LMFDB - Embedded newform 6025.2.a.k.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.410249 q^{2} +0.0956416 q^{3} -1.83170 q^{4} +0.0392369 q^{6} +2.86768 q^{7} -1.57195 q^{8} -2.99085 q^{9} +O(q^{10})$	\(q+0.410249 q^{2} +0.0956416 q^{3} -1.83170 q^{4} +0.0392369 q^{6} +2.86768 q^{7} -1.57195 q^{8} -2.99085 q^{9} -3.49164 q^{11} -0.175186 q^{12} -5.64568 q^{13} +1.17646 q^{14} +3.01850 q^{16} +4.62135 q^{17} -1.22699 q^{18} -0.926962 q^{19} +0.274269 q^{21} -1.43244 q^{22} +4.23292 q^{23} -0.150344 q^{24} -2.31613 q^{26} -0.572975 q^{27} -5.25272 q^{28} -5.97466 q^{29} +4.15677 q^{31} +4.38224 q^{32} -0.333946 q^{33} +1.89591 q^{34} +5.47833 q^{36} -6.57325 q^{37} -0.380285 q^{38} -0.539961 q^{39} +5.53158 q^{41} +0.112519 q^{42} -11.2505 q^{43} +6.39562 q^{44} +1.73655 q^{46} -10.4496 q^{47} +0.288694 q^{48} +1.22358 q^{49} +0.441993 q^{51} +10.3412 q^{52} +1.42576 q^{53} -0.235062 q^{54} -4.50785 q^{56} -0.0886561 q^{57} -2.45110 q^{58} +6.67323 q^{59} -4.08418 q^{61} +1.70531 q^{62} -8.57681 q^{63} -4.23919 q^{64} -0.137001 q^{66} +10.1991 q^{67} -8.46491 q^{68} +0.404844 q^{69} +6.09650 q^{71} +4.70147 q^{72} +14.6125 q^{73} -2.69667 q^{74} +1.69791 q^{76} -10.0129 q^{77} -0.221519 q^{78} +14.6628 q^{79} +8.91776 q^{81} +2.26933 q^{82} -6.91913 q^{83} -0.502378 q^{84} -4.61549 q^{86} -0.571426 q^{87} +5.48868 q^{88} +1.90236 q^{89} -16.1900 q^{91} -7.75343 q^{92} +0.397560 q^{93} -4.28693 q^{94} +0.419124 q^{96} +9.02466 q^{97} +0.501973 q^{98} +10.4430 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9	$ 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) $ 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9 + 10 * q^11 - 22 * q^12 - 10 * q^13 + 13 * q^14 + 54 * q^16 - q^17 + 13 * q^18 + 50 * q^19 + 9 * q^21 - 11 * q^22 + 31 * q^23 + 22 * q^24 + 8 * q^26 - 42 * q^27 - 14 * q^28 + 4 * q^29 + 34 * q^31 + 44 * q^32 - 28 * q^33 + 33 * q^34 + 83 * q^36 - 14 * q^37 + 10 * q^38 + 23 * q^39 + 11 * q^41 - 23 * q^42 - 49 * q^43 + 20 * q^44 + 27 * q^46 + 28 * q^47 - 30 * q^48 + 66 * q^49 + 49 * q^51 - 39 * q^52 + 16 * q^53 + 5 * q^54 + 51 * q^56 - 10 * q^57 + 8 * q^58 + 30 * q^59 + 35 * q^61 + 18 * q^62 + 73 * q^64 - 13 * q^66 - 37 * q^67 - 11 * q^68 - 4 * q^69 + 12 * q^71 + 90 * q^72 - 36 * q^73 - 12 * q^74 + 57 * q^76 + 31 * q^77 + 9 * q^78 + 16 * q^79 + 65 * q^81 + 11 * q^82 - 43 * q^83 - 62 * q^84 - 9 * q^86 + 22 * q^87 - 20 * q^88 + 38 * q^89 + 86 * q^91 + 119 * q^92 - 10 * q^93 - 18 * q^94 - 34 * q^96 - 17 * q^97 + 32 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.410249	0.290090	0.145045	−	0.989425i	$-0.453667\pi$
$2$	0.410249	0.290090	0.145045	+	0.989425i	$0.453667\pi$
$3$	0.0956416	0.0552187	0.0276093	−	0.999619i	$-0.491211\pi$
$3$	0.0956416	0.0552187	0.0276093	+	0.999619i	$0.491211\pi$
$4$	−1.83170	−0.915848
$5$	0	0
$5$	0	0
$6$	0.0392369	0.0160184
$7$	2.86768	1.08388	0.541940	−	0.840417i	$-0.317690\pi$
$7$	2.86768	1.08388	0.541940	+	0.840417i	$0.317690\pi$
$8$	−1.57195	−0.555768
$9$	−2.99085	−0.996951
$10$	0	0
$11$	−3.49164	−1.05277	−0.526385	−	0.850247i	$-0.676453\pi$
$11$	−3.49164	−1.05277	−0.526385	+	0.850247i	$0.676453\pi$
$12$	−0.175186	−0.0505719
$13$	−5.64568	−1.56583	−0.782914	−	0.622129i	$-0.786268\pi$
$13$	−5.64568	−1.56583	−0.782914	+	0.622129i	$0.786268\pi$
$14$	1.17646	0.314423
$15$	0	0
$16$	3.01850	0.754625
$17$	4.62135	1.12084	0.560421	−	0.828208i	$-0.310639\pi$
$17$	4.62135	1.12084	0.560421	+	0.828208i	$0.310639\pi$
$18$	−1.22699	−0.289205
$19$	−0.926962	−0.212660	−0.106330	−	0.994331i	$-0.533910\pi$
$19$	−0.926962	−0.212660	−0.106330	+	0.994331i	$0.533910\pi$
$20$	0	0
$21$	0.274269	0.0598505
$22$	−1.43244	−0.305398
$23$	4.23292	0.882626	0.441313	−	0.897353i	$-0.354513\pi$
$23$	4.23292	0.882626	0.441313	+	0.897353i	$0.354513\pi$
$24$	−0.150344	−0.0306888
$25$	0	0
$26$	−2.31613	−0.454231
$27$	−0.572975	−0.110269
$28$	−5.25272	−0.992670
$29$	−5.97466	−1.10947	−0.554733	−	0.832028i	$-0.687180\pi$
$29$	−5.97466	−1.10947	−0.554733	+	0.832028i	$0.687180\pi$
$30$	0	0
$31$	4.15677	0.746578	0.373289	−	0.927715i	$-0.378230\pi$
$31$	4.15677	0.746578	0.373289	+	0.927715i	$0.378230\pi$
$32$	4.38224	0.774677
$33$	−0.333946	−0.0581325
$34$	1.89591	0.325145
$35$	0	0
$36$	5.47833	0.913055
$37$	−6.57325	−1.08064	−0.540318	−	0.841461i	$-0.681696\pi$
$37$	−6.57325	−1.08064	−0.540318	+	0.841461i	$0.681696\pi$
$38$	−0.380285	−0.0616904
$39$	−0.539961	−0.0864630
$40$	0	0
$41$	5.53158	0.863888	0.431944	−	0.901901i	$-0.357828\pi$
$41$	5.53158	0.863888	0.431944	+	0.901901i	$0.357828\pi$
$42$	0.112519	0.0173620
$43$	−11.2505	−1.71568	−0.857839	−	0.513919i	$-0.828193\pi$
$43$	−11.2505	−1.71568	−0.857839	+	0.513919i	$0.828193\pi$
$44$	6.39562	0.964177
$45$	0	0
$46$	1.73655	0.256041
$47$	−10.4496	−1.52423	−0.762113	−	0.647444i	$-0.775838\pi$
$47$	−10.4496	−1.52423	−0.762113	+	0.647444i	$0.775838\pi$
$48$	0.288694	0.0416694
$49$	1.22358	0.174797
$50$	0	0
$51$	0.441993	0.0618915
$52$	10.3412	1.43406
$53$	1.42576	0.195843	0.0979216	−	0.995194i	$-0.468781\pi$
$53$	1.42576	0.195843	0.0979216	+	0.995194i	$0.468781\pi$
$54$	−0.235062	−0.0319879
$55$	0	0
$56$	−4.50785	−0.602386
$57$	−0.0886561	−0.0117428
$58$	−2.45110	−0.321845
$59$	6.67323	0.868781	0.434391	−	0.900725i	$-0.356964\pi$
$59$	6.67323	0.868781	0.434391	+	0.900725i	$0.356964\pi$
$60$	0	0
$61$	−4.08418	−0.522925	−0.261463	−	0.965214i	$-0.584205\pi$
$61$	−4.08418	−0.522925	−0.261463	+	0.965214i	$0.584205\pi$
$62$	1.70531	0.216575
$63$	−8.57681	−1.08058
$64$	−4.23919	−0.529899
$65$	0	0
$66$	−0.137001	−0.0168637
$67$	10.1991	1.24602	0.623012	−	0.782213i	$-0.285909\pi$
$67$	10.1991	1.24602	0.623012	+	0.782213i	$0.285909\pi$
$68$	−8.46491	−1.02652
$69$	0.404844	0.0487374
$70$	0	0
$71$	6.09650	0.723522	0.361761	−	0.932271i	$-0.382176\pi$
$71$	6.09650	0.723522	0.361761	+	0.932271i	$0.382176\pi$
$72$	4.70147	0.554073
$73$	14.6125	1.71027	0.855134	−	0.518407i	$-0.173475\pi$
$73$	14.6125	1.71027	0.855134	+	0.518407i	$0.173475\pi$
$74$	−2.69667	−0.313482
$75$	0	0
$76$	1.69791	0.194764
$77$	−10.0129	−1.14108
$78$	−0.221519	−0.0250820
$79$	14.6628	1.64969	0.824844	−	0.565360i	$-0.191263\pi$
$79$	14.6628	1.64969	0.824844	+	0.565360i	$0.191263\pi$
$80$	0	0
$81$	8.91776	0.990862
$82$	2.26933	0.250605
$83$	−6.91913	−0.759473	−0.379736	−	0.925095i	$-0.623985\pi$
$83$	−6.91913	−0.759473	−0.379736	+	0.925095i	$0.623985\pi$
$84$	−0.502378	−0.0548139
$85$	0	0
$86$	−4.61549	−0.497701
$87$	−0.571426	−0.0612633
$88$	5.48868	0.585096
$89$	1.90236	0.201650	0.100825	−	0.994904i	$-0.467852\pi$
$89$	1.90236	0.201650	0.100825	+	0.994904i	$0.467852\pi$
$90$	0	0
$91$	−16.1900	−1.69717
$92$	−7.75343	−0.808351
$93$	0.397560	0.0412251
$94$	−4.28693	−0.442163
$95$	0	0
$96$	0.419124	0.0427767
$97$	9.02466	0.916315	0.458158	−	0.888871i	$-0.348509\pi$
$97$	9.02466	0.916315	0.458158	+	0.888871i	$0.348509\pi$
$98$	0.501973	0.0507070
$99$	10.4430	1.04956
$100$	0	0
$101$	−7.24075	−0.720481	−0.360241	−	0.932859i	$-0.617305\pi$
$101$	−7.24075	−0.720481	−0.360241	+	0.932859i	$0.617305\pi$
$102$	0.181327	0.0179541
$103$	−12.9407	−1.27509	−0.637543	−	0.770415i	$-0.720049\pi$
$103$	−12.9407	−1.27509	−0.637543	+	0.770415i	$0.720049\pi$
$104$	8.87472	0.870238
$105$	0	0
$106$	0.584917	0.0568121
$107$	8.80643	0.851350	0.425675	−	0.904876i	$-0.360037\pi$
$107$	8.80643	0.851350	0.425675	+	0.904876i	$0.360037\pi$
$108$	1.04952	0.100990
$109$	13.6029	1.30292	0.651461	−	0.758682i	$-0.274156\pi$
$109$	13.6029	1.30292	0.651461	+	0.758682i	$0.274156\pi$
$110$	0	0
$111$	−0.628676	−0.0596713
$112$	8.65609	0.817924
$113$	4.35845	0.410008	0.205004	−	0.978761i	$-0.434279\pi$
$113$	4.35845	0.410008	0.205004	+	0.978761i	$0.434279\pi$
$114$	−0.0363711	−0.00340646
$115$	0	0
$116$	10.9438	1.01610
$117$	16.8854	1.56105
$118$	2.73769	0.252025
$119$	13.2526	1.21486
$120$	0	0
$121$	1.19156	0.108323
$122$	−1.67553	−0.151695
$123$	0.529049	0.0477027
$124$	−7.61394	−0.683752
$125$	0	0
$126$	−3.51863	−0.313464
$127$	0.124520	0.0110494	0.00552468	−	0.999985i	$-0.498241\pi$
$127$	0.124520	0.0110494	0.00552468	+	0.999985i	$0.498241\pi$
$128$	−10.5036	−0.928396
$129$	−1.07601	−0.0947375
$130$	0	0
$131$	−8.37090	−0.731369	−0.365684	−	0.930739i	$-0.619165\pi$
$131$	−8.37090	−0.731369	−0.365684	+	0.930739i	$0.619165\pi$
$132$	0.611687	0.0532406
$133$	−2.65823	−0.230498
$134$	4.18419	0.361459
$135$	0	0
$136$	−7.26453	−0.622929
$137$	−19.5551	−1.67070	−0.835351	−	0.549717i	$-0.814735\pi$
$137$	−19.5551	−1.67070	−0.835351	+	0.549717i	$0.814735\pi$
$138$	0.166087	0.0141382
$139$	11.7294	0.994877	0.497439	−	0.867499i	$-0.334274\pi$
$139$	11.7294	0.994877	0.497439	+	0.867499i	$0.334274\pi$
$140$	0	0
$141$	−0.999413	−0.0841658
$142$	2.50108	0.209886
$143$	19.7127	1.64846
$144$	−9.02789	−0.752324
$145$	0	0
$146$	5.99478	0.496131
$147$	0.117025	0.00965208
$148$	12.0402	0.989698
$149$	6.57271	0.538457	0.269228	−	0.963076i	$-0.413231\pi$
$149$	6.57271	0.538457	0.269228	+	0.963076i	$0.413231\pi$
$150$	0	0
$151$	14.9535	1.21690	0.608451	−	0.793591i	$-0.291791\pi$
$151$	14.9535	1.21690	0.608451	+	0.793591i	$0.291791\pi$
$152$	1.45714	0.118189
$153$	−13.8218	−1.11743
$154$	−4.10778	−0.331015
$155$	0	0
$156$	0.989045	0.0791870
$157$	9.78375	0.780829	0.390414	−	0.920639i	$-0.372332\pi$
$157$	9.78375	0.780829	0.390414	+	0.920639i	$0.372332\pi$
$158$	6.01538	0.478558
$159$	0.136362	0.0108142
$160$	0	0
$161$	12.1387	0.956661
$162$	3.65850	0.287439
$163$	−8.81431	−0.690390	−0.345195	−	0.938531i	$-0.612187\pi$
$163$	−8.81431	−0.690390	−0.345195	+	0.938531i	$0.612187\pi$
$164$	−10.1322	−0.791190
$165$	0	0
$166$	−2.83856	−0.220315
$167$	19.6245	1.51859	0.759293	−	0.650749i	$-0.225545\pi$
$167$	19.6245	1.51859	0.759293	+	0.650749i	$0.225545\pi$
$168$	−0.431137	−0.0332630
$169$	18.8737	1.45182
$170$	0	0
$171$	2.77241	0.212011
$172$	20.6074	1.57130
$173$	11.9204	0.906288	0.453144	−	0.891437i	$-0.350302\pi$
$173$	11.9204	0.906288	0.453144	+	0.891437i	$0.350302\pi$
$174$	−0.234427	−0.0177719
$175$	0	0
$176$	−10.5395	−0.794446
$177$	0.638239	0.0479730
$178$	0.780442	0.0584966
$179$	−20.6139	−1.54076	−0.770378	−	0.637588i	$-0.779932\pi$
$179$	−20.6139	−1.54076	−0.770378	+	0.637588i	$0.779932\pi$
$180$	0	0
$181$	−6.38627	−0.474687	−0.237344	−	0.971426i	$-0.576277\pi$
$181$	−6.38627	−0.474687	−0.237344	+	0.971426i	$0.576277\pi$
$182$	−6.64193	−0.492332
$183$	−0.390617	−0.0288753
$184$	−6.65394	−0.490535
$185$	0	0
$186$	0.163099	0.0119590
$187$	−16.1361	−1.17999
$188$	19.1404	1.39596
$189$	−1.64311	−0.119518
$190$	0	0
$191$	11.5045	0.832434	0.416217	−	0.909265i	$-0.363356\pi$
$191$	11.5045	0.832434	0.416217	+	0.909265i	$0.363356\pi$
$192$	−0.405443	−0.0292603
$193$	20.6759	1.48828	0.744142	−	0.668022i	$-0.232859\pi$
$193$	20.6759	1.48828	0.744142	+	0.668022i	$0.232859\pi$
$194$	3.70236	0.265814
$195$	0	0
$196$	−2.24123	−0.160088
$197$	2.68142	0.191044	0.0955218	−	0.995427i	$-0.469548\pi$
$197$	2.68142	0.191044	0.0955218	+	0.995427i	$0.469548\pi$
$198$	4.28422	0.304466
$199$	7.10471	0.503639	0.251820	−	0.967774i	$-0.418971\pi$
$199$	7.10471	0.503639	0.251820	+	0.967774i	$0.418971\pi$
$200$	0	0
$201$	0.975462	0.0688038
$202$	−2.97051	−0.209004
$203$	−17.1334	−1.20253
$204$	−0.809598	−0.0566832
$205$	0	0
$206$	−5.30892	−0.369890
$207$	−12.6601	−0.879935
$208$	−17.0415	−1.18161
$209$	3.23662	0.223882
$210$	0	0
$211$	3.48701	0.240056	0.120028	−	0.992771i	$-0.461702\pi$
$211$	3.48701	0.240056	0.120028	+	0.992771i	$0.461702\pi$
$212$	−2.61156	−0.179363
$213$	0.583079	0.0399519
$214$	3.61283	0.246968
$215$	0	0
$216$	0.900687	0.0612840
$217$	11.9203	0.809201
$218$	5.58058	0.377964
$219$	1.39757	0.0944387
$220$	0	0
$221$	−26.0907	−1.75505
$222$	−0.257914	−0.0173100
$223$	−4.11962	−0.275870	−0.137935	−	0.990441i	$-0.544047\pi$
$223$	−4.11962	−0.275870	−0.137935	+	0.990441i	$0.544047\pi$
$224$	12.5668	0.839658
$225$	0	0
$226$	1.78805	0.118939
$227$	12.3258	0.818091	0.409046	−	0.912514i	$-0.365862\pi$
$227$	12.3258	0.818091	0.409046	+	0.912514i	$0.365862\pi$
$228$	0.162391	0.0107546
$229$	9.46344	0.625362	0.312681	−	0.949858i	$-0.398773\pi$
$229$	9.46344	0.625362	0.312681	+	0.949858i	$0.398773\pi$
$230$	0	0
$231$	−0.957650	−0.0630087
$232$	9.39186	0.616606
$233$	−0.0510957	−0.00334739	−0.00167369	−	0.999999i	$-0.500533\pi$
$233$	−0.0510957	−0.00334739	−0.00167369	+	0.999999i	$0.500533\pi$
$234$	6.92721	0.452846
$235$	0	0
$236$	−12.2233	−0.795671
$237$	1.40237	0.0910936
$238$	5.43685	0.352418
$239$	−16.7457	−1.08319	−0.541596	−	0.840639i	$-0.682180\pi$
$239$	−16.7457	−1.08319	−0.541596	+	0.840639i	$0.682180\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	0.488834	0.0314235
$243$	2.57183	0.164983
$244$	7.48097	0.478920
$245$	0	0
$246$	0.217042	0.0138381
$247$	5.23333	0.332989
$248$	−6.53423	−0.414924
$249$	−0.661756	−0.0419371
$250$	0	0
$251$	16.8630	1.06438	0.532190	−	0.846625i	$-0.321369\pi$
$251$	16.8630	1.06438	0.532190	+	0.846625i	$0.321369\pi$
$252$	15.7101	0.989643
$253$	−14.7799	−0.929201
$254$	0.0510842	0.00320531
$255$	0	0
$256$	4.16930	0.260581
$257$	−10.4151	−0.649675	−0.324838	−	0.945770i	$-0.605310\pi$
$257$	−10.4151	−0.649675	−0.324838	+	0.945770i	$0.605310\pi$
$258$	−0.441432	−0.0274824
$259$	−18.8500	−1.17128
$260$	0	0
$261$	17.8693	1.10608
$262$	−3.43415	−0.212163
$263$	2.25119	0.138814	0.0694070	−	0.997588i	$-0.477889\pi$
$263$	2.25119	0.138814	0.0694070	+	0.997588i	$0.477889\pi$
$264$	0.524946	0.0323082
$265$	0	0
$266$	−1.09054	−0.0668651
$267$	0.181945	0.0111348
$268$	−18.6817	−1.14117
$269$	18.9188	1.15350	0.576749	−	0.816921i	$-0.304321\pi$
$269$	18.9188	1.15350	0.576749	+	0.816921i	$0.304321\pi$
$270$	0	0
$271$	24.4211	1.48347	0.741737	−	0.670691i	$-0.234002\pi$
$271$	24.4211	1.48347	0.741737	+	0.670691i	$0.234002\pi$
$272$	13.9496	0.845816
$273$	−1.54844	−0.0937156
$274$	−8.02244	−0.484654
$275$	0	0
$276$	−0.741550	−0.0446361
$277$	13.8794	0.833932	0.416966	−	0.908922i	$-0.363093\pi$
$277$	13.8794	0.833932	0.416966	+	0.908922i	$0.363093\pi$
$278$	4.81199	0.288604
$279$	−12.4323	−0.744302
$280$	0	0
$281$	23.0875	1.37728	0.688642	−	0.725101i	$-0.258207\pi$
$281$	23.0875	1.37728	0.688642	+	0.725101i	$0.258207\pi$
$282$	−0.410008	−0.0244156
$283$	−3.69078	−0.219394	−0.109697	−	0.993965i	$-0.534988\pi$
$283$	−3.69078	−0.219394	−0.109697	+	0.993965i	$0.534988\pi$
$284$	−11.1669	−0.662636
$285$	0	0
$286$	8.08710	0.478201
$287$	15.8628	0.936351
$288$	−13.1066	−0.772315
$289$	4.35690	0.256288
$290$	0	0
$291$	0.863133	0.0505977
$292$	−26.7657	−1.56635
$293$	15.4854	0.904667	0.452334	−	0.891849i	$-0.350592\pi$
$293$	15.4854	0.904667	0.452334	+	0.891849i	$0.350592\pi$
$294$	0.0480095	0.00279997
$295$	0	0
$296$	10.3328	0.600583
$297$	2.00062	0.116088
$298$	2.69645	0.156201
$299$	−23.8977	−1.38204
$300$	0	0
$301$	−32.2627	−1.85959
$302$	6.13468	0.353011
$303$	−0.692516	−0.0397840
$304$	−2.79804	−0.160478
$305$	0	0
$306$	−5.67037	−0.324154
$307$	−8.83112	−0.504019	−0.252009	−	0.967725i	$-0.581091\pi$
$307$	−8.83112	−0.504019	−0.252009	+	0.967725i	$0.581091\pi$
$308$	18.3406	1.04505
$309$	−1.23767	−0.0704086
$310$	0	0
$311$	−16.6249	−0.942710	−0.471355	−	0.881944i	$-0.656235\pi$
$311$	−16.6249	−0.942710	−0.471355	+	0.881944i	$0.656235\pi$
$312$	0.848792	0.0480534
$313$	−10.9670	−0.619893	−0.309947	−	0.950754i	$-0.600311\pi$
$313$	−10.9670	−0.619893	−0.309947	+	0.950754i	$0.600311\pi$
$314$	4.01377	0.226510
$315$	0	0
$316$	−26.8577	−1.51086
$317$	−16.0125	−0.899352	−0.449676	−	0.893192i	$-0.648461\pi$
$317$	−16.0125	−0.899352	−0.449676	+	0.893192i	$0.648461\pi$
$318$	0.0559423	0.00313709
$319$	20.8614	1.16801
$320$	0	0
$321$	0.842261	0.0470104
$322$	4.97988	0.277518
$323$	−4.28382	−0.238358
$324$	−16.3346	−0.907479
$325$	0	0
$326$	−3.61606	−0.200275
$327$	1.30100	0.0719456
$328$	−8.69536	−0.480121
$329$	−29.9660	−1.65208
$330$	0	0
$331$	−13.3293	−0.732644	−0.366322	−	0.930488i	$-0.619383\pi$
$331$	−13.3293	−0.732644	−0.366322	+	0.930488i	$0.619383\pi$
$332$	12.6737	0.695561
$333$	19.6596	1.07734
$334$	8.05091	0.440526
$335$	0	0
$336$	0.827882	0.0451647
$337$	−10.4867	−0.571247	−0.285624	−	0.958342i	$-0.592201\pi$
$337$	−10.4867	−0.571247	−0.285624	+	0.958342i	$0.592201\pi$
$338$	7.74290	0.421158
$339$	0.416849	0.0226401
$340$	0	0
$341$	−14.5139	−0.785974
$342$	1.13738	0.0615023
$343$	−16.5649	−0.894421
$344$	17.6851	0.953519
$345$	0	0
$346$	4.89031	0.262905
$347$	−23.3184	−1.25180	−0.625898	−	0.779905i	$-0.715268\pi$
$347$	−23.3184	−1.25180	−0.625898	+	0.779905i	$0.715268\pi$
$348$	1.04668	0.0561079
$349$	−19.4939	−1.04349	−0.521743	−	0.853103i	$-0.674718\pi$
$349$	−19.4939	−1.04349	−0.521743	+	0.853103i	$0.674718\pi$
$350$	0	0
$351$	3.23483	0.172662
$352$	−15.3012	−0.815556
$353$	31.1294	1.65685	0.828426	−	0.560098i	$-0.189237\pi$
$353$	31.1294	1.65685	0.828426	+	0.560098i	$0.189237\pi$
$354$	0.261837	0.0139165
$355$	0	0
$356$	−3.48455	−0.184681
$357$	1.26750	0.0670830
$358$	−8.45684	−0.446958
$359$	−6.88319	−0.363281	−0.181640	−	0.983365i	$-0.558141\pi$
$359$	−6.88319	−0.363281	−0.181640	+	0.983365i	$0.558141\pi$
$360$	0	0
$361$	−18.1407	−0.954776
$362$	−2.61996	−0.137702
$363$	0.113962	0.00598147
$364$	29.6551	1.55435
$365$	0	0
$366$	−0.160250	−0.00837642
$367$	12.4951	0.652239	0.326119	−	0.945329i	$-0.394259\pi$
$367$	12.4951	0.652239	0.326119	+	0.945329i	$0.394259\pi$
$368$	12.7771	0.666052
$369$	−16.5441	−0.861254
$370$	0	0
$371$	4.08862	0.212271
$372$	−0.728209	−0.0377559
$373$	25.8877	1.34041	0.670207	−	0.742174i	$-0.266205\pi$
$373$	25.8877	1.34041	0.670207	+	0.742174i	$0.266205\pi$
$374$	−6.61982	−0.342303
$375$	0	0
$376$	16.4262	0.847116
$377$	33.7310	1.73724
$378$	−0.674083	−0.0346711
$379$	6.19039	0.317979	0.158989	−	0.987280i	$-0.449176\pi$
$379$	6.19039	0.317979	0.158989	+	0.987280i	$0.449176\pi$
$380$	0	0
$381$	0.0119093	0.000610131 0
$382$	4.71970	0.241481
$383$	−13.0841	−0.668567	−0.334283	−	0.942473i	$-0.608494\pi$
$383$	−13.0841	−0.668567	−0.334283	+	0.942473i	$0.608494\pi$
$384$	−1.00458	−0.0512648
$385$	0	0
$386$	8.48227	0.431736
$387$	33.6484	1.71045
$388$	−16.5304	−0.839206
$389$	33.1098	1.67874	0.839368	−	0.543564i	$-0.182926\pi$
$389$	33.1098	1.67874	0.839368	+	0.543564i	$0.182926\pi$
$390$	0	0
$391$	19.5618	0.989285
$392$	−1.92341	−0.0971468
$393$	−0.800606	−0.0403852
$394$	1.10005	0.0554198
$395$	0	0
$396$	−19.1284	−0.961237
$397$	−15.3334	−0.769561	−0.384780	−	0.923008i	$-0.625723\pi$
$397$	−15.3334	−0.769561	−0.384780	+	0.923008i	$0.625723\pi$
$398$	2.91470	0.146101
$399$	−0.254237	−0.0127278
$400$	0	0
$401$	22.8097	1.13906	0.569531	−	0.821970i	$-0.307125\pi$
$401$	22.8097	1.13906	0.569531	+	0.821970i	$0.307125\pi$
$402$	0.400182	0.0199593
$403$	−23.4678	−1.16901
$404$	13.2628	0.659851
$405$	0	0
$406$	−7.02896	−0.348842
$407$	22.9514	1.13766
$408$	−0.694791	−0.0343973
$409$	8.90902	0.440523	0.220261	−	0.975441i	$-0.429309\pi$
$409$	8.90902	0.440523	0.220261	+	0.975441i	$0.429309\pi$
$410$	0	0
$411$	−1.87028	−0.0922539
$412$	23.7035	1.16779
$413$	19.1367	0.941655
$414$	−5.19377	−0.255260
$415$	0	0
$416$	−24.7407	−1.21301
$417$	1.12182	0.0549358
$418$	1.32782	0.0649458
$419$	14.6214	0.714302	0.357151	−	0.934047i	$-0.383748\pi$
$419$	14.6214	0.714302	0.357151	+	0.934047i	$0.383748\pi$
$420$	0	0
$421$	38.8904	1.89540	0.947702	−	0.319157i	$-0.103400\pi$
$421$	38.8904	1.89540	0.947702	+	0.319157i	$0.103400\pi$
$422$	1.43054	0.0696377
$423$	31.2531	1.51958
$424$	−2.24122	−0.108843
$425$	0	0
$426$	0.239208	0.0115896
$427$	−11.7121	−0.566789
$428$	−16.1307	−0.779707
$429$	1.88535	0.0910256
$430$	0	0
$431$	14.1828	0.683162	0.341581	−	0.939852i	$-0.389038\pi$
$431$	14.1828	0.683162	0.341581	+	0.939852i	$0.389038\pi$
$432$	−1.72952	−0.0832118
$433$	5.28263	0.253867	0.126933	−	0.991911i	$-0.459487\pi$
$433$	5.28263	0.253867	0.126933	+	0.991911i	$0.459487\pi$
$434$	4.89028	0.234741
$435$	0	0
$436$	−24.9164	−1.19328
$437$	−3.92376	−0.187699
$438$	0.573350	0.0273957
$439$	16.8906	0.806147	0.403073	−	0.915168i	$-0.367942\pi$
$439$	16.8906	0.806147	0.403073	+	0.915168i	$0.367942\pi$
$440$	0	0
$441$	−3.65955	−0.174264
$442$	−10.7037	−0.509122
$443$	−5.47869	−0.260301	−0.130150	−	0.991494i	$-0.541546\pi$
$443$	−5.47869	−0.260301	−0.130150	+	0.991494i	$0.541546\pi$
$444$	1.15154	0.0546498
$445$	0	0
$446$	−1.69007	−0.0800271
$447$	0.628624	0.0297329
$448$	−12.1566	−0.574348
$449$	13.6071	0.642157	0.321078	−	0.947053i	$-0.395955\pi$
$449$	13.6071	0.642157	0.321078	+	0.947053i	$0.395955\pi$
$450$	0	0
$451$	−19.3143	−0.909474
$452$	−7.98335	−0.375505
$453$	1.43018	0.0671958
$454$	5.05664	0.237320
$455$	0	0
$456$	0.139363	0.00652627
$457$	−22.0235	−1.03022	−0.515109	−	0.857125i	$-0.672249\pi$
$457$	−22.0235	−1.03022	−0.515109	+	0.857125i	$0.672249\pi$
$458$	3.88237	0.181411
$459$	−2.64792	−0.123594
$460$	0	0
$461$	33.2858	1.55027	0.775137	−	0.631793i	$-0.217681\pi$
$461$	33.2858	1.55027	0.775137	+	0.631793i	$0.217681\pi$
$462$	−0.392875	−0.0182782
$463$	−31.9292	−1.48387	−0.741937	−	0.670469i	$-0.766093\pi$
$463$	−31.9292	−1.48387	−0.741937	+	0.670469i	$0.766093\pi$
$464$	−18.0345	−0.837232
$465$	0	0
$466$	−0.0209619	−0.000971043 0
$467$	29.1306	1.34800	0.674001	−	0.738730i	$-0.264574\pi$
$467$	29.1306	1.34800	0.674001	+	0.738730i	$0.264574\pi$
$468$	−30.9289	−1.42969
$469$	29.2479	1.35054
$470$	0	0
$471$	0.935734	0.0431163
$472$	−10.4900	−0.482841
$473$	39.2825	1.80621
$474$	0.575320	0.0264253
$475$	0	0
$476$	−24.2747	−1.11263
$477$	−4.26424	−0.195246
$478$	−6.86993	−0.314223
$479$	9.68123	0.442347	0.221173	−	0.975235i	$-0.429011\pi$
$479$	9.68123	0.442347	0.221173	+	0.975235i	$0.429011\pi$
$480$	0	0
$481$	37.1105	1.69209
$482$	0.410249	0.0186863
$483$	1.16096	0.0528256
$484$	−2.18257	−0.0992076
$485$	0	0
$486$	1.05509	0.0478599
$487$	−21.8135	−0.988464	−0.494232	−	0.869330i	$-0.664551\pi$
$487$	−21.8135	−0.988464	−0.494232	+	0.869330i	$0.664551\pi$
$488$	6.42012	0.290625
$489$	−0.843014	−0.0381224
$490$	0	0
$491$	10.8171	0.488168	0.244084	−	0.969754i	$-0.421513\pi$
$491$	10.8171	0.488168	0.244084	+	0.969754i	$0.421513\pi$
$492$	−0.969057	−0.0436885
$493$	−27.6110	−1.24354
$494$	2.14697	0.0965967
$495$	0	0
$496$	12.5472	0.563387
$497$	17.4828	0.784211
$498$	−0.271485	−0.0121655
$499$	−42.2233	−1.89018	−0.945088	−	0.326817i	$-0.894024\pi$
$499$	−42.2233	−1.89018	−0.945088	+	0.326817i	$0.894024\pi$
$500$	0	0
$501$	1.87691	0.0838543
$502$	6.91801	0.308766
$503$	21.5095	0.959061	0.479530	−	0.877525i	$-0.340807\pi$
$503$	21.5095	0.959061	0.479530	+	0.877525i	$0.340807\pi$
$504$	13.4823	0.600549
$505$	0	0
$506$	−6.06342	−0.269552
$507$	1.80511	0.0801676
$508$	−0.228083	−0.0101195
$509$	−39.2556	−1.73998	−0.869988	−	0.493073i	$-0.835873\pi$
$509$	−39.2556	−1.73998	−0.869988	+	0.493073i	$0.835873\pi$
$510$	0	0
$511$	41.9041	1.85373
$512$	22.7176	1.00399
$513$	0.531126	0.0234498
$514$	−4.27278	−0.188464
$515$	0	0
$516$	1.97092	0.0867651
$517$	36.4861	1.60466
$518$	−7.73318	−0.339777
$519$	1.14008	0.0500440
$520$	0	0
$521$	−0.520785	−0.0228160	−0.0114080	−	0.999935i	$-0.503631\pi$
$521$	−0.520785	−0.0228160	−0.0114080	+	0.999935i	$0.503631\pi$
$522$	7.33087	0.320864
$523$	−4.73930	−0.207235	−0.103618	−	0.994617i	$-0.533042\pi$
$523$	−4.73930	−0.207235	−0.103618	+	0.994617i	$0.533042\pi$
$524$	15.3329	0.669823
$525$	0	0
$526$	0.923547	0.0402685
$527$	19.2099	0.836796
$528$	−1.00802	−0.0438683
$529$	−5.08235	−0.220972
$530$	0	0
$531$	−19.9587	−0.866132
$532$	4.86907	0.211101
$533$	−31.2295	−1.35270
$534$	0.0746427	0.00323011
$535$	0	0
$536$	−16.0325	−0.692500
$537$	−1.97155	−0.0850785
$538$	7.76141	0.334618
$539$	−4.27231	−0.184021
$540$	0	0
$541$	9.47701	0.407449	0.203724	−	0.979028i	$-0.434695\pi$
$541$	9.47701	0.407449	0.203724	+	0.979028i	$0.434695\pi$
$542$	10.0187	0.430341
$543$	−0.610793	−0.0262116
$544$	20.2519	0.868291
$545$	0	0
$546$	−0.635244	−0.0271859
$547$	16.7331	0.715454	0.357727	−	0.933826i	$-0.383552\pi$
$547$	16.7331	0.715454	0.357727	+	0.933826i	$0.383552\pi$
$548$	35.8189	1.53011
$549$	12.2152	0.521331
$550$	0	0
$551$	5.53829	0.235939
$552$	−0.636394	−0.0270867
$553$	42.0481	1.78807
$554$	5.69401	0.241915
$555$	0	0
$556$	−21.4848	−0.911156
$557$	−10.1962	−0.432026	−0.216013	−	0.976390i	$-0.569305\pi$
$557$	−10.1962	−0.432026	−0.216013	+	0.976390i	$0.569305\pi$
$558$	−5.10033	−0.215914
$559$	63.5164	2.68646
$560$	0	0
$561$	−1.54328	−0.0651574
$562$	9.47162	0.399536
$563$	−2.06949	−0.0872187	−0.0436093	−	0.999049i	$-0.513886\pi$
$563$	−2.06949	−0.0872187	−0.0436093	+	0.999049i	$0.513886\pi$
$564$	1.83062	0.0770830
$565$	0	0
$566$	−1.51414	−0.0636441
$567$	25.5733	1.07398
$568$	−9.58340	−0.402110
$569$	25.9665	1.08857	0.544287	−	0.838899i	$-0.316800\pi$
$569$	25.9665	1.08857	0.544287	+	0.838899i	$0.316800\pi$
$570$	0	0
$571$	41.1264	1.72109	0.860543	−	0.509378i	$-0.170124\pi$
$571$	41.1264	1.72109	0.860543	+	0.509378i	$0.170124\pi$
$572$	−36.1076	−1.50974
$573$	1.10031	0.0459659
$574$	6.50770	0.271626
$575$	0	0
$576$	12.6788	0.528284
$577$	30.3316	1.26272	0.631360	−	0.775490i	$-0.282497\pi$
$577$	30.3316	1.26272	0.631360	+	0.775490i	$0.282497\pi$
$578$	1.78741	0.0743467
$579$	1.97748	0.0821811
$580$	0	0
$581$	−19.8418	−0.823178
$582$	0.354099	0.0146779
$583$	−4.97824	−0.206178
$584$	−22.9702	−0.950512
$585$	0	0
$586$	6.35287	0.262435
$587$	−16.7714	−0.692228	−0.346114	−	0.938193i	$-0.612499\pi$
$587$	−16.7714	−0.692228	−0.346114	+	0.938193i	$0.612499\pi$
$588$	−0.214355	−0.00883984
$589$	−3.85317	−0.158767
$590$	0	0
$591$	0.256456	0.0105492
$592$	−19.8414	−0.815475
$593$	−15.7090	−0.645091	−0.322546	−	0.946554i	$-0.604539\pi$
$593$	−15.7090	−0.645091	−0.322546	+	0.946554i	$0.604539\pi$
$594$	0.820753	0.0336759
$595$	0	0
$596$	−12.0392	−0.493145
$597$	0.679505	0.0278103
$598$	−9.80402	−0.400916
$599$	37.9618	1.55108	0.775539	−	0.631300i	$-0.217478\pi$
$599$	37.9618	1.55108	0.775539	+	0.631300i	$0.217478\pi$
$600$	0	0
$601$	41.4595	1.69117	0.845583	−	0.533844i	$-0.179253\pi$
$601$	41.4595	1.69117	0.845583	+	0.533844i	$0.179253\pi$
$602$	−13.2357	−0.539448
$603$	−30.5041	−1.24222
$604$	−27.3904	−1.11450
$605$	0	0
$606$	−0.284104	−0.0115409
$607$	−27.1265	−1.10103	−0.550515	−	0.834825i	$-0.685569\pi$
$607$	−27.1265	−1.10103	−0.550515	+	0.834825i	$0.685569\pi$
$608$	−4.06217	−0.164743
$609$	−1.63867	−0.0664021
$610$	0	0
$611$	58.9949	2.38668
$612$	25.3173	1.02339
$613$	−5.17732	−0.209110	−0.104555	−	0.994519i	$-0.533342\pi$
$613$	−5.17732	−0.209110	−0.104555	+	0.994519i	$0.533342\pi$
$614$	−3.62296	−0.146211
$615$	0	0
$616$	15.7398	0.634174
$617$	−15.8742	−0.639072	−0.319536	−	0.947574i	$-0.603527\pi$
$617$	−15.8742	−0.639072	−0.319536	+	0.947574i	$0.603527\pi$
$618$	−0.507753	−0.0204248
$619$	30.4799	1.22509	0.612546	−	0.790435i	$-0.290145\pi$
$619$	30.4799	1.22509	0.612546	+	0.790435i	$0.290145\pi$
$620$	0	0
$621$	−2.42536	−0.0973263
$622$	−6.82034	−0.273471
$623$	5.45536	0.218565
$624$	−1.62987	−0.0652472
$625$	0	0
$626$	−4.49921	−0.179825
$627$	0.309555	0.0123625
$628$	−17.9209	−0.715120
$629$	−30.3773	−1.21122
$630$	0	0
$631$	−48.1327	−1.91613	−0.958065	−	0.286550i	$-0.907492\pi$
$631$	−48.1327	−1.91613	−0.958065	+	0.286550i	$0.907492\pi$
$632$	−23.0491	−0.916844
$633$	0.333503	0.0132556
$634$	−6.56911	−0.260893
$635$	0	0
$636$	−0.249774	−0.00990417
$637$	−6.90795	−0.273703
$638$	8.55836	0.338829
$639$	−18.2337	−0.721316
$640$	0	0
$641$	−28.3595	−1.12013	−0.560066	−	0.828448i	$-0.689224\pi$
$641$	−28.3595	−1.12013	−0.560066	+	0.828448i	$0.689224\pi$
$642$	0.345537	0.0136372
$643$	−12.7707	−0.503628	−0.251814	−	0.967776i	$-0.581027\pi$
$643$	−12.7707	−0.503628	−0.251814	+	0.967776i	$0.581027\pi$
$644$	−22.2343	−0.876156
$645$	0	0
$646$	−1.75743	−0.0691453
$647$	−16.1474	−0.634821	−0.317411	−	0.948288i	$-0.602813\pi$
$647$	−16.1474	−0.634821	−0.317411	+	0.948288i	$0.602813\pi$
$648$	−14.0183	−0.550689
$649$	−23.3005	−0.914626
$650$	0	0
$651$	1.14007	0.0446830
$652$	16.1451	0.632292
$653$	18.9470	0.741455	0.370728	−	0.928742i	$-0.379108\pi$
$653$	18.9470	0.741455	0.370728	+	0.928742i	$0.379108\pi$
$654$	0.533735	0.0208707
$655$	0	0
$656$	16.6971	0.651911
$657$	−43.7039	−1.70505
$658$	−12.2935	−0.479252
$659$	5.15863	0.200952	0.100476	−	0.994940i	$-0.467963\pi$
$659$	5.15863	0.200952	0.100476	+	0.994940i	$0.467963\pi$
$660$	0	0
$661$	12.5884	0.489632	0.244816	−	0.969569i	$-0.421272\pi$
$661$	12.5884	0.489632	0.244816	+	0.969569i	$0.421272\pi$
$662$	−5.46833	−0.212533
$663$	−2.49535	−0.0969114
$664$	10.8765	0.422091
$665$	0	0
$666$	8.06534	0.312526
$667$	−25.2903	−0.979244
$668$	−35.9460	−1.39079
$669$	−0.394007	−0.0152332
$670$	0	0
$671$	14.2605	0.550520
$672$	1.20191	0.0463648
$673$	−34.8101	−1.34183	−0.670916	−	0.741534i	$-0.734099\pi$
$673$	−34.8101	−1.34183	−0.670916	+	0.741534i	$0.734099\pi$
$674$	−4.30216	−0.165713
$675$	0	0
$676$	−34.5708	−1.32965
$677$	−1.97563	−0.0759297	−0.0379648	−	0.999279i	$-0.512087\pi$
$677$	−1.97563	−0.0759297	−0.0379648	+	0.999279i	$0.512087\pi$
$678$	0.171012	0.00656767
$679$	25.8798	0.993177
$680$	0	0
$681$	1.17886	0.0451739
$682$	−5.95433	−0.228003
$683$	−30.1662	−1.15428	−0.577138	−	0.816646i	$-0.695831\pi$
$683$	−30.1662	−1.15428	−0.577138	+	0.816646i	$0.695831\pi$
$684$	−5.07821	−0.194170
$685$	0	0
$686$	−6.79574	−0.259462
$687$	0.905098	0.0345316
$688$	−33.9595	−1.29469
$689$	−8.04938	−0.306657
$690$	0	0
$691$	5.09033	0.193645	0.0968227	−	0.995302i	$-0.469132\pi$
$691$	5.09033	0.193645	0.0968227	+	0.995302i	$0.469132\pi$
$692$	−21.8345	−0.830022
$693$	29.9471	1.13760
$694$	−9.56634	−0.363133
$695$	0	0
$696$	0.898253	0.0340482
$697$	25.5634	0.968282
$698$	−7.99736	−0.302705
$699$	−0.00488687	−0.000184838 0
$700$	0	0
$701$	1.56801	0.0592228	0.0296114	−	0.999561i	$-0.490573\pi$
$701$	1.56801	0.0592228	0.0296114	+	0.999561i	$0.490573\pi$
$702$	1.32709	0.0500876
$703$	6.09316	0.229808
$704$	14.8017	0.557862
$705$	0	0
$706$	12.7708	0.480636
$707$	−20.7641	−0.780916
$708$	−1.16906	−0.0439359
$709$	−41.0120	−1.54024	−0.770119	−	0.637900i	$-0.779803\pi$
$709$	−41.0120	−1.54024	−0.770119	+	0.637900i	$0.779803\pi$
$710$	0	0
$711$	−43.8541	−1.64466
$712$	−2.99042	−0.112071
$713$	17.5953	0.658949
$714$	0.519989	0.0194601
$715$	0	0
$716$	37.7584	1.41110
$717$	−1.60159	−0.0598125
$718$	−2.82382	−0.105384
$719$	16.2498	0.606017	0.303008	−	0.952988i	$-0.402009\pi$
$719$	16.2498	0.606017	0.303008	+	0.952988i	$0.402009\pi$
$720$	0	0
$721$	−37.1098	−1.38204
$722$	−7.44222	−0.276971
$723$	0.0956416	0.00355695
$724$	11.6977	0.434742
$725$	0	0
$726$	0.0467529	0.00173516
$727$	−10.3421	−0.383566	−0.191783	−	0.981437i	$-0.561427\pi$
$727$	−10.3421	−0.383566	−0.191783	+	0.981437i	$0.561427\pi$
$728$	25.4498	0.943234
$729$	−26.5073	−0.981752
$730$	0	0
$731$	−51.9923	−1.92300
$732$	0.715492	0.0264453
$733$	−29.9872	−1.10760	−0.553801	−	0.832649i	$-0.686823\pi$
$733$	−29.9872	−1.10760	−0.553801	+	0.832649i	$0.686823\pi$
$734$	5.12610	0.189208
$735$	0	0
$736$	18.5497	0.683750
$737$	−35.6117	−1.31177
$738$	−6.78722	−0.249841
$739$	35.4009	1.30224	0.651121	−	0.758974i	$-0.274299\pi$
$739$	35.4009	1.30224	0.651121	+	0.758974i	$0.274299\pi$
$740$	0	0
$741$	0.500524	0.0183872
$742$	1.67735	0.0615776
$743$	35.5809	1.30534	0.652669	−	0.757643i	$-0.273649\pi$
$743$	35.5809	1.30534	0.652669	+	0.757643i	$0.273649\pi$
$744$	−0.624944	−0.0229116
$745$	0	0
$746$	10.6204	0.388841
$747$	20.6941	0.757157
$748$	29.5564	1.08069
$749$	25.2540	0.922762
$750$	0	0
$751$	−48.2481	−1.76060	−0.880298	−	0.474420i	$-0.842658\pi$
$751$	−48.2481	−1.76060	−0.880298	+	0.474420i	$0.842658\pi$
$752$	−31.5420	−1.15022
$753$	1.61280	0.0587737
$754$	13.8381	0.503954
$755$	0	0
$756$	3.00967	0.109461
$757$	−19.4363	−0.706424	−0.353212	−	0.935543i	$-0.614911\pi$
$757$	−19.4363	−0.706424	−0.353212	+	0.935543i	$0.614911\pi$
$758$	2.53960	0.0922425
$759$	−1.41357	−0.0513093
$760$	0	0
$761$	23.2081	0.841292	0.420646	−	0.907225i	$-0.361803\pi$
$761$	23.2081	0.841292	0.420646	+	0.907225i	$0.361803\pi$
$762$	0.00488577	0.000176993 0
$763$	39.0088	1.41221
$764$	−21.0727	−0.762383
$765$	0	0
$766$	−5.36774	−0.193944
$767$	−37.6749	−1.36036
$768$	0.398758	0.0143889
$769$	−40.4257	−1.45779	−0.728893	−	0.684627i	$-0.759965\pi$
$769$	−40.4257	−1.45779	−0.728893	+	0.684627i	$0.759965\pi$
$770$	0	0
$771$	−0.996115	−0.0358742
$772$	−37.8720	−1.36304
$773$	−41.9952	−1.51046	−0.755231	−	0.655458i	$-0.772475\pi$
$773$	−41.9952	−1.51046	−0.755231	+	0.655458i	$0.772475\pi$
$774$	13.8042	0.496183
$775$	0	0
$776$	−14.1863	−0.509259
$777$	−1.80284	−0.0646766
$778$	13.5833	0.486984
$779$	−5.12757	−0.183714
$780$	0	0
$781$	−21.2868	−0.761702
$782$	8.02522	0.286981
$783$	3.42333	0.122340
$784$	3.69338	0.131907
$785$	0	0
$786$	−0.328448	−0.0117153
$787$	−42.3623	−1.51005	−0.755027	−	0.655693i	$-0.772376\pi$
$787$	−42.3623	−1.51005	−0.755027	+	0.655693i	$0.772376\pi$
$788$	−4.91155	−0.174967
$789$	0.215307	0.00766513
$790$	0	0
$791$	12.4986	0.444400
$792$	−16.4158	−0.583311
$793$	23.0579	0.818812
$794$	−6.29051	−0.223242
$795$	0	0
$796$	−13.0137	−0.461257
$797$	12.0023	0.425144	0.212572	−	0.977145i	$-0.431816\pi$
$797$	12.0023	0.425144	0.212572	+	0.977145i	$0.431816\pi$
$798$	−0.104301	−0.00369220
$799$	−48.2911	−1.70842
$800$	0	0
$801$	−5.68969	−0.201035
$802$	9.35766	0.330430
$803$	−51.0217	−1.80052
$804$	−1.78675	−0.0630138
$805$	0	0
$806$	−9.62763	−0.339119
$807$	1.80942	0.0636947
$808$	11.3821	0.400420
$809$	3.91715	0.137720	0.0688598	−	0.997626i	$-0.478064\pi$
$809$	3.91715	0.137720	0.0688598	+	0.997626i	$0.478064\pi$
$810$	0	0
$811$	−20.5026	−0.719945	−0.359973	−	0.932963i	$-0.617214\pi$
$811$	−20.5026	−0.719945	−0.359973	+	0.932963i	$0.617214\pi$
$812$	31.3832	1.10133
$813$	2.33567	0.0819155
$814$	9.41580	0.330024
$815$	0	0
$816$	1.33416	0.0467049
$817$	10.4287	0.364856
$818$	3.65492	0.127791
$819$	48.4219	1.69200
$820$	0	0
$821$	−40.1467	−1.40113	−0.700564	−	0.713589i	$-0.747068\pi$
$821$	−40.1467	−1.40113	−0.700564	+	0.713589i	$0.747068\pi$
$822$	−0.767279	−0.0267619
$823$	44.8166	1.56221	0.781104	−	0.624401i	$-0.214657\pi$
$823$	44.8166	1.56221	0.781104	+	0.624401i	$0.214657\pi$
$824$	20.3421	0.708652
$825$	0	0
$826$	7.85081	0.273165
$827$	−44.8318	−1.55895	−0.779477	−	0.626431i	$-0.784515\pi$
$827$	−44.8318	−1.55895	−0.779477	+	0.626431i	$0.784515\pi$
$828$	23.1894	0.805886
$829$	−18.3135	−0.636053	−0.318026	−	0.948082i	$-0.603020\pi$
$829$	−18.3135	−0.636053	−0.318026	+	0.948082i	$0.603020\pi$
$830$	0	0
$831$	1.32745	0.0460486
$832$	23.9331	0.829732
$833$	5.65460	0.195920
$834$	0.460226	0.0159363
$835$	0	0
$836$	−5.92850	−0.205042
$837$	−2.38172	−0.0823244
$838$	5.99842	0.207212
$839$	−23.4533	−0.809697	−0.404848	−	0.914384i	$-0.632676\pi$
$839$	−23.4533	−0.809697	−0.404848	+	0.914384i	$0.632676\pi$
$840$	0	0
$841$	6.69657	0.230916
$842$	15.9548	0.549837
$843$	2.20812	0.0760518
$844$	−6.38714	−0.219854
$845$	0	0
$846$	12.8216	0.440814
$847$	3.41700	0.117409
$848$	4.30366	0.147788
$849$	−0.352992	−0.0121147
$850$	0	0
$851$	−27.8241	−0.953797
$852$	−1.06802	−0.0365899
$853$	44.5712	1.52609	0.763044	−	0.646347i	$-0.223704\pi$
$853$	44.5712	1.52609	0.763044	+	0.646347i	$0.223704\pi$
$854$	−4.80488	−0.164420
$855$	0	0
$856$	−13.8433	−0.473153
$857$	16.8801	0.576613	0.288306	−	0.957538i	$-0.406908\pi$
$857$	16.8801	0.576613	0.288306	+	0.957538i	$0.406908\pi$
$858$	0.773463	0.0264056
$859$	43.4122	1.48121	0.740603	−	0.671943i	$-0.234540\pi$
$859$	43.4122	1.48121	0.740603	+	0.671943i	$0.234540\pi$
$860$	0	0
$861$	1.51714	0.0517041
$862$	5.81849	0.198178
$863$	−4.44408	−0.151278	−0.0756392	−	0.997135i	$-0.524100\pi$
$863$	−4.44408	−0.151278	−0.0756392	+	0.997135i	$0.524100\pi$
$864$	−2.51091	−0.0854229
$865$	0	0
$866$	2.16719	0.0736442
$867$	0.416701	0.0141519
$868$	−21.8343	−0.741105
$869$	−51.1971	−1.73674
$870$	0	0
$871$	−57.5810	−1.95106
$872$	−21.3831	−0.724122
$873$	−26.9914	−0.913521
$874$	−1.60972	−0.0544496
$875$	0	0
$876$	−2.55992	−0.0864915
$877$	13.1827	0.445147	0.222573	−	0.974916i	$-0.428554\pi$
$877$	13.1827	0.445147	0.222573	+	0.974916i	$0.428554\pi$
$878$	6.92937	0.233855
$879$	1.48105	0.0499545
$880$	0	0
$881$	−28.6955	−0.966777	−0.483389	−	0.875406i	$-0.660594\pi$
$881$	−28.6955	−0.966777	−0.483389	+	0.875406i	$0.660594\pi$
$882$	−1.50133	−0.0505524
$883$	10.3730	0.349080	0.174540	−	0.984650i	$-0.444156\pi$
$883$	10.3730	0.349080	0.174540	+	0.984650i	$0.444156\pi$
$884$	47.7902	1.60736
$885$	0	0
$886$	−2.24763	−0.0755106
$887$	33.1854	1.11426	0.557129	−	0.830426i	$-0.311903\pi$
$887$	33.1854	1.11426	0.557129	+	0.830426i	$0.311903\pi$
$888$	0.988247	0.0331634
$889$	0.357083	0.0119762
$890$	0	0
$891$	−31.1376	−1.04315
$892$	7.54589	0.252655
$893$	9.68636	0.324142
$894$	0.257892	0.00862521
$895$	0	0
$896$	−30.1209	−1.00627
$897$	−2.28562	−0.0763145
$898$	5.58228	0.186283
$899$	−24.8353	−0.828303
$900$	0	0
$901$	6.58894	0.219509
$902$	−7.92367	−0.263829
$903$	−3.08565	−0.102684
$904$	−6.85126	−0.227870
$905$	0	0
$906$	0.586730	0.0194928
$907$	−40.7469	−1.35298	−0.676489	−	0.736453i	$-0.736499\pi$
$907$	−40.7469	−1.35298	−0.676489	+	0.736453i	$0.736499\pi$
$908$	−22.5771	−0.749247
$909$	21.6560	0.718284
$910$	0	0
$911$	43.4509	1.43959	0.719797	−	0.694185i	$-0.244235\pi$
$911$	43.4509	1.43959	0.719797	+	0.694185i	$0.244235\pi$
$912$	−0.267609	−0.00886141
$913$	24.1591	0.799549
$914$	−9.03514	−0.298856
$915$	0	0
$916$	−17.3341	−0.572736
$917$	−24.0051	−0.792717
$918$	−1.08631	−0.0358534
$919$	−10.7876	−0.355849	−0.177924	−	0.984044i	$-0.556938\pi$
$919$	−10.7876	−0.355849	−0.177924	+	0.984044i	$0.556938\pi$
$920$	0	0
$921$	−0.844622	−0.0278312
$922$	13.6555	0.449719
$923$	−34.4189	−1.13291
$924$	1.75412	0.0577064
$925$	0	0
$926$	−13.0989	−0.430457
$927$	38.7038	1.27120
$928$	−26.1824	−0.859478
$929$	44.2212	1.45085	0.725426	−	0.688301i	$-0.241643\pi$
$929$	44.2212	1.45085	0.725426	+	0.688301i	$0.241643\pi$
$930$	0	0
$931$	−1.13421	−0.0371724
$932$	0.0935917	0.00306570
$933$	−1.59003	−0.0520552
$934$	11.9508	0.391042
$935$	0	0
$936$	−26.5430	−0.867584
$937$	−4.40256	−0.143825	−0.0719127	−	0.997411i	$-0.522910\pi$
$937$	−4.40256	−0.143825	−0.0719127	+	0.997411i	$0.522910\pi$
$938$	11.9989	0.391778
$939$	−1.04890	−0.0342297
$940$	0	0
$941$	−1.62108	−0.0528459	−0.0264229	−	0.999651i	$-0.508412\pi$
$941$	−1.62108	−0.0528459	−0.0264229	+	0.999651i	$0.508412\pi$
$942$	0.383884	0.0125076
$943$	23.4148	0.762490
$944$	20.1432	0.655604
$945$	0	0
$946$	16.1156	0.523964
$947$	55.9249	1.81731	0.908657	−	0.417543i	$-0.137109\pi$
$947$	55.9249	1.81731	0.908657	+	0.417543i	$0.137109\pi$
$948$	−2.56871	−0.0834279
$949$	−82.4976	−2.67799
$950$	0	0
$951$	−1.53146	−0.0496610
$952$	−20.8323	−0.675180
$953$	−9.68270	−0.313653	−0.156827	−	0.987626i	$-0.550126\pi$
$953$	−9.68270	−0.313653	−0.156827	+	0.987626i	$0.550126\pi$
$954$	−1.74940	−0.0566389
$955$	0	0
$956$	30.6731	0.992039
$957$	1.99521	0.0644961
$958$	3.97171	0.128320
$959$	−56.0776	−1.81084
$960$	0	0
$961$	−13.7213	−0.442621
$962$	15.2245	0.490858
$963$	−26.3387	−0.848754
$964$	−1.83170	−0.0589949
$965$	0	0
$966$	0.476283	0.0153242
$967$	−10.0438	−0.322985	−0.161493	−	0.986874i	$-0.551631\pi$
$967$	−10.0438	−0.322985	−0.161493	+	0.986874i	$0.551631\pi$
$968$	−1.87306	−0.0602026
$969$	−0.409711	−0.0131618
$970$	0	0
$971$	33.8437	1.08609	0.543047	−	0.839702i	$-0.317270\pi$
$971$	33.8437	1.08609	0.543047	+	0.839702i	$0.317270\pi$
$972$	−4.71081	−0.151099
$973$	33.6362	1.07833
$974$	−8.94897	−0.286743
$975$	0	0
$976$	−12.3281	−0.394613
$977$	23.6776	0.757515	0.378757	−	0.925496i	$-0.376351\pi$
$977$	23.6776	0.757515	0.378757	+	0.925496i	$0.376351\pi$
$978$	−0.345846	−0.0110589
$979$	−6.64237	−0.212291
$980$	0	0
$981$	−40.6843	−1.29895
$982$	4.43770	0.141613
$983$	−24.1936	−0.771656	−0.385828	−	0.922571i	$-0.626084\pi$
$983$	−24.1936	−0.771656	−0.385828	+	0.922571i	$0.626084\pi$
$984$	−0.831638	−0.0265117
$985$	0	0
$986$	−11.3274	−0.360738
$987$	−2.86600	−0.0912257
$988$	−9.58587	−0.304967
$989$	−47.6223	−1.51430
$990$	0	0
$991$	40.0106	1.27098	0.635489	−	0.772110i	$-0.280799\pi$
$991$	40.0106	1.27098	0.635489	+	0.772110i	$0.280799\pi$
$992$	18.2159	0.578357
$993$	−1.27483	−0.0404556
$994$	7.17231	0.227492
$995$	0	0
$996$	1.21214	0.0384080
$997$	−46.1127	−1.46040	−0.730202	−	0.683232i	$-0.760574\pi$
$997$	−46.1127	−1.46040	−0.730202	+	0.683232i	$0.760574\pi$
$998$	−17.3221	−0.548321
$999$	3.76631	0.119161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.k.1.13		25
5.4	even	2		1205.2.a.d.1.13	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.13	✓	25	5.4	even	2
6025.2.a.k.1.13		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.410249 q^{2} +0.0956416 q^{3} -1.83170 q^{4} +0.0392369 q^{6} +2.86768 q^{7} -1.57195 q^{8} -2.99085 q^{9} +O(q^{10})\)	\(q+0.410249 q^{2} +0.0956416 q^{3} -1.83170 q^{4} +0.0392369 q^{6} +2.86768 q^{7} -1.57195 q^{8} -2.99085 q^{9} -3.49164 q^{11} -0.175186 q^{12} -5.64568 q^{13} +1.17646 q^{14} +3.01850 q^{16} +4.62135 q^{17} -1.22699 q^{18} -0.926962 q^{19} +0.274269 q^{21} -1.43244 q^{22} +4.23292 q^{23} -0.150344 q^{24} -2.31613 q^{26} -0.572975 q^{27} -5.25272 q^{28} -5.97466 q^{29} +4.15677 q^{31} +4.38224 q^{32} -0.333946 q^{33} +1.89591 q^{34} +5.47833 q^{36} -6.57325 q^{37} -0.380285 q^{38} -0.539961 q^{39} +5.53158 q^{41} +0.112519 q^{42} -11.2505 q^{43} +6.39562 q^{44} +1.73655 q^{46} -10.4496 q^{47} +0.288694 q^{48} +1.22358 q^{49} +0.441993 q^{51} +10.3412 q^{52} +1.42576 q^{53} -0.235062 q^{54} -4.50785 q^{56} -0.0886561 q^{57} -2.45110 q^{58} +6.67323 q^{59} -4.08418 q^{61} +1.70531 q^{62} -8.57681 q^{63} -4.23919 q^{64} -0.137001 q^{66} +10.1991 q^{67} -8.46491 q^{68} +0.404844 q^{69} +6.09650 q^{71} +4.70147 q^{72} +14.6125 q^{73} -2.69667 q^{74} +1.69791 q^{76} -10.0129 q^{77} -0.221519 q^{78} +14.6628 q^{79} +8.91776 q^{81} +2.26933 q^{82} -6.91913 q^{83} -0.502378 q^{84} -4.61549 q^{86} -0.571426 q^{87} +5.48868 q^{88} +1.90236 q^{89} -16.1900 q^{91} -7.75343 q^{92} +0.397560 q^{93} -4.28693 q^{94} +0.419124 q^{96} +9.02466 q^{97} +0.501973 q^{98} +10.4430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9	\( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9 + 10 * q^11 - 22 * q^12 - 10 * q^13 + 13 * q^14 + 54 * q^16 - q^17 + 13 * q^18 + 50 * q^19 + 9 * q^21 - 11 * q^22 + 31 * q^23 + 22 * q^24 + 8 * q^26 - 42 * q^27 - 14 * q^28 + 4 * q^29 + 34 * q^31 + 44 * q^32 - 28 * q^33 + 33 * q^34 + 83 * q^36 - 14 * q^37 + 10 * q^38 + 23 * q^39 + 11 * q^41 - 23 * q^42 - 49 * q^43 + 20 * q^44 + 27 * q^46 + 28 * q^47 - 30 * q^48 + 66 * q^49 + 49 * q^51 - 39 * q^52 + 16 * q^53 + 5 * q^54 + 51 * q^56 - 10 * q^57 + 8 * q^58 + 30 * q^59 + 35 * q^61 + 18 * q^62 + 73 * q^64 - 13 * q^66 - 37 * q^67 - 11 * q^68 - 4 * q^69 + 12 * q^71 + 90 * q^72 - 36 * q^73 - 12 * q^74 + 57 * q^76 + 31 * q^77 + 9 * q^78 + 16 * q^79 + 65 * q^81 + 11 * q^82 - 43 * q^83 - 62 * q^84 - 9 * q^86 + 22 * q^87 - 20 * q^88 + 38 * q^89 + 86 * q^91 + 119 * q^92 - 10 * q^93 - 18 * q^94 - 34 * q^96 - 17 * q^97 + 32 * q^98 + 26 * q^99

Introduction

L-functions

Modular forms

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Database

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