LMFDB - Embedded newform 1875.2.b.e.1249.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1249,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1875.1249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 23x^{10} + 199x^{8} + 794x^{6} + 1399x^{4} + 783x^{2} + 81 $ x^12 + 23x^10 + 199x^8 + 794x^6 + 1399x^4 + 783*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.11
Root			$2.38719i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.e.1249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38719i q^{2} -1.00000i q^{3} -3.69868 q^{4} +2.38719 q^{6} +3.31671i q^{7} -4.05506i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.38719i q^{2} -1.00000i q^{3} -3.69868 q^{4} +2.38719 q^{6} +3.31671i q^{7} -4.05506i q^{8} -1.00000 q^{9} -4.36655 q^{11} +3.69868i q^{12} -5.85502i q^{13} -7.91762 q^{14} +2.28286 q^{16} +0.407830i q^{17} -2.38719i q^{18} +6.64447 q^{19} +3.31671 q^{21} -10.4238i q^{22} -4.61860i q^{23} -4.05506 q^{24} +13.9771 q^{26} +1.00000i q^{27} -12.2674i q^{28} -3.30132 q^{29} -8.77495 q^{31} -2.66052i q^{32} +4.36655i q^{33} -0.973567 q^{34} +3.69868 q^{36} +3.09911i q^{37} +15.8616i q^{38} -5.85502 q^{39} +2.89349 q^{41} +7.91762i q^{42} -1.33270i q^{43} +16.1505 q^{44} +11.0255 q^{46} -11.0609i q^{47} -2.28286i q^{48} -4.00057 q^{49} +0.407830 q^{51} +21.6558i q^{52} -2.70021i q^{53} -2.38719 q^{54} +13.4495 q^{56} -6.64447i q^{57} -7.88089i q^{58} +5.80518 q^{59} +11.2366 q^{61} -20.9475i q^{62} -3.31671i q^{63} +10.9169 q^{64} -10.4238 q^{66} -0.0418484i q^{67} -1.50843i q^{68} -4.61860 q^{69} -16.2062 q^{71} +4.05506i q^{72} -5.35799i q^{73} -7.39817 q^{74} -24.5757 q^{76} -14.4826i q^{77} -13.9771i q^{78} +3.55370 q^{79} +1.00000 q^{81} +6.90732i q^{82} -4.98952i q^{83} -12.2674 q^{84} +3.18140 q^{86} +3.30132i q^{87} +17.7066i q^{88} +1.94025 q^{89} +19.4194 q^{91} +17.0827i q^{92} +8.77495i q^{93} +26.4044 q^{94} -2.66052 q^{96} +5.99258i q^{97} -9.55012i q^{98} +4.36655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times$.

$n$	$626$	$1252$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.38719i	1.68800i	0.536345	+	0.843999i	$0.319805\pi$
$2$	2.38719i	1.68800i	−0.536345	+	0.843999i	$0.680195\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−3.69868	−1.84934
$5$	0	0
$5$	0	0
$6$	2.38719	0.974566
$7$	3.31671i	1.25360i	0.779181	+	0.626799i	$0.215635\pi$
$7$	3.31671i	1.25360i	−0.779181	+	0.626799i	$0.784365\pi$
$8$	− 4.05506i	− 1.43368i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−4.36655	−1.31656	−0.658282	−	0.752771i	$-0.728717\pi$
$11$	−4.36655	−1.31656	−0.658282	+	0.752771i	$0.728717\pi$
$12$	3.69868i	1.06772i
$13$	− 5.85502i	− 1.62389i	−0.583733	−	0.811946i	$-0.698409\pi$
$13$	− 5.85502i	− 1.62389i	0.583733	−	0.811946i	$-0.301591\pi$
$14$	−7.91762	−2.11607
$15$	0	0
$16$	2.28286	0.570714
$17$	0.407830i	0.0989132i	0.998776	+	0.0494566i	$0.0157490\pi$
$17$	0.407830i	0.0989132i	−0.998776	+	0.0494566i	$0.984251\pi$
$18$	− 2.38719i	− 0.562666i
$19$	6.64447	1.52435	0.762173	−	0.647374i	$-0.224133\pi$
$19$	6.64447	1.52435	0.762173	+	0.647374i	$0.224133\pi$
$20$	0	0
$21$	3.31671	0.723766
$22$	− 10.4238i	− 2.22236i
$23$	− 4.61860i	− 0.963045i	−0.876434	−	0.481523i	$-0.840084\pi$
$23$	− 4.61860i	− 0.963045i	0.876434	−	0.481523i	$-0.159916\pi$
$24$	−4.05506	−0.827736
$25$	0	0
$26$	13.9771	2.74113
$27$	1.00000i	0.192450i
$28$	− 12.2674i	− 2.31833i
$29$	−3.30132	−0.613040	−0.306520	−	0.951864i	$-0.599165\pi$
$29$	−3.30132	−0.613040	−0.306520	+	0.951864i	$0.599165\pi$
$30$	0	0
$31$	−8.77495	−1.57603	−0.788014	−	0.615658i	$-0.788890\pi$
$31$	−8.77495	−1.57603	−0.788014	+	0.615658i	$0.788890\pi$
$32$	− 2.66052i	− 0.470318i
$33$	4.36655i	0.760119i
$34$	−0.973567	−0.166965
$35$	0	0
$36$	3.69868	0.616446
$37$	3.09911i	0.509491i	0.967008	+	0.254745i	$0.0819916\pi$
$37$	3.09911i	0.509491i	−0.967008	+	0.254745i	$0.918008\pi$
$38$	15.8616i	2.57309i
$39$	−5.85502	−0.937554
$40$	0	0
$41$	2.89349	0.451888	0.225944	−	0.974140i	$-0.427453\pi$
$41$	2.89349	0.451888	0.225944	+	0.974140i	$0.427453\pi$
$42$	7.91762i	1.22172i
$43$	− 1.33270i	− 0.203234i	−0.994824	−	0.101617i	$-0.967598\pi$
$43$	− 1.33270i	− 0.203234i	0.994824	−	0.101617i	$-0.0324016\pi$
$44$	16.1505	2.43477
$45$	0	0
$46$	11.0255	1.62562
$47$	− 11.0609i	− 1.61339i	−0.590967	−	0.806696i	$-0.701254\pi$
$47$	− 11.0609i	− 1.61339i	0.590967	−	0.806696i	$-0.298746\pi$
$48$	− 2.28286i	− 0.329502i
$49$	−4.00057	−0.571510
$50$	0	0
$51$	0.407830	0.0571076
$52$	21.6558i	3.00312i
$53$	− 2.70021i	− 0.370903i	−0.982653	−	0.185451i	$-0.940625\pi$
$53$	− 2.70021i	− 0.370903i	0.982653	−	0.185451i	$-0.0593747\pi$
$54$	−2.38719	−0.324855
$55$	0	0
$56$	13.4495	1.79726
$57$	− 6.64447i	− 0.880081i
$58$	− 7.88089i	− 1.03481i
$59$	5.80518	0.755770	0.377885	−	0.925852i	$-0.376651\pi$
$59$	5.80518	0.755770	0.377885	+	0.925852i	$0.376651\pi$
$60$	0	0
$61$	11.2366	1.43870	0.719352	−	0.694646i	$-0.244439\pi$
$61$	11.2366	1.43870	0.719352	+	0.694646i	$0.244439\pi$
$62$	− 20.9475i	− 2.66033i
$63$	− 3.31671i	− 0.417866i
$64$	10.9169	1.36461
$65$	0	0
$66$	−10.4238	−1.28308
$67$	− 0.0418484i	− 0.00511260i	−0.999997	−	0.00255630i	$-0.999186\pi$
$67$	− 0.0418484i	− 0.00511260i	0.999997	−	0.00255630i	$-0.000813696\pi$
$68$	− 1.50843i	− 0.182924i
$69$	−4.61860	−0.556014
$70$	0	0
$71$	−16.2062	−1.92332	−0.961659	−	0.274250i	$-0.911571\pi$
$71$	−16.2062	−1.92332	−0.961659	+	0.274250i	$0.911571\pi$
$72$	4.05506i	0.477894i
$73$	− 5.35799i	− 0.627105i	−0.949571	−	0.313553i	$-0.898481\pi$
$73$	− 5.35799i	− 0.627105i	0.949571	−	0.313553i	$-0.101519\pi$
$74$	−7.39817	−0.860019
$75$	0	0
$76$	−24.5757	−2.81903
$77$	− 14.4826i	− 1.65044i
$78$	− 13.9771i	− 1.58259i
$79$	3.55370	0.399822	0.199911	−	0.979814i	$-0.435935\pi$
$79$	3.55370	0.399822	0.199911	+	0.979814i	$0.435935\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	6.90732i	0.762786i
$83$	− 4.98952i	− 0.547671i	−0.961776	−	0.273836i	$-0.911708\pi$
$83$	− 4.98952i	− 0.547671i	0.961776	−	0.273836i	$-0.0882924\pi$
$84$	−12.2674	−1.33849
$85$	0	0
$86$	3.18140	0.343059
$87$	3.30132i	0.353939i
$88$	17.7066i	1.88753i
$89$	1.94025	0.205666	0.102833	−	0.994699i	$-0.467209\pi$
$89$	1.94025	0.205666	0.102833	+	0.994699i	$0.467209\pi$
$90$	0	0
$91$	19.4194	2.03571
$92$	17.0827i	1.78100i
$93$	8.77495i	0.909920i
$94$	26.4044	2.72340
$95$	0	0
$96$	−2.66052	−0.271538
$97$	5.99258i	0.608454i	0.952600	+	0.304227i	$0.0983981\pi$
$97$	5.99258i	0.608454i	−0.952600	+	0.304227i	$0.901602\pi$
$98$	− 9.55012i	− 0.964708i
$99$	4.36655	0.438855
$100$	0	0
$101$	5.06181	0.503669	0.251834	−	0.967770i	$-0.418966\pi$
$101$	5.06181	0.503669	0.251834	+	0.967770i	$0.418966\pi$
$102$	0.973567i	0.0963975i
$103$	− 6.90359i	− 0.680231i	−0.940384	−	0.340115i	$-0.889534\pi$
$103$	− 6.90359i	− 0.680231i	0.940384	−	0.340115i	$-0.110466\pi$
$104$	−23.7425	−2.32814
$105$	0	0
$106$	6.44592	0.626083
$107$	− 17.2723i	− 1.66978i	−0.550417	−	0.834890i	$-0.685531\pi$
$107$	− 17.2723i	− 1.66978i	0.550417	−	0.834890i	$-0.314469\pi$
$108$	− 3.69868i	− 0.355905i
$109$	6.54439	0.626839	0.313419	−	0.949615i	$-0.398525\pi$
$109$	6.54439	0.626839	0.313419	+	0.949615i	$0.398525\pi$
$110$	0	0
$111$	3.09911	0.294155
$112$	7.57157i	0.715446i
$113$	− 8.66993i	− 0.815599i	−0.913072	−	0.407799i	$-0.866296\pi$
$113$	− 8.66993i	− 0.815599i	0.913072	−	0.407799i	$-0.133704\pi$
$114$	15.8616	1.48558
$115$	0	0
$116$	12.2105	1.13372
$117$	5.85502i	0.541297i
$118$	13.8581i	1.27574i
$119$	−1.35265	−0.123998
$120$	0	0
$121$	8.06676	0.733342
$122$	26.8240i	2.42853i
$123$	− 2.89349i	− 0.260898i
$124$	32.4557	2.91461
$125$	0	0
$126$	7.91762	0.705358
$127$	− 3.24595i	− 0.288031i	−0.989575	−	0.144016i	$-0.953998\pi$
$127$	− 3.24595i	− 0.288031i	0.989575	−	0.144016i	$-0.0460016\pi$
$128$	20.7396i	1.83314i
$129$	−1.33270	−0.117337
$130$	0	0
$131$	−4.40192	−0.384598	−0.192299	−	0.981336i	$-0.561594\pi$
$131$	−4.40192	−0.384598	−0.192299	+	0.981336i	$0.561594\pi$
$132$	− 16.1505i	− 1.40572i
$133$	22.0378i	1.91092i
$134$	0.0999001	0.00863005
$135$	0	0
$136$	1.65378	0.141810
$137$	1.06523i	0.0910085i	0.998964	+	0.0455042i	$0.0144895\pi$
$137$	1.06523i	0.0910085i	−0.998964	+	0.0455042i	$0.985511\pi$
$138$	− 11.0255i	− 0.938551i
$139$	3.77286	0.320010	0.160005	−	0.987116i	$-0.448849\pi$
$139$	3.77286	0.320010	0.160005	+	0.987116i	$0.448849\pi$
$140$	0	0
$141$	−11.0609	−0.931492
$142$	− 38.6872i	− 3.24656i
$143$	25.5663i	2.13796i
$144$	−2.28286	−0.190238
$145$	0	0
$146$	12.7905	1.05855
$147$	4.00057i	0.329961i
$148$	− 11.4626i	− 0.942221i
$149$	7.88089	0.645627	0.322814	−	0.946463i	$-0.395371\pi$
$149$	7.88089	0.645627	0.322814	+	0.946463i	$0.395371\pi$
$150$	0	0
$151$	7.46432	0.607437	0.303719	−	0.952762i	$-0.401772\pi$
$151$	7.46432	0.607437	0.303719	+	0.952762i	$0.401772\pi$
$152$	− 26.9437i	− 2.18543i
$153$	− 0.407830i	− 0.0329711i
$154$	34.5727	2.78595
$155$	0	0
$156$	21.6558	1.73385
$157$	0.268958i	0.0214652i	0.999942	+	0.0107326i	$0.00341636\pi$
$157$	0.268958i	0.0214652i	−0.999942	+	0.0107326i	$0.996584\pi$
$158$	8.48336i	0.674900i
$159$	−2.70021	−0.214141
$160$	0	0
$161$	15.3186	1.20727
$162$	2.38719i	0.187555i
$163$	− 10.3496i	− 0.810645i	−0.914174	−	0.405322i	$-0.867159\pi$
$163$	− 10.3496i	− 0.810645i	0.914174	−	0.405322i	$-0.132841\pi$
$164$	−10.7021	−0.835693
$165$	0	0
$166$	11.9109	0.924468
$167$	− 4.26896i	− 0.330342i	−0.986265	−	0.165171i	$-0.947182\pi$
$167$	− 4.26896i	− 0.330342i	0.986265	−	0.165171i	$-0.0528176\pi$
$168$	− 13.4495i	− 1.03765i
$169$	−21.2813	−1.63702
$170$	0	0
$171$	−6.64447	−0.508115
$172$	4.92921i	0.375849i
$173$	23.5031i	1.78691i	0.449154	+	0.893454i	$0.351725\pi$
$173$	23.5031i	1.78691i	−0.449154	+	0.893454i	$0.648275\pi$
$174$	−7.88089	−0.597448
$175$	0	0
$176$	−9.96820	−0.751382
$177$	− 5.80518i	− 0.436344i
$178$	4.63175i	0.347164i
$179$	−19.6897	−1.47168	−0.735840	−	0.677155i	$-0.763212\pi$
$179$	−19.6897	−1.47168	−0.735840	+	0.677155i	$0.763212\pi$
$180$	0	0
$181$	−12.8221	−0.953060	−0.476530	−	0.879158i	$-0.658106\pi$
$181$	−12.8221	−0.953060	−0.476530	+	0.879158i	$0.658106\pi$
$182$	46.3578i	3.43627i
$183$	− 11.2366i	− 0.830636i
$184$	−18.7287	−1.38070
$185$	0	0
$186$	−20.9475	−1.53594
$187$	− 1.78081i	− 0.130226i
$188$	40.9105i	2.98371i
$189$	−3.31671	−0.241255
$190$	0	0
$191$	−19.0583	−1.37901	−0.689507	−	0.724279i	$-0.742173\pi$
$191$	−19.0583	−1.37901	−0.689507	+	0.724279i	$0.742173\pi$
$192$	− 10.9169i	− 0.787857i
$193$	− 16.9842i	− 1.22255i	−0.791418	−	0.611275i	$-0.790657\pi$
$193$	− 16.9842i	− 1.22255i	0.791418	−	0.611275i	$-0.209343\pi$
$194$	−14.3054	−1.02707
$195$	0	0
$196$	14.7968	1.05692
$197$	− 0.469462i	− 0.0334478i	−0.999860	−	0.0167239i	$-0.994676\pi$
$197$	− 0.469462i	− 0.0334478i	0.999860	−	0.0167239i	$-0.00532363\pi$
$198$	10.4238i	0.740786i
$199$	−7.02491	−0.497983	−0.248991	−	0.968506i	$-0.580099\pi$
$199$	−7.02491	−0.497983	−0.248991	+	0.968506i	$0.580099\pi$
$200$	0	0
$201$	−0.0418484	−0.00295176
$202$	12.0835i	0.850192i
$203$	− 10.9495i	− 0.768507i
$204$	−1.50843	−0.105611
$205$	0	0
$206$	16.4802	1.14823
$207$	4.61860i	0.321015i
$208$	− 13.3662i	− 0.926777i
$209$	−29.0134	−2.00690
$210$	0	0
$211$	15.7531	1.08449	0.542243	−	0.840222i	$-0.317575\pi$
$211$	15.7531	1.08449	0.542243	+	0.840222i	$0.317575\pi$
$212$	9.98721i	0.685925i
$213$	16.2062i	1.11043i
$214$	41.2323	2.81859
$215$	0	0
$216$	4.05506	0.275912
$217$	− 29.1040i	− 1.97571i
$218$	15.6227i	1.05810i
$219$	−5.35799	−0.362059
$220$	0	0
$221$	2.38785	0.160624
$222$	7.39817i	0.496532i
$223$	2.27697i	0.152477i	0.997090	+	0.0762385i	$0.0242910\pi$
$223$	2.27697i	0.152477i	−0.997090	+	0.0762385i	$0.975709\pi$
$224$	8.82417	0.589590
$225$	0	0
$226$	20.6968	1.37673
$227$	− 20.2674i	− 1.34520i	−0.740007	−	0.672599i	$-0.765178\pi$
$227$	− 20.2674i	− 1.34520i	0.740007	−	0.672599i	$-0.234822\pi$
$228$	24.5757i	1.62757i
$229$	−19.6358	−1.29757	−0.648786	−	0.760971i	$-0.724723\pi$
$229$	−19.6358	−1.29757	−0.648786	+	0.760971i	$0.724723\pi$
$230$	0	0
$231$	−14.4826	−0.952884
$232$	13.3871i	0.878905i
$233$	17.1468i	1.12333i	0.827366	+	0.561663i	$0.189838\pi$
$233$	17.1468i	1.12333i	−0.827366	+	0.561663i	$0.810162\pi$
$234$	−13.9771	−0.913709
$235$	0	0
$236$	−21.4715	−1.39768
$237$	− 3.55370i	− 0.230838i
$238$	− 3.22904i	− 0.209308i
$239$	−21.7654	−1.40789	−0.703945	−	0.710255i	$-0.748580\pi$
$239$	−21.7654	−1.40789	−0.703945	+	0.710255i	$0.748580\pi$
$240$	0	0
$241$	3.90067	0.251264	0.125632	−	0.992077i	$-0.459904\pi$
$241$	3.90067	0.251264	0.125632	+	0.992077i	$0.459904\pi$
$242$	19.2569i	1.23788i
$243$	− 1.00000i	− 0.0641500i
$244$	−41.5607	−2.66065
$245$	0	0
$246$	6.90732	0.440395
$247$	− 38.9035i	− 2.47537i
$248$	35.5830i	2.25952i
$249$	−4.98952	−0.316198
$250$	0	0
$251$	−21.8389	−1.37846	−0.689230	−	0.724543i	$-0.742051\pi$
$251$	−21.8389	−1.37846	−0.689230	+	0.724543i	$0.742051\pi$
$252$	12.2674i	0.772776i
$253$	20.1674i	1.26791i
$254$	7.74869	0.486196
$255$	0	0
$256$	−27.6757	−1.72973
$257$	17.1453i	1.06949i	0.845012	+	0.534747i	$0.179593\pi$
$257$	17.1453i	1.06949i	−0.845012	+	0.534747i	$0.820407\pi$
$258$	− 3.18140i	− 0.198065i
$259$	−10.2789	−0.638697
$260$	0	0
$261$	3.30132	0.204347
$262$	− 10.5082i	− 0.649201i
$263$	− 17.6266i	− 1.08690i	−0.839441	−	0.543451i	$-0.817117\pi$
$263$	− 17.6266i	− 1.08690i	0.839441	−	0.543451i	$-0.182883\pi$
$264$	17.7066	1.08977
$265$	0	0
$266$	−52.6084	−3.22563
$267$	− 1.94025i	− 0.118742i
$268$	0.154784i	0.00945492i
$269$	−1.94772	−0.118755	−0.0593773	−	0.998236i	$-0.518912\pi$
$269$	−1.94772	−0.118755	−0.0593773	+	0.998236i	$0.518912\pi$
$270$	0	0
$271$	−13.8707	−0.842583	−0.421292	−	0.906925i	$-0.638423\pi$
$271$	−13.8707	−0.842583	−0.421292	+	0.906925i	$0.638423\pi$
$272$	0.931016i	0.0564512i
$273$	− 19.4194i	− 1.17532i
$274$	−2.54290	−0.153622
$275$	0	0
$276$	17.0827	1.02826
$277$	− 26.4814i	− 1.59111i	−0.605880	−	0.795556i	$-0.707179\pi$
$277$	− 26.4814i	− 1.59111i	0.605880	−	0.795556i	$-0.292821\pi$
$278$	9.00654i	0.540177i
$279$	8.77495	0.525342
$280$	0	0
$281$	−21.6050	−1.28885	−0.644425	−	0.764668i	$-0.722903\pi$
$281$	−21.6050	−1.28885	−0.644425	+	0.764668i	$0.722903\pi$
$282$	− 26.4044i	− 1.57236i
$283$	2.05287i	0.122030i	0.998137	+	0.0610151i	$0.0194338\pi$
$283$	2.05287i	0.122030i	−0.998137	+	0.0610151i	$0.980566\pi$
$284$	59.9413	3.55686
$285$	0	0
$286$	−61.0315	−3.60887
$287$	9.59688i	0.566486i
$288$	2.66052i	0.156773i
$289$	16.8337	0.990216
$290$	0	0
$291$	5.99258	0.351291
$292$	19.8175i	1.15973i
$293$	− 11.9787i	− 0.699805i	−0.936786	−	0.349902i	$-0.886215\pi$
$293$	− 11.9787i	− 0.699805i	0.936786	−	0.349902i	$-0.113785\pi$
$294$	−9.55012	−0.556974
$295$	0	0
$296$	12.5671	0.730447
$297$	− 4.36655i	− 0.253373i
$298$	18.8132i	1.08982i
$299$	−27.0420	−1.56388
$300$	0	0
$301$	4.42016	0.254774
$302$	17.8187i	1.02535i
$303$	− 5.06181i	− 0.290793i
$304$	15.1684	0.869965
$305$	0	0
$306$	0.973567	0.0556551
$307$	7.07969i	0.404059i	0.979379	+	0.202030i	$0.0647538\pi$
$307$	7.07969i	0.404059i	−0.979379	+	0.202030i	$0.935246\pi$
$308$	53.5664i	3.05223i
$309$	−6.90359	−0.392732
$310$	0	0
$311$	−11.4130	−0.647171	−0.323586	−	0.946199i	$-0.604888\pi$
$311$	−11.4130	−0.647171	−0.323586	+	0.946199i	$0.604888\pi$
$312$	23.7425i	1.34415i
$313$	11.9077i	0.673064i	0.941672	+	0.336532i	$0.109254\pi$
$313$	11.9077i	0.673064i	−0.941672	+	0.336532i	$0.890746\pi$
$314$	−0.642054	−0.0362332
$315$	0	0
$316$	−13.1440	−0.739407
$317$	− 12.7719i	− 0.717340i	−0.933465	−	0.358670i	$-0.883230\pi$
$317$	− 12.7719i	− 0.717340i	0.933465	−	0.358670i	$-0.116770\pi$
$318$	− 6.44592i	− 0.361469i
$319$	14.4154	0.807107
$320$	0	0
$321$	−17.2723	−0.964048
$322$	36.5683i	2.03787i
$323$	2.70981i	0.150778i
$324$	−3.69868	−0.205482
$325$	0	0
$326$	24.7065	1.36837
$327$	− 6.54439i	− 0.361906i
$328$	− 11.7333i	− 0.647863i
$329$	36.6857	2.02255
$330$	0	0
$331$	8.66041	0.476019	0.238010	−	0.971263i	$-0.423505\pi$
$331$	8.66041	0.476019	0.238010	+	0.971263i	$0.423505\pi$
$332$	18.4546i	1.01283i
$333$	− 3.09911i	− 0.169830i
$334$	10.1908	0.557617
$335$	0	0
$336$	7.57157	0.413063
$337$	15.2564i	0.831069i	0.909577	+	0.415534i	$0.136405\pi$
$337$	15.2564i	0.831069i	−0.909577	+	0.415534i	$0.863595\pi$
$338$	− 50.8025i	− 2.76329i
$339$	−8.66993	−0.470886
$340$	0	0
$341$	38.3163	2.07494
$342$	− 15.8616i	− 0.857697i
$343$	9.94824i	0.537155i
$344$	−5.40416	−0.291373
$345$	0	0
$346$	−56.1064	−3.01630
$347$	21.8540i	1.17319i	0.809882	+	0.586593i	$0.199531\pi$
$347$	21.8540i	1.17319i	−0.809882	+	0.586593i	$0.800469\pi$
$348$	− 12.2105i	− 0.654553i
$349$	−7.29614	−0.390553	−0.195277	−	0.980748i	$-0.562560\pi$
$349$	−7.29614	−0.390553	−0.195277	+	0.980748i	$0.562560\pi$
$350$	0	0
$351$	5.85502	0.312518
$352$	11.6173i	0.619203i
$353$	− 30.5320i	− 1.62506i	−0.582923	−	0.812528i	$-0.698091\pi$
$353$	− 30.5320i	− 1.62506i	0.582923	−	0.812528i	$-0.301909\pi$
$354$	13.8581	0.736548
$355$	0	0
$356$	−7.17637	−0.380347
$357$	1.35265i	0.0715900i
$358$	− 47.0031i	− 2.48419i
$359$	−3.06747	−0.161895	−0.0809473	−	0.996718i	$-0.525795\pi$
$359$	−3.06747	−0.161895	−0.0809473	+	0.996718i	$0.525795\pi$
$360$	0	0
$361$	25.1489	1.32363
$362$	− 30.6088i	− 1.60876i
$363$	− 8.06676i	− 0.423395i
$364$	−71.8261	−3.76471
$365$	0	0
$366$	26.8240	1.40211
$367$	31.6035i	1.64969i	0.565358	+	0.824845i	$0.308738\pi$
$367$	31.6035i	1.64969i	−0.565358	+	0.824845i	$0.691262\pi$
$368$	− 10.5436i	− 0.549623i
$369$	−2.89349	−0.150629
$370$	0	0
$371$	8.95582	0.464963
$372$	− 32.4557i	− 1.68275i
$373$	− 22.4904i	− 1.16451i	−0.813007	−	0.582254i	$-0.802171\pi$
$373$	− 22.4904i	− 1.16451i	0.813007	−	0.582254i	$-0.197829\pi$
$374$	4.25113	0.219821
$375$	0	0
$376$	−44.8525	−2.31309
$377$	19.3293i	0.995511i
$378$	− 7.91762i	− 0.407238i
$379$	−30.1612	−1.54928	−0.774638	−	0.632404i	$-0.782068\pi$
$379$	−30.1612	−1.54928	−0.774638	+	0.632404i	$0.782068\pi$
$380$	0	0
$381$	−3.24595	−0.166295
$382$	− 45.4959i	− 2.32777i
$383$	16.7725i	0.857034i	0.903534	+	0.428517i	$0.140964\pi$
$383$	16.7725i	0.857034i	−0.903534	+	0.428517i	$0.859036\pi$
$384$	20.7396	1.05836
$385$	0	0
$386$	40.5445	2.06366
$387$	1.33270i	0.0677447i
$388$	− 22.1646i	− 1.12524i
$389$	−22.4835	−1.13996	−0.569980	−	0.821659i	$-0.693049\pi$
$389$	−22.4835	−1.13996	−0.569980	+	0.821659i	$0.693049\pi$
$390$	0	0
$391$	1.88360	0.0952579
$392$	16.2226i	0.819363i
$393$	4.40192i	0.222048i
$394$	1.12069	0.0564598
$395$	0	0
$396$	−16.1505	−0.811591
$397$	− 3.65800i	− 0.183590i	−0.995778	−	0.0917948i	$-0.970740\pi$
$397$	− 3.65800i	− 0.183590i	0.995778	−	0.0917948i	$-0.0292604\pi$
$398$	− 16.7698i	− 0.840594i
$399$	22.0378	1.10327
$400$	0	0
$401$	−25.3774	−1.26729	−0.633643	−	0.773626i	$-0.718441\pi$
$401$	−25.3774	−1.26729	−0.633643	+	0.773626i	$0.718441\pi$
$402$	− 0.0999001i	− 0.00498256i
$403$	51.3775i	2.55930i
$404$	−18.7220	−0.931454
$405$	0	0
$406$	26.1386	1.29724
$407$	− 13.5324i	− 0.670777i
$408$	− 1.65378i	− 0.0818741i
$409$	27.8011	1.37468	0.687339	−	0.726337i	$-0.258779\pi$
$409$	27.8011	1.37468	0.687339	+	0.726337i	$0.258779\pi$
$410$	0	0
$411$	1.06523	0.0525438
$412$	25.5341i	1.25798i
$413$	19.2541i	0.947433i
$414$	−11.0255	−0.541873
$415$	0	0
$416$	−15.5774	−0.763745
$417$	− 3.77286i	− 0.184758i
$418$	− 69.2605i	− 3.38764i
$419$	0.119817	0.00585344	0.00292672	−	0.999996i	$-0.499068\pi$
$419$	0.119817	0.00585344	0.00292672	+	0.999996i	$0.499068\pi$
$420$	0	0
$421$	−0.0393633	−0.00191845	−0.000959225	−	1.00000i	$-0.500305\pi$
$421$	−0.0393633	−0.00191845	−0.000959225		1.00000i	$0.500305\pi$
$422$	37.6056i	1.83061i
$423$	11.0609i	0.537797i
$424$	−10.9495	−0.531756
$425$	0	0
$426$	−38.6872	−1.87440
$427$	37.2687i	1.80356i
$428$	63.8848i	3.08799i
$429$	25.5663	1.23435
$430$	0	0
$431$	16.3869	0.789328	0.394664	−	0.918825i	$-0.370861\pi$
$431$	16.3869	0.789328	0.394664	+	0.918825i	$0.370861\pi$
$432$	2.28286i	0.109834i
$433$	− 17.5610i	− 0.843930i	−0.906612	−	0.421965i	$-0.861340\pi$
$433$	− 17.5610i	− 0.843930i	0.906612	−	0.421965i	$-0.138660\pi$
$434$	69.4767	3.33499
$435$	0	0
$436$	−24.2056	−1.15924
$437$	− 30.6882i	− 1.46801i
$438$	− 12.7905i	− 0.611156i
$439$	31.1577	1.48708	0.743538	−	0.668694i	$-0.233146\pi$
$439$	31.1577	1.48708	0.743538	+	0.668694i	$0.233146\pi$
$440$	0	0
$441$	4.00057	0.190503
$442$	5.70026i	0.271134i
$443$	− 13.1787i	− 0.626141i	−0.949730	−	0.313071i	$-0.898642\pi$
$443$	− 13.1787i	− 0.626141i	0.949730	−	0.313071i	$-0.101358\pi$
$444$	−11.4626	−0.543991
$445$	0	0
$446$	−5.43555	−0.257381
$447$	− 7.88089i	− 0.372753i
$448$	36.2081i	1.71067i
$449$	29.2119	1.37859	0.689297	−	0.724479i	$-0.257920\pi$
$449$	29.2119	1.37859	0.689297	+	0.724479i	$0.257920\pi$
$450$	0	0
$451$	−12.6346	−0.594939
$452$	32.0673i	1.50832i
$453$	− 7.46432i	− 0.350704i
$454$	48.3822	2.27069
$455$	0	0
$456$	−26.9437	−1.26176
$457$	− 35.8001i	− 1.67466i	−0.546698	−	0.837330i	$-0.684115\pi$
$457$	− 35.8001i	− 1.67466i	0.546698	−	0.837330i	$-0.315885\pi$
$458$	− 46.8745i	− 2.19030i
$459$	−0.407830	−0.0190359
$460$	0	0
$461$	6.01315	0.280060	0.140030	−	0.990147i	$-0.455280\pi$
$461$	6.01315	0.280060	0.140030	+	0.990147i	$0.455280\pi$
$462$	− 34.5727i	− 1.60847i
$463$	− 41.2139i	− 1.91537i	−0.287813	−	0.957687i	$-0.592928\pi$
$463$	− 41.2139i	− 1.91537i	0.287813	−	0.957687i	$-0.407072\pi$
$464$	−7.53644	−0.349871
$465$	0	0
$466$	−40.9328	−1.89617
$467$	29.9663i	1.38667i	0.720614	+	0.693337i	$0.243860\pi$
$467$	29.9663i	1.38667i	−0.720614	+	0.693337i	$0.756140\pi$
$468$	− 21.6558i	− 1.00104i
$469$	0.138799	0.00640914
$470$	0	0
$471$	0.268958	0.0123929
$472$	− 23.5404i	− 1.08353i
$473$	5.81928i	0.267571i
$474$	8.48336	0.389653
$475$	0	0
$476$	5.00303	0.229313
$477$	2.70021i	0.123634i
$478$	− 51.9582i	− 2.37651i
$479$	−8.33937	−0.381036	−0.190518	−	0.981684i	$-0.561017\pi$
$479$	−8.33937	−0.381036	−0.190518	+	0.981684i	$0.561017\pi$
$480$	0	0
$481$	18.1454	0.827357
$482$	9.31165i	0.424134i
$483$	− 15.3186i	− 0.697019i
$484$	−29.8363	−1.35620
$485$	0	0
$486$	2.38719	0.108285
$487$	4.91110i	0.222543i	0.993790	+	0.111272i	$0.0354924\pi$
$487$	4.91110i	0.222543i	−0.993790	+	0.111272i	$0.964508\pi$
$488$	− 45.5653i	− 2.06264i
$489$	−10.3496	−0.468026
$490$	0	0
$491$	4.33484	0.195629	0.0978144	−	0.995205i	$-0.468815\pi$
$491$	4.33484	0.195629	0.0978144	+	0.995205i	$0.468815\pi$
$492$	10.7021i	0.482488i
$493$	− 1.34638i	− 0.0606378i
$494$	92.8701	4.17842
$495$	0	0
$496$	−20.0319	−0.899461
$497$	− 53.7511i	− 2.41107i
$498$	− 11.9109i	− 0.533742i
$499$	−36.1803	−1.61965	−0.809826	−	0.586671i	$-0.800438\pi$
$499$	−36.1803	−1.61965	−0.809826	+	0.586671i	$0.800438\pi$
$500$	0	0
$501$	−4.26896	−0.190723
$502$	− 52.1336i	− 2.32684i
$503$	− 37.3990i	− 1.66754i	−0.552113	−	0.833769i	$-0.686178\pi$
$503$	− 37.3990i	− 1.66754i	0.552113	−	0.833769i	$-0.313822\pi$
$504$	−13.4495	−0.599087
$505$	0	0
$506$	−48.1433	−2.14023
$507$	21.2813i	0.945135i
$508$	12.0057i	0.532667i
$509$	26.2959	1.16555	0.582773	−	0.812635i	$-0.301968\pi$
$509$	26.2959	1.16555	0.582773	+	0.812635i	$0.301968\pi$
$510$	0	0
$511$	17.7709	0.786138
$512$	− 24.5878i	− 1.08664i
$513$	6.64447i	0.293360i
$514$	−40.9291	−1.80530
$515$	0	0
$516$	4.92921	0.216996
$517$	48.2978i	2.12413i
$518$	− 24.5376i	− 1.07812i
$519$	23.5031	1.03167
$520$	0	0
$521$	7.02231	0.307653	0.153826	−	0.988098i	$-0.450840\pi$
$521$	7.02231	0.307653	0.153826	+	0.988098i	$0.450840\pi$
$522$	7.88089i	0.344937i
$523$	13.0796i	0.571933i	0.958240	+	0.285967i	$0.0923146\pi$
$523$	13.0796i	0.571933i	−0.958240	+	0.285967i	$0.907685\pi$
$524$	16.2813	0.711252
$525$	0	0
$526$	42.0780	1.83469
$527$	− 3.57869i	− 0.155890i
$528$	9.96820i	0.433810i
$529$	1.66851	0.0725437
$530$	0	0
$531$	−5.80518	−0.251923
$532$	− 81.5106i	− 3.53393i
$533$	− 16.9415i	− 0.733817i
$534$	4.63175	0.200436
$535$	0	0
$536$	−0.169698	−0.00732984
$537$	19.6897i	0.849675i
$538$	− 4.64958i	− 0.200458i
$539$	17.4687	0.752430
$540$	0	0
$541$	−2.08066	−0.0894546	−0.0447273	−	0.998999i	$-0.514242\pi$
$541$	−2.08066	−0.0894546	−0.0447273	+	0.998999i	$0.514242\pi$
$542$	− 33.1119i	− 1.42228i
$543$	12.8221i	0.550249i
$544$	1.08504	0.0465206
$545$	0	0
$546$	46.3578	1.98393
$547$	36.9553i	1.58009i	0.613047	+	0.790046i	$0.289944\pi$
$547$	36.9553i	1.58009i	−0.613047	+	0.790046i	$0.710056\pi$
$548$	− 3.93993i	− 0.168305i
$549$	−11.2366	−0.479568
$550$	0	0
$551$	−21.9355	−0.934485
$552$	18.7287i	0.797148i
$553$	11.7866i	0.501217i
$554$	63.2161	2.68579
$555$	0	0
$556$	−13.9546	−0.591807
$557$	2.67455i	0.113324i	0.998393	+	0.0566621i	$0.0180458\pi$
$557$	2.67455i	0.113324i	−0.998393	+	0.0566621i	$0.981954\pi$
$558$	20.9475i	0.886777i
$559$	−7.80296	−0.330030
$560$	0	0
$561$	−1.78081	−0.0751858
$562$	− 51.5754i	− 2.17557i
$563$	13.8746i	0.584745i	0.956305	+	0.292372i	$0.0944447\pi$
$563$	13.8746i	0.584745i	−0.956305	+	0.292372i	$0.905555\pi$
$564$	40.9105	1.72264
$565$	0	0
$566$	−4.90058	−0.205987
$567$	3.31671i	0.139289i
$568$	65.7170i	2.75742i
$569$	−33.3404	−1.39770	−0.698852	−	0.715266i	$-0.746305\pi$
$569$	−33.3404	−1.39770	−0.698852	+	0.715266i	$0.746305\pi$
$570$	0	0
$571$	35.3794	1.48058	0.740291	−	0.672287i	$-0.234688\pi$
$571$	35.3794	1.48058	0.740291	+	0.672287i	$0.234688\pi$
$572$	− 94.5613i	− 3.95381i
$573$	19.0583i	0.796174i
$574$	−22.9096	−0.956227
$575$	0	0
$576$	−10.9169	−0.454870
$577$	− 16.6041i	− 0.691239i	−0.938375	−	0.345620i	$-0.887669\pi$
$577$	− 16.6041i	− 0.691239i	0.938375	−	0.345620i	$-0.112331\pi$
$578$	40.1852i	1.67148i
$579$	−16.9842	−0.705839
$580$	0	0
$581$	16.5488	0.686560
$582$	14.3054i	0.592979i
$583$	11.7906i	0.488317i
$584$	−21.7270	−0.899069
$585$	0	0
$586$	28.5955	1.18127
$587$	26.9696i	1.11315i	0.830796	+	0.556576i	$0.187885\pi$
$587$	26.9696i	1.11315i	−0.830796	+	0.556576i	$0.812115\pi$
$588$	− 14.7968i	− 0.610210i
$589$	−58.3049	−2.40241
$590$	0	0
$591$	−0.469462	−0.0193111
$592$	7.07482i	0.290773i
$593$	12.7895i	0.525201i	0.964905	+	0.262600i	$0.0845801\pi$
$593$	12.7895i	0.525201i	−0.964905	+	0.262600i	$0.915420\pi$
$594$	10.4238	0.427693
$595$	0	0
$596$	−29.1489	−1.19398
$597$	7.02491i	0.287511i
$598$	− 64.5545i	− 2.63983i
$599$	−31.1978	−1.27471	−0.637354	−	0.770571i	$-0.719971\pi$
$599$	−31.1978	−1.27471	−0.637354	+	0.770571i	$0.719971\pi$
$600$	0	0
$601$	19.2310	0.784450	0.392225	−	0.919869i	$-0.371705\pi$
$601$	19.2310	0.784450	0.392225	+	0.919869i	$0.371705\pi$
$602$	10.5518i	0.430058i
$603$	0.0418484i	0.00170420i
$604$	−27.6081	−1.12336
$605$	0	0
$606$	12.0835	0.490858
$607$	8.01104i	0.325158i	0.986696	+	0.162579i	$0.0519813\pi$
$607$	8.01104i	0.325158i	−0.986696	+	0.162579i	$0.948019\pi$
$608$	− 17.6777i	− 0.716926i
$609$	−10.9495	−0.443698
$610$	0	0
$611$	−64.7616	−2.61997
$612$	1.50843i	0.0609747i
$613$	11.3203i	0.457224i	0.973518	+	0.228612i	$0.0734187\pi$
$613$	11.3203i	0.457224i	−0.973518	+	0.228612i	$0.926581\pi$
$614$	−16.9006	−0.682052
$615$	0	0
$616$	−58.7278	−2.36621
$617$	9.71325i	0.391041i	0.980700	+	0.195520i	$0.0626396\pi$
$617$	9.71325i	0.391041i	−0.980700	+	0.195520i	$0.937360\pi$
$618$	− 16.4802i	− 0.662930i
$619$	−20.4652	−0.822567	−0.411284	−	0.911507i	$-0.634919\pi$
$619$	−20.4652	−0.822567	−0.411284	+	0.911507i	$0.634919\pi$
$620$	0	0
$621$	4.61860	0.185338
$622$	− 27.2450i	− 1.09242i
$623$	6.43526i	0.257823i
$624$	−13.3662	−0.535075
$625$	0	0
$626$	−28.4260	−1.13613
$627$	29.0134i	1.15868i
$628$	− 0.994789i	− 0.0396964i
$629$	−1.26391	−0.0503954
$630$	0	0
$631$	2.46405	0.0980924	0.0490462	−	0.998797i	$-0.484382\pi$
$631$	2.46405	0.0980924	0.0490462	+	0.998797i	$0.484382\pi$
$632$	− 14.4105i	− 0.573218i
$633$	− 15.7531i	− 0.626128i
$634$	30.4889	1.21087
$635$	0	0
$636$	9.98721	0.396019
$637$	23.4234i	0.928070i
$638$	34.4123i	1.36240i
$639$	16.2062	0.641106
$640$	0	0
$641$	31.7217	1.25293	0.626465	−	0.779449i	$-0.284501\pi$
$641$	31.7217	1.25293	0.626465	+	0.779449i	$0.284501\pi$
$642$	− 41.2323i	− 1.62731i
$643$	− 11.5574i	− 0.455779i	−0.973687	−	0.227889i	$-0.926818\pi$
$643$	− 11.5574i	− 0.455779i	0.973687	−	0.227889i	$-0.0731824\pi$
$644$	−56.6584	−2.23266
$645$	0	0
$646$	−6.46883	−0.254513
$647$	− 6.06222i	− 0.238330i	−0.992874	−	0.119165i	$-0.961978\pi$
$647$	− 6.06222i	− 0.238330i	0.992874	−	0.119165i	$-0.0380218\pi$
$648$	− 4.05506i	− 0.159298i
$649$	−25.3486	−0.995021
$650$	0	0
$651$	−29.1040	−1.14067
$652$	38.2799i	1.49916i
$653$	26.3569i	1.03143i	0.856762	+	0.515713i	$0.172473\pi$
$653$	26.3569i	1.03143i	−0.856762	+	0.515713i	$0.827527\pi$
$654$	15.6227	0.610896
$655$	0	0
$656$	6.60543	0.257899
$657$	5.35799i	0.209035i
$658$	87.5756i	3.41405i
$659$	−16.2879	−0.634487	−0.317243	−	0.948344i	$-0.602757\pi$
$659$	−16.2879	−0.634487	−0.317243	+	0.948344i	$0.602757\pi$
$660$	0	0
$661$	−20.4308	−0.794665	−0.397332	−	0.917675i	$-0.630064\pi$
$661$	−20.4308	−0.794665	−0.397332	+	0.917675i	$0.630064\pi$
$662$	20.6740i	0.803519i
$663$	− 2.38785i	− 0.0927365i
$664$	−20.2328	−0.785186
$665$	0	0
$666$	7.39817	0.286673
$667$	15.2475i	0.590386i
$668$	15.7895i	0.610914i
$669$	2.27697	0.0880326
$670$	0	0
$671$	−49.0653	−1.89415
$672$	− 8.82417i	− 0.340400i
$673$	− 20.7479i	− 0.799772i	−0.916565	−	0.399886i	$-0.869050\pi$
$673$	− 20.7479i	− 0.799772i	0.916565	−	0.399886i	$-0.130950\pi$
$674$	−36.4199	−1.40284
$675$	0	0
$676$	78.7126	3.02741
$677$	− 20.1892i	− 0.775935i	−0.921673	−	0.387967i	$-0.873177\pi$
$677$	− 20.1892i	− 0.775935i	0.921673	−	0.387967i	$-0.126823\pi$
$678$	− 20.6968i	− 0.794855i
$679$	−19.8756	−0.762757
$680$	0	0
$681$	−20.2674	−0.776650
$682$	91.4682i	3.50250i
$683$	− 6.69431i	− 0.256151i	−0.991764	−	0.128075i	$-0.959120\pi$
$683$	− 6.69431i	− 0.256151i	0.991764	−	0.128075i	$-0.0408799\pi$
$684$	24.5757	0.939677
$685$	0	0
$686$	−23.7484	−0.906716
$687$	19.6358i	0.749154i
$688$	− 3.04235i	− 0.115989i
$689$	−15.8098	−0.602306
$690$	0	0
$691$	−7.86690	−0.299271	−0.149635	−	0.988741i	$-0.547810\pi$
$691$	−7.86690	−0.299271	−0.149635	+	0.988741i	$0.547810\pi$
$692$	− 86.9304i	− 3.30460i
$693$	14.4826i	0.550148i
$694$	−52.1697	−1.98034
$695$	0	0
$696$	13.3871	0.507436
$697$	1.18005i	0.0446977i
$698$	− 17.4173i	− 0.659254i
$699$	17.1468	0.648553
$700$	0	0
$701$	11.5944	0.437916	0.218958	−	0.975734i	$-0.429734\pi$
$701$	11.5944	0.437916	0.218958	+	0.975734i	$0.429734\pi$
$702$	13.9771i	0.527530i
$703$	20.5919i	0.776640i
$704$	−47.6691	−1.79660
$705$	0	0
$706$	72.8857	2.74309
$707$	16.7885i	0.631398i
$708$	21.4715i	0.806948i
$709$	−37.6176	−1.41276	−0.706379	−	0.707834i	$-0.749673\pi$
$709$	−37.6176	−1.41276	−0.706379	+	0.707834i	$0.749673\pi$
$710$	0	0
$711$	−3.55370	−0.133274
$712$	− 7.86785i	− 0.294860i
$713$	40.5280i	1.51779i
$714$	−3.22904	−0.120844
$715$	0	0
$716$	72.8260	2.72163
$717$	21.7654i	0.812845i
$718$	− 7.32263i	− 0.273278i
$719$	21.0855	0.786355	0.393177	−	0.919463i	$-0.371376\pi$
$719$	21.0855	0.786355	0.393177	+	0.919463i	$0.371376\pi$
$720$	0	0
$721$	22.8972	0.852737
$722$	60.0353i	2.23428i
$723$	− 3.90067i	− 0.145068i
$724$	47.4248	1.76253
$725$	0	0
$726$	19.2569	0.714690
$727$	− 26.1113i	− 0.968416i	−0.874953	−	0.484208i	$-0.839108\pi$
$727$	− 26.1113i	− 0.968416i	0.874953	−	0.484208i	$-0.160892\pi$
$728$	− 78.7470i	− 2.91856i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	0.543513	0.0201025
$732$	41.5607i	1.53613i
$733$	13.4461i	0.496642i	0.968678	+	0.248321i	$0.0798788\pi$
$733$	13.4461i	0.496642i	−0.968678	+	0.248321i	$0.920121\pi$
$734$	−75.4436	−2.78468
$735$	0	0
$736$	−12.2879	−0.452937
$737$	0.182733i	0.00673106i
$738$	− 6.90732i	− 0.254262i
$739$	53.9014	1.98279	0.991397	−	0.130887i	$-0.0417824\pi$
$739$	53.9014	1.98279	0.991397	+	0.130887i	$0.0417824\pi$
$740$	0	0
$741$	−38.9035	−1.42916
$742$	21.3793i	0.784857i
$743$	4.33521i	0.159043i	0.996833	+	0.0795216i	$0.0253393\pi$
$743$	4.33521i	0.159043i	−0.996833	+	0.0795216i	$0.974661\pi$
$744$	35.5830	1.30454
$745$	0	0
$746$	53.6888	1.96569
$747$	4.98952i	0.182557i
$748$	6.58664i	0.240831i
$749$	57.2873	2.09323
$750$	0	0
$751$	−2.87653	−0.104966	−0.0524831	−	0.998622i	$-0.516714\pi$
$751$	−2.87653	−0.104966	−0.0524831	+	0.998622i	$0.516714\pi$
$752$	− 25.2503i	− 0.920785i
$753$	21.8389i	0.795854i
$754$	−46.1428	−1.68042
$755$	0	0
$756$	12.2674	0.446162
$757$	16.0480i	0.583275i	0.956529	+	0.291637i	$0.0942000\pi$
$757$	16.0480i	0.583275i	−0.956529	+	0.291637i	$0.905800\pi$
$758$	− 72.0005i	− 2.61518i
$759$	20.1674	0.732029
$760$	0	0
$761$	−43.5182	−1.57753	−0.788767	−	0.614692i	$-0.789280\pi$
$761$	−43.5182	−1.57753	−0.788767	+	0.614692i	$0.789280\pi$
$762$	− 7.74869i	− 0.280706i
$763$	21.7058i	0.785804i
$764$	70.4907	2.55026
$765$	0	0
$766$	−40.0391	−1.44667
$767$	− 33.9895i	− 1.22729i
$768$	27.6757i	0.998659i
$769$	25.9575	0.936052	0.468026	−	0.883715i	$-0.344965\pi$
$769$	25.9575	0.936052	0.468026	+	0.883715i	$0.344965\pi$
$770$	0	0
$771$	17.1453	0.617473
$772$	62.8191i	2.26091i
$773$	− 52.9965i	− 1.90615i	−0.302731	−	0.953076i	$-0.597898\pi$
$773$	− 52.9965i	− 1.90615i	0.302731	−	0.953076i	$-0.402102\pi$
$774$	−3.18140	−0.114353
$775$	0	0
$776$	24.3003	0.872329
$777$	10.2789i	0.368752i
$778$	− 53.6724i	− 1.92425i
$779$	19.2257	0.688833
$780$	0	0
$781$	70.7650	2.53217
$782$	4.49652i	0.160795i
$783$	− 3.30132i	− 0.117980i
$784$	−9.13272	−0.326169
$785$	0	0
$786$	−10.5082	−0.374816
$787$	13.1832i	0.469929i	0.972004	+	0.234964i	$0.0754974\pi$
$787$	13.1832i	0.469929i	−0.972004	+	0.234964i	$0.924503\pi$
$788$	1.73639i	0.0618562i
$789$	−17.6266	−0.627523
$790$	0	0
$791$	28.7557	1.02243
$792$	− 17.7066i	− 0.629178i
$793$	− 65.7908i	− 2.33630i
$794$	8.73233	0.309899
$795$	0	0
$796$	25.9829	0.920939
$797$	− 15.6197i	− 0.553280i	−0.960974	−	0.276640i	$-0.910779\pi$
$797$	− 15.6197i	− 0.553280i	0.960974	−	0.276640i	$-0.0892209\pi$
$798$	52.6084i	1.86232i
$799$	4.51095	0.159586
$800$	0	0
$801$	−1.94025	−0.0685555
$802$	− 60.5806i	− 2.13918i
$803$	23.3959i	0.825625i
$804$	0.154784	0.00545880
$805$	0	0
$806$	−122.648	−4.32009
$807$	1.94772i	0.0685630i
$808$	− 20.5259i	− 0.722100i
$809$	−11.7683	−0.413750	−0.206875	−	0.978367i	$-0.566329\pi$
$809$	−11.7683	−0.413750	−0.206875	+	0.978367i	$0.566329\pi$
$810$	0	0
$811$	−38.3050	−1.34507	−0.672536	−	0.740065i	$-0.734795\pi$
$811$	−38.3050	−1.34507	−0.672536	+	0.740065i	$0.734795\pi$
$812$	40.4988i	1.42123i
$813$	13.8707i	0.486466i
$814$	32.3045	1.13227
$815$	0	0
$816$	0.931016	0.0325921
$817$	− 8.85505i	− 0.309799i
$818$	66.3666i	2.32045i
$819$	−19.4194	−0.678569
$820$	0	0
$821$	22.4713	0.784254	0.392127	−	0.919911i	$-0.371739\pi$
$821$	22.4713	0.784254	0.392127	+	0.919911i	$0.371739\pi$
$822$	2.54290i	0.0886938i
$823$	19.8645i	0.692434i	0.938155	+	0.346217i	$0.112534\pi$
$823$	19.8645i	0.692434i	−0.938155	+	0.346217i	$0.887466\pi$
$824$	−27.9945	−0.975235
$825$	0	0
$826$	−45.9632	−1.59927
$827$	− 21.4039i	− 0.744288i	−0.928175	−	0.372144i	$-0.878623\pi$
$827$	− 21.4039i	− 0.744288i	0.928175	−	0.372144i	$-0.121377\pi$
$828$	− 17.0827i	− 0.593666i
$829$	24.6676	0.856743	0.428371	−	0.903603i	$-0.359088\pi$
$829$	24.6676	0.856743	0.428371	+	0.903603i	$0.359088\pi$
$830$	0	0
$831$	−26.4814	−0.918629
$832$	− 63.9185i	− 2.21598i
$833$	− 1.63155i	− 0.0565299i
$834$	9.00654	0.311871
$835$	0	0
$836$	107.311	3.71143
$837$	− 8.77495i	− 0.303307i
$838$	0.286026i	0.00988060i
$839$	4.60054	0.158828	0.0794142	−	0.996842i	$-0.474695\pi$
$839$	4.60054	0.158828	0.0794142	+	0.996842i	$0.474695\pi$
$840$	0	0
$841$	−18.1013	−0.624182
$842$	− 0.0939677i	− 0.00323834i
$843$	21.6050i	0.744117i
$844$	−58.2655	−2.00558
$845$	0	0
$846$	−26.4044	−0.907801
$847$	26.7551i	0.919317i
$848$	− 6.16419i	− 0.211679i
$849$	2.05287	0.0704542
$850$	0	0
$851$	14.3136	0.490663
$852$	− 59.9413i	− 2.05356i
$853$	− 27.1689i	− 0.930245i	−0.885246	−	0.465122i	$-0.846010\pi$
$853$	− 27.1689i	− 0.930245i	0.885246	−	0.465122i	$-0.153990\pi$
$854$	−88.9674	−3.04440
$855$	0	0
$856$	−70.0404	−2.39393
$857$	− 7.66692i	− 0.261897i	−0.991389	−	0.130949i	$-0.958198\pi$
$857$	− 7.66692i	− 0.261897i	0.991389	−	0.130949i	$-0.0418023\pi$
$858$	61.0315i	2.08358i
$859$	−9.09944	−0.310469	−0.155234	−	0.987878i	$-0.549613\pi$
$859$	−9.09944	−0.310469	−0.155234	+	0.987878i	$0.549613\pi$
$860$	0	0
$861$	9.59688	0.327061
$862$	39.1186i	1.33238i
$863$	21.7471i	0.740279i	0.928976	+	0.370140i	$0.120690\pi$
$863$	21.7471i	0.740279i	−0.928976	+	0.370140i	$0.879310\pi$
$864$	2.66052	0.0905127
$865$	0	0
$866$	41.9216	1.42455
$867$	− 16.8337i	− 0.571702i
$868$	107.646i	3.65375i
$869$	−15.5174	−0.526392
$870$	0	0
$871$	−0.245023	−0.00830230
$872$	− 26.5379i	− 0.898687i
$873$	− 5.99258i	− 0.202818i
$874$	73.2585	2.47800
$875$	0	0
$876$	19.8175	0.669570
$877$	20.9781i	0.708379i	0.935174	+	0.354190i	$0.115243\pi$
$877$	20.9781i	0.708379i	−0.935174	+	0.354190i	$0.884757\pi$
$878$	74.3794i	2.51018i
$879$	−11.9787	−0.404032
$880$	0	0
$881$	40.6001	1.36785	0.683927	−	0.729551i	$-0.260271\pi$
$881$	40.6001	1.36785	0.683927	+	0.729551i	$0.260271\pi$
$882$	9.55012i	0.321569i
$883$	− 44.2689i	− 1.48977i	−0.667195	−	0.744883i	$-0.732505\pi$
$883$	− 44.2689i	− 1.48977i	0.667195	−	0.744883i	$-0.267495\pi$
$884$	−8.83189	−0.297049
$885$	0	0
$886$	31.4602	1.05693
$887$	− 21.2137i	− 0.712285i	−0.934432	−	0.356142i	$-0.884092\pi$
$887$	− 21.2137i	− 0.712285i	0.934432	−	0.356142i	$-0.115908\pi$
$888$	− 12.5671i	− 0.421724i
$889$	10.7659	0.361076
$890$	0	0
$891$	−4.36655	−0.146285
$892$	− 8.42177i	− 0.281982i
$893$	− 73.4935i	− 2.45937i
$894$	18.8132	0.629207
$895$	0	0
$896$	−68.7873	−2.29802
$897$	27.0420i	0.902907i
$898$	69.7343i	2.32706i
$899$	28.9689	0.966168
$900$	0	0
$901$	1.10123	0.0366872
$902$	− 30.1612i	− 1.00426i
$903$	− 4.42016i	− 0.147094i
$904$	−35.1571	−1.16931
$905$	0	0
$906$	17.8187	0.591988
$907$	42.8598i	1.42314i	0.702617	+	0.711568i	$0.252015\pi$
$907$	42.8598i	1.42314i	−0.702617	+	0.711568i	$0.747985\pi$
$908$	74.9627i	2.48772i
$909$	−5.06181	−0.167890
$910$	0	0
$911$	52.6870	1.74560	0.872800	−	0.488078i	$-0.162302\pi$
$911$	52.6870	1.74560	0.872800	+	0.488078i	$0.162302\pi$
$912$	− 15.1684i	− 0.502274i
$913$	21.7870i	0.721045i
$914$	85.4617	2.82682
$915$	0	0
$916$	72.6266	2.39965
$917$	− 14.5999i	− 0.482131i
$918$	− 0.973567i	− 0.0321325i
$919$	17.5655	0.579434	0.289717	−	0.957112i	$-0.406439\pi$
$919$	17.5655	0.579434	0.289717	+	0.957112i	$0.406439\pi$
$920$	0	0
$921$	7.07969	0.233284
$922$	14.3545i	0.472741i
$923$	94.8874i	3.12326i
$924$	53.5664	1.76221
$925$	0	0
$926$	98.3855	3.23315
$927$	6.90359i	0.226744i
$928$	8.78323i	0.288324i
$929$	58.2546	1.91127	0.955636	−	0.294550i	$-0.0951699\pi$
$929$	58.2546	1.91127	0.955636	+	0.294550i	$0.0951699\pi$
$930$	0	0
$931$	−26.5816	−0.871178
$932$	− 63.4206i	− 2.07741i
$933$	11.4130i	0.373644i
$934$	−71.5352	−2.34070
$935$	0	0
$936$	23.7425	0.776048
$937$	− 21.6766i	− 0.708142i	−0.935218	−	0.354071i	$-0.884797\pi$
$937$	− 21.6766i	− 0.708142i	0.935218	−	0.354071i	$-0.115203\pi$
$938$	0.331340i	0.0108186i
$939$	11.9077	0.388594
$940$	0	0
$941$	−41.9457	−1.36739	−0.683695	−	0.729768i	$-0.739628\pi$
$941$	−41.9457	−1.36739	−0.683695	+	0.729768i	$0.739628\pi$
$942$	0.642054i	0.0209193i
$943$	− 13.3639i	− 0.435188i
$944$	13.2524	0.431329
$945$	0	0
$946$	−13.8917	−0.451659
$947$	40.0301i	1.30080i	0.759591	+	0.650401i	$0.225399\pi$
$947$	40.0301i	1.30080i	−0.759591	+	0.650401i	$0.774601\pi$
$948$	13.1440i	0.426897i
$949$	−31.3712	−1.01835
$950$	0	0
$951$	−12.7719	−0.414156
$952$	5.48510i	0.177773i
$953$	− 33.1969i	− 1.07535i	−0.843151	−	0.537677i	$-0.819302\pi$
$953$	− 33.1969i	− 1.07535i	0.843151	−	0.537677i	$-0.180698\pi$
$954$	−6.44592	−0.208694
$955$	0	0
$956$	80.5033	2.60366
$957$	− 14.4154i	− 0.465984i
$958$	− 19.9077i	− 0.643187i
$959$	−3.53305	−0.114088
$960$	0	0
$961$	45.9997	1.48386
$962$	43.3164i	1.39658i
$963$	17.2723i	0.556593i
$964$	−14.4273	−0.464673
$965$	0	0
$966$	36.5683	1.17657
$967$	− 20.5477i	− 0.660770i	−0.943846	−	0.330385i	$-0.892821\pi$
$967$	− 20.5477i	− 0.660770i	0.943846	−	0.330385i	$-0.107179\pi$
$968$	− 32.7112i	− 1.05138i
$969$	2.70981	0.0870517
$970$	0	0
$971$	20.4201	0.655312	0.327656	−	0.944797i	$-0.393741\pi$
$971$	20.4201	0.655312	0.327656	+	0.944797i	$0.393741\pi$
$972$	3.69868i	0.118635i
$973$	12.5135i	0.401164i
$974$	−11.7237	−0.375653
$975$	0	0
$976$	25.6516	0.821088
$977$	27.7767i	0.888655i	0.895864	+	0.444327i	$0.146557\pi$
$977$	27.7767i	0.888655i	−0.895864	+	0.444327i	$0.853443\pi$
$978$	− 24.7065i	− 0.790027i
$979$	−8.47221	−0.270773
$980$	0	0
$981$	−6.54439	−0.208946
$982$	10.3481i	0.330221i
$983$	− 15.7171i	− 0.501298i	−0.968078	−	0.250649i	$-0.919356\pi$
$983$	− 15.7171i	− 0.501298i	0.968078	−	0.250649i	$-0.0806439\pi$
$984$	−11.7333	−0.374044
$985$	0	0
$986$	3.21406	0.102357
$987$	− 36.6857i	− 1.16772i
$988$	143.891i	4.57780i
$989$	−6.15519	−0.195724
$990$	0	0
$991$	−6.18035	−0.196325	−0.0981627	−	0.995170i	$-0.531297\pi$
$991$	−6.18035	−0.196325	−0.0981627	+	0.995170i	$0.531297\pi$
$992$	23.3459i	0.741233i
$993$	− 8.66041i	− 0.274830i
$994$	128.314	4.06988
$995$	0	0
$996$	18.4546	0.584757
$997$	60.9412i	1.93003i	0.262200	+	0.965014i	$0.415552\pi$
$997$	60.9412i	1.93003i	−0.262200	+	0.965014i	$0.584448\pi$
$998$	− 86.3692i	− 2.73397i
$999$	−3.09911	−0.0980515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.e.1249.11		12
5.2	odd	4		1875.2.a.l.1.1	yes	6
5.3	odd	4		1875.2.a.i.1.6	✓	6
5.4	even	2	inner	1875.2.b.e.1249.2		12
15.2	even	4		5625.2.a.o.1.6		6
15.8	even	4		5625.2.a.r.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.6	✓	6	5.3	odd	4
1875.2.a.l.1.1	yes	6	5.2	odd	4
1875.2.b.e.1249.2		12	5.4	even	2	inner
1875.2.b.e.1249.11		12	1.1	even	1	trivial
5625.2.a.o.1.6		6	15.2	even	4
5625.2.a.r.1.1		6	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.38719i q^{2} -1.00000i q^{3} -3.69868 q^{4} +2.38719 q^{6} +3.31671i q^{7} -4.05506i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.38719i q^{2} -1.00000i q^{3} -3.69868 q^{4} +2.38719 q^{6} +3.31671i q^{7} -4.05506i q^{8} -1.00000 q^{9} -4.36655 q^{11} +3.69868i q^{12} -5.85502i q^{13} -7.91762 q^{14} +2.28286 q^{16} +0.407830i q^{17} -2.38719i q^{18} +6.64447 q^{19} +3.31671 q^{21} -10.4238i q^{22} -4.61860i q^{23} -4.05506 q^{24} +13.9771 q^{26} +1.00000i q^{27} -12.2674i q^{28} -3.30132 q^{29} -8.77495 q^{31} -2.66052i q^{32} +4.36655i q^{33} -0.973567 q^{34} +3.69868 q^{36} +3.09911i q^{37} +15.8616i q^{38} -5.85502 q^{39} +2.89349 q^{41} +7.91762i q^{42} -1.33270i q^{43} +16.1505 q^{44} +11.0255 q^{46} -11.0609i q^{47} -2.28286i q^{48} -4.00057 q^{49} +0.407830 q^{51} +21.6558i q^{52} -2.70021i q^{53} -2.38719 q^{54} +13.4495 q^{56} -6.64447i q^{57} -7.88089i q^{58} +5.80518 q^{59} +11.2366 q^{61} -20.9475i q^{62} -3.31671i q^{63} +10.9169 q^{64} -10.4238 q^{66} -0.0418484i q^{67} -1.50843i q^{68} -4.61860 q^{69} -16.2062 q^{71} +4.05506i q^{72} -5.35799i q^{73} -7.39817 q^{74} -24.5757 q^{76} -14.4826i q^{77} -13.9771i q^{78} +3.55370 q^{79} +1.00000 q^{81} +6.90732i q^{82} -4.98952i q^{83} -12.2674 q^{84} +3.18140 q^{86} +3.30132i q^{87} +17.7066i q^{88} +1.94025 q^{89} +19.4194 q^{91} +17.0827i q^{92} +8.77495i q^{93} +26.4044 q^{94} -2.66052 q^{96} +5.99258i q^{97} -9.55012i q^{98} +4.36655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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