LMFDB - Embedded newform 640.3.t.a.417.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,3,Mod(353,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("640.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	640.t (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.4387369191$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			417.4
Character	$\chi$	$=$	640.417
Dual form			640.3.t.a.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.50609 q^{3} +(-4.65788 + 1.81773i) q^{5} +(1.52625 - 1.52625i) q^{7} +11.3048 q^{9} +O(q^{10})$	\(q-4.50609 q^{3} +(-4.65788 + 1.81773i) q^{5} +(1.52625 - 1.52625i) q^{7} +11.3048 q^{9} +(10.2610 - 10.2610i) q^{11} -21.4526 q^{13} +(20.9888 - 8.19085i) q^{15} +(-18.5474 - 18.5474i) q^{17} +(6.86774 - 6.86774i) q^{19} +(-6.87740 + 6.87740i) q^{21} +(4.81049 + 4.81049i) q^{23} +(18.3917 - 16.9335i) q^{25} -10.3858 q^{27} +(7.30552 - 7.30552i) q^{29} -24.8935 q^{31} +(-46.2368 + 46.2368i) q^{33} +(-4.33477 + 9.88337i) q^{35} -0.818619 q^{37} +96.6671 q^{39} +36.1925i q^{41} +35.2864i q^{43} +(-52.6566 + 20.5491i) q^{45} +(9.49981 + 9.49981i) q^{47} +44.3412i q^{49} +(83.5763 + 83.5763i) q^{51} +81.0314i q^{53} +(-29.1427 + 66.4460i) q^{55} +(-30.9466 + 30.9466i) q^{57} +(-8.65405 - 8.65405i) q^{59} +(16.3705 + 16.3705i) q^{61} +(17.2539 - 17.2539i) q^{63} +(99.9235 - 38.9949i) q^{65} -46.6786i q^{67} +(-21.6765 - 21.6765i) q^{69} +80.8598i q^{71} +(27.4939 + 27.4939i) q^{73} +(-82.8748 + 76.3040i) q^{75} -31.3215i q^{77} -79.6266i q^{79} -54.9442 q^{81} -29.4998 q^{83} +(120.106 + 52.6775i) q^{85} +(-32.9193 + 32.9193i) q^{87} -29.5008 q^{89} +(-32.7419 + 32.7419i) q^{91} +112.173 q^{93} +(-19.5054 + 44.4728i) q^{95} +(11.6094 + 11.6094i) q^{97} +(115.999 - 115.999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9	$ 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 40 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{35} + 4 q^{37} + 72 q^{39} + 70 q^{45} + 4 q^{47} - 100 q^{51} - 36 q^{57} - 64 q^{59} + 36 q^{61} + 200 q^{63} - 4 q^{65} - 60 q^{69} - 48 q^{73} - 324 q^{75} + 100 q^{81} + 156 q^{83} + 52 q^{85} + 36 q^{87} + 188 q^{91} + 40 q^{93} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 40 * q^27 + 8 * q^31 - 4 * q^33 - 4 * q^35 + 4 * q^37 + 72 * q^39 + 70 * q^45 + 4 * q^47 - 100 * q^51 - 36 * q^57 - 64 * q^59 + 36 * q^61 + 200 * q^63 - 4 * q^65 - 60 * q^69 - 48 * q^73 - 324 * q^75 + 100 * q^81 + 156 * q^83 + 52 * q^85 + 36 * q^87 + 188 * q^91 + 40 * q^93 - 380 * q^95 - 4 * q^97 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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			0
$2$		0			0
$3$	−4.50609			−1.50203			−0.751015	−	0.660285i	$-0.770435\pi$
$3$	−4.50609			−1.50203			−0.751015	+	0.660285i	$0.770435\pi$
$4$		0			0
$5$	−4.65788	+	1.81773i	−0.931576	+	0.363546i
$5$	−4.65788	+	1.81773i	−0.931576	+	0.363546i
$6$		0			0
$7$	1.52625	−	1.52625i	0.218035	−	0.218035i	−0.589635	−	0.807670i	$-0.700728\pi$
$7$	1.52625	−	1.52625i	0.218035	−	0.218035i	0.807670	+	0.589635i	$0.200728\pi$
$8$		0			0
$9$	11.3048			1.25609
$10$		0			0
$11$	10.2610	−	10.2610i	0.932816	−	0.932816i	−0.0650655	−	0.997881i	$-0.520726\pi$
$11$	10.2610	−	10.2610i	0.932816	−	0.932816i	0.997881	+	0.0650655i	$0.0207256\pi$
$12$		0			0
$13$	−21.4526			−1.65020			−0.825098	−	0.564989i	$-0.808880\pi$
$13$	−21.4526			−1.65020			−0.825098	+	0.564989i	$0.808880\pi$
$14$		0			0
$15$	20.9888	−	8.19085i	1.39926	−	0.546056i
$16$		0			0
$17$	−18.5474	−	18.5474i	−1.09102	−	1.09102i	−0.995419	−	0.0956051i	$-0.969521\pi$
$17$	−18.5474	−	18.5474i	−1.09102	−	1.09102i	−0.0956051	−	0.995419i	$-0.530479\pi$
$18$		0			0
$19$	6.86774	−	6.86774i	0.361460	−	0.361460i	−0.502890	−	0.864350i	$-0.667730\pi$
$19$	6.86774	−	6.86774i	0.361460	−	0.361460i	0.864350	+	0.502890i	$0.167730\pi$
$20$		0			0
$21$	−6.87740	+	6.87740i	−0.327495	+	0.327495i
$22$		0			0
$23$	4.81049	+	4.81049i	0.209152	+	0.209152i	0.803907	−	0.594755i	$-0.202751\pi$
$23$	4.81049	+	4.81049i	0.209152	+	0.209152i	−0.594755	+	0.803907i	$0.702751\pi$
$24$		0			0
$25$	18.3917	−	16.9335i	0.735669	−	0.677341i
$26$		0			0
$27$	−10.3858			−0.384659
$28$		0			0
$29$	7.30552	−	7.30552i	0.251915	−	0.251915i	−0.569841	−	0.821755i	$-0.692995\pi$
$29$	7.30552	−	7.30552i	0.251915	−	0.251915i	0.821755	+	0.569841i	$0.192995\pi$
$30$		0			0
$31$	−24.8935			−0.803018			−0.401509	−	0.915855i	$-0.631514\pi$
$31$	−24.8935			−0.803018			−0.401509	+	0.915855i	$0.631514\pi$
$32$		0			0
$33$	−46.2368	+	46.2368i	−1.40112	+	1.40112i
$34$		0			0
$35$	−4.33477	+	9.88337i	−0.123851	+	0.282382i
$36$		0			0
$37$	−0.818619			−0.0221248			−0.0110624	−	0.999939i	$-0.503521\pi$
$37$	−0.818619			−0.0221248			−0.0110624	+	0.999939i	$0.503521\pi$
$38$		0			0
$39$	96.6671			2.47864
$40$		0			0
$41$			36.1925i			0.882744i	0.897324	+	0.441372i	$0.145508\pi$
$41$			36.1925i			0.882744i	−0.897324	+	0.441372i	$0.854492\pi$
$42$		0			0
$43$			35.2864i			0.820615i	0.911947	+	0.410307i	$0.134579\pi$
$43$			35.2864i			0.820615i	−0.911947	+	0.410307i	$0.865421\pi$
$44$		0			0
$45$	−52.6566	+	20.5491i	−1.17015	+	0.456647i
$46$		0			0
$47$	9.49981	+	9.49981i	0.202124	+	0.202124i	0.800909	−	0.598786i	$-0.204350\pi$
$47$	9.49981	+	9.49981i	0.202124	+	0.202124i	−0.598786	+	0.800909i	$0.704350\pi$
$48$		0			0
$49$			44.3412i			0.904921i
$50$		0			0
$51$	83.5763	+	83.5763i	1.63875	+	1.63875i
$52$		0			0
$53$			81.0314i			1.52889i	0.644686	+	0.764447i	$0.276988\pi$
$53$			81.0314i			1.52889i	−0.644686	+	0.764447i	$0.723012\pi$
$54$		0			0
$55$	−29.1427	+	66.4460i	−0.529868	+	1.20811i
$56$		0			0
$57$	−30.9466	+	30.9466i	−0.542924	+	0.542924i
$58$		0			0
$59$	−8.65405	−	8.65405i	−0.146679	−	0.146679i	0.629954	−	0.776633i	$-0.283074\pi$
$59$	−8.65405	−	8.65405i	−0.146679	−	0.146679i	−0.776633	+	0.629954i	$0.783074\pi$
$60$		0			0
$61$	16.3705	+	16.3705i	0.268368	+	0.268368i	0.828442	−	0.560074i	$-0.189227\pi$
$61$	16.3705	+	16.3705i	0.268368	+	0.268368i	−0.560074	+	0.828442i	$0.689227\pi$
$62$		0			0
$63$	17.2539	−	17.2539i	0.273872	−	0.273872i
$64$		0			0
$65$	99.9235	−	38.9949i	1.53728	−	0.599922i
$66$		0			0
$67$		−	46.6786i		−	0.696695i	−0.937365	−	0.348348i	$-0.886743\pi$
$67$		−	46.6786i		−	0.696695i	0.937365	−	0.348348i	$-0.113257\pi$
$68$		0			0
$69$	−21.6765	−	21.6765i	−0.314152	−	0.314152i
$70$		0			0
$71$			80.8598i			1.13887i	0.822036	+	0.569435i	$0.192838\pi$
$71$			80.8598i			1.13887i	−0.822036	+	0.569435i	$0.807162\pi$
$72$		0			0
$73$	27.4939	+	27.4939i	0.376629	+	0.376629i	0.869884	−	0.493256i	$-0.164193\pi$
$73$	27.4939	+	27.4939i	0.376629	+	0.376629i	−0.493256	+	0.869884i	$0.664193\pi$
$74$		0			0
$75$	−82.8748	+	76.3040i	−1.10500	+	1.01739i
$76$		0			0
$77$		−	31.3215i		−	0.406773i
$78$		0			0
$79$		−	79.6266i		−	1.00793i	−0.863724	−	0.503966i	$-0.831874\pi$
$79$		−	79.6266i		−	1.00793i	0.863724	−	0.503966i	$-0.168126\pi$
$80$		0			0
$81$	−54.9442			−0.678324
$82$		0			0
$83$	−29.4998			−0.355420			−0.177710	−	0.984083i	$-0.556869\pi$
$83$	−29.4998			−0.355420			−0.177710	+	0.984083i	$0.556869\pi$
$84$		0			0
$85$	120.106	+	52.6775i	1.41301	+	0.619735i
$86$		0			0
$87$	−32.9193	+	32.9193i	−0.378383	+	0.378383i
$88$		0			0
$89$	−29.5008			−0.331469			−0.165735	−	0.986170i	$-0.553000\pi$
$89$	−29.5008			−0.331469			−0.165735	+	0.986170i	$0.553000\pi$
$90$		0			0
$91$	−32.7419	+	32.7419i	−0.359801	+	0.359801i
$92$		0			0
$93$	112.173			1.20616
$94$		0			0
$95$	−19.5054	+	44.4728i	−0.205320	+	0.468135i
$96$		0			0
$97$	11.6094	+	11.6094i	0.119685	+	0.119685i	0.764412	−	0.644728i	$-0.223029\pi$
$97$	11.6094	+	11.6094i	0.119685	+	0.119685i	−0.644728	+	0.764412i	$0.723029\pi$
$98$		0			0
$99$	115.999	−	115.999i	1.17170	−	1.17170i
$100$		0			0
$101$	16.5754	−	16.5754i	0.164113	−	0.164113i	−0.620273	−	0.784386i	$-0.712978\pi$
$101$	16.5754	−	16.5754i	0.164113	−	0.164113i	0.784386	+	0.620273i	$0.212978\pi$
$102$		0			0
$103$	−99.5646	−	99.5646i	−0.966647	−	0.966647i	0.0328145	−	0.999461i	$-0.489553\pi$
$103$	−99.5646	−	99.5646i	−0.966647	−	0.966647i	−0.999461	+	0.0328145i	$0.989553\pi$
$104$		0			0
$105$	19.5329	−	44.5353i	0.186027	−	0.424146i
$106$		0			0
$107$	157.800			1.47477			0.737384	−	0.675474i	$-0.236061\pi$
$107$	157.800			1.47477			0.737384	+	0.675474i	$0.236061\pi$
$108$		0			0
$109$	38.8130	−	38.8130i	0.356083	−	0.356083i	−0.506284	−	0.862367i	$-0.668981\pi$
$109$	38.8130	−	38.8130i	0.356083	−	0.356083i	0.862367	+	0.506284i	$0.168981\pi$
$110$		0			0
$111$	3.68877			0.0332322
$112$		0			0
$113$	−131.857	+	131.857i	−1.16688	+	1.16688i	−0.183938	+	0.982938i	$0.558884\pi$
$113$	−131.857	+	131.857i	−1.16688	+	1.16688i	−0.982938	+	0.183938i	$0.941116\pi$
$114$		0			0
$115$	−31.1508	−	13.6625i	−0.270877	−	0.118805i
$116$		0			0
$117$	−242.518			−2.07280
$118$		0			0
$119$	−56.6158			−0.475763
$120$		0			0
$121$		−	89.5750i		−	0.740290i
$122$		0			0
$123$		−	163.087i		−	1.32591i
$124$		0			0
$125$	−54.8859	+	112.306i	−0.439087	+	0.898444i
$126$		0			0
$127$	154.162	+	154.162i	1.21388	+	1.21388i	0.969741	+	0.244136i	$0.0785044\pi$
$127$	154.162	+	154.162i	1.21388	+	1.21388i	0.244136	+	0.969741i	$0.421496\pi$
$128$		0			0
$129$		−	159.004i		−	1.23259i
$130$		0			0
$131$	128.318	+	128.318i	0.979530	+	0.979530i	0.999795	−	0.0202649i	$-0.00645095\pi$
$131$	128.318	+	128.318i	0.979530	+	0.979530i	−0.0202649	+	0.999795i	$0.506451\pi$
$132$		0			0
$133$		−	20.9637i		−	0.157622i
$134$		0			0
$135$	48.3758	−	18.8786i	0.358339	−	0.139841i
$136$		0			0
$137$	−98.3855	+	98.3855i	−0.718142	+	0.718142i	−0.968225	−	0.250082i	$-0.919542\pi$
$137$	−98.3855	+	98.3855i	−0.718142	+	0.718142i	0.250082	+	0.968225i	$0.419542\pi$
$138$		0			0
$139$	89.3606	+	89.3606i	0.642882	+	0.642882i	0.951263	−	0.308381i	$-0.0997871\pi$
$139$	89.3606	+	89.3606i	0.642882	+	0.642882i	−0.308381	+	0.951263i	$0.599787\pi$
$140$		0			0
$141$	−42.8070	−	42.8070i	−0.303596	−	0.303596i
$142$		0			0
$143$	−220.124	+	220.124i	−1.53933	+	1.53933i
$144$		0			0
$145$	−20.7488	+	47.3077i	−0.143095	+	0.326260i
$146$		0			0
$147$		−	199.805i		−	1.35922i
$148$		0			0
$149$	135.878	+	135.878i	0.911932	+	0.911932i	0.996424	−	0.0844918i	$-0.0269267\pi$
$149$	135.878	+	135.878i	0.911932	+	0.911932i	−0.0844918	+	0.996424i	$0.526927\pi$
$150$		0			0
$151$		−	174.395i		−	1.15493i	−0.816415	−	0.577466i	$-0.804042\pi$
$151$		−	174.395i		−	1.15493i	0.816415	−	0.577466i	$-0.195958\pi$
$152$		0			0
$153$	−209.675	−	209.675i	−1.37043	−	1.37043i
$154$		0			0
$155$	115.951	−	45.2497i	0.748072	−	0.291934i
$156$		0			0
$157$		−	230.146i		−	1.46590i	−0.680285	−	0.732948i	$-0.738144\pi$
$157$		−	230.146i		−	1.46590i	0.680285	−	0.732948i	$-0.261856\pi$
$158$		0			0
$159$		−	365.135i		−	2.29645i
$160$		0			0
$161$	14.6840			0.0912047
$162$		0			0
$163$	−205.854			−1.26291			−0.631453	−	0.775414i	$-0.717541\pi$
$163$	−205.854			−1.26291			−0.631453	+	0.775414i	$0.717541\pi$
$164$		0			0
$165$	131.320	−	299.412i	0.795877	−	1.81462i
$166$		0			0
$167$	52.8722	−	52.8722i	0.316600	−	0.316600i	−0.530860	−	0.847460i	$-0.678131\pi$
$167$	52.8722	−	52.8722i	0.316600	−	0.316600i	0.847460	+	0.530860i	$0.178131\pi$
$168$		0			0
$169$	291.212			1.72315
$170$		0			0
$171$	77.6387	−	77.6387i	0.454027	−	0.454027i
$172$		0			0
$173$	−138.325			−0.799567			−0.399783	−	0.916610i	$-0.630915\pi$
$173$	−138.325			−0.799567			−0.399783	+	0.916610i	$0.630915\pi$
$174$		0			0
$175$	2.22557	−	53.9150i	0.0127175	−	0.308086i
$176$		0			0
$177$	38.9959	+	38.9959i	0.220316	+	0.220316i
$178$		0			0
$179$	−103.785	+	103.785i	−0.579802	+	0.579802i	−0.934849	−	0.355047i	$-0.884465\pi$
$179$	−103.785	+	103.785i	−0.579802	+	0.579802i	0.355047	+	0.934849i	$0.384465\pi$
$180$		0			0
$181$	−79.6876	+	79.6876i	−0.440263	+	0.440263i	−0.892100	−	0.451837i	$-0.850769\pi$
$181$	−79.6876	+	79.6876i	−0.440263	+	0.440263i	0.451837	+	0.892100i	$0.350769\pi$
$182$		0			0
$183$	−73.7668	−	73.7668i	−0.403097	−	0.403097i
$184$		0			0
$185$	3.81303	−	1.48803i	0.0206110	−	0.00804339i
$186$		0			0
$187$	−380.629			−2.03545
$188$		0			0
$189$	−15.8513	+	15.8513i	−0.0838691	+	0.0838691i
$190$		0			0
$191$	113.437			0.593911			0.296956	−	0.954891i	$-0.404029\pi$
$191$	113.437			0.593911			0.296956	+	0.954891i	$0.404029\pi$
$192$		0			0
$193$	207.468	−	207.468i	1.07496	−	1.07496i	0.0780092	−	0.996953i	$-0.475144\pi$
$193$	207.468	−	207.468i	1.07496	−	1.07496i	0.996953	−	0.0780092i	$-0.0248564\pi$
$194$		0			0
$195$	−450.264	+	175.715i	−2.30905	+	0.901100i
$196$		0			0
$197$	−30.4535			−0.154586			−0.0772932	−	0.997008i	$-0.524628\pi$
$197$	−30.4535			−0.154586			−0.0772932	+	0.997008i	$0.524628\pi$
$198$		0			0
$199$	227.899			1.14522			0.572611	−	0.819827i	$-0.305931\pi$
$199$	227.899			1.14522			0.572611	+	0.819827i	$0.305931\pi$
$200$		0			0
$201$			210.338i			1.04646i
$202$		0			0
$203$		−	22.3000i		−	0.109852i
$204$		0			0
$205$	−65.7882	−	168.580i	−0.320918	−	0.822344i
$206$		0			0
$207$	54.3818	+	54.3818i	0.262714	+	0.262714i
$208$		0			0
$209$		−	140.939i		−	0.674351i
$210$		0			0
$211$	−162.639	−	162.639i	−0.770801	−	0.770801i	0.207445	−	0.978247i	$-0.433485\pi$
$211$	−162.639	−	162.639i	−0.770801	−	0.770801i	−0.978247	+	0.207445i	$0.933485\pi$
$212$		0			0
$213$		−	364.361i		−	1.71062i
$214$		0			0
$215$	−64.1412	−	164.360i	−0.298331	−	0.764465i
$216$		0			0
$217$	−37.9937	+	37.9937i	−0.175086	+	0.175086i
$218$		0			0
$219$	−123.890	−	123.890i	−0.565707	−	0.565707i
$220$		0			0
$221$	397.889	+	397.889i	1.80040	+	1.80040i
$222$		0			0
$223$	−14.2230	+	14.2230i	−0.0637803	+	0.0637803i	−0.738277	−	0.674497i	$-0.764360\pi$
$223$	−14.2230	+	14.2230i	−0.0637803	+	0.0637803i	0.674497	+	0.738277i	$0.264360\pi$
$224$		0			0
$225$	207.915	−	191.431i	0.924069	−	0.850803i
$226$		0			0
$227$			284.554i			1.25354i	0.779203	+	0.626771i	$0.215624\pi$
$227$			284.554i			1.25354i	−0.779203	+	0.626771i	$0.784376\pi$
$228$		0			0
$229$	20.0023	+	20.0023i	0.0873464	+	0.0873464i	0.749430	−	0.662084i	$-0.230328\pi$
$229$	20.0023	+	20.0023i	0.0873464	+	0.0873464i	−0.662084	+	0.749430i	$0.730328\pi$
$230$		0			0
$231$			141.138i			0.610985i
$232$		0			0
$233$	147.800	+	147.800i	0.634336	+	0.634336i	0.949153	−	0.314817i	$-0.101943\pi$
$233$	147.800	+	147.800i	0.634336	+	0.634336i	−0.314817	+	0.949153i	$0.601943\pi$
$234$		0			0
$235$	−61.5171	−	26.9809i	−0.261775	−	0.114812i
$236$		0			0
$237$			358.805i			1.51394i
$238$		0			0
$239$			230.738i			0.965433i	0.875777	+	0.482716i	$0.160350\pi$
$239$			230.738i			0.965433i	−0.875777	+	0.482716i	$0.839650\pi$
$240$		0			0
$241$	165.848			0.688167			0.344083	−	0.938939i	$-0.388190\pi$
$241$	165.848			0.688167			0.344083	+	0.938939i	$0.388190\pi$
$242$		0			0
$243$	341.056			1.40352
$244$		0			0
$245$	−80.6002	−	206.536i	−0.328980	−	0.843003i
$246$		0			0
$247$	−147.331	+	147.331i	−0.596480	+	0.596480i
$248$		0			0
$249$	132.929			0.533851
$250$		0			0
$251$	74.6924	−	74.6924i	0.297579	−	0.297579i	−0.542486	−	0.840065i	$-0.682517\pi$
$251$	74.6924	−	74.6924i	0.297579	−	0.297579i	0.840065	+	0.542486i	$0.182517\pi$
$252$		0			0
$253$	98.7205			0.390200
$254$		0			0
$255$	−541.208	−	237.369i	−2.12238	−	0.930861i
$256$		0			0
$257$	136.830	+	136.830i	0.532413	+	0.532413i	0.921290	−	0.388876i	$-0.127137\pi$
$257$	136.830	+	136.830i	0.532413	+	0.532413i	−0.388876	+	0.921290i	$0.627137\pi$
$258$		0			0
$259$	−1.24941	+	1.24941i	−0.00482399	+	0.00482399i
$260$		0			0
$261$	82.5877	−	82.5877i	0.316428	−	0.316428i
$262$		0			0
$263$	20.0534	+	20.0534i	0.0762487	+	0.0762487i	0.744203	−	0.667954i	$-0.232830\pi$
$263$	20.0534	+	20.0534i	0.0762487	+	0.0762487i	−0.667954	+	0.744203i	$0.732830\pi$
$264$		0			0
$265$	−147.293	−	377.435i	−0.555823	−	1.42428i
$266$		0			0
$267$	132.933			0.497877
$268$		0			0
$269$	−104.051	+	104.051i	−0.386807	+	0.386807i	−0.873547	−	0.486740i	$-0.838186\pi$
$269$	−104.051	+	104.051i	−0.386807	+	0.386807i	0.486740	+	0.873547i	$0.338186\pi$
$270$		0			0
$271$	91.2232			0.336617			0.168308	−	0.985734i	$-0.446170\pi$
$271$	91.2232			0.336617			0.168308	+	0.985734i	$0.446170\pi$
$272$		0			0
$273$	147.538	−	147.538i	0.540431	−	0.540431i
$274$		0			0
$275$	14.9625	−	362.471i	0.0544092	−	1.31808i
$276$		0			0
$277$	−87.2400			−0.314946			−0.157473	−	0.987523i	$-0.550335\pi$
$277$	−87.2400			−0.314946			−0.157473	+	0.987523i	$0.550335\pi$
$278$		0			0
$279$	−281.417			−1.00866
$280$		0			0
$281$		−	163.799i		−	0.582915i	−0.956584	−	0.291458i	$-0.905860\pi$
$281$		−	163.799i		−	0.582915i	0.956584	−	0.291458i	$-0.0941402\pi$
$282$		0			0
$283$			234.667i			0.829213i	0.910001	+	0.414607i	$0.136081\pi$
$283$			234.667i			0.829213i	−0.910001	+	0.414607i	$0.863919\pi$
$284$		0			0
$285$	87.8932	−	200.398i	0.308397	−	0.703152i
$286$		0			0
$287$	55.2387	+	55.2387i	0.192469	+	0.192469i
$288$		0			0
$289$			399.013i			1.38067i
$290$		0			0
$291$	−52.3131	−	52.3131i	−0.179770	−	0.179770i
$292$		0			0
$293$		−	305.403i		−	1.04233i	−0.853455	−	0.521166i	$-0.825497\pi$
$293$		−	305.403i		−	1.04233i	0.853455	−	0.521166i	$-0.174503\pi$
$294$		0			0
$295$	56.0402	+	24.5788i	0.189967	+	0.0833180i
$296$		0			0
$297$	−106.568	+	106.568i	−0.358816	+	0.358816i
$298$		0			0
$299$	−103.197	−	103.197i	−0.345141	−	0.345141i
$300$		0			0
$301$	53.8557	+	53.8557i	0.178923	+	0.178923i
$302$		0			0
$303$	−74.6904	+	74.6904i	−0.246503	+	0.246503i
$304$		0			0
$305$	−106.009	−	46.4946i	−0.347570	−	0.152441i
$306$		0			0
$307$			495.760i			1.61485i	0.589967	+	0.807427i	$0.299141\pi$
$307$			495.760i			1.61485i	−0.589967	+	0.807427i	$0.700859\pi$
$308$		0			0
$309$	448.647	+	448.647i	1.45193	+	1.45193i
$310$		0			0
$311$		−	38.1349i		−	0.122620i	−0.998119	−	0.0613101i	$-0.980472\pi$
$311$		−	38.1349i		−	0.122620i	0.998119	−	0.0613101i	$-0.0195279\pi$
$312$		0			0
$313$	30.8202	+	30.8202i	0.0984671	+	0.0984671i	0.754624	−	0.656157i	$-0.227819\pi$
$313$	30.8202	+	30.8202i	0.0984671	+	0.0984671i	−0.656157	+	0.754624i	$0.727819\pi$
$314$		0			0
$315$	−49.0039	+	111.730i	−0.155568	+	0.354698i
$316$		0			0
$317$		−	194.056i		−	0.612164i	−0.952005	−	0.306082i	$-0.900982\pi$
$317$		−	194.056i		−	0.612164i	0.952005	−	0.306082i	$-0.0990182\pi$
$318$		0			0
$319$		−	149.924i		−	0.469980i
$320$		0			0
$321$	−711.062			−2.21515
$322$		0			0
$323$	−254.758			−0.788723
$324$		0			0
$325$	−394.550	+	363.267i	−1.21400	+	1.11775i
$326$		0			0
$327$	−174.895	+	174.895i	−0.534847	+	0.534847i
$328$		0			0
$329$	28.9981			0.0881401
$330$		0			0
$331$	−109.097	+	109.097i	−0.329598	+	0.329598i	−0.852434	−	0.522836i	$-0.824874\pi$
$331$	−109.097	+	109.097i	−0.329598	+	0.329598i	0.522836	+	0.852434i	$0.324874\pi$
$332$		0			0
$333$	−9.25435			−0.0277909
$334$		0			0
$335$	84.8490	+	217.423i	0.253281	+	0.649025i
$336$		0			0
$337$	−73.7614	−	73.7614i	−0.218877	−	0.218877i	0.589148	−	0.808025i	$-0.299463\pi$
$337$	−73.7614	−	73.7614i	−0.218877	−	0.218877i	−0.808025	+	0.589148i	$0.799463\pi$
$338$		0			0
$339$	594.159	−	594.159i	1.75268	−	1.75268i
$340$		0			0
$341$	−255.432	+	255.432i	−0.749067	+	0.749067i
$342$		0			0
$343$	142.461	+	142.461i	0.415340	+	0.415340i
$344$		0			0
$345$	140.368	+	61.5645i	0.406865	+	0.178448i
$346$		0			0
$347$	644.536			1.85745			0.928726	−	0.370767i	$-0.120905\pi$
$347$	644.536			1.85745			0.928726	+	0.370767i	$0.120905\pi$
$348$		0			0
$349$	−161.816	+	161.816i	−0.463657	+	0.463657i	−0.899852	−	0.436195i	$-0.856326\pi$
$349$	−161.816	+	161.816i	−0.463657	+	0.463657i	0.436195	+	0.899852i	$0.356326\pi$
$350$		0			0
$351$	222.802			0.634763
$352$		0			0
$353$	91.5785	−	91.5785i	0.259429	−	0.259429i	−0.565393	−	0.824822i	$-0.691275\pi$
$353$	91.5785	−	91.5785i	0.259429	−	0.259429i	0.824822	+	0.565393i	$0.191275\pi$
$354$		0			0
$355$	−146.981	−	376.635i	−0.414031	−	1.06094i
$356$		0			0
$357$	255.116			0.714610
$358$		0			0
$359$	218.109			0.607545			0.303772	−	0.952745i	$-0.401754\pi$
$359$	218.109			0.607545			0.303772	+	0.952745i	$0.401754\pi$
$360$		0			0
$361$			266.668i			0.738693i
$362$		0			0
$363$			403.633i			1.11194i
$364$		0			0
$365$	−178.040	−	78.0869i	−0.487780	−	0.213937i
$366$		0			0
$367$	232.108	+	232.108i	0.632446	+	0.632446i	0.948681	−	0.316235i	$-0.102419\pi$
$367$	232.108	+	232.108i	0.632446	+	0.632446i	−0.316235	+	0.948681i	$0.602419\pi$
$368$		0			0
$369$			409.150i			1.10881i
$370$		0			0
$371$	123.674	+	123.674i	0.333353	+	0.333353i
$372$		0			0
$373$			71.3315i			0.191237i	0.995418	+	0.0956187i	$0.0304829\pi$
$373$			71.3315i			0.191237i	−0.995418	+	0.0956187i	$0.969517\pi$
$374$		0			0
$375$	247.321	−	506.059i	0.659522	−	1.34949i
$376$		0			0
$377$	−156.722	+	156.722i	−0.415709	+	0.415709i
$378$		0			0
$379$	−449.527	−	449.527i	−1.18609	−	1.18609i	−0.978140	−	0.207946i	$-0.933322\pi$
$379$	−449.527	−	449.527i	−1.18609	−	1.18609i	−0.207946	−	0.978140i	$-0.566678\pi$
$380$		0			0
$381$	−694.669	−	694.669i	−1.82328	−	1.82328i
$382$		0			0
$383$	392.032	−	392.032i	1.02358	−	1.02358i	0.0238677	−	0.999715i	$-0.492402\pi$
$383$	392.032	−	392.032i	1.02358	−	1.02358i	0.999715	−	0.0238677i	$-0.00759805\pi$
$384$		0			0
$385$	56.9340	+	145.892i	0.147881	+	0.378940i
$386$		0			0
$387$			398.907i			1.03077i
$388$		0			0
$389$	0.333140	+	0.333140i	0.000856400	+	0.000856400i	0.707535	−	0.706678i	$-0.249807\pi$
$389$	0.333140	+	0.333140i	0.000856400	+	0.000856400i	−0.706678	+	0.707535i	$0.749807\pi$
$390$		0			0
$391$		−	178.444i		−	0.456379i
$392$		0			0
$393$	−578.214	−	578.214i	−1.47128	−	1.47128i
$394$		0			0
$395$	144.740	+	370.891i	0.366429	+	0.938965i
$396$		0			0
$397$			3.73338i			0.00940399i	0.999989	+	0.00470199i	$0.00149670\pi$
$397$			3.73338i			0.00940399i	−0.999989	+	0.00470199i	$0.998503\pi$
$398$		0			0
$399$			94.4643i			0.236753i
$400$		0			0
$401$	−327.705			−0.817219			−0.408609	−	0.912709i	$-0.633986\pi$
$401$	−327.705			−0.817219			−0.408609	+	0.912709i	$0.633986\pi$
$402$		0			0
$403$	534.030			1.32514
$404$		0			0
$405$	255.924	−	99.8737i	0.631910	−	0.246602i
$406$		0			0
$407$	−8.39983	+	8.39983i	−0.0206384	+	0.0206384i
$408$		0			0
$409$	192.834			0.471478			0.235739	−	0.971816i	$-0.424249\pi$
$409$	192.834			0.471478			0.235739	+	0.971816i	$0.424249\pi$
$410$		0			0
$411$	443.334	−	443.334i	1.07867	−	1.07867i
$412$		0			0
$413$	−26.4164			−0.0639622
$414$		0			0
$415$	137.407	−	53.6227i	0.331101	−	0.129211i
$416$		0			0
$417$	−402.667	−	402.667i	−0.965628	−	0.965628i
$418$		0			0
$419$	−100.155	+	100.155i	−0.239034	+	0.239034i	−0.816450	−	0.577416i	$-0.804061\pi$
$419$	−100.155	+	100.155i	−0.239034	+	0.239034i	0.577416	+	0.816450i	$0.304061\pi$
$420$		0			0
$421$	−281.009	+	281.009i	−0.667479	+	0.667479i	−0.957132	−	0.289653i	$-0.906460\pi$
$421$	−281.009	+	281.009i	−0.667479	+	0.667479i	0.289653	+	0.957132i	$0.406460\pi$
$422$		0			0
$423$	107.394	+	107.394i	0.253886	+	0.253886i
$424$		0			0
$425$	−655.192	−	27.0458i	−1.54163	−	0.0636371i
$426$		0			0
$427$	49.9707			0.117027
$428$		0			0
$429$	991.898	−	991.898i	2.31212	−	2.31212i
$430$		0			0
$431$	−33.2755			−0.0772054			−0.0386027	−	0.999255i	$-0.512291\pi$
$431$	−33.2755			−0.0772054			−0.0386027	+	0.999255i	$0.512291\pi$
$432$		0			0
$433$	210.976	−	210.976i	0.487243	−	0.487243i	−0.420192	−	0.907435i	$-0.638037\pi$
$433$	210.976	−	210.976i	0.487243	−	0.487243i	0.907435	+	0.420192i	$0.138037\pi$
$434$		0			0
$435$	93.4960	−	213.173i	0.214933	−	0.490052i
$436$		0			0
$437$	66.0743			0.151200
$438$		0			0
$439$	−533.725			−1.21577			−0.607887	−	0.794023i	$-0.707983\pi$
$439$	−533.725			−1.21577			−0.607887	+	0.794023i	$0.707983\pi$
$440$		0			0
$441$			501.269i			1.13667i
$442$		0			0
$443$		−	79.6496i		−	0.179796i	−0.995951	−	0.0898979i	$-0.971346\pi$
$443$		−	79.6496i		−	0.179796i	0.995951	−	0.0898979i	$-0.0286541\pi$
$444$		0			0
$445$	137.411	−	53.6244i	0.308789	−	0.120504i
$446$		0			0
$447$	−612.278	−	612.278i	−1.36975	−	1.36975i
$448$		0			0
$449$			816.938i			1.81946i	0.415200	+	0.909730i	$0.363712\pi$
$449$			816.938i			1.81946i	−0.415200	+	0.909730i	$0.636288\pi$
$450$		0			0
$451$	371.370	+	371.370i	0.823438	+	0.823438i
$452$		0			0
$453$			785.838i			1.73474i
$454$		0			0
$455$	92.9919	−	212.024i	0.204378	−	0.465986i
$456$		0			0
$457$	238.754	−	238.754i	0.522437	−	0.522437i	−0.395870	−	0.918307i	$-0.629557\pi$
$457$	238.754	−	238.754i	0.522437	−	0.522437i	0.918307	+	0.395870i	$0.129557\pi$
$458$		0			0
$459$	192.630	+	192.630i	0.419672	+	0.419672i
$460$		0			0
$461$	243.794	+	243.794i	0.528837	+	0.528837i	0.920225	−	0.391389i	$-0.128005\pi$
$461$	243.794	+	243.794i	0.528837	+	0.528837i	−0.391389	+	0.920225i	$0.628005\pi$
$462$		0			0
$463$	−195.645	+	195.645i	−0.422559	+	0.422559i	−0.886084	−	0.463525i	$-0.846585\pi$
$463$	−195.645	+	195.645i	−0.422559	+	0.422559i	0.463525	+	0.886084i	$0.346585\pi$
$464$		0			0
$465$	−522.486	+	203.899i	−1.12363	+	0.438493i
$466$		0			0
$467$			108.782i			0.232938i	0.993194	+	0.116469i	$0.0371576\pi$
$467$			108.782i			0.232938i	−0.993194	+	0.116469i	$0.962842\pi$
$468$		0			0
$469$	−71.2430	−	71.2430i	−0.151904	−	0.151904i
$470$		0			0
$471$			1037.06i			2.20182i
$472$		0			0
$473$	362.073	+	362.073i	0.765482	+	0.765482i
$474$		0			0
$475$	10.0145	−	242.605i	0.0210832	−	0.510747i
$476$		0			0
$477$			916.047i			1.92043i
$478$		0			0
$479$		−	186.555i		−	0.389467i	−0.980856	−	0.194733i	$-0.937616\pi$
$479$		−	186.555i		−	0.389467i	0.980856	−	0.194733i	$-0.0623842\pi$
$480$		0			0
$481$	17.5615			0.0365103
$482$		0			0
$483$	−66.1672			−0.136992
$484$		0			0
$485$	−75.1781	−	32.9725i	−0.155006	−	0.0679846i
$486$		0			0
$487$	87.5337	−	87.5337i	0.179741	−	0.179741i	−0.611502	−	0.791243i	$-0.709434\pi$
$487$	87.5337	−	87.5337i	0.179741	−	0.179741i	0.791243	+	0.611502i	$0.209434\pi$
$488$		0			0
$489$	927.595			1.89692
$490$		0			0
$491$	−481.445	+	481.445i	−0.980540	+	0.980540i	−0.999814	−	0.0192739i	$-0.993865\pi$
$491$	−481.445	+	481.445i	−0.980540	+	0.980540i	0.0192739	+	0.999814i	$0.493865\pi$
$492$		0			0
$493$	−270.997			−0.549690
$494$		0			0
$495$	−329.454	+	751.162i	−0.665563	+	1.51750i
$496$		0			0
$497$	123.412	+	123.412i	0.248314	+	0.248314i
$498$		0			0
$499$	263.132	−	263.132i	0.527319	−	0.527319i	−0.392453	−	0.919772i	$-0.628373\pi$
$499$	263.132	−	263.132i	0.527319	−	0.527319i	0.919772	+	0.392453i	$0.128373\pi$
$500$		0			0
$501$	−238.247	+	238.247i	−0.475543	+	0.475543i
$502$		0			0
$503$	433.805	+	433.805i	0.862435	+	0.862435i	0.991620	−	0.129186i	$-0.0412363\pi$
$503$	433.805	+	433.805i	0.862435	+	0.862435i	−0.129186	+	0.991620i	$0.541236\pi$
$504$		0			0
$505$	−47.0768	+	107.336i	−0.0932213	+	0.212547i
$506$		0			0
$507$	−1312.23			−2.58822
$508$		0			0
$509$	−513.368	+	513.368i	−1.00858	+	1.00858i	−0.00861858	+	0.999963i	$0.502743\pi$
$509$	−513.368	+	513.368i	−1.00858	+	1.00858i	−0.999963	+	0.00861858i	$0.997257\pi$
$510$		0			0
$511$	83.9248			0.164236
$512$		0			0
$513$	−71.3269	+	71.3269i	−0.139039	+	0.139039i
$514$		0			0
$515$	644.742	+	282.779i	1.25193	+	0.549085i
$516$		0			0
$517$	194.955			0.377088
$518$		0			0
$519$	623.305			1.20097
$520$		0			0
$521$			228.528i			0.438633i	0.975654	+	0.219316i	$0.0703827\pi$
$521$			228.528i			0.438633i	−0.975654	+	0.219316i	$0.929617\pi$
$522$		0			0
$523$			42.0347i			0.0803723i	0.999192	+	0.0401862i	$0.0127951\pi$
$523$			42.0347i			0.0803723i	−0.999192	+	0.0401862i	$0.987205\pi$
$524$		0			0
$525$	−10.0286	+	242.946i	−0.0191021	+	0.462754i
$526$		0			0
$527$	461.711	+	461.711i	0.876112	+	0.876112i
$528$		0			0
$529$		−	482.718i		−	0.912511i
$530$		0			0
$531$	−97.8326	−	97.8326i	−0.184242	−	0.184242i
$532$		0			0
$533$		−	776.422i		−	1.45670i
$534$		0			0
$535$	−735.015	+	286.838i	−1.37386	+	0.536146i
$536$		0			0
$537$	467.662	−	467.662i	0.870879	−	0.870879i
$538$		0			0
$539$	454.983	+	454.983i	0.844125	+	0.844125i
$540$		0			0
$541$	−300.583	−	300.583i	−0.555607	−	0.555607i	0.372446	−	0.928054i	$-0.378519\pi$
$541$	−300.583	−	300.583i	−0.555607	−	0.555607i	−0.928054	+	0.372446i	$0.878519\pi$
$542$		0			0
$543$	359.079	−	359.079i	0.661288	−	0.661288i
$544$		0			0
$545$	−110.235	+	251.338i	−0.202266	+	0.461170i
$546$		0			0
$547$		−	565.276i		−	1.03341i	−0.856163	−	0.516706i	$-0.827158\pi$
$547$		−	565.276i		−	1.03341i	0.856163	−	0.516706i	$-0.172842\pi$
$548$		0			0
$549$	185.065	+	185.065i	0.337096	+	0.337096i
$550$		0			0
$551$		−	100.345i		−	0.182114i
$552$		0			0
$553$	−121.530	−	121.530i	−0.219764	−	0.219764i
$554$		0			0
$555$	−17.1819	+	6.70518i	−0.0309583	+	0.0120814i
$556$		0			0
$557$			972.870i			1.74662i	0.487161	+	0.873312i	$0.338032\pi$
$557$			972.870i			1.74662i	−0.487161	+	0.873312i	$0.661968\pi$
$558$		0			0
$559$		−	756.984i		−	1.35418i
$560$		0			0
$561$	1715.15			3.05730
$562$		0			0
$563$	−827.358			−1.46955			−0.734776	−	0.678310i	$-0.762713\pi$
$563$	−827.358			−1.46955			−0.734776	+	0.678310i	$0.762713\pi$
$564$		0			0
$565$	374.494	−	853.854i	0.662821	−	1.51125i
$566$		0			0
$567$	−83.8583	+	83.8583i	−0.147898	+	0.147898i
$568$		0			0
$569$	−1016.20			−1.78594			−0.892970	−	0.450115i	$-0.851383\pi$
$569$	−1016.20			−1.78594			−0.892970	+	0.450115i	$0.851383\pi$
$570$		0			0
$571$	−381.530	+	381.530i	−0.668178	+	0.668178i	−0.957294	−	0.289116i	$-0.906639\pi$
$571$	−381.530	+	381.530i	−0.668178	+	0.668178i	0.289116	+	0.957294i	$0.406639\pi$
$572$		0			0
$573$	−511.157			−0.892072
$574$		0			0
$575$	169.932	+	7.01464i	0.295533	+	0.0121994i
$576$		0			0
$577$	−494.447	−	494.447i	−0.856928	−	0.856928i	0.134047	−	0.990975i	$-0.457203\pi$
$577$	−494.447	−	494.447i	−0.856928	−	0.856928i	−0.990975	+	0.134047i	$0.957203\pi$
$578$		0			0
$579$	−934.868	+	934.868i	−1.61462	+	1.61462i
$580$		0			0
$581$	−45.0240	+	45.0240i	−0.0774939	+	0.0774939i
$582$		0			0
$583$	831.461	+	831.461i	1.42618	+	1.42618i
$584$		0			0
$585$	1129.62	−	440.831i	1.93097	−	0.753558i
$586$		0			0
$587$	1106.40			1.88485			0.942423	−	0.334423i	$-0.108541\pi$
$587$	1106.40			1.88485			0.942423	+	0.334423i	$0.108541\pi$
$588$		0			0
$589$	−170.962	+	170.962i	−0.290259	+	0.290259i
$590$		0			0
$591$	137.226			0.232193
$592$		0			0
$593$	−312.835	+	312.835i	−0.527546	+	0.527546i	−0.919840	−	0.392294i	$-0.871682\pi$
$593$	−312.835	+	312.835i	−0.527546	+	0.527546i	0.392294	+	0.919840i	$0.371682\pi$
$594$		0			0
$595$	263.710	−	102.912i	0.443210	−	0.172962i
$596$		0			0
$597$	−1026.93			−1.72016
$598$		0			0
$599$	406.395			0.678457			0.339228	−	0.940704i	$-0.389834\pi$
$599$	406.395			0.678457			0.339228	+	0.940704i	$0.389834\pi$
$600$		0			0
$601$			172.522i			0.287058i	0.989646	+	0.143529i	$0.0458451\pi$
$601$			172.522i			0.287058i	−0.989646	+	0.143529i	$0.954155\pi$
$602$		0			0
$603$		−	527.694i		−	0.875114i
$604$		0			0
$605$	162.823	+	417.230i	0.269129	+	0.689636i
$606$		0			0
$607$	−434.724	−	434.724i	−0.716185	−	0.716185i	0.251636	−	0.967822i	$-0.419031\pi$
$607$	−434.724	−	434.724i	−0.716185	−	0.716185i	−0.967822	+	0.251636i	$0.919031\pi$
$608$		0			0
$609$			100.486i			0.165002i
$610$		0			0
$611$	−203.795	−	203.795i	−0.333544	−	0.333544i
$612$		0			0
$613$			540.620i			0.881925i	0.897525	+	0.440963i	$0.145363\pi$
$613$			540.620i			0.881925i	−0.897525	+	0.440963i	$0.854637\pi$
$614$		0			0
$615$	296.447	+	759.639i	0.482028	+	1.23518i
$616$		0			0
$617$	−840.793	+	840.793i	−1.36271	+	1.36271i	−0.492266	+	0.870445i	$0.663831\pi$
$617$	−840.793	+	840.793i	−1.36271	+	1.36271i	−0.870445	+	0.492266i	$0.836169\pi$
$618$		0			0
$619$	379.330	+	379.330i	0.612810	+	0.612810i	0.943677	−	0.330867i	$-0.107341\pi$
$619$	379.330	+	379.330i	0.612810	+	0.612810i	−0.330867	+	0.943677i	$0.607341\pi$
$620$		0			0
$621$	−49.9607	−	49.9607i	−0.0804520	−	0.0804520i
$622$		0			0
$623$	−45.0254	+	45.0254i	−0.0722719	+	0.0722719i
$624$		0			0
$625$	51.5112	−	622.874i	0.0824179	−	0.996598i
$626$		0			0
$627$			635.085i			1.01290i
$628$		0			0
$629$	15.1833	+	15.1833i	0.0241387	+	0.0241387i
$630$		0			0
$631$		−	685.081i		−	1.08571i	−0.839827	−	0.542853i	$-0.817344\pi$
$631$		−	685.081i		−	1.08571i	0.839827	−	0.542853i	$-0.182656\pi$
$632$		0			0
$633$	732.866	+	732.866i	1.15777	+	1.15777i
$634$		0			0
$635$	−998.296	−	437.845i	−1.57212	−	0.689519i
$636$		0			0
$637$		−	951.231i		−	1.49330i
$638$		0			0
$639$			914.107i			1.43053i
$640$		0			0
$641$	510.792			0.796868			0.398434	−	0.917197i	$-0.369554\pi$
$641$	510.792			0.796868			0.398434	+	0.917197i	$0.369554\pi$
$642$		0			0
$643$	−566.933			−0.881700			−0.440850	−	0.897581i	$-0.645323\pi$
$643$	−566.933			−0.881700			−0.440850	+	0.897581i	$0.645323\pi$
$644$		0			0
$645$	289.026	+	740.621i	0.448102	+	1.14825i
$646$		0			0
$647$	270.517	−	270.517i	0.418109	−	0.418109i	−0.466442	−	0.884552i	$-0.654464\pi$
$647$	270.517	−	270.517i	0.418109	−	0.418109i	0.884552	+	0.466442i	$0.154464\pi$
$648$		0			0
$649$	−177.598			−0.273648
$650$		0			0
$651$	171.203	−	171.203i	0.262984	−	0.262984i
$652$		0			0
$653$	724.152			1.10896			0.554481	−	0.832197i	$-0.312917\pi$
$653$	724.152			1.10896			0.554481	+	0.832197i	$0.312917\pi$
$654$		0			0
$655$	−830.940	−	364.444i	−1.26861	−	0.556403i
$656$		0			0
$657$	310.814	+	310.814i	0.473080	+	0.473080i
$658$		0			0
$659$	641.423	−	641.423i	0.973328	−	0.973328i	−0.0263257	−	0.999653i	$-0.508381\pi$
$659$	641.423	−	641.423i	0.973328	−	0.973328i	0.999653	+	0.0263257i	$0.00838070\pi$
$660$		0			0
$661$	699.865	−	699.865i	1.05880	−	1.05880i	0.0606382	−	0.998160i	$-0.480686\pi$
$661$	699.865	−	699.865i	1.05880	−	1.05880i	0.998160	−	0.0606382i	$-0.0193136\pi$
$662$		0			0
$663$	−1792.93	−	1792.93i	−2.70426	−	2.70426i
$664$		0			0
$665$	38.1063	+	97.6465i	0.0573028	+	0.146837i
$666$		0			0
$667$	70.2862			0.105377
$668$		0			0
$669$	64.0902	−	64.0902i	0.0958000	−	0.0958000i
$670$		0			0
$671$	335.954			0.500676
$672$		0			0
$673$	−439.226	+	439.226i	−0.652639	+	0.652639i	−0.953628	−	0.300989i	$-0.902683\pi$
$673$	−439.226	+	439.226i	−0.652639	+	0.652639i	0.300989	+	0.953628i	$0.402683\pi$
$674$		0			0
$675$	−191.013	+	175.868i	−0.282982	+	0.260545i
$676$		0			0
$677$	−372.736			−0.550570			−0.275285	−	0.961363i	$-0.588772\pi$
$677$	−372.736			−0.550570			−0.275285	+	0.961363i	$0.588772\pi$
$678$		0			0
$679$	35.4376			0.0521909
$680$		0			0
$681$		−	1282.23i		−	1.88286i
$682$		0			0
$683$			2.98479i			0.00437012i	0.999998	+	0.00218506i	$0.000695527\pi$
$683$			2.98479i			0.00437012i	−0.999998	+	0.00218506i	$0.999304\pi$
$684$		0			0
$685$	279.430	−	637.106i	0.407927	−	0.930082i
$686$		0			0
$687$	−90.1323	−	90.1323i	−0.131197	−	0.131197i
$688$		0			0
$689$		−	1738.33i		−	2.52298i
$690$		0			0
$691$	−153.000	−	153.000i	−0.221418	−	0.221418i	0.587678	−	0.809095i	$-0.300042\pi$
$691$	−153.000	−	153.000i	−0.221418	−	0.221418i	−0.809095	+	0.587678i	$0.800042\pi$
$692$		0			0
$693$		−	354.085i		−	0.510945i
$694$		0			0
$695$	−578.664	−	253.798i	−0.832611	−	0.365177i
$696$		0			0
$697$	671.278	−	671.278i	0.963096	−	0.963096i
$698$		0			0
$699$	−666.001	−	666.001i	−0.952791	−	0.952791i
$700$		0			0
$701$	−374.594	−	374.594i	−0.534371	−	0.534371i	0.387499	−	0.921870i	$-0.373339\pi$
$701$	−374.594	−	374.594i	−0.534371	−	0.534371i	−0.921870	+	0.387499i	$0.873339\pi$
$702$		0			0
$703$	−5.62206	+	5.62206i	−0.00799724	+	0.00799724i
$704$		0			0
$705$	277.201	+	121.578i	0.393194	+	0.172452i
$706$		0			0
$707$		−	50.5964i		−	0.0715649i
$708$		0			0
$709$	−841.096	−	841.096i	−1.18631	−	1.18631i	−0.978079	−	0.208233i	$-0.933229\pi$
$709$	−841.096	−	841.096i	−1.18631	−	1.18631i	−0.208233	−	0.978079i	$-0.566771\pi$
$710$		0			0
$711$		−	900.166i		−	1.26606i
$712$		0			0
$713$	−119.750	−	119.750i	−0.167952	−	0.167952i
$714$		0			0
$715$	625.186	−	1425.44i	0.874386	−	1.99362i
$716$		0			0
$717$		−	1039.73i		−	1.45011i
$718$		0			0
$719$		−	28.8722i		−	0.0401560i	−0.999798	−	0.0200780i	$-0.993609\pi$
$719$		−	28.8722i		−	0.0401560i	0.999798	−	0.0200780i	$-0.00639146\pi$
$720$		0			0
$721$	−303.920			−0.421526
$722$		0			0
$723$	−747.327			−1.03365
$724$		0			0
$725$	10.6529	−	258.069i	0.0146936	−	0.355958i
$726$		0			0
$727$	896.554	−	896.554i	1.23322	−	1.23322i	0.270506	−	0.962718i	$-0.412809\pi$
$727$	896.554	−	896.554i	1.23322	−	1.23322i	0.962718	−	0.270506i	$-0.0871909\pi$
$728$		0			0
$729$	−1042.33			−1.42981
$730$		0			0
$731$	654.472	−	654.472i	0.895311	−	0.895311i
$732$		0			0
$733$	−83.0751			−0.113336			−0.0566678	−	0.998393i	$-0.518048\pi$
$733$	−83.0751			−0.113336			−0.0566678	+	0.998393i	$0.518048\pi$
$734$		0			0
$735$	363.192	+	930.669i	0.494138	+	1.26622i
$736$		0			0
$737$	−478.968	−	478.968i	−0.649888	−	0.649888i
$738$		0			0
$739$	148.263	−	148.263i	0.200626	−	0.200626i	−0.599642	−	0.800268i	$-0.704690\pi$
$739$	148.263	−	148.263i	0.200626	−	0.200626i	0.800268	+	0.599642i	$0.204690\pi$
$740$		0			0
$741$	663.885	−	663.885i	0.895931	−	0.895931i
$742$		0			0
$743$	−613.895	−	613.895i	−0.826238	−	0.826238i	0.160756	−	0.986994i	$-0.448607\pi$
$743$	−613.895	−	613.895i	−0.826238	−	0.826238i	−0.986994	+	0.160756i	$0.948607\pi$
$744$		0			0
$745$	−879.893	−	385.914i	−1.18106	−	0.518006i
$746$		0			0
$747$	−333.491			−0.446440
$748$		0			0
$749$	240.842	−	240.842i	0.321551	−	0.321551i
$750$		0			0
$751$	−516.621			−0.687911			−0.343956	−	0.938986i	$-0.611767\pi$
$751$	−516.621			−0.687911			−0.343956	+	0.938986i	$0.611767\pi$
$752$		0			0
$753$	−336.570	+	336.570i	−0.446973	+	0.446973i
$754$		0			0
$755$	317.002	+	812.310i	0.419870	+	1.07591i
$756$		0			0
$757$	1230.47			1.62545			0.812727	−	0.582644i	$-0.197982\pi$
$757$	1230.47			1.62545			0.812727	+	0.582644i	$0.197982\pi$
$758$		0			0
$759$	−444.843			−0.586091
$760$		0			0
$761$		−	129.224i		−	0.169808i	−0.996389	−	0.0849040i	$-0.972942\pi$
$761$		−	129.224i		−	0.169808i	0.996389	−	0.0849040i	$-0.0270584\pi$
$762$		0			0
$763$		−	118.476i		−	0.155277i
$764$		0			0
$765$	1357.78	+	595.510i	1.77487	+	0.778445i
$766$		0			0
$767$	185.651	+	185.651i	0.242049	+	0.242049i
$768$		0			0
$769$			247.035i			0.321242i	0.987016	+	0.160621i	$0.0513496\pi$
$769$			247.035i			0.321242i	−0.987016	+	0.160621i	$0.948650\pi$
$770$		0			0
$771$	−616.569	−	616.569i	−0.799701	−	0.799701i
$772$		0			0
$773$		−	149.770i		−	0.193751i	−0.995296	−	0.0968756i	$-0.969115\pi$
$773$		−	149.770i		−	0.193751i	0.995296	−	0.0968756i	$-0.0308849\pi$
$774$		0			0
$775$	−457.835	+	421.536i	−0.590755	+	0.543917i
$776$		0			0
$777$	5.62997	−	5.62997i	0.00724577	−	0.00724577i
$778$		0			0
$779$	248.561	+	248.561i	0.319077	+	0.319077i
$780$		0			0
$781$	829.700	+	829.700i	1.06236	+	1.06236i
$782$		0			0
$783$	−75.8737	+	75.8737i	−0.0969012	+	0.0969012i
$784$		0			0
$785$	418.342	+	1071.99i	0.532920	+	1.36559i
$786$		0			0
$787$		−	1010.58i		−	1.28409i	−0.766668	−	0.642044i	$-0.778087\pi$
$787$		−	1010.58i		−	1.28409i	0.766668	−	0.642044i	$-0.221913\pi$
$788$		0			0
$789$	−90.3624	−	90.3624i	−0.114528	−	0.114528i
$790$		0			0
$791$			402.492i			0.508839i
$792$		0			0
$793$	−351.188	−	351.188i	−0.442861	−	0.442861i
$794$		0			0
$795$	663.716	+	1700.75i	0.834863	+	2.13931i
$796$		0			0
$797$		−	627.322i		−	0.787105i	−0.919302	−	0.393552i	$-0.871246\pi$
$797$		−	627.322i		−	0.787105i	0.919302	−	0.393552i	$-0.128754\pi$
$798$		0			0
$799$		−	352.394i		−	0.441044i
$800$		0			0
$801$	−333.501			−0.416356
$802$		0			0
$803$	564.228			0.702650
$804$		0			0
$805$	−68.3962	+	26.6915i	−0.0849642	+	0.0331571i
$806$		0			0
$807$	468.864	−	468.864i	0.580996	−	0.580996i
$808$		0			0
$809$	−1040.62			−1.28631			−0.643155	−	0.765736i	$-0.722375\pi$
$809$	−1040.62			−1.28631			−0.643155	+	0.765736i	$0.722375\pi$
$810$		0			0
$811$	51.2843	−	51.2843i	0.0632359	−	0.0632359i	−0.674782	−	0.738018i	$-0.735762\pi$
$811$	51.2843	−	51.2843i	0.0632359	−	0.0632359i	0.738018	+	0.674782i	$0.235762\pi$
$812$		0			0
$813$	−411.060			−0.505609
$814$		0			0
$815$	958.843	−	374.186i	1.17649	−	0.459124i
$816$		0			0
$817$	242.338	+	242.338i	0.296619	+	0.296619i
$818$		0			0
$819$	−370.141	+	370.141i	−0.451943	+	0.451943i
$820$		0			0
$821$	−981.049	+	981.049i	−1.19494	+	1.19494i	−0.219282	+	0.975661i	$0.570372\pi$
$821$	−981.049	+	981.049i	−1.19494	+	1.19494i	−0.975661	+	0.219282i	$0.929628\pi$
$822$		0			0
$823$	−175.154	−	175.154i	−0.212823	−	0.212823i	0.592642	−	0.805466i	$-0.298085\pi$
$823$	−175.154	−	175.154i	−0.212823	−	0.212823i	−0.805466	+	0.592642i	$0.798085\pi$
$824$		0			0
$825$	−67.4224	+	1633.33i	−0.0817242	+	1.97979i
$826$		0			0
$827$	386.856			0.467782			0.233891	−	0.972263i	$-0.424854\pi$
$827$	386.856			0.467782			0.233891	+	0.972263i	$0.424854\pi$
$828$		0			0
$829$	94.0409	−	94.0409i	0.113439	−	0.113439i	−0.648109	−	0.761548i	$-0.724440\pi$
$829$	94.0409	−	94.0409i	0.113439	−	0.113439i	0.761548	+	0.648109i	$0.224440\pi$
$830$		0			0
$831$	393.111			0.473058
$832$		0			0
$833$	822.414	−	822.414i	0.987291	−	0.987291i
$834$		0			0
$835$	−150.165	+	342.380i	−0.179839	+	0.410036i
$836$		0			0
$837$	258.539			0.308888
$838$		0			0
$839$	−1049.59			−1.25100			−0.625499	−	0.780225i	$-0.715105\pi$
$839$	−1049.59			−1.25100			−0.625499	+	0.780225i	$0.715105\pi$
$840$		0			0
$841$			734.259i			0.873078i
$842$		0			0
$843$			738.093i			0.875556i
$844$		0			0
$845$	−1356.43	+	529.345i	−1.60524	+	0.626443i
$846$		0			0
$847$	−136.713	−	136.713i	−0.161409	−	0.161409i
$848$		0			0
$849$		−	1057.43i		−	1.24550i
$850$		0			0
$851$	−3.93796	−	3.93796i	−0.00462745	−	0.00462745i
$852$		0			0
$853$			1697.19i			1.98967i	0.101505	+	0.994835i	$0.467634\pi$
$853$			1697.19i			1.98967i	−0.101505	+	0.994835i	$0.532366\pi$
$854$		0			0
$855$	−220.506	+	502.758i	−0.257901	+	0.588021i
$856$		0			0
$857$	835.829	−	835.829i	0.975296	−	0.975296i	−0.0244059	−	0.999702i	$-0.507769\pi$
$857$	835.829	−	835.829i	0.975296	−	0.975296i	0.999702	+	0.0244059i	$0.00776940\pi$
$858$		0			0
$859$	101.258	+	101.258i	0.117879	+	0.117879i	0.763586	−	0.645707i	$-0.223437\pi$
$859$	101.258	+	101.258i	0.117879	+	0.117879i	−0.645707	+	0.763586i	$0.723437\pi$
$860$		0			0
$861$	−248.910	−	248.910i	−0.289094	−	0.289094i
$862$		0			0
$863$	−866.298	+	866.298i	−1.00382	+	1.00382i	−0.00382915	+	0.999993i	$0.501219\pi$
$863$	−866.298	+	866.298i	−1.00382	+	1.00382i	−0.999993	+	0.00382915i	$0.998781\pi$
$864$		0			0
$865$	644.302	−	251.437i	0.744858	−	0.290679i
$866$		0			0
$867$		−	1797.99i		−	2.07380i
$868$		0			0
$869$	−817.046	−	817.046i	−0.940214	−	0.940214i
$870$		0			0
$871$			1001.37i			1.14968i
$872$		0			0
$873$	131.243	+	131.243i	0.150335	+	0.150335i
$874$		0			0
$875$	87.6364	+	255.175i	0.100156	+	0.291629i
$876$		0			0
$877$			708.097i			0.807408i	0.914890	+	0.403704i	$0.132277\pi$
$877$			708.097i			0.807408i	−0.914890	+	0.403704i	$0.867723\pi$
$878$		0			0
$879$			1376.17i			1.56561i
$880$		0			0
$881$	678.953			0.770662			0.385331	−	0.922778i	$-0.374087\pi$
$881$	678.953			0.770662			0.385331	+	0.922778i	$0.374087\pi$
$882$		0			0
$883$	−302.033			−0.342053			−0.171027	−	0.985266i	$-0.554708\pi$
$883$	−302.033			−0.342053			−0.171027	+	0.985266i	$0.554708\pi$
$884$		0			0
$885$	−252.522	−	110.754i	−0.285336	−	0.125146i
$886$		0			0
$887$	−961.511	+	961.511i	−1.08400	+	1.08400i	−0.0878714	+	0.996132i	$0.528006\pi$
$887$	−961.511	+	961.511i	−1.08400	+	1.08400i	−0.996132	+	0.0878714i	$0.971994\pi$
$888$		0			0
$889$	470.579			0.529335
$890$		0			0
$891$	−563.781	+	563.781i	−0.632751	+	0.632751i
$892$		0			0
$893$	130.485			0.146119
$894$		0			0
$895$	294.764	−	672.068i	0.329345	−	0.750914i
$896$		0			0
$897$	465.016	+	465.016i	0.518412	+	0.518412i
$898$		0			0
$899$	−181.860	+	181.860i	−0.202292	+	0.202292i
$900$		0			0
$901$	1502.92	−	1502.92i	1.66806	−	1.66806i
$902$		0			0
$903$	−242.679	−	242.679i	−0.268747	−	0.268747i
$904$		0			0
$905$	226.325	−	516.026i	0.250083	−	0.570194i
$906$		0			0
$907$	−504.237			−0.555940			−0.277970	−	0.960590i	$-0.589662\pi$
$907$	−504.237			−0.555940			−0.277970	+	0.960590i	$0.589662\pi$
$908$		0			0
$909$	187.383	−	187.383i	0.206141	−	0.206141i
$910$		0			0
$911$	−1061.71			−1.16544			−0.582718	−	0.812675i	$-0.698011\pi$
$911$	−1061.71			−1.16544			−0.582718	+	0.812675i	$0.698011\pi$
$912$		0			0
$913$	−302.697	+	302.697i	−0.331541	+	0.331541i
$914$		0			0
$915$	477.685	+	209.509i	0.522060	+	0.228972i
$916$		0			0
$917$	391.691			0.427144
$918$		0			0
$919$	216.839			0.235951			0.117975	−	0.993017i	$-0.462360\pi$
$919$	216.839			0.235951			0.117975	+	0.993017i	$0.462360\pi$
$920$		0			0
$921$		−	2233.94i		−	2.42556i
$922$		0			0
$923$		−	1734.65i		−	1.87936i
$924$		0			0
$925$	−15.0558	+	13.8621i	−0.0162766	+	0.0149861i
$926$		0			0
$927$	−1125.56	−	1125.56i	−1.21420	−	1.21420i
$928$		0			0
$929$			173.225i			0.186464i	0.995644	+	0.0932321i	$0.0297198\pi$
$929$			173.225i			0.186464i	−0.995644	+	0.0932321i	$0.970280\pi$
$930$		0			0
$931$	304.524	+	304.524i	0.327093	+	0.327093i
$932$		0			0
$933$			171.839i			0.184179i
$934$		0			0
$935$	1772.92	−	691.880i	1.89618	−	0.739979i
$936$		0			0
$937$	−681.081	+	681.081i	−0.726874	+	0.726874i	−0.969996	−	0.243122i	$-0.921829\pi$
$937$	−681.081	+	681.081i	−0.726874	+	0.726874i	0.243122	+	0.969996i	$0.421829\pi$
$938$		0			0
$939$	−138.879	−	138.879i	−0.147900	−	0.147900i
$940$		0			0
$941$	622.205	+	622.205i	0.661217	+	0.661217i	0.955667	−	0.294450i	$-0.0951364\pi$
$941$	622.205	+	622.205i	0.661217	+	0.661217i	−0.294450	+	0.955667i	$0.595136\pi$
$942$		0			0
$943$	−174.104	+	174.104i	−0.184627	+	0.184627i
$944$		0			0
$945$	45.0200	−	102.647i	0.0476402	−	0.108621i
$946$		0			0
$947$		−	334.816i		−	0.353555i	−0.984251	−	0.176777i	$-0.943433\pi$
$947$		−	334.816i		−	0.353555i	0.984251	−	0.176777i	$-0.0565672\pi$
$948$		0			0
$949$	−589.814	−	589.814i	−0.621511	−	0.621511i
$950$		0			0
$951$			874.434i			0.919489i
$952$		0			0
$953$	503.098	+	503.098i	0.527909	+	0.527909i	0.919949	−	0.392039i	$-0.128230\pi$
$953$	503.098	+	503.098i	0.527909	+	0.527909i	−0.392039	+	0.919949i	$0.628230\pi$
$954$		0			0
$955$	−528.376	+	206.198i	−0.553274	+	0.215914i
$956$		0			0
$957$			675.569i			0.705923i
$958$		0			0
$959$			300.321i			0.313160i
$960$		0			0
$961$	−341.311			−0.355163
$962$		0			0
$963$	1783.91			1.85245
$964$		0			0
$965$	−589.240	+	1343.48i	−0.610611	+	1.39221i
$966$		0			0
$967$	−855.714	+	855.714i	−0.884916	+	0.884916i	−0.994029	−	0.109113i	$-0.965199\pi$
$967$	−855.714	+	855.714i	−0.884916	+	0.884916i	0.109113	+	0.994029i	$0.465199\pi$
$968$		0			0
$969$	1147.96			1.18469
$970$		0			0
$971$	−1101.75	+	1101.75i	−1.13466	+	1.13466i	−0.145267	+	0.989392i	$0.546404\pi$
$971$	−1101.75	+	1101.75i	−1.13466	+	1.13466i	−0.989392	+	0.145267i	$0.953596\pi$
$972$		0			0
$973$	272.772			0.280342
$974$		0			0
$975$	1777.88	−	1636.92i	1.82346	−	1.67889i
$976$		0			0
$977$	287.755	+	287.755i	0.294530	+	0.294530i	0.838867	−	0.544337i	$-0.183219\pi$
$977$	287.755	+	287.755i	0.294530	+	0.294530i	−0.544337	+	0.838867i	$0.683219\pi$
$978$		0			0
$979$	−302.707	+	302.707i	−0.309200	+	0.309200i
$980$		0			0
$981$	438.775	−	438.775i	0.447273	−	0.447273i
$982$		0			0
$983$	1237.43	+	1237.43i	1.25883	+	1.25883i	0.951653	+	0.307176i	$0.0993842\pi$
$983$	1237.43	+	1237.43i	1.25883	+	1.25883i	0.307176	+	0.951653i	$0.400616\pi$
$984$		0			0
$985$	141.849	−	55.3563i	0.144009	−	0.0561992i
$986$		0			0
$987$	−130.668			−0.132389
$988$		0			0
$989$	−169.745	+	169.745i	−0.171633	+	0.171633i
$990$		0			0
$991$	−1513.43			−1.52717			−0.763586	−	0.645706i	$-0.776563\pi$
$991$	−1513.43			−1.52717			−0.763586	+	0.645706i	$0.776563\pi$
$992$		0			0
$993$	491.600	−	491.600i	0.495066	−	0.495066i
$994$		0			0
$995$	−1061.53	+	414.259i	−1.06686	+	0.416341i
$996$		0			0
$997$	764.377			0.766677			0.383339	−	0.923608i	$-0.374774\pi$
$997$	764.377			0.766677			0.383339	+	0.923608i	$0.374774\pi$
$998$		0			0
$999$	8.50201			0.00851052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.3.t.a.417.4		44
4.3	odd	2		640.3.t.b.417.19		44
5.3	odd	4		640.3.i.a.33.4		44
8.3	odd	2		80.3.t.a.77.6	yes	44
8.5	even	2		320.3.t.a.17.19		44
16.3	odd	4		80.3.i.a.37.18	yes	44
16.5	even	4		640.3.i.a.97.19		44
16.11	odd	4		640.3.i.b.97.4		44
16.13	even	4		320.3.i.a.177.4		44
20.3	even	4		640.3.i.b.33.19		44
40.3	even	4		80.3.i.a.13.18	✓	44
40.13	odd	4		320.3.i.a.273.19		44
40.19	odd	2		400.3.t.b.157.17		44
40.27	even	4		400.3.i.b.93.5		44
80.3	even	4		80.3.t.a.53.6	yes	44
80.13	odd	4		320.3.t.a.113.19		44
80.19	odd	4		400.3.i.b.357.5		44
80.43	even	4		640.3.t.b.353.19		44
80.53	odd	4	inner	640.3.t.a.353.4		44
80.67	even	4		400.3.t.b.293.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.18	✓	44	40.3	even	4
80.3.i.a.37.18	yes	44	16.3	odd	4
80.3.t.a.53.6	yes	44	80.3	even	4
80.3.t.a.77.6	yes	44	8.3	odd	2
320.3.i.a.177.4		44	16.13	even	4
320.3.i.a.273.19		44	40.13	odd	4
320.3.t.a.17.19		44	8.5	even	2
320.3.t.a.113.19		44	80.13	odd	4
400.3.i.b.93.5		44	40.27	even	4
400.3.i.b.357.5		44	80.19	odd	4
400.3.t.b.157.17		44	40.19	odd	2
400.3.t.b.293.17		44	80.67	even	4
640.3.i.a.33.4		44	5.3	odd	4
640.3.i.a.97.19		44	16.5	even	4
640.3.i.b.33.19		44	20.3	even	4
640.3.i.b.97.4		44	16.11	odd	4
640.3.t.a.353.4		44	80.53	odd	4	inner
640.3.t.a.417.4		44	1.1	even	1	trivial
640.3.t.b.353.19		44	80.43	even	4
640.3.t.b.417.19		44	4.3	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	640.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-4.50609 q^{3} +(-4.65788 + 1.81773i) q^{5} +(1.52625 - 1.52625i) q^{7} +11.3048 q^{9} +O(q^{10})\)	\(q-4.50609 q^{3} +(-4.65788 + 1.81773i) q^{5} +(1.52625 - 1.52625i) q^{7} +11.3048 q^{9} +(10.2610 - 10.2610i) q^{11} -21.4526 q^{13} +(20.9888 - 8.19085i) q^{15} +(-18.5474 - 18.5474i) q^{17} +(6.86774 - 6.86774i) q^{19} +(-6.87740 + 6.87740i) q^{21} +(4.81049 + 4.81049i) q^{23} +(18.3917 - 16.9335i) q^{25} -10.3858 q^{27} +(7.30552 - 7.30552i) q^{29} -24.8935 q^{31} +(-46.2368 + 46.2368i) q^{33} +(-4.33477 + 9.88337i) q^{35} -0.818619 q^{37} +96.6671 q^{39} +36.1925i q^{41} +35.2864i q^{43} +(-52.6566 + 20.5491i) q^{45} +(9.49981 + 9.49981i) q^{47} +44.3412i q^{49} +(83.5763 + 83.5763i) q^{51} +81.0314i q^{53} +(-29.1427 + 66.4460i) q^{55} +(-30.9466 + 30.9466i) q^{57} +(-8.65405 - 8.65405i) q^{59} +(16.3705 + 16.3705i) q^{61} +(17.2539 - 17.2539i) q^{63} +(99.9235 - 38.9949i) q^{65} -46.6786i q^{67} +(-21.6765 - 21.6765i) q^{69} +80.8598i q^{71} +(27.4939 + 27.4939i) q^{73} +(-82.8748 + 76.3040i) q^{75} -31.3215i q^{77} -79.6266i q^{79} -54.9442 q^{81} -29.4998 q^{83} +(120.106 + 52.6775i) q^{85} +(-32.9193 + 32.9193i) q^{87} -29.5008 q^{89} +(-32.7419 + 32.7419i) q^{91} +112.173 q^{93} +(-19.5054 + 44.4728i) q^{95} +(11.6094 + 11.6094i) q^{97} +(115.999 - 115.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9	\( 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 40 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{35} + 4 q^{37} + 72 q^{39} + 70 q^{45} + 4 q^{47} - 100 q^{51} - 36 q^{57} - 64 q^{59} + 36 q^{61} + 200 q^{63} - 4 q^{65} - 60 q^{69} - 48 q^{73} - 324 q^{75} + 100 q^{81} + 156 q^{83} + 52 q^{85} + 36 q^{87} + 188 q^{91} + 40 q^{93} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 40 * q^27 + 8 * q^31 - 4 * q^33 - 4 * q^35 + 4 * q^37 + 72 * q^39 + 70 * q^45 + 4 * q^47 - 100 * q^51 - 36 * q^57 - 64 * q^59 + 36 * q^61 + 200 * q^63 - 4 * q^65 - 60 * q^69 - 48 * q^73 - 324 * q^75 + 100 * q^81 + 156 * q^83 + 52 * q^85 + 36 * q^87 + 188 * q^91 + 40 * q^93 - 380 * q^95 - 4 * q^97 + 92 * q^99

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