LMFDB - Embedded newform 16.6.e.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, 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:	$2.56614111701$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.8
Root			$3.95408 + 0.604357i$ of defining polynomial
Character	$\chi$	$=$	16.13
Dual form			16.6.e.a.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.55844 - 3.34972i) q^{2} +(14.5768 + 14.5768i) q^{3} +(9.55871 - 30.5390i) q^{4} +(-33.9573 + 33.9573i) q^{5} +(115.276 + 17.6192i) q^{6} -141.886i q^{7} +(-58.7245 - 171.229i) q^{8} +181.969i q^{9} +O(q^{10})$	\(q+(4.55844 - 3.34972i) q^{2} +(14.5768 + 14.5768i) q^{3} +(9.55871 - 30.5390i) q^{4} +(-33.9573 + 33.9573i) q^{5} +(115.276 + 17.6192i) q^{6} -141.886i q^{7} +(-58.7245 - 171.229i) q^{8} +181.969i q^{9} +(-41.0447 + 268.540i) q^{10} +(-509.792 + 509.792i) q^{11} +(584.498 - 305.827i) q^{12} +(0.484929 + 0.484929i) q^{13} +(-475.280 - 646.780i) q^{14} -989.980 q^{15} +(-841.262 - 583.827i) q^{16} +1559.58 q^{17} +(609.544 + 829.492i) q^{18} +(92.6701 + 92.6701i) q^{19} +(712.434 + 1361.61i) q^{20} +(2068.25 - 2068.25i) q^{21} +(-616.194 + 4031.52i) q^{22} -2630.63i q^{23} +(1639.96 - 3352.00i) q^{24} +818.803i q^{25} +(3.83490 + 0.586141i) q^{26} +(889.645 - 889.645i) q^{27} +(-4333.07 - 1356.25i) q^{28} +(3984.50 + 3984.50i) q^{29} +(-4512.76 + 3316.16i) q^{30} -3882.73 q^{31} +(-5790.50 + 156.657i) q^{32} -14862.3 q^{33} +(7109.25 - 5224.16i) q^{34} +(4818.07 + 4818.07i) q^{35} +(5557.14 + 1739.38i) q^{36} +(7806.14 - 7806.14i) q^{37} +(732.850 + 112.012i) q^{38} +14.1375i q^{39} +(7808.61 + 3820.36i) q^{40} +7658.37i q^{41} +(2499.93 - 16356.1i) q^{42} +(-3947.03 + 3947.03i) q^{43} +(10695.6 + 20441.5i) q^{44} +(-6179.16 - 6179.16i) q^{45} +(-8811.87 - 11991.5i) q^{46} +525.728 q^{47} +(-3752.59 - 20773.3i) q^{48} -3324.71 q^{49} +(2742.76 + 3732.46i) q^{50} +(22733.7 + 22733.7i) q^{51} +(19.4446 - 10.1740i) q^{52} +(-15545.1 + 15545.1i) q^{53} +(1075.33 - 7035.46i) q^{54} -34622.4i q^{55} +(-24295.1 + 8332.19i) q^{56} +2701.67i q^{57} +(31510.1 + 4816.13i) q^{58} +(7088.71 - 7088.71i) q^{59} +(-9462.93 + 30233.0i) q^{60} +(-19344.7 - 19344.7i) q^{61} +(-17699.2 + 13006.1i) q^{62} +25818.8 q^{63} +(-25870.9 + 20110.7i) q^{64} -32.9338 q^{65} +(-67749.0 + 49784.7i) q^{66} +(-21154.5 - 21154.5i) q^{67} +(14907.6 - 47628.0i) q^{68} +(38346.2 - 38346.2i) q^{69} +(38102.1 + 5823.68i) q^{70} +24047.5i q^{71} +(31158.3 - 10686.0i) q^{72} -11057.8i q^{73} +(9435.39 - 61732.2i) q^{74} +(-11935.6 + 11935.6i) q^{75} +(3715.86 - 1944.25i) q^{76} +(72332.5 + 72332.5i) q^{77} +(47.3566 + 64.4448i) q^{78} -63378.0 q^{79} +(48392.2 - 8741.80i) q^{80} +70154.8 q^{81} +(25653.4 + 34910.2i) q^{82} +(-49588.7 - 49588.7i) q^{83} +(-43392.6 - 82932.2i) q^{84} +(-52959.1 + 52959.1i) q^{85} +(-4770.83 + 31213.7i) q^{86} +116163. i q^{87} +(117229. + 57354.1i) q^{88} -67262.1i q^{89} +(-48865.8 - 7468.84i) q^{90} +(68.8048 - 68.8048i) q^{91} +(-80336.7 - 25145.4i) q^{92} +(-56598.0 - 56598.0i) q^{93} +(2396.50 - 1761.04i) q^{94} -6293.65 q^{95} +(-86690.8 - 82123.6i) q^{96} -9709.53 q^{97} +(-15155.5 + 11136.9i) q^{98} +(-92766.2 - 92766.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	4.55844	−	3.34972i	0.805826	−	0.592153i
$2$	4.55844	−	3.34972i	0.805826	−	0.592153i
$3$	14.5768	+	14.5768i	0.935105	+	0.935105i	0.998019	−	0.0629142i	$-0.0200394\pi$
$3$	14.5768	+	14.5768i	0.935105	+	0.935105i	−0.0629142	+	0.998019i	$0.520039\pi$
$4$	9.55871	−	30.5390i	0.298710	−	0.954344i
$5$	−33.9573	+	33.9573i	−0.607447	+	0.607447i	−0.942278	−	0.334831i	$-0.891321\pi$
$5$	−33.9573	+	33.9573i	−0.607447	+	0.607447i	0.334831	+	0.942278i	$0.391321\pi$
$6$	115.276	+	17.6192i	1.30726	+	0.199806i
$7$		−	141.886i		−	1.09445i	−0.836986	−	0.547224i	$-0.815685\pi$
$7$		−	141.886i		−	1.09445i	0.836986	−	0.547224i	$-0.184315\pi$
$8$	−58.7245	−	171.229i	−0.324410	−	0.945917i
$9$			181.969i			0.748842i
$10$	−41.0447	+	268.540i	−0.129795	+	0.849197i
$11$	−509.792	+	509.792i	−1.27032	+	1.27032i	−0.324394	+	0.945922i	$0.605160\pi$
$11$	−509.792	+	509.792i	−1.27032	+	1.27032i	−0.945922	+	0.324394i	$0.894840\pi$
$12$	584.498	−	305.827i	1.17174	−	0.613087i
$13$	0.484929	+	0.484929i	0.000795829	+	0.000795829i	0.707505	−	0.706709i	$-0.249821\pi$
$13$	0.484929	+	0.484929i	0.000795829	+	0.000795829i	−0.706709	+	0.707505i	$0.749821\pi$
$14$	−475.280	−	646.780i	−0.648081	−	0.881934i
$15$	−989.980			−1.13605
$16$	−841.262	−	583.827i	−0.821545	−	0.570144i
$17$	1559.58			1.30884			0.654418	−	0.756133i	$-0.272914\pi$
$17$	1559.58			1.30884			0.654418	+	0.756133i	$0.272914\pi$
$18$	609.544	+	829.492i	0.443429	+	0.603436i
$19$	92.6701	+	92.6701i	0.0588919	+	0.0588919i	0.735939	−	0.677047i	$-0.236741\pi$
$19$	92.6701	+	92.6701i	0.0588919	+	0.0588919i	−0.677047	+	0.735939i	$0.736741\pi$
$20$	712.434	+	1361.61i	0.398263	+	0.761163i
$21$	2068.25	−	2068.25i	1.02342	−	1.02342i
$22$	−616.194	+	4031.52i	−0.271432	+	1.77587i
$23$		−	2630.63i		−	1.03691i	−0.855106	−	0.518453i	$-0.826508\pi$
$23$		−	2630.63i		−	1.03691i	0.855106	−	0.518453i	$-0.173492\pi$
$24$	1639.96	−	3352.00i	0.581174	−	1.18789i
$25$			818.803i			0.262017i
$26$	3.83490	+	0.586141i	0.00111255	+	0.000170047i
$27$	889.645	−	889.645i	0.234859	−	0.234859i
$28$	−4333.07	−	1356.25i	−1.04448	−	0.326922i
$29$	3984.50	+	3984.50i	0.879790	+	0.879790i	0.993513	−	0.113722i	$-0.0362775\pi$
$29$	3984.50	+	3984.50i	0.879790	+	0.879790i	−0.113722	+	0.993513i	$0.536277\pi$
$30$	−4512.76	+	3316.16i	−0.915460	+	0.672717i
$31$	−3882.73			−0.725660			−0.362830	−	0.931855i	$-0.618189\pi$
$31$	−3882.73			−0.725660			−0.362830	+	0.931855i	$0.618189\pi$
$32$	−5790.50	+	156.657i	−0.999634	+	0.0270442i
$33$	−14862.3			−2.37576
$34$	7109.25	−	5224.16i	1.05469	−	0.775031i
$35$	4818.07	+	4818.07i	0.664819	+	0.664819i
$36$	5557.14	+	1739.38i	0.714653	+	0.223686i
$37$	7806.14	−	7806.14i	0.937415	−	0.937415i	−0.0607387	−	0.998154i	$-0.519346\pi$
$37$	7806.14	−	7806.14i	0.937415	−	0.937415i	0.998154	+	0.0607387i	$0.0193456\pi$
$38$	732.850	+	112.012i	0.0823296	+	0.0125836i
$39$			14.1375i			0.00148837i
$40$	7808.61	+	3820.36i	0.771656	+	0.377532i
$41$			7658.37i			0.711503i	0.934581	+	0.355751i	$0.115775\pi$
$41$			7658.37i			0.711503i	−0.934581	+	0.355751i	$0.884225\pi$
$42$	2499.93	−	16356.1i	0.218678	−	1.43072i
$43$	−3947.03	+	3947.03i	−0.325536	+	0.325536i	−0.850886	−	0.525350i	$-0.823934\pi$
$43$	−3947.03	+	3947.03i	−0.325536	+	0.325536i	0.525350	+	0.850886i	$0.323934\pi$
$44$	10695.6	+	20441.5i	0.832863	+	1.59177i
$45$	−6179.16	−	6179.16i	−0.454881	−	0.454881i
$46$	−8811.87	−	11991.5i	−0.614007	−	0.835566i
$47$	525.728			0.0347150			0.0173575	−	0.999849i	$-0.494475\pi$
$47$	525.728			0.0347150			0.0173575	+	0.999849i	$0.494475\pi$
$48$	−3752.59	−	20773.3i	−0.235087	−	1.30137i
$49$	−3324.71			−0.197817
$50$	2742.76	+	3732.46i	0.155154	+	0.211140i
$51$	22733.7	+	22733.7i	1.22390	+	1.22390i
$52$	19.4446	−	10.1740i	0.000997217	−	0.000521773i
$53$	−15545.1	+	15545.1i	−0.760160	+	0.760160i	−0.976351	−	0.216191i	$-0.930637\pi$
$53$	−15545.1	+	15545.1i	−0.760160	+	0.760160i	0.216191	+	0.976351i	$0.430637\pi$
$54$	1075.33	−	7035.46i	0.0501830	−	0.328328i
$55$		−	34622.4i		−	1.54330i
$56$	−24295.1	+	8332.19i	−1.03526	+	0.355050i
$57$			2701.67i			0.110140i
$58$	31510.1	+	4816.13i	1.22993	+	0.187987i
$59$	7088.71	−	7088.71i	0.265117	−	0.265117i	−0.562012	−	0.827129i	$-0.689973\pi$
$59$	7088.71	−	7088.71i	0.265117	−	0.265117i	0.827129	+	0.562012i	$0.189973\pi$
$60$	−9462.93	+	30233.0i	−0.339350	+	1.08418i
$61$	−19344.7	−	19344.7i	−0.665638	−	0.665638i	0.291066	−	0.956703i	$-0.405990\pi$
$61$	−19344.7	−	19344.7i	−0.665638	−	0.665638i	−0.956703	+	0.291066i	$0.905990\pi$
$62$	−17699.2	+	13006.1i	−0.584756	+	0.429702i
$63$	25818.8			0.819569
$64$	−25870.9	+	20110.7i	−0.789517	+	0.613729i
$65$	−32.9338			−0.000966848
$66$	−67749.0	+	49784.7i	−1.91445	+	1.40681i
$67$	−21154.5	−	21154.5i	−0.575727	−	0.575727i	0.357996	−	0.933723i	$-0.383460\pi$
$67$	−21154.5	−	21154.5i	−0.575727	−	0.575727i	−0.933723	+	0.357996i	$0.883460\pi$
$68$	14907.6	−	47628.0i	0.390962	−	1.24908i
$69$	38346.2	−	38346.2i	0.969616	−	0.969616i
$70$	38102.1	+	5823.68i	0.929403	+	0.142054i
$71$			24047.5i			0.566140i	0.959099	+	0.283070i	$0.0913529\pi$
$71$			24047.5i			0.566140i	−0.959099	+	0.283070i	$0.908647\pi$
$72$	31158.3	−	10686.0i	0.708342	−	0.242932i
$73$		−	11057.8i		−	0.242863i	−0.992600	−	0.121431i	$-0.961252\pi$
$73$		−	11057.8i		−	0.242863i	0.992600	−	0.121431i	$-0.0387484\pi$
$74$	9435.39	−	61732.2i	0.200300	−	1.31049i
$75$	−11935.6	+	11935.6i	−0.245013	+	0.245013i
$76$	3715.86	−	1944.25i	0.0737947	−	0.0386115i
$77$	72332.5	+	72332.5i	1.39030	+	1.39030i
$78$	47.3566	+	64.4448i	0.000881341	+	0.00119936i
$79$	−63378.0			−1.14254			−0.571269	−	0.820763i	$-0.693549\pi$
$79$	−63378.0			−1.14254			−0.571269	+	0.820763i	$0.693549\pi$
$80$	48392.2	−	8741.80i	0.845377	−	0.152713i
$81$	70154.8			1.18808
$82$	25653.4	+	34910.2i	0.421319	+	0.573347i
$83$	−49588.7	−	49588.7i	−0.790110	−	0.790110i	0.191402	−	0.981512i	$-0.438697\pi$
$83$	−49588.7	−	49588.7i	−0.790110	−	0.790110i	−0.981512	+	0.191402i	$0.938697\pi$
$84$	−43392.6	−	82932.2i	−0.670992	−	1.28240i
$85$	−52959.1	+	52959.1i	−0.795048	+	0.795048i
$86$	−4770.83	+	31213.7i	−0.0695581	+	0.455092i
$87$			116163.i			1.64539i
$88$	117229.	+	57354.1i	1.61372	+	0.789510i
$89$		−	67262.1i		−	0.900110i	−0.893001	−	0.450055i	$-0.851404\pi$
$89$		−	67262.1i		−	0.900110i	0.893001	−	0.450055i	$-0.148596\pi$
$90$	−48865.8	−	7468.84i	−0.635915	−	0.0971957i
$91$	68.8048	−	68.8048i	0.000870994	−	0.000870994i
$92$	−80336.7	−	25145.4i	−0.989566	−	0.309734i
$93$	−56598.0	−	56598.0i	−0.678568	−	0.678568i
$94$	2396.50	−	1761.04i	0.0279742	−	0.0205566i
$95$	−6293.65			−0.0715474
$96$	−86690.8	−	82123.6i	−0.960052	−	0.909474i
$97$	−9709.53			−0.104778			−0.0523889	−	0.998627i	$-0.516684\pi$
$97$	−9709.53			−0.104778			−0.0523889	+	0.998627i	$0.516684\pi$
$98$	−15155.5	+	11136.9i	−0.159406	+	0.117138i
$99$	−92766.2	−	92766.2i	−0.951266	−	0.951266i
$100$	25005.4	+	7826.70i	0.250054	+	0.0782670i
$101$	−67901.1	+	67901.1i	−0.662329	+	0.662329i	−0.955928	−	0.293600i	$-0.905147\pi$
$101$	−67901.1	+	67901.1i	−0.662329	+	0.662329i	0.293600	+	0.955928i	$0.405147\pi$
$102$	179782.	+	27478.6i	1.71098	+	0.261514i
$103$			48496.8i			0.450423i	0.974310	+	0.225211i	$0.0723073\pi$
$103$			48496.8i			0.450423i	−0.974310	+	0.225211i	$0.927693\pi$
$104$	54.5568	−	111.511i	0.000494613	−	0.00101096i
$105$			140465.i			1.24335i
$106$	−18789.6	+	122934.i	−0.162425	+	1.06269i
$107$	77963.3	−	77963.3i	0.658310	−	0.658310i	−0.296670	−	0.954980i	$-0.595876\pi$
$107$	77963.3	−	77963.3i	0.658310	−	0.658310i	0.954980	+	0.296670i	$0.0958760\pi$
$108$	−18665.0	−	35672.7i	−0.153982	−	0.294291i
$109$	3671.58	+	3671.58i	0.0295997	+	0.0295997i	0.721752	−	0.692152i	$-0.243337\pi$
$109$	3671.58	+	3671.58i	0.0295997	+	0.0295997i	−0.692152	+	0.721752i	$0.743337\pi$
$110$	−115975.	−	157824.i	−0.913869	−	1.24363i
$111$	227578.			1.75316
$112$	−82837.0	+	119364.i	−0.623993	+	0.899139i
$113$	166660.			1.22782			0.613910	−	0.789376i	$-0.289596\pi$
$113$	166660.			1.22782			0.613910	+	0.789376i	$0.289596\pi$
$114$	9049.86	+	12315.4i	0.0652198	+	0.0887538i
$115$	89329.0	+	89329.0i	0.629865	+	0.629865i
$116$	159769.	−	83596.1i	1.10242	−	0.576821i
$117$	−88.2419	+	88.2419i	−0.000595950	+	0.000595950i
$118$	8568.23	−	56058.7i	0.0566482	−	0.370628i
$119$		−	221283.i		−	1.43245i
$120$	58136.1	+	169514.i	0.368547	+	1.07461i
$121$		−	358726.i		−	2.22740i
$122$	−152981.	−	23382.2i	−0.930547	−	0.142228i
$123$	−111635.	+	111635.i	−0.665330	+	0.665330i
$124$	−37113.9	+	118575.i	−0.216762	+	0.692530i
$125$	−133921.	−	133921.i	−0.766608	−	0.766608i
$126$	117694.	−	86486.0i	0.660429	−	0.485310i
$127$	−28044.5			−0.154290			−0.0771452	−	0.997020i	$-0.524581\pi$
$127$	−28044.5			−0.154290			−0.0771452	+	0.997020i	$0.524581\pi$
$128$	−50565.6	+	178334.i	−0.272791	+	0.962073i
$129$	−115070.			−0.608821
$130$	−150.127	+	110.319i	−0.000779111	+	0.000572522i
$131$	128867.	+	128867.i	0.656092	+	0.656092i	0.954453	−	0.298361i	$-0.0964400\pi$
$131$	128867.	+	128867.i	0.656092	+	0.656092i	−0.298361	+	0.954453i	$0.596440\pi$
$132$	−142065.	+	453881.i	−0.709661	+	2.26729i
$133$	13148.6	−	13148.6i	0.0644541	−	0.0644541i
$134$	−167294.	−	25569.8i	−0.804854	−	0.123017i
$135$			60419.9i			0.285329i
$136$	−91585.5	−	267046.i	−0.424599	−	1.23805i
$137$			305421.i			1.39027i	0.718881	+	0.695133i	$0.244655\pi$
$137$			305421.i			1.39027i	−0.718881	+	0.695133i	$0.755345\pi$
$138$	46349.6	−	303248.i	0.207180	−	1.35550i
$139$	49520.2	−	49520.2i	0.217393	−	0.217393i	−0.590006	−	0.807399i	$-0.700875\pi$
$139$	49520.2	−	49520.2i	0.217393	−	0.217393i	0.807399	+	0.590006i	$0.200875\pi$
$140$	193194.	−	101085.i	0.833054	−	0.435878i
$141$	7663.46	+	7663.46i	0.0324621	+	0.0324621i
$142$	80552.5	+	109619.i	0.335242	+	0.456210i
$143$	−494.427			−0.00202191
$144$	106238.	−	153083.i	0.426947	−	0.615207i
$145$	−270606.			−1.06885
$146$	−37040.5	−	50406.2i	−0.143812	−	0.195705i
$147$	−48463.8	−	48463.8i	−0.184980	−	0.184980i
$148$	−163775.	−	313008.i	−0.614602	−	1.17463i
$149$	−91591.5	+	91591.5i	−0.337979	+	0.337979i	−0.855606	−	0.517627i	$-0.826815\pi$
$149$	−91591.5	+	91591.5i	−0.337979	+	0.337979i	0.517627	+	0.855606i	$0.326815\pi$
$150$	−14426.7	+	94388.4i	−0.0523526	+	0.342524i
$151$			151711.i			0.541469i	0.962654	+	0.270735i	$0.0872666\pi$
$151$			151711.i			0.541469i	−0.962654	+	0.270735i	$0.912733\pi$
$152$	10425.8	−	21309.8i	0.0366017	−	0.0748119i
$153$			283795.i			0.980111i
$154$	572017.	+	87429.4i	1.94360	+	0.297068i
$155$	131847.	−	131847.i	0.440800	−	0.440800i
$156$	431.744	+	135.136i	0.00142041	+	0.000444590i
$157$	240579.	+	240579.i	0.778948	+	0.778948i	0.979652	−	0.200704i	$-0.0643230\pi$
$157$	240579.	+	240579.i	0.778948	+	0.778948i	−0.200704	+	0.979652i	$0.564323\pi$
$158$	−288905.	+	212299.i	−0.920687	+	0.676558i
$159$	−453198.			−1.42166
$160$	191310.	−	201949.i	0.590797	−	0.623652i
$161$	−373250.			−1.13484
$162$	319796.	−	234999.i	0.957383	−	0.703524i
$163$	35449.6	+	35449.6i	0.104506	+	0.104506i	0.757427	−	0.652920i	$-0.226456\pi$
$163$	35449.6	+	35449.6i	0.104506	+	0.104506i	−0.652920	+	0.757427i	$0.726456\pi$
$164$	233879.	+	73204.1i	0.679019	+	0.212533i
$165$	504685.	−	504685.i	1.44315	−	1.44315i
$166$	−392155.	−	59938.6i	−1.10456	−	0.168825i
$167$		−	142411.i		−	0.395141i	−0.980289	−	0.197571i	$-0.936695\pi$
$167$		−	142411.i		−	0.395141i	0.980289	−	0.197571i	$-0.0633052\pi$
$168$	−475602.	−	232688.i	−1.30008	−	0.636065i
$169$		−	371293.i		−	0.999999i
$170$	−64012.5	+	418809.i	−0.169880	+	1.11146i
$171$	−16863.0	+	16863.0i	−0.0441007	+	0.0441007i
$172$	82809.8	+	158267.i	0.213433	+	0.407914i
$173$	242417.	+	242417.i	0.615811	+	0.615811i	0.944454	−	0.328643i	$-0.106591\pi$
$173$	242417.	+	242417.i	0.615811	+	0.615811i	−0.328643	+	0.944454i	$0.606591\pi$
$174$	389114.	+	529521.i	0.974324	+	1.32590i
$175$	116177.			0.286764
$176$	726500.	−	131239.i	1.76788	−	0.319359i
$177$	206662.			0.495824
$178$	−225309.	−	306610.i	−0.533003	−	0.725332i
$179$	146175.	+	146175.i	0.340989	+	0.340989i	0.856739	−	0.515750i	$-0.172487\pi$
$179$	146175.	+	146175.i	0.340989	+	0.340989i	−0.515750	+	0.856739i	$0.672487\pi$
$180$	−247770.	+	129641.i	−0.569991	+	0.298236i
$181$	298363.	−	298363.i	0.676936	−	0.676936i	−0.282369	−	0.959306i	$-0.591120\pi$
$181$	298363.	−	298363.i	0.676936	−	0.676936i	0.959306	+	0.282369i	$0.0911204\pi$
$182$	83.1653	−	544.119i	0.000186108	−	0.00121763i
$183$		−	563970.i		−	1.24488i
$184$	−450440.	+	154482.i	−0.980827	+	0.336383i
$185$			530151.i			1.13886i
$186$	−447586.	−	68410.8i	−0.948624	−	0.144991i
$187$	−795062.	+	795062.i	−1.66264	+	1.66264i
$188$	5025.28	−	16055.2i	0.0103697	−	0.0331300i
$189$	−126228.	−	126228.i	−0.257041	−	0.257041i
$190$	−28689.2	+	21082.0i	−0.0576547	+	0.0423670i
$191$	−733661.			−1.45516			−0.727582	−	0.686021i	$-0.759356\pi$
$191$	−733661.			−1.45516			−0.727582	+	0.686021i	$0.759356\pi$
$192$	−670266.	−	83965.5i	−1.31218	−	0.164379i
$193$	610124.			1.17903			0.589515	−	0.807757i	$-0.299319\pi$
$193$	610124.			1.17903			0.589515	+	0.807757i	$0.299319\pi$
$194$	−44260.3	+	32524.3i	−0.0844326	+	0.0620445i
$195$	−480.070	−	480.070i	−0.000904104	−	0.000904104i
$196$	−31779.9	+	101533.i	−0.0590898	+	0.188785i
$197$	−60939.9	+	60939.9i	−0.111876	+	0.111876i	−0.760829	−	0.648953i	$-0.775207\pi$
$197$	−60939.9	+	60939.9i	−0.111876	+	0.111876i	0.648953	+	0.760829i	$0.275207\pi$
$198$	−733610.	−	112128.i	−1.32985	−	0.203259i
$199$		−	284263.i		−	0.508848i	−0.967093	−	0.254424i	$-0.918114\pi$
$199$		−	284263.i		−	0.508848i	0.967093	−	0.254424i	$-0.0818859\pi$
$200$	140203.	−	48083.8i	0.247846	−	0.0850009i
$201$		−	616733.i		−	1.07673i
$202$	−82073.1	+	536973.i	−0.141521	+	0.925921i
$203$	565346.	−	565346.i	0.962885	−	0.962885i
$204$	911571.	−	476961.i	1.53361	−	0.802430i
$205$	−260058.	−	260058.i	−0.432200	−	0.432200i
$206$	162451.	+	221070.i	0.266719	+	0.362962i
$207$	478691.			0.776479
$208$	−124.838	−	691.067i	−0.000200073	−	0.00110755i
$209$	−94485.0			−0.149623
$210$	470518.	+	640299.i	0.736254	+	1.00192i
$211$	393620.	+	393620.i	0.608655	+	0.608655i	0.942595	−	0.333939i	$-0.108378\pi$
$211$	393620.	+	393620.i	0.608655	+	0.608655i	−0.333939	+	0.942595i	$0.608378\pi$
$212$	326142.	+	623325.i	0.498387	+	0.952522i
$213$	−350537.	+	350537.i	−0.529400	+	0.529400i
$214$	94235.4	−	616546.i	0.140663	−	0.920304i
$215$		−	268061.i		−	0.395492i
$216$	−204577.	−	100089.i	−0.298348	−	0.145967i
$217$			550907.i			0.794198i
$218$	29035.4	+	4437.89i	0.0413797	+	0.00632463i
$219$	161187.	−	161187.i	0.227102	−	0.227102i
$220$	−1.05733e6	−	330945.i	−1.47284	−	0.460998i
$221$	756.286	+	756.286i	0.00104161	+	0.00104161i
$222$	1.03740e6	−	762322.i	1.41274	−	1.03814i
$223$	1.30899e6			1.76269			0.881344	−	0.472475i	$-0.156639\pi$
$223$	1.30899e6			1.76269			0.881344	+	0.472475i	$0.156639\pi$
$224$	22227.4	+	821592.i	0.0295985	+	1.09405i
$225$	−148996.			−0.196209
$226$	759709.	−	558264.i	0.989409	−	0.727058i
$227$	−1.02649e6	−	1.02649e6i	−1.32218	−	1.32218i	−0.912006	−	0.410176i	$-0.865467\pi$
$227$	−1.02649e6	−	1.02649e6i	−1.32218	−	1.32218i	−0.410176	−	0.912006i	$-0.634533\pi$
$228$	82506.4	+	25824.5i	0.105112	+	0.0328999i
$229$	−935677.	+	935677.i	−1.17906	+	1.17906i	−0.199081	+	0.979983i	$0.563796\pi$
$229$	−935677.	+	935677.i	−1.17906	+	1.17906i	−0.979983	+	0.199081i	$0.936204\pi$
$230$	706428.	+	107973.i	0.880538	+	0.134585i
$231$			2.10876e6i			2.60014i
$232$	448275.	−	916251.i	0.546796	−	1.11762i
$233$			302991.i			0.365628i	0.983148	+	0.182814i	$0.0585206\pi$
$233$			302991.i			0.365628i	−0.983148	+	0.182814i	$0.941479\pi$
$234$	−106.659	+	697.831i	−0.000127338	+	0.000833126i
$235$	−17852.3	+	17852.3i	−0.0210875	+	0.0210875i
$236$	−148723.	−	284241.i	−0.173820	−	0.332206i
$237$	−923851.	−	923851.i	−1.06839	−	1.06839i
$238$	−741237.	−	1.00870e6i	−0.848232	−	1.15431i
$239$	−82683.0			−0.0936313			−0.0468157	−	0.998904i	$-0.514907\pi$
$239$	−82683.0			−0.0936313			−0.0468157	+	0.998904i	$0.514907\pi$
$240$	832833.	+	577977.i	0.933318	+	0.647713i
$241$	−817254.			−0.906388			−0.453194	−	0.891412i	$-0.649716\pi$
$241$	−817254.			−0.906388			−0.453194	+	0.891412i	$0.649716\pi$
$242$	−1.20163e6	−	1.63523e6i	−1.31896	−	1.79490i
$243$	806452.	+	806452.i	0.876118	+	0.876118i
$244$	−775679.	+	405858.i	−0.834080	+	0.436415i
$245$	112898.	−	112898.i	0.120163	−	0.120163i
$246$	−134935.	+	882826.i	−0.142163	+	0.930117i
$247$			89.8768i			9.37358e-5i
$248$	228011.	+	664837.i	0.235411	+	0.686414i
$249$		−	1.44569e6i		−	1.47767i
$250$	−1.05907e6	−	161872.i	−1.07170	−	0.163803i
$251$	120643.	−	120643.i	0.120870	−	0.120870i	−0.644085	−	0.764954i	$-0.722762\pi$
$251$	120643.	−	120643.i	0.120870	−	0.120870i	0.764954	+	0.644085i	$0.222762\pi$
$252$	246795.	−	788482.i	0.244813	−	0.782150i
$253$	1.34107e6	+	1.34107e6i	1.31720	+	1.31720i
$254$	−127839.	+	93941.4i	−0.124331	+	0.0913635i
$255$	−1.54395e6			−1.48691
$256$	366868.	+	982303.i	0.349873	+	0.936797i
$257$	929323.			0.877675			0.438838	−	0.898566i	$-0.355390\pi$
$257$	929323.			0.877675			0.438838	+	0.898566i	$0.355390\pi$
$258$	−524541.	+	385454.i	−0.490603	+	0.360515i
$259$	−1.10758e6	−	1.10758e6i	−1.02595	−	1.02595i
$260$	−314.804	+	1005.76i	−0.000288807	+	0.000922705i
$261$	−725054.	+	725054.i	−0.658824	+	0.658824i
$262$	1.01910e6	+	155764.i	0.917202	+	0.140189i
$263$			725830.i			0.647061i	0.946218	+	0.323531i	$0.104870\pi$
$263$			725830.i			0.647061i	−0.946218	+	0.323531i	$0.895130\pi$
$264$	872782.	+	2.54486e6i	0.770719	+	2.24727i
$265$		−	1.05574e6i		−	0.923514i
$266$	15892.9	−	103981.i	0.0137721	−	0.0901055i
$267$	980469.	−	980469.i	0.841697	−	0.841697i
$268$	−848249.	+	443829.i	−0.721417	+	0.377467i
$269$	−467451.	−	467451.i	−0.393872	−	0.393872i	0.482193	−	0.876065i	$-0.339840\pi$
$269$	−467451.	−	467451.i	−0.393872	−	0.393872i	−0.876065	+	0.482193i	$0.839840\pi$
$270$	202390.	+	275420.i	0.168958	+	0.229925i
$271$	2.31563e6			1.91534			0.957670	−	0.287868i	$-0.0929466\pi$
$271$	2.31563e6			1.91534			0.957670	+	0.287868i	$0.0929466\pi$
$272$	−1.31202e6	−	910525.i	−1.07527	−	0.746225i
$273$	2005.91			0.00162894
$274$	1.02308e6	+	1.39224e6i	0.823250	+	1.12031i
$275$	−417420.	−	417420.i	−0.332844	−	0.332844i
$276$	−804515.	−	1.53760e6i	−0.635714	−	1.21498i
$277$	1.51343e6	−	1.51343e6i	1.18513	−	1.18513i	0.206727	−	0.978399i	$-0.433719\pi$
$277$	1.51343e6	−	1.51343e6i	1.18513	−	1.18513i	0.978399	−	0.206727i	$-0.0662811\pi$
$278$	59855.8	−	391614.i	0.0464509	−	0.303911i
$279$		−	706536.i		−	0.543405i
$280$	542056.	−	1.10793e6i	0.413189	−	0.844537i
$281$			830122.i			0.627157i	0.949562	+	0.313578i	$0.101528\pi$
$281$			830122.i			0.627157i	−0.949562	+	0.313578i	$0.898472\pi$
$282$	60603.9	+	9262.93i	0.0453814	+	0.00693627i
$283$	−600416.	+	600416.i	−0.445642	+	0.445642i	−0.893903	−	0.448261i	$-0.852044\pi$
$283$	−600416.	+	600416.i	−0.445642	+	0.445642i	0.448261	+	0.893903i	$0.352044\pi$
$284$	734387.	+	229863.i	0.540293	+	0.169112i
$285$	−91741.5	−	91741.5i	−0.0669043	−	0.0669043i
$286$	−2253.81	+	1656.19i	−0.00162931	+	0.00119728i
$287$	1.08662e6			0.778703
$288$	−28506.6	−	1.05369e6i	−0.0202518	−	0.748568i
$289$	1.01243e6			0.713052
$290$	−1.23354e6	+	906455.i	−0.861308	+	0.632923i
$291$	−141534.	−	141534.i	−0.0979782	−	0.0979782i
$292$	−337694.	−	105698.i	−0.231774	−	0.0725454i
$293$	−712048.	+	712048.i	−0.484552	+	0.484552i	−0.906582	−	0.422030i	$-0.861318\pi$
$293$	−712048.	+	712048.i	−0.484552	+	0.484552i	0.422030	+	0.906582i	$0.361318\pi$
$294$	−383259.	−	58578.9i	−0.258598	−	0.0395251i
$295$			481427.i			0.322089i
$296$	−1.79505e6	−	878228.i	−1.19082	−	0.582610i
$297$			907069.i			0.596691i
$298$	−110708.	+	724321.i	−0.0722168	+	0.472487i
$299$	1275.67	−	1275.67i	0.000825201	−	0.000825201i
$300$	250412.	+	478589.i	0.160639	+	0.307015i
$301$	560029.	+	560029.i	0.356282	+	0.356282i
$302$	508189.	+	691564.i	0.320633	+	0.436330i
$303$	−1.97957e6			−1.23869
$304$	−23856.5	−	132063.i	−0.0148055	−	0.0819592i
$305$	1.31379e6			0.808679
$306$	950633.	+	1.29366e6i	0.580376	+	0.789799i
$307$	167442.	+	167442.i	0.101395	+	0.101395i	0.755985	−	0.654589i	$-0.227158\pi$
$307$	167442.	+	167442.i	0.101395	+	0.101395i	−0.654589	+	0.755985i	$0.727158\pi$
$308$	2.90037e6	−	1.51756e6i	1.74211	−	0.911525i
$309$	−706930.	+	706930.i	−0.421192	+	0.421192i
$310$	159366.	−	1.04267e6i	0.0941868	−	0.616229i
$311$		−	2.10277e6i		−	1.23279i	−0.787435	−	0.616397i	$-0.788591\pi$
$311$		−	2.10277e6i		−	1.23279i	0.787435	−	0.616397i	$-0.211409\pi$
$312$	2420.75	−	830.215i	0.00140787	−	0.000482841i
$313$			49135.8i			0.0283490i	0.999900	+	0.0141745i	$0.00451203\pi$
$313$			49135.8i			0.0283490i	−0.999900	+	0.0141745i	$0.995488\pi$
$314$	1.90254e6	+	290791.i	1.08895	+	0.166440i
$315$	−876738.	+	876738.i	−0.497844	+	0.497844i
$316$	−605812.	+	1.93550e6i	−0.341287	+	1.09038i
$317$	−1.73077e6	−	1.73077e6i	−0.967369	−	0.967369i	0.0321147	−	0.999484i	$-0.489776\pi$
$317$	−1.73077e6	−	1.73077e6i	−0.967369	−	0.967369i	−0.999484	+	0.0321147i	$0.989776\pi$
$318$	−2.06588e6	+	1.51809e6i	−1.14561	+	0.841840i
$319$	−4.06254e6			−2.23522
$320$	195601.	−	1.56141e6i	0.106781	−	0.852397i
$321$	2.27292e6			1.23118
$322$	−1.70144e6	+	1.25028e6i	−0.914484	+	0.671999i
$323$	144526.	+	144526.i	0.0770798	+	0.0770798i
$324$	670589.	−	2.14246e6i	0.354890	−	1.13383i
$325$	−397.062	+	397.062i	−0.000208521	+	0.000208521i
$326$	280341.	+	42848.4i	0.146097	+	0.0223301i
$327$			107040.i			0.0553576i
$328$	1.31134e6	−	449734.i	0.673022	−	0.230819i
$329$		−	74593.6i		−	0.0379937i
$330$	610020.	−	3.99113e6i	0.308361	−	2.01749i
$331$	−2.07628e6	+	2.07628e6i	−1.04164	+	1.04164i	−0.0425407	+	0.999095i	$0.513545\pi$
$331$	−2.07628e6	+	2.07628e6i	−1.04164	+	1.04164i	−0.999095	+	0.0425407i	$0.986455\pi$
$332$	−1.98839e6	+	1.04039e6i	−0.990050	+	0.518023i
$333$	1.42047e6	+	1.42047e6i	0.701976	+	0.701976i
$334$	−477037.	−	649172.i	−0.233984	−	0.318415i
$335$	1.43670e6			0.699447
$336$	−2.94745e6	+	532441.i	−1.42429	+	0.257290i
$337$	−4.03966e6			−1.93763			−0.968814	−	0.247790i	$-0.920296\pi$
$337$	−4.03966e6			−1.93763			−0.968814	+	0.247790i	$0.920296\pi$
$338$	−1.24373e6	−	1.69251e6i	−0.592152	−	0.805825i
$339$	2.42937e6	+	2.42937e6i	1.14814	+	1.14814i
$340$	1.11110e6	+	2.12354e6i	0.521261	+	0.996238i
$341$	1.97939e6	−	1.97939e6i	0.921818	−	0.921818i
$342$	−20382.6	+	133356.i	−0.00942311	+	0.0616518i
$343$		−	1.91295e6i		−	0.877948i
$344$	907633.	+	444059.i	0.413537	+	0.202323i
$345$			2.60427e6i			1.17798i
$346$	1.91707e6	+	293012.i	0.860890	+	0.131582i
$347$	−1.31394e6	+	1.31394e6i	−0.585803	+	0.585803i	−0.936492	−	0.350689i	$-0.885948\pi$
$347$	−1.31394e6	+	1.31394e6i	−0.585803	+	0.585803i	0.350689	+	0.936492i	$0.385948\pi$
$348$	3.54750e6	+	1.11037e6i	1.57027	+	0.491494i
$349$	1.15878e6	+	1.15878e6i	0.509256	+	0.509256i	0.914298	−	0.405042i	$-0.132743\pi$
$349$	1.15878e6	+	1.15878e6i	0.509256	+	0.509256i	−0.405042	+	0.914298i	$0.632743\pi$
$350$	529585.	−	389161.i	0.231082	−	0.169808i
$351$	862.830			0.000373816
$352$	2.87209e6	−	3.03182e6i	1.23550	−	1.30421i
$353$	−3.63541e6			−1.55280			−0.776402	−	0.630238i	$-0.782957\pi$
$353$	−3.63541e6			−1.55280			−0.776402	+	0.630238i	$0.782957\pi$
$354$	942056.	−	692261.i	0.399548	−	0.293604i
$355$	−816588.	−	816588.i	−0.343900	−	0.343900i
$356$	−2.05412e6	−	642939.i	−0.859014	−	0.268871i
$357$	3.22561e6	−	3.22561e6i	1.33949	−	1.33949i
$358$	1.15597e6	+	176684.i	0.476695	+	0.0728599i
$359$			3.78539e6i			1.55015i	0.631867	+	0.775077i	$0.282289\pi$
$359$			3.78539e6i			1.55015i	−0.631867	+	0.775077i	$0.717711\pi$
$360$	−695185.	+	1.42092e6i	−0.282712	+	0.577848i
$361$		−	2.45892e6i		−	0.993063i
$362$	360635.	−	2.35950e6i	0.144643	−	0.946342i
$363$	5.22909e6	−	5.22909e6i	2.08286	−	2.08286i
$364$	−1443.55	−	2758.92i	−0.000571054	−	0.00109140i
$365$	375492.	+	375492.i	0.147526	+	0.147526i
$366$	−1.88914e6	−	2.57082e6i	−0.737160	−	1.00316i
$367$	4.50582e6			1.74626			0.873130	−	0.487488i	$-0.162087\pi$
$367$	4.50582e6			1.74626			0.873130	+	0.487488i	$0.162087\pi$
$368$	−1.53583e6	+	2.21305e6i	−0.591186	+	0.851866i
$369$	−1.39358e6			−0.532803
$370$	1.77586e6	+	2.41666e6i	0.674379	+	0.917722i
$371$	2.20564e6	+	2.20564e6i	0.831956	+	0.831956i
$372$	−2.26945e6	+	1.18744e6i	−0.850283	+	0.444893i
$373$	−2.41809e6	+	2.41809e6i	−0.899912	+	0.899912i	−0.995428	−	0.0955160i	$-0.969550\pi$
$373$	−2.41809e6	+	2.41809e6i	−0.899912	+	0.899912i	0.0955160	+	0.995428i	$0.469550\pi$
$374$	−961003.	+	6.28748e6i	−0.355260	+	2.32433i
$375$		−	3.90429e6i		−	1.43372i
$376$	−30873.1	−	90020.1i	−0.0112619	−	0.0328375i
$377$			3864.40i			0.00140033i
$378$	−998235.	−	152574.i	−0.359338	−	0.0549226i
$379$	980618.	−	980618.i	0.350673	−	0.350673i	−0.509687	−	0.860360i	$-0.670239\pi$
$379$	980618.	−	980618.i	0.350673	−	0.350673i	0.860360	+	0.509687i	$0.170239\pi$
$380$	−60159.2	+	192202.i	−0.0213719	+	0.0682808i
$381$	−408801.	−	408801.i	−0.144278	−	0.144278i
$382$	−3.34435e6	+	2.45756e6i	−1.17261	+	0.861680i
$383$	−4.07800e6			−1.42053			−0.710265	−	0.703935i	$-0.751425\pi$
$383$	−4.07800e6			−1.42053			−0.710265	+	0.703935i	$0.751425\pi$
$384$	−3.33663e6	+	1.86245e6i	−1.15473	+	0.644551i
$385$	−4.91244e6			−1.68906
$386$	2.78121e6	−	2.04375e6i	0.950092	−	0.698166i
$387$	−718235.	−	718235.i	−0.243775	−	0.243775i
$388$	−92810.6	+	296520.i	−0.0312981	+	0.0999940i
$389$	1.40683e6	−	1.40683e6i	0.471376	−	0.471376i	−0.430984	−	0.902360i	$-0.641833\pi$
$389$	1.40683e6	−	1.40683e6i	0.471376	−	0.471376i	0.902360	+	0.430984i	$0.141833\pi$
$390$	−3796.47	−	580.268i	−0.00126392	−	0.000193182i
$391$		−	4.10267e6i		−	1.35714i
$392$	195242.	+	569287.i	0.0641738	+	0.187118i
$393$			3.75696e6i			1.22703i
$394$	−73659.0	+	481923.i	−0.0239048	+	0.156400i
$395$	2.15215e6	−	2.15215e6i	0.694031	−	0.694031i
$396$	−3.71971e6	+	1.94626e6i	−1.19199	+	0.623683i
$397$	−1.87867e6	−	1.87867e6i	−0.598237	−	0.598237i	0.341606	−	0.939843i	$-0.389029\pi$
$397$	−1.87867e6	−	1.87867e6i	−0.598237	−	0.598237i	−0.939843	+	0.341606i	$0.889029\pi$
$398$	−952204.	−	1.29580e6i	−0.301316	−	0.410043i
$399$	383330.			0.120543
$400$	478040.	−	688828.i	0.149387	−	0.215259i
$401$	4.69189e6			1.45709			0.728547	−	0.684996i	$-0.240196\pi$
$401$	4.69189e6			1.45709			0.728547	+	0.684996i	$0.240196\pi$
$402$	−2.06588e6	−	2.81134e6i	−0.637589	−	0.867657i
$403$	−1882.85	−	1882.85i	−0.000577502	−	0.000577502i
$404$	1.42459e6	+	2.72268e6i	0.434245	+	0.829933i
$405$	−2.38227e6	+	2.38227e6i	−0.721694	+	0.721694i
$406$	683342.	−	4.47085e6i	0.205742	−	1.34609i
$407$			7.95902e6i			2.38163i
$408$	2.55765e6	−	5.22771e6i	0.760662	−	1.55475i
$409$		−	4.50870e6i		−	1.33273i	−0.745624	−	0.666366i	$-0.767849\pi$
$409$		−	4.50870e6i		−	1.33273i	0.745624	−	0.666366i	$-0.232151\pi$
$410$	−2.05658e6	−	314335.i	−0.604206	−	0.0923493i
$411$	−4.45208e6	+	4.45208e6i	−1.30004	+	1.30004i
$412$	1.48104e6	+	463567.i	0.429858	+	0.134546i
$413$	−1.00579e6	−	1.00579e6i	−0.290157	−	0.290157i
$414$	2.18208e6	−	1.60348e6i	0.625707	−	0.459794i
$415$	3.36780e6			0.959899
$416$	−2883.95	−	2732.02i	−0.000817061	−	0.000774016i
$417$	1.44370e6			0.406571
$418$	−430704.	+	316499.i	−0.120570	+	0.0885995i
$419$	3.28478e6	+	3.28478e6i	0.914054	+	0.914054i	0.996588	−	0.0825343i	$-0.0263014\pi$
$419$	3.28478e6	+	3.28478e6i	0.914054	+	0.914054i	−0.0825343	+	0.996588i	$0.526301\pi$
$420$	4.28965e6	+	1.34266e6i	1.18658	+	0.371401i
$421$	170138.	−	170138.i	0.0467838	−	0.0467838i	−0.683328	−	0.730112i	$-0.739468\pi$
$421$	170138.	−	170138.i	0.0467838	−	0.0467838i	0.730112	+	0.683328i	$0.239468\pi$
$422$	3.11281e6	+	475774.i	0.850887	+	0.130053i
$423$			95666.1i			0.0259960i
$424$	3.57466e6	+	1.74890e6i	0.965652	+	0.472445i
$425$			1.27699e6i			0.342937i
$426$	−423699.	+	2.77210e6i	−0.113118	+	0.740091i
$427$	−2.74475e6	+	2.74475e6i	−0.728506	+	0.728506i
$428$	−1.63569e6	−	3.12615e6i	−0.431611	−	0.824898i
$429$	−7207.18	−	7207.18i	−0.00189070	−	0.00189070i
$430$	−897930.	−	1.22194e6i	−0.234192	−	0.318697i
$431$	−1.88220e6			−0.488058			−0.244029	−	0.969768i	$-0.578469\pi$
$431$	−1.88220e6			−0.488058			−0.244029	+	0.969768i	$0.578469\pi$
$432$	−1.26782e6	+	229026.i	−0.326851	+	0.0590440i
$433$	5.65106e6			1.44847			0.724237	−	0.689552i	$-0.242192\pi$
$433$	5.65106e6			1.44847			0.724237	+	0.689552i	$0.242192\pi$
$434$	1.84538e6	+	2.51127e6i	0.470287	+	0.639985i
$435$	−3.94458e6	−	3.94458e6i	−0.999488	−	0.999488i
$436$	147222.	−	77030.8i	0.0370900	−	0.0194066i
$437$	243780.	−	243780.i	0.0610654	−	0.0610654i
$438$	194830.	−	1.27470e6i	0.0485255	−	0.317484i
$439$		−	5.65397e6i		−	1.40021i	−0.714042	−	0.700103i	$-0.753137\pi$
$439$		−	5.65397e6i		−	1.40021i	0.714042	−	0.700103i	$-0.246863\pi$
$440$	−5.92836e6	+	2.03318e6i	−1.45983	+	0.500661i
$441$		−	604993.i		−	0.148134i
$442$	5980.83	+	914.134i	0.00145615	+	0.000222564i
$443$	−1.09538e6	+	1.09538e6i	−0.265189	+	0.265189i	−0.827158	−	0.561969i	$-0.810044\pi$
$443$	−1.09538e6	+	1.09538e6i	−0.265189	+	0.265189i	0.561969	+	0.827158i	$0.310044\pi$
$444$	2.17535e6	−	6.95000e6i	0.523687	−	1.67312i
$445$	2.28404e6	+	2.28404e6i	0.546769	+	0.546769i
$446$	5.96697e6	−	4.38477e6i	1.42042	−	1.04378i
$447$	−2.67023e6			−0.632091
$448$	2.85343e6	+	3.67072e6i	0.671695	+	0.864085i
$449$	−670790.			−0.157026			−0.0785129	−	0.996913i	$-0.525017\pi$
$449$	−670790.			−0.157026			−0.0785129	+	0.996913i	$0.525017\pi$
$450$	−679191.	+	499097.i	−0.158111	+	0.116186i
$451$	−3.90418e6	−	3.90418e6i	−0.903833	−	0.903833i
$452$	1.59305e6	−	5.08963e6i	0.366762	−	1.17176i
$453$	−2.21146e6	+	2.21146e6i	−0.506331	+	0.506331i
$454$	−8.11767e6	−	1.24074e6i	−1.84838	−	0.282514i
$455$			4672.85i			0.00105816i
$456$	462605.	−	158654.i	0.104183	−	0.0357306i
$457$			2.97763e6i			0.666929i	0.942763	+	0.333464i	$0.108218\pi$
$457$			2.97763e6i			0.666929i	−0.942763	+	0.333464i	$0.891782\pi$
$458$	−1.13097e6	+	7.39949e6i	−0.251934	+	1.64831i
$459$	1.38747e6	−	1.38747e6i	0.307392	−	0.307392i
$460$	3.58189e6	−	1.87415e6i	0.789255	−	0.412961i
$461$	137930.	+	137930.i	0.0302278	+	0.0302278i	0.722059	−	0.691831i	$-0.243196\pi$
$461$	137930.	+	137930.i	0.0302278	+	0.0302278i	−0.691831	+	0.722059i	$0.743196\pi$
$462$	7.06376e6	+	9.61265e6i	1.53968	+	2.09526i
$463$	1.31655e6			0.285420			0.142710	−	0.989765i	$-0.454418\pi$
$463$	1.31655e6			0.285420			0.142710	+	0.989765i	$0.454418\pi$
$464$	−1.02575e6	−	5.67827e6i	−0.221181	−	1.22439i
$465$	3.84383e6			0.824388
$466$	1.01493e6	+	1.38116e6i	0.216508	+	0.294632i
$467$	1.40289e6	+	1.40289e6i	0.297666	+	0.297666i	0.840099	−	0.542433i	$-0.182497\pi$
$467$	1.40289e6	+	1.40289e6i	0.297666	+	0.297666i	−0.542433	+	0.840099i	$0.682497\pi$
$468$	1851.34	+	3538.30i	0.000390726	+	0.000746758i
$469$	−3.00154e6	+	3.00154e6i	−0.630104	+	0.630104i
$470$	−21578.4	+	141179.i	−0.00450582	+	0.0294799i
$471$			7.01376e6i			1.45680i
$472$	−1.63008e6	−	797514.i	−0.336785	−	0.164772i
$473$		−	4.02433e6i		−	0.827067i
$474$	−7.30597e6	−	1.11667e6i	−1.49359	−	0.228286i
$475$	−75878.6	+	75878.6i	−0.0154307	+	0.0154307i
$476$	−6.75776e6	−	2.11518e6i	−1.36705	−	0.427888i
$477$	−2.82873e6	−	2.82873e6i	−0.569240	−	0.569240i
$478$	−376905.	+	276965.i	−0.0754505	+	0.0554441i
$479$	−809409.			−0.161187			−0.0805933	−	0.996747i	$-0.525682\pi$
$479$	−809409.			−0.161187			−0.0805933	+	0.996747i	$0.525682\pi$
$480$	5.73248e6	−	155087.i	1.13564	−	0.0307236i
$481$	7570.85			0.00149204
$482$	−3.72540e6	+	2.73757e6i	−0.730391	+	0.536721i
$483$	−5.44080e6	−	5.44080e6i	−1.06119	−	1.06119i
$484$	−1.09551e7	−	3.42896e6i	−2.12571	−	0.665347i
$485$	329710.	−	329710.i	0.0636469	−	0.0636469i
$486$	6.37755e6	+	974770.i	1.22479	+	0.187202i
$487$			5.82444e6i			1.11284i	0.830902	+	0.556419i	$0.187825\pi$
$487$			5.82444e6i			1.11284i	−0.830902	+	0.556419i	$0.812175\pi$
$488$	−2.17637e6	+	4.44839e6i	−0.413698	+	0.845577i
$489$			1.03349e6i			0.195449i
$490$	136462.	−	892817.i	0.0256756	−	0.167986i
$491$	1.45884e6	−	1.45884e6i	0.273089	−	0.273089i	−0.557253	−	0.830343i	$-0.688145\pi$
$491$	1.45884e6	−	1.45884e6i	0.273089	−	0.273089i	0.830343	+	0.557253i	$0.188145\pi$
$492$	2.34213e6	+	4.47630e6i	0.436213	+	0.833694i
$493$	6.21415e6	+	6.21415e6i	1.15150	+	1.15150i
$494$	301.063	+	409.698i	5.55059e−5	+	7.55347e-5i
$495$	6.30018e6			1.15569
$496$	3.26640e6	+	2.26684e6i	0.596163	+	0.413731i
$497$	3.41201e6			0.619611
$498$	−4.84267e6	−	6.59010e6i	−0.875007	−	1.19074i
$499$	−761593.	−	761593.i	−0.136921	−	0.136921i	0.635324	−	0.772246i	$-0.280867\pi$
$499$	−761593.	−	761593.i	−0.136921	−	0.136921i	−0.772246	+	0.635324i	$0.780867\pi$
$500$	−5.36992e6	+	2.80970e6i	−0.960601	+	0.502615i
$501$	2.07590e6	−	2.07590e6i	0.369498	−	0.369498i
$502$	145823.	−	954063.i	0.0258265	−	0.168973i
$503$		−	7.27846e6i		−	1.28268i	−0.767255	−	0.641342i	$-0.778378\pi$
$503$		−	7.27846e6i		−	1.28268i	0.767255	−	0.641342i	$-0.221622\pi$
$504$	−1.51620e6	−	4.42094e6i	−0.265876	−	0.775244i
$505$		−	4.61148e6i		−	0.804659i
$506$	1.06054e7	+	1.62098e6i	1.84142	+	0.281449i
$507$	5.41227e6	−	5.41227e6i	0.935104	−	0.935104i
$508$	−268070.	+	856452.i	−0.0460880	+	0.147246i
$509$	−5.49916e6	−	5.49916e6i	−0.940811	−	0.940811i	0.0575329	−	0.998344i	$-0.481677\pi$
$509$	−5.49916e6	−	5.49916e6i	−0.940811	−	0.940811i	−0.998344	+	0.0575329i	$0.981677\pi$
$510$	−7.03802e6	+	5.17182e6i	−1.19819	+	0.880476i
$511$	−1.56895e6			−0.265801
$512$	4.96279e6	+	3.24886e6i	0.836664	+	0.547717i
$513$	164887.			0.0276626
$514$	4.23626e6	−	3.11297e6i	0.707253	−	0.519718i
$515$	−1.64682e6	−	1.64682e6i	−0.273608	−	0.273608i
$516$	−1.09992e6	+	3.51414e6i	−0.181861	+	0.581024i
$517$	−268012.	+	268012.i	−0.0440990	+	0.0440990i
$518$	−8.75895e6	−	1.33875e6i	−1.43426	−	0.219218i
$519$			7.06734e6i			1.15169i
$520$	1934.02	+	5639.22i	0.000313655	+	0.000914557i
$521$		−	9.09886e6i		−	1.46856i	−0.678845	−	0.734282i	$-0.737519\pi$
$521$		−	9.09886e6i		−	1.46856i	0.678845	−	0.734282i	$-0.262481\pi$
$522$	−876383.	+	5.73385e6i	−0.140773	+	0.921021i
$523$	1.65237e6	−	1.65237e6i	0.264152	−	0.264152i	−0.562587	−	0.826738i	$-0.690194\pi$
$523$	1.65237e6	−	1.65237e6i	0.264152	−	0.264152i	0.826738	+	0.562587i	$0.190194\pi$
$524$	5.16729e6	−	2.70368e6i	0.822118	−	0.430156i
$525$	1.69349e6	+	1.69349e6i	0.268155	+	0.268155i
$526$	2.43133e6	+	3.30865e6i	0.383159	+	0.521419i
$527$	−6.05543e6			−0.949771
$528$	1.25031e7	+	8.67703e6i	1.95179	+	1.35452i
$529$	−483854.			−0.0751753
$530$	−3.53645e6	−	4.81254e6i	−0.546861	−	0.744191i
$531$	1.28992e6	+	1.28992e6i	0.198531	+	0.198531i
$532$	−275862.	−	527229.i	−0.0422583	−	0.0807645i
$533$	−3713.77	+	3713.77i	−0.000566235	+	0.000566235i
$534$	1.18511e6	−	7.75371e6i	0.179848	−	1.17667i
$535$			5.29485e6i			0.799777i
$536$	−2.37999e6	+	4.86456e6i	−0.357818	+	0.731361i
$537$			4.26153e6i			0.637720i
$538$	−3.69668e6	−	565015.i	−0.550625	−	0.0841597i
$539$	1.69491e6	−	1.69491e6i	0.251290	−	0.251290i
$540$	1.84516e6	+	577536.i	0.272302	+	0.0852305i
$541$	3.94802e6	+	3.94802e6i	0.579944	+	0.579944i	0.934888	−	0.354944i	$-0.115500\pi$
$541$	3.94802e6	+	3.94802e6i	0.579944	+	0.579944i	−0.354944	+	0.934888i	$0.615500\pi$
$542$	1.05557e7	−	7.75672e6i	1.54343	−	1.13417i
$543$	8.69837e6			1.26601
$544$	−9.03075e6	+	244318.i	−1.30836	+	0.0353964i
$545$	−249354.			−0.0359604
$546$	9143.83	−	6719.25i	0.00131264	−	0.000964583i
$547$	5.90578e6	+	5.90578e6i	0.843935	+	0.843935i	0.989368	−	0.145433i	$-0.0464575\pi$
$547$	5.90578e6	+	5.90578e6i	0.843935	+	0.843935i	−0.145433	+	0.989368i	$0.546457\pi$
$548$	9.32726e6	+	2.91943e6i	1.32679	+	0.415286i
$549$	3.52013e6	−	3.52013e6i	0.498457	−	0.498457i
$550$	−3.30102e6	−	504541.i	−0.465309	−	0.0711197i
$551$			738488.i			0.103625i
$552$	−8.81785e6	−	4.31413e6i	−1.23173	−	0.602623i
$553$			8.99247e6i			1.25045i
$554$	1.82931e6	−	1.19685e7i	0.253229	−	1.65678i
$555$	−7.72792e6	+	7.72792e6i	−1.06495	+	1.06495i
$556$	−1.03895e6	−	1.98565e6i	−0.142530	−	0.272405i
$557$	−3.36194e6	−	3.36194e6i	−0.459147	−	0.459147i	0.439228	−	0.898375i	$-0.355252\pi$
$557$	−3.36194e6	−	3.36194e6i	−0.459147	−	0.459147i	−0.898375	+	0.439228i	$0.855252\pi$
$558$	−2.36670e6	−	3.22070e6i	−0.321779	−	0.437890i
$559$	−3828.06			−0.000518142
$560$	−1.24034e6	−	6.86619e6i	−0.167137	−	0.925221i
$561$	−2.31790e7			−3.10948
$562$	2.78068e6	+	3.78406e6i	0.371373	+	0.505379i
$563$	−1.45833e6	−	1.45833e6i	−0.193903	−	0.193903i	0.603477	−	0.797380i	$-0.293781\pi$
$563$	−1.45833e6	−	1.45833e6i	−0.193903	−	0.193903i	−0.797380	+	0.603477i	$0.793781\pi$
$564$	307287.	−	160782.i	0.0406768	−	0.0212833i
$565$	−5.65932e6	+	5.65932e6i	−0.745836	+	0.745836i
$566$	−725732.	+	4.74819e6i	−0.0952215	+	0.622998i
$567$		−	9.95400e6i		−	1.30029i
$568$	4.11763e6	−	1.41218e6i	0.535521	−	0.183661i
$569$			9.83779e6i			1.27385i	0.770928	+	0.636923i	$0.219793\pi$
$569$			9.83779e6i			1.27385i	−0.770928	+	0.636923i	$0.780207\pi$
$570$	−725507.	−	110889.i	−0.0935307	−	0.0142956i
$571$	−2.69114e6	+	2.69114e6i	−0.345419	+	0.345419i	−0.858400	−	0.512981i	$-0.828541\pi$
$571$	−2.69114e6	+	2.69114e6i	−0.345419	+	0.345419i	0.512981	+	0.858400i	$0.328541\pi$
$572$	−4726.08	+	15099.3i	−0.000603964	+	0.00192960i
$573$	−1.06945e7	−	1.06945e7i	−1.36073	−	1.36073i
$574$	4.95328e6	−	3.63987e6i	0.627499	−	0.461111i
$575$	2.15397e6			0.271687
$576$	−3.65951e6	−	4.70769e6i	−0.459586	−	0.591223i
$577$	1.66049e6			0.207634			0.103817	−	0.994596i	$-0.466894\pi$
$577$	1.66049e6			0.207634			0.103817	+	0.994596i	$0.466894\pi$
$578$	4.61511e6	−	3.39137e6i	0.574596	−	0.422236i
$579$	8.89368e6	+	8.89368e6i	1.10252	+	1.10252i
$580$	−2.58664e6	+	8.26404e6i	−0.319276	+	1.02005i
$581$	−7.03595e6	+	7.03595e6i	−0.864734	+	0.864734i
$582$	−1.11928e6	−	171075.i	−0.136971	−	0.0209352i
$583$		−	1.58496e7i		−	1.93129i
$584$	−1.89341e6	+	649362.i	−0.229728	+	0.0787870i
$585$		−	5992.91i		−	0.000724016i
$586$	−860663.	+	5.63099e6i	−0.103535	+	0.677393i
$587$	−3.14201e6	+	3.14201e6i	−0.376368	+	0.376368i	−0.869790	−	0.493422i	$-0.835746\pi$
$587$	−3.14201e6	+	3.14201e6i	−0.376368	+	0.376368i	0.493422	+	0.869790i	$0.335746\pi$
$588$	−1.94329e6	+	1.01678e6i	−0.231789	+	0.121279i
$589$	−359813.	−	359813.i	−0.0427355	−	0.0427355i
$590$	1.61265e6	+	2.19456e6i	0.190726	+	0.259547i
$591$	−1.77662e6			−0.209231
$592$	−1.11244e7	+	2.00957e6i	−1.30459	+	0.235668i
$593$	−2.72965e6			−0.318765			−0.159382	−	0.987217i	$-0.550950\pi$
$593$	−2.72965e6			−0.318765			−0.159382	+	0.987217i	$0.550950\pi$
$594$	3.03843e6	+	4.13482e6i	0.353332	+	0.480829i
$595$	7.51417e6	+	7.51417e6i	0.870139	+	0.870139i
$596$	1.92162e6	+	3.67261e6i	0.221591	+	0.423506i
$597$	4.14366e6	−	4.14366e6i	0.475827	−	0.475827i
$598$	1541.92	−	10088.2i	0.000176323	−	0.00115361i
$599$		−	3.91871e6i		−	0.446248i	−0.974790	−	0.223124i	$-0.928375\pi$
$599$		−	3.91871e6i		−	0.446248i	0.974790	−	0.223124i	$-0.0716254\pi$
$600$	2.74463e6	+	1.34281e6i	0.311247	+	0.152278i
$601$		−	1.02527e7i		−	1.15785i	−0.815381	−	0.578924i	$-0.803473\pi$
$601$		−	1.02527e7i		−	1.15785i	0.815381	−	0.578924i	$-0.196527\pi$
$602$	4.42880e6	+	676915.i	0.498075	+	0.0761278i
$603$	3.84946e6	−	3.84946e6i	0.431129	−	0.431129i
$604$	4.63309e6	+	1.45016e6i	0.516748	+	0.161742i
$605$	1.21814e7	+	1.21814e7i	1.35303	+	1.35303i
$606$	−9.02374e6	+	6.63100e6i	−0.998171	+	0.733496i
$607$	−2.72186e6			−0.299843			−0.149922	−	0.988698i	$-0.547902\pi$
$607$	−2.72186e6			−0.299843			−0.149922	+	0.988698i	$0.547902\pi$
$608$	−551123.	−	522089.i	−0.0604630	−	0.0572777i
$609$	1.64819e7			1.80080
$610$	5.98882e6	−	4.40083e6i	0.651654	−	0.478861i
$611$	254.941	+	254.941i	2.76272e−5	+	2.76272e-5i
$612$	8.66680e6	+	2.71271e6i	0.935363	+	0.292769i
$613$	6.86839e6	−	6.86839e6i	0.738251	−	0.738251i	−0.233989	−	0.972239i	$-0.575178\pi$
$613$	6.86839e6	−	6.86839e6i	0.738251	−	0.738251i	0.972239	+	0.233989i	$0.0751778\pi$
$614$	1.32416e6	+	202389.i	0.141748	+	0.0216654i
$615$		−	7.58164e6i		−	0.808305i
$616$	8.13776e6	−	1.66331e7i	0.864078	−	1.76613i
$617$		−	3.04363e6i		−	0.321868i	−0.986965	−	0.160934i	$-0.948549\pi$
$617$		−	3.04363e6i		−	0.321868i	0.986965	−	0.160934i	$-0.0514507\pi$
$618$	−854477.	+	5.59052e6i	−0.0899972	+	0.588818i
$619$	1.02826e6	−	1.02826e6i	0.107864	−	0.107864i	−0.651115	−	0.758979i	$-0.725699\pi$
$619$	1.02826e6	−	1.02826e6i	0.107864	−	0.107864i	0.758979	+	0.651115i	$0.225699\pi$
$620$	−2.76619e6	−	5.28677e6i	−0.289004	−	0.552346i
$621$	−2.34032e6	−	2.34032e6i	−0.243527	−	0.243527i
$622$	−7.04370e6	−	9.58535e6i	−0.730003	−	0.993418i
$623$	−9.54357e6			−0.985124
$624$	8253.84	−	11893.3i	0.000848583	−	0.00122276i
$625$	6.53643e6			0.669330
$626$	164591.	+	223983.i	0.0167869	+	0.0228443i
$627$	−1.37729e6	−	1.37729e6i	−0.139913	−	0.139913i
$628$	9.64666e6	−	5.04742e6i	0.976063	−	0.510705i
$629$	1.21743e7	−	1.21743e7i	1.22692	−	1.22692i
$630$	−1.05973e6	+	6.93339e6i	−0.106376	+	0.695976i
$631$			1.53609e7i			1.53583i	0.640549	+	0.767917i	$0.278707\pi$
$631$			1.53609e7i			1.53583i	−0.640549	+	0.767917i	$0.721293\pi$
$632$	3.72184e6	+	1.08522e7i	0.370651	+	1.08075i
$633$			1.14755e7i			1.13831i
$634$	−1.36872e7	−	2.09201e6i	−1.35236	−	0.206700i
$635$	952317.	−	952317.i	0.0937232	−	0.0937232i
$636$	−4.33199e6	+	1.38402e7i	−0.424663	+	1.35675i
$637$	−1612.25	−	1612.25i	−0.000157429	−	0.000157429i
$638$	−1.85188e7	+	1.36084e7i	−1.80120	+	1.32359i
$639$	−4.37589e6			−0.423950
$640$	−4.33866e6	−	7.77280e6i	−0.418702	−	0.750114i
$641$	−1.05544e7			−1.01458			−0.507292	−	0.861774i	$-0.669353\pi$
$641$	−1.05544e7			−1.01458			−0.507292	+	0.861774i	$0.669353\pi$
$642$	1.03610e7	−	7.61364e6i	0.992115	−	0.729046i
$643$	−4.06540e6	−	4.06540e6i	−0.387772	−	0.387772i	0.486120	−	0.873892i	$-0.338412\pi$
$643$	−4.06540e6	−	4.06540e6i	−0.387772	−	0.387772i	−0.873892	+	0.486120i	$0.838412\pi$
$644$	−3.56779e6	+	1.13987e7i	−0.338988	+	1.08303i
$645$	3.90748e6	−	3.90748e6i	0.369826	−	0.369826i
$646$	1.14294e6	+	174691.i	0.107756	+	0.0164698i
$647$			1.76648e6i			0.165901i	0.996554	+	0.0829503i	$0.0264343\pi$
$647$			1.76648e6i			0.165901i	−0.996554	+	0.0829503i	$0.973566\pi$
$648$	−4.11980e6	−	1.20126e7i	−0.385424	−	1.12382i
$649$			7.22755e6i			0.673564i
$650$	−479.934	+	3140.03i	−4.45552e−5	+	0.000291508i
$651$	−8.03048e6	+	8.03048e6i	−0.742658	+	0.742658i
$652$	1.42145e6	−	743743.i	0.130952	−	0.0685179i
$653$	−965221.	−	965221.i	−0.0885816	−	0.0885816i	0.661427	−	0.750009i	$-0.269951\pi$
$653$	−965221.	−	965221.i	−0.0885816	−	0.0885816i	−0.750009	+	0.661427i	$0.769951\pi$
$654$	358555.	+	487935.i	0.0327801	+	0.0446085i
$655$	−8.75197e6			−0.797082
$656$	4.47116e6	−	6.44270e6i	0.405659	−	0.584532i
$657$	2.01217e6			0.181866
$658$	−249868.	−	340030.i	−0.0224981	−	0.0306163i
$659$	−1.29347e7	−	1.29347e7i	−1.16022	−	1.16022i	−0.984426	−	0.175797i	$-0.943750\pi$
$659$	−1.29347e7	−	1.29347e7i	−1.16022	−	1.16022i	−0.175797	−	0.984426i	$-0.556250\pi$
$660$	−1.05884e7	−	2.02367e7i	−0.946176	−	1.80834i
$661$	1.53039e7	−	1.53039e7i	1.36238	−	1.36238i	0.491502	−	0.870876i	$-0.336448\pi$
$661$	1.53039e7	−	1.53039e7i	1.36238	−	1.36238i	0.870876	−	0.491502i	$-0.163552\pi$
$662$	−2.50963e6	+	1.64195e7i	−0.222569	+	1.45618i
$663$			22048.5i			0.00194803i
$664$	−5.57896e6	+	1.14031e7i	−0.491058	+	1.00370i
$665$			892983.i			0.0783049i
$666$	1.12333e7	+	1.71694e6i	0.981347	+	0.149993i
$667$	1.04817e7	−	1.04817e7i	0.912260	−	0.912260i
$668$	−4.34909e6	−	1.36127e6i	−0.377101	−	0.118032i
$669$	1.90810e7	+	1.90810e7i	1.64830	+	1.64830i
$670$	6.54912e6	−	4.81256e6i	0.563632	−	0.414180i
$671$	1.97236e7			1.69114
$672$	−1.16522e7	+	1.23002e7i	−0.995372	+	1.05073i
$673$	−1.45460e7			−1.23796			−0.618979	−	0.785407i	$-0.712454\pi$
$673$	−1.45460e7			−1.23796			−0.618979	+	0.785407i	$0.712454\pi$
$674$	−1.84145e7	+	1.35317e7i	−1.56139	+	1.14737i
$675$	728445.	+	728445.i	0.0615371	+	0.0615371i
$676$	−1.13389e7	−	3.54908e6i	−0.954343	−	0.298709i
$677$	−1.08525e7	+	1.08525e7i	−0.910032	+	0.910032i	−0.996274	−	0.0862426i	$-0.972514\pi$
$677$	−1.08525e7	+	1.08525e7i	−0.910032	+	0.910032i	0.0862426	+	0.996274i	$0.472514\pi$
$678$	1.92119e7	+	2.93642e6i	1.60508	+	0.245326i
$679$			1.37765e6i			0.114674i
$680$	1.21781e7	+	5.95815e6i	1.00997	+	0.494128i
$681$		−	2.99260e7i		−	2.47276i
$682$	2.39252e6	−	1.56533e7i	0.196967	−	1.28868i
$683$	−826804.	+	826804.i	−0.0678189	+	0.0678189i	−0.740203	−	0.672384i	$-0.765270\pi$
$683$	−826804.	+	826804.i	−0.0678189	+	0.0678189i	0.672384	+	0.740203i	$0.265270\pi$
$684$	353792.	+	676169.i	0.0289139	+	0.0552606i
$685$	−1.03713e7	−	1.03713e7i	−0.844512	−	0.844512i
$686$	−6.40786e6	−	8.72007e6i	−0.519879	−	0.707473i
$687$	−2.72784e7			−2.20510
$688$	5.62487e6	−	1.01610e6i	0.453045	−	0.0818403i
$689$	−15076.6			−0.00120992
$690$	8.72358e6	+	1.18714e7i	0.697545	+	0.949247i
$691$	5.92461e6	+	5.92461e6i	0.472024	+	0.472024i	0.902569	−	0.430545i	$-0.141679\pi$
$691$	5.92461e6	+	5.92461e6i	0.472024	+	0.472024i	−0.430545	+	0.902569i	$0.641679\pi$
$692$	9.72035e6	−	5.08597e6i	0.771644	−	0.403747i
$693$	−1.31623e7	+	1.31623e7i	−1.04111	+	1.04111i
$694$	−1.58818e6	+	1.03909e7i	−0.125170	+	0.818941i
$695$			3.36315e6i			0.264109i
$696$	1.98905e7	−	6.82160e6i	1.55640	−	0.533781i
$697$			1.19438e7i			0.931241i
$698$	9.16380e6	+	1.40063e6i	0.711929	+	0.108814i
$699$	−4.41665e6	+	4.41665e6i	−0.341900	+	0.341900i
$700$	1.11050e6	−	3.54793e6i	0.0856592	−	0.273672i
$701$	9.66889e6	+	9.66889e6i	0.743159	+	0.743159i	0.973185	−	0.230026i	$-0.0738810\pi$
$701$	9.66889e6	+	9.66889e6i	0.743159	+	0.743159i	−0.230026	+	0.973185i	$0.573881\pi$
$702$	3933.16	−	2890.24i	0.000301230	−	0.000221356i
$703$	1.44679e6			0.110412
$704$	2.93650e6	−	2.34411e7i	0.223305	−	1.78257i
$705$	−520461.			−0.0394380
$706$	−1.65718e7	+	1.21776e7i	−1.25129	+	0.919498i
$707$	9.63424e6	+	9.63424e6i	0.724884	+	0.724884i
$708$	1.97542e6	−	6.31126e6i	0.148107	−	0.473187i
$709$	−1.03764e7	+	1.03764e7i	−0.775234	+	0.775234i	−0.979016	−	0.203782i	$-0.934677\pi$
$709$	−1.03764e7	+	1.03764e7i	−0.775234	+	0.775234i	0.203782	+	0.979016i	$0.434677\pi$
$710$	−6.45771e6	−	987022.i	−0.480765	−	0.0734820i
$711$		−	1.15328e7i		−	0.855581i
$712$	−1.15172e7	+	3.94993e6i	−0.851429	+	0.292004i
$713$			1.02140e7i			0.752442i
$714$	3.89884e6	−	2.55086e7i	0.286213	−	1.87258i
$715$	16789.4	−	16789.4i	0.00122820	−	0.00122820i
$716$	5.86128e6	−	3.06679e6i	0.427277	−	0.223564i
$717$	−1.20526e6	−	1.20526e6i	−0.0875551	−	0.0875551i
$718$	1.26800e7	+	1.72555e7i	0.917928	+	1.24915i
$719$	2.61135e7			1.88383			0.941916	−	0.335847i	$-0.109023\pi$
$719$	2.61135e7			1.88383			0.941916	+	0.335847i	$0.109023\pi$
$720$	1.59073e6	+	8.80586e6i	0.114358	+	0.633053i
$721$	6.88103e6			0.492964
$722$	−8.23671e6	−	1.12088e7i	−0.588046	−	0.800236i
$723$	−1.19130e7	−	1.19130e7i	−0.847568	−	0.847568i
$724$	−6.25974e6	−	1.19637e7i	−0.443823	−	0.848238i
$725$	−3.26252e6	+	3.26252e6i	−0.230520	+	0.230520i
$726$	6.32047e6	−	4.13525e7i	0.445049	−	2.91179i
$727$			1.21217e7i			0.850602i	0.905052	+	0.425301i	$0.139832\pi$
$727$			1.21217e7i			0.850602i	−0.905052	+	0.425301i	$0.860168\pi$
$728$	−15821.9	−	7740.87i	−0.00110645	−	0.000541329i
$729$			6.46341e6i			0.450446i
$730$	2.96945e6	+	453863.i	0.206238	+	0.0315223i
$731$	−6.15571e6	+	6.15571e6i	−0.426073	+	0.426073i
$732$	−1.72231e7	−	5.39082e6i	−1.18805	−	0.371858i
$733$	−1.61927e7	−	1.61927e7i	−1.11317	−	1.11317i	−0.992720	−	0.120446i	$-0.961568\pi$
$733$	−1.61927e7	−	1.61927e7i	−1.11317	−	1.11317i	−0.120446	−	0.992720i	$-0.538432\pi$
$734$	2.05395e7	−	1.50933e7i	1.40718	−	1.03405i
$735$	3.29140e6			0.224731
$736$	412105.	+	1.52326e7i	0.0280423	+	1.03653i
$737$	2.15689e7			1.46271
$738$	−6.35256e6	+	4.66812e6i	−0.429346	+	0.315501i
$739$	−3.92497e6	−	3.92497e6i	−0.264378	−	0.264378i	0.562452	−	0.826830i	$-0.309858\pi$
$739$	−3.92497e6	−	3.92497e6i	−0.264378	−	0.264378i	−0.826830	+	0.562452i	$0.809858\pi$
$740$	1.61903e7	+	5.06756e6i	1.08686	+	0.340188i
$741$	−1310.12	+	1310.12i	−8.76528e−5	+	8.76528e-5i
$742$	1.74426e7	+	2.66599e6i	1.16306	+	0.177766i
$743$		−	5.95124e6i		−	0.395490i	−0.980254	−	0.197745i	$-0.936638\pi$
$743$		−	5.95124e6i		−	0.395490i	0.980254	−	0.197745i	$-0.0633618\pi$
$744$	−6.36754e6	+	1.30149e7i	−0.421735	+	0.862003i
$745$		−	6.22040e6i		−	0.410608i
$746$	−2.92278e6	+	1.91226e7i	−0.192286	+	1.25806i
$747$	9.02358e6	−	9.02358e6i	0.591667	−	0.591667i
$748$	1.66806e7	+	3.18802e7i	1.09008	+	2.08337i
$749$	−1.10619e7	−	1.10619e7i	−0.720487	−	0.720487i
$750$	−1.30783e7	−	1.77975e7i	−0.848980	−	1.15533i
$751$	1.30705e7			0.845656			0.422828	−	0.906210i	$-0.361037\pi$
$751$	1.30705e7			0.845656			0.422828	+	0.906210i	$0.361037\pi$
$752$	−442275.	−	306934.i	−0.0285199	−	0.0197925i
$753$	3.51718e6			0.226052
$754$	12944.7	+	17615.6i	0.000829207	+	0.00112842i
$755$	−5.15169e6	−	5.15169e6i	−0.328914	−	0.328914i
$756$	−5.06147e6	+	2.64831e6i	−0.322086	+	0.168525i
$757$	−2.84481e6	+	2.84481e6i	−0.180432	+	0.180432i	−0.791544	−	0.611112i	$-0.790722\pi$
$757$	−2.84481e6	+	2.84481e6i	−0.180432	+	0.180432i	0.611112	+	0.791544i	$0.290722\pi$
$758$	1.18529e6	−	7.75488e6i	0.0749291	−	0.490233i
$759$			3.90972e7i			2.46344i
$760$	369591.	+	1.07766e6i	0.0232107	+	0.0676778i
$761$		−	8.93791e6i		−	0.559467i	−0.960078	−	0.279734i	$-0.909754\pi$
$761$		−	8.93791e6i		−	0.559467i	0.960078	−	0.279734i	$-0.0902461\pi$
$762$	−3.23286e6	−	494123.i	−0.201697	−	0.0308282i
$763$	520947.	−	520947.i	0.0323953	−	0.0323953i
$764$	−7.01285e6	+	2.24053e7i	−0.434671	+	1.38873i
$765$	−9.63690e6	−	9.63690e6i	−0.595365	−	0.595365i
$766$	−1.85893e7	+	1.36602e7i	−1.14470	+	0.841171i
$767$	6875.05			0.000421976
$768$	−8.97110e6	+	1.96667e7i	−0.548836	+	1.20317i
$769$	1.24168e7			0.757171			0.378586	−	0.925566i	$-0.376411\pi$
$769$	1.24168e7			0.757171			0.378586	+	0.925566i	$0.376411\pi$
$770$	−2.23930e7	+	1.64553e7i	−1.36109	+	1.00018i
$771$	1.35466e7	+	1.35466e7i	0.820718	+	0.820718i
$772$	5.83200e6	−	1.86326e7i	0.352188	−	1.12520i
$773$	−9.38994e6	+	9.38994e6i	−0.565216	+	0.565216i	−0.930784	−	0.365569i	$-0.880875\pi$
$773$	−9.38994e6	+	9.38994e6i	−0.565216	+	0.565216i	0.365569	+	0.930784i	$0.380875\pi$
$774$	−5.67992e6	−	868141.i	−0.340792	−	0.0520880i
$775$		−	3.17920e6i		−	0.190135i
$776$	570187.	+	1.66256e6i	0.0339909	+	0.0991110i
$777$		−	3.22901e7i		−	1.91875i
$778$	1.70046e6	−	1.11254e7i	0.100720	−	0.658974i
$779$	−709702.	+	709702.i	−0.0419017	+	0.0419017i
$780$	−19249.7	+	10072.0i	−0.00113289	+	0.000592762i
$781$	−1.22592e7	−	1.22592e7i	−0.719177	−	0.719177i
$782$	−1.37428e7	−	1.87018e7i	−0.803635	−	1.09362i
$783$	7.08959e6			0.413254
$784$	2.79695e6	+	1.94106e6i	0.162516	+	0.112784i
$785$	−1.63388e7			−0.946339
$786$	1.25848e7	+	1.71259e7i	0.726589	+	0.988771i
$787$	−1.86499e7	−	1.86499e7i	−1.07335	−	1.07335i	−0.997088	−	0.0762608i	$-0.975702\pi$
$787$	−1.86499e7	−	1.86499e7i	−1.07335	−	1.07335i	−0.0762608	−	0.997088i	$-0.524298\pi$
$788$	1.27854e6	+	2.44355e6i	0.0733497	+	0.140186i
$789$	−1.05803e7	+	1.05803e7i	−0.605070	+	0.605070i
$790$	2.60133e6	−	1.70195e7i	0.148295	−	0.970241i
$791$		−	2.36467e7i		−	1.34379i
$792$	−1.04366e7	+	2.13319e7i	−0.591218	+	1.20842i
$793$		−	18761.6i		−	0.00105947i
$794$	−1.48568e7	−	2.27077e6i	−0.836323	−	0.127827i
$795$	1.53894e7	−	1.53894e7i	0.863582	−	0.863582i
$796$	−8.68112e6	−	2.71719e6i	−0.485616	−	0.151998i
$797$	8.94275e6	+	8.94275e6i	0.498684	+	0.498684i	0.911028	−	0.412344i	$-0.135290\pi$
$797$	8.94275e6	+	8.94275e6i	0.498684	+	0.498684i	−0.412344	+	0.911028i	$0.635290\pi$
$798$	1.74739e6	−	1.28405e6i	0.0971364	−	0.0713797i
$799$	819915.			0.0454362
$800$	−128271.	−	4.74128e6i	−0.00708604	−	0.261921i
$801$	1.22396e7			0.674040
$802$	2.13877e7	−	1.57165e7i	1.17416	−	0.862822i
$803$	5.63717e6	+	5.63717e6i	0.308512	+	0.308512i
$804$	−1.88344e7	−	5.89517e6i	−1.02757	−	0.321630i
$805$	1.26746e7	−	1.26746e7i	0.689355	−	0.689355i
$806$	−14889.9	−	2275.83i	−0.000807335	−	0.000123396i
$807$		−	1.36279e7i		−	0.736624i
$808$	1.56141e7	+	7.63920e6i	0.841373	+	0.411642i
$809$			3.04492e7i			1.63570i	0.575429	+	0.817852i	$0.304835\pi$
$809$			3.04492e7i			1.63570i	−0.575429	+	0.817852i	$0.695165\pi$
$810$	−2.87948e6	+	1.88394e7i	−0.154206	+	1.00891i
$811$	−1.53360e7	+	1.53360e7i	−0.818766	+	0.818766i	−0.985929	−	0.167163i	$-0.946539\pi$
$811$	−1.53360e7	+	1.53360e7i	−0.818766	+	0.818766i	0.167163	+	0.985929i	$0.446539\pi$
$812$	−1.18611e7	−	2.26691e7i	−0.631300	−	1.20655i
$813$	3.37546e7	+	3.37546e7i	1.79104	+	1.79104i
$814$	2.66605e7	+	3.62807e7i	1.41029	+	1.91918i
$815$	−2.40754e6			−0.126964
$816$	−5.85247e6	−	3.23976e7i	−0.307690	−	1.70329i
$817$	−731543.			−0.0383429
$818$	−1.51029e7	−	2.05526e7i	−0.789182	−	1.07395i
$819$	12520.3	+	12520.3i	0.000652237	+	0.000652237i
$820$	−1.04277e7	+	5.45609e6i	−0.541570	+	0.283365i
$821$	−1.12989e7	+	1.12989e7i	−0.585033	+	0.585033i	−0.936282	−	0.351249i	$-0.885757\pi$
$821$	−1.12989e7	+	1.12989e7i	−0.585033	+	0.585033i	0.351249	+	0.936282i	$0.385757\pi$
$822$	−5.38129e6	+	3.52077e7i	−0.277784	+	1.81743i
$823$			2.53026e7i			1.30216i	0.759008	+	0.651081i	$0.225684\pi$
$823$			2.53026e7i			1.30216i	−0.759008	+	0.651081i	$0.774316\pi$
$824$	8.30407e6	−	2.84795e6i	0.426062	−	0.146122i
$825$		−	1.21693e7i		−	0.622489i
$826$	−7.95396e6	−	1.21571e6i	−0.405633	−	0.0619985i
$827$	2.47271e7	−	2.47271e7i	1.25721	−	1.25721i	0.304794	−	0.952418i	$-0.401412\pi$
$827$	2.47271e7	−	2.47271e7i	1.25721	−	1.25721i	0.952418	−	0.304794i	$-0.0985877\pi$
$828$	4.57567e6	−	1.46188e7i	0.231942	−	0.741028i
$829$	−2.30371e7	−	2.30371e7i	−1.16424	−	1.16424i	−0.983538	−	0.180699i	$-0.942164\pi$
$829$	−2.30371e7	−	2.30371e7i	−1.16424	−	1.16424i	−0.180699	−	0.983538i	$-0.557836\pi$
$830$	1.53519e7	−	1.12812e7i	0.773511	−	0.568407i
$831$	4.41222e7			2.21643
$832$	−22297.8	−	2793.29i	−0.00111674	−	0.000139897i
$833$	−5.18515e6			−0.258910
$834$	6.58100e6	−	4.83599e6i	0.327625	−	0.240752i
$835$	4.83589e6	+	4.83589e6i	0.240027	+	0.240027i
$836$	−903155.	+	2.88548e6i	−0.0446937	+	0.142791i
$837$	−3.45426e6	+	3.45426e6i	−0.170428	+	0.170428i
$838$	2.59766e7	+	3.97037e6i	1.27783	+	0.195308i
$839$			805150.i			0.0394886i	0.999805	+	0.0197443i	$0.00628522\pi$
$839$			805150.i			0.0394886i	−0.999805	+	0.0197443i	$0.993715\pi$
$840$	2.40516e7	−	8.24871e6i	1.17611	−	0.403355i
$841$			1.12414e7i			0.548061i
$842$	205648.	−	1.34548e6i	0.00999642	−	0.0654028i
$843$	−1.21006e7	+	1.21006e7i	−0.586457	+	0.586457i
$844$	1.57833e7	−	8.25827e6i	0.762678	−	0.399055i
$845$	1.26081e7	+	1.26081e7i	0.607446	+	0.607446i
$846$	320455.	+	436088.i	0.0153936	+	0.0209483i
$847$	−5.08983e7			−2.43778
$848$	2.21532e7	−	4.00187e6i	1.05791	−	0.191106i
$849$	−1.75043e7			−0.833444
$850$	4.27756e6	+	5.82108e6i	0.203071	+	0.276348i
$851$	−2.05350e7	−	2.05350e7i	−0.972012	−	0.972012i
$852$	7.35436e6	+	1.40557e7i	0.347093	+	0.663367i
$853$	2.30704e7	−	2.30704e7i	1.08563	−	1.08563i	0.0896579	−	0.995973i	$-0.471423\pi$
$853$	2.30704e7	−	2.30704e7i	1.08563	−	1.08563i	0.995973	−	0.0896579i	$-0.0285774\pi$
$854$	−3.31762e6	+	2.17059e7i	−0.155662	+	1.01844i
$855$		−	1.14525e6i		−	0.0535777i
$856$	−1.79279e7	−	8.77124e6i	−0.836269	−	0.409144i
$857$		−	6.68963e6i		−	0.311136i	−0.987825	−	0.155568i	$-0.950279\pi$
$857$		−	6.68963e6i		−	0.311136i	0.987825	−	0.155568i	$-0.0497207\pi$
$858$	−56995.5	−	8711.42i	−0.00264315	−	0.000403990i
$859$	8.68603e6	−	8.68603e6i	0.401641	−	0.401641i	−0.477170	−	0.878811i	$-0.658337\pi$
$859$	8.68603e6	−	8.68603e6i	0.401641	−	0.401641i	0.878811	+	0.477170i	$0.158337\pi$
$860$	−8.18631e6	−	2.56232e6i	−0.377435	−	0.118137i
$861$	1.58394e7	+	1.58394e7i	0.728169	+	0.728169i
$862$	−8.57987e6	+	6.30483e6i	−0.393290	+	0.289005i
$863$	−2.89560e7			−1.32346			−0.661732	−	0.749741i	$-0.730178\pi$
$863$	−2.89560e7			−1.32346			−0.661732	+	0.749741i	$0.730178\pi$
$864$	−5.01212e6	+	5.29086e6i	−0.228422	+	0.241125i
$865$	−1.64636e7			−0.748144
$866$	2.57600e7	−	1.89295e7i	1.16722	−	0.857718i
$867$	1.47581e7	+	1.47581e7i	0.666779	+	0.666779i
$868$	1.68241e7	+	5.26596e6i	0.757938	+	0.237235i
$869$	3.23096e7	−	3.23096e7i	1.45139	−	1.45139i
$870$	−3.11944e7	−	4.76787e6i	−1.39726	−	0.213563i
$871$		−	20516.9i		−	0.000916361i
$872$	413070.	−	844293.i	0.0183964	−	0.0376012i
$873$		−	1.76683e6i		−	0.0784620i
$874$	294661.	−	1.92785e6i	0.0130480	−	0.0853681i
$875$	−1.90015e7	+	1.90015e7i	−0.839013	+	0.839013i
$876$	−3.38176e6	−	6.46325e6i	−0.148896	−	0.284571i
$877$	6.77915e6	+	6.77915e6i	0.297630	+	0.297630i	0.840085	−	0.542455i	$-0.182505\pi$
$877$	6.77915e6	+	6.77915e6i	0.297630	+	0.297630i	−0.542455	+	0.840085i	$0.682505\pi$
$878$	−1.89392e7	−	2.57732e7i	−0.829136	−	1.12832i
$879$	−2.07588e7			−0.906213
$880$	−2.02135e7	+	2.91265e7i	−0.879902	+	1.26789i
$881$	−2.43828e6			−0.105838			−0.0529192	−	0.998599i	$-0.516853\pi$
$881$	−2.43828e6			−0.105838			−0.0529192	+	0.998599i	$0.516853\pi$
$882$	−2.02656e6	−	2.75782e6i	−0.0877178	−	0.119370i
$883$	969798.	+	969798.i	0.0418581	+	0.0418581i	0.727726	−	0.685868i	$-0.240577\pi$
$883$	969798.	+	969798.i	0.0418581	+	0.0418581i	−0.685868	+	0.727726i	$0.740577\pi$
$884$	30325.3	−	15867.1i	0.00130519	−	0.000682916i
$885$	−7.01769e6	+	7.01769e6i	−0.301187	+	0.301187i
$886$	−1.32400e6	+	8.66243e6i	−0.0566635	+	0.370728i
$887$			1.12002e7i			0.477986i	0.971021	+	0.238993i	$0.0768173\pi$
$887$			1.12002e7i			0.477986i	−0.971021	+	0.238993i	$0.923183\pi$
$888$	−1.33644e7	−	3.89679e7i	−0.568743	−	1.65835i
$889$			3.97913e6i			0.168863i
$890$	1.80626e7	+	2.76075e6i	0.764371	+	0.116829i
$891$	−3.57644e7	+	3.57644e7i	−1.50923	+	1.50923i
$892$	1.25123e7	−	3.99754e7i	0.526532	−	1.68221i
$893$	48719.3	+	48719.3i	0.00204443	+	0.00204443i
$894$	−1.21721e7	+	8.94453e6i	−0.509355	+	0.374295i
$895$	−9.92740e6			−0.414265
$896$	2.53031e7	+	7.17456e6i	1.05294	+	0.298556i
$897$	37190.4			0.00154330
$898$	−3.05776e6	+	2.24696e6i	−0.126535	+	0.0929833i
$899$	−1.54708e7	−	1.54708e7i	−0.638429	−	0.638429i
$900$	−1.42421e6	+	4.55021e6i	−0.0586096	+	0.187251i
$901$	−2.42439e7	+	2.42439e7i	−0.994925	+	0.994925i
$902$	−3.08749e7	−	4.71904e6i	−1.26354	−	0.193124i
$903$			1.63269e7i			0.666323i
$904$	−9.78701e6	−	2.85370e7i	−0.398317	−	1.16142i
$905$			2.02632e7i			0.822405i
$906$	−2.67303e6	+	1.74886e7i	−0.108189	+	0.707839i
$907$	1.40221e7	−	1.40221e7i	0.565973	−	0.565973i	−0.365025	−	0.930998i	$-0.618940\pi$
$907$	1.40221e7	−	1.40221e7i	0.565973	−	0.565973i	0.930998	+	0.365025i	$0.118940\pi$
$908$	−4.11600e7	+	2.15361e7i	−1.65677	+	0.866868i
$909$	−1.23559e7	−	1.23559e7i	−0.495979	−	0.495979i
$910$	15652.8	+	21300.9i	0.000626596	+	0.000852696i
$911$	2.60096e6			0.103834			0.0519168	−	0.998651i	$-0.483467\pi$
$911$	2.60096e6			0.103834			0.0519168	+	0.998651i	$0.483467\pi$
$912$	1.57731e6	−	2.27282e6i	0.0627957	−	0.0904851i
$913$	5.05599e7			2.00738
$914$	9.97422e6	+	1.35733e7i	0.394924	+	0.537428i
$915$	1.91509e7	+	1.91509e7i	0.756199	+	0.756199i
$916$	1.96308e7	+	3.75185e7i	0.773035	+	1.47743i
$917$	1.82845e7	−	1.82845e7i	0.718059	−	0.718059i
$918$	1.67706e6	−	1.09724e7i	0.0656813	−	0.429728i
$919$		−	2.82623e7i		−	1.10387i	−0.833886	−	0.551937i	$-0.813889\pi$
$919$		−	2.82623e7i		−	1.10387i	0.833886	−	0.551937i	$-0.186111\pi$
$920$	1.00499e7	−	2.05415e7i	0.391466	−	0.800135i
$921$			4.88154e6i			0.189630i
$922$	1.09077e6	+	166718.i	0.0422578	+	0.00645885i
$923$	−11661.3	+	11661.3i	−0.000450551	+	0.000450551i
$924$	6.43994e7	+	2.01570e7i	2.48143	+	0.776688i
$925$	6.39169e6	+	6.39169e6i	0.245619	+	0.245619i
$926$	6.00141e6	−	4.41008e6i	0.229999	−	0.169012i
$927$	−8.82490e6			−0.337295
$928$	−2.36965e7	−	2.24481e7i	−0.903262	−	0.855675i
$929$	−2.72647e7			−1.03648			−0.518240	−	0.855235i	$-0.673413\pi$
$929$	−2.72647e7			−1.03648			−0.518240	+	0.855235i	$0.673413\pi$
$930$	1.75219e7	−	1.28758e7i	0.664313	−	0.488164i
$931$	−308101.	−	308101.i	−0.0116498	−	0.0116498i
$932$	9.25303e6	+	2.89620e6i	0.348935	+	0.109217i
$933$	3.06517e7	−	3.06517e7i	1.15279	−	1.15279i
$934$	1.10942e7	+	1.69569e6i	0.416131	+	0.0636032i
$935$		−	5.39963e7i		−	2.01992i
$936$	20291.5	+	9927.63i	0.000757052	+	0.000370387i
$937$			3.99155e7i			1.48523i	0.669720	+	0.742614i	$0.266414\pi$
$937$			3.99155e7i			1.48523i	−0.669720	+	0.742614i	$0.733586\pi$
$938$	−3.62800e6	+	2.37367e7i	−0.134636	+	0.880871i
$939$	−716245.	+	716245.i	−0.0265093	+	0.0265093i
$940$	374547.	+	715837.i	0.0138257	+	0.0264238i
$941$	1.72696e7	+	1.72696e7i	0.635784	+	0.635784i	0.949513	−	0.313729i	$-0.101578\pi$
$941$	1.72696e7	+	1.72696e7i	0.635784	+	0.635784i	−0.313729	+	0.949513i	$0.601578\pi$
$942$	2.34942e7	+	3.19718e7i	0.862646	+	1.17392i
$943$	2.01463e7			0.737762
$944$	−1.01020e7	+	1.82488e6i	−0.368960	+	0.0666508i
$945$	8.57276e6			0.312278
$946$	−1.34804e7	−	1.83447e7i	−0.489750	−	0.666472i
$947$	2.86531e7	+	2.86531e7i	1.03824	+	1.03824i	0.999239	+	0.0389965i	$0.0124161\pi$
$947$	2.86531e7	+	2.86531e7i	1.03824	+	1.03824i	0.0389965	+	0.999239i	$0.487584\pi$
$948$	−3.70443e7	+	1.93827e7i	−1.33875	+	0.700476i
$949$	5362.24	−	5362.24i	0.000193277	−	0.000193277i
$950$	−91715.5	+	600060.i	−0.00329711	+	0.0215718i
$951$		−	5.04585e7i		−	1.80918i
$952$	−3.78901e7	+	1.29947e7i	−1.35498	+	0.464702i
$953$		−	5.02248e7i		−	1.79137i	−0.444686	−	0.895687i	$-0.646685\pi$
$953$		−	5.02248e7i		−	1.79137i	0.444686	−	0.895687i	$-0.353315\pi$
$954$	−2.23700e7	−	3.41913e6i	−0.795785	−	0.121631i
$955$	2.49131e7	−	2.49131e7i	0.883934	−	0.883934i
$956$	−790342.	+	2.52506e6i	−0.0279686	+	0.0893565i
$957$	−5.92190e7	−	5.92190e7i	−2.09017	−	2.09017i
$958$	−3.68964e6	+	2.71129e6i	−0.129888	+	0.0954471i
$959$	4.33351e7			1.52157
$960$	2.56117e7	−	1.99092e7i	0.896932	−	0.697229i
$961$	−1.35535e7			−0.473417
$962$	34511.2	−	25360.2i	0.00120233	−	0.000883519i
$963$	1.41869e7	+	1.41869e7i	0.492970	+	0.492970i
$964$	−7.81189e6	+	2.49581e7i	−0.270747	+	0.865006i
$965$	−2.07182e7	+	2.07182e7i	−0.716198	+	0.716198i
$966$	−4.30267e7	−	6.57638e6i	−1.48353	−	0.226748i
$967$		−	3.14877e6i		−	0.108287i	−0.998533	−	0.0541434i	$-0.982757\pi$
$967$		−	3.14877e6i		−	0.108287i	0.998533	−	0.0541434i	$-0.0172428\pi$
$968$	−6.14243e7	+	2.10660e7i	−2.10694	+	0.722592i
$969$			4.21348e6i			0.144155i
$970$	398525.	−	2.60740e6i	0.0135996	−	0.0889770i
$971$	−8.06923e6	+	8.06923e6i	−0.274653	+	0.274653i	−0.830970	−	0.556317i	$-0.812214\pi$
$971$	−8.06923e6	+	8.06923e6i	−0.274653	+	0.274653i	0.556317	+	0.830970i	$0.312214\pi$
$972$	3.23369e7	−	1.69196e7i	1.09782	−	0.574413i
$973$	−7.02624e6	−	7.02624e6i	−0.237925	−	0.237925i
$974$	1.95103e7	+	2.65504e7i	0.658970	+	0.896753i
$975$	−11575.8			−0.000389978
$976$	4.98001e6	+	2.75679e7i	0.167342	+	0.926360i
$977$	1.11153e7			0.372550			0.186275	−	0.982498i	$-0.440358\pi$
$977$	1.11153e7			0.372550			0.186275	+	0.982498i	$0.440358\pi$
$978$	3.46189e6	+	4.71108e6i	0.115735	+	0.157497i
$979$	3.42897e7	+	3.42897e7i	1.14342	+	1.14342i
$980$	−2.36864e6	−	4.52696e6i	−0.0787832	−	0.150571i
$981$	−668112.	+	668112.i	−0.0221655	+	0.0221655i
$982$	1.76332e6	−	1.15368e7i	0.0583517	−	0.381773i
$983$			1.72608e7i			0.569740i	0.958566	+	0.284870i	$0.0919505\pi$
$983$			1.72608e7i			0.569740i	−0.958566	+	0.284870i	$0.908050\pi$
$984$	2.56708e7	+	1.25594e7i	0.845186	+	0.413507i
$985$		−	4.13871e6i		−	0.135917i
$986$	4.91425e7	+	7.51113e6i	1.60977	+	0.246044i
$987$	1.08734e6	−	1.08734e6i	0.0355281	−	0.0355281i
$988$	2744.75	+	859.107i	8.94562e−5	+	2.79998e-5i
$989$	1.03832e7	+	1.03832e7i	0.337550	+	0.337550i
$990$	2.87190e7	−	2.11039e7i	0.931282	−	0.684343i
$991$	−1.74040e7			−0.562944			−0.281472	−	0.959569i	$-0.590823\pi$
$991$	−1.74040e7			−0.562944			−0.281472	+	0.959569i	$0.590823\pi$
$992$	2.24830e7	−	608256.i	0.725395	−	0.0196249i
$993$	−6.05312e7			−1.94808
$994$	1.55534e7	−	1.14293e7i	0.499299	−	0.366905i
$995$	9.65282e6	+	9.65282e6i	0.309098	+	0.309098i
$996$	−4.41500e7	−	1.38190e7i	−1.41021	−	0.441394i
$997$	−2.49728e6	+	2.49728e6i	−0.0795665	+	0.0795665i	−0.745770	−	0.666204i	$-0.767918\pi$
$997$	−2.49728e6	+	2.49728e6i	−0.0795665	+	0.0795665i	0.666204	+	0.745770i	$0.267918\pi$
$998$	−6.02280e6	−	920549.i	−0.191413	−	0.0292564i
$999$		−	1.38894e7i		−	0.440321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.13.8	yes	18
3.2	odd	2		144.6.k.a.109.2		18
4.3	odd	2		64.6.e.a.17.2		18
8.3	odd	2		128.6.e.a.33.8		18
8.5	even	2		128.6.e.b.33.2		18
12.11	even	2		576.6.k.a.145.8		18
16.3	odd	4		128.6.e.a.97.8		18
16.5	even	4	inner	16.6.e.a.5.8	✓	18
16.11	odd	4		64.6.e.a.49.2		18
16.13	even	4		128.6.e.b.97.2		18
32.5	even	8		1024.6.a.k.1.3		18
32.11	odd	8		1024.6.a.l.1.3		18
32.21	even	8		1024.6.a.k.1.16		18
32.27	odd	8		1024.6.a.l.1.16		18
48.5	odd	4		144.6.k.a.37.2		18
48.11	even	4		576.6.k.a.433.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.8	✓	18	16.5	even	4	inner
16.6.e.a.13.8	yes	18	1.1	even	1	trivial
64.6.e.a.17.2		18	4.3	odd	2
64.6.e.a.49.2		18	16.11	odd	4
128.6.e.a.33.8		18	8.3	odd	2
128.6.e.a.97.8		18	16.3	odd	4
128.6.e.b.33.2		18	8.5	even	2
128.6.e.b.97.2		18	16.13	even	4
144.6.k.a.37.2		18	48.5	odd	4
144.6.k.a.109.2		18	3.2	odd	2
576.6.k.a.145.8		18	12.11	even	2
576.6.k.a.433.8		18	48.11	even	4
1024.6.a.k.1.3		18	32.5	even	8
1024.6.a.k.1.16		18	32.21	even	8
1024.6.a.l.1.3		18	32.11	odd	8
1024.6.a.l.1.16		18	32.27	odd	8

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.55844 - 3.34972i) q^{2} +(14.5768 + 14.5768i) q^{3} +(9.55871 - 30.5390i) q^{4} +(-33.9573 + 33.9573i) q^{5} +(115.276 + 17.6192i) q^{6} -141.886i q^{7} +(-58.7245 - 171.229i) q^{8} +181.969i q^{9} +O(q^{10})\)	\(q+(4.55844 - 3.34972i) q^{2} +(14.5768 + 14.5768i) q^{3} +(9.55871 - 30.5390i) q^{4} +(-33.9573 + 33.9573i) q^{5} +(115.276 + 17.6192i) q^{6} -141.886i q^{7} +(-58.7245 - 171.229i) q^{8} +181.969i q^{9} +(-41.0447 + 268.540i) q^{10} +(-509.792 + 509.792i) q^{11} +(584.498 - 305.827i) q^{12} +(0.484929 + 0.484929i) q^{13} +(-475.280 - 646.780i) q^{14} -989.980 q^{15} +(-841.262 - 583.827i) q^{16} +1559.58 q^{17} +(609.544 + 829.492i) q^{18} +(92.6701 + 92.6701i) q^{19} +(712.434 + 1361.61i) q^{20} +(2068.25 - 2068.25i) q^{21} +(-616.194 + 4031.52i) q^{22} -2630.63i q^{23} +(1639.96 - 3352.00i) q^{24} +818.803i q^{25} +(3.83490 + 0.586141i) q^{26} +(889.645 - 889.645i) q^{27} +(-4333.07 - 1356.25i) q^{28} +(3984.50 + 3984.50i) q^{29} +(-4512.76 + 3316.16i) q^{30} -3882.73 q^{31} +(-5790.50 + 156.657i) q^{32} -14862.3 q^{33} +(7109.25 - 5224.16i) q^{34} +(4818.07 + 4818.07i) q^{35} +(5557.14 + 1739.38i) q^{36} +(7806.14 - 7806.14i) q^{37} +(732.850 + 112.012i) q^{38} +14.1375i q^{39} +(7808.61 + 3820.36i) q^{40} +7658.37i q^{41} +(2499.93 - 16356.1i) q^{42} +(-3947.03 + 3947.03i) q^{43} +(10695.6 + 20441.5i) q^{44} +(-6179.16 - 6179.16i) q^{45} +(-8811.87 - 11991.5i) q^{46} +525.728 q^{47} +(-3752.59 - 20773.3i) q^{48} -3324.71 q^{49} +(2742.76 + 3732.46i) q^{50} +(22733.7 + 22733.7i) q^{51} +(19.4446 - 10.1740i) q^{52} +(-15545.1 + 15545.1i) q^{53} +(1075.33 - 7035.46i) q^{54} -34622.4i q^{55} +(-24295.1 + 8332.19i) q^{56} +2701.67i q^{57} +(31510.1 + 4816.13i) q^{58} +(7088.71 - 7088.71i) q^{59} +(-9462.93 + 30233.0i) q^{60} +(-19344.7 - 19344.7i) q^{61} +(-17699.2 + 13006.1i) q^{62} +25818.8 q^{63} +(-25870.9 + 20110.7i) q^{64} -32.9338 q^{65} +(-67749.0 + 49784.7i) q^{66} +(-21154.5 - 21154.5i) q^{67} +(14907.6 - 47628.0i) q^{68} +(38346.2 - 38346.2i) q^{69} +(38102.1 + 5823.68i) q^{70} +24047.5i q^{71} +(31158.3 - 10686.0i) q^{72} -11057.8i q^{73} +(9435.39 - 61732.2i) q^{74} +(-11935.6 + 11935.6i) q^{75} +(3715.86 - 1944.25i) q^{76} +(72332.5 + 72332.5i) q^{77} +(47.3566 + 64.4448i) q^{78} -63378.0 q^{79} +(48392.2 - 8741.80i) q^{80} +70154.8 q^{81} +(25653.4 + 34910.2i) q^{82} +(-49588.7 - 49588.7i) q^{83} +(-43392.6 - 82932.2i) q^{84} +(-52959.1 + 52959.1i) q^{85} +(-4770.83 + 31213.7i) q^{86} +116163. i q^{87} +(117229. + 57354.1i) q^{88} -67262.1i q^{89} +(-48865.8 - 7468.84i) q^{90} +(68.8048 - 68.8048i) q^{91} +(-80336.7 - 25145.4i) q^{92} +(-56598.0 - 56598.0i) q^{93} +(2396.50 - 1761.04i) q^{94} -6293.65 q^{95} +(-86690.8 - 82123.6i) q^{96} -9709.53 q^{97} +(-15155.5 + 11136.9i) q^{98} +(-92766.2 - 92766.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

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