LMFDB - Embedded newform 585.2.ca.a.58.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(58,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.58"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.ca (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$80$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			58.1
Character	$\chi$	$=$	585.58
Dual form			585.2.ca.a.232.80

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.74212i q^{2} +(-0.788234 - 1.54230i) q^{3} -5.51923 q^{4} +(1.63311 + 1.52740i) q^{5} +(-4.22917 + 2.16143i) q^{6} +(-0.999815 + 1.73173i) q^{7} +9.65015i q^{8} +(-1.75738 + 2.43139i) q^{9} +(4.18831 - 4.47819i) q^{10} +(2.92709 + 2.92709i) q^{11} +(4.35044 + 8.51230i) q^{12} +(-3.35467 - 1.32144i) q^{13} +(4.74861 + 2.74161i) q^{14} +(1.06843 - 3.72269i) q^{15} +15.4234 q^{16} +(0.123121 - 0.459493i) q^{17} +(6.66715 + 4.81894i) q^{18} +(-1.10499 + 4.12388i) q^{19} +(-9.01352 - 8.43006i) q^{20} +(3.45893 + 0.177006i) q^{21} +(8.02643 - 8.02643i) q^{22} +(-5.40565 - 1.44844i) q^{23} +(14.8834 - 7.60658i) q^{24} +(0.334109 + 4.98882i) q^{25} +(-3.62356 + 9.19890i) q^{26} +(5.13515 + 0.793899i) q^{27} +(5.51821 - 9.55782i) q^{28} +8.53407i q^{29} +(-10.2081 - 2.92977i) q^{30} +(-0.732032 - 2.73198i) q^{31} -22.9926i q^{32} +(2.20722 - 6.82168i) q^{33} +(-1.25999 - 0.337612i) q^{34} +(-4.27785 + 1.30099i) q^{35} +(9.69935 - 13.4194i) q^{36} +(-2.66413 + 4.61440i) q^{37} +(11.3082 + 3.03002i) q^{38} +(0.606199 + 6.21551i) q^{39} +(-14.7396 + 15.7598i) q^{40} +(-7.91919 - 2.12194i) q^{41} +(0.485371 - 9.48482i) q^{42} +(0.658274 + 2.45671i) q^{43} +(-16.1553 - 16.1553i) q^{44} +(-6.58368 + 1.28651i) q^{45} +(-3.97180 + 14.8230i) q^{46} +(-5.61106 - 9.71864i) q^{47} +(-12.1573 - 23.7875i) q^{48} +(1.50074 + 2.59936i) q^{49} +(13.6800 - 0.916166i) q^{50} +(-0.805724 + 0.172299i) q^{51} +(18.5152 + 7.29335i) q^{52} +(5.21679 + 5.21679i) q^{53} +(2.17697 - 14.0812i) q^{54} +(0.309433 + 9.25109i) q^{55} +(-16.7115 - 9.64837i) q^{56} +(7.23125 - 1.54636i) q^{57} +23.4014 q^{58} +(-1.73531 + 1.73531i) q^{59} +(-5.89692 + 20.5464i) q^{60} +(1.75899 - 3.04666i) q^{61} +(-7.49142 + 2.00732i) q^{62} +(-2.45345 - 5.47424i) q^{63} -32.2017 q^{64} +(-3.46017 - 7.28198i) q^{65} +(-18.7059 - 6.05246i) q^{66} +(2.57441 - 1.48634i) q^{67} +(-0.679532 + 2.53605i) q^{68} +(2.02699 + 9.47885i) q^{69} +(3.56748 + 11.7304i) q^{70} +(3.28037 + 0.878973i) q^{71} +(-23.4632 - 16.9589i) q^{72} +1.33164i q^{73} +(12.6533 + 7.30536i) q^{74} +(7.43091 - 4.44766i) q^{75} +(6.09869 - 22.7606i) q^{76} +(-7.99548 + 2.14238i) q^{77} +(17.0437 - 1.66227i) q^{78} +(4.70323 - 2.71541i) q^{79} +(25.1882 + 23.5577i) q^{80} +(-2.82327 - 8.54571i) q^{81} +(-5.81862 + 21.7154i) q^{82} +(-3.23684 - 5.60637i) q^{83} +(-19.0907 - 0.976935i) q^{84} +(0.902899 - 0.562349i) q^{85} +(6.73660 - 1.80507i) q^{86} +(13.1621 - 6.72684i) q^{87} +(-28.2468 + 28.2468i) q^{88} +(0.382500 + 1.42751i) q^{89} +(3.52777 + 18.0533i) q^{90} +(5.64243 - 4.48818i) q^{91} +(29.8350 + 7.99427i) q^{92} +(-3.63652 + 3.28245i) q^{93} +(-26.6497 + 15.3862i) q^{94} +(-8.10338 + 5.04700i) q^{95} +(-35.4615 + 18.1235i) q^{96} +(5.72842 + 3.30730i) q^{97} +(7.12775 - 4.11521i) q^{98} +(-12.2609 + 1.97289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 2 q^{3} - 304 q^{4} - 2 q^{5} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{10} - 12 q^{11} - 14 q^{12} - 2 q^{13} + 48 q^{14} - 6 q^{15} + 264 q^{16} - 12 q^{17} + 4 q^{18} - 30 q^{20} - 16 q^{21} - 4 q^{22}+ \cdots - 20 q^{99}+O(q^{100}) $ 320 * q - 2 * q^3 - 304 * q^4 - 2 * q^5 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^10 - 12 * q^11 - 14 * q^12 - 2 * q^13 + 48 * q^14 - 6 * q^15 + 264 * q^16 - 12 * q^17 + 4 * q^18 - 30 * q^20 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 56 * q^24 - 20 * q^27 - 24 * q^28 - 2 * q^30 - 4 * q^31 - 6 * q^33 + 8 * q^34 - 46 * q^35 - 60 * q^36 - 4 * q^37 - 40 * q^38 - 4 * q^39 + 28 * q^40 + 4 * q^41 + 22 * q^42 - 6 * q^43 + 8 * q^44 + 4 * q^45 - 16 * q^46 - 14 * q^47 + 2 * q^48 - 112 * q^49 + 56 * q^50 - 30 * q^52 - 16 * q^53 - 4 * q^55 - 108 * q^56 - 72 * q^57 + 28 * q^58 - 16 * q^59 + 10 * q^60 + 4 * q^61 - 28 * q^62 - 18 * q^63 - 192 * q^64 + 58 * q^65 - 6 * q^67 + 62 * q^68 + 24 * q^69 + 10 * q^70 - 2 * q^72 - 34 * q^75 - 20 * q^76 - 44 * q^77 - 42 * q^78 + 4 * q^80 + 8 * q^81 + 20 * q^82 + 8 * q^83 + 124 * q^84 - 16 * q^85 + 68 * q^86 + 38 * q^87 - 8 * q^88 + 64 * q^90 - 16 * q^91 - 32 * q^92 - 70 * q^93 + 48 * q^94 - 64 * q^96 - 6 * q^97 - 282 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$		−	2.74212i		−	1.93897i	−0.245146	−	0.969486i	$-0.578836\pi$
$2$		−	2.74212i		−	1.93897i	0.245146	−	0.969486i	$-0.421164\pi$
$3$	−0.788234	−	1.54230i	−0.455087	−	0.890447i
$3$	−0.788234	−	1.54230i	−0.455087	−	0.890447i
$4$	−5.51923			−2.75961
$5$	1.63311	+	1.52740i	0.730350	+	0.683073i
$5$	1.63311	+	1.52740i	0.730350	+	0.683073i
$6$	−4.22917	+	2.16143i	−1.72655	+	0.882401i
$7$	−0.999815	+	1.73173i	−0.377895	+	0.654533i	−0.990756	−	0.135658i	$-0.956685\pi$
$7$	−0.999815	+	1.73173i	−0.377895	+	0.654533i	0.612861	+	0.790191i	$0.290018\pi$
$8$			9.65015i			3.41184i
$9$	−1.75738	+	2.43139i	−0.585792	+	0.810462i
$10$	4.18831	−	4.47819i	1.32446	−	1.41613i
$11$	2.92709	+	2.92709i	0.882550	+	0.882550i	0.993793	−	0.111243i	$-0.0354831\pi$
$11$	2.92709	+	2.92709i	0.882550	+	0.882550i	−0.111243	+	0.993793i	$0.535483\pi$
$12$	4.35044	+	8.51230i	1.25586	+	2.45729i
$13$	−3.35467	−	1.32144i	−0.930417	−	0.366503i
$13$	−3.35467	−	1.32144i	−0.930417	−	0.366503i
$14$	4.74861	+	2.74161i	1.26912	+	0.732727i
$15$	1.06843	−	3.72269i	0.275868	−	0.961196i
$16$	15.4234			3.85586
$17$	0.123121	−	0.459493i	0.0298612	−	0.111443i	−0.949387	−	0.314110i	$-0.898294\pi$
$17$	0.123121	−	0.459493i	0.0298612	−	0.111443i	0.979248	+	0.202666i	$0.0649607\pi$
$18$	6.66715	+	4.81894i	1.57146	+	1.13583i
$19$	−1.10499	+	4.12388i	−0.253502	+	0.946083i	0.715415	+	0.698699i	$0.246237\pi$
$19$	−1.10499	+	4.12388i	−0.253502	+	0.946083i	−0.968918	+	0.247384i	$0.920429\pi$
$20$	−9.01352	−	8.43006i	−2.01548	−	1.88502i
$21$	3.45893	+	0.177006i	0.754801	+	0.0386258i
$22$	8.02643	−	8.02643i	1.71124	−	1.71124i
$23$	−5.40565	−	1.44844i	−1.12716	−	0.302021i	−0.353380	−	0.935480i	$-0.614968\pi$
$23$	−5.40565	−	1.44844i	−1.12716	−	0.302021i	−0.773776	+	0.633459i	$0.781635\pi$
$24$	14.8834	−	7.60658i	3.03807	−	1.55269i
$25$	0.334109	+	4.98882i	0.0668217	+	0.997765i
$26$	−3.62356	+	9.19890i	−0.710638	+	1.80405i
$27$	5.13515	+	0.793899i	0.988259	+	0.152786i
$28$	5.51821	−	9.55782i	1.04284	−	1.80626i
$29$			8.53407i			1.58474i	0.610043	+	0.792368i	$0.291152\pi$
$29$			8.53407i			1.58474i	−0.610043	+	0.792368i	$0.708848\pi$
$30$	−10.2081	−	2.92977i	−1.86373	−	0.534900i
$31$	−0.732032	−	2.73198i	−0.131477	−	0.490678i	0.868511	−	0.495670i	$-0.165078\pi$
$31$	−0.732032	−	2.73198i	−0.131477	−	0.490678i	−0.999988	+	0.00499226i	$0.998411\pi$
$32$		−	22.9926i		−	4.06456i
$33$	2.20722	−	6.82168i	0.384227	−	1.18750i
$34$	−1.25999	−	0.337612i	−0.216086	−	0.0579000i
$35$	−4.27785	+	1.30099i	−0.723089	+	0.219908i
$36$	9.69935	−	13.4194i	1.61656	−	2.23656i
$37$	−2.66413	+	4.61440i	−0.437980	+	0.758603i	−0.997534	−	0.0701907i	$-0.977639\pi$
$37$	−2.66413	+	4.61440i	−0.437980	+	0.758603i	0.559554	+	0.828794i	$0.310973\pi$
$38$	11.3082	+	3.03002i	1.83443	+	0.491534i
$39$	0.606199	+	6.21551i	0.0970695	+	0.995278i
$40$	−14.7396	+	15.7598i	−2.33054	+	2.49184i
$41$	−7.91919	−	2.12194i	−1.23677	−	0.331392i	−0.419558	−	0.907729i	$-0.637815\pi$
$41$	−7.91919	−	2.12194i	−1.23677	−	0.331392i	−0.817212	+	0.576337i	$0.804482\pi$
$42$	0.485371	−	9.48482i	0.0748944	−	1.46354i
$43$	0.658274	+	2.45671i	0.100386	+	0.374645i	0.997781	−	0.0665829i	$-0.0212097\pi$
$43$	0.658274	+	2.45671i	0.100386	+	0.374645i	−0.897395	+	0.441228i	$0.854543\pi$
$44$	−16.1553	−	16.1553i	−2.43550	−	2.43550i
$45$	−6.58368	+	1.28651i	−0.981438	+	0.191782i
$46$	−3.97180	+	14.8230i	−0.585610	+	2.18553i
$47$	−5.61106	−	9.71864i	−0.818457	−	1.41761i	−0.906818	−	0.421521i	$-0.861496\pi$
$47$	−5.61106	−	9.71864i	−0.818457	−	1.41761i	0.0883610	−	0.996089i	$-0.471837\pi$
$48$	−12.1573	−	23.7875i	−1.75475	−	3.43344i
$49$	1.50074	+	2.59936i	0.214391	+	0.371337i
$50$	13.6800	−	0.916166i	1.93464	−	0.129565i
$51$	−0.805724	+	0.172299i	−0.112824	+	0.0241267i
$52$	18.5152	+	7.29335i	2.56759	+	1.01141i
$53$	5.21679	+	5.21679i	0.716581	+	0.716581i	0.967903	−	0.251322i	$-0.0808654\pi$
$53$	5.21679	+	5.21679i	0.716581	+	0.716581i	−0.251322	+	0.967903i	$0.580865\pi$
$54$	2.17697	−	14.0812i	0.296248	−	1.91621i
$55$	0.309433	+	9.25109i	0.0417239	+	1.24742i
$56$	−16.7115	−	9.64837i	−2.23316	−	1.28932i
$57$	7.23125	−	1.54636i	0.957802	−	0.204820i
$58$	23.4014			3.07276
$59$	−1.73531	+	1.73531i	−0.225918	+	0.225918i	−0.810985	−	0.585067i	$-0.801068\pi$
$59$	−1.73531	+	1.73531i	−0.225918	+	0.225918i	0.585067	+	0.810985i	$0.301068\pi$
$60$	−5.89692	+	20.5464i	−0.761289	+	2.65253i
$61$	1.75899	−	3.04666i	0.225215	−	0.390084i	−0.731169	−	0.682197i	$-0.761025\pi$
$61$	1.75899	−	3.04666i	0.225215	−	0.390084i	0.956384	+	0.292112i	$0.0943581\pi$
$62$	−7.49142	+	2.00732i	−0.951411	+	0.254930i
$63$	−2.45345	−	5.47424i	−0.309106	−	0.689689i
$64$	−32.2017			−4.02521
$65$	−3.46017	−	7.28198i	−0.429182	−	0.903218i
$66$	−18.7059	−	6.05246i	−2.30253	−	0.745006i
$67$	2.57441	−	1.48634i	0.314515	−	0.181585i	−0.334430	−	0.942421i	$-0.608544\pi$
$67$	2.57441	−	1.48634i	0.314515	−	0.181585i	0.648945	+	0.760835i	$0.275211\pi$
$68$	−0.679532	+	2.53605i	−0.0824053	+	0.307541i
$69$	2.02699	+	9.47885i	0.244021	+	1.14112i
$70$	3.56748	+	11.7304i	0.426396	+	1.40205i
$71$	3.28037	+	0.878973i	0.389309	+	0.104315i	0.448163	−	0.893952i	$-0.352078\pi$
$71$	3.28037	+	0.878973i	0.389309	+	0.104315i	−0.0588548	+	0.998267i	$0.518745\pi$
$72$	−23.4632	−	16.9589i	−2.76517	−	1.99863i
$73$			1.33164i			0.155856i	0.996959	+	0.0779281i	$0.0248305\pi$
$73$			1.33164i			0.155856i	−0.996959	+	0.0779281i	$0.975170\pi$
$74$	12.6533	+	7.30536i	1.47091	+	0.849231i
$75$	7.43091	−	4.44766i	0.858047	−	0.513571i
$76$	6.09869	−	22.7606i	0.699568	−	2.61082i
$77$	−7.99548	+	2.14238i	−0.911169	+	0.244147i
$78$	17.0437	−	1.66227i	1.92982	−	0.188215i
$79$	4.70323	−	2.71541i	0.529155	−	0.305508i	−0.211517	−	0.977374i	$-0.567840\pi$
$79$	4.70323	−	2.71541i	0.529155	−	0.305508i	0.740672	+	0.671866i	$0.234507\pi$
$80$	25.1882	+	23.5577i	2.81612	+	2.63383i
$81$	−2.82327	−	8.54571i	−0.313696	−	0.949523i
$82$	−5.81862	+	21.7154i	−0.642559	+	2.39806i
$83$	−3.23684	−	5.60637i	−0.355289	−	0.615379i	0.631878	−	0.775068i	$-0.282284\pi$
$83$	−3.23684	−	5.60637i	−0.355289	−	0.615379i	−0.987167	+	0.159689i	$0.948951\pi$
$84$	−19.0907	−	0.976935i	−2.08296	−	0.106592i
$85$	0.902899	−	0.562349i	0.0979332	−	0.0609953i
$86$	6.73660	−	1.80507i	0.726427	−	0.194645i
$87$	13.1621	−	6.72684i	1.41112	−	0.721193i
$88$	−28.2468	+	28.2468i	−3.01112	+	3.01112i
$89$	0.382500	+	1.42751i	0.0405449	+	0.151316i	0.983231	−	0.182366i	$-0.0583756\pi$
$89$	0.382500	+	1.42751i	0.0405449	+	0.151316i	−0.942686	+	0.333682i	$0.891709\pi$
$90$	3.52777	+	18.0533i	0.371860	+	1.90298i
$91$	5.64243	−	4.48818i	0.591487	−	0.470489i
$92$	29.8350	+	7.99427i	3.11052	+	0.833461i
$93$	−3.63652	+	3.28245i	−0.377089	+	0.340374i
$94$	−26.6497	+	15.3862i	−2.74871	+	1.58697i
$95$	−8.10338	+	5.04700i	−0.831389	+	0.517811i
$96$	−35.4615	+	18.1235i	−3.61927	+	1.84973i
$97$	5.72842	+	3.30730i	0.581633	+	0.335806i	0.761782	−	0.647834i	$-0.224325\pi$
$97$	5.72842	+	3.30730i	0.581633	+	0.335806i	−0.180149	+	0.983639i	$0.557658\pi$
$98$	7.12775	−	4.11521i	0.720012	−	0.415699i
$99$	−12.2609	+	1.97289i	−1.23226	+	0.198283i
$100$	−1.84402	−	27.5345i	−0.184402	−	2.75345i
$101$			6.72688i			0.669349i	0.942334	+	0.334675i	$0.108626\pi$
$101$			6.72688i			0.669349i	−0.942334	+	0.334675i	$0.891374\pi$
$102$	0.472464	+	2.20939i	0.0467809	+	0.218762i
$103$	−0.593658	−	2.21556i	−0.0584949	−	0.218306i	0.930491	−	0.366314i	$-0.119380\pi$
$103$	−0.593658	−	2.21556i	−0.0584949	−	0.218306i	−0.988986	+	0.148008i	$0.952714\pi$
$104$	12.7521	−	32.3730i	1.25045	−	3.17444i
$105$	5.37847	+	5.57224i	0.524885	+	0.543795i
$106$	14.3051	−	14.3051i	1.38943	−	1.38943i
$107$	0.988611	+	3.68954i	0.0955726	+	0.356682i	0.997106	−	0.0760285i	$-0.0242240\pi$
$107$	0.988611	+	3.68954i	0.0955726	+	0.356682i	−0.901533	+	0.432710i	$0.857557\pi$
$108$	−28.3420	−	4.38171i	−2.72721	−	0.421630i
$109$	−2.11040	−	2.11040i	−0.202140	−	0.202140i	0.598776	−	0.800916i	$-0.295654\pi$
$109$	−2.11040	−	2.11040i	−0.202140	−	0.202140i	−0.800916	+	0.598776i	$0.795654\pi$
$110$	25.3676	−	0.848502i	2.41871	−	0.0809015i
$111$	9.21675	+	0.471653i	0.874815	+	0.0447673i
$112$	−15.4206	+	26.7092i	−1.45711	+	2.52378i
$113$	−2.63708	−	2.63708i	−0.248075	−	0.248075i	0.572105	−	0.820180i	$-0.306127\pi$
$113$	−2.63708	−	2.63708i	−0.248075	−	0.248075i	−0.820180	+	0.572105i	$0.806127\pi$
$114$	−4.24029	−	19.8290i	−0.397140	−	1.85715i
$115$	−6.61569	−	10.6221i	−0.616916	−	0.990511i
$116$		−	47.1015i		−	4.37326i
$117$	9.10835	−	5.83421i	0.842067	−	0.539373i
$118$	4.75844	+	4.75844i	0.438050	+	0.438050i
$119$	0.672620	+	0.672620i	0.0616590	+	0.0616590i
$120$	35.9246	+	10.3105i	3.27945	+	0.941218i
$121$			6.13569i			0.557790i
$122$	−8.35430	−	4.82336i	−0.756363	−	0.436686i
$123$	2.96951	+	13.8864i	0.267751	+	1.25209i
$124$	4.04025	+	15.0784i	0.362825	+	1.35408i
$125$	−7.07429	+	8.65763i	−0.632743	+	0.774362i
$126$	−15.0110	+	6.72767i	−1.33729	+	0.599348i
$127$	16.9733	−	4.54798i	1.50614	−	0.403568i	0.590985	−	0.806682i	$-0.298739\pi$
$127$	16.9733	−	4.54798i	1.50614	−	0.403568i	0.915150	+	0.403115i	$0.132072\pi$
$128$			42.3156i			3.74021i
$129$	3.27011	−	2.95172i	0.287917	−	0.259884i
$130$	−19.9681	+	9.48822i	−1.75132	+	0.832172i
$131$	1.35851	−	2.35300i	0.118693	−	0.205583i	−0.800557	−	0.599257i	$-0.795463\pi$
$131$	1.35851	−	2.35300i	0.118693	−	0.205583i	0.919250	+	0.393674i	$0.128796\pi$
$132$	−12.1821	+	37.6504i	−1.06032	+	3.27705i
$133$	−6.03666	−	6.03666i	−0.523445	−	0.523445i
$134$	−4.07572	−	7.05936i	−0.352089	−	0.609836i
$135$	7.17367	+	9.13994i	0.617411	+	0.786641i
$136$	4.43418	+	1.18813i	0.380228	+	0.101882i
$137$	−8.21755	+	14.2332i	−0.702072	+	1.21603i	0.265665	+	0.964065i	$0.414408\pi$
$137$	−8.21755	+	14.2332i	−0.702072	+	1.21603i	−0.967738	+	0.251960i	$0.918925\pi$
$138$	25.9921	−	5.55825i	2.21260	−	0.473150i
$139$		−	9.09815i		−	0.771695i	−0.922563	−	0.385847i	$-0.873909\pi$
$139$		−	9.09815i		−	0.771695i	0.922563	−	0.385847i	$-0.126091\pi$
$140$	23.6104	−	7.18048i	1.99545	−	0.606861i
$141$	−10.5662	+	16.3145i	−0.889837	+	1.37393i
$142$	2.41025	−	8.99518i	0.202264	−	0.754859i
$143$	−5.95142	−	13.6874i	−0.497683	−	1.14460i
$144$	−27.1047	+	37.5003i	−2.25873	+	3.12502i
$145$	−13.0349	+	13.9371i	−1.08249	+	1.15741i
$146$	3.65151			0.302201
$147$	2.82605	−	4.36349i	0.233089	−	0.359895i
$148$	14.7039	−	25.4680i	1.20866	−	2.09345i
$149$	3.09930	+	3.09930i	0.253905	+	0.253905i	0.822569	−	0.568665i	$-0.192540\pi$
$149$	3.09930	+	3.09930i	0.253905	+	0.253905i	−0.568665	+	0.822569i	$0.692540\pi$
$150$	−12.1960	−	20.3764i	−0.995800	−	1.66373i
$151$	−5.82405	+	21.7356i	−0.473954	+	1.76882i	0.151392	+	0.988474i	$0.451624\pi$
$151$	−5.82405	+	21.7356i	−0.473954	+	1.76882i	−0.625346	+	0.780347i	$0.715042\pi$
$152$	−39.7961	−	10.6633i	−3.22789	−	0.864910i
$153$	0.900835	+	1.10686i	0.0728282	+	0.0894840i
$154$	5.87467	+	21.9246i	0.473394	+	1.76673i
$155$	2.97733	−	5.57973i	0.239145	−	0.448175i
$156$	−3.34575	−	34.3048i	−0.267874	−	2.74658i
$157$	1.82877	+	6.82507i	0.145952	+	0.544700i	0.999711	+	0.0240321i	$0.00765038\pi$
$157$	1.82877	+	6.82507i	0.145952	+	0.544700i	−0.853759	+	0.520668i	$0.825683\pi$
$158$	−7.44599	−	12.8968i	−0.592371	−	1.02602i
$159$	3.93380	−	12.1579i	0.311971	−	0.964185i
$160$	35.1189	−	37.5495i	2.77639	−	2.96855i
$161$	7.91296	−	7.91296i	0.623629	−	0.623629i
$162$	−23.4334	+	7.74174i	−1.84110	+	0.608248i
$163$	15.9125	−	9.18707i	1.24636	−	0.719587i	0.275980	−	0.961164i	$-0.410998\pi$
$163$	15.9125	−	9.18707i	1.24636	−	0.719587i	0.970382	+	0.241576i	$0.0776645\pi$
$164$	43.7078	+	11.7115i	3.41301	+	0.914513i
$165$	14.0241	−	7.76926i	1.09177	−	0.604836i
$166$	−15.3733	+	8.87580i	−1.19320	+	0.688896i
$167$	5.42718	+	9.40015i	0.419968	+	0.727405i	0.995936	−	0.0900669i	$-0.0287081\pi$
$167$	5.42718	+	9.40015i	0.419968	+	0.727405i	−0.575968	+	0.817472i	$0.695375\pi$
$168$	−1.70813	+	33.3792i	−0.131785	+	2.57526i
$169$	9.50757	+	8.86601i	0.731352	+	0.682001i
$170$	−1.54203	−	2.47586i	−0.118268	−	0.189890i
$171$	−8.08486	−	9.93386i	−0.618264	−	0.759661i
$172$	−3.63317	−	13.5592i	−0.277026	−	1.03388i
$173$	2.52977	+	9.44125i	0.192335	+	0.717805i	0.992941	+	0.118613i	$0.0378447\pi$
$173$	2.52977	+	9.44125i	0.192335	+	0.717805i	−0.800605	+	0.599192i	$0.795489\pi$
$174$	−18.4458	−	36.0920i	−1.39837	−	2.73613i
$175$	−8.97335	−	4.40932i	−0.678321	−	0.333313i
$176$	45.1457	+	45.1457i	3.40299	+	3.40299i
$177$	4.04420	+	1.30854i	0.303981	+	0.0983558i
$178$	3.91440	−	1.04886i	0.293397	−	0.0786154i
$179$	2.55427	−	4.42412i	0.190915	−	0.330674i	−0.754639	−	0.656140i	$-0.772188\pi$
$179$	2.55427	−	4.42412i	0.190915	−	0.330674i	0.945554	+	0.325466i	$0.105521\pi$
$180$	36.3369	−	7.10055i	2.70839	−	0.529244i
$181$			13.5530i			1.00739i	0.863883	+	0.503693i	$0.168026\pi$
$181$			13.5530i			1.00739i	−0.863883	+	0.503693i	$0.831974\pi$
$182$	−12.3071	−	15.4722i	−0.912265	−	1.14688i
$183$	−6.08535	−	0.311409i	−0.449842	−	0.0230200i
$184$	13.9777	−	52.1654i	1.03045	−	3.84568i
$185$	−11.3989	+	3.46665i	−0.838060	+	0.254873i
$186$	9.00088	+	9.97178i	0.659976	+	0.731166i
$187$	1.70536	−	0.984592i	0.124708	−	0.0720005i
$188$	30.9687	+	53.6394i	2.25863	+	3.91206i
$189$	−6.50901	+	8.09894i	−0.473461	+	0.589111i
$190$	13.8395	+	22.2204i	1.00402	+	1.61204i
$191$	−2.95703	+	5.12172i	−0.213963	+	0.370595i	−0.952951	−	0.303124i	$-0.901970\pi$
$191$	−2.95703	+	5.12172i	−0.213963	+	0.370595i	0.738988	+	0.673718i	$0.235304\pi$
$192$	25.3824	+	49.6646i	1.83182	+	3.58423i
$193$	−7.90816	+	4.56578i	−0.569242	+	0.328652i	−0.756846	−	0.653593i	$-0.773261\pi$
$193$	−7.90816	+	4.56578i	−0.569242	+	0.328652i	0.187605	+	0.982245i	$0.439928\pi$
$194$	9.06902	−	15.7080i	0.651118	−	1.12777i
$195$	−8.50356	+	11.0765i	−0.608953	+	0.793206i
$196$	−8.28293	−	14.3464i	−0.591638	−	1.02475i
$197$	−11.8447	−	6.83856i	−0.843902	−	0.487227i	0.0146864	−	0.999892i	$-0.495325\pi$
$197$	−11.8447	−	6.83856i	−0.843902	−	0.487227i	−0.858589	+	0.512665i	$0.828658\pi$
$198$	5.40990	+	33.6208i	0.384465	+	2.38933i
$199$	−9.39722	−	16.2765i	−0.666151	−	1.15381i	−0.978972	−	0.203995i	$-0.934607\pi$
$199$	−9.39722	−	16.2765i	−0.666151	−	1.15381i	0.312821	−	0.949812i	$-0.398726\pi$
$200$	−48.1429	+	3.22420i	−3.40422	+	0.227985i
$201$	−4.32162	−	2.79894i	−0.304824	−	0.197422i
$202$	18.4459			1.29785
$203$	−14.7787	−	8.53249i	−1.03726	−	0.598863i
$204$	4.44697	−	0.950957i	0.311351	−	0.0665803i
$205$	−9.69188	−	15.5611i	−0.676910	−	1.08684i
$206$	−6.07534	+	1.62788i	−0.423289	+	0.113420i
$207$	13.0215	−	10.5978i	0.905055	−	0.736596i
$208$	−51.7405	−	20.3812i	−3.58755	−	1.41318i
$209$	−15.3054	+	8.83656i	−1.05869	+	0.611237i
$210$	15.2798	−	14.7484i	1.05440	−	1.01774i
$211$	−2.46671	−	4.27246i	−0.169815	−	0.294128i	0.768540	−	0.639802i	$-0.220984\pi$
$211$	−2.46671	−	4.27246i	−0.169815	−	0.294128i	−0.938355	+	0.345674i	$0.887650\pi$
$212$	−28.7927	−	28.7927i	−1.97749	−	1.97749i
$213$	−1.23006	−	5.75215i	−0.0842824	−	0.394131i
$214$	10.1172	−	2.71089i	0.691596	−	0.185313i
$215$	−2.67734	+	5.01753i	−0.182593	+	0.342193i
$216$	−7.66124	+	49.5549i	−0.521282	+	3.37179i
$217$	5.46295	+	1.46379i	0.370849	+	0.0993687i
$218$	−5.78697	+	5.78697i	−0.391943	+	0.391943i
$219$	2.05378	−	1.04964i	0.138782	−	0.0709281i
$220$	−1.70783	−	51.0589i	−0.115142	−	3.44239i
$221$	−1.02022	+	1.37875i	−0.0686277	+	0.0927447i
$222$	1.29333	−	25.2734i	0.0868026	−	1.69624i
$223$	12.9588			0.867789			0.433894	−	0.900964i	$-0.357139\pi$
$223$	12.9588			0.867789			0.433894	+	0.900964i	$0.357139\pi$
$224$	39.8170	+	22.9884i	2.66038	+	1.53597i
$225$	−12.7169	−	7.95489i	−0.847794	−	0.530326i
$226$	−7.23119	+	7.23119i	−0.481011	+	0.481011i
$227$	−12.4055	−	7.16232i	−0.823382	−	0.475380i	0.0281991	−	0.999602i	$-0.491023\pi$
$227$	−12.4055	−	7.16232i	−0.823382	−	0.475380i	−0.851581	+	0.524222i	$0.824356\pi$
$228$	−39.9109	+	8.53469i	−2.64316	+	0.565224i
$229$	−0.730761	−	2.72724i	−0.0482900	−	0.180221i	0.937568	−	0.347801i	$-0.113071\pi$
$229$	−0.730761	−	2.72724i	−0.0482900	−	0.180221i	−0.985858	+	0.167580i	$0.946405\pi$
$230$	−29.1270	+	18.1410i	−1.92057	+	1.19618i
$231$	9.60650	+	10.6427i	0.632061	+	0.700240i
$232$	−82.3550			−5.40687
$233$	−8.80062	+	8.80062i	−0.576548	+	0.576548i	−0.933950	−	0.357403i	$-0.883662\pi$
$233$	−8.80062	+	8.80062i	−0.576548	+	0.576548i	0.357403	+	0.933950i	$0.383662\pi$
$234$	−15.9981	−	24.9762i	−1.04583	−	1.63274i
$235$	5.68075	−	24.4420i	0.370571	−	1.59442i
$236$	9.57759	−	9.57759i	0.623448	−	0.623448i
$237$	−7.89523	−	5.11341i	−0.512850	−	0.332152i
$238$	1.84441	−	1.84441i	0.119555	−	0.119555i
$239$	−23.8049	+	6.37852i	−1.53981	+	0.412592i	−0.926206	−	0.377019i	$-0.876949\pi$
$239$	−23.8049	+	6.37852i	−1.53981	+	0.412592i	−0.613608	+	0.789611i	$0.710283\pi$
$240$	16.4789	−	57.4167i	1.06371	−	3.70623i
$241$	−22.4936	+	6.02714i	−1.44894	+	0.388242i	−0.895655	−	0.444750i	$-0.853292\pi$
$241$	−22.4936	+	6.02714i	−1.44894	+	0.388242i	−0.553285	+	0.832992i	$0.686626\pi$
$242$	16.8248			1.08154
$243$	−10.9547	+	11.0903i	−0.702741	+	0.711446i
$244$	−9.70826	+	16.8152i	−0.621508	+	1.07648i
$245$	−1.51938	+	6.53727i	−0.0970695	+	0.417651i
$246$	38.0781	−	8.14275i	2.42777	−	0.519163i
$247$	9.15635	−	12.3741i	0.582605	−	0.787342i
$248$	26.3640	−	7.06422i	1.67412	−	0.448578i
$249$	−6.09531	+	9.41130i	−0.386275	+	0.596417i
$250$	23.7403	+	19.3985i	1.50147	+	1.22687i
$251$	15.4206	−	8.90307i	0.973338	−	0.561957i	0.0730855	−	0.997326i	$-0.476715\pi$
$251$	15.4206	−	8.90307i	0.973338	−	0.561957i	0.900252	+	0.435369i	$0.143382\pi$
$252$	13.5412	+	30.2136i	0.853014	+	1.90328i
$253$	−11.5831	−	20.0625i	−0.728224	−	1.26132i
$254$	−12.4711	−	46.5428i	−0.782507	−	2.92035i
$255$	−1.57901	−	0.949278i	−0.0988812	−	0.0594461i
$256$	51.6313			3.22695
$257$	−1.87160	+	6.98492i	−0.116747	+	0.435707i	−0.999412	−	0.0342968i	$-0.989081\pi$
$257$	−1.87160	+	6.98492i	−0.116747	+	0.435707i	0.882664	+	0.470004i	$0.155748\pi$
$258$	−8.09397	−	8.96704i	−0.503909	−	0.558264i
$259$	−5.32727	−	9.22710i	−0.331020	−	0.573344i
$260$	19.0975	+	40.1909i	1.18438	+	2.49253i
$261$	−20.7496	−	14.9976i	−1.28437	−	0.928325i
$262$	−6.45221	−	3.72519i	−0.398619	−	0.230143i
$263$	−20.9500	−	20.9500i	−1.29183	−	1.29183i	−0.933652	−	0.358181i	$-0.883397\pi$
$263$	−20.9500	−	20.9500i	−1.29183	−	1.29183i	−0.358181	−	0.933652i	$-0.616603\pi$
$264$	65.8302	+	21.3000i	4.05157	+	1.31092i
$265$	0.551485	+	16.4877i	0.0338775	+	1.01283i
$266$	−16.5533	+	16.5533i	−1.01495	+	1.01495i
$267$	1.90015	−	1.71514i	0.116287	−	0.104965i
$268$	−14.2088	+	8.20345i	−0.867940	+	0.501105i
$269$	−21.2565	+	12.2725i	−1.29603	+	0.748265i	−0.979717	−	0.200388i	$-0.935780\pi$
$269$	−21.2565	+	12.2725i	−1.29603	+	0.748265i	−0.316317	+	0.948654i	$0.602446\pi$
$270$	25.0628	−	19.6711i	1.52527	−	1.19714i
$271$	21.9750	−	5.88819i	1.33489	−	0.357682i	0.480352	−	0.877076i	$-0.340509\pi$
$271$	21.9750	−	5.88819i	1.33489	−	0.357682i	0.854535	+	0.519394i	$0.173842\pi$
$272$	1.89894	−	7.08696i	0.115140	−	0.429710i
$273$	−11.3697	−	5.16458i	−0.688124	−	0.312575i
$274$	39.0292	+	22.5335i	2.35784	+	1.36130i
$275$	−13.6248	+	15.5807i	−0.821604	+	0.939551i
$276$	−11.1874	−	52.3159i	−0.673404	−	3.14905i
$277$	1.10210	−	0.295306i	0.0662186	−	0.0177432i	−0.225558	−	0.974230i	$-0.572420\pi$
$277$	1.10210	−	0.295306i	0.0662186	−	0.0177432i	0.291776	+	0.956487i	$0.405754\pi$
$278$	−24.9482			−1.49630
$279$	7.92895	+	3.02126i	0.474694	+	0.180878i
$280$	−12.5548	−	41.2819i	−0.750292	−	2.46707i
$281$	7.20104	−	26.8746i	0.429578	−	1.60321i	−0.324140	−	0.946009i	$-0.605075\pi$
$281$	7.20104	−	26.8746i	0.429578	−	1.60321i	0.753718	−	0.657198i	$-0.228258\pi$
$282$	44.7363	+	28.9739i	2.66401	+	1.72537i
$283$	26.6940	+	7.15265i	1.58680	+	0.425181i	0.941021	−	0.338347i	$-0.109868\pi$
$283$	26.6940	+	7.15265i	1.58680	+	0.425181i	0.645775	+	0.763528i	$0.276535\pi$
$284$	−18.1051	−	4.85125i	−1.07434	−	0.287869i
$285$	14.1713	+	8.51962i	0.839438	+	0.504659i
$286$	−37.5325	+	16.3195i	−2.21934	+	0.964993i
$287$	11.5924	−	11.5924i	0.684275	−	0.684275i
$288$	55.9039	+	40.4066i	3.29417	+	2.38098i
$289$	14.5265	+	8.38685i	0.854497	+	0.493344i
$290$	38.2172	+	35.7433i	2.24419	+	2.09892i
$291$	0.585520	−	11.4419i	0.0343238	−	0.670734i
$292$		−	7.34960i		−	0.430103i
$293$			1.44772i			0.0845770i	0.999105	+	0.0422885i	$0.0134649\pi$
$293$			1.44772i			0.0845770i	−0.999105	+	0.0422885i	$0.986535\pi$
$294$	−11.9652	−	7.74938i	−0.697826	−	0.451953i
$295$	−5.48447	+	0.183446i	−0.319318	+	0.0106806i
$296$	−44.5297	−	25.7092i	−2.58824	−	1.49432i
$297$	12.7072	+	17.3548i	0.737347	+	1.00703i
$298$	8.49867	−	8.49867i	0.492314	−	0.492314i
$299$	16.2201	+	12.0023i	0.938034	+	0.694111i
$300$	−41.0129	+	24.5476i	−2.36788	+	1.41726i
$301$	−4.91252	−	1.31630i	−0.283153	−	0.0758705i
$302$	59.6018	+	15.9702i	3.42970	+	0.918984i
$303$	10.3749	−	5.30235i	0.596020	−	0.304612i
$304$	−17.0427	+	63.6044i	−0.977468	+	3.64796i
$305$	7.52608	−	2.28886i	0.430942	−	0.131060i
$306$	3.03513	−	2.47020i	0.173507	−	0.141212i
$307$	−5.54271			−0.316339			−0.158170	−	0.987412i	$-0.550559\pi$
$307$	−5.54271			−0.316339			−0.158170	+	0.987412i	$0.550559\pi$
$308$	44.1289	−	11.8243i	2.51448	−	0.673752i
$309$	−2.94912	+	2.66198i	−0.167770	+	0.151435i
$310$	−15.3003	−	8.16420i	−0.868999	−	0.463696i
$311$	8.14715	+	4.70376i	0.461983	+	0.266726i	0.712878	−	0.701289i	$-0.247392\pi$
$311$	8.14715	+	4.70376i	0.461983	+	0.266726i	−0.250895	+	0.968014i	$0.580725\pi$
$312$	−59.9806	+	5.84991i	−3.39573	+	0.331186i
$313$	3.65688	−	13.6477i	0.206699	−	0.771412i	−0.782226	−	0.622995i	$-0.785916\pi$
$313$	3.65688	−	13.6477i	0.206699	−	0.771412i	0.988925	−	0.148417i	$-0.0474177\pi$
$314$	18.7152	−	5.01472i	1.05616	−	0.282997i
$315$	4.35457	−	12.6874i	0.245352	−	0.714856i
$316$	−25.9582	+	14.9870i	−1.46026	+	0.843084i
$317$	23.7072	−	13.6874i	1.33153	−	0.768759i	0.345996	−	0.938236i	$-0.387541\pi$
$317$	23.7072	−	13.6874i	1.33153	−	0.768759i	0.985534	+	0.169477i	$0.0542079\pi$
$318$	−33.3384	−	10.7870i	−1.86953	−	0.604903i
$319$	−24.9800	+	24.9800i	−1.39861	+	1.39861i
$320$	−52.5889	−	49.1848i	−2.93981	−	2.74951i
$321$	4.91113	−	4.43296i	0.274112	−	0.247424i
$322$	−21.6983	−	21.6983i	−1.20920	−	1.20920i
$323$	1.75885	+	1.01547i	0.0978649	+	0.0565023i
$324$	15.5823	+	47.1657i	0.865681	+	2.62032i
$325$	5.47163	−	17.1773i	0.303511	−	0.952828i
$326$	−25.1921	−	43.6339i	−1.39526	−	2.41666i
$327$	−1.59138	+	4.91836i	−0.0880035	+	0.271986i
$328$	20.4771	−	76.4214i	1.13066	−	4.21967i
$329$	22.4401			1.23716
$330$	−21.3043	−	38.4556i	−1.17276	−	2.11691i
$331$	5.10580	+	19.0551i	0.280640	+	1.04736i	0.951967	+	0.306202i	$0.0990582\pi$
$331$	5.10580	+	19.0551i	0.280640	+	1.04736i	−0.671326	+	0.741162i	$0.734275\pi$
$332$	17.8648	+	30.9428i	0.980461	+	1.69821i
$333$	−6.53752	−	14.5868i	−0.358254	−	0.799349i
$334$	25.7763	−	14.8820i	1.41042	−	0.814306i
$335$	6.47454	+	1.50480i	0.353742	+	0.0822160i
$336$	53.3486	+	2.73003i	2.91041	+	0.148936i
$337$	12.5939	−	3.37452i	0.686032	−	0.183822i	0.101066	−	0.994880i	$-0.467775\pi$
$337$	12.5939	−	3.37452i	0.686032	−	0.183822i	0.584966	+	0.811058i	$0.301108\pi$
$338$	24.3117	−	26.0709i	1.32238	−	1.41807i
$339$	−1.98853	+	6.14580i	−0.108002	+	0.333794i
$340$	−4.98331	+	3.10373i	−0.270258	+	0.168324i
$341$	5.85403	−	10.1395i	0.317013	−	0.549083i
$342$	−27.2398	+	22.1697i	−1.47296	+	1.19880i
$343$	−19.9993			−1.07986
$344$	−23.7076	+	6.35244i	−1.27823	+	0.342501i
$345$	−11.1677	+	18.5760i	−0.601247	+	1.00010i
$346$	25.8890	−	6.93695i	1.39180	−	0.372933i
$347$	−15.5673	+	15.5673i	−0.835695	+	0.835695i	−0.988289	−	0.152594i	$-0.951237\pi$
$347$	−15.5673	+	15.5673i	−0.835695	+	0.835695i	0.152594	+	0.988289i	$0.451237\pi$
$348$	−72.6446	+	37.1270i	−3.89416	+	1.99021i
$349$	12.5388	−	12.5388i	0.671187	−	0.671187i	−0.286803	−	0.957990i	$-0.592593\pi$
$349$	12.5388	−	12.5388i	0.671187	−	0.671187i	0.957990	+	0.286803i	$0.0925925\pi$
$350$	−12.0909	+	24.6060i	−0.646285	+	1.31525i
$351$	−16.1776	−	9.44907i	−0.863497	−	0.504354i
$352$	67.3014	−	67.3014i	3.58718	−	3.58718i
$353$	23.2905			1.23963			0.619814	−	0.784749i	$-0.287208\pi$
$353$	23.2905			1.23963			0.619814	+	0.784749i	$0.287208\pi$
$354$	3.58817	−	11.0897i	0.190709	−	0.589411i
$355$	4.01467	+	6.44590i	0.213077	+	0.342113i
$356$	−2.11110	−	7.87875i	−0.111888	−	0.417573i
$357$	0.507200	−	1.56756i	0.0268439	−	0.0829643i
$358$	−12.1315	−	7.00411i	−0.641169	−	0.370179i
$359$	16.0905	−	16.0905i	0.849224	−	0.849224i	−0.140812	−	0.990036i	$-0.544971\pi$
$359$	16.0905	−	16.0905i	0.849224	−	0.849224i	0.990036	+	0.140812i	$0.0449713\pi$
$360$	−12.4150	−	63.5335i	−0.654330	−	3.34851i
$361$	0.669104	+	0.386307i	0.0352160	+	0.0203320i
$362$	37.1639			1.95329
$363$	9.46308	−	4.83636i	0.496683	−	0.253843i
$364$	−31.1419	+	24.7713i	−1.63228	+	1.29837i
$365$	−2.03394	+	2.17471i	−0.106461	+	0.113830i
$366$	−0.853920	+	16.6868i	−0.0446351	+	0.872231i
$367$	−4.61049	+	4.61049i	−0.240665	+	0.240665i	−0.817125	−	0.576460i	$-0.804434\pi$
$367$	−4.61049	+	4.61049i	−0.240665	+	0.240665i	0.576460	+	0.817125i	$0.304434\pi$
$368$	−83.3737	−	22.3399i	−4.34615	−	1.16455i
$369$	19.0762	−	15.5256i	0.993070	−	0.808228i
$370$	9.50599	+	31.2570i	0.494193	+	1.62498i
$371$	−14.2499	+	3.81825i	−0.739818	+	0.198234i
$372$	20.0708	−	18.1166i	1.04062	−	0.939302i
$373$	−1.92953	−	1.92953i	−0.0999074	−	0.0999074i	0.655386	−	0.755294i	$-0.272506\pi$
$373$	−1.92953	−	1.92953i	−0.0999074	−	0.0999074i	−0.755294	+	0.655386i	$0.772506\pi$
$374$	−2.69987	−	4.67631i	−0.139607	−	0.241806i
$375$	18.9288	+	4.08643i	0.977481	+	0.211023i
$376$	93.7864	−	54.1476i	4.83666	−	2.79245i
$377$	11.2773	−	28.6289i	0.580810	−	1.47447i
$378$	22.2083	+	17.8485i	1.14227	+	0.918028i
$379$	−9.89075	+	2.65022i	−0.508054	+	0.136133i	−0.503735	−	0.863858i	$-0.668041\pi$
$379$	−9.89075	+	2.65022i	−0.508054	+	0.136133i	−0.00431858	+	0.999991i	$0.501375\pi$
$380$	44.7244	−	27.8555i	2.29431	−	1.42896i
$381$	−20.3933	−	22.5930i	−1.04478	−	1.15747i
$382$	14.0444	+	8.10852i	0.718573	+	0.414868i
$383$	−21.9308			−1.12061			−0.560305	−	0.828286i	$-0.689316\pi$
$383$	−21.9308			−1.12061			−0.560305	+	0.828286i	$0.689316\pi$
$384$	65.2634	−	33.3546i	3.33046	−	1.70212i
$385$	−16.3298	−	8.71353i	−0.832242	−	0.444082i
$386$	12.5199	+	21.6851i	0.637247	+	1.10374i
$387$	−7.13005	−	2.71685i	−0.362441	−	0.138105i
$388$	−31.6164	−	18.2538i	−1.60508	−	0.926694i
$389$	−2.69357	−	4.66539i	−0.136569	−	0.236545i	0.789627	−	0.613588i	$-0.210274\pi$
$389$	−2.69357	−	4.66539i	−0.136569	−	0.236545i	−0.926196	+	0.377043i	$0.876941\pi$
$390$	30.3732	+	23.3178i	1.53801	+	1.18074i
$391$	−1.33110	+	2.30553i	−0.0673165	+	0.116596i
$392$	−25.0842	+	14.4824i	−1.26694	+	0.731470i
$393$	−4.69985	−	0.240508i	−0.237076	−	0.0121320i
$394$	−18.7522	+	32.4797i	−0.944720	+	1.63630i
$395$	11.8284	+	2.74914i	0.595152	+	0.138324i
$396$	67.6706	−	10.8888i	3.40057	−	0.547184i
$397$	1.65564	+	2.86765i	0.0830942	+	0.143923i	0.904578	−	0.426309i	$-0.140186\pi$
$397$	1.65564	+	2.86765i	0.0830942	+	0.143923i	−0.821483	+	0.570233i	$0.806853\pi$
$398$	−44.6320	+	25.7683i	−2.23720	+	1.29165i
$399$	−4.55204	+	14.0686i	−0.227887	+	0.704313i
$400$	5.15310	+	76.9448i	0.257655	+	3.84724i
$401$	−5.55561	+	20.7338i	−0.277434	+	1.03540i	0.676759	+	0.736204i	$0.263384\pi$
$401$	−5.55561	+	20.7338i	−0.277434	+	1.03540i	−0.954193	+	0.299192i	$0.903283\pi$
$402$	−7.67502	+	11.8504i	−0.382795	+	0.591045i
$403$	−1.15444	+	10.1322i	−0.0575066	+	0.504722i
$404$		−	37.1272i		−	1.84715i
$405$	8.44199	−	18.2684i	0.419486	−	0.907762i
$406$	−23.3971	+	40.5250i	−1.16118	+	2.01122i
$407$	−21.3049	+	5.70863i	−1.05604	+	0.282966i
$408$	−1.66271	−	7.77536i	−0.0823164	−	0.384938i
$409$	17.0501	+	17.0501i	0.843074	+	0.843074i	0.989257	−	0.146184i	$-0.0466991\pi$
$409$	17.0501	+	17.0501i	0.843074	+	0.843074i	−0.146184	+	0.989257i	$0.546699\pi$
$410$	−42.6705	+	26.5763i	−2.10735	+	1.31251i
$411$	28.4292	+	1.45482i	1.40231	+	0.0717611i
$412$	3.27654	+	12.2282i	0.161423	+	0.602440i
$413$	−1.27010	−	4.74008i	−0.0624976	−	0.233244i
$414$	−29.0604	−	35.7065i	−1.42824	−	1.75488i
$415$	3.27704	−	14.0998i	0.160863	−	0.692130i
$416$	−30.3834	+	77.1325i	−1.48967	+	3.78173i
$417$	−14.0321	+	7.17147i	−0.687153	+	0.351188i
$418$	24.2309	+	41.9692i	1.18517	+	2.05278i
$419$	−4.17877	+	2.41262i	−0.204146	+	0.117864i	−0.598588	−	0.801057i	$-0.704271\pi$
$419$	−4.17877	+	2.41262i	−0.204146	+	0.117864i	0.394442	+	0.918921i	$0.370938\pi$
$420$	−29.6850	−	30.7545i	−1.44848	−	1.50066i
$421$	−1.32785	−	0.355796i	−0.0647153	−	0.0173404i	0.226316	−	0.974054i	$-0.427332\pi$
$421$	−1.32785	−	0.355796i	−0.0647153	−	0.0173404i	−0.291031	+	0.956713i	$0.593998\pi$
$422$	−11.7156	+	6.76401i	−0.570307	+	0.329267i
$423$	33.4905	+	3.43665i	1.62836	+	0.167096i
$424$	−50.3428	+	50.3428i	−2.44486	+	2.44486i
$425$	2.33347	+	0.460708i	0.113190	+	0.0223476i
$426$	−15.7731	+	3.37298i	−0.764209	+	0.163421i
$427$	3.51733	+	6.09219i	0.170215	+	0.294822i
$428$	−5.45637	−	20.3634i	−0.263743	−	0.984304i
$429$	−16.4189	+	19.9677i	−0.792714	+	0.964051i
$430$	13.7587	+	7.34160i	0.663503	+	0.354043i
$431$	5.16202	+	19.2649i	0.248646	+	0.927958i	0.971516	+	0.236974i	$0.0761558\pi$
$431$	5.16202	+	19.2649i	0.248646	+	0.927958i	−0.722870	+	0.690984i	$0.757178\pi$
$432$	79.2016	+	12.2446i	3.81059	+	0.589120i
$433$	6.33678	+	1.69793i	0.304526	+	0.0815975i	0.407846	−	0.913051i	$-0.366280\pi$
$433$	6.33678	+	1.69793i	0.304526	+	0.0815975i	−0.103320	+	0.994648i	$0.532947\pi$
$434$	4.01390	−	14.9801i	0.192673	−	0.719066i
$435$	31.7697	+	9.11807i	1.52324	+	0.437178i
$436$	11.6478	+	11.6478i	0.557828	+	0.557828i
$437$	11.9464	−	20.6917i	0.571473	−	0.989821i
$438$	−2.87824	−	5.63172i	−0.137528	−	0.269094i
$439$	25.6614			1.22475			0.612377	−	0.790566i	$-0.290214\pi$
$439$	25.6614			1.22475			0.612377	+	0.790566i	$0.290214\pi$
$440$	−89.2745	+	2.98607i	−4.25599	+	0.142355i
$441$	−8.95740	−	0.919170i	−0.426543	−	0.0437700i
$442$	3.78070	+	2.79758i	0.179829	+	0.133067i
$443$	1.59651	−	5.95826i	0.0758526	−	0.283086i	−0.917573	−	0.397568i	$-0.869854\pi$
$443$	1.59651	−	5.95826i	0.0758526	−	0.283086i	0.993425	+	0.114482i	$0.0365209\pi$
$444$	−50.8693	−	2.60316i	−2.41415	−	0.123541i
$445$	−1.55571	+	2.91551i	−0.0737477	+	0.138208i
$446$		−	35.5347i		−	1.68262i
$447$	2.33708	−	7.22303i	0.110540	−	0.341638i
$448$	32.1957	−	55.7646i	1.52110	−	2.63463i
$449$	19.0634	+	5.10802i	0.899657	+	0.241062i	0.678869	−	0.734259i	$-0.262470\pi$
$449$	19.0634	+	5.10802i	0.899657	+	0.241062i	0.220788	+	0.975322i	$0.429137\pi$
$450$	−21.8133	+	34.8713i	−1.02829	+	1.64385i
$451$	−16.9691	−	29.3913i	−0.799042	−	1.38398i
$452$	14.5546	+	14.5546i	0.684593	+	0.684593i
$453$	38.1136	−	8.15034i	1.79073	−	0.382936i
$454$	−19.6400	+	34.0174i	−0.921749	+	1.59652i
$455$	16.0700	+	1.28854i	0.753371	+	0.0604078i
$456$	14.9226	+	69.7826i	0.698813	+	3.26787i
$457$			14.1634i			0.662538i	0.943536	+	0.331269i	$0.107477\pi$
$457$			14.1634i			0.662538i	−0.943536	+	0.331269i	$0.892523\pi$
$458$	−7.47841	+	2.00384i	−0.349443	+	0.0936331i
$459$	0.997034	−	2.26182i	0.0465376	−	0.105573i
$460$	36.5135	+	58.6255i	1.70245	+	2.73343i
$461$	−8.92087	−	33.2932i	−0.415487	−	1.55062i	−0.783859	−	0.620939i	$-0.786752\pi$
$461$	−8.92087	−	33.2932i	−0.415487	−	1.55062i	0.368373	−	0.929678i	$-0.379915\pi$
$462$	29.1836	−	26.3422i	1.35775	−	1.22555i
$463$	−24.8807	−	14.3649i	−1.15630	−	0.667592i	−0.205888	−	0.978576i	$-0.566008\pi$
$463$	−24.8807	−	14.3649i	−1.15630	−	0.667592i	−0.950415	+	0.310983i	$0.899342\pi$
$464$			131.625i			6.11052i
$465$	−10.9525	−	0.193803i	−0.507908	−	0.00898740i
$466$	24.1324	+	24.1324i	1.11791	+	1.11791i
$467$	21.2208	+	21.2208i	0.981979	+	0.981979i	0.999840	−	0.0178611i	$-0.00568566\pi$
$467$	21.2208	+	21.2208i	0.981979	+	0.981979i	−0.0178611	+	0.999840i	$0.505686\pi$
$468$	−50.2710	+	32.2004i	−2.32378	+	1.48846i
$469$			5.94426i			0.274480i
$470$	−67.0228	−	15.5773i	−3.09153	−	0.718527i
$471$	9.08480	−	8.20027i	0.418606	−	0.377848i
$472$	−16.7460	−	16.7460i	−0.770798	−	0.770798i
$473$	−5.26419	+	9.11784i	−0.242048	+	0.419239i
$474$	−14.0216	+	21.6497i	−0.644033	+	0.994402i
$475$	−20.9425	−	4.13478i	−0.960908	−	0.189717i
$476$	−3.71234	−	3.71234i	−0.170155	−	0.170155i
$477$	−21.8519	+	3.51617i	−1.00053	+	0.160994i
$478$	17.4907	+	65.2760i	0.800004	+	2.98566i
$479$	−3.78891	+	3.78891i	−0.173120	+	0.173120i	−0.788349	−	0.615229i	$-0.789064\pi$
$479$	−3.78891	+	3.78891i	−0.173120	+	0.173120i	0.615229	+	0.788349i	$0.289064\pi$
$480$	−85.5944	−	24.5660i	−3.90683	−	1.12128i
$481$	15.0349	−	11.9593i	0.685534	−	0.545297i
$482$	16.5271	+	61.6801i	0.752791	+	2.80945i
$483$	−18.4414	−	5.96689i	−0.839114	−	0.271503i
$484$		−	33.8643i		−	1.53929i
$485$	4.30358	+	14.1508i	0.195415	+	0.642553i
$486$	30.4111	+	30.0390i	1.37947	+	1.36260i
$487$	−10.5615	+	6.09767i	−0.478586	+	0.276312i	−0.719827	−	0.694153i	$-0.755779\pi$
$487$	−10.5615	+	6.09767i	−0.478586	+	0.276312i	0.241241	+	0.970465i	$0.422446\pi$
$488$	29.4007	+	16.9745i	1.33091	+	0.768400i
$489$	−26.7120	−	17.3002i	−1.20796	−	0.782344i
$490$	17.9260	+	4.16632i	0.809813	+	0.188215i
$491$	20.5600	−	11.8703i	0.927861	−	0.535701i	0.0417268	−	0.999129i	$-0.486714\pi$
$491$	20.5600	−	11.8703i	0.927861	−	0.535701i	0.886135	+	0.463428i	$0.153381\pi$
$492$	−16.3894	−	76.6419i	−0.738890	−	3.45529i
$493$	3.92134	+	1.05072i	0.176608	+	0.0473221i
$494$	−33.9312	−	25.1078i	−1.52664	−	1.12965i
$495$	−23.0368	−	15.5053i	−1.03543	−	0.696911i
$496$	−11.2904	−	42.1365i	−0.506956	−	1.89198i
$497$	−4.80191	+	4.80191i	−0.215395	+	0.215395i
$498$	25.8069	+	16.7141i	1.15644	+	0.748976i
$499$	25.3030	−	6.77993i	1.13272	−	0.303511i	0.356700	−	0.934219i	$-0.383902\pi$
$499$	25.3030	−	6.77993i	1.13272	−	0.303511i	0.776020	+	0.630708i	$0.217235\pi$
$500$	39.0446	−	47.7834i	1.74613	−	2.13694i
$501$	10.2200	−	15.7798i	0.456594	−	0.704992i
$502$	−24.4133	−	42.2851i	−1.08962	−	1.88727i
$503$	−0.00185907	+	0.00693813i	−8.28917e−5	+	0.000309356i	−0.965967	−	0.258664i	$-0.916718\pi$
$503$	−0.00185907	+	0.00693813i	−8.28917e−5	+	0.000309356i	0.965884	+	0.258974i	$0.0833843\pi$
$504$	52.8272	−	23.6762i	2.35311	−	1.05462i
$505$	−10.2746	+	10.9857i	−0.457214	+	0.488859i
$506$	−55.0139	+	31.7623i	−2.44567	+	1.41201i
$507$	6.17985	−	21.6520i	0.274457	−	0.961599i
$508$	−93.6794	+	25.1013i	−4.15635	+	1.11369i
$509$	6.41780	−	23.9516i	0.284464	−	1.06163i	−0.664766	−	0.747052i	$-0.731469\pi$
$509$	6.41780	−	23.9516i	0.284464	−	1.06163i	0.949230	−	0.314583i	$-0.101865\pi$
$510$	−2.60304	+	4.32983i	−0.115264	+	0.191728i
$511$	−2.30603	−	1.33139i	−0.102013	−	0.0588972i
$512$		−	56.9480i		−	2.51677i
$513$	−8.94823	+	20.2995i	−0.395074	+	0.896244i
$514$	19.1535	+	5.13216i	0.844824	+	0.226370i
$515$	2.41454	−	4.52502i	0.106397	−	0.199396i
$516$	−18.0485	+	16.2912i	−0.794541	+	0.717181i
$517$	12.0233	−	44.8714i	0.528782	−	1.97344i
$518$	−25.3018	+	14.6080i	−1.11170	+	0.641839i
$519$	12.5672	−	11.3436i	0.551638	−	0.497928i
$520$	70.2722	−	33.3912i	3.08164	−	1.46430i
$521$	25.4621			1.11552			0.557758	−	0.830003i	$-0.311662\pi$
$521$	25.4621			1.11552			0.557758	+	0.830003i	$0.311662\pi$
$522$	−41.1251	+	56.8979i	−1.80000	+	2.49035i
$523$	−14.2922	+	3.82958i	−0.624953	+	0.167456i	−0.557379	−	0.830258i	$-0.688193\pi$
$523$	−14.2922	+	3.82958i	−0.624953	+	0.167456i	−0.0675748	+	0.997714i	$0.521526\pi$
$524$	−7.49790	+	12.9867i	−0.327547	+	0.567329i
$525$	0.272610	+	17.3152i	0.0118977	+	0.755695i
$526$	−57.4475	+	57.4475i	−2.50483	+	2.50483i
$527$	−1.34545			−0.0586089
$528$	34.0429	−	105.214i	1.48152	−	4.57884i
$529$	7.20452	+	4.15953i	0.313240	+	0.180849i
$530$	45.2113	−	1.51224i	1.96385	−	0.0656875i
$531$	−1.16962	−	7.26881i	−0.0507571	−	0.315439i
$532$	33.3177	+	33.3177i	1.44451	+	1.44451i
$533$	23.7622	+	17.5832i	1.02926	+	0.761612i
$534$	−4.70312	−	5.21043i	−0.203524	−	0.225477i
$535$	−4.02089	+	7.53544i	−0.173838	+	0.325786i
$536$	14.3434	+	24.8435i	0.619540	+	1.07308i
$537$	−8.83668	−	0.452204i	−0.381331	−	0.0195140i
$538$	33.6526	+	58.2880i	1.45087	+	2.51297i
$539$	−3.21575	+	12.0013i	−0.138512	+	0.516935i
$540$	−39.5931	−	50.4454i	−1.70382	−	2.17082i
$541$	−27.9857	−	27.9857i	−1.20320	−	1.20320i	−0.973188	−	0.230013i	$-0.926123\pi$
$541$	−27.9857	−	27.9857i	−1.20320	−	1.20320i	−0.230013	−	0.973188i	$-0.573877\pi$
$542$	−16.1461	−	60.2581i	−0.693535	−	2.58831i
$543$	20.9028	−	10.6829i	0.897023	−	0.458448i
$544$	−10.5649	−	2.83087i	−0.452968	−	0.121372i
$545$	−0.223098	−	6.66994i	−0.00955646	−	0.285709i
$546$	−14.1619	+	31.1770i	−0.606074	+	1.33425i
$547$	1.41869	+	0.380138i	0.0606590	+	0.0162535i	0.289021	−	0.957323i	$-0.406670\pi$
$547$	1.41869	+	0.380138i	0.0606590	+	0.0162535i	−0.228362	+	0.973576i	$0.573337\pi$
$548$	45.3545	−	78.5563i	1.93745	−	3.35576i
$549$	4.31639	+	9.63090i	0.184219	+	0.411037i
$550$	42.7242	+	37.3608i	1.82176	+	1.59307i
$551$	−35.1935	−	9.43006i	−1.49929	−	0.401734i
$552$	−91.4723	+	19.5608i	−3.89332	+	0.832561i
$553$			10.8596i			0.461799i
$554$	−0.809765	−	3.02208i	−0.0344036	−	0.128396i
$555$	14.3316	+	14.8479i	0.608342	+	0.630259i
$556$			50.2148i			2.12958i
$557$	−11.7643	+	20.3764i	−0.498470	+	0.863375i	−0.999998	−	0.00176626i	$-0.999438\pi$
$557$	−11.7643	+	20.3764i	−0.498470	+	0.863375i	0.501529	+	0.865141i	$0.332771\pi$
$558$	8.28467	−	21.7421i	0.350718	−	0.920418i
$559$	1.03812	−	9.11132i	0.0439077	−	0.385368i
$560$	−65.9791	+	20.0658i	−2.78813	+	0.847934i
$561$	−2.86276	−	1.85409i	−0.120866	−	0.0782798i
$562$	−73.6935	−	19.7461i	−3.10857	−	0.832940i
$563$	−5.70944	+	5.70944i	−0.240624	+	0.240624i	−0.817108	−	0.576484i	$-0.804424\pi$
$563$	−5.70944	+	5.70944i	−0.240624	+	0.240624i	0.576484	+	0.817108i	$0.304424\pi$
$564$	58.3174	−	90.0435i	2.45561	−	3.79151i
$565$	−0.278775	−	8.33451i	−0.0117281	−	0.350636i
$566$	19.6134	−	73.1983i	0.824414	−	3.07675i
$567$	17.6216	+	3.65499i	0.740038	+	0.153495i
$568$	−8.48223	+	31.6561i	−0.355906	+	1.32826i
$569$	−22.3188			−0.935651			−0.467826	−	0.883821i	$-0.654963\pi$
$569$	−22.3188			−0.935651			−0.467826	+	0.883821i	$0.654963\pi$
$570$	23.3618	−	38.8595i	0.978520	−	1.62765i
$571$	4.13139	+	2.38526i	0.172893	+	0.0998201i	0.583949	−	0.811790i	$-0.301507\pi$
$571$	4.13139	+	2.38526i	0.172893	+	0.0998201i	−0.411056	+	0.911610i	$0.634840\pi$
$572$	32.8473	+	75.5438i	1.37341	+	3.15865i
$573$	10.2301	+	0.523507i	0.427367	+	0.0218698i
$574$	−31.7876	−	31.7876i	−1.32679	−	1.32679i
$575$	5.41994	−	27.4518i	0.226027	−	1.14482i
$576$	56.5904	−	78.2946i	2.35793	−	3.26228i
$577$			11.2004i			0.466277i	0.972444	+	0.233138i	$0.0748995\pi$
$577$			11.2004i			0.466277i	−0.972444	+	0.233138i	$0.925100\pi$
$578$	22.9978	−	39.8333i	0.956581	−	1.65685i
$579$	13.2753	+	8.59785i	0.551702	+	0.357314i
$580$	71.9427	−	76.9220i	2.98726	−	3.19401i
$581$	12.9450			0.537047
$582$	−31.3750	−	1.60557i	−1.30053	−	0.0665529i
$583$			30.5400i			1.26484i
$584$	−12.8505			−0.531757
$585$	23.7861	+	4.38415i	0.983435	+	0.181262i
$586$	3.96984			0.163992
$587$			1.62479i			0.0670623i	0.999438	+	0.0335311i	$0.0106753\pi$
$587$			1.62479i			0.0670623i	−0.999438	+	0.0335311i	$0.989325\pi$
$588$	−15.5976	+	24.0831i	−0.643236	+	0.993171i
$589$	12.0752			0.497552
$590$	0.503031	+	15.0391i	0.0207095	+	0.619149i
$591$	−1.21069	+	23.6585i	−0.0498011	+	0.973181i
$592$	−41.0900	+	71.1699i	−1.68879	+	2.92507i
$593$			4.65301i			0.191076i	0.995426	+	0.0955380i	$0.0304572\pi$
$593$			4.65301i			0.191076i	−0.995426	+	0.0955380i	$0.969543\pi$
$594$	47.5891	−	34.8447i	1.95260	−	1.42970i
$595$	0.0711050	+	2.12582i	0.00291502	+	0.0871502i
$596$	−17.1058	−	17.1058i	−0.700679	−	0.700679i
$597$	−17.6960	+	27.3230i	−0.724248	+	1.11826i
$598$	32.9118	−	44.4776i	1.34586	−	1.81882i
$599$	−4.07812	−	2.35451i	−0.166628	−	0.0962025i	0.414367	−	0.910110i	$-0.364003\pi$
$599$	−4.07812	−	2.35451i	−0.166628	−	0.0962025i	−0.580995	+	0.813907i	$0.697336\pi$
$600$	42.9206	+	71.7094i	1.75222	+	2.92752i
$601$	33.6180			1.37131			0.685654	−	0.727927i	$-0.259516\pi$
$601$	33.6180			1.37131			0.685654	+	0.727927i	$0.259516\pi$
$602$	−3.60947	+	13.4707i	−0.147111	+	0.549025i
$603$	−0.910350	+	8.87145i	−0.0370723	+	0.361273i
$604$	32.1442	−	119.964i	1.30793	−	4.88126i
$605$	−9.37165	+	10.0203i	−0.381012	+	0.407382i
$606$	−14.5397	−	28.4491i	−0.590634	−	1.15567i
$607$	−7.39589	+	7.39589i	−0.300190	+	0.300190i	−0.841088	−	0.540898i	$-0.818084\pi$
$607$	−7.39589	+	7.39589i	−0.300190	+	0.300190i	0.540898	+	0.841088i	$0.318084\pi$
$608$	94.8187	+	25.4066i	3.84541	+	1.03037i
$609$	−1.51058	+	29.5188i	−0.0612117	+	1.19616i
$610$	−6.27632	−	20.6374i	−0.254121	−	0.835585i
$611$	5.98060	+	40.0175i	0.241949	+	1.61894i
$612$	−4.97192	−	6.10899i	−0.200978	−	0.246941i
$613$	−6.20902	+	10.7543i	−0.250780	+	0.434363i	−0.963741	−	0.266840i	$-0.914020\pi$
$613$	−6.20902	+	10.7543i	−0.250780	+	0.434363i	0.712961	+	0.701204i	$0.247354\pi$
$614$			15.1988i			0.613373i
$615$	−16.3605	+	27.2136i	−0.659717	+	1.09736i
$616$	−20.6743	−	77.1575i	−0.832991	−	3.10877i
$617$			12.7705i			0.514122i	0.966395	+	0.257061i	$0.0827541\pi$
$617$			12.7705i			0.514122i	−0.966395	+	0.257061i	$0.917246\pi$
$618$	7.29947	+	8.08685i	0.293628	+	0.325301i
$619$	1.33743	+	0.358363i	0.0537559	+	0.0144038i	0.285597	−	0.958350i	$-0.407808\pi$
$619$	1.33743	+	0.358363i	0.0537559	+	0.0144038i	−0.231841	+	0.972754i	$0.574475\pi$
$620$	−16.4326	+	30.7958i	−0.659948	+	1.23679i
$621$	−26.6089	−	11.7295i	−1.06778	−	0.470688i
$622$	12.8983	−	22.3405i	0.517174	−	0.895772i
$623$	−2.85449	−	0.764858i	−0.114363	−	0.0306434i
$624$	9.34967	+	95.8644i	0.374286	+	3.83765i
$625$	−24.7767	+	3.33362i	−0.991070	+	0.133345i
$626$	−37.4236	−	10.0276i	−1.49575	−	0.400784i
$627$	25.6928	+	16.6402i	1.02607	+	0.664545i
$628$	−10.0934	−	37.6691i	−0.402771	−	1.50316i
$629$	1.79228	+	1.79228i	0.0714628	+	0.0714628i
$630$	−34.7905	−	11.9408i	−1.38609	−	0.475732i
$631$	9.75070	−	36.3901i	0.388169	−	1.44867i	−0.444940	−	0.895560i	$-0.646775\pi$
$631$	9.75070	−	36.3901i	0.388169	−	1.44867i	0.833110	−	0.553108i	$-0.186558\pi$
$632$	26.2041	+	45.3869i	1.04234	+	1.80539i
$633$	−4.64507	+	7.17210i	−0.184625	+	0.285065i
$634$	−37.5324	−	65.0081i	−1.49060	−	2.58180i
$635$	34.6658	+	18.4976i	1.37567	+	0.734055i
$636$	−21.7116	+	67.1023i	−0.860919	+	2.66078i
$637$	−1.59958	−	10.7031i	−0.0633775	−	0.424073i
$638$	68.4981	+	68.4981i	2.71187	+	2.71187i
$639$	−7.90197	+	6.43116i	−0.312597	+	0.254413i
$640$	−64.6328	+	69.1062i	−2.55484	+	2.73166i
$641$	36.7914	+	21.2415i	1.45317	+	0.838989i	0.998660	−	0.0517520i	$-0.0164805\pi$
$641$	36.7914	+	21.2415i	1.45317	+	0.838989i	0.454511	+	0.890741i	$0.349814\pi$
$642$	−12.1557	−	13.4669i	−0.479747	−	0.531496i
$643$	43.0311			1.69698			0.848490	−	0.529212i	$-0.177512\pi$
$643$	43.0311			1.69698			0.848490	+	0.529212i	$0.177512\pi$
$644$	−43.6734	+	43.6734i	−1.72097	+	1.72097i
$645$	9.84891	+	0.174276i	0.387800	+	0.00686211i
$646$	2.78454	−	4.82297i	0.109556	−	0.189757i
$647$	−24.6944	+	6.61684i	−0.970836	+	0.260135i	−0.709181	−	0.705027i	$-0.750935\pi$
$647$	−24.6944	+	6.61684i	−0.970836	+	0.260135i	−0.261655	+	0.965161i	$0.584268\pi$
$648$	82.4674	−	27.2449i	3.23963	−	1.07028i
$649$	−10.1588			−0.398769
$650$	−47.1024	−	15.0039i	−1.84751	−	0.588500i
$651$	−2.04847	−	9.57931i	−0.0802860	−	0.375443i
$652$	−87.8246	+	50.7056i	−3.43948	+	1.98578i
$653$	8.28689	−	30.9271i	0.324291	−	1.21027i	−0.590732	−	0.806868i	$-0.701161\pi$
$653$	8.28689	−	30.9271i	0.324291	−	1.21027i	0.915023	−	0.403402i	$-0.132172\pi$
$654$	13.4867	+	4.36376i	0.527373	+	0.170636i
$655$	5.81256	−	1.76773i	0.227116	−	0.0690711i
$656$	−122.141	−	32.7276i	−4.76881	−	1.27780i
$657$	−3.23772	−	2.34018i	−0.126316	−	0.0912993i
$658$		−	61.5335i		−	2.39882i
$659$	−6.50554	−	3.75598i	−0.253420	−	0.146312i	0.367909	−	0.929862i	$-0.380074\pi$
$659$	−6.50554	−	3.75598i	−0.253420	−	0.146312i	−0.621329	+	0.783550i	$0.713407\pi$
$660$	−77.4019	+	42.8803i	−3.01287	+	1.66911i
$661$	−7.45876	+	27.8365i	−0.290112	+	1.08271i	0.654910	+	0.755707i	$0.272706\pi$
$661$	−7.45876	+	27.8365i	−0.290112	+	1.08271i	−0.945022	+	0.327006i	$0.893960\pi$
$662$	52.2514	−	14.0007i	2.03081	−	0.544154i
$663$	2.93062	+	0.486714i	0.113816	+	0.0189024i
$664$	54.1023	−	31.2360i	2.09958	−	1.21219i
$665$	−0.638157	−	19.0789i	−0.0247467	−	0.739849i
$666$	−39.9987	+	17.9267i	−1.54992	+	0.694645i
$667$	12.3611	−	46.1322i	0.478623	−	1.78625i
$668$	−29.9538	−	51.8816i	−1.15895	−	2.00736i
$669$	−10.2146	−	19.9864i	−0.394919	−	0.772720i
$670$	4.12634	−	17.7540i	0.159414	−	0.685896i
$671$	14.0665	−	3.76912i	0.543033	−	0.145505i
$672$	4.06982	−	79.5299i	0.156997	−	3.06793i
$673$	20.3748	−	20.3748i	0.785391	−	0.785391i	−0.195344	−	0.980735i	$-0.562582\pi$
$673$	20.3748	−	20.3748i	0.785391	−	0.785391i	0.980735	+	0.195344i	$0.0625823\pi$
$674$	−9.25334	−	34.5339i	−0.356425	−	1.33020i
$675$	−2.24492	+	25.8836i	−0.0864072	+	0.996260i
$676$	−52.4745	−	48.9335i	−2.01825	−	1.88206i
$677$	−1.84561	−	0.494531i	−0.0709327	−	0.0190064i	0.223178	−	0.974778i	$-0.428357\pi$
$677$	−1.84561	−	0.494531i	−0.0709327	−	0.0190064i	−0.294111	+	0.955771i	$0.595023\pi$
$678$	16.8525	+	5.45279i	0.647217	+	0.209413i
$679$	−11.4547	+	6.61338i	−0.439592	+	0.253798i
$680$	5.42675	+	8.71311i	0.208107	+	0.334133i
$681$	−1.26801	+	24.7786i	−0.0485901	+	0.949518i
$682$	−27.8037	−	16.0524i	−1.06466	−	0.614680i
$683$	−4.34302	+	2.50744i	−0.166181	+	0.0959447i	−0.580784	−	0.814058i	$-0.697254\pi$
$683$	−4.34302	+	2.50744i	−0.166181	+	0.0959447i	0.414603	+	0.910002i	$0.363921\pi$
$684$	44.6222	+	54.8272i	1.70617	+	2.09637i
$685$	−35.1600	+	10.6930i	−1.34339	+	0.408557i
$686$			54.8404i			2.09382i
$687$	−3.63021	+	3.27675i	−0.138501	+	0.125016i
$688$	10.1528	+	37.8909i	0.387074	+	1.44458i
$689$	−10.6069	−	24.3943i	−0.404091	−	0.929348i
$690$	50.9377	+	30.6231i	1.93917	+	1.16580i
$691$	−21.2280	+	21.2280i	−0.807551	+	0.807551i	−0.984263	−	0.176712i	$-0.943454\pi$
$691$	−21.2280	+	21.2280i	−0.807551	+	0.807551i	0.176712	+	0.984263i	$0.443454\pi$
$692$	−13.9624	−	52.1084i	−0.530771	−	1.98086i
$693$	8.84210	−	23.2050i	0.335883	−	0.881487i
$694$	42.6873	+	42.6873i	1.62039	+	1.62039i
$695$	13.8965	−	14.8583i	0.527124	−	0.563607i
$696$	64.9150	+	127.016i	2.46060	+	4.81453i
$697$	−1.95003	+	3.37756i	−0.0738628	+	0.127934i
$698$	−34.3829	−	34.3829i	−1.30141	−	1.30141i
$699$	20.5101	+	6.63625i	0.775765	+	0.251006i
$700$	49.5260	+	24.3360i	1.87190	+	0.919815i
$701$			47.1597i			1.78120i	0.454791	+	0.890598i	$0.349714\pi$
$701$			47.1597i			1.78120i	−0.454791	+	0.890598i	$0.650286\pi$
$702$	−25.9105	+	44.3610i	−0.977929	+	1.67430i
$703$	−16.0854	−	16.0854i	−0.606673	−	0.606673i
$704$	−94.2571	−	94.2571i	−3.55245	−	3.55245i
$705$	−42.1746	+	10.5046i	−1.58839	+	0.395625i
$706$		−	63.8654i		−	2.40361i
$707$	−11.6491	−	6.72563i	−0.438111	−	0.252943i
$708$	−22.3209	−	7.22213i	−0.838870	−	0.271424i
$709$	−7.32886	−	27.3517i	−0.275241	−	1.02721i	−0.955680	−	0.294409i	$-0.904877\pi$
$709$	−7.32886	−	27.3517i	−0.275241	−	1.02721i	0.680438	−	0.732805i	$-0.261789\pi$
$710$	17.6754	−	11.0087i	0.663347	−	0.413150i
$711$	−1.66313	+	16.2074i	−0.0623722	+	0.607824i
$712$	−13.7757	+	3.69118i	−0.516265	+	0.138333i
$713$			15.8284i			0.592780i
$714$	−4.29845	−	1.39080i	−0.160865	−	0.0520495i
$715$	11.1868	−	31.4432i	0.418361	−	1.17591i
$716$	−14.0976	+	24.4177i	−0.526852	+	0.912534i
$717$	28.6014	+	31.6866i	1.06814	+	1.18336i
$718$	−44.1221	−	44.1221i	−1.64662	−	1.64662i
$719$	−10.9565	−	18.9771i	−0.408607	−	0.707728i	0.586127	−	0.810219i	$-0.300652\pi$
$719$	−10.9565	−	18.9771i	−0.408607	−	0.707728i	−0.994734	+	0.102491i	$0.967319\pi$
$720$	−101.543	+	19.8424i	−3.78428	+	0.739484i
$721$	4.43031	+	1.18710i	0.164993	+	0.0442098i
$722$	1.05930	−	1.83476i	0.0394231	−	0.0682829i
$723$	27.0259	+	29.9411i	1.00510	+	1.11352i
$724$		−	74.8020i		−	2.78000i
$725$	−42.5750	+	2.85131i	−1.58119	+	0.105895i
$726$	−13.2619	−	25.9489i	−0.492195	−	0.963054i
$727$	9.77461	−	36.4793i	0.362520	−	1.35294i	−0.508231	−	0.861221i	$-0.669700\pi$
$727$	9.77461	−	36.4793i	0.362520	−	1.35294i	0.870752	−	0.491723i	$-0.163633\pi$
$728$	43.3116	+	54.4503i	1.60523	+	2.01806i
$729$	25.7394	+	8.15357i	0.953313	+	0.301984i
$730$	5.96332	+	5.57731i	0.220712	+	0.206425i
$731$	1.20989			0.0447494
$732$	33.5864	+	1.71874i	1.24139	+	0.0635263i
$733$	5.21024	−	9.02440i	0.192445	−	0.333324i	−0.753615	−	0.657316i	$-0.771692\pi$
$733$	5.21024	−	9.02440i	0.192445	−	0.333324i	0.946060	+	0.323992i	$0.105025\pi$
$734$	12.6425	+	12.6425i	0.466644	+	0.466644i
$735$	11.2801	−	2.80956i	0.416071	−	0.103632i
$736$	−33.3034	+	124.290i	−1.22758	+	4.58139i
$737$	11.8862	+	3.18489i	0.437833	+	0.117317i
$738$	−42.5730	−	52.3094i	−1.56713	−	1.92553i
$739$	10.0709	+	37.5852i	0.370465	+	1.38259i	0.859859	+	0.510531i	$0.170551\pi$
$739$	10.0709	+	37.5852i	0.370465	+	1.38259i	−0.489394	+	0.872063i	$0.662782\pi$
$740$	62.9129	−	19.1333i	2.31272	−	0.703353i
$741$	−26.3018	−	4.36818i	−0.966222	−	0.160469i
$742$	10.4701	+	39.0750i	0.384370	+	1.43449i
$743$	23.2694	+	40.3038i	0.853673	+	1.47860i	0.877871	+	0.478897i	$0.158963\pi$
$743$	23.2694	+	40.3038i	0.853673	+	1.47860i	−0.0241986	+	0.999707i	$0.507703\pi$
$744$	−31.6762	−	35.0930i	−1.16130	−	1.28657i
$745$	0.327638	+	9.79538i	0.0120037	+	0.358875i
$746$	−5.29101	+	5.29101i	−0.193718	+	0.193718i
$747$	19.3196	+	1.98249i	0.706866	+	0.0725355i
$748$	−9.41229	+	5.43419i	−0.344147	+	0.198694i
$749$	−7.37772	−	1.97686i	−0.269576	−	0.0722327i
$750$	11.2055	−	51.9052i	0.409167	−	1.89531i
$751$	17.2606	−	9.96539i	0.629847	−	0.363642i	−0.150846	−	0.988557i	$-0.548200\pi$
$751$	17.2606	−	9.96539i	0.629847	−	0.363642i	0.780693	+	0.624915i	$0.214866\pi$
$752$	−86.5418	−	149.895i	−3.15585	−	5.46610i
$753$	−25.8862	−	16.7654i	−0.943346	−	0.610966i
$754$	−78.5040	−	30.9237i	−2.85895	−	1.12617i
$755$	−42.7103	+	26.6011i	−1.55439	+	0.968113i
$756$	35.9247	−	44.6999i	1.30657	−	1.62572i
$757$	−4.16825	−	15.5561i	−0.151498	−	0.565396i	−0.999380	−	0.0352120i	$-0.988789\pi$
$757$	−4.16825	−	15.5561i	−0.151498	−	0.565396i	0.847882	−	0.530184i	$-0.177877\pi$
$758$	7.26722	+	27.1216i	0.263957	+	0.985103i
$759$	−21.8122	+	33.6786i	−0.791734	+	1.22246i
$760$	−48.7043	−	78.1988i	−1.76669	−	2.83657i
$761$	−19.4488	−	19.4488i	−0.705017	−	0.705017i	0.260466	−	0.965483i	$-0.416124\pi$
$761$	−19.4488	−	19.4488i	−0.705017	−	0.705017i	−0.965483	+	0.260466i	$0.916124\pi$
$762$	−61.9528	+	55.9208i	−2.24431	+	2.02580i
$763$	5.76465	−	1.54463i	0.208694	−	0.0559195i
$764$	16.3205	−	28.2679i	0.590455	−	1.02270i
$765$	−0.219445	+	3.18355i	−0.00793405	+	0.115102i
$766$			60.1368i			2.17283i
$767$	8.11451	−	3.52828i	0.292998	−	0.127399i
$768$	−40.6975	−	79.6309i	−1.46855	−	2.87343i
$769$	−1.92844	+	7.19703i	−0.0695413	+	0.259532i	−0.991940	−	0.126707i	$-0.959559\pi$
$769$	−1.92844	+	7.19703i	−0.0695413	+	0.259532i	0.922399	+	0.386239i	$0.126226\pi$
$770$	−23.8935	+	44.7782i	−0.861064	+	1.61370i
$771$	12.2481	−	2.61918i	0.441104	−	0.0943273i
$772$	43.6469	−	25.1996i	1.57089	−	0.906953i
$773$	−24.7380	−	42.8475i	−0.889764	−	1.54112i	−0.840154	−	0.542348i	$-0.817535\pi$
$773$	−24.7380	−	42.8475i	−0.889764	−	1.54112i	−0.0496102	−	0.998769i	$-0.515798\pi$
$774$	−7.44992	+	19.5515i	−0.267782	+	0.702763i
$775$	13.3848	−	4.56476i	0.480796	−	0.163971i
$776$	−31.9160	+	55.2801i	−1.14572	+	1.98444i
$777$	−10.0318	+	15.4894i	−0.359889	+	0.555678i
$778$	−12.7931	+	7.38609i	−0.458654	+	0.264804i
$779$	17.5013	−	30.3131i	0.627048	−	1.08608i
$780$	46.9331	−	61.1339i	1.68048	−	2.18894i
$781$	7.02911	+	12.1748i	0.251521	+	0.435648i
$782$	6.32204	+	3.65003i	0.226076	+	0.130525i
$783$	−6.77518	+	43.8237i	−0.242125	+	1.56613i
$784$	23.1466	+	40.0910i	0.826663	+	1.43182i
$785$	−7.43801	+	13.9394i	−0.265474	+	0.497517i
$786$	−0.659501	+	12.8876i	−0.0235236	+	0.459684i
$787$	29.6351			1.05638			0.528189	−	0.849127i	$-0.322871\pi$
$787$	29.6351			1.05638			0.528189	+	0.849127i	$0.322871\pi$
$788$	65.3738	+	37.7436i	2.32885	+	1.34456i
$789$	−15.7977	+	48.8247i	−0.562412	+	1.73821i
$790$	7.53847	−	32.4350i	0.268207	−	1.15398i
$791$	7.20330	−	1.93012i	0.256120	−	0.0686271i
$792$	−19.0387	−	118.319i	−0.676509	−	4.20429i
$793$	−9.92680	+	7.89611i	−0.352511	+	0.280399i
$794$	7.86345	−	4.53997i	0.279063	−	0.161117i
$795$	24.9943	−	13.8467i	0.886457	−	0.491093i
$796$	51.8654	+	89.8335i	1.83832	+	3.18406i
$797$	−6.95712	−	6.95712i	−0.246434	−	0.246434i	0.573072	−	0.819505i	$-0.305752\pi$
$797$	−6.95712	−	6.95712i	−0.246434	−	0.246434i	−0.819505	+	0.573072i	$0.805752\pi$
$798$	38.5779	+	12.4822i	1.36564	+	0.441867i
$799$	−5.15649	+	1.38168i	−0.182423	+	0.0488802i
$800$	114.706	−	7.68203i	4.05547	−	0.271601i
$801$	−4.14302	−	1.57866i	−0.146386	−	0.0557793i
$802$	56.8546	+	15.2341i	2.00761	+	0.537936i
$803$	−3.89782	+	3.89782i	−0.137551	+	0.137551i
$804$	23.8520	+	15.4480i	0.841196	+	0.544808i
$805$	25.0090	−	0.836507i	0.881451	−	0.0294830i
$806$	27.7838	+	3.16560i	0.978642	+	0.111504i
$807$	35.6829	+	23.1104i	1.25610	+	0.813523i
$808$	−64.9154			−2.28371
$809$	46.4170	+	26.7989i	1.63193	+	0.942198i	0.983496	+	0.180930i	$0.0579108\pi$
$809$	46.4170	+	26.7989i	1.63193	+	0.942198i	0.648438	+	0.761267i	$0.275423\pi$
$810$	−50.0940	−	23.1490i	−1.76013	−	0.813372i
$811$	0.526292	−	0.526292i	0.0184806	−	0.0184806i	−0.697806	−	0.716287i	$-0.745840\pi$
$811$	0.526292	−	0.526292i	0.0184806	−	0.0184806i	0.716287	+	0.697806i	$0.245840\pi$
$812$	81.5670	+	47.0928i	2.86244	+	1.65263i
$813$	−26.4028	−	29.2508i	−0.925986	−	1.02587i
$814$	15.6538	+	58.4206i	0.548664	+	2.04764i
$815$	40.0192	+	9.30117i	1.40181	+	0.325806i
$816$	−12.4270	+	2.65744i	−0.435033	+	0.0930290i
$817$	−10.8586			−0.379893
$818$	46.7535	−	46.7535i	1.63470	−	1.63470i
$819$	0.996623	+	21.6063i	0.0348248	+	0.754986i
$820$	53.4917	+	85.8854i	1.86801	+	2.99925i
$821$	13.4822	−	13.4822i	0.470531	−	0.470531i	−0.431555	−	0.902086i	$-0.642035\pi$
$821$	13.4822	−	13.4822i	0.470531	−	0.470531i	0.902086	+	0.431555i	$0.142035\pi$
$822$	3.98930	−	77.9564i	0.139143	−	2.71904i
$823$	14.5269	−	14.5269i	0.506376	−	0.506376i	−0.407036	−	0.913412i	$-0.633438\pi$
$823$	14.5269	−	14.5269i	0.506376	−	0.506376i	0.913412	+	0.407036i	$0.133438\pi$
$824$	21.3805	−	5.72889i	0.744826	−	0.199575i
$825$	34.7696	+	8.73224i	1.21052	+	0.304017i
$826$	−12.9979	+	3.48277i	−0.452254	+	0.121181i
$827$	42.7184			1.48546			0.742732	−	0.669589i	$-0.233530\pi$
$827$	42.7184			1.48546			0.742732	+	0.669589i	$0.233530\pi$
$828$	−71.8685	+	58.4915i	−2.49760	+	2.03272i
$829$	−3.17533	+	5.49983i	−0.110284	+	0.191017i	−0.915885	−	0.401442i	$-0.868509\pi$
$829$	−3.17533	+	5.49983i	−0.110284	+	0.191017i	0.805601	+	0.592459i	$0.201843\pi$
$830$	−38.6633	−	8.98603i	−1.34202	−	0.311910i
$831$	−1.32416	−	1.46699i	−0.0459346	−	0.0508894i
$832$	108.026	+	42.5527i	3.74512	+	1.47525i
$833$	1.37916	−	0.369545i	0.0477850	−	0.0128040i
$834$	19.6650	+	38.4776i	0.680945	+	1.33237i
$835$	−5.49458	+	23.6410i	−0.190148	+	0.818129i
$836$	84.4738	−	48.7710i	2.92159	−	1.68678i
$837$	−1.59018	−	14.6103i	−0.0549645	−	0.505005i
$838$	6.61569	+	11.4587i	0.228535	+	0.395834i
$839$	0.208412	+	0.777804i	0.00719518	+	0.0268528i	0.969430	−	0.245368i	$-0.0789087\pi$
$839$	0.208412	+	0.777804i	0.00719518	+	0.0268528i	−0.962235	+	0.272220i	$0.912242\pi$
$840$	−53.7730	+	51.9030i	−1.85534	+	1.79083i
$841$	−43.8303			−1.51139
$842$	−0.975635	+	3.64112i	−0.0336226	+	0.125481i
$843$	−47.1248	+	10.0773i	−1.62307	+	0.347082i
$844$	13.6143	+	23.5807i	0.468624	+	0.811681i
$845$	1.98500	+	29.0010i	0.0682862	+	0.997666i
$846$	9.42371	−	91.8350i	0.323994	−	3.15735i
$847$	−10.6254	−	6.13456i	−0.365092	−	0.210786i
$848$	80.4608	+	80.4608i	2.76304	+	2.76304i
$849$	−10.0096	−	46.8082i	−0.343529	−	1.60645i
$850$	1.26332	−	6.39865i	0.0433314	−	0.219472i
$851$	21.0850	−	21.0850i	0.722786	−	0.722786i
$852$	6.78899	+	31.7475i	0.232587	+	1.08765i
$853$	30.6107	−	17.6731i	1.04809	−	0.605115i	0.125976	−	0.992033i	$-0.459794\pi$
$853$	30.6107	−	17.6731i	1.04809	−	0.605115i	0.922114	+	0.386918i	$0.126460\pi$
$854$	16.7055	−	9.64493i	0.571651	−	0.330043i
$855$	1.96948	−	28.5719i	0.0673550	−	0.977138i
$856$	−35.6047	+	9.54024i	−1.21694	+	0.326079i
$857$	12.9963	−	48.5029i	0.443946	−	1.65683i	−0.274760	−	0.961513i	$-0.588598\pi$
$857$	12.9963	−	48.5029i	0.443946	−	1.65683i	0.718705	−	0.695315i	$-0.244735\pi$
$858$	54.7540	+	45.0227i	1.86927	+	1.53705i
$859$	−27.8812	−	16.0972i	−0.951295	−	0.549230i	−0.0578119	−	0.998327i	$-0.518412\pi$
$859$	−27.8812	−	16.0972i	−0.951295	−	0.549230i	−0.893483	+	0.449097i	$0.851746\pi$
$860$	14.7769	−	27.6929i	0.503887	−	0.944320i
$861$	−27.0164	−	8.74140i	−0.920716	−	0.297906i
$862$	52.8267	−	14.1549i	1.79929	−	0.482117i
$863$	1.77605			0.0604575			0.0302288	−	0.999543i	$-0.490376\pi$
$863$	1.77605			0.0604575			0.0302288	+	0.999543i	$0.490376\pi$
$864$	18.2538	−	118.070i	0.621007	−	4.01684i
$865$	−10.2891	+	19.2826i	−0.349841	+	0.655628i
$866$	4.65594	−	17.3762i	0.158215	−	0.590468i
$867$	1.48480	−	29.0149i	0.0504263	−	0.985399i
$868$	−30.1513	−	8.07901i	−1.02340	−	0.274219i
$869$	21.7150	+	5.81852i	0.736632	+	0.197380i
$870$	25.0028	−	87.1164i	0.847676	−	2.95352i
$871$	−10.6004	+	1.58423i	−0.359181	+	0.0536795i
$872$	20.3657	−	20.3657i	0.689669	−	0.689669i
$873$	−18.1083	+	8.11581i	−0.612873	+	0.274679i
$874$	−56.7393	−	32.7584i	−1.91923	−	1.10807i
$875$	−7.91970	−	20.9068i	−0.267735	−	0.706778i
$876$	−11.3353	+	5.79321i	−0.382984	+	0.195734i
$877$			41.9475i			1.41647i	0.705979	+	0.708233i	$0.250507\pi$
$877$			41.9475i			1.41647i	−0.705979	+	0.708233i	$0.749493\pi$
$878$		−	70.3667i		−	2.37476i
$879$	2.23282	−	1.14115i	0.0753113	−	0.0384899i
$880$	4.77251	+	142.684i	0.160881	+	4.80986i
$881$	33.3901	+	19.2778i	1.12494	+	0.649486i	0.942658	−	0.333760i	$-0.108318\pi$
$881$	33.3901	+	19.2778i	1.12494	+	0.649486i	0.182284	+	0.983246i	$0.441651\pi$
$882$	−2.52048	+	24.5623i	−0.0848688	+	0.827055i
$883$	−2.25048	+	2.25048i	−0.0757348	+	0.0757348i	−0.743959	−	0.668225i	$-0.767054\pi$
$883$	−2.25048	+	2.25048i	−0.0757348	+	0.0757348i	0.668225	+	0.743959i	$0.267054\pi$
$884$	5.63085	−	7.60963i	0.189386	−	0.255940i
$885$	4.60598	+	8.31410i	0.154828	+	0.279475i
$886$	−16.3383	−	4.37783i	−0.548895	−	0.147076i
$887$	−55.9686	−	14.9967i	−1.87924	−	0.503541i	−0.999611	−	0.0278828i	$-0.991123\pi$
$887$	−55.9686	−	14.9967i	−1.87924	−	0.503541i	−0.879630	−	0.475658i	$-0.842210\pi$
$888$	−4.55152	+	88.9430i	−0.152739	+	2.98473i
$889$	−9.09427	+	33.9403i	−0.305012	+	1.13832i
$890$	7.99468	+	4.26594i	0.267982	+	0.142995i
$891$	16.7501	−	33.2780i	0.561150	−	1.11485i
$892$	−71.5228			−2.39476
$893$	46.2787	−	12.4003i	1.54866	−	0.414961i
$894$	−19.8064	−	6.40855i	−0.662426	−	0.214334i
$895$	10.9288	−	3.32370i	0.365310	−	0.111099i
$896$	−73.2793	−	42.3078i	−2.44809	−	1.41340i
$897$	5.72589	−	34.4769i	0.191182	−	1.15115i
$898$	14.0068	−	52.2741i	0.467413	−	1.74441i
$899$	23.3149	−	6.24721i	0.777595	−	0.208356i
$900$	70.1875	+	43.9049i	2.33958	+	1.46350i
$901$	3.03938	−	1.75478i	0.101256	−	0.0584603i
$902$	−80.5945	+	46.5312i	−2.68350	+	1.54932i
$903$	1.84208	+	8.61413i	0.0613004	+	0.286660i
$904$	25.4482	−	25.4482i	0.846395	−	0.846395i
$905$	−20.7008	+	22.1335i	−0.688118	+	0.735744i
$906$	−22.3492	−	104.512i	−0.742503	−	3.47218i
$907$	−19.6523	−	19.6523i	−0.652545	−	0.652545i	0.301060	−	0.953605i	$-0.402659\pi$
$907$	−19.6523	−	19.6523i	−0.652545	−	0.652545i	−0.953605	+	0.301060i	$0.902659\pi$
$908$	68.4688	+	39.5305i	2.27222	+	1.31187i
$909$	−16.3556	−	11.8216i	−0.542482	−	0.392099i
$910$	3.53334	−	44.0658i	0.117129	−	1.46077i
$911$	1.02106	+	1.76852i	0.0338291	+	0.0585937i	0.882444	−	0.470417i	$-0.155896\pi$
$911$	1.02106	+	1.76852i	0.0338291	+	0.0585937i	−0.848615	+	0.529011i	$0.822563\pi$
$912$	111.531	−	23.8501i	3.69315	−	0.789756i
$913$	6.93582	−	25.8848i	0.229542	−	0.856663i
$914$	38.8379			1.28464
$915$	−9.46241	−	9.80332i	−0.312818	−	0.324088i
$916$	4.03324	+	15.0522i	0.133262	+	0.497340i
$917$	2.71651	+	4.70513i	0.0897070	+	0.155377i
$918$	−6.20218	−	2.73399i	−0.204702	−	0.0902351i
$919$	−15.0397	+	8.68320i	−0.496115	+	0.286432i	−0.727108	−	0.686523i	$-0.759136\pi$
$919$	−15.0397	+	8.68320i	−0.496115	+	0.286432i	0.230993	+	0.972955i	$0.425803\pi$
$920$	102.504	−	63.8424i	3.37947	−	2.10482i
$921$	4.36895	+	8.54852i	0.143962	+	0.281683i
$922$	−91.2939	+	24.4621i	−3.00660	+	0.805617i
$923$	−9.84304	−	7.28349i	−0.323988	−	0.239739i
$924$	−53.0205	−	58.7396i	−1.74424	−	1.93239i
$925$	−23.9106	−	11.7492i	−0.786174	−	0.386310i
$926$	−39.3902	+	68.2259i	−1.29444	+	2.24204i
$927$	6.43017	+	2.45016i	0.211194	+	0.0804739i
$928$	196.220			6.44125
$929$	−2.58340	+	0.692219i	−0.0847585	+	0.0227110i	−0.300949	−	0.953640i	$-0.597303\pi$
$929$	−2.58340	+	0.692219i	−0.0847585	+	0.0227110i	0.216191	+	0.976351i	$0.430637\pi$
$930$	−0.531431	+	30.0330i	−0.0174263	+	0.984819i
$931$	−12.3777	+	3.31661i	−0.405664	+	0.108697i
$932$	48.5726	−	48.5726i	1.59105	−	1.59105i
$933$	0.832747	−	16.2730i	0.0272629	−	0.532754i
$934$	58.1899	−	58.1899i	1.90403	−	1.90403i
$935$	4.28891	+	0.996820i	0.140262	+	0.0325995i
$936$	56.3010	+	87.8969i	1.84026	+	2.87300i
$937$	−32.0751	+	32.0751i	−1.04785	+	1.04785i	−0.0490507	+	0.998796i	$0.515620\pi$
$937$	−32.0751	+	32.0751i	−1.04785	+	1.04785i	−0.998796	+	0.0490507i	$0.984380\pi$
$938$	16.2999			0.532210
$939$	−23.9313	+	5.11755i	−0.780967	+	0.167005i
$940$	−31.3534	+	134.901i	−1.02263	+	4.39998i
$941$	12.3814	+	46.2081i	0.403623	+	1.50634i	0.806581	+	0.591124i	$0.201316\pi$
$941$	12.3814	+	46.2081i	0.403623	+	1.50634i	−0.402958	+	0.915219i	$0.632018\pi$
$942$	−22.4861	−	24.9116i	−0.732638	−	0.811665i
$943$	39.7349	+	22.9410i	1.29395	+	0.747060i
$944$	−26.7645	+	26.7645i	−0.871109	+	0.871109i
$945$	−23.0003	+	3.28461i	−0.748198	+	0.106848i
$946$	25.0022	+	14.4350i	0.812892	+	0.469324i
$947$	24.9812			0.811779			0.405890	−	0.913922i	$-0.366962\pi$
$947$	24.9812			0.811779			0.405890	+	0.913922i	$0.366962\pi$
$948$	43.5756	+	28.2221i	1.41527	+	0.916611i
$949$	1.75968	−	4.46720i	0.0571217	−	0.145011i
$950$	−11.3381	+	57.4269i	−0.367855	+	1.86317i
$951$	−39.7968	−	25.7748i	−1.29050	−	0.835804i
$952$	−6.49089	+	6.49089i	−0.210371	+	0.210371i
$953$	−43.1683	−	11.5669i	−1.39836	−	0.374689i	−0.520603	−	0.853799i	$-0.674293\pi$
$953$	−43.1683	−	11.5669i	−1.39836	−	0.374689i	−0.877755	+	0.479111i	$0.840959\pi$
$954$	9.64176	+	59.9205i	0.312164	+	1.94000i
$955$	−12.6521	+	3.84778i	−0.409411	+	0.124511i
$956$	131.385	−	35.2045i	4.24929	−	1.13859i
$957$	58.2166	+	18.8365i	1.88188	+	0.608899i
$958$	10.3896	+	10.3896i	0.335674	+	0.335674i
$959$	−16.4321	−	28.4612i	−0.530619	−	0.919059i
$960$	−34.4053	+	119.877i	−1.11043	+	3.86901i
$961$	19.9189	−	11.5002i	0.642547	−	0.370974i
$962$	−32.7938	−	41.2276i	−1.05732	−	1.32923i
$963$	−10.7081	−	4.08022i	−0.345063	−	0.131483i
$964$	124.147	−	33.2652i	3.99851	−	1.07140i
$965$	−19.8887	−	4.62248i	−0.640239	−	0.148803i
$966$	−16.3619	+	50.5686i	−0.526437	+	1.62702i
$967$	−33.0914	−	19.1053i	−1.06415	−	0.614386i	−0.137572	−	0.990492i	$-0.543930\pi$
$967$	−33.0914	−	19.1053i	−1.06415	−	0.614386i	−0.926577	+	0.376105i	$0.877263\pi$
$968$	−59.2104			−1.90309
$969$	0.179777	−	3.51310i	0.00577528	−	0.112857i
$970$	38.8031	−	11.8009i	1.24589	−	0.378905i
$971$	6.07113	+	10.5155i	0.194832	+	0.337458i	0.946845	−	0.321689i	$-0.104251\pi$
$971$	6.07113	+	10.5155i	0.194832	+	0.337458i	−0.752014	+	0.659148i	$0.770917\pi$
$972$	60.4612	−	61.2101i	1.93929	−	1.96332i
$973$	15.7555	+	9.09647i	0.505099	+	0.291619i
$974$	16.7206	+	28.9609i	0.535761	+	0.927966i
$975$	−30.8055	+	5.10088i	−0.986567	+	0.163359i
$976$	27.1296	−	46.9899i	0.868398	−	1.50411i
$977$	−10.0543	+	5.80484i	−0.321665	+	0.185713i	−0.652134	−	0.758103i	$-0.726126\pi$
$977$	−10.0543	+	5.80484i	−0.321665	+	0.185713i	0.330470	+	0.943817i	$0.392793\pi$
$978$	−47.4394	+	73.2475i	−1.51694	+	2.34220i
$979$	−3.05883	+	5.29805i	−0.0977607	+	0.169327i
$980$	8.38580	−	36.0807i	0.267874	−	1.15256i
$981$	8.83996	−	1.42243i	0.282238	−	0.0454147i
$982$	−32.5499	−	56.3781i	−1.03871	−	1.79910i
$983$	−40.5629	+	23.4190i	−1.29376	+	0.746950i	−0.979318	−	0.202328i	$-0.935149\pi$
$983$	−40.5629	+	23.4190i	−1.29376	+	0.746950i	−0.314437	+	0.949278i	$0.601816\pi$
$984$	−134.005	+	28.6562i	−4.27194	+	0.913526i
$985$	−8.89857	−	29.2598i	−0.283532	−	0.932294i
$986$	2.88120	−	10.7528i	0.0917563	−	0.342439i
$987$	−17.6880	−	34.6093i	−0.563017	−	1.10163i
$988$	−50.5360	+	68.2952i	−1.60776	+	2.17276i
$989$		−	14.2336i		−	0.452602i
$990$	−42.5174	+	63.1696i	−1.35129	+	2.00766i
$991$	15.4378	−	26.7391i	0.490399	−	0.849395i	−0.509540	−	0.860447i	$-0.670185\pi$
$991$	15.4378	−	26.7391i	0.490399	−	0.849395i	0.999939	+	0.0110515i	$0.00351786\pi$
$992$	−62.8153	+	16.8313i	−1.99439	+	0.534395i
$993$	25.3641	−	22.8946i	0.804906	−	0.726537i
$994$	13.1674	+	13.1674i	0.417645	+	0.417645i
$995$	9.51393	−	40.9346i	0.301612	−	1.29771i
$996$	33.6414	−	51.9431i	1.06597	−	1.64588i
$997$	5.16415	+	19.2729i	0.163550	+	0.610377i	0.998221	+	0.0596279i	$0.0189914\pi$
$997$	5.16415	+	19.2729i	0.163550	+	0.610377i	−0.834671	+	0.550750i	$0.814342\pi$
$998$	−18.5914	−	69.3840i	−0.588500	−	2.19631i
$999$	−17.3441	+	21.5806i	−0.548742	+	0.682780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.ca.a.58.1	✓	320
5.2	odd	4		585.2.dv.a.292.80	yes	320
9.7	even	3		585.2.dt.a.448.1	yes	320
13.11	odd	12		585.2.cc.a.193.1	yes	320
45.7	odd	12		585.2.cc.a.97.1	yes	320
65.37	even	12		585.2.dt.a.427.1	yes	320
117.115	odd	12		585.2.dv.a.583.80	yes	320
585.232	even	12	inner	585.2.ca.a.232.80	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.ca.a.58.1	✓	320	1.1	even	1	trivial
585.2.ca.a.232.80	yes	320	585.232	even	12	inner
585.2.cc.a.97.1	yes	320	45.7	odd	12
585.2.cc.a.193.1	yes	320	13.11	odd	12
585.2.dt.a.427.1	yes	320	65.37	even	12
585.2.dt.a.448.1	yes	320	9.7	even	3
585.2.dv.a.292.80	yes	320	5.2	odd	4
585.2.dv.a.583.80	yes	320	117.115	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.74212i q^{2} +(-0.788234 - 1.54230i) q^{3} -5.51923 q^{4} +(1.63311 + 1.52740i) q^{5} +(-4.22917 + 2.16143i) q^{6} +(-0.999815 + 1.73173i) q^{7} +9.65015i q^{8} +(-1.75738 + 2.43139i) q^{9} +(4.18831 - 4.47819i) q^{10} +(2.92709 + 2.92709i) q^{11} +(4.35044 + 8.51230i) q^{12} +(-3.35467 - 1.32144i) q^{13} +(4.74861 + 2.74161i) q^{14} +(1.06843 - 3.72269i) q^{15} +15.4234 q^{16} +(0.123121 - 0.459493i) q^{17} +(6.66715 + 4.81894i) q^{18} +(-1.10499 + 4.12388i) q^{19} +(-9.01352 - 8.43006i) q^{20} +(3.45893 + 0.177006i) q^{21} +(8.02643 - 8.02643i) q^{22} +(-5.40565 - 1.44844i) q^{23} +(14.8834 - 7.60658i) q^{24} +(0.334109 + 4.98882i) q^{25} +(-3.62356 + 9.19890i) q^{26} +(5.13515 + 0.793899i) q^{27} +(5.51821 - 9.55782i) q^{28} +8.53407i q^{29} +(-10.2081 - 2.92977i) q^{30} +(-0.732032 - 2.73198i) q^{31} -22.9926i q^{32} +(2.20722 - 6.82168i) q^{33} +(-1.25999 - 0.337612i) q^{34} +(-4.27785 + 1.30099i) q^{35} +(9.69935 - 13.4194i) q^{36} +(-2.66413 + 4.61440i) q^{37} +(11.3082 + 3.03002i) q^{38} +(0.606199 + 6.21551i) q^{39} +(-14.7396 + 15.7598i) q^{40} +(-7.91919 - 2.12194i) q^{41} +(0.485371 - 9.48482i) q^{42} +(0.658274 + 2.45671i) q^{43} +(-16.1553 - 16.1553i) q^{44} +(-6.58368 + 1.28651i) q^{45} +(-3.97180 + 14.8230i) q^{46} +(-5.61106 - 9.71864i) q^{47} +(-12.1573 - 23.7875i) q^{48} +(1.50074 + 2.59936i) q^{49} +(13.6800 - 0.916166i) q^{50} +(-0.805724 + 0.172299i) q^{51} +(18.5152 + 7.29335i) q^{52} +(5.21679 + 5.21679i) q^{53} +(2.17697 - 14.0812i) q^{54} +(0.309433 + 9.25109i) q^{55} +(-16.7115 - 9.64837i) q^{56} +(7.23125 - 1.54636i) q^{57} +23.4014 q^{58} +(-1.73531 + 1.73531i) q^{59} +(-5.89692 + 20.5464i) q^{60} +(1.75899 - 3.04666i) q^{61} +(-7.49142 + 2.00732i) q^{62} +(-2.45345 - 5.47424i) q^{63} -32.2017 q^{64} +(-3.46017 - 7.28198i) q^{65} +(-18.7059 - 6.05246i) q^{66} +(2.57441 - 1.48634i) q^{67} +(-0.679532 + 2.53605i) q^{68} +(2.02699 + 9.47885i) q^{69} +(3.56748 + 11.7304i) q^{70} +(3.28037 + 0.878973i) q^{71} +(-23.4632 - 16.9589i) q^{72} +1.33164i q^{73} +(12.6533 + 7.30536i) q^{74} +(7.43091 - 4.44766i) q^{75} +(6.09869 - 22.7606i) q^{76} +(-7.99548 + 2.14238i) q^{77} +(17.0437 - 1.66227i) q^{78} +(4.70323 - 2.71541i) q^{79} +(25.1882 + 23.5577i) q^{80} +(-2.82327 - 8.54571i) q^{81} +(-5.81862 + 21.7154i) q^{82} +(-3.23684 - 5.60637i) q^{83} +(-19.0907 - 0.976935i) q^{84} +(0.902899 - 0.562349i) q^{85} +(6.73660 - 1.80507i) q^{86} +(13.1621 - 6.72684i) q^{87} +(-28.2468 + 28.2468i) q^{88} +(0.382500 + 1.42751i) q^{89} +(3.52777 + 18.0533i) q^{90} +(5.64243 - 4.48818i) q^{91} +(29.8350 + 7.99427i) q^{92} +(-3.63652 + 3.28245i) q^{93} +(-26.6497 + 15.3862i) q^{94} +(-8.10338 + 5.04700i) q^{95} +(-35.4615 + 18.1235i) q^{96} +(5.72842 + 3.30730i) q^{97} +(7.12775 - 4.11521i) q^{98} +(-12.2609 + 1.97289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 2 q^{3} - 304 q^{4} - 2 q^{5} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{10} - 12 q^{11} - 14 q^{12} - 2 q^{13} + 48 q^{14} - 6 q^{15} + 264 q^{16} - 12 q^{17} + 4 q^{18} - 30 q^{20} - 16 q^{21} - 4 q^{22}+ \cdots - 20 q^{99}+O(q^{100}) \) 320 * q - 2 * q^3 - 304 * q^4 - 2 * q^5 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^10 - 12 * q^11 - 14 * q^12 - 2 * q^13 + 48 * q^14 - 6 * q^15 + 264 * q^16 - 12 * q^17 + 4 * q^18 - 30 * q^20 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 56 * q^24 - 20 * q^27 - 24 * q^28 - 2 * q^30 - 4 * q^31 - 6 * q^33 + 8 * q^34 - 46 * q^35 - 60 * q^36 - 4 * q^37 - 40 * q^38 - 4 * q^39 + 28 * q^40 + 4 * q^41 + 22 * q^42 - 6 * q^43 + 8 * q^44 + 4 * q^45 - 16 * q^46 - 14 * q^47 + 2 * q^48 - 112 * q^49 + 56 * q^50 - 30 * q^52 - 16 * q^53 - 4 * q^55 - 108 * q^56 - 72 * q^57 + 28 * q^58 - 16 * q^59 + 10 * q^60 + 4 * q^61 - 28 * q^62 - 18 * q^63 - 192 * q^64 + 58 * q^65 - 6 * q^67 + 62 * q^68 + 24 * q^69 + 10 * q^70 - 2 * q^72 - 34 * q^75 - 20 * q^76 - 44 * q^77 - 42 * q^78 + 4 * q^80 + 8 * q^81 + 20 * q^82 + 8 * q^83 + 124 * q^84 - 16 * q^85 + 68 * q^86 + 38 * q^87 - 8 * q^88 + 64 * q^90 - 16 * q^91 - 32 * q^92 - 70 * q^93 + 48 * q^94 - 64 * q^96 - 6 * q^97 - 282 * q^98 - 20 * q^99

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