LMFDB - Embedded newform 320.3.i.a.177.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(177,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("320.177");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.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:	$8.71936845953$
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			177.20
Character	$\chi$	$=$	320.177
Dual form			320.3.i.a.273.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.38426i q^{3} +(-4.75384 + 1.54952i) q^{5} +(-3.84157 + 3.84157i) q^{7} -10.2217 q^{9} +O(q^{10})$	\(q+4.38426i q^{3} +(-4.75384 + 1.54952i) q^{5} +(-3.84157 + 3.84157i) q^{7} -10.2217 q^{9} +(-1.14088 - 1.14088i) q^{11} -9.68938i q^{13} +(-6.79348 - 20.8421i) q^{15} +(-12.6460 - 12.6460i) q^{17} +(24.3373 + 24.3373i) q^{19} +(-16.8424 - 16.8424i) q^{21} +(-24.0032 - 24.0032i) q^{23} +(20.1980 - 14.7323i) q^{25} -5.35627i q^{27} +(21.4101 + 21.4101i) q^{29} -42.4278 q^{31} +(5.00192 - 5.00192i) q^{33} +(12.3096 - 24.2148i) q^{35} -37.4340i q^{37} +42.4807 q^{39} -2.23637i q^{41} -37.4392 q^{43} +(48.5924 - 15.8387i) q^{45} +(-17.4520 - 17.4520i) q^{47} +19.4847i q^{49} +(55.4434 - 55.4434i) q^{51} -32.3677 q^{53} +(7.19138 + 3.65575i) q^{55} +(-106.701 + 106.701i) q^{57} +(-21.2720 + 21.2720i) q^{59} +(-52.5704 + 52.5704i) q^{61} +(39.2674 - 39.2674i) q^{63} +(15.0139 + 46.0618i) q^{65} -82.6126 q^{67} +(105.236 - 105.236i) q^{69} -14.2246i q^{71} +(10.2704 + 10.2704i) q^{73} +(64.5903 + 88.5532i) q^{75} +8.76554 q^{77} +55.6719i q^{79} -68.5121 q^{81} +38.4377i q^{83} +(79.7123 + 40.5219i) q^{85} +(-93.8675 + 93.8675i) q^{87} -138.133 q^{89} +(37.2224 + 37.2224i) q^{91} -186.014i q^{93} +(-153.407 - 77.9845i) q^{95} +(113.344 + 113.344i) q^{97} +(11.6618 + 11.6618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$			4.38426i			1.46142i	0.682689	+	0.730709i	$0.260811\pi$
$3$			4.38426i			1.46142i	−0.682689	+	0.730709i	$0.739189\pi$
$4$		0			0
$5$	−4.75384	+	1.54952i	−0.950768	+	0.309904i
$5$	−4.75384	+	1.54952i	−0.950768	+	0.309904i
$6$		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	0.653344	−	0.757061i	$-0.273365\pi$
$11$	−1.14088	−	1.14088i	−0.103716	−	0.103716i	−0.757061	+	0.653344i	$0.773365\pi$
$12$		0			0
$13$		−	9.68938i		−	0.745337i	−0.927965	−	0.372668i	$-0.878443\pi$
$13$		−	9.68938i		−	0.745337i	0.927965	−	0.372668i	$-0.121557\pi$
$14$		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	0.940150	+	0.340760i	$0.110684\pi$
$19$	24.3373	+	24.3373i	1.28091	+	1.28091i	0.340760	+	0.940150i	$0.389316\pi$
$20$		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
$27$		−	5.35627i		−	0.198381i
$28$		0			0
$29$	21.4101	+	21.4101i	0.738280	+	0.738280i	0.972245	−	0.233965i	$-0.0751701\pi$
$29$	21.4101	+	21.4101i	0.738280	+	0.738280i	−0.233965	+	0.972245i	$0.575170\pi$
$30$		0			0
$31$	−42.4278			−1.36864			−0.684319	−	0.729183i	$-0.739900\pi$
$31$	−42.4278			−1.36864			−0.684319	+	0.729183i	$0.739900\pi$
$32$		0			0
$33$	5.00192	−	5.00192i	0.151573	−	0.151573i
$34$		0			0
$35$	12.3096	−	24.2148i	0.351703	−	0.691850i
$36$		0			0
$37$		−	37.4340i		−	1.01173i	−0.862613	−	0.505865i	$-0.831174\pi$
$37$		−	37.4340i		−	1.01173i	0.862613	−	0.505865i	$-0.168826\pi$
$38$		0			0
$39$	42.4807			1.08925
$40$		0			0
$41$		−	2.23637i		−	0.0545457i	−0.999628	−	0.0272728i	$-0.991318\pi$
$41$		−	2.23637i		−	0.0545457i	0.999628	−	0.0272728i	$-0.00868229\pi$
$42$		0			0
$43$	−37.4392			−0.870679			−0.435339	−	0.900266i	$-0.643372\pi$
$43$	−37.4392			−0.870679			−0.435339	+	0.900266i	$0.643372\pi$
$44$		0			0
$45$	48.5924	−	15.8387i	1.07983	−	0.351971i
$46$		0			0
$47$	−17.4520	−	17.4520i	−0.371319	−	0.371319i	0.496638	−	0.867958i	$-0.334568\pi$
$47$	−17.4520	−	17.4520i	−0.371319	−	0.371319i	−0.867958	+	0.496638i	$0.834568\pi$
$48$		0			0
$49$			19.4847i			0.397648i
$50$		0			0
$51$	55.4434	−	55.4434i	1.08712	−	1.08712i
$52$		0			0
$53$	−32.3677			−0.610712			−0.305356	−	0.952238i	$-0.598775\pi$
$53$	−32.3677			−0.610712			−0.305356	+	0.952238i	$0.598775\pi$
$54$		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	$-0.832056\pi$
$59$	−21.2720	+	21.2720i	−0.360543	+	0.360543i	0.503470	+	0.864013i	$0.332056\pi$
$60$		0			0
$61$	−52.5704	+	52.5704i	−0.861809	+	0.861809i	−0.991548	−	0.129739i	$-0.958586\pi$
$61$	−52.5704	+	52.5704i	−0.861809	+	0.861809i	0.129739	+	0.991548i	$0.458586\pi$
$62$		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
$67$	−82.6126			−1.23302			−0.616512	−	0.787346i	$-0.711455\pi$
$67$	−82.6126			−1.23302			−0.616512	+	0.787346i	$0.711455\pi$
$68$		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	0.773944	−	0.633254i	$-0.218281\pi$
$73$	10.2704	+	10.2704i	0.140690	+	0.140690i	−0.633254	+	0.773944i	$0.718281\pi$
$74$		0			0
$75$	64.5903	+	88.5532i	0.861204	+	1.18071i
$76$		0			0
$77$	8.76554			0.113838
$78$		0			0
$79$			55.6719i			0.704707i	0.935867	+	0.352354i	$0.114619\pi$
$79$			55.6719i			0.704707i	−0.935867	+	0.352354i	$0.885381\pi$
$80$		0			0
$81$	−68.5121			−0.845828
$82$		0			0
$83$			38.4377i			0.463105i	0.972822	+	0.231553i	$0.0743805\pi$
$83$			38.4377i			0.463105i	−0.972822	+	0.231553i	$0.925619\pi$
$84$		0			0
$85$	79.7123	+	40.5219i	0.937792	+	0.476728i
$86$		0			0
$87$	−93.8675	+	93.8675i	−1.07894	+	1.07894i
$88$		0			0
$89$	−138.133			−1.55206			−0.776030	−	0.630696i	$-0.782769\pi$
$89$	−138.133			−1.55206			−0.776030	+	0.630696i	$0.782769\pi$
$90$		0			0
$91$	37.2224	+	37.2224i	0.409037	+	0.409037i
$92$		0			0
$93$		−	186.014i		−	2.00015i
$94$		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	$-0.220302\pi$
$101$	13.3073	+	13.3073i	0.131755	+	0.131755i	−0.638154	+	0.769909i	$0.720302\pi$
$102$		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
$107$		−	6.15039i		−	0.0574803i	−0.999587	−	0.0287401i	$-0.990850\pi$
$107$		−	6.15039i		−	0.0574803i	0.999587	−	0.0287401i	$-0.00914953\pi$
$108$		0			0
$109$	115.185	+	115.185i	1.05674	+	1.05674i	0.998290	+	0.0584506i	$0.0186160\pi$
$109$	115.185	+	115.185i	1.05674	+	1.05674i	0.0584506	+	0.998290i	$0.481384\pi$
$110$		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
$115$	151.301	+	76.9139i	1.31566	+	0.668817i
$116$		0			0
$117$			99.0420i			0.846513i
$118$		0			0
$119$	97.1610			0.816479
$120$		0			0
$121$		−	118.397i		−	0.978486i
$122$		0			0
$123$	9.80484			0.0797141
$124$		0			0
$125$	−73.1900	+	101.332i	−0.585520	+	0.810658i
$126$		0			0
$127$	80.3378	+	80.3378i	0.632581	+	0.632581i	0.948715	−	0.316133i	$-0.102385\pi$
$127$	80.3378	+	80.3378i	0.632581	+	0.632581i	−0.316133	+	0.948715i	$0.602385\pi$
$128$		0			0
$129$		−	164.143i		−	1.27243i
$130$		0			0
$131$	18.5843	−	18.5843i	0.141865	−	0.141865i	−0.632608	−	0.774472i	$-0.718015\pi$
$131$	18.5843	−	18.5843i	0.141865	−	0.141865i	0.774472	+	0.632608i	$0.218015\pi$
$132$		0			0
$133$	−186.987			−1.40591
$134$		0			0
$135$	8.29964	+	25.4629i	0.0614788	+	0.188614i
$136$		0			0
$137$	83.5138	−	83.5138i	0.609590	−	0.609590i	−0.333249	−	0.942839i	$-0.608145\pi$
$137$	83.5138	−	83.5138i	0.609590	−	0.609590i	0.942839	+	0.333249i	$0.108145\pi$
$138$		0			0
$139$	0.886367	−	0.886367i	0.00637674	−	0.00637674i	−0.703911	−	0.710288i	$-0.748565\pi$
$139$	0.886367	−	0.886367i	0.00637674	−	0.00637674i	0.710288	+	0.703911i	$0.248565\pi$
$140$		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
$147$	−85.4261			−0.581130
$148$		0			0
$149$	−126.231	+	126.231i	−0.847186	+	0.847186i	−0.989781	−	0.142595i	$-0.954455\pi$
$149$	−126.231	+	126.231i	−0.847186	+	0.847186i	0.142595	+	0.989781i	$0.454455\pi$
$150$		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
$155$	201.695	−	65.7426i	1.30126	−	0.424146i
$156$		0			0
$157$	−222.987			−1.42030			−0.710148	−	0.704052i	$-0.751372\pi$
$157$	−222.987			−1.42030			−0.710148	+	0.704052i	$0.751372\pi$
$158$		0			0
$159$		−	141.908i		−	0.892506i
$160$		0			0
$161$	184.420			1.14546
$162$		0			0
$163$			114.176i			0.700465i	0.936663	+	0.350233i	$0.113897\pi$
$163$			114.176i			0.700465i	−0.936663	+	0.350233i	$0.886103\pi$
$164$		0			0
$165$	−16.0277	+	31.5289i	−0.0971379	+	0.191084i
$166$		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
$173$		−	31.8309i		−	0.183993i	−0.995759	−	0.0919967i	$-0.970675\pi$
$173$		−	31.8309i		−	0.183993i	0.995759	−	0.0919967i	$-0.0293249\pi$
$174$		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	−0.993975	−	0.109605i	$-0.965041\pi$
$179$	−197.541	−	197.541i	−1.10358	−	1.10358i	−0.109605	−	0.993975i	$-0.534959\pi$
$180$		0			0
$181$	85.6404	+	85.6404i	0.473151	+	0.473151i	0.902933	−	0.429782i	$-0.141409\pi$
$181$	85.6404	+	85.6404i	0.473151	+	0.473151i	−0.429782	+	0.902933i	$0.641409\pi$
$182$		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
$187$			28.8552i			0.154306i
$188$		0			0
$189$	20.5765	+	20.5765i	0.108870	+	0.108870i
$190$		0			0
$191$	−6.70134			−0.0350856			−0.0175428	−	0.999846i	$-0.505584\pi$
$191$	−6.70134			−0.0350856			−0.0175428	+	0.999846i	$0.505584\pi$
$192$		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
$195$	−201.947	+	65.8247i	−1.03562	+	0.337562i
$196$		0			0
$197$			54.1842i			0.275047i	0.990499	+	0.137523i	$0.0439142\pi$
$197$			54.1842i			0.275047i	−0.990499	+	0.137523i	$0.956086\pi$
$198$		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
$203$	−164.497			−0.810329
$204$		0			0
$205$	3.46530	+	10.6314i	0.0169039	+	0.0518603i
$206$		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	−0.503919	−	0.863751i	$-0.668109\pi$
$211$	75.9246	−	75.9246i	0.359832	−	0.359832i	0.863751	+	0.503919i	$0.168109\pi$
$212$		0			0
$213$	62.3645			0.292791
$214$		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	−0.899329	−	0.437273i	$-0.855944\pi$
$223$	−103.038	+	103.038i	−0.462056	+	0.462056i	0.437273	+	0.899329i	$0.355944\pi$
$224$		0			0
$225$	−206.458	+	150.589i	−0.917591	+	0.669286i
$226$		0			0
$227$	−98.3454			−0.433240			−0.216620	−	0.976256i	$-0.569503\pi$
$227$	−98.3454			−0.433240			−0.216620	+	0.976256i	$0.569503\pi$
$228$		0			0
$229$	176.947	−	176.947i	0.772695	−	0.772695i	−0.205882	−	0.978577i	$-0.566006\pi$
$229$	176.947	−	176.947i	0.772695	−	0.772695i	0.978577	+	0.205882i	$0.0660061\pi$
$230$		0			0
$231$			38.4304i			0.166365i
$232$		0			0
$233$	−177.619	−	177.619i	−0.762312	−	0.762312i	0.214427	−	0.976740i	$-0.431211\pi$
$233$	−177.619	−	177.619i	−0.762312	−	0.762312i	−0.976740	+	0.214427i	$0.931211\pi$
$234$		0			0
$235$	110.006	+	55.9218i	0.468112	+	0.237965i
$236$		0			0
$237$	−244.080			−1.02987
$238$		0			0
$239$		−	232.519i		−	0.972881i	−0.873714	−	0.486440i	$-0.838295\pi$
$239$		−	232.519i		−	0.972881i	0.873714	−	0.486440i	$-0.161705\pi$
$240$		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
$243$		−	348.581i		−	1.43449i
$244$		0			0
$245$	−30.1919	−	92.6273i	−0.123232	−	0.378071i
$246$		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	0.275440	−	0.961318i	$-0.411176\pi$
$251$	−172.155	−	172.155i	−0.685878	−	0.685878i	−0.961318	+	0.275440i	$0.911176\pi$
$252$		0			0
$253$			54.7695i			0.216480i
$254$		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
$267$		−	605.612i		−	2.26821i
$268$		0			0
$269$	51.7648	+	51.7648i	0.192434	+	0.192434i	0.796747	−	0.604313i	$-0.206552\pi$
$269$	51.7648	+	51.7648i	0.192434	+	0.192434i	−0.604313	+	0.796747i	$0.706552\pi$
$270$		0			0
$271$	92.2487			0.340401			0.170201	−	0.985409i	$-0.445558\pi$
$271$	92.2487			0.340401			0.170201	+	0.985409i	$0.445558\pi$
$272$		0			0
$273$	−163.193	+	163.193i	−0.597775	+	0.597775i
$274$		0			0
$275$	−39.8513	−	6.23568i	−0.144914	−	0.0226752i
$276$		0			0
$277$			169.623i			0.612357i	0.951974	+	0.306179i	$0.0990505\pi$
$277$			169.623i			0.612357i	−0.951974	+	0.306179i	$0.900949\pi$
$278$		0			0
$279$	433.684			1.55442
$280$		0			0
$281$		−	194.385i		−	0.691761i	−0.938278	−	0.345881i	$-0.887580\pi$
$281$		−	194.385i		−	0.691761i	0.938278	−	0.345881i	$-0.112420\pi$
$282$		0			0
$283$	523.679			1.85046			0.925229	−	0.379410i	$-0.123873\pi$
$283$	523.679			1.85046			0.925229	+	0.379410i	$0.123873\pi$
$284$		0			0
$285$	341.904	−	672.574i	1.19966	−	2.35991i
$286$		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
$293$	272.325			0.929435			0.464718	−	0.885459i	$-0.346156\pi$
$293$	272.325			0.929435			0.464718	+	0.885459i	$0.346156\pi$
$294$		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
$307$	112.655			0.366954			0.183477	−	0.983024i	$-0.441265\pi$
$307$	112.655			0.366954			0.183477	+	0.983024i	$0.441265\pi$
$308$		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	0.670264	−	0.742122i	$-0.266181\pi$
$313$	−22.4916	−	22.4916i	−0.0718580	−	0.0718580i	−0.742122	+	0.670264i	$0.766181\pi$
$314$		0			0
$315$	−125.825	+	247.516i	−0.399445	+	0.785766i
$316$		0			0
$317$	−379.973			−1.19865			−0.599327	−	0.800504i	$-0.704565\pi$
$317$	−379.973			−1.19865			−0.599327	+	0.800504i	$0.704565\pi$
$318$		0			0
$319$		−	48.8528i		−	0.153144i
$320$		0			0
$321$	26.9649			0.0840028
$322$		0			0
$323$		−	615.539i		−	1.90569i
$324$		0			0
$325$	−142.747	−	195.706i	−0.439222	−	0.602172i
$326$		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	0.787573	−	0.616222i	$-0.211337\pi$
$331$	56.7172	+	56.7172i	0.171351	+	0.171351i	−0.616222	+	0.787573i	$0.711337\pi$
$332$		0			0
$333$			382.639i			1.14907i
$334$		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
$347$			512.927i			1.47817i	0.673610	+	0.739087i	$0.264743\pi$
$347$			512.927i			1.47817i	−0.673610	+	0.739087i	$0.735257\pi$
$348$		0			0
$349$	335.325	+	335.325i	0.960817	+	0.960817i	0.999261	−	0.0384442i	$-0.0122402\pi$
$349$	335.325	+	335.325i	0.960817	+	0.960817i	−0.0384442	+	0.999261i	$0.512240\pi$
$350$		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
$355$	22.0413	+	67.6217i	0.0620883	+	0.190484i
$356$		0			0
$357$			425.979i			1.19322i
$358$		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
$363$	519.082			1.42998
$364$		0			0
$365$	−64.7380	−	32.9096i	−0.177364	−	0.0901634i
$366$		0			0
$367$	−185.365	−	185.365i	−0.505081	−	0.505081i	0.407931	−	0.913013i	$-0.366250\pi$
$367$	−185.365	−	185.365i	−0.505081	−	0.505081i	−0.913013	+	0.407931i	$0.866250\pi$
$368$		0			0
$369$			22.8596i			0.0619500i
$370$		0			0
$371$	124.343	−	124.343i	0.335156	−	0.335156i
$372$		0			0
$373$	−16.1719			−0.0433562			−0.0216781	−	0.999765i	$-0.506901\pi$
$373$	−16.1719			−0.0433562			−0.0216781	+	0.999765i	$0.506901\pi$
$374$		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	−0.271998	+	0.962298i	$0.587684\pi$
$379$	−467.798	+	467.798i	−1.23430	+	1.23430i	−0.962298	+	0.271998i	$0.912316\pi$
$380$		0			0
$381$	−352.222	+	352.222i	−0.924466	+	0.924466i
$382$		0			0
$383$	−138.301	+	138.301i	−0.361100	+	0.361100i	−0.864218	−	0.503118i	$-0.832186\pi$
$383$	−138.301	+	138.301i	−0.361100	+	0.361100i	0.503118	+	0.864218i	$0.332186\pi$
$384$		0			0
$385$	−41.6700	+	13.5824i	−0.108234	+	0.0352789i
$386$		0			0
$387$	382.692			0.988869
$388$		0			0
$389$	−356.792	+	356.792i	−0.917202	+	0.917202i	−0.996825	−	0.0796230i	$-0.974628\pi$
$389$	−356.792	+	356.792i	−0.917202	+	0.917202i	0.0796230	+	0.996825i	$0.474628\pi$
$390$		0			0
$391$			607.089i			1.55266i
$392$		0			0
$393$	81.4783	+	81.4783i	0.207324	+	0.207324i
$394$		0			0
$395$	−86.2646	−	264.655i	−0.218391	−	0.670013i
$396$		0			0
$397$	287.234			0.723511			0.361755	−	0.932273i	$-0.382178\pi$
$397$	287.234			0.723511			0.361755	+	0.932273i	$0.382178\pi$
$398$		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
$403$			411.099i			1.02010i
$404$		0			0
$405$	325.695	−	106.161i	0.804186	−	0.262125i
$406$		0			0
$407$	−42.7077	+	42.7077i	−0.104933	+	0.104933i
$408$		0			0
$409$	60.0556			0.146835			0.0734176	−	0.997301i	$-0.476609\pi$
$409$	60.0556			0.146835			0.0734176	+	0.997301i	$0.476609\pi$
$410$		0			0
$411$	366.146	+	366.146i	0.890866	+	0.890866i
$412$		0			0
$413$		−	163.436i		−	0.395728i
$414$		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	$-0.106086\pi$
$419$	258.872	+	258.872i	0.617833	+	0.617833i	−0.327142	+	0.944975i	$0.606086\pi$
$420$		0			0
$421$	429.322	+	429.322i	1.01977	+	1.01977i	0.999801	+	0.0199654i	$0.00635560\pi$
$421$	429.322	+	429.322i	1.01977	+	1.01977i	0.0199654	+	0.999801i	$0.493644\pi$
$422$		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
$427$		−	403.905i		−	0.945914i
$428$		0			0
$429$	−48.4655	−	48.4655i	−0.112973	−	0.112973i
$430$		0			0
$431$	412.636			0.957392			0.478696	−	0.877981i	$-0.341110\pi$
$431$	412.636			0.957392			0.478696	+	0.877981i	$0.341110\pi$
$432$		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
$435$	300.782	−	591.680i	0.691452	−	1.36018i
$436$		0			0
$437$		−	1168.34i		−	2.67356i
$438$		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
$443$	−255.432			−0.576595			−0.288298	−	0.957541i	$-0.593089\pi$
$443$	−255.432			−0.576595			−0.288298	+	0.957541i	$0.593089\pi$
$444$		0			0
$445$	656.664	−	214.040i	1.47565	−	0.480989i
$446$		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
$453$	376.450			0.831016
$454$		0			0
$455$	−234.626	−	119.273i	−0.515662	−	0.262137i
$456$		0			0
$457$	−288.400	+	288.400i	−0.631072	+	0.631072i	−0.948337	−	0.317265i	$-0.897236\pi$
$457$	−288.400	+	288.400i	−0.631072	+	0.631072i	0.317265	+	0.948337i	$0.397236\pi$
$458$		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	$-0.841417\pi$
$461$	−184.673	+	184.673i	−0.400593	+	0.400593i	0.477849	+	0.878442i	$0.341417\pi$
$462$		0			0
$463$	−232.357	+	232.357i	−0.501850	+	0.501850i	−0.912013	−	0.410162i	$-0.865472\pi$
$463$	−232.357	+	232.357i	−0.501850	+	0.501850i	0.410162	+	0.912013i	$0.365472\pi$
$464$		0			0
$465$	288.232	+	884.282i	0.619855	+	1.90168i
$466$		0			0
$467$	360.961			0.772937			0.386468	−	0.922303i	$-0.373695\pi$
$467$	360.961			0.772937			0.386468	+	0.922303i	$0.373695\pi$
$468$		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
$475$	850.109	+	133.020i	1.78970	+	0.280041i
$476$		0			0
$477$	330.853			0.693613
$478$		0			0
$479$			111.130i			0.232005i	0.993249	+	0.116003i	$0.0370081\pi$
$479$			111.130i			0.232005i	−0.993249	+	0.116003i	$0.962992\pi$
$480$		0			0
$481$	−362.712			−0.754079
$482$		0			0
$483$			808.543i			1.67400i
$484$		0			0
$485$	−714.450	−	363.192i	−1.47309	−	0.748850i
$486$		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	0.280382	−	0.959889i	$-0.409539\pi$
$491$	−333.638	−	333.638i	−0.679507	−	0.679507i	−0.959889	+	0.280382i	$0.909539\pi$
$492$		0			0
$493$		−	541.505i		−	1.09839i
$494$		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	$-0.328881\pi$
$499$	−173.095	−	173.095i	−0.346884	−	0.346884i	−0.858947	+	0.512064i	$0.828881\pi$
$500$		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
$507$			329.327i			0.649561i
$508$		0			0
$509$	519.035	+	519.035i	1.01972	+	1.01972i	0.999802	+	0.0199135i	$0.00633909\pi$
$509$	519.035	+	519.035i	1.01972	+	1.01972i	0.0199135	+	0.999802i	$0.493661\pi$
$510$		0			0
$511$	−78.9088			−0.154420
$512$		0			0
$513$	130.357	−	130.357i	0.254108	−	0.254108i
$514$		0			0
$515$	−236.143	−	120.044i	−0.458529	−	0.233094i
$516$		0			0
$517$			39.8213i			0.0770238i
$518$		0			0
$519$	139.555			0.268891
$520$		0			0
$521$			687.482i			1.31954i	0.751467	+	0.659771i	$0.229347\pi$
$521$			687.482i			1.31954i	−0.751467	+	0.659771i	$0.770653\pi$
$522$		0			0
$523$	−472.937			−0.904277			−0.452139	−	0.891948i	$-0.649339\pi$
$523$	−472.937			−0.904277			−0.452139	+	0.891948i	$0.649339\pi$
$524$		0			0
$525$	−588.311	−	92.0550i	−1.12059	−	0.175343i
$526$		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
$533$	−21.6691			−0.0406549
$534$		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	$-0.711645\pi$
$541$	91.9662	−	91.9662i	0.169993	−	0.169993i	0.786976	+	0.616983i	$0.211645\pi$
$542$		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
$547$	−238.842			−0.436640			−0.218320	−	0.975877i	$-0.570058\pi$
$547$	−238.842			−0.436640			−0.218320	+	0.975877i	$0.570058\pi$
$548$		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
$555$	−780.201	+	254.307i	−1.40577	+	0.458211i
$556$		0			0
$557$	181.535			0.325915			0.162958	−	0.986633i	$-0.447897\pi$
$557$	181.535			0.325915			0.162958	+	0.986633i	$0.447897\pi$
$558$		0			0
$559$			362.763i			0.648949i
$560$		0			0
$561$	−126.509			−0.225505
$562$		0			0
$563$		−	759.434i		−	1.34891i	−0.738318	−	0.674453i	$-0.764379\pi$
$563$		−	759.434i		−	1.34891i	0.738318	−	0.674453i	$-0.235621\pi$
$564$		0			0
$565$	−234.770	+	461.826i	−0.415523	+	0.817392i
$566$		0			0
$567$	263.194	−	263.194i	0.464186	−	0.464186i
$568$		0			0
$569$	−1063.33			−1.86878			−0.934388	−	0.356258i	$-0.884053\pi$
$569$	−1063.33			−1.86878			−0.934388	+	0.356258i	$0.884053\pi$
$570$		0			0
$571$	−342.578	−	342.578i	−0.599962	−	0.599962i	0.340341	−	0.940302i	$-0.389458\pi$
$571$	−342.578	−	342.578i	−0.599962	−	0.599962i	−0.940302	+	0.340341i	$0.889458\pi$
$572$		0			0
$573$		−	29.3804i		−	0.0512747i
$574$		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
$587$		−	236.253i		−	0.402476i	−0.979542	−	0.201238i	$-0.935504\pi$
$587$		−	236.253i		−	0.402476i	0.979542	−	0.201238i	$-0.0644964\pi$
$588$		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
$595$	−461.888	+	150.553i	−0.776282	+	0.253030i
$596$		0			0
$597$		−	360.561i		−	0.603955i
$598$		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	$-0.949522\pi$
$601$		−	189.816i		−	0.315834i	0.987452	−	0.157917i	$-0.0504778\pi$
$602$		0			0
$603$	844.442			1.40040
$604$		0			0
$605$	183.458	+	562.839i	0.303236	+	0.930313i
$606$		0			0
$607$	−288.020	−	288.020i	−0.474498	−	0.474498i	0.428869	−	0.903367i	$-0.358912\pi$
$607$	−288.020	−	288.020i	−0.474498	−	0.474498i	−0.903367	+	0.428869i	$0.858912\pi$
$608$		0			0
$609$		−	721.196i		−	1.18423i
$610$		0			0
$611$	−169.099	+	169.099i	−0.276758	+	0.276758i
$612$		0			0
$613$	−194.536			−0.317351			−0.158676	−	0.987331i	$-0.550722\pi$
$613$	−194.536			−0.317351			−0.158676	+	0.987331i	$0.550722\pi$
$614$		0			0
$615$	−46.6106	+	15.1928i	−0.0757896	+	0.0247037i
$616$		0			0
$617$	89.2331	−	89.2331i	0.144624	−	0.144624i	−0.631087	−	0.775712i	$-0.717391\pi$
$617$	89.2331	−	89.2331i	0.144624	−	0.144624i	0.775712	+	0.631087i	$0.217391\pi$
$618$		0			0
$619$	98.7690	−	98.7690i	0.159562	−	0.159562i	−0.622811	−	0.782373i	$-0.714009\pi$
$619$	98.7690	−	98.7690i	0.159562	−	0.159562i	0.782373	+	0.622811i	$0.214009\pi$
$620$		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
$627$	243.466			0.388303
$628$		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
$635$	−506.398	−	257.428i	−0.797477	−	0.405399i
$636$		0			0
$637$	188.795			0.296382
$638$		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
$643$			1219.79i			1.89703i	0.316731	+	0.948515i	$0.397415\pi$
$643$			1219.79i			1.89703i	−0.316731	+	0.948515i	$0.602585\pi$
$644$		0			0
$645$	254.343	+	780.310i	0.394330	+	1.20978i
$646$		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
$653$			652.961i			0.999940i	0.866043	+	0.499970i	$0.166656\pi$
$653$			652.961i			0.999940i	−0.866043	+	0.499970i	$0.833344\pi$
$654$		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	$-0.0423434\pi$
$659$	565.772	+	565.772i	0.858532	+	0.858532i	−0.132634	+	0.991165i	$0.542343\pi$
$660$		0			0
$661$	−304.268	−	304.268i	−0.460315	−	0.460315i	0.438443	−	0.898759i	$-0.355530\pi$
$661$	−304.268	−	304.268i	−0.460315	−	0.460315i	−0.898759	+	0.438443i	$0.855530\pi$
$662$		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
$667$		−	1027.82i		−	1.54096i
$668$		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
$675$	−78.9103	−	108.186i	−0.116904	−	0.160276i
$676$		0			0
$677$			796.004i			1.17578i	0.808941	+	0.587890i	$0.200041\pi$
$677$			796.004i			1.17578i	−0.808941	+	0.587890i	$0.799959\pi$
$678$		0			0
$679$	−870.840			−1.28253
$680$		0			0
$681$		−	431.172i		−	0.633145i
$682$		0			0
$683$	−949.934			−1.39083			−0.695413	−	0.718610i	$-0.744778\pi$
$683$	−949.934			−1.39083			−0.695413	+	0.718610i	$0.744778\pi$
$684$		0			0
$685$	−267.605	+	526.417i	−0.390664	+	0.768492i
$686$		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	0.334908	−	0.942251i	$-0.391295\pi$
$691$	882.517	−	882.517i	1.27716	−	1.27716i	0.942251	−	0.334908i	$-0.108705\pi$
$692$		0			0
$693$	−89.5988			−0.129291
$694$		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	$-0.763742\pi$
$701$	−42.7867	+	42.7867i	−0.0610367	+	0.0610367i	0.675930	+	0.736966i	$0.263742\pi$
$702$		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
$707$	−102.242			−0.144613
$708$		0			0
$709$	239.953	−	239.953i	0.338439	−	0.338439i	−0.517341	−	0.855780i	$-0.673078\pi$
$709$	239.953	−	239.953i	0.338439	−	0.338439i	0.855780	+	0.517341i	$0.173078\pi$
$710$		0			0
$711$		−	569.062i		−	0.800368i
$712$		0			0
$713$	1018.40	+	1018.40i	1.42833	+	1.42833i
$714$		0			0
$715$	35.4220	−	69.6800i	0.0495412	−	0.0974546i
$716$		0			0
$717$	1019.42			1.42179
$718$		0			0
$719$			840.915i			1.16956i	0.811191	+	0.584781i	$0.198819\pi$
$719$			840.915i			1.16956i	−0.811191	+	0.584781i	$0.801181\pi$
$720$		0			0
$721$	−287.833			−0.399214
$722$		0			0
$723$			641.742i			0.887610i
$724$		0			0
$725$	747.862	+	117.021i	1.03153	+	0.161408i
$726$		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
$733$		−	65.3306i		−	0.0891277i	−0.999007	−	0.0445639i	$-0.985810\pi$
$733$		−	65.3306i		−	0.0891277i	0.999007	−	0.0445639i	$-0.0141898\pi$
$734$		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	$-0.328208\pi$
$739$	−254.204	−	254.204i	−0.343984	−	0.343984i	−0.857863	+	0.513879i	$0.828208\pi$
$740$		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
$747$		−	392.899i		−	0.525969i
$748$		0			0
$749$	23.6271	+	23.6271i	0.0315449	+	0.0315449i
$750$		0			0
$751$	512.529			0.682462			0.341231	−	0.939979i	$-0.389156\pi$
$751$	512.529			0.682462			0.341231	+	0.939979i	$0.389156\pi$
$752$		0			0
$753$	754.774	−	754.774i	1.00236	−	1.00236i
$754$		0			0
$755$	133.048	+	408.184i	0.176222	+	0.540641i
$756$		0			0
$757$		−	109.439i		−	0.144570i	−0.997384	−	0.0722849i	$-0.976971\pi$
$757$		−	109.439i		−	0.144570i	0.997384	−	0.0722849i	$-0.0230291\pi$
$758$		0			0
$759$	−240.124			−0.316369
$760$		0			0
$761$		−	737.899i		−	0.969644i	−0.874613	−	0.484822i	$-0.838884\pi$
$761$		−	737.899i		−	0.969644i	0.874613	−	0.484822i	$-0.161116\pi$
$762$		0			0
$763$	−884.980			−1.15987
$764$		0			0
$765$	−814.796	−	414.203i	−1.06509	−	0.541442i
$766$		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
$773$	−1341.89			−1.73595			−0.867973	−	0.496612i	$-0.834577\pi$
$773$	−1341.89			−1.73595			−0.867973	+	0.496612i	$0.834577\pi$
$774$		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
$787$	−1158.29			−1.47178			−0.735892	−	0.677099i	$-0.763237\pi$
$787$	−1158.29			−1.47178			−0.735892	+	0.677099i	$0.763237\pi$
$788$		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
$795$	219.890	+	674.610i	0.276591	+	0.848566i
$796$		0			0
$797$	−67.0596			−0.0841400			−0.0420700	−	0.999115i	$-0.513395\pi$
$797$	−67.0596			−0.0841400			−0.0420700	+	0.999115i	$0.513395\pi$
$798$		0			0
$799$			441.396i			0.552436i
$800$		0			0
$801$	1411.96			1.76274
$802$		0			0
$803$		−	23.4346i		−	0.0291838i
$804$		0			0
$805$	−876.701	+	285.761i	−1.08907	+	0.354983i
$806$		0			0
$807$	−226.950	+	226.950i	−0.281227	+	0.281227i
$808$		0			0
$809$	602.411			0.744637			0.372318	−	0.928105i	$-0.378563\pi$
$809$	602.411			0.744637			0.372318	+	0.928105i	$0.378563\pi$
$810$		0			0
$811$	47.6019	+	47.6019i	0.0586953	+	0.0586953i	0.735845	−	0.677150i	$-0.236785\pi$
$811$	47.6019	+	47.6019i	0.0586953	+	0.0586953i	−0.677150	+	0.735845i	$0.736785\pi$
$812$		0			0
$813$			404.442i			0.497469i
$814$		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	$-0.0868040\pi$
$821$	569.537	+	569.537i	0.693711	+	0.693711i	−0.269335	+	0.963046i	$0.586804\pi$
$822$		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
$827$			829.310i			1.00279i	0.865217	+	0.501397i	$0.167180\pi$
$827$			829.310i			1.00279i	−0.865217	+	0.501397i	$0.832820\pi$
$828$		0			0
$829$	178.863	+	178.863i	0.215758	+	0.215758i	0.806708	−	0.590950i	$-0.201247\pi$
$829$	178.863	+	178.863i	0.215758	+	0.215758i	−0.590950	+	0.806708i	$0.701247\pi$
$830$		0			0
$831$	−743.671			−0.894911
$832$		0			0
$833$	246.404	−	246.404i	0.295803	−	0.295803i
$834$		0			0
$835$	266.393	−	524.034i	0.319034	−	0.627585i
$836$		0			0
$837$			227.255i			0.271511i
$838$		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
$843$	852.234			1.01095
$844$		0			0
$845$	−357.089	+	116.393i	−0.422591	+	0.137744i
$846$		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
$853$	1087.76			1.27522			0.637608	−	0.770361i	$-0.279924\pi$
$853$	1087.76			1.27522			0.637608	+	0.770361i	$0.279924\pi$
$854$		0			0
$855$	1568.08	+	797.135i	1.83401	+	0.932322i
$856$		0			0
$857$	−753.252	+	753.252i	−0.878940	+	0.878940i	−0.993425	−	0.114485i	$-0.963478\pi$
$857$	−753.252	+	753.252i	−0.878940	+	0.878940i	0.114485	+	0.993425i	$0.463478\pi$
$858$		0			0
$859$	656.780	−	656.780i	0.764587	−	0.764587i	−0.212561	−	0.977148i	$-0.568180\pi$
$859$	656.780	−	656.780i	0.764587	−	0.764587i	0.977148	+	0.212561i	$0.0681804\pi$
$860$		0			0
$861$	−37.6659	+	37.6659i	−0.0437467	+	0.0437467i
$862$		0			0
$863$	6.97025	−	6.97025i	0.00807676	−	0.00807676i	−0.703057	−	0.711134i	$-0.748182\pi$
$863$	6.97025	−	6.97025i	0.00807676	−	0.00807676i	0.711134	+	0.703057i	$0.248182\pi$
$864$		0			0
$865$	49.3225	+	151.319i	0.0570202	+	0.174935i
$866$		0			0
$867$	−135.225			−0.155968
$868$		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
$875$	−108.110	−	670.439i	−0.123555	−	0.766216i
$876$		0			0
$877$	−1467.43			−1.67324			−0.836618	−	0.547787i	$-0.815471\pi$
$877$	−1467.43			−1.67324			−0.836618	+	0.547787i	$0.815471\pi$
$878$		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
$883$		−	1602.95i		−	1.81535i	−0.419675	−	0.907674i	$-0.637856\pi$
$883$		−	1602.95i		−	1.81535i	0.419675	−	0.907674i	$-0.362144\pi$
$884$		0			0
$885$	587.864	+	298.842i	0.664253	+	0.337674i
$886$		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
$893$		−	849.469i		−	0.951253i
$894$		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
$907$			1609.72i			1.77478i	0.461024	+	0.887388i	$0.347482\pi$
$907$			1609.72i			1.77478i	−0.461024	+	0.887388i	$0.652518\pi$
$908$		0			0
$909$	−136.023	−	136.023i	−0.149641	−	0.149641i
$910$		0			0
$911$	−1117.02			−1.22615			−0.613074	−	0.790025i	$-0.710067\pi$
$911$	−1117.02			−1.22615			−0.613074	+	0.790025i	$0.710067\pi$
$912$		0			0
$913$	43.8529	−	43.8529i	0.0480316	−	0.0480316i
$914$		0			0
$915$	1452.81	+	738.539i	1.58777	+	0.807146i
$916$		0			0
$917$			142.786i			0.155709i
$918$		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
$923$	−137.828			−0.149326
$924$		0			0
$925$	−551.489	−	756.091i	−0.596205	−	0.817396i
$926$		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
$933$	−1113.74			−1.19372
$934$		0			0
$935$	−44.7116	−	137.173i	−0.0478199	−	0.146709i
$936$		0			0
$937$	−514.395	+	514.395i	−0.548980	+	0.548980i	−0.926146	−	0.377166i	$-0.876899\pi$
$937$	−514.395	+	514.395i	−0.548980	+	0.548980i	0.377166	+	0.926146i	$0.376899\pi$
$938$		0			0
$939$	98.6087	−	98.6087i	0.105015	−	0.105015i
$940$		0			0
$941$	1074.54	−	1074.54i	1.14191	−	1.14191i	0.153808	−	0.988101i	$-0.450846\pi$
$941$	1074.54	−	1074.54i	1.14191	−	1.14191i	0.988101	−	0.153808i	$-0.0491538\pi$
$942$		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
$947$	−173.864			−0.183595			−0.0917974	−	0.995778i	$-0.529261\pi$
$947$	−173.864			−0.183595			−0.0917974	+	0.995778i	$0.529261\pi$
$948$		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	0.320263	−	0.947329i	$-0.396229\pi$
$953$	−597.594	−	597.594i	−0.627066	−	0.627066i	−0.947329	+	0.320263i	$0.896229\pi$
$954$		0			0
$955$	31.8571	−	10.3839i	0.0333582	−	0.0108731i
$956$		0			0
$957$	214.183			0.223807
$958$		0			0
$959$			641.648i			0.669080i
$960$		0			0
$961$	839.116			0.873170
$962$		0			0
$963$			62.8675i			0.0652830i
$964$		0			0
$965$	644.981	−	1268.77i	0.668374	−	1.31479i
$966$		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	0.164748	−	0.986336i	$-0.447319\pi$
$971$	−797.762	−	797.762i	−0.821588	−	0.821588i	−0.986336	+	0.164748i	$0.947319\pi$
$972$		0			0
$973$			6.81008i			0.00699905i
$974$		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
$987$			587.868i			0.595611i
$988$		0			0
$989$	898.659	+	898.659i	0.908655	+	0.908655i
$990$		0			0
$991$	−504.008			−0.508585			−0.254293	−	0.967127i	$-0.581843\pi$
$991$	−504.008			−0.508585			−0.254293	+	0.967127i	$0.581843\pi$
$992$		0			0
$993$	−248.663	+	248.663i	−0.250416	+	0.250416i
$994$		0			0
$995$	390.956	−	127.432i	0.392920	−	0.128073i
$996$		0			0
$997$		−	1524.58i		−	1.52917i	−0.644526	−	0.764583i	$-0.722945\pi$
$997$		−	1524.58i		−	1.52917i	0.644526	−	0.764583i	$-0.277055\pi$
$998$		0			0
$999$	−200.507			−0.200707

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.10	✓	44	80.3	even	4
80.3.i.a.37.10	yes	44	4.3	odd	2
80.3.t.a.53.2	yes	44	20.3	even	4
80.3.t.a.77.2	yes	44	16.3	odd	4
320.3.i.a.177.20		44	1.1	even	1	trivial
320.3.i.a.273.3		44	80.13	odd	4	inner
320.3.t.a.17.3		44	16.13	even	4
320.3.t.a.113.3		44	5.3	odd	4
400.3.i.b.93.13		44	80.67	even	4
400.3.i.b.357.13		44	20.19	odd	2
400.3.t.b.157.21		44	80.19	odd	4
400.3.t.b.293.21		44	20.7	even	4
640.3.i.a.33.20		44	80.53	odd	4
640.3.i.a.97.3		44	8.5	even	2
640.3.i.b.33.3		44	80.43	even	4
640.3.i.b.97.20		44	8.3	odd	2
640.3.t.a.353.20		44	40.13	odd	4
640.3.t.a.417.20		44	16.5	even	4
640.3.t.b.353.3		44	40.3	even	4
640.3.t.b.417.3		44	16.11	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.i (of order \(4\), degree \(2\), not minimal)

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