LMFDB - Embedded newform 100.9.b.g.51.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,9,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, 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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 94 x^{18} + 5343 x^{16} - 172772 x^{14} + 36131456 x^{12} - 3044563968 x^{10} + \cdots + 11\!\cdots\!76 $ x^20 - 94x^18 + 5343x^16 - 172772x^14 + 36131456x^12 - 3044563968x^10 + 147994443776x^8 - 2898633162752x^6 + 367168164200448x^4 - 26458647810801664*x^2 + 1152921504606846976
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{75}\cdot 3^{4}\cdot 5^{14} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.17
Root			$7.17826 - 3.53165i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.g.51.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.3565 - 7.06329i) q^{2} +134.970i q^{3} +(156.220 - 202.809i) q^{4} +(953.329 + 1937.69i) q^{6} -1863.96i q^{7} +(810.276 - 4015.06i) q^{8} -11655.8 q^{9} +O(q^{10})$	\(q+(14.3565 - 7.06329i) q^{2} +134.970i q^{3} +(156.220 - 202.809i) q^{4} +(953.329 + 1937.69i) q^{6} -1863.96i q^{7} +(810.276 - 4015.06i) q^{8} -11655.8 q^{9} -5278.32i q^{11} +(27373.0 + 21084.9i) q^{12} -33338.9 q^{13} +(-13165.7 - 26760.0i) q^{14} +(-16726.8 - 63365.5i) q^{16} -142617. q^{17} +(-167336. + 82328.1i) q^{18} -70346.9i q^{19} +251578. q^{21} +(-37282.3 - 75778.3i) q^{22} +255957. i q^{23} +(541910. + 109363. i) q^{24} +(-478630. + 235482. i) q^{26} -687639. i q^{27} +(-378027. - 291187. i) q^{28} -534050. q^{29} -1.24954e6i q^{31} +(-687707. - 791562. i) q^{32} +712412. q^{33} +(-2.04748e6 + 1.00735e6i) q^{34} +(-1.82086e6 + 2.36389e6i) q^{36} -169861. q^{37} +(-496881. - 1.00994e6i) q^{38} -4.49973e6i q^{39} +2.36651e6 q^{41} +(3.61178e6 - 1.77697e6i) q^{42} -4.03853e6i q^{43} +(-1.07049e6 - 824577. i) q^{44} +(1.80790e6 + 3.67465e6i) q^{46} -1.65928e6i q^{47} +(8.55241e6 - 2.25760e6i) q^{48} +2.29046e6 q^{49} -1.92489e7i q^{51} +(-5.20819e6 + 6.76141e6i) q^{52} +981179. q^{53} +(-4.85699e6 - 9.87210e6i) q^{54} +(-7.48390e6 - 1.51032e6i) q^{56} +9.49469e6 q^{57} +(-7.66710e6 + 3.77215e6i) q^{58} -7.47526e6i q^{59} -1.41028e7 q^{61} +(-8.82589e6 - 1.79391e7i) q^{62} +2.17259e7i q^{63} +(-1.54641e7 - 6.50660e6i) q^{64} +(1.02278e7 - 5.03197e6i) q^{66} +3.75634e7i q^{67} +(-2.22796e7 + 2.89240e7i) q^{68} -3.45463e7 q^{69} +3.57630e7i q^{71} +(-9.44439e6 + 4.67986e7i) q^{72} +7.26944e6 q^{73} +(-2.43862e6 + 1.19978e6i) q^{74} +(-1.42670e7 - 1.09896e7i) q^{76} -9.83857e6 q^{77} +(-3.17829e7 - 6.46005e7i) q^{78} -3.72731e7i q^{79} +1.63368e7 q^{81} +(3.39749e7 - 1.67154e7i) q^{82} +2.09461e7i q^{83} +(3.93014e7 - 5.10222e7i) q^{84} +(-2.85253e7 - 5.79792e7i) q^{86} -7.20805e7i q^{87} +(-2.11927e7 - 4.27689e6i) q^{88} -2.52812e7 q^{89} +6.21423e7i q^{91} +(5.19102e7 + 3.99855e7i) q^{92} +1.68650e8 q^{93} +(-1.17199e7 - 2.38214e7i) q^{94} +(1.06837e8 - 9.28195e7i) q^{96} +1.35709e6 q^{97} +(3.28830e7 - 1.61782e7i) q^{98} +6.15229e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9}+O(q^{10}) $ 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9	$ 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9} - 8848 q^{14} - 59200 q^{16} + 410256 q^{21} + 156672 q^{24} - 440448 q^{26} - 660136 q^{29} - 4342528 q^{34} - 7191312 q^{36} + 7068520 q^{41} - 2666880 q^{44} + 561168 q^{46} - 11719036 q^{49} - 37110816 q^{54} - 35044352 q^{56} - 17660440 q^{61} - 20201728 q^{64} + 31902720 q^{66} - 111747216 q^{69} - 19114368 q^{74} - 54998400 q^{76} - 154212444 q^{81} - 101289216 q^{84} + 94429648 q^{86} - 105006376 q^{89} + 192757872 q^{94} + 28850688 q^{96}+O(q^{100}) $ 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9 - 8848 * q^14 - 59200 * q^16 + 410256 * q^21 + 156672 * q^24 - 440448 * q^26 - 660136 * q^29 - 4342528 * q^34 - 7191312 * q^36 + 7068520 * q^41 - 2666880 * q^44 + 561168 * q^46 - 11719036 * q^49 - 37110816 * q^54 - 35044352 * q^56 - 17660440 * q^61 - 20201728 * q^64 + 31902720 * q^66 - 111747216 * q^69 - 19114368 * q^74 - 54998400 * q^76 - 154212444 * q^81 - 101289216 * q^84 + 94429648 * q^86 - 105006376 * q^89 + 192757872 * q^94 + 28850688 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	14.3565	−	7.06329i	0.897283	−	0.441456i
$2$	14.3565	−	7.06329i	0.897283	−	0.441456i
$3$			134.970i			1.66629i	0.553054	+	0.833145i	$0.313462\pi$
$3$			134.970i			1.66629i	−0.553054	+	0.833145i	$0.686538\pi$
$4$	156.220	−	202.809i	0.610233	−	0.792222i
$5$		0			0
$5$		0			0
$6$	953.329	+	1937.69i	0.735594	+	1.49513i
$7$		−	1863.96i		−	0.776326i	−0.921591	−	0.388163i	$-0.873110\pi$
$7$		−	1863.96i		−	0.776326i	0.921591	−	0.388163i	$-0.126890\pi$
$8$	810.276	−	4015.06i	0.197821	−	0.980238i
$9$	−11655.8			−1.77652
$10$		0			0
$11$		−	5278.32i		−	0.360516i	−0.983619	−	0.180258i	$-0.942307\pi$
$11$		−	5278.32i		−	0.360516i	0.983619	−	0.180258i	$-0.0576933\pi$
$12$	27373.0	+	21084.9i	1.32007	+	1.01683i
$13$	−33338.9			−1.16729			−0.583643	−	0.812010i	$-0.698373\pi$
$13$	−33338.9			−1.16729			−0.583643	+	0.812010i	$0.698373\pi$
$14$	−13165.7	−	26760.0i	−0.342714	−	0.696584i
$15$		0			0
$16$	−16726.8	−	63365.5i	−0.255230	−	0.966880i
$17$	−142617.			−1.70756			−0.853779	−	0.520636i	$-0.825695\pi$
$17$	−142617.			−1.70756			−0.853779	+	0.520636i	$0.825695\pi$
$18$	−167336.	+	82328.1i	−1.59404	+	0.784257i
$19$		−	70346.9i		−	0.539797i	−0.962889	−	0.269899i	$-0.913010\pi$
$19$		−	70346.9i		−	0.539797i	0.962889	−	0.269899i	$-0.0869902\pi$
$20$		0			0
$21$	251578.			1.29359
$22$	−37282.3	−	75778.3i	−0.159152	−	0.323485i
$23$			255957.i			0.914650i	0.889300	+	0.457325i	$0.151192\pi$
$23$			255957.i			0.914650i	−0.889300	+	0.457325i	$0.848808\pi$
$24$	541910.	+	109363.i	1.63336	+	0.329628i
$25$		0			0
$26$	−478630.	+	235482.i	−1.04739	+	0.515305i
$27$		−	687639.i		−	1.29391i
$28$	−378027.	−	291187.i	−0.615023	−	0.473740i
$29$	−534050.			−0.755075			−0.377537	−	0.925994i	$-0.623229\pi$
$29$	−534050.			−0.755075			−0.377537	+	0.925994i	$0.623229\pi$
$30$		0			0
$31$		−	1.24954e6i		−	1.35302i	−0.736433	−	0.676511i	$-0.763491\pi$
$31$		−	1.24954e6i		−	1.35302i	0.736433	−	0.676511i	$-0.236509\pi$
$32$	−687707.	−	791562.i	−0.655849	−	0.754892i
$33$	712412.			0.600725
$34$	−2.04748e6	+	1.00735e6i	−1.53216	+	0.753811i
$35$		0			0
$36$	−1.82086e6	+	2.36389e6i	−1.08409	+	1.40740i
$37$	−169861.			−0.0906332			−0.0453166	−	0.998973i	$-0.514430\pi$
$37$	−169861.			−0.0906332			−0.0453166	+	0.998973i	$0.514430\pi$
$38$	−496881.	−	1.00994e6i	−0.238297	−	0.484351i
$39$		−	4.49973e6i		−	1.94504i
$40$		0			0
$41$	2.36651e6			0.837479			0.418739	−	0.908106i	$-0.362472\pi$
$41$	2.36651e6			0.837479			0.418739	+	0.908106i	$0.362472\pi$
$42$	3.61178e6	−	1.77697e6i	1.16071	−	0.571061i
$43$		−	4.03853e6i		−	1.18127i	−0.806939	−	0.590635i	$-0.798877\pi$
$43$		−	4.03853e6i		−	1.18127i	0.806939	−	0.590635i	$-0.201123\pi$
$44$	−1.07049e6	−	824577.i	−0.285609	−	0.219999i
$45$		0			0
$46$	1.80790e6	+	3.67465e6i	0.403778	+	0.820700i
$47$		−	1.65928e6i		−	0.340038i	−0.985441	−	0.170019i	$-0.945617\pi$
$47$		−	1.65928e6i		−	0.340038i	0.985441	−	0.170019i	$-0.0543829\pi$
$48$	8.55241e6	−	2.25760e6i	1.61110	−	0.425288i
$49$	2.29046e6			0.397317
$50$		0			0
$51$		−	1.92489e7i		−	2.84529i
$52$	−5.20819e6	+	6.76141e6i	−0.712317	+	0.924749i
$53$	981179.			0.124350			0.0621748	−	0.998065i	$-0.480196\pi$
$53$	981179.			0.124350			0.0621748	+	0.998065i	$0.480196\pi$
$54$	−4.85699e6	−	9.87210e6i	−0.571206	−	1.16101i
$55$		0			0
$56$	−7.48390e6	−	1.51032e6i	−0.760985	−	0.153574i
$57$	9.49469e6			0.899459
$58$	−7.66710e6	+	3.77215e6i	−0.677516	+	0.333332i
$59$		−	7.47526e6i		−	0.616905i	−0.951240	−	0.308453i	$-0.900189\pi$
$59$		−	7.47526e6i		−	0.616905i	0.951240	−	0.308453i	$-0.0998111\pi$
$60$		0			0
$61$	−1.41028e7			−1.01856			−0.509280	−	0.860601i	$-0.670088\pi$
$61$	−1.41028e7			−1.01856			−0.509280	+	0.860601i	$0.670088\pi$
$62$	−8.82589e6	−	1.79391e7i	−0.597299	−	1.21404i
$63$			2.17259e7i			1.37916i
$64$	−1.54641e7	−	6.50660e6i	−0.921734	−	0.387824i
$65$		0			0
$66$	1.02278e7	−	5.03197e6i	0.539020	−	0.265193i
$67$			3.75634e7i			1.86409i	0.362347	+	0.932043i	$0.381976\pi$
$67$			3.75634e7i			1.86409i	−0.362347	+	0.932043i	$0.618024\pi$
$68$	−2.22796e7	+	2.89240e7i	−1.04201	+	1.35276i
$69$	−3.45463e7			−1.52407
$70$		0			0
$71$			3.57630e7i			1.40734i	0.710524	+	0.703672i	$0.248458\pi$
$71$			3.57630e7i			1.40734i	−0.710524	+	0.703672i	$0.751542\pi$
$72$	−9.44439e6	+	4.67986e7i	−0.351434	+	1.74142i
$73$	7.26944e6			0.255982			0.127991	−	0.991775i	$-0.459147\pi$
$73$	7.26944e6			0.255982			0.127991	+	0.991775i	$0.459147\pi$
$74$	−2.43862e6	+	1.19978e6i	−0.0813236	+	0.0400106i
$75$		0			0
$76$	−1.42670e7	−	1.09896e7i	−0.427639	−	0.329402i
$77$	−9.83857e6			−0.279878
$78$	−3.17829e7	−	6.46005e7i	−0.858648	−	1.74525i
$79$		−	3.72731e7i		−	0.956945i	−0.878102	−	0.478473i	$-0.841191\pi$
$79$		−	3.72731e7i		−	0.956945i	0.878102	−	0.478473i	$-0.158809\pi$
$80$		0			0
$81$	1.63368e7			0.379512
$82$	3.39749e7	−	1.67154e7i	0.751455	−	0.369710i
$83$			2.09461e7i			0.441357i	0.975347	+	0.220679i	$0.0708272\pi$
$83$			2.09461e7i			0.441357i	−0.975347	+	0.220679i	$0.929173\pi$
$84$	3.93014e7	−	5.10222e7i	0.789389	−	1.02481i
$85$		0			0
$86$	−2.85253e7	−	5.79792e7i	−0.521479	−	1.05993i
$87$		−	7.20805e7i		−	1.25817i
$88$	−2.11927e7	−	4.27689e6i	−0.353392	−	0.0713177i
$89$	−2.52812e7			−0.402938			−0.201469	−	0.979495i	$-0.564571\pi$
$89$	−2.52812e7			−0.402938			−0.201469	+	0.979495i	$0.564571\pi$
$90$		0			0
$91$			6.21423e7i			0.906195i
$92$	5.19102e7	+	3.99855e7i	0.724606	+	0.558150i
$93$	1.68650e8			2.25453
$94$	−1.17199e7	−	2.38214e7i	−0.150112	−	0.305110i
$95$		0			0
$96$	1.06837e8	−	9.28195e7i	1.25787	−	1.09283i
$97$	1.35709e6			0.0153293			0.00766465	−	0.999971i	$-0.497560\pi$
$97$	1.35709e6			0.0153293			0.00766465	+	0.999971i	$0.497560\pi$
$98$	3.28830e7	−	1.61782e7i	0.356506	−	0.175398i
$99$			6.15229e7i			0.640465i
$100$		0			0
$101$	−1.25091e8			−1.20210			−0.601052	−	0.799210i	$-0.705251\pi$
$101$	−1.25091e8			−1.20210			−0.601052	+	0.799210i	$0.705251\pi$
$102$	−1.35961e8	−	2.76348e8i	−1.25607	−	2.55303i
$103$		−	4.55443e7i		−	0.404655i	−0.979318	−	0.202327i	$-0.935149\pi$
$103$		−	4.55443e7i		−	0.404655i	0.979318	−	0.202327i	$-0.0648505\pi$
$104$	−2.70137e7	+	1.33857e8i	−0.230914	+	1.14422i
$105$		0			0
$106$	1.40863e7	−	6.93035e6i	0.111577	−	0.0548949i
$107$			1.11806e7i			0.0852959i	0.999090	+	0.0426480i	$0.0135794\pi$
$107$			1.11806e7i			0.0852959i	−0.999090	+	0.0426480i	$0.986421\pi$
$108$	−1.39459e8	−	1.07423e8i	−1.02507	−	0.789589i
$109$	3.48944e7			0.247201			0.123600	−	0.992332i	$-0.460556\pi$
$109$	3.48944e7			0.247201			0.123600	+	0.992332i	$0.460556\pi$
$110$		0			0
$111$		−	2.29261e7i		−	0.151021i
$112$	−1.18111e8	+	3.11780e7i	−0.750615	+	0.198142i
$113$	1.55089e8			0.951187			0.475594	−	0.879665i	$-0.342233\pi$
$113$	1.55089e8			0.951187			0.475594	+	0.879665i	$0.342233\pi$
$114$	1.36311e8	−	6.70638e7i	0.807069	−	0.397071i
$115$		0			0
$116$	−8.34292e7	+	1.08310e8i	−0.460772	+	0.598187i
$117$	3.88590e8			2.07371
$118$	−5.28000e7	−	1.07319e8i	−0.272336	−	0.553539i
$119$			2.65832e8i			1.32562i
$120$		0			0
$121$	1.86498e8			0.870028
$122$	−2.02467e8	+	9.96123e7i	−0.913936	+	0.449649i
$123$			3.19407e8i			1.39548i
$124$	−2.53418e8	−	1.95203e8i	−1.07189	−	0.825659i
$125$		0			0
$126$	1.53456e8	+	3.11908e8i	0.608839	+	1.23750i
$127$			2.11442e8i			0.812786i	0.913698	+	0.406393i	$0.133214\pi$
$127$			2.11442e8i			0.812786i	−0.913698	+	0.406393i	$0.866786\pi$
$128$	−2.67969e8	+	1.58154e7i	−0.998263	+	0.0589170i
$129$	5.45078e8			1.96834
$130$		0			0
$131$		−	1.14013e8i		−	0.387140i	−0.981086	−	0.193570i	$-0.937993\pi$
$131$		−	1.14013e8i		−	0.387140i	0.981086	−	0.193570i	$-0.0620067\pi$
$132$	1.11293e8	−	1.44483e8i	0.366582	−	0.475907i
$133$	−1.31124e8			−0.419059
$134$	2.65322e8	+	5.39281e8i	0.822912	+	1.67261i
$135$		0			0
$136$	−1.15559e8	+	5.72615e8i	−0.337791	+	1.67381i
$137$	−3.96731e8			−1.12620			−0.563098	−	0.826390i	$-0.690391\pi$
$137$	−3.96731e8			−1.12620			−0.563098	+	0.826390i	$0.690391\pi$
$138$	−4.95966e8	+	2.44011e8i	−1.36752	+	0.672811i
$139$		−	2.81838e8i		−	0.754988i	−0.926012	−	0.377494i	$-0.876786\pi$
$139$		−	2.81838e8i		−	0.754988i	0.926012	−	0.377494i	$-0.123214\pi$
$140$		0			0
$141$	2.23952e8			0.566601
$142$	2.52605e8	+	5.13433e8i	0.621281	+	1.26279i
$143$			1.75973e8i			0.420825i
$144$	1.94963e8	+	7.38573e8i	0.453423	+	1.71769i
$145$		0			0
$146$	1.04364e8	−	5.13462e7i	0.229688	−	0.113005i
$147$			3.09142e8i			0.662046i
$148$	−2.65357e7	+	3.44493e7i	−0.0553074	+	0.0718016i
$149$	−4.38854e8			−0.890379			−0.445190	−	0.895436i	$-0.646864\pi$
$149$	−4.38854e8			−0.890379			−0.445190	+	0.895436i	$0.646864\pi$
$150$		0			0
$151$		−	7.34766e8i		−	1.41332i	−0.707552	−	0.706662i	$-0.750200\pi$
$151$		−	7.34766e8i		−	1.41332i	0.707552	−	0.706662i	$-0.249800\pi$
$152$	−2.82447e8	−	5.70004e7i	−0.529130	−	0.106783i
$153$	1.66231e9			3.03352
$154$	−1.41248e8	+	6.94927e7i	−0.251130	+	0.123554i
$155$		0			0
$156$	−9.12584e8	−	7.02947e8i	−1.54090	−	1.18693i
$157$	3.92920e8			0.646704			0.323352	−	0.946279i	$-0.395190\pi$
$157$	3.92920e8			0.646704			0.323352	+	0.946279i	$0.395190\pi$
$158$	−2.63271e8	−	5.35112e8i	−0.422449	−	0.858651i
$159$			1.32429e8i			0.207203i
$160$		0			0
$161$	4.77093e8			0.710067
$162$	2.34539e8	−	1.15391e8i	0.340530	−	0.167538i
$163$			8.78730e8i			1.24482i	0.782693	+	0.622408i	$0.213845\pi$
$163$			8.78730e8i			1.24482i	−0.782693	+	0.622408i	$0.786155\pi$
$164$	3.69696e8	−	4.79950e8i	0.511057	−	0.663469i
$165$		0			0
$166$	1.47948e8	+	3.00713e8i	0.194840	+	0.396022i
$167$		−	4.28526e8i		−	0.550948i	−0.961308	−	0.275474i	$-0.911165\pi$
$167$		−	4.28526e8i		−	0.550948i	0.961308	−	0.275474i	$-0.0888349\pi$
$168$	2.03847e8	−	1.01010e9i	0.255899	−	1.26802i
$169$	2.95749e8			0.362557
$170$		0			0
$171$			8.19947e8i			0.958962i
$172$	−8.19049e8	−	6.30898e8i	−0.935828	−	0.720851i
$173$	3.08766e8			0.344703			0.172352	−	0.985035i	$-0.444863\pi$
$173$	3.08766e8			0.344703			0.172352	+	0.985035i	$0.444863\pi$
$174$	−5.09126e8	−	1.03483e9i	−0.555428	−	1.12894i
$175$		0			0
$176$	−3.34463e8	+	8.82892e7i	−0.348576	+	0.0920146i
$177$	1.00893e9			1.02794
$178$	−3.62950e8	+	1.78569e8i	−0.361549	+	0.177879i
$179$			2.34312e8i			0.228235i	0.993467	+	0.114117i	$0.0364040\pi$
$179$			2.34312e8i			0.228235i	−0.993467	+	0.114117i	$0.963596\pi$
$180$		0			0
$181$	−1.98225e8			−0.184691			−0.0923454	−	0.995727i	$-0.529436\pi$
$181$	−1.98225e8			−0.184691			−0.0923454	+	0.995727i	$0.529436\pi$
$182$	4.38929e8	+	8.92147e8i	0.400045	+	0.813113i
$183$		−	1.90345e9i		−	1.69722i
$184$	1.02768e9	+	2.07395e8i	0.896575	+	0.180937i
$185$		0			0
$186$	2.42123e9	−	1.19123e9i	2.02295	−	0.995274i
$187$			7.52778e8i			0.615602i
$188$	−3.36516e8	−	2.59212e8i	−0.269385	−	0.207502i
$189$	−1.28173e9			−1.00450
$190$		0			0
$191$			2.29845e9i			1.72704i	0.504317	+	0.863518i	$0.331744\pi$
$191$			2.29845e9i			1.72704i	−0.504317	+	0.863518i	$0.668256\pi$
$192$	8.78193e8	−	2.08719e9i	0.646227	−	1.53588i
$193$	−6.50744e8			−0.469009			−0.234505	−	0.972115i	$-0.575347\pi$
$193$	−6.50744e8			−0.469009			−0.234505	+	0.972115i	$0.575347\pi$
$194$	1.94831e7	−	9.58554e6i	0.0137547	−	0.00676721i
$195$		0			0
$196$	3.57814e8	−	4.64524e8i	0.242456	−	0.314763i
$197$	−1.18078e9			−0.783981			−0.391990	−	0.919969i	$-0.628213\pi$
$197$	−1.18078e9			−0.783981			−0.391990	+	0.919969i	$0.628213\pi$
$198$	4.34554e8	+	8.83255e8i	0.282737	+	0.574679i
$199$		−	8.61830e8i		−	0.549553i	−0.961508	−	0.274776i	$-0.911396\pi$
$199$		−	8.61830e8i		−	0.549553i	0.961508	−	0.274776i	$-0.0886038\pi$
$200$		0			0
$201$	−5.06992e9			−3.10611
$202$	−1.79588e9	+	8.83557e8i	−1.07863	+	0.530676i
$203$			9.95448e8i			0.586185i
$204$	−3.90385e9	−	3.00707e9i	−2.25410	−	1.73629i
$205$		0			0
$206$	−3.21693e8	−	6.53858e8i	−0.178637	−	0.363090i
$207$		−	2.98337e9i		−	1.62490i
$208$	5.57651e8	+	2.11253e9i	0.297927	+	1.12863i
$209$	−3.71313e8			−0.194606
$210$		0			0
$211$		−	1.94443e9i		−	0.980985i	−0.871445	−	0.490493i	$-0.836817\pi$
$211$		−	1.94443e9i		−	0.980985i	0.871445	−	0.490493i	$-0.163183\pi$
$212$	1.53280e8	−	1.98992e8i	0.0758823	−	0.0985125i
$213$	−4.82691e9			−2.34505
$214$	7.89716e7	+	1.60514e8i	0.0376544	+	0.0765346i
$215$		0			0
$216$	−2.76091e9	−	5.57177e8i	−1.26834	−	0.255964i
$217$	−2.32910e9			−1.05039
$218$	5.00962e8	−	2.46469e8i	0.221809	−	0.109128i
$219$			9.81153e8i			0.426541i
$220$		0			0
$221$	4.75469e9			1.99321
$222$	−1.61934e8	−	3.29139e8i	−0.0666692	−	0.135509i
$223$			5.65989e8i			0.228870i	0.993431	+	0.114435i	$0.0365058\pi$
$223$			5.65989e8i			0.228870i	−0.993431	+	0.114435i	$0.963494\pi$
$224$	−1.47544e9	+	1.28186e9i	−0.586043	+	0.509153i
$225$		0			0
$226$	2.22653e9	−	1.09544e9i	0.853484	−	0.419907i
$227$			2.24952e9i			0.847200i	0.905849	+	0.423600i	$0.139234\pi$
$227$			2.24952e9i			0.847200i	−0.905849	+	0.423600i	$0.860766\pi$
$228$	1.48326e9	−	1.92561e9i	0.548880	−	0.712571i
$229$	1.02108e9			0.371295			0.185648	−	0.982616i	$-0.440562\pi$
$229$	1.02108e9			0.371295			0.185648	+	0.982616i	$0.440562\pi$
$230$		0			0
$231$		−	1.32791e9i		−	0.466358i
$232$	−4.32728e8	+	2.14424e9i	−0.149370	+	0.740153i
$233$	1.60926e9			0.546013			0.273007	−	0.962012i	$-0.411982\pi$
$233$	1.60926e9			0.546013			0.273007	+	0.962012i	$0.411982\pi$
$234$	5.57880e9	−	2.74473e9i	1.86071	−	0.915452i
$235$		0			0
$236$	−1.51605e9	−	1.16778e9i	−0.488726	−	0.376456i
$237$	5.03073e9			1.59455
$238$	1.87765e9	+	3.81643e9i	0.585204	+	1.18946i
$239$		−	6.14150e9i		−	1.88227i	−0.338027	−	0.941136i	$-0.609760\pi$
$239$		−	6.14150e9i		−	1.88227i	0.338027	−	0.941136i	$-0.390240\pi$
$240$		0			0
$241$	−1.57617e9			−0.467234			−0.233617	−	0.972329i	$-0.575056\pi$
$241$	−1.57617e9			−0.467234			−0.233617	+	0.972329i	$0.575056\pi$
$242$	2.67747e9	−	1.31729e9i	0.780661	−	0.384079i
$243$		−	2.30663e9i		−	0.661536i
$244$	−2.20314e9	+	2.86017e9i	−0.621559	+	0.806925i
$245$		0			0
$246$	2.25607e9	+	4.58558e9i	0.616044	+	1.25214i
$247$			2.34528e9i			0.630098i
$248$	−5.01699e9	−	1.01247e9i	−1.32628	−	0.267656i
$249$	−2.82708e9			−0.735429
$250$		0			0
$251$		−	6.05238e8i		−	0.152486i	−0.997089	−	0.0762432i	$-0.975707\pi$
$251$		−	6.05238e8i		−	0.152486i	0.997089	−	0.0762432i	$-0.0242925\pi$
$252$	4.40620e9	+	3.39401e9i	1.09260	+	0.841611i
$253$	1.35102e9			0.329746
$254$	1.49348e9	+	3.03557e9i	0.358809	+	0.729299i
$255$		0			0
$256$	−3.73540e9	+	2.11980e9i	−0.869715	+	0.493554i
$257$	−7.33383e9			−1.68112			−0.840559	−	0.541720i	$-0.817773\pi$
$257$	−7.33383e9			−1.68112			−0.840559	+	0.541720i	$0.817773\pi$
$258$	7.82543e9	−	3.85005e9i	1.76616	−	0.868935i
$259$			3.16614e8i			0.0703609i
$260$		0			0
$261$	6.22476e9			1.34141
$262$	−8.05305e8	−	1.63683e9i	−0.170905	−	0.347374i
$263$		−	8.11216e9i		−	1.69556i	−0.530348	−	0.847780i	$-0.677939\pi$
$263$		−	8.11216e9i		−	1.69556i	0.530348	−	0.847780i	$-0.322061\pi$
$264$	5.77250e8	−	2.86037e9i	0.118836	−	0.588853i
$265$		0			0
$266$	−1.88248e9	+	9.26166e8i	−0.376014	+	0.184996i
$267$		−	3.41219e9i		−	0.671411i
$268$	7.61819e9	+	5.86815e9i	1.47677	+	1.13753i
$269$	−1.31912e9			−0.251927			−0.125964	−	0.992035i	$-0.540202\pi$
$269$	−1.31912e9			−0.251927			−0.125964	+	0.992035i	$0.540202\pi$
$270$		0			0
$271$		−	3.01624e9i		−	0.559228i	−0.960113	−	0.279614i	$-0.909794\pi$
$271$		−	3.01624e9i		−	0.559228i	0.960113	−	0.279614i	$-0.0902064\pi$
$272$	2.38552e9	+	9.03699e9i	0.435821	+	1.65100i
$273$	−8.38731e9			−1.50998
$274$	−5.69568e9	+	2.80223e9i	−1.01052	+	0.497166i
$275$		0			0
$276$	−5.39682e9	+	7.00630e9i	−0.930040	+	1.20740i
$277$	−1.19710e9			−0.203334			−0.101667	−	0.994818i	$-0.532418\pi$
$277$	−1.19710e9			−0.203334			−0.101667	+	0.994818i	$0.532418\pi$
$278$	−1.99070e9	−	4.04621e9i	−0.333294	−	0.677438i
$279$			1.45644e10i			2.40367i
$280$		0			0
$281$	2.05582e9			0.329732			0.164866	−	0.986316i	$-0.447281\pi$
$281$	2.05582e9			0.329732			0.164866	+	0.986316i	$0.447281\pi$
$282$	3.21517e9	−	1.58184e9i	0.508402	−	0.250130i
$283$			1.21382e10i			1.89238i	0.323616	+	0.946189i	$0.395102\pi$
$283$			1.21382e10i			1.89238i	−0.323616	+	0.946189i	$0.604898\pi$
$284$	7.25305e9	+	5.58689e9i	1.11493	+	0.858809i
$285$		0			0
$286$	1.24295e9	+	2.52636e9i	0.185776	+	0.377600i
$287$		−	4.41109e9i		−	0.650157i
$288$	8.01576e9	+	9.22626e9i	1.16513	+	1.34108i
$289$	1.33638e10			1.91575
$290$		0			0
$291$			1.83166e8i			0.0255431i
$292$	1.13563e9	−	1.47431e9i	0.156209	−	0.202795i
$293$	−8.85830e9			−1.20193			−0.600966	−	0.799275i	$-0.705217\pi$
$293$	−8.85830e9			−1.20193			−0.600966	+	0.799275i	$0.705217\pi$
$294$	2.18356e9	+	4.43820e9i	0.292264	+	0.594043i
$295$		0			0
$296$	−1.37634e8	+	6.82002e8i	−0.0179292	+	0.0888421i
$297$	−3.62958e9			−0.466477
$298$	−6.30042e9	+	3.09975e9i	−0.798922	+	0.393063i
$299$		−	8.53330e9i		−	1.06766i
$300$		0			0
$301$	−7.52765e9			−0.917051
$302$	−5.18987e9	−	1.05487e10i	−0.623920	−	1.26815i
$303$		−	1.68835e10i		−	2.00305i
$304$	−4.45756e9	+	1.17668e9i	−0.521919	+	0.137773i
$305$		0			0
$306$	2.38650e10	−	1.17414e10i	2.72192	−	1.33916i
$307$			2.27115e9i			0.255678i	0.991795	+	0.127839i	$0.0408040\pi$
$307$			2.27115e9i			0.255678i	−0.991795	+	0.127839i	$0.959196\pi$
$308$	−1.53698e9	+	1.99535e9i	−0.170791	+	0.221726i
$309$	6.14709e9			0.674273
$310$		0			0
$311$		−	9.95031e8i		−	0.106364i	−0.998585	−	0.0531820i	$-0.983064\pi$
$311$		−	9.95031e8i		−	0.106364i	0.998585	−	0.0531820i	$-0.0169364\pi$
$312$	−1.80667e10	−	3.64602e9i	−1.90660	−	0.384770i
$313$	−9.67741e9			−1.00828			−0.504141	−	0.863621i	$-0.668191\pi$
$313$	−9.67741e9			−1.00828			−0.504141	+	0.863621i	$0.668191\pi$
$314$	5.64096e9	−	2.77531e9i	0.580276	−	0.285491i
$315$		0			0
$316$	−7.55931e9	−	5.82279e9i	−0.758113	−	0.583960i
$317$	5.41589e9			0.536330			0.268165	−	0.963373i	$-0.413583\pi$
$317$	5.41589e9			0.536330			0.268165	+	0.963373i	$0.413583\pi$
$318$	9.35386e8	+	1.90122e9i	0.0914708	+	0.185919i
$319$			2.81889e9i			0.272217i
$320$		0			0
$321$	−1.50903e9			−0.142128
$322$	6.84940e9	−	3.36985e9i	0.637131	−	0.313463i
$323$			1.00327e10i			0.921735i
$324$	2.55212e9	−	3.31324e9i	0.231591	−	0.300658i
$325$		0			0
$326$	6.20673e9	+	1.26155e10i	0.549531	+	1.11695i
$327$			4.70968e9i			0.411908i
$328$	1.91753e9	−	9.50169e9i	0.165671	−	0.820928i
$329$	−3.09282e9			−0.263980
$330$		0			0
$331$			1.61383e10i			1.34445i	0.740345	+	0.672227i	$0.234662\pi$
$331$			1.61383e10i			1.34445i	−0.740345	+	0.672227i	$0.765338\pi$
$332$	4.24805e9	+	3.27219e9i	0.349653	+	0.269331i
$333$	1.97986e9			0.161012
$334$	−3.02680e9	−	6.15214e9i	−0.243219	−	0.494357i
$335$		0			0
$336$	−4.20808e9	−	1.59413e10i	−0.330162	−	1.25074i
$337$	1.60080e10			1.24113			0.620566	−	0.784154i	$-0.286903\pi$
$337$	1.60080e10			1.24113			0.620566	+	0.784154i	$0.286903\pi$
$338$	4.24592e9	−	2.08896e9i	0.325316	−	0.160053i
$339$			2.09322e10i			1.58495i
$340$		0			0
$341$	−6.59549e9			−0.487786
$342$	5.79153e9	+	1.17716e10i	0.423339	+	0.860460i
$343$		−	1.50147e10i		−	1.08477i
$344$	−1.62149e10	−	3.27232e9i	−1.15793	−	0.233680i
$345$		0			0
$346$	4.43281e9	−	2.18091e9i	0.309297	−	0.152171i
$347$		−	1.34569e10i		−	0.928168i	−0.885791	−	0.464084i	$-0.846384\pi$
$347$		−	1.34569e10i		−	0.928168i	0.885791	−	0.464084i	$-0.153616\pi$
$348$	−1.46186e10	−	1.12604e10i	−0.996753	−	0.767780i
$349$	−1.78901e10			−1.20590			−0.602951	−	0.797779i	$-0.706008\pi$
$349$	−1.78901e10			−1.20590			−0.602951	+	0.797779i	$0.706008\pi$
$350$		0			0
$351$			2.29251e10i			1.51037i
$352$	−4.17812e9	+	3.62994e9i	−0.272151	+	0.236444i
$353$	2.70557e10			1.74245			0.871224	−	0.490886i	$-0.163327\pi$
$353$	2.70557e10			1.74245			0.871224	+	0.490886i	$0.163327\pi$
$354$	1.44848e10	−	7.12639e9i	0.922356	−	0.453792i
$355$		0			0
$356$	−3.94942e9	+	5.12725e9i	−0.245886	+	0.319216i
$357$	−3.58793e10			−2.20887
$358$	1.65501e9	+	3.36390e9i	0.100756	+	0.204791i
$359$		−	5.50402e9i		−	0.331361i	−0.986179	−	0.165681i	$-0.947018\pi$
$359$		−	5.50402e9i		−	0.331361i	0.986179	−	0.165681i	$-0.0529821\pi$
$360$		0			0
$361$	1.20349e10			0.708619
$362$	−2.84583e9	+	1.40012e9i	−0.165720	+	0.0815328i
$363$			2.51716e10i			1.44972i
$364$	1.26030e10	+	9.70785e9i	0.717907	+	0.552991i
$365$		0			0
$366$	−1.34446e10	−	2.73269e10i	−0.749246	−	1.52288i
$367$		−	9.67406e9i		−	0.533267i	−0.963798	−	0.266633i	$-0.914089\pi$
$367$		−	9.67406e9i		−	0.533267i	0.963798	−	0.266633i	$-0.0859112\pi$
$368$	1.62188e10	−	4.28133e9i	0.884357	−	0.233446i
$369$	−2.75835e10			−1.48780
$370$		0			0
$371$		−	1.82888e9i		−	0.0965359i
$372$	2.63465e10	−	3.42038e10i	1.37579	−	1.78608i
$373$	2.57338e10			1.32944			0.664720	−	0.747093i	$-0.268551\pi$
$373$	2.57338e10			1.32944			0.664720	+	0.747093i	$0.268551\pi$
$374$	5.31709e9	+	1.08073e10i	0.271761	+	0.552369i
$375$		0			0
$376$	−6.66208e9	−	1.34447e9i	−0.333318	−	0.0672667i
$377$	1.78046e10			0.881388
$378$	−1.84012e10	+	9.05324e9i	−0.901320	+	0.443442i
$379$		−	3.39099e10i		−	1.64350i	−0.569849	−	0.821749i	$-0.692998\pi$
$379$		−	3.39099e10i		−	1.64350i	0.569849	−	0.821749i	$-0.307002\pi$
$380$		0			0
$381$	−2.85382e10			−1.35434
$382$	1.62346e10	+	3.29978e10i	0.762411	+	1.54964i
$383$		−	1.07466e10i		−	0.499433i	−0.968319	−	0.249717i	$-0.919663\pi$
$383$		−	1.07466e10i		−	0.499433i	0.968319	−	0.249717i	$-0.0803375\pi$
$384$	−2.13460e9	−	3.61677e10i	−0.0981729	−	1.66340i
$385$		0			0
$386$	−9.34243e9	+	4.59640e9i	−0.420834	+	0.207047i
$387$			4.70722e10i			2.09855i
$388$	2.12005e8	−	2.75230e8i	0.00935446	−	0.0121442i
$389$	4.17407e10			1.82289			0.911446	−	0.411419i	$-0.134967\pi$
$389$	4.17407e10			1.82289			0.911446	+	0.411419i	$0.134967\pi$
$390$		0			0
$391$		−	3.65038e10i		−	1.56182i
$392$	1.85590e9	−	9.19630e9i	0.0785978	−	0.389466i
$393$	1.53882e10			0.645088
$394$	−1.69520e10	+	8.34022e9i	−0.703453	+	0.346093i
$395$		0			0
$396$	1.24774e10	+	9.61109e9i	0.507391	+	0.390833i
$397$	1.28145e10			0.515871			0.257936	−	0.966162i	$-0.416958\pi$
$397$	1.28145e10			0.515871			0.257936	+	0.966162i	$0.416958\pi$
$398$	−6.08736e9	−	1.23729e10i	−0.242603	−	0.493104i
$399$		−	1.76977e10i		−	0.698274i
$400$		0			0
$401$	4.75527e10			1.83907			0.919533	−	0.393013i	$-0.128567\pi$
$401$	4.75527e10			1.83907			0.919533	+	0.393013i	$0.128567\pi$
$402$	−7.27864e10	+	3.58103e10i	−2.78706	+	1.37121i
$403$			4.16584e10i			1.57936i
$404$	−1.95417e10	+	2.53696e10i	−0.733564	+	0.952332i
$405$		0			0
$406$	7.03114e9	+	1.42912e10i	0.258775	+	0.525973i
$407$			8.96581e8i			0.0326747i
$408$	−7.72856e10	−	1.55969e10i	−2.78906	−	0.562858i
$409$	−2.44716e10			−0.874518			−0.437259	−	0.899336i	$-0.644051\pi$
$409$	−2.44716e10			−0.874518			−0.437259	+	0.899336i	$0.644051\pi$
$410$		0			0
$411$		−	5.35466e10i		−	1.87657i
$412$	−9.23678e9	−	7.11492e9i	−0.320576	−	0.246934i
$413$	−1.39336e10			−0.478920
$414$	−2.10724e10	−	4.28309e10i	−0.717321	−	1.45799i
$415$		0			0
$416$	2.29274e10	+	2.63898e10i	0.765563	+	0.881175i
$417$	3.80395e10			1.25803
$418$	−5.33077e9	+	2.62269e9i	−0.174616	+	0.0859098i
$419$		−	3.99144e9i		−	0.129501i	−0.997901	−	0.0647505i	$-0.979375\pi$
$419$		−	3.99144e9i		−	0.129501i	0.997901	−	0.0647505i	$-0.0206252\pi$
$420$		0			0
$421$	−8.14500e9			−0.259276			−0.129638	−	0.991561i	$-0.541382\pi$
$421$	−8.14500e9			−0.259276			−0.129638	+	0.991561i	$0.541382\pi$
$422$	−1.37341e10	−	2.79153e10i	−0.433062	−	0.880222i
$423$			1.93401e10i			0.604085i
$424$	7.95025e8	−	3.93949e9i	0.0245990	−	0.121892i
$425$		0			0
$426$	−6.92977e10	+	3.40939e10i	−2.10417	+	1.03523i
$427$			2.62871e10i			0.790734i
$428$	2.26752e9	+	1.74662e9i	0.0675733	+	0.0520504i
$429$	−2.37510e10			−0.701217
$430$		0			0
$431$		−	4.14023e9i		−	0.119982i	−0.998199	−	0.0599909i	$-0.980893\pi$
$431$		−	4.14023e9i		−	0.119982i	0.998199	−	0.0599909i	$-0.0191072\pi$
$432$	−4.35725e10	+	1.15020e10i	−1.25106	+	0.330246i
$433$	−2.45166e10			−0.697443			−0.348722	−	0.937226i	$-0.613384\pi$
$433$	−2.45166e10			−0.697443			−0.348722	+	0.937226i	$0.613384\pi$
$434$	−3.34378e10	+	1.64511e10i	−0.942494	+	0.463699i
$435$		0			0
$436$	5.45119e9	−	7.07689e9i	0.150850	−	0.195838i
$437$	1.80058e10			0.493726
$438$	6.93017e9	+	1.40860e10i	0.188299	+	0.382728i
$439$		−	5.66902e10i		−	1.52633i	−0.646201	−	0.763167i	$-0.723643\pi$
$439$		−	5.66902e10i		−	1.52633i	0.646201	−	0.763167i	$-0.276357\pi$
$440$		0			0
$441$	−2.66970e10			−0.705843
$442$	6.82608e10	−	3.35837e10i	1.78847	−	0.879914i
$443$		−	2.12919e10i		−	0.552840i	−0.961037	−	0.276420i	$-0.910852\pi$
$443$		−	2.12919e10i		−	0.552840i	0.961037	−	0.276420i	$-0.0891481\pi$
$444$	−4.64961e9	−	3.58151e9i	−0.119642	−	0.0921582i
$445$		0			0
$446$	3.99775e9	+	8.12564e9i	0.101036	+	0.205361i
$447$		−	5.92319e10i		−	1.48363i
$448$	−1.21280e10	+	2.88245e10i	−0.301078	+	0.715566i
$449$	5.16478e10			1.27077			0.635384	−	0.772196i	$-0.280842\pi$
$449$	5.16478e10			1.27077			0.635384	+	0.772196i	$0.280842\pi$
$450$		0			0
$451$		−	1.24912e10i		−	0.301925i
$452$	2.42279e10	−	3.14533e10i	0.580446	−	0.753551i
$453$	9.91711e10			2.35501
$454$	1.58890e10	+	3.22953e10i	0.374001	+	0.760178i
$455$		0			0
$456$	7.69331e9	−	3.81217e10i	0.177932	−	0.881684i
$457$	−6.18862e10			−1.41883			−0.709413	−	0.704793i	$-0.751040\pi$
$457$	−6.18862e10			−1.41883			−0.709413	+	0.704793i	$0.751040\pi$
$458$	1.46592e10	−	7.21221e9i	0.333157	−	0.163910i
$459$			9.80689e10i			2.20943i
$460$		0			0
$461$	1.84997e9			0.0409601			0.0204800	−	0.999790i	$-0.493481\pi$
$461$	1.84997e9			0.0409601			0.0204800	+	0.999790i	$0.493481\pi$
$462$	−9.37940e9	−	1.90641e10i	−0.205877	−	0.418455i
$463$		−	4.89801e10i		−	1.06585i	−0.846163	−	0.532924i	$-0.821093\pi$
$463$		−	4.89801e10i		−	1.06585i	0.846163	−	0.532924i	$-0.178907\pi$
$464$	8.93293e9	+	3.38403e10i	0.192718	+	0.730067i
$465$		0			0
$466$	2.31034e10	−	1.13667e10i	0.489928	−	0.241041i
$467$		−	2.58985e9i		−	0.0544511i	−0.999629	−	0.0272255i	$-0.991333\pi$
$467$		−	2.58985e9i		−	0.0544511i	0.999629	−	0.0272255i	$-0.00866723\pi$
$468$	6.07054e10	−	7.88095e10i	1.26545	−	1.64284i
$469$	7.00167e10			1.44714
$470$		0			0
$471$			5.30322e10i			1.07760i
$472$	−3.00136e10	−	6.05702e9i	−0.604714	−	0.122037i
$473$	−2.13166e10			−0.425867
$474$	7.22238e10	−	3.55335e10i	1.43076	−	0.703923i
$475$		0			0
$476$	5.39131e10	+	4.15283e10i	1.05019	+	0.808939i
$477$	−1.14364e10			−0.220910
$478$	−4.33792e10	−	8.81705e10i	−0.830940	−	1.68893i
$479$			7.24642e10i			1.37652i	0.725466	+	0.688258i	$0.241624\pi$
$479$			7.24642e10i			1.37652i	−0.725466	+	0.688258i	$0.758376\pi$
$480$		0			0
$481$	5.66298e9			0.105795
$482$	−2.26283e10	+	1.11329e10i	−0.419241	+	0.206263i
$483$			6.43930e10i			1.18318i
$484$	2.91347e10	−	3.78235e10i	0.530920	−	0.689255i
$485$		0			0
$486$	−1.62924e10	−	3.31153e10i	−0.292039	−	0.593585i
$487$		−	6.78628e10i		−	1.20647i	−0.797564	−	0.603234i	$-0.793879\pi$
$487$		−	6.78628e10i		−	1.20647i	0.797564	−	0.603234i	$-0.206121\pi$
$488$	−1.14272e10	+	5.66235e10i	−0.201493	+	0.998430i
$489$	−1.18602e11			−2.07422
$490$		0			0
$491$			1.04720e11i			1.80179i	0.434032	+	0.900897i	$0.357090\pi$
$491$			1.04720e11i			1.80179i	−0.434032	+	0.900897i	$0.642910\pi$
$492$	6.47786e10	+	4.98977e10i	1.10553	+	0.851570i
$493$	7.61646e10			1.28933
$494$	1.65654e10	+	3.36701e10i	0.278160	+	0.565376i
$495$		0			0
$496$	−7.91779e10	+	2.09008e10i	−1.30821	+	0.345332i
$497$	6.66608e10			1.09256
$498$	−4.05871e10	+	1.99685e10i	−0.659888	+	0.324659i
$499$		−	5.70756e10i		−	0.920552i	−0.887776	−	0.460276i	$-0.847750\pi$
$499$		−	5.70756e10i		−	0.920552i	0.887776	−	0.460276i	$-0.152250\pi$
$500$		0			0
$501$	5.78379e10			0.918040
$502$	−4.27497e9	−	8.68911e9i	−0.0673160	−	0.136823i
$503$		−	1.65834e10i		−	0.259061i	−0.991575	−	0.129531i	$-0.958653\pi$
$503$		−	1.65834e10i		−	0.259061i	0.991575	−	0.129531i	$-0.0413471\pi$
$504$	8.72306e10	+	1.76040e10i	1.35191	+	0.272827i
$505$		0			0
$506$	1.93960e10	−	9.54265e9i	0.295876	−	0.145568i
$507$			3.99171e10i			0.604125i
$508$	4.28823e10	+	3.30314e10i	0.643907	+	0.495989i
$509$	−3.82746e9			−0.0570216			−0.0285108	−	0.999593i	$-0.509076\pi$
$509$	−3.82746e9			−0.0570216			−0.0285108	+	0.999593i	$0.509076\pi$
$510$		0			0
$511$		−	1.35499e10i		−	0.198726i
$512$	−3.86546e10	+	5.68172e10i	−0.562498	+	0.826799i
$513$	−4.83732e10			−0.698451
$514$	−1.05288e11	+	5.18010e10i	−1.50844	+	0.742140i
$515$		0			0
$516$	8.51520e10	−	1.10547e11i	1.20115	−	1.55936i
$517$	−8.75818e9			−0.122589
$518$	2.23634e9	+	4.54548e9i	0.0310613	+	0.0631337i
$519$			4.16740e10i			0.574376i
$520$		0			0
$521$	−7.15272e10			−0.970779			−0.485389	−	0.874298i	$-0.661322\pi$
$521$	−7.15272e10			−0.970779			−0.485389	+	0.874298i	$0.661322\pi$
$522$	8.93660e10	−	4.39673e10i	1.20362	−	0.592172i
$523$		−	2.30293e10i		−	0.307803i	−0.988086	−	0.153902i	$-0.950816\pi$
$523$		−	2.30293e10i		−	0.307803i	0.988086	−	0.153902i	$-0.0491839\pi$
$524$	−2.31228e10	−	1.78110e10i	−0.306701	−	0.236246i
$525$		0			0
$526$	−5.72985e10	−	1.16462e11i	−0.748515	−	1.52140i
$527$			1.78206e11i			2.31036i
$528$	−1.19164e10	−	4.51423e10i	−0.153323	−	0.580829i
$529$	1.27972e10			0.163415
$530$		0			0
$531$			8.71300e10i			1.09595i
$532$	−2.04841e10	+	2.65930e10i	−0.255724	+	0.331987i
$533$	−7.88969e10			−0.977577
$534$	−2.41013e10	−	4.89872e10i	−0.296398	−	0.602446i
$535$		0			0
$536$	1.50819e11	+	3.04367e10i	1.82725	+	0.368756i
$537$	−3.16250e10			−0.380306
$538$	−1.89380e10	+	9.31733e9i	−0.226050	+	0.111215i
$539$		−	1.20897e10i		−	0.143239i
$540$		0			0
$541$	5.52906e10			0.645450			0.322725	−	0.946493i	$-0.395401\pi$
$541$	5.52906e10			0.645450			0.322725	+	0.946493i	$0.395401\pi$
$542$	−2.13046e10	−	4.33027e10i	−0.246874	−	0.501786i
$543$		−	2.67544e10i		−	0.307748i
$544$	9.80787e10	+	1.12890e11i	1.11990	+	1.28902i
$545$		0			0
$546$	−1.20413e11	+	5.92421e10i	−1.35488	+	0.666591i
$547$		−	8.25380e10i		−	0.921945i	−0.887415	−	0.460972i	$-0.847501\pi$
$547$		−	8.25380e10i		−	0.921945i	0.887415	−	0.460972i	$-0.152499\pi$
$548$	−6.19772e10	+	8.04605e10i	−0.687242	+	0.892196i
$549$	1.64379e11			1.80949
$550$		0			0
$551$			3.75688e10i			0.407587i
$552$	−2.79921e10	+	1.38705e11i	−0.301494	+	1.49395i
$553$	−6.94755e10			−0.742902
$554$	−1.71862e10	+	8.45545e9i	−0.182448	+	0.0897631i
$555$		0			0
$556$	−5.71592e10	−	4.40286e10i	−0.598118	−	0.460719i
$557$	−6.76291e10			−0.702608			−0.351304	−	0.936261i	$-0.614262\pi$
$557$	−6.76291e10			−0.702608			−0.351304	+	0.936261i	$0.614262\pi$
$558$	1.02873e11	+	2.09094e11i	1.06112	+	2.15678i
$559$			1.34640e11i			1.37888i
$560$		0			0
$561$	−1.01602e11			−1.02577
$562$	2.95145e10	−	1.45209e10i	0.295863	−	0.145562i
$563$			1.16824e11i			1.16278i	0.813624	+	0.581391i	$0.197491\pi$
$563$			1.16824e11i			1.16278i	−0.813624	+	0.581391i	$0.802509\pi$
$564$	3.49857e10	−	4.54193e10i	0.345759	−	0.448874i
$565$		0			0
$566$	8.57355e10	+	1.74262e11i	0.835401	+	1.69800i
$567$		−	3.04510e10i		−	0.294625i
$568$	1.43590e11	+	2.89779e10i	1.37953	+	0.278403i
$569$	1.83290e9			0.0174860			0.00874298	−	0.999962i	$-0.497217\pi$
$569$	1.83290e9			0.0174860			0.00874298	+	0.999962i	$0.497217\pi$
$570$		0			0
$571$		−	1.83754e11i		−	1.72859i	−0.502984	−	0.864296i	$-0.667765\pi$
$571$		−	1.83754e11i		−	1.72859i	0.502984	−	0.864296i	$-0.332235\pi$
$572$	3.56889e10	+	2.74905e10i	0.333387	+	0.256802i
$573$	−3.10221e11			−2.87774
$574$	−3.11568e10	−	6.33279e10i	−0.287016	−	0.583375i
$575$		0			0
$576$	1.80246e11	+	7.58395e10i	1.63748	+	0.688978i
$577$	−1.07447e11			−0.969374			−0.484687	−	0.874688i	$-0.661066\pi$
$577$	−1.07447e11			−0.969374			−0.484687	+	0.874688i	$0.661066\pi$
$578$	1.91858e11	−	9.43927e10i	1.71897	−	0.845721i
$579$		−	8.78307e10i		−	0.781505i
$580$		0			0
$581$	3.90426e10			0.342637
$582$	1.29376e9	+	2.62963e9i	0.0112761	+	0.0229194i
$583$		−	5.17897e9i		−	0.0448301i
$584$	5.89025e9	−	2.91872e10i	0.0506387	−	0.250923i
$585$		0			0
$586$	−1.27174e11	+	6.25688e10i	−1.07847	+	0.530600i
$587$		−	8.33835e10i		−	0.702308i	−0.936318	−	0.351154i	$-0.885789\pi$
$587$		−	8.33835e10i		−	0.702308i	0.936318	−	0.351154i	$-0.114211\pi$
$588$	6.26966e10	+	4.82940e10i	0.524487	+	0.404003i
$589$	−8.79015e10			−0.730357
$590$		0			0
$591$		−	1.59370e11i		−	1.30634i
$592$	2.84123e9	+	1.07633e10i	0.0231323	+	0.0876315i
$593$	8.33128e10			0.673741			0.336871	−	0.941551i	$-0.390631\pi$
$593$	8.33128e10			0.673741			0.336871	+	0.941551i	$0.390631\pi$
$594$	−5.21081e10	+	2.56368e10i	−0.418562	+	0.205929i
$595$		0			0
$596$	−6.85577e10	+	8.90034e10i	−0.543339	+	0.705378i
$597$	1.16321e11			0.915714
$598$	−6.02732e10	−	1.22509e11i	−0.471324	−	0.957992i
$599$		−	7.46618e10i		−	0.579951i	−0.957034	−	0.289976i	$-0.906353\pi$
$599$		−	7.46618e10i		−	0.579951i	0.957034	−	0.289976i	$-0.0936472\pi$
$600$		0			0
$601$	−1.14915e11			−0.880803			−0.440401	−	0.897801i	$-0.645164\pi$
$601$	−1.14915e11			−0.880803			−0.440401	+	0.897801i	$0.645164\pi$
$602$	−1.08071e11	+	5.31700e10i	−0.822855	+	0.404838i
$603$		−	4.37831e11i		−	3.31159i
$604$	−1.49017e11	−	1.14785e11i	−1.11967	−	0.862457i
$605$		0			0
$606$	−1.19253e11	−	2.42389e11i	−0.884259	−	1.79731i
$607$			3.63432e10i			0.267712i	0.991001	+	0.133856i	$0.0427360\pi$
$607$			3.63432e10i			0.267712i	−0.991001	+	0.133856i	$0.957264\pi$
$608$	−5.56839e10	+	4.83781e10i	−0.407489	+	0.354025i
$609$	−1.34355e11			−0.976754
$610$		0			0
$611$			5.53183e10i			0.396921i
$612$	2.59686e11	−	3.37131e11i	1.85115	−	2.40322i
$613$	−4.54903e10			−0.322164			−0.161082	−	0.986941i	$-0.551498\pi$
$613$	−4.54903e10			−0.322164			−0.161082	+	0.986941i	$0.551498\pi$
$614$	1.60418e10	+	3.26059e10i	0.112870	+	0.229415i
$615$		0			0
$616$	−7.97195e9	+	3.95024e10i	−0.0553658	+	0.274347i
$617$	9.39914e10			0.648556			0.324278	−	0.945962i	$-0.394879\pi$
$617$	9.39914e10			0.648556			0.324278	+	0.945962i	$0.394879\pi$
$618$	8.82508e10	−	4.34187e10i	0.605013	−	0.297662i
$619$		−	6.86980e10i		−	0.467931i	−0.972245	−	0.233965i	$-0.924830\pi$
$619$		−	6.86980e10i		−	0.467931i	0.972245	−	0.233965i	$-0.0751702\pi$
$620$		0			0
$621$	1.76006e11			1.18348
$622$	−7.02820e9	−	1.42852e10i	−0.0469550	−	0.0954387i
$623$			4.71232e10i			0.312811i
$624$	−2.85127e11	+	7.52659e10i	−1.88062	+	0.496432i
$625$		0			0
$626$	−1.38934e11	+	6.83544e10i	−0.904714	+	0.445112i
$627$		−	5.01160e10i		−	0.324269i
$628$	6.13818e10	−	7.96876e10i	0.394640	−	0.512333i
$629$	2.42251e10			0.154761
$630$		0			0
$631$		−	3.95536e10i		−	0.249499i	−0.992188	−	0.124750i	$-0.960187\pi$
$631$		−	3.95536e10i		−	0.249499i	0.992188	−	0.124750i	$-0.0398128\pi$
$632$	−1.49654e11	−	3.02015e10i	−0.938034	−	0.189304i
$633$	2.62439e11			1.63461
$634$	7.77533e10	−	3.82540e10i	0.481240	−	0.236766i
$635$		0			0
$636$	2.68578e10	+	2.06881e10i	0.164150	+	0.126442i
$637$	−7.63612e10			−0.463783
$638$	1.99106e10	+	4.04694e10i	0.120172	+	0.244255i
$639$		−	4.16845e11i		−	2.50018i
$640$		0			0
$641$	3.16726e11			1.87608			0.938040	−	0.346526i	$-0.112639\pi$
$641$	3.16726e11			1.87608			0.938040	+	0.346526i	$0.112639\pi$
$642$	−2.16645e10	+	1.06588e10i	−0.127529	+	0.0627432i
$643$		−	2.41563e11i		−	1.41315i	−0.707640	−	0.706574i	$-0.750240\pi$
$643$		−	2.41563e11i		−	1.41315i	0.707640	−	0.706574i	$-0.249760\pi$
$644$	7.45313e10	−	9.67586e10i	0.433307	−	0.562531i
$645$		0			0
$646$	7.08636e10	+	1.44034e11i	0.406905	+	0.827057i
$647$		−	1.42487e11i		−	0.813124i	−0.913623	−	0.406562i	$-0.866728\pi$
$647$		−	1.42487e11i		−	0.813124i	0.913623	−	0.406562i	$-0.133272\pi$
$648$	1.32373e10	−	6.55930e10i	0.0750755	−	0.372012i
$649$	−3.94568e10			−0.222404
$650$		0			0
$651$		−	3.14357e11i		−	1.75025i
$652$	1.78214e11	+	1.37275e11i	0.986170	+	0.759628i
$653$	−1.22267e11			−0.672447			−0.336224	−	0.941782i	$-0.609150\pi$
$653$	−1.22267e11			−0.672447			−0.336224	+	0.941782i	$0.609150\pi$
$654$	3.32658e10	+	6.76146e10i	0.181839	+	0.369598i
$655$		0			0
$656$	−3.95841e10	−	1.49955e11i	−0.213750	−	0.809742i
$657$	−8.47310e10			−0.454758
$658$	−4.44022e10	+	2.18455e10i	−0.236865	+	0.116536i
$659$			1.05381e11i			0.558753i	0.960182	+	0.279377i	$0.0901278\pi$
$659$			1.05381e11i			0.558753i	−0.960182	+	0.279377i	$0.909872\pi$
$660$		0			0
$661$	−2.12360e11			−1.11242			−0.556209	−	0.831043i	$-0.687745\pi$
$661$	−2.12360e11			−1.11242			−0.556209	+	0.831043i	$0.687745\pi$
$662$	1.13990e11	+	2.31690e11i	0.593517	+	1.20636i
$663$			6.41738e11i			3.32126i
$664$	8.40996e10	+	1.69721e10i	0.432635	+	0.0873098i
$665$		0			0
$666$	2.84240e10	−	1.39844e10i	0.144473	−	0.0710797i
$667$		−	1.36694e11i		−	0.690629i
$668$	−8.69088e10	−	6.69442e10i	−0.436473	−	0.336207i
$669$	−7.63913e10			−0.381364
$670$		0			0
$671$			7.44391e10i			0.367207i
$672$	−1.73012e11	−	1.99139e11i	−0.848396	−	0.976518i
$673$	−3.80972e11			−1.85709			−0.928545	−	0.371219i	$-0.878940\pi$
$673$	−3.80972e11			−1.85709			−0.928545	+	0.371219i	$0.878940\pi$
$674$	2.29819e11	−	1.13069e11i	1.11365	−	0.547905i
$675$		0			0
$676$	4.62018e10	−	5.99804e10i	0.221244	−	0.287225i
$677$	−2.80516e11			−1.33538			−0.667688	−	0.744441i	$-0.732716\pi$
$677$	−2.80516e11			−1.33538			−0.667688	+	0.744441i	$0.732716\pi$
$678$	1.47850e11	+	3.00514e11i	0.699687	+	1.42215i
$679$		−	2.52957e9i		−	0.0119005i
$680$		0			0
$681$	−3.03616e11			−1.41168
$682$	−9.46883e10	+	4.65859e10i	−0.437682	+	0.215336i
$683$		−	5.79360e10i		−	0.266235i	−0.991100	−	0.133118i	$-0.957501\pi$
$683$		−	5.79360e10i		−	0.266235i	0.991100	−	0.133118i	$-0.0424988\pi$
$684$	1.66292e11	+	1.28092e11i	0.759711	+	0.585191i
$685$		0			0
$686$	−1.06053e11	−	2.15559e11i	−0.478880	−	0.973350i
$687$			1.37815e11i			0.618686i
$688$	−2.55903e11	+	6.75515e10i	−1.14215	+	0.301496i
$689$	−3.27114e10			−0.145152
$690$		0			0
$691$			2.55640e11i			1.12129i	0.828057	+	0.560644i	$0.189446\pi$
$691$			2.55640e11i			1.12129i	−0.828057	+	0.560644i	$0.810554\pi$
$692$	4.82354e10	−	6.26205e10i	0.210350	−	0.273082i
$693$	1.14676e11			0.497210
$694$	−9.50499e10	−	1.93194e11i	−0.409745	−	0.832829i
$695$		0			0
$696$	−2.89407e11	−	5.84051e10i	−1.23331	−	0.248893i
$697$	−3.37505e11			−1.43004
$698$	−2.56840e11	+	1.26363e11i	−1.08203	+	0.532352i
$699$			2.17201e11i			0.909817i
$700$		0			0
$701$	1.52264e11			0.630556			0.315278	−	0.948999i	$-0.397902\pi$
$701$	1.52264e11			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$702$	1.61927e11	+	3.29125e11i	0.666760	+	1.35523i
$703$			1.19492e10i			0.0489235i
$704$	−3.43439e10	+	8.16245e10i	−0.139817	+	0.332300i
$705$		0			0
$706$	3.88426e11	−	1.91102e11i	1.56347	−	0.769214i
$707$			2.33165e11i			0.933225i
$708$	1.57615e11	−	2.04620e11i	0.627285	−	0.814359i
$709$	−8.99510e10			−0.355976			−0.177988	−	0.984033i	$-0.556959\pi$
$709$	−8.99510e10			−0.355976			−0.177988	+	0.984033i	$0.556959\pi$
$710$		0			0
$711$			4.34447e11i			1.70004i
$712$	−2.04847e10	+	1.01505e11i	−0.0797096	+	0.394975i
$713$	3.19829e11			1.23754
$714$	−5.15101e11	+	2.53426e11i	−1.98198	+	0.975119i
$715$		0			0
$716$	4.75205e10	+	3.66041e10i	0.180813	+	0.139277i
$717$	8.28915e11			3.13641
$718$	−3.88765e10	−	7.90186e10i	−0.146281	−	0.297325i
$719$			3.34871e11i			1.25303i	0.779409	+	0.626515i	$0.215519\pi$
$719$			3.34871e11i			1.25303i	−0.779409	+	0.626515i	$0.784481\pi$
$720$		0			0
$721$	−8.48927e10			−0.314144
$722$	1.72779e11	−	8.50059e10i	0.635832	−	0.312824i
$723$		−	2.12735e11i		−	0.778547i
$724$	−3.09667e10	+	4.02019e10i	−0.112704	+	0.146316i
$725$		0			0
$726$	1.77794e11	+	3.61376e11i	0.639987	+	1.30081i
$727$			4.68905e11i			1.67860i	0.543669	+	0.839300i	$0.317035\pi$
$727$			4.68905e11i			1.67860i	−0.543669	+	0.839300i	$0.682965\pi$
$728$	2.49505e11	+	5.03524e10i	0.888287	+	0.179265i
$729$	4.18511e11			1.48182
$730$		0			0
$731$			5.75963e11i			2.01709i
$732$	−3.86036e11	−	2.97356e11i	−1.34457	−	1.03570i
$733$	−6.30452e10			−0.218392			−0.109196	−	0.994020i	$-0.534828\pi$
$733$	−6.30452e10			−0.218392			−0.109196	+	0.994020i	$0.534828\pi$
$734$	−6.83307e10	−	1.38886e11i	−0.235414	−	0.478491i
$735$		0			0
$736$	2.02606e11	−	1.76023e11i	0.690463	−	0.599872i
$737$	1.98272e11			0.672033
$738$	−3.96004e11	+	1.94831e11i	−1.33498	+	0.656798i
$739$			2.09954e11i			0.703959i	0.936008	+	0.351979i	$0.114491\pi$
$739$			2.09954e11i			0.703959i	−0.936008	+	0.351979i	$0.885509\pi$
$740$		0			0
$741$	−3.16542e11			−1.04993
$742$	−1.29179e10	−	2.62563e10i	−0.0426164	−	0.0866200i
$743$			2.18225e11i			0.716060i	0.933710	+	0.358030i	$0.116552\pi$
$743$			2.18225e11i			0.716060i	−0.933710	+	0.358030i	$0.883448\pi$
$744$	1.36653e11	−	6.77140e11i	0.445993	−	2.20997i
$745$		0			0
$746$	3.69448e11	−	1.81765e11i	1.19288	−	0.586889i
$747$		−	2.44143e11i		−	0.784081i
$748$	1.52670e11	+	1.17599e11i	0.487693	+	0.375661i
$749$	2.08401e10			0.0662175
$750$		0			0
$751$		−	5.33771e10i		−	0.167801i	−0.996474	−	0.0839006i	$-0.973262\pi$
$751$		−	5.33771e10i		−	0.167801i	0.996474	−	0.0839006i	$-0.0267378\pi$
$752$	−1.05141e11	+	2.77543e10i	−0.328776	+	0.0867879i
$753$	8.16886e10			0.254087
$754$	2.55612e11	−	1.25759e11i	0.790855	−	0.389094i
$755$		0			0
$756$	−2.00232e11	+	2.59946e11i	−0.612979	+	0.795786i
$757$	2.91321e11			0.887132			0.443566	−	0.896242i	$-0.353713\pi$
$757$	2.91321e11			0.887132			0.443566	+	0.896242i	$0.353713\pi$
$758$	−2.39515e11	−	4.86828e11i	−0.725532	−	1.47468i
$759$			1.82347e11i			0.549453i
$760$		0			0
$761$	1.92349e10			0.0573523			0.0286762	−	0.999589i	$-0.490871\pi$
$761$	1.92349e10			0.0573523			0.0286762	+	0.999589i	$0.490871\pi$
$762$	−4.09710e11	+	2.01574e11i	−1.21522	+	0.597880i
$763$		−	6.50417e10i		−	0.191908i
$764$	4.66146e11	+	3.59063e11i	1.36820	+	1.05390i
$765$		0			0
$766$	−7.59066e10	−	1.54284e11i	−0.220478	−	0.448133i
$767$			2.49217e11i			0.720105i
$768$	−2.86108e11	−	5.04165e11i	−0.822405	−	1.44920i
$769$	−3.49604e11			−0.999703			−0.499852	−	0.866111i	$-0.666612\pi$
$769$	−3.49604e11			−0.999703			−0.499852	+	0.866111i	$0.666612\pi$
$770$		0			0
$771$		−	9.89843e11i		−	2.80123i
$772$	−1.01659e11	+	1.31977e11i	−0.286205	+	0.371559i
$773$	6.52120e11			1.82646			0.913229	−	0.407447i	$-0.133581\pi$
$773$	6.52120e11			1.82646			0.913229	+	0.407447i	$0.133581\pi$
$774$	3.32484e11	+	6.75793e11i	0.926419	+	1.88300i
$775$		0			0
$776$	1.09962e9	−	5.44880e9i	0.00303246	−	0.0150264i
$777$	−4.27333e10			−0.117242
$778$	5.99251e11	−	2.94827e11i	1.63565	−	0.804727i
$779$		−	1.66477e11i		−	0.452068i
$780$		0			0
$781$	1.88768e11			0.507371
$782$	−2.57837e11	−	5.24067e11i	−0.689474	−	1.40139i
$783$			3.67233e11i			0.977001i
$784$	−3.83119e10	−	1.45136e11i	−0.101407	−	0.384158i
$785$		0			0
$786$	2.20922e11	−	1.08692e11i	0.578826	−	0.284778i
$787$		−	3.62094e11i		−	0.943892i	−0.881627	−	0.471946i	$-0.843552\pi$
$787$		−	3.62094e11i		−	0.943892i	0.881627	−	0.471946i	$-0.156448\pi$
$788$	−1.84462e11	+	2.39473e11i	−0.478411	+	0.621087i
$789$	1.09489e12			2.82530
$790$		0			0
$791$		−	2.89079e11i		−	0.738432i
$792$	2.47018e11	+	4.98505e10i	0.627809	+	0.126698i
$793$	4.70171e11			1.18895
$794$	1.83972e11	−	9.05129e10i	0.462882	−	0.227734i
$795$		0			0
$796$	−1.74787e11	−	1.34635e11i	−0.435368	−	0.335355i
$797$	−1.33733e11			−0.331440			−0.165720	−	0.986173i	$-0.552995\pi$
$797$	−1.33733e11			−0.331440			−0.165720	+	0.986173i	$0.552995\pi$
$798$	−1.25004e11	−	2.54078e11i	−0.308257	−	0.626549i
$799$			2.36641e11i			0.580634i
$800$		0			0
$801$	2.94672e11			0.715828
$802$	6.82691e11	−	3.35878e11i	1.65016	−	0.811866i
$803$		−	3.83704e10i		−	0.0922857i
$804$	−7.92022e11	+	1.02822e12i	−1.89545	+	2.46073i
$805$		0			0
$806$	2.94245e11	+	5.98069e11i	0.697219	+	1.41714i
$807$		−	1.78041e11i		−	0.419784i
$808$	−1.01358e11	+	5.02249e11i	−0.237801	+	1.17835i
$809$	−4.11621e11			−0.960956			−0.480478	−	0.877007i	$-0.659537\pi$
$809$	−4.11621e11			−0.960956			−0.480478	+	0.877007i	$0.659537\pi$
$810$		0			0
$811$			7.23209e11i			1.67178i	0.548894	+	0.835892i	$0.315049\pi$
$811$			7.23209e11i			1.67178i	−0.548894	+	0.835892i	$0.684951\pi$
$812$	2.01886e11	+	1.55509e11i	0.464388	+	0.357709i
$813$	4.07100e11			0.931836
$814$	6.33282e9	+	1.28718e10i	0.0144245	+	0.0293185i
$815$		0			0
$816$	−1.21972e12	+	3.21973e11i	−2.75105	+	0.726203i
$817$	−2.84098e11			−0.637646
$818$	−3.51327e11	+	1.72850e11i	−0.784691	+	0.386061i
$819$		−	7.24316e11i		−	1.60988i
$820$		0			0
$821$	6.38146e11			1.40458			0.702291	−	0.711890i	$-0.252160\pi$
$821$	6.38146e11			1.40458			0.702291	+	0.711890i	$0.252160\pi$
$822$	−3.78215e11	−	7.68743e11i	−0.828422	−	1.68381i
$823$		−	2.86794e11i		−	0.625130i	−0.949896	−	0.312565i	$-0.898812\pi$
$823$		−	2.86794e11i		−	0.625130i	0.949896	−	0.312565i	$-0.101188\pi$
$824$	−1.82863e11	−	3.69034e10i	−0.396658	−	0.0800493i
$825$		0			0
$826$	−2.00038e11	+	9.84171e10i	−0.429727	+	0.211422i
$827$		−	6.21880e11i		−	1.32949i	−0.747071	−	0.664745i	$-0.768540\pi$
$827$		−	6.21880e11i		−	1.32949i	0.747071	−	0.664745i	$-0.231460\pi$
$828$	−6.05054e11	−	4.66062e11i	−1.28728	−	0.991567i
$829$	5.50205e11			1.16495			0.582474	−	0.812849i	$-0.302085\pi$
$829$	5.50205e11			1.16495			0.582474	+	0.812849i	$0.302085\pi$
$830$		0			0
$831$		−	1.61572e11i		−	0.338814i
$832$	5.15556e11	+	2.16923e11i	1.07593	+	0.452701i
$833$	−3.26658e11			−0.678442
$834$	5.46115e11	−	2.68684e11i	1.12881	−	0.555364i
$835$		0			0
$836$	−5.80065e10	+	7.53056e10i	−0.118755	+	0.154171i
$837$	−8.59235e11			−1.75069
$838$	−2.81927e10	−	5.73032e10i	−0.0571690	−	0.116199i
$839$			9.29570e9i			0.0187601i	0.999956	+	0.00938003i	$0.00298580\pi$
$839$			9.29570e9i			0.0187601i	−0.999956	+	0.00938003i	$0.997014\pi$
$840$		0			0
$841$	−2.15037e11			−0.429862
$842$	−1.16934e11	+	5.75305e10i	−0.232644	+	0.114459i
$843$			2.77474e11i			0.549429i
$844$	−3.94347e11	−	3.03758e11i	−0.777158	−	0.598630i
$845$		0			0
$846$	1.36605e11	+	2.77657e11i	0.266677	+	0.542035i
$847$		−	3.47625e11i		−	0.675426i
$848$	−1.64120e10	−	6.21728e10i	−0.0317378	−	0.120231i
$849$	−1.63828e12			−3.15325
$850$		0			0
$851$		−	4.34771e10i		−	0.0828977i
$852$	−7.54059e11	+	9.78941e11i	−1.43103	+	1.85780i
$853$	−2.76680e11			−0.522615			−0.261308	−	0.965256i	$-0.584154\pi$
$853$	−2.76680e11			−0.522615			−0.261308	+	0.965256i	$0.584154\pi$
$854$	1.85673e11	+	3.77391e11i	0.349074	+	0.709512i
$855$		0			0
$856$	4.48906e10	+	9.05933e9i	0.0836103	+	0.0168733i
$857$	8.09328e11			1.50038			0.750190	−	0.661223i	$-0.229962\pi$
$857$	8.09328e11			1.50038			0.750190	+	0.661223i	$0.229962\pi$
$858$	−3.40982e11	+	1.67760e11i	−0.629190	+	0.309557i
$859$			2.89123e11i			0.531020i	0.964108	+	0.265510i	$0.0855403\pi$
$859$			2.89123e11i			0.531020i	−0.964108	+	0.265510i	$0.914460\pi$
$860$		0			0
$861$	5.95362e11			1.08335
$862$	−2.92436e10	−	5.94393e10i	−0.0529666	−	0.107658i
$863$			6.16481e11i			1.11142i	0.831378	+	0.555708i	$0.187553\pi$
$863$			6.16481e11i			1.11142i	−0.831378	+	0.555708i	$0.812447\pi$
$864$	−5.44309e11	+	4.72894e11i	−0.976765	+	0.848612i
$865$		0			0
$866$	−3.51973e11	+	1.73168e11i	−0.625804	+	0.307890i
$867$			1.80371e12i			3.19220i
$868$	−3.63851e11	+	4.72362e11i	−0.640981	+	0.832139i
$869$	−1.96739e11			−0.344994
$870$		0			0
$871$		−	1.25232e12i		−	2.17592i
$872$	2.82741e10	−	1.40103e11i	0.0489015	−	0.242315i
$873$	−1.58180e10			−0.0272329
$874$	2.58500e11	−	1.27180e11i	0.443012	−	0.217958i
$875$		0			0
$876$	1.98986e11	+	1.53276e11i	0.337915	+	0.260289i
$877$	6.46830e10			0.109343			0.0546716	−	0.998504i	$-0.482589\pi$
$877$	6.46830e10			0.109343			0.0546716	+	0.998504i	$0.482589\pi$
$878$	−4.00419e11	−	8.13874e11i	−0.673809	−	1.36955i
$879$		−	1.19560e12i		−	2.00277i
$880$		0			0
$881$	−9.16075e11			−1.52064			−0.760322	−	0.649547i	$-0.774959\pi$
$881$	−9.16075e11			−1.52064			−0.760322	+	0.649547i	$0.774959\pi$
$882$	−3.83276e11	+	1.88569e11i	−0.633341	+	0.311599i
$883$			7.21518e11i			1.18687i	0.804881	+	0.593437i	$0.202229\pi$
$883$			7.21518e11i			1.18687i	−0.804881	+	0.593437i	$0.797771\pi$
$884$	7.42776e11	−	9.64292e11i	1.21632	−	1.57906i
$885$		0			0
$886$	−1.50391e11	−	3.05678e11i	−0.244055	−	0.496054i
$887$		−	1.56512e10i		−	0.0252844i	−0.999920	−	0.0126422i	$-0.995976\pi$
$887$		−	1.56512e10i		−	0.0252844i	0.999920	−	0.0126422i	$-0.00402425\pi$
$888$	−9.20495e10	−	1.85764e10i	−0.148037	−	0.0298752i
$889$	3.94119e11			0.630987
$890$		0			0
$891$		−	8.62306e10i		−	0.136820i
$892$	1.14788e11	+	8.84187e10i	0.181316	+	0.139664i
$893$	−1.16725e11			−0.183551
$894$	−4.18372e11	−	8.50364e11i	−0.654957	−	1.33124i
$895$		0			0
$896$	2.94793e10	+	4.99484e11i	0.0457389	+	0.774978i
$897$	1.15174e12			1.77903
$898$	7.41483e11	−	3.64804e11i	1.14024	−	0.560988i
$899$			6.67319e11i			1.02163i
$900$		0			0
$901$	−1.39933e11			−0.212334
$902$	−8.82291e10	−	1.79330e11i	−0.133286	−	0.270912i
$903$		−	1.01600e12i		−	1.52807i
$904$	1.25664e11	−	6.22689e11i	0.188165	−	0.932390i
$905$		0			0
$906$	1.42375e12	−	7.00474e11i	2.11311	−	1.03963i
$907$		−	7.40442e11i		−	1.09411i	−0.837096	−	0.547056i	$-0.815748\pi$
$907$		−	7.40442e11i		−	1.09411i	0.837096	−	0.547056i	$-0.184252\pi$
$908$	4.56222e11	+	3.51419e11i	0.671170	+	0.516990i
$909$	1.45804e12			2.13556
$910$		0			0
$911$			1.11646e12i			1.62095i	0.585770	+	0.810477i	$0.300792\pi$
$911$			1.11646e12i			1.62095i	−0.585770	+	0.810477i	$0.699208\pi$
$912$	−1.58815e11	−	6.01635e11i	−0.229569	−	0.869669i
$913$	1.10560e11			0.159116
$914$	−8.88471e11	+	4.37121e11i	−1.27309	+	0.626349i
$915$		0			0
$916$	1.59513e11	−	2.07085e11i	0.226577	−	0.294148i
$917$	−2.12515e11			−0.300547
$918$	6.92690e11	+	1.40793e12i	0.975367	+	1.98249i
$919$			4.29970e11i			0.602804i	0.953497	+	0.301402i	$0.0974546\pi$
$919$			4.29970e11i			0.602804i	−0.953497	+	0.301402i	$0.902545\pi$
$920$		0			0
$921$	−3.06536e11			−0.426033
$922$	2.65591e10	−	1.30669e10i	0.0367528	−	0.0180821i
$923$		−	1.19230e12i		−	1.64277i
$924$	−2.69311e11	−	2.07445e11i	−0.369459	−	0.284587i
$925$		0			0
$926$	−3.45961e11	−	7.03184e11i	−0.470525	−	0.956368i
$927$			5.30854e11i			0.718879i
$928$	3.67270e11	+	4.22734e11i	0.495215	+	0.570000i
$929$	−1.03621e12			−1.39119			−0.695594	−	0.718435i	$-0.744859\pi$
$929$	−1.03621e12			−1.39119			−0.695594	+	0.718435i	$0.744859\pi$
$930$		0			0
$931$		−	1.61126e11i		−	0.214471i
$932$	2.51399e11	−	3.26372e11i	0.333196	−	0.432564i
$933$	1.34299e11			0.177233
$934$	−1.82928e10	−	3.71812e10i	−0.0240377	−	0.0488580i
$935$		0			0
$936$	3.14865e11	−	1.56021e12i	0.410224	−	2.03273i
$937$	−9.79343e11			−1.27051			−0.635253	−	0.772304i	$-0.719104\pi$
$937$	−9.79343e11			−1.27051			−0.635253	+	0.772304i	$0.719104\pi$
$938$	1.00520e12	−	4.94549e11i	1.29849	−	0.638848i
$939$		−	1.30616e12i		−	1.68009i
$940$		0			0
$941$	−3.95736e11			−0.504715			−0.252358	−	0.967634i	$-0.581206\pi$
$941$	−3.95736e11			−0.504715			−0.252358	+	0.967634i	$0.581206\pi$
$942$	3.74582e11	+	7.61358e11i	0.475711	+	0.966909i
$943$			6.05725e11i			0.766000i
$944$	−4.73674e11	+	1.25037e11i	−0.596474	+	0.157453i
$945$		0			0
$946$	−3.06033e11	+	1.50566e11i	−0.382123	+	0.188001i
$947$			7.08577e11i			0.881022i	0.897747	+	0.440511i	$0.145203\pi$
$947$			7.08577e11i			0.881022i	−0.897747	+	0.440511i	$0.854797\pi$
$948$	7.85900e11	−	1.02028e12i	0.973047	−	1.26324i
$949$	−2.42355e11			−0.298804
$950$		0			0
$951$			7.30979e11i			0.893682i
$952$	1.06733e12	+	2.15397e11i	1.29943	+	0.262236i
$953$	−4.04943e11			−0.490932			−0.245466	−	0.969405i	$-0.578941\pi$
$953$	−4.04943e11			−0.490932			−0.245466	+	0.969405i	$0.578941\pi$
$954$	−1.64187e11	+	8.07786e10i	−0.198219	+	0.0975221i
$955$		0			0
$956$	−1.24555e12	−	9.59423e11i	−1.49118	−	1.14863i
$957$	−3.80464e11			−0.453592
$958$	5.11836e11	+	1.04033e12i	0.607671	+	1.23512i
$959$			7.39490e11i			0.874295i
$960$		0			0
$961$	−7.08468e11			−0.830667
$962$	8.13007e10	−	3.99993e10i	0.0949279	−	0.0467038i
$963$		−	1.30318e11i		−	0.151530i
$964$	−2.46228e11	+	3.19660e11i	−0.285122	+	0.370153i
$965$		0			0
$966$	4.54827e11	+	9.24460e11i	0.522321	+	1.06165i
$967$		−	1.36193e12i		−	1.55758i	−0.627286	−	0.778789i	$-0.715834\pi$
$967$		−	1.36193e12i		−	1.55758i	0.627286	−	0.778789i	$-0.284166\pi$
$968$	1.51115e11	−	7.48801e11i	0.172110	−	0.852835i
$969$	−1.35410e12			−1.53588
$970$		0			0
$971$		−	1.12453e12i		−	1.26501i	−0.774556	−	0.632505i	$-0.782027\pi$
$971$		−	1.12453e12i		−	1.26501i	0.774556	−	0.632505i	$-0.217973\pi$
$972$	−4.67806e11	−	3.60342e11i	−0.524083	−	0.403691i
$973$	−5.25334e11			−0.586117
$974$	−4.79335e11	−	9.74274e11i	−0.532602	−	1.08254i
$975$		0			0
$976$	2.35894e11	+	8.93631e11i	0.259967	+	0.984825i
$977$	1.36587e12			1.49910			0.749549	−	0.661949i	$-0.230270\pi$
$977$	1.36587e12			1.49910			0.749549	+	0.661949i	$0.230270\pi$
$978$	−1.70271e12	+	8.37719e11i	−1.86117	+	0.915678i
$979$			1.33442e11i			0.145266i
$980$		0			0
$981$	−4.06721e11			−0.439158
$982$	7.39671e11	+	1.50342e12i	0.795413	+	1.61672i
$983$		−	1.23632e12i		−	1.32409i	−0.749463	−	0.662046i	$-0.769688\pi$
$983$		−	1.23632e12i		−	1.32409i	0.749463	−	0.662046i	$-0.230312\pi$
$984$	1.28244e12	+	2.58808e11i	1.36791	+	0.276056i
$985$		0			0
$986$	1.09346e12	−	5.37973e11i	1.15690	−	0.569184i
$987$		−	4.17437e11i		−	0.439868i
$988$	4.75644e11	+	3.66380e11i	0.499177	+	0.384507i
$989$	1.03369e12			1.08045
$990$		0			0
$991$			1.30551e12i			1.35359i	0.736172	+	0.676794i	$0.236631\pi$
$991$			1.30551e12i			1.35359i	−0.736172	+	0.676794i	$0.763369\pi$
$992$	−9.89091e11	+	8.59320e11i	−1.02139	+	0.887377i
$993$	−2.17818e12			−2.24025
$994$	9.57018e11	−	4.70845e11i	0.980335	−	0.482317i
$995$		0			0
$996$	−4.41646e11	+	5.73357e11i	−0.448783	+	0.582623i
$997$	−1.69693e12			−1.71744			−0.858722	−	0.512441i	$-0.828741\pi$
$997$	−1.69693e12			−1.71744			−0.858722	+	0.512441i	$0.828741\pi$
$998$	−4.03142e11	−	8.19408e11i	−0.406383	−	0.825996i
$999$			1.16803e11i			0.117272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.g.51.17		20
4.3	odd	2	inner	100.9.b.g.51.18		20
5.2	odd	4		20.9.d.c.19.14	yes	20
5.3	odd	4		20.9.d.c.19.7	✓	20
5.4	even	2	inner	100.9.b.g.51.4		20
20.3	even	4		20.9.d.c.19.13	yes	20
20.7	even	4		20.9.d.c.19.8	yes	20
20.19	odd	2	inner	100.9.b.g.51.3		20
40.3	even	4		320.9.h.g.319.2		20
40.13	odd	4		320.9.h.g.319.20		20
40.27	even	4		320.9.h.g.319.19		20
40.37	odd	4		320.9.h.g.319.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.7	✓	20	5.3	odd	4
20.9.d.c.19.8	yes	20	20.7	even	4
20.9.d.c.19.13	yes	20	20.3	even	4
20.9.d.c.19.14	yes	20	5.2	odd	4
100.9.b.g.51.3		20	20.19	odd	2	inner
100.9.b.g.51.4		20	5.4	even	2	inner
100.9.b.g.51.17		20	1.1	even	1	trivial
100.9.b.g.51.18		20	4.3	odd	2	inner
320.9.h.g.319.1		20	40.37	odd	4
320.9.h.g.319.2		20	40.3	even	4
320.9.h.g.319.19		20	40.27	even	4
320.9.h.g.319.20		20	40.13	odd	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(14.3565 - 7.06329i) q^{2} +134.970i q^{3} +(156.220 - 202.809i) q^{4} +(953.329 + 1937.69i) q^{6} -1863.96i q^{7} +(810.276 - 4015.06i) q^{8} -11655.8 q^{9} +O(q^{10})\)	\(q+(14.3565 - 7.06329i) q^{2} +134.970i q^{3} +(156.220 - 202.809i) q^{4} +(953.329 + 1937.69i) q^{6} -1863.96i q^{7} +(810.276 - 4015.06i) q^{8} -11655.8 q^{9} -5278.32i q^{11} +(27373.0 + 21084.9i) q^{12} -33338.9 q^{13} +(-13165.7 - 26760.0i) q^{14} +(-16726.8 - 63365.5i) q^{16} -142617. q^{17} +(-167336. + 82328.1i) q^{18} -70346.9i q^{19} +251578. q^{21} +(-37282.3 - 75778.3i) q^{22} +255957. i q^{23} +(541910. + 109363. i) q^{24} +(-478630. + 235482. i) q^{26} -687639. i q^{27} +(-378027. - 291187. i) q^{28} -534050. q^{29} -1.24954e6i q^{31} +(-687707. - 791562. i) q^{32} +712412. q^{33} +(-2.04748e6 + 1.00735e6i) q^{34} +(-1.82086e6 + 2.36389e6i) q^{36} -169861. q^{37} +(-496881. - 1.00994e6i) q^{38} -4.49973e6i q^{39} +2.36651e6 q^{41} +(3.61178e6 - 1.77697e6i) q^{42} -4.03853e6i q^{43} +(-1.07049e6 - 824577. i) q^{44} +(1.80790e6 + 3.67465e6i) q^{46} -1.65928e6i q^{47} +(8.55241e6 - 2.25760e6i) q^{48} +2.29046e6 q^{49} -1.92489e7i q^{51} +(-5.20819e6 + 6.76141e6i) q^{52} +981179. q^{53} +(-4.85699e6 - 9.87210e6i) q^{54} +(-7.48390e6 - 1.51032e6i) q^{56} +9.49469e6 q^{57} +(-7.66710e6 + 3.77215e6i) q^{58} -7.47526e6i q^{59} -1.41028e7 q^{61} +(-8.82589e6 - 1.79391e7i) q^{62} +2.17259e7i q^{63} +(-1.54641e7 - 6.50660e6i) q^{64} +(1.02278e7 - 5.03197e6i) q^{66} +3.75634e7i q^{67} +(-2.22796e7 + 2.89240e7i) q^{68} -3.45463e7 q^{69} +3.57630e7i q^{71} +(-9.44439e6 + 4.67986e7i) q^{72} +7.26944e6 q^{73} +(-2.43862e6 + 1.19978e6i) q^{74} +(-1.42670e7 - 1.09896e7i) q^{76} -9.83857e6 q^{77} +(-3.17829e7 - 6.46005e7i) q^{78} -3.72731e7i q^{79} +1.63368e7 q^{81} +(3.39749e7 - 1.67154e7i) q^{82} +2.09461e7i q^{83} +(3.93014e7 - 5.10222e7i) q^{84} +(-2.85253e7 - 5.79792e7i) q^{86} -7.20805e7i q^{87} +(-2.11927e7 - 4.27689e6i) q^{88} -2.52812e7 q^{89} +6.21423e7i q^{91} +(5.19102e7 + 3.99855e7i) q^{92} +1.68650e8 q^{93} +(-1.17199e7 - 2.38214e7i) q^{94} +(1.06837e8 - 9.28195e7i) q^{96} +1.35709e6 q^{97} +(3.28830e7 - 1.61782e7i) q^{98} +6.15229e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9}+O(q^{10}) \) 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9	\( 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9} - 8848 q^{14} - 59200 q^{16} + 410256 q^{21} + 156672 q^{24} - 440448 q^{26} - 660136 q^{29} - 4342528 q^{34} - 7191312 q^{36} + 7068520 q^{41} - 2666880 q^{44} + 561168 q^{46} - 11719036 q^{49} - 37110816 q^{54} - 35044352 q^{56} - 17660440 q^{61} - 20201728 q^{64} + 31902720 q^{66} - 111747216 q^{69} - 19114368 q^{74} - 54998400 q^{76} - 154212444 q^{81} - 101289216 q^{84} + 94429648 q^{86} - 105006376 q^{89} + 192757872 q^{94} + 28850688 q^{96}+O(q^{100}) \) 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9 - 8848 * q^14 - 59200 * q^16 + 410256 * q^21 + 156672 * q^24 - 440448 * q^26 - 660136 * q^29 - 4342528 * q^34 - 7191312 * q^36 + 7068520 * q^41 - 2666880 * q^44 + 561168 * q^46 - 11719036 * q^49 - 37110816 * q^54 - 35044352 * q^56 - 17660440 * q^61 - 20201728 * q^64 + 31902720 * q^66 - 111747216 * q^69 - 19114368 * q^74 - 54998400 * q^76 - 154212444 * q^81 - 101289216 * q^84 + 94429648 * q^86 - 105006376 * q^89 + 192757872 * q^94 + 28850688 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more