LMFDB - Embedded newform 1190.2.a.l.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(1,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-3,0,3,-3,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.837.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 1 $ x^3 - 6*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.36147$ of defining polynomial
Character	$\chi$	$=$	1190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -2.36147 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.36147 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.57653 q^{9} +1.00000 q^{10} -3.36147 q^{11} -2.36147 q^{12} +6.93800 q^{13} -1.00000 q^{14} +2.36147 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.57653 q^{18} -6.29947 q^{19} -1.00000 q^{20} -2.36147 q^{21} +3.36147 q^{22} -5.29947 q^{23} +2.36147 q^{24} +1.00000 q^{25} -6.93800 q^{26} +1.00000 q^{27} +1.00000 q^{28} -2.79160 q^{29} -2.36147 q^{30} -3.14640 q^{31} -1.00000 q^{32} +7.93800 q^{33} +1.00000 q^{34} -1.00000 q^{35} +2.57653 q^{36} +8.72294 q^{37} +6.29947 q^{38} -16.3839 q^{39} +1.00000 q^{40} -3.36147 q^{41} +2.36147 q^{42} +3.42347 q^{43} -3.36147 q^{44} -2.57653 q^{45} +5.29947 q^{46} -3.51454 q^{47} -2.36147 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.36147 q^{51} +6.93800 q^{52} +5.94467 q^{53} -1.00000 q^{54} +3.36147 q^{55} -1.00000 q^{56} +14.8760 q^{57} +2.79160 q^{58} +10.2375 q^{59} +2.36147 q^{60} -10.3839 q^{61} +3.14640 q^{62} +2.57653 q^{63} +1.00000 q^{64} -6.93800 q^{65} -7.93800 q^{66} +12.0844 q^{67} -1.00000 q^{68} +12.5145 q^{69} +1.00000 q^{70} +14.8140 q^{71} -2.57653 q^{72} -15.2441 q^{73} -8.72294 q^{74} -2.36147 q^{75} -6.29947 q^{76} -3.36147 q^{77} +16.3839 q^{78} +5.56987 q^{79} -1.00000 q^{80} -10.0911 q^{81} +3.36147 q^{82} -13.7520 q^{83} -2.36147 q^{84} +1.00000 q^{85} -3.42347 q^{86} +6.59228 q^{87} +3.36147 q^{88} +10.9380 q^{89} +2.57653 q^{90} +6.93800 q^{91} -5.29947 q^{92} +7.43013 q^{93} +3.51454 q^{94} +6.29947 q^{95} +2.36147 q^{96} +14.3839 q^{97} -1.00000 q^{98} -8.66094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} + 9 q^{13} - 3 q^{14} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{20} + 3 q^{22} + 3 q^{23} + 3 q^{25} - 9 q^{26} + 3 q^{27}+ \cdots - 3 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 + 9 * q^13 - 3 * q^14 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^20 + 3 * q^22 + 3 * q^23 + 3 * q^25 - 9 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^29 - 3 * q^32 + 12 * q^33 + 3 * q^34 - 3 * q^35 + 3 * q^36 + 12 * q^37 - 9 * q^39 + 3 * q^40 - 3 * q^41 + 15 * q^43 - 3 * q^44 - 3 * q^45 - 3 * q^46 + 6 * q^47 + 3 * q^49 - 3 * q^50 + 9 * q^52 + 6 * q^53 - 3 * q^54 + 3 * q^55 - 3 * q^56 + 21 * q^57 + 6 * q^58 + 9 * q^61 + 3 * q^63 + 3 * q^64 - 9 * q^65 - 12 * q^66 + 15 * q^67 - 3 * q^68 + 21 * q^69 + 3 * q^70 + 9 * q^71 - 3 * q^72 - 15 * q^73 - 12 * q^74 - 3 * q^77 + 9 * q^78 + 12 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 6 * q^83 + 3 * q^85 - 15 * q^86 - 18 * q^87 + 3 * q^88 + 21 * q^89 + 3 * q^90 + 9 * q^91 + 3 * q^92 + 27 * q^93 - 6 * q^94 + 3 * q^97 - 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.36147	−1.36339	−0.681697	−	0.731634i	$-0.738758\pi$
$3$	−2.36147	−1.36339	−0.681697	+	0.731634i	$0.738758\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.36147	0.964066
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	2.57653	0.858845
$10$	1.00000	0.316228
$11$	−3.36147	−1.01352	−0.506760	−	0.862087i	$-0.669157\pi$
$11$	−3.36147	−1.01352	−0.506760	+	0.862087i	$0.669157\pi$
$12$	−2.36147	−0.681697
$13$	6.93800	1.92426	0.962128	−	0.272598i	$-0.0878830\pi$
$13$	6.93800	1.92426	0.962128	+	0.272598i	$0.0878830\pi$
$14$	−1.00000	−0.267261
$15$	2.36147	0.609729
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.57653	−0.607295
$19$	−6.29947	−1.44520	−0.722599	−	0.691267i	$-0.757053\pi$
$19$	−6.29947	−1.44520	−0.722599	+	0.691267i	$0.757053\pi$
$20$	−1.00000	−0.223607
$21$	−2.36147	−0.515315
$22$	3.36147	0.716668
$23$	−5.29947	−1.10502	−0.552508	−	0.833507i	$-0.686329\pi$
$23$	−5.29947	−1.10502	−0.552508	+	0.833507i	$0.686329\pi$
$24$	2.36147	0.482033
$25$	1.00000	0.200000
$26$	−6.93800	−1.36065
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−2.79160	−0.518387	−0.259194	−	0.965825i	$-0.583457\pi$
$29$	−2.79160	−0.518387	−0.259194	+	0.965825i	$0.583457\pi$
$30$	−2.36147	−0.431143
$31$	−3.14640	−0.565111	−0.282555	−	0.959251i	$-0.591182\pi$
$31$	−3.14640	−0.565111	−0.282555	+	0.959251i	$0.591182\pi$
$32$	−1.00000	−0.176777
$33$	7.93800	1.38183
$34$	1.00000	0.171499
$35$	−1.00000	−0.169031
$36$	2.57653	0.429422
$37$	8.72294	1.43404	0.717021	−	0.697052i	$-0.245505\pi$
$37$	8.72294	1.43404	0.717021	+	0.697052i	$0.245505\pi$
$38$	6.29947	1.02191
$39$	−16.3839	−2.62352
$40$	1.00000	0.158114
$41$	−3.36147	−0.524973	−0.262487	−	0.964936i	$-0.584543\pi$
$41$	−3.36147	−0.524973	−0.262487	+	0.964936i	$0.584543\pi$
$42$	2.36147	0.364383
$43$	3.42347	0.522074	0.261037	−	0.965329i	$-0.415936\pi$
$43$	3.42347	0.522074	0.261037	+	0.965329i	$0.415936\pi$
$44$	−3.36147	−0.506760
$45$	−2.57653	−0.384087
$46$	5.29947	0.781365
$47$	−3.51454	−0.512648	−0.256324	−	0.966591i	$-0.582511\pi$
$47$	−3.51454	−0.512648	−0.256324	+	0.966591i	$0.582511\pi$
$48$	−2.36147	−0.340849
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	2.36147	0.330672
$52$	6.93800	0.962128
$53$	5.94467	0.816563	0.408282	−	0.912856i	$-0.366128\pi$
$53$	5.94467	0.816563	0.408282	+	0.912856i	$0.366128\pi$
$54$	−1.00000	−0.136083
$55$	3.36147	0.453260
$56$	−1.00000	−0.133631
$57$	14.8760	1.97038
$58$	2.79160	0.366555
$59$	10.2375	1.33281	0.666403	−	0.745592i	$-0.267833\pi$
$59$	10.2375	1.33281	0.666403	+	0.745592i	$0.267833\pi$
$60$	2.36147	0.304864
$61$	−10.3839	−1.32952	−0.664760	−	0.747057i	$-0.731466\pi$
$61$	−10.3839	−1.32952	−0.664760	+	0.747057i	$0.731466\pi$
$62$	3.14640	0.399594
$63$	2.57653	0.324613
$64$	1.00000	0.125000
$65$	−6.93800	−0.860553
$66$	−7.93800	−0.977101
$67$	12.0844	1.47635	0.738173	−	0.674612i	$-0.235689\pi$
$67$	12.0844	1.47635	0.738173	+	0.674612i	$0.235689\pi$
$68$	−1.00000	−0.121268
$69$	12.5145	1.50657
$70$	1.00000	0.119523
$71$	14.8140	1.75810	0.879050	−	0.476730i	$-0.158178\pi$
$71$	14.8140	1.75810	0.879050	+	0.476730i	$0.158178\pi$
$72$	−2.57653	−0.303648
$73$	−15.2441	−1.78419	−0.892096	−	0.451846i	$-0.850766\pi$
$73$	−15.2441	−1.78419	−0.892096	+	0.451846i	$0.850766\pi$
$74$	−8.72294	−1.01402
$75$	−2.36147	−0.272679
$76$	−6.29947	−0.722599
$77$	−3.36147	−0.383075
$78$	16.3839	1.85511
$79$	5.56987	0.626659	0.313330	−	0.949644i	$-0.398556\pi$
$79$	5.56987	0.626659	0.313330	+	0.949644i	$0.398556\pi$
$80$	−1.00000	−0.111803
$81$	−10.0911	−1.12123
$82$	3.36147	0.371212
$83$	−13.7520	−1.50948	−0.754740	−	0.656024i	$-0.772237\pi$
$83$	−13.7520	−1.50948	−0.754740	+	0.656024i	$0.772237\pi$
$84$	−2.36147	−0.257657
$85$	1.00000	0.108465
$86$	−3.42347	−0.369162
$87$	6.59228	0.706766
$88$	3.36147	0.358334
$89$	10.9380	1.15943	0.579713	−	0.814821i	$-0.303165\pi$
$89$	10.9380	1.15943	0.579713	+	0.814821i	$0.303165\pi$
$90$	2.57653	0.271591
$91$	6.93800	0.727300
$92$	−5.29947	−0.552508
$93$	7.43013	0.770469
$94$	3.51454	0.362497
$95$	6.29947	0.646312
$96$	2.36147	0.241016
$97$	14.3839	1.46046	0.730231	−	0.683201i	$-0.239413\pi$
$97$	14.3839	1.46046	0.730231	+	0.683201i	$0.239413\pi$
$98$	−1.00000	−0.101015
$99$	−8.66094	−0.870457
$100$	1.00000	0.100000
$101$	14.6834	1.46105	0.730524	−	0.682887i	$-0.239276\pi$
$101$	14.6834	1.46105	0.730524	+	0.682887i	$0.239276\pi$
$102$	−2.36147	−0.233820
$103$	12.5765	1.23920	0.619601	−	0.784917i	$-0.287294\pi$
$103$	12.5765	1.23920	0.619601	+	0.784917i	$0.287294\pi$
$104$	−6.93800	−0.680327
$105$	2.36147	0.230456
$106$	−5.94467	−0.577397
$107$	6.30614	0.609637	0.304819	−	0.952410i	$-0.401404\pi$
$107$	6.30614	0.609637	0.304819	+	0.952410i	$0.401404\pi$
$108$	1.00000	0.0962250
$109$	17.0224	1.63045	0.815226	−	0.579144i	$-0.196613\pi$
$109$	17.0224	1.63045	0.815226	+	0.579144i	$0.196613\pi$
$110$	−3.36147	−0.320503
$111$	−20.5989	−1.95517
$112$	1.00000	0.0944911
$113$	15.4392	1.45240	0.726199	−	0.687484i	$-0.241285\pi$
$113$	15.4392	1.45240	0.726199	+	0.687484i	$0.241285\pi$
$114$	−14.8760	−1.39327
$115$	5.29947	0.494178
$116$	−2.79160	−0.259194
$117$	17.8760	1.65264
$118$	−10.2375	−0.942436
$119$	−1.00000	−0.0916698
$120$	−2.36147	−0.215572
$121$	0.299472	0.0272248
$122$	10.3839	0.940112
$123$	7.93800	0.715746
$124$	−3.14640	−0.282555
$125$	−1.00000	−0.0894427
$126$	−2.57653	−0.229536
$127$	2.33906	0.207558	0.103779	−	0.994600i	$-0.466907\pi$
$127$	2.33906	0.207558	0.103779	+	0.994600i	$0.466907\pi$
$128$	−1.00000	−0.0883883
$129$	−8.08441	−0.711792
$130$	6.93800	0.608503
$131$	8.16881	0.713712	0.356856	−	0.934159i	$-0.383849\pi$
$131$	8.16881	0.713712	0.356856	+	0.934159i	$0.383849\pi$
$132$	7.93800	0.690915
$133$	−6.29947	−0.546234
$134$	−12.0844	−1.04393
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	16.2928	1.39199	0.695994	−	0.718047i	$-0.254964\pi$
$137$	16.2928	1.39199	0.695994	+	0.718047i	$0.254964\pi$
$138$	−12.5145	−1.06531
$139$	1.27706	0.108319	0.0541595	−	0.998532i	$-0.482752\pi$
$139$	1.27706	0.108319	0.0541595	+	0.998532i	$0.482752\pi$
$140$	−1.00000	−0.0845154
$141$	8.29947	0.698942
$142$	−14.8140	−1.24316
$143$	−23.3219	−1.95027
$144$	2.57653	0.214711
$145$	2.79160	0.231830
$146$	15.2441	1.26161
$147$	−2.36147	−0.194771
$148$	8.72294	0.717021
$149$	−7.02908	−0.575844	−0.287922	−	0.957654i	$-0.592964\pi$
$149$	−7.02908	−0.575844	−0.287922	+	0.957654i	$0.592964\pi$
$150$	2.36147	0.192813
$151$	−10.9313	−0.889580	−0.444790	−	0.895635i	$-0.646722\pi$
$151$	−10.9313	−0.889580	−0.444790	+	0.895635i	$0.646722\pi$
$152$	6.29947	0.510955
$153$	−2.57653	−0.208300
$154$	3.36147	0.270875
$155$	3.14640	0.252725
$156$	−16.3839	−1.31176
$157$	−0.430132	−0.0343283	−0.0171641	−	0.999853i	$-0.505464\pi$
$157$	−0.430132	−0.0343283	−0.0171641	+	0.999853i	$0.505464\pi$
$158$	−5.56987	−0.443115
$159$	−14.0382	−1.11330
$160$	1.00000	0.0790569
$161$	−5.29947	−0.417657
$162$	10.0911	0.792830
$163$	17.1531	1.34353	0.671766	−	0.740763i	$-0.265536\pi$
$163$	17.1531	1.34353	0.671766	+	0.740763i	$0.265536\pi$
$164$	−3.36147	−0.262487
$165$	−7.93800	−0.617973
$166$	13.7520	1.06736
$167$	−23.0157	−1.78101	−0.890506	−	0.454972i	$-0.849649\pi$
$167$	−23.0157	−1.78101	−0.890506	+	0.454972i	$0.849649\pi$
$168$	2.36147	0.182191
$169$	35.1359	2.70276
$170$	−1.00000	−0.0766965
$171$	−16.2308	−1.24120
$172$	3.42347	0.261037
$173$	2.63853	0.200604	0.100302	−	0.994957i	$-0.468019\pi$
$173$	2.63853	0.200604	0.100302	+	0.994957i	$0.468019\pi$
$174$	−6.59228	−0.499759
$175$	1.00000	0.0755929
$176$	−3.36147	−0.253380
$177$	−24.1755	−1.81714
$178$	−10.9380	−0.819838
$179$	6.72294	0.502496	0.251248	−	0.967923i	$-0.419159\pi$
$179$	6.72294	0.502496	0.251248	+	0.967923i	$0.419159\pi$
$180$	−2.57653	−0.192044
$181$	−20.5989	−1.53111	−0.765554	−	0.643372i	$-0.777535\pi$
$181$	−20.5989	−1.53111	−0.765554	+	0.643372i	$0.777535\pi$
$182$	−6.93800	−0.514279
$183$	24.5212	1.81266
$184$	5.29947	0.390682
$185$	−8.72294	−0.641323
$186$	−7.43013	−0.544804
$187$	3.36147	0.245815
$188$	−3.51454	−0.256324
$189$	1.00000	0.0727393
$190$	−6.29947	−0.457012
$191$	−25.2375	−1.82612	−0.913060	−	0.407826i	$-0.866287\pi$
$191$	−25.2375	−1.82612	−0.913060	+	0.407826i	$0.866287\pi$
$192$	−2.36147	−0.170424
$193$	−26.6214	−1.91625	−0.958124	−	0.286355i	$-0.907556\pi$
$193$	−26.6214	−1.91625	−0.958124	+	0.286355i	$0.907556\pi$
$194$	−14.3839	−1.03270
$195$	16.3839	1.17327
$196$	1.00000	0.0714286
$197$	16.2928	1.16081	0.580407	−	0.814326i	$-0.302893\pi$
$197$	16.2928	1.16081	0.580407	+	0.814326i	$0.302893\pi$
$198$	8.66094	0.615506
$199$	−16.3615	−1.15983	−0.579917	−	0.814676i	$-0.696915\pi$
$199$	−16.3615	−1.15983	−0.579917	+	0.814676i	$0.696915\pi$
$200$	−1.00000	−0.0707107
$201$	−28.5369	−2.01284
$202$	−14.6834	−1.03312
$203$	−2.79160	−0.195932
$204$	2.36147	0.165336
$205$	3.36147	0.234775
$206$	−12.5765	−0.876249
$207$	−13.6543	−0.949038
$208$	6.93800	0.481064
$209$	21.1755	1.46474
$210$	−2.36147	−0.162957
$211$	3.13974	0.216148	0.108074	−	0.994143i	$-0.465532\pi$
$211$	3.13974	0.216148	0.108074	+	0.994143i	$0.465532\pi$
$212$	5.94467	0.408282
$213$	−34.9828	−2.39698
$214$	−6.30614	−0.431079
$215$	−3.42347	−0.233478
$216$	−1.00000	−0.0680414
$217$	−3.14640	−0.213592
$218$	−17.0224	−1.15290
$219$	35.9986	2.43256
$220$	3.36147	0.226630
$221$	−6.93800	−0.466701
$222$	20.5989	1.38251
$223$	1.24414	0.0833139	0.0416570	−	0.999132i	$-0.486736\pi$
$223$	1.24414	0.0833139	0.0416570	+	0.999132i	$0.486736\pi$
$224$	−1.00000	−0.0668153
$225$	2.57653	0.171769
$226$	−15.4392	−1.02700
$227$	−10.4235	−0.691830	−0.345915	−	0.938266i	$-0.612431\pi$
$227$	−10.4235	−0.691830	−0.345915	+	0.938266i	$0.612431\pi$
$228$	14.8760	0.985188
$229$	15.4235	1.01921	0.509606	−	0.860408i	$-0.329791\pi$
$229$	15.4235	1.01921	0.509606	+	0.860408i	$0.329791\pi$
$230$	−5.29947	−0.349437
$231$	7.93800	0.522282
$232$	2.79160	0.183278
$233$	16.2599	1.06522	0.532610	−	0.846361i	$-0.321211\pi$
$233$	16.2599	1.06522	0.532610	+	0.846361i	$0.321211\pi$
$234$	−17.8760	−1.16859
$235$	3.51454	0.229263
$236$	10.2375	0.666403
$237$	−13.1531	−0.854384
$238$	1.00000	0.0648204
$239$	6.93134	0.448351	0.224175	−	0.974549i	$-0.428031\pi$
$239$	6.93134	0.448351	0.224175	+	0.974549i	$0.428031\pi$
$240$	2.36147	0.152432
$241$	−8.57653	−0.552463	−0.276232	−	0.961091i	$-0.589086\pi$
$241$	−8.57653	−0.552463	−0.276232	+	0.961091i	$0.589086\pi$
$242$	−0.299472	−0.0192508
$243$	20.8298	1.33623
$244$	−10.3839	−0.664760
$245$	−1.00000	−0.0638877
$246$	−7.93800	−0.506109
$247$	−43.7058	−2.78093
$248$	3.14640	0.199797
$249$	32.4750	2.05802
$250$	1.00000	0.0632456
$251$	21.4063	1.35115	0.675576	−	0.737290i	$-0.263895\pi$
$251$	21.4063	1.35115	0.675576	+	0.737290i	$0.263895\pi$
$252$	2.57653	0.162306
$253$	17.8140	1.11996
$254$	−2.33906	−0.146766
$255$	−2.36147	−0.147881
$256$	1.00000	0.0625000
$257$	−15.5923	−0.972620	−0.486310	−	0.873786i	$-0.661657\pi$
$257$	−15.5923	−0.972620	−0.486310	+	0.873786i	$0.661657\pi$
$258$	8.08441	0.503313
$259$	8.72294	0.542017
$260$	−6.93800	−0.430277
$261$	−7.19266	−0.445214
$262$	−8.16881	−0.504671
$263$	−15.1201	−0.932348	−0.466174	−	0.884693i	$-0.654368\pi$
$263$	−15.1201	−0.932348	−0.466174	+	0.884693i	$0.654368\pi$
$264$	−7.93800	−0.488550
$265$	−5.94467	−0.365178
$266$	6.29947	0.386245
$267$	−25.8298	−1.58076
$268$	12.0844	0.738173
$269$	16.2599	0.991383	0.495691	−	0.868499i	$-0.334915\pi$
$269$	16.2599	0.991383	0.495691	+	0.868499i	$0.334915\pi$
$270$	1.00000	0.0608581
$271$	−5.70719	−0.346687	−0.173344	−	0.984861i	$-0.555457\pi$
$271$	−5.70719	−0.346687	−0.173344	+	0.984861i	$0.555457\pi$
$272$	−1.00000	−0.0606339
$273$	−16.3839	−0.991597
$274$	−16.2928	−0.984284
$275$	−3.36147	−0.202704
$276$	12.5145	0.753287
$277$	9.13974	0.549154	0.274577	−	0.961565i	$-0.411462\pi$
$277$	9.13974	0.549154	0.274577	+	0.961565i	$0.411462\pi$
$278$	−1.27706	−0.0765931
$279$	−8.10682	−0.485342
$280$	1.00000	0.0597614
$281$	19.6967	1.17501	0.587503	−	0.809222i	$-0.300111\pi$
$281$	19.6967	1.17501	0.587503	+	0.809222i	$0.300111\pi$
$282$	−8.29947	−0.494226
$283$	1.24414	0.0739566	0.0369783	−	0.999316i	$-0.488227\pi$
$283$	1.24414	0.0739566	0.0369783	+	0.999316i	$0.488227\pi$
$284$	14.8140	0.879050
$285$	−14.8760	−0.881179
$286$	23.3219	1.37905
$287$	−3.36147	−0.198421
$288$	−2.57653	−0.151824
$289$	1.00000	0.0588235
$290$	−2.79160	−0.163928
$291$	−33.9671	−1.99119
$292$	−15.2441	−0.892096
$293$	14.0911	0.823209	0.411605	−	0.911363i	$-0.364968\pi$
$293$	14.0911	0.823209	0.411605	+	0.911363i	$0.364968\pi$
$294$	2.36147	0.137724
$295$	−10.2375	−0.596049
$296$	−8.72294	−0.507010
$297$	−3.36147	−0.195052
$298$	7.02908	0.407183
$299$	−36.7678	−2.12633
$300$	−2.36147	−0.136339
$301$	3.42347	0.197325
$302$	10.9313	0.629028
$303$	−34.6743	−1.99199
$304$	−6.29947	−0.361300
$305$	10.3839	0.594579
$306$	2.57653	0.147291
$307$	22.4750	1.28271	0.641357	−	0.767243i	$-0.278372\pi$
$307$	22.4750	1.28271	0.641357	+	0.767243i	$0.278372\pi$
$308$	−3.36147	−0.191537
$309$	−29.6991	−1.68952
$310$	−3.14640	−0.178704
$311$	−9.85360	−0.558746	−0.279373	−	0.960183i	$-0.590127\pi$
$311$	−9.85360	−0.558746	−0.279373	+	0.960183i	$0.590127\pi$
$312$	16.3839	0.927554
$313$	5.45921	0.308573	0.154286	−	0.988026i	$-0.450692\pi$
$313$	5.45921	0.308573	0.154286	+	0.988026i	$0.450692\pi$
$314$	0.430132	0.0242737
$315$	−2.57653	−0.145171
$316$	5.56987	0.313330
$317$	−15.1531	−0.851081	−0.425541	−	0.904939i	$-0.639916\pi$
$317$	−15.1531	−0.851081	−0.425541	+	0.904939i	$0.639916\pi$
$318$	14.0382	0.787221
$319$	9.38388	0.525396
$320$	−1.00000	−0.0559017
$321$	−14.8918	−0.831176
$322$	5.29947	0.295328
$323$	6.29947	0.350512
$324$	−10.0911	−0.560615
$325$	6.93800	0.384851
$326$	−17.1531	−0.950021
$327$	−40.1979	−2.22295
$328$	3.36147	0.185606
$329$	−3.51454	−0.193763
$330$	7.93800	0.436973
$331$	8.38388	0.460820	0.230410	−	0.973094i	$-0.425993\pi$
$331$	8.38388	0.460820	0.230410	+	0.973094i	$0.425993\pi$
$332$	−13.7520	−0.754740
$333$	22.4750	1.23162
$334$	23.0157	1.25937
$335$	−12.0844	−0.660242
$336$	−2.36147	−0.128829
$337$	−9.94467	−0.541721	−0.270860	−	0.962619i	$-0.587308\pi$
$337$	−9.94467	−0.541721	−0.270860	+	0.962619i	$0.587308\pi$
$338$	−35.1359	−1.91114
$339$	−36.4592	−1.98019
$340$	1.00000	0.0542326
$341$	10.5765	0.572751
$342$	16.2308	0.877662
$343$	1.00000	0.0539949
$344$	−3.42347	−0.184581
$345$	−12.5145	−0.673760
$346$	−2.63853	−0.141848
$347$	4.21507	0.226277	0.113138	−	0.993579i	$-0.463910\pi$
$347$	4.21507	0.226277	0.113138	+	0.993579i	$0.463910\pi$
$348$	6.59228	0.353383
$349$	5.56987	0.298148	0.149074	−	0.988826i	$-0.452371\pi$
$349$	5.56987	0.298148	0.149074	+	0.988826i	$0.452371\pi$
$350$	−1.00000	−0.0534522
$351$	6.93800	0.370323
$352$	3.36147	0.179167
$353$	−1.34814	−0.0717540	−0.0358770	−	0.999356i	$-0.511422\pi$
$353$	−1.34814	−0.0717540	−0.0358770	+	0.999356i	$0.511422\pi$
$354$	24.1755	1.28491
$355$	−14.8140	−0.786246
$356$	10.9380	0.579713
$357$	2.36147	0.124982
$358$	−6.72294	−0.355318
$359$	9.89842	0.522418	0.261209	−	0.965282i	$-0.415879\pi$
$359$	9.89842	0.522418	0.261209	+	0.965282i	$0.415879\pi$
$360$	2.57653	0.135795
$361$	20.6834	1.08860
$362$	20.5989	1.08266
$363$	−0.707194	−0.0371181
$364$	6.93800	0.363650
$365$	15.2441	0.797915
$366$	−24.5212	−1.28174
$367$	30.4883	1.59148	0.795738	−	0.605641i	$-0.207083\pi$
$367$	30.4883	1.59148	0.795738	+	0.605641i	$0.207083\pi$
$368$	−5.29947	−0.276254
$369$	−8.66094	−0.450871
$370$	8.72294	0.453484
$371$	5.94467	0.308632
$372$	7.43013	0.385234
$373$	10.8693	0.562793	0.281397	−	0.959592i	$-0.409202\pi$
$373$	10.8693	0.562793	0.281397	+	0.959592i	$0.409202\pi$
$374$	−3.36147	−0.173817
$375$	2.36147	0.121946
$376$	3.51454	0.181248
$377$	−19.3681	−0.997510
$378$	−1.00000	−0.0514344
$379$	−18.7587	−0.963569	−0.481784	−	0.876290i	$-0.660011\pi$
$379$	−18.7587	−0.963569	−0.481784	+	0.876290i	$0.660011\pi$
$380$	6.29947	0.323156
$381$	−5.52361	−0.282983
$382$	25.2375	1.29126
$383$	21.7453	1.11114	0.555568	−	0.831471i	$-0.312501\pi$
$383$	21.7453	1.11114	0.555568	+	0.831471i	$0.312501\pi$
$384$	2.36147	0.120508
$385$	3.36147	0.171316
$386$	26.6214	1.35499
$387$	8.82068	0.448380
$388$	14.3839	0.730231
$389$	−9.45921	−0.479601	−0.239800	−	0.970822i	$-0.577082\pi$
$389$	−9.45921	−0.479601	−0.239800	+	0.970822i	$0.577082\pi$
$390$	−16.3839	−0.829630
$391$	5.29947	0.268006
$392$	−1.00000	−0.0505076
$393$	−19.2904	−0.973072
$394$	−16.2928	−0.820820
$395$	−5.56987	−0.280250
$396$	−8.66094	−0.435229
$397$	25.6056	1.28511	0.642554	−	0.766240i	$-0.277875\pi$
$397$	25.6056	1.28511	0.642554	+	0.766240i	$0.277875\pi$
$398$	16.3615	0.820126
$399$	14.8760	0.744732
$400$	1.00000	0.0500000
$401$	1.40106	0.0699654	0.0349827	−	0.999388i	$-0.488862\pi$
$401$	1.40106	0.0699654	0.0349827	+	0.999388i	$0.488862\pi$
$402$	28.5369	1.42329
$403$	−21.8298	−1.08742
$404$	14.6834	0.730524
$405$	10.0911	0.501429
$406$	2.79160	0.138545
$407$	−29.3219	−1.45343
$408$	−2.36147	−0.116910
$409$	8.49454	0.420028	0.210014	−	0.977698i	$-0.432649\pi$
$409$	8.49454	0.420028	0.210014	+	0.977698i	$0.432649\pi$
$410$	−3.36147	−0.166011
$411$	−38.4750	−1.89783
$412$	12.5765	0.619601
$413$	10.2375	0.503753
$414$	13.6543	0.671071
$415$	13.7520	0.675060
$416$	−6.93800	−0.340164
$417$	−3.01574	−0.147682
$418$	−21.1755	−1.03573
$419$	11.0157	0.538154	0.269077	−	0.963119i	$-0.413281\pi$
$419$	11.0157	0.538154	0.269077	+	0.963119i	$0.413281\pi$
$420$	2.36147	0.115228
$421$	−29.7968	−1.45221	−0.726104	−	0.687584i	$-0.758671\pi$
$421$	−29.7968	−1.45221	−0.726104	+	0.687584i	$0.758671\pi$
$422$	−3.13974	−0.152840
$423$	−9.05533	−0.440285
$424$	−5.94467	−0.288699
$425$	−1.00000	−0.0485071
$426$	34.9828	1.69492
$427$	−10.3839	−0.502511
$428$	6.30614	0.304819
$429$	55.0739	2.65899
$430$	3.42347	0.165094
$431$	−19.1397	−0.921929	−0.460964	−	0.887419i	$-0.652496\pi$
$431$	−19.1397	−0.921929	−0.460964	+	0.887419i	$0.652496\pi$
$432$	1.00000	0.0481125
$433$	−24.0582	−1.15616	−0.578081	−	0.815980i	$-0.696198\pi$
$433$	−24.0582	−1.15616	−0.578081	+	0.815980i	$0.696198\pi$
$434$	3.14640	0.151032
$435$	−6.59228	−0.316076
$436$	17.0224	0.815226
$437$	33.3839	1.59697
$438$	−35.9986	−1.72008
$439$	5.89842	0.281516	0.140758	−	0.990044i	$-0.455046\pi$
$439$	5.89842	0.281516	0.140758	+	0.990044i	$0.455046\pi$
$440$	−3.36147	−0.160252
$441$	2.57653	0.122692
$442$	6.93800	0.330007
$443$	−13.1621	−0.625352	−0.312676	−	0.949860i	$-0.601225\pi$
$443$	−13.1621	−0.625352	−0.312676	+	0.949860i	$0.601225\pi$
$444$	−20.5989	−0.977583
$445$	−10.9380	−0.518511
$446$	−1.24414	−0.0589119
$447$	16.5989	0.785103
$448$	1.00000	0.0472456
$449$	7.44588	0.351393	0.175696	−	0.984444i	$-0.443782\pi$
$449$	7.44588	0.351393	0.175696	+	0.984444i	$0.443782\pi$
$450$	−2.57653	−0.121459
$451$	11.2995	0.532071
$452$	15.4392	0.726199
$453$	25.8140	1.21285
$454$	10.4235	0.489197
$455$	−6.93800	−0.325259
$456$	−14.8760	−0.696633
$457$	27.0291	1.26437	0.632183	−	0.774819i	$-0.282159\pi$
$457$	27.0291	1.26437	0.632183	+	0.774819i	$0.282159\pi$
$458$	−15.4235	−0.720691
$459$	−1.00000	−0.0466760
$460$	5.29947	0.247089
$461$	−29.4196	−1.37021	−0.685104	−	0.728445i	$-0.740243\pi$
$461$	−29.4196	−1.37021	−0.685104	+	0.728445i	$0.740243\pi$
$462$	−7.93800	−0.369309
$463$	12.2151	0.567682	0.283841	−	0.958871i	$-0.408391\pi$
$463$	12.2151	0.567682	0.283841	+	0.958871i	$0.408391\pi$
$464$	−2.79160	−0.129597
$465$	−7.43013	−0.344564
$466$	−16.2599	−0.753225
$467$	12.1555	0.562488	0.281244	−	0.959636i	$-0.409253\pi$
$467$	12.1555	0.562488	0.281244	+	0.959636i	$0.409253\pi$
$468$	17.8760	0.826319
$469$	12.0844	0.558006
$470$	−3.51454	−0.162114
$471$	1.01574	0.0468030
$472$	−10.2375	−0.471218
$473$	−11.5079	−0.529132
$474$	13.1531	0.604140
$475$	−6.29947	−0.289040
$476$	−1.00000	−0.0458349
$477$	15.3166	0.701301
$478$	−6.93134	−0.317032
$479$	12.3839	0.565834	0.282917	−	0.959144i	$-0.408698\pi$
$479$	12.3839	0.565834	0.282917	+	0.959144i	$0.408698\pi$
$480$	−2.36147	−0.107786
$481$	60.5198	2.75946
$482$	8.57653	0.390650
$483$	12.5145	0.569431
$484$	0.299472	0.0136124
$485$	−14.3839	−0.653138
$486$	−20.8298	−0.944857
$487$	20.5145	0.929602	0.464801	−	0.885415i	$-0.346126\pi$
$487$	20.5145	0.929602	0.464801	+	0.885415i	$0.346126\pi$
$488$	10.3839	0.470056
$489$	−40.5064	−1.83176
$490$	1.00000	0.0451754
$491$	−8.20173	−0.370139	−0.185070	−	0.982725i	$-0.559251\pi$
$491$	−8.20173	−0.370139	−0.185070	+	0.982725i	$0.559251\pi$
$492$	7.93800	0.357873
$493$	2.79160	0.125727
$494$	43.7058	1.96642
$495$	8.66094	0.389280
$496$	−3.14640	−0.141278
$497$	14.8140	0.664499
$498$	−32.4750	−1.45524
$499$	22.9447	1.02714	0.513572	−	0.858046i	$-0.328322\pi$
$499$	22.9447	1.02714	0.513572	+	0.858046i	$0.328322\pi$
$500$	−1.00000	−0.0447214
$501$	54.3510	2.42822
$502$	−21.4063	−0.955409
$503$	−7.33522	−0.327061	−0.163531	−	0.986538i	$-0.552288\pi$
$503$	−7.33522	−0.327061	−0.163531	+	0.986538i	$0.552288\pi$
$504$	−2.57653	−0.114768
$505$	−14.6834	−0.653401
$506$	−17.8140	−0.791929
$507$	−82.9723	−3.68493
$508$	2.33906	0.103779
$509$	−3.89842	−0.172794	−0.0863971	−	0.996261i	$-0.527535\pi$
$509$	−3.89842	−0.172794	−0.0863971	+	0.996261i	$0.527535\pi$
$510$	2.36147	0.104568
$511$	−15.2441	−0.674361
$512$	−1.00000	−0.0441942
$513$	−6.29947	−0.278128
$514$	15.5923	0.687746
$515$	−12.5765	−0.554188
$516$	−8.08441	−0.355896
$517$	11.8140	0.519580
$518$	−8.72294	−0.383264
$519$	−6.23081	−0.273502
$520$	6.93800	0.304252
$521$	−7.46828	−0.327192	−0.163596	−	0.986527i	$-0.552309\pi$
$521$	−7.46828	−0.327192	−0.163596	+	0.986527i	$0.552309\pi$
$522$	7.19266	0.314814
$523$	−31.7653	−1.38900	−0.694501	−	0.719492i	$-0.744375\pi$
$523$	−31.7653	−1.38900	−0.694501	+	0.719492i	$0.744375\pi$
$524$	8.16881	0.356856
$525$	−2.36147	−0.103063
$526$	15.1201	0.659270
$527$	3.14640	0.137059
$528$	7.93800	0.345457
$529$	5.08441	0.221061
$530$	5.94467	0.258220
$531$	26.3772	1.14467
$532$	−6.29947	−0.273117
$533$	−23.3219	−1.01018
$534$	25.8298	1.11776
$535$	−6.30614	−0.272638
$536$	−12.0844	−0.521967
$537$	−15.8760	−0.685100
$538$	−16.2599	−0.701013
$539$	−3.36147	−0.144789
$540$	−1.00000	−0.0430331
$541$	−29.3930	−1.26370	−0.631851	−	0.775090i	$-0.717705\pi$
$541$	−29.3930	−1.26370	−0.631851	+	0.775090i	$0.717705\pi$
$542$	5.70719	0.245145
$543$	48.6438	2.08750
$544$	1.00000	0.0428746
$545$	−17.0224	−0.729160
$546$	16.3839	0.701165
$547$	25.6609	1.09718	0.548591	−	0.836091i	$-0.315164\pi$
$547$	25.6609	1.09718	0.548591	+	0.836091i	$0.315164\pi$
$548$	16.2928	0.695994
$549$	−26.7544	−1.14185
$550$	3.36147	0.143334
$551$	17.5856	0.749172
$552$	−12.5145	−0.532654
$553$	5.56987	0.236855
$554$	−9.13974	−0.388310
$555$	20.5989	0.874376
$556$	1.27706	0.0541595
$557$	−4.46828	−0.189327	−0.0946637	−	0.995509i	$-0.530178\pi$
$557$	−4.46828	−0.189327	−0.0946637	+	0.995509i	$0.530178\pi$
$558$	8.10682	0.343189
$559$	23.7520	1.00460
$560$	−1.00000	−0.0422577
$561$	−7.93800	−0.335143
$562$	−19.6967	−0.830854
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	8.29947	0.349471
$565$	−15.4392	−0.649532
$566$	−1.24414	−0.0522952
$567$	−10.0911	−0.423785
$568$	−14.8140	−0.621582
$569$	7.99333	0.335098	0.167549	−	0.985864i	$-0.446415\pi$
$569$	7.99333	0.335098	0.167549	+	0.985864i	$0.446415\pi$
$570$	14.8760	0.623087
$571$	13.4855	0.564349	0.282175	−	0.959363i	$-0.408944\pi$
$571$	13.4855	0.564349	0.282175	+	0.959363i	$0.408944\pi$
$572$	−23.3219	−0.975137
$573$	59.5975	2.48972
$574$	3.36147	0.140305
$575$	−5.29947	−0.221003
$576$	2.57653	0.107356
$577$	−13.7783	−0.573597	−0.286798	−	0.957991i	$-0.592591\pi$
$577$	−13.7783	−0.573597	−0.286798	+	0.957991i	$0.592591\pi$
$578$	−1.00000	−0.0415945
$579$	62.8655	2.61260
$580$	2.79160	0.115915
$581$	−13.7520	−0.570530
$582$	33.9671	1.40798
$583$	−19.9828	−0.827604
$584$	15.2441	0.630807
$585$	−17.8760	−0.739082
$586$	−14.0911	−0.582097
$587$	31.1846	1.28712	0.643562	−	0.765394i	$-0.277456\pi$
$587$	31.1846	1.28712	0.643562	+	0.765394i	$0.277456\pi$
$588$	−2.36147	−0.0973853
$589$	19.8207	0.816697
$590$	10.2375	0.421470
$591$	−38.4750	−1.58265
$592$	8.72294	0.358511
$593$	8.56320	0.351649	0.175824	−	0.984422i	$-0.443741\pi$
$593$	8.56320	0.351649	0.175824	+	0.984422i	$0.443741\pi$
$594$	3.36147	0.137923
$595$	1.00000	0.0409960
$596$	−7.02908	−0.287922
$597$	38.6371	1.58131
$598$	36.7678	1.50355
$599$	−33.2203	−1.35734	−0.678672	−	0.734441i	$-0.737444\pi$
$599$	−33.2203	−1.35734	−0.678672	+	0.734441i	$0.737444\pi$
$600$	2.36147	0.0964066
$601$	5.25081	0.214185	0.107092	−	0.994249i	$-0.465846\pi$
$601$	5.25081	0.214185	0.107092	+	0.994249i	$0.465846\pi$
$602$	−3.42347	−0.139530
$603$	31.1359	1.26795
$604$	−10.9313	−0.444790
$605$	−0.299472	−0.0121753
$606$	34.6743	1.40855
$607$	16.0582	0.651780	0.325890	−	0.945408i	$-0.394336\pi$
$607$	16.0582	0.651780	0.325890	+	0.945408i	$0.394336\pi$
$608$	6.29947	0.255477
$609$	6.59228	0.267133
$610$	−10.3839	−0.420431
$611$	−24.3839	−0.986466
$612$	−2.57653	−0.104150
$613$	−0.507872	−0.0205127	−0.0102564	−	0.999947i	$-0.503265\pi$
$613$	−0.507872	−0.0205127	−0.0102564	+	0.999947i	$0.503265\pi$
$614$	−22.4750	−0.907015
$615$	−7.93800	−0.320091
$616$	3.36147	0.135437
$617$	14.5303	0.584967	0.292484	−	0.956271i	$-0.405518\pi$
$617$	14.5303	0.584967	0.292484	+	0.956271i	$0.405518\pi$
$618$	29.6991	1.19467
$619$	−11.7072	−0.470552	−0.235276	−	0.971929i	$-0.575599\pi$
$619$	−11.7072	−0.470552	−0.235276	+	0.971929i	$0.575599\pi$
$620$	3.14640	0.126363
$621$	−5.29947	−0.212660
$622$	9.85360	0.395093
$623$	10.9380	0.438222
$624$	−16.3839	−0.655880
$625$	1.00000	0.0400000
$626$	−5.45921	−0.218194
$627$	−50.0052	−1.99702
$628$	−0.430132	−0.0171641
$629$	−8.72294	−0.347806
$630$	2.57653	0.102652
$631$	−16.9762	−0.675810	−0.337905	−	0.941180i	$-0.609718\pi$
$631$	−16.9762	−0.675810	−0.337905	+	0.941180i	$0.609718\pi$
$632$	−5.56987	−0.221557
$633$	−7.41439	−0.294695
$634$	15.1531	0.601805
$635$	−2.33906	−0.0928227
$636$	−14.0382	−0.556649
$637$	6.93800	0.274894
$638$	−9.38388	−0.371511
$639$	38.1688	1.50993
$640$	1.00000	0.0395285
$641$	−22.7544	−0.898746	−0.449373	−	0.893344i	$-0.648353\pi$
$641$	−22.7544	−0.898746	−0.449373	+	0.893344i	$0.648353\pi$
$642$	14.8918	0.587730
$643$	−3.38772	−0.133599	−0.0667994	−	0.997766i	$-0.521279\pi$
$643$	−3.38772	−0.133599	−0.0667994	+	0.997766i	$0.521279\pi$
$644$	−5.29947	−0.208828
$645$	8.08441	0.318323
$646$	−6.29947	−0.247849
$647$	3.18599	0.125254	0.0626271	−	0.998037i	$-0.480052\pi$
$647$	3.18599	0.125254	0.0626271	+	0.998037i	$0.480052\pi$
$648$	10.0911	0.396415
$649$	−34.4130	−1.35083
$650$	−6.93800	−0.272131
$651$	7.43013	0.291210
$652$	17.1531	0.671766
$653$	−32.6304	−1.27693	−0.638464	−	0.769652i	$-0.720430\pi$
$653$	−32.6304	−1.27693	−0.638464	+	0.769652i	$0.720430\pi$
$654$	40.1979	1.57186
$655$	−8.16881	−0.319182
$656$	−3.36147	−0.131243
$657$	−39.2771	−1.53234
$658$	3.51454	0.137011
$659$	−9.23081	−0.359581	−0.179791	−	0.983705i	$-0.557542\pi$
$659$	−9.23081	−0.359581	−0.179791	+	0.983705i	$0.557542\pi$
$660$	−7.93800	−0.308986
$661$	49.9919	1.94446	0.972230	−	0.234028i	$-0.0751909\pi$
$661$	49.9919	1.94446	0.972230	+	0.234028i	$0.0751909\pi$
$662$	−8.38388	−0.325849
$663$	16.3839	0.636297
$664$	13.7520	0.533682
$665$	6.29947	0.244283
$666$	−22.4750	−0.870887
$667$	14.7940	0.572826
$668$	−23.0157	−0.890506
$669$	−2.93800	−0.113590
$670$	12.0844	0.466861
$671$	34.9051	1.34750
$672$	2.36147	0.0910956
$673$	−25.3285	−0.976344	−0.488172	−	0.872747i	$-0.662336\pi$
$673$	−25.3285	−0.976344	−0.488172	+	0.872747i	$0.662336\pi$
$674$	9.94467	0.383054
$675$	1.00000	0.0384900
$676$	35.1359	1.35138
$677$	−30.4392	−1.16987	−0.584937	−	0.811079i	$-0.698881\pi$
$677$	−30.4392	−1.16987	−0.584937	+	0.811079i	$0.698881\pi$
$678$	36.4592	1.40021
$679$	14.3839	0.552003
$680$	−1.00000	−0.0383482
$681$	24.6147	0.943237
$682$	−10.5765	−0.404996
$683$	33.1201	1.26731	0.633654	−	0.773617i	$-0.281554\pi$
$683$	33.1201	1.26731	0.633654	+	0.773617i	$0.281554\pi$
$684$	−16.2308	−0.620600
$685$	−16.2928	−0.622516
$686$	−1.00000	−0.0381802
$687$	−36.4220	−1.38959
$688$	3.42347	0.130518
$689$	41.2441	1.57128
$690$	12.5145	0.476420
$691$	30.7544	1.16995	0.584977	−	0.811050i	$-0.301104\pi$
$691$	30.7544	1.16995	0.584977	+	0.811050i	$0.301104\pi$
$692$	2.63853	0.100302
$693$	−8.66094	−0.329002
$694$	−4.21507	−0.160002
$695$	−1.27706	−0.0484417
$696$	−6.59228	−0.249880
$697$	3.36147	0.127325
$698$	−5.56987	−0.210823
$699$	−38.3972	−1.45232
$700$	1.00000	0.0377964
$701$	−22.4883	−0.849371	−0.424685	−	0.905341i	$-0.639615\pi$
$701$	−22.4883	−0.849371	−0.424685	+	0.905341i	$0.639615\pi$
$702$	−6.93800	−0.261858
$703$	−54.9499	−2.07247
$704$	−3.36147	−0.126690
$705$	−8.29947	−0.312576
$706$	1.34814	0.0507377
$707$	14.6834	0.552224
$708$	−24.1755	−0.908570
$709$	−23.1292	−0.868636	−0.434318	−	0.900760i	$-0.643011\pi$
$709$	−23.1292	−0.868636	−0.434318	+	0.900760i	$0.643011\pi$
$710$	14.8140	0.555960
$711$	14.3510	0.538203
$712$	−10.9380	−0.409919
$713$	16.6743	0.624456
$714$	−2.36147	−0.0883757
$715$	23.3219	0.872189
$716$	6.72294	0.251248
$717$	−16.3681	−0.611279
$718$	−9.89842	−0.369406
$719$	−1.00908	−0.0376322	−0.0188161	−	0.999823i	$-0.505990\pi$
$719$	−1.00908	−0.0376322	−0.0188161	+	0.999823i	$0.505990\pi$
$720$	−2.57653	−0.0960218
$721$	12.5765	0.468375
$722$	−20.6834	−0.769755
$723$	20.2532	0.753225
$724$	−20.5989	−0.765554
$725$	−2.79160	−0.103677
$726$	0.707194	0.0262464
$727$	−24.3748	−0.904011	−0.452006	−	0.892015i	$-0.649291\pi$
$727$	−24.3748	−0.904011	−0.452006	+	0.892015i	$0.649291\pi$
$728$	−6.93800	−0.257140
$729$	−18.9156	−0.700578
$730$	−15.2441	−0.564211
$731$	−3.42347	−0.126621
$732$	24.5212	0.906330
$733$	−7.15307	−0.264205	−0.132102	−	0.991236i	$-0.542173\pi$
$733$	−7.15307	−0.264205	−0.132102	+	0.991236i	$0.542173\pi$
$734$	−30.4883	−1.12534
$735$	2.36147	0.0871041
$736$	5.29947	0.195341
$737$	−40.6214	−1.49631
$738$	8.66094	0.318814
$739$	7.92226	0.291425	0.145713	−	0.989327i	$-0.453453\pi$
$739$	7.92226	0.291425	0.145713	+	0.989327i	$0.453453\pi$
$740$	−8.72294	−0.320662
$741$	103.210	3.79151
$742$	−5.94467	−0.218236
$743$	−7.59653	−0.278690	−0.139345	−	0.990244i	$-0.544500\pi$
$743$	−7.59653	−0.278690	−0.139345	+	0.990244i	$0.544500\pi$
$744$	−7.43013	−0.272402
$745$	7.02908	0.257525
$746$	−10.8693	−0.397955
$747$	−35.4325	−1.29641
$748$	3.36147	0.122907
$749$	6.30614	0.230421
$750$	−2.36147	−0.0862286
$751$	45.1516	1.64761	0.823803	−	0.566876i	$-0.191848\pi$
$751$	45.1516	1.64761	0.823803	+	0.566876i	$0.191848\pi$
$752$	−3.51454	−0.128162
$753$	−50.5503	−1.84215
$754$	19.3681	0.705346
$755$	10.9313	0.397832
$756$	1.00000	0.0363696
$757$	38.3839	1.39509	0.697543	−	0.716543i	$-0.254277\pi$
$757$	38.3839	1.39509	0.697543	+	0.716543i	$0.254277\pi$
$758$	18.7587	0.681346
$759$	−42.0672	−1.52694
$760$	−6.29947	−0.228506
$761$	20.0582	0.727107	0.363554	−	0.931573i	$-0.381563\pi$
$761$	20.0582	0.727107	0.363554	+	0.931573i	$0.381563\pi$
$762$	5.52361	0.200099
$763$	17.0224	0.616253
$764$	−25.2375	−0.913060
$765$	2.57653	0.0931548
$766$	−21.7453	−0.785691
$767$	71.0276	2.56466
$768$	−2.36147	−0.0852122
$769$	−14.9828	−0.540294	−0.270147	−	0.962819i	$-0.587072\pi$
$769$	−14.9828	−0.540294	−0.270147	+	0.962819i	$0.587072\pi$
$770$	−3.36147	−0.121139
$771$	36.8207	1.32606
$772$	−26.6214	−0.958124
$773$	33.8760	1.21844	0.609218	−	0.793003i	$-0.291484\pi$
$773$	33.8760	1.21844	0.609218	+	0.793003i	$0.291484\pi$
$774$	−8.82068	−0.317053
$775$	−3.14640	−0.113022
$776$	−14.3839	−0.516351
$777$	−20.5989	−0.738983
$778$	9.45921	0.339129
$779$	21.1755	0.758690
$780$	16.3839	0.586637
$781$	−49.7968	−1.78187
$782$	−5.29947	−0.189509
$783$	−2.79160	−0.0997637
$784$	1.00000	0.0357143
$785$	0.430132	0.0153521
$786$	19.2904	0.688066
$787$	−6.60561	−0.235465	−0.117732	−	0.993045i	$-0.537562\pi$
$787$	−6.60561	−0.235465	−0.117732	+	0.993045i	$0.537562\pi$
$788$	16.2928	0.580407
$789$	35.7058	1.27116
$790$	5.56987	0.198167
$791$	15.4392	0.548955
$792$	8.66094	0.307753
$793$	−72.0434	−2.55834
$794$	−25.6056	−0.908709
$795$	14.0382	0.497882
$796$	−16.3615	−0.579917
$797$	−18.4616	−0.653944	−0.326972	−	0.945034i	$-0.606028\pi$
$797$	−18.4616	−0.653944	−0.326972	+	0.945034i	$0.606028\pi$
$798$	−14.8760	−0.526605
$799$	3.51454	0.124335
$800$	−1.00000	−0.0353553
$801$	28.1821	0.995767
$802$	−1.40106	−0.0494730
$803$	51.2427	1.80832
$804$	−28.5369	−1.00642
$805$	5.29947	0.186782
$806$	21.8298	0.768920
$807$	−38.3972	−1.35165
$808$	−14.6834	−0.516558
$809$	28.9499	1.01782	0.508912	−	0.860818i	$-0.330048\pi$
$809$	28.9499	1.01782	0.508912	+	0.860818i	$0.330048\pi$
$810$	−10.0911	−0.354564
$811$	−51.6280	−1.81291	−0.906453	−	0.422308i	$-0.861220\pi$
$811$	−51.6280	−1.81291	−0.906453	+	0.422308i	$0.861220\pi$
$812$	−2.79160	−0.0979660
$813$	13.4774	0.472672
$814$	29.3219	1.02773
$815$	−17.1531	−0.600846
$816$	2.36147	0.0826679
$817$	−21.5660	−0.754500
$818$	−8.49454	−0.297005
$819$	17.8760	0.624638
$820$	3.36147	0.117388
$821$	−10.5660	−0.368757	−0.184378	−	0.982855i	$-0.559027\pi$
$821$	−10.5660	−0.368757	−0.184378	+	0.982855i	$0.559027\pi$
$822$	38.4750	1.34197
$823$	−28.0977	−0.979426	−0.489713	−	0.871884i	$-0.662898\pi$
$823$	−28.0977	−0.979426	−0.489713	+	0.871884i	$0.662898\pi$
$824$	−12.5765	−0.438124
$825$	7.93800	0.276366
$826$	−10.2375	−0.356207
$827$	−8.54079	−0.296992	−0.148496	−	0.988913i	$-0.547443\pi$
$827$	−8.54079	−0.296992	−0.148496	+	0.988913i	$0.547443\pi$
$828$	−13.6543	−0.474519
$829$	15.2823	0.530776	0.265388	−	0.964142i	$-0.414500\pi$
$829$	15.2823	0.530776	0.265388	+	0.964142i	$0.414500\pi$
$830$	−13.7520	−0.477339
$831$	−21.5832	−0.748713
$832$	6.93800	0.240532
$833$	−1.00000	−0.0346479
$834$	3.01574	0.104427
$835$	23.0157	0.796493
$836$	21.1755	0.732369
$837$	−3.14640	−0.108756
$838$	−11.0157	−0.380533
$839$	−10.3481	−0.357257	−0.178629	−	0.983917i	$-0.557166\pi$
$839$	−10.3481	−0.357257	−0.178629	+	0.983917i	$0.557166\pi$
$840$	−2.36147	−0.0814784
$841$	−21.2070	−0.731275
$842$	29.7968	1.02687
$843$	−46.5131	−1.60200
$844$	3.13974	0.108074
$845$	−35.1359	−1.20871
$846$	9.05533	0.311329
$847$	0.299472	0.0102900
$848$	5.94467	0.204141
$849$	−2.93800	−0.100832
$850$	1.00000	0.0342997
$851$	−46.2270	−1.58464
$852$	−34.9828	−1.19849
$853$	−26.0091	−0.890534	−0.445267	−	0.895398i	$-0.646891\pi$
$853$	−26.0091	−0.890534	−0.445267	+	0.895398i	$0.646891\pi$
$854$	10.3839	0.355329
$855$	16.2308	0.555082
$856$	−6.30614	−0.215539
$857$	8.24655	0.281697	0.140848	−	0.990031i	$-0.455017\pi$
$857$	8.24655	0.281697	0.140848	+	0.990031i	$0.455017\pi$
$858$	−55.0739	−1.88019
$859$	−42.5975	−1.45341	−0.726704	−	0.686951i	$-0.758949\pi$
$859$	−42.5975	−1.45341	−0.726704	+	0.686951i	$0.758949\pi$
$860$	−3.42347	−0.116739
$861$	7.93800	0.270526
$862$	19.1397	0.651902
$863$	25.4011	0.864662	0.432331	−	0.901715i	$-0.357691\pi$
$863$	25.4011	0.864662	0.432331	+	0.901715i	$0.357691\pi$
$864$	−1.00000	−0.0340207
$865$	−2.63853	−0.0897128
$866$	24.0582	0.817529
$867$	−2.36147	−0.0801997
$868$	−3.14640	−0.106796
$869$	−18.7229	−0.635132
$870$	6.59228	0.223499
$871$	83.8417	2.84087
$872$	−17.0224	−0.576452
$873$	37.0606	1.25431
$874$	−33.3839	−1.12923
$875$	−1.00000	−0.0338062
$876$	35.9986	1.21628
$877$	25.2771	0.853546	0.426773	−	0.904359i	$-0.359650\pi$
$877$	25.2771	0.853546	0.426773	+	0.904359i	$0.359650\pi$
$878$	−5.89842	−0.199062
$879$	−33.2756	−1.12236
$880$	3.36147	0.113315
$881$	−28.5107	−0.960550	−0.480275	−	0.877118i	$-0.659463\pi$
$881$	−28.5107	−0.960550	−0.480275	+	0.877118i	$0.659463\pi$
$882$	−2.57653	−0.0867564
$883$	17.1979	0.578755	0.289378	−	0.957215i	$-0.406552\pi$
$883$	17.1979	0.578755	0.289378	+	0.957215i	$0.406552\pi$
$884$	−6.93800	−0.233350
$885$	24.1755	0.812650
$886$	13.1621	0.442191
$887$	53.4115	1.79338	0.896692	−	0.442656i	$-0.145964\pi$
$887$	53.4115	1.79338	0.896692	+	0.442656i	$0.145964\pi$
$888$	20.5989	0.691255
$889$	2.33906	0.0784495
$890$	10.9380	0.366643
$891$	33.9208	1.13639
$892$	1.24414	0.0416570
$893$	22.1397	0.740878
$894$	−16.5989	−0.555152
$895$	−6.72294	−0.224723
$896$	−1.00000	−0.0334077
$897$	86.8259	2.89903
$898$	−7.44588	−0.248472
$899$	8.78350	0.292946
$900$	2.57653	0.0858845
$901$	−5.94467	−0.198046
$902$	−11.2995	−0.376231
$903$	−8.08441	−0.269032
$904$	−15.4392	−0.513500
$905$	20.5989	0.684732
$906$	−25.8140	−0.857613
$907$	2.80068	0.0929950	0.0464975	−	0.998918i	$-0.485194\pi$
$907$	2.80068	0.0929950	0.0464975	+	0.998918i	$0.485194\pi$
$908$	−10.4235	−0.345915
$909$	37.8322	1.25481
$910$	6.93800	0.229993
$911$	21.5699	0.714642	0.357321	−	0.933982i	$-0.383690\pi$
$911$	21.5699	0.714642	0.357321	+	0.933982i	$0.383690\pi$
$912$	14.8760	0.492594
$913$	46.2270	1.52989
$914$	−27.0291	−0.894042
$915$	−24.5212	−0.810646
$916$	15.4235	0.509606
$917$	8.16881	0.269758
$918$	1.00000	0.0330049
$919$	18.5765	0.612783	0.306392	−	0.951906i	$-0.400878\pi$
$919$	18.5765	0.612783	0.306392	+	0.951906i	$0.400878\pi$
$920$	−5.29947	−0.174718
$921$	−53.0739	−1.74884
$922$	29.4196	0.968884
$923$	102.780	3.38303
$924$	7.93800	0.261141
$925$	8.72294	0.286808
$926$	−12.2151	−0.401412
$927$	32.4039	1.06428
$928$	2.79160	0.0916388
$929$	−13.7520	−0.451189	−0.225594	−	0.974221i	$-0.572432\pi$
$929$	−13.7520	−0.451189	−0.225594	+	0.974221i	$0.572432\pi$
$930$	7.43013	0.243644
$931$	−6.29947	−0.206457
$932$	16.2599	0.532610
$933$	23.2690	0.761792
$934$	−12.1555	−0.397739
$935$	−3.36147	−0.109932
$936$	−17.8760	−0.584296
$937$	−37.8536	−1.23662	−0.618312	−	0.785933i	$-0.712183\pi$
$937$	−37.8536	−1.23662	−0.618312	+	0.785933i	$0.712183\pi$
$938$	−12.0844	−0.394570
$939$	−12.8918	−0.420706
$940$	3.51454	0.114632
$941$	31.2175	1.01766	0.508830	−	0.860867i	$-0.330078\pi$
$941$	31.2175	1.01766	0.508830	+	0.860867i	$0.330078\pi$
$942$	−1.01574	−0.0330947
$943$	17.8140	0.580104
$944$	10.2375	0.333201
$945$	−1.00000	−0.0325300
$946$	11.5079	0.374153
$947$	−20.9695	−0.681417	−0.340708	−	0.940169i	$-0.610667\pi$
$947$	−20.9695	−0.681417	−0.340708	+	0.940169i	$0.610667\pi$
$948$	−13.1531	−0.427192
$949$	−105.764	−3.43324
$950$	6.29947	0.204382
$951$	35.7835	1.16036
$952$	1.00000	0.0324102
$953$	−10.7096	−0.346918	−0.173459	−	0.984841i	$-0.555494\pi$
$953$	−10.7096	−0.346918	−0.173459	+	0.984841i	$0.555494\pi$
$954$	−15.3166	−0.495895
$955$	25.2375	0.816666
$956$	6.93134	0.224175
$957$	−22.1597	−0.716323
$958$	−12.3839	−0.400105
$959$	16.2928	0.526122
$960$	2.36147	0.0762161
$961$	−21.1001	−0.680650
$962$	−60.5198	−1.95124
$963$	16.2480	0.523584
$964$	−8.57653	−0.276232
$965$	26.6214	0.856972
$966$	−12.5145	−0.402649
$967$	−7.45921	−0.239872	−0.119936	−	0.992782i	$-0.538269\pi$
$967$	−7.45921	−0.239872	−0.119936	+	0.992782i	$0.538269\pi$
$968$	−0.299472	−0.00962540
$969$	−14.8760	−0.477886
$970$	14.3839	0.461839
$971$	43.5107	1.39632	0.698162	−	0.715940i	$-0.254001\pi$
$971$	43.5107	1.39632	0.698162	+	0.715940i	$0.254001\pi$
$972$	20.8298	0.668115
$973$	1.27706	0.0409407
$974$	−20.5145	−0.657328
$975$	−16.3839	−0.524704
$976$	−10.3839	−0.332380
$977$	43.6414	1.39621	0.698105	−	0.715995i	$-0.254027\pi$
$977$	43.6414	1.39621	0.698105	+	0.715995i	$0.254027\pi$
$978$	40.5064	1.29525
$979$	−36.7678	−1.17510
$980$	−1.00000	−0.0319438
$981$	43.8588	1.40030
$982$	8.20173	0.261728
$983$	−22.7544	−0.725753	−0.362877	−	0.931837i	$-0.618205\pi$
$983$	−22.7544	−0.725753	−0.362877	+	0.931837i	$0.618205\pi$
$984$	−7.93800	−0.253054
$985$	−16.2928	−0.519132
$986$	−2.79160	−0.0889027
$987$	8.29947	0.264175
$988$	−43.7058	−1.39047
$989$	−18.1426	−0.576900
$990$	−8.66094	−0.275263
$991$	4.65853	0.147983	0.0739916	−	0.997259i	$-0.476426\pi$
$991$	4.65853	0.147983	0.0739916	+	0.997259i	$0.476426\pi$
$992$	3.14640	0.0998984
$993$	−19.7983	−0.628279
$994$	−14.8140	−0.469872
$995$	16.3615	0.518693
$996$	32.4750	1.02901
$997$	−41.0739	−1.30082	−0.650412	−	0.759582i	$-0.725404\pi$
$997$	−41.0739	−1.30082	−0.650412	+	0.759582i	$0.725404\pi$
$998$	−22.9447	−0.726301
$999$	8.72294	0.275982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.a.l.1.1	✓	3
4.3	odd	2		9520.2.a.u.1.3		3
5.4	even	2		5950.2.a.bk.1.3		3
7.6	odd	2		8330.2.a.bs.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.a.l.1.1	✓	3	1.1	even	1	trivial
5950.2.a.bk.1.3		3	5.4	even	2
8330.2.a.bs.1.3		3	7.6	odd	2
9520.2.a.u.1.3		3	4.3	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:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.36147 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.36147 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.57653 q^{9} +1.00000 q^{10} -3.36147 q^{11} -2.36147 q^{12} +6.93800 q^{13} -1.00000 q^{14} +2.36147 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.57653 q^{18} -6.29947 q^{19} -1.00000 q^{20} -2.36147 q^{21} +3.36147 q^{22} -5.29947 q^{23} +2.36147 q^{24} +1.00000 q^{25} -6.93800 q^{26} +1.00000 q^{27} +1.00000 q^{28} -2.79160 q^{29} -2.36147 q^{30} -3.14640 q^{31} -1.00000 q^{32} +7.93800 q^{33} +1.00000 q^{34} -1.00000 q^{35} +2.57653 q^{36} +8.72294 q^{37} +6.29947 q^{38} -16.3839 q^{39} +1.00000 q^{40} -3.36147 q^{41} +2.36147 q^{42} +3.42347 q^{43} -3.36147 q^{44} -2.57653 q^{45} +5.29947 q^{46} -3.51454 q^{47} -2.36147 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.36147 q^{51} +6.93800 q^{52} +5.94467 q^{53} -1.00000 q^{54} +3.36147 q^{55} -1.00000 q^{56} +14.8760 q^{57} +2.79160 q^{58} +10.2375 q^{59} +2.36147 q^{60} -10.3839 q^{61} +3.14640 q^{62} +2.57653 q^{63} +1.00000 q^{64} -6.93800 q^{65} -7.93800 q^{66} +12.0844 q^{67} -1.00000 q^{68} +12.5145 q^{69} +1.00000 q^{70} +14.8140 q^{71} -2.57653 q^{72} -15.2441 q^{73} -8.72294 q^{74} -2.36147 q^{75} -6.29947 q^{76} -3.36147 q^{77} +16.3839 q^{78} +5.56987 q^{79} -1.00000 q^{80} -10.0911 q^{81} +3.36147 q^{82} -13.7520 q^{83} -2.36147 q^{84} +1.00000 q^{85} -3.42347 q^{86} +6.59228 q^{87} +3.36147 q^{88} +10.9380 q^{89} +2.57653 q^{90} +6.93800 q^{91} -5.29947 q^{92} +7.43013 q^{93} +3.51454 q^{94} +6.29947 q^{95} +2.36147 q^{96} +14.3839 q^{97} -1.00000 q^{98} -8.66094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} + 9 q^{13} - 3 q^{14} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{20} + 3 q^{22} + 3 q^{23} + 3 q^{25} - 9 q^{26} + 3 q^{27}+ \cdots - 3 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 + 9 * q^13 - 3 * q^14 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^20 + 3 * q^22 + 3 * q^23 + 3 * q^25 - 9 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^29 - 3 * q^32 + 12 * q^33 + 3 * q^34 - 3 * q^35 + 3 * q^36 + 12 * q^37 - 9 * q^39 + 3 * q^40 - 3 * q^41 + 15 * q^43 - 3 * q^44 - 3 * q^45 - 3 * q^46 + 6 * q^47 + 3 * q^49 - 3 * q^50 + 9 * q^52 + 6 * q^53 - 3 * q^54 + 3 * q^55 - 3 * q^56 + 21 * q^57 + 6 * q^58 + 9 * q^61 + 3 * q^63 + 3 * q^64 - 9 * q^65 - 12 * q^66 + 15 * q^67 - 3 * q^68 + 21 * q^69 + 3 * q^70 + 9 * q^71 - 3 * q^72 - 15 * q^73 - 12 * q^74 - 3 * q^77 + 9 * q^78 + 12 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 6 * q^83 + 3 * q^85 - 15 * q^86 - 18 * q^87 + 3 * q^88 + 21 * q^89 + 3 * q^90 + 9 * q^91 + 3 * q^92 + 27 * q^93 - 6 * q^94 + 3 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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