LMFDB - Embedded newform 3751.2.a.l.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3751,2,Mod(1,3751)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3751, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("3751.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3751 = 11^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3751.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-1,2,17,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$29.9518857982$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 21 x^{12} + 204 x^{11} - 160 x^{10} - 880 x^{9} + 535 x^{8} + 1918 x^{7} + \cdots + 4 $ x^15 - x^14 - 23x^13 + 21x^12 + 204x^11 - 160x^10 - 880x^9 + 535x^8 + 1918x^7 - 751x^6 - 1980x^5 + 313x^4 + 845x^3 + 37x^2 - 72*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 23 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.15277$ of defining polynomial
Character	$\chi$	$=$	3751.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.15277 q^{2} +0.107389 q^{3} -0.671122 q^{4} +3.27597 q^{5} -0.123795 q^{6} +2.63305 q^{7} +3.07919 q^{8} -2.98847 q^{9} -3.77644 q^{10} -0.0720712 q^{12} +0.342173 q^{13} -3.03530 q^{14} +0.351804 q^{15} -2.20735 q^{16} -6.90058 q^{17} +3.44501 q^{18} -1.85785 q^{19} -2.19858 q^{20} +0.282760 q^{21} +1.56779 q^{23} +0.330671 q^{24} +5.73201 q^{25} -0.394447 q^{26} -0.643096 q^{27} -1.76710 q^{28} -0.183838 q^{29} -0.405549 q^{30} -1.00000 q^{31} -3.61381 q^{32} +7.95478 q^{34} +8.62579 q^{35} +2.00563 q^{36} +7.43409 q^{37} +2.14168 q^{38} +0.0367457 q^{39} +10.0873 q^{40} +4.54923 q^{41} -0.325958 q^{42} -1.46404 q^{43} -9.79014 q^{45} -1.80730 q^{46} +5.77796 q^{47} -0.237045 q^{48} -0.0670632 q^{49} -6.60768 q^{50} -0.741046 q^{51} -0.229640 q^{52} +7.49877 q^{53} +0.741341 q^{54} +8.10765 q^{56} -0.199513 q^{57} +0.211923 q^{58} +13.2244 q^{59} -0.236103 q^{60} +2.86416 q^{61} +1.15277 q^{62} -7.86878 q^{63} +8.58059 q^{64} +1.12095 q^{65} +3.84775 q^{67} +4.63113 q^{68} +0.168364 q^{69} -9.94355 q^{70} +4.34068 q^{71} -9.20206 q^{72} +12.3659 q^{73} -8.56980 q^{74} +0.615555 q^{75} +1.24685 q^{76} -0.0423593 q^{78} -13.5159 q^{79} -7.23122 q^{80} +8.89634 q^{81} -5.24421 q^{82} +9.82792 q^{83} -0.189767 q^{84} -22.6061 q^{85} +1.68771 q^{86} -0.0197422 q^{87} +9.23024 q^{89} +11.2858 q^{90} +0.900959 q^{91} -1.05218 q^{92} -0.107389 q^{93} -6.66066 q^{94} -6.08628 q^{95} -0.388084 q^{96} +5.92141 q^{97} +0.0773084 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - q^{2} + 2 q^{3} + 17 q^{4} + 8 q^{5} + 2 q^{6} - 3 q^{8} + 25 q^{9} + 15 q^{10} + 11 q^{12} + 4 q^{13} + 9 q^{14} + 15 q^{15} + 29 q^{16} + 2 q^{17} - 4 q^{18} - 5 q^{19} + 17 q^{20} + 15 q^{21}+ \cdots + 31 q^{98}+O(q^{100}) $ 15 * q - q^2 + 2 * q^3 + 17 * q^4 + 8 * q^5 + 2 * q^6 - 3 * q^8 + 25 * q^9 + 15 * q^10 + 11 * q^12 + 4 * q^13 + 9 * q^14 + 15 * q^15 + 29 * q^16 + 2 * q^17 - 4 * q^18 - 5 * q^19 + 17 * q^20 + 15 * q^21 + 17 * q^23 + 18 * q^24 + 27 * q^25 + 22 * q^26 + 17 * q^27 - 35 * q^28 - 7 * q^29 - 27 * q^30 - 15 * q^31 + 23 * q^32 + 15 * q^34 - 9 * q^35 - 3 * q^36 + 17 * q^37 + 4 * q^38 - 18 * q^39 + 51 * q^40 + 7 * q^41 - 17 * q^42 + 12 * q^43 + 18 * q^45 - 20 * q^46 - 8 * q^47 + 21 * q^48 + 37 * q^49 - 16 * q^50 + 52 * q^51 - 35 * q^52 + 26 * q^53 + 48 * q^54 + 8 * q^56 - 44 * q^57 - 55 * q^58 + 11 * q^59 + 108 * q^60 - 17 * q^61 + q^62 - 22 * q^63 - 3 * q^64 + 12 * q^65 - 31 * q^67 - 30 * q^68 - 16 * q^69 - 8 * q^70 + 35 * q^71 - 59 * q^72 + q^73 - 5 * q^74 + 61 * q^75 + 12 * q^76 + q^78 - 14 * q^79 + 27 * q^80 + 83 * q^81 + 39 * q^82 - 26 * q^83 + 46 * q^84 - 16 * q^85 + 51 * q^86 - 43 * q^87 + 73 * q^89 + 45 * q^90 - 23 * q^91 + 19 * q^92 - 2 * q^93 - 46 * q^94 + 59 * q^95 - 53 * q^96 + 34 * q^97 + 31 * q^98

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 $

$2$	−1.15277	−0.815131	−0.407566	−	0.913176i	$-0.633622\pi$
$2$	−1.15277	−0.815131	−0.407566	+	0.913176i	$0.633622\pi$
$3$	0.107389	0.0620011	0.0310005	−	0.999519i	$-0.490131\pi$
$3$	0.107389	0.0620011	0.0310005	+	0.999519i	$0.490131\pi$
$4$	−0.671122	−0.335561
$5$	3.27597	1.46506	0.732530	−	0.680735i	$-0.238339\pi$
$5$	3.27597	1.46506	0.732530	+	0.680735i	$0.238339\pi$
$6$	−0.123795	−0.0505390
$7$	2.63305	0.995198	0.497599	−	0.867407i	$-0.334215\pi$
$7$	2.63305	0.995198	0.497599	+	0.867407i	$0.334215\pi$
$8$	3.07919	1.08866
$9$	−2.98847	−0.996156
$10$	−3.77644	−1.19422
$11$	0	0
$11$	0	0
$12$	−0.0720712	−0.0208052
$13$	0.342173	0.0949019	0.0474509	−	0.998874i	$-0.484890\pi$
$13$	0.342173	0.0949019	0.0474509	+	0.998874i	$0.484890\pi$
$14$	−3.03530	−0.811217
$15$	0.351804	0.0908353
$16$	−2.20735	−0.551838
$17$	−6.90058	−1.67364	−0.836818	−	0.547481i	$-0.815587\pi$
$17$	−6.90058	−1.67364	−0.836818	+	0.547481i	$0.815587\pi$
$18$	3.44501	0.811998
$19$	−1.85785	−0.426221	−0.213110	−	0.977028i	$-0.568359\pi$
$19$	−1.85785	−0.426221	−0.213110	+	0.977028i	$0.568359\pi$
$20$	−2.19858	−0.491617
$21$	0.282760	0.0617034
$22$	0	0
$23$	1.56779	0.326908	0.163454	−	0.986551i	$-0.447737\pi$
$23$	1.56779	0.326908	0.163454	+	0.986551i	$0.447737\pi$
$24$	0.330671	0.0674980
$25$	5.73201	1.14640
$26$	−0.394447	−0.0773575
$27$	−0.643096	−0.123764
$28$	−1.76710	−0.333950
$29$	−0.183838	−0.0341379	−0.0170690	−	0.999854i	$-0.505433\pi$
$29$	−0.183838	−0.0341379	−0.0170690	+	0.999854i	$0.505433\pi$
$30$	−0.405549	−0.0740427
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−3.61381	−0.638837
$33$	0	0
$34$	7.95478	1.36423
$35$	8.62579	1.45803
$36$	2.00563	0.334271
$37$	7.43409	1.22216	0.611079	−	0.791570i	$-0.290736\pi$
$37$	7.43409	1.22216	0.611079	+	0.791570i	$0.290736\pi$
$38$	2.14168	0.347426
$39$	0.0367457	0.00588402
$40$	10.0873	1.59495
$41$	4.54923	0.710470	0.355235	−	0.934777i	$-0.384401\pi$
$41$	4.54923	0.710470	0.355235	+	0.934777i	$0.384401\pi$
$42$	−0.325958	−0.0502964
$43$	−1.46404	−0.223265	−0.111632	−	0.993750i	$-0.535608\pi$
$43$	−1.46404	−0.223265	−0.111632	+	0.993750i	$0.535608\pi$
$44$	0	0
$45$	−9.79014	−1.45943
$46$	−1.80730	−0.266473
$47$	5.77796	0.842802	0.421401	−	0.906874i	$-0.361538\pi$
$47$	5.77796	0.842802	0.421401	+	0.906874i	$0.361538\pi$
$48$	−0.237045	−0.0342145
$49$	−0.0670632	−0.00958045
$50$	−6.60768	−0.934467
$51$	−0.741046	−0.103767
$52$	−0.229640	−0.0318454
$53$	7.49877	1.03003	0.515017	−	0.857180i	$-0.327785\pi$
$53$	7.49877	1.03003	0.515017	+	0.857180i	$0.327785\pi$
$54$	0.741341	0.100884
$55$	0	0
$56$	8.10765	1.08343
$57$	−0.199513	−0.0264262
$58$	0.211923	0.0278269
$59$	13.2244	1.72167	0.860837	−	0.508881i	$-0.169941\pi$
$59$	13.2244	1.72167	0.860837	+	0.508881i	$0.169941\pi$
$60$	−0.236103	−0.0304808
$61$	2.86416	0.366718	0.183359	−	0.983046i	$-0.441303\pi$
$61$	2.86416	0.366718	0.183359	+	0.983046i	$0.441303\pi$
$62$	1.15277	0.146402
$63$	−7.86878	−0.991373
$64$	8.58059	1.07257
$65$	1.12095	0.139037
$66$	0	0
$67$	3.84775	0.470077	0.235039	−	0.971986i	$-0.424478\pi$
$67$	3.84775	0.470077	0.235039	+	0.971986i	$0.424478\pi$
$68$	4.63113	0.561607
$69$	0.168364	0.0202686
$70$	−9.94355	−1.18848
$71$	4.34068	0.515144	0.257572	−	0.966259i	$-0.417077\pi$
$71$	4.34068	0.515144	0.257572	+	0.966259i	$0.417077\pi$
$72$	−9.20206	−1.08447
$73$	12.3659	1.44731	0.723657	−	0.690160i	$-0.242460\pi$
$73$	12.3659	1.44731	0.723657	+	0.690160i	$0.242460\pi$
$74$	−8.56980	−0.996218
$75$	0.615555	0.0710781
$76$	1.24685	0.143023
$77$	0	0
$78$	−0.0423593	−0.00479625
$79$	−13.5159	−1.52065	−0.760327	−	0.649540i	$-0.774961\pi$
$79$	−13.5159	−1.52065	−0.760327	+	0.649540i	$0.774961\pi$
$80$	−7.23122	−0.808475
$81$	8.89634	0.988482
$82$	−5.24421	−0.579126
$83$	9.82792	1.07875	0.539377	−	0.842064i	$-0.318660\pi$
$83$	9.82792	1.07875	0.539377	+	0.842064i	$0.318660\pi$
$84$	−0.189767	−0.0207053
$85$	−22.6061	−2.45198
$86$	1.68771	0.181990
$87$	−0.0197422	−0.00211659
$88$	0	0
$89$	9.23024	0.978404	0.489202	−	0.872171i	$-0.337288\pi$
$89$	9.23024	0.978404	0.489202	+	0.872171i	$0.337288\pi$
$90$	11.2858	1.18963
$91$	0.900959	0.0944462
$92$	−1.05218	−0.109697
$93$	−0.107389	−0.0111357
$94$	−6.66066	−0.686995
$95$	−6.08628	−0.624439
$96$	−0.388084	−0.0396086
$97$	5.92141	0.601228	0.300614	−	0.953746i	$-0.402808\pi$
$97$	5.92141	0.601228	0.300614	+	0.953746i	$0.402808\pi$
$98$	0.0773084	0.00780933
$99$	0	0
$100$	−3.84688	−0.384688
$101$	−7.06692	−0.703185	−0.351592	−	0.936153i	$-0.614360\pi$
$101$	−7.06692	−0.703185	−0.351592	+	0.936153i	$0.614360\pi$
$102$	0.854256	0.0845839
$103$	9.46983	0.933090	0.466545	−	0.884497i	$-0.345499\pi$
$103$	9.46983	0.933090	0.466545	+	0.884497i	$0.345499\pi$
$104$	1.05362	0.103316
$105$	0.926316	0.0903992
$106$	−8.64435	−0.839613
$107$	−12.5151	−1.20988	−0.604942	−	0.796270i	$-0.706804\pi$
$107$	−12.5151	−1.20988	−0.604942	+	0.796270i	$0.706804\pi$
$108$	0.431596	0.0415303
$109$	−1.73913	−0.166578	−0.0832891	−	0.996525i	$-0.526543\pi$
$109$	−1.73913	−0.166578	−0.0832891	+	0.996525i	$0.526543\pi$
$110$	0	0
$111$	0.798340	0.0757751
$112$	−5.81206	−0.549188
$113$	−7.29603	−0.686353	−0.343176	−	0.939271i	$-0.611503\pi$
$113$	−7.29603	−0.686353	−0.343176	+	0.939271i	$0.611503\pi$
$114$	0.229993	0.0215408
$115$	5.13605	0.478939
$116$	0.123378	0.0114554
$117$	−1.02257	−0.0945370
$118$	−15.2447	−1.40339
$119$	−18.1695	−1.66560
$120$	1.08327	0.0988886
$121$	0	0
$122$	−3.30171	−0.298923
$123$	0.488537	0.0440499
$124$	0.671122	0.0602685
$125$	2.39803	0.214486
$126$	9.07089	0.808099
$127$	9.10026	0.807517	0.403759	−	0.914866i	$-0.367704\pi$
$127$	9.10026	0.807517	0.403759	+	0.914866i	$0.367704\pi$
$128$	−2.66383	−0.235451
$129$	−0.157222	−0.0138427
$130$	−1.29220	−0.113333
$131$	15.2130	1.32916	0.664582	−	0.747215i	$-0.268610\pi$
$131$	15.2130	1.32916	0.664582	+	0.747215i	$0.268610\pi$
$132$	0	0
$133$	−4.89182	−0.424174
$134$	−4.43557	−0.383175
$135$	−2.10677	−0.181321
$136$	−21.2482	−1.82202
$137$	1.70017	0.145255	0.0726275	−	0.997359i	$-0.476862\pi$
$137$	1.70017	0.145255	0.0726275	+	0.997359i	$0.476862\pi$
$138$	−0.194085	−0.0165216
$139$	12.3211	1.04506	0.522532	−	0.852620i	$-0.324987\pi$
$139$	12.3211	1.04506	0.522532	+	0.852620i	$0.324987\pi$
$140$	−5.78896	−0.489257
$141$	0.620490	0.0522547
$142$	−5.00381	−0.419910
$143$	0	0
$144$	6.59660	0.549716
$145$	−0.602250	−0.0500141
$146$	−14.2550	−1.17975
$147$	−0.00720185	−0.000593999 0
$148$	−4.98918	−0.410108
$149$	−23.2285	−1.90295	−0.951475	−	0.307728i	$-0.900431\pi$
$149$	−23.2285	−1.90295	−0.951475	+	0.307728i	$0.900431\pi$
$150$	−0.709593	−0.0579380
$151$	12.4737	1.01510	0.507549	−	0.861623i	$-0.330552\pi$
$151$	12.4737	1.01510	0.507549	+	0.861623i	$0.330552\pi$
$152$	−5.72068	−0.464009
$153$	20.6221	1.66720
$154$	0	0
$155$	−3.27597	−0.263133
$156$	−0.0246608	−0.00197445
$157$	13.7145	1.09453	0.547266	−	0.836959i	$-0.315668\pi$
$157$	13.7145	1.09453	0.547266	+	0.836959i	$0.315668\pi$
$158$	15.5807	1.23953
$159$	0.805285	0.0638633
$160$	−11.8387	−0.935935
$161$	4.12807	0.325338
$162$	−10.2554	−0.805743
$163$	1.00329	0.0785834	0.0392917	−	0.999228i	$-0.487490\pi$
$163$	1.00329	0.0785834	0.0392917	+	0.999228i	$0.487490\pi$
$164$	−3.05309	−0.238406
$165$	0	0
$166$	−11.3293	−0.879327
$167$	2.30657	0.178488	0.0892440	−	0.996010i	$-0.471555\pi$
$167$	2.30657	0.178488	0.0892440	+	0.996010i	$0.471555\pi$
$168$	0.870673	0.0671739
$169$	−12.8829	−0.990994
$170$	26.0596	1.99868
$171$	5.55214	0.424583
$172$	0.982552	0.0749189
$173$	−8.11715	−0.617135	−0.308568	−	0.951202i	$-0.599850\pi$
$173$	−8.11715	−0.617135	−0.308568	+	0.951202i	$0.599850\pi$
$174$	0.0227582	0.00172530
$175$	15.0926	1.14090
$176$	0	0
$177$	1.42016	0.106746
$178$	−10.6403	−0.797528
$179$	−14.6013	−1.09135	−0.545675	−	0.837997i	$-0.683727\pi$
$179$	−14.6013	−1.09135	−0.545675	+	0.837997i	$0.683727\pi$
$180$	6.57038	0.489727
$181$	24.4581	1.81796	0.908978	−	0.416843i	$-0.136864\pi$
$181$	24.4581	1.81796	0.908978	+	0.416843i	$0.136864\pi$
$182$	−1.03860	−0.0769860
$183$	0.307579	0.0227369
$184$	4.82753	0.355890
$185$	24.3539	1.79053
$186$	0.123795	0.00907708
$187$	0	0
$188$	−3.87772	−0.282812
$189$	−1.69330	−0.123170
$190$	7.01608	0.509000
$191$	1.99534	0.144378	0.0721889	−	0.997391i	$-0.477002\pi$
$191$	1.99534	0.144378	0.0721889	+	0.997391i	$0.477002\pi$
$192$	0.921462	0.0665008
$193$	−14.2850	−1.02826	−0.514128	−	0.857713i	$-0.671884\pi$
$193$	−14.2850	−1.02826	−0.514128	+	0.857713i	$0.671884\pi$
$194$	−6.82603	−0.490080
$195$	0.120378	0.00862044
$196$	0.0450076	0.00321483
$197$	7.47401	0.532501	0.266251	−	0.963904i	$-0.414215\pi$
$197$	7.47401	0.532501	0.266251	+	0.963904i	$0.414215\pi$
$198$	0	0
$199$	−27.8678	−1.97550	−0.987749	−	0.156049i	$-0.950124\pi$
$199$	−27.8678	−1.97550	−0.987749	+	0.156049i	$0.950124\pi$
$200$	17.6499	1.24804
$201$	0.413206	0.0291453
$202$	8.14653	0.573188
$203$	−0.484055	−0.0339740
$204$	0.497333	0.0348202
$205$	14.9031	1.04088
$206$	−10.9165	−0.760591
$207$	−4.68530	−0.325651
$208$	−0.755297	−0.0523704
$209$	0	0
$210$	−1.06783	−0.0736872
$211$	−2.74406	−0.188909	−0.0944543	−	0.995529i	$-0.530111\pi$
$211$	−2.74406	−0.188909	−0.0944543	+	0.995529i	$0.530111\pi$
$212$	−5.03259	−0.345640
$213$	0.466142	0.0319395
$214$	14.4271	0.986214
$215$	−4.79617	−0.327096
$216$	−1.98021	−0.134736
$217$	−2.63305	−0.178743
$218$	2.00481	0.135783
$219$	1.32796	0.0897351
$220$	0	0
$221$	−2.36119	−0.158831
$222$	−0.920302	−0.0617666
$223$	18.4742	1.23713	0.618564	−	0.785735i	$-0.287715\pi$
$223$	18.4742	1.23713	0.618564	+	0.785735i	$0.287715\pi$
$224$	−9.51533	−0.635770
$225$	−17.1299	−1.14199
$226$	8.41064	0.559468
$227$	16.7025	1.10858	0.554292	−	0.832322i	$-0.312989\pi$
$227$	16.7025	1.10858	0.554292	+	0.832322i	$0.312989\pi$
$228$	0.133898	0.00886759
$229$	7.17201	0.473940	0.236970	−	0.971517i	$-0.423846\pi$
$229$	7.17201	0.473940	0.236970	+	0.971517i	$0.423846\pi$
$230$	−5.92068	−0.390398
$231$	0	0
$232$	−0.566073	−0.0371645
$233$	−19.5627	−1.28160	−0.640798	−	0.767709i	$-0.721397\pi$
$233$	−19.5627	−1.28160	−0.640798	+	0.767709i	$0.721397\pi$
$234$	1.17879	0.0770601
$235$	18.9285	1.23476
$236$	−8.87521	−0.577727
$237$	−1.45146	−0.0942823
$238$	20.9453	1.35768
$239$	27.7470	1.79480	0.897401	−	0.441216i	$-0.145453\pi$
$239$	27.7470	1.79480	0.897401	+	0.441216i	$0.145453\pi$
$240$	−0.776554	−0.0501264
$241$	−17.6551	−1.13726	−0.568631	−	0.822593i	$-0.692527\pi$
$241$	−17.6551	−1.13726	−0.568631	+	0.822593i	$0.692527\pi$
$242$	0	0
$243$	2.88466	0.185051
$244$	−1.92220	−0.123056
$245$	−0.219697	−0.0140359
$246$	−0.563171	−0.0359064
$247$	−0.635708	−0.0404492
$248$	−3.07919	−0.195529
$249$	1.05541	0.0668840
$250$	−2.76438	−0.174835
$251$	−16.6714	−1.05229	−0.526144	−	0.850396i	$-0.676363\pi$
$251$	−16.6714	−1.05229	−0.526144	+	0.850396i	$0.676363\pi$
$252$	5.28091	0.332666
$253$	0	0
$254$	−10.4905	−0.658233
$255$	−2.42765	−0.152025
$256$	−14.0904	−0.880650
$257$	−16.3614	−1.02060	−0.510299	−	0.859997i	$-0.670465\pi$
$257$	−16.3614	−1.02060	−0.510299	+	0.859997i	$0.670465\pi$
$258$	0.181241	0.0112836
$259$	19.5743	1.21629
$260$	−0.752295	−0.0466554
$261$	0.549395	0.0340067
$262$	−17.5371	−1.08344
$263$	−9.37200	−0.577902	−0.288951	−	0.957344i	$-0.593307\pi$
$263$	−9.37200	−0.577902	−0.288951	+	0.957344i	$0.593307\pi$
$264$	0	0
$265$	24.5658	1.50906
$266$	5.63914	0.345758
$267$	0.991227	0.0606621
$268$	−2.58231	−0.157740
$269$	14.5309	0.885964	0.442982	−	0.896531i	$-0.353921\pi$
$269$	14.5309	0.885964	0.442982	+	0.896531i	$0.353921\pi$
$270$	2.42861	0.147801
$271$	7.68414	0.466779	0.233389	−	0.972383i	$-0.425018\pi$
$271$	7.68414	0.466779	0.233389	+	0.972383i	$0.425018\pi$
$272$	15.2320	0.923575
$273$	0.0967531	0.00585577
$274$	−1.95990	−0.118402
$275$	0	0
$276$	−0.112993	−0.00680136
$277$	12.1756	0.731563	0.365781	−	0.930701i	$-0.380802\pi$
$277$	12.1756	0.731563	0.365781	+	0.930701i	$0.380802\pi$
$278$	−14.2034	−0.851864
$279$	2.98847	0.178915
$280$	26.5604	1.58729
$281$	15.6056	0.930950	0.465475	−	0.885061i	$-0.345884\pi$
$281$	15.6056	0.930950	0.465475	+	0.885061i	$0.345884\pi$
$282$	−0.715282	−0.0425944
$283$	8.35173	0.496459	0.248230	−	0.968701i	$-0.420151\pi$
$283$	8.35173	0.496459	0.248230	+	0.968701i	$0.420151\pi$
$284$	−2.91313	−0.172862
$285$	−0.653600	−0.0387159
$286$	0	0
$287$	11.9783	0.707058
$288$	10.7998	0.636382
$289$	30.6180	1.80106
$290$	0.694255	0.0407681
$291$	0.635895	0.0372768
$292$	−8.29900	−0.485662
$293$	31.3717	1.83276	0.916378	−	0.400313i	$-0.131099\pi$
$293$	31.3717	1.83276	0.916378	+	0.400313i	$0.131099\pi$
$294$	0.00830207	0.000484187 0
$295$	43.3229	2.52236
$296$	22.8910	1.33051
$297$	0	0
$298$	26.7771	1.55115
$299$	0.536457	0.0310241
$300$	−0.413112	−0.0238511
$301$	−3.85490	−0.222193
$302$	−14.3793	−0.827438
$303$	−0.758909	−0.0435982
$304$	4.10094	0.235205
$305$	9.38290	0.537263
$306$	−23.7726	−1.35899
$307$	20.3687	1.16250	0.581251	−	0.813724i	$-0.302563\pi$
$307$	20.3687	1.16250	0.581251	+	0.813724i	$0.302563\pi$
$308$	0	0
$309$	1.01696	0.0578526
$310$	3.77644	0.214488
$311$	−29.6459	−1.68106	−0.840531	−	0.541763i	$-0.817757\pi$
$311$	−29.6459	−1.68106	−0.840531	+	0.541763i	$0.817757\pi$
$312$	0.113147	0.00640568
$313$	21.5561	1.21842	0.609212	−	0.793008i	$-0.291486\pi$
$313$	21.5561	1.21842	0.609212	+	0.793008i	$0.291486\pi$
$314$	−15.8096	−0.892188
$315$	−25.7779	−1.45242
$316$	9.07080	0.510272
$317$	19.2133	1.07912	0.539562	−	0.841946i	$-0.318590\pi$
$317$	19.2133	1.07912	0.539562	+	0.841946i	$0.318590\pi$
$318$	−0.928308	−0.0520570
$319$	0	0
$320$	28.1098	1.57139
$321$	−1.34399	−0.0750141
$322$	−4.75872	−0.265193
$323$	12.8203	0.713339
$324$	−5.97053	−0.331696
$325$	1.96134	0.108796
$326$	−1.15656	−0.0640558
$327$	−0.186763	−0.0103280
$328$	14.0079	0.773458
$329$	15.2136	0.838755
$330$	0	0
$331$	−0.0130451	−0.000717023 0	−0.000358512	−	1.00000i	$-0.500114\pi$
$331$	−0.0130451	−0.000717023 0	−0.000358512		1.00000i	$0.500114\pi$
$332$	−6.59574	−0.361988
$333$	−22.2165	−1.21746
$334$	−2.65895	−0.145491
$335$	12.6051	0.688691
$336$	−0.624151	−0.0340503
$337$	−11.6798	−0.636242	−0.318121	−	0.948050i	$-0.603052\pi$
$337$	−11.6798	−0.636242	−0.318121	+	0.948050i	$0.603052\pi$
$338$	14.8510	0.807790
$339$	−0.783514	−0.0425546
$340$	15.1715	0.822788
$341$	0	0
$342$	−6.40033	−0.346090
$343$	−18.6079	−1.00473
$344$	−4.50807	−0.243059
$345$	0.551556	0.0296948
$346$	9.35720	0.503046
$347$	−5.75926	−0.309173	−0.154587	−	0.987979i	$-0.549405\pi$
$347$	−5.75926	−0.309173	−0.154587	+	0.987979i	$0.549405\pi$
$348$	0.0132494	0.000710245 0
$349$	−29.8101	−1.59570	−0.797849	−	0.602857i	$-0.794029\pi$
$349$	−29.8101	−1.59570	−0.797849	+	0.602857i	$0.794029\pi$
$350$	−17.3983	−0.929980
$351$	−0.220050	−0.0117454
$352$	0	0
$353$	36.0545	1.91899	0.959493	−	0.281734i	$-0.0909095\pi$
$353$	36.0545	1.91899	0.959493	+	0.281734i	$0.0909095\pi$
$354$	−1.63712	−0.0870117
$355$	14.2200	0.754718
$356$	−6.19462	−0.328314
$357$	−1.95121	−0.103269
$358$	16.8319	0.889593
$359$	3.54787	0.187250	0.0936248	−	0.995608i	$-0.470155\pi$
$359$	3.54787	0.187250	0.0936248	+	0.995608i	$0.470155\pi$
$360$	−30.1457	−1.58882
$361$	−15.5484	−0.818336
$362$	−28.1946	−1.48187
$363$	0	0
$364$	−0.604653	−0.0316925
$365$	40.5102	2.12040
$366$	−0.354568	−0.0185336
$367$	−3.51477	−0.183469	−0.0917347	−	0.995783i	$-0.529241\pi$
$367$	−3.51477	−0.183469	−0.0917347	+	0.995783i	$0.529241\pi$
$368$	−3.46067	−0.180400
$369$	−13.5952	−0.707739
$370$	−28.0744	−1.45952
$371$	19.7446	1.02509
$372$	0.0720712	0.00373672
$373$	−17.5147	−0.906877	−0.453438	−	0.891288i	$-0.649803\pi$
$373$	−17.5147	−0.906877	−0.453438	+	0.891288i	$0.649803\pi$
$374$	0	0
$375$	0.257522	0.0132984
$376$	17.7914	0.917523
$377$	−0.0629046	−0.00323975
$378$	1.95199	0.100399
$379$	−23.2999	−1.19684	−0.598418	−	0.801184i	$-0.704204\pi$
$379$	−23.2999	−1.19684	−0.598418	+	0.801184i	$0.704204\pi$
$380$	4.08464	0.209538
$381$	0.977268	0.0500670
$382$	−2.30017	−0.117687
$383$	33.8396	1.72912	0.864562	−	0.502526i	$-0.167596\pi$
$383$	33.8396	1.72912	0.864562	+	0.502526i	$0.167596\pi$
$384$	−0.286066	−0.0145982
$385$	0	0
$386$	16.4673	0.838164
$387$	4.37525	0.222406
$388$	−3.97399	−0.201749
$389$	−20.4381	−1.03625	−0.518126	−	0.855304i	$-0.673370\pi$
$389$	−20.4381	−1.03625	−0.518126	+	0.855304i	$0.673370\pi$
$390$	−0.138768	−0.00702679
$391$	−10.8187	−0.547124
$392$	−0.206500	−0.0104298
$393$	1.63371	0.0824096
$394$	−8.61581	−0.434058
$395$	−44.2777	−2.22785
$396$	0	0
$397$	−11.1155	−0.557869	−0.278934	−	0.960310i	$-0.589981\pi$
$397$	−11.1155	−0.557869	−0.278934	+	0.960310i	$0.589981\pi$
$398$	32.1252	1.61029
$399$	−0.525328	−0.0262993
$400$	−12.6525	−0.632627
$401$	−30.2195	−1.50909	−0.754545	−	0.656249i	$-0.772142\pi$
$401$	−30.2195	−1.50909	−0.754545	+	0.656249i	$0.772142\pi$
$402$	−0.476331	−0.0237572
$403$	−0.342173	−0.0170449
$404$	4.74276	0.235961
$405$	29.1442	1.44819
$406$	0.558004	0.0276933
$407$	0	0
$408$	−2.28182	−0.112967
$409$	−28.5272	−1.41058	−0.705290	−	0.708919i	$-0.749183\pi$
$409$	−28.5272	−1.41058	−0.705290	+	0.708919i	$0.749183\pi$
$410$	−17.1799	−0.848454
$411$	0.182579	0.00900596
$412$	−6.35541	−0.313109
$413$	34.8205	1.71341
$414$	5.40107	0.265448
$415$	32.1960	1.58044
$416$	−1.23655	−0.0606269
$417$	1.32315	0.0647951
$418$	0	0
$419$	−9.56270	−0.467169	−0.233584	−	0.972337i	$-0.575045\pi$
$419$	−9.56270	−0.467169	−0.233584	+	0.972337i	$0.575045\pi$
$420$	−0.621671	−0.0303344
$421$	7.66340	0.373491	0.186746	−	0.982408i	$-0.440206\pi$
$421$	7.66340	0.373491	0.186746	+	0.982408i	$0.440206\pi$
$422$	3.16326	0.153985
$423$	−17.2673	−0.839562
$424$	23.0901	1.12136
$425$	−39.5541	−1.91866
$426$	−0.537354	−0.0260349
$427$	7.54146	0.364957
$428$	8.39918	0.405990
$429$	0	0
$430$	5.52888	0.266626
$431$	14.6736	0.706800	0.353400	−	0.935472i	$-0.385025\pi$
$431$	14.6736	0.706800	0.353400	+	0.935472i	$0.385025\pi$
$432$	1.41954	0.0682976
$433$	4.75175	0.228354	0.114177	−	0.993460i	$-0.463577\pi$
$433$	4.75175	0.228354	0.114177	+	0.993460i	$0.463577\pi$
$434$	3.03530	0.145699
$435$	−0.0646750	−0.00310093
$436$	1.16717	0.0558972
$437$	−2.91273	−0.139335
$438$	−1.53083	−0.0731459
$439$	−13.9499	−0.665793	−0.332897	−	0.942963i	$-0.608026\pi$
$439$	−13.9499	−0.665793	−0.332897	+	0.942963i	$0.608026\pi$
$440$	0	0
$441$	0.200416	0.00954363
$442$	2.72191	0.129468
$443$	41.4538	1.96953	0.984766	−	0.173886i	$-0.0556325\pi$
$443$	41.4538	1.96953	0.984766	+	0.173886i	$0.0556325\pi$
$444$	−0.535784	−0.0254272
$445$	30.2380	1.43342
$446$	−21.2966	−1.00842
$447$	−2.49448	−0.117985
$448$	22.5931	1.06742
$449$	32.8894	1.55215	0.776074	−	0.630642i	$-0.217208\pi$
$449$	32.8894	1.55215	0.776074	+	0.630642i	$0.217208\pi$
$450$	19.7468	0.930875
$451$	0	0
$452$	4.89653	0.230313
$453$	1.33954	0.0629372
$454$	−19.2541	−0.903641
$455$	2.95152	0.138369
$456$	−0.614339	−0.0287690
$457$	−27.9961	−1.30960	−0.654802	−	0.755801i	$-0.727248\pi$
$457$	−27.9961	−1.30960	−0.654802	+	0.755801i	$0.727248\pi$
$458$	−8.26768	−0.386323
$459$	4.43773	0.207136
$460$	−3.44692	−0.160713
$461$	18.4278	0.858268	0.429134	−	0.903241i	$-0.358819\pi$
$461$	18.4278	0.858268	0.429134	+	0.903241i	$0.358819\pi$
$462$	0	0
$463$	−26.2380	−1.21938	−0.609691	−	0.792639i	$-0.708707\pi$
$463$	−26.2380	−1.21938	−0.609691	+	0.792639i	$0.708707\pi$
$464$	0.405796	0.0188386
$465$	−0.351804	−0.0163145
$466$	22.5513	1.04467
$467$	−34.4708	−1.59512	−0.797559	−	0.603241i	$-0.793876\pi$
$467$	−34.4708	−1.59512	−0.797559	+	0.603241i	$0.793876\pi$
$468$	0.686272	0.0317229
$469$	10.1313	0.467820
$470$	−21.8201	−1.00649
$471$	1.47278	0.0678622
$472$	40.7205	1.87431
$473$	0	0
$474$	1.67320	0.0768524
$475$	−10.6492	−0.488620
$476$	12.1940	0.558910
$477$	−22.4098	−1.02608
$478$	−31.9859	−1.46300
$479$	−34.1531	−1.56050	−0.780248	−	0.625470i	$-0.784907\pi$
$479$	−34.1531	−1.56050	−0.780248	+	0.625470i	$0.784907\pi$
$480$	−1.27135	−0.0580290
$481$	2.54375	0.115985
$482$	20.3522	0.927018
$483$	0.443310	0.0201713
$484$	0	0
$485$	19.3984	0.880836
$486$	−3.32535	−0.150841
$487$	9.48784	0.429935	0.214968	−	0.976621i	$-0.431035\pi$
$487$	9.48784	0.429935	0.214968	+	0.976621i	$0.431035\pi$
$488$	8.81928	0.399230
$489$	0.107742	0.00487226
$490$	0.253260	0.0114411
$491$	−14.2933	−0.645049	−0.322524	−	0.946561i	$-0.604531\pi$
$491$	−14.2933	−0.645049	−0.322524	+	0.946561i	$0.604531\pi$
$492$	−0.327868	−0.0147814
$493$	1.26859	0.0571344
$494$	0.732825	0.0329714
$495$	0	0
$496$	2.20735	0.0991130
$497$	11.4292	0.512671
$498$	−1.21665	−0.0545192
$499$	2.89660	0.129670	0.0648348	−	0.997896i	$-0.479348\pi$
$499$	2.89660	0.129670	0.0648348	+	0.997896i	$0.479348\pi$
$500$	−1.60937	−0.0719733
$501$	0.247701	0.0110664
$502$	19.2182	0.857752
$503$	25.4083	1.13290	0.566449	−	0.824097i	$-0.308317\pi$
$503$	25.4083	1.13290	0.566449	+	0.824097i	$0.308317\pi$
$504$	−24.2294	−1.07927
$505$	−23.1510	−1.03021
$506$	0	0
$507$	−1.38348	−0.0614427
$508$	−6.10738	−0.270971
$509$	31.0667	1.37701	0.688504	−	0.725232i	$-0.258268\pi$
$509$	31.0667	1.37701	0.688504	+	0.725232i	$0.258268\pi$
$510$	2.79852	0.123921
$511$	32.5599	1.44036
$512$	21.5706	0.953297
$513$	1.19478	0.0527507
$514$	18.8609	0.831921
$515$	31.0229	1.36703
$516$	0.105515	0.00464506
$517$	0	0
$518$	−22.5647	−0.991435
$519$	−0.871693	−0.0382631
$520$	3.45162	0.151364
$521$	−1.23390	−0.0540581	−0.0270290	−	0.999635i	$-0.508605\pi$
$521$	−1.23390	−0.0540581	−0.0270290	+	0.999635i	$0.508605\pi$
$522$	−0.633326	−0.0277199
$523$	1.97777	0.0864817	0.0432409	−	0.999065i	$-0.486232\pi$
$523$	1.97777	0.0864817	0.0432409	+	0.999065i	$0.486232\pi$
$524$	−10.2098	−0.446016
$525$	1.62078	0.0707368
$526$	10.8038	0.471066
$527$	6.90058	0.300594
$528$	0	0
$529$	−20.5420	−0.893131
$530$	−28.3187	−1.23008
$531$	−39.5208	−1.71506
$532$	3.28301	0.142336
$533$	1.55662	0.0674249
$534$	−1.14266	−0.0494476
$535$	−40.9992	−1.77255
$536$	11.8479	0.511753
$537$	−1.56801	−0.0676648
$538$	−16.7508	−0.722177
$539$	0	0
$540$	1.41390	0.0608444
$541$	34.8968	1.50033	0.750166	−	0.661249i	$-0.229973\pi$
$541$	34.8968	1.50033	0.750166	+	0.661249i	$0.229973\pi$
$542$	−8.85805	−0.380486
$543$	2.62653	0.112715
$544$	24.9374	1.06918
$545$	−5.69734	−0.244047
$546$	−0.111534	−0.00477322
$547$	−13.4432	−0.574792	−0.287396	−	0.957812i	$-0.592790\pi$
$547$	−13.4432	−0.574792	−0.287396	+	0.957812i	$0.592790\pi$
$548$	−1.14102	−0.0487419
$549$	−8.55944	−0.365308
$550$	0	0
$551$	0.341545	0.0145503
$552$	0.518424	0.0220656
$553$	−35.5879	−1.51335
$554$	−14.0357	−0.596319
$555$	2.61534	0.111015
$556$	−8.26898	−0.350683
$557$	39.1484	1.65877	0.829386	−	0.558675i	$-0.188690\pi$
$557$	39.1484	1.65877	0.829386	+	0.558675i	$0.188690\pi$
$558$	−3.44501	−0.145839
$559$	−0.500957	−0.0211882
$560$	−19.0402	−0.804593
$561$	0	0
$562$	−17.9896	−0.758846
$563$	−17.4664	−0.736121	−0.368060	−	0.929802i	$-0.619978\pi$
$563$	−17.4664	−0.736121	−0.368060	+	0.929802i	$0.619978\pi$
$564$	−0.416424	−0.0175346
$565$	−23.9016	−1.00555
$566$	−9.62763	−0.404679
$567$	23.4245	0.983736
$568$	13.3658	0.560816
$569$	10.7176	0.449304	0.224652	−	0.974439i	$-0.427876\pi$
$569$	10.7176	0.449304	0.224652	+	0.974439i	$0.427876\pi$
$570$	0.753450	0.0315586
$571$	−41.8928	−1.75316	−0.876580	−	0.481256i	$-0.840181\pi$
$571$	−41.8928	−1.75316	−0.876580	+	0.481256i	$0.840181\pi$
$572$	0	0
$573$	0.214278	0.00895158
$574$	−13.8082	−0.576345
$575$	8.98660	0.374767
$576$	−25.6428	−1.06845
$577$	−8.79461	−0.366124	−0.183062	−	0.983101i	$-0.558601\pi$
$577$	−8.79461	−0.366124	−0.183062	+	0.983101i	$0.558601\pi$
$578$	−35.2954	−1.46810
$579$	−1.53405	−0.0637530
$580$	0.404183	0.0167828
$581$	25.8774	1.07357
$582$	−0.733040	−0.0303855
$583$	0	0
$584$	38.0768	1.57563
$585$	−3.34993	−0.138502
$586$	−36.1644	−1.49394
$587$	−30.5869	−1.26246	−0.631228	−	0.775598i	$-0.717449\pi$
$587$	−30.5869	−1.26246	−0.631228	+	0.775598i	$0.717449\pi$
$588$	0.00483332	0.000199323 0
$589$	1.85785	0.0765515
$590$	−49.9413	−2.05605
$591$	0.802627	0.0330157
$592$	−16.4096	−0.674432
$593$	32.2636	1.32491	0.662453	−	0.749104i	$-0.269516\pi$
$593$	32.2636	1.32491	0.662453	+	0.749104i	$0.269516\pi$
$594$	0	0
$595$	−59.5229	−2.44020
$596$	15.5891	0.638556
$597$	−2.99270	−0.122483
$598$	−0.618412	−0.0252887
$599$	−25.2799	−1.03291	−0.516455	−	0.856314i	$-0.672749\pi$
$599$	−25.2799	−1.03291	−0.516455	+	0.856314i	$0.672749\pi$
$600$	1.89541	0.0773797
$601$	1.67048	0.0681405	0.0340702	−	0.999419i	$-0.489153\pi$
$601$	1.67048	0.0681405	0.0340702	+	0.999419i	$0.489153\pi$
$602$	4.44381	0.181116
$603$	−11.4989	−0.468270
$604$	−8.37140	−0.340627
$605$	0	0
$606$	0.874848	0.0355383
$607$	−25.0906	−1.01840	−0.509198	−	0.860650i	$-0.670058\pi$
$607$	−25.0906	−1.01840	−0.509198	+	0.860650i	$0.670058\pi$
$608$	6.71393	0.272286
$609$	−0.0519822	−0.00210643
$610$	−10.8163	−0.437940
$611$	1.97707	0.0799835
$612$	−13.8400	−0.559448
$613$	−4.95539	−0.200146	−0.100073	−	0.994980i	$-0.531908\pi$
$613$	−4.95539	−0.200146	−0.100073	+	0.994980i	$0.531908\pi$
$614$	−23.4804	−0.947592
$615$	1.60043	0.0645357
$616$	0	0
$617$	−39.7247	−1.59926	−0.799628	−	0.600495i	$-0.794970\pi$
$617$	−39.7247	−1.59926	−0.799628	+	0.600495i	$0.794970\pi$
$618$	−1.17232	−0.0471575
$619$	32.5556	1.30852	0.654260	−	0.756270i	$-0.272980\pi$
$619$	32.5556	1.30852	0.654260	+	0.756270i	$0.272980\pi$
$620$	2.19858	0.0882970
$621$	−1.00824	−0.0404593
$622$	34.1748	1.37029
$623$	24.3037	0.973706
$624$	−0.0811106	−0.00324702
$625$	−20.8041	−0.832166
$626$	−24.8492	−0.993175
$627$	0	0
$628$	−9.20407	−0.367283
$629$	−51.2995	−2.04545
$630$	29.7160	1.18391
$631$	−27.2465	−1.08467	−0.542333	−	0.840164i	$-0.682459\pi$
$631$	−27.2465	−1.08467	−0.542333	+	0.840164i	$0.682459\pi$
$632$	−41.6179	−1.65547
$633$	−0.294682	−0.0117125
$634$	−22.1485	−0.879628
$635$	29.8122	1.18306
$636$	−0.540445	−0.0214300
$637$	−0.0229472	−0.000909203 0
$638$	0	0
$639$	−12.9720	−0.513164
$640$	−8.72662	−0.344950
$641$	−9.63386	−0.380514	−0.190257	−	0.981734i	$-0.560932\pi$
$641$	−9.63386	−0.380514	−0.190257	+	0.981734i	$0.560932\pi$
$642$	1.54931	0.0611463
$643$	22.4579	0.885653	0.442827	−	0.896607i	$-0.353976\pi$
$643$	22.4579	0.885653	0.442827	+	0.896607i	$0.353976\pi$
$644$	−2.77044	−0.109171
$645$	−0.515056	−0.0202803
$646$	−14.7788	−0.581465
$647$	−47.5680	−1.87009	−0.935046	−	0.354525i	$-0.884642\pi$
$647$	−47.5680	−1.87009	−0.935046	+	0.354525i	$0.884642\pi$
$648$	27.3935	1.07612
$649$	0	0
$650$	−2.26097	−0.0886827
$651$	−0.282760	−0.0110823
$652$	−0.673327	−0.0263695
$653$	47.0874	1.84267	0.921337	−	0.388766i	$-0.127098\pi$
$653$	47.0874	1.84267	0.921337	+	0.388766i	$0.127098\pi$
$654$	0.215295	0.00841870
$655$	49.8373	1.94730
$656$	−10.0417	−0.392064
$657$	−36.9550	−1.44175
$658$	−17.5378	−0.683696
$659$	−9.75425	−0.379971	−0.189986	−	0.981787i	$-0.560844\pi$
$659$	−9.75425	−0.379971	−0.189986	+	0.981787i	$0.560844\pi$
$660$	0	0
$661$	−20.9488	−0.814813	−0.407407	−	0.913247i	$-0.633567\pi$
$661$	−20.9488	−0.814813	−0.407407	+	0.913247i	$0.633567\pi$
$662$	0.0150380	0.000584468 0
$663$	−0.253566	−0.00984770
$664$	30.2620	1.17439
$665$	−16.0255	−0.621441
$666$	25.6106	0.992389
$667$	−0.288221	−0.0111599
$668$	−1.54799	−0.0598936
$669$	1.98393	0.0767032
$670$	−14.5308	−0.561374
$671$	0	0
$672$	−1.02184	−0.0394184
$673$	4.53121	0.174665	0.0873327	−	0.996179i	$-0.472166\pi$
$673$	4.53121	0.174665	0.0873327	+	0.996179i	$0.472166\pi$
$674$	13.4642	0.518620
$675$	−3.68623	−0.141883
$676$	8.64601	0.332539
$677$	24.7951	0.952955	0.476477	−	0.879187i	$-0.341913\pi$
$677$	24.7951	0.952955	0.476477	+	0.879187i	$0.341913\pi$
$678$	0.903211	0.0346876
$679$	15.5914	0.598342
$680$	−69.6085	−2.66936
$681$	1.79366	0.0687334
$682$	0	0
$683$	−3.58738	−0.137267	−0.0686336	−	0.997642i	$-0.521864\pi$
$683$	−3.58738	−0.137267	−0.0686336	+	0.997642i	$0.521864\pi$
$684$	−3.72616	−0.142473
$685$	5.56970	0.212807
$686$	21.4506	0.818989
$687$	0.770196	0.0293848
$688$	3.23166	0.123206
$689$	2.56588	0.0977522
$690$	−0.635817	−0.0242051
$691$	−40.1663	−1.52800	−0.763999	−	0.645217i	$-0.776767\pi$
$691$	−40.1663	−1.52800	−0.763999	+	0.645217i	$0.776767\pi$
$692$	5.44760	0.207087
$693$	0	0
$694$	6.63910	0.252017
$695$	40.3637	1.53108
$696$	−0.0607900	−0.00230424
$697$	−31.3923	−1.18907
$698$	34.3642	1.30070
$699$	−2.10082	−0.0794604
$700$	−10.1290	−0.382840
$701$	24.4163	0.922189	0.461095	−	0.887351i	$-0.347457\pi$
$701$	24.4163	0.922189	0.461095	+	0.887351i	$0.347457\pi$
$702$	0.253667	0.00957406
$703$	−13.8115	−0.520909
$704$	0	0
$705$	2.03271	0.0765562
$706$	−41.5625	−1.56422
$707$	−18.6075	−0.699808
$708$	−0.953100	−0.0358197
$709$	−6.87752	−0.258290	−0.129145	−	0.991626i	$-0.541223\pi$
$709$	−6.87752	−0.258290	−0.129145	+	0.991626i	$0.541223\pi$
$710$	−16.3923	−0.615194
$711$	40.3918	1.51481
$712$	28.4217	1.06515
$713$	−1.56779	−0.0587143
$714$	2.24930	0.0841778
$715$	0	0
$716$	9.79923	0.366214
$717$	2.97972	0.111280
$718$	−4.08988	−0.152633
$719$	−1.77394	−0.0661566	−0.0330783	−	0.999453i	$-0.510531\pi$
$719$	−1.77394	−0.0661566	−0.0330783	+	0.999453i	$0.510531\pi$
$720$	21.6103	0.805368
$721$	24.9345	0.928610
$722$	17.9237	0.667051
$723$	−1.89596	−0.0705115
$724$	−16.4144	−0.610036
$725$	−1.05376	−0.0391357
$726$	0	0
$727$	13.6200	0.505139	0.252569	−	0.967579i	$-0.418724\pi$
$727$	13.6200	0.505139	0.252569	+	0.967579i	$0.418724\pi$
$728$	2.77422	0.102820
$729$	−26.3792	−0.977009
$730$	−46.6990	−1.72841
$731$	10.1027	0.373664
$732$	−0.206423	−0.00762962
$733$	−23.9566	−0.884856	−0.442428	−	0.896804i	$-0.645883\pi$
$733$	−23.9566	−0.884856	−0.442428	+	0.896804i	$0.645883\pi$
$734$	4.05172	0.149552
$735$	−0.0235931	−0.000870244 0
$736$	−5.66571	−0.208841
$737$	0	0
$738$	15.6721	0.576900
$739$	32.2523	1.18642	0.593210	−	0.805048i	$-0.297861\pi$
$739$	32.2523	1.18642	0.593210	+	0.805048i	$0.297861\pi$
$740$	−16.3444	−0.600833
$741$	−0.0682681	−0.00250789
$742$	−22.7610	−0.835582
$743$	44.9374	1.64859	0.824296	−	0.566159i	$-0.191571\pi$
$743$	44.9374	1.64859	0.824296	+	0.566159i	$0.191571\pi$
$744$	−0.330671	−0.0121230
$745$	−76.0958	−2.78793
$746$	20.1904	0.739223
$747$	−29.3704	−1.07461
$748$	0	0
$749$	−32.9529	−1.20407
$750$	−0.296864	−0.0108399
$751$	26.6343	0.971898	0.485949	−	0.873987i	$-0.338474\pi$
$751$	26.6343	0.971898	0.485949	+	0.873987i	$0.338474\pi$
$752$	−12.7540	−0.465090
$753$	−1.79032	−0.0652430
$754$	0.0725145	0.00264082
$755$	40.8636	1.48718
$756$	1.13641	0.0413309
$757$	33.5729	1.22023	0.610113	−	0.792314i	$-0.291124\pi$
$757$	33.5729	1.22023	0.610113	+	0.792314i	$0.291124\pi$
$758$	26.8594	0.975578
$759$	0	0
$760$	−18.7408	−0.679801
$761$	−4.80013	−0.174005	−0.0870023	−	0.996208i	$-0.527729\pi$
$761$	−4.80013	−0.174005	−0.0870023	+	0.996208i	$0.527729\pi$
$762$	−1.12656	−0.0408111
$763$	−4.57921	−0.165778
$764$	−1.33912	−0.0484476
$765$	67.5576	2.44255
$766$	−39.0093	−1.40946
$767$	4.52505	0.163390
$768$	−1.51316	−0.0546013
$769$	34.9209	1.25928	0.629640	−	0.776887i	$-0.283202\pi$
$769$	34.9209	1.25928	0.629640	+	0.776887i	$0.283202\pi$
$770$	0	0
$771$	−1.75704	−0.0632781
$772$	9.58698	0.345043
$773$	29.7126	1.06869	0.534344	−	0.845267i	$-0.320559\pi$
$773$	29.7126	1.06869	0.534344	+	0.845267i	$0.320559\pi$
$774$	−5.04365	−0.181290
$775$	−5.73201	−0.205900
$776$	18.2331	0.654532
$777$	2.10207	0.0754112
$778$	23.5604	0.844682
$779$	−8.45180	−0.302817
$780$	−0.0807883	−0.00289268
$781$	0	0
$782$	12.4714	0.445978
$783$	0.118226	0.00422504
$784$	0.148032	0.00528686
$785$	44.9282	1.60356
$786$	−1.88329	−0.0671746
$787$	−47.1544	−1.68087	−0.840436	−	0.541911i	$-0.817701\pi$
$787$	−47.1544	−1.68087	−0.840436	+	0.541911i	$0.817701\pi$
$788$	−5.01598	−0.178687
$789$	−1.00645	−0.0358306
$790$	51.0419	1.81599
$791$	−19.2108	−0.683057
$792$	0	0
$793$	0.980038	0.0348022
$794$	12.8136	0.454736
$795$	2.63809	0.0935635
$796$	18.7027	0.662900
$797$	2.69124	0.0953287	0.0476644	−	0.998863i	$-0.484822\pi$
$797$	2.69124	0.0953287	0.0476644	+	0.998863i	$0.484822\pi$
$798$	0.605582	0.0214374
$799$	−39.8713	−1.41054
$800$	−20.7144	−0.732364
$801$	−27.5843	−0.974643
$802$	34.8361	1.23011
$803$	0	0
$804$	−0.277312	−0.00978003
$805$	13.5235	0.476639
$806$	0.394447	0.0138938
$807$	1.56046	0.0549307
$808$	−21.7604	−0.765527
$809$	2.06674	0.0726628	0.0363314	−	0.999340i	$-0.488433\pi$
$809$	2.06674	0.0726628	0.0363314	+	0.999340i	$0.488433\pi$
$810$	−33.5965	−1.18046
$811$	0.783325	0.0275063	0.0137531	−	0.999905i	$-0.495622\pi$
$811$	0.783325	0.0275063	0.0137531	+	0.999905i	$0.495622\pi$
$812$	0.324860	0.0114004
$813$	0.825193	0.0289408
$814$	0	0
$815$	3.28674	0.115129
$816$	1.63575	0.0572627
$817$	2.71998	0.0951601
$818$	32.8853	1.14981
$819$	−2.69249	−0.0940831
$820$	−10.0018	−0.349279
$821$	22.4309	0.782845	0.391423	−	0.920211i	$-0.371983\pi$
$821$	22.4309	0.782845	0.391423	+	0.920211i	$0.371983\pi$
$822$	−0.210472	−0.00734104
$823$	−21.4831	−0.748853	−0.374426	−	0.927257i	$-0.622160\pi$
$823$	−21.4831	−0.748853	−0.374426	+	0.927257i	$0.622160\pi$
$824$	29.1594	1.01582
$825$	0	0
$826$	−40.1401	−1.39665
$827$	−40.8268	−1.41969	−0.709844	−	0.704359i	$-0.751235\pi$
$827$	−40.8268	−1.41969	−0.709844	+	0.704359i	$0.751235\pi$
$828$	3.14441	0.109276
$829$	14.7640	0.512774	0.256387	−	0.966574i	$-0.417468\pi$
$829$	14.7640	0.512774	0.256387	+	0.966574i	$0.417468\pi$
$830$	−37.1146	−1.28827
$831$	1.30753	0.0453577
$832$	2.93605	0.101789
$833$	0.462775	0.0160342
$834$	−1.52529	−0.0528165
$835$	7.55627	0.261496
$836$	0	0
$837$	0.643096	0.0222286
$838$	11.0236	0.380804
$839$	28.5773	0.986598	0.493299	−	0.869860i	$-0.335791\pi$
$839$	28.5773	0.986598	0.493299	+	0.869860i	$0.335791\pi$
$840$	2.85230	0.0984137
$841$	−28.9662	−0.998835
$842$	−8.83414	−0.304444
$843$	1.67587	0.0577199
$844$	1.84160	0.0633904
$845$	−42.2041	−1.45187
$846$	19.9052	0.684354
$847$	0	0
$848$	−16.5524	−0.568412
$849$	0.896885	0.0307810
$850$	45.5968	1.56396
$851$	11.6551	0.399532
$852$	−0.312838	−0.0107177
$853$	29.2738	1.00232	0.501158	−	0.865356i	$-0.332907\pi$
$853$	29.2738	1.00232	0.501158	+	0.865356i	$0.332907\pi$
$854$	−8.69356	−0.297488
$855$	18.1887	0.622039
$856$	−38.5364	−1.31715
$857$	−10.2407	−0.349815	−0.174907	−	0.984585i	$-0.555963\pi$
$857$	−10.2407	−0.349815	−0.174907	+	0.984585i	$0.555963\pi$
$858$	0	0
$859$	0.0382432	0.00130484	0.000652421	−	1.00000i	$-0.499792\pi$
$859$	0.0382432	0.00130484	0.000652421		1.00000i	$0.499792\pi$
$860$	3.21882	0.109761
$861$	1.28634	0.0438384
$862$	−16.9152	−0.576135
$863$	−51.8036	−1.76341	−0.881707	−	0.471798i	$-0.843605\pi$
$863$	−51.8036	−1.76341	−0.881707	+	0.471798i	$0.843605\pi$
$864$	2.32403	0.0790650
$865$	−26.5916	−0.904140
$866$	−5.47767	−0.186139
$867$	3.28803	0.111667
$868$	1.76710	0.0599792
$869$	0	0
$870$	0.0745554	0.00252766
$871$	1.31660	0.0446112
$872$	−5.35510	−0.181347
$873$	−17.6960	−0.598917
$874$	3.35771	0.113576
$875$	6.31413	0.213457
$876$	−0.891222	−0.0301116
$877$	−7.78611	−0.262918	−0.131459	−	0.991322i	$-0.541966\pi$
$877$	−7.78611	−0.262918	−0.131459	+	0.991322i	$0.541966\pi$
$878$	16.0810	0.542709
$879$	3.36898	0.113633
$880$	0	0
$881$	12.4817	0.420519	0.210259	−	0.977646i	$-0.432569\pi$
$881$	12.4817	0.420519	0.210259	+	0.977646i	$0.432569\pi$
$882$	−0.231034	−0.00777931
$883$	−25.8967	−0.871493	−0.435746	−	0.900069i	$-0.643516\pi$
$883$	−25.8967	−0.871493	−0.435746	+	0.900069i	$0.643516\pi$
$884$	1.58465	0.0532975
$885$	4.65240	0.156389
$886$	−47.7867	−1.60543
$887$	35.2744	1.18440	0.592200	−	0.805791i	$-0.298260\pi$
$887$	35.2744	1.18440	0.592200	+	0.805791i	$0.298260\pi$
$888$	2.45824	0.0824931
$889$	23.9614	0.803640
$890$	−34.8575	−1.16843
$891$	0	0
$892$	−12.3985	−0.415132
$893$	−10.7346	−0.359220
$894$	2.87556	0.0961732
$895$	−47.8333	−1.59889
$896$	−7.01398	−0.234321
$897$	0.0576096	0.00192353
$898$	−37.9139	−1.26520
$899$	0.183838	0.00613135
$900$	11.4963	0.383209
$901$	−51.7458	−1.72390
$902$	0	0
$903$	−0.413974	−0.0137762
$904$	−22.4659	−0.747203
$905$	80.1241	2.66342
$906$	−1.54418	−0.0513021
$907$	−15.1372	−0.502622	−0.251311	−	0.967906i	$-0.580862\pi$
$907$	−15.1372	−0.502622	−0.251311	+	0.967906i	$0.580862\pi$
$908$	−11.2094	−0.371997
$909$	21.1193	0.700481
$910$	−3.40242	−0.112789
$911$	−49.4855	−1.63953	−0.819764	−	0.572701i	$-0.805896\pi$
$911$	−49.4855	−1.63953	−0.819764	+	0.572701i	$0.805896\pi$
$912$	0.440396	0.0145830
$913$	0	0
$914$	32.2731	1.06750
$915$	1.00762	0.0333109
$916$	−4.81330	−0.159036
$917$	40.0565	1.32278
$918$	−5.11568	−0.168843
$919$	15.0994	0.498082	0.249041	−	0.968493i	$-0.419885\pi$
$919$	15.0994	0.498082	0.249041	+	0.968493i	$0.419885\pi$
$920$	15.8149	0.521401
$921$	2.18737	0.0720764
$922$	−21.2430	−0.699601
$923$	1.48527	0.0488882
$924$	0	0
$925$	42.6123	1.40108
$926$	30.2464	0.993957
$927$	−28.3003	−0.929503
$928$	0.664357	0.0218086
$929$	−25.3815	−0.832740	−0.416370	−	0.909195i	$-0.636698\pi$
$929$	−25.3815	−0.832740	−0.416370	+	0.909195i	$0.636698\pi$
$930$	0.405549	0.0132985
$931$	0.124594	0.00408339
$932$	13.1290	0.430054
$933$	−3.18364	−0.104228
$934$	39.7369	1.30023
$935$	0	0
$936$	−3.14870	−0.102918
$937$	31.1915	1.01898	0.509492	−	0.860476i	$-0.329834\pi$
$937$	31.1915	1.01898	0.509492	+	0.860476i	$0.329834\pi$
$938$	−11.6791	−0.381335
$939$	2.31489	0.0755436
$940$	−12.7033	−0.414336
$941$	22.9835	0.749242	0.374621	−	0.927178i	$-0.377773\pi$
$941$	22.9835	0.749242	0.374621	+	0.927178i	$0.377773\pi$
$942$	−1.69778	−0.0553166
$943$	7.13225	0.232258
$944$	−29.1910	−0.950085
$945$	−5.54721	−0.180451
$946$	0	0
$947$	−2.18255	−0.0709233	−0.0354617	−	0.999371i	$-0.511290\pi$
$947$	−2.18255	−0.0709233	−0.0354617	+	0.999371i	$0.511290\pi$
$948$	0.974105	0.0316375
$949$	4.23127	0.137353
$950$	12.2761	0.398290
$951$	2.06329	0.0669069
$952$	−55.9474	−1.81327
$953$	−15.1240	−0.489915	−0.244958	−	0.969534i	$-0.578774\pi$
$953$	−15.1240	−0.489915	−0.244958	+	0.969534i	$0.578774\pi$
$954$	25.8334	0.836386
$955$	6.53669	0.211522
$956$	−18.6216	−0.602266
$957$	0	0
$958$	39.3707	1.27201
$959$	4.47661	0.144557
$960$	3.01868	0.0974276
$961$	1.00000	0.0322581
$962$	−2.93236	−0.0945430
$963$	37.4011	1.20523
$964$	11.8487	0.381621
$965$	−46.7973	−1.50646
$966$	−0.511034	−0.0164423
$967$	−23.8152	−0.765847	−0.382923	−	0.923780i	$-0.625083\pi$
$967$	−23.8152	−0.765847	−0.382923	+	0.923780i	$0.625083\pi$
$968$	0	0
$969$	1.37676	0.0442278
$970$	−22.3619	−0.717997
$971$	30.7573	0.987047	0.493524	−	0.869732i	$-0.335709\pi$
$971$	30.7573	0.987047	0.493524	+	0.869732i	$0.335709\pi$
$972$	−1.93596	−0.0620959
$973$	32.4421	1.04005
$974$	−10.9373	−0.350454
$975$	0.210626	0.00674545
$976$	−6.32220	−0.202369
$977$	30.7283	0.983087	0.491543	−	0.870853i	$-0.336433\pi$
$977$	30.7283	0.983087	0.491543	+	0.870853i	$0.336433\pi$
$978$	−0.124202	−0.00397153
$979$	0	0
$980$	0.147444	0.00470992
$981$	5.19733	0.165938
$982$	16.4769	0.525799
$983$	−42.0295	−1.34053	−0.670267	−	0.742120i	$-0.733820\pi$
$983$	−42.0295	−1.34053	−0.670267	+	0.742120i	$0.733820\pi$
$984$	1.50430	0.0479553
$985$	24.4847	0.780146
$986$	−1.46239	−0.0465721
$987$	1.63378	0.0520038
$988$	0.426638	0.0135732
$989$	−2.29532	−0.0729869
$990$	0	0
$991$	11.9371	0.379195	0.189598	−	0.981862i	$-0.439282\pi$
$991$	11.9371	0.379195	0.189598	+	0.981862i	$0.439282\pi$
$992$	3.61381	0.114739
$993$	−0.00140090	−4.44562e−5 0
$994$	−13.1753	−0.417894
$995$	−91.2943	−2.89422
$996$	−0.708310	−0.0224437
$997$	−19.8817	−0.629661	−0.314830	−	0.949148i	$-0.601948\pi$
$997$	−19.8817	−0.629661	−0.314830	+	0.949148i	$0.601948\pi$
$998$	−3.33911	−0.105698
$999$	−4.78083	−0.151259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3751.2.a.l.1.5	✓	15
11.10	odd	2		3751.2.a.m.1.11	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3751.2.a.l.1.5	✓	15	1.1	even	1	trivial
3751.2.a.m.1.11	yes	15	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.a (trivial)

\(f(q)\)	\(=\)	\(q-1.15277 q^{2} +0.107389 q^{3} -0.671122 q^{4} +3.27597 q^{5} -0.123795 q^{6} +2.63305 q^{7} +3.07919 q^{8} -2.98847 q^{9} -3.77644 q^{10} -0.0720712 q^{12} +0.342173 q^{13} -3.03530 q^{14} +0.351804 q^{15} -2.20735 q^{16} -6.90058 q^{17} +3.44501 q^{18} -1.85785 q^{19} -2.19858 q^{20} +0.282760 q^{21} +1.56779 q^{23} +0.330671 q^{24} +5.73201 q^{25} -0.394447 q^{26} -0.643096 q^{27} -1.76710 q^{28} -0.183838 q^{29} -0.405549 q^{30} -1.00000 q^{31} -3.61381 q^{32} +7.95478 q^{34} +8.62579 q^{35} +2.00563 q^{36} +7.43409 q^{37} +2.14168 q^{38} +0.0367457 q^{39} +10.0873 q^{40} +4.54923 q^{41} -0.325958 q^{42} -1.46404 q^{43} -9.79014 q^{45} -1.80730 q^{46} +5.77796 q^{47} -0.237045 q^{48} -0.0670632 q^{49} -6.60768 q^{50} -0.741046 q^{51} -0.229640 q^{52} +7.49877 q^{53} +0.741341 q^{54} +8.10765 q^{56} -0.199513 q^{57} +0.211923 q^{58} +13.2244 q^{59} -0.236103 q^{60} +2.86416 q^{61} +1.15277 q^{62} -7.86878 q^{63} +8.58059 q^{64} +1.12095 q^{65} +3.84775 q^{67} +4.63113 q^{68} +0.168364 q^{69} -9.94355 q^{70} +4.34068 q^{71} -9.20206 q^{72} +12.3659 q^{73} -8.56980 q^{74} +0.615555 q^{75} +1.24685 q^{76} -0.0423593 q^{78} -13.5159 q^{79} -7.23122 q^{80} +8.89634 q^{81} -5.24421 q^{82} +9.82792 q^{83} -0.189767 q^{84} -22.6061 q^{85} +1.68771 q^{86} -0.0197422 q^{87} +9.23024 q^{89} +11.2858 q^{90} +0.900959 q^{91} -1.05218 q^{92} -0.107389 q^{93} -6.66066 q^{94} -6.08628 q^{95} -0.388084 q^{96} +5.92141 q^{97} +0.0773084 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - q^{2} + 2 q^{3} + 17 q^{4} + 8 q^{5} + 2 q^{6} - 3 q^{8} + 25 q^{9} + 15 q^{10} + 11 q^{12} + 4 q^{13} + 9 q^{14} + 15 q^{15} + 29 q^{16} + 2 q^{17} - 4 q^{18} - 5 q^{19} + 17 q^{20} + 15 q^{21}+ \cdots + 31 q^{98}+O(q^{100}) \) 15 * q - q^2 + 2 * q^3 + 17 * q^4 + 8 * q^5 + 2 * q^6 - 3 * q^8 + 25 * q^9 + 15 * q^10 + 11 * q^12 + 4 * q^13 + 9 * q^14 + 15 * q^15 + 29 * q^16 + 2 * q^17 - 4 * q^18 - 5 * q^19 + 17 * q^20 + 15 * q^21 + 17 * q^23 + 18 * q^24 + 27 * q^25 + 22 * q^26 + 17 * q^27 - 35 * q^28 - 7 * q^29 - 27 * q^30 - 15 * q^31 + 23 * q^32 + 15 * q^34 - 9 * q^35 - 3 * q^36 + 17 * q^37 + 4 * q^38 - 18 * q^39 + 51 * q^40 + 7 * q^41 - 17 * q^42 + 12 * q^43 + 18 * q^45 - 20 * q^46 - 8 * q^47 + 21 * q^48 + 37 * q^49 - 16 * q^50 + 52 * q^51 - 35 * q^52 + 26 * q^53 + 48 * q^54 + 8 * q^56 - 44 * q^57 - 55 * q^58 + 11 * q^59 + 108 * q^60 - 17 * q^61 + q^62 - 22 * q^63 - 3 * q^64 + 12 * q^65 - 31 * q^67 - 30 * q^68 - 16 * q^69 - 8 * q^70 + 35 * q^71 - 59 * q^72 + q^73 - 5 * q^74 + 61 * q^75 + 12 * q^76 + q^78 - 14 * q^79 + 27 * q^80 + 83 * q^81 + 39 * q^82 - 26 * q^83 + 46 * q^84 - 16 * q^85 + 51 * q^86 - 43 * q^87 + 73 * q^89 + 45 * q^90 - 23 * q^91 + 19 * q^92 - 2 * q^93 - 46 * q^94 + 59 * q^95 - 53 * q^96 + 34 * q^97 + 31 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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