LMFDB - Embedded newform 637.2.h.b.471.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, 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:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.b.165.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.82843 q^{4} +(0.914214 - 1.58346i) q^{5} +(-0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+0.414214 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.82843 q^{4} +(0.914214 - 1.58346i) q^{5} +(-0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.378680 - 0.655892i) q^{10} +(-0.292893 + 0.507306i) q^{11} +(1.29289 - 2.23936i) q^{12} +(-3.50000 + 0.866025i) q^{13} +(1.29289 + 2.23936i) q^{15} +3.00000 q^{16} -5.82843 q^{17} +(0.207107 + 0.358719i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-1.67157 + 2.89525i) q^{20} +(-0.121320 + 0.210133i) q^{22} -1.41421 q^{23} +(1.12132 - 1.94218i) q^{24} +(0.828427 + 1.43488i) q^{25} +(-1.44975 + 0.358719i) q^{26} -5.65685 q^{27} +(-2.08579 - 3.61269i) q^{29} +(0.535534 + 0.927572i) q^{30} +(-1.29289 - 2.23936i) q^{31} +4.41421 q^{32} +(-0.414214 - 0.717439i) q^{33} -2.41421 q^{34} +(-0.914214 - 1.58346i) q^{36} -9.48528 q^{37} +(-1.24264 - 2.15232i) q^{38} +(1.41421 - 4.89898i) q^{39} +(-1.44975 + 2.51104i) q^{40} +(-0.0857864 - 0.148586i) q^{41} +(-1.70711 + 2.95680i) q^{43} +(0.535534 - 0.927572i) q^{44} +1.82843 q^{45} -0.585786 q^{46} +(1.82843 - 3.16693i) q^{47} +(-2.12132 + 3.67423i) q^{48} +(0.343146 + 0.594346i) q^{50} +(4.12132 - 7.13834i) q^{51} +(6.39949 - 1.58346i) q^{52} +(1.50000 + 2.59808i) q^{53} -2.34315 q^{54} +(0.535534 + 0.927572i) q^{55} +8.48528 q^{57} +(-0.863961 - 1.49642i) q^{58} -10.2426 q^{59} +(-2.36396 - 4.09450i) q^{60} +(-2.08579 - 3.61269i) q^{61} +(-0.535534 - 0.927572i) q^{62} -4.17157 q^{64} +(-1.82843 + 6.33386i) q^{65} +(-0.171573 - 0.297173i) q^{66} +(-2.12132 + 3.67423i) q^{67} +10.6569 q^{68} +(1.00000 - 1.73205i) q^{69} +(5.82843 - 10.0951i) q^{71} +(-0.792893 - 1.37333i) q^{72} +(5.32843 + 9.22911i) q^{73} -3.92893 q^{74} -2.34315 q^{75} +(5.48528 + 9.50079i) q^{76} +(0.585786 - 2.02922i) q^{78} +(-0.878680 + 1.52192i) q^{79} +(2.74264 - 4.75039i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-0.0355339 - 0.0615465i) q^{82} +1.07107 q^{83} +(-5.32843 + 9.22911i) q^{85} +(-0.707107 + 1.22474i) q^{86} +5.89949 q^{87} +(0.464466 - 0.804479i) q^{88} +15.3137 q^{89} +0.757359 q^{90} +2.58579 q^{92} +3.65685 q^{93} +(0.757359 - 1.31178i) q^{94} -10.9706 q^{95} +(-3.12132 + 5.40629i) q^{96} +(5.41421 - 9.37769i) q^{97} -0.585786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9} + 10 q^{10} - 4 q^{11} + 8 q^{12} - 14 q^{13} + 8 q^{15} + 12 q^{16} - 12 q^{17} - 2 q^{18} - 12 q^{19} - 18 q^{20} + 8 q^{22} - 4 q^{24} - 8 q^{25} + 14 q^{26} - 14 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} + 12 q^{38} + 14 q^{40} - 6 q^{41} - 4 q^{43} - 12 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} + 24 q^{50} + 8 q^{51} - 14 q^{52} + 6 q^{53} - 32 q^{54} - 12 q^{55} + 22 q^{58} - 24 q^{59} + 16 q^{60} - 14 q^{61} + 12 q^{62} - 28 q^{64} + 4 q^{65} - 12 q^{66} + 20 q^{68} + 4 q^{69} + 12 q^{71} - 6 q^{72} + 10 q^{73} - 44 q^{74} - 32 q^{75} - 12 q^{76} + 8 q^{78} - 12 q^{79} - 6 q^{80} + 10 q^{81} + 14 q^{82} - 24 q^{83} - 10 q^{85} - 16 q^{87} + 16 q^{88} + 16 q^{89} + 20 q^{90} + 16 q^{92} - 8 q^{93} + 20 q^{94} + 24 q^{95} - 4 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9 + 10 * q^10 - 4 * q^11 + 8 * q^12 - 14 * q^13 + 8 * q^15 + 12 * q^16 - 12 * q^17 - 2 * q^18 - 12 * q^19 - 18 * q^20 + 8 * q^22 - 4 * q^24 - 8 * q^25 + 14 * q^26 - 14 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 + 12 * q^38 + 14 * q^40 - 6 * q^41 - 4 * q^43 - 12 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 + 24 * q^50 + 8 * q^51 - 14 * q^52 + 6 * q^53 - 32 * q^54 - 12 * q^55 + 22 * q^58 - 24 * q^59 + 16 * q^60 - 14 * q^61 + 12 * q^62 - 28 * q^64 + 4 * q^65 - 12 * q^66 + 20 * q^68 + 4 * q^69 + 12 * q^71 - 6 * q^72 + 10 * q^73 - 44 * q^74 - 32 * q^75 - 12 * q^76 + 8 * q^78 - 12 * q^79 - 6 * q^80 + 10 * q^81 + 14 * q^82 - 24 * q^83 - 10 * q^85 - 16 * q^87 + 16 * q^88 + 16 * q^89 + 20 * q^90 + 16 * q^92 - 8 * q^93 + 20 * q^94 + 24 * q^95 - 4 * q^96 + 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.414214			0.292893			0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214			0.292893			0.146447	+	0.989219i	$0.453216\pi$
$3$	−0.707107	+	1.22474i	−0.408248	+	0.707107i	−0.994694	−	0.102882i	$-0.967194\pi$
$3$	−0.707107	+	1.22474i	−0.408248	+	0.707107i	0.586445	+	0.809989i	$0.300527\pi$
$4$	−1.82843			−0.914214
$5$	0.914214	−	1.58346i	0.408849	−	0.708147i	−0.585912	−	0.810374i	$-0.699264\pi$
$5$	0.914214	−	1.58346i	0.408849	−	0.708147i	0.994761	+	0.102228i	$0.0325970\pi$
$6$	−0.292893	+	0.507306i	−0.119573	+	0.207107i
$7$		0			0
$7$		0			0
$8$	−1.58579			−0.560660
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.378680	−	0.655892i	0.119749	−	0.207411i
$11$	−0.292893	+	0.507306i	−0.0883106	+	0.152958i	−0.906797	−	0.421567i	$-0.861480\pi$
$11$	−0.292893	+	0.507306i	−0.0883106	+	0.152958i	0.818487	+	0.574526i	$0.194813\pi$
$12$	1.29289	−	2.23936i	0.373226	−	0.646447i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$		0			0
$15$	1.29289	+	2.23936i	0.333824	+	0.578199i
$16$	3.00000			0.750000
$17$	−5.82843			−1.41360			−0.706801	−	0.707413i	$-0.749862\pi$
$17$	−5.82843			−1.41360			−0.706801	+	0.707413i	$0.749862\pi$
$18$	0.207107	+	0.358719i	0.0488155	+	0.0845510i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	−1.67157	+	2.89525i	−0.373775	+	0.647397i
$21$		0			0
$22$	−0.121320	+	0.210133i	−0.0258656	+	0.0448005i
$23$	−1.41421			−0.294884			−0.147442	−	0.989071i	$-0.547104\pi$
$23$	−1.41421			−0.294884			−0.147442	+	0.989071i	$0.547104\pi$
$24$	1.12132	−	1.94218i	0.228889	−	0.396447i
$25$	0.828427	+	1.43488i	0.165685	+	0.286976i
$26$	−1.44975	+	0.358719i	−0.284319	+	0.0703507i
$27$	−5.65685			−1.08866
$28$		0			0
$29$	−2.08579	−	3.61269i	−0.387321	−	0.670859i	0.604767	−	0.796402i	$-0.293266\pi$
$29$	−2.08579	−	3.61269i	−0.387321	−	0.670859i	−0.992088	+	0.125543i	$0.959933\pi$
$30$	0.535534	+	0.927572i	0.0977747	+	0.169351i
$31$	−1.29289	−	2.23936i	−0.232210	−	0.402200i	0.726248	−	0.687433i	$-0.241262\pi$
$31$	−1.29289	−	2.23936i	−0.232210	−	0.402200i	−0.958458	+	0.285233i	$0.907929\pi$
$32$	4.41421			0.780330
$33$	−0.414214	−	0.717439i	−0.0721053	−	0.124890i
$34$	−2.41421			−0.414034
$35$		0			0
$36$	−0.914214	−	1.58346i	−0.152369	−	0.263911i
$37$	−9.48528			−1.55937			−0.779685	−	0.626172i	$-0.784621\pi$
$37$	−9.48528			−1.55937			−0.779685	+	0.626172i	$0.784621\pi$
$38$	−1.24264	−	2.15232i	−0.201583	−	0.349152i
$39$	1.41421	−	4.89898i	0.226455	−	0.784465i
$40$	−1.44975	+	2.51104i	−0.229225	+	0.397030i
$41$	−0.0857864	−	0.148586i	−0.0133976	−	0.0232053i	0.859249	−	0.511558i	$-0.170931\pi$
$41$	−0.0857864	−	0.148586i	−0.0133976	−	0.0232053i	−0.872646	+	0.488352i	$0.837598\pi$
$42$		0			0
$43$	−1.70711	+	2.95680i	−0.260331	+	0.450907i	−0.966330	−	0.257306i	$-0.917165\pi$
$43$	−1.70711	+	2.95680i	−0.260331	+	0.450907i	0.705999	+	0.708213i	$0.250498\pi$
$44$	0.535534	−	0.927572i	0.0807348	−	0.139837i
$45$	1.82843			0.272566
$46$	−0.585786			−0.0863695
$47$	1.82843	−	3.16693i	0.266704	−	0.461944i	−0.701305	−	0.712861i	$-0.747399\pi$
$47$	1.82843	−	3.16693i	0.266704	−	0.461944i	0.968009	+	0.250917i	$0.0807322\pi$
$48$	−2.12132	+	3.67423i	−0.306186	+	0.530330i
$49$		0			0
$50$	0.343146	+	0.594346i	0.0485281	+	0.0840532i
$51$	4.12132	−	7.13834i	0.577100	−	0.999567i
$52$	6.39949	−	1.58346i	0.887450	−	0.219587i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$	−2.34315			−0.318862
$55$	0.535534	+	0.927572i	0.0722114	+	0.125074i
$56$		0			0
$57$	8.48528			1.12390
$58$	−0.863961	−	1.49642i	−0.113444	−	0.196490i
$59$	−10.2426			−1.33348			−0.666739	−	0.745291i	$-0.732310\pi$
$59$	−10.2426			−1.33348			−0.666739	+	0.745291i	$0.732310\pi$
$60$	−2.36396	−	4.09450i	−0.305186	−	0.528598i
$61$	−2.08579	−	3.61269i	−0.267058	−	0.462557i	0.701043	−	0.713119i	$-0.252718\pi$
$61$	−2.08579	−	3.61269i	−0.267058	−	0.462557i	−0.968101	+	0.250562i	$0.919385\pi$
$62$	−0.535534	−	0.927572i	−0.0680129	−	0.117802i
$63$		0			0
$64$	−4.17157			−0.521447
$65$	−1.82843	+	6.33386i	−0.226788	+	0.785618i
$66$	−0.171573	−	0.297173i	−0.0211192	−	0.0365795i
$67$	−2.12132	+	3.67423i	−0.259161	+	0.448879i	−0.966017	−	0.258478i	$-0.916779\pi$
$67$	−2.12132	+	3.67423i	−0.259161	+	0.448879i	0.706857	+	0.707357i	$0.250113\pi$
$68$	10.6569			1.29233
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$		0			0
$71$	5.82843	−	10.0951i	0.691707	−	1.19807i	−0.279571	−	0.960125i	$-0.590192\pi$
$71$	5.82843	−	10.0951i	0.691707	−	1.19807i	0.971278	−	0.237947i	$-0.0764744\pi$
$72$	−0.792893	−	1.37333i	−0.0934434	−	0.161849i
$73$	5.32843	+	9.22911i	0.623645	+	1.08019i	0.988801	+	0.149239i	$0.0476823\pi$
$73$	5.32843	+	9.22911i	0.623645	+	1.08019i	−0.365156	+	0.930946i	$0.618984\pi$
$74$	−3.92893			−0.456729
$75$	−2.34315			−0.270563
$76$	5.48528	+	9.50079i	0.629205	+	1.08981i
$77$		0			0
$78$	0.585786	−	2.02922i	0.0663273	−	0.229764i
$79$	−0.878680	+	1.52192i	−0.0988592	+	0.171229i	−0.911213	−	0.411936i	$-0.864853\pi$
$79$	−0.878680	+	1.52192i	−0.0988592	+	0.171229i	0.812354	+	0.583165i	$0.198186\pi$
$80$	2.74264	−	4.75039i	0.306637	−	0.531110i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	−0.0355339	−	0.0615465i	−0.00392406	−	0.00679668i
$83$	1.07107			0.117565			0.0587825	−	0.998271i	$-0.481278\pi$
$83$	1.07107			0.117565			0.0587825	+	0.998271i	$0.481278\pi$
$84$		0			0
$85$	−5.32843	+	9.22911i	−0.577949	+	1.00104i
$86$	−0.707107	+	1.22474i	−0.0762493	+	0.132068i
$87$	5.89949			0.632492
$88$	0.464466	−	0.804479i	0.0495123	−	0.0857577i
$89$	15.3137			1.62325			0.811625	−	0.584179i	$-0.198583\pi$
$89$	15.3137			1.62325			0.811625	+	0.584179i	$0.198583\pi$
$90$	0.757359			0.0798327
$91$		0			0
$92$	2.58579			0.269587
$93$	3.65685			0.379198
$94$	0.757359	−	1.31178i	0.0781156	−	0.135300i
$95$	−10.9706			−1.12556
$96$	−3.12132	+	5.40629i	−0.318568	+	0.551777i
$97$	5.41421	−	9.37769i	0.549730	−	0.952160i	−0.448563	−	0.893751i	$-0.648064\pi$
$97$	5.41421	−	9.37769i	0.549730	−	0.952160i	0.998293	−	0.0584091i	$-0.0186028\pi$
$98$		0			0
$99$	−0.585786			−0.0588738
$100$	−1.51472	−	2.62357i	−0.151472	−	0.262357i
$101$	−7.32843	+	12.6932i	−0.729206	+	1.26302i	0.228014	+	0.973658i	$0.426777\pi$
$101$	−7.32843	+	12.6932i	−0.729206	+	1.26302i	−0.957219	+	0.289363i	$0.906556\pi$
$102$	1.70711	−	2.95680i	0.169029	−	0.292766i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	5.55025	−	1.37333i	0.544247	−	0.134666i
$105$		0			0
$106$	0.621320	+	1.07616i	0.0603480	+	0.104526i
$107$	17.3137			1.67378			0.836890	−	0.547372i	$-0.184372\pi$
$107$	17.3137			1.67378			0.836890	+	0.547372i	$0.184372\pi$
$108$	10.3431			0.995270
$109$	6.82843	+	11.8272i	0.654045	+	1.13284i	0.982132	+	0.188191i	$0.0602625\pi$
$109$	6.82843	+	11.8272i	0.654045	+	1.13284i	−0.328088	+	0.944647i	$0.606404\pi$
$110$	0.221825	+	0.384213i	0.0211502	+	0.0366333i
$111$	6.70711	−	11.6170i	0.636610	−	1.10264i
$112$		0			0
$113$	−10.1569	+	17.5922i	−0.955476	+	1.65493i	−0.222202	+	0.975001i	$0.571325\pi$
$113$	−10.1569	+	17.5922i	−0.955476	+	1.65493i	−0.733274	+	0.679933i	$0.762009\pi$
$114$	3.51472			0.329184
$115$	−1.29289	+	2.23936i	−0.120563	+	0.208821i
$116$	3.81371	+	6.60554i	0.354094	+	0.613309i
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	−4.24264			−0.390567
$119$		0			0
$120$	−2.05025	−	3.55114i	−0.187162	−	0.324173i
$121$	5.32843	+	9.22911i	0.484402	+	0.839010i
$122$	−0.863961	−	1.49642i	−0.0782194	−	0.135480i
$123$	0.242641			0.0218782
$124$	2.36396	+	4.09450i	0.212290	+	0.367697i
$125$	12.1716			1.08866
$126$		0			0
$127$	−6.65685	−	11.5300i	−0.590700	−	1.02312i	−0.994138	−	0.108116i	$-0.965518\pi$
$127$	−6.65685	−	11.5300i	−0.590700	−	1.02312i	0.403438	−	0.915007i	$-0.367815\pi$
$128$	−10.5563			−0.933058
$129$	−2.41421	−	4.18154i	−0.212560	−	0.368164i
$130$	−0.757359	+	2.62357i	−0.0664248	+	0.230102i
$131$	−10.6569	+	18.4582i	−0.931094	+	1.61270i	−0.149638	+	0.988741i	$0.547811\pi$
$131$	−10.6569	+	18.4582i	−0.931094	+	1.61270i	−0.781456	+	0.623961i	$0.785523\pi$
$132$	0.757359	+	1.31178i	0.0659197	+	0.114176i
$133$		0			0
$134$	−0.878680	+	1.52192i	−0.0759064	+	0.131474i
$135$	−5.17157	+	8.95743i	−0.445098	+	0.770933i
$136$	9.24264			0.792550
$137$	−0.171573			−0.0146585			−0.00732923	−	0.999973i	$-0.502333\pi$
$137$	−0.171573			−0.0146585			−0.00732923	+	0.999973i	$0.502333\pi$
$138$	0.414214	−	0.717439i	0.0352602	−	0.0610725i
$139$	5.94975	−	10.3053i	0.504651	−	0.874081i	−0.495335	−	0.868702i	$-0.664955\pi$
$139$	5.94975	−	10.3053i	0.504651	−	0.874081i	0.999986	−	0.00537886i	$-0.00171215\pi$
$140$		0			0
$141$	2.58579	+	4.47871i	0.217763	+	0.377176i
$142$	2.41421	−	4.18154i	0.202596	−	0.350907i
$143$	0.585786	−	2.02922i	0.0489859	−	0.169692i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−7.62742			−0.633423
$146$	2.20711	+	3.82282i	0.182661	+	0.316379i
$147$		0			0
$148$	17.3431			1.42560
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$	−0.970563			−0.0792461
$151$	−7.48528	−	12.9649i	−0.609144	−	1.05507i	−0.991382	−	0.131004i	$-0.958180\pi$
$151$	−7.48528	−	12.9649i	−0.609144	−	1.05507i	0.382238	−	0.924064i	$-0.375153\pi$
$152$	4.75736	+	8.23999i	0.385873	+	0.668351i
$153$	−2.91421	−	5.04757i	−0.235600	−	0.408072i
$154$		0			0
$155$	−4.72792			−0.379756
$156$	−2.58579	+	8.95743i	−0.207029	+	0.717168i
$157$	−2.74264	−	4.75039i	−0.218887	−	0.379123i	0.735581	−	0.677436i	$-0.236909\pi$
$157$	−2.74264	−	4.75039i	−0.218887	−	0.379123i	−0.954468	+	0.298314i	$0.903576\pi$
$158$	−0.363961	+	0.630399i	−0.0289552	+	0.0501519i
$159$	−4.24264			−0.336463
$160$	4.03553	−	6.98975i	0.319037	−	0.552588i
$161$		0			0
$162$	1.03553	−	1.79360i	0.0813592	−	0.140918i
$163$	−6.29289	−	10.8996i	−0.492897	−	0.853723i	0.507069	−	0.861905i	$-0.330729\pi$
$163$	−6.29289	−	10.8996i	−0.492897	−	0.853723i	−0.999967	+	0.00818201i	$0.997396\pi$
$164$	0.156854	+	0.271680i	0.0122483	+	0.0212146i
$165$	−1.51472			−0.117921
$166$	0.443651			0.0344340
$167$	−3.36396	−	5.82655i	−0.260311	−	0.450872i	0.706013	−	0.708198i	$-0.250492\pi$
$167$	−3.36396	−	5.82655i	−0.260311	−	0.450872i	−0.966325	+	0.257326i	$0.917158\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−2.20711	+	3.82282i	−0.169277	+	0.293197i
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	3.12132	−	5.40629i	0.237998	−	0.412225i
$173$	5.07107	+	8.78335i	0.385546	+	0.667786i	0.991845	−	0.127452i	$-0.0406797\pi$
$173$	5.07107	+	8.78335i	0.385546	+	0.667786i	−0.606299	+	0.795237i	$0.707346\pi$
$174$	2.44365			0.185253
$175$		0			0
$176$	−0.878680	+	1.52192i	−0.0662330	+	0.114719i
$177$	7.24264	−	12.5446i	0.544390	−	0.942912i
$178$	6.34315			0.475439
$179$	2.82843	−	4.89898i	0.211407	−	0.366167i	−0.740748	−	0.671783i	$-0.765529\pi$
$179$	2.82843	−	4.89898i	0.211407	−	0.366167i	0.952155	+	0.305616i	$0.0988623\pi$
$180$	−3.34315			−0.249183
$181$	9.14214			0.679530			0.339765	−	0.940510i	$-0.389653\pi$
$181$	9.14214			0.679530			0.339765	+	0.940510i	$0.389653\pi$
$182$		0			0
$183$	5.89949			0.436103
$184$	2.24264			0.165330
$185$	−8.67157	+	15.0196i	−0.637547	+	1.10426i
$186$	1.51472			0.111065
$187$	1.70711	−	2.95680i	0.124836	−	0.216222i
$188$	−3.34315	+	5.79050i	−0.243824	+	0.422315i
$189$		0			0
$190$	−4.54416			−0.329668
$191$	−8.12132	−	14.0665i	−0.587638	−	1.01782i	−0.994541	−	0.104348i	$-0.966725\pi$
$191$	−8.12132	−	14.0665i	−0.587638	−	1.01782i	0.406903	−	0.913471i	$-0.366609\pi$
$192$	2.94975	−	5.10911i	0.212880	−	0.368718i
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	−0.965451	−	0.260586i	$-0.916084\pi$
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	0.708400	+	0.705812i	$0.249418\pi$
$194$	2.24264	−	3.88437i	0.161012	−	0.278881i
$195$	−6.46447	−	6.71807i	−0.462930	−	0.481091i
$196$		0			0
$197$	−7.41421	−	12.8418i	−0.528241	−	0.914940i	−0.999458	−	0.0329227i	$-0.989518\pi$
$197$	−7.41421	−	12.8418i	−0.528241	−	0.914940i	0.471217	−	0.882017i	$-0.343815\pi$
$198$	−0.242641			−0.0172437
$199$	−14.9706			−1.06124			−0.530618	−	0.847611i	$-0.678040\pi$
$199$	−14.9706			−1.06124			−0.530618	+	0.847611i	$0.678040\pi$
$200$	−1.31371	−	2.27541i	−0.0928932	−	0.160896i
$201$	−3.00000	−	5.19615i	−0.211604	−	0.366508i
$202$	−3.03553	+	5.25770i	−0.213579	+	0.369930i
$203$		0			0
$204$	−7.53553	+	13.0519i	−0.527593	+	0.913818i
$205$	−0.313708			−0.0219104
$206$	−2.89949	+	5.02207i	−0.202017	+	0.349904i
$207$	−0.707107	−	1.22474i	−0.0491473	−	0.0851257i
$208$	−10.5000	+	2.59808i	−0.728044	+	0.180144i
$209$	3.51472			0.243118
$210$		0			0
$211$	−12.3640	−	21.4150i	−0.851170	−	1.47427i	−0.880153	−	0.474690i	$-0.842560\pi$
$211$	−12.3640	−	21.4150i	−0.851170	−	1.47427i	0.0289828	−	0.999580i	$-0.490773\pi$
$212$	−2.74264	−	4.75039i	−0.188365	−	0.326258i
$213$	8.24264	+	14.2767i	0.564776	+	0.978221i
$214$	7.17157			0.490239
$215$	3.12132	+	5.40629i	0.212872	+	0.368706i
$216$	8.97056			0.610369
$217$		0			0
$218$	2.82843	+	4.89898i	0.191565	+	0.331801i
$219$	−15.0711			−1.01841
$220$	−0.979185	−	1.69600i	−0.0660166	−	0.114344i
$221$	20.3995	−	5.04757i	1.37222	−	0.339536i
$222$	2.77817	−	4.81194i	0.186459	−	0.322956i
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$		0			0
$225$	−0.828427	+	1.43488i	−0.0552285	+	0.0956585i
$226$	−4.20711	+	7.28692i	−0.279853	+	0.484719i
$227$	5.89949			0.391563			0.195782	−	0.980648i	$-0.437276\pi$
$227$	5.89949			0.391563			0.195782	+	0.980648i	$0.437276\pi$
$228$	−15.5147			−1.02749
$229$	6.24264	−	10.8126i	0.412525	−	0.714515i	−0.582640	−	0.812730i	$-0.697980\pi$
$229$	6.24264	−	10.8126i	0.412525	−	0.714515i	0.995165	+	0.0982157i	$0.0313135\pi$
$230$	−0.535534	+	0.927572i	−0.0353121	+	0.0611623i
$231$		0			0
$232$	3.30761	+	5.72895i	0.217155	+	0.376124i
$233$	−1.41421	+	2.44949i	−0.0926482	+	0.160471i	−0.908625	−	0.417614i	$-0.862867\pi$
$233$	−1.41421	+	2.44949i	−0.0926482	+	0.160471i	0.815976	+	0.578085i	$0.196200\pi$
$234$	−1.03553	−	1.07616i	−0.0676950	−	0.0703507i
$235$	−3.34315	−	5.79050i	−0.218083	−	0.377730i
$236$	18.7279			1.21908
$237$	−1.24264	−	2.15232i	−0.0807182	−	0.139808i
$238$		0			0
$239$	24.3848			1.57732			0.788660	−	0.614830i	$-0.210775\pi$
$239$	24.3848			1.57732			0.788660	+	0.614830i	$0.210775\pi$
$240$	3.87868	+	6.71807i	0.250368	+	0.433650i
$241$	15.4853			0.997495			0.498747	−	0.866747i	$-0.333794\pi$
$241$	15.4853			0.997495			0.498747	+	0.866747i	$0.333794\pi$
$242$	2.20711	+	3.82282i	0.141878	+	0.245740i
$243$	−4.94975	−	8.57321i	−0.317526	−	0.549972i
$244$	3.81371	+	6.60554i	0.244148	+	0.422876i
$245$		0			0
$246$	0.100505			0.00640797
$247$	15.0000	+	15.5885i	0.954427	+	0.991870i
$248$	2.05025	+	3.55114i	0.130191	+	0.225498i
$249$	−0.757359	+	1.31178i	−0.0479957	+	0.0831310i
$250$	5.04163			0.318861
$251$	−11.4853	+	19.8931i	−0.724945	+	1.25564i	0.234052	+	0.972224i	$0.424801\pi$
$251$	−11.4853	+	19.8931i	−0.724945	+	1.25564i	−0.958997	+	0.283417i	$0.908532\pi$
$252$		0			0
$253$	0.414214	−	0.717439i	0.0260414	−	0.0451050i
$254$	−2.75736	−	4.77589i	−0.173012	−	0.299666i
$255$	−7.53553	−	13.0519i	−0.471893	−	0.817343i
$256$	3.97056			0.248160
$257$	15.0000			0.935674			0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000			0.935674			0.467837	+	0.883815i	$0.345033\pi$
$258$	−1.00000	−	1.73205i	−0.0622573	−	0.107833i
$259$		0			0
$260$	3.34315	−	11.5810i	0.207333	−	0.718223i
$261$	2.08579	−	3.61269i	0.129107	−	0.223620i
$262$	−4.41421	+	7.64564i	−0.272711	+	0.472349i
$263$	3.36396	−	5.82655i	0.207431	−	0.359281i	−0.743474	−	0.668765i	$-0.766823\pi$
$263$	3.36396	−	5.82655i	0.207431	−	0.359281i	0.950904	+	0.309485i	$0.100157\pi$
$264$	0.656854	+	1.13770i	0.0404266	+	0.0700209i
$265$	5.48528			0.336958
$266$		0			0
$267$	−10.8284	+	18.7554i	−0.662689	+	1.14781i
$268$	3.87868	−	6.71807i	0.236928	−	0.410371i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$	−2.14214	+	3.71029i	−0.130366	+	0.225801i
$271$	−21.0711			−1.27998			−0.639988	−	0.768385i	$-0.721061\pi$
$271$	−21.0711			−1.27998			−0.639988	+	0.768385i	$0.721061\pi$
$272$	−17.4853			−1.06020
$273$		0			0
$274$	−0.0710678			−0.00429336
$275$	−0.970563			−0.0585271
$276$	−1.82843	+	3.16693i	−0.110058	+	0.190627i
$277$	1.97056			0.118400			0.0591998	−	0.998246i	$-0.481145\pi$
$277$	1.97056			0.118400			0.0591998	+	0.998246i	$0.481145\pi$
$278$	2.46447	−	4.26858i	0.147809	−	0.256012i
$279$	1.29289	−	2.23936i	0.0774035	−	0.134067i
$280$		0			0
$281$	−17.4853			−1.04308			−0.521542	−	0.853225i	$-0.674643\pi$
$281$	−17.4853			−1.04308			−0.521542	+	0.853225i	$0.674643\pi$
$282$	1.07107	+	1.85514i	0.0637812	+	0.110472i
$283$	9.94975	−	17.2335i	0.591451	−	1.02442i	−0.402586	−	0.915382i	$-0.631889\pi$
$283$	9.94975	−	17.2335i	0.591451	−	1.02442i	0.994037	−	0.109041i	$-0.0347781\pi$
$284$	−10.6569	+	18.4582i	−0.632368	+	1.09529i
$285$	7.75736	−	13.4361i	0.459506	−	0.795888i
$286$	0.242641	−	0.840532i	0.0143476	−	0.0497017i
$287$		0			0
$288$	2.20711	+	3.82282i	0.130055	+	0.225262i
$289$	16.9706			0.998268
$290$	−3.15938			−0.185525
$291$	7.65685	+	13.2621i	0.448853	+	0.777436i
$292$	−9.74264	−	16.8747i	−0.570145	−	0.987520i
$293$	−14.2279	+	24.6435i	−0.831204	+	1.43969i	0.0658799	+	0.997828i	$0.479015\pi$
$293$	−14.2279	+	24.6435i	−0.831204	+	1.43969i	−0.897084	+	0.441860i	$0.854319\pi$
$294$		0			0
$295$	−9.36396	+	16.2189i	−0.545191	+	0.944298i
$296$	15.0416			0.874277
$297$	1.65685	−	2.86976i	0.0961404	−	0.166520i
$298$	−0.621320	−	1.07616i	−0.0359921	−	0.0623402i
$299$	4.94975	−	1.22474i	0.286251	−	0.0708288i
$300$	4.28427			0.247353
$301$		0			0
$302$	−3.10051	−	5.37023i	−0.178414	−	0.309022i
$303$	−10.3640	−	17.9509i	−0.595394	−	1.03125i
$304$	−9.00000	−	15.5885i	−0.516185	−	0.894059i
$305$	−7.62742			−0.436745
$306$	−1.20711	−	2.09077i	−0.0690057	−	0.119521i
$307$	−32.7279			−1.86788			−0.933941	−	0.357428i	$-0.883654\pi$
$307$	−32.7279			−1.86788			−0.933941	+	0.357428i	$0.883654\pi$
$308$		0			0
$309$	−9.89949	−	17.1464i	−0.563163	−	0.975426i
$310$	−1.95837			−0.111228
$311$	6.46447	+	11.1968i	0.366566	+	0.634911i	0.989026	−	0.147740i	$-0.0472000\pi$
$311$	6.46447	+	11.1968i	0.366566	+	0.634911i	−0.622460	+	0.782652i	$0.713867\pi$
$312$	−2.24264	+	7.76874i	−0.126965	+	0.439818i
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	−1.13604	−	1.96768i	−0.0641104	−	0.111042i
$315$		0			0
$316$	1.60660	−	2.78272i	0.0903784	−	0.156540i
$317$	−16.3284	+	28.2817i	−0.917096	+	1.58846i	−0.113292	+	0.993562i	$0.536140\pi$
$317$	−16.3284	+	28.2817i	−0.917096	+	1.58846i	−0.803804	+	0.594895i	$0.797194\pi$
$318$	−1.75736			−0.0985478
$319$	2.44365			0.136818
$320$	−3.81371	+	6.60554i	−0.213193	+	0.369261i
$321$	−12.2426	+	21.2049i	−0.683318	+	1.18354i
$322$		0			0
$323$	17.4853	+	30.2854i	0.972907	+	1.68512i
$324$	−4.57107	+	7.91732i	−0.253948	+	0.439851i
$325$	−4.14214	−	4.30463i	−0.229764	−	0.238778i
$326$	−2.60660	−	4.51477i	−0.144366	−	0.250050i
$327$	−19.3137			−1.06805
$328$	0.136039	+	0.235626i	0.00751150	+	0.0130103i
$329$		0			0
$330$	−0.627417			−0.0345382
$331$	12.4350	+	21.5381i	0.683491	+	1.18384i	0.973908	+	0.226941i	$0.0728725\pi$
$331$	12.4350	+	21.5381i	0.683491	+	1.18384i	−0.290417	+	0.956900i	$0.593794\pi$
$332$	−1.95837			−0.107479
$333$	−4.74264	−	8.21449i	−0.259895	−	0.450152i
$334$	−1.39340	−	2.41344i	−0.0762434	−	0.132057i
$335$	3.87868	+	6.71807i	0.211915	+	0.367047i
$336$		0			0
$337$	−3.48528			−0.189855			−0.0949277	−	0.995484i	$-0.530262\pi$
$337$	−3.48528			−0.189855			−0.0949277	+	0.995484i	$0.530262\pi$
$338$	4.76346	−	2.51104i	0.259098	−	0.136582i
$339$	−14.3640	−	24.8791i	−0.780143	−	1.35125i
$340$	9.74264	−	16.8747i	0.528369	−	0.915162i
$341$	1.51472			0.0820266
$342$	1.24264	−	2.15232i	0.0671943	−	0.116384i
$343$		0			0
$344$	2.70711	−	4.68885i	0.145957	−	0.252806i
$345$	−1.82843	−	3.16693i	−0.0984392	−	0.170502i
$346$	2.10051	+	3.63818i	0.112924	+	0.195590i
$347$	−6.10051			−0.327492			−0.163746	−	0.986503i	$-0.552358\pi$
$347$	−6.10051			−0.327492			−0.163746	+	0.986503i	$0.552358\pi$
$348$	−10.7868			−0.578233
$349$	−4.65685	−	8.06591i	−0.249276	−	0.431758i	0.714049	−	0.700095i	$-0.246859\pi$
$349$	−4.65685	−	8.06591i	−0.249276	−	0.431758i	−0.963325	+	0.268337i	$0.913526\pi$
$350$		0			0
$351$	19.7990	−	4.89898i	1.05679	−	0.261488i
$352$	−1.29289	+	2.23936i	−0.0689114	+	0.119358i
$353$	−2.91421	+	5.04757i	−0.155108	+	0.268655i	−0.933098	−	0.359621i	$-0.882906\pi$
$353$	−2.91421	+	5.04757i	−0.155108	+	0.268655i	0.777990	+	0.628276i	$0.216239\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$	−10.6569	−	18.4582i	−0.565607	−	0.979660i
$356$	−28.0000			−1.48400
$357$		0			0
$358$	1.17157	−	2.02922i	0.0619196	−	0.107248i
$359$	8.48528	−	14.6969i	0.447836	−	0.775675i	−0.550409	−	0.834895i	$-0.685528\pi$
$359$	8.48528	−	14.6969i	0.447836	−	0.775675i	0.998245	+	0.0592205i	$0.0188615\pi$
$360$	−2.89949			−0.152817
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	3.78680			0.199030
$363$	−15.0711			−0.791026
$364$		0			0
$365$	19.4853			1.01991
$366$	2.44365			0.127732
$367$	14.3640	−	24.8791i	0.749793	−	1.29868i	−0.198129	−	0.980176i	$-0.563487\pi$
$367$	14.3640	−	24.8791i	0.749793	−	1.29868i	0.947922	−	0.318503i	$-0.103180\pi$
$368$	−4.24264			−0.221163
$369$	0.0857864	−	0.148586i	0.00446586	−	0.00773510i
$370$	−3.59188	+	6.22132i	−0.186733	+	0.323431i
$371$		0			0
$372$	−6.68629			−0.346668
$373$	−13.2279	−	22.9114i	−0.684916	−	1.18631i	−0.973463	−	0.228843i	$-0.926506\pi$
$373$	−13.2279	−	22.9114i	−0.684916	−	1.18631i	0.288547	−	0.957466i	$-0.406828\pi$
$374$	0.707107	−	1.22474i	0.0365636	−	0.0633300i
$375$	−8.60660	+	14.9071i	−0.444443	+	0.769798i
$376$	−2.89949	+	5.02207i	−0.149530	+	0.258994i
$377$	10.4289	+	10.8381i	0.537117	+	0.558189i
$378$		0			0
$379$	0.121320	+	0.210133i	0.00623181	+	0.0107938i	0.869124	−	0.494593i	$-0.164683\pi$
$379$	0.121320	+	0.210133i	0.00623181	+	0.0107938i	−0.862893	+	0.505387i	$0.831350\pi$
$380$	20.0589			1.02900
$381$	18.8284			0.964610
$382$	−3.36396	−	5.82655i	−0.172115	−	0.298112i
$383$	17.0208	+	29.4809i	0.869723	+	1.50640i	0.862280	+	0.506432i	$0.169036\pi$
$383$	17.0208	+	29.4809i	0.869723	+	1.50640i	0.00744324	+	0.999972i	$0.497631\pi$
$384$	7.46447	−	12.9288i	0.380919	−	0.659772i
$385$		0			0
$386$	−1.47918	+	2.56202i	−0.0752885	+	0.130404i
$387$	−3.41421			−0.173554
$388$	−9.89949	+	17.1464i	−0.502571	+	0.870478i
$389$	−13.5711	−	23.5058i	−0.688080	−	1.19179i	−0.972458	−	0.233078i	$-0.925120\pi$
$389$	−13.5711	−	23.5058i	−0.688080	−	1.19179i	0.284378	−	0.958712i	$-0.408213\pi$
$390$	−2.67767	−	2.78272i	−0.135589	−	0.140908i
$391$	8.24264			0.416848
$392$		0			0
$393$	−15.0711	−	26.1039i	−0.760235	−	1.31677i
$394$	−3.07107	−	5.31925i	−0.154718	−	0.267980i
$395$	1.60660	+	2.78272i	0.0808369	+	0.140014i
$396$	1.07107			0.0538232
$397$	−3.31371	−	5.73951i	−0.166310	−	0.288058i	0.770810	−	0.637066i	$-0.219852\pi$
$397$	−3.31371	−	5.73951i	−0.166310	−	0.288058i	−0.937120	+	0.349008i	$0.886519\pi$
$398$	−6.20101			−0.310829
$399$		0			0
$400$	2.48528	+	4.30463i	0.124264	+	0.215232i
$401$	8.79899			0.439401			0.219700	−	0.975567i	$-0.429492\pi$
$401$	8.79899			0.439401			0.219700	+	0.975567i	$0.429492\pi$
$402$	−1.24264	−	2.15232i	−0.0619773	−	0.107348i
$403$	6.46447	+	6.71807i	0.322018	+	0.334651i
$404$	13.3995	−	23.2086i	0.666650	−	1.15467i
$405$	−4.57107	−	7.91732i	−0.227138	−	0.393415i
$406$		0			0
$407$	2.77817	−	4.81194i	0.137709	−	0.238519i
$408$	−6.53553	+	11.3199i	−0.323557	+	0.560417i
$409$	−21.9706			−1.08637			−0.543187	−	0.839612i	$-0.682783\pi$
$409$	−21.9706			−1.08637			−0.543187	+	0.839612i	$0.682783\pi$
$410$	−0.129942			−0.00641739
$411$	0.121320	−	0.210133i	0.00598429	−	0.0103651i
$412$	12.7990	−	22.1685i	0.630561	−	1.09216i
$413$		0			0
$414$	−0.292893	−	0.507306i	−0.0143949	−	0.0249327i
$415$	0.979185	−	1.69600i	0.0480663	−	0.0832533i
$416$	−15.4497	+	3.82282i	−0.757486	+	0.187429i
$417$	8.41421	+	14.5738i	0.412046	+	0.713684i
$418$	1.45584			0.0712077
$419$	5.77817	+	10.0081i	0.282282	+	0.488927i	0.971946	−	0.235202i	$-0.0755752\pi$
$419$	5.77817	+	10.0081i	0.282282	+	0.488927i	−0.689664	+	0.724129i	$0.742242\pi$
$420$		0			0
$421$	21.4853			1.04713			0.523564	−	0.851986i	$-0.324602\pi$
$421$	21.4853			1.04713			0.523564	+	0.851986i	$0.324602\pi$
$422$	−5.12132	−	8.87039i	−0.249302	−	0.431804i
$423$	3.65685			0.177802
$424$	−2.37868	−	4.11999i	−0.115519	−	0.200085i
$425$	−4.82843	−	8.36308i	−0.234213	−	0.405669i
$426$	3.41421	+	5.91359i	0.165419	+	0.286514i
$427$		0			0
$428$	−31.6569			−1.53019
$429$	2.07107	+	2.15232i	0.0999921	+	0.103915i
$430$	1.29289	+	2.23936i	0.0623488	+	0.107991i
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	−16.9706			−0.816497
$433$	−8.74264	+	15.1427i	−0.420144	+	0.727712i	−0.995953	−	0.0898728i	$-0.971354\pi$
$433$	−8.74264	+	15.1427i	−0.420144	+	0.727712i	0.575809	+	0.817584i	$0.304687\pi$
$434$		0			0
$435$	5.39340	−	9.34164i	0.258594	−	0.447897i
$436$	−12.4853	−	21.6251i	−0.597937	−	1.03566i
$437$	4.24264	+	7.34847i	0.202953	+	0.351525i
$438$	−6.24264			−0.298285
$439$	−1.27208			−0.0607130			−0.0303565	−	0.999539i	$-0.509664\pi$
$439$	−1.27208			−0.0607130			−0.0303565	+	0.999539i	$0.509664\pi$
$440$	−0.849242	−	1.47093i	−0.0404860	−	0.0701239i
$441$		0			0
$442$	8.44975	−	2.09077i	0.401914	−	0.0994478i
$443$	−12.8284	+	22.2195i	−0.609497	+	1.05568i	0.381826	+	0.924234i	$0.375295\pi$
$443$	−12.8284	+	22.2195i	−0.609497	+	1.05568i	−0.991323	+	0.131446i	$0.958038\pi$
$444$	−12.2635	+	21.2409i	−0.581998	+	1.00805i
$445$	14.0000	−	24.2487i	0.663664	−	1.14950i
$446$	−0.414214	−	0.717439i	−0.0196136	−	0.0339717i
$447$	4.24264			0.200670
$448$		0			0
$449$	−16.2426	+	28.1331i	−0.766538	+	1.32768i	0.172892	+	0.984941i	$0.444689\pi$
$449$	−16.2426	+	28.1331i	−0.766538	+	1.32768i	−0.939430	+	0.342741i	$0.888645\pi$
$450$	−0.343146	+	0.594346i	−0.0161760	+	0.0280177i
$451$	0.100505			0.00473260
$452$	18.5711	−	32.1660i	0.873510	−	1.51296i
$453$	21.1716			0.994727
$454$	2.44365			0.114686
$455$		0			0
$456$	−13.4558			−0.630128
$457$	−25.0000			−1.16945			−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000			−1.16945			−0.584725	+	0.811231i	$0.698798\pi$
$458$	2.58579	−	4.47871i	0.120826	−	0.209277i
$459$	32.9706			1.53893
$460$	2.36396	−	4.09450i	0.110220	−	0.190907i
$461$	−0.671573	+	1.16320i	−0.0312783	+	0.0541755i	−0.881241	−	0.472668i	$-0.843291\pi$
$461$	−0.671573	+	1.16320i	−0.0312783	+	0.0541755i	0.849963	+	0.526843i	$0.176624\pi$
$462$		0			0
$463$	6.72792			0.312673			0.156337	−	0.987704i	$-0.450032\pi$
$463$	6.72792			0.312673			0.156337	+	0.987704i	$0.450032\pi$
$464$	−6.25736	−	10.8381i	−0.290491	−	0.503145i
$465$	3.34315	−	5.79050i	0.155035	−	0.268528i
$466$	−0.585786	+	1.01461i	−0.0271360	+	0.0470010i
$467$	−5.70711	+	9.88500i	−0.264093	+	0.457423i	−0.967326	−	0.253537i	$-0.918406\pi$
$467$	−5.70711	+	9.88500i	−0.264093	+	0.457423i	0.703232	+	0.710960i	$0.251739\pi$
$468$	4.57107	+	4.75039i	0.211298	+	0.219587i
$469$		0			0
$470$	−1.38478	−	2.39850i	−0.0638750	−	0.110635i
$471$	7.75736			0.357440
$472$	16.2426			0.747628
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$	−0.514719	−	0.891519i	−0.0236418	−	0.0409488i
$475$	4.97056	−	8.60927i	0.228065	−	0.395020i
$476$		0			0
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	10.1005			0.461986
$479$	0.807612	−	1.39882i	0.0369007	−	0.0639139i	−0.846985	−	0.531616i	$-0.821585\pi$
$479$	0.807612	−	1.39882i	0.0369007	−	0.0639139i	0.883886	+	0.467703i	$0.154918\pi$
$480$	5.70711	+	9.88500i	0.260493	+	0.451186i
$481$	33.1985	−	8.21449i	1.51372	−	0.374549i
$482$	6.41421			0.292159
$483$		0			0
$484$	−9.74264	−	16.8747i	−0.442847	−	0.767034i
$485$	−9.89949	−	17.1464i	−0.449513	−	0.778579i
$486$	−2.05025	−	3.55114i	−0.0930013	−	0.161083i
$487$	−12.9706			−0.587752			−0.293876	−	0.955844i	$-0.594945\pi$
$487$	−12.9706			−0.587752			−0.293876	+	0.955844i	$0.594945\pi$
$488$	3.30761	+	5.72895i	0.149729	+	0.259337i
$489$	17.7990			0.804898
$490$		0			0
$491$	−6.34315	−	10.9867i	−0.286262	−	0.495821i	0.686652	−	0.726986i	$-0.259079\pi$
$491$	−6.34315	−	10.9867i	−0.286262	−	0.495821i	−0.972914	+	0.231165i	$0.925746\pi$
$492$	−0.443651			−0.0200013
$493$	12.1569	+	21.0563i	0.547517	+	0.948328i
$494$	6.21320	+	6.45695i	0.279545	+	0.290512i
$495$	−0.535534	+	0.927572i	−0.0240705	+	0.0416913i
$496$	−3.87868	−	6.71807i	−0.174158	−	0.301650i
$497$		0			0
$498$	−0.313708	+	0.543359i	−0.0140576	+	0.0243485i
$499$	−10.0208	+	17.3566i	−0.448593	+	0.776986i	−0.998295	−	0.0583748i	$-0.981408\pi$
$499$	−10.0208	+	17.3566i	−0.448593	+	0.776986i	0.549701	+	0.835361i	$0.314741\pi$
$500$	−22.2548			−0.995266
$501$	9.51472			0.425086
$502$	−4.75736	+	8.23999i	−0.212331	+	0.367769i
$503$	1.22183	−	2.11626i	0.0544785	−	0.0943595i	−0.837500	−	0.546437i	$-0.815984\pi$
$503$	1.22183	−	2.11626i	0.0544785	−	0.0943595i	0.891979	+	0.452078i	$0.149317\pi$
$504$		0			0
$505$	13.3995	+	23.2086i	0.596270	+	1.03277i
$506$	0.171573	−	0.297173i	0.00762734	−	0.0132109i
$507$	−0.707107	+	18.3712i	−0.0314037	+	0.815892i
$508$	12.1716	+	21.0818i	0.540026	+	0.935353i
$509$	4.65685			0.206411			0.103206	−	0.994660i	$-0.467090\pi$
$509$	4.65685			0.206411			0.103206	+	0.994660i	$0.467090\pi$
$510$	−3.12132	−	5.40629i	−0.138214	−	0.239394i
$511$		0			0
$512$	22.7574			1.00574
$513$	16.9706	+	29.3939i	0.749269	+	1.29777i
$514$	6.21320			0.274053
$515$	12.7990	+	22.1685i	0.563991	+	0.976861i
$516$	4.41421	+	7.64564i	0.194325	+	0.336581i
$517$	1.07107	+	1.85514i	0.0471055	+	0.0815891i
$518$		0			0
$519$	−14.3431			−0.629594
$520$	2.89949	−	10.0441i	0.127151	−	0.440465i
$521$	12.3284	+	21.3535i	0.540118	+	0.935512i	0.998897	+	0.0469615i	$0.0149538\pi$
$521$	12.3284	+	21.3535i	0.540118	+	0.935512i	−0.458779	+	0.888551i	$0.651713\pi$
$522$	0.863961	−	1.49642i	0.0378145	−	0.0654967i
$523$	−16.9706			−0.742071			−0.371035	−	0.928619i	$-0.620997\pi$
$523$	−16.9706			−0.742071			−0.371035	+	0.928619i	$0.620997\pi$
$524$	19.4853	−	33.7495i	0.851218	−	1.47435i
$525$		0			0
$526$	1.39340	−	2.41344i	0.0607551	−	0.105231i
$527$	7.53553	+	13.0519i	0.328253	+	0.568551i
$528$	−1.24264	−	2.15232i	−0.0540790	−	0.0936676i
$529$	−21.0000			−0.913043
$530$	2.27208			0.0986928
$531$	−5.12132	−	8.87039i	−0.222246	−	0.384942i
$532$		0			0
$533$	0.428932	+	0.445759i	0.0185791	+	0.0193080i
$534$	−4.48528	+	7.76874i	−0.194097	+	0.336186i
$535$	15.8284	−	27.4156i	0.684323	−	1.18528i
$536$	3.36396	−	5.82655i	0.145301	−	0.251669i
$537$	4.00000	+	6.92820i	0.172613	+	0.298974i
$538$	−7.45584			−0.321444
$539$		0			0
$540$	9.45584	−	16.3780i	0.406915	−	0.704797i
$541$	5.74264	−	9.94655i	0.246895	−	0.427635i	−0.715767	−	0.698339i	$-0.753923\pi$
$541$	5.74264	−	9.94655i	0.246895	−	0.427635i	0.962663	+	0.270703i	$0.0872563\pi$
$542$	−8.72792			−0.374896
$543$	−6.46447	+	11.1968i	−0.277417	+	0.480500i
$544$	−25.7279			−1.10308
$545$	24.9706			1.06962
$546$		0			0
$547$	0.928932			0.0397183			0.0198591	−	0.999803i	$-0.493678\pi$
$547$	0.928932			0.0397183			0.0198591	+	0.999803i	$0.493678\pi$
$548$	0.313708			0.0134010
$549$	2.08579	−	3.61269i	0.0890192	−	0.154186i
$550$	−0.402020			−0.0171422
$551$	−12.5147	+	21.6761i	−0.533145	+	0.923434i
$552$	−1.58579	+	2.74666i	−0.0674956	+	0.116906i
$553$		0			0
$554$	0.816234			0.0346785
$555$	−12.2635	−	21.2409i	−0.520555	−	0.901627i
$556$	−10.8787	+	18.8424i	−0.461359	+	0.799097i
$557$	−6.15685	+	10.6640i	−0.260874	+	0.451848i	−0.966474	−	0.256763i	$-0.917344\pi$
$557$	−6.15685	+	10.6640i	−0.260874	+	0.451848i	0.705600	+	0.708610i	$0.250677\pi$
$558$	0.535534	−	0.927572i	0.0226710	−	0.0392673i
$559$	3.41421	−	11.8272i	0.144406	−	0.500237i
$560$		0			0
$561$	2.41421	+	4.18154i	0.101928	+	0.176545i
$562$	−7.24264			−0.305512
$563$	0.100505			0.00423578			0.00211789	−	0.999998i	$-0.499326\pi$
$563$	0.100505			0.00423578			0.00211789	+	0.999998i	$0.499326\pi$
$564$	−4.72792	−	8.18900i	−0.199081	−	0.344819i
$565$	18.5711	+	32.1660i	0.781291	+	1.35324i
$566$	4.12132	−	7.13834i	0.173232	−	0.300047i
$567$		0			0
$568$	−9.24264	+	16.0087i	−0.387813	+	0.671711i
$569$	18.8284			0.789329			0.394664	−	0.918825i	$-0.370861\pi$
$569$	18.8284			0.789329			0.394664	+	0.918825i	$0.370861\pi$
$570$	3.21320	−	5.56543i	0.134586	−	0.233110i
$571$	−14.4853	−	25.0892i	−0.606190	−	1.04995i	−0.991862	−	0.127316i	$-0.959364\pi$
$571$	−14.4853	−	25.0892i	−0.606190	−	1.04995i	0.385672	−	0.922636i	$-0.373970\pi$
$572$	−1.07107	+	3.71029i	−0.0447836	+	0.155135i
$573$	22.9706			0.959609
$574$		0			0
$575$	−1.17157	−	2.02922i	−0.0488580	−	0.0846245i
$576$	−2.08579	−	3.61269i	−0.0869078	−	0.150529i
$577$	6.84315	+	11.8527i	0.284884	+	0.493433i	0.972581	−	0.232564i	$-0.0747116\pi$
$577$	6.84315	+	11.8527i	0.284884	+	0.493433i	−0.687697	+	0.725998i	$0.741378\pi$
$578$	7.02944			0.292386
$579$	−5.05025	−	8.74729i	−0.209881	−	0.363525i
$580$	13.9462			0.579083
$581$		0			0
$582$	3.17157	+	5.49333i	0.131466	+	0.227706i
$583$	−1.75736			−0.0727824
$584$	−8.44975	−	14.6354i	−0.349653	−	0.605617i
$585$	−6.39949	+	1.58346i	−0.264587	+	0.0654682i
$586$	−5.89340	+	10.2077i	−0.243454	+	0.421675i
$587$	14.8284	+	25.6836i	0.612035	+	1.06008i	0.990897	+	0.134622i	$0.0429821\pi$
$587$	14.8284	+	25.6836i	0.612035	+	1.06008i	−0.378862	+	0.925453i	$0.623685\pi$
$588$		0			0
$589$	−7.75736	+	13.4361i	−0.319636	+	0.553627i
$590$	−3.87868	+	6.71807i	−0.159683	+	0.276579i
$591$	20.9706			0.862614
$592$	−28.4558			−1.16953
$593$	−12.6421	+	21.8968i	−0.519150	+	0.899195i	0.480602	+	0.876939i	$0.340418\pi$
$593$	−12.6421	+	21.8968i	−0.519150	+	0.899195i	−0.999752	+	0.0222559i	$0.992915\pi$
$594$	0.686292	−	1.18869i	0.0281589	−	0.0487726i
$595$		0			0
$596$	2.74264	+	4.75039i	0.112343	+	0.194584i
$597$	10.5858	−	18.3351i	0.433247	−	0.750407i
$598$	2.05025	−	0.507306i	0.0838411	−	0.0207453i
$599$	−14.1716	−	24.5459i	−0.579035	−	1.00292i	−0.995590	−	0.0938074i	$-0.970096\pi$
$599$	−14.1716	−	24.5459i	−0.579035	−	1.00292i	0.416556	−	0.909110i	$-0.363237\pi$
$600$	3.71573			0.151694
$601$	−15.4706	−	26.7958i	−0.631057	−	1.09302i	−0.987336	−	0.158644i	$-0.949288\pi$
$601$	−15.4706	−	26.7958i	−0.631057	−	1.09302i	0.356278	−	0.934380i	$-0.384045\pi$
$602$		0			0
$603$	−4.24264			−0.172774
$604$	13.6863	+	23.7054i	0.556887	+	0.964557i
$605$	19.4853			0.792189
$606$	−4.29289	−	7.43551i	−0.174387	−	0.302047i
$607$	16.1716	+	28.0100i	0.656384	+	1.13689i	0.981545	+	0.191232i	$0.0612482\pi$
$607$	16.1716	+	28.0100i	0.656384	+	1.13689i	−0.325161	+	0.945659i	$0.605419\pi$
$608$	−13.2426	−	22.9369i	−0.537060	−	0.930215i
$609$		0			0
$610$	−3.15938			−0.127920
$611$	−3.65685	+	12.6677i	−0.147940	+	0.512481i
$612$	5.32843	+	9.22911i	0.215389	+	0.373065i
$613$	7.39949	−	12.8163i	0.298863	−	0.517646i	−0.677013	−	0.735971i	$-0.736726\pi$
$613$	7.39949	−	12.8163i	0.298863	−	0.517646i	0.975876	+	0.218325i	$0.0700594\pi$
$614$	−13.5563			−0.547090
$615$	0.221825	−	0.384213i	0.00894486	−	0.0154930i
$616$		0			0
$617$	15.5711	−	26.9699i	0.626868	−	1.08577i	−0.361309	−	0.932446i	$-0.617670\pi$
$617$	15.5711	−	26.9699i	0.626868	−	1.08577i	0.988177	−	0.153320i	$-0.0489966\pi$
$618$	−4.10051	−	7.10228i	−0.164947	−	0.285696i
$619$	−20.7782	−	35.9889i	−0.835145	−	1.44651i	−0.893912	−	0.448242i	$-0.852050\pi$
$619$	−20.7782	−	35.9889i	−0.835145	−	1.44651i	0.0587667	−	0.998272i	$-0.481283\pi$
$620$	8.64466			0.347178
$621$	8.00000			0.321029
$622$	2.67767	+	4.63786i	0.107365	+	0.185961i
$623$		0			0
$624$	4.24264	−	14.6969i	0.169842	−	0.588348i
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	2.89949	−	5.02207i	0.115887	−	0.200722i
$627$	−2.48528	+	4.30463i	−0.0992526	+	0.171911i
$628$	5.01472	+	8.68575i	0.200109	+	0.346599i
$629$	55.2843			2.20433
$630$		0			0
$631$	−12.1421	+	21.0308i	−0.483371	+	0.837223i	−0.999818	−	0.0190965i	$-0.993921\pi$
$631$	−12.1421	+	21.0308i	−0.483371	+	0.837223i	0.516447	+	0.856319i	$0.327254\pi$
$632$	1.39340	−	2.41344i	0.0554264	−	0.0960014i
$633$	34.9706			1.38996
$634$	−6.76346	+	11.7146i	−0.268611	+	0.465248i
$635$	−24.3431			−0.966028
$636$	7.75736			0.307599
$637$		0			0
$638$	1.01219			0.0400731
$639$	11.6569			0.461138
$640$	−9.65076	+	16.7156i	−0.381480	+	0.660742i
$641$	−14.7990			−0.584525			−0.292262	−	0.956338i	$-0.594408\pi$
$641$	−14.7990			−0.584525			−0.292262	+	0.956338i	$0.594408\pi$
$642$	−5.07107	+	8.78335i	−0.200139	+	0.346651i
$643$	−7.51472	+	13.0159i	−0.296352	+	0.513296i	−0.975298	−	0.220891i	$-0.929103\pi$
$643$	−7.51472	+	13.0159i	−0.296352	+	0.513296i	0.678947	+	0.734187i	$0.262437\pi$
$644$		0			0
$645$	−8.82843			−0.347619
$646$	7.24264	+	12.5446i	0.284958	+	0.493562i
$647$	8.65685	−	14.9941i	0.340336	−	0.589479i	−0.644159	−	0.764892i	$-0.722793\pi$
$647$	8.65685	−	14.9941i	0.340336	−	0.589479i	0.984495	+	0.175412i	$0.0561258\pi$
$648$	−3.96447	+	6.86666i	−0.155739	+	0.269748i
$649$	3.00000	−	5.19615i	0.117760	−	0.203967i
$650$	−1.71573	−	1.78304i	−0.0672964	−	0.0699365i
$651$		0			0
$652$	11.5061	+	19.9291i	0.450614	+	0.780486i
$653$	26.1421			1.02302			0.511510	−	0.859277i	$-0.329086\pi$
$653$	26.1421			1.02302			0.511510	+	0.859277i	$0.329086\pi$
$654$	−8.00000			−0.312825
$655$	19.4853	+	33.7495i	0.761353	+	1.31870i
$656$	−0.257359	−	0.445759i	−0.0100482	−	0.0174040i
$657$	−5.32843	+	9.22911i	−0.207882	+	0.360062i
$658$		0			0
$659$	7.65685	−	13.2621i	0.298269	−	0.516617i	−0.677471	−	0.735549i	$-0.736924\pi$
$659$	7.65685	−	13.2621i	0.298269	−	0.516617i	0.975740	+	0.218933i	$0.0702575\pi$
$660$	2.76955			0.107805
$661$	16.5711	−	28.7019i	0.644540	−	1.11638i	−0.339868	−	0.940473i	$-0.610382\pi$
$661$	16.5711	−	28.7019i	0.644540	−	1.11638i	0.984408	−	0.175903i	$-0.0562843\pi$
$662$	5.15076	+	8.92137i	0.200190	+	0.346739i
$663$	−8.24264	+	28.5533i	−0.320118	+	1.10892i
$664$	−1.69848			−0.0659140
$665$		0			0
$666$	−1.96447	−	3.40256i	−0.0761215	−	0.131846i
$667$	2.94975	+	5.10911i	0.114215	+	0.197826i
$668$	6.15076	+	10.6534i	0.237980	+	0.412193i
$669$	2.82843			0.109353
$670$	1.60660	+	2.78272i	0.0620684	+	0.107506i
$671$	2.44365			0.0943361
$672$		0			0
$673$	−7.25736	−	12.5701i	−0.279751	−	0.484542i	0.691572	−	0.722308i	$-0.256918\pi$
$673$	−7.25736	−	12.5701i	−0.279751	−	0.484542i	−0.971323	+	0.237765i	$0.923585\pi$
$674$	−1.44365			−0.0556074
$675$	−4.68629	−	8.11689i	−0.180375	−	0.312419i
$676$	−21.0269	+	11.0843i	−0.808727	+	0.426317i
$677$	8.82843	−	15.2913i	0.339304	−	0.587692i	−0.644998	−	0.764184i	$-0.723142\pi$
$677$	8.82843	−	15.2913i	0.339304	−	0.587692i	0.984302	+	0.176492i	$0.0564751\pi$
$678$	−5.94975	−	10.3053i	−0.228499	−	0.395771i
$679$		0			0
$680$	8.44975	−	14.6354i	0.324033	−	0.561242i
$681$	−4.17157	+	7.22538i	−0.159855	+	0.276877i
$682$	0.627417			0.0240250
$683$	5.31371			0.203323			0.101662	−	0.994819i	$-0.467584\pi$
$683$	5.31371			0.203323			0.101662	+	0.994819i	$0.467584\pi$
$684$	−5.48528	+	9.50079i	−0.209735	+	0.363272i
$685$	−0.156854	+	0.271680i	−0.00599309	+	0.0103803i
$686$		0			0
$687$	8.82843	+	15.2913i	0.336826	+	0.583399i
$688$	−5.12132	+	8.87039i	−0.195249	+	0.338180i
$689$	−7.50000	−	7.79423i	−0.285727	−	0.296936i
$690$	−0.757359	−	1.31178i	−0.0288322	−	0.0499388i
$691$	29.9411			1.13901			0.569507	−	0.821986i	$-0.307134\pi$
$691$	29.9411			1.13901			0.569507	+	0.821986i	$0.307134\pi$
$692$	−9.27208	−	16.0597i	−0.352472	−	0.610499i
$693$		0			0
$694$	−2.52691			−0.0959203
$695$	−10.8787	−	18.8424i	−0.412652	−	0.714734i
$696$	−9.35534			−0.354613
$697$	0.500000	+	0.866025i	0.0189389	+	0.0328031i
$698$	−1.92893	−	3.34101i	−0.0730112	−	0.126459i
$699$	−2.00000	−	3.46410i	−0.0756469	−	0.131024i
$700$		0			0
$701$	13.8579			0.523404			0.261702	−	0.965149i	$-0.415716\pi$
$701$	13.8579			0.523404			0.261702	+	0.965149i	$0.415716\pi$
$702$	8.20101	−	2.02922i	0.309527	−	0.0765881i
$703$	28.4558	+	49.2870i	1.07323	+	1.85889i
$704$	1.22183	−	2.11626i	0.0460493	−	0.0797597i
$705$	9.45584			0.356128
$706$	−1.20711	+	2.09077i	−0.0454301	+	0.0786872i
$707$		0			0
$708$	−13.2426	+	22.9369i	−0.497689	+	0.862022i
$709$	−8.81371	−	15.2658i	−0.331006	−	0.573319i	0.651704	−	0.758474i	$-0.274055\pi$
$709$	−8.81371	−	15.2658i	−0.331006	−	0.573319i	−0.982709	+	0.185155i	$0.940721\pi$
$710$	−4.41421	−	7.64564i	−0.165662	−	0.286936i
$711$	−1.75736			−0.0659061
$712$	−24.2843			−0.910092
$713$	1.82843	+	3.16693i	0.0684751	+	0.118602i
$714$		0			0
$715$	−2.67767	−	2.78272i	−0.100139	−	0.104068i
$716$	−5.17157	+	8.95743i	−0.193271	+	0.334755i
$717$	−17.2426	+	29.8651i	−0.643938	+	1.11533i
$718$	3.51472	−	6.08767i	0.131168	−	0.227190i
$719$	−0.192388	−	0.333226i	−0.00717487	−	0.0124272i	0.862416	−	0.506201i	$-0.168951\pi$
$719$	−0.192388	−	0.333226i	−0.00717487	−	0.0124272i	−0.869591	+	0.493774i	$0.835617\pi$
$720$	5.48528			0.204424
$721$		0			0
$722$	−3.52082	+	6.09823i	−0.131031	+	0.226953i
$723$	−10.9497	+	18.9655i	−0.407225	+	0.705335i
$724$	−16.7157			−0.621235
$725$	3.45584	−	5.98570i	0.128347	−	0.222303i
$726$	−6.24264			−0.231686
$727$	24.9706			0.926107			0.463053	−	0.886330i	$-0.346754\pi$
$727$	24.9706			0.926107			0.463053	+	0.886330i	$0.346754\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	8.07107			0.298724
$731$	9.94975	−	17.2335i	0.368005	−	0.637403i
$732$	−10.7868			−0.398691
$733$	10.5000	−	18.1865i	0.387826	−	0.671735i	−0.604331	−	0.796734i	$-0.706559\pi$
$733$	10.5000	−	18.1865i	0.387826	−	0.671735i	0.992157	+	0.124999i	$0.0398927\pi$
$734$	5.94975	−	10.3053i	0.219609	−	0.380374i
$735$		0			0
$736$	−6.24264			−0.230107
$737$	−1.24264	−	2.15232i	−0.0457733	−	0.0792816i
$738$	0.0355339	−	0.0615465i	0.00130802	−	0.00226556i
$739$	10.1421	−	17.5667i	0.373084	−	0.646201i	−0.616954	−	0.786999i	$-0.711633\pi$
$739$	10.1421	−	17.5667i	0.373084	−	0.646201i	0.990038	+	0.140798i	$0.0449668\pi$
$740$	15.8553	−	27.4623i	0.582854	−	1.00953i
$741$	−29.6985	+	7.34847i	−1.09100	+	0.269953i
$742$		0			0
$743$	−15.7990	−	27.3647i	−0.579609	−	1.00391i	−0.995524	−	0.0945084i	$-0.969872\pi$
$743$	−15.7990	−	27.3647i	−0.579609	−	1.00391i	0.415915	−	0.909403i	$-0.363461\pi$
$744$	−5.79899			−0.212601
$745$	−5.48528			−0.200965
$746$	−5.47918	−	9.49023i	−0.200607	−	0.347462i
$747$	0.535534	+	0.927572i	0.0195942	+	0.0339381i
$748$	−3.12132	+	5.40629i	−0.114127	+	0.197673i
$749$		0			0
$750$	−3.56497	+	6.17471i	−0.130174	+	0.225469i
$751$	−17.5563			−0.640640			−0.320320	−	0.947309i	$-0.603790\pi$
$751$	−17.5563			−0.640640			−0.320320	+	0.947309i	$0.603790\pi$
$752$	5.48528	−	9.50079i	0.200028	−	0.346458i
$753$	−16.2426	−	28.1331i	−0.591915	−	1.02523i
$754$	4.31981	+	4.48927i	0.157318	+	0.163490i
$755$	−27.3726			−0.996190
$756$		0			0
$757$	−14.7279	−	25.5095i	−0.535295	−	0.927159i	−0.999149	−	0.0412470i	$-0.986867\pi$
$757$	−14.7279	−	25.5095i	−0.535295	−	0.927159i	0.463854	−	0.885912i	$-0.346466\pi$
$758$	0.0502525	+	0.0870399i	0.00182525	+	0.00316143i
$759$	0.585786	+	1.01461i	0.0212627	+	0.0368281i
$760$	17.3970			0.631054
$761$	−8.92893	−	15.4654i	−0.323674	−	0.560619i	0.657569	−	0.753394i	$-0.271585\pi$
$761$	−8.92893	−	15.4654i	−0.323674	−	0.560619i	−0.981243	+	0.192775i	$0.938251\pi$
$762$	7.79899			0.282528
$763$		0			0
$764$	14.8492	+	25.7196i	0.537227	+	0.930504i
$765$	−10.6569			−0.385299
$766$	7.05025	+	12.2114i	0.254736	+	0.441216i
$767$	35.8492	−	8.87039i	1.29444	−	0.320291i
$768$	−2.80761	+	4.86293i	−0.101311	+	0.175476i
$769$	24.7279	+	42.8300i	0.891712	+	1.54449i	0.837822	+	0.545943i	$0.183828\pi$
$769$	24.7279	+	42.8300i	0.891712	+	1.54449i	0.0538894	+	0.998547i	$0.482838\pi$
$770$		0			0
$771$	−10.6066	+	18.3712i	−0.381987	+	0.661622i
$772$	6.52944	−	11.3093i	0.235000	−	0.407031i
$773$	6.34315			0.228147			0.114074	−	0.993472i	$-0.463610\pi$
$773$	6.34315			0.228147			0.114074	+	0.993472i	$0.463610\pi$
$774$	−1.41421			−0.0508329
$775$	2.14214	−	3.71029i	0.0769478	−	0.133277i
$776$	−8.58579	+	14.8710i	−0.308212	+	0.533838i
$777$		0			0
$778$	−5.62132	−	9.73641i	−0.201534	−	0.349067i
$779$	−0.514719	+	0.891519i	−0.0184417	+	0.0319420i
$780$	11.8198	+	12.2835i	0.423217	+	0.439820i
$781$	3.41421	+	5.91359i	0.122170	+	0.211605i
$782$	3.41421			0.122092
$783$	11.7990	+	20.4364i	0.421661	+	0.730339i
$784$		0			0
$785$	−10.0294			−0.357966
$786$	−6.24264	−	10.8126i	−0.222668	−	0.385672i
$787$	−13.8995			−0.495463			−0.247732	−	0.968829i	$-0.579685\pi$
$787$	−13.8995			−0.495463			−0.247732	+	0.968829i	$0.579685\pi$
$788$	13.5563	+	23.4803i	0.482925	+	0.836451i
$789$	4.75736	+	8.23999i	0.169366	+	0.293351i
$790$	0.665476	+	1.15264i	0.0236766	+	0.0410090i
$791$		0			0
$792$	0.928932			0.0330082
$793$	10.4289	+	10.8381i	0.370342	+	0.384871i
$794$	−1.37258	−	2.37738i	−0.0487111	−	0.0843702i
$795$	−3.87868	+	6.71807i	−0.137563	+	0.238265i
$796$	27.3726			0.970195
$797$	9.07107	−	15.7116i	0.321314	−	0.556532i	−0.659446	−	0.751752i	$-0.729209\pi$
$797$	9.07107	−	15.7116i	0.321314	−	0.556532i	0.980759	+	0.195221i	$0.0625423\pi$
$798$		0			0
$799$	−10.6569	+	18.4582i	−0.377012	+	0.653005i
$800$	3.65685	+	6.33386i	0.129289	+	0.223936i
$801$	7.65685	+	13.2621i	0.270542	+	0.468592i
$802$	3.64466			0.128697
$803$	−6.24264			−0.220298
$804$	5.48528	+	9.50079i	0.193451	+	0.335067i
$805$		0			0
$806$	2.67767	+	2.78272i	0.0943169	+	0.0980170i
$807$	12.7279	−	22.0454i	0.448044	−	0.776035i
$808$	11.6213	−	20.1287i	0.408837	−	0.708126i
$809$	−17.5711	+	30.4340i	−0.617766	+	1.07000i	0.372127	+	0.928182i	$0.378629\pi$
$809$	−17.5711	+	30.4340i	−0.617766	+	1.07000i	−0.989892	+	0.141820i	$0.954705\pi$
$810$	−1.89340	−	3.27946i	−0.0665272	−	0.115229i
$811$	−42.1838			−1.48127			−0.740636	−	0.671906i	$-0.765476\pi$
$811$	−42.1838			−1.48127			−0.740636	+	0.671906i	$0.765476\pi$
$812$		0			0
$813$	14.8995	−	25.8067i	0.522548	−	0.905080i
$814$	1.15076	−	1.99317i	0.0403340	−	0.0698606i
$815$	−23.0122			−0.806082
$816$	12.3640	−	21.4150i	0.432825	−	0.749675i
$817$	20.4853			0.716689
$818$	−9.10051			−0.318192
$819$		0			0
$820$	0.573593			0.0200307
$821$	−39.9411			−1.39395			−0.696977	−	0.717093i	$-0.745472\pi$
$821$	−39.9411			−1.39395			−0.696977	+	0.717093i	$0.745472\pi$
$822$	0.0502525	−	0.0870399i	0.00175276	−	0.00303587i
$823$	19.3137			0.673234			0.336617	−	0.941642i	$-0.390717\pi$
$823$	19.3137			0.673234			0.336617	+	0.941642i	$0.390717\pi$
$824$	11.1005	−	19.2266i	0.386704	−	0.669792i
$825$	0.686292	−	1.18869i	0.0238936	−	0.0413849i
$826$		0			0
$827$	−52.6690			−1.83148			−0.915741	−	0.401769i	$-0.868396\pi$
$827$	−52.6690			−1.83148			−0.915741	+	0.401769i	$0.868396\pi$
$828$	1.29289	+	2.23936i	0.0449311	+	0.0778230i
$829$	−23.1569	+	40.1088i	−0.804271	+	1.39304i	0.112511	+	0.993650i	$0.464111\pi$
$829$	−23.1569	+	40.1088i	−0.804271	+	1.39304i	−0.916782	+	0.399387i	$0.869223\pi$
$830$	0.405592	−	0.702505i	0.0140783	−	0.0243843i
$831$	−1.39340	+	2.41344i	−0.0483365	+	0.0837212i
$832$	14.6005	−	3.61269i	0.506181	−	0.125247i
$833$		0			0
$834$	3.48528	+	6.03668i	0.120685	+	0.209033i
$835$	−12.3015			−0.425711
$836$	−6.42641			−0.222262
$837$	7.31371	+	12.6677i	0.252799	+	0.437860i
$838$	2.39340	+	4.14549i	0.0826786	+	0.143203i
$839$	20.7990	−	36.0249i	0.718061	−	1.24372i	−0.243706	−	0.969849i	$-0.578363\pi$
$839$	20.7990	−	36.0249i	0.718061	−	1.24372i	0.961767	−	0.273869i	$-0.0883034\pi$
$840$		0			0
$841$	5.79899	−	10.0441i	0.199965	−	0.346350i
$842$	8.89949			0.306697
$843$	12.3640	−	21.4150i	0.425837	−	0.737572i
$844$	22.6066	+	39.1558i	0.778151	+	1.34780i
$845$	0.914214	−	23.7520i	0.0314499	−	0.817092i
$846$	1.51472			0.0520771
$847$		0			0
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$	14.0711	+	24.3718i	0.482918	+	0.836438i
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	13.4142			0.459833
$852$	−15.0711	−	26.1039i	−0.516326	−	0.894303i
$853$	−35.0000			−1.19838			−0.599189	−	0.800608i	$-0.704510\pi$
$853$	−35.0000			−1.19838			−0.599189	+	0.800608i	$0.704510\pi$
$854$		0			0
$855$	−5.48528	−	9.50079i	−0.187593	−	0.324920i
$856$	−27.4558			−0.938421
$857$	−0.600505	−	1.04011i	−0.0205129	−	0.0355293i	0.855587	−	0.517659i	$-0.173197\pi$
$857$	−0.600505	−	1.04011i	−0.0205129	−	0.0355293i	−0.876100	+	0.482130i	$0.839863\pi$
$858$	0.857864	+	0.891519i	0.0292870	+	0.0304360i
$859$	6.46447	−	11.1968i	0.220565	−	0.382029i	−0.734415	−	0.678701i	$-0.762543\pi$
$859$	6.46447	−	11.1968i	0.220565	−	0.382029i	0.954980	+	0.296672i	$0.0958766\pi$
$860$	−5.70711	−	9.88500i	−0.194611	−	0.337076i
$861$		0			0
$862$	−2.48528	+	4.30463i	−0.0846490	+	0.146616i
$863$	10.0919	−	17.4797i	0.343532	−	0.595014i	−0.641554	−	0.767078i	$-0.721710\pi$
$863$	10.0919	−	17.4797i	0.343532	−	0.595014i	0.985086	+	0.172063i	$0.0550434\pi$
$864$	−24.9706			−0.849516
$865$	18.5442			0.630520
$866$	−3.62132	+	6.27231i	−0.123057	+	0.213142i
$867$	−12.0000	+	20.7846i	−0.407541	+	0.705882i
$868$		0			0
$869$	−0.514719	−	0.891519i	−0.0174606	−	0.0302427i
$870$	2.23402	−	3.86943i	0.0757403	−	0.131186i
$871$	4.24264	−	14.6969i	0.143756	−	0.497987i
$872$	−10.8284	−	18.7554i	−0.366697	−	0.635138i
$873$	10.8284			0.366487
$874$	1.75736	+	3.04384i	0.0594436	+	0.102959i
$875$		0			0
$876$	27.5563			0.931043
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	0.686074	−	0.727532i	$-0.259333\pi$
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	−0.973098	+	0.230391i	$0.925999\pi$
$878$	−0.526912			−0.0177824
$879$	−20.1213	−	34.8511i	−0.678675	−	1.17550i
$880$	1.60660	+	2.78272i	0.0541585	+	0.0938053i
$881$	−2.22792	−	3.85887i	−0.0750606	−	0.130009i	0.826052	−	0.563594i	$-0.190582\pi$
$881$	−2.22792	−	3.85887i	−0.0750606	−	0.130009i	−0.901113	+	0.433585i	$0.857248\pi$
$882$		0			0
$883$	56.0416			1.88595			0.942976	−	0.332862i	$-0.108014\pi$
$883$	56.0416			1.88595			0.942976	+	0.332862i	$0.108014\pi$
$884$	−37.2990	+	9.22911i	−1.25450	+	0.310408i
$885$	−13.2426	−	22.9369i	−0.445146	−	0.771016i
$886$	−5.31371	+	9.20361i	−0.178518	+	0.309201i
$887$	−34.6274			−1.16267			−0.581337	−	0.813663i	$-0.697470\pi$
$887$	−34.6274			−1.16267			−0.581337	+	0.813663i	$0.697470\pi$
$888$	−10.6360	+	18.4222i	−0.356922	+	0.618207i
$889$		0			0
$890$	5.79899	−	10.0441i	0.194383	−	0.336681i
$891$	1.46447	+	2.53653i	0.0490615	+	0.0849769i
$892$	1.82843	+	3.16693i	0.0612203	+	0.106037i
$893$	−21.9411			−0.734232
$894$	1.75736			0.0587749
$895$	−5.17157	−	8.95743i	−0.172867	−	0.299414i
$896$		0			0
$897$	−2.00000	+	6.92820i	−0.0667781	+	0.231326i
$898$	−6.72792	+	11.6531i	−0.224514	+	0.388869i
$899$	−5.39340	+	9.34164i	−0.179880	+	0.311561i
$900$	1.51472	−	2.62357i	0.0504906	−	0.0874523i
$901$	−8.74264	−	15.1427i	−0.291260	−	0.504476i
$902$	0.0416306			0.00138615
$903$		0			0
$904$	16.1066	−	27.8975i	0.535698	−	0.927855i
$905$	8.35786	−	14.4762i	0.277825	−	0.481207i
$906$	8.76955			0.291349
$907$	3.36396	−	5.82655i	0.111698	−	0.193467i	−0.804757	−	0.593605i	$-0.797704\pi$
$907$	3.36396	−	5.82655i	0.111698	−	0.193467i	0.916455	+	0.400137i	$0.131038\pi$
$908$	−10.7868			−0.357972
$909$	−14.6569			−0.486137
$910$		0			0
$911$	−29.6569			−0.982575			−0.491288	−	0.870997i	$-0.663474\pi$
$911$	−29.6569			−0.982575			−0.491288	+	0.870997i	$0.663474\pi$
$912$	25.4558			0.842927
$913$	−0.313708	+	0.543359i	−0.0103822	+	0.0179826i
$914$	−10.3553			−0.342524
$915$	5.39340	−	9.34164i	0.178300	−	0.308825i
$916$	−11.4142	+	19.7700i	−0.377136	+	0.653219i
$917$		0			0
$918$	13.6569			0.450743
$919$	−1.34315	−	2.32640i	−0.0443063	−	0.0767407i	0.843022	−	0.537879i	$-0.180774\pi$
$919$	−1.34315	−	2.32640i	−0.0443063	−	0.0767407i	−0.887328	+	0.461139i	$0.847441\pi$
$920$	2.05025	−	3.55114i	0.0675948	−	0.117078i
$921$	23.1421	−	40.0834i	0.762559	−	1.32079i
$922$	−0.278175	+	0.481813i	−0.00916119	+	0.0158677i
$923$	−11.6569	+	40.3805i	−0.383690	+	1.32914i
$924$		0			0
$925$	−7.85786	−	13.6102i	−0.258365	−	0.447501i
$926$	2.78680			0.0915798
$927$	−14.0000			−0.459820
$928$	−9.20711	−	15.9472i	−0.302238	−	0.523492i
$929$	−24.4706	−	42.3843i	−0.802853	−	1.39058i	−0.917731	−	0.397203i	$-0.869981\pi$
$929$	−24.4706	−	42.3843i	−0.802853	−	1.39058i	0.114878	−	0.993380i	$-0.463352\pi$
$930$	1.38478	−	2.39850i	0.0454086	−	0.0786500i
$931$		0			0
$932$	2.58579	−	4.47871i	0.0847003	−	0.146705i
$933$	−18.2843			−0.598600
$934$	−2.36396	+	4.09450i	−0.0773512	+	0.133976i
$935$	−3.12132	−	5.40629i	−0.102078	−	0.176804i
$936$	3.96447	+	4.11999i	0.129583	+	0.134666i
$937$	−37.1421			−1.21338			−0.606690	−	0.794938i	$-0.707503\pi$
$937$	−37.1421			−1.21338			−0.606690	+	0.794938i	$0.707503\pi$
$938$		0			0
$939$	9.89949	+	17.1464i	0.323058	+	0.559553i
$940$	6.11270	+	10.5875i	0.199374	+	0.345326i
$941$	−26.4853	−	45.8739i	−0.863395	−	1.49544i	−0.868632	−	0.495459i	$-0.835000\pi$
$941$	−26.4853	−	45.8739i	−0.863395	−	1.49544i	0.00523607	−	0.999986i	$-0.498333\pi$
$942$	3.21320			0.104692
$943$	0.121320	+	0.210133i	0.00395073	+	0.00684287i
$944$	−30.7279			−1.00011
$945$		0			0
$946$	−0.414214	−	0.717439i	−0.0134672	−	0.0233260i
$947$	21.4142			0.695868			0.347934	−	0.937519i	$-0.386883\pi$
$947$	21.4142			0.695868			0.347934	+	0.937519i	$0.386883\pi$
$948$	2.27208	+	3.93535i	0.0737937	+	0.127814i
$949$	−26.6421	−	27.6873i	−0.864840	−	0.898768i
$950$	2.05887	−	3.56608i	0.0667987	−	0.115699i
$951$	−23.0919	−	39.9963i	−0.748806	−	1.29697i
$952$		0			0
$953$	−3.31371	+	5.73951i	−0.107342	+	0.185921i	−0.914692	−	0.404151i	$-0.867567\pi$
$953$	−3.31371	+	5.73951i	−0.107342	+	0.185921i	0.807351	+	0.590072i	$0.200900\pi$
$954$	−0.621320	+	1.07616i	−0.0201160	+	0.0348419i
$955$	−29.6985			−0.961020
$956$	−44.5858			−1.44201
$957$	−1.72792	+	2.99285i	−0.0558558	+	0.0967451i
$958$	0.334524	−	0.579412i	0.0108080	−	0.0187200i
$959$		0			0
$960$	−5.39340	−	9.34164i	−0.174071	−	0.301500i
$961$	12.1569	−	21.0563i	0.392157	−	0.679235i
$962$	13.7513	−	3.40256i	0.443359	−	0.109703i
$963$	8.65685	+	14.9941i	0.278963	+	0.483178i
$964$	−28.3137			−0.911923
$965$	6.52944	+	11.3093i	0.210190	+	0.364060i
$966$		0			0
$967$	−19.7574			−0.635354			−0.317677	−	0.948199i	$-0.602903\pi$
$967$	−19.7574			−0.635354			−0.317677	+	0.948199i	$0.602903\pi$
$968$	−8.44975	−	14.6354i	−0.271585	−	0.470399i
$969$	−49.4558			−1.58875
$970$	−4.10051	−	7.10228i	−0.131659	−	0.228041i
$971$	−25.8284	−	44.7361i	−0.828874	−	1.43565i	−0.898922	−	0.438108i	$-0.855649\pi$
$971$	−25.8284	−	44.7361i	−0.828874	−	1.43565i	0.0700488	−	0.997544i	$-0.477685\pi$
$972$	9.05025	+	15.6755i	0.290287	+	0.502792i
$973$		0			0
$974$	−5.37258			−0.172149
$975$	8.20101	−	2.02922i	0.262643	−	0.0649872i
$976$	−6.25736	−	10.8381i	−0.200293	−	0.346918i
$977$	−15.2990	+	26.4986i	−0.489458	+	0.847766i	−0.999926	−	0.0121303i	$-0.996139\pi$
$977$	−15.2990	+	26.4986i	−0.489458	+	0.847766i	0.510468	+	0.859897i	$0.329472\pi$
$978$	7.37258			0.235749
$979$	−4.48528	+	7.76874i	−0.143350	+	0.248290i
$980$		0			0
$981$	−6.82843	+	11.8272i	−0.218015	+	0.377613i
$982$	−2.62742	−	4.55082i	−0.0838442	−	0.145222i
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	0.977961	+	0.208788i	$0.0669518\pi$
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	−0.308165	+	0.951333i	$0.599715\pi$
$984$	−0.384776			−0.0122662
$985$	−27.1127			−0.863882
$986$	5.03553	+	8.72180i	0.160364	+	0.277759i
$987$		0			0
$988$	−27.4264	−	28.5024i	−0.872550	−	0.906781i
$989$	2.41421	−	4.18154i	0.0767675	−	0.132965i
$990$	−0.221825	+	0.384213i	−0.00705007	+	0.0122111i
$991$	−9.87868	+	17.1104i	−0.313807	+	0.543529i	−0.979183	−	0.202979i	$-0.934938\pi$
$991$	−9.87868	+	17.1104i	−0.313807	+	0.543529i	0.665376	+	0.746508i	$0.268271\pi$
$992$	−5.70711	−	9.88500i	−0.181201	−	0.313849i
$993$	−35.1716			−1.11614
$994$		0			0
$995$	−13.6863	+	23.7054i	−0.433885	+	0.751510i
$996$	1.38478	−	2.39850i	0.0438783	−	0.0759995i
$997$	13.9706			0.442452			0.221226	−	0.975223i	$-0.428994\pi$
$997$	13.9706			0.442452			0.221226	+	0.975223i	$0.428994\pi$
$998$	−4.15076	+	7.18932i	−0.131390	+	0.227574i
$999$	53.6569			1.69763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.b.471.2		4
7.2	even	3		637.2.f.f.393.1	yes	4
7.3	odd	6		637.2.g.g.263.1		4
7.4	even	3		637.2.g.f.263.1		4
7.5	odd	6		637.2.f.e.393.1	yes	4
7.6	odd	2		637.2.h.c.471.2		4
13.9	even	3		637.2.g.f.373.1		4
91.9	even	3		637.2.f.f.295.1	yes	4
91.16	even	3		8281.2.a.p.1.2		2
91.23	even	6		8281.2.a.x.1.1		2
91.48	odd	6		637.2.g.g.373.1		4
91.61	odd	6		637.2.f.e.295.1	✓	4
91.68	odd	6		8281.2.a.o.1.2		2
91.74	even	3	inner	637.2.h.b.165.2		4
91.75	odd	6		8281.2.a.y.1.1		2
91.87	odd	6		637.2.h.c.165.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.e.295.1	✓	4	91.61	odd	6
637.2.f.e.393.1	yes	4	7.5	odd	6
637.2.f.f.295.1	yes	4	91.9	even	3
637.2.f.f.393.1	yes	4	7.2	even	3
637.2.g.f.263.1		4	7.4	even	3
637.2.g.f.373.1		4	13.9	even	3
637.2.g.g.263.1		4	7.3	odd	6
637.2.g.g.373.1		4	91.48	odd	6
637.2.h.b.165.2		4	91.74	even	3	inner
637.2.h.b.471.2		4	1.1	even	1	trivial
637.2.h.c.165.2		4	91.87	odd	6
637.2.h.c.471.2		4	7.6	odd	2
8281.2.a.o.1.2		2	91.68	odd	6
8281.2.a.p.1.2		2	91.16	even	3
8281.2.a.x.1.1		2	91.23	even	6
8281.2.a.y.1.1		2	91.75	odd	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.82843 q^{4} +(0.914214 - 1.58346i) q^{5} +(-0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.82843 q^{4} +(0.914214 - 1.58346i) q^{5} +(-0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.378680 - 0.655892i) q^{10} +(-0.292893 + 0.507306i) q^{11} +(1.29289 - 2.23936i) q^{12} +(-3.50000 + 0.866025i) q^{13} +(1.29289 + 2.23936i) q^{15} +3.00000 q^{16} -5.82843 q^{17} +(0.207107 + 0.358719i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-1.67157 + 2.89525i) q^{20} +(-0.121320 + 0.210133i) q^{22} -1.41421 q^{23} +(1.12132 - 1.94218i) q^{24} +(0.828427 + 1.43488i) q^{25} +(-1.44975 + 0.358719i) q^{26} -5.65685 q^{27} +(-2.08579 - 3.61269i) q^{29} +(0.535534 + 0.927572i) q^{30} +(-1.29289 - 2.23936i) q^{31} +4.41421 q^{32} +(-0.414214 - 0.717439i) q^{33} -2.41421 q^{34} +(-0.914214 - 1.58346i) q^{36} -9.48528 q^{37} +(-1.24264 - 2.15232i) q^{38} +(1.41421 - 4.89898i) q^{39} +(-1.44975 + 2.51104i) q^{40} +(-0.0857864 - 0.148586i) q^{41} +(-1.70711 + 2.95680i) q^{43} +(0.535534 - 0.927572i) q^{44} +1.82843 q^{45} -0.585786 q^{46} +(1.82843 - 3.16693i) q^{47} +(-2.12132 + 3.67423i) q^{48} +(0.343146 + 0.594346i) q^{50} +(4.12132 - 7.13834i) q^{51} +(6.39949 - 1.58346i) q^{52} +(1.50000 + 2.59808i) q^{53} -2.34315 q^{54} +(0.535534 + 0.927572i) q^{55} +8.48528 q^{57} +(-0.863961 - 1.49642i) q^{58} -10.2426 q^{59} +(-2.36396 - 4.09450i) q^{60} +(-2.08579 - 3.61269i) q^{61} +(-0.535534 - 0.927572i) q^{62} -4.17157 q^{64} +(-1.82843 + 6.33386i) q^{65} +(-0.171573 - 0.297173i) q^{66} +(-2.12132 + 3.67423i) q^{67} +10.6569 q^{68} +(1.00000 - 1.73205i) q^{69} +(5.82843 - 10.0951i) q^{71} +(-0.792893 - 1.37333i) q^{72} +(5.32843 + 9.22911i) q^{73} -3.92893 q^{74} -2.34315 q^{75} +(5.48528 + 9.50079i) q^{76} +(0.585786 - 2.02922i) q^{78} +(-0.878680 + 1.52192i) q^{79} +(2.74264 - 4.75039i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-0.0355339 - 0.0615465i) q^{82} +1.07107 q^{83} +(-5.32843 + 9.22911i) q^{85} +(-0.707107 + 1.22474i) q^{86} +5.89949 q^{87} +(0.464466 - 0.804479i) q^{88} +15.3137 q^{89} +0.757359 q^{90} +2.58579 q^{92} +3.65685 q^{93} +(0.757359 - 1.31178i) q^{94} -10.9706 q^{95} +(-3.12132 + 5.40629i) q^{96} +(5.41421 - 9.37769i) q^{97} -0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9} + 10 q^{10} - 4 q^{11} + 8 q^{12} - 14 q^{13} + 8 q^{15} + 12 q^{16} - 12 q^{17} - 2 q^{18} - 12 q^{19} - 18 q^{20} + 8 q^{22} - 4 q^{24} - 8 q^{25} + 14 q^{26} - 14 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} + 12 q^{38} + 14 q^{40} - 6 q^{41} - 4 q^{43} - 12 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} + 24 q^{50} + 8 q^{51} - 14 q^{52} + 6 q^{53} - 32 q^{54} - 12 q^{55} + 22 q^{58} - 24 q^{59} + 16 q^{60} - 14 q^{61} + 12 q^{62} - 28 q^{64} + 4 q^{65} - 12 q^{66} + 20 q^{68} + 4 q^{69} + 12 q^{71} - 6 q^{72} + 10 q^{73} - 44 q^{74} - 32 q^{75} - 12 q^{76} + 8 q^{78} - 12 q^{79} - 6 q^{80} + 10 q^{81} + 14 q^{82} - 24 q^{83} - 10 q^{85} - 16 q^{87} + 16 q^{88} + 16 q^{89} + 20 q^{90} + 16 q^{92} - 8 q^{93} + 20 q^{94} + 24 q^{95} - 4 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9 + 10 * q^10 - 4 * q^11 + 8 * q^12 - 14 * q^13 + 8 * q^15 + 12 * q^16 - 12 * q^17 - 2 * q^18 - 12 * q^19 - 18 * q^20 + 8 * q^22 - 4 * q^24 - 8 * q^25 + 14 * q^26 - 14 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 + 12 * q^38 + 14 * q^40 - 6 * q^41 - 4 * q^43 - 12 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 + 24 * q^50 + 8 * q^51 - 14 * q^52 + 6 * q^53 - 32 * q^54 - 12 * q^55 + 22 * q^58 - 24 * q^59 + 16 * q^60 - 14 * q^61 + 12 * q^62 - 28 * q^64 + 4 * q^65 - 12 * q^66 + 20 * q^68 + 4 * q^69 + 12 * q^71 - 6 * q^72 + 10 * q^73 - 44 * q^74 - 32 * q^75 - 12 * q^76 + 8 * q^78 - 12 * q^79 - 6 * q^80 + 10 * q^81 + 14 * q^82 - 24 * q^83 - 10 * q^85 - 16 * q^87 + 16 * q^88 + 16 * q^89 + 20 * q^90 + 16 * q^92 - 8 * q^93 + 20 * q^94 + 24 * q^95 - 4 * q^96 + 16 * q^97 - 8 * q^99

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