LMFDB - Embedded newform 360.4.m.c.179.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.40
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17972 + 2.57066i) q^{2} +(-5.21654 + 6.06528i) q^{4} +(8.70998 + 7.00973i) q^{5} +3.04837 q^{7} +(-21.7458 - 6.25463i) q^{8} +O(q^{10})$	\(q+(1.17972 + 2.57066i) q^{2} +(-5.21654 + 6.06528i) q^{4} +(8.70998 + 7.00973i) q^{5} +3.04837 q^{7} +(-21.7458 - 6.25463i) q^{8} +(-7.74430 + 30.6598i) q^{10} +54.7844i q^{11} +6.02360 q^{13} +(3.59620 + 7.83630i) q^{14} +(-9.57536 - 63.2796i) q^{16} +70.4789 q^{17} -97.7106 q^{19} +(-87.9520 + 16.2620i) q^{20} +(-140.832 + 64.6300i) q^{22} +12.4765i q^{23} +(26.7275 + 122.109i) q^{25} +(7.10614 + 15.4846i) q^{26} +(-15.9019 + 18.4892i) q^{28} -191.066 q^{29} +185.083i q^{31} +(151.374 - 99.2669i) q^{32} +(83.1450 + 181.177i) q^{34} +(26.5512 + 21.3682i) q^{35} -15.2023 q^{37} +(-115.271 - 251.180i) q^{38} +(-145.562 - 206.910i) q^{40} +61.0901i q^{41} +100.920i q^{43} +(-332.283 - 285.785i) q^{44} +(-32.0728 + 14.7187i) q^{46} -479.967i q^{47} -333.707 q^{49} +(-282.370 + 212.761i) q^{50} +(-31.4224 + 36.5349i) q^{52} -629.394i q^{53} +(-384.023 + 477.171i) q^{55} +(-66.2891 - 19.0664i) q^{56} +(-225.403 - 491.164i) q^{58} +515.626i q^{59} -68.2593i q^{61} +(-475.785 + 218.345i) q^{62} +(433.759 + 272.024i) q^{64} +(52.4654 + 42.2238i) q^{65} +785.021i q^{67} +(-367.656 + 427.474i) q^{68} +(-23.6074 + 93.4624i) q^{70} +374.645 q^{71} -469.268i q^{73} +(-17.9344 - 39.0799i) q^{74} +(509.711 - 592.642i) q^{76} +167.003i q^{77} +274.276i q^{79} +(360.172 - 618.285i) q^{80} +(-157.042 + 72.0689i) q^{82} -1023.14 q^{83} +(613.869 + 494.037i) q^{85} +(-259.430 + 119.057i) q^{86} +(342.656 - 1191.33i) q^{88} -337.508i q^{89} +18.3621 q^{91} +(-75.6734 - 65.0841i) q^{92} +(1233.83 - 566.225i) q^{94} +(-851.057 - 684.924i) q^{95} +862.964i q^{97} +(-393.680 - 857.847i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	1.17972	+	2.57066i	0.417092	+	0.908864i
$2$	1.17972	+	2.57066i	0.417092	+	0.908864i
$3$		0			0
$3$		0			0
$4$	−5.21654	+	6.06528i	−0.652068	+	0.758161i
$5$	8.70998	+	7.00973i	0.779044	+	0.626969i
$5$	8.70998	+	7.00973i	0.779044	+	0.626969i
$6$		0			0
$7$	3.04837			0.164596			0.0822981	−	0.996608i	$-0.473774\pi$
$7$	3.04837			0.164596			0.0822981	+	0.996608i	$0.473774\pi$
$8$	−21.7458	−	6.25463i	−0.961038	−	0.276418i
$9$		0			0
$10$	−7.74430	+	30.6598i	−0.244896	+	0.969549i
$11$			54.7844i			1.50165i	0.660504	+	0.750823i	$0.270343\pi$
$11$			54.7844i			1.50165i	−0.660504	+	0.750823i	$0.729657\pi$
$12$		0			0
$13$	6.02360			0.128511			0.0642556	−	0.997933i	$-0.479533\pi$
$13$	6.02360			0.128511			0.0642556	+	0.997933i	$0.479533\pi$
$14$	3.59620	+	7.83630i	0.0686519	+	0.149596i
$15$		0			0
$16$	−9.57536	−	63.2796i	−0.149615	−	0.988744i
$17$	70.4789			1.00551			0.502754	−	0.864430i	$-0.332320\pi$
$17$	70.4789			1.00551			0.502754	+	0.864430i	$0.332320\pi$
$18$		0			0
$19$	−97.7106			−1.17981			−0.589904	−	0.807474i	$-0.700834\pi$
$19$	−97.7106			−1.17981			−0.589904	+	0.807474i	$0.700834\pi$
$20$	−87.9520	+	16.2620i	−0.983333	+	0.181814i
$21$		0			0
$22$	−140.832	+	64.6300i	−1.36479	+	0.626325i
$23$			12.4765i			0.113110i	0.998399	+	0.0565549i	$0.0180116\pi$
$23$			12.4765i			0.113110i	−0.998399	+	0.0565549i	$0.981988\pi$
$24$		0			0
$25$	26.7275	+	122.109i	0.213820	+	0.976873i
$26$	7.10614	+	15.4846i	0.0536011	+	0.116799i
$27$		0			0
$28$	−15.9019	+	18.4892i	−0.107328	+	0.124790i
$29$	−191.066			−1.22345			−0.611724	−	0.791071i	$-0.709524\pi$
$29$	−191.066			−1.22345			−0.611724	+	0.791071i	$0.709524\pi$
$30$		0			0
$31$			185.083i			1.07232i	0.844117	+	0.536159i	$0.180125\pi$
$31$			185.083i			1.07232i	−0.844117	+	0.536159i	$0.819875\pi$
$32$	151.374	−	99.2669i	0.836231	−	0.548378i
$33$		0			0
$34$	83.1450	+	181.177i	0.419390	+	0.913870i
$35$	26.5512	+	21.3682i	0.128228	+	0.103197i
$36$		0			0
$37$	−15.2023			−0.0675471			−0.0337736	−	0.999430i	$-0.510753\pi$
$37$	−15.2023			−0.0675471			−0.0337736	+	0.999430i	$0.510753\pi$
$38$	−115.271	−	251.180i	−0.492089	−	1.07228i
$39$		0			0
$40$	−145.562	−	206.910i	−0.575385	−	0.817883i
$41$			61.0901i			0.232699i	0.993208	+	0.116350i	$0.0371193\pi$
$41$			61.0901i			0.232699i	−0.993208	+	0.116350i	$0.962881\pi$
$42$		0			0
$43$			100.920i			0.357910i	0.983857	+	0.178955i	$0.0572717\pi$
$43$			100.920i			0.357910i	−0.983857	+	0.178955i	$0.942728\pi$
$44$	−332.283	−	285.785i	−1.13849	−	0.979175i
$45$		0			0
$46$	−32.0728	+	14.7187i	−0.102802	+	0.0471773i
$47$		−	479.967i		−	1.48958i	−0.667297	−	0.744791i	$-0.732549\pi$
$47$		−	479.967i		−	1.48958i	0.667297	−	0.744791i	$-0.267451\pi$
$48$		0			0
$49$	−333.707			−0.972908
$50$	−282.370	+	212.761i	−0.798662	+	0.601780i
$51$		0			0
$52$	−31.4224	+	36.5349i	−0.0837981	+	0.0974322i
$53$		−	629.394i		−	1.63121i	−0.578612	−	0.815603i	$-0.696406\pi$
$53$		−	629.394i		−	1.63121i	0.578612	−	0.815603i	$-0.303594\pi$
$54$		0			0
$55$	−384.023	+	477.171i	−0.941485	+	1.16985i
$56$	−66.2891	−	19.0664i	−0.158183	−	0.0454974i
$57$		0			0
$58$	−225.403	−	491.164i	−0.510291	−	1.11195i
$59$			515.626i			1.13778i	0.822415	+	0.568888i	$0.192626\pi$
$59$			515.626i			1.13778i	−0.822415	+	0.568888i	$0.807374\pi$
$60$		0			0
$61$		−	68.2593i		−	0.143274i	−0.997431	−	0.0716370i	$-0.977178\pi$
$61$		−	68.2593i		−	0.143274i	0.997431	−	0.0716370i	$-0.0228223\pi$
$62$	−475.785	+	218.345i	−0.974592	+	0.447256i
$63$		0			0
$64$	433.759	+	272.024i	0.847186	+	0.531296i
$65$	52.4654	+	42.2238i	0.100116	+	0.0805726i
$66$		0			0
$67$			785.021i			1.43143i	0.698395	+	0.715713i	$0.253898\pi$
$67$			785.021i			1.43143i	−0.698395	+	0.715713i	$0.746102\pi$
$68$	−367.656	+	427.474i	−0.655659	+	0.762336i
$69$		0			0
$70$	−23.6074	+	93.4624i	−0.0403090	+	0.159584i
$71$	374.645			0.626228			0.313114	−	0.949716i	$-0.398628\pi$
$71$	374.645			0.626228			0.313114	+	0.949716i	$0.398628\pi$
$72$		0			0
$73$		−	469.268i		−	0.752379i	−0.926543	−	0.376190i	$-0.877234\pi$
$73$		−	469.268i		−	0.752379i	0.926543	−	0.376190i	$-0.122766\pi$
$74$	−17.9344	−	39.0799i	−0.0281734	−	0.0613912i
$75$		0			0
$76$	509.711	−	592.642i	0.769314	−	0.894483i
$77$			167.003i			0.247165i
$78$		0			0
$79$			274.276i			0.390614i	0.980742	+	0.195307i	$0.0625703\pi$
$79$			274.276i			0.390614i	−0.980742	+	0.195307i	$0.937430\pi$
$80$	360.172	−	618.285i	0.503355	−	0.864080i
$81$		0			0
$82$	−157.042	+	72.0689i	−0.211492	+	0.0970571i
$83$	−1023.14			−1.35306			−0.676532	−	0.736414i	$-0.736518\pi$
$83$	−1023.14			−1.35306			−0.676532	+	0.736414i	$0.736518\pi$
$84$		0			0
$85$	613.869	+	494.037i	0.783335	+	0.630422i
$86$	−259.430	+	119.057i	−0.325292	+	0.149282i
$87$		0			0
$88$	342.656	−	1191.33i	0.415082	−	1.44314i
$89$		−	337.508i		−	0.401975i	−0.979594	−	0.200987i	$-0.935585\pi$
$89$		−	337.508i		−	0.401975i	0.979594	−	0.200987i	$-0.0644150\pi$
$90$		0			0
$91$	18.3621			0.0211525
$92$	−75.6734	−	65.0841i	−0.0857555	−	0.0737553i
$93$		0			0
$94$	1233.83	−	566.225i	1.35383	−	0.621294i
$95$	−851.057	−	684.924i	−0.919122	−	0.739703i
$96$		0			0
$97$			862.964i			0.903307i	0.892193	+	0.451653i	$0.149166\pi$
$97$			862.964i			0.903307i	−0.892193	+	0.451653i	$0.850834\pi$
$98$	−393.680	−	857.847i	−0.405793	−	0.884241i
$99$		0			0
$100$	−880.052	−	474.878i	−0.880052	−	0.474878i
$101$	1589.73			1.56618			0.783091	−	0.621907i	$-0.213642\pi$
$101$	1589.73			1.56618			0.783091	+	0.621907i	$0.213642\pi$
$102$		0			0
$103$	1329.26			1.27161			0.635804	−	0.771851i	$-0.280669\pi$
$103$	1329.26			1.27161			0.635804	+	0.771851i	$0.280669\pi$
$104$	−130.988	−	37.6754i	−0.123504	−	0.0355228i
$105$		0			0
$106$	1617.95	−	742.506i	1.48254	−	0.680363i
$107$	760.234			0.686865			0.343433	−	0.939177i	$-0.388410\pi$
$107$	760.234			0.686865			0.343433	+	0.939177i	$0.388410\pi$
$108$		0			0
$109$			989.226i			0.869272i	0.900606	+	0.434636i	$0.143123\pi$
$109$			989.226i			0.869272i	−0.900606	+	0.434636i	$0.856877\pi$
$110$	−1679.68	−	424.266i	−1.45592	−	0.367747i
$111$		0			0
$112$	−29.1892	−	192.899i	−0.0246261	−	0.162744i
$113$	1604.32			1.33559			0.667794	−	0.744346i	$-0.267239\pi$
$113$	1604.32			1.33559			0.667794	+	0.744346i	$0.267239\pi$
$114$		0			0
$115$	−87.4567	+	108.670i	−0.0709164	+	0.0881176i
$116$	996.702	−	1158.87i	0.797771	−	0.927570i
$117$		0			0
$118$	−1325.50	+	608.292i	−1.03408	+	0.474557i
$119$	214.845			0.165503
$120$		0			0
$121$	−1670.33			−1.25494
$122$	175.471	−	80.5266i	0.130217	−	0.0597585i
$123$		0			0
$124$	−1122.58	−	965.493i	−0.812990	−	0.699225i
$125$	−623.156	+	1250.92i	−0.445894	+	0.895086i
$126$		0			0
$127$	33.5163			0.0234181			0.0117090	−	0.999931i	$-0.496273\pi$
$127$	33.5163			0.0234181			0.0117090	+	0.999931i	$0.496273\pi$
$128$	−187.567	+	1435.96i	−0.129521	+	0.991577i
$129$		0			0
$130$	−46.6485	+	184.683i	−0.0314719	+	0.124598i
$131$			1933.63i			1.28963i	0.764337	+	0.644817i	$0.223066\pi$
$131$			1933.63i			1.28963i	−0.764337	+	0.644817i	$0.776934\pi$
$132$		0			0
$133$	−297.857			−0.194192
$134$	−2018.02	+	926.101i	−1.30097	+	0.597037i
$135$		0			0
$136$	−1532.62	−	440.819i	−0.966331	−	0.277940i
$137$	2964.07			1.84845			0.924225	−	0.381848i	$-0.124712\pi$
$137$	2964.07			1.84845			0.924225	+	0.381848i	$0.124712\pi$
$138$		0			0
$139$	−258.266			−0.157596			−0.0787980	−	0.996891i	$-0.525108\pi$
$139$	−258.266			−0.157596			−0.0787980	+	0.996891i	$0.525108\pi$
$140$	−268.110	+	49.5724i	−0.161853	+	0.0299260i
$141$		0			0
$142$	441.975	+	963.084i	0.261195	+	0.569156i
$143$			329.999i			0.192978i
$144$		0			0
$145$	−1664.18	−	1339.32i	−0.953120	−	0.767064i
$146$	1206.33	−	553.603i	0.683811	−	0.313812i
$147$		0			0
$148$	79.3035	−	92.2063i	0.0440453	−	0.0512116i
$149$	3245.49			1.78443			0.892217	−	0.451607i	$-0.149149\pi$
$149$	3245.49			1.78443			0.892217	+	0.451607i	$0.149149\pi$
$150$		0			0
$151$		−	984.814i		−	0.530748i	−0.964145	−	0.265374i	$-0.914504\pi$
$151$		−	984.814i		−	0.530748i	0.964145	−	0.265374i	$-0.0854955\pi$
$152$	2124.79	+	611.143i	1.13384	+	0.326120i
$153$		0			0
$154$	−429.307	+	197.016i	−0.224640	+	0.103091i
$155$	−1297.38	+	1612.07i	−0.672311	+	0.835384i
$156$		0			0
$157$	3712.76			1.88733			0.943663	−	0.330908i	$-0.107355\pi$
$157$	3712.76			1.88733			0.943663	+	0.330908i	$0.107355\pi$
$158$	−705.070	+	323.568i	−0.355015	+	0.162922i
$159$		0			0
$160$	2014.30	+	196.477i	0.995277	+	0.0970805i
$161$			38.0329i			0.0186175i
$162$		0			0
$163$			2850.58i			1.36978i	0.728645	+	0.684892i	$0.240150\pi$
$163$			2850.58i			1.36978i	−0.728645	+	0.684892i	$0.759850\pi$
$164$	−370.529	−	318.679i	−0.176423	−	0.151736i
$165$		0			0
$166$	−1207.01	−	2630.14i	−0.564352	−	1.22975i
$167$		−	750.365i		−	0.347694i	−0.984773	−	0.173847i	$-0.944380\pi$
$167$		−	750.365i		−	0.347694i	0.984773	−	0.173847i	$-0.0556199\pi$
$168$		0			0
$169$	−2160.72			−0.983485
$170$	−545.809	+	2160.87i	−0.246245	+	0.974889i
$171$		0			0
$172$	−612.108	−	526.453i	−0.271353	−	0.233382i
$173$			2509.45i			1.10283i	0.834230	+	0.551416i	$0.185912\pi$
$173$			2509.45i			1.10283i	−0.834230	+	0.551416i	$0.814088\pi$
$174$		0			0
$175$	81.4751	+	372.233i	0.0351940	+	0.160790i
$176$	3466.73	−	524.580i	1.48474	−	0.224669i
$177$		0			0
$178$	867.617	−	398.163i	0.365341	−	0.167661i
$179$		−	165.661i		−	0.0691736i	−0.999402	−	0.0345868i	$-0.988988\pi$
$179$		−	165.661i		−	0.0691736i	0.999402	−	0.0345868i	$-0.0110115\pi$
$180$		0			0
$181$		−	1303.77i		−	0.535407i	−0.963501	−	0.267703i	$-0.913735\pi$
$181$		−	1303.77i		−	0.535407i	0.963501	−	0.267703i	$-0.0862647\pi$
$182$	21.6621	+	47.2027i	0.00882254	+	0.0192247i
$183$		0			0
$184$	78.0357	−	271.311i	0.0312656	−	0.108703i
$185$	−132.412	−	106.564i	−0.0526222	−	0.0423500i
$186$		0			0
$187$			3861.14i			1.50992i
$188$	2911.14	+	2503.77i	1.12934	+	0.971309i
$189$		0			0
$190$	756.699	−	2995.79i	0.288930	−	1.14388i
$191$	1414.91			0.536018			0.268009	−	0.963416i	$-0.413634\pi$
$191$	1414.91			0.536018			0.268009	+	0.963416i	$0.413634\pi$
$192$		0			0
$193$		−	2550.20i		−	0.951125i	−0.879682	−	0.475563i	$-0.842245\pi$
$193$		−	2550.20i		−	0.951125i	0.879682	−	0.475563i	$-0.157755\pi$
$194$	−2218.38	+	1018.05i	−0.820983	+	0.376762i
$195$		0			0
$196$	1740.80	−	2024.03i	0.634402	−	0.737621i
$197$			161.851i			0.0585350i	0.999572	+	0.0292675i	$0.00931747\pi$
$197$			161.851i			0.0585350i	−0.999572	+	0.0292675i	$0.990683\pi$
$198$		0			0
$199$			1363.22i			0.485609i	0.970075	+	0.242805i	$0.0780674\pi$
$199$			1363.22i			0.485609i	−0.970075	+	0.242805i	$0.921933\pi$
$200$	182.536	−	2822.53i	0.0645364	−	0.997915i
$201$		0			0
$202$	1875.43	+	4086.66i	0.653243	+	1.42345i
$203$	−582.438			−0.201375
$204$		0			0
$205$	−428.225	+	532.093i	−0.145895	+	0.181283i
$206$	1568.15	+	3417.06i	0.530378	+	1.15572i
$207$		0			0
$208$	−57.6782	−	381.171i	−0.0192272	−	0.127065i
$209$		−	5353.01i		−	1.77165i
$210$		0			0
$211$	2460.62			0.802825			0.401412	−	0.915897i	$-0.368519\pi$
$211$	2460.62			0.802825			0.401412	+	0.915897i	$0.368519\pi$
$212$	3817.45	+	3283.26i	1.23672	+	1.06366i
$213$		0			0
$214$	896.860	+	1954.30i	0.286486	+	0.624267i
$215$	−707.421	+	879.010i	−0.224399	+	0.278828i
$216$		0			0
$217$			564.201i			0.176500i
$218$	−2542.96	+	1167.01i	−0.790050	+	0.362567i
$219$		0			0
$220$	−890.902	−	4818.39i	−0.273021	−	1.47662i
$221$	424.537			0.129219
$222$		0			0
$223$	−3381.16			−1.01533			−0.507666	−	0.861554i	$-0.669492\pi$
$223$	−3381.16			−1.01533			−0.507666	+	0.861554i	$0.669492\pi$
$224$	461.443	−	302.602i	0.137640	−	0.0902609i
$225$		0			0
$226$	1892.64	+	4124.15i	0.557064	+	1.21387i
$227$	−4908.25			−1.43512			−0.717560	−	0.696497i	$-0.754741\pi$
$227$	−4908.25			−1.43512			−0.717560	+	0.696497i	$0.754741\pi$
$228$		0			0
$229$		−	5896.22i		−	1.70145i	−0.525608	−	0.850727i	$-0.676162\pi$
$229$		−	5896.22i		−	1.70145i	0.525608	−	0.850727i	$-0.323838\pi$
$230$	−382.527	−	96.6216i	−0.109666	−	0.0277002i
$231$		0			0
$232$	4154.87	+	1195.04i	1.17578	+	0.338183i
$233$	231.563			0.0651081			0.0325541	−	0.999470i	$-0.489636\pi$
$233$	231.563			0.0651081			0.0325541	+	0.999470i	$0.489636\pi$
$234$		0			0
$235$	3364.44	−	4180.50i	0.933922	−	1.16045i
$236$	−3127.42	−	2689.78i	−0.862616	−	0.741907i
$237$		0			0
$238$	253.456	+	552.293i	0.0690300	+	0.150420i
$239$	−1008.10			−0.272839			−0.136419	−	0.990651i	$-0.543559\pi$
$239$	−1008.10			−0.272839			−0.136419	+	0.990651i	$0.543559\pi$
$240$		0			0
$241$	1710.82			0.457277			0.228639	−	0.973511i	$-0.426573\pi$
$241$	1710.82			0.457277			0.228639	+	0.973511i	$0.426573\pi$
$242$	−1970.51	−	4293.83i	−0.523426	−	1.14057i
$243$		0			0
$244$	414.012	+	356.078i	0.108625	+	0.0934244i
$245$	−2906.59	−	2339.20i	−0.757938	−	0.609983i
$246$		0			0
$247$	−588.569			−0.151619
$248$	1157.62	−	4024.78i	0.296408	−	1.03054i
$249$		0			0
$250$	−3950.83	−	126.189i	−0.999490	−	0.0319235i
$251$			2529.40i			0.636073i	0.948078	+	0.318037i	$0.103023\pi$
$251$			2529.40i			0.636073i	−0.948078	+	0.318037i	$0.896977\pi$
$252$		0			0
$253$	−683.516			−0.169851
$254$	39.5397	+	86.1590i	0.00976750	+	0.0212838i
$255$		0			0
$256$	−3912.62	+	1211.85i	−0.955231	+	0.295862i
$257$	5703.45			1.38432			0.692162	−	0.721742i	$-0.256658\pi$
$257$	5703.45			1.38432			0.692162	+	0.721742i	$0.256658\pi$
$258$		0			0
$259$	−46.3422			−0.0111180
$260$	−529.788	+	97.9556i	−0.126369	+	0.0233652i
$261$		0			0
$262$	−4970.70	+	2281.13i	−1.17210	+	0.537897i
$263$		−	6283.42i		−	1.47320i	−0.676327	−	0.736602i	$-0.736429\pi$
$263$		−	6283.42i		−	1.47320i	0.676327	−	0.736602i	$-0.263571\pi$
$264$		0			0
$265$	4411.88	−	5482.01i	1.02272	−	1.27078i
$266$	−351.387	−	765.689i	−0.0809960	−	0.176494i
$267$		0			0
$268$	−4761.37	−	4095.09i	−1.08525	−	0.933387i
$269$	−716.767			−0.162461			−0.0812306	−	0.996695i	$-0.525885\pi$
$269$	−716.767			−0.162461			−0.0812306	+	0.996695i	$0.525885\pi$
$270$		0			0
$271$			4212.49i			0.944245i	0.881533	+	0.472123i	$0.156512\pi$
$271$			4212.49i			0.944245i	−0.881533	+	0.472123i	$0.843488\pi$
$272$	−674.861	−	4459.88i	−0.150439	−	0.994190i
$273$		0			0
$274$	3496.76	+	7619.61i	0.770975	+	1.67999i
$275$	−6689.67	+	1464.25i	−1.46692	+	0.321082i
$276$		0			0
$277$	−2415.15			−0.523872			−0.261936	−	0.965085i	$-0.584361\pi$
$277$	−2415.15			−0.523872			−0.261936	+	0.965085i	$0.584361\pi$
$278$	−304.681	−	663.913i	−0.0657321	−	0.143233i
$279$		0			0
$280$	−443.727	−	630.736i	−0.0947063	−	0.134620i
$281$		−	7101.14i		−	1.50754i	−0.657138	−	0.753770i	$-0.728233\pi$
$281$		−	7101.14i		−	1.50754i	0.657138	−	0.753770i	$-0.271767\pi$
$282$		0			0
$283$		−	4895.59i		−	1.02831i	−0.857696	−	0.514157i	$-0.828105\pi$
$283$		−	4895.59i		−	1.02831i	0.857696	−	0.514157i	$-0.171895\pi$
$284$	−1954.35	+	2272.33i	−0.408343	+	0.474781i
$285$		0			0
$286$	−848.314	+	389.305i	−0.175391	+	0.0804898i
$287$			186.225i			0.0383014i
$288$		0			0
$289$	54.2687			0.0110459
$290$	1479.67	−	5858.04i	0.299618	−	1.18619i
$291$		0			0
$292$	2846.25	+	2447.96i	0.570424	+	0.490602i
$293$			7319.56i			1.45943i	0.683751	+	0.729715i	$0.260347\pi$
$293$			7319.56i			1.45943i	−0.683751	+	0.729715i	$0.739653\pi$
$294$		0			0
$295$	−3614.39	+	4491.09i	−0.713350	+	0.886377i
$296$	330.586	+	95.0848i	0.0649153	+	0.0186712i
$297$		0			0
$298$	3828.75	+	8343.03i	0.744274	+	1.62181i
$299$			75.1534i			0.0145359i
$300$		0			0
$301$			307.641i			0.0589107i
$302$	2531.62	−	1161.80i	0.482378	−	0.221371i
$303$		0			0
$304$	935.614	+	6183.09i	0.176517	+	1.16653i
$305$	478.479	−	594.537i	0.0898283	−	0.111617i
$306$		0			0
$307$			5314.75i			0.988042i	0.869450	+	0.494021i	$0.164473\pi$
$307$			5314.75i			0.988042i	−0.869450	+	0.494021i	$0.835527\pi$
$308$	−1012.92	−	871.177i	−0.187391	−	0.161169i
$309$		0			0
$310$	−5674.61	−	1433.34i	−1.03967	−	0.262607i
$311$	−10611.0			−1.93470			−0.967351	−	0.253441i	$-0.918438\pi$
$311$	−10611.0			−1.93470			−0.967351	+	0.253441i	$0.918438\pi$
$312$		0			0
$313$		−	5003.85i		−	0.903623i	−0.892113	−	0.451812i	$-0.850778\pi$
$313$		−	5003.85i		−	0.903623i	0.892113	−	0.451812i	$-0.149222\pi$
$314$	4380.00	+	9544.22i	0.787189	+	1.71532i
$315$		0			0
$316$	−1663.56	−	1430.77i	−0.296148	−	0.254707i
$317$		−	1934.35i		−	0.342724i	−0.985208	−	0.171362i	$-0.945183\pi$
$317$		−	1934.35i		−	0.342724i	0.985208	−	0.171362i	$-0.0548168\pi$
$318$		0			0
$319$		−	10467.4i		−	1.83719i
$320$	1871.22	+	5409.85i	0.326889	+	0.945063i
$321$		0			0
$322$	−97.7695	+	44.8680i	−0.0169207	+	0.00776520i
$323$	−6886.53			−1.18631
$324$		0			0
$325$	160.996	+	735.537i	0.0274783	+	0.125539i
$326$	−7327.86	+	3362.87i	−1.24495	+	0.571326i
$327$		0			0
$328$	382.096	−	1328.45i	0.0643223	−	0.223633i
$329$		−	1463.12i		−	0.245180i
$330$		0			0
$331$	5272.57			0.875549			0.437774	−	0.899085i	$-0.355767\pi$
$331$	5272.57			0.875549			0.437774	+	0.899085i	$0.355767\pi$
$332$	5337.26	−	6205.64i	0.882289	−	1.02584i
$333$		0			0
$334$	1928.93	−	885.217i	0.316007	−	0.145021i
$335$	−5502.78	+	6837.51i	−0.897460	+	1.11514i
$336$		0			0
$337$			1466.69i			0.237080i	0.992949	+	0.118540i	$0.0378213\pi$
$337$			1466.69i			0.237080i	−0.992949	+	0.118540i	$0.962179\pi$
$338$	−2549.03	−	5554.46i	−0.410204	−	0.893854i
$339$		0			0
$340$	−6198.75	+	1146.13i	−0.988749	+	0.182816i
$341$	−10139.7			−1.61024
$342$		0			0
$343$	−2062.85			−0.324733
$344$	631.216	−	2194.58i	0.0989328	−	0.343965i
$345$		0			0
$346$	−6450.93	+	2960.44i	−1.00232	+	0.459983i
$347$	8934.40			1.38220			0.691100	−	0.722759i	$-0.257126\pi$
$347$	8934.40			1.38220			0.691100	+	0.722759i	$0.257126\pi$
$348$		0			0
$349$		−	4604.02i		−	0.706154i	−0.935594	−	0.353077i	$-0.885135\pi$
$349$		−	4604.02i		−	0.706154i	0.935594	−	0.353077i	$-0.114865\pi$
$350$	−860.766	+	648.574i	−0.131457	+	0.0990507i
$351$		0			0
$352$	5438.27	+	8292.92i	0.823469	+	1.25572i
$353$	−6511.64			−0.981813			−0.490906	−	0.871212i	$-0.663334\pi$
$353$	−6511.64			−0.981813			−0.490906	+	0.871212i	$0.663334\pi$
$354$		0			0
$355$	3263.15	+	2626.16i	0.487859	+	0.392626i
$356$	2047.08	+	1760.62i	0.304762	+	0.262115i
$357$		0			0
$358$	425.857	−	195.433i	0.0628694	−	0.0288518i
$359$	8623.71			1.26781			0.633903	−	0.773413i	$-0.281452\pi$
$359$	8623.71			1.26781			0.633903	+	0.773413i	$0.281452\pi$
$360$		0			0
$361$	2688.35			0.391945
$362$	3351.55	−	1538.08i	0.486612	−	0.223314i
$363$		0			0
$364$	−95.7869	+	111.372i	−0.0137928	+	0.0160370i
$365$	3289.44	−	4087.32i	0.471718	−	0.586137i
$366$		0			0
$367$	−1842.26			−0.262030			−0.131015	−	0.991380i	$-0.541824\pi$
$367$	−1842.26			−0.262030			−0.131015	+	0.991380i	$0.541824\pi$
$368$	789.507	−	119.467i	0.111837	−	0.0169229i
$369$		0			0
$370$	117.731	−	466.100i	0.0165420	−	0.0654903i
$371$		−	1918.62i		−	0.268490i
$372$		0			0
$373$	−3486.20			−0.483937			−0.241969	−	0.970284i	$-0.577793\pi$
$373$	−3486.20			−0.483937			−0.241969	+	0.970284i	$0.577793\pi$
$374$	−9925.66	+	4555.04i	−1.37231	+	0.629775i
$375$		0			0
$376$	−3002.01	+	10437.3i	−0.411748	+	1.43155i
$377$	−1150.90			−0.157227
$378$		0			0
$379$	2778.85			0.376623			0.188312	−	0.982109i	$-0.439699\pi$
$379$	2778.85			0.376623			0.188312	+	0.982109i	$0.439699\pi$
$380$	8593.84	−	1588.97i	1.16014	−	0.214506i
$381$		0			0
$382$	1669.19	+	3637.25i	0.223569	+	0.487167i
$383$		−	6873.36i		−	0.917004i	−0.888693	−	0.458502i	$-0.848386\pi$
$383$		−	6873.36i		−	0.917004i	0.888693	−	0.458502i	$-0.151614\pi$
$384$		0			0
$385$	−1170.64	+	1454.59i	−0.154965	+	0.192553i
$386$	6555.68	−	3008.51i	0.864444	−	0.396707i
$387$		0			0
$388$	−5234.13	−	4501.69i	−0.684852	−	0.589017i
$389$	7589.77			0.989246			0.494623	−	0.869108i	$-0.335306\pi$
$389$	7589.77			0.989246			0.494623	+	0.869108i	$0.335306\pi$
$390$		0			0
$391$			879.328i			0.113733i
$392$	7256.73	+	2087.22i	0.935001	+	0.268929i
$393$		0			0
$394$	−416.063	+	190.938i	−0.0532004	+	0.0244145i
$395$	−1922.60	+	2388.94i	−0.244903	+	0.304305i
$396$		0			0
$397$	−4629.43			−0.585250			−0.292625	−	0.956227i	$-0.594529\pi$
$397$	−4629.43			−0.585250			−0.292625	+	0.956227i	$0.594529\pi$
$398$	−3504.37	+	1608.21i	−0.441353	+	0.202544i
$399$		0			0
$400$	7471.10	−	2860.54i	0.933887	−	0.357568i
$401$			12943.8i			1.61193i	0.591962	+	0.805966i	$0.298353\pi$
$401$			12943.8i			1.61193i	−0.591962	+	0.805966i	$0.701647\pi$
$402$		0			0
$403$			1114.87i			0.137805i
$404$	−8292.91	+	9642.19i	−1.02126	+	1.18742i
$405$		0			0
$406$	−687.111	−	1497.25i	−0.0839920	−	0.183022i
$407$		−	832.849i		−	0.101432i
$408$		0			0
$409$	−10252.0			−1.23944			−0.619718	−	0.784825i	$-0.712753\pi$
$409$	−10252.0			−1.23944			−0.619718	+	0.784825i	$0.712753\pi$
$410$	−1873.01	−	473.100i	−0.225613	−	0.0569871i
$411$		0			0
$412$	−6934.13	+	8062.32i	−0.829175	+	0.964083i
$413$			1571.82i			0.187274i
$414$		0			0
$415$	−8911.53	−	7171.93i	−1.05410	−	0.848329i
$416$	911.816	−	597.944i	0.107465	−	0.0704727i
$417$		0			0
$418$	13760.7	−	6315.03i	1.61019	−	0.738943i
$419$		−	12097.1i		−	1.41046i	−0.708981	−	0.705228i	$-0.750845\pi$
$419$		−	12097.1i		−	1.41046i	0.708981	−	0.705228i	$-0.249155\pi$
$420$		0			0
$421$			9325.94i			1.07962i	0.841788	+	0.539808i	$0.181503\pi$
$421$			9325.94i			1.07962i	−0.841788	+	0.539808i	$0.818497\pi$
$422$	2902.83	+	6325.40i	0.334852	+	0.729658i
$423$		0			0
$424$	−3936.62	+	13686.7i	−0.450895	+	1.56765i
$425$	1883.72	+	8606.11i	0.214998	+	0.982254i
$426$		0			0
$427$		−	208.079i		−	0.0235824i
$428$	−3965.79	+	4611.03i	−0.447883	+	0.520754i
$429$		0			0
$430$	−3094.19	−	781.553i	−0.347012	−	0.0876508i
$431$	−10892.9			−1.21738			−0.608689	−	0.793409i	$-0.708304\pi$
$431$	−10892.9			−1.21738			−0.608689	+	0.793409i	$0.708304\pi$
$432$		0			0
$433$		−	6598.11i		−	0.732297i	−0.930556	−	0.366149i	$-0.880676\pi$
$433$		−	6598.11i		−	0.732297i	0.930556	−	0.366149i	$-0.119324\pi$
$434$	−1450.37	+	665.596i	−0.160414	+	0.0736167i
$435$		0			0
$436$	−5999.94	−	5160.34i	−0.659048	−	0.566824i
$437$		−	1219.08i		−	0.133448i
$438$		0			0
$439$		−	5456.53i		−	0.593225i	−0.954998	−	0.296613i	$-0.904143\pi$
$439$		−	5456.53i		−	0.593225i	0.954998	−	0.296613i	$-0.0958570\pi$
$440$	11335.4	−	7974.53i	1.22817	−	0.864025i
$441$		0			0
$442$	500.832	+	1091.34i	0.0538963	+	0.117443i
$443$	7139.56			0.765713			0.382856	−	0.923808i	$-0.374940\pi$
$443$	7139.56			0.765713			0.382856	+	0.923808i	$0.374940\pi$
$444$		0			0
$445$	2365.84	−	2939.69i	0.252026	−	0.313156i
$446$	−3988.80	−	8691.79i	−0.423487	−	0.922799i
$447$		0			0
$448$	1322.26	+	829.227i	0.139444	+	0.0874494i
$449$		−	18493.8i		−	1.94383i	−0.235342	−	0.971913i	$-0.575621\pi$
$449$		−	18493.8i		−	1.94383i	0.235342	−	0.971913i	$-0.424379\pi$
$450$		0			0
$451$	−3346.78			−0.349432
$452$	−8368.99	+	9730.64i	−0.870894	+	1.01259i
$453$		0			0
$454$	−5790.34	−	12617.4i	−0.598577	−	1.30433i
$455$	159.934	+	128.714i	0.0164787	+	0.0132619i
$456$		0			0
$457$			6937.45i			0.710110i	0.934845	+	0.355055i	$0.115538\pi$
$457$			6937.45i			0.710110i	−0.934845	+	0.355055i	$0.884462\pi$
$458$	15157.1	−	6955.86i	1.54639	−	0.709663i
$459$		0			0
$460$	−202.892	−	1097.33i	−0.0205650	−	0.111225i
$461$	−2454.34			−0.247961			−0.123980	−	0.992285i	$-0.539566\pi$
$461$	−2454.34			−0.247961			−0.123980	+	0.992285i	$0.539566\pi$
$462$		0			0
$463$	18655.5			1.87256			0.936280	−	0.351255i	$-0.114245\pi$
$463$	18655.5			1.87256			0.936280	+	0.351255i	$0.114245\pi$
$464$	1829.52	+	12090.6i	0.183046	+	1.20968i
$465$		0			0
$466$	273.178	+	595.268i	0.0271561	+	0.0591744i
$467$	−8711.27			−0.863189			−0.431595	−	0.902068i	$-0.642049\pi$
$467$	−8711.27			−0.863189			−0.431595	+	0.902068i	$0.642049\pi$
$468$		0			0
$469$			2393.03i			0.235607i
$470$	14715.7	+	3717.01i	1.44422	+	0.364793i
$471$		0			0
$472$	3225.05	−	11212.7i	0.314502	−	1.09344i
$473$	−5528.83			−0.537454
$474$		0			0
$475$	−2611.56	−	11931.4i	−0.252266	−	1.15252i
$476$	−1120.75	+	1303.10i	−0.107919	+	0.125478i
$477$		0			0
$478$	−1189.27	−	2591.48i	−0.113799	−	0.247973i
$479$	14564.1			1.38925			0.694627	−	0.719370i	$-0.255569\pi$
$479$	14564.1			1.38925			0.694627	+	0.719370i	$0.255569\pi$
$480$		0			0
$481$	−91.5727			−0.00868057
$482$	2018.28	+	4397.94i	0.190727	+	0.415603i
$483$		0			0
$484$	8713.33	−	10131.0i	0.818306	−	0.951446i
$485$	−6049.14	+	7516.40i	−0.566345	+	0.703716i
$486$		0			0
$487$	1532.44			0.142591			0.0712953	−	0.997455i	$-0.477287\pi$
$487$	1532.44			0.142591			0.0712953	+	0.997455i	$0.477287\pi$
$488$	−426.937	+	1484.35i	−0.0396035	+	0.137692i
$489$		0			0
$490$	2584.33	−	10231.4i	0.238261	−	0.943282i
$491$			1830.42i			0.168240i	0.996456	+	0.0841201i	$0.0268079\pi$
$491$			1830.42i			0.168240i	−0.996456	+	0.0841201i	$0.973192\pi$
$492$		0			0
$493$	−13466.1			−1.23019
$494$	−694.344	−	1513.01i	−0.0632389	−	0.137801i
$495$		0			0
$496$	11712.0	−	1772.24i	1.06025	−	0.160435i
$497$	1142.06			0.103075
$498$		0			0
$499$	−9894.04			−0.887611			−0.443806	−	0.896123i	$-0.646372\pi$
$499$	−9894.04			−0.887611			−0.443806	+	0.896123i	$0.646372\pi$
$500$	−4336.47	−	10305.1i	−0.387866	−	0.921716i
$501$		0			0
$502$	−6502.22	+	2983.97i	−0.578104	+	0.265301i
$503$			11702.0i			1.03731i	0.854983	+	0.518657i	$0.173568\pi$
$503$			11702.0i			1.03731i	−0.854983	+	0.518657i	$0.826432\pi$
$504$		0			0
$505$	13846.5	+	11143.6i	1.22013	+	0.981948i
$506$	−806.355	−	1757.08i	−0.0708436	−	0.154371i
$507$		0			0
$508$	−174.839	+	203.286i	−0.0152702	+	0.0177547i
$509$	19391.1			1.68860			0.844298	−	0.535875i	$-0.180018\pi$
$509$	19391.1			1.68860			0.844298	+	0.535875i	$0.180018\pi$
$510$		0			0
$511$		−	1430.50i		−	0.123839i
$512$	−7731.04	−	8628.37i	−0.667318	−	0.744773i
$513$		0			0
$514$	6728.45	+	14661.6i	0.577391	+	1.25816i
$515$	11577.8	+	9317.73i	0.990639	+	0.797259i
$516$		0			0
$517$	26294.7			2.23683
$518$	−54.6706	−	119.130i	−0.00463724	−	0.0101048i
$519$		0			0
$520$	−876.809	−	1246.34i	−0.0739435	−	0.105107i
$521$		−	5978.90i		−	0.502765i	−0.967888	−	0.251382i	$-0.919115\pi$
$521$		−	5978.90i		−	0.502765i	0.967888	−	0.251382i	$-0.0808851\pi$
$522$		0			0
$523$			3209.92i			0.268375i	0.990956	+	0.134187i	$0.0428424\pi$
$523$			3209.92i			0.268375i	−0.990956	+	0.134187i	$0.957158\pi$
$524$	−11728.0	−	10086.9i	−0.977750	−	0.840929i
$525$		0			0
$526$	16152.5	−	7412.65i	1.33894	−	0.614462i
$527$			13044.4i			1.07822i
$528$		0			0
$529$	12011.3			0.987206
$530$	19297.1	+	4874.21i	1.58153	+	0.399476i
$531$		0			0
$532$	1553.79	−	1806.59i	0.126626	−	0.147229i
$533$			367.982i			0.0299045i
$534$		0			0
$535$	6621.62	+	5329.03i	0.535098	+	0.430643i
$536$	4910.01	−	17070.9i	0.395672	−	1.37565i
$537$		0			0
$538$	−845.581	−	1842.56i	−0.0677613	−	0.147655i
$539$		−	18281.9i		−	1.46096i
$540$		0			0
$541$		−	730.645i		−	0.0580645i	−0.999578	−	0.0290322i	$-0.990757\pi$
$541$		−	730.645i		−	0.0580645i	0.999578	−	0.0290322i	$-0.00924255\pi$
$542$	−10828.9	+	4969.54i	−0.858190	+	0.393837i
$543$		0			0
$544$	10668.7	−	6996.22i	0.840837	−	0.551398i
$545$	−6934.20	+	8616.14i	−0.545007	+	0.677201i
$546$		0			0
$547$		−	21172.4i		−	1.65497i	−0.561491	−	0.827483i	$-0.689772\pi$
$547$		−	21172.4i		−	1.65497i	0.561491	−	0.827483i	$-0.310228\pi$
$548$	−15462.2	+	17977.9i	−1.20532	+	1.40142i
$549$		0			0
$550$	−11656.0	−	15469.4i	−0.903660	−	1.19931i
$551$	18669.1			1.44343
$552$		0			0
$553$			836.094i			0.0642935i
$554$	−2849.19	−	6208.53i	−0.218503	−	0.476128i
$555$		0			0
$556$	1347.26	−	1566.46i	0.102763	−	0.119483i
$557$		−	772.589i		−	0.0587713i	−0.999568	−	0.0293857i	$-0.990645\pi$
$557$		−	772.589i		−	0.0587713i	0.999568	−	0.0293857i	$-0.00935510\pi$
$558$		0			0
$559$			607.901i			0.0459955i
$560$	1097.93	−	1884.76i	0.0828504	−	0.142224i
$561$		0			0
$562$	18254.6	−	8377.33i	1.37015	−	0.628784i
$563$	18014.6			1.34854			0.674268	−	0.738486i	$-0.264459\pi$
$563$	18014.6			1.34854			0.674268	+	0.738486i	$0.264459\pi$
$564$		0			0
$565$	13973.6	+	11245.8i	1.04048	+	0.837372i
$566$	12584.9	−	5775.41i	0.934597	−	0.428902i
$567$		0			0
$568$	−8146.96	−	2343.26i	−0.601829	−	0.173101i
$569$			23132.6i			1.70434i	0.523266	+	0.852170i	$0.324713\pi$
$569$			23132.6i			1.70434i	−0.523266	+	0.852170i	$0.675287\pi$
$570$		0			0
$571$	−7076.17			−0.518614			−0.259307	−	0.965795i	$-0.583494\pi$
$571$	−7076.17			−0.518614			−0.259307	+	0.965795i	$0.583494\pi$
$572$	−2001.54	−	1721.45i	−0.146309	−	0.125835i
$573$		0			0
$574$	−478.720	+	219.692i	−0.0348108	+	0.0159752i
$575$	−1523.49	+	333.465i	−0.110494	+	0.0241851i
$576$		0			0
$577$			5616.89i			0.405258i	0.979256	+	0.202629i	$0.0649486\pi$
$577$			5616.89i			0.405258i	−0.979256	+	0.202629i	$0.935051\pi$
$578$	64.0216	+	139.506i	0.00460717	+	0.0100392i
$579$		0			0
$580$	16804.6	−	3107.10i	1.20306	−	0.222440i
$581$	−3118.91			−0.222709
$582$		0			0
$583$	34480.9			2.44949
$584$	−2935.10	+	10204.6i	−0.207971	+	0.723065i
$585$		0			0
$586$	−18816.1	+	8635.00i	−1.32642	+	0.608718i
$587$	17604.0			1.23781			0.618905	−	0.785466i	$-0.287577\pi$
$587$	17604.0			1.23781			0.618905	+	0.785466i	$0.287577\pi$
$588$		0			0
$589$		−	18084.6i		−	1.26513i
$590$	−15809.0	−	3993.16i	−1.10313	−	0.278637i
$591$		0			0
$592$	145.568	+	961.997i	0.0101061	+	0.0667869i
$593$	1017.20			0.0704410			0.0352205	−	0.999380i	$-0.488787\pi$
$593$	1017.20			0.0704410			0.0352205	+	0.999380i	$0.488787\pi$
$594$		0			0
$595$	1871.30	+	1506.01i	0.128934	+	0.103765i
$596$	−16930.2	+	19684.8i	−1.16357	+	1.35289i
$597$		0			0
$598$	−193.193	+	88.6596i	−0.0132112	+	0.00606281i
$599$	19133.7			1.30515			0.652574	−	0.757725i	$-0.273689\pi$
$599$	19133.7			1.30515			0.652574	+	0.757725i	$0.273689\pi$
$600$		0			0
$601$	5425.28			0.368223			0.184111	−	0.982905i	$-0.441059\pi$
$601$	5425.28			0.368223			0.184111	+	0.982905i	$0.441059\pi$
$602$	−790.838	+	362.928i	−0.0535418	+	0.0245712i
$603$		0			0
$604$	5973.18	+	5137.32i	0.402393	+	0.346084i
$605$	−14548.5	−	11708.5i	−0.977654	−	0.786809i
$606$		0			0
$607$	−20254.8			−1.35439			−0.677196	−	0.735803i	$-0.736805\pi$
$607$	−20254.8			−1.35439			−0.677196	+	0.735803i	$0.736805\pi$
$608$	−14790.8	+	9699.43i	−0.986591	+	0.646980i
$609$		0			0
$610$	2092.82	+	528.620i	0.138911	+	0.0350872i
$611$		−	2891.13i		−	0.191428i
$612$		0			0
$613$	−24005.4			−1.58168			−0.790838	−	0.612025i	$-0.790355\pi$
$613$	−24005.4			−1.58168			−0.790838	+	0.612025i	$0.790355\pi$
$614$	−13662.4	+	6269.89i	−0.897996	+	0.412105i
$615$		0			0
$616$	1044.54	−	3631.61i	0.0683209	−	0.237535i
$617$	−7647.46			−0.498988			−0.249494	−	0.968376i	$-0.580264\pi$
$617$	−7647.46			−0.498988			−0.249494	+	0.968376i	$0.580264\pi$
$618$		0			0
$619$	−28648.3			−1.86021			−0.930105	−	0.367293i	$-0.880285\pi$
$619$	−28648.3			−1.86021			−0.930105	+	0.367293i	$0.880285\pi$
$620$	−3009.81	−	16278.4i	−0.194963	−	1.05445i
$621$		0			0
$622$	−12517.9	−	27277.1i	−0.806949	−	1.75838i
$623$		−	1028.85i		−	0.0661636i
$624$		0			0
$625$	−14196.3	+	6527.34i	−0.908562	+	0.417750i
$626$	12863.2	−	5903.11i	0.821271	−	0.376894i
$627$		0			0
$628$	−19367.8	+	22518.9i	−1.23066	+	1.43090i
$629$	−1071.44			−0.0679192
$630$		0			0
$631$			20493.5i			1.29292i	0.762947	+	0.646461i	$0.223752\pi$
$631$			20493.5i			1.29292i	−0.762947	+	0.646461i	$0.776248\pi$
$632$	1715.49	−	5964.35i	0.107973	−	0.375394i
$633$		0			0
$634$	4972.54	−	2281.98i	0.311490	−	0.142948i
$635$	291.927	+	234.940i	0.0182437	+	0.0146824i
$636$		0			0
$637$	−2010.12			−0.125030
$638$	26908.1	−	12348.6i	1.66975	−	0.766276i
$639$		0			0
$640$	−11699.4	+	11192.4i	−0.722590	+	0.691276i
$641$			29538.9i			1.82015i	0.414446	+	0.910074i	$0.363975\pi$
$641$			29538.9i			1.82015i	−0.414446	+	0.910074i	$0.636025\pi$
$642$		0			0
$643$			25933.9i			1.59056i	0.606239	+	0.795282i	$0.292677\pi$
$643$			25933.9i			1.59056i	−0.606239	+	0.795282i	$0.707323\pi$
$644$	−230.680	−	198.400i	−0.0141150	−	0.0121398i
$645$		0			0
$646$	−8124.14	−	17702.9i	−0.494799	−	1.07819i
$647$			373.073i			0.0226693i	0.999936	+	0.0113346i	$0.00360800\pi$
$647$			373.073i			0.0226693i	−0.999936	+	0.0113346i	$0.996392\pi$
$648$		0			0
$649$	−28248.2			−1.70854
$650$	−1700.88	+	1281.59i	−0.102637	+	0.0773355i
$651$		0			0
$652$	−17289.6	−	14870.2i	−1.03852	−	0.893192i
$653$		−	9267.82i		−	0.555403i	−0.960667	−	0.277701i	$-0.910427\pi$
$653$		−	9267.82i		−	0.555403i	0.960667	−	0.277701i	$-0.0895726\pi$
$654$		0			0
$655$	−13554.2	+	16841.9i	−0.808561	+	1.00468i
$656$	3865.76	−	584.960i	0.230080	−	0.0348153i
$657$		0			0
$658$	3761.17	−	1726.06i	0.222835	−	0.102263i
$659$			915.098i			0.0540928i	0.999634	+	0.0270464i	$0.00861019\pi$
$659$			915.098i			0.0540928i	−0.999634	+	0.0270464i	$0.991390\pi$
$660$		0			0
$661$			7444.12i			0.438038i	0.975721	+	0.219019i	$0.0702856\pi$
$661$			7444.12i			0.438038i	−0.975721	+	0.219019i	$0.929714\pi$
$662$	6220.13	+	13554.0i	0.365185	+	0.795755i
$663$		0			0
$664$	22249.0	+	6399.36i	1.30034	+	0.374011i
$665$	−2594.33	−	2087.90i	−0.151284	−	0.121752i
$666$		0			0
$667$		−	2383.83i		−	0.138384i
$668$	4551.18	+	3914.31i	0.263608	+	0.226720i
$669$		0			0
$670$	−24068.6	−	6079.43i	−1.38784	−	0.350551i
$671$	3739.54			0.215147
$672$		0			0
$673$			26971.0i			1.54481i	0.635133	+	0.772403i	$0.280945\pi$
$673$			26971.0i			1.54481i	−0.635133	+	0.772403i	$0.719055\pi$
$674$	−3770.36	+	1730.28i	−0.215473	+	0.0988841i
$675$		0			0
$676$	11271.5	−	13105.4i	0.641299	−	0.745639i
$677$		−	23165.6i		−	1.31510i	−0.753409	−	0.657552i	$-0.771592\pi$
$677$		−	23165.6i		−	1.31510i	0.753409	−	0.657552i	$-0.228408\pi$
$678$		0			0
$679$			2630.63i			0.148681i
$680$	−10259.1	−	14582.8i	−0.578554	−	0.822387i
$681$		0			0
$682$	−11961.9	−	26065.6i	−0.671620	−	1.46349i
$683$	14047.0			0.786962			0.393481	−	0.919333i	$-0.371271\pi$
$683$	14047.0			0.786962			0.393481	+	0.919333i	$0.371271\pi$
$684$		0			0
$685$	25817.0	+	20777.3i	1.44002	+	1.15892i
$686$	−2433.58	−	5302.88i	−0.135444	−	0.295138i
$687$		0			0
$688$	6386.17	−	966.345i	0.353882	−	0.0535488i
$689$		−	3791.22i		−	0.209628i
$690$		0			0
$691$	−10957.6			−0.603250			−0.301625	−	0.953427i	$-0.597529\pi$
$691$	−10957.6			−0.603250			−0.301625	+	0.953427i	$0.597529\pi$
$692$	−15220.5	−	13090.7i	−0.836124	−	0.719121i
$693$		0			0
$694$	10540.0	+	22967.3i	0.576505	+	1.25623i
$695$	−2249.49	−	1810.37i	−0.122774	−	0.0988078i
$696$		0			0
$697$			4305.56i			0.233981i
$698$	11835.4	−	5431.44i	0.641798	−	0.294531i
$699$		0			0
$700$	−2682.72	−	1447.60i	−0.144853	−	0.0781631i
$701$	−8450.42			−0.455304			−0.227652	−	0.973743i	$-0.573105\pi$
$701$	−8450.42			−0.455304			−0.227652	+	0.973743i	$0.573105\pi$
$702$		0			0
$703$	1485.43			0.0796926
$704$	−14902.6	+	23763.2i	−0.797819	+	1.27217i
$705$		0			0
$706$	−7681.89	−	16739.2i	−0.409507	−	0.892334i
$707$	4846.09			0.257788
$708$		0			0
$709$		−	3000.63i		−	0.158944i	−0.996837	−	0.0794719i	$-0.974677\pi$
$709$		−	3000.63i		−	0.158944i	0.996837	−	0.0794719i	$-0.0253234\pi$
$710$	−2901.36	+	11486.6i	−0.153361	+	0.607159i
$711$		0			0
$712$	−2110.99	+	7339.38i	−0.111113	+	0.386313i
$713$	−2309.19			−0.121290
$714$		0			0
$715$	−2313.20	+	2874.29i	−0.120991	+	0.150339i
$716$	1004.78	+	864.177i	0.0524447	+	0.0451059i
$717$		0			0
$718$	10173.5	+	22168.6i	0.528792	+	1.15226i
$719$	−13034.1			−0.676061			−0.338031	−	0.941135i	$-0.609761\pi$
$719$	−13034.1			−0.676061			−0.338031	+	0.941135i	$0.609761\pi$
$720$		0			0
$721$	4052.06			0.209302
$722$	3171.49	+	6910.83i	0.163477	+	0.356225i
$723$		0			0
$724$	7907.75	+	6801.18i	0.405924	+	0.349121i
$725$	−5106.70	−	23330.9i	−0.261597	−	1.19515i
$726$		0			0
$727$	16646.7			0.849232			0.424616	−	0.905373i	$-0.360409\pi$
$727$	16646.7			0.849232			0.424616	+	0.905373i	$0.360409\pi$
$728$	−399.299	−	114.848i	−0.0203283	−	0.00584692i
$729$		0			0
$730$	14387.7	+	3634.15i	0.729469	+	0.184255i
$731$			7112.72i			0.359881i
$732$		0			0
$733$	−21887.0			−1.10289			−0.551444	−	0.834212i	$-0.685923\pi$
$733$	−21887.0			−1.10289			−0.551444	+	0.834212i	$0.685923\pi$
$734$	−2173.34	−	4735.81i	−0.109291	−	0.238150i
$735$		0			0
$736$	1238.50	+	1888.62i	0.0620269	+	0.0945860i
$737$	−43006.9			−2.14949
$738$		0			0
$739$	−16888.3			−0.840659			−0.420329	−	0.907372i	$-0.638085\pi$
$739$	−16888.3			−0.840659			−0.420329	+	0.907372i	$0.638085\pi$
$740$	1337.07	−	247.220i	0.0664213	−	0.0122810i
$741$		0			0
$742$	4932.12	−	2263.43i	0.244021	−	0.111985i
$743$		−	37788.5i		−	1.86585i	−0.360071	−	0.932925i	$-0.617247\pi$
$743$		−	37788.5i		−	1.86585i	0.360071	−	0.932925i	$-0.382753\pi$
$744$		0			0
$745$	28268.1	+	22750.0i	1.39015	+	1.11878i
$746$	−4112.72	−	8961.82i	−0.201847	−	0.439833i
$747$		0			0
$748$	−23418.9	−	20141.8i	−1.14476	−	0.984568i
$749$	2317.47			0.113055
$750$		0			0
$751$		−	25256.4i		−	1.22719i	−0.789620	−	0.613596i	$-0.789722\pi$
$751$		−	25256.4i		−	1.22719i	0.789620	−	0.613596i	$-0.210278\pi$
$752$	−30372.1	+	4595.86i	−1.47282	+	0.222864i
$753$		0			0
$754$	−1357.74	−	2958.58i	−0.0655781	−	0.142898i
$755$	6903.28	−	8577.71i	0.332763	−	0.413477i
$756$		0			0
$757$	−24978.2			−1.19927			−0.599635	−	0.800274i	$-0.704687\pi$
$757$	−24978.2			−1.19927			−0.599635	+	0.800274i	$0.704687\pi$
$758$	3278.26	+	7143.48i	0.157087	+	0.342299i
$759$		0			0
$760$	14223.0	+	20217.3i	0.678844	+	0.964944i
$761$			10048.1i			0.478636i	0.970941	+	0.239318i	$0.0769239\pi$
$761$			10048.1i			0.478636i	−0.970941	+	0.239318i	$0.923076\pi$
$762$		0			0
$763$			3015.52i			0.143079i
$764$	−7380.94	+	8581.84i	−0.349520	+	0.406387i
$765$		0			0
$766$	17669.1	−	8108.61i	0.833432	−	0.382475i
$767$			3105.92i			0.146217i
$768$		0			0
$769$	9573.24			0.448920			0.224460	−	0.974483i	$-0.427938\pi$
$769$	9573.24			0.448920			0.224460	+	0.974483i	$0.427938\pi$
$770$	−5120.28	−	1293.32i	−0.239639	−	0.0605298i
$771$		0			0
$772$	15467.7	+	13303.2i	0.721106	+	0.620198i
$773$			15067.4i			0.701083i	0.936547	+	0.350542i	$0.114002\pi$
$773$			15067.4i			0.701083i	−0.936547	+	0.350542i	$0.885998\pi$
$774$		0			0
$775$	−22600.3	+	4946.80i	−1.04752	+	0.229283i
$776$	5397.52	−	18765.8i	0.249690	−	0.868112i
$777$		0			0
$778$	8953.77	+	19510.7i	0.412607	+	0.899090i
$779$		−	5969.15i		−	0.274540i
$780$		0			0
$781$			20524.7i			0.940373i
$782$	−2260.45	+	1037.36i	−0.103368	+	0.0474371i
$783$		0			0
$784$	3195.37	+	21116.9i	0.145562	+	0.961957i
$785$	32338.0	+	26025.4i	1.47031	+	1.18329i
$786$		0			0
$787$		−	33994.6i		−	1.53974i	−0.638199	−	0.769872i	$-0.720320\pi$
$787$		−	33994.6i		−	1.53974i	0.638199	−	0.769872i	$-0.279680\pi$
$788$	−981.672	−	844.302i	−0.0443789	−	0.0381688i
$789$		0			0
$790$	−8409.26	−	2124.08i	−0.378719	−	0.0956598i
$791$	4890.55			0.219833
$792$		0			0
$793$		−	411.167i		−	0.0184123i
$794$	−5461.41	−	11900.7i	−0.244103	−	0.531913i
$795$		0			0
$796$	−8268.33	−	7111.31i	−0.368170	−	0.316650i
$797$			977.710i			0.0434533i	0.999764	+	0.0217266i	$0.00691635\pi$
$797$			977.710i			0.0434533i	−0.999764	+	0.0217266i	$0.993084\pi$
$798$		0			0
$799$		−	33827.5i		−	1.49779i
$800$	16167.2	+	15831.0i	0.714498	+	0.699637i
$801$		0			0
$802$	−33274.2	+	15270.0i	−1.46503	+	0.672324i
$803$	25708.6			1.12981
$804$		0			0
$805$	−266.600	+	331.266i	−0.0116726	+	0.0145038i
$806$	−2865.94	+	1315.22i	−0.125246	+	0.0574774i
$807$		0			0
$808$	−34570.0	−	9943.19i	−1.50516	−	0.432921i
$809$		−	2061.22i		−	0.0895780i	−0.998996	−	0.0447890i	$-0.985738\pi$
$809$		−	2061.22i		−	0.0895780i	0.998996	−	0.0447890i	$-0.0142616\pi$
$810$		0			0
$811$	7805.66			0.337970			0.168985	−	0.985619i	$-0.445951\pi$
$811$	7805.66			0.337970			0.168985	+	0.985619i	$0.445951\pi$
$812$	3038.31	−	3532.65i	0.131310	−	0.152675i
$813$		0			0
$814$	2140.97	−	982.525i	0.0921878	−	0.0423065i
$815$	−19981.8	+	24828.5i	−0.858812	+	1.06712i
$816$		0			0
$817$		−	9860.94i		−	0.422265i
$818$	−12094.5	−	26354.4i	−0.516959	−	1.12648i
$819$		0			0
$820$	−993.445	−	5372.99i	−0.0423081	−	0.228821i
$821$	28089.7			1.19408			0.597038	−	0.802213i	$-0.296344\pi$
$821$	28089.7			1.19408			0.597038	+	0.802213i	$0.296344\pi$
$822$		0			0
$823$	31744.7			1.34453			0.672267	−	0.740309i	$-0.265321\pi$
$823$	31744.7			1.34453			0.672267	+	0.740309i	$0.265321\pi$
$824$	−28905.8	−	8314.01i	−1.22206	−	0.351495i
$825$		0			0
$826$	−4040.60	+	1854.29i	−0.170206	+	0.0781104i
$827$	−40210.2			−1.69074			−0.845371	−	0.534179i	$-0.820621\pi$
$827$	−40210.2			−1.69074			−0.845371	+	0.534179i	$0.820621\pi$
$828$		0			0
$829$			38128.7i			1.59742i	0.601714	+	0.798711i	$0.294485\pi$
$829$			38128.7i			1.59742i	−0.601714	+	0.798711i	$0.705515\pi$
$830$	7923.50	−	31369.3i	0.331360	−	1.31186i
$831$		0			0
$832$	2612.79	+	1638.56i	0.108873	+	0.0682775i
$833$	−23519.3			−0.978267
$834$		0			0
$835$	5259.85	−	6535.66i	0.217994	−	0.270869i
$836$	32467.5	+	27924.2i	1.34320	+	1.15524i
$837$		0			0
$838$	31097.4	−	14271.1i	1.28191	−	0.588290i
$839$	10728.3			0.441456			0.220728	−	0.975335i	$-0.429157\pi$
$839$	10728.3			0.441456			0.220728	+	0.975335i	$0.429157\pi$
$840$		0			0
$841$	12117.1			0.496825
$842$	−23973.8	+	11002.0i	−0.981224	+	0.450300i
$843$		0			0
$844$	−12835.9	+	14924.4i	−0.523496	+	0.608670i
$845$	−18819.8	−	15146.0i	−0.766178	−	0.616614i
$846$		0			0
$847$	−5091.76			−0.206558
$848$	−39827.8	+	6026.67i	−1.61285	+	0.244053i
$849$		0			0
$850$	−19901.1	+	14995.2i	−0.803061	+	0.605094i
$851$		−	189.671i		−	0.00764025i
$852$		0			0
$853$	−11849.6			−0.475641			−0.237820	−	0.971309i	$-0.576433\pi$
$853$	−11849.6			−0.475641			−0.237820	+	0.971309i	$0.576433\pi$
$854$	534.901	−	245.474i	0.0214332	−	0.00983602i
$855$		0			0
$856$	−16531.9	−	4754.98i	−0.660103	−	0.189862i
$857$	834.989			0.0332820			0.0166410	−	0.999862i	$-0.494703\pi$
$857$	834.989			0.0332820			0.0166410	+	0.999862i	$0.494703\pi$
$858$		0			0
$859$	23881.8			0.948587			0.474294	−	0.880367i	$-0.342703\pi$
$859$	23881.8			0.948587			0.474294	+	0.880367i	$0.342703\pi$
$860$	−1641.16	−	8876.10i	−0.0650732	−	0.351945i
$861$		0			0
$862$	−12850.5	−	28001.8i	−0.507759	−	1.10643i
$863$		−	11775.2i		−	0.464464i	−0.972660	−	0.232232i	$-0.925397\pi$
$863$		−	11775.2i		−	0.464464i	0.972660	−	0.232232i	$-0.0746029\pi$
$864$		0			0
$865$	−17590.6	+	21857.3i	−0.691442	+	0.859155i
$866$	16961.5	−	7783.89i	0.665559	−	0.305436i
$867$		0			0
$868$	−3422.04	−	2943.18i	−0.133815	−	0.115090i
$869$	−15026.0			−0.586563
$870$		0			0
$871$			4728.65i			0.183954i
$872$	6187.24	−	21511.5i	0.240282	−	0.835403i
$873$		0			0
$874$	3133.85	−	1438.17i	0.121286	−	0.0556601i
$875$	−1899.61	+	3813.26i	−0.0733925	+	0.147328i
$876$		0			0
$877$	25544.4			0.983548			0.491774	−	0.870723i	$-0.336349\pi$
$877$	25544.4			0.983548			0.491774	+	0.870723i	$0.336349\pi$
$878$	14026.9	−	6437.15i	0.539161	−	0.247430i
$879$		0			0
$880$	33872.3	+	19731.8i	1.29754	+	0.755861i
$881$		−	11317.2i		−	0.432786i	−0.976306	−	0.216393i	$-0.930571\pi$
$881$		−	11317.2i		−	0.432786i	0.976306	−	0.216393i	$-0.0694293\pi$
$882$		0			0
$883$		−	11165.3i		−	0.425529i	−0.977103	−	0.212765i	$-0.931753\pi$
$883$		−	11165.3i		−	0.425529i	0.977103	−	0.212765i	$-0.0682468\pi$
$884$	−2214.61	+	2574.94i	−0.0842596	+	0.0979688i
$885$		0			0
$886$	8422.65	+	18353.4i	0.319373	+	0.695929i
$887$			8025.56i			0.303802i	0.988396	+	0.151901i	$0.0485394\pi$
$887$			8025.56i			0.303802i	−0.988396	+	0.151901i	$0.951461\pi$
$888$		0			0
$889$	102.170			0.00385453
$890$	10347.9	+	2613.76i	0.389734	+	0.0984421i
$891$		0			0
$892$	17638.0	−	20507.7i	0.662066	−	0.769785i
$893$			46897.9i			1.75742i
$894$		0			0
$895$	1161.24	−	1442.90i	0.0433697	−	0.0538893i
$896$	−571.771	+	4377.32i	−0.0213187	+	0.163210i
$897$		0			0
$898$	47541.3	−	21817.4i	1.76667	−	0.810755i
$899$		−	35363.0i		−	1.31193i
$900$		0			0
$901$		−	44359.0i		−	1.64019i
$902$	−3948.25	−	8603.42i	−0.145745	−	0.317586i
$903$		0			0
$904$	−34887.2	−	10034.4i	−1.28355	−	0.369181i
$905$	9139.08	−	11355.8i	0.335683	−	0.417105i
$906$		0			0
$907$		−	15137.9i		−	0.554186i	−0.960843	−	0.277093i	$-0.910629\pi$
$907$		−	15137.9i		−	0.554186i	0.960843	−	0.277093i	$-0.0893711\pi$
$908$	25604.1	−	29769.9i	0.935795	−	1.08805i
$909$		0			0
$910$	−142.202	+	562.980i	−0.00518016	+	0.0205084i
$911$	−22730.3			−0.826660			−0.413330	−	0.910581i	$-0.635634\pi$
$911$	−22730.3			−0.826660			−0.413330	+	0.910581i	$0.635634\pi$
$912$		0			0
$913$		−	56052.1i		−	2.03182i
$914$	−17833.8	+	8184.21i	−0.645393	+	0.296181i
$915$		0			0
$916$	35762.2	+	30757.9i	1.28998	+	1.10946i
$917$			5894.41i			0.212269i
$918$		0			0
$919$			26742.0i			0.959889i	0.877299	+	0.479945i	$0.159343\pi$
$919$			26742.0i			0.959889i	−0.877299	+	0.479945i	$0.840657\pi$
$920$	2581.51	−	1816.11i	0.0925106	−	0.0650818i
$921$		0			0
$922$	−2895.42	−	6309.26i	−0.103423	−	0.225363i
$923$	2256.71			0.0804774
$924$		0			0
$925$	−406.319	−	1856.34i	−0.0144429	−	0.0659850i
$926$	22008.2	+	47956.9i	0.781030	+	1.70190i
$927$		0			0
$928$	−28922.4	+	18966.5i	−1.02308	+	0.670911i
$929$		−	34992.3i		−	1.23580i	−0.786256	−	0.617901i	$-0.787983\pi$
$929$		−	34992.3i		−	1.23580i	0.786256	−	0.617901i	$-0.212017\pi$
$930$		0			0
$931$	32606.7			1.14784
$932$	−1207.96	+	1404.49i	−0.0424549	+	0.0493624i
$933$		0			0
$934$	−10276.8	−	22393.7i	−0.360030	−	0.784522i
$935$	−27065.5	+	33630.4i	−0.946671	+	1.17629i
$936$		0			0
$937$		−	43046.2i		−	1.50081i	−0.660978	−	0.750405i	$-0.729858\pi$
$937$		−	43046.2i		−	1.50081i	0.660978	−	0.750405i	$-0.270142\pi$
$938$	−6151.66	+	2823.09i	−0.214135	+	0.0982700i
$939$		0			0
$940$	7805.21	+	42214.1i	0.270828	+	1.46476i
$941$	−870.023			−0.0301402			−0.0150701	−	0.999886i	$-0.504797\pi$
$941$	−870.023			−0.0301402			−0.0150701	+	0.999886i	$0.504797\pi$
$942$		0			0
$943$	−762.190			−0.0263206
$944$	32628.6	−	4937.30i	1.12497	−	0.170228i
$945$		0			0
$946$	−6522.45	−	14212.7i	−0.224168	−	0.488473i
$947$	3409.34			0.116989			0.0584945	−	0.998288i	$-0.481370\pi$
$947$	3409.34			0.116989			0.0584945	+	0.998288i	$0.481370\pi$
$948$		0			0
$949$		−	2826.68i		−	0.0966892i
$950$	27590.5	−	20789.0i	0.942268	−	0.709984i
$951$		0			0
$952$	−4671.98	−	1343.78i	−0.159054	−	0.0457480i
$953$	−38280.7			−1.30119			−0.650595	−	0.759425i	$-0.725480\pi$
$953$	−38280.7			−1.30119			−0.650595	+	0.759425i	$0.725480\pi$
$954$		0			0
$955$	12323.8	+	9918.14i	0.417581	+	0.336066i
$956$	5258.79	−	6114.41i	0.177909	−	0.206856i
$957$		0			0
$958$	17181.6	+	37439.4i	0.579448	+	1.26264i
$959$	9035.57			0.304248
$960$		0			0
$961$	−4464.71			−0.149868
$962$	−108.030	−	235.402i	−0.00362060	−	0.00788946i
$963$		0			0
$964$	−8924.58	+	10376.6i	−0.298176	+	0.346690i
$965$	17876.2	−	22212.2i	0.596326	−	0.740969i
$966$		0			0
$967$	−47491.1			−1.57933			−0.789664	−	0.613540i	$-0.789745\pi$
$967$	−47491.1			−1.57933			−0.789664	+	0.613540i	$0.789745\pi$
$968$	36322.6	+	10447.3i	1.20604	+	0.346888i
$969$		0			0
$970$	−26458.4	−	6683.05i	−0.875801	−	0.221216i
$971$		−	36930.4i		−	1.22055i	−0.792190	−	0.610275i	$-0.791059\pi$
$971$		−	36930.4i		−	1.22055i	0.792190	−	0.610275i	$-0.208941\pi$
$972$		0			0
$973$	−787.290			−0.0259397
$974$	1807.85	+	3939.38i	0.0594735	+	0.129595i
$975$		0			0
$976$	−4319.43	+	653.608i	−0.141661	+	0.0214359i
$977$	40349.4			1.32128			0.660640	−	0.750703i	$-0.270285\pi$
$977$	40349.4			1.32128			0.660640	+	0.750703i	$0.270285\pi$
$978$		0			0
$979$	18490.2			0.603624
$980$	29350.2	−	5426.74i	0.956692	−	0.176889i
$981$		0			0
$982$	−4705.39	+	2159.38i	−0.152907	+	0.0701717i
$983$		−	54548.2i		−	1.76991i	−0.465681	−	0.884953i	$-0.654191\pi$
$983$		−	54548.2i		−	1.76991i	0.465681	−	0.884953i	$-0.345809\pi$
$984$		0			0
$985$	−1134.53	+	1409.72i	−0.0366996	+	0.0456014i
$986$	−15886.1	−	34616.7i	−0.513101	−	1.11807i
$987$		0			0
$988$	3070.30	−	3569.84i	0.0988656	−	0.114951i
$989$	−1259.13			−0.0404832
$990$		0			0
$991$		−	55545.9i		−	1.78050i	−0.455473	−	0.890249i	$-0.650530\pi$
$991$		−	55545.9i		−	1.78050i	0.455473	−	0.890249i	$-0.349470\pi$
$992$	18372.6	+	28016.7i	0.588036	+	0.896706i
$993$		0			0
$994$	1347.30	+	2935.83i	0.0429917	+	0.0936810i
$995$	−9555.81	+	11873.6i	−0.304462	+	0.378311i
$996$		0			0
$997$	−25594.6			−0.813027			−0.406513	−	0.913645i	$-0.633256\pi$
$997$	−25594.6			−0.813027			−0.406513	+	0.913645i	$0.633256\pi$
$998$	−11672.2	−	25434.2i	−0.370216	−	0.806718i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.40	yes	64
3.2	odd	2	inner	360.4.m.c.179.25	✓	64
4.3	odd	2		1440.4.m.c.719.51		64
5.4	even	2	inner	360.4.m.c.179.26	yes	64
8.3	odd	2	inner	360.4.m.c.179.37	yes	64
8.5	even	2		1440.4.m.c.719.14		64
12.11	even	2		1440.4.m.c.719.13		64
15.14	odd	2	inner	360.4.m.c.179.39	yes	64
20.19	odd	2		1440.4.m.c.719.50		64
24.5	odd	2		1440.4.m.c.719.52		64
24.11	even	2	inner	360.4.m.c.179.28	yes	64
40.19	odd	2	inner	360.4.m.c.179.27	yes	64
40.29	even	2		1440.4.m.c.719.15		64
60.59	even	2		1440.4.m.c.719.16		64
120.29	odd	2		1440.4.m.c.719.49		64
120.59	even	2	inner	360.4.m.c.179.38	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.25	✓	64	3.2	odd	2	inner
360.4.m.c.179.26	yes	64	5.4	even	2	inner
360.4.m.c.179.27	yes	64	40.19	odd	2	inner
360.4.m.c.179.28	yes	64	24.11	even	2	inner
360.4.m.c.179.37	yes	64	8.3	odd	2	inner
360.4.m.c.179.38	yes	64	120.59	even	2	inner
360.4.m.c.179.39	yes	64	15.14	odd	2	inner
360.4.m.c.179.40	yes	64	1.1	even	1	trivial
1440.4.m.c.719.13		64	12.11	even	2
1440.4.m.c.719.14		64	8.5	even	2
1440.4.m.c.719.15		64	40.29	even	2
1440.4.m.c.719.16		64	60.59	even	2
1440.4.m.c.719.49		64	120.29	odd	2
1440.4.m.c.719.50		64	20.19	odd	2
1440.4.m.c.719.51		64	4.3	odd	2
1440.4.m.c.719.52		64	24.5	odd	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17972 + 2.57066i) q^{2} +(-5.21654 + 6.06528i) q^{4} +(8.70998 + 7.00973i) q^{5} +3.04837 q^{7} +(-21.7458 - 6.25463i) q^{8} +O(q^{10})\)	\(q+(1.17972 + 2.57066i) q^{2} +(-5.21654 + 6.06528i) q^{4} +(8.70998 + 7.00973i) q^{5} +3.04837 q^{7} +(-21.7458 - 6.25463i) q^{8} +(-7.74430 + 30.6598i) q^{10} +54.7844i q^{11} +6.02360 q^{13} +(3.59620 + 7.83630i) q^{14} +(-9.57536 - 63.2796i) q^{16} +70.4789 q^{17} -97.7106 q^{19} +(-87.9520 + 16.2620i) q^{20} +(-140.832 + 64.6300i) q^{22} +12.4765i q^{23} +(26.7275 + 122.109i) q^{25} +(7.10614 + 15.4846i) q^{26} +(-15.9019 + 18.4892i) q^{28} -191.066 q^{29} +185.083i q^{31} +(151.374 - 99.2669i) q^{32} +(83.1450 + 181.177i) q^{34} +(26.5512 + 21.3682i) q^{35} -15.2023 q^{37} +(-115.271 - 251.180i) q^{38} +(-145.562 - 206.910i) q^{40} +61.0901i q^{41} +100.920i q^{43} +(-332.283 - 285.785i) q^{44} +(-32.0728 + 14.7187i) q^{46} -479.967i q^{47} -333.707 q^{49} +(-282.370 + 212.761i) q^{50} +(-31.4224 + 36.5349i) q^{52} -629.394i q^{53} +(-384.023 + 477.171i) q^{55} +(-66.2891 - 19.0664i) q^{56} +(-225.403 - 491.164i) q^{58} +515.626i q^{59} -68.2593i q^{61} +(-475.785 + 218.345i) q^{62} +(433.759 + 272.024i) q^{64} +(52.4654 + 42.2238i) q^{65} +785.021i q^{67} +(-367.656 + 427.474i) q^{68} +(-23.6074 + 93.4624i) q^{70} +374.645 q^{71} -469.268i q^{73} +(-17.9344 - 39.0799i) q^{74} +(509.711 - 592.642i) q^{76} +167.003i q^{77} +274.276i q^{79} +(360.172 - 618.285i) q^{80} +(-157.042 + 72.0689i) q^{82} -1023.14 q^{83} +(613.869 + 494.037i) q^{85} +(-259.430 + 119.057i) q^{86} +(342.656 - 1191.33i) q^{88} -337.508i q^{89} +18.3621 q^{91} +(-75.6734 - 65.0841i) q^{92} +(1233.83 - 566.225i) q^{94} +(-851.057 - 684.924i) q^{95} +862.964i q^{97} +(-393.680 - 857.847i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

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