LMFDB - Embedded newform 6.20.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,20,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	6.a (trivial)

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:	yes
Analytic conductor:	$13.7290017934$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-512.000 q^{2} +19683.0 q^{3} +262144. q^{4} -5.84949e6 q^{5} -1.00777e7 q^{6} +1.73531e8 q^{7} -1.34218e8 q^{8} +3.87420e8 q^{9} +O(q^{10})$

\(q-512.000 q^{2} +19683.0 q^{3} +262144. q^{4} -5.84949e6 q^{5} -1.00777e7 q^{6} +1.73531e8 q^{7} -1.34218e8 q^{8} +3.87420e8 q^{9} +2.99494e9 q^{10} -7.31283e9 q^{11} +5.15978e9 q^{12} -4.18451e10 q^{13} -8.88478e10 q^{14} -1.15136e11 q^{15} +6.87195e10 q^{16} -9.58344e10 q^{17} -1.98359e11 q^{18} -2.41907e12 q^{19} -1.53341e12 q^{20} +3.41561e12 q^{21} +3.74417e12 q^{22} -1.32185e13 q^{23} -2.64181e12 q^{24} +1.51430e13 q^{25} +2.14247e13 q^{26} +7.62560e12 q^{27} +4.54901e13 q^{28} +2.20967e13 q^{29} +5.89494e13 q^{30} +5.42050e13 q^{31} -3.51844e13 q^{32} -1.43938e14 q^{33} +4.90672e13 q^{34} -1.01507e15 q^{35} +1.01560e14 q^{36} -7.54675e14 q^{37} +1.23857e15 q^{38} -8.23636e14 q^{39} +7.85105e14 q^{40} +1.01551e15 q^{41} -1.74879e15 q^{42} +2.30740e15 q^{43} -1.91701e15 q^{44} -2.26621e15 q^{45} +6.76789e15 q^{46} +7.36560e13 q^{47} +1.35261e15 q^{48} +1.87141e16 q^{49} -7.75324e15 q^{50} -1.88631e15 q^{51} -1.09694e16 q^{52} -5.77230e15 q^{53} -3.90431e15 q^{54} +4.27763e16 q^{55} -2.32909e16 q^{56} -4.76146e16 q^{57} -1.13135e16 q^{58} -1.29569e17 q^{59} -3.01821e16 q^{60} +1.14049e17 q^{61} -2.77530e16 q^{62} +6.72294e16 q^{63} +1.80144e16 q^{64} +2.44772e17 q^{65} +7.36965e16 q^{66} -1.31077e17 q^{67} -2.51224e16 q^{68} -2.60181e17 q^{69} +5.19715e17 q^{70} +5.32257e17 q^{71} -5.19987e16 q^{72} -8.01680e17 q^{73} +3.86394e17 q^{74} +2.98061e17 q^{75} -6.34145e17 q^{76} -1.26900e18 q^{77} +4.21702e17 q^{78} -7.99387e17 q^{79} -4.01974e17 q^{80} +1.50095e17 q^{81} -5.19939e17 q^{82} +1.02105e18 q^{83} +8.95382e17 q^{84} +5.60582e17 q^{85} -1.18139e18 q^{86} +4.34930e17 q^{87} +9.81511e17 q^{88} +4.06479e18 q^{89} +1.16030e18 q^{90} -7.26141e18 q^{91} -3.46516e18 q^{92} +1.06692e18 q^{93} -3.77119e16 q^{94} +1.41503e19 q^{95} -6.92534e17 q^{96} +1.10150e19 q^{97} -9.58162e18 q^{98} -2.83314e18 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	−512.000	−0.707107
$2$	−512.000	−0.707107
$3$	19683.0	0.577350
$3$	19683.0	0.577350
$4$	262144.	0.500000
$5$	−5.84949e6	−1.33938	−0.669689	−	0.742642i	$-0.733572\pi$
$5$	−5.84949e6	−1.33938	−0.669689	+	0.742642i	$0.733572\pi$
$6$	−1.00777e7	−0.408248
$7$	1.73531e8	1.62535	0.812673	−	0.582721i	$-0.198012\pi$
$7$	1.73531e8	1.62535	0.812673	+	0.582721i	$0.198012\pi$
$8$	−1.34218e8	−0.353553
$9$	3.87420e8	0.333333
$10$	2.99494e9	0.947083
$11$	−7.31283e9	−0.935093	−0.467547	−	0.883968i	$-0.654862\pi$
$11$	−7.31283e9	−0.935093	−0.467547	+	0.883968i	$0.654862\pi$
$12$	5.15978e9	0.288675
$13$	−4.18451e10	−1.09442	−0.547208	−	0.836997i	$-0.684309\pi$
$13$	−4.18451e10	−1.09442	−0.547208	+	0.836997i	$0.684309\pi$
$14$	−8.88478e10	−1.14929
$15$	−1.15136e11	−0.773290
$16$	6.87195e10	0.250000
$17$	−9.58344e10	−0.196000	−0.0980001	−	0.995186i	$-0.531245\pi$
$17$	−9.58344e10	−0.196000	−0.0980001	+	0.995186i	$0.531245\pi$
$18$	−1.98359e11	−0.235702
$19$	−2.41907e12	−1.71985	−0.859923	−	0.510423i	$-0.829489\pi$
$19$	−2.41907e12	−1.71985	−0.859923	+	0.510423i	$0.829489\pi$
$20$	−1.53341e12	−0.669689
$21$	3.41561e12	0.938393
$22$	3.74417e12	0.661211
$23$	−1.32185e13	−1.53027	−0.765137	−	0.643867i	$-0.777329\pi$
$23$	−1.32185e13	−1.53027	−0.765137	+	0.643867i	$0.777329\pi$
$24$	−2.64181e12	−0.204124
$25$	1.51430e13	0.793932
$26$	2.14247e13	0.773869
$27$	7.62560e12	0.192450
$28$	4.54901e13	0.812673
$29$	2.20967e13	0.282844	0.141422	−	0.989949i	$-0.454833\pi$
$29$	2.20967e13	0.282844	0.141422	+	0.989949i	$0.454833\pi$
$30$	5.89494e13	0.546799
$31$	5.42050e13	0.368217	0.184108	−	0.982906i	$-0.441060\pi$
$31$	5.42050e13	0.368217	0.184108	+	0.982906i	$0.441060\pi$
$32$	−3.51844e13	−0.176777
$33$	−1.43938e14	−0.539876
$34$	4.90672e13	0.138593
$35$	−1.01507e15	−2.17695
$36$	1.01560e14	0.166667
$37$	−7.54675e14	−0.954649	−0.477325	−	0.878727i	$-0.658393\pi$
$37$	−7.54675e14	−0.954649	−0.477325	+	0.878727i	$0.658393\pi$
$38$	1.23857e15	1.21612
$39$	−8.23636e14	−0.631861
$40$	7.85105e14	0.473541
$41$	1.01551e15	0.484435	0.242218	−	0.970222i	$-0.422125\pi$
$41$	1.01551e15	0.484435	0.242218	+	0.970222i	$0.422125\pi$
$42$	−1.74879e15	−0.663544
$43$	2.30740e15	0.700121	0.350060	−	0.936727i	$-0.386161\pi$
$43$	2.30740e15	0.700121	0.350060	+	0.936727i	$0.386161\pi$
$44$	−1.91701e15	−0.467547
$45$	−2.26621e15	−0.446459
$46$	6.76789e15	1.08207
$47$	7.36560e13	0.00960016	0.00480008	−	0.999988i	$-0.498472\pi$
$47$	7.36560e13	0.00960016	0.00480008	+	0.999988i	$0.498472\pi$
$48$	1.35261e15	0.144338
$49$	1.87141e16	1.64175
$50$	−7.75324e15	−0.561395
$51$	−1.88631e15	−0.113161
$52$	−1.09694e16	−0.547208
$53$	−5.77230e15	−0.240286	−0.120143	−	0.992757i	$-0.538335\pi$
$53$	−5.77230e15	−0.240286	−0.120143	+	0.992757i	$0.538335\pi$
$54$	−3.90431e15	−0.136083
$55$	4.27763e16	1.25244
$56$	−2.32909e16	−0.574646
$57$	−4.76146e16	−0.992954
$58$	−1.13135e16	−0.200001
$59$	−1.29569e17	−1.94718	−0.973592	−	0.228294i	$-0.926685\pi$
$59$	−1.29569e17	−1.94718	−0.973592	+	0.228294i	$0.926685\pi$
$60$	−3.01821e16	−0.386645
$61$	1.14049e17	1.24870	0.624351	−	0.781144i	$-0.285363\pi$
$61$	1.14049e17	1.24870	0.624351	+	0.781144i	$0.285363\pi$
$62$	−2.77530e16	−0.260368
$63$	6.72294e16	0.541782
$64$	1.80144e16	0.125000
$65$	2.44772e17	1.46584
$66$	7.36965e16	0.381750
$67$	−1.31077e17	−0.588594	−0.294297	−	0.955714i	$-0.595085\pi$
$67$	−1.31077e17	−0.588594	−0.294297	+	0.955714i	$0.595085\pi$
$68$	−2.51224e16	−0.0980001
$69$	−2.60181e17	−0.883504
$70$	5.19715e17	1.53934
$71$	5.32257e17	1.37774	0.688869	−	0.724886i	$-0.258107\pi$
$71$	5.32257e17	1.37774	0.688869	+	0.724886i	$0.258107\pi$
$72$	−5.19987e16	−0.117851
$73$	−8.01680e17	−1.59380	−0.796900	−	0.604111i	$-0.793528\pi$
$73$	−8.01680e17	−1.59380	−0.796900	+	0.604111i	$0.793528\pi$
$74$	3.86394e17	0.675039
$75$	2.98061e17	0.458377
$76$	−6.34145e17	−0.859923
$77$	−1.26900e18	−1.51985
$78$	4.21702e17	0.446793
$79$	−7.99387e17	−0.750411	−0.375206	−	0.926942i	$-0.622428\pi$
$79$	−7.99387e17	−0.750411	−0.375206	+	0.926942i	$0.622428\pi$
$80$	−4.01974e17	−0.334844
$81$	1.50095e17	0.111111
$82$	−5.19939e17	−0.342548
$83$	1.02105e18	0.599522	0.299761	−	0.954014i	$-0.403093\pi$
$83$	1.02105e18	0.599522	0.299761	+	0.954014i	$0.403093\pi$
$84$	8.95382e17	0.469197
$85$	5.60582e17	0.262518
$86$	−1.18139e18	−0.495060
$87$	4.34930e17	0.163300
$88$	9.81511e17	0.330605
$89$	4.06479e18	1.22979	0.614897	−	0.788607i	$-0.289197\pi$
$89$	4.06479e18	1.22979	0.614897	+	0.788607i	$0.289197\pi$
$90$	1.16030e18	0.315694
$91$	−7.26141e18	−1.77880
$92$	−3.46516e18	−0.765137
$93$	1.06692e18	0.212590
$94$	−3.77119e16	−0.00678834
$95$	1.41503e19	2.30352
$96$	−6.92534e17	−0.102062
$97$	1.10150e19	1.47113	0.735566	−	0.677453i	$-0.236916\pi$
$97$	1.10150e19	1.47113	0.735566	+	0.677453i	$0.236916\pi$
$98$	−9.58162e18	−1.16089
$99$	−2.83314e18	−0.311698
$100$	3.96966e18	0.396966
$101$	−1.40290e19	−1.27636	−0.638181	−	0.769886i	$-0.720313\pi$
$101$	−1.40290e19	−1.27636	−0.638181	+	0.769886i	$0.720313\pi$
$102$	9.65790e17	0.0800168
$103$	−7.92032e17	−0.0598121	−0.0299060	−	0.999553i	$-0.509521\pi$
$103$	−7.92032e17	−0.0598121	−0.0299060	+	0.999553i	$0.509521\pi$
$104$	5.61635e18	0.386934
$105$	−1.99796e19	−1.25686
$106$	2.95542e18	0.169908
$107$	5.91177e18	0.310865	0.155432	−	0.987847i	$-0.450323\pi$
$107$	5.91177e18	0.310865	0.155432	+	0.987847i	$0.450323\pi$
$108$	1.99900e18	0.0962250
$109$	−3.41020e19	−1.50393	−0.751966	−	0.659201i	$-0.770894\pi$
$109$	−3.41020e19	−1.50393	−0.751966	+	0.659201i	$0.770894\pi$
$110$	−2.19015e19	−0.885611
$111$	−1.48543e19	−0.551167
$112$	1.19250e19	0.406336
$113$	6.36367e18	0.199279	0.0996397	−	0.995024i	$-0.468231\pi$
$113$	6.36367e18	0.199279	0.0996397	+	0.995024i	$0.468231\pi$
$114$	2.43787e19	0.702124
$115$	7.73217e19	2.04961
$116$	5.79252e18	0.141422
$117$	−1.62116e19	−0.364805
$118$	6.63393e19	1.37687
$119$	−1.66302e19	−0.318568
$120$	1.54532e19	0.273399
$121$	−7.68163e18	−0.125601
$122$	−5.83932e19	−0.882966
$123$	1.99882e19	0.279689
$124$	1.42095e19	0.184108
$125$	2.29911e19	0.276003
$126$	−3.44215e19	−0.383097
$127$	2.66753e18	0.0275406	0.0137703	−	0.999905i	$-0.495617\pi$
$127$	2.66753e18	0.0275406	0.0137703	+	0.999905i	$0.495617\pi$
$128$	−9.22337e18	−0.0883883
$129$	4.54166e19	0.404215
$130$	−1.25323e20	−1.03650
$131$	1.07481e20	0.826525	0.413263	−	0.910612i	$-0.364389\pi$
$131$	1.07481e20	0.826525	0.413263	+	0.910612i	$0.364389\pi$
$132$	−3.77326e19	−0.269938
$133$	−4.19784e20	−2.79534
$134$	6.71114e19	0.416199
$135$	−4.46059e19	−0.257763
$136$	1.28627e19	0.0692966
$137$	4.17804e19	0.209956	0.104978	−	0.994475i	$-0.466523\pi$
$137$	4.17804e19	0.209956	0.104978	+	0.994475i	$0.466523\pi$
$138$	1.33212e20	0.624732
$139$	3.37928e20	1.47973	0.739866	−	0.672754i	$-0.234889\pi$
$139$	3.37928e20	1.47973	0.739866	+	0.672754i	$0.234889\pi$
$140$	−2.66094e20	−1.08848
$141$	1.44977e18	0.00554266
$142$	−2.72515e20	−0.974208
$143$	3.06006e20	1.02338
$144$	2.66233e19	0.0833333
$145$	−1.29254e20	−0.378835
$146$	4.10460e20	1.12699
$147$	3.68350e20	0.947863
$148$	−1.97834e20	−0.477325
$149$	−2.06483e20	−0.467320	−0.233660	−	0.972318i	$-0.575070\pi$
$149$	−2.06483e20	−0.467320	−0.233660	+	0.972318i	$0.575070\pi$
$150$	−1.52607e20	−0.324121
$151$	−5.10180e19	−0.101728	−0.0508642	−	0.998706i	$-0.516198\pi$
$151$	−5.10180e19	−0.101728	−0.0508642	+	0.998706i	$0.516198\pi$
$152$	3.24682e20	0.608058
$153$	−3.71282e19	−0.0653334
$154$	6.49729e20	1.07470
$155$	−3.17072e20	−0.493181
$156$	−2.15911e20	−0.315931
$157$	4.90280e20	0.675146	0.337573	−	0.941299i	$-0.390394\pi$
$157$	4.90280e20	0.675146	0.337573	+	0.941299i	$0.390394\pi$
$158$	4.09286e20	0.530621
$159$	−1.13616e20	−0.138729
$160$	2.05811e20	0.236771
$161$	−2.29383e21	−2.48722
$162$	−7.68485e19	−0.0785674
$163$	−3.88083e20	−0.374233	−0.187116	−	0.982338i	$-0.559914\pi$
$163$	−3.88083e20	−0.374233	−0.187116	+	0.982338i	$0.559914\pi$
$164$	2.66209e20	0.242218
$165$	8.41966e20	0.723098
$166$	−5.22777e20	−0.423926
$167$	3.07051e20	0.235182	0.117591	−	0.993062i	$-0.462483\pi$
$167$	3.07051e20	0.235182	0.117591	+	0.993062i	$0.462483\pi$
$168$	−4.58435e20	−0.331772
$169$	2.89089e20	0.197746
$170$	−2.87018e20	−0.185628
$171$	−9.37198e20	−0.573282
$172$	6.04871e20	0.350060
$173$	−1.72716e21	−0.946008	−0.473004	−	0.881060i	$-0.656830\pi$
$173$	−1.72716e21	−0.946008	−0.473004	+	0.881060i	$0.656830\pi$
$174$	−2.22684e20	−0.115470
$175$	2.62779e21	1.29041
$176$	−5.02534e20	−0.233773
$177$	−2.55031e21	−1.12421
$178$	−2.08117e21	−0.869596
$179$	2.22976e21	0.883395	0.441697	−	0.897164i	$-0.354376\pi$
$179$	2.22976e21	0.883395	0.441697	+	0.897164i	$0.354376\pi$
$180$	−5.94074e20	−0.223230
$181$	3.93656e21	1.40337	0.701683	−	0.712489i	$-0.252432\pi$
$181$	3.93656e21	1.40337	0.701683	+	0.712489i	$0.252432\pi$
$182$	3.71784e21	1.25780
$183$	2.24483e21	0.720938
$184$	1.77416e21	0.541034
$185$	4.41447e21	1.27864
$186$	−5.46262e20	−0.150324
$187$	7.00821e20	0.183279
$188$	1.93085e19	0.00480008
$189$	1.32328e21	0.312798
$190$	−7.24497e21	−1.62884
$191$	−6.72054e21	−1.43743	−0.718716	−	0.695304i	$-0.755270\pi$
$191$	−6.72054e21	−1.43743	−0.718716	+	0.695304i	$0.755270\pi$
$192$	3.54577e20	0.0721688
$193$	−4.56360e21	−0.884124	−0.442062	−	0.896985i	$-0.645753\pi$
$193$	−4.56360e21	−0.884124	−0.442062	+	0.896985i	$0.645753\pi$
$194$	−5.63966e21	−1.04025
$195$	4.81785e21	0.846301
$196$	4.90579e21	0.820873
$197$	−6.63320e20	−0.105753	−0.0528766	−	0.998601i	$-0.516839\pi$
$197$	−6.63320e20	−0.105753	−0.0528766	+	0.998601i	$0.516839\pi$
$198$	1.45057e21	0.220404
$199$	−1.22836e22	−1.77919	−0.889595	−	0.456750i	$-0.849013\pi$
$199$	−1.22836e22	−1.77919	−0.889595	+	0.456750i	$0.849013\pi$
$200$	−2.03247e21	−0.280697
$201$	−2.57999e21	−0.339825
$202$	7.18285e21	0.902524
$203$	3.83446e21	0.459719
$204$	−4.94484e20	−0.0565804
$205$	−5.94019e21	−0.648842
$206$	4.05520e20	0.0422935
$207$	−5.12114e21	−0.510091
$208$	−2.87557e21	−0.273604
$209$	1.76903e22	1.60822
$210$	1.02295e22	0.888736
$211$	−4.36762e21	−0.362711	−0.181356	−	0.983418i	$-0.558049\pi$
$211$	−4.36762e21	−0.362711	−0.181356	+	0.983418i	$0.558049\pi$
$212$	−1.51317e21	−0.120143
$213$	1.04764e22	0.795438
$214$	−3.02682e21	−0.219815
$215$	−1.34971e22	−0.937726
$216$	−1.02349e21	−0.0680414
$217$	9.40625e21	0.598479
$218$	1.74602e22	1.06344
$219$	−1.57795e22	−0.920181
$220$	1.12136e22	0.626221
$221$	4.01020e21	0.214506
$222$	7.60539e21	0.389734
$223$	−8.36561e21	−0.410772	−0.205386	−	0.978681i	$-0.565845\pi$
$223$	−8.36561e21	−0.410772	−0.205386	+	0.978681i	$0.565845\pi$
$224$	−6.10558e21	−0.287323
$225$	5.86673e21	0.264644
$226$	−3.25820e21	−0.140912
$227$	1.46611e22	0.608026	0.304013	−	0.952668i	$-0.401673\pi$
$227$	1.46611e22	0.608026	0.304013	+	0.952668i	$0.401673\pi$
$228$	−1.24819e22	−0.496477
$229$	2.25010e22	0.858548	0.429274	−	0.903174i	$-0.358769\pi$
$229$	2.25010e22	0.858548	0.429274	+	0.903174i	$0.358769\pi$
$230$	−3.95887e22	−1.44930
$231$	−2.49778e22	−0.877485
$232$	−2.96577e21	−0.100000
$233$	3.79109e22	1.22711	0.613553	−	0.789653i	$-0.289740\pi$
$233$	3.79109e22	1.22711	0.613553	+	0.789653i	$0.289740\pi$
$234$	8.30036e21	0.257956
$235$	−4.30850e20	−0.0128582
$236$	−3.39657e22	−0.973592
$237$	−1.57343e22	−0.433250
$238$	8.51468e21	0.225262
$239$	5.79683e21	0.147370	0.0736852	−	0.997282i	$-0.476524\pi$
$239$	5.79683e21	0.147370	0.0736852	+	0.997282i	$0.476524\pi$
$240$	−7.91205e21	−0.193322
$241$	−4.01115e22	−0.942121	−0.471060	−	0.882101i	$-0.656129\pi$
$241$	−4.01115e22	−0.942121	−0.471060	+	0.882101i	$0.656129\pi$
$242$	3.93300e21	0.0888132
$243$	2.95431e21	0.0641500
$244$	2.98973e22	0.624351
$245$	−1.09468e23	−2.19892
$246$	−1.02340e22	−0.197770
$247$	1.01226e23	1.88223
$248$	−7.27527e21	−0.130184
$249$	2.00973e22	0.346134
$250$	−1.17714e22	−0.195164
$251$	−1.96223e22	−0.313220	−0.156610	−	0.987660i	$-0.550057\pi$
$251$	−1.96223e22	−0.313220	−0.156610	+	0.987660i	$0.550057\pi$
$252$	1.76238e22	0.270891
$253$	9.66649e22	1.43095
$254$	−1.36578e21	−0.0194742
$255$	1.10339e22	0.151565
$256$	4.72237e21	0.0625000
$257$	7.08266e22	0.903300	0.451650	−	0.892195i	$-0.350836\pi$
$257$	7.08266e22	0.903300	0.451650	+	0.892195i	$0.350836\pi$
$258$	−2.32533e22	−0.285823
$259$	−1.30960e23	−1.55163
$260$	6.41656e22	0.732918
$261$	8.56072e21	0.0942813
$262$	−5.50305e22	−0.584442
$263$	4.62083e22	0.473305	0.236652	−	0.971594i	$-0.423950\pi$
$263$	4.62083e22	0.473305	0.236652	+	0.971594i	$0.423950\pi$
$264$	1.93191e22	0.190875
$265$	3.37650e22	0.321833
$266$	2.14929e23	1.97661
$267$	8.00072e22	0.710022
$268$	−3.43610e22	−0.294297
$269$	−8.39443e22	−0.693976	−0.346988	−	0.937870i	$-0.612796\pi$
$269$	−8.39443e22	−0.693976	−0.346988	+	0.937870i	$0.612796\pi$
$270$	2.28382e22	0.182266
$271$	−1.51682e23	−1.16876	−0.584380	−	0.811480i	$-0.698662\pi$
$271$	−1.51682e23	−1.16876	−0.584380	+	0.811480i	$0.698662\pi$
$272$	−6.58569e21	−0.0490001
$273$	−1.42926e23	−1.02699
$274$	−2.13916e22	−0.148461
$275$	−1.10739e23	−0.742400
$276$	−6.82048e22	−0.441752
$277$	−1.58000e23	−0.988781	−0.494391	−	0.869240i	$-0.664609\pi$
$277$	−1.58000e23	−0.988781	−0.494391	+	0.869240i	$0.664609\pi$
$278$	−1.73019e23	−1.04633
$279$	2.10001e22	0.122739
$280$	1.36240e23	0.769668
$281$	−2.15511e22	−0.117695	−0.0588476	−	0.998267i	$-0.518743\pi$
$281$	−2.15511e22	−0.117695	−0.0588476	+	0.998267i	$0.518743\pi$
$282$	−7.42283e20	−0.00391925
$283$	−5.48833e22	−0.280201	−0.140100	−	0.990137i	$-0.544743\pi$
$283$	−5.48833e22	−0.280201	−0.140100	+	0.990137i	$0.544743\pi$
$284$	1.39528e23	0.688869
$285$	2.78521e23	1.32994
$286$	−1.56675e23	−0.723640
$287$	1.76222e23	0.787375
$288$	−1.36311e22	−0.0589256
$289$	−2.29888e23	−0.961584
$290$	6.61783e22	0.267876
$291$	2.16808e23	0.849358
$292$	−2.10156e23	−0.796900
$293$	−2.47778e23	−0.909536	−0.454768	−	0.890610i	$-0.650278\pi$
$293$	−2.47778e23	−0.909536	−0.454768	+	0.890610i	$0.650278\pi$
$294$	−1.88595e23	−0.670240
$295$	7.57913e23	2.60802
$296$	1.01291e23	0.337519
$297$	−5.57647e22	−0.179959
$298$	1.05719e23	0.330445
$299$	5.53131e23	1.67476
$300$	7.81348e22	0.229188
$301$	4.00406e23	1.13794
$302$	2.61212e22	0.0719328
$303$	−2.76133e23	−0.736908
$304$	−1.66237e23	−0.429962
$305$	−6.67130e23	−1.67248
$306$	1.90096e22	0.0461977
$307$	−1.10901e22	−0.0261290	−0.0130645	−	0.999915i	$-0.504159\pi$
$307$	−1.10901e22	−0.0261290	−0.0130645	+	0.999915i	$0.504159\pi$
$308$	−3.32661e23	−0.759924
$309$	−1.55896e22	−0.0345325
$310$	1.62341e23	0.348732
$311$	−2.46930e23	−0.514458	−0.257229	−	0.966350i	$-0.582810\pi$
$311$	−2.46930e23	−0.514458	−0.257229	+	0.966350i	$0.582810\pi$
$312$	1.10547e23	0.223397
$313$	2.99103e23	0.586339	0.293170	−	0.956060i	$-0.405290\pi$
$313$	2.99103e23	0.586339	0.293170	+	0.956060i	$0.405290\pi$
$314$	−2.51023e23	−0.477400
$315$	−3.93258e23	−0.725650
$316$	−2.09554e23	−0.375206
$317$	2.31714e22	0.0402614	0.0201307	−	0.999797i	$-0.493592\pi$
$317$	2.31714e22	0.0402614	0.0201307	+	0.999797i	$0.493592\pi$
$318$	5.81714e22	0.0980962
$319$	−1.61589e23	−0.264485
$320$	−1.05375e23	−0.167422
$321$	1.16361e23	0.179478
$322$	1.17444e24	1.75873
$323$	2.31830e23	0.337090
$324$	3.93464e22	0.0555556
$325$	−6.33662e23	−0.868892
$326$	1.98698e23	0.264623
$327$	−6.71230e23	−0.868296
$328$	−1.36299e23	−0.171274
$329$	1.27816e22	0.0156036
$330$	−4.31087e23	−0.511308
$331$	−7.69802e23	−0.887182	−0.443591	−	0.896229i	$-0.646296\pi$
$331$	−7.69802e23	−0.887182	−0.443591	+	0.896229i	$0.646296\pi$
$332$	2.67662e23	0.299761
$333$	−2.92377e23	−0.318216
$334$	−1.57210e23	−0.166299
$335$	7.66733e23	0.788349
$336$	2.34719e23	0.234598
$337$	−2.46339e23	−0.239359	−0.119679	−	0.992813i	$-0.538187\pi$
$337$	−2.46339e23	−0.239359	−0.119679	+	0.992813i	$0.538187\pi$
$338$	−1.48014e23	−0.139828
$339$	1.25256e23	0.115054
$340$	1.46953e23	0.131259
$341$	−3.96392e23	−0.344317
$342$	4.79846e23	0.405372
$343$	1.26941e24	1.04306
$344$	−3.09694e23	−0.247530
$345$	1.52192e24	1.18335
$346$	8.84306e23	0.668929
$347$	2.35373e24	1.73231	0.866157	−	0.499773i	$-0.166583\pi$
$347$	2.35373e24	1.73231	0.866157	+	0.499773i	$0.166583\pi$
$348$	1.14014e23	0.0816500
$349$	−7.20631e23	−0.502194	−0.251097	−	0.967962i	$-0.580791\pi$
$349$	−7.20631e23	−0.502194	−0.251097	+	0.967962i	$0.580791\pi$
$350$	−1.34543e24	−0.912460
$351$	−3.19094e23	−0.210620
$352$	2.57297e23	0.165303
$353$	−7.47328e22	−0.0467360	−0.0233680	−	0.999727i	$-0.507439\pi$
$353$	−7.47328e22	−0.0467360	−0.0233680	+	0.999727i	$0.507439\pi$
$354$	1.30576e24	0.794935
$355$	−3.11343e24	−1.84531
$356$	1.06556e24	0.614897
$357$	−3.27333e23	−0.183925
$358$	−1.14164e24	−0.624654
$359$	−2.75374e24	−1.46732	−0.733660	−	0.679516i	$-0.762190\pi$
$359$	−2.75374e24	−1.46732	−0.733660	+	0.679516i	$0.762190\pi$
$360$	3.04166e23	0.157847
$361$	3.87349e24	1.95787
$362$	−2.01552e24	−0.992330
$363$	−1.51198e23	−0.0725157
$364$	−1.90354e24	−0.889402
$365$	4.68942e24	2.13470
$366$	−1.14935e24	−0.509780
$367$	−1.21541e24	−0.525284	−0.262642	−	0.964893i	$-0.584594\pi$
$367$	−1.21541e24	−0.525284	−0.262642	+	0.964893i	$0.584594\pi$
$368$	−9.08371e23	−0.382569
$369$	3.93428e23	0.161478
$370$	−2.26021e24	−0.904132
$371$	−1.00167e24	−0.390547
$372$	2.79686e23	0.106295
$373$	−2.98671e24	−1.10652	−0.553259	−	0.833009i	$-0.686616\pi$
$373$	−2.98671e24	−1.10652	−0.553259	+	0.833009i	$0.686616\pi$
$374$	−3.58820e23	−0.129597
$375$	4.52533e23	0.159350
$376$	−9.88595e21	−0.00339417
$377$	−9.24638e23	−0.309549
$378$	−6.77518e23	−0.221181
$379$	−4.01605e24	−1.27858	−0.639288	−	0.768968i	$-0.720771\pi$
$379$	−4.01605e24	−1.27858	−0.639288	+	0.768968i	$0.720771\pi$
$380$	3.70943e24	1.15176
$381$	5.25050e22	0.0159006
$382$	3.44092e24	1.01642
$383$	2.15253e24	0.620241	0.310121	−	0.950697i	$-0.399631\pi$
$383$	2.15253e24	0.620241	0.310121	+	0.950697i	$0.399631\pi$
$384$	−1.81544e23	−0.0510310
$385$	7.42301e24	2.03565
$386$	2.33656e24	0.625170
$387$	8.93935e23	0.233374
$388$	2.88751e24	0.735566
$389$	−7.09755e24	−1.76436	−0.882180	−	0.470913i	$-0.843925\pi$
$389$	−7.09755e24	−1.76436	−0.882180	+	0.470913i	$0.843925\pi$
$390$	−2.46674e24	−0.598425
$391$	1.26679e24	0.299934
$392$	−2.51176e24	−0.580445
$393$	2.11556e24	0.477195
$394$	3.39620e23	0.0747788
$395$	4.67600e24	1.00508
$396$	−7.42691e23	−0.155849
$397$	7.68951e24	1.57539	0.787696	−	0.616064i	$-0.211274\pi$
$397$	7.68951e24	1.57539	0.787696	+	0.616064i	$0.211274\pi$
$398$	6.28922e24	1.25808
$399$	−8.26261e24	−1.61389
$400$	1.04062e24	0.198483
$401$	−6.56792e24	−1.22337	−0.611683	−	0.791103i	$-0.709507\pi$
$401$	−6.56792e24	−1.22337	−0.611683	+	0.791103i	$0.709507\pi$
$402$	1.32095e24	0.240292
$403$	−2.26821e24	−0.402982
$404$	−3.67762e24	−0.638181
$405$	−8.77977e23	−0.148820
$406$	−1.96324e24	−0.325070
$407$	5.51881e24	0.892686
$408$	2.53176e23	0.0400084
$409$	−1.12209e24	−0.173242	−0.0866212	−	0.996241i	$-0.527607\pi$
$409$	−1.12209e24	−0.173242	−0.0866212	+	0.996241i	$0.527607\pi$
$410$	3.04138e24	0.458800
$411$	8.22364e23	0.121218
$412$	−2.07626e23	−0.0299060
$413$	−2.24842e25	−3.16485
$414$	2.62202e24	0.360689
$415$	−5.97262e24	−0.802986
$416$	1.47229e24	0.193467
$417$	6.65143e24	0.854324
$418$	−9.05741e24	−1.13718
$419$	1.74471e24	0.214136	0.107068	−	0.994252i	$-0.465854\pi$
$419$	1.74471e24	0.214136	0.107068	+	0.994252i	$0.465854\pi$
$420$	−5.23753e24	−0.628431
$421$	8.39638e24	0.984946	0.492473	−	0.870328i	$-0.336093\pi$
$421$	8.39638e24	0.984946	0.492473	+	0.870328i	$0.336093\pi$
$422$	2.23622e24	0.256476
$423$	2.85359e22	0.00320005
$424$	7.74744e23	0.0849538
$425$	−1.45122e24	−0.155611
$426$	−5.36392e24	−0.562459
$427$	1.97911e25	2.02957
$428$	1.54973e24	0.155432
$429$	6.02311e24	0.590849
$430$	6.91053e24	0.663072
$431$	−1.30565e25	−1.22544	−0.612721	−	0.790300i	$-0.709925\pi$
$431$	−1.30565e25	−1.22544	−0.612721	+	0.790300i	$0.709925\pi$
$432$	5.24027e23	0.0481125
$433$	−1.31390e25	−1.18012	−0.590060	−	0.807360i	$-0.700896\pi$
$433$	−1.31390e25	−1.18012	−0.590060	+	0.807360i	$0.700896\pi$
$434$	−4.81600e24	−0.423188
$435$	−2.54412e24	−0.218720
$436$	−8.93964e24	−0.751966
$437$	3.19766e25	2.63184
$438$	8.07909e24	0.650666
$439$	−6.28375e24	−0.495229	−0.247614	−	0.968859i	$-0.579647\pi$
$439$	−6.28375e24	−0.495229	−0.247614	+	0.968859i	$0.579647\pi$
$440$	−5.74134e24	−0.442805
$441$	7.25022e24	0.547249
$442$	−2.05322e24	−0.151679
$443$	2.44870e25	1.77051	0.885257	−	0.465102i	$-0.153982\pi$
$443$	2.44870e25	1.77051	0.885257	+	0.465102i	$0.153982\pi$
$444$	−3.89396e24	−0.275583
$445$	−2.37769e25	−1.64716
$446$	4.28319e24	0.290460
$447$	−4.06420e24	−0.269807
$448$	3.12606e24	0.203168
$449$	−8.80163e23	−0.0560045	−0.0280022	−	0.999608i	$-0.508915\pi$
$449$	−8.80163e23	−0.0560045	−0.0280022	+	0.999608i	$0.508915\pi$
$450$	−3.00376e24	−0.187132
$451$	−7.42622e24	−0.452992
$452$	1.66820e24	0.0996397
$453$	−1.00419e24	−0.0587329
$454$	−7.50651e24	−0.429939
$455$	4.24756e25	2.38249
$456$	6.39072e24	0.351062
$457$	9.21395e24	0.495727	0.247863	−	0.968795i	$-0.420272\pi$
$457$	9.21395e24	0.495727	0.247863	+	0.968795i	$0.420272\pi$
$458$	−1.15205e25	−0.607085
$459$	−7.30795e23	−0.0377203
$460$	2.02694e25	1.02481
$461$	−3.77928e25	−1.87176	−0.935881	−	0.352317i	$-0.885394\pi$
$461$	−3.77928e25	−1.87176	−0.935881	+	0.352317i	$0.885394\pi$
$462$	1.27886e25	0.620476
$463$	7.07724e24	0.336391	0.168196	−	0.985754i	$-0.446206\pi$
$463$	7.07724e24	0.336391	0.168196	+	0.985754i	$0.446206\pi$
$464$	1.51847e24	0.0707109
$465$	−6.24092e24	−0.284738
$466$	−1.94104e25	−0.867695
$467$	−3.34015e25	−1.46304	−0.731518	−	0.681822i	$-0.761188\pi$
$467$	−3.34015e25	−1.46304	−0.731518	+	0.681822i	$0.761188\pi$
$468$	−4.24978e24	−0.182403
$469$	−2.27459e25	−0.956668
$470$	2.20595e23	0.00909215
$471$	9.65018e24	0.389796
$472$	1.73905e25	0.688434
$473$	−1.68736e25	−0.654678
$474$	8.05597e24	0.306354
$475$	−3.66321e25	−1.36544
$476$	−4.35952e24	−0.159284
$477$	−2.23631e24	−0.0800952
$478$	−2.96798e24	−0.104207
$479$	2.78353e25	0.958093	0.479047	−	0.877789i	$-0.340982\pi$
$479$	2.78353e25	0.958093	0.479047	+	0.877789i	$0.340982\pi$
$480$	4.05097e24	0.136700
$481$	3.15794e25	1.04478
$482$	2.05371e25	0.666180
$483$	−4.51494e25	−1.43600
$484$	−2.01369e24	−0.0628004
$485$	−6.44319e25	−1.97040
$486$	−1.51261e24	−0.0453609
$487$	4.44276e25	1.30656	0.653278	−	0.757118i	$-0.273393\pi$
$487$	4.44276e25	1.30656	0.653278	+	0.757118i	$0.273393\pi$
$488$	−1.53074e25	−0.441483
$489$	−7.63863e24	−0.216063
$490$	5.60476e25	1.55487
$491$	5.06809e25	1.37902	0.689509	−	0.724277i	$-0.257826\pi$
$491$	5.06809e25	1.37902	0.689509	+	0.724277i	$0.257826\pi$
$492$	5.23979e24	0.139844
$493$	−2.11762e24	−0.0554375
$494$	−5.18278e25	−1.33094
$495$	1.65724e25	0.417481
$496$	3.72494e24	0.0920541
$497$	9.23630e25	2.23930
$498$	−1.02898e25	−0.244754
$499$	3.54622e25	0.827580	0.413790	−	0.910372i	$-0.364205\pi$
$499$	3.54622e25	0.827580	0.413790	+	0.910372i	$0.364205\pi$
$500$	6.02697e24	0.138002
$501$	6.04368e24	0.135782
$502$	1.00466e25	0.221480
$503$	2.04986e25	0.443434	0.221717	−	0.975111i	$-0.428834\pi$
$503$	2.04986e25	0.443434	0.221717	+	0.975111i	$0.428834\pi$
$504$	−9.02338e24	−0.191549
$505$	8.20625e25	1.70953
$506$	−4.94925e25	−1.01183
$507$	5.69014e24	0.114169
$508$	6.99277e23	0.0137703
$509$	−8.73938e25	−1.68912	−0.844562	−	0.535457i	$-0.820139\pi$
$509$	−8.73938e25	−1.68912	−0.844562	+	0.535457i	$0.820139\pi$
$510$	−5.64938e24	−0.107173
$511$	−1.39116e26	−2.59048
$512$	−2.41785e24	−0.0441942
$513$	−1.84469e25	−0.330985
$514$	−3.62632e25	−0.638729
$515$	4.63298e24	0.0801109
$516$	1.19057e25	0.202107
$517$	−5.38634e23	−0.00897705
$518$	6.70513e25	1.09717
$519$	−3.39957e25	−0.546178
$520$	−3.28528e25	−0.518251
$521$	2.50510e25	0.388031	0.194016	−	0.980998i	$-0.437849\pi$
$521$	2.50510e25	0.388031	0.194016	+	0.980998i	$0.437849\pi$
$522$	−4.38309e24	−0.0666669
$523$	−9.23396e24	−0.137918	−0.0689591	−	0.997619i	$-0.521968\pi$
$523$	−9.23396e24	−0.137918	−0.0689591	+	0.997619i	$0.521968\pi$
$524$	2.81756e25	0.413263
$525$	5.17227e25	0.745020
$526$	−2.36587e25	−0.334677
$527$	−5.19470e24	−0.0721705
$528$	−9.89137e24	−0.134969
$529$	1.00114e26	1.34174
$530$	−1.72877e25	−0.227570
$531$	−5.01977e25	−0.649062
$532$	−1.10044e26	−1.39767
$533$	−4.24939e25	−0.530174
$534$	−4.09637e25	−0.502061
$535$	−3.45808e25	−0.416365
$536$	1.75928e25	0.208099
$537$	4.38884e25	0.510028
$538$	4.29795e25	0.490715
$539$	−1.36853e26	−1.53519
$540$	−1.16932e25	−0.128882
$541$	−2.64716e25	−0.286686	−0.143343	−	0.989673i	$-0.545785\pi$
$541$	−2.64716e25	−0.286686	−0.143343	+	0.989673i	$0.545785\pi$
$542$	7.76611e25	0.826438
$543$	7.74834e25	0.810234
$544$	3.37187e24	0.0346483
$545$	1.99479e26	2.01433
$546$	7.31783e25	0.726193
$547$	1.51798e25	0.148042	0.0740211	−	0.997257i	$-0.476417\pi$
$547$	1.51798e25	0.148042	0.0740211	+	0.997257i	$0.476417\pi$
$548$	1.09525e25	0.104978
$549$	4.41850e25	0.416234
$550$	5.66981e25	0.524956
$551$	−5.34535e25	−0.486448
$552$	3.49209e25	0.312366
$553$	−1.38718e26	−1.21968
$554$	8.08962e25	0.699174
$555$	8.68899e25	0.738221
$556$	8.85857e25	0.739866
$557$	−1.25393e26	−1.02956	−0.514778	−	0.857324i	$-0.672126\pi$
$557$	−1.25393e26	−1.02956	−0.514778	+	0.857324i	$0.672126\pi$
$558$	−1.07521e25	−0.0867895
$559$	−9.65534e25	−0.766223
$560$	−6.97549e25	−0.544238
$561$	1.37943e25	0.105816
$562$	1.10341e25	0.0832231
$563$	4.25965e25	0.315896	0.157948	−	0.987447i	$-0.449512\pi$
$563$	4.25965e25	0.315896	0.157948	+	0.987447i	$0.449512\pi$
$564$	3.80049e23	0.00277133
$565$	−3.72242e25	−0.266910
$566$	2.81003e25	0.198132
$567$	2.60461e25	0.180594
$568$	−7.14383e25	−0.487104
$569$	1.41504e25	0.0948861	0.0474431	−	0.998874i	$-0.484893\pi$
$569$	1.41504e25	0.0948861	0.0474431	+	0.998874i	$0.484893\pi$
$570$	−1.42603e26	−0.940410
$571$	2.27682e26	1.47668	0.738338	−	0.674431i	$-0.235611\pi$
$571$	2.27682e26	1.47668	0.738338	+	0.674431i	$0.235611\pi$
$572$	8.02176e25	0.511690
$573$	−1.32280e26	−0.829902
$574$	−9.02255e25	−0.556758
$575$	−2.00169e26	−1.21493
$576$	6.97915e24	0.0416667
$577$	1.24028e25	0.0728363	0.0364182	−	0.999337i	$-0.488405\pi$
$577$	1.24028e25	0.0728363	0.0364182	+	0.999337i	$0.488405\pi$
$578$	1.17703e26	0.679942
$579$	−8.98253e25	−0.510449
$580$	−3.38833e25	−0.189417
$581$	1.77184e26	0.974429
$582$	−1.11005e26	−0.600587
$583$	4.22118e25	0.224689
$584$	1.07600e26	0.563494
$585$	9.48298e25	0.488612
$586$	1.26862e26	0.643139
$587$	−2.54582e26	−1.26989	−0.634943	−	0.772559i	$-0.718977\pi$
$587$	−2.54582e26	−1.26989	−0.634943	+	0.772559i	$0.718977\pi$
$588$	9.65606e25	0.473931
$589$	−1.31126e26	−0.633276
$590$	−3.88051e26	−1.84415
$591$	−1.30561e25	−0.0610567
$592$	−5.18609e25	−0.238662
$593$	1.65796e26	0.750853	0.375426	−	0.926852i	$-0.377496\pi$
$593$	1.65796e26	0.750853	0.375426	+	0.926852i	$0.377496\pi$
$594$	2.85515e25	0.127250
$595$	9.72784e25	0.426683
$596$	−5.41282e25	−0.233660
$597$	−2.41779e26	−1.02722
$598$	−2.83203e26	−1.18423
$599$	1.15640e26	0.475942	0.237971	−	0.971272i	$-0.423518\pi$
$599$	1.15640e26	0.475942	0.237971	+	0.971272i	$0.423518\pi$
$600$	−4.00050e25	−0.162061
$601$	4.05444e26	1.61668	0.808339	−	0.588718i	$-0.200367\pi$
$601$	4.05444e26	1.61668	0.808339	+	0.588718i	$0.200367\pi$
$602$	−2.05008e26	−0.804643
$603$	−5.07819e25	−0.196198
$604$	−1.33741e25	−0.0508642
$605$	4.49336e25	0.168227
$606$	1.41380e26	0.521073
$607$	3.22398e26	1.16977	0.584884	−	0.811117i	$-0.301140\pi$
$607$	3.22398e26	1.16977	0.584884	+	0.811117i	$0.301140\pi$
$608$	8.51135e25	0.304029
$609$	7.54737e25	0.265419
$610$	3.41570e26	1.18262
$611$	−3.08214e24	−0.0105066
$612$	−9.73294e24	−0.0326667
$613$	−1.03291e26	−0.341342	−0.170671	−	0.985328i	$-0.554594\pi$
$613$	−1.03291e26	−0.341342	−0.170671	+	0.985328i	$0.554594\pi$
$614$	5.67815e24	0.0184760
$615$	−1.16921e26	−0.374609
$616$	1.70323e26	0.537348
$617$	−1.56088e26	−0.484909	−0.242455	−	0.970163i	$-0.577953\pi$
$617$	−1.56088e26	−0.484909	−0.242455	+	0.970163i	$0.577953\pi$
$618$	7.98185e24	0.0244182
$619$	1.16594e26	0.351249	0.175624	−	0.984457i	$-0.443806\pi$
$619$	1.16594e26	0.351249	0.175624	+	0.984457i	$0.443806\pi$
$620$	−8.31184e25	−0.246590
$621$	−1.00799e26	−0.294501
$622$	1.26428e26	0.363777
$623$	7.05366e26	1.99884
$624$	−5.65999e25	−0.157965
$625$	−4.23317e26	−1.16360
$626$	−1.53141e26	−0.414604
$627$	3.48197e26	0.928504
$628$	1.28524e26	0.337573
$629$	7.23239e25	0.187112
$630$	2.01348e26	0.513112
$631$	−1.76820e26	−0.443866	−0.221933	−	0.975062i	$-0.571237\pi$
$631$	−1.76820e26	−0.443866	−0.221933	+	0.975062i	$0.571237\pi$
$632$	1.07292e26	0.265311
$633$	−8.59678e25	−0.209411
$634$	−1.18637e25	−0.0284691
$635$	−1.56037e25	−0.0368873
$636$	−2.97838e25	−0.0693645
$637$	−7.83093e26	−1.79675
$638$	8.27338e25	0.187019
$639$	2.06207e26	0.459246
$640$	5.39520e25	0.118385
$641$	−7.99922e26	−1.72940	−0.864701	−	0.502286i	$-0.832492\pi$
$641$	−7.99922e26	−1.72940	−0.864701	+	0.502286i	$0.832492\pi$
$642$	−5.95770e25	−0.126910
$643$	−4.51740e26	−0.948165	−0.474082	−	0.880480i	$-0.657220\pi$
$643$	−4.51740e26	−0.948165	−0.474082	+	0.880480i	$0.657220\pi$
$644$	−6.01313e26	−1.24361
$645$	−2.65664e26	−0.541396
$646$	−1.18697e26	−0.238359
$647$	−7.36280e26	−1.45698	−0.728488	−	0.685058i	$-0.759777\pi$
$647$	−7.36280e26	−1.45698	−0.728488	+	0.685058i	$0.759777\pi$
$648$	−2.01454e25	−0.0392837
$649$	9.47516e26	1.82080
$650$	3.24435e26	0.614399
$651$	1.85143e26	0.345532
$652$	−1.01734e26	−0.187116
$653$	1.02602e26	0.185986	0.0929928	−	0.995667i	$-0.470357\pi$
$653$	1.02602e26	0.185986	0.0929928	+	0.995667i	$0.470357\pi$
$654$	3.43670e26	0.613978
$655$	−6.28712e26	−1.10703
$656$	6.97850e25	0.121109
$657$	−3.10587e26	−0.531267
$658$	−6.54418e24	−0.0110334
$659$	1.08377e27	1.80105	0.900523	−	0.434808i	$-0.143184\pi$
$659$	1.08377e27	1.80105	0.900523	+	0.434808i	$0.143184\pi$
$660$	2.20716e26	0.361549
$661$	−8.74444e26	−1.41195	−0.705973	−	0.708238i	$-0.749490\pi$
$661$	−8.74444e26	−1.41195	−0.705973	+	0.708238i	$0.749490\pi$
$662$	3.94138e26	0.627333
$663$	7.89327e25	0.123845
$664$	−1.37043e26	−0.211963
$665$	2.45552e27	3.74402
$666$	1.49697e26	0.225013
$667$	−2.92086e26	−0.432828
$668$	8.04916e25	0.117591
$669$	−1.64660e26	−0.237160
$670$	−3.92567e26	−0.557447
$671$	−8.34022e26	−1.16765
$672$	−1.20176e26	−0.165886
$673$	−7.45888e25	−0.101515	−0.0507575	−	0.998711i	$-0.516164\pi$
$673$	−7.45888e25	−0.101515	−0.0507575	+	0.998711i	$0.516164\pi$
$674$	1.26126e26	0.169252
$675$	1.15475e26	0.152792
$676$	7.57830e25	0.0988731
$677$	−2.73338e26	−0.351648	−0.175824	−	0.984422i	$-0.556259\pi$
$677$	−2.73338e26	−0.351648	−0.175824	+	0.984422i	$0.556259\pi$
$678$	−6.41311e25	−0.0813554
$679$	1.91144e27	2.39110
$680$	−7.52401e25	−0.0928142
$681$	2.88575e26	0.351044
$682$	2.02953e26	0.243469
$683$	−1.31536e26	−0.155614	−0.0778070	−	0.996968i	$-0.524792\pi$
$683$	−1.31536e26	−0.155614	−0.0778070	+	0.996968i	$0.524792\pi$
$684$	−2.45681e26	−0.286641
$685$	−2.44394e26	−0.281210
$686$	−6.49940e26	−0.737554
$687$	4.42887e26	0.495683
$688$	1.58563e26	0.175030
$689$	2.41542e26	0.262972
$690$	−7.79225e26	−0.836752
$691$	1.24536e27	1.31903	0.659514	−	0.751693i	$-0.270762\pi$
$691$	1.24536e27	1.31903	0.659514	+	0.751693i	$0.270762\pi$
$692$	−4.52765e26	−0.473004
$693$	−4.91637e26	−0.506616
$694$	−1.20511e27	−1.22493
$695$	−1.97670e27	−1.98192
$696$	−5.83753e25	−0.0577352
$697$	−9.73204e25	−0.0949495
$698$	3.68963e26	0.355105
$699$	7.46199e26	0.708470
$700$	6.88859e26	0.645207
$701$	−2.73106e25	−0.0252354	−0.0126177	−	0.999920i	$-0.504016\pi$
$701$	−2.73106e25	−0.0252354	−0.0126177	+	0.999920i	$0.504016\pi$
$702$	1.63376e26	0.148931
$703$	1.82561e27	1.64185
$704$	−1.31736e26	−0.116887
$705$	−8.48043e24	−0.00742371
$706$	3.82632e25	0.0330473
$707$	−2.43447e27	−2.07453
$708$	−6.68548e26	−0.562104
$709$	−5.31078e26	−0.440574	−0.220287	−	0.975435i	$-0.570699\pi$
$709$	−5.31078e26	−0.440574	−0.220287	+	0.975435i	$0.570699\pi$
$710$	1.59408e27	1.30483
$711$	−3.09699e26	−0.250137
$712$	−5.45566e26	−0.434798
$713$	−7.16511e26	−0.563472
$714$	1.67594e26	0.130055
$715$	−1.78998e27	−1.37069
$716$	5.84519e26	0.441697
$717$	1.14099e26	0.0850843
$718$	1.40991e27	1.03755
$719$	1.35673e27	0.985304	0.492652	−	0.870226i	$-0.336028\pi$
$719$	1.35673e27	0.985304	0.492652	+	0.870226i	$0.336028\pi$
$720$	−1.55733e26	−0.111615
$721$	−1.37442e26	−0.0972153
$722$	−1.98323e27	−1.38442
$723$	−7.89514e26	−0.543934
$724$	1.03195e27	0.701683
$725$	3.34611e26	0.224559
$726$	7.74131e25	0.0512763
$727$	−2.08184e26	−0.136104	−0.0680518	−	0.997682i	$-0.521678\pi$
$727$	−2.08184e26	−0.136104	−0.0680518	+	0.997682i	$0.521678\pi$
$728$	9.74610e26	0.628902
$729$	5.81497e25	0.0370370
$730$	−2.40098e27	−1.50946
$731$	−2.21128e26	−0.137224
$732$	5.88469e26	0.360469
$733$	2.95872e27	1.78902	0.894511	−	0.447046i	$-0.147524\pi$
$733$	2.95872e27	1.78902	0.894511	+	0.447046i	$0.147524\pi$
$734$	6.22288e26	0.371432
$735$	−2.15466e27	−1.26955
$736$	4.65086e26	0.270517
$737$	9.58543e26	0.550390
$738$	−2.01435e26	−0.114183
$739$	1.44513e26	0.0808695	0.0404347	−	0.999182i	$-0.487126\pi$
$739$	1.44513e26	0.0808695	0.0404347	+	0.999182i	$0.487126\pi$
$740$	1.15723e27	0.639318
$741$	1.99244e27	1.08670
$742$	5.12856e26	0.276158
$743$	−3.03048e27	−1.61108	−0.805541	−	0.592540i	$-0.798125\pi$
$743$	−3.03048e27	−1.61108	−0.805541	+	0.592540i	$0.798125\pi$
$744$	−1.43199e26	−0.0751619
$745$	1.20782e27	0.625918
$746$	1.52919e27	0.782427
$747$	3.95575e26	0.199841
$748$	1.83716e26	0.0916393
$749$	1.02587e27	0.505262
$750$	−2.31697e26	−0.112678
$751$	−1.46434e27	−0.703174	−0.351587	−	0.936155i	$-0.614358\pi$
$751$	−1.46434e27	−0.703174	−0.351587	+	0.936155i	$0.614358\pi$
$752$	5.06160e24	0.00240004
$753$	−3.86226e26	−0.180838
$754$	4.73415e26	0.218884
$755$	2.98429e26	0.136253
$756$	3.46889e26	0.156399
$757$	3.25829e26	0.145070	0.0725351	−	0.997366i	$-0.476891\pi$
$757$	3.25829e26	0.145070	0.0725351	+	0.997366i	$0.476891\pi$
$758$	2.05622e27	0.904089
$759$	1.90266e27	0.826159
$760$	−1.89923e27	−0.814419
$761$	−9.57431e26	−0.405465	−0.202732	−	0.979234i	$-0.564982\pi$
$761$	−9.57431e26	−0.405465	−0.202732	+	0.979234i	$0.564982\pi$
$762$	−2.68826e25	−0.0112434
$763$	−5.91776e27	−2.44441
$764$	−1.76175e27	−0.718716
$765$	2.17181e26	0.0875061
$766$	−1.10209e27	−0.438577
$767$	5.42182e27	2.13103
$768$	9.29503e25	0.0360844
$769$	−1.07414e27	−0.411870	−0.205935	−	0.978566i	$-0.566024\pi$
$769$	−1.07414e27	−0.411870	−0.205935	+	0.978566i	$0.566024\pi$
$770$	−3.80058e27	−1.43942
$771$	1.39408e27	0.521520
$772$	−1.19632e27	−0.442062
$773$	4.04134e27	1.47509	0.737547	−	0.675295i	$-0.235984\pi$
$773$	4.04134e27	1.47509	0.737547	+	0.675295i	$0.235984\pi$
$774$	−4.57695e26	−0.165020
$775$	8.20829e26	0.292339
$776$	−1.47840e27	−0.520124
$777$	−2.57768e27	−0.895837
$778$	3.63394e27	1.24759
$779$	−2.45658e27	−0.833154
$780$	1.26297e27	0.423150
$781$	−3.89230e27	−1.28831
$782$	−6.48597e26	−0.212085
$783$	1.68501e26	0.0544333
$784$	1.28602e27	0.410437
$785$	−2.86789e27	−0.904275
$786$	−1.08317e27	−0.337428
$787$	2.25240e27	0.693242	0.346621	−	0.938005i	$-0.387329\pi$
$787$	2.25240e27	0.693242	0.346621	+	0.938005i	$0.387329\pi$
$788$	−1.73885e26	−0.0528766
$789$	9.09519e26	0.273263
$790$	−2.39411e27	−0.710702
$791$	1.10429e27	0.323898
$792$	3.80258e26	0.110202
$793$	−4.77240e27	−1.36660
$794$	−3.93703e27	−1.11397
$795$	6.64596e26	0.185810
$796$	−3.22008e27	−0.889595
$797$	−3.52672e27	−0.962757	−0.481379	−	0.876513i	$-0.659864\pi$
$797$	−3.52672e27	−0.962757	−0.481379	+	0.876513i	$0.659864\pi$
$798$	4.23046e27	1.14119
$799$	−7.05878e24	−0.00188163
$800$	−5.32799e26	−0.140349
$801$	1.57478e27	0.409931
$802$	3.36277e27	0.865050
$803$	5.86255e27	1.49035
$804$	−6.76328e26	−0.169912
$805$	1.34177e28	3.33133
$806$	1.16132e27	0.284951
$807$	−1.65228e27	−0.400667
$808$	1.88294e27	0.451262
$809$	7.00961e27	1.66029	0.830143	−	0.557550i	$-0.188259\pi$
$809$	7.00961e27	1.66029	0.830143	+	0.557550i	$0.188259\pi$
$810$	4.49524e26	0.105231
$811$	7.37922e27	1.70731	0.853655	−	0.520838i	$-0.174381\pi$
$811$	7.37922e27	1.70731	0.853655	+	0.520838i	$0.174381\pi$
$812$	1.00518e27	0.229859
$813$	−2.98555e27	−0.674784
$814$	−2.82563e27	−0.631224
$815$	2.27009e27	0.501239
$816$	−1.29626e26	−0.0282902
$817$	−5.58177e27	−1.20410
$818$	5.74508e26	0.122501
$819$	−2.81322e27	−0.592934
$820$	−1.55719e27	−0.324421
$821$	−9.26688e27	−1.90842	−0.954209	−	0.299141i	$-0.903300\pi$
$821$	−9.26688e27	−1.90842	−0.954209	+	0.299141i	$0.903300\pi$
$822$	−4.21051e26	−0.0857140
$823$	−6.38372e27	−1.28462	−0.642311	−	0.766444i	$-0.722024\pi$
$823$	−6.38372e27	−1.28462	−0.642311	+	0.766444i	$0.722024\pi$
$824$	1.06305e26	0.0211468
$825$	−2.17967e27	−0.428625
$826$	1.15119e28	2.23788
$827$	−1.32238e27	−0.254129	−0.127064	−	0.991894i	$-0.540556\pi$
$827$	−1.32238e27	−0.254129	−0.127064	+	0.991894i	$0.540556\pi$
$828$	−1.34247e27	−0.255046
$829$	3.02476e27	0.568097	0.284049	−	0.958810i	$-0.408322\pi$
$829$	3.02476e27	0.568097	0.284049	+	0.958810i	$0.408322\pi$
$830$	3.05798e27	0.567797
$831$	−3.10992e27	−0.570873
$832$	−7.53814e26	−0.136802
$833$	−1.79345e27	−0.321783
$834$	−3.40553e27	−0.604098
$835$	−1.79609e27	−0.314997
$836$	4.63740e27	0.804108
$837$	4.13346e26	0.0708633
$838$	−8.93293e26	−0.151417
$839$	−2.48470e27	−0.416423	−0.208212	−	0.978084i	$-0.566764\pi$
$839$	−2.48470e27	−0.416423	−0.208212	+	0.978084i	$0.566764\pi$
$840$	2.68161e27	0.444368
$841$	−5.61500e27	−0.919999
$842$	−4.29895e27	−0.696462
$843$	−4.24190e26	−0.0679513
$844$	−1.14494e27	−0.181356
$845$	−1.69102e27	−0.264857
$846$	−1.46104e25	−0.00226278
$847$	−1.33300e27	−0.204145
$848$	−3.96669e26	−0.0600714
$849$	−1.08027e27	−0.161774
$850$	7.43027e26	0.110033
$851$	9.97571e27	1.46087
$852$	2.74633e27	0.397719
$853$	−5.61792e27	−0.804562	−0.402281	−	0.915516i	$-0.631783\pi$
$853$	−5.61792e27	−0.804562	−0.402281	+	0.915516i	$0.631783\pi$
$854$	−1.01330e28	−1.43512
$855$	5.48213e27	0.767841
$856$	−7.93464e26	−0.109907
$857$	−9.20716e27	−1.26127	−0.630635	−	0.776080i	$-0.717205\pi$
$857$	−9.20716e27	−1.26127	−0.630635	+	0.776080i	$0.717205\pi$
$858$	−3.08383e27	−0.417793
$859$	8.80243e27	1.17942	0.589709	−	0.807616i	$-0.299242\pi$
$859$	8.80243e27	1.17942	0.589709	+	0.807616i	$0.299242\pi$
$860$	−3.53819e27	−0.468863
$861$	3.46857e27	0.454591
$862$	6.68493e27	0.866518
$863$	−6.52182e27	−0.836116	−0.418058	−	0.908420i	$-0.637289\pi$
$863$	−6.52182e27	−0.836116	−0.418058	+	0.908420i	$0.637289\pi$
$864$	−2.68302e26	−0.0340207
$865$	1.01030e28	1.26706
$866$	6.72715e27	0.834471
$867$	−4.52489e27	−0.555171
$868$	2.46579e27	0.299239
$869$	5.84578e27	0.701705
$870$	1.30259e27	0.154659
$871$	5.48492e27	0.644166
$872$	4.57710e27	0.531721
$873$	4.26742e27	0.490377
$874$	−1.63720e28	−1.86099
$875$	3.98966e27	0.448600
$876$	−4.13649e27	−0.460091
$877$	2.73862e26	0.0301326	0.0150663	−	0.999886i	$-0.495204\pi$
$877$	2.73862e26	0.0301326	0.0150663	+	0.999886i	$0.495204\pi$
$878$	3.21728e27	0.350179
$879$	−4.87701e27	−0.525121
$880$	2.93957e27	0.313111
$881$	−1.32037e28	−1.39132	−0.695659	−	0.718373i	$-0.744887\pi$
$881$	−1.32037e28	−1.39132	−0.695659	+	0.718373i	$0.744887\pi$
$882$	−3.71211e27	−0.386963
$883$	−3.43259e27	−0.353993	−0.176997	−	0.984211i	$-0.556638\pi$
$883$	−3.43259e27	−0.353993	−0.176997	+	0.984211i	$0.556638\pi$
$884$	1.05125e27	0.107253
$885$	1.49180e28	1.50574
$886$	−1.25373e28	−1.25194
$887$	1.63516e28	1.61542	0.807709	−	0.589581i	$-0.200707\pi$
$887$	1.63516e28	1.61542	0.807709	+	0.589581i	$0.200707\pi$
$888$	1.99371e27	0.194867
$889$	4.62899e26	0.0447631
$890$	1.21738e28	1.16472
$891$	−1.09762e27	−0.103899
$892$	−2.19299e27	−0.205386
$893$	−1.78179e26	−0.0165108
$894$	2.08087e27	0.190783
$895$	−1.30430e28	−1.18320
$896$	−1.60054e27	−0.143662
$897$	1.08873e28	0.966921
$898$	4.50643e26	0.0396011
$899$	1.19775e27	0.104148
$900$	1.53793e27	0.132322
$901$	5.53185e26	0.0470961
$902$	3.80222e27	0.320314
$903$	7.88118e27	0.656989
$904$	−8.54117e26	−0.0704559
$905$	−2.30269e28	−1.87964
$906$	5.14144e26	0.0415304
$907$	1.74989e28	1.39875	0.699377	−	0.714753i	$-0.253461\pi$
$907$	1.74989e28	1.39875	0.699377	+	0.714753i	$0.253461\pi$
$908$	3.84333e27	0.304013
$909$	−5.43512e27	−0.425454
$910$	−2.17475e28	−1.68467
$911$	1.57852e28	1.21011	0.605055	−	0.796184i	$-0.293151\pi$
$911$	1.57852e28	1.21011	0.605055	+	0.796184i	$0.293151\pi$
$912$	−3.27205e27	−0.248238
$913$	−7.46676e27	−0.560608
$914$	−4.71754e27	−0.350532
$915$	−1.31311e28	−0.965609
$916$	5.89850e27	0.429274
$917$	1.86514e28	1.34339
$918$	3.74167e26	0.0266723
$919$	−7.61316e27	−0.537115	−0.268558	−	0.963264i	$-0.586547\pi$
$919$	−7.61316e27	−0.537115	−0.268558	+	0.963264i	$0.586547\pi$
$920$	−1.03779e28	−0.724648
$921$	−2.18287e26	−0.0150856
$922$	1.93499e28	1.32353
$923$	−2.22723e28	−1.50782
$924$	−6.54777e27	−0.438743
$925$	−1.14281e28	−0.757926
$926$	−3.62355e27	−0.237864
$927$	−3.06849e26	−0.0199374
$928$	−7.77459e26	−0.0500002
$929$	−1.20652e28	−0.768044	−0.384022	−	0.923324i	$-0.625461\pi$
$929$	−1.20652e28	−0.768044	−0.384022	+	0.923324i	$0.625461\pi$
$930$	3.19535e27	0.201340
$931$	−4.52708e28	−2.82355
$932$	9.93810e27	0.613553
$933$	−4.86032e27	−0.297023
$934$	1.71015e28	1.03452
$935$	−4.09944e27	−0.245479
$936$	2.17589e27	0.128978
$937$	2.77032e28	1.62557	0.812783	−	0.582567i	$-0.197951\pi$
$937$	2.77032e28	1.62557	0.812783	+	0.582567i	$0.197951\pi$
$938$	1.16459e28	0.676466
$939$	5.88724e27	0.338523
$940$	−1.12945e26	−0.00642912
$941$	3.28090e28	1.84880	0.924402	−	0.381419i	$-0.124564\pi$
$941$	3.28090e28	1.84880	0.924402	+	0.381419i	$0.124564\pi$
$942$	−4.94089e27	−0.275627
$943$	−1.34235e28	−0.741319
$944$	−8.90392e27	−0.486796
$945$	−7.74050e27	−0.418954
$946$	8.63930e27	0.462927
$947$	−1.15089e28	−0.610533	−0.305267	−	0.952267i	$-0.598746\pi$
$947$	−1.15089e28	−0.610533	−0.305267	+	0.952267i	$0.598746\pi$
$948$	−4.12466e27	−0.216625
$949$	3.35464e28	1.74428
$950$	1.87556e28	0.965512
$951$	4.56082e26	0.0232449
$952$	2.23207e27	0.112631
$953$	−3.28534e28	−1.64134	−0.820669	−	0.571404i	$-0.806399\pi$
$953$	−3.28534e28	−1.64134	−0.820669	+	0.571404i	$0.806399\pi$
$954$	1.14499e27	0.0566359
$955$	3.93117e28	1.92526
$956$	1.51960e27	0.0736852
$957$	−3.18056e27	−0.152701
$958$	−1.42517e28	−0.677474
$959$	7.25020e27	0.341250
$960$	−2.07410e27	−0.0966612
$961$	−1.87325e28	−0.864417
$962$	−1.61687e28	−0.738773
$963$	2.29034e27	0.103622
$964$	−1.05150e28	−0.471060
$965$	2.66947e28	1.18418
$966$	2.31165e28	1.01540
$967$	2.20019e28	0.956994	0.478497	−	0.878089i	$-0.341182\pi$
$967$	2.20019e28	0.956994	0.478497	+	0.878089i	$0.341182\pi$
$968$	1.03101e27	0.0444066
$969$	4.56312e27	0.194619
$970$	3.29891e28	1.39328
$971$	−3.09095e28	−1.29274	−0.646368	−	0.763026i	$-0.723713\pi$
$971$	−3.09095e28	−1.29274	−0.646368	+	0.763026i	$0.723713\pi$
$972$	7.74455e26	0.0320750
$973$	5.86409e28	2.40507
$974$	−2.27469e28	−0.923874
$975$	−1.24724e28	−0.501655
$976$	7.83740e27	0.312176
$977$	7.54223e27	0.297510	0.148755	−	0.988874i	$-0.452473\pi$
$977$	7.54223e27	0.297510	0.148755	+	0.988874i	$0.452473\pi$
$978$	3.91098e27	0.152780
$979$	−2.97251e28	−1.14997
$980$	−2.86964e28	−1.09946
$981$	−1.32118e28	−0.501311
$982$	−2.59486e28	−0.975113
$983$	−5.25429e27	−0.195549	−0.0977744	−	0.995209i	$-0.531172\pi$
$983$	−5.25429e27	−0.195549	−0.0977744	+	0.995209i	$0.531172\pi$
$984$	−2.68277e27	−0.0988850
$985$	3.88008e27	0.141643
$986$	1.08422e27	0.0392002
$987$	2.51580e26	0.00900873
$988$	2.65359e28	0.941114
$989$	−3.05005e28	−1.07138
$990$	−8.48508e27	−0.295204
$991$	−4.37144e28	−1.50635	−0.753173	−	0.657823i	$-0.771478\pi$
$991$	−4.37144e28	−1.50635	−0.753173	+	0.657823i	$0.771478\pi$
$992$	−1.90717e27	−0.0650921
$993$	−1.51520e28	−0.512215
$994$	−4.72899e28	−1.58342
$995$	7.18530e28	2.38301
$996$	5.26839e27	0.173067
$997$	−2.92957e28	−0.953236	−0.476618	−	0.879110i	$-0.658138\pi$
$997$	−2.92957e28	−0.953236	−0.476618	+	0.879110i	$0.658138\pi$
$998$	−1.81566e28	−0.585188
$999$	−5.75485e27	−0.183722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.20.a.b.1.1	✓	1
3.2	odd	2		18.20.a.g.1.1		1
4.3	odd	2		48.20.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.20.a.b.1.1	✓	1	1.1	even	1	trivial
18.20.a.g.1.1		1	3.2	odd	2
48.20.a.a.1.1		1	4.3	odd	2

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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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