LMFDB - Embedded newform 3750.2.c.e.1249.7

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			1249.7
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	3750.1249
Dual form			3750.2.c.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)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -0.273457i q^{7} -1.00000i q^{8} -1.00000 q^{9} -4.79360 q^{11} -1.00000i q^{12} -1.73311i q^{13} +0.273457 q^{14} +1.00000 q^{16} +1.89149i q^{17} -1.00000i q^{18} +3.01062 q^{19} +0.273457 q^{21} -4.79360i q^{22} +4.64584i q^{23} +1.00000 q^{24} +1.73311 q^{26} -1.00000i q^{27} +0.273457i q^{28} -9.08715 q^{29} +3.83390 q^{31} +1.00000i q^{32} -4.79360i q^{33} -1.89149 q^{34} +1.00000 q^{36} -9.00947i q^{37} +3.01062i q^{38} +1.73311 q^{39} -7.58064 q^{41} +0.273457i q^{42} +2.88963i q^{43} +4.79360 q^{44} -4.64584 q^{46} -1.18806i q^{47} +1.00000i q^{48} +6.92522 q^{49} -1.89149 q^{51} +1.73311i q^{52} -11.6150i q^{53} +1.00000 q^{54} -0.273457 q^{56} +3.01062i q^{57} -9.08715i q^{58} +14.2895 q^{59} -5.15131 q^{61} +3.83390i q^{62} +0.273457i q^{63} -1.00000 q^{64} +4.79360 q^{66} -6.29000i q^{67} -1.89149i q^{68} -4.64584 q^{69} -1.40217 q^{71} +1.00000i q^{72} +1.78112i q^{73} +9.00947 q^{74} -3.01062 q^{76} +1.31085i q^{77} +1.73311i q^{78} +16.0593 q^{79} +1.00000 q^{81} -7.58064i q^{82} -15.1392i q^{83} -0.273457 q^{84} -2.88963 q^{86} -9.08715i q^{87} +4.79360i q^{88} +14.8273 q^{89} -0.473931 q^{91} -4.64584i q^{92} +3.83390i q^{93} +1.18806 q^{94} -1.00000 q^{96} +5.88597i q^{97} +6.92522i q^{98} +4.79360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	− 0.273457i	− 0.103357i	−0.998664	−	0.0516786i	$-0.983543\pi$
$7$	− 0.273457i	− 0.103357i	0.998664	−	0.0516786i	$-0.0164571\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−4.79360	−1.44533	−0.722663	−	0.691200i	$-0.757082\pi$
$11$	−4.79360	−1.44533	−0.722663	+	0.691200i	$0.757082\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 1.73311i	− 0.480677i	−0.970689	−	0.240339i	$-0.922741\pi$
$13$	− 1.73311i	− 0.480677i	0.970689	−	0.240339i	$-0.0772585\pi$
$14$	0.273457	0.0730846
$15$	0	0
$16$	1.00000	0.250000
$17$	1.89149i	0.458754i	0.973338	+	0.229377i	$0.0736689\pi$
$17$	1.89149i	0.458754i	−0.973338	+	0.229377i	$0.926331\pi$
$18$	− 1.00000i	− 0.235702i
$19$	3.01062	0.690684	0.345342	−	0.938477i	$-0.387763\pi$
$19$	3.01062	0.690684	0.345342	+	0.938477i	$0.387763\pi$
$20$	0	0
$21$	0.273457	0.0596733
$22$	− 4.79360i	− 1.02200i
$23$	4.64584i	0.968725i	0.874867	+	0.484362i	$0.160948\pi$
$23$	4.64584i	0.968725i	−0.874867	+	0.484362i	$0.839052\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	1.73311	0.339890
$27$	− 1.00000i	− 0.192450i
$28$	0.273457i	0.0516786i
$29$	−9.08715	−1.68744	−0.843721	−	0.536782i	$-0.819640\pi$
$29$	−9.08715	−1.68744	−0.843721	+	0.536782i	$0.819640\pi$
$30$	0	0
$31$	3.83390	0.688589	0.344294	−	0.938862i	$-0.388118\pi$
$31$	3.83390	0.688589	0.344294	+	0.938862i	$0.388118\pi$
$32$	1.00000i	0.176777i
$33$	− 4.79360i	− 0.834459i
$34$	−1.89149	−0.324388
$35$	0	0
$36$	1.00000	0.166667
$37$	− 9.00947i	− 1.48115i	−0.671975	−	0.740574i	$-0.734554\pi$
$37$	− 9.00947i	− 1.48115i	0.671975	−	0.740574i	$-0.265446\pi$
$38$	3.01062i	0.488387i
$39$	1.73311	0.277519
$40$	0	0
$41$	−7.58064	−1.18390	−0.591949	−	0.805976i	$-0.701641\pi$
$41$	−7.58064	−1.18390	−0.591949	+	0.805976i	$0.701641\pi$
$42$	0.273457i	0.0421954i
$43$	2.88963i	0.440664i	0.975425	+	0.220332i	$0.0707141\pi$
$43$	2.88963i	0.440664i	−0.975425	+	0.220332i	$0.929286\pi$
$44$	4.79360	0.722663
$45$	0	0
$46$	−4.64584	−0.684992
$47$	− 1.18806i	− 0.173296i	−0.996239	−	0.0866480i	$-0.972384\pi$
$47$	− 1.18806i	− 0.173296i	0.996239	−	0.0866480i	$-0.0276155\pi$
$48$	1.00000i	0.144338i
$49$	6.92522	0.989317
$50$	0	0
$51$	−1.89149	−0.264862
$52$	1.73311i	0.240339i
$53$	− 11.6150i	− 1.59545i	−0.603025	−	0.797723i	$-0.706038\pi$
$53$	− 11.6150i	− 1.59545i	0.603025	−	0.797723i	$-0.293962\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−0.273457	−0.0365423
$57$	3.01062i	0.398767i
$58$	− 9.08715i	− 1.19320i
$59$	14.2895	1.86033	0.930167	−	0.367138i	$-0.119662\pi$
$59$	14.2895	1.86033	0.930167	+	0.367138i	$0.119662\pi$
$60$	0	0
$61$	−5.15131	−0.659558	−0.329779	−	0.944058i	$-0.606974\pi$
$61$	−5.15131	−0.659558	−0.329779	+	0.944058i	$0.606974\pi$
$62$	3.83390i	0.486906i
$63$	0.273457i	0.0344524i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.79360	0.590052
$67$	− 6.29000i	− 0.768446i	−0.923240	−	0.384223i	$-0.874469\pi$
$67$	− 6.29000i	− 0.768446i	0.923240	−	0.384223i	$-0.125531\pi$
$68$	− 1.89149i	− 0.229377i
$69$	−4.64584	−0.559294
$70$	0	0
$71$	−1.40217	−0.166407	−0.0832034	−	0.996533i	$-0.526515\pi$
$71$	−1.40217	−0.166407	−0.0832034	+	0.996533i	$0.526515\pi$
$72$	1.00000i	0.117851i
$73$	1.78112i	0.208464i	0.994553	+	0.104232i	$0.0332385\pi$
$73$	1.78112i	0.208464i	−0.994553	+	0.104232i	$0.966762\pi$
$74$	9.00947	1.04733
$75$	0	0
$76$	−3.01062	−0.345342
$77$	1.31085i	0.149385i
$78$	1.73311i	0.196236i
$79$	16.0593	1.80682	0.903409	−	0.428780i	$-0.141057\pi$
$79$	16.0593	1.80682	0.903409	+	0.428780i	$0.141057\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 7.58064i	− 0.837142i
$83$	− 15.1392i	− 1.66175i	−0.556463	−	0.830873i	$-0.687842\pi$
$83$	− 15.1392i	− 1.66175i	0.556463	−	0.830873i	$-0.312158\pi$
$84$	−0.273457	−0.0298367
$85$	0	0
$86$	−2.88963	−0.311596
$87$	− 9.08715i	− 0.974245i
$88$	4.79360i	0.511000i
$89$	14.8273	1.57169	0.785847	−	0.618421i	$-0.212227\pi$
$89$	14.8273	1.57169	0.785847	+	0.618421i	$0.212227\pi$
$90$	0	0
$91$	−0.473931	−0.0496815
$92$	− 4.64584i	− 0.484362i
$93$	3.83390i	0.397557i
$94$	1.18806	0.122539
$95$	0	0
$96$	−1.00000	−0.102062
$97$	5.88597i	0.597629i	0.954311	+	0.298815i	$0.0965912\pi$
$97$	5.88597i	0.597629i	−0.954311	+	0.298815i	$0.903409\pi$
$98$	6.92522i	0.699553i
$99$	4.79360	0.481775
$100$	0	0
$101$	4.83576	0.481176	0.240588	−	0.970627i	$-0.422660\pi$
$101$	4.83576	0.481176	0.240588	+	0.970627i	$0.422660\pi$
$102$	− 1.89149i	− 0.187286i
$103$	− 0.0729839i	− 0.00719132i	−0.999994	−	0.00359566i	$-0.998855\pi$
$103$	− 0.0729839i	− 0.00719132i	0.999994	−	0.00359566i	$-0.00114454\pi$
$104$	−1.73311	−0.169945
$105$	0	0
$106$	11.6150	1.12815
$107$	− 5.84754i	− 0.565303i	−0.959223	−	0.282651i	$-0.908786\pi$
$107$	− 5.84754i	− 0.565303i	0.959223	−	0.282651i	$-0.0912140\pi$
$108$	1.00000i	0.0962250i
$109$	9.80609	0.939253	0.469627	−	0.882865i	$-0.344389\pi$
$109$	9.80609	0.939253	0.469627	+	0.882865i	$0.344389\pi$
$110$	0	0
$111$	9.00947	0.855141
$112$	− 0.273457i	− 0.0258393i
$113$	− 17.3291i	− 1.63019i	−0.579328	−	0.815094i	$-0.696685\pi$
$113$	− 17.3291i	− 1.63019i	0.579328	−	0.815094i	$-0.303315\pi$
$114$	−3.01062	−0.281971
$115$	0	0
$116$	9.08715	0.843721
$117$	1.73311i	0.160226i
$118$	14.2895i	1.31545i
$119$	0.517242	0.0474155
$120$	0	0
$121$	11.9786	1.08897
$122$	− 5.15131i	− 0.466378i
$123$	− 7.58064i	− 0.683524i
$124$	−3.83390	−0.344294
$125$	0	0
$126$	−0.273457	−0.0243615
$127$	− 18.3677i	− 1.62987i	−0.579553	−	0.814934i	$-0.696773\pi$
$127$	− 18.3677i	− 1.62987i	0.579553	−	0.814934i	$-0.303227\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−2.88963	−0.254417
$130$	0	0
$131$	−7.57357	−0.661706	−0.330853	−	0.943682i	$-0.607336\pi$
$131$	−7.57357	−0.661706	−0.330853	+	0.943682i	$0.607336\pi$
$132$	4.79360i	0.417230i
$133$	− 0.823277i	− 0.0713872i
$134$	6.29000	0.543373
$135$	0	0
$136$	1.89149	0.162194
$137$	19.6095i	1.67535i	0.546168	+	0.837676i	$0.316086\pi$
$137$	19.6095i	1.67535i	−0.546168	+	0.837676i	$0.683914\pi$
$138$	− 4.64584i	− 0.395480i
$139$	−9.56514	−0.811305	−0.405652	−	0.914027i	$-0.632956\pi$
$139$	−9.56514	−0.811305	−0.405652	+	0.914027i	$0.632956\pi$
$140$	0	0
$141$	1.18806	0.100052
$142$	− 1.40217i	− 0.117667i
$143$	8.30783i	0.694736i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−1.78112	−0.147406
$147$	6.92522i	0.571183i
$148$	9.00947i	0.740574i
$149$	4.64398	0.380449	0.190225	−	0.981741i	$-0.439078\pi$
$149$	4.64398	0.380449	0.190225	+	0.981741i	$0.439078\pi$
$150$	0	0
$151$	−16.7881	−1.36619	−0.683097	−	0.730327i	$-0.739368\pi$
$151$	−16.7881	−1.36619	−0.683097	+	0.730327i	$0.739368\pi$
$152$	− 3.01062i	− 0.244194i
$153$	− 1.89149i	− 0.152918i
$154$	−1.31085	−0.105631
$155$	0	0
$156$	−1.73311	−0.138760
$157$	− 5.57763i	− 0.445143i	−0.974916	−	0.222572i	$-0.928555\pi$
$157$	− 5.57763i	− 0.445143i	0.974916	−	0.222572i	$-0.0714451\pi$
$158$	16.0593i	1.27761i
$159$	11.6150	0.921131
$160$	0	0
$161$	1.27044	0.100125
$162$	1.00000i	0.0785674i
$163$	− 18.3753i	− 1.43926i	−0.694356	−	0.719632i	$-0.744311\pi$
$163$	− 18.3753i	− 1.43926i	0.694356	−	0.719632i	$-0.255689\pi$
$164$	7.58064	0.591949
$165$	0	0
$166$	15.1392	1.17503
$167$	− 8.94427i	− 0.692129i	−0.938211	−	0.346064i	$-0.887518\pi$
$167$	− 8.94427i	− 0.692129i	0.938211	−	0.346064i	$-0.112482\pi$
$168$	− 0.273457i	− 0.0210977i
$169$	9.99634	0.768949
$170$	0	0
$171$	−3.01062	−0.230228
$172$	− 2.88963i	− 0.220332i
$173$	11.9151i	0.905890i	0.891538	+	0.452945i	$0.149627\pi$
$173$	11.9151i	0.905890i	−0.891538	+	0.452945i	$0.850373\pi$
$174$	9.08715	0.688895
$175$	0	0
$176$	−4.79360	−0.361332
$177$	14.2895i	1.07406i
$178$	14.8273i	1.11136i
$179$	3.75621	0.280753	0.140376	−	0.990098i	$-0.455169\pi$
$179$	3.75621	0.280753	0.140376	+	0.990098i	$0.455169\pi$
$180$	0	0
$181$	−18.0626	−1.34258	−0.671290	−	0.741194i	$-0.734260\pi$
$181$	−18.0626	−1.34258	−0.671290	+	0.741194i	$0.734260\pi$
$182$	− 0.473931i	− 0.0351301i
$183$	− 5.15131i	− 0.380796i
$184$	4.64584	0.342496
$185$	0	0
$186$	−3.83390	−0.281115
$187$	− 9.06706i	− 0.663049i
$188$	1.18806i	0.0866480i
$189$	−0.273457	−0.0198911
$190$	0	0
$191$	−16.6007	−1.20119	−0.600594	−	0.799555i	$-0.705069\pi$
$191$	−16.6007	−1.20119	−0.600594	+	0.799555i	$0.705069\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	3.84858i	0.277027i	0.990361	+	0.138513i	$0.0442324\pi$
$193$	3.84858i	0.277027i	−0.990361	+	0.138513i	$0.955768\pi$
$194$	−5.88597	−0.422588
$195$	0	0
$196$	−6.92522	−0.494659
$197$	− 10.7432i	− 0.765423i	−0.923868	−	0.382711i	$-0.874990\pi$
$197$	− 10.7432i	− 0.765423i	0.923868	−	0.382711i	$-0.125010\pi$
$198$	4.79360i	0.340667i
$199$	−2.49808	−0.177084	−0.0885421	−	0.996072i	$-0.528221\pi$
$199$	−2.49808	−0.177084	−0.0885421	+	0.996072i	$0.528221\pi$
$200$	0	0
$201$	6.29000	0.443662
$202$	4.83576i	0.340243i
$203$	2.48495i	0.174409i
$204$	1.89149	0.132431
$205$	0	0
$206$	0.0729839	0.00508503
$207$	− 4.64584i	− 0.322908i
$208$	− 1.73311i	− 0.120169i
$209$	−14.4317	−0.998264
$210$	0	0
$211$	24.2741	1.67109	0.835547	−	0.549418i	$-0.185151\pi$
$211$	24.2741	1.67109	0.835547	+	0.549418i	$0.185151\pi$
$212$	11.6150i	0.797723i
$213$	− 1.40217i	− 0.0960751i
$214$	5.84754	0.399729
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	− 1.04841i	− 0.0711706i
$218$	9.80609i	0.664152i
$219$	−1.78112	−0.120357
$220$	0	0
$221$	3.27816	0.220513
$222$	9.00947i	0.604676i
$223$	13.0539i	0.874156i	0.899424	+	0.437078i	$0.143987\pi$
$223$	13.0539i	0.874156i	−0.899424	+	0.437078i	$0.856013\pi$
$224$	0.273457	0.0182711
$225$	0	0
$226$	17.3291	1.15272
$227$	− 7.06154i	− 0.468691i	−0.972153	−	0.234345i	$-0.924705\pi$
$227$	− 7.06154i	− 0.468691i	0.972153	−	0.234345i	$-0.0752946\pi$
$228$	− 3.01062i	− 0.199383i
$229$	12.5771	0.831119	0.415560	−	0.909566i	$-0.363586\pi$
$229$	12.5771	0.831119	0.415560	+	0.909566i	$0.363586\pi$
$230$	0	0
$231$	−1.31085	−0.0862474
$232$	9.08715i	0.596601i
$233$	− 9.80527i	− 0.642364i	−0.947017	−	0.321182i	$-0.895920\pi$
$233$	− 9.80527i	− 0.642364i	0.947017	−	0.321182i	$-0.104080\pi$
$234$	−1.73311	−0.113297
$235$	0	0
$236$	−14.2895	−0.930167
$237$	16.0593i	1.04317i
$238$	0.517242i	0.0335278i
$239$	−5.04029	−0.326030	−0.163015	−	0.986624i	$-0.552122\pi$
$239$	−5.04029	−0.326030	−0.163015	+	0.986624i	$0.552122\pi$
$240$	0	0
$241$	6.84097	0.440666	0.220333	−	0.975425i	$-0.429286\pi$
$241$	6.84097	0.440666	0.220333	+	0.975425i	$0.429286\pi$
$242$	11.9786i	0.770016i
$243$	1.00000i	0.0641500i
$244$	5.15131	0.329779
$245$	0	0
$246$	7.58064	0.483324
$247$	− 5.21773i	− 0.331996i
$248$	− 3.83390i	− 0.243453i
$249$	15.1392	0.959409
$250$	0	0
$251$	−7.07549	−0.446601	−0.223301	−	0.974750i	$-0.571683\pi$
$251$	−7.07549	−0.446601	−0.223301	+	0.974750i	$0.571683\pi$
$252$	− 0.273457i	− 0.0172262i
$253$	− 22.2703i	− 1.40012i
$254$	18.3677	1.15249
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 4.47318i	− 0.279029i	−0.990220	−	0.139515i	$-0.955446\pi$
$257$	− 4.47318i	− 0.279029i	0.990220	−	0.139515i	$-0.0445542\pi$
$258$	− 2.88963i	− 0.179900i
$259$	−2.46371	−0.153087
$260$	0	0
$261$	9.08715	0.562481
$262$	− 7.57357i	− 0.467897i
$263$	2.50232i	0.154300i	0.997020	+	0.0771498i	$0.0245820\pi$
$263$	2.50232i	0.154300i	−0.997020	+	0.0771498i	$0.975418\pi$
$264$	−4.79360	−0.295026
$265$	0	0
$266$	0.823277	0.0504783
$267$	14.8273i	0.907418i
$268$	6.29000i	0.384223i
$269$	−6.18870	−0.377332	−0.188666	−	0.982041i	$-0.560416\pi$
$269$	−6.18870	−0.377332	−0.188666	+	0.982041i	$0.560416\pi$
$270$	0	0
$271$	13.1689	0.799953	0.399977	−	0.916525i	$-0.369018\pi$
$271$	13.1689	0.799953	0.399977	+	0.916525i	$0.369018\pi$
$272$	1.89149i	0.114689i
$273$	− 0.473931i	− 0.0286836i
$274$	−19.6095	−1.18465
$275$	0	0
$276$	4.64584	0.279647
$277$	5.16714i	0.310463i	0.987878	+	0.155232i	$0.0496124\pi$
$277$	5.16714i	0.310463i	−0.987878	+	0.155232i	$0.950388\pi$
$278$	− 9.56514i	− 0.573679i
$279$	−3.83390	−0.229530
$280$	0	0
$281$	−0.0469714	−0.00280208	−0.00140104	−	0.999999i	$-0.500446\pi$
$281$	−0.0469714	−0.00280208	−0.00140104	+	0.999999i	$0.500446\pi$
$282$	1.18806i	0.0707478i
$283$	− 21.8712i	− 1.30011i	−0.759889	−	0.650053i	$-0.774747\pi$
$283$	− 21.8712i	− 1.30011i	0.759889	−	0.650053i	$-0.225253\pi$
$284$	1.40217	0.0832034
$285$	0	0
$286$	−8.30783	−0.491252
$287$	2.07298i	0.122364i
$288$	− 1.00000i	− 0.0589256i
$289$	13.4223	0.789545
$290$	0	0
$291$	−5.88597	−0.345041
$292$	− 1.78112i	− 0.104232i
$293$	8.35289i	0.487981i	0.969778	+	0.243991i	$0.0784566\pi$
$293$	8.35289i	0.487981i	−0.969778	+	0.243991i	$0.921543\pi$
$294$	−6.92522	−0.403887
$295$	0	0
$296$	−9.00947	−0.523665
$297$	4.79360i	0.278153i
$298$	4.64398i	0.269018i
$299$	8.05174	0.465644
$300$	0	0
$301$	0.790190	0.0455458
$302$	− 16.7881i	− 0.966045i
$303$	4.83576i	0.277807i
$304$	3.01062	0.172671
$305$	0	0
$306$	1.89149	0.108129
$307$	2.28918i	0.130650i	0.997864	+	0.0653251i	$0.0208084\pi$
$307$	2.28918i	0.130650i	−0.997864	+	0.0653251i	$0.979192\pi$
$308$	− 1.31085i	− 0.0746924i
$309$	0.0729839	0.00415191
$310$	0	0
$311$	25.6673	1.45546	0.727729	−	0.685865i	$-0.240576\pi$
$311$	25.6673	1.45546	0.727729	+	0.685865i	$0.240576\pi$
$312$	− 1.73311i	− 0.0981179i
$313$	30.2110i	1.70763i	0.520580	+	0.853813i	$0.325716\pi$
$313$	30.2110i	1.70763i	−0.520580	+	0.853813i	$0.674284\pi$
$314$	5.57763	0.314764
$315$	0	0
$316$	−16.0593	−0.903409
$317$	25.8613i	1.45251i	0.687424	+	0.726257i	$0.258742\pi$
$317$	25.8613i	1.45251i	−0.687424	+	0.726257i	$0.741258\pi$
$318$	11.6150i	0.651338i
$319$	43.5602	2.43890
$320$	0	0
$321$	5.84754	0.326378
$322$	1.27044i	0.0707989i
$323$	5.69456i	0.316854i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	18.3753	1.01771
$327$	9.80609i	0.542278i
$328$	7.58064i	0.418571i
$329$	−0.324883	−0.0179114
$330$	0	0
$331$	14.5094	0.797509	0.398755	−	0.917058i	$-0.369442\pi$
$331$	14.5094	0.797509	0.398755	+	0.917058i	$0.369442\pi$
$332$	15.1392i	0.830873i
$333$	9.00947i	0.493716i
$334$	8.94427	0.489409
$335$	0	0
$336$	0.273457	0.0149183
$337$	− 11.0676i	− 0.602889i	−0.953484	−	0.301445i	$-0.902531\pi$
$337$	− 11.0676i	− 0.602889i	0.953484	−	0.301445i	$-0.0974688\pi$
$338$	9.99634i	0.543729i
$339$	17.3291	0.941190
$340$	0	0
$341$	−18.3782	−0.995235
$342$	− 3.01062i	− 0.162796i
$343$	− 3.80796i	− 0.205610i
$344$	2.88963	0.155798
$345$	0	0
$346$	−11.9151	−0.640561
$347$	− 1.01062i	− 0.0542530i	−0.999632	−	0.0271265i	$-0.991364\pi$
$347$	− 1.01062i	− 0.0542530i	0.999632	−	0.0271265i	$-0.00863569\pi$
$348$	9.08715i	0.487123i
$349$	−30.4268	−1.62871	−0.814356	−	0.580366i	$-0.802910\pi$
$349$	−30.4268	−1.62871	−0.814356	+	0.580366i	$0.802910\pi$
$350$	0	0
$351$	−1.73311	−0.0925064
$352$	− 4.79360i	− 0.255500i
$353$	15.6597i	0.833481i	0.909026	+	0.416740i	$0.136828\pi$
$353$	15.6597i	0.833481i	−0.909026	+	0.416740i	$0.863172\pi$
$354$	−14.2895	−0.759478
$355$	0	0
$356$	−14.8273	−0.785847
$357$	0.517242i	0.0273754i
$358$	3.75621i	0.198522i
$359$	−4.37321	−0.230809	−0.115405	−	0.993319i	$-0.536816\pi$
$359$	−4.37321	−0.230809	−0.115405	+	0.993319i	$0.536816\pi$
$360$	0	0
$361$	−9.93616	−0.522956
$362$	− 18.0626i	− 0.949348i
$363$	11.9786i	0.628716i
$364$	0.473931	0.0248407
$365$	0	0
$366$	5.15131	0.269263
$367$	− 21.8334i	− 1.13969i	−0.821751	−	0.569847i	$-0.807003\pi$
$367$	− 21.8334i	− 1.13969i	0.821751	−	0.569847i	$-0.192997\pi$
$368$	4.64584i	0.242181i
$369$	7.58064	0.394633
$370$	0	0
$371$	−3.17621	−0.164901
$372$	− 3.83390i	− 0.198778i
$373$	− 1.41871i	− 0.0734582i	−0.999325	−	0.0367291i	$-0.988306\pi$
$373$	− 1.41871i	− 0.0734582i	0.999325	−	0.0367291i	$-0.0116939\pi$
$374$	9.06706	0.468847
$375$	0	0
$376$	−1.18806	−0.0612694
$377$	15.7490i	0.811115i
$378$	− 0.273457i	− 0.0140651i
$379$	26.0806	1.33967	0.669835	−	0.742510i	$-0.266365\pi$
$379$	26.0806	1.33967	0.669835	+	0.742510i	$0.266365\pi$
$380$	0	0
$381$	18.3677	0.941005
$382$	− 16.6007i	− 0.849367i
$383$	− 32.7645i	− 1.67419i	−0.547058	−	0.837095i	$-0.684252\pi$
$383$	− 32.7645i	− 1.67419i	0.547058	−	0.837095i	$-0.315748\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−3.84858	−0.195887
$387$	− 2.88963i	− 0.146888i
$388$	− 5.88597i	− 0.298815i
$389$	4.46133	0.226199	0.113099	−	0.993584i	$-0.463922\pi$
$389$	4.46133	0.226199	0.113099	+	0.993584i	$0.463922\pi$
$390$	0	0
$391$	−8.78757	−0.444407
$392$	− 6.92522i	− 0.349776i
$393$	− 7.57357i	− 0.382036i
$394$	10.7432	0.541236
$395$	0	0
$396$	−4.79360	−0.240888
$397$	2.11727i	0.106262i	0.998588	+	0.0531312i	$0.0169202\pi$
$397$	2.11727i	0.106262i	−0.998588	+	0.0531312i	$0.983080\pi$
$398$	− 2.49808i	− 0.125217i
$399$	0.823277	0.0412154
$400$	0	0
$401$	−28.6530	−1.43086	−0.715431	−	0.698683i	$-0.753770\pi$
$401$	−28.6530	−1.43086	−0.715431	+	0.698683i	$0.753770\pi$
$402$	6.29000i	0.313717i
$403$	− 6.64456i	− 0.330989i
$404$	−4.83576	−0.240588
$405$	0	0
$406$	−2.48495	−0.123326
$407$	43.1878i	2.14074i
$408$	1.89149i	0.0936428i
$409$	−39.3546	−1.94596	−0.972979	−	0.230893i	$-0.925835\pi$
$409$	−39.3546	−1.94596	−0.972979	+	0.230893i	$0.925835\pi$
$410$	0	0
$411$	−19.6095	−0.967265
$412$	0.0729839i	0.00359566i
$413$	− 3.90757i	− 0.192279i
$414$	4.64584	0.228331
$415$	0	0
$416$	1.73311	0.0849726
$417$	− 9.56514i	− 0.468407i
$418$	− 14.4317i	− 0.705879i
$419$	−14.1068	−0.689165	−0.344582	−	0.938756i	$-0.611979\pi$
$419$	−14.1068	−0.689165	−0.344582	+	0.938756i	$0.611979\pi$
$420$	0	0
$421$	16.3046	0.794636	0.397318	−	0.917681i	$-0.369941\pi$
$421$	16.3046	0.794636	0.397318	+	0.917681i	$0.369941\pi$
$422$	24.2741i	1.18164i
$423$	1.18806i	0.0577653i
$424$	−11.6150	−0.564075
$425$	0	0
$426$	1.40217	0.0679353
$427$	1.40866i	0.0681700i
$428$	5.84754i	0.282651i
$429$	−8.30783	−0.401106
$430$	0	0
$431$	−1.98217	−0.0954778	−0.0477389	−	0.998860i	$-0.515202\pi$
$431$	−1.98217	−0.0954778	−0.0477389	+	0.998860i	$0.515202\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 4.48943i	− 0.215748i	−0.994165	−	0.107874i	$-0.965596\pi$
$433$	− 4.48943i	− 0.215748i	0.994165	−	0.107874i	$-0.0344044\pi$
$434$	1.04841	0.0503252
$435$	0	0
$436$	−9.80609	−0.469627
$437$	13.9869i	0.669083i
$438$	− 1.78112i	− 0.0851051i
$439$	−25.7158	−1.22735	−0.613674	−	0.789559i	$-0.710309\pi$
$439$	−25.7158	−1.22735	−0.613674	+	0.789559i	$0.710309\pi$
$440$	0	0
$441$	−6.92522	−0.329772
$442$	3.27816i	0.155926i
$443$	− 29.1477i	− 1.38485i	−0.721491	−	0.692423i	$-0.756543\pi$
$443$	− 29.1477i	− 1.38485i	0.721491	−	0.692423i	$-0.243457\pi$
$444$	−9.00947	−0.427570
$445$	0	0
$446$	−13.0539	−0.618122
$447$	4.64398i	0.219653i
$448$	0.273457i	0.0129197i
$449$	5.14037	0.242589	0.121295	−	0.992617i	$-0.461295\pi$
$449$	5.14037	0.242589	0.121295	+	0.992617i	$0.461295\pi$
$450$	0	0
$451$	36.3386	1.71112
$452$	17.3291i	0.815094i
$453$	− 16.7881i	− 0.788773i
$454$	7.06154	0.331414
$455$	0	0
$456$	3.01062	0.140985
$457$	− 20.8445i	− 0.975066i	−0.873105	−	0.487533i	$-0.837897\pi$
$457$	− 20.8445i	− 0.975066i	0.873105	−	0.487533i	$-0.162103\pi$
$458$	12.5771i	0.587690i
$459$	1.89149	0.0882873
$460$	0	0
$461$	−4.96989	−0.231471	−0.115735	−	0.993280i	$-0.536922\pi$
$461$	−4.96989	−0.231471	−0.115735	+	0.993280i	$0.536922\pi$
$462$	− 1.31085i	− 0.0609861i
$463$	7.10664i	0.330274i	0.986271	+	0.165137i	$0.0528066\pi$
$463$	7.10664i	0.330274i	−0.986271	+	0.165137i	$0.947193\pi$
$464$	−9.08715	−0.421860
$465$	0	0
$466$	9.80527	0.454220
$467$	30.1821i	1.39666i	0.715775	+	0.698331i	$0.246074\pi$
$467$	30.1821i	1.39666i	−0.715775	+	0.698331i	$0.753926\pi$
$468$	− 1.73311i	− 0.0801129i
$469$	−1.72005	−0.0794244
$470$	0	0
$471$	5.57763	0.257003
$472$	− 14.2895i	− 0.657727i
$473$	− 13.8517i	− 0.636903i
$474$	−16.0593	−0.737630
$475$	0	0
$476$	−0.517242	−0.0237078
$477$	11.6150i	0.531815i
$478$	− 5.04029i	− 0.230538i
$479$	−27.8415	−1.27211	−0.636055	−	0.771643i	$-0.719435\pi$
$479$	−27.8415	−1.27211	−0.636055	+	0.771643i	$0.719435\pi$
$480$	0	0
$481$	−15.6144	−0.711954
$482$	6.84097i	0.311598i
$483$	1.27044i	0.0578070i
$484$	−11.9786	−0.544484
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	1.29951i	0.0588866i	0.999566	+	0.0294433i	$0.00937344\pi$
$487$	1.29951i	0.0588866i	−0.999566	+	0.0294433i	$0.990627\pi$
$488$	5.15131i	0.233189i
$489$	18.3753	0.830959
$490$	0	0
$491$	19.1650	0.864905	0.432453	−	0.901657i	$-0.357648\pi$
$491$	19.1650	0.864905	0.432453	+	0.901657i	$0.357648\pi$
$492$	7.58064i	0.341762i
$493$	− 17.1883i	− 0.774121i
$494$	5.21773	0.234757
$495$	0	0
$496$	3.83390	0.172147
$497$	0.383434i	0.0171994i
$498$	15.1392i	0.678405i
$499$	−6.41339	−0.287103	−0.143551	−	0.989643i	$-0.545852\pi$
$499$	−6.41339	−0.287103	−0.143551	+	0.989643i	$0.545852\pi$
$500$	0	0
$501$	8.94427	0.399601
$502$	− 7.07549i	− 0.315795i
$503$	35.7696i	1.59489i	0.603392	+	0.797444i	$0.293815\pi$
$503$	35.7696i	1.59489i	−0.603392	+	0.797444i	$0.706185\pi$
$504$	0.273457	0.0121808
$505$	0	0
$506$	22.2703	0.990037
$507$	9.99634i	0.443953i
$508$	18.3677i	0.814934i
$509$	−12.0587	−0.534493	−0.267246	−	0.963628i	$-0.586114\pi$
$509$	−12.0587	−0.534493	−0.267246	+	0.963628i	$0.586114\pi$
$510$	0	0
$511$	0.487060	0.0215463
$512$	1.00000i	0.0441942i
$513$	− 3.01062i	− 0.132922i
$514$	4.47318	0.197303
$515$	0	0
$516$	2.88963	0.127209
$517$	5.69507i	0.250469i
$518$	− 2.46371i	− 0.108249i
$519$	−11.9151	−0.523016
$520$	0	0
$521$	3.51319	0.153915	0.0769577	−	0.997034i	$-0.475479\pi$
$521$	3.51319	0.153915	0.0769577	+	0.997034i	$0.475479\pi$
$522$	9.08715i	0.397734i
$523$	− 24.4468i	− 1.06898i	−0.845174	−	0.534492i	$-0.820503\pi$
$523$	− 24.4468i	− 1.06898i	0.845174	−	0.534492i	$-0.179497\pi$
$524$	7.57357	0.330853
$525$	0	0
$526$	−2.50232	−0.109106
$527$	7.25179i	0.315893i
$528$	− 4.79360i	− 0.208615i
$529$	1.41616	0.0615720
$530$	0	0
$531$	−14.2895	−0.620111
$532$	0.823277i	0.0356936i
$533$	13.1381i	0.569073i
$534$	−14.8273	−0.641641
$535$	0	0
$536$	−6.29000	−0.271687
$537$	3.75621i	0.162093i
$538$	− 6.18870i	− 0.266814i
$539$	−33.1968	−1.42989
$540$	0	0
$541$	−38.7392	−1.66553	−0.832765	−	0.553627i	$-0.813243\pi$
$541$	−38.7392	−1.66553	−0.832765	+	0.553627i	$0.813243\pi$
$542$	13.1689i	0.565652i
$543$	− 18.0626i	− 0.775139i
$544$	−1.89149	−0.0810970
$545$	0	0
$546$	0.473931	0.0202824
$547$	− 30.3218i	− 1.29646i	−0.761443	−	0.648232i	$-0.775509\pi$
$547$	− 30.3218i	− 1.29646i	0.761443	−	0.648232i	$-0.224491\pi$
$548$	− 19.6095i	− 0.837676i
$549$	5.15131	0.219853
$550$	0	0
$551$	−27.3580	−1.16549
$552$	4.64584i	0.197740i
$553$	− 4.39155i	− 0.186748i
$554$	−5.16714	−0.219531
$555$	0	0
$556$	9.56514	0.405652
$557$	25.7254i	1.09002i	0.838430	+	0.545010i	$0.183474\pi$
$557$	25.7254i	1.09002i	−0.838430	+	0.545010i	$0.816526\pi$
$558$	− 3.83390i	− 0.162302i
$559$	5.00803	0.211817
$560$	0	0
$561$	9.06706	0.382812
$562$	− 0.0469714i	− 0.00198137i
$563$	− 30.6333i	− 1.29104i	−0.763743	−	0.645520i	$-0.776641\pi$
$563$	− 30.6333i	− 1.29104i	0.763743	−	0.645520i	$-0.223359\pi$
$564$	−1.18806	−0.0500262
$565$	0	0
$566$	21.8712	0.919314
$567$	− 0.273457i	− 0.0114841i
$568$	1.40217i	0.0588337i
$569$	−12.4856	−0.523423	−0.261712	−	0.965146i	$-0.584287\pi$
$569$	−12.4856	−0.523423	−0.261712	+	0.965146i	$0.584287\pi$
$570$	0	0
$571$	−24.3564	−1.01929	−0.509643	−	0.860386i	$-0.670222\pi$
$571$	−24.3564	−1.01929	−0.509643	+	0.860386i	$0.670222\pi$
$572$	− 8.30783i	− 0.347368i
$573$	− 16.6007i	− 0.693506i
$574$	−2.07298	−0.0865247
$575$	0	0
$576$	1.00000	0.0416667
$577$	3.21252i	0.133739i	0.997762	+	0.0668695i	$0.0213011\pi$
$577$	3.21252i	0.133739i	−0.997762	+	0.0668695i	$0.978699\pi$
$578$	13.4223i	0.558292i
$579$	−3.84858	−0.159941
$580$	0	0
$581$	−4.13993	−0.171753
$582$	− 5.88597i	− 0.243981i
$583$	55.6778i	2.30594i
$584$	1.78112	0.0737032
$585$	0	0
$586$	−8.35289	−0.345055
$587$	− 15.1892i	− 0.626924i	−0.949601	−	0.313462i	$-0.898511\pi$
$587$	− 15.1892i	− 0.626924i	0.949601	−	0.313462i	$-0.101489\pi$
$588$	− 6.92522i	− 0.285591i
$589$	11.5424	0.475597
$590$	0	0
$591$	10.7432	0.441917
$592$	− 9.00947i	− 0.370287i
$593$	4.96989i	0.204089i	0.994780	+	0.102044i	$0.0325384\pi$
$593$	4.96989i	0.204089i	−0.994780	+	0.102044i	$0.967462\pi$
$594$	−4.79360	−0.196684
$595$	0	0
$596$	−4.64398	−0.190225
$597$	− 2.49808i	− 0.102240i
$598$	8.05174i	0.329260i
$599$	3.23524	0.132188	0.0660942	−	0.997813i	$-0.478946\pi$
$599$	3.23524	0.132188	0.0660942	+	0.997813i	$0.478946\pi$
$600$	0	0
$601$	−8.78152	−0.358205	−0.179103	−	0.983830i	$-0.557319\pi$
$601$	−8.78152	−0.358205	−0.179103	+	0.983830i	$0.557319\pi$
$602$	0.790190i	0.0322057i
$603$	6.29000i	0.256149i
$604$	16.7881	0.683097
$605$	0	0
$606$	−4.83576	−0.196439
$607$	− 39.5692i	− 1.60606i	−0.595937	−	0.803031i	$-0.703219\pi$
$607$	− 39.5692i	− 1.60606i	0.595937	−	0.803031i	$-0.296781\pi$
$608$	3.01062i	0.122097i
$609$	−2.48495	−0.100695
$610$	0	0
$611$	−2.05903	−0.0832994
$612$	1.89149i	0.0764590i
$613$	− 46.8849i	− 1.89366i	−0.321730	−	0.946831i	$-0.604264\pi$
$613$	− 46.8849i	− 1.89366i	0.321730	−	0.946831i	$-0.395736\pi$
$614$	−2.28918	−0.0923836
$615$	0	0
$616$	1.31085	0.0528155
$617$	− 14.1520i	− 0.569739i	−0.958566	−	0.284869i	$-0.908050\pi$
$617$	− 14.1520i	− 0.569739i	0.958566	−	0.284869i	$-0.0919503\pi$
$618$	0.0729839i	0.00293584i
$619$	6.54669	0.263134	0.131567	−	0.991307i	$-0.457999\pi$
$619$	6.54669	0.263134	0.131567	+	0.991307i	$0.457999\pi$
$620$	0	0
$621$	4.64584	0.186431
$622$	25.6673i	1.02916i
$623$	− 4.05465i	− 0.162446i
$624$	1.73311	0.0693798
$625$	0	0
$626$	−30.2110	−1.20747
$627$	− 14.4317i	− 0.576348i
$628$	5.57763i	0.222572i
$629$	17.0413	0.679482
$630$	0	0
$631$	6.04884	0.240800	0.120400	−	0.992725i	$-0.461582\pi$
$631$	6.04884	0.240800	0.120400	+	0.992725i	$0.461582\pi$
$632$	− 16.0593i	− 0.638806i
$633$	24.2741i	0.964807i
$634$	−25.8613	−1.02708
$635$	0	0
$636$	−11.6150	−0.460565
$637$	− 12.0021i	− 0.475542i
$638$	43.5602i	1.72457i
$639$	1.40217	0.0554690
$640$	0	0
$641$	32.2843	1.27515	0.637576	−	0.770388i	$-0.279937\pi$
$641$	32.2843	1.27515	0.637576	+	0.770388i	$0.279937\pi$
$642$	5.84754i	0.230784i
$643$	− 12.1187i	− 0.477914i	−0.971030	−	0.238957i	$-0.923194\pi$
$643$	− 12.1187i	− 0.477914i	0.971030	−	0.238957i	$-0.0768056\pi$
$644$	−1.27044	−0.0500624
$645$	0	0
$646$	−5.69456	−0.224050
$647$	20.2287i	0.795271i	0.917543	+	0.397635i	$0.130169\pi$
$647$	20.2287i	0.795271i	−0.917543	+	0.397635i	$0.869831\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−68.4982	−2.68879
$650$	0	0
$651$	1.04841	0.0410904
$652$	18.3753i	0.719632i
$653$	− 33.3838i	− 1.30641i	−0.757182	−	0.653204i	$-0.773424\pi$
$653$	− 33.3838i	− 1.30641i	0.757182	−	0.653204i	$-0.226576\pi$
$654$	−9.80609	−0.383448
$655$	0	0
$656$	−7.58064	−0.295974
$657$	− 1.78112i	− 0.0694880i
$658$	− 0.324883i	− 0.0126653i
$659$	30.3942	1.18399	0.591995	−	0.805941i	$-0.298340\pi$
$659$	30.3942	1.18399	0.591995	+	0.805941i	$0.298340\pi$
$660$	0	0
$661$	24.9370	0.969935	0.484968	−	0.874532i	$-0.338831\pi$
$661$	24.9370	0.969935	0.484968	+	0.874532i	$0.338831\pi$
$662$	14.5094i	0.563924i
$663$	3.27816i	0.127313i
$664$	−15.1392	−0.587516
$665$	0	0
$666$	−9.00947	−0.349110
$667$	− 42.2175i	− 1.63467i
$668$	8.94427i	0.346064i
$669$	−13.0539	−0.504694
$670$	0	0
$671$	24.6933	0.953276
$672$	0.273457i	0.0105489i
$673$	− 46.0697i	− 1.77586i	−0.459983	−	0.887928i	$-0.652145\pi$
$673$	− 46.0697i	− 1.77586i	0.459983	−	0.887928i	$-0.347855\pi$
$674$	11.0676	0.426307
$675$	0	0
$676$	−9.99634	−0.384475
$677$	− 28.5921i	− 1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$677$	− 28.5921i	− 1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$678$	17.3291i	0.665522i
$679$	1.60956	0.0617693
$680$	0	0
$681$	7.06154	0.270599
$682$	− 18.3782i	− 0.703737i
$683$	8.92741i	0.341598i	0.985306	+	0.170799i	$0.0546349\pi$
$683$	8.92741i	0.341598i	−0.985306	+	0.170799i	$0.945365\pi$
$684$	3.01062	0.115114
$685$	0	0
$686$	3.80796	0.145388
$687$	12.5771i	0.479847i
$688$	2.88963i	0.110166i
$689$	−20.1301	−0.766894
$690$	0	0
$691$	−1.31278	−0.0499406	−0.0249703	−	0.999688i	$-0.507949\pi$
$691$	−1.31278	−0.0499406	−0.0249703	+	0.999688i	$0.507949\pi$
$692$	− 11.9151i	− 0.452945i
$693$	− 1.31085i	− 0.0497950i
$694$	1.01062	0.0383627
$695$	0	0
$696$	−9.08715	−0.344448
$697$	− 14.3387i	− 0.543118i
$698$	− 30.4268i	− 1.15167i
$699$	9.80527	0.370869
$700$	0	0
$701$	22.5267	0.850822	0.425411	−	0.905000i	$-0.360130\pi$
$701$	22.5267	0.850822	0.425411	+	0.905000i	$0.360130\pi$
$702$	− 1.73311i	− 0.0654119i
$703$	− 27.1241i	− 1.02300i
$704$	4.79360	0.180666
$705$	0	0
$706$	−15.6597	−0.589360
$707$	− 1.32238i	− 0.0497331i
$708$	− 14.2895i	− 0.537032i
$709$	6.89619	0.258992	0.129496	−	0.991580i	$-0.458664\pi$
$709$	6.89619	0.258992	0.129496	+	0.991580i	$0.458664\pi$
$710$	0	0
$711$	−16.0593	−0.602272
$712$	− 14.8273i	− 0.555678i
$713$	17.8117i	0.667053i
$714$	−0.517242	−0.0193573
$715$	0	0
$716$	−3.75621	−0.140376
$717$	− 5.04029i	− 0.188233i
$718$	− 4.37321i	− 0.163207i
$719$	−28.3423	−1.05699	−0.528495	−	0.848936i	$-0.677244\pi$
$719$	−28.3423	−1.05699	−0.528495	+	0.848936i	$0.677244\pi$
$720$	0	0
$721$	−0.0199580	−0.000743274 0
$722$	− 9.93616i	− 0.369786i
$723$	6.84097i	0.254419i
$724$	18.0626	0.671290
$725$	0	0
$726$	−11.9786	−0.444569
$727$	− 17.0802i	− 0.633469i	−0.948514	−	0.316735i	$-0.897414\pi$
$727$	− 17.0802i	− 0.633469i	0.948514	−	0.316735i	$-0.102586\pi$
$728$	0.473931i	0.0175651i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−5.46570	−0.202156
$732$	5.15131i	0.190398i
$733$	− 11.8923i	− 0.439251i	−0.975584	−	0.219626i	$-0.929516\pi$
$733$	− 11.8923i	− 0.439251i	0.975584	−	0.219626i	$-0.0704836\pi$
$734$	21.8334	0.805885
$735$	0	0
$736$	−4.64584	−0.171248
$737$	30.1518i	1.11065i
$738$	7.58064i	0.279047i
$739$	−11.4605	−0.421581	−0.210791	−	0.977531i	$-0.567604\pi$
$739$	−11.4605	−0.421581	−0.210791	+	0.977531i	$0.567604\pi$
$740$	0	0
$741$	5.21773	0.191678
$742$	− 3.17621i	− 0.116602i
$743$	8.64114i	0.317013i	0.987358	+	0.158506i	$0.0506678\pi$
$743$	8.64114i	0.317013i	−0.987358	+	0.158506i	$0.949332\pi$
$744$	3.83390	0.140558
$745$	0	0
$746$	1.41871	0.0519428
$747$	15.1392i	0.553915i
$748$	9.06706i	0.331525i
$749$	−1.59905	−0.0584281
$750$	0	0
$751$	−8.45998	−0.308709	−0.154354	−	0.988016i	$-0.549330\pi$
$751$	−8.45998	−0.308709	−0.154354	+	0.988016i	$0.549330\pi$
$752$	− 1.18806i	− 0.0433240i
$753$	− 7.07549i	− 0.257845i
$754$	−15.7490	−0.573545
$755$	0	0
$756$	0.273457	0.00994555
$757$	53.6675i	1.95058i	0.220932	+	0.975289i	$0.429090\pi$
$757$	53.6675i	1.95058i	−0.220932	+	0.975289i	$0.570910\pi$
$758$	26.0806i	0.947290i
$759$	22.2703	0.808362
$760$	0	0
$761$	11.7714	0.426713	0.213357	−	0.976974i	$-0.431560\pi$
$761$	11.7714	0.426713	0.213357	+	0.976974i	$0.431560\pi$
$762$	18.3677i	0.665391i
$763$	− 2.68155i	− 0.0970786i
$764$	16.6007	0.600594
$765$	0	0
$766$	32.7645	1.18383
$767$	− 24.7652i	− 0.894220i
$768$	1.00000i	0.0360844i
$769$	−5.09591	−0.183763	−0.0918816	−	0.995770i	$-0.529288\pi$
$769$	−5.09591	−0.183763	−0.0918816	+	0.995770i	$0.529288\pi$
$770$	0	0
$771$	4.47318	0.161097
$772$	− 3.84858i	− 0.138513i
$773$	− 12.6222i	− 0.453990i	−0.973896	−	0.226995i	$-0.927110\pi$
$773$	− 12.6222i	− 0.453990i	0.973896	−	0.226995i	$-0.0728901\pi$
$774$	2.88963	0.103865
$775$	0	0
$776$	5.88597	0.211294
$777$	− 2.46371i	− 0.0883850i
$778$	4.46133i	0.159946i
$779$	−22.8225	−0.817699
$780$	0	0
$781$	6.72145	0.240512
$782$	− 8.78757i	− 0.314243i
$783$	9.08715i	0.324748i
$784$	6.92522	0.247329
$785$	0	0
$786$	7.57357	0.270140
$787$	44.2098i	1.57591i	0.615734	+	0.787954i	$0.288860\pi$
$787$	44.2098i	1.57591i	−0.615734	+	0.787954i	$0.711140\pi$
$788$	10.7432i	0.382711i
$789$	−2.50232	−0.0890849
$790$	0	0
$791$	−4.73878	−0.168492
$792$	− 4.79360i	− 0.170333i
$793$	8.92777i	0.317034i
$794$	−2.11727	−0.0751389
$795$	0	0
$796$	2.49808	0.0885421
$797$	46.3400i	1.64145i	0.571326	+	0.820723i	$0.306429\pi$
$797$	46.3400i	1.64145i	−0.571326	+	0.820723i	$0.693571\pi$
$798$	0.823277i	0.0291437i
$799$	2.24720	0.0795002
$800$	0	0
$801$	−14.8273	−0.523898
$802$	− 28.6530i	− 1.01177i
$803$	− 8.53798i	− 0.301299i
$804$	−6.29000	−0.221831
$805$	0	0
$806$	6.64456	0.234045
$807$	− 6.18870i	− 0.217853i
$808$	− 4.83576i	− 0.170122i
$809$	−49.4913	−1.74002	−0.870011	−	0.493033i	$-0.835888\pi$
$809$	−49.4913	−1.74002	−0.870011	+	0.493033i	$0.835888\pi$
$810$	0	0
$811$	−2.80756	−0.0985867	−0.0492934	−	0.998784i	$-0.515697\pi$
$811$	−2.80756	−0.0985867	−0.0492934	+	0.998784i	$0.515697\pi$
$812$	− 2.48495i	− 0.0872046i
$813$	13.1689i	0.461853i
$814$	−43.1878	−1.51373
$815$	0	0
$816$	−1.89149	−0.0662154
$817$	8.69957i	0.304360i
$818$	− 39.3546i	− 1.37600i
$819$	0.473931	0.0165605
$820$	0	0
$821$	−37.3643	−1.30402	−0.652011	−	0.758209i	$-0.726075\pi$
$821$	−37.3643	−1.30402	−0.652011	+	0.758209i	$0.726075\pi$
$822$	− 19.6095i	− 0.683960i
$823$	− 22.8380i	− 0.796082i	−0.917368	−	0.398041i	$-0.869690\pi$
$823$	− 22.8380i	− 0.796082i	0.917368	−	0.398041i	$-0.130310\pi$
$824$	−0.0729839	−0.00254251
$825$	0	0
$826$	3.90757	0.135962
$827$	− 10.7107i	− 0.372448i	−0.982507	−	0.186224i	$-0.940375\pi$
$827$	− 10.7107i	− 0.372448i	0.982507	−	0.186224i	$-0.0596250\pi$
$828$	4.64584i	0.161454i
$829$	27.5959	0.958445	0.479223	−	0.877693i	$-0.340919\pi$
$829$	27.5959	0.958445	0.479223	+	0.877693i	$0.340919\pi$
$830$	0	0
$831$	−5.16714	−0.179246
$832$	1.73311i	0.0600847i
$833$	13.0990i	0.453853i
$834$	9.56514	0.331214
$835$	0	0
$836$	14.4317	0.499132
$837$	− 3.83390i	− 0.132519i
$838$	− 14.1068i	− 0.487313i
$839$	9.93655	0.343048	0.171524	−	0.985180i	$-0.445131\pi$
$839$	9.93655	0.343048	0.171524	+	0.985180i	$0.445131\pi$
$840$	0	0
$841$	53.5763	1.84746
$842$	16.3046i	0.561892i
$843$	− 0.0469714i	− 0.00161778i
$844$	−24.2741	−0.835547
$845$	0	0
$846$	−1.18806	−0.0408462
$847$	− 3.27565i	− 0.112553i
$848$	− 11.6150i	− 0.398861i
$849$	21.8712	0.750617
$850$	0	0
$851$	41.8566	1.43482
$852$	1.40217i	0.0480375i
$853$	45.0081i	1.54105i	0.637412	+	0.770524i	$0.280005\pi$
$853$	45.0081i	1.54105i	−0.637412	+	0.770524i	$0.719995\pi$
$854$	−1.40866	−0.0482035
$855$	0	0
$856$	−5.84754	−0.199865
$857$	− 24.6986i	− 0.843686i	−0.906669	−	0.421843i	$-0.861383\pi$
$857$	− 24.6986i	− 0.843686i	0.906669	−	0.421843i	$-0.138617\pi$
$858$	− 8.30783i	− 0.283625i
$859$	17.3400	0.591632	0.295816	−	0.955245i	$-0.404408\pi$
$859$	17.3400	0.591632	0.295816	+	0.955245i	$0.404408\pi$
$860$	0	0
$861$	−2.07298	−0.0706471
$862$	− 1.98217i	− 0.0675130i
$863$	− 25.8867i	− 0.881195i	−0.897705	−	0.440598i	$-0.854767\pi$
$863$	− 25.8867i	− 0.881195i	0.897705	−	0.440598i	$-0.145233\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	4.48943	0.152557
$867$	13.4223i	0.455844i
$868$	1.04841i	0.0355853i
$869$	−76.9821	−2.61144
$870$	0	0
$871$	−10.9012	−0.369375
$872$	− 9.80609i	− 0.332076i
$873$	− 5.88597i	− 0.199210i
$874$	−13.9869	−0.473113
$875$	0	0
$876$	1.78112	0.0601784
$877$	− 20.1898i	− 0.681761i	−0.940107	−	0.340881i	$-0.889275\pi$
$877$	− 20.1898i	− 0.681761i	0.940107	−	0.340881i	$-0.110725\pi$
$878$	− 25.7158i	− 0.867866i
$879$	−8.35289	−0.281736
$880$	0	0
$881$	23.7732	0.800940	0.400470	−	0.916310i	$-0.368847\pi$
$881$	23.7732	0.800940	0.400470	+	0.916310i	$0.368847\pi$
$882$	− 6.92522i	− 0.233184i
$883$	32.5787i	1.09636i	0.836361	+	0.548180i	$0.184679\pi$
$883$	32.5787i	1.09636i	−0.836361	+	0.548180i	$0.815321\pi$
$884$	−3.27816	−0.110256
$885$	0	0
$886$	29.1477	0.979234
$887$	− 56.3177i	− 1.89096i	−0.325678	−	0.945481i	$-0.605592\pi$
$887$	− 56.3177i	− 1.89096i	0.325678	−	0.945481i	$-0.394408\pi$
$888$	− 9.00947i	− 0.302338i
$889$	−5.02278	−0.168459
$890$	0	0
$891$	−4.79360	−0.160592
$892$	− 13.0539i	− 0.437078i
$893$	− 3.57679i	− 0.119693i
$894$	−4.64398	−0.155318
$895$	0	0
$896$	−0.273457	−0.00913557
$897$	8.05174i	0.268840i
$898$	5.14037i	0.171536i
$899$	−34.8392	−1.16195
$900$	0	0
$901$	21.9697	0.731917
$902$	36.3386i	1.20994i
$903$	0.790190i	0.0262959i
$904$	−17.3291	−0.576359
$905$	0	0
$906$	16.7881	0.557747
$907$	− 46.7617i	− 1.55270i	−0.630304	−	0.776349i	$-0.717070\pi$
$907$	− 46.7617i	− 1.55270i	0.630304	−	0.776349i	$-0.282930\pi$
$908$	7.06154i	0.234345i
$909$	−4.83576	−0.160392
$910$	0	0
$911$	−16.7472	−0.554858	−0.277429	−	0.960746i	$-0.589482\pi$
$911$	−16.7472	−0.554858	−0.277429	+	0.960746i	$0.589482\pi$
$912$	3.01062i	0.0996916i
$913$	72.5714i	2.40176i
$914$	20.8445	0.689475
$915$	0	0
$916$	−12.5771	−0.415560
$917$	2.07105i	0.0683921i
$918$	1.89149i	0.0624285i
$919$	5.12507	0.169061	0.0845303	−	0.996421i	$-0.473061\pi$
$919$	5.12507	0.169061	0.0845303	+	0.996421i	$0.473061\pi$
$920$	0	0
$921$	−2.28918	−0.0754309
$922$	− 4.96989i	− 0.163675i
$923$	2.43011i	0.0799880i
$924$	1.31085	0.0431237
$925$	0	0
$926$	−7.10664	−0.233539
$927$	0.0729839i	0.00239711i
$928$	− 9.08715i	− 0.298300i
$929$	−45.3434	−1.48767	−0.743834	−	0.668364i	$-0.766995\pi$
$929$	−45.3434	−1.48767	−0.743834	+	0.668364i	$0.766995\pi$
$930$	0	0
$931$	20.8492	0.683306
$932$	9.80527i	0.321182i
$933$	25.6673i	0.840309i
$934$	−30.1821	−0.987590
$935$	0	0
$936$	1.73311	0.0566484
$937$	− 31.0119i	− 1.01311i	−0.862207	−	0.506557i	$-0.830918\pi$
$937$	− 31.0119i	− 1.01311i	0.862207	−	0.506557i	$-0.169082\pi$
$938$	− 1.72005i	− 0.0561616i
$939$	−30.2110	−0.985898
$940$	0	0
$941$	−48.3113	−1.57490	−0.787452	−	0.616377i	$-0.788600\pi$
$941$	−48.3113	−1.57490	−0.787452	+	0.616377i	$0.788600\pi$
$942$	5.57763i	0.181729i
$943$	− 35.2185i	− 1.14687i
$944$	14.2895	0.465083
$945$	0	0
$946$	13.8517	0.450358
$947$	− 33.3872i	− 1.08494i	−0.840075	−	0.542470i	$-0.817489\pi$
$947$	− 33.3872i	− 1.08494i	0.840075	−	0.542470i	$-0.182511\pi$
$948$	− 16.0593i	− 0.521583i
$949$	3.08687	0.100204
$950$	0	0
$951$	−25.8613	−0.838609
$952$	− 0.517242i	− 0.0167639i
$953$	21.8525i	0.707872i	0.935270	+	0.353936i	$0.115157\pi$
$953$	21.8525i	0.707872i	−0.935270	+	0.353936i	$0.884843\pi$
$954$	−11.6150	−0.376050
$955$	0	0
$956$	5.04029	0.163015
$957$	43.5602i	1.40810i
$958$	− 27.8415i	− 0.899518i
$959$	5.36236	0.173160
$960$	0	0
$961$	−16.3012	−0.525846
$962$	− 15.6144i	− 0.503428i
$963$	5.84754i	0.188434i
$964$	−6.84097	−0.220333
$965$	0	0
$966$	−1.27044	−0.0408757
$967$	32.2205i	1.03614i	0.855338	+	0.518071i	$0.173350\pi$
$967$	32.2205i	1.03614i	−0.855338	+	0.518071i	$0.826650\pi$
$968$	− 11.9786i	− 0.385008i
$969$	−5.69456	−0.182936
$970$	0	0
$971$	35.6114	1.14282	0.571411	−	0.820664i	$-0.306396\pi$
$971$	35.6114	1.14282	0.571411	+	0.820664i	$0.306396\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	2.61566i	0.0838542i
$974$	−1.29951	−0.0416391
$975$	0	0
$976$	−5.15131	−0.164889
$977$	9.85880i	0.315411i	0.987486	+	0.157706i	$0.0504097\pi$
$977$	9.85880i	0.315411i	−0.987486	+	0.157706i	$0.949590\pi$
$978$	18.3753i	0.587577i
$979$	−71.0764	−2.27161
$980$	0	0
$981$	−9.80609	−0.313084
$982$	19.1650i	0.611580i
$983$	30.4129i	0.970020i	0.874509	+	0.485010i	$0.161184\pi$
$983$	30.4129i	0.970020i	−0.874509	+	0.485010i	$0.838816\pi$
$984$	−7.58064	−0.241662
$985$	0	0
$986$	17.1883	0.547386
$987$	− 0.324883i	− 0.0103411i
$988$	5.21773i	0.165998i
$989$	−13.4247	−0.426882
$990$	0	0
$991$	−41.0077	−1.30265	−0.651327	−	0.758798i	$-0.725787\pi$
$991$	−41.0077	−1.30265	−0.651327	+	0.758798i	$0.725787\pi$
$992$	3.83390i	0.121726i
$993$	14.5094i	0.460442i
$994$	−0.383434	−0.0121618
$995$	0	0
$996$	−15.1392	−0.479705
$997$	− 8.00811i	− 0.253620i	−0.991927	−	0.126810i	$-0.959526\pi$
$997$	− 8.00811i	− 0.253620i	0.991927	−	0.126810i	$-0.0404738\pi$
$998$	− 6.41339i	− 0.203012i
$999$	−9.00947	−0.285047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.c.e.1249.7		8
5.2	odd	4		3750.2.a.m.1.2		4
5.3	odd	4		3750.2.a.o.1.3		4
5.4	even	2	inner	3750.2.c.e.1249.2		8
25.3	odd	20		750.2.g.c.451.2		8
25.4	even	10		150.2.h.a.109.1	✓	8
25.6	even	5		150.2.h.a.139.1	yes	8
25.8	odd	20		750.2.g.c.301.2		8
25.17	odd	20		750.2.g.e.301.1		8
25.19	even	10		750.2.h.c.199.2		8
25.21	even	5		750.2.h.c.49.2		8
25.22	odd	20		750.2.g.e.451.1		8
75.29	odd	10		450.2.l.a.109.2		8
75.56	odd	10		450.2.l.a.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.109.1	✓	8	25.4	even	10
150.2.h.a.139.1	yes	8	25.6	even	5
450.2.l.a.109.2		8	75.29	odd	10
450.2.l.a.289.2		8	75.56	odd	10
750.2.g.c.301.2		8	25.8	odd	20
750.2.g.c.451.2		8	25.3	odd	20
750.2.g.e.301.1		8	25.17	odd	20
750.2.g.e.451.1		8	25.22	odd	20
750.2.h.c.49.2		8	25.21	even	5
750.2.h.c.199.2		8	25.19	even	10
3750.2.a.m.1.2		4	5.2	odd	4
3750.2.a.o.1.3		4	5.3	odd	4
3750.2.c.e.1249.2		8	5.4	even	2	inner
3750.2.c.e.1249.7		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -0.273457i q^{7} -1.00000i q^{8} -1.00000 q^{9} -4.79360 q^{11} -1.00000i q^{12} -1.73311i q^{13} +0.273457 q^{14} +1.00000 q^{16} +1.89149i q^{17} -1.00000i q^{18} +3.01062 q^{19} +0.273457 q^{21} -4.79360i q^{22} +4.64584i q^{23} +1.00000 q^{24} +1.73311 q^{26} -1.00000i q^{27} +0.273457i q^{28} -9.08715 q^{29} +3.83390 q^{31} +1.00000i q^{32} -4.79360i q^{33} -1.89149 q^{34} +1.00000 q^{36} -9.00947i q^{37} +3.01062i q^{38} +1.73311 q^{39} -7.58064 q^{41} +0.273457i q^{42} +2.88963i q^{43} +4.79360 q^{44} -4.64584 q^{46} -1.18806i q^{47} +1.00000i q^{48} +6.92522 q^{49} -1.89149 q^{51} +1.73311i q^{52} -11.6150i q^{53} +1.00000 q^{54} -0.273457 q^{56} +3.01062i q^{57} -9.08715i q^{58} +14.2895 q^{59} -5.15131 q^{61} +3.83390i q^{62} +0.273457i q^{63} -1.00000 q^{64} +4.79360 q^{66} -6.29000i q^{67} -1.89149i q^{68} -4.64584 q^{69} -1.40217 q^{71} +1.00000i q^{72} +1.78112i q^{73} +9.00947 q^{74} -3.01062 q^{76} +1.31085i q^{77} +1.73311i q^{78} +16.0593 q^{79} +1.00000 q^{81} -7.58064i q^{82} -15.1392i q^{83} -0.273457 q^{84} -2.88963 q^{86} -9.08715i q^{87} +4.79360i q^{88} +14.8273 q^{89} -0.473931 q^{91} -4.64584i q^{92} +3.83390i q^{93} +1.18806 q^{94} -1.00000 q^{96} +5.88597i q^{97} +6.92522i q^{98} +4.79360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{6} - 8 q^{9} - 20 q^{11} + 8 q^{14} + 8 q^{16} + 12 q^{19} + 8 q^{21} + 8 q^{24} + 4 q^{26} + 28 q^{29} - 36 q^{31} - 12 q^{34} + 8 q^{36} + 4 q^{39} - 28 q^{41} + 20 q^{44} + 8 q^{49}+ \cdots + 20 q^{99}+O(q^{100}) \) 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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