LMFDB - Embedded newform 640.3.t.b.417.3

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			417.3
Character	$\chi$	$=$	640.417
Dual form			640.3.t.b.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.38426 q^{3} +(-1.54952 - 4.75384i) q^{5} +(-3.84157 + 3.84157i) q^{7} +10.2217 q^{9} +O(q^{10})$	\(q-4.38426 q^{3} +(-1.54952 - 4.75384i) q^{5} +(-3.84157 + 3.84157i) q^{7} +10.2217 q^{9} +(-1.14088 + 1.14088i) q^{11} -9.68938 q^{13} +(6.79348 + 20.8421i) q^{15} +(-12.6460 - 12.6460i) q^{17} +(-24.3373 + 24.3373i) q^{19} +(16.8424 - 16.8424i) q^{21} +(-24.0032 - 24.0032i) q^{23} +(-20.1980 + 14.7323i) q^{25} -5.35627 q^{27} +(21.4101 - 21.4101i) q^{29} +42.4278 q^{31} +(5.00192 - 5.00192i) q^{33} +(24.2148 + 12.3096i) q^{35} +37.4340 q^{37} +42.4807 q^{39} +2.23637i q^{41} +37.4392i q^{43} +(-15.8387 - 48.5924i) q^{45} +(17.4520 + 17.4520i) q^{47} +19.4847i q^{49} +(55.4434 + 55.4434i) q^{51} -32.3677i q^{53} +(7.19138 + 3.65575i) q^{55} +(106.701 - 106.701i) q^{57} +(21.2720 + 21.2720i) q^{59} +(52.5704 + 52.5704i) q^{61} +(-39.2674 + 39.2674i) q^{63} +(15.0139 + 46.0618i) q^{65} -82.6126i q^{67} +(105.236 + 105.236i) q^{69} -14.2246i q^{71} +(-10.2704 - 10.2704i) q^{73} +(88.5532 - 64.5903i) q^{75} -8.76554i q^{77} -55.6719i q^{79} -68.5121 q^{81} -38.4377 q^{83} +(-40.5219 + 79.7123i) q^{85} +(-93.8675 + 93.8675i) q^{87} +138.133 q^{89} +(37.2224 - 37.2224i) q^{91} -186.014 q^{93} +(153.407 + 77.9845i) q^{95} +(113.344 + 113.344i) q^{97} +(-11.6618 + 11.6618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−4.38426			−1.46142			−0.730709	−	0.682689i	$-0.760811\pi$
$3$	−4.38426			−1.46142			−0.730709	+	0.682689i	$0.760811\pi$
$4$		0			0
$5$	−1.54952	−	4.75384i	−0.309904	−	0.950768i
$5$	−1.54952	−	4.75384i	−0.309904	−	0.950768i
$6$		0			0
$7$	−3.84157	+	3.84157i	−0.548795	+	0.548795i	−0.926092	−	0.377297i	$-0.876854\pi$
$7$	−3.84157	+	3.84157i	−0.548795	+	0.548795i	0.377297	+	0.926092i	$0.376854\pi$
$8$		0			0
$9$	10.2217			1.13575
$10$		0			0
$11$	−1.14088	+	1.14088i	−0.103716	+	0.103716i	−0.757061	−	0.653344i	$-0.773365\pi$
$11$	−1.14088	+	1.14088i	−0.103716	+	0.103716i	0.653344	+	0.757061i	$0.273365\pi$
$12$		0			0
$13$	−9.68938			−0.745337			−0.372668	−	0.927965i	$-0.621557\pi$
$13$	−9.68938			−0.745337			−0.372668	+	0.927965i	$0.621557\pi$
$14$		0			0
$15$	6.79348	+	20.8421i	0.452899	+	1.38947i
$16$		0			0
$17$	−12.6460	−	12.6460i	−0.743883	−	0.743883i	0.229440	−	0.973323i	$-0.426311\pi$
$17$	−12.6460	−	12.6460i	−0.743883	−	0.743883i	−0.973323	+	0.229440i	$0.926311\pi$
$18$		0			0
$19$	−24.3373	+	24.3373i	−1.28091	+	1.28091i	−0.340760	+	0.940150i	$0.610684\pi$
$19$	−24.3373	+	24.3373i	−1.28091	+	1.28091i	−0.940150	+	0.340760i	$0.889316\pi$
$20$		0			0
$21$	16.8424	−	16.8424i	0.802020	−	0.802020i
$22$		0			0
$23$	−24.0032	−	24.0032i	−1.04362	−	1.04362i	−0.999004	−	0.0446119i	$-0.985795\pi$
$23$	−24.0032	−	24.0032i	−1.04362	−	1.04362i	−0.0446119	−	0.999004i	$-0.514205\pi$
$24$		0			0
$25$	−20.1980	+	14.7323i	−0.807920	+	0.589293i
$26$		0			0
$27$	−5.35627			−0.198381
$28$		0			0
$29$	21.4101	−	21.4101i	0.738280	−	0.738280i	−0.233965	−	0.972245i	$-0.575170\pi$
$29$	21.4101	−	21.4101i	0.738280	−	0.738280i	0.972245	+	0.233965i	$0.0751701\pi$
$30$		0			0
$31$	42.4278			1.36864			0.684319	−	0.729183i	$-0.260100\pi$
$31$	42.4278			1.36864			0.684319	+	0.729183i	$0.260100\pi$
$32$		0			0
$33$	5.00192	−	5.00192i	0.151573	−	0.151573i
$34$		0			0
$35$	24.2148	+	12.3096i	0.691850	+	0.351703i
$36$		0			0
$37$	37.4340			1.01173			0.505865	−	0.862613i	$-0.331174\pi$
$37$	37.4340			1.01173			0.505865	+	0.862613i	$0.331174\pi$
$38$		0			0
$39$	42.4807			1.08925
$40$		0			0
$41$			2.23637i			0.0545457i	0.999628	+	0.0272728i	$0.00868229\pi$
$41$			2.23637i			0.0545457i	−0.999628	+	0.0272728i	$0.991318\pi$
$42$		0			0
$43$			37.4392i			0.870679i	0.900266	+	0.435339i	$0.143372\pi$
$43$			37.4392i			0.870679i	−0.900266	+	0.435339i	$0.856628\pi$
$44$		0			0
$45$	−15.8387	−	48.5924i	−0.351971	−	1.07983i
$46$		0			0
$47$	17.4520	+	17.4520i	0.371319	+	0.371319i	0.867958	−	0.496638i	$-0.165432\pi$
$47$	17.4520	+	17.4520i	0.371319	+	0.371319i	−0.496638	+	0.867958i	$0.665432\pi$
$48$		0			0
$49$			19.4847i			0.397648i
$50$		0			0
$51$	55.4434	+	55.4434i	1.08712	+	1.08712i
$52$		0			0
$53$		−	32.3677i		−	0.610712i	−0.952238	−	0.305356i	$-0.901225\pi$
$53$		−	32.3677i		−	0.610712i	0.952238	−	0.305356i	$-0.0987754\pi$
$54$		0			0
$55$	7.19138	+	3.65575i	0.130752	+	0.0664682i
$56$		0			0
$57$	106.701	−	106.701i	1.87195	−	1.87195i
$58$		0			0
$59$	21.2720	+	21.2720i	0.360543	+	0.360543i	0.864013	−	0.503470i	$-0.167944\pi$
$59$	21.2720	+	21.2720i	0.360543	+	0.360543i	−0.503470	+	0.864013i	$0.667944\pi$
$60$		0			0
$61$	52.5704	+	52.5704i	0.861809	+	0.861809i	0.991548	−	0.129739i	$-0.0414139\pi$
$61$	52.5704	+	52.5704i	0.861809	+	0.861809i	−0.129739	+	0.991548i	$0.541414\pi$
$62$		0			0
$63$	−39.2674	+	39.2674i	−0.623291	+	0.623291i
$64$		0			0
$65$	15.0139	+	46.0618i	0.230983	+	0.708642i
$66$		0			0
$67$		−	82.6126i		−	1.23302i	−0.787346	−	0.616512i	$-0.788545\pi$
$67$		−	82.6126i		−	1.23302i	0.787346	−	0.616512i	$-0.211455\pi$
$68$		0			0
$69$	105.236	+	105.236i	1.52516	+	1.52516i
$70$		0			0
$71$		−	14.2246i		−	0.200347i	−0.994970	−	0.100174i	$-0.968060\pi$
$71$		−	14.2246i		−	0.200347i	0.994970	−	0.100174i	$-0.0319398\pi$
$72$		0			0
$73$	−10.2704	−	10.2704i	−0.140690	−	0.140690i	0.633254	−	0.773944i	$-0.281719\pi$
$73$	−10.2704	−	10.2704i	−0.140690	−	0.140690i	−0.773944	+	0.633254i	$0.781719\pi$
$74$		0			0
$75$	88.5532	−	64.5903i	1.18071	−	0.861204i
$76$		0			0
$77$		−	8.76554i		−	0.113838i
$78$		0			0
$79$		−	55.6719i		−	0.704707i	−0.935867	−	0.352354i	$-0.885381\pi$
$79$		−	55.6719i		−	0.704707i	0.935867	−	0.352354i	$-0.114619\pi$
$80$		0			0
$81$	−68.5121			−0.845828
$82$		0			0
$83$	−38.4377			−0.463105			−0.231553	−	0.972822i	$-0.574381\pi$
$83$	−38.4377			−0.463105			−0.231553	+	0.972822i	$0.574381\pi$
$84$		0			0
$85$	−40.5219	+	79.7123i	−0.476728	+	0.937792i
$86$		0			0
$87$	−93.8675	+	93.8675i	−1.07894	+	1.07894i
$88$		0			0
$89$	138.133			1.55206			0.776030	−	0.630696i	$-0.217231\pi$
$89$	138.133			1.55206			0.776030	+	0.630696i	$0.217231\pi$
$90$		0			0
$91$	37.2224	−	37.2224i	0.409037	−	0.409037i
$92$		0			0
$93$	−186.014			−2.00015
$94$		0			0
$95$	153.407	+	77.9845i	1.61481	+	0.820890i
$96$		0			0
$97$	113.344	+	113.344i	1.16850	+	1.16850i	0.982562	+	0.185938i	$0.0595323\pi$
$97$	113.344	+	113.344i	1.16850	+	1.16850i	0.185938	+	0.982562i	$0.440468\pi$
$98$		0			0
$99$	−11.6618	+	11.6618i	−0.117795	+	0.117795i
$100$		0			0
$101$	−13.3073	+	13.3073i	−0.131755	+	0.131755i	−0.769909	−	0.638154i	$-0.779698\pi$
$101$	−13.3073	+	13.3073i	−0.131755	+	0.131755i	0.638154	+	0.769909i	$0.279698\pi$
$102$		0			0
$103$	37.4630	+	37.4630i	0.363718	+	0.363718i	0.865180	−	0.501462i	$-0.167204\pi$
$103$	37.4630	+	37.4630i	0.363718	+	0.363718i	−0.501462	+	0.865180i	$0.667204\pi$
$104$		0			0
$105$	−106.164	−	53.9685i	−1.01108	−	0.513986i
$106$		0			0
$107$	−6.15039			−0.0574803			−0.0287401	−	0.999587i	$-0.509150\pi$
$107$	−6.15039			−0.0574803			−0.0287401	+	0.999587i	$0.509150\pi$
$108$		0			0
$109$	115.185	−	115.185i	1.05674	−	1.05674i	0.0584506	−	0.998290i	$-0.481384\pi$
$109$	115.185	−	115.185i	1.05674	−	1.05674i	0.998290	−	0.0584506i	$-0.0186160\pi$
$110$		0			0
$111$	−164.120			−1.47856
$112$		0			0
$113$	73.2667	−	73.2667i	0.648378	−	0.648378i	−0.304223	−	0.952601i	$-0.598397\pi$
$113$	73.2667	−	73.2667i	0.648378	−	0.648378i	0.952601	+	0.304223i	$0.0983967\pi$
$114$		0			0
$115$	−76.9139	+	151.301i	−0.668817	+	1.31566i
$116$		0			0
$117$	−99.0420			−0.846513
$118$		0			0
$119$	97.1610			0.816479
$120$		0			0
$121$			118.397i			0.978486i
$122$		0			0
$123$		−	9.80484i		−	0.0797141i
$124$		0			0
$125$	101.332	+	73.1900i	0.810658	+	0.585520i
$126$		0			0
$127$	−80.3378	−	80.3378i	−0.632581	−	0.632581i	0.316133	−	0.948715i	$-0.397615\pi$
$127$	−80.3378	−	80.3378i	−0.632581	−	0.632581i	−0.948715	+	0.316133i	$0.897615\pi$
$128$		0			0
$129$		−	164.143i		−	1.27243i
$130$		0			0
$131$	18.5843	+	18.5843i	0.141865	+	0.141865i	0.774472	−	0.632608i	$-0.218015\pi$
$131$	18.5843	+	18.5843i	0.141865	+	0.141865i	−0.632608	+	0.774472i	$0.718015\pi$
$132$		0			0
$133$		−	186.987i		−	1.40591i
$134$		0			0
$135$	8.29964	+	25.4629i	0.0614788	+	0.188614i
$136$		0			0
$137$	−83.5138	+	83.5138i	−0.609590	+	0.609590i	−0.942839	−	0.333249i	$-0.891855\pi$
$137$	−83.5138	+	83.5138i	−0.609590	+	0.609590i	0.333249	+	0.942839i	$0.391855\pi$
$138$		0			0
$139$	−0.886367	−	0.886367i	−0.00637674	−	0.00637674i	0.703911	−	0.710288i	$-0.251435\pi$
$139$	−0.886367	−	0.886367i	−0.00637674	−	0.00637674i	−0.710288	+	0.703911i	$0.751435\pi$
$140$		0			0
$141$	−76.5141	−	76.5141i	−0.542653	−	0.542653i
$142$		0			0
$143$	11.0544	−	11.0544i	0.0773037	−	0.0773037i
$144$		0			0
$145$	−134.956	−	68.6049i	−0.930729	−	0.473137i
$146$		0			0
$147$		−	85.4261i		−	0.581130i
$148$		0			0
$149$	−126.231	−	126.231i	−0.847186	−	0.847186i	0.142595	−	0.989781i	$-0.454455\pi$
$149$	−126.231	−	126.231i	−0.847186	−	0.847186i	−0.989781	+	0.142595i	$0.954455\pi$
$150$		0			0
$151$		−	85.8641i		−	0.568636i	−0.958730	−	0.284318i	$-0.908233\pi$
$151$		−	85.8641i		−	0.568636i	0.958730	−	0.284318i	$-0.0917672\pi$
$152$		0			0
$153$	−129.264	−	129.264i	−0.844862	−	0.844862i
$154$		0			0
$155$	−65.7426	−	201.695i	−0.424146	−	1.30126i
$156$		0			0
$157$			222.987i			1.42030i	0.704052	+	0.710148i	$0.251372\pi$
$157$			222.987i			1.42030i	−0.704052	+	0.710148i	$0.748628\pi$
$158$		0			0
$159$			141.908i			0.892506i
$160$		0			0
$161$	184.420			1.14546
$162$		0			0
$163$	−114.176			−0.700465			−0.350233	−	0.936663i	$-0.613897\pi$
$163$	−114.176			−0.700465			−0.350233	+	0.936663i	$0.613897\pi$
$164$		0			0
$165$	−31.5289	−	16.0277i	−0.191084	−	0.0971379i
$166$		0			0
$167$	−83.1357	+	83.1357i	−0.497818	+	0.497818i	−0.910758	−	0.412940i	$-0.864502\pi$
$167$	−83.1357	+	83.1357i	−0.497818	+	0.497818i	0.412940	+	0.910758i	$0.364502\pi$
$168$		0			0
$169$	−75.1159			−0.444473
$170$		0			0
$171$	−248.769	+	248.769i	−1.45479	+	1.45479i
$172$		0			0
$173$	−31.8309			−0.183993			−0.0919967	−	0.995759i	$-0.529325\pi$
$173$	−31.8309			−0.183993			−0.0919967	+	0.995759i	$0.529325\pi$
$174$		0			0
$175$	20.9967	−	134.187i	0.119981	−	0.766783i
$176$		0			0
$177$	−93.2620	−	93.2620i	−0.526904	−	0.526904i
$178$		0			0
$179$	197.541	−	197.541i	1.10358	−	1.10358i	0.109605	−	0.993975i	$-0.465041\pi$
$179$	197.541	−	197.541i	1.10358	−	1.10358i	0.993975	−	0.109605i	$-0.0349586\pi$
$180$		0			0
$181$	−85.6404	+	85.6404i	−0.473151	+	0.473151i	−0.902933	−	0.429782i	$-0.858591\pi$
$181$	−85.6404	+	85.6404i	−0.473151	+	0.473151i	0.429782	+	0.902933i	$0.358591\pi$
$182$		0			0
$183$	−230.482	−	230.482i	−1.25946	−	1.25946i
$184$		0			0
$185$	−58.0046	−	177.955i	−0.313538	−	0.961920i
$186$		0			0
$187$	28.8552			0.154306
$188$		0			0
$189$	20.5765	−	20.5765i	0.108870	−	0.108870i
$190$		0			0
$191$	6.70134			0.0350856			0.0175428	−	0.999846i	$-0.494416\pi$
$191$	6.70134			0.0350856			0.0175428	+	0.999846i	$0.494416\pi$
$192$		0			0
$193$	−201.285	+	201.285i	−1.04293	+	1.04293i	−0.0438900	+	0.999036i	$0.513975\pi$
$193$	−201.285	+	201.285i	−1.04293	+	1.04293i	−0.999036	+	0.0438900i	$0.986025\pi$
$194$		0			0
$195$	−65.8247	−	201.947i	−0.337562	−	1.03562i
$196$		0			0
$197$	−54.1842			−0.275047			−0.137523	−	0.990499i	$-0.543914\pi$
$197$	−54.1842			−0.275047			−0.137523	+	0.990499i	$0.543914\pi$
$198$		0			0
$199$	−82.2399			−0.413266			−0.206633	−	0.978419i	$-0.566251\pi$
$199$	−82.2399			−0.413266			−0.206633	+	0.978419i	$0.566251\pi$
$200$		0			0
$201$			362.195i			1.80196i
$202$		0			0
$203$			164.497i			0.810329i
$204$		0			0
$205$	10.6314	−	3.46530i	0.0518603	−	0.0169039i
$206$		0			0
$207$	−245.353	−	245.353i	−1.18528	−	1.18528i
$208$		0			0
$209$		−	55.5319i		−	0.265703i
$210$		0			0
$211$	75.9246	+	75.9246i	0.359832	+	0.359832i	0.863751	−	0.503919i	$-0.168109\pi$
$211$	75.9246	+	75.9246i	0.359832	+	0.359832i	−0.503919	+	0.863751i	$0.668109\pi$
$212$		0			0
$213$			62.3645i			0.292791i
$214$		0			0
$215$	177.980	−	58.0127i	0.827814	−	0.269826i
$216$		0			0
$217$	−162.989	+	162.989i	−0.751102	+	0.751102i
$218$		0			0
$219$	45.0280	+	45.0280i	0.205607	+	0.205607i
$220$		0			0
$221$	122.532	+	122.532i	0.554444	+	0.554444i
$222$		0			0
$223$	103.038	−	103.038i	0.462056	−	0.462056i	−0.437273	−	0.899329i	$-0.644056\pi$
$223$	103.038	−	103.038i	0.462056	−	0.462056i	0.899329	+	0.437273i	$0.144056\pi$
$224$		0			0
$225$	−206.458	+	150.589i	−0.917591	+	0.669286i
$226$		0			0
$227$		−	98.3454i		−	0.433240i	−0.976256	−	0.216620i	$-0.930497\pi$
$227$		−	98.3454i		−	0.433240i	0.976256	−	0.216620i	$-0.0695032\pi$
$228$		0			0
$229$	176.947	+	176.947i	0.772695	+	0.772695i	0.978577	−	0.205882i	$-0.0660061\pi$
$229$	176.947	+	176.947i	0.772695	+	0.772695i	−0.205882	+	0.978577i	$0.566006\pi$
$230$		0			0
$231$			38.4304i			0.166365i
$232$		0			0
$233$	177.619	+	177.619i	0.762312	+	0.762312i	0.976740	−	0.214427i	$-0.0687885\pi$
$233$	177.619	+	177.619i	0.762312	+	0.762312i	−0.214427	+	0.976740i	$0.568789\pi$
$234$		0			0
$235$	55.9218	−	110.006i	0.237965	−	0.468112i
$236$		0			0
$237$			244.080i			1.02987i
$238$		0			0
$239$			232.519i			0.972881i	0.873714	+	0.486440i	$0.161705\pi$
$239$			232.519i			0.972881i	−0.873714	+	0.486440i	$0.838295\pi$
$240$		0			0
$241$	146.374			0.607362			0.303681	−	0.952774i	$-0.401784\pi$
$241$	146.374			0.607362			0.303681	+	0.952774i	$0.401784\pi$
$242$		0			0
$243$	348.581			1.43449
$244$		0			0
$245$	92.6273	−	30.1919i	0.378071	−	0.123232i
$246$		0			0
$247$	235.813	−	235.813i	0.954710	−	0.954710i
$248$		0			0
$249$	168.521			0.676791
$250$		0			0
$251$	−172.155	+	172.155i	−0.685878	+	0.685878i	−0.961318	−	0.275440i	$-0.911176\pi$
$251$	−172.155	+	172.155i	−0.685878	+	0.685878i	0.275440	+	0.961318i	$0.411176\pi$
$252$		0			0
$253$	54.7695			0.216480
$254$		0			0
$255$	177.658	−	349.479i	0.696700	−	1.37051i
$256$		0			0
$257$	73.6289	+	73.6289i	0.286494	+	0.286494i	0.835692	−	0.549198i	$-0.185067\pi$
$257$	73.6289	+	73.6289i	0.286494	+	0.286494i	−0.549198	+	0.835692i	$0.685067\pi$
$258$		0			0
$259$	−143.805	+	143.805i	−0.555232	+	0.555232i
$260$		0			0
$261$	218.848	−	218.848i	0.838498	−	0.838498i
$262$		0			0
$263$	141.657	+	141.657i	0.538620	+	0.538620i	0.923123	−	0.384504i	$-0.125627\pi$
$263$	141.657	+	141.657i	0.538620	+	0.538620i	−0.384504	+	0.923123i	$0.625627\pi$
$264$		0			0
$265$	−153.871	+	50.1544i	−0.580645	+	0.189262i
$266$		0			0
$267$	−605.612			−2.26821
$268$		0			0
$269$	51.7648	−	51.7648i	0.192434	−	0.192434i	−0.604313	−	0.796747i	$-0.706552\pi$
$269$	51.7648	−	51.7648i	0.192434	−	0.192434i	0.796747	+	0.604313i	$0.206552\pi$
$270$		0			0
$271$	−92.2487			−0.340401			−0.170201	−	0.985409i	$-0.554442\pi$
$271$	−92.2487			−0.340401			−0.170201	+	0.985409i	$0.554442\pi$
$272$		0			0
$273$	−163.193	+	163.193i	−0.597775	+	0.597775i
$274$		0			0
$275$	6.23568	−	39.8513i	0.0226752	−	0.144914i
$276$		0			0
$277$	−169.623			−0.612357			−0.306179	−	0.951974i	$-0.599051\pi$
$277$	−169.623			−0.612357			−0.306179	+	0.951974i	$0.599051\pi$
$278$		0			0
$279$	433.684			1.55442
$280$		0			0
$281$			194.385i			0.691761i	0.938278	+	0.345881i	$0.112420\pi$
$281$			194.385i			0.691761i	−0.938278	+	0.345881i	$0.887580\pi$
$282$		0			0
$283$		−	523.679i		−	1.85046i	−0.379410	−	0.925229i	$-0.623873\pi$
$283$		−	523.679i		−	1.85046i	0.379410	−	0.925229i	$-0.376127\pi$
$284$		0			0
$285$	−672.574	−	341.904i	−2.35991	−	1.19966i
$286$		0			0
$287$	−8.59118	−	8.59118i	−0.0299344	−	0.0299344i
$288$		0			0
$289$			30.8432i			0.106724i
$290$		0			0
$291$	−496.931	−	496.931i	−1.70767	−	1.70767i
$292$		0			0
$293$			272.325i			0.929435i	0.885459	+	0.464718i	$0.153844\pi$
$293$			272.325i			0.929435i	−0.885459	+	0.464718i	$0.846156\pi$
$294$		0			0
$295$	68.1624	−	134.085i	0.231059	−	0.454526i
$296$		0			0
$297$	6.11087	−	6.11087i	0.0205753	−	0.0205753i
$298$		0			0
$299$	232.576	+	232.576i	0.777846	+	0.777846i
$300$		0			0
$301$	−143.825	−	143.825i	−0.477824	−	0.477824i
$302$		0			0
$303$	58.3426	−	58.3426i	0.192550	−	0.192550i
$304$		0			0
$305$	168.452	−	331.370i	0.552303	−	1.08646i
$306$		0			0
$307$			112.655i			0.366954i	0.983024	+	0.183477i	$0.0587353\pi$
$307$			112.655i			0.366954i	−0.983024	+	0.183477i	$0.941265\pi$
$308$		0			0
$309$	−164.247	−	164.247i	−0.531545	−	0.531545i
$310$		0			0
$311$			254.031i			0.816820i	0.912799	+	0.408410i	$0.133917\pi$
$311$			254.031i			0.816820i	−0.912799	+	0.408410i	$0.866083\pi$
$312$		0			0
$313$	22.4916	+	22.4916i	0.0718580	+	0.0718580i	0.742122	−	0.670264i	$-0.233819\pi$
$313$	22.4916	+	22.4916i	0.0718580	+	0.0718580i	−0.670264	+	0.742122i	$0.733819\pi$
$314$		0			0
$315$	247.516	+	125.825i	0.785766	+	0.399445i
$316$		0			0
$317$			379.973i			1.19865i	0.800504	+	0.599327i	$0.204565\pi$
$317$			379.973i			1.19865i	−0.800504	+	0.599327i	$0.795435\pi$
$318$		0			0
$319$			48.8528i			0.153144i
$320$		0			0
$321$	26.9649			0.0840028
$322$		0			0
$323$	615.539			1.90569
$324$		0			0
$325$	195.706	−	142.747i	0.602172	−	0.439222i
$326$		0			0
$327$	−505.000	+	505.000i	−1.54434	+	1.54434i
$328$		0			0
$329$	−134.086			−0.407556
$330$		0			0
$331$	56.7172	−	56.7172i	0.171351	−	0.171351i	−0.616222	−	0.787573i	$-0.711337\pi$
$331$	56.7172	−	56.7172i	0.171351	−	0.171351i	0.787573	+	0.616222i	$0.211337\pi$
$332$		0			0
$333$	382.639			1.14907
$334$		0			0
$335$	−392.727	+	128.010i	−1.17232	+	0.382118i
$336$		0			0
$337$	6.90955	+	6.90955i	0.0205031	+	0.0205031i	0.717284	−	0.696781i	$-0.245385\pi$
$337$	6.90955	+	6.90955i	0.0205031	+	0.0205031i	−0.696781	+	0.717284i	$0.745385\pi$
$338$		0			0
$339$	−321.220	+	321.220i	−0.947552	+	0.947552i
$340$		0			0
$341$	−48.4050	+	48.4050i	−0.141950	+	0.141950i
$342$		0			0
$343$	−263.089	−	263.089i	−0.767022	−	0.767022i
$344$		0			0
$345$	337.210	−	663.341i	0.977421	−	1.92273i
$346$		0			0
$347$	512.927			1.47817			0.739087	−	0.673610i	$-0.235257\pi$
$347$	512.927			1.47817			0.739087	+	0.673610i	$0.235257\pi$
$348$		0			0
$349$	335.325	−	335.325i	0.960817	−	0.960817i	−0.0384442	−	0.999261i	$-0.512240\pi$
$349$	335.325	−	335.325i	0.960817	−	0.960817i	0.999261	+	0.0384442i	$0.0122402\pi$
$350$		0			0
$351$	51.8990			0.147860
$352$		0			0
$353$	304.970	−	304.970i	0.863938	−	0.863938i	−0.127855	−	0.991793i	$-0.540809\pi$
$353$	304.970	−	304.970i	0.863938	−	0.863938i	0.991793	+	0.127855i	$0.0408092\pi$
$354$		0			0
$355$	−67.6217	+	22.0413i	−0.190484	+	0.0620883i
$356$		0			0
$357$	−425.979			−1.19322
$358$		0			0
$359$	−55.6486			−0.155010			−0.0775050	−	0.996992i	$-0.524695\pi$
$359$	−55.6486			−0.155010			−0.0775050	+	0.996992i	$0.524695\pi$
$360$		0			0
$361$		−	823.608i		−	2.28146i
$362$		0			0
$363$		−	519.082i		−	1.42998i
$364$		0			0
$365$	−32.9096	+	64.7380i	−0.0901634	+	0.177364i
$366$		0			0
$367$	185.365	+	185.365i	0.505081	+	0.505081i	0.913013	−	0.407931i	$-0.133750\pi$
$367$	185.365	+	185.365i	0.505081	+	0.505081i	−0.407931	+	0.913013i	$0.633750\pi$
$368$		0			0
$369$			22.8596i			0.0619500i
$370$		0			0
$371$	124.343	+	124.343i	0.335156	+	0.335156i
$372$		0			0
$373$		−	16.1719i		−	0.0433562i	−0.999765	−	0.0216781i	$-0.993099\pi$
$373$		−	16.1719i		−	0.0433562i	0.999765	−	0.0216781i	$-0.00690090\pi$
$374$		0			0
$375$	−444.267	−	320.884i	−1.18471	−	0.855690i
$376$		0			0
$377$	−207.451	+	207.451i	−0.550267	+	0.550267i
$378$		0			0
$379$	467.798	+	467.798i	1.23430	+	1.23430i	0.962298	+	0.271998i	$0.0876843\pi$
$379$	467.798	+	467.798i	1.23430	+	1.23430i	0.271998	+	0.962298i	$0.412316\pi$
$380$		0			0
$381$	352.222	+	352.222i	0.924466	+	0.924466i
$382$		0			0
$383$	138.301	−	138.301i	0.361100	−	0.361100i	−0.503118	−	0.864218i	$-0.667814\pi$
$383$	138.301	−	138.301i	0.361100	−	0.361100i	0.864218	+	0.503118i	$0.167814\pi$
$384$		0			0
$385$	−41.6700	+	13.5824i	−0.108234	+	0.0352789i
$386$		0			0
$387$			382.692i			0.988869i
$388$		0			0
$389$	−356.792	−	356.792i	−0.917202	−	0.917202i	0.0796230	−	0.996825i	$-0.474628\pi$
$389$	−356.792	−	356.792i	−0.917202	−	0.917202i	−0.996825	+	0.0796230i	$0.974628\pi$
$390$		0			0
$391$			607.089i			1.55266i
$392$		0			0
$393$	−81.4783	−	81.4783i	−0.207324	−	0.207324i
$394$		0			0
$395$	−264.655	+	86.2646i	−0.670013	+	0.218391i
$396$		0			0
$397$		−	287.234i		−	0.723511i	−0.932273	−	0.361755i	$-0.882178\pi$
$397$		−	287.234i		−	0.723511i	0.932273	−	0.361755i	$-0.117822\pi$
$398$		0			0
$399$			819.797i			2.05463i
$400$		0			0
$401$	178.508			0.445157			0.222579	−	0.974915i	$-0.428553\pi$
$401$	178.508			0.445157			0.222579	+	0.974915i	$0.428553\pi$
$402$		0			0
$403$	−411.099			−1.02010
$404$		0			0
$405$	106.161	+	325.695i	0.262125	+	0.804186i
$406$		0			0
$407$	−42.7077	+	42.7077i	−0.104933	+	0.104933i
$408$		0			0
$409$	−60.0556			−0.146835			−0.0734176	−	0.997301i	$-0.523391\pi$
$409$	−60.0556			−0.146835			−0.0734176	+	0.997301i	$0.523391\pi$
$410$		0			0
$411$	366.146	−	366.146i	0.890866	−	0.890866i
$412$		0			0
$413$	−163.436			−0.395728
$414$		0			0
$415$	59.5599	+	182.727i	0.143518	+	0.440306i
$416$		0			0
$417$	3.88606	+	3.88606i	0.00931909	+	0.00931909i
$418$		0			0
$419$	−258.872	+	258.872i	−0.617833	+	0.617833i	−0.944975	−	0.327142i	$-0.893914\pi$
$419$	−258.872	+	258.872i	−0.617833	+	0.617833i	0.327142	+	0.944975i	$0.393914\pi$
$420$		0			0
$421$	−429.322	+	429.322i	−1.01977	+	1.01977i	−0.0199654	+	0.999801i	$0.506356\pi$
$421$	−429.322	+	429.322i	−1.01977	+	1.01977i	−0.999801	+	0.0199654i	$0.993644\pi$
$422$		0			0
$423$	178.389	+	178.389i	0.421724	+	0.421724i
$424$		0			0
$425$	441.729	+	69.1189i	1.03936	+	0.162633i
$426$		0			0
$427$	−403.905			−0.945914
$428$		0			0
$429$	−48.4655	+	48.4655i	−0.112973	+	0.112973i
$430$		0			0
$431$	−412.636			−0.957392			−0.478696	−	0.877981i	$-0.658890\pi$
$431$	−412.636			−0.957392			−0.478696	+	0.877981i	$0.658890\pi$
$432$		0			0
$433$	−203.596	+	203.596i	−0.470200	+	0.470200i	−0.901979	−	0.431780i	$-0.857886\pi$
$433$	−203.596	+	203.596i	−0.470200	+	0.470200i	0.431780	+	0.901979i	$0.357886\pi$
$434$		0			0
$435$	591.680	+	300.782i	1.36018	+	0.691452i
$436$		0			0
$437$	1168.34			2.67356
$438$		0			0
$439$	−190.193			−0.433241			−0.216621	−	0.976256i	$-0.569503\pi$
$439$	−190.193			−0.433241			−0.216621	+	0.976256i	$0.569503\pi$
$440$		0			0
$441$			199.167i			0.451626i
$442$		0			0
$443$			255.432i			0.576595i	0.957541	+	0.288298i	$0.0930892\pi$
$443$			255.432i			0.576595i	−0.957541	+	0.288298i	$0.906911\pi$
$444$		0			0
$445$	−214.040	−	656.664i	−0.480989	−	1.47565i
$446$		0			0
$447$	553.428	+	553.428i	1.23809	+	1.23809i
$448$		0			0
$449$		−	569.939i		−	1.26935i	−0.772778	−	0.634676i	$-0.781133\pi$
$449$		−	569.939i		−	1.26935i	0.772778	−	0.634676i	$-0.218867\pi$
$450$		0			0
$451$	−2.55144	−	2.55144i	−0.00565729	−	0.00565729i
$452$		0			0
$453$			376.450i			0.831016i
$454$		0			0
$455$	−234.626	−	119.273i	−0.515662	−	0.262137i
$456$		0			0
$457$	288.400	−	288.400i	0.631072	−	0.631072i	−0.317265	−	0.948337i	$-0.602764\pi$
$457$	288.400	−	288.400i	0.631072	−	0.631072i	0.948337	+	0.317265i	$0.102764\pi$
$458$		0			0
$459$	67.7355	+	67.7355i	0.147572	+	0.147572i
$460$		0			0
$461$	184.673	+	184.673i	0.400593	+	0.400593i	0.878442	−	0.477849i	$-0.158583\pi$
$461$	184.673	+	184.673i	0.400593	+	0.400593i	−0.477849	+	0.878442i	$0.658583\pi$
$462$		0			0
$463$	232.357	−	232.357i	0.501850	−	0.501850i	−0.410162	−	0.912013i	$-0.634528\pi$
$463$	232.357	−	232.357i	0.501850	−	0.501850i	0.912013	+	0.410162i	$0.134528\pi$
$464$		0			0
$465$	288.232	+	884.282i	0.619855	+	1.90168i
$466$		0			0
$467$			360.961i			0.772937i	0.922303	+	0.386468i	$0.126305\pi$
$467$			360.961i			0.772937i	−0.922303	+	0.386468i	$0.873695\pi$
$468$		0			0
$469$	317.362	+	317.362i	0.676677	+	0.676677i
$470$		0			0
$471$		−	977.631i		−	2.07565i
$472$		0			0
$473$	−42.7137	−	42.7137i	−0.0903037	−	0.0903037i
$474$		0			0
$475$	133.020	−	850.109i	0.280041	−	1.78970i
$476$		0			0
$477$		−	330.853i		−	0.693613i
$478$		0			0
$479$		−	111.130i		−	0.232005i	−0.993249	−	0.116003i	$-0.962992\pi$
$479$		−	111.130i		−	0.232005i	0.993249	−	0.116003i	$-0.0370081\pi$
$480$		0			0
$481$	−362.712			−0.754079
$482$		0			0
$483$	−808.543			−1.67400
$484$		0			0
$485$	363.192	−	714.450i	0.748850	−	1.47309i
$486$		0			0
$487$	467.586	−	467.586i	0.960135	−	0.960135i	−0.0391007	−	0.999235i	$-0.512449\pi$
$487$	467.586	−	467.586i	0.960135	−	0.960135i	0.999235	+	0.0391007i	$0.0124493\pi$
$488$		0			0
$489$	500.576			1.02367
$490$		0			0
$491$	−333.638	+	333.638i	−0.679507	+	0.679507i	−0.959889	−	0.280382i	$-0.909539\pi$
$491$	−333.638	+	333.638i	−0.679507	+	0.679507i	0.280382	+	0.959889i	$0.409539\pi$
$492$		0			0
$493$	−541.505			−1.09839
$494$		0			0
$495$	73.5082	+	37.3680i	0.148501	+	0.0754909i
$496$		0			0
$497$	54.6449	+	54.6449i	0.109950	+	0.109950i
$498$		0			0
$499$	173.095	−	173.095i	0.346884	−	0.346884i	−0.512064	−	0.858947i	$-0.671119\pi$
$499$	173.095	−	173.095i	0.346884	−	0.346884i	0.858947	+	0.512064i	$0.171119\pi$
$500$		0			0
$501$	364.488	−	364.488i	0.727521	−	0.727521i
$502$		0			0
$503$	618.020	+	618.020i	1.22867	+	1.22867i	0.964468	+	0.264201i	$0.0851083\pi$
$503$	618.020	+	618.020i	1.22867	+	1.22867i	0.264201	+	0.964468i	$0.414892\pi$
$504$		0			0
$505$	83.8807	+	42.6409i	0.166100	+	0.0844374i
$506$		0			0
$507$	329.327			0.649561
$508$		0			0
$509$	519.035	−	519.035i	1.01972	−	1.01972i	0.0199135	−	0.999802i	$-0.493661\pi$
$509$	519.035	−	519.035i	1.01972	−	1.01972i	0.999802	−	0.0199135i	$-0.00633909\pi$
$510$		0			0
$511$	78.9088			0.154420
$512$		0			0
$513$	130.357	−	130.357i	0.254108	−	0.254108i
$514$		0			0
$515$	120.044	−	236.143i	0.233094	−	0.458529i
$516$		0			0
$517$	−39.8213			−0.0770238
$518$		0			0
$519$	139.555			0.268891
$520$		0			0
$521$		−	687.482i		−	1.31954i	−0.751467	−	0.659771i	$-0.770653\pi$
$521$		−	687.482i		−	1.31954i	0.751467	−	0.659771i	$-0.229347\pi$
$522$		0			0
$523$			472.937i			0.904277i	0.891948	+	0.452139i	$0.149339\pi$
$523$			472.937i			0.904277i	−0.891948	+	0.452139i	$0.850661\pi$
$524$		0			0
$525$	−92.0550	+	588.311i	−0.175343	+	1.12059i
$526$		0			0
$527$	−536.542	−	536.542i	−1.01811	−	1.01811i
$528$		0			0
$529$			623.305i			1.17827i
$530$		0			0
$531$	217.436	+	217.436i	0.409485	+	0.409485i
$532$		0			0
$533$		−	21.6691i		−	0.0406549i
$534$		0			0
$535$	9.53014	+	29.2380i	0.0178133	+	0.0546504i
$536$		0			0
$537$	−866.070	+	866.070i	−1.61279	+	1.61279i
$538$		0			0
$539$	−22.2298	−	22.2298i	−0.0412426	−	0.0412426i
$540$		0			0
$541$	−91.9662	−	91.9662i	−0.169993	−	0.169993i	0.616983	−	0.786976i	$-0.288355\pi$
$541$	−91.9662	−	91.9662i	−0.169993	−	0.169993i	−0.786976	+	0.616983i	$0.788355\pi$
$542$		0			0
$543$	375.469	−	375.469i	0.691472	−	0.691472i
$544$		0			0
$545$	−726.051	−	369.089i	−1.33220	−	0.677228i
$546$		0			0
$547$		−	238.842i		−	0.436640i	−0.975877	−	0.218320i	$-0.929942\pi$
$547$		−	238.842i		−	0.436640i	0.975877	−	0.218320i	$-0.0700577\pi$
$548$		0			0
$549$	537.359	+	537.359i	0.978796	+	0.978796i
$550$		0			0
$551$			1042.13i			1.89134i
$552$		0			0
$553$	213.867	+	213.867i	0.386740	+	0.386740i
$554$		0			0
$555$	254.307	+	780.201i	0.458211	+	1.40577i
$556$		0			0
$557$		−	181.535i		−	0.325915i	−0.986633	−	0.162958i	$-0.947897\pi$
$557$		−	181.535i		−	0.325915i	0.986633	−	0.162958i	$-0.0521034\pi$
$558$		0			0
$559$		−	362.763i		−	0.648949i
$560$		0			0
$561$	−126.509			−0.225505
$562$		0			0
$563$	759.434			1.34891			0.674453	−	0.738318i	$-0.264379\pi$
$563$	759.434			1.34891			0.674453	+	0.738318i	$0.264379\pi$
$564$		0			0
$565$	−461.826	−	234.770i	−0.817392	−	0.415523i
$566$		0			0
$567$	263.194	−	263.194i	0.464186	−	0.464186i
$568$		0			0
$569$	1063.33			1.86878			0.934388	−	0.356258i	$-0.115947\pi$
$569$	1063.33			1.86878			0.934388	+	0.356258i	$0.115947\pi$
$570$		0			0
$571$	−342.578	+	342.578i	−0.599962	+	0.599962i	−0.940302	−	0.340341i	$-0.889458\pi$
$571$	−342.578	+	342.578i	−0.599962	+	0.599962i	0.340341	+	0.940302i	$0.389458\pi$
$572$		0			0
$573$	−29.3804			−0.0512747
$574$		0			0
$575$	838.438	+	131.193i	1.45815	+	0.228162i
$576$		0			0
$577$	465.865	+	465.865i	0.807392	+	0.807392i	0.984239	−	0.176846i	$-0.0565895\pi$
$577$	465.865	+	465.865i	0.807392	+	0.807392i	−0.176846	+	0.984239i	$0.556590\pi$
$578$		0			0
$579$	882.484	−	882.484i	1.52415	−	1.52415i
$580$		0			0
$581$	147.661	−	147.661i	0.254150	−	0.254150i
$582$		0			0
$583$	36.9277	+	36.9277i	0.0633409	+	0.0633409i
$584$		0			0
$585$	153.467	+	470.830i	0.262337	+	0.804837i
$586$		0			0
$587$	−236.253			−0.402476			−0.201238	−	0.979542i	$-0.564496\pi$
$587$	−236.253			−0.402476			−0.201238	+	0.979542i	$0.564496\pi$
$588$		0			0
$589$	−1032.58	+	1032.58i	−1.75310	+	1.75310i
$590$		0			0
$591$	237.558			0.401959
$592$		0			0
$593$	208.498	−	208.498i	0.351599	−	0.351599i	−0.509106	−	0.860704i	$-0.670024\pi$
$593$	208.498	−	208.498i	0.351599	−	0.351599i	0.860704	+	0.509106i	$0.170024\pi$
$594$		0			0
$595$	−150.553	−	461.888i	−0.253030	−	0.776282i
$596$		0			0
$597$	360.561			0.603955
$598$		0			0
$599$	−100.435			−0.167670			−0.0838352	−	0.996480i	$-0.526717\pi$
$599$	−100.435			−0.167670			−0.0838352	+	0.996480i	$0.526717\pi$
$600$		0			0
$601$			189.816i			0.315834i	0.987452	+	0.157917i	$0.0504778\pi$
$601$			189.816i			0.315834i	−0.987452	+	0.157917i	$0.949522\pi$
$602$		0			0
$603$		−	844.442i		−	1.40040i
$604$		0			0
$605$	562.839	−	183.458i	0.930313	−	0.303236i
$606$		0			0
$607$	288.020	+	288.020i	0.474498	+	0.474498i	0.903367	−	0.428869i	$-0.141088\pi$
$607$	288.020	+	288.020i	0.474498	+	0.474498i	−0.428869	+	0.903367i	$0.641088\pi$
$608$		0			0
$609$		−	721.196i		−	1.18423i
$610$		0			0
$611$	−169.099	−	169.099i	−0.276758	−	0.276758i
$612$		0			0
$613$		−	194.536i		−	0.317351i	−0.987331	−	0.158676i	$-0.949278\pi$
$613$		−	194.536i		−	0.317351i	0.987331	−	0.158676i	$-0.0507224\pi$
$614$		0			0
$615$	−46.6106	+	15.1928i	−0.0757896	+	0.0247037i
$616$		0			0
$617$	−89.2331	+	89.2331i	−0.144624	+	0.144624i	−0.775712	−	0.631087i	$-0.782609\pi$
$617$	−89.2331	+	89.2331i	−0.144624	+	0.144624i	0.631087	+	0.775712i	$0.282609\pi$
$618$		0			0
$619$	−98.7690	−	98.7690i	−0.159562	−	0.159562i	0.622811	−	0.782373i	$-0.285991\pi$
$619$	−98.7690	−	98.7690i	−0.159562	−	0.159562i	−0.782373	+	0.622811i	$0.785991\pi$
$620$		0			0
$621$	128.568	+	128.568i	0.207033	+	0.207033i
$622$		0			0
$623$	−530.648	+	530.648i	−0.851763	+	0.851763i
$624$		0			0
$625$	190.917	−	595.126i	0.305468	−	0.952202i
$626$		0			0
$627$			243.466i			0.388303i
$628$		0			0
$629$	−473.390	−	473.390i	−0.752608	−	0.752608i
$630$		0			0
$631$		−	361.528i		−	0.572945i	−0.958089	−	0.286472i	$-0.907517\pi$
$631$		−	361.528i		−	0.572945i	0.958089	−	0.286472i	$-0.0924827\pi$
$632$		0			0
$633$	−332.873	−	332.873i	−0.525866	−	0.525866i
$634$		0			0
$635$	−257.428	+	506.398i	−0.405399	+	0.797477i
$636$		0			0
$637$		−	188.795i		−	0.296382i
$638$		0			0
$639$		−	145.400i		−	0.227543i
$640$		0			0
$641$	−225.925			−0.352458			−0.176229	−	0.984349i	$-0.556390\pi$
$641$	−225.925			−0.352458			−0.176229	+	0.984349i	$0.556390\pi$
$642$		0			0
$643$	−1219.79			−1.89703			−0.948515	−	0.316731i	$-0.897415\pi$
$643$	−1219.79			−1.89703			−0.948515	+	0.316731i	$0.897415\pi$
$644$		0			0
$645$	−780.310	+	254.343i	−1.20978	+	0.394330i
$646$		0			0
$647$	406.190	−	406.190i	0.627806	−	0.627806i	−0.319710	−	0.947516i	$-0.603585\pi$
$647$	406.190	−	406.190i	0.627806	−	0.627806i	0.947516	+	0.319710i	$0.103585\pi$
$648$		0			0
$649$	−48.5377			−0.0747885
$650$		0			0
$651$	714.586	−	714.586i	1.09767	−	1.09767i
$652$		0			0
$653$	652.961			0.999940			0.499970	−	0.866043i	$-0.333344\pi$
$653$	652.961			0.999940			0.499970	+	0.866043i	$0.333344\pi$
$654$		0			0
$655$	59.5500	−	117.143i	0.0909161	−	0.178845i
$656$		0			0
$657$	−104.981	−	104.981i	−0.159788	−	0.159788i
$658$		0			0
$659$	−565.772	+	565.772i	−0.858532	+	0.858532i	−0.991165	−	0.132634i	$-0.957657\pi$
$659$	−565.772	+	565.772i	−0.858532	+	0.858532i	0.132634	+	0.991165i	$0.457657\pi$
$660$		0			0
$661$	304.268	−	304.268i	0.460315	−	0.460315i	−0.438443	−	0.898759i	$-0.644470\pi$
$661$	304.268	−	304.268i	0.460315	−	0.460315i	0.898759	+	0.438443i	$0.144470\pi$
$662$		0			0
$663$	−537.212	−	537.212i	−0.810274	−	0.810274i
$664$		0			0
$665$	−888.905	+	289.739i	−1.33670	+	0.435698i
$666$		0			0
$667$	−1027.82			−1.54096
$668$		0			0
$669$	−451.747	+	451.747i	−0.675257	+	0.675257i
$670$		0			0
$671$	−119.953			−0.178768
$672$		0			0
$673$	−822.674	+	822.674i	−1.22240	+	1.22240i	−0.255621	+	0.966777i	$0.582280\pi$
$673$	−822.674	+	822.674i	−1.22240	+	1.22240i	−0.966777	+	0.255621i	$0.917720\pi$
$674$		0			0
$675$	108.186	−	78.9103i	0.160276	−	0.116904i
$676$		0			0
$677$	−796.004			−1.17578			−0.587890	−	0.808941i	$-0.700041\pi$
$677$	−796.004			−1.17578			−0.587890	+	0.808941i	$0.700041\pi$
$678$		0			0
$679$	−870.840			−1.28253
$680$		0			0
$681$			431.172i			0.633145i
$682$		0			0
$683$			949.934i			1.39083i	0.718610	+	0.695413i	$0.244778\pi$
$683$			949.934i			1.39083i	−0.718610	+	0.695413i	$0.755222\pi$
$684$		0			0
$685$	526.417	+	267.605i	0.768492	+	0.390664i
$686$		0			0
$687$	−775.782	−	775.782i	−1.12923	−	1.12923i
$688$		0			0
$689$			313.623i			0.455186i
$690$		0			0
$691$	882.517	+	882.517i	1.27716	+	1.27716i	0.942251	+	0.334908i	$0.108705\pi$
$691$	882.517	+	882.517i	1.27716	+	1.27716i	0.334908	+	0.942251i	$0.391295\pi$
$692$		0			0
$693$		−	89.5988i		−	0.129291i
$694$		0			0
$695$	−2.84021	+	5.58709i	−0.00408663	+	0.00803898i
$696$		0			0
$697$	28.2812	−	28.2812i	0.0405756	−	0.0405756i
$698$		0			0
$699$	−778.726	−	778.726i	−1.11406	−	1.11406i
$700$		0			0
$701$	42.7867	+	42.7867i	0.0610367	+	0.0610367i	0.736966	−	0.675930i	$-0.236258\pi$
$701$	42.7867	+	42.7867i	0.0610367	+	0.0610367i	−0.675930	+	0.736966i	$0.736258\pi$
$702$		0			0
$703$	−911.042	+	911.042i	−1.29593	+	1.29593i
$704$		0			0
$705$	−245.176	+	482.295i	−0.347767	+	0.684107i
$706$		0			0
$707$		−	102.242i		−	0.144613i
$708$		0			0
$709$	239.953	+	239.953i	0.338439	+	0.338439i	0.855780	−	0.517341i	$-0.173078\pi$
$709$	239.953	+	239.953i	0.338439	+	0.338439i	−0.517341	+	0.855780i	$0.673078\pi$
$710$		0			0
$711$		−	569.062i		−	0.800368i
$712$		0			0
$713$	−1018.40	−	1018.40i	−1.42833	−	1.42833i
$714$		0			0
$715$	−69.6800	−	35.4220i	−0.0974546	−	0.0495412i
$716$		0			0
$717$		−	1019.42i		−	1.42179i
$718$		0			0
$719$		−	840.915i		−	1.16956i	−0.811191	−	0.584781i	$-0.801181\pi$
$719$		−	840.915i		−	1.16956i	0.811191	−	0.584781i	$-0.198819\pi$
$720$		0			0
$721$	−287.833			−0.399214
$722$		0			0
$723$	−641.742			−0.887610
$724$		0			0
$725$	−117.021	+	747.862i	−0.161408	+	1.03153i
$726$		0			0
$727$	−8.90967	+	8.90967i	−0.0122554	+	0.0122554i	−0.713208	−	0.700953i	$-0.752758\pi$
$727$	−8.90967	+	8.90967i	−0.0122554	+	0.0122554i	0.700953	+	0.713208i	$0.252758\pi$
$728$		0			0
$729$	−911.660			−1.25056
$730$		0			0
$731$	473.456	−	473.456i	0.647683	−	0.647683i
$732$		0			0
$733$	−65.3306			−0.0891277			−0.0445639	−	0.999007i	$-0.514190\pi$
$733$	−65.3306			−0.0891277			−0.0445639	+	0.999007i	$0.514190\pi$
$734$		0			0
$735$	−406.102	+	132.369i	−0.552520	+	0.180094i
$736$		0			0
$737$	94.2511	+	94.2511i	0.127885	+	0.127885i
$738$		0			0
$739$	254.204	−	254.204i	0.343984	−	0.343984i	−0.513879	−	0.857863i	$-0.671792\pi$
$739$	254.204	−	254.204i	0.343984	−	0.343984i	0.857863	+	0.513879i	$0.171792\pi$
$740$		0			0
$741$	−1033.87	+	1033.87i	−1.39523	+	1.39523i
$742$		0			0
$743$	−6.53981	−	6.53981i	−0.00880189	−	0.00880189i	0.702692	−	0.711494i	$-0.251981\pi$
$743$	−6.53981	−	6.53981i	−0.00880189	−	0.00880189i	−0.711494	+	0.702692i	$0.751981\pi$
$744$		0			0
$745$	−404.484	+	795.678i	−0.542931	+	1.06802i
$746$		0			0
$747$	−392.899			−0.525969
$748$		0			0
$749$	23.6271	−	23.6271i	0.0315449	−	0.0315449i
$750$		0			0
$751$	−512.529			−0.682462			−0.341231	−	0.939979i	$-0.610844\pi$
$751$	−512.529			−0.682462			−0.341231	+	0.939979i	$0.610844\pi$
$752$		0			0
$753$	754.774	−	754.774i	1.00236	−	1.00236i
$754$		0			0
$755$	−408.184	+	133.048i	−0.540641	+	0.176222i
$756$		0			0
$757$	109.439			0.144570			0.0722849	−	0.997384i	$-0.476971\pi$
$757$	109.439			0.144570			0.0722849	+	0.997384i	$0.476971\pi$
$758$		0			0
$759$	−240.124			−0.316369
$760$		0			0
$761$			737.899i			0.969644i	0.874613	+	0.484822i	$0.161116\pi$
$761$			737.899i			0.969644i	−0.874613	+	0.484822i	$0.838884\pi$
$762$		0			0
$763$			884.980i			1.15987i
$764$		0			0
$765$	−414.203	+	814.796i	−0.541442	+	1.06509i
$766$		0			0
$767$	−206.113	−	206.113i	−0.268726	−	0.268726i
$768$		0			0
$769$		−	1218.07i		−	1.58396i	−0.610545	−	0.791981i	$-0.709050\pi$
$769$		−	1218.07i		−	1.58396i	0.610545	−	0.791981i	$-0.290950\pi$
$770$		0			0
$771$	−322.808	−	322.808i	−0.418687	−	0.418687i
$772$		0			0
$773$		−	1341.89i		−	1.73595i	−0.496612	−	0.867973i	$-0.665423\pi$
$773$		−	1341.89i		−	1.73595i	0.496612	−	0.867973i	$-0.334577\pi$
$774$		0			0
$775$	−856.956	+	625.060i	−1.10575	+	0.806529i
$776$		0			0
$777$	630.478	−	630.478i	0.811427	−	0.811427i
$778$		0			0
$779$	−54.4273	−	54.4273i	−0.0698681	−	0.0698681i
$780$		0			0
$781$	16.2286	+	16.2286i	0.0207793	+	0.0207793i
$782$		0			0
$783$	−114.678	+	114.678i	−0.146460	+	0.146460i
$784$		0			0
$785$	1060.04	−	345.522i	1.35037	−	0.440155i
$786$		0			0
$787$		−	1158.29i		−	1.47178i	−0.677099	−	0.735892i	$-0.736763\pi$
$787$		−	1158.29i		−	1.47178i	0.677099	−	0.735892i	$-0.263237\pi$
$788$		0			0
$789$	−621.060	−	621.060i	−0.787149	−	0.787149i
$790$		0			0
$791$			562.918i			0.711654i
$792$		0			0
$793$	−509.374	−	509.374i	−0.642338	−	0.642338i
$794$		0			0
$795$	674.610	−	219.890i	0.848566	−	0.276591i
$796$		0			0
$797$			67.0596i			0.0841400i	0.999115	+	0.0420700i	$0.0133952\pi$
$797$			67.0596i			0.0841400i	−0.999115	+	0.0420700i	$0.986605\pi$
$798$		0			0
$799$		−	441.396i		−	0.552436i
$800$		0			0
$801$	1411.96			1.76274
$802$		0			0
$803$	23.4346			0.0291838
$804$		0			0
$805$	−285.761	−	876.701i	−0.354983	−	1.08907i
$806$		0			0
$807$	−226.950	+	226.950i	−0.281227	+	0.281227i
$808$		0			0
$809$	−602.411			−0.744637			−0.372318	−	0.928105i	$-0.621437\pi$
$809$	−602.411			−0.744637			−0.372318	+	0.928105i	$0.621437\pi$
$810$		0			0
$811$	47.6019	−	47.6019i	0.0586953	−	0.0586953i	−0.677150	−	0.735845i	$-0.736785\pi$
$811$	47.6019	−	47.6019i	0.0586953	−	0.0586953i	0.735845	+	0.677150i	$0.236785\pi$
$812$		0			0
$813$	404.442			0.497469
$814$		0			0
$815$	176.918	+	542.774i	0.217077	+	0.665980i
$816$		0			0
$817$	−911.169	−	911.169i	−1.11526	−	1.11526i
$818$		0			0
$819$	380.476	−	380.476i	0.464562	−	0.464562i
$820$		0			0
$821$	−569.537	+	569.537i	−0.693711	+	0.693711i	−0.963046	−	0.269335i	$-0.913196\pi$
$821$	−569.537	+	569.537i	−0.693711	+	0.693711i	0.269335	+	0.963046i	$0.413196\pi$
$822$		0			0
$823$	−142.304	−	142.304i	−0.172909	−	0.172909i	0.615347	−	0.788256i	$-0.289016\pi$
$823$	−142.304	−	142.304i	−0.172909	−	0.172909i	−0.788256	+	0.615347i	$0.789016\pi$
$824$		0			0
$825$	−27.3388	+	174.718i	−0.0331380	+	0.211780i
$826$		0			0
$827$	829.310			1.00279			0.501397	−	0.865217i	$-0.332820\pi$
$827$	829.310			1.00279			0.501397	+	0.865217i	$0.332820\pi$
$828$		0			0
$829$	178.863	−	178.863i	0.215758	−	0.215758i	−0.590950	−	0.806708i	$-0.701247\pi$
$829$	178.863	−	178.863i	0.215758	−	0.215758i	0.806708	+	0.590950i	$0.201247\pi$
$830$		0			0
$831$	743.671			0.894911
$832$		0			0
$833$	246.404	−	246.404i	0.295803	−	0.295803i
$834$		0			0
$835$	524.034	+	266.393i	0.627585	+	0.319034i
$836$		0			0
$837$	−227.255			−0.271511
$838$		0			0
$839$	1632.17			1.94537			0.972686	−	0.232127i	$-0.0745685\pi$
$839$	1632.17			1.94537			0.972686	+	0.232127i	$0.0745685\pi$
$840$		0			0
$841$		−	75.7868i		−	0.0901151i
$842$		0			0
$843$		−	852.234i		−	1.01095i
$844$		0			0
$845$	116.393	+	357.089i	0.137744	+	0.422591i
$846$		0			0
$847$	−454.829	−	454.829i	−0.536988	−	0.536988i
$848$		0			0
$849$			2295.94i			2.70429i
$850$		0			0
$851$	−898.534	−	898.534i	−1.05586	−	1.05586i
$852$		0			0
$853$			1087.76i			1.27522i	0.770361	+	0.637608i	$0.220076\pi$
$853$			1087.76i			1.27522i	−0.770361	+	0.637608i	$0.779924\pi$
$854$		0			0
$855$	1568.08	+	797.135i	1.83401	+	0.932322i
$856$		0			0
$857$	753.252	−	753.252i	0.878940	−	0.878940i	−0.114485	−	0.993425i	$-0.536522\pi$
$857$	753.252	−	753.252i	0.878940	−	0.878940i	0.993425	+	0.114485i	$0.0365218\pi$
$858$		0			0
$859$	−656.780	−	656.780i	−0.764587	−	0.764587i	0.212561	−	0.977148i	$-0.431820\pi$
$859$	−656.780	−	656.780i	−0.764587	−	0.764587i	−0.977148	+	0.212561i	$0.931820\pi$
$860$		0			0
$861$	37.6659	+	37.6659i	0.0437467	+	0.0437467i
$862$		0			0
$863$	−6.97025	+	6.97025i	−0.00807676	+	0.00807676i	−0.711134	−	0.703057i	$-0.751818\pi$
$863$	−6.97025	+	6.97025i	−0.00807676	+	0.00807676i	0.703057	+	0.711134i	$0.251818\pi$
$864$		0			0
$865$	49.3225	+	151.319i	0.0570202	+	0.174935i
$866$		0			0
$867$		−	135.225i		−	0.155968i
$868$		0			0
$869$	63.5150	+	63.5150i	0.0730898	+	0.0730898i
$870$		0			0
$871$			800.465i			0.919018i
$872$		0			0
$873$	1158.57	+	1158.57i	1.32712	+	1.32712i
$874$		0			0
$875$	−670.439	+	108.110i	−0.766216	+	0.123555i
$876$		0			0
$877$			1467.43i			1.67324i	0.547787	+	0.836618i	$0.315471\pi$
$877$			1467.43i			1.67324i	−0.547787	+	0.836618i	$0.684529\pi$
$878$		0			0
$879$		−	1193.94i		−	1.35829i
$880$		0			0
$881$	−889.409			−1.00954			−0.504772	−	0.863252i	$-0.668424\pi$
$881$	−889.409			−1.00954			−0.504772	+	0.863252i	$0.668424\pi$
$882$		0			0
$883$	1602.95			1.81535			0.907674	−	0.419675i	$-0.137856\pi$
$883$	1602.95			1.81535			0.907674	+	0.419675i	$0.137856\pi$
$884$		0			0
$885$	−298.842	+	587.864i	−0.337674	+	0.664253i
$886$		0			0
$887$	−428.954	+	428.954i	−0.483601	+	0.483601i	−0.906280	−	0.422679i	$-0.861090\pi$
$887$	−428.954	+	428.954i	−0.483601	+	0.483601i	0.422679	+	0.906280i	$0.361090\pi$
$888$		0			0
$889$	617.246			0.694315
$890$		0			0
$891$	78.1641	−	78.1641i	0.0877263	−	0.0877263i
$892$		0			0
$893$	−849.469			−0.951253
$894$		0			0
$895$	−1245.17	−	632.985i	−1.39125	−	0.707245i
$896$		0			0
$897$	−1019.67	−	1019.67i	−1.13676	−	1.13676i
$898$		0			0
$899$	908.384	−	908.384i	1.01044	−	1.01044i
$900$		0			0
$901$	−409.323	+	409.323i	−0.454298	+	0.454298i
$902$		0			0
$903$	630.566	+	630.566i	0.698302	+	0.698302i
$904$		0			0
$905$	539.822	+	274.419i	0.596488	+	0.303226i
$906$		0			0
$907$	1609.72			1.77478			0.887388	−	0.461024i	$-0.152518\pi$
$907$	1609.72			1.77478			0.887388	+	0.461024i	$0.152518\pi$
$908$		0			0
$909$	−136.023	+	136.023i	−0.149641	+	0.149641i
$910$		0			0
$911$	1117.02			1.22615			0.613074	−	0.790025i	$-0.289933\pi$
$911$	1117.02			1.22615			0.613074	+	0.790025i	$0.289933\pi$
$912$		0			0
$913$	43.8529	−	43.8529i	0.0480316	−	0.0480316i
$914$		0			0
$915$	−738.539	+	1452.81i	−0.807146	+	1.58777i
$916$		0			0
$917$	−142.786			−0.155709
$918$		0			0
$919$	−750.127			−0.816242			−0.408121	−	0.912928i	$-0.633816\pi$
$919$	−750.127			−0.816242			−0.408121	+	0.912928i	$0.633816\pi$
$920$		0			0
$921$		−	493.908i		−	0.536273i
$922$		0			0
$923$			137.828i			0.149326i
$924$		0			0
$925$	−756.091	+	551.489i	−0.817396	+	0.596205i
$926$		0			0
$927$	382.936	+	382.936i	0.413091	+	0.413091i
$928$		0			0
$929$			1640.80i			1.76620i	0.469181	+	0.883102i	$0.344549\pi$
$929$			1640.80i			1.76620i	−0.469181	+	0.883102i	$0.655451\pi$
$930$		0			0
$931$	−474.206	−	474.206i	−0.509351	−	0.509351i
$932$		0			0
$933$		−	1113.74i		−	1.19372i
$934$		0			0
$935$	−44.7116	−	137.173i	−0.0478199	−	0.146709i
$936$		0			0
$937$	514.395	−	514.395i	0.548980	−	0.548980i	−0.377166	−	0.926146i	$-0.623101\pi$
$937$	514.395	−	514.395i	0.548980	−	0.548980i	0.926146	+	0.377166i	$0.123101\pi$
$938$		0			0
$939$	−98.6087	−	98.6087i	−0.105015	−	0.105015i
$940$		0			0
$941$	−1074.54	−	1074.54i	−1.14191	−	1.14191i	−0.988101	−	0.153808i	$-0.950846\pi$
$941$	−1074.54	−	1074.54i	−1.14191	−	1.14191i	−0.153808	−	0.988101i	$-0.549154\pi$
$942$		0			0
$943$	53.6801	−	53.6801i	0.0569248	−	0.0569248i
$944$		0			0
$945$	−129.701	−	65.9337i	−0.137250	−	0.0697711i
$946$		0			0
$947$		−	173.864i		−	0.183595i	−0.995778	−	0.0917974i	$-0.970739\pi$
$947$		−	173.864i		−	0.183595i	0.995778	−	0.0917974i	$-0.0292612\pi$
$948$		0			0
$949$	99.5137	+	99.5137i	0.104862	+	0.104862i
$950$		0			0
$951$		−	1665.90i		−	1.75174i
$952$		0			0
$953$	597.594	+	597.594i	0.627066	+	0.627066i	0.947329	−	0.320263i	$-0.103771\pi$
$953$	597.594	+	597.594i	0.627066	+	0.627066i	−0.320263	+	0.947329i	$0.603771\pi$
$954$		0			0
$955$	−10.3839	−	31.8571i	−0.0108731	−	0.0333582i
$956$		0			0
$957$		−	214.183i		−	0.223807i
$958$		0			0
$959$		−	641.648i		−	0.669080i
$960$		0			0
$961$	839.116			0.873170
$962$		0			0
$963$	−62.8675			−0.0652830
$964$		0			0
$965$	1268.77	+	644.981i	1.31479	+	0.668374i
$966$		0			0
$967$	734.726	−	734.726i	0.759800	−	0.759800i	−0.216486	−	0.976286i	$-0.569460\pi$
$967$	734.726	−	734.726i	0.759800	−	0.759800i	0.976286	+	0.216486i	$0.0694595\pi$
$968$		0			0
$969$	−2698.68			−2.78502
$970$		0			0
$971$	−797.762	+	797.762i	−0.821588	+	0.821588i	−0.986336	−	0.164748i	$-0.947319\pi$
$971$	−797.762	+	797.762i	−0.821588	+	0.821588i	0.164748	+	0.986336i	$0.447319\pi$
$972$		0			0
$973$	6.81008			0.00699905
$974$		0			0
$975$	−858.025	+	625.840i	−0.880026	+	0.641887i
$976$		0			0
$977$	1242.00	+	1242.00i	1.27124	+	1.27124i	0.945440	+	0.325795i	$0.105632\pi$
$977$	1242.00	+	1242.00i	1.27124	+	1.27124i	0.325795	+	0.945440i	$0.394368\pi$
$978$		0			0
$979$	−157.594	+	157.594i	−0.160974	+	0.160974i
$980$		0			0
$981$	1177.38	−	1177.38i	1.20019	−	1.20019i
$982$		0			0
$983$	−17.3080	−	17.3080i	−0.0176073	−	0.0176073i	0.698248	−	0.715856i	$-0.253963\pi$
$983$	−17.3080	−	17.3080i	−0.0176073	−	0.0176073i	−0.715856	+	0.698248i	$0.753963\pi$
$984$		0			0
$985$	83.9594	+	257.583i	0.0852380	+	0.261506i
$986$		0			0
$987$	587.868			0.595611
$988$		0			0
$989$	898.659	−	898.659i	0.908655	−	0.908655i
$990$		0			0
$991$	504.008			0.508585			0.254293	−	0.967127i	$-0.418157\pi$
$991$	504.008			0.508585			0.254293	+	0.967127i	$0.418157\pi$
$992$		0			0
$993$	−248.663	+	248.663i	−0.250416	+	0.250416i
$994$		0			0
$995$	127.432	+	390.956i	0.128073	+	0.392920i
$996$		0			0
$997$	1524.58			1.52917			0.764583	−	0.644526i	$-0.222945\pi$
$997$	1524.58			1.52917			0.764583	+	0.644526i	$0.222945\pi$
$998$		0			0
$999$	−200.507			−0.200707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.3.t.b.417.3		44
4.3	odd	2		640.3.t.a.417.20		44
5.3	odd	4		640.3.i.b.33.3		44
8.3	odd	2		320.3.t.a.17.3		44
8.5	even	2		80.3.t.a.77.2	yes	44
16.3	odd	4		320.3.i.a.177.20		44
16.5	even	4		640.3.i.b.97.20		44
16.11	odd	4		640.3.i.a.97.3		44
16.13	even	4		80.3.i.a.37.10	yes	44
20.3	even	4		640.3.i.a.33.20		44
40.3	even	4		320.3.i.a.273.3		44
40.13	odd	4		80.3.i.a.13.10	✓	44
40.29	even	2		400.3.t.b.157.21		44
40.37	odd	4		400.3.i.b.93.13		44
80.3	even	4		320.3.t.a.113.3		44
80.13	odd	4		80.3.t.a.53.2	yes	44
80.29	even	4		400.3.i.b.357.13		44
80.43	even	4		640.3.t.a.353.20		44
80.53	odd	4	inner	640.3.t.b.353.3		44
80.77	odd	4		400.3.t.b.293.21		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.10	✓	44	40.13	odd	4
80.3.i.a.37.10	yes	44	16.13	even	4
80.3.t.a.53.2	yes	44	80.13	odd	4
80.3.t.a.77.2	yes	44	8.5	even	2
320.3.i.a.177.20		44	16.3	odd	4
320.3.i.a.273.3		44	40.3	even	4
320.3.t.a.17.3		44	8.3	odd	2
320.3.t.a.113.3		44	80.3	even	4
400.3.i.b.93.13		44	40.37	odd	4
400.3.i.b.357.13		44	80.29	even	4
400.3.t.b.157.21		44	40.29	even	2
400.3.t.b.293.21		44	80.77	odd	4
640.3.i.a.33.20		44	20.3	even	4
640.3.i.a.97.3		44	16.11	odd	4
640.3.i.b.33.3		44	5.3	odd	4
640.3.i.b.97.20		44	16.5	even	4
640.3.t.a.353.20		44	80.43	even	4
640.3.t.a.417.20		44	4.3	odd	2
640.3.t.b.353.3		44	80.53	odd	4	inner
640.3.t.b.417.3		44	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-4.38426 q^{3} +(-1.54952 - 4.75384i) q^{5} +(-3.84157 + 3.84157i) q^{7} +10.2217 q^{9} +O(q^{10})\)	\(q-4.38426 q^{3} +(-1.54952 - 4.75384i) q^{5} +(-3.84157 + 3.84157i) q^{7} +10.2217 q^{9} +(-1.14088 + 1.14088i) q^{11} -9.68938 q^{13} +(6.79348 + 20.8421i) q^{15} +(-12.6460 - 12.6460i) q^{17} +(-24.3373 + 24.3373i) q^{19} +(16.8424 - 16.8424i) q^{21} +(-24.0032 - 24.0032i) q^{23} +(-20.1980 + 14.7323i) q^{25} -5.35627 q^{27} +(21.4101 - 21.4101i) q^{29} +42.4278 q^{31} +(5.00192 - 5.00192i) q^{33} +(24.2148 + 12.3096i) q^{35} +37.4340 q^{37} +42.4807 q^{39} +2.23637i q^{41} +37.4392i q^{43} +(-15.8387 - 48.5924i) q^{45} +(17.4520 + 17.4520i) q^{47} +19.4847i q^{49} +(55.4434 + 55.4434i) q^{51} -32.3677i q^{53} +(7.19138 + 3.65575i) q^{55} +(106.701 - 106.701i) q^{57} +(21.2720 + 21.2720i) q^{59} +(52.5704 + 52.5704i) q^{61} +(-39.2674 + 39.2674i) q^{63} +(15.0139 + 46.0618i) q^{65} -82.6126i q^{67} +(105.236 + 105.236i) q^{69} -14.2246i q^{71} +(-10.2704 - 10.2704i) q^{73} +(88.5532 - 64.5903i) q^{75} -8.76554i q^{77} -55.6719i q^{79} -68.5121 q^{81} -38.4377 q^{83} +(-40.5219 + 79.7123i) q^{85} +(-93.8675 + 93.8675i) q^{87} +138.133 q^{89} +(37.2224 - 37.2224i) q^{91} -186.014 q^{93} +(153.407 + 77.9845i) q^{95} +(113.344 + 113.344i) q^{97} +(-11.6618 + 11.6618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) \) 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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