LMFDB - Embedded newform 640.3.i.b.33.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,3,Mod(33,640)]

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, 3, 3]))

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

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

chi := DirichletCharacter("640.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	640.i (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			33.19
Character	$\chi$	$=$	640.33
Dual form			640.3.i.b.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.50609i q^{3} +(-1.81773 + 4.65788i) q^{5} +(1.52625 + 1.52625i) q^{7} -11.3048 q^{9} +O(q^{10})$	\(q+4.50609i q^{3} +(-1.81773 + 4.65788i) q^{5} +(1.52625 + 1.52625i) q^{7} -11.3048 q^{9} +(-10.2610 + 10.2610i) q^{11} -21.4526i q^{13} +(-20.9888 - 8.19085i) q^{15} +(-18.5474 + 18.5474i) q^{17} +(6.86774 - 6.86774i) q^{19} +(-6.87740 + 6.87740i) q^{21} +(4.81049 - 4.81049i) q^{23} +(-18.3917 - 16.9335i) q^{25} -10.3858i q^{27} +(-7.30552 + 7.30552i) q^{29} +24.8935 q^{31} +(-46.2368 - 46.2368i) q^{33} +(-9.88337 + 4.33477i) q^{35} +0.818619i q^{37} +96.6671 q^{39} +36.1925i q^{41} +35.2864 q^{43} +(20.5491 - 52.6566i) q^{45} +(-9.49981 + 9.49981i) q^{47} -44.3412i q^{49} +(-83.5763 - 83.5763i) q^{51} -81.0314 q^{53} +(-29.1427 - 66.4460i) q^{55} +(30.9466 + 30.9466i) q^{57} +(-8.65405 - 8.65405i) q^{59} +(16.3705 + 16.3705i) q^{61} +(-17.2539 - 17.2539i) q^{63} +(99.9235 + 38.9949i) q^{65} +46.6786 q^{67} +(21.6765 + 21.6765i) q^{69} -80.8598i q^{71} +(-27.4939 + 27.4939i) q^{73} +(76.3040 - 82.8748i) q^{75} -31.3215 q^{77} -79.6266i q^{79} -54.9442 q^{81} +29.4998i q^{83} +(-52.6775 - 120.106i) q^{85} +(-32.9193 - 32.9193i) q^{87} +29.5008 q^{89} +(32.7419 - 32.7419i) q^{91} +112.173i q^{93} +(19.5054 + 44.4728i) q^{95} +(11.6094 - 11.6094i) q^{97} +(115.999 - 115.999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{5} - 108 q^{9}+O(q^{10}) $ 44 * q + 2 * q^5 - 108 * q^9	$ 44 q + 2 q^{5} - 108 q^{9} + 4 q^{11} - 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 8 q^{31} - 4 q^{33} - 96 q^{35} + 72 q^{39} - 124 q^{43} + 34 q^{45} - 4 q^{47} + 100 q^{51} + 4 q^{53} + 36 q^{57} - 64 q^{59} + 36 q^{61} - 200 q^{63} - 4 q^{65} + 292 q^{67} + 60 q^{69} + 48 q^{73} - 96 q^{75} - 192 q^{77} + 100 q^{81} - 48 q^{85} + 36 q^{87} - 188 q^{91} + 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q + 2 * q^5 - 108 * q^9 + 4 * q^11 - 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 8 * q^31 - 4 * q^33 - 96 * q^35 + 72 * q^39 - 124 * q^43 + 34 * q^45 - 4 * q^47 + 100 * q^51 + 4 * q^53 + 36 * q^57 - 64 * q^59 + 36 * q^61 - 200 * q^63 - 4 * q^65 + 292 * q^67 + 60 * q^69 + 48 * q^73 - 96 * q^75 - 192 * q^77 + 100 * q^81 - 48 * q^85 + 36 * q^87 - 188 * q^91 + 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

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

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
$3$			4.50609i			1.50203i	0.660285	+	0.751015i	$0.270435\pi$
$3$			4.50609i			1.50203i	−0.660285	+	0.751015i	$0.729565\pi$
$4$		0			0
$5$	−1.81773	+	4.65788i	−0.363546	+	0.931576i
$5$	−1.81773	+	4.65788i	−0.363546	+	0.931576i
$6$		0			0
$7$	1.52625	+	1.52625i	0.218035	+	0.218035i	0.807670	−	0.589635i	$-0.200728\pi$
$7$	1.52625	+	1.52625i	0.218035	+	0.218035i	−0.589635	+	0.807670i	$0.700728\pi$
$8$		0			0
$9$	−11.3048			−1.25609
$10$		0			0
$11$	−10.2610	+	10.2610i	−0.932816	+	0.932816i	−0.997881	−	0.0650655i	$-0.979274\pi$
$11$	−10.2610	+	10.2610i	−0.932816	+	0.932816i	0.0650655	+	0.997881i	$0.479274\pi$
$12$		0			0
$13$		−	21.4526i		−	1.65020i	−0.564989	−	0.825098i	$-0.691120\pi$
$13$		−	21.4526i		−	1.65020i	0.564989	−	0.825098i	$-0.308880\pi$
$14$		0			0
$15$	−20.9888	−	8.19085i	−1.39926	−	0.546056i
$16$		0			0
$17$	−18.5474	+	18.5474i	−1.09102	+	1.09102i	−0.0956051	+	0.995419i	$0.530479\pi$
$17$	−18.5474	+	18.5474i	−1.09102	+	1.09102i	−0.995419	+	0.0956051i	$0.969521\pi$
$18$		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	−0.594755	−	0.803907i	$-0.702751\pi$
$23$	4.81049	−	4.81049i	0.209152	−	0.209152i	0.803907	+	0.594755i	$0.202751\pi$
$24$		0			0
$25$	−18.3917	−	16.9335i	−0.735669	−	0.677341i
$26$		0			0
$27$		−	10.3858i		−	0.384659i
$28$		0			0
$29$	−7.30552	+	7.30552i	−0.251915	+	0.251915i	−0.821755	−	0.569841i	$-0.807005\pi$
$29$	−7.30552	+	7.30552i	−0.251915	+	0.251915i	0.569841	+	0.821755i	$0.307005\pi$
$30$		0			0
$31$	24.8935			0.803018			0.401509	−	0.915855i	$-0.368486\pi$
$31$	24.8935			0.803018			0.401509	+	0.915855i	$0.368486\pi$
$32$		0			0
$33$	−46.2368	−	46.2368i	−1.40112	−	1.40112i
$34$		0			0
$35$	−9.88337	+	4.33477i	−0.282382	+	0.123851i
$36$		0			0
$37$			0.818619i			0.0221248i	0.999939	+	0.0110624i	$0.00352135\pi$
$37$			0.818619i			0.0221248i	−0.999939	+	0.0110624i	$0.996479\pi$
$38$		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
$43$	35.2864			0.820615			0.410307	−	0.911947i	$-0.365421\pi$
$43$	35.2864			0.820615			0.410307	+	0.911947i	$0.365421\pi$
$44$		0			0
$45$	20.5491	−	52.6566i	0.456647	−	1.17015i
$46$		0			0
$47$	−9.49981	+	9.49981i	−0.202124	+	0.202124i	−0.800909	−	0.598786i	$-0.795650\pi$
$47$	−9.49981	+	9.49981i	−0.202124	+	0.202124i	0.598786	+	0.800909i	$0.295650\pi$
$48$		0			0
$49$		−	44.3412i		−	0.904921i
$50$		0			0
$51$	−83.5763	−	83.5763i	−1.63875	−	1.63875i
$52$		0			0
$53$	−81.0314			−1.52889			−0.764447	−	0.644686i	$-0.776988\pi$
$53$	−81.0314			−1.52889			−0.764447	+	0.644686i	$0.776988\pi$
$54$		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
$67$	46.6786			0.696695			0.348348	−	0.937365i	$-0.386743\pi$
$67$	46.6786			0.696695			0.348348	+	0.937365i	$0.386743\pi$
$68$		0			0
$69$	21.6765	+	21.6765i	0.314152	+	0.314152i
$70$		0			0
$71$		−	80.8598i		−	1.13887i	−0.822036	−	0.569435i	$-0.807162\pi$
$71$		−	80.8598i		−	1.13887i	0.822036	−	0.569435i	$-0.192838\pi$
$72$		0			0
$73$	−27.4939	+	27.4939i	−0.376629	+	0.376629i	−0.869884	−	0.493256i	$-0.835807\pi$
$73$	−27.4939	+	27.4939i	−0.376629	+	0.376629i	0.493256	+	0.869884i	$0.335807\pi$
$74$		0			0
$75$	76.3040	−	82.8748i	1.01739	−	1.10500i
$76$		0			0
$77$	−31.3215			−0.406773
$78$		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
$83$			29.4998i			0.355420i	0.984083	+	0.177710i	$0.0568688\pi$
$83$			29.4998i			0.355420i	−0.984083	+	0.177710i	$0.943131\pi$
$84$		0			0
$85$	−52.6775	−	120.106i	−0.619735	−	1.41301i
$86$		0			0
$87$	−32.9193	−	32.9193i	−0.378383	−	0.378383i
$88$		0			0
$89$	29.5008			0.331469			0.165735	−	0.986170i	$-0.447000\pi$
$89$	29.5008			0.331469			0.165735	+	0.986170i	$0.447000\pi$
$90$		0			0
$91$	32.7419	−	32.7419i	0.359801	−	0.359801i
$92$		0			0
$93$			112.173i			1.20616i
$94$		0			0
$95$	19.5054	+	44.4728i	0.205320	+	0.468135i
$96$		0			0
$97$	11.6094	−	11.6094i	0.119685	−	0.119685i	−0.644728	−	0.764412i	$-0.723029\pi$
$97$	11.6094	−	11.6094i	0.119685	−	0.119685i	0.764412	+	0.644728i	$0.223029\pi$
$98$		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	−0.999461	−	0.0328145i	$-0.989553\pi$
$103$	−99.5646	+	99.5646i	−0.966647	+	0.966647i	0.0328145	+	0.999461i	$0.489553\pi$
$104$		0			0
$105$	−19.5329	−	44.5353i	−0.186027	−	0.424146i
$106$		0			0
$107$			157.800i			1.47477i	0.675474	+	0.737384i	$0.263939\pi$
$107$			157.800i			1.47477i	−0.675474	+	0.737384i	$0.736061\pi$
$108$		0			0
$109$	−38.8130	+	38.8130i	−0.356083	+	0.356083i	−0.862367	−	0.506284i	$-0.831019\pi$
$109$	−38.8130	+	38.8130i	−0.356083	+	0.356083i	0.506284	+	0.862367i	$0.331019\pi$
$110$		0			0
$111$	−3.68877			−0.0332322
$112$		0			0
$113$	−131.857	−	131.857i	−1.16688	−	1.16688i	−0.982938	−	0.183938i	$-0.941116\pi$
$113$	−131.857	−	131.857i	−1.16688	−	1.16688i	−0.183938	−	0.982938i	$-0.558884\pi$
$114$		0			0
$115$	13.6625	+	31.1508i	0.118805	+	0.270877i
$116$		0			0
$117$			242.518i			2.07280i
$118$		0			0
$119$	−56.6158			−0.475763
$120$		0			0
$121$		−	89.5750i		−	0.740290i
$122$		0			0
$123$	−163.087			−1.32591
$124$		0			0
$125$	112.306	−	54.8859i	0.898444	−	0.439087i
$126$		0			0
$127$	−154.162	+	154.162i	−1.21388	+	1.21388i	−0.244136	+	0.969741i	$0.578504\pi$
$127$	−154.162	+	154.162i	−1.21388	+	1.21388i	−0.969741	+	0.244136i	$0.921496\pi$
$128$		0			0
$129$			159.004i			1.23259i
$130$		0			0
$131$	−128.318	−	128.318i	−0.979530	−	0.979530i	0.0202649	−	0.999795i	$-0.493549\pi$
$131$	−128.318	−	128.318i	−0.979530	−	0.979530i	−0.999795	+	0.0202649i	$0.993549\pi$
$132$		0			0
$133$	20.9637			0.157622
$134$		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	$-0.0804576\pi$
$137$	98.3855	+	98.3855i	0.718142	+	0.718142i	−0.250082	+	0.968225i	$0.580458\pi$
$138$		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
$147$	199.805			1.35922
$148$		0			0
$149$	−135.878	−	135.878i	−0.911932	−	0.911932i	0.0844918	−	0.996424i	$-0.473073\pi$
$149$	−135.878	−	135.878i	−0.911932	−	0.911932i	−0.996424	+	0.0844918i	$0.973073\pi$
$150$		0			0
$151$			174.395i			1.15493i	0.816415	+	0.577466i	$0.195958\pi$
$151$			174.395i			1.15493i	−0.816415	+	0.577466i	$0.804042\pi$
$152$		0			0
$153$	209.675	−	209.675i	1.37043	−	1.37043i
$154$		0			0
$155$	−45.2497	+	115.951i	−0.291934	+	0.748072i
$156$		0			0
$157$	−230.146			−1.46590			−0.732948	−	0.680285i	$-0.761856\pi$
$157$	−230.146			−1.46590			−0.732948	+	0.680285i	$0.761856\pi$
$158$		0			0
$159$		−	365.135i		−	2.29645i
$160$		0			0
$161$	14.6840			0.0912047
$162$		0			0
$163$			205.854i			1.26291i	0.775414	+	0.631453i	$0.217541\pi$
$163$			205.854i			1.26291i	−0.775414	+	0.631453i	$0.782459\pi$
$164$		0			0
$165$	299.412	−	131.320i	1.81462	−	0.795877i
$166$		0			0
$167$	52.8722	+	52.8722i	0.316600	+	0.316600i	0.847460	−	0.530860i	$-0.178131\pi$
$167$	52.8722	+	52.8722i	0.316600	+	0.316600i	−0.530860	+	0.847460i	$0.678131\pi$
$168$		0			0
$169$	−291.212			−1.72315
$170$		0			0
$171$	−77.6387	+	77.6387i	−0.454027	+	0.454027i
$172$		0			0
$173$		−	138.325i		−	0.799567i	−0.916610	−	0.399783i	$-0.869085\pi$
$173$		−	138.325i		−	0.799567i	0.916610	−	0.399783i	$-0.130915\pi$
$174$		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
$187$		−	380.629i		−	2.03545i
$188$		0			0
$189$	15.8513	−	15.8513i	0.0838691	−	0.0838691i
$190$		0			0
$191$	−113.437			−0.593911			−0.296956	−	0.954891i	$-0.595971\pi$
$191$	−113.437			−0.593911			−0.296956	+	0.954891i	$0.595971\pi$
$192$		0			0
$193$	207.468	+	207.468i	1.07496	+	1.07496i	0.996953	+	0.0780092i	$0.0248564\pi$
$193$	207.468	+	207.468i	1.07496	+	1.07496i	0.0780092	+	0.996953i	$0.475144\pi$
$194$		0			0
$195$	−175.715	+	450.264i	−0.901100	+	2.30905i
$196$		0			0
$197$			30.4535i			0.154586i	0.997008	+	0.0772932i	$0.0246278\pi$
$197$			30.4535i			0.154586i	−0.997008	+	0.0772932i	$0.975372\pi$
$198$		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
$203$	−22.3000			−0.109852
$204$		0			0
$205$	−168.580	−	65.7882i	−0.822344	−	0.320918i
$206$		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	0.978247	−	0.207445i	$-0.0665149\pi$
$211$	162.639	+	162.639i	0.770801	+	0.770801i	−0.207445	+	0.978247i	$0.566515\pi$
$212$		0			0
$213$	364.361			1.71062
$214$		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	$-0.235640\pi$
$223$	14.2230	+	14.2230i	0.0637803	+	0.0637803i	−0.674497	+	0.738277i	$0.735640\pi$
$224$		0			0
$225$	207.915	+	191.431i	0.924069	+	0.850803i
$226$		0			0
$227$	−284.554			−1.25354			−0.626771	−	0.779203i	$-0.715624\pi$
$227$	−284.554			−1.25354			−0.626771	+	0.779203i	$0.715624\pi$
$228$		0			0
$229$	−20.0023	−	20.0023i	−0.0873464	−	0.0873464i	0.662084	−	0.749430i	$-0.269672\pi$
$229$	−20.0023	−	20.0023i	−0.0873464	−	0.0873464i	−0.749430	+	0.662084i	$0.769672\pi$
$230$		0			0
$231$		−	141.138i		−	0.610985i
$232$		0			0
$233$	−147.800	+	147.800i	−0.634336	+	0.634336i	−0.949153	−	0.314817i	$-0.898057\pi$
$233$	−147.800	+	147.800i	−0.634336	+	0.634336i	0.314817	+	0.949153i	$0.398057\pi$
$234$		0			0
$235$	−26.9809	−	61.5171i	−0.114812	−	0.261775i
$236$		0			0
$237$	358.805			1.51394
$238$		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
$243$		−	341.056i		−	1.40352i
$244$		0			0
$245$	206.536	+	80.6002i	0.843003	+	0.328980i
$246$		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	−0.840065	−	0.542486i	$-0.817483\pi$
$251$	−74.6924	+	74.6924i	−0.297579	+	0.297579i	0.542486	+	0.840065i	$0.317483\pi$
$252$		0			0
$253$			98.7205i			0.390200i
$254$		0			0
$255$	541.208	−	237.369i	2.12238	−	0.930861i
$256$		0			0
$257$	136.830	−	136.830i	0.532413	−	0.532413i	−0.388876	−	0.921290i	$-0.627137\pi$
$257$	136.830	−	136.830i	0.532413	−	0.532413i	0.921290	+	0.388876i	$0.127137\pi$
$258$		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	−0.667954	−	0.744203i	$-0.732830\pi$
$263$	20.0534	−	20.0534i	0.0762487	−	0.0762487i	0.744203	+	0.667954i	$0.232830\pi$
$264$		0			0
$265$	147.293	−	377.435i	0.555823	−	1.42428i
$266$		0			0
$267$			132.933i			0.497877i
$268$		0			0
$269$	104.051	−	104.051i	0.386807	−	0.386807i	−0.486740	−	0.873547i	$-0.661814\pi$
$269$	104.051	−	104.051i	0.386807	−	0.386807i	0.873547	+	0.486740i	$0.161814\pi$
$270$		0			0
$271$	−91.2232			−0.336617			−0.168308	−	0.985734i	$-0.553830\pi$
$271$	−91.2232			−0.336617			−0.168308	+	0.985734i	$0.553830\pi$
$272$		0			0
$273$	147.538	+	147.538i	0.540431	+	0.540431i
$274$		0			0
$275$	362.471	−	14.9625i	1.31808	−	0.0544092i
$276$		0			0
$277$			87.2400i			0.314946i	0.987523	+	0.157473i	$0.0503347\pi$
$277$			87.2400i			0.314946i	−0.987523	+	0.157473i	$0.949665\pi$
$278$		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
$283$	234.667			0.829213			0.414607	−	0.910001i	$-0.363919\pi$
$283$	234.667			0.829213			0.414607	+	0.910001i	$0.363919\pi$
$284$		0			0
$285$	−200.398	+	87.8932i	−0.703152	+	0.308397i
$286$		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
$293$	305.403			1.04233			0.521166	−	0.853455i	$-0.325497\pi$
$293$	305.403			1.04233			0.521166	+	0.853455i	$0.325497\pi$
$294$		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
$307$	−495.760			−1.61485			−0.807427	−	0.589967i	$-0.799141\pi$
$307$	−495.760			−1.61485			−0.807427	+	0.589967i	$0.799141\pi$
$308$		0			0
$309$	−448.647	−	448.647i	−1.45193	−	1.45193i
$310$		0			0
$311$			38.1349i			0.122620i	0.998119	+	0.0613101i	$0.0195279\pi$
$311$			38.1349i			0.122620i	−0.998119	+	0.0613101i	$0.980472\pi$
$312$		0			0
$313$	−30.8202	+	30.8202i	−0.0984671	+	0.0984671i	−0.754624	−	0.656157i	$-0.772181\pi$
$313$	−30.8202	+	30.8202i	−0.0984671	+	0.0984671i	0.656157	+	0.754624i	$0.272181\pi$
$314$		0			0
$315$	111.730	−	49.0039i	0.354698	−	0.155568i
$316$		0			0
$317$	−194.056			−0.612164			−0.306082	−	0.952005i	$-0.599018\pi$
$317$	−194.056			−0.612164			−0.306082	+	0.952005i	$0.599018\pi$
$318$		0			0
$319$		−	149.924i		−	0.469980i
$320$		0			0
$321$	−711.062			−2.21515
$322$		0			0
$323$			254.758i			0.788723i
$324$		0			0
$325$	−363.267	+	394.550i	−1.11775	+	1.21400i
$326$		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	−0.522836	−	0.852434i	$-0.675126\pi$
$331$	109.097	−	109.097i	0.329598	−	0.329598i	0.852434	+	0.522836i	$0.175126\pi$
$332$		0			0
$333$		−	9.25435i		−	0.0277909i
$334$		0			0
$335$	−84.8490	+	217.423i	−0.253281	+	0.649025i
$336$		0			0
$337$	−73.7614	+	73.7614i	−0.218877	+	0.218877i	−0.808025	−	0.589148i	$-0.799463\pi$
$337$	−73.7614	+	73.7614i	−0.218877	+	0.218877i	0.589148	+	0.808025i	$0.299463\pi$
$338$		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
$347$			644.536i			1.85745i	0.370767	+	0.928726i	$0.379095\pi$
$347$			644.536i			1.85745i	−0.370767	+	0.928726i	$0.620905\pi$
$348$		0			0
$349$	161.816	−	161.816i	0.463657	−	0.463657i	−0.436195	−	0.899852i	$-0.643674\pi$
$349$	161.816	−	161.816i	0.463657	−	0.463657i	0.899852	+	0.436195i	$0.143674\pi$
$350$		0			0
$351$	−222.802			−0.634763
$352$		0			0
$353$	91.5785	+	91.5785i	0.259429	+	0.259429i	0.824822	−	0.565393i	$-0.191275\pi$
$353$	91.5785	+	91.5785i	0.259429	+	0.259429i	−0.565393	+	0.824822i	$0.691275\pi$
$354$		0			0
$355$	376.635	+	146.981i	1.06094	+	0.414031i
$356$		0			0
$357$		−	255.116i		−	0.714610i
$358$		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
$363$	403.633			1.11194
$364$		0			0
$365$	−78.0869	−	178.040i	−0.213937	−	0.487780i
$366$		0			0
$367$	−232.108	+	232.108i	−0.632446	+	0.632446i	−0.948681	−	0.316235i	$-0.897581\pi$
$367$	−232.108	+	232.108i	−0.632446	+	0.632446i	0.316235	+	0.948681i	$0.397581\pi$
$368$		0			0
$369$		−	409.150i		−	1.10881i
$370$		0			0
$371$	−123.674	−	123.674i	−0.333353	−	0.333353i
$372$		0			0
$373$	−71.3315			−0.191237			−0.0956187	−	0.995418i	$-0.530483\pi$
$373$	−71.3315			−0.191237			−0.0956187	+	0.995418i	$0.530483\pi$
$374$		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	−0.999715	−	0.0238677i	$-0.992402\pi$
$383$	−392.032	−	392.032i	−1.02358	−	1.02358i	−0.0238677	−	0.999715i	$-0.507598\pi$
$384$		0			0
$385$	56.9340	−	145.892i	0.147881	−	0.378940i
$386$		0			0
$387$	−398.907			−1.03077
$388$		0			0
$389$	−0.333140	−	0.333140i	−0.000856400	−	0.000856400i	0.706678	−	0.707535i	$-0.250193\pi$
$389$	−0.333140	−	0.333140i	−0.000856400	−	0.000856400i	−0.707535	+	0.706678i	$0.750193\pi$
$390$		0			0
$391$			178.444i			0.456379i
$392$		0			0
$393$	578.214	−	578.214i	1.47128	−	1.47128i
$394$		0			0
$395$	370.891	+	144.740i	0.938965	+	0.366429i
$396$		0			0
$397$	3.73338			0.00940399			0.00470199	−	0.999989i	$-0.498503\pi$
$397$	3.73338			0.00940399			0.00470199	+	0.999989i	$0.498503\pi$
$398$		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
$403$		−	534.030i		−	1.32514i
$404$		0			0
$405$	99.8737	−	255.924i	0.246602	−	0.631910i
$406$		0			0
$407$	−8.39983	−	8.39983i	−0.0206384	−	0.0206384i
$408$		0			0
$409$	−192.834			−0.471478			−0.235739	−	0.971816i	$-0.575751\pi$
$409$	−192.834			−0.471478			−0.235739	+	0.971816i	$0.575751\pi$
$410$		0			0
$411$	−443.334	+	443.334i	−1.07867	+	1.07867i
$412$		0			0
$413$		−	26.4164i		−	0.0639622i
$414$		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
$427$			49.9707i			0.117027i
$428$		0			0
$429$	−991.898	+	991.898i	−2.31212	+	2.31212i
$430$		0			0
$431$	33.2755			0.0772054			0.0386027	−	0.999255i	$-0.487709\pi$
$431$	33.2755			0.0772054			0.0386027	+	0.999255i	$0.487709\pi$
$432$		0			0
$433$	210.976	+	210.976i	0.487243	+	0.487243i	0.907435	−	0.420192i	$-0.138037\pi$
$433$	210.976	+	210.976i	0.487243	+	0.487243i	−0.420192	+	0.907435i	$0.638037\pi$
$434$		0			0
$435$	213.173	−	93.4960i	0.490052	−	0.214933i
$436$		0			0
$437$		−	66.0743i		−	0.151200i
$438$		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
$443$	−79.6496			−0.179796			−0.0898979	−	0.995951i	$-0.528654\pi$
$443$	−79.6496			−0.179796			−0.0898979	+	0.995951i	$0.528654\pi$
$444$		0			0
$445$	−53.6244	+	137.411i	−0.120504	+	0.308789i
$446$		0			0
$447$	612.278	−	612.278i	1.36975	−	1.36975i
$448$		0			0
$449$		−	816.938i		−	1.81946i	−0.415200	−	0.909730i	$-0.636288\pi$
$449$		−	816.938i		−	1.81946i	0.415200	−	0.909730i	$-0.363712\pi$
$450$		0			0
$451$	−371.370	−	371.370i	−0.823438	−	0.823438i
$452$		0			0
$453$	−785.838			−1.73474
$454$		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	$-0.370443\pi$
$457$	−238.754	−	238.754i	−0.522437	−	0.522437i	−0.918307	+	0.395870i	$0.870443\pi$
$458$		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	$-0.153415\pi$
$463$	195.645	+	195.645i	0.422559	+	0.422559i	−0.463525	+	0.886084i	$0.653415\pi$
$464$		0			0
$465$	−522.486	−	203.899i	−1.12363	−	0.438493i
$466$		0			0
$467$	−108.782			−0.232938			−0.116469	−	0.993194i	$-0.537158\pi$
$467$	−108.782			−0.232938			−0.116469	+	0.993194i	$0.537158\pi$
$468$		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
$475$	−242.605	+	10.0145i	−0.510747	+	0.0210832i
$476$		0			0
$477$	916.047			1.92043
$478$		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
$483$			66.1672i			0.136992i
$484$		0			0
$485$	32.9725	+	75.1781i	0.0679846	+	0.155006i
$486$		0			0
$487$	87.5337	+	87.5337i	0.179741	+	0.179741i	0.791243	−	0.611502i	$-0.209434\pi$
$487$	87.5337	+	87.5337i	0.179741	+	0.179741i	−0.611502	+	0.791243i	$0.709434\pi$
$488$		0			0
$489$	−927.595			−1.89692
$490$		0			0
$491$	481.445	−	481.445i	0.980540	−	0.980540i	−0.0192739	−	0.999814i	$-0.506135\pi$
$491$	481.445	−	481.445i	0.980540	−	0.980540i	0.999814	+	0.0192739i	$0.00613544\pi$
$492$		0			0
$493$		−	270.997i		−	0.549690i
$494$		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	−0.129186	−	0.991620i	$-0.541236\pi$
$503$	433.805	−	433.805i	0.862435	−	0.862435i	0.991620	+	0.129186i	$0.0412363\pi$
$504$		0			0
$505$	47.0768	+	107.336i	0.0932213	+	0.212547i
$506$		0			0
$507$		−	1312.23i		−	2.58822i
$508$		0			0
$509$	513.368	−	513.368i	1.00858	−	1.00858i	0.00861858	−	0.999963i	$-0.497257\pi$
$509$	513.368	−	513.368i	1.00858	−	1.00858i	0.999963	−	0.00861858i	$-0.00274341\pi$
$510$		0			0
$511$	−83.9248			−0.164236
$512$		0			0
$513$	−71.3269	−	71.3269i	−0.139039	−	0.139039i
$514$		0			0
$515$	−282.779	−	644.742i	−0.549085	−	1.25193i
$516$		0			0
$517$		−	194.955i		−	0.377088i
$518$		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
$523$	42.0347			0.0803723			0.0401862	−	0.999192i	$-0.487205\pi$
$523$	42.0347			0.0803723			0.0401862	+	0.999192i	$0.487205\pi$
$524$		0			0
$525$	242.946	−	10.0286i	0.462754	−	0.0191021i
$526$		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
$533$	776.422			1.45670
$534$		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
$547$	565.276			1.03341			0.516706	−	0.856163i	$-0.327158\pi$
$547$	565.276			1.03341			0.516706	+	0.856163i	$0.327158\pi$
$548$		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
$555$	6.70518	−	17.1819i	0.0120814	−	0.0309583i
$556$		0			0
$557$	972.870			1.74662			0.873312	−	0.487161i	$-0.161968\pi$
$557$	972.870			1.74662			0.873312	+	0.487161i	$0.161968\pi$
$558$		0			0
$559$		−	756.984i		−	1.35418i
$560$		0			0
$561$	1715.15			3.05730
$562$		0			0
$563$			827.358i			1.46955i	0.678310	+	0.734776i	$0.262713\pi$
$563$			827.358i			1.46955i	−0.678310	+	0.734776i	$0.737287\pi$
$564$		0			0
$565$	853.854	−	374.494i	1.51125	−	0.662821i
$566$		0			0
$567$	−83.8583	−	83.8583i	−0.147898	−	0.147898i
$568$		0			0
$569$	1016.20			1.78594			0.892970	−	0.450115i	$-0.148617\pi$
$569$	1016.20			1.78594			0.892970	+	0.450115i	$0.148617\pi$
$570$		0			0
$571$	381.530	−	381.530i	0.668178	−	0.668178i	−0.289116	−	0.957294i	$-0.593361\pi$
$571$	381.530	−	381.530i	0.668178	−	0.668178i	0.957294	+	0.289116i	$0.0933614\pi$
$572$		0			0
$573$		−	511.157i		−	0.892072i
$574$		0			0
$575$	−169.932	+	7.01464i	−0.295533	+	0.0121994i
$576$		0			0
$577$	−494.447	+	494.447i	−0.856928	+	0.856928i	−0.990975	−	0.134047i	$-0.957203\pi$
$577$	−494.447	+	494.447i	−0.856928	+	0.856928i	0.134047	+	0.990975i	$0.457203\pi$
$578$		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
$587$			1106.40i			1.88485i	0.334423	+	0.942423i	$0.391459\pi$
$587$			1106.40i			1.88485i	−0.334423	+	0.942423i	$0.608541\pi$
$588$		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	0.392294	−	0.919840i	$-0.371682\pi$
$593$	−312.835	−	312.835i	−0.527546	−	0.527546i	−0.919840	+	0.392294i	$0.871682\pi$
$594$		0			0
$595$	102.912	−	263.710i	0.172962	−	0.443210i
$596$		0			0
$597$			1026.93i			1.72016i
$598$		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
$603$	−527.694			−0.875114
$604$		0			0
$605$	417.230	+	162.823i	0.689636	+	0.269129i
$606$		0			0
$607$	434.724	−	434.724i	0.716185	−	0.716185i	−0.251636	−	0.967822i	$-0.580969\pi$
$607$	434.724	−	434.724i	0.716185	−	0.716185i	0.967822	+	0.251636i	$0.0809687\pi$
$608$		0			0
$609$		−	100.486i		−	0.165002i
$610$		0			0
$611$	203.795	+	203.795i	0.333544	+	0.333544i
$612$		0			0
$613$	−540.620			−0.881925			−0.440963	−	0.897525i	$-0.645363\pi$
$613$	−540.620			−0.881925			−0.440963	+	0.897525i	$0.645363\pi$
$614$		0			0
$615$	296.447	−	759.639i	0.482028	−	1.23518i
$616$		0			0
$617$	840.793	+	840.793i	1.36271	+	1.36271i	0.870445	+	0.492266i	$0.163831\pi$
$617$	840.793	+	840.793i	1.36271	+	1.36271i	0.492266	+	0.870445i	$0.336169\pi$
$618$		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
$627$	−635.085			−1.01290
$628$		0			0
$629$	−15.1833	−	15.1833i	−0.0241387	−	0.0241387i
$630$		0			0
$631$			685.081i			1.08571i	0.839827	+	0.542853i	$0.182656\pi$
$631$			685.081i			1.08571i	−0.839827	+	0.542853i	$0.817344\pi$
$632$		0			0
$633$	−732.866	+	732.866i	−1.15777	+	1.15777i
$634$		0			0
$635$	−437.845	−	998.296i	−0.689519	−	1.57212i
$636$		0			0
$637$	−951.231			−1.49330
$638$		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
$643$			566.933i			0.881700i	0.897581	+	0.440850i	$0.145323\pi$
$643$			566.933i			0.881700i	−0.897581	+	0.440850i	$0.854677\pi$
$644$		0			0
$645$	−740.621	−	289.026i	−1.14825	−	0.448102i
$646$		0			0
$647$	270.517	+	270.517i	0.418109	+	0.418109i	0.884552	−	0.466442i	$-0.154464\pi$
$647$	270.517	+	270.517i	0.418109	+	0.418109i	−0.466442	+	0.884552i	$0.654464\pi$
$648$		0			0
$649$	177.598			0.273648
$650$		0			0
$651$	−171.203	+	171.203i	−0.262984	+	0.262984i
$652$		0			0
$653$			724.152i			1.10896i	0.832197	+	0.554481i	$0.187083\pi$
$653$			724.152i			1.10896i	−0.832197	+	0.554481i	$0.812917\pi$
$654$		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
$667$			70.2862i			0.105377i
$668$		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	0.300989	−	0.953628i	$-0.402683\pi$
$673$	−439.226	−	439.226i	−0.652639	−	0.652639i	−0.953628	+	0.300989i	$0.902683\pi$
$674$		0			0
$675$	−175.868	+	191.013i	−0.260545	+	0.282982i
$676$		0			0
$677$			372.736i			0.550570i	0.961363	+	0.275285i	$0.0887722\pi$
$677$			372.736i			0.550570i	−0.961363	+	0.275285i	$0.911228\pi$
$678$		0			0
$679$	35.4376			0.0521909
$680$		0			0
$681$		−	1282.23i		−	1.88286i
$682$		0			0
$683$	2.98479			0.00437012			0.00218506	−	0.999998i	$-0.499304\pi$
$683$	2.98479			0.00437012			0.00218506	+	0.999998i	$0.499304\pi$
$684$		0			0
$685$	−637.106	+	279.430i	−0.930082	+	0.407927i
$686$		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	0.809095	−	0.587678i	$-0.199958\pi$
$691$	153.000	+	153.000i	0.221418	+	0.221418i	−0.587678	+	0.809095i	$0.699958\pi$
$692$		0			0
$693$	354.085			0.510945
$694$		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
$707$	50.5964			0.0715649
$708$		0			0
$709$	841.096	+	841.096i	1.18631	+	1.18631i	0.978079	+	0.208233i	$0.0667713\pi$
$709$	841.096	+	841.096i	1.18631	+	1.18631i	0.208233	+	0.978079i	$0.433229\pi$
$710$		0			0
$711$			900.166i			1.26606i
$712$		0			0
$713$	119.750	−	119.750i	0.167952	−	0.167952i
$714$		0			0
$715$	−1425.44	+	625.186i	−1.99362	+	0.874386i
$716$		0			0
$717$	−1039.73			−1.45011
$718$		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
$723$			747.327i			1.03365i
$724$		0			0
$725$	258.069	−	10.6529i	0.355958	−	0.0146936i
$726$		0			0
$727$	896.554	+	896.554i	1.23322	+	1.23322i	0.962718	+	0.270506i	$0.0871909\pi$
$727$	896.554	+	896.554i	1.23322	+	1.23322i	0.270506	+	0.962718i	$0.412809\pi$
$728$		0			0
$729$	1042.33			1.42981
$730$		0			0
$731$	−654.472	+	654.472i	−0.895311	+	0.895311i
$732$		0			0
$733$		−	83.0751i		−	0.113336i	−0.998393	−	0.0566678i	$-0.981952\pi$
$733$		−	83.0751i		−	0.113336i	0.998393	−	0.0566678i	$-0.0180476\pi$
$734$		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	−0.986994	−	0.160756i	$-0.948607\pi$
$743$	−613.895	+	613.895i	−0.826238	+	0.826238i	0.160756	+	0.986994i	$0.448607\pi$
$744$		0			0
$745$	879.893	−	385.914i	1.18106	−	0.518006i
$746$		0			0
$747$		−	333.491i		−	0.446440i
$748$		0			0
$749$	−240.842	+	240.842i	−0.321551	+	0.321551i
$750$		0			0
$751$	516.621			0.687911			0.343956	−	0.938986i	$-0.388233\pi$
$751$	516.621			0.687911			0.343956	+	0.938986i	$0.388233\pi$
$752$		0			0
$753$	−336.570	−	336.570i	−0.446973	−	0.446973i
$754$		0			0
$755$	−812.310	−	317.002i	−1.07591	−	0.419870i
$756$		0			0
$757$		−	1230.47i		−	1.62545i	−0.582644	−	0.812727i	$-0.697982\pi$
$757$		−	1230.47i		−	1.62545i	0.582644	−	0.812727i	$-0.302018\pi$
$758$		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
$763$	−118.476			−0.155277
$764$		0			0
$765$	595.510	+	1357.78i	0.778445	+	1.77487i
$766$		0			0
$767$	−185.651	+	185.651i	−0.242049	+	0.242049i
$768$		0			0
$769$		−	247.035i		−	0.321242i	−0.987016	−	0.160621i	$-0.948650\pi$
$769$		−	247.035i		−	0.321242i	0.987016	−	0.160621i	$-0.0513496\pi$
$770$		0			0
$771$	616.569	+	616.569i	0.799701	+	0.799701i
$772$		0			0
$773$	149.770			0.193751			0.0968756	−	0.995296i	$-0.469115\pi$
$773$	149.770			0.193751			0.0968756	+	0.995296i	$0.469115\pi$
$774$		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
$787$	1010.58			1.28409			0.642044	−	0.766668i	$-0.278087\pi$
$787$	1010.58			1.28409			0.642044	+	0.766668i	$0.278087\pi$
$788$		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
$795$	1700.75	+	663.716i	2.13931	+	0.834863i
$796$		0			0
$797$	−627.322			−0.787105			−0.393552	−	0.919302i	$-0.628754\pi$
$797$	−627.322			−0.787105			−0.393552	+	0.919302i	$0.628754\pi$
$798$		0			0
$799$		−	352.394i		−	0.441044i
$800$		0			0
$801$	−333.501			−0.416356
$802$		0			0
$803$		−	564.228i		−	0.702650i
$804$		0			0
$805$	−26.6915	+	68.3962i	−0.0331571	+	0.0849642i
$806$		0			0
$807$	468.864	+	468.864i	0.580996	+	0.580996i
$808$		0			0
$809$	1040.62			1.28631			0.643155	−	0.765736i	$-0.277625\pi$
$809$	1040.62			1.28631			0.643155	+	0.765736i	$0.277625\pi$
$810$		0			0
$811$	−51.2843	+	51.2843i	−0.0632359	+	0.0632359i	−0.738018	−	0.674782i	$-0.764238\pi$
$811$	−51.2843	+	51.2843i	−0.0632359	+	0.0632359i	0.674782	+	0.738018i	$0.264238\pi$
$812$		0			0
$813$		−	411.060i		−	0.505609i
$814$		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	−0.805466	−	0.592642i	$-0.798085\pi$
$823$	−175.154	+	175.154i	−0.212823	+	0.212823i	0.592642	+	0.805466i	$0.298085\pi$
$824$		0			0
$825$	67.4224	+	1633.33i	0.0817242	+	1.97979i
$826$		0			0
$827$			386.856i			0.467782i	0.972263	+	0.233891i	$0.0751459\pi$
$827$			386.856i			0.467782i	−0.972263	+	0.233891i	$0.924854\pi$
$828$		0			0
$829$	−94.0409	+	94.0409i	−0.113439	+	0.113439i	−0.761548	−	0.648109i	$-0.775560\pi$
$829$	−94.0409	+	94.0409i	−0.113439	+	0.113439i	0.648109	+	0.761548i	$0.275560\pi$
$830$		0			0
$831$	−393.111			−0.473058
$832$		0			0
$833$	822.414	+	822.414i	0.987291	+	0.987291i
$834$		0			0
$835$	−342.380	+	150.165i	−0.410036	+	0.179839i
$836$		0			0
$837$		−	258.539i		−	0.308888i
$838$		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
$843$	738.093			0.875556
$844$		0			0
$845$	529.345	−	1356.43i	0.626443	−	1.60524i
$846$		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
$853$	−1697.19			−1.98967			−0.994835	−	0.101505i	$-0.967634\pi$
$853$	−1697.19			−1.98967			−0.994835	+	0.101505i	$0.967634\pi$
$854$		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	$-0.492231\pi$
$857$	−835.829	−	835.829i	−0.975296	−	0.975296i	−0.999702	+	0.0244059i	$0.992231\pi$
$858$		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	0.999993	+	0.00382915i	$0.00121886\pi$
$863$	866.298	+	866.298i	1.00382	+	1.00382i	0.00382915	+	0.999993i	$0.498781\pi$
$864$		0			0
$865$	644.302	+	251.437i	0.744858	+	0.290679i
$866$		0			0
$867$	1797.99			2.07380
$868$		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
$875$	255.175	+	87.6364i	0.291629	+	0.100156i
$876$		0			0
$877$	708.097			0.807408			0.403704	−	0.914890i	$-0.367723\pi$
$877$	708.097			0.807408			0.403704	+	0.914890i	$0.367723\pi$
$878$		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
$883$			302.033i			0.342053i	0.985266	+	0.171027i	$0.0547085\pi$
$883$			302.033i			0.342053i	−0.985266	+	0.171027i	$0.945292\pi$
$884$		0			0
$885$	110.754	+	252.522i	0.125146	+	0.285336i
$886$		0			0
$887$	−961.511	−	961.511i	−1.08400	−	1.08400i	−0.996132	−	0.0878714i	$-0.971994\pi$
$887$	−961.511	−	961.511i	−1.08400	−	1.08400i	−0.0878714	−	0.996132i	$-0.528006\pi$
$888$		0			0
$889$	−470.579			−0.529335
$890$		0			0
$891$	563.781	−	563.781i	0.632751	−	0.632751i
$892$		0			0
$893$			130.485i			0.146119i
$894$		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
$907$		−	504.237i		−	0.555940i	−0.960590	−	0.277970i	$-0.910338\pi$
$907$		−	504.237i		−	0.555940i	0.960590	−	0.277970i	$-0.0896615\pi$
$908$		0			0
$909$	−187.383	+	187.383i	−0.206141	+	0.206141i
$910$		0			0
$911$	1061.71			1.16544			0.582718	−	0.812675i	$-0.301989\pi$
$911$	1061.71			1.16544			0.582718	+	0.812675i	$0.301989\pi$
$912$		0			0
$913$	−302.697	−	302.697i	−0.331541	−	0.331541i
$914$		0			0
$915$	−209.509	−	477.685i	−0.228972	−	0.522060i
$916$		0			0
$917$		−	391.691i		−	0.427144i
$918$		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
$923$	−1734.65			−1.87936
$924$		0			0
$925$	13.8621	−	15.0558i	0.0149861	−	0.0162766i
$926$		0			0
$927$	1125.56	−	1125.56i	1.21420	−	1.21420i
$928$		0			0
$929$		−	173.225i		−	0.186464i	−0.995644	−	0.0932321i	$-0.970280\pi$
$929$		−	173.225i		−	0.186464i	0.995644	−	0.0932321i	$-0.0297198\pi$
$930$		0			0
$931$	−304.524	−	304.524i	−0.327093	−	0.327093i
$932$		0			0
$933$	−171.839			−0.184179
$934$		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	$-0.0781715\pi$
$937$	681.081	+	681.081i	0.726874	+	0.726874i	−0.243122	+	0.969996i	$0.578171\pi$
$938$		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
$947$	334.816			0.353555			0.176777	−	0.984251i	$-0.443433\pi$
$947$	334.816			0.353555			0.176777	+	0.984251i	$0.443433\pi$
$948$		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	$-0.871770\pi$
$953$	−503.098	+	503.098i	−0.527909	+	0.527909i	0.392039	+	0.919949i	$0.371770\pi$
$954$		0			0
$955$	206.198	−	528.376i	0.215914	−	0.553274i
$956$		0			0
$957$	675.569			0.705923
$958$		0			0
$959$			300.321i			0.313160i
$960$		0			0
$961$	−341.311			−0.355163
$962$		0			0
$963$		−	1783.91i		−	1.85245i
$964$		0			0
$965$	−1343.48	+	589.240i	−1.39221	+	0.610611i
$966$		0			0
$967$	−855.714	−	855.714i	−0.884916	−	0.884916i	0.109113	−	0.994029i	$-0.465199\pi$
$967$	−855.714	−	855.714i	−0.884916	−	0.884916i	−0.994029	+	0.109113i	$0.965199\pi$
$968$		0			0
$969$	−1147.96			−1.18469
$970$		0			0
$971$	1101.75	−	1101.75i	1.13466	−	1.13466i	0.145267	−	0.989392i	$-0.453596\pi$
$971$	1101.75	−	1101.75i	1.13466	−	1.13466i	0.989392	−	0.145267i	$-0.0464043\pi$
$972$		0			0
$973$			272.772i			0.280342i
$974$		0			0
$975$	−1777.88	−	1636.92i	−1.82346	−	1.67889i
$976$		0			0
$977$	287.755	−	287.755i	0.294530	−	0.294530i	−0.544337	−	0.838867i	$-0.683219\pi$
$977$	287.755	−	287.755i	0.294530	−	0.294530i	0.838867	+	0.544337i	$0.183219\pi$
$978$		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	0.307176	−	0.951653i	$-0.400616\pi$
$983$	1237.43	−	1237.43i	1.25883	−	1.25883i	0.951653	−	0.307176i	$-0.0993842\pi$
$984$		0			0
$985$	−141.849	−	55.3563i	−0.144009	−	0.0561992i
$986$		0			0
$987$		−	130.668i		−	0.132389i
$988$		0			0
$989$	169.745	−	169.745i	0.171633	−	0.171633i
$990$		0			0
$991$	1513.43			1.52717			0.763586	−	0.645706i	$-0.223437\pi$
$991$	1513.43			1.52717			0.763586	+	0.645706i	$0.223437\pi$
$992$		0			0
$993$	491.600	+	491.600i	0.495066	+	0.495066i
$994$		0			0
$995$	−414.259	+	1061.53i	−0.416341	+	1.06686i
$996$		0			0
$997$		−	764.377i		−	0.766677i	−0.923608	−	0.383339i	$-0.874774\pi$
$997$		−	764.377i		−	0.766677i	0.923608	−	0.383339i	$-0.125226\pi$
$998$		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.i.b.33.19		44
4.3	odd	2		640.3.i.a.33.4		44
5.2	odd	4		640.3.t.b.417.19		44
8.3	odd	2		320.3.i.a.273.19		44
8.5	even	2		80.3.i.a.13.18	✓	44
16.3	odd	4		320.3.t.a.113.19		44
16.5	even	4		640.3.t.b.353.19		44
16.11	odd	4		640.3.t.a.353.4		44
16.13	even	4		80.3.t.a.53.6	yes	44
20.7	even	4		640.3.t.a.417.4		44
40.13	odd	4		400.3.t.b.157.17		44
40.27	even	4		320.3.t.a.17.19		44
40.29	even	2		400.3.i.b.93.5		44
40.37	odd	4		80.3.t.a.77.6	yes	44
80.13	odd	4		400.3.i.b.357.5		44
80.27	even	4		640.3.i.a.97.19		44
80.29	even	4		400.3.t.b.293.17		44
80.37	odd	4	inner	640.3.i.b.97.4		44
80.67	even	4		320.3.i.a.177.4		44
80.77	odd	4		80.3.i.a.37.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.18	✓	44	8.5	even	2
80.3.i.a.37.18	yes	44	80.77	odd	4
80.3.t.a.53.6	yes	44	16.13	even	4
80.3.t.a.77.6	yes	44	40.37	odd	4
320.3.i.a.177.4		44	80.67	even	4
320.3.i.a.273.19		44	8.3	odd	2
320.3.t.a.17.19		44	40.27	even	4
320.3.t.a.113.19		44	16.3	odd	4
400.3.i.b.93.5		44	40.29	even	2
400.3.i.b.357.5		44	80.13	odd	4
400.3.t.b.157.17		44	40.13	odd	4
400.3.t.b.293.17		44	80.29	even	4
640.3.i.a.33.4		44	4.3	odd	2
640.3.i.a.97.19		44	80.27	even	4
640.3.i.b.33.19		44	1.1	even	1	trivial
640.3.i.b.97.4		44	80.37	odd	4	inner
640.3.t.a.353.4		44	16.11	odd	4
640.3.t.a.417.4		44	20.7	even	4
640.3.t.b.353.19		44	16.5	even	4
640.3.t.b.417.19		44	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.50609i q^{3} +(-1.81773 + 4.65788i) q^{5} +(1.52625 + 1.52625i) q^{7} -11.3048 q^{9} +O(q^{10})\)	\(q+4.50609i q^{3} +(-1.81773 + 4.65788i) q^{5} +(1.52625 + 1.52625i) q^{7} -11.3048 q^{9} +(-10.2610 + 10.2610i) q^{11} -21.4526i q^{13} +(-20.9888 - 8.19085i) q^{15} +(-18.5474 + 18.5474i) q^{17} +(6.86774 - 6.86774i) q^{19} +(-6.87740 + 6.87740i) q^{21} +(4.81049 - 4.81049i) q^{23} +(-18.3917 - 16.9335i) q^{25} -10.3858i q^{27} +(-7.30552 + 7.30552i) q^{29} +24.8935 q^{31} +(-46.2368 - 46.2368i) q^{33} +(-9.88337 + 4.33477i) q^{35} +0.818619i q^{37} +96.6671 q^{39} +36.1925i q^{41} +35.2864 q^{43} +(20.5491 - 52.6566i) q^{45} +(-9.49981 + 9.49981i) q^{47} -44.3412i q^{49} +(-83.5763 - 83.5763i) q^{51} -81.0314 q^{53} +(-29.1427 - 66.4460i) q^{55} +(30.9466 + 30.9466i) q^{57} +(-8.65405 - 8.65405i) q^{59} +(16.3705 + 16.3705i) q^{61} +(-17.2539 - 17.2539i) q^{63} +(99.9235 + 38.9949i) q^{65} +46.6786 q^{67} +(21.6765 + 21.6765i) q^{69} -80.8598i q^{71} +(-27.4939 + 27.4939i) q^{73} +(76.3040 - 82.8748i) q^{75} -31.3215 q^{77} -79.6266i q^{79} -54.9442 q^{81} +29.4998i q^{83} +(-52.6775 - 120.106i) q^{85} +(-32.9193 - 32.9193i) q^{87} +29.5008 q^{89} +(32.7419 - 32.7419i) q^{91} +112.173i q^{93} +(19.5054 + 44.4728i) q^{95} +(11.6094 - 11.6094i) q^{97} +(115.999 - 115.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{5} - 108 q^{9}+O(q^{10}) \) 44 * q + 2 * q^5 - 108 * q^9	\( 44 q + 2 q^{5} - 108 q^{9} + 4 q^{11} - 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 8 q^{31} - 4 q^{33} - 96 q^{35} + 72 q^{39} - 124 q^{43} + 34 q^{45} - 4 q^{47} + 100 q^{51} + 4 q^{53} + 36 q^{57} - 64 q^{59} + 36 q^{61} - 200 q^{63} - 4 q^{65} + 292 q^{67} + 60 q^{69} + 48 q^{73} - 96 q^{75} - 192 q^{77} + 100 q^{81} - 48 q^{85} + 36 q^{87} - 188 q^{91} + 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q + 2 * q^5 - 108 * q^9 + 4 * q^11 - 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 8 * q^31 - 4 * q^33 - 96 * q^35 + 72 * q^39 - 124 * q^43 + 34 * q^45 - 4 * q^47 + 100 * q^51 + 4 * q^53 + 36 * q^57 - 64 * q^59 + 36 * q^61 - 200 * q^63 - 4 * q^65 + 292 * q^67 + 60 * q^69 + 48 * q^73 - 96 * q^75 - 192 * q^77 + 100 * q^81 - 48 * q^85 + 36 * q^87 - 188 * q^91 + 380 * q^95 - 4 * q^97 + 92 * q^99

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