LMFDB - Embedded newform 650.2.t.h.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(7,650)]

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([3, 11]))

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

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

chi := DirichletCharacter("650.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.4
Root			$-2.05387i$ of defining polynomial
Character	$\chi$	$=$	650.7
Dual form			650.2.t.h.93.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.531582 + 1.98389i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.531582 - 1.98389i) q^{6} +(-1.54650 - 2.67861i) q^{7} -1.00000i q^{8} +(-1.05516 + 0.609199i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.531582 + 1.98389i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.531582 - 1.98389i) q^{6} +(-1.54650 - 2.67861i) q^{7} -1.00000i q^{8} +(-1.05516 + 0.609199i) q^{9} +(-0.858184 - 3.20278i) q^{11} +(-1.45231 + 1.45231i) q^{12} +(-3.30770 - 1.43497i) q^{13} +3.09300i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.40200 - 1.44746i) q^{17} +1.21840 q^{18} +(-0.296610 - 0.0794764i) q^{19} +(4.49199 - 4.49199i) q^{21} +(-0.858184 + 3.20278i) q^{22} +(-5.05047 + 1.35327i) q^{23} +(1.98389 - 0.531582i) q^{24} +(2.14706 + 2.89657i) q^{26} +(2.58743 + 2.58743i) q^{27} +(1.54650 - 2.67861i) q^{28} +(-6.38628 - 3.68712i) q^{29} +(-1.42975 - 1.42975i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.89778 - 3.40508i) q^{33} +(3.95454 + 3.95454i) q^{34} +(-1.05516 - 0.609199i) q^{36} +(-1.84285 + 3.19191i) q^{37} +(0.217134 + 0.217134i) q^{38} +(1.08852 - 7.32491i) q^{39} +(9.05057 - 2.42509i) q^{41} +(-6.13617 + 1.64418i) q^{42} +(2.48315 - 9.26725i) q^{43} +(2.34460 - 2.34460i) q^{44} +(5.05047 + 1.35327i) q^{46} +5.28553 q^{47} +(-1.98389 - 0.531582i) q^{48} +(-1.28332 + 2.22277i) q^{49} -11.4864i q^{51} +(-0.411124 - 3.58204i) q^{52} +(-2.01746 + 2.01746i) q^{53} +(-0.947067 - 3.53450i) q^{54} +(-2.67861 + 1.54650i) q^{56} -0.630690i q^{57} +(3.68712 + 6.38628i) q^{58} +(0.224282 - 0.837031i) q^{59} +(2.36485 + 4.09605i) q^{61} +(0.523324 + 1.95307i) q^{62} +(3.26362 + 1.88425i) q^{63} -1.00000 q^{64} -6.81017 q^{66} +(2.81947 + 1.62782i) q^{67} +(-1.44746 - 5.40200i) q^{68} +(-5.36948 - 9.30021i) q^{69} +(-1.79018 + 6.68104i) q^{71} +(0.609199 + 1.05516i) q^{72} -11.2058i q^{73} +(3.19191 - 1.84285i) q^{74} +(-0.0794764 - 0.296610i) q^{76} +(-7.25185 + 7.25185i) q^{77} +(-4.60514 + 5.79930i) q^{78} +4.04811i q^{79} +(-5.58535 + 9.67411i) q^{81} +(-9.05057 - 2.42509i) q^{82} -5.45554 q^{83} +(6.13617 + 1.64418i) q^{84} +(-6.78410 + 6.78410i) q^{86} +(3.92001 - 14.6297i) q^{87} +(-3.20278 + 0.858184i) q^{88} +(-7.03958 + 1.88625i) q^{89} +(1.27160 + 11.0792i) q^{91} +(-3.69720 - 3.69720i) q^{92} +(2.07643 - 3.59649i) q^{93} +(-4.57740 - 2.64276i) q^{94} +(1.45231 + 1.45231i) q^{96} +(12.2608 - 7.07877i) q^{97} +(2.22277 - 1.28332i) q^{98} +(2.85666 + 2.85666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33} + 16 q^{34} + 24 q^{36} - 20 q^{37} - 4 q^{38} + 32 q^{41} - 4 q^{42} - 8 q^{44} + 4 q^{46} + 32 q^{47} - 16 q^{49} - 12 q^{52} - 44 q^{53} - 36 q^{54} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 20 q^{61} - 16 q^{62} + 108 q^{63} - 16 q^{64} + 8 q^{68} - 24 q^{69} + 16 q^{71} + 4 q^{72} + 36 q^{74} - 20 q^{76} + 16 q^{77} + 4 q^{78} + 16 q^{81} - 32 q^{82} - 80 q^{83} + 4 q^{84} - 36 q^{86} + 12 q^{87} + 4 q^{88} + 28 q^{89} - 44 q^{91} - 8 q^{92} - 24 q^{94} + 96 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.531582	+	1.98389i	0.306909	+	1.14540i	0.931290	+	0.364279i	$0.118685\pi$
$3$	0.531582	+	1.98389i	0.306909	+	1.14540i	−0.624381	+	0.781120i	$0.714649\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.531582	−	1.98389i	0.217017	−	0.809920i
$7$	−1.54650	−	2.67861i	−0.584522	−	1.01242i	−0.994935	−	0.100522i	$-0.967949\pi$
$7$	−1.54650	−	2.67861i	−0.584522	−	1.01242i	0.410413	−	0.911900i	$-0.365384\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−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
$13$	−3.30770	−	1.43497i	−0.917390	−	0.397990i
$13$	−3.30770	−	1.43497i	−0.917390	−	0.397990i
$14$			3.09300i			0.826638i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.40200	−	1.44746i	−1.31018	−	0.351061i	−0.464887	−	0.885370i	$-0.653905\pi$
$17$	−5.40200	−	1.44746i	−1.31018	−	0.351061i	−0.845289	+	0.534309i	$0.820572\pi$
$18$	1.21840			0.287179
$19$	−0.296610	−	0.0794764i	−0.0680470	−	0.0182331i	0.224635	−	0.974443i	$-0.427881\pi$
$19$	−0.296610	−	0.0794764i	−0.0680470	−	0.0182331i	−0.292682	+	0.956210i	$0.594548\pi$
$20$		0			0
$21$	4.49199	−	4.49199i	0.980232	−	0.980232i
$22$	−0.858184	+	3.20278i	−0.182965	+	0.682836i
$23$	−5.05047	+	1.35327i	−1.05310	+	0.282176i	−0.743531	−	0.668702i	$-0.766850\pi$
$23$	−5.05047	+	1.35327i	−1.05310	+	0.282176i	−0.309566	+	0.950878i	$0.600184\pi$
$24$	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
$28$	1.54650	−	2.67861i	0.292261	−	0.506211i
$29$	−6.38628	−	3.68712i	−1.18590	−	0.684682i	−0.228530	−	0.973537i	$-0.573392\pi$
$29$	−6.38628	−	3.68712i	−1.18590	−	0.684682i	−0.957373	+	0.288855i	$0.906725\pi$
$30$		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	$0.808121\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	5.89778	−	3.40508i	1.02667	−	0.592749i
$34$	3.95454	+	3.95454i	0.678197	+	0.678197i
$35$		0			0
$36$	−1.05516	−	0.609199i	−0.175861	−	0.101533i
$37$	−1.84285	+	3.19191i	−0.302963	+	0.524747i	−0.976806	−	0.214128i	$-0.931309\pi$
$37$	−1.84285	+	3.19191i	−0.302963	+	0.524747i	0.673843	+	0.738875i	$0.264642\pi$
$38$	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	$0.155412\pi$
$42$	−6.13617	+	1.64418i	−0.946831	+	0.253703i
$43$	2.48315	−	9.26725i	0.378677	−	1.41324i	−0.469220	−	0.883081i	$-0.655465\pi$
$43$	2.48315	−	9.26725i	0.378677	−	1.41324i	0.847897	−	0.530161i	$-0.177868\pi$
$44$	2.34460	−	2.34460i	0.353462	−	0.353462i
$45$		0			0
$46$	5.05047	+	1.35327i	0.744651	+	0.199529i
$47$	5.28553			0.770973			0.385487	−	0.922713i	$-0.374034\pi$
$47$	5.28553			0.770973			0.385487	+	0.922713i	$0.374034\pi$
$48$	−1.98389	−	0.531582i	−0.286350	−	0.0767272i
$49$	−1.28332	+	2.22277i	−0.183331	+	0.317539i
$50$		0			0
$51$		−	11.4864i		−	1.60842i
$52$	−0.411124	−	3.58204i	−0.0570126	−	0.496739i
$53$	−2.01746	+	2.01746i	−0.277119	+	0.277119i	−0.831958	−	0.554839i	$-0.812780\pi$
$53$	−2.01746	+	2.01746i	−0.277119	+	0.277119i	0.554839	+	0.831958i	$0.312780\pi$
$54$	−0.947067	−	3.53450i	−0.128879	−	0.480985i
$55$		0			0
$56$	−2.67861	+	1.54650i	−0.357945	+	0.206660i
$57$		−	0.630690i		−	0.0835369i
$58$	3.68712	+	6.38628i	0.484143	+	0.838560i
$59$	0.224282	−	0.837031i	0.0291990	−	0.108972i	−0.949788	−	0.312893i	$-0.898702\pi$
$59$	0.224282	−	0.837031i	0.0291990	−	0.108972i	0.978987	+	0.203921i	$0.0653685\pi$
$60$		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	$0.735416\pi$
$62$	0.523324	+	1.95307i	0.0664622	+	0.248040i
$63$	3.26362	+	1.88425i	0.411178	+	0.237393i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.81017			−0.838274
$67$	2.81947	+	1.62782i	0.344454	+	0.198870i	0.662240	−	0.749292i	$-0.269606\pi$
$67$	2.81947	+	1.62782i	0.344454	+	0.198870i	−0.317786	+	0.948162i	$0.602939\pi$
$68$	−1.44746	−	5.40200i	−0.175530	−	0.655088i
$69$	−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	$0.948711\pi$
$72$	0.609199	+	1.05516i	0.0717948	+	0.124352i
$73$		−	11.2058i		−	1.31154i	−0.754962	−	0.655769i	$-0.772345\pi$
$73$		−	11.2058i		−	1.31154i	0.754962	−	0.655769i	$-0.227655\pi$
$74$	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
$78$	−4.60514	+	5.79930i	−0.521430	+	0.656641i
$79$			4.04811i			0.455447i	0.973726	+	0.227724i	$0.0731283\pi$
$79$			4.04811i			0.455447i	−0.973726	+	0.227724i	$0.926872\pi$
$80$		0			0
$81$	−5.58535	+	9.67411i	−0.620594	+	1.07490i
$82$	−9.05057	−	2.42509i	−0.999469	−	0.267807i
$83$	−5.45554			−0.598824			−0.299412	−	0.954124i	$-0.596790\pi$
$83$	−5.45554			−0.598824			−0.299412	+	0.954124i	$0.596790\pi$
$84$	6.13617	+	1.64418i	0.669511	+	0.179395i
$85$		0			0
$86$	−6.78410	+	6.78410i	−0.731548	+	0.731548i
$87$	3.92001	−	14.6297i	0.420270	−	1.56847i
$88$	−3.20278	+	0.858184i	−0.341418	+	0.0914827i
$89$	−7.03958	+	1.88625i	−0.746195	+	0.199942i	−0.611829	−	0.790990i	$-0.709566\pi$
$89$	−7.03958	+	1.88625i	−0.746195	+	0.199942i	−0.134365	+	0.990932i	$0.542899\pi$
$90$		0			0
$91$	1.27160	+	11.0792i	0.133300	+	1.16142i
$92$	−3.69720	−	3.69720i	−0.385460	−	0.385460i
$93$	2.07643	−	3.59649i	0.215316	−	0.372939i
$94$	−4.57740	−	2.64276i	−0.472123	−	0.272580i
$95$		0			0
$96$	1.45231	+	1.45231i	0.148226	+	0.148226i
$97$	12.2608	−	7.07877i	1.24490	−	0.718741i	0.274808	−	0.961499i	$-0.411386\pi$
$97$	12.2608	−	7.07877i	1.24490	−	0.718741i	0.970087	+	0.242758i	$0.0780523\pi$
$98$	2.22277	−	1.28332i	0.224534	−	0.129635i
$99$	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	$-0.736706\pi$
$102$	−5.74321	+	9.94752i	−0.568662	+	0.984952i
$103$	12.8600	+	12.8600i	1.26713	+	1.26713i	0.947562	+	0.319572i	$0.103539\pi$
$103$	12.8600	+	12.8600i	1.26713	+	1.26713i	0.319572	+	0.947562i	$0.396461\pi$
$104$	−1.43497	+	3.30770i	−0.140711	+	0.324346i
$105$		0			0
$106$	2.75590	−	0.738441i	0.267677	−	0.0717238i
$107$	14.4928	−	3.88333i	1.40107	−	0.375416i	0.522342	−	0.852736i	$-0.325059\pi$
$107$	14.4928	−	3.88333i	1.40107	−	0.375416i	0.878729	+	0.477321i	$0.158392\pi$
$108$	−0.947067	+	3.53450i	−0.0911315	+	0.340108i
$109$	−11.0597	+	11.0597i	−1.05933	+	1.05933i	−0.0612039	+	0.998125i	$0.519494\pi$
$109$	−11.0597	+	11.0597i	−1.05933	+	1.05933i	−0.998125	+	0.0612039i	$0.980506\pi$
$110$		0			0
$111$	−7.31203	−	1.95925i	−0.694027	−	0.185964i
$112$	3.09300			0.292261
$113$	−19.8948	−	5.33080i	−1.87155	−	0.501480i	−0.999936	−	0.0112824i	$-0.996409\pi$
$113$	−19.8948	−	5.33080i	−1.87155	−	0.501480i	−0.871611	−	0.490197i	$-0.836925\pi$
$114$	−0.315345	+	0.546193i	−0.0295347	+	0.0511557i
$115$		0			0
$116$		−	7.37425i		−	0.684682i
$117$	4.36435	−	0.500913i	0.403484	−	0.0463094i
$118$	−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
$122$		−	4.72971i		−	0.428208i
$123$	9.62224	+	16.6662i	0.867608	+	1.50274i
$124$	0.523324	−	1.95307i	0.0469959	−	0.175391i
$125$		0			0
$126$	−1.88425	−	3.26362i	−0.167863	−	0.290746i
$127$	5.21043	+	19.4456i	0.462351	+	1.72552i	0.665526	+	0.746375i	$0.268207\pi$
$127$	5.21043	+	19.4456i	0.462351	+	1.72552i	−0.203175	+	0.979143i	$0.565126\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	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	$0.615500\pi$
$132$	5.89778	+	3.40508i	0.513336	+	0.296374i
$133$	0.245820	+	0.917414i	0.0213153	+	0.0795499i
$134$	−1.62782	−	2.81947i	−0.140623	−	0.243565i
$135$		0			0
$136$	−1.44746	+	5.40200i	−0.124119	+	0.463217i
$137$	−10.3583	−	17.9411i	−0.884967	−	1.53281i	−0.845751	−	0.533578i	$-0.820847\pi$
$137$	−10.3583	−	17.9411i	−0.884967	−	1.53281i	−0.0392164	−	0.999231i	$-0.512486\pi$
$138$			10.7390i			0.914161i
$139$	1.21848	−	0.703489i	0.103350	−	0.0596691i	−0.447434	−	0.894317i	$-0.647662\pi$
$139$	1.21848	−	0.703489i	0.103350	−	0.0596691i	0.550784	+	0.834648i	$0.314329\pi$
$140$		0			0
$141$	2.80969	+	10.4859i	0.236619	+	0.883072i
$142$	4.89086	−	4.89086i	0.410432	−	0.410432i
$143$	−1.75730	+	11.8253i	−0.146953	+	0.988882i
$144$		−	1.21840i		−	0.101533i
$145$		0			0
$146$	−5.60289	+	9.70449i	−0.463699	+	0.803149i
$147$	−5.09193	−	1.36438i	−0.419975	−	0.112532i
$148$	−3.68570			−0.302963
$149$	−0.934559	−	0.250414i	−0.0765621	−	0.0205147i	0.220335	−	0.975424i	$-0.429285\pi$
$149$	−0.934559	−	0.250414i	−0.0765621	−	0.0205147i	−0.296897	+	0.954910i	$0.595952\pi$
$150$		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	$-0.100110\pi$
$152$	−0.0794764	+	0.296610i	−0.00644639	+	0.0240582i
$153$	6.58179	−	1.76358i	0.532106	−	0.142577i
$154$	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	$-0.0392267\pi$
$157$	10.8947	+	10.8947i	0.869494	+	0.869494i	−0.122923	+	0.992416i	$0.539227\pi$
$158$	2.02405	−	3.50576i	0.161025	−	0.278903i
$159$	−5.07486	−	2.92997i	−0.402463	−	0.232362i
$160$		0			0
$161$	11.4354	+	11.4354i	0.901239	+	0.901239i
$162$	9.67411	−	5.58535i	0.760070	−	0.438827i
$163$	15.9984	−	9.23667i	1.25309	−	0.723472i	0.281368	−	0.959600i	$-0.409212\pi$
$163$	15.9984	−	9.23667i	1.25309	−	0.723472i	0.971722	+	0.236128i	$0.0758785\pi$
$164$	6.62548	+	6.62548i	0.517363	+	0.517363i
$165$		0			0
$166$	4.72464	+	2.72777i	0.366703	+	0.211716i
$167$	5.02084	−	8.69635i	0.388524	−	0.672944i	−0.603727	−	0.797191i	$-0.706318\pi$
$167$	5.02084	−	8.69635i	0.388524	−	0.672944i	0.992251	+	0.124247i	$0.0396516\pi$
$168$	−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
$172$	9.26725	−	2.48315i	0.706621	−	0.189338i
$173$	−1.81473	+	6.77265i	−0.137971	+	0.514915i	0.861997	+	0.506914i	$0.169214\pi$
$173$	−1.81473	+	6.77265i	−0.137971	+	0.514915i	−0.999968	+	0.00800159i	$0.997453\pi$
$174$	−10.7097	+	10.7097i	−0.811899	+	0.811899i
$175$		0			0
$176$	3.20278	+	0.858184i	0.241419	+	0.0646880i
$177$	1.77980			0.133778
$178$	7.03958	+	1.88625i	0.527639	+	0.141380i
$179$	5.58297	−	9.66999i	0.417291	−	0.722769i	−0.578375	−	0.815771i	$-0.696313\pi$
$179$	5.58297	−	9.66999i	0.417291	−	0.722769i	0.995666	+	0.0930022i	$0.0296464\pi$
$180$		0			0
$181$			8.49811i			0.631659i	0.948816	+	0.315830i	$0.102283\pi$
$181$			8.49811i			0.631659i	−0.948816	+	0.315830i	$0.897717\pi$
$182$	4.43837	−	10.2307i	0.328994	−	0.758350i
$183$	−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
$187$			18.5436i			1.35604i
$188$	2.64276	+	4.57740i	0.192743	+	0.333841i
$189$	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	$0.929727\pi$
$192$	−0.531582	−	1.98389i	−0.0383636	−	0.143175i
$193$	−16.7576	−	9.67501i	−1.20624	−	0.696422i	−0.244303	−	0.969699i	$-0.578559\pi$
$193$	−16.7576	−	9.67501i	−1.20624	−	0.696422i	−0.961936	+	0.273276i	$0.911893\pi$
$194$	−14.1575			−1.01645
$195$		0			0
$196$	−2.56664			−0.183331
$197$	−2.40599	−	1.38910i	−0.171419	−	0.0989691i	0.411836	−	0.911258i	$-0.364888\pi$
$197$	−2.40599	−	1.38910i	−0.171419	−	0.0989691i	−0.583255	+	0.812289i	$0.698221\pi$
$198$	−1.04561	−	3.90227i	−0.0743082	−	0.277322i
$199$	−6.86305	−	11.8872i	−0.486509	−	0.842658i	0.513371	−	0.858167i	$-0.328397\pi$
$199$	−6.86305	−	11.8872i	−0.486509	−	0.842658i	−0.999880	+	0.0155087i	$0.995063\pi$
$200$		0			0
$201$	−1.73064	+	6.45885i	−0.122070	+	0.455572i
$202$	9.59037	+	16.6110i	0.674776	+	1.16875i
$203$			22.8085i			1.60084i
$204$	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
$208$	2.89657	−	2.14706i	0.200841	−	0.148872i
$209$			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	$0.240039\pi$
$212$	−2.75590	−	0.738441i	−0.189276	−	0.0507164i
$213$	−14.2061			−0.973385
$214$	−14.4928	−	3.88333i	−0.990707	−	0.265459i
$215$		0			0
$216$	2.58743	−	2.58743i	0.176053	−	0.176053i
$217$	−1.61864	+	6.04085i	−0.109880	+	0.410079i
$218$	15.1079	−	4.04814i	1.02323	−	0.274175i
$219$	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
$223$	6.67804	−	11.5667i	0.447195	−	0.774564i	−0.551007	−	0.834500i	$-0.685756\pi$
$223$	6.67804	−	11.5667i	0.447195	−	0.774564i	0.998202	+	0.0599362i	$0.0190897\pi$
$224$	−2.67861	−	1.54650i	−0.178972	−	0.103330i
$225$		0			0
$226$	14.5640	+	14.5640i	0.968784	+	0.968784i
$227$	−19.5630	+	11.2947i	−1.29844	+	0.749654i	−0.980134	−	0.198335i	$-0.936447\pi$
$227$	−19.5630	+	11.2947i	−1.29844	+	0.749654i	−0.318304	+	0.947989i	$0.603113\pi$
$228$	0.546193	−	0.315345i	0.0361725	−	0.0208842i
$229$	−9.24789	−	9.24789i	−0.611118	−	0.611118i	0.332120	−	0.943237i	$-0.392236\pi$
$229$	−9.24789	−	9.24789i	−0.611118	−	0.611118i	−0.943237	+	0.332120i	$0.892236\pi$
$230$		0			0
$231$	−18.2418	−	10.5319i	−1.20022	−	0.692949i
$232$	−3.68712	+	6.38628i	−0.242071	+	0.419280i
$233$	4.35174	+	4.35174i	0.285092	+	0.285092i	0.835136	−	0.550044i	$-0.185389\pi$
$233$	4.35174	+	4.35174i	0.285092	+	0.285092i	−0.550044	+	0.835136i	$0.685389\pi$
$234$	−4.03009	−	1.74837i	−0.263455	−	0.114295i
$235$		0			0
$236$	0.837031	−	0.224282i	0.0544861	−	0.0145995i
$237$	−8.03100	+	2.15190i	−0.521669	+	0.139781i
$238$	4.47699	−	16.7084i	0.290200	−	1.08304i
$239$	−8.69193	+	8.69193i	−0.562234	+	0.562234i	−0.929942	−	0.367707i	$-0.880143\pi$
$239$	−8.69193	+	8.69193i	−0.562234	+	0.562234i	0.367707	+	0.929942i	$0.380143\pi$
$240$		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	$0.711672\pi$
$242$	−0.00569267			−0.000365939
$243$	−11.5579	−	3.09694i	−0.741442	−	0.198669i
$244$	−2.36485	+	4.09605i	−0.151394	+	0.262223i
$245$		0			0
$246$		−	19.2445i		−	1.22698i
$247$	0.867049	+	0.688511i	0.0551690	+	0.0438089i
$248$	−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	$0.418900\pi$
$252$			3.76850i			0.237393i
$253$	8.66846	+	15.0142i	0.544982	+	0.943936i
$254$	5.21043	−	19.4456i	0.326932	−	1.22013i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.73118	+	10.1929i	0.170366	+	0.635815i	0.997295	+	0.0735078i	$0.0234194\pi$
$257$	2.73118	+	10.1929i	0.170366	+	0.635815i	−0.826929	+	0.562307i	$0.809914\pi$
$258$	−17.0652	−	9.85260i	−1.06243	−	0.613396i
$259$	11.3999			0.708353
$260$		0			0
$261$	8.98477			0.556143
$262$	7.03650	+	4.06252i	0.434716	+	0.250984i
$263$	0.638074	+	2.38132i	0.0393453	+	0.146839i	0.982804	−	0.184651i	$-0.0591155\pi$
$263$	0.638074	+	2.38132i	0.0393453	+	0.146839i	−0.943459	+	0.331490i	$0.892449\pi$
$264$	−3.40508	−	5.89778i	−0.209568	−	0.362983i
$265$		0			0
$266$	0.245820	−	0.917414i	0.0150722	−	0.0562503i
$267$	−7.48423	−	12.9631i	−0.458027	−	0.793327i
$268$			3.25565i			0.198870i
$269$	−3.93326	+	2.27087i	−0.239815	+	0.138457i	−0.615092	−	0.788456i	$-0.710881\pi$
$269$	−3.93326	+	2.27087i	−0.239815	+	0.138457i	0.375277	+	0.926913i	$0.377548\pi$
$270$		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
$273$	−21.3040	+	8.41224i	−1.28938	+	0.509132i
$274$			20.7166i			1.25153i
$275$		0			0
$276$	5.36948	−	9.30021i	0.323205	−	0.559807i
$277$	−19.2027	−	5.14536i	−1.15378	−	0.309154i	−0.369301	−	0.929310i	$-0.620403\pi$
$277$	−19.2027	−	5.14536i	−1.15378	−	0.309154i	−0.784479	+	0.620155i	$0.787070\pi$
$278$	−1.40698			−0.0843849
$279$	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	$0.140281\pi$
$282$	2.80969	−	10.4859i	0.167315	−	0.624426i
$283$	23.6504	−	6.33709i	1.40587	−	0.376701i	0.525419	−	0.850843i	$-0.323908\pi$
$283$	23.6504	−	6.33709i	1.40587	−	0.376701i	0.880448	+	0.474142i	$0.157242\pi$
$284$	−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
$288$	−0.609199	+	1.05516i	−0.0358974	+	0.0621762i
$289$	12.3640	+	7.13836i	0.727294	+	0.419903i
$290$		0			0
$291$	20.5611	+	20.5611i	1.20531	+	1.20531i
$292$	9.70449	−	5.60289i	0.567912	−	0.327884i
$293$	−7.26980	+	4.19722i	−0.424706	+	0.245204i	−0.697089	−	0.716985i	$-0.745522\pi$
$293$	−7.26980	+	4.19722i	−0.424706	+	0.245204i	0.272383	+	0.962189i	$0.412188\pi$
$294$	3.72755	+	3.72755i	0.217395	+	0.217395i
$295$		0			0
$296$	3.19191	+	1.84285i	0.185526	+	0.107114i
$297$	6.06650	−	10.5075i	0.352014	−	0.609706i
$298$	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
$302$	−21.1553	+	5.66855i	−1.21735	+	0.326188i
$303$	10.1961	−	38.0525i	0.585752	−	2.18606i
$304$	0.217134	−	0.217134i	0.0124535	−	0.0124535i
$305$		0			0
$306$	−6.58179	−	1.76358i	−0.376256	−	0.100817i
$307$	−12.9555			−0.739411			−0.369705	−	0.929149i	$-0.620541\pi$
$307$	−12.9555			−0.739411			−0.369705	+	0.929149i	$0.620541\pi$
$308$	−9.90621	−	2.65436i	−0.564458	−	0.151246i
$309$	−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	$-0.223487\pi$
$312$	−7.32491	−	1.08852i	−0.414691	−	0.0616253i
$313$	21.0763	−	21.0763i	1.19130	−	1.19130i	0.214598	−	0.976702i	$-0.431156\pi$
$313$	21.0763	−	21.0763i	1.19130	−	1.19130i	0.976702	−	0.214598i	$-0.0688442\pi$
$314$	−3.98775	−	14.8825i	−0.225042	−	0.839866i
$315$		0			0
$316$	−3.50576	+	2.02405i	−0.197215	+	0.113862i
$317$			8.94845i			0.502595i	0.967910	+	0.251298i	$0.0808573\pi$
$317$			8.94845i			0.502595i	−0.967910	+	0.251298i	$0.919143\pi$
$318$	2.92997	+	5.07486i	0.164305	+	0.284584i
$319$	−6.32846	+	23.6181i	−0.354326	+	1.32236i
$320$		0			0
$321$	15.4082	+	26.6878i	0.860002	+	1.48957i
$322$	−4.18566	−	15.6211i	−0.233258	−	0.870530i
$323$	1.48725	+	0.858662i	0.0827526	+	0.0477772i
$324$	−11.1707			−0.620594
$325$		0			0
$326$	−18.4733			−1.02314
$327$	−27.8204	−	16.0621i	−1.53847	−	0.888238i
$328$	−2.42509	−	9.05057i	−0.133903	−	0.499734i
$329$	−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	$-0.137326\pi$
$332$	−2.72777	−	4.72464i	−0.149706	−	0.259298i
$333$		−	4.49065i		−	0.246086i
$334$	−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	−0.758047	−	0.652199i	$-0.773846\pi$
$337$	−1.94311	+	1.94311i	−0.105848	+	0.105848i	0.652199	+	0.758047i	$0.273846\pi$
$338$	−2.94532	−	12.6620i	−0.160204	−	0.688720i
$339$		−	42.3029i		−	2.29758i
$340$		0			0
$341$	−3.35219	+	5.80616i	−0.181531	+	0.314421i
$342$	−0.361389	−	0.0968339i	−0.0195417	−	0.00523618i
$343$	−13.7124			−0.740399
$344$	−9.26725	−	2.48315i	−0.499656	−	0.133883i
$345$		0			0
$346$	4.95792	−	4.95792i	0.266540	−	0.266540i
$347$	−1.30034	+	4.85295i	−0.0698062	+	0.260520i	−0.992005	−	0.126195i	$-0.959724\pi$
$347$	−1.30034	+	4.85295i	−0.0698062	+	0.260520i	0.922199	+	0.386715i	$0.126390\pi$
$348$	14.6297	−	3.92001i	0.784234	−	0.210135i
$349$	−4.75638	+	1.27447i	−0.254603	+	0.0682207i	−0.383863	−	0.923390i	$-0.625407\pi$
$349$	−4.75638	+	1.27447i	−0.254603	+	0.0682207i	0.129260	+	0.991611i	$0.458740\pi$
$350$		0			0
$351$	−4.84554	−	12.2713i	−0.258636	−	0.654996i
$352$	−2.34460	−	2.34460i	−0.124968	−	0.124968i
$353$	9.71447	−	16.8260i	0.517049	−	0.895556i	−0.482755	−	0.875756i	$-0.660364\pi$
$353$	9.71447	−	16.8260i	0.517049	−	0.895556i	0.999804	−	0.0198000i	$-0.00630293\pi$
$354$	−1.54135	−	0.889901i	−0.0819220	−	0.0472977i
$355$		0			0
$356$	−5.15333	−	5.15333i	−0.273126	−	0.273126i
$357$	−30.7677	+	17.7637i	−1.62840	+	0.940156i
$358$	−9.66999	+	5.58297i	−0.511075	+	0.295069i
$359$	9.43437	+	9.43437i	0.497927	+	0.497927i	0.910792	−	0.412865i	$-0.135472\pi$
$359$	9.43437	+	9.43437i	0.497927	+	0.497927i	−0.412865	+	0.910792i	$0.635472\pi$
$360$		0			0
$361$	−16.3728	−	9.45285i	−0.861727	−	0.497519i
$362$	4.24905	−	7.35958i	0.223325	−	0.386811i
$363$	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
$367$	−12.9097	+	3.45913i	−0.673879	+	0.180565i	−0.579501	−	0.814971i	$-0.696753\pi$
$367$	−12.9097	+	3.45913i	−0.673879	+	0.180565i	−0.0943773	+	0.995537i	$0.530086\pi$
$368$	1.35327	−	5.05047i	0.0705441	−	0.263274i
$369$	−8.07248	+	8.07248i	−0.420236	+	0.420236i
$370$		0			0
$371$	8.52400	+	2.28400i	0.442544	+	0.118579i
$372$	4.15287			0.215316
$373$	−11.3685	−	3.04619i	−0.588640	−	0.157726i	−0.0478083	−	0.998857i	$-0.515224\pi$
$373$	−11.3685	−	3.04619i	−0.588640	−	0.157726i	−0.540831	+	0.841131i	$0.681890\pi$
$374$	9.27181	−	16.0592i	0.479434	−	0.830404i
$375$		0			0
$376$		−	5.28553i		−	0.272580i
$377$	15.8330	+	21.3600i	0.815439	+	1.10010i
$378$	−8.00293	+	8.00293i	−0.411626	+	0.411626i
$379$	9.33409	+	34.8353i	0.479460	+	1.78937i	0.603806	+	0.797131i	$0.293650\pi$
$379$	9.33409	+	34.8353i	0.479460	+	1.78937i	−0.124346	+	0.992239i	$0.539683\pi$
$380$		0			0
$381$	−35.8082	+	20.6738i	−1.83451	+	1.05915i
$382$			8.24304i			0.421750i
$383$	−7.19342	−	12.4594i	−0.367567	−	0.636644i	0.621618	−	0.783321i	$-0.286476\pi$
$383$	−7.19342	−	12.4594i	−0.367567	−	0.636644i	−0.989185	+	0.146676i	$0.953142\pi$
$384$	−0.531582	+	1.98389i	−0.0271272	+	0.101240i
$385$		0			0
$386$	9.67501	+	16.7576i	0.492445	+	0.852940i
$387$	3.02547	+	11.2912i	0.153793	+	0.573964i
$388$	12.2608	+	7.07877i	0.622448	+	0.359370i
$389$	25.0361			1.26938			0.634690	−	0.772767i	$-0.281128\pi$
$389$	25.0361			1.26938			0.634690	+	0.772767i	$0.281128\pi$
$390$		0			0
$391$	29.2414			1.47880
$392$	2.22277	+	1.28332i	0.112267	+	0.0648174i
$393$	−4.31913	−	16.1192i	−0.217871	−	0.813106i
$394$	1.38910	+	2.40599i	0.0699817	+	0.121212i
$395$		0			0
$396$	−1.04561	+	3.90227i	−0.0525439	+	0.196096i
$397$	0.575967	+	0.997605i	0.0289070	+	0.0500683i	0.880117	−	0.474757i	$-0.157464\pi$
$397$	0.575967	+	0.997605i	0.0289070	+	0.0500683i	−0.851210	+	0.524825i	$0.824131\pi$
$398$			13.7261i			0.688027i
$399$	−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
$403$	2.67752	+	6.78082i	0.133377	+	0.337777i
$404$		−	19.1807i		−	0.954278i
$405$		0			0
$406$	11.4043	−	19.7528i	0.565984	−	0.980313i
$407$	11.8045	+	3.16301i	0.585128	+	0.156784i
$408$	−11.4864			−0.568662
$409$	0.850870	+	0.227990i	0.0420728	+	0.0112734i	0.279794	−	0.960060i	$-0.409734\pi$
$409$	0.850870	+	0.227990i	0.0420728	+	0.0112734i	−0.237721	+	0.971333i	$0.576400\pi$
$410$		0			0
$411$	30.0868	−	30.0868i	1.48407	−	1.48407i
$412$	−4.70709	+	17.5671i	−0.231902	+	0.865469i
$413$	−2.58894	+	0.693703i	−0.127393	+	0.0341349i
$414$	−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
$418$	0.509091	−	0.881772i	0.0249005	−	0.0431289i
$419$	−5.40969	−	3.12329i	−0.264281	−	0.152583i	0.362005	−	0.932176i	$-0.382092\pi$
$419$	−5.40969	−	3.12329i	−0.264281	−	0.152583i	−0.626286	+	0.779594i	$0.715426\pi$
$420$		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	$0.623011\pi$
$422$	5.74821	−	3.31873i	0.279819	−	0.161553i
$423$	−5.57710	+	3.21994i	−0.271168	+	0.156559i
$424$	2.01746	+	2.01746i	0.0979765	+	0.0979765i
$425$		0			0
$426$	12.3028	+	7.10304i	0.596074	+	0.344144i
$427$	7.31449	−	12.6691i	0.353973	−	0.613099i
$428$	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	$0.265775\pi$
$432$	−3.53450	+	0.947067i	−0.170054	+	0.0455658i
$433$	−0.252419	+	0.942040i	−0.0121305	+	0.0452715i	−0.971726	−	0.236112i	$-0.924127\pi$
$433$	−0.252419	+	0.942040i	−0.0121305	+	0.0452715i	0.959595	+	0.281384i	$0.0907934\pi$
$434$	4.42221	−	4.42221i	0.212273	−	0.212273i
$435$		0			0
$436$	−15.1079	−	4.04814i	−0.723535	−	0.193871i
$437$	1.60557			0.0768050
$438$	−22.2310	−	5.95679i	−1.06224	−	0.284626i
$439$	14.2275	−	24.6428i	0.679042	−	1.17614i	−0.296228	−	0.955117i	$-0.595729\pi$
$439$	14.2275	−	24.6428i	0.679042	−	1.17614i	0.975270	−	0.221018i	$-0.0709379\pi$
$440$		0			0
$441$		−	3.12719i		−	0.148914i
$442$	−7.40574	−	18.7551i	−0.352255	−	0.892087i
$443$	2.04110	−	2.04110i	0.0969755	−	0.0969755i	−0.656955	−	0.753930i	$-0.728156\pi$
$443$	2.04110	−	2.04110i	0.0969755	−	0.0969755i	0.753930	+	0.656955i	$0.228156\pi$
$444$	−1.95925	−	7.31203i	−0.0929819	−	0.347013i
$445$		0			0
$446$	−11.5667	+	6.67804i	−0.547700	+	0.316214i
$447$		−	1.98718i		−	0.0939903i
$448$	1.54650	+	2.67861i	0.0730652	+	0.126553i
$449$	−1.94578	+	7.26176i	−0.0918272	+	0.342704i	−0.996519	−	0.0833622i	$-0.973434\pi$
$449$	−1.94578	+	7.26176i	−0.0918272	+	0.342704i	0.904692	+	0.426066i	$0.140101\pi$
$450$		0			0
$451$	−15.5341	−	26.9059i	−0.731472	−	1.26695i
$452$	−5.33080	−	19.8948i	−0.250740	−	0.935774i
$453$	38.9565	+	22.4916i	1.83034	+	1.05675i
$454$	22.5894			1.06017
$455$		0			0
$456$	−0.630690			−0.0295347
$457$	25.7545	+	14.8694i	1.20474	+	0.695559i	0.961606	−	0.274433i	$-0.0884902\pi$
$457$	25.7545	+	14.8694i	1.20474	+	0.695559i	0.243137	+	0.969992i	$0.421823\pi$
$458$	3.38496	+	12.6329i	0.158169	+	0.590294i
$459$	−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	$-0.293225\pi$
$462$	10.5319	+	18.2418i	0.489989	+	0.848686i
$463$		−	7.01939i		−	0.326219i	−0.986608	−	0.163109i	$-0.947848\pi$
$463$		−	7.01939i		−	0.326219i	0.986608	−	0.163109i	$-0.0521523\pi$
$464$	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	−0.753010	−	0.658009i	$-0.771399\pi$
$467$	−2.05301	+	2.05301i	−0.0950020	+	0.0950020i	0.658009	+	0.753010i	$0.271399\pi$
$468$	2.61598	+	3.52918i	0.120924	+	0.163136i
$469$		−	10.0697i		−	0.464976i
$470$		0			0
$471$	−15.8225	+	27.4054i	−0.729062	+	1.26277i
$472$	−0.837031	−	0.224282i	−0.0385275	−	0.0103234i
$473$	−31.8120			−1.46272
$474$	8.03100	+	2.15190i	0.368876	+	0.0988400i
$475$		0			0
$476$	−12.2314	+	12.2314i	−0.560624	+	0.560624i
$477$	0.899716	−	3.35779i	0.0411952	−	0.153742i
$478$	11.8734	−	3.18147i	0.543077	−	0.145517i
$479$	2.82518	−	0.757005i	0.129086	−	0.0345885i	−0.193698	−	0.981061i	$-0.562048\pi$
$479$	2.82518	−	0.757005i	0.129086	−	0.0345885i	0.322784	+	0.946473i	$0.395381\pi$
$480$		0			0
$481$	10.6759	−	7.91343i	0.486779	−	0.360821i
$482$	8.61388	+	8.61388i	0.392351	+	0.392351i
$483$	−16.6078	+	28.7655i	−0.755680	+	1.30888i
$484$	0.00493000	+	0.00284634i	0.000224091	+	0.000129379i
$485$		0			0
$486$	8.46100	+	8.46100i	0.383799	+	0.383799i
$487$	9.89253	−	5.71146i	0.448274	−	0.258811i	−0.258827	−	0.965924i	$-0.583336\pi$
$487$	9.89253	−	5.71146i	0.448274	−	0.258811i	0.707101	+	0.707113i	$0.250003\pi$
$488$	4.09605	−	2.36485i	0.185419	−	0.107052i
$489$	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	$0.458842\pi$
$492$	−9.62224	+	16.6662i	−0.433804	+	0.751371i
$493$	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
$497$	20.6645	−	5.53702i	0.926928	−	0.248370i
$498$	−2.90007	+	10.8232i	−0.129955	+	0.484999i
$499$	−4.16213	+	4.16213i	−0.186323	+	0.186323i	−0.794104	−	0.607782i	$-0.792060\pi$
$499$	−4.16213	+	4.16213i	−0.186323	+	0.186323i	0.607782	+	0.794104i	$0.292060\pi$
$500$		0			0
$501$	19.9216	+	5.33797i	0.890031	+	0.238483i
$502$	8.41551			0.375603
$503$	36.0038	+	9.64719i	1.60533	+	0.430147i	0.946647	−	0.322273i	$-0.104447\pi$
$503$	36.0038	+	9.64719i	1.60533	+	0.430147i	0.658684	+	0.752420i	$0.271114\pi$
$504$	1.88425	−	3.26362i	0.0839313	−	0.145373i
$505$		0			0
$506$		−	17.3369i		−	0.770720i
$507$	−14.1115	+	22.6666i	−0.626716	+	1.00666i
$508$	−14.2352	+	14.2352i	−0.631583	+	0.631583i
$509$	−5.55465	−	20.7303i	−0.246206	−	0.918852i	−0.972774	−	0.231758i	$-0.925552\pi$
$509$	−5.55465	−	20.7303i	−0.246206	−	0.918852i	0.726568	−	0.687095i	$-0.241114\pi$
$510$		0			0
$511$	−30.0160	+	17.3297i	−1.32783	+	0.766622i
$512$			1.00000i			0.0441942i
$513$	−0.561819	−	0.973099i	−0.0248049	−	0.0429633i
$514$	2.73118	−	10.1929i	0.120467	−	0.449589i
$515$		0			0
$516$	9.85260	+	17.0652i	0.433736	+	0.751254i
$517$	−4.53595	−	16.9284i	−0.199491	−	0.744510i
$518$	−9.87257	−	5.69993i	−0.433776	−	0.250441i
$519$	−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	$0.424447\pi$
$522$	−7.78104	−	4.49239i	−0.340567	−	0.196626i
$523$	−2.96161	−	11.0529i	−0.129502	−	0.483309i	0.870458	−	0.492243i	$-0.163823\pi$
$523$	−2.96161	−	11.0529i	−0.129502	−	0.483309i	−0.999960	+	0.00893386i	$0.997156\pi$
$524$	−4.06252	−	7.03650i	−0.177472	−	0.307391i
$525$		0			0
$526$	0.638074	−	2.38132i	0.0278213	−	0.103831i
$527$	5.65399	+	9.79300i	0.246292	+	0.426590i
$528$			6.81017i			0.296374i
$529$	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
$533$	−33.4165	−	4.96587i	−1.44743	−	0.215096i
$534$			14.9685i			0.647749i
$535$		0			0
$536$	1.62782	−	2.81947i	0.0703113	−	0.121783i
$537$	22.1520	+	5.93561i	0.955929	+	0.256140i
$538$	4.54174			0.195808
$539$	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	$0.290855\pi$
$542$	−3.40254	+	12.6985i	−0.146152	+	0.545445i
$543$	−16.8593	+	4.51744i	−0.723502	+	0.193862i
$544$	−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	$-0.275034\pi$
$547$	−2.59861	−	2.59861i	−0.111109	−	0.111109i	−0.760475	+	0.649367i	$0.775034\pi$
$548$	10.3583	−	17.9411i	0.442484	−	0.766404i
$549$	−4.99062	−	2.88134i	−0.212995	−	0.122972i
$550$		0			0
$551$	1.60120	+	1.60120i	0.0682132	+	0.0682132i
$552$	−9.30021	+	5.36948i	−0.395843	+	0.228540i
$553$	10.8433	−	6.26039i	0.461105	−	0.266219i
$554$	14.0574	+	14.0574i	0.597241	+	0.597241i
$555$		0			0
$556$	1.21848	+	0.703489i	0.0516750	+	0.0298346i
$557$	19.5475	−	33.8572i	0.828253	−	1.43458i	−0.0711544	−	0.997465i	$-0.522668\pi$
$557$	19.5475	−	33.8572i	0.828253	−	1.43458i	0.899407	−	0.437111i	$-0.143998\pi$
$558$	−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
$562$	−10.9427	+	2.93209i	−0.461590	+	0.123683i
$563$	−1.21560	+	4.53668i	−0.0512314	+	0.191198i	−0.986799	−	0.161949i	$-0.948222\pi$
$563$	−1.21560	+	4.53668i	−0.0512314	+	0.191198i	0.935568	+	0.353147i	$0.114889\pi$
$564$	−7.67621	+	7.67621i	−0.323227	+	0.323227i
$565$		0			0
$566$	−23.6504	−	6.33709i	−0.994099	−	0.266368i
$567$	34.5510			1.45100
$568$	6.68104	+	1.79018i	0.280330	+	0.0751143i
$569$	12.7418	−	22.0694i	0.534163	−	0.925197i	−0.465041	−	0.885289i	$-0.653960\pi$
$569$	12.7418	−	22.0694i	0.534163	−	0.925197i	0.999203	−	0.0399078i	$-0.0127064\pi$
$570$		0			0
$571$			40.9077i			1.71193i	0.517031	+	0.855967i	$0.327037\pi$
$571$			40.9077i			1.71193i	−0.517031	+	0.855967i	$0.672963\pi$
$572$	−11.1197	+	4.39078i	−0.464937	+	0.183588i
$573$	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
$577$		−	26.6995i		−	1.11151i	−0.831345	−	0.555757i	$-0.812429\pi$
$577$		−	26.6995i		−	1.11151i	0.831345	−	0.555757i	$-0.187571\pi$
$578$	−7.13836	−	12.3640i	−0.296916	−	0.514274i
$579$	10.2861	−	38.3883i	0.427476	−	1.59536i
$580$		0			0
$581$	8.43699	+	14.6133i	0.350025	+	0.606262i
$582$	−7.52589	−	28.0870i	−0.311958	−	1.16424i
$583$	8.19284	+	4.73014i	0.339313	+	0.195902i
$584$	−11.2058			−0.463699
$585$		0			0
$586$	8.39444			0.346771
$587$	17.7692	+	10.2591i	0.733414	+	0.423437i	0.819670	−	0.572836i	$-0.194157\pi$
$587$	17.7692	+	10.2591i	0.733414	+	0.423437i	−0.0862556	+	0.996273i	$0.527490\pi$
$588$	−1.36438	−	5.09193i	−0.0562660	−	0.209987i
$589$	0.310446	+	0.537709i	0.0127917	+	0.0221559i
$590$		0			0
$591$	1.47684	−	5.51163i	0.0607490	−	0.226718i
$592$	−1.84285	−	3.19191i	−0.0757407	−	0.131187i
$593$			38.3032i			1.57293i	0.617638	+	0.786463i	$0.288090\pi$
$593$			38.3032i			1.57293i	−0.617638	+	0.786463i	$0.711910\pi$
$594$	−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
$598$	−14.7635	−	11.7235i	−0.603725	−	0.479410i
$599$			34.5762i			1.41274i	0.707841	+	0.706372i	$0.249670\pi$
$599$			34.5762i			1.41274i	−0.707841	+	0.706372i	$0.750330\pi$
$600$		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	$0.324508\pi$
$602$	28.6636	+	7.68038i	1.16824	+	0.313029i
$603$	−3.96668			−0.161536
$604$	21.1553	+	5.66855i	0.860798	+	0.230650i
$605$		0			0
$606$	−27.8563	+	27.8563i	−1.13159	+	1.13159i
$607$	2.26734	−	8.46183i	0.0920286	−	0.343455i	−0.904524	−	0.426424i	$-0.859773\pi$
$607$	2.26734	−	8.46183i	0.0920286	−	0.343455i	0.996552	+	0.0829682i	$0.0264400\pi$
$608$	−0.296610	+	0.0794764i	−0.0120291	+	0.00322319i
$609$	−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
$613$	−6.72783	+	11.6529i	−0.271734	+	0.470658i	−0.969306	−	0.245857i	$-0.920931\pi$
$613$	−6.72783	+	11.6529i	−0.271734	+	0.470658i	0.697572	+	0.716515i	$0.254264\pi$
$614$	11.2198	+	6.47776i	0.452795	+	0.261421i
$615$		0			0
$616$	7.25185	+	7.25185i	0.292185	+	0.292185i
$617$	−17.5781	+	10.1487i	−0.707666	+	0.408571i	−0.810196	−	0.586159i	$-0.800639\pi$
$617$	−17.5781	+	10.1487i	−0.707666	+	0.408571i	0.102530	+	0.994730i	$0.467306\pi$
$618$	32.3490	−	18.6767i	1.30127	−	0.751287i
$619$	−5.02632	−	5.02632i	−0.202025	−	0.202025i	0.598842	−	0.800867i	$-0.295628\pi$
$619$	−5.02632	−	5.02632i	−0.202025	−	0.202025i	−0.800867	+	0.598842i	$0.795628\pi$
$620$		0			0
$621$	−16.5693	−	9.56627i	−0.664902	−	0.383881i
$622$	−11.3893	+	19.7268i	−0.456669	+	0.790973i
$623$	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
$627$	−2.01996	+	0.541247i	−0.0806695	+	0.0216153i
$628$	−3.98775	+	14.8825i	−0.159128	+	0.593875i
$629$	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	$0.998027\pi$
$632$	4.04811			0.161025
$633$	−13.1680	−	3.52836i	−0.523381	−	0.140240i
$634$	4.47423	−	7.74959i	0.177694	−	0.307775i
$635$		0			0
$636$		−	5.85995i		−	0.232362i
$637$	7.43445	−	5.51073i	0.294564	−	0.218343i
$638$	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	$0.198702\pi$
$642$		−	30.8164i		−	1.21623i
$643$	−24.2955	−	42.0811i	−0.958122	−	1.65952i	−0.727056	−	0.686578i	$-0.759112\pi$
$643$	−24.2955	−	42.0811i	−0.958122	−	1.65952i	−0.231066	−	0.972938i	$-0.574221\pi$
$644$	−4.18566	+	15.6211i	−0.164938	+	0.615558i
$645$		0			0
$646$	−0.858662	−	1.48725i	−0.0337836	−	0.0585149i
$647$	−12.2931	−	45.8784i	−0.483291	−	1.80367i	−0.587636	−	0.809125i	$-0.699941\pi$
$647$	−12.2931	−	45.8784i	−0.483291	−	1.80367i	0.104345	−	0.994541i	$-0.466725\pi$
$648$	9.67411	+	5.58535i	0.380035	+	0.219413i
$649$	−2.87330			−0.112787
$650$		0			0
$651$	−12.8448			−0.503428
$652$	15.9984	+	9.23667i	0.626545	+	0.361736i
$653$	−1.40889	−	5.25805i	−0.0551341	−	0.205763i	0.932864	−	0.360228i	$-0.117301\pi$
$653$	−1.40889	−	5.25805i	−0.0551341	−	0.205763i	−0.987998	+	0.154465i	$0.950635\pi$
$654$	16.0621	+	27.8204i	0.628079	+	1.08786i
$655$		0			0
$656$	−2.42509	+	9.05057i	−0.0946840	+	0.353366i
$657$	6.82655	+	11.8239i	0.266329	+	0.461296i
$658$			16.3481i			0.637316i
$659$	−7.60592	+	4.39128i	−0.296285	+	0.171060i	−0.640773	−	0.767731i	$-0.721386\pi$
$659$	−7.60592	+	4.39128i	−0.296285	+	0.171060i	0.344488	+	0.938791i	$0.388053\pi$
$660$		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
$663$	−16.4827	+	37.9935i	−0.640135	+	1.47555i
$664$			5.45554i			0.211716i
$665$		0			0
$666$	−2.24533	+	3.88902i	−0.0870046	+	0.150696i
$667$	37.2434	+	9.97934i	1.44207	+	0.386402i
$668$	10.0417			0.388524
$669$	26.4970	+	7.09985i	1.02443	+	0.274496i
$670$		0			0
$671$	11.0893	−	11.0893i	0.428097	−	0.428097i
$672$	1.64418	−	6.13617i	0.0634257	−	0.236708i
$673$	−11.5910	+	3.10579i	−0.446799	+	0.119720i	−0.475201	−	0.879877i	$-0.657625\pi$
$673$	−11.5910	+	3.10579i	−0.446799	+	0.119720i	0.0284021	+	0.999597i	$0.490958\pi$
$674$	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	$-0.191083\pi$
$677$	6.77198	+	6.77198i	0.260268	+	0.260268i	−0.564895	+	0.825163i	$0.691083\pi$
$678$	−21.1515	+	36.6354i	−0.812317	+	1.40697i
$679$	−37.9226	−	21.8946i	−1.45534	−	0.840239i
$680$		0			0
$681$	−32.8067	−	32.8067i	−1.25716	−	1.25716i
$682$	5.80616	−	3.35219i	0.222329	−	0.128362i
$683$	9.63149	−	5.56074i	0.368539	−	0.212776i	−0.304281	−	0.952582i	$-0.598416\pi$
$683$	9.63149	−	5.56074i	0.368539	−	0.212776i	0.672820	+	0.739806i	$0.265083\pi$
$684$	0.264555	+	0.264555i	0.0101155	+	0.0101155i
$685$		0			0
$686$	11.8753	+	6.85619i	0.453400	+	0.261771i
$687$	13.4308	−	23.2628i	0.512416	−	0.887531i
$688$	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	$0.306412\pi$
$692$	−6.77265	+	1.81473i	−0.257458	+	0.0689856i
$693$	3.23407	−	12.0697i	0.122852	−	0.458490i
$694$	3.55261	−	3.55261i	0.134855	−	0.134855i
$695$		0			0
$696$	−14.6297	−	3.92001i	−0.554537	−	0.148588i
$697$	−52.4014			−1.98484
$698$	4.75638	+	1.27447i	0.180032	+	0.0482393i
$699$	−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	$-0.0176503\pi$
$702$	−1.93931	+	13.0501i	−0.0731945	+	0.492543i
$703$	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
$707$			59.3260i			2.23118i
$708$	0.889901	+	1.54135i	0.0334445	+	0.0579276i
$709$	−8.59544	+	32.0786i	−0.322809	+	1.20474i	0.593688	+	0.804696i	$0.297671\pi$
$709$	−8.59544	+	32.0786i	−0.322809	+	1.20474i	−0.916496	+	0.400043i	$0.868995\pi$
$710$		0			0
$711$	−2.46610	−	4.27142i	−0.0924861	−	0.160191i
$712$	1.88625	+	7.03958i	0.0706902	+	0.263820i
$713$	9.15574	+	5.28607i	0.342885	+	0.197965i
$714$	35.5274			1.32958
$715$		0			0
$716$	11.1659			0.417291
$717$	−21.8643	−	12.6234i	−0.816538	−	0.471428i
$718$	−3.45322	−	12.8876i	−0.128873	−	0.480960i
$719$	1.02490	+	1.77519i	0.0382225	+	0.0662033i	0.884504	−	0.466533i	$-0.154497\pi$
$719$	1.02490	+	1.77519i	0.0382225	+	0.0662033i	−0.846281	+	0.532736i	$0.821164\pi$
$720$		0			0
$721$	14.5590	−	54.3350i	0.542206	−	2.02354i
$722$	9.45285	+	16.3728i	0.351799	+	0.609333i
$723$		−	25.0200i		−	0.930504i
$724$	−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	−0.103642	−	0.994615i	$-0.533050\pi$
$727$	24.0232	−	24.0232i	0.890972	−	0.890972i	0.994615	+	0.103642i	$0.0330498\pi$
$728$	11.0792	−	1.27160i	0.410624	−	0.0471288i
$729$			8.93615i			0.330968i
$730$		0			0
$731$	−26.8279	+	46.4674i	−0.992268	+	1.71866i
$732$	−9.38322	−	2.51423i	−0.346814	−	0.0929285i
$733$	−18.4922			−0.683026			−0.341513	−	0.939877i	$-0.610939\pi$
$733$	−18.4922			−0.683026			−0.341513	+	0.939877i	$0.610939\pi$
$734$	12.9097	+	3.45913i	0.476504	+	0.127679i
$735$		0			0
$736$	−3.69720	+	3.69720i	−0.136281	+	0.136281i
$737$	2.79394	−	10.4271i	0.102916	−	0.384089i
$738$	11.0272	−	2.95473i	0.405917	−	0.108765i
$739$	29.9685	−	8.03003i	1.10241	−	0.295389i	0.338663	−	0.940908i	$-0.390025\pi$
$739$	29.9685	−	8.03003i	1.10241	−	0.295389i	0.763745	+	0.645518i	$0.223359\pi$
$740$		0			0
$741$	−0.905023	+	2.08613i	−0.0332469	+	0.0766359i
$742$	−6.24000	−	6.24000i	−0.229078	−	0.229078i
$743$	−6.60401	+	11.4385i	−0.242278	+	0.419637i	−0.961363	−	0.275285i	$-0.911228\pi$
$743$	−6.60401	+	11.4385i	−0.242278	+	0.419637i	0.719085	+	0.694922i	$0.244561\pi$
$744$	−3.59649	−	2.07643i	−0.131854	−	0.0761258i
$745$		0			0
$746$	8.32234	+	8.32234i	0.304702	+	0.304702i
$747$	5.75649	−	3.32351i	0.210619	−	0.121601i
$748$	−16.0592	+	9.27181i	−0.587184	+	0.339011i
$749$	−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	$0.691432\pi$
$752$	−2.64276	+	4.57740i	−0.0963717	+	0.166921i
$753$	−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
$757$	−7.24553	+	1.94143i	−0.263343	+	0.0705626i	−0.388075	−	0.921628i	$-0.626860\pi$
$757$	−7.24553	+	1.94143i	−0.263343	+	0.0705626i	0.124731	+	0.992191i	$0.460193\pi$
$758$	9.33409	−	34.8353i	0.339030	−	1.26528i
$759$	−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	$0.758294\pi$
$762$	41.3477			1.49787
$763$	46.7286	+	12.5209i	1.69169	+	0.453287i
$764$	4.12152	−	7.13868i	0.149111	−	0.258268i
$765$		0			0
$766$			14.3868i			0.519818i
$767$	−1.94297	+	2.44680i	−0.0701567	+	0.0883490i
$768$	1.45231	−	1.45231i	0.0524057	−	0.0524057i
$769$	−8.69883	−	32.4645i	−0.313688	−	1.17070i	−0.925205	−	0.379468i	$-0.876107\pi$
$769$	−8.69883	−	32.4645i	−0.313688	−	1.17070i	0.611517	−	0.791231i	$-0.290560\pi$
$770$		0			0
$771$	−18.7697	+	10.8367i	−0.675975	+	0.390274i
$772$		−	19.3500i		−	0.696422i
$773$	12.8802	+	22.3092i	0.463269	+	0.802406i	0.999122	−	0.0419060i	$-0.0133430\pi$
$773$	12.8802	+	22.3092i	0.463269	+	0.802406i	−0.535852	+	0.844312i	$0.680010\pi$
$774$	3.02547	−	11.2912i	0.108748	−	0.405854i
$775$		0			0
$776$	−7.07877	−	12.2608i	−0.254113	−	0.440137i
$777$	6.05996	+	22.6161i	0.217400	+	0.811347i
$778$	−21.6819	−	12.5180i	−0.777333	−	0.448793i
$779$	−2.87723			−0.103087
$780$		0			0
$781$	22.9342			0.820652
$782$	−25.3238	−	14.6207i	−0.905578	−	0.522836i
$783$	−6.98390	−	26.0643i	−0.249584	−	0.931461i
$784$	−1.28332	−	2.22277i	−0.0458328	−	0.0793847i
$785$		0			0
$786$	−4.31913	+	16.1192i	−0.154058	+	0.574953i
$787$	−2.77643	−	4.80892i	−0.0989690	−	0.171419i	0.812289	−	0.583255i	$-0.198221\pi$
$787$	−2.77643	−	4.80892i	−0.0989690	−	0.171419i	−0.911258	+	0.411836i	$0.864888\pi$
$788$		−	2.77819i		−	0.0989691i
$789$	−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
$793$	−1.94450	−	16.9420i	−0.0690511	−	0.601628i
$794$		−	1.15193i		−	0.0408806i
$795$		0			0
$796$	6.86305	−	11.8872i	0.243254	−	0.421329i
$797$	16.9489	+	4.54144i	0.600360	+	0.160866i	0.546184	−	0.837665i	$-0.316080\pi$
$797$	16.9489	+	4.54144i	0.600360	+	0.160866i	0.0541763	+	0.998531i	$0.482747\pi$
$798$	1.95072			0.0690548
$799$	−28.5524	−	7.65059i	−1.01011	−	0.270658i
$800$		0			0
$801$	6.27882	−	6.27882i	0.221851	−	0.221851i
$802$	0.140834	−	0.525598i	0.00497301	−	0.0185595i
$803$	−35.8897	+	9.61662i	−1.26652	+	0.339363i
$804$	−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
$808$	−9.59037	+	16.6110i	−0.337388	+	0.584373i
$809$	−23.4884	−	13.5610i	−0.825807	−	0.476780i	0.0266077	−	0.999646i	$-0.491529\pi$
$809$	−23.4884	−	13.5610i	−0.825807	−	0.476780i	−0.852415	+	0.522866i	$0.824863\pi$
$810$		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	$0.484491\pi$
$812$	−19.7528	+	11.4043i	−0.693186	+	0.400211i
$813$	23.3836	−	13.5005i	0.820099	−	0.473484i
$814$	−8.64150	−	8.64150i	−0.302884	−	0.302884i
$815$		0			0
$816$	9.94752	+	5.74321i	0.348233	+	0.201052i
$817$	−1.47305	+	2.55141i	−0.0515356	+	0.0892624i
$818$	−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	$0.176803\pi$
$822$	−41.0994	+	11.0125i	−1.43351	+	0.384107i
$823$	0.871770	−	3.25349i	0.0303880	−	0.113409i	−0.949066	−	0.315077i	$-0.897970\pi$
$823$	0.871770	−	3.25349i	0.0303880	−	0.113409i	0.979454	+	0.201668i	$0.0646362\pi$
$824$	12.8600	−	12.8600i	0.448000	−	0.448000i
$825$		0			0
$826$	2.58894	+	0.693703i	0.0900806	+	0.0241370i
$827$	−24.4923			−0.851680			−0.425840	−	0.904799i	$-0.640021\pi$
$827$	−24.4923			−0.851680			−0.425840	+	0.904799i	$0.640021\pi$
$828$	6.15349	+	1.64882i	0.213849	+	0.0573005i
$829$	23.7780	−	41.1847i	0.825844	−	1.43040i	−0.0754282	−	0.997151i	$-0.524032\pi$
$829$	23.7780	−	41.1847i	0.825844	−	1.43040i	0.901272	−	0.433253i	$-0.142634\pi$
$830$		0			0
$831$		−	40.8313i		−	1.41642i
$832$	3.30770	+	1.43497i	0.114674	+	0.0497488i
$833$	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
$837$		−	7.39876i		−	0.255738i
$838$	3.12329	+	5.40969i	0.107892	+	0.186875i
$839$	6.14365	−	22.9284i	0.212102	−	0.791577i	−0.775064	−	0.631883i	$-0.782282\pi$
$839$	6.14365	−	22.9284i	0.212102	−	0.791577i	0.987166	−	0.159694i	$-0.0510509\pi$
$840$		0			0
$841$	12.6897	+	21.9793i	0.437578	+	0.757907i
$842$	−4.12574	−	15.3975i	−0.142182	−	0.530631i
$843$	20.1505	+	11.6339i	0.694019	+	0.400692i
$844$	−6.63747			−0.228471
$845$		0			0
$846$	6.43988			0.221408
$847$	−0.0152485	−	0.00880371i	−0.000523944	−	0.000302499i
$848$	−0.738441	−	2.75590i	−0.0253582	−	0.0946380i
$849$	25.1442	+	43.5510i	0.862946	+	1.49467i
$850$		0			0
$851$	4.98775	−	18.6145i	0.170978	−	0.638098i
$852$	−7.10304	−	12.3028i	−0.243346	−	0.421488i
$853$		−	42.9175i		−	1.46947i	−0.678356	−	0.734733i	$-0.737307\pi$
$853$		−	42.9175i		−	1.46947i	0.678356	−	0.734733i	$-0.262693\pi$
$854$	−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	−0.483983	−	0.875078i	$-0.660810\pi$
$857$	11.4491	−	11.4491i	0.391095	−	0.391095i	0.875078	+	0.483983i	$0.160810\pi$
$858$	22.5260	+	9.77241i	0.769024	+	0.333625i
$859$		−	27.2713i		−	0.930484i	−0.885184	−	0.465242i	$-0.845967\pi$
$859$		−	27.2713i		−	0.930484i	0.885184	−	0.465242i	$-0.154033\pi$
$860$		0			0
$861$	29.7616	−	51.5485i	1.01427	−	1.75677i
$862$	−18.3079	−	4.90558i	−0.623569	−	0.167085i
$863$	0.705520			0.0240162			0.0120081	−	0.999928i	$-0.496178\pi$
$863$	0.705520			0.0240162			0.0120081	+	0.999928i	$0.496178\pi$
$864$	3.53450	+	0.947067i	0.120246	+	0.0322199i
$865$		0			0
$866$	0.689621	−	0.689621i	0.0234343	−	0.0234343i
$867$	−7.58924	+	28.3234i	−0.257744	+	0.961914i
$868$	−6.04085	+	1.61864i	−0.205040	+	0.0549402i
$869$	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
$873$	−8.62477	+	14.9385i	−0.291904	+	0.505593i
$874$	−1.39047	−	0.802786i	−0.0470332	−	0.0271547i
$875$		0			0
$876$	16.2742	+	16.2742i	0.549856	+	0.549856i
$877$	26.0064	−	15.0148i	0.878175	−	0.507014i	0.00811852	−	0.999967i	$-0.497416\pi$
$877$	26.0064	−	15.0148i	0.878175	−	0.507014i	0.870056	+	0.492953i	$0.164082\pi$
$878$	−24.6428	+	14.2275i	−0.831653	+	0.480155i
$879$	−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	$0.575580\pi$
$882$	−1.56359	+	2.70822i	−0.0526489	+	0.0911906i
$883$	8.90010	+	8.90010i	0.299512	+	0.299512i	0.840823	−	0.541311i	$-0.182072\pi$
$883$	8.90010	+	8.90010i	0.299512	+	0.299512i	−0.541311	+	0.840823i	$0.682072\pi$
$884$	−2.96397	+	19.9452i	−0.0996890	+	0.670831i
$885$		0			0
$886$	−2.78819	+	0.747094i	−0.0936712	+	0.0250991i
$887$	18.0718	−	4.84233i	0.606792	−	0.162589i	0.0576758	−	0.998335i	$-0.481631\pi$
$887$	18.0718	−	4.84233i	0.606792	−	0.162589i	0.549116	+	0.835746i	$0.314964\pi$
$888$	−1.95925	+	7.31203i	−0.0657482	+	0.245375i
$889$	44.0293	−	44.0293i	1.47670	−	1.47670i
$890$		0			0
$891$	35.7773	+	9.58651i	1.19859	+	0.321160i
$892$	13.3561			0.447195
$893$	−1.56774	−	0.420075i	−0.0524624	−	0.0140573i
$894$	−0.993589	+	1.72095i	−0.0332306	+	0.0575571i
$895$		0			0
$896$		−	3.09300i		−	0.103330i
$897$	4.41504	+	38.4673i	0.147414	+	1.28439i
$898$	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
$902$			31.0682i			1.03446i
$903$	−30.4741	−	52.7826i	−1.01411	−	1.75650i
$904$	−5.33080	+	19.8948i	−0.177300	+	0.661692i
$905$		0			0
$906$	−22.4916	−	38.9565i	−0.747232	−	1.29424i
$907$	10.5177	+	39.2525i	0.349234	+	1.30336i	0.887587	+	0.460639i	$0.152380\pi$
$907$	10.5177	+	39.2525i	0.349234	+	1.30336i	−0.538353	+	0.842719i	$0.680953\pi$
$908$	−19.5630	−	11.2947i	−0.649219	−	0.374827i
$909$	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	$0.557453\pi$
$912$	0.546193	+	0.315345i	0.0180863	+	0.0104421i
$913$	4.68186	+	17.4729i	0.154947	+	0.578270i
$914$	−14.8694	−	25.7545i	−0.491834	−	0.851882i
$915$		0			0
$916$	3.38496	−	12.6329i	0.111842	−	0.417401i
$917$	12.5654	+	21.7639i	0.414945	+	0.718706i
$918$			20.4642i			0.675419i
$919$	−10.1608	+	5.86633i	−0.335173	+	0.193512i	−0.658136	−	0.752899i	$-0.728655\pi$
$919$	−10.1608	+	5.86633i	−0.335173	+	0.193512i	0.322962	+	0.946412i	$0.395321\pi$
$920$		0			0
$921$	−6.88692	−	25.7023i	−0.226932	−	0.846921i
$922$	−28.1096	+	28.1096i	−0.925742	+	0.925742i
$923$	15.5085	−	19.5300i	0.510468	−	0.642838i
$924$		−	21.0638i		−	0.692949i
$925$		0			0
$926$	−3.50969	+	6.07897i	−0.115336	+	0.199767i
$927$	−21.4037	−	5.73511i	−0.702991	−	0.188366i
$928$	−7.37425			−0.242071
$929$	5.95839	+	1.59655i	0.195488	+	0.0523810i	0.355235	−	0.934777i	$-0.384401\pi$
$929$	5.95839	+	1.59655i	0.195488	+	0.0523810i	−0.159746	+	0.987158i	$0.551068\pi$
$930$		0			0
$931$	0.557303	−	0.557303i	0.0182649	−	0.0182649i
$932$	−1.59285	+	5.94459i	−0.0521755	+	0.194722i
$933$	45.1902	−	12.1087i	1.47946	−	0.396420i
$934$	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	−0.985819	−	0.167812i	$-0.946330\pi$
$937$	−35.3132	−	35.3132i	−1.15363	−	1.15363i	−0.167812	−	0.985819i	$-0.553670\pi$
$938$	−5.03486	+	8.72063i	−0.164394	+	0.284739i
$939$	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	$-0.530204\pi$
$942$	27.4054	−	15.8225i	0.892915	−	0.515525i
$943$	−42.4279	+	24.4957i	−1.38164	+	0.797691i
$944$	0.612749	+	0.612749i	0.0199433	+	0.0199433i
$945$		0			0
$946$	27.5500	+	15.9060i	0.895728	+	0.517149i
$947$	−28.8472	+	49.9648i	−0.937408	+	1.62364i	−0.167126	+	0.985936i	$0.553449\pi$
$947$	−28.8472	+	49.9648i	−0.937408	+	1.62364i	−0.770282	+	0.637703i	$0.779885\pi$
$948$	−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
$952$	16.7084	−	4.47699i	0.541521	−	0.145100i
$953$	−3.04318	+	11.3573i	−0.0985782	+	0.367899i	−0.997538	−	0.0701330i	$-0.977658\pi$
$953$	−3.04318	+	11.3573i	−0.0985782	+	0.367899i	0.898959	+	0.438032i	$0.144324\pi$
$954$	−2.45807	+	2.45807i	−0.0795830	+	0.0795830i
$955$		0			0
$956$	−11.8734	−	3.18147i	−0.384013	−	0.102896i
$957$	−50.2198			−1.62338
$958$	−2.82518	−	0.757005i	−0.0912775	−	0.0244577i
$959$	−32.0381	+	55.4917i	−1.03457	+	1.79192i
$960$		0			0
$961$		−	26.9116i		−	0.868117i
$962$	−13.2023	+	1.51528i	−0.425660	+	0.0488546i
$963$	−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
$967$		−	18.0712i		−	0.581130i	−0.956855	−	0.290565i	$-0.906157\pi$
$967$		−	18.0712i		−	0.581130i	0.956855	−	0.290565i	$-0.0938433\pi$
$968$	−0.00284634	−	0.00493000i	−9.14847e−5	−	0.000158456i
$969$	−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	$0.638186\pi$
$972$	−3.09694	−	11.5579i	−0.0993344	−	0.370721i
$973$	−3.76875	−	2.17589i	−0.120821	−	0.0697558i
$974$	−11.4229			−0.366014
$975$		0			0
$976$	−4.72971			−0.151394
$977$	−6.77703	−	3.91272i	−0.216816	−	0.125179i	0.387659	−	0.921803i	$-0.373284\pi$
$977$	−6.77703	−	3.91272i	−0.216816	−	0.125179i	−0.604475	+	0.796624i	$0.706617\pi$
$978$	−9.82009	−	36.6491i	−0.314012	−	1.17191i
$979$	12.0825	+	20.9275i	0.386159	+	0.668847i
$980$		0			0
$981$	4.93225	−	18.4074i	0.157475	−	0.587703i
$982$	−13.4612	−	23.3154i	−0.429563	−	0.744024i
$983$			0.969383i			0.0309185i	0.999880	+	0.0154593i	$0.00492103\pi$
$983$			0.969383i			0.0309185i	−0.999880	+	0.0154593i	$0.995079\pi$
$984$	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
$988$	−0.162744	+	1.09514i	−0.00517757	+	0.0348411i
$989$			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	$0.0293516\pi$
$992$	−1.95307	−	0.523324i	−0.0620101	−	0.0166156i
$993$	47.7564			1.51550
$994$	−20.6645	−	5.53702i	−0.655437	−	0.175624i
$995$		0			0
$996$	7.92313	−	7.92313i	0.251054	−	0.251054i
$997$	−9.18510	+	34.2793i	−0.290895	+	1.08564i	0.653528	+	0.756902i	$0.273288\pi$
$997$	−9.18510	+	34.2793i	−0.290895	+	1.08564i	−0.944423	+	0.328733i	$0.893378\pi$
$998$	5.68558	−	1.52345i	0.179974	−	0.0482238i
$999$	−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.t.h.7.4	yes	16
5.2	odd	4		650.2.w.h.293.4	yes	16
5.3	odd	4		650.2.w.f.293.1	yes	16
5.4	even	2		650.2.t.f.7.1	✓	16
13.2	odd	12		650.2.w.f.457.1	yes	16
65.2	even	12		650.2.t.f.93.1	yes	16
65.28	even	12	inner	650.2.t.h.93.4	yes	16
65.54	odd	12		650.2.w.h.457.4	yes	16

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.531582 + 1.98389i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.531582 - 1.98389i) q^{6} +(-1.54650 - 2.67861i) q^{7} -1.00000i q^{8} +(-1.05516 + 0.609199i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.531582 + 1.98389i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.531582 - 1.98389i) q^{6} +(-1.54650 - 2.67861i) q^{7} -1.00000i q^{8} +(-1.05516 + 0.609199i) q^{9} +(-0.858184 - 3.20278i) q^{11} +(-1.45231 + 1.45231i) q^{12} +(-3.30770 - 1.43497i) q^{13} +3.09300i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.40200 - 1.44746i) q^{17} +1.21840 q^{18} +(-0.296610 - 0.0794764i) q^{19} +(4.49199 - 4.49199i) q^{21} +(-0.858184 + 3.20278i) q^{22} +(-5.05047 + 1.35327i) q^{23} +(1.98389 - 0.531582i) q^{24} +(2.14706 + 2.89657i) q^{26} +(2.58743 + 2.58743i) q^{27} +(1.54650 - 2.67861i) q^{28} +(-6.38628 - 3.68712i) q^{29} +(-1.42975 - 1.42975i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.89778 - 3.40508i) q^{33} +(3.95454 + 3.95454i) q^{34} +(-1.05516 - 0.609199i) q^{36} +(-1.84285 + 3.19191i) q^{37} +(0.217134 + 0.217134i) q^{38} +(1.08852 - 7.32491i) q^{39} +(9.05057 - 2.42509i) q^{41} +(-6.13617 + 1.64418i) q^{42} +(2.48315 - 9.26725i) q^{43} +(2.34460 - 2.34460i) q^{44} +(5.05047 + 1.35327i) q^{46} +5.28553 q^{47} +(-1.98389 - 0.531582i) q^{48} +(-1.28332 + 2.22277i) q^{49} -11.4864i q^{51} +(-0.411124 - 3.58204i) q^{52} +(-2.01746 + 2.01746i) q^{53} +(-0.947067 - 3.53450i) q^{54} +(-2.67861 + 1.54650i) q^{56} -0.630690i q^{57} +(3.68712 + 6.38628i) q^{58} +(0.224282 - 0.837031i) q^{59} +(2.36485 + 4.09605i) q^{61} +(0.523324 + 1.95307i) q^{62} +(3.26362 + 1.88425i) q^{63} -1.00000 q^{64} -6.81017 q^{66} +(2.81947 + 1.62782i) q^{67} +(-1.44746 - 5.40200i) q^{68} +(-5.36948 - 9.30021i) q^{69} +(-1.79018 + 6.68104i) q^{71} +(0.609199 + 1.05516i) q^{72} -11.2058i q^{73} +(3.19191 - 1.84285i) q^{74} +(-0.0794764 - 0.296610i) q^{76} +(-7.25185 + 7.25185i) q^{77} +(-4.60514 + 5.79930i) q^{78} +4.04811i q^{79} +(-5.58535 + 9.67411i) q^{81} +(-9.05057 - 2.42509i) q^{82} -5.45554 q^{83} +(6.13617 + 1.64418i) q^{84} +(-6.78410 + 6.78410i) q^{86} +(3.92001 - 14.6297i) q^{87} +(-3.20278 + 0.858184i) q^{88} +(-7.03958 + 1.88625i) q^{89} +(1.27160 + 11.0792i) q^{91} +(-3.69720 - 3.69720i) q^{92} +(2.07643 - 3.59649i) q^{93} +(-4.57740 - 2.64276i) q^{94} +(1.45231 + 1.45231i) q^{96} +(12.2608 - 7.07877i) q^{97} +(2.22277 - 1.28332i) q^{98} +(2.85666 + 2.85666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33} + 16 q^{34} + 24 q^{36} - 20 q^{37} - 4 q^{38} + 32 q^{41} - 4 q^{42} - 8 q^{44} + 4 q^{46} + 32 q^{47} - 16 q^{49} - 12 q^{52} - 44 q^{53} - 36 q^{54} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 20 q^{61} - 16 q^{62} + 108 q^{63} - 16 q^{64} + 8 q^{68} - 24 q^{69} + 16 q^{71} + 4 q^{72} + 36 q^{74} - 20 q^{76} + 16 q^{77} + 4 q^{78} + 16 q^{81} - 32 q^{82} - 80 q^{83} + 4 q^{84} - 36 q^{86} + 12 q^{87} + 4 q^{88} + 28 q^{89} - 44 q^{91} - 8 q^{92} - 24 q^{94} + 96 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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