LMFDB - Embedded newform 18.14.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,14,Mod(7,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.3015672113$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 70059 x^{10} + 5065444 x^{9} + 4093250893 x^{8} + 217797867390 x^{7} + \cdots + 18\!\cdots\!00 $ x^12 - 2x^11 + 70059x^10 + 5065444x^9 + 4093250893x^8 + 217797867390x^7 + 63708924992805x^6 + 3895447778197164x^5 + 788586885260894475x^4 + 36120700348479454374x^3 + 1423630529500671020169x^2 + 17839110274779505783500*x + 180081901433575820250000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{31} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$127.635 + 221.070i$ of defining polynomial
Character	$\chi$	$=$	18.7
Dual form			18.14.c.a.13.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 - 55.4256i) q^{2} +(-908.101 + 877.312i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(-10927.3 - 18926.7i) q^{5} +(19566.3 + 78406.0i) q^{6} +(-146006. + 252890. i) q^{7} -262144. q^{8} +(54970.7 - 1.59338e6i) q^{9} +O(q^{10})$	\(q+(32.0000 - 55.4256i) q^{2} +(-908.101 + 877.312i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(-10927.3 - 18926.7i) q^{5} +(19566.3 + 78406.0i) q^{6} +(-146006. + 252890. i) q^{7} -262144. q^{8} +(54970.7 - 1.59338e6i) q^{9} -1.39870e6 q^{10} +(1.12078e6 - 1.94125e6i) q^{11} +(4.97183e6 + 1.42452e6i) q^{12} +(8.69332e6 + 1.50573e7i) q^{13} +(9.34440e6 + 1.61850e7i) q^{14} +(2.65277e7 + 7.60065e6i) q^{15} +(-8.38861e6 + 1.45295e7i) q^{16} +1.02646e8 q^{17} +(-8.65547e7 - 5.40348e7i) q^{18} +2.84600e8 q^{19} +(-4.47583e7 + 7.75236e7i) q^{20} +(-8.92752e7 - 3.57743e8i) q^{21} +(-7.17298e7 - 1.24240e8i) q^{22} +(-1.29161e8 - 2.23713e8i) q^{23} +(2.38053e8 - 2.29982e8i) q^{24} +(3.71539e8 - 6.43525e8i) q^{25} +1.11274e9 q^{26} +(1.34797e9 + 1.49517e9i) q^{27} +1.19608e9 q^{28} +(1.74217e9 - 3.01753e9i) q^{29} +(1.27016e9 - 1.22709e9i) q^{30} +(4.05701e9 + 7.02694e9i) q^{31} +(5.36871e8 + 9.29888e8i) q^{32} +(6.85298e8 + 2.74612e9i) q^{33} +(3.28468e9 - 5.68923e9i) q^{34} +6.38182e9 q^{35} +(-5.76466e9 + 3.06824e9i) q^{36} -1.28194e10 q^{37} +(9.10720e9 - 1.57741e10i) q^{38} +(-2.11043e10 - 6.04676e9i) q^{39} +(2.86453e9 + 4.96151e9i) q^{40} +(2.35711e9 + 4.08263e9i) q^{41} +(-2.26849e10 - 6.49963e9i) q^{42} +(-1.66397e10 + 2.88208e10i) q^{43} -9.18142e9 q^{44} +(-3.07580e10 + 1.63709e10i) q^{45} -1.65326e10 q^{46} +(1.52063e9 - 2.63380e9i) q^{47} +(-5.12920e9 - 2.05537e10i) q^{48} +(5.80889e9 + 1.00613e10i) q^{49} +(-2.37785e10 - 4.11856e10i) q^{50} +(-9.32130e10 + 9.00527e10i) q^{51} +(3.56078e10 - 6.16746e10i) q^{52} -5.94638e10 q^{53} +(1.26006e11 - 2.68665e10i) q^{54} -4.89884e10 q^{55} +(3.82746e10 - 6.62936e10i) q^{56} +(-2.58445e11 + 2.49683e11i) q^{57} +(-1.11499e11 - 1.93122e11i) q^{58} +(2.89332e11 + 5.01138e11i) q^{59} +(-2.73674e10 - 1.09666e11i) q^{60} +(1.43544e11 - 2.48625e11i) q^{61} +5.19297e11 q^{62} +(3.94923e11 + 2.46544e11i) q^{63} +6.87195e10 q^{64} +(1.89989e11 - 3.29071e11i) q^{65} +(1.74135e11 + 4.98927e10i) q^{66} +(-4.37420e11 - 7.57634e11i) q^{67} +(-2.10219e11 - 3.64110e11i) q^{68} +(3.13557e11 + 8.98396e10i) q^{69} +(2.04218e11 - 3.53716e11i) q^{70} +1.64422e12 q^{71} +(-1.44102e10 + 4.17694e11i) q^{72} -1.62988e12 q^{73} +(-4.10222e11 + 7.10525e11i) q^{74} +(2.27177e11 + 9.10341e11i) q^{75} +(-5.82861e11 - 1.00954e12i) q^{76} +(3.27281e11 + 5.66868e11i) q^{77} +(-1.01048e12 + 9.76224e11i) q^{78} +(1.51346e12 - 2.62139e12i) q^{79} +3.66660e11 q^{80} +(-2.53582e12 - 1.75178e11i) q^{81} +3.01710e11 q^{82} +(-4.62483e11 + 8.01045e11i) q^{83} +(-1.08616e12 + 1.04934e12i) q^{84} +(-1.12165e12 - 1.94275e12i) q^{85} +(1.06494e12 + 1.84453e12i) q^{86} +(1.06525e12 + 4.26865e12i) q^{87} +(-2.93805e11 + 5.08886e11i) q^{88} +6.03750e12 q^{89} +(-7.68873e10 + 2.22865e12i) q^{90} -5.07711e12 q^{91} +(-5.29042e11 + 9.16328e11i) q^{92} +(-9.84899e12 - 2.82191e12i) q^{93} +(-9.73201e10 - 1.68563e11i) q^{94} +(-3.10991e12 - 5.38653e12i) q^{95} +(-1.30333e12 - 3.73428e11i) q^{96} +(-5.99631e11 + 1.03859e12i) q^{97} +7.43538e11 q^{98} +(-3.03152e12 - 1.89253e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 384 q^{2} + 1836 q^{3} - 24576 q^{4} - 36504 q^{5} + 102528 q^{6} + 153942 q^{7} - 3145728 q^{8} - 5622426 q^{9}+O(q^{10}) $ 12 * q + 384 * q^2 + 1836 * q^3 - 24576 * q^4 - 36504 * q^5 + 102528 * q^6 + 153942 * q^7 - 3145728 * q^8 - 5622426 * q^9	\( 12 q + 384 q^{2} + 1836 q^{3} - 24576 q^{4} - 36504 q^{5} + 102528 q^{6} + 153942 q^{7} - 3145728 q^{8} - 5622426 q^{9} - 4672512 q^{10} - 1456506 q^{11} - 958464 q^{12} + 24033660 q^{13} - 9852288 q^{14} - 25621002 q^{15} - 100663296 q^{16} - 1079532 q^{17} - 119093760 q^{18} + 337140888 q^{19} - 149520384 q^{20} + 386320356 q^{21} + 93216384 q^{22} + 445386186 q^{23} - 481296384 q^{24} - 2193691326 q^{25} + 3076308480 q^{26} + 5101396200 q^{27} - 1261092864 q^{28} - 9171393012 q^{29} + 4197353472 q^{30} + 4264851066 q^{31} + 6442450944 q^{32} - 23566590198 q^{33} - 34545024 q^{34} + 5180969412 q^{35} + 15407456256 q^{36} - 49108850688 q^{37} + 10788508416 q^{38} - 43492658274 q^{39} + 9569304576 q^{40} - 15964345782 q^{41} + 3573347328 q^{42} + 78379952838 q^{43} + 11931697152 q^{44} + 175634070336 q^{45} + 57009431808 q^{46} + 94117799358 q^{47} - 26877100032 q^{48} - 15284873538 q^{49} + 140396244864 q^{50} - 93672459180 q^{51} + 98441871360 q^{52} - 592790415264 q^{53} + 453285652608 q^{54} - 1108282558212 q^{55} - 40354971648 q^{56} - 1485104020362 q^{57} + 586969152768 q^{58} + 46698155010 q^{59} + 373574246400 q^{60} + 928192122600 q^{61} + 545900936448 q^{62} + 1292399354358 q^{63} + 824633720832 q^{64} - 1327744890468 q^{65} - 1308420898560 q^{66} + 2282039666898 q^{67} + 2210881536 q^{68} - 1791810302256 q^{69} + 165791021184 q^{70} + 2360122970688 q^{71} + 1473885241344 q^{72} + 1355834901228 q^{73} - 1571483222016 q^{74} - 2580299891100 q^{75} - 690464538624 q^{76} - 3622976109756 q^{77} - 3601561950720 q^{78} + 2457538059750 q^{79} + 1224870985728 q^{80} + 3601735790598 q^{81} - 2043436260096 q^{82} - 9950916891942 q^{83} - 1353673949184 q^{84} - 576987174720 q^{85} - 5016316981632 q^{86} + 10025707613994 q^{87} + 381814308864 q^{88} + 22604686696296 q^{89} - 2251213959168 q^{90} + 14791528659540 q^{91} + 1824301817856 q^{92} - 19426418885880 q^{93} - 6023539158912 q^{94} - 7488669126384 q^{95} + 251255586816 q^{96} + 1124429902242 q^{97} - 1956463812864 q^{98} + 12314866399002 q^{99}+O(q^{100}) \) 12 * q + 384 * q^2 + 1836 * q^3 - 24576 * q^4 - 36504 * q^5 + 102528 * q^6 + 153942 * q^7 - 3145728 * q^8 - 5622426 * q^9 - 4672512 * q^10 - 1456506 * q^11 - 958464 * q^12 + 24033660 * q^13 - 9852288 * q^14 - 25621002 * q^15 - 100663296 * q^16 - 1079532 * q^17 - 119093760 * q^18 + 337140888 * q^19 - 149520384 * q^20 + 386320356 * q^21 + 93216384 * q^22 + 445386186 * q^23 - 481296384 * q^24 - 2193691326 * q^25 + 3076308480 * q^26 + 5101396200 * q^27 - 1261092864 * q^28 - 9171393012 * q^29 + 4197353472 * q^30 + 4264851066 * q^31 + 6442450944 * q^32 - 23566590198 * q^33 - 34545024 * q^34 + 5180969412 * q^35 + 15407456256 * q^36 - 49108850688 * q^37 + 10788508416 * q^38 - 43492658274 * q^39 + 9569304576 * q^40 - 15964345782 * q^41 + 3573347328 * q^42 + 78379952838 * q^43 + 11931697152 * q^44 + 175634070336 * q^45 + 57009431808 * q^46 + 94117799358 * q^47 - 26877100032 * q^48 - 15284873538 * q^49 + 140396244864 * q^50 - 93672459180 * q^51 + 98441871360 * q^52 - 592790415264 * q^53 + 453285652608 * q^54 - 1108282558212 * q^55 - 40354971648 * q^56 - 1485104020362 * q^57 + 586969152768 * q^58 + 46698155010 * q^59 + 373574246400 * q^60 + 928192122600 * q^61 + 545900936448 * q^62 + 1292399354358 * q^63 + 824633720832 * q^64 - 1327744890468 * q^65 - 1308420898560 * q^66 + 2282039666898 * q^67 + 2210881536 * q^68 - 1791810302256 * q^69 + 165791021184 * q^70 + 2360122970688 * q^71 + 1473885241344 * q^72 + 1355834901228 * q^73 - 1571483222016 * q^74 - 2580299891100 * q^75 - 690464538624 * q^76 - 3622976109756 * q^77 - 3601561950720 * q^78 + 2457538059750 * q^79 + 1224870985728 * q^80 + 3601735790598 * q^81 - 2043436260096 * q^82 - 9950916891942 * q^83 - 1353673949184 * q^84 - 576987174720 * q^85 - 5016316981632 * q^86 + 10025707613994 * q^87 + 381814308864 * q^88 + 22604686696296 * q^89 - 2251213959168 * q^90 + 14791528659540 * q^91 + 1824301817856 * q^92 - 19426418885880 * q^93 - 6023539158912 * q^94 - 7488669126384 * q^95 + 251255586816 * q^96 + 1124429902242 * q^97 - 1956463812864 * q^98 + 12314866399002 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	32.0000	−	55.4256i	0.353553	−	0.612372i
$2$	32.0000	−	55.4256i	0.353553	−	0.612372i
$3$	−908.101	+	877.312i	−0.719194	+	0.694810i
$3$	−908.101	+	877.312i	−0.719194	+	0.694810i
$4$	−2048.00	−	3547.24i	−0.250000	−	0.433013i
$5$	−10927.3	−	18926.7i	−0.312758	−	0.541713i	0.666200	−	0.745773i	$-0.267920\pi$
$5$	−10927.3	−	18926.7i	−0.312758	−	0.541713i	−0.978958	+	0.204060i	$0.934586\pi$
$6$	19566.3	+	78406.0i	0.171209	+	0.686067i
$7$	−146006.	+	252890.i	−0.469066	+	0.812446i	−0.999375	−	0.0353584i	$-0.988743\pi$
$7$	−146006.	+	252890.i	−0.469066	+	0.812446i	0.530309	+	0.847805i	$0.322076\pi$
$8$	−262144.			−0.353553
$9$	54970.7	−	1.59338e6i	0.0344790	−	0.999405i
$10$	−1.39870e6			−0.442307
$11$	1.12078e6	−	1.94125e6i	0.190751	−	0.330391i	−0.754748	−	0.656015i	$-0.772241\pi$
$11$	1.12078e6	−	1.94125e6i	0.190751	−	0.330391i	0.945499	+	0.325624i	$0.105574\pi$
$12$	4.97183e6	+	1.42452e6i	0.480660	+	0.137718i
$13$	8.69332e6	+	1.50573e7i	0.499521	+	0.865196i	1.00000		0.000553009i	$-0.000176028\pi$
$13$	8.69332e6	+	1.50573e7i	0.499521	+	0.865196i	−0.500479	+	0.865749i	$0.666843\pi$
$14$	9.34440e6	+	1.61850e7i	0.331680	+	0.574486i
$15$	2.65277e7	+	7.60065e6i	0.601321	+	0.172289i
$16$	−8.38861e6	+	1.45295e7i	−0.125000	+	0.216506i
$17$	1.02646e8			1.03139			0.515697	−	0.856771i	$-0.327533\pi$
$17$	1.02646e8			1.03139			0.515697	+	0.856771i	$0.327533\pi$
$18$	−8.65547e7	−	5.40348e7i	−0.599818	−	0.374457i
$19$	2.84600e8			1.38783			0.693915	−	0.720057i	$-0.255884\pi$
$19$	2.84600e8			1.38783			0.693915	+	0.720057i	$0.255884\pi$
$20$	−4.47583e7	+	7.75236e7i	−0.156379	+	0.270856i
$21$	−8.92752e7	−	3.57743e8i	−0.227146	−	0.910218i
$22$	−7.17298e7	−	1.24240e8i	−0.134882	−	0.233622i
$23$	−1.29161e8	−	2.23713e8i	−0.181928	−	0.315108i	0.760609	−	0.649210i	$-0.224900\pi$
$23$	−1.29161e8	−	2.23713e8i	−0.181928	−	0.315108i	−0.942537	+	0.334102i	$0.891567\pi$
$24$	2.38053e8	−	2.29982e8i	0.254273	−	0.245652i
$25$	3.71539e8	−	6.43525e8i	0.304365	−	0.527175i
$26$	1.11274e9			0.706429
$27$	1.34797e9	+	1.49517e9i	0.669599	+	0.742722i
$28$	1.19608e9			0.469066
$29$	1.74217e9	−	3.01753e9i	0.543881	−	0.942030i	−0.454795	−	0.890596i	$-0.650287\pi$
$29$	1.74217e9	−	3.01753e9i	0.543881	−	0.942030i	0.998676	−	0.0514340i	$-0.0163792\pi$
$30$	1.27016e9	−	1.22709e9i	0.318104	−	0.307319i
$31$	4.05701e9	+	7.02694e9i	0.821022	+	1.42205i	0.904922	+	0.425578i	$0.139929\pi$
$31$	4.05701e9	+	7.02694e9i	0.821022	+	1.42205i	−0.0838996	+	0.996474i	$0.526738\pi$
$32$	5.36871e8	+	9.29888e8i	0.0883883	+	0.153093i
$33$	6.85298e8	+	2.74612e9i	0.0923717	+	0.370151i
$34$	3.28468e9	−	5.68923e9i	0.364653	−	0.631597i
$35$	6.38182e9			0.586817
$36$	−5.76466e9	+	3.06824e9i	−0.441375	+	0.234921i
$37$	−1.28194e10			−0.821405			−0.410703	−	0.911769i	$-0.634717\pi$
$37$	−1.28194e10			−0.821405			−0.410703	+	0.911769i	$0.634717\pi$
$38$	9.10720e9	−	1.57741e10i	0.490672	−	0.849869i
$39$	−2.11043e10	−	6.04676e9i	−0.960399	−	0.275171i
$40$	2.86453e9	+	4.96151e9i	0.110577	+	0.191524i
$41$	2.35711e9	+	4.08263e9i	0.0774970	+	0.134229i	0.902169	−	0.431382i	$-0.141974\pi$
$41$	2.35711e9	+	4.08263e9i	0.0774970	+	0.134229i	−0.824672	+	0.565611i	$0.808641\pi$
$42$	−2.26849e10	−	6.49963e9i	−0.637701	−	0.182713i
$43$	−1.66397e10	+	2.88208e10i	−0.401422	+	0.695283i	−0.993898	−	0.110305i	$-0.964817\pi$
$43$	−1.66397e10	+	2.88208e10i	−0.401422	+	0.695283i	0.592476	+	0.805588i	$0.298151\pi$
$44$	−9.18142e9			−0.190751
$45$	−3.07580e10	+	1.63709e10i	−0.552174	+	0.293894i
$46$	−1.65326e10			−0.257285
$47$	1.52063e9	−	2.63380e9i	0.0205772	−	0.0356408i	−0.855553	−	0.517715i	$-0.826783\pi$
$47$	1.52063e9	−	2.63380e9i	0.0205772	−	0.0356408i	0.876131	+	0.482074i	$0.160116\pi$
$48$	−5.12920e9	−	2.05537e10i	−0.0605315	−	0.242561i
$49$	5.80889e9	+	1.00613e10i	0.0599541	+	0.103843i
$50$	−2.37785e10	−	4.11856e10i	−0.215218	−	0.372769i
$51$	−9.32130e10	+	9.00527e10i	−0.741772	+	0.716623i
$52$	3.56078e10	−	6.16746e10i	0.249761	−	0.432598i
$53$	−5.94638e10			−0.368519			−0.184259	−	0.982878i	$-0.558989\pi$
$53$	−5.94638e10			−0.368519			−0.184259	+	0.982878i	$0.558989\pi$
$54$	1.26006e11	−	2.68665e10i	0.691562	−	0.147452i
$55$	−4.89884e10			−0.238636
$56$	3.82746e10	−	6.62936e10i	0.165840	−	0.287243i
$57$	−2.58445e11	+	2.49683e11i	−0.998119	+	0.964278i
$58$	−1.11499e11	−	1.93122e11i	−0.384582	−	0.666116i
$59$	2.89332e11	+	5.01138e11i	0.893015	+	1.54675i	0.836242	+	0.548361i	$0.184748\pi$
$59$	2.89332e11	+	5.01138e11i	0.893015	+	1.54675i	0.0567738	+	0.998387i	$0.481919\pi$
$60$	−2.73674e10	−	1.09666e11i	−0.0757268	−	0.303452i
$61$	1.43544e11	−	2.48625e11i	0.356731	−	0.617876i	−0.630682	−	0.776041i	$-0.717225\pi$
$61$	1.43544e11	−	2.48625e11i	0.356731	−	0.617876i	0.987413	+	0.158166i	$0.0505581\pi$
$62$	5.19297e11			1.16110
$63$	3.94923e11	+	2.46544e11i	0.795790	+	0.496800i
$64$	6.87195e10			0.125000
$65$	1.89989e11	−	3.29071e11i	0.312458	−	0.541194i
$66$	1.74135e11	+	4.98927e10i	0.259329	+	0.0743022i
$67$	−4.37420e11	−	7.57634e11i	−0.590762	−	1.02323i	−0.994130	−	0.108192i	$-0.965494\pi$
$67$	−4.37420e11	−	7.57634e11i	−0.590762	−	1.02323i	0.403368	−	0.915038i	$-0.367839\pi$
$68$	−2.10219e11	−	3.64110e11i	−0.257849	−	0.446607i
$69$	3.13557e11	+	8.98396e10i	0.349782	+	0.100219i
$70$	2.04218e11	−	3.53716e11i	0.207471	−	0.359350i
$71$	1.64422e12			1.52329			0.761644	−	0.647996i	$-0.224393\pi$
$71$	1.64422e12			1.52329			0.761644	+	0.647996i	$0.224393\pi$
$72$	−1.44102e10	+	4.17694e11i	−0.0121902	+	0.353343i
$73$	−1.62988e12			−1.26054			−0.630270	−	0.776376i	$-0.717056\pi$
$73$	−1.62988e12			−1.26054			−0.630270	+	0.776376i	$0.717056\pi$
$74$	−4.10222e11	+	7.10525e11i	−0.290411	+	0.503006i
$75$	2.27177e11	+	9.10341e11i	0.147389	+	0.590617i
$76$	−5.82861e11	−	1.00954e12i	−0.346958	−	0.600948i
$77$	3.27281e11	+	5.66868e11i	0.178950	+	0.309950i
$78$	−1.01048e12	+	9.76224e11i	−0.508060	+	0.490834i
$79$	1.51346e12	−	2.62139e12i	0.700478	−	1.21326i	−0.267821	−	0.963469i	$-0.586304\pi$
$79$	1.51346e12	−	2.62139e12i	0.700478	−	1.21326i	0.968299	−	0.249795i	$-0.0803632\pi$
$80$	3.66660e11			0.156379
$81$	−2.53582e12	−	1.75178e11i	−0.997622	−	0.0689171i
$82$	3.01710e11			0.109597
$83$	−4.62483e11	+	8.01045e11i	−0.155270	+	0.268936i	−0.933157	−	0.359468i	$-0.882958\pi$
$83$	−4.62483e11	+	8.01045e11i	−0.155270	+	0.268936i	0.777887	+	0.628404i	$0.216292\pi$
$84$	−1.08616e12	+	1.04934e12i	−0.337349	+	0.325912i
$85$	−1.12165e12	−	1.94275e12i	−0.322577	−	0.558719i
$86$	1.06494e12	+	1.84453e12i	0.283848	+	0.491639i
$87$	1.06525e12	+	4.26865e12i	0.263376	+	1.05540i
$88$	−2.93805e11	+	5.08886e11i	−0.0674408	+	0.116811i
$89$	6.03750e12			1.28772			0.643861	−	0.765143i	$-0.277332\pi$
$89$	6.03750e12			1.28772			0.643861	+	0.765143i	$0.277332\pi$
$90$	−7.68873e10	+	2.22865e12i	−0.0152503	+	0.442044i
$91$	−5.07711e12			−0.937233
$92$	−5.29042e11	+	9.16328e11i	−0.0909640	+	0.157554i
$93$	−9.84899e12	−	2.82191e12i	−1.57853	−	0.452277i
$94$	−9.73201e10	−	1.68563e11i	−0.0145503	−	0.0252018i
$95$	−3.10991e12	−	5.38653e12i	−0.434055	−	0.751805i
$96$	−1.30333e12	−	3.73428e11i	−0.169939	−	0.0486905i
$97$	−5.99631e11	+	1.03859e12i	−0.0730916	+	0.126598i	−0.900255	−	0.435363i	$-0.856620\pi$
$97$	−5.99631e11	+	1.03859e12i	−0.0730916	+	0.126598i	0.827163	+	0.561962i	$0.189953\pi$
$98$	7.43538e11			0.0847878
$99$	−3.03152e12	−	1.89253e12i	−0.323618	−	0.202029i
$100$	−3.04365e12			−0.304365
$101$	6.16075e12	−	1.06707e13i	0.577490	−	1.00024i	−0.418276	−	0.908320i	$-0.637366\pi$
$101$	6.16075e12	−	1.06707e13i	0.577490	−	1.00024i	0.995766	−	0.0919222i	$-0.0293011\pi$
$102$	2.00841e12	+	8.04808e12i	0.176584	+	0.707605i
$103$	−1.90932e12	−	3.30704e12i	−0.157557	−	0.272897i	0.776430	−	0.630203i	$-0.217028\pi$
$103$	−1.90932e12	−	3.30704e12i	−0.157557	−	0.272897i	−0.933987	+	0.357307i	$0.883695\pi$
$104$	−2.27890e12	−	3.94717e12i	−0.176607	−	0.305893i
$105$	−5.79534e12	+	5.59885e12i	−0.422035	+	0.407726i
$106$	−1.90284e12	+	3.29582e12i	−0.130291	+	0.225671i
$107$	2.89672e13			1.86600			0.933002	−	0.359872i	$-0.117179\pi$
$107$	2.89672e13			1.86600			0.933002	+	0.359872i	$0.117179\pi$
$108$	2.54309e12	−	7.84368e12i	0.154208	−	0.475626i
$109$	2.01531e13			1.15099			0.575494	−	0.817806i	$-0.304810\pi$
$109$	2.01531e13			1.15099			0.575494	+	0.817806i	$0.304810\pi$
$110$	−1.56763e12	+	2.71521e12i	−0.0843705	+	0.146134i
$111$	1.16413e13	−	1.12466e13i	0.590749	−	0.570720i
$112$	−2.44958e12	−	4.24279e12i	−0.117267	−	0.203112i
$113$	7.37102e12	+	1.27670e13i	0.333056	+	0.576870i	0.983110	−	0.183018i	$-0.0585867\pi$
$113$	7.37102e12	+	1.27670e13i	0.333056	+	0.576870i	−0.650053	+	0.759889i	$0.725253\pi$
$114$	5.56858e12	+	2.23143e13i	0.237609	+	0.952144i
$115$	−2.82276e12	+	4.88916e12i	−0.113799	+	0.197105i
$116$	−1.42719e13			−0.543881
$117$	2.44698e13	−	1.30240e13i	0.881904	−	0.469393i
$118$	3.70345e13			1.26291
$119$	−1.49870e13	+	2.59582e13i	−0.483792	+	0.837952i
$120$	−6.95407e12	−	1.99247e12i	−0.212599	−	0.0609134i
$121$	1.47491e13	+	2.55461e13i	0.427228	+	0.739980i
$122$	−9.18680e12	−	1.59120e13i	−0.252247	−	0.436904i
$123$	−5.72224e12	−	1.63952e12i	−0.148999	−	0.0426908i
$124$	1.66175e13	−	2.87824e13i	0.410511	−	0.711026i
$125$	−4.29177e13			−1.00629
$126$	2.63024e13	−	1.39994e13i	0.585581	−	0.311675i
$127$	−6.27677e13			−1.32743			−0.663715	−	0.747985i	$-0.731021\pi$
$127$	−6.27677e13			−1.32743			−0.663715	+	0.747985i	$0.731021\pi$
$128$	2.19902e12	−	3.80882e12i	0.0441942	−	0.0765466i
$129$	−1.01743e13	−	4.07704e13i	−0.194389	−	0.778955i
$130$	−1.21593e13	−	2.10605e13i	−0.220941	−	0.382682i
$131$	−2.97023e13	−	5.14459e13i	−0.513484	−	0.889380i	−0.999878	−	0.0156407i	$-0.995021\pi$
$131$	−2.97023e13	−	5.14459e13i	−0.513484	−	0.889380i	0.486394	−	0.873740i	$-0.338312\pi$
$132$	8.33765e12	−	8.05497e12i	0.137187	−	0.132536i
$133$	−4.15533e13	+	7.19725e13i	−0.650984	+	1.12754i
$134$	−5.59898e13			−0.835463
$135$	1.35689e13	−	4.18507e13i	0.192920	−	0.595023i
$136$	−2.69081e13			−0.364653
$137$	−6.70609e13	+	1.16153e14i	−0.866535	+	1.50088i	−0.00101949	+	0.999999i	$0.500325\pi$
$137$	−6.70609e13	+	1.16153e14i	−0.866535	+	1.50088i	−0.865515	+	0.500883i	$0.833009\pi$
$138$	1.50132e13	−	1.45042e13i	0.185038	−	0.178764i
$139$	7.44053e13	+	1.28874e14i	0.874999	+	1.51554i	0.856764	+	0.515709i	$0.172472\pi$
$139$	7.44053e13	+	1.28874e14i	0.874999	+	1.51554i	0.0182356	+	0.999834i	$0.494195\pi$
$140$	−1.30700e13	−	2.26379e13i	−0.146704	−	0.254099i
$141$	9.29784e11	+	3.72582e12i	0.00996456	+	0.0399299i
$142$	5.26152e13	−	9.11322e13i	0.538563	−	0.932819i
$143$	3.89731e13			0.381137
$144$	2.26898e13	+	1.41649e13i	0.212068	+	0.132391i
$145$	−7.61491e13			−0.680413
$146$	−5.21561e13	+	9.03370e13i	−0.445668	+	0.771920i
$147$	−1.41019e13	−	4.04046e12i	−0.115270	−	0.0330269i
$148$	2.62542e13	+	4.54736e13i	0.205351	+	0.355679i
$149$	−1.10148e13	−	1.90782e13i	−0.0824645	−	0.142833i	0.821843	−	0.569713i	$-0.192946\pi$
$149$	−1.10148e13	−	1.90782e13i	−0.0824645	−	0.142833i	−0.904308	+	0.426881i	$0.859612\pi$
$150$	5.77259e13	+	1.65395e13i	0.413787	+	0.118557i
$151$	−2.09503e13	+	3.62870e13i	−0.143827	+	0.249116i	−0.928935	−	0.370244i	$-0.879274\pi$
$151$	−2.09503e13	+	3.62870e13i	−0.143827	+	0.249116i	0.785108	+	0.619359i	$0.212608\pi$
$152$	−7.46062e13			−0.490672
$153$	5.64253e12	−	1.63554e14i	0.0355615	−	1.03078i
$154$	4.18920e13			0.253073
$155$	8.86644e13	−	1.53571e14i	0.513562	−	0.889516i
$156$	2.17723e13	+	8.72459e13i	0.120947	+	0.484658i
$157$	6.74371e13	+	1.16805e14i	0.359378	+	0.622461i	0.987857	−	0.155366i	$-0.0496556\pi$
$157$	6.74371e13	+	1.16805e14i	0.359378	+	0.622461i	−0.628479	+	0.777826i	$0.716322\pi$
$158$	−9.68614e13	−	1.67769e14i	−0.495313	−	0.857907i
$159$	5.39991e13	−	5.21683e13i	0.265036	−	0.256050i
$160$	1.17331e13	−	2.03224e13i	0.0552883	−	0.0957622i
$161$	7.54330e13			0.341345
$162$	−9.08557e13	+	1.34944e14i	−0.394916	+	0.586551i
$163$	1.65656e14			0.691813			0.345907	−	0.938269i	$-0.387571\pi$
$163$	1.65656e14			0.691813			0.345907	+	0.938269i	$0.387571\pi$
$164$	9.65472e12	−	1.67225e13i	0.0387485	−	0.0671143i
$165$	4.44864e13	−	4.29781e13i	0.171625	−	0.165807i
$166$	2.95989e13	+	5.12669e13i	0.109793	+	0.190167i
$167$	8.10102e13	+	1.40314e14i	0.288990	+	0.500545i	0.973569	−	0.228393i	$-0.0733473\pi$
$167$	8.10102e13	+	1.40314e14i	0.288990	+	0.500545i	−0.684579	+	0.728939i	$0.740014\pi$
$168$	2.34030e13	+	9.37801e13i	0.0803083	+	0.321811i
$169$	2.90013e11	−	5.02318e11i	0.000957534	−	0.00165850i
$170$	−1.43571e14			−0.456192
$171$	1.56447e13	−	4.53474e14i	0.0478510	−	1.38700i
$172$	1.36313e14			0.401422
$173$	1.33981e14	−	2.32062e14i	0.379964	−	0.658118i	−0.611092	−	0.791559i	$-0.709270\pi$
$173$	1.33981e14	−	2.32062e14i	0.379964	−	0.658118i	0.991057	+	0.133442i	$0.0426029\pi$
$174$	2.70681e14	+	7.75548e13i	0.739413	+	0.211855i
$175$	1.08494e14	+	1.87917e14i	0.285534	+	0.494560i
$176$	1.88035e13	+	3.25687e13i	0.0476878	+	0.0825977i
$177$	−7.02398e14	−	2.01249e14i	−1.71695	−	0.491936i
$178$	1.93200e14	−	3.34632e14i	0.455278	−	0.788565i
$179$	8.14358e14			1.85042			0.925211	−	0.379454i	$-0.123888\pi$
$179$	8.14358e14			1.85042			0.925211	+	0.379454i	$0.123888\pi$
$180$	1.21064e14	+	7.55783e13i	0.265304	+	0.165625i
$181$	−6.82572e14			−1.44291			−0.721453	−	0.692464i	$-0.756525\pi$
$181$	−6.82572e14			−1.44291			−0.721453	+	0.692464i	$0.756525\pi$
$182$	−1.62468e14	+	2.81402e14i	−0.331362	+	0.573936i
$183$	8.77696e13	+	3.51709e14i	0.172748	+	0.692232i
$184$	3.38587e13	+	5.86450e13i	0.0643212	+	0.111408i
$185$	1.40082e14	+	2.42629e14i	0.256901	+	0.444966i
$186$	−4.71574e14	+	4.55585e14i	−0.835056	+	0.806744i
$187$	1.15044e14	−	1.99261e14i	0.196740	−	0.340763i
$188$	−1.24570e13			−0.0205772
$189$	−5.74926e14	+	1.22584e14i	−0.917508	+	0.195628i
$190$	−3.98069e14			−0.613846
$191$	2.97121e14	−	5.14629e14i	0.442809	−	0.766968i	−0.555087	−	0.831792i	$-0.687315\pi$
$191$	2.97121e14	−	5.14629e14i	0.442809	−	0.766968i	0.997897	+	0.0648238i	$0.0206485\pi$
$192$	−6.24042e13	+	6.02884e13i	−0.0898992	+	0.0868512i
$193$	−4.17764e14	−	7.23589e14i	−0.581847	−	1.00779i	−0.995260	−	0.0972448i	$-0.968997\pi$
$193$	−4.17764e14	−	7.23589e14i	−0.581847	−	1.00779i	0.413414	−	0.910543i	$-0.364336\pi$
$194$	3.83764e13	+	6.64698e13i	0.0516836	+	0.0895186i
$195$	1.16169e14	+	4.65509e14i	0.151309	+	0.606322i
$196$	2.37932e13	−	4.12111e13i	0.0299770	−	0.0519217i
$197$	−9.13748e14			−1.11377			−0.556886	−	0.830589i	$-0.688004\pi$
$197$	−9.13748e14			−1.11377			−0.556886	+	0.830589i	$0.688004\pi$
$198$	−2.01904e14	+	1.07463e14i	−0.238133	+	0.126746i
$199$	−5.29824e14			−0.604765			−0.302382	−	0.953187i	$-0.597782\pi$
$199$	−5.29824e14			−0.604765			−0.302382	+	0.953187i	$0.597782\pi$
$200$	−9.73968e13	+	1.68696e14i	−0.107609	+	0.186385i
$201$	1.06190e15	+	3.04254e14i	1.13582	+	0.325433i
$202$	−3.94288e14	−	6.82927e14i	−0.408347	−	0.707278i
$203$	5.08736e14	+	8.81157e14i	0.510233	+	0.883749i
$204$	5.10339e14	+	1.46221e14i	0.495750	+	0.142041i
$205$	5.15138e13	−	8.92244e13i	0.0484756	−	0.0839622i
$206$	−2.44393e14			−0.222819
$207$	−3.63559e14	+	1.93504e14i	−0.321194	+	0.170955i
$208$	−2.91699e14			−0.249761
$209$	3.18974e14	−	5.52478e14i	0.264730	−	0.458526i
$210$	1.24869e14	+	5.00373e14i	0.100468	+	0.402595i
$211$	1.98238e13	+	3.43358e13i	0.0154650	+	0.0267862i	0.873654	−	0.486547i	$-0.161744\pi$
$211$	1.98238e13	+	3.43358e13i	0.0154650	+	0.0267862i	−0.858189	+	0.513333i	$0.828410\pi$
$212$	1.21782e14	+	2.10932e14i	0.0921297	+	0.159573i
$213$	−1.49312e15	+	1.44250e15i	−1.09554	+	1.05839i
$214$	9.26952e14	−	1.60553e15i	0.659732	−	1.14269i
$215$	7.27310e14			0.502192
$216$	−3.53362e14	−	3.91950e14i	−0.236739	−	0.262592i
$217$	−2.36939e15			−1.54045
$218$	6.44901e14	−	1.11700e15i	0.406936	−	0.704833i
$219$	1.48009e15	−	1.42991e15i	0.906572	−	0.875835i
$220$	1.00328e14	+	1.73774e14i	0.0596590	+	0.103332i
$221$	8.92335e14	+	1.54557e15i	0.515203	+	0.892358i
$222$	−2.50829e14	−	1.00512e15i	−0.140632	−	0.563539i
$223$	1.67180e15	−	2.89564e15i	0.910337	−	1.57675i	0.0967496	−	0.995309i	$-0.469155\pi$
$223$	1.67180e15	−	2.89564e15i	0.910337	−	1.57675i	0.813588	−	0.581442i	$-0.197511\pi$
$224$	−3.13546e14			−0.165840
$225$	−1.00495e15	−	6.27376e14i	−0.516368	−	0.322360i
$226$	9.43490e14			0.471013
$227$	−7.83386e14	+	1.35686e15i	−0.380021	+	0.658216i	−0.991065	−	0.133381i	$-0.957417\pi$
$227$	−7.83386e14	+	1.35686e15i	−0.380021	+	0.658216i	0.611044	+	0.791597i	$0.290750\pi$
$228$	1.41498e15	+	4.05417e14i	0.667074	+	0.191129i
$229$	1.93486e15	+	3.35128e15i	0.886582	+	1.53561i	0.843890	+	0.536517i	$0.180260\pi$
$229$	1.93486e15	+	3.35128e15i	0.886582	+	1.53561i	0.0426925	+	0.999088i	$0.486406\pi$
$230$	1.80657e14	+	3.12906e14i	0.0804679	+	0.139375i
$231$	−7.94524e14	−	2.27645e14i	−0.344056	−	0.0985782i
$232$	−4.56700e14	+	7.91028e14i	−0.192291	+	0.333058i
$233$	5.09381e14			0.208559			0.104280	−	0.994548i	$-0.466746\pi$
$233$	5.09381e14			0.208559			0.104280	+	0.994548i	$0.466746\pi$
$234$	6.11684e13	−	1.77302e15i	0.0243570	−	0.706009i
$235$	−6.64655e13			−0.0257428
$236$	1.18511e15	−	2.05266e15i	0.446508	−	0.773374i
$237$	9.25401e14	+	3.70826e15i	0.339208	+	1.35927i
$238$	9.59166e14	+	1.66132e15i	0.342093	+	0.592522i
$239$	−7.94675e14	−	1.37642e15i	−0.275806	−	0.477709i	0.694532	−	0.719461i	$-0.255611\pi$
$239$	−7.94675e14	−	1.37642e15i	−0.275806	−	0.477709i	−0.970338	+	0.241752i	$0.922278\pi$
$240$	−3.32964e14	+	3.21675e14i	−0.112467	+	0.108654i
$241$	1.97767e14	−	3.42542e14i	0.0650193	−	0.112617i	−0.831683	−	0.555250i	$-0.812622\pi$
$241$	1.97767e14	−	3.42542e14i	0.0650193	−	0.112617i	0.896703	+	0.442634i	$0.145956\pi$
$242$	1.88788e15			0.604191
$243$	2.45647e15	−	2.06563e15i	0.765368	−	0.643593i
$244$	−1.17591e15			−0.356731
$245$	1.26951e14	−	2.19886e14i	0.0375022	−	0.0649558i
$246$	−2.73983e14	+	2.64694e14i	−0.0788217	+	0.0761492i
$247$	2.47412e15	+	4.28530e15i	0.693250	+	1.20074i
$248$	−1.06352e15	−	1.84207e15i	−0.290275	−	0.502771i
$249$	−2.82785e14	−	1.13317e15i	−0.0751900	−	0.301301i
$250$	−1.37337e15	+	2.37874e15i	−0.355776	+	0.616222i
$251$	−2.94268e15			−0.742786			−0.371393	−	0.928476i	$-0.621120\pi$
$251$	−2.94268e15			−0.742786			−0.371393	+	0.928476i	$0.621120\pi$
$252$	6.57495e13	−	1.90581e15i	0.0161729	−	0.468787i
$253$	−5.79042e14			−0.138812
$254$	−2.00857e15	+	3.47894e15i	−0.469318	+	0.812882i
$255$	2.72296e15	+	7.80178e14i	0.620199	+	0.177698i
$256$	−1.40737e14	−	2.43764e14i	−0.0312500	−	0.0541266i
$257$	−4.25116e15	−	7.36322e15i	−0.920326	−	1.59405i	−0.798910	−	0.601450i	$-0.794590\pi$
$257$	−4.25116e15	−	7.36322e15i	−0.920326	−	1.59405i	−0.121416	−	0.992602i	$-0.538743\pi$
$258$	−2.58531e15	−	7.40736e14i	−0.545738	−	0.156364i
$259$	1.87172e15	−	3.24191e15i	0.385293	−	0.667348i
$260$	−1.55639e15			−0.312458
$261$	−4.71229e15	−	2.94181e15i	−0.922718	−	0.576038i
$262$	−3.80190e15			−0.726176
$263$	−4.13547e14	+	7.16284e14i	−0.0770570	+	0.133467i	−0.901979	−	0.431780i	$-0.857886\pi$
$263$	−4.13547e14	+	7.16284e14i	−0.0770570	+	0.133467i	0.824922	+	0.565247i	$0.191219\pi$
$264$	−1.79647e14	−	7.19879e14i	−0.0326583	−	0.130868i
$265$	6.49780e14	+	1.12545e15i	0.115257	+	0.199631i
$266$	2.65941e15	+	4.60624e15i	0.460315	+	0.797289i
$267$	−5.48266e15	+	5.29677e15i	−0.926121	+	0.894721i
$268$	−1.79167e15	+	3.10327e15i	−0.295381	+	0.511615i
$269$	−1.21446e16			−1.95431			−0.977156	−	0.212521i	$-0.931833\pi$
$269$	−1.21446e16			−1.95431			−0.977156	+	0.212521i	$0.931833\pi$
$270$	−1.88540e15	−	2.09129e15i	−0.296168	−	0.328511i
$271$	−8.66147e14			−0.132828			−0.0664142	−	0.997792i	$-0.521156\pi$
$271$	−8.66147e14			−0.132828			−0.0664142	+	0.997792i	$0.521156\pi$
$272$	−8.61058e14	+	1.49140e15i	−0.128924	+	0.223303i
$273$	4.61053e15	−	4.45421e15i	0.674052	−	0.651199i
$274$	4.29190e15	+	7.43379e15i	0.612733	+	1.06128i
$275$	−8.32826e14	−	1.44250e15i	−0.116116	−	0.201119i
$276$	−3.23482e14	−	1.29625e15i	−0.0440495	−	0.176515i
$277$	1.11698e15	−	1.93467e15i	0.148569	−	0.257329i	−0.782130	−	0.623116i	$-0.785867\pi$
$277$	1.11698e15	−	1.93467e15i	0.148569	−	0.257329i	0.930699	+	0.365787i	$0.119200\pi$
$278$	9.52388e15			1.23744
$279$	1.14196e16	−	6.07806e15i	1.44951	−	0.771503i
$280$	−1.67296e15			−0.207471
$281$	−2.37385e15	+	4.11163e15i	−0.287649	+	0.498222i	−0.973248	−	0.229757i	$-0.926207\pi$
$281$	−2.37385e15	+	4.11163e15i	−0.287649	+	0.498222i	0.685599	+	0.727979i	$0.259540\pi$
$282$	2.36259e14	+	6.76924e13i	0.0279750	+	0.00801532i
$283$	3.28026e15	+	5.68158e15i	0.379574	+	0.657442i	0.991000	−	0.133860i	$-0.0427371\pi$
$283$	3.28026e15	+	5.68158e15i	0.379574	+	0.657442i	−0.611426	+	0.791302i	$0.709404\pi$
$284$	−3.36737e15	−	5.83246e15i	−0.380822	−	0.659603i
$285$	7.54978e15	+	2.16315e15i	0.834531	+	0.239108i
$286$	1.24714e15	−	2.16011e15i	0.134752	−	0.233398i
$287$	−1.37661e15			−0.145405
$288$	1.51117e15	−	8.04320e14i	0.156050	−	0.0830573i
$289$	6.31651e14			0.0637736
$290$	−2.43677e15	+	4.22061e15i	−0.240562	+	0.416666i
$291$	−3.66643e14	−	1.46921e15i	−0.0353948	−	0.141834i
$292$	3.33799e15	+	5.78157e15i	0.315135	+	0.545830i
$293$	5.53057e15	+	9.57923e15i	0.510658	+	0.884486i	0.999924	+	0.0123510i	$0.00393155\pi$
$293$	5.53057e15	+	9.57923e15i	0.510658	+	0.884486i	−0.489266	+	0.872135i	$0.662735\pi$
$294$	−6.75207e14	+	6.52315e14i	−0.0609789	+	0.0589114i
$295$	6.32325e15	−	1.09522e16i	0.558595	−	0.967516i
$296$	3.36054e15			0.290411
$297$	4.41327e15	−	9.40981e14i	0.373116	−	0.0795543i
$298$	−1.40990e15			−0.116622
$299$	2.24567e15	−	3.88961e15i	0.181754	−	0.314807i
$300$	2.76394e15	−	2.67023e15i	0.218897	−	0.211476i
$301$	−4.85900e15	−	8.41604e15i	−0.376587	−	0.652267i
$302$	1.34082e15	+	2.32237e15i	0.101701	+	0.176151i
$303$	3.76698e15	+	1.50950e16i	0.279651	+	1.12061i
$304$	−2.38740e15	+	4.13509e15i	−0.173479	+	0.300474i
$305$	−6.27419e15			−0.446281
$306$	−8.88451e15	−	5.54646e15i	−0.618649	−	0.386213i
$307$	−4.85853e15			−0.331211			−0.165606	−	0.986192i	$-0.552958\pi$
$307$	−4.85853e15			−0.331211			−0.165606	+	0.986192i	$0.552958\pi$
$308$	1.34054e15	−	2.32189e15i	0.0894749	−	0.154975i
$309$	4.63517e15	+	1.32806e15i	0.302925	+	0.0867934i
$310$	−5.67452e15	−	9.82856e15i	−0.363144	−	0.628983i
$311$	−3.88280e15	−	6.72520e15i	−0.243334	−	0.421466i	0.718328	−	0.695704i	$-0.244908\pi$
$311$	−3.88280e15	−	6.72520e15i	−0.243334	−	0.421466i	−0.961662	+	0.274238i	$0.911574\pi$
$312$	5.53237e15	+	1.58512e15i	0.339552	+	0.0972877i
$313$	1.24807e16	−	2.16172e16i	0.750241	−	1.29945i	−0.197465	−	0.980310i	$-0.563271\pi$
$313$	1.24807e16	−	2.16172e16i	0.750241	−	1.29945i	0.947706	−	0.319145i	$-0.103396\pi$
$314$	8.63195e15			0.508237
$315$	3.50813e14	−	1.01686e16i	0.0202329	−	0.586468i
$316$	−1.23983e16			−0.700478
$317$	−5.36996e14	+	9.30105e14i	−0.0297226	+	0.0514810i	−0.880504	−	0.474039i	$-0.842796\pi$
$317$	−5.36996e14	+	9.30105e14i	−0.0297226	+	0.0514810i	0.850782	+	0.525520i	$0.176129\pi$
$318$	−1.16349e15	−	4.66232e15i	−0.0630937	−	0.252829i
$319$	−3.90518e15	−	6.76397e15i	−0.207492	−	0.359387i
$320$	−7.50919e14	−	1.30063e15i	−0.0390947	−	0.0677141i
$321$	−2.63052e16	+	2.54133e16i	−1.34202	+	1.29652i
$322$	2.41386e15	−	4.18092e15i	0.120684	−	0.209030i
$323$	2.92131e16			1.43140
$324$	4.57197e15	+	9.35393e15i	0.219564	+	0.449212i
$325$	1.29196e16			0.608147
$326$	5.30101e15	−	9.18161e15i	0.244593	−	0.423648i
$327$	−1.83011e16	+	1.76806e16i	−0.827783	+	0.799717i
$328$	−6.17902e14	−	1.07024e15i	−0.0273993	−	0.0474570i
$329$	4.44042e14	+	7.69103e14i	0.0193041	+	0.0334358i
$330$	−9.58524e14	−	3.84099e15i	−0.0408566	−	0.163720i
$331$	−1.86953e16	+	3.23811e16i	−0.781357	+	1.35335i	0.149795	+	0.988717i	$0.452139\pi$
$331$	−1.86953e16	+	3.23811e16i	−0.781357	+	1.35335i	−0.931152	+	0.364632i	$0.881195\pi$
$332$	3.78866e15			0.155270
$333$	−7.04693e14	+	2.04262e16i	−0.0283213	+	0.820917i
$334$	1.03693e16			0.408693
$335$	−9.55965e15	+	1.65578e16i	−0.369531	+	0.640046i
$336$	5.94672e15	+	1.70384e15i	0.225461	+	0.0645986i
$337$	−4.45382e15	−	7.71424e15i	−0.165630	−	0.286879i	0.771249	−	0.636533i	$-0.219632\pi$
$337$	−4.45382e15	−	7.71424e15i	−0.165630	−	0.286879i	−0.936879	+	0.349655i	$0.886299\pi$
$338$	−1.85608e13	−	3.21483e13i	−0.000677079	−	0.00117274i
$339$	−1.78943e16	−	5.12702e15i	−0.640347	−	0.183471i
$340$	−4.59426e15	+	7.95750e15i	−0.161288	+	0.279360i
$341$	1.81880e16			0.626444
$342$	−2.46335e16	−	1.53783e16i	−0.832446	−	0.519683i
$343$	−3.16853e16			−1.05062
$344$	4.36200e15	−	7.55521e15i	0.141924	−	0.245820i
$345$	−1.72597e15	−	6.91629e15i	−0.0551073	−	0.220825i
$346$	−8.57477e15	−	1.48519e16i	−0.268675	−	0.465359i
$347$	8.89968e15	+	1.54147e16i	0.273674	+	0.474017i	0.969800	−	0.243903i	$-0.0784279\pi$
$347$	8.89968e15	+	1.54147e16i	0.273674	+	0.474017i	−0.696126	+	0.717920i	$0.745095\pi$
$348$	1.29603e16	−	1.25209e16i	0.391156	−	0.377894i
$349$	−2.02979e16	+	3.51571e16i	−0.601294	+	1.04147i	0.391332	+	0.920250i	$0.372014\pi$
$349$	−2.02979e16	+	3.51571e16i	−0.601294	+	1.04147i	−0.992625	+	0.121222i	$0.961319\pi$
$350$	1.38872e16			0.403807
$351$	−1.07949e16	+	3.32947e16i	−0.308121	+	0.950340i
$352$	2.40685e15			0.0674408
$353$	2.52713e16	−	4.37711e16i	0.695170	−	1.20407i	−0.274953	−	0.961458i	$-0.588662\pi$
$353$	2.52713e16	−	4.37711e16i	0.695170	−	1.20407i	0.970123	−	0.242613i	$-0.0780044\pi$
$354$	−3.36311e16	+	3.24908e16i	−0.908280	+	0.877485i
$355$	−1.79670e16	−	3.11197e16i	−0.476420	−	0.825184i
$356$	−1.23648e16	−	2.14165e16i	−0.321930	−	0.557600i
$357$	−9.16375e15	−	3.67209e16i	−0.234277	−	0.938793i
$358$	2.60595e16	−	4.51363e16i	0.654223	−	1.13315i
$359$	−4.12005e16			−1.01575			−0.507877	−	0.861430i	$-0.669570\pi$
$359$	−4.12005e16			−1.01575			−0.507877	+	0.861430i	$0.669570\pi$
$360$	8.06301e15	−	4.29153e15i	0.195223	−	0.103907i
$361$	3.89441e16			0.926073
$362$	−2.18423e16	+	3.78320e16i	−0.510144	+	0.883595i
$363$	−3.58056e16	−	1.02589e16i	−0.821405	−	0.235347i
$364$	1.03979e16	+	1.80097e16i	0.234308	+	0.405834i
$365$	1.78102e16	+	3.08481e16i	0.394244	+	0.682850i
$366$	2.23023e16	+	6.39001e15i	0.484979	+	0.138955i
$367$	1.92069e16	−	3.32673e16i	0.410325	−	0.710703i	−0.584600	−	0.811321i	$-0.698749\pi$
$367$	1.92069e16	−	3.32673e16i	0.410325	−	0.710703i	0.994925	+	0.100618i	$0.0320820\pi$
$368$	4.33391e15			0.0909640
$369$	6.63474e15	−	3.53133e15i	0.136821	−	0.0728228i
$370$	1.79305e16			0.363313
$371$	8.68209e15	−	1.50378e16i	0.172860	−	0.299402i
$372$	1.01607e16	+	4.07160e16i	0.198791	+	0.796593i
$373$	2.62379e16	+	4.54454e16i	0.504455	+	0.873741i	0.999987	+	0.00515150i	$0.00163978\pi$
$373$	2.62379e16	+	4.54454e16i	0.504455	+	0.873741i	−0.495532	+	0.868590i	$0.665027\pi$
$374$	−7.36279e15	−	1.27527e16i	−0.139116	−	0.240956i
$375$	3.89736e16	−	3.76522e16i	0.723715	−	0.699177i
$376$	−3.98623e14	+	6.90436e14i	−0.00727514	+	0.0126009i
$377$	6.05810e16			1.08672
$378$	−1.16034e16	+	3.57883e16i	−0.204591	+	0.631022i
$379$	−3.80121e16			−0.658820			−0.329410	−	0.944187i	$-0.606850\pi$
$379$	−3.80121e16			−0.658820			−0.329410	+	0.944187i	$0.606850\pi$
$380$	−1.27382e16	+	2.20632e16i	−0.217027	+	0.375903i
$381$	5.69994e16	−	5.50668e16i	0.954680	−	0.922312i
$382$	−1.90158e16	−	3.29363e16i	−0.313113	−	0.542328i
$383$	9.58764e15	+	1.66063e16i	0.155210	+	0.268832i	0.933135	−	0.359525i	$-0.117061\pi$
$383$	9.58764e15	+	1.66063e16i	0.155210	+	0.268832i	−0.777926	+	0.628357i	$0.783728\pi$
$384$	1.34459e15	+	5.38802e15i	0.0214011	+	0.0857583i
$385$	7.15261e15	−	1.23887e16i	0.111936	−	0.193879i
$386$	−5.34738e16			−0.822856
$387$	4.50077e16	+	2.80976e16i	0.681029	+	0.425156i
$388$	4.91218e15			0.0730916
$389$	3.75175e16	−	6.49823e16i	0.548987	−	0.950873i	−0.449358	−	0.893352i	$-0.648347\pi$
$389$	3.75175e16	−	6.49823e16i	0.548987	−	0.950873i	0.998344	−	0.0575208i	$-0.0183195\pi$
$390$	2.95185e16	+	8.45759e15i	0.424791	+	0.121710i
$391$	−1.32578e16	−	2.29633e16i	−0.187639	−	0.325001i
$392$	−1.52277e15	−	2.63751e15i	−0.0211970	−	0.0367142i
$393$	7.21068e16	+	2.06599e16i	0.987245	+	0.282863i
$394$	−2.92399e16	+	5.06451e16i	−0.393778	+	0.682043i
$395$	−6.61522e16			−0.876320
$396$	−5.04709e14	+	1.46294e16i	−0.00657692	+	0.190638i
$397$	6.62792e16			0.849647			0.424824	−	0.905276i	$-0.360336\pi$
$397$	6.62792e16			0.849647			0.424824	+	0.905276i	$0.360336\pi$
$398$	−1.69544e16	+	2.93658e16i	−0.213817	+	0.370341i
$399$	−2.54077e16	−	1.01814e17i	−0.315240	−	1.26323i
$400$	6.23339e15	+	1.07966e16i	0.0760912	+	0.131794i
$401$	4.76233e15	+	8.24860e15i	0.0571980	+	0.0990699i	0.893207	−	0.449646i	$-0.148450\pi$
$401$	4.76233e15	+	8.24860e15i	0.0571980	+	0.0990699i	−0.836009	+	0.548716i	$0.815117\pi$
$402$	5.08443e16	−	4.91205e16i	0.600860	−	0.580488i
$403$	−7.05377e16	+	1.22175e17i	−0.820236	+	1.42069i
$404$	−5.04688e16			−0.577490
$405$	2.43942e16	+	4.99089e16i	0.274681	+	0.561979i
$406$	6.51182e16			0.721578
$407$	−1.43677e16	+	2.48857e16i	−0.156684	+	0.271385i
$408$	2.44352e16	−	2.36068e16i	0.262256	−	0.253364i
$409$	−8.61134e15	−	1.49153e16i	−0.0909639	−	0.157554i	0.816953	−	0.576704i	$-0.195661\pi$
$409$	−8.61134e15	−	1.49153e16i	−0.0909639	−	0.157554i	−0.907917	+	0.419150i	$0.862328\pi$
$410$	−3.29688e15	−	5.71036e15i	−0.0342774	−	0.0593702i
$411$	−4.10043e16	−	1.64312e17i	−0.419621	−	1.68150i
$412$	−7.82059e15	+	1.35457e16i	−0.0787784	+	0.136448i
$413$	−1.68977e17			−1.67553
$414$	−9.08807e14	+	2.63426e16i	−0.00887094	+	0.257132i
$415$	2.02148e16			0.194248
$416$	−9.33438e15	+	1.61676e16i	−0.0883037	+	0.152946i
$417$	−1.80630e17	−	5.17537e16i	−1.68231	−	0.482011i
$418$	−2.04143e16	−	3.53586e16i	−0.187193	−	0.324227i
$419$	7.14576e16	+	1.23768e17i	0.645145	+	1.11742i	0.984268	+	0.176682i	$0.0565365\pi$
$419$	7.14576e16	+	1.23768e17i	0.645145	+	1.11742i	−0.339123	+	0.940742i	$0.610130\pi$
$420$	3.17293e16	+	9.09101e15i	0.282059	+	0.0808150i
$421$	−5.30966e16	+	9.19660e16i	−0.464765	+	0.804996i	−0.999191	−	0.0402192i	$-0.987194\pi$
$421$	−5.30966e16	+	9.19660e16i	−0.464765	+	0.804996i	0.534426	+	0.845215i	$0.320528\pi$
$422$	2.53744e15			0.0218708
$423$	−4.11305e15	−	2.56771e15i	−0.0349101	−	0.0217938i
$424$	1.55881e16			0.130291
$425$	3.81371e16	−	6.60553e16i	0.313920	−	0.543726i
$426$	3.21714e16	+	1.28917e17i	0.260800	+	1.04508i
$427$	4.19166e16	+	7.26016e16i	0.334660	+	0.579649i
$428$	−5.93249e16	−	1.02754e17i	−0.466501	−	0.808003i
$429$	−3.53915e16	+	3.41916e16i	−0.274111	+	0.264818i
$430$	2.32739e16	−	4.03116e16i	0.177552	−	0.307528i
$431$	−9.79018e16			−0.735679			−0.367840	−	0.929889i	$-0.619902\pi$
$431$	−9.79018e16			−0.735679			−0.367840	+	0.929889i	$0.619902\pi$
$432$	−3.30317e16	+	7.04289e15i	−0.244504	+	0.0521322i
$433$	1.01860e17			0.742736			0.371368	−	0.928486i	$-0.378889\pi$
$433$	1.01860e17			0.742736			0.371368	+	0.928486i	$0.378889\pi$
$434$	−7.58206e16	+	1.31325e17i	−0.544633	+	0.943332i
$435$	6.91510e16	−	6.68065e16i	0.489349	−	0.472758i
$436$	−4.12736e16	−	7.14880e16i	−0.287747	−	0.498392i
$437$	−3.67591e16	−	6.36687e16i	−0.252485	−	0.437317i
$438$	−3.18907e16	−	1.27792e17i	−0.215816	−	0.864814i
$439$	−7.75733e16	+	1.34361e17i	−0.517241	+	0.895887i	0.482559	+	0.875864i	$0.339707\pi$
$439$	−7.75733e16	+	1.34361e17i	−0.517241	+	0.895887i	−0.999800	+	0.0200235i	$0.993626\pi$
$440$	1.28420e16			0.0843705
$441$	1.63507e16	−	8.70266e15i	0.105849	−	0.0563380i
$442$	1.14219e17			0.728607
$443$	4.10565e15	−	7.11119e15i	0.0258082	−	0.0447011i	−0.852833	−	0.522184i	$-0.825117\pi$
$443$	4.10565e15	−	7.11119e15i	0.0258082	−	0.0447011i	0.878641	+	0.477483i	$0.158451\pi$
$444$	−6.37360e16	−	1.82615e16i	−0.394817	−	0.113122i
$445$	−6.59736e16	−	1.14270e17i	−0.402745	−	0.697575i
$446$	−1.06995e17	−	1.85321e17i	−0.643706	−	1.11493i
$447$	2.67401e16	+	7.66152e15i	0.158549	+	0.0454272i
$448$	−1.00335e16	+	1.73785e16i	−0.0586333	+	0.101556i
$449$	−2.94000e16			−0.169335			−0.0846675	−	0.996409i	$-0.526983\pi$
$449$	−2.94000e16			−0.169335			−0.0846675	+	0.996409i	$0.526983\pi$
$450$	−6.69312e16	+	3.56241e16i	−0.379968	+	0.202238i
$451$	1.05672e16			0.0591306
$452$	3.01917e16	−	5.22935e16i	0.166528	−	0.288435i
$453$	−1.28100e16	−	5.13322e16i	−0.0696485	−	0.279095i
$454$	5.01367e16	+	8.68393e16i	0.268715	+	0.465429i
$455$	5.54792e16	+	9.60928e16i	0.293127	+	0.507711i
$456$	6.77499e16	−	6.54529e16i	0.352888	−	0.340924i
$457$	−1.27616e17	+	2.21038e17i	−0.655316	+	1.13504i	0.326499	+	0.945198i	$0.394131\pi$
$457$	−1.27616e17	+	2.21038e17i	−0.655316	+	1.13504i	−0.981815	+	0.189842i	$0.939202\pi$
$458$	2.47662e17			1.25382
$459$	1.38364e17	+	1.53474e17i	0.690621	+	0.766039i
$460$	2.31240e16			0.113799
$461$	6.15012e16	−	1.06523e17i	0.298420	−	0.516878i	−0.677355	−	0.735656i	$-0.736874\pi$
$461$	6.15012e16	−	1.06523e17i	0.298420	−	0.516878i	0.975775	+	0.218778i	$0.0702072\pi$
$462$	−3.80422e16	+	3.67524e16i	−0.182009	+	0.175838i
$463$	2.63262e16	+	4.55984e16i	0.124197	+	0.215116i	0.921419	−	0.388571i	$-0.127031\pi$
$463$	2.63262e16	+	4.55984e16i	0.124197	+	0.215116i	−0.797222	+	0.603687i	$0.793698\pi$
$464$	2.92288e16	+	5.06258e16i	0.135970	+	0.235508i
$465$	5.42137e16	+	2.17245e17i	0.248694	+	0.996563i
$466$	1.63002e16	−	2.82328e16i	0.0737368	−	0.127716i
$467$	3.35303e17			1.49581			0.747907	−	0.663803i	$-0.231059\pi$
$467$	3.35303e17			1.49581			0.747907	+	0.663803i	$0.231059\pi$
$468$	−9.63133e16	−	6.01269e16i	−0.423729	−	0.264528i
$469$	2.55464e17			1.10843
$470$	−2.12690e15	+	3.68389e15i	−0.00910144	+	0.0157642i
$471$	−1.63714e17	−	4.69069e16i	−0.690954	−	0.197971i
$472$	−7.58468e16	−	1.31370e17i	−0.315729	−	0.546858i
$473$	3.72989e16	+	6.46036e16i	0.153143	+	0.265252i
$474$	2.35145e17	+	6.73733e16i	0.952308	+	0.272853i
$475$	1.05740e17	−	1.83147e17i	0.422407	−	0.731630i
$476$	1.22773e17			0.483792
$477$	−3.26877e15	+	9.47482e16i	−0.0127062	+	0.368300i
$478$	−1.01718e17			−0.390048
$479$	1.28704e17	−	2.22922e17i	0.486869	−	0.843282i	−0.513017	−	0.858378i	$-0.671472\pi$
$479$	1.28704e17	−	2.22922e17i	0.486869	−	0.843282i	0.999886	+	0.0150967i	$0.00480562\pi$
$480$	7.17419e15	+	2.87483e16i	0.0267735	+	0.107286i
$481$	−1.11443e17	−	1.93026e17i	−0.410309	−	0.710676i
$482$	−1.26571e16	−	2.19227e16i	−0.0459756	−	0.0796321i
$483$	−6.85008e16	+	6.61783e16i	−0.245493	+	0.237170i
$484$	6.04122e16	−	1.04637e17i	0.213614	−	0.369990i
$485$	2.62094e16			0.0914400
$486$	−3.58817e16	−	2.02251e17i	−0.123520	−	0.696235i
$487$	−1.57963e17			−0.536560			−0.268280	−	0.963341i	$-0.586455\pi$
$487$	−1.57963e17			−0.536560			−0.268280	+	0.963341i	$0.586455\pi$
$488$	−3.76291e16	+	6.51756e16i	−0.126123	+	0.218452i
$489$	−1.50433e17	+	1.45332e17i	−0.497548	+	0.480679i
$490$	−8.12487e15	−	1.40727e16i	−0.0265181	−	0.0459307i
$491$	9.68006e16	+	1.67664e17i	0.311780	+	0.540019i	0.978748	−	0.205068i	$-0.0657414\pi$
$491$	9.68006e16	+	1.67664e17i	0.311780	+	0.540019i	−0.666968	+	0.745087i	$0.732408\pi$
$492$	5.90336e15	+	2.36559e16i	0.0187640	+	0.0751910i
$493$	1.78827e17	−	3.09738e17i	0.560956	−	0.971604i
$494$	3.16687e17			0.980404
$495$	−2.69293e15	+	7.80569e16i	−0.00822794	+	0.238494i
$496$	−1.36131e17			−0.410511
$497$	−2.40067e17	+	4.15808e17i	−0.714522	+	1.23759i
$498$	−7.18559e16	−	2.05880e16i	−0.211092	−	0.0604816i
$499$	−2.03789e17	−	3.52972e17i	−0.590917	−	1.02350i	−0.994109	−	0.108383i	$-0.965433\pi$
$499$	−2.03789e17	−	3.52972e17i	−0.590917	−	1.02350i	0.403192	−	0.915115i	$-0.367901\pi$
$500$	8.78955e16	+	1.52239e17i	0.251572	+	0.435735i
$501$	−1.96664e17	−	5.63478e16i	−0.555623	−	0.159196i
$502$	−9.41657e16	+	1.63100e17i	−0.262615	+	0.454862i
$503$	−3.41866e17			−0.941162			−0.470581	−	0.882357i	$-0.655956\pi$
$503$	−3.41866e17			−0.941162			−0.470581	+	0.882357i	$0.655956\pi$
$504$	−1.03527e17	−	6.46301e16i	−0.281354	−	0.175645i
$505$	−2.69282e17			−0.722458
$506$	−1.85294e16	+	3.20938e16i	−0.0490774	+	0.0850046i
$507$	1.77328e14	+	7.10587e14i	0.000463688	+	0.00185809i
$508$	1.28548e17	+	2.22652e17i	0.331858	+	0.574794i
$509$	−3.30769e17	−	5.72909e17i	−0.843062	−	1.46023i	−0.887294	−	0.461205i	$-0.847417\pi$
$509$	−3.30769e17	−	5.72909e17i	−0.843062	−	1.46023i	0.0442315	−	0.999021i	$-0.485916\pi$
$510$	1.30377e17	−	1.25956e17i	0.328091	−	0.316967i
$511$	2.37972e17	−	4.12180e17i	0.591276	−	1.02412i
$512$	−1.80144e16			−0.0441942
$513$	3.83632e17	+	4.25526e17i	0.929290	+	1.03077i
$514$	−5.44148e17			−1.30154
$515$	−4.17275e16	+	7.22742e16i	−0.0985543	+	0.170701i
$516$	−1.23786e17	+	1.19589e17i	−0.288700	+	0.278912i
$517$	−3.40857e15	−	5.90382e15i	−0.00785026	−	0.0135970i
$518$	−1.19790e17	−	2.07482e17i	−0.272444	−	0.471886i
$519$	8.19223e16	+	3.28278e17i	0.183999	+	0.737317i
$520$	−4.98045e16	+	8.62640e16i	−0.110471	+	0.191341i
$521$	1.27627e17			0.279575			0.139787	−	0.990182i	$-0.455358\pi$
$521$	1.27627e17			0.279575			0.139787	+	0.990182i	$0.455358\pi$
$522$	−3.13845e17	+	1.67044e17i	−0.678980	+	0.361387i
$523$	−1.90574e17			−0.407196			−0.203598	−	0.979055i	$-0.565264\pi$
$523$	−1.90574e17			−0.407196			−0.203598	+	0.979055i	$0.565264\pi$
$524$	−1.21661e17	+	2.10723e17i	−0.256742	+	0.444690i
$525$	−2.63385e17	−	7.54646e16i	−0.548980	−	0.157292i
$526$	2.64670e16	+	4.58422e16i	0.0544875	+	0.0943752i
$527$	4.16436e17	+	7.21289e17i	0.846797	+	1.46670i
$528$	−4.56484e16	−	1.30791e16i	−0.0916865	−	0.0262698i
$529$	2.18653e17	−	3.78718e17i	0.433804	−	0.751371i
$530$	8.31718e16			0.162998
$531$	8.14406e17	−	4.33467e17i	1.57662	−	0.839154i
$532$	3.40405e17			0.650984
$533$	−4.09822e16	+	7.09833e16i	−0.0774227	+	0.134100i
$534$	1.18132e17	+	4.73376e17i	0.220469	+	0.883463i
$535$	−3.16534e17	−	5.48253e17i	−0.583608	−	1.01084i
$536$	1.14667e17	+	1.98609e17i	0.208866	+	0.361766i
$537$	−7.39519e17	+	7.14446e17i	−1.33081	+	1.28569i
$538$	−3.88628e17	+	6.73123e17i	−0.690954	+	1.19677i
$539$	2.60419e16			0.0457453
$540$	−1.76244e17	+	3.75780e16i	−0.305882	+	0.0652191i
$541$	6.46355e17			1.10838			0.554191	−	0.832390i	$-0.313028\pi$
$541$	6.46355e17			1.10838			0.554191	+	0.832390i	$0.313028\pi$
$542$	−2.77167e16	+	4.80067e16i	−0.0469619	+	0.0813405i
$543$	6.19844e17	−	5.98829e17i	1.03773	−	1.00254i
$544$	5.51077e16	+	9.54494e16i	0.0911632	+	0.157899i
$545$	−2.20220e17	−	3.81432e17i	−0.359981	−	0.623505i
$546$	−9.93405e16	−	3.98076e17i	−0.160463	−	0.643005i
$547$	−1.79901e17	+	3.11598e17i	−0.287155	+	0.497367i	−0.973129	−	0.230259i	$-0.926043\pi$
$547$	−1.79901e17	+	3.11598e17i	−0.287155	+	0.497367i	0.685975	+	0.727625i	$0.259376\pi$
$548$	5.49363e17			0.866535
$549$	−3.88262e17	−	2.42386e17i	−0.605209	−	0.377822i
$550$	−1.06602e17			−0.164213
$551$	4.95822e17	−	8.58789e17i	0.754815	−	1.30738i
$552$	−8.21971e16	−	2.35509e16i	−0.123667	−	0.0354327i
$553$	4.41949e17	+	7.65478e17i	0.657141	+	1.13820i
$554$	−7.14869e16	−	1.23819e17i	−0.105054	−	0.181959i
$555$	−3.40070e17	−	9.74360e16i	−0.493928	−	0.141519i
$556$	3.04764e17	−	5.27867e17i	0.437500	−	0.757772i
$557$	−1.20436e18			−1.70883			−0.854413	−	0.519595i	$-0.826083\pi$
$557$	−1.20436e18			−1.70883			−0.854413	+	0.519595i	$0.826083\pi$
$558$	2.85461e16	−	8.27435e17i	0.0400336	−	1.16041i
$559$	−5.78617e17			−0.802075
$560$	−5.35346e16	+	9.27247e16i	−0.0733521	+	0.127050i
$561$	7.03432e16	+	2.81879e17i	0.0952716	+	0.381771i
$562$	1.51926e17	+	2.63144e17i	0.203398	+	0.352296i
$563$	−7.49238e15	−	1.29772e16i	−0.00991551	−	0.0171742i	0.861025	−	0.508563i	$-0.169823\pi$
$563$	−7.49238e15	−	1.29772e16i	−0.00991551	−	0.0171742i	−0.870941	+	0.491388i	$0.836490\pi$
$564$	1.13122e16	−	1.09287e16i	0.0147990	−	0.0142972i
$565$	1.61091e17	−	2.79018e17i	0.208332	−	0.360842i
$566$	4.19874e17			0.536799
$567$	4.14547e17	−	6.15707e17i	0.523942	−	0.778188i
$568$	−4.31024e17			−0.538563
$569$	3.97144e17	−	6.87874e17i	0.490590	−	0.849727i	−0.509351	−	0.860559i	$-0.670115\pi$
$569$	3.97144e17	−	6.87874e17i	0.490590	−	0.849727i	0.999941	+	0.0108318i	$0.00344793\pi$
$570$	3.61487e17	−	3.49230e17i	0.441474	−	0.426506i
$571$	4.75009e17	+	8.22740e17i	0.573545	+	0.993408i	0.996198	+	0.0871169i	$0.0277654\pi$
$571$	4.75009e17	+	8.22740e17i	0.573545	+	0.993408i	−0.422654	+	0.906291i	$0.638901\pi$
$572$	−7.98170e16	−	1.38247e17i	−0.0952843	−	0.165037i
$573$	1.81674e17	+	7.28003e17i	0.214431	+	0.859267i
$574$	−4.40515e16	+	7.62995e16i	−0.0514084	+	0.0890419i
$575$	−1.91953e17			−0.221490
$576$	3.77756e15	−	1.09496e17i	0.00430988	−	0.124926i
$577$	2.58846e17			0.292011			0.146005	−	0.989284i	$-0.453358\pi$
$577$	2.58846e17			0.292011			0.146005	+	0.989284i	$0.453358\pi$
$578$	2.02128e16	−	3.50097e16i	0.0225474	−	0.0390532i
$579$	1.01418e18	+	2.90582e17i	1.11868	+	0.320522i
$580$	1.55953e17	+	2.70119e17i	0.170103	+	0.294627i
$581$	−1.35051e17	−	2.33915e17i	−0.145664	−	0.252298i
$582$	−9.31644e16	−	2.66933e16i	−0.0993689	−	0.0284710i
$583$	−6.66458e16	+	1.15434e17i	−0.0702954	+	0.121755i
$584$	4.27263e17			0.445668
$585$	−5.13890e17	−	3.20813e17i	−0.530099	−	0.330932i
$586$	7.07913e17			0.722180
$587$	−6.50180e17	+	1.12614e18i	−0.655973	+	1.13618i	0.325676	+	0.945481i	$0.394408\pi$
$587$	−6.50180e17	+	1.12614e18i	−0.655973	+	1.13618i	−0.981649	+	0.190697i	$0.938925\pi$
$588$	1.45483e16	+	5.82979e16i	0.0145164	+	0.0581701i
$589$	1.15462e18	+	1.99987e18i	1.13944	+	1.97357i
$590$	−4.04688e17	−	7.00940e17i	−0.394987	−	0.684137i
$591$	8.29775e17	−	8.01642e17i	0.801017	−	0.773859i
$592$	1.07537e17	−	1.86260e17i	0.102676	−	0.177839i
$593$	−1.53388e18			−1.44855			−0.724277	−	0.689509i	$-0.757826\pi$
$593$	−1.53388e18			−1.44855			−0.724277	+	0.689509i	$0.757826\pi$
$594$	8.90702e16	−	2.74720e17i	0.0831994	−	0.256612i
$595$	6.55069e17			0.605239
$596$	−4.51167e16	+	7.81445e16i	−0.0412322	+	0.0714163i
$597$	4.81133e17	−	4.64821e17i	0.434943	−	0.420196i
$598$	−1.43723e17	−	2.48935e17i	−0.128519	−	0.222602i
$599$	4.15847e17	+	7.20268e17i	0.367840	+	0.637118i	0.989228	−	0.146386i	$-0.0467641\pi$
$599$	4.15847e17	+	7.20268e17i	0.367840	+	0.637118i	−0.621388	+	0.783503i	$0.713431\pi$
$600$	−5.95531e16	−	2.38640e17i	−0.0521100	−	0.208815i
$601$	3.69383e17	−	6.39790e17i	0.319737	−	0.553800i	−0.660696	−	0.750653i	$-0.729739\pi$
$601$	3.69383e17	−	6.39790e17i	0.319737	−	0.553800i	0.980433	+	0.196853i	$0.0630722\pi$
$602$	−6.21953e17			−0.532574
$603$	−1.23124e18	+	6.55326e17i	−1.04299	+	0.555131i
$604$	1.71625e17			0.143827
$605$	3.22335e17	−	5.58301e17i	0.267238	−	0.462870i
$606$	9.57193e17	+	2.74253e17i	0.785104	+	0.224946i
$607$	9.65998e16	+	1.67316e17i	0.0783880	+	0.135772i	0.902555	−	0.430575i	$-0.141689\pi$
$607$	9.65998e16	+	1.67316e17i	0.0783880	+	0.135772i	−0.824167	+	0.566347i	$0.808356\pi$
$608$	1.52793e17	+	2.64646e17i	0.122668	+	0.212467i
$609$	−1.23503e18	−	3.53859e17i	−0.980993	−	0.281072i
$610$	−2.00774e17	+	3.47751e17i	−0.157784	+	0.273290i
$611$	5.28772e16			0.0411150
$612$	−5.91720e17	+	3.14943e17i	−0.455232	+	0.242297i
$613$	−1.81666e18			−1.38286			−0.691432	−	0.722441i	$-0.743020\pi$
$613$	−1.81666e18			−1.38286			−0.691432	+	0.722441i	$0.743020\pi$
$614$	−1.55473e17	+	2.69287e17i	−0.117101	+	0.202825i
$615$	3.14980e16	+	1.26218e17i	0.0234744	+	0.0940664i
$616$	−8.57948e16	−	1.48601e17i	−0.0632683	−	0.109584i
$617$	1.96368e17	+	3.40119e17i	0.143290	+	0.248186i	0.928734	−	0.370747i	$-0.120898\pi$
$617$	1.96368e17	+	3.40119e17i	0.143290	+	0.248186i	−0.785443	+	0.618934i	$0.787565\pi$
$618$	2.21934e17	−	2.14409e17i	0.160250	−	0.154817i
$619$	−1.15858e17	+	2.00672e17i	−0.0827822	+	0.143383i	−0.904444	−	0.426592i	$-0.859714\pi$
$619$	−1.15858e17	+	2.00672e17i	−0.0827822	+	0.143383i	0.821662	+	0.569975i	$0.193047\pi$
$620$	−7.26339e17			−0.513562
$621$	1.60385e17	−	4.94675e17i	0.112219	−	0.346118i
$622$	−4.96998e17			−0.344126
$623$	−8.81512e17	+	1.52682e18i	−0.604026	+	1.04620i
$624$	2.64892e17	−	2.55911e17i	0.179626	−	0.173536i
$625$	1.54363e16	+	2.67365e16i	0.0103591	+	0.0179426i
$626$	−7.98764e17	−	1.38350e18i	−0.530500	−	0.918853i
$627$	1.95036e17	+	7.81545e17i	0.128196	+	0.513707i
$628$	2.76222e17	−	4.78431e17i	0.179689	−	0.311230i
$629$	−1.31586e18			−0.847193
$630$	−5.52377e17	−	3.44840e17i	−0.351983	−	0.219738i
$631$	−3.03856e18			−1.91636			−0.958180	−	0.286165i	$-0.907620\pi$
$631$	−3.03856e18			−1.91636			−0.958180	+	0.286165i	$0.907620\pi$
$632$	−3.96744e17	+	6.87181e17i	−0.247656	+	0.428953i
$633$	−4.81251e16	−	1.37887e16i	−0.0297336	−	0.00851921i
$634$	3.43678e16	+	5.95267e16i	0.0210170	+	0.0364026i
$635$	6.85882e17	+	1.18798e18i	0.415165	+	0.719086i
$636$	−2.95644e17	−	8.47072e16i	−0.177132	−	0.0507515i
$637$	−1.00997e17	+	1.74932e17i	−0.0598966	+	0.103744i
$638$	−4.99863e17			−0.293438
$639$	9.03842e16	−	2.61987e18i	0.0525215	−	1.52238i
$640$	−9.61177e16			−0.0552883
$641$	1.47678e18	−	2.55785e18i	0.840887	−	1.45646i	−0.0482578	−	0.998835i	$-0.515367\pi$
$641$	1.47678e18	−	2.55785e18i	0.840887	−	1.45646i	0.889145	−	0.457625i	$-0.151300\pi$
$642$	5.66783e17	+	2.27121e18i	0.319477	+	1.28020i
$643$	−5.96115e17	−	1.03250e18i	−0.332628	−	0.576129i	0.650398	−	0.759593i	$-0.274602\pi$
$643$	−5.96115e17	−	1.03250e18i	−0.332628	−	0.576129i	−0.983026	+	0.183465i	$0.941269\pi$
$644$	−1.54487e17	−	2.67579e17i	−0.0853362	−	0.147807i
$645$	−6.60471e17	+	6.38078e17i	−0.361173	+	0.348928i
$646$	9.34819e17	−	1.61915e18i	0.506076	−	0.876550i
$647$	2.23653e18			1.19866			0.599331	−	0.800502i	$-0.295433\pi$
$647$	2.23653e18			1.19866			0.599331	+	0.800502i	$0.295433\pi$
$648$	6.64751e17	+	4.59218e16i	0.352713	+	0.0243659i
$649$	1.29711e18			0.681375
$650$	4.13428e17	−	7.16079e17i	0.215012	−	0.372412i
$651$	2.15165e18	−	2.07870e18i	1.10789	−	1.07032i
$652$	−3.39264e17	−	5.87623e17i	−0.172953	−	0.299564i
$653$	2.19229e17	+	3.79715e17i	0.110653	+	0.191656i	0.916034	−	0.401102i	$-0.131373\pi$
$653$	2.19229e17	+	3.79715e17i	0.110653	+	0.191656i	−0.805381	+	0.592758i	$0.798039\pi$
$654$	3.94323e17	+	1.58013e18i	0.197059	+	0.789654i
$655$	−6.49133e17	+	1.12433e18i	−0.321192	+	0.556322i
$656$	−7.90915e16			−0.0387485
$657$	−8.95955e16	+	2.59701e18i	−0.0434622	+	1.25979i
$658$	5.68374e16			0.0273002
$659$	−6.64942e17	+	1.15171e18i	−0.316248	+	0.547758i	−0.979702	−	0.200459i	$-0.935757\pi$
$659$	−6.64942e17	+	1.15171e18i	−0.316248	+	0.547758i	0.663454	+	0.748217i	$0.269090\pi$
$660$	−2.43562e17	−	6.97848e16i	−0.114703	−	0.0328644i
$661$	−2.57315e17	−	4.45682e17i	−0.119993	−	0.207834i	0.799772	−	0.600304i	$-0.204954\pi$
$661$	−2.57315e17	−	4.45682e17i	−0.119993	−	0.207834i	−0.919765	+	0.392471i	$0.871620\pi$
$662$	1.19650e18	+	2.07239e18i	0.552503	+	0.956963i
$663$	−2.16628e18	−	6.20677e17i	−0.990550	−	0.283810i
$664$	1.21237e17	−	2.09989e17i	0.0548964	−	0.0950833i
$665$	1.81627e18			0.814402
$666$	1.10958e18	+	6.92695e17i	0.492694	+	0.307581i
$667$	−9.00081e17			−0.395789
$668$	3.31818e17	−	5.74725e17i	0.144495	−	0.250273i
$669$	1.02222e18	+	4.09622e18i	0.440833	+	1.76650i
$670$	6.11818e17	+	1.05970e18i	0.261298	+	0.452581i
$671$	−3.21762e17	−	5.57307e17i	−0.136094	−	0.235721i
$672$	2.84731e17	−	2.75078e17i	0.119271	−	0.115227i
$673$	1.89072e18	−	3.27482e18i	0.784384	−	1.35859i	−0.144982	−	0.989434i	$-0.546312\pi$
$673$	1.89072e18	−	3.27482e18i	0.784384	−	1.35859i	0.929366	−	0.369159i	$-0.120354\pi$
$674$	−5.70089e17			−0.234236
$675$	1.46300e18	−	3.11936e17i	0.595348	−	0.126938i
$676$	−2.37579e15			−0.000957534
$677$	8.47886e17	−	1.46858e18i	0.338463	−	0.586235i	−0.645681	−	0.763607i	$-0.723426\pi$
$677$	8.47886e17	−	1.46858e18i	0.338463	−	0.586235i	0.984144	+	0.177372i	$0.0567597\pi$
$678$	−8.56784e17	+	8.27735e17i	−0.338749	+	0.327264i
$679$	−1.75100e17	−	3.03282e17i	−0.0685696	−	0.118766i
$680$	2.94033e17	+	5.09280e17i	0.114048	+	0.197537i
$681$	−4.79000e17	−	1.91944e18i	−0.184026	−	0.737427i
$682$	5.82017e17	−	1.00808e18i	0.221481	−	0.383617i
$683$	3.06899e18			1.15681			0.578404	−	0.815750i	$-0.303676\pi$
$683$	3.06899e18			1.15681			0.578404	+	0.815750i	$0.303676\pi$
$684$	−1.64062e18	+	8.73220e17i	−0.612554	+	0.326031i
$685$	2.93118e18			1.08406
$686$	−1.01393e18	+	1.75618e18i	−0.371451	+	0.643372i
$687$	−4.69716e18	−	1.34582e18i	−1.70458	−	0.488392i
$688$	−2.79168e17	−	4.83533e17i	−0.100355	−	0.173821i
$689$	−5.16938e17	−	8.95363e17i	−0.184083	−	0.318841i
$690$	−4.38571e17	−	1.25658e17i	−0.154711	−	0.0443274i
$691$	2.86999e17	−	4.97097e17i	0.100294	−	0.173714i	−0.811512	−	0.584336i	$-0.801355\pi$
$691$	2.86999e17	−	4.97097e17i	0.100294	−	0.173714i	0.911806	+	0.410622i	$0.134688\pi$
$692$	−1.09757e18			−0.379964
$693$	9.21224e17	−	4.90321e17i	0.315936	−	0.168157i
$694$	1.13916e18			0.387033
$695$	1.62610e18	−	2.81649e18i	0.547326	−	0.947996i
$696$	−2.79248e17	−	1.11900e18i	−0.0931174	−	0.373139i
$697$	2.41948e17	+	4.19067e17i	0.0799299	+	0.138443i
$698$	1.29907e18	+	2.25005e18i	0.425179	+	0.736431i
$699$	−4.62569e17	+	4.46886e17i	−0.149994	+	0.144909i
$700$	4.44392e17	−	7.69709e17i	0.142767	−	0.247280i
$701$	5.78307e18			1.84073			0.920367	−	0.391056i	$-0.127890\pi$
$701$	5.78307e18			1.84073			0.920367	+	0.391056i	$0.127890\pi$
$702$	1.49994e18	+	1.66374e18i	0.473025	+	0.524681i
$703$	−3.64841e18			−1.13997
$704$	7.70193e16	−	1.33401e17i	0.0238439	−	0.0412989i
$705$	6.03573e16	−	5.83110e16i	0.0185140	−	0.0178863i
$706$	−1.61736e18	−	2.80135e18i	−0.491560	−	0.851406i
$707$	1.79901e18	+	3.11598e18i	0.541762	+	0.938359i
$708$	7.24630e17	+	2.90373e18i	0.216222	+	0.866444i
$709$	−1.04576e18	+	1.81130e18i	−0.309193	+	0.535538i	−0.978186	−	0.207731i	$-0.933392\pi$
$709$	−1.04576e18	+	1.81130e18i	−0.309193	+	0.535538i	0.668993	+	0.743269i	$0.266726\pi$
$710$	−2.29977e18			−0.673760
$711$	−4.09366e18	−	2.55561e18i	−1.18839	−	0.741894i
$712$	−1.58269e18			−0.455278
$713$	1.04801e18	−	1.81521e18i	0.298734	−	0.517422i
$714$	−2.32852e18	−	6.67162e17i	−0.657721	−	0.188449i
$715$	−4.25872e17	−	7.37632e17i	−0.119204	−	0.206467i
$716$	−1.66781e18	−	2.88872e18i	−0.462605	−	0.801256i
$717$	1.92919e18	+	5.52748e17i	0.530275	+	0.151933i
$718$	−1.31842e18	+	2.28356e18i	−0.359123	+	0.622020i
$719$	−2.54253e18			−0.686321			−0.343161	−	0.939277i	$-0.611498\pi$
$719$	−2.54253e18			−0.686321			−0.343161	+	0.939277i	$0.611498\pi$
$720$	2.01556e16	−	5.84227e17i	0.00539180	−	0.156286i
$721$	1.11509e18			0.295618
$722$	1.24621e18	−	2.15850e18i	0.327416	−	0.567101i
$723$	1.20924e17	+	4.84566e17i	0.0314857	+	0.126169i
$724$	1.39791e18	+	2.42125e18i	0.360726	+	0.624796i
$725$	−1.29457e18	−	2.24226e18i	−0.331077	−	0.573442i
$726$	−1.71439e18	+	1.65626e18i	−0.434531	+	0.419798i
$727$	−2.67471e18	+	4.63273e18i	−0.671897	+	1.16376i	0.305469	+	0.952202i	$0.401187\pi$
$727$	−2.67471e18	+	4.63273e18i	−0.671897	+	1.16376i	−0.977366	+	0.211557i	$0.932147\pi$
$728$	1.33093e18			0.331362
$729$	−4.18520e17	+	4.03089e18i	−0.103273	+	0.994653i
$730$	2.27970e18			0.557545
$731$	−1.70800e18	+	2.95835e18i	−0.414024	+	0.717111i
$732$	1.06785e18	−	1.03164e18i	0.256558	−	0.247860i
$733$	5.07526e17	+	8.79060e17i	0.120860	+	0.209335i	0.920107	−	0.391667i	$-0.128101\pi$
$733$	5.07526e17	+	8.79060e17i	0.120860	+	0.209335i	−0.799247	+	0.601003i	$0.794768\pi$
$734$	−1.22924e18	−	2.12911e18i	−0.290143	−	0.502543i
$735$	7.76240e16	+	3.11054e17i	0.0181605	+	0.0727727i
$736$	1.38685e17	−	2.40210e17i	0.0321606	−	0.0557038i
$737$	−1.96100e18			−0.450754
$738$	1.65852e16	−	4.80737e17i	0.00377881	−	0.109532i
$739$	−4.21697e18			−0.952384			−0.476192	−	0.879341i	$-0.657983\pi$
$739$	−4.21697e18			−0.952384			−0.476192	+	0.879341i	$0.657983\pi$
$740$	5.73776e17	−	9.93809e17i	0.128451	−	0.222483i
$741$	−6.00629e18	−	1.72091e18i	−1.33287	−	0.381891i
$742$	−5.55654e17	−	9.62420e17i	−0.122230	−	0.211709i
$743$	−6.27655e17	−	1.08713e18i	−0.136865	−	0.237058i	0.789443	−	0.613824i	$-0.210369\pi$
$743$	−6.27655e17	−	1.08713e18i	−0.136865	−	0.237058i	−0.926309	+	0.376766i	$0.877036\pi$
$744$	2.58185e18	+	7.39747e17i	0.558094	+	0.159904i
$745$	−2.40725e17	+	4.16948e17i	−0.0515829	+	0.0893441i
$746$	3.35846e18			0.713407
$747$	1.25094e18	+	7.80944e17i	0.263423	+	0.164451i
$748$	−9.42437e17			−0.196740
$749$	−4.22940e18	+	7.32553e18i	−0.875279	+	1.51603i
$750$	−8.39743e17	−	3.36501e18i	−0.172285	−	0.690379i
$751$	−4.76700e18	−	8.25669e18i	−0.969584	−	1.67937i	−0.696759	−	0.717306i	$-0.745375\pi$
$751$	−4.76700e18	−	8.25669e18i	−0.969584	−	1.67937i	−0.272826	−	0.962064i	$-0.587958\pi$
$752$	2.55119e16	+	4.41879e16i	0.00514430	+	0.00891020i
$753$	2.67225e18	−	2.58165e18i	0.534207	−	0.516095i
$754$	1.93859e18	−	3.35774e18i	0.384214	−	0.665478i
$755$	9.15722e17			0.179932
$756$	1.61228e18	+	1.78835e18i	0.314086	+	0.348386i
$757$	8.60869e18			1.66270			0.831350	−	0.555749i	$-0.187569\pi$
$757$	8.60869e18			1.66270			0.831350	+	0.555749i	$0.187569\pi$
$758$	−1.21639e18	+	2.10684e18i	−0.232928	+	0.403443i
$759$	5.25829e17	−	5.08001e17i	0.0998327	−	0.0964479i
$760$	8.15245e17	+	1.41205e18i	0.153462	+	0.265803i
$761$	−2.59150e18	−	4.48862e18i	−0.483673	−	0.837746i	0.516151	−	0.856497i	$-0.327364\pi$
$761$	−2.59150e18	−	4.48862e18i	−0.483673	−	0.837746i	−0.999824	+	0.0187517i	$0.994031\pi$
$762$	−1.22813e18	−	4.92136e18i	−0.227268	−	0.910706i
$763$	−2.94248e18	+	5.09653e18i	−0.539889	+	0.935116i
$764$	−2.43402e18			−0.442809
$765$	−3.15719e18	+	1.68041e18i	−0.569509	+	0.303121i
$766$	1.22722e18			0.219500
$767$	−5.03052e18	+	8.71311e18i	−0.892160	+	1.54527i
$768$	3.41661e17	+	9.78920e16i	0.0600825	+	0.0172147i
$769$	2.02951e18	+	3.51522e18i	0.353892	+	0.612959i	0.986928	−	0.161164i	$-0.0515247\pi$
$769$	2.02951e18	+	3.51522e18i	0.353892	+	0.612959i	−0.633036	+	0.774123i	$0.718191\pi$
$770$	−4.57767e17	−	7.92876e17i	−0.0791507	−	0.137093i
$771$	1.03203e19	+	2.95695e18i	1.76946	+	0.506980i
$772$	−1.71116e18	+	2.96382e18i	−0.290923	+	0.503894i
$773$	1.51385e18			0.255221			0.127610	−	0.991824i	$-0.459269\pi$
$773$	1.51385e18			0.255221			0.127610	+	0.991824i	$0.459269\pi$
$774$	2.99757e18	−	1.59546e18i	0.501134	−	0.266728i
$775$	6.02935e18			0.999561
$776$	1.57190e17	−	2.72260e17i	0.0258418	−	0.0447593i
$777$	1.14446e18	+	4.58606e18i	0.186579	+	0.747658i
$778$	−2.40112e18	−	4.15886e18i	−0.388192	−	0.672369i
$779$	6.70833e17	+	1.16192e18i	0.107553	+	0.186287i
$780$	1.41336e18	−	1.36544e18i	0.224718	−	0.217099i
$781$	1.84281e18	−	3.19184e18i	0.290569	−	0.503280i
$782$	−1.69700e18			−0.265362
$783$	6.86012e18	−	1.46269e18i	1.06385	−	0.226830i
$784$	−1.94914e17			−0.0299770
$785$	1.47381e18	−	2.55272e18i	0.224797	−	0.389359i
$786$	3.45251e18	−	3.33545e18i	0.522261	−	0.504554i
$787$	2.55698e18	+	4.42882e18i	0.383612	+	0.664435i	0.991576	−	0.129530i	$-0.0413467\pi$
$787$	2.55698e18	+	4.42882e18i	0.383612	+	0.664435i	−0.607964	+	0.793965i	$0.708013\pi$
$788$	1.87136e18	+	3.24128e18i	0.278443	+	0.482277i
$789$	−2.52862e17	−	1.01327e18i	−0.0373150	−	0.149528i
$790$	−2.11687e18	+	3.66652e18i	−0.309826	+	0.536634i
$791$	−4.30486e18			−0.624902
$792$	7.94695e17	+	4.96116e17i	0.114416	+	0.0714282i
$793$	4.99149e18			0.712778
$794$	2.12093e18	−	3.67356e18i	0.300396	−	0.520301i
$795$	−1.57744e18	−	4.51964e17i	−0.221598	−	0.0634918i
$796$	1.08508e18	+	1.87941e18i	0.151191	+	0.261871i
$797$	−5.54336e18	−	9.60138e18i	−0.766115	−	1.32695i	−0.939655	−	0.342123i	$-0.888854\pi$
$797$	−5.54336e18	−	9.60138e18i	−0.766115	−	1.32695i	0.173540	−	0.984827i	$-0.444479\pi$
$798$	−6.45613e18	−	1.84979e18i	−0.885020	−	0.253574i
$799$	1.56086e17	−	2.70350e17i	0.0212232	−	0.0367597i
$800$	7.97874e17			0.107609
$801$	3.31886e17	−	9.62000e18i	0.0443994	−	1.28696i
$802$	6.09578e17			0.0808902
$803$	−1.82673e18	+	3.16399e18i	−0.240449	+	0.416471i
$804$	−1.09551e18	−	4.38994e18i	−0.143039	−	0.573184i
$805$	−8.24281e17	−	1.42770e18i	−0.106758	−	0.184911i
$806$	4.51441e18	+	7.81919e18i	0.579994	+	1.00458i
$807$	1.10285e19	−	1.06546e19i	1.40553	−	1.35788i
$808$	−1.61500e18	+	2.79727e18i	−0.204174	+	0.353639i
$809$	−1.01551e19			−1.27356			−0.636778	−	0.771047i	$-0.719733\pi$
$809$	−1.01551e19			−1.27356			−0.636778	+	0.771047i	$0.719733\pi$
$810$	3.54685e18	+	2.45021e17i	0.441255	+	0.0304825i
$811$	8.70589e18			1.07443			0.537214	−	0.843446i	$-0.319477\pi$
$811$	8.70589e18			1.07443			0.537214	+	0.843446i	$0.319477\pi$
$812$	2.08378e18	−	3.60922e18i	0.255116	−	0.441874i
$813$	7.86548e17	−	7.59881e17i	0.0955294	−	0.0922905i
$814$	9.19536e17	+	1.59268e18i	0.110792	+	0.191898i
$815$	−1.81018e18	−	3.13532e18i	−0.216370	−	0.374764i
$816$	−5.26492e17	−	2.10975e18i	−0.0624318	−	0.250176i
$817$	−4.73566e18	+	8.20241e18i	−0.557105	+	0.964935i
$818$	−1.10225e18			−0.128642
$819$	−2.79093e17	+	8.08974e18i	−0.0323149	+	0.936676i
$820$	−4.22001e17			−0.0484756
$821$	−3.57522e17	+	6.19247e17i	−0.0407448	+	0.0705721i	−0.885679	−	0.464299i	$-0.846306\pi$
$821$	−3.57522e17	+	6.19247e17i	−0.0407448	+	0.0705721i	0.844934	+	0.534871i	$0.179640\pi$
$822$	−1.04192e19	−	2.98529e18i	−1.17806	−	0.337536i
$823$	−6.22452e18	−	1.07812e19i	−0.698244	−	1.20939i	−0.969075	−	0.246767i	$-0.920632\pi$
$823$	−6.22452e18	−	1.07812e19i	−0.698244	−	1.20939i	0.270831	−	0.962627i	$-0.412701\pi$
$824$	5.00517e17	+	8.66922e17i	0.0557048	+	0.0964835i
$825$	2.02181e18	+	5.79285e17i	0.223249	+	0.0639648i
$826$	−5.40727e18	+	9.36567e18i	−0.592390	+	1.02605i
$827$	4.42505e18			0.480986			0.240493	−	0.970651i	$-0.422691\pi$
$827$	4.42505e18			0.480986			0.240493	+	0.970651i	$0.422691\pi$
$828$	1.43097e18	+	8.93334e17i	0.154324	+	0.0963422i
$829$	1.96050e18			0.209779			0.104890	−	0.994484i	$-0.466551\pi$
$829$	1.96050e18			0.209779			0.104890	+	0.994484i	$0.466551\pi$
$830$	6.46874e17	−	1.12042e18i	0.0686771	−	0.118952i
$831$	6.82977e17	+	2.73682e18i	0.0719448	+	0.288297i
$832$	5.97400e17	+	1.03473e18i	0.0624401	+	0.108149i
$833$	5.96260e17	+	1.03275e18i	0.0618363	+	0.107104i
$834$	−8.64864e18	+	8.35541e18i	−0.889956	+	0.859782i
$835$	1.77045e18	−	3.06651e18i	0.180768	−	0.313099i
$836$	−2.61303e18			−0.264730
$837$	−5.03777e18	+	1.55380e19i	−0.506434	+	1.56200i
$838$	9.14658e18			0.912373
$839$	4.88000e18	−	8.45241e18i	0.483022	−	0.836619i	−0.516788	−	0.856114i	$-0.672872\pi$
$839$	4.88000e18	−	8.45241e18i	0.483022	−	0.836619i	0.999810	+	0.0194945i	$0.00620569\pi$
$840$	1.51921e18	−	1.46770e18i	0.149212	−	0.144153i
$841$	−9.40017e17	−	1.62816e18i	−0.0916139	−	0.158680i
$842$	3.39818e18	+	5.88582e18i	0.328638	+	0.569218i
$843$	−1.45149e18	−	5.81638e18i	−0.139294	−	0.558179i
$844$	8.11981e16	−	1.40639e17i	0.00773250	−	0.0133931i
$845$	−1.26763e16			−0.00119791
$846$	−2.73934e17	+	1.45801e17i	−0.0256885	+	0.0136727i
$847$	−8.61382e18			−0.801592
$848$	4.98819e17	−	8.63980e17i	0.0460649	−	0.0797867i
$849$	−7.96333e18	−	2.28163e18i	−0.729784	−	0.209096i
$850$	−2.44077e18	−	4.22754e18i	−0.221975	−	0.384472i
$851$	1.65577e18	+	2.86787e18i	0.149437	+	0.258832i
$852$	8.17480e18	+	2.34222e18i	0.732183	+	0.209783i
$853$	1.17246e18	−	2.03076e18i	0.104215	−	0.180506i	−0.809202	−	0.587530i	$-0.800100\pi$
$853$	1.17246e18	−	2.03076e18i	0.104215	−	0.180506i	0.913417	+	0.407025i	$0.133434\pi$
$854$	5.36532e18			0.473281
$855$	−8.75371e18	+	4.65916e18i	−0.766324	+	0.407875i
$856$	−7.59359e18			−0.659732
$857$	−5.33861e18	+	9.24675e18i	−0.460313	+	0.797285i	−0.998976	−	0.0452360i	$-0.985596\pi$
$857$	−5.33861e18	+	9.24675e18i	−0.460313	+	0.797285i	0.538664	+	0.842521i	$0.318929\pi$
$858$	7.62562e17	+	3.05573e18i	0.0652541	+	0.261485i
$859$	8.60207e18	+	1.48992e19i	0.730546	+	1.26534i	0.956650	+	0.291239i	$0.0940675\pi$
$859$	8.60207e18	+	1.48992e19i	0.730546	+	1.26534i	−0.226105	+	0.974103i	$0.572599\pi$
$860$	−1.48953e18	−	2.57994e18i	−0.125548	−	0.217455i
$861$	1.25010e18	−	1.20772e18i	0.104574	−	0.101029i
$862$	−3.13286e18	+	5.42627e18i	−0.260102	+	0.450510i
$863$	−1.42851e18			−0.117710			−0.0588548	−	0.998267i	$-0.518745\pi$
$863$	−1.42851e18			−0.117710			−0.0588548	+	0.998267i	$0.518745\pi$
$864$	−6.66657e17	+	2.05617e18i	−0.0545209	+	0.168159i
$865$	−5.85620e18			−0.475348
$866$	3.25953e18	−	5.64568e18i	0.262597	−	0.454831i
$867$	−5.73603e17	+	5.54155e17i	−0.0458656	+	0.0443105i
$868$	4.85252e18	+	8.40481e18i	0.385114	+	0.667036i
$869$	−3.39250e18	−	5.87599e18i	−0.267234	−	0.462863i
$870$	−1.48996e18	−	5.97055e18i	−0.116493	−	0.466809i
$871$	7.60526e18	−	1.31727e19i	0.590196	−	1.02225i
$872$	−5.28303e18			−0.406936
$873$	1.62190e18	+	1.01253e18i	0.124003	+	0.0774132i
$874$	−4.70517e18			−0.357068
$875$	6.26625e18	−	1.08535e19i	0.472015	−	0.817553i
$876$	−8.10347e18	−	2.32179e18i	−0.605891	−	0.173598i
$877$	−6.22801e18	−	1.07872e19i	−0.462223	−	0.800594i	0.536848	−	0.843679i	$-0.319615\pi$
$877$	−6.22801e18	−	1.07872e19i	−0.462223	−	0.800594i	−0.999071	+	0.0430847i	$0.986281\pi$
$878$	4.96469e18	+	8.59909e18i	0.365744	+	0.633488i
$879$	−1.34263e19	−	3.84687e18i	−0.981811	−	0.281306i
$880$	4.10945e17	−	7.11777e17i	0.0298295	−	0.0516662i
$881$	−3.63494e18			−0.261911			−0.130956	−	0.991388i	$-0.541805\pi$
$881$	−3.63494e18			−0.261911			−0.130956	+	0.991388i	$0.541805\pi$
$882$	4.08728e16	−	1.18473e18i	0.00292340	−	0.0847374i
$883$	−1.55878e18			−0.110673			−0.0553364	−	0.998468i	$-0.517623\pi$
$883$	−1.55878e18			−0.110673			−0.0553364	+	0.998468i	$0.517623\pi$
$884$	3.65501e18	−	6.33066e18i	0.257601	−	0.446179i
$885$	3.86634e18	+	1.54932e19i	0.270501	+	1.08395i
$886$	−2.62762e17	−	4.55116e17i	−0.0182491	−	0.0316085i
$887$	−4.28354e18	−	7.41931e18i	−0.295325	−	0.511517i	0.679736	−	0.733457i	$-0.262094\pi$
$887$	−4.28354e18	−	7.41931e18i	−0.295325	−	0.511517i	−0.975060	+	0.221940i	$0.928761\pi$
$888$	−3.05171e18	+	2.94824e18i	−0.208861	+	0.201780i
$889$	9.16447e18	−	1.58733e19i	0.622653	−	1.07847i
$890$	−8.44462e18			−0.569568
$891$	−3.18216e18	+	4.72632e18i	−0.213067	+	0.316459i
$892$	−1.36954e19			−0.910337
$893$	4.32770e17	−	7.49580e17i	0.0285577	−	0.0494634i
$894$	1.28033e18	−	1.23692e18i	0.0838741	−	0.0810304i
$895$	−8.89875e18	−	1.54131e19i	−0.578734	−	1.00240i
$896$	6.42142e17	+	1.11222e18i	0.0414600	+	0.0718108i
$897$	1.37311e18	+	5.50231e18i	0.0880146	+	0.352691i
$898$	−9.40801e17	+	1.62952e18i	−0.0598690	+	0.103696i
$899$	2.82720e19			1.78615
$900$	−1.67312e17	+	4.84967e18i	−0.0104942	+	0.304184i
$901$	−6.10373e18			−0.380088
$902$	3.38150e17	−	5.85693e17i	0.0209058	−	0.0362099i
$903$	1.17960e19	+	3.37975e18i	0.724041	+	0.207450i
$904$	−1.93227e18	−	3.34679e18i	−0.117753	−	0.203954i
$905$	7.45868e18	+	1.29188e19i	0.451280	+	0.781640i
$906$	−3.25504e18	−	9.32627e17i	−0.195534	−	0.0560241i
$907$	−3.41915e18	+	5.92214e18i	−0.203925	+	0.353209i	−0.949790	−	0.312889i	$-0.898703\pi$
$907$	−3.41915e18	+	5.92214e18i	−0.203925	+	0.353209i	0.745865	+	0.666098i	$0.232037\pi$
$908$	6.41749e18			0.380021
$909$	−1.66638e19	−	1.04030e19i	−0.979736	−	0.611634i
$910$	7.10134e18			0.414545
$911$	−2.67920e18	+	4.64050e18i	−0.155287	+	0.268965i	−0.933163	−	0.359452i	$-0.882964\pi$
$911$	−2.67920e18	+	4.64050e18i	−0.155287	+	0.268965i	0.777876	+	0.628417i	$0.216297\pi$
$912$	−1.45977e18	−	5.84957e18i	−0.0840074	−	0.336634i
$913$	1.03668e18	+	1.79559e18i	0.0592360	+	0.102600i
$914$	8.16744e18	+	1.41464e19i	0.463378	+	0.802594i
$915$	5.69760e18	−	5.50442e18i	0.320963	−	0.310081i
$916$	7.92519e18	−	1.37268e19i	0.443291	−	0.767803i
$917$	1.73469e19			0.963432
$918$	1.29340e19	−	2.75774e18i	0.713273	−	0.152081i
$919$	2.65287e19			1.45266			0.726332	−	0.687344i	$-0.241224\pi$
$919$	2.65287e19			1.45266			0.726332	+	0.687344i	$0.241224\pi$
$920$	7.39969e17	−	1.28166e18i	0.0402340	−	0.0696873i
$921$	4.41203e18	−	4.26244e18i	0.238205	−	0.230129i
$922$	−3.93608e18	−	6.81748e18i	−0.211015	−	0.365488i
$923$	1.42938e19	+	2.47575e19i	0.760914	+	1.31794i
$924$	8.19673e17	+	3.28459e18i	0.0433284	+	0.173625i
$925$	−4.76292e18	+	8.24962e18i	−0.250007	+	0.433025i
$926$	3.36976e18			0.175642
$927$	−5.37432e18	+	2.86048e18i	−0.278167	+	0.148054i
$928$	3.74129e18			0.192291
$929$	−1.11800e18	+	1.93644e18i	−0.0570613	+	0.0988330i	−0.893145	−	0.449769i	$-0.851506\pi$
$929$	−1.11800e18	+	1.93644e18i	−0.0570613	+	0.0988330i	0.836084	+	0.548602i	$0.184840\pi$
$930$	1.37758e19	+	3.94700e18i	0.698194	+	0.200045i
$931$	1.65321e18	+	2.86344e18i	0.0832061	+	0.144117i
$932$	−1.04321e18	−	1.80690e18i	−0.0521398	−	0.0903087i
$933$	9.42607e18	+	2.70074e18i	0.467843	+	0.134045i
$934$	1.07297e19	−	1.85844e19i	0.528850	−	0.915996i
$935$	−5.02847e18			−0.246128
$936$	−6.41460e18	+	3.41417e18i	−0.311800	+	0.165955i
$937$	−9.93409e18			−0.479536			−0.239768	−	0.970830i	$-0.577071\pi$
$937$	−9.93409e18			−0.479536			−0.239768	+	0.970830i	$0.577071\pi$
$938$	8.17485e18	−	1.41593e19i	0.391888	−	0.678769i
$939$	7.63130e18	+	3.05801e19i	0.363305	+	1.45583i
$940$	1.36121e17	+	2.35769e17i	0.00643569	+	0.0111469i
$941$	−1.37093e18	−	2.37453e18i	−0.0643700	−	0.111492i	0.832044	−	0.554709i	$-0.187170\pi$
$941$	−1.37093e18	−	2.37453e18i	−0.0643700	−	0.111492i	−0.896414	+	0.443217i	$0.853837\pi$
$942$	−7.83868e18	+	7.57291e18i	−0.365521	+	0.353128i
$943$	6.08892e17	−	1.05463e18i	0.0281977	−	0.0488399i
$944$	−9.70838e18			−0.446508
$945$	8.60249e18	+	9.54192e18i	0.392932	+	0.435842i
$946$	4.77426e18			0.216578
$947$	−6.52057e18	+	1.12940e19i	−0.293772	+	0.508828i	−0.974698	−	0.223524i	$-0.928244\pi$
$947$	−6.52057e18	+	1.12940e19i	−0.293772	+	0.508828i	0.680926	+	0.732352i	$0.261577\pi$
$948$	1.12589e19	−	1.08771e19i	0.503779	−	0.486699i
$949$	−1.41690e19	−	2.45415e19i	−0.629666	−	1.09061i
$950$	−6.76736e18	−	1.17214e19i	−0.298687	−	0.517341i
$951$	−3.28345e17	−	1.31574e18i	−0.0143932	−	0.0576763i
$952$	3.92874e18	−	6.80479e18i	0.171046	−	0.296261i
$953$	1.23319e19			0.533243			0.266621	−	0.963801i	$-0.414093\pi$
$953$	1.23319e19			0.533243			0.266621	+	0.963801i	$0.414093\pi$
$954$	5.14688e18	+	3.21312e18i	0.221044	+	0.137995i
$955$	−1.29869e19			−0.553969
$956$	−3.25499e18	+	5.63781e18i	−0.137903	+	0.238855i
$957$	9.48041e18	+	2.71631e18i	0.398933	+	0.114301i
$958$	−8.23707e18	−	1.42670e19i	−0.344268	−	0.596290i
$959$	−1.95826e19	−	3.39181e19i	−0.812924	−	1.40803i
$960$	1.82297e18	+	5.22313e17i	0.0751651	+	0.0215361i
$961$	−2.07099e19	+	3.58705e19i	−0.848155	+	1.46905i
$962$	−1.42648e19			−0.580265
$963$	1.59235e18	−	4.61557e19i	0.0643380	−	1.86489i
$964$	−1.62010e18			−0.0650193
$965$	−9.13008e18	+	1.58138e19i	−0.363954	+	0.630388i
$966$	1.47595e18	+	5.91441e18i	0.0584413	+	0.234185i
$967$	1.53868e19	+	2.66507e19i	0.605167	+	1.04818i	0.992025	+	0.126041i	$0.0402270\pi$
$967$	1.53868e19	+	2.66507e19i	0.605167	+	1.04818i	−0.386858	+	0.922139i	$0.626440\pi$
$968$	−3.86638e18	−	6.69677e18i	−0.151048	−	0.261623i
$969$	−2.65284e19	+	2.56290e19i	−1.02945	+	0.994550i
$970$	8.38702e17	−	1.45267e18i	0.0323289	−	0.0559953i
$971$	−2.27430e19			−0.870809			−0.435404	−	0.900235i	$-0.643395\pi$
$971$	−2.27430e19			−0.870809			−0.435404	+	0.900235i	$0.643395\pi$
$972$	−1.23581e19	−	4.48327e18i	−0.470026	−	0.170516i
$973$	−4.34545e19			−1.64173
$974$	−5.05483e18	+	8.75521e18i	−0.189702	+	0.328574i
$975$	−1.17323e19	+	1.13345e19i	−0.437375	+	0.422546i
$976$	2.40826e18	+	4.17124e18i	0.0891827	+	0.154469i
$977$	1.35929e18	+	2.35436e18i	0.0500033	+	0.0866082i	0.889944	−	0.456070i	$-0.150743\pi$
$977$	1.35929e18	+	2.35436e18i	0.0500033	+	0.0866082i	−0.839940	+	0.542679i	$0.817410\pi$
$978$	3.24129e18	+	1.29885e19i	0.118445	+	0.474630i
$979$	6.76670e18	−	1.17203e19i	0.245634	−	0.425451i
$980$	−1.03998e18			−0.0375022
$981$	1.10783e18	−	3.21115e19i	0.0396849	−	1.15030i
$982$	1.23905e19			0.440924
$983$	1.05770e19	−	1.83199e19i	0.373908	−	0.647627i	−0.616255	−	0.787546i	$-0.711351\pi$
$983$	1.05770e19	−	1.83199e19i	0.373908	−	0.647627i	0.990163	+	0.139920i	$0.0446844\pi$
$984$	1.50005e18	+	4.29791e17i	0.0526790	+	0.0150935i
$985$	9.98481e18	+	1.72942e19i	0.348341	+	0.603344i
$986$	−1.14449e19	−	1.98232e19i	−0.396656	−	0.687028i
$987$	−1.07798e18	−	3.08860e17i	−0.0371149	−	0.0106341i
$988$	1.01340e19	−	1.75526e19i	0.346625	−	0.600372i
$989$	8.59679e18			0.292119
$990$	4.24018e18	+	2.64708e18i	0.143138	+	0.0893589i
$991$	−2.51495e19			−0.843434			−0.421717	−	0.906727i	$-0.638572\pi$
$991$	−2.51495e19			−0.843434			−0.421717	+	0.906727i	$0.638572\pi$
$992$	−4.35618e18	+	7.54512e18i	−0.145138	+	0.251386i
$993$	−1.14312e19	−	4.58069e19i	−0.378374	−	1.51621i
$994$	1.53643e19	+	2.66117e19i	0.505244	+	0.875108i
$995$	5.78955e18	+	1.00278e19i	0.189145	+	0.327609i
$996$	−3.44049e18	+	3.32384e18i	−0.111669	+	0.107883i
$997$	2.35308e18	−	4.07565e18i	0.0758783	−	0.131425i	−0.825590	−	0.564271i	$-0.809157\pi$
$997$	2.35308e18	−	4.07565e18i	0.0758783	−	0.131425i	0.901468	+	0.432846i	$0.142491\pi$
$998$	−2.60849e19			−0.835683
$999$	−1.72802e19	−	1.91672e19i	−0.550013	−	0.610076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.14.c.a.7.1	✓	12
3.2	odd	2		54.14.c.a.19.4		12
9.2	odd	6		162.14.a.h.1.3		6
9.4	even	3	inner	18.14.c.a.13.1	yes	12
9.5	odd	6		54.14.c.a.37.4		12
9.7	even	3		162.14.a.e.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.14.c.a.7.1	✓	12	1.1	even	1	trivial
18.14.c.a.13.1	yes	12	9.4	even	3	inner
54.14.c.a.19.4		12	3.2	odd	2
54.14.c.a.37.4		12	9.5	odd	6
162.14.a.e.1.4		6	9.7	even	3
162.14.a.h.1.3		6	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(32.0000 - 55.4256i) q^{2} +(-908.101 + 877.312i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(-10927.3 - 18926.7i) q^{5} +(19566.3 + 78406.0i) q^{6} +(-146006. + 252890. i) q^{7} -262144. q^{8} +(54970.7 - 1.59338e6i) q^{9} +O(q^{10})\)	\(q+(32.0000 - 55.4256i) q^{2} +(-908.101 + 877.312i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(-10927.3 - 18926.7i) q^{5} +(19566.3 + 78406.0i) q^{6} +(-146006. + 252890. i) q^{7} -262144. q^{8} +(54970.7 - 1.59338e6i) q^{9} -1.39870e6 q^{10} +(1.12078e6 - 1.94125e6i) q^{11} +(4.97183e6 + 1.42452e6i) q^{12} +(8.69332e6 + 1.50573e7i) q^{13} +(9.34440e6 + 1.61850e7i) q^{14} +(2.65277e7 + 7.60065e6i) q^{15} +(-8.38861e6 + 1.45295e7i) q^{16} +1.02646e8 q^{17} +(-8.65547e7 - 5.40348e7i) q^{18} +2.84600e8 q^{19} +(-4.47583e7 + 7.75236e7i) q^{20} +(-8.92752e7 - 3.57743e8i) q^{21} +(-7.17298e7 - 1.24240e8i) q^{22} +(-1.29161e8 - 2.23713e8i) q^{23} +(2.38053e8 - 2.29982e8i) q^{24} +(3.71539e8 - 6.43525e8i) q^{25} +1.11274e9 q^{26} +(1.34797e9 + 1.49517e9i) q^{27} +1.19608e9 q^{28} +(1.74217e9 - 3.01753e9i) q^{29} +(1.27016e9 - 1.22709e9i) q^{30} +(4.05701e9 + 7.02694e9i) q^{31} +(5.36871e8 + 9.29888e8i) q^{32} +(6.85298e8 + 2.74612e9i) q^{33} +(3.28468e9 - 5.68923e9i) q^{34} +6.38182e9 q^{35} +(-5.76466e9 + 3.06824e9i) q^{36} -1.28194e10 q^{37} +(9.10720e9 - 1.57741e10i) q^{38} +(-2.11043e10 - 6.04676e9i) q^{39} +(2.86453e9 + 4.96151e9i) q^{40} +(2.35711e9 + 4.08263e9i) q^{41} +(-2.26849e10 - 6.49963e9i) q^{42} +(-1.66397e10 + 2.88208e10i) q^{43} -9.18142e9 q^{44} +(-3.07580e10 + 1.63709e10i) q^{45} -1.65326e10 q^{46} +(1.52063e9 - 2.63380e9i) q^{47} +(-5.12920e9 - 2.05537e10i) q^{48} +(5.80889e9 + 1.00613e10i) q^{49} +(-2.37785e10 - 4.11856e10i) q^{50} +(-9.32130e10 + 9.00527e10i) q^{51} +(3.56078e10 - 6.16746e10i) q^{52} -5.94638e10 q^{53} +(1.26006e11 - 2.68665e10i) q^{54} -4.89884e10 q^{55} +(3.82746e10 - 6.62936e10i) q^{56} +(-2.58445e11 + 2.49683e11i) q^{57} +(-1.11499e11 - 1.93122e11i) q^{58} +(2.89332e11 + 5.01138e11i) q^{59} +(-2.73674e10 - 1.09666e11i) q^{60} +(1.43544e11 - 2.48625e11i) q^{61} +5.19297e11 q^{62} +(3.94923e11 + 2.46544e11i) q^{63} +6.87195e10 q^{64} +(1.89989e11 - 3.29071e11i) q^{65} +(1.74135e11 + 4.98927e10i) q^{66} +(-4.37420e11 - 7.57634e11i) q^{67} +(-2.10219e11 - 3.64110e11i) q^{68} +(3.13557e11 + 8.98396e10i) q^{69} +(2.04218e11 - 3.53716e11i) q^{70} +1.64422e12 q^{71} +(-1.44102e10 + 4.17694e11i) q^{72} -1.62988e12 q^{73} +(-4.10222e11 + 7.10525e11i) q^{74} +(2.27177e11 + 9.10341e11i) q^{75} +(-5.82861e11 - 1.00954e12i) q^{76} +(3.27281e11 + 5.66868e11i) q^{77} +(-1.01048e12 + 9.76224e11i) q^{78} +(1.51346e12 - 2.62139e12i) q^{79} +3.66660e11 q^{80} +(-2.53582e12 - 1.75178e11i) q^{81} +3.01710e11 q^{82} +(-4.62483e11 + 8.01045e11i) q^{83} +(-1.08616e12 + 1.04934e12i) q^{84} +(-1.12165e12 - 1.94275e12i) q^{85} +(1.06494e12 + 1.84453e12i) q^{86} +(1.06525e12 + 4.26865e12i) q^{87} +(-2.93805e11 + 5.08886e11i) q^{88} +6.03750e12 q^{89} +(-7.68873e10 + 2.22865e12i) q^{90} -5.07711e12 q^{91} +(-5.29042e11 + 9.16328e11i) q^{92} +(-9.84899e12 - 2.82191e12i) q^{93} +(-9.73201e10 - 1.68563e11i) q^{94} +(-3.10991e12 - 5.38653e12i) q^{95} +(-1.30333e12 - 3.73428e11i) q^{96} +(-5.99631e11 + 1.03859e12i) q^{97} +7.43538e11 q^{98} +(-3.03152e12 - 1.89253e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 384 q^{2} + 1836 q^{3} - 24576 q^{4} - 36504 q^{5} + 102528 q^{6} + 153942 q^{7} - 3145728 q^{8} - 5622426 q^{9}+O(q^{10}) \) 12 * q + 384 * q^2 + 1836 * q^3 - 24576 * q^4 - 36504 * q^5 + 102528 * q^6 + 153942 * q^7 - 3145728 * q^8 - 5622426 * q^9	\( 12 q + 384 q^{2} + 1836 q^{3} - 24576 q^{4} - 36504 q^{5} + 102528 q^{6} + 153942 q^{7} - 3145728 q^{8} - 5622426 q^{9} - 4672512 q^{10} - 1456506 q^{11} - 958464 q^{12} + 24033660 q^{13} - 9852288 q^{14} - 25621002 q^{15} - 100663296 q^{16} - 1079532 q^{17} - 119093760 q^{18} + 337140888 q^{19} - 149520384 q^{20} + 386320356 q^{21} + 93216384 q^{22} + 445386186 q^{23} - 481296384 q^{24} - 2193691326 q^{25} + 3076308480 q^{26} + 5101396200 q^{27} - 1261092864 q^{28} - 9171393012 q^{29} + 4197353472 q^{30} + 4264851066 q^{31} + 6442450944 q^{32} - 23566590198 q^{33} - 34545024 q^{34} + 5180969412 q^{35} + 15407456256 q^{36} - 49108850688 q^{37} + 10788508416 q^{38} - 43492658274 q^{39} + 9569304576 q^{40} - 15964345782 q^{41} + 3573347328 q^{42} + 78379952838 q^{43} + 11931697152 q^{44} + 175634070336 q^{45} + 57009431808 q^{46} + 94117799358 q^{47} - 26877100032 q^{48} - 15284873538 q^{49} + 140396244864 q^{50} - 93672459180 q^{51} + 98441871360 q^{52} - 592790415264 q^{53} + 453285652608 q^{54} - 1108282558212 q^{55} - 40354971648 q^{56} - 1485104020362 q^{57} + 586969152768 q^{58} + 46698155010 q^{59} + 373574246400 q^{60} + 928192122600 q^{61} + 545900936448 q^{62} + 1292399354358 q^{63} + 824633720832 q^{64} - 1327744890468 q^{65} - 1308420898560 q^{66} + 2282039666898 q^{67} + 2210881536 q^{68} - 1791810302256 q^{69} + 165791021184 q^{70} + 2360122970688 q^{71} + 1473885241344 q^{72} + 1355834901228 q^{73} - 1571483222016 q^{74} - 2580299891100 q^{75} - 690464538624 q^{76} - 3622976109756 q^{77} - 3601561950720 q^{78} + 2457538059750 q^{79} + 1224870985728 q^{80} + 3601735790598 q^{81} - 2043436260096 q^{82} - 9950916891942 q^{83} - 1353673949184 q^{84} - 576987174720 q^{85} - 5016316981632 q^{86} + 10025707613994 q^{87} + 381814308864 q^{88} + 22604686696296 q^{89} - 2251213959168 q^{90} + 14791528659540 q^{91} + 1824301817856 q^{92} - 19426418885880 q^{93} - 6023539158912 q^{94} - 7488669126384 q^{95} + 251255586816 q^{96} + 1124429902242 q^{97} - 1956463812864 q^{98} + 12314866399002 q^{99}+O(q^{100}) \) 12 * q + 384 * q^2 + 1836 * q^3 - 24576 * q^4 - 36504 * q^5 + 102528 * q^6 + 153942 * q^7 - 3145728 * q^8 - 5622426 * q^9 - 4672512 * q^10 - 1456506 * q^11 - 958464 * q^12 + 24033660 * q^13 - 9852288 * q^14 - 25621002 * q^15 - 100663296 * q^16 - 1079532 * q^17 - 119093760 * q^18 + 337140888 * q^19 - 149520384 * q^20 + 386320356 * q^21 + 93216384 * q^22 + 445386186 * q^23 - 481296384 * q^24 - 2193691326 * q^25 + 3076308480 * q^26 + 5101396200 * q^27 - 1261092864 * q^28 - 9171393012 * q^29 + 4197353472 * q^30 + 4264851066 * q^31 + 6442450944 * q^32 - 23566590198 * q^33 - 34545024 * q^34 + 5180969412 * q^35 + 15407456256 * q^36 - 49108850688 * q^37 + 10788508416 * q^38 - 43492658274 * q^39 + 9569304576 * q^40 - 15964345782 * q^41 + 3573347328 * q^42 + 78379952838 * q^43 + 11931697152 * q^44 + 175634070336 * q^45 + 57009431808 * q^46 + 94117799358 * q^47 - 26877100032 * q^48 - 15284873538 * q^49 + 140396244864 * q^50 - 93672459180 * q^51 + 98441871360 * q^52 - 592790415264 * q^53 + 453285652608 * q^54 - 1108282558212 * q^55 - 40354971648 * q^56 - 1485104020362 * q^57 + 586969152768 * q^58 + 46698155010 * q^59 + 373574246400 * q^60 + 928192122600 * q^61 + 545900936448 * q^62 + 1292399354358 * q^63 + 824633720832 * q^64 - 1327744890468 * q^65 - 1308420898560 * q^66 + 2282039666898 * q^67 + 2210881536 * q^68 - 1791810302256 * q^69 + 165791021184 * q^70 + 2360122970688 * q^71 + 1473885241344 * q^72 + 1355834901228 * q^73 - 1571483222016 * q^74 - 2580299891100 * q^75 - 690464538624 * q^76 - 3622976109756 * q^77 - 3601561950720 * q^78 + 2457538059750 * q^79 + 1224870985728 * q^80 + 3601735790598 * q^81 - 2043436260096 * q^82 - 9950916891942 * q^83 - 1353673949184 * q^84 - 576987174720 * q^85 - 5016316981632 * q^86 + 10025707613994 * q^87 + 381814308864 * q^88 + 22604686696296 * q^89 - 2251213959168 * q^90 + 14791528659540 * q^91 + 1824301817856 * q^92 - 19426418885880 * q^93 - 6023539158912 * q^94 - 7488669126384 * q^95 + 251255586816 * q^96 + 1124429902242 * q^97 - 1956463812864 * q^98 + 12314866399002 * q^99

Introduction

L-functions

Modular forms

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