LMFDB - Embedded newform 650.2.w.h.293.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(193,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("650.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 294x^{12} + 1516x^{10} + 4147x^{8} + 6012x^{6} + 4338x^{4} + 1296x^{2} + 81 $ x^16 + 28x^14 + 294x^12 + 1516x^10 + 4147x^8 + 6012x^6 + 4338x^4 + 1296*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.4
Root			$2.05387i$ of defining polynomial
Character	$\chi$	$=$	650.293
Dual form			650.2.w.h.457.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(1.98389 - 0.531582i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.531582 - 1.98389i) q^{6} +(2.67861 - 1.54650i) q^{7} -1.00000 q^{8} +(1.05516 - 0.609199i) q^{9} +(-0.858184 - 3.20278i) q^{11} +(-1.45231 - 1.45231i) q^{12} +(-1.43497 + 3.30770i) q^{13} -3.09300i q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.44746 - 5.40200i) q^{17} -1.21840i q^{18} +(0.296610 + 0.0794764i) q^{19} +(4.49199 - 4.49199i) q^{21} +(-3.20278 - 0.858184i) q^{22} +(1.35327 + 5.05047i) q^{23} +(-1.98389 + 0.531582i) q^{24} +(2.14706 + 2.89657i) q^{26} +(-2.58743 + 2.58743i) q^{27} +(-2.67861 - 1.54650i) q^{28} +(6.38628 + 3.68712i) q^{29} +(-1.42975 - 1.42975i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.40508 - 5.89778i) q^{33} +(-3.95454 - 3.95454i) q^{34} +(-1.05516 - 0.609199i) q^{36} +(-3.19191 - 1.84285i) q^{37} +(0.217134 - 0.217134i) q^{38} +(-1.08852 + 7.32491i) q^{39} +(9.05057 - 2.42509i) q^{41} +(-1.64418 - 6.13617i) q^{42} +(-9.26725 - 2.48315i) q^{43} +(-2.34460 + 2.34460i) q^{44} +(5.05047 + 1.35327i) q^{46} +5.28553i q^{47} +(-0.531582 + 1.98389i) q^{48} +(1.28332 - 2.22277i) q^{49} -11.4864i q^{51} +(3.58204 - 0.411124i) q^{52} +(2.01746 + 2.01746i) q^{53} +(0.947067 + 3.53450i) q^{54} +(-2.67861 + 1.54650i) q^{56} +0.630690 q^{57} +(6.38628 - 3.68712i) q^{58} +(-0.224282 + 0.837031i) q^{59} +(2.36485 + 4.09605i) q^{61} +(-1.95307 + 0.523324i) q^{62} +(1.88425 - 3.26362i) q^{63} +1.00000 q^{64} -6.81017 q^{66} +(-1.62782 + 2.81947i) q^{67} +(-5.40200 + 1.44746i) q^{68} +(5.36948 + 9.30021i) q^{69} +(-1.79018 + 6.68104i) q^{71} +(-1.05516 + 0.609199i) q^{72} -11.2058 q^{73} +(-3.19191 + 1.84285i) q^{74} +(-0.0794764 - 0.296610i) q^{76} +(-7.25185 - 7.25185i) q^{77} +(5.79930 + 4.60514i) q^{78} -4.04811i q^{79} +(-5.58535 + 9.67411i) q^{81} +(2.42509 - 9.05057i) q^{82} +5.45554i q^{83} +(-6.13617 - 1.64418i) q^{84} +(-6.78410 + 6.78410i) q^{86} +(14.6297 + 3.92001i) q^{87} +(0.858184 + 3.20278i) q^{88} +(7.03958 - 1.88625i) q^{89} +(1.27160 + 11.0792i) q^{91} +(3.69720 - 3.69720i) q^{92} +(-3.59649 - 2.07643i) q^{93} +(4.57740 + 2.64276i) q^{94} +(1.45231 + 1.45231i) q^{96} +(7.07877 + 12.2608i) q^{97} +(-1.28332 - 2.22277i) q^{98} +(-2.85666 - 2.85666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.98389	−	0.531582i	1.14540	−	0.306909i	0.364279	−	0.931290i	$-0.381315\pi$
$3$	1.98389	−	0.531582i	1.14540	−	0.306909i	0.781120	+	0.624381i	$0.214649\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.531582	−	1.98389i	0.217017	−	0.809920i
$7$	2.67861	−	1.54650i	1.01242	−	0.584522i	0.100522	−	0.994935i	$-0.467949\pi$
$7$	2.67861	−	1.54650i	1.01242	−	0.584522i	0.911900	+	0.410413i	$0.134616\pi$
$8$	−1.00000			−0.353553
$9$	1.05516	−	0.609199i	0.351721	−	0.203066i
$10$		0			0
$11$	−0.858184	−	3.20278i	−0.258752	−	0.965676i	−0.965964	−	0.258675i	$-0.916714\pi$
$11$	−0.858184	−	3.20278i	−0.258752	−	0.965676i	0.707212	−	0.707001i	$-0.249952\pi$
$12$	−1.45231	−	1.45231i	−0.419245	−	0.419245i
$13$	−1.43497	+	3.30770i	−0.397990	+	0.917390i
$13$	−1.43497	+	3.30770i	−0.397990	+	0.917390i
$14$		−	3.09300i		−	0.826638i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.44746	−	5.40200i	0.351061	−	1.31018i	−0.534309	−	0.845289i	$-0.679428\pi$
$17$	1.44746	−	5.40200i	0.351061	−	1.31018i	0.885370	−	0.464887i	$-0.153905\pi$
$18$		−	1.21840i		−	0.287179i
$19$	0.296610	+	0.0794764i	0.0680470	+	0.0182331i	0.292682	−	0.956210i	$-0.405452\pi$
$19$	0.296610	+	0.0794764i	0.0680470	+	0.0182331i	−0.224635	+	0.974443i	$0.572119\pi$
$20$		0			0
$21$	4.49199	−	4.49199i	0.980232	−	0.980232i
$22$	−3.20278	−	0.858184i	−0.682836	−	0.182965i
$23$	1.35327	+	5.05047i	0.282176	+	1.05310i	0.950878	+	0.309566i	$0.100184\pi$
$23$	1.35327	+	5.05047i	0.282176	+	1.05310i	−0.668702	+	0.743531i	$0.733150\pi$
$24$	−1.98389	+	0.531582i	−0.404960	+	0.108509i
$25$		0			0
$26$	2.14706	+	2.89657i	0.421073	+	0.568064i
$27$	−2.58743	+	2.58743i	−0.497952	+	0.497952i
$28$	−2.67861	−	1.54650i	−0.506211	−	0.292261i
$29$	6.38628	+	3.68712i	1.18590	+	0.684682i	0.957373	−	0.288855i	$-0.0932746\pi$
$29$	6.38628	+	3.68712i	1.18590	+	0.684682i	0.228530	+	0.973537i	$0.426608\pi$
$30$		0			0
$31$	−1.42975	−	1.42975i	−0.256790	−	0.256790i	0.566957	−	0.823747i	$-0.308121\pi$
$31$	−1.42975	−	1.42975i	−0.256790	−	0.256790i	−0.823747	+	0.566957i	$0.808121\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.40508	−	5.89778i	−0.592749	−	1.02667i
$34$	−3.95454	−	3.95454i	−0.678197	−	0.678197i
$35$		0			0
$36$	−1.05516	−	0.609199i	−0.175861	−	0.101533i
$37$	−3.19191	−	1.84285i	−0.524747	−	0.302963i	0.214128	−	0.976806i	$-0.431309\pi$
$37$	−3.19191	−	1.84285i	−0.524747	−	0.302963i	−0.738875	+	0.673843i	$0.764642\pi$
$38$	0.217134	−	0.217134i	0.0352237	−	0.0352237i
$39$	−1.08852	+	7.32491i	−0.174303	+	1.17292i
$40$		0			0
$41$	9.05057	−	2.42509i	1.41346	−	0.378736i	0.530302	−	0.847809i	$-0.322078\pi$
$41$	9.05057	−	2.42509i	1.41346	−	0.378736i	0.883160	+	0.469073i	$0.155412\pi$
$42$	−1.64418	−	6.13617i	−0.253703	−	0.946831i
$43$	−9.26725	−	2.48315i	−1.41324	−	0.378677i	−0.530161	−	0.847897i	$-0.677868\pi$
$43$	−9.26725	−	2.48315i	−1.41324	−	0.378677i	−0.883081	+	0.469220i	$0.844535\pi$
$44$	−2.34460	+	2.34460i	−0.353462	+	0.353462i
$45$		0			0
$46$	5.05047	+	1.35327i	0.744651	+	0.199529i
$47$			5.28553i			0.770973i	0.922713	+	0.385487i	$0.125966\pi$
$47$			5.28553i			0.770973i	−0.922713	+	0.385487i	$0.874034\pi$
$48$	−0.531582	+	1.98389i	−0.0767272	+	0.286350i
$49$	1.28332	−	2.22277i	0.183331	−	0.317539i
$50$		0			0
$51$		−	11.4864i		−	1.60842i
$52$	3.58204	−	0.411124i	0.496739	−	0.0570126i
$53$	2.01746	+	2.01746i	0.277119	+	0.277119i	0.831958	−	0.554839i	$-0.187220\pi$
$53$	2.01746	+	2.01746i	0.277119	+	0.277119i	−0.554839	+	0.831958i	$0.687220\pi$
$54$	0.947067	+	3.53450i	0.128879	+	0.480985i
$55$		0			0
$56$	−2.67861	+	1.54650i	−0.357945	+	0.206660i
$57$	0.630690			0.0835369
$58$	6.38628	−	3.68712i	0.838560	−	0.484143i
$59$	−0.224282	+	0.837031i	−0.0291990	+	0.108972i	−0.978987	−	0.203921i	$-0.934631\pi$
$59$	−0.224282	+	0.837031i	−0.0291990	+	0.108972i	0.949788	+	0.312893i	$0.101298\pi$
$60$		0			0
$61$	2.36485	+	4.09605i	0.302789	+	0.524445i	0.976767	−	0.214306i	$-0.0687490\pi$
$61$	2.36485	+	4.09605i	0.302789	+	0.524445i	−0.673978	+	0.738752i	$0.735416\pi$
$62$	−1.95307	+	0.523324i	−0.248040	+	0.0664622i
$63$	1.88425	−	3.26362i	0.237393	−	0.411178i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.81017			−0.838274
$67$	−1.62782	+	2.81947i	−0.198870	+	0.344454i	−0.948162	−	0.317786i	$-0.897061\pi$
$67$	−1.62782	+	2.81947i	−0.198870	+	0.344454i	0.749292	+	0.662240i	$0.230394\pi$
$68$	−5.40200	+	1.44746i	−0.655088	+	0.175530i
$69$	5.36948	+	9.30021i	0.646409	+	1.11961i
$70$		0			0
$71$	−1.79018	+	6.68104i	−0.212455	+	0.792894i	0.774592	+	0.632462i	$0.217955\pi$
$71$	−1.79018	+	6.68104i	−0.212455	+	0.792894i	−0.987047	+	0.160432i	$0.948711\pi$
$72$	−1.05516	+	0.609199i	−0.124352	+	0.0717948i
$73$	−11.2058			−1.31154			−0.655769	−	0.754962i	$-0.727655\pi$
$73$	−11.2058			−1.31154			−0.655769	+	0.754962i	$0.727655\pi$
$74$	−3.19191	+	1.84285i	−0.371052	+	0.214227i
$75$		0			0
$76$	−0.0794764	−	0.296610i	−0.00911657	−	0.0340235i
$77$	−7.25185	−	7.25185i	−0.826425	−	0.826425i
$78$	5.79930	+	4.60514i	0.656641	+	0.521430i
$79$		−	4.04811i		−	0.455447i	−0.973726	−	0.227724i	$-0.926872\pi$
$79$		−	4.04811i		−	0.455447i	0.973726	−	0.227724i	$-0.0731283\pi$
$80$		0			0
$81$	−5.58535	+	9.67411i	−0.620594	+	1.07490i
$82$	2.42509	−	9.05057i	0.267807	−	0.999469i
$83$			5.45554i			0.598824i	0.954124	+	0.299412i	$0.0967904\pi$
$83$			5.45554i			0.598824i	−0.954124	+	0.299412i	$0.903210\pi$
$84$	−6.13617	−	1.64418i	−0.669511	−	0.179395i
$85$		0			0
$86$	−6.78410	+	6.78410i	−0.731548	+	0.731548i
$87$	14.6297	+	3.92001i	1.56847	+	0.420270i
$88$	0.858184	+	3.20278i	0.0914827	+	0.341418i
$89$	7.03958	−	1.88625i	0.746195	−	0.199942i	0.134365	−	0.990932i	$-0.457101\pi$
$89$	7.03958	−	1.88625i	0.746195	−	0.199942i	0.611829	+	0.790990i	$0.290434\pi$
$90$		0			0
$91$	1.27160	+	11.0792i	0.133300	+	1.16142i
$92$	3.69720	−	3.69720i	0.385460	−	0.385460i
$93$	−3.59649	−	2.07643i	−0.372939	−	0.215316i
$94$	4.57740	+	2.64276i	0.472123	+	0.272580i
$95$		0			0
$96$	1.45231	+	1.45231i	0.148226	+	0.148226i
$97$	7.07877	+	12.2608i	0.718741	+	1.24490i	0.961499	+	0.274808i	$0.0886144\pi$
$97$	7.07877	+	12.2608i	0.718741	+	1.24490i	−0.242758	+	0.970087i	$0.578052\pi$
$98$	−1.28332	−	2.22277i	−0.129635	−	0.224534i
$99$	−2.85666	−	2.85666i	−0.287105	−	0.287105i
$100$		0			0
$101$	−16.6110	−	9.59037i	−1.65286	−	0.954278i	−0.975890	−	0.218265i	$-0.929960\pi$
$101$	−16.6110	−	9.59037i	−1.65286	−	0.954278i	−0.676967	−	0.736013i	$-0.736706\pi$
$102$	−9.94752	−	5.74321i	−0.984952	−	0.568662i
$103$	12.8600	−	12.8600i	1.26713	−	1.26713i	0.319572	−	0.947562i	$-0.396461\pi$
$103$	12.8600	−	12.8600i	1.26713	−	1.26713i	0.947562	−	0.319572i	$-0.103539\pi$
$104$	1.43497	−	3.30770i	0.140711	−	0.324346i
$105$		0			0
$106$	2.75590	−	0.738441i	0.267677	−	0.0717238i
$107$	3.88333	+	14.4928i	0.375416	+	1.40107i	0.852736	+	0.522342i	$0.174941\pi$
$107$	3.88333	+	14.4928i	0.375416	+	1.40107i	−0.477321	+	0.878729i	$0.658392\pi$
$108$	3.53450	+	0.947067i	0.340108	+	0.0911315i
$109$	11.0597	−	11.0597i	1.05933	−	1.05933i	0.0612039	−	0.998125i	$-0.480506\pi$
$109$	11.0597	−	11.0597i	1.05933	−	1.05933i	0.998125	−	0.0612039i	$-0.0194940\pi$
$110$		0			0
$111$	−7.31203	−	1.95925i	−0.694027	−	0.185964i
$112$			3.09300i			0.292261i
$113$	−5.33080	+	19.8948i	−0.501480	+	1.87155i	−0.0112824	+	0.999936i	$0.503591\pi$
$113$	−5.33080	+	19.8948i	−0.501480	+	1.87155i	−0.490197	+	0.871611i	$0.663075\pi$
$114$	0.315345	−	0.546193i	0.0295347	−	0.0511557i
$115$		0			0
$116$		−	7.37425i		−	0.684682i
$117$	0.500913	+	4.36435i	0.0463094	+	0.403484i
$118$	0.612749	+	0.612749i	0.0564081	+	0.0564081i
$119$	−4.47699	−	16.7084i	−0.410405	−	1.53165i
$120$		0			0
$121$	0.00493000	−	0.00284634i	0.000448182	−	0.000258758i
$122$	4.72971			0.428208
$123$	16.6662	−	9.62224i	1.50274	−	0.867608i
$124$	−0.523324	+	1.95307i	−0.0469959	+	0.175391i
$125$		0			0
$126$	−1.88425	−	3.26362i	−0.167863	−	0.290746i
$127$	−19.4456	+	5.21043i	−1.72552	+	0.462351i	−0.979143	−	0.203175i	$-0.934874\pi$
$127$	−19.4456	+	5.21043i	−1.72552	+	0.462351i	−0.746375	+	0.665526i	$0.768207\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−19.7052			−1.73495
$130$		0			0
$131$	−8.12505			−0.709889			−0.354944	−	0.934887i	$-0.615500\pi$
$131$	−8.12505			−0.709889			−0.354944	+	0.934887i	$0.615500\pi$
$132$	−3.40508	+	5.89778i	−0.296374	+	0.513336i
$133$	0.917414	−	0.245820i	0.0795499	−	0.0213153i
$134$	1.62782	+	2.81947i	0.140623	+	0.243565i
$135$		0			0
$136$	−1.44746	+	5.40200i	−0.124119	+	0.463217i
$137$	17.9411	−	10.3583i	1.53281	−	0.884967i	0.533578	−	0.845751i	$-0.320847\pi$
$137$	17.9411	−	10.3583i	1.53281	−	0.884967i	0.999231	−	0.0392164i	$-0.0124862\pi$
$138$	10.7390			0.914161
$139$	−1.21848	+	0.703489i	−0.103350	+	0.0596691i	−0.550784	−	0.834648i	$-0.685671\pi$
$139$	−1.21848	+	0.703489i	−0.103350	+	0.0596691i	0.447434	+	0.894317i	$0.352338\pi$
$140$		0			0
$141$	2.80969	+	10.4859i	0.236619	+	0.883072i
$142$	4.89086	+	4.89086i	0.410432	+	0.410432i
$143$	11.8253	+	1.75730i	0.988882	+	0.146953i
$144$			1.21840i			0.101533i
$145$		0			0
$146$	−5.60289	+	9.70449i	−0.463699	+	0.803149i
$147$	1.36438	−	5.09193i	0.112532	−	0.419975i
$148$			3.68570i			0.302963i
$149$	0.934559	+	0.250414i	0.0765621	+	0.0205147i	0.296897	−	0.954910i	$-0.404048\pi$
$149$	0.934559	+	0.250414i	0.0765621	+	0.0205147i	−0.220335	+	0.975424i	$0.570715\pi$
$150$		0			0
$151$	15.4868	−	15.4868i	1.26030	−	1.26030i	0.309346	−	0.950950i	$-0.399890\pi$
$151$	15.4868	−	15.4868i	1.26030	−	1.26030i	0.950950	−	0.309346i	$-0.100110\pi$
$152$	−0.296610	−	0.0794764i	−0.0240582	−	0.00644639i
$153$	−1.76358	−	6.58179i	−0.142577	−	0.532106i
$154$	−9.90621	+	2.65436i	−0.798265	+	0.213894i
$155$		0			0
$156$	6.88782	−	2.71977i	0.551467	−	0.217756i
$157$	−10.8947	+	10.8947i	−0.869494	+	0.869494i	−0.992416	−	0.122923i	$-0.960773\pi$
$157$	−10.8947	+	10.8947i	−0.869494	+	0.869494i	0.122923	+	0.992416i	$0.460773\pi$
$158$	−3.50576	−	2.02405i	−0.278903	−	0.161025i
$159$	5.07486	+	2.92997i	0.402463	+	0.232362i
$160$		0			0
$161$	11.4354	+	11.4354i	0.901239	+	0.901239i
$162$	5.58535	+	9.67411i	0.438827	+	0.760070i
$163$	−9.23667	−	15.9984i	−0.723472	−	1.25309i	−0.959600	−	0.281368i	$-0.909212\pi$
$163$	−9.23667	−	15.9984i	−0.723472	−	1.25309i	0.236128	−	0.971722i	$-0.424122\pi$
$164$	−6.62548	−	6.62548i	−0.517363	−	0.517363i
$165$		0			0
$166$	4.72464	+	2.72777i	0.366703	+	0.211716i
$167$	8.69635	+	5.02084i	0.672944	+	0.388524i	0.797191	−	0.603727i	$-0.206318\pi$
$167$	8.69635	+	5.02084i	0.672944	+	0.388524i	−0.124247	+	0.992251i	$0.539652\pi$
$168$	−4.49199	+	4.49199i	−0.346564	+	0.346564i
$169$	−8.88170	−	9.49291i	−0.683208	−	0.730224i
$170$		0			0
$171$	0.361389	−	0.0968339i	0.0276361	−	0.00740508i
$172$	2.48315	+	9.26725i	0.189338	+	0.706621i
$173$	6.77265	+	1.81473i	0.514915	+	0.137971i	0.506914	−	0.861997i	$-0.330786\pi$
$173$	6.77265	+	1.81473i	0.514915	+	0.137971i	0.00800159	+	0.999968i	$0.497453\pi$
$174$	10.7097	−	10.7097i	0.811899	−	0.811899i
$175$		0			0
$176$	3.20278	+	0.858184i	0.241419	+	0.0646880i
$177$			1.77980i			0.133778i
$178$	1.88625	−	7.03958i	0.141380	−	0.527639i
$179$	−5.58297	+	9.66999i	−0.417291	+	0.722769i	−0.995666	−	0.0930022i	$-0.970354\pi$
$179$	−5.58297	+	9.66999i	−0.417291	+	0.722769i	0.578375	+	0.815771i	$0.303687\pi$
$180$		0			0
$181$			8.49811i			0.631659i	0.948816	+	0.315830i	$0.102283\pi$
$181$			8.49811i			0.631659i	−0.948816	+	0.315830i	$0.897717\pi$
$182$	10.2307	+	4.43837i	0.758350	+	0.328994i
$183$	6.86900	+	6.86900i	0.507771	+	0.507771i
$184$	−1.35327	−	5.05047i	−0.0997644	−	0.372326i
$185$		0			0
$186$	−3.59649	+	2.07643i	−0.263707	+	0.152252i
$187$	−18.5436			−1.35604
$188$	4.57740	−	2.64276i	0.333841	−	0.192743i
$189$	−2.92928	+	10.9322i	−0.213073	+	0.795201i
$190$		0			0
$191$	−4.12152	−	7.13868i	−0.298223	−	0.516537i	0.677507	−	0.735517i	$-0.263060\pi$
$191$	−4.12152	−	7.13868i	−0.298223	−	0.516537i	−0.975729	+	0.218980i	$0.929727\pi$
$192$	1.98389	−	0.531582i	0.143175	−	0.0383636i
$193$	−9.67501	+	16.7576i	−0.696422	+	1.20624i	0.273276	+	0.961936i	$0.411893\pi$
$193$	−9.67501	+	16.7576i	−0.696422	+	1.20624i	−0.969699	+	0.244303i	$0.921441\pi$
$194$	14.1575			1.01645
$195$		0			0
$196$	−2.56664			−0.183331
$197$	1.38910	−	2.40599i	0.0989691	−	0.171419i	−0.812289	−	0.583255i	$-0.801779\pi$
$197$	1.38910	−	2.40599i	0.0989691	−	0.171419i	0.911258	+	0.411836i	$0.135112\pi$
$198$	−3.90227	+	1.04561i	−0.277322	+	0.0743082i
$199$	6.86305	+	11.8872i	0.486509	+	0.842658i	0.999880	−	0.0155087i	$-0.00493678\pi$
$199$	6.86305	+	11.8872i	0.486509	+	0.842658i	−0.513371	+	0.858167i	$0.671603\pi$
$200$		0			0
$201$	−1.73064	+	6.45885i	−0.122070	+	0.455572i
$202$	−16.6110	+	9.59037i	−1.16875	+	0.674776i
$203$	22.8085			1.60084
$204$	−9.94752	+	5.74321i	−0.696466	+	0.402105i
$205$		0			0
$206$	−4.70709	−	17.5671i	−0.327958	−	1.22396i
$207$	4.50467	+	4.50467i	0.313096	+	0.313096i
$208$	−2.14706	−	2.89657i	−0.148872	−	0.200841i
$209$		−	1.01818i		−	0.0704292i
$210$		0			0
$211$	−3.31873	+	5.74821i	−0.228471	+	0.395723i	−0.957355	−	0.288914i	$-0.906706\pi$
$211$	−3.31873	+	5.74821i	−0.228471	+	0.395723i	0.728884	+	0.684637i	$0.240039\pi$
$212$	0.738441	−	2.75590i	0.0507164	−	0.189276i
$213$			14.2061i			0.973385i
$214$	14.4928	+	3.88333i	0.990707	+	0.265459i
$215$		0			0
$216$	2.58743	−	2.58743i	0.176053	−	0.176053i
$217$	−6.04085	−	1.61864i	−0.410079	−	0.109880i
$218$	−4.04814	−	15.1079i	−0.274175	−	1.02323i
$219$	−22.2310	+	5.95679i	−1.50223	+	0.402522i
$220$		0			0
$221$	15.7911	+	12.5395i	1.06222	+	0.843497i
$222$	−5.35277	+	5.35277i	−0.359255	+	0.359255i
$223$	−11.5667	−	6.67804i	−0.774564	−	0.447195i	0.0599362	−	0.998202i	$-0.480910\pi$
$223$	−11.5667	−	6.67804i	−0.774564	−	0.447195i	−0.834500	+	0.551007i	$0.814244\pi$
$224$	2.67861	+	1.54650i	0.178972	+	0.103330i
$225$		0			0
$226$	14.5640	+	14.5640i	0.968784	+	0.968784i
$227$	−11.2947	−	19.5630i	−0.749654	−	1.29844i	−0.947989	−	0.318304i	$-0.896887\pi$
$227$	−11.2947	−	19.5630i	−0.749654	−	1.29844i	0.198335	−	0.980134i	$-0.436447\pi$
$228$	−0.315345	−	0.546193i	−0.0208842	−	0.0361725i
$229$	9.24789	+	9.24789i	0.611118	+	0.611118i	0.943237	−	0.332120i	$-0.107764\pi$
$229$	9.24789	+	9.24789i	0.611118	+	0.611118i	−0.332120	+	0.943237i	$0.607764\pi$
$230$		0			0
$231$	−18.2418	−	10.5319i	−1.20022	−	0.692949i
$232$	−6.38628	−	3.68712i	−0.419280	−	0.242071i
$233$	4.35174	−	4.35174i	0.285092	−	0.285092i	−0.550044	−	0.835136i	$-0.685389\pi$
$233$	4.35174	−	4.35174i	0.285092	−	0.285092i	0.835136	+	0.550044i	$0.185389\pi$
$234$	4.03009	+	1.74837i	0.263455	+	0.114295i
$235$		0			0
$236$	0.837031	−	0.224282i	0.0544861	−	0.0145995i
$237$	−2.15190	−	8.03100i	−0.139781	−	0.521669i
$238$	−16.7084	−	4.47699i	−1.08304	−	0.290200i
$239$	8.69193	−	8.69193i	0.562234	−	0.562234i	−0.367707	−	0.929942i	$-0.619857\pi$
$239$	8.69193	−	8.69193i	0.562234	−	0.562234i	0.929942	+	0.367707i	$0.119857\pi$
$240$		0			0
$241$	−11.7668	−	3.15290i	−0.757965	−	0.203096i	−0.140917	−	0.990021i	$-0.545005\pi$
$241$	−11.7668	−	3.15290i	−0.757965	−	0.203096i	−0.617048	+	0.786925i	$0.711672\pi$
$242$		−	0.00569267i		−	0.000365939i
$243$	−3.09694	+	11.5579i	−0.198669	+	0.741442i
$244$	2.36485	−	4.09605i	0.151394	−	0.262223i
$245$		0			0
$246$		−	19.2445i		−	1.22698i
$247$	−0.688511	+	0.867049i	−0.0438089	+	0.0551690i
$248$	1.42975	+	1.42975i	0.0907891	+	0.0907891i
$249$	2.90007	+	10.8232i	0.183784	+	0.685892i
$250$		0			0
$251$	−7.28805	+	4.20776i	−0.460017	+	0.265591i	−0.712052	−	0.702127i	$-0.752234\pi$
$251$	−7.28805	+	4.20776i	−0.460017	+	0.265591i	0.252034	+	0.967718i	$0.418900\pi$
$252$	−3.76850			−0.237393
$253$	15.0142	−	8.66846i	0.943936	−	0.544982i
$254$	−5.21043	+	19.4456i	−0.326932	+	1.22013i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.1929	+	2.73118i	−0.635815	+	0.170366i	−0.562307	−	0.826929i	$-0.690086\pi$
$257$	−10.1929	+	2.73118i	−0.635815	+	0.170366i	−0.0735078	+	0.997295i	$0.523419\pi$
$258$	−9.85260	+	17.0652i	−0.613396	+	1.06243i
$259$	−11.3999			−0.708353
$260$		0			0
$261$	8.98477			0.556143
$262$	−4.06252	+	7.03650i	−0.250984	+	0.434716i
$263$	2.38132	−	0.638074i	0.146839	−	0.0393453i	−0.184651	−	0.982804i	$-0.559115\pi$
$263$	2.38132	−	0.638074i	0.146839	−	0.0393453i	0.331490	+	0.943459i	$0.392449\pi$
$264$	3.40508	+	5.89778i	0.209568	+	0.362983i
$265$		0			0
$266$	0.245820	−	0.917414i	0.0150722	−	0.0562503i
$267$	12.9631	−	7.48423i	0.793327	−	0.458027i
$268$	3.25565			0.198870
$269$	3.93326	−	2.27087i	0.239815	−	0.138457i	−0.375277	−	0.926913i	$-0.622452\pi$
$269$	3.93326	−	2.27087i	0.239815	−	0.138457i	0.615092	+	0.788456i	$0.289119\pi$
$270$		0			0
$271$	−3.40254	−	12.6985i	−0.206690	−	0.771376i	−0.988928	−	0.148397i	$-0.952589\pi$
$271$	−3.40254	−	12.6985i	−0.206690	−	0.771376i	0.782238	−	0.622979i	$-0.214078\pi$
$272$	3.95454	+	3.95454i	0.239779	+	0.239779i
$273$	8.41224	+	21.3040i	0.509132	+	1.28938i
$274$		−	20.7166i		−	1.25153i
$275$		0			0
$276$	5.36948	−	9.30021i	0.323205	−	0.559807i
$277$	5.14536	−	19.2027i	0.309154	−	1.15378i	−0.620155	−	0.784479i	$-0.712930\pi$
$277$	5.14536	−	19.2027i	0.309154	−	1.15378i	0.929310	−	0.369301i	$-0.120403\pi$
$278$			1.40698i			0.0843849i
$279$	−2.37962	−	0.637617i	−0.142464	−	0.0381732i
$280$		0			0
$281$	8.01061	−	8.01061i	0.477873	−	0.477873i	−0.426578	−	0.904451i	$-0.640281\pi$
$281$	8.01061	−	8.01061i	0.477873	−	0.477873i	0.904451	+	0.426578i	$0.140281\pi$
$282$	10.4859	+	2.80969i	0.624426	+	0.167315i
$283$	−6.33709	−	23.6504i	−0.376701	−	1.40587i	−0.850843	−	0.525419i	$-0.823908\pi$
$283$	−6.33709	−	23.6504i	−0.376701	−	1.40587i	0.474142	−	0.880448i	$-0.342758\pi$
$284$	6.68104	−	1.79018i	0.396447	−	0.106228i
$285$		0			0
$286$	7.43452	−	9.36236i	0.439613	−	0.553608i
$287$	20.4926	−	20.4926i	1.20964	−	1.20964i
$288$	1.05516	+	0.609199i	0.0621762	+	0.0358974i
$289$	−12.3640	−	7.13836i	−0.727294	−	0.419903i
$290$		0			0
$291$	20.5611	+	20.5611i	1.20531	+	1.20531i
$292$	5.60289	+	9.70449i	0.327884	+	0.567912i
$293$	4.19722	+	7.26980i	0.245204	+	0.424706i	0.962189	−	0.272383i	$-0.0878116\pi$
$293$	4.19722	+	7.26980i	0.245204	+	0.424706i	−0.716985	+	0.697089i	$0.754478\pi$
$294$	−3.72755	−	3.72755i	−0.217395	−	0.217395i
$295$		0			0
$296$	3.19191	+	1.84285i	0.185526	+	0.107114i
$297$	10.5075	+	6.06650i	0.609706	+	0.352014i
$298$	0.684145	−	0.684145i	0.0396314	−	0.0396314i
$299$	−18.6473	−	2.77109i	−1.07840	−	0.160256i
$300$		0			0
$301$	−28.6636	+	7.68038i	−1.65214	+	0.442690i
$302$	−5.66855	−	21.1553i	−0.326188	−	1.21735i
$303$	−38.0525	−	10.1961i	−2.18606	−	0.585752i
$304$	−0.217134	+	0.217134i	−0.0124535	+	0.0124535i
$305$		0			0
$306$	−6.58179	−	1.76358i	−0.376256	−	0.100817i
$307$		−	12.9555i		−	0.739411i	−0.929149	−	0.369705i	$-0.879459\pi$
$307$		−	12.9555i		−	0.739411i	0.929149	−	0.369705i	$-0.120541\pi$
$308$	−2.65436	+	9.90621i	−0.151246	+	0.564458i
$309$	18.6767	−	32.3490i	1.06248	−	1.84027i
$310$		0			0
$311$		−	22.7786i		−	1.29165i	−0.763484	−	0.645827i	$-0.776513\pi$
$311$		−	22.7786i		−	1.29165i	0.763484	−	0.645827i	$-0.223487\pi$
$312$	1.08852	−	7.32491i	0.0616253	−	0.414691i
$313$	−21.0763	−	21.0763i	−1.19130	−	1.19130i	−0.976702	−	0.214598i	$-0.931156\pi$
$313$	−21.0763	−	21.0763i	−1.19130	−	1.19130i	−0.214598	−	0.976702i	$-0.568844\pi$
$314$	3.98775	+	14.8825i	0.225042	+	0.839866i
$315$		0			0
$316$	−3.50576	+	2.02405i	−0.197215	+	0.113862i
$317$	−8.94845			−0.502595			−0.251298	−	0.967910i	$-0.580857\pi$
$317$	−8.94845			−0.502595			−0.251298	+	0.967910i	$0.580857\pi$
$318$	5.07486	−	2.92997i	0.284584	−	0.164305i
$319$	6.32846	−	23.6181i	0.354326	−	1.32236i
$320$		0			0
$321$	15.4082	+	26.6878i	0.860002	+	1.48957i
$322$	15.6211	−	4.18566i	0.870530	−	0.233258i
$323$	0.858662	−	1.48725i	0.0477772	−	0.0827526i
$324$	11.1707			0.620594
$325$		0			0
$326$	−18.4733			−1.02314
$327$	16.0621	−	27.8204i	0.888238	−	1.53847i
$328$	−9.05057	+	2.42509i	−0.499734	+	0.133903i
$329$	8.17406	+	14.1579i	0.450651	+	0.780550i
$330$		0			0
$331$	6.01802	−	22.4596i	0.330780	−	1.23449i	−0.577592	−	0.816326i	$-0.696007\pi$
$331$	6.01802	−	22.4596i	0.330780	−	1.23449i	0.908372	−	0.418163i	$-0.137326\pi$
$332$	4.72464	−	2.72777i	0.259298	−	0.149706i
$333$	−4.49065			−0.246086
$334$	8.69635	−	5.02084i	0.475843	−	0.274728i
$335$		0			0
$336$	1.64418	+	6.13617i	0.0896974	+	0.334755i
$337$	−1.94311	−	1.94311i	−0.105848	−	0.105848i	0.652199	−	0.758047i	$-0.273846\pi$
$337$	−1.94311	−	1.94311i	−0.105848	−	0.105848i	−0.758047	+	0.652199i	$0.773846\pi$
$338$	−12.6620	+	2.94532i	−0.688720	+	0.160204i
$339$			42.3029i			2.29758i
$340$		0			0
$341$	−3.35219	+	5.80616i	−0.181531	+	0.314421i
$342$	0.0968339	−	0.361389i	0.00523618	−	0.0195417i
$343$			13.7124i			0.740399i
$344$	9.26725	+	2.48315i	0.499656	+	0.133883i
$345$		0			0
$346$	4.95792	−	4.95792i	0.266540	−	0.266540i
$347$	−4.85295	−	1.30034i	−0.260520	−	0.0698062i	0.126195	−	0.992005i	$-0.459724\pi$
$347$	−4.85295	−	1.30034i	−0.260520	−	0.0698062i	−0.386715	+	0.922199i	$0.626390\pi$
$348$	−3.92001	−	14.6297i	−0.210135	−	0.784234i
$349$	4.75638	−	1.27447i	0.254603	−	0.0682207i	−0.129260	−	0.991611i	$-0.541260\pi$
$349$	4.75638	−	1.27447i	0.254603	−	0.0682207i	0.383863	+	0.923390i	$0.374593\pi$
$350$		0			0
$351$	−4.84554	−	12.2713i	−0.258636	−	0.654996i
$352$	2.34460	−	2.34460i	0.124968	−	0.124968i
$353$	−16.8260	−	9.71447i	−0.895556	−	0.517049i	−0.0198000	−	0.999804i	$-0.506303\pi$
$353$	−16.8260	−	9.71447i	−0.895556	−	0.517049i	−0.875756	+	0.482755i	$0.839636\pi$
$354$	1.54135	+	0.889901i	0.0819220	+	0.0472977i
$355$		0			0
$356$	−5.15333	−	5.15333i	−0.273126	−	0.273126i
$357$	−17.7637	−	30.7677i	−0.940156	−	1.62840i
$358$	5.58297	+	9.66999i	0.295069	+	0.511075i
$359$	−9.43437	−	9.43437i	−0.497927	−	0.497927i	0.412865	−	0.910792i	$-0.364528\pi$
$359$	−9.43437	−	9.43437i	−0.497927	−	0.497927i	−0.910792	+	0.412865i	$0.864528\pi$
$360$		0			0
$361$	−16.3728	−	9.45285i	−0.861727	−	0.497519i
$362$	7.35958	+	4.24905i	0.386811	+	0.223325i
$363$	0.00826752	−	0.00826752i	0.000433932	−	0.000433932i
$364$	8.95909	−	6.64086i	0.469584	−	0.348075i
$365$		0			0
$366$	9.38322	−	2.51423i	0.490469	−	0.131421i
$367$	−3.45913	−	12.9097i	−0.180565	−	0.673879i	−0.995537	−	0.0943773i	$-0.969914\pi$
$367$	−3.45913	−	12.9097i	−0.180565	−	0.673879i	0.814971	−	0.579501i	$-0.196753\pi$
$368$	−5.05047	−	1.35327i	−0.263274	−	0.0705441i
$369$	8.07248	−	8.07248i	0.420236	−	0.420236i
$370$		0			0
$371$	8.52400	+	2.28400i	0.442544	+	0.118579i
$372$			4.15287i			0.215316i
$373$	−3.04619	+	11.3685i	−0.157726	+	0.588640i	0.841131	+	0.540831i	$0.181890\pi$
$373$	−3.04619	+	11.3685i	−0.157726	+	0.588640i	−0.998857	+	0.0478083i	$0.984776\pi$
$374$	−9.27181	+	16.0592i	−0.479434	+	0.830404i
$375$		0			0
$376$		−	5.28553i		−	0.272580i
$377$	−21.3600	+	15.8330i	−1.10010	+	0.815439i
$378$	8.00293	+	8.00293i	0.411626	+	0.411626i
$379$	−9.33409	−	34.8353i	−0.479460	−	1.78937i	−0.603806	−	0.797131i	$-0.706350\pi$
$379$	−9.33409	−	34.8353i	−0.479460	−	1.78937i	0.124346	−	0.992239i	$-0.460317\pi$
$380$		0			0
$381$	−35.8082	+	20.6738i	−1.83451	+	1.05915i
$382$	−8.24304			−0.421750
$383$	−12.4594	+	7.19342i	−0.636644	+	0.367567i	−0.783321	−	0.621618i	$-0.786476\pi$
$383$	−12.4594	+	7.19342i	−0.636644	+	0.367567i	0.146676	+	0.989185i	$0.453142\pi$
$384$	0.531582	−	1.98389i	0.0271272	−	0.101240i
$385$		0			0
$386$	9.67501	+	16.7576i	0.492445	+	0.852940i
$387$	−11.2912	+	3.02547i	−0.573964	+	0.153793i
$388$	7.07877	−	12.2608i	0.359370	−	0.622448i
$389$	−25.0361			−1.26938			−0.634690	−	0.772767i	$-0.718872\pi$
$389$	−25.0361			−1.26938			−0.634690	+	0.772767i	$0.718872\pi$
$390$		0			0
$391$	29.2414			1.47880
$392$	−1.28332	+	2.22277i	−0.0648174	+	0.112267i
$393$	−16.1192	+	4.31913i	−0.813106	+	0.217871i
$394$	−1.38910	−	2.40599i	−0.0699817	−	0.121212i
$395$		0			0
$396$	−1.04561	+	3.90227i	−0.0525439	+	0.196096i
$397$	−0.997605	+	0.575967i	−0.0500683	+	0.0289070i	−0.524825	−	0.851210i	$-0.675869\pi$
$397$	−0.997605	+	0.575967i	−0.0500683	+	0.0289070i	0.474757	+	0.880117i	$0.342536\pi$
$398$	13.7261			0.688027
$399$	1.68937	−	0.975361i	0.0845745	−	0.0488291i
$400$		0			0
$401$	0.140834	+	0.525598i	0.00703290	+	0.0262471i	0.969353	−	0.245672i	$-0.0790085\pi$
$401$	0.140834	+	0.525598i	0.00703290	+	0.0262471i	−0.962320	+	0.271919i	$0.912342\pi$
$402$	4.72820	+	4.72820i	0.235821	+	0.235821i
$403$	6.78082	−	2.67752i	0.337777	−	0.133377i
$404$			19.1807i			0.954278i
$405$		0			0
$406$	11.4043	−	19.7528i	0.565984	−	0.980313i
$407$	−3.16301	+	11.8045i	−0.156784	+	0.585128i
$408$			11.4864i			0.568662i
$409$	−0.850870	−	0.227990i	−0.0420728	−	0.0112734i	0.237721	−	0.971333i	$-0.423600\pi$
$409$	−0.850870	−	0.227990i	−0.0420728	−	0.0112734i	−0.279794	+	0.960060i	$0.590266\pi$
$410$		0			0
$411$	30.0868	−	30.0868i	1.48407	−	1.48407i
$412$	−17.5671	−	4.70709i	−0.865469	−	0.231902i
$413$	0.693703	+	2.58894i	0.0341349	+	0.127393i
$414$	6.15349	−	1.64882i	0.302427	−	0.0810352i
$415$		0			0
$416$	−3.58204	+	0.411124i	−0.175624	+	0.0201570i
$417$	−2.04336	+	2.04336i	−0.100064	+	0.100064i
$418$	−0.881772	−	0.509091i	−0.0431289	−	0.0249005i
$419$	5.40969	+	3.12329i	0.264281	+	0.152583i	0.626286	−	0.779594i	$-0.284574\pi$
$419$	5.40969	+	3.12329i	0.264281	+	0.152583i	−0.362005	+	0.932176i	$0.617908\pi$
$420$		0			0
$421$	11.2717	+	11.2717i	0.549350	+	0.549350i	0.926253	−	0.376903i	$-0.123011\pi$
$421$	11.2717	+	11.2717i	0.549350	+	0.549350i	−0.376903	+	0.926253i	$0.623011\pi$
$422$	3.31873	+	5.74821i	0.161553	+	0.279819i
$423$	3.21994	+	5.57710i	0.156559	+	0.271168i
$424$	−2.01746	−	2.01746i	−0.0979765	−	0.0979765i
$425$		0			0
$426$	12.3028	+	7.10304i	0.596074	+	0.344144i
$427$	12.6691	+	7.31449i	0.613099	+	0.353973i
$428$	10.6095	−	10.6095i	0.512828	−	0.512828i
$429$	24.3943	−	2.79982i	1.17777	−	0.135177i
$430$		0			0
$431$	18.3079	−	4.90558i	0.881859	−	0.236293i	0.210650	−	0.977562i	$-0.432442\pi$
$431$	18.3079	−	4.90558i	0.881859	−	0.236293i	0.671209	+	0.741268i	$0.265775\pi$
$432$	−0.947067	−	3.53450i	−0.0455658	−	0.170054i
$433$	0.942040	+	0.252419i	0.0452715	+	0.0121305i	0.281384	−	0.959595i	$-0.409207\pi$
$433$	0.942040	+	0.252419i	0.0452715	+	0.0121305i	−0.236112	+	0.971726i	$0.575873\pi$
$434$	−4.42221	+	4.42221i	−0.212273	+	0.212273i
$435$		0			0
$436$	−15.1079	−	4.04814i	−0.723535	−	0.193871i
$437$			1.60557i			0.0768050i
$438$	−5.95679	+	22.2310i	−0.284626	+	1.06224i
$439$	−14.2275	+	24.6428i	−0.679042	+	1.17614i	0.296228	+	0.955117i	$0.404271\pi$
$439$	−14.2275	+	24.6428i	−0.679042	+	1.17614i	−0.975270	+	0.221018i	$0.929062\pi$
$440$		0			0
$441$		−	3.12719i		−	0.148914i
$442$	18.7551	−	7.40574i	0.892087	−	0.352255i
$443$	−2.04110	−	2.04110i	−0.0969755	−	0.0969755i	0.656955	−	0.753930i	$-0.271844\pi$
$443$	−2.04110	−	2.04110i	−0.0969755	−	0.0969755i	−0.753930	+	0.656955i	$0.771844\pi$
$444$	1.95925	+	7.31203i	0.0929819	+	0.347013i
$445$		0			0
$446$	−11.5667	+	6.67804i	−0.547700	+	0.316214i
$447$	1.98718			0.0939903
$448$	2.67861	−	1.54650i	0.126553	−	0.0730652i
$449$	1.94578	−	7.26176i	0.0918272	−	0.342704i	−0.904692	−	0.426066i	$-0.859899\pi$
$449$	1.94578	−	7.26176i	0.0918272	−	0.342704i	0.996519	+	0.0833622i	$0.0265658\pi$
$450$		0			0
$451$	−15.5341	−	26.9059i	−0.731472	−	1.26695i
$452$	19.8948	−	5.33080i	0.935774	−	0.250740i
$453$	22.4916	−	38.9565i	1.05675	−	1.83034i
$454$	−22.5894			−1.06017
$455$		0			0
$456$	−0.630690			−0.0295347
$457$	−14.8694	+	25.7545i	−0.695559	+	1.20474i	0.274433	+	0.961606i	$0.411510\pi$
$457$	−14.8694	+	25.7545i	−0.695559	+	1.20474i	−0.969992	+	0.243137i	$0.921823\pi$
$458$	12.6329	−	3.38496i	0.590294	−	0.158169i
$459$	10.2321	+	17.7225i	0.477594	+	0.827216i
$460$		0			0
$461$	10.2888	−	38.3985i	0.479199	−	1.78840i	−0.125671	−	0.992072i	$-0.540108\pi$
$461$	10.2888	−	38.3985i	0.479199	−	1.78840i	0.604870	−	0.796324i	$-0.293225\pi$
$462$	−18.2418	+	10.5319i	−0.848686	+	0.489989i
$463$	−7.01939			−0.326219			−0.163109	−	0.986608i	$-0.552152\pi$
$463$	−7.01939			−0.326219			−0.163109	+	0.986608i	$0.552152\pi$
$464$	−6.38628	+	3.68712i	−0.296476	+	0.171170i
$465$		0			0
$466$	−1.59285	−	5.94459i	−0.0737873	−	0.275378i
$467$	−2.05301	−	2.05301i	−0.0950020	−	0.0950020i	0.658009	−	0.753010i	$-0.271399\pi$
$467$	−2.05301	−	2.05301i	−0.0950020	−	0.0950020i	−0.753010	+	0.658009i	$0.771399\pi$
$468$	3.52918	−	2.61598i	0.163136	−	0.120924i
$469$			10.0697i			0.464976i
$470$		0			0
$471$	−15.8225	+	27.4054i	−0.729062	+	1.26277i
$472$	0.224282	−	0.837031i	0.0103234	−	0.0385275i
$473$			31.8120i			1.46272i
$474$	−8.03100	−	2.15190i	−0.368876	−	0.0988400i
$475$		0			0
$476$	−12.2314	+	12.2314i	−0.560624	+	0.560624i
$477$	3.35779	+	0.899716i	0.153742	+	0.0411952i
$478$	−3.18147	−	11.8734i	−0.145517	−	0.543077i
$479$	−2.82518	+	0.757005i	−0.129086	+	0.0345885i	−0.322784	−	0.946473i	$-0.604619\pi$
$479$	−2.82518	+	0.757005i	−0.129086	+	0.0345885i	0.193698	+	0.981061i	$0.437952\pi$
$480$		0			0
$481$	10.6759	−	7.91343i	0.486779	−	0.360821i
$482$	−8.61388	+	8.61388i	−0.392351	+	0.392351i
$483$	28.7655	+	16.6078i	1.30888	+	0.755680i
$484$	−0.00493000	−	0.00284634i	−0.000224091	−	0.000129379i
$485$		0			0
$486$	8.46100	+	8.46100i	0.383799	+	0.383799i
$487$	5.71146	+	9.89253i	0.258811	+	0.448274i	0.965924	−	0.258827i	$-0.0833360\pi$
$487$	5.71146	+	9.89253i	0.258811	+	0.448274i	−0.707113	+	0.707101i	$0.750003\pi$
$488$	−2.36485	−	4.09605i	−0.107052	−	0.185419i
$489$	−26.8290	−	26.8290i	−1.21325	−	1.21325i
$490$		0			0
$491$	23.3154	+	13.4612i	1.05221	+	0.607493i	0.923267	−	0.384159i	$-0.125508\pi$
$491$	23.3154	+	13.4612i	1.05221	+	0.607493i	0.128942	+	0.991652i	$0.458842\pi$
$492$	−16.6662	−	9.62224i	−0.751371	−	0.433804i
$493$	29.1617	−	29.1617i	1.31338	−	1.31338i
$494$	0.406631	+	1.02979i	0.0182952	+	0.0463326i
$495$		0			0
$496$	1.95307	−	0.523324i	0.0876955	−	0.0234979i
$497$	5.53702	+	20.6645i	0.248370	+	0.926928i
$498$	10.8232	+	2.90007i	0.484999	+	0.129955i
$499$	4.16213	−	4.16213i	0.186323	−	0.186323i	−0.607782	−	0.794104i	$-0.707940\pi$
$499$	4.16213	−	4.16213i	0.186323	−	0.186323i	0.794104	+	0.607782i	$0.207940\pi$
$500$		0			0
$501$	19.9216	+	5.33797i	0.890031	+	0.238483i
$502$			8.41551i			0.375603i
$503$	9.64719	−	36.0038i	0.430147	−	1.60533i	−0.322273	−	0.946647i	$-0.604447\pi$
$503$	9.64719	−	36.0038i	0.430147	−	1.60533i	0.752420	−	0.658684i	$-0.228886\pi$
$504$	−1.88425	+	3.26362i	−0.0839313	+	0.145373i
$505$		0			0
$506$		−	17.3369i		−	0.770720i
$507$	−22.6666	−	14.1115i	−1.00666	−	0.626716i
$508$	14.2352	+	14.2352i	0.631583	+	0.631583i
$509$	5.55465	+	20.7303i	0.246206	+	0.918852i	0.972774	+	0.231758i	$0.0744476\pi$
$509$	5.55465	+	20.7303i	0.246206	+	0.918852i	−0.726568	+	0.687095i	$0.758886\pi$
$510$		0			0
$511$	−30.0160	+	17.3297i	−1.32783	+	0.766622i
$512$	−1.00000			−0.0441942
$513$	−0.973099	+	0.561819i	−0.0429633	+	0.0248049i
$514$	−2.73118	+	10.1929i	−0.120467	+	0.449589i
$515$		0			0
$516$	9.85260	+	17.0652i	0.433736	+	0.751254i
$517$	16.9284	−	4.53595i	0.744510	−	0.199491i
$518$	−5.69993	+	9.87257i	−0.250441	+	0.433776i
$519$	14.4009			0.632128
$520$		0			0
$521$	10.7341			0.470271			0.235136	−	0.971963i	$-0.424447\pi$
$521$	10.7341			0.470271			0.235136	+	0.971963i	$0.424447\pi$
$522$	4.49239	−	7.78104i	0.196626	−	0.340567i
$523$	−11.0529	+	2.96161i	−0.483309	+	0.129502i	−0.492243	−	0.870458i	$-0.663823\pi$
$523$	−11.0529	+	2.96161i	−0.483309	+	0.129502i	0.00893386	+	0.999960i	$0.497156\pi$
$524$	4.06252	+	7.03650i	0.177472	+	0.307391i
$525$		0			0
$526$	0.638074	−	2.38132i	0.0278213	−	0.103831i
$527$	−9.79300	+	5.65399i	−0.426590	+	0.246292i
$528$	6.81017			0.296374
$529$	−3.75734	+	2.16930i	−0.163363	+	0.0943176i
$530$		0			0
$531$	0.273265	+	1.01984i	0.0118587	+	0.0442572i
$532$	−0.671594	−	0.671594i	−0.0291173	−	0.0291173i
$533$	−4.96587	+	33.4165i	−0.215096	+	1.44743i
$534$		−	14.9685i		−	0.647749i
$535$		0			0
$536$	1.62782	−	2.81947i	0.0703113	−	0.121783i
$537$	−5.93561	+	22.1520i	−0.256140	+	0.955929i
$538$		−	4.54174i		−	0.195808i
$539$	−8.22038	−	2.20265i	−0.354077	−	0.0948747i
$540$		0			0
$541$	−4.21032	+	4.21032i	−0.181016	+	0.181016i	−0.791798	−	0.610783i	$-0.790855\pi$
$541$	−4.21032	+	4.21032i	−0.181016	+	0.181016i	0.610783	+	0.791798i	$0.290855\pi$
$542$	−12.6985	−	3.40254i	−0.545445	−	0.146152i
$543$	4.51744	+	16.8593i	0.193862	+	0.723502i
$544$	5.40200	−	1.44746i	0.231609	−	0.0620594i
$545$		0			0
$546$	22.6559	+	3.36679i	0.969584	+	0.144085i
$547$	2.59861	−	2.59861i	0.111109	−	0.111109i	−0.649367	−	0.760475i	$-0.724966\pi$
$547$	2.59861	−	2.59861i	0.111109	−	0.111109i	0.760475	+	0.649367i	$0.224966\pi$
$548$	−17.9411	−	10.3583i	−0.766404	−	0.442484i
$549$	4.99062	+	2.88134i	0.212995	+	0.122972i
$550$		0			0
$551$	1.60120	+	1.60120i	0.0682132	+	0.0682132i
$552$	−5.36948	−	9.30021i	−0.228540	−	0.395843i
$553$	−6.26039	−	10.8433i	−0.266219	−	0.461105i
$554$	−14.0574	−	14.0574i	−0.597241	−	0.597241i
$555$		0			0
$556$	1.21848	+	0.703489i	0.0516750	+	0.0298346i
$557$	33.8572	+	19.5475i	1.43458	+	0.828253i	0.997465	−	0.0711544i	$-0.0226683\pi$
$557$	33.8572	+	19.5475i	1.43458	+	0.828253i	0.437111	+	0.899407i	$0.356002\pi$
$558$	−1.74200	+	1.74200i	−0.0737449	+	0.0737449i
$559$	21.5118	−	27.0900i	0.909851	−	1.14578i
$560$		0			0
$561$	−36.7885	+	9.85745i	−1.55321	+	0.416182i
$562$	−2.93209	−	10.9427i	−0.123683	−	0.461590i
$563$	4.53668	+	1.21560i	0.191198	+	0.0512314i	0.353147	−	0.935568i	$-0.385111\pi$
$563$	4.53668	+	1.21560i	0.191198	+	0.0512314i	−0.161949	+	0.986799i	$0.551778\pi$
$564$	7.67621	−	7.67621i	0.323227	−	0.323227i
$565$		0			0
$566$	−23.6504	−	6.33709i	−0.994099	−	0.266368i
$567$			34.5510i			1.45100i
$568$	1.79018	−	6.68104i	0.0751143	−	0.280330i
$569$	−12.7418	+	22.0694i	−0.534163	+	0.925197i	0.465041	+	0.885289i	$0.346040\pi$
$569$	−12.7418	+	22.0694i	−0.534163	+	0.925197i	−0.999203	+	0.0399078i	$0.987294\pi$
$570$		0			0
$571$			40.9077i			1.71193i	0.517031	+	0.855967i	$0.327037\pi$
$571$			40.9077i			1.71193i	−0.517031	+	0.855967i	$0.672963\pi$
$572$	−4.39078	−	11.1197i	−0.183588	−	0.464937i
$573$	−11.9714	−	11.9714i	−0.500114	−	0.500114i
$574$	−7.50081	−	27.9934i	−0.313078	−	1.16842i
$575$		0			0
$576$	1.05516	−	0.609199i	0.0439652	−	0.0253833i
$577$	26.6995			1.11151			0.555757	−	0.831345i	$-0.312429\pi$
$577$	26.6995			1.11151			0.555757	+	0.831345i	$0.312429\pi$
$578$	−12.3640	+	7.13836i	−0.514274	+	0.296916i
$579$	−10.2861	+	38.3883i	−0.427476	+	1.59536i
$580$		0			0
$581$	8.43699	+	14.6133i	0.350025	+	0.606262i
$582$	28.0870	−	7.52589i	1.16424	−	0.311958i
$583$	4.73014	−	8.19284i	0.195902	−	0.339313i
$584$	11.2058			0.463699
$585$		0			0
$586$	8.39444			0.346771
$587$	−10.2591	+	17.7692i	−0.423437	+	0.733414i	−0.996273	−	0.0862556i	$-0.972510\pi$
$587$	−10.2591	+	17.7692i	−0.423437	+	0.733414i	0.572836	+	0.819670i	$0.305843\pi$
$588$	−5.09193	+	1.36438i	−0.209987	+	0.0562660i
$589$	−0.310446	−	0.537709i	−0.0127917	−	0.0221559i
$590$		0			0
$591$	1.47684	−	5.51163i	0.0607490	−	0.226718i
$592$	3.19191	−	1.84285i	0.131187	−	0.0757407i
$593$	38.3032			1.57293			0.786463	−	0.617638i	$-0.211910\pi$
$593$	38.3032			1.57293			0.786463	+	0.617638i	$0.211910\pi$
$594$	10.5075	−	6.06650i	0.431127	−	0.248912i
$595$		0			0
$596$	−0.250414	−	0.934559i	−0.0102574	−	0.0382810i
$597$	19.9345	+	19.9345i	0.815866	+	0.815866i
$598$	−11.7235	+	14.7635i	−0.479410	+	0.603725i
$599$		−	34.5762i		−	1.41274i	−0.707841	−	0.706372i	$-0.750330\pi$
$599$		−	34.5762i		−	1.41274i	0.707841	−	0.706372i	$-0.249670\pi$
$600$		0			0
$601$	−11.6644	+	20.2033i	−0.475800	+	0.824111i	−0.999616	−	0.0277213i	$-0.991175\pi$
$601$	−11.6644	+	20.2033i	−0.475800	+	0.824111i	0.523815	+	0.851832i	$0.324508\pi$
$602$	−7.68038	+	28.6636i	−0.313029	+	1.16824i
$603$			3.96668i			0.161536i
$604$	−21.1553	−	5.66855i	−0.860798	−	0.230650i
$605$		0			0
$606$	−27.8563	+	27.8563i	−1.13159	+	1.13159i
$607$	8.46183	+	2.26734i	0.343455	+	0.0920286i	0.426424	−	0.904524i	$-0.359773\pi$
$607$	8.46183	+	2.26734i	0.343455	+	0.0920286i	−0.0829682	+	0.996552i	$0.526440\pi$
$608$	0.0794764	+	0.296610i	0.00322319	+	0.0120291i
$609$	45.2496	−	12.1246i	1.83361	−	0.491313i
$610$		0			0
$611$	−17.4829	−	7.58459i	−0.707283	−	0.306840i
$612$	−4.81820	+	4.81820i	−0.194764	+	0.194764i
$613$	11.6529	+	6.72783i	0.470658	+	0.271734i	0.716515	−	0.697572i	$-0.245736\pi$
$613$	11.6529	+	6.72783i	0.470658	+	0.271734i	−0.245857	+	0.969306i	$0.579069\pi$
$614$	−11.2198	−	6.47776i	−0.452795	−	0.261421i
$615$		0			0
$616$	7.25185	+	7.25185i	0.292185	+	0.292185i
$617$	−10.1487	−	17.5781i	−0.408571	−	0.707666i	0.586159	−	0.810196i	$-0.300639\pi$
$617$	−10.1487	−	17.5781i	−0.408571	−	0.707666i	−0.994730	+	0.102530i	$0.967306\pi$
$618$	−18.6767	−	32.3490i	−0.751287	−	1.30127i
$619$	5.02632	+	5.02632i	0.202025	+	0.202025i	0.800867	−	0.598842i	$-0.204372\pi$
$619$	5.02632	+	5.02632i	0.202025	+	0.202025i	−0.598842	+	0.800867i	$0.704372\pi$
$620$		0			0
$621$	−16.5693	−	9.56627i	−0.664902	−	0.383881i
$622$	−19.7268	−	11.3893i	−0.790973	−	0.456669i
$623$	15.9393	−	15.9393i	0.638593	−	0.638593i
$624$	−5.79930	−	4.60514i	−0.232158	−	0.184353i
$625$		0			0
$626$	−28.7907	+	7.71445i	−1.15071	+	0.308331i
$627$	−0.541247	−	2.01996i	−0.0216153	−	0.0806695i
$628$	14.8825	+	3.98775i	0.593875	+	0.159128i
$629$	−14.5752	+	14.5752i	−0.581153	+	0.581153i
$630$		0			0
$631$	−46.7953	−	12.5388i	−1.86289	−	0.499160i	−0.862909	−	0.505359i	$-0.831360\pi$
$631$	−46.7953	−	12.5388i	−1.86289	−	0.499160i	−0.999981	+	0.00619928i	$0.998027\pi$
$632$			4.04811i			0.161025i
$633$	−3.52836	+	13.1680i	−0.140240	+	0.523381i
$634$	−4.47423	+	7.74959i	−0.177694	+	0.307775i
$635$		0			0
$636$		−	5.85995i		−	0.232362i
$637$	5.51073	+	7.43445i	0.218343	+	0.294564i
$638$	−17.2897	−	17.2897i	−0.684504	−	0.684504i
$639$	2.18115	+	8.14018i	0.0862851	+	0.322020i
$640$		0			0
$641$	17.9994	−	10.3919i	0.710933	−	0.410457i	−0.100473	−	0.994940i	$-0.532036\pi$
$641$	17.9994	−	10.3919i	0.710933	−	0.410457i	0.811406	+	0.584482i	$0.198702\pi$
$642$	30.8164			1.21623
$643$	−42.0811	+	24.2955i	−1.65952	+	0.958122i	−0.686578	+	0.727056i	$0.740888\pi$
$643$	−42.0811	+	24.2955i	−1.65952	+	0.958122i	−0.972938	+	0.231066i	$0.925779\pi$
$644$	4.18566	−	15.6211i	0.164938	−	0.615558i
$645$		0			0
$646$	−0.858662	−	1.48725i	−0.0337836	−	0.0585149i
$647$	45.8784	−	12.2931i	1.80367	−	0.483291i	0.809125	−	0.587636i	$-0.199941\pi$
$647$	45.8784	−	12.2931i	1.80367	−	0.483291i	0.994541	+	0.104345i	$0.0332748\pi$
$648$	5.58535	−	9.67411i	0.219413	−	0.380035i
$649$	2.87330			0.112787
$650$		0			0
$651$	−12.8448			−0.503428
$652$	−9.23667	+	15.9984i	−0.361736	+	0.626545i
$653$	−5.25805	+	1.40889i	−0.205763	+	0.0551341i	−0.360228	−	0.932864i	$-0.617301\pi$
$653$	−5.25805	+	1.40889i	−0.205763	+	0.0551341i	0.154465	+	0.987998i	$0.450635\pi$
$654$	−16.0621	−	27.8204i	−0.628079	−	1.08786i
$655$		0			0
$656$	−2.42509	+	9.05057i	−0.0946840	+	0.353366i
$657$	−11.8239	+	6.82655i	−0.461296	+	0.266329i
$658$	16.3481			0.637316
$659$	7.60592	−	4.39128i	0.296285	−	0.171060i	−0.344488	−	0.938791i	$-0.611947\pi$
$659$	7.60592	−	4.39128i	0.296285	−	0.171060i	0.640773	+	0.767731i	$0.278614\pi$
$660$		0			0
$661$	8.59123	+	32.0629i	0.334160	+	1.24710i	0.904777	+	0.425886i	$0.140038\pi$
$661$	8.59123	+	32.0629i	0.334160	+	1.24710i	−0.570617	+	0.821217i	$0.693296\pi$
$662$	−16.4415	−	16.4415i	−0.639018	−	0.639018i
$663$	37.9935	+	16.4827i	1.47555	+	0.640135i
$664$		−	5.45554i		−	0.211716i
$665$		0			0
$666$	−2.24533	+	3.88902i	−0.0870046	+	0.150696i
$667$	−9.97934	+	37.2434i	−0.386402	+	1.44207i
$668$		−	10.0417i		−	0.388524i
$669$	−26.4970	−	7.09985i	−1.02443	−	0.274496i
$670$		0			0
$671$	11.0893	−	11.0893i	0.428097	−	0.428097i
$672$	6.13617	+	1.64418i	0.236708	+	0.0634257i
$673$	3.10579	+	11.5910i	0.119720	+	0.446799i	0.999597	−	0.0284021i	$-0.00904188\pi$
$673$	3.10579	+	11.5910i	0.119720	+	0.446799i	−0.879877	+	0.475201i	$0.842375\pi$
$674$	−2.65434	+	0.711228i	−0.102241	+	0.0273955i
$675$		0			0
$676$	−3.78026	+	12.4382i	−0.145394	+	0.478394i
$677$	−6.77198	+	6.77198i	−0.260268	+	0.260268i	−0.825163	−	0.564895i	$-0.808917\pi$
$677$	−6.77198	+	6.77198i	−0.260268	+	0.260268i	0.564895	+	0.825163i	$0.308917\pi$
$678$	36.6354	+	21.1515i	1.40697	+	0.812317i
$679$	37.9226	+	21.8946i	1.45534	+	0.840239i
$680$		0			0
$681$	−32.8067	−	32.8067i	−1.25716	−	1.25716i
$682$	3.35219	+	5.80616i	0.128362	+	0.222329i
$683$	−5.56074	−	9.63149i	−0.212776	−	0.368539i	0.739806	−	0.672820i	$-0.234917\pi$
$683$	−5.56074	−	9.63149i	−0.212776	−	0.368539i	−0.952582	+	0.304281i	$0.901584\pi$
$684$	−0.264555	−	0.264555i	−0.0101155	−	0.0101155i
$685$		0			0
$686$	11.8753	+	6.85619i	0.453400	+	0.261771i
$687$	23.2628	+	13.4308i	0.887531	+	0.512416i
$688$	6.78410	−	6.78410i	0.258641	−	0.258641i
$689$	−9.56814	+	3.77814i	−0.364517	+	0.143936i
$690$		0			0
$691$	17.2401	−	4.61947i	0.655845	−	0.175733i	0.0844748	−	0.996426i	$-0.473079\pi$
$691$	17.2401	−	4.61947i	0.655845	−	0.175733i	0.571370	+	0.820693i	$0.306412\pi$
$692$	−1.81473	−	6.77265i	−0.0689856	−	0.257458i
$693$	−12.0697	−	3.23407i	−0.458490	−	0.122852i
$694$	−3.55261	+	3.55261i	−0.134855	+	0.134855i
$695$		0			0
$696$	−14.6297	−	3.92001i	−0.554537	−	0.148588i
$697$		−	52.4014i		−	1.98484i
$698$	1.27447	−	4.75638i	0.0482393	−	0.180032i
$699$	6.32007	−	10.9467i	0.239047	−	0.414042i
$700$		0			0
$701$		−	2.93473i		−	0.110843i	−0.998463	−	0.0554216i	$-0.982350\pi$
$701$		−	2.93473i		−	0.110843i	0.998463	−	0.0554216i	$-0.0176503\pi$
$702$	−13.0501	−	1.93931i	−0.492543	−	0.0731945i
$703$	−0.800289	−	0.800289i	−0.0301835	−	0.0301835i
$704$	−0.858184	−	3.20278i	−0.0323440	−	0.120709i
$705$		0			0
$706$	−16.8260	+	9.71447i	−0.633253	+	0.365609i
$707$	−59.3260			−2.23118
$708$	1.54135	−	0.889901i	0.0579276	−	0.0334445i
$709$	8.59544	−	32.0786i	0.322809	−	1.20474i	−0.593688	−	0.804696i	$-0.702329\pi$
$709$	8.59544	−	32.0786i	0.322809	−	1.20474i	0.916496	−	0.400043i	$-0.131005\pi$
$710$		0			0
$711$	−2.46610	−	4.27142i	−0.0924861	−	0.160191i
$712$	−7.03958	+	1.88625i	−0.263820	+	0.0706902i
$713$	5.28607	−	9.15574i	0.197965	−	0.342885i
$714$	−35.5274			−1.32958
$715$		0			0
$716$	11.1659			0.417291
$717$	12.6234	−	21.8643i	0.471428	−	0.816538i
$718$	−12.8876	+	3.45322i	−0.480960	+	0.128873i
$719$	−1.02490	−	1.77519i	−0.0382225	−	0.0662033i	0.846281	−	0.532736i	$-0.178836\pi$
$719$	−1.02490	−	1.77519i	−0.0382225	−	0.0662033i	−0.884504	+	0.466533i	$0.845503\pi$
$720$		0			0
$721$	14.5590	−	54.3350i	0.542206	−	2.02354i
$722$	−16.3728	+	9.45285i	−0.609333	+	0.351799i
$723$	−25.0200			−0.930504
$724$	7.35958	−	4.24905i	0.273517	−	0.157915i
$725$		0			0
$726$	−0.00302612	−	0.0112936i	−0.000112310	−	0.000419146i
$727$	24.0232	+	24.0232i	0.890972	+	0.890972i	0.994615	−	0.103642i	$-0.0330498\pi$
$727$	24.0232	+	24.0232i	0.890972	+	0.890972i	−0.103642	+	0.994615i	$0.533050\pi$
$728$	−1.27160	−	11.0792i	−0.0471288	−	0.410624i
$729$		−	8.93615i		−	0.330968i
$730$		0			0
$731$	−26.8279	+	46.4674i	−0.992268	+	1.71866i
$732$	2.51423	−	9.38322i	0.0929285	−	0.346814i
$733$			18.4922i			0.683026i	0.939877	+	0.341513i	$0.110939\pi$
$733$			18.4922i			0.683026i	−0.939877	+	0.341513i	$0.889061\pi$
$734$	−12.9097	−	3.45913i	−0.476504	−	0.127679i
$735$		0			0
$736$	−3.69720	+	3.69720i	−0.136281	+	0.136281i
$737$	10.4271	+	2.79394i	0.384089	+	0.102916i
$738$	−2.95473	−	11.0272i	−0.108765	−	0.405917i
$739$	−29.9685	+	8.03003i	−1.10241	+	0.295389i	−0.763745	−	0.645518i	$-0.776641\pi$
$739$	−29.9685	+	8.03003i	−1.10241	+	0.295389i	−0.338663	+	0.940908i	$0.609975\pi$
$740$		0			0
$741$	−0.905023	+	2.08613i	−0.0332469	+	0.0766359i
$742$	6.24000	−	6.24000i	0.229078	−	0.229078i
$743$	11.4385	+	6.60401i	0.419637	+	0.242278i	0.694922	−	0.719085i	$-0.255439\pi$
$743$	11.4385	+	6.60401i	0.419637	+	0.242278i	−0.275285	+	0.961363i	$0.588772\pi$
$744$	3.59649	+	2.07643i	0.131854	+	0.0761258i
$745$		0			0
$746$	8.32234	+	8.32234i	0.304702	+	0.304702i
$747$	3.32351	+	5.75649i	0.121601	+	0.210619i
$748$	9.27181	+	16.0592i	0.339011	+	0.587184i
$749$	32.8150	+	32.8150i	1.19904	+	1.19904i
$750$		0			0
$751$	−3.68919	−	2.12995i	−0.134620	−	0.0777231i	0.431177	−	0.902267i	$-0.358098\pi$
$751$	−3.68919	−	2.12995i	−0.134620	−	0.0777231i	−0.565798	+	0.824544i	$0.691432\pi$
$752$	−4.57740	−	2.64276i	−0.166921	−	0.0963717i
$753$	−12.2219	+	12.2219i	−0.445391	+	0.445391i
$754$	3.03173	+	26.4148i	0.110409	+	0.961971i
$755$		0			0
$756$	10.9322	−	2.92928i	0.397600	−	0.106537i
$757$	−1.94143	−	7.24553i	−0.0705626	−	0.263343i	0.921628	−	0.388075i	$-0.126860\pi$
$757$	−1.94143	−	7.24553i	−0.0705626	−	0.263343i	−0.992191	+	0.124731i	$0.960193\pi$
$758$	−34.8353	−	9.33409i	−1.26528	−	0.339030i
$759$	25.1786	−	25.1786i	0.913924	−	0.913924i
$760$		0			0
$761$	−27.8397	−	7.45963i	−1.00919	−	0.270411i	−0.283898	−	0.958854i	$-0.591628\pi$
$761$	−27.8397	−	7.45963i	−1.00919	−	0.270411i	−0.725290	+	0.688443i	$0.758294\pi$
$762$			41.3477i			1.49787i
$763$	12.5209	−	46.7286i	0.453287	−	1.69169i
$764$	−4.12152	+	7.13868i	−0.149111	+	0.258268i
$765$		0			0
$766$			14.3868i			0.519818i
$767$	−2.44680	−	1.94297i	−0.0883490	−	0.0701567i
$768$	−1.45231	−	1.45231i	−0.0524057	−	0.0524057i
$769$	8.69883	+	32.4645i	0.313688	+	1.17070i	0.925205	+	0.379468i	$0.123893\pi$
$769$	8.69883	+	32.4645i	0.313688	+	1.17070i	−0.611517	+	0.791231i	$0.709440\pi$
$770$		0			0
$771$	−18.7697	+	10.8367i	−0.675975	+	0.390274i
$772$	19.3500			0.696422
$773$	22.3092	−	12.8802i	0.802406	−	0.463269i	−0.0419060	−	0.999122i	$-0.513343\pi$
$773$	22.3092	−	12.8802i	0.802406	−	0.463269i	0.844312	+	0.535852i	$0.180010\pi$
$774$	−3.02547	+	11.2912i	−0.108748	+	0.405854i
$775$		0			0
$776$	−7.07877	−	12.2608i	−0.254113	−	0.440137i
$777$	−22.6161	+	6.05996i	−0.811347	+	0.217400i
$778$	−12.5180	+	21.6819i	−0.448793	+	0.777333i
$779$	2.87723			0.103087
$780$		0			0
$781$	22.9342			0.820652
$782$	14.6207	−	25.3238i	0.522836	−	0.905578i
$783$	−26.0643	+	6.98390i	−0.931461	+	0.249584i
$784$	1.28332	+	2.22277i	0.0458328	+	0.0793847i
$785$		0			0
$786$	−4.31913	+	16.1192i	−0.154058	+	0.574953i
$787$	4.80892	−	2.77643i	0.171419	−	0.0989690i	−0.411836	−	0.911258i	$-0.635112\pi$
$787$	4.80892	−	2.77643i	0.171419	−	0.0989690i	0.583255	+	0.812289i	$0.301779\pi$
$788$	−2.77819			−0.0989691
$789$	4.38510	−	2.53174i	0.156114	−	0.0901322i
$790$		0			0
$791$	16.4882	+	61.5347i	0.586252	+	2.18792i
$792$	2.85666	+	2.85666i	0.101507	+	0.101507i
$793$	−16.9420	+	1.94450i	−0.601628	+	0.0690511i
$794$			1.15193i			0.0408806i
$795$		0			0
$796$	6.86305	−	11.8872i	0.243254	−	0.421329i
$797$	−4.54144	+	16.9489i	−0.160866	+	0.600360i	0.837665	+	0.546184i	$0.183920\pi$
$797$	−4.54144	+	16.9489i	−0.160866	+	0.600360i	−0.998531	+	0.0541763i	$0.982747\pi$
$798$		−	1.95072i		−	0.0690548i
$799$	28.5524	+	7.65059i	1.01011	+	0.270658i
$800$		0			0
$801$	6.27882	−	6.27882i	0.221851	−	0.221851i
$802$	0.525598	+	0.140834i	0.0185595	+	0.00497301i
$803$	9.61662	+	35.8897i	0.339363	+	1.26652i
$804$	6.45885	−	1.73064i	0.227786	−	0.0610351i
$805$		0			0
$806$	1.07161	−	7.21112i	0.0377459	−	0.254001i
$807$	6.59600	−	6.59600i	0.232190	−	0.232190i
$808$	16.6110	+	9.59037i	0.584373	+	0.337388i
$809$	23.4884	+	13.5610i	0.825807	+	0.476780i	0.852415	−	0.522866i	$-0.175137\pi$
$809$	23.4884	+	13.5610i	0.825807	+	0.476780i	−0.0266077	+	0.999646i	$0.508471\pi$
$810$		0			0
$811$	29.8312	+	29.8312i	1.04752	+	1.04752i	0.998813	+	0.0487028i	$0.0155087\pi$
$811$	29.8312	+	29.8312i	1.04752	+	1.04752i	0.0487028	+	0.998813i	$0.484491\pi$
$812$	−11.4043	−	19.7528i	−0.400211	−	0.693186i
$813$	−13.5005	−	23.3836i	−0.473484	−	0.820099i
$814$	8.64150	+	8.64150i	0.302884	+	0.302884i
$815$		0			0
$816$	9.94752	+	5.74321i	0.348233	+	0.201052i
$817$	−2.55141	−	1.47305i	−0.0892624	−	0.0515356i
$818$	−0.622880	+	0.622880i	−0.0217785	+	0.0217785i
$819$	8.09121	+	10.9157i	0.282730	+	0.381427i
$820$		0			0
$821$	37.8748	−	10.1485i	1.32184	−	0.354186i	0.472173	−	0.881506i	$-0.343470\pi$
$821$	37.8748	−	10.1485i	1.32184	−	0.354186i	0.849667	+	0.527320i	$0.176803\pi$
$822$	−11.0125	−	41.0994i	−0.384107	−	1.43351i
$823$	−3.25349	−	0.871770i	−0.113409	−	0.0303880i	0.201668	−	0.979454i	$-0.435364\pi$
$823$	−3.25349	−	0.871770i	−0.113409	−	0.0303880i	−0.315077	+	0.949066i	$0.602030\pi$
$824$	−12.8600	+	12.8600i	−0.448000	+	0.448000i
$825$		0			0
$826$	2.58894	+	0.693703i	0.0900806	+	0.0241370i
$827$		−	24.4923i		−	0.851680i	−0.904799	−	0.425840i	$-0.859979\pi$
$827$		−	24.4923i		−	0.851680i	0.904799	−	0.425840i	$-0.140021\pi$
$828$	1.64882	−	6.15349i	0.0573005	−	0.213849i
$829$	−23.7780	+	41.1847i	−0.825844	+	1.43040i	0.0754282	+	0.997151i	$0.475968\pi$
$829$	−23.7780	+	41.1847i	−0.825844	+	1.43040i	−0.901272	+	0.433253i	$0.857366\pi$
$830$		0			0
$831$		−	40.8313i		−	1.41642i
$832$	−1.43497	+	3.30770i	−0.0497488	+	0.114674i
$833$	−10.1499	−	10.1499i	−0.351672	−	0.351672i
$834$	0.747923	+	2.79129i	0.0258985	+	0.0966544i
$835$		0			0
$836$	−0.881772	+	0.509091i	−0.0304967	+	0.0176073i
$837$	7.39876			0.255738
$838$	5.40969	−	3.12329i	0.186875	−	0.107892i
$839$	−6.14365	+	22.9284i	−0.212102	+	0.791577i	0.775064	+	0.631883i	$0.217718\pi$
$839$	−6.14365	+	22.9284i	−0.212102	+	0.791577i	−0.987166	+	0.159694i	$0.948949\pi$
$840$		0			0
$841$	12.6897	+	21.9793i	0.437578	+	0.757907i
$842$	15.3975	−	4.12574i	0.530631	−	0.142182i
$843$	11.6339	−	20.1505i	0.400692	−	0.694019i
$844$	6.63747			0.228471
$845$		0			0
$846$	6.43988			0.221408
$847$	0.00880371	−	0.0152485i	0.000302499	−	0.000523944i
$848$	−2.75590	+	0.738441i	−0.0946380	+	0.0253582i
$849$	−25.1442	−	43.5510i	−0.862946	−	1.49467i
$850$		0			0
$851$	4.98775	−	18.6145i	0.170978	−	0.638098i
$852$	12.3028	−	7.10304i	0.421488	−	0.243346i
$853$	−42.9175			−1.46947			−0.734733	−	0.678356i	$-0.762693\pi$
$853$	−42.9175			−1.46947			−0.734733	+	0.678356i	$0.762693\pi$
$854$	12.6691	−	7.31449i	0.433527	−	0.250297i
$855$		0			0
$856$	−3.88333	−	14.4928i	−0.132730	−	0.495353i
$857$	11.4491	+	11.4491i	0.391095	+	0.391095i	0.875078	−	0.483983i	$-0.160810\pi$
$857$	11.4491	+	11.4491i	0.391095	+	0.391095i	−0.483983	+	0.875078i	$0.660810\pi$
$858$	9.77241	−	22.5260i	0.333625	−	0.769024i
$859$			27.2713i			0.930484i	0.885184	+	0.465242i	$0.154033\pi$
$859$			27.2713i			0.930484i	−0.885184	+	0.465242i	$0.845967\pi$
$860$		0			0
$861$	29.7616	−	51.5485i	1.01427	−	1.75677i
$862$	4.90558	−	18.3079i	0.167085	−	0.623569i
$863$		−	0.705520i		−	0.0240162i	−0.999928	−	0.0120081i	$-0.996178\pi$
$863$		−	0.705520i		−	0.0240162i	0.999928	−	0.0120081i	$-0.00382239\pi$
$864$	−3.53450	−	0.947067i	−0.120246	−	0.0322199i
$865$		0			0
$866$	0.689621	−	0.689621i	0.0234343	−	0.0234343i
$867$	−28.3234	−	7.58924i	−0.961914	−	0.257744i
$868$	1.61864	+	6.04085i	0.0549402	+	0.205040i
$869$	−12.9652	+	3.47402i	−0.439815	+	0.117848i
$870$		0			0
$871$	−6.99007	−	9.43022i	−0.236850	−	0.319531i
$872$	−11.0597	+	11.0597i	−0.374529	+	0.374529i
$873$	14.9385	+	8.62477i	0.505593	+	0.291904i
$874$	1.39047	+	0.802786i	0.0470332	+	0.0271547i
$875$		0			0
$876$	16.2742	+	16.2742i	0.549856	+	0.549856i
$877$	15.0148	+	26.0064i	0.507014	+	0.878175i	0.999967	+	0.00811852i	$0.00258423\pi$
$877$	15.0148	+	26.0064i	0.507014	+	0.878175i	−0.492953	+	0.870056i	$0.664082\pi$
$878$	14.2275	+	24.6428i	0.480155	+	0.831653i
$879$	12.1913	+	12.1913i	0.411203	+	0.411203i
$880$		0			0
$881$	14.5114	+	8.37819i	0.488903	+	0.282268i	0.724119	−	0.689675i	$-0.242246\pi$
$881$	14.5114	+	8.37819i	0.488903	+	0.282268i	−0.235216	+	0.971943i	$0.575580\pi$
$882$	−2.70822	−	1.56359i	−0.0911906	−	0.0526489i
$883$	8.90010	−	8.90010i	0.299512	−	0.299512i	−0.541311	−	0.840823i	$-0.682072\pi$
$883$	8.90010	−	8.90010i	0.299512	−	0.299512i	0.840823	+	0.541311i	$0.182072\pi$
$884$	2.96397	−	19.9452i	0.0996890	−	0.670831i
$885$		0			0
$886$	−2.78819	+	0.747094i	−0.0936712	+	0.0250991i
$887$	4.84233	+	18.0718i	0.162589	+	0.606792i	0.998335	+	0.0576758i	$0.0183690\pi$
$887$	4.84233	+	18.0718i	0.162589	+	0.606792i	−0.835746	+	0.549116i	$0.814964\pi$
$888$	7.31203	+	1.95925i	0.245375	+	0.0657482i
$889$	−44.0293	+	44.0293i	−1.47670	+	1.47670i
$890$		0			0
$891$	35.7773	+	9.58651i	1.19859	+	0.321160i
$892$			13.3561i			0.447195i
$893$	−0.420075	+	1.56774i	−0.0140573	+	0.0524624i
$894$	0.993589	−	1.72095i	0.0332306	−	0.0575571i
$895$		0			0
$896$		−	3.09300i		−	0.103330i
$897$	−38.4673	+	4.41504i	−1.28439	+	0.147414i
$898$	−5.31598	−	5.31598i	−0.177396	−	0.177396i
$899$	−3.85912	−	14.4024i	−0.128709	−	0.480348i
$900$		0			0
$901$	13.8185	−	7.97812i	0.460361	−	0.265790i
$902$	−31.0682			−1.03446
$903$	−52.7826	+	30.4741i	−1.75650	+	1.01411i
$904$	5.33080	−	19.8948i	0.177300	−	0.661692i
$905$		0			0
$906$	−22.4916	−	38.9565i	−0.747232	−	1.29424i
$907$	−39.2525	+	10.5177i	−1.30336	+	0.349234i	−0.842719	−	0.538353i	$-0.819047\pi$
$907$	−39.2525	+	10.5177i	−1.30336	+	0.349234i	−0.460639	+	0.887587i	$0.652380\pi$
$908$	−11.2947	+	19.5630i	−0.374827	+	0.649219i
$909$	−23.3698			−0.775127
$910$		0			0
$911$	−10.8365			−0.359029			−0.179515	−	0.983755i	$-0.557453\pi$
$911$	−10.8365			−0.359029			−0.179515	+	0.983755i	$0.557453\pi$
$912$	−0.315345	+	0.546193i	−0.0104421	+	0.0180863i
$913$	17.4729	−	4.68186i	0.578270	−	0.154947i
$914$	14.8694	+	25.7545i	0.491834	+	0.851882i
$915$		0			0
$916$	3.38496	−	12.6329i	0.111842	−	0.417401i
$917$	−21.7639	+	12.5654i	−0.718706	+	0.414945i
$918$	20.4642			0.675419
$919$	10.1608	−	5.86633i	0.335173	−	0.193512i	−0.322962	−	0.946412i	$-0.604679\pi$
$919$	10.1608	−	5.86633i	0.335173	−	0.193512i	0.658136	+	0.752899i	$0.271345\pi$
$920$		0			0
$921$	−6.88692	−	25.7023i	−0.226932	−	0.846921i
$922$	−28.1096	−	28.1096i	−0.925742	−	0.925742i
$923$	−19.5300	−	15.5085i	−0.642838	−	0.510468i
$924$			21.0638i			0.692949i
$925$		0			0
$926$	−3.50969	+	6.07897i	−0.115336	+	0.199767i
$927$	5.73511	−	21.4037i	0.188366	−	0.702991i
$928$			7.37425i			0.242071i
$929$	−5.95839	−	1.59655i	−0.195488	−	0.0523810i	0.159746	−	0.987158i	$-0.448932\pi$
$929$	−5.95839	−	1.59655i	−0.195488	−	0.0523810i	−0.355235	+	0.934777i	$0.615599\pi$
$930$		0			0
$931$	0.557303	−	0.557303i	0.0182649	−	0.0182649i
$932$	−5.94459	−	1.59285i	−0.194722	−	0.0521755i
$933$	−12.1087	−	45.1902i	−0.396420	−	1.47946i
$934$	−2.80446	+	0.751454i	−0.0917649	+	0.0245883i
$935$		0			0
$936$	−0.500913	−	4.36435i	−0.0163728	−	0.142653i
$937$	35.3132	−	35.3132i	1.15363	−	1.15363i	0.167812	−	0.985819i	$-0.446330\pi$
$937$	35.3132	−	35.3132i	1.15363	−	1.15363i	0.985819	−	0.167812i	$-0.0536701\pi$
$938$	8.72063	+	5.03486i	0.284739	+	0.164394i
$939$	−53.0167	−	30.6092i	−1.73014	−	0.998894i
$940$		0			0
$941$	−33.4441	−	33.4441i	−1.09025	−	1.09025i	−0.995501	−	0.0947459i	$-0.969796\pi$
$941$	−33.4441	−	33.4441i	−1.09025	−	1.09025i	−0.0947459	−	0.995501i	$-0.530204\pi$
$942$	15.8225	+	27.4054i	0.515525	+	0.892915i
$943$	24.4957	+	42.4279i	0.797691	+	1.38164i
$944$	−0.612749	−	0.612749i	−0.0199433	−	0.0199433i
$945$		0			0
$946$	27.5500	+	15.9060i	0.895728	+	0.517149i
$947$	−49.9648	−	28.8472i	−1.62364	−	0.937408i	−0.985936	−	0.167126i	$-0.946551\pi$
$947$	−49.9648	−	28.8472i	−1.62364	−	0.937408i	−0.637703	−	0.770282i	$-0.720115\pi$
$948$	−5.87910	+	5.87910i	−0.190944	+	0.190944i
$949$	16.0800	−	37.0653i	0.521979	−	1.20319i
$950$		0			0
$951$	−17.7527	+	4.75683i	−0.575672	+	0.154251i
$952$	4.47699	+	16.7084i	0.145100	+	0.541521i
$953$	11.3573	+	3.04318i	0.367899	+	0.0985782i	0.438032	−	0.898959i	$-0.355676\pi$
$953$	11.3573	+	3.04318i	0.367899	+	0.0985782i	−0.0701330	+	0.997538i	$0.522342\pi$
$954$	2.45807	−	2.45807i	0.0795830	−	0.0795830i
$955$		0			0
$956$	−11.8734	−	3.18147i	−0.384013	−	0.102896i
$957$		−	50.2198i		−	1.62338i
$958$	−0.757005	+	2.82518i	−0.0244577	+	0.0912775i
$959$	32.0381	−	55.4917i	1.03457	−	1.79192i
$960$		0			0
$961$		−	26.9116i		−	0.868117i
$962$	−1.51528	−	13.2023i	−0.0488546	−	0.425660i
$963$	12.9266	+	12.9266i	0.416552	+	0.416552i
$964$	3.15290	+	11.7668i	0.101548	+	0.378982i
$965$		0			0
$966$	28.7655	−	16.6078i	0.925516	−	0.534347i
$967$	18.0712			0.581130			0.290565	−	0.956855i	$-0.406157\pi$
$967$	18.0712			0.581130			0.290565	+	0.956855i	$0.406157\pi$
$968$	−0.00493000	+	0.00284634i	−0.000158456	+	9.14847e-5i
$969$	0.912898	−	3.40698i	0.0293265	−	0.109448i
$970$		0			0
$971$	17.9295	+	31.0547i	0.575383	+	0.996593i	0.996000	+	0.0893548i	$0.0284805\pi$
$971$	17.9295	+	31.0547i	0.575383	+	0.996593i	−0.420616	+	0.907239i	$0.638186\pi$
$972$	11.5579	−	3.09694i	0.370721	−	0.0993344i
$973$	−2.17589	+	3.76875i	−0.0697558	+	0.120821i
$974$	11.4229			0.366014
$975$		0			0
$976$	−4.72971			−0.151394
$977$	3.91272	−	6.77703i	0.125179	−	0.216816i	−0.796624	−	0.604475i	$-0.793383\pi$
$977$	3.91272	−	6.77703i	0.125179	−	0.216816i	0.921803	+	0.387659i	$0.126716\pi$
$978$	−36.6491	+	9.82009i	−1.17191	+	0.314012i
$979$	−12.0825	−	20.9275i	−0.386159	−	0.668847i
$980$		0			0
$981$	4.93225	−	18.4074i	0.157475	−	0.587703i
$982$	23.3154	−	13.4612i	0.744024	−	0.429563i
$983$	0.969383			0.0309185			0.0154593	−	0.999880i	$-0.495079\pi$
$983$	0.969383			0.0309185			0.0154593	+	0.999880i	$0.495079\pi$
$984$	−16.6662	+	9.62224i	−0.531299	+	0.306746i
$985$		0			0
$986$	−10.6739	−	39.8357i	−0.339927	−	1.26863i
$987$	23.7425	+	23.7425i	0.755733	+	0.755733i
$988$	1.09514	+	0.162744i	0.0348411	+	0.00517757i
$989$		−	50.1643i		−	1.59513i
$990$		0			0
$991$	13.1629	−	22.7988i	0.418132	−	0.724226i	−0.577619	−	0.816306i	$-0.696018\pi$
$991$	13.1629	−	22.7988i	0.418132	−	0.724226i	0.995752	+	0.0920800i	$0.0293516\pi$
$992$	0.523324	−	1.95307i	0.0166156	−	0.0620101i
$993$		−	47.7564i		−	1.51550i
$994$	20.6645	+	5.53702i	0.655437	+	0.175624i
$995$		0			0
$996$	7.92313	−	7.92313i	0.251054	−	0.251054i
$997$	−34.2793	−	9.18510i	−1.08564	−	0.290895i	−0.328733	−	0.944423i	$-0.606622\pi$
$997$	−34.2793	−	9.18510i	−1.08564	−	0.290895i	−0.756902	+	0.653528i	$0.773288\pi$
$998$	−1.52345	−	5.68558i	−0.0482238	−	0.179974i
$999$	13.0271	−	3.49060i	0.412160	−	0.110438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.h.293.4	yes	16
5.2	odd	4		650.2.t.f.7.1	✓	16
5.3	odd	4		650.2.t.h.7.4	yes	16
5.4	even	2		650.2.w.f.293.1	yes	16
13.2	odd	12		650.2.t.f.93.1	yes	16
65.2	even	12	inner	650.2.w.h.457.4	yes	16
65.28	even	12		650.2.w.f.457.1	yes	16
65.54	odd	12		650.2.t.h.93.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.7.1	✓	16	5.2	odd	4
650.2.t.f.93.1	yes	16	13.2	odd	12
650.2.t.h.7.4	yes	16	5.3	odd	4
650.2.t.h.93.4	yes	16	65.54	odd	12
650.2.w.f.293.1	yes	16	5.4	even	2
650.2.w.f.457.1	yes	16	65.28	even	12
650.2.w.h.293.4	yes	16	1.1	even	1	trivial
650.2.w.h.457.4	yes	16	65.2	even	12	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.98389 - 0.531582i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.531582 - 1.98389i) q^{6} +(2.67861 - 1.54650i) q^{7} -1.00000 q^{8} +(1.05516 - 0.609199i) q^{9} +(-0.858184 - 3.20278i) q^{11} +(-1.45231 - 1.45231i) q^{12} +(-1.43497 + 3.30770i) q^{13} -3.09300i q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.44746 - 5.40200i) q^{17} -1.21840i q^{18} +(0.296610 + 0.0794764i) q^{19} +(4.49199 - 4.49199i) q^{21} +(-3.20278 - 0.858184i) q^{22} +(1.35327 + 5.05047i) q^{23} +(-1.98389 + 0.531582i) q^{24} +(2.14706 + 2.89657i) q^{26} +(-2.58743 + 2.58743i) q^{27} +(-2.67861 - 1.54650i) q^{28} +(6.38628 + 3.68712i) q^{29} +(-1.42975 - 1.42975i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.40508 - 5.89778i) q^{33} +(-3.95454 - 3.95454i) q^{34} +(-1.05516 - 0.609199i) q^{36} +(-3.19191 - 1.84285i) q^{37} +(0.217134 - 0.217134i) q^{38} +(-1.08852 + 7.32491i) q^{39} +(9.05057 - 2.42509i) q^{41} +(-1.64418 - 6.13617i) q^{42} +(-9.26725 - 2.48315i) q^{43} +(-2.34460 + 2.34460i) q^{44} +(5.05047 + 1.35327i) q^{46} +5.28553i q^{47} +(-0.531582 + 1.98389i) q^{48} +(1.28332 - 2.22277i) q^{49} -11.4864i q^{51} +(3.58204 - 0.411124i) q^{52} +(2.01746 + 2.01746i) q^{53} +(0.947067 + 3.53450i) q^{54} +(-2.67861 + 1.54650i) q^{56} +0.630690 q^{57} +(6.38628 - 3.68712i) q^{58} +(-0.224282 + 0.837031i) q^{59} +(2.36485 + 4.09605i) q^{61} +(-1.95307 + 0.523324i) q^{62} +(1.88425 - 3.26362i) q^{63} +1.00000 q^{64} -6.81017 q^{66} +(-1.62782 + 2.81947i) q^{67} +(-5.40200 + 1.44746i) q^{68} +(5.36948 + 9.30021i) q^{69} +(-1.79018 + 6.68104i) q^{71} +(-1.05516 + 0.609199i) q^{72} -11.2058 q^{73} +(-3.19191 + 1.84285i) q^{74} +(-0.0794764 - 0.296610i) q^{76} +(-7.25185 - 7.25185i) q^{77} +(5.79930 + 4.60514i) q^{78} -4.04811i q^{79} +(-5.58535 + 9.67411i) q^{81} +(2.42509 - 9.05057i) q^{82} +5.45554i q^{83} +(-6.13617 - 1.64418i) q^{84} +(-6.78410 + 6.78410i) q^{86} +(14.6297 + 3.92001i) q^{87} +(0.858184 + 3.20278i) q^{88} +(7.03958 - 1.88625i) q^{89} +(1.27160 + 11.0792i) q^{91} +(3.69720 - 3.69720i) q^{92} +(-3.59649 - 2.07643i) q^{93} +(4.57740 + 2.64276i) q^{94} +(1.45231 + 1.45231i) q^{96} +(7.07877 + 12.2608i) q^{97} +(-1.28332 - 2.22277i) q^{98} +(-2.85666 - 2.85666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Introduction

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