LMFDB - Embedded newform 312.4.m.a.181.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, 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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.38
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.481589 + 2.78713i) q^{2} +3.00000i q^{3} +(-7.53614 - 2.68450i) q^{4} -21.7286 q^{5} +(-8.36138 - 1.44477i) q^{6} +13.0550i q^{7} +(11.1114 - 19.7114i) q^{8} -9.00000 q^{9} +(10.4643 - 60.5604i) q^{10} -21.2862 q^{11} +(8.05349 - 22.6084i) q^{12} +(29.0436 - 36.7895i) q^{13} +(-36.3859 - 6.28713i) q^{14} -65.1858i q^{15} +(49.5870 + 40.4615i) q^{16} -41.3375 q^{17} +(4.33430 - 25.0841i) q^{18} -147.281 q^{19} +(163.750 + 58.3304i) q^{20} -39.1649 q^{21} +(10.2512 - 59.3273i) q^{22} +58.4571 q^{23} +(59.1341 + 33.3341i) q^{24} +347.133 q^{25} +(88.5499 + 98.6656i) q^{26} -27.0000i q^{27} +(35.0460 - 98.3842i) q^{28} +180.566i q^{29} +(181.681 + 31.3928i) q^{30} +272.316i q^{31} +(-136.652 + 118.719i) q^{32} -63.8585i q^{33} +(19.9077 - 115.213i) q^{34} -283.666i q^{35} +(67.8253 + 24.1605i) q^{36} +337.223 q^{37} +(70.9287 - 410.490i) q^{38} +(110.369 + 87.1309i) q^{39} +(-241.434 + 428.301i) q^{40} -118.629i q^{41} +(18.8614 - 109.158i) q^{42} -404.289i q^{43} +(160.416 + 57.1427i) q^{44} +195.558 q^{45} +(-28.1523 + 162.927i) q^{46} +145.629i q^{47} +(-121.385 + 148.761i) q^{48} +172.568 q^{49} +(-167.175 + 967.503i) q^{50} -124.012i q^{51} +(-317.638 + 199.284i) q^{52} -409.695i q^{53} +(75.2524 + 13.0029i) q^{54} +462.519 q^{55} +(257.331 + 145.058i) q^{56} -441.842i q^{57} +(-503.260 - 86.9586i) q^{58} -809.386 q^{59} +(-174.991 + 491.250i) q^{60} +34.5359i q^{61} +(-758.979 - 131.144i) q^{62} -117.495i q^{63} +(-265.076 - 438.040i) q^{64} +(-631.078 + 799.385i) q^{65} +(177.982 + 30.7535i) q^{66} +750.048 q^{67} +(311.525 + 110.970i) q^{68} +175.371i q^{69} +(790.614 + 136.611i) q^{70} -455.788i q^{71} +(-100.002 + 177.402i) q^{72} -130.323i q^{73} +(-162.403 + 939.883i) q^{74} +1041.40i q^{75} +(1109.93 + 395.375i) q^{76} -277.890i q^{77} +(-295.997 + 265.650i) q^{78} +108.684 q^{79} +(-1077.46 - 879.173i) q^{80} +81.0000 q^{81} +(330.634 + 57.1304i) q^{82} +201.602 q^{83} +(295.153 + 105.138i) q^{84} +898.206 q^{85} +(1126.81 + 194.701i) q^{86} -541.698 q^{87} +(-236.518 + 419.580i) q^{88} -1268.20i q^{89} +(-94.1783 + 545.043i) q^{90} +(480.286 + 379.164i) q^{91} +(-440.541 - 156.928i) q^{92} -816.948 q^{93} +(-405.887 - 70.1333i) q^{94} +3200.21 q^{95} +(-356.158 - 409.956i) q^{96} -1421.15i q^{97} +(-83.1066 + 480.968i) q^{98} +191.576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.481589	+	2.78713i	−0.170267	+	0.985398i
$2$	−0.481589	+	2.78713i	−0.170267	+	0.985398i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−7.53614	−	2.68450i	−0.942018	−	0.335562i
$5$	−21.7286			−1.94347			−0.971733	−	0.236082i	$-0.924137\pi$
$5$	−21.7286			−1.94347			−0.971733	+	0.236082i	$0.924137\pi$
$6$	−8.36138	−	1.44477i	−0.568920	−	0.0983039i
$7$			13.0550i			0.704902i	0.935830	+	0.352451i	$0.114652\pi$
$7$			13.0550i			0.704902i	−0.935830	+	0.352451i	$0.885348\pi$
$8$	11.1114	−	19.7114i	0.491057	−	0.871127i
$9$	−9.00000			−0.333333
$10$	10.4643	−	60.5604i	0.330909	−	1.91509i
$11$	−21.2862			−0.583457			−0.291728	−	0.956501i	$-0.594230\pi$
$11$	−21.2862			−0.583457			−0.291728	+	0.956501i	$0.594230\pi$
$12$	8.05349	−	22.6084i	0.193737	−	0.543874i
$13$	29.0436	−	36.7895i	0.619635	−	0.784890i
$13$	29.0436	−	36.7895i	0.619635	−	0.784890i
$14$	−36.3859	−	6.28713i	−0.694609	−	0.120022i
$15$		−	65.1858i		−	1.12206i
$16$	49.5870	+	40.4615i	0.774796	+	0.632211i
$17$	−41.3375			−0.589754			−0.294877	−	0.955535i	$-0.595279\pi$
$17$	−41.3375			−0.589754			−0.294877	+	0.955535i	$0.595279\pi$
$18$	4.33430	−	25.0841i	0.0567558	−	0.328466i
$19$	−147.281			−1.77834			−0.889171	−	0.457574i	$-0.848718\pi$
$19$	−147.281			−1.77834			−0.889171	+	0.457574i	$0.848718\pi$
$20$	163.750	+	58.3304i	1.83078	+	0.652154i
$21$	−39.1649			−0.406976
$22$	10.2512	−	59.3273i	0.0993436	−	0.574937i
$23$	58.4571			0.529963			0.264981	−	0.964254i	$-0.414634\pi$
$23$	58.4571			0.529963			0.264981	+	0.964254i	$0.414634\pi$
$24$	59.1341	+	33.3341i	0.502946	+	0.283512i
$25$	347.133			2.77706
$26$	88.5499	+	98.6656i	0.667926	+	0.744228i
$27$		−	27.0000i		−	0.192450i
$28$	35.0460	−	98.3842i	0.236538	−	0.664031i
$29$			180.566i			1.15622i	0.815960	+	0.578108i	$0.196209\pi$
$29$			180.566i			1.15622i	−0.815960	+	0.578108i	$0.803791\pi$
$30$	181.681	+	31.3928i	1.10568	+	0.191050i
$31$			272.316i			1.57772i	0.614571	+	0.788861i	$0.289329\pi$
$31$			272.316i			1.57772i	−0.614571	+	0.788861i	$0.710671\pi$
$32$	−136.652	+	118.719i	−0.754902	+	0.655838i
$33$		−	63.8585i		−	0.336859i
$34$	19.9077	−	115.213i	0.100416	−	0.581142i
$35$		−	283.666i		−	1.36995i
$36$	67.8253	+	24.1605i	0.314006	+	0.111854i
$37$	337.223			1.49835			0.749177	−	0.662370i	$-0.230449\pi$
$37$	337.223			1.49835			0.749177	+	0.662370i	$0.230449\pi$
$38$	70.9287	−	410.490i	0.302794	−	1.75238i
$39$	110.369	+	87.1309i	0.453157	+	0.357746i
$40$	−241.434	+	428.301i	−0.954353	+	1.69301i
$41$		−	118.629i		−	0.451871i	−0.974142	−	0.225936i	$-0.927456\pi$
$41$		−	118.629i		−	0.451871i	0.974142	−	0.225936i	$-0.0725439\pi$
$42$	18.8614	−	109.158i	0.0692946	−	0.401033i
$43$		−	404.289i		−	1.43380i	−0.697174	−	0.716902i	$-0.745560\pi$
$43$		−	404.289i		−	1.43380i	0.697174	−	0.716902i	$-0.254440\pi$
$44$	160.416	+	57.1427i	0.549627	+	0.195786i
$45$	195.558			0.647822
$46$	−28.1523	+	162.927i	−0.0902353	+	0.522224i
$47$			145.629i			0.451961i	0.974132	+	0.225981i	$0.0725586\pi$
$47$			145.629i			0.451961i	−0.974132	+	0.225981i	$0.927441\pi$
$48$	−121.385	+	148.761i	−0.365007	+	0.447329i
$49$	172.568			0.503113
$50$	−167.175	+	967.503i	−0.472843	+	2.73651i
$51$		−	124.012i		−	0.340495i
$52$	−317.638	+	199.284i	−0.847087	+	0.531455i
$53$		−	409.695i		−	1.06181i	−0.847432	−	0.530905i	$-0.821852\pi$
$53$		−	409.695i		−	1.06181i	0.847432	−	0.530905i	$-0.178148\pi$
$54$	75.2524	+	13.0029i	0.189640	+	0.0327680i
$55$	462.519			1.13393
$56$	257.331	+	145.058i	0.614060	+	0.346147i
$57$		−	441.842i		−	1.02673i
$58$	−503.260	−	86.9586i	−1.13933	−	0.196866i
$59$	−809.386			−1.78599			−0.892993	−	0.450071i	$-0.851399\pi$
$59$	−809.386			−1.78599			−0.892993	+	0.450071i	$0.851399\pi$
$60$	−174.991	+	491.250i	−0.376521	+	1.05700i
$61$			34.5359i			0.0724896i	0.999343	+	0.0362448i	$0.0115396\pi$
$61$			34.5359i			0.0724896i	−0.999343	+	0.0362448i	$0.988460\pi$
$62$	−758.979	−	131.144i	−1.55468	−	0.268635i
$63$		−	117.495i		−	0.234967i
$64$	−265.076	−	438.040i	−0.517726	−	0.855547i
$65$	−631.078	+	799.385i	−1.20424	+	1.52541i
$66$	177.982	+	30.7535i	0.331940	+	0.0573561i
$67$	750.048			1.36766			0.683828	−	0.729643i	$-0.260314\pi$
$67$	750.048			1.36766			0.683828	+	0.729643i	$0.260314\pi$
$68$	311.525	+	110.970i	0.555559	+	0.197899i
$69$			175.371i			0.305974i
$70$	790.614	+	136.611i	1.34995	+	0.233258i
$71$		−	455.788i		−	0.761861i	−0.924604	−	0.380930i	$-0.875604\pi$
$71$		−	455.788i		−	0.761861i	0.924604	−	0.380930i	$-0.124396\pi$
$72$	−100.002	+	177.402i	−0.163686	+	0.290376i
$73$		−	130.323i		−	0.208947i	−0.994528	−	0.104473i	$-0.966684\pi$
$73$		−	130.323i		−	0.208947i	0.994528	−	0.104473i	$-0.0333157\pi$
$74$	−162.403	+	939.883i	−0.255121	+	1.47648i
$75$			1041.40i			1.60334i
$76$	1109.93	+	395.375i	1.67523	+	0.596744i
$77$		−	277.890i		−	0.411280i
$78$	−295.997	+	265.650i	−0.429680	+	0.385627i
$79$	108.684			0.154784			0.0773918	−	0.997001i	$-0.475341\pi$
$79$	108.684			0.154784			0.0773918	+	0.997001i	$0.475341\pi$
$80$	−1077.46	−	879.173i	−1.50579	−	1.22868i
$81$	81.0000			0.111111
$82$	330.634	+	57.1304i	0.445273	+	0.0769389i
$83$	201.602			0.266611			0.133306	−	0.991075i	$-0.457441\pi$
$83$	201.602			0.266611			0.133306	+	0.991075i	$0.457441\pi$
$84$	295.153	+	105.138i	0.383378	+	0.136566i
$85$	898.206			1.14617
$86$	1126.81	+	194.701i	1.41287	+	0.244130i
$87$	−541.698			−0.667542
$88$	−236.518	+	419.580i	−0.286511	+	0.508265i
$89$		−	1268.20i		−	1.51044i	−0.655470	−	0.755221i	$-0.727529\pi$
$89$		−	1268.20i		−	1.51044i	0.655470	−	0.755221i	$-0.272471\pi$
$90$	−94.1783	+	545.043i	−0.110303	+	0.638363i
$91$	480.286	+	379.164i	0.553271	+	0.436782i
$92$	−440.541	−	156.928i	−0.499235	−	0.177835i
$93$	−816.948			−0.910899
$94$	−405.887	−	70.1333i	−0.445362	−	0.0769543i
$95$	3200.21			3.45615
$96$	−356.158	−	409.956i	−0.378648	−	0.435843i
$97$		−	1421.15i		−	1.48759i	−0.668410	−	0.743793i	$-0.733025\pi$
$97$		−	1421.15i		−	1.48759i	0.668410	−	0.743793i	$-0.266975\pi$
$98$	−83.1066	+	480.968i	−0.0856636	+	0.495766i
$99$	191.576			0.194486
$100$	−2616.04	−	931.876i	−2.61604	−	0.931876i
$101$		−	655.469i		−	0.645759i	−0.946440	−	0.322879i	$-0.895349\pi$
$101$		−	655.469i		−	0.645759i	0.946440	−	0.322879i	$-0.104651\pi$
$102$	345.638	+	59.7230i	0.335523	+	0.0579751i
$103$	464.213			0.444080			0.222040	−	0.975038i	$-0.428728\pi$
$103$	464.213			0.444080			0.222040	+	0.975038i	$0.428728\pi$
$104$	−402.458	−	981.271i	−0.379464	−	0.925207i
$105$	850.999			0.790943
$106$	1141.87	+	197.304i	1.04630	+	0.180791i
$107$			283.880i			0.256484i	0.991743	+	0.128242i	$0.0409334\pi$
$107$			283.880i			0.256484i	−0.991743	+	0.128242i	$0.959067\pi$
$108$	−72.4814	+	203.476i	−0.0645790	+	0.181291i
$109$	−422.005			−0.370833			−0.185416	−	0.982660i	$-0.559363\pi$
$109$	−422.005			−0.370833			−0.185416	+	0.982660i	$0.559363\pi$
$110$	−222.744	+	1289.10i	−0.193071	+	1.11737i
$111$			1011.67i			0.865075i
$112$	−528.224	+	647.356i	−0.445647	+	0.546156i
$113$	−873.891			−0.727511			−0.363755	−	0.931495i	$-0.618506\pi$
$113$	−873.891			−0.727511			−0.363755	+	0.931495i	$0.618506\pi$
$114$	1231.47	+	212.786i	1.01173	+	0.174818i
$115$	−1270.19			−1.02996
$116$	484.729	−	1360.77i	0.387982	−	1.08918i
$117$	−261.393	+	331.106i	−0.206545	+	0.261630i
$118$	389.791	−	2255.86i	0.304095	−	1.75991i
$119$		−	539.660i		−	0.415719i
$120$	−1284.90	−	724.303i	−0.977458	−	0.550996i
$121$	−877.899			−0.659578
$122$	−96.2558	−	16.6321i	−0.0714311	−	0.0123426i
$123$	355.887			0.260888
$124$	731.031	−	2052.21i	0.529424	−	1.48624i
$125$	−4826.63			−3.45366
$126$	327.473	+	56.5841i	0.231536	+	0.0400073i
$127$	−535.808			−0.374372			−0.187186	−	0.982324i	$-0.559937\pi$
$127$	−535.808			−0.374372			−0.187186	+	0.982324i	$0.559937\pi$
$128$	1348.53	−	527.844i	0.931206	−	0.364494i
$129$	1212.87			0.827807
$130$	−1924.07	−	2143.87i	−1.29809	−	1.44638i
$131$			1795.81i			1.19772i	0.800855	+	0.598859i	$0.204379\pi$
$131$			1795.81i			1.19772i	−0.800855	+	0.598859i	$0.795621\pi$
$132$	−171.428	+	481.247i	−0.113037	+	0.317327i
$133$		−	1922.75i		−	1.25356i
$134$	−361.215	+	2090.48i	−0.232867	+	1.34769i
$135$			586.673i			0.374020i
$136$	−459.315	+	814.818i	−0.289603	+	0.513751i
$137$			818.868i			0.510662i	0.966854	+	0.255331i	$0.0821844\pi$
$137$			818.868i			0.510662i	−0.966854	+	0.255331i	$0.917816\pi$
$138$	−488.782	−	84.4568i	−0.301506	−	0.0520974i
$139$			688.906i			0.420376i	0.977661	+	0.210188i	$0.0674076\pi$
$139$			688.906i			0.420376i	−0.977661	+	0.210188i	$0.932592\pi$
$140$	−761.502	+	2137.75i	−0.459705	+	1.29052i
$141$	−436.887			−0.260940
$142$	1270.34	+	219.502i	0.750736	+	0.129720i
$143$	−618.228	+	783.108i	−0.361530	+	0.457950i
$144$	−446.283	−	364.154i	−0.258265	−	0.210737i
$145$		−	3923.45i		−	2.24707i
$146$	363.226	+	62.7619i	0.205896	+	0.0355768i
$147$			517.703i			0.290472i
$148$	−2541.36	−	905.274i	−1.41148	−	0.502791i
$149$	1873.85			1.03028			0.515140	−	0.857106i	$-0.327740\pi$
$149$	1873.85			1.03028			0.515140	+	0.857106i	$0.327740\pi$
$150$	−2902.51	−	501.525i	−1.57992	−	0.272996i
$151$		−	2042.90i		−	1.10098i	−0.834841	−	0.550492i	$-0.814440\pi$
$151$		−	2042.90i		−	1.10098i	0.834841	−	0.550492i	$-0.185560\pi$
$152$	−1636.49	+	2903.10i	−0.873268	+	1.54916i
$153$	372.037			0.196585
$154$	774.516	+	133.829i	0.405274	+	0.0700275i
$155$		−	5917.05i		−	3.06625i
$156$	−597.851	−	952.915i	−0.306836	−	0.489066i
$157$			416.042i			0.211489i	0.994393	+	0.105744i	$0.0337225\pi$
$157$			416.042i			0.211489i	−0.994393	+	0.105744i	$0.966277\pi$
$158$	−52.3409	+	302.916i	−0.0263546	+	0.152523i
$159$	1229.08			0.613036
$160$	2969.26	−	2579.61i	1.46713	−	1.27460i
$161$			763.156i			0.373572i
$162$	−39.0087	+	225.757i	−0.0189186	+	0.109489i
$163$	1218.69			0.585615			0.292808	−	0.956171i	$-0.405410\pi$
$163$	1218.69			0.585615			0.292808	+	0.956171i	$0.405410\pi$
$164$	−318.459	+	894.005i	−0.151631	+	0.425671i
$165$			1387.56i			0.654674i
$166$	−97.0894	+	561.891i	−0.0453952	+	0.262718i
$167$		−	2020.62i		−	0.936287i	−0.883653	−	0.468143i	$-0.844923\pi$
$167$		−	2020.62i		−	0.936287i	0.883653	−	0.468143i	$-0.155077\pi$
$168$	−435.175	+	771.994i	−0.199848	+	0.354528i
$169$	−509.936	−	2137.00i	−0.232106	−	0.972691i
$170$	−432.566	+	2503.41i	−0.195155	+	1.12943i
$171$	1325.53			0.592781
$172$	−1085.31	+	3046.78i	−0.481130	+	1.35067i
$173$			2227.75i			0.979031i	0.871995	+	0.489516i	$0.162826\pi$
$173$			2227.75i			0.979031i	−0.871995	+	0.489516i	$0.837174\pi$
$174$	260.876	−	1509.78i	0.113661	−	0.657794i
$175$			4531.81i			1.95756i
$176$	−1055.52	−	861.271i	−0.452060	−	0.368868i
$177$		−	2428.16i		−	1.03114i
$178$	3534.65	+	610.753i	1.48839	+	0.257179i
$179$		−	141.910i		−	0.0592560i	−0.999561	−	0.0296280i	$-0.990568\pi$
$179$		−	141.910i		−	0.0592560i	0.999561	−	0.0296280i	$-0.00943227\pi$
$180$	−1473.75	−	524.974i	−0.610260	−	0.217385i
$181$		−	701.384i		−	0.288030i	−0.989575	−	0.144015i	$-0.953999\pi$
$181$		−	701.384i		−	0.288030i	0.989575	−	0.144015i	$-0.0460014\pi$
$182$	−1288.08	+	1156.02i	−0.524608	+	0.470822i
$183$	−103.608			−0.0418519
$184$	649.537	−	1152.27i	0.260242	−	0.461665i
$185$	−7327.39			−2.91200
$186$	393.433	−	2276.94i	0.155096	−	0.897598i
$187$	879.917			0.344096
$188$	390.941	−	1097.48i	0.151661	−	0.425756i
$189$	352.484			0.135659
$190$	−1541.18	+	8919.38i	−0.588469	+	3.40568i
$191$	2179.85			0.825803			0.412902	−	0.910776i	$-0.364515\pi$
$191$	2179.85			0.825803			0.412902	+	0.910776i	$0.364515\pi$
$192$	1314.12	−	795.227i	0.493950	−	0.298909i
$193$		−	3338.36i		−	1.24508i	−0.782588	−	0.622540i	$-0.786101\pi$
$193$		−	3338.36i		−	1.24508i	0.782588	−	0.622540i	$-0.213899\pi$
$194$	3960.92	+	684.409i	1.46586	+	0.253287i
$195$	−2398.16	−	1893.23i	−0.880695	−	0.695268i
$196$	−1300.49	−	463.257i	−0.473941	−	0.168826i
$197$	2468.85			0.892885			0.446443	−	0.894812i	$-0.352691\pi$
$197$	2468.85			0.892885			0.446443	+	0.894812i	$0.352691\pi$
$198$	−92.2606	+	533.945i	−0.0331145	+	0.191646i
$199$	−959.929			−0.341948			−0.170974	−	0.985276i	$-0.554691\pi$
$199$	−959.929			−0.341948			−0.170974	+	0.985276i	$0.554691\pi$
$200$	3857.11	−	6842.46i	1.36370	−	2.41917i
$201$			2250.15i			0.789617i
$202$	1826.88	+	315.667i	0.636329	+	0.109952i
$203$	−2357.28			−0.815020
$204$	−332.911	+	934.576i	−0.114257	+	0.320752i
$205$			2577.64i			0.878197i
$206$	−223.560	+	1293.82i	−0.0756123	+	0.437596i
$207$	−526.114			−0.176654
$208$	2928.74	−	649.131i	0.976307	−	0.216390i
$209$	3135.04			1.03759
$210$	−409.832	+	2371.84i	−0.134672	+	0.779394i
$211$		−	821.620i		−	0.268070i	−0.990977	−	0.134035i	$-0.957207\pi$
$211$		−	821.620i		−	0.268070i	0.990977	−	0.134035i	$-0.0427934\pi$
$212$	−1099.82	+	3087.52i	−0.356303	+	1.00024i
$213$	1367.37			0.439861
$214$	−791.211	−	136.714i	−0.252739	−	0.0436708i
$215$			8784.65i			2.78655i
$216$	−532.207	−	300.007i	−0.167649	−	0.0945040i
$217$	−3555.08			−1.11214
$218$	203.233	−	1176.18i	0.0631407	−	0.365418i
$219$	390.968			0.120635
$220$	−3485.61	−	1241.63i	−1.06818	−	0.380503i
$221$	−1200.59	+	1520.79i	−0.365432	+	0.462892i
$222$	−2819.65	−	487.208i	−0.852443	−	0.147294i
$223$		−	3360.91i		−	1.00925i	−0.863338	−	0.504626i	$-0.831630\pi$
$223$		−	3360.91i		−	1.00925i	0.863338	−	0.504626i	$-0.168370\pi$
$224$	−1549.88	−	1783.99i	−0.462301	−	0.532132i
$225$	−3124.19			−0.925687
$226$	420.856	−	2435.64i	0.123871	−	0.716888i
$227$	3682.56			1.07674			0.538371	−	0.842708i	$-0.319040\pi$
$227$	3682.56			1.07674			0.538371	+	0.842708i	$0.319040\pi$
$228$	−1186.12	+	3329.79i	−0.344531	+	0.967195i
$229$	4219.89			1.21772			0.608861	−	0.793277i	$-0.291627\pi$
$229$	4219.89			1.21772			0.608861	+	0.793277i	$0.291627\pi$
$230$	611.710	−	3540.18i	0.175369	−	1.01493i
$231$	833.671			0.237453
$232$	3559.20	+	2006.33i	1.00721	+	0.567768i
$233$	379.674			0.106752			0.0533761	−	0.998574i	$-0.483002\pi$
$233$	379.674			0.106752			0.0533761	+	0.998574i	$0.483002\pi$
$234$	−796.949	−	887.991i	−0.222642	−	0.248076i
$235$		−	3164.32i		−	0.878372i
$236$	6099.65	+	2172.80i	1.68243	+	0.599309i
$237$			326.052i			0.0893643i
$238$	1504.10	+	259.894i	0.409648	+	0.0707833i
$239$			2710.64i			0.733626i	0.930295	+	0.366813i	$0.119551\pi$
$239$			2710.64i			0.733626i	−0.930295	+	0.366813i	$0.880449\pi$
$240$	2637.52	−	3232.37i	0.709379	−	0.869368i
$241$			4760.79i			1.27249i	0.771489	+	0.636243i	$0.219513\pi$
$241$			4760.79i			1.27249i	−0.771489	+	0.636243i	$0.780487\pi$
$242$	422.786	−	2446.81i	0.112305	−	0.649947i
$243$			243.000i			0.0641500i
$244$	92.7114	−	260.267i	0.0243248	−	0.0682865i
$245$	−3749.66			−0.977783
$246$	−171.391	+	991.902i	−0.0444207	+	0.257079i
$247$	−4277.57	+	5418.39i	−1.10192	+	1.39580i
$248$	5367.72	+	3025.80i	1.37440	+	0.774752i
$249$			604.807i			0.153928i
$250$	2324.45	−	13452.4i	0.588045	−	3.40323i
$251$		−	2592.76i		−	0.652006i	−0.945369	−	0.326003i	$-0.894298\pi$
$251$		−	2592.76i		−	0.652006i	0.945369	−	0.326003i	$-0.105702\pi$
$252$	−315.414	+	885.458i	−0.0788462	+	0.221344i
$253$	−1244.33			−0.309210
$254$	258.039	−	1493.36i	0.0637434	−	0.368906i
$255$			2694.62i			0.661740i
$256$	821.732	+	4012.73i	0.200618	+	0.979669i
$257$	3934.89			0.955065			0.477533	−	0.878614i	$-0.341531\pi$
$257$	3934.89			0.955065			0.477533	+	0.878614i	$0.341531\pi$
$258$	−584.104	+	3380.42i	−0.140948	+	0.815719i
$259$			4402.44i			1.05619i
$260$	6901.84	−	4330.16i	1.64628	−	1.03286i
$261$		−	1625.09i		−	0.385405i
$262$	−5005.16	−	864.844i	−1.18023	−	0.203932i
$263$	−457.722			−0.107317			−0.0536585	−	0.998559i	$-0.517088\pi$
$263$	−457.722			−0.107317			−0.0536585	+	0.998559i	$0.517088\pi$
$264$	−1258.74	−	709.555i	−0.293447	−	0.165417i
$265$			8902.10i			2.06359i
$266$	5358.94	+	925.973i	1.23525	+	0.213440i
$267$	3804.61			0.872055
$268$	−5652.47	−	2013.50i	−1.28836	−	0.458934i
$269$		−	1601.26i		−	0.362940i	−0.983397	−	0.181470i	$-0.941915\pi$
$269$		−	1601.26i		−	0.362940i	0.983397	−	0.181470i	$-0.0580855\pi$
$270$	−1635.13	−	282.535i	−0.368559	−	0.0636834i
$271$			2202.46i			0.493691i	0.969055	+	0.246845i	$0.0793940\pi$
$271$			2202.46i			0.493691i	−0.969055	+	0.246845i	$0.920606\pi$
$272$	−2049.80	−	1672.58i	−0.456939	−	0.372849i
$273$	−1137.49	+	1440.86i	−0.252176	+	0.319431i
$274$	−2282.29	−	394.358i	−0.503205	−	0.0869490i
$275$	−7389.13			−1.62030
$276$	470.784	−	1321.62i	0.102673	−	0.288233i
$277$			4581.89i			0.993860i	0.867791	+	0.496930i	$0.165540\pi$
$277$			4581.89i			0.993860i	−0.867791	+	0.496930i	$0.834460\pi$
$278$	−1920.07	−	331.769i	−0.414238	−	0.0715763i
$279$		−	2450.84i		−	0.525908i
$280$	−5591.45	−	3151.92i	−1.19340	−	0.672725i
$281$		−	7994.12i		−	1.69711i	−0.529103	−	0.848557i	$-0.677472\pi$
$281$		−	7994.12i		−	1.69711i	0.529103	−	0.848557i	$-0.322528\pi$
$282$	210.400	−	1217.66i	0.0444296	−	0.257130i
$283$			7605.59i			1.59755i	0.601632	+	0.798773i	$0.294517\pi$
$283$			7605.59i			1.59755i	−0.601632	+	0.798773i	$0.705483\pi$
$284$	−1223.56	+	3434.89i	−0.255652	+	0.717687i
$285$			9600.62i			1.99541i
$286$	−1884.89	−	2100.21i	−0.389706	−	0.434225i
$287$	1548.70			0.318525
$288$	1229.87	−	1068.47i	0.251634	−	0.218613i
$289$	−3204.21			−0.652190
$290$	10935.2	+	1889.49i	2.21426	+	0.382602i
$291$	4263.45			0.858858
$292$	−349.851	+	982.130i	−0.0701146	+	0.196832i
$293$	−1970.45			−0.392883			−0.196442	−	0.980516i	$-0.562939\pi$
$293$	−1970.45			−0.392883			−0.196442	+	0.980516i	$0.562939\pi$
$294$	−1442.90	−	249.320i	−0.286231	−	0.0494579i
$295$	17586.8			3.47100
$296$	3747.00	−	6647.12i	0.735777	−	1.30526i
$297$			574.727i			0.112286i
$298$	−902.424	+	5222.65i	−0.175423	+	1.01523i
$299$	1697.81	−	2150.61i	0.328383	−	0.415963i
$300$	2795.63	−	7848.13i	0.538019	−	1.51037i
$301$	5277.99			1.01069
$302$	5693.81	+	983.835i	1.08491	+	0.187461i
$303$	1966.41			0.372829
$304$	−7303.20	−	5959.20i	−1.37785	−	1.12429i
$305$		−	750.416i		−	0.140881i
$306$	−179.169	+	1036.92i	−0.0334719	+	0.193714i
$307$	−4874.65			−0.906224			−0.453112	−	0.891453i	$-0.649686\pi$
$307$	−4874.65			−0.906224			−0.453112	+	0.891453i	$0.649686\pi$
$308$	−745.996	+	2094.22i	−0.138010	+	0.387433i
$309$			1392.64i			0.256390i
$310$	16491.6	+	2849.58i	3.02148	+	0.522082i
$311$	−6585.69			−1.20077			−0.600386	−	0.799710i	$-0.704986\pi$
$311$	−6585.69			−1.20077			−0.600386	+	0.799710i	$0.704986\pi$
$312$	2943.81	−	1207.37i	0.534168	−	0.219083i
$313$	−1307.67			−0.236147			−0.118074	−	0.993005i	$-0.537672\pi$
$313$	−1307.67			−0.236147			−0.118074	+	0.993005i	$0.537672\pi$
$314$	−1159.56	−	200.361i	−0.208401	−	0.0360096i
$315$			2553.00i			0.456651i
$316$	−819.058	−	291.762i	−0.145809	−	0.0519395i
$317$	−5262.79			−0.932454			−0.466227	−	0.884665i	$-0.654387\pi$
$317$	−5262.79			−0.932454			−0.466227	+	0.884665i	$0.654387\pi$
$318$	−591.913	+	3425.61i	−0.104380	+	0.604084i
$319$		−	3843.56i		−	0.674602i
$320$	5759.73	+	9518.00i	1.00618	+	1.66273i
$321$	−851.641			−0.148081
$322$	−2127.01	−	367.527i	−0.368117	−	0.0636071i
$323$	6088.22			1.04878
$324$	−610.428	−	217.444i	−0.104669	−	0.0372847i
$325$	10082.0	−	12770.8i	1.72076	−	2.17969i
$326$	−586.908	+	3396.65i	−0.0997112	+	0.577064i
$327$		−	1266.02i		−	0.214100i
$328$	−2338.34	−	1318.13i	−0.393638	−	0.221895i
$329$	−1901.18			−0.318589
$330$	−3867.30	−	668.232i	−0.645114	−	0.111470i
$331$	189.140			0.0314080			0.0157040	−	0.999877i	$-0.495001\pi$
$331$	189.140			0.0314080			0.0157040	+	0.999877i	$0.495001\pi$
$332$	−1519.30	−	541.201i	−0.251153	−	0.0894646i
$333$	−3035.01			−0.499451
$334$	5631.71	+	973.105i	0.922615	+	0.159419i
$335$	−16297.5			−2.65799
$336$	−1942.07	−	1584.67i	−0.315323	−	0.257294i
$337$	−8991.25			−1.45337			−0.726683	−	0.686973i	$-0.758939\pi$
$337$	−8991.25			−1.45337			−0.726683	+	0.686973i	$0.758939\pi$
$338$	6201.67	−	392.101i	0.998007	−	0.0630991i
$339$		−	2621.67i		−	0.420029i
$340$	−6769.01	−	2411.23i	−1.07971	−	0.384610i
$341$		−	5796.57i		−	0.920533i
$342$	−638.358	+	3694.41i	−0.100931	+	0.584125i
$343$			6730.72i			1.05955i
$344$	−7969.09	−	4492.20i	−1.24903	−	0.704079i
$345$		−	3810.57i		−	0.594650i
$346$	−6209.01	−	1072.86i	−0.964735	−	0.166697i
$347$		−	1000.54i		−	0.154788i	−0.997001	−	0.0773942i	$-0.975340\pi$
$347$		−	1000.54i		−	0.154788i	0.997001	−	0.0773942i	$-0.0246600\pi$
$348$	4082.32	+	1454.19i	0.628836	+	0.224002i
$349$	619.676			0.0950444			0.0475222	−	0.998870i	$-0.484868\pi$
$349$	619.676			0.0950444			0.0475222	+	0.998870i	$0.484868\pi$
$350$	−12630.7	−	2182.47i	−1.92897	−	0.333308i
$351$	−993.317	−	784.178i	−0.151052	−	0.119249i
$352$	2908.80	−	2527.08i	0.440453	−	0.382653i
$353$			1894.83i			0.285698i	0.989744	+	0.142849i	$0.0456263\pi$
$353$			1894.83i			0.285698i	−0.989744	+	0.142849i	$0.954374\pi$
$354$	6767.59	+	1169.37i	1.01608	+	0.175569i
$355$			9903.65i			1.48065i
$356$	−3404.49	+	9557.37i	−0.506847	+	1.42286i
$357$	1618.98			0.240015
$358$	395.520	+	68.3421i	0.0583908	+	0.0100894i
$359$			7682.08i			1.12937i	0.825306	+	0.564686i	$0.191003\pi$
$359$			7682.08i			1.12937i	−0.825306	+	0.564686i	$0.808997\pi$
$360$	2172.91	−	3854.71i	0.318118	−	0.564336i
$361$	14832.6			2.16250
$362$	1954.85	+	337.779i	0.283824	+	0.0490421i
$363$		−	2633.70i		−	0.380808i
$364$	−2601.64	−	4146.76i	−0.374624	−	0.597113i
$365$			2831.73i			0.406081i
$366$	49.8962	−	288.767i	0.00712601	−	0.0412407i
$367$	4776.32			0.679351			0.339676	−	0.940543i	$-0.389683\pi$
$367$	4776.32			0.679351			0.339676	+	0.940543i	$0.389683\pi$
$368$	2898.71	+	2365.26i	0.410613	+	0.335048i
$369$			1067.66i			0.150624i
$370$	3528.79	−	20422.3i	0.495818	−	2.86948i
$371$	5348.55			0.748472
$372$	6156.64	+	2193.09i	0.858083	+	0.305663i
$373$		−	10048.1i		−	1.39482i	−0.716671	−	0.697412i	$-0.754335\pi$
$373$		−	10048.1i		−	1.39482i	0.716671	−	0.697412i	$-0.245665\pi$
$374$	−423.758	+	2452.44i	−0.0585883	+	0.339071i
$375$		−	14479.9i		−	1.99397i
$376$	2870.55	+	1618.14i	0.393716	+	0.221939i
$377$	6642.94	+	5244.29i	0.907503	+	0.716432i
$378$	−169.752	+	982.418i	−0.0230982	+	0.133678i
$379$	−5194.68			−0.704044			−0.352022	−	0.935992i	$-0.614506\pi$
$379$	−5194.68			−0.704044			−0.352022	+	0.935992i	$0.614506\pi$
$380$	−24117.2	−	8590.94i	−3.25576	−	1.15975i
$381$		−	1607.42i		−	0.216144i
$382$	−1049.79	+	6075.52i	−0.140607	+	0.813745i
$383$		−	1411.54i		−	0.188319i	−0.995557	−	0.0941594i	$-0.969984\pi$
$383$		−	1411.54i		−	0.188319i	0.995557	−	0.0941594i	$-0.0300163\pi$
$384$	1583.53	+	4045.59i	0.210441	+	0.537632i
$385$			6038.17i			0.799309i
$386$	9304.43	+	1607.72i	1.22690	+	0.211996i
$387$			3638.60i			0.477935i
$388$	−3815.07	+	10710.0i	−0.499177	+	1.40133i
$389$		−	14787.7i		−	1.92742i	−0.266947	−	0.963711i	$-0.586015\pi$
$389$		−	14787.7i		−	1.92742i	0.266947	−	0.963711i	$-0.413985\pi$
$390$	6431.60	−	5772.20i	0.835069	−	0.749453i
$391$	−2416.47			−0.312548
$392$	1917.46	−	3401.54i	0.247057	−	0.438275i
$393$	−5387.44			−0.691503
$394$	−1188.97	+	6881.00i	−0.152029	+	0.879847i
$395$	−2361.55			−0.300817
$396$	−1443.74	−	514.284i	−0.183209	−	0.0652620i
$397$	−10111.9			−1.27834			−0.639172	−	0.769064i	$-0.720723\pi$
$397$	−10111.9			−1.27834			−0.639172	+	0.769064i	$0.720723\pi$
$398$	462.291	−	2675.44i	0.0582225	−	0.336954i
$399$	5768.24			0.723742
$400$	17213.3	+	14045.5i	2.15166	+	1.75569i
$401$		−	7313.73i		−	0.910799i	−0.890287	−	0.455400i	$-0.849496\pi$
$401$		−	7313.73i		−	0.910799i	0.890287	−	0.455400i	$-0.150504\pi$
$402$	−6271.44	−	1083.64i	−0.778087	−	0.134446i
$403$	10018.4	+	7909.04i	1.23834	+	0.977612i
$404$	−1759.60	+	4939.71i	−0.216692	+	0.608316i
$405$	−1760.02			−0.215941
$406$	1135.24	−	6570.05i	0.138771	−	0.803119i
$407$	−7178.19			−0.874225
$408$	−2444.46	−	1377.95i	−0.296614	−	0.167202i
$409$		−	13472.1i		−	1.62873i	−0.580352	−	0.814366i	$-0.697085\pi$
$409$		−	13472.1i		−	1.62873i	0.580352	−	0.814366i	$-0.302915\pi$
$410$	−7184.22	−	1241.36i	−0.865373	−	0.149528i
$411$	−2456.60			−0.294831
$412$	−3498.38	−	1246.18i	−0.418332	−	0.149016i
$413$		−	10566.5i		−	1.25895i
$414$	253.370	−	1466.35i	0.0300784	−	0.174075i
$415$	−4380.54			−0.518150
$416$	398.761	+	8475.39i	0.0469972	+	0.998895i
$417$	−2066.72			−0.242704
$418$	−1509.80	+	8737.76i	−0.176667	+	1.02244i
$419$		−	5187.31i		−	0.604813i	−0.953179	−	0.302406i	$-0.902210\pi$
$419$		−	5187.31i		−	0.604813i	0.953179	−	0.302406i	$-0.0977900\pi$
$420$	−6413.25	−	2284.51i	−0.745083	−	0.265411i
$421$	7353.20			0.851243			0.425621	−	0.904901i	$-0.360056\pi$
$421$	7353.20			0.851243			0.425621	+	0.904901i	$0.360056\pi$
$422$	2289.96	+	395.683i	0.264155	+	0.0456435i
$423$		−	1310.66i		−	0.150654i
$424$	−8075.64	−	4552.26i	−0.924971	−	0.521409i
$425$	−14349.6			−1.63778
$426$	−658.507	+	3811.02i	−0.0748939	+	0.433438i
$427$	−450.865			−0.0510981
$428$	762.076	−	2139.36i	0.0860662	−	0.241612i
$429$	−2349.32	−	1854.68i	−0.264397	−	0.208729i
$430$	−24483.9	−	4230.59i	−2.74586	−	0.474458i
$431$			2116.23i			0.236508i	0.992983	+	0.118254i	$0.0377298\pi$
$431$			2116.23i			0.236508i	−0.992983	+	0.118254i	$0.962270\pi$
$432$	1092.46	−	1338.85i	0.121669	−	0.149110i
$433$	828.728			0.0919772			0.0459886	−	0.998942i	$-0.485356\pi$
$433$	828.728			0.0919772			0.0459886	+	0.998942i	$0.485356\pi$
$434$	1712.09	−	9908.45i	0.189361	−	1.09590i
$435$	11770.3			1.29735
$436$	3180.29	+	1132.87i	0.349331	+	0.124437i
$437$	−8609.60			−0.942456
$438$	−188.286	+	1089.68i	−0.0205403	+	0.118874i
$439$	−1702.92			−0.185139			−0.0925694	−	0.995706i	$-0.529508\pi$
$439$	−1702.92			−0.185139			−0.0925694	+	0.995706i	$0.529508\pi$
$440$	5139.21	−	9116.88i	0.556824	−	0.987796i
$441$	−1553.11			−0.167704
$442$	−3660.43	−	4078.59i	−0.393912	−	0.438911i
$443$			10502.3i			1.12637i	0.826332	+	0.563184i	$0.190424\pi$
$443$			10502.3i			1.12637i	−0.826332	+	0.563184i	$0.809576\pi$
$444$	2715.82	−	7624.08i	0.290286	−	0.814916i
$445$			27556.3i			2.93549i
$446$	9367.29	+	1618.58i	0.994516	+	0.171843i
$447$			5621.54i			0.594832i
$448$	5718.60	−	3460.56i	0.603077	−	0.364946i
$449$			5700.06i			0.599114i	0.954078	+	0.299557i	$0.0968389\pi$
$449$			5700.06i			0.599114i	−0.954078	+	0.299557i	$0.903161\pi$
$450$	1504.58	−	8707.52i	0.157614	−	0.912170i
$451$			2525.16i			0.263647i
$452$	6585.77	+	2345.96i	0.685328	+	0.244125i
$453$	6128.69			0.635653
$454$	−1773.48	+	10263.8i	−0.183334	+	1.06102i
$455$	−10436.0	−	8238.70i	−1.07526	−	0.848871i
$456$	−8709.31	−	4909.46i	−0.894410	−	0.504181i
$457$			7723.44i			0.790563i	0.918560	+	0.395281i	$0.129353\pi$
$457$			7723.44i			0.790563i	−0.918560	+	0.395281i	$0.870647\pi$
$458$	−2032.25	+	11761.4i	−0.207338	+	1.19994i
$459$			1116.11i			0.113498i
$460$	9572.35	+	3409.82i	0.970246	+	0.345617i
$461$	5681.04			0.573953			0.286976	−	0.957938i	$-0.407350\pi$
$461$	5681.04			0.573953			0.286976	+	0.957938i	$0.407350\pi$
$462$	−401.487	+	2323.55i	−0.0404304	+	0.233985i
$463$		−	8410.25i		−	0.844185i	−0.906553	−	0.422092i	$-0.861296\pi$
$463$		−	8410.25i		−	0.844185i	0.906553	−	0.422092i	$-0.138704\pi$
$464$	−7305.98	+	8953.72i	−0.730973	+	0.895832i
$465$	17751.2			1.77030
$466$	−182.847	+	1058.20i	−0.0181764	+	0.105193i
$467$		−	15102.6i		−	1.49650i	−0.663416	−	0.748251i	$-0.730894\pi$
$467$		−	15102.6i		−	1.49650i	0.663416	−	0.748251i	$-0.269106\pi$
$468$	2858.74	−	1793.55i	0.282362	−	0.177152i
$469$			9791.86i			0.964064i
$470$	8819.36	+	1523.90i	0.865546	+	0.149558i
$471$	−1248.13			−0.122103
$472$	−8993.38	+	15954.1i	−0.877021	+	1.55582i
$473$			8605.78i			0.836562i
$474$	−908.748	−	157.023i	−0.0880594	−	0.0152158i
$475$	−51125.9			−4.93857
$476$	−1448.72	+	4066.96i	−0.139499	+	0.391615i
$477$			3687.25i			0.353936i
$478$	−7554.89	−	1305.41i	−0.722913	−	0.124912i
$479$		−	6424.97i		−	0.612869i	−0.951892	−	0.306435i	$-0.900864\pi$
$479$		−	6424.97i		−	0.612869i	0.951892	−	0.306435i	$-0.0991361\pi$
$480$	7738.82	+	8907.77i	0.735890	+	0.847046i
$481$	9794.17	−	12406.3i	0.928432	−	1.17604i
$482$	−13268.9	−	2292.74i	−1.25391	−	0.216663i
$483$	−2289.47			−0.215682
$484$	6615.97	+	2356.72i	0.621335	+	0.221329i
$485$			30879.6i			2.89107i
$486$	−677.272	−	117.026i	−0.0632133	−	0.0109227i
$487$		−	9662.31i		−	0.899058i	−0.893266	−	0.449529i	$-0.851592\pi$
$487$		−	9662.31i		−	0.899058i	0.893266	−	0.449529i	$-0.148408\pi$
$488$	680.749	+	383.740i	0.0631477	+	0.0355965i
$489$			3656.08i			0.338105i
$490$	1805.79	−	10450.8i	0.166484	−	0.963505i
$491$		−	4536.18i		−	0.416934i	−0.978029	−	0.208467i	$-0.933153\pi$
$491$		−	4536.18i		−	0.416934i	0.978029	−	0.208467i	$-0.0668474\pi$
$492$	−2682.02	−	955.377i	−0.245761	−	0.0875442i
$493$		−	7464.15i		−	0.681883i
$494$	−13041.7	−	14531.5i	−1.18780	−	1.32349i
$495$	−4162.67			−0.377976
$496$	−11018.3	+	13503.3i	−0.997454	+	1.22241i
$497$	5950.30			0.537037
$498$	−1685.67	−	291.268i	−0.151680	−	0.0262089i
$499$	−9717.54			−0.871778			−0.435889	−	0.900001i	$-0.643566\pi$
$499$	−9717.54			−0.871778			−0.435889	+	0.900001i	$0.643566\pi$
$500$	36374.2	+	12957.1i	3.25341	+	1.15892i
$501$	6061.85			0.540565
$502$	7226.35	+	1248.64i	0.642485	+	0.111015i
$503$	19916.9			1.76550			0.882752	−	0.469839i	$-0.155688\pi$
$503$	19916.9			1.76550			0.882752	+	0.469839i	$0.155688\pi$
$504$	−2315.98	−	1305.53i	−0.204687	−	0.115382i
$505$			14242.4i			1.25501i
$506$	599.254	−	3468.10i	0.0526484	−	0.304695i
$507$	6411.00	−	1529.81i	0.561583	−	0.134006i
$508$	4037.93	+	1438.38i	0.352666	+	0.125625i
$509$	−13960.8			−1.21572			−0.607862	−	0.794043i	$-0.707972\pi$
$509$	−13960.8			−1.21572			−0.607862	+	0.794043i	$0.707972\pi$
$510$	−7510.24	−	1297.70i	−0.652077	−	0.112673i
$511$	1701.36			0.147287
$512$	−11579.7	+	357.788i	−0.999523	+	0.0308831i
$513$			3976.58i			0.342242i
$514$	−1895.00	+	10967.0i	−0.162616	+	0.941119i
$515$	−10086.7			−0.863055
$516$	−9140.35	−	3255.94i	−0.779809	−	0.277781i
$517$		−	3099.89i		−	0.263700i
$518$	−12270.1	−	2120.16i	−1.04077	−	0.179835i
$519$	−6683.24			−0.565244
$520$	8744.84	+	21321.6i	0.737475	+	1.79811i
$521$	17146.9			1.44188			0.720941	−	0.692997i	$-0.243710\pi$
$521$	17146.9			1.44188			0.720941	+	0.692997i	$0.243710\pi$
$522$	4529.34	+	782.627i	0.379778	+	0.0656219i
$523$		−	1202.54i		−	0.100542i	−0.998736	−	0.0502711i	$-0.983991\pi$
$523$		−	1202.54i		−	0.100542i	0.998736	−	0.0502711i	$-0.0160085\pi$
$524$	4820.86	−	13533.5i	0.401909	−	1.12827i
$525$	−13595.4			−1.13020
$526$	220.434	−	1275.73i	0.0182726	−	0.105750i
$527$		−	11256.9i		−	0.930468i
$528$	2583.81	−	3166.55i	0.212966	−	0.260997i
$529$	−8749.77			−0.719139
$530$	−24811.3	−	4287.15i	−2.03346	−	0.351362i
$531$	7284.48			0.595328
$532$	−5161.60	+	14490.1i	−0.420647	+	1.18087i
$533$	−4364.30	−	3445.41i	−0.354670	−	0.279995i
$534$	−1832.26	+	10603.9i	−0.148482	+	0.859321i
$535$		−	6168.33i		−	0.498467i
$536$	8334.05	−	14784.5i	0.671598	−	1.19140i
$537$	425.729			0.0342115
$538$	4462.92	+	771.150i	0.357640	+	0.0617967i
$539$	−3673.31			−0.293545
$540$	1574.92	−	4421.25i	0.125507	−	0.352334i
$541$	3911.67			0.310861			0.155430	−	0.987847i	$-0.450324\pi$
$541$	3911.67			0.310861			0.155430	+	0.987847i	$0.450324\pi$
$542$	−6138.55	−	1060.68i	−0.486482	−	0.0840594i
$543$	2104.15			0.166294
$544$	5648.85	−	4907.56i	0.445206	−	0.386783i
$545$	9169.59			0.720701
$546$	−3468.05	−	3864.23i	−0.271829	−	0.302883i
$547$		−	2123.59i		−	0.165993i	−0.996550	−	0.0829966i	$-0.973551\pi$
$547$		−	2123.59i		−	0.165993i	0.996550	−	0.0829966i	$-0.0264491\pi$
$548$	2198.25	−	6171.11i	0.171359	−	0.481052i
$549$		−	310.823i		−	0.0241632i
$550$	3558.52	−	20594.4i	0.275883	−	1.59664i
$551$		−	26593.9i		−	2.05615i
$552$	3456.81	+	1948.61i	0.266542	+	0.150251i
$553$			1418.87i			0.109107i
$554$	−12770.3	−	2206.59i	−0.979348	−	0.169222i
$555$		−	21982.2i		−	1.68124i
$556$	1849.37	−	5191.70i	0.141062	−	0.396002i
$557$	11396.8			0.866960			0.433480	−	0.901163i	$-0.357285\pi$
$557$	11396.8			0.866960			0.433480	+	0.901163i	$0.357285\pi$
$558$	6830.81	+	1180.30i	0.518228	+	0.0895449i
$559$	−14873.6	−	11742.0i	−1.12538	−	0.888434i
$560$	11477.6	−	14066.2i	0.866100	−	1.06144i
$561$			2639.75i			0.198664i
$562$	22280.6	+	3849.88i	1.67233	+	0.288963i
$563$		−	22958.8i		−	1.71865i	−0.511432	−	0.859324i	$-0.670885\pi$
$563$		−	22958.8i		−	1.71865i	0.511432	−	0.859324i	$-0.329115\pi$
$564$	3292.45	+	1172.82i	0.245810	+	0.0875616i
$565$	18988.4			1.41389
$566$	−21197.8	−	3662.77i	−1.57422	−	0.272010i
$567$			1057.45i			0.0783225i
$568$	−8984.21	−	5064.42i	−0.663678	−	0.374117i
$569$	1997.33			0.147157			0.0735786	−	0.997289i	$-0.476558\pi$
$569$	1997.33			0.147157			0.0735786	+	0.997289i	$0.476558\pi$
$570$	−26758.1	−	4623.55i	−1.96627	−	0.339753i
$571$		−	1360.30i		−	0.0996963i	−0.998757	−	0.0498482i	$-0.984126\pi$
$571$		−	1360.30i		−	0.0996963i	0.998757	−	0.0498482i	$-0.0158737\pi$
$572$	6761.30	−	4241.99i	0.494238	−	0.310081i
$573$			6539.55i			0.476778i
$574$	−745.835	+	4316.42i	−0.0542344	+	0.313874i
$575$	20292.4			1.47174
$576$	2385.68	+	3942.36i	0.172575	+	0.285182i
$577$		−	12943.8i		−	0.933892i	−0.884286	−	0.466946i	$-0.845354\pi$
$577$		−	12943.8i		−	0.933892i	0.884286	−	0.466946i	$-0.154646\pi$
$578$	1543.11	−	8930.54i	0.111047	−	0.642667i
$579$	10015.1			0.718847
$580$	−10532.5	+	29567.7i	−0.754031	+	2.11678i
$581$			2631.91i			0.187935i
$582$	−2053.23	+	11882.8i	−0.146235	+	0.846317i
$583$			8720.83i			0.619520i
$584$	−2568.84	−	1448.06i	−0.182019	−	0.102605i
$585$	5679.70	−	7194.47i	0.401413	−	0.508469i
$586$	948.945	−	5491.88i	0.0668951	−	0.387146i
$587$	21749.2			1.52928			0.764638	−	0.644459i	$-0.222918\pi$
$587$	21749.2			1.52928			0.764638	+	0.644459i	$0.222918\pi$
$588$	1389.77	−	3901.48i	0.0974715	−	0.273630i
$589$		−	40106.9i		−	2.80573i
$590$	−8469.62	+	49016.8i	−0.590998	+	3.42032i
$591$			7406.55i			0.515507i
$592$	16721.9	+	13644.5i	1.16092	+	0.947276i
$593$			11525.0i			0.798102i	0.916929	+	0.399051i	$0.130660\pi$
$593$			11525.0i			0.798102i	−0.916929	+	0.399051i	$0.869340\pi$
$594$	−1601.84	−	276.782i	−0.110647	−	0.0191187i
$595$			11726.1i			0.807936i
$596$	−14121.6	−	5030.34i	−0.970542	−	0.345723i
$597$		−	2879.79i		−	0.197424i
$598$	5176.37	+	5767.71i	0.353976	+	0.394413i
$599$	3056.30			0.208476			0.104238	−	0.994552i	$-0.466760\pi$
$599$	3056.30			0.208476			0.104238	+	0.994552i	$0.466760\pi$
$600$	20527.4	+	11571.3i	1.39671	+	0.787330i
$601$	−19514.8			−1.32450			−0.662251	−	0.749282i	$-0.730399\pi$
$601$	−19514.8			−1.32450			−0.662251	+	0.749282i	$0.730399\pi$
$602$	−2541.82	+	14710.4i	−0.172088	+	0.995933i
$603$	−6750.44			−0.455886
$604$	−5484.15	+	15395.6i	−0.369448	+	1.03715i
$605$	19075.5			1.28187
$606$	−947.000	+	5480.63i	−0.0634806	+	0.367385i
$607$	−7121.66			−0.476210			−0.238105	−	0.971239i	$-0.576526\pi$
$607$	−7121.66			−0.476210			−0.238105	+	0.971239i	$0.576526\pi$
$608$	20126.2	−	17485.1i	1.34247	−	1.16630i
$609$		−	7071.85i		−	0.470552i
$610$	2091.51	+	361.392i	0.138824	+	0.0239874i
$611$	5357.62	+	4229.60i	0.354740	+	0.280051i
$612$	−2803.73	−	998.733i	−0.185186	−	0.0659663i
$613$	13806.8			0.909709			0.454855	−	0.890566i	$-0.349691\pi$
$613$	13806.8			0.909709			0.454855	+	0.890566i	$0.349691\pi$
$614$	2347.58	−	13586.3i	0.154300	−	0.892992i
$615$	−7732.93			−0.507027
$616$	−5477.60	−	3087.74i	−0.358277	−	0.201962i
$617$		−	8301.27i		−	0.541648i	−0.962629	−	0.270824i	$-0.912704\pi$
$617$		−	8301.27i		−	0.541648i	0.962629	−	0.270824i	$-0.0872961\pi$
$618$	−3881.46	−	670.679i	−0.252646	−	0.0436548i
$619$	23396.1			1.51917			0.759587	−	0.650406i	$-0.225401\pi$
$619$	23396.1			1.51917			0.759587	+	0.650406i	$0.225401\pi$
$620$	−15884.3	+	44591.7i	−1.02892	+	2.88846i
$621$		−	1578.34i		−	0.101991i
$622$	3171.59	−	18355.1i	0.204452	−	1.18324i
$623$	16556.4			1.06471
$624$	1947.39	+	8786.23i	0.124933	+	0.563671i
$625$	61484.5			3.93501
$626$	629.761	−	3644.65i	0.0402082	−	0.232699i
$627$			9405.13i			0.599051i
$628$	1116.86	−	3135.35i	0.0709676	−	0.199226i
$629$	−13940.0			−0.883660
$630$	−7115.53	−	1229.49i	−0.449983	−	0.0777528i
$631$			22309.5i			1.40749i	0.710451	+	0.703747i	$0.248491\pi$
$631$			22309.5i			1.40749i	−0.710451	+	0.703747i	$0.751509\pi$
$632$	1207.63	−	2142.31i	0.0760075	−	0.134836i
$633$	2464.86			0.154770
$634$	2534.50	−	14668.1i	0.158766	−	0.918839i
$635$	11642.4			0.727580
$636$	−9262.55	−	3299.47i	−0.577491	−	0.205712i
$637$	5011.99	−	6348.68i	0.311746	−	0.394888i
$638$	10712.5	+	1851.02i	0.664752	+	0.114863i
$639$			4102.10i			0.253954i
$640$	−29301.7	+	11469.3i	−1.80977	+	0.708383i
$641$	11515.3			0.709559			0.354780	−	0.934950i	$-0.384556\pi$
$641$	11515.3			0.709559			0.354780	+	0.934950i	$0.384556\pi$
$642$	410.141	−	2373.63i	0.0252133	−	0.145919i
$643$	−20112.3			−1.23351			−0.616757	−	0.787153i	$-0.711554\pi$
$643$	−20112.3			−1.23351			−0.616757	+	0.787153i	$0.711554\pi$
$644$	2048.69	−	5751.25i	0.125357	−	0.351912i
$645$	−26353.9			−1.60881
$646$	−2932.02	+	16968.6i	−0.178574	+	1.03347i
$647$	−15844.9			−0.962794			−0.481397	−	0.876503i	$-0.659870\pi$
$647$	−15844.9			−0.962794			−0.481397	+	0.876503i	$0.659870\pi$
$648$	900.020	−	1596.62i	0.0545619	−	0.0967919i
$649$	17228.7			1.04205
$650$	30738.6	+	34250.1i	1.85487	+	2.06677i
$651$		−	10665.2i		−	0.642095i
$652$	−9184.24	−	3271.57i	−0.551660	−	0.196510i
$653$			26540.8i			1.59054i	0.606257	+	0.795269i	$0.292670\pi$
$653$			26540.8i			1.59054i	−0.606257	+	0.795269i	$0.707330\pi$
$654$	3528.54	+	609.699i	0.210974	+	0.0364543i
$655$		−	39020.6i		−	2.32772i
$656$	4799.91	−	5882.45i	0.285678	−	0.350108i
$657$			1172.90i			0.0696489i
$658$	915.589	−	5298.84i	0.0542452	−	0.313937i
$659$			13346.4i			0.788926i	0.918912	+	0.394463i	$0.129069\pi$
$659$			13346.4i			0.788926i	−0.918912	+	0.394463i	$0.870931\pi$
$660$	3724.89	−	10456.8i	0.219684	−	0.616715i
$661$	937.788			0.0551826			0.0275913	−	0.999619i	$-0.491216\pi$
$661$	937.788			0.0551826			0.0275913	+	0.999619i	$0.491216\pi$
$662$	−91.0876	+	527.156i	−0.00534776	+	0.0309494i
$663$	−4562.36	−	3601.77i	−0.267251	−	0.210982i
$664$	2240.07	−	3973.86i	0.130921	−	0.232252i
$665$			41778.6i			2.43625i
$666$	1461.62	−	8458.94i	0.0850402	−	0.492158i
$667$			10555.4i			0.612752i
$668$	−5424.33	+	15227.6i	−0.314182	+	0.881999i
$669$	10082.7			0.582692
$670$	7848.70	−	45423.2i	0.452570	−	2.61918i
$671$		−	735.136i		−	0.0422945i
$672$	5351.96	−	4649.63i	0.307227	−	0.266910i
$673$	−3267.28			−0.187139			−0.0935693	−	0.995613i	$-0.529828\pi$
$673$	−3267.28			−0.187139			−0.0935693	+	0.995613i	$0.529828\pi$
$674$	4330.08	−	25059.7i	0.247461	−	1.43214i
$675$		−	9372.58i		−	0.534446i
$676$	−1893.82	+	17473.7i	−0.107750	+	0.994178i
$677$		−	20225.8i		−	1.14821i	−0.818780	−	0.574107i	$-0.805349\pi$
$677$		−	20225.8i		−	1.14821i	0.818780	−	0.574107i	$-0.194651\pi$
$678$	7306.93	+	1262.57i	0.413895	+	0.0715171i
$679$	18553.1			1.04860
$680$	9980.29	−	17704.9i	0.562833	−	0.998457i
$681$			11047.7i			0.621657i
$682$	16155.8	+	2791.56i	0.907091	+	0.156737i
$683$	4942.54			0.276897			0.138449	−	0.990370i	$-0.455788\pi$
$683$	4942.54			0.276897			0.138449	+	0.990370i	$0.455788\pi$
$684$	−9989.36	−	3558.37i	−0.558410	−	0.198915i
$685$		−	17792.9i		−	0.992454i
$686$	−18759.4	−	3241.44i	−1.04408	−	0.180406i
$687$			12659.7i			0.703052i
$688$	16358.2	−	20047.5i	0.906467	−	1.11091i
$689$	−15072.5	−	11899.0i	−0.833404	−	0.657934i
$690$	10620.6	+	1835.13i	0.585967	+	0.101250i
$691$	5672.16			0.312271			0.156135	−	0.987736i	$-0.450096\pi$
$691$	5672.16			0.312271			0.156135	+	0.987736i	$0.450096\pi$
$692$	5980.38	−	16788.6i	0.328526	−	0.922265i
$693$			2501.01i			0.137093i
$694$	2788.62	+	481.846i	0.152528	+	0.0263554i
$695$		−	14969.0i		−	0.816986i
$696$	−6019.00	+	10677.6i	−0.327801	+	0.581514i
$697$			4903.82i			0.266493i
$698$	−298.429	+	1727.12i	−0.0161830	+	0.0936566i
$699$			1139.02i			0.0616334i
$700$	12165.6	−	34152.4i	0.656882	−	1.84405i
$701$		−	14703.7i		−	0.792226i	−0.918202	−	0.396113i	$-0.870359\pi$
$701$		−	14703.7i		−	0.792226i	0.918202	−	0.396113i	$-0.129641\pi$
$702$	2663.97	−	2390.85i	0.143227	−	0.128542i
$703$	−49666.4			−2.66459
$704$	5642.45	+	9324.19i	0.302071	+	0.499174i
$705$	9492.96			0.507128
$706$	−5281.12	−	912.527i	−0.281526	−	0.0486450i
$707$	8557.13			0.455197
$708$	−6518.39	+	18299.0i	−0.346011	+	0.971352i
$709$	−35465.0			−1.87858			−0.939291	−	0.343122i	$-0.888516\pi$
$709$	−35465.0			−1.87858			−0.939291	+	0.343122i	$0.888516\pi$
$710$	−27602.7	−	4769.48i	−1.45903	−	0.252106i
$711$	−978.155			−0.0515945
$712$	−24998.0	−	14091.5i	−1.31579	−	0.741714i
$713$			15918.8i			0.836134i
$714$	−779.682	+	4512.30i	−0.0408668	+	0.236511i
$715$	13433.2	−	17015.9i	0.702621	−	0.890010i
$716$	−380.956	+	1069.45i	−0.0198841	+	0.0558202i
$717$	−8131.91			−0.423559
$718$	−21410.9	−	3699.60i	−1.11288	−	0.192295i
$719$	31867.9			1.65295			0.826476	−	0.562971i	$-0.190342\pi$
$719$	31867.9			1.65295			0.826476	+	0.562971i	$0.190342\pi$
$720$	9697.10	+	7912.55i	0.501930	+	0.409560i
$721$			6060.29i			0.313033i
$722$	−7143.22	+	41340.4i	−0.368204	+	2.13093i
$723$	−14282.4			−0.734670
$724$	−1882.86	+	5285.73i	−0.0966521	+	0.271330i
$725$			62680.4i			3.21088i
$726$	7340.44	+	1268.36i	0.375247	+	0.0648391i
$727$	16752.6			0.854633			0.427317	−	0.904102i	$-0.359459\pi$
$727$	16752.6			0.854633			0.427317	+	0.904102i	$0.359459\pi$
$728$	12810.5	−	5254.07i	0.652180	−	0.267485i
$729$	−729.000			−0.0370370
$730$	−7892.39	−	1363.73i	−0.400151	−	0.0691423i
$731$			16712.3i			0.845591i
$732$	780.802	+	278.134i	0.0394252	+	0.0140439i
$733$	7015.46			0.353509			0.176754	−	0.984255i	$-0.443440\pi$
$733$	7015.46			0.353509			0.176754	+	0.984255i	$0.443440\pi$
$734$	−2300.22	+	13312.2i	−0.115671	+	0.669431i
$735$		−	11249.0i		−	0.564523i
$736$	−7988.27	+	6939.98i	−0.400070	+	0.347570i
$737$	−15965.7			−0.797969
$738$	−2975.70	−	514.173i	−0.148424	−	0.0256463i
$739$	1456.76			0.0725138			0.0362569	−	0.999343i	$-0.488457\pi$
$739$	1456.76			0.0725138			0.0362569	+	0.999343i	$0.488457\pi$
$740$	55220.2	+	19670.3i	2.74316	+	0.977157i
$741$	−16255.2	−	12832.7i	−0.805868	−	0.636195i
$742$	−2575.80	+	14907.1i	−0.127440	+	0.737543i
$743$		−	8657.84i		−	0.427491i	−0.976889	−	0.213745i	$-0.931434\pi$
$743$		−	8657.84i		−	0.427491i	0.976889	−	0.213745i	$-0.0685663\pi$
$744$	−9077.40	+	16103.2i	−0.447303	+	0.793509i
$745$	−40716.1			−2.00231
$746$	28005.2	+	4839.03i	1.37446	+	0.237493i
$747$	−1814.42			−0.0888704
$748$	−6631.18	−	2362.13i	−0.324145	−	0.115466i
$749$	−3706.05			−0.180796
$750$	40357.3	+	6973.36i	1.96485	+	0.339508i
$751$	1217.68			0.0591664			0.0295832	−	0.999562i	$-0.490582\pi$
$751$	1217.68			0.0591664			0.0295832	+	0.999562i	$0.490582\pi$
$752$	−5892.37	+	7221.30i	−0.285735	+	0.350178i
$753$	7778.28			0.376436
$754$	−17815.7	+	15989.1i	−0.860488	+	0.772267i
$755$			44389.3i			2.13972i
$756$	−2656.37	−	946.243i	−0.127793	−	0.0455219i
$757$		−	27866.0i		−	1.33792i	−0.743297	−	0.668962i	$-0.766739\pi$
$757$		−	27866.0i		−	1.33792i	0.743297	−	0.668962i	$-0.233261\pi$
$758$	2501.70	−	14478.2i	0.119876	−	0.693763i
$759$		−	3732.98i		−	0.178523i
$760$	35558.6	−	63080.4i	1.69717	−	3.01075i
$761$		−	7301.63i		−	0.347811i	−0.984762	−	0.173905i	$-0.944361\pi$
$761$		−	7301.63i		−	0.347811i	0.984762	−	0.173905i	$-0.0556387\pi$
$762$	4480.09	+	774.117i	0.212988	+	0.0368022i
$763$		−	5509.27i		−	0.261401i
$764$	−16427.7	−	5851.80i	−0.777922	−	0.277108i
$765$	−8083.86			−0.382056
$766$	3934.13	+	679.780i	0.185569	+	0.0320645i
$767$	−23507.5	+	29776.9i	−1.10666	+	1.40180i
$768$	−12038.2	+	2465.20i	−0.565612	+	0.115827i
$769$		−	8632.60i		−	0.404811i	−0.979302	−	0.202405i	$-0.935124\pi$
$769$		−	8632.60i		−	0.404811i	0.979302	−	0.202405i	$-0.0648759\pi$
$770$	−16829.2	−	2907.92i	−0.787637	−	0.136096i
$771$			11804.7i			0.551407i
$772$	−8961.82	+	25158.4i	−0.417802	+	1.17289i
$773$	4072.53			0.189494			0.0947470	−	0.995501i	$-0.469796\pi$
$773$	4072.53			0.189494			0.0947470	+	0.995501i	$0.469796\pi$
$774$	−10141.2	−	1752.31i	−0.470956

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.481589 + 2.78713i) q^{2} +3.00000i q^{3} +(-7.53614 - 2.68450i) q^{4} -21.7286 q^{5} +(-8.36138 - 1.44477i) q^{6} +13.0550i q^{7} +(11.1114 - 19.7114i) q^{8} -9.00000 q^{9} +(10.4643 - 60.5604i) q^{10} -21.2862 q^{11} +(8.05349 - 22.6084i) q^{12} +(29.0436 - 36.7895i) q^{13} +(-36.3859 - 6.28713i) q^{14} -65.1858i q^{15} +(49.5870 + 40.4615i) q^{16} -41.3375 q^{17} +(4.33430 - 25.0841i) q^{18} -147.281 q^{19} +(163.750 + 58.3304i) q^{20} -39.1649 q^{21} +(10.2512 - 59.3273i) q^{22} +58.4571 q^{23} +(59.1341 + 33.3341i) q^{24} +347.133 q^{25} +(88.5499 + 98.6656i) q^{26} -27.0000i q^{27} +(35.0460 - 98.3842i) q^{28} +180.566i q^{29} +(181.681 + 31.3928i) q^{30} +272.316i q^{31} +(-136.652 + 118.719i) q^{32} -63.8585i q^{33} +(19.9077 - 115.213i) q^{34} -283.666i q^{35} +(67.8253 + 24.1605i) q^{36} +337.223 q^{37} +(70.9287 - 410.490i) q^{38} +(110.369 + 87.1309i) q^{39} +(-241.434 + 428.301i) q^{40} -118.629i q^{41} +(18.8614 - 109.158i) q^{42} -404.289i q^{43} +(160.416 + 57.1427i) q^{44} +195.558 q^{45} +(-28.1523 + 162.927i) q^{46} +145.629i q^{47} +(-121.385 + 148.761i) q^{48} +172.568 q^{49} +(-167.175 + 967.503i) q^{50} -124.012i q^{51} +(-317.638 + 199.284i) q^{52} -409.695i q^{53} +(75.2524 + 13.0029i) q^{54} +462.519 q^{55} +(257.331 + 145.058i) q^{56} -441.842i q^{57} +(-503.260 - 86.9586i) q^{58} -809.386 q^{59} +(-174.991 + 491.250i) q^{60} +34.5359i q^{61} +(-758.979 - 131.144i) q^{62} -117.495i q^{63} +(-265.076 - 438.040i) q^{64} +(-631.078 + 799.385i) q^{65} +(177.982 + 30.7535i) q^{66} +750.048 q^{67} +(311.525 + 110.970i) q^{68} +175.371i q^{69} +(790.614 + 136.611i) q^{70} -455.788i q^{71} +(-100.002 + 177.402i) q^{72} -130.323i q^{73} +(-162.403 + 939.883i) q^{74} +1041.40i q^{75} +(1109.93 + 395.375i) q^{76} -277.890i q^{77} +(-295.997 + 265.650i) q^{78} +108.684 q^{79} +(-1077.46 - 879.173i) q^{80} +81.0000 q^{81} +(330.634 + 57.1304i) q^{82} +201.602 q^{83} +(295.153 + 105.138i) q^{84} +898.206 q^{85} +(1126.81 + 194.701i) q^{86} -541.698 q^{87} +(-236.518 + 419.580i) q^{88} -1268.20i q^{89} +(-94.1783 + 545.043i) q^{90} +(480.286 + 379.164i) q^{91} +(-440.541 - 156.928i) q^{92} -816.948 q^{93} +(-405.887 - 70.1333i) q^{94} +3200.21 q^{95} +(-356.158 - 409.956i) q^{96} -1421.15i q^{97} +(-83.1066 + 480.968i) q^{98} +191.576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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