LMFDB - Embedded newform 5819.2.a.u.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.56762 q^{2} -1.86277 q^{3} +4.59270 q^{4} +2.06282 q^{5} +4.78289 q^{6} +4.15023 q^{7} -6.65707 q^{8} +0.469907 q^{9} -5.29655 q^{10} +1.00000 q^{11} -8.55513 q^{12} +6.78320 q^{13} -10.6562 q^{14} -3.84256 q^{15} +7.90746 q^{16} +6.01773 q^{17} -1.20655 q^{18} -0.387363 q^{19} +9.47392 q^{20} -7.73091 q^{21} -2.56762 q^{22} +12.4006 q^{24} -0.744761 q^{25} -17.4167 q^{26} +4.71298 q^{27} +19.0607 q^{28} -2.15648 q^{29} +9.86626 q^{30} +5.57670 q^{31} -6.98925 q^{32} -1.86277 q^{33} -15.4513 q^{34} +8.56119 q^{35} +2.15814 q^{36} -0.497911 q^{37} +0.994603 q^{38} -12.6355 q^{39} -13.7324 q^{40} +6.02933 q^{41} +19.8501 q^{42} +2.60332 q^{43} +4.59270 q^{44} +0.969335 q^{45} -11.6609 q^{47} -14.7298 q^{48} +10.2244 q^{49} +1.91227 q^{50} -11.2096 q^{51} +31.1532 q^{52} -5.78450 q^{53} -12.1012 q^{54} +2.06282 q^{55} -27.6283 q^{56} +0.721568 q^{57} +5.53702 q^{58} +0.0787985 q^{59} -17.6477 q^{60} +1.37371 q^{61} -14.3189 q^{62} +1.95022 q^{63} +2.13085 q^{64} +13.9925 q^{65} +4.78289 q^{66} +8.27533 q^{67} +27.6376 q^{68} -21.9819 q^{70} -5.73161 q^{71} -3.12820 q^{72} +5.77935 q^{73} +1.27845 q^{74} +1.38732 q^{75} -1.77904 q^{76} +4.15023 q^{77} +32.4433 q^{78} +1.22499 q^{79} +16.3117 q^{80} -10.1889 q^{81} -15.4810 q^{82} +11.5638 q^{83} -35.5057 q^{84} +12.4135 q^{85} -6.68434 q^{86} +4.01702 q^{87} -6.65707 q^{88} +12.4007 q^{89} -2.48889 q^{90} +28.1518 q^{91} -10.3881 q^{93} +29.9407 q^{94} -0.799062 q^{95} +13.0194 q^{96} +5.98575 q^{97} -26.2524 q^{98} +0.469907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * 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 $

$2$	−2.56762	−1.81558	−0.907792	−	0.419420i	$-0.862233\pi$
$2$	−2.56762	−1.81558	−0.907792	+	0.419420i	$0.862233\pi$
$3$	−1.86277	−1.07547	−0.537735	−	0.843114i	$-0.680720\pi$
$3$	−1.86277	−1.07547	−0.537735	+	0.843114i	$0.680720\pi$
$4$	4.59270	2.29635
$5$	2.06282	0.922523	0.461261	−	0.887264i	$-0.347397\pi$
$5$	2.06282	0.922523	0.461261	+	0.887264i	$0.347397\pi$
$6$	4.78289	1.95261
$7$	4.15023	1.56864	0.784319	−	0.620357i	$-0.213012\pi$
$7$	4.15023	1.56864	0.784319	+	0.620357i	$0.213012\pi$
$8$	−6.65707	−2.35363
$9$	0.469907	0.156636
$10$	−5.29655	−1.67492
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−8.55513	−2.46965
$13$	6.78320	1.88132	0.940660	−	0.339349i	$-0.110207\pi$
$13$	6.78320	1.88132	0.940660	+	0.339349i	$0.110207\pi$
$14$	−10.6562	−2.84800
$15$	−3.84256	−0.992145
$16$	7.90746	1.97686
$17$	6.01773	1.45951	0.729757	−	0.683706i	$-0.239633\pi$
$17$	6.01773	1.45951	0.729757	+	0.683706i	$0.239633\pi$
$18$	−1.20655	−0.284385
$19$	−0.387363	−0.0888672	−0.0444336	−	0.999012i	$-0.514148\pi$
$19$	−0.387363	−0.0888672	−0.0444336	+	0.999012i	$0.514148\pi$
$20$	9.47392	2.11843
$21$	−7.73091	−1.68702
$22$	−2.56762	−0.547419
$23$	0	0
$23$	0	0
$24$	12.4006	2.53126
$25$	−0.744761	−0.148952
$26$	−17.4167	−3.41570
$27$	4.71298	0.907013
$28$	19.0607	3.60214
$29$	−2.15648	−0.400448	−0.200224	−	0.979750i	$-0.564167\pi$
$29$	−2.15648	−0.400448	−0.200224	+	0.979750i	$0.564167\pi$
$30$	9.86626	1.80132
$31$	5.57670	1.00160	0.500802	−	0.865562i	$-0.333038\pi$
$31$	5.57670	1.00160	0.500802	+	0.865562i	$0.333038\pi$
$32$	−6.98925	−1.23554
$33$	−1.86277	−0.324266
$34$	−15.4513	−2.64987
$35$	8.56119	1.44710
$36$	2.15814	0.359690
$37$	−0.497911	−0.0818560	−0.0409280	−	0.999162i	$-0.513031\pi$
$37$	−0.497911	−0.0818560	−0.0409280	+	0.999162i	$0.513031\pi$
$38$	0.994603	0.161346
$39$	−12.6355	−2.02330
$40$	−13.7324	−2.17128
$41$	6.02933	0.941623	0.470811	−	0.882234i	$-0.343961\pi$
$41$	6.02933	0.941623	0.470811	+	0.882234i	$0.343961\pi$
$42$	19.8501	3.06293
$43$	2.60332	0.397002	0.198501	−	0.980101i	$-0.436393\pi$
$43$	2.60332	0.397002	0.198501	+	0.980101i	$0.436393\pi$
$44$	4.59270	0.692375
$45$	0.969335	0.144500
$46$	0	0
$47$	−11.6609	−1.70091	−0.850456	−	0.526046i	$-0.823674\pi$
$47$	−11.6609	−1.70091	−0.850456	+	0.526046i	$0.823674\pi$
$48$	−14.7298	−2.12606
$49$	10.2244	1.46063
$50$	1.91227	0.270435
$51$	−11.2096	−1.56966
$52$	31.1532	4.32017
$53$	−5.78450	−0.794562	−0.397281	−	0.917697i	$-0.630046\pi$
$53$	−5.78450	−0.794562	−0.397281	+	0.917697i	$0.630046\pi$
$54$	−12.1012	−1.64676
$55$	2.06282	0.278151
$56$	−27.6283	−3.69199
$57$	0.721568	0.0955740
$58$	5.53702	0.727047
$59$	0.0787985	0.0102587	0.00512934	−	0.999987i	$-0.498367\pi$
$59$	0.0787985	0.0102587	0.00512934	+	0.999987i	$0.498367\pi$
$60$	−17.6477	−2.27831
$61$	1.37371	0.175885	0.0879425	−	0.996126i	$-0.471971\pi$
$61$	1.37371	0.175885	0.0879425	+	0.996126i	$0.471971\pi$
$62$	−14.3189	−1.81850
$63$	1.95022	0.245705
$64$	2.13085	0.266356
$65$	13.9925	1.73556
$66$	4.78289	0.588733
$67$	8.27533	1.01099	0.505496	−	0.862829i	$-0.331309\pi$
$67$	8.27533	1.01099	0.505496	+	0.862829i	$0.331309\pi$
$68$	27.6376	3.35155
$69$	0	0
$70$	−21.9819	−2.62734
$71$	−5.73161	−0.680216	−0.340108	−	0.940386i	$-0.610464\pi$
$71$	−5.73161	−0.680216	−0.340108	+	0.940386i	$0.610464\pi$
$72$	−3.12820	−0.368662
$73$	5.77935	0.676422	0.338211	−	0.941070i	$-0.390178\pi$
$73$	5.77935	0.676422	0.338211	+	0.941070i	$0.390178\pi$
$74$	1.27845	0.148616
$75$	1.38732	0.160194
$76$	−1.77904	−0.204070
$77$	4.15023	0.472962
$78$	32.4433	3.67348
$79$	1.22499	0.137822	0.0689108	−	0.997623i	$-0.478048\pi$
$79$	1.22499	0.137822	0.0689108	+	0.997623i	$0.478048\pi$
$80$	16.3117	1.82370
$81$	−10.1889	−1.13210
$82$	−15.4810	−1.70960
$83$	11.5638	1.26930	0.634648	−	0.772801i	$-0.281145\pi$
$83$	11.5638	1.26930	0.634648	+	0.772801i	$0.281145\pi$
$84$	−35.5057	−3.87399
$85$	12.4135	1.34644
$86$	−6.68434	−0.720791
$87$	4.01702	0.430670
$88$	−6.65707	−0.709646
$89$	12.4007	1.31447	0.657237	−	0.753684i	$-0.271725\pi$
$89$	12.4007	1.31447	0.657237	+	0.753684i	$0.271725\pi$
$90$	−2.48889	−0.262352
$91$	28.1518	2.95111
$92$	0	0
$93$	−10.3881	−1.07720
$94$	29.9407	3.08815
$95$	−0.799062	−0.0819820
$96$	13.0194	1.32878
$97$	5.98575	0.607761	0.303881	−	0.952710i	$-0.401718\pi$
$97$	5.98575	0.607761	0.303881	+	0.952710i	$0.401718\pi$
$98$	−26.2524	−2.65189
$99$	0.469907	0.0472274
$100$	−3.42046	−0.342046
$101$	3.76839	0.374969	0.187484	−	0.982268i	$-0.439967\pi$
$101$	3.76839	0.374969	0.187484	+	0.982268i	$0.439967\pi$
$102$	28.7822	2.84986
$103$	2.18621	0.215414	0.107707	−	0.994183i	$-0.465649\pi$
$103$	2.18621	0.215414	0.107707	+	0.994183i	$0.465649\pi$
$104$	−45.1562	−4.42793
$105$	−15.9475	−1.55632
$106$	14.8524	1.44259
$107$	8.60392	0.831772	0.415886	−	0.909417i	$-0.363472\pi$
$107$	8.60392	0.831772	0.415886	+	0.909417i	$0.363472\pi$
$108$	21.6453	2.08282
$109$	−6.33957	−0.607221	−0.303611	−	0.952796i	$-0.598192\pi$
$109$	−6.33957	−0.607221	−0.303611	+	0.952796i	$0.598192\pi$
$110$	−5.29655	−0.505007
$111$	0.927492	0.0880337
$112$	32.8178	3.10099
$113$	4.22845	0.397780	0.198890	−	0.980022i	$-0.436266\pi$
$113$	4.22845	0.397780	0.198890	+	0.980022i	$0.436266\pi$
$114$	−1.85272	−0.173523
$115$	0	0
$116$	−9.90404	−0.919567
$117$	3.18747	0.294682
$118$	−0.202325	−0.0186255
$119$	24.9750	2.28945
$120$	25.5802	2.33514
$121$	1.00000	0.0909091
$122$	−3.52716	−0.319334
$123$	−11.2312	−1.01269
$124$	25.6121	2.30003
$125$	−11.8504	−1.05993
$126$	−5.00744	−0.446098
$127$	0.00579766	0.000514459 0	0.000257230	−	1.00000i	$-0.499918\pi$
$127$	0.00579766	0.000514459 0	0.000257230		1.00000i	$0.499918\pi$
$128$	8.50728	0.751944
$129$	−4.84938	−0.426964
$130$	−35.9276	−3.15106
$131$	−1.96462	−0.171650	−0.0858250	−	0.996310i	$-0.527353\pi$
$131$	−1.96462	−0.171650	−0.0858250	+	0.996310i	$0.527353\pi$
$132$	−8.55513	−0.744628
$133$	−1.60765	−0.139401
$134$	−21.2479	−1.83554
$135$	9.72204	0.836740
$136$	−40.0605	−3.43516
$137$	−7.94836	−0.679075	−0.339537	−	0.940593i	$-0.610270\pi$
$137$	−7.94836	−0.679075	−0.339537	+	0.940593i	$0.610270\pi$
$138$	0	0
$139$	−9.04226	−0.766954	−0.383477	−	0.923550i	$-0.625274\pi$
$139$	−9.04226	−0.766954	−0.383477	+	0.923550i	$0.625274\pi$
$140$	39.3189	3.32305
$141$	21.7215	1.82928
$142$	14.7166	1.23499
$143$	6.78320	0.567240
$144$	3.71577	0.309648
$145$	−4.44843	−0.369422
$146$	−14.8392	−1.22810
$147$	−19.0457	−1.57086
$148$	−2.28675	−0.187970
$149$	5.94347	0.486908	0.243454	−	0.969912i	$-0.421720\pi$
$149$	5.94347	0.486908	0.243454	+	0.969912i	$0.421720\pi$
$150$	−3.56211	−0.290845
$151$	12.8807	1.04821	0.524107	−	0.851653i	$-0.324399\pi$
$151$	12.8807	1.04821	0.524107	+	0.851653i	$0.324399\pi$
$152$	2.57870	0.209160
$153$	2.82778	0.228612
$154$	−10.6562	−0.858703
$155$	11.5037	0.924003
$156$	−58.0311	−4.64621
$157$	22.4478	1.79153	0.895763	−	0.444531i	$-0.146630\pi$
$157$	22.4478	1.79153	0.895763	+	0.444531i	$0.146630\pi$
$158$	−3.14530	−0.250227
$159$	10.7752	0.854528
$160$	−14.4176	−1.13981
$161$	0	0
$162$	26.1613	2.05543
$163$	−19.4165	−1.52082	−0.760408	−	0.649445i	$-0.775001\pi$
$163$	−19.4165	−1.52082	−0.760408	+	0.649445i	$0.775001\pi$
$164$	27.6909	2.16229
$165$	−3.84256	−0.299143
$166$	−29.6916	−2.30452
$167$	−2.97517	−0.230225	−0.115113	−	0.993352i	$-0.536723\pi$
$167$	−2.97517	−0.230225	−0.115113	+	0.993352i	$0.536723\pi$
$168$	51.4652	3.97063
$169$	33.0118	2.53937
$170$	−31.8733	−2.44457
$171$	−0.182025	−0.0139198
$172$	11.9562	0.911655
$173$	−19.0196	−1.44604	−0.723018	−	0.690829i	$-0.757246\pi$
$173$	−19.0196	−1.44604	−0.723018	+	0.690829i	$0.757246\pi$
$174$	−10.3142	−0.781917
$175$	−3.09093	−0.233652
$176$	7.90746	0.596047
$177$	−0.146783	−0.0110329
$178$	−31.8404	−2.38654
$179$	−1.46061	−0.109171	−0.0545855	−	0.998509i	$-0.517384\pi$
$179$	−1.46061	−0.109171	−0.0545855	+	0.998509i	$0.517384\pi$
$180$	4.45186	0.331822
$181$	20.6644	1.53598	0.767988	−	0.640465i	$-0.221258\pi$
$181$	20.6644	1.53598	0.767988	+	0.640465i	$0.221258\pi$
$182$	−72.2833	−5.35800
$183$	−2.55890	−0.189159
$184$	0	0
$185$	−1.02710	−0.0755140
$186$	26.6727	1.95574
$187$	6.01773	0.440060
$188$	−53.5548	−3.90589
$189$	19.5599	1.42278
$190$	2.05169	0.148845
$191$	−21.8392	−1.58023	−0.790113	−	0.612961i	$-0.789978\pi$
$191$	−21.8392	−1.58023	−0.790113	+	0.612961i	$0.789978\pi$
$192$	−3.96928	−0.286458
$193$	3.54506	0.255179	0.127589	−	0.991827i	$-0.459276\pi$
$193$	3.54506	0.255179	0.127589	+	0.991827i	$0.459276\pi$
$194$	−15.3692	−1.10344
$195$	−26.0649	−1.86654
$196$	46.9575	3.35411
$197$	−22.5614	−1.60743	−0.803716	−	0.595013i	$-0.797147\pi$
$197$	−22.5614	−1.60743	−0.803716	+	0.595013i	$0.797147\pi$
$198$	−1.20655	−0.0857454
$199$	1.91593	0.135817	0.0679085	−	0.997692i	$-0.478367\pi$
$199$	1.91593	0.135817	0.0679085	+	0.997692i	$0.478367\pi$
$200$	4.95793	0.350578
$201$	−15.4150	−1.08729
$202$	−9.67581	−0.680788
$203$	−8.94987	−0.628158
$204$	−51.4825	−3.60449
$205$	12.4374	0.868668
$206$	−5.61338	−0.391103
$207$	0	0
$208$	53.6379	3.71912
$209$	−0.387363	−0.0267945
$210$	40.9472	2.82563
$211$	6.45913	0.444665	0.222332	−	0.974971i	$-0.428633\pi$
$211$	6.45913	0.444665	0.222332	+	0.974971i	$0.428633\pi$
$212$	−26.5664	−1.82459
$213$	10.6767	0.731552
$214$	−22.0916	−1.51015
$215$	5.37018	0.366244
$216$	−31.3746	−2.13477
$217$	23.1446	1.57116
$218$	16.2776	1.10246
$219$	−10.7656	−0.727471
$220$	9.47392	0.638731
$221$	40.8195	2.74582
$222$	−2.38145	−0.159833
$223$	−17.4228	−1.16672	−0.583360	−	0.812214i	$-0.698262\pi$
$223$	−17.4228	−1.16672	−0.583360	+	0.812214i	$0.698262\pi$
$224$	−29.0070	−1.93811
$225$	−0.349969	−0.0233312
$226$	−10.8571	−0.722202
$227$	−18.5779	−1.23306	−0.616531	−	0.787331i	$-0.711462\pi$
$227$	−18.5779	−1.23306	−0.616531	+	0.787331i	$0.711462\pi$
$228$	3.31394	0.219471
$229$	2.94024	0.194297	0.0971484	−	0.995270i	$-0.469028\pi$
$229$	2.94024	0.194297	0.0971484	+	0.995270i	$0.469028\pi$
$230$	0	0
$231$	−7.73091	−0.508657
$232$	14.3558	0.942505
$233$	−5.55070	−0.363638	−0.181819	−	0.983332i	$-0.558199\pi$
$233$	−5.55070	−0.363638	−0.181819	+	0.983332i	$0.558199\pi$
$234$	−8.18423	−0.535020
$235$	−24.0543	−1.56913
$236$	0.361897	0.0235575
$237$	−2.28186	−0.148223
$238$	−64.1263	−4.15669
$239$	−9.69764	−0.627288	−0.313644	−	0.949541i	$-0.601550\pi$
$239$	−9.69764	−0.627288	−0.313644	+	0.949541i	$0.601550\pi$
$240$	−30.3849	−1.96134
$241$	−6.09670	−0.392723	−0.196361	−	0.980532i	$-0.562913\pi$
$241$	−6.09670	−0.392723	−0.196361	+	0.980532i	$0.562913\pi$
$242$	−2.56762	−0.165053
$243$	4.84065	0.310528
$244$	6.30901	0.403893
$245$	21.0911	1.34746
$246$	28.8376	1.83862
$247$	−2.62756	−0.167188
$248$	−37.1245	−2.35741
$249$	−21.5408	−1.36509
$250$	30.4274	1.92440
$251$	−14.2801	−0.901349	−0.450675	−	0.892688i	$-0.648816\pi$
$251$	−14.2801	−0.901349	−0.450675	+	0.892688i	$0.648816\pi$
$252$	8.95677	0.564224
$253$	0	0
$254$	−0.0148862	−0.000934044 0
$255$	−23.1235	−1.44805
$256$	−26.1052	−1.63157
$257$	−22.8786	−1.42713	−0.713565	−	0.700589i	$-0.752921\pi$
$257$	−22.8786	−1.42713	−0.713565	+	0.700589i	$0.752921\pi$
$258$	12.4514	0.775189
$259$	−2.06644	−0.128402
$260$	64.2635	3.98545
$261$	−1.01334	−0.0627244
$262$	5.04441	0.311645
$263$	18.8419	1.16184	0.580919	−	0.813961i	$-0.302693\pi$
$263$	18.8419	1.16184	0.580919	+	0.813961i	$0.302693\pi$
$264$	12.4006	0.763203
$265$	−11.9324	−0.733001
$266$	4.12783	0.253094
$267$	−23.0997	−1.41368
$268$	38.0061	2.32159
$269$	15.5010	0.945113	0.472556	−	0.881300i	$-0.343331\pi$
$269$	15.5010	0.945113	0.472556	+	0.881300i	$0.343331\pi$
$270$	−24.9625	−1.51917
$271$	−11.5914	−0.704127	−0.352063	−	0.935976i	$-0.614520\pi$
$271$	−11.5914	−0.704127	−0.352063	+	0.935976i	$0.614520\pi$
$272$	47.5850	2.88526
$273$	−52.4403	−3.17383
$274$	20.4084	1.23292
$275$	−0.744761	−0.0449108
$276$	0	0
$277$	−11.1964	−0.672728	−0.336364	−	0.941732i	$-0.609197\pi$
$277$	−11.1964	−0.672728	−0.336364	+	0.941732i	$0.609197\pi$
$278$	23.2171	1.39247
$279$	2.62053	0.156887
$280$	−56.9924	−3.40595
$281$	−10.7042	−0.638559	−0.319279	−	0.947661i	$-0.603441\pi$
$281$	−10.7042	−0.638559	−0.319279	+	0.947661i	$0.603441\pi$
$282$	−55.7727	−3.32121
$283$	−18.5884	−1.10497	−0.552484	−	0.833524i	$-0.686320\pi$
$283$	−18.5884	−1.10497	−0.552484	+	0.833524i	$0.686320\pi$
$284$	−26.3235	−1.56201
$285$	1.48847	0.0881692
$286$	−17.4167	−1.02987
$287$	25.0231	1.47707
$288$	−3.28430	−0.193529
$289$	19.2131	1.13018
$290$	11.4219	0.670717
$291$	−11.1501	−0.653629
$292$	26.5428	1.55330
$293$	14.0388	0.820155	0.410077	−	0.912051i	$-0.365502\pi$
$293$	14.0388	0.820155	0.410077	+	0.912051i	$0.365502\pi$
$294$	48.9021	2.85203
$295$	0.162547	0.00946387
$296$	3.31462	0.192659
$297$	4.71298	0.273475
$298$	−15.2606	−0.884023
$299$	0	0
$300$	6.37153	0.367860
$301$	10.8044	0.622753
$302$	−33.0727	−1.90312
$303$	−7.01964	−0.403268
$304$	−3.06306	−0.175678
$305$	2.83371	0.162258
$306$	−7.26067	−0.415065
$307$	−33.1886	−1.89417	−0.947086	−	0.320979i	$-0.895988\pi$
$307$	−33.1886	−1.89417	−0.947086	+	0.320979i	$0.895988\pi$
$308$	19.0607	1.08609
$309$	−4.07241	−0.231671
$310$	−29.5373	−1.67761
$311$	−30.0708	−1.70516	−0.852578	−	0.522600i	$-0.824962\pi$
$311$	−30.0708	−1.70516	−0.852578	+	0.522600i	$0.824962\pi$
$312$	84.1156	4.76211
$313$	−29.4359	−1.66382	−0.831908	−	0.554913i	$-0.812752\pi$
$313$	−29.4359	−1.66382	−0.831908	+	0.554913i	$0.812752\pi$
$314$	−57.6374	−3.25267
$315$	4.02296	0.226668
$316$	5.62598	0.316486
$317$	−10.1262	−0.568742	−0.284371	−	0.958714i	$-0.591785\pi$
$317$	−10.1262	−0.568742	−0.284371	+	0.958714i	$0.591785\pi$
$318$	−27.6666	−1.55147
$319$	−2.15648	−0.120740
$320$	4.39556	0.245719
$321$	−16.0271	−0.894546
$322$	0	0
$323$	−2.33105	−0.129703
$324$	−46.7946	−2.59970
$325$	−5.05186	−0.280227
$326$	49.8542	2.76117
$327$	11.8092	0.653048
$328$	−40.1376	−2.21623
$329$	−48.3953	−2.66812
$330$	9.86626	0.543120
$331$	−5.11497	−0.281144	−0.140572	−	0.990070i	$-0.544894\pi$
$331$	−5.11497	−0.281144	−0.140572	+	0.990070i	$0.544894\pi$
$332$	53.1092	2.91475
$333$	−0.233972	−0.0128216
$334$	7.63911	0.417994
$335$	17.0705	0.932663
$336$	−61.1319	−3.33502
$337$	11.7630	0.640774	0.320387	−	0.947287i	$-0.396187\pi$
$337$	11.7630	0.640774	0.320387	+	0.947287i	$0.396187\pi$
$338$	−84.7619	−4.61044
$339$	−7.87663	−0.427800
$340$	57.0115	3.09188
$341$	5.57670	0.301995
$342$	0.467371	0.0252725
$343$	13.3820	0.722558
$344$	−17.3305	−0.934396
$345$	0	0
$346$	48.8353	2.62540
$347$	18.3528	0.985232	0.492616	−	0.870247i	$-0.336041\pi$
$347$	18.3528	0.985232	0.492616	+	0.870247i	$0.336041\pi$
$348$	18.4489	0.988967
$349$	13.8377	0.740717	0.370358	−	0.928889i	$-0.379235\pi$
$349$	13.8377	0.740717	0.370358	+	0.928889i	$0.379235\pi$
$350$	7.93634	0.424215
$351$	31.9691	1.70638
$352$	−6.98925	−0.372528
$353$	2.57511	0.137059	0.0685297	−	0.997649i	$-0.478169\pi$
$353$	2.57511	0.137059	0.0685297	+	0.997649i	$0.478169\pi$
$354$	0.376884	0.0200312
$355$	−11.8233	−0.627515
$356$	56.9527	3.01849
$357$	−46.5226	−2.46224
$358$	3.75030	0.198209
$359$	4.17268	0.220226	0.110113	−	0.993919i	$-0.464879\pi$
$359$	4.17268	0.220226	0.110113	+	0.993919i	$0.464879\pi$
$360$	−6.45293	−0.340099
$361$	−18.8499	−0.992103
$362$	−53.0585	−2.78869
$363$	−1.86277	−0.0977700
$364$	129.293	6.77678
$365$	11.9218	0.624014
$366$	6.57028	0.343434
$367$	28.8419	1.50553	0.752767	−	0.658287i	$-0.228719\pi$
$367$	28.8419	1.50553	0.752767	+	0.658287i	$0.228719\pi$
$368$	0	0
$369$	2.83322	0.147492
$370$	2.63721	0.137102
$371$	−24.0070	−1.24638
$372$	−47.7094	−2.47362
$373$	−9.13105	−0.472788	−0.236394	−	0.971657i	$-0.575966\pi$
$373$	−9.13105	−0.472788	−0.236394	+	0.971657i	$0.575966\pi$
$374$	−15.4513	−0.798967
$375$	22.0746	1.13993
$376$	77.6272	4.00332
$377$	−14.6278	−0.753371
$378$	−50.2226	−2.58317
$379$	21.5169	1.10525	0.552625	−	0.833430i	$-0.313626\pi$
$379$	21.5169	1.10525	0.552625	+	0.833430i	$0.313626\pi$
$380$	−3.66985	−0.188259
$381$	−0.0107997	−0.000553286 0
$382$	56.0748	2.86904
$383$	3.97421	0.203073	0.101536	−	0.994832i	$-0.467624\pi$
$383$	3.97421	0.203073	0.101536	+	0.994832i	$0.467624\pi$
$384$	−15.8471	−0.808694
$385$	8.56119	0.436318
$386$	−9.10238	−0.463299
$387$	1.22332	0.0621847
$388$	27.4907	1.39563
$389$	4.71656	0.239139	0.119569	−	0.992826i	$-0.461849\pi$
$389$	4.71656	0.239139	0.119569	+	0.992826i	$0.461849\pi$
$390$	66.9248	3.38887
$391$	0	0
$392$	−68.0645	−3.43777
$393$	3.65964	0.184604
$394$	57.9292	2.91843
$395$	2.52693	0.127144
$396$	2.15814	0.108451
$397$	−0.622192	−0.0312269	−0.0156135	−	0.999878i	$-0.504970\pi$
$397$	−0.622192	−0.0312269	−0.0156135	+	0.999878i	$0.504970\pi$
$398$	−4.91940	−0.246587
$399$	2.99467	0.149921
$400$	−5.88917	−0.294458
$401$	25.9004	1.29341	0.646703	−	0.762742i	$-0.276147\pi$
$401$	25.9004	1.29341	0.646703	+	0.762742i	$0.276147\pi$
$402$	39.5800	1.97407
$403$	37.8279	1.88434
$404$	17.3071	0.861059
$405$	−21.0179	−1.04439
$406$	22.9799	1.14047
$407$	−0.497911	−0.0246805
$408$	74.6234	3.69441
$409$	24.9272	1.23257	0.616286	−	0.787523i	$-0.288637\pi$
$409$	24.9272	1.23257	0.616286	+	0.787523i	$0.288637\pi$
$410$	−31.9347	−1.57714
$411$	14.8060	0.730324
$412$	10.0406	0.494666
$413$	0.327032	0.0160922
$414$	0	0
$415$	23.8542	1.17095
$416$	−47.4095	−2.32444
$417$	16.8436	0.824837
$418$	0.994603	0.0486476
$419$	8.12831	0.397094	0.198547	−	0.980091i	$-0.436378\pi$
$419$	8.12831	0.397094	0.198547	+	0.980091i	$0.436378\pi$
$420$	−73.2420	−3.57385
$421$	7.83432	0.381821	0.190911	−	0.981607i	$-0.438856\pi$
$421$	7.83432	0.381821	0.190911	+	0.981607i	$0.438856\pi$
$422$	−16.5846	−0.807326
$423$	−5.47953	−0.266424
$424$	38.5078	1.87010
$425$	−4.48177	−0.217398
$426$	−27.4136	−1.32820
$427$	5.70119	0.275900
$428$	39.5152	1.91004
$429$	−12.6355	−0.610049
$430$	−13.7886	−0.664946
$431$	10.1312	0.488000	0.244000	−	0.969775i	$-0.421540\pi$
$431$	10.1312	0.488000	0.244000	+	0.969775i	$0.421540\pi$
$432$	37.2677	1.79304
$433$	−32.5790	−1.56565	−0.782823	−	0.622244i	$-0.786221\pi$
$433$	−32.5790	−1.56565	−0.782823	+	0.622244i	$0.786221\pi$
$434$	−59.4266	−2.85257
$435$	8.28640	0.397302
$436$	−29.1157	−1.39439
$437$	0	0
$438$	27.6420	1.32079
$439$	−37.0097	−1.76638	−0.883189	−	0.469017i	$-0.844608\pi$
$439$	−37.0097	−1.76638	−0.883189	+	0.469017i	$0.844608\pi$
$440$	−13.7324	−0.654664
$441$	4.80452	0.228786
$442$	−104.809	−4.98526
$443$	−37.6868	−1.79056	−0.895278	−	0.445509i	$-0.853023\pi$
$443$	−37.6868	−1.79056	−0.895278	+	0.445509i	$0.853023\pi$
$444$	4.25969	0.202156
$445$	25.5805	1.21263
$446$	44.7353	2.11828
$447$	−11.0713	−0.523655
$448$	8.84351	0.417816
$449$	27.5213	1.29881	0.649406	−	0.760442i	$-0.275018\pi$
$449$	27.5213	1.29881	0.649406	+	0.760442i	$0.275018\pi$
$450$	0.898588	0.0423598
$451$	6.02933	0.283910
$452$	19.4200	0.913440
$453$	−23.9937	−1.12732
$454$	47.7012	2.23873
$455$	58.0722	2.72247
$456$	−4.80353	−0.224946
$457$	−35.5934	−1.66499	−0.832495	−	0.554033i	$-0.813088\pi$
$457$	−35.5934	−1.66499	−0.832495	+	0.554033i	$0.813088\pi$
$458$	−7.54944	−0.352762
$459$	28.3614	1.32380
$460$	0	0
$461$	−8.98085	−0.418280	−0.209140	−	0.977886i	$-0.567066\pi$
$461$	−8.98085	−0.418280	−0.209140	+	0.977886i	$0.567066\pi$
$462$	19.8501	0.923510
$463$	12.8747	0.598340	0.299170	−	0.954200i	$-0.403290\pi$
$463$	12.8747	0.598340	0.299170	+	0.954200i	$0.403290\pi$
$464$	−17.0523	−0.791631
$465$	−21.4288	−0.993738
$466$	14.2521	0.660216
$467$	12.5074	0.578775	0.289387	−	0.957212i	$-0.406548\pi$
$467$	12.5074	0.578775	0.289387	+	0.957212i	$0.406548\pi$
$468$	14.6391	0.676692
$469$	34.3445	1.58588
$470$	61.7624	2.84889
$471$	−41.8150	−1.92673
$472$	−0.524567	−0.0241451
$473$	2.60332	0.119701
$474$	5.85897	0.269111
$475$	0.288493	0.0132370
$476$	114.702	5.25738
$477$	−2.71818	−0.124457
$478$	24.8999	1.13890
$479$	−38.7395	−1.77005	−0.885026	−	0.465542i	$-0.845859\pi$
$479$	−38.7395	−1.77005	−0.885026	+	0.465542i	$0.845859\pi$
$480$	26.8566	1.22583
$481$	−3.37743	−0.153997
$482$	15.6540	0.713022
$483$	0	0
$484$	4.59270	0.208759
$485$	12.3476	0.560673
$486$	−12.4290	−0.563789
$487$	22.8787	1.03673	0.518366	−	0.855159i	$-0.326540\pi$
$487$	22.8787	1.03673	0.518366	+	0.855159i	$0.326540\pi$
$488$	−9.14485	−0.413968
$489$	36.1684	1.63559
$490$	−54.1541	−2.44643
$491$	11.1112	0.501440	0.250720	−	0.968060i	$-0.419333\pi$
$491$	11.1112	0.501440	0.250720	+	0.968060i	$0.419333\pi$
$492$	−51.5817	−2.32548
$493$	−12.9771	−0.584459
$494$	6.74659	0.303544
$495$	0.969335	0.0435684
$496$	44.0975	1.98004
$497$	−23.7875	−1.06701
$498$	55.3086	2.47844
$499$	33.4000	1.49519	0.747594	−	0.664156i	$-0.231209\pi$
$499$	33.4000	1.49519	0.747594	+	0.664156i	$0.231209\pi$
$500$	−54.4254	−2.43398
$501$	5.54205	0.247600
$502$	36.6658	1.63648
$503$	−17.7350	−0.790764	−0.395382	−	0.918517i	$-0.629388\pi$
$503$	−17.7350	−0.790764	−0.395382	+	0.918517i	$0.629388\pi$
$504$	−12.9828	−0.578298
$505$	7.77352	0.345917
$506$	0	0
$507$	−61.4933	−2.73101
$508$	0.0266269	0.00118138
$509$	12.4946	0.553816	0.276908	−	0.960897i	$-0.410690\pi$
$509$	12.4946	0.553816	0.276908	+	0.960897i	$0.410690\pi$
$510$	59.3725	2.62906
$511$	23.9856	1.06106
$512$	50.0138	2.21032
$513$	−1.82563	−0.0806037
$514$	58.7437	2.59107
$515$	4.50977	0.198724
$516$	−22.2717	−0.980458
$517$	−11.6609	−0.512845
$518$	5.30585	0.233126
$519$	35.4292	1.55517
$520$	−93.1493	−4.08487
$521$	3.11513	0.136476	0.0682382	−	0.997669i	$-0.478262\pi$
$521$	3.11513	0.136476	0.0682382	+	0.997669i	$0.478262\pi$
$522$	2.60189	0.113882
$523$	2.12799	0.0930505	0.0465252	−	0.998917i	$-0.485185\pi$
$523$	2.12799	0.0930505	0.0465252	+	0.998917i	$0.485185\pi$
$524$	−9.02292	−0.394168
$525$	5.75769	0.251286
$526$	−48.3788	−2.10942
$527$	33.5591	1.46186
$528$	−14.7298	−0.641031
$529$	0	0
$530$	30.6379	1.33083
$531$	0.0370280	0.00160688
$532$	−7.38343	−0.320112
$533$	40.8981	1.77149
$534$	59.3113	2.56665
$535$	17.7484	0.767328
$536$	−55.0894	−2.37950
$537$	2.72078	0.117410
$538$	−39.8007	−1.71593
$539$	10.2244	0.440396
$540$	44.6504	1.92145
$541$	17.7330	0.762401	0.381201	−	0.924492i	$-0.375511\pi$
$541$	17.7330	0.762401	0.381201	+	0.924492i	$0.375511\pi$
$542$	29.7623	1.27840
$543$	−38.4931	−1.65190
$544$	−42.0594	−1.80328
$545$	−13.0774	−0.560175
$546$	134.647	5.76236
$547$	−20.0968	−0.859279	−0.429639	−	0.903001i	$-0.641359\pi$
$547$	−20.0968	−0.859279	−0.429639	+	0.903001i	$0.641359\pi$
$548$	−36.5044	−1.55939
$549$	0.645514	0.0275499
$550$	1.91227	0.0815393
$551$	0.835340	0.0355867
$552$	0	0
$553$	5.08397	0.216192
$554$	28.7482	1.22139
$555$	1.91325	0.0812130
$556$	−41.5283	−1.76119
$557$	0.640386	0.0271340	0.0135670	−	0.999908i	$-0.495681\pi$
$557$	0.640386	0.0271340	0.0135670	+	0.999908i	$0.495681\pi$
$558$	−6.72854	−0.284842
$559$	17.6588	0.746889
$560$	67.6972	2.86073
$561$	−11.2096	−0.473272
$562$	27.4843	1.15936
$563$	−38.3904	−1.61796	−0.808981	−	0.587835i	$-0.799981\pi$
$563$	−38.3904	−1.61796	−0.808981	+	0.587835i	$0.799981\pi$
$564$	99.7603	4.20066
$565$	8.72255	0.366961
$566$	47.7281	2.00616
$567$	−42.2863	−1.77586
$568$	38.1557	1.60098
$569$	9.31893	0.390670	0.195335	−	0.980737i	$-0.437421\pi$
$569$	9.31893	0.390670	0.195335	+	0.980737i	$0.437421\pi$
$570$	−3.82182	−0.160079
$571$	12.3062	0.514999	0.257499	−	0.966278i	$-0.417101\pi$
$571$	12.3062	0.514999	0.257499	+	0.966278i	$0.417101\pi$
$572$	31.1532	1.30258
$573$	40.6813	1.69949
$574$	−64.2499	−2.68174
$575$	0	0
$576$	1.00130	0.0417209
$577$	−10.5450	−0.438993	−0.219497	−	0.975613i	$-0.570441\pi$
$577$	−10.5450	−0.438993	−0.219497	+	0.975613i	$0.570441\pi$
$578$	−49.3320	−2.05194
$579$	−6.60362	−0.274437
$580$	−20.4303	−0.848322
$581$	47.9926	1.99107
$582$	28.6292	1.18672
$583$	−5.78450	−0.239570
$584$	−38.4735	−1.59205
$585$	6.57519	0.271851
$586$	−36.0463	−1.48906
$587$	9.83741	0.406033	0.203017	−	0.979175i	$-0.434925\pi$
$587$	9.83741	0.406033	0.203017	+	0.979175i	$0.434925\pi$
$588$	−87.4710	−3.60724
$589$	−2.16021	−0.0890098
$590$	−0.417360	−0.0171825
$591$	42.0267	1.72875
$592$	−3.93721	−0.161818
$593$	21.6558	0.889296	0.444648	−	0.895705i	$-0.353329\pi$
$593$	21.6558	0.889296	0.444648	+	0.895705i	$0.353329\pi$
$594$	−12.1012	−0.496516
$595$	51.5189	2.11207
$596$	27.2965	1.11811
$597$	−3.56894	−0.146067
$598$	0	0
$599$	7.51262	0.306957	0.153479	−	0.988152i	$-0.450952\pi$
$599$	7.51262	0.306957	0.153479	+	0.988152i	$0.450952\pi$
$600$	−9.23547	−0.377036
$601$	35.6521	1.45428	0.727140	−	0.686489i	$-0.240849\pi$
$601$	35.6521	1.45428	0.727140	+	0.686489i	$0.240849\pi$
$602$	−27.7416	−1.13066
$603$	3.88864	0.158358
$604$	59.1570	2.40706
$605$	2.06282	0.0838657
$606$	18.0238	0.732167
$607$	29.8716	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$607$	29.8716	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$608$	2.70738	0.109799
$609$	16.6715	0.675565
$610$	−7.27591	−0.294593
$611$	−79.0980	−3.19996
$612$	12.9871	0.524973
$613$	−30.1249	−1.21673	−0.608366	−	0.793657i	$-0.708175\pi$
$613$	−30.1249	−1.21673	−0.608366	+	0.793657i	$0.708175\pi$
$614$	85.2158	3.43903
$615$	−23.1681	−0.934226
$616$	−27.6283	−1.11318
$617$	−10.8409	−0.436439	−0.218220	−	0.975900i	$-0.570025\pi$
$617$	−10.8409	−0.436439	−0.218220	+	0.975900i	$0.570025\pi$
$618$	10.4564	0.420619
$619$	−15.6049	−0.627213	−0.313606	−	0.949553i	$-0.601537\pi$
$619$	−15.6049	−0.627213	−0.313606	+	0.949553i	$0.601537\pi$
$620$	52.8332	2.12183
$621$	0	0
$622$	77.2104	3.09585
$623$	51.4658	2.06194
$624$	−99.9149	−3.99980
$625$	−20.7215	−0.828861
$626$	75.5804	3.02080
$627$	0.721568	0.0288167
$628$	103.096	4.11397
$629$	−2.99629	−0.119470
$630$	−10.3295	−0.411535
$631$	−17.3015	−0.688762	−0.344381	−	0.938830i	$-0.611911\pi$
$631$	−17.3015	−0.688762	−0.344381	+	0.938830i	$0.611911\pi$
$632$	−8.15481	−0.324381
$633$	−12.0319	−0.478224
$634$	26.0002	1.03260
$635$	0.0119595	0.000474600 0
$636$	49.4871	1.96229
$637$	69.3541	2.74791
$638$	5.53702	0.219213
$639$	−2.69332	−0.106546
$640$	17.5490	0.693686
$641$	26.5099	1.04708	0.523539	−	0.852001i	$-0.324611\pi$
$641$	26.5099	1.04708	0.523539	+	0.852001i	$0.324611\pi$
$642$	41.1516	1.62412
$643$	−9.94102	−0.392035	−0.196018	−	0.980600i	$-0.562801\pi$
$643$	−9.94102	−0.392035	−0.196018	+	0.980600i	$0.562801\pi$
$644$	0	0
$645$	−10.0034	−0.393884
$646$	5.98526	0.235487
$647$	4.15705	0.163431	0.0817153	−	0.996656i	$-0.473960\pi$
$647$	4.15705	0.163431	0.0817153	+	0.996656i	$0.473960\pi$
$648$	67.8283	2.66455
$649$	0.0787985	0.00309311
$650$	12.9713	0.508776
$651$	−43.1130	−1.68973
$652$	−89.1740	−3.49232
$653$	−18.1110	−0.708737	−0.354369	−	0.935106i	$-0.615304\pi$
$653$	−18.1110	−0.708737	−0.354369	+	0.935106i	$0.615304\pi$
$654$	−30.3215	−1.18566
$655$	−4.05267	−0.158351
$656$	47.6766	1.86146
$657$	2.71576	0.105952
$658$	124.261	4.84419
$659$	−18.6817	−0.727737	−0.363869	−	0.931450i	$-0.618544\pi$
$659$	−18.6817	−0.727737	−0.363869	+	0.931450i	$0.618544\pi$
$660$	−17.6477	−0.686936
$661$	26.2985	1.02289	0.511446	−	0.859316i	$-0.329110\pi$
$661$	26.2985	1.02289	0.511446	+	0.859316i	$0.329110\pi$
$662$	13.1333	0.510441
$663$	−76.0372	−2.95304
$664$	−76.9813	−2.98745
$665$	−3.31629	−0.128600
$666$	0.600752	0.0232787
$667$	0	0
$668$	−13.6640	−0.528677
$669$	32.4547	1.25477
$670$	−43.8307	−1.69333
$671$	1.37371	0.0530313
$672$	54.0333	2.08438
$673$	14.9810	0.577475	0.288738	−	0.957408i	$-0.406764\pi$
$673$	14.9810	0.577475	0.288738	+	0.957408i	$0.406764\pi$
$674$	−30.2031	−1.16338
$675$	−3.51004	−0.135102
$676$	151.613	5.83127
$677$	−36.7407	−1.41206	−0.706029	−	0.708182i	$-0.749515\pi$
$677$	−36.7407	−1.41206	−0.706029	+	0.708182i	$0.749515\pi$
$678$	20.2242	0.776707
$679$	24.8422	0.953358
$680$	−82.6376	−3.16901
$681$	34.6064	1.32612
$682$	−14.3189	−0.548298
$683$	−13.4535	−0.514784	−0.257392	−	0.966307i	$-0.582863\pi$
$683$	−13.4535	−0.514784	−0.257392	+	0.966307i	$0.582863\pi$
$684$	−0.835984	−0.0319647
$685$	−16.3961	−0.626462
$686$	−34.3599	−1.31187
$687$	−5.47699	−0.208960
$688$	20.5856	0.784820
$689$	−39.2374	−1.49483
$690$	0	0
$691$	25.0061	0.951276	0.475638	−	0.879641i	$-0.342217\pi$
$691$	25.0061	0.951276	0.475638	+	0.879641i	$0.342217\pi$
$692$	−87.3514	−3.32060
$693$	1.95022	0.0740828
$694$	−47.1232	−1.78877
$695$	−18.6526	−0.707533
$696$	−26.7416	−1.01364
$697$	36.2829	1.37431
$698$	−35.5301	−1.34483
$699$	10.3397	0.391082
$700$	−14.1957	−0.536547
$701$	6.21329	0.234673	0.117336	−	0.993092i	$-0.462564\pi$
$701$	6.21329	0.234673	0.117336	+	0.993092i	$0.462564\pi$
$702$	−82.0846	−3.09808
$703$	0.192872	0.00727431
$704$	2.13085	0.0803094
$705$	44.8076	1.68755
$706$	−6.61192	−0.248843
$707$	15.6397	0.588191
$708$	−0.674131	−0.0253354
$709$	−27.2196	−1.02225	−0.511126	−	0.859506i	$-0.670771\pi$
$709$	−27.2196	−1.02225	−0.511126	+	0.859506i	$0.670771\pi$
$710$	30.3578	1.13931
$711$	0.575629	0.0215878
$712$	−82.5525	−3.09378
$713$	0	0
$714$	119.453	4.47040
$715$	13.9925	0.523291
$716$	−6.70813	−0.250695
$717$	18.0645	0.674630
$718$	−10.7139	−0.399838
$719$	−43.7502	−1.63161	−0.815804	−	0.578329i	$-0.803705\pi$
$719$	−43.7502	−1.63161	−0.815804	+	0.578329i	$0.803705\pi$
$720$	7.66498	0.285657
$721$	9.07329	0.337907
$722$	48.3996	1.80125
$723$	11.3567	0.422362
$724$	94.9054	3.52713
$725$	1.60606	0.0596476
$726$	4.78289	0.177510
$727$	28.3391	1.05104	0.525519	−	0.850782i	$-0.323871\pi$
$727$	28.3391	1.05104	0.525519	+	0.850782i	$0.323871\pi$
$728$	−187.409	−6.94582
$729$	21.5497	0.798138
$730$	−30.6106	−1.13295
$731$	15.6661	0.579431
$732$	−11.7522	−0.434375
$733$	24.4551	0.903271	0.451635	−	0.892203i	$-0.350841\pi$
$733$	24.4551	0.903271	0.451635	+	0.892203i	$0.350841\pi$
$734$	−74.0551	−2.73342
$735$	−39.2879	−1.44915
$736$	0	0
$737$	8.27533	0.304826
$738$	−7.27465	−0.267784
$739$	−39.6213	−1.45749	−0.728747	−	0.684783i	$-0.759897\pi$
$739$	−39.6213	−1.45749	−0.728747	+	0.684783i	$0.759897\pi$
$740$	−4.71716	−0.173406
$741$	4.89454	0.179805
$742$	61.6409	2.26291
$743$	−9.79560	−0.359366	−0.179683	−	0.983725i	$-0.557507\pi$
$743$	−9.79560	−0.359366	−0.179683	+	0.983725i	$0.557507\pi$
$744$	69.1543	2.53532
$745$	12.2603	0.449184
$746$	23.4451	0.858386
$747$	5.43393	0.198817
$748$	27.6376	1.01053
$749$	35.7082	1.30475
$750$	−56.6793	−2.06963
$751$	9.44609	0.344693	0.172346	−	0.985036i	$-0.444865\pi$
$751$	9.44609	0.344693	0.172346	+	0.985036i	$0.444865\pi$
$752$	−92.2079	−3.36247
$753$	26.6004	0.969374
$754$	37.5587	1.36781
$755$	26.5705	0.967000
$756$	89.8328	3.26719
$757$	−21.7912	−0.792014	−0.396007	−	0.918247i	$-0.629604\pi$
$757$	−21.7912	−0.792014	−0.396007	+	0.918247i	$0.629604\pi$
$758$	−55.2474	−2.00668
$759$	0	0
$760$	5.31941	0.192955
$761$	−7.66206	−0.277749	−0.138875	−	0.990310i	$-0.544349\pi$
$761$	−7.66206	−0.277749	−0.138875	+	0.990310i	$0.544349\pi$
$762$	0.0277296	0.00100454
$763$	−26.3107	−0.952511
$764$	−100.301	−3.62875
$765$	5.83320	0.210900
$766$	−10.2043	−0.368695
$767$	0.534506	0.0192999
$768$	48.6279	1.75471
$769$	−49.3907	−1.78107	−0.890537	−	0.454911i	$-0.849671\pi$
$769$	−49.3907	−1.78107	−0.890537	+	0.454911i	$0.849671\pi$
$770$	−21.9819	−0.792173
$771$	42.6176	1.53483
$772$	16.2814	0.585979
$773$	−43.5127	−1.56504	−0.782521	−	0.622624i	$-0.786067\pi$
$773$	−43.5127	−1.56504	−0.782521	+	0.622624i	$0.786067\pi$
$774$	−3.14102	−0.112902
$775$	−4.15331	−0.149191
$776$	−39.8476	−1.43044
$777$	3.84930	0.138093
$778$	−12.1103	−0.434177
$779$	−2.33554	−0.0836794
$780$	−119.708	−4.28623
$781$	−5.73161	−0.205093
$782$	0	0
$783$	−10.1634	−0.363211
$784$	80.8490	2.88746
$785$	46.3058	1.65272
$786$	−9.39658	−0.335165
$787$	−14.6738	−0.523064	−0.261532	−	0.965195i	$-0.584228\pi$
$787$	−14.6738	−0.523064	−0.261532	+	0.965195i	$0.584228\pi$
$788$	−103.618	−3.69122
$789$	−35.0980	−1.24952
$790$	−6.48820	−0.230840
$791$	17.5490	0.623972
$792$	−3.12820	−0.111156
$793$	9.31812	0.330896
$794$	1.59755	0.0566951
$795$	22.2273	0.788321
$796$	8.79930	0.311883
$797$	45.1987	1.60102	0.800510	−	0.599319i	$-0.204562\pi$
$797$	45.1987	1.60102	0.800510	+	0.599319i	$0.204562\pi$
$798$	−7.68919	−0.272194
$799$	−70.1720	−2.48251
$800$	5.20532	0.184036
$801$	5.82719	0.205894
$802$	−66.5026	−2.34829
$803$	5.77935	0.203949
$804$	−70.7965	−2.49680
$805$	0	0
$806$	−97.1278	−3.42118
$807$	−28.8748	−1.01644
$808$	−25.0864	−0.882537
$809$	32.5409	1.14408	0.572038	−	0.820227i	$-0.306153\pi$
$809$	32.5409	1.14408	0.572038	+	0.820227i	$0.306153\pi$
$810$	53.9661	1.89618
$811$	−50.4931	−1.77305	−0.886526	−	0.462680i	$-0.846888\pi$
$811$	−50.4931	−1.77305	−0.886526	+	0.462680i	$0.846888\pi$
$812$	−41.1040	−1.44247
$813$	21.5921	0.757267
$814$	1.27845	0.0448096
$815$	−40.0528	−1.40299
$816$	−88.6398	−3.10301
$817$	−1.00843	−0.0352805
$818$	−64.0037	−2.23784
$819$	13.2287	0.462250
$820$	57.1213	1.99476
$821$	−19.9307	−0.695586	−0.347793	−	0.937571i	$-0.613069\pi$
$821$	−19.9307	−0.695586	−0.347793	+	0.937571i	$0.613069\pi$
$822$	−38.0162	−1.32597
$823$	−20.2426	−0.705614	−0.352807	−	0.935696i	$-0.614773\pi$
$823$	−20.2426	−0.705614	−0.352807	+	0.935696i	$0.614773\pi$
$824$	−14.5538	−0.507005
$825$	1.38732	0.0483002
$826$	−0.839694	−0.0292167
$827$	27.0085	0.939176	0.469588	−	0.882886i	$-0.344402\pi$
$827$	27.0085	0.939176	0.469588	+	0.882886i	$0.344402\pi$
$828$	0	0
$829$	−46.9795	−1.63167	−0.815833	−	0.578288i	$-0.803721\pi$
$829$	−46.9795	−1.63167	−0.815833	+	0.578288i	$0.803721\pi$
$830$	−61.2485	−2.12597
$831$	20.8564	0.723499
$832$	14.4540	0.501101
$833$	61.5277	2.13181
$834$	−43.2481	−1.49756
$835$	−6.13724	−0.212388
$836$	−1.77904	−0.0615294
$837$	26.2829	0.908469
$838$	−20.8704	−0.720958
$839$	21.9464	0.757674	0.378837	−	0.925463i	$-0.376324\pi$
$839$	21.9464	0.757674	0.378837	+	0.925463i	$0.376324\pi$
$840$	106.164	3.66299
$841$	−24.3496	−0.839642
$842$	−20.1156	−0.693229
$843$	19.9394	0.686751
$844$	29.6648	1.02110
$845$	68.0975	2.34262
$846$	14.0694	0.483715
$847$	4.15023	0.142604
$848$	−45.7407	−1.57074
$849$	34.6259	1.18836
$850$	11.5075	0.394704
$851$	0	0
$852$	49.0346	1.67990
$853$	−12.3162	−0.421699	−0.210849	−	0.977519i	$-0.567623\pi$
$853$	−12.3162	−0.421699	−0.210849	+	0.977519i	$0.567623\pi$
$854$	−14.6385	−0.500920
$855$	−0.375485	−0.0128413
$856$	−57.2769	−1.95768
$857$	12.3110	0.420536	0.210268	−	0.977644i	$-0.432566\pi$
$857$	12.3110	0.420536	0.210268	+	0.977644i	$0.432566\pi$
$858$	32.4433	1.10760
$859$	−9.05383	−0.308913	−0.154456	−	0.988000i	$-0.549363\pi$
$859$	−9.05383	−0.308913	−0.154456	+	0.988000i	$0.549363\pi$
$860$	24.6636	0.841023
$861$	−46.6122	−1.58854
$862$	−26.0130	−0.886006
$863$	3.37903	0.115024	0.0575118	−	0.998345i	$-0.481683\pi$
$863$	3.37903	0.115024	0.0575118	+	0.998345i	$0.481683\pi$
$864$	−32.9402	−1.12065
$865$	−39.2342	−1.33400
$866$	83.6506	2.84256
$867$	−35.7896	−1.21548
$868$	106.296	3.60792
$869$	1.22499	0.0415548
$870$	−21.2764	−0.721336
$871$	56.1332	1.90200
$872$	42.2030	1.42917
$873$	2.81275	0.0951971
$874$	0	0
$875$	−49.1820	−1.66265
$876$	−49.4431	−1.67053
$877$	53.9276	1.82101	0.910504	−	0.413501i	$-0.135694\pi$
$877$	53.9276	1.82101	0.910504	+	0.413501i	$0.135694\pi$
$878$	95.0271	3.20701
$879$	−26.1510	−0.882052
$880$	16.3117	0.549867
$881$	34.5622	1.16443	0.582215	−	0.813035i	$-0.302186\pi$
$881$	34.5622	1.16443	0.582215	+	0.813035i	$0.302186\pi$
$882$	−12.3362	−0.415381
$883$	19.5480	0.657844	0.328922	−	0.944357i	$-0.393315\pi$
$883$	19.5480	0.657844	0.328922	+	0.944357i	$0.393315\pi$
$884$	187.471	6.30535
$885$	−0.302788	−0.0101781
$886$	96.7656	3.25090
$887$	12.2485	0.411264	0.205632	−	0.978629i	$-0.434075\pi$
$887$	12.2485	0.411264	0.205632	+	0.978629i	$0.434075\pi$
$888$	−6.17438	−0.207199
$889$	0.0240616	0.000807001 0
$890$	−65.6811	−2.20164
$891$	−10.1889	−0.341341
$892$	−80.0178	−2.67919
$893$	4.51699	0.151155
$894$	28.4270	0.950740
$895$	−3.01298	−0.100713
$896$	35.3071	1.17953
$897$	0	0
$898$	−70.6644	−2.35810
$899$	−12.0260	−0.401091
$900$	−1.60730	−0.0535766
$901$	−34.8096	−1.15968
$902$	−15.4810	−0.515462
$903$	−20.1260	−0.669752
$904$	−28.1491	−0.936225
$905$	42.6271	1.41697
$906$	61.6068	2.04675
$907$	55.9809	1.85881	0.929407	−	0.369057i	$-0.120319\pi$
$907$	55.9809	1.85881	0.929407	+	0.369057i	$0.120319\pi$
$908$	−85.3228	−2.83154
$909$	1.77079	0.0587335
$910$	−149.108	−4.94287
$911$	−13.8998	−0.460522	−0.230261	−	0.973129i	$-0.573958\pi$
$911$	−13.8998	−0.460522	−0.230261	+	0.973129i	$0.573958\pi$
$912$	5.70577	0.188937
$913$	11.5638	0.382707
$914$	91.3905	3.02293
$915$	−5.27855	−0.174503
$916$	13.5036	0.446173
$917$	−8.15363	−0.269257
$918$	−72.8215	−2.40347
$919$	29.8027	0.983101	0.491551	−	0.870849i	$-0.336430\pi$
$919$	29.8027	0.983101	0.491551	+	0.870849i	$0.336430\pi$
$920$	0	0
$921$	61.8227	2.03713
$922$	23.0595	0.759423
$923$	−38.8786	−1.27971
$924$	−35.5057	−1.16805
$925$	0.370824	0.0121926
$926$	−33.0575	−1.08634
$927$	1.02732	0.0337416
$928$	15.0722	0.494768
$929$	−5.80521	−0.190463	−0.0952315	−	0.995455i	$-0.530359\pi$
$929$	−5.80521	−0.190463	−0.0952315	+	0.995455i	$0.530359\pi$
$930$	55.0212	1.80421
$931$	−3.96055	−0.129802
$932$	−25.4927	−0.835040
$933$	56.0149	1.83384
$934$	−32.1144	−1.05081
$935$	12.4135	0.405965
$936$	−21.2192	−0.693572
$937$	−6.35465	−0.207598	−0.103799	−	0.994598i	$-0.533100\pi$
$937$	−6.35465	−0.207598	−0.103799	+	0.994598i	$0.533100\pi$
$938$	−88.1838	−2.87930
$939$	54.8323	1.78939
$940$	−110.474	−3.60327
$941$	−6.07766	−0.198126	−0.0990630	−	0.995081i	$-0.531585\pi$
$941$	−6.07766	−0.198126	−0.0990630	+	0.995081i	$0.531585\pi$
$942$	107.365	3.49815
$943$	0	0
$944$	0.623096	0.0202800
$945$	40.3487	1.31254
$946$	−6.68434	−0.217327
$947$	38.4954	1.25093	0.625467	−	0.780251i	$-0.284909\pi$
$947$	38.4954	1.25093	0.625467	+	0.780251i	$0.284909\pi$
$948$	−10.4799	−0.340372
$949$	39.2025	1.27257
$950$	−0.740742	−0.0240328
$951$	18.8627	0.611665
$952$	−166.260	−5.38852
$953$	−14.6604	−0.474896	−0.237448	−	0.971400i	$-0.576311\pi$
$953$	−14.6604	−0.474896	−0.237448	+	0.971400i	$0.576311\pi$
$954$	6.97926	0.225962
$955$	−45.0503	−1.45779
$956$	−44.5383	−1.44047
$957$	4.01702	0.129852
$958$	99.4684	3.21368
$959$	−32.9875	−1.06522
$960$	−8.18792	−0.264264
$961$	0.0995872	0.00321249
$962$	8.67196	0.279595
$963$	4.04304	0.130285
$964$	−28.0003	−0.901828
$965$	7.31283	0.235408
$966$	0	0
$967$	−23.7829	−0.764805	−0.382403	−	0.923996i	$-0.624903\pi$
$967$	−23.7829	−0.764805	−0.382403	+	0.923996i	$0.624903\pi$
$968$	−6.65707	−0.213966
$969$	4.34220	0.139492
$970$	−31.7039	−1.01795
$971$	20.6653	0.663181	0.331591	−	0.943423i	$-0.392415\pi$
$971$	20.6653	0.663181	0.331591	+	0.943423i	$0.392415\pi$
$972$	22.2316	0.713079
$973$	−37.5274	−1.20307
$974$	−58.7439	−1.88228
$975$	9.41045	0.301376
$976$	10.8625	0.347701
$977$	−24.8167	−0.793956	−0.396978	−	0.917828i	$-0.629941\pi$
$977$	−24.8167	−0.793956	−0.396978	+	0.917828i	$0.629941\pi$
$978$	−92.8669	−2.96956
$979$	12.4007	0.396329
$980$	96.8651	3.09424
$981$	−2.97901	−0.0951125
$982$	−28.5293	−0.910406
$983$	−9.12258	−0.290965	−0.145482	−	0.989361i	$-0.546473\pi$
$983$	−9.12258	−0.290965	−0.145482	+	0.989361i	$0.546473\pi$
$984$	74.7671	2.38349
$985$	−46.5402	−1.48289
$986$	33.3203	1.06114
$987$	90.1492	2.86948
$988$	−12.0676	−0.383921
$989$	0	0
$990$	−2.48889	−0.0791021
$991$	−51.5648	−1.63801	−0.819004	−	0.573787i	$-0.805474\pi$
$991$	−51.5648	−1.63801	−0.819004	+	0.573787i	$0.805474\pi$
$992$	−38.9769	−1.23752
$993$	9.52801	0.302362
$994$	61.0773	1.93725
$995$	3.95223	0.125294
$996$	−98.9302	−3.13472
$997$	31.6978	1.00388	0.501940	−	0.864903i	$-0.332620\pi$
$997$	31.6978	1.00388	0.501940	+	0.864903i	$0.332620\pi$
$998$	−85.7586	−2.71464
$999$	−2.34664	−0.0742445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.4		60
23.9	even	11		253.2.i.b.12.1	✓	120
23.18	even	11		253.2.i.b.232.1	yes	120
23.22	odd	2		5819.2.a.t.1.4		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.12.1	✓	120	23.9	even	11
253.2.i.b.232.1	yes	120	23.18	even	11
5819.2.a.t.1.4		60	23.22	odd	2
5819.2.a.u.1.4		60	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:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56762 q^{2} -1.86277 q^{3} +4.59270 q^{4} +2.06282 q^{5} +4.78289 q^{6} +4.15023 q^{7} -6.65707 q^{8} +0.469907 q^{9} -5.29655 q^{10} +1.00000 q^{11} -8.55513 q^{12} +6.78320 q^{13} -10.6562 q^{14} -3.84256 q^{15} +7.90746 q^{16} +6.01773 q^{17} -1.20655 q^{18} -0.387363 q^{19} +9.47392 q^{20} -7.73091 q^{21} -2.56762 q^{22} +12.4006 q^{24} -0.744761 q^{25} -17.4167 q^{26} +4.71298 q^{27} +19.0607 q^{28} -2.15648 q^{29} +9.86626 q^{30} +5.57670 q^{31} -6.98925 q^{32} -1.86277 q^{33} -15.4513 q^{34} +8.56119 q^{35} +2.15814 q^{36} -0.497911 q^{37} +0.994603 q^{38} -12.6355 q^{39} -13.7324 q^{40} +6.02933 q^{41} +19.8501 q^{42} +2.60332 q^{43} +4.59270 q^{44} +0.969335 q^{45} -11.6609 q^{47} -14.7298 q^{48} +10.2244 q^{49} +1.91227 q^{50} -11.2096 q^{51} +31.1532 q^{52} -5.78450 q^{53} -12.1012 q^{54} +2.06282 q^{55} -27.6283 q^{56} +0.721568 q^{57} +5.53702 q^{58} +0.0787985 q^{59} -17.6477 q^{60} +1.37371 q^{61} -14.3189 q^{62} +1.95022 q^{63} +2.13085 q^{64} +13.9925 q^{65} +4.78289 q^{66} +8.27533 q^{67} +27.6376 q^{68} -21.9819 q^{70} -5.73161 q^{71} -3.12820 q^{72} +5.77935 q^{73} +1.27845 q^{74} +1.38732 q^{75} -1.77904 q^{76} +4.15023 q^{77} +32.4433 q^{78} +1.22499 q^{79} +16.3117 q^{80} -10.1889 q^{81} -15.4810 q^{82} +11.5638 q^{83} -35.5057 q^{84} +12.4135 q^{85} -6.68434 q^{86} +4.01702 q^{87} -6.65707 q^{88} +12.4007 q^{89} -2.48889 q^{90} +28.1518 q^{91} -10.3881 q^{93} +29.9407 q^{94} -0.799062 q^{95} +13.0194 q^{96} +5.98575 q^{97} -26.2524 q^{98} +0.469907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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