LMFDB - Embedded newform 1020.3.bc.a.701.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(701,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))

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

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

chi := DirichletCharacter("1020.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bc (of order $4$, degree $2$, 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:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			701.11
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43789 - 1.74834i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-8.85638 - 8.85638i) q^{7} +(2.88662 + 8.52452i) q^{9} +O(q^{10})$	\(q+(-2.43789 - 1.74834i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-8.85638 - 8.85638i) q^{7} +(2.88662 + 8.52452i) q^{9} +(2.63770 - 2.63770i) q^{11} +20.5134 q^{13} +(-1.09028 - 6.61901i) q^{15} +(-4.55641 + 16.3780i) q^{17} +35.8936i q^{19} +(6.10693 + 37.0748i) q^{21} +(8.94022 - 8.94022i) q^{23} +5.00000i q^{25} +(7.86648 - 25.8286i) q^{27} +(-16.1433 - 16.1433i) q^{29} +(10.9229 - 10.9229i) q^{31} +(-11.0420 + 1.81883i) q^{33} -28.0063i q^{35} +(-12.8349 + 12.8349i) q^{37} +(-50.0094 - 35.8644i) q^{39} +(20.1796 - 20.1796i) q^{41} +7.77261i q^{43} +(-8.91430 + 18.0426i) q^{45} -86.9167i q^{47} +107.871i q^{49} +(39.7423 - 31.9616i) q^{51} +32.6491 q^{53} +8.34115 q^{55} +(62.7541 - 87.5046i) q^{57} +43.9125 q^{59} +(49.0492 + 49.0492i) q^{61} +(49.9313 - 101.061i) q^{63} +(32.4345 + 32.4345i) q^{65} +15.4506 q^{67} +(-37.4258 + 6.16475i) q^{69} +(-96.5031 - 96.5031i) q^{71} +(49.2069 - 49.2069i) q^{73} +(8.74169 - 12.1895i) q^{75} -46.7210 q^{77} +(24.4138 + 24.4138i) q^{79} +(-64.3348 + 49.2141i) q^{81} +112.951 q^{83} +(-33.1002 + 18.6916i) q^{85} +(11.1317 + 67.5796i) q^{87} -73.1486i q^{89} +(-181.674 - 181.674i) q^{91} +(-45.7259 + 7.53192i) q^{93} +(-56.7527 + 56.7527i) q^{95} +(132.453 - 132.453i) q^{97} +(30.0992 + 14.8711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{3}+O(q^{10}) $ 96 * q - 8 * q^3	$ 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) $ 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.43789	−	1.74834i	−0.812630	−	0.582780i
$3$	−2.43789	−	1.74834i	−0.812630	−	0.582780i
$4$		0			0
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$		0			0
$7$	−8.85638	−	8.85638i	−1.26520	−	1.26520i	−0.948540	−	0.316656i	$-0.897440\pi$
$7$	−8.85638	−	8.85638i	−1.26520	−	1.26520i	−0.316656	−	0.948540i	$-0.602560\pi$
$8$		0			0
$9$	2.88662	+	8.52452i	0.320736	+	0.947169i
$10$		0			0
$11$	2.63770	−	2.63770i	0.239791	−	0.239791i	−0.576972	−	0.816764i	$-0.695766\pi$
$11$	2.63770	−	2.63770i	0.239791	−	0.239791i	0.816764	+	0.576972i	$0.195766\pi$
$12$		0			0
$13$	20.5134			1.57795			0.788977	−	0.614423i	$-0.210611\pi$
$13$	20.5134			1.57795			0.788977	+	0.614423i	$0.210611\pi$
$14$		0			0
$15$	−1.09028	−	6.61901i	−0.0726851	−	0.441267i
$16$		0			0
$17$	−4.55641	+	16.3780i	−0.268024	+	0.963412i
$17$	−4.55641	+	16.3780i	−0.268024	+	0.963412i
$18$		0			0
$19$			35.8936i			1.88914i	0.328317	+	0.944568i	$0.393519\pi$
$19$			35.8936i			1.88914i	−0.328317	+	0.944568i	$0.606481\pi$
$20$		0			0
$21$	6.10693	+	37.0748i	0.290806	+	1.76547i
$22$		0			0
$23$	8.94022	−	8.94022i	0.388705	−	0.388705i	−0.485520	−	0.874225i	$-0.661370\pi$
$23$	8.94022	−	8.94022i	0.388705	−	0.388705i	0.874225	+	0.485520i	$0.161370\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	7.86648	−	25.8286i	0.291351	−	0.956616i
$28$		0			0
$29$	−16.1433	−	16.1433i	−0.556666	−	0.556666i	0.371690	−	0.928357i	$-0.378778\pi$
$29$	−16.1433	−	16.1433i	−0.556666	−	0.556666i	−0.928357	+	0.371690i	$0.878778\pi$
$30$		0			0
$31$	10.9229	−	10.9229i	0.352352	−	0.352352i	−0.508632	−	0.860984i	$-0.669849\pi$
$31$	10.9229	−	10.9229i	0.352352	−	0.352352i	0.860984	+	0.508632i	$0.169849\pi$
$32$		0			0
$33$	−11.0420	+	1.81883i	−0.334607	+	0.0551161i
$34$		0			0
$35$		−	28.0063i		−	0.800181i
$36$		0			0
$37$	−12.8349	+	12.8349i	−0.346889	+	0.346889i	−0.858949	−	0.512061i	$-0.828882\pi$
$37$	−12.8349	+	12.8349i	−0.346889	+	0.346889i	0.512061	+	0.858949i	$0.328882\pi$
$38$		0			0
$39$	−50.0094	−	35.8644i	−1.28229	−	0.919599i
$40$		0			0
$41$	20.1796	−	20.1796i	0.492184	−	0.492184i	−0.416810	−	0.908994i	$-0.636852\pi$
$41$	20.1796	−	20.1796i	0.492184	−	0.492184i	0.908994	+	0.416810i	$0.136852\pi$
$42$		0			0
$43$			7.77261i			0.180758i	0.995907	+	0.0903792i	$0.0288079\pi$
$43$			7.77261i			0.180758i	−0.995907	+	0.0903792i	$0.971192\pi$
$44$		0			0
$45$	−8.91430	+	18.0426i	−0.198095	+	0.400947i
$46$		0			0
$47$		−	86.9167i		−	1.84929i	−0.380827	−	0.924646i	$-0.624361\pi$
$47$		−	86.9167i		−	1.84929i	0.380827	−	0.924646i	$-0.375639\pi$
$48$		0			0
$49$			107.871i			2.20145i
$50$		0			0
$51$	39.7423	−	31.9616i	0.779262	−	0.626699i
$52$		0			0
$53$	32.6491			0.616021			0.308011	−	0.951383i	$-0.400337\pi$
$53$	32.6491			0.616021			0.308011	+	0.951383i	$0.400337\pi$
$54$		0			0
$55$	8.34115			0.151657
$56$		0			0
$57$	62.7541	−	87.5046i	1.10095	−	1.53517i
$58$		0			0
$59$	43.9125			0.744279			0.372140	−	0.928177i	$-0.378624\pi$
$59$	43.9125			0.744279			0.372140	+	0.928177i	$0.378624\pi$
$60$		0			0
$61$	49.0492	+	49.0492i	0.804085	+	0.804085i	0.983731	−	0.179646i	$-0.0574952\pi$
$61$	49.0492	+	49.0492i	0.804085	+	0.804085i	−0.179646	+	0.983731i	$0.557495\pi$
$62$		0			0
$63$	49.9313	−	101.061i	0.792561	−	1.60415i
$64$		0			0
$65$	32.4345	+	32.4345i	0.498993	+	0.498993i
$66$		0			0
$67$	15.4506			0.230606			0.115303	−	0.993330i	$-0.463216\pi$
$67$	15.4506			0.230606			0.115303	+	0.993330i	$0.463216\pi$
$68$		0			0
$69$	−37.4258	+	6.16475i	−0.542403	+	0.0893441i
$70$		0			0
$71$	−96.5031	−	96.5031i	−1.35920	−	1.35920i	−0.874907	−	0.484291i	$-0.839078\pi$
$71$	−96.5031	−	96.5031i	−1.35920	−	1.35920i	−0.484291	−	0.874907i	$-0.660922\pi$
$72$		0			0
$73$	49.2069	−	49.2069i	0.674067	−	0.674067i	−0.284584	−	0.958651i	$-0.591856\pi$
$73$	49.2069	−	49.2069i	0.674067	−	0.674067i	0.958651	+	0.284584i	$0.0918556\pi$
$74$		0			0
$75$	8.74169	−	12.1895i	0.116556	−	0.162526i
$76$		0			0
$77$	−46.7210			−0.606766
$78$		0			0
$79$	24.4138	+	24.4138i	0.309035	+	0.309035i	0.844535	−	0.535500i	$-0.179877\pi$
$79$	24.4138	+	24.4138i	0.309035	+	0.309035i	−0.535500	+	0.844535i	$0.679877\pi$
$80$		0			0
$81$	−64.3348	+	49.2141i	−0.794257	+	0.607582i
$82$		0			0
$83$	112.951			1.36085			0.680425	−	0.732818i	$-0.261795\pi$
$83$	112.951			1.36085			0.680425	+	0.732818i	$0.261795\pi$
$84$		0			0
$85$	−33.1002	+	18.6916i	−0.389414	+	0.219901i
$86$		0			0
$87$	11.1317	+	67.5796i	0.127950	+	0.776778i
$88$		0			0
$89$		−	73.1486i		−	0.821894i	−0.911659	−	0.410947i	$-0.865198\pi$
$89$		−	73.1486i		−	0.821894i	0.911659	−	0.410947i	$-0.134802\pi$
$90$		0			0
$91$	−181.674	−	181.674i	−1.99642	−	1.99642i
$92$		0			0
$93$	−45.7259	+	7.53192i	−0.491676	+	0.0809884i
$94$		0			0
$95$	−56.7527	+	56.7527i	−0.597397	+	0.597397i
$96$		0			0
$97$	132.453	−	132.453i	1.36550	−	1.36550i	0.498749	−	0.866746i	$-0.333793\pi$
$97$	132.453	−	132.453i	1.36550	−	1.36550i	0.866746	−	0.498749i	$-0.166207\pi$
$98$		0			0
$99$	30.0992	+	14.8711i	0.304032	+	0.150213i
$100$		0			0
$101$		−	0.728047i		−	0.00720838i	−0.999994	−	0.00360419i	$-0.998853\pi$
$101$		−	0.728047i		−	0.00720838i	0.999994	−	0.00360419i	$-0.00114725\pi$
$102$		0			0
$103$	−56.1529			−0.545174			−0.272587	−	0.962131i	$-0.587879\pi$
$103$	−56.1529			−0.545174			−0.272587	+	0.962131i	$0.587879\pi$
$104$		0			0
$105$	−48.9645	+	68.2764i	−0.466329	+	0.650251i
$106$		0			0
$107$	10.5589	+	10.5589i	0.0986816	+	0.0986816i	0.754724	−	0.656042i	$-0.227771\pi$
$107$	10.5589	+	10.5589i	0.0986816	+	0.0986816i	−0.656042	+	0.754724i	$0.727771\pi$
$108$		0			0
$109$	−83.2132	−	83.2132i	−0.763424	−	0.763424i	0.213515	−	0.976940i	$-0.431509\pi$
$109$	−83.2132	−	83.2132i	−0.763424	−	0.763424i	−0.976940	+	0.213515i	$0.931509\pi$
$110$		0			0
$111$	53.7298	−	8.85032i	0.484052	−	0.0797326i
$112$		0			0
$113$	62.9357	−	62.9357i	0.556953	−	0.556953i	−0.371486	−	0.928439i	$-0.621152\pi$
$113$	62.9357	−	62.9357i	0.556953	−	0.556953i	0.928439	+	0.371486i	$0.121152\pi$
$114$		0			0
$115$	28.2715			0.245839
$116$		0			0
$117$	59.2144	+	174.867i	0.506106	+	1.49459i
$118$		0			0
$119$	185.403	−	104.697i	1.55801	−	0.879803i
$120$		0			0
$121$			107.085i			0.885000i
$122$		0			0
$123$	−84.4763	+	13.9149i	−0.686799	+	0.113129i
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	33.4779i		−	0.263606i	−0.991276	−	0.131803i	$-0.957923\pi$
$127$		−	33.4779i		−	0.263606i	0.991276	−	0.131803i	$-0.0420766\pi$
$128$		0			0
$129$	13.5892	−	18.9488i	0.105342	−	0.146890i
$130$		0			0
$131$	98.9764	+	98.9764i	0.755545	+	0.755545i	0.975508	−	0.219963i	$-0.0705936\pi$
$131$	98.9764	+	98.9764i	0.755545	+	0.755545i	−0.219963	+	0.975508i	$0.570594\pi$
$132$		0			0
$133$	317.887	−	317.887i	2.39013	−	2.39013i
$134$		0			0
$135$	53.2767	−	28.4007i	0.394642	−	0.210375i
$136$		0			0
$137$		−	65.4036i		−	0.477399i	−0.971093	−	0.238699i	$-0.923279\pi$
$137$		−	65.4036i		−	0.477399i	0.971093	−	0.238699i	$-0.0767211\pi$
$138$		0			0
$139$	41.7540	−	41.7540i	0.300388	−	0.300388i	−0.540777	−	0.841166i	$-0.681870\pi$
$139$	41.7540	−	41.7540i	0.300388	−	0.300388i	0.841166	+	0.540777i	$0.181870\pi$
$140$		0			0
$141$	−151.960	+	211.894i	−1.07773	+	1.50279i
$142$		0			0
$143$	54.1083	−	54.1083i	0.378379	−	0.378379i
$144$		0			0
$145$		−	51.0497i		−	0.352067i
$146$		0			0
$147$	188.595	−	262.977i	1.28296	−	1.78896i
$148$		0			0
$149$		−	81.5492i		−	0.547310i	−0.961828	−	0.273655i	$-0.911767\pi$
$149$		−	81.5492i		−	0.547310i	0.961828	−	0.273655i	$-0.0882326\pi$
$150$		0			0
$151$		−	32.5225i		−	0.215381i	−0.994184	−	0.107691i	$-0.965654\pi$
$151$		−	32.5225i		−	0.215381i	0.994184	−	0.107691i	$-0.0343456\pi$
$152$		0			0
$153$	−152.767	+	8.43591i	−0.998479	+	0.0551367i
$154$		0			0
$155$	34.5413			0.222847
$156$		0			0
$157$	90.9864			0.579531			0.289766	−	0.957098i	$-0.406423\pi$
$157$	90.9864			0.579531			0.289766	+	0.957098i	$0.406423\pi$
$158$		0			0
$159$	−79.5950	−	57.0817i	−0.500597	−	0.359005i
$160$		0			0
$161$	−158.356			−0.983577
$162$		0			0
$163$	77.3212	+	77.3212i	0.474363	+	0.474363i	0.903323	−	0.428960i	$-0.141120\pi$
$163$	77.3212	+	77.3212i	0.474363	+	0.474363i	−0.428960	+	0.903323i	$0.641120\pi$
$164$		0			0
$165$	−20.3348	−	14.5832i	−0.123241	−	0.0883827i
$166$		0			0
$167$	−182.197	−	182.197i	−1.09100	−	1.09100i	−0.995422	−	0.0955785i	$-0.969530\pi$
$167$	−182.197	−	182.197i	−1.09100	−	1.09100i	−0.0955785	−	0.995422i	$-0.530470\pi$
$168$		0			0
$169$	251.800			1.48994
$170$		0			0
$171$	−305.975	+	103.611i	−1.78933	+	0.605913i
$172$		0			0
$173$	−207.045	−	207.045i	−1.19679	−	1.19679i	−0.975121	−	0.221673i	$-0.928848\pi$
$173$	−207.045	−	207.045i	−1.19679	−	1.19679i	−0.221673	−	0.975121i	$-0.571152\pi$
$174$		0			0
$175$	44.2819	−	44.2819i	0.253039	−	0.253039i
$176$		0			0
$177$	−107.054	−	76.7739i	−0.604824	−	0.433751i
$178$		0			0
$179$	130.210			0.727429			0.363715	−	0.931510i	$-0.381508\pi$
$179$	130.210			0.727429			0.363715	+	0.931510i	$0.381508\pi$
$180$		0			0
$181$	−100.898	−	100.898i	−0.557449	−	0.557449i	0.371132	−	0.928580i	$-0.378970\pi$
$181$	−100.898	−	100.898i	−0.557449	−	0.557449i	−0.928580	+	0.371132i	$0.878970\pi$
$182$		0			0
$183$	−33.8220	−	205.331i	−0.184820	−	1.12203i
$184$		0			0
$185$	−40.5875			−0.219392
$186$		0			0
$187$	31.1819	+	55.2188i	0.166748	+	0.295288i
$188$		0			0
$189$	−298.417	+	159.080i	−1.57892	+	0.841691i
$190$		0			0
$191$			48.2512i			0.252624i	0.991991	+	0.126312i	$0.0403141\pi$
$191$			48.2512i			0.252624i	−0.991991	+	0.126312i	$0.959686\pi$
$192$		0			0
$193$	121.207	+	121.207i	0.628018	+	0.628018i	0.947569	−	0.319551i	$-0.103532\pi$
$193$	121.207	+	121.207i	0.628018	+	0.628018i	−0.319551	+	0.947569i	$0.603532\pi$
$194$		0			0
$195$	−22.3653	−	135.778i	−0.114694	−	0.696300i
$196$		0			0
$197$	−135.270	+	135.270i	−0.686650	+	0.686650i	−0.961490	−	0.274840i	$-0.911375\pi$
$197$	−135.270	+	135.270i	−0.686650	+	0.686650i	0.274840	+	0.961490i	$0.411375\pi$
$198$		0			0
$199$	75.2582	−	75.2582i	0.378182	−	0.378182i	−0.492264	−	0.870446i	$-0.663831\pi$
$199$	75.2582	−	75.2582i	0.378182	−	0.378182i	0.870446	+	0.492264i	$0.163831\pi$
$200$		0			0
$201$	−37.6668	−	27.0128i	−0.187397	−	0.134392i
$202$		0			0
$203$			285.943i			1.40858i
$204$		0			0
$205$	63.8134			0.311285
$206$		0			0
$207$	102.018	+	50.4040i	0.492841	+	0.243498i
$208$		0			0
$209$	94.6766	+	94.6766i	0.452998	+	0.452998i
$210$		0			0
$211$	251.425	+	251.425i	1.19159	+	1.19159i	0.976622	+	0.214964i	$0.0689634\pi$
$211$	251.425	+	251.425i	1.19159	+	1.19159i	0.214964	+	0.976622i	$0.431037\pi$
$212$		0			0
$213$	66.5439	+	403.984i	0.312413	+	1.89664i
$214$		0			0
$215$	−12.2896	+	12.2896i	−0.0571608	+	0.0571608i
$216$		0			0
$217$	−193.475			−0.891590
$218$		0			0
$219$	−205.991	+	33.9307i	−0.940599	+	0.154935i
$220$		0			0
$221$	−93.4675	+	335.969i	−0.422930	+	1.52022i
$222$		0			0
$223$			141.824i			0.635981i	0.948094	+	0.317991i	$0.103008\pi$
$223$			141.824i			0.635981i	−0.948094	+	0.317991i	$0.896992\pi$
$224$		0			0
$225$	−42.6226	+	14.4331i	−0.189434	+	0.0641472i
$226$		0			0
$227$	−126.548	+	126.548i	−0.557479	+	0.557479i	−0.928589	−	0.371110i	$-0.878977\pi$
$227$	−126.548	+	126.548i	−0.557479	+	0.557479i	0.371110	+	0.928589i	$0.378977\pi$
$228$		0			0
$229$		−	374.463i		−	1.63521i	−0.575781	−	0.817604i	$-0.695302\pi$
$229$		−	374.463i		−	1.63521i	0.575781	−	0.817604i	$-0.304698\pi$
$230$		0			0
$231$	113.901	+	81.6841i	0.493076	+	0.353611i
$232$		0			0
$233$	301.645	+	301.645i	1.29461	+	1.29461i	0.931901	+	0.362712i	$0.118149\pi$
$233$	301.645	+	301.645i	1.29461	+	1.29461i	0.362712	+	0.931901i	$0.381851\pi$
$234$		0			0
$235$	137.427	−	137.427i	0.584798	−	0.584798i
$236$		0			0
$237$	−16.8346	−	102.202i	−0.0710320	−	0.431231i
$238$		0			0
$239$		−	345.222i		−	1.44444i	−0.691662	−	0.722222i	$-0.743121\pi$
$239$		−	345.222i		−	1.44444i	0.691662	−	0.722222i	$-0.256879\pi$
$240$		0			0
$241$	−213.411	+	213.411i	−0.885522	+	0.885522i	−0.994089	−	0.108567i	$-0.965374\pi$
$241$	−213.411	+	213.411i	−0.885522	+	0.885522i	0.108567	+	0.994089i	$0.465374\pi$
$242$		0			0
$243$	242.884	−	7.49960i	0.999524	−	0.0308626i
$244$		0			0
$245$	−170.559	+	170.559i	−0.696158	+	0.696158i
$246$		0			0
$247$			736.299i			2.98097i
$248$		0			0
$249$	−275.361	−	197.476i	−1.10587	−	0.793075i
$250$		0			0
$251$			68.2085i			0.271747i	0.990726	+	0.135873i	$0.0433841\pi$
$251$			68.2085i			0.271747i	−0.990726	+	0.135873i	$0.956616\pi$
$252$		0			0
$253$		−	47.1633i		−	0.186416i
$254$		0			0
$255$	113.374	+	12.3024i	0.444604	+	0.0482446i
$256$		0			0
$257$	324.065			1.26095			0.630477	−	0.776208i	$-0.282859\pi$
$257$	324.065			1.26095			0.630477	+	0.776208i	$0.282859\pi$
$258$		0			0
$259$	227.341			0.877765
$260$		0			0
$261$	91.0144	−	184.214i	0.348714	−	0.705800i
$262$		0			0
$263$	−43.3793			−0.164940			−0.0824702	−	0.996594i	$-0.526281\pi$
$263$	−43.3793			−0.164940			−0.0824702	+	0.996594i	$0.526281\pi$
$264$		0			0
$265$	51.6228	+	51.6228i	0.194803	+	0.194803i
$266$		0			0
$267$	−127.889	+	178.328i	−0.478983	+	0.667896i
$268$		0			0
$269$	319.025	+	319.025i	1.18597	+	1.18597i	0.978173	+	0.207794i	$0.0666282\pi$
$269$	319.025	+	319.025i	1.18597	+	1.18597i	0.207794	+	0.978173i	$0.433372\pi$
$270$		0			0
$271$	−134.147			−0.495007			−0.247504	−	0.968887i	$-0.579610\pi$
$271$	−134.147			−0.495007			−0.247504	+	0.968887i	$0.579610\pi$
$272$		0			0
$273$	125.274	+	760.531i	0.458879	+	2.78583i
$274$		0			0
$275$	13.1885	+	13.1885i	0.0479582	+	0.0479582i
$276$		0			0
$277$	−110.241	+	110.241i	−0.397983	+	0.397983i	−0.877521	−	0.479538i	$-0.840804\pi$
$277$	−110.241	+	110.241i	−0.397983	+	0.397983i	0.479538	+	0.877521i	$0.340804\pi$
$278$		0			0
$279$	124.643	+	61.5823i	0.446749	+	0.220725i
$280$		0			0
$281$	−274.334			−0.976276			−0.488138	−	0.872766i	$-0.662324\pi$
$281$	−274.334			−0.976276			−0.488138	+	0.872766i	$0.662324\pi$
$282$		0			0
$283$	−182.973	−	182.973i	−0.646549	−	0.646549i	0.305608	−	0.952157i	$-0.401140\pi$
$283$	−182.973	−	182.973i	−0.646549	−	0.646549i	−0.952157	+	0.305608i	$0.901140\pi$
$284$		0			0
$285$	237.580	−	39.1339i	0.833614	−	0.137312i
$286$		0			0
$287$	−357.436			−1.24542
$288$		0			0
$289$	−247.478	−	149.250i	−0.856326	−	0.516436i
$290$		0			0
$291$	−554.479	+	91.3333i	−1.90543	+	0.313860i
$292$		0			0
$293$		−	268.265i		−	0.915580i	−0.889060	−	0.457790i	$-0.848641\pi$
$293$		−	268.265i		−	0.915580i	0.889060	−	0.457790i	$-0.151359\pi$
$294$		0			0
$295$	69.4317	+	69.4317i	0.235362	+	0.235362i
$296$		0			0
$297$	−47.3788	−	88.8777i	−0.159525	−	0.299251i
$298$		0			0
$299$	183.394	−	183.394i	0.613359	−	0.613359i
$300$		0			0
$301$	68.8371	−	68.8371i	0.228695	−	0.228695i
$302$		0			0
$303$	−1.27287	+	1.77490i	−0.00420090	+	0.00585775i
$304$		0			0
$305$			155.107i			0.508548i
$306$		0			0
$307$	−263.660			−0.858827			−0.429413	−	0.903108i	$-0.641280\pi$
$307$	−263.660			−0.858827			−0.429413	+	0.903108i	$0.641280\pi$
$308$		0			0
$309$	136.895	+	98.1743i	0.443025	+	0.317716i
$310$		0			0
$311$	227.337	+	227.337i	0.730986	+	0.730986i	0.970815	−	0.239829i	$-0.0770915\pi$
$311$	227.337	+	227.337i	0.730986	+	0.730986i	−0.239829	+	0.970815i	$0.577091\pi$
$312$		0			0
$313$	334.016	+	334.016i	1.06714	+	1.06714i	0.997577	+	0.0695661i	$0.0221615\pi$
$313$	334.016	+	334.016i	1.06714	+	1.06714i	0.0695661	+	0.997577i	$0.477839\pi$
$314$		0			0
$315$	238.740	−	80.8437i	0.757906	−	0.256647i
$316$		0			0
$317$	−25.5377	+	25.5377i	−0.0805606	+	0.0805606i	−0.746239	−	0.665678i	$-0.768142\pi$
$317$	−25.5377	+	25.5377i	−0.0805606	+	0.0805606i	0.665678	+	0.746239i	$0.268142\pi$
$318$		0			0
$319$	−85.1626			−0.266967
$320$		0			0
$321$	−7.28093	−	44.2021i	−0.0226820	−	0.137701i
$322$		0			0
$323$	−587.865	−	163.546i	−1.82002	−	0.506334i
$324$		0			0
$325$			102.567i			0.315591i
$326$		0			0
$327$	57.3798	+	348.350i	0.175474	+	1.06529i
$328$		0			0
$329$	−769.767	+	769.767i	−2.33972	+	2.33972i
$330$		0			0
$331$		−	75.4304i		−	0.227886i	−0.993487	−	0.113943i	$-0.963652\pi$
$331$		−	75.4304i		−	0.227886i	0.993487	−	0.113943i	$-0.0363482\pi$
$332$		0			0
$333$	−146.461	−	72.3617i	−0.439822	−	0.217303i
$334$		0			0
$335$	24.4295	+	24.4295i	0.0729239	+	0.0729239i
$336$		0			0
$337$	364.081	−	364.081i	1.08036	−	1.08036i	0.0838834	−	0.996476i	$-0.473268\pi$
$337$	364.081	−	364.081i	1.08036	−	1.08036i	0.996476	−	0.0838834i	$-0.0267323\pi$
$338$		0			0
$339$	−263.463	+	43.3974i	−0.777177	+	0.128016i
$340$		0			0
$341$		−	57.6229i		−	0.168982i
$342$		0			0
$343$	521.382	−	521.382i	1.52006	−	1.52006i
$344$		0			0
$345$	−68.9227	−	49.4281i	−0.199776	−	0.143270i
$346$		0			0
$347$	87.3452	−	87.3452i	0.251715	−	0.251715i	−0.569958	−	0.821674i	$-0.693041\pi$
$347$	87.3452	−	87.3452i	0.251715	−	0.251715i	0.821674	+	0.569958i	$0.193041\pi$
$348$		0			0
$349$			74.1562i			0.212482i	0.994340	+	0.106241i	$0.0338815\pi$
$349$			74.1562i			0.212482i	−0.994340	+	0.106241i	$0.966118\pi$
$350$		0			0
$351$	161.368	−	529.833i	0.459738	−	1.50950i
$352$		0			0
$353$			336.737i			0.953930i	0.878922	+	0.476965i	$0.158263\pi$
$353$			336.737i			0.953930i	−0.878922	+	0.476965i	$0.841737\pi$
$354$		0			0
$355$		−	305.169i		−	0.859632i
$356$		0			0
$357$	−635.037	−	68.9088i	−1.77882	−	0.193022i
$358$		0			0
$359$	384.960			1.07231			0.536156	−	0.844119i	$-0.319876\pi$
$359$	384.960			1.07231			0.536156	+	0.844119i	$0.319876\pi$
$360$		0			0
$361$	−927.349			−2.56883
$362$		0			0
$363$	187.221	−	261.062i	0.515760	−	0.719178i
$364$		0			0
$365$	155.606			0.426317
$366$		0			0
$367$	68.4299	+	68.4299i	0.186458	+	0.186458i	0.794163	−	0.607705i	$-0.207910\pi$
$367$	68.4299	+	68.4299i	0.186458	+	0.186458i	−0.607705	+	0.794163i	$0.707910\pi$
$368$		0			0
$369$	230.272	+	113.770i	0.624043	+	0.308320i
$370$		0			0
$371$	−289.153	−	289.153i	−0.779388	−	0.779388i
$372$		0			0
$373$	387.454			1.03875			0.519375	−	0.854546i	$-0.326165\pi$
$373$	387.454			1.03875			0.519375	+	0.854546i	$0.326165\pi$
$374$		0			0
$375$	33.0951	−	5.45139i	0.0882535	−	0.0145370i
$376$		0			0
$377$	−331.154	−	331.154i	−0.878394	−	0.878394i
$378$		0			0
$379$	−203.015	+	203.015i	−0.535659	+	0.535659i	−0.922251	−	0.386592i	$-0.873652\pi$
$379$	−203.015	+	203.015i	−0.535659	+	0.535659i	0.386592	+	0.922251i	$0.373652\pi$
$380$		0			0
$381$	−58.5308	+	81.6156i	−0.153624	+	0.214214i
$382$		0			0
$383$	−171.377			−0.447460			−0.223730	−	0.974651i	$-0.571823\pi$
$383$	−171.377			−0.447460			−0.223730	+	0.974651i	$0.571823\pi$
$384$		0			0
$385$	−73.8723	−	73.8723i	−0.191876	−	0.191876i
$386$		0			0
$387$	−66.2577	+	22.4366i	−0.171209	+	0.0579757i
$388$		0			0
$389$	466.221			1.19851			0.599256	−	0.800557i	$-0.295463\pi$
$389$	466.221			1.19851			0.599256	+	0.800557i	$0.295463\pi$
$390$		0			0
$391$	105.688	+	187.158i	0.270301	+	0.478666i
$392$		0			0
$393$	−68.2494	−	414.338i	−0.173663	−	1.05430i
$394$		0			0
$395$			77.2032i			0.195451i
$396$		0			0
$397$	−309.896	−	309.896i	−0.780595	−	0.780595i	0.199336	−	0.979931i	$-0.436122\pi$
$397$	−309.896	−	309.896i	−0.780595	−	0.780595i	−0.979931	+	0.199336i	$0.936122\pi$
$398$		0			0
$399$	−1330.75	+	219.200i	−3.33521	+	0.549372i
$400$		0			0
$401$	265.041	−	265.041i	0.660949	−	0.660949i	−0.294655	−	0.955604i	$-0.595205\pi$
$401$	265.041	−	265.041i	0.660949	−	0.660949i	0.955604	+	0.294655i	$0.0952046\pi$
$402$		0			0
$403$	224.066	−	224.066i	0.555996	−	0.555996i
$404$		0			0
$405$	−179.537	−	23.9079i	−0.443300	−	0.0590319i
$406$		0			0
$407$			67.7092i			0.166362i
$408$		0			0
$409$	625.462			1.52925			0.764624	−	0.644477i	$-0.222925\pi$
$409$	625.462			1.52925			0.764624	+	0.644477i	$0.222925\pi$
$410$		0			0
$411$	−114.348	+	159.447i	−0.278218	+	0.387949i
$412$		0			0
$413$	−388.905	−	388.905i	−0.941659	−	0.941659i
$414$		0			0
$415$	178.590	+	178.590i	0.430338	+	0.430338i
$416$		0			0
$417$	−174.792	+	28.7915i	−0.419165	+	0.0690444i
$418$		0			0
$419$	331.448	−	331.448i	0.791046	−	0.791046i	−0.190619	−	0.981664i	$-0.561049\pi$
$419$	331.448	−	331.448i	0.791046	−	0.791046i	0.981664	+	0.190619i	$0.0610494\pi$
$420$		0			0
$421$	519.977			1.23510			0.617550	−	0.786532i	$-0.288125\pi$
$421$	519.977			1.23510			0.617550	+	0.786532i	$0.288125\pi$
$422$		0			0
$423$	740.923	−	250.896i	1.75159	−	0.593134i
$424$		0			0
$425$	−81.8900	−	22.7821i	−0.192682	−	0.0536048i
$426$		0			0
$427$		−	868.796i		−	2.03465i
$428$		0			0
$429$	−226.510	+	37.3104i	−0.527994	+	0.0869707i
$430$		0			0
$431$	−288.633	+	288.633i	−0.669681	+	0.669681i	−0.957642	−	0.287961i	$-0.907023\pi$
$431$	−288.633	+	288.633i	−0.669681	+	0.669681i	0.287961	+	0.957642i	$0.407023\pi$
$432$		0			0
$433$		−	374.300i		−	0.864435i	−0.901769	−	0.432217i	$-0.857731\pi$
$433$		−	374.300i		−	0.864435i	0.901769	−	0.432217i	$-0.142269\pi$
$434$		0			0
$435$	−89.2521	+	124.453i	−0.205177	+	0.286100i
$436$		0			0
$437$	320.896	+	320.896i	0.734317	+	0.734317i
$438$		0			0
$439$	−418.428	+	418.428i	−0.953138	+	0.953138i	−0.998950	−	0.0458122i	$-0.985412\pi$
$439$	−418.428	+	418.428i	−0.953138	+	0.953138i	0.0458122	+	0.998950i	$0.485412\pi$
$440$		0			0
$441$	−919.547	+	311.382i	−2.08514	+	0.706082i
$442$		0			0
$443$			206.922i			0.467093i	0.972346	+	0.233546i	$0.0750330\pi$
$443$			206.922i			0.467093i	−0.972346	+	0.233546i	$0.924967\pi$
$444$		0			0
$445$	115.658	−	115.658i	0.259906	−	0.259906i
$446$		0			0
$447$	−142.576	+	198.808i	−0.318961	+	0.444761i
$448$		0			0
$449$	−351.654	+	351.654i	−0.783194	+	0.783194i	−0.980368	−	0.197174i	$-0.936824\pi$
$449$	−351.654	+	351.654i	−0.783194	+	0.783194i	0.197174	+	0.980368i	$0.436824\pi$
$450$		0			0
$451$		−	106.455i		−	0.236043i
$452$		0			0
$453$	−56.8604	+	79.2864i	−0.125520	+	0.175025i
$454$		0			0
$455$		−	574.505i		−	1.26265i
$456$		0			0
$457$			5.43919i			0.0119020i	0.999982	+	0.00595098i	$0.00189427\pi$
$457$			5.43919i			0.0119020i	−0.999982	+	0.00595098i	$0.998106\pi$
$458$		0			0
$459$	387.179	+	246.523i	0.843527	+	0.537087i
$460$		0			0
$461$	370.706			0.804134			0.402067	−	0.915610i	$-0.368292\pi$
$461$	370.706			0.804134			0.402067	+	0.915610i	$0.368292\pi$
$462$		0			0
$463$	698.277			1.50816			0.754079	−	0.656784i	$-0.228084\pi$
$463$	698.277			1.50816			0.754079	+	0.656784i	$0.228084\pi$
$464$		0			0
$465$	−84.2080	−	60.3899i	−0.181092	−	0.129871i
$466$		0			0
$467$	601.287			1.28755			0.643776	−	0.765214i	$-0.277367\pi$
$467$	601.287			1.28755			0.643776	+	0.765214i	$0.277367\pi$
$468$		0			0
$469$	−136.836	−	136.836i	−0.291761	−	0.291761i
$470$		0			0
$471$	−221.815	−	159.075i	−0.470945	−	0.337739i
$472$		0			0
$473$	20.5018	+	20.5018i	0.0433442	+	0.0433442i
$474$		0			0
$475$	−179.468			−0.377827
$476$		0			0
$477$	94.2457	+	278.318i	0.197580	+	0.583476i
$478$		0			0
$479$	−373.010	−	373.010i	−0.778727	−	0.778727i	0.200887	−	0.979614i	$-0.435617\pi$
$479$	−373.010	−	373.010i	−0.778727	−	0.778727i	−0.979614	+	0.200887i	$0.935617\pi$
$480$		0			0
$481$	−263.287	+	263.287i	−0.547374	+	0.547374i
$482$		0			0
$483$	386.054	+	276.860i	0.799285	+	0.573209i
$484$		0			0
$485$	418.853			0.863615
$486$		0			0
$487$	171.121	+	171.121i	0.351378	+	0.351378i	0.860622	−	0.509244i	$-0.170075\pi$
$487$	171.121	+	171.121i	0.351378	+	0.351378i	−0.509244	+	0.860622i	$0.670075\pi$
$488$		0			0
$489$	−53.3170	−	323.684i	−0.109033	−	0.661931i
$490$		0			0
$491$	701.356			1.42842			0.714212	−	0.699930i	$-0.246785\pi$
$491$	701.356			1.42842			0.714212	+	0.699930i	$0.246785\pi$
$492$		0			0
$493$	337.951	−	190.840i	0.685499	−	0.387099i
$494$		0			0
$495$	24.0777	+	71.1043i	0.0486419	+	0.143645i
$496$		0			0
$497$			1709.33i			3.43931i
$498$		0			0
$499$	−48.4461	−	48.4461i	−0.0970864	−	0.0970864i	0.656895	−	0.753982i	$-0.271869\pi$
$499$	−48.4461	−	48.4461i	−0.0970864	−	0.0970864i	−0.753982	+	0.656895i	$0.771869\pi$
$500$		0			0
$501$	125.634	+	762.719i	0.250767	+	1.52239i
$502$		0			0
$503$	−565.024	+	565.024i	−1.12331	+	1.12331i	−0.132068	+	0.991241i	$0.542162\pi$
$503$	−565.024	+	565.024i	−1.12331	+	1.12331i	−0.991241	+	0.132068i	$0.957838\pi$
$504$		0			0
$505$	1.15114	−	1.15114i	0.00227949	−	0.00227949i
$506$		0			0
$507$	−613.860	−	440.231i	−1.21077	−	0.868306i
$508$		0			0
$509$			856.414i			1.68254i	0.540613	+	0.841272i	$0.318192\pi$
$509$			856.414i			1.68254i	−0.540613	+	0.841272i	$0.681808\pi$
$510$		0			0
$511$	−871.589			−1.70565
$512$		0			0
$513$	927.082	+	282.356i	1.80718	+	0.550401i
$514$		0			0
$515$	−88.7855	−	88.7855i	−0.172399	−	0.172399i
$516$		0			0
$517$	−229.261	−	229.261i	−0.443444	−	0.443444i
$518$		0			0
$519$	142.768	+	866.739i	0.275084	+	1.67002i
$520$		0			0
$521$	235.284	−	235.284i	0.451602	−	0.451602i	−0.444284	−	0.895886i	$-0.646542\pi$
$521$	235.284	−	235.284i	0.451602	−	0.451602i	0.895886	+	0.444284i	$0.146542\pi$
$522$		0			0
$523$	381.786			0.729993			0.364996	−	0.931009i	$-0.381070\pi$
$523$	381.786			0.729993			0.364996	+	0.931009i	$0.381070\pi$
$524$		0			0
$525$	−185.374	+	30.5347i	−0.353094	+	0.0581612i
$526$		0			0
$527$	129.126	+	228.665i	0.245022	+	0.433900i
$528$		0			0
$529$			369.145i			0.697816i
$530$		0			0
$531$	126.759	+	374.333i	0.238717	+	0.704958i
$532$		0			0
$533$	413.951	−	413.951i	0.776644	−	0.776644i
$534$		0			0
$535$			33.3903i			0.0624117i
$536$		0			0
$537$	−317.437	−	227.651i	−0.591131	−	0.423931i
$538$		0			0
$539$	284.531	+	284.531i	0.527887	+	0.527887i
$540$		0			0
$541$	65.0221	−	65.0221i	0.120189	−	0.120189i	−0.644454	−	0.764643i	$-0.722915\pi$
$541$	65.0221	−	65.0221i	0.120189	−	0.120189i	0.764643	+	0.644454i	$0.222915\pi$
$542$		0			0
$543$	69.5746	+	422.383i	0.128130	+	0.777870i
$544$		0			0
$545$		−	263.143i		−	0.482832i
$546$		0			0
$547$	295.170	−	295.170i	0.539616	−	0.539616i	−0.383800	−	0.923416i	$-0.625385\pi$
$547$	295.170	−	295.170i	0.539616	−	0.539616i	0.923416	+	0.383800i	$0.125385\pi$
$548$		0			0
$549$	−276.534	+	559.707i	−0.503705	+	1.01950i
$550$		0			0
$551$	579.441	−	579.441i	1.05162	−	1.05162i
$552$		0			0
$553$		−	432.435i		−	0.781981i
$554$		0			0
$555$	98.9478	+	70.9606i	0.178284	+	0.127857i
$556$		0			0
$557$		−	634.216i		−	1.13863i	−0.822120	−	0.569314i	$-0.807209\pi$
$557$		−	634.216i		−	1.13863i	0.822120	−	0.569314i	$-0.192791\pi$
$558$		0			0
$559$			159.443i			0.285228i
$560$		0			0
$561$	20.5232	−	189.134i	0.0365832	−	0.337137i
$562$		0			0
$563$	68.5748			0.121802			0.0609012	−	0.998144i	$-0.480603\pi$
$563$	68.5748			0.121802			0.0609012	+	0.998144i	$0.480603\pi$
$564$		0			0
$565$	199.020			0.352248
$566$		0			0
$567$	1005.63	+	133.915i	1.77360	+	0.236181i
$568$		0			0
$569$	−937.748			−1.64806			−0.824031	−	0.566544i	$-0.808280\pi$
$569$	−937.748			−1.64806			−0.824031	+	0.566544i	$0.808280\pi$
$570$		0			0
$571$	−343.962	−	343.962i	−0.602385	−	0.602385i	0.338560	−	0.940945i	$-0.390060\pi$
$571$	−343.962	−	343.962i	−0.602385	−	0.602385i	−0.940945	+	0.338560i	$0.890060\pi$
$572$		0			0
$573$	84.3595	−	117.631i	0.147224	−	0.205290i
$574$		0			0
$575$	44.7011	+	44.7011i	0.0777411	+	0.0777411i
$576$		0			0
$577$	−949.918			−1.64630			−0.823152	−	0.567821i	$-0.807787\pi$
$577$	−949.918			−1.64630			−0.823152	+	0.567821i	$0.807787\pi$
$578$		0			0
$579$	−83.5788	−	507.402i	−0.144350	−	0.876342i
$580$		0			0
$581$	−1000.33	−	1000.33i	−1.72174	−	1.72174i
$582$		0			0
$583$	86.1187	−	86.1187i	0.147716	−	0.147716i
$584$		0			0
$585$	−182.863	+	370.115i	−0.312586	+	0.632675i
$586$		0			0
$587$	−358.662			−0.611008			−0.305504	−	0.952191i	$-0.598825\pi$
$587$	−358.662			−0.611008			−0.305504	+	0.952191i	$0.598825\pi$
$588$		0			0
$589$	392.063	+	392.063i	0.665641	+	0.665641i
$590$		0			0
$591$	566.272	−	93.2757i	0.958158	−	0.157827i
$592$		0			0
$593$	−147.937			−0.249472			−0.124736	−	0.992190i	$-0.539808\pi$
$593$	−147.937			−0.249472			−0.124736	+	0.992190i	$0.539808\pi$
$594$		0			0
$595$	458.688	+	127.608i	0.770904	+	0.214468i
$596$		0			0
$597$	−315.048	+	51.8944i	−0.527719	+	0.0869254i
$598$		0			0
$599$		−	99.4383i		−	0.166007i	−0.996549	−	0.0830036i	$-0.973549\pi$
$599$		−	99.4383i		−	0.166007i	0.996549	−	0.0830036i	$-0.0264513\pi$
$600$		0			0
$601$	509.073	+	509.073i	0.847044	+	0.847044i	0.989763	−	0.142719i	$-0.0455847\pi$
$601$	509.073	+	509.073i	0.847044	+	0.847044i	−0.142719	+	0.989763i	$0.545585\pi$
$602$		0			0
$603$	44.6000	+	131.709i	0.0739635	+	0.218422i
$604$		0			0
$605$	−169.316	+	169.316i	−0.279862	+	0.279862i
$606$		0			0
$607$	3.52307	−	3.52307i	0.00580408	−	0.00580408i	−0.704199	−	0.710003i	$-0.748694\pi$
$607$	3.52307	−	3.52307i	0.00580408	−	0.00580408i	0.710003	+	0.704199i	$0.248694\pi$
$608$		0			0
$609$	499.925	−	697.097i	0.820894	−	1.14466i
$610$		0			0
$611$		−	1782.96i		−	2.91810i
$612$		0			0
$613$	706.009			1.15173			0.575864	−	0.817545i	$-0.304666\pi$
$613$	706.009			1.15173			0.575864	+	0.817545i	$0.304666\pi$
$614$		0			0
$615$	−155.570	−	111.567i	−0.252959	−	0.181410i
$616$		0			0
$617$	−263.929	−	263.929i	−0.427762	−	0.427762i	0.460103	−	0.887865i	$-0.347812\pi$
$617$	−263.929	−	263.929i	−0.427762	−	0.427762i	−0.887865	+	0.460103i	$0.847812\pi$
$618$		0			0
$619$	−138.275	−	138.275i	−0.223385	−	0.223385i	0.586537	−	0.809922i	$-0.300491\pi$
$619$	−138.275	−	138.275i	−0.223385	−	0.223385i	−0.809922	+	0.586537i	$0.800491\pi$
$620$		0			0
$621$	−160.586	−	301.242i	−0.258592	−	0.485091i
$622$		0			0
$623$	−647.831	+	647.831i	−1.03986	+	1.03986i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−65.2844	−	396.338i	−0.104122	−	0.632118i
$628$		0			0
$629$	−151.729	−	268.691i	−0.241222	−	0.427171i
$630$		0			0
$631$			64.5220i			0.102254i	0.998692	+	0.0511268i	$0.0162813\pi$
$631$			64.5220i			0.102254i	−0.998692	+	0.0511268i	$0.983719\pi$
$632$		0			0
$633$	−173.370	−	1052.52i	−0.273887	−	1.66275i
$634$		0			0
$635$	52.9333	−	52.9333i	0.0833595	−	0.0833595i
$636$		0			0
$637$			2212.80i			3.47378i
$638$		0			0
$639$	544.074	−	1101.21i	0.851446	−	1.72333i
$640$		0			0
$641$	−617.291	−	617.291i	−0.963013	−	0.963013i	0.0363270	−	0.999340i	$-0.488434\pi$
$641$	−617.291	−	617.291i	−0.963013	−	0.963013i	−0.999340	+	0.0363270i	$0.988434\pi$
$642$		0			0
$643$	−393.111	+	393.111i	−0.611370	+	0.611370i	−0.943303	−	0.331933i	$-0.892299\pi$
$643$	−393.111	+	393.111i	−0.611370	+	0.611370i	0.331933	+	0.943303i	$0.392299\pi$
$644$		0			0
$645$	51.4470	−	8.47430i	0.0797627	−	0.0131384i
$646$		0			0
$647$		−	511.133i		−	0.790004i	−0.918680	−	0.395002i	$-0.870744\pi$
$647$		−	511.133i		−	0.790004i	0.918680	−	0.395002i	$-0.129256\pi$
$648$		0			0
$649$	115.828	−	115.828i	0.178472	−	0.178472i
$650$		0			0
$651$	471.671	+	338.260i	0.724533	+	0.519601i
$652$		0			0
$653$	724.214	−	724.214i	1.10906	−	1.10906i	0.115782	−	0.993275i	$-0.463063\pi$
$653$	724.214	−	724.214i	1.10906	−	1.10906i	0.993275	−	0.115782i	$-0.0369373\pi$
$654$		0			0
$655$			312.991i			0.477849i
$656$		0			0
$657$	561.506	+	277.423i	0.854652	+	0.422257i
$658$		0			0
$659$		−	484.139i		−	0.734657i	−0.930091	−	0.367329i	$-0.880272\pi$
$659$		−	484.139i		−	0.734657i	0.930091	−	0.367329i	$-0.119728\pi$
$660$		0			0
$661$		−	723.650i		−	1.09478i	−0.836877	−	0.547391i	$-0.815621\pi$
$661$		−	723.650i		−	1.09478i	0.836877	−	0.547391i	$-0.184379\pi$
$662$		0			0
$663$	815.251	−	655.642i	1.22964	−	0.988902i
$664$		0			0
$665$	1005.25			1.51165
$666$		0			0
$667$	−288.650			−0.432758
$668$		0			0
$669$	247.956	−	345.751i	0.370637	−	0.516818i
$670$		0			0
$671$	258.754			0.385625
$672$		0			0
$673$	−431.676	−	431.676i	−0.641420	−	0.641420i	0.309485	−	0.950904i	$-0.399843\pi$
$673$	−431.676	−	431.676i	−0.641420	−	0.641420i	−0.950904	+	0.309485i	$0.899843\pi$
$674$		0			0
$675$	129.143	+	39.3324i	0.191323	+	0.0582702i
$676$		0			0
$677$	−497.799	−	497.799i	−0.735301	−	0.735301i	0.236363	−	0.971665i	$-0.424044\pi$
$677$	−497.799	−	497.799i	−0.735301	−	0.735301i	−0.971665	+	0.236363i	$0.924044\pi$
$678$		0			0
$679$	−2346.11			−3.45524
$680$		0			0
$681$	529.758	−	87.2612i	0.777911	−	0.128137i
$682$		0			0
$683$	−136.626	−	136.626i	−0.200038	−	0.200038i	0.599978	−	0.800016i	$-0.295176\pi$
$683$	−136.626	−	136.626i	−0.200038	−	0.200038i	−0.800016	+	0.599978i	$0.795176\pi$
$684$		0			0
$685$	103.412	−	103.412i	0.150967	−	0.150967i
$686$		0			0
$687$	−654.688	+	912.899i	−0.952966	+	1.32882i
$688$		0			0
$689$	669.745			0.972053
$690$		0			0
$691$	596.546	+	596.546i	0.863309	+	0.863309i	0.991721	−	0.128412i	$-0.0409881\pi$
$691$	596.546	+	596.546i	0.863309	+	0.863309i	−0.128412	+	0.991721i	$0.540988\pi$
$692$		0			0
$693$	−134.866	−	398.274i	−0.194612	−	0.574710i
$694$		0			0
$695$	132.038			0.189982
$696$		0			0
$697$	238.555	+	422.447i	0.342259	+	0.606094i
$698$		0			0
$699$	−208.000	−	1262.76i	−0.297568	−	1.80652i
$700$		0			0
$701$			661.689i			0.943922i	0.881619	+	0.471961i	$0.156454\pi$
$701$			661.689i			0.943922i	−0.881619	+	0.471961i	$0.843546\pi$
$702$		0			0
$703$	−460.690	−	460.690i	−0.655320	−	0.655320i
$704$		0			0
$705$	−575.303	+	94.7633i	−0.816032	+	0.134416i
$706$		0			0
$707$	−6.44786	+	6.44786i	−0.00912002	+	0.00912002i
$708$		0			0
$709$	768.813	−	768.813i	1.08436	−	1.08436i	0.0882654	−	0.996097i	$-0.471868\pi$
$709$	768.813	−	768.813i	1.08436	−	1.08436i	0.996097	−	0.0882654i	$-0.0281324\pi$
$710$		0			0
$711$	−137.642	+	278.589i	−0.193590	+	0.391827i
$712$		0			0
$713$		−	195.307i		−	0.273922i
$714$		0			0
$715$	171.105			0.239308
$716$		0			0
$717$	−603.565	+	841.614i	−0.841792	+	1.17380i
$718$		0			0
$719$	920.822	+	920.822i	1.28070	+	1.28070i	0.940271	+	0.340427i	$0.110572\pi$
$719$	920.822	+	920.822i	1.28070	+	1.28070i	0.340427	+	0.940271i	$0.389428\pi$
$720$		0			0
$721$	497.311	+	497.311i	0.689752	+	0.689752i
$722$		0			0
$723$	893.386	−	147.158i	1.23567	−	0.203538i
$724$		0			0
$725$	80.7166	−	80.7166i	0.111333	−	0.111333i
$726$		0			0
$727$	−589.587			−0.810986			−0.405493	−	0.914098i	$-0.632900\pi$
$727$	−589.587			−0.810986			−0.405493	+	0.914098i	$0.632900\pi$
$728$		0			0
$729$	−605.237	−	406.361i	−0.830229	−	0.557422i
$730$		0			0
$731$	−127.300	−	35.4152i	−0.174145	−	0.0484476i
$732$		0			0
$733$		−	842.724i		−	1.14969i	−0.818262	−	0.574846i	$-0.805062\pi$
$733$		−	842.724i		−	1.14969i	0.818262	−	0.574846i	$-0.194938\pi$
$734$		0			0
$735$	713.998	−	117.609i	0.971426	−	0.160012i
$736$		0			0
$737$	40.7540	−	40.7540i	0.0552972	−	0.0552972i
$738$		0			0
$739$			406.489i			0.550053i	0.961437	+	0.275027i	$0.0886866\pi$
$739$			406.489i			0.550053i	−0.961437	+	0.275027i	$0.911313\pi$
$740$		0			0
$741$	1287.30	−	1795.02i	1.73725	−	2.42243i
$742$		0			0
$743$	473.160	+	473.160i	0.636823	+	0.636823i	0.949771	−	0.312947i	$-0.101316\pi$
$743$	473.160	+	473.160i	0.636823	+	0.636823i	−0.312947	+	0.949771i	$0.601316\pi$
$744$		0			0
$745$	128.941	−	128.941i	0.173075	−	0.173075i
$746$		0			0
$747$	326.045	+	962.849i	0.436473	+	1.28895i
$748$		0			0
$749$		−	187.028i		−	0.249703i
$750$		0			0
$751$	−210.388	+	210.388i	−0.280144	+	0.280144i	−0.833166	−	0.553022i	$-0.813474\pi$
$751$	−210.388	+	210.388i	−0.280144	+	0.280144i	0.553022	+	0.833166i	$0.313474\pi$
$752$		0			0
$753$	119.252	−	166.285i	0.158369	−	0.220830i
$754$		0			0
$755$	51.4227	−	51.4227i	0.0681095	−	0.0681095i
$756$		0			0
$757$			44.8000i			0.0591810i	0.999562	+	0.0295905i	$0.00942033\pi$
$757$			44.8000i			0.0591810i	−0.999562	+	0.0295905i	$0.990580\pi$
$758$		0			0
$759$	−82.4574	+	114.979i	−0.108640	+	0.151487i
$760$		0			0
$761$			1196.59i			1.57239i	0.617980	+	0.786193i	$0.287951\pi$
$761$			1196.59i			1.57239i	−0.617980	+	0.786193i	$0.712049\pi$
$762$		0			0
$763$			1473.94i			1.93176i
$764$		0			0
$765$	−254.885	−	228.208i	−0.333182	−	0.298311i
$766$		0			0
$767$	900.794			1.17444
$768$		0			0
$769$	−612.641			−0.796672			−0.398336	−	0.917240i	$-0.630412\pi$
$769$	−612.641			−0.796672			−0.398336	+	0.917240i	$0.630412\pi$
$770$		0			0
$771$	−790.036	−	566.576i	−1.02469	−	0.734858i
$772$		0			0
$773$	−822.220			−1.06367			−0.531837	−	0.846847i	$-0.678498\pi$
$773$	−822.220			−1.06367			−0.531837	+	0.846847i	$0.678498\pi$
$774$		0			0
$775$	54.6146	+	54.6146i	0.0704705	+	0.0704705i
$776$		0			0
$777$	−554.233	−	397.469i	−0.713298	−	0.511544i
$778$		0			0
$779$	724.316	+	724.316i	0.929803	+	0.929803i
$780$		0			0
$781$	−509.093			−0.651847
$782$		0			0
$783$	−543.951	+	289.969i	−0.694701	+	0.370331i
$784$		0			0
$785$	143.862	+	143.862i	0.183264	+	0.183264i
$786$		0			0
$787$	−173.027	+	173.027i	−0.219857	+	0.219857i	−0.808438	−	0.588581i	$-0.799687\pi$
$787$	−173.027	+	173.027i	−0.219857	+	0.219857i	0.588581	+	0.808438i	$0.299687\pi$
$788$		0			0
$789$	105.754	+	75.8417i	0.134035	+	0.0961238i
$790$		0			0
$791$	−1114.76			−1.40931
$792$		0			0
$793$	1006.17	+	1006.17i	1.26881	+	1.26881i
$794$		0			0
$795$	−35.5966	−	216.105i	−0.0447756	−	0.271830i
$796$		0			0
$797$	263.816			0.331011			0.165506	−	0.986209i	$-0.447074\pi$
$797$	263.816			0.331011			0.165506	+	0.986209i	$0.447074\pi$
$798$		0			0
$799$	1423.52	+	396.028i	1.78163	+	0.495655i
$800$		0			0
$801$	623.556	−	211.152i	0.778472	−	0.263611i
$802$		0			0
$803$		−	259.586i		−	0.323270i
$804$		0			0
$805$	−250.383	−	250.383i	−0.311034	−	0.311034i
$806$		0			0
$807$	−219.984	−	1335.51i	−0.272595	−	1.65491i
$808$		0			0
$809$	506.963	−	506.963i	0.626654	−	0.626654i	−0.320571	−	0.947225i	$-0.603875\pi$
$809$	506.963	−	506.963i	0.626654	−	0.626654i	0.947225	+	0.320571i	$0.103875\pi$
$810$		0			0
$811$	−799.377	+	799.377i	−0.985668	+	0.985668i	−0.999899	−	0.0142308i	$-0.995470\pi$
$811$	−799.377	+	799.377i	−0.985668	+	0.985668i	0.0142308	+	0.999899i	$0.495470\pi$
$812$		0			0
$813$	327.036	+	234.534i	0.402258	+	0.288480i
$814$		0			0
$815$			244.511i			0.300014i
$816$		0			0
$817$	−278.987			−0.341477
$818$		0			0
$819$	1024.26	−	2073.11i	1.25062	−	2.53127i
$820$		0			0
$821$	404.895	+	404.895i	0.493173	+	0.493173i	0.909304	−	0.416132i	$-0.136614\pi$
$821$	404.895	+	404.895i	0.493173	+	0.493173i	−0.416132	+	0.909304i	$0.636614\pi$
$822$		0			0
$823$	60.9416	+	60.9416i	0.0740481	+	0.0740481i	0.743161	−	0.669113i	$-0.233326\pi$
$823$	60.9416	+	60.9416i	0.0740481	+	0.0740481i	−0.669113	+	0.743161i	$0.733326\pi$
$824$		0			0
$825$	−9.09416	−	55.2101i	−0.0110232	−	0.0669214i
$826$		0			0
$827$	1035.92	−	1035.92i	1.25262	−	1.25262i	0.298084	−	0.954540i	$-0.403653\pi$
$827$	1035.92	−	1035.92i	1.25262	−	1.25262i	0.954540	−	0.298084i	$-0.0963474\pi$
$828$		0			0
$829$	−747.750			−0.901991			−0.450995	−	0.892526i	$-0.648931\pi$
$829$	−747.750			−0.901991			−0.450995	+	0.892526i	$0.648931\pi$
$830$		0			0
$831$	461.496	−	76.0172i	0.555350	−	0.0914767i
$832$		0			0
$833$	−1766.71	−	491.504i	−2.12090	−	0.590041i
$834$		0			0
$835$		−	576.158i		−	0.690009i
$836$		0			0
$837$	−196.199	−	368.049i	−0.234408	−	0.439724i
$838$		0			0
$839$	−528.142	+	528.142i	−0.629490	+	0.629490i	−0.947940	−	0.318449i	$-0.896838\pi$
$839$	−528.142	+	528.142i	−0.629490	+	0.629490i	0.318449	+	0.947940i	$0.396838\pi$
$840$		0			0
$841$		−	319.786i		−	0.380245i
$842$		0			0
$843$	668.795	+	479.628i	0.793352	+	0.568954i
$844$		0			0
$845$	398.130	+	398.130i	0.471160	+	0.471160i
$846$		0			0
$847$	948.386	−	948.386i	1.11970	−	1.11970i
$848$		0			0
$849$	126.170	+	765.969i	0.148610	+	0.902201i
$850$		0			0
$851$			229.493i			0.269675i
$852$		0			0
$853$	−822.928	+	822.928i	−0.964746	+	0.964746i	−0.999399	−	0.0346538i	$-0.988967\pi$
$853$	−822.928	+	822.928i	−0.964746	+	0.964746i	0.0346538	+	0.999399i	$0.488967\pi$
$854$		0			0
$855$	−647.613	−	319.966i	−0.757442	−	0.374229i
$856$		0			0
$857$	188.907	−	188.907i	0.220429	−	0.220429i	−0.588250	−	0.808679i	$-0.700183\pi$
$857$	188.907	−	188.907i	0.220429	−	0.220429i	0.808679	+	0.588250i	$0.200183\pi$
$858$		0			0
$859$		−	1071.56i		−	1.24745i	−0.781643	−	0.623726i	$-0.785618\pi$
$859$		−	1071.56i		−	1.24745i	0.781643	−	0.623726i	$-0.214382\pi$
$860$		0			0
$861$	871.389	+	624.918i	1.01207	+	0.725805i
$862$		0			0
$863$		−	371.527i		−	0.430506i	−0.976558	−	0.215253i	$-0.930942\pi$
$863$		−	371.527i		−	0.430506i	0.976558	−	0.215253i	$-0.0690576\pi$
$864$		0			0
$865$		−	654.735i		−	0.756919i
$866$		0			0
$867$	342.386	+	796.531i	0.394908	+	0.918721i
$868$		0			0
$869$	128.793			0.148208
$870$		0			0
$871$	316.944			0.363885
$872$		0			0
$873$	1511.44	+	746.757i	1.73132	+	0.855391i
$874$		0			0
$875$	140.032			0.160036
$876$		0			0
$877$	−456.739	−	456.739i	−0.520797	−	0.520797i	0.397015	−	0.917812i	$-0.370046\pi$
$877$	−456.739	−	456.739i	−0.520797	−	0.520797i	−0.917812	+	0.397015i	$0.870046\pi$
$878$		0			0
$879$	−469.018	+	654.000i	−0.533581	+	0.744028i
$880$		0			0
$881$	−531.403	−	531.403i	−0.603181	−	0.603181i	0.337974	−	0.941155i	$-0.390258\pi$
$881$	−531.403	−	531.403i	−0.603181	−	0.603181i	−0.941155	+	0.337974i	$0.890258\pi$
$882$		0			0
$883$	−1527.80			−1.73024			−0.865120	−	0.501565i	$-0.832758\pi$
$883$	−1527.80			−1.73024			−0.865120	+	0.501565i	$0.832758\pi$
$884$		0			0
$885$	−47.8768	−	290.657i	−0.0540980	−	0.328426i
$886$		0			0
$887$	265.589	+	265.589i	0.299424	+	0.299424i	0.840788	−	0.541364i	$-0.182092\pi$
$887$	265.589	+	265.589i	0.299424	+	0.299424i	−0.541364	+	0.840788i	$0.682092\pi$
$888$		0			0
$889$	−296.493	+	296.493i	−0.333513	+	0.333513i
$890$		0			0
$891$	−39.8839	+	299.508i	−0.0447631	+	0.336149i
$892$		0			0
$893$	3119.75			3.49356
$894$		0			0
$895$	205.880	+	205.880i	0.230033	+	0.230033i
$896$		0			0
$897$	−767.731	+	126.460i	−0.855887	+	0.140981i
$898$		0			0
$899$	−352.665			−0.392285
$900$		0			0
$901$	−148.763	+	534.728i	−0.165109	+	0.593482i
$902$		0			0
$903$	−288.168	+	47.4668i	−0.319123	+	0.0525656i
$904$		0			0
$905$		−	319.068i		−	0.352562i
$906$		0			0
$907$	−982.684	−	982.684i	−1.08344	−	1.08344i	−0.996186	−	0.0872582i	$-0.972189\pi$
$907$	−982.684	−	982.684i	−1.08344	−	1.08344i	−0.0872582	−	0.996186i	$-0.527811\pi$
$908$		0			0
$909$	6.20625	−	2.10160i	0.00682756	−	0.00231199i
$910$		0			0
$911$	−104.963	+	104.963i	−0.115217	+	0.115217i	−0.762365	−	0.647148i	$-0.775962\pi$
$911$	−104.963	+	104.963i	−0.115217	+	0.115217i	0.647148	+	0.762365i	$0.275962\pi$
$912$		0			0
$913$	297.930	−	297.930i	0.326320	−	0.326320i
$914$		0			0
$915$	271.180	−	378.134i	0.296372	−	0.413262i
$916$		0			0
$917$		−	1753.15i		−	1.91183i
$918$		0			0
$919$	833.689			0.907170			0.453585	−	0.891213i	$-0.350145\pi$
$919$	833.689			0.907170			0.453585	+	0.891213i	$0.350145\pi$
$920$		0			0
$921$	642.774	+	460.967i	0.697909	+	0.500507i
$922$		0			0
$923$	−1979.61	−	1979.61i	−2.14475	−	2.14475i
$924$		0			0
$925$	−64.1744	−	64.1744i	−0.0693777	−	0.0693777i
$926$		0			0
$927$	−162.092	−	478.676i	−0.174857	−	0.516371i
$928$		0			0
$929$	267.842	−	267.842i	0.288312	−	0.288312i	−0.548101	−	0.836412i	$-0.684649\pi$
$929$	267.842	−	267.842i	0.288312	−	0.288312i	0.836412	+	0.548101i	$0.184649\pi$
$930$		0			0
$931$	−3871.87			−4.15883
$932$		0			0
$933$	−156.760	−	951.683i	−0.168018	−	1.02002i
$934$		0			0
$935$	−38.0057	+	136.611i	−0.0406478	+	0.146108i
$936$		0			0
$937$			32.1304i			0.0342907i	0.999853	+	0.0171453i	$0.00545780\pi$
$937$			32.1304i			0.0342907i	−0.999853	+	0.0171453i	$0.994542\pi$
$938$		0			0
$939$	−230.321	−	1398.27i	−0.245284	−	1.48910i
$940$		0			0
$941$	−461.125	+	461.125i	−0.490038	+	0.490038i	−0.908318	−	0.418280i	$-0.862633\pi$
$941$	−461.125	+	461.125i	−0.490038	+	0.490038i	0.418280	+	0.908318i	$0.362633\pi$
$942$		0			0
$943$		−	360.819i		−	0.382629i
$944$		0			0
$945$	−723.365	−	220.311i	−0.765466	−	0.233133i
$946$		0			0
$947$	−641.692	−	641.692i	−0.677605	−	0.677605i	0.281853	−	0.959458i	$-0.409051\pi$
$947$	−641.692	−	641.692i	−0.677605	−	0.677605i	−0.959458	+	0.281853i	$0.909051\pi$
$948$		0			0
$949$	1009.40	−	1009.40i	1.06365	−	1.06365i
$950$		0			0
$951$	106.907	−	17.6096i	0.112415	−	0.0185169i
$952$		0			0
$953$			1122.84i			1.17822i	0.808054	+	0.589108i	$0.200521\pi$
$953$			1122.84i			1.17822i	−0.808054	+	0.589108i	$0.799479\pi$
$954$		0			0
$955$	−76.2919	+	76.2919i	−0.0798868	+	0.0798868i
$956$		0			0
$957$	207.617	+	148.893i	0.216946	+	0.155583i
$958$		0			0
$959$	−579.239	+	579.239i	−0.604003	+	0.604003i
$960$		0			0
$961$			722.379i			0.751696i
$962$		0			0
$963$	−59.5302	+	120.489i	−0.0618174	+	0.125119i
$964$		0			0
$965$			383.292i			0.397193i
$966$		0			0
$967$		−	659.738i		−	0.682253i	−0.940017	−	0.341126i	$-0.889192\pi$
$967$		−	659.738i		−	0.682253i	0.940017	−	0.341126i	$-0.110808\pi$
$968$		0			0
$969$	1147.22	+	1426.49i	1.18392	+	1.47213i
$970$		0			0
$971$	−1805.24			−1.85916			−0.929578	−	0.368624i	$-0.879829\pi$
$971$	−1805.24			−1.85916			−0.929578	+	0.368624i	$0.879829\pi$
$972$		0			0
$973$	−739.578			−0.760100
$974$		0			0
$975$	179.322	−	250.047i	0.183920	−	0.256459i
$976$		0			0
$977$	989.215			1.01250			0.506251	−	0.862386i	$-0.331031\pi$
$977$	989.215			1.01250			0.506251	+	0.862386i	$0.331031\pi$
$978$		0			0
$979$	−192.944	−	192.944i	−0.197083	−	0.197083i
$980$		0			0
$981$	469.148	−	949.558i	0.478234	−	0.967949i
$982$		0			0
$983$	320.473	+	320.473i	0.326016	+	0.326016i	0.851069	−	0.525053i	$-0.175955\pi$
$983$	320.473	+	320.473i	0.326016	+	0.326016i	−0.525053	+	0.851069i	$0.675955\pi$
$984$		0			0
$985$	−427.762			−0.434276
$986$		0			0
$987$	3222.42	−	530.795i	3.26487	−	0.537786i
$988$		0			0
$989$	69.4888	+	69.4888i	0.0702617	+	0.0702617i
$990$		0			0
$991$	82.6684	−	82.6684i	0.0834192	−	0.0834192i	−0.664166	−	0.747585i	$-0.731213\pi$
$991$	82.6684	−	82.6684i	0.0834192	−	0.0834192i	0.747585	+	0.664166i	$0.231213\pi$
$992$		0			0
$993$	−131.878	+	183.891i	−0.132808	+	0.185187i
$994$		0			0
$995$	237.987			0.239183
$996$		0			0
$997$	640.833	+	640.833i	0.642762	+	0.642762i	0.951233	−	0.308472i	$-0.0998176\pi$
$997$	640.833	+	640.833i	0.642762	+	0.642762i	−0.308472	+	0.951233i	$0.599818\pi$
$998$		0			0
$999$	230.542	+	432.473i	0.230773	+	0.432906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.11	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.35	yes	96
17.13	even	4	inner	1020.3.bc.a.761.35	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.11	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.35	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.11	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.35	yes	96	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43789 - 1.74834i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-8.85638 - 8.85638i) q^{7} +(2.88662 + 8.52452i) q^{9} +O(q^{10})\)	\(q+(-2.43789 - 1.74834i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-8.85638 - 8.85638i) q^{7} +(2.88662 + 8.52452i) q^{9} +(2.63770 - 2.63770i) q^{11} +20.5134 q^{13} +(-1.09028 - 6.61901i) q^{15} +(-4.55641 + 16.3780i) q^{17} +35.8936i q^{19} +(6.10693 + 37.0748i) q^{21} +(8.94022 - 8.94022i) q^{23} +5.00000i q^{25} +(7.86648 - 25.8286i) q^{27} +(-16.1433 - 16.1433i) q^{29} +(10.9229 - 10.9229i) q^{31} +(-11.0420 + 1.81883i) q^{33} -28.0063i q^{35} +(-12.8349 + 12.8349i) q^{37} +(-50.0094 - 35.8644i) q^{39} +(20.1796 - 20.1796i) q^{41} +7.77261i q^{43} +(-8.91430 + 18.0426i) q^{45} -86.9167i q^{47} +107.871i q^{49} +(39.7423 - 31.9616i) q^{51} +32.6491 q^{53} +8.34115 q^{55} +(62.7541 - 87.5046i) q^{57} +43.9125 q^{59} +(49.0492 + 49.0492i) q^{61} +(49.9313 - 101.061i) q^{63} +(32.4345 + 32.4345i) q^{65} +15.4506 q^{67} +(-37.4258 + 6.16475i) q^{69} +(-96.5031 - 96.5031i) q^{71} +(49.2069 - 49.2069i) q^{73} +(8.74169 - 12.1895i) q^{75} -46.7210 q^{77} +(24.4138 + 24.4138i) q^{79} +(-64.3348 + 49.2141i) q^{81} +112.951 q^{83} +(-33.1002 + 18.6916i) q^{85} +(11.1317 + 67.5796i) q^{87} -73.1486i q^{89} +(-181.674 - 181.674i) q^{91} +(-45.7259 + 7.53192i) q^{93} +(-56.7527 + 56.7527i) q^{95} +(132.453 - 132.453i) q^{97} +(30.0992 + 14.8711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 96 * q - 8 * q^3	\( 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) \) 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Introduction

L-functions

Modular forms

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