LMFDB - Embedded newform 320.3.i.a.177.19

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			177.19
Character	$\chi$	$=$	320.177
Dual form			320.3.i.a.273.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.83124i q^{3} +(0.146974 + 4.99784i) q^{5} +(1.69668 - 1.69668i) q^{7} -5.67842 q^{9} +O(q^{10})$	\(q+3.83124i q^{3} +(0.146974 + 4.99784i) q^{5} +(1.69668 - 1.69668i) q^{7} -5.67842 q^{9} +(6.09580 + 6.09580i) q^{11} +14.9024i q^{13} +(-19.1479 + 0.563095i) q^{15} +(10.0145 + 10.0145i) q^{17} +(-4.15403 - 4.15403i) q^{19} +(6.50038 + 6.50038i) q^{21} +(-31.1044 - 31.1044i) q^{23} +(-24.9568 + 1.46911i) q^{25} +12.7258i q^{27} +(-38.9751 - 38.9751i) q^{29} +15.2616 q^{31} +(-23.3545 + 23.3545i) q^{33} +(8.72908 + 8.23034i) q^{35} +10.0034i q^{37} -57.0947 q^{39} -17.1555i q^{41} +41.2482 q^{43} +(-0.834582 - 28.3798i) q^{45} +(35.1314 + 35.1314i) q^{47} +43.2426i q^{49} +(-38.3679 + 38.3679i) q^{51} -5.40107 q^{53} +(-29.5699 + 31.3618i) q^{55} +(15.9151 - 15.9151i) q^{57} +(-13.6188 + 13.6188i) q^{59} +(55.0109 - 55.0109i) q^{61} +(-9.63443 + 9.63443i) q^{63} +(-74.4798 + 2.19027i) q^{65} +67.6058 q^{67} +(119.168 - 119.168i) q^{69} +68.8740i q^{71} +(84.8652 + 84.8652i) q^{73} +(-5.62851 - 95.6155i) q^{75} +20.6852 q^{77} -89.5060i q^{79} -99.8613 q^{81} +128.441i q^{83} +(-48.5789 + 51.5226i) q^{85} +(149.323 - 149.323i) q^{87} -43.6449 q^{89} +(25.2845 + 25.2845i) q^{91} +58.4708i q^{93} +(20.1507 - 21.3717i) q^{95} +(50.0681 + 50.0681i) q^{97} +(-34.6145 - 34.6145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			3.83124i			1.27708i	0.769588	+	0.638540i	$0.220461\pi$
$3$			3.83124i			1.27708i	−0.769588	+	0.638540i	$0.779539\pi$
$4$		0			0
$5$	0.146974	+	4.99784i	0.0293949	+	0.999568i
$5$	0.146974	+	4.99784i	0.0293949	+	0.999568i
$6$		0			0
$7$	1.69668	−	1.69668i	0.242382	−	0.242382i	−0.575453	−	0.817835i	$-0.695174\pi$
$7$	1.69668	−	1.69668i	0.242382	−	0.242382i	0.817835	+	0.575453i	$0.195174\pi$
$8$		0			0
$9$	−5.67842			−0.630935
$10$		0			0
$11$	6.09580	+	6.09580i	0.554164	+	0.554164i	0.927640	−	0.373476i	$-0.121834\pi$
$11$	6.09580	+	6.09580i	0.554164	+	0.554164i	−0.373476	+	0.927640i	$0.621834\pi$
$12$		0			0
$13$			14.9024i			1.14634i	0.819437	+	0.573169i	$0.194286\pi$
$13$			14.9024i			1.14634i	−0.819437	+	0.573169i	$0.805714\pi$
$14$		0			0
$15$	−19.1479	+	0.563095i	−1.27653	+	0.0375396i
$16$		0			0
$17$	10.0145	+	10.0145i	0.589087	+	0.589087i	0.937384	−	0.348297i	$-0.113240\pi$
$17$	10.0145	+	10.0145i	0.589087	+	0.589087i	−0.348297	+	0.937384i	$0.613240\pi$
$18$		0			0
$19$	−4.15403	−	4.15403i	−0.218633	−	0.218633i	0.589289	−	0.807922i	$-0.299408\pi$
$19$	−4.15403	−	4.15403i	−0.218633	−	0.218633i	−0.807922	+	0.589289i	$0.799408\pi$
$20$		0			0
$21$	6.50038	+	6.50038i	0.309542	+	0.309542i
$22$		0			0
$23$	−31.1044	−	31.1044i	−1.35237	−	1.35237i	−0.883009	−	0.469356i	$-0.844486\pi$
$23$	−31.1044	−	31.1044i	−1.35237	−	1.35237i	−0.469356	−	0.883009i	$-0.655514\pi$
$24$		0			0
$25$	−24.9568	+	1.46911i	−0.998272	+	0.0587644i
$26$		0			0
$27$			12.7258i			0.471325i
$28$		0			0
$29$	−38.9751	−	38.9751i	−1.34397	−	1.34397i	−0.892068	−	0.451901i	$-0.850746\pi$
$29$	−38.9751	−	38.9751i	−1.34397	−	1.34397i	−0.451901	−	0.892068i	$-0.649254\pi$
$30$		0			0
$31$	15.2616			0.492309			0.246154	−	0.969231i	$-0.420833\pi$
$31$	15.2616			0.492309			0.246154	+	0.969231i	$0.420833\pi$
$32$		0			0
$33$	−23.3545	+	23.3545i	−0.707712	+	0.707712i
$34$		0			0
$35$	8.72908	+	8.23034i	0.249402	+	0.235153i
$36$		0			0
$37$			10.0034i			0.270363i	0.990821	+	0.135181i	$0.0431617\pi$
$37$			10.0034i			0.270363i	−0.990821	+	0.135181i	$0.956838\pi$
$38$		0			0
$39$	−57.0947			−1.46397
$40$		0			0
$41$		−	17.1555i		−	0.418427i	−0.977870	−	0.209213i	$-0.932910\pi$
$41$		−	17.1555i		−	0.418427i	0.977870	−	0.209213i	$-0.0670903\pi$
$42$		0			0
$43$	41.2482			0.959261			0.479630	−	0.877471i	$-0.340771\pi$
$43$	41.2482			0.959261			0.479630	+	0.877471i	$0.340771\pi$
$44$		0			0
$45$	−0.834582	−	28.3798i	−0.0185463	−	0.630663i
$46$		0			0
$47$	35.1314	+	35.1314i	0.747476	+	0.747476i	0.974004	−	0.226529i	$-0.0727377\pi$
$47$	35.1314	+	35.1314i	0.747476	+	0.747476i	−0.226529	+	0.974004i	$0.572738\pi$
$48$		0			0
$49$			43.2426i			0.882502i
$50$		0			0
$51$	−38.3679	+	38.3679i	−0.752311	+	0.752311i
$52$		0			0
$53$	−5.40107			−0.101907			−0.0509535	−	0.998701i	$-0.516226\pi$
$53$	−5.40107			−0.101907			−0.0509535	+	0.998701i	$0.516226\pi$
$54$		0			0
$55$	−29.5699	+	31.3618i	−0.537635	+	0.570214i
$56$		0			0
$57$	15.9151	−	15.9151i	0.279212	−	0.279212i
$58$		0			0
$59$	−13.6188	+	13.6188i	−0.230827	+	0.230827i	−0.813038	−	0.582211i	$-0.802188\pi$
$59$	−13.6188	+	13.6188i	−0.230827	+	0.230827i	0.582211	+	0.813038i	$0.302188\pi$
$60$		0			0
$61$	55.0109	−	55.0109i	0.901818	−	0.901818i	−0.0937755	−	0.995593i	$-0.529894\pi$
$61$	55.0109	−	55.0109i	0.901818	−	0.901818i	0.995593	+	0.0937755i	$0.0298936\pi$
$62$		0			0
$63$	−9.63443	+	9.63443i	−0.152928	+	0.152928i
$64$		0			0
$65$	−74.4798	+	2.19027i	−1.14584	+	0.0336965i
$66$		0			0
$67$	67.6058			1.00904			0.504521	−	0.863400i	$-0.331669\pi$
$67$	67.6058			1.00904			0.504521	+	0.863400i	$0.331669\pi$
$68$		0			0
$69$	119.168	−	119.168i	1.72708	−	1.72708i
$70$		0			0
$71$			68.8740i			0.970057i	0.874498	+	0.485028i	$0.161191\pi$
$71$			68.8740i			0.970057i	−0.874498	+	0.485028i	$0.838809\pi$
$72$		0			0
$73$	84.8652	+	84.8652i	1.16254	+	1.16254i	0.983918	+	0.178619i	$0.0571630\pi$
$73$	84.8652	+	84.8652i	1.16254	+	1.16254i	0.178619	+	0.983918i	$0.442837\pi$
$74$		0			0
$75$	−5.62851	−	95.6155i	−0.0750468	−	1.27487i
$76$		0			0
$77$	20.6852			0.268639
$78$		0			0
$79$		−	89.5060i		−	1.13299i	−0.824066	−	0.566494i	$-0.808300\pi$
$79$		−	89.5060i		−	1.13299i	0.824066	−	0.566494i	$-0.191700\pi$
$80$		0			0
$81$	−99.8613			−1.23286
$82$		0			0
$83$			128.441i			1.54748i	0.633504	+	0.773740i	$0.281616\pi$
$83$			128.441i			1.54748i	−0.633504	+	0.773740i	$0.718384\pi$
$84$		0			0
$85$	−48.5789	+	51.5226i	−0.571516	+	0.606148i
$86$		0			0
$87$	149.323	−	149.323i	1.71636	−	1.71636i
$88$		0			0
$89$	−43.6449			−0.490392			−0.245196	−	0.969474i	$-0.578852\pi$
$89$	−43.6449			−0.490392			−0.245196	+	0.969474i	$0.578852\pi$
$90$		0			0
$91$	25.2845	+	25.2845i	0.277852	+	0.277852i
$92$		0			0
$93$			58.4708i			0.628718i
$94$		0			0
$95$	20.1507	−	21.3717i	0.212112	−	0.224966i
$96$		0			0
$97$	50.0681	+	50.0681i	0.516166	+	0.516166i	0.916409	−	0.400243i	$-0.131074\pi$
$97$	50.0681	+	50.0681i	0.516166	+	0.516166i	−0.400243	+	0.916409i	$0.631074\pi$
$98$		0			0
$99$	−34.6145	−	34.6145i	−0.349642	−	0.349642i
$100$		0			0
$101$	72.5051	+	72.5051i	0.717872	+	0.717872i	0.968169	−	0.250297i	$-0.0805282\pi$
$101$	72.5051	+	72.5051i	0.717872	+	0.717872i	−0.250297	+	0.968169i	$0.580528\pi$
$102$		0			0
$103$	−35.2795	−	35.2795i	−0.342520	−	0.342520i	0.514794	−	0.857314i	$-0.327868\pi$
$103$	−35.2795	−	35.2795i	−0.342520	−	0.342520i	−0.857314	+	0.514794i	$0.827868\pi$
$104$		0			0
$105$	−31.5324	+	33.4432i	−0.300309	+	0.318507i
$106$		0			0
$107$		−	82.1016i		−	0.767304i	−0.923478	−	0.383652i	$-0.874666\pi$
$107$		−	82.1016i		−	0.767304i	0.923478	−	0.383652i	$-0.125334\pi$
$108$		0			0
$109$	21.7299	+	21.7299i	0.199357	+	0.199357i	0.799724	−	0.600367i	$-0.204979\pi$
$109$	21.7299	+	21.7299i	0.199357	+	0.199357i	−0.600367	+	0.799724i	$0.704979\pi$
$110$		0			0
$111$	−38.3256			−0.345275
$112$		0			0
$113$	126.862	−	126.862i	1.12267	−	1.12267i	0.131331	−	0.991339i	$-0.458075\pi$
$113$	126.862	−	126.862i	1.12267	−	1.12267i	0.991339	−	0.131331i	$-0.0419249\pi$
$114$		0			0
$115$	150.883	−	160.026i	1.31203	−	1.39153i
$116$		0			0
$117$		−	84.6221i		−	0.723266i
$118$		0			0
$119$	33.9826			0.285568
$120$		0			0
$121$		−	46.6824i		−	0.385805i
$122$		0			0
$123$	65.7268			0.534364
$124$		0			0
$125$	−11.0104	−	124.514i	−0.0880830	−	0.996113i
$126$		0			0
$127$	−12.9872	−	12.9872i	−0.102261	−	0.102261i	0.654125	−	0.756386i	$-0.273037\pi$
$127$	−12.9872	−	12.9872i	−0.102261	−	0.102261i	−0.756386	+	0.654125i	$0.773037\pi$
$128$		0			0
$129$			158.032i			1.22505i
$130$		0			0
$131$	−79.1439	+	79.1439i	−0.604152	+	0.604152i	−0.941412	−	0.337260i	$-0.890500\pi$
$131$	−79.1439	+	79.1439i	−0.604152	+	0.604152i	0.337260	+	0.941412i	$0.390500\pi$
$132$		0			0
$133$	−14.0961			−0.105986
$134$		0			0
$135$	−63.6014	+	1.87036i	−0.471122	+	0.0138545i
$136$		0			0
$137$	156.302	−	156.302i	1.14089	−	1.14089i	0.152600	−	0.988288i	$-0.451235\pi$
$137$	156.302	−	156.302i	1.14089	−	1.14089i	0.988288	−	0.152600i	$-0.0487646\pi$
$138$		0			0
$139$	10.6258	−	10.6258i	0.0764446	−	0.0764446i	−0.667851	−	0.744295i	$-0.732786\pi$
$139$	10.6258	−	10.6258i	0.0764446	−	0.0764446i	0.744295	+	0.667851i	$0.232786\pi$
$140$		0			0
$141$	−134.597	+	134.597i	−0.954587	+	0.954587i
$142$		0			0
$143$	−90.8421	+	90.8421i	−0.635259	+	0.635259i
$144$		0			0
$145$	189.063	−	200.520i	1.30388	−	1.38289i
$146$		0			0
$147$	−165.673			−1.12703
$148$		0			0
$149$	−59.6091	+	59.6091i	−0.400061	+	0.400061i	−0.878255	−	0.478193i	$-0.841292\pi$
$149$	−59.6091	+	59.6091i	−0.400061	+	0.400061i	0.478193	+	0.878255i	$0.341292\pi$
$150$		0			0
$151$			3.55134i			0.0235188i	0.999931	+	0.0117594i	$0.00374322\pi$
$151$			3.55134i			0.0235188i	−0.999931	+	0.0117594i	$0.996257\pi$
$152$		0			0
$153$	−56.8664	−	56.8664i	−0.371676	−	0.371676i
$154$		0			0
$155$	2.24306	+	76.2749i	0.0144714	+	0.492096i
$156$		0			0
$157$	2.28360			0.0145453			0.00727263	−	0.999974i	$-0.497685\pi$
$157$	2.28360			0.0145453			0.00727263	+	0.999974i	$0.497685\pi$
$158$		0			0
$159$		−	20.6928i		−	0.130143i
$160$		0			0
$161$	−105.548			−0.655579
$162$		0			0
$163$		−	116.769i		−	0.716375i	−0.933650	−	0.358188i	$-0.883395\pi$
$163$		−	116.769i		−	0.716375i	0.933650	−	0.358188i	$-0.116605\pi$
$164$		0			0
$165$	−120.155	−	113.289i	−0.728209	−	0.686603i
$166$		0			0
$167$	20.9709	−	20.9709i	0.125574	−	0.125574i	−0.641527	−	0.767101i	$-0.721699\pi$
$167$	20.9709	−	20.9709i	0.125574	−	0.125574i	0.767101	+	0.641527i	$0.221699\pi$
$168$		0			0
$169$	−53.0817			−0.314093
$170$		0			0
$171$	23.5883	+	23.5883i	0.137944	+	0.137944i
$172$		0			0
$173$			242.412i			1.40122i	0.713543	+	0.700612i	$0.247090\pi$
$173$			242.412i			1.40122i	−0.713543	+	0.700612i	$0.752910\pi$
$174$		0			0
$175$	−39.8510	+	44.8362i	−0.227720	+	0.256207i
$176$		0			0
$177$	−52.1770	−	52.1770i	−0.294785	−	0.294785i
$178$		0			0
$179$	177.009	+	177.009i	0.988880	+	0.988880i	0.999939	−	0.0110592i	$-0.00352031\pi$
$179$	177.009	+	177.009i	0.988880	+	0.988880i	−0.0110592	+	0.999939i	$0.503520\pi$
$180$		0			0
$181$	−24.0528	−	24.0528i	−0.132888	−	0.132888i	0.637534	−	0.770422i	$-0.279955\pi$
$181$	−24.0528	−	24.0528i	−0.132888	−	0.132888i	−0.770422	+	0.637534i	$0.779955\pi$
$182$		0			0
$183$	210.760	+	210.760i	1.15169	+	1.15169i
$184$		0			0
$185$	−49.9955	+	1.47025i	−0.270246	+	0.00794729i
$186$		0			0
$187$			122.092i			0.652901i
$188$		0			0
$189$	21.5915	+	21.5915i	0.114241	+	0.114241i
$190$		0			0
$191$	23.7935			0.124573			0.0622867	−	0.998058i	$-0.480161\pi$
$191$	23.7935			0.124573			0.0622867	+	0.998058i	$0.480161\pi$
$192$		0			0
$193$	72.7930	−	72.7930i	0.377166	−	0.377166i	−0.492913	−	0.870079i	$-0.664068\pi$
$193$	72.7930	−	72.7930i	0.377166	−	0.377166i	0.870079	+	0.492913i	$0.164068\pi$
$194$		0			0
$195$	−8.39146	−	285.350i	−0.0430331	−	1.46333i
$196$		0			0
$197$			211.841i			1.07533i	0.843157	+	0.537667i	$0.180694\pi$
$197$			211.841i			1.07533i	−0.843157	+	0.537667i	$0.819306\pi$
$198$		0			0
$199$	−106.366			−0.534502			−0.267251	−	0.963627i	$-0.586115\pi$
$199$	−106.366			−0.534502			−0.267251	+	0.963627i	$0.586115\pi$
$200$		0			0
$201$			259.014i			1.28863i
$202$		0			0
$203$	−132.256			−0.651508
$204$		0			0
$205$	85.7404	−	2.52142i	0.418246	−	0.0122996i
$206$		0			0
$207$	176.624	+	176.624i	0.853255	+	0.853255i
$208$		0			0
$209$		−	50.6443i		−	0.242317i
$210$		0			0
$211$	5.13143	−	5.13143i	0.0243196	−	0.0243196i	−0.694842	−	0.719162i	$-0.744526\pi$
$211$	5.13143	−	5.13143i	0.0243196	−	0.0243196i	0.719162	+	0.694842i	$0.244526\pi$
$212$		0			0
$213$	−263.873			−1.23884
$214$		0			0
$215$	6.06243	+	206.152i	0.0281974	+	0.958846i
$216$		0			0
$217$	25.8939	−	25.8939i	0.119327	−	0.119327i
$218$		0			0
$219$	−325.139	+	325.139i	−1.48465	+	1.48465i
$220$		0			0
$221$	−149.240	+	149.240i	−0.675293	+	0.675293i
$222$		0			0
$223$	116.577	−	116.577i	0.522765	−	0.522765i	−0.395640	−	0.918406i	$-0.629477\pi$
$223$	116.577	−	116.577i	0.522765	−	0.522765i	0.918406	+	0.395640i	$0.129477\pi$
$224$		0			0
$225$	141.715	−	8.34222i	0.629845	−	0.0370765i
$226$		0			0
$227$	−256.557			−1.13021			−0.565104	−	0.825020i	$-0.691164\pi$
$227$	−256.557			−1.13021			−0.565104	+	0.825020i	$0.691164\pi$
$228$		0			0
$229$	15.0848	−	15.0848i	0.0658724	−	0.0658724i	−0.673403	−	0.739275i	$-0.735168\pi$
$229$	15.0848	−	15.0848i	0.0658724	−	0.0658724i	0.739275	+	0.673403i	$0.235168\pi$
$230$		0			0
$231$			79.2500i			0.343074i
$232$		0			0
$233$	106.551	+	106.551i	0.457298	+	0.457298i	0.897768	−	0.440469i	$-0.145188\pi$
$233$	106.551	+	106.551i	0.457298	+	0.457298i	−0.440469	+	0.897768i	$0.645188\pi$
$234$		0			0
$235$	−170.417	+	180.744i	−0.725181	+	0.769125i
$236$		0			0
$237$	342.919			1.44692
$238$		0			0
$239$			8.02920i			0.0335950i	0.999859	+	0.0167975i	$0.00534706\pi$
$239$			8.02920i			0.0335950i	−0.999859	+	0.0167975i	$0.994653\pi$
$240$		0			0
$241$	9.19588			0.0381572			0.0190786	−	0.999818i	$-0.493927\pi$
$241$	9.19588			0.0381572			0.0190786	+	0.999818i	$0.493927\pi$
$242$		0			0
$243$		−	268.061i		−	1.10313i
$244$		0			0
$245$	−216.119	+	6.35555i	−0.882120	+	0.0259410i
$246$		0			0
$247$	61.9051	−	61.9051i	0.250628	−	0.250628i
$248$		0			0
$249$	−492.088			−1.97626
$250$		0			0
$251$	−326.061	−	326.061i	−1.29905	−	1.29905i	−0.929022	−	0.370024i	$-0.879349\pi$
$251$	−326.061	−	326.061i	−1.29905	−	1.29905i	−0.370024	−	0.929022i	$-0.620651\pi$
$252$		0			0
$253$		−	379.212i		−	1.49886i
$254$		0			0
$255$	−197.396	−	186.117i	−0.774100	−	0.729872i
$256$		0			0
$257$	−185.092	−	185.092i	−0.720204	−	0.720204i	0.248443	−	0.968647i	$-0.420081\pi$
$257$	−185.092	−	185.092i	−0.720204	−	0.720204i	−0.968647	+	0.248443i	$0.920081\pi$
$258$		0			0
$259$	16.9726	+	16.9726i	0.0655312	+	0.0655312i
$260$		0			0
$261$	221.317	+	221.317i	0.847958	+	0.847958i
$262$		0			0
$263$	202.165	+	202.165i	0.768689	+	0.768689i	0.977876	−	0.209187i	$-0.0670816\pi$
$263$	202.165	+	202.165i	0.768689	+	0.768689i	−0.209187	+	0.977876i	$0.567082\pi$
$264$		0			0
$265$	−0.793819	−	26.9937i	−0.00299554	−	0.101863i
$266$		0			0
$267$		−	167.214i		−	0.626270i
$268$		0			0
$269$	−135.481	−	135.481i	−0.503647	−	0.503647i	0.408922	−	0.912569i	$-0.365905\pi$
$269$	−135.481	−	135.481i	−0.503647	−	0.503647i	−0.912569	+	0.408922i	$0.865905\pi$
$270$		0			0
$271$	276.220			1.01926			0.509632	−	0.860393i	$-0.329782\pi$
$271$	276.220			1.01926			0.509632	+	0.860393i	$0.329782\pi$
$272$		0			0
$273$	−96.8712	+	96.8712i	−0.354840	+	0.354840i
$274$		0			0
$275$	−161.087	−	143.176i	−0.585771	−	0.520641i
$276$		0			0
$277$			184.706i			0.666808i	0.942784	+	0.333404i	$0.108197\pi$
$277$			184.706i			0.666808i	−0.942784	+	0.333404i	$0.891803\pi$
$278$		0			0
$279$	−86.6616			−0.310615
$280$		0			0
$281$		−	173.967i		−	0.619100i	−0.950883	−	0.309550i	$-0.899822\pi$
$281$		−	173.967i		−	0.619100i	0.950883	−	0.309550i	$-0.100178\pi$
$282$		0			0
$283$	−33.1982			−0.117308			−0.0586541	−	0.998278i	$-0.518681\pi$
$283$	−33.1982			−0.117308			−0.0586541	+	0.998278i	$0.518681\pi$
$284$		0			0
$285$	81.8803	+	77.2020i	0.287299	+	0.270884i
$286$		0			0
$287$	−29.1073	−	29.1073i	−0.101419	−	0.101419i
$288$		0			0
$289$		−	88.4206i		−	0.305954i
$290$		0			0
$291$	−191.823	+	191.823i	−0.659185	+	0.659185i
$292$		0			0
$293$	−194.502			−0.663829			−0.331915	−	0.943309i	$-0.607695\pi$
$293$	−194.502			−0.663829			−0.331915	+	0.943309i	$0.607695\pi$
$294$		0			0
$295$	−70.0662	−	66.0630i	−0.237513	−	0.223942i
$296$		0			0
$297$	−77.5738	+	77.5738i	−0.261191	+	0.261191i
$298$		0			0
$299$	463.530	−	463.530i	1.55027	−	1.55027i
$300$		0			0
$301$	69.9848	−	69.9848i	0.232508	−	0.232508i
$302$		0			0
$303$	−277.785	+	277.785i	−0.916781	+	0.916781i
$304$		0			0
$305$	283.021	+	266.850i	0.927937	+	0.874919i
$306$		0			0
$307$	517.509			1.68570			0.842849	−	0.538150i	$-0.180877\pi$
$307$	517.509			1.68570			0.842849	+	0.538150i	$0.180877\pi$
$308$		0			0
$309$	135.164	−	135.164i	0.437426	−	0.437426i
$310$		0			0
$311$		−	482.841i		−	1.55254i	−0.630399	−	0.776271i	$-0.717109\pi$
$311$		−	482.841i		−	1.55254i	0.630399	−	0.776271i	$-0.282891\pi$
$312$		0			0
$313$	96.1945	+	96.1945i	0.307331	+	0.307331i	0.843873	−	0.536543i	$-0.180270\pi$
$313$	96.1945	+	96.1945i	0.307331	+	0.307331i	−0.536543	+	0.843873i	$0.680270\pi$
$314$		0			0
$315$	−49.5674	−	46.7353i	−0.157357	−	0.148366i
$316$		0			0
$317$	−344.707			−1.08740			−0.543702	−	0.839278i	$-0.682978\pi$
$317$	−344.707			−1.08740			−0.543702	+	0.839278i	$0.682978\pi$
$318$		0			0
$319$		−	475.169i		−	1.48956i
$320$		0			0
$321$	314.551			0.979910
$322$		0			0
$323$		−	83.2009i		−	0.257588i
$324$		0			0
$325$	−21.8933	−	371.916i	−0.0673639	−	1.14436i
$326$		0			0
$327$	−83.2525	+	83.2525i	−0.254595	+	0.254595i
$328$		0			0
$329$	119.213			0.362350
$330$		0			0
$331$	204.460	+	204.460i	0.617704	+	0.617704i	0.944942	−	0.327238i	$-0.106118\pi$
$331$	204.460	+	204.460i	0.617704	+	0.617704i	−0.327238	+	0.944942i	$0.606118\pi$
$332$		0			0
$333$		−	56.8037i		−	0.170582i
$334$		0			0
$335$	9.93632	+	337.883i	0.0296606	+	1.00861i
$336$		0			0
$337$	−200.716	−	200.716i	−0.595598	−	0.595598i	0.343540	−	0.939138i	$-0.388374\pi$
$337$	−200.716	−	200.716i	−0.595598	−	0.595598i	−0.939138	+	0.343540i	$0.888374\pi$
$338$		0			0
$339$	486.038	+	486.038i	1.43374	+	1.43374i
$340$		0			0
$341$	93.0315	+	93.0315i	0.272820	+	0.272820i
$342$		0			0
$343$	156.506	+	156.506i	0.456285	+	0.456285i
$344$		0			0
$345$	613.100	+	578.070i	1.77710	+	1.67557i
$346$		0			0
$347$			187.616i			0.540681i	0.962765	+	0.270341i	$0.0871363\pi$
$347$			187.616i			0.540681i	−0.962765	+	0.270341i	$0.912864\pi$
$348$		0			0
$349$	316.337	+	316.337i	0.906409	+	0.906409i	0.995980	−	0.0895710i	$-0.0285496\pi$
$349$	316.337	+	316.337i	0.906409	+	0.906409i	−0.0895710	+	0.995980i	$0.528550\pi$
$350$		0			0
$351$	−189.645			−0.540299
$352$		0			0
$353$	−284.733	+	284.733i	−0.806610	+	0.806610i	−0.984119	−	0.177509i	$-0.943196\pi$
$353$	−284.733	+	284.733i	−0.806610	+	0.806610i	0.177509	+	0.984119i	$0.443196\pi$
$354$		0			0
$355$	−344.221	+	10.1227i	−0.969637	+	0.0285147i
$356$		0			0
$357$			130.196i			0.364694i
$358$		0			0
$359$	−425.478			−1.18518			−0.592588	−	0.805506i	$-0.701894\pi$
$359$	−425.478			−1.18518			−0.592588	+	0.805506i	$0.701894\pi$
$360$		0			0
$361$		−	326.488i		−	0.904399i
$362$		0			0
$363$	178.852			0.492704
$364$		0			0
$365$	−411.670	+	436.616i	−1.12786	+	1.19621i
$366$		0			0
$367$	203.918	+	203.918i	0.555635	+	0.555635i	0.928062	−	0.372427i	$-0.121474\pi$
$367$	203.918	+	203.918i	0.555635	+	0.555635i	−0.372427	+	0.928062i	$0.621474\pi$
$368$		0			0
$369$			97.4160i			0.264000i
$370$		0			0
$371$	−9.16386	+	9.16386i	−0.0247004	+	0.0247004i
$372$		0			0
$373$	601.037			1.61136			0.805680	−	0.592351i	$-0.201800\pi$
$373$	601.037			1.61136			0.805680	+	0.592351i	$0.201800\pi$
$374$		0			0
$375$	477.044	−	42.1834i	1.27212	−	0.112489i
$376$		0			0
$377$	580.823	−	580.823i	1.54064	−	1.54064i
$378$		0			0
$379$	300.652	−	300.652i	0.793276	−	0.793276i	−0.188750	−	0.982025i	$-0.560443\pi$
$379$	300.652	−	300.652i	0.793276	−	0.793276i	0.982025	+	0.188750i	$0.0604434\pi$
$380$		0			0
$381$	49.7570	−	49.7570i	0.130596	−	0.130596i
$382$		0			0
$383$	135.792	−	135.792i	0.354547	−	0.354547i	−0.507251	−	0.861798i	$-0.669338\pi$
$383$	135.792	−	135.792i	0.354547	−	0.354547i	0.861798	+	0.507251i	$0.169338\pi$
$384$		0			0
$385$	3.04019	+	103.381i	0.00789661	+	0.268523i
$386$		0			0
$387$	−234.225			−0.605232
$388$		0			0
$389$	428.756	−	428.756i	1.10220	−	1.10220i	0.108054	−	0.994145i	$-0.465538\pi$
$389$	428.756	−	428.756i	1.10220	−	1.10220i	0.994145	−	0.108054i	$-0.0344620\pi$
$390$		0			0
$391$		−	622.988i		−	1.59332i
$392$		0			0
$393$	−303.219	−	303.219i	−0.771551	−	0.771551i
$394$		0			0
$395$	447.337	−	13.1551i	1.13250	−	0.0333040i
$396$		0			0
$397$	194.112			0.488947			0.244474	−	0.969656i	$-0.421385\pi$
$397$	194.112			0.488947			0.244474	+	0.969656i	$0.421385\pi$
$398$		0			0
$399$		−	54.0055i		−	0.135352i
$400$		0			0
$401$	−285.335			−0.711560			−0.355780	−	0.934570i	$-0.615785\pi$
$401$	−285.335			−0.711560			−0.355780	+	0.934570i	$0.615785\pi$
$402$		0			0
$403$			227.434i			0.564353i
$404$		0			0
$405$	−14.6771	−	499.091i	−0.0362397	−	1.23232i
$406$		0			0
$407$	−60.9789	+	60.9789i	−0.149825	+	0.149825i
$408$		0			0
$409$	−219.624			−0.536978			−0.268489	−	0.963283i	$-0.586524\pi$
$409$	−219.624			−0.536978			−0.268489	+	0.963283i	$0.586524\pi$
$410$		0			0
$411$	598.830	+	598.830i	1.45701	+	1.45701i
$412$		0			0
$413$			46.2134i			0.111897i
$414$		0			0
$415$	−641.926	+	18.8775i	−1.54681	+	0.0454880i
$416$		0			0
$417$	40.7100	+	40.7100i	0.0976259	+	0.0976259i
$418$		0			0
$419$	−92.3158	−	92.3158i	−0.220324	−	0.220324i	0.588311	−	0.808635i	$-0.299793\pi$
$419$	−92.3158	−	92.3158i	−0.220324	−	0.220324i	−0.808635	+	0.588311i	$0.799793\pi$
$420$		0			0
$421$	−203.067	−	203.067i	−0.482345	−	0.482345i	0.423535	−	0.905880i	$-0.360789\pi$
$421$	−203.067	−	203.067i	−0.482345	−	0.482345i	−0.905880	+	0.423535i	$0.860789\pi$
$422$		0			0
$423$	−199.491	−	199.491i	−0.471609	−	0.471609i
$424$		0			0
$425$	−264.642	−	235.217i	−0.622686	−	0.553451i
$426$		0			0
$427$		−	186.671i		−	0.437169i
$428$		0			0
$429$	−348.038	−	348.038i	−0.811278	−	0.811278i
$430$		0			0
$431$	468.188			1.08628			0.543142	−	0.839641i	$-0.317235\pi$
$431$	468.188			1.08628			0.543142	+	0.839641i	$0.317235\pi$
$432$		0			0
$433$	55.1786	−	55.1786i	0.127433	−	0.127433i	−0.640514	−	0.767947i	$-0.721278\pi$
$433$	55.1786	−	55.1786i	0.127433	−	0.127433i	0.767947	+	0.640514i	$0.221278\pi$
$434$		0			0
$435$	768.239	+	724.346i	1.76607	+	1.66516i
$436$		0			0
$437$			258.417i			0.591344i
$438$		0			0
$439$	−40.4072			−0.0920437			−0.0460219	−	0.998940i	$-0.514654\pi$
$439$	−40.4072			−0.0920437			−0.0460219	+	0.998940i	$0.514654\pi$
$440$		0			0
$441$		−	245.550i		−	0.556802i
$442$		0			0
$443$	−551.916			−1.24586			−0.622930	−	0.782277i	$-0.714058\pi$
$443$	−551.916			−1.24586			−0.622930	+	0.782277i	$0.714058\pi$
$444$		0			0
$445$	−6.41468	−	218.130i	−0.0144150	−	0.490180i
$446$		0			0
$447$	−228.377	−	228.377i	−0.510911	−	0.510911i
$448$		0			0
$449$		−	161.753i		−	0.360252i	−0.983644	−	0.180126i	$-0.942349\pi$
$449$		−	161.753i		−	0.360252i	0.983644	−	0.180126i	$-0.0576506\pi$
$450$		0			0
$451$	104.576	−	104.576i	0.231877	−	0.231877i
$452$		0			0
$453$	−13.6060			−0.0300354
$454$		0			0
$455$	−122.652	+	130.084i	−0.269565	+	0.285900i
$456$		0			0
$457$	−397.309	+	397.309i	−0.869384	+	0.869384i	−0.992404	−	0.123020i	$-0.960742\pi$
$457$	−397.309	+	397.309i	−0.869384	+	0.869384i	0.123020	+	0.992404i	$0.460742\pi$
$458$		0			0
$459$	−127.442	+	127.442i	−0.277651	+	0.277651i
$460$		0			0
$461$	426.786	−	426.786i	0.925784	−	0.925784i	−0.0716461	−	0.997430i	$-0.522825\pi$
$461$	426.786	−	426.786i	0.925784	−	0.925784i	0.997430	+	0.0716461i	$0.0228252\pi$
$462$		0			0
$463$	−33.0173	+	33.0173i	−0.0713118	+	0.0713118i	−0.741863	−	0.670551i	$-0.766058\pi$
$463$	−33.0173	+	33.0173i	−0.0713118	+	0.0713118i	0.670551	+	0.741863i	$0.266058\pi$
$464$		0			0
$465$	−292.228	+	8.59371i	−0.628447	+	0.0184811i
$466$		0			0
$467$	−771.151			−1.65129			−0.825644	−	0.564192i	$-0.809188\pi$
$467$	−771.151			−1.65129			−0.825644	+	0.564192i	$0.809188\pi$
$468$		0			0
$469$	114.705	−	114.705i	0.244574	−	0.244574i
$470$		0			0
$471$			8.74904i			0.0185755i
$472$		0			0
$473$	251.441	+	251.441i	0.531588	+	0.531588i
$474$		0			0
$475$	109.774	+	97.5686i	0.231103	+	0.205408i
$476$		0			0
$477$	30.6695			0.0642967
$478$		0			0
$479$		−	210.902i		−	0.440295i	−0.975467	−	0.220148i	$-0.929346\pi$
$479$		−	210.902i		−	0.440295i	0.975467	−	0.220148i	$-0.0706539\pi$
$480$		0			0
$481$	−149.075			−0.309928
$482$		0			0
$483$		−	404.381i		−	0.837227i
$484$		0			0
$485$	−242.873	+	257.591i	−0.500770	+	0.531115i
$486$		0			0
$487$	−196.542	+	196.542i	−0.403578	+	0.403578i	−0.879492	−	0.475914i	$-0.842117\pi$
$487$	−196.542	+	196.542i	−0.403578	+	0.403578i	0.475914	+	0.879492i	$0.342117\pi$
$488$		0			0
$489$	447.371			0.914869
$490$		0			0
$491$	−391.245	−	391.245i	−0.796833	−	0.796833i	0.185762	−	0.982595i	$-0.440525\pi$
$491$	−391.245	−	391.245i	−0.796833	−	0.796833i	−0.982595	+	0.185762i	$0.940525\pi$
$492$		0			0
$493$		−	780.630i		−	1.58343i
$494$		0			0
$495$	167.910	−	178.085i	0.339213	−	0.359768i
$496$		0			0
$497$	116.857	+	116.857i	0.235124	+	0.235124i
$498$		0			0
$499$	240.105	+	240.105i	0.481173	+	0.481173i	0.905506	−	0.424333i	$-0.139491\pi$
$499$	240.105	+	240.105i	0.481173	+	0.481173i	−0.424333	+	0.905506i	$0.639491\pi$
$500$		0			0
$501$	80.3446	+	80.3446i	0.160368	+	0.160368i
$502$		0			0
$503$	−459.843	−	459.843i	−0.914200	−	0.914200i	0.0823992	−	0.996599i	$-0.473742\pi$
$503$	−459.843	−	459.843i	−0.914200	−	0.914200i	−0.996599	+	0.0823992i	$0.973742\pi$
$504$		0			0
$505$	−351.713	+	373.025i	−0.696460	+	0.738664i
$506$		0			0
$507$		−	203.369i		−	0.401122i
$508$		0			0
$509$	348.808	+	348.808i	0.685281	+	0.685281i	0.961185	−	0.275904i	$-0.0889772\pi$
$509$	348.808	+	348.808i	0.685281	+	0.685281i	−0.275904	+	0.961185i	$0.588977\pi$
$510$		0			0
$511$	287.978			0.563557
$512$		0			0
$513$	52.8633	−	52.8633i	0.103047	−	0.103047i
$514$		0			0
$515$	171.136	−	181.507i	0.332304	−	0.352440i
$516$		0			0
$517$			428.308i			0.828448i
$518$		0			0
$519$	−928.738			−1.78948
$520$		0			0
$521$			54.0067i			0.103660i	0.998656	+	0.0518298i	$0.0165053\pi$
$521$			54.0067i			0.103660i	−0.998656	+	0.0518298i	$0.983495\pi$
$522$		0			0
$523$	367.680			0.703022			0.351511	−	0.936184i	$-0.385668\pi$
$523$	367.680			0.703022			0.351511	+	0.936184i	$0.385668\pi$
$524$		0			0
$525$	−171.778	−	152.679i	−0.327197	−	0.290817i
$526$		0			0
$527$	152.837	+	152.837i	0.290013	+	0.290013i
$528$		0			0
$529$			1405.97i			2.65778i
$530$		0			0
$531$	77.3333	−	77.3333i	0.145637	−	0.145637i
$532$		0			0
$533$	255.658			0.479659
$534$		0			0
$535$	410.330	−	12.0668i	0.766973	−	0.0225548i
$536$		0			0
$537$	−678.166	+	678.166i	−1.26288	+	1.26288i
$538$		0			0
$539$	−263.598	+	263.598i	−0.489050	+	0.489050i
$540$		0			0
$541$	−39.4092	+	39.4092i	−0.0728451	+	0.0728451i	−0.742591	−	0.669746i	$-0.766403\pi$
$541$	−39.4092	+	39.4092i	−0.0728451	+	0.0728451i	0.669746	+	0.742591i	$0.266403\pi$
$542$		0			0
$543$	92.1521	−	92.1521i	0.169709	−	0.169709i
$544$		0			0
$545$	−105.409	+	111.796i	−0.193411	+	0.205131i
$546$		0			0
$547$	−428.552			−0.783459			−0.391730	−	0.920080i	$-0.628123\pi$
$547$	−428.552			−0.783459			−0.391730	+	0.920080i	$0.628123\pi$
$548$		0			0
$549$	−312.375	+	312.375i	−0.568989	+	0.568989i
$550$		0			0
$551$			323.808i			0.587673i
$552$		0			0
$553$	−151.863	−	151.863i	−0.274616	−	0.274616i
$554$		0			0
$555$	−5.63288	−	191.545i	−0.0101493	−	0.345126i
$556$		0			0
$557$	−816.333			−1.46559			−0.732794	−	0.680450i	$-0.761784\pi$
$557$	−816.333			−1.46559			−0.732794	+	0.680450i	$0.761784\pi$
$558$		0			0
$559$			614.698i			1.09964i
$560$		0			0
$561$	−467.766			−0.833807
$562$		0			0
$563$		−	242.788i		−	0.431240i	−0.976477	−	0.215620i	$-0.930823\pi$
$563$		−	242.788i		−	0.431240i	0.976477	−	0.215620i	$-0.0691772\pi$
$564$		0			0
$565$	652.679	+	615.389i	1.15518	+	1.08918i
$566$		0			0
$567$	−169.432	+	169.432i	−0.298822	+	0.298822i
$568$		0			0
$569$	310.112			0.545011			0.272506	−	0.962154i	$-0.412148\pi$
$569$	310.112			0.545011			0.272506	+	0.962154i	$0.412148\pi$
$570$		0			0
$571$	−403.169	−	403.169i	−0.706075	−	0.706075i	0.259632	−	0.965708i	$-0.416399\pi$
$571$	−403.169	−	403.169i	−0.706075	−	0.706075i	−0.965708	+	0.259632i	$0.916399\pi$
$572$		0			0
$573$			91.1587i			0.159090i
$574$		0			0
$575$	821.962	+	730.570i	1.42950	+	1.27056i
$576$		0			0
$577$	−47.9244	−	47.9244i	−0.0830580	−	0.0830580i	0.664357	−	0.747415i	$-0.268705\pi$
$577$	−47.9244	−	47.9244i	−0.0830580	−	0.0830580i	−0.747415	+	0.664357i	$0.768705\pi$
$578$		0			0
$579$	278.888	+	278.888i	0.481671	+	0.481671i
$580$		0			0
$581$	217.922	+	217.922i	0.375081	+	0.375081i
$582$		0			0
$583$	−32.9238	−	32.9238i	−0.0564732	−	0.0564732i
$584$		0			0
$585$	422.928	−	12.4373i	0.722953	−	0.0212603i
$586$		0			0
$587$		−	466.709i		−	0.795075i	−0.917586	−	0.397538i	$-0.869865\pi$
$587$		−	466.709i		−	0.795075i	0.917586	−	0.397538i	$-0.130135\pi$
$588$		0			0
$589$	−63.3971	−	63.3971i	−0.107635	−	0.107635i
$590$		0			0
$591$	−811.614			−1.37329
$592$		0			0
$593$	−214.674	+	214.674i	−0.362013	+	0.362013i	−0.864554	−	0.502541i	$-0.832399\pi$
$593$	−214.674	+	214.674i	−0.362013	+	0.362013i	0.502541	+	0.864554i	$0.332399\pi$
$594$		0			0
$595$	4.99458	+	169.840i	0.00839425	+	0.285445i
$596$		0			0
$597$		−	407.514i		−	0.682603i
$598$		0			0
$599$	1167.57			1.94920			0.974600	−	0.223954i	$-0.0718964\pi$
$599$	1167.57			1.94920			0.974600	+	0.223954i	$0.0718964\pi$
$600$		0			0
$601$		−	82.0258i		−	0.136482i	−0.997669	−	0.0682411i	$-0.978261\pi$
$601$		−	82.0258i		−	0.136482i	0.997669	−	0.0682411i	$-0.0217387\pi$
$602$		0			0
$603$	−383.894			−0.636640
$604$		0			0
$605$	233.311	−	6.86112i	0.385639	−	0.0113407i
$606$		0			0
$607$	−419.964	−	419.964i	−0.691869	−	0.691869i	0.270774	−	0.962643i	$-0.412720\pi$
$607$	−419.964	−	419.964i	−0.691869	−	0.691869i	−0.962643	+	0.270774i	$0.912720\pi$
$608$		0			0
$609$		−	506.706i		−	0.832029i
$610$		0			0
$611$	−523.542	+	523.542i	−0.856861	+	0.856861i
$612$		0			0
$613$	−725.219			−1.18307			−0.591533	−	0.806281i	$-0.701477\pi$
$613$	−725.219			−1.18307			−0.591533	+	0.806281i	$0.701477\pi$
$614$		0			0
$615$	9.66016	+	328.492i	0.0157076	+	0.534134i
$616$		0			0
$617$	−321.786	+	321.786i	−0.521534	+	0.521534i	−0.918034	−	0.396501i	$-0.870224\pi$
$617$	−321.786	+	321.786i	−0.521534	+	0.521534i	0.396501	+	0.918034i	$0.370224\pi$
$618$		0			0
$619$	−161.377	+	161.377i	−0.260706	+	0.260706i	−0.825341	−	0.564635i	$-0.809017\pi$
$619$	−161.377	+	161.377i	−0.260706	+	0.260706i	0.564635	+	0.825341i	$0.309017\pi$
$620$		0			0
$621$	395.828	−	395.828i	0.637404	−	0.637404i
$622$		0			0
$623$	−74.0512	+	74.0512i	−0.118862	+	0.118862i
$624$		0			0
$625$	620.683	−	73.3285i	0.993094	−	0.117326i
$626$		0			0
$627$	194.031			0.309459
$628$		0			0
$629$	−100.179	+	100.179i	−0.159267	+	0.159267i
$630$		0			0
$631$			620.361i			0.983140i	0.870838	+	0.491570i	$0.163577\pi$
$631$			620.361i			0.983140i	−0.870838	+	0.491570i	$0.836423\pi$
$632$		0			0
$633$	19.6598	+	19.6598i	0.0310581	+	0.0310581i
$634$		0			0
$635$	62.9990	−	66.8165i	0.0992110	−	0.105223i
$636$		0			0
$637$	−644.419			−1.01165
$638$		0			0
$639$		−	391.096i		−	0.612043i
$640$		0			0
$641$	890.879			1.38983			0.694914	−	0.719093i	$-0.255443\pi$
$641$	890.879			1.38983			0.694914	+	0.719093i	$0.255443\pi$
$642$		0			0
$643$		−	304.169i		−	0.473047i	−0.971626	−	0.236523i	$-0.923992\pi$
$643$		−	304.169i		−	0.473047i	0.971626	−	0.236523i	$-0.0760080\pi$
$644$		0			0
$645$	−789.818	+	23.2266i	−1.22452	+	0.0360103i
$646$		0			0
$647$	−71.6597	+	71.6597i	−0.110757	+	0.110757i	−0.760313	−	0.649556i	$-0.774955\pi$
$647$	−71.6597	+	71.6597i	−0.110757	+	0.110757i	0.649556	+	0.760313i	$0.274955\pi$
$648$		0			0
$649$	−166.035			−0.255832
$650$		0			0
$651$	99.2060	+	99.2060i	0.152390	+	0.152390i
$652$		0			0
$653$			304.063i			0.465640i	0.972520	+	0.232820i	$0.0747953\pi$
$653$			304.063i			0.465640i	−0.972520	+	0.232820i	$0.925205\pi$
$654$		0			0
$655$	−407.181	−	383.916i	−0.621650	−	0.586132i
$656$		0			0
$657$	−481.900	−	481.900i	−0.733486	−	0.733486i
$658$		0			0
$659$	−560.205	−	560.205i	−0.850083	−	0.850083i	0.140060	−	0.990143i	$-0.455270\pi$
$659$	−560.205	−	560.205i	−0.850083	−	0.850083i	−0.990143	+	0.140060i	$0.955270\pi$
$660$		0			0
$661$	−863.183	−	863.183i	−1.30588	−	1.30588i	−0.924364	−	0.381511i	$-0.875404\pi$
$661$	−863.183	−	863.183i	−1.30588	−	1.30588i	−0.381511	−	0.924364i	$-0.624596\pi$
$662$		0			0
$663$	−571.774	−	571.774i	−0.862404	−	0.862404i
$664$		0			0
$665$	−2.07176	−	70.4500i	−0.00311544	−	0.105940i
$666$		0			0
$667$			2424.59i			3.63507i
$668$		0			0
$669$	446.634	+	446.634i	0.667614	+	0.667614i
$670$		0			0
$671$	670.671			0.999509
$672$		0			0
$673$	720.376	−	720.376i	1.07040	−	1.07040i	0.0730683	−	0.997327i	$-0.476721\pi$
$673$	720.376	−	720.376i	1.07040	−	1.07040i	0.997327	−	0.0730683i	$-0.0232791\pi$
$674$		0			0
$675$	−18.6956	−	317.595i	−0.0276971	−	0.470511i
$676$		0			0
$677$		−	110.173i		−	0.162738i	−0.996684	−	0.0813688i	$-0.974071\pi$
$677$		−	110.173i		−	0.162738i	0.996684	−	0.0813688i	$-0.0259292\pi$
$678$		0			0
$679$	169.899			0.250219
$680$		0			0
$681$		−	982.933i		−	1.44337i
$682$		0			0
$683$	537.997			0.787697			0.393849	−	0.919175i	$-0.371143\pi$
$683$	537.997			0.787697			0.393849	+	0.919175i	$0.371143\pi$
$684$		0			0
$685$	804.143	+	758.198i	1.17393	+	1.10686i
$686$		0			0
$687$	57.7934	+	57.7934i	0.0841244	+	0.0841244i
$688$		0			0
$689$		−	80.4890i		−	0.116820i
$690$		0			0
$691$	433.458	−	433.458i	0.627290	−	0.627290i	−0.320095	−	0.947385i	$-0.603715\pi$
$691$	433.458	−	433.458i	0.627290	−	0.627290i	0.947385	+	0.320095i	$0.103715\pi$
$692$		0			0
$693$	−117.459			−0.169494
$694$		0			0
$695$	54.6678	+	51.5443i	0.0786587	+	0.0741645i
$696$		0			0
$697$	171.803	−	171.803i	0.246490	−	0.246490i
$698$		0			0
$699$	−408.221	+	408.221i	−0.584007	+	0.584007i
$700$		0			0
$701$	−390.739	+	390.739i	−0.557402	+	0.557402i	−0.928567	−	0.371165i	$-0.878958\pi$
$701$	−390.739	+	390.739i	−0.557402	+	0.557402i	0.371165	+	0.928567i	$0.378958\pi$
$702$		0			0
$703$	41.5546	−	41.5546i	0.0591103	−	0.0591103i
$704$		0			0
$705$	−692.475	−	652.911i	−0.982234	−	0.926115i
$706$		0			0
$707$	246.035			0.347999
$708$		0			0
$709$	340.829	−	340.829i	0.480718	−	0.480718i	−0.424643	−	0.905361i	$-0.639600\pi$
$709$	340.829	−	340.829i	0.480718	−	0.480718i	0.905361	+	0.424643i	$0.139600\pi$
$710$		0			0
$711$			508.252i			0.714842i
$712$		0			0
$713$	−474.702	−	474.702i	−0.665782	−	0.665782i
$714$		0			0
$715$	−467.366	−	440.663i	−0.653658	−	0.616312i
$716$		0			0
$717$	−30.7618			−0.0429035
$718$		0			0
$719$			1185.79i			1.64922i	0.565702	+	0.824609i	$0.308605\pi$
$719$			1185.79i			1.64922i	−0.565702	+	0.824609i	$0.691395\pi$
$720$		0			0
$721$	−119.716			−0.166041
$722$		0			0
$723$			35.2316i			0.0487298i
$724$		0			0
$725$	1029.95	+	915.435i	1.42062	+	1.26267i
$726$		0			0
$727$	493.648	−	493.648i	0.679021	−	0.679021i	−0.280758	−	0.959779i	$-0.590586\pi$
$727$	493.648	−	493.648i	0.679021	−	0.679021i	0.959779	+	0.280758i	$0.0905857\pi$
$728$		0			0
$729$	128.254			0.175932
$730$		0			0
$731$	413.079	+	413.079i	0.565088	+	0.565088i
$732$		0			0
$733$			864.330i			1.17917i	0.807707	+	0.589584i	$0.200708\pi$
$733$			864.330i			1.17917i	−0.807707	+	0.589584i	$0.799292\pi$
$734$		0			0
$735$	−24.3497	−	828.006i	−0.0331288	−	1.12654i
$736$		0			0
$737$	412.111	+	412.111i	0.559174	+	0.559174i
$738$		0			0
$739$	−667.334	−	667.334i	−0.903023	−	0.903023i	0.0926732	−	0.995697i	$-0.470459\pi$
$739$	−667.334	−	667.334i	−0.903023	−	0.903023i	−0.995697	+	0.0926732i	$0.970459\pi$
$740$		0			0
$741$	237.173	+	237.173i	0.320072	+	0.320072i
$742$		0			0
$743$	−87.5208	−	87.5208i	−0.117794	−	0.117794i	0.645753	−	0.763547i	$-0.276544\pi$
$743$	−87.5208	−	87.5208i	−0.117794	−	0.117794i	−0.763547	+	0.645753i	$0.776544\pi$
$744$		0			0
$745$	−306.678	−	289.156i	−0.411648	−	0.388129i
$746$		0			0
$747$		−	729.341i		−	0.976360i
$748$		0			0
$749$	−139.300	−	139.300i	−0.185981	−	0.185981i
$750$		0			0
$751$	−809.874			−1.07839			−0.539197	−	0.842180i	$-0.681272\pi$
$751$	−809.874			−1.07839			−0.539197	+	0.842180i	$0.681272\pi$
$752$		0			0
$753$	1249.22	−	1249.22i	1.65899	−	1.65899i
$754$		0			0
$755$	−17.7490	+	0.521956i	−0.0235086	+	0.000691332i
$756$		0			0
$757$		−	1268.47i		−	1.67565i	−0.545937	−	0.837827i	$-0.683826\pi$
$757$		−	1268.47i		−	1.67565i	0.545937	−	0.837827i	$-0.316174\pi$
$758$		0			0
$759$	1452.85			1.91417
$760$		0			0
$761$		−	332.602i		−	0.437059i	−0.975830	−	0.218529i	$-0.929874\pi$
$761$		−	332.602i		−	0.437059i	0.975830	−	0.218529i	$-0.0701259\pi$
$762$		0			0
$763$	73.7372			0.0966411
$764$		0			0
$765$	275.851	−	292.567i	0.360590	−	0.382440i
$766$		0			0
$767$	−202.953	−	202.953i	−0.264606	−	0.264606i
$768$		0			0
$769$		−	519.527i		−	0.675588i	−0.941220	−	0.337794i	$-0.890319\pi$
$769$		−	519.527i		−	0.675588i	0.941220	−	0.337794i	$-0.109681\pi$
$770$		0			0
$771$	709.134	−	709.134i	0.919759	−	0.919759i
$772$		0			0
$773$	−895.057			−1.15790			−0.578950	−	0.815363i	$-0.696537\pi$
$773$	−895.057			−1.15790			−0.578950	+	0.815363i	$0.696537\pi$
$774$		0			0
$775$	−380.880	+	22.4209i	−0.491458	+	0.0289302i
$776$		0			0
$777$	−65.0260	+	65.0260i	−0.0836886	+	0.0836886i
$778$		0			0
$779$	−71.2645	+	71.2645i	−0.0914820	+	0.0914820i
$780$		0			0
$781$	−419.842	+	419.842i	−0.537570	+	0.537570i
$782$		0			0
$783$	495.989	−	495.989i	0.633447	−	0.633447i
$784$		0			0
$785$	0.335631	+	11.4131i	0.000427556	+	0.0145390i
$786$		0			0
$787$	58.1451			0.0738820			0.0369410	−	0.999317i	$-0.488239\pi$
$787$	58.1451			0.0738820			0.0369410	+	0.999317i	$0.488239\pi$
$788$		0			0
$789$	−774.544	+	774.544i	−0.981678	+	0.981678i
$790$		0			0
$791$		−	430.486i		−	0.544230i
$792$		0			0
$793$	819.795	+	819.795i	1.03379	+	1.03379i
$794$		0			0
$795$	103.419	−	3.04131i	0.130087	−	0.00382555i
$796$		0			0
$797$	−238.679			−0.299472			−0.149736	−	0.988726i	$-0.547842\pi$
$797$	−238.679			−0.299472			−0.149736	+	0.988726i	$0.547842\pi$
$798$		0			0
$799$			703.644i			0.880656i
$800$		0			0
$801$	247.834			0.309406
$802$		0			0
$803$			1034.64i			1.28847i
$804$		0			0
$805$	−15.5129	−	527.513i	−0.0192707	−	0.655295i
$806$		0			0
$807$	519.060	−	519.060i	0.643197	−	0.643197i
$808$		0			0
$809$	612.464			0.757062			0.378531	−	0.925589i	$-0.376429\pi$
$809$	612.464			0.757062			0.378531	+	0.925589i	$0.376429\pi$
$810$		0			0
$811$	−618.905	−	618.905i	−0.763138	−	0.763138i	0.213750	−	0.976888i	$-0.431432\pi$
$811$	−618.905	−	618.905i	−0.763138	−	0.763138i	−0.976888	+	0.213750i	$0.931432\pi$
$812$		0			0
$813$			1058.27i			1.30168i
$814$		0			0
$815$	583.594	−	17.1621i	0.716066	−	0.0210578i
$816$		0			0
$817$	−171.346	−	171.346i	−0.209726	−	0.209726i
$818$		0			0
$819$	−143.576	−	143.576i	−0.175307	−	0.175307i
$820$		0			0
$821$	67.0385	+	67.0385i	0.0816547	+	0.0816547i	0.746755	−	0.665100i	$-0.231611\pi$
$821$	67.0385	+	67.0385i	0.0816547	+	0.0816547i	−0.665100	+	0.746755i	$0.731611\pi$
$822$		0			0
$823$	720.633	+	720.633i	0.875617	+	0.875617i	0.993078	−	0.117461i	$-0.0374754\pi$
$823$	720.633	+	720.633i	0.875617	+	0.875617i	−0.117461	+	0.993078i	$0.537475\pi$
$824$		0			0
$825$	548.543	−	617.164i	0.664901	−	0.748077i
$826$		0			0
$827$		−	1189.91i		−	1.43883i	−0.694582	−	0.719413i	$-0.744411\pi$
$827$		−	1189.91i		−	1.43883i	0.694582	−	0.719413i	$-0.255589\pi$
$828$		0			0
$829$	−77.7453	−	77.7453i	−0.0937821	−	0.0937821i	0.658659	−	0.752441i	$-0.271124\pi$
$829$	−77.7453	−	77.7453i	−0.0937821	−	0.0937821i	−0.752441	+	0.658659i	$0.771124\pi$
$830$		0			0
$831$	−707.653			−0.851567
$832$		0			0
$833$	−433.052	+	433.052i	−0.519870	+	0.519870i
$834$		0			0
$835$	107.891	+	101.727i	0.129211	+	0.121829i
$836$		0			0
$837$			194.216i			0.232038i
$838$		0			0
$839$	1281.90			1.52789			0.763947	−	0.645279i	$-0.223259\pi$
$839$	1281.90			1.52789			0.763947	+	0.645279i	$0.223259\pi$
$840$		0			0
$841$			2197.12i			2.61251i
$842$		0			0
$843$	666.511			0.790641
$844$		0			0
$845$	−7.80165	−	265.294i	−0.00923273	−	0.313957i
$846$		0			0
$847$	−79.2049	−	79.2049i	−0.0935123	−	0.0935123i
$848$		0			0
$849$		−	127.191i		−	0.149812i
$850$		0			0
$851$	311.151	−	311.151i	0.365629	−	0.365629i
$852$		0			0
$853$	−62.5726			−0.0733559			−0.0366779	−	0.999327i	$-0.511678\pi$
$853$	−62.5726			−0.0733559			−0.0366779	+	0.999327i	$0.511678\pi$
$854$		0			0
$855$	−114.424	+	121.358i	−0.133829	+	0.141939i
$856$		0			0
$857$	1102.12	−	1102.12i	1.28602	−	1.28602i	0.348838	−	0.937183i	$-0.386577\pi$
$857$	1102.12	−	1102.12i	1.28602	−	1.28602i	0.937183	−	0.348838i	$-0.113423\pi$
$858$		0			0
$859$	677.212	−	677.212i	0.788373	−	0.788373i	−0.192855	−	0.981227i	$-0.561775\pi$
$859$	677.212	−	677.212i	0.788373	−	0.788373i	0.981227	+	0.192855i	$0.0617746\pi$
$860$		0			0
$861$	111.517	−	111.517i	0.129520	−	0.129520i
$862$		0			0
$863$	448.822	−	448.822i	0.520072	−	0.520072i	−0.397521	−	0.917593i	$-0.630129\pi$
$863$	448.822	−	448.822i	0.520072	−	0.520072i	0.917593	+	0.397521i	$0.130129\pi$
$864$		0			0
$865$	−1211.53	+	35.6283i	−1.40062	+	0.0411888i
$866$		0			0
$867$	338.761			0.390728
$868$		0			0
$869$	545.611	−	545.611i	0.627860	−	0.627860i
$870$		0			0
$871$			1007.49i			1.15670i
$872$		0			0
$873$	−284.307	−	284.307i	−0.325667	−	0.325667i
$874$		0			0
$875$	−229.941	−	192.579i	−0.262790	−	0.220090i
$876$		0			0
$877$	834.366			0.951387			0.475693	−	0.879611i	$-0.342197\pi$
$877$	834.366			0.951387			0.475693	+	0.879611i	$0.342197\pi$
$878$		0			0
$879$		−	745.184i		−	0.847764i
$880$		0			0
$881$	678.979			0.770691			0.385346	−	0.922772i	$-0.374082\pi$
$881$	678.979			0.770691			0.385346	+	0.922772i	$0.374082\pi$
$882$		0			0
$883$			708.993i			0.802937i	0.915873	+	0.401468i	$0.131500\pi$
$883$			708.993i			0.802937i	−0.915873	+	0.401468i	$0.868500\pi$
$884$		0			0
$885$	253.103	−	268.441i	0.285993	−	0.303323i
$886$		0			0
$887$	−472.922	+	472.922i	−0.533170	+	0.533170i	−0.921514	−	0.388344i	$-0.873047\pi$
$887$	−472.922	+	472.922i	−0.533170	+	0.533170i	0.388344	+	0.921514i	$0.373047\pi$
$888$		0			0
$889$	−44.0700			−0.0495726
$890$		0			0
$891$	−608.735	−	608.735i	−0.683204	−	0.683204i
$892$		0			0
$893$		−	291.874i		−	0.326846i
$894$		0			0
$895$	−858.649	+	910.681i	−0.959384	+	1.01752i
$896$		0			0
$897$	1775.90	+	1775.90i	1.97982	+	1.97982i
$898$		0			0
$899$	−594.822	−	594.822i	−0.661648	−	0.661648i
$900$		0			0
$901$	−54.0889	−	54.0889i	−0.0600321	−	0.0600321i
$902$		0			0
$903$	268.129	+	268.129i	0.296931	+	0.296931i
$904$		0			0
$905$	116.677	−	123.747i	0.128925	−	0.136737i
$906$		0			0
$907$		−	27.0583i		−	0.0298328i	−0.999889	−	0.0149164i	$-0.995252\pi$
$907$		−	27.0583i		−	0.0298328i	0.999889	−	0.0149164i	$-0.00474821\pi$
$908$		0			0
$909$	−411.714	−	411.714i	−0.452931	−	0.452931i
$910$		0			0
$911$	51.9221			0.0569946			0.0284973	−	0.999594i	$-0.490928\pi$
$911$	51.9221			0.0569946			0.0284973	+	0.999594i	$0.490928\pi$
$912$		0			0
$913$	−782.949	+	782.949i	−0.857557	+	0.857557i
$914$		0			0
$915$	−1022.37	+	1084.32i	−1.11734	+	1.18505i
$916$		0			0
$917$			268.563i			0.292871i
$918$		0			0
$919$	−365.843			−0.398089			−0.199044	−	0.979990i	$-0.563784\pi$
$919$	−365.843			−0.398089			−0.199044	+	0.979990i	$0.563784\pi$
$920$		0			0
$921$			1982.70i			2.15277i
$922$		0			0
$923$	−1026.39			−1.11201
$924$		0			0
$925$	−14.6961	−	249.654i	−0.0158877	−	0.269896i
$926$		0			0
$927$	200.332	+	200.332i	0.216108	+	0.216108i
$928$		0			0
$929$		−	1736.63i		−	1.86936i	−0.355491	−	0.934680i	$-0.615686\pi$
$929$		−	1736.63i		−	1.86936i	0.355491	−	0.934680i	$-0.384314\pi$
$930$		0			0
$931$	179.631	−	179.631i	0.192944	−	0.192944i
$932$		0			0
$933$	1849.88			1.98272
$934$		0			0
$935$	−610.199	+	17.9445i	−0.652619	+	0.0191919i
$936$		0			0
$937$	−26.5779	+	26.5779i	−0.0283649	+	0.0283649i	−0.721147	−	0.692782i	$-0.756385\pi$
$937$	−26.5779	+	26.5779i	−0.0283649	+	0.0283649i	0.692782	+	0.721147i	$0.256385\pi$
$938$		0			0
$939$	−368.544	+	368.544i	−0.392486	+	0.392486i
$940$		0			0
$941$	770.144	−	770.144i	0.818431	−	0.818431i	−0.167450	−	0.985881i	$-0.553553\pi$
$941$	770.144	−	770.144i	0.818431	−	0.818431i	0.985881	+	0.167450i	$0.0535532\pi$
$942$		0			0
$943$	−533.611	+	533.611i	−0.565865	+	0.565865i
$944$		0			0
$945$	−104.738	+	111.084i	−0.110833	+	0.117550i
$946$		0			0
$947$	585.598			0.618372			0.309186	−	0.951002i	$-0.399943\pi$
$947$	585.598			0.618372			0.309186	+	0.951002i	$0.399943\pi$
$948$		0			0
$949$	−1264.70	+	1264.70i	−1.33266	+	1.33266i
$950$		0			0
$951$		−	1320.66i		−	1.38870i
$952$		0			0
$953$	−1209.67	−	1209.67i	−1.26933	−	1.26933i	−0.946434	−	0.322897i	$-0.895343\pi$
$953$	−1209.67	−	1209.67i	−1.26933	−	1.26933i	−0.322897	−	0.946434i	$-0.604657\pi$
$954$		0			0
$955$	3.49704	+	118.916i	0.00366182	+	0.124520i
$956$		0			0
$957$	1820.49			1.90229
$958$		0			0
$959$		−	530.386i		−	0.553062i
$960$		0			0
$961$	−728.084			−0.757632
$962$		0			0
$963$			466.207i			0.484120i
$964$		0			0
$965$	374.507	+	353.109i	0.388090	+	0.365916i
$966$		0			0
$967$	−265.767	+	265.767i	−0.274837	+	0.274837i	−0.831044	−	0.556207i	$-0.812256\pi$
$967$	−265.767	+	265.767i	−0.274837	+	0.274837i	0.556207	+	0.831044i	$0.312256\pi$
$968$		0			0
$969$	318.763			0.328961
$970$		0			0
$971$	703.377	+	703.377i	0.724384	+	0.724384i	0.969495	−	0.245111i	$-0.0788245\pi$
$971$	703.377	+	703.377i	0.724384	+	0.724384i	−0.245111	+	0.969495i	$0.578824\pi$
$972$		0			0
$973$		−	36.0571i		−	0.0370576i
$974$		0			0
$975$	1424.90	−	83.8784i	1.46144	−	0.0860291i
$976$		0			0
$977$	−320.028	−	320.028i	−0.327562	−	0.327562i	0.524097	−	0.851659i	$-0.324403\pi$
$977$	−320.028	−	320.028i	−0.327562	−	0.327562i	−0.851659	+	0.524097i	$0.824403\pi$
$978$		0			0
$979$	−266.050	−	266.050i	−0.271757	−	0.271757i
$980$		0			0
$981$	−123.391	−	123.391i	−0.125781	−	0.125781i
$982$		0			0
$983$	331.430	+	331.430i	0.337162	+	0.337162i	0.855298	−	0.518136i	$-0.173374\pi$
$983$	331.430	+	331.430i	0.337162	+	0.337162i	−0.518136	+	0.855298i	$0.673374\pi$
$984$		0			0
$985$	−1058.75	+	31.1352i	−1.07487	+	0.0316093i
$986$		0			0
$987$			456.734i			0.462750i
$988$		0			0
$989$	−1283.00	−	1283.00i	−1.29727	−	1.29727i
$990$		0			0
$991$	1610.77			1.62540			0.812699	−	0.582684i	$-0.197997\pi$
$991$	1610.77			1.62540			0.812699	+	0.582684i	$0.197997\pi$
$992$		0			0
$993$	−783.336	+	783.336i	−0.788858	+	0.788858i
$994$		0			0
$995$	−15.6331	−	531.600i	−0.0157116	−	0.534271i
$996$		0			0
$997$		−	513.114i		−	0.514658i	−0.966324	−	0.257329i	$-0.917158\pi$
$997$		−	513.114i		−	0.514658i	0.966324	−	0.257329i	$-0.0828425\pi$
$998$		0			0
$999$	−127.301			−0.127429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.i.a.177.19		44
4.3	odd	2		80.3.i.a.37.19	yes	44
5.3	odd	4		320.3.t.a.113.4		44
8.3	odd	2		640.3.i.b.97.19		44
8.5	even	2		640.3.i.a.97.4		44
16.3	odd	4		80.3.t.a.77.9	yes	44
16.5	even	4		640.3.t.a.417.19		44
16.11	odd	4		640.3.t.b.417.4		44
16.13	even	4		320.3.t.a.17.4		44
20.3	even	4		80.3.t.a.53.9	yes	44
20.7	even	4		400.3.t.b.293.14		44
20.19	odd	2		400.3.i.b.357.4		44
40.3	even	4		640.3.t.b.353.4		44
40.13	odd	4		640.3.t.a.353.19		44
80.3	even	4		80.3.i.a.13.19	✓	44
80.13	odd	4	inner	320.3.i.a.273.4		44
80.19	odd	4		400.3.t.b.157.14		44
80.43	even	4		640.3.i.b.33.4		44
80.53	odd	4		640.3.i.a.33.19		44
80.67	even	4		400.3.i.b.93.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.19	✓	44	80.3	even	4
80.3.i.a.37.19	yes	44	4.3	odd	2
80.3.t.a.53.9	yes	44	20.3	even	4
80.3.t.a.77.9	yes	44	16.3	odd	4
320.3.i.a.177.19		44	1.1	even	1	trivial
320.3.i.a.273.4		44	80.13	odd	4	inner
320.3.t.a.17.4		44	16.13	even	4
320.3.t.a.113.4		44	5.3	odd	4
400.3.i.b.93.4		44	80.67	even	4
400.3.i.b.357.4		44	20.19	odd	2
400.3.t.b.157.14		44	80.19	odd	4
400.3.t.b.293.14		44	20.7	even	4
640.3.i.a.33.19		44	80.53	odd	4
640.3.i.a.97.4		44	8.5	even	2
640.3.i.b.33.4		44	80.43	even	4
640.3.i.b.97.19		44	8.3	odd	2
640.3.t.a.353.19		44	40.13	odd	4
640.3.t.a.417.19		44	16.5	even	4
640.3.t.b.353.4		44	40.3	even	4
640.3.t.b.417.4		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)

\(f(q)\)	\(=\)	\(q+3.83124i q^{3} +(0.146974 + 4.99784i) q^{5} +(1.69668 - 1.69668i) q^{7} -5.67842 q^{9} +O(q^{10})\)	\(q+3.83124i q^{3} +(0.146974 + 4.99784i) q^{5} +(1.69668 - 1.69668i) q^{7} -5.67842 q^{9} +(6.09580 + 6.09580i) q^{11} +14.9024i q^{13} +(-19.1479 + 0.563095i) q^{15} +(10.0145 + 10.0145i) q^{17} +(-4.15403 - 4.15403i) q^{19} +(6.50038 + 6.50038i) q^{21} +(-31.1044 - 31.1044i) q^{23} +(-24.9568 + 1.46911i) q^{25} +12.7258i q^{27} +(-38.9751 - 38.9751i) q^{29} +15.2616 q^{31} +(-23.3545 + 23.3545i) q^{33} +(8.72908 + 8.23034i) q^{35} +10.0034i q^{37} -57.0947 q^{39} -17.1555i q^{41} +41.2482 q^{43} +(-0.834582 - 28.3798i) q^{45} +(35.1314 + 35.1314i) q^{47} +43.2426i q^{49} +(-38.3679 + 38.3679i) q^{51} -5.40107 q^{53} +(-29.5699 + 31.3618i) q^{55} +(15.9151 - 15.9151i) q^{57} +(-13.6188 + 13.6188i) q^{59} +(55.0109 - 55.0109i) q^{61} +(-9.63443 + 9.63443i) q^{63} +(-74.4798 + 2.19027i) q^{65} +67.6058 q^{67} +(119.168 - 119.168i) q^{69} +68.8740i q^{71} +(84.8652 + 84.8652i) q^{73} +(-5.62851 - 95.6155i) q^{75} +20.6852 q^{77} -89.5060i q^{79} -99.8613 q^{81} +128.441i q^{83} +(-48.5789 + 51.5226i) q^{85} +(149.323 - 149.323i) q^{87} -43.6449 q^{89} +(25.2845 + 25.2845i) q^{91} +58.4708i q^{93} +(20.1507 - 21.3717i) q^{95} +(50.0681 + 50.0681i) q^{97} +(-34.6145 - 34.6145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) \) 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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