LMFDB - Embedded newform 312.4.m.a.181.37

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.481589 - 2.78713i) q^{2} -3.00000i q^{3} +(-7.53614 + 2.68450i) q^{4} -21.7286 q^{5} +(-8.36138 + 1.44477i) q^{6} -13.0550i q^{7} +(11.1114 + 19.7114i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 84 * q - 756 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.885348\pi$
$7$		−	13.0550i		−	0.704902i	0.935830	−	0.352451i	$-0.114652\pi$
$8$	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	$-0.803791\pi$
$29$		−	180.566i		−	1.15622i	0.815960	−	0.578108i	$-0.196209\pi$
$30$	181.681	−	31.3928i	1.10568	−	0.191050i
$31$		−	272.316i		−	1.57772i	−0.614571	−	0.788861i	$-0.710671\pi$
$31$		−	272.316i		−	1.57772i	0.614571	−	0.788861i	$-0.289329\pi$
$32$	−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	$0.0725439\pi$
$41$			118.629i			0.451871i	−0.974142	+	0.225936i	$0.927456\pi$
$42$	18.8614	+	109.158i	0.0692946	+	0.401033i
$43$			404.289i			1.43380i	0.697174	+	0.716902i	$0.254440\pi$
$43$			404.289i			1.43380i	−0.697174	+	0.716902i	$0.745560\pi$
$44$	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	$-0.927441\pi$
$47$		−	145.629i		−	0.451961i	0.974132	−	0.225981i	$-0.0725586\pi$
$48$	−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	$0.178148\pi$
$53$			409.695i			1.06181i	−0.847432	+	0.530905i	$0.821852\pi$
$54$	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	$-0.988460\pi$
$61$		−	34.5359i		−	0.0724896i	0.999343	−	0.0362448i	$-0.0115396\pi$
$62$	−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	$0.124396\pi$
$71$			455.788i			0.761861i	−0.924604	+	0.380930i	$0.875604\pi$
$72$	−100.002	−	177.402i	−0.163686	−	0.290376i
$73$			130.323i			0.208947i	0.994528	+	0.104473i	$0.0333157\pi$
$73$			130.323i			0.208947i	−0.994528	+	0.104473i	$0.966684\pi$
$74$	−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	$0.272471\pi$
$89$			1268.20i			1.51044i	−0.655470	+	0.755221i	$0.727529\pi$
$90$	−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	$0.266975\pi$
$97$			1421.15i			1.48759i	−0.668410	+	0.743793i	$0.733025\pi$
$98$	−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	$0.104651\pi$
$101$			655.469i			0.645759i	−0.946440	+	0.322879i	$0.895349\pi$
$102$	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	$-0.959067\pi$
$107$		−	283.880i		−	0.256484i	0.991743	−	0.128242i	$-0.0409334\pi$
$108$	−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	$-0.795621\pi$
$131$		−	1795.81i		−	1.19772i	0.800855	−	0.598859i	$-0.204379\pi$
$132$	−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	$-0.917816\pi$
$137$		−	818.868i		−	0.510662i	0.966854	−	0.255331i	$-0.0821844\pi$
$138$	−488.782	+	84.4568i	−0.301506	+	0.0520974i
$139$		−	688.906i		−	0.420376i	−0.977661	−	0.210188i	$-0.932592\pi$
$139$		−	688.906i		−	0.420376i	0.977661	−	0.210188i	$-0.0674076\pi$
$140$	−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	$0.185560\pi$
$151$			2042.90i			1.10098i	−0.834841	+	0.550492i	$0.814440\pi$
$152$	−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	$-0.966277\pi$
$157$		−	416.042i		−	0.211489i	0.994393	−	0.105744i	$-0.0337225\pi$
$158$	−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	$0.155077\pi$
$167$			2020.62i			0.936287i	−0.883653	+	0.468143i	$0.844923\pi$
$168$	−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	$-0.837174\pi$
$173$		−	2227.75i		−	0.979031i	0.871995	−	0.489516i	$-0.162826\pi$
$174$	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	$0.00943227\pi$
$179$			141.910i			0.0592560i	−0.999561	+	0.0296280i	$0.990568\pi$
$180$	−1473.75	+	524.974i	−0.610260	+	0.217385i
$181$			701.384i			0.288030i	0.989575	+	0.144015i	$0.0460014\pi$
$181$			701.384i			0.288030i	−0.989575	+	0.144015i	$0.953999\pi$
$182$	−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	$0.213899\pi$
$193$			3338.36i			1.24508i	−0.782588	+	0.622540i	$0.786101\pi$
$194$	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	$0.0427934\pi$
$211$			821.620i			0.268070i	−0.990977	+	0.134035i	$0.957207\pi$
$212$	−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	$0.168370\pi$
$223$			3360.91i			1.00925i	−0.863338	+	0.504626i	$0.831630\pi$
$224$	−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	$-0.880449\pi$
$239$		−	2710.64i		−	0.733626i	0.930295	−	0.366813i	$-0.119551\pi$
$240$	2637.52	+	3232.37i	0.709379	+	0.869368i
$241$		−	4760.79i		−	1.27249i	−0.771489	−	0.636243i	$-0.780487\pi$
$241$		−	4760.79i		−	1.27249i	0.771489	−	0.636243i	$-0.219513\pi$
$242$	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	$0.105702\pi$
$251$			2592.76i			0.652006i	−0.945369	+	0.326003i	$0.894298\pi$
$252$	−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	$0.0580855\pi$
$269$			1601.26i			0.362940i	−0.983397	+	0.181470i	$0.941915\pi$
$270$	−1635.13	+	282.535i	−0.368559	+	0.0636834i
$271$		−	2202.46i		−	0.493691i	−0.969055	−	0.246845i	$-0.920606\pi$
$271$		−	2202.46i		−	0.493691i	0.969055	−	0.246845i	$-0.0793940\pi$
$272$	−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	$-0.834460\pi$
$277$		−	4581.89i		−	0.993860i	0.867791	−	0.496930i	$-0.165540\pi$
$278$	−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	$0.322528\pi$
$281$			7994.12i			1.69711i	−0.529103	+	0.848557i	$0.677472\pi$
$282$	210.400	+	1217.66i	0.0444296	+	0.257130i
$283$		−	7605.59i		−	1.59755i	−0.601632	−	0.798773i	$-0.705483\pi$
$283$		−	7605.59i		−	1.59755i	0.601632	−	0.798773i	$-0.294517\pi$
$284$	−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	$0.0246600\pi$
$347$			1000.54i			0.154788i	−0.997001	+	0.0773942i	$0.975340\pi$
$348$	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	$-0.954374\pi$
$353$		−	1894.83i		−	0.285698i	0.989744	−	0.142849i	$-0.0456263\pi$
$354$	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	$-0.808997\pi$
$359$		−	7682.08i		−	1.12937i	0.825306	−	0.564686i	$-0.191003\pi$
$360$	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	$0.245665\pi$
$373$			10048.1i			1.39482i	−0.716671	+	0.697412i	$0.754335\pi$
$374$	−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	$0.0300163\pi$
$383$			1411.54i			0.188319i	−0.995557	+	0.0941594i	$0.969984\pi$
$384$	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	$0.413985\pi$
$389$			14787.7i			1.92742i	−0.266947	+	0.963711i	$0.586015\pi$
$390$	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	$0.150504\pi$
$401$			7313.73i			0.910799i	−0.890287	+	0.455400i	$0.849496\pi$
$402$	−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	$0.302915\pi$
$409$			13472.1i			1.62873i	−0.580352	+	0.814366i	$0.697085\pi$
$410$	−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	$0.0977900\pi$
$419$			5187.31i			0.604813i	−0.953179	+	0.302406i	$0.902210\pi$
$420$	−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	$-0.962270\pi$
$431$		−	2116.23i		−	0.236508i	0.992983	−	0.118254i	$-0.0377298\pi$
$432$	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	$-0.809576\pi$
$443$		−	10502.3i		−	1.12637i	0.826332	−	0.563184i	$-0.190424\pi$
$444$	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	$-0.903161\pi$
$449$		−	5700.06i		−	0.599114i	0.954078	−	0.299557i	$-0.0968389\pi$
$450$	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	$-0.870647\pi$
$457$		−	7723.44i		−	0.790563i	0.918560	−	0.395281i	$-0.129353\pi$
$458$	−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	$0.138704\pi$
$463$			8410.25i			0.844185i	−0.906553	+	0.422092i	$0.861296\pi$
$464$	−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	$0.269106\pi$
$467$			15102.6i			1.49650i	−0.663416	+	0.748251i	$0.730894\pi$
$468$	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	$0.0991361\pi$
$479$			6424.97i			0.612869i	−0.951892	+	0.306435i	$0.900864\pi$
$480$	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	$0.148408\pi$
$487$			9662.31i			0.899058i	−0.893266	+	0.449529i	$0.851592\pi$
$488$	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	$0.0668474\pi$
$491$			4536.18i			0.416934i	−0.978029	+	0.208467i	$0.933153\pi$
$492$	−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	$0.0160085\pi$
$523$			1202.54i			0.100542i	−0.998736	+	0.0502711i	$0.983991\pi$
$524$	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	$0.0264491\pi$
$547$			2123.59i			0.165993i	−0.996550	+	0.0829966i	$0.973551\pi$
$548$	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	$0.329115\pi$
$563$			22958.8i			1.71865i	−0.511432	+	0.859324i	$0.670885\pi$
$564$	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	$0.0158737\pi$
$571$			1360.30i			0.0996963i	−0.998757	+	0.0498482i	$0.984126\pi$
$572$	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	$0.154646\pi$
$577$			12943.8i			0.933892i	−0.884286	+	0.466946i	$0.845354\pi$
$578$	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	$-0.869340\pi$
$593$		−	11525.0i		−	0.798102i	0.916929	−	0.399051i	$-0.130660\pi$
$594$	−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	$0.0872961\pi$
$617$			8301.27i			0.541648i	−0.962629	+	0.270824i	$0.912704\pi$
$618$	−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	$-0.751509\pi$
$631$		−	22309.5i		−	1.40749i	0.710451	−	0.703747i	$-0.248491\pi$
$632$	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	$-0.707330\pi$
$653$		−	26540.8i		−	1.59054i	0.606257	−	0.795269i	$-0.292670\pi$
$654$	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	$-0.870931\pi$
$659$		−	13346.4i		−	0.788926i	0.918912	−	0.394463i	$-0.129069\pi$
$660$	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	$0.194651\pi$
$677$			20225.8i			1.14821i	−0.818780	+	0.574107i	$0.805349\pi$
$678$	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	$0.129641\pi$
$701$			14703.7i			0.792226i	−0.918202	+	0.396113i	$0.870359\pi$
$702$	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	$0.0685663\pi$
$743$			8657.84i			0.427491i	−0.976889	+	0.213745i	$0.931434\pi$
$744$	−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	$0.233261\pi$
$757$			27866.0i			1.33792i	−0.743297	+	0.668962i	$0.766739\pi$
$758$	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	$0.0556387\pi$
$761$			7301.63i			0.347811i	−0.984762	+	0.173905i	$0.944361\pi$
$762$	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	$0.0648759\pi$
$769$			8632.60i			0.404811i	−0.979302	+	0.202405i	$0.935124\pi$
$770$	−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

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)

\(f(q)\)	\(=\)	\(q+(-0.481589 - 2.78713i) q^{2} -3.00000i q^{3} +(-7.53614 + 2.68450i) q^{4} -21.7286 q^{5} +(-8.36138 + 1.44477i) q^{6} -13.0550i q^{7} +(11.1114 + 19.7114i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 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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