LMFDB - Embedded newform 950.4.b.i.799.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,4,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$56.0518145055$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 37x^{2} + 324 $ x^4 + 37*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.2
Root			$3.77200i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.4.b.i.799.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +8.77200i q^{3} -4.00000 q^{4} +17.5440 q^{6} +26.0880i q^{7} +8.00000i q^{8} -49.9480 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +8.77200i q^{3} -4.00000 q^{4} +17.5440 q^{6} +26.0880i q^{7} +8.00000i q^{8} -49.9480 q^{9} -4.22800 q^{11} -35.0880i q^{12} +64.0360i q^{13} +52.1760 q^{14} +16.0000 q^{16} +48.5440i q^{17} +99.8960i q^{18} -19.0000 q^{19} -228.844 q^{21} +8.45600i q^{22} +92.0360i q^{23} -70.1760 q^{24} +128.072 q^{26} -201.300i q^{27} -104.352i q^{28} +88.2120 q^{29} -81.9681 q^{31} -32.0000i q^{32} -37.0880i q^{33} +97.0880 q^{34} +199.792 q^{36} +23.6161i q^{37} +38.0000i q^{38} -561.724 q^{39} +17.7200 q^{41} +457.688i q^{42} +368.404i q^{43} +16.9120 q^{44} +184.072 q^{46} +497.812i q^{47} +140.352i q^{48} -337.584 q^{49} -425.828 q^{51} -256.144i q^{52} -536.876i q^{53} -402.600 q^{54} -208.704 q^{56} -166.668i q^{57} -176.424i q^{58} +36.7000 q^{59} +630.692 q^{61} +163.936i q^{62} -1303.04i q^{63} -64.0000 q^{64} -74.1760 q^{66} -282.556i q^{67} -194.176i q^{68} -807.340 q^{69} +595.552 q^{71} -399.584i q^{72} -597.048i q^{73} +47.2321 q^{74} +76.0000 q^{76} -110.300i q^{77} +1123.45i q^{78} -427.224 q^{79} +417.208 q^{81} -35.4400i q^{82} +493.768i q^{83} +915.376 q^{84} +736.808 q^{86} +773.796i q^{87} -33.8240i q^{88} +921.136 q^{89} -1670.57 q^{91} -368.144i q^{92} -719.024i q^{93} +995.624 q^{94} +280.704 q^{96} -1082.74i q^{97} +675.168i q^{98} +211.180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9}+O(q^{10}) $ 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9	$ 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9} - 34 q^{11} + 72 q^{14} + 64 q^{16} - 76 q^{19} - 454 q^{21} - 144 q^{24} + 68 q^{26} - 6 q^{29} + 424 q^{31} + 320 q^{34} + 184 q^{36} - 1102 q^{39} - 100 q^{41} + 136 q^{44} + 292 q^{46} - 120 q^{49} - 866 q^{51} - 756 q^{54} - 288 q^{56} + 574 q^{59} + 626 q^{61} - 256 q^{64} - 160 q^{66} - 1606 q^{69} + 400 q^{71} - 768 q^{74} + 304 q^{76} - 2700 q^{79} + 2284 q^{81} + 1816 q^{84} + 2708 q^{86} + 472 q^{89} - 4102 q^{91} + 1556 q^{94} + 576 q^{96} - 266 q^{99}+O(q^{100}) $ 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9 - 34 * q^11 + 72 * q^14 + 64 * q^16 - 76 * q^19 - 454 * q^21 - 144 * q^24 + 68 * q^26 - 6 * q^29 + 424 * q^31 + 320 * q^34 + 184 * q^36 - 1102 * q^39 - 100 * q^41 + 136 * q^44 + 292 * q^46 - 120 * q^49 - 866 * q^51 - 756 * q^54 - 288 * q^56 + 574 * q^59 + 626 * q^61 - 256 * q^64 - 160 * q^66 - 1606 * q^69 + 400 * q^71 - 768 * q^74 + 304 * q^76 - 2700 * q^79 + 2284 * q^81 + 1816 * q^84 + 2708 * q^86 + 472 * q^89 - 4102 * q^91 + 1556 * q^94 + 576 * q^96 - 266 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	8.77200i	1.68817i	0.536207	+	0.844086i	$0.319856\pi$
$3$	8.77200i	1.68817i	−0.536207	+	0.844086i	$0.680144\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	17.5440	1.19372
$7$	26.0880i	1.40862i	0.709893	+	0.704310i	$0.248743\pi$
$7$	26.0880i	1.40862i	−0.709893	+	0.704310i	$0.751257\pi$
$8$	8.00000i	0.353553i
$9$	−49.9480	−1.84993
$10$	0	0
$11$	−4.22800	−0.115890	−0.0579450	−	0.998320i	$-0.518455\pi$
$11$	−4.22800	−0.115890	−0.0579450	+	0.998320i	$0.518455\pi$
$12$	− 35.0880i	− 0.844086i
$13$	64.0360i	1.36618i	0.730332	+	0.683092i	$0.239365\pi$
$13$	64.0360i	1.36618i	−0.730332	+	0.683092i	$0.760635\pi$
$14$	52.1760	0.996045
$15$	0	0
$16$	16.0000	0.250000
$17$	48.5440i	0.692568i	0.938130	+	0.346284i	$0.112557\pi$
$17$	48.5440i	0.692568i	−0.938130	+	0.346284i	$0.887443\pi$
$18$	99.8960i	1.30810i
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	−228.844	−2.37799
$22$	8.45600i	0.0819466i
$23$	92.0360i	0.834384i	0.908818	+	0.417192i	$0.136986\pi$
$23$	92.0360i	0.834384i	−0.908818	+	0.417192i	$0.863014\pi$
$24$	−70.1760	−0.596859
$25$	0	0
$26$	128.072	0.966038
$27$	− 201.300i	− 1.43482i
$28$	− 104.352i	− 0.704310i
$29$	88.2120	0.564847	0.282424	−	0.959290i	$-0.408862\pi$
$29$	88.2120	0.564847	0.282424	+	0.959290i	$0.408862\pi$
$30$	0	0
$31$	−81.9681	−0.474900	−0.237450	−	0.971400i	$-0.576312\pi$
$31$	−81.9681	−0.474900	−0.237450	+	0.971400i	$0.576312\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 37.0880i	− 0.195642i
$34$	97.0880	0.489719
$35$	0	0
$36$	199.792	0.924963
$37$	23.6161i	0.104931i	0.998623	+	0.0524656i	$0.0167080\pi$
$37$	23.6161i	0.104931i	−0.998623	+	0.0524656i	$0.983292\pi$
$38$	38.0000i	0.162221i
$39$	−561.724	−2.30636
$40$	0	0
$41$	17.7200	0.0674976	0.0337488	−	0.999430i	$-0.489255\pi$
$41$	17.7200	0.0674976	0.0337488	+	0.999430i	$0.489255\pi$
$42$	457.688i	1.68150i
$43$	368.404i	1.30654i	0.757126	+	0.653268i	$0.226603\pi$
$43$	368.404i	1.30654i	−0.757126	+	0.653268i	$0.773397\pi$
$44$	16.9120	0.0579450
$45$	0	0
$46$	184.072	0.589999
$47$	497.812i	1.54497i	0.635036	+	0.772483i	$0.280985\pi$
$47$	497.812i	1.54497i	−0.635036	+	0.772483i	$0.719015\pi$
$48$	140.352i	0.422043i
$49$	−337.584	−0.984210
$50$	0	0
$51$	−425.828	−1.16917
$52$	− 256.144i	− 0.683092i
$53$	− 536.876i	− 1.39143i	−0.718320	−	0.695713i	$-0.755089\pi$
$53$	− 536.876i	− 1.39143i	0.718320	−	0.695713i	$-0.244911\pi$
$54$	−402.600	−1.01457
$55$	0	0
$56$	−208.704	−0.498022
$57$	− 166.668i	− 0.387293i
$58$	− 176.424i	− 0.399407i
$59$	36.7000	0.0809818	0.0404909	−	0.999180i	$-0.487108\pi$
$59$	36.7000	0.0809818	0.0404909	+	0.999180i	$0.487108\pi$
$60$	0	0
$61$	630.692	1.32380	0.661901	−	0.749592i	$-0.269750\pi$
$61$	630.692	1.32380	0.661901	+	0.749592i	$0.269750\pi$
$62$	163.936i	0.335805i
$63$	− 1303.04i	− 2.60584i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−74.1760	−0.138340
$67$	− 282.556i	− 0.515219i	−0.966249	−	0.257610i	$-0.917065\pi$
$67$	− 282.556i	− 0.515219i	0.966249	−	0.257610i	$-0.0829349\pi$
$68$	− 194.176i	− 0.346284i
$69$	−807.340	−1.40858
$70$	0	0
$71$	595.552	0.995480	0.497740	−	0.867326i	$-0.334163\pi$
$71$	595.552	0.995480	0.497740	+	0.867326i	$0.334163\pi$
$72$	− 399.584i	− 0.654048i
$73$	− 597.048i	− 0.957250i	−0.878020	−	0.478625i	$-0.841135\pi$
$73$	− 597.048i	− 0.957250i	0.878020	−	0.478625i	$-0.158865\pi$
$74$	47.2321	0.0741976
$75$	0	0
$76$	76.0000	0.114708
$77$	− 110.300i	− 0.163245i
$78$	1123.45i	1.63084i
$79$	−427.224	−0.608436	−0.304218	−	0.952602i	$-0.598395\pi$
$79$	−427.224	−0.608436	−0.304218	+	0.952602i	$0.598395\pi$
$80$	0	0
$81$	417.208	0.572302
$82$	− 35.4400i	− 0.0477280i
$83$	493.768i	0.652989i	0.945199	+	0.326495i	$0.105868\pi$
$83$	493.768i	0.652989i	−0.945199	+	0.326495i	$0.894132\pi$
$84$	915.376	1.18900
$85$	0	0
$86$	736.808	0.923861
$87$	773.796i	0.953559i
$88$	− 33.8240i	− 0.0409733i
$89$	921.136	1.09708	0.548541	−	0.836124i	$-0.315184\pi$
$89$	921.136	1.09708	0.548541	+	0.836124i	$0.315184\pi$
$90$	0	0
$91$	−1670.57	−1.92443
$92$	− 368.144i	− 0.417192i
$93$	− 719.024i	− 0.801713i
$94$	995.624	1.09246
$95$	0	0
$96$	280.704	0.298430
$97$	− 1082.74i	− 1.13336i	−0.823938	−	0.566680i	$-0.808227\pi$
$97$	− 1082.74i	− 1.13336i	0.823938	−	0.566680i	$-0.191773\pi$
$98$	675.168i	0.695942i
$99$	211.180	0.214388
$100$	0	0
$101$	−712.448	−0.701893	−0.350947	−	0.936395i	$-0.614140\pi$
$101$	−712.448	−0.701893	−0.350947	+	0.936395i	$0.614140\pi$
$102$	851.656i	0.826731i
$103$	− 26.4797i	− 0.0253313i	−0.999920	−	0.0126656i	$-0.995968\pi$
$103$	− 26.4797i	− 0.0253313i	0.999920	−	0.0126656i	$-0.00403171\pi$
$104$	−512.288	−0.483019
$105$	0	0
$106$	−1073.75	−0.983887
$107$	740.996i	0.669484i	0.942310	+	0.334742i	$0.108649\pi$
$107$	740.996i	0.669484i	−0.942310	+	0.334742i	$0.891351\pi$
$108$	805.200i	0.717411i
$109$	1983.08	1.74261	0.871304	−	0.490744i	$-0.163275\pi$
$109$	1983.08	1.74261	0.871304	+	0.490744i	$0.163275\pi$
$110$	0	0
$111$	−207.160	−0.177142
$112$	417.408i	0.352155i
$113$	− 718.720i	− 0.598332i	−0.954201	−	0.299166i	$-0.903292\pi$
$113$	− 718.720i	− 0.598332i	0.954201	−	0.299166i	$-0.0967085\pi$
$114$	−333.336	−0.273858
$115$	0	0
$116$	−352.848	−0.282424
$117$	− 3198.47i	− 2.52734i
$118$	− 73.3999i	− 0.0572628i
$119$	−1266.42	−0.975565
$120$	0	0
$121$	−1313.12	−0.986570
$122$	− 1261.38i	− 0.936069i
$123$	155.440i	0.113948i
$124$	327.872	0.237450
$125$	0	0
$126$	−2606.09	−1.84261
$127$	− 2610.72i	− 1.82413i	−0.410050	−	0.912063i	$-0.634489\pi$
$127$	− 2610.72i	− 1.82413i	0.410050	−	0.912063i	$-0.365511\pi$
$128$	128.000i	0.0883883i
$129$	−3231.64	−2.20566
$130$	0	0
$131$	−1216.69	−0.811472	−0.405736	−	0.913990i	$-0.632985\pi$
$131$	−1216.69	−0.811472	−0.405736	+	0.913990i	$0.632985\pi$
$132$	148.352i	0.0978211i
$133$	− 495.672i	− 0.323160i
$134$	−565.112	−0.364315
$135$	0	0
$136$	−388.352	−0.244860
$137$	− 1170.67i	− 0.730053i	−0.930997	−	0.365026i	$-0.881060\pi$
$137$	− 1170.67i	− 0.730053i	0.930997	−	0.365026i	$-0.118940\pi$
$138$	1614.68i	0.996020i
$139$	271.083	0.165417	0.0827086	−	0.996574i	$-0.473643\pi$
$139$	271.083	0.165417	0.0827086	+	0.996574i	$0.473643\pi$
$140$	0	0
$141$	−4366.81	−2.60817
$142$	− 1191.10i	− 0.703910i
$143$	− 270.744i	− 0.158327i
$144$	−799.168	−0.462482
$145$	0	0
$146$	−1194.10	−0.676878
$147$	− 2961.29i	− 1.66152i
$148$	− 94.4642i	− 0.0524656i
$149$	−1841.19	−1.01232	−0.506161	−	0.862439i	$-0.668936\pi$
$149$	−1841.19	−1.01232	−0.506161	+	0.862439i	$0.668936\pi$
$150$	0	0
$151$	3322.32	1.79051	0.895254	−	0.445557i	$-0.146994\pi$
$151$	3322.32	1.79051	0.895254	+	0.445557i	$0.146994\pi$
$152$	− 152.000i	− 0.0811107i
$153$	− 2424.68i	− 1.28120i
$154$	−220.600	−0.115432
$155$	0	0
$156$	2246.90	1.15318
$157$	− 243.616i	− 0.123839i	−0.998081	−	0.0619194i	$-0.980278\pi$
$157$	− 243.616i	− 0.123839i	0.998081	−	0.0619194i	$-0.0197222\pi$
$158$	854.448i	0.430229i
$159$	4709.48	2.34897
$160$	0	0
$161$	−2401.04	−1.17533
$162$	− 834.416i	− 0.404678i
$163$	− 2598.11i	− 1.24847i	−0.781238	−	0.624233i	$-0.785412\pi$
$163$	− 2598.11i	− 1.24847i	0.781238	−	0.624233i	$-0.214588\pi$
$164$	−70.8801	−0.0337488
$165$	0	0
$166$	987.537	0.461733
$167$	491.064i	0.227543i	0.993507	+	0.113772i	$0.0362932\pi$
$167$	491.064i	0.227543i	−0.993507	+	0.113772i	$0.963707\pi$
$168$	− 1830.75i	− 0.840748i
$169$	−1903.61	−0.866460
$170$	0	0
$171$	949.012	0.424402
$172$	− 1473.62i	− 0.653268i
$173$	1648.56i	0.724496i	0.932082	+	0.362248i	$0.117991\pi$
$173$	1648.56i	0.724496i	−0.932082	+	0.362248i	$0.882009\pi$
$174$	1547.59	0.674268
$175$	0	0
$176$	−67.6480	−0.0289725
$177$	321.932i	0.136711i
$178$	− 1842.27i	− 0.775754i
$179$	−2326.81	−0.971586	−0.485793	−	0.874074i	$-0.661469\pi$
$179$	−2326.81	−0.971586	−0.485793	+	0.874074i	$0.661469\pi$
$180$	0	0
$181$	−4637.46	−1.90442	−0.952208	−	0.305449i	$-0.901193\pi$
$181$	−4637.46	−1.90442	−0.952208	+	0.305449i	$0.901193\pi$
$182$	3341.14i	1.36078i
$183$	5532.43i	2.23480i
$184$	−736.288	−0.294999
$185$	0	0
$186$	−1438.05	−0.566897
$187$	− 205.244i	− 0.0802616i
$188$	− 1991.25i	− 0.772483i
$189$	5251.52	2.02112
$190$	0	0
$191$	5260.38	1.99281	0.996407	−	0.0846903i	$-0.0269901\pi$
$191$	5260.38	1.99281	0.996407	+	0.0846903i	$0.0269901\pi$
$192$	− 561.408i	− 0.211022i
$193$	16.1833i	0.00603575i	0.999995	+	0.00301787i	$0.000960620\pi$
$193$	16.1833i	0.00603575i	−0.999995	+	0.00301787i	$0.999039\pi$
$194$	−2165.49	−0.801407
$195$	0	0
$196$	1350.34	0.492105
$197$	− 3784.71i	− 1.36878i	−0.729116	−	0.684390i	$-0.760069\pi$
$197$	− 3784.71i	− 1.36878i	0.729116	−	0.684390i	$-0.239931\pi$
$198$	− 422.360i	− 0.151595i
$199$	−73.2079	−0.0260783	−0.0130391	−	0.999915i	$-0.504151\pi$
$199$	−73.2079	−0.0260783	−0.0130391	+	0.999915i	$0.504151\pi$
$200$	0	0
$201$	2478.58	0.869779
$202$	1424.90i	0.496313i
$203$	2301.28i	0.795655i
$204$	1703.31	0.584587
$205$	0	0
$206$	−52.9594	−0.0179119
$207$	− 4597.02i	− 1.54355i
$208$	1024.58i	0.341546i
$209$	80.3320	0.0265870
$210$	0	0
$211$	−2945.44	−0.961006	−0.480503	−	0.876993i	$-0.659546\pi$
$211$	−2945.44	−0.961006	−0.480503	+	0.876993i	$0.659546\pi$
$212$	2147.50i	0.695713i
$213$	5224.19i	1.68054i
$214$	1481.99	0.473397
$215$	0	0
$216$	1610.40	0.507286
$217$	− 2138.38i	− 0.668954i
$218$	− 3966.15i	− 1.23221i
$219$	5237.31	1.61600
$220$	0	0
$221$	−3108.57	−0.946175
$222$	414.320i	0.125258i
$223$	3125.30i	0.938499i	0.883066	+	0.469250i	$0.155476\pi$
$223$	3125.30i	0.938499i	−0.883066	+	0.469250i	$0.844524\pi$
$224$	834.816	0.249011
$225$	0	0
$226$	−1437.44	−0.423085
$227$	3577.80i	1.04611i	0.852299	+	0.523055i	$0.175208\pi$
$227$	3577.80i	1.04611i	−0.852299	+	0.523055i	$0.824792\pi$
$228$	666.672i	0.193647i
$229$	4802.00	1.38570	0.692850	−	0.721082i	$-0.256355\pi$
$229$	4802.00	1.38570	0.692850	+	0.721082i	$0.256355\pi$
$230$	0	0
$231$	967.552	0.275586
$232$	705.696i	0.199704i
$233$	5829.49i	1.63907i	0.573031	+	0.819534i	$0.305768\pi$
$233$	5829.49i	1.63907i	−0.573031	+	0.819534i	$0.694232\pi$
$234$	−6396.94	−1.78710
$235$	0	0
$236$	−146.800	−0.0404909
$237$	− 3747.61i	− 1.02714i
$238$	2532.83i	0.689828i
$239$	−1364.33	−0.369251	−0.184625	−	0.982809i	$-0.559107\pi$
$239$	−1364.33	−0.369251	−0.184625	+	0.982809i	$0.559107\pi$
$240$	0	0
$241$	−2647.22	−0.707563	−0.353782	−	0.935328i	$-0.615104\pi$
$241$	−2647.22	−0.707563	−0.353782	+	0.935328i	$0.615104\pi$
$242$	2626.25i	0.697610i
$243$	− 1775.35i	− 0.468679i
$244$	−2522.77	−0.661901
$245$	0	0
$246$	310.880	0.0805731
$247$	− 1216.68i	− 0.313424i
$248$	− 655.745i	− 0.167903i
$249$	−4331.34	−1.10236
$250$	0	0
$251$	1970.73	0.495582	0.247791	−	0.968814i	$-0.420295\pi$
$251$	1970.73	0.495582	0.247791	+	0.968814i	$0.420295\pi$
$252$	5212.18i	1.30292i
$253$	− 389.128i	− 0.0966967i
$254$	−5221.44	−1.28985
$255$	0	0
$256$	256.000	0.0625000
$257$	7915.82i	1.92131i	0.277752	+	0.960653i	$0.410411\pi$
$257$	7915.82i	1.92131i	−0.277752	+	0.960653i	$0.589589\pi$
$258$	6463.28i	1.55964i
$259$	−616.096	−0.147808
$260$	0	0
$261$	−4406.02	−1.04493
$262$	2433.38i	0.573798i
$263$	3287.96i	0.770892i	0.922730	+	0.385446i	$0.125952\pi$
$263$	3287.96i	0.770892i	−0.922730	+	0.385446i	$0.874048\pi$
$264$	296.704	0.0691700
$265$	0	0
$266$	−991.344	−0.228508
$267$	8080.21i	1.85206i
$268$	1130.22i	0.257610i
$269$	4749.61	1.07654	0.538269	−	0.842773i	$-0.319078\pi$
$269$	4749.61	1.07654	0.538269	+	0.842773i	$0.319078\pi$
$270$	0	0
$271$	242.661	0.0543933	0.0271967	−	0.999630i	$-0.491342\pi$
$271$	242.661	0.0543933	0.0271967	+	0.999630i	$0.491342\pi$
$272$	776.704i	0.173142i
$273$	− 14654.3i	− 3.24878i
$274$	−2341.34	−0.516225
$275$	0	0
$276$	3229.36	0.704292
$277$	4131.13i	0.896086i	0.894012	+	0.448043i	$0.147879\pi$
$277$	4131.13i	0.896086i	−0.894012	+	0.448043i	$0.852121\pi$
$278$	− 542.167i	− 0.116968i
$279$	4094.14	0.878530
$280$	0	0
$281$	1007.19	0.213822	0.106911	−	0.994269i	$-0.465904\pi$
$281$	1007.19	0.213822	0.106911	+	0.994269i	$0.465904\pi$
$282$	8733.62i	1.84425i
$283$	2333.63i	0.490176i	0.969501	+	0.245088i	$0.0788169\pi$
$283$	2333.63i	0.490176i	−0.969501	+	0.245088i	$0.921183\pi$
$284$	−2382.21	−0.497740
$285$	0	0
$286$	−541.488	−0.111954
$287$	462.280i	0.0950785i
$288$	1598.34i	0.327024i
$289$	2556.48	0.520350
$290$	0	0
$291$	9497.83	1.91331
$292$	2388.19i	0.478625i
$293$	− 1588.68i	− 0.316763i	−0.987378	−	0.158381i	$-0.949372\pi$
$293$	− 1588.68i	− 0.316763i	0.987378	−	0.158381i	$-0.0506275\pi$
$294$	−5922.58	−1.17487
$295$	0	0
$296$	−188.928	−0.0370988
$297$	851.096i	0.166282i
$298$	3682.38i	0.715820i
$299$	−5893.62	−1.13992
$300$	0	0
$301$	−9610.93	−1.84041
$302$	− 6644.64i	− 1.26608i
$303$	− 6249.59i	− 1.18492i
$304$	−304.000	−0.0573539
$305$	0	0
$306$	−4849.35	−0.905945
$307$	− 4057.46i	− 0.754304i	−0.926151	−	0.377152i	$-0.876903\pi$
$307$	− 4057.46i	− 0.754304i	0.926151	−	0.377152i	$-0.123097\pi$
$308$	441.200i	0.0816224i
$309$	232.280	0.0427636
$310$	0	0
$311$	2871.92	0.523638	0.261819	−	0.965117i	$-0.415678\pi$
$311$	2871.92	0.523638	0.261819	+	0.965117i	$0.415678\pi$
$312$	− 4493.79i	− 0.815420i
$313$	4322.67i	0.780612i	0.920685	+	0.390306i	$0.127631\pi$
$313$	4322.67i	0.780612i	−0.920685	+	0.390306i	$0.872369\pi$
$314$	−487.232	−0.0875672
$315$	0	0
$316$	1708.90	0.304218
$317$	− 2513.56i	− 0.445349i	−0.974893	−	0.222674i	$-0.928521\pi$
$317$	− 2513.56i	− 0.445349i	0.974893	−	0.222674i	$-0.0714786\pi$
$318$	− 9418.95i	− 1.66097i
$319$	−372.960	−0.0654601
$320$	0	0
$321$	−6500.02	−1.13021
$322$	4802.07i	0.831084i
$323$	− 922.336i	− 0.158886i
$324$	−1668.83	−0.286151
$325$	0	0
$326$	−5196.22	−0.882798
$327$	17395.6i	2.94182i
$328$	141.760i	0.0238640i
$329$	−12986.9	−2.17627
$330$	0	0
$331$	−4573.78	−0.759509	−0.379754	−	0.925087i	$-0.623992\pi$
$331$	−4573.78	−0.759509	−0.379754	+	0.925087i	$0.623992\pi$
$332$	− 1975.07i	− 0.326495i
$333$	− 1179.57i	− 0.194115i
$334$	982.129	0.160897
$335$	0	0
$336$	−3661.50	−0.594498
$337$	− 9001.71i	− 1.45506i	−0.686077	−	0.727529i	$-0.740669\pi$
$337$	− 9001.71i	− 1.45506i	0.686077	−	0.727529i	$-0.259331\pi$
$338$	3807.22i	0.612680i
$339$	6304.62	1.01009
$340$	0	0
$341$	346.561	0.0550361
$342$	− 1898.02i	− 0.300098i
$343$	141.289i	0.0222417i
$344$	−2947.23	−0.461931
$345$	0	0
$346$	3297.12	0.512296
$347$	− 9358.68i	− 1.44784i	−0.689884	−	0.723920i	$-0.742339\pi$
$347$	− 9358.68i	− 1.44784i	0.689884	−	0.723920i	$-0.257661\pi$
$348$	− 3095.18i	− 0.476780i
$349$	−5787.76	−0.887712	−0.443856	−	0.896098i	$-0.646390\pi$
$349$	−5787.76	−0.887712	−0.443856	+	0.896098i	$0.646390\pi$
$350$	0	0
$351$	12890.5	1.96023
$352$	135.296i	0.0204866i
$353$	5784.59i	0.872188i	0.899901	+	0.436094i	$0.143639\pi$
$353$	5784.59i	0.872188i	−0.899901	+	0.436094i	$0.856361\pi$
$354$	643.864	0.0966695
$355$	0	0
$356$	−3684.55	−0.548541
$357$	− 11109.0i	− 1.64692i
$358$	4653.62i	0.687015i
$359$	10132.3	1.48959	0.744796	−	0.667292i	$-0.232547\pi$
$359$	10132.3	1.48959	0.744796	+	0.667292i	$0.232547\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	9274.91i	1.34663i
$363$	− 11518.7i	− 1.66550i
$364$	6682.29	0.962217
$365$	0	0
$366$	11064.9	1.58025
$367$	6993.81i	0.994752i	0.867535	+	0.497376i	$0.165703\pi$
$367$	6993.81i	0.994752i	−0.867535	+	0.497376i	$0.834297\pi$
$368$	1472.58i	0.208596i
$369$	−885.080	−0.124866
$370$	0	0
$371$	14006.0	1.95999
$372$	2876.10i	0.400857i
$373$	6523.15i	0.905512i	0.891634	+	0.452756i	$0.149559\pi$
$373$	6523.15i	0.905512i	−0.891634	+	0.452756i	$0.850441\pi$
$374$	−410.488	−0.0567535
$375$	0	0
$376$	−3982.50	−0.546228
$377$	5648.75i	0.771685i
$378$	− 10503.0i	− 1.42915i
$379$	9782.00	1.32577	0.662886	−	0.748720i	$-0.269331\pi$
$379$	9782.00	1.32577	0.662886	+	0.748720i	$0.269331\pi$
$380$	0	0
$381$	22901.2	3.07944
$382$	− 10520.8i	− 1.40913i
$383$	9878.11i	1.31788i	0.752196	+	0.658940i	$0.228995\pi$
$383$	9878.11i	1.31788i	−0.752196	+	0.658940i	$0.771005\pi$
$384$	−1122.82	−0.149215
$385$	0	0
$386$	32.3666	0.00426792
$387$	− 18401.0i	− 2.41700i
$388$	4330.98i	0.566680i
$389$	7891.25	1.02854	0.514270	−	0.857628i	$-0.328063\pi$
$389$	7891.25	1.02854	0.514270	+	0.857628i	$0.328063\pi$
$390$	0	0
$391$	−4467.80	−0.577868
$392$	− 2700.67i	− 0.347971i
$393$	− 10672.8i	− 1.36991i
$394$	−7569.43	−0.967874
$395$	0	0
$396$	−844.720	−0.107194
$397$	2787.84i	0.352437i	0.984351	+	0.176219i	$0.0563865\pi$
$397$	2787.84i	0.352437i	−0.984351	+	0.176219i	$0.943613\pi$
$398$	146.416i	0.0184401i
$399$	4348.04	0.545549
$400$	0	0
$401$	1264.42	0.157461	0.0787306	−	0.996896i	$-0.474913\pi$
$401$	1264.42	0.157461	0.0787306	+	0.996896i	$0.474913\pi$
$402$	− 4957.16i	− 0.615027i
$403$	− 5248.91i	− 0.648801i
$404$	2849.79	0.350947
$405$	0	0
$406$	4602.55	0.562613
$407$	− 99.8486i	− 0.0121605i
$408$	− 3406.62i	− 0.413365i
$409$	8140.55	0.984166	0.492083	−	0.870548i	$-0.336236\pi$
$409$	8140.55	0.984166	0.492083	+	0.870548i	$0.336236\pi$
$410$	0	0
$411$	10269.1	1.23246
$412$	105.919i	0.0126656i
$413$	957.429i	0.114073i
$414$	−9194.03	−1.09145
$415$	0	0
$416$	2049.15	0.241510
$417$	2377.94i	0.279253i
$418$	− 160.664i	− 0.0187998i
$419$	9601.15	1.11944	0.559722	−	0.828680i	$-0.310908\pi$
$419$	9601.15	1.11944	0.559722	+	0.828680i	$0.310908\pi$
$420$	0	0
$421$	5702.48	0.660147	0.330074	−	0.943955i	$-0.392926\pi$
$421$	5702.48	0.660147	0.330074	+	0.943955i	$0.392926\pi$
$422$	5890.87i	0.679534i
$423$	− 24864.7i	− 2.85807i
$424$	4295.01	0.491943
$425$	0	0
$426$	10448.4	1.18832
$427$	16453.5i	1.86473i
$428$	− 2963.99i	− 0.334742i
$429$	2374.97	0.267283
$430$	0	0
$431$	−4025.72	−0.449912	−0.224956	−	0.974369i	$-0.572224\pi$
$431$	−4025.72	−0.449912	−0.224956	+	0.974369i	$0.572224\pi$
$432$	− 3220.80i	− 0.358706i
$433$	− 1347.10i	− 0.149510i	−0.997202	−	0.0747548i	$-0.976183\pi$
$433$	− 1347.10i	− 0.149510i	0.997202	−	0.0747548i	$-0.0238174\pi$
$434$	−4276.77	−0.473022
$435$	0	0
$436$	−7932.31	−0.871304
$437$	− 1748.68i	− 0.191421i
$438$	− 10474.6i	− 1.14269i
$439$	−4109.36	−0.446763	−0.223381	−	0.974731i	$-0.571710\pi$
$439$	−4109.36	−0.446763	−0.223381	+	0.974731i	$0.571710\pi$
$440$	0	0
$441$	16861.7	1.82072
$442$	6217.13i	0.669047i
$443$	6964.84i	0.746974i	0.927635	+	0.373487i	$0.121838\pi$
$443$	6964.84i	0.746974i	−0.927635	+	0.373487i	$0.878162\pi$
$444$	828.640	0.0885710
$445$	0	0
$446$	6250.59	0.663619
$447$	− 16150.9i	− 1.70897i
$448$	− 1669.63i	− 0.176078i
$449$	−3041.21	−0.319652	−0.159826	−	0.987145i	$-0.551093\pi$
$449$	−3041.21	−0.319652	−0.159826	+	0.987145i	$0.551093\pi$
$450$	0	0
$451$	−74.9202	−0.00782229
$452$	2874.88i	0.299166i
$453$	29143.4i	3.02269i
$454$	7155.60	0.739711
$455$	0	0
$456$	1333.34	0.136929
$457$	− 11984.3i	− 1.22670i	−0.789810	−	0.613352i	$-0.789821\pi$
$457$	− 11984.3i	− 1.22670i	0.789810	−	0.613352i	$-0.210179\pi$
$458$	− 9604.01i	− 0.979838i
$459$	9771.91	0.993712
$460$	0	0
$461$	−12126.7	−1.22515	−0.612577	−	0.790411i	$-0.709867\pi$
$461$	−12126.7	−1.22515	−0.612577	+	0.790411i	$0.709867\pi$
$462$	− 1935.10i	− 0.194868i
$463$	− 6399.19i	− 0.642323i	−0.947024	−	0.321162i	$-0.895927\pi$
$463$	− 6399.19i	− 0.642323i	0.947024	−	0.321162i	$-0.104073\pi$
$464$	1411.39	0.141212
$465$	0	0
$466$	11659.0	1.15900
$467$	− 993.366i	− 0.0984315i	−0.998788	−	0.0492157i	$-0.984328\pi$
$467$	− 993.366i	− 0.0984315i	0.998788	−	0.0492157i	$-0.0156722\pi$
$468$	12793.9i	1.26367i
$469$	7371.32	0.725748
$470$	0	0
$471$	2137.00	0.209061
$472$	293.600i	0.0286314i
$473$	− 1557.61i	− 0.151414i
$474$	−7495.22	−0.726301
$475$	0	0
$476$	5065.67	0.487782
$477$	26815.9i	2.57404i
$478$	2728.65i	0.261100i
$479$	−6639.36	−0.633320	−0.316660	−	0.948539i	$-0.602561\pi$
$479$	−6639.36	−0.633320	−0.316660	+	0.948539i	$0.602561\pi$
$480$	0	0
$481$	−1512.28	−0.143355
$482$	5294.45i	0.500323i
$483$	− 21061.9i	− 1.98416i
$484$	5252.50	0.493285
$485$	0	0
$486$	−3550.70	−0.331406
$487$	11088.8i	1.03179i	0.856652	+	0.515894i	$0.172540\pi$
$487$	11088.8i	1.03179i	−0.856652	+	0.515894i	$0.827460\pi$
$488$	5045.54i	0.468034i
$489$	22790.6	2.10762
$490$	0	0
$491$	−13215.2	−1.21465	−0.607324	−	0.794454i	$-0.707757\pi$
$491$	−13215.2	−1.21465	−0.607324	+	0.794454i	$0.707757\pi$
$492$	− 621.760i	− 0.0569738i
$493$	4282.17i	0.391195i
$494$	−2433.37	−0.221624
$495$	0	0
$496$	−1311.49	−0.118725
$497$	15536.8i	1.40225i
$498$	8662.67i	0.779485i
$499$	−410.640	−0.0368393	−0.0184196	−	0.999830i	$-0.505863\pi$
$499$	−410.640	−0.0368393	−0.0184196	+	0.999830i	$0.505863\pi$
$500$	0	0
$501$	−4307.62	−0.384132
$502$	− 3941.45i	− 0.350429i
$503$	− 9407.88i	− 0.833950i	−0.908918	−	0.416975i	$-0.863090\pi$
$503$	− 9407.88i	− 0.833950i	0.908918	−	0.416975i	$-0.136910\pi$
$504$	10424.4	0.921305
$505$	0	0
$506$	−778.256	−0.0683749
$507$	− 16698.5i	− 1.46273i
$508$	10442.9i	0.912063i
$509$	−10482.2	−0.912803	−0.456402	−	0.889774i	$-0.650862\pi$
$509$	−10482.2	−0.912803	−0.456402	+	0.889774i	$0.650862\pi$
$510$	0	0
$511$	15575.8	1.34840
$512$	− 512.000i	− 0.0441942i
$513$	3824.70i	0.329171i
$514$	15831.6	1.35857
$515$	0	0
$516$	12926.6	1.10283
$517$	− 2104.75i	− 0.179046i
$518$	1232.19i	0.104516i
$519$	−14461.2	−1.22307
$520$	0	0
$521$	−3181.02	−0.267492	−0.133746	−	0.991016i	$-0.542701\pi$
$521$	−3181.02	−0.267492	−0.133746	+	0.991016i	$0.542701\pi$
$522$	8812.03i	0.738874i
$523$	− 4360.12i	− 0.364541i	−0.983248	−	0.182270i	$-0.941655\pi$
$523$	− 4360.12i	− 0.364541i	0.983248	−	0.182270i	$-0.0583446\pi$
$524$	4866.77	0.405736
$525$	0	0
$526$	6575.93	0.545103
$527$	− 3979.06i	− 0.328900i
$528$	− 593.408i	− 0.0489106i
$529$	3696.37	0.303803
$530$	0	0
$531$	−1833.09	−0.149810
$532$	1982.69i	0.161580i
$533$	1134.72i	0.0922142i
$534$	16160.4	1.30961
$535$	0	0
$536$	2260.45	0.182158
$537$	− 20410.8i	− 1.64020i
$538$	− 9499.22i	− 0.761227i
$539$	1427.31	0.114060
$540$	0	0
$541$	−23681.2	−1.88195	−0.940973	−	0.338481i	$-0.890087\pi$
$541$	−23681.2	−1.88195	−0.940973	+	0.338481i	$0.890087\pi$
$542$	− 485.322i	− 0.0384619i
$543$	− 40679.8i	− 3.21498i
$544$	1553.41	0.122430
$545$	0	0
$546$	−29308.5	−2.29723
$547$	7373.25i	0.576339i	0.957579	+	0.288169i	$0.0930466\pi$
$547$	7373.25i	0.576339i	−0.957579	+	0.288169i	$0.906953\pi$
$548$	4682.69i	0.365026i
$549$	−31501.8	−2.44893
$550$	0	0
$551$	−1676.03	−0.129585
$552$	− 6458.72i	− 0.498010i
$553$	− 11145.4i	− 0.857055i
$554$	8262.27	0.633628
$555$	0	0
$556$	−1084.33	−0.0827086
$557$	− 4772.14i	− 0.363020i	−0.983389	−	0.181510i	$-0.941902\pi$
$557$	− 4772.14i	− 0.363020i	0.983389	−	0.181510i	$-0.0580984\pi$
$558$	− 8188.29i	− 0.621215i
$559$	−23591.1	−1.78497
$560$	0	0
$561$	1800.40	0.135495
$562$	− 2014.38i	− 0.151195i
$563$	7276.49i	0.544702i	0.962198	+	0.272351i	$0.0878012\pi$
$563$	7276.49i	0.544702i	−0.962198	+	0.272351i	$0.912199\pi$
$564$	17467.2	1.30408
$565$	0	0
$566$	4667.26	0.346607
$567$	10884.1i	0.806156i
$568$	4764.42i	0.351955i
$569$	10685.1	0.787245	0.393622	−	0.919272i	$-0.371222\pi$
$569$	10685.1	0.787245	0.393622	+	0.919272i	$0.371222\pi$
$570$	0	0
$571$	14856.1	1.08881	0.544404	−	0.838823i	$-0.316756\pi$
$571$	14856.1	1.08881	0.544404	+	0.838823i	$0.316756\pi$
$572$	1082.98i	0.0791635i
$573$	46144.0i	3.36421i
$574$	924.560	0.0672306
$575$	0	0
$576$	3196.67	0.231241
$577$	− 3212.67i	− 0.231794i	−0.993261	−	0.115897i	$-0.963026\pi$
$577$	− 3212.67i	− 0.231794i	0.993261	−	0.115897i	$-0.0369742\pi$
$578$	− 5112.96i	− 0.367943i
$579$	−141.960	−0.0101894
$580$	0	0
$581$	−12881.4	−0.919814
$582$	− 18995.7i	− 1.35291i
$583$	2269.91i	0.161252i
$584$	4776.39	0.338439
$585$	0	0
$586$	−3177.35	−0.223985
$587$	22321.1i	1.56949i	0.619818	+	0.784745i	$0.287206\pi$
$587$	22321.1i	1.56949i	−0.619818	+	0.784745i	$0.712794\pi$
$588$	11845.2i	0.830758i
$589$	1557.39	0.108950
$590$	0	0
$591$	33199.5	2.31074
$592$	377.857i	0.0262328i
$593$	− 8202.50i	− 0.568021i	−0.958821	−	0.284010i	$-0.908335\pi$
$593$	− 8202.50i	− 0.568021i	0.958821	−	0.284010i	$-0.0916650\pi$
$594$	1702.19	0.117579
$595$	0	0
$596$	7364.75	0.506161
$597$	− 642.180i	− 0.0440246i
$598$	11787.2i	0.806047i
$599$	−10583.3	−0.721906	−0.360953	−	0.932584i	$-0.617548\pi$
$599$	−10583.3	−0.721906	−0.360953	+	0.932584i	$0.617548\pi$
$600$	0	0
$601$	−9051.94	−0.614370	−0.307185	−	0.951650i	$-0.599387\pi$
$601$	−9051.94	−0.614370	−0.307185	+	0.951650i	$0.599387\pi$
$602$	19221.9i	1.30137i
$603$	14113.1i	0.953118i
$604$	−13289.3	−0.895254
$605$	0	0
$606$	−12499.2	−0.837863
$607$	− 8123.48i	− 0.543199i	−0.962410	−	0.271599i	$-0.912447\pi$
$607$	− 8123.48i	− 0.543199i	0.962410	−	0.271599i	$-0.0875526\pi$
$608$	608.000i	0.0405554i
$609$	−20186.8	−1.34320
$610$	0	0
$611$	−31877.9	−2.11071
$612$	9698.71i	0.640600i
$613$	22384.7i	1.47490i	0.675404	+	0.737448i	$0.263969\pi$
$613$	22384.7i	1.47490i	−0.675404	+	0.737448i	$0.736031\pi$
$614$	−8114.91	−0.533373
$615$	0	0
$616$	882.400	0.0577158
$617$	− 11349.1i	− 0.740517i	−0.928929	−	0.370259i	$-0.879269\pi$
$617$	− 11349.1i	− 0.740517i	0.928929	−	0.370259i	$-0.120731\pi$
$618$	− 464.560i	− 0.0302384i
$619$	9106.25	0.591294	0.295647	−	0.955297i	$-0.404465\pi$
$619$	9106.25	0.591294	0.295647	+	0.955297i	$0.404465\pi$
$620$	0	0
$621$	18526.9	1.19719
$622$	− 5743.84i	− 0.370268i
$623$	24030.6i	1.54537i
$624$	−8987.59	−0.576589
$625$	0	0
$626$	8645.34	0.551976
$627$	704.672i	0.0448834i
$628$	974.464i	0.0619194i
$629$	−1146.42	−0.0726720
$630$	0	0
$631$	−27784.2	−1.75289	−0.876444	−	0.481505i	$-0.840090\pi$
$631$	−27784.2	−1.75289	−0.876444	+	0.481505i	$0.840090\pi$
$632$	− 3417.79i	− 0.215115i
$633$	− 25837.4i	− 1.62234i
$634$	−5027.12	−0.314909
$635$	0	0
$636$	−18837.9	−1.17448
$637$	− 21617.5i	− 1.34461i
$638$	745.921i	0.0462873i
$639$	−29746.7	−1.84156
$640$	0	0
$641$	−16958.3	−1.04495	−0.522476	−	0.852654i	$-0.674992\pi$
$641$	−16958.3	−1.04495	−0.522476	+	0.852654i	$0.674992\pi$
$642$	13000.0i	0.799176i
$643$	4754.37i	0.291592i	0.989315	+	0.145796i	$0.0465744\pi$
$643$	4754.37i	0.291592i	−0.989315	+	0.145796i	$0.953426\pi$
$644$	9604.15	0.587665
$645$	0	0
$646$	−1844.67	−0.112349
$647$	11254.0i	0.683831i	0.939731	+	0.341916i	$0.111076\pi$
$647$	11254.0i	0.683831i	−0.939731	+	0.341916i	$0.888924\pi$
$648$	3337.66i	0.202339i
$649$	−155.167	−0.00938498
$650$	0	0
$651$	18757.9	1.12931
$652$	10392.4i	0.624233i
$653$	− 15515.1i	− 0.929793i	−0.885365	−	0.464896i	$-0.846092\pi$
$653$	− 15515.1i	− 0.929793i	0.885365	−	0.464896i	$-0.153908\pi$
$654$	34791.1	2.08018
$655$	0	0
$656$	283.520	0.0168744
$657$	29821.4i	1.77084i
$658$	25973.9i	1.53885i
$659$	−17203.2	−1.01691	−0.508453	−	0.861090i	$-0.669783\pi$
$659$	−17203.2	−1.01691	−0.508453	+	0.861090i	$0.669783\pi$
$660$	0	0
$661$	2305.65	0.135672	0.0678361	−	0.997696i	$-0.478390\pi$
$661$	2305.65	0.135672	0.0678361	+	0.997696i	$0.478390\pi$
$662$	9147.55i	0.537054i
$663$	− 27268.3i	− 1.59731i
$664$	−3950.15	−0.230867
$665$	0	0
$666$	−2359.15	−0.137260
$667$	8118.69i	0.471299i
$668$	− 1964.26i	− 0.113772i
$669$	−27415.1	−1.58435
$670$	0	0
$671$	−2666.57	−0.153415
$672$	7323.01i	0.420374i
$673$	− 14242.8i	− 0.815782i	−0.913031	−	0.407891i	$-0.866264\pi$
$673$	− 14242.8i	− 0.815782i	0.913031	−	0.407891i	$-0.133736\pi$
$674$	−18003.4	−1.02888
$675$	0	0
$676$	7614.45	0.433230
$677$	13480.0i	0.765256i	0.923902	+	0.382628i	$0.124981\pi$
$677$	13480.0i	0.765256i	−0.923902	+	0.382628i	$0.875019\pi$
$678$	− 12609.2i	− 0.714240i
$679$	28246.6	1.59647
$680$	0	0
$681$	−31384.5	−1.76601
$682$	− 693.122i	− 0.0389164i
$683$	27626.1i	1.54771i	0.633365	+	0.773854i	$0.281673\pi$
$683$	27626.1i	1.54771i	−0.633365	+	0.773854i	$0.718327\pi$
$684$	−3796.05	−0.212201
$685$	0	0
$686$	282.578	0.0157272
$687$	42123.2i	2.33930i
$688$	5894.46i	0.326634i
$689$	34379.4	1.90094
$690$	0	0
$691$	17419.7	0.959009	0.479505	−	0.877539i	$-0.340816\pi$
$691$	17419.7	0.959009	0.479505	+	0.877539i	$0.340816\pi$
$692$	− 6594.24i	− 0.362248i
$693$	5509.27i	0.301991i
$694$	−18717.4	−1.02378
$695$	0	0
$696$	−6190.37	−0.337134
$697$	860.201i	0.0467467i
$698$	11575.5i	0.627707i
$699$	−51136.3	−2.76703
$700$	0	0
$701$	5069.39	0.273136	0.136568	−	0.990631i	$-0.456393\pi$
$701$	5069.39	0.273136	0.136568	+	0.990631i	$0.456393\pi$
$702$	− 25780.9i	− 1.38609i
$703$	− 448.705i	− 0.0240729i
$704$	270.592	0.0144862
$705$	0	0
$706$	11569.2	0.616730
$707$	− 18586.3i	− 0.988701i
$708$	− 1287.73i	− 0.0683556i
$709$	16758.9	0.887719	0.443860	−	0.896096i	$-0.353609\pi$
$709$	16758.9	0.887719	0.443860	+	0.896096i	$0.353609\pi$
$710$	0	0
$711$	21339.0	1.12556
$712$	7369.09i	0.387877i
$713$	− 7544.02i	− 0.396249i
$714$	−22218.0	−1.16455
$715$	0	0
$716$	9307.24	0.485793
$717$	− 11967.9i	− 0.623359i
$718$	− 20264.6i	− 1.05330i
$719$	3885.84	0.201554	0.100777	−	0.994909i	$-0.467867\pi$
$719$	3885.84	0.201554	0.100777	+	0.994909i	$0.467867\pi$
$720$	0	0
$721$	690.803	0.0356822
$722$	− 722.000i	− 0.0372161i
$723$	− 23221.5i	− 1.19449i
$724$	18549.8	0.952208
$725$	0	0
$726$	−23037.5	−1.17769
$727$	− 6468.37i	− 0.329984i	−0.986295	−	0.164992i	$-0.947240\pi$
$727$	− 6468.37i	− 0.329984i	0.986295	−	0.164992i	$-0.0527598\pi$
$728$	− 13364.6i	− 0.680390i
$729$	26838.0	1.36351
$730$	0	0
$731$	−17883.8	−0.904865
$732$	− 22129.7i	− 1.11740i
$733$	25245.5i	1.27212i	0.771640	+	0.636059i	$0.219437\pi$
$733$	25245.5i	1.27212i	−0.771640	+	0.636059i	$0.780563\pi$
$734$	13987.6	0.703396
$735$	0	0
$736$	2945.15	0.147500
$737$	1194.65i	0.0597087i
$738$	1770.16i	0.0882933i
$739$	−3229.28	−0.160746	−0.0803728	−	0.996765i	$-0.525611\pi$
$739$	−3229.28	−0.160746	−0.0803728	+	0.996765i	$0.525611\pi$
$740$	0	0
$741$	10672.8	0.529114
$742$	− 28012.0i	− 1.38592i
$743$	18876.2i	0.932033i	0.884776	+	0.466016i	$0.154311\pi$
$743$	18876.2i	0.932033i	−0.884776	+	0.466016i	$0.845689\pi$
$744$	5752.19	0.283448
$745$	0	0
$746$	13046.3	0.640294
$747$	− 24662.8i	− 1.20798i
$748$	820.976i	0.0401308i
$749$	−19331.1	−0.943049
$750$	0	0
$751$	24895.8	1.20967	0.604833	−	0.796352i	$-0.293240\pi$
$751$	24895.8	1.20967	0.604833	+	0.796352i	$0.293240\pi$
$752$	7964.99i	0.386241i
$753$	17287.2i	0.836628i
$754$	11297.5	0.545664
$755$	0	0
$756$	−21006.1	−1.01056
$757$	36203.2i	1.73821i	0.494624	+	0.869107i	$0.335306\pi$
$757$	36203.2i	1.73821i	−0.494624	+	0.869107i	$0.664694\pi$
$758$	− 19564.0i	− 0.937462i
$759$	3413.43	0.163241
$760$	0	0
$761$	11417.5	0.543868	0.271934	−	0.962316i	$-0.412337\pi$
$761$	11417.5	0.543868	0.271934	+	0.962316i	$0.412337\pi$
$762$	− 45802.5i	− 2.17749i
$763$	51734.5i	2.45467i
$764$	−21041.5	−0.996407
$765$	0	0
$766$	19756.2	0.931881
$767$	2350.12i	0.110636i
$768$	2245.63i	0.105511i
$769$	−39414.5	−1.84828	−0.924138	−	0.382058i	$-0.875215\pi$
$769$	−39414.5	−1.84828	−0.924138	+	0.382058i	$0.875215\pi$
$770$	0	0
$771$	−69437.6	−3.24350
$772$	− 64.7332i	− 0.00301787i
$773$	− 14268.5i	− 0.663910i	−0.943295	−	0.331955i	$-0.892292\pi$
$773$	− 14268.5i	− 0.663910i	0.943295	−	0.331955i	$-0.107708\pi$
$774$	−36802.1	−1.70908
$775$	0	0
$776$	8661.95	0.400704
$777$	− 5404.39i	− 0.249526i
$778$	− 15782.5i	− 0.727288i
$779$	−336.680	−0.0154850
$780$	0	0
$781$	−2517.99	−0.115366
$782$	8935.59i	0.408614i
$783$	− 17757.1i	− 0.810455i
$784$	−5401.35	−0.246053
$785$	0	0
$786$	−21345.7	−0.968669
$787$	2922.28i	0.132361i	0.997808	+	0.0661804i	$0.0210813\pi$
$787$	2922.28i	0.132361i	−0.997808	+	0.0661804i	$0.978919\pi$
$788$	15138.9i	0.684390i
$789$	−28842.0	−1.30140
$790$	0	0
$791$	18750.0	0.842823
$792$	1689.44i	0.0757976i
$793$	40387.0i	1.80856i
$794$	5575.67	0.249211
$795$	0	0
$796$	292.832	0.0130391
$797$	7724.25i	0.343296i	0.985158	+	0.171648i	$0.0549092\pi$
$797$	7724.25i	0.343296i	−0.985158	+	0.171648i	$0.945091\pi$
$798$	− 8696.07i	− 0.385762i
$799$	−24165.8	−1.06999
$800$	0	0
$801$	−46008.9	−2.02952
$802$	− 2528.83i	− 0.111342i
$803$	2524.32i	0.110936i
$804$	−9914.32	−0.434890
$805$	0	0
$806$	−10497.8	−0.458772
$807$	41663.6i	1.81738i
$808$	− 5699.58i	− 0.248157i
$809$	−42980.8	−1.86789	−0.933947	−	0.357412i	$-0.883659\pi$
$809$	−42980.8	−1.86789	−0.933947	+	0.357412i	$0.883659\pi$
$810$	0	0
$811$	28749.5	1.24480	0.622398	−	0.782701i	$-0.286158\pi$
$811$	28749.5	1.24480	0.622398	+	0.782701i	$0.286158\pi$
$812$	− 9205.11i	− 0.397827i
$813$	2128.62i	0.0918253i
$814$	−199.697	−0.00859875
$815$	0	0
$816$	−6813.25	−0.292293
$817$	− 6999.68i	− 0.299740i
$818$	− 16281.1i	− 0.695911i
$819$	83441.8	3.56006
$820$	0	0
$821$	−30274.8	−1.28696	−0.643482	−	0.765461i	$-0.722511\pi$
$821$	−30274.8	−1.28696	−0.643482	+	0.765461i	$0.722511\pi$
$822$	− 20538.3i	− 0.871477i
$823$	17296.1i	0.732568i	0.930503	+	0.366284i	$0.119370\pi$
$823$	17296.1i	0.732568i	−0.930503	+	0.366284i	$0.880630\pi$
$824$	211.838	0.00895596
$825$	0	0
$826$	1914.86	0.0806615
$827$	2022.80i	0.0850541i	0.999095	+	0.0425271i	$0.0135409\pi$
$827$	2022.80i	0.0850541i	−0.999095	+	0.0425271i	$0.986459\pi$
$828$	18388.1i	0.771775i
$829$	43239.0	1.81152	0.905762	−	0.423786i	$-0.139299\pi$
$829$	43239.0	1.81152	0.905762	+	0.423786i	$0.139299\pi$
$830$	0	0
$831$	−36238.3	−1.51275
$832$	− 4098.31i	− 0.170773i
$833$	− 16387.7i	− 0.681632i
$834$	4755.89	0.197462
$835$	0	0
$836$	−321.328	−0.0132935
$837$	16500.2i	0.681397i
$838$	− 19202.3i	− 0.791567i
$839$	−27435.9	−1.12895	−0.564477	−	0.825449i	$-0.690922\pi$
$839$	−27435.9	−1.12895	−0.564477	+	0.825449i	$0.690922\pi$
$840$	0	0
$841$	−16607.6	−0.680948
$842$	− 11405.0i	− 0.466795i
$843$	8835.09i	0.360969i
$844$	11781.7	0.480503
$845$	0	0
$846$	−49729.5	−2.02096
$847$	− 34256.8i	− 1.38970i
$848$	− 8590.02i	− 0.347857i
$849$	−20470.6	−0.827502
$850$	0	0
$851$	−2173.53	−0.0875530
$852$	− 20896.7i	− 0.840271i
$853$	− 20978.4i	− 0.842071i	−0.907044	−	0.421035i	$-0.861667\pi$
$853$	− 20978.4i	− 0.842071i	0.907044	−	0.421035i	$-0.138333\pi$
$854$	32907.0	1.31857
$855$	0	0
$856$	−5927.97	−0.236698
$857$	30822.4i	1.22856i	0.789089	+	0.614279i	$0.210553\pi$
$857$	30822.4i	1.22856i	−0.789089	+	0.614279i	$0.789447\pi$
$858$	− 4749.94i	− 0.188998i
$859$	39267.6	1.55971	0.779856	−	0.625959i	$-0.215292\pi$
$859$	39267.6	1.55971	0.779856	+	0.625959i	$0.215292\pi$
$860$	0	0
$861$	−4055.12	−0.160509
$862$	8051.45i	0.318136i
$863$	− 24131.3i	− 0.951842i	−0.879488	−	0.475921i	$-0.842115\pi$
$863$	− 24131.3i	− 0.951842i	0.879488	−	0.475921i	$-0.157885\pi$
$864$	−6441.60	−0.253643
$865$	0	0
$866$	−2694.21	−0.105719
$867$	22425.4i	0.878441i
$868$	8553.54i	0.334477i
$869$	1806.30	0.0705116
$870$	0	0
$871$	18093.8	0.703885
$872$	15864.6i	0.616105i
$873$	54080.9i	2.09663i
$874$	−3497.37	−0.135355
$875$	0	0
$876$	−20949.2	−0.808001
$877$	− 39380.6i	− 1.51629i	−0.652084	−	0.758147i	$-0.726105\pi$
$877$	− 39380.6i	− 1.51629i	0.652084	−	0.758147i	$-0.273895\pi$
$878$	8218.71i	0.315909i
$879$	13935.9	0.534750
$880$	0	0
$881$	30887.5	1.18119	0.590595	−	0.806968i	$-0.298893\pi$
$881$	30887.5	1.18119	0.590595	+	0.806968i	$0.298893\pi$
$882$	− 33723.3i	− 1.28744i
$883$	28191.9i	1.07444i	0.843441	+	0.537221i	$0.180526\pi$
$883$	28191.9i	1.07444i	−0.843441	+	0.537221i	$0.819474\pi$
$884$	12434.3	0.473088
$885$	0	0
$886$	13929.7	0.528190
$887$	− 2760.58i	− 0.104500i	−0.998634	−	0.0522498i	$-0.983361\pi$
$887$	− 2760.58i	− 0.104500i	0.998634	−	0.0522498i	$-0.0166392\pi$
$888$	− 1657.28i	− 0.0626292i
$889$	68108.5	2.56950
$890$	0	0
$891$	−1763.95	−0.0663240
$892$	− 12501.2i	− 0.469250i
$893$	− 9458.43i	− 0.354439i
$894$	−32301.8	−1.20843
$895$	0	0
$896$	−3339.26	−0.124506
$897$	− 51698.9i	− 1.92439i
$898$	6082.42i	0.226028i
$899$	−7230.57	−0.268246
$900$	0	0
$901$	26062.1	0.963657
$902$	149.840i	0.00553120i
$903$	− 84307.1i	− 3.10694i
$904$	5749.76	0.211542
$905$	0	0
$906$	58286.8	2.13736
$907$	18969.1i	0.694443i	0.937783	+	0.347222i	$0.112875\pi$
$907$	18969.1i	0.694443i	−0.937783	+	0.347222i	$0.887125\pi$
$908$	− 14311.2i	− 0.523055i
$909$	35585.4	1.29845
$910$	0	0
$911$	−48732.9	−1.77233	−0.886164	−	0.463371i	$-0.846640\pi$
$911$	−48732.9	−1.77233	−0.886164	+	0.463371i	$0.846640\pi$
$912$	− 2666.69i	− 0.0968233i
$913$	− 2087.65i	− 0.0756749i
$914$	−23968.7	−0.867411
$915$	0	0
$916$	−19208.0	−0.692850
$917$	− 31741.1i	− 1.14306i
$918$	− 19543.8i	− 0.702660i
$919$	35850.4	1.28683	0.643414	−	0.765518i	$-0.277517\pi$
$919$	35850.4	1.28683	0.643414	+	0.765518i	$0.277517\pi$
$920$	0	0
$921$	35592.0	1.27340
$922$	24253.4i	0.866315i
$923$	38136.8i	1.36001i
$924$	−3870.21	−0.137793
$925$	0	0
$926$	−12798.4	−0.454191
$927$	1322.61i	0.0468610i
$928$	− 2822.79i	− 0.0998518i
$929$	−22936.8	−0.810044	−0.405022	−	0.914307i	$-0.632736\pi$
$929$	−22936.8	−0.810044	−0.405022	+	0.914307i	$0.632736\pi$
$930$	0	0
$931$	6414.10	0.225793
$932$	− 23318.0i	− 0.819534i
$933$	25192.5i	0.883992i
$934$	−1986.73	−0.0696016
$935$	0	0
$936$	25587.8	0.893550
$937$	− 47925.4i	− 1.67092i	−0.549548	−	0.835462i	$-0.685200\pi$
$937$	− 47925.4i	− 1.67092i	0.549548	−	0.835462i	$-0.314800\pi$
$938$	− 14742.6i	− 0.513181i
$939$	−37918.5	−1.31781
$940$	0	0
$941$	−25842.2	−0.895251	−0.447626	−	0.894221i	$-0.647730\pi$
$941$	−25842.2	−0.895251	−0.447626	+	0.894221i	$0.647730\pi$
$942$	− 4274.00i	− 0.147829i
$943$	1630.88i	0.0563189i
$944$	587.199	0.0202455
$945$	0	0
$946$	−3115.22	−0.107066
$947$	− 36562.8i	− 1.25463i	−0.778766	−	0.627314i	$-0.784154\pi$
$947$	− 36562.8i	− 1.25463i	0.778766	−	0.627314i	$-0.215846\pi$
$948$	14990.4i	0.513572i
$949$	38232.6	1.30778
$950$	0	0
$951$	22048.9	0.751825
$952$	− 10131.3i	− 0.344914i
$953$	29813.1i	1.01337i	0.862132	+	0.506684i	$0.169129\pi$
$953$	29813.1i	1.01337i	−0.862132	+	0.506684i	$0.830871\pi$
$954$	53631.8	1.82012
$955$	0	0
$956$	5457.31	0.184625
$957$	− 3271.61i	− 0.110508i
$958$	13278.7i	0.447825i
$959$	30540.5	1.02837
$960$	0	0
$961$	−23072.2	−0.774470
$962$	3024.56i	0.101368i
$963$	− 37011.3i	− 1.23850i
$964$	10588.9	0.353782
$965$	0	0
$966$	−42123.8	−1.40301
$967$	− 30315.5i	− 1.00815i	−0.863660	−	0.504075i	$-0.831833\pi$
$967$	− 30315.5i	− 1.00815i	0.863660	−	0.504075i	$-0.168167\pi$
$968$	− 10505.0i	− 0.348805i
$969$	8090.73	0.268227
$970$	0	0
$971$	26455.6	0.874357	0.437178	−	0.899375i	$-0.355978\pi$
$971$	26455.6	0.874357	0.437178	+	0.899375i	$0.355978\pi$
$972$	7101.41i	0.234339i
$973$	7072.03i	0.233010i
$974$	22177.6	0.729584
$975$	0	0
$976$	10091.1	0.330950
$977$	− 30207.7i	− 0.989183i	−0.869126	−	0.494591i	$-0.835318\pi$
$977$	− 30207.7i	− 0.989183i	0.869126	−	0.494591i	$-0.164682\pi$
$978$	− 45581.3i	− 1.49032i
$979$	−3894.56	−0.127141
$980$	0	0
$981$	−99050.7	−3.22370
$982$	26430.3i	0.858886i
$983$	− 5878.48i	− 0.190737i	−0.995442	−	0.0953685i	$-0.969597\pi$
$983$	− 5878.48i	− 0.190737i	0.995442	−	0.0953685i	$-0.0304029\pi$
$984$	−1243.52	−0.0402866
$985$	0	0
$986$	8564.33	0.276616
$987$	− 113921.i	− 3.67392i
$988$	4866.74i	0.156712i
$989$	−33906.4	−1.09015
$990$	0	0
$991$	−42532.3	−1.36335	−0.681676	−	0.731654i	$-0.738749\pi$
$991$	−42532.3	−1.36335	−0.681676	+	0.731654i	$0.738749\pi$
$992$	2622.98i	0.0839513i
$993$	− 40121.2i	− 1.28218i
$994$	31073.5	0.991542
$995$	0	0
$996$	17325.3	0.551179
$997$	− 6320.28i	− 0.200767i	−0.994949	−	0.100384i	$-0.967993\pi$
$997$	− 6320.28i	− 0.200767i	0.994949	−	0.100384i	$-0.0320070\pi$
$998$	821.281i	0.0260493i
$999$	4753.91	0.150558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.4.b.i.799.2		4
5.2	odd	4		38.4.a.c.1.2	✓	2
5.3	odd	4		950.4.a.e.1.1		2
5.4	even	2	inner	950.4.b.i.799.3		4
15.2	even	4		342.4.a.h.1.2		2
20.7	even	4		304.4.a.c.1.1		2
35.27	even	4		1862.4.a.e.1.1		2
40.27	even	4		1216.4.a.p.1.2		2
40.37	odd	4		1216.4.a.g.1.1		2
95.37	even	4		722.4.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.a.c.1.2	✓	2	5.2	odd	4
304.4.a.c.1.1		2	20.7	even	4
342.4.a.h.1.2		2	15.2	even	4
722.4.a.f.1.1		2	95.37	even	4
950.4.a.e.1.1		2	5.3	odd	4
950.4.b.i.799.2		4	1.1	even	1	trivial
950.4.b.i.799.3		4	5.4	even	2	inner
1216.4.a.g.1.1		2	40.37	odd	4
1216.4.a.p.1.2		2	40.27	even	4
1862.4.a.e.1.1		2	35.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +8.77200i q^{3} -4.00000 q^{4} +17.5440 q^{6} +26.0880i q^{7} +8.00000i q^{8} -49.9480 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +8.77200i q^{3} -4.00000 q^{4} +17.5440 q^{6} +26.0880i q^{7} +8.00000i q^{8} -49.9480 q^{9} -4.22800 q^{11} -35.0880i q^{12} +64.0360i q^{13} +52.1760 q^{14} +16.0000 q^{16} +48.5440i q^{17} +99.8960i q^{18} -19.0000 q^{19} -228.844 q^{21} +8.45600i q^{22} +92.0360i q^{23} -70.1760 q^{24} +128.072 q^{26} -201.300i q^{27} -104.352i q^{28} +88.2120 q^{29} -81.9681 q^{31} -32.0000i q^{32} -37.0880i q^{33} +97.0880 q^{34} +199.792 q^{36} +23.6161i q^{37} +38.0000i q^{38} -561.724 q^{39} +17.7200 q^{41} +457.688i q^{42} +368.404i q^{43} +16.9120 q^{44} +184.072 q^{46} +497.812i q^{47} +140.352i q^{48} -337.584 q^{49} -425.828 q^{51} -256.144i q^{52} -536.876i q^{53} -402.600 q^{54} -208.704 q^{56} -166.668i q^{57} -176.424i q^{58} +36.7000 q^{59} +630.692 q^{61} +163.936i q^{62} -1303.04i q^{63} -64.0000 q^{64} -74.1760 q^{66} -282.556i q^{67} -194.176i q^{68} -807.340 q^{69} +595.552 q^{71} -399.584i q^{72} -597.048i q^{73} +47.2321 q^{74} +76.0000 q^{76} -110.300i q^{77} +1123.45i q^{78} -427.224 q^{79} +417.208 q^{81} -35.4400i q^{82} +493.768i q^{83} +915.376 q^{84} +736.808 q^{86} +773.796i q^{87} -33.8240i q^{88} +921.136 q^{89} -1670.57 q^{91} -368.144i q^{92} -719.024i q^{93} +995.624 q^{94} +280.704 q^{96} -1082.74i q^{97} +675.168i q^{98} +211.180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9}+O(q^{10}) \) 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9	\( 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9} - 34 q^{11} + 72 q^{14} + 64 q^{16} - 76 q^{19} - 454 q^{21} - 144 q^{24} + 68 q^{26} - 6 q^{29} + 424 q^{31} + 320 q^{34} + 184 q^{36} - 1102 q^{39} - 100 q^{41} + 136 q^{44} + 292 q^{46} - 120 q^{49} - 866 q^{51} - 756 q^{54} - 288 q^{56} + 574 q^{59} + 626 q^{61} - 256 q^{64} - 160 q^{66} - 1606 q^{69} + 400 q^{71} - 768 q^{74} + 304 q^{76} - 2700 q^{79} + 2284 q^{81} + 1816 q^{84} + 2708 q^{86} + 472 q^{89} - 4102 q^{91} + 1556 q^{94} + 576 q^{96} - 266 q^{99}+O(q^{100}) \) 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9 - 34 * q^11 + 72 * q^14 + 64 * q^16 - 76 * q^19 - 454 * q^21 - 144 * q^24 + 68 * q^26 - 6 * q^29 + 424 * q^31 + 320 * q^34 + 184 * q^36 - 1102 * q^39 - 100 * q^41 + 136 * q^44 + 292 * q^46 - 120 * q^49 - 866 * q^51 - 756 * q^54 - 288 * q^56 + 574 * q^59 + 626 * q^61 - 256 * q^64 - 160 * q^66 - 1606 * q^69 + 400 * q^71 - 768 * q^74 + 304 * q^76 - 2700 * q^79 + 2284 * q^81 + 1816 * q^84 + 2708 * q^86 + 472 * q^89 - 4102 * q^91 + 1556 * q^94 + 576 * q^96 - 266 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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