LMFDB - Embedded newform 9.10.c.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,10,Mod(4,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	9.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:	$4.63532252547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{28}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$0.500000 + 23.8209i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.10.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.8795 - 34.4322i) q^{2} +(-14.1649 + 139.579i) q^{3} +(-534.387 + 925.585i) q^{4} +(423.223 - 733.045i) q^{5} +(5087.62 - 2287.03i) q^{6} +(3521.99 + 6100.27i) q^{7} +22136.7 q^{8} +(-19281.7 - 3954.24i) q^{9} +O(q^{10})$	\(q+(-19.8795 - 34.4322i) q^{2} +(-14.1649 + 139.579i) q^{3} +(-534.387 + 925.585i) q^{4} +(423.223 - 733.045i) q^{5} +(5087.62 - 2287.03i) q^{6} +(3521.99 + 6100.27i) q^{7} +22136.7 q^{8} +(-19281.7 - 3954.24i) q^{9} -33653.8 q^{10} +(45051.5 + 78031.5i) q^{11} +(-121623. - 87700.0i) q^{12} +(-34294.5 + 59399.8i) q^{13} +(140031. - 242540. i) q^{14} +(96322.9 + 69456.7i) q^{15} +(-166460. - 288317. i) q^{16} -235749. q^{17} +(247157. + 742521. i) q^{18} -232999. q^{19} +(452330. + 783458. i) q^{20} +(-901359. + 405187. i) q^{21} +(1.79120e6 - 3.10245e6i) q^{22} +(133126. - 230581. i) q^{23} +(-313563. + 3.08982e6i) q^{24} +(618326. + 1.07097e6i) q^{25} +2.72703e6 q^{26} +(825053. - 2.63532e6i) q^{27} -7.52842e6 q^{28} +(-1.53091e6 - 2.65162e6i) q^{29} +(476702. - 4.69737e6i) q^{30} +(-1.79575e6 + 3.11033e6i) q^{31} +(-951277. + 1.64766e6i) q^{32} +(-1.15297e7 + 5.18295e6i) q^{33} +(4.68656e6 + 8.11736e6i) q^{34} +5.96236e6 q^{35} +(1.39639e7 - 1.57338e7i) q^{36} +5.13436e6 q^{37} +(4.63189e6 + 8.02267e6i) q^{38} +(-7.80521e6 - 5.62819e6i) q^{39} +(9.36877e6 - 1.62272e7i) q^{40} +(2.25103e6 - 3.89890e6i) q^{41} +(3.18701e7 + 2.29809e7i) q^{42} +(1.64956e7 + 2.85712e7i) q^{43} -9.62997e7 q^{44} +(-1.10591e7 + 1.24608e7i) q^{45} -1.05859e7 q^{46} +(-6.21541e6 - 1.07654e7i) q^{47} +(4.26010e7 - 1.91504e7i) q^{48} +(-4.63206e6 + 8.02297e6i) q^{49} +(2.45840e7 - 4.25807e7i) q^{50} +(3.33935e6 - 3.29056e7i) q^{51} +(-3.66530e7 - 6.34849e7i) q^{52} +3.42506e7 q^{53} +(-1.07141e8 + 2.39802e7i) q^{54} +7.62674e7 q^{55} +(7.79653e7 + 1.35040e8i) q^{56} +(3.30039e6 - 3.25218e7i) q^{57} +(-6.08675e7 + 1.05426e8i) q^{58} +(2.27808e7 - 3.94575e7i) q^{59} +(-1.15762e8 + 5.20383e7i) q^{60} +(-3.08230e7 - 5.33870e7i) q^{61} +1.42794e8 q^{62} +(-4.37881e7 - 1.31550e8i) q^{63} -9.48116e7 q^{64} +(2.90285e7 + 5.02788e7i) q^{65} +(4.07665e8 + 2.93960e8i) q^{66} +(-2.92242e6 + 5.06178e6i) q^{67} +(1.25981e8 - 2.18205e8i) q^{68} +(3.02986e7 + 2.18477e7i) q^{69} +(-1.18529e8 - 2.05297e8i) q^{70} -2.53018e8 q^{71} +(-4.26834e8 - 8.75338e7i) q^{72} +3.59593e8 q^{73} +(-1.02068e8 - 1.76788e8i) q^{74} +(-1.58244e8 + 7.11353e7i) q^{75} +(1.24511e8 - 2.15660e8i) q^{76} +(-3.17342e8 + 5.49653e8i) q^{77} +(-3.86280e7 + 3.80636e8i) q^{78} +(-1.44462e8 - 2.50215e8i) q^{79} -2.81799e8 q^{80} +(3.56148e8 + 1.52489e8i) q^{81} -1.78997e8 q^{82} +(2.26650e8 + 3.92569e8i) q^{83} +(1.06639e8 - 1.05081e9i) q^{84} +(-9.97744e7 + 1.72814e8i) q^{85} +(6.55848e8 - 1.13596e9i) q^{86} +(3.91796e8 - 1.76124e8i) q^{87} +(9.97292e8 + 1.72736e9i) q^{88} -5.93996e8 q^{89} +(6.48903e8 + 1.33075e8i) q^{90} -4.83140e8 q^{91} +(1.42281e8 + 2.46438e8i) q^{92} +(-4.08701e8 - 2.94707e8i) q^{93} +(-2.47118e8 + 4.28021e8i) q^{94} +(-9.86105e7 + 1.70798e8i) q^{95} +(-2.16504e8 - 1.56117e8i) q^{96} +(1.49505e8 + 2.58951e8i) q^{97} +3.68332e8 q^{98} +(-5.60115e8 - 1.68273e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9}+O(q^{10}) $ 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16} - 831078 q^{17} - 1039500 q^{18} - 170554 q^{19} + 1855164 q^{20} - 503475 q^{21} + 529359 q^{22} + 1064559 q^{23} - 2686059 q^{24} - 2293229 q^{25} + 2436312 q^{26} - 6176520 q^{27} + 1225724 q^{28} - 1309053 q^{29} + 30713544 q^{30} - 2359819 q^{31} + 5760063 q^{32} - 19931472 q^{33} + 981801 q^{34} - 31066554 q^{35} - 48894093 q^{36} + 16391516 q^{37} + 39490203 q^{38} + 74528535 q^{39} - 16760496 q^{40} + 54747318 q^{41} + 25242354 q^{42} + 15249608 q^{43} - 332509926 q^{44} - 139865967 q^{45} + 2390520 q^{46} + 156295545 q^{47} + 312045027 q^{48} + 15239583 q^{49} + 315590163 q^{50} + 3098385 q^{51} - 19773358 q^{52} - 525516228 q^{53} - 591710103 q^{54} - 7579770 q^{55} + 470339790 q^{56} + 581271465 q^{57} + 55408560 q^{58} + 307774074 q^{59} - 430082172 q^{60} + 69192125 q^{61} - 914436924 q^{62} - 693544725 q^{63} - 403588478 q^{64} + 482470359 q^{65} + 1912534074 q^{66} + 14328044 q^{67} + 915409575 q^{68} - 724756329 q^{69} - 229271934 q^{70} - 1239601392 q^{71} - 1729340037 q^{72} + 598613198 q^{73} + 1022736000 q^{74} + 1477690413 q^{75} + 119954093 q^{76} + 717995541 q^{77} + 243023958 q^{78} + 30257531 q^{79} - 2927826528 q^{80} - 1055378241 q^{81} - 202376022 q^{82} + 1176168291 q^{83} + 1383634866 q^{84} + 4818366 q^{85} + 1426944009 q^{86} + 617958567 q^{87} + 911312427 q^{88} - 3317041296 q^{89} - 981417492 q^{90} - 739230122 q^{91} - 76813998 q^{92} - 552731577 q^{93} - 1954316784 q^{94} - 391400652 q^{95} + 1854064512 q^{96} - 267311278 q^{97} + 4827300318 q^{98} + 1672014609 q^{99}+O(q^{100}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−19.8795	−	34.4322i	−0.878557	−	1.52170i	−0.852925	−	0.522033i	$-0.825174\pi$
$2$	−19.8795	−	34.4322i	−0.878557	−	1.52170i	−0.0256316	−	0.999671i	$-0.508160\pi$
$3$	−14.1649	+	139.579i	−0.100964	+	0.994890i
$3$	−14.1649	+	139.579i	−0.100964	+	0.994890i
$4$	−534.387	+	925.585i	−1.04372	+	1.80778i
$5$	423.223	−	733.045i	0.302834	−	0.524524i	−0.673943	−	0.738784i	$-0.735401\pi$
$5$	423.223	−	733.045i	0.302834	−	0.524524i	0.976777	+	0.214260i	$0.0687339\pi$
$6$	5087.62	−	2287.03i	1.60263	−	0.720430i
$7$	3521.99	+	6100.27i	0.554431	+	0.960302i	0.997948	+	0.0640361i	$0.0203973\pi$
$7$	3521.99	+	6100.27i	0.554431	+	0.960302i	−0.443517	+	0.896266i	$0.646269\pi$
$8$	22136.7			1.91077
$9$	−19281.7	−	3954.24i	−0.979613	−	0.200896i
$10$	−33653.8			−1.06423
$11$	45051.5	+	78031.5i	0.927774	+	1.60695i	0.787037	+	0.616905i	$0.211614\pi$
$11$	45051.5	+	78031.5i	0.927774	+	1.60695i	0.140737	+	0.990047i	$0.455053\pi$
$12$	−121623.	−	87700.0i	−1.69317	−	1.22091i
$13$	−34294.5	+	59399.8i	−0.333027	+	0.576820i	−0.983104	−	0.183049i	$-0.941403\pi$
$13$	−34294.5	+	59399.8i	−0.333027	+	0.576820i	0.650077	+	0.759869i	$0.274737\pi$
$14$	140031.	−	242540.i	0.974198	−	1.68736i
$15$	96322.9	+	69456.7i	0.491268	+	0.354245i
$16$	−166460.	−	288317.i	−0.634995	−	1.09984i
$17$	−235749.			−0.684588			−0.342294	−	0.939593i	$-0.611204\pi$
$17$	−235749.			−0.684588			−0.342294	+	0.939593i	$0.611204\pi$
$18$	247157.	+	742521.i	0.554940	+	1.66718i
$19$	−232999.			−0.410168			−0.205084	−	0.978744i	$-0.565747\pi$
$19$	−232999.			−0.410168			−0.205084	+	0.978744i	$0.565747\pi$
$20$	452330.	+	783458.i	0.632150	+	1.09492i
$21$	−901359.	+	405187.i	−1.01137	+	0.454642i
$22$	1.79120e6	−	3.10245e6i	1.63020	−	2.82360i
$23$	133126.	−	230581.i	0.0991944	−	0.171810i	−0.812157	−	0.583439i	$-0.801707\pi$
$23$	133126.	−	230581.i	0.0991944	−	0.171810i	0.911351	+	0.411629i	$0.135040\pi$
$24$	−313563.	+	3.08982e6i	−0.192919	+	1.90100i
$25$	618326.	+	1.07097e6i	0.316583	+	0.548338i
$26$	2.72703e6			1.17033
$27$	825053.	−	2.63532e6i	0.298775	−	0.954323i
$28$	−7.52842e6			−2.31469
$29$	−1.53091e6	−	2.65162e6i	−0.401938	−	0.696178i	0.592021	−	0.805922i	$-0.298330\pi$
$29$	−1.53091e6	−	2.65162e6i	−0.401938	−	0.696178i	−0.993960	+	0.109744i	$0.964997\pi$
$30$	476702.	−	4.69737e6i	0.107449	−	1.05879i
$31$	−1.79575e6	+	3.11033e6i	−0.349235	+	0.604893i	−0.986114	−	0.166071i	$-0.946892\pi$
$31$	−1.79575e6	+	3.11033e6i	−0.349235	+	0.604893i	0.636879	+	0.770964i	$0.280225\pi$
$32$	−951277.	+	1.64766e6i	−0.160373	+	0.277775i
$33$	−1.15297e7	+	5.18295e6i	−1.69241	+	0.760789i
$34$	4.68656e6	+	8.11736e6i	0.601449	+	1.04174i
$35$	5.96236e6			0.671602
$36$	1.39639e7	−	1.57338e7i	1.38562	−	1.56125i
$37$	5.13436e6			0.450380			0.225190	−	0.974315i	$-0.427700\pi$
$37$	5.13436e6			0.450380			0.225190	+	0.974315i	$0.427700\pi$
$38$	4.63189e6	+	8.02267e6i	0.360356	+	0.624155i
$39$	−7.80521e6	−	5.62819e6i	−0.540249	−	0.389563i
$40$	9.36877e6	−	1.62272e7i	0.578646	−	1.00224i
$41$	2.25103e6	−	3.89890e6i	0.124410	−	0.215484i	−0.797092	−	0.603857i	$-0.793630\pi$
$41$	2.25103e6	−	3.89890e6i	0.124410	−	0.215484i	0.921502	+	0.388374i	$0.126963\pi$
$42$	3.18701e7	+	2.29809e7i	1.58038	+	1.13958i
$43$	1.64956e7	+	2.85712e7i	0.735801	+	1.27444i	0.954371	+	0.298623i	$0.0965273\pi$
$43$	1.64956e7	+	2.85712e7i	0.735801	+	1.27444i	−0.218571	+	0.975821i	$0.570139\pi$
$44$	−9.62997e7			−3.87336
$45$	−1.10591e7	+	1.24608e7i	−0.402035	+	0.452992i
$46$	−1.05859e7			−0.348592
$47$	−6.21541e6	−	1.07654e7i	−0.185793	−	0.321803i	0.758050	−	0.652196i	$-0.226152\pi$
$47$	−6.21541e6	−	1.07654e7i	−0.185793	−	0.321803i	−0.943843	+	0.330393i	$0.892819\pi$
$48$	4.26010e7	−	1.91504e7i	1.15833	−	0.520705i
$49$	−4.63206e6	+	8.02297e6i	−0.114787	+	0.198817i
$50$	2.45840e7	−	4.25807e7i	0.556272	−	0.963492i
$51$	3.33935e6	−	3.29056e7i	0.0691187	−	0.681090i
$52$	−3.66530e7	−	6.34849e7i	−0.695176	−	1.20408i
$53$	3.42506e7			0.596248			0.298124	−	0.954527i	$-0.403639\pi$
$53$	3.42506e7			0.596248			0.298124	+	0.954527i	$0.403639\pi$
$54$	−1.07141e8	+	2.39802e7i	−1.71469	+	0.383780i
$55$	7.62674e7			1.12385
$56$	7.79653e7	+	1.35040e8i	1.05939	+	1.83491i
$57$	3.30039e6	−	3.25218e7i	0.0414122	−	0.408072i
$58$	−6.08675e7	+	1.05426e8i	−0.706251	+	1.22326i
$59$	2.27808e7	−	3.94575e7i	0.244757	−	0.423932i	−0.717306	−	0.696758i	$-0.754625\pi$
$59$	2.27808e7	−	3.94575e7i	0.244757	−	0.423932i	0.962063	+	0.272826i	$0.0879585\pi$
$60$	−1.15762e8	+	5.20383e7i	−1.15315	+	0.518373i
$61$	−3.08230e7	−	5.33870e7i	−0.285030	−	0.493686i	0.687587	−	0.726102i	$-0.258670\pi$
$61$	−3.08230e7	−	5.33870e7i	−0.285030	−	0.493686i	−0.972616	+	0.232416i	$0.925337\pi$
$62$	1.42794e8			1.22729
$63$	−4.37881e7	−	1.31550e8i	−0.350206	−	1.05211i
$64$	−9.48116e7			−0.706401
$65$	2.90285e7	+	5.02788e7i	0.201704	+	0.349361i
$66$	4.07665e8	+	2.93960e8i	2.64458	+	1.90696i
$67$	−2.92242e6	+	5.06178e6i	−0.0177176	+	0.0306879i	−0.874748	−	0.484578i	$-0.838973\pi$
$67$	−2.92242e6	+	5.06178e6i	−0.0177176	+	0.0306879i	0.857031	+	0.515265i	$0.172307\pi$
$68$	1.25981e8	−	2.18205e8i	0.714520	−	1.23759i
$69$	3.02986e7	+	2.18477e7i	0.160917	+	0.116034i
$70$	−1.18529e8	−	2.05297e8i	−0.590040	−	1.02198i
$71$	−2.53018e8			−1.18165			−0.590825	−	0.806800i	$-0.701198\pi$
$71$	−2.53018e8			−1.18165			−0.590825	+	0.806800i	$0.701198\pi$
$72$	−4.26834e8	−	8.75338e7i	−1.87181	−	0.383866i
$73$	3.59593e8			1.48203			0.741017	−	0.671486i	$-0.234344\pi$
$73$	3.59593e8			1.48203			0.741017	+	0.671486i	$0.234344\pi$
$74$	−1.02068e8	−	1.76788e8i	−0.395684	−	0.685345i
$75$	−1.58244e8	+	7.11353e7i	−0.577500	+	0.259603i
$76$	1.24511e8	−	2.15660e8i	0.428102	−	0.741495i
$77$	−3.17342e8	+	5.49653e8i	−1.02877	+	1.78189i
$78$	−3.86280e7	+	3.80636e8i	−0.118161	+	1.16435i
$79$	−1.44462e8	−	2.50215e8i	−0.417283	−	0.722755i	0.578382	−	0.815766i	$-0.303684\pi$
$79$	−1.44462e8	−	2.50215e8i	−0.417283	−	0.722755i	−0.995665	+	0.0930107i	$0.970351\pi$
$80$	−2.81799e8			−0.769192
$81$	3.56148e8	+	1.52489e8i	0.919281	+	0.393601i
$82$	−1.78997e8			−0.437204
$83$	2.26650e8	+	3.92569e8i	0.524208	+	0.907956i	0.999603	+	0.0281829i	$0.00897208\pi$
$83$	2.26650e8	+	3.92569e8i	0.524208	+	0.907956i	−0.475394	+	0.879773i	$0.657695\pi$
$84$	1.06639e8	−	1.05081e9i	0.233700	−	2.30286i
$85$	−9.97744e7	+	1.72814e8i	−0.207316	+	0.359083i
$86$	6.55848e8	−	1.13596e9i	1.29289	−	2.23934i
$87$	3.91796e8	−	1.76124e8i	0.733202	−	0.329596i
$88$	9.97292e8	+	1.72736e9i	1.77276	+	3.07051i
$89$	−5.93996e8			−1.00353			−0.501763	−	0.865005i	$-0.667315\pi$
$89$	−5.93996e8			−1.00353			−0.501763	+	0.865005i	$0.667315\pi$
$90$	6.48903e8	+	1.33075e8i	1.04253	+	0.213799i
$91$	−4.83140e8			−0.738562
$92$	1.42281e8	+	2.46438e8i	0.207063	+	0.358644i
$93$	−4.08701e8	−	2.94707e8i	−0.566542	−	0.408523i
$94$	−2.47118e8	+	4.28021e8i	−0.326460	+	0.565445i
$95$	−9.86105e7	+	1.70798e8i	−0.124213	+	0.215143i
$96$	−2.16504e8	−	1.56117e8i	−0.260163	−	0.187599i
$97$	1.49505e8	+	2.58951e8i	0.171468	+	0.296992i	0.938933	−	0.344099i	$-0.111816\pi$
$97$	1.49505e8	+	2.58951e8i	0.171468	+	0.296992i	−0.767465	+	0.641091i	$0.778482\pi$
$98$	3.68332e8			0.403387
$99$	−5.60115e8	−	1.68273e9i	−0.586029	−	1.76058i
$100$	−1.32170e9			−1.32170
$101$	3.93716e6	+	6.81936e6i	0.00376476	+	0.00652075i	0.867902	−	0.496736i	$-0.165468\pi$
$101$	3.93716e6	+	6.81936e6i	0.00376476	+	0.00652075i	−0.864137	+	0.503257i	$0.832135\pi$
$102$	−1.19940e9	+	5.39165e8i	−1.09714	+	0.493197i
$103$	9.12453e8	−	1.58041e9i	0.798809	−	1.38358i	−0.121583	−	0.992581i	$-0.538797\pi$
$103$	9.12453e8	−	1.58041e9i	0.798809	−	1.38358i	0.920392	−	0.390996i	$-0.127869\pi$
$104$	−7.59167e8	+	1.31492e9i	−0.636338	+	1.10217i
$105$	−8.44560e7	+	8.32221e8i	−0.0678076	+	0.668170i
$106$	−6.80884e8	−	1.17933e9i	−0.523838	−	0.907313i
$107$	4.67288e8			0.344634			0.172317	−	0.985042i	$-0.444875\pi$
$107$	4.67288e8			0.344634			0.172317	+	0.985042i	$0.444875\pi$
$108$	1.99831e9	+	2.17193e9i	1.41337	+	1.53617i
$109$	1.80762e9			1.22656			0.613279	−	0.789866i	$-0.289850\pi$
$109$	1.80762e9			1.22656			0.613279	+	0.789866i	$0.289850\pi$
$110$	−1.51616e9	−	2.62606e9i	−0.987363	−	1.71016i
$111$	−7.27275e7	+	7.16650e8i	−0.0454722	+	0.448078i
$112$	1.17254e9	−	2.03090e9i	0.704121	−	1.21957i
$113$	−5.18834e8	+	8.98647e8i	−0.299347	+	0.518485i	−0.975987	−	0.217830i	$-0.930102\pi$
$113$	−5.18834e8	+	8.98647e8i	−0.299347	+	0.518485i	0.676639	+	0.736315i	$0.263436\pi$
$114$	−1.18541e9	+	5.32875e8i	−0.657349	+	0.295498i
$115$	−1.12684e8	−	1.95174e8i	−0.0600789	−	0.104060i
$116$	3.27240e9			1.67805
$117$	8.96138e8	−	1.00972e9i	0.442118	−	0.498156i
$118$	−1.81148e9			−0.860132
$119$	−8.30305e8	−	1.43813e9i	−0.379556	−	0.657411i
$120$	2.13227e9	+	1.53754e9i	0.938700	+	0.676879i
$121$	−2.88030e9	+	4.98883e9i	−1.22153	+	2.11575i
$122$	−1.22549e9	+	2.12261e9i	−0.500830	+	0.867463i
$123$	5.12320e8	+	3.69424e8i	0.201822	+	0.145530i
$124$	−1.91925e9	−	3.32423e9i	−0.729010	−	1.26268i
$125$	2.69998e9			0.989157
$126$	−3.65909e9	+	4.12288e9i	−1.29332	+	1.45725i
$127$	5.65026e9			1.92731			0.963655	−	0.267150i	$-0.0860818\pi$
$127$	5.65026e9			1.92731			0.963655	+	0.267150i	$0.0860818\pi$
$128$	2.37186e9	+	4.10818e9i	0.780987	+	1.35271i
$129$	−4.22161e9	+	1.89774e9i	−1.34222	+	0.603368i
$130$	1.15414e9	−	1.99903e9i	0.354417	−	0.613867i
$131$	3.24241e9	−	5.61602e9i	0.961939	−	1.66613i	0.244314	−	0.969696i	$-0.421437\pi$
$131$	3.24241e9	−	5.61602e9i	0.961939	−	1.66613i	0.717625	−	0.696430i	$-0.245229\pi$
$132$	1.36407e9	−	1.34414e10i	0.391070	−	3.85357i
$133$	−8.20619e8	−	1.42135e9i	−0.227410	−	0.393886i
$134$	2.32385e8			0.0622638
$135$	−1.58262e9	−	1.72013e9i	−0.410086	−	0.445716i
$136$	−5.21870e9			−1.30809
$137$	1.29715e9	+	2.24673e9i	0.314592	+	0.544889i	0.979351	−	0.202169i	$-0.0647990\pi$
$137$	1.29715e9	+	2.24673e9i	0.314592	+	0.544889i	−0.664759	+	0.747058i	$0.731466\pi$
$138$	1.49948e8	−	1.47757e9i	0.0351952	−	0.346810i
$139$	−2.19078e9	+	3.79454e9i	−0.497773	+	0.862169i	−0.999997	−	0.00256931i	$-0.999182\pi$
$139$	−2.19078e9	+	3.79454e9i	−0.497773	+	0.862169i	0.502223	+	0.864738i	$0.332515\pi$
$140$	−3.18620e9	+	5.51867e9i	−0.700967	+	1.21411i
$141$	1.59067e9	−	7.15052e8i	0.338917	−	0.152353i
$142$	5.02986e9	+	8.71198e9i	1.03815	+	1.79812i
$143$	−6.18008e9			−1.23590
$144$	2.06956e9	+	6.21747e9i	0.401094	+	1.20499i
$145$	−2.59167e9			−0.486883
$146$	−7.14852e9	−	1.23816e10i	−1.30205	−	2.25522i
$147$	−1.05423e9	−	7.60184e8i	−0.186211	−	0.134274i
$148$	−2.74373e9	+	4.75229e9i	−0.470072	+	0.814189i
$149$	1.88301e9	−	3.26147e9i	0.312978	−	0.542094i	−0.666028	−	0.745927i	$-0.732007\pi$
$149$	1.88301e9	−	3.26147e9i	0.312978	−	0.542094i	0.979006	+	0.203833i	$0.0653400\pi$
$150$	5.59516e9	+	4.03457e9i	0.902405	+	0.650708i
$151$	−4.60600e9	−	7.97783e9i	−0.720988	−	1.24879i	−0.960604	−	0.277920i	$-0.910355\pi$
$151$	−4.60600e9	−	7.97783e9i	−0.720988	−	1.24879i	0.239616	−	0.970868i	$-0.422978\pi$
$152$	−5.15782e9			−0.783737
$153$	4.54564e9	+	9.32207e8i	0.670631	+	0.137531i
$154$	2.52344e10			3.61534
$155$	1.52001e9	+	2.63273e9i	0.211521	+	0.366364i
$156$	9.38036e9	−	4.21675e9i	1.26812	−	0.570055i
$157$	1.74126e9	−	3.01595e9i	0.228726	−	0.396165i	−0.728705	−	0.684828i	$-0.759877\pi$
$157$	1.74126e9	−	3.01595e9i	0.228726	−	0.396165i	0.957431	+	0.288663i	$0.0932107\pi$
$158$	−5.74364e9	+	9.94828e9i	−0.733213	+	1.26996i
$159$	−4.85155e8	+	4.78067e9i	−0.0601996	+	0.593201i
$160$	8.05205e8	+	1.39466e9i	0.0971330	+	0.168239i
$161$	1.87547e9			0.219986
$162$	−1.82950e9	−	1.52944e10i	−0.208696	−	1.74468i
$163$	−6.34728e9			−0.704277			−0.352139	−	0.935948i	$-0.614545\pi$
$163$	−6.34728e9			−0.704277			−0.352139	+	0.935948i	$0.614545\pi$
$164$	2.40584e9	+	4.16704e9i	0.259699	+	0.449811i
$165$	−1.08032e9	+	1.06453e10i	−0.113468	+	1.11810i
$166$	9.01136e9	−	1.56081e10i	0.921094	−	1.59538i
$167$	−3.40727e9	+	5.90156e9i	−0.338986	+	0.587142i	−0.984242	−	0.176825i	$-0.943417\pi$
$167$	−3.40727e9	+	5.90156e9i	−0.338986	+	0.587142i	0.645256	+	0.763966i	$0.276751\pi$
$168$	−1.99531e10	+	8.96952e9i	−1.93250	+	0.868715i
$169$	2.95002e9	+	5.10959e9i	0.278186	+	0.481832i
$170$	7.93385e9			0.728557
$171$	4.49261e9	+	9.21332e8i	0.401806	+	0.0824013i
$172$	−3.52601e10			−3.07189
$173$	−4.95185e9	−	8.57685e9i	−0.420300	−	0.727982i	0.575668	−	0.817683i	$-0.304742\pi$
$173$	−4.95185e9	−	8.57685e9i	−0.420300	−	0.727982i	−0.995969	+	0.0897016i	$0.971409\pi$
$174$	−1.38530e10	−	9.98917e9i	−1.14571	−	0.826148i
$175$	−4.35548e9	+	7.54392e9i	−0.351047	+	0.608031i
$176$	1.49986e10	−	2.59783e10i	1.17826	−	2.04081i
$177$	5.18476e9	+	3.73864e9i	0.397054	+	0.286308i
$178$	1.18083e10	+	2.04526e10i	0.881654	+	1.52707i
$179$	1.34679e9			0.0980532			0.0490266	−	0.998797i	$-0.484388\pi$
$179$	1.34679e9			0.0980532			0.0490266	+	0.998797i	$0.484388\pi$
$180$	−5.62371e9	−	1.68950e10i	−0.399298	−	1.19959i
$181$	−1.53579e10			−1.06360			−0.531800	−	0.846870i	$-0.678484\pi$
$181$	−1.53579e10			−1.06360			−0.531800	+	0.846870i	$0.678484\pi$
$182$	9.60457e9	+	1.66356e10i	0.648868	+	1.12387i
$183$	7.88831e9	−	3.54603e9i	0.519941	−	0.233729i
$184$	2.94697e9	−	5.10430e9i	0.189538	−	0.328289i
$185$	2.17298e9	−	3.76372e9i	0.136390	−	0.236235i
$186$	−2.02266e9	+	1.99311e10i	−0.123912	+	1.22102i
$187$	−1.06208e10	−	1.83958e10i	−0.635143	−	1.10010i
$188$	1.32857e10			0.775667
$189$	1.89820e10	−	4.24852e9i	1.08209	−	0.242192i
$190$	7.84130e9			0.436512
$191$	1.39313e10	+	2.41297e10i	0.757429	+	1.31191i	0.944158	+	0.329494i	$0.106878\pi$
$191$	1.39313e10	+	2.41297e10i	0.757429	+	1.31191i	−0.186729	+	0.982412i	$0.559789\pi$
$192$	1.34299e9	−	1.32337e10i	0.0713211	−	0.702791i
$193$	7.38764e9	−	1.27958e10i	0.383264	−	0.663832i	−0.608263	−	0.793736i	$-0.708133\pi$
$193$	7.38764e9	−	1.27958e10i	0.383264	−	0.663832i	0.991527	+	0.129903i	$0.0414667\pi$
$194$	5.94417e9	−	1.02956e10i	0.301289	−	0.521848i
$195$	−7.42906e9	+	3.33958e9i	−0.367941	+	0.165400i
$196$	−4.95062e9	−	8.57473e9i	−0.239611	−	0.415019i
$197$	−2.08977e10			−0.988554			−0.494277	−	0.869304i	$-0.664567\pi$
$197$	−2.08977e10			−0.988554			−0.494277	+	0.869304i	$0.664567\pi$
$198$	−4.68052e10	+	5.27377e10i	−2.16422	+	2.43853i
$199$	2.77242e10			1.25320			0.626600	−	0.779341i	$-0.284446\pi$
$199$	2.77242e10			1.25320			0.626600	+	0.779341i	$0.284446\pi$
$200$	1.36877e10	+	2.37078e10i	0.604917	+	1.04775i
$201$	−6.65123e8	−	4.79608e8i	−0.0287422	−	0.0207255i
$202$	1.56537e8	−	2.71131e8i	0.00661510	−	0.0114577i
$203$	1.07837e10	−	1.86780e10i	0.445694	−	0.771965i
$204$	2.86724e10	+	2.06752e10i	1.15912	+	0.835821i
$205$	−1.90538e9	−	3.30021e9i	−0.0753509	−	0.130512i
$206$	−7.25563e10			−2.80720
$207$	−3.47867e9	+	3.91958e9i	−0.131688	+	0.148379i
$208$	2.28347e10			0.845881
$209$	−1.04969e10	−	1.81812e10i	−0.380544	−	0.659121i
$210$	3.03342e10	−	1.36361e10i	1.07633	−	0.483842i
$211$	5.45826e9	−	9.45399e9i	0.189576	−	0.328355i	−0.755533	−	0.655111i	$-0.772622\pi$
$211$	5.45826e9	−	9.45399e9i	0.189576	−	0.328355i	0.945109	+	0.326755i	$0.105955\pi$
$212$	−1.83031e10	+	3.17018e10i	−0.622318	+	1.07789i
$213$	3.58397e9	−	3.53161e10i	0.119304	−	1.17561i
$214$	−9.28944e9	−	1.60898e10i	−0.302780	−	0.524431i
$215$	2.79253e10			0.891302
$216$	1.82639e10	−	5.83372e10i	0.570890	−	1.82349i
$217$	−2.52985e10			−0.774507
$218$	−3.59346e10	−	6.22405e10i	−1.07760	−	1.86646i
$219$	−5.09358e9	+	5.01917e10i	−0.149632	+	1.47446i
$220$	−4.07563e10	+	7.05920e10i	−1.17299	+	2.03167i
$221$	8.08489e9	−	1.40034e10i	0.227986	−	0.394884i
$222$	2.61217e10	−	1.17425e10i	0.721793	−	0.324467i
$223$	2.80127e10	+	4.85194e10i	0.758547	+	1.31384i	0.943591	+	0.331113i	$0.107424\pi$
$223$	2.80127e10	+	4.85194e10i	0.758547	+	1.31384i	−0.185044	+	0.982730i	$0.559243\pi$
$224$	−1.34016e10			−0.355663
$225$	−7.68751e9	−	2.30952e10i	−0.199970	−	0.600759i
$226$	4.12566e10			1.05197
$227$	1.28104e10	+	2.21883e10i	0.320219	+	0.554636i	0.980533	−	0.196354i	$-0.0629101\pi$
$227$	1.28104e10	+	2.21883e10i	0.320219	+	0.554636i	−0.660314	+	0.750990i	$0.729577\pi$
$228$	2.83380e10	+	2.04340e10i	0.694483	+	0.500779i
$229$	−4.04705e9	+	7.00970e9i	−0.0972477	+	0.168438i	−0.910544	−	0.413411i	$-0.864337\pi$
$229$	−4.04705e9	+	7.00970e9i	−0.0972477	+	0.168438i	0.813297	+	0.581849i	$0.197671\pi$
$230$	−4.48019e9	+	7.75992e9i	−0.105565	+	0.182845i
$231$	−7.22250e10	−	5.20801e10i	−1.66891	−	1.20342i
$232$	−3.38894e10	−	5.86981e10i	−0.768011	−	1.33023i
$233$	−2.40857e10			−0.535374			−0.267687	−	0.963506i	$-0.586259\pi$
$233$	−2.40857e10			−0.535374			−0.267687	+	0.963506i	$0.586259\pi$
$234$	−5.25817e10	−	1.07833e10i	−1.14647	−	0.235115i
$235$	−1.05220e10			−0.225058
$236$	2.43475e10	+	4.21711e10i	0.510917	+	0.884935i
$237$	3.69711e10	−	1.66196e10i	0.761192	−	0.342178i
$238$	−3.30121e10	+	5.71785e10i	−0.666924	+	1.15515i
$239$	−1.83170e10	+	3.17260e10i	−0.363132	+	0.628963i	−0.988475	−	0.151387i	$-0.951626\pi$
$239$	−1.83170e10	+	3.17260e10i	−0.363132	+	0.628963i	0.625342	+	0.780350i	$0.284959\pi$
$240$	3.99165e9	−	3.93333e10i	0.0776607	−	0.765261i
$241$	4.13227e10	+	7.15730e10i	0.789063	+	1.36670i	0.926542	+	0.376193i	$0.122767\pi$
$241$	4.13227e10	+	7.15730e10i	0.789063	+	1.36670i	−0.137478	+	0.990505i	$0.543900\pi$
$242$	2.29036e11			4.29273
$243$	−2.63291e10	+	4.75509e10i	−0.484404	+	0.874844i
$244$	6.58855e10			1.18997
$245$	3.92079e9	+	6.79102e9i	0.0695227	+	0.120417i
$246$	2.53547e9	−	2.49843e10i	0.0441418	−	0.434970i
$247$	7.99057e9	−	1.38401e10i	0.136597	−	0.236593i
$248$	−3.97520e10	+	6.88524e10i	−0.667307	+	1.15581i
$249$	−5.80049e10	+	2.60749e10i	−0.956242	+	0.429859i
$250$	−5.36741e10	−	9.29663e10i	−0.869030	−	1.50520i
$251$	−8.40180e10			−1.33611			−0.668053	−	0.744114i	$-0.732872\pi$
$251$	−8.40180e10			−1.33611			−0.668053	+	0.744114i	$0.732872\pi$
$252$	1.45161e11	+	2.97692e10i	2.26750	+	0.465012i
$253$	2.39901e10			0.368120
$254$	−1.12324e11	−	1.94551e11i	−1.69325	−	2.93280i
$255$	−2.27080e10	−	1.63743e10i	−0.336316	−	0.242512i
$256$	7.00307e10	−	1.21297e11i	1.01908	−	1.76510i
$257$	6.19866e10	−	1.07364e11i	0.886337	−	1.53518i	0.0421632	−	0.999111i	$-0.486575\pi$
$257$	6.19866e10	−	1.07364e11i	0.886337	−	1.53518i	0.844174	−	0.536070i	$-0.180092\pi$
$258$	1.49267e11	+	1.07633e11i	2.09736	+	1.51237i
$259$	1.80832e10	+	3.13210e10i	0.249704	+	0.432501i
$260$	−6.20497e10			−0.842092
$261$	1.90335e10	+	5.71814e10i	0.253884	+	0.762732i
$262$	−2.57830e11			−3.38047
$263$	5.38774e10	+	9.33183e10i	0.694393	+	1.20272i	0.970385	+	0.241564i	$0.0776604\pi$
$263$	5.38774e10	+	9.33183e10i	0.694393	+	1.20272i	−0.275992	+	0.961160i	$0.589006\pi$
$264$	−2.55230e11	+	1.14733e11i	−3.23381	+	1.45369i
$265$	1.44957e10	−	2.51072e10i	0.180564	−	0.312746i
$266$	−3.26270e10	+	5.65115e10i	−0.399585	+	0.692101i
$267$	8.41387e9	−	8.29095e10i	0.101320	−	0.998398i
$268$	−3.12340e9	−	5.40989e9i	−0.0369846	−	0.0640593i
$269$	−5.47369e10			−0.637375			−0.318688	−	0.947860i	$-0.603242\pi$
$269$	−5.47369e10			−0.637375			−0.318688	+	0.947860i	$0.603242\pi$
$270$	−2.77662e10	+	8.86884e10i	−0.317965	+	1.01562i
$271$	7.34345e9			0.0827063			0.0413531	−	0.999145i	$-0.486833\pi$
$271$	7.34345e9			0.0827063			0.0413531	+	0.999145i	$0.486833\pi$
$272$	3.92427e10	+	6.79704e10i	0.434709	+	0.752939i
$273$	6.84361e9	−	6.74363e10i	0.0745682	−	0.734788i
$274$	5.15733e10	−	8.93276e10i	0.552774	−	0.957432i
$275$	−5.57131e10	+	9.64979e10i	−0.587435	+	1.01747i
$276$	−3.64131e10	+	1.63687e10i	−0.377717	+	0.169795i
$277$	−3.80128e10	−	6.58400e10i	−0.387945	−	0.671941i	0.604228	−	0.796812i	$-0.293482\pi$
$277$	−3.80128e10	−	6.58400e10i	−0.387945	−	0.671941i	−0.992173	+	0.124871i	$0.960148\pi$
$278$	1.74206e11			1.74929
$279$	4.69241e10	−	5.28716e10i	0.463636	−	0.522401i
$280$	1.31987e11			1.28328
$281$	−1.14192e10	−	1.97787e10i	−0.109259	−	0.189243i	0.806211	−	0.591628i	$-0.201515\pi$
$281$	−1.14192e10	−	1.97787e10i	−0.109259	−	0.189243i	−0.915470	+	0.402385i	$0.868181\pi$
$282$	−5.62425e10	−	4.05554e10i	−0.529595	−	0.381881i
$283$	9.92192e10	−	1.71853e11i	0.919511	−	1.59264i	0.119352	−	0.992852i	$-0.461918\pi$
$283$	9.92192e10	−	1.71853e11i	0.919511	−	1.59264i	0.800159	−	0.599788i	$-0.204748\pi$
$284$	1.35209e11	−	2.34190e11i	1.23332	−	2.13617i
$285$	−2.24431e10	−	1.61833e10i	−0.201503	−	0.145300i
$286$	1.22857e11	+	2.12794e11i	1.08580	+	1.88067i
$287$	3.17124e10			0.275906
$288$	2.48575e10	−	2.80081e10i	0.212908	−	0.239893i
$289$	−6.30104e10			−0.531340
$290$	5.15211e10	+	8.92371e10i	0.427754	+	0.740892i
$291$	−3.82619e10	+	1.71998e10i	−0.312786	+	0.140607i
$292$	−1.92162e11	+	3.32834e11i	−1.54683	+	2.67920i
$293$	−2.07685e10	+	3.59722e10i	−0.164627	+	0.285143i	−0.936523	−	0.350607i	$-0.885975\pi$
$293$	−2.07685e10	+	3.59722e10i	−0.164627	+	0.285143i	0.771896	+	0.635749i	$0.219309\pi$
$294$	−5.21737e9	+	5.14115e10i	−0.0407276	+	0.401326i
$295$	−1.92828e10	−	3.33987e10i	−0.148242	−	0.256762i
$296$	1.13658e11			0.860571
$297$	2.42808e11	−	5.43448e10i	1.81075	−	0.405279i
$298$	−1.49733e11			−1.09988
$299$	9.13097e9	+	1.58153e10i	0.0660688	+	0.114435i
$300$	1.87217e10	−	1.84482e11i	0.133444	−	1.31495i
$301$	−1.16195e11	+	2.01255e11i	−0.815901	+	1.41318i
$302$	−1.83130e11	+	3.17190e11i	−1.26686	+	2.19426i
$303$	−1.00761e9	+	4.52950e8i	−0.00686753	+	0.00308716i
$304$	3.87849e10	+	6.71775e10i	0.260455	+	0.451121i
$305$	−5.21800e10			−0.345267
$306$	−5.82669e10	−	1.75048e11i	−0.379905	−	1.14133i
$307$	1.45036e10			0.0931864			0.0465932	−	0.998914i	$-0.485164\pi$
$307$	1.45036e10			0.0931864			0.0465932	+	0.998914i	$0.485164\pi$
$308$	−3.39167e11	−	5.87454e11i	−2.14751	−	3.71960i
$309$	2.07668e11	+	1.49746e11i	1.29586	+	0.934419i
$310$	6.04338e10	−	1.04674e11i	0.371666	−	0.643744i
$311$	1.48065e10	−	2.56457e10i	0.0897494	−	0.155450i	−0.817656	−	0.575707i	$-0.804727\pi$
$311$	1.48065e10	−	2.56457e10i	0.0897494	−	0.155450i	0.907405	+	0.420257i	$0.138060\pi$
$312$	−1.72782e11	−	1.24590e11i	−1.03229	−	0.744365i
$313$	4.63427e10	+	8.02679e10i	0.272918	+	0.472707i	0.969608	−	0.244665i	$-0.0786780\pi$
$313$	4.63427e10	+	8.02679e10i	0.272918	+	0.472707i	−0.696690	+	0.717372i	$0.745345\pi$
$314$	−1.38461e11			−0.803795
$315$	−1.14965e11	−	2.35766e10i	−0.657910	−	0.134922i
$316$	3.08793e11			1.74211
$317$	6.83738e10	+	1.18427e11i	0.380297	+	0.658694i	0.991105	−	0.133085i	$-0.0424884\pi$
$317$	6.83738e10	+	1.18427e11i	0.380297	+	0.658694i	−0.610807	+	0.791779i	$0.709155\pi$
$318$	1.74254e11	−	7.83323e10i	0.955566	−	0.429555i
$319$	1.37940e11	−	2.38919e11i	0.745816	−	1.29179i
$320$	−4.01265e10	+	6.95011e10i	−0.213922	+	0.370524i
$321$	−6.61907e9	+	6.52237e10i	−0.0347956	+	0.342873i
$322$	−3.72834e10	−	6.45768e10i	−0.193270	−	0.334753i
$323$	5.49291e10			0.280796
$324$	−3.31462e11	+	2.48157e11i	−1.67102	+	1.25105i
$325$	−8.48208e10			−0.421723
$326$	1.26181e11	+	2.18551e11i	0.618747	+	1.07170i
$327$	−2.56047e10	+	2.52306e11i	−0.123838	+	1.22029i
$328$	4.98304e10	−	8.63088e10i	0.237718	−	0.411740i
$329$	4.37813e10	−	7.58314e10i	0.206019	−	0.356835i
$330$	3.88019e11	−	1.74426e11i	1.80111	−	0.809653i
$331$	−1.56804e11	−	2.71592e11i	−0.718009	−	1.24363i	−0.961787	−	0.273797i	$-0.911720\pi$
$331$	−1.56804e11	−	2.71592e11i	−0.718009	−	1.24363i	0.243778	−	0.969831i	$-0.421613\pi$
$332$	−4.84475e11			−2.18852
$333$	−9.89993e10	−	2.03025e10i	−0.441198	−	0.0904796i
$334$	2.70939e11			1.19128
$335$	2.47367e9	+	4.28453e9i	0.0107310	+	0.0185867i
$336$	2.66863e11	+	1.92430e11i	1.14225	+	0.823656i
$337$	−1.44549e11	+	2.50366e11i	−0.610493	+	1.05740i	0.380664	+	0.924713i	$0.375695\pi$
$337$	−1.44549e11	+	2.50366e11i	−0.610493	+	1.05740i	−0.991157	+	0.132692i	$0.957638\pi$
$338$	1.17290e11	−	2.03152e11i	0.488804	−	0.846634i
$339$	−1.18083e11	−	8.51477e10i	−0.485612	−	0.350166i
$340$	−1.06636e11	−	1.84699e11i	−0.432762	−	0.749566i
$341$	−3.23605e11			−1.29605
$342$	−5.75872e10	−	1.73006e11i	−0.227619	−	0.683824i
$343$	2.18994e11			0.854296
$344$	3.65158e11	+	6.32473e11i	1.40594	+	2.43517i
$345$	2.88384e10	−	1.29637e10i	0.109594	−	0.0492656i
$346$	−1.96880e11	+	3.41007e11i	−0.738516	+	1.27915i
$347$	1.12430e11	−	1.94734e11i	0.416293	−	0.721040i	−0.579271	−	0.815135i	$-0.696663\pi$
$347$	1.12430e11	−	1.94734e11i	0.416293	−	0.721040i	0.995563	+	0.0940954i	$0.0299959\pi$
$348$	−4.63531e10	+	4.56759e11i	−0.169423	+	1.66948i
$349$	4.39959e10	+	7.62031e10i	0.158744	+	0.274953i	0.934416	−	0.356183i	$-0.115922\pi$
$349$	4.39959e10	+	7.62031e10i	0.158744	+	0.274953i	−0.775672	+	0.631136i	$0.782589\pi$
$350$	3.46339e11			1.23366
$351$	1.28243e11	+	1.39385e11i	0.450972	+	0.490155i
$352$	−1.71426e11			−0.595161
$353$	−1.91051e11	−	3.30911e11i	−0.654884	−	1.13429i	−0.981923	−	0.189281i	$-0.939384\pi$
$353$	−1.91051e11	−	3.30911e11i	−0.654884	−	1.13429i	0.327039	−	0.945011i	$-0.393949\pi$
$354$	2.56594e10	−	2.52845e11i	0.0868424	−	0.855737i
$355$	−1.07083e11	+	1.85473e11i	−0.357844	+	0.619804i
$356$	3.17424e11	−	5.49794e11i	1.04740	−	1.81416i
$357$	2.12494e11	−	9.55224e10i	0.692373	−	0.311242i
$358$	−2.67735e10	−	4.63731e10i	−0.0861453	−	0.149208i
$359$	4.78348e11			1.51991			0.759957	−	0.649973i	$-0.225220\pi$
$359$	4.78348e11			1.51991			0.759957	+	0.649973i	$0.225220\pi$
$360$	−2.44812e11	+	2.75842e11i	−0.768196	+	0.865563i
$361$	−2.68399e11			−0.831762
$362$	3.05307e11	+	5.28807e11i	0.934433	+	1.61849i
$363$	−6.55538e11	−	4.72697e11i	−1.98161	−	1.42890i
$364$	2.58184e11	−	4.47187e11i	0.770854	−	1.33516i
$365$	1.52188e11	−	2.63598e11i	0.448811	−	0.777363i
$366$	−2.78913e11	−	2.01119e11i	−0.812464	−	0.585853i
$367$	−1.13258e11	−	1.96169e11i	−0.325892	−	0.564461i	0.655801	−	0.754934i	$-0.272331\pi$
$367$	−1.13258e11	−	1.96169e11i	−0.325892	−	0.564461i	−0.981692	+	0.190473i	$0.938998\pi$
$368$	−8.86405e10			−0.251952
$369$	−5.88209e10	+	6.62763e10i	−0.165163	+	0.186097i
$370$	−1.72791e11			−0.479307
$371$	1.20630e11	+	2.08938e11i	0.330578	+	0.572578i
$372$	4.91180e11	−	2.20800e11i	1.32983	−	0.597799i
$373$	−2.38579e11	+	4.13231e11i	−0.638180	+	1.10536i	0.347652	+	0.937624i	$0.386979\pi$
$373$	−2.38579e11	+	4.13231e11i	−0.638180	+	1.10536i	−0.985832	+	0.167736i	$0.946354\pi$
$374$	−4.22273e11	+	7.31399e11i	−1.11602	+	1.93300i
$375$	−3.82448e10	+	3.76861e11i	−0.0998692	+	0.984102i
$376$	−1.37589e11	−	2.38311e11i	−0.355008	−	0.614891i
$377$	2.10008e11			0.535426
$378$	−5.23637e11	−	5.69133e11i	−1.31922	−	1.43384i
$379$	−5.69565e10			−0.141797			−0.0708985	−	0.997484i	$-0.522587\pi$
$379$	−5.69565e10			−0.141797			−0.0708985	+	0.997484i	$0.522587\pi$
$380$	−1.05392e11	−	1.82545e11i	−0.259288	−	0.449100i
$381$	−8.00351e10	+	7.88659e11i	−0.194589	+	1.91746i
$382$	5.53894e11	−	9.59373e11i	1.33089	−	2.30517i
$383$	1.11903e10	−	1.93822e10i	0.0265734	−	0.0460265i	−0.852433	−	0.522837i	$-0.824874\pi$
$383$	1.11903e10	−	1.93822e10i	0.0265734	−	0.0460265i	0.879006	+	0.476810i	$0.158207\pi$
$384$	−6.07013e11	+	2.72870e11i	−1.42465	+	0.640421i
$385$	2.68613e11	+	4.65252e11i	0.623095	+	1.07923i
$386$	−5.87449e11			−1.34688
$387$	−2.05086e11	−	6.16130e11i	−0.464769	−	1.39628i
$388$	−3.19575e11			−0.715862
$389$	−2.11354e11	−	3.66075e11i	−0.467990	−	0.810583i	0.531341	−	0.847158i	$-0.321688\pi$
$389$	−2.11354e11	−	3.66075e11i	−0.467990	−	0.810583i	−0.999331	+	0.0365755i	$0.988355\pi$
$390$	2.62675e11	+	1.89410e11i	0.574947	+	0.414584i
$391$	−3.13842e10	+	5.43591e10i	−0.0679073	+	0.117619i
$392$	−1.02539e11	+	1.77602e11i	−0.219331	+	0.379892i
$393$	7.37952e11	+	5.32123e11i	1.56049	+	1.12524i
$394$	4.15435e11	+	7.19555e11i	0.868501	+	1.50429i
$395$	−2.44558e11			−0.505470
$396$	1.85682e12	+	3.80792e11i	3.79439	+	0.778143i
$397$	5.15461e11			1.04145			0.520725	−	0.853724i	$-0.325662\pi$
$397$	5.15461e11			1.04145			0.520725	+	0.853724i	$0.325662\pi$
$398$	−5.51143e11	−	9.54608e11i	−1.10101	−	1.90700i
$399$	2.10015e11	−	9.44081e10i	0.414833	−	0.186480i
$400$	2.05853e11	−	3.56548e11i	0.402057	−	0.696383i
$401$	−3.20829e9	+	5.55693e9i	−0.00619619	+	0.0107321i	−0.869107	−	0.494624i	$-0.835306\pi$
$401$	−3.20829e9	+	5.55693e9i	−0.00619619	+	0.0107321i	0.862911	+	0.505356i	$0.168639\pi$
$402$	−3.29169e9	+	3.24361e10i	−0.00628640	+	0.0619456i
$403$	−1.23169e11	−	2.13334e11i	−0.232610	−	0.402891i
$404$	−8.41586e9			−0.0157175
$405$	2.62512e11	−	1.96536e11i	0.484843	−	0.362989i
$406$	−8.57499e11			−1.56627
$407$	2.31311e11	+	4.00642e11i	0.417851	+	0.723739i
$408$	7.39221e10	−	7.28422e11i	0.132070	−	1.30140i
$409$	1.74242e11	−	3.01796e11i	0.307891	−	0.533284i	−0.670009	−	0.742353i	$-0.733710\pi$
$409$	1.74242e11	−	3.01796e11i	0.307891	−	0.533284i	0.977901	+	0.209069i	$0.0670433\pi$
$410$	−7.57558e10	+	1.31213e11i	−0.132400	+	0.229324i
$411$	−3.31971e11	+	1.49231e11i	−0.573867	+	0.257970i
$412$	9.75205e11	+	1.68910e12i	1.66747	+	2.88815i
$413$	3.20935e11			0.542803
$414$	2.04114e11	+	4.18591e10i	0.341485	+	0.0700307i
$415$	3.83694e11			0.634993
$416$	−6.52471e10	−	1.13011e11i	−0.106817	−	0.185013i
$417$	−4.98606e11	−	3.59536e11i	−0.807506	−	0.582278i
$418$	−4.17347e11	+	7.22867e11i	−0.668658	+	1.15815i
$419$	−1.89634e11	+	3.28456e11i	−0.300575	+	0.520611i	−0.976266	−	0.216573i	$-0.930512\pi$
$419$	−1.89634e11	+	3.28456e11i	−0.300575	+	0.520611i	0.675691	+	0.737185i	$0.263845\pi$
$420$	−7.25159e11	−	5.22899e11i	−1.13713	−	0.819966i
$421$	−5.72178e11	−	9.91041e11i	−0.887690	−	1.53752i	−0.842599	−	0.538542i	$-0.818975\pi$
$421$	−5.72178e11	−	9.91041e11i	−0.887690	−	1.53752i	−0.0450917	−	0.998983i	$-0.514358\pi$
$422$	−4.34030e11			−0.666213
$423$	7.72748e10	+	2.32153e11i	0.117356	+	0.352567i
$424$	7.58196e11			1.13929
$425$	−1.45770e11	−	2.52480e11i	−0.216729	−	0.375385i
$426$	−1.28726e12	+	5.78660e11i	−1.89375	+	0.851296i
$427$	2.17117e11	−	3.76057e11i	0.316059	−	0.547430i
$428$	−2.49713e11	+	4.32515e11i	−0.359703	+	0.623023i
$429$	8.75400e10	−	8.62611e11i	0.124781	−	1.22958i
$430$	−5.55140e11	−	9.61531e11i	−0.783059	−	1.35630i
$431$	−3.08594e11			−0.430764			−0.215382	−	0.976530i	$-0.569100\pi$
$431$	−3.08594e11			−0.430764			−0.215382	+	0.976530i	$0.569100\pi$
$432$	−8.97145e11	+	2.00798e11i	−1.23933	+	0.277384i
$433$	−3.53112e11			−0.482744			−0.241372	−	0.970433i	$-0.577597\pi$
$433$	−3.53112e11			−0.482744			−0.241372	+	0.970433i	$0.577597\pi$
$434$	5.02920e11	+	8.71083e11i	0.680448	+	1.17857i
$435$	3.67107e10	−	3.61744e11i	0.0491576	−	0.484395i
$436$	−9.65969e11	+	1.67311e12i	−1.28019	+	2.21735i
$437$	−3.10181e10	+	5.37250e10i	−0.0406864	+	0.0704709i
$438$	1.82947e12	−	8.22401e11i	2.37516	−	1.06770i
$439$	2.97352e11	+	5.15030e11i	0.382104	+	0.661823i	0.991363	−	0.131148i	$-0.0418664\pi$
$439$	2.97352e11	+	5.15030e11i	0.382104	+	0.661823i	−0.609259	+	0.792971i	$0.708533\pi$
$440$	1.68831e12			2.14741
$441$	1.21039e11	−	1.36380e11i	0.152388	−	0.171703i
$442$	−6.42893e11			−0.801195
$443$	9.53500e10	+	1.65151e11i	0.117626	+	0.203735i	0.918827	−	0.394662i	$-0.129138\pi$
$443$	9.53500e10	+	1.65151e11i	0.117626	+	0.203735i	−0.801200	+	0.598396i	$0.795805\pi$
$444$	−6.24456e11	−	4.50284e11i	−0.762568	−	0.549874i
$445$	−2.51393e11	+	4.35426e11i	−0.303902	+	0.526373i
$446$	1.11375e12	−	1.92908e12i	1.33285	−	2.30857i
$447$	4.28560e11	+	3.09027e11i	0.507724	+	0.366111i
$448$	−3.33926e11	−	5.78376e11i	−0.391650	−	0.678358i
$449$	2.55836e11			0.297066			0.148533	−	0.988907i	$-0.452545\pi$
$449$	2.55836e11			0.297066			0.148533	+	0.988907i	$0.452545\pi$
$450$	−6.42396e11	+	7.23818e11i	−0.738493	+	0.832096i
$451$	4.05649e11			0.461696
$452$	−5.54516e11	−	9.60450e11i	−0.624872	−	1.08231i
$453$	1.17878e12	−	5.29897e11i	1.31520	−	0.591221i
$454$	5.09329e11	−	8.82184e11i	0.562662	−	0.974559i
$455$	−2.04476e11	+	3.54163e11i	−0.223662	+	0.387393i
$456$	7.30598e10	−	7.19925e11i	0.0791292	−	0.779732i
$457$	−2.02347e11	−	3.50475e11i	−0.217007	−	0.375867i	0.736885	−	0.676019i	$-0.236296\pi$
$457$	−2.02347e11	−	3.50475e11i	−0.217007	−	0.375867i	−0.953892	+	0.300152i	$0.902963\pi$
$458$	3.21813e11			0.341750
$459$	−1.94505e11	+	6.21272e11i	−0.204538	+	0.653318i
$460$	2.40867e11			0.250823
$461$	−2.83018e11	−	4.90201e11i	−0.291850	−	0.505499i	0.682397	−	0.730982i	$-0.260937\pi$
$461$	−2.83018e11	−	4.90201e11i	−0.291850	−	0.505499i	−0.974247	+	0.225483i	$0.927604\pi$
$462$	−3.57441e11	+	3.52219e12i	−0.365019	+	3.59687i
$463$	2.30932e11	−	3.99986e11i	0.233544	−	0.404511i	−0.725304	−	0.688428i	$-0.758301\pi$
$463$	2.30932e11	−	3.99986e11i	0.233544	−	0.404511i	0.958849	+	0.283918i	$0.0916343\pi$
$464$	−5.09672e11	+	8.82777e11i	−0.510457	+	0.884138i
$465$	−3.89005e11	+	1.74869e11i	−0.385848	+	0.173450i
$466$	4.78811e11	+	8.29324e11i	0.470357	+	0.814682i
$467$	−1.14378e12			−1.11280			−0.556398	−	0.830916i	$-0.687817\pi$
$467$	−1.14378e12			−1.11280			−0.556398	+	0.830916i	$0.687817\pi$
$468$	4.55699e11	+	1.36903e12i	0.439108	+	1.31919i
$469$	−4.11710e10			−0.0392928
$470$	2.09172e11	+	3.62297e11i	0.197726	+	0.342472i
$471$	3.96300e11	+	2.85764e11i	0.371048	+	0.267556i
$472$	5.04292e11	−	8.73460e11i	0.467674	−	0.810035i
$473$	−1.48630e12	+	2.57435e12i	−1.36531	+	2.36479i
$474$	−1.30721e12	−	9.42609e11i	−1.18945	−	0.857687i
$475$	−1.44069e11	−	2.49535e11i	−0.129852	−	0.224911i
$476$	1.77482e12			1.58461
$477$	−6.60410e11	−	1.35435e11i	−0.584092	−	0.119784i
$478$	1.45653e12			1.27613
$479$	7.19646e11	+	1.24646e12i	0.624610	+	1.08186i	0.988616	+	0.150460i	$0.0480756\pi$
$479$	7.19646e11	+	1.24646e12i	0.624610	+	1.08186i	−0.364006	+	0.931397i	$0.618591\pi$
$480$	−2.06071e11	+	9.26348e10i	−0.177186	+	0.0796505i
$481$	−1.76080e11	+	3.04980e11i	−0.149989	+	0.259788i
$482$	1.64295e12	−	2.84567e12i	1.38647	−	2.40144i
$483$	−2.65658e10	+	2.61777e11i	−0.0222106	+	0.218862i
$484$	−3.07839e12	−	5.33193e12i	−2.54988	−	4.41652i
$485$	2.53097e11			0.207706
$486$	2.16069e12	−	3.87173e10i	1.75683	−	0.0314806i
$487$	3.07201e11			0.247481			0.123740	−	0.992315i	$-0.460511\pi$
$487$	3.07201e11			0.247481			0.123740	+	0.992315i	$0.460511\pi$
$488$	−6.82319e11	−	1.18181e12i	−0.544626	−	0.943320i
$489$	8.99084e10	−	8.85948e11i	0.0711066	−	0.700678i
$490$	1.55887e11	−	2.70004e11i	0.122159	−	0.211586i
$491$	−6.64994e11	+	1.15180e12i	−0.516358	+	0.894358i	0.483462	+	0.875365i	$0.339379\pi$
$491$	−6.64994e11	+	1.15180e12i	−0.516358	+	0.894358i	−0.999820	+	0.0189926i	$0.993954\pi$
$492$	−6.15710e11	+	2.76780e11i	−0.473733	+	0.212957i
$493$	3.60911e11	+	6.25116e11i	0.275162	+	0.476595i
$494$	−6.35393e11			−0.480033
$495$	−1.47057e12	−	3.01580e11i	−1.10093	−	0.225777i
$496$	1.19568e12			0.887050
$497$	−8.91128e11	−	1.54348e12i	−0.655143	−	1.13474i
$498$	2.05093e12	+	1.47889e12i	1.49423	+	1.07746i
$499$	1.35791e11	−	2.35197e11i	0.0980433	−	0.169816i	−0.812831	−	0.582499i	$-0.802075\pi$
$499$	1.35791e11	−	2.35197e11i	0.0980433	−	0.169816i	0.910875	+	0.412683i	$0.135408\pi$
$500$	−1.44283e12	+	2.49906e12i	−1.03241	+	1.78818i
$501$	−7.75472e11	−	5.59179e11i	−0.549916	−	0.396534i
$502$	1.67023e12	+	2.89293e12i	1.17384	+	2.03316i
$503$	2.43504e12			1.69610			0.848049	−	0.529917i	$-0.177777\pi$
$503$	2.43504e12			1.69610			0.848049	+	0.529917i	$0.177777\pi$
$504$	−9.69325e11	−	2.91209e12i	−0.669163	−	2.01033i
$505$	6.66519e9			0.00456039
$506$	−4.76910e11	−	8.26033e11i	−0.323414	−	0.560170i
$507$	−7.54979e11	+	3.39385e11i	−0.507457	+	0.228117i
$508$	−3.01942e12	+	5.22979e12i	−2.01158	+	3.48416i
$509$	1.24976e12	−	2.16465e12i	0.825272	−	1.42941i	−0.0764398	−	0.997074i	$-0.524355\pi$
$509$	1.24976e12	−	2.16465e12i	0.825272	−	1.42941i	0.901711	−	0.432338i	$-0.142311\pi$
$510$	−1.12382e11	+	1.10740e12i	−0.0735581	+	0.724834i
$511$	1.26648e12	+	2.19361e12i	0.821686	+	1.42320i
$512$	−3.13991e12			−2.01931
$513$	−1.92236e11	+	6.14025e11i	−0.122548	+	0.391433i
$514$	−4.92904e12			−3.11479
$515$	−7.72343e11	−	1.33774e12i	−0.483813	−	0.837989i
$516$	4.99455e11	−	4.92158e12i	0.310150	−	3.05619i
$517$	5.60028e11	−	9.69996e11i	0.344748	−	0.597121i
$518$	7.18968e11	−	1.24529e12i	0.438759	−	0.759953i
$519$	1.26729e12	−	5.69685e11i	0.766697	−	0.344653i
$520$	6.42595e11	+	1.11301e12i	0.385409	+	0.667549i
$521$	1.97181e11			0.117245			0.0586225	−	0.998280i	$-0.481329\pi$
$521$	1.97181e11			0.117245			0.0586225	+	0.998280i	$0.481329\pi$
$522$	1.59051e12	−	1.79210e12i	0.937602	−	1.05644i
$523$	−1.84314e12			−1.07721			−0.538606	−	0.842558i	$-0.681049\pi$
$523$	−1.84314e12			−1.07721			−0.538606	+	0.842558i	$0.681049\pi$
$524$	3.46540e12	+	6.00225e12i	2.00800	+	3.47795i
$525$	−9.91279e11	−	7.14793e11i	−0.569481	−	0.410642i
$526$	2.14211e12	−	3.71024e12i	1.22013	−	2.11332i
$527$	4.23345e11	−	7.33256e11i	0.239082	−	0.414102i
$528$	3.41357e12	+	2.46146e12i	1.91142	+	1.37829i
$529$	8.65131e11	+	1.49845e12i	0.480321	+	0.831940i
$530$	−1.15266e12			−0.634543
$531$	−5.95278e11	+	6.70728e11i	−0.324933	+	0.366118i
$532$	1.75411e12			0.949412
$533$	1.54396e11	+	2.67422e11i	0.0828635	+	0.143524i
$534$	−3.02202e12	+	1.35849e12i	−1.60828	+	0.722970i
$535$	1.97767e11	−	3.42543e11i	0.104367	−	0.180769i
$536$	−6.46927e10	+	1.12051e11i	−0.0338543	+	0.0586374i
$537$	−1.90771e10	+	1.87984e11i	−0.00989985	+	0.0975522i
$538$	1.08814e12	+	1.88472e12i	0.559970	+	0.969897i
$539$	−8.34726e11			−0.425985
$540$	2.43786e12	−	5.45637e11i	1.23378	−	0.276142i
$541$	1.54291e12			0.774378			0.387189	−	0.922000i	$-0.373446\pi$
$541$	1.54291e12			0.774378			0.387189	+	0.922000i	$0.373446\pi$
$542$	−1.45984e11	−	2.52852e11i	−0.0726621	−	0.125855i
$543$	2.17543e11	−	2.14364e12i	0.107385	−	1.05817i
$544$	2.24262e11	−	3.88434e11i	0.109790	−	0.190161i
$545$	7.65028e11	−	1.32507e12i	0.371444	−	0.643359i
$546$	−2.45803e12	+	1.10496e12i	−1.18364	+	0.532082i
$547$	−5.29052e11	−	9.16345e11i	−0.252671	−	0.437639i	0.711589	−	0.702596i	$-0.247976\pi$
$547$	−5.29052e11	−	9.16345e11i	−0.252671	−	0.437639i	−0.964260	+	0.264957i	$0.914642\pi$
$548$	−2.77272e12			−1.31339
$549$	3.83215e11	+	1.15127e12i	0.180039	+	0.540883i
$550$	4.43019e12			2.06438
$551$	3.56701e11	+	6.17824e11i	0.164862	+	0.285550i
$552$	6.70710e11	+	4.83637e11i	0.307475	+	0.221714i
$553$	1.01759e12	−	1.76251e12i	0.462709	−	0.801435i
$554$	−1.51135e12	+	2.61773e12i	−0.681664	+	1.18068i
$555$	4.94557e11	+	3.56616e11i	0.221257	+	0.159545i
$556$	−2.34144e12	−	4.05550e12i	−1.03908	−	1.79973i
$557$	3.41690e11			0.150413			0.0752063	−	0.997168i	$-0.476038\pi$
$557$	3.41690e11			0.150413			0.0752063	+	0.997168i	$0.476038\pi$
$558$	−2.75332e12	−	5.64642e11i	−1.20227	−	0.246558i
$559$	−2.26283e12			−0.980166
$560$	−9.92494e11	−	1.71905e12i	−0.426464	−	0.738657i
$561$	2.71812e12	−	1.22187e12i	1.15861	−	0.520827i
$562$	−4.54017e11	+	7.86380e11i	−0.191981	+	0.332521i
$563$	1.19658e12	−	2.07253e12i	0.501941	−	0.869387i	−0.498056	−	0.867145i	$-0.665953\pi$
$563$	1.19658e12	−	2.07253e12i	0.501941	−	0.869387i	0.999997	−	0.00224278i	$-0.000713900\pi$
$564$	−1.88191e11	+	1.85441e12i	−0.0783144	+	0.771703i
$565$	4.39166e11	+	7.60657e11i	0.181305	+	0.314030i
$566$	−7.88970e12			−3.23137
$567$	3.24128e11	+	2.70967e12i	0.131702	+	1.10101i
$568$	−5.60099e12			−2.25786
$569$	6.66747e11	+	1.15484e12i	0.266659	+	0.461866i	0.967997	−	0.250962i	$-0.0807471\pi$
$569$	6.66747e11	+	1.15484e12i	0.266659	+	0.461866i	−0.701338	+	0.712829i	$0.747414\pi$
$570$	−1.11071e11	+	1.09448e12i	−0.0440720	+	0.434282i
$571$	−7.84355e11	+	1.35854e12i	−0.308781	+	0.534824i	−0.978096	−	0.208155i	$-0.933254\pi$
$571$	−7.84355e11	+	1.35854e12i	−0.308781	+	0.534824i	0.669315	+	0.742979i	$0.266588\pi$
$572$	3.30255e12	−	5.72019e12i	1.28993	−	2.23423i
$573$	−3.56535e12	+	1.60273e12i	−1.38167	+	0.621103i
$574$	−6.30427e11	−	1.09193e12i	−0.242399	−	0.419848i
$575$	3.29261e11			0.125613
$576$	1.82813e12	+	3.74908e11i	0.691999	+	0.141913i
$577$	−1.18747e12			−0.445996			−0.222998	−	0.974819i	$-0.571584\pi$
$577$	−1.18747e12			−0.445996			−0.222998	+	0.974819i	$0.571584\pi$
$578$	1.25261e12	+	2.16959e12i	0.466812	+	0.808542i
$579$	1.68138e12	+	1.21241e12i	0.621744	+	0.448329i
$580$	1.38496e12	−	2.39881e12i	0.508171	−	0.880178i
$581$	−1.59652e12	+	2.76525e12i	−0.581275	+	1.00680i
$582$	1.35285e12	+	9.75519e11i	0.488762	+	0.352438i
$583$	1.54304e12	+	2.67263e12i	0.553184	+	0.958142i
$584$	7.96020e12			2.83182
$585$	−3.60904e11	−	1.08425e12i	−0.127406	−	0.382760i
$586$	1.65147e12			0.578537
$587$	−2.78979e12	−	4.83205e12i	−0.969839	−	1.67981i	−0.696010	−	0.718032i	$-0.745043\pi$
$587$	−2.78979e12	−	4.83205e12i	−0.969839	−	1.67981i	−0.273829	−	0.961778i	$-0.588290\pi$
$588$	1.26698e12	−	5.69544e11i	0.437091	−	0.196485i
$589$	4.18407e11	−	7.24702e11i	0.143245	−	0.248108i
$590$	−7.66662e11	+	1.32790e12i	−0.260477	+	0.451160i
$591$	2.96013e11	−	2.91688e12i	0.0998084	−	0.983503i
$592$	−8.54666e11	−	1.48033e12i	−0.285989	−	0.495347i
$593$	3.44549e12			1.14421			0.572105	−	0.820181i	$-0.306127\pi$
$593$	3.44549e12			1.14421			0.572105	+	0.820181i	$0.306127\pi$
$594$	−6.69810e12	−	7.28006e12i	−2.20756	−	2.39936i
$595$	−1.40562e12			−0.459771
$596$	2.01251e12	+	3.48577e12i	0.653325	+	1.13159i
$597$	−3.92710e11	+	3.86973e12i	−0.126528	+	1.24680i
$598$	3.63038e11	−	6.28800e11i	0.116090	−	0.201075i
$599$	−9.21832e11	+	1.59666e12i	−0.292571	+	0.506748i	−0.974417	−	0.224748i	$-0.927844\pi$
$599$	−9.21832e11	+	1.59666e12i	−0.292571	+	0.506748i	0.681846	+	0.731496i	$0.261177\pi$
$600$	−3.50300e12	+	1.57470e12i	−1.10347	+	0.496041i
$601$	−2.52084e12	−	4.36622e12i	−0.788152	−	1.36512i	−0.927098	−	0.374819i	$-0.877705\pi$
$601$	−2.52084e12	−	4.36622e12i	−0.788152	−	1.36512i	0.138946	−	0.990300i	$-0.455628\pi$
$602$	9.23956e12			2.86726
$603$	7.63647e10	−	8.60438e10i	0.0235215	−	0.0265028i
$604$	9.84554e12			3.01005
$605$	2.43802e12	+	4.22278e12i	0.739842	+	1.28144i
$606$	3.56269e10	+	2.56899e10i	0.0107313	+	0.00773812i
$607$	−4.91499e11	+	8.51302e11i	−0.146951	+	0.254527i	−0.930099	−	0.367308i	$-0.880279\pi$
$607$	−4.91499e11	+	8.51302e11i	−0.146951	+	0.254527i	0.783148	+	0.621836i	$0.213613\pi$
$608$	2.21646e11	−	3.83902e11i	0.0657800	−	0.113934i
$609$	2.45431e12	+	1.76976e12i	0.723021	+	0.521357i
$610$	1.03731e12	+	1.79668e12i	0.303337	+	0.525394i
$611$	8.52618e11			0.247497
$612$	−3.29196e12	+	3.70921e12i	−0.948579	+	1.06881i
$613$	−5.27728e12			−1.50952			−0.754758	−	0.656003i	$-0.772246\pi$
$613$	−5.27728e12			−1.50952			−0.754758	+	0.656003i	$0.772246\pi$
$614$	−2.88324e11	−	4.99391e11i	−0.0818696	−	0.141802i
$615$	4.87630e11	−	2.19204e11i	0.137452	−	0.0617889i
$616$	−7.02491e12	+	1.21675e13i	−1.96575	+	3.40477i
$617$	−2.50229e12	+	4.33409e12i	−0.695111	+	1.20397i	0.275032	+	0.961435i	$0.411312\pi$
$617$	−2.50229e12	+	4.33409e12i	−0.695111	+	1.20397i	−0.970143	+	0.242533i	$0.922022\pi$
$618$	1.02775e12	−	1.01274e13i	0.283426	−	2.79285i
$619$	−2.62154e12	−	4.54063e12i	−0.717708	−	1.24311i	−0.961906	−	0.273382i	$-0.911858\pi$
$619$	−2.62154e12	−	4.54063e12i	−0.717708	−	1.24311i	0.244197	−	0.969726i	$-0.421476\pi$
$620$	−3.24908e12			−0.883076
$621$	−4.97817e11	−	5.41070e11i	−0.134325	−	0.145996i
$622$	−1.17738e12			−0.315400
$623$	−2.09205e12	−	3.62354e12i	−0.556386	−	0.963688i
$624$	−3.23450e11	+	3.18724e12i	−0.0854036	+	0.841559i
$625$	−6.49748e10	+	1.12540e11i	−0.0170328	+	0.0295016i
$626$	1.84254e12	−	3.19137e12i	0.479548	−	0.830601i
$627$	2.68641e12	−	1.20762e12i	0.694174	−	0.312052i
$628$	1.86101e12	+	3.22337e12i	0.477453	+	0.826974i
$629$	−1.21042e12			−0.308324
$630$	1.47364e12	+	4.42718e12i	0.372699	+	1.11968i
$631$	4.84088e12			1.21560			0.607802	−	0.794089i	$-0.292052\pi$
$631$	4.84088e12			1.21560			0.607802	+	0.794089i	$0.292052\pi$
$632$	−3.19790e12	−	5.53893e12i	−0.797331	−	1.38102i
$633$	1.24226e12	+	8.95775e11i	0.307537	+	0.221759i
$634$	2.71847e12	−	4.70853e12i	0.668225	−	1.15740i
$635$	2.39132e12	−	4.14189e12i	0.583655	−	1.01092i
$636$	−4.16566e12	−	3.00378e12i	−1.00955	−	0.727966i
$637$	−3.17709e11	−	5.50287e11i	−0.0764542	−	0.132423i
$638$	−1.09687e13			−2.62097
$639$	4.87862e12	+	1.00049e12i	1.15756	+	0.237389i
$640$	4.01530e12			0.946037
$641$	−1.22108e12	−	2.11497e12i	−0.285682	−	0.494816i	0.687092	−	0.726570i	$-0.258887\pi$
$641$	−1.22108e12	−	2.11497e12i	−0.285682	−	0.494816i	−0.972774	+	0.231754i	$0.925553\pi$
$642$	2.37738e12	−	1.06870e12i	0.552321	−	0.248285i
$643$	−2.79975e12	+	4.84930e12i	−0.645906	+	1.11874i	0.338185	+	0.941080i	$0.390187\pi$
$643$	−2.79975e12	+	4.84930e12i	−0.645906	+	1.11874i	−0.984091	+	0.177663i	$0.943146\pi$
$644$	−1.00223e12	+	1.73591e12i	−0.229604	+	0.397686i
$645$	−3.95558e11	+	3.89779e12i	−0.0899894	+	0.886747i
$646$	−1.09196e12	−	1.89133e12i	−0.246695	−	0.427289i
$647$	−7.09599e12			−1.59200			−0.796002	−	0.605295i	$-0.793055\pi$
$647$	−7.09599e12			−1.59200			−0.796002	+	0.605295i	$0.793055\pi$
$648$	7.88395e12	+	3.37561e12i	1.75653	+	0.752080i
$649$	4.10524e12			0.908317
$650$	1.68619e12	+	2.92057e12i	0.370507	+	0.641738i
$651$	3.58349e11	−	3.53114e12i	0.0781973	−	0.770549i
$652$	3.39190e12	−	5.87495e12i	0.735071	−	1.27318i
$653$	9.88559e10	−	1.71223e11i	0.0212762	−	0.0368514i	−0.855191	−	0.518313i	$-0.826560\pi$
$653$	9.88559e10	−	1.71223e11i	0.0212762	−	0.0368514i	0.876467	+	0.481461i	$0.159894\pi$
$654$	9.19648e12	−	4.13409e12i	1.96572	−	0.883649i
$655$	−2.74453e12	−	4.75366e12i	−0.582615	−	1.00912i
$656$	−1.49883e12			−0.315998
$657$	−6.93357e12	−	1.42192e12i	−1.45182	−	0.297735i
$658$	−3.48139e12			−0.723997
$659$	2.47784e12	+	4.29174e12i	0.511786	+	0.886440i	0.999907	+	0.0136635i	$0.00434936\pi$
$659$	2.47784e12	+	4.29174e12i	0.511786	+	0.886440i	−0.488120	+	0.872776i	$0.662317\pi$
$660$	−9.27586e12	−	6.68866e12i	−1.90286	−	1.37212i
$661$	1.81202e12	−	3.13852e12i	0.369196	−	0.639467i	−0.620244	−	0.784409i	$-0.712966\pi$
$661$	1.81202e12	−	3.13852e12i	0.369196	−	0.639467i	0.989440	+	0.144942i	$0.0462997\pi$
$662$	−6.23434e12	+	1.07982e13i	−1.26162	+	2.18520i
$663$	1.84007e12	+	1.32684e12i	0.369848	+	0.266690i
$664$	5.01728e12	+	8.69019e12i	1.00164	+	1.73489i
$665$	−1.38922e12			−0.275470
$666$	1.26899e12	+	3.81237e12i	0.249934	+	0.750864i
$667$	−8.15216e11			−0.159480
$668$	−3.64160e12	−	6.30743e12i	−0.707616	−	1.22563i
$669$	−7.16909e12	+	3.22272e12i	−1.38372	+	0.622021i
$670$	9.83506e10	−	1.70348e11i	0.0188556	−	0.0326589i
$671$	2.77724e12	−	4.81033e12i	0.528887	−	0.916059i
$672$	1.89831e11	−	1.87058e12i	0.0359092	−	0.353846i
$673$	1.66766e12	+	2.88846e12i	0.313356	+	0.542749i	0.979087	−	0.203443i	$-0.0652132\pi$
$673$	1.66766e12	+	2.88846e12i	0.313356	+	0.542749i	−0.665730	+	0.746192i	$0.731880\pi$
$674$	1.14942e13			2.14541
$675$	3.33250e12	−	7.45876e11i	0.617879	−	0.138293i
$676$	−6.30581e12			−1.16140
$677$	2.09334e12	+	3.62577e12i	0.382993	+	0.663363i	0.991489	−	0.130194i	$-0.0415600\pi$
$677$	2.09334e12	+	3.62577e12i	0.382993	+	0.663363i	−0.608496	+	0.793557i	$0.708227\pi$
$678$	−5.84394e11	+	5.75856e12i	−0.106212	+	1.04660i
$679$	−1.05311e12	+	1.82405e12i	−0.190135	+	0.329323i
$680$	−2.20868e12	+	3.82554e12i	−0.396134	+	0.686124i
$681$	−3.27849e12	+	1.47378e12i	−0.584133	+	0.262585i
$682$	6.43309e12	+	1.11424e13i	1.13865	+	1.97220i
$683$	3.28484e12			0.577591			0.288796	−	0.957391i	$-0.406745\pi$
$683$	3.28484e12			0.577591			0.288796	+	0.957391i	$0.406745\pi$
$684$	−3.25356e12	+	3.66595e12i	−0.568338	+	0.640374i
$685$	2.19594e12			0.381077
$686$	−4.35348e12	−	7.54045e12i	−0.750548	−	1.29999i
$687$	−9.21083e11	−	6.64176e11i	−0.157759	−	0.113757i
$688$	5.49172e12	−	9.51193e12i	0.934459	−	1.61853i
$689$	−1.17461e12	+	2.03448e12i	−0.198567	+	0.343928i
$690$	−1.01966e12	−	7.35260e11i	−0.171252	−	0.123487i
$691$	1.34766e12	+	2.33422e12i	0.224869	+	0.389485i	0.956280	−	0.292452i	$-0.0944712\pi$
$691$	1.34766e12	+	2.33422e12i	0.224869	+	0.389485i	−0.731411	+	0.681937i	$0.761138\pi$
$692$	1.05848e13			1.75471
$693$	8.29236e12	−	9.34340e12i	1.36577	−	1.53888i
$694$	−8.94018e12			−1.46295
$695$	1.85438e12	+	3.21187e12i	0.301485	+	0.522188i
$696$	8.67307e12	−	3.89880e12i	1.40098	−	0.629781i
$697$	−5.30677e11	+	9.19160e11i	−0.0851693	+	0.147518i
$698$	1.74923e12	−	3.02975e12i	0.278931	−	0.483123i
$699$	3.41170e11	−	3.36186e12i	0.0540535	−	0.532638i
$700$	−4.65502e12	−	8.06273e12i	−0.732792	−	1.26923i
$701$	8.26238e12			1.29233			0.646166	−	0.763197i	$-0.276372\pi$
$701$	8.26238e12			1.29233			0.646166	+	0.763197i	$0.276372\pi$
$702$	2.24994e12	−	7.18657e12i	0.349666	−	1.11688i
$703$	−1.19630e12			−0.184732
$704$	−4.27140e12	−	7.39829e12i	−0.655381	−	1.13515i
$705$	1.49043e11	−	1.46866e12i	0.0227228	−	0.223908i
$706$	−7.59600e12	+	1.31567e13i	−1.15070	+	1.99308i
$707$	−2.77333e10	+	4.80355e10i	−0.00417459	+	0.00723061i
$708$	−6.23109e12	+	2.80106e12i	−0.931997	+	0.418960i
$709$	3.94697e12	+	6.83635e12i	0.586619	+	1.01605i	0.994672	+	0.103095i	$0.0328745\pi$
$709$	3.94697e12	+	6.83635e12i	0.586619	+	1.01605i	−0.408053	+	0.912958i	$0.633792\pi$
$710$	8.51503e12			1.25754
$711$	1.79606e12	+	5.39581e12i	0.263577	+	0.791851i
$712$	−1.31491e13			−1.91751
$713$	4.78121e11	+	8.28130e11i	0.0692843	+	0.120004i
$714$	−7.51333e12	−	5.41772e12i	−1.08191	−	0.780144i
$715$	−2.61555e12	+	4.53027e12i	−0.374271	+	0.648257i
$716$	−7.19708e11	+	1.24657e12i	−0.102340	+	0.177259i
$717$	−4.16884e12	−	3.00607e12i	−0.589086	−	0.424779i
$718$	−9.50931e12	−	1.64706e13i	−1.33533	−	2.31286i
$719$	−9.37950e12			−1.30888			−0.654440	−	0.756114i	$-0.727096\pi$
$719$	−9.37950e12			−1.30888			−0.654440	+	0.756114i	$0.727096\pi$
$720$	5.43357e12	+	1.11430e12i	0.753510	+	0.154528i
$721$	1.28546e13			1.77154
$722$	5.33564e12	+	9.24159e12i	0.730750	+	1.26570i
$723$	−1.05754e13	+	4.75396e12i	−1.43938	+	0.647044i
$724$	8.20706e12	−	1.42150e13i	1.11010	−	1.92276i
$725$	1.89321e12	−	3.27913e12i	0.254494	−	0.440796i
$726$	−3.24426e12	+	3.19686e13i	−0.433412	+	4.27080i
$727$	−1.89555e11	−	3.28319e11i	−0.0251670	−	0.0435905i	0.853168	−	0.521637i	$-0.174678\pi$
$727$	−1.89555e11	−	3.28319e11i	−0.0251670	−	0.0435905i	−0.878335	+	0.478046i	$0.841345\pi$
$728$	−1.06951e13			−1.41122
$729$	−6.26417e12	−	4.34855e12i	−0.821467	−	0.570257i
$730$	−1.21017e13			−1.57722
$731$	−3.88882e12	−	6.73563e12i	−0.503720	−	0.872469i
$732$	−9.33259e11	+	9.19625e12i	−0.120144	+	1.18389i
$733$	4.04935e12	−	7.01368e12i	0.518104	−	0.897383i	−0.481674	−	0.876350i	$-0.659971\pi$
$733$	4.04935e12	−	7.01368e12i	0.518104	−	0.897383i	0.999779	−	0.0210328i	$-0.00669544\pi$
$734$	−4.50304e12	+	7.79949e12i	−0.572629	+	0.991822i
$735$	−1.00342e12	+	4.51068e11i	−0.126821	+	0.0570097i
$736$	2.53279e11	+	4.38692e11i	0.0318163	+	0.0551074i
$737$	−5.26638e11			−0.0657519
$738$	3.45137e12	+	7.07798e11i	0.428290	+	0.0878325i
$739$	5.44252e12			0.671274			0.335637	−	0.941991i	$-0.391048\pi$
$739$	5.44252e12			0.671274			0.335637	+	0.941991i	$0.391048\pi$
$740$	2.32243e12	+	4.02256e12i	0.284708	+	0.493128i
$741$	1.81860e12	+	1.31136e12i	0.221593	+	0.159787i
$742$	4.79614e12	−	8.30715e12i	0.580863	−	1.00608i
$743$	5.15614e12	−	8.93070e12i	0.620691	−	1.07507i	−0.368667	−	0.929562i	$-0.620186\pi$
$743$	5.15614e12	−	8.93070e12i	0.620691	−	1.07507i	0.989357	−	0.145506i	$-0.0464810\pi$
$744$	−9.04728e12	−	6.52383e12i	−1.08253	−	0.780593i
$745$	−1.59387e12	−	2.76066e12i	−0.189561	−	0.328329i
$746$	1.89713e13			2.24271
$747$	−2.81789e12	−	8.46563e12i	−0.331116	−	0.994756i
$748$	2.27025e13			2.65165
$749$	1.64579e12	+	2.85059e12i	0.191076	+	0.330953i
$750$	1.37364e13	−	6.17494e12i	1.58525	−	0.712618i
$751$	1.31578e12	−	2.27900e12i	0.150940	−	0.261435i	−0.780633	−	0.624989i	$-0.785103\pi$
$751$	1.31578e12	−	2.27900e12i	0.150940	−	0.261435i	0.931573	+	0.363554i	$0.118437\pi$
$752$	−2.06924e12	+	3.58402e12i	−0.235955	+	0.408686i
$753$	1.19010e12	−	1.17272e13i	0.134899	−	1.32928i
$754$	−4.17484e12	−	7.23104e12i	−0.470402	−	0.814760i
$755$	−7.79747e12			−0.873359
$756$	−6.21134e12	+	1.98398e13i	−0.691572	+	2.20896i
$757$	−4.56786e12			−0.505570			−0.252785	−	0.967523i	$-0.581346\pi$
$757$	−4.56786e12			−0.505570			−0.252785	+	0.967523i	$0.581346\pi$
$758$	1.13226e12	+	1.96114e12i	0.124577	+	0.215773i
$759$	−3.39816e11	+	3.34852e12i	−0.0371669	+	0.366239i
$760$	−2.18291e12	+	3.78091e12i	−0.237342	+	0.411089i
$761$	−2.74282e12	+	4.75071e12i	−0.296461	+	0.513485i	−0.975324	−	0.220780i	$-0.929140\pi$
$761$	−2.74282e12	+	4.75071e12i	−0.296461	+	0.513485i	0.678863	+	0.734265i	$0.262473\pi$
$762$	2.87463e13	−	1.29223e13i	3.08877	−	1.38849i
$763$	6.36643e12	+	1.10270e13i	0.680042	+	1.17787i
$764$	−2.97788e13			−3.16219
$765$	2.60717e12	−	2.93762e12i	0.275228	−	0.310113i
$766$	−8.89830e11			−0.0933851
$767$	1.56251e12	+	2.70635e12i	0.163021	+	0.282361i
$768$	1.59385e13	+	1.14930e13i	1.65319	+	1.19209i
$769$	−4.54800e12	+	7.87737e12i	−0.468977	+	0.812293i	−0.999371	−	0.0354588i	$-0.988711\pi$
$769$	−4.54800e12	+	7.87737e12i	−0.468977	+	0.812293i	0.530394	+	0.847751i	$0.322044\pi$
$770$	1.06798e13	−	1.84979e13i	1.09485	−	1.89633i
$771$	1.41077e13	+	1.01728e13i	1.43785	+	1.03681i
$772$	7.89571e12	+	1.36758e13i	0.800043	+	1.38572i
$773$	−4.56540e12			−0.459908			−0.229954	−	0.973202i	$-0.573858\pi$
$773$	−4.56540e12			−0.459908			−0.229954	+	0.973202i	$0.573858\pi$
$774$	−1.71377e13	+	1.93099e13i	−1.71640	+	1.93395i
$775$	−4.44143e12			−0.442248
$776$	3.30955e12	+	5.73232e12i	0.327636	+	0.567483i
$777$	−4.62791e12	+	2.08038e12i	−0.455502	+	0.204761i
$778$	−8.40320e12	+	1.45548e13i	−0.822312	+	1.42429i
$779$	−5.24487e11	+	9.08438e11i	−0.0510289	+	0.0883846i
$780$	8.78926e11	−	8.66085e12i	0.0850210	−	0.837789i
$781$	−1.13988e13	−	1.97434e13i	−1.09630	−	1.89886i
$782$	2.49561e12			0.238642
$783$	−8.25094e12	+	1.84671e12i	−0.784468	+	0.175579i
$784$	3.08421e12			0.291556
$785$	−1.47389e12	−	2.55284e12i	−0.138532	−	0.239944i
$786$	3.65212e12	−	3.59877e13i	0.341306	−	3.36320i
$787$	−1.46658e12	+	2.54020e12i	−0.136276	+	0.236037i	−0.926084	−	0.377317i	$-0.876847\pi$
$787$	−1.46658e12	+	2.54020e12i	−0.136276	+	0.236037i	0.789808	+	0.613354i	$0.210180\pi$
$788$	1.11675e13	−	1.93426e13i	1.03178	−	1.78709i
$789$	−1.37885e13	+	6.19832e12i	−1.26669	+	0.569413i
$790$	4.86169e12	+	8.42069e12i	0.444084	+	0.769176i
$791$	−7.30932e12			−0.663870
$792$	−1.23991e13	−	3.72500e13i	−1.11977	−	3.36405i
$793$	4.22824e12			0.379691
$794$	−1.02471e13	−	1.77485e13i	−0.914973	−	1.58478i
$795$	3.29912e12	+	2.37893e12i	0.292918	+	0.211218i
$796$	−1.48155e13	+	2.56611e13i	−1.30800	+	2.26551i
$797$	−8.53371e12	+	1.47808e13i	−0.749162	+	1.29759i	0.199063	+	0.979987i	$0.436210\pi$
$797$	−8.53371e12	+	1.47808e13i	−0.749162	+	1.29759i	−0.948225	+	0.317600i	$0.897123\pi$
$798$	−7.42568e12	−	5.35452e12i	−0.648221	−	0.467420i
$799$	1.46528e12	+	2.53793e12i	0.127192	+	0.220302i
$800$	−2.35280e12			−0.203086
$801$	1.14533e13	+	2.34880e12i	0.983066	+	0.201605i
$802$	2.55117e11			0.0217748
$803$	1.62002e13	+	2.80596e13i	1.37499	+	2.38156i
$804$	7.99351e11	−	3.59332e11i	0.0674661	−	0.0303280i
$805$	7.93744e11	−	1.37481e12i	0.0666192	−	0.115388i
$806$	−4.89705e12	+	8.48195e12i	−0.408721	+	0.707926i
$807$	7.75341e11	−	7.64014e12i	0.0643520	−	0.634118i
$808$	8.71557e10	+	1.50958e11i	0.00719358	+	0.0124596i
$809$	1.70485e13			1.39932			0.699662	−	0.714474i	$-0.253334\pi$
$809$	1.70485e13			1.39932			0.699662	+	0.714474i	$0.253334\pi$
$810$	−1.19858e13	−	5.13184e12i	−0.978325	−	0.418881i
$811$	1.00699e13			0.817390			0.408695	−	0.912671i	$-0.365984\pi$
$811$	1.00699e13			0.817390			0.408695	+	0.912671i	$0.365984\pi$
$812$	1.15254e13	+	1.99625e13i	0.930363	+	1.61144i
$813$	−1.04019e11	+	1.02499e12i	−0.00835036	+	0.0822836i
$814$	9.19667e12	−	1.59291e13i	0.734211	−	1.27169i
$815$	−2.68632e12	+	4.65284e12i	−0.213279	+	0.369410i
$816$	−1.00431e13	+	4.51468e12i	−0.792981	+	0.356468i
$817$	−3.84345e12	−	6.65706e12i	−0.301802	−	0.522737i
$818$	−1.38553e13			−1.08200
$819$	9.31577e12	+	1.91045e12i	0.723504	+	0.148374i
$820$	4.07283e12			0.314582
$821$	−6.38604e12	−	1.10610e13i	−0.490555	−	0.849666i	0.509386	−	0.860538i	$-0.329873\pi$
$821$	−6.38604e12	−	1.10610e13i	−0.490555	−	0.849666i	−0.999941	+	0.0108721i	$0.996539\pi$
$822$	1.17377e13	+	8.46387e12i	0.896730	+	0.646615i
$823$	−4.34146e12	+	7.51964e12i	−0.329865	+	0.571344i	−0.982485	−	0.186342i	$-0.940337\pi$
$823$	−4.34146e12	+	7.51964e12i	−0.329865	+	0.571344i	0.652619	+	0.757686i	$0.273670\pi$
$824$	2.01987e13	−	3.49852e13i	1.52634	−	2.64370i
$825$	−1.26799e13	−	9.14327e12i	−0.952959	−	0.687161i
$826$	−6.38003e12	−	1.10505e13i	−0.476883	−	0.825986i
$827$	−1.72868e13			−1.28511			−0.642554	−	0.766240i	$-0.722125\pi$
$827$	−1.72868e13			−1.28511			−0.642554	+	0.766240i	$0.722125\pi$
$828$	−1.76895e12	−	5.31437e12i	−0.130791	−	0.392930i
$829$	1.88685e12			0.138753			0.0693763	−	0.997591i	$-0.477899\pi$
$829$	1.88685e12			0.138753			0.0693763	+	0.997591i	$0.477899\pi$
$830$	−7.62764e12	−	1.32115e13i	−0.557877	−	0.966271i
$831$	9.72834e12	−	4.37318e12i	0.707676	−	0.318121i
$832$	3.25152e12	−	5.63179e12i	0.235251	−	0.407466i
$833$	1.09200e12	−	1.89140e12i	0.0785817	−	0.136107i
$834$	−2.46760e12	+	2.43155e13i	−0.176615	+	1.74035i
$835$	2.88407e12	+	4.99536e12i	0.205313	+	0.355613i
$836$	2.24377e13			1.58873
$837$	6.71511e12	+	7.29855e12i	0.472921	+	0.514010i
$838$	1.50793e13			1.05629
$839$	−4.82969e12	−	8.36527e12i	−0.336504	−	0.582843i	0.647268	−	0.762262i	$-0.275911\pi$
$839$	−4.82969e12	−	8.36527e12i	−0.336504	−	0.582843i	−0.983773	+	0.179420i	$0.942578\pi$
$840$	−1.86958e12	+	1.84226e13i	−0.129565	+	1.27672i
$841$	2.56618e12	−	4.44476e12i	0.176891	−	0.306384i
$842$	−2.27492e13	+	3.94027e13i	−1.55977	+	2.70161i
$843$	2.92245e12	−	1.31373e12i	0.199307	−	0.0895944i
$844$	5.83364e12	+	1.01042e13i	0.395730	+	0.685424i
$845$	4.99408e12			0.336977
$846$	6.45736e12	−	7.27582e12i	0.433400	−	0.488332i
$847$	−4.05776e13			−2.70902
$848$	−5.70136e12	−	9.87504e12i	−0.378614	−	0.655779i
$849$	2.25816e13	+	1.62832e13i	1.49166	+	1.07561i
$850$	−5.79564e12	+	1.00384e13i	−0.380817	+	0.659595i
$851$	6.83517e11	−	1.18389e12i	0.0446751	−	0.0773796i
$852$	3.07728e13	+	2.21897e13i	2.00073	+	1.44269i
$853$	−6.32883e12	−	1.09619e13i	−0.409311	−	0.708947i	0.585502	−	0.810671i	$-0.300897\pi$
$853$	−6.32883e12	−	1.09619e13i	−0.409311	−	0.708947i	−0.994813	+	0.101724i	$0.967564\pi$
$854$	−1.72647e13			−1.11070
$855$	2.57676e12	−	2.90336e12i	0.164902	−	0.185803i
$856$	1.03442e13			0.658515
$857$	−8.15121e12	−	1.41183e13i	−0.516189	−	0.894065i	−0.999823	−	0.0187949i	$-0.994017\pi$
$857$	−8.15121e12	−	1.41183e13i	−0.516189	−	0.894065i	0.483635	−	0.875270i	$-0.339316\pi$
$858$	−3.14419e13	+	1.41340e13i	−1.98069	+	0.890376i
$859$	1.32805e13	−	2.30024e13i	0.832231	−	1.44147i	−0.0640344	−	0.997948i	$-0.520397\pi$
$859$	1.32805e13	−	2.30024e13i	0.832231	−	1.44147i	0.896265	−	0.443518i	$-0.146270\pi$
$860$	−1.49229e13	+	2.58472e13i	−0.930273	+	1.61128i
$861$	−4.49202e11	+	4.42640e12i	−0.0278566	+	0.274496i
$862$	6.13468e12	+	1.06256e13i	0.378450	+	0.655495i
$863$	1.50602e13			0.924234			0.462117	−	0.886819i	$-0.347090\pi$
$863$	1.50602e13			0.924234			0.462117	+	0.886819i	$0.347090\pi$
$864$	3.55725e12	+	3.86632e12i	0.217171	+	0.236040i
$865$	−8.38295e12			−0.509125
$866$	7.01968e12	+	1.21584e13i	0.424118	+	0.734594i
$867$	8.92534e11	−	8.79495e12i	0.0536462	−	0.528624i
$868$	1.35192e13	−	2.34159e13i	0.808371	−	1.40014i
$869$	1.30164e13	−	2.25451e13i	0.774289	−	1.34111i
$870$	−1.31854e13	+	5.92724e12i	−0.780293	+	0.350765i
$871$	−2.00446e11	−	3.47182e11i	−0.0118009	−	0.0204398i
$872$	4.00148e13			2.34367
$873$	−1.85877e12	−	5.58420e12i	−0.108308	−	0.325384i
$874$	2.46650e12			0.142981
$875$	9.50930e12	+	1.64706e13i	0.548419	+	0.949889i
$876$	−4.37347e13	−	3.15363e13i	−2.50933	−	1.80943i
$877$	1.33232e13	−	2.30765e13i	0.760520	−	1.31726i	−0.182064	−	0.983287i	$-0.558278\pi$
$877$	1.33232e13	−	2.30765e13i	0.760520	−	1.31726i	0.942583	−	0.333972i	$-0.108389\pi$
$878$	1.18224e13	−	2.04770e13i	0.671399	−	1.16290i
$879$	−4.72678e12	−	3.40840e12i	−0.267064	−	0.192575i
$880$	−1.26955e13	−	2.19892e13i	−0.713636	−	1.23605i
$881$	−3.46233e13			−1.93632			−0.968159	−	0.250336i	$-0.919459\pi$
$881$	−3.46233e13			−1.93632			−0.968159	+	0.250336i	$0.919459\pi$
$882$	−7.10207e12	−	1.45647e12i	−0.395163	−	0.0810389i
$883$	5.22763e12			0.289389			0.144694	−	0.989476i	$-0.453780\pi$
$883$	5.22763e12			0.289389			0.144694	+	0.989476i	$0.453780\pi$
$884$	8.64091e12	+	1.49665e13i	0.475909	+	0.824299i
$885$	4.93490e12	−	2.21838e12i	0.270417	−	0.121560i
$886$	3.79102e12	−	6.56623e12i	0.206683	−	0.357985i
$887$	1.70993e13	−	2.96169e13i	0.927518	−	1.60651i	0.140057	−	0.990143i	$-0.455271\pi$
$887$	1.70993e13	−	2.96169e13i	0.927518	−	1.60651i	0.787461	−	0.616365i	$-0.211395\pi$
$888$	−1.60995e12	+	1.58643e13i	−0.0868867	+	0.856174i
$889$	1.99002e13	+	3.44681e13i	1.06856	+	1.85080i
$890$	1.99902e13			1.06798
$891$	4.14608e12	+	3.46607e13i	0.220388	+	1.84241i
$892$	−5.98784e13			−3.16686
$893$	1.44818e12	+	2.50833e12i	0.0762064	+	0.131993i
$894$	2.12094e12	−	2.08996e13i	0.111048	−	1.09426i
$895$	5.69994e11	−	9.87259e11i	0.0296939	−	0.0514313i
$896$	−1.67073e13	+	2.89379e13i	−0.866006	+	1.49997i
$897$	−2.33683e12	+	1.05047e12i	−0.120520	+	0.0541775i
$898$	−5.08589e12	−	8.80901e12i	−0.260990	−	0.452047i
$899$	1.09965e13			0.561484
$900$	2.54847e13	+	5.22632e12i	1.29475	+	0.265525i
$901$	−8.07454e12			−0.408184
$902$	−8.06409e12	−	1.39674e13i	−0.405626	−	0.702565i
$903$	−2.64452e13	−	1.90691e13i	−1.32358	−	0.954412i
$904$	−1.14853e13	+	1.98931e13i	−0.571984	+	0.990705i
$905$	−6.49982e12	+	1.12580e13i	−0.322094	+	0.557884i
$906$	−4.16791e13	−	3.00541e13i	−2.05514	−	1.48193i
$907$	3.67941e12	+	6.37292e12i	0.180528	+	0.312684i	0.942061	−	0.335443i	$-0.108886\pi$
$907$	3.67941e12	+	6.37292e12i	0.180528	+	0.312684i	−0.761532	+	0.648127i	$0.775553\pi$
$908$	−2.73829e13			−1.33688
$909$	−4.89498e10	−	1.47057e11i	−0.00237801	−	0.00714413i
$910$	1.62595e13			0.785998
$911$	6.52165e12	+	1.12958e13i	0.313708	+	0.543358i	0.979162	−	0.203081i	$-0.0650955\pi$
$911$	6.52165e12	+	1.12958e13i	0.313708	+	0.543358i	−0.665454	+	0.746439i	$0.731762\pi$
$912$	−9.92597e12	+	4.46201e12i	−0.475112	+	0.213577i
$913$	−2.04218e13	+	3.53717e13i	−0.972694	+	1.68476i
$914$	−8.04509e12	+	1.39345e13i	−0.381306	+	0.660441i
$915$	7.39123e11	−	7.28325e12i	0.0348595	−	0.343503i
$916$	−4.32538e12	−	7.49178e12i	−0.202999	−	0.351605i
$917$	4.56790e13			2.13331
$918$	2.52585e13	−	5.65331e12i	1.17386	−	0.262731i
$919$	−6.75575e12			−0.312431			−0.156215	−	0.987723i	$-0.549929\pi$
$919$	−6.75575e12			−0.312431			−0.156215	+	0.987723i	$0.549929\pi$
$920$	−2.49445e12	−	4.32052e12i	−0.114797	−	0.198834i
$921$	−2.05441e11	+	2.02440e12i	−0.00940848	+	0.0927102i
$922$	−1.12525e13	+	1.94899e13i	−0.512813	+	0.888219i
$923$	8.67713e12	−	1.50292e13i	0.393521	−	0.681599i
$924$	8.68006e13	−	3.90194e13i	3.91741	−	1.76099i
$925$	3.17471e12	+	5.49876e12i	0.142583	+	0.246960i
$926$	−1.83632e13			−0.820727
$927$	−2.38430e13	+	2.68650e13i	−1.06048	+	1.19489i
$928$	5.82529e12			0.257841
$929$	−8.69637e12	−	1.50625e13i	−0.383060	−	0.663480i	0.608438	−	0.793602i	$-0.291796\pi$
$929$	−8.69637e12	−	1.50625e13i	−0.383060	−	0.663480i	−0.991498	+	0.130122i	$0.958463\pi$
$930$	1.37543e13	+	9.91800e12i	0.602929	+	0.434761i
$931$	1.07926e12	−	1.86934e12i	0.0470819	−	0.0815483i
$932$	1.28711e13	−	2.22933e13i	0.558783	−	0.967840i
$933$	3.36987e12	+	2.42995e12i	0.145595	+	0.104986i
$934$	2.27377e13	+	3.93828e13i	0.977654	+	1.69335i
$935$	−1.79799e13			−0.769372
$936$	1.98375e13	−	2.23519e13i	0.844786	−	0.951861i
$937$	−6.24202e12			−0.264544			−0.132272	−	0.991213i	$-0.542227\pi$
$937$	−6.24202e12			−0.264544			−0.132272	+	0.991213i	$0.542227\pi$
$938$	8.18457e11	+	1.41761e12i	0.0345210	+	0.0597921i
$939$	−1.18602e13	+	5.33149e12i	−0.497847	+	0.223797i
$940$	5.62283e12	−	9.73903e12i	0.234898	−	0.406856i
$941$	−3.56277e12	+	6.17090e12i	−0.148127	+	0.256564i	−0.930535	−	0.366202i	$-0.880658\pi$
$941$	−3.56277e12	+	6.17090e12i	−0.148127	+	0.256564i	0.782408	+	0.622766i	$0.213991\pi$
$942$	1.96129e12	−	1.93263e13i	0.0811544	−	0.799688i
$943$	−5.99341e11	−	1.03809e12i	−0.0246815	−	0.0427496i
$944$	−1.51684e13			−0.621678
$945$	4.91926e12	−	1.57127e13i	0.200658	−	0.640926i
$946$	1.18188e14			4.79802
$947$	−9.20632e12	−	1.59458e13i	−0.371973	−	0.644276i	0.617896	−	0.786260i	$-0.287985\pi$
$947$	−9.20632e12	−	1.59458e13i	−0.371973	−	0.644276i	−0.989869	+	0.141984i	$0.954652\pi$
$948$	−4.37402e12	+	4.31011e13i	−0.175891	+	1.73321i
$949$	−1.23321e13	+	2.13598e13i	−0.493558	+	0.854867i
$950$	−5.72804e12	+	9.92125e12i	−0.228165	+	0.395194i
$951$	−1.74984e13	+	7.86606e12i	−0.693724	+	0.311849i
$952$	−1.83802e13	−	3.18355e13i	−0.725244	−	1.25616i
$953$	8.34892e12			0.327878			0.163939	−	0.986470i	$-0.447580\pi$
$953$	8.34892e12			0.327878			0.163939	+	0.986470i	$0.447580\pi$
$954$	8.46527e12	+	2.54318e13i	0.330882	+	0.994053i
$955$	2.35842e13			0.917501
$956$	−1.95768e13	−	3.39079e13i	−0.758019	−	1.31293i
$957$	3.13942e13	+	2.26378e13i	1.20989	+	0.872430i
$958$	2.86124e13	−	4.95581e13i	1.09751	−	1.90095i
$959$	−9.13711e12	+	1.58259e13i	−0.348839	+	0.604207i
$960$	−9.13252e12	−	6.58529e12i	−0.347032	−	0.250239i
$961$	6.77038e12	+	1.17266e13i	0.256070	+	0.443526i
$962$	1.40015e13			0.527094
$963$	−9.01012e12	−	1.84777e12i	−0.337608	−	0.0692356i
$964$	−8.83291e13			−3.29426
$965$	−6.25325e12	−	1.08309e13i	−0.232131	−	0.402062i
$966$	9.54169e12	−	4.28927e12i	0.352556	−	0.158484i
$967$	1.50380e13	−	2.60466e13i	0.553059	−	0.957927i	−0.444992	−	0.895534i	$-0.646794\pi$
$967$	1.50380e13	−	2.60466e13i	0.553059	−	0.957927i	0.998052	−	0.0623927i	$-0.0198731\pi$
$968$	−6.37605e13	+	1.10436e14i	−2.33406	+	4.04271i
$969$	−7.78063e11	+	7.66696e12i	−0.0283503	+	0.279361i
$970$	−5.03143e12	−	8.71469e12i	−0.182481	−	0.316067i
$971$	−4.68313e12			−0.169064			−0.0845318	−	0.996421i	$-0.526939\pi$
$971$	−4.68313e12			−0.169064			−0.0845318	+	0.996421i	$0.526939\pi$
$972$	−2.99425e13	−	4.97804e13i	−1.07594	−	1.78879i
$973$	−3.08636e13			−1.10392
$974$	−6.10699e12	−	1.05776e13i	−0.217426	−	0.376593i
$975$	1.20147e12	−	1.18392e13i	0.0425788	−	0.419568i
$976$	−1.02616e13	+	1.77736e13i	−0.361985	+	0.626976i
$977$	−7.81803e12	+	1.35412e13i	−0.274519	+	0.475480i	−0.970014	−	0.243051i	$-0.921852\pi$
$977$	−7.81803e12	+	1.35412e13i	−0.274519	+	0.475480i	0.695495	+	0.718531i	$0.255185\pi$
$978$	−3.22925e13	+	1.45164e13i	−1.12870	+	0.507382i
$979$	−2.67604e13	−	4.63504e13i	−0.931045	−	1.61262i
$980$	−8.38088e12			−0.290250
$981$	−3.48540e13	−	7.14777e12i	−1.20155	−	0.246411i
$982$	5.28789e13			1.81460
$983$	2.31834e12	+	4.01548e12i	0.0791929	+	0.137166i	0.902902	−	0.429847i	$-0.141432\pi$
$983$	2.31834e12	+	4.01548e12i	0.0791929	+	0.137166i	−0.823709	+	0.567013i	$0.808099\pi$
$984$	1.13411e13	+	8.17784e12i	0.385635	+	0.278074i
$985$	−8.84440e12	+	1.53189e13i	−0.299368	+	0.518520i
$986$	1.43494e13	−	2.48539e13i	0.483491	−	0.837431i
$987$	9.96433e12	+	7.18510e12i	0.334211	+	0.240994i
$988$	8.54011e12	+	1.47919e13i	0.285139	+	0.493876i
$989$	8.78397e12			0.291949
$990$	1.88500e13	+	5.66302e13i	0.623668	+	1.87365i
$991$	2.04024e13			0.671970			0.335985	−	0.941867i	$-0.390931\pi$
$991$	2.04024e13			0.671970			0.335985	+	0.941867i	$0.390931\pi$
$992$	−3.41651e12	−	5.91756e12i	−0.112016	−	0.194017i
$993$	4.01297e13	−	1.80395e13i	1.30977	−	0.588778i
$994$	−3.54303e13	+	6.13671e13i	−1.15116	+	1.99387i
$995$	1.17335e13	−	2.03231e13i	0.379512	−	0.657334i
$996$	6.86251e12	−	6.76226e13i	0.220961	−	2.17733i
$997$	1.05858e13	+	1.83351e13i	0.339308	+	0.587699i	0.984303	−	0.176488i	$-0.0564738\pi$
$997$	1.05858e13	+	1.83351e13i	0.339308	+	0.587699i	−0.644995	+	0.764187i	$0.723140\pi$
$998$	−1.07978e13			−0.344547
$999$	4.23612e12	−	1.35307e13i	0.134562	−	0.429808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.10.c.a.4.1	✓	16
3.2	odd	2		27.10.c.a.10.8		16
9.2	odd	6		27.10.c.a.19.8		16
9.4	even	3		81.10.a.c.1.8		8
9.5	odd	6		81.10.a.d.1.1		8
9.7	even	3	inner	9.10.c.a.7.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.1	✓	16	1.1	even	1	trivial
9.10.c.a.7.1	yes	16	9.7	even	3	inner
27.10.c.a.10.8		16	3.2	odd	2
27.10.c.a.19.8		16	9.2	odd	6
81.10.a.c.1.8		8	9.4	even	3
81.10.a.d.1.1		8	9.5	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.8795 - 34.4322i) q^{2} +(-14.1649 + 139.579i) q^{3} +(-534.387 + 925.585i) q^{4} +(423.223 - 733.045i) q^{5} +(5087.62 - 2287.03i) q^{6} +(3521.99 + 6100.27i) q^{7} +22136.7 q^{8} +(-19281.7 - 3954.24i) q^{9} +O(q^{10})\)	\(q+(-19.8795 - 34.4322i) q^{2} +(-14.1649 + 139.579i) q^{3} +(-534.387 + 925.585i) q^{4} +(423.223 - 733.045i) q^{5} +(5087.62 - 2287.03i) q^{6} +(3521.99 + 6100.27i) q^{7} +22136.7 q^{8} +(-19281.7 - 3954.24i) q^{9} -33653.8 q^{10} +(45051.5 + 78031.5i) q^{11} +(-121623. - 87700.0i) q^{12} +(-34294.5 + 59399.8i) q^{13} +(140031. - 242540. i) q^{14} +(96322.9 + 69456.7i) q^{15} +(-166460. - 288317. i) q^{16} -235749. q^{17} +(247157. + 742521. i) q^{18} -232999. q^{19} +(452330. + 783458. i) q^{20} +(-901359. + 405187. i) q^{21} +(1.79120e6 - 3.10245e6i) q^{22} +(133126. - 230581. i) q^{23} +(-313563. + 3.08982e6i) q^{24} +(618326. + 1.07097e6i) q^{25} +2.72703e6 q^{26} +(825053. - 2.63532e6i) q^{27} -7.52842e6 q^{28} +(-1.53091e6 - 2.65162e6i) q^{29} +(476702. - 4.69737e6i) q^{30} +(-1.79575e6 + 3.11033e6i) q^{31} +(-951277. + 1.64766e6i) q^{32} +(-1.15297e7 + 5.18295e6i) q^{33} +(4.68656e6 + 8.11736e6i) q^{34} +5.96236e6 q^{35} +(1.39639e7 - 1.57338e7i) q^{36} +5.13436e6 q^{37} +(4.63189e6 + 8.02267e6i) q^{38} +(-7.80521e6 - 5.62819e6i) q^{39} +(9.36877e6 - 1.62272e7i) q^{40} +(2.25103e6 - 3.89890e6i) q^{41} +(3.18701e7 + 2.29809e7i) q^{42} +(1.64956e7 + 2.85712e7i) q^{43} -9.62997e7 q^{44} +(-1.10591e7 + 1.24608e7i) q^{45} -1.05859e7 q^{46} +(-6.21541e6 - 1.07654e7i) q^{47} +(4.26010e7 - 1.91504e7i) q^{48} +(-4.63206e6 + 8.02297e6i) q^{49} +(2.45840e7 - 4.25807e7i) q^{50} +(3.33935e6 - 3.29056e7i) q^{51} +(-3.66530e7 - 6.34849e7i) q^{52} +3.42506e7 q^{53} +(-1.07141e8 + 2.39802e7i) q^{54} +7.62674e7 q^{55} +(7.79653e7 + 1.35040e8i) q^{56} +(3.30039e6 - 3.25218e7i) q^{57} +(-6.08675e7 + 1.05426e8i) q^{58} +(2.27808e7 - 3.94575e7i) q^{59} +(-1.15762e8 + 5.20383e7i) q^{60} +(-3.08230e7 - 5.33870e7i) q^{61} +1.42794e8 q^{62} +(-4.37881e7 - 1.31550e8i) q^{63} -9.48116e7 q^{64} +(2.90285e7 + 5.02788e7i) q^{65} +(4.07665e8 + 2.93960e8i) q^{66} +(-2.92242e6 + 5.06178e6i) q^{67} +(1.25981e8 - 2.18205e8i) q^{68} +(3.02986e7 + 2.18477e7i) q^{69} +(-1.18529e8 - 2.05297e8i) q^{70} -2.53018e8 q^{71} +(-4.26834e8 - 8.75338e7i) q^{72} +3.59593e8 q^{73} +(-1.02068e8 - 1.76788e8i) q^{74} +(-1.58244e8 + 7.11353e7i) q^{75} +(1.24511e8 - 2.15660e8i) q^{76} +(-3.17342e8 + 5.49653e8i) q^{77} +(-3.86280e7 + 3.80636e8i) q^{78} +(-1.44462e8 - 2.50215e8i) q^{79} -2.81799e8 q^{80} +(3.56148e8 + 1.52489e8i) q^{81} -1.78997e8 q^{82} +(2.26650e8 + 3.92569e8i) q^{83} +(1.06639e8 - 1.05081e9i) q^{84} +(-9.97744e7 + 1.72814e8i) q^{85} +(6.55848e8 - 1.13596e9i) q^{86} +(3.91796e8 - 1.76124e8i) q^{87} +(9.97292e8 + 1.72736e9i) q^{88} -5.93996e8 q^{89} +(6.48903e8 + 1.33075e8i) q^{90} -4.83140e8 q^{91} +(1.42281e8 + 2.46438e8i) q^{92} +(-4.08701e8 - 2.94707e8i) q^{93} +(-2.47118e8 + 4.28021e8i) q^{94} +(-9.86105e7 + 1.70798e8i) q^{95} +(-2.16504e8 - 1.56117e8i) q^{96} +(1.49505e8 + 2.58951e8i) q^{97} +3.68332e8 q^{98} +(-5.60115e8 - 1.68273e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9}+O(q^{10}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16} - 831078 q^{17} - 1039500 q^{18} - 170554 q^{19} + 1855164 q^{20} - 503475 q^{21} + 529359 q^{22} + 1064559 q^{23} - 2686059 q^{24} - 2293229 q^{25} + 2436312 q^{26} - 6176520 q^{27} + 1225724 q^{28} - 1309053 q^{29} + 30713544 q^{30} - 2359819 q^{31} + 5760063 q^{32} - 19931472 q^{33} + 981801 q^{34} - 31066554 q^{35} - 48894093 q^{36} + 16391516 q^{37} + 39490203 q^{38} + 74528535 q^{39} - 16760496 q^{40} + 54747318 q^{41} + 25242354 q^{42} + 15249608 q^{43} - 332509926 q^{44} - 139865967 q^{45} + 2390520 q^{46} + 156295545 q^{47} + 312045027 q^{48} + 15239583 q^{49} + 315590163 q^{50} + 3098385 q^{51} - 19773358 q^{52} - 525516228 q^{53} - 591710103 q^{54} - 7579770 q^{55} + 470339790 q^{56} + 581271465 q^{57} + 55408560 q^{58} + 307774074 q^{59} - 430082172 q^{60} + 69192125 q^{61} - 914436924 q^{62} - 693544725 q^{63} - 403588478 q^{64} + 482470359 q^{65} + 1912534074 q^{66} + 14328044 q^{67} + 915409575 q^{68} - 724756329 q^{69} - 229271934 q^{70} - 1239601392 q^{71} - 1729340037 q^{72} + 598613198 q^{73} + 1022736000 q^{74} + 1477690413 q^{75} + 119954093 q^{76} + 717995541 q^{77} + 243023958 q^{78} + 30257531 q^{79} - 2927826528 q^{80} - 1055378241 q^{81} - 202376022 q^{82} + 1176168291 q^{83} + 1383634866 q^{84} + 4818366 q^{85} + 1426944009 q^{86} + 617958567 q^{87} + 911312427 q^{88} - 3317041296 q^{89} - 981417492 q^{90} - 739230122 q^{91} - 76813998 q^{92} - 552731577 q^{93} - 1954316784 q^{94} - 391400652 q^{95} + 1854064512 q^{96} - 267311278 q^{97} + 4827300318 q^{98} + 1672014609 q^{99}+O(q^{100}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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