LMFDB - Embedded newform 7935.2.a.bw.1.8

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)

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")

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);

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 = [25,11,25,31,25,11,7] 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			1.8
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)

$f(q)$	$=$	\(q-1.08036 q^{2} +1.00000 q^{3} -0.832828 q^{4} +1.00000 q^{5} -1.08036 q^{6} +2.50098 q^{7} +3.06047 q^{8} +1.00000 q^{9} -1.08036 q^{10} +3.09908 q^{11} -0.832828 q^{12} +5.05600 q^{13} -2.70195 q^{14} +1.00000 q^{15} -1.64074 q^{16} -4.41362 q^{17} -1.08036 q^{18} -8.37165 q^{19} -0.832828 q^{20} +2.50098 q^{21} -3.34811 q^{22} +3.06047 q^{24} +1.00000 q^{25} -5.46229 q^{26} +1.00000 q^{27} -2.08288 q^{28} -1.05068 q^{29} -1.08036 q^{30} -5.62498 q^{31} -4.34835 q^{32} +3.09908 q^{33} +4.76829 q^{34} +2.50098 q^{35} -0.832828 q^{36} +6.45154 q^{37} +9.04437 q^{38} +5.05600 q^{39} +3.06047 q^{40} +3.14288 q^{41} -2.70195 q^{42} +11.6301 q^{43} -2.58100 q^{44} +1.00000 q^{45} +8.62851 q^{47} -1.64074 q^{48} -0.745113 q^{49} -1.08036 q^{50} -4.41362 q^{51} -4.21078 q^{52} -9.34955 q^{53} -1.08036 q^{54} +3.09908 q^{55} +7.65416 q^{56} -8.37165 q^{57} +1.13511 q^{58} +11.3835 q^{59} -0.832828 q^{60} -12.0138 q^{61} +6.07699 q^{62} +2.50098 q^{63} +7.97925 q^{64} +5.05600 q^{65} -3.34811 q^{66} -7.01792 q^{67} +3.67579 q^{68} -2.70195 q^{70} -6.26637 q^{71} +3.06047 q^{72} +15.4649 q^{73} -6.96997 q^{74} +1.00000 q^{75} +6.97214 q^{76} +7.75072 q^{77} -5.46229 q^{78} +6.74139 q^{79} -1.64074 q^{80} +1.00000 q^{81} -3.39543 q^{82} +14.2778 q^{83} -2.08288 q^{84} -4.41362 q^{85} -12.5647 q^{86} -1.05068 q^{87} +9.48462 q^{88} +5.93666 q^{89} -1.08036 q^{90} +12.6449 q^{91} -5.62498 q^{93} -9.32188 q^{94} -8.37165 q^{95} -4.34835 q^{96} +11.6599 q^{97} +0.804988 q^{98} +3.09908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} + 25 q^{5} + 11 q^{6} + 7 q^{7} + 33 q^{8} + 25 q^{9} + 11 q^{10} + 9 q^{11} + 31 q^{12} + 18 q^{13} + 11 q^{14} + 25 q^{15} + 39 q^{16} - 8 q^{17} + 11 q^{18} + 11 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) $ 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 + 25 * q^5 + 11 * q^6 + 7 * q^7 + 33 * q^8 + 25 * q^9 + 11 * q^10 + 9 * q^11 + 31 * q^12 + 18 * q^13 + 11 * q^14 + 25 * q^15 + 39 * q^16 - 8 * q^17 + 11 * q^18 + 11 * q^19 + 31 * q^20 + 7 * q^21 + 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 - 5 * q^28 + 33 * q^29 + 11 * q^30 + 14 * q^31 + 77 * q^32 + 9 * q^33 + 13 * q^34 + 7 * q^35 + 31 * q^36 + 4 * q^37 - 23 * q^38 + 18 * q^39 + 33 * q^40 + 56 * q^41 + 11 * q^42 - 4 * q^43 - 18 * q^44 + 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 - 8 * q^51 + 49 * q^52 + 2 * q^53 + 11 * q^54 + 9 * q^55 + 33 * q^56 + 11 * q^57 + 26 * q^58 + 61 * q^59 + 31 * q^60 + 21 * q^61 + 51 * q^62 + 7 * q^63 + 71 * q^64 + 18 * q^65 + 9 * q^66 + 2 * q^67 - 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 - 47 * q^74 + 25 * q^75 - 8 * q^76 + 49 * q^77 + 35 * q^78 + 35 * q^79 + 39 * q^80 + 25 * q^81 + 35 * q^82 - 26 * q^83 - 5 * q^84 - 8 * q^85 - 33 * q^86 + 33 * q^87 + 9 * q^88 - 7 * q^89 + 11 * q^90 + 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 - 54 * q^97 + 88 * q^98 + 9 * 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 $

$2$	−1.08036	−0.763928	−0.381964	−	0.924177i	$-0.624752\pi$
$2$	−1.08036	−0.763928	−0.381964	+	0.924177i	$0.624752\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.832828	−0.416414
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.08036	−0.441054
$7$	2.50098	0.945281	0.472640	−	0.881255i	$-0.343301\pi$
$7$	2.50098	0.945281	0.472640	+	0.881255i	$0.343301\pi$
$8$	3.06047	1.08204
$9$	1.00000	0.333333
$10$	−1.08036	−0.341639
$11$	3.09908	0.934407	0.467203	−	0.884150i	$-0.345262\pi$
$11$	3.09908	0.934407	0.467203	+	0.884150i	$0.345262\pi$
$12$	−0.832828	−0.240417
$13$	5.05600	1.40228	0.701141	−	0.713023i	$-0.252674\pi$
$13$	5.05600	1.40228	0.701141	+	0.713023i	$0.252674\pi$
$14$	−2.70195	−0.722126
$15$	1.00000	0.258199
$16$	−1.64074	−0.410185
$17$	−4.41362	−1.07046	−0.535230	−	0.844706i	$-0.679775\pi$
$17$	−4.41362	−1.07046	−0.535230	+	0.844706i	$0.679775\pi$
$18$	−1.08036	−0.254643
$19$	−8.37165	−1.92059	−0.960294	−	0.278990i	$-0.910000\pi$
$19$	−8.37165	−1.92059	−0.960294	+	0.278990i	$0.910000\pi$
$20$	−0.832828	−0.186226
$21$	2.50098	0.545758
$22$	−3.34811	−0.713820
$23$	0	0
$23$	0	0
$24$	3.06047	0.624715
$25$	1.00000	0.200000
$26$	−5.46229	−1.07124
$27$	1.00000	0.192450
$28$	−2.08288	−0.393628
$29$	−1.05068	−0.195107	−0.0975535	−	0.995230i	$-0.531102\pi$
$29$	−1.05068	−0.195107	−0.0975535	+	0.995230i	$0.531102\pi$
$30$	−1.08036	−0.197245
$31$	−5.62498	−1.01028	−0.505138	−	0.863038i	$-0.668559\pi$
$31$	−5.62498	−1.01028	−0.505138	+	0.863038i	$0.668559\pi$
$32$	−4.34835	−0.768686
$33$	3.09908	0.539480
$34$	4.76829	0.817754
$35$	2.50098	0.422742
$36$	−0.832828	−0.138805
$37$	6.45154	1.06063	0.530313	−	0.847802i	$-0.322074\pi$
$37$	6.45154	1.06063	0.530313	+	0.847802i	$0.322074\pi$
$38$	9.04437	1.46719
$39$	5.05600	0.809608
$40$	3.06047	0.483902
$41$	3.14288	0.490835	0.245418	−	0.969417i	$-0.421075\pi$
$41$	3.14288	0.490835	0.245418	+	0.969417i	$0.421075\pi$
$42$	−2.70195	−0.416920
$43$	11.6301	1.77357	0.886786	−	0.462180i	$-0.152932\pi$
$43$	11.6301	1.77357	0.886786	+	0.462180i	$0.152932\pi$
$44$	−2.58100	−0.389100
$45$	1.00000	0.149071
$46$	0	0
$47$	8.62851	1.25860	0.629299	−	0.777163i	$-0.283342\pi$
$47$	8.62851	1.25860	0.629299	+	0.777163i	$0.283342\pi$
$48$	−1.64074	−0.236821
$49$	−0.745113	−0.106445
$50$	−1.08036	−0.152786
$51$	−4.41362	−0.618030
$52$	−4.21078	−0.583930
$53$	−9.34955	−1.28426	−0.642130	−	0.766596i	$-0.721949\pi$
$53$	−9.34955	−1.28426	−0.642130	+	0.766596i	$0.721949\pi$
$54$	−1.08036	−0.147018
$55$	3.09908	0.417879
$56$	7.65416	1.02283
$57$	−8.37165	−1.10885
$58$	1.13511	0.149048
$59$	11.3835	1.48200	0.741000	−	0.671505i	$-0.234352\pi$
$59$	11.3835	1.48200	0.741000	+	0.671505i	$0.234352\pi$
$60$	−0.832828	−0.107518
$61$	−12.0138	−1.53821	−0.769105	−	0.639122i	$-0.779298\pi$
$61$	−12.0138	−1.53821	−0.769105	+	0.639122i	$0.779298\pi$
$62$	6.07699	0.771779
$63$	2.50098	0.315094
$64$	7.97925	0.997406
$65$	5.05600	0.627120
$66$	−3.34811	−0.412124
$67$	−7.01792	−0.857375	−0.428687	−	0.903453i	$-0.641024\pi$
$67$	−7.01792	−0.857375	−0.428687	+	0.903453i	$0.641024\pi$
$68$	3.67579	0.445754
$69$	0	0
$70$	−2.70195	−0.322945
$71$	−6.26637	−0.743681	−0.371841	−	0.928297i	$-0.621273\pi$
$71$	−6.26637	−0.743681	−0.371841	+	0.928297i	$0.621273\pi$
$72$	3.06047	0.360679
$73$	15.4649	1.81002	0.905012	−	0.425386i	$-0.139862\pi$
$73$	15.4649	1.81002	0.905012	+	0.425386i	$0.139862\pi$
$74$	−6.96997	−0.810243
$75$	1.00000	0.115470
$76$	6.97214	0.799760
$77$	7.75072	0.883277
$78$	−5.46229	−0.618482
$79$	6.74139	0.758466	0.379233	−	0.925301i	$-0.376188\pi$
$79$	6.74139	0.758466	0.379233	+	0.925301i	$0.376188\pi$
$80$	−1.64074	−0.183440
$81$	1.00000	0.111111
$82$	−3.39543	−0.374963
$83$	14.2778	1.56719	0.783595	−	0.621273i	$-0.213384\pi$
$83$	14.2778	1.56719	0.783595	+	0.621273i	$0.213384\pi$
$84$	−2.08288	−0.227261
$85$	−4.41362	−0.478724
$86$	−12.5647	−1.35488
$87$	−1.05068	−0.112645
$88$	9.48462	1.01106
$89$	5.93666	0.629285	0.314643	−	0.949210i	$-0.398115\pi$
$89$	5.93666	0.629285	0.314643	+	0.949210i	$0.398115\pi$
$90$	−1.08036	−0.113880
$91$	12.6449	1.32555
$92$	0	0
$93$	−5.62498	−0.583283
$94$	−9.32188	−0.961478
$95$	−8.37165	−0.858913
$96$	−4.34835	−0.443801
$97$	11.6599	1.18389	0.591943	−	0.805980i	$-0.298361\pi$
$97$	11.6599	1.18389	0.591943	+	0.805980i	$0.298361\pi$
$98$	0.804988	0.0813161
$99$	3.09908	0.311469
$100$	−0.832828	−0.0832828
$101$	4.15654	0.413591	0.206795	−	0.978384i	$-0.433697\pi$
$101$	4.15654	0.413591	0.206795	+	0.978384i	$0.433697\pi$
$102$	4.76829	0.472131
$103$	5.37402	0.529518	0.264759	−	0.964315i	$-0.414708\pi$
$103$	5.37402	0.529518	0.264759	+	0.964315i	$0.414708\pi$
$104$	15.4737	1.51732
$105$	2.50098	0.244070
$106$	10.1009	0.981082
$107$	−4.28544	−0.414289	−0.207145	−	0.978310i	$-0.566417\pi$
$107$	−4.28544	−0.414289	−0.207145	+	0.978310i	$0.566417\pi$
$108$	−0.832828	−0.0801389
$109$	2.96583	0.284075	0.142038	−	0.989861i	$-0.454635\pi$
$109$	2.96583	0.284075	0.142038	+	0.989861i	$0.454635\pi$
$110$	−3.34811	−0.319230
$111$	6.45154	0.612353
$112$	−4.10346	−0.387740
$113$	17.0982	1.60846	0.804231	−	0.594317i	$-0.202578\pi$
$113$	17.0982	1.60846	0.804231	+	0.594317i	$0.202578\pi$
$114$	9.04437	0.847083
$115$	0	0
$116$	0.875039	0.0812453
$117$	5.05600	0.467427
$118$	−12.2982	−1.13214
$119$	−11.0384	−1.01188
$120$	3.06047	0.279381
$121$	−1.39572	−0.126884
$122$	12.9792	1.17508
$123$	3.14288	0.283384
$124$	4.68464	0.420693
$125$	1.00000	0.0894427
$126$	−2.70195	−0.240709
$127$	0.164913	0.0146336	0.00731682	−	0.999973i	$-0.497671\pi$
$127$	0.164913	0.0146336	0.00731682	+	0.999973i	$0.497671\pi$
$128$	0.0762499	0.00673960
$129$	11.6301	1.02397
$130$	−5.46229	−0.479074
$131$	−11.6425	−1.01721	−0.508603	−	0.861001i	$-0.669838\pi$
$131$	−11.6425	−1.01721	−0.508603	+	0.861001i	$0.669838\pi$
$132$	−2.58100	−0.224647
$133$	−20.9373	−1.81549
$134$	7.58186	0.654973
$135$	1.00000	0.0860663
$136$	−13.5077	−1.15828
$137$	3.02846	0.258739	0.129369	−	0.991596i	$-0.458705\pi$
$137$	3.02846	0.258739	0.129369	+	0.991596i	$0.458705\pi$
$138$	0	0
$139$	9.83875	0.834512	0.417256	−	0.908789i	$-0.362992\pi$
$139$	9.83875	0.834512	0.417256	+	0.908789i	$0.362992\pi$
$140$	−2.08288	−0.176036
$141$	8.62851	0.726652
$142$	6.76992	0.568119
$143$	15.6689	1.31030
$144$	−1.64074	−0.136728
$145$	−1.05068	−0.0872545
$146$	−16.7076	−1.38273
$147$	−0.745113	−0.0614559
$148$	−5.37302	−0.441660
$149$	−16.1199	−1.32060	−0.660298	−	0.751004i	$-0.729570\pi$
$149$	−16.1199	−1.32060	−0.660298	+	0.751004i	$0.729570\pi$
$150$	−1.08036	−0.0882108
$151$	−5.10744	−0.415638	−0.207819	−	0.978167i	$-0.566636\pi$
$151$	−5.10744	−0.415638	−0.207819	+	0.978167i	$0.566636\pi$
$152$	−25.6212	−2.07815
$153$	−4.41362	−0.356820
$154$	−8.37355	−0.674760
$155$	−5.62498	−0.451809
$156$	−4.21078	−0.337132
$157$	6.41640	0.512084	0.256042	−	0.966666i	$-0.417581\pi$
$157$	6.41640	0.512084	0.256042	+	0.966666i	$0.417581\pi$
$158$	−7.28311	−0.579413
$159$	−9.34955	−0.741467
$160$	−4.34835	−0.343767
$161$	0	0
$162$	−1.08036	−0.0848809
$163$	−14.9480	−1.17082	−0.585411	−	0.810737i	$-0.699067\pi$
$163$	−14.9480	−1.17082	−0.585411	+	0.810737i	$0.699067\pi$
$164$	−2.61748	−0.204391
$165$	3.09908	0.241263
$166$	−15.4251	−1.19722
$167$	6.49021	0.502228	0.251114	−	0.967958i	$-0.419203\pi$
$167$	6.49021	0.502228	0.251114	+	0.967958i	$0.419203\pi$
$168$	7.65416	0.590531
$169$	12.5631	0.966395
$170$	4.76829	0.365711
$171$	−8.37165	−0.640196
$172$	−9.68587	−0.738540
$173$	6.24433	0.474748	0.237374	−	0.971418i	$-0.423713\pi$
$173$	6.24433	0.474748	0.237374	+	0.971418i	$0.423713\pi$
$174$	1.13511	0.0860528
$175$	2.50098	0.189056
$176$	−5.08478	−0.383280
$177$	11.3835	0.855633
$178$	−6.41372	−0.480729
$179$	3.67740	0.274862	0.137431	−	0.990511i	$-0.456116\pi$
$179$	3.67740	0.274862	0.137431	+	0.990511i	$0.456116\pi$
$180$	−0.832828	−0.0620753
$181$	−11.8608	−0.881610	−0.440805	−	0.897603i	$-0.645307\pi$
$181$	−11.8608	−0.881610	−0.440805	+	0.897603i	$0.645307\pi$
$182$	−13.6611	−1.01262
$183$	−12.0138	−0.888087
$184$	0	0
$185$	6.45154	0.474327
$186$	6.07699	0.445587
$187$	−13.6781	−1.00025
$188$	−7.18607	−0.524098
$189$	2.50098	0.181919
$190$	9.04437	0.656148
$191$	6.51802	0.471627	0.235814	−	0.971798i	$-0.424224\pi$
$191$	6.51802	0.471627	0.235814	+	0.971798i	$0.424224\pi$
$192$	7.97925	0.575853
$193$	−7.15270	−0.514862	−0.257431	−	0.966297i	$-0.582876\pi$
$193$	−7.15270	−0.514862	−0.257431	+	0.966297i	$0.582876\pi$
$194$	−12.5969	−0.904403
$195$	5.05600	0.362068
$196$	0.620551	0.0443251
$197$	−2.86150	−0.203874	−0.101937	−	0.994791i	$-0.532504\pi$
$197$	−2.86150	−0.203874	−0.101937	+	0.994791i	$0.532504\pi$
$198$	−3.34811	−0.237940
$199$	−5.81290	−0.412066	−0.206033	−	0.978545i	$-0.566055\pi$
$199$	−5.81290	−0.412066	−0.206033	+	0.978545i	$0.566055\pi$
$200$	3.06047	0.216408
$201$	−7.01792	−0.495006
$202$	−4.49055	−0.315954
$203$	−2.62774	−0.184431
$204$	3.67579	0.257356
$205$	3.14288	0.219508
$206$	−5.80586	−0.404514
$207$	0	0
$208$	−8.29559	−0.575196
$209$	−25.9444	−1.79461
$210$	−2.70195	−0.186452
$211$	14.7073	1.01249	0.506246	−	0.862389i	$-0.331033\pi$
$211$	14.7073	1.01249	0.506246	+	0.862389i	$0.331033\pi$
$212$	7.78657	0.534784
$213$	−6.26637	−0.429365
$214$	4.62981	0.316487
$215$	11.6301	0.793166
$216$	3.06047	0.208238
$217$	−14.0680	−0.954995
$218$	−3.20416	−0.217013
$219$	15.4649	1.04502
$220$	−2.58100	−0.174011
$221$	−22.3153	−1.50109
$222$	−6.96997	−0.467794
$223$	27.4144	1.83580	0.917902	−	0.396807i	$-0.129882\pi$
$223$	27.4144	1.83580	0.917902	+	0.396807i	$0.129882\pi$
$224$	−10.8751	−0.726624
$225$	1.00000	0.0666667
$226$	−18.4721	−1.22875
$227$	−3.20691	−0.212850	−0.106425	−	0.994321i	$-0.533940\pi$
$227$	−3.20691	−0.212850	−0.106425	+	0.994321i	$0.533940\pi$
$228$	6.97214	0.461741
$229$	−9.14163	−0.604096	−0.302048	−	0.953293i	$-0.597670\pi$
$229$	−9.14163	−0.604096	−0.302048	+	0.953293i	$0.597670\pi$
$230$	0	0
$231$	7.75072	0.509960
$232$	−3.21558	−0.211113
$233$	7.54366	0.494202	0.247101	−	0.968990i	$-0.420522\pi$
$233$	7.54366	0.494202	0.247101	+	0.968990i	$0.420522\pi$
$234$	−5.46229	−0.357081
$235$	8.62851	0.562862
$236$	−9.48047	−0.617126
$237$	6.74139	0.437900
$238$	11.9254	0.773007
$239$	10.7392	0.694661	0.347330	−	0.937743i	$-0.387088\pi$
$239$	10.7392	0.694661	0.347330	+	0.937743i	$0.387088\pi$
$240$	−1.64074	−0.105909
$241$	3.41230	0.219805	0.109903	−	0.993942i	$-0.464946\pi$
$241$	3.41230	0.219805	0.109903	+	0.993942i	$0.464946\pi$
$242$	1.50788	0.0969300
$243$	1.00000	0.0641500
$244$	10.0054	0.640533
$245$	−0.745113	−0.0476035
$246$	−3.39543	−0.216485
$247$	−42.3271	−2.69321
$248$	−17.2151	−1.09316
$249$	14.2778	0.904817
$250$	−1.08036	−0.0683278
$251$	−26.0111	−1.64181	−0.820905	−	0.571065i	$-0.806530\pi$
$251$	−26.0111	−1.64181	−0.820905	+	0.571065i	$0.806530\pi$
$252$	−2.08288	−0.131209
$253$	0	0
$254$	−0.178165	−0.0111790
$255$	−4.41362	−0.276392
$256$	−16.0409	−1.00255
$257$	17.5574	1.09520	0.547599	−	0.836741i	$-0.315542\pi$
$257$	17.5574	1.09520	0.547599	+	0.836741i	$0.315542\pi$
$258$	−12.5647	−0.782241
$259$	16.1352	1.00259
$260$	−4.21078	−0.261141
$261$	−1.05068	−0.0650357
$262$	12.5780	0.777072
$263$	20.8332	1.28463	0.642316	−	0.766440i	$-0.277974\pi$
$263$	20.8332	1.28463	0.642316	+	0.766440i	$0.277974\pi$
$264$	9.48462	0.583738
$265$	−9.34955	−0.574338
$266$	22.6198	1.38691
$267$	5.93666	0.363318
$268$	5.84472	0.357023
$269$	−4.72683	−0.288200	−0.144100	−	0.989563i	$-0.546029\pi$
$269$	−4.72683	−0.288200	−0.144100	+	0.989563i	$0.546029\pi$
$270$	−1.08036	−0.0657485
$271$	−21.6896	−1.31755	−0.658775	−	0.752340i	$-0.728925\pi$
$271$	−21.6896	−1.31755	−0.658775	+	0.752340i	$0.728925\pi$
$272$	7.24161	0.439087
$273$	12.6449	0.765307
$274$	−3.27182	−0.197658
$275$	3.09908	0.186881
$276$	0	0
$277$	9.27565	0.557320	0.278660	−	0.960390i	$-0.410110\pi$
$277$	9.27565	0.557320	0.278660	+	0.960390i	$0.410110\pi$
$278$	−10.6294	−0.637507
$279$	−5.62498	−0.336759
$280$	7.65416	0.457423
$281$	−2.25086	−0.134275	−0.0671376	−	0.997744i	$-0.521387\pi$
$281$	−2.25086	−0.134275	−0.0671376	+	0.997744i	$0.521387\pi$
$282$	−9.32188	−0.555110
$283$	10.7197	0.637218	0.318609	−	0.947886i	$-0.396784\pi$
$283$	10.7197	0.637218	0.318609	+	0.947886i	$0.396784\pi$
$284$	5.21881	0.309679
$285$	−8.37165	−0.495894
$286$	−16.9280	−1.00098
$287$	7.86027	0.463977
$288$	−4.34835	−0.256229
$289$	2.48003	0.145884
$290$	1.13511	0.0666562
$291$	11.6599	0.683517
$292$	−12.8796	−0.753719
$293$	−16.8568	−0.984787	−0.492393	−	0.870373i	$-0.663878\pi$
$293$	−16.8568	−0.984787	−0.492393	+	0.870373i	$0.663878\pi$
$294$	0.804988	0.0469479
$295$	11.3835	0.662771
$296$	19.7447	1.14764
$297$	3.09908	0.179827
$298$	17.4153	1.00884
$299$	0	0
$300$	−0.832828	−0.0480833
$301$	29.0866	1.67652
$302$	5.51786	0.317517
$303$	4.15654	0.238787
$304$	13.7357	0.787797
$305$	−12.0138	−0.687909
$306$	4.76829	0.272585
$307$	−8.01764	−0.457591	−0.228795	−	0.973475i	$-0.573479\pi$
$307$	−8.01764	−0.457591	−0.228795	+	0.973475i	$0.573479\pi$
$308$	−6.45502	−0.367809
$309$	5.37402	0.305717
$310$	6.07699	0.345150
$311$	−0.268117	−0.0152035	−0.00760176	−	0.999971i	$-0.502420\pi$
$311$	−0.268117	−0.0152035	−0.00760176	+	0.999971i	$0.502420\pi$
$312$	15.4737	0.876027
$313$	2.72810	0.154201	0.0771006	−	0.997023i	$-0.475434\pi$
$313$	2.72810	0.154201	0.0771006	+	0.997023i	$0.475434\pi$
$314$	−6.93200	−0.391196
$315$	2.50098	0.140914
$316$	−5.61442	−0.315836
$317$	20.8543	1.17130	0.585648	−	0.810565i	$-0.300840\pi$
$317$	20.8543	1.17130	0.585648	+	0.810565i	$0.300840\pi$
$318$	10.1009	0.566428
$319$	−3.25615	−0.182309
$320$	7.97925	0.446054
$321$	−4.28544	−0.239190
$322$	0	0
$323$	36.9493	2.05591
$324$	−0.832828	−0.0462682
$325$	5.05600	0.280456
$326$	16.1492	0.894423
$327$	2.96583	0.164011
$328$	9.61868	0.531103
$329$	21.5797	1.18973
$330$	−3.34811	−0.184307
$331$	7.76342	0.426716	0.213358	−	0.976974i	$-0.431560\pi$
$331$	7.76342	0.426716	0.213358	+	0.976974i	$0.431560\pi$
$332$	−11.8909	−0.652599
$333$	6.45154	0.353542
$334$	−7.01175	−0.383666
$335$	−7.01792	−0.383430
$336$	−4.10346	−0.223862
$337$	−12.6100	−0.686909	−0.343455	−	0.939169i	$-0.611597\pi$
$337$	−12.6100	−0.686909	−0.343455	+	0.939169i	$0.611597\pi$
$338$	−13.5727	−0.738256
$339$	17.0982	0.928646
$340$	3.67579	0.199347
$341$	−17.4323	−0.944009
$342$	9.04437	0.489064
$343$	−19.3704	−1.04590
$344$	35.5935	1.91907
$345$	0	0
$346$	−6.74611	−0.362673
$347$	29.1850	1.56674	0.783368	−	0.621559i	$-0.213500\pi$
$347$	29.1850	1.56674	0.783368	+	0.621559i	$0.213500\pi$
$348$	0.875039	0.0469070
$349$	−0.964660	−0.0516371	−0.0258185	−	0.999667i	$-0.508219\pi$
$349$	−0.964660	−0.0516371	−0.0258185	+	0.999667i	$0.508219\pi$
$350$	−2.70195	−0.144425
$351$	5.05600	0.269869
$352$	−13.4759	−0.718266
$353$	23.1117	1.23011	0.615055	−	0.788484i	$-0.289134\pi$
$353$	23.1117	1.23011	0.615055	+	0.788484i	$0.289134\pi$
$354$	−12.2982	−0.653642
$355$	−6.26637	−0.332584
$356$	−4.94422	−0.262043
$357$	−11.0384	−0.584212
$358$	−3.97290	−0.209974
$359$	7.99373	0.421893	0.210946	−	0.977498i	$-0.432345\pi$
$359$	7.99373	0.421893	0.210946	+	0.977498i	$0.432345\pi$
$360$	3.06047	0.161301
$361$	51.0845	2.68866
$362$	12.8140	0.673486
$363$	−1.39572	−0.0732564
$364$	−10.5311	−0.551978
$365$	15.4649	0.809467
$366$	12.9792	0.678434
$367$	15.5771	0.813119	0.406559	−	0.913624i	$-0.366728\pi$
$367$	15.5771	0.813119	0.406559	+	0.913624i	$0.366728\pi$
$368$	0	0
$369$	3.14288	0.163612
$370$	−6.96997	−0.362351
$371$	−23.3830	−1.21399
$372$	4.68464	0.242887
$373$	−9.49846	−0.491811	−0.245906	−	0.969294i	$-0.579085\pi$
$373$	−9.49846	−0.491811	−0.245906	+	0.969294i	$0.579085\pi$
$374$	14.7773	0.764115
$375$	1.00000	0.0516398
$376$	26.4073	1.36185
$377$	−5.31226	−0.273595
$378$	−2.70195	−0.138973
$379$	−31.5484	−1.62053	−0.810266	−	0.586062i	$-0.800677\pi$
$379$	−31.5484	−1.62053	−0.810266	+	0.586062i	$0.800677\pi$
$380$	6.97214	0.357663
$381$	0.164913	0.00844874
$382$	−7.04179	−0.360289
$383$	−19.6603	−1.00460	−0.502298	−	0.864695i	$-0.667512\pi$
$383$	−19.6603	−1.00460	−0.502298	+	0.864695i	$0.667512\pi$
$384$	0.0762499	0.00389111
$385$	7.75072	0.395013
$386$	7.72747	0.393318
$387$	11.6301	0.591191
$388$	−9.71071	−0.492986
$389$	14.8422	0.752531	0.376265	−	0.926512i	$-0.377208\pi$
$389$	14.8422	0.752531	0.376265	+	0.926512i	$0.377208\pi$
$390$	−5.46229	−0.276594
$391$	0	0
$392$	−2.28039	−0.115177
$393$	−11.6425	−0.587284
$394$	3.09145	0.155745
$395$	6.74139	0.339196
$396$	−2.58100	−0.129700
$397$	−5.27400	−0.264694	−0.132347	−	0.991203i	$-0.542251\pi$
$397$	−5.27400	−0.264694	−0.132347	+	0.991203i	$0.542251\pi$
$398$	6.28001	0.314789
$399$	−20.9373	−1.04818
$400$	−1.64074	−0.0820371
$401$	−7.21849	−0.360474	−0.180237	−	0.983623i	$-0.557686\pi$
$401$	−7.21849	−0.360474	−0.180237	+	0.983623i	$0.557686\pi$
$402$	7.58186	0.378149
$403$	−28.4399	−1.41669
$404$	−3.46168	−0.172225
$405$	1.00000	0.0496904
$406$	2.83889	0.140892
$407$	19.9938	0.991057
$408$	−13.5077	−0.668732
$409$	−9.42270	−0.465922	−0.232961	−	0.972486i	$-0.574842\pi$
$409$	−9.42270	−0.465922	−0.232961	+	0.972486i	$0.574842\pi$
$410$	−3.39543	−0.167689
$411$	3.02846	0.149383
$412$	−4.47564	−0.220499
$413$	28.4698	1.40091
$414$	0	0
$415$	14.2778	0.700868
$416$	−21.9852	−1.07791
$417$	9.83875	0.481806
$418$	28.0292	1.37095
$419$	−21.6652	−1.05842	−0.529208	−	0.848492i	$-0.677511\pi$
$419$	−21.6652	−1.05842	−0.529208	+	0.848492i	$0.677511\pi$
$420$	−2.08288	−0.101634
$421$	22.4027	1.09184	0.545920	−	0.837838i	$-0.316180\pi$
$421$	22.4027	1.09184	0.545920	+	0.837838i	$0.316180\pi$
$422$	−15.8891	−0.773471
$423$	8.62851	0.419533
$424$	−28.6140	−1.38962
$425$	−4.41362	−0.214092
$426$	6.76992	0.328004
$427$	−30.0463	−1.45404
$428$	3.56904	0.172516
$429$	15.6689	0.756503
$430$	−12.5647	−0.605922
$431$	−3.91046	−0.188360	−0.0941800	−	0.995555i	$-0.530023\pi$
$431$	−3.91046	−0.188360	−0.0941800	+	0.995555i	$0.530023\pi$
$432$	−1.64074	−0.0789402
$433$	3.99400	0.191940	0.0959698	−	0.995384i	$-0.469405\pi$
$433$	3.99400	0.191940	0.0959698	+	0.995384i	$0.469405\pi$
$434$	15.1984	0.729547
$435$	−1.05068	−0.0503764
$436$	−2.47003	−0.118293
$437$	0	0
$438$	−16.7076	−0.798318
$439$	−28.8414	−1.37652	−0.688262	−	0.725462i	$-0.741626\pi$
$439$	−28.8414	−1.37652	−0.688262	+	0.725462i	$0.741626\pi$
$440$	9.48462	0.452162
$441$	−0.745113	−0.0354816
$442$	24.1085	1.14672
$443$	33.8971	1.61050	0.805249	−	0.592936i	$-0.202031\pi$
$443$	33.8971	1.61050	0.805249	+	0.592936i	$0.202031\pi$
$444$	−5.37302	−0.254992
$445$	5.93666	0.281425
$446$	−29.6173	−1.40242
$447$	−16.1199	−0.762446
$448$	19.9559	0.942829
$449$	33.0196	1.55829	0.779147	−	0.626841i	$-0.215653\pi$
$449$	33.0196	1.55829	0.779147	+	0.626841i	$0.215653\pi$
$450$	−1.08036	−0.0509285
$451$	9.74003	0.458640
$452$	−14.2398	−0.669786
$453$	−5.10744	−0.239969
$454$	3.46461	0.162602
$455$	12.6449	0.592804
$456$	−25.6212	−1.19982
$457$	−27.9667	−1.30823	−0.654114	−	0.756396i	$-0.726958\pi$
$457$	−27.9667	−1.30823	−0.654114	+	0.756396i	$0.726958\pi$
$458$	9.87623	0.461486
$459$	−4.41362	−0.206010
$460$	0	0
$461$	33.4177	1.55642	0.778209	−	0.628005i	$-0.216128\pi$
$461$	33.4177	1.55642	0.778209	+	0.628005i	$0.216128\pi$
$462$	−8.37355	−0.389573
$463$	16.6628	0.774388	0.387194	−	0.921998i	$-0.373444\pi$
$463$	16.6628	0.774388	0.387194	+	0.921998i	$0.373444\pi$
$464$	1.72390	0.0800301
$465$	−5.62498	−0.260852
$466$	−8.14985	−0.377534
$467$	−15.5251	−0.718416	−0.359208	−	0.933258i	$-0.616953\pi$
$467$	−15.5251	−0.718416	−0.359208	+	0.933258i	$0.616953\pi$
$468$	−4.21078	−0.194643
$469$	−17.5516	−0.810460
$470$	−9.32188	−0.429986
$471$	6.41640	0.295652
$472$	34.8387	1.60358
$473$	36.0426	1.65724
$474$	−7.28311	−0.334524
$475$	−8.37165	−0.384118
$476$	9.19306	0.421363
$477$	−9.34955	−0.428086
$478$	−11.6022	−0.530671
$479$	31.5511	1.44160	0.720802	−	0.693141i	$-0.243774\pi$
$479$	31.5511	1.44160	0.720802	+	0.693141i	$0.243774\pi$
$480$	−4.34835	−0.198474
$481$	32.6190	1.48730
$482$	−3.68650	−0.167915
$483$	0	0
$484$	1.16240	0.0528362
$485$	11.6599	0.529450
$486$	−1.08036	−0.0490060
$487$	−28.6551	−1.29849	−0.649244	−	0.760580i	$-0.724915\pi$
$487$	−28.6551	−1.29849	−0.649244	+	0.760580i	$0.724915\pi$
$488$	−36.7679	−1.66440
$489$	−14.9480	−0.675974
$490$	0.804988	0.0363657
$491$	10.5686	0.476955	0.238478	−	0.971148i	$-0.423352\pi$
$491$	10.5686	0.476955	0.238478	+	0.971148i	$0.423352\pi$
$492$	−2.61748	−0.118005
$493$	4.63732	0.208854
$494$	45.7283	2.05742
$495$	3.09908	0.139293
$496$	9.22914	0.414401
$497$	−15.6721	−0.702988
$498$	−15.4251	−0.691215
$499$	−34.6530	−1.55128	−0.775640	−	0.631176i	$-0.782573\pi$
$499$	−34.6530	−1.55128	−0.775640	+	0.631176i	$0.782573\pi$
$500$	−0.832828	−0.0372452
$501$	6.49021	0.289961
$502$	28.1013	1.25422
$503$	−22.1075	−0.985725	−0.492863	−	0.870107i	$-0.664049\pi$
$503$	−22.1075	−0.985725	−0.492863	+	0.870107i	$0.664049\pi$
$504$	7.65416	0.340943
$505$	4.15654	0.184963
$506$	0	0
$507$	12.5631	0.557949
$508$	−0.137344	−0.00609365
$509$	4.19975	0.186151	0.0930754	−	0.995659i	$-0.470330\pi$
$509$	4.19975	0.186151	0.0930754	+	0.995659i	$0.470330\pi$
$510$	4.76829	0.211143
$511$	38.6772	1.71098
$512$	17.1774	0.759140
$513$	−8.37165	−0.369617
$514$	−18.9682	−0.836653
$515$	5.37402	0.236808
$516$	−9.68587	−0.426397
$517$	26.7404	1.17604
$518$	−17.4317	−0.765907
$519$	6.24433	0.274096
$520$	15.4737	0.678567
$521$	−28.9172	−1.26689	−0.633443	−	0.773790i	$-0.718359\pi$
$521$	−28.9172	−1.26689	−0.633443	+	0.773790i	$0.718359\pi$
$522$	1.13511	0.0496826
$523$	12.8802	0.563213	0.281607	−	0.959530i	$-0.409133\pi$
$523$	12.8802	0.563213	0.281607	+	0.959530i	$0.409133\pi$
$524$	9.69616	0.423579
$525$	2.50098	0.109152
$526$	−22.5073	−0.981366
$527$	24.8265	1.08146
$528$	−5.08478	−0.221287
$529$	0	0
$530$	10.1009	0.438753
$531$	11.3835	0.494000
$532$	17.4372	0.755997
$533$	15.8904	0.688290
$534$	−6.41372	−0.277549
$535$	−4.28544	−0.185276
$536$	−21.4781	−0.927713
$537$	3.67740	0.158691
$538$	5.10666	0.220164
$539$	−2.30916	−0.0994627
$540$	−0.832828	−0.0358392
$541$	14.4495	0.621233	0.310617	−	0.950535i	$-0.399464\pi$
$541$	14.4495	0.621233	0.310617	+	0.950535i	$0.399464\pi$
$542$	23.4325	1.00651
$543$	−11.8608	−0.508998
$544$	19.1919	0.822848
$545$	2.96583	0.127042
$546$	−13.6611	−0.584639
$547$	−28.2358	−1.20728	−0.603639	−	0.797258i	$-0.706283\pi$
$547$	−28.2358	−1.20728	−0.603639	+	0.797258i	$0.706283\pi$
$548$	−2.52219	−0.107742
$549$	−12.0138	−0.512737
$550$	−3.34811	−0.142764
$551$	8.79595	0.374720
$552$	0	0
$553$	16.8601	0.716963
$554$	−10.0210	−0.425752
$555$	6.45154	0.273853
$556$	−8.19398	−0.347502
$557$	−4.08724	−0.173182	−0.0865910	−	0.996244i	$-0.527597\pi$
$557$	−4.08724	−0.173182	−0.0865910	+	0.996244i	$0.527597\pi$
$558$	6.07699	0.257260
$559$	58.8018	2.48705
$560$	−4.10346	−0.173403
$561$	−13.6781	−0.577492
$562$	2.43174	0.102577
$563$	−16.0327	−0.675697	−0.337848	−	0.941201i	$-0.609699\pi$
$563$	−16.0327	−0.675697	−0.337848	+	0.941201i	$0.609699\pi$
$564$	−7.18607	−0.302588
$565$	17.0982	0.719326
$566$	−11.5811	−0.486789
$567$	2.50098	0.105031
$568$	−19.1780	−0.804692
$569$	13.6709	0.573112	0.286556	−	0.958063i	$-0.407490\pi$
$569$	13.6709	0.573112	0.286556	+	0.958063i	$0.407490\pi$
$570$	9.04437	0.378827
$571$	−2.03500	−0.0851619	−0.0425810	−	0.999093i	$-0.513558\pi$
$571$	−2.03500	−0.0851619	−0.0425810	+	0.999093i	$0.513558\pi$
$572$	−13.0495	−0.545628
$573$	6.51802	0.272294
$574$	−8.49190	−0.354445
$575$	0	0
$576$	7.97925	0.332469
$577$	9.34661	0.389104	0.194552	−	0.980892i	$-0.437675\pi$
$577$	9.34661	0.389104	0.194552	+	0.980892i	$0.437675\pi$
$578$	−2.67932	−0.111445
$579$	−7.15270	−0.297256
$580$	0.875039	0.0363340
$581$	35.7084	1.48143
$582$	−12.5969	−0.522157
$583$	−28.9750	−1.20002
$584$	47.3297	1.95852
$585$	5.05600	0.209040
$586$	18.2114	0.752306
$587$	42.1764	1.74081	0.870403	−	0.492339i	$-0.163858\pi$
$587$	42.1764	1.74081	0.870403	+	0.492339i	$0.163858\pi$
$588$	0.620551	0.0255911
$589$	47.0904	1.94033
$590$	−12.2982	−0.506309
$591$	−2.86150	−0.117707
$592$	−10.5853	−0.435054
$593$	12.2241	0.501984	0.250992	−	0.967989i	$-0.419243\pi$
$593$	12.2241	0.501984	0.250992	+	0.967989i	$0.419243\pi$
$594$	−3.34811	−0.137375
$595$	−11.0384	−0.452529
$596$	13.4251	0.549914
$597$	−5.81290	−0.237906
$598$	0	0
$599$	−25.6961	−1.04991	−0.524957	−	0.851129i	$-0.675919\pi$
$599$	−25.6961	−1.04991	−0.524957	+	0.851129i	$0.675919\pi$
$600$	3.06047	0.124943
$601$	6.13585	0.250287	0.125143	−	0.992139i	$-0.460061\pi$
$601$	6.13585	0.250287	0.125143	+	0.992139i	$0.460061\pi$
$602$	−31.4239	−1.28074
$603$	−7.01792	−0.285792
$604$	4.25362	0.173077
$605$	−1.39572	−0.0567441
$606$	−4.49055	−0.182416
$607$	−6.22427	−0.252635	−0.126318	−	0.991990i	$-0.540316\pi$
$607$	−6.22427	−0.252635	−0.126318	+	0.991990i	$0.540316\pi$
$608$	36.4028	1.47633
$609$	−2.62774	−0.106481
$610$	12.9792	0.525513
$611$	43.6258	1.76491
$612$	3.67579	0.148585
$613$	29.2823	1.18270	0.591350	−	0.806415i	$-0.298595\pi$
$613$	29.2823	1.18270	0.591350	+	0.806415i	$0.298595\pi$
$614$	8.66191	0.349566
$615$	3.14288	0.126733
$616$	23.7208	0.955739
$617$	−17.6688	−0.711321	−0.355660	−	0.934615i	$-0.615744\pi$
$617$	−17.6688	−0.711321	−0.355660	+	0.934615i	$0.615744\pi$
$618$	−5.80586	−0.233546
$619$	−28.7800	−1.15677	−0.578384	−	0.815765i	$-0.696316\pi$
$619$	−28.7800	−1.15677	−0.578384	+	0.815765i	$0.696316\pi$
$620$	4.68464	0.188140
$621$	0	0
$622$	0.289662	0.0116144
$623$	14.8475	0.594851
$624$	−8.29559	−0.332089
$625$	1.00000	0.0400000
$626$	−2.94732	−0.117799
$627$	−25.9444	−1.03612
$628$	−5.34376	−0.213239
$629$	−28.4746	−1.13536
$630$	−2.70195	−0.107648
$631$	−11.6466	−0.463642	−0.231821	−	0.972758i	$-0.574468\pi$
$631$	−11.6466	−0.463642	−0.231821	+	0.972758i	$0.574468\pi$
$632$	20.6318	0.820689
$633$	14.7073	0.584563
$634$	−22.5301	−0.894786
$635$	0.164913	0.00654436
$636$	7.78657	0.308757
$637$	−3.76729	−0.149266
$638$	3.51781	0.139271
$639$	−6.26637	−0.247894
$640$	0.0762499	0.00301404
$641$	−19.8577	−0.784331	−0.392166	−	0.919895i	$-0.628274\pi$
$641$	−19.8577	−0.784331	−0.392166	+	0.919895i	$0.628274\pi$
$642$	4.62981	0.182724
$643$	13.5334	0.533705	0.266853	−	0.963737i	$-0.414016\pi$
$643$	13.5334	0.533705	0.266853	+	0.963737i	$0.414016\pi$
$644$	0	0
$645$	11.6301	0.457934
$646$	−39.9184	−1.57057
$647$	−5.75874	−0.226399	−0.113200	−	0.993572i	$-0.536110\pi$
$647$	−5.75874	−0.226399	−0.113200	+	0.993572i	$0.536110\pi$
$648$	3.06047	0.120226
$649$	35.2782	1.38479
$650$	−5.46229	−0.214249
$651$	−14.0680	−0.551367
$652$	12.4491	0.487546
$653$	−26.7082	−1.04517	−0.522586	−	0.852586i	$-0.675033\pi$
$653$	−26.7082	−1.04517	−0.522586	+	0.852586i	$0.675033\pi$
$654$	−3.20416	−0.125293
$655$	−11.6425	−0.454908
$656$	−5.15665	−0.201334
$657$	15.4649	0.603341
$658$	−23.3138	−0.908867
$659$	−0.749871	−0.0292108	−0.0146054	−	0.999893i	$-0.504649\pi$
$659$	−0.749871	−0.0292108	−0.0146054	+	0.999893i	$0.504649\pi$
$660$	−2.58100	−0.100465
$661$	1.89109	0.0735550	0.0367775	−	0.999323i	$-0.488291\pi$
$661$	1.89109	0.0735550	0.0367775	+	0.999323i	$0.488291\pi$
$662$	−8.38727	−0.325980
$663$	−22.3153	−0.866653
$664$	43.6966	1.69576
$665$	−20.9373	−0.811914
$666$	−6.96997	−0.270081
$667$	0	0
$668$	−5.40523	−0.209135
$669$	27.4144	1.05990
$670$	7.58186	0.292913
$671$	−37.2317	−1.43731
$672$	−10.8751	−0.419517
$673$	29.7313	1.14606	0.573029	−	0.819535i	$-0.305768\pi$
$673$	29.7313	1.14606	0.573029	+	0.819535i	$0.305768\pi$
$674$	13.6233	0.524749
$675$	1.00000	0.0384900
$676$	−10.4629	−0.402421
$677$	−3.75385	−0.144272	−0.0721361	−	0.997395i	$-0.522982\pi$
$677$	−3.75385	−0.144272	−0.0721361	+	0.997395i	$0.522982\pi$
$678$	−18.4721	−0.709418
$679$	29.1612	1.11910
$680$	−13.5077	−0.517998
$681$	−3.20691	−0.122889
$682$	18.8331	0.721155
$683$	46.6404	1.78465	0.892323	−	0.451398i	$-0.149074\pi$
$683$	46.6404	1.78465	0.892323	+	0.451398i	$0.149074\pi$
$684$	6.97214	0.266587
$685$	3.02846	0.115712
$686$	20.9269	0.798993
$687$	−9.14163	−0.348775
$688$	−19.0820	−0.727494
$689$	−47.2713	−1.80089
$690$	0	0
$691$	−39.2320	−1.49245	−0.746227	−	0.665692i	$-0.768137\pi$
$691$	−39.2320	−1.49245	−0.746227	+	0.665692i	$0.768137\pi$
$692$	−5.20045	−0.197692
$693$	7.75072	0.294426
$694$	−31.5303	−1.19687
$695$	9.83875	0.373205
$696$	−3.21558	−0.121886
$697$	−13.8715	−0.525420
$698$	1.04218	0.0394470
$699$	7.54366	0.285327
$700$	−2.08288	−0.0787256
$701$	6.57424	0.248306	0.124153	−	0.992263i	$-0.460379\pi$
$701$	6.57424	0.248306	0.124153	+	0.992263i	$0.460379\pi$
$702$	−5.46229	−0.206161
$703$	−54.0100	−2.03703
$704$	24.7283	0.931983
$705$	8.62851	0.324969
$706$	−24.9689	−0.939716
$707$	10.3954	0.390959
$708$	−9.48047	−0.356298
$709$	−11.7329	−0.440638	−0.220319	−	0.975428i	$-0.570710\pi$
$709$	−11.7329	−0.440638	−0.220319	+	0.975428i	$0.570710\pi$
$710$	6.76992	0.254071
$711$	6.74139	0.252822
$712$	18.1690	0.680911
$713$	0	0
$714$	11.9254	0.446296
$715$	15.6689	0.585985
$716$	−3.06264	−0.114456
$717$	10.7392	0.401063
$718$	−8.63609	−0.322296
$719$	10.3636	0.386498	0.193249	−	0.981150i	$-0.438097\pi$
$719$	10.3636	0.386498	0.193249	+	0.981150i	$0.438097\pi$
$720$	−1.64074	−0.0611468
$721$	13.4403	0.500543
$722$	−55.1895	−2.05394
$723$	3.41230	0.126905
$724$	9.87804	0.367115
$725$	−1.05068	−0.0390214
$726$	1.50788	0.0559626
$727$	−34.1589	−1.26688	−0.633442	−	0.773790i	$-0.718359\pi$
$727$	−34.1589	−1.26688	−0.633442	+	0.773790i	$0.718359\pi$
$728$	38.6994	1.43430
$729$	1.00000	0.0370370
$730$	−16.7076	−0.618375
$731$	−51.3308	−1.89854
$732$	10.0054	0.369812
$733$	−12.9923	−0.479882	−0.239941	−	0.970787i	$-0.577128\pi$
$733$	−12.9923	−0.479882	−0.239941	+	0.970787i	$0.577128\pi$
$734$	−16.8288	−0.621164
$735$	−0.745113	−0.0274839
$736$	0	0
$737$	−21.7491	−0.801137
$738$	−3.39543	−0.124988
$739$	−23.6637	−0.870484	−0.435242	−	0.900314i	$-0.643337\pi$
$739$	−23.6637	−0.870484	−0.435242	+	0.900314i	$0.643337\pi$
$740$	−5.37302	−0.197516
$741$	−42.3271	−1.55492
$742$	25.2620	0.927397
$743$	6.83604	0.250790	0.125395	−	0.992107i	$-0.459980\pi$
$743$	6.83604	0.250790	0.125395	+	0.992107i	$0.459980\pi$
$744$	−17.2151	−0.631135
$745$	−16.1199	−0.590588
$746$	10.2617	0.375709
$747$	14.2778	0.522396
$748$	11.3915	0.416516
$749$	−10.7178	−0.391620
$750$	−1.08036	−0.0394491
$751$	37.0810	1.35310	0.676552	−	0.736394i	$-0.263473\pi$
$751$	37.0810	1.35310	0.676552	+	0.736394i	$0.263473\pi$
$752$	−14.1572	−0.516258
$753$	−26.0111	−0.947899
$754$	5.73914	0.209007
$755$	−5.10744	−0.185879
$756$	−2.08288	−0.0757538
$757$	−41.9753	−1.52562	−0.762809	−	0.646624i	$-0.776180\pi$
$757$	−41.9753	−1.52562	−0.762809	+	0.646624i	$0.776180\pi$
$758$	34.0835	1.23797
$759$	0	0
$760$	−25.6212	−0.929377
$761$	18.7013	0.677921	0.338960	−	0.940801i	$-0.389925\pi$
$761$	18.7013	0.677921	0.338960	+	0.940801i	$0.389925\pi$
$762$	−0.178165	−0.00645423
$763$	7.41748	0.268531
$764$	−5.42839	−0.196392
$765$	−4.41362	−0.159575
$766$	21.2402	0.767439
$767$	57.5548	2.07818
$768$	−16.0409	−0.578825
$769$	−49.7505	−1.79405	−0.897024	−	0.441982i	$-0.854276\pi$
$769$	−49.7505	−1.79405	−0.897024	+	0.441982i	$0.854276\pi$
$770$	−8.37355	−0.301762
$771$	17.5574	0.632313
$772$	5.95697	0.214396
$773$	4.96532	0.178590	0.0892951	−	0.996005i	$-0.471539\pi$
$773$	4.96532	0.178590	0.0892951	+	0.996005i	$0.471539\pi$
$774$	−12.5647	−0.451627
$775$	−5.62498	−0.202055
$776$	35.6848	1.28101
$777$	16.1352	0.578846
$778$	−16.0349	−0.574879
$779$	−26.3111	−0.942693
$780$	−4.21078	−0.150770
$781$	−19.4200	−0.694901
$782$	0	0
$783$	−1.05068	−0.0375484
$784$	1.22254	0.0436621
$785$	6.41640	0.229011
$786$	12.5780	0.448643
$787$	1.34048	0.0477830	0.0238915	−	0.999715i	$-0.492394\pi$
$787$	1.34048	0.0477830	0.0238915	+	0.999715i	$0.492394\pi$
$788$	2.38314	0.0848959
$789$	20.8332	0.741682
$790$	−7.28311	−0.259122
$791$	42.7622	1.52045
$792$	9.48462	0.337021
$793$	−60.7418	−2.15701
$794$	5.69780	0.202207
$795$	−9.34955	−0.331594
$796$	4.84115	0.171590
$797$	−5.42680	−0.192227	−0.0961135	−	0.995370i	$-0.530641\pi$
$797$	−5.42680	−0.192227	−0.0961135	+	0.995370i	$0.530641\pi$
$798$	22.6198	0.800731
$799$	−38.0830	−1.34728
$800$	−4.34835	−0.153737
$801$	5.93666	0.209762
$802$	7.79855	0.275376
$803$	47.9268	1.69130
$804$	5.84472	0.206127
$805$	0	0
$806$	30.7253	1.08225
$807$	−4.72683	−0.166392
$808$	12.7209	0.447521
$809$	1.40730	0.0494781	0.0247391	−	0.999694i	$-0.492125\pi$
$809$	1.40730	0.0494781	0.0247391	+	0.999694i	$0.492125\pi$
$810$	−1.08036	−0.0379599
$811$	24.1912	0.849466	0.424733	−	0.905319i	$-0.360368\pi$
$811$	24.1912	0.849466	0.424733	+	0.905319i	$0.360368\pi$
$812$	2.18845	0.0767996
$813$	−21.6896	−0.760688
$814$	−21.6005	−0.757096
$815$	−14.9480	−0.523607
$816$	7.24161	0.253507
$817$	−97.3631	−3.40630
$818$	10.1799	0.355931
$819$	12.6449	0.441850
$820$	−2.61748	−0.0914063
$821$	4.73150	0.165131	0.0825653	−	0.996586i	$-0.473689\pi$
$821$	4.73150	0.165131	0.0825653	+	0.996586i	$0.473689\pi$
$822$	−3.27182	−0.114118
$823$	−0.537068	−0.0187210	−0.00936052	−	0.999956i	$-0.502980\pi$
$823$	−0.537068	−0.0187210	−0.00936052	+	0.999956i	$0.502980\pi$
$824$	16.4470	0.572959
$825$	3.09908	0.107896
$826$	−30.7575	−1.07019
$827$	17.4962	0.608401	0.304200	−	0.952608i	$-0.401611\pi$
$827$	17.4962	0.608401	0.304200	+	0.952608i	$0.401611\pi$
$828$	0	0
$829$	10.9294	0.379594	0.189797	−	0.981823i	$-0.439217\pi$
$829$	10.9294	0.379594	0.189797	+	0.981823i	$0.439217\pi$
$830$	−15.4251	−0.535413
$831$	9.27565	0.321769
$832$	40.3431	1.39865
$833$	3.28865	0.113945
$834$	−10.6294	−0.368065
$835$	6.49021	0.224603
$836$	21.6072	0.747301
$837$	−5.62498	−0.194428
$838$	23.4062	0.808553
$839$	26.9960	0.932007	0.466003	−	0.884783i	$-0.345693\pi$
$839$	26.9960	0.932007	0.466003	+	0.884783i	$0.345693\pi$
$840$	7.65416	0.264094
$841$	−27.8961	−0.961933
$842$	−24.2029	−0.834087
$843$	−2.25086	−0.0775238
$844$	−12.2487	−0.421616
$845$	12.5631	0.432185
$846$	−9.32188	−0.320493
$847$	−3.49067	−0.119941
$848$	15.3402	0.526784
$849$	10.7197	0.367898
$850$	4.76829	0.163551
$851$	0	0
$852$	5.21881	0.178793
$853$	−27.9913	−0.958403	−0.479201	−	0.877705i	$-0.659074\pi$
$853$	−27.9913	−0.958403	−0.479201	+	0.877705i	$0.659074\pi$
$854$	32.4607	1.11078
$855$	−8.37165	−0.286304
$856$	−13.1155	−0.448277
$857$	−26.6611	−0.910726	−0.455363	−	0.890306i	$-0.650490\pi$
$857$	−26.6611	−0.910726	−0.455363	+	0.890306i	$0.650490\pi$
$858$	−16.9280	−0.577914
$859$	−8.09971	−0.276358	−0.138179	−	0.990407i	$-0.544125\pi$
$859$	−8.09971	−0.276358	−0.138179	+	0.990407i	$0.544125\pi$
$860$	−9.68587	−0.330285
$861$	7.86027	0.267877
$862$	4.22469	0.143894
$863$	−19.1373	−0.651443	−0.325721	−	0.945466i	$-0.605607\pi$
$863$	−19.1373	−0.651443	−0.325721	+	0.945466i	$0.605607\pi$
$864$	−4.34835	−0.147934
$865$	6.24433	0.212314
$866$	−4.31495	−0.146628
$867$	2.48003	0.0842264
$868$	11.7162	0.397673
$869$	20.8921	0.708716
$870$	1.13511	0.0384840
$871$	−35.4826	−1.20228
$872$	9.07683	0.307380
$873$	11.6599	0.394628
$874$	0	0
$875$	2.50098	0.0845485
$876$	−12.8796	−0.435160
$877$	−15.0875	−0.509468	−0.254734	−	0.967011i	$-0.581988\pi$
$877$	−15.0875	−0.509468	−0.254734	+	0.967011i	$0.581988\pi$
$878$	31.1590	1.05156
$879$	−16.8568	−0.568567
$880$	−5.08478	−0.171408
$881$	−32.4938	−1.09474	−0.547372	−	0.836890i	$-0.684372\pi$
$881$	−32.4938	−1.09474	−0.547372	+	0.836890i	$0.684372\pi$
$882$	0.804988	0.0271054
$883$	−6.16160	−0.207354	−0.103677	−	0.994611i	$-0.533061\pi$
$883$	−6.16160	−0.207354	−0.103677	+	0.994611i	$0.533061\pi$
$884$	18.5848	0.625074
$885$	11.3835	0.382651
$886$	−36.6210	−1.23031
$887$	4.20145	0.141071	0.0705355	−	0.997509i	$-0.477529\pi$
$887$	4.20145	0.141071	0.0705355	+	0.997509i	$0.477529\pi$
$888$	19.7447	0.662590
$889$	0.412443	0.0138329
$890$	−6.41372	−0.214988
$891$	3.09908	0.103823
$892$	−22.8315	−0.764454
$893$	−72.2349	−2.41725
$894$	17.4153	0.582454
$895$	3.67740	0.122922
$896$	0.190699	0.00637081
$897$	0	0
$898$	−35.6730	−1.19042
$899$	5.91008	0.197112
$900$	−0.832828	−0.0277609
$901$	41.2653	1.37475
$902$	−10.5227	−0.350368
$903$	29.0866	0.967941
$904$	52.3284	1.74042
$905$	−11.8608	−0.394268
$906$	5.51786	0.183319
$907$	9.59705	0.318665	0.159332	−	0.987225i	$-0.449066\pi$
$907$	9.59705	0.318665	0.159332	+	0.987225i	$0.449066\pi$
$908$	2.67081	0.0886338
$909$	4.15654	0.137864
$910$	−13.6611	−0.452860
$911$	5.13714	0.170201	0.0851005	−	0.996372i	$-0.472879\pi$
$911$	5.13714	0.170201	0.0851005	+	0.996372i	$0.472879\pi$
$912$	13.7357	0.454835
$913$	44.2479	1.46439
$914$	30.2140	0.999391
$915$	−12.0138	−0.397164
$916$	7.61340	0.251554
$917$	−29.1175	−0.961545
$918$	4.76829	0.157377
$919$	−36.9375	−1.21846	−0.609228	−	0.792995i	$-0.708521\pi$
$919$	−36.9375	−1.21846	−0.609228	+	0.792995i	$0.708521\pi$
$920$	0	0
$921$	−8.01764	−0.264190
$922$	−36.1031	−1.18899
$923$	−31.6828	−1.04285
$924$	−6.45502	−0.212354
$925$	6.45154	0.212125
$926$	−18.0018	−0.591576
$927$	5.37402	0.176506
$928$	4.56874	0.149976
$929$	11.6066	0.380800	0.190400	−	0.981707i	$-0.439022\pi$
$929$	11.6066	0.380800	0.190400	+	0.981707i	$0.439022\pi$
$930$	6.07699	0.199272
$931$	6.23782	0.204436
$932$	−6.28257	−0.205792
$933$	−0.268117	−0.00877775
$934$	16.7727	0.548818
$935$	−13.6781	−0.447323
$936$	15.4737	0.505774
$937$	26.1152	0.853146	0.426573	−	0.904453i	$-0.359721\pi$
$937$	26.1152	0.853146	0.426573	+	0.904453i	$0.359721\pi$
$938$	18.9621	0.619133
$939$	2.72810	0.0890281
$940$	−7.18607	−0.234384
$941$	50.9626	1.66133	0.830667	−	0.556770i	$-0.187960\pi$
$941$	50.9626	1.66133	0.830667	+	0.556770i	$0.187960\pi$
$942$	−6.93200	−0.225857
$943$	0	0
$944$	−18.6773	−0.607895
$945$	2.50098	0.0813568
$946$	−38.9388	−1.26601
$947$	40.7038	1.32269	0.661347	−	0.750080i	$-0.269985\pi$
$947$	40.7038	1.32269	0.661347	+	0.750080i	$0.269985\pi$
$948$	−5.61442	−0.182348
$949$	78.1903	2.53816
$950$	9.04437	0.293438
$951$	20.8543	0.676248
$952$	−33.7825	−1.09490
$953$	−2.61359	−0.0846626	−0.0423313	−	0.999104i	$-0.513479\pi$
$953$	−2.61359	−0.0846626	−0.0423313	+	0.999104i	$0.513479\pi$
$954$	10.1009	0.327027
$955$	6.51802	0.210918
$956$	−8.94390	−0.289266
$957$	−3.25615	−0.105256
$958$	−34.0864	−1.10128
$959$	7.57411	0.244581
$960$	7.97925	0.257529
$961$	0.640424	0.0206588
$962$	−35.2402	−1.13619
$963$	−4.28544	−0.138096
$964$	−2.84186	−0.0915300
$965$	−7.15270	−0.230253
$966$	0	0
$967$	−18.2175	−0.585834	−0.292917	−	0.956138i	$-0.594626\pi$
$967$	−18.2175	−0.585834	−0.292917	+	0.956138i	$0.594626\pi$
$968$	−4.27156	−0.137293
$969$	36.9493	1.18698
$970$	−12.5969	−0.404461
$971$	16.5227	0.530239	0.265120	−	0.964216i	$-0.414589\pi$
$971$	16.5227	0.530239	0.265120	+	0.964216i	$0.414589\pi$
$972$	−0.832828	−0.0267130
$973$	24.6065	0.788848
$974$	30.9578	0.991951
$975$	5.05600	0.161922
$976$	19.7116	0.630952
$977$	−31.5625	−1.00977	−0.504887	−	0.863186i	$-0.668466\pi$
$977$	−31.5625	−1.00977	−0.504887	+	0.863186i	$0.668466\pi$
$978$	16.1492	0.516395
$979$	18.3982	0.588008
$980$	0.620551	0.0198228
$981$	2.96583	0.0946918
$982$	−11.4179	−0.364359
$983$	15.1549	0.483366	0.241683	−	0.970355i	$-0.422301\pi$
$983$	15.1549	0.483366	0.241683	+	0.970355i	$0.422301\pi$
$984$	9.61868	0.306632
$985$	−2.86150	−0.0911751
$986$	−5.00996	−0.159550
$987$	21.5797	0.686890
$988$	35.2512	1.12149
$989$	0	0
$990$	−3.34811	−0.106410
$991$	25.8354	0.820687	0.410343	−	0.911931i	$-0.365409\pi$
$991$	25.8354	0.820687	0.410343	+	0.911931i	$0.365409\pi$
$992$	24.4594	0.776586
$993$	7.76342	0.246365
$994$	16.9314	0.537032
$995$	−5.81290	−0.184281
$996$	−11.8909	−0.376778
$997$	56.8799	1.80140	0.900702	−	0.434438i	$-0.143053\pi$
$997$	56.8799	1.80140	0.900702	+	0.434438i	$0.143053\pi$
$998$	37.4376	1.18507
$999$	6.45154	0.204118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bw.1.8		25
23.17	odd	22		345.2.m.c.151.4	yes	50
23.19	odd	22		345.2.m.c.16.4	✓	50
23.22	odd	2		7935.2.a.bv.1.8		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.4	✓	50	23.19	odd	22
345.2.m.c.151.4	yes	50	23.17	odd	22
7935.2.a.bv.1.8		25	23.22	odd	2
7935.2.a.bw.1.8		25	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.08036 q^{2} +1.00000 q^{3} -0.832828 q^{4} +1.00000 q^{5} -1.08036 q^{6} +2.50098 q^{7} +3.06047 q^{8} +1.00000 q^{9} -1.08036 q^{10} +3.09908 q^{11} -0.832828 q^{12} +5.05600 q^{13} -2.70195 q^{14} +1.00000 q^{15} -1.64074 q^{16} -4.41362 q^{17} -1.08036 q^{18} -8.37165 q^{19} -0.832828 q^{20} +2.50098 q^{21} -3.34811 q^{22} +3.06047 q^{24} +1.00000 q^{25} -5.46229 q^{26} +1.00000 q^{27} -2.08288 q^{28} -1.05068 q^{29} -1.08036 q^{30} -5.62498 q^{31} -4.34835 q^{32} +3.09908 q^{33} +4.76829 q^{34} +2.50098 q^{35} -0.832828 q^{36} +6.45154 q^{37} +9.04437 q^{38} +5.05600 q^{39} +3.06047 q^{40} +3.14288 q^{41} -2.70195 q^{42} +11.6301 q^{43} -2.58100 q^{44} +1.00000 q^{45} +8.62851 q^{47} -1.64074 q^{48} -0.745113 q^{49} -1.08036 q^{50} -4.41362 q^{51} -4.21078 q^{52} -9.34955 q^{53} -1.08036 q^{54} +3.09908 q^{55} +7.65416 q^{56} -8.37165 q^{57} +1.13511 q^{58} +11.3835 q^{59} -0.832828 q^{60} -12.0138 q^{61} +6.07699 q^{62} +2.50098 q^{63} +7.97925 q^{64} +5.05600 q^{65} -3.34811 q^{66} -7.01792 q^{67} +3.67579 q^{68} -2.70195 q^{70} -6.26637 q^{71} +3.06047 q^{72} +15.4649 q^{73} -6.96997 q^{74} +1.00000 q^{75} +6.97214 q^{76} +7.75072 q^{77} -5.46229 q^{78} +6.74139 q^{79} -1.64074 q^{80} +1.00000 q^{81} -3.39543 q^{82} +14.2778 q^{83} -2.08288 q^{84} -4.41362 q^{85} -12.5647 q^{86} -1.05068 q^{87} +9.48462 q^{88} +5.93666 q^{89} -1.08036 q^{90} +12.6449 q^{91} -5.62498 q^{93} -9.32188 q^{94} -8.37165 q^{95} -4.34835 q^{96} +11.6599 q^{97} +0.804988 q^{98} +3.09908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} + 25 q^{5} + 11 q^{6} + 7 q^{7} + 33 q^{8} + 25 q^{9} + 11 q^{10} + 9 q^{11} + 31 q^{12} + 18 q^{13} + 11 q^{14} + 25 q^{15} + 39 q^{16} - 8 q^{17} + 11 q^{18} + 11 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 + 25 * q^5 + 11 * q^6 + 7 * q^7 + 33 * q^8 + 25 * q^9 + 11 * q^10 + 9 * q^11 + 31 * q^12 + 18 * q^13 + 11 * q^14 + 25 * q^15 + 39 * q^16 - 8 * q^17 + 11 * q^18 + 11 * q^19 + 31 * q^20 + 7 * q^21 + 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 - 5 * q^28 + 33 * q^29 + 11 * q^30 + 14 * q^31 + 77 * q^32 + 9 * q^33 + 13 * q^34 + 7 * q^35 + 31 * q^36 + 4 * q^37 - 23 * q^38 + 18 * q^39 + 33 * q^40 + 56 * q^41 + 11 * q^42 - 4 * q^43 - 18 * q^44 + 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 - 8 * q^51 + 49 * q^52 + 2 * q^53 + 11 * q^54 + 9 * q^55 + 33 * q^56 + 11 * q^57 + 26 * q^58 + 61 * q^59 + 31 * q^60 + 21 * q^61 + 51 * q^62 + 7 * q^63 + 71 * q^64 + 18 * q^65 + 9 * q^66 + 2 * q^67 - 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 - 47 * q^74 + 25 * q^75 - 8 * q^76 + 49 * q^77 + 35 * q^78 + 35 * q^79 + 39 * q^80 + 25 * q^81 + 35 * q^82 - 26 * q^83 - 5 * q^84 - 8 * q^85 - 33 * q^86 + 33 * q^87 + 9 * q^88 - 7 * q^89 + 11 * q^90 + 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 - 54 * q^97 + 88 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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