LMFDB - Embedded newform 637.2.x.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	637.19
Dual form			637.2.x.a.570.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.263976 + 0.0707322i) q^{2} +2.50625i q^{3} +(-1.66737 - 0.962657i) q^{4} +(1.43012 - 0.383199i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} -3.28130 q^{9} +O(q^{10})$	\(q+(0.263976 + 0.0707322i) q^{2} +2.50625i q^{3} +(-1.66737 - 0.962657i) q^{4} +(1.43012 - 0.383199i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} -3.28130 q^{9} +0.404621 q^{10} +(3.24588 + 3.24588i) q^{11} +(2.41266 - 4.17885i) q^{12} +(-2.80779 + 2.26193i) q^{13} +(0.960393 + 3.58423i) q^{15} +(1.77873 + 3.08085i) q^{16} +(-1.17081 + 2.02791i) q^{17} +(-0.866185 - 0.232094i) q^{18} +(1.19817 + 1.19817i) q^{19} +(-2.75342 - 0.737778i) q^{20} +(0.627247 + 1.08642i) q^{22} +(-4.15065 + 2.39638i) q^{23} +(1.90110 - 1.90110i) q^{24} +(-2.43173 + 1.40396i) q^{25} +(-0.901181 + 0.398494i) q^{26} -0.705008i q^{27} +(-2.87534 + 4.98024i) q^{29} +1.01408i q^{30} +(1.52668 - 5.69764i) q^{31} +(0.806919 + 3.01146i) q^{32} +(-8.13500 + 8.13500i) q^{33} +(-0.452505 + 0.452505i) q^{34} +(5.47114 + 3.15877i) q^{36} +(2.20859 - 8.24256i) q^{37} +(0.231540 + 0.401038i) q^{38} +(-5.66896 - 7.03703i) q^{39} +(-1.37548 - 0.794133i) q^{40} +(-0.829479 + 0.222258i) q^{41} +(1.70069 - 0.981895i) q^{43} +(-2.28742 - 8.53676i) q^{44} +(-4.69264 + 1.25739i) q^{45} +(-1.26518 + 0.339003i) q^{46} +(-2.07859 - 7.75739i) q^{47} +(-7.72139 + 4.45794i) q^{48} +(-0.741225 + 0.198611i) q^{50} +(-5.08245 - 2.93435i) q^{51} +(6.85909 - 1.06853i) q^{52} +(6.54133 + 11.3299i) q^{53} +(0.0498668 - 0.186105i) q^{54} +(5.88581 + 3.39817i) q^{55} +(-3.00292 + 3.00292i) q^{57} +(-1.11129 + 1.11129i) q^{58} +(0.400951 + 1.49637i) q^{59} +(1.84906 - 6.90078i) q^{60} +9.76025i q^{61} +(0.806013 - 1.39606i) q^{62} -6.26289i q^{64} +(-3.14870 + 4.31076i) q^{65} +(-2.72285 + 1.57204i) q^{66} +(-0.385736 + 0.385736i) q^{67} +(3.90436 - 2.25418i) q^{68} +(-6.00594 - 10.4026i) q^{69} +(1.77061 + 0.474435i) q^{71} +(2.48901 + 2.48901i) q^{72} +(2.28234 + 0.611552i) q^{73} +(1.16603 - 2.01962i) q^{74} +(-3.51868 - 6.09453i) q^{75} +(-0.844368 - 3.15123i) q^{76} +(-0.998725 - 2.25859i) q^{78} +(-2.13339 + 3.69514i) q^{79} +(3.72437 + 3.72437i) q^{80} -8.07697 q^{81} -0.234683 q^{82} +(3.88518 + 3.88518i) q^{83} +(-0.897309 + 3.34880i) q^{85} +(0.518394 - 0.138903i) q^{86} +(-12.4817 - 7.20634i) q^{87} -4.92428i q^{88} +(13.5517 + 3.63117i) q^{89} -1.32768 q^{90} +9.22757 q^{92} +(14.2797 + 3.82624i) q^{93} -2.19479i q^{94} +(2.17267 + 1.25439i) q^{95} +(-7.54749 + 2.02234i) q^{96} +(0.734114 - 2.73975i) q^{97} +(-10.6507 - 10.6507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.263976	+	0.0707322i	0.186659	+	0.0500152i	0.350938	−	0.936399i	$-0.385863\pi$
$2$	0.263976	+	0.0707322i	0.186659	+	0.0500152i	−0.164278	+	0.986414i	$0.552530\pi$
$3$			2.50625i			1.44699i	0.690332	+	0.723493i	$0.257464\pi$
$3$			2.50625i			1.44699i	−0.690332	+	0.723493i	$0.742536\pi$
$4$	−1.66737	−	0.962657i	−0.833685	−	0.481328i
$5$	1.43012	−	0.383199i	0.639568	−	0.171372i	0.0755602	−	0.997141i	$-0.475925\pi$
$5$	1.43012	−	0.383199i	0.639568	−	0.171372i	0.564008	+	0.825770i	$0.309259\pi$
$6$	−0.177273	+	0.661591i	−0.0723713	+	0.270093i
$7$		0			0
$7$		0			0
$8$	−0.758543	−	0.758543i	−0.268186	−	0.268186i
$9$	−3.28130			−1.09377
$10$	0.404621			0.127953
$11$	3.24588	+	3.24588i	0.978670	+	0.978670i	0.999777	−	0.0211071i	$-0.00671910\pi$
$11$	3.24588	+	3.24588i	0.978670	+	0.978670i	−0.0211071	+	0.999777i	$0.506719\pi$
$12$	2.41266	−	4.17885i	0.696475	−	1.20633i
$13$	−2.80779	+	2.26193i	−0.778741	+	0.627346i
$13$	−2.80779	+	2.26193i	−0.778741	+	0.627346i
$14$		0			0
$15$	0.960393	+	3.58423i	0.247972	+	0.925445i
$16$	1.77873	+	3.08085i	0.444682	+	0.770213i
$17$	−1.17081	+	2.02791i	−0.283964	+	0.491840i	−0.972357	−	0.233497i	$-0.924983\pi$
$17$	−1.17081	+	2.02791i	−0.283964	+	0.491840i	0.688393	+	0.725337i	$0.258316\pi$
$18$	−0.866185	−	0.232094i	−0.204162	−	0.0547050i
$19$	1.19817	+	1.19817i	0.274880	+	0.274880i	0.831061	−	0.556181i	$-0.187734\pi$
$19$	1.19817	+	1.19817i	0.274880	+	0.274880i	−0.556181	+	0.831061i	$0.687734\pi$
$20$	−2.75342	−	0.737778i	−0.615684	−	0.164972i
$21$		0			0
$22$	0.627247	+	1.08642i	0.133730	+	0.231626i
$23$	−4.15065	+	2.39638i	−0.865471	+	0.499680i	−0.865841	−	0.500320i	$-0.833216\pi$
$23$	−4.15065	+	2.39638i	−0.865471	+	0.499680i	0.000369324		1.00000i	$0.499882\pi$
$24$	1.90110	−	1.90110i	0.388061	−	0.388061i
$25$	−2.43173	+	1.40396i	−0.486347	+	0.280792i
$26$	−0.901181	+	0.398494i	−0.176736	+	0.0781510i
$27$		−	0.705008i		−	0.135679i
$28$		0			0
$29$	−2.87534	+	4.98024i	−0.533938	+	0.924808i	0.465276	+	0.885166i	$0.345955\pi$
$29$	−2.87534	+	4.98024i	−0.533938	+	0.924808i	−0.999214	+	0.0396419i	$0.987378\pi$
$30$			1.01408i			0.185145i
$31$	1.52668	−	5.69764i	0.274199	−	1.02333i	−0.682177	−	0.731187i	$-0.738967\pi$
$31$	1.52668	−	5.69764i	0.274199	−	1.02333i	0.956376	−	0.292139i	$-0.0943668\pi$
$32$	0.806919	+	3.01146i	0.142644	+	0.532356i
$33$	−8.13500	+	8.13500i	−1.41612	+	1.41612i
$34$	−0.452505	+	0.452505i	−0.0776040	+	0.0776040i
$35$		0			0
$36$	5.47114	+	3.15877i	0.911857	+	0.526461i
$37$	2.20859	−	8.24256i	0.363090	−	1.35507i	−0.506902	−	0.862003i	$-0.669210\pi$
$37$	2.20859	−	8.24256i	0.363090	−	1.35507i	0.869992	−	0.493066i	$-0.164124\pi$
$38$	0.231540	+	0.401038i	0.0375607	+	0.0650570i
$39$	−5.66896	−	7.03703i	−0.907760	−	1.12683i
$40$	−1.37548	−	0.794133i	−0.217482	−	0.125563i
$41$	−0.829479	+	0.222258i	−0.129543	+	0.0347109i	−0.323008	−	0.946396i	$-0.604694\pi$
$41$	−0.829479	+	0.222258i	−0.129543	+	0.0347109i	0.193465	+	0.981107i	$0.438027\pi$
$42$		0			0
$43$	1.70069	−	0.981895i	0.259353	−	0.149738i	−0.364686	−	0.931130i	$-0.618824\pi$
$43$	1.70069	−	0.981895i	0.259353	−	0.149738i	0.624039	+	0.781393i	$0.285490\pi$
$44$	−2.28742	−	8.53676i	−0.344841	−	1.28696i
$45$	−4.69264	+	1.25739i	−0.699538	+	0.187441i
$46$	−1.26518	+	0.339003i	−0.186540	+	0.0499832i
$47$	−2.07859	−	7.75739i	−0.303193	−	1.13153i	−0.934490	−	0.355990i	$-0.884144\pi$
$47$	−2.07859	−	7.75739i	−0.303193	−	1.13153i	0.631297	−	0.775542i	$-0.282523\pi$
$48$	−7.72139	+	4.45794i	−1.11449	+	0.643449i
$49$		0			0
$50$	−0.741225	+	0.198611i	−0.104825	+	0.0280878i
$51$	−5.08245	−	2.93435i	−0.711685	−	0.410892i
$52$	6.85909	−	1.06853i	0.951184	−	0.148179i
$53$	6.54133	+	11.3299i	0.898521	+	1.55628i	0.829386	+	0.558677i	$0.188691\pi$
$53$	6.54133	+	11.3299i	0.898521	+	1.55628i	0.0691354	+	0.997607i	$0.477976\pi$
$54$	0.0498668	−	0.186105i	0.00678601	−	0.0253257i
$55$	5.88581	+	3.39817i	0.793642	+	0.458210i
$56$		0			0
$57$	−3.00292	+	3.00292i	−0.397747	+	0.397747i
$58$	−1.11129	+	1.11129i	−0.145919	+	0.145919i
$59$	0.400951	+	1.49637i	0.0521994	+	0.194811i	0.987102	−	0.160094i	$-0.0511798\pi$
$59$	0.400951	+	1.49637i	0.0521994	+	0.194811i	−0.934902	+	0.354905i	$0.884513\pi$
$60$	1.84906	−	6.90078i	0.238712	−	0.890886i
$61$			9.76025i			1.24967i	0.780756	+	0.624836i	$0.214834\pi$
$61$			9.76025i			1.24967i	−0.780756	+	0.624836i	$0.785166\pi$
$62$	0.806013	−	1.39606i	0.102364	−	0.177299i
$63$		0			0
$64$		−	6.26289i		−	0.782861i
$65$	−3.14870	+	4.31076i	−0.390548	+	0.534684i
$66$	−2.72285	+	1.57204i	−0.335160	+	0.193505i
$67$	−0.385736	+	0.385736i	−0.0471252	+	0.0471252i	−0.730277	−	0.683152i	$-0.760609\pi$
$67$	−0.385736	+	0.385736i	−0.0471252	+	0.0471252i	0.683152	+	0.730277i	$0.260609\pi$
$68$	3.90436	−	2.25418i	0.473473	−	0.273360i
$69$	−6.00594	−	10.4026i	−0.723030	−	1.25232i
$70$		0			0
$71$	1.77061	+	0.474435i	0.210133	+	0.0563050i	0.362350	−	0.932042i	$-0.381975\pi$
$71$	1.77061	+	0.474435i	0.210133	+	0.0563050i	−0.152217	+	0.988347i	$0.548641\pi$
$72$	2.48901	+	2.48901i	0.293332	+	0.293332i
$73$	2.28234	+	0.611552i	0.267128	+	0.0715768i	0.389897	−	0.920859i	$-0.372511\pi$
$73$	2.28234	+	0.611552i	0.267128	+	0.0715768i	−0.122769	+	0.992435i	$0.539177\pi$
$74$	1.16603	−	2.01962i	0.135548	−	0.234776i
$75$	−3.51868	−	6.09453i	−0.406302	−	0.703736i
$76$	−0.844368	−	3.15123i	−0.0968557	−	0.361470i
$77$		0			0
$78$	−0.998725	−	2.25859i	−0.113083	−	0.255735i
$79$	−2.13339	+	3.69514i	−0.240025	+	0.415736i	−0.960721	−	0.277516i	$-0.910489\pi$
$79$	−2.13339	+	3.69514i	−0.240025	+	0.415736i	0.720696	+	0.693251i	$0.243822\pi$
$80$	3.72437	+	3.72437i	0.416397	+	0.416397i
$81$	−8.07697			−0.897441
$82$	−0.234683			−0.0259165
$83$	3.88518	+	3.88518i	0.426454	+	0.426454i	0.887419	−	0.460965i	$-0.152496\pi$
$83$	3.88518	+	3.88518i	0.426454	+	0.426454i	−0.460965	+	0.887419i	$0.652496\pi$
$84$		0			0
$85$	−0.897309	+	3.34880i	−0.0973268	+	0.363228i
$86$	0.518394	−	0.138903i	0.0558998	−	0.0149783i
$87$	−12.4817	−	7.20634i	−1.33818	−	0.772600i
$88$		−	4.92428i		−	0.524930i
$89$	13.5517	+	3.63117i	1.43648	+	0.384904i	0.891299	−	0.453415i	$-0.149795\pi$
$89$	13.5517	+	3.63117i	1.43648	+	0.384904i	0.545180	+	0.838319i	$0.316461\pi$
$90$	−1.32768			−0.139950
$91$		0			0
$92$	9.22757			0.962041
$93$	14.2797	+	3.82624i	1.48074	+	0.396762i
$94$		−	2.19479i		−	0.226375i
$95$	2.17267	+	1.25439i	0.222911	+	0.128698i
$96$	−7.54749	+	2.02234i	−0.770312	+	0.206404i
$97$	0.734114	−	2.73975i	0.0745380	−	0.278180i	−0.918590	−	0.395212i	$-0.870671\pi$
$97$	0.734114	−	2.73975i	0.0745380	−	0.278180i	0.993128	+	0.117032i	$0.0373380\pi$
$98$		0			0
$99$	−10.6507	−	10.6507i	−1.07044	−	1.07044i
$100$	5.40613			0.540613
$101$	10.6403			1.05875			0.529374	−	0.848388i	$-0.322427\pi$
$101$	10.6403			1.05875			0.529374	+	0.848388i	$0.322427\pi$
$102$	−1.13409	−	1.13409i	−0.112292	−	0.112292i
$103$	8.60773	−	14.9090i	0.848145	−	1.46903i	−0.0347173	−	0.999397i	$-0.511053\pi$
$103$	8.60773	−	14.9090i	0.848145	−	1.46903i	0.882862	−	0.469633i	$-0.155614\pi$
$104$	3.84560	+	0.414061i	0.377092	+	0.0406020i
$105$		0			0
$106$	0.925366	+	3.45351i	0.0898794	+	0.335435i
$107$	2.02845	+	3.51338i	0.196097	+	0.339651i	0.947260	−	0.320467i	$-0.103840\pi$
$107$	2.02845	+	3.51338i	0.196097	+	0.339651i	−0.751162	+	0.660118i	$0.770506\pi$
$108$	−0.678681	+	1.17551i	−0.0653061	+	0.113113i
$109$	7.65154	+	2.05022i	0.732885	+	0.196376i	0.605914	−	0.795531i	$-0.292808\pi$
$109$	7.65154	+	2.05022i	0.732885	+	0.196376i	0.126971	+	0.991906i	$0.459474\pi$
$110$	1.31335	+	1.31335i	0.125223	+	0.125223i
$111$	20.6579	+	5.53528i	1.96077	+	0.525385i
$112$		0			0
$113$	−9.23138	−	15.9892i	−0.868415	−	1.50414i	−0.863616	−	0.504150i	$-0.831806\pi$
$113$	−9.23138	−	15.9892i	−0.868415	−	1.50414i	−0.00479920	−	0.999988i	$-0.501528\pi$
$114$	−1.00510	+	0.580297i	−0.0941365	+	0.0543497i
$115$	−5.01763	+	5.01763i	−0.467897	+	0.467897i
$116$	9.58853	−	5.53594i	0.890272	−	0.513999i
$117$	9.21320	−	7.42206i	0.851761	−	0.686170i
$118$			0.423366i			0.0389740i
$119$		0			0
$120$	1.99030	−	3.44730i	0.181688	−	0.314694i
$121$			10.0715i			0.915590i
$122$	−0.690364	+	2.57647i	−0.0625026	+	0.233263i
$123$	−0.557035	−	2.07888i	−0.0502262	−	0.187447i
$124$	−8.03041	+	8.03041i	−0.721152	+	0.721152i
$125$	−8.17426	+	8.17426i	−0.731128	+	0.731128i
$126$		0			0
$127$	−2.52084	−	1.45541i	−0.223689	−	0.129147i	0.383968	−	0.923346i	$-0.374557\pi$
$127$	−2.52084	−	1.45541i	−0.223689	−	0.129147i	−0.607657	+	0.794200i	$0.707890\pi$
$128$	2.05683	−	7.67618i	0.181799	−	0.678485i
$129$	2.46088	+	4.26236i	0.216668	+	0.375280i
$130$	−1.13609	+	0.915224i	−0.0996419	+	0.0802705i
$131$	8.58252	+	4.95512i	0.749858	+	0.432931i	0.825643	−	0.564194i	$-0.190813\pi$
$131$	8.58252	+	4.95512i	0.749858	+	0.432931i	−0.0757847	+	0.997124i	$0.524146\pi$
$132$	21.3953	−	5.73284i	1.86222	−	0.498980i
$133$		0			0
$134$	−0.129109	+	0.0745412i	−0.0111533	+	0.00643938i
$135$	−0.270158	−	1.00824i	−0.0232515	−	0.0867758i
$136$	2.42637	−	0.650144i	0.208059	−	0.0557493i
$137$	0.526114	−	0.140972i	0.0449489	−	0.0120440i	−0.236275	−	0.971686i	$-0.575926\pi$
$137$	0.526114	−	0.140972i	0.0449489	−	0.0120440i	0.281223	+	0.959642i	$0.409260\pi$
$138$	−0.849626	−	3.17085i	−0.0723250	−	0.269921i
$139$	3.32499	−	1.91968i	0.282022	−	0.162825i	−0.352317	−	0.935881i	$-0.614606\pi$
$139$	3.32499	−	1.91968i	0.282022	−	0.162825i	0.634338	+	0.773056i	$0.281273\pi$
$140$		0			0
$141$	19.4420	−	5.20946i	1.63731	−	0.438716i
$142$	0.433842	+	0.250479i	0.0364072	+	0.0210197i
$143$	−16.4557	−	1.77181i	−1.37609	−	0.148166i
$144$	−5.83654	−	10.1092i	−0.486379	−	0.842433i
$145$	−2.20366	+	8.22416i	−0.183004	+	0.682979i
$146$	0.559228	+	0.322870i	0.0462820	+	0.0267210i
$147$		0			0
$148$	−11.6173	+	11.6173i	−0.954936	+	0.954936i
$149$	16.5393	−	16.5393i	1.35495	−	1.35495i	0.474919	−	0.880029i	$-0.342477\pi$
$149$	16.5393	−	16.5393i	1.35495	−	1.35495i	0.880029	−	0.474919i	$-0.157523\pi$
$150$	−0.497768	−	1.85770i	−0.0406426	−	0.151680i
$151$	−1.70623	+	6.36774i	−0.138851	+	0.518200i	0.861101	+	0.508434i	$0.169775\pi$
$151$	−1.70623	+	6.36774i	−0.138851	+	0.518200i	−0.999952	+	0.00976596i	$0.996891\pi$
$152$		−	1.81773i		−	0.147437i
$153$	3.84179	−	6.65417i	0.310590	−	0.537958i
$154$		0			0
$155$		−	8.73331i		−	0.701476i
$156$	2.67801	+	17.1906i	0.214412	+	1.37635i
$157$	−9.49287	+	5.48071i	−0.757613	+	0.437408i	−0.828438	−	0.560081i	$-0.810770\pi$
$157$	−9.49287	+	5.48071i	−0.757613	+	0.437408i	0.0708249	+	0.997489i	$0.477437\pi$
$158$	−0.824529	+	0.824529i	−0.0655960	+	0.0655960i
$159$	−28.3956	+	16.3942i	−2.25192	+	1.30015i
$160$	2.30798	+	3.99754i	0.182462	+	0.316033i
$161$		0			0
$162$	−2.13213	−	0.571302i	−0.167516	−	0.0448857i
$163$	2.73418	+	2.73418i	0.214157	+	0.214157i	0.806031	−	0.591874i	$-0.201612\pi$
$163$	2.73418	+	2.73418i	0.214157	+	0.214157i	−0.591874	+	0.806031i	$0.701612\pi$
$164$	1.59701	+	0.427917i	0.124705	+	0.0334147i
$165$	−8.51668	+	14.7513i	−0.663023	+	1.14839i
$166$	0.750788	+	1.30040i	0.0582724	+	0.100931i
$167$	−6.30900	−	23.5455i	−0.488205	−	1.82201i	−0.565172	−	0.824973i	$-0.691190\pi$
$167$	−6.30900	−	23.5455i	−0.488205	−	1.82201i	0.0769673	−	0.997034i	$-0.475476\pi$
$168$		0			0
$169$	2.76737	−	12.7020i	0.212875	−	0.977079i
$170$	−0.473736	+	0.820535i	−0.0363339	+	0.0629322i
$171$	−3.93156	−	3.93156i	−0.300654	−	0.300654i
$172$	−3.78091			−0.288292
$173$	4.79982			0.364924			0.182462	−	0.983213i	$-0.441593\pi$
$173$	4.79982			0.364924			0.182462	+	0.983213i	$0.441593\pi$
$174$	−2.78516	−	2.78516i	−0.211143	−	0.211143i
$175$		0			0
$176$	−4.22653	+	15.7736i	−0.318587	+	1.18898i
$177$	−3.75028	+	1.00488i	−0.281888	+	0.0755317i
$178$	3.32049	+	1.91709i	0.248881	+	0.143692i
$179$		−	11.1404i		−	0.832672i	−0.909211	−	0.416336i	$-0.863314\pi$
$179$		−	11.1404i		−	0.832672i	0.909211	−	0.416336i	$-0.136686\pi$
$180$	9.03481	+	2.42087i	0.673415	+	0.180441i
$181$	4.32449			0.321437			0.160718	−	0.987000i	$-0.448619\pi$
$181$	4.32449			0.321437			0.160718	+	0.987000i	$0.448619\pi$
$182$		0			0
$183$	−24.4616			−1.80826
$184$	4.96621	+	1.33069i	0.366114	+	0.0980999i
$185$		−	12.6342i		−	0.928882i
$186$	3.49887	+	2.02007i	0.256549	+	0.148119i
$187$	−10.3827	+	2.78203i	−0.759256	+	0.203442i
$188$	−4.00193	+	14.9354i	−0.291871	+	1.08928i
$189$		0			0
$190$	0.484806	+	0.484806i	0.0351715	+	0.0351715i
$191$	−6.31947			−0.457261			−0.228630	−	0.973513i	$-0.573425\pi$
$191$	−6.31947			−0.457261			−0.228630	+	0.973513i	$0.573425\pi$
$192$	15.6964			1.13279
$193$	8.42328	+	8.42328i	0.606321	+	0.606321i	0.941983	−	0.335662i	$-0.108960\pi$
$193$	8.42328	+	8.42328i	0.606321	+	0.606321i	−0.335662	+	0.941983i	$0.608960\pi$
$194$	0.387577	−	0.671304i	0.0278264	−	0.0481968i
$195$	−10.8039	−	7.89144i	−0.773680	−	0.565118i
$196$		0			0
$197$	−0.533499	−	1.99105i	−0.0380103	−	0.141856i	0.944313	−	0.329048i	$-0.106728\pi$
$197$	−0.533499	−	1.99105i	−0.0380103	−	0.141856i	−0.982323	+	0.187192i	$0.940061\pi$
$198$	−2.05819	−	3.56488i	−0.146269	−	0.253345i
$199$	9.28142	−	16.0759i	0.657942	−	1.13959i	−0.323205	−	0.946329i	$-0.604760\pi$
$199$	9.28142	−	16.0759i	0.657942	−	1.13959i	0.981147	−	0.193261i	$-0.0619063\pi$
$200$	2.90954	+	0.779609i	0.205736	+	0.0551267i
$201$	−0.966752	−	0.966752i	−0.0681894	−	0.0681894i
$202$	2.80878	+	0.752611i	0.197625	+	0.0529536i
$203$		0			0
$204$	5.64955	+	9.78531i	0.395548	+	0.685109i
$205$	−1.10108	+	0.635711i	−0.0769030	+	0.0443999i
$206$	3.32678	−	3.32678i	0.231788	−	0.231788i
$207$	13.6195	−	7.86325i	0.946624	−	0.546533i
$208$	−11.9630	−	4.62703i	−0.829482	−	0.320826i
$209$			7.77825i			0.538033i
$210$		0			0
$211$	−1.40368	+	2.43124i	−0.0966332	+	0.167374i	−0.910289	−	0.413973i	$-0.864141\pi$
$211$	−1.40368	+	2.43124i	−0.0966332	+	0.167374i	0.813656	+	0.581347i	$0.197474\pi$
$212$		−	25.1882i		−	1.72993i
$213$	−1.18905	+	4.43761i	−0.0814726	+	0.304060i
$214$	0.286953	+	1.07092i	0.0196157	+	0.0732069i
$215$	2.05593	−	2.05593i	0.140213	−	0.140213i
$216$	−0.534779	+	0.534779i	−0.0363871	+	0.0363871i
$217$		0			0
$218$	1.87481	+	1.08242i	0.126978	+	0.0733108i
$219$	−1.53270	+	5.72013i	−0.103571	+	0.386531i
$220$	−6.54255	−	11.3320i	−0.441099	−	0.764005i
$221$	−1.29958	−	8.34224i	−0.0874193	−	0.561160i
$222$	5.06168	+	2.92236i	0.339718	+	0.196136i
$223$	−15.6678	+	4.19816i	−1.04919	+	0.281130i	−0.741917	−	0.670491i	$-0.766083\pi$
$223$	−15.6678	+	4.19816i	−1.04919	+	0.281130i	−0.307274	+	0.951621i	$0.599417\pi$
$224$		0			0
$225$	7.97924	−	4.60682i	0.531950	−	0.307121i
$226$	−1.30591	−	4.87373i	−0.0868679	−	0.324196i
$227$	−1.69538	+	0.454277i	−0.112527	+	0.0301514i	−0.314643	−	0.949210i	$-0.601885\pi$
$227$	−1.69538	+	0.454277i	−0.112527	+	0.0301514i	0.202116	+	0.979362i	$0.435218\pi$
$228$	7.89777	−	2.11620i	0.523042	−	0.140149i
$229$	−2.88434	−	10.7645i	−0.190602	−	0.711338i	−0.993362	−	0.115034i	$-0.963302\pi$
$229$	−2.88434	−	10.7645i	−0.190602	−	0.711338i	0.802759	−	0.596304i	$-0.203365\pi$
$230$	−1.67944	+	0.969627i	−0.110739	+	0.0639353i
$231$		0			0
$232$	5.95880	−	1.59666i	0.391214	−	0.104826i
$233$	−17.6370	−	10.1827i	−1.15544	−	0.667091i	−0.205230	−	0.978714i	$-0.565794\pi$
$233$	−17.6370	−	10.1827i	−1.15544	−	0.667091i	−0.950206	+	0.311623i	$0.899128\pi$
$234$	2.95704	−	1.30758i	0.193308	−	0.0854790i
$235$	−5.94525	−	10.2975i	−0.387825	−	0.671733i
$236$	0.771957	−	2.88098i	0.0502501	−	0.187536i
$237$	−9.26095	−	5.34681i	−0.601563	−	0.347313i
$238$		0			0
$239$	14.6160	−	14.6160i	0.945430	−	0.945430i	−0.0531558	−	0.998586i	$-0.516928\pi$
$239$	14.6160	−	14.6160i	0.945430	−	0.945430i	0.998586	+	0.0531558i	$0.0169280\pi$
$240$	−9.33421	+	9.33421i	−0.602521	+	0.602521i
$241$	3.69524	+	13.7908i	0.238031	+	0.888345i	0.976759	+	0.214341i	$0.0687604\pi$
$241$	3.69524	+	13.7908i	0.238031	+	0.888345i	−0.738728	+	0.674004i	$0.764573\pi$
$242$	−0.712379	+	2.65863i	−0.0457935	+	0.170904i
$243$		−	22.3580i		−	1.43426i
$244$	9.39577	−	16.2740i	0.601503	−	1.04183i
$245$		0			0
$246$		−	0.588176i		−	0.0375007i
$247$	−6.07439	−	0.654039i	−0.386504	−	0.0416155i
$248$	−5.47995	+	3.16385i	−0.347977	+	0.200905i
$249$	−9.73724	+	9.73724i	−0.617073	+	0.617073i
$250$	−2.73599	+	1.57963i	−0.173039	+	0.0999043i
$251$	−3.24540	−	5.62120i	−0.204848	−	0.354807i	0.745236	−	0.666801i	$-0.232337\pi$
$251$	−3.24540	−	5.62120i	−0.204848	−	0.354807i	−0.950084	+	0.311993i	$0.899003\pi$
$252$		0			0
$253$	−21.2509	−	5.69416i	−1.33603	−	0.357989i
$254$	−0.562498	−	0.562498i	−0.0352943	−	0.0352943i
$255$	−8.39294	−	2.24888i	−0.525586	−	0.140830i
$256$	−5.17698	+	8.96680i	−0.323561	+	0.560425i
$257$	11.0980	+	19.2224i	0.692277	+	1.19906i	0.971090	+	0.238713i	$0.0767257\pi$
$257$	11.0980	+	19.2224i	0.692277	+	1.19906i	−0.278813	+	0.960345i	$0.589941\pi$
$258$	0.348126	+	1.29923i	0.0216734	+	0.0808862i
$259$		0			0
$260$	9.39984	−	4.15652i	0.582953	−	0.257776i
$261$	9.43486	−	16.3417i	0.584003	−	1.01152i
$262$	1.91509	+	1.91509i	0.118315	+	0.118315i
$263$	10.1064			0.623187			0.311594	−	0.950215i	$-0.399137\pi$
$263$	10.1064			0.623187			0.311594	+	0.950215i	$0.399137\pi$
$264$	12.3415			0.759566
$265$	13.6965	+	13.6965i	0.841368	+	0.841368i
$266$		0			0
$267$	−9.10063	+	33.9640i	−0.556950	+	2.07857i
$268$	1.01450	−	0.271834i	0.0619702	−	0.0166049i
$269$	8.97049	+	5.17912i	0.546940	+	0.315776i	0.747887	−	0.663826i	$-0.231068\pi$
$269$	8.97049	+	5.17912i	0.546940	+	0.315776i	−0.200947	+	0.979602i	$0.564402\pi$
$270$		−	0.285261i		−	0.0173604i
$271$	3.15801	+	0.846186i	0.191835	+	0.0514022i	0.353458	−	0.935451i	$-0.385006\pi$
$271$	3.15801	+	0.846186i	0.191835	+	0.0514022i	−0.161622	+	0.986853i	$0.551673\pi$
$272$	−8.33024			−0.505095
$273$		0			0
$274$	0.148853			0.00899252
$275$	−12.4502	−	3.33602i	−0.750776	−	0.201170i
$276$			23.1266i			1.39206i
$277$	−14.4303	−	8.33132i	−0.867030	−	0.500580i	−0.000670170	−	1.00000i	$-0.500213\pi$
$277$	−14.4303	−	8.33132i	−0.867030	−	0.500580i	−0.866360	+	0.499420i	$0.833547\pi$
$278$	1.01350	−	0.271567i	0.0607857	−	0.0162875i
$279$	−5.00949	+	18.6957i	−0.299910	+	1.11928i
$280$		0			0
$281$	8.02095	+	8.02095i	0.478490	+	0.478490i	0.904648	−	0.426159i	$-0.140134\pi$
$281$	8.02095	+	8.02095i	0.478490	+	0.478490i	−0.426159	+	0.904648i	$0.640134\pi$
$282$	5.50070			0.327562
$283$	−14.4404			−0.858390			−0.429195	−	0.903212i	$-0.641203\pi$
$283$	−14.4404			−0.858390			−0.429195	+	0.903212i	$0.641203\pi$
$284$	−2.49555	−	2.49555i	−0.148084	−	0.148084i
$285$	−3.14381	+	5.44525i	−0.186223	+	0.322549i
$286$	−4.21859	−	1.63166i	−0.249450	−	0.0964823i
$287$		0			0
$288$	−2.64774	−	9.88151i	−0.156020	−	0.582274i
$289$	5.75839	+	9.97383i	0.338729	+	0.586696i
$290$	−1.16343	+	2.01511i	−0.0683187	+	0.118331i
$291$	6.86651	+	1.83988i	0.402522	+	0.107855i
$292$	−3.21680	−	3.21680i	−0.188249	−	0.188249i
$293$	15.9091	+	4.26283i	0.929420	+	0.249037i	0.691607	−	0.722274i	$-0.256903\pi$
$293$	15.9091	+	4.26283i	0.929420	+	0.249037i	0.237812	+	0.971311i	$0.423570\pi$
$294$		0			0
$295$	1.14681	+	1.98634i	0.0667701	+	0.115649i
$296$	−7.92765	+	4.57703i	−0.460785	+	0.266035i
$297$	2.28837	−	2.28837i	0.132785	−	0.132785i
$298$	5.53583	−	3.19611i	0.320682	−	0.185146i
$299$	6.23373	−	16.1170i	0.360506	−	0.932071i
$300$			13.5491i			0.782259i
$301$		0			0
$302$	−0.900809	+	1.56025i	−0.0518357	+	0.0897821i
$303$			26.6673i			1.53199i
$304$	−1.56016	+	5.82261i	−0.0894816	+	0.333950i
$305$	3.74012	+	13.9583i	0.214158	+	0.799250i
$306$	1.48481	−	1.48481i	0.0848807	−	0.0848807i
$307$	−8.27574	+	8.27574i	−0.472322	+	0.472322i	−0.902665	−	0.430344i	$-0.858392\pi$
$307$	−8.27574	+	8.27574i	−0.472322	+	0.472322i	0.430344	+	0.902665i	$0.358392\pi$
$308$		0			0
$309$	37.3658	+	21.5731i	2.12566	+	1.22725i
$310$	0.617726	−	2.30539i	0.0350845	−	0.130937i
$311$	6.45124	+	11.1739i	0.365816	+	0.633612i	0.988907	−	0.148538i	$-0.0474566\pi$
$311$	6.45124	+	11.1739i	0.365816	+	0.633612i	−0.623091	+	0.782150i	$0.714123\pi$
$312$	−1.03774	+	9.63804i	−0.0587506	+	0.545647i
$313$	−5.16307	−	2.98090i	−0.291834	−	0.168490i	0.346935	−	0.937889i	$-0.387223\pi$
$313$	−5.16307	−	2.98090i	−0.291834	−	0.168490i	−0.638769	+	0.769399i	$0.720556\pi$
$314$	−2.89355	+	0.775325i	−0.163293	+	0.0437541i
$315$		0			0
$316$	7.11430	−	4.10744i	0.400211	−	0.231062i
$317$	3.34843	+	12.4965i	0.188066	+	0.701873i	0.993953	+	0.109804i	$0.0350223\pi$
$317$	3.34843	+	12.4965i	0.188066	+	0.701873i	−0.805887	+	0.592070i	$0.798311\pi$
$318$	−8.65537	+	2.31920i	−0.485369	+	0.130054i
$319$	−25.4983	+	6.83225i	−1.42763	+	0.382532i
$320$	−2.39993	−	8.95667i	−0.134160	−	0.500693i
$321$	−8.80540	+	5.08380i	−0.491470	+	0.283750i
$322$		0			0
$323$	−3.83262	+	1.02695i	−0.213253	+	0.0571409i
$324$	13.4673	+	7.77535i	0.748184	+	0.431964i
$325$	3.65214	−	9.44243i	0.202584	−	0.523772i
$326$	0.528363	+	0.915152i	0.0292633	+	0.0506856i
$327$	−5.13838	+	19.1767i	−0.284153	+	1.06047i
$328$	0.797788	+	0.460603i	0.0440505	+	0.0254325i
$329$		0			0
$330$	−3.29159	+	3.29159i	−0.181196	+	0.181196i
$331$	−7.06614	+	7.06614i	−0.388390	+	0.388390i	−0.874113	−	0.485723i	$-0.838556\pi$
$331$	−7.06614	+	7.06614i	−0.388390	+	0.388390i	0.485723	+	0.874113i	$0.338556\pi$
$332$	−2.73794	−	10.2181i	−0.150264	−	0.560793i
$333$	−7.24704	+	27.0463i	−0.397135	+	1.48213i
$334$		−	6.66170i		−	0.364512i
$335$	−0.403834	+	0.699462i	−0.0220638	+	0.0382157i
$336$		0			0
$337$			17.5327i			0.955069i	0.878613	+	0.477534i	$0.158469\pi$
$337$			17.5327i			0.955069i	−0.878613	+	0.477534i	$0.841531\pi$
$338$	1.62896	−	3.15729i	0.0886039	−	0.171734i
$339$	40.0730	−	23.1362i	2.17647	−	1.25658i
$340$	4.71989	−	4.71989i	0.255972	−	0.255972i
$341$	23.4493	−	13.5384i	1.26985	−	0.733148i
$342$	−0.759751	−	1.31593i	−0.0410826	−	0.0711572i
$343$		0			0
$344$	−2.03486	−	0.545238i	−0.109712	−	0.0293973i
$345$	−12.5755	−	12.5755i	−0.677040	−	0.677040i
$346$	1.26704	+	0.339502i	0.0681164	+	0.0182517i
$347$	13.1271	−	22.7368i	0.704700	−	1.22058i	−0.262100	−	0.965041i	$-0.584415\pi$
$347$	13.1271	−	22.7368i	0.704700	−	1.22058i	0.966800	−	0.255535i	$-0.0822516\pi$
$348$	13.8745	+	24.0313i	0.743749	+	1.28821i
$349$	2.90133	+	10.8279i	0.155304	+	0.579604i	0.999079	+	0.0429064i	$0.0136617\pi$
$349$	2.90133	+	10.8279i	0.155304	+	0.579604i	−0.843775	+	0.536698i	$0.819672\pi$
$350$		0			0
$351$	1.59468	+	1.97951i	0.0851175	+	0.105659i
$352$	−7.15569	+	12.3940i	−0.381399	+	0.660603i
$353$	4.95246	+	4.95246i	0.263593	+	0.263593i	0.826512	−	0.562919i	$-0.190322\pi$
$353$	4.95246	+	4.95246i	0.263593	+	0.263593i	−0.562919	+	0.826512i	$0.690322\pi$
$354$	−1.06106			−0.0563948
$355$	2.71399			0.144044
$356$	−19.1002	−	19.1002i	−1.01231	−	1.01231i
$357$		0			0
$358$	0.787984	−	2.94080i	0.0416463	−	0.155426i
$359$	−4.93737	+	1.32297i	−0.260585	+	0.0698234i	−0.386746	−	0.922186i	$-0.626401\pi$
$359$	−4.93737	+	1.32297i	−0.260585	+	0.0698234i	0.126161	+	0.992010i	$0.459734\pi$
$360$	4.51336	+	2.60579i	0.237875	+	0.137337i
$361$		−	16.1288i		−	0.848882i
$362$	1.14156	+	0.305881i	0.0599992	+	0.0160767i
$363$	−25.2417			−1.32485
$364$		0			0
$365$	3.49837			0.183113
$366$	−6.45729	−	1.73023i	−0.337528	−	0.0904404i
$367$			18.3774i			0.959291i	0.877462	+	0.479645i	$0.159235\pi$
$367$			18.3774i			0.959291i	−0.877462	+	0.479645i	$0.840765\pi$
$368$	−14.7658	−	8.52503i	−0.769720	−	0.444398i
$369$	2.72177	−	0.729296i	0.141690	−	0.0379656i
$370$	0.893642	−	3.33512i	0.0464582	−	0.173385i
$371$		0			0
$372$	−20.1262	−	20.1262i	−1.04350	−	1.04350i
$373$	20.8520			1.07967			0.539837	−	0.841770i	$-0.318486\pi$
$373$	20.8520			1.07967			0.539837	+	0.841770i	$0.318486\pi$
$374$	−2.93756			−0.151897
$375$	−20.4868	−	20.4868i	−1.05793	−	1.05793i
$376$	−4.30762	+	7.46101i	−0.222148	+	0.384772i
$377$	−3.19158	−	20.4873i	−0.164375	−	1.05515i
$378$		0			0
$379$	7.22021	+	26.9462i	0.370877	+	1.38413i	0.859276	+	0.511512i	$0.170914\pi$
$379$	7.22021	+	26.9462i	0.370877	+	1.38413i	−0.488399	+	0.872620i	$0.662419\pi$
$380$	−2.41509	−	4.18306i	−0.123892	−	0.214587i
$381$	3.64762	−	6.31787i	0.186873	−	0.323674i
$382$	−1.66819	−	0.446990i	−0.0853520	−	0.0228700i
$383$	−17.3797	−	17.3797i	−0.888063	−	0.888063i	0.106274	−	0.994337i	$-0.466108\pi$
$383$	−17.3797	−	17.3797i	−0.888063	−	0.888063i	−0.994337	+	0.106274i	$0.966108\pi$
$384$	19.2384	+	5.15492i	0.981758	+	0.263061i
$385$		0			0
$386$	1.62775	+	2.81934i	0.0828502	+	0.143501i
$387$	−5.58048	+	3.22189i	−0.283672	+	0.163778i
$388$	−3.86148	+	3.86148i	−0.196037	+	0.196037i
$389$	−21.2079	+	12.2444i	−1.07528	+	0.620815i	−0.929620	−	0.368519i	$-0.879865\pi$
$389$	−21.2079	+	12.2444i	−1.07528	+	0.620815i	−0.145663	+	0.989334i	$0.546532\pi$
$390$	−2.29378	−	2.84733i	−0.116150	−	0.144180i
$391$		−	11.2229i		−	0.567565i
$392$		0			0
$393$	−12.4188	+	21.5099i	−0.626444	+	1.08503i
$394$		−	0.563325i		−	0.0283799i
$395$	−1.63502	+	6.10199i	−0.0822670	+	0.307025i
$396$	7.50570	+	28.0117i	0.377176	+	1.40764i
$397$	−13.6915	+	13.6915i	−0.687155	+	0.687155i	−0.961602	−	0.274448i	$-0.911505\pi$
$397$	−13.6915	+	13.6915i	−0.687155	+	0.687155i	0.274448	+	0.961602i	$0.411505\pi$
$398$	3.58716	−	3.58716i	0.179808	−	0.179808i
$399$		0			0
$400$	−8.65079	−	4.99454i	−0.432539	−	0.249727i
$401$	−3.42360	+	12.7770i	−0.170966	+	0.638055i	0.826237	+	0.563322i	$0.190477\pi$
$401$	−3.42360	+	12.7770i	−0.170966	+	0.638055i	−0.997204	+	0.0747328i	$0.976190\pi$
$402$	−0.186819	−	0.323580i	−0.00931768	−	0.0161387i
$403$	8.60105	+	19.4510i	0.428449	+	0.968924i
$404$	−17.7413	−	10.2430i	−0.882663	−	0.509606i
$405$	−11.5510	+	3.09509i	−0.573975	+	0.153796i
$406$		0			0
$407$	33.9232	−	19.5856i	1.68151	−	0.970821i
$408$	1.62942	+	6.08109i	0.0806685	+	0.301059i
$409$	−24.0538	+	6.44521i	−1.18939	+	0.318695i	−0.798643	−	0.601805i	$-0.794449\pi$
$409$	−24.0538	+	6.44521i	−1.18939	+	0.318695i	−0.390743	+	0.920500i	$0.627782\pi$
$410$	−0.335625	+	0.0899304i	−0.0165753	+	0.00444135i
$411$	0.353311	+	1.31857i	0.0174275	+	0.0650405i
$412$	−28.7045	+	16.5726i	−1.41417	+	0.816472i
$413$		0			0
$414$	4.15142	−	1.11237i	0.204031	−	0.0546700i
$415$	7.04506	+	4.06747i	0.345828	+	0.199664i
$416$	−9.07737	−	6.63037i	−0.445055	−	0.325080i
$417$	4.81121	+	8.33325i	0.235606	+	0.408081i
$418$	−0.550173	+	2.05327i	−0.0269098	+	0.100429i
$419$	13.9899	+	8.07708i	0.683452	+	0.394591i	0.801154	−	0.598458i	$-0.204220\pi$
$419$	13.9899	+	8.07708i	0.683452	+	0.394591i	−0.117703	+	0.993049i	$0.537553\pi$
$420$		0			0
$421$	−12.8050	+	12.8050i	−0.624080	+	0.624080i	−0.946572	−	0.322492i	$-0.895479\pi$
$421$	−12.8050	+	12.8050i	−0.624080	+	0.624080i	0.322492	+	0.946572i	$0.395479\pi$
$422$	−0.542505	+	0.542505i	−0.0264087	+	0.0264087i
$423$	6.82047	+	25.4543i	0.331622	+	1.23763i
$424$	3.63235	−	13.5561i	0.176403	−	0.658343i
$425$		−	6.57511i		−	0.318940i
$426$	−0.627763	+	1.08732i	−0.0304152	+	0.0526807i
$427$		0			0
$428$		−	7.81080i		−	0.377549i
$429$	4.44060	−	41.2421i	0.214394	−	1.99119i
$430$	0.688136	−	0.397296i	0.0331849	−	0.0191593i
$431$	15.8111	−	15.8111i	0.761594	−	0.761594i	−0.215016	−	0.976611i	$-0.568980\pi$
$431$	15.8111	−	15.8111i	0.761594	−	0.761594i	0.976611	+	0.215016i	$0.0689804\pi$
$432$	2.17202	−	1.25402i	0.104502	−	0.0603340i
$433$	−9.21467	−	15.9603i	−0.442829	−	0.767002i	0.555069	−	0.831804i	$-0.312692\pi$
$433$	−9.21467	−	15.9603i	−0.442829	−	0.767002i	−0.997898	+	0.0648019i	$0.979358\pi$
$434$		0			0
$435$	−20.6118	−	5.52292i	−0.988261	−	0.264804i
$436$	−10.7843	−	10.7843i	−0.516474	−	0.516474i
$437$	−7.84448	−	2.10192i	−0.375252	−	0.100549i
$438$	−0.809195	+	1.40157i	−0.0386648	+	0.0669694i
$439$	7.79998	+	13.5100i	0.372273	+	0.644795i	0.989915	−	0.141664i	$-0.0452453\pi$
$439$	7.79998	+	13.5100i	0.372273	+	0.644795i	−0.617642	+	0.786459i	$0.711912\pi$
$440$	−1.88698	−	7.04230i	−0.0899582	−	0.335729i
$441$		0			0
$442$	0.247006	−	2.29407i	0.0117489	−	0.109118i
$443$	14.7949	−	25.6255i	0.702926	−	1.21750i	−0.264509	−	0.964383i	$-0.585210\pi$
$443$	14.7949	−	25.6255i	0.702926	−	1.21750i	0.967435	−	0.253120i	$-0.0814567\pi$
$444$	−29.1159	−	29.1159i	−1.38178	−	1.38178i
$445$	20.7720			0.984688
$446$	−4.43286			−0.209902
$447$	41.4515	+	41.4515i	1.96059	+	1.96059i
$448$		0			0
$449$	−2.50811	+	9.36041i	−0.118365	+	0.441745i	−0.999517	−	0.0310893i	$-0.990102\pi$
$449$	−2.50811	+	9.36041i	−0.118365	+	0.441745i	0.881151	+	0.472834i	$0.156769\pi$
$450$	2.43218	−	0.651701i	0.114654	−	0.0307215i
$451$	−3.41381	−	1.97097i	−0.160750	−	0.0928092i
$452$			35.5466i			1.67197i
$453$	−15.9592	−	4.27625i	−0.749827	−	0.200916i
$454$	−0.479673			−0.0225122
$455$		0			0
$456$	4.55569			0.213340
$457$	−33.4816	−	8.97136i	−1.56620	−	0.419663i	−0.631582	−	0.775309i	$-0.717594\pi$
$457$	−33.4816	−	8.97136i	−1.56620	−	0.419663i	−0.934621	+	0.355646i	$0.884261\pi$
$458$		−	3.04559i		−	0.142311i
$459$	1.42969	+	0.825433i	0.0667323	+	0.0385279i
$460$	13.1965	−	3.53599i	0.615291	−	0.164867i
$461$	2.45042	−	9.14508i	0.114127	−	0.425929i	−0.885093	−	0.465414i	$-0.845905\pi$
$461$	2.45042	−	9.14508i	0.114127	−	0.425929i	0.999220	+	0.0394858i	$0.0125720\pi$
$462$		0			0
$463$	3.59580	+	3.59580i	0.167111	+	0.167111i	0.785708	−	0.618597i	$-0.212299\pi$
$463$	3.59580	+	3.59580i	0.167111	+	0.167111i	−0.618597	+	0.785708i	$0.712299\pi$
$464$	−20.4578			−0.949731
$465$	21.8879			1.01503
$466$	−3.93549	−	3.93549i	−0.182308	−	0.182308i
$467$	−12.0623	+	20.8926i	−0.558179	+	0.966794i	0.439470	+	0.898257i	$0.355166\pi$
$467$	−12.0623	+	20.8926i	−0.558179	+	0.966794i	−0.997649	+	0.0685368i	$0.978167\pi$
$468$	−22.5067	+	3.50617i	−1.04037	+	0.162073i
$469$		0			0
$470$	−0.841041	−	3.13881i	−0.0387943	−	0.144782i
$471$	−13.7360	−	23.7915i	−0.632923	−	1.09626i
$472$	0.830922	−	1.43920i	0.0382463	−	0.0662445i
$473$	8.70736	+	2.33313i	0.400365	+	0.107277i
$474$	−2.06648	−	2.06648i	−0.0949165	−	0.0949165i
$475$	−4.59582	−	1.23145i	−0.210871	−	0.0565027i
$476$		0			0
$477$	−21.4641	−	37.1769i	−0.982772	−	1.70221i
$478$	4.89210	−	2.82445i	0.223759	−	0.129188i
$479$	17.3217	−	17.3217i	0.791451	−	0.791451i	−0.190279	−	0.981730i	$-0.560939\pi$
$479$	17.3217	−	17.3217i	0.791451	−	0.791451i	0.981730	+	0.190279i	$0.0609394\pi$
$480$	−10.0188	+	5.78437i	−0.457295	+	0.264019i
$481$	12.4428	+	28.1391i	0.567344	+	1.28303i
$482$			3.90182i			0.177723i
$483$		0			0
$484$	9.69539	−	16.7929i	0.440700	−	0.763314i
$485$		−	4.19948i		−	0.190689i
$486$	1.58143	−	5.90197i	0.0717350	−	0.267719i
$487$	−9.89230	−	36.9186i	−0.448263	−	1.67294i	−0.707174	−	0.707039i	$-0.750030\pi$
$487$	−9.89230	−	36.9186i	−0.448263	−	1.67294i	0.258911	−	0.965901i	$-0.416636\pi$
$488$	7.40357	−	7.40357i	0.335144	−	0.335144i
$489$	−6.85254	+	6.85254i	−0.309883	+	0.309883i
$490$		0			0
$491$	10.2155	+	5.89793i	0.461020	+	0.266170i	0.712473	−	0.701700i	$-0.247575\pi$
$491$	10.2155	+	5.89793i	0.461020	+	0.266170i	−0.251453	+	0.967869i	$0.580908\pi$
$492$	−1.07247	+	4.00250i	−0.0483505	+	0.180447i
$493$	−6.73298	−	11.6619i	−0.303238	−	0.525224i
$494$	−1.55723	−	0.602306i	−0.0700633	−	0.0270990i
$495$	−19.3131	−	11.1504i	−0.868060	−	0.501174i
$496$	20.2691	−	5.43109i	0.910110	−	0.243863i
$497$		0			0
$498$	−3.25914	+	1.88166i	−0.146045	+	0.0843193i
$499$	3.96298	+	14.7901i	0.177408	+	0.662094i	0.996129	+	0.0879031i	$0.0280166\pi$
$499$	3.96298	+	14.7901i	0.177408	+	0.662094i	−0.818722	+	0.574191i	$0.805317\pi$
$500$	21.4985	−	5.76051i	0.961443	−	0.257618i
$501$	59.0110	−	15.8119i	2.63642	−	0.706426i
$502$	−0.459109	−	1.71342i	−0.0204910	−	0.0764736i
$503$	21.5683	−	12.4524i	0.961682	−	0.555227i	0.0649915	−	0.997886i	$-0.479298\pi$
$503$	21.5683	−	12.4524i	0.961682	−	0.555227i	0.896690	+	0.442659i	$0.145965\pi$
$504$		0			0
$505$	15.2169	−	4.07735i	0.677142	−	0.181440i
$506$	−5.20697	−	3.00625i	−0.231478	−	0.133644i
$507$	31.8345	+	6.93574i	1.41382	+	0.308027i
$508$	2.80212	+	4.85341i	0.124324	+	0.215335i
$509$	8.66796	−	32.3493i	0.384201	−	1.43386i	−0.455222	−	0.890378i	$-0.650440\pi$
$509$	8.66796	−	32.3493i	0.384201	−	1.43386i	0.839423	−	0.543478i	$-0.182893\pi$
$510$	−2.05647	−	1.18730i	−0.0910619	−	0.0525746i
$511$		0			0
$512$	−13.2395	+	13.2395i	−0.585111	+	0.585111i
$513$	0.844721	−	0.844721i	0.0372953	−	0.0372953i
$514$	1.56998	+	5.85924i	0.0692488	+	0.258440i
$515$	6.59694	−	24.6201i	0.290696	−	1.08489i
$516$		−	9.47591i		−	0.417154i
$517$	18.4327	−	31.9264i	0.810670	−	1.40412i
$518$		0			0
$519$			12.0296i			0.528039i
$520$	5.65833	−	0.881473i	0.248134	−	0.0386551i
$521$	−19.8845	+	11.4803i	−0.871155	+	0.502962i	−0.867732	−	0.497032i	$-0.834423\pi$
$521$	−19.8845	+	11.4803i	−0.871155	+	0.502962i	−0.00342331	+	0.999994i	$0.501090\pi$
$522$	3.64646	−	3.64646i	0.159601	−	0.159601i
$523$	2.92715	−	1.68999i	0.127995	−	0.0738980i	−0.434635	−	0.900607i	$-0.643123\pi$
$523$	2.92715	−	1.68999i	0.127995	−	0.0738980i	0.562630	+	0.826709i	$0.309789\pi$
$524$	−9.54015	−	16.5240i	−0.416764	−	0.721856i
$525$		0			0
$526$	2.66785	+	0.714848i	0.116324	+	0.0311688i
$527$	9.76683	+	9.76683i	0.425450	+	0.425450i
$528$	−39.5327	−	10.5927i	−1.72044	−	0.460990i
$529$	−0.0147097	+	0.0254780i	−0.000639552	+	0.00110774i
$530$	2.64676	+	4.58433i	0.114968	+	0.199130i
$531$	−1.31564	−	4.91004i	−0.0570939	−	0.213078i
$532$		0			0
$533$	1.82627	−	2.50027i	0.0791046	−	0.108299i
$534$	−4.80470	+	8.32199i	−0.207920	+	0.360128i
$535$	4.24724	+	4.24724i	0.183624	+	0.183624i
$536$	0.585195			0.0252766
$537$	27.9206			1.20486
$538$	2.00167	+	2.00167i	0.0862979	+	0.0862979i
$539$		0			0
$540$	−0.520139	+	1.94119i	−0.0223832	+	0.0835353i
$541$	31.0743	−	8.32634i	1.33599	−	0.357977i	0.481044	−	0.876696i	$-0.340258\pi$
$541$	31.0743	−	8.32634i	1.33599	−	0.357977i	0.854945	+	0.518719i	$0.173591\pi$
$542$	0.773787	+	0.446746i	0.0332370	+	0.0191894i
$543$			10.8383i			0.465114i
$544$	−7.05172	−	1.88950i	−0.302340	−	0.0810118i
$545$	11.7282			0.502383
$546$		0			0
$547$	−13.1782			−0.563460			−0.281730	−	0.959494i	$-0.590908\pi$
$547$	−13.1782			−0.563460			−0.281730	+	0.959494i	$0.590908\pi$
$548$	−1.01293	−	0.271415i	−0.0432704	−	0.0115943i
$549$		−	32.0263i		−	1.36685i
$550$	−3.05059	−	1.76126i	−0.130078	−	0.0751004i
$551$	−9.41234	+	2.52203i	−0.400979	+	0.107442i
$552$	−3.33505	+	12.4466i	−0.141949	+	0.529761i
$553$		0			0
$554$	−3.21995	−	3.21995i	−0.136803	−	0.136803i
$555$	31.6644			1.34408
$556$	−7.39198			−0.313490
$557$	−2.88728	−	2.88728i	−0.122338	−	0.122338i	0.643287	−	0.765625i	$-0.277570\pi$
$557$	−2.88728	−	2.88728i	−0.122338	−	0.122338i	−0.765625	+	0.643287i	$0.777570\pi$
$558$	−2.64477	+	4.58088i	−0.111962	+	0.193924i
$559$	−2.55421	+	6.60379i	−0.108032	+	0.279311i
$560$		0			0
$561$	−6.97247	−	26.0216i	−0.294378	−	1.09863i
$562$	1.55000	+	2.68468i	0.0653828	+	0.113246i
$563$	−10.2301	+	17.7191i	−0.431149	+	0.746772i	−0.996973	−	0.0777545i	$-0.975225\pi$
$563$	−10.2301	+	17.7191i	−0.431149	+	0.746772i	0.565824	+	0.824526i	$0.308558\pi$
$564$	−37.4319	−	10.0298i	−1.57617	−	0.422333i
$565$	−19.3290	−	19.3290i	−0.813177	−	0.813177i
$566$	−3.81191	−	1.02140i	−0.160227	−	0.0429326i
$567$		0			0
$568$	−0.983208	−	1.70297i	−0.0412545	−	0.0714549i
$569$	8.00992	−	4.62453i	0.335793	−	0.193870i	−0.322617	−	0.946530i	$-0.604563\pi$
$569$	8.00992	−	4.62453i	0.335793	−	0.193870i	0.658410	+	0.752659i	$0.271229\pi$
$570$	−1.21505	+	1.21505i	−0.0508927	+	0.0508927i
$571$	−35.2658	+	20.3607i	−1.47583	+	0.852069i	−0.999628	−	0.0272690i	$-0.991319\pi$
$571$	−35.2658	+	20.3607i	−1.47583	+	0.852069i	−0.476198	+	0.879338i	$0.657986\pi$
$572$	25.7321	+	18.7955i	1.07591	+	0.785877i
$573$		−	15.8382i		−	0.661650i
$574$		0			0
$575$	6.72885	−	11.6547i	0.280613	−	0.486035i
$576$			20.5504i			0.856267i
$577$	−2.82885	+	10.5574i	−0.117767	+	0.439511i	−0.999479	−	0.0322762i	$-0.989724\pi$
$577$	−2.82885	+	10.5574i	−0.117767	+	0.439511i	0.881712	+	0.471788i	$0.156391\pi$
$578$	0.814608	+	3.04016i	0.0338832	+	0.126454i
$579$	−21.1109	+	21.1109i	−0.877337	+	0.877337i
$580$	11.5914	−	11.5914i	0.481305	−	0.481305i
$581$		0			0
$582$	1.68246	+	0.971367i	0.0697401	+	0.0402644i
$583$	−15.5432	+	58.0080i	−0.643733	+	2.40244i
$584$	−1.26737	−	2.19515i	−0.0524441	−	0.0908358i
$585$	10.3318	−	14.1449i	0.427169	−	0.584820i
$586$	3.89810	+	2.25057i	0.161029	+	0.0929703i
$587$	15.6037	−	4.18099i	0.644033	−	0.172568i	0.0780032	−	0.996953i	$-0.475146\pi$
$587$	15.6037	−	4.18099i	0.644033	−	0.172568i	0.566029	+	0.824385i	$0.308479\pi$
$588$		0			0
$589$	8.65597	−	4.99753i	0.356663	−	0.205920i
$590$	0.162233	+	0.605463i	0.00667904	+	0.0249265i
$591$	4.99007	−	1.33708i	0.205264	−	0.0550003i
$592$	29.3226	−	7.85696i	1.20515	−	0.322919i
$593$	11.9735	+	44.6856i	0.491691	+	1.83502i	0.547824	+	0.836594i	$0.315456\pi$
$593$	11.9735	+	44.6856i	0.491691	+	1.83502i	−0.0561324	+	0.998423i	$0.517877\pi$
$594$	0.765937	−	0.442214i	0.0314268	−	0.0181443i
$595$		0			0
$596$	−43.4987	+	11.6554i	−1.78178	+	0.477425i
$597$	40.2902	+	23.2616i	1.64897	+	0.952033i
$598$	2.78555	−	3.81358i	0.113910	−	0.155949i
$599$	5.89887	+	10.2171i	0.241021	+	0.417461i	0.961005	−	0.276529i	$-0.0891843\pi$
$599$	5.89887	+	10.2171i	0.241021	+	0.417461i	−0.719984	+	0.693990i	$0.755851\pi$
$600$	−1.95390	+	7.29204i	−0.0797675	+	0.297696i
$601$	11.5727	+	6.68152i	0.472062	+	0.272545i	0.717102	−	0.696968i	$-0.245468\pi$
$601$	11.5727	+	6.68152i	0.472062	+	0.272545i	−0.245041	+	0.969513i	$0.578801\pi$
$602$		0			0
$603$	1.26572	−	1.26572i	0.0515439	−	0.0515439i
$604$	8.97487	−	8.97487i	0.365182	−	0.365182i
$605$	3.85938	+	14.4034i	0.156906	+	0.585582i
$606$	−1.88623	+	7.03952i	−0.0766230	+	0.285961i
$607$		−	34.1174i		−	1.38478i	−0.721522	−	0.692392i	$-0.756557\pi$
$607$		−	34.1174i		−	1.38478i	0.721522	−	0.692392i	$-0.243443\pi$
$608$	−2.64142	+	4.57508i	−0.107124	+	0.185544i
$609$		0			0
$610$			3.94921i			0.159899i
$611$	23.3829	+	17.0795i	0.945970	+	0.690963i
$612$	−12.8114	+	7.39665i	−0.517869	+	0.298992i
$613$	−2.87688	+	2.87688i	−0.116196	+	0.116196i	−0.762814	−	0.646618i	$-0.776183\pi$
$613$	−2.87688	+	2.87688i	−0.116196	+	0.116196i	0.646618	+	0.762814i	$0.276183\pi$
$614$	−2.76996	+	1.59924i	−0.111787	+	0.0645400i
$615$	−1.59325	−	2.75959i	−0.0642461	−	0.111277i
$616$		0			0
$617$	−17.7169	−	4.74724i	−0.713257	−	0.191117i	−0.116096	−	0.993238i	$-0.537038\pi$
$617$	−17.7169	−	4.74724i	−0.713257	−	0.191117i	−0.597161	+	0.802121i	$0.703705\pi$
$618$	8.33776	+	8.33776i	0.335394	+	0.335394i
$619$	35.0270	+	9.38547i	1.40786	+	0.377234i	0.881159	−	0.472820i	$-0.156764\pi$
$619$	35.0270	+	9.38547i	1.40786	+	0.377234i	0.526697	+	0.850053i	$0.323430\pi$
$620$	−8.40718	+	14.5617i	−0.337641	+	0.584811i
$621$	1.68947	+	2.92624i	0.0677960	+	0.117426i
$622$	0.912620	+	3.40595i	0.0365927	+	0.136566i
$623$		0			0
$624$	11.5965	−	29.9822i	0.464231	−	1.20025i
$625$	−1.53798	+	2.66385i	−0.0615191	+	0.106554i
$626$	−1.15208	−	1.15208i	−0.0460465	−	0.0460465i
$627$	−19.4943			−0.778526
$628$	21.1042			0.842148
$629$	14.1293	+	14.1293i	0.563373	+	0.563373i
$630$		0			0
$631$	6.52992	−	24.3700i	0.259952	−	0.970153i	−0.705316	−	0.708893i	$-0.749195\pi$
$631$	6.52992	−	24.3700i	0.259952	−	0.970153i	0.965268	−	0.261261i	$-0.0841383\pi$
$632$	4.42119	−	1.18465i	0.175866	−	0.0471230i
$633$	−6.09330	−	3.51797i	−0.242187	−	0.139827i
$634$			3.53562i			0.140417i
$635$	−4.16281	−	1.11542i	−0.165196	−	0.0442642i
$636$	63.1280			2.50319
$637$		0			0
$638$	−7.21420			−0.285613
$639$	−5.80992	−	1.55676i	−0.229837	−	0.0615846i
$640$		−	11.7660i		−	0.465092i
$641$	−9.82660	−	5.67339i	−0.388127	−	0.224085i	0.293221	−	0.956045i	$-0.405273\pi$
$641$	−9.82660	−	5.67339i	−0.388127	−	0.224085i	−0.681348	+	0.731959i	$0.738606\pi$
$642$	−2.68401	+	0.719177i	−0.105929	+	0.0283837i
$643$	−2.92632	+	10.9212i	−0.115403	+	0.430690i	−0.999317	−	0.0369602i	$-0.988233\pi$
$643$	−2.92632	+	10.9212i	−0.115403	+	0.430690i	0.883914	+	0.467650i	$0.154899\pi$
$644$		0			0
$645$	5.15267	+	5.15267i	0.202886	+	0.202886i
$646$	−1.08436			−0.0426635
$647$	−19.2816			−0.758039			−0.379020	−	0.925389i	$-0.623739\pi$
$647$	−19.2816			−0.758039			−0.379020	+	0.925389i	$0.623739\pi$
$648$	6.12673	+	6.12673i	0.240681	+	0.240681i
$649$	−3.55560	+	6.15848i	−0.139569	+	0.241741i
$650$	1.63196	−	2.23425i	0.0640108	−	0.0876346i
$651$		0			0
$652$	−1.92681	−	7.19096i	−0.0754598	−	0.281620i
$653$	−1.99409	−	3.45386i	−0.0780346	−	0.135160i	0.824367	−	0.566055i	$-0.191531\pi$
$653$	−1.99409	−	3.45386i	−0.0780346	−	0.135160i	−0.902402	+	0.430895i	$0.858198\pi$
$654$	−2.71282	+	4.69874i	−0.106080	+	0.183735i
$655$	14.1728	+	3.79759i	0.553777	+	0.148384i
$656$	−2.16016	−	2.16016i	−0.0843402	−	0.0843402i
$657$	−7.48906	−	2.00669i	−0.292176	−	0.0782883i
$658$		0			0
$659$	−13.3526	−	23.1273i	−0.520143	−	0.900913i	−0.999726	−	0.0234170i	$-0.992545\pi$
$659$	−13.3526	−	23.1273i	−0.520143	−	0.900913i	0.479583	−	0.877496i	$-0.340788\pi$
$660$	28.4009	−	16.3973i	1.10550	−	0.638263i
$661$	−10.0407	+	10.0407i	−0.390539	+	0.390539i	−0.874880	−	0.484340i	$-0.839060\pi$
$661$	−10.0407	+	10.0407i	−0.390539	+	0.390539i	0.484340	+	0.874880i	$0.339060\pi$
$662$	−2.36509	+	1.36549i	−0.0919220	+	0.0530712i
$663$	20.9077	−	3.25708i	0.811990	−	0.126494i
$664$		−	5.89415i		−	0.228738i
$665$		0			0
$666$	−3.82609	+	6.62699i	−0.148258	+	0.256790i
$667$		−	27.5617i		−	1.06719i
$668$	−12.1468	+	45.3325i	−0.469974	+	1.75397i
$669$	−10.5217	−	39.2674i	−0.406791	−	1.51816i
$670$	−0.156077	+	0.156077i	−0.00602978	+	0.00602978i
$671$	−31.6806	+	31.6806i	−1.22302	+	1.22302i
$672$		0			0
$673$	34.5521	+	19.9487i	1.33189	+	0.768965i	0.985589	−	0.169159i	$-0.0541052\pi$
$673$	34.5521	+	19.9487i	1.33189	+	0.768965i	0.346298	+	0.938124i	$0.387439\pi$
$674$	−1.24013	+	4.62822i	−0.0477680	+	0.178273i
$675$	0.989804	+	1.71439i	0.0380976	+	0.0659869i
$676$	−16.8419	+	18.5150i	−0.647767	+	0.712114i
$677$	−5.68825	−	3.28411i	−0.218617	−	0.126219i	0.386693	−	0.922209i	$-0.373617\pi$
$677$	−5.68825	−	3.28411i	−0.218617	−	0.126219i	−0.605310	+	0.795990i	$0.706951\pi$
$678$	12.2148	−	3.27294i	0.469106	−	0.125697i
$679$		0			0
$680$	3.22086	−	1.85956i	0.123514	−	0.0713110i
$681$	−1.13853	−	4.24906i	−0.0436286	−	0.162824i
$682$	7.14765	−	1.91521i	0.273698	−	0.0733371i
$683$	−11.2790	+	3.02219i	−0.431578	+	0.115641i	−0.468067	−	0.883693i	$-0.655049\pi$
$683$	−11.2790	+	3.02219i	−0.431578	+	0.115641i	0.0364888	+	0.999334i	$0.488383\pi$
$684$	2.77063	+	10.3401i	0.105938	+	0.395364i
$685$	0.698384	−	0.403212i	0.0266839	−	0.0154060i
$686$		0			0
$687$	26.9785	−	7.22888i	1.02930	−	0.275799i
$688$	6.05014	+	3.49305i	0.230659	+	0.133171i
$689$	−43.9941	−	17.0160i	−1.67604	−	0.648259i
$690$	−2.43013	−	4.20911i	−0.0925135	−	0.160238i
$691$	5.09630	−	19.0196i	0.193872	−	0.723541i	−0.798684	−	0.601751i	$-0.794470\pi$
$691$	5.09630	−	19.0196i	0.193872	−	0.723541i	0.992556	−	0.121790i	$-0.0388635\pi$
$692$	−8.00308	−	4.62058i	−0.304231	−	0.175648i
$693$		0			0
$694$	5.07347	−	5.07347i	0.192586	−	0.192586i
$695$	4.01950	−	4.01950i	0.152468	−	0.152468i
$696$	4.00162	+	14.9343i	0.151681	+	0.566081i
$697$	0.520446	−	1.94233i	0.0197133	−	0.0735710i
$698$			3.06352i			0.115956i
$699$	25.5204	−	44.2027i	0.965271	−	1.67190i
$700$		0			0
$701$		−	1.58634i		−	0.0599153i	−0.999551	−	0.0299577i	$-0.990463\pi$
$701$		−	1.58634i		−	0.0599153i	0.999551	−	0.0299577i	$-0.00953725\pi$
$702$	0.280941	+	0.635340i	0.0106034	+	0.0239793i
$703$	12.5223	−	7.22974i	0.472287	−	0.272675i
$704$	20.3286	−	20.3286i	0.766163	−	0.766163i
$705$	25.8081	−	14.9003i	0.971988	−	0.561177i
$706$	0.957033	+	1.65763i	0.0360184	+	0.0623857i
$707$		0			0
$708$	7.22047	+	1.93472i	0.271362	+	0.0727111i
$709$	−12.2017	−	12.2017i	−0.458246	−	0.458246i	0.439834	−	0.898079i	$-0.355037\pi$
$709$	−12.2017	−	12.2017i	−0.458246	−	0.458246i	−0.898079	+	0.439834i	$0.855037\pi$
$710$	0.716428	+	0.191966i	0.0268871	+	0.00720437i
$711$	7.00029	−	12.1249i	0.262531	−	0.454718i
$712$	−7.52517	−	13.0340i	−0.282017	−	0.488469i
$713$	7.31700	+	27.3074i	0.274024	+	1.02267i
$714$		0			0
$715$	−24.2125	+	3.77191i	−0.905498	+	0.141061i
$716$	−10.7244	+	18.5751i	−0.400788	+	0.694186i
$717$	36.6314	+	36.6314i	1.36802	+	1.36802i
$718$	−1.39693			−0.0521328
$719$	−23.1711			−0.864137			−0.432069	−	0.901841i	$-0.642216\pi$
$719$	−23.1711			−0.864137			−0.432069	+	0.901841i	$0.642216\pi$
$720$	−12.2208	−	12.2208i	−0.455441	−	0.455441i
$721$		0			0
$722$	1.14082	−	4.25761i	0.0424570	−	0.158452i
$723$	−34.5633	+	9.26120i	−1.28542	+	0.344428i
$724$	−7.21053	−	4.16300i	−0.267977	−	0.154717i
$725$		−	16.1475i		−	0.599703i
$726$	−6.66321	−	1.78540i	−0.247295	−	0.0662625i
$727$	−18.3365			−0.680062			−0.340031	−	0.940414i	$-0.610438\pi$
$727$	−18.3365			−0.680062			−0.340031	+	0.940414i	$0.610438\pi$
$728$		0			0
$729$	31.8037			1.17792
$730$	0.923485	+	0.247447i	0.0341797	+	0.00915843i
$731$			4.59846i			0.170080i
$732$	40.7866	+	23.5482i	1.50752	+	0.870365i
$733$	19.6316	−	5.26026i	0.725108	−	0.194292i	0.122658	−	0.992449i	$-0.460858\pi$
$733$	19.6316	−	5.26026i	0.725108	−	0.194292i	0.602450	+	0.798157i	$0.294191\pi$
$734$	−1.29987	+	4.85119i	−0.0479791	+	0.179061i
$735$		0			0
$736$	−10.5659	−	10.5659i	−0.389463	−	0.389463i
$737$	−2.50411			−0.0922400
$738$	0.770067			0.0283465
$739$	−23.4876	−	23.4876i	−0.864004	−	0.864004i	0.127797	−	0.991800i	$-0.459209\pi$
$739$	−23.4876	−	23.4876i	−0.864004	−	0.864004i	−0.991800	+	0.127797i	$0.959209\pi$
$740$	−12.1624	+	21.0658i	−0.447097	+	0.774395i
$741$	1.63919	−	15.2240i	0.0602170	−	0.559266i
$742$		0			0
$743$	1.88756	+	7.04445i	0.0692477	+	0.258436i	0.991868	−	0.127275i	$-0.0406230\pi$
$743$	1.88756	+	7.04445i	0.0692477	+	0.258436i	−0.922620	+	0.385711i	$0.873956\pi$
$744$	−7.92941	−	13.7341i	−0.290706	−	0.503518i
$745$	17.3153	−	29.9909i	0.634382	−	1.09878i
$746$	5.50442	+	1.47491i	0.201531	+	0.0540001i
$747$	−12.7484	−	12.7484i	−0.466441	−	0.466441i
$748$	19.9899	+	5.35628i	0.730903	+	0.195845i
$749$		0			0
$750$	−3.95894	−	6.85709i	−0.144560	−	0.250385i
$751$	6.19866	−	3.57880i	0.226192	−	0.130592i	−0.382622	−	0.923905i	$-0.624979\pi$
$751$	6.19866	−	3.57880i	0.226192	−	0.130592i	0.608814	+	0.793313i	$0.291645\pi$
$752$	20.2021	−	20.2021i	0.736695	−	0.736695i
$753$	14.0882	−	8.13380i	0.513401	−	0.296412i
$754$	0.606610	−	5.63390i	0.0220915	−	0.205175i
$755$			9.76045i			0.355219i
$756$		0			0
$757$	7.08185	−	12.2661i	0.257394	−	0.445820i	−0.708149	−	0.706063i	$-0.750469\pi$
$757$	7.08185	−	12.2661i	0.257394	−	0.445820i	0.965543	+	0.260243i	$0.0838027\pi$
$758$			7.62385i			0.276911i
$759$	14.2710	−	53.2601i	0.518005	−	1.93322i
$760$	−0.696552	−	2.59957i	−0.0252666	−	0.0942963i
$761$	10.2079	−	10.2079i	0.370038	−	0.370038i	−0.497453	−	0.867491i	$-0.665731\pi$
$761$	10.2079	−	10.2079i	0.370038	−	0.370038i	0.867491	+	0.497453i	$0.165731\pi$
$762$	1.40976	−	1.40976i	0.0510703	−	0.0510703i
$763$		0			0
$764$	10.5369	+	6.08348i	0.381212	+	0.220093i
$765$	2.94434	−	10.9884i	0.106453	−	0.397287i
$766$	−3.35853	−	5.81714i	−0.121349	−	0.210182i
$767$	−4.51047	−	3.29457i	−0.162863	−	0.118960i
$768$	−22.4731	−	12.9748i	−0.810926	−	0.468189i
$769$	−48.9223	+	13.1087i	−1.76418	+	0.472711i	−0.987559	−	0.157252i	$-0.949737\pi$
$769$	−48.9223	+	13.1087i	−1.76418	+	0.472711i	−0.776625	+	0.629963i	$0.783070\pi$
$770$		0			0
$771$	−48.1761	+	27.8145i	−1.73502	+	1.00171i
$772$	−5.93600	−	22.1535i	−0.213641	−	0.797320i
$773$	11.3142	−	3.03164i	0.406944	−	0.109040i	−0.0495394	−	0.998772i	$-0.515775\pi$
$773$	11.3142	−	3.03164i	0.406944	−	0.109040i	0.456484	+	0.889732i	$0.349109\pi$
$774$	−1.70100	+	0.455783i	−0.0611414	+	0.0163828i
$775$	4.28679	+	15.9985i	0.153986	+	0.574684i
$776$	−2.63508	+	1.52136i	−0.0945938	+	0.0546137i
$777$		0			0
$778$	−6.46445	+	1.73215i	−0.231762	+	0.0621004i
$779$	−1.26016	−	0.727555i	−0.0451500	−	0.0260674i
$780$	10.4173	+	23.5584i	0.372999	+	0.843525i
$781$	4.20725	+	7.28716i	0.150547	+	0.260755i
$782$	0.793818	−	2.96257i	0.0283869	−	0.105941i
$783$	3.51111	+	2.02714i	0.125477	+	0.0724441i
$784$		0			0
$785$	−11.4757	+	11.4757i	−0.409586	+	0.409586i
$786$	−4.79971	+	4.79971i	−0.171200	+	0.171200i
$787$	−9.10172	−	33.9681i	−0.324441	−	1.21083i	−0.914872	−	0.403743i	$-0.867709\pi$
$787$	−9.10172	−	33.9681i	−0.324441	−	1.21083i	0.590431	−	0.807088i	$-0.298958\pi$
$788$	−1.02715	+	3.83339i	−0.0365908	+	0.136559i
$789$			25.3292i			0.901743i
$790$	−0.863215	+	1.49513i	−0.0307118	+	0.0531944i
$791$		0			0
$792$			16.1580i			0.574151i
$793$	−22.0770	−	27.4047i	−0.783976	−	0.973171i
$794$	−4.58265	+	2.64579i	−0.162632	+	0.0938956i
$795$	−34.3268	+	34.3268i	−1.21745	+	1.21745i
$796$	−30.9511	+	17.8696i	−1.09703	+	0.633373i
$797$	4.21417	+	7.29915i	0.149273	+	0.258549i	0.930959	−	0.365123i	$-0.118973\pi$
$797$	4.21417	+	7.29915i	0.149273	+	0.258549i	−0.781686	+	0.623673i	$0.785640\pi$
$798$		0			0
$799$	18.1649	+	4.86727i	0.642629	+	0.172192i
$800$	−6.19019	−	6.19019i	−0.218856	−	0.218856i
$801$	−44.4673	−	11.9150i	−1.57117	−	0.420995i
$802$	−1.80750	+	3.13068i	−0.0638249	+	0.110548i
$803$	5.42319	+	9.39325i	0.191380	+	0.331480i
$804$	0.681283	+	2.54258i	0.0240270	+	0.0896700i
$805$		0			0
$806$	0.894660	+	5.74297i	0.0315130	+	0.202288i
$807$	−12.9802	+	22.4823i	−0.456924	+	0.791415i
$808$	−8.07112	−	8.07112i	−0.283941	−	0.283941i
$809$	38.9122			1.36808			0.684040	−	0.729445i	$-0.260222\pi$
$809$	38.9122			1.36808			0.684040	+	0.729445i	$0.260222\pi$
$810$	−3.26812			−0.114830
$811$	−33.4503	−	33.4503i	−1.17460	−	1.17460i	−0.981101	−	0.193499i	$-0.938016\pi$
$811$	−33.4503	−	33.4503i	−1.17460	−	1.17460i	−0.193499	−	0.981101i	$-0.561984\pi$
$812$		0			0
$813$	−2.12076	+	7.91477i	−0.0743782	+	0.277583i
$814$	10.3402	−	2.77066i	0.362425	−	0.0971116i
$815$	4.95793	+	2.86246i	0.173669	+	0.100268i
$816$		−	20.8777i		−	0.730865i
$817$	3.21420	+	0.861242i	0.112451	+	0.0301311i
$818$	−6.80553			−0.237950
$819$		0			0
$820$	2.44788			0.0854838
$821$	45.9251	+	12.3056i	1.60280	+	0.429468i	0.945886	−	0.324499i	$-0.105196\pi$
$821$	45.9251	+	12.3056i	1.60280	+	0.429468i	0.656912	+	0.753968i	$0.271862\pi$
$822$			0.373063i			0.0130121i
$823$	31.5629	+	18.2229i	1.10022	+	0.635210i	0.936278	−	0.351261i	$-0.114247\pi$
$823$	31.5629	+	18.2229i	1.10022	+	0.635210i	0.163938	+	0.986471i	$0.447580\pi$
$824$	−17.8385	+	4.77980i	−0.621433	+	0.166512i
$825$	8.36092	−	31.2034i	0.291090	−	1.08636i
$826$		0			0
$827$	4.04107	+	4.04107i	0.140522	+	0.140522i	0.773868	−	0.633347i	$-0.218319\pi$
$827$	4.04107	+	4.04107i	0.140522	+	0.140522i	−0.633347	+	0.773868i	$0.718319\pi$
$828$	−30.2784			−1.05225
$829$	35.5680			1.23533			0.617664	−	0.786442i	$-0.288079\pi$
$829$	35.5680			1.23533			0.617664	+	0.786442i	$0.288079\pi$
$830$	1.57203	+	1.57203i	0.0545659	+	0.0545659i
$831$	20.8804	−	36.1659i	0.724332	−	1.25458i
$832$	14.1662	+	17.5849i	0.491124	+	0.609646i
$833$		0			0
$834$	0.680614	+	2.54009i	0.0235677	+	0.0879560i
$835$	−18.0452	−	31.2552i	−0.624481	−	1.08163i
$836$	7.48778	−	12.9692i	0.258970	−	0.448550i
$837$	−4.01688	−	1.07632i	−0.138844	−	0.0372030i
$838$	3.12169	+	3.12169i	0.107837	+	0.107837i
$839$	−14.5158	−	3.88950i	−0.501142	−	0.134280i	−0.000611847	−	1.00000i	$-0.500195\pi$
$839$	−14.5158	−	3.88950i	−0.501142	−	0.134280i	−0.500530	+	0.865719i	$0.666861\pi$
$840$		0			0
$841$	−2.03520	−	3.52507i	−0.0701793	−	0.121554i
$842$	−4.28596	+	2.47450i	−0.147704	+	0.0852769i
$843$	−20.1025	+	20.1025i	−0.692367	+	0.692367i
$844$	4.68090	−	2.70252i	0.161123	−	0.0930246i
$845$	−0.909733	−	19.2259i	−0.0312958	−	0.661389i
$846$			7.20176i			0.247602i
$847$		0			0
$848$	−23.2705	+	40.3057i	−0.799113	+	1.38410i
$849$		−	36.1912i		−	1.24208i
$850$	0.465072	−	1.73567i	0.0159518	−	0.0595331i
$851$	10.5852	+	39.5047i	0.362857	+	1.35420i
$852$	6.25448	−	6.25448i	0.214275	−	0.214275i
$853$	11.5963	−	11.5963i	0.397050	−	0.397050i	−0.480141	−	0.877191i	$-0.659415\pi$
$853$	11.5963	−	11.5963i	0.397050	−	0.397050i	0.877191	+	0.480141i	$0.159415\pi$
$854$		0			0
$855$	−7.12916	−	4.11603i	−0.243812	−	0.140765i
$856$	1.12638	−	4.20371i	0.0384989	−	0.143680i
$857$	−23.4161	−	40.5579i	−0.799880	−	1.38543i	−0.919694	−	0.392637i	$-0.871563\pi$
$857$	−23.4161	−	40.5579i	−0.799880	−	1.38543i	0.119814	−	0.992796i	$-0.461770\pi$
$858$	4.08936	−	10.5728i	0.139608	−	0.360951i
$859$	17.1191	+	9.88371i	0.584095	+	0.337228i	0.762759	−	0.646683i	$-0.223844\pi$
$859$	17.1191	+	9.88371i	0.584095	+	0.337228i	−0.178664	+	0.983910i	$0.557177\pi$
$860$	−5.40715	+	1.44884i	−0.184382	+	0.0494050i
$861$		0			0
$862$	5.29211	−	3.05540i	0.180250	−	0.104067i
$863$	1.86062	+	6.94395i	0.0633364	+	0.236375i	0.990336	−	0.138687i	$-0.0442882\pi$
$863$	1.86062	+	6.94395i	0.0633364	+	0.236375i	−0.927000	+	0.375062i	$0.877622\pi$
$864$	2.12311	−	0.568884i	0.0722295	−	0.0193538i
$865$	6.86431	−	1.83929i	0.233393	−	0.0625376i
$866$	−1.30355	−	4.86491i	−0.0442964	−	0.165316i
$867$	−24.9969	+	14.4320i	−0.848940	+	0.490136i
$868$		0			0
$869$	−18.9187	+	5.06925i	−0.641773	+	0.171963i
$870$	−5.05038	−	2.91584i	−0.171224	−	0.0988562i
$871$	0.210559	−	1.95557i	0.00713453	−	0.0662621i
$872$	−4.24884	−	7.35921i	−0.143884	−	0.249214i
$873$	−2.40885	+	8.98995i	−0.0815272	+	0.304264i
$874$	−1.92208	−	1.10971i	−0.0650154	−	0.0375366i
$875$		0			0
$876$	8.06211	−	8.06211i	0.272393	−	0.272393i
$877$	−22.4699	+	22.4699i	−0.758755	+	0.758755i	−0.976096	−	0.217341i	$-0.930262\pi$
$877$	−22.4699	+	22.4699i	−0.758755	+	0.758755i	0.217341	+	0.976096i	$0.430262\pi$
$878$	1.10342	+	4.11802i	0.0372386	+	0.138976i
$879$	−10.6837	+	39.8722i	−0.360353	+	1.34486i
$880$			24.1777i			0.815031i
$881$	−8.45038	+	14.6365i	−0.284701	+	0.493116i	−0.972537	−	0.232750i	$-0.925228\pi$
$881$	−8.45038	+	14.6365i	−0.284701	+	0.493116i	0.687836	+	0.725866i	$0.258561\pi$
$882$		0			0
$883$		−	21.1502i		−	0.711760i	−0.934532	−	0.355880i	$-0.884181\pi$
$883$		−	21.1502i		−	0.711760i	0.934532	−	0.355880i	$-0.115819\pi$
$884$	−5.86383	+	15.1606i	−0.197222	+	0.509908i
$885$	−4.97827	+	2.87421i	−0.167343	+	0.0966154i
$886$	5.71804	−	5.71804i	0.192101	−	0.192101i
$887$	8.83730	−	5.10222i	0.296727	−	0.171316i	−0.344244	−	0.938880i	$-0.611865\pi$
$887$	8.83730	−	5.10222i	0.296727	−	0.171316i	0.640972	+	0.767564i	$0.278532\pi$
$888$	−11.4712	−	19.8687i	−0.384948	−	0.666750i
$889$		0			0
$890$	5.48332	+	1.46925i	0.183801	+	0.0492494i
$891$	−26.2169	−	26.2169i	−0.878299	−	0.878299i
$892$	30.1654	+	8.08278i	1.01001	+	0.270632i
$893$	6.80419	−	11.7852i	0.227693	−	0.394377i
$894$	8.01026	+	13.8742i	0.267903	+	0.464022i
$895$	−4.26898	−	15.9321i	−0.142696	−	0.532550i
$896$		0			0
$897$	40.3933	+	15.6233i	1.34869	+	0.521647i
$898$	−1.32416	+	2.29352i	−0.0441879	+	0.0765357i
$899$	23.9859	+	23.9859i	0.799974	+	0.799974i
$900$	−17.7391			−0.591305
$901$	−30.6347			−1.02059
$902$	−0.761755	−	0.761755i	−0.0253637	−	0.0253637i
$903$		0			0
$904$	−5.12611	+	19.1309i	−0.170492	+	0.636285i
$905$	6.18453	−	1.65714i	0.205581	−	0.0550852i
$906$	−3.91037	−	2.25765i	−0.129913	−	0.0750056i
$907$			15.6924i			0.521059i	0.965466	+	0.260529i	$0.0838971\pi$
$907$			15.6924i			0.521059i	−0.965466	+	0.260529i	$0.916103\pi$
$908$	3.26415	+	0.874625i	0.108324	+	0.0290255i
$909$	−34.9140			−1.15802
$910$		0			0
$911$	−23.8232			−0.789296			−0.394648	−	0.918832i	$-0.629134\pi$
$911$	−23.8232			−0.789296			−0.394648	+	0.918832i	$0.629134\pi$
$912$	−14.5929	−	3.91017i	−0.483220	−	0.129479i
$913$			25.2217i			0.834715i
$914$	−8.20378	−	4.73645i	−0.271357	−	0.156668i
$915$	−34.9830	+	9.37367i	−1.15650	+	0.309884i
$916$	−5.55326	+	20.7250i	−0.183485	+	0.684774i
$917$		0			0
$918$	0.319020	+	0.319020i	0.0105292	+	0.0105292i
$919$	−8.03295			−0.264983			−0.132491	−	0.991184i	$-0.542298\pi$
$919$	−8.03295			−0.264983			−0.132491	+	0.991184i	$0.542298\pi$
$920$	7.61218			0.250966
$921$	−20.7411	−	20.7411i	−0.683442	−	0.683442i
$922$	1.29370	−	2.24076i	0.0426058	−	0.0737955i
$923$	−6.04465	+	2.67289i	−0.198962	+	0.0879791i
$924$		0			0
$925$	6.20155	+	23.1445i	0.203906	+	0.760986i
$926$	0.694867	+	1.20355i	0.0228348	+	0.0395509i
$927$	−28.2445	+	48.9210i	−0.927672	+	1.60678i
$928$	−17.3180	−	4.64034i	−0.568491	−	0.152327i
$929$	9.07632	+	9.07632i	0.297785	+	0.297785i	0.840146	−	0.542361i	$-0.182469\pi$
$929$	9.07632	+	9.07632i	0.297785	+	0.297785i	−0.542361	+	0.840146i	$0.682469\pi$
$930$	5.77788	+	1.54818i	0.189464	+	0.0507668i
$931$		0			0
$932$	19.6049	+	33.9567i	0.642180	+	1.11229i
$933$	−28.0045	+	16.1684i	−0.916827	+	0.529331i
$934$	−4.66195	+	4.66195i	−0.152544	+	0.152544i
$935$	−13.7824	+	7.95725i	−0.450732	+	0.260230i
$936$	−12.6186	−	1.35866i	−0.412451	−	0.0444092i
$937$			19.3918i			0.633501i	0.948509	+	0.316751i	$0.102592\pi$
$937$			19.3918i			0.633501i	−0.948509	+	0.316751i	$0.897408\pi$
$938$		0			0
$939$	7.47089	−	12.9400i	0.243803	−	0.422279i
$940$			22.8929i			0.746685i
$941$	0.688857	−	2.57085i	0.0224561	−	0.0838073i	−0.953788	−	0.300479i	$-0.902853\pi$
$941$	0.688857	−	2.57085i	0.0224561	−	0.0838073i	0.976245	+	0.216672i	$0.0695201\pi$
$942$	−1.94316	−	7.25197i	−0.0633116	−	0.236282i
$943$	2.91026	−	2.91026i	0.0947713	−	0.0947713i
$944$	−3.89691	+	3.89691i	−0.126834	+	0.126834i
$945$		0			0
$946$	2.13351	+	1.23178i	0.0693663	+	0.0400487i
$947$	5.20734	−	19.4341i	0.169216	−	0.631523i	−0.828249	−	0.560360i	$-0.810663\pi$
$947$	5.20734	−	19.4341i	0.169216	−	0.631523i	0.997465	−	0.0711620i	$-0.0226707\pi$
$948$	10.2943	+	17.8302i	0.334343	+	0.579099i
$949$	−7.79163	+	3.44538i	−0.252927	+	0.111842i
$950$	−1.12608	−	0.650145i	−0.0365350	−	0.0210935i
$951$	−31.3194	+	8.39200i	−1.01560	+	0.272129i
$952$		0			0
$953$	24.0417	−	13.8805i	0.778788	−	0.449634i	−0.0572123	−	0.998362i	$-0.518221\pi$
$953$	24.0417	−	13.8805i	0.778788	−	0.449634i	0.836001	+	0.548728i	$0.184888\pi$
$954$	−3.03640	−	11.3320i	−0.0983071	−	0.366887i
$955$	−9.03758	+	2.42161i	−0.292449	+	0.0783616i
$956$	−38.4405	+	10.3001i	−1.24325	+	0.333129i
$957$	−17.1233	−	63.9052i	−0.553519	−	2.06576i
$958$	5.79773	−	3.34732i	0.187316	−	0.108147i
$959$		0			0
$960$	22.4477	−	6.01483i	0.724495	−	0.194128i
$961$	−3.28554	−	1.89691i	−0.105985	−	0.0611906i
$962$	1.29427	+	8.30815i	0.0417290	+	0.267865i
$963$	−6.65595	−	11.5284i	−0.214485	−	0.371499i
$964$	7.11450	−	26.5517i	0.229143	−	0.855171i
$965$	15.2741	+	8.81849i	0.491690	+	0.283877i
$966$		0			0
$967$	−4.10934	+	4.10934i	−0.132147	+	0.132147i	−0.770087	−	0.637939i	$-0.779787\pi$
$967$	−4.10934	+	4.10934i	−0.132147	+	0.132147i	0.637939	+	0.770087i	$0.279787\pi$
$968$	7.63966	−	7.63966i	0.245548	−	0.245548i
$969$	−2.57379	−	9.60551i	−0.0826820	−	0.308573i
$970$	0.297038	−	1.10856i	0.00953733	−	0.0355938i
$971$			21.7688i			0.698593i	0.937012	+	0.349296i	$0.113579\pi$
$971$			21.7688i			0.698593i	−0.937012	+	0.349296i	$0.886421\pi$
$972$	−21.5230	+	37.2790i	−0.690352	+	1.19572i
$973$		0			0
$974$		−	10.4453i		−	0.334690i
$975$	23.6651	+	9.15318i	0.757890	+	0.293136i
$976$	−30.0699	+	17.3608i	−0.962513	+	0.555707i
$977$	−6.54075	+	6.54075i	−0.209257	+	0.209257i	−0.803952	−	0.594695i	$-0.797273\pi$
$977$	−6.54075	+	6.54075i	−0.209257	+	0.209257i	0.594695	+	0.803952i	$0.297273\pi$
$978$	−2.29360	+	1.32421i	−0.0733413	+	0.0423436i
$979$	32.2009	+	55.7736i	1.02915	+	1.78253i
$980$		0			0
$981$	−25.1070	−	6.72740i	−0.801605	−	0.214789i
$982$	2.27948	+	2.27948i	0.0727411	+	0.0727411i
$983$	53.1178	+	14.2329i	1.69420	+	0.453958i	0.971467	−	0.237174i	$-0.0762210\pi$
$983$	53.1178	+	14.2329i	1.69420	+	0.453958i	0.722729	+	0.691132i	$0.242888\pi$
$984$	−1.15439	+	1.99946i	−0.0368005	+	0.0637404i
$985$	−1.52593	−	2.64299i	−0.0486203	−	0.0842128i
$986$	−0.952477	−	3.55469i	−0.0303331	−	0.113205i
$987$		0			0
$988$	9.49865	+	6.93808i	0.302192	+	0.220730i
$989$	−4.70599	+	8.15101i	−0.149642	+	0.259187i
$990$	−4.30951	−	4.30951i	−0.136965	−	0.136965i
$991$	−4.69901			−0.149269			−0.0746345	−	0.997211i	$-0.523779\pi$
$991$	−4.69901			−0.149269			−0.0746345	+	0.997211i	$0.523779\pi$
$992$	18.3901			0.583887
$993$	−17.7095	−	17.7095i	−0.561995	−	0.561995i
$994$		0			0
$995$	7.11326	−	26.5470i	0.225505	−	0.841598i
$996$	25.6092	−	6.86197i	0.811459	−	0.217430i
$997$	−14.6274	−	8.44515i	−0.463255	−	0.267461i	0.250157	−	0.968205i	$-0.419518\pi$
$997$	−14.6274	−	8.44515i	−0.463255	−	0.267461i	−0.713412	+	0.700745i	$0.752851\pi$
$998$			4.18453i			0.132459i
$999$	−5.81107	−	1.55707i	−0.183854	−	0.0492636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.a.19.4		28
7.2	even	3		637.2.bd.b.97.4		28
7.3	odd	6		637.2.bb.a.227.4		28
7.4	even	3		91.2.ba.a.45.4	yes	28
7.5	odd	6		637.2.bd.a.97.4		28
7.6	odd	2		91.2.w.a.19.4	✓	28
13.11	odd	12		637.2.bb.a.362.4		28
21.11	odd	6		819.2.et.b.136.4		28
21.20	even	2		819.2.gh.b.19.4		28
91.11	odd	12		91.2.w.a.24.4	yes	28
91.24	even	12	inner	637.2.x.a.570.4		28
91.37	odd	12		637.2.bd.a.440.4		28
91.76	even	12		91.2.ba.a.89.4	yes	28
91.89	even	12		637.2.bd.b.440.4		28
273.11	even	12		819.2.gh.b.388.4		28
273.167	odd	12		819.2.et.b.271.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.4	✓	28	7.6	odd	2
91.2.w.a.24.4	yes	28	91.11	odd	12
91.2.ba.a.45.4	yes	28	7.4	even	3
91.2.ba.a.89.4	yes	28	91.76	even	12
637.2.x.a.19.4		28	1.1	even	1	trivial
637.2.x.a.570.4		28	91.24	even	12	inner
637.2.bb.a.227.4		28	7.3	odd	6
637.2.bb.a.362.4		28	13.11	odd	12
637.2.bd.a.97.4		28	7.5	odd	6
637.2.bd.a.440.4		28	91.37	odd	12
637.2.bd.b.97.4		28	7.2	even	3
637.2.bd.b.440.4		28	91.89	even	12
819.2.et.b.136.4		28	21.11	odd	6
819.2.et.b.271.4		28	273.167	odd	12
819.2.gh.b.19.4		28	21.20	even	2
819.2.gh.b.388.4		28	273.11	even	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.263976 + 0.0707322i) q^{2} +2.50625i q^{3} +(-1.66737 - 0.962657i) q^{4} +(1.43012 - 0.383199i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} -3.28130 q^{9} +O(q^{10})\)	\(q+(0.263976 + 0.0707322i) q^{2} +2.50625i q^{3} +(-1.66737 - 0.962657i) q^{4} +(1.43012 - 0.383199i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} -3.28130 q^{9} +0.404621 q^{10} +(3.24588 + 3.24588i) q^{11} +(2.41266 - 4.17885i) q^{12} +(-2.80779 + 2.26193i) q^{13} +(0.960393 + 3.58423i) q^{15} +(1.77873 + 3.08085i) q^{16} +(-1.17081 + 2.02791i) q^{17} +(-0.866185 - 0.232094i) q^{18} +(1.19817 + 1.19817i) q^{19} +(-2.75342 - 0.737778i) q^{20} +(0.627247 + 1.08642i) q^{22} +(-4.15065 + 2.39638i) q^{23} +(1.90110 - 1.90110i) q^{24} +(-2.43173 + 1.40396i) q^{25} +(-0.901181 + 0.398494i) q^{26} -0.705008i q^{27} +(-2.87534 + 4.98024i) q^{29} +1.01408i q^{30} +(1.52668 - 5.69764i) q^{31} +(0.806919 + 3.01146i) q^{32} +(-8.13500 + 8.13500i) q^{33} +(-0.452505 + 0.452505i) q^{34} +(5.47114 + 3.15877i) q^{36} +(2.20859 - 8.24256i) q^{37} +(0.231540 + 0.401038i) q^{38} +(-5.66896 - 7.03703i) q^{39} +(-1.37548 - 0.794133i) q^{40} +(-0.829479 + 0.222258i) q^{41} +(1.70069 - 0.981895i) q^{43} +(-2.28742 - 8.53676i) q^{44} +(-4.69264 + 1.25739i) q^{45} +(-1.26518 + 0.339003i) q^{46} +(-2.07859 - 7.75739i) q^{47} +(-7.72139 + 4.45794i) q^{48} +(-0.741225 + 0.198611i) q^{50} +(-5.08245 - 2.93435i) q^{51} +(6.85909 - 1.06853i) q^{52} +(6.54133 + 11.3299i) q^{53} +(0.0498668 - 0.186105i) q^{54} +(5.88581 + 3.39817i) q^{55} +(-3.00292 + 3.00292i) q^{57} +(-1.11129 + 1.11129i) q^{58} +(0.400951 + 1.49637i) q^{59} +(1.84906 - 6.90078i) q^{60} +9.76025i q^{61} +(0.806013 - 1.39606i) q^{62} -6.26289i q^{64} +(-3.14870 + 4.31076i) q^{65} +(-2.72285 + 1.57204i) q^{66} +(-0.385736 + 0.385736i) q^{67} +(3.90436 - 2.25418i) q^{68} +(-6.00594 - 10.4026i) q^{69} +(1.77061 + 0.474435i) q^{71} +(2.48901 + 2.48901i) q^{72} +(2.28234 + 0.611552i) q^{73} +(1.16603 - 2.01962i) q^{74} +(-3.51868 - 6.09453i) q^{75} +(-0.844368 - 3.15123i) q^{76} +(-0.998725 - 2.25859i) q^{78} +(-2.13339 + 3.69514i) q^{79} +(3.72437 + 3.72437i) q^{80} -8.07697 q^{81} -0.234683 q^{82} +(3.88518 + 3.88518i) q^{83} +(-0.897309 + 3.34880i) q^{85} +(0.518394 - 0.138903i) q^{86} +(-12.4817 - 7.20634i) q^{87} -4.92428i q^{88} +(13.5517 + 3.63117i) q^{89} -1.32768 q^{90} +9.22757 q^{92} +(14.2797 + 3.82624i) q^{93} -2.19479i q^{94} +(2.17267 + 1.25439i) q^{95} +(-7.54749 + 2.02234i) q^{96} +(0.734114 - 2.73975i) q^{97} +(-10.6507 - 10.6507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

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