LMFDB - Embedded newform 320.3.t.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(17,320)]

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, 3, 1]))

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

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

chi := DirichletCharacter("320.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.t (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.71936845953$
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			17.4
Character	$\chi$	$=$	320.17
Dual form			320.3.t.a.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.83124 q^{3} +(4.99784 - 0.146974i) q^{5} +(-1.69668 + 1.69668i) q^{7} +5.67842 q^{9} +O(q^{10})$	\(q-3.83124 q^{3} +(4.99784 - 0.146974i) q^{5} +(-1.69668 + 1.69668i) q^{7} +5.67842 q^{9} +(6.09580 - 6.09580i) q^{11} -14.9024 q^{13} +(-19.1479 + 0.563095i) q^{15} +(10.0145 + 10.0145i) q^{17} +(4.15403 - 4.15403i) q^{19} +(6.50038 - 6.50038i) q^{21} +(31.1044 + 31.1044i) q^{23} +(24.9568 - 1.46911i) q^{25} +12.7258 q^{27} +(38.9751 - 38.9751i) q^{29} +15.2616 q^{31} +(-23.3545 + 23.3545i) q^{33} +(-8.23034 + 8.72908i) q^{35} +10.0034 q^{37} +57.0947 q^{39} +17.1555i q^{41} -41.2482i q^{43} +(28.3798 - 0.834582i) q^{45} +(35.1314 + 35.1314i) q^{47} +43.2426i q^{49} +(-38.3679 - 38.3679i) q^{51} +5.40107i q^{53} +(29.5699 - 31.3618i) q^{55} +(-15.9151 + 15.9151i) q^{57} +(13.6188 + 13.6188i) q^{59} +(55.0109 + 55.0109i) q^{61} +(-9.63443 + 9.63443i) q^{63} +(-74.4798 + 2.19027i) q^{65} +67.6058i q^{67} +(-119.168 - 119.168i) q^{69} -68.8740i q^{71} +(-84.8652 - 84.8652i) q^{73} +(-95.6155 + 5.62851i) q^{75} +20.6852i q^{77} -89.5060i q^{79} -99.8613 q^{81} -128.441 q^{83} +(51.5226 + 48.5789i) q^{85} +(-149.323 + 149.323i) q^{87} +43.6449 q^{89} +(25.2845 - 25.2845i) q^{91} -58.4708 q^{93} +(20.1507 - 21.3717i) q^{95} +(50.0681 + 50.0681i) q^{97} +(34.6145 - 34.6145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−3.83124			−1.27708			−0.638540	−	0.769588i	$-0.720461\pi$
$3$	−3.83124			−1.27708			−0.638540	+	0.769588i	$0.720461\pi$
$4$		0			0
$5$	4.99784	−	0.146974i	0.999568	−	0.0293949i
$5$	4.99784	−	0.146974i	0.999568	−	0.0293949i
$6$		0			0
$7$	−1.69668	+	1.69668i	−0.242382	+	0.242382i	−0.817835	−	0.575453i	$-0.804826\pi$
$7$	−1.69668	+	1.69668i	−0.242382	+	0.242382i	0.575453	+	0.817835i	$0.304826\pi$
$8$		0			0
$9$	5.67842			0.630935
$10$		0			0
$11$	6.09580	−	6.09580i	0.554164	−	0.554164i	−0.373476	−	0.927640i	$-0.621834\pi$
$11$	6.09580	−	6.09580i	0.554164	−	0.554164i	0.927640	+	0.373476i	$0.121834\pi$
$12$		0			0
$13$	−14.9024			−1.14634			−0.573169	−	0.819437i	$-0.694286\pi$
$13$	−14.9024			−1.14634			−0.573169	+	0.819437i	$0.694286\pi$
$14$		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	$-0.700592\pi$
$19$	4.15403	−	4.15403i	0.218633	−	0.218633i	0.807922	+	0.589289i	$0.200592\pi$
$20$		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	$0.155514\pi$
$23$	31.1044	+	31.1044i	1.35237	+	1.35237i	0.469356	+	0.883009i	$0.344486\pi$
$24$		0			0
$25$	24.9568	−	1.46911i	0.998272	−	0.0587644i
$26$		0			0
$27$	12.7258			0.471325
$28$		0			0
$29$	38.9751	−	38.9751i	1.34397	−	1.34397i	0.451901	−	0.892068i	$-0.350746\pi$
$29$	38.9751	−	38.9751i	1.34397	−	1.34397i	0.892068	−	0.451901i	$-0.149254\pi$
$30$		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
$35$	−8.23034	+	8.72908i	−0.235153	+	0.249402i
$36$		0			0
$37$	10.0034			0.270363			0.135181	−	0.990821i	$-0.456838\pi$
$37$	10.0034			0.270363			0.135181	+	0.990821i	$0.456838\pi$
$38$		0			0
$39$	57.0947			1.46397
$40$		0			0
$41$			17.1555i			0.418427i	0.977870	+	0.209213i	$0.0670903\pi$
$41$			17.1555i			0.418427i	−0.977870	+	0.209213i	$0.932910\pi$
$42$		0			0
$43$		−	41.2482i		−	0.959261i	−0.877471	−	0.479630i	$-0.840771\pi$
$43$		−	41.2482i		−	0.959261i	0.877471	−	0.479630i	$-0.159229\pi$
$44$		0			0
$45$	28.3798	−	0.834582i	0.630663	−	0.0185463i
$46$		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
$53$			5.40107i			0.101907i	0.998701	+	0.0509535i	$0.0162260\pi$
$53$			5.40107i			0.101907i	−0.998701	+	0.0509535i	$0.983774\pi$
$54$		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	$-0.197812\pi$
$59$	13.6188	+	13.6188i	0.230827	+	0.230827i	−0.582211	+	0.813038i	$0.697812\pi$
$60$		0			0
$61$	55.0109	+	55.0109i	0.901818	+	0.901818i	0.995593	−	0.0937755i	$-0.0298936\pi$
$61$	55.0109	+	55.0109i	0.901818	+	0.901818i	−0.0937755	+	0.995593i	$0.529894\pi$
$62$		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
$67$			67.6058i			1.00904i	0.863400	+	0.504521i	$0.168331\pi$
$67$			67.6058i			1.00904i	−0.863400	+	0.504521i	$0.831669\pi$
$68$		0			0
$69$	−119.168	−	119.168i	−1.72708	−	1.72708i
$70$		0			0
$71$		−	68.8740i		−	0.970057i	−0.874498	−	0.485028i	$-0.838809\pi$
$71$		−	68.8740i		−	0.970057i	0.874498	−	0.485028i	$-0.161191\pi$
$72$		0			0
$73$	−84.8652	−	84.8652i	−1.16254	−	1.16254i	−0.983918	−	0.178619i	$-0.942837\pi$
$73$	−84.8652	−	84.8652i	−1.16254	−	1.16254i	−0.178619	−	0.983918i	$-0.557163\pi$
$74$		0			0
$75$	−95.6155	+	5.62851i	−1.27487	+	0.0750468i
$76$		0			0
$77$			20.6852i			0.268639i
$78$		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
$83$	−128.441			−1.54748			−0.773740	−	0.633504i	$-0.781616\pi$
$83$	−128.441			−1.54748			−0.773740	+	0.633504i	$0.781616\pi$
$84$		0			0
$85$	51.5226	+	48.5789i	0.606148	+	0.571516i
$86$		0			0
$87$	−149.323	+	149.323i	−1.71636	+	1.71636i
$88$		0			0
$89$	43.6449			0.490392			0.245196	−	0.969474i	$-0.421148\pi$
$89$	43.6449			0.490392			0.245196	+	0.969474i	$0.421148\pi$
$90$		0			0
$91$	25.2845	−	25.2845i	0.277852	−	0.277852i
$92$		0			0
$93$	−58.4708			−0.628718
$94$		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	−0.250297	−	0.968169i	$-0.580528\pi$
$101$	72.5051	−	72.5051i	0.717872	−	0.717872i	0.968169	+	0.250297i	$0.0805282\pi$
$102$		0			0
$103$	35.2795	+	35.2795i	0.342520	+	0.342520i	0.857314	−	0.514794i	$-0.172132\pi$
$103$	35.2795	+	35.2795i	0.342520	+	0.342520i	−0.514794	+	0.857314i	$0.672132\pi$
$104$		0			0
$105$	31.5324	−	33.4432i	0.300309	−	0.318507i
$106$		0			0
$107$	−82.1016			−0.767304			−0.383652	−	0.923478i	$-0.625334\pi$
$107$	−82.1016			−0.767304			−0.383652	+	0.923478i	$0.625334\pi$
$108$		0			0
$109$	−21.7299	+	21.7299i	−0.199357	+	0.199357i	−0.799724	−	0.600367i	$-0.795021\pi$
$109$	−21.7299	+	21.7299i	−0.199357	+	0.199357i	0.600367	+	0.799724i	$0.295021\pi$
$110$		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
$115$	160.026	+	150.883i	1.39153	+	1.31203i
$116$		0			0
$117$	−84.6221			−0.723266
$118$		0			0
$119$	−33.9826			−0.285568
$120$		0			0
$121$			46.6824i			0.385805i
$122$		0			0
$123$		−	65.7268i		−	0.534364i
$124$		0			0
$125$	124.514	−	11.0104i	0.996113	−	0.0880830i
$126$		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	0.337260	−	0.941412i	$-0.390500\pi$
$131$	−79.1439	−	79.1439i	−0.604152	−	0.604152i	−0.941412	+	0.337260i	$0.890500\pi$
$132$		0			0
$133$			14.0961i			0.105986i
$134$		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	$0.548765\pi$
$137$	−156.302	+	156.302i	−1.14089	+	1.14089i	−0.988288	+	0.152600i	$0.951235\pi$
$138$		0			0
$139$	−10.6258	−	10.6258i	−0.0764446	−	0.0764446i	0.667851	−	0.744295i	$-0.267214\pi$
$139$	−10.6258	−	10.6258i	−0.0764446	−	0.0764446i	−0.744295	+	0.667851i	$0.767214\pi$
$140$		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
$147$		−	165.673i		−	1.12703i
$148$		0			0
$149$	59.6091	+	59.6091i	0.400061	+	0.400061i	0.878255	−	0.478193i	$-0.158708\pi$
$149$	59.6091	+	59.6091i	0.400061	+	0.400061i	−0.478193	+	0.878255i	$0.658708\pi$
$150$		0			0
$151$		−	3.55134i		−	0.0235188i	−0.999931	−	0.0117594i	$-0.996257\pi$
$151$		−	3.55134i		−	0.0235188i	0.999931	−	0.0117594i	$-0.00374322\pi$
$152$		0			0
$153$	56.8664	+	56.8664i	0.371676	+	0.371676i
$154$		0			0
$155$	76.2749	−	2.24306i	0.492096	−	0.0144714i
$156$		0			0
$157$			2.28360i			0.0145453i	0.999974	+	0.00727263i	$0.00231497\pi$
$157$			2.28360i			0.0145453i	−0.999974	+	0.00727263i	$0.997685\pi$
$158$		0			0
$159$		−	20.6928i		−	0.130143i
$160$		0			0
$161$	−105.548			−0.655579
$162$		0			0
$163$	116.769			0.716375			0.358188	−	0.933650i	$-0.383395\pi$
$163$	116.769			0.716375			0.358188	+	0.933650i	$0.383395\pi$
$164$		0			0
$165$	−113.289	+	120.155i	−0.686603	+	0.728209i
$166$		0			0
$167$	−20.9709	+	20.9709i	−0.125574	+	0.125574i	−0.767101	−	0.641527i	$-0.778301\pi$
$167$	−20.9709	+	20.9709i	−0.125574	+	0.125574i	0.641527	+	0.767101i	$0.278301\pi$
$168$		0			0
$169$	53.0817			0.314093
$170$		0			0
$171$	23.5883	−	23.5883i	0.137944	−	0.137944i
$172$		0			0
$173$	−242.412			−1.40122			−0.700612	−	0.713543i	$-0.747090\pi$
$173$	−242.412			−1.40122			−0.700612	+	0.713543i	$0.747090\pi$
$174$		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	$-0.996480\pi$
$179$	−177.009	+	177.009i	−0.988880	+	0.988880i	0.0110592	+	0.999939i	$0.496480\pi$
$180$		0			0
$181$	−24.0528	+	24.0528i	−0.132888	+	0.132888i	−0.770422	−	0.637534i	$-0.779955\pi$
$181$	−24.0528	+	24.0528i	−0.132888	+	0.132888i	0.637534	+	0.770422i	$0.279955\pi$
$182$		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
$187$	122.092			0.652901
$188$		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
$195$	285.350	−	8.39146i	1.46333	−	0.0430331i
$196$		0			0
$197$	211.841			1.07533			0.537667	−	0.843157i	$-0.319306\pi$
$197$	211.841			1.07533			0.537667	+	0.843157i	$0.319306\pi$
$198$		0			0
$199$	106.366			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$199$	106.366			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$200$		0			0
$201$		−	259.014i		−	1.28863i
$202$		0			0
$203$			132.256i			0.651508i
$204$		0			0
$205$	2.52142	+	85.7404i	0.0122996	+	0.418246i
$206$		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	0.719162	−	0.694842i	$-0.244526\pi$
$211$	5.13143	+	5.13143i	0.0243196	+	0.0243196i	−0.694842	+	0.719162i	$0.744526\pi$
$212$		0			0
$213$			263.873i			1.23884i
$214$		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
$227$		−	256.557i		−	1.13021i	−0.825020	−	0.565104i	$-0.808836\pi$
$227$		−	256.557i		−	1.13021i	0.825020	−	0.565104i	$-0.191164\pi$
$228$		0			0
$229$	−15.0848	−	15.0848i	−0.0658724	−	0.0658724i	0.673403	−	0.739275i	$-0.264832\pi$
$229$	−15.0848	−	15.0848i	−0.0658724	−	0.0658724i	−0.739275	+	0.673403i	$0.764832\pi$
$230$		0			0
$231$		−	79.2500i		−	0.343074i
$232$		0			0
$233$	−106.551	−	106.551i	−0.457298	−	0.457298i	0.440469	−	0.897768i	$-0.354812\pi$
$233$	−106.551	−	106.551i	−0.457298	−	0.457298i	−0.897768	+	0.440469i	$0.854812\pi$
$234$		0			0
$235$	180.744	+	170.417i	0.769125	+	0.725181i
$236$		0			0
$237$			342.919i			1.44692i
$238$		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
$243$	268.061			1.10313
$244$		0			0
$245$	6.35555	+	216.119i	0.0259410	+	0.882120i
$246$		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	−0.370024	+	0.929022i	$0.620651\pi$
$251$	−326.061	+	326.061i	−1.29905	+	1.29905i	−0.929022	+	0.370024i	$0.879349\pi$
$252$		0			0
$253$	379.212			1.49886
$254$		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	0.209187	−	0.977876i	$-0.432918\pi$
$263$	−202.165	−	202.165i	−0.768689	−	0.768689i	−0.977876	+	0.209187i	$0.932918\pi$
$264$		0			0
$265$	0.793819	+	26.9937i	0.00299554	+	0.101863i
$266$		0			0
$267$	−167.214			−0.626270
$268$		0			0
$269$	135.481	−	135.481i	0.503647	−	0.503647i	−0.408922	−	0.912569i	$-0.634095\pi$
$269$	135.481	−	135.481i	0.503647	−	0.503647i	0.912569	+	0.408922i	$0.134095\pi$
$270$		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
$275$	143.176	−	161.087i	0.520641	−	0.585771i
$276$		0			0
$277$	184.706			0.666808			0.333404	−	0.942784i	$-0.391803\pi$
$277$	184.706			0.666808			0.333404	+	0.942784i	$0.391803\pi$
$278$		0			0
$279$	86.6616			0.310615
$280$		0			0
$281$			173.967i			0.619100i	0.950883	+	0.309550i	$0.100178\pi$
$281$			173.967i			0.619100i	−0.950883	+	0.309550i	$0.899822\pi$
$282$		0			0
$283$			33.1982i			0.117308i	0.998278	+	0.0586541i	$0.0186809\pi$
$283$			33.1982i			0.117308i	−0.998278	+	0.0586541i	$0.981319\pi$
$284$		0			0
$285$	−77.2020	+	81.8803i	−0.270884	+	0.287299i
$286$		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
$293$			194.502i			0.663829i	0.943309	+	0.331915i	$0.107695\pi$
$293$			194.502i			0.663829i	−0.943309	+	0.331915i	$0.892305\pi$
$294$		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
$307$			517.509i			1.68570i	0.538150	+	0.842849i	$0.319123\pi$
$307$			517.509i			1.68570i	−0.538150	+	0.842849i	$0.680877\pi$
$308$		0			0
$309$	−135.164	−	135.164i	−0.437426	−	0.437426i
$310$		0			0
$311$			482.841i			1.55254i	0.630399	+	0.776271i	$0.282891\pi$
$311$			482.841i			1.55254i	−0.630399	+	0.776271i	$0.717109\pi$
$312$		0			0
$313$	−96.1945	−	96.1945i	−0.307331	−	0.307331i	0.536543	−	0.843873i	$-0.319730\pi$
$313$	−96.1945	−	96.1945i	−0.307331	−	0.307331i	−0.843873	+	0.536543i	$0.819730\pi$
$314$		0			0
$315$	−46.7353	+	49.5674i	−0.148366	+	0.157357i
$316$		0			0
$317$		−	344.707i		−	1.08740i	−0.839278	−	0.543702i	$-0.817022\pi$
$317$		−	344.707i		−	1.08740i	0.839278	−	0.543702i	$-0.182978\pi$
$318$		0			0
$319$		−	475.169i		−	1.48956i
$320$		0			0
$321$	314.551			0.979910
$322$		0			0
$323$	83.2009			0.257588
$324$		0			0
$325$	−371.916	+	21.8933i	−1.14436	+	0.0673639i
$326$		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	−0.327238	−	0.944942i	$-0.606118\pi$
$331$	204.460	−	204.460i	0.617704	−	0.617704i	0.944942	+	0.327238i	$0.106118\pi$
$332$		0			0
$333$	56.8037			0.170582
$334$		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
$347$	187.616			0.540681			0.270341	−	0.962765i	$-0.412864\pi$
$347$	187.616			0.540681			0.270341	+	0.962765i	$0.412864\pi$
$348$		0			0
$349$	−316.337	+	316.337i	−0.906409	+	0.906409i	−0.995980	−	0.0895710i	$-0.971450\pi$
$349$	−316.337	+	316.337i	−0.906409	+	0.906409i	0.0895710	+	0.995980i	$0.471450\pi$
$350$		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
$355$	−10.1227	−	344.221i	−0.0285147	−	0.969637i
$356$		0			0
$357$	130.196			0.364694
$358$		0			0
$359$	425.478			1.18518			0.592588	−	0.805506i	$-0.298106\pi$
$359$	425.478			1.18518			0.592588	+	0.805506i	$0.298106\pi$
$360$		0			0
$361$			326.488i			0.904399i
$362$		0			0
$363$		−	178.852i		−	0.492704i
$364$		0			0
$365$	−436.616	−	411.670i	−1.19621	−	1.12786i
$366$		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
$373$		−	601.037i		−	1.61136i	−0.592351	−	0.805680i	$-0.701800\pi$
$373$		−	601.037i		−	1.61136i	0.592351	−	0.805680i	$-0.298200\pi$
$374$		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	$-0.439557\pi$
$379$	−300.652	−	300.652i	−0.793276	−	0.793276i	−0.982025	+	0.188750i	$0.939557\pi$
$380$		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
$387$		−	234.225i		−	0.605232i
$388$		0			0
$389$	−428.756	−	428.756i	−1.10220	−	1.10220i	−0.994145	−	0.108054i	$-0.965538\pi$
$389$	−428.756	−	428.756i	−1.10220	−	1.10220i	−0.108054	−	0.994145i	$-0.534462\pi$
$390$		0			0
$391$			622.988i			1.59332i
$392$		0			0
$393$	303.219	+	303.219i	0.771551	+	0.771551i
$394$		0			0
$395$	−13.1551	−	447.337i	−0.0333040	−	1.13250i
$396$		0			0
$397$			194.112i			0.488947i	0.969656	+	0.244474i	$0.0786152\pi$
$397$			194.112i			0.488947i	−0.969656	+	0.244474i	$0.921385\pi$
$398$		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
$403$	−227.434			−0.564353
$404$		0			0
$405$	−499.091	+	14.6771i	−1.23232	+	0.0362397i
$406$		0			0
$407$	60.9789	−	60.9789i	0.149825	−	0.149825i
$408$		0			0
$409$	219.624			0.536978			0.268489	−	0.963283i	$-0.413476\pi$
$409$	219.624			0.536978			0.268489	+	0.963283i	$0.413476\pi$
$410$		0			0
$411$	598.830	−	598.830i	1.45701	−	1.45701i
$412$		0			0
$413$	−46.2134			−0.111897
$414$		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	$-0.700207\pi$
$419$	92.3158	−	92.3158i	0.220324	−	0.220324i	0.808635	+	0.588311i	$0.200207\pi$
$420$		0			0
$421$	−203.067	+	203.067i	−0.482345	+	0.482345i	−0.905880	−	0.423535i	$-0.860789\pi$
$421$	−203.067	+	203.067i	−0.482345	+	0.482345i	0.423535	+	0.905880i	$0.360789\pi$
$422$		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
$427$	−186.671			−0.437169
$428$		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
$435$	−724.346	+	768.239i	−1.66516	+	1.76607i
$436$		0			0
$437$	258.417			0.591344
$438$		0			0
$439$	40.4072			0.0920437			0.0460219	−	0.998940i	$-0.485346\pi$
$439$	40.4072			0.0920437			0.0460219	+	0.998940i	$0.485346\pi$
$440$		0			0
$441$			245.550i			0.556802i
$442$		0			0
$443$			551.916i			1.24586i	0.782277	+	0.622930i	$0.214058\pi$
$443$			551.916i			1.24586i	−0.782277	+	0.622930i	$0.785942\pi$
$444$		0			0
$445$	218.130	−	6.41468i	0.490180	−	0.0144150i
$446$		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
$453$			13.6060i			0.0300354i
$454$		0			0
$455$	122.652	−	130.084i	0.269565	−	0.285900i
$456$		0			0
$457$	397.309	−	397.309i	0.869384	−	0.869384i	−0.123020	−	0.992404i	$-0.539258\pi$
$457$	397.309	−	397.309i	0.869384	−	0.869384i	0.992404	+	0.123020i	$0.0392579\pi$
$458$		0			0
$459$	127.442	+	127.442i	0.277651	+	0.277651i
$460$		0			0
$461$	426.786	+	426.786i	0.925784	+	0.925784i	0.997430	−	0.0716461i	$-0.0228252\pi$
$461$	426.786	+	426.786i	0.925784	+	0.925784i	−0.0716461	+	0.997430i	$0.522825\pi$
$462$		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
$467$		−	771.151i		−	1.65129i	−0.564192	−	0.825644i	$-0.690812\pi$
$467$		−	771.151i		−	1.65129i	0.564192	−	0.825644i	$-0.309188\pi$
$468$		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
$475$	97.5686	−	109.774i	0.205408	−	0.231103i
$476$		0			0
$477$			30.6695i			0.0642967i
$478$		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
$483$	404.381			0.837227
$484$		0			0
$485$	257.591	+	242.873i	0.531115	+	0.500770i
$486$		0			0
$487$	196.542	−	196.542i	0.403578	−	0.403578i	−0.475914	−	0.879492i	$-0.657883\pi$
$487$	196.542	−	196.542i	0.403578	−	0.403578i	0.879492	+	0.475914i	$0.157883\pi$
$488$		0			0
$489$	−447.371			−0.914869
$490$		0			0
$491$	−391.245	+	391.245i	−0.796833	+	0.796833i	−0.982595	−	0.185762i	$-0.940525\pi$
$491$	−391.245	+	391.245i	−0.796833	+	0.796833i	0.185762	+	0.982595i	$0.440525\pi$
$492$		0			0
$493$	780.630			1.58343
$494$		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	$-0.860509\pi$
$499$	−240.105	+	240.105i	−0.481173	+	0.481173i	0.424333	+	0.905506i	$0.360509\pi$
$500$		0			0
$501$	80.3446	−	80.3446i	0.160368	−	0.160368i
$502$		0			0
$503$	459.843	+	459.843i	0.914200	+	0.914200i	0.996599	−	0.0823992i	$-0.0262582\pi$
$503$	459.843	+	459.843i	0.914200	+	0.914200i	−0.0823992	+	0.996599i	$0.526258\pi$
$504$		0			0
$505$	351.713	−	373.025i	0.696460	−	0.738664i
$506$		0			0
$507$	−203.369			−0.401122
$508$		0			0
$509$	−348.808	+	348.808i	−0.685281	+	0.685281i	−0.961185	−	0.275904i	$-0.911023\pi$
$509$	−348.808	+	348.808i	−0.685281	+	0.685281i	0.275904	+	0.961185i	$0.411023\pi$
$510$		0			0
$511$	287.978			0.563557
$512$		0			0
$513$	52.8633	−	52.8633i	0.103047	−	0.103047i
$514$		0			0
$515$	181.507	+	171.136i	0.352440	+	0.332304i
$516$		0			0
$517$	428.308			0.828448
$518$		0			0
$519$	928.738			1.78948
$520$		0			0
$521$		−	54.0067i		−	0.103660i	−0.998656	−	0.0518298i	$-0.983495\pi$
$521$		−	54.0067i		−	0.103660i	0.998656	−	0.0518298i	$-0.0165053\pi$
$522$		0			0
$523$		−	367.680i		−	0.703022i	−0.936184	−	0.351511i	$-0.885668\pi$
$523$		−	367.680i		−	0.703022i	0.936184	−	0.351511i	$-0.114332\pi$
$524$		0			0
$525$	152.679	−	171.778i	0.290817	−	0.327197i
$526$		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
$533$		−	255.658i		−	0.479659i
$534$		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	0.669746	−	0.742591i	$-0.266403\pi$
$541$	−39.4092	−	39.4092i	−0.0728451	−	0.0728451i	−0.742591	+	0.669746i	$0.766403\pi$
$542$		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
$547$		−	428.552i		−	0.783459i	−0.920080	−	0.391730i	$-0.871877\pi$
$547$		−	428.552i		−	0.783459i	0.920080	−	0.391730i	$-0.128123\pi$
$548$		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
$555$	−191.545	+	5.63288i	−0.345126	+	0.0101493i
$556$		0			0
$557$		−	816.333i		−	1.46559i	−0.680450	−	0.732794i	$-0.738216\pi$
$557$		−	816.333i		−	1.46559i	0.680450	−	0.732794i	$-0.261784\pi$
$558$		0			0
$559$			614.698i			1.09964i
$560$		0			0
$561$	−467.766			−0.833807
$562$		0			0
$563$	242.788			0.431240			0.215620	−	0.976477i	$-0.430823\pi$
$563$	242.788			0.431240			0.215620	+	0.976477i	$0.430823\pi$
$564$		0			0
$565$	615.389	−	652.679i	1.08918	−	1.15518i
$566$		0			0
$567$	169.432	−	169.432i	0.298822	−	0.298822i
$568$		0			0
$569$	−310.112			−0.545011			−0.272506	−	0.962154i	$-0.587852\pi$
$569$	−310.112			−0.545011			−0.272506	+	0.962154i	$0.587852\pi$
$570$		0			0
$571$	−403.169	+	403.169i	−0.706075	+	0.706075i	−0.965708	−	0.259632i	$-0.916399\pi$
$571$	−403.169	+	403.169i	−0.706075	+	0.706075i	0.259632	+	0.965708i	$0.416399\pi$
$572$		0			0
$573$	−91.1587			−0.159090
$574$		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
$587$	−466.709			−0.795075			−0.397538	−	0.917586i	$-0.630135\pi$
$587$	−466.709			−0.795075			−0.397538	+	0.917586i	$0.630135\pi$
$588$		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
$595$	−169.840	+	4.99458i	−0.285445	+	0.00839425i
$596$		0			0
$597$	−407.514			−0.682603
$598$		0			0
$599$	−1167.57			−1.94920			−0.974600	−	0.223954i	$-0.928104\pi$
$599$	−1167.57			−1.94920			−0.974600	+	0.223954i	$0.928104\pi$
$600$		0			0
$601$			82.0258i			0.136482i	0.997669	+	0.0682411i	$0.0217387\pi$
$601$			82.0258i			0.136482i	−0.997669	+	0.0682411i	$0.978261\pi$
$602$		0			0
$603$			383.894i			0.636640i
$604$		0			0
$605$	6.86112	+	233.311i	0.0113407	+	0.385639i
$606$		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
$613$			725.219i			1.18307i	0.806281	+	0.591533i	$0.201477\pi$
$613$			725.219i			1.18307i	−0.806281	+	0.591533i	$0.798523\pi$
$614$		0			0
$615$	−9.66016	−	328.492i	−0.0157076	−	0.534134i
$616$		0			0
$617$	321.786	−	321.786i	0.521534	−	0.521534i	−0.396501	−	0.918034i	$-0.629776\pi$
$617$	321.786	−	321.786i	0.521534	−	0.521534i	0.918034	+	0.396501i	$0.129776\pi$
$618$		0			0
$619$	161.377	+	161.377i	0.260706	+	0.260706i	0.825341	−	0.564635i	$-0.190983\pi$
$619$	161.377	+	161.377i	0.260706	+	0.260706i	−0.564635	+	0.825341i	$0.690983\pi$
$620$		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
$627$			194.031i			0.309459i
$628$		0			0
$629$	100.179	+	100.179i	0.159267	+	0.159267i
$630$		0			0
$631$		−	620.361i		−	0.983140i	−0.870838	−	0.491570i	$-0.836423\pi$
$631$		−	620.361i		−	0.983140i	0.870838	−	0.491570i	$-0.163577\pi$
$632$		0			0
$633$	−19.6598	−	19.6598i	−0.0310581	−	0.0310581i
$634$		0			0
$635$	−66.8165	−	62.9990i	−0.105223	−	0.0992110i
$636$		0			0
$637$		−	644.419i		−	1.01165i
$638$		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
$643$	304.169			0.473047			0.236523	−	0.971626i	$-0.423992\pi$
$643$	304.169			0.473047			0.236523	+	0.971626i	$0.423992\pi$
$644$		0			0
$645$	23.2266	+	789.818i	0.0360103	+	1.22452i
$646$		0			0
$647$	71.6597	−	71.6597i	0.110757	−	0.110757i	−0.649556	−	0.760313i	$-0.725045\pi$
$647$	71.6597	−	71.6597i	0.110757	−	0.110757i	0.760313	+	0.649556i	$0.225045\pi$
$648$		0			0
$649$	166.035			0.255832
$650$		0			0
$651$	99.2060	−	99.2060i	0.152390	−	0.152390i
$652$		0			0
$653$	−304.063			−0.465640			−0.232820	−	0.972520i	$-0.574795\pi$
$653$	−304.063			−0.465640			−0.232820	+	0.972520i	$0.574795\pi$
$654$		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	$-0.544730\pi$
$659$	560.205	−	560.205i	0.850083	−	0.850083i	0.990143	+	0.140060i	$0.0447296\pi$
$660$		0			0
$661$	−863.183	+	863.183i	−1.30588	+	1.30588i	−0.381511	+	0.924364i	$0.624596\pi$
$661$	−863.183	+	863.183i	−1.30588	+	1.30588i	−0.924364	+	0.381511i	$0.875404\pi$
$662$		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
$667$	2424.59			3.63507
$668$		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
$675$	317.595	−	18.6956i	0.470511	−	0.0276971i
$676$		0			0
$677$	−110.173			−0.162738			−0.0813688	−	0.996684i	$-0.525929\pi$
$677$	−110.173			−0.162738			−0.0813688	+	0.996684i	$0.525929\pi$
$678$		0			0
$679$	−169.899			−0.250219
$680$		0			0
$681$			982.933i			1.44337i
$682$		0			0
$683$		−	537.997i		−	0.787697i	−0.919175	−	0.393849i	$-0.871143\pi$
$683$		−	537.997i		−	0.787697i	0.919175	−	0.393849i	$-0.128857\pi$
$684$		0			0
$685$	−758.198	+	804.143i	−1.10686	+	1.17393i
$686$		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	0.947385	−	0.320095i	$-0.103715\pi$
$691$	433.458	+	433.458i	0.627290	+	0.627290i	−0.320095	+	0.947385i	$0.603715\pi$
$692$		0			0
$693$			117.459i			0.169494i
$694$		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	0.371165	−	0.928567i	$-0.378958\pi$
$701$	−390.739	−	390.739i	−0.557402	−	0.557402i	−0.928567	+	0.371165i	$0.878958\pi$
$702$		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
$707$			246.035i			0.347999i
$708$		0			0
$709$	−340.829	−	340.829i	−0.480718	−	0.480718i	0.424643	−	0.905361i	$-0.360400\pi$
$709$	−340.829	−	340.829i	−0.480718	−	0.480718i	−0.905361	+	0.424643i	$0.860400\pi$
$710$		0			0
$711$		−	508.252i		−	0.714842i
$712$		0			0
$713$	474.702	+	474.702i	0.665782	+	0.665782i
$714$		0			0
$715$	−440.663	+	467.366i	−0.616312	+	0.653658i
$716$		0			0
$717$		−	30.7618i		−	0.0429035i
$718$		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
$723$	−35.2316			−0.0487298
$724$		0			0
$725$	915.435	−	1029.95i	1.26267	−	1.42062i
$726$		0			0
$727$	−493.648	+	493.648i	−0.679021	+	0.679021i	−0.959779	−	0.280758i	$-0.909414\pi$
$727$	−493.648	+	493.648i	−0.679021	+	0.679021i	0.280758	+	0.959779i	$0.409414\pi$
$728$		0			0
$729$	−128.254			−0.175932
$730$		0			0
$731$	413.079	−	413.079i	0.565088	−	0.565088i
$732$		0			0
$733$	−864.330			−1.17917			−0.589584	−	0.807707i	$-0.700708\pi$
$733$	−864.330			−1.17917			−0.589584	+	0.807707i	$0.700708\pi$
$734$		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	$-0.529541\pi$
$739$	667.334	−	667.334i	0.903023	−	0.903023i	0.995697	+	0.0926732i	$0.0295412\pi$
$740$		0			0
$741$	237.173	−	237.173i	0.320072	−	0.320072i
$742$		0			0
$743$	87.5208	+	87.5208i	0.117794	+	0.117794i	0.763547	−	0.645753i	$-0.223456\pi$
$743$	87.5208	+	87.5208i	0.117794	+	0.117794i	−0.645753	+	0.763547i	$0.723456\pi$
$744$		0			0
$745$	306.678	+	289.156i	0.411648	+	0.388129i
$746$		0			0
$747$	−729.341			−0.976360
$748$		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
$755$	−0.521956	−	17.7490i	−0.000691332	−	0.0235086i
$756$		0			0
$757$	−1268.47			−1.67565			−0.837827	−	0.545937i	$-0.816174\pi$
$757$	−1268.47			−1.67565			−0.837827	+	0.545937i	$0.816174\pi$
$758$		0			0
$759$	−1452.85			−1.91417
$760$		0			0
$761$			332.602i			0.437059i	0.975830	+	0.218529i	$0.0701259\pi$
$761$			332.602i			0.437059i	−0.975830	+	0.218529i	$0.929874\pi$
$762$		0			0
$763$		−	73.7372i		−	0.0966411i
$764$		0			0
$765$	292.567	+	275.851i	0.382440	+	0.360590i
$766$		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
$773$			895.057i			1.15790i	0.815363	+	0.578950i	$0.196537\pi$
$773$			895.057i			1.15790i	−0.815363	+	0.578950i	$0.803463\pi$
$774$		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
$787$			58.1451i			0.0738820i	0.999317	+	0.0369410i	$0.0117614\pi$
$787$			58.1451i			0.0738820i	−0.999317	+	0.0369410i	$0.988239\pi$
$788$		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
$795$	−3.04131	−	103.419i	−0.00382555	−	0.130087i
$796$		0			0
$797$		−	238.679i		−	0.299472i	−0.988726	−	0.149736i	$-0.952158\pi$
$797$		−	238.679i		−	0.299472i	0.988726	−	0.149736i	$-0.0478423\pi$
$798$		0			0
$799$			703.644i			0.880656i
$800$		0			0
$801$	247.834			0.309406
$802$		0			0
$803$	−1034.64			−1.28847
$804$		0			0
$805$	−527.513	+	15.5129i	−0.655295	+	0.0192707i
$806$		0			0
$807$	−519.060	+	519.060i	−0.643197	+	0.643197i
$808$		0			0
$809$	−612.464			−0.757062			−0.378531	−	0.925589i	$-0.623571\pi$
$809$	−612.464			−0.757062			−0.378531	+	0.925589i	$0.623571\pi$
$810$		0			0
$811$	−618.905	+	618.905i	−0.763138	+	0.763138i	−0.976888	−	0.213750i	$-0.931432\pi$
$811$	−618.905	+	618.905i	−0.763138	+	0.763138i	0.213750	+	0.976888i	$0.431432\pi$
$812$		0			0
$813$	−1058.27			−1.30168
$814$		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	−0.665100	−	0.746755i	$-0.731611\pi$
$821$	67.0385	−	67.0385i	0.0816547	−	0.0816547i	0.746755	+	0.665100i	$0.231611\pi$
$822$		0			0
$823$	−720.633	−	720.633i	−0.875617	−	0.875617i	0.117461	−	0.993078i	$-0.462525\pi$
$823$	−720.633	−	720.633i	−0.875617	−	0.875617i	−0.993078	+	0.117461i	$0.962525\pi$
$824$		0			0
$825$	−548.543	+	617.164i	−0.664901	+	0.748077i
$826$		0			0
$827$	−1189.91			−1.43883			−0.719413	−	0.694582i	$-0.755589\pi$
$827$	−1189.91			−1.43883			−0.719413	+	0.694582i	$0.755589\pi$
$828$		0			0
$829$	77.7453	−	77.7453i	0.0937821	−	0.0937821i	−0.658659	−	0.752441i	$-0.728876\pi$
$829$	77.7453	−	77.7453i	0.0937821	−	0.0937821i	0.752441	+	0.658659i	$0.228876\pi$
$830$		0			0
$831$	−707.653			−0.851567
$832$		0			0
$833$	−433.052	+	433.052i	−0.519870	+	0.519870i
$834$		0			0
$835$	−101.727	+	107.891i	−0.121829	+	0.129211i
$836$		0			0
$837$	194.216			0.232038
$838$		0			0
$839$	−1281.90			−1.52789			−0.763947	−	0.645279i	$-0.776741\pi$
$839$	−1281.90			−1.52789			−0.763947	+	0.645279i	$0.776741\pi$
$840$		0			0
$841$		−	2197.12i		−	2.61251i
$842$		0			0
$843$		−	666.511i		−	0.790641i
$844$		0			0
$845$	265.294	−	7.80165i	0.313957	−	0.00923273i
$846$		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
$853$			62.5726i			0.0733559i	0.999327	+	0.0366779i	$0.0116776\pi$
$853$			62.5726i			0.0733559i	−0.999327	+	0.0366779i	$0.988322\pi$
$854$		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	$0.613423\pi$
$857$	−1102.12	+	1102.12i	−1.28602	+	1.28602i	−0.937183	+	0.348838i	$0.886577\pi$
$858$		0			0
$859$	−677.212	−	677.212i	−0.788373	−	0.788373i	0.192855	−	0.981227i	$-0.438225\pi$
$859$	−677.212	−	677.212i	−0.788373	−	0.788373i	−0.981227	+	0.192855i	$0.938225\pi$
$860$		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
$867$			338.761i			0.390728i
$868$		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
$875$	−192.579	+	229.941i	−0.220090	+	0.262790i
$876$		0			0
$877$			834.366i			0.951387i	0.879611	+	0.475693i	$0.157803\pi$
$877$			834.366i			0.951387i	−0.879611	+	0.475693i	$0.842197\pi$
$878$		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
$883$	−708.993			−0.802937			−0.401468	−	0.915873i	$-0.631500\pi$
$883$	−708.993			−0.802937			−0.401468	+	0.915873i	$0.631500\pi$
$884$		0			0
$885$	−268.441	−	253.103i	−0.303323	−	0.285993i
$886$		0			0
$887$	472.922	−	472.922i	0.533170	−	0.533170i	−0.388344	−	0.921514i	$-0.626953\pi$
$887$	472.922	−	472.922i	0.533170	−	0.533170i	0.921514	+	0.388344i	$0.126953\pi$
$888$		0			0
$889$	44.0700			0.0495726
$890$		0			0
$891$	−608.735	+	608.735i	−0.683204	+	0.683204i
$892$		0			0
$893$	291.874			0.326846
$894$		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
$907$	−27.0583			−0.0298328			−0.0149164	−	0.999889i	$-0.504748\pi$
$907$	−27.0583			−0.0298328			−0.0149164	+	0.999889i	$0.504748\pi$
$908$		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
$915$	−1084.32	−	1022.37i	−1.18505	−	1.11734i
$916$		0			0
$917$	268.563			0.292871
$918$		0			0
$919$	365.843			0.398089			0.199044	−	0.979990i	$-0.436216\pi$
$919$	365.843			0.398089			0.199044	+	0.979990i	$0.436216\pi$
$920$		0			0
$921$		−	1982.70i		−	2.15277i
$922$		0			0
$923$			1026.39i			1.11201i
$924$		0			0
$925$	249.654	−	14.6961i	0.269896	−	0.0158877i
$926$		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
$933$		−	1849.88i		−	1.98272i
$934$		0			0
$935$	610.199	−	17.9445i	0.652619	−	0.0191919i
$936$		0			0
$937$	26.5779	−	26.5779i	0.0283649	−	0.0283649i	−0.692782	−	0.721147i	$-0.743615\pi$
$937$	26.5779	−	26.5779i	0.0283649	−	0.0283649i	0.721147	+	0.692782i	$0.243615\pi$
$938$		0			0
$939$	368.544	+	368.544i	0.392486	+	0.392486i
$940$		0			0
$941$	770.144	+	770.144i	0.818431	+	0.818431i	0.985881	−	0.167450i	$-0.0535532\pi$
$941$	770.144	+	770.144i	0.818431	+	0.818431i	−0.167450	+	0.985881i	$0.553553\pi$
$942$		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
$947$			585.598i			0.618372i	0.951002	+	0.309186i	$0.100057\pi$
$947$			585.598i			0.618372i	−0.951002	+	0.309186i	$0.899943\pi$
$948$		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	$0.104657\pi$
$953$	1209.67	+	1209.67i	1.26933	+	1.26933i	0.322897	+	0.946434i	$0.395343\pi$
$954$		0			0
$955$	118.916	−	3.49704i	0.124520	−	0.00366182i
$956$		0			0
$957$			1820.49i			1.90229i
$958$		0			0
$959$		−	530.386i		−	0.553062i
$960$		0			0
$961$	−728.084			−0.757632
$962$		0			0
$963$	−466.207			−0.484120
$964$		0			0
$965$	353.109	−	374.507i	0.365916	−	0.388090i
$966$		0			0
$967$	265.767	−	265.767i	0.274837	−	0.274837i	−0.556207	−	0.831044i	$-0.687744\pi$
$967$	265.767	−	265.767i	0.274837	−	0.274837i	0.831044	+	0.556207i	$0.187744\pi$
$968$		0			0
$969$	−318.763			−0.328961
$970$		0			0
$971$	703.377	−	703.377i	0.724384	−	0.724384i	−0.245111	−	0.969495i	$-0.578824\pi$
$971$	703.377	−	703.377i	0.724384	−	0.724384i	0.969495	+	0.245111i	$0.0788245\pi$
$972$		0			0
$973$	36.0571			0.0370576
$974$		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	0.518136	−	0.855298i	$-0.326626\pi$
$983$	−331.430	−	331.430i	−0.337162	−	0.337162i	−0.855298	+	0.518136i	$0.826626\pi$
$984$		0			0
$985$	1058.75	−	31.1352i	1.07487	−	0.0316093i
$986$		0			0
$987$	456.734			0.462750
$988$		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
$995$	531.600	−	15.6331i	0.534271	−	0.0157116i
$996$		0			0
$997$	−513.114			−0.514658			−0.257329	−	0.966324i	$-0.582842\pi$
$997$	−513.114			−0.514658			−0.257329	+	0.966324i	$0.582842\pi$
$998$		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.t.a.17.4		44
4.3	odd	2		80.3.t.a.77.9	yes	44
5.3	odd	4		320.3.i.a.273.4		44
8.3	odd	2		640.3.t.b.417.4		44
8.5	even	2		640.3.t.a.417.19		44
16.3	odd	4		640.3.i.b.97.19		44
16.5	even	4		320.3.i.a.177.19		44
16.11	odd	4		80.3.i.a.37.19	yes	44
16.13	even	4		640.3.i.a.97.4		44
20.3	even	4		80.3.i.a.13.19	✓	44
20.7	even	4		400.3.i.b.93.4		44
20.19	odd	2		400.3.t.b.157.14		44
40.3	even	4		640.3.i.b.33.4		44
40.13	odd	4		640.3.i.a.33.19		44
80.3	even	4		640.3.t.b.353.4		44
80.13	odd	4		640.3.t.a.353.19		44
80.27	even	4		400.3.t.b.293.14		44
80.43	even	4		80.3.t.a.53.9	yes	44
80.53	odd	4	inner	320.3.t.a.113.4		44
80.59	odd	4		400.3.i.b.357.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.19	✓	44	20.3	even	4
80.3.i.a.37.19	yes	44	16.11	odd	4
80.3.t.a.53.9	yes	44	80.43	even	4
80.3.t.a.77.9	yes	44	4.3	odd	2
320.3.i.a.177.19		44	16.5	even	4
320.3.i.a.273.4		44	5.3	odd	4
320.3.t.a.17.4		44	1.1	even	1	trivial
320.3.t.a.113.4		44	80.53	odd	4	inner
400.3.i.b.93.4		44	20.7	even	4
400.3.i.b.357.4		44	80.59	odd	4
400.3.t.b.157.14		44	20.19	odd	2
400.3.t.b.293.14		44	80.27	even	4
640.3.i.a.33.19		44	40.13	odd	4
640.3.i.a.97.4		44	16.13	even	4
640.3.i.b.33.4		44	40.3	even	4
640.3.i.b.97.19		44	16.3	odd	4
640.3.t.a.353.19		44	80.13	odd	4
640.3.t.a.417.19		44	8.5	even	2
640.3.t.b.353.4		44	80.3	even	4
640.3.t.b.417.4		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.83124 q^{3} +(4.99784 - 0.146974i) q^{5} +(-1.69668 + 1.69668i) q^{7} +5.67842 q^{9} +O(q^{10})\)	\(q-3.83124 q^{3} +(4.99784 - 0.146974i) q^{5} +(-1.69668 + 1.69668i) q^{7} +5.67842 q^{9} +(6.09580 - 6.09580i) q^{11} -14.9024 q^{13} +(-19.1479 + 0.563095i) q^{15} +(10.0145 + 10.0145i) q^{17} +(4.15403 - 4.15403i) q^{19} +(6.50038 - 6.50038i) q^{21} +(31.1044 + 31.1044i) q^{23} +(24.9568 - 1.46911i) q^{25} +12.7258 q^{27} +(38.9751 - 38.9751i) q^{29} +15.2616 q^{31} +(-23.3545 + 23.3545i) q^{33} +(-8.23034 + 8.72908i) q^{35} +10.0034 q^{37} +57.0947 q^{39} +17.1555i q^{41} -41.2482i q^{43} +(28.3798 - 0.834582i) q^{45} +(35.1314 + 35.1314i) q^{47} +43.2426i q^{49} +(-38.3679 - 38.3679i) q^{51} +5.40107i q^{53} +(29.5699 - 31.3618i) q^{55} +(-15.9151 + 15.9151i) q^{57} +(13.6188 + 13.6188i) q^{59} +(55.0109 + 55.0109i) q^{61} +(-9.63443 + 9.63443i) q^{63} +(-74.4798 + 2.19027i) q^{65} +67.6058i q^{67} +(-119.168 - 119.168i) q^{69} -68.8740i q^{71} +(-84.8652 - 84.8652i) q^{73} +(-95.6155 + 5.62851i) q^{75} +20.6852i q^{77} -89.5060i q^{79} -99.8613 q^{81} -128.441 q^{83} +(51.5226 + 48.5789i) q^{85} +(-149.323 + 149.323i) q^{87} +43.6449 q^{89} +(25.2845 - 25.2845i) q^{91} -58.4708 q^{93} +(20.1507 - 21.3717i) q^{95} +(50.0681 + 50.0681i) q^{97} +(34.6145 - 34.6145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

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