LMFDB - Embedded newform 9409.2.a.q.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9409,2,Mod(1,9409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9409, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("9409.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 9409 = 97^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9409.a (trivial)

Newform invariants

comment:select newform

sage:traces = [168,0,0,168,42] 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:	$75.1312432618$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	9409.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.69259 q^{2} -2.04647 q^{3} +5.25006 q^{4} -1.47101 q^{5} +5.51032 q^{6} -4.98771 q^{7} -8.75110 q^{8} +1.18805 q^{9} +3.96083 q^{10} +1.63431 q^{11} -10.7441 q^{12} +0.394431 q^{13} +13.4299 q^{14} +3.01038 q^{15} +13.0630 q^{16} -1.95633 q^{17} -3.19893 q^{18} +2.39756 q^{19} -7.72289 q^{20} +10.2072 q^{21} -4.40053 q^{22} +6.20684 q^{23} +17.9089 q^{24} -2.83613 q^{25} -1.06204 q^{26} +3.70811 q^{27} -26.1858 q^{28} +0.717805 q^{29} -8.10573 q^{30} -3.12057 q^{31} -17.6713 q^{32} -3.34457 q^{33} +5.26760 q^{34} +7.33697 q^{35} +6.23732 q^{36} +5.68856 q^{37} -6.45566 q^{38} -0.807191 q^{39} +12.8730 q^{40} +5.97273 q^{41} -27.4839 q^{42} -0.777988 q^{43} +8.58022 q^{44} -1.74763 q^{45} -16.7125 q^{46} +4.88471 q^{47} -26.7332 q^{48} +17.8773 q^{49} +7.63655 q^{50} +4.00357 q^{51} +2.07079 q^{52} -6.68787 q^{53} -9.98444 q^{54} -2.40408 q^{55} +43.6480 q^{56} -4.90654 q^{57} -1.93276 q^{58} -0.201460 q^{59} +15.8047 q^{60} +9.97347 q^{61} +8.40243 q^{62} -5.92563 q^{63} +21.4555 q^{64} -0.580211 q^{65} +9.00556 q^{66} +0.930700 q^{67} -10.2709 q^{68} -12.7021 q^{69} -19.7555 q^{70} +13.1728 q^{71} -10.3967 q^{72} +11.4791 q^{73} -15.3170 q^{74} +5.80407 q^{75} +12.5873 q^{76} -8.15146 q^{77} +2.17344 q^{78} +9.92001 q^{79} -19.2159 q^{80} -11.1527 q^{81} -16.0821 q^{82} -15.0787 q^{83} +53.5885 q^{84} +2.87778 q^{85} +2.09481 q^{86} -1.46897 q^{87} -14.3020 q^{88} -6.38242 q^{89} +4.70565 q^{90} -1.96731 q^{91} +32.5863 q^{92} +6.38616 q^{93} -13.1525 q^{94} -3.52683 q^{95} +36.1638 q^{96} -48.1362 q^{98} +1.94164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 168 q^{4} + 42 q^{5} + 42 q^{7} + 168 q^{9} + 42 q^{10} + 42 q^{13} + 70 q^{14} + 84 q^{15} + 140 q^{16} + 49 q^{17} - 49 q^{18} + 84 q^{19} + 98 q^{20} + 84 q^{21} - 35 q^{22} + 126 q^{23} + 168 q^{25}+ \cdots - 84 q^{99}+O(q^{100}) $ 168 * q + 168 * q^4 + 42 * q^5 + 42 * q^7 + 168 * q^9 + 42 * q^10 + 42 * q^13 + 70 * q^14 + 84 * q^15 + 140 * q^16 + 49 * q^17 - 49 * q^18 + 84 * q^19 + 98 * q^20 + 84 * q^21 - 35 * q^22 + 126 * q^23 + 168 * q^25 + 105 * q^26 + 84 * q^28 + 126 * q^29 + 84 * q^30 + 84 * q^34 + 168 * q^36 + 42 * q^37 + 112 * q^38 + 168 * q^39 + 126 * q^40 + 154 * q^41 + 28 * q^42 - 63 * q^44 + 91 * q^45 - 21 * q^46 - 42 * q^47 - 56 * q^48 + 126 * q^49 - 28 * q^50 + 168 * q^51 + 63 * q^52 - 28 * q^53 - 42 * q^54 + 168 * q^55 + 140 * q^56 + 56 * q^57 - 77 * q^58 + 238 * q^59 + 168 * q^60 - 56 * q^61 - 91 * q^62 + 210 * q^63 + 112 * q^64 - 49 * q^65 - 133 * q^66 + 28 * q^67 + 126 * q^68 + 105 * q^69 - 147 * q^70 + 252 * q^71 - 98 * q^72 + 77 * q^73 + 147 * q^74 + 14 * q^75 + 196 * q^76 + 77 * q^77 - 63 * q^78 + 56 * q^79 + 133 * q^80 + 168 * q^81 + 56 * q^82 + 203 * q^83 + 252 * q^84 - 56 * q^85 - 56 * q^86 + 182 * q^87 - 182 * q^88 + 84 * q^90 - 42 * q^91 + 189 * q^92 + 84 * q^93 - 154 * q^94 - 28 * q^95 - 21 * q^96 + 84 * q^98 - 84 * q^99

Coefficient data

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

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

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

$2$	−2.69259	−1.90395	−0.951976	−	0.306173i	$-0.900951\pi$
$2$	−2.69259	−1.90395	−0.951976	+	0.306173i	$0.900951\pi$
$3$	−2.04647	−1.18153	−0.590766	−	0.806843i	$-0.701174\pi$
$3$	−2.04647	−1.18153	−0.590766	+	0.806843i	$0.701174\pi$
$4$	5.25006	2.62503
$5$	−1.47101	−0.657855	−0.328928	−	0.944355i	$-0.606687\pi$
$5$	−1.47101	−0.657855	−0.328928	+	0.944355i	$0.606687\pi$
$6$	5.51032	2.24958
$7$	−4.98771	−1.88518	−0.942589	−	0.333956i	$-0.891616\pi$
$7$	−4.98771	−1.88518	−0.942589	+	0.333956i	$0.891616\pi$
$8$	−8.75110	−3.09398
$9$	1.18805	0.396016
$10$	3.96083	1.25252
$11$	1.63431	0.492763	0.246381	−	0.969173i	$-0.420758\pi$
$11$	1.63431	0.492763	0.246381	+	0.969173i	$0.420758\pi$
$12$	−10.7441	−3.10156
$13$	0.394431	0.109395	0.0546977	−	0.998503i	$-0.482580\pi$
$13$	0.394431	0.109395	0.0546977	+	0.998503i	$0.482580\pi$
$14$	13.4299	3.58929
$15$	3.01038	0.777276
$16$	13.0630	3.26576
$17$	−1.95633	−0.474479	−0.237240	−	0.971451i	$-0.576243\pi$
$17$	−1.95633	−0.474479	−0.237240	+	0.971451i	$0.576243\pi$
$18$	−3.19893	−0.753995
$19$	2.39756	0.550038	0.275019	−	0.961439i	$-0.411316\pi$
$19$	2.39756	0.550038	0.275019	+	0.961439i	$0.411316\pi$
$20$	−7.72289	−1.72689
$21$	10.2072	2.22740
$22$	−4.40053	−0.938196
$23$	6.20684	1.29422	0.647108	−	0.762399i	$-0.275978\pi$
$23$	6.20684	1.29422	0.647108	+	0.762399i	$0.275978\pi$
$24$	17.9089	3.65564
$25$	−2.83613	−0.567226
$26$	−1.06204	−0.208284
$27$	3.70811	0.713626
$28$	−26.1858	−4.94865
$29$	0.717805	0.133293	0.0666466	−	0.997777i	$-0.478770\pi$
$29$	0.717805	0.133293	0.0666466	+	0.997777i	$0.478770\pi$
$30$	−8.10573	−1.47990
$31$	−3.12057	−0.560471	−0.280235	−	0.959931i	$-0.590413\pi$
$31$	−3.12057	−0.560471	−0.280235	+	0.959931i	$0.590413\pi$
$32$	−17.6713	−3.12387
$33$	−3.34457	−0.582214
$34$	5.26760	0.903386
$35$	7.33697	1.24017
$36$	6.23732	1.03955
$37$	5.68856	0.935193	0.467597	−	0.883942i	$-0.345120\pi$
$37$	5.68856	0.935193	0.467597	+	0.883942i	$0.345120\pi$
$38$	−6.45566	−1.04725
$39$	−0.807191	−0.129254
$40$	12.8730	2.03539
$41$	5.97273	0.932784	0.466392	−	0.884578i	$-0.345554\pi$
$41$	5.97273	0.932784	0.466392	+	0.884578i	$0.345554\pi$
$42$	−27.4839	−4.24085
$43$	−0.777988	−0.118642	−0.0593210	−	0.998239i	$-0.518894\pi$
$43$	−0.777988	−0.118642	−0.0593210	+	0.998239i	$0.518894\pi$
$44$	8.58022	1.29352
$45$	−1.74763	−0.260521
$46$	−16.7125	−2.46412
$47$	4.88471	0.712507	0.356254	−	0.934389i	$-0.384054\pi$
$47$	4.88471	0.712507	0.356254	+	0.934389i	$0.384054\pi$
$48$	−26.7332	−3.85860
$49$	17.8773	2.55389
$50$	7.63655	1.07997
$51$	4.00357	0.560612
$52$	2.07079	0.287166
$53$	−6.68787	−0.918650	−0.459325	−	0.888268i	$-0.651909\pi$
$53$	−6.68787	−0.918650	−0.459325	+	0.888268i	$0.651909\pi$
$54$	−9.98444	−1.35871
$55$	−2.40408	−0.324166
$56$	43.6480	5.83271
$57$	−4.90654	−0.649887
$58$	−1.93276	−0.253784
$59$	−0.201460	−0.0262279	−0.0131139	−	0.999914i	$-0.504174\pi$
$59$	−0.201460	−0.0262279	−0.0131139	+	0.999914i	$0.504174\pi$
$60$	15.8047	2.04038
$61$	9.97347	1.27697	0.638486	−	0.769633i	$-0.279561\pi$
$61$	9.97347	1.27697	0.638486	+	0.769633i	$0.279561\pi$
$62$	8.40243	1.06711
$63$	−5.92563	−0.746560
$64$	21.4555	2.68193
$65$	−0.580211	−0.0719663
$66$	9.00556	1.10851
$67$	0.930700	0.113703	0.0568516	−	0.998383i	$-0.481894\pi$
$67$	0.930700	0.113703	0.0568516	+	0.998383i	$0.481894\pi$
$68$	−10.2709	−1.24552
$69$	−12.7021	−1.52916
$70$	−19.7555	−2.36123
$71$	13.1728	1.56332	0.781660	−	0.623704i	$-0.214373\pi$
$71$	13.1728	1.56332	0.781660	+	0.623704i	$0.214373\pi$
$72$	−10.3967	−1.22527
$73$	11.4791	1.34353	0.671764	−	0.740766i	$-0.265537\pi$
$73$	11.4791	1.34353	0.671764	+	0.740766i	$0.265537\pi$
$74$	−15.3170	−1.78056
$75$	5.80407	0.670196
$76$	12.5873	1.44387
$77$	−8.15146	−0.928945
$78$	2.17344	0.246093
$79$	9.92001	1.11609	0.558044	−	0.829811i	$-0.311552\pi$
$79$	9.92001	1.11609	0.558044	+	0.829811i	$0.311552\pi$
$80$	−19.2159	−2.14840
$81$	−11.1527	−1.23919
$82$	−16.0821	−1.77598
$83$	−15.0787	−1.65510	−0.827551	−	0.561390i	$-0.810267\pi$
$83$	−15.0787	−1.65510	−0.827551	+	0.561390i	$0.810267\pi$
$84$	53.5885	5.84698
$85$	2.87778	0.312139
$86$	2.09481	0.225889
$87$	−1.46897	−0.157490
$88$	−14.3020	−1.52460
$89$	−6.38242	−0.676535	−0.338268	−	0.941050i	$-0.609841\pi$
$89$	−6.38242	−0.676535	−0.338268	+	0.941050i	$0.609841\pi$
$90$	4.70565	0.496019
$91$	−1.96731	−0.206230
$92$	32.5863	3.39736
$93$	6.38616	0.662214
$94$	−13.1525	−1.35658
$95$	−3.52683	−0.361845
$96$	36.1638	3.69095
$97$	0	0
$97$	0	0
$98$	−48.1362	−4.86249
$99$	1.94164	0.195142
$100$	−14.8899	−1.48899
$101$	0.906821	0.0902321	0.0451160	−	0.998982i	$-0.485634\pi$
$101$	0.906821	0.0902321	0.0451160	+	0.998982i	$0.485634\pi$
$102$	−10.7800	−1.06738
$103$	−7.54245	−0.743180	−0.371590	−	0.928397i	$-0.621187\pi$
$103$	−7.54245	−0.743180	−0.371590	+	0.928397i	$0.621187\pi$
$104$	−3.45170	−0.338467
$105$	−15.0149	−1.46530
$106$	18.0077	1.74907
$107$	0.880623	0.0851330	0.0425665	−	0.999094i	$-0.486447\pi$
$107$	0.880623	0.0851330	0.0425665	+	0.999094i	$0.486447\pi$
$108$	19.4678	1.87329
$109$	7.52228	0.720504	0.360252	−	0.932855i	$-0.382691\pi$
$109$	7.52228	0.720504	0.360252	+	0.932855i	$0.382691\pi$
$110$	6.47322	0.617197
$111$	−11.6415	−1.10496
$112$	−65.1547	−6.15654
$113$	−3.42317	−0.322025	−0.161012	−	0.986952i	$-0.551476\pi$
$113$	−3.42317	−0.322025	−0.161012	+	0.986952i	$0.551476\pi$
$114$	13.2113	1.23735
$115$	−9.13032	−0.851407
$116$	3.76852	0.349899
$117$	0.468602	0.0433223
$118$	0.542451	0.0499366
$119$	9.75760	0.894478
$120$	−26.3441	−2.40488
$121$	−8.32904	−0.757185
$122$	−26.8545	−2.43129
$123$	−12.2230	−1.10211
$124$	−16.3832	−1.47125
$125$	11.5270	1.03101
$126$	15.9553	1.42141
$127$	−13.5398	−1.20147	−0.600734	−	0.799449i	$-0.705125\pi$
$127$	−13.5398	−1.20147	−0.600734	+	0.799449i	$0.705125\pi$
$128$	−22.4283	−1.98240
$129$	1.59213	0.140179
$130$	1.56227	0.137020
$131$	13.6673	1.19412	0.597060	−	0.802197i	$-0.296336\pi$
$131$	13.6673	1.19412	0.597060	+	0.802197i	$0.296336\pi$
$132$	−17.5592	−1.52833
$133$	−11.9583	−1.03692
$134$	−2.50600	−0.216485
$135$	−5.45466	−0.469463
$136$	17.1200	1.46803
$137$	20.5879	1.75894	0.879470	−	0.475955i	$-0.157897\pi$
$137$	20.5879	1.75894	0.879470	+	0.475955i	$0.157897\pi$
$138$	34.2017	2.91144
$139$	−2.99496	−0.254029	−0.127015	−	0.991901i	$-0.540539\pi$
$139$	−2.99496	−0.254029	−0.127015	+	0.991901i	$0.540539\pi$
$140$	38.5195	3.25550
$141$	−9.99641	−0.841850
$142$	−35.4689	−2.97649
$143$	0.644621	0.0539060
$144$	15.5195	1.29329
$145$	−1.05590	−0.0876876
$146$	−30.9086	−2.55801
$147$	−36.5853	−3.01750
$148$	29.8653	2.45491
$149$	−8.78274	−0.719510	−0.359755	−	0.933047i	$-0.617140\pi$
$149$	−8.78274	−0.719510	−0.359755	+	0.933047i	$0.617140\pi$
$150$	−15.6280	−1.27602
$151$	−20.5024	−1.66846	−0.834230	−	0.551417i	$-0.814087\pi$
$151$	−20.5024	−1.66846	−0.834230	+	0.551417i	$0.814087\pi$
$152$	−20.9813	−1.70181
$153$	−2.32421	−0.187901
$154$	21.9486	1.76867
$155$	4.59039	0.368709
$156$	−4.23781	−0.339296
$157$	−11.8274	−0.943927	−0.471963	−	0.881618i	$-0.656455\pi$
$157$	−11.8274	−0.943927	−0.471963	+	0.881618i	$0.656455\pi$
$158$	−26.7106	−2.12498
$159$	13.6865	1.08541
$160$	25.9946	2.05505
$161$	−30.9579	−2.43983
$162$	30.0297	2.35935
$163$	−22.7670	−1.78325	−0.891624	−	0.452776i	$-0.850434\pi$
$163$	−22.7670	−1.78325	−0.891624	+	0.452776i	$0.850434\pi$
$164$	31.3572	2.44859
$165$	4.91989	0.383013
$166$	40.6008	3.15124
$167$	19.0137	1.47132	0.735662	−	0.677349i	$-0.236871\pi$
$167$	19.0137	1.47132	0.735662	+	0.677349i	$0.236871\pi$
$168$	−89.3243	−6.89152
$169$	−12.8444	−0.988033
$170$	−7.74869	−0.594297
$171$	2.84841	0.217824
$172$	−4.08449	−0.311439
$173$	14.9241	1.13466	0.567328	−	0.823492i	$-0.307977\pi$
$173$	14.9241	1.13466	0.567328	+	0.823492i	$0.307977\pi$
$174$	3.95534	0.299853
$175$	14.1458	1.06932
$176$	21.3490	1.60924
$177$	0.412283	0.0309891
$178$	17.1853	1.28809
$179$	5.30962	0.396860	0.198430	−	0.980115i	$-0.436416\pi$
$179$	5.30962	0.396860	0.198430	+	0.980115i	$0.436416\pi$
$180$	−9.17516	−0.683876
$181$	3.71460	0.276104	0.138052	−	0.990425i	$-0.455916\pi$
$181$	3.71460	0.276104	0.138052	+	0.990425i	$0.455916\pi$
$182$	5.29716	0.392651
$183$	−20.4104	−1.50878
$184$	−54.3167	−4.00428
$185$	−8.36792	−0.615222
$186$	−17.1953	−1.26082
$187$	−3.19724	−0.233806
$188$	25.6450	1.87035
$189$	−18.4950	−1.34531
$190$	9.49633	0.688936
$191$	13.8693	1.00354	0.501772	−	0.865000i	$-0.332682\pi$
$191$	13.8693	1.00354	0.501772	+	0.865000i	$0.332682\pi$
$192$	−43.9080	−3.16879
$193$	7.81575	0.562590	0.281295	−	0.959621i	$-0.409236\pi$
$193$	7.81575	0.562590	0.281295	+	0.959621i	$0.409236\pi$
$194$	0	0
$195$	1.18739	0.0850305
$196$	93.8567	6.70405
$197$	−6.70183	−0.477486	−0.238743	−	0.971083i	$-0.576735\pi$
$197$	−6.70183	−0.477486	−0.238743	+	0.971083i	$0.576735\pi$
$198$	−5.22804	−0.371540
$199$	5.52805	0.391873	0.195937	−	0.980617i	$-0.437225\pi$
$199$	5.52805	0.391873	0.195937	+	0.980617i	$0.437225\pi$
$200$	24.8193	1.75499
$201$	−1.90465	−0.134344
$202$	−2.44170	−0.171797
$203$	−3.58021	−0.251281
$204$	21.0190	1.47162
$205$	−8.78594	−0.613637
$206$	20.3088	1.41498
$207$	7.37402	0.512530
$208$	5.15247	0.357259
$209$	3.91835	0.271038
$210$	40.4290	2.78987
$211$	26.2987	1.81048	0.905238	−	0.424905i	$-0.139693\pi$
$211$	26.2987	1.81048	0.905238	+	0.424905i	$0.139693\pi$
$212$	−35.1118	−2.41149
$213$	−26.9577	−1.84711
$214$	−2.37116	−0.162089
$215$	1.14443	0.0780493
$216$	−32.4501	−2.20795
$217$	15.5645	1.05659
$218$	−20.2544	−1.37180
$219$	−23.4917	−1.58742
$220$	−12.6216	−0.850947
$221$	−0.771636	−0.0519059
$222$	31.3458	2.10379
$223$	−19.0046	−1.27265	−0.636323	−	0.771423i	$-0.719545\pi$
$223$	−19.0046	−1.27265	−0.636323	+	0.771423i	$0.719545\pi$
$224$	88.1392	5.88905
$225$	−3.36946	−0.224631
$226$	9.21721	0.613120
$227$	−10.9138	−0.724376	−0.362188	−	0.932105i	$-0.617970\pi$
$227$	−10.9138	−0.724376	−0.362188	+	0.932105i	$0.617970\pi$
$228$	−25.7596	−1.70597
$229$	2.76447	0.182682	0.0913408	−	0.995820i	$-0.470885\pi$
$229$	2.76447	0.182682	0.0913408	+	0.995820i	$0.470885\pi$
$230$	24.5842	1.62104
$231$	16.6817	1.09758
$232$	−6.28159	−0.412407
$233$	−1.65967	−0.108729	−0.0543643	−	0.998521i	$-0.517313\pi$
$233$	−1.65967	−0.108729	−0.0543643	+	0.998521i	$0.517313\pi$
$234$	−1.26176	−0.0824835
$235$	−7.18545	−0.468727
$236$	−1.05768	−0.0688491
$237$	−20.3010	−1.31869
$238$	−26.2733	−1.70304
$239$	7.36870	0.476642	0.238321	−	0.971186i	$-0.423403\pi$
$239$	7.36870	0.476642	0.238321	+	0.971186i	$0.423403\pi$
$240$	39.3247	2.53840
$241$	−3.87983	−0.249922	−0.124961	−	0.992162i	$-0.539881\pi$
$241$	−3.87983	−0.249922	−0.124961	+	0.992162i	$0.539881\pi$
$242$	22.4267	1.44164
$243$	11.6993	0.750512
$244$	52.3614	3.35209
$245$	−26.2976	−1.68009
$246$	32.9116	2.09837
$247$	0.945671	0.0601716
$248$	27.3084	1.73409
$249$	30.8581	1.95556
$250$	−31.0376	−1.96299
$251$	24.9984	1.57789	0.788943	−	0.614466i	$-0.210628\pi$
$251$	24.9984	1.57789	0.788943	+	0.614466i	$0.210628\pi$
$252$	−31.1100	−1.95974
$253$	10.1439	0.637741
$254$	36.4573	2.28754
$255$	−5.88929	−0.368802
$256$	17.4795	1.09247
$257$	−5.48633	−0.342228	−0.171114	−	0.985251i	$-0.554737\pi$
$257$	−5.48633	−0.342228	−0.171114	+	0.985251i	$0.554737\pi$
$258$	−4.28696	−0.266895
$259$	−28.3729	−1.76300
$260$	−3.04615	−0.188914
$261$	0.852787	0.0527862
$262$	−36.8005	−2.27355
$263$	0.157856	0.00973382	0.00486691	−	0.999988i	$-0.498451\pi$
$263$	0.157856	0.00973382	0.00486691	+	0.999988i	$0.498451\pi$
$264$	29.2686	1.80136
$265$	9.83792	0.604339
$266$	32.1989	1.97424
$267$	13.0614	0.799347
$268$	4.88623	0.298474
$269$	−24.3675	−1.48571	−0.742857	−	0.669450i	$-0.766530\pi$
$269$	−24.3675	−1.48571	−0.742857	+	0.669450i	$0.766530\pi$
$270$	14.6872	0.893834
$271$	−13.9802	−0.849238	−0.424619	−	0.905372i	$-0.639592\pi$
$271$	−13.9802	−0.849238	−0.424619	+	0.905372i	$0.639592\pi$
$272$	−25.5556	−1.54954
$273$	4.02604	0.243667
$274$	−55.4348	−3.34894
$275$	−4.63512	−0.279508
$276$	−66.6870	−4.01408
$277$	10.1741	0.611304	0.305652	−	0.952143i	$-0.401126\pi$
$277$	10.1741	0.611304	0.305652	+	0.952143i	$0.401126\pi$
$278$	8.06421	0.483659
$279$	−3.70738	−0.221955
$280$	−64.2066	−3.83708
$281$	1.44370	0.0861239	0.0430620	−	0.999072i	$-0.486289\pi$
$281$	1.44370	0.0861239	0.0430620	+	0.999072i	$0.486289\pi$
$282$	26.9163	1.60284
$283$	26.3777	1.56799	0.783996	−	0.620765i	$-0.213178\pi$
$283$	26.3777	1.56799	0.783996	+	0.620765i	$0.213178\pi$
$284$	69.1579	4.10377
$285$	7.21756	0.427532
$286$	−1.73570	−0.102634
$287$	−29.7903	−1.75846
$288$	−20.9943	−1.23710
$289$	−13.1728	−0.774869
$290$	2.84311	0.166953
$291$	0	0
$292$	60.2660	3.52680
$293$	−4.49227	−0.262441	−0.131221	−	0.991353i	$-0.541890\pi$
$293$	−4.49227	−0.262441	−0.131221	+	0.991353i	$0.541890\pi$
$294$	98.5094	5.74518
$295$	0.296350	0.0172542
$296$	−49.7812	−2.89347
$297$	6.06020	0.351648
$298$	23.6484	1.36991
$299$	2.44817	0.141581
$300$	30.4717	1.75929
$301$	3.88038	0.223661
$302$	55.2046	3.17667
$303$	−1.85578	−0.106612
$304$	31.3194	1.79629
$305$	−14.6711	−0.840063
$306$	6.25816	0.357755
$307$	5.99831	0.342341	0.171171	−	0.985241i	$-0.445245\pi$
$307$	5.99831	0.342341	0.171171	+	0.985241i	$0.445245\pi$
$308$	−42.7957	−2.43851
$309$	15.4354	0.878090
$310$	−12.3600	−0.702004
$311$	9.88911	0.560760	0.280380	−	0.959889i	$-0.409540\pi$
$311$	9.88911	0.560760	0.280380	+	0.959889i	$0.409540\pi$
$312$	7.06381	0.399910
$313$	8.03444	0.454133	0.227067	−	0.973879i	$-0.427086\pi$
$313$	8.03444	0.454133	0.227067	+	0.973879i	$0.427086\pi$
$314$	31.8463	1.79719
$315$	8.71666	0.491128
$316$	52.0807	2.92977
$317$	12.9753	0.728764	0.364382	−	0.931250i	$-0.381280\pi$
$317$	12.9753	0.728764	0.364382	+	0.931250i	$0.381280\pi$
$318$	−36.8523	−2.06657
$319$	1.17312	0.0656819
$320$	−31.5612	−1.76432
$321$	−1.80217	−0.100587
$322$	83.3571	4.64531
$323$	−4.69042	−0.260982
$324$	−58.5523	−3.25291
$325$	−1.11866	−0.0620520
$326$	61.3023	3.39522
$327$	−15.3941	−0.851298
$328$	−52.2680	−2.88602
$329$	−24.3635	−1.34320
$330$	−13.2473	−0.729238
$331$	−24.8848	−1.36779	−0.683895	−	0.729580i	$-0.739716\pi$
$331$	−24.8848	−1.36779	−0.683895	+	0.729580i	$0.739716\pi$
$332$	−79.1642	−4.34470
$333$	6.75827	0.370351
$334$	−51.1962	−2.80133
$335$	−1.36907	−0.0748002
$336$	133.337	7.27414
$337$	0.136525	0.00743700	0.00371850	−	0.999993i	$-0.498816\pi$
$337$	0.136525	0.00743700	0.00371850	+	0.999993i	$0.498816\pi$
$338$	34.5848	1.88117
$339$	7.00542	0.380482
$340$	15.1085	0.819374
$341$	−5.09997	−0.276179
$342$	−7.66962	−0.414726
$343$	−54.2526	−2.92936
$344$	6.80825	0.367076
$345$	18.6849	1.00596
$346$	−40.1845	−2.16033
$347$	17.4869	0.938748	0.469374	−	0.883000i	$-0.344480\pi$
$347$	17.4869	0.938748	0.469374	+	0.883000i	$0.344480\pi$
$348$	−7.71218	−0.413416
$349$	−30.3412	−1.62413	−0.812063	−	0.583570i	$-0.801655\pi$
$349$	−30.3412	−1.62413	−0.812063	+	0.583570i	$0.801655\pi$
$350$	−38.0889	−2.03594
$351$	1.46259	0.0780674
$352$	−28.8803	−1.53933
$353$	5.01161	0.266741	0.133371	−	0.991066i	$-0.457420\pi$
$353$	5.01161	0.266741	0.133371	+	0.991066i	$0.457420\pi$
$354$	−1.11011	−0.0590017
$355$	−19.3773	−1.02844
$356$	−33.5081	−1.77593
$357$	−19.9687	−1.05685
$358$	−14.2967	−0.755602
$359$	7.13450	0.376544	0.188272	−	0.982117i	$-0.439711\pi$
$359$	7.13450	0.376544	0.188272	+	0.982117i	$0.439711\pi$
$360$	15.2937	0.806047
$361$	−13.2517	−0.697458
$362$	−10.0019	−0.525688
$363$	17.0451	0.894638
$364$	−10.3285	−0.541360
$365$	−16.8859	−0.883846
$366$	54.9570	2.87265
$367$	−32.0433	−1.67264	−0.836322	−	0.548238i	$-0.815299\pi$
$367$	−32.0433	−1.67264	−0.836322	+	0.548238i	$0.815299\pi$
$368$	81.0802	4.22660
$369$	7.09589	0.369397
$370$	22.5314	1.17135
$371$	33.3572	1.73182
$372$	33.5277	1.73833
$373$	−4.09375	−0.211967	−0.105983	−	0.994368i	$-0.533799\pi$
$373$	−4.09375	−0.211967	−0.105983	+	0.994368i	$0.533799\pi$
$374$	8.60888	0.445155
$375$	−23.5897	−1.21817
$376$	−42.7466	−2.20449
$377$	0.283124	0.0145817
$378$	49.7995	2.56141
$379$	−14.6298	−0.751483	−0.375741	−	0.926725i	$-0.622612\pi$
$379$	−14.6298	−0.751483	−0.375741	+	0.926725i	$0.622612\pi$
$380$	−18.5161	−0.949856
$381$	27.7089	1.41957
$382$	−37.3443	−1.91070
$383$	24.7668	1.26552	0.632761	−	0.774347i	$-0.281922\pi$
$383$	24.7668	1.26552	0.632761	+	0.774347i	$0.281922\pi$
$384$	45.8990	2.34227
$385$	11.9909	0.611111
$386$	−21.0446	−1.07114
$387$	−0.924286	−0.0469841
$388$	0	0
$389$	26.5138	1.34430	0.672151	−	0.740414i	$-0.265371\pi$
$389$	26.5138	1.34430	0.672151	+	0.740414i	$0.265371\pi$
$390$	−3.19715	−0.161894
$391$	−12.1426	−0.614079
$392$	−156.446	−7.90170
$393$	−27.9698	−1.41089
$394$	18.0453	0.909110
$395$	−14.5924	−0.734224
$396$	10.1937	0.512253
$397$	−31.2216	−1.56697	−0.783485	−	0.621411i	$-0.786560\pi$
$397$	−31.2216	−1.56697	−0.783485	+	0.621411i	$0.786560\pi$
$398$	−14.8848	−0.746108
$399$	24.4724	1.22515
$400$	−37.0485	−1.85243
$401$	−26.2883	−1.31278	−0.656388	−	0.754424i	$-0.727916\pi$
$401$	−26.2883	−1.31278	−0.656388	+	0.754424i	$0.727916\pi$
$402$	5.12845	0.255784
$403$	−1.23085	−0.0613129
$404$	4.76087	0.236862
$405$	16.4057	0.815206
$406$	9.64004	0.478427
$407$	9.29686	0.460828
$408$	−35.0357	−1.73452
$409$	13.9549	0.690026	0.345013	−	0.938598i	$-0.387875\pi$
$409$	13.9549	0.690026	0.345013	+	0.938598i	$0.387875\pi$
$410$	23.6570	1.16833
$411$	−42.1325	−2.07824
$412$	−39.5983	−1.95087
$413$	1.00483	0.0494442
$414$	−19.8552	−0.975832
$415$	22.1809	1.08882
$416$	−6.97009	−0.341737
$417$	6.12910	0.300143
$418$	−10.5505	−0.516044
$419$	−20.1940	−0.986543	−0.493271	−	0.869875i	$-0.664199\pi$
$419$	−20.1940	−0.986543	−0.493271	+	0.869875i	$0.664199\pi$
$420$	−78.8292	−3.84647
$421$	5.36867	0.261653	0.130826	−	0.991405i	$-0.458237\pi$
$421$	5.36867	0.261653	0.130826	+	0.991405i	$0.458237\pi$
$422$	−70.8117	−3.44706
$423$	5.80326	0.282164
$424$	58.5263	2.84229
$425$	5.54841	0.269137
$426$	72.5862	3.51681
$427$	−49.7448	−2.40732
$428$	4.62333	0.223477
$429$	−1.31920	−0.0636916
$430$	−3.08148	−0.148602
$431$	−35.1983	−1.69544	−0.847721	−	0.530442i	$-0.822026\pi$
$431$	−35.1983	−1.69544	−0.847721	+	0.530442i	$0.822026\pi$
$432$	48.4392	2.33053
$433$	−7.62295	−0.366336	−0.183168	−	0.983082i	$-0.558635\pi$
$433$	−7.62295	−0.366336	−0.183168	+	0.983082i	$0.558635\pi$
$434$	−41.9089	−2.01169
$435$	2.16087	0.103606
$436$	39.4925	1.89135
$437$	14.8813	0.711868
$438$	63.2535	3.02237
$439$	−15.2362	−0.727183	−0.363592	−	0.931558i	$-0.618450\pi$
$439$	−15.2362	−0.727183	−0.363592	+	0.931558i	$0.618450\pi$
$440$	21.0384	1.00297
$441$	21.2390	1.01138
$442$	2.07770	0.0988263
$443$	13.0668	0.620824	0.310412	−	0.950602i	$-0.399533\pi$
$443$	13.0668	0.620824	0.310412	+	0.950602i	$0.399533\pi$
$444$	−61.1185	−2.90055
$445$	9.38860	0.445062
$446$	51.1718	2.42306
$447$	17.9736	0.850124
$448$	−107.014	−5.05592
$449$	22.5393	1.06369	0.531847	−	0.846841i	$-0.321498\pi$
$449$	22.5393	1.06369	0.531847	+	0.846841i	$0.321498\pi$
$450$	9.07259	0.427686
$451$	9.76129	0.459641
$452$	−17.9719	−0.845325
$453$	41.9575	1.97134
$454$	29.3865	1.37918
$455$	2.89392	0.135669
$456$	42.9376	2.01074
$457$	7.21425	0.337469	0.168734	−	0.985662i	$-0.446032\pi$
$457$	7.21425	0.337469	0.168734	+	0.985662i	$0.446032\pi$
$458$	−7.44361	−0.347817
$459$	−7.25428	−0.338601
$460$	−47.9348	−2.23497
$461$	5.69103	0.265058	0.132529	−	0.991179i	$-0.457690\pi$
$461$	5.69103	0.265058	0.132529	+	0.991179i	$0.457690\pi$
$462$	−44.9171	−2.08973
$463$	−18.5383	−0.861550	−0.430775	−	0.902459i	$-0.641760\pi$
$463$	−18.5383	−0.861550	−0.430775	+	0.902459i	$0.641760\pi$
$464$	9.37672	0.435303
$465$	−9.39410	−0.435641
$466$	4.46882	0.207014
$467$	−11.8179	−0.546869	−0.273435	−	0.961891i	$-0.588160\pi$
$467$	−11.8179	−0.546869	−0.273435	+	0.961891i	$0.588160\pi$
$468$	2.46019	0.113722
$469$	−4.64206	−0.214351
$470$	19.3475	0.892433
$471$	24.2044	1.11528
$472$	1.76300	0.0811486
$473$	−1.27147	−0.0584624
$474$	54.6624	2.51073
$475$	−6.79980	−0.311996
$476$	51.2280	2.34803
$477$	−7.94551	−0.363800
$478$	−19.8409	−0.907503
$479$	14.4516	0.660310	0.330155	−	0.943927i	$-0.392899\pi$
$479$	14.4516	0.660310	0.330155	+	0.943927i	$0.392899\pi$
$480$	−53.1972	−2.42811
$481$	2.24374	0.102306
$482$	10.4468	0.475839
$483$	63.3545	2.88273
$484$	−43.7280	−1.98763
$485$	0	0
$486$	−31.5015	−1.42894
$487$	7.53160	0.341289	0.170645	−	0.985333i	$-0.445415\pi$
$487$	7.53160	0.341289	0.170645	+	0.985333i	$0.445415\pi$
$488$	−87.2789	−3.95093
$489$	46.5920	2.10696
$490$	70.8088	3.19881
$491$	9.67614	0.436678	0.218339	−	0.975873i	$-0.429936\pi$
$491$	9.67614	0.436678	0.218339	+	0.975873i	$0.429936\pi$
$492$	−64.1717	−2.89308
$493$	−1.40426	−0.0632448
$494$	−2.54631	−0.114564
$495$	−2.85616	−0.128375
$496$	−40.7641	−1.83036
$497$	−65.7020	−2.94714
$498$	−83.0885	−3.72328
$499$	30.6551	1.37231	0.686156	−	0.727455i	$-0.259297\pi$
$499$	30.6551	1.37231	0.686156	+	0.727455i	$0.259297\pi$
$500$	60.5176	2.70643
$501$	−38.9110	−1.73841
$502$	−67.3106	−3.00422
$503$	24.9778	1.11370	0.556852	−	0.830612i	$-0.312009\pi$
$503$	24.9778	1.11370	0.556852	+	0.830612i	$0.312009\pi$
$504$	51.8558	2.30984
$505$	−1.33394	−0.0593596
$506$	−27.3134	−1.21423
$507$	26.2858	1.16739
$508$	−71.0851	−3.15389
$509$	−17.0991	−0.757904	−0.378952	−	0.925416i	$-0.623715\pi$
$509$	−17.0991	−0.757904	−0.378952	+	0.925416i	$0.623715\pi$
$510$	15.8575	0.702181
$511$	−57.2544	−2.53279
$512$	−2.20848	−0.0976021
$513$	8.89042	0.392522
$514$	14.7725	0.651585
$515$	11.0950	0.488905
$516$	8.35879	0.367975
$517$	7.98312	0.351097
$518$	76.3966	3.35668
$519$	−30.5417	−1.34063
$520$	5.07749	0.222663
$521$	−29.6657	−1.29968	−0.649838	−	0.760073i	$-0.725163\pi$
$521$	−29.6657	−1.29968	−0.649838	+	0.760073i	$0.725163\pi$
$522$	−2.29621	−0.100502
$523$	26.1781	1.14469	0.572344	−	0.820014i	$-0.306034\pi$
$523$	26.1781	1.14469	0.572344	+	0.820014i	$0.306034\pi$
$524$	71.7543	3.13460
$525$	−28.9490	−1.26344
$526$	−0.425042	−0.0185327
$527$	6.10486	0.265932
$528$	−43.6902	−1.90137
$529$	15.5249	0.674994
$530$	−26.4895	−1.15063
$531$	−0.239344	−0.0103867
$532$	−62.7820	−2.72195
$533$	2.35583	0.102042
$534$	−35.1692	−1.52192
$535$	−1.29540	−0.0560052
$536$	−8.14465	−0.351795
$537$	−10.8660	−0.468902
$538$	65.6119	2.82873
$539$	29.2170	1.25846
$540$	−28.6373	−1.23235
$541$	−11.1292	−0.478484	−0.239242	−	0.970960i	$-0.576899\pi$
$541$	−11.1292	−0.478484	−0.239242	+	0.970960i	$0.576899\pi$
$542$	37.6431	1.61691
$543$	−7.60181	−0.326225
$544$	34.5708	1.48221
$545$	−11.0653	−0.473987
$546$	−10.8405	−0.463930
$547$	34.2377	1.46390	0.731950	−	0.681359i	$-0.238611\pi$
$547$	34.2377	1.46390	0.731950	+	0.681359i	$0.238611\pi$
$548$	108.088	4.61727
$549$	11.8490	0.505701
$550$	12.4805	0.532170
$551$	1.72098	0.0733163
$552$	111.158	4.73118
$553$	−49.4781	−2.10402
$554$	−27.3948	−1.16389
$555$	17.1247	0.726903
$556$	−15.7237	−0.666835
$557$	−28.3086	−1.19947	−0.599737	−	0.800197i	$-0.704728\pi$
$557$	−28.3086	−1.19947	−0.599737	+	0.800197i	$0.704728\pi$
$558$	9.98248	0.422592
$559$	−0.306862	−0.0129789
$560$	95.8431	4.05011
$561$	6.54307	0.276249
$562$	−3.88730	−0.163976
$563$	−20.0249	−0.843948	−0.421974	−	0.906608i	$-0.638663\pi$
$563$	−20.0249	−0.843948	−0.421974	+	0.906608i	$0.638663\pi$
$564$	−52.4818	−2.20988
$565$	5.03551	0.211846
$566$	−71.0245	−2.98538
$567$	55.6264	2.33609
$568$	−115.276	−4.83689
$569$	−3.66114	−0.153483	−0.0767415	−	0.997051i	$-0.524452\pi$
$569$	−3.66114	−0.153483	−0.0767415	+	0.997051i	$0.524452\pi$
$570$	−19.4340	−0.813999
$571$	−9.24230	−0.386778	−0.193389	−	0.981122i	$-0.561948\pi$
$571$	−9.24230	−0.386778	−0.193389	+	0.981122i	$0.561948\pi$
$572$	3.38430	0.141505
$573$	−28.3830	−1.18572
$574$	80.2131	3.34803
$575$	−17.6034	−0.734113
$576$	25.4901	1.06209
$577$	−7.23763	−0.301307	−0.150653	−	0.988587i	$-0.548138\pi$
$577$	−7.23763	−0.301307	−0.150653	+	0.988587i	$0.548138\pi$
$578$	35.4689	1.47531
$579$	−15.9947	−0.664717
$580$	−5.54353	−0.230183
$581$	75.2082	3.12016
$582$	0	0
$583$	−10.9300	−0.452676
$584$	−100.455	−4.15685
$585$	−0.689318	−0.0284998
$586$	12.0959	0.499676
$587$	−8.71013	−0.359506	−0.179753	−	0.983712i	$-0.557530\pi$
$587$	−8.71013	−0.359506	−0.179753	+	0.983712i	$0.557530\pi$
$588$	−192.075	−7.92105
$589$	−7.48175	−0.308280
$590$	−0.797950	−0.0328511
$591$	13.7151	0.564165
$592$	74.3099	3.05412
$593$	13.8689	0.569529	0.284765	−	0.958597i	$-0.408085\pi$
$593$	13.8689	0.569529	0.284765	+	0.958597i	$0.408085\pi$
$594$	−16.3177	−0.669521
$595$	−14.3535	−0.588437
$596$	−46.1100	−1.88874
$597$	−11.3130	−0.463010
$598$	−6.59192	−0.269564
$599$	29.4768	1.20439	0.602196	−	0.798349i	$-0.294293\pi$
$599$	29.4768	1.20439	0.602196	+	0.798349i	$0.294293\pi$
$600$	−50.7920	−2.07357
$601$	−32.3744	−1.32058	−0.660290	−	0.751010i	$-0.729567\pi$
$601$	−32.3744	−1.32058	−0.660290	+	0.751010i	$0.729567\pi$
$602$	−10.4483	−0.425840
$603$	1.10572	0.0450282
$604$	−107.639	−4.37976
$605$	12.2521	0.498118
$606$	4.99687	0.202984
$607$	16.1725	0.656420	0.328210	−	0.944605i	$-0.393555\pi$
$607$	16.1725	0.656420	0.328210	+	0.944605i	$0.393555\pi$
$608$	−42.3679	−1.71825
$609$	7.32679	0.296896
$610$	39.5032	1.59944
$611$	1.92668	0.0779450
$612$	−12.2023	−0.493247
$613$	−37.1735	−1.50143	−0.750713	−	0.660629i	$-0.770290\pi$
$613$	−37.1735	−1.50143	−0.750713	+	0.660629i	$0.770290\pi$
$614$	−16.1510	−0.651802
$615$	17.9802	0.725031
$616$	71.3343	2.87414
$617$	−36.7190	−1.47825	−0.739125	−	0.673568i	$-0.764761\pi$
$617$	−36.7190	−1.47825	−0.739125	+	0.673568i	$0.764761\pi$
$618$	−41.5613	−1.67184
$619$	0.911585	0.0366397	0.0183199	−	0.999832i	$-0.494168\pi$
$619$	0.911585	0.0366397	0.0183199	+	0.999832i	$0.494168\pi$
$620$	24.0998	0.967872
$621$	23.0156	0.923586
$622$	−26.6274	−1.06766
$623$	31.8337	1.27539
$624$	−10.5444	−0.422113
$625$	−2.77569	−0.111028
$626$	−21.6335	−0.864648
$627$	−8.01880	−0.320240
$628$	−62.0944	−2.47784
$629$	−11.1287	−0.443730
$630$	−23.4704	−0.935085
$631$	−32.3199	−1.28664	−0.643318	−	0.765599i	$-0.722443\pi$
$631$	−32.3199	−1.28664	−0.643318	+	0.765599i	$0.722443\pi$
$632$	−86.8110	−3.45316
$633$	−53.8195	−2.13913
$634$	−34.9371	−1.38753
$635$	19.9172	0.790392
$636$	71.8552	2.84925
$637$	7.05134	0.279384
$638$	−3.15872	−0.125055
$639$	15.6499	0.619099
$640$	32.9923	1.30414
$641$	11.0204	0.435280	0.217640	−	0.976029i	$-0.430164\pi$
$641$	11.0204	0.435280	0.217640	+	0.976029i	$0.430164\pi$
$642$	4.85251	0.191513
$643$	23.7598	0.936995	0.468497	−	0.883465i	$-0.344796\pi$
$643$	23.7598	0.936995	0.468497	+	0.883465i	$0.344796\pi$
$644$	−162.531	−6.40462
$645$	−2.34204	−0.0922177
$646$	12.6294	0.496897
$647$	−36.1055	−1.41945	−0.709727	−	0.704477i	$-0.751182\pi$
$647$	−36.1055	−1.41945	−0.709727	+	0.704477i	$0.751182\pi$
$648$	97.5983	3.83402
$649$	−0.329248	−0.0129241
$650$	3.01209	0.118144
$651$	−31.8523	−1.24839
$652$	−119.528	−4.68108
$653$	24.7500	0.968543	0.484272	−	0.874918i	$-0.339085\pi$
$653$	24.7500	0.968543	0.484272	+	0.874918i	$0.339085\pi$
$654$	41.4502	1.62083
$655$	−20.1047	−0.785558
$656$	78.0221	3.04625
$657$	13.6377	0.532058
$658$	65.6010	2.55739
$659$	25.4931	0.993071	0.496536	−	0.868016i	$-0.334605\pi$
$659$	25.4931	0.993071	0.496536	+	0.868016i	$0.334605\pi$
$660$	25.8297	1.00542
$661$	−27.2336	−1.05926	−0.529632	−	0.848227i	$-0.677670\pi$
$661$	−27.2336	−1.05926	−0.529632	+	0.848227i	$0.677670\pi$
$662$	67.0046	2.60421
$663$	1.57913	0.0613284
$664$	131.955	5.12086
$665$	17.5908	0.682143
$666$	−18.1973	−0.705131
$667$	4.45530	0.172510
$668$	99.8231	3.86227
$669$	38.8925	1.50367
$670$	3.68634	0.142416
$671$	16.2997	0.629244
$672$	−180.374	−6.95809
$673$	−26.7436	−1.03089	−0.515445	−	0.856923i	$-0.672373\pi$
$673$	−26.7436	−1.03089	−0.515445	+	0.856923i	$0.672373\pi$
$674$	−0.367607	−0.0141597
$675$	−10.5167	−0.404788
$676$	−67.4341	−2.59362
$677$	31.1081	1.19558	0.597791	−	0.801652i	$-0.296045\pi$
$677$	31.1081	1.19558	0.597791	+	0.801652i	$0.296045\pi$
$678$	−18.8628	−0.724420
$679$	0	0
$680$	−25.1837	−0.965752
$681$	22.3348	0.855872
$682$	13.7322	0.525832
$683$	46.6151	1.78368	0.891839	−	0.452352i	$-0.149415\pi$
$683$	46.6151	1.78368	0.891839	+	0.452352i	$0.149415\pi$
$684$	14.9544	0.571794
$685$	−30.2849	−1.15713
$686$	146.080	5.57737
$687$	−5.65742	−0.215844
$688$	−10.1629	−0.387457
$689$	−2.63790	−0.100496
$690$	−50.3110	−1.91531
$691$	49.9428	1.89991	0.949957	−	0.312381i	$-0.101127\pi$
$691$	49.9428	1.89991	0.949957	+	0.312381i	$0.101127\pi$
$692$	78.3523	2.97851
$693$	−9.68432	−0.367877
$694$	−47.0852	−1.78733
$695$	4.40561	0.167114
$696$	12.8551	0.487271
$697$	−11.6846	−0.442587
$698$	81.6964	3.09226
$699$	3.39647	0.128466
$700$	74.2664	2.80701
$701$	46.8949	1.77119	0.885597	−	0.464454i	$-0.153749\pi$
$701$	46.8949	1.77119	0.885597	+	0.464454i	$0.153749\pi$
$702$	−3.93817	−0.148637
$703$	13.6387	0.514392
$704$	35.0649	1.32156
$705$	14.7048	0.553815
$706$	−13.4942	−0.507862
$707$	−4.52296	−0.170103
$708$	2.16451	0.0813473
$709$	18.4018	0.691093	0.345547	−	0.938402i	$-0.387693\pi$
$709$	18.4018	0.691093	0.345547	+	0.938402i	$0.387693\pi$
$710$	52.1751	1.95810
$711$	11.7854	0.441988
$712$	55.8532	2.09319
$713$	−19.3689	−0.725370
$714$	53.7675	2.01220
$715$	−0.948244	−0.0354623
$716$	27.8759	1.04177
$717$	−15.0798	−0.563167
$718$	−19.2103	−0.716922
$719$	17.7015	0.660154	0.330077	−	0.943954i	$-0.392925\pi$
$719$	17.7015	0.660154	0.330077	+	0.943954i	$0.392925\pi$
$720$	−22.8293	−0.850799
$721$	37.6196	1.40103
$722$	35.6815	1.32793
$723$	7.93997	0.295291
$724$	19.5019	0.724781
$725$	−2.03579	−0.0756074
$726$	−45.8956	−1.70335
$727$	−7.33162	−0.271915	−0.135957	−	0.990715i	$-0.543411\pi$
$727$	−7.33162	−0.271915	−0.135957	+	0.990715i	$0.543411\pi$
$728$	17.2161	0.638071
$729$	9.51572	0.352434
$730$	45.4668	1.68280
$731$	1.52200	0.0562932
$732$	−107.156	−3.96060
$733$	−15.6386	−0.577624	−0.288812	−	0.957386i	$-0.593260\pi$
$733$	−15.6386	−0.577624	−0.288812	+	0.957386i	$0.593260\pi$
$734$	86.2795	3.18463
$735$	53.8173	1.98508
$736$	−109.683	−4.04296
$737$	1.52105	0.0560286
$738$	−19.1063	−0.703314
$739$	36.6096	1.34670	0.673352	−	0.739322i	$-0.264854\pi$
$739$	36.6096	1.34670	0.673352	+	0.739322i	$0.264854\pi$
$740$	−43.9321	−1.61498
$741$	−1.93529	−0.0710946
$742$	−89.8173	−3.29730
$743$	15.6458	0.573989	0.286994	−	0.957932i	$-0.407344\pi$
$743$	15.6458	0.573989	0.286994	+	0.957932i	$0.407344\pi$
$744$	−55.8859	−2.04888
$745$	12.9195	0.473334
$746$	11.0228	0.403574
$747$	−17.9142	−0.655447
$748$	−16.7857	−0.613747
$749$	−4.39229	−0.160491
$750$	63.5176	2.31933
$751$	−53.6546	−1.95788	−0.978942	−	0.204136i	$-0.934561\pi$
$751$	−53.6546	−1.95788	−0.978942	+	0.204136i	$0.934561\pi$
$752$	63.8091	2.32688
$753$	−51.1586	−1.86432
$754$	−0.762339	−0.0277628
$755$	30.1592	1.09760
$756$	−97.0998	−3.53149
$757$	35.4909	1.28994	0.644970	−	0.764208i	$-0.276870\pi$
$757$	35.4909	1.28994	0.644970	+	0.764208i	$0.276870\pi$
$758$	39.3921	1.43079
$759$	−20.7592	−0.753511
$760$	30.8637	1.11954
$761$	4.14974	0.150428	0.0752139	−	0.997167i	$-0.476036\pi$
$761$	4.14974	0.150428	0.0752139	+	0.997167i	$0.476036\pi$
$762$	−74.6089	−2.70279
$763$	−37.5190	−1.35828
$764$	72.8145	2.63434
$765$	3.41893	0.123612
$766$	−66.6868	−2.40949
$767$	−0.0794621	−0.00286921
$768$	−35.7713	−1.29079
$769$	41.1185	1.48277	0.741386	−	0.671079i	$-0.234169\pi$
$769$	41.1185	1.48277	0.741386	+	0.671079i	$0.234169\pi$
$770$	−32.2865	−1.16353
$771$	11.2276	0.404353
$772$	41.0332	1.47682
$773$	16.6185	0.597724	0.298862	−	0.954296i	$-0.403393\pi$
$773$	16.6185	0.597724	0.298862	+	0.954296i	$0.403393\pi$
$774$	2.48873	0.0894555
$775$	8.85035	0.317914
$776$	0	0
$777$	58.0643	2.08304
$778$	−71.3908	−2.55949
$779$	14.3200	0.513067
$780$	6.23385	0.223208
$781$	21.5284	0.770346
$782$	32.6951	1.16918
$783$	2.66170	0.0951215
$784$	233.531	8.34041
$785$	17.3982	0.620967
$786$	75.3113	2.68626
$787$	−2.21215	−0.0788548	−0.0394274	−	0.999222i	$-0.512553\pi$
$787$	−2.21215	−0.0788548	−0.0394274	+	0.999222i	$0.512553\pi$
$788$	−35.1851	−1.25342
$789$	−0.323048	−0.0115008
$790$	39.2915	1.39793
$791$	17.0738	0.607074
$792$	−16.9915	−0.603765
$793$	3.93384	0.139695
$794$	84.0672	2.98343
$795$	−20.1330	−0.714045
$796$	29.0226	1.02868
$797$	−45.9770	−1.62859	−0.814294	−	0.580453i	$-0.802876\pi$
$797$	−45.9770	−1.62859	−0.814294	+	0.580453i	$0.802876\pi$
$798$	−65.8942	−2.33263
$799$	−9.55609	−0.338070
$800$	50.1181	1.77194
$801$	−7.58261	−0.267918
$802$	70.7838	2.49946
$803$	18.7604	0.662040
$804$	−9.99954	−0.352657
$805$	45.5394	1.60505
$806$	3.31418	0.116737
$807$	49.8675	1.75542
$808$	−7.93569	−0.279176
$809$	−43.9409	−1.54488	−0.772440	−	0.635087i	$-0.780964\pi$
$809$	−43.9409	−1.54488	−0.772440	+	0.635087i	$0.780964\pi$
$810$	−44.1739	−1.55211
$811$	−23.0354	−0.808884	−0.404442	−	0.914564i	$-0.632534\pi$
$811$	−23.0354	−0.808884	−0.404442	+	0.914564i	$0.632534\pi$
$812$	−18.7963	−0.659621
$813$	28.6101	1.00340
$814$	−25.0327	−0.877394
$815$	33.4904	1.17312
$816$	52.2988	1.83083
$817$	−1.86527	−0.0652576
$818$	−37.5749	−1.31378
$819$	−2.33725	−0.0816702
$820$	−46.1268	−1.61082
$821$	−32.7239	−1.14207	−0.571037	−	0.820924i	$-0.693459\pi$
$821$	−32.7239	−1.14207	−0.571037	+	0.820924i	$0.693459\pi$
$822$	113.446	3.95687
$823$	−10.8486	−0.378159	−0.189079	−	0.981962i	$-0.560550\pi$
$823$	−10.8486	−0.378159	−0.189079	+	0.981962i	$0.560550\pi$
$824$	66.0048	2.29939
$825$	9.48563	0.330247
$826$	−2.70559	−0.0941394
$827$	−8.33487	−0.289832	−0.144916	−	0.989444i	$-0.546291\pi$
$827$	−8.33487	−0.289832	−0.144916	+	0.989444i	$0.546291\pi$
$828$	38.7141	1.34541
$829$	20.7219	0.719702	0.359851	−	0.933010i	$-0.382828\pi$
$829$	20.7219	0.719702	0.359851	+	0.933010i	$0.382828\pi$
$830$	−59.7242	−2.07306
$831$	−20.8210	−0.722274
$832$	8.46270	0.293391
$833$	−34.9738	−1.21177
$834$	−16.5032	−0.571458
$835$	−27.9693	−0.967918
$836$	20.5716	0.711484
$837$	−11.5714	−0.399967
$838$	54.3743	1.87833
$839$	25.0473	0.864728	0.432364	−	0.901699i	$-0.357680\pi$
$839$	25.0473	0.864728	0.432364	+	0.901699i	$0.357680\pi$
$840$	131.397	4.53362
$841$	−28.4848	−0.982233
$842$	−14.4556	−0.498175
$843$	−2.95449	−0.101758
$844$	138.070	4.75256
$845$	18.8943	0.649982
$846$	−15.6258	−0.537227
$847$	41.5428	1.42743
$848$	−87.3640	−3.00009
$849$	−53.9813	−1.85263
$850$	−14.9396	−0.512424
$851$	35.3080	1.21034
$852$	−141.530	−4.84873
$853$	15.6218	0.534881	0.267441	−	0.963574i	$-0.413822\pi$
$853$	15.6218	0.534881	0.267441	+	0.963574i	$0.413822\pi$
$854$	133.943	4.58342
$855$	−4.19004	−0.143296
$856$	−7.70642	−0.263400
$857$	41.3279	1.41173	0.705867	−	0.708344i	$-0.250557\pi$
$857$	41.3279	1.41173	0.705867	+	0.708344i	$0.250557\pi$
$858$	3.55207	0.121266
$859$	41.3999	1.41255	0.706274	−	0.707939i	$-0.250375\pi$
$859$	41.3999	1.41255	0.706274	+	0.707939i	$0.250375\pi$
$860$	6.00832	0.204882
$861$	60.9649	2.07768
$862$	94.7747	3.22804
$863$	−14.7679	−0.502704	−0.251352	−	0.967896i	$-0.580875\pi$
$863$	−14.7679	−0.502704	−0.251352	+	0.967896i	$0.580875\pi$
$864$	−65.5270	−2.22927
$865$	−21.9534	−0.746440
$866$	20.5255	0.697485
$867$	26.9577	0.915532
$868$	81.7146	2.77357
$869$	16.2124	0.549966
$870$	−5.81833	−0.197260
$871$	0.367097	0.0124386
$872$	−65.8283	−2.22923
$873$	0	0
$874$	−40.0692	−1.35536
$875$	−57.4934	−1.94363
$876$	−123.333	−4.16703
$877$	−7.75035	−0.261711	−0.130855	−	0.991401i	$-0.541772\pi$
$877$	−7.75035	−0.261711	−0.130855	+	0.991401i	$0.541772\pi$
$878$	41.0248	1.38452
$879$	9.19331	0.310083
$880$	−31.4046	−1.05865
$881$	12.8664	0.433481	0.216740	−	0.976229i	$-0.430457\pi$
$881$	12.8664	0.433481	0.216740	+	0.976229i	$0.430457\pi$
$882$	−57.1881	−1.92562
$883$	−25.0240	−0.842126	−0.421063	−	0.907031i	$-0.638343\pi$
$883$	−25.0240	−0.842126	−0.421063	+	0.907031i	$0.638343\pi$
$884$	−4.05114	−0.136255
$885$	−0.606472	−0.0203863
$886$	−35.1837	−1.18202
$887$	45.2802	1.52036	0.760180	−	0.649713i	$-0.225111\pi$
$887$	45.2802	1.52036	0.760180	+	0.649713i	$0.225111\pi$
$888$	101.876	3.41873
$889$	67.5328	2.26498
$890$	−25.2797	−0.847377
$891$	−18.2269	−0.610625
$892$	−99.7756	−3.34073
$893$	11.7114	0.391906
$894$	−48.3957	−1.61859
$895$	−7.81050	−0.261076
$896$	111.866	3.73718
$897$	−5.01011	−0.167283
$898$	−60.6891	−2.02522
$899$	−2.23996	−0.0747069
$900$	−17.6899	−0.589663
$901$	13.0837	0.435880
$902$	−26.2832	−0.875134
$903$	−7.94109	−0.264263
$904$	29.9565	0.996339
$905$	−5.46420	−0.181636
$906$	−112.975	−3.75333
$907$	32.9162	1.09296	0.546482	−	0.837471i	$-0.315967\pi$
$907$	32.9162	1.09296	0.546482	+	0.837471i	$0.315967\pi$
$908$	−57.2983	−1.90151
$909$	1.07735	0.0357333
$910$	−7.79217	−0.258308
$911$	−38.8873	−1.28839	−0.644197	−	0.764860i	$-0.722808\pi$
$911$	−38.8873	−1.28839	−0.644197	+	0.764860i	$0.722808\pi$
$912$	−64.0943	−2.12238
$913$	−24.6433	−0.815573
$914$	−19.4251	−0.642524
$915$	30.0239	0.992561
$916$	14.5137	0.479545
$917$	−68.1686	−2.25113
$918$	19.5328	0.644680
$919$	42.8726	1.41424	0.707118	−	0.707096i	$-0.249995\pi$
$919$	42.8726	1.41424	0.707118	+	0.707096i	$0.249995\pi$
$920$	79.9004	2.63424
$921$	−12.2754	−0.404487
$922$	−15.3236	−0.504657
$923$	5.19575	0.171020
$924$	87.5801	2.88118
$925$	−16.1335	−0.530466
$926$	49.9162	1.64035
$927$	−8.96079	−0.294311
$928$	−12.6845	−0.416390
$929$	1.08277	0.0355246	0.0177623	−	0.999842i	$-0.494346\pi$
$929$	1.08277	0.0355246	0.0177623	+	0.999842i	$0.494346\pi$
$930$	25.2945	0.829439
$931$	42.8618	1.40474
$932$	−8.71337	−0.285416
$933$	−20.2378	−0.662555
$934$	31.8209	1.04121
$935$	4.70318	0.153810
$936$	−4.10079	−0.134038
$937$	0.565168	0.0184632	0.00923162	−	0.999957i	$-0.497061\pi$
$937$	0.565168	0.0184632	0.00923162	+	0.999957i	$0.497061\pi$
$938$	12.4992	0.408113
$939$	−16.4422	−0.536572
$940$	−37.7240	−1.23042
$941$	−2.55466	−0.0832794	−0.0416397	−	0.999133i	$-0.513258\pi$
$941$	−2.55466	−0.0832794	−0.0416397	+	0.999133i	$0.513258\pi$
$942$	−65.1726	−2.12344
$943$	37.0718	1.20722
$944$	−2.63168	−0.0856540
$945$	27.2063	0.885021
$946$	3.42356	0.111310
$947$	1.29198	0.0419838	0.0209919	−	0.999780i	$-0.493318\pi$
$947$	1.29198	0.0419838	0.0209919	+	0.999780i	$0.493318\pi$
$948$	−106.582	−3.46161
$949$	4.52771	0.146976
$950$	18.3091	0.594026
$951$	−26.5535	−0.861057
$952$	−85.3898	−2.76750
$953$	−10.5851	−0.342884	−0.171442	−	0.985194i	$-0.554843\pi$
$953$	−10.5851	−0.342884	−0.171442	+	0.985194i	$0.554843\pi$
$954$	21.3940	0.692657
$955$	−20.4018	−0.660187
$956$	38.6861	1.25120
$957$	−2.40075	−0.0776052
$958$	−38.9123	−1.25720
$959$	−102.686	−3.31591
$960$	64.5891	2.08460
$961$	−21.2620	−0.685872
$962$	−6.04149	−0.194785
$963$	1.04622	0.0337140
$964$	−20.3694	−0.656053
$965$	−11.4970	−0.370103
$966$	−170.588	−5.48858
$967$	3.76453	0.121059	0.0605295	−	0.998166i	$-0.480721\pi$
$967$	3.76453	0.121059	0.0605295	+	0.998166i	$0.480721\pi$
$968$	72.8883	2.34272
$969$	9.59880	0.308358
$970$	0	0
$971$	−31.9964	−1.02681	−0.513407	−	0.858145i	$-0.671617\pi$
$971$	−31.9964	−1.02681	−0.513407	+	0.858145i	$0.671617\pi$
$972$	61.4222	1.97012
$973$	14.9380	0.478890
$974$	−20.2795	−0.649799
$975$	2.28930	0.0733163
$976$	130.284	4.17029
$977$	7.01307	0.224368	0.112184	−	0.993687i	$-0.464215\pi$
$977$	7.01307	0.224368	0.112184	+	0.993687i	$0.464215\pi$
$978$	−125.453	−4.01156
$979$	−10.4308	−0.333371
$980$	−138.064	−4.41030
$981$	8.93682	0.285331
$982$	−26.0539	−0.831414
$983$	6.30841	0.201207	0.100603	−	0.994927i	$-0.467923\pi$
$983$	6.30841	0.201207	0.100603	+	0.994927i	$0.467923\pi$
$984$	106.965	3.40992
$985$	9.85846	0.314117
$986$	3.78111	0.120415
$987$	49.8592	1.58704
$988$	4.96483	0.157952
$989$	−4.82885	−0.153548
$990$	7.69049	0.244420
$991$	21.3503	0.678216	0.339108	−	0.940747i	$-0.389875\pi$
$991$	21.3503	0.678216	0.339108	+	0.940747i	$0.389875\pi$
$992$	55.1444	1.75084
$993$	50.9260	1.61609
$994$	176.909	5.61121
$995$	−8.13181	−0.257796
$996$	162.007	5.13340
$997$	−15.2836	−0.484038	−0.242019	−	0.970272i	$-0.577810\pi$
$997$	−15.2836	−0.484038	−0.242019	+	0.970272i	$0.577810\pi$
$998$	−82.5418	−2.61282
$999$	21.0938	0.667378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9409.2.a.q.1.4	yes	168
97.96	even	2		9409.2.a.p.1.4	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9409.2.a.p.1.4	✓	168	97.96	even	2
9409.2.a.q.1.4	yes	168	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9409 = 97^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9409.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69259 q^{2} -2.04647 q^{3} +5.25006 q^{4} -1.47101 q^{5} +5.51032 q^{6} -4.98771 q^{7} -8.75110 q^{8} +1.18805 q^{9} +3.96083 q^{10} +1.63431 q^{11} -10.7441 q^{12} +0.394431 q^{13} +13.4299 q^{14} +3.01038 q^{15} +13.0630 q^{16} -1.95633 q^{17} -3.19893 q^{18} +2.39756 q^{19} -7.72289 q^{20} +10.2072 q^{21} -4.40053 q^{22} +6.20684 q^{23} +17.9089 q^{24} -2.83613 q^{25} -1.06204 q^{26} +3.70811 q^{27} -26.1858 q^{28} +0.717805 q^{29} -8.10573 q^{30} -3.12057 q^{31} -17.6713 q^{32} -3.34457 q^{33} +5.26760 q^{34} +7.33697 q^{35} +6.23732 q^{36} +5.68856 q^{37} -6.45566 q^{38} -0.807191 q^{39} +12.8730 q^{40} +5.97273 q^{41} -27.4839 q^{42} -0.777988 q^{43} +8.58022 q^{44} -1.74763 q^{45} -16.7125 q^{46} +4.88471 q^{47} -26.7332 q^{48} +17.8773 q^{49} +7.63655 q^{50} +4.00357 q^{51} +2.07079 q^{52} -6.68787 q^{53} -9.98444 q^{54} -2.40408 q^{55} +43.6480 q^{56} -4.90654 q^{57} -1.93276 q^{58} -0.201460 q^{59} +15.8047 q^{60} +9.97347 q^{61} +8.40243 q^{62} -5.92563 q^{63} +21.4555 q^{64} -0.580211 q^{65} +9.00556 q^{66} +0.930700 q^{67} -10.2709 q^{68} -12.7021 q^{69} -19.7555 q^{70} +13.1728 q^{71} -10.3967 q^{72} +11.4791 q^{73} -15.3170 q^{74} +5.80407 q^{75} +12.5873 q^{76} -8.15146 q^{77} +2.17344 q^{78} +9.92001 q^{79} -19.2159 q^{80} -11.1527 q^{81} -16.0821 q^{82} -15.0787 q^{83} +53.5885 q^{84} +2.87778 q^{85} +2.09481 q^{86} -1.46897 q^{87} -14.3020 q^{88} -6.38242 q^{89} +4.70565 q^{90} -1.96731 q^{91} +32.5863 q^{92} +6.38616 q^{93} -13.1525 q^{94} -3.52683 q^{95} +36.1638 q^{96} -48.1362 q^{98} +1.94164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 168 q^{4} + 42 q^{5} + 42 q^{7} + 168 q^{9} + 42 q^{10} + 42 q^{13} + 70 q^{14} + 84 q^{15} + 140 q^{16} + 49 q^{17} - 49 q^{18} + 84 q^{19} + 98 q^{20} + 84 q^{21} - 35 q^{22} + 126 q^{23} + 168 q^{25}+ \cdots - 84 q^{99}+O(q^{100}) \) 168 * q + 168 * q^4 + 42 * q^5 + 42 * q^7 + 168 * q^9 + 42 * q^10 + 42 * q^13 + 70 * q^14 + 84 * q^15 + 140 * q^16 + 49 * q^17 - 49 * q^18 + 84 * q^19 + 98 * q^20 + 84 * q^21 - 35 * q^22 + 126 * q^23 + 168 * q^25 + 105 * q^26 + 84 * q^28 + 126 * q^29 + 84 * q^30 + 84 * q^34 + 168 * q^36 + 42 * q^37 + 112 * q^38 + 168 * q^39 + 126 * q^40 + 154 * q^41 + 28 * q^42 - 63 * q^44 + 91 * q^45 - 21 * q^46 - 42 * q^47 - 56 * q^48 + 126 * q^49 - 28 * q^50 + 168 * q^51 + 63 * q^52 - 28 * q^53 - 42 * q^54 + 168 * q^55 + 140 * q^56 + 56 * q^57 - 77 * q^58 + 238 * q^59 + 168 * q^60 - 56 * q^61 - 91 * q^62 + 210 * q^63 + 112 * q^64 - 49 * q^65 - 133 * q^66 + 28 * q^67 + 126 * q^68 + 105 * q^69 - 147 * q^70 + 252 * q^71 - 98 * q^72 + 77 * q^73 + 147 * q^74 + 14 * q^75 + 196 * q^76 + 77 * q^77 - 63 * q^78 + 56 * q^79 + 133 * q^80 + 168 * q^81 + 56 * q^82 + 203 * q^83 + 252 * q^84 - 56 * q^85 - 56 * q^86 + 182 * q^87 - 182 * q^88 + 84 * q^90 - 42 * q^91 + 189 * q^92 + 84 * q^93 - 154 * q^94 - 28 * q^95 - 21 * q^96 + 84 * q^98 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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