LMFDB - Embedded newform 7935.2.a.bt.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,1,-25,31,-25,-1,15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.587229 q^{2} -1.00000 q^{3} -1.65516 q^{4} -1.00000 q^{5} +0.587229 q^{6} -1.98135 q^{7} +2.14642 q^{8} +1.00000 q^{9} +0.587229 q^{10} +1.32641 q^{11} +1.65516 q^{12} -4.37911 q^{13} +1.16351 q^{14} +1.00000 q^{15} +2.04988 q^{16} +6.01632 q^{17} -0.587229 q^{18} -8.00370 q^{19} +1.65516 q^{20} +1.98135 q^{21} -0.778910 q^{22} -2.14642 q^{24} +1.00000 q^{25} +2.57154 q^{26} -1.00000 q^{27} +3.27946 q^{28} -1.61945 q^{29} -0.587229 q^{30} +1.47039 q^{31} -5.49659 q^{32} -1.32641 q^{33} -3.53296 q^{34} +1.98135 q^{35} -1.65516 q^{36} -0.666505 q^{37} +4.70001 q^{38} +4.37911 q^{39} -2.14642 q^{40} +3.57137 q^{41} -1.16351 q^{42} +8.48841 q^{43} -2.19543 q^{44} -1.00000 q^{45} -9.62613 q^{47} -2.04988 q^{48} -3.07423 q^{49} -0.587229 q^{50} -6.01632 q^{51} +7.24813 q^{52} +2.20910 q^{53} +0.587229 q^{54} -1.32641 q^{55} -4.25282 q^{56} +8.00370 q^{57} +0.950988 q^{58} +7.22150 q^{59} -1.65516 q^{60} -12.7396 q^{61} -0.863454 q^{62} -1.98135 q^{63} -0.872010 q^{64} +4.37911 q^{65} +0.778910 q^{66} -12.0280 q^{67} -9.95799 q^{68} -1.16351 q^{70} +13.4980 q^{71} +2.14642 q^{72} -6.96019 q^{73} +0.391392 q^{74} -1.00000 q^{75} +13.2474 q^{76} -2.62810 q^{77} -2.57154 q^{78} -12.3272 q^{79} -2.04988 q^{80} +1.00000 q^{81} -2.09721 q^{82} +11.5024 q^{83} -3.27946 q^{84} -6.01632 q^{85} -4.98464 q^{86} +1.61945 q^{87} +2.84704 q^{88} +5.21463 q^{89} +0.587229 q^{90} +8.67656 q^{91} -1.47039 q^{93} +5.65275 q^{94} +8.00370 q^{95} +5.49659 q^{96} -5.95363 q^{97} +1.80528 q^{98} +1.32641 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19}+ \cdots - 15 q^{99}+O(q^{100}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9 - q^10 - 15 * q^11 - 31 * q^12 + 24 * q^13 - 5 * q^14 + 25 * q^15 + 39 * q^16 + 6 * q^17 + q^18 - 13 * q^19 - 31 * q^20 - 15 * q^21 + 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 + 41 * q^28 + q^29 + q^30 + 18 * q^31 + 17 * q^32 + 15 * q^33 - 7 * q^34 - 15 * q^35 + 31 * q^36 + 8 * q^37 - 15 * q^38 - 24 * q^39 - 3 * q^40 + 36 * q^41 + 5 * q^42 + 36 * q^43 - 90 * q^44 - 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 - 6 * q^51 + 35 * q^52 - 6 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 13 * q^57 + 42 * q^58 - 3 * q^59 + 31 * q^60 - 71 * q^61 - 7 * q^62 + 15 * q^63 + 47 * q^64 - 24 * q^65 - 21 * q^66 + 10 * q^67 + 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 - 67 * q^74 - 25 * q^75 + 12 * q^76 + 27 * q^77 - 21 * q^78 - 33 * q^79 - 39 * q^80 + 25 * q^81 + 49 * q^82 + 2 * q^83 - 41 * q^84 - 6 * q^85 + 35 * q^86 - q^87 + 33 * q^88 - 11 * q^89 - q^90 - 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 + 48 * q^97 + 4 * q^98 - 15 * 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 $

$2$	−0.587229	−0.415234	−0.207617	−	0.978210i	$-0.566571\pi$
$2$	−0.587229	−0.415234	−0.207617	+	0.978210i	$0.566571\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.65516	−0.827581
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.587229	0.239735
$7$	−1.98135	−0.748882	−0.374441	−	0.927251i	$-0.622165\pi$
$7$	−1.98135	−0.748882	−0.374441	+	0.927251i	$0.622165\pi$
$8$	2.14642	0.758873
$9$	1.00000	0.333333
$10$	0.587229	0.185698
$11$	1.32641	0.399929	0.199965	−	0.979803i	$-0.435917\pi$
$11$	1.32641	0.399929	0.199965	+	0.979803i	$0.435917\pi$
$12$	1.65516	0.477804
$13$	−4.37911	−1.21455	−0.607273	−	0.794493i	$-0.707737\pi$
$13$	−4.37911	−1.21455	−0.607273	+	0.794493i	$0.707737\pi$
$14$	1.16351	0.310961
$15$	1.00000	0.258199
$16$	2.04988	0.512471
$17$	6.01632	1.45917	0.729586	−	0.683889i	$-0.239713\pi$
$17$	6.01632	1.45917	0.729586	+	0.683889i	$0.239713\pi$
$18$	−0.587229	−0.138411
$19$	−8.00370	−1.83617	−0.918087	−	0.396379i	$-0.870267\pi$
$19$	−8.00370	−1.83617	−0.918087	+	0.396379i	$0.870267\pi$
$20$	1.65516	0.370105
$21$	1.98135	0.432367
$22$	−0.778910	−0.166064
$23$	0	0
$23$	0	0
$24$	−2.14642	−0.438136
$25$	1.00000	0.200000
$26$	2.57154	0.504321
$27$	−1.00000	−0.192450
$28$	3.27946	0.619760
$29$	−1.61945	−0.300724	−0.150362	−	0.988631i	$-0.548044\pi$
$29$	−1.61945	−0.300724	−0.150362	+	0.988631i	$0.548044\pi$
$30$	−0.587229	−0.107213
$31$	1.47039	0.264089	0.132045	−	0.991244i	$-0.457846\pi$
$31$	1.47039	0.264089	0.132045	+	0.991244i	$0.457846\pi$
$32$	−5.49659	−0.971669
$33$	−1.32641	−0.230899
$34$	−3.53296	−0.605898
$35$	1.98135	0.334910
$36$	−1.65516	−0.275860
$37$	−0.666505	−0.109573	−0.0547864	−	0.998498i	$-0.517448\pi$
$37$	−0.666505	−0.109573	−0.0547864	+	0.998498i	$0.517448\pi$
$38$	4.70001	0.762442
$39$	4.37911	0.701218
$40$	−2.14642	−0.339378
$41$	3.57137	0.557754	0.278877	−	0.960327i	$-0.410038\pi$
$41$	3.57137	0.557754	0.278877	+	0.960327i	$0.410038\pi$
$42$	−1.16351	−0.179533
$43$	8.48841	1.29447	0.647235	−	0.762290i	$-0.275925\pi$
$43$	8.48841	1.29447	0.647235	+	0.762290i	$0.275925\pi$
$44$	−2.19543	−0.330974
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−9.62613	−1.40412	−0.702058	−	0.712120i	$-0.747735\pi$
$47$	−9.62613	−1.40412	−0.702058	+	0.712120i	$0.747735\pi$
$48$	−2.04988	−0.295875
$49$	−3.07423	−0.439176
$50$	−0.587229	−0.0830468
$51$	−6.01632	−0.842454
$52$	7.24813	1.00513
$53$	2.20910	0.303443	0.151722	−	0.988423i	$-0.451518\pi$
$53$	2.20910	0.303443	0.151722	+	0.988423i	$0.451518\pi$
$54$	0.587229	0.0799118
$55$	−1.32641	−0.178854
$56$	−4.25282	−0.568306
$57$	8.00370	1.06012
$58$	0.950988	0.124871
$59$	7.22150	0.940160	0.470080	−	0.882624i	$-0.344225\pi$
$59$	7.22150	0.940160	0.470080	+	0.882624i	$0.344225\pi$
$60$	−1.65516	−0.213680
$61$	−12.7396	−1.63114	−0.815568	−	0.578661i	$-0.803575\pi$
$61$	−12.7396	−1.63114	−0.815568	+	0.578661i	$0.803575\pi$
$62$	−0.863454	−0.109659
$63$	−1.98135	−0.249627
$64$	−0.872010	−0.109001
$65$	4.37911	0.543161
$66$	0.778910	0.0958771
$67$	−12.0280	−1.46945	−0.734727	−	0.678363i	$-0.762690\pi$
$67$	−12.0280	−1.46945	−0.734727	+	0.678363i	$0.762690\pi$
$68$	−9.95799	−1.20758
$69$	0	0
$70$	−1.16351	−0.139066
$71$	13.4980	1.60192	0.800958	−	0.598721i	$-0.204324\pi$
$71$	13.4980	1.60192	0.800958	+	0.598721i	$0.204324\pi$
$72$	2.14642	0.252958
$73$	−6.96019	−0.814629	−0.407315	−	0.913288i	$-0.633535\pi$
$73$	−6.96019	−0.814629	−0.407315	+	0.913288i	$0.633535\pi$
$74$	0.391392	0.0454983
$75$	−1.00000	−0.115470
$76$	13.2474	1.51958
$77$	−2.62810	−0.299500
$78$	−2.57154	−0.291170
$79$	−12.3272	−1.38692	−0.693458	−	0.720497i	$-0.743914\pi$
$79$	−12.3272	−1.38692	−0.693458	+	0.720497i	$0.743914\pi$
$80$	−2.04988	−0.229184
$81$	1.00000	0.111111
$82$	−2.09721	−0.231598
$83$	11.5024	1.26256	0.631278	−	0.775556i	$-0.282531\pi$
$83$	11.5024	1.26256	0.631278	+	0.775556i	$0.282531\pi$
$84$	−3.27946	−0.357819
$85$	−6.01632	−0.652562
$86$	−4.98464	−0.537508
$87$	1.61945	0.173623
$88$	2.84704	0.303496
$89$	5.21463	0.552749	0.276375	−	0.961050i	$-0.410867\pi$
$89$	5.21463	0.552749	0.276375	+	0.961050i	$0.410867\pi$
$90$	0.587229	0.0618994
$91$	8.67656	0.909551
$92$	0	0
$93$	−1.47039	−0.152472
$94$	5.65275	0.583036
$95$	8.00370	0.821162
$96$	5.49659	0.560993
$97$	−5.95363	−0.604500	−0.302250	−	0.953229i	$-0.597738\pi$
$97$	−5.95363	−0.604500	−0.302250	+	0.953229i	$0.597738\pi$
$98$	1.80528	0.182361
$99$	1.32641	0.133310
$100$	−1.65516	−0.165516
$101$	−14.4844	−1.44126	−0.720628	−	0.693322i	$-0.756147\pi$
$101$	−14.4844	−1.44126	−0.720628	+	0.693322i	$0.756147\pi$
$102$	3.53296	0.349815
$103$	−18.3810	−1.81113	−0.905565	−	0.424207i	$-0.860553\pi$
$103$	−18.3810	−1.81113	−0.905565	+	0.424207i	$0.860553\pi$
$104$	−9.39939	−0.921687
$105$	−1.98135	−0.193360
$106$	−1.29725	−0.126000
$107$	−4.48711	−0.433785	−0.216893	−	0.976195i	$-0.569592\pi$
$107$	−4.48711	−0.433785	−0.216893	+	0.976195i	$0.569592\pi$
$108$	1.65516	0.159268
$109$	0.977068	0.0935861	0.0467931	−	0.998905i	$-0.485100\pi$
$109$	0.977068	0.0935861	0.0467931	+	0.998905i	$0.485100\pi$
$110$	0.778910	0.0742661
$111$	0.666505	0.0632619
$112$	−4.06155	−0.383780
$113$	6.08822	0.572732	0.286366	−	0.958120i	$-0.407553\pi$
$113$	6.08822	0.572732	0.286366	+	0.958120i	$0.407553\pi$
$114$	−4.70001	−0.440196
$115$	0	0
$116$	2.68045	0.248874
$117$	−4.37911	−0.404849
$118$	−4.24068	−0.390386
$119$	−11.9205	−1.09275
$120$	2.14642	0.195940
$121$	−9.24062	−0.840057
$122$	7.48106	0.677303
$123$	−3.57137	−0.322019
$124$	−2.43373	−0.218555
$125$	−1.00000	−0.0894427
$126$	1.16351	0.103654
$127$	−5.17999	−0.459650	−0.229825	−	0.973232i	$-0.573815\pi$
$127$	−5.17999	−0.459650	−0.229825	+	0.973232i	$0.573815\pi$
$128$	11.5052	1.01693
$129$	−8.48841	−0.747363
$130$	−2.57154	−0.225539
$131$	6.34097	0.554013	0.277007	−	0.960868i	$-0.410658\pi$
$131$	6.34097	0.554013	0.277007	+	0.960868i	$0.410658\pi$
$132$	2.19543	0.191088
$133$	15.8582	1.37508
$134$	7.06319	0.610167
$135$	1.00000	0.0860663
$136$	12.9135	1.10733
$137$	6.38278	0.545317	0.272659	−	0.962111i	$-0.412097\pi$
$137$	6.38278	0.545317	0.272659	+	0.962111i	$0.412097\pi$
$138$	0	0
$139$	−7.86494	−0.667096	−0.333548	−	0.942733i	$-0.608246\pi$
$139$	−7.86494	−0.667096	−0.333548	+	0.942733i	$0.608246\pi$
$140$	−3.27946	−0.277165
$141$	9.62613	0.810666
$142$	−7.92641	−0.665169
$143$	−5.80851	−0.485732
$144$	2.04988	0.170824
$145$	1.61945	0.134488
$146$	4.08723	0.338262
$147$	3.07423	0.253559
$148$	1.10317	0.0906804
$149$	−13.8792	−1.13703	−0.568513	−	0.822674i	$-0.692481\pi$
$149$	−13.8792	−1.13703	−0.568513	+	0.822674i	$0.692481\pi$
$150$	0.587229	0.0479471
$151$	0.653845	0.0532092	0.0266046	−	0.999646i	$-0.491530\pi$
$151$	0.653845	0.0532092	0.0266046	+	0.999646i	$0.491530\pi$
$152$	−17.1793	−1.39342
$153$	6.01632	0.486391
$154$	1.54330	0.124362
$155$	−1.47039	−0.118104
$156$	−7.24813	−0.580315
$157$	−2.87719	−0.229624	−0.114812	−	0.993387i	$-0.536627\pi$
$157$	−2.87719	−0.229624	−0.114812	+	0.993387i	$0.536627\pi$
$158$	7.23888	0.575895
$159$	−2.20910	−0.175193
$160$	5.49659	0.434543
$161$	0	0
$162$	−0.587229	−0.0461371
$163$	−12.8468	−1.00624	−0.503118	−	0.864218i	$-0.667814\pi$
$163$	−12.8468	−1.00624	−0.503118	+	0.864218i	$0.667814\pi$
$164$	−5.91119	−0.461586
$165$	1.32641	0.103261
$166$	−6.75457	−0.524256
$167$	11.9470	0.924489	0.462244	−	0.886753i	$-0.347044\pi$
$167$	11.9470	0.924489	0.462244	+	0.886753i	$0.347044\pi$
$168$	4.25282	0.328112
$169$	6.17658	0.475122
$170$	3.53296	0.270966
$171$	−8.00370	−0.612058
$172$	−14.0497	−1.07128
$173$	17.8127	1.35428	0.677138	−	0.735856i	$-0.263220\pi$
$173$	17.8127	1.35428	0.677138	+	0.735856i	$0.263220\pi$
$174$	−0.950988	−0.0720943
$175$	−1.98135	−0.149776
$176$	2.71900	0.204952
$177$	−7.22150	−0.542801
$178$	−3.06218	−0.229520
$179$	−19.0494	−1.42382	−0.711909	−	0.702272i	$-0.752169\pi$
$179$	−19.0494	−1.42382	−0.711909	+	0.702272i	$0.752169\pi$
$180$	1.65516	0.123368
$181$	20.7929	1.54552	0.772761	−	0.634697i	$-0.218875\pi$
$181$	20.7929	1.54552	0.772761	+	0.634697i	$0.218875\pi$
$182$	−5.09513	−0.377676
$183$	12.7396	0.941737
$184$	0	0
$185$	0.666505	0.0490025
$186$	0.863454	0.0633115
$187$	7.98014	0.583565
$188$	15.9328	1.16202
$189$	1.98135	0.144122
$190$	−4.70001	−0.340974
$191$	−11.5210	−0.833633	−0.416816	−	0.908991i	$-0.636854\pi$
$191$	−11.5210	−0.833633	−0.416816	+	0.908991i	$0.636854\pi$
$192$	0.872010	0.0629319
$193$	−10.6100	−0.763725	−0.381862	−	0.924219i	$-0.624717\pi$
$193$	−10.6100	−0.763725	−0.381862	+	0.924219i	$0.624717\pi$
$194$	3.49615	0.251009
$195$	−4.37911	−0.313594
$196$	5.08835	0.363454
$197$	−9.41984	−0.671136	−0.335568	−	0.942016i	$-0.608928\pi$
$197$	−9.41984	−0.671136	−0.335568	+	0.942016i	$0.608928\pi$
$198$	−0.778910	−0.0553547
$199$	−14.5331	−1.03022	−0.515112	−	0.857123i	$-0.672250\pi$
$199$	−14.5331	−1.03022	−0.515112	+	0.857123i	$0.672250\pi$
$200$	2.14642	0.151775
$201$	12.0280	0.848389
$202$	8.50569	0.598458
$203$	3.20870	0.225207
$204$	9.95799	0.697198
$205$	−3.57137	−0.249435
$206$	10.7938	0.752043
$207$	0	0
$208$	−8.97666	−0.622419
$209$	−10.6162	−0.734339
$210$	1.16351	0.0802898
$211$	−16.1442	−1.11141	−0.555707	−	0.831378i	$-0.687552\pi$
$211$	−16.1442	−1.11141	−0.555707	+	0.831378i	$0.687552\pi$
$212$	−3.65642	−0.251124
$213$	−13.4980	−0.924866
$214$	2.63496	0.180122
$215$	−8.48841	−0.578905
$216$	−2.14642	−0.146045
$217$	−2.91336	−0.197771
$218$	−0.573763	−0.0388601
$219$	6.96019	0.470326
$220$	2.19543	0.148016
$221$	−26.3461	−1.77223
$222$	−0.391392	−0.0262685
$223$	21.2636	1.42392	0.711959	−	0.702221i	$-0.247808\pi$
$223$	21.2636	1.42392	0.711959	+	0.702221i	$0.247808\pi$
$224$	10.8907	0.727665
$225$	1.00000	0.0666667
$226$	−3.57518	−0.237818
$227$	−13.0490	−0.866092	−0.433046	−	0.901372i	$-0.642561\pi$
$227$	−13.0490	−0.866092	−0.433046	+	0.901372i	$0.642561\pi$
$228$	−13.2474	−0.877331
$229$	−3.53598	−0.233664	−0.116832	−	0.993152i	$-0.537274\pi$
$229$	−3.53598	−0.233664	−0.116832	+	0.993152i	$0.537274\pi$
$230$	0	0
$231$	2.62810	0.172916
$232$	−3.47602	−0.228212
$233$	19.4283	1.27279	0.636397	−	0.771362i	$-0.280424\pi$
$233$	19.4283	1.27279	0.636397	+	0.771362i	$0.280424\pi$
$234$	2.57154	0.168107
$235$	9.62613	0.627940
$236$	−11.9528	−0.778058
$237$	12.3272	0.800736
$238$	7.00005	0.453746
$239$	0.106901	0.00691482	0.00345741	−	0.999994i	$-0.498899\pi$
$239$	0.106901	0.00691482	0.00345741	+	0.999994i	$0.498899\pi$
$240$	2.04988	0.132319
$241$	14.2230	0.916186	0.458093	−	0.888904i	$-0.348533\pi$
$241$	14.2230	0.916186	0.458093	+	0.888904i	$0.348533\pi$
$242$	5.42637	0.348820
$243$	−1.00000	−0.0641500
$244$	21.0861	1.34990
$245$	3.07423	0.196406
$246$	2.09721	0.133713
$247$	35.0491	2.23012
$248$	3.15606	0.200410
$249$	−11.5024	−0.728937
$250$	0.587229	0.0371396
$251$	0.794786	0.0501665	0.0250832	−	0.999685i	$-0.492015\pi$
$251$	0.794786	0.0501665	0.0250832	+	0.999685i	$0.492015\pi$
$252$	3.27946	0.206587
$253$	0	0
$254$	3.04184	0.190862
$255$	6.01632	0.376757
$256$	−5.01220	−0.313262
$257$	−6.77389	−0.422543	−0.211272	−	0.977427i	$-0.567760\pi$
$257$	−6.77389	−0.422543	−0.211272	+	0.977427i	$0.567760\pi$
$258$	4.98464	0.310330
$259$	1.32058	0.0820571
$260$	−7.24813	−0.449510
$261$	−1.61945	−0.100241
$262$	−3.72361	−0.230045
$263$	−1.60108	−0.0987268	−0.0493634	−	0.998781i	$-0.515719\pi$
$263$	−1.60108	−0.0987268	−0.0493634	+	0.998781i	$0.515719\pi$
$264$	−2.84704	−0.175223
$265$	−2.20910	−0.135704
$266$	−9.31238	−0.570979
$267$	−5.21463	−0.319130
$268$	19.9083	1.21609
$269$	17.3308	1.05668	0.528340	−	0.849033i	$-0.322815\pi$
$269$	17.3308	1.05668	0.528340	+	0.849033i	$0.322815\pi$
$270$	−0.587229	−0.0357376
$271$	5.72514	0.347778	0.173889	−	0.984765i	$-0.444367\pi$
$271$	5.72514	0.347778	0.173889	+	0.984765i	$0.444367\pi$
$272$	12.3328	0.747783
$273$	−8.67656	−0.525130
$274$	−3.74815	−0.226434
$275$	1.32641	0.0799858
$276$	0	0
$277$	4.21841	0.253460	0.126730	−	0.991937i	$-0.459552\pi$
$277$	4.21841	0.253460	0.126730	+	0.991937i	$0.459552\pi$
$278$	4.61852	0.277001
$279$	1.47039	0.0880297
$280$	4.25282	0.254154
$281$	−5.53117	−0.329962	−0.164981	−	0.986297i	$-0.552756\pi$
$281$	−5.53117	−0.329962	−0.164981	+	0.986297i	$0.552756\pi$
$282$	−5.65275	−0.336616
$283$	28.1991	1.67626	0.838130	−	0.545471i	$-0.183649\pi$
$283$	28.1991	1.67626	0.838130	+	0.545471i	$0.183649\pi$
$284$	−22.3413	−1.32571
$285$	−8.00370	−0.474098
$286$	3.41093	0.201692
$287$	−7.07614	−0.417691
$288$	−5.49659	−0.323890
$289$	19.1961	1.12918
$290$	−0.950988	−0.0558440
$291$	5.95363	0.349008
$292$	11.5202	0.674172
$293$	19.0595	1.11347	0.556734	−	0.830691i	$-0.312054\pi$
$293$	19.0595	1.11347	0.556734	+	0.830691i	$0.312054\pi$
$294$	−1.80528	−0.105286
$295$	−7.22150	−0.420452
$296$	−1.43060	−0.0831519
$297$	−1.32641	−0.0769664
$298$	8.15026	0.472132
$299$	0	0
$300$	1.65516	0.0955608
$301$	−16.8186	−0.969405
$302$	−0.383957	−0.0220942
$303$	14.4844	0.832110
$304$	−16.4067	−0.940986
$305$	12.7396	0.729466
$306$	−3.53296	−0.201966
$307$	31.3691	1.79033	0.895163	−	0.445739i	$-0.147059\pi$
$307$	31.3691	1.79033	0.895163	+	0.445739i	$0.147059\pi$
$308$	4.34993	0.247860
$309$	18.3810	1.04566
$310$	0.863454	0.0490409
$311$	−23.0310	−1.30597	−0.652984	−	0.757372i	$-0.726483\pi$
$311$	−23.0310	−1.30597	−0.652984	+	0.757372i	$0.726483\pi$
$312$	9.39939	0.532136
$313$	8.36516	0.472827	0.236413	−	0.971653i	$-0.424028\pi$
$313$	8.36516	0.472827	0.236413	+	0.971653i	$0.424028\pi$
$314$	1.68957	0.0953478
$315$	1.98135	0.111637
$316$	20.4035	1.14779
$317$	15.3262	0.860803	0.430402	−	0.902638i	$-0.358372\pi$
$317$	15.3262	0.860803	0.430402	+	0.902638i	$0.358372\pi$
$318$	1.29725	0.0727460
$319$	−2.14806	−0.120268
$320$	0.872010	0.0487469
$321$	4.48711	0.250446
$322$	0	0
$323$	−48.1528	−2.67929
$324$	−1.65516	−0.0919534
$325$	−4.37911	−0.242909
$326$	7.54399	0.417823
$327$	−0.977068	−0.0540320
$328$	7.66564	0.423264
$329$	19.0728	1.05152
$330$	−0.778910	−0.0428776
$331$	17.4539	0.959353	0.479677	−	0.877445i	$-0.340754\pi$
$331$	17.4539	0.959353	0.479677	+	0.877445i	$0.340754\pi$
$332$	−19.0384	−1.04487
$333$	−0.666505	−0.0365243
$334$	−7.01565	−0.383879
$335$	12.0280	0.657160
$336$	4.06155	0.221576
$337$	−7.54403	−0.410949	−0.205475	−	0.978662i	$-0.565874\pi$
$337$	−7.54403	−0.410949	−0.205475	+	0.978662i	$0.565874\pi$
$338$	−3.62707	−0.197287
$339$	−6.08822	−0.330667
$340$	9.95799	0.540048
$341$	1.95034	0.105617
$342$	4.70001	0.254147
$343$	19.9606	1.07777
$344$	18.2197	0.982339
$345$	0	0
$346$	−10.4602	−0.562341
$347$	5.52837	0.296778	0.148389	−	0.988929i	$-0.452591\pi$
$347$	5.52837	0.296778	0.148389	+	0.988929i	$0.452591\pi$
$348$	−2.68045	−0.143687
$349$	17.9725	0.962043	0.481022	−	0.876709i	$-0.340266\pi$
$349$	17.9725	0.962043	0.481022	+	0.876709i	$0.340266\pi$
$350$	1.16351	0.0621922
$351$	4.37911	0.233739
$352$	−7.29076	−0.388599
$353$	−14.1660	−0.753982	−0.376991	−	0.926217i	$-0.623041\pi$
$353$	−14.1660	−0.753982	−0.376991	+	0.926217i	$0.623041\pi$
$354$	4.24068	0.225390
$355$	−13.4980	−0.716398
$356$	−8.63105	−0.457445
$357$	11.9205	0.630898
$358$	11.1864	0.591217
$359$	−30.0163	−1.58420	−0.792100	−	0.610391i	$-0.791012\pi$
$359$	−30.0163	−1.58420	−0.792100	+	0.610391i	$0.791012\pi$
$360$	−2.14642	−0.113126
$361$	45.0592	2.37154
$362$	−12.2102	−0.641753
$363$	9.24062	0.485007
$364$	−14.3611	−0.752727
$365$	6.96019	0.364313
$366$	−7.48106	−0.391041
$367$	4.90179	0.255871	0.127936	−	0.991782i	$-0.459165\pi$
$367$	4.90179	0.255871	0.127936	+	0.991782i	$0.459165\pi$
$368$	0	0
$369$	3.57137	0.185918
$370$	−0.391392	−0.0203475
$371$	−4.37701	−0.227243
$372$	2.43373	0.126183
$373$	−9.77213	−0.505982	−0.252991	−	0.967469i	$-0.581414\pi$
$373$	−9.77213	−0.505982	−0.252991	+	0.967469i	$0.581414\pi$
$374$	−4.68617	−0.242316
$375$	1.00000	0.0516398
$376$	−20.6617	−1.06555
$377$	7.09175	0.365243
$378$	−1.16351	−0.0598445
$379$	−29.8768	−1.53467	−0.767334	−	0.641248i	$-0.778417\pi$
$379$	−29.8768	−1.53467	−0.767334	+	0.641248i	$0.778417\pi$
$380$	−13.2474	−0.679578
$381$	5.17999	0.265379
$382$	6.76549	0.346152
$383$	−29.7415	−1.51972	−0.759860	−	0.650087i	$-0.774732\pi$
$383$	−29.7415	−1.51972	−0.759860	+	0.650087i	$0.774732\pi$
$384$	−11.5052	−0.587125
$385$	2.62810	0.133940
$386$	6.23051	0.317124
$387$	8.48841	0.431490
$388$	9.85422	0.500272
$389$	−25.0386	−1.26951	−0.634753	−	0.772715i	$-0.718898\pi$
$389$	−25.0386	−1.26951	−0.634753	+	0.772715i	$0.718898\pi$
$390$	2.57154	0.130215
$391$	0	0
$392$	−6.59859	−0.333279
$393$	−6.34097	−0.319860
$394$	5.53160	0.278678
$395$	12.3272	0.620248
$396$	−2.19543	−0.110325
$397$	25.1925	1.26438	0.632188	−	0.774815i	$-0.282157\pi$
$397$	25.1925	1.26438	0.632188	+	0.774815i	$0.282157\pi$
$398$	8.53426	0.427784
$399$	−15.8582	−0.793901
$400$	2.04988	0.102494
$401$	28.9392	1.44515	0.722577	−	0.691290i	$-0.242957\pi$
$401$	28.9392	1.44515	0.722577	+	0.691290i	$0.242957\pi$
$402$	−7.06319	−0.352280
$403$	−6.43898	−0.320748
$404$	23.9741	1.19276
$405$	−1.00000	−0.0496904
$406$	−1.88425	−0.0935135
$407$	−0.884063	−0.0438214
$408$	−12.9135	−0.639316
$409$	22.0972	1.09263	0.546317	−	0.837578i	$-0.316029\pi$
$409$	22.0972	1.09263	0.546317	+	0.837578i	$0.316029\pi$
$410$	2.09721	0.103574
$411$	−6.38278	−0.314839
$412$	30.4235	1.49886
$413$	−14.3084	−0.704068
$414$	0	0
$415$	−11.5024	−0.564632
$416$	24.0701	1.18014
$417$	7.86494	0.385148
$418$	6.23416	0.304923
$419$	25.5345	1.24744	0.623722	−	0.781646i	$-0.285620\pi$
$419$	25.5345	1.24744	0.623722	+	0.781646i	$0.285620\pi$
$420$	3.27946	0.160021
$421$	−20.3717	−0.992854	−0.496427	−	0.868079i	$-0.665355\pi$
$421$	−20.3717	−0.992854	−0.496427	+	0.868079i	$0.665355\pi$
$422$	9.48036	0.461497
$423$	−9.62613	−0.468038
$424$	4.74165	0.230275
$425$	6.01632	0.291834
$426$	7.92641	0.384036
$427$	25.2416	1.22153
$428$	7.42689	0.358992
$429$	5.80851	0.280438
$430$	4.98464	0.240381
$431$	5.97602	0.287855	0.143927	−	0.989588i	$-0.454027\pi$
$431$	5.97602	0.287855	0.143927	+	0.989588i	$0.454027\pi$
$432$	−2.04988	−0.0986251
$433$	11.1843	0.537485	0.268743	−	0.963212i	$-0.413392\pi$
$433$	11.1843	0.537485	0.268743	+	0.963212i	$0.413392\pi$
$434$	1.71081	0.0821214
$435$	−1.61945	−0.0776467
$436$	−1.61721	−0.0774501
$437$	0	0
$438$	−4.08723	−0.195295
$439$	24.8487	1.18596	0.592982	−	0.805216i	$-0.297950\pi$
$439$	24.8487	1.18596	0.592982	+	0.805216i	$0.297950\pi$
$440$	−2.84704	−0.135727
$441$	−3.07423	−0.146392
$442$	15.4712	0.735891
$443$	15.9117	0.755989	0.377994	−	0.925808i	$-0.376614\pi$
$443$	15.9117	0.755989	0.377994	+	0.925808i	$0.376614\pi$
$444$	−1.10317	−0.0523543
$445$	−5.21463	−0.247197
$446$	−12.4866	−0.591259
$447$	13.8792	0.656463
$448$	1.72776	0.0816291
$449$	28.6982	1.35435	0.677177	−	0.735820i	$-0.263203\pi$
$449$	28.6982	1.35435	0.677177	+	0.735820i	$0.263203\pi$
$450$	−0.587229	−0.0276823
$451$	4.73711	0.223062
$452$	−10.0770	−0.473982
$453$	−0.653845	−0.0307203
$454$	7.66275	0.359631
$455$	−8.67656	−0.406764
$456$	17.1793	0.804494
$457$	16.1635	0.756095	0.378048	−	0.925786i	$-0.376596\pi$
$457$	16.1635	0.756095	0.378048	+	0.925786i	$0.376596\pi$
$458$	2.07643	0.0970252
$459$	−6.01632	−0.280818
$460$	0	0
$461$	−18.4103	−0.857454	−0.428727	−	0.903434i	$-0.641038\pi$
$461$	−18.4103	−0.857454	−0.428727	+	0.903434i	$0.641038\pi$
$462$	−1.54330	−0.0718006
$463$	−5.52604	−0.256817	−0.128408	−	0.991721i	$-0.540987\pi$
$463$	−5.52604	−0.256817	−0.128408	+	0.991721i	$0.540987\pi$
$464$	−3.31968	−0.154112
$465$	1.47039	0.0681875
$466$	−11.4089	−0.528507
$467$	22.2337	1.02885	0.514427	−	0.857534i	$-0.328005\pi$
$467$	22.2337	1.02885	0.514427	+	0.857534i	$0.328005\pi$
$468$	7.24813	0.335045
$469$	23.8317	1.10045
$470$	−5.65275	−0.260742
$471$	2.87719	0.132574
$472$	15.5004	0.713462
$473$	11.2592	0.517696
$474$	−7.23888	−0.332493
$475$	−8.00370	−0.367235
$476$	19.7303	0.904337
$477$	2.20910	0.101148
$478$	−0.0627751	−0.00287127
$479$	−4.99165	−0.228074	−0.114037	−	0.993476i	$-0.536378\pi$
$479$	−4.99165	−0.228074	−0.114037	+	0.993476i	$0.536378\pi$
$480$	−5.49659	−0.250884
$481$	2.91870	0.133081
$482$	−8.35218	−0.380432
$483$	0	0
$484$	15.2947	0.695215
$485$	5.95363	0.270340
$486$	0.587229	0.0266373
$487$	−12.9466	−0.586665	−0.293332	−	0.956011i	$-0.594764\pi$
$487$	−12.9466	−0.586665	−0.293332	+	0.956011i	$0.594764\pi$
$488$	−27.3445	−1.23783
$489$	12.8468	0.580950
$490$	−1.80528	−0.0815542
$491$	7.29988	0.329439	0.164719	−	0.986340i	$-0.447328\pi$
$491$	7.29988	0.329439	0.164719	+	0.986340i	$0.447328\pi$
$492$	5.91119	0.266497
$493$	−9.74313	−0.438809
$494$	−20.5818	−0.926020
$495$	−1.32641	−0.0596179
$496$	3.01412	0.135338
$497$	−26.7443	−1.19965
$498$	6.75457	0.302679
$499$	−17.3869	−0.778346	−0.389173	−	0.921165i	$-0.627239\pi$
$499$	−17.3869	−0.778346	−0.389173	+	0.921165i	$0.627239\pi$
$500$	1.65516	0.0740211
$501$	−11.9470	−0.533754
$502$	−0.466722	−0.0208308
$503$	−11.5414	−0.514606	−0.257303	−	0.966331i	$-0.582834\pi$
$503$	−11.5414	−0.514606	−0.257303	+	0.966331i	$0.582834\pi$
$504$	−4.25282	−0.189435
$505$	14.4844	0.644549
$506$	0	0
$507$	−6.17658	−0.274312
$508$	8.57372	0.380397
$509$	25.8737	1.14683	0.573416	−	0.819265i	$-0.305618\pi$
$509$	25.8737	1.14683	0.573416	+	0.819265i	$0.305618\pi$
$510$	−3.53296	−0.156442
$511$	13.7906	0.610061
$512$	−20.0672	−0.886853
$513$	8.00370	0.353372
$514$	3.97783	0.175454
$515$	18.3810	0.809962
$516$	14.0497	0.618503
$517$	−12.7682	−0.561547
$518$	−0.775485	−0.0340729
$519$	−17.8127	−0.781892
$520$	9.39939	0.412191
$521$	34.5640	1.51428	0.757138	−	0.653255i	$-0.226597\pi$
$521$	34.5640	1.51428	0.757138	+	0.653255i	$0.226597\pi$
$522$	0.950988	0.0416236
$523$	−33.0218	−1.44394	−0.721972	−	0.691922i	$-0.756764\pi$
$523$	−33.0218	−1.44394	−0.721972	+	0.691922i	$0.756764\pi$
$524$	−10.4953	−0.458491
$525$	1.98135	0.0864734
$526$	0.940201	0.0409947
$527$	8.84631	0.385351
$528$	−2.71900	−0.118329
$529$	0	0
$530$	1.29725	0.0563488
$531$	7.22150	0.313387
$532$	−26.2478	−1.13799
$533$	−15.6394	−0.677417
$534$	3.06218	0.132514
$535$	4.48711	0.193995
$536$	−25.8171	−1.11513
$537$	19.0494	0.822041
$538$	−10.1772	−0.438769
$539$	−4.07771	−0.175639
$540$	−1.65516	−0.0712268
$541$	17.6617	0.759334	0.379667	−	0.925123i	$-0.376039\pi$
$541$	17.6617	0.759334	0.379667	+	0.925123i	$0.376039\pi$
$542$	−3.36197	−0.144409
$543$	−20.7929	−0.892307
$544$	−33.0692	−1.41783
$545$	−0.977068	−0.0418530
$546$	5.09513	0.218052
$547$	27.0659	1.15725	0.578627	−	0.815593i	$-0.303589\pi$
$547$	27.0659	1.15725	0.578627	+	0.815593i	$0.303589\pi$
$548$	−10.5645	−0.451294
$549$	−12.7396	−0.543712
$550$	−0.778910	−0.0332128
$551$	12.9616	0.552182
$552$	0	0
$553$	24.4245	1.03864
$554$	−2.47718	−0.105245
$555$	−0.666505	−0.0282916
$556$	13.0178	0.552076
$557$	7.34400	0.311175	0.155588	−	0.987822i	$-0.450273\pi$
$557$	7.34400	0.311175	0.155588	+	0.987822i	$0.450273\pi$
$558$	−0.863454	−0.0365529
$559$	−37.1717	−1.57219
$560$	4.06155	0.171632
$561$	−7.98014	−0.336922
$562$	3.24807	0.137011
$563$	29.0669	1.22503	0.612513	−	0.790461i	$-0.290159\pi$
$563$	29.0669	1.22503	0.612513	+	0.790461i	$0.290159\pi$
$564$	−15.9328	−0.670892
$565$	−6.08822	−0.256133
$566$	−16.5593	−0.696040
$567$	−1.98135	−0.0832091
$568$	28.9723	1.21565
$569$	0.910447	0.0381679	0.0190840	−	0.999818i	$-0.493925\pi$
$569$	0.910447	0.0381679	0.0190840	+	0.999818i	$0.493925\pi$
$570$	4.70001	0.196862
$571$	−38.9204	−1.62877	−0.814384	−	0.580326i	$-0.802925\pi$
$571$	−38.9204	−1.62877	−0.814384	+	0.580326i	$0.802925\pi$
$572$	9.61403	0.401983
$573$	11.5210	0.481298
$574$	4.15532	0.173440
$575$	0	0
$576$	−0.872010	−0.0363338
$577$	46.4750	1.93478	0.967390	−	0.253292i	$-0.0815134\pi$
$577$	46.4750	1.93478	0.967390	+	0.253292i	$0.0815134\pi$
$578$	−11.2725	−0.468875
$579$	10.6100	0.440937
$580$	−2.68045	−0.111300
$581$	−22.7904	−0.945505
$582$	−3.49615	−0.144920
$583$	2.93018	0.121356
$584$	−14.9395	−0.618200
$585$	4.37911	0.181054
$586$	−11.1923	−0.462350
$587$	29.6971	1.22573	0.612866	−	0.790187i	$-0.290017\pi$
$587$	29.6971	1.22573	0.612866	+	0.790187i	$0.290017\pi$
$588$	−5.08835	−0.209840
$589$	−11.7685	−0.484914
$590$	4.24068	0.174586
$591$	9.41984	0.387480
$592$	−1.36626	−0.0561529
$593$	40.7972	1.67534	0.837669	−	0.546178i	$-0.183918\pi$
$593$	40.7972	1.67534	0.837669	+	0.546178i	$0.183918\pi$
$594$	0.778910	0.0319590
$595$	11.9205	0.488691
$596$	22.9723	0.940982
$597$	14.5331	0.594800
$598$	0	0
$599$	25.0894	1.02513	0.512564	−	0.858649i	$-0.328696\pi$
$599$	25.0894	1.02513	0.512564	+	0.858649i	$0.328696\pi$
$600$	−2.14642	−0.0876272
$601$	37.4790	1.52880	0.764400	−	0.644742i	$-0.223035\pi$
$601$	37.4790	1.52880	0.764400	+	0.644742i	$0.223035\pi$
$602$	9.87635	0.402530
$603$	−12.0280	−0.489818
$604$	−1.08222	−0.0440349
$605$	9.24062	0.375685
$606$	−8.50569	−0.345520
$607$	40.7022	1.65205	0.826026	−	0.563632i	$-0.190596\pi$
$607$	40.7022	1.65205	0.826026	+	0.563632i	$0.190596\pi$
$608$	43.9930	1.78415
$609$	−3.20870	−0.130023
$610$	−7.48106	−0.302899
$611$	42.1539	1.70536
$612$	−9.95799	−0.402528
$613$	−28.5579	−1.15344	−0.576721	−	0.816941i	$-0.695668\pi$
$613$	−28.5579	−1.15344	−0.576721	+	0.816941i	$0.695668\pi$
$614$	−18.4208	−0.743404
$615$	3.57137	0.144011
$616$	−5.64100	−0.227282
$617$	−22.9966	−0.925810	−0.462905	−	0.886408i	$-0.653193\pi$
$617$	−22.9966	−0.925810	−0.462905	+	0.886408i	$0.653193\pi$
$618$	−10.7938	−0.434192
$619$	−23.8429	−0.958328	−0.479164	−	0.877725i	$-0.659060\pi$
$619$	−23.8429	−0.958328	−0.479164	+	0.877725i	$0.659060\pi$
$620$	2.43373	0.0977408
$621$	0	0
$622$	13.5245	0.542282
$623$	−10.3320	−0.413944
$624$	8.97666	0.359354
$625$	1.00000	0.0400000
$626$	−4.91227	−0.196334
$627$	10.6162	0.423971
$628$	4.76221	0.190033
$629$	−4.00991	−0.159886
$630$	−1.16351	−0.0463553
$631$	−11.3594	−0.452209	−0.226104	−	0.974103i	$-0.572599\pi$
$631$	−11.3594	−0.452209	−0.226104	+	0.974103i	$0.572599\pi$
$632$	−26.4593	−1.05249
$633$	16.1442	0.641675
$634$	−8.99997	−0.357435
$635$	5.17999	0.205562
$636$	3.65642	0.144986
$637$	13.4624	0.533400
$638$	1.26141	0.0499395
$639$	13.4980	0.533972
$640$	−11.5052	−0.454785
$641$	2.81009	0.110992	0.0554958	−	0.998459i	$-0.482326\pi$
$641$	2.81009	0.110992	0.0554958	+	0.998459i	$0.482326\pi$
$642$	−2.63496	−0.103994
$643$	−17.8375	−0.703443	−0.351721	−	0.936105i	$-0.614404\pi$
$643$	−17.8375	−0.703443	−0.351721	+	0.936105i	$0.614404\pi$
$644$	0	0
$645$	8.48841	0.334231
$646$	28.2767	1.11253
$647$	25.3959	0.998415	0.499207	−	0.866483i	$-0.333625\pi$
$647$	25.3959	0.998415	0.499207	+	0.866483i	$0.333625\pi$
$648$	2.14642	0.0843193
$649$	9.57871	0.375997
$650$	2.57154	0.100864
$651$	2.91336	0.114183
$652$	21.2635	0.832741
$653$	−26.1383	−1.02287	−0.511436	−	0.859321i	$-0.670886\pi$
$653$	−26.1383	−1.02287	−0.511436	+	0.859321i	$0.670886\pi$
$654$	0.573763	0.0224359
$655$	−6.34097	−0.247762
$656$	7.32089	0.285833
$657$	−6.96019	−0.271543
$658$	−11.2001	−0.436625
$659$	−9.65589	−0.376140	−0.188070	−	0.982156i	$-0.560223\pi$
$659$	−9.65589	−0.376140	−0.188070	+	0.982156i	$0.560223\pi$
$660$	−2.19543	−0.0854570
$661$	0.841121	0.0327158	0.0163579	−	0.999866i	$-0.494793\pi$
$661$	0.841121	0.0327158	0.0163579	+	0.999866i	$0.494793\pi$
$662$	−10.2494	−0.398356
$663$	26.3461	1.02320
$664$	24.6890	0.958120
$665$	−15.8582	−0.614953
$666$	0.391392	0.0151661
$667$	0	0
$668$	−19.7743	−0.765089
$669$	−21.2636	−0.822100
$670$	−7.06319	−0.272875
$671$	−16.8980	−0.652339
$672$	−10.8907	−0.420118
$673$	4.90785	0.189184	0.0945919	−	0.995516i	$-0.469845\pi$
$673$	4.90785	0.189184	0.0945919	+	0.995516i	$0.469845\pi$
$674$	4.43007	0.170640
$675$	−1.00000	−0.0384900
$676$	−10.2232	−0.393202
$677$	−25.1996	−0.968498	−0.484249	−	0.874930i	$-0.660907\pi$
$677$	−25.1996	−0.968498	−0.484249	+	0.874930i	$0.660907\pi$
$678$	3.57518	0.137304
$679$	11.7963	0.452699
$680$	−12.9135	−0.495212
$681$	13.0490	0.500038
$682$	−1.14530	−0.0438557
$683$	−8.09321	−0.309678	−0.154839	−	0.987940i	$-0.549486\pi$
$683$	−8.09321	−0.309678	−0.154839	+	0.987940i	$0.549486\pi$
$684$	13.2474	0.506528
$685$	−6.38278	−0.243873
$686$	−11.7215	−0.447528
$687$	3.53598	0.134906
$688$	17.4003	0.663378
$689$	−9.67388	−0.368545
$690$	0	0
$691$	−12.3228	−0.468782	−0.234391	−	0.972142i	$-0.575310\pi$
$691$	−12.3228	−0.468782	−0.234391	+	0.972142i	$0.575310\pi$
$692$	−29.4829	−1.12077
$693$	−2.62810	−0.0998332
$694$	−3.24642	−0.123232
$695$	7.86494	0.298334
$696$	3.47602	0.131758
$697$	21.4865	0.813859
$698$	−10.5540	−0.399473
$699$	−19.4283	−0.734848
$700$	3.27946	0.123952
$701$	29.7304	1.12290	0.561451	−	0.827510i	$-0.310243\pi$
$701$	29.7304	1.12290	0.561451	+	0.827510i	$0.310243\pi$
$702$	−2.57154	−0.0970565
$703$	5.33451	0.201195
$704$	−1.15665	−0.0435928
$705$	−9.62613	−0.362541
$706$	8.31871	0.313079
$707$	28.6988	1.07933
$708$	11.9528	0.449212
$709$	−46.6564	−1.75222	−0.876108	−	0.482114i	$-0.839869\pi$
$709$	−46.6564	−1.75222	−0.876108	+	0.482114i	$0.839869\pi$
$710$	7.92641	0.297473
$711$	−12.3272	−0.462305
$712$	11.1928	0.419467
$713$	0	0
$714$	−7.00005	−0.261970
$715$	5.80851	0.217226
$716$	31.5298	1.17832
$717$	−0.106901	−0.00399227
$718$	17.6265	0.657814
$719$	−15.8828	−0.592328	−0.296164	−	0.955137i	$-0.595707\pi$
$719$	−15.8828	−0.592328	−0.296164	+	0.955137i	$0.595707\pi$
$720$	−2.04988	−0.0763947
$721$	36.4192	1.35632
$722$	−26.4601	−0.984742
$723$	−14.2230	−0.528960
$724$	−34.4156	−1.27904
$725$	−1.61945	−0.0601449
$726$	−5.42637	−0.201391
$727$	18.5158	0.686714	0.343357	−	0.939205i	$-0.388436\pi$
$727$	18.5158	0.686714	0.343357	+	0.939205i	$0.388436\pi$
$728$	18.6235	0.690234
$729$	1.00000	0.0370370
$730$	−4.08723	−0.151275
$731$	51.0690	1.88886
$732$	−21.0861	−0.779363
$733$	3.77761	0.139529	0.0697646	−	0.997563i	$-0.477775\pi$
$733$	3.77761	0.139529	0.0697646	+	0.997563i	$0.477775\pi$
$734$	−2.87847	−0.106246
$735$	−3.07423	−0.113395
$736$	0	0
$737$	−15.9541	−0.587677
$738$	−2.09721	−0.0771994
$739$	−4.03829	−0.148551	−0.0742755	−	0.997238i	$-0.523664\pi$
$739$	−4.03829	−0.148551	−0.0742755	+	0.997238i	$0.523664\pi$
$740$	−1.10317	−0.0405535
$741$	−35.0491	−1.28756
$742$	2.57031	0.0943589
$743$	−11.3382	−0.415958	−0.207979	−	0.978133i	$-0.566689\pi$
$743$	−11.3382	−0.415958	−0.207979	+	0.978133i	$0.566689\pi$
$744$	−3.15606	−0.115707
$745$	13.8792	0.508494
$746$	5.73848	0.210101
$747$	11.5024	0.420852
$748$	−13.2084	−0.482948
$749$	8.89056	0.324854
$750$	−0.587229	−0.0214426
$751$	25.3428	0.924772	0.462386	−	0.886679i	$-0.346993\pi$
$751$	25.3428	0.924772	0.462386	+	0.886679i	$0.346993\pi$
$752$	−19.7325	−0.719568
$753$	−0.794786	−0.0289636
$754$	−4.16448	−0.151661
$755$	−0.653845	−0.0237959
$756$	−3.27946	−0.119273
$757$	−12.5531	−0.456249	−0.228125	−	0.973632i	$-0.573259\pi$
$757$	−12.5531	−0.456249	−0.228125	+	0.973632i	$0.573259\pi$
$758$	17.5445	0.637246
$759$	0	0
$760$	17.1793	0.623158
$761$	−54.0891	−1.96073	−0.980363	−	0.197200i	$-0.936815\pi$
$761$	−54.0891	−1.96073	−0.980363	+	0.197200i	$0.936815\pi$
$762$	−3.04184	−0.110194
$763$	−1.93592	−0.0700849
$764$	19.0692	0.689898
$765$	−6.01632	−0.217521
$766$	17.4651	0.631039
$767$	−31.6237	−1.14187
$768$	5.01220	0.180862
$769$	−31.5517	−1.13778	−0.568892	−	0.822412i	$-0.692628\pi$
$769$	−31.5517	−1.13778	−0.568892	+	0.822412i	$0.692628\pi$
$770$	−1.54330	−0.0556165
$771$	6.77389	0.243956
$772$	17.5613	0.632044
$773$	−9.60816	−0.345581	−0.172791	−	0.984959i	$-0.555278\pi$
$773$	−9.60816	−0.345581	−0.172791	+	0.984959i	$0.555278\pi$
$774$	−4.98464	−0.179169
$775$	1.47039	0.0528178
$776$	−12.7790	−0.458739
$777$	−1.32058	−0.0473757
$778$	14.7034	0.527141
$779$	−28.5841	−1.02413
$780$	7.24813	0.259525
$781$	17.9039	0.640653
$782$	0	0
$783$	1.61945	0.0578744
$784$	−6.30182	−0.225065
$785$	2.87719	0.102691
$786$	3.72361	0.132817
$787$	6.21337	0.221483	0.110741	−	0.993849i	$-0.464677\pi$
$787$	6.21337	0.221483	0.110741	+	0.993849i	$0.464677\pi$
$788$	15.5914	0.555419
$789$	1.60108	0.0570000
$790$	−7.23888	−0.257548
$791$	−12.0629	−0.428908
$792$	2.84704	0.101165
$793$	55.7880	1.98109
$794$	−14.7938	−0.525011
$795$	2.20910	0.0783487
$796$	24.0546	0.852594
$797$	32.3141	1.14462	0.572312	−	0.820036i	$-0.306046\pi$
$797$	32.3141	1.14462	0.572312	+	0.820036i	$0.306046\pi$
$798$	9.31238	0.329655
$799$	−57.9139	−2.04885
$800$	−5.49659	−0.194334
$801$	5.21463	0.184250
$802$	−16.9939	−0.600077
$803$	−9.23211	−0.325794
$804$	−19.9083	−0.702111
$805$	0	0
$806$	3.78116	0.133186
$807$	−17.3308	−0.610074
$808$	−31.0897	−1.09373
$809$	−20.8406	−0.732716	−0.366358	−	0.930474i	$-0.619395\pi$
$809$	−20.8406	−0.732716	−0.366358	+	0.930474i	$0.619395\pi$
$810$	0.587229	0.0206331
$811$	11.2665	0.395620	0.197810	−	0.980240i	$-0.436617\pi$
$811$	11.2665	0.395620	0.197810	+	0.980240i	$0.436617\pi$
$812$	−5.31093	−0.186377
$813$	−5.72514	−0.200789
$814$	0.519147	0.0181961
$815$	12.8468	0.450002
$816$	−12.3328	−0.431733
$817$	−67.9387	−2.37687
$818$	−12.9761	−0.453699
$819$	8.67656	0.303184
$820$	5.91119	0.206428
$821$	−50.9227	−1.77721	−0.888607	−	0.458670i	$-0.848326\pi$
$821$	−50.9227	−1.77721	−0.888607	+	0.458670i	$0.848326\pi$
$822$	3.74815	0.130732
$823$	44.4162	1.54825	0.774125	−	0.633032i	$-0.218190\pi$
$823$	44.4162	1.54825	0.774125	+	0.633032i	$0.218190\pi$
$824$	−39.4532	−1.37442
$825$	−1.32641	−0.0461798
$826$	8.40229	0.292353
$827$	6.97399	0.242510	0.121255	−	0.992621i	$-0.461308\pi$
$827$	6.97399	0.242510	0.121255	+	0.992621i	$0.461308\pi$
$828$	0	0
$829$	21.8823	0.760004	0.380002	−	0.924986i	$-0.375923\pi$
$829$	21.8823	0.760004	0.380002	+	0.924986i	$0.375923\pi$
$830$	6.75457	0.234454
$831$	−4.21841	−0.146335
$832$	3.81863	0.132387
$833$	−18.4956	−0.640834
$834$	−4.61852	−0.159926
$835$	−11.9470	−0.413444
$836$	17.5716	0.607725
$837$	−1.47039	−0.0508240
$838$	−14.9946	−0.517981
$839$	29.3202	1.01225	0.506123	−	0.862461i	$-0.331078\pi$
$839$	29.3202	1.01225	0.506123	+	0.862461i	$0.331078\pi$
$840$	−4.25282	−0.146736
$841$	−26.3774	−0.909565
$842$	11.9628	0.412266
$843$	5.53117	0.190504
$844$	26.7213	0.919785
$845$	−6.17658	−0.212481
$846$	5.65275	0.194345
$847$	18.3090	0.629103
$848$	4.52840	0.155506
$849$	−28.1991	−0.967789
$850$	−3.53296	−0.121180
$851$	0	0
$852$	22.3413	0.765402
$853$	29.6748	1.01605	0.508023	−	0.861343i	$-0.330376\pi$
$853$	29.6748	1.01605	0.508023	+	0.861343i	$0.330376\pi$
$854$	−14.8226	−0.507220
$855$	8.00370	0.273721
$856$	−9.63121	−0.329188
$857$	19.7671	0.675231	0.337616	−	0.941284i	$-0.390380\pi$
$857$	19.7671	0.675231	0.337616	+	0.941284i	$0.390380\pi$
$858$	−3.41093	−0.116447
$859$	−36.9601	−1.26106	−0.630531	−	0.776164i	$-0.717163\pi$
$859$	−36.9601	−1.26106	−0.630531	+	0.776164i	$0.717163\pi$
$860$	14.0497	0.479090
$861$	7.07614	0.241154
$862$	−3.50929	−0.119527
$863$	43.1825	1.46995	0.734975	−	0.678094i	$-0.237194\pi$
$863$	43.1825	1.46995	0.734975	+	0.678094i	$0.237194\pi$
$864$	5.49659	0.186998
$865$	−17.8127	−0.605651
$866$	−6.56777	−0.223182
$867$	−19.1961	−0.651935
$868$	4.82207	0.163672
$869$	−16.3510	−0.554668
$870$	0.950988	0.0322415
$871$	52.6719	1.78472
$872$	2.09720	0.0710200
$873$	−5.95363	−0.201500
$874$	0	0
$875$	1.98135	0.0669820
$876$	−11.5202	−0.389233
$877$	−14.4857	−0.489147	−0.244573	−	0.969631i	$-0.578648\pi$
$877$	−14.4857	−0.489147	−0.244573	+	0.969631i	$0.578648\pi$
$878$	−14.5919	−0.492452
$879$	−19.0595	−0.642861
$880$	−2.71900	−0.0916573
$881$	−13.7756	−0.464111	−0.232055	−	0.972703i	$-0.574545\pi$
$881$	−13.7756	−0.464111	−0.232055	+	0.972703i	$0.574545\pi$
$882$	1.80528	0.0607869
$883$	−6.02573	−0.202782	−0.101391	−	0.994847i	$-0.532329\pi$
$883$	−6.02573	−0.202782	−0.101391	+	0.994847i	$0.532329\pi$
$884$	43.6071	1.46666
$885$	7.22150	0.242748
$886$	−9.34383	−0.313912
$887$	3.55204	0.119266	0.0596329	−	0.998220i	$-0.481007\pi$
$887$	3.55204	0.119266	0.0596329	+	0.998220i	$0.481007\pi$
$888$	1.43060	0.0480078
$889$	10.2634	0.344223
$890$	3.06218	0.102645
$891$	1.32641	0.0444366
$892$	−35.1948	−1.17841
$893$	77.0446	2.57820
$894$	−8.15026	−0.272586
$895$	19.0494	0.636751
$896$	−22.7960	−0.761560
$897$	0	0
$898$	−16.8524	−0.562373
$899$	−2.38122	−0.0794180
$900$	−1.65516	−0.0551721
$901$	13.2906	0.442776
$902$	−2.78177	−0.0926229
$903$	16.8186	0.559686
$904$	13.0679	0.434631
$905$	−20.7929	−0.691178
$906$	0.383957	0.0127561
$907$	15.2309	0.505733	0.252867	−	0.967501i	$-0.418627\pi$
$907$	15.2309	0.505733	0.252867	+	0.967501i	$0.418627\pi$
$908$	21.5982	0.716761
$909$	−14.4844	−0.480419
$910$	5.09513	0.168902
$911$	0.923469	0.0305959	0.0152979	−	0.999883i	$-0.495130\pi$
$911$	0.923469	0.0305959	0.0152979	+	0.999883i	$0.495130\pi$
$912$	16.4067	0.543279
$913$	15.2570	0.504933
$914$	−9.49166	−0.313956
$915$	−12.7396	−0.421158
$916$	5.85262	0.193376
$917$	−12.5637	−0.414891
$918$	3.53296	0.116605
$919$	24.1622	0.797038	0.398519	−	0.917160i	$-0.369524\pi$
$919$	24.1622	0.797038	0.398519	+	0.917160i	$0.369524\pi$
$920$	0	0
$921$	−31.3691	−1.03365
$922$	10.8111	0.356044
$923$	−59.1091	−1.94560
$924$	−4.34993	−0.143102
$925$	−0.666505	−0.0219146
$926$	3.24505	0.106639
$927$	−18.3810	−0.603710
$928$	8.90145	0.292204
$929$	44.8830	1.47256	0.736281	−	0.676676i	$-0.236580\pi$
$929$	44.8830	1.47256	0.736281	+	0.676676i	$0.236580\pi$
$930$	−0.863454	−0.0283138
$931$	24.6052	0.806404
$932$	−32.1571	−1.05334
$933$	23.0310	0.754001
$934$	−13.0563	−0.427215
$935$	−7.98014	−0.260978
$936$	−9.39939	−0.307229
$937$	−35.7587	−1.16819	−0.584093	−	0.811687i	$-0.698550\pi$
$937$	−35.7587	−1.16819	−0.584093	+	0.811687i	$0.698550\pi$
$938$	−13.9947	−0.456943
$939$	−8.36516	−0.272987
$940$	−15.9328	−0.519671
$941$	12.2723	0.400064	0.200032	−	0.979789i	$-0.435895\pi$
$941$	12.2723	0.400064	0.200032	+	0.979789i	$0.435895\pi$
$942$	−1.68957	−0.0550491
$943$	0	0
$944$	14.8032	0.481805
$945$	−1.98135	−0.0644535
$946$	−6.61170	−0.214965
$947$	16.4496	0.534542	0.267271	−	0.963621i	$-0.413878\pi$
$947$	16.4496	0.534542	0.267271	+	0.963621i	$0.413878\pi$
$948$	−20.4035	−0.662674
$949$	30.4794	0.989404
$950$	4.70001	0.152488
$951$	−15.3262	−0.496985
$952$	−25.5863	−0.829257
$953$	44.4403	1.43956	0.719781	−	0.694202i	$-0.244242\pi$
$953$	44.4403	1.43956	0.719781	+	0.694202i	$0.244242\pi$
$954$	−1.29725	−0.0419999
$955$	11.5210	0.372812
$956$	−0.176938	−0.00572257
$957$	2.14806	0.0694370
$958$	2.93124	0.0947041
$959$	−12.6465	−0.408378
$960$	−0.872010	−0.0281440
$961$	−28.8380	−0.930257
$962$	−1.71395	−0.0552598
$963$	−4.48711	−0.144595
$964$	−23.5414	−0.758218
$965$	10.6100	0.341548
$966$	0	0
$967$	−47.5786	−1.53003	−0.765013	−	0.644015i	$-0.777267\pi$
$967$	−47.5786	−1.53003	−0.765013	+	0.644015i	$0.777267\pi$
$968$	−19.8342	−0.637497
$969$	48.1528	1.54689
$970$	−3.49615	−0.112254
$971$	−19.0649	−0.611820	−0.305910	−	0.952060i	$-0.598961\pi$
$971$	−19.0649	−0.611820	−0.305910	+	0.952060i	$0.598961\pi$
$972$	1.65516	0.0530893
$973$	15.5832	0.499576
$974$	7.60260	0.243603
$975$	4.37911	0.140244
$976$	−26.1147	−0.835910
$977$	−34.1970	−1.09406	−0.547029	−	0.837114i	$-0.684241\pi$
$977$	−34.1970	−1.09406	−0.547029	+	0.837114i	$0.684241\pi$
$978$	−7.54399	−0.241230
$979$	6.91676	0.221061
$980$	−5.08835	−0.162541
$981$	0.977068	0.0311954
$982$	−4.28670	−0.136794
$983$	−3.65780	−0.116666	−0.0583329	−	0.998297i	$-0.518578\pi$
$983$	−3.65780	−0.116666	−0.0583329	+	0.998297i	$0.518578\pi$
$984$	−7.66564	−0.244372
$985$	9.41984	0.300141
$986$	5.72145	0.182208
$987$	−19.0728	−0.607093
$988$	−58.0118	−1.84560
$989$	0	0
$990$	0.778910	0.0247554
$991$	39.2208	1.24589	0.622945	−	0.782265i	$-0.285936\pi$
$991$	39.2208	1.24589	0.622945	+	0.782265i	$0.285936\pi$
$992$	−8.08210	−0.256607
$993$	−17.4539	−0.553883
$994$	15.7050	0.498133
$995$	14.5331	0.460730
$996$	19.0384	0.603255
$997$	37.1319	1.17598	0.587990	−	0.808868i	$-0.299919\pi$
$997$	37.1319	1.17598	0.587990	+	0.808868i	$0.299919\pi$
$998$	10.2101	0.323196
$999$	0.666505	0.0210873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bt.1.11		25
23.11	odd	22		345.2.m.d.121.2	✓	50
23.21	odd	22		345.2.m.d.211.2	yes	50
23.22	odd	2		7935.2.a.bu.1.11		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.121.2	✓	50	23.11	odd	22
345.2.m.d.211.2	yes	50	23.21	odd	22
7935.2.a.bt.1.11		25	1.1	even	1	trivial
7935.2.a.bu.1.11		25	23.22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-0.587229 q^{2} -1.00000 q^{3} -1.65516 q^{4} -1.00000 q^{5} +0.587229 q^{6} -1.98135 q^{7} +2.14642 q^{8} +1.00000 q^{9} +0.587229 q^{10} +1.32641 q^{11} +1.65516 q^{12} -4.37911 q^{13} +1.16351 q^{14} +1.00000 q^{15} +2.04988 q^{16} +6.01632 q^{17} -0.587229 q^{18} -8.00370 q^{19} +1.65516 q^{20} +1.98135 q^{21} -0.778910 q^{22} -2.14642 q^{24} +1.00000 q^{25} +2.57154 q^{26} -1.00000 q^{27} +3.27946 q^{28} -1.61945 q^{29} -0.587229 q^{30} +1.47039 q^{31} -5.49659 q^{32} -1.32641 q^{33} -3.53296 q^{34} +1.98135 q^{35} -1.65516 q^{36} -0.666505 q^{37} +4.70001 q^{38} +4.37911 q^{39} -2.14642 q^{40} +3.57137 q^{41} -1.16351 q^{42} +8.48841 q^{43} -2.19543 q^{44} -1.00000 q^{45} -9.62613 q^{47} -2.04988 q^{48} -3.07423 q^{49} -0.587229 q^{50} -6.01632 q^{51} +7.24813 q^{52} +2.20910 q^{53} +0.587229 q^{54} -1.32641 q^{55} -4.25282 q^{56} +8.00370 q^{57} +0.950988 q^{58} +7.22150 q^{59} -1.65516 q^{60} -12.7396 q^{61} -0.863454 q^{62} -1.98135 q^{63} -0.872010 q^{64} +4.37911 q^{65} +0.778910 q^{66} -12.0280 q^{67} -9.95799 q^{68} -1.16351 q^{70} +13.4980 q^{71} +2.14642 q^{72} -6.96019 q^{73} +0.391392 q^{74} -1.00000 q^{75} +13.2474 q^{76} -2.62810 q^{77} -2.57154 q^{78} -12.3272 q^{79} -2.04988 q^{80} +1.00000 q^{81} -2.09721 q^{82} +11.5024 q^{83} -3.27946 q^{84} -6.01632 q^{85} -4.98464 q^{86} +1.61945 q^{87} +2.84704 q^{88} +5.21463 q^{89} +0.587229 q^{90} +8.67656 q^{91} -1.47039 q^{93} +5.65275 q^{94} +8.00370 q^{95} +5.49659 q^{96} -5.95363 q^{97} +1.80528 q^{98} +1.32641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19}+ \cdots - 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9 - q^10 - 15 * q^11 - 31 * q^12 + 24 * q^13 - 5 * q^14 + 25 * q^15 + 39 * q^16 + 6 * q^17 + q^18 - 13 * q^19 - 31 * q^20 - 15 * q^21 + 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 + 41 * q^28 + q^29 + q^30 + 18 * q^31 + 17 * q^32 + 15 * q^33 - 7 * q^34 - 15 * q^35 + 31 * q^36 + 8 * q^37 - 15 * q^38 - 24 * q^39 - 3 * q^40 + 36 * q^41 + 5 * q^42 + 36 * q^43 - 90 * q^44 - 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 - 6 * q^51 + 35 * q^52 - 6 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 13 * q^57 + 42 * q^58 - 3 * q^59 + 31 * q^60 - 71 * q^61 - 7 * q^62 + 15 * q^63 + 47 * q^64 - 24 * q^65 - 21 * q^66 + 10 * q^67 + 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 - 67 * q^74 - 25 * q^75 + 12 * q^76 + 27 * q^77 - 21 * q^78 - 33 * q^79 - 39 * q^80 + 25 * q^81 + 49 * q^82 + 2 * q^83 - 41 * q^84 - 6 * q^85 + 35 * q^86 - q^87 + 33 * q^88 - 11 * q^89 - q^90 - 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 + 48 * q^97 + 4 * q^98 - 15 * q^99

Introduction

L-functions

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Database

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