LMFDB - Embedded newform 4655.2.a.br.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4655,2,Mod(1,4655)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4655, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4655.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4655 = 5 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4655.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:	$37.1703621409$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.21870 q^{2} -2.59660 q^{3} -0.514774 q^{4} -1.00000 q^{5} +3.16448 q^{6} +3.06475 q^{8} +3.74235 q^{9} +1.21870 q^{10} +1.34660 q^{11} +1.33666 q^{12} -4.31575 q^{13} +2.59660 q^{15} -2.70546 q^{16} -6.29921 q^{17} -4.56080 q^{18} +1.00000 q^{19} +0.514774 q^{20} -1.64110 q^{22} +8.99673 q^{23} -7.95795 q^{24} +1.00000 q^{25} +5.25960 q^{26} -1.92760 q^{27} +6.18505 q^{29} -3.16448 q^{30} +3.48591 q^{31} -2.83236 q^{32} -3.49659 q^{33} +7.67684 q^{34} -1.92647 q^{36} -2.65974 q^{37} -1.21870 q^{38} +11.2063 q^{39} -3.06475 q^{40} -7.39767 q^{41} -4.40794 q^{43} -0.693194 q^{44} -3.74235 q^{45} -10.9643 q^{46} +9.10868 q^{47} +7.02501 q^{48} -1.21870 q^{50} +16.3566 q^{51} +2.22163 q^{52} -4.06456 q^{53} +2.34917 q^{54} -1.34660 q^{55} -2.59660 q^{57} -7.53772 q^{58} -0.439715 q^{59} -1.33666 q^{60} +11.4698 q^{61} -4.24827 q^{62} +8.86272 q^{64} +4.31575 q^{65} +4.26129 q^{66} -10.1027 q^{67} +3.24267 q^{68} -23.3609 q^{69} +7.65157 q^{71} +11.4694 q^{72} -11.0854 q^{73} +3.24142 q^{74} -2.59660 q^{75} -0.514774 q^{76} -13.6571 q^{78} -17.5813 q^{79} +2.70546 q^{80} -6.22185 q^{81} +9.01553 q^{82} +3.61540 q^{83} +6.29921 q^{85} +5.37195 q^{86} -16.0601 q^{87} +4.12699 q^{88} -2.45819 q^{89} +4.56080 q^{90} -4.63128 q^{92} -9.05153 q^{93} -11.1007 q^{94} -1.00000 q^{95} +7.35452 q^{96} +7.31121 q^{97} +5.03946 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) $ 26 * q + 4 * q^2 - 6 * q^3 + 36 * q^4 - 26 * q^5 + 4 * q^6 + 12 * q^8 + 44 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 14 * q^13 + 6 * q^15 + 64 * q^16 - 18 * q^17 + 8 * q^18 + 26 * q^19 - 36 * q^20 + 36 * q^22 + 44 * q^24 + 26 * q^25 + 8 * q^26 - 30 * q^27 + 22 * q^29 - 4 * q^30 + 28 * q^32 - 38 * q^33 + 68 * q^36 + 48 * q^37 + 4 * q^38 + 26 * q^39 - 12 * q^40 - 4 * q^41 + 16 * q^43 + 44 * q^44 - 44 * q^45 + 48 * q^46 - 22 * q^47 - 48 * q^48 + 4 * q^50 + 34 * q^51 - 32 * q^52 + 28 * q^53 + 28 * q^54 - 14 * q^55 - 6 * q^57 + 52 * q^58 + 8 * q^59 + 20 * q^60 + 28 * q^61 + 16 * q^62 + 52 * q^64 + 14 * q^65 + 24 * q^66 + 60 * q^67 - 52 * q^68 + 4 * q^69 + 8 * q^71 + 36 * q^72 + 4 * q^73 + 8 * q^74 - 6 * q^75 + 36 * q^76 - 76 * q^78 + 50 * q^79 - 64 * q^80 + 114 * q^81 + 36 * q^82 - 20 * q^83 + 18 * q^85 + 40 * q^86 - 18 * q^87 + 108 * q^88 + 20 * q^89 - 8 * q^90 - 48 * q^92 + 32 * q^93 + 80 * q^94 - 26 * q^95 + 140 * q^96 - 26 * q^97 + 24 * q^99

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 $

$2$	−1.21870	−0.861750	−0.430875	−	0.902412i	$-0.641795\pi$
$2$	−1.21870	−0.861750	−0.430875	+	0.902412i	$0.641795\pi$
$3$	−2.59660	−1.49915	−0.749575	−	0.661919i	$-0.769742\pi$
$3$	−2.59660	−1.49915	−0.749575	+	0.661919i	$0.769742\pi$
$4$	−0.514774	−0.257387
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.16448	1.29189
$7$	0	0
$7$	0	0
$8$	3.06475	1.08355
$9$	3.74235	1.24745
$10$	1.21870	0.385386
$11$	1.34660	0.406015	0.203008	−	0.979177i	$-0.434928\pi$
$11$	1.34660	0.406015	0.203008	+	0.979177i	$0.434928\pi$
$12$	1.33666	0.385861
$13$	−4.31575	−1.19697	−0.598487	−	0.801133i	$-0.704231\pi$
$13$	−4.31575	−1.19697	−0.598487	+	0.801133i	$0.704231\pi$
$14$	0	0
$15$	2.59660	0.670440
$16$	−2.70546	−0.676365
$17$	−6.29921	−1.52778	−0.763891	−	0.645345i	$-0.776714\pi$
$17$	−6.29921	−1.52778	−0.763891	+	0.645345i	$0.776714\pi$
$18$	−4.56080	−1.07499
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.514774	0.115107
$21$	0	0
$22$	−1.64110	−0.349884
$23$	8.99673	1.87595	0.937974	−	0.346706i	$-0.112700\pi$
$23$	8.99673	1.87595	0.937974	+	0.346706i	$0.112700\pi$
$24$	−7.95795	−1.62441
$25$	1.00000	0.200000
$26$	5.25960	1.03149
$27$	−1.92760	−0.370967
$28$	0	0
$29$	6.18505	1.14854	0.574268	−	0.818668i	$-0.305287\pi$
$29$	6.18505	1.14854	0.574268	+	0.818668i	$0.305287\pi$
$30$	−3.16448	−0.577752
$31$	3.48591	0.626088	0.313044	−	0.949739i	$-0.398651\pi$
$31$	3.48591	0.626088	0.313044	+	0.949739i	$0.398651\pi$
$32$	−2.83236	−0.500695
$33$	−3.49659	−0.608678
$34$	7.67684	1.31657
$35$	0	0
$36$	−1.92647	−0.321078
$37$	−2.65974	−0.437259	−0.218629	−	0.975808i	$-0.570159\pi$
$37$	−2.65974	−0.437259	−0.218629	+	0.975808i	$0.570159\pi$
$38$	−1.21870	−0.197699
$39$	11.2063	1.79444
$40$	−3.06475	−0.484580
$41$	−7.39767	−1.15532	−0.577661	−	0.816277i	$-0.696034\pi$
$41$	−7.39767	−1.15532	−0.577661	+	0.816277i	$0.696034\pi$
$42$	0	0
$43$	−4.40794	−0.672205	−0.336102	−	0.941825i	$-0.609109\pi$
$43$	−4.40794	−0.672205	−0.336102	+	0.941825i	$0.609109\pi$
$44$	−0.693194	−0.104503
$45$	−3.74235	−0.557877
$46$	−10.9643	−1.61660
$47$	9.10868	1.32864	0.664319	−	0.747449i	$-0.268722\pi$
$47$	9.10868	1.32864	0.664319	+	0.747449i	$0.268722\pi$
$48$	7.02501	1.01397
$49$	0	0
$50$	−1.21870	−0.172350
$51$	16.3566	2.29038
$52$	2.22163	0.308085
$53$	−4.06456	−0.558310	−0.279155	−	0.960246i	$-0.590054\pi$
$53$	−4.06456	−0.558310	−0.279155	+	0.960246i	$0.590054\pi$
$54$	2.34917	0.319681
$55$	−1.34660	−0.181576
$56$	0	0
$57$	−2.59660	−0.343929
$58$	−7.53772	−0.989751
$59$	−0.439715	−0.0572460	−0.0286230	−	0.999590i	$-0.509112\pi$
$59$	−0.439715	−0.0572460	−0.0286230	+	0.999590i	$0.509112\pi$
$60$	−1.33666	−0.172562
$61$	11.4698	1.46855	0.734277	−	0.678850i	$-0.237521\pi$
$61$	11.4698	1.46855	0.734277	+	0.678850i	$0.237521\pi$
$62$	−4.24827	−0.539531
$63$	0	0
$64$	8.86272	1.10784
$65$	4.31575	0.535303
$66$	4.26129	0.524528
$67$	−10.1027	−1.23424	−0.617122	−	0.786868i	$-0.711701\pi$
$67$	−10.1027	−1.23424	−0.617122	+	0.786868i	$0.711701\pi$
$68$	3.24267	0.393231
$69$	−23.3609	−2.81233
$70$	0	0
$71$	7.65157	0.908075	0.454037	−	0.890983i	$-0.349983\pi$
$71$	7.65157	0.908075	0.454037	+	0.890983i	$0.349983\pi$
$72$	11.4694	1.35168
$73$	−11.0854	−1.29745	−0.648725	−	0.761023i	$-0.724697\pi$
$73$	−11.0854	−1.29745	−0.648725	+	0.761023i	$0.724697\pi$
$74$	3.24142	0.376808
$75$	−2.59660	−0.299830
$76$	−0.514774	−0.0590486
$77$	0	0
$78$	−13.6571	−1.54636
$79$	−17.5813	−1.97805	−0.989025	−	0.147747i	$-0.952798\pi$
$79$	−17.5813	−1.97805	−0.989025	+	0.147747i	$0.952798\pi$
$80$	2.70546	0.302480
$81$	−6.22185	−0.691316
$82$	9.01553	0.995599
$83$	3.61540	0.396842	0.198421	−	0.980117i	$-0.436419\pi$
$83$	3.61540	0.396842	0.198421	+	0.980117i	$0.436419\pi$
$84$	0	0
$85$	6.29921	0.683245
$86$	5.37195	0.579272
$87$	−16.0601	−1.72183
$88$	4.12699	0.439939
$89$	−2.45819	−0.260568	−0.130284	−	0.991477i	$-0.541589\pi$
$89$	−2.45819	−0.260568	−0.130284	+	0.991477i	$0.541589\pi$
$90$	4.56080	0.480751
$91$	0	0
$92$	−4.63128	−0.482844
$93$	−9.05153	−0.938600
$94$	−11.1007	−1.14495
$95$	−1.00000	−0.102598
$96$	7.35452	0.750618
$97$	7.31121	0.742341	0.371171	−	0.928565i	$-0.378956\pi$
$97$	7.31121	0.742341	0.371171	+	0.928565i	$0.378956\pi$
$98$	0	0
$99$	5.03946	0.506484
$100$	−0.514774	−0.0514774
$101$	−7.95595	−0.791647	−0.395824	−	0.918327i	$-0.629541\pi$
$101$	−7.95595	−0.791647	−0.395824	+	0.918327i	$0.629541\pi$
$102$	−19.9337	−1.97373
$103$	−0.476109	−0.0469124	−0.0234562	−	0.999725i	$-0.507467\pi$
$103$	−0.476109	−0.0469124	−0.0234562	+	0.999725i	$0.507467\pi$
$104$	−13.2267	−1.29698
$105$	0	0
$106$	4.95347	0.481124
$107$	−5.19385	−0.502108	−0.251054	−	0.967973i	$-0.580777\pi$
$107$	−5.19385	−0.502108	−0.251054	+	0.967973i	$0.580777\pi$
$108$	0.992278	0.0954820
$109$	19.8446	1.90077	0.950386	−	0.311074i	$-0.100689\pi$
$109$	19.8446	1.90077	0.950386	+	0.311074i	$0.100689\pi$
$110$	1.64110	0.156473
$111$	6.90630	0.655517
$112$	0	0
$113$	−3.33367	−0.313606	−0.156803	−	0.987630i	$-0.550119\pi$
$113$	−3.33367	−0.313606	−0.156803	+	0.987630i	$0.550119\pi$
$114$	3.16448	0.296381
$115$	−8.99673	−0.838949
$116$	−3.18390	−0.295618
$117$	−16.1511	−1.49317
$118$	0.535880	0.0493317
$119$	0	0
$120$	7.95795	0.726458
$121$	−9.18667	−0.835152
$122$	−13.9782	−1.26553
$123$	19.2088	1.73200
$124$	−1.79445	−0.161147
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−1.70529	−0.151320	−0.0756599	−	0.997134i	$-0.524106\pi$
$127$	−1.70529	−0.151320	−0.0756599	+	0.997134i	$0.524106\pi$
$128$	−5.13626	−0.453985
$129$	11.4457	1.00774
$130$	−5.25960	−0.461297
$131$	−11.7277	−1.02466	−0.512329	−	0.858789i	$-0.671217\pi$
$131$	−11.7277	−1.02466	−0.512329	+	0.858789i	$0.671217\pi$
$132$	1.79995	0.156666
$133$	0	0
$134$	12.3122	1.06361
$135$	1.92760	0.165902
$136$	−19.3055	−1.65543
$137$	−7.43129	−0.634898	−0.317449	−	0.948275i	$-0.602826\pi$
$137$	−7.43129	−0.634898	−0.317449	+	0.948275i	$0.602826\pi$
$138$	28.4700	2.42352
$139$	6.05613	0.513674	0.256837	−	0.966455i	$-0.417320\pi$
$139$	6.05613	0.513674	0.256837	+	0.966455i	$0.417320\pi$
$140$	0	0
$141$	−23.6516	−1.99183
$142$	−9.32496	−0.782533
$143$	−5.81159	−0.485989
$144$	−10.1248	−0.843733
$145$	−6.18505	−0.513641
$146$	13.5098	1.11808
$147$	0	0
$148$	1.36916	0.112545
$149$	−3.91575	−0.320790	−0.160395	−	0.987053i	$-0.551277\pi$
$149$	−3.91575	−0.320790	−0.160395	+	0.987053i	$0.551277\pi$
$150$	3.16448	0.258379
$151$	−16.1392	−1.31339	−0.656693	−	0.754158i	$-0.728045\pi$
$151$	−16.1392	−1.31339	−0.656693	+	0.754158i	$0.728045\pi$
$152$	3.06475	0.248584
$153$	−23.5739	−1.90583
$154$	0	0
$155$	−3.48591	−0.279995
$156$	−5.76870	−0.461866
$157$	−15.5675	−1.24242	−0.621211	−	0.783644i	$-0.713359\pi$
$157$	−15.5675	−1.24242	−0.621211	+	0.783644i	$0.713359\pi$
$158$	21.4263	1.70459
$159$	10.5540	0.836990
$160$	2.83236	0.223918
$161$	0	0
$162$	7.58255	0.595742
$163$	−10.7167	−0.839398	−0.419699	−	0.907663i	$-0.637864\pi$
$163$	−10.7167	−0.839398	−0.419699	+	0.907663i	$0.637864\pi$
$164$	3.80812	0.297365
$165$	3.49659	0.272209
$166$	−4.40609	−0.341979
$167$	−15.8611	−1.22737	−0.613684	−	0.789552i	$-0.710313\pi$
$167$	−15.8611	−1.22737	−0.613684	+	0.789552i	$0.710313\pi$
$168$	0	0
$169$	5.62569	0.432745
$170$	−7.67684	−0.588786
$171$	3.74235	0.286185
$172$	2.26909	0.173017
$173$	1.46256	0.111196	0.0555981	−	0.998453i	$-0.482293\pi$
$173$	1.46256	0.111196	0.0555981	+	0.998453i	$0.482293\pi$
$174$	19.5725	1.48378
$175$	0	0
$176$	−3.64317	−0.274615
$177$	1.14176	0.0858203
$178$	2.99580	0.224544
$179$	9.52438	0.711886	0.355943	−	0.934508i	$-0.384160\pi$
$179$	9.52438	0.711886	0.355943	+	0.934508i	$0.384160\pi$
$180$	1.92647	0.143590
$181$	−23.9915	−1.78327	−0.891635	−	0.452754i	$-0.850441\pi$
$181$	−23.9915	−1.78327	−0.891635	+	0.452754i	$0.850441\pi$
$182$	0	0
$183$	−29.7825	−2.20158
$184$	27.5727	2.03269
$185$	2.65974	0.195548
$186$	11.0311	0.808839
$187$	−8.48251	−0.620303
$188$	−4.68891	−0.341974
$189$	0	0
$190$	1.21870	0.0884137
$191$	8.43884	0.610613	0.305306	−	0.952254i	$-0.401241\pi$
$191$	8.43884	0.610613	0.305306	+	0.952254i	$0.401241\pi$
$192$	−23.0130	−1.66082
$193$	24.4605	1.76071	0.880354	−	0.474318i	$-0.157305\pi$
$193$	24.4605	1.76071	0.880354	+	0.474318i	$0.157305\pi$
$194$	−8.91017	−0.639713
$195$	−11.2063	−0.802499
$196$	0	0
$197$	−22.5738	−1.60832	−0.804158	−	0.594416i	$-0.797383\pi$
$197$	−22.5738	−1.60832	−0.804158	+	0.594416i	$0.797383\pi$
$198$	−6.14158	−0.436463
$199$	8.25872	0.585445	0.292723	−	0.956197i	$-0.405439\pi$
$199$	8.25872	0.585445	0.292723	+	0.956197i	$0.405439\pi$
$200$	3.06475	0.216711
$201$	26.2328	1.85032
$202$	9.69591	0.682202
$203$	0	0
$204$	−8.41992	−0.589512
$205$	7.39767	0.516676
$206$	0.580233	0.0404268
$207$	33.6689	2.34015
$208$	11.6761	0.809591
$209$	1.34660	0.0931463
$210$	0	0
$211$	8.12000	0.559004	0.279502	−	0.960145i	$-0.409831\pi$
$211$	8.12000	0.559004	0.279502	+	0.960145i	$0.409831\pi$
$212$	2.09233	0.143702
$213$	−19.8681	−1.36134
$214$	6.32974	0.432692
$215$	4.40794	0.300619
$216$	−5.90762	−0.401963
$217$	0	0
$218$	−24.1846	−1.63799
$219$	28.7844	1.94507
$220$	0.693194	0.0467351
$221$	27.1858	1.82871
$222$	−8.41669	−0.564891
$223$	22.6800	1.51876	0.759381	−	0.650646i	$-0.225502\pi$
$223$	22.6800	1.51876	0.759381	+	0.650646i	$0.225502\pi$
$224$	0	0
$225$	3.74235	0.249490
$226$	4.06274	0.270250
$227$	−1.82891	−0.121389	−0.0606944	−	0.998156i	$-0.519332\pi$
$227$	−1.82891	−0.121389	−0.0606944	+	0.998156i	$0.519332\pi$
$228$	1.33666	0.0885227
$229$	−0.187466	−0.0123881	−0.00619405	−	0.999981i	$-0.501972\pi$
$229$	−0.187466	−0.0123881	−0.00619405	+	0.999981i	$0.501972\pi$
$230$	10.9643	0.722965
$231$	0	0
$232$	18.9556	1.24450
$233$	−0.267637	−0.0175335	−0.00876675	−	0.999962i	$-0.502791\pi$
$233$	−0.267637	−0.0175335	−0.00876675	+	0.999962i	$0.502791\pi$
$234$	19.6833	1.28674
$235$	−9.10868	−0.594185
$236$	0.226353	0.0147344
$237$	45.6517	2.96539
$238$	0	0
$239$	19.1664	1.23977	0.619887	−	0.784691i	$-0.287178\pi$
$239$	19.1664	1.23977	0.619887	+	0.784691i	$0.287178\pi$
$240$	−7.02501	−0.453463
$241$	5.42779	0.349635	0.174817	−	0.984601i	$-0.444066\pi$
$241$	5.42779	0.349635	0.174817	+	0.984601i	$0.444066\pi$
$242$	11.1958	0.719692
$243$	21.9385	1.40735
$244$	−5.90434	−0.377986
$245$	0	0
$246$	−23.4098	−1.49255
$247$	−4.31575	−0.274605
$248$	10.6834	0.678400
$249$	−9.38777	−0.594926
$250$	1.21870	0.0770773
$251$	13.5886	0.857703	0.428851	−	0.903375i	$-0.358918\pi$
$251$	13.5886	0.857703	0.428851	+	0.903375i	$0.358918\pi$
$252$	0	0
$253$	12.1150	0.761663
$254$	2.07823	0.130400
$255$	−16.3566	−1.02429
$256$	−11.4659	−0.716617
$257$	−15.2880	−0.953638	−0.476819	−	0.879001i	$-0.658210\pi$
$257$	−15.2880	−0.953638	−0.476819	+	0.879001i	$0.658210\pi$
$258$	−13.9488	−0.868416
$259$	0	0
$260$	−2.22163	−0.137780
$261$	23.1467	1.43274
$262$	14.2926	0.882999
$263$	14.4321	0.889921	0.444960	−	0.895550i	$-0.353218\pi$
$263$	14.4321	0.889921	0.444960	+	0.895550i	$0.353218\pi$
$264$	−10.7162	−0.659535
$265$	4.06456	0.249684
$266$	0	0
$267$	6.38296	0.390631
$268$	5.20061	0.317678
$269$	8.70066	0.530488	0.265244	−	0.964181i	$-0.414547\pi$
$269$	8.70066	0.530488	0.265244	+	0.964181i	$0.414547\pi$
$270$	−2.34917	−0.142966
$271$	22.1555	1.34585	0.672924	−	0.739712i	$-0.265038\pi$
$271$	22.1555	1.34585	0.672924	+	0.739712i	$0.265038\pi$
$272$	17.0423	1.03334
$273$	0	0
$274$	9.05650	0.547123
$275$	1.34660	0.0812031
$276$	12.0256	0.723856
$277$	22.6124	1.35864	0.679322	−	0.733840i	$-0.262274\pi$
$277$	22.6124	1.35864	0.679322	+	0.733840i	$0.262274\pi$
$278$	−7.38060	−0.442659
$279$	13.0455	0.781014
$280$	0	0
$281$	30.6197	1.82662	0.913308	−	0.407269i	$-0.133519\pi$
$281$	30.6197	1.82662	0.913308	+	0.407269i	$0.133519\pi$
$282$	28.8242	1.71646
$283$	14.3623	0.853751	0.426876	−	0.904310i	$-0.359614\pi$
$283$	14.3623	0.853751	0.426876	+	0.904310i	$0.359614\pi$
$284$	−3.93883	−0.233726
$285$	2.59660	0.153810
$286$	7.08258	0.418801
$287$	0	0
$288$	−10.5997	−0.624593
$289$	22.6800	1.33412
$290$	7.53772	0.442630
$291$	−18.9843	−1.11288
$292$	5.70648	0.333946
$293$	14.0391	0.820171	0.410086	−	0.912047i	$-0.365499\pi$
$293$	14.0391	0.820171	0.410086	+	0.912047i	$0.365499\pi$
$294$	0	0
$295$	0.439715	0.0256012
$296$	−8.15144	−0.473793
$297$	−2.59571	−0.150618
$298$	4.77212	0.276441
$299$	−38.8276	−2.24546
$300$	1.33666	0.0771723
$301$	0	0
$302$	19.6688	1.13181
$303$	20.6585	1.18680
$304$	−2.70546	−0.155169
$305$	−11.4698	−0.656757
$306$	28.7294	1.64235
$307$	−30.7563	−1.75536	−0.877678	−	0.479251i	$-0.840908\pi$
$307$	−30.7563	−1.75536	−0.877678	+	0.479251i	$0.840908\pi$
$308$	0	0
$309$	1.23627	0.0703288
$310$	4.24827	0.241286
$311$	16.5154	0.936500	0.468250	−	0.883596i	$-0.344885\pi$
$311$	16.5154	0.936500	0.468250	+	0.883596i	$0.344885\pi$
$312$	34.3445	1.94437
$313$	−11.0388	−0.623950	−0.311975	−	0.950090i	$-0.600991\pi$
$313$	−11.0388	−0.623950	−0.311975	+	0.950090i	$0.600991\pi$
$314$	18.9721	1.07066
$315$	0	0
$316$	9.05039	0.509124
$317$	−23.5720	−1.32394	−0.661968	−	0.749532i	$-0.730279\pi$
$317$	−23.5720	−1.32394	−0.661968	+	0.749532i	$0.730279\pi$
$318$	−12.8622	−0.721277
$319$	8.32879	0.466323
$320$	−8.86272	−0.495441
$321$	13.4864	0.752736
$322$	0	0
$323$	−6.29921	−0.350497
$324$	3.20284	0.177936
$325$	−4.31575	−0.239395
$326$	13.0605	0.723352
$327$	−51.5287	−2.84954
$328$	−22.6720	−1.25185
$329$	0	0
$330$	−4.26129	−0.234576
$331$	−8.88565	−0.488400	−0.244200	−	0.969725i	$-0.578525\pi$
$331$	−8.88565	−0.488400	−0.244200	+	0.969725i	$0.578525\pi$
$332$	−1.86111	−0.102142
$333$	−9.95369	−0.545459
$334$	19.3299	1.05768
$335$	10.1027	0.551971
$336$	0	0
$337$	4.27124	0.232669	0.116335	−	0.993210i	$-0.462886\pi$
$337$	4.27124	0.232669	0.116335	+	0.993210i	$0.462886\pi$
$338$	−6.85602	−0.372918
$339$	8.65623	0.470142
$340$	−3.24267	−0.175858
$341$	4.69413	0.254201
$342$	−4.56080	−0.246620
$343$	0	0
$344$	−13.5092	−0.728370
$345$	23.3609	1.25771
$346$	−1.78242	−0.0958233
$347$	−33.7353	−1.81101	−0.905504	−	0.424339i	$-0.860507\pi$
$347$	−33.7353	−1.81101	−0.905504	+	0.424339i	$0.860507\pi$
$348$	8.26733	0.443176
$349$	35.8204	1.91742	0.958710	−	0.284386i	$-0.0917898\pi$
$349$	35.8204	1.91742	0.958710	+	0.284386i	$0.0917898\pi$
$350$	0	0
$351$	8.31904	0.444038
$352$	−3.81406	−0.203290
$353$	4.81697	0.256382	0.128191	−	0.991750i	$-0.459083\pi$
$353$	4.81697	0.256382	0.128191	+	0.991750i	$0.459083\pi$
$354$	−1.39147	−0.0739557
$355$	−7.65157	−0.406103
$356$	1.26541	0.0670668
$357$	0	0
$358$	−11.6074	−0.613468
$359$	31.0854	1.64062	0.820312	−	0.571917i	$-0.193800\pi$
$359$	31.0854	1.64062	0.820312	+	0.571917i	$0.193800\pi$
$360$	−11.4694	−0.604490
$361$	1.00000	0.0526316
$362$	29.2383	1.53673
$363$	23.8541	1.25202
$364$	0	0
$365$	11.0854	0.580237
$366$	36.2959	1.89721
$367$	4.65599	0.243041	0.121520	−	0.992589i	$-0.461223\pi$
$367$	4.65599	0.243041	0.121520	+	0.992589i	$0.461223\pi$
$368$	−24.3403	−1.26883
$369$	−27.6847	−1.44121
$370$	−3.24142	−0.168514
$371$	0	0
$372$	4.65949	0.241583
$373$	−3.63513	−0.188220	−0.0941099	−	0.995562i	$-0.530001\pi$
$373$	−3.63513	−0.188220	−0.0941099	+	0.995562i	$0.530001\pi$
$374$	10.3376	0.534546
$375$	2.59660	0.134088
$376$	27.9158	1.43965
$377$	−26.6931	−1.37477
$378$	0	0
$379$	−13.9090	−0.714458	−0.357229	−	0.934017i	$-0.616279\pi$
$379$	−13.9090	−0.714458	−0.357229	+	0.934017i	$0.616279\pi$
$380$	0.514774	0.0264073
$381$	4.42796	0.226851
$382$	−10.2844	−0.526196
$383$	14.0305	0.716927	0.358464	−	0.933544i	$-0.383301\pi$
$383$	14.0305	0.716927	0.358464	+	0.933544i	$0.383301\pi$
$384$	13.3368	0.680592
$385$	0	0
$386$	−29.8100	−1.51729
$387$	−16.4961	−0.838543
$388$	−3.76362	−0.191069
$389$	36.4415	1.84766	0.923829	−	0.382806i	$-0.125042\pi$
$389$	36.4415	1.84766	0.923829	+	0.382806i	$0.125042\pi$
$390$	13.6571	0.691554
$391$	−56.6723	−2.86604
$392$	0	0
$393$	30.4523	1.53612
$394$	27.5106	1.38597
$395$	17.5813	0.884611
$396$	−2.59418	−0.130362
$397$	31.2870	1.57025	0.785125	−	0.619337i	$-0.212599\pi$
$397$	31.2870	1.57025	0.785125	+	0.619337i	$0.212599\pi$
$398$	−10.0649	−0.504508
$399$	0	0
$400$	−2.70546	−0.135273
$401$	−26.8571	−1.34118	−0.670589	−	0.741829i	$-0.733959\pi$
$401$	−26.8571	−1.34118	−0.670589	+	0.741829i	$0.733959\pi$
$402$	−31.9698	−1.59451
$403$	−15.0443	−0.749411
$404$	4.09551	0.203759
$405$	6.22185	0.309166
$406$	0	0
$407$	−3.58161	−0.177534
$408$	50.1288	2.48174
$409$	−9.94796	−0.491895	−0.245947	−	0.969283i	$-0.579099\pi$
$409$	−9.94796	−0.491895	−0.245947	+	0.969283i	$0.579099\pi$
$410$	−9.01553	−0.445245
$411$	19.2961	0.951807
$412$	0.245088	0.0120746
$413$	0	0
$414$	−41.0323	−2.01663
$415$	−3.61540	−0.177473
$416$	12.2238	0.599319
$417$	−15.7254	−0.770075
$418$	−1.64110	−0.0802688
$419$	−13.6597	−0.667319	−0.333659	−	0.942694i	$-0.608284\pi$
$419$	−13.6597	−0.667319	−0.333659	+	0.942694i	$0.608284\pi$
$420$	0	0
$421$	−10.0275	−0.488711	−0.244356	−	0.969686i	$-0.578576\pi$
$421$	−10.0275	−0.488711	−0.244356	+	0.969686i	$0.578576\pi$
$422$	−9.89583	−0.481721
$423$	34.0879	1.65741
$424$	−12.4569	−0.604958
$425$	−6.29921	−0.305556
$426$	24.2132	1.17314
$427$	0	0
$428$	2.67366	0.129236
$429$	15.0904	0.728571
$430$	−5.37195	−0.259059
$431$	−20.7275	−0.998410	−0.499205	−	0.866484i	$-0.666375\pi$
$431$	−20.7275	−0.998410	−0.499205	+	0.866484i	$0.666375\pi$
$432$	5.21505	0.250909
$433$	25.2058	1.21131	0.605657	−	0.795726i	$-0.292910\pi$
$433$	25.2058	1.21131	0.605657	+	0.795726i	$0.292910\pi$
$434$	0	0
$435$	16.0601	0.770025
$436$	−10.2155	−0.489233
$437$	8.99673	0.430372
$438$	−35.0795	−1.67617
$439$	0.410047	0.0195705	0.00978525	−	0.999952i	$-0.496885\pi$
$439$	0.410047	0.0195705	0.00978525	+	0.999952i	$0.496885\pi$
$440$	−4.12699	−0.196747
$441$	0	0
$442$	−33.1313	−1.57590
$443$	−15.5041	−0.736622	−0.368311	−	0.929703i	$-0.620064\pi$
$443$	−15.5041	−0.736622	−0.368311	+	0.929703i	$0.620064\pi$
$444$	−3.55518	−0.168721
$445$	2.45819	0.116530
$446$	−27.6400	−1.30879
$447$	10.1676	0.480913
$448$	0	0
$449$	13.9261	0.657212	0.328606	−	0.944467i	$-0.393421\pi$
$449$	13.9261	0.657212	0.328606	+	0.944467i	$0.393421\pi$
$450$	−4.56080	−0.214998
$451$	−9.96170	−0.469078
$452$	1.71609	0.0807179
$453$	41.9070	1.96896
$454$	2.22889	0.104607
$455$	0	0
$456$	−7.95795	−0.372665
$457$	32.8812	1.53812	0.769058	−	0.639179i	$-0.220726\pi$
$457$	32.8812	1.53812	0.769058	+	0.639179i	$0.220726\pi$
$458$	0.228464	0.0106754
$459$	12.1424	0.566757
$460$	4.63128	0.215934
$461$	21.2325	0.988896	0.494448	−	0.869207i	$-0.335370\pi$
$461$	21.2325	0.988896	0.494448	+	0.869207i	$0.335370\pi$
$462$	0	0
$463$	−5.41515	−0.251663	−0.125832	−	0.992052i	$-0.540160\pi$
$463$	−5.41515	−0.251663	−0.125832	+	0.992052i	$0.540160\pi$
$464$	−16.7334	−0.776830
$465$	9.05153	0.419755
$466$	0.326169	0.0151095
$467$	−26.5030	−1.22641	−0.613206	−	0.789923i	$-0.710120\pi$
$467$	−26.5030	−1.22641	−0.613206	+	0.789923i	$0.710120\pi$
$468$	8.31414	0.384321
$469$	0	0
$470$	11.1007	0.512039
$471$	40.4226	1.86258
$472$	−1.34762	−0.0620291
$473$	−5.93573	−0.272925
$474$	−55.6356	−2.55543
$475$	1.00000	0.0458831
$476$	0	0
$477$	−15.2110	−0.696465
$478$	−23.3581	−1.06838
$479$	14.9268	0.682021	0.341011	−	0.940059i	$-0.389231\pi$
$479$	14.9268	0.682021	0.341011	+	0.940059i	$0.389231\pi$
$480$	−7.35452	−0.335686
$481$	11.4788	0.523387
$482$	−6.61484	−0.301298
$483$	0	0
$484$	4.72905	0.214957
$485$	−7.31121	−0.331985
$486$	−26.7364	−1.21279
$487$	11.1025	0.503101	0.251550	−	0.967844i	$-0.419060\pi$
$487$	11.1025	0.503101	0.251550	+	0.967844i	$0.419060\pi$
$488$	35.1520	1.59126
$489$	27.8271	1.25838
$490$	0	0
$491$	−20.3610	−0.918880	−0.459440	−	0.888209i	$-0.651950\pi$
$491$	−20.3610	−0.918880	−0.459440	+	0.888209i	$0.651950\pi$
$492$	−9.88819	−0.445794
$493$	−38.9609	−1.75471
$494$	5.25960	0.236640
$495$	−5.03946	−0.226507
$496$	−9.43099	−0.423464
$497$	0	0
$498$	11.4409	0.512677
$499$	−19.3442	−0.865967	−0.432984	−	0.901402i	$-0.642539\pi$
$499$	−19.3442	−0.865967	−0.432984	+	0.901402i	$0.642539\pi$
$500$	0.514774	0.0230214
$501$	41.1850	1.84001
$502$	−16.5604	−0.739125
$503$	−25.7994	−1.15034	−0.575170	−	0.818034i	$-0.695064\pi$
$503$	−25.7994	−1.15034	−0.575170	+	0.818034i	$0.695064\pi$
$504$	0	0
$505$	7.95595	0.354035
$506$	−14.7645	−0.656363
$507$	−14.6077	−0.648750
$508$	0.877837	0.0389477
$509$	−19.0053	−0.842396	−0.421198	−	0.906969i	$-0.638390\pi$
$509$	−19.0053	−0.842396	−0.421198	+	0.906969i	$0.638390\pi$
$510$	19.9337	0.882679
$511$	0	0
$512$	24.2460	1.07153
$513$	−1.92760	−0.0851057
$514$	18.6314	0.821798
$515$	0.476109	0.0209799
$516$	−5.89193	−0.259378
$517$	12.2658	0.539447
$518$	0	0
$519$	−3.79768	−0.166700
$520$	13.2267	0.580029
$521$	−27.7992	−1.21791	−0.608953	−	0.793206i	$-0.708410\pi$
$521$	−27.7992	−1.21791	−0.608953	+	0.793206i	$0.708410\pi$
$522$	−28.2088	−1.23467
$523$	2.83110	0.123796	0.0618978	−	0.998082i	$-0.480285\pi$
$523$	2.83110	0.123796	0.0618978	+	0.998082i	$0.480285\pi$
$524$	6.03713	0.263733
$525$	0	0
$526$	−17.5884	−0.766889
$527$	−21.9585	−0.956526
$528$	9.45988	0.411689
$529$	57.9411	2.51918
$530$	−4.95347	−0.215165
$531$	−1.64557	−0.0714116
$532$	0	0
$533$	31.9265	1.38289
$534$	−7.77890	−0.336626
$535$	5.19385	0.224550
$536$	−30.9623	−1.33737
$537$	−24.7311	−1.06722
$538$	−10.6035	−0.457149
$539$	0	0
$540$	−0.992278	−0.0427009
$541$	14.5758	0.626663	0.313331	−	0.949644i	$-0.398555\pi$
$541$	14.5758	0.626663	0.313331	+	0.949644i	$0.398555\pi$
$542$	−27.0008	−1.15978
$543$	62.2963	2.67339
$544$	17.8416	0.764953
$545$	−19.8446	−0.850051
$546$	0	0
$547$	−1.26617	−0.0541377	−0.0270688	−	0.999634i	$-0.508617\pi$
$547$	−1.26617	−0.0541377	−0.0270688	+	0.999634i	$0.508617\pi$
$548$	3.82543	0.163414
$549$	42.9240	1.83195
$550$	−1.64110	−0.0699767
$551$	6.18505	0.263492
$552$	−71.5955	−3.04731
$553$	0	0
$554$	−27.5577	−1.17081
$555$	−6.90630	−0.293156
$556$	−3.11753	−0.132213
$557$	−28.0971	−1.19051	−0.595255	−	0.803537i	$-0.702949\pi$
$557$	−28.0971	−1.19051	−0.595255	+	0.803537i	$0.702949\pi$
$558$	−15.8985	−0.673039
$559$	19.0236	0.804611
$560$	0	0
$561$	22.0257	0.929927
$562$	−37.3162	−1.57409
$563$	21.3119	0.898191	0.449096	−	0.893484i	$-0.351746\pi$
$563$	21.3119	0.898191	0.449096	+	0.893484i	$0.351746\pi$
$564$	12.1752	0.512670
$565$	3.33367	0.140249
$566$	−17.5033	−0.735720
$567$	0	0
$568$	23.4502	0.983947
$569$	−31.8597	−1.33563	−0.667815	−	0.744327i	$-0.732770\pi$
$569$	−31.8597	−1.33563	−0.667815	+	0.744327i	$0.732770\pi$
$570$	−3.16448	−0.132545
$571$	22.6689	0.948666	0.474333	−	0.880346i	$-0.342689\pi$
$571$	22.6689	0.948666	0.474333	+	0.880346i	$0.342689\pi$
$572$	2.99165	0.125087
$573$	−21.9123	−0.915401
$574$	0	0
$575$	8.99673	0.375189
$576$	33.1674	1.38198
$577$	23.6964	0.986492	0.493246	−	0.869890i	$-0.335810\pi$
$577$	23.6964	0.986492	0.493246	+	0.869890i	$0.335810\pi$
$578$	−27.6401	−1.14968
$579$	−63.5143	−2.63956
$580$	3.18390	0.132204
$581$	0	0
$582$	23.1362	0.959025
$583$	−5.47333	−0.226682
$584$	−33.9740	−1.40586
$585$	16.1511	0.667764
$586$	−17.1094	−0.706783
$587$	−2.44246	−0.100811	−0.0504055	−	0.998729i	$-0.516051\pi$
$587$	−2.44246	−0.100811	−0.0504055	+	0.998729i	$0.516051\pi$
$588$	0	0
$589$	3.48591	0.143634
$590$	−0.535880	−0.0220618
$591$	58.6152	2.41111
$592$	7.19583	0.295747
$593$	−8.05391	−0.330734	−0.165367	−	0.986232i	$-0.552881\pi$
$593$	−8.05391	−0.330734	−0.165367	+	0.986232i	$0.552881\pi$
$594$	3.16339	0.129795
$595$	0	0
$596$	2.01572	0.0825672
$597$	−21.4446	−0.877671
$598$	47.3192	1.93502
$599$	−14.0509	−0.574106	−0.287053	−	0.957915i	$-0.592676\pi$
$599$	−14.0509	−0.574106	−0.287053	+	0.957915i	$0.592676\pi$
$600$	−7.95795	−0.324882
$601$	12.3953	0.505615	0.252807	−	0.967517i	$-0.418646\pi$
$601$	12.3953	0.505615	0.252807	+	0.967517i	$0.418646\pi$
$602$	0	0
$603$	−37.8080	−1.53966
$604$	8.30801	0.338048
$605$	9.18667	0.373491
$606$	−25.1764	−1.02272
$607$	−9.54948	−0.387602	−0.193801	−	0.981041i	$-0.562082\pi$
$607$	−9.54948	−0.387602	−0.193801	+	0.981041i	$0.562082\pi$
$608$	−2.83236	−0.114867
$609$	0	0
$610$	13.9782	0.565961
$611$	−39.3108	−1.59034
$612$	12.1352	0.490537
$613$	10.0870	0.407409	0.203705	−	0.979032i	$-0.434702\pi$
$613$	10.0870	0.407409	0.203705	+	0.979032i	$0.434702\pi$
$614$	37.4827	1.51268
$615$	−19.2088	−0.774574
$616$	0	0
$617$	44.2405	1.78106	0.890529	−	0.454927i	$-0.150335\pi$
$617$	44.2405	1.78106	0.890529	+	0.454927i	$0.150335\pi$
$618$	−1.50664	−0.0606058
$619$	−28.3095	−1.13786	−0.568928	−	0.822388i	$-0.692642\pi$
$619$	−28.3095	−1.13786	−0.568928	+	0.822388i	$0.692642\pi$
$620$	1.79445	0.0720670
$621$	−17.3421	−0.695915
$622$	−20.1273	−0.807029
$623$	0	0
$624$	−30.3182	−1.21370
$625$	1.00000	0.0400000
$626$	13.4530	0.537689
$627$	−3.49659	−0.139640
$628$	8.01374	0.319783
$629$	16.7543	0.668036
$630$	0	0
$631$	20.8647	0.830610	0.415305	−	0.909682i	$-0.363675\pi$
$631$	20.8647	0.830610	0.415305	+	0.909682i	$0.363675\pi$
$632$	−53.8823	−2.14332
$633$	−21.0844	−0.838031
$634$	28.7272	1.14090
$635$	1.70529	0.0676723
$636$	−5.43294	−0.215430
$637$	0	0
$638$	−10.1503	−0.401854
$639$	28.6349	1.13278
$640$	5.13626	0.203028
$641$	−4.61134	−0.182137	−0.0910686	−	0.995845i	$-0.529028\pi$
$641$	−4.61134	−0.182137	−0.0910686	+	0.995845i	$0.529028\pi$
$642$	−16.4358	−0.648670
$643$	9.85158	0.388508	0.194254	−	0.980951i	$-0.437771\pi$
$643$	9.85158	0.388508	0.194254	+	0.980951i	$0.437771\pi$
$644$	0	0
$645$	−11.4457	−0.450673
$646$	7.67684	0.302041
$647$	−12.3295	−0.484723	−0.242362	−	0.970186i	$-0.577922\pi$
$647$	−12.3295	−0.484723	−0.242362	+	0.970186i	$0.577922\pi$
$648$	−19.0684	−0.749078
$649$	−0.592120	−0.0232427
$650$	5.25960	0.206298
$651$	0	0
$652$	5.51668	0.216050
$653$	24.9967	0.978197	0.489098	−	0.872229i	$-0.337326\pi$
$653$	24.9967	0.978197	0.489098	+	0.872229i	$0.337326\pi$
$654$	62.7979	2.45559
$655$	11.7277	0.458241
$656$	20.0141	0.781420
$657$	−41.4855	−1.61851
$658$	0	0
$659$	−10.3506	−0.403201	−0.201600	−	0.979468i	$-0.564614\pi$
$659$	−10.3506	−0.403201	−0.201600	+	0.979468i	$0.564614\pi$
$660$	−1.79995	−0.0700630
$661$	12.2629	0.476973	0.238486	−	0.971146i	$-0.423349\pi$
$661$	12.2629	0.476973	0.238486	+	0.971146i	$0.423349\pi$
$662$	10.8289	0.420878
$663$	−70.5908	−2.74152
$664$	11.0803	0.429999
$665$	0	0
$666$	12.1306	0.470049
$667$	55.6452	2.15459
$668$	8.16487	0.315908
$669$	−58.8909	−2.27685
$670$	−12.3122	−0.475661
$671$	15.4452	0.596255
$672$	0	0
$673$	18.7370	0.722258	0.361129	−	0.932516i	$-0.382391\pi$
$673$	18.7370	0.722258	0.361129	+	0.932516i	$0.382391\pi$
$674$	−5.20535	−0.200503
$675$	−1.92760	−0.0741934
$676$	−2.89596	−0.111383
$677$	−38.3777	−1.47498	−0.737488	−	0.675360i	$-0.763988\pi$
$677$	−38.3777	−1.47498	−0.737488	+	0.675360i	$0.763988\pi$
$678$	−10.5493	−0.405145
$679$	0	0
$680$	19.3055	0.740332
$681$	4.74895	0.181980
$682$	−5.72073	−0.219058
$683$	−7.86791	−0.301057	−0.150529	−	0.988606i	$-0.548098\pi$
$683$	−7.86791	−0.301057	−0.150529	+	0.988606i	$0.548098\pi$
$684$	−1.92647	−0.0736602
$685$	7.43129	0.283935
$686$	0	0
$687$	0.486775	0.0185716
$688$	11.9255	0.454656
$689$	17.5416	0.668282
$690$	−28.4700	−1.08383
$691$	−41.4312	−1.57612	−0.788059	−	0.615600i	$-0.788914\pi$
$691$	−41.4312	−1.57612	−0.788059	+	0.615600i	$0.788914\pi$
$692$	−0.752886	−0.0286204
$693$	0	0
$694$	41.1132	1.56064
$695$	−6.05613	−0.229722
$696$	−49.2203	−1.86569
$697$	46.5995	1.76508
$698$	−43.6542	−1.65234
$699$	0.694948	0.0262853
$700$	0	0
$701$	18.4630	0.697337	0.348668	−	0.937246i	$-0.386634\pi$
$701$	18.4630	0.697337	0.348668	+	0.937246i	$0.386634\pi$
$702$	−10.1384	−0.382650
$703$	−2.65974	−0.100314
$704$	11.9345	0.449800
$705$	23.6516	0.890772
$706$	−5.87044	−0.220937
$707$	0	0
$708$	−0.587750	−0.0220890
$709$	−9.71093	−0.364701	−0.182351	−	0.983234i	$-0.558371\pi$
$709$	−9.71093	−0.364701	−0.182351	+	0.983234i	$0.558371\pi$
$710$	9.32496	0.349960
$711$	−65.7954	−2.46752
$712$	−7.53375	−0.282339
$713$	31.3618	1.17451
$714$	0	0
$715$	5.81159	0.217341
$716$	−4.90290	−0.183230
$717$	−49.7677	−1.85861
$718$	−37.8837	−1.41381
$719$	3.88966	0.145060	0.0725299	−	0.997366i	$-0.476893\pi$
$719$	3.88966	0.145060	0.0725299	+	0.997366i	$0.476893\pi$
$720$	10.1248	0.377329
$721$	0	0
$722$	−1.21870	−0.0453553
$723$	−14.0938	−0.524155
$724$	12.3502	0.458990
$725$	6.18505	0.229707
$726$	−29.0710	−1.07893
$727$	43.9305	1.62929	0.814646	−	0.579958i	$-0.196931\pi$
$727$	43.9305	1.62929	0.814646	+	0.579958i	$0.196931\pi$
$728$	0	0
$729$	−38.3000	−1.41852
$730$	−13.5098	−0.500019
$731$	27.7665	1.02698
$732$	15.3312	0.566658
$733$	30.0305	1.10920	0.554601	−	0.832116i	$-0.312871\pi$
$733$	30.0305	1.10920	0.554601	+	0.832116i	$0.312871\pi$
$734$	−5.67425	−0.209441
$735$	0	0
$736$	−25.4820	−0.939278
$737$	−13.6043	−0.501122
$738$	33.7393	1.24196
$739$	−26.1955	−0.963617	−0.481808	−	0.876277i	$-0.660020\pi$
$739$	−26.1955	−0.963617	−0.481808	+	0.876277i	$0.660020\pi$
$740$	−1.36916	−0.0503315
$741$	11.2063	0.411673
$742$	0	0
$743$	−7.24377	−0.265748	−0.132874	−	0.991133i	$-0.542421\pi$
$743$	−7.24377	−0.265748	−0.132874	+	0.991133i	$0.542421\pi$
$744$	−27.7407	−1.01702
$745$	3.91575	0.143462
$746$	4.43013	0.162198
$747$	13.5301	0.495041
$748$	4.36657	0.159658
$749$	0	0
$750$	−3.16448	−0.115550
$751$	33.7313	1.23087	0.615436	−	0.788187i	$-0.288980\pi$
$751$	33.7313	1.23087	0.615436	+	0.788187i	$0.288980\pi$
$752$	−24.6432	−0.898644
$753$	−35.2841	−1.28582
$754$	32.5309	1.18471
$755$	16.1392	0.587364
$756$	0	0
$757$	40.4892	1.47160	0.735802	−	0.677196i	$-0.236805\pi$
$757$	40.4892	1.47160	0.735802	+	0.677196i	$0.236805\pi$
$758$	16.9509	0.615685
$759$	−31.4579	−1.14185
$760$	−3.06475	−0.111170
$761$	12.1473	0.440341	0.220170	−	0.975461i	$-0.429339\pi$
$761$	12.1473	0.440341	0.220170	+	0.975461i	$0.429339\pi$
$762$	−5.39635	−0.195489
$763$	0	0
$764$	−4.34409	−0.157164
$765$	23.5739	0.852315
$766$	−17.0990	−0.617812
$767$	1.89770	0.0685219
$768$	29.7724	1.07432
$769$	26.4500	0.953811	0.476906	−	0.878954i	$-0.341758\pi$
$769$	26.4500	0.953811	0.476906	+	0.878954i	$0.341758\pi$
$770$	0	0
$771$	39.6969	1.42965
$772$	−12.5916	−0.453183
$773$	−22.4933	−0.809028	−0.404514	−	0.914532i	$-0.632559\pi$
$773$	−22.4933	−0.809028	−0.404514	+	0.914532i	$0.632559\pi$
$774$	20.1037	0.722614
$775$	3.48591	0.125218
$776$	22.4071	0.804366
$777$	0	0
$778$	−44.4112	−1.59222
$779$	−7.39767	−0.265049
$780$	5.76870	0.206553
$781$	10.3036	0.368692
$782$	69.0664	2.46981
$783$	−11.9223	−0.426069
$784$	0	0
$785$	15.5675	0.555628
$786$	−37.1122	−1.32375
$787$	−11.1505	−0.397472	−0.198736	−	0.980053i	$-0.563684\pi$
$787$	−11.1505	−0.397472	−0.198736	+	0.980053i	$0.563684\pi$
$788$	11.6204	0.413959
$789$	−37.4744	−1.33412
$790$	−21.4263	−0.762314
$791$	0	0
$792$	15.4447	0.548803
$793$	−49.5007	−1.75782
$794$	−38.1295	−1.35316
$795$	−10.5540	−0.374313
$796$	−4.25137	−0.150686
$797$	−2.00143	−0.0708944	−0.0354472	−	0.999372i	$-0.511286\pi$
$797$	−2.00143	−0.0708944	−0.0354472	+	0.999372i	$0.511286\pi$
$798$	0	0
$799$	−57.3775	−2.02987
$800$	−2.83236	−0.100139
$801$	−9.19943	−0.325046
$802$	32.7307	1.15576
$803$	−14.9276	−0.526784
$804$	−13.5039	−0.476247
$805$	0	0
$806$	18.3345	0.645805
$807$	−22.5922	−0.795282
$808$	−24.3830	−0.857792
$809$	27.3887	0.962934	0.481467	−	0.876464i	$-0.340104\pi$
$809$	27.3887	0.962934	0.481467	+	0.876464i	$0.340104\pi$
$810$	−7.58255	−0.266424
$811$	−49.9883	−1.75533	−0.877664	−	0.479277i	$-0.840899\pi$
$811$	−49.9883	−1.75533	−0.877664	+	0.479277i	$0.840899\pi$
$812$	0	0
$813$	−57.5289	−2.01763
$814$	4.36490	0.152990
$815$	10.7167	0.375390
$816$	−44.2520	−1.54913
$817$	−4.40794	−0.154214
$818$	12.1236	0.423890
$819$	0	0
$820$	−3.80812	−0.132985
$821$	−33.4012	−1.16571	−0.582855	−	0.812576i	$-0.698064\pi$
$821$	−33.4012	−1.16571	−0.582855	+	0.812576i	$0.698064\pi$
$822$	−23.5161	−0.820220
$823$	4.64616	0.161955	0.0809775	−	0.996716i	$-0.474196\pi$
$823$	4.64616	0.161955	0.0809775	+	0.996716i	$0.474196\pi$
$824$	−1.45916	−0.0508321
$825$	−3.49659	−0.121736
$826$	0	0
$827$	5.64229	0.196201	0.0981007	−	0.995176i	$-0.468723\pi$
$827$	5.64229	0.196201	0.0981007	+	0.995176i	$0.468723\pi$
$828$	−17.3319	−0.602325
$829$	39.9143	1.38628	0.693141	−	0.720802i	$-0.256226\pi$
$829$	39.9143	1.38628	0.693141	+	0.720802i	$0.256226\pi$
$830$	4.40609	0.152937
$831$	−58.7154	−2.03681
$832$	−38.2493	−1.32605
$833$	0	0
$834$	19.1645	0.663612
$835$	15.8611	0.548896
$836$	−0.693194	−0.0239746
$837$	−6.71945	−0.232258
$838$	16.6470	0.575062
$839$	23.4423	0.809317	0.404659	−	0.914468i	$-0.367390\pi$
$839$	23.4423	0.809317	0.404659	+	0.914468i	$0.367390\pi$
$840$	0	0
$841$	9.25488	0.319134
$842$	12.2205	0.421147
$843$	−79.5072	−2.73837
$844$	−4.17996	−0.143880
$845$	−5.62569	−0.193530
$846$	−41.5429	−1.42827
$847$	0	0
$848$	10.9965	0.377621
$849$	−37.2933	−1.27990
$850$	7.67684	0.263313
$851$	−23.9290	−0.820274
$852$	10.2276	0.350391
$853$	−23.1897	−0.793999	−0.396999	−	0.917819i	$-0.629949\pi$
$853$	−23.1897	−0.793999	−0.396999	+	0.917819i	$0.629949\pi$
$854$	0	0
$855$	−3.74235	−0.127986
$856$	−15.9179	−0.544061
$857$	−14.1698	−0.484033	−0.242016	−	0.970272i	$-0.577809\pi$
$857$	−14.1698	−0.484033	−0.242016	+	0.970272i	$0.577809\pi$
$858$	−18.3906	−0.627846
$859$	28.2375	0.963451	0.481726	−	0.876322i	$-0.340010\pi$
$859$	28.2375	0.963451	0.481726	+	0.876322i	$0.340010\pi$
$860$	−2.26909	−0.0773754
$861$	0	0
$862$	25.2606	0.860380
$863$	43.0648	1.46594	0.732972	−	0.680259i	$-0.238133\pi$
$863$	43.0648	1.46594	0.732972	+	0.680259i	$0.238133\pi$
$864$	5.45966	0.185741
$865$	−1.46256	−0.0497284
$866$	−30.7183	−1.04385
$867$	−58.8910	−2.00004
$868$	0	0
$869$	−23.6750	−0.803119
$870$	−19.5725	−0.663569
$871$	43.6008	1.47736
$872$	60.8189	2.05959
$873$	27.3612	0.926035
$874$	−10.9643	−0.370873
$875$	0	0
$876$	−14.8175	−0.500636
$877$	−40.9748	−1.38362	−0.691810	−	0.722080i	$-0.743186\pi$
$877$	−40.9748	−1.38362	−0.691810	+	0.722080i	$0.743186\pi$
$878$	−0.499724	−0.0168649
$879$	−36.4539	−1.22956
$880$	3.64317	0.122811
$881$	8.65739	0.291675	0.145837	−	0.989309i	$-0.453412\pi$
$881$	8.65739	0.291675	0.145837	+	0.989309i	$0.453412\pi$
$882$	0	0
$883$	43.8087	1.47428	0.737140	−	0.675740i	$-0.236176\pi$
$883$	43.8087	1.47428	0.737140	+	0.675740i	$0.236176\pi$
$884$	−13.9945	−0.470687
$885$	−1.14176	−0.0383800
$886$	18.8948	0.634784
$887$	30.6402	1.02880	0.514398	−	0.857552i	$-0.328015\pi$
$887$	30.6402	1.02880	0.514398	+	0.857552i	$0.328015\pi$
$888$	21.1661	0.710287
$889$	0	0
$890$	−2.99580	−0.100419
$891$	−8.37834	−0.280685
$892$	−11.6750	−0.390909
$893$	9.10868	0.304810
$894$	−12.3913	−0.414427
$895$	−9.52438	−0.318365
$896$	0	0
$897$	100.820	3.36628
$898$	−16.9717	−0.566353
$899$	21.5605	0.719084
$900$	−1.92647	−0.0642155
$901$	25.6035	0.852976
$902$	12.1403	0.404228
$903$	0	0
$904$	−10.2169	−0.339808
$905$	23.9915	0.797503
$906$	−51.0720	−1.69675
$907$	−18.7440	−0.622386	−0.311193	−	0.950347i	$-0.600729\pi$
$907$	−18.7440	−0.622386	−0.311193	+	0.950347i	$0.600729\pi$
$908$	0.941473	0.0312439
$909$	−29.7740	−0.987541
$910$	0	0
$911$	41.6954	1.38143	0.690715	−	0.723127i	$-0.257296\pi$
$911$	41.6954	1.38143	0.690715	+	0.723127i	$0.257296\pi$
$912$	7.02501	0.232621
$913$	4.86850	0.161124
$914$	−40.0722	−1.32547
$915$	29.7825	0.984578
$916$	0.0965025	0.00318853
$917$	0	0
$918$	−14.7979	−0.488403
$919$	48.1289	1.58763	0.793813	−	0.608162i	$-0.208093\pi$
$919$	48.1289	1.58763	0.793813	+	0.608162i	$0.208093\pi$
$920$	−27.5727	−0.909046
$921$	79.8620	2.63154
$922$	−25.8760	−0.852181
$923$	−33.0223	−1.08694
$924$	0	0
$925$	−2.65974	−0.0874518
$926$	6.59944	0.216871
$927$	−1.78177	−0.0585210
$928$	−17.5183	−0.575066
$929$	−14.5530	−0.477470	−0.238735	−	0.971085i	$-0.576733\pi$
$929$	−14.5530	−0.477470	−0.238735	+	0.971085i	$0.576733\pi$
$930$	−11.0311	−0.361724
$931$	0	0
$932$	0.137773	0.00451289
$933$	−42.8839	−1.40395
$934$	32.2992	1.05686
$935$	8.48251	0.277408
$936$	−49.4990	−1.61793
$937$	−30.5187	−0.997002	−0.498501	−	0.866889i	$-0.666116\pi$
$937$	−30.5187	−0.997002	−0.498501	+	0.866889i	$0.666116\pi$
$938$	0	0
$939$	28.6634	0.935395
$940$	4.68891	0.152935
$941$	47.1839	1.53815	0.769076	−	0.639157i	$-0.220717\pi$
$941$	47.1839	1.53815	0.769076	+	0.639157i	$0.220717\pi$
$942$	−49.2630	−1.60508
$943$	−66.5548	−2.16732
$944$	1.18963	0.0387192
$945$	0	0
$946$	7.23387	0.235193
$947$	29.9827	0.974308	0.487154	−	0.873316i	$-0.338035\pi$
$947$	29.9827	0.974308	0.487154	+	0.873316i	$0.338035\pi$
$948$	−23.5003	−0.763253
$949$	47.8419	1.55301
$950$	−1.21870	−0.0395398
$951$	61.2072	1.98478
$952$	0	0
$953$	−29.4974	−0.955515	−0.477757	−	0.878492i	$-0.658550\pi$
$953$	−29.4974	−0.955515	−0.477757	+	0.878492i	$0.658550\pi$
$954$	18.5376	0.600178
$955$	−8.43884	−0.273074
$956$	−9.86638	−0.319101
$957$	−21.6266	−0.699088
$958$	−18.1912	−0.587732
$959$	0	0
$960$	23.0130	0.742740
$961$	−18.8484	−0.608014
$962$	−13.9892	−0.451029
$963$	−19.4372	−0.626356
$964$	−2.79408	−0.0899914
$965$	−24.4605	−0.787412
$966$	0	0
$967$	49.4422	1.58996	0.794978	−	0.606639i	$-0.207483\pi$
$967$	49.4422	1.58996	0.794978	+	0.606639i	$0.207483\pi$
$968$	−28.1549	−0.904931
$969$	16.3566	0.525448
$970$	8.91017	0.286088
$971$	21.0324	0.674961	0.337481	−	0.941333i	$-0.390425\pi$
$971$	21.0324	0.674961	0.337481	+	0.941333i	$0.390425\pi$
$972$	−11.2933	−0.362234
$973$	0	0
$974$	−13.5306	−0.433547
$975$	11.2063	0.358889
$976$	−31.0310	−0.993279
$977$	−7.12218	−0.227859	−0.113929	−	0.993489i	$-0.536344\pi$
$977$	−7.12218	−0.227859	−0.113929	+	0.993489i	$0.536344\pi$
$978$	−33.9128	−1.08441
$979$	−3.31020	−0.105795
$980$	0	0
$981$	74.2657	2.37112
$982$	24.8140	0.791845
$983$	35.4689	1.13128	0.565641	−	0.824652i	$-0.308629\pi$
$983$	35.4689	1.13128	0.565641	+	0.824652i	$0.308629\pi$
$984$	58.8703	1.87672
$985$	22.5738	0.719260
$986$	47.4816	1.51212
$987$	0	0
$988$	2.22163	0.0706796
$989$	−39.6570	−1.26102
$990$	6.14158	0.195192
$991$	−35.0928	−1.11476	−0.557380	−	0.830258i	$-0.688193\pi$
$991$	−35.0928	−1.11476	−0.557380	+	0.830258i	$0.688193\pi$
$992$	−9.87335	−0.313479
$993$	23.0725	0.732184
$994$	0	0
$995$	−8.25872	−0.261819
$996$	4.83258	0.153126
$997$	51.0328	1.61622	0.808112	−	0.589029i	$-0.200490\pi$
$997$	51.0328	1.61622	0.808112	+	0.589029i	$0.200490\pi$
$998$	23.5748	0.746247
$999$	5.12692	0.162209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4655.2.a.br.1.8	✓	26
7.6	odd	2		4655.2.a.bs.1.8	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4655.2.a.br.1.8	✓	26	1.1	even	1	trivial
4655.2.a.bs.1.8	yes	26	7.6	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:	\( N \)	\(=\)	\( 4655 = 5 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4655.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21870 q^{2} -2.59660 q^{3} -0.514774 q^{4} -1.00000 q^{5} +3.16448 q^{6} +3.06475 q^{8} +3.74235 q^{9} +1.21870 q^{10} +1.34660 q^{11} +1.33666 q^{12} -4.31575 q^{13} +2.59660 q^{15} -2.70546 q^{16} -6.29921 q^{17} -4.56080 q^{18} +1.00000 q^{19} +0.514774 q^{20} -1.64110 q^{22} +8.99673 q^{23} -7.95795 q^{24} +1.00000 q^{25} +5.25960 q^{26} -1.92760 q^{27} +6.18505 q^{29} -3.16448 q^{30} +3.48591 q^{31} -2.83236 q^{32} -3.49659 q^{33} +7.67684 q^{34} -1.92647 q^{36} -2.65974 q^{37} -1.21870 q^{38} +11.2063 q^{39} -3.06475 q^{40} -7.39767 q^{41} -4.40794 q^{43} -0.693194 q^{44} -3.74235 q^{45} -10.9643 q^{46} +9.10868 q^{47} +7.02501 q^{48} -1.21870 q^{50} +16.3566 q^{51} +2.22163 q^{52} -4.06456 q^{53} +2.34917 q^{54} -1.34660 q^{55} -2.59660 q^{57} -7.53772 q^{58} -0.439715 q^{59} -1.33666 q^{60} +11.4698 q^{61} -4.24827 q^{62} +8.86272 q^{64} +4.31575 q^{65} +4.26129 q^{66} -10.1027 q^{67} +3.24267 q^{68} -23.3609 q^{69} +7.65157 q^{71} +11.4694 q^{72} -11.0854 q^{73} +3.24142 q^{74} -2.59660 q^{75} -0.514774 q^{76} -13.6571 q^{78} -17.5813 q^{79} +2.70546 q^{80} -6.22185 q^{81} +9.01553 q^{82} +3.61540 q^{83} +6.29921 q^{85} +5.37195 q^{86} -16.0601 q^{87} +4.12699 q^{88} -2.45819 q^{89} +4.56080 q^{90} -4.63128 q^{92} -9.05153 q^{93} -11.1007 q^{94} -1.00000 q^{95} +7.35452 q^{96} +7.31121 q^{97} +5.03946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 - 6 * q^3 + 36 * q^4 - 26 * q^5 + 4 * q^6 + 12 * q^8 + 44 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 14 * q^13 + 6 * q^15 + 64 * q^16 - 18 * q^17 + 8 * q^18 + 26 * q^19 - 36 * q^20 + 36 * q^22 + 44 * q^24 + 26 * q^25 + 8 * q^26 - 30 * q^27 + 22 * q^29 - 4 * q^30 + 28 * q^32 - 38 * q^33 + 68 * q^36 + 48 * q^37 + 4 * q^38 + 26 * q^39 - 12 * q^40 - 4 * q^41 + 16 * q^43 + 44 * q^44 - 44 * q^45 + 48 * q^46 - 22 * q^47 - 48 * q^48 + 4 * q^50 + 34 * q^51 - 32 * q^52 + 28 * q^53 + 28 * q^54 - 14 * q^55 - 6 * q^57 + 52 * q^58 + 8 * q^59 + 20 * q^60 + 28 * q^61 + 16 * q^62 + 52 * q^64 + 14 * q^65 + 24 * q^66 + 60 * q^67 - 52 * q^68 + 4 * q^69 + 8 * q^71 + 36 * q^72 + 4 * q^73 + 8 * q^74 - 6 * q^75 + 36 * q^76 - 76 * q^78 + 50 * q^79 - 64 * q^80 + 114 * q^81 + 36 * q^82 - 20 * q^83 + 18 * q^85 + 40 * q^86 - 18 * q^87 + 108 * q^88 + 20 * q^89 - 8 * q^90 - 48 * q^92 + 32 * q^93 + 80 * q^94 - 26 * q^95 + 140 * q^96 - 26 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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