LMFDB - Embedded newform 6.26.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,26,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, 26, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 26 $
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:	$23.7598067971$
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)

$f(q)$

$=$

$q-4096.00 q^{2} -531441. q^{3} +1.67772e7 q^{4} -2.92755e8 q^{5} +2.17678e9 q^{6} +3.58064e9 q^{7} -6.87195e10 q^{8} +2.82430e11 q^{9} +O(q^{10})$

\(q-4096.00 q^{2} -531441. q^{3} +1.67772e7 q^{4} -2.92755e8 q^{5} +2.17678e9 q^{6} +3.58064e9 q^{7} -6.87195e10 q^{8} +2.82430e11 q^{9} +1.19912e12 q^{10} +1.51116e13 q^{11} -8.91610e12 q^{12} +1.22107e12 q^{13} -1.46663e13 q^{14} +1.55582e14 q^{15} +2.81475e14 q^{16} +2.51825e15 q^{17} -1.15683e15 q^{18} -7.99269e15 q^{19} -4.91161e15 q^{20} -1.90290e15 q^{21} -6.18970e16 q^{22} -9.96456e16 q^{23} +3.65203e16 q^{24} -2.12318e17 q^{25} -5.00151e15 q^{26} -1.50095e17 q^{27} +6.00732e16 q^{28} -2.08067e18 q^{29} -6.37264e17 q^{30} -4.93767e18 q^{31} -1.15292e18 q^{32} -8.03091e18 q^{33} -1.03148e19 q^{34} -1.04825e18 q^{35} +4.73838e18 q^{36} +1.98292e19 q^{37} +3.27381e19 q^{38} -6.48928e17 q^{39} +2.01180e19 q^{40} +2.24696e20 q^{41} +7.79428e18 q^{42} -7.22210e19 q^{43} +2.53530e20 q^{44} -8.26826e19 q^{45} +4.08149e20 q^{46} +1.89872e20 q^{47} -1.49587e20 q^{48} -1.32825e21 q^{49} +8.69654e20 q^{50} -1.33830e21 q^{51} +2.04862e19 q^{52} -2.64568e21 q^{53} +6.14788e20 q^{54} -4.42399e21 q^{55} -2.46060e20 q^{56} +4.24764e21 q^{57} +8.52244e21 q^{58} -1.64546e22 q^{59} +2.61023e21 q^{60} -3.55470e22 q^{61} +2.02247e22 q^{62} +1.01128e21 q^{63} +4.72237e21 q^{64} -3.57475e20 q^{65} +3.28946e22 q^{66} +1.06704e23 q^{67} +4.22492e22 q^{68} +5.29558e22 q^{69} +4.29364e21 q^{70} +7.36720e22 q^{71} -1.94084e22 q^{72} -2.62403e23 q^{73} -8.12202e22 q^{74} +1.12834e23 q^{75} -1.34095e23 q^{76} +5.41092e22 q^{77} +2.65801e21 q^{78} -1.00264e24 q^{79} -8.24032e22 q^{80} +7.97664e22 q^{81} -9.20355e23 q^{82} +1.55859e24 q^{83} -3.19254e22 q^{84} -7.37230e23 q^{85} +2.95817e23 q^{86} +1.10575e24 q^{87} -1.03846e24 q^{88} +2.18167e24 q^{89} +3.38668e23 q^{90} +4.37222e21 q^{91} -1.67178e24 q^{92} +2.62408e24 q^{93} -7.77717e23 q^{94} +2.33990e24 q^{95} +6.12710e23 q^{96} -4.40165e23 q^{97} +5.44050e24 q^{98} +4.26795e24 q^{99} +O(q^{100})\)

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 $

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	−531441.	−0.577350
$3$	−531441.	−0.577350
$4$	1.67772e7	0.500000
$5$	−2.92755e8	−0.536264	−0.268132	−	0.963382i	$-0.586406\pi$
$5$	−2.92755e8	−0.536264	−0.268132	+	0.963382i	$0.586406\pi$
$6$	2.17678e9	0.408248
$7$	3.58064e9	0.0977768	0.0488884	−	0.998804i	$-0.484432\pi$
$7$	3.58064e9	0.0977768	0.0488884	+	0.998804i	$0.484432\pi$
$8$	−6.87195e10	−0.353553
$9$	2.82430e11	0.333333
$10$	1.19912e12	0.379196
$11$	1.51116e13	1.45178	0.725891	−	0.687810i	$-0.241428\pi$
$11$	1.51116e13	1.45178	0.725891	+	0.687810i	$0.241428\pi$
$12$	−8.91610e12	−0.288675
$13$	1.22107e12	0.0145361	0.00726807	−	0.999974i	$-0.497686\pi$
$13$	1.22107e12	0.0145361	0.00726807	+	0.999974i	$0.497686\pi$
$14$	−1.46663e13	−0.0691386
$15$	1.55582e14	0.309612
$16$	2.81475e14	0.250000
$17$	2.51825e15	1.04830	0.524152	−	0.851625i	$-0.324382\pi$
$17$	2.51825e15	1.04830	0.524152	+	0.851625i	$0.324382\pi$
$18$	−1.15683e15	−0.235702
$19$	−7.99269e15	−0.828463	−0.414232	−	0.910172i	$-0.635950\pi$
$19$	−7.99269e15	−0.828463	−0.414232	+	0.910172i	$0.635950\pi$
$20$	−4.91161e15	−0.268132
$21$	−1.90290e15	−0.0564514
$22$	−6.18970e16	−1.02656
$23$	−9.96456e16	−0.948114	−0.474057	−	0.880494i	$-0.657211\pi$
$23$	−9.96456e16	−0.948114	−0.474057	+	0.880494i	$0.657211\pi$
$24$	3.65203e16	0.204124
$25$	−2.12318e17	−0.712420
$26$	−5.00151e15	−0.0102786
$27$	−1.50095e17	−0.192450
$28$	6.00732e16	0.0488884
$29$	−2.08067e18	−1.09202	−0.546008	−	0.837780i	$-0.683853\pi$
$29$	−2.08067e18	−1.09202	−0.546008	+	0.837780i	$0.683853\pi$
$30$	−6.37264e17	−0.218929
$31$	−4.93767e18	−1.12590	−0.562952	−	0.826490i	$-0.690334\pi$
$31$	−4.93767e18	−1.12590	−0.562952	+	0.826490i	$0.690334\pi$
$32$	−1.15292e18	−0.176777
$33$	−8.03091e18	−0.838186
$34$	−1.03148e19	−0.741263
$35$	−1.04825e18	−0.0524342
$36$	4.73838e18	0.166667
$37$	1.98292e19	0.495202	0.247601	−	0.968862i	$-0.420358\pi$
$37$	1.98292e19	0.495202	0.247601	+	0.968862i	$0.420358\pi$
$38$	3.27381e19	0.585812
$39$	−6.48928e17	−0.00839245
$40$	2.01180e19	0.189598
$41$	2.24696e20	1.55524	0.777620	−	0.628735i	$-0.216427\pi$
$41$	2.24696e20	1.55524	0.777620	+	0.628735i	$0.216427\pi$
$42$	7.79428e18	0.0399172
$43$	−7.22210e19	−0.275618	−0.137809	−	0.990459i	$-0.544006\pi$
$43$	−7.22210e19	−0.275618	−0.137809	+	0.990459i	$0.544006\pi$
$44$	2.53530e20	0.725891
$45$	−8.26826e19	−0.178755
$46$	4.08149e20	0.670418
$47$	1.89872e20	0.238363	0.119181	−	0.992872i	$-0.461973\pi$
$47$	1.89872e20	0.238363	0.119181	+	0.992872i	$0.461973\pi$
$48$	−1.49587e20	−0.144338
$49$	−1.32825e21	−0.990440
$50$	8.69654e20	0.503757
$51$	−1.33830e21	−0.605239
$52$	2.04862e19	0.00726807
$53$	−2.64568e21	−0.739756	−0.369878	−	0.929080i	$-0.620600\pi$
$53$	−2.64568e21	−0.739756	−0.369878	+	0.929080i	$0.620600\pi$
$54$	6.14788e20	0.136083
$55$	−4.42399e21	−0.778539
$56$	−2.46060e20	−0.0345693
$57$	4.24764e21	0.478313
$58$	8.52244e21	0.772172
$59$	−1.64546e22	−1.20403	−0.602015	−	0.798485i	$-0.705635\pi$
$59$	−1.64546e22	−1.20403	−0.602015	+	0.798485i	$0.705635\pi$
$60$	2.61023e21	0.154806
$61$	−3.55470e22	−1.71467	−0.857333	−	0.514762i	$-0.827880\pi$
$61$	−3.55470e22	−1.71467	−0.857333	+	0.514762i	$0.827880\pi$
$62$	2.02247e22	0.796134
$63$	1.01128e21	0.0325923
$64$	4.72237e21	0.125000
$65$	−3.57475e20	−0.00779522
$66$	3.28946e22	0.592687
$67$	1.06704e23	1.59311	0.796553	−	0.604569i	$-0.206655\pi$
$67$	1.06704e23	1.59311	0.796553	+	0.604569i	$0.206655\pi$
$68$	4.22492e22	0.524152
$69$	5.29558e22	0.547394
$70$	4.29364e21	0.0370766
$71$	7.36720e22	0.532811	0.266405	−	0.963861i	$-0.414164\pi$
$71$	7.36720e22	0.532811	0.266405	+	0.963861i	$0.414164\pi$
$72$	−1.94084e22	−0.117851
$73$	−2.62403e23	−1.34101	−0.670506	−	0.741904i	$-0.733923\pi$
$73$	−2.62403e23	−1.34101	−0.670506	+	0.741904i	$0.733923\pi$
$74$	−8.12202e22	−0.350161
$75$	1.12834e23	0.411316
$76$	−1.34095e23	−0.414232
$77$	5.41092e22	0.141950
$78$	2.65801e21	0.00593436
$79$	−1.00264e24	−1.90901	−0.954503	−	0.298201i	$-0.903613\pi$
$79$	−1.00264e24	−1.90901	−0.954503	+	0.298201i	$0.903613\pi$
$80$	−8.24032e22	−0.134066
$81$	7.97664e22	0.111111
$82$	−9.20355e23	−1.09972
$83$	1.55859e24	1.60050	0.800249	−	0.599667i	$-0.204700\pi$
$83$	1.55859e24	1.60050	0.800249	+	0.599667i	$0.204700\pi$
$84$	−3.19254e22	−0.0282257
$85$	−7.37230e23	−0.562169
$86$	2.95817e23	0.194891
$87$	1.10575e24	0.630475
$88$	−1.03846e24	−0.513282
$89$	2.18167e24	0.936298	0.468149	−	0.883650i	$-0.344921\pi$
$89$	2.18167e24	0.936298	0.468149	+	0.883650i	$0.344921\pi$
$90$	3.38668e23	0.126399
$91$	4.37222e21	0.00142130
$92$	−1.67178e24	−0.474057
$93$	2.62408e24	0.650041
$94$	−7.77717e23	−0.168548
$95$	2.33990e24	0.444275
$96$	6.12710e23	0.102062
$97$	−4.40165e23	−0.0644123	−0.0322062	−	0.999481i	$-0.510253\pi$
$97$	−4.40165e23	−0.0644123	−0.0322062	+	0.999481i	$0.510253\pi$
$98$	5.44050e24	0.700347
$99$	4.26795e24	0.483927
$100$	−3.56210e24	−0.356210
$101$	−5.02582e24	−0.443802	−0.221901	−	0.975069i	$-0.571226\pi$
$101$	−5.02582e24	−0.443802	−0.221901	+	0.975069i	$0.571226\pi$
$102$	5.48168e24	0.427969
$103$	−1.52311e25	−1.05261	−0.526304	−	0.850296i	$-0.676423\pi$
$103$	−1.52311e25	−1.05261	−0.526304	+	0.850296i	$0.676423\pi$
$104$	−8.39114e22	−0.00513930
$105$	5.57084e23	0.0302729
$106$	1.08367e25	0.523086
$107$	−2.47232e25	−1.06123	−0.530613	−	0.847614i	$-0.678038\pi$
$107$	−2.47232e25	−1.06123	−0.530613	+	0.847614i	$0.678038\pi$
$108$	−2.51817e24	−0.0962250
$109$	−2.85771e25	−0.973166	−0.486583	−	0.873634i	$-0.661757\pi$
$109$	−2.85771e25	−0.973166	−0.486583	+	0.873634i	$0.661757\pi$
$110$	1.81206e25	0.550510
$111$	−1.05380e25	−0.285905
$112$	1.00786e24	0.0244442
$113$	−1.73240e25	−0.375982	−0.187991	−	0.982171i	$-0.560198\pi$
$113$	−1.73240e25	−0.375982	−0.187991	+	0.982171i	$0.560198\pi$
$114$	−1.73984e25	−0.338219
$115$	2.91717e25	0.508440
$116$	−3.49079e25	−0.546008
$117$	3.44867e23	0.00484538
$118$	6.73981e25	0.851378
$119$	9.01696e24	0.102500
$120$	−1.06915e25	−0.109465
$121$	1.20013e26	1.10767
$122$	1.45600e26	1.21245
$123$	−1.19413e26	−0.897918
$124$	−8.28404e25	−0.562952
$125$	1.49405e26	0.918310
$126$	−4.14220e24	−0.0230462
$127$	3.23349e26	1.62976	0.814882	−	0.579627i	$-0.196802\pi$
$127$	3.23349e26	1.62976	0.814882	+	0.579627i	$0.196802\pi$
$128$	−1.93428e25	−0.0883883
$129$	3.83812e25	0.159128
$130$	1.46422e24	0.00551205
$131$	−3.63273e26	−1.24263	−0.621315	−	0.783561i	$-0.713401\pi$
$131$	−3.63273e26	−1.24263	−0.621315	+	0.783561i	$0.713401\pi$
$132$	−1.34736e26	−0.419093
$133$	−2.86190e25	−0.0810044
$134$	−4.37059e26	−1.12650
$135$	4.39409e25	0.103204
$136$	−1.73053e26	−0.370632
$137$	−6.56742e26	−1.28348	−0.641738	−	0.766924i	$-0.721786\pi$
$137$	−6.56742e26	−1.28348	−0.641738	+	0.766924i	$0.721786\pi$
$138$	−2.16907e26	−0.387066
$139$	6.72509e26	1.09651	0.548256	−	0.836311i	$-0.315292\pi$
$139$	6.72509e26	1.09651	0.548256	+	0.836311i	$0.315292\pi$
$140$	−1.75867e25	−0.0262171
$141$	−1.00906e26	−0.137619
$142$	−3.01761e26	−0.376754
$143$	1.84523e25	0.0211033
$144$	7.94968e25	0.0833333
$145$	6.09127e26	0.585609
$146$	1.07480e27	0.948239
$147$	7.05885e26	0.571831
$148$	3.32678e26	0.247601
$149$	−7.98627e26	−0.546406	−0.273203	−	0.961956i	$-0.588083\pi$
$149$	−7.98627e26	−0.546406	−0.273203	+	0.961956i	$0.588083\pi$
$150$	−4.62170e26	−0.290844
$151$	−1.03633e27	−0.600187	−0.300093	−	0.953910i	$-0.597018\pi$
$151$	−1.03633e27	−0.600187	−0.300093	+	0.953910i	$0.597018\pi$
$152$	5.49254e26	0.292906
$153$	7.11228e26	0.349435
$154$	−2.21631e26	−0.100374
$155$	1.44553e27	0.603782
$156$	−1.08872e25	−0.00419622
$157$	−3.36346e27	−1.19685	−0.598427	−	0.801178i	$-0.704207\pi$
$157$	−3.36346e27	−1.19685	−0.598427	+	0.801178i	$0.704207\pi$
$158$	4.10682e27	1.34987
$159$	1.40602e27	0.427098
$160$	3.37523e26	0.0947991
$161$	−3.56796e26	−0.0927035
$162$	−3.26723e26	−0.0785674
$163$	8.00443e26	0.178232	0.0891159	−	0.996021i	$-0.471596\pi$
$163$	8.00443e26	0.178232	0.0891159	+	0.996021i	$0.471596\pi$
$164$	3.76977e27	0.777620
$165$	2.35109e27	0.449489
$166$	−6.38398e27	−1.13172
$167$	−5.17982e27	−0.851842	−0.425921	−	0.904760i	$-0.640050\pi$
$167$	−5.17982e27	−0.851842	−0.425921	+	0.904760i	$0.640050\pi$
$168$	1.30766e26	0.0199586
$169$	−7.05492e27	−0.999789
$170$	3.01969e27	0.397513
$171$	−2.25737e27	−0.276154
$172$	−1.21167e27	−0.137809
$173$	−3.40880e27	−0.360599	−0.180300	−	0.983612i	$-0.557707\pi$
$173$	−3.40880e27	−0.360599	−0.180300	+	0.983612i	$0.557707\pi$
$174$	−4.52917e27	−0.445813
$175$	−7.60235e26	−0.0696582
$176$	4.25353e27	0.362945
$177$	8.74465e27	0.695147
$178$	−8.93612e27	−0.662063
$179$	−1.23610e28	−0.853870	−0.426935	−	0.904282i	$-0.640407\pi$
$179$	−1.23610e28	−0.853870	−0.426935	+	0.904282i	$0.640407\pi$
$180$	−1.38718e27	−0.0893774
$181$	3.38516e27	0.203516	0.101758	−	0.994809i	$-0.467553\pi$
$181$	3.38516e27	0.203516	0.101758	+	0.994809i	$0.467553\pi$
$182$	−1.79086e25	−0.00100501
$183$	1.88911e28	0.989963
$184$	6.84760e27	0.335209
$185$	−5.80508e27	−0.265559
$186$	−1.07482e28	−0.459648
$187$	3.80547e28	1.52191
$188$	3.18553e27	0.119181
$189$	−5.37435e26	−0.0188171
$190$	−9.58423e27	−0.314150
$191$	3.81140e28	1.16995	0.584975	−	0.811052i	$-0.301104\pi$
$191$	3.81140e28	1.16995	0.584975	+	0.811052i	$0.301104\pi$
$192$	−2.50966e27	−0.0721688
$193$	6.38842e28	1.72158	0.860790	−	0.508961i	$-0.169970\pi$
$193$	6.38842e28	1.72158	0.860790	+	0.508961i	$0.169970\pi$
$194$	1.80292e27	0.0455464
$195$	1.89977e26	0.00450057
$196$	−2.22843e28	−0.495220
$197$	−8.73680e28	−1.82190	−0.910950	−	0.412517i	$-0.864650\pi$
$197$	−8.73680e28	−1.82190	−0.910950	+	0.412517i	$0.864650\pi$
$198$	−1.74815e28	−0.342188
$199$	2.76766e28	0.508686	0.254343	−	0.967114i	$-0.418141\pi$
$199$	2.76766e28	0.508686	0.254343	+	0.967114i	$0.418141\pi$
$200$	1.45904e28	0.251879
$201$	−5.67067e28	−0.919780
$202$	2.05857e28	0.313816
$203$	−7.45015e27	−0.106774
$204$	−2.24530e28	−0.302619
$205$	−6.57809e28	−0.834020
$206$	6.23867e28	0.744307
$207$	−2.81429e28	−0.316038
$208$	3.43701e26	0.00363404
$209$	−1.20782e29	−1.20275
$210$	−2.28181e27	−0.0214062
$211$	−2.08479e28	−0.184303	−0.0921513	−	0.995745i	$-0.529374\pi$
$211$	−2.08479e28	−0.184303	−0.0921513	+	0.995745i	$0.529374\pi$
$212$	−4.43871e28	−0.369878
$213$	−3.91523e28	−0.307619
$214$	1.01266e29	0.750400
$215$	2.11431e28	0.147804
$216$	1.03144e28	0.0680414
$217$	−1.76800e28	−0.110087
$218$	1.17052e29	0.688132
$219$	1.39452e29	0.774234
$220$	−7.42222e28	−0.389269
$221$	3.07496e27	0.0152383
$222$	4.31638e28	0.202165
$223$	2.90506e29	1.28630	0.643152	−	0.765739i	$-0.277626\pi$
$223$	2.90506e29	1.28630	0.643152	+	0.765739i	$0.277626\pi$
$224$	−4.12820e27	−0.0172847
$225$	−5.99648e28	−0.237473
$226$	7.09591e28	0.265860
$227$	3.23765e29	1.14791	0.573954	−	0.818887i	$-0.305409\pi$
$227$	3.23765e29	1.14791	0.573954	+	0.818887i	$0.305409\pi$
$228$	7.12637e28	0.239157
$229$	−5.11099e29	−1.62391	−0.811954	−	0.583721i	$-0.801596\pi$
$229$	−5.11099e29	−1.62391	−0.811954	+	0.583721i	$0.801596\pi$
$230$	−1.19487e29	−0.359521
$231$	−2.87558e28	−0.0819551
$232$	1.42983e29	0.386086
$233$	−1.20130e29	−0.307399	−0.153700	−	0.988118i	$-0.549119\pi$
$233$	−1.20130e29	−0.307399	−0.153700	+	0.988118i	$0.549119\pi$
$234$	−1.41257e27	−0.00342620
$235$	−5.55861e28	−0.127826
$236$	−2.76063e29	−0.602015
$237$	5.32845e29	1.10217
$238$	−3.69335e28	−0.0724783
$239$	3.34916e29	0.623681	0.311840	−	0.950135i	$-0.399055\pi$
$239$	3.34916e29	0.623681	0.311840	+	0.950135i	$0.399055\pi$
$240$	4.37924e28	0.0774031
$241$	−3.53238e29	−0.592727	−0.296363	−	0.955075i	$-0.595774\pi$
$241$	−3.53238e29	−0.592727	−0.296363	+	0.955075i	$0.595774\pi$
$242$	−4.91572e29	−0.783240
$243$	−4.23912e28	−0.0641500
$244$	−5.96379e29	−0.857333
$245$	3.88851e29	0.531138
$246$	4.89114e29	0.634924
$247$	−9.75965e27	−0.0120427
$248$	3.39314e29	0.398067
$249$	−8.28298e29	−0.924048
$250$	−6.11962e29	−0.649343
$251$	1.07603e30	1.08619	0.543093	−	0.839673i	$-0.317253\pi$
$251$	1.07603e30	1.08619	0.543093	+	0.839673i	$0.317253\pi$
$252$	1.69665e28	0.0162961
$253$	−1.50580e30	−1.37645
$254$	−1.32444e30	−1.15242
$255$	3.91794e29	0.324568
$256$	7.92282e28	0.0625000
$257$	6.56258e27	0.00493073	0.00246536	−	0.999997i	$-0.499215\pi$
$257$	6.56258e27	0.00493073	0.00246536	+	0.999997i	$0.499215\pi$
$258$	−1.57209e29	−0.112521
$259$	7.10011e28	0.0484193
$260$	−5.99743e27	−0.00389761
$261$	−5.87643e29	−0.364005
$262$	1.48797e30	0.878673
$263$	2.03818e30	1.14761	0.573807	−	0.818990i	$-0.305466\pi$
$263$	2.03818e30	1.14761	0.573807	+	0.818990i	$0.305466\pi$
$264$	5.51880e29	0.296344
$265$	7.74534e29	0.396705
$266$	1.17223e29	0.0572788
$267$	−1.15943e30	−0.540572
$268$	1.79019e30	0.796553
$269$	1.30216e30	0.553046	0.276523	−	0.961007i	$-0.410818\pi$
$269$	1.30216e30	0.553046	0.276523	+	0.961007i	$0.410818\pi$
$270$	−1.79982e29	−0.0729764
$271$	2.73384e30	1.05842	0.529209	−	0.848492i	$-0.322489\pi$
$271$	2.73384e30	1.05842	0.529209	+	0.848492i	$0.322489\pi$
$272$	7.08825e29	0.262076
$273$	−2.32358e27	−0.000820586 0
$274$	2.69002e30	0.907554
$275$	−3.20846e30	−1.03428
$276$	8.88451e29	0.273697
$277$	−4.83846e29	−0.142466	−0.0712329	−	0.997460i	$-0.522693\pi$
$277$	−4.83846e29	−0.142466	−0.0712329	+	0.997460i	$0.522693\pi$
$278$	−2.75460e30	−0.775351
$279$	−1.39454e30	−0.375301
$280$	7.20353e28	0.0185383
$281$	−7.57818e30	−1.86525	−0.932623	−	0.360853i	$-0.882486\pi$
$281$	−7.57818e30	−1.86525	−0.932623	+	0.360853i	$0.882486\pi$
$282$	4.13311e29	0.0973113
$283$	−1.30443e30	−0.293827	−0.146914	−	0.989149i	$-0.546934\pi$
$283$	−1.30443e30	−0.293827	−0.146914	+	0.989149i	$0.546934\pi$
$284$	1.23601e30	0.266405
$285$	−1.24352e30	−0.256502
$286$	−7.55807e28	−0.0149223
$287$	8.04557e29	0.152066
$288$	−3.25619e29	−0.0589256
$289$	5.70960e29	0.0989424
$290$	−2.49498e30	−0.414088
$291$	2.33922e29	0.0371885
$292$	−4.40239e30	−0.670506
$293$	−4.04021e29	−0.0589601	−0.0294800	−	0.999565i	$-0.509385\pi$
$293$	−4.04021e29	−0.0589601	−0.0294800	+	0.999565i	$0.509385\pi$
$294$	−2.89131e30	−0.404345
$295$	4.81717e30	0.645679
$296$	−1.36265e30	−0.175080
$297$	−2.26817e30	−0.279395
$298$	3.27118e30	0.386367
$299$	−1.21674e29	−0.0137819
$300$	1.89305e30	0.205658
$301$	−2.58598e29	−0.0269491
$302$	4.24481e30	0.424396
$303$	2.67092e30	0.256229
$304$	−2.24974e30	−0.207116
$305$	1.04065e31	0.919514
$306$	−2.91319e30	−0.247088
$307$	6.95636e30	0.566438	0.283219	−	0.959055i	$-0.408598\pi$
$307$	6.95636e30	0.566438	0.283219	+	0.959055i	$0.408598\pi$
$308$	9.07801e29	0.0709752
$309$	8.09445e30	0.607724
$310$	−5.92088e30	−0.426938
$311$	2.74913e30	0.190410	0.0952051	−	0.995458i	$-0.469649\pi$
$311$	2.74913e30	0.190410	0.0952051	+	0.995458i	$0.469649\pi$
$312$	4.45940e28	0.00296718
$313$	9.39383e30	0.600535	0.300267	−	0.953855i	$-0.402924\pi$
$313$	9.39383e30	0.600535	0.300267	+	0.953855i	$0.402924\pi$
$314$	1.37767e31	0.846303
$315$	−2.96057e29	−0.0174781
$316$	−1.68215e31	−0.954503
$317$	1.86543e31	1.01751	0.508755	−	0.860912i	$-0.330106\pi$
$317$	1.86543e31	1.01751	0.508755	+	0.860912i	$0.330106\pi$
$318$	−5.75906e30	−0.302004
$319$	−3.14422e31	−1.58537
$320$	−1.38250e30	−0.0670331
$321$	1.31389e31	0.612699
$322$	1.46143e30	0.0655513
$323$	−2.01276e31	−0.868482
$324$	1.33826e30	0.0555556
$325$	−2.59255e29	−0.0103558
$326$	−3.27861e30	−0.126029
$327$	1.51870e31	0.561857
$328$	−1.54410e31	−0.549860
$329$	6.79866e29	0.0233064
$330$	−9.63006e30	−0.317837
$331$	−4.71638e31	−1.49885	−0.749426	−	0.662088i	$-0.769670\pi$
$331$	−4.71638e31	−1.49885	−0.749426	+	0.662088i	$0.769670\pi$
$332$	2.61488e31	0.800249
$333$	5.60034e30	0.165067
$334$	2.12166e31	0.602343
$335$	−3.12380e31	−0.854326
$336$	−5.35619e29	−0.0141129
$337$	1.85792e31	0.471686	0.235843	−	0.971791i	$-0.424215\pi$
$337$	1.85792e31	0.471686	0.235843	+	0.971791i	$0.424215\pi$
$338$	2.88969e31	0.706957
$339$	9.20668e30	0.217074
$340$	−1.23687e31	−0.281084
$341$	−7.46160e31	−1.63456
$342$	9.24620e30	0.195271
$343$	−9.55787e30	−0.194619
$344$	4.96299e30	0.0974457
$345$	−1.55031e31	−0.293548
$346$	1.39624e31	0.254982
$347$	−7.27635e31	−1.28173	−0.640863	−	0.767655i	$-0.721423\pi$
$347$	−7.27635e31	−1.28173	−0.640863	+	0.767655i	$0.721423\pi$
$348$	1.85515e31	0.315238
$349$	1.19713e32	1.96256	0.981282	−	0.192574i	$-0.0616835\pi$
$349$	1.19713e32	1.96256	0.981282	+	0.192574i	$0.0616835\pi$
$350$	3.11392e30	0.0492558
$351$	−1.83276e29	−0.00279748
$352$	−1.74225e31	−0.256641
$353$	6.99722e31	0.994813	0.497407	−	0.867517i	$-0.334286\pi$
$353$	6.99722e31	0.994813	0.497407	+	0.867517i	$0.334286\pi$
$354$	−3.58181e31	−0.491543
$355$	−2.15678e31	−0.285728
$356$	3.66024e31	0.468149
$357$	−4.79198e30	−0.0591783
$358$	5.06308e31	0.603777
$359$	6.06364e31	0.698317	0.349159	−	0.937064i	$-0.386467\pi$
$359$	6.06364e31	0.698317	0.349159	+	0.937064i	$0.386467\pi$
$360$	5.68191e30	0.0631994
$361$	−2.91933e31	−0.313649
$362$	−1.38656e31	−0.143907
$363$	−6.37796e31	−0.639513
$364$	7.33537e28	0.000710649 0
$365$	7.68197e31	0.719137
$366$	−7.73780e31	−0.700009
$367$	2.22539e32	1.94572	0.972860	−	0.231394i	$-0.0743287\pi$
$367$	2.22539e32	1.94572	0.972860	+	0.231394i	$0.0743287\pi$
$368$	−2.80478e31	−0.237028
$369$	6.34608e31	0.518413
$370$	2.37776e31	0.187779
$371$	−9.47322e30	−0.0723309
$372$	4.40248e31	0.325020
$373$	−1.15379e32	−0.823695	−0.411848	−	0.911253i	$-0.635116\pi$
$373$	−1.15379e32	−0.823695	−0.411848	+	0.911253i	$0.635116\pi$
$374$	−1.55872e32	−1.07615
$375$	−7.93998e31	−0.530187
$376$	−1.30479e31	−0.0842740
$377$	−2.54065e30	−0.0158737
$378$	2.20134e30	0.0133057
$379$	5.47213e31	0.320012	0.160006	−	0.987116i	$-0.448849\pi$
$379$	5.47213e31	0.320012	0.160006	+	0.987116i	$0.448849\pi$
$380$	3.92570e31	0.222138
$381$	−1.71841e32	−0.940945
$382$	−1.56115e32	−0.827279
$383$	−1.98130e32	−1.01617	−0.508085	−	0.861307i	$-0.669646\pi$
$383$	−1.98130e32	−1.01617	−0.508085	+	0.861307i	$0.669646\pi$
$384$	1.02796e31	0.0510310
$385$	−1.58407e31	−0.0761230
$386$	−2.61670e32	−1.21734
$387$	−2.03973e31	−0.0918727
$388$	−7.38475e30	−0.0322062
$389$	4.19098e31	0.176989	0.0884945	−	0.996077i	$-0.471794\pi$
$389$	4.19098e31	0.176989	0.0884945	+	0.996077i	$0.471794\pi$
$390$	−7.78145e29	−0.00318238
$391$	−2.50933e32	−0.993912
$392$	9.12765e31	0.350173
$393$	1.93058e32	0.717433
$394$	3.57859e32	1.28828
$395$	2.93528e32	1.02373
$396$	7.16044e31	0.241964
$397$	2.64500e32	0.866053	0.433027	−	0.901381i	$-0.357446\pi$
$397$	2.64500e32	0.866053	0.433027	+	0.901381i	$0.357446\pi$
$398$	−1.13363e32	−0.359695
$399$	1.52093e31	0.0467679
$400$	−5.97622e31	−0.178105
$401$	2.33767e32	0.675273	0.337636	−	0.941277i	$-0.390373\pi$
$401$	2.33767e32	0.675273	0.337636	+	0.941277i	$0.390373\pi$
$402$	2.32271e32	0.650383
$403$	−6.02925e30	−0.0163663
$404$	−8.43192e31	−0.221901
$405$	−2.33520e31	−0.0595849
$406$	3.05158e31	0.0755004
$407$	2.99650e32	0.718925
$408$	9.19674e31	0.213984
$409$	−5.48497e32	−1.23775	−0.618875	−	0.785490i	$-0.712411\pi$
$409$	−5.48497e32	−1.23775	−0.618875	+	0.785490i	$0.712411\pi$
$410$	2.69438e32	0.589741
$411$	3.49020e32	0.741015
$412$	−2.55536e32	−0.526304
$413$	−5.89181e31	−0.117726
$414$	1.15273e32	0.223473
$415$	−4.56284e32	−0.858291
$416$	−1.40780e30	−0.00256965
$417$	−3.57399e32	−0.633071
$418$	4.94724e32	0.850471
$419$	3.41488e31	0.0569771	0.0284885	−	0.999594i	$-0.490931\pi$
$419$	3.41488e31	0.0569771	0.0284885	+	0.999594i	$0.490931\pi$
$420$	9.34631e30	0.0151365
$421$	−5.71127e32	−0.897856	−0.448928	−	0.893568i	$-0.648194\pi$
$421$	−5.71127e32	−0.897856	−0.448928	+	0.893568i	$0.648194\pi$
$422$	8.53930e31	0.130322
$423$	5.36256e31	0.0794543
$424$	1.81809e32	0.261543
$425$	−5.34670e32	−0.746834
$426$	1.60368e32	0.217519
$427$	−1.27281e32	−0.167654
$428$	−4.14787e32	−0.530613
$429$	−9.80632e30	−0.0121840
$430$	−8.66019e31	−0.104513
$431$	5.26390e32	0.617081	0.308540	−	0.951211i	$-0.400160\pi$
$431$	5.26390e32	0.617081	0.308540	+	0.951211i	$0.400160\pi$
$432$	−4.22479e31	−0.0481125
$433$	−7.00633e32	−0.775160	−0.387580	−	0.921836i	$-0.626689\pi$
$433$	−7.00633e32	−0.775160	−0.387580	+	0.921836i	$0.626689\pi$
$434$	7.24175e31	0.0778434
$435$	−3.23715e32	−0.338102
$436$	−4.79444e32	−0.486583
$437$	7.96437e32	0.785477
$438$	−5.71194e32	−0.547466
$439$	5.29542e32	0.493280	0.246640	−	0.969107i	$-0.420673\pi$
$439$	5.29542e32	0.493280	0.246640	+	0.969107i	$0.420673\pi$
$440$	3.04014e32	0.275255
$441$	−3.75136e32	−0.330147
$442$	−1.25951e31	−0.0107751
$443$	4.49792e32	0.374080	0.187040	−	0.982352i	$-0.440111\pi$
$443$	4.49792e32	0.374080	0.187040	+	0.982352i	$0.440111\pi$
$444$	−1.76799e32	−0.142953
$445$	−6.38695e32	−0.502103
$446$	−1.18991e33	−0.909554
$447$	4.24423e32	0.315468
$448$	1.69091e31	0.0122221
$449$	−9.88741e32	−0.695030	−0.347515	−	0.937674i	$-0.612974\pi$
$449$	−9.88741e32	−0.695030	−0.347515	+	0.937674i	$0.612974\pi$
$450$	2.45616e32	0.167919
$451$	3.39551e33	2.25787
$452$	−2.90648e32	−0.187991
$453$	5.50748e32	0.346518
$454$	−1.32614e33	−0.811694
$455$	−1.27999e30	−0.000762191 0
$456$	−2.91896e32	−0.169109
$457$	2.93791e33	1.65610	0.828050	−	0.560654i	$-0.189450\pi$
$457$	2.93791e33	1.65610	0.828050	+	0.560654i	$0.189450\pi$
$458$	2.09346e33	1.14828
$459$	−3.77976e32	−0.201746
$460$	4.89421e32	0.254220
$461$	−2.14053e33	−1.08208	−0.541039	−	0.840997i	$-0.681969\pi$
$461$	−2.14053e33	−1.08208	−0.541039	+	0.840997i	$0.681969\pi$
$462$	1.17784e32	0.0579510
$463$	8.71982e32	0.417585	0.208793	−	0.977960i	$-0.433047\pi$
$463$	8.71982e32	0.417585	0.208793	+	0.977960i	$0.433047\pi$
$464$	−5.85657e32	−0.273004
$465$	−7.68213e32	−0.348594
$466$	4.92053e32	0.217364
$467$	−6.01153e32	−0.258538	−0.129269	−	0.991610i	$-0.541263\pi$
$467$	−6.01153e32	−0.258538	−0.129269	+	0.991610i	$0.541263\pi$
$468$	5.78590e30	0.00242269
$469$	3.82068e32	0.155769
$470$	2.27681e32	0.0903863
$471$	1.78748e33	0.691003
$472$	1.13075e33	0.425689
$473$	−1.09137e33	−0.400137
$474$	−2.18253e33	−0.779348
$475$	1.69699e33	0.590214
$476$	1.51279e32	0.0512499
$477$	−7.47217e32	−0.246585
$478$	−1.37182e33	−0.441009
$479$	−3.01870e33	−0.945423	−0.472711	−	0.881217i	$-0.656725\pi$
$479$	−3.01870e33	−0.945423	−0.472711	+	0.881217i	$0.656725\pi$
$480$	−1.79374e32	−0.0547323
$481$	2.42128e31	0.00719833
$482$	1.44686e33	0.419121
$483$	1.89616e32	0.0535224
$484$	2.01348e33	0.553834
$485$	1.28861e32	0.0345421
$486$	1.73634e32	0.0453609
$487$	−5.24137e33	−1.33454	−0.667272	−	0.744814i	$-0.732538\pi$
$487$	−5.24137e33	−1.33454	−0.667272	+	0.744814i	$0.732538\pi$
$488$	2.44277e33	0.606226
$489$	−4.25388e32	−0.102902
$490$	−1.59273e33	−0.375571
$491$	−3.08172e33	−0.708393	−0.354197	−	0.935171i	$-0.615246\pi$
$491$	−3.08172e33	−0.708393	−0.354197	+	0.935171i	$0.615246\pi$
$492$	−2.00341e33	−0.448959
$493$	−5.23966e33	−1.14476
$494$	3.99755e31	0.00851545
$495$	−1.24946e33	−0.259513
$496$	−1.38983e33	−0.281476
$497$	2.63793e32	0.0520965
$498$	3.39271e33	0.653401
$499$	−1.64910e33	−0.309734	−0.154867	−	0.987935i	$-0.549495\pi$
$499$	−1.64910e33	−0.309734	−0.154867	+	0.987935i	$0.549495\pi$
$500$	2.50660e33	0.459155
$501$	2.75277e33	0.491811
$502$	−4.40743e33	−0.768049
$503$	−2.47162e32	−0.0420128	−0.0210064	−	0.999779i	$-0.506687\pi$
$503$	−2.47162e32	−0.0420128	−0.0210064	+	0.999779i	$0.506687\pi$
$504$	−6.94946e31	−0.0115231
$505$	1.47133e33	0.237995
$506$	6.16777e33	0.973299
$507$	3.74927e33	0.577228
$508$	5.42489e33	0.814882
$509$	6.26740e33	0.918577	0.459288	−	0.888287i	$-0.348105\pi$
$509$	6.26740e33	0.918577	0.459288	+	0.888287i	$0.348105\pi$
$510$	−1.60479e33	−0.229504
$511$	−9.39571e32	−0.131120
$512$	−3.24519e32	−0.0441942
$513$	1.19966e33	0.159438
$514$	−2.68803e31	−0.00348655
$515$	4.45899e33	0.564477
$516$	6.43930e32	0.0795641
$517$	2.86927e33	0.346051
$518$	−2.90821e32	−0.0342376
$519$	1.81158e33	0.208192
$520$	2.45655e31	0.00275603
$521$	1.64678e34	1.80370	0.901850	−	0.432049i	$-0.142209\pi$
$521$	1.64678e34	1.80370	0.901850	+	0.432049i	$0.142209\pi$
$522$	2.40699e33	0.257391
$523$	−3.45969e33	−0.361216	−0.180608	−	0.983555i	$-0.557806\pi$
$523$	−3.45969e33	−0.361216	−0.180608	+	0.983555i	$0.557806\pi$
$524$	−6.09471e33	−0.621315
$525$	4.04020e32	0.0402172
$526$	−8.34839e33	−0.811486
$527$	−1.24343e34	−1.18029
$528$	−2.26050e33	−0.209547
$529$	−1.11651e33	−0.101081
$530$	−3.17249e33	−0.280513
$531$	−4.64727e33	−0.401343
$532$	−4.80147e32	−0.0405022
$533$	2.74370e32	0.0226072
$534$	4.74902e33	0.382242
$535$	7.23785e33	0.569098
$536$	−7.33263e33	−0.563248
$537$	6.56916e33	0.492982
$538$	−5.33365e33	−0.391062
$539$	−2.00719e34	−1.43790
$540$	7.37207e32	0.0516021
$541$	−2.31144e33	−0.158094	−0.0790472	−	0.996871i	$-0.525188\pi$
$541$	−2.31144e33	−0.158094	−0.0790472	+	0.996871i	$0.525188\pi$
$542$	−1.11978e34	−0.748414
$543$	−1.79902e33	−0.117500
$544$	−2.90335e33	−0.185316
$545$	8.36608e33	0.521874
$546$	9.51738e30	0.000580242 0
$547$	−4.04733e33	−0.241172	−0.120586	−	0.992703i	$-0.538477\pi$
$547$	−4.04733e33	−0.241172	−0.120586	+	0.992703i	$0.538477\pi$
$548$	−1.10183e34	−0.641738
$549$	−1.00395e34	−0.571555
$550$	1.31418e34	0.731345
$551$	1.66302e34	0.904694
$552$	−3.63909e33	−0.193533
$553$	−3.59010e33	−0.186656
$554$	1.98183e33	0.100738
$555$	3.08506e33	0.153321
$556$	1.12828e34	0.548256
$557$	2.32181e34	1.10315	0.551577	−	0.834124i	$-0.314026\pi$
$557$	2.32181e34	1.10315	0.551577	+	0.834124i	$0.314026\pi$
$558$	5.71205e33	0.265378
$559$	−8.81870e31	−0.00400643
$560$	−2.95056e32	−0.0131086
$561$	−2.02238e34	−0.878674
$562$	3.10402e34	1.31893
$563$	−2.70103e34	−1.12247	−0.561235	−	0.827656i	$-0.689674\pi$
$563$	−2.70103e34	−1.12247	−0.561235	+	0.827656i	$0.689674\pi$
$564$	−1.69292e33	−0.0688094
$565$	5.07168e33	0.201626
$566$	5.34296e33	0.207767
$567$	2.85615e32	0.0108641
$568$	−5.06270e33	−0.188377
$569$	−2.32147e33	−0.0845007	−0.0422504	−	0.999107i	$-0.513453\pi$
$569$	−2.32147e33	−0.0845007	−0.0422504	+	0.999107i	$0.513453\pi$
$570$	5.09345e33	0.181375
$571$	2.55837e34	0.891276	0.445638	−	0.895213i	$-0.352977\pi$
$571$	2.55837e34	0.891276	0.445638	+	0.895213i	$0.352977\pi$
$572$	3.09578e32	0.0105516
$573$	−2.02553e34	−0.675470
$574$	−3.29546e33	−0.107527
$575$	2.11565e34	0.675455
$576$	1.33374e33	0.0416667
$577$	1.95952e34	0.599035	0.299517	−	0.954091i	$-0.403174\pi$
$577$	1.95952e34	0.599035	0.299517	+	0.954091i	$0.403174\pi$
$578$	−2.33865e33	−0.0699629
$579$	−3.39507e34	−0.993954
$580$	1.02195e34	0.292805
$581$	5.58075e33	0.156492
$582$	−9.58144e32	−0.0262962
$583$	−3.99803e34	−1.07396
$584$	1.80322e34	0.474119
$585$	−1.00961e32	−0.00259841
$586$	1.65487e33	0.0416911
$587$	5.98783e33	0.147670	0.0738352	−	0.997270i	$-0.476476\pi$
$587$	5.98783e33	0.147670	0.0738352	+	0.997270i	$0.476476\pi$
$588$	1.18428e34	0.285915
$589$	3.94653e34	0.932769
$590$	−1.97311e34	−0.456564
$591$	4.64309e34	1.05187
$592$	5.58141e33	0.123801
$593$	1.57169e34	0.341338	0.170669	−	0.985328i	$-0.445407\pi$
$593$	1.57169e34	0.341338	0.170669	+	0.985328i	$0.445407\pi$
$594$	9.29041e33	0.197562
$595$	−2.63976e33	−0.0549670
$596$	−1.33987e34	−0.273203
$597$	−1.47085e34	−0.293690
$598$	4.98379e32	0.00974529
$599$	−7.90989e34	−1.51473	−0.757364	−	0.652992i	$-0.773513\pi$
$599$	−7.90989e34	−1.51473	−0.757364	+	0.652992i	$0.773513\pi$
$600$	−7.75392e33	−0.145422
$601$	−9.50067e34	−1.74511	−0.872556	−	0.488514i	$-0.837539\pi$
$601$	−9.50067e34	−1.74511	−0.872556	+	0.488514i	$0.837539\pi$
$602$	1.05922e33	0.0190559
$603$	3.01363e34	0.531035
$604$	−1.73867e34	−0.300093
$605$	−3.51343e34	−0.594003
$606$	−1.09401e34	−0.181181
$607$	−3.98588e32	−0.00646644	−0.00323322	−	0.999995i	$-0.501029\pi$
$607$	−3.98588e32	−0.00646644	−0.00323322	+	0.999995i	$0.501029\pi$
$608$	9.21495e33	0.146453
$609$	3.95931e33	0.0616458
$610$	−4.26252e34	−0.650195
$611$	2.31848e32	0.00346488
$612$	1.19324e34	0.174717
$613$	−6.82592e34	−0.979276	−0.489638	−	0.871926i	$-0.662871\pi$
$613$	−6.82592e34	−0.979276	−0.489638	+	0.871926i	$0.662871\pi$
$614$	−2.84932e34	−0.400532
$615$	3.49586e34	0.481521
$616$	−3.71835e33	−0.0501871
$617$	1.15084e35	1.52212	0.761062	−	0.648679i	$-0.224678\pi$
$617$	1.15084e35	1.52212	0.761062	+	0.648679i	$0.224678\pi$
$618$	−3.31549e34	−0.429726
$619$	4.34788e34	0.552261	0.276131	−	0.961120i	$-0.410948\pi$
$619$	4.34788e34	0.552261	0.276131	+	0.961120i	$0.410948\pi$
$620$	2.42519e34	0.301891
$621$	1.49563e34	0.182465
$622$	−1.12604e34	−0.134640
$623$	7.81178e33	0.0915482
$624$	−1.82657e32	−0.00209811
$625$	1.95367e34	0.219963
$626$	−3.84771e34	−0.424642
$627$	6.41886e34	0.694406
$628$	−5.64295e34	−0.598427
$629$	4.99348e34	0.519123
$630$	1.21265e33	0.0123589
$631$	1.27302e35	1.27195	0.635974	−	0.771711i	$-0.280599\pi$
$631$	1.27302e35	1.27195	0.635974	+	0.771711i	$0.280599\pi$
$632$	6.89010e34	0.674936
$633$	1.10794e34	0.106407
$634$	−7.64080e34	−0.719488
$635$	−9.46619e34	−0.873985
$636$	2.35891e34	0.213549
$637$	−1.62189e33	−0.0143972
$638$	1.28787e35	1.12102
$639$	2.08072e34	0.177604
$640$	5.66270e33	0.0473995
$641$	−9.45454e33	−0.0776096	−0.0388048	−	0.999247i	$-0.512355\pi$
$641$	−9.45454e33	−0.0776096	−0.0388048	+	0.999247i	$0.512355\pi$
$642$	−5.38171e34	−0.433244
$643$	8.31941e34	0.656834	0.328417	−	0.944533i	$-0.393485\pi$
$643$	8.31941e34	0.656834	0.328417	+	0.944533i	$0.393485\pi$
$644$	−5.98604e33	−0.0463517
$645$	−1.12363e34	−0.0853348
$646$	8.24427e34	0.614109
$647$	2.34992e35	1.71692	0.858460	−	0.512880i	$-0.171421\pi$
$647$	2.34992e35	1.71692	0.858460	+	0.512880i	$0.171421\pi$
$648$	−5.48151e33	−0.0392837
$649$	−2.48655e35	−1.74799
$650$	1.06191e33	0.00732269
$651$	9.39590e33	0.0635589
$652$	1.34292e34	0.0891159
$653$	−1.75276e35	−1.14106	−0.570530	−	0.821277i	$-0.693262\pi$
$653$	−1.75276e35	−1.14106	−0.570530	+	0.821277i	$0.693262\pi$
$654$	−6.22061e34	−0.397293
$655$	1.06350e35	0.666379
$656$	6.32463e34	0.388810
$657$	−7.41103e34	−0.447004
$658$	−2.78473e33	−0.0164801
$659$	−2.48211e35	−1.44130	−0.720648	−	0.693301i	$-0.756156\pi$
$659$	−2.48211e35	−1.44130	−0.720648	+	0.693301i	$0.756156\pi$
$660$	3.94447e34	0.224745
$661$	−3.37345e35	−1.88606	−0.943030	−	0.332707i	$-0.892038\pi$
$661$	−3.37345e35	−1.88606	−0.943030	+	0.332707i	$0.892038\pi$
$662$	1.93183e35	1.05985
$663$	−1.63416e33	−0.00879784
$664$	−1.07105e35	−0.565862
$665$	8.37835e33	0.0434398
$666$	−2.29390e34	−0.116720
$667$	2.07330e35	1.03535
$668$	−8.69030e34	−0.425921
$669$	−1.54387e35	−0.742648
$670$	1.27951e35	0.604100
$671$	−5.37170e35	−2.48932
$672$	2.19390e33	0.00997930
$673$	2.99045e35	1.33521	0.667604	−	0.744517i	$-0.267320\pi$
$673$	2.99045e35	1.33521	0.667604	+	0.744517i	$0.267320\pi$
$674$	−7.61004e34	−0.333533
$675$	3.18678e34	0.137105
$676$	−1.18362e35	−0.499894
$677$	5.69058e34	0.235938	0.117969	−	0.993017i	$-0.462362\pi$
$677$	5.69058e34	0.235938	0.117969	+	0.993017i	$0.462362\pi$
$678$	−3.77106e34	−0.153494
$679$	−1.57608e33	−0.00629803
$680$	5.06621e34	0.198757
$681$	−1.72062e35	−0.662745
$682$	3.05627e35	1.15581
$683$	1.38059e35	0.512633	0.256317	−	0.966593i	$-0.417491\pi$
$683$	1.38059e35	0.512633	0.256317	+	0.966593i	$0.417491\pi$
$684$	−3.78724e34	−0.138077
$685$	1.92264e35	0.688283
$686$	3.91490e34	0.137616
$687$	2.71619e35	0.937564
$688$	−2.03284e34	−0.0689045
$689$	−3.23056e33	−0.0107532
$690$	6.35005e34	0.207570
$691$	1.16343e35	0.373479	0.186739	−	0.982409i	$-0.440208\pi$
$691$	1.16343e35	0.373479	0.186739	+	0.982409i	$0.440208\pi$
$692$	−5.71901e34	−0.180300
$693$	1.52820e34	0.0473168
$694$	2.98039e35	0.906317
$695$	−1.96880e35	−0.588020
$696$	−7.59869e34	−0.222907
$697$	5.65841e35	1.63036
$698$	−4.90345e35	−1.38774
$699$	6.38421e34	0.177477
$700$	−1.27546e34	−0.0348291
$701$	6.30496e35	1.69125	0.845624	−	0.533779i	$-0.179229\pi$
$701$	6.30496e35	1.69125	0.845624	+	0.533779i	$0.179229\pi$
$702$	7.50700e32	0.00197812
$703$	−1.58488e35	−0.410257
$704$	7.13624e34	0.181473
$705$	2.95407e34	0.0738001
$706$	−2.86606e35	−0.703439
$707$	−1.79957e34	−0.0433935
$708$	1.46711e35	0.347574
$709$	−7.52844e35	−1.75238	−0.876188	−	0.481970i	$-0.839921\pi$
$709$	−7.52844e35	−1.75238	−0.876188	+	0.481970i	$0.839921\pi$
$710$	8.83419e34	0.202040
$711$	−2.83176e35	−0.636335
$712$	−1.49923e35	−0.331031
$713$	4.92018e35	1.06748
$714$	1.96280e34	0.0418454
$715$	−5.40200e33	−0.0113170
$716$	−2.07384e35	−0.426935
$717$	−1.77988e35	−0.360082
$718$	−2.48367e35	−0.493785
$719$	−1.28708e35	−0.251475	−0.125738	−	0.992064i	$-0.540130\pi$
$719$	−1.28708e35	−0.251475	−0.125738	+	0.992064i	$0.540130\pi$
$720$	−2.32731e34	−0.0446887
$721$	−5.45373e34	−0.102921
$722$	1.19576e35	0.221783
$723$	1.87725e35	0.342211
$724$	5.67936e34	0.101758
$725$	4.41764e35	0.777974
$726$	2.61241e35	0.452204
$727$	4.39640e35	0.748027	0.374014	−	0.927423i	$-0.377981\pi$
$727$	4.39640e35	0.748027	0.374014	+	0.927423i	$0.377981\pi$
$728$	−3.00457e32	−0.000502504 0
$729$	2.25284e34	0.0370370
$730$	−3.14654e35	−0.508507
$731$	−1.81871e35	−0.288932
$732$	3.16940e35	0.494981
$733$	−1.18297e36	−1.81625	−0.908124	−	0.418702i	$-0.862485\pi$
$733$	−1.18297e36	−1.81625	−0.908124	+	0.418702i	$0.862485\pi$
$734$	−9.11520e35	−1.37583
$735$	−2.06651e35	−0.306652
$736$	1.14884e35	0.167604
$737$	1.61246e36	2.31284
$738$	−2.59935e35	−0.366573
$739$	−8.13836e35	−1.12845	−0.564224	−	0.825622i	$-0.690825\pi$
$739$	−8.13836e35	−1.12845	−0.564224	+	0.825622i	$0.690825\pi$
$740$	−9.73931e34	−0.132780
$741$	5.18668e33	0.00695283
$742$	3.88023e34	0.0511457
$743$	−1.02640e36	−1.33033	−0.665164	−	0.746698i	$-0.731638\pi$
$743$	−1.02640e36	−1.33033	−0.665164	+	0.746698i	$0.731638\pi$
$744$	−1.80325e35	−0.229824
$745$	2.33802e35	0.293018
$746$	4.72593e35	0.582440
$747$	4.40191e35	0.533500
$748$	6.38452e35	0.760954
$749$	−8.85251e34	−0.103763
$750$	3.25222e35	0.374899
$751$	−1.43129e36	−1.62266	−0.811332	−	0.584586i	$-0.801257\pi$
$751$	−1.43129e36	−1.62266	−0.811332	+	0.584586i	$0.801257\pi$
$752$	5.34443e34	0.0595907
$753$	−5.71848e35	−0.627110
$754$	1.04065e34	0.0112244
$755$	3.03391e35	0.321859
$756$	−9.01667e33	−0.00940857
$757$	8.68697e35	0.891600	0.445800	−	0.895133i	$-0.352919\pi$
$757$	8.68697e35	0.891600	0.445800	+	0.895133i	$0.352919\pi$
$758$	−2.24138e35	−0.226283
$759$	8.00245e35	0.794696
$760$	−1.60797e35	−0.157075
$761$	5.51250e34	0.0529713	0.0264857	−	0.999649i	$-0.491568\pi$
$761$	5.51250e34	0.0529713	0.0264857	+	0.999649i	$0.491568\pi$
$762$	7.03860e35	0.665348
$763$	−1.02324e35	−0.0951530
$764$	6.39446e35	0.584975
$765$	−2.08216e35	−0.187390
$766$	8.11541e35	0.718540
$767$	−2.00923e34	−0.0175020
$768$	−4.21051e34	−0.0360844
$769$	−4.98681e35	−0.420479	−0.210239	−	0.977650i	$-0.567424\pi$
$769$	−4.98681e35	−0.420479	−0.210239	+	0.977650i	$0.567424\pi$
$770$	6.48836e34	0.0538271
$771$	−3.48763e33	−0.00284676
$772$	1.07180e36	0.860790
$773$	4.79467e35	0.378892	0.189446	−	0.981891i	$-0.439331\pi$
$773$	4.79467e35	0.378892	0.189446	+	0.981891i	$0.439331\pi$
$774$	8.35475e34	0.0649638
$775$	1.04836e36	0.802116
$776$	3.02479e34	0.0227732
$777$	−3.77329e34	−0.0279549
$778$	−1.71663e35	−0.125150
$779$	−1.79593e36	−1.28846
$780$	3.18728e33	0.00225029
$781$	1.11330e36	0.773525
$782$	1.02782e36	0.702802
$783$	3.12298e35	0.210158
$784$	−3.73868e35	−0.247610
$785$	9.84670e35	0.641830
$786$	−7.90767e35	−0.507302
$787$	1.22599e36	0.774111	0.387055	−	0.922056i	$-0.373492\pi$
$787$	1.22599e36	0.774111	0.387055	+	0.922056i	$0.373492\pi$
$788$	−1.46579e36	−0.910950
$789$	−1.08317e36	−0.662576
$790$	−1.20229e36	−0.723888
$791$	−6.20311e34	−0.0367623
$792$	−2.93292e35	−0.171094
$793$	−4.34054e34	−0.0249246
$794$	−1.08339e36	−0.612392
$795$	−4.11619e35	−0.229038
$796$	4.64337e35	0.254343
$797$	−3.12403e36	−1.68456	−0.842278	−	0.539043i	$-0.818786\pi$
$797$	−3.12403e36	−1.68456	−0.842278	+	0.539043i	$0.818786\pi$
$798$	−6.22973e34	−0.0330699
$799$	4.78146e35	0.249877
$800$	2.44786e35	0.125939
$801$	6.16168e35	0.312099
$802$	−9.57511e35	−0.477490
$803$	−3.96532e36	−1.94686
$804$	−9.51381e35	−0.459890
$805$	1.04454e35	0.0497136
$806$	2.46958e34	0.0115727
$807$	−6.92021e35	−0.319301
$808$	3.45371e35	0.156908
$809$	4.16982e36	1.86535	0.932675	−	0.360717i	$-0.117468\pi$
$809$	4.16982e36	1.86535	0.932675	+	0.360717i	$0.117468\pi$
$810$	9.56498e34	0.0421329
$811$	7.93102e35	0.344008	0.172004	−	0.985096i	$-0.444976\pi$
$811$	7.93102e35	0.344008	0.172004	+	0.985096i	$0.444976\pi$
$812$	−1.24993e35	−0.0533869
$813$	−1.45287e36	−0.611078
$814$	−1.22737e36	−0.508357
$815$	−2.34334e35	−0.0955794
$816$	−3.76698e35	−0.151310
$817$	5.77240e35	0.228339
$818$	2.24664e36	0.875221
$819$	1.23484e33	0.000473766 0
$820$	−1.10362e36	−0.417010
$821$	2.22198e35	0.0826896	0.0413448	−	0.999145i	$-0.486836\pi$
$821$	2.22198e35	0.0826896	0.0413448	+	0.999145i	$0.486836\pi$
$822$	−1.42958e36	−0.523977
$823$	4.63197e36	1.67212	0.836061	−	0.548637i	$-0.184853\pi$
$823$	4.63197e36	1.67212	0.836061	+	0.548637i	$0.184853\pi$
$824$	1.04668e36	0.372153
$825$	1.70511e36	0.597141
$826$	2.41329e35	0.0832450
$827$	5.60825e36	1.90550	0.952748	−	0.303760i	$-0.0982422\pi$
$827$	5.60825e36	1.90550	0.952748	+	0.303760i	$0.0982422\pi$
$828$	−4.72159e35	−0.158019
$829$	−3.61387e36	−1.19135	−0.595677	−	0.803224i	$-0.703116\pi$
$829$	−3.61387e36	−1.19135	−0.595677	+	0.803224i	$0.703116\pi$
$830$	1.86894e36	0.606903
$831$	2.57136e35	0.0822526
$832$	5.76635e33	0.00181702
$833$	−3.34486e36	−1.03828
$834$	1.46391e36	0.447649
$835$	1.51642e36	0.456813
$836$	−2.02639e36	−0.601373
$837$	7.41118e35	0.216680
$838$	−1.39873e35	−0.0402889
$839$	−3.53738e36	−1.00382	−0.501911	−	0.864919i	$-0.667370\pi$
$839$	−3.53738e36	−1.00382	−0.501911	+	0.864919i	$0.667370\pi$
$840$	−3.82825e34	−0.0107031
$841$	6.98837e35	0.192498
$842$	2.33934e36	0.634880
$843$	4.02736e36	1.07690
$844$	−3.49770e35	−0.0921513
$845$	2.06536e36	0.536151
$846$	−2.19650e35	−0.0561827
$847$	4.29722e35	0.108304
$848$	−7.44692e35	−0.184939
$849$	6.93230e35	0.169641
$850$	2.19001e36	0.528091
$851$	−1.97589e36	−0.469508
$852$	−6.56867e35	−0.153809
$853$	−5.36485e36	−1.23792	−0.618962	−	0.785421i	$-0.712447\pi$
$853$	−5.36485e36	−1.23792	−0.618962	+	0.785421i	$0.712447\pi$
$854$	5.21343e35	0.118550
$855$	6.60857e35	0.148092
$856$	1.69897e36	0.375200
$857$	1.12850e36	0.245607	0.122803	−	0.992431i	$-0.460812\pi$
$857$	1.12850e36	0.245607	0.122803	+	0.992431i	$0.460812\pi$
$858$	4.01667e34	0.00861539
$859$	−6.05620e36	−1.28022	−0.640111	−	0.768282i	$-0.721112\pi$
$859$	−6.05620e36	−1.28022	−0.640111	+	0.768282i	$0.721112\pi$
$860$	3.54722e35	0.0739021
$861$	−4.27574e35	−0.0877955
$862$	−2.15609e36	−0.436342
$863$	5.30956e35	0.105907	0.0529533	−	0.998597i	$-0.483137\pi$
$863$	5.30956e35	0.105907	0.0529533	+	0.998597i	$0.483137\pi$
$864$	1.73047e35	0.0340207
$865$	9.97942e35	0.193377
$866$	2.86979e36	0.548121
$867$	−3.03432e35	−0.0571244
$868$	−2.96622e35	−0.0550436
$869$	−1.51515e37	−2.77146
$870$	1.32594e36	0.239074
$871$	1.30293e35	0.0231576
$872$	1.96380e36	0.344066
$873$	−1.24316e35	−0.0214708
$874$	−3.26221e36	−0.555416
$875$	5.34965e35	0.0897894
$876$	2.33961e36	0.387117
$877$	−5.83031e36	−0.951035	−0.475518	−	0.879706i	$-0.657739\pi$
$877$	−5.83031e36	−0.951035	−0.475518	+	0.879706i	$0.657739\pi$
$878$	−2.16900e36	−0.348802
$879$	2.14713e35	0.0340406
$880$	−1.24524e36	−0.194635
$881$	7.57293e36	1.16698	0.583492	−	0.812119i	$-0.301686\pi$
$881$	7.57293e36	1.16698	0.583492	+	0.812119i	$0.301686\pi$
$882$	1.53656e36	0.233449
$883$	−2.59184e36	−0.388239	−0.194119	−	0.980978i	$-0.562185\pi$
$883$	−2.59184e36	−0.388239	−0.194119	+	0.980978i	$0.562185\pi$
$884$	5.15893e34	0.00761915
$885$	−2.56004e36	−0.372783
$886$	−1.84235e36	−0.264515
$887$	7.96686e36	1.12782	0.563912	−	0.825835i	$-0.309296\pi$
$887$	7.96686e36	1.12782	0.563912	+	0.825835i	$0.309296\pi$
$888$	7.24168e35	0.101083
$889$	1.15780e36	0.159353
$890$	2.61609e36	0.355041
$891$	1.20540e36	0.161309
$892$	4.87387e36	0.643152
$893$	−1.51759e36	−0.197475
$894$	−1.73844e36	−0.223069
$895$	3.61875e36	0.457900
$896$	−6.92597e34	−0.00864233
$897$	6.46628e34	0.00795699
$898$	4.04988e36	0.491460
$899$	1.02737e37	1.22950
$900$	−1.00604e36	−0.118737
$901$	−6.66248e36	−0.775489
$902$	−1.39080e37	−1.59655
$903$	1.37429e35	0.0155590
$904$	1.19050e36	0.132930
$905$	−9.91023e35	−0.109138
$906$	−2.25586e36	−0.245025
$907$	−4.86506e36	−0.521191	−0.260596	−	0.965448i	$-0.583919\pi$
$907$	−4.86506e36	−0.521191	−0.260596	+	0.965448i	$0.583919\pi$
$908$	5.43188e36	0.573954
$909$	−1.41944e36	−0.147934
$910$	5.24284e33	0.000538951 0
$911$	1.10036e37	1.11572	0.557859	−	0.829936i	$-0.311623\pi$
$911$	1.10036e37	1.11572	0.557859	+	0.829936i	$0.311623\pi$
$912$	1.19561e36	0.119578
$913$	2.35527e37	2.32357
$914$	−1.20337e37	−1.17104
$915$	−5.53046e36	−0.530882
$916$	−8.57482e36	−0.811954
$917$	−1.30075e36	−0.121500
$918$	1.54819e36	0.142656
$919$	1.10577e37	1.00513	0.502564	−	0.864540i	$-0.332390\pi$
$919$	1.10577e37	1.00513	0.502564	+	0.864540i	$0.332390\pi$
$920$	−2.00467e36	−0.179761
$921$	−3.69689e36	−0.327033
$922$	8.76759e36	0.765145
$923$	8.99588e34	0.00774502
$924$	−4.82443e35	−0.0409776
$925$	−4.21008e36	−0.352792
$926$	−3.57164e36	−0.295277
$927$	−4.30172e36	−0.350870
$928$	2.39885e36	0.193043
$929$	1.82435e37	1.44848	0.724239	−	0.689549i	$-0.242191\pi$
$929$	1.82435e37	1.44848	0.724239	+	0.689549i	$0.242191\pi$
$930$	3.14660e36	0.246493
$931$	1.06163e37	0.820543
$932$	−2.01545e36	−0.153700
$933$	−1.46100e36	−0.109933
$934$	2.46232e36	0.182814
$935$	−1.11407e37	−0.816146
$936$	−2.36991e34	−0.00171310
$937$	9.54074e36	0.680514	0.340257	−	0.940332i	$-0.389486\pi$
$937$	9.54074e36	0.680514	0.340257	+	0.940332i	$0.389486\pi$
$938$	−1.56495e36	−0.110145
$939$	−4.99226e36	−0.346719
$940$	−9.32580e35	−0.0639128
$941$	−7.72127e36	−0.522178	−0.261089	−	0.965315i	$-0.584082\pi$
$941$	−7.72127e36	−0.522178	−0.261089	+	0.965315i	$0.584082\pi$
$942$	−7.32152e36	−0.488613
$943$	−2.23900e37	−1.47454
$944$	−4.63156e36	−0.301008
$945$	1.57337e35	0.0100910
$946$	4.47026e36	0.282940
$947$	−1.89183e37	−1.18170	−0.590849	−	0.806782i	$-0.701207\pi$
$947$	−1.89183e37	−1.18170	−0.590849	+	0.806782i	$0.701207\pi$
$948$	8.93966e36	0.551083
$949$	−3.20413e35	−0.0194932
$950$	−6.95088e36	−0.417344
$951$	−9.91366e36	−0.587459
$952$	−6.19641e35	−0.0362392
$953$	−1.61494e37	−0.932172	−0.466086	−	0.884739i	$-0.654336\pi$
$953$	−1.61494e37	−0.932172	−0.466086	+	0.884739i	$0.654336\pi$
$954$	3.06060e36	0.174362
$955$	−1.11580e37	−0.627402
$956$	5.61896e36	0.311840
$957$	1.67097e37	0.915312
$958$	1.23646e37	0.668515
$959$	−2.35156e36	−0.125494
$960$	7.34715e35	0.0387016
$961$	5.14781e36	0.267658
$962$	−9.91757e34	−0.00508999
$963$	−6.98257e36	−0.353742
$964$	−5.92635e36	−0.296363
$965$	−1.87024e37	−0.923222
$966$	−7.76666e35	−0.0378460
$967$	−2.64645e37	−1.27301	−0.636507	−	0.771271i	$-0.719621\pi$
$967$	−2.64645e37	−1.27301	−0.636507	+	0.771271i	$0.719621\pi$
$968$	−8.24720e36	−0.391620
$969$	1.06966e37	0.501418
$970$	−5.27813e35	−0.0244249
$971$	2.73601e37	1.24990	0.624952	−	0.780663i	$-0.285118\pi$
$971$	2.73601e37	1.24990	0.624952	+	0.780663i	$0.285118\pi$
$972$	−7.11206e35	−0.0320750
$973$	2.40802e36	0.107213
$974$	2.14687e37	0.943665
$975$	1.37779e35	0.00597895
$976$	−1.00056e37	−0.428666
$977$	3.04743e37	1.28900	0.644498	−	0.764606i	$-0.277066\pi$
$977$	3.04743e37	1.28900	0.644498	+	0.764606i	$0.277066\pi$
$978$	1.74239e36	0.0727629
$979$	3.29685e37	1.35930
$980$	6.52384e36	0.265569
$981$	−8.07101e36	−0.324389
$982$	1.26227e37	0.500910
$983$	3.84516e36	0.150659	0.0753296	−	0.997159i	$-0.475999\pi$
$983$	3.84516e36	0.150659	0.0753296	+	0.997159i	$0.475999\pi$
$984$	8.20598e36	0.317462
$985$	2.55774e37	0.977020
$986$	2.14616e37	0.809471
$987$	−3.61308e35	−0.0134559
$988$	−1.63740e35	−0.00602133
$989$	7.19651e36	0.261317
$990$	5.11781e36	0.183503
$991$	−4.30043e37	−1.52262	−0.761309	−	0.648389i	$-0.775443\pi$
$991$	−4.30043e37	−1.52262	−0.761309	+	0.648389i	$0.775443\pi$
$992$	5.69275e36	0.199033
$993$	2.50648e37	0.865363
$994$	−1.08050e36	−0.0368378
$995$	−8.10246e36	−0.272790
$996$	−1.38965e37	−0.462024
$997$	−1.52317e37	−0.500103	−0.250051	−	0.968233i	$-0.580447\pi$
$997$	−1.52317e37	−0.500103	−0.250051	+	0.968233i	$0.580447\pi$
$998$	6.75470e36	0.219015
$999$	−2.97625e36	−0.0953017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.26.a.a.1.1	✓	1
3.2	odd	2		18.26.a.d.1.1		1
4.3	odd	2		48.26.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.26.a.a.1.1	✓	1	1.1	even	1	trivial
18.26.a.d.1.1		1	3.2	odd	2
48.26.a.c.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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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