LMFDB - Embedded newform 3750.2.c.e.1249.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3750,2,Mod(1249,3750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3750, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3750.1249"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,-8,0,0,-8,0,-20,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.5
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	3750.1249
Dual form			3750.2.c.e.1249.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -4.07768i q^{7} -1.00000i q^{8} -1.00000 q^{9} -3.28408 q^{11} -1.00000i q^{12} -5.42226i q^{13} +4.07768 q^{14} +1.00000 q^{16} +3.45965i q^{17} -1.00000i q^{18} -1.63522 q^{19} +4.07768 q^{21} -3.28408i q^{22} +0.611469i q^{23} +1.00000 q^{24} +5.42226 q^{26} -1.00000i q^{27} +4.07768i q^{28} +4.67447 q^{29} -8.30313 q^{31} +1.00000i q^{32} -3.28408i q^{33} -3.45965 q^{34} +1.00000 q^{36} +2.40102i q^{37} -1.63522i q^{38} +5.42226 q^{39} +2.93179 q^{41} +4.07768i q^{42} +8.64114i q^{43} +3.28408 q^{44} -0.611469 q^{46} +6.91460i q^{47} +1.00000i q^{48} -9.62750 q^{49} -3.45965 q^{51} +5.42226i q^{52} -6.79766i q^{53} +1.00000 q^{54} -4.07768 q^{56} -1.63522i q^{57} +4.67447i q^{58} +14.1766 q^{59} -12.5882 q^{61} -8.30313i q^{62} +4.07768i q^{63} -1.00000 q^{64} +3.28408 q^{66} +10.8742i q^{67} -3.45965i q^{68} -0.611469 q^{69} -9.06706 q^{71} +1.00000i q^{72} +9.10079i q^{73} -2.40102 q^{74} +1.63522 q^{76} +13.3914i q^{77} +5.42226i q^{78} +4.09602 q^{79} +1.00000 q^{81} +2.93179i q^{82} +7.13111i q^{83} -4.07768 q^{84} -8.64114 q^{86} +4.67447i q^{87} +3.28408i q^{88} -4.80307 q^{89} -22.1103 q^{91} -0.611469i q^{92} -8.30313i q^{93} -6.91460 q^{94} -1.00000 q^{96} -14.7598i q^{97} -9.62750i q^{98} +3.28408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{6} - 8 q^{9} - 20 q^{11} + 8 q^{14} + 8 q^{16} + 12 q^{19} + 8 q^{21} + 8 q^{24} + 4 q^{26} + 28 q^{29} - 36 q^{31} - 12 q^{34} + 8 q^{36} + 4 q^{39} - 28 q^{41} + 20 q^{44} + 8 q^{49}+ \cdots + 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^6 - 8 * q^9 - 20 * q^11 + 8 * q^14 + 8 * q^16 + 12 * q^19 + 8 * q^21 + 8 * q^24 + 4 * q^26 + 28 * q^29 - 36 * q^31 - 12 * q^34 + 8 * q^36 + 4 * q^39 - 28 * q^41 + 20 * q^44 + 8 * q^49 - 12 * q^51 + 8 * q^54 - 8 * q^56 + 40 * q^59 - 8 * q^64 + 20 * q^66 - 60 * q^71 - 4 * q^74 - 12 * q^76 + 56 * q^79 + 8 * q^81 - 8 * q^84 - 28 * q^86 + 56 * q^89 - 44 * q^91 - 20 * q^94 - 8 * q^96 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3750\mathbb{Z}\right)^\times$.

$n$	$2501$	$3127$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	− 4.07768i	− 1.54122i	−0.637307	−	0.770610i	$-0.719952\pi$
$7$	− 4.07768i	− 1.54122i	0.637307	−	0.770610i	$-0.280048\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.28408	−0.990187	−0.495094	−	0.868840i	$-0.664866\pi$
$11$	−3.28408	−0.990187	−0.495094	+	0.868840i	$0.664866\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 5.42226i	− 1.50386i	−0.659240	−	0.751932i	$-0.729122\pi$
$13$	− 5.42226i	− 1.50386i	0.659240	−	0.751932i	$-0.270878\pi$
$14$	4.07768	1.08981
$15$	0	0
$16$	1.00000	0.250000
$17$	3.45965i	0.839088i	0.907735	+	0.419544i	$0.137810\pi$
$17$	3.45965i	0.839088i	−0.907735	+	0.419544i	$0.862190\pi$
$18$	− 1.00000i	− 0.235702i
$19$	−1.63522	−0.375145	−0.187573	−	0.982251i	$-0.560062\pi$
$19$	−1.63522	−0.375145	−0.187573	+	0.982251i	$0.560062\pi$
$20$	0	0
$21$	4.07768	0.889823
$22$	− 3.28408i	− 0.700168i
$23$	0.611469i	0.127500i	0.997966	+	0.0637501i	$0.0203061\pi$
$23$	0.611469i	0.127500i	−0.997966	+	0.0637501i	$0.979694\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	5.42226	1.06339
$27$	− 1.00000i	− 0.192450i
$28$	4.07768i	0.770610i
$29$	4.67447	0.868028	0.434014	−	0.900906i	$-0.357097\pi$
$29$	4.67447	0.868028	0.434014	+	0.900906i	$0.357097\pi$
$30$	0	0
$31$	−8.30313	−1.49129	−0.745643	−	0.666346i	$-0.767858\pi$
$31$	−8.30313	−1.49129	−0.745643	+	0.666346i	$0.767858\pi$
$32$	1.00000i	0.176777i
$33$	− 3.28408i	− 0.571685i
$34$	−3.45965	−0.593325
$35$	0	0
$36$	1.00000	0.166667
$37$	2.40102i	0.394725i	0.980331	+	0.197362i	$0.0632376\pi$
$37$	2.40102i	0.394725i	−0.980331	+	0.197362i	$0.936762\pi$
$38$	− 1.63522i	− 0.265268i
$39$	5.42226	0.868256
$40$	0	0
$41$	2.93179	0.457868	0.228934	−	0.973442i	$-0.426476\pi$
$41$	2.93179	0.457868	0.228934	+	0.973442i	$0.426476\pi$
$42$	4.07768i	0.629200i
$43$	8.64114i	1.31776i	0.752247	+	0.658881i	$0.228970\pi$
$43$	8.64114i	1.31776i	−0.752247	+	0.658881i	$0.771030\pi$
$44$	3.28408	0.495094
$45$	0	0
$46$	−0.611469	−0.0901563
$47$	6.91460i	1.00860i	0.863529	+	0.504299i	$0.168249\pi$
$47$	6.91460i	1.00860i	−0.863529	+	0.504299i	$0.831751\pi$
$48$	1.00000i	0.144338i
$49$	−9.62750	−1.37536
$50$	0	0
$51$	−3.45965	−0.484448
$52$	5.42226i	0.751932i
$53$	− 6.79766i	− 0.933731i	−0.884328	−	0.466865i	$-0.845383\pi$
$53$	− 6.79766i	− 0.933731i	0.884328	−	0.466865i	$-0.154617\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−4.07768	−0.544903
$57$	− 1.63522i	− 0.216590i
$58$	4.67447i	0.613789i
$59$	14.1766	1.84564	0.922819	−	0.385234i	$-0.125879\pi$
$59$	14.1766	1.84564	0.922819	+	0.385234i	$0.125879\pi$
$60$	0	0
$61$	−12.5882	−1.61176	−0.805880	−	0.592079i	$-0.798307\pi$
$61$	−12.5882	−1.61176	−0.805880	+	0.592079i	$0.798307\pi$
$62$	− 8.30313i	− 1.05450i
$63$	4.07768i	0.513740i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	3.28408	0.404242
$67$	10.8742i	1.32849i	0.747513	+	0.664247i	$0.231248\pi$
$67$	10.8742i	1.32849i	−0.747513	+	0.664247i	$0.768752\pi$
$68$	− 3.45965i	− 0.419544i
$69$	−0.611469	−0.0736123
$70$	0	0
$71$	−9.06706	−1.07606	−0.538031	−	0.842925i	$-0.680832\pi$
$71$	−9.06706	−1.07606	−0.538031	+	0.842925i	$0.680832\pi$
$72$	1.00000i	0.117851i
$73$	9.10079i	1.06517i	0.846377	+	0.532584i	$0.178779\pi$
$73$	9.10079i	1.06517i	−0.846377	+	0.532584i	$0.821221\pi$
$74$	−2.40102	−0.279113
$75$	0	0
$76$	1.63522	0.187573
$77$	13.3914i	1.52610i
$78$	5.42226i	0.613950i
$79$	4.09602	0.460838	0.230419	−	0.973091i	$-0.425990\pi$
$79$	4.09602	0.460838	0.230419	+	0.973091i	$0.425990\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.93179i	0.323762i
$83$	7.13111i	0.782741i	0.920233	+	0.391370i	$0.127999\pi$
$83$	7.13111i	0.782741i	−0.920233	+	0.391370i	$0.872001\pi$
$84$	−4.07768	−0.444912
$85$	0	0
$86$	−8.64114	−0.931798
$87$	4.67447i	0.501156i
$88$	3.28408i	0.350084i
$89$	−4.80307	−0.509125	−0.254562	−	0.967056i	$-0.581931\pi$
$89$	−4.80307	−0.509125	−0.254562	+	0.967056i	$0.581931\pi$
$90$	0	0
$91$	−22.1103	−2.31779
$92$	− 0.611469i	− 0.0637501i
$93$	− 8.30313i	− 0.860994i
$94$	−6.91460	−0.713186
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 14.7598i	− 1.49863i	−0.662216	−	0.749313i	$-0.730384\pi$
$97$	− 14.7598i	− 1.49863i	0.662216	−	0.749313i	$-0.269616\pi$
$98$	− 9.62750i	− 0.972525i
$99$	3.28408	0.330062
$100$	0	0
$101$	−11.4846	−1.14276	−0.571381	−	0.820685i	$-0.693592\pi$
$101$	−11.4846	−1.14276	−0.571381	+	0.820685i	$0.693592\pi$
$102$	− 3.45965i	− 0.342556i
$103$	13.9549i	1.37502i	0.726177	+	0.687508i	$0.241295\pi$
$103$	13.9549i	1.37502i	−0.726177	+	0.687508i	$0.758705\pi$
$104$	−5.42226	−0.531696
$105$	0	0
$106$	6.79766	0.660247
$107$	8.35405i	0.807616i	0.914844	+	0.403808i	$0.132314\pi$
$107$	8.35405i	0.807616i	−0.914844	+	0.403808i	$0.867686\pi$
$108$	1.00000i	0.0962250i
$109$	−0.532633	−0.0510170	−0.0255085	−	0.999675i	$-0.508120\pi$
$109$	−0.532633	−0.0510170	−0.0255085	+	0.999675i	$0.508120\pi$
$110$	0	0
$111$	−2.40102	−0.227894
$112$	− 4.07768i	− 0.385305i
$113$	17.2272i	1.62060i	0.586016	+	0.810299i	$0.300695\pi$
$113$	17.2272i	1.62060i	−0.586016	+	0.810299i	$0.699305\pi$
$114$	1.63522	0.153152
$115$	0	0
$116$	−4.67447	−0.434014
$117$	5.42226i	0.501288i
$118$	14.1766i	1.30506i
$119$	14.1074	1.29322
$120$	0	0
$121$	−0.214825	−0.0195295
$122$	− 12.5882i	− 1.13969i
$123$	2.93179i	0.264350i
$124$	8.30313	0.745643
$125$	0	0
$126$	−4.07768	−0.363269
$127$	1.14765i	0.101837i	0.998703	+	0.0509187i	$0.0162149\pi$
$127$	1.14765i	0.101837i	−0.998703	+	0.0509187i	$0.983785\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−8.64114	−0.760810
$130$	0	0
$131$	−6.61907	−0.578311	−0.289156	−	0.957282i	$-0.593374\pi$
$131$	−6.61907	−0.578311	−0.289156	+	0.957282i	$0.593374\pi$
$132$	3.28408i	0.285842i
$133$	6.66791i	0.578181i
$134$	−10.8742	−0.939387
$135$	0	0
$136$	3.45965	0.296663
$137$	− 7.42175i	− 0.634083i	−0.948412	−	0.317041i	$-0.897311\pi$
$137$	− 7.42175i	− 0.634083i	0.948412	−	0.317041i	$-0.102689\pi$
$138$	− 0.611469i	− 0.0520517i
$139$	−5.30062	−0.449593	−0.224796	−	0.974406i	$-0.572172\pi$
$139$	−5.30062	−0.449593	−0.224796	+	0.974406i	$0.572172\pi$
$140$	0	0
$141$	−6.91460	−0.582314
$142$	− 9.06706i	− 0.760891i
$143$	17.8071i	1.48911i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−9.10079	−0.753187
$147$	− 9.62750i	− 0.794063i
$148$	− 2.40102i	− 0.197362i
$149$	4.79296	0.392655	0.196327	−	0.980538i	$-0.437098\pi$
$149$	4.79296	0.392655	0.196327	+	0.980538i	$0.437098\pi$
$150$	0	0
$151$	6.93533	0.564389	0.282195	−	0.959357i	$-0.408938\pi$
$151$	6.93533	0.564389	0.282195	+	0.959357i	$0.408938\pi$
$152$	1.63522i	0.132634i
$153$	− 3.45965i	− 0.279696i
$154$	−13.3914	−1.07911
$155$	0	0
$156$	−5.42226	−0.434128
$157$	7.51609i	0.599849i	0.953963	+	0.299925i	$0.0969615\pi$
$157$	7.51609i	0.599849i	−0.953963	+	0.299925i	$0.903038\pi$
$158$	4.09602i	0.325862i
$159$	6.79766	0.539090
$160$	0	0
$161$	2.49338	0.196506
$162$	1.00000i	0.0785674i
$163$	8.36717i	0.655368i	0.944787	+	0.327684i	$0.106268\pi$
$163$	8.36717i	0.655368i	−0.944787	+	0.327684i	$0.893732\pi$
$164$	−2.93179	−0.228934
$165$	0	0
$166$	−7.13111	−0.553481
$167$	8.94427i	0.692129i	0.938211	+	0.346064i	$0.112482\pi$
$167$	8.94427i	0.692129i	−0.938211	+	0.346064i	$0.887518\pi$
$168$	− 4.07768i	− 0.314600i
$169$	−16.4009	−1.26161
$170$	0	0
$171$	1.63522	0.125048
$172$	− 8.64114i	− 0.658881i
$173$	2.33905i	0.177835i	0.996039	+	0.0889174i	$0.0283407\pi$
$173$	2.33905i	0.177835i	−0.996039	+	0.0889174i	$0.971659\pi$
$174$	−4.67447	−0.354371
$175$	0	0
$176$	−3.28408	−0.247547
$177$	14.1766i	1.06558i
$178$	− 4.80307i	− 0.360006i
$179$	−6.02967	−0.450679	−0.225339	−	0.974280i	$-0.572349\pi$
$179$	−6.02967	−0.450679	−0.225339	+	0.974280i	$0.572349\pi$
$180$	0	0
$181$	16.5771	1.23217	0.616084	−	0.787681i	$-0.288718\pi$
$181$	16.5771	1.23217	0.616084	+	0.787681i	$0.288718\pi$
$182$	− 22.1103i	− 1.63892i
$183$	− 12.5882i	− 0.930550i
$184$	0.611469	0.0450781
$185$	0	0
$186$	8.30313	0.608815
$187$	− 11.3618i	− 0.830854i
$188$	− 6.91460i	− 0.504299i
$189$	−4.07768	−0.296608
$190$	0	0
$191$	9.96802	0.721261	0.360630	−	0.932709i	$-0.382562\pi$
$191$	9.96802	0.721261	0.360630	+	0.932709i	$0.382562\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 25.0735i	− 1.80483i	−0.430867	−	0.902416i	$-0.641792\pi$
$193$	− 25.0735i	− 1.80483i	0.430867	−	0.902416i	$-0.358208\pi$
$194$	14.7598	1.05969
$195$	0	0
$196$	9.62750	0.687679
$197$	− 26.8378i	− 1.91212i	−0.293176	−	0.956059i	$-0.594712\pi$
$197$	− 26.8378i	− 1.91212i	0.293176	−	0.956059i	$-0.405288\pi$
$198$	3.28408i	0.233389i
$199$	4.06114	0.287887	0.143943	−	0.989586i	$-0.454022\pi$
$199$	4.06114	0.287887	0.143943	+	0.989586i	$0.454022\pi$
$200$	0	0
$201$	−10.8742	−0.767006
$202$	− 11.4846i	− 0.808055i
$203$	− 19.0610i	− 1.33782i
$204$	3.45965	0.242224
$205$	0	0
$206$	−13.9549	−0.972283
$207$	− 0.611469i	− 0.0425001i
$208$	− 5.42226i	− 0.375966i
$209$	5.37019	0.371464
$210$	0	0
$211$	−4.35487	−0.299802	−0.149901	−	0.988701i	$-0.547895\pi$
$211$	−4.35487	−0.299802	−0.149901	+	0.988701i	$0.547895\pi$
$212$	6.79766i	0.466865i
$213$	− 9.06706i	− 0.621265i
$214$	−8.35405	−0.571071
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	33.8575i	2.29840i
$218$	− 0.532633i	− 0.0360745i
$219$	−9.10079	−0.614975
$220$	0	0
$221$	18.7591	1.26187
$222$	− 2.40102i	− 0.161146i
$223$	0.361875i	0.0242330i	0.999927	+	0.0121165i	$0.00385689\pi$
$223$	0.361875i	0.0242330i	−0.999927	+	0.0121165i	$0.996143\pi$
$224$	4.07768	0.272452
$225$	0	0
$226$	−17.2272	−1.14594
$227$	12.8576i	0.853392i	0.904395	+	0.426696i	$0.140323\pi$
$227$	12.8576i	0.853392i	−0.904395	+	0.426696i	$0.859677\pi$
$228$	1.63522i	0.108295i
$229$	16.5347	1.09264	0.546322	−	0.837575i	$-0.316027\pi$
$229$	16.5347	1.09264	0.546322	+	0.837575i	$0.316027\pi$
$230$	0	0
$231$	−13.3914	−0.881092
$232$	− 4.67447i	− 0.306894i
$233$	11.0706i	0.725260i	0.931933	+	0.362630i	$0.118121\pi$
$233$	11.0706i	0.725260i	−0.931933	+	0.362630i	$0.881879\pi$
$234$	−5.42226	−0.354464
$235$	0	0
$236$	−14.1766	−0.922819
$237$	4.09602i	0.266065i
$238$	14.1074i	0.914444i
$239$	5.58721	0.361407	0.180703	−	0.983538i	$-0.442163\pi$
$239$	5.58721	0.361407	0.180703	+	0.983538i	$0.442163\pi$
$240$	0	0
$241$	−14.8540	−0.956830	−0.478415	−	0.878134i	$-0.658788\pi$
$241$	−14.8540	−0.956830	−0.478415	+	0.878134i	$0.658788\pi$
$242$	− 0.214825i	− 0.0138095i
$243$	1.00000i	0.0641500i
$244$	12.5882	0.805880
$245$	0	0
$246$	−2.93179	−0.186924
$247$	8.86659i	0.564168i
$248$	8.30313i	0.527249i
$249$	−7.13111	−0.451916
$250$	0	0
$251$	−12.6802	−0.800368	−0.400184	−	0.916435i	$-0.631054\pi$
$251$	−12.6802	−0.800368	−0.400184	+	0.916435i	$0.631054\pi$
$252$	− 4.07768i	− 0.256870i
$253$	− 2.00811i	− 0.126249i
$254$	−1.14765	−0.0720100
$255$	0	0
$256$	1.00000	0.0625000
$257$	19.1916i	1.19714i	0.801071	+	0.598570i	$0.204264\pi$
$257$	19.1916i	1.19714i	−0.801071	+	0.598570i	$0.795736\pi$
$258$	− 8.64114i	− 0.537974i
$259$	9.79059	0.608357
$260$	0	0
$261$	−4.67447	−0.289343
$262$	− 6.61907i	− 0.408928i
$263$	− 29.4749i	− 1.81750i	−0.417339	−	0.908751i	$-0.637037\pi$
$263$	− 29.4749i	− 1.81750i	0.417339	−	0.908751i	$-0.362963\pi$
$264$	−3.28408	−0.202121
$265$	0	0
$266$	−6.66791	−0.408836
$267$	− 4.80307i	− 0.293943i
$268$	− 10.8742i	− 0.664247i
$269$	−21.9020	−1.33539	−0.667694	−	0.744436i	$-0.732719\pi$
$269$	−21.9020	−1.33539	−0.667694	+	0.744436i	$0.732719\pi$
$270$	0	0
$271$	−15.0831	−0.916233	−0.458116	−	0.888892i	$-0.651476\pi$
$271$	−15.0831	−0.916233	−0.458116	+	0.888892i	$0.651476\pi$
$272$	3.45965i	0.209772i
$273$	− 22.1103i	− 1.33817i
$274$	7.42175	0.448364
$275$	0	0
$276$	0.611469	0.0368061
$277$	2.58366i	0.155237i	0.996983	+	0.0776186i	$0.0247316\pi$
$277$	2.58366i	0.155237i	−0.996983	+	0.0776186i	$0.975268\pi$
$278$	− 5.30062i	− 0.317910i
$279$	8.30313	0.497095
$280$	0	0
$281$	−18.3980	−1.09753	−0.548766	−	0.835976i	$-0.684902\pi$
$281$	−18.3980	−1.09753	−0.548766	+	0.835976i	$0.684902\pi$
$282$	− 6.91460i	− 0.411758i
$283$	3.47464i	0.206546i	0.994653	+	0.103273i	$0.0329315\pi$
$283$	3.47464i	0.206546i	−0.994653	+	0.103273i	$0.967068\pi$
$284$	9.06706	0.538031
$285$	0	0
$286$	−17.8071	−1.05296
$287$	− 11.9549i	− 0.705675i
$288$	− 1.00000i	− 0.0589256i
$289$	5.03083	0.295931
$290$	0	0
$291$	14.7598	0.865233
$292$	− 9.10079i	− 0.532584i
$293$	− 15.8625i	− 0.926699i	−0.886176	−	0.463349i	$-0.846647\pi$
$293$	− 15.8625i	− 0.926699i	0.886176	−	0.463349i	$-0.153353\pi$
$294$	9.62750	0.561487
$295$	0	0
$296$	2.40102	0.139556
$297$	3.28408i	0.190562i
$298$	4.79296i	0.277649i
$299$	3.31555	0.191743
$300$	0	0
$301$	35.2358	2.03096
$302$	6.93533i	0.399084i
$303$	− 11.4846i	− 0.659774i
$304$	−1.63522	−0.0937863
$305$	0	0
$306$	3.45965	0.197775
$307$	− 25.4122i	− 1.45035i	−0.688565	−	0.725175i	$-0.741759\pi$
$307$	− 25.4122i	− 1.45035i	0.688565	−	0.725175i	$-0.258241\pi$
$308$	− 13.3914i	− 0.763048i
$309$	−13.9549	−0.793866
$310$	0	0
$311$	18.4445	1.04589	0.522947	−	0.852365i	$-0.324833\pi$
$311$	18.4445	1.04589	0.522947	+	0.852365i	$0.324833\pi$
$312$	− 5.42226i	− 0.306975i
$313$	21.9121i	1.23854i	0.785176	+	0.619272i	$0.212572\pi$
$313$	21.9121i	1.23854i	−0.785176	+	0.619272i	$0.787428\pi$
$314$	−7.51609	−0.424157
$315$	0	0
$316$	−4.09602	−0.230419
$317$	− 5.78671i	− 0.325014i	−0.986707	−	0.162507i	$-0.948042\pi$
$317$	− 5.78671i	− 0.325014i	0.986707	−	0.162507i	$-0.0519580\pi$
$318$	6.79766i	0.381194i
$319$	−15.3513	−0.859510
$320$	0	0
$321$	−8.35405	−0.466277
$322$	2.49338i	0.138951i
$323$	− 5.65729i	− 0.314780i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−8.36717	−0.463415
$327$	− 0.532633i	− 0.0294547i
$328$	− 2.93179i	− 0.161881i
$329$	28.1955	1.55447
$330$	0	0
$331$	−7.64365	−0.420133	−0.210066	−	0.977687i	$-0.567368\pi$
$331$	−7.64365	−0.420133	−0.210066	+	0.977687i	$0.567368\pi$
$332$	− 7.13111i	− 0.391370i
$333$	− 2.40102i	− 0.131575i
$334$	−8.94427	−0.489409
$335$	0	0
$336$	4.07768	0.222456
$337$	3.68904i	0.200955i	0.994939	+	0.100477i	$0.0320370\pi$
$337$	3.68904i	0.200955i	−0.994939	+	0.100477i	$0.967963\pi$
$338$	− 16.4009i	− 0.892092i
$339$	−17.2272	−0.935653
$340$	0	0
$341$	27.2681	1.47665
$342$	1.63522i	0.0884226i
$343$	10.7141i	0.578508i
$344$	8.64114	0.465899
$345$	0	0
$346$	−2.33905	−0.125748
$347$	3.63522i	0.195149i	0.995228	+	0.0975744i	$0.0311084\pi$
$347$	3.63522i	0.195149i	−0.995228	+	0.0975744i	$0.968892\pi$
$348$	− 4.67447i	− 0.250578i
$349$	−12.2270	−0.654496	−0.327248	−	0.944938i	$-0.606121\pi$
$349$	−12.2270	−0.654496	−0.327248	+	0.944938i	$0.606121\pi$
$350$	0	0
$351$	−5.42226	−0.289419
$352$	− 3.28408i	− 0.175042i
$353$	15.6641i	0.833714i	0.908972	+	0.416857i	$0.136868\pi$
$353$	15.6641i	0.833714i	−0.908972	+	0.416857i	$0.863132\pi$
$354$	−14.1766	−0.753478
$355$	0	0
$356$	4.80307	0.254562
$357$	14.1074i	0.746640i
$358$	− 6.02967i	− 0.318678i
$359$	−7.07176	−0.373233	−0.186617	−	0.982433i	$-0.559752\pi$
$359$	−7.07176	−0.373233	−0.186617	+	0.982433i	$0.559752\pi$
$360$	0	0
$361$	−16.3261	−0.859266
$362$	16.5771i	0.871274i
$363$	− 0.214825i	− 0.0112754i
$364$	22.1103	1.15889
$365$	0	0
$366$	12.5882	0.657998
$367$	− 26.7477i	− 1.39622i	−0.715992	−	0.698109i	$-0.754025\pi$
$367$	− 26.7477i	− 1.39622i	0.715992	−	0.698109i	$-0.245975\pi$
$368$	0.611469i	0.0318751i
$369$	−2.93179	−0.152623
$370$	0	0
$371$	−27.7187	−1.43908
$372$	8.30313i	0.430497i
$373$	11.8848i	0.615372i	0.951488	+	0.307686i	$0.0995547\pi$
$373$	11.8848i	0.615372i	−0.951488	+	0.307686i	$0.900445\pi$
$374$	11.3618	0.587503
$375$	0	0
$376$	6.91460	0.356593
$377$	− 25.3462i	− 1.30540i
$378$	− 4.07768i	− 0.209733i
$379$	4.82558	0.247873	0.123937	−	0.992290i	$-0.460448\pi$
$379$	4.82558	0.247873	0.123937	+	0.992290i	$0.460448\pi$
$380$	0	0
$381$	−1.14765	−0.0587959
$382$	9.96802i	0.510008i
$383$	− 4.80351i	− 0.245448i	−0.992441	−	0.122724i	$-0.960837\pi$
$383$	− 4.80351i	− 0.245448i	0.992441	−	0.122724i	$-0.0391630\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	25.0735	1.27621
$387$	− 8.64114i	− 0.439254i
$388$	14.7598i	0.749313i
$389$	13.4417	0.681522	0.340761	−	0.940150i	$-0.389315\pi$
$389$	13.4417	0.681522	0.340761	+	0.940150i	$0.389315\pi$
$390$	0	0
$391$	−2.11547	−0.106984
$392$	9.62750i	0.486262i
$393$	− 6.61907i	− 0.333888i
$394$	26.8378	1.35207
$395$	0	0
$396$	−3.28408	−0.165031
$397$	0.0866228i	0.00434747i	0.999998	+	0.00217374i	$0.000691923\pi$
$397$	0.0866228i	0.00434747i	−0.999998	+	0.00217374i	$0.999308\pi$
$398$	4.06114i	0.203567i
$399$	−6.66791	−0.333813
$400$	0	0
$401$	0.321141	0.0160370	0.00801851	−	0.999968i	$-0.497448\pi$
$401$	0.321141	0.0160370	0.00801851	+	0.999968i	$0.497448\pi$
$402$	− 10.8742i	− 0.542355i
$403$	45.0217i	2.24269i
$404$	11.4846	0.571381
$405$	0	0
$406$	19.0610	0.945983
$407$	− 7.88513i	− 0.390851i
$408$	3.45965i	0.171278i
$409$	−24.2346	−1.19832	−0.599162	−	0.800628i	$-0.704499\pi$
$409$	−24.2346	−1.19832	−0.599162	+	0.800628i	$0.704499\pi$
$410$	0	0
$411$	7.42175	0.366088
$412$	− 13.9549i	− 0.687508i
$413$	− 57.8077i	− 2.84453i
$414$	0.611469	0.0300521
$415$	0	0
$416$	5.42226	0.265848
$417$	− 5.30062i	− 0.259573i
$418$	5.37019i	0.262665i
$419$	−22.8254	−1.11509	−0.557546	−	0.830146i	$-0.688257\pi$
$419$	−22.8254	−1.11509	−0.557546	+	0.830146i	$0.688257\pi$
$420$	0	0
$421$	−39.1298	−1.90707	−0.953536	−	0.301279i	$-0.902586\pi$
$421$	−39.1298	−1.90707	−0.953536	+	0.301279i	$0.902586\pi$
$422$	− 4.35487i	− 0.211992i
$423$	− 6.91460i	− 0.336199i
$424$	−6.79766	−0.330124
$425$	0	0
$426$	9.06706	0.439301
$427$	51.3309i	2.48408i
$428$	− 8.35405i	− 0.403808i
$429$	−17.8071	−0.859736
$430$	0	0
$431$	24.6813	1.18886	0.594429	−	0.804148i	$-0.297378\pi$
$431$	24.6813	1.18886	0.594429	+	0.804148i	$0.297378\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 19.8779i	− 0.955269i	−0.878559	−	0.477634i	$-0.841494\pi$
$433$	− 19.8779i	− 0.955269i	0.878559	−	0.477634i	$-0.158506\pi$
$434$	−33.8575	−1.62521
$435$	0	0
$436$	0.532633	0.0255085
$437$	− 0.999887i	− 0.0478311i
$438$	− 9.10079i	− 0.434853i
$439$	−5.07227	−0.242086	−0.121043	−	0.992647i	$-0.538624\pi$
$439$	−5.07227	−0.242086	−0.121043	+	0.992647i	$0.538624\pi$
$440$	0	0
$441$	9.62750	0.458453
$442$	18.7591i	0.892280i
$443$	− 10.1873i	− 0.484015i	−0.970274	−	0.242008i	$-0.922194\pi$
$443$	− 10.1873i	− 0.484015i	0.970274	−	0.242008i	$-0.0778059\pi$
$444$	2.40102	0.113947
$445$	0	0
$446$	−0.361875	−0.0171353
$447$	4.79296i	0.226699i
$448$	4.07768i	0.192652i
$449$	−10.3653	−0.489169	−0.244585	−	0.969628i	$-0.578652\pi$
$449$	−10.3653	−0.489169	−0.244585	+	0.969628i	$0.578652\pi$
$450$	0	0
$451$	−9.62822	−0.453375
$452$	− 17.2272i	− 0.810299i
$453$	6.93533i	0.325850i
$454$	−12.8576	−0.603439
$455$	0	0
$456$	−1.63522	−0.0765762
$457$	− 4.06165i	− 0.189996i	−0.995477	−	0.0949980i	$-0.969716\pi$
$457$	− 4.06165i	− 0.189996i	0.995477	−	0.0949980i	$-0.0302845\pi$
$458$	16.5347i	0.772616i
$459$	3.45965	0.161483
$460$	0	0
$461$	6.76110	0.314896	0.157448	−	0.987527i	$-0.449673\pi$
$461$	6.76110	0.314896	0.157448	+	0.987527i	$0.449673\pi$
$462$	− 13.3914i	− 0.623026i
$463$	9.72184i	0.451812i	0.974149	+	0.225906i	$0.0725343\pi$
$463$	9.72184i	0.451812i	−0.974149	+	0.225906i	$0.927466\pi$
$464$	4.67447	0.217007
$465$	0	0
$466$	−11.0706	−0.512836
$467$	38.4021i	1.77704i	0.458842	+	0.888518i	$0.348264\pi$
$467$	38.4021i	1.77704i	−0.458842	+	0.888518i	$0.651736\pi$
$468$	− 5.42226i	− 0.250644i
$469$	44.3415	2.04750
$470$	0	0
$471$	−7.51609	−0.346323
$472$	− 14.1766i	− 0.652531i
$473$	− 28.3782i	− 1.30483i
$474$	−4.09602	−0.188137
$475$	0	0
$476$	−14.1074	−0.646610
$477$	6.79766i	0.311244i
$478$	5.58721i	0.255553i
$479$	−8.47735	−0.387340	−0.193670	−	0.981067i	$-0.562039\pi$
$479$	−8.47735	−0.387340	−0.193670	+	0.981067i	$0.562039\pi$
$480$	0	0
$481$	13.0189	0.593612
$482$	− 14.8540i	− 0.676581i
$483$	2.49338i	0.113453i
$484$	0.214825	0.00976477
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	28.9739i	1.31293i	0.754354	+	0.656467i	$0.227950\pi$
$487$	28.9739i	1.31293i	−0.754354	+	0.656467i	$0.772050\pi$
$488$	12.5882i	0.569843i
$489$	−8.36717	−0.378377
$490$	0	0
$491$	−10.2266	−0.461518	−0.230759	−	0.973011i	$-0.574121\pi$
$491$	−10.2266	−0.461518	−0.230759	+	0.973011i	$0.574121\pi$
$492$	− 2.93179i	− 0.132175i
$493$	16.1720i	0.728352i
$494$	−8.86659	−0.398927
$495$	0	0
$496$	−8.30313	−0.372822
$497$	36.9726i	1.65845i
$498$	− 7.13111i	− 0.319553i
$499$	23.0007	1.02965	0.514827	−	0.857294i	$-0.327856\pi$
$499$	23.0007	1.02965	0.514827	+	0.857294i	$0.327856\pi$
$500$	0	0
$501$	−8.94427	−0.399601
$502$	− 12.6802i	− 0.565946i
$503$	− 19.0511i	− 0.849447i	−0.905323	−	0.424724i	$-0.860371\pi$
$503$	− 19.0511i	− 0.849447i	0.905323	−	0.424724i	$-0.139629\pi$
$504$	4.07768	0.181634
$505$	0	0
$506$	2.00811	0.0892716
$507$	− 16.4009i	− 0.728390i
$508$	− 1.14765i	− 0.0509187i
$509$	23.7206	1.05140	0.525698	−	0.850671i	$-0.323804\pi$
$509$	23.7206	1.05140	0.525698	+	0.850671i	$0.323804\pi$
$510$	0	0
$511$	37.1101	1.64166
$512$	1.00000i	0.0441942i
$513$	1.63522i	0.0721967i
$514$	−19.1916	−0.846505
$515$	0	0
$516$	8.64114	0.380405
$517$	− 22.7081i	− 0.998701i
$518$	9.79059i	0.430174i
$519$	−2.33905	−0.102673
$520$	0	0
$521$	29.2425	1.28114	0.640569	−	0.767901i	$-0.278699\pi$
$521$	29.2425	1.28114	0.640569	+	0.767901i	$0.278699\pi$
$522$	− 4.67447i	− 0.204596i
$523$	19.3157i	0.844616i	0.906452	+	0.422308i	$0.138780\pi$
$523$	19.3157i	0.844616i	−0.906452	+	0.422308i	$0.861220\pi$
$524$	6.61907	0.289156
$525$	0	0
$526$	29.4749	1.28517
$527$	− 28.7259i	− 1.25132i
$528$	− 3.28408i	− 0.142921i
$529$	22.6261	0.983744
$530$	0	0
$531$	−14.1766	−0.615212
$532$	− 6.66791i	− 0.289091i
$533$	− 15.8969i	− 0.688571i
$534$	4.80307	0.207849
$535$	0	0
$536$	10.8742	0.469694
$537$	− 6.02967i	− 0.260200i
$538$	− 21.9020i	− 0.944262i
$539$	31.6175	1.36186
$540$	0	0
$541$	−32.2091	−1.38478	−0.692389	−	0.721524i	$-0.743442\pi$
$541$	−32.2091	−1.38478	−0.692389	+	0.721524i	$0.743442\pi$
$542$	− 15.0831i	− 0.647874i
$543$	16.5771i	0.711392i
$544$	−3.45965	−0.148331
$545$	0	0
$546$	22.1103	0.946232
$547$	22.2651i	0.951988i	0.879449	+	0.475994i	$0.157912\pi$
$547$	22.2651i	0.951988i	−0.879449	+	0.475994i	$0.842088\pi$
$548$	7.42175i	0.317041i
$549$	12.5882	0.537253
$550$	0	0
$551$	−7.64379	−0.325637
$552$	0.611469i	0.0260259i
$553$	− 16.7023i	− 0.710253i
$554$	−2.58366	−0.109769
$555$	0	0
$556$	5.30062	0.224796
$557$	15.1565i	0.642202i	0.947045	+	0.321101i	$0.104053\pi$
$557$	15.1565i	0.642202i	−0.947045	+	0.321101i	$0.895947\pi$
$558$	8.30313i	0.351500i
$559$	46.8545	1.98173
$560$	0	0
$561$	11.3618	0.479694
$562$	− 18.3980i	− 0.776073i
$563$	20.8210i	0.877499i	0.898609	+	0.438750i	$0.144579\pi$
$563$	20.8210i	0.877499i	−0.898609	+	0.438750i	$0.855421\pi$
$564$	6.91460	0.291157
$565$	0	0
$566$	−3.47464	−0.146050
$567$	− 4.07768i	− 0.171247i
$568$	9.06706i	0.380445i
$569$	−14.7556	−0.618586	−0.309293	−	0.950967i	$-0.600092\pi$
$569$	−14.7556	−0.618586	−0.309293	+	0.950967i	$0.600092\pi$
$570$	0	0
$571$	−5.05311	−0.211466	−0.105733	−	0.994395i	$-0.533719\pi$
$571$	−5.05311	−0.211466	−0.105733	+	0.994395i	$0.533719\pi$
$572$	− 17.8071i	− 0.744554i
$573$	9.96802i	0.416420i
$574$	11.9549	0.498988
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 5.49722i	− 0.228852i	−0.993432	−	0.114426i	$-0.963497\pi$
$577$	− 5.49722i	− 0.228852i	0.993432	−	0.114426i	$-0.0365029\pi$
$578$	5.03083i	0.209255i
$579$	25.0735	1.04202
$580$	0	0
$581$	29.0784	1.20638
$582$	14.7598i	0.611812i
$583$	22.3241i	0.924568i
$584$	9.10079	0.376593
$585$	0	0
$586$	15.8625	0.655275
$587$	42.3980i	1.74995i	0.484167	+	0.874975i	$0.339123\pi$
$587$	42.3980i	1.74995i	−0.484167	+	0.874975i	$0.660877\pi$
$588$	9.62750i	0.397032i
$589$	13.5774	0.559449
$590$	0	0
$591$	26.8378	1.10396
$592$	2.40102i	0.0986812i
$593$	− 6.76110i	− 0.277645i	−0.990317	−	0.138822i	$-0.955668\pi$
$593$	− 6.76110i	− 0.277645i	0.990317	−	0.138822i	$-0.0443317\pi$
$594$	−3.28408	−0.134747
$595$	0	0
$596$	−4.79296	−0.196327
$597$	4.06114i	0.166211i
$598$	3.31555i	0.135583i
$599$	−11.7740	−0.481074	−0.240537	−	0.970640i	$-0.577324\pi$
$599$	−11.7740	−0.481074	−0.240537	+	0.970640i	$0.577324\pi$
$600$	0	0
$601$	22.4353	0.915154	0.457577	−	0.889170i	$-0.348717\pi$
$601$	22.4353	0.915154	0.457577	+	0.889170i	$0.348717\pi$
$602$	35.2358i	1.43611i
$603$	− 10.8742i	− 0.442831i
$604$	−6.93533	−0.282195
$605$	0	0
$606$	11.4846	0.466531
$607$	33.0837i	1.34283i	0.741083	+	0.671413i	$0.234312\pi$
$607$	33.0837i	1.34283i	−0.741083	+	0.671413i	$0.765688\pi$
$608$	− 1.63522i	− 0.0663169i
$609$	19.0610	0.772392
$610$	0	0
$611$	37.4928	1.51679
$612$	3.45965i	0.139848i
$613$	15.2894i	0.617535i	0.951138	+	0.308767i	$0.0999165\pi$
$613$	15.2894i	0.617535i	−0.951138	+	0.308767i	$0.900084\pi$
$614$	25.4122	1.02555
$615$	0	0
$616$	13.3914	0.539556
$617$	− 10.6410i	− 0.428389i	−0.976791	−	0.214194i	$-0.931287\pi$
$617$	− 10.6410i	− 0.428389i	0.976791	−	0.214194i	$-0.0687126\pi$
$618$	− 13.9549i	− 0.561348i
$619$	−28.8152	−1.15818	−0.579090	−	0.815264i	$-0.696592\pi$
$619$	−28.8152	−1.15818	−0.579090	+	0.815264i	$0.696592\pi$
$620$	0	0
$621$	0.611469	0.0245374
$622$	18.4445i	0.739559i
$623$	19.5854i	0.784673i
$624$	5.42226	0.217064
$625$	0	0
$626$	−21.9121	−0.875783
$627$	5.37019i	0.214465i
$628$	− 7.51609i	− 0.299925i
$629$	−8.30668	−0.331209
$630$	0	0
$631$	20.2165	0.804806	0.402403	−	0.915463i	$-0.368175\pi$
$631$	20.2165	0.804806	0.402403	+	0.915463i	$0.368175\pi$
$632$	− 4.09602i	− 0.162931i
$633$	− 4.35487i	− 0.173091i
$634$	5.78671	0.229820
$635$	0	0
$636$	−6.79766	−0.269545
$637$	52.2028i	2.06835i
$638$	− 15.3513i	− 0.607766i
$639$	9.06706	0.358687
$640$	0	0
$641$	−50.0641	−1.97741	−0.988707	−	0.149860i	$-0.952118\pi$
$641$	−50.0641	−1.97741	−0.988707	+	0.149860i	$0.952118\pi$
$642$	− 8.35405i	− 0.329708i
$643$	11.8080i	0.465660i	0.972517	+	0.232830i	$0.0747986\pi$
$643$	11.8080i	0.465660i	−0.972517	+	0.232830i	$0.925201\pi$
$644$	−2.49338	−0.0982529
$645$	0	0
$646$	5.65729	0.222583
$647$	29.0870i	1.14353i	0.820419	+	0.571763i	$0.193740\pi$
$647$	29.0870i	1.14353i	−0.820419	+	0.571763i	$0.806260\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−46.5571	−1.82753
$650$	0	0
$651$	−33.8575	−1.32698
$652$	− 8.36717i	− 0.327684i
$653$	24.8126i	0.970993i	0.874239	+	0.485496i	$0.161361\pi$
$653$	24.8126i	0.970993i	−0.874239	+	0.485496i	$0.838639\pi$
$654$	0.532633	0.0208276
$655$	0	0
$656$	2.93179	0.114467
$657$	− 9.10079i	− 0.355056i
$658$	28.1955i	1.09918i
$659$	−19.1692	−0.746726	−0.373363	−	0.927685i	$-0.621795\pi$
$659$	−19.1692	−0.746726	−0.373363	+	0.927685i	$0.621795\pi$
$660$	0	0
$661$	−45.7461	−1.77932	−0.889658	−	0.456627i	$-0.849057\pi$
$661$	−45.7461	−1.77932	−0.889658	+	0.456627i	$0.849057\pi$
$662$	− 7.64365i	− 0.297079i
$663$	18.7591i	0.728544i
$664$	7.13111	0.276741
$665$	0	0
$666$	2.40102	0.0930375
$667$	2.85830i	0.110674i
$668$	− 8.94427i	− 0.346064i
$669$	−0.361875	−0.0139909
$670$	0	0
$671$	41.3408	1.59594
$672$	4.07768i	0.157300i
$673$	− 21.2542i	− 0.819288i	−0.912246	−	0.409644i	$-0.865653\pi$
$673$	− 21.2542i	− 0.819288i	0.912246	−	0.409644i	$-0.134347\pi$
$674$	−3.68904	−0.142097
$675$	0	0
$676$	16.4009	0.630804
$677$	− 43.3531i	− 1.66620i	−0.553126	−	0.833098i	$-0.686565\pi$
$677$	− 43.3531i	− 1.66620i	0.553126	−	0.833098i	$-0.313435\pi$
$678$	− 17.2272i	− 0.661607i
$679$	−60.1856	−2.30971
$680$	0	0
$681$	−12.8576	−0.492706
$682$	27.2681i	1.04415i
$683$	− 15.5812i	− 0.596197i	−0.954535	−	0.298099i	$-0.903648\pi$
$683$	− 15.5812i	− 0.596197i	0.954535	−	0.298099i	$-0.0963524\pi$
$684$	−1.63522	−0.0625242
$685$	0	0
$686$	−10.7141	−0.409067
$687$	16.5347i	0.630839i
$688$	8.64114i	0.329440i
$689$	−36.8587	−1.40420
$690$	0	0
$691$	25.5539	0.972118	0.486059	−	0.873926i	$-0.338434\pi$
$691$	25.5539	0.972118	0.486059	+	0.873926i	$0.338434\pi$
$692$	− 2.33905i	− 0.0889174i
$693$	− 13.3914i	− 0.508699i
$694$	−3.63522	−0.137991
$695$	0	0
$696$	4.67447	0.177185
$697$	10.1430i	0.384192i
$698$	− 12.2270i	− 0.462799i
$699$	−11.0706	−0.418729
$700$	0	0
$701$	24.7063	0.933146	0.466573	−	0.884483i	$-0.345489\pi$
$701$	24.7063	0.933146	0.466573	+	0.884483i	$0.345489\pi$
$702$	− 5.42226i	− 0.204650i
$703$	− 3.92619i	− 0.148079i
$704$	3.28408	0.123773
$705$	0	0
$706$	−15.6641	−0.589525
$707$	46.8307i	1.76125i
$708$	− 14.1766i	− 0.532790i
$709$	20.1411	0.756414	0.378207	−	0.925721i	$-0.376541\pi$
$709$	20.1411	0.756414	0.378207	+	0.925721i	$0.376541\pi$
$710$	0	0
$711$	−4.09602	−0.153613
$712$	4.80307i	0.180003i
$713$	− 5.07711i	− 0.190139i
$714$	−14.1074	−0.527955
$715$	0	0
$716$	6.02967	0.225339
$717$	5.58721i	0.208658i
$718$	− 7.07176i	− 0.263916i
$719$	25.9912	0.969308	0.484654	−	0.874706i	$-0.338945\pi$
$719$	25.9912	0.969308	0.484654	+	0.874706i	$0.338945\pi$
$720$	0	0
$721$	56.9036	2.11920
$722$	− 16.3261i	− 0.607593i
$723$	− 14.8540i	− 0.552426i
$724$	−16.5771	−0.616084
$725$	0	0
$726$	0.214825	0.00797290
$727$	− 34.3616i	− 1.27440i	−0.770697	−	0.637202i	$-0.780092\pi$
$727$	− 34.3616i	− 1.27440i	0.770697	−	0.637202i	$-0.219908\pi$
$728$	22.1103i	0.819461i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−29.8953	−1.10572
$732$	12.5882i	0.465275i
$733$	32.2515i	1.19124i	0.803267	+	0.595619i	$0.203093\pi$
$733$	32.2515i	1.19124i	−0.803267	+	0.595619i	$0.796907\pi$
$734$	26.7477	0.987275
$735$	0	0
$736$	−0.611469	−0.0225391
$737$	− 35.7117i	− 1.31546i
$738$	− 2.93179i	− 0.107921i
$739$	−41.2647	−1.51795	−0.758973	−	0.651122i	$-0.774299\pi$
$739$	−41.2647	−1.51795	−0.758973	+	0.651122i	$0.774299\pi$
$740$	0	0
$741$	−8.86659	−0.325722
$742$	− 27.7187i	− 1.01759i
$743$	− 7.06997i	− 0.259372i	−0.991555	−	0.129686i	$-0.958603\pi$
$743$	− 7.06997i	− 0.259372i	0.991555	−	0.129686i	$-0.0413969\pi$
$744$	−8.30313	−0.304408
$745$	0	0
$746$	−11.8848	−0.435134
$747$	− 7.13111i	− 0.260914i
$748$	11.3618i	0.415427i
$749$	34.0652	1.24471
$750$	0	0
$751$	−4.57240	−0.166849	−0.0834246	−	0.996514i	$-0.526586\pi$
$751$	−4.57240	−0.166849	−0.0834246	+	0.996514i	$0.526586\pi$
$752$	6.91460i	0.252149i
$753$	− 12.6802i	− 0.462093i
$754$	25.3462	0.923055
$755$	0	0
$756$	4.07768	0.148304
$757$	21.1871i	0.770058i	0.922904	+	0.385029i	$0.125809\pi$
$757$	21.1871i	0.770058i	−0.922904	+	0.385029i	$0.874191\pi$
$758$	4.82558i	0.175273i
$759$	2.00811	0.0728899
$760$	0	0
$761$	−31.8509	−1.15459	−0.577296	−	0.816535i	$-0.695892\pi$
$761$	−31.8509	−1.15459	−0.577296	+	0.816535i	$0.695892\pi$
$762$	− 1.14765i	− 0.0415750i
$763$	2.17191i	0.0786284i
$764$	−9.96802	−0.360630
$765$	0	0
$766$	4.80351	0.173558
$767$	− 76.8693i	− 2.77559i
$768$	1.00000i	0.0360844i
$769$	9.12820	0.329171	0.164586	−	0.986363i	$-0.447371\pi$
$769$	9.12820	0.329171	0.164586	+	0.986363i	$0.447371\pi$
$770$	0	0
$771$	−19.1916	−0.691169
$772$	25.0735i	0.902416i
$773$	− 39.1142i	− 1.40684i	−0.710774	−	0.703420i	$-0.751655\pi$
$773$	− 39.1142i	− 1.40684i	0.710774	−	0.703420i	$-0.248345\pi$
$774$	8.64114	0.310599
$775$	0	0
$776$	−14.7598	−0.529845
$777$	9.79059i	0.351235i
$778$	13.4417i	0.481909i
$779$	−4.79411	−0.171767
$780$	0	0
$781$	29.7769	1.06550
$782$	− 2.11547i	− 0.0756491i
$783$	− 4.67447i	− 0.167052i
$784$	−9.62750	−0.343839
$785$	0	0
$786$	6.61907	0.236095
$787$	− 27.1029i	− 0.966113i	−0.875589	−	0.483056i	$-0.839527\pi$
$787$	− 27.1029i	− 0.966113i	0.875589	−	0.483056i	$-0.160473\pi$
$788$	26.8378i	0.956059i
$789$	29.4749	1.04934
$790$	0	0
$791$	70.2471	2.49770
$792$	− 3.28408i	− 0.116695i
$793$	68.2568i	2.42387i
$794$	−0.0866228	−0.00307413
$795$	0	0
$796$	−4.06114	−0.143943
$797$	13.2411i	0.469024i	0.972113	+	0.234512i	$0.0753492\pi$
$797$	13.2411i	0.469024i	−0.972113	+	0.234512i	$0.924651\pi$
$798$	− 6.66791i	− 0.236041i
$799$	−23.9221	−0.846303
$800$	0	0
$801$	4.80307	0.169708
$802$	0.321141i	0.0113399i
$803$	− 29.8877i	− 1.05471i
$804$	10.8742	0.383503
$805$	0	0
$806$	−45.0217	−1.58582
$807$	− 21.9020i	− 0.770987i
$808$	11.4846i	0.404028i
$809$	7.53161	0.264797	0.132399	−	0.991197i	$-0.457732\pi$
$809$	7.53161	0.264797	0.132399	+	0.991197i	$0.457732\pi$
$810$	0	0
$811$	−26.8219	−0.941846	−0.470923	−	0.882174i	$-0.656079\pi$
$811$	−26.8219	−0.941846	−0.470923	+	0.882174i	$0.656079\pi$
$812$	19.0610i	0.668911i
$813$	− 15.0831i	− 0.528987i
$814$	7.88513	0.276374
$815$	0	0
$816$	−3.45965	−0.121112
$817$	− 14.1302i	− 0.494352i
$818$	− 24.2346i	− 0.847343i
$819$	22.1103	0.772595
$820$	0	0
$821$	37.2089	1.29860	0.649300	−	0.760532i	$-0.275062\pi$
$821$	37.2089	1.29860	0.649300	+	0.760532i	$0.275062\pi$
$822$	7.42175i	0.258863i
$823$	− 17.9438i	− 0.625483i	−0.949838	−	0.312742i	$-0.898753\pi$
$823$	− 17.9438i	− 0.625483i	0.949838	−	0.312742i	$-0.101247\pi$
$824$	13.9549	0.486142
$825$	0	0
$826$	57.8077	2.01139
$827$	− 16.9269i	− 0.588606i	−0.955712	−	0.294303i	$-0.904913\pi$
$827$	− 16.9269i	− 0.588606i	0.955712	−	0.294303i	$-0.0950875\pi$
$828$	0.611469i	0.0212500i
$829$	−51.5169	−1.78925	−0.894627	−	0.446813i	$-0.852559\pi$
$829$	−51.5169	−1.78925	−0.894627	+	0.446813i	$0.852559\pi$
$830$	0	0
$831$	−2.58366	−0.0896262
$832$	5.42226i	0.187983i
$833$	− 33.3078i	− 1.15405i
$834$	5.30062	0.183546
$835$	0	0
$836$	−5.37019	−0.185732
$837$	8.30313i	0.286998i
$838$	− 22.8254i	− 0.788489i
$839$	−22.2100	−0.766775	−0.383387	−	0.923588i	$-0.625243\pi$
$839$	−22.2100	−0.766775	−0.383387	+	0.923588i	$0.625243\pi$
$840$	0	0
$841$	−7.14929	−0.246527
$842$	− 39.1298i	− 1.34850i
$843$	− 18.3980i	− 0.633661i
$844$	4.35487	0.149901
$845$	0	0
$846$	6.91460	0.237729
$847$	0.875988i	0.0300993i
$848$	− 6.79766i	− 0.233433i
$849$	−3.47464	−0.119249
$850$	0	0
$851$	−1.46815	−0.0503275
$852$	9.06706i	0.310632i
$853$	− 35.5195i	− 1.21616i	−0.793874	−	0.608082i	$-0.791939\pi$
$853$	− 35.5195i	− 1.21616i	0.793874	−	0.608082i	$-0.208061\pi$
$854$	−51.3309	−1.75651
$855$	0	0
$856$	8.35405	0.285535
$857$	− 35.9714i	− 1.22876i	−0.789010	−	0.614380i	$-0.789406\pi$
$857$	− 35.9714i	− 1.22876i	0.789010	−	0.614380i	$-0.210594\pi$
$858$	− 17.8071i	− 0.607925i
$859$	−47.1199	−1.60771	−0.803854	−	0.594826i	$-0.797221\pi$
$859$	−47.1199	−1.60771	−0.803854	+	0.594826i	$0.797221\pi$
$860$	0	0
$861$	11.9549	0.407422
$862$	24.6813i	0.840649i
$863$	40.4709i	1.37765i	0.724929	+	0.688823i	$0.241872\pi$
$863$	40.4709i	1.37765i	−0.724929	+	0.688823i	$0.758128\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	19.8779	0.675477
$867$	5.03083i	0.170856i
$868$	− 33.8575i	− 1.14920i
$869$	−13.4517	−0.456316
$870$	0	0
$871$	58.9627	1.99787
$872$	0.532633i	0.0180372i
$873$	14.7598i	0.499542i
$874$	0.999887	0.0338217
$875$	0	0
$876$	9.10079	0.307487
$877$	13.5814i	0.458610i	0.973355	+	0.229305i	$0.0736453\pi$
$877$	13.5814i	0.458610i	−0.973355	+	0.229305i	$0.926355\pi$
$878$	− 5.07227i	− 0.171181i
$879$	15.8625	0.535030
$880$	0	0
$881$	30.1137	1.01456	0.507278	−	0.861783i	$-0.330652\pi$
$881$	30.1137	1.01456	0.507278	+	0.861783i	$0.330652\pi$
$882$	9.62750i	0.324175i
$883$	4.76444i	0.160336i	0.996781	+	0.0801681i	$0.0255457\pi$
$883$	4.76444i	0.160336i	−0.996781	+	0.0801681i	$0.974454\pi$
$884$	−18.7591	−0.630937
$885$	0	0
$886$	10.1873	0.342251
$887$	40.3791i	1.35580i	0.735155	+	0.677899i	$0.237109\pi$
$887$	40.3791i	1.35580i	−0.735155	+	0.677899i	$0.762891\pi$
$888$	2.40102i	0.0805729i
$889$	4.67975	0.156954
$890$	0	0
$891$	−3.28408	−0.110021
$892$	− 0.361875i	− 0.0121165i
$893$	− 11.3069i	− 0.378371i
$894$	−4.79296	−0.160301
$895$	0	0
$896$	−4.07768	−0.136226
$897$	3.31555i	0.110703i
$898$	− 10.3653i	− 0.345895i
$899$	−38.8128	−1.29448
$900$	0	0
$901$	23.5175	0.783482
$902$	− 9.62822i	− 0.320585i
$903$	35.2358i	1.17258i
$904$	17.2272	0.572968
$905$	0	0
$906$	−6.93533	−0.230411
$907$	− 22.3227i	− 0.741214i	−0.928790	−	0.370607i	$-0.879150\pi$
$907$	− 22.3227i	− 0.741214i	0.928790	−	0.370607i	$-0.120850\pi$
$908$	− 12.8576i	− 0.426696i
$909$	11.4846	0.380921
$910$	0	0
$911$	0.782586	0.0259282	0.0129641	−	0.999916i	$-0.495873\pi$
$911$	0.782586	0.0259282	0.0129641	+	0.999916i	$0.495873\pi$
$912$	− 1.63522i	− 0.0541475i
$913$	− 23.4191i	− 0.775060i
$914$	4.06165	0.134347
$915$	0	0
$916$	−16.5347	−0.546322
$917$	26.9905i	0.891304i
$918$	3.45965i	0.114185i
$919$	1.97061	0.0650045	0.0325022	−	0.999472i	$-0.489652\pi$
$919$	1.97061	0.0650045	0.0325022	+	0.999472i	$0.489652\pi$
$920$	0	0
$921$	25.4122	0.837359
$922$	6.76110i	0.222665i
$923$	49.1640i	1.61825i
$924$	13.3914	0.440546
$925$	0	0
$926$	−9.72184	−0.319480
$927$	− 13.9549i	− 0.458339i
$928$	4.67447i	0.153447i
$929$	23.7107	0.777922	0.388961	−	0.921254i	$-0.372834\pi$
$929$	23.7107	0.777922	0.388961	+	0.921254i	$0.372834\pi$
$930$	0	0
$931$	15.7431	0.515959
$932$	− 11.0706i	− 0.362630i
$933$	18.4445i	0.603847i
$934$	−38.4021	−1.25655
$935$	0	0
$936$	5.42226	0.177232
$937$	− 17.7488i	− 0.579829i	−0.957053	−	0.289914i	$-0.906373\pi$
$937$	− 17.7488i	− 0.579829i	0.957053	−	0.289914i	$-0.0936268\pi$
$938$	44.3415i	1.44780i
$939$	−21.9121	−0.715074
$940$	0	0
$941$	49.7755	1.62264	0.811318	−	0.584605i	$-0.198750\pi$
$941$	49.7755	1.62264	0.811318	+	0.584605i	$0.198750\pi$
$942$	− 7.51609i	− 0.244887i
$943$	1.79270i	0.0583783i
$944$	14.1766	0.461409
$945$	0	0
$946$	28.3782	0.922655
$947$	4.51522i	0.146725i	0.997305	+	0.0733625i	$0.0233730\pi$
$947$	4.51522i	0.146725i	−0.997305	+	0.0733625i	$0.976627\pi$
$948$	− 4.09602i	− 0.133033i
$949$	49.3469	1.60187
$950$	0	0
$951$	5.78671	0.187647
$952$	− 14.1074i	− 0.457222i
$953$	− 9.33298i	− 0.302325i	−0.988509	−	0.151163i	$-0.951698\pi$
$953$	− 9.33298i	− 0.302325i	0.988509	−	0.151163i	$-0.0483017\pi$
$954$	−6.79766	−0.220082
$955$	0	0
$956$	−5.58721	−0.180703
$957$	− 15.3513i	− 0.496238i
$958$	− 8.47735i	− 0.273891i
$959$	−30.2635	−0.977261
$960$	0	0
$961$	37.9420	1.22393
$962$	13.0189i	0.419747i
$963$	− 8.35405i	− 0.269205i
$964$	14.8540	0.478415
$965$	0	0
$966$	−2.49338	−0.0802232
$967$	− 22.2528i	− 0.715602i	−0.933798	−	0.357801i	$-0.883527\pi$
$967$	− 22.2528i	− 0.715602i	0.933798	−	0.357801i	$-0.116473\pi$
$968$	0.214825i	0.00690473i
$969$	5.65729	0.181738
$970$	0	0
$971$	4.39676	0.141099	0.0705493	−	0.997508i	$-0.477525\pi$
$971$	4.39676	0.141099	0.0705493	+	0.997508i	$0.477525\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	21.6143i	0.692921i
$974$	−28.9739	−0.928385
$975$	0	0
$976$	−12.5882	−0.402940
$977$	14.8273i	0.474368i	0.971465	+	0.237184i	$0.0762245\pi$
$977$	14.8273i	0.474368i	−0.971465	+	0.237184i	$0.923775\pi$
$978$	− 8.36717i	− 0.267553i
$979$	15.7737	0.504129
$980$	0	0
$981$	0.532633	0.0170057
$982$	− 10.2266i	− 0.326343i
$983$	18.0501i	0.575708i	0.957674	+	0.287854i	$0.0929419\pi$
$983$	18.0501i	0.575708i	−0.957674	+	0.287854i	$0.907058\pi$
$984$	2.93179	0.0934619
$985$	0	0
$986$	−16.1720	−0.515023
$987$	28.1955i	0.897474i
$988$	− 8.86659i	− 0.282084i
$989$	−5.28379	−0.168015
$990$	0	0
$991$	−55.2657	−1.75557	−0.877787	−	0.479051i	$-0.840981\pi$
$991$	−55.2657	−1.75557	−0.877787	+	0.479051i	$0.840981\pi$
$992$	− 8.30313i	− 0.263625i
$993$	− 7.64365i	− 0.242564i
$994$	−36.9726	−1.17270
$995$	0	0
$996$	7.13111	0.225958
$997$	16.2703i	0.515286i	0.966240	+	0.257643i	$0.0829459\pi$
$997$	16.2703i	0.515286i	−0.966240	+	0.257643i	$0.917054\pi$
$998$	23.0007i	0.728075i
$999$	2.40102	0.0759648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.c.e.1249.5		8
5.2	odd	4		3750.2.a.m.1.4		4
5.3	odd	4		3750.2.a.o.1.1		4
5.4	even	2	inner	3750.2.c.e.1249.4		8
25.2	odd	20		750.2.g.e.601.2		8
25.9	even	10		750.2.h.c.349.2		8
25.11	even	5		750.2.h.c.649.2		8
25.12	odd	20		750.2.g.e.151.2		8
25.13	odd	20		750.2.g.c.151.1		8
25.14	even	10		150.2.h.a.79.1	yes	8
25.16	even	5		150.2.h.a.19.1	✓	8
25.23	odd	20		750.2.g.c.601.1		8
75.14	odd	10		450.2.l.a.379.2		8
75.41	odd	10		450.2.l.a.19.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.19.1	✓	8	25.16	even	5
150.2.h.a.79.1	yes	8	25.14	even	10
450.2.l.a.19.2		8	75.41	odd	10
450.2.l.a.379.2		8	75.14	odd	10
750.2.g.c.151.1		8	25.13	odd	20
750.2.g.c.601.1		8	25.23	odd	20
750.2.g.e.151.2		8	25.12	odd	20
750.2.g.e.601.2		8	25.2	odd	20
750.2.h.c.349.2		8	25.9	even	10
750.2.h.c.649.2		8	25.11	even	5
3750.2.a.m.1.4		4	5.2	odd	4
3750.2.a.o.1.1		4	5.3	odd	4
3750.2.c.e.1249.4		8	5.4	even	2	inner
3750.2.c.e.1249.5		8	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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -4.07768i q^{7} -1.00000i q^{8} -1.00000 q^{9} -3.28408 q^{11} -1.00000i q^{12} -5.42226i q^{13} +4.07768 q^{14} +1.00000 q^{16} +3.45965i q^{17} -1.00000i q^{18} -1.63522 q^{19} +4.07768 q^{21} -3.28408i q^{22} +0.611469i q^{23} +1.00000 q^{24} +5.42226 q^{26} -1.00000i q^{27} +4.07768i q^{28} +4.67447 q^{29} -8.30313 q^{31} +1.00000i q^{32} -3.28408i q^{33} -3.45965 q^{34} +1.00000 q^{36} +2.40102i q^{37} -1.63522i q^{38} +5.42226 q^{39} +2.93179 q^{41} +4.07768i q^{42} +8.64114i q^{43} +3.28408 q^{44} -0.611469 q^{46} +6.91460i q^{47} +1.00000i q^{48} -9.62750 q^{49} -3.45965 q^{51} +5.42226i q^{52} -6.79766i q^{53} +1.00000 q^{54} -4.07768 q^{56} -1.63522i q^{57} +4.67447i q^{58} +14.1766 q^{59} -12.5882 q^{61} -8.30313i q^{62} +4.07768i q^{63} -1.00000 q^{64} +3.28408 q^{66} +10.8742i q^{67} -3.45965i q^{68} -0.611469 q^{69} -9.06706 q^{71} +1.00000i q^{72} +9.10079i q^{73} -2.40102 q^{74} +1.63522 q^{76} +13.3914i q^{77} +5.42226i q^{78} +4.09602 q^{79} +1.00000 q^{81} +2.93179i q^{82} +7.13111i q^{83} -4.07768 q^{84} -8.64114 q^{86} +4.67447i q^{87} +3.28408i q^{88} -4.80307 q^{89} -22.1103 q^{91} -0.611469i q^{92} -8.30313i q^{93} -6.91460 q^{94} -1.00000 q^{96} -14.7598i q^{97} -9.62750i q^{98} +3.28408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{6} - 8 q^{9} - 20 q^{11} + 8 q^{14} + 8 q^{16} + 12 q^{19} + 8 q^{21} + 8 q^{24} + 4 q^{26} + 28 q^{29} - 36 q^{31} - 12 q^{34} + 8 q^{36} + 4 q^{39} - 28 q^{41} + 20 q^{44} + 8 q^{49}+ \cdots + 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^6 - 8 * q^9 - 20 * q^11 + 8 * q^14 + 8 * q^16 + 12 * q^19 + 8 * q^21 + 8 * q^24 + 4 * q^26 + 28 * q^29 - 36 * q^31 - 12 * q^34 + 8 * q^36 + 4 * q^39 - 28 * q^41 + 20 * q^44 + 8 * q^49 - 12 * q^51 + 8 * q^54 - 8 * q^56 + 40 * q^59 - 8 * q^64 + 20 * q^66 - 60 * q^71 - 4 * q^74 - 12 * q^76 + 56 * q^79 + 8 * q^81 - 8 * q^84 - 28 * q^86 + 56 * q^89 - 44 * q^91 - 20 * q^94 - 8 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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