LMFDB - Embedded newform 637.2.f.f.393.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	$4$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.f.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 - 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.82843 q^{5} +(-0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.82843 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} -2.58579 q^{12} +(-3.50000 + 0.866025i) q^{13} +(1.29289 + 2.23936i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.91421 - 5.04757i) q^{17} -0.414214 q^{18} +(-3.00000 + 5.19615i) q^{19} +(-1.67157 + 2.89525i) q^{20} +(-0.121320 + 0.210133i) q^{22} +(0.707107 + 1.22474i) q^{23} +(1.12132 + 1.94218i) q^{24} -1.65685 q^{25} +(1.03553 + 1.07616i) q^{26} -5.65685 q^{27} +(-2.08579 - 3.61269i) q^{29} +(0.535534 - 0.927572i) q^{30} +2.58579 q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.414214 + 0.717439i) q^{33} -2.41421 q^{34} +(-0.914214 - 1.58346i) q^{36} +(4.74264 + 8.21449i) q^{37} +2.48528 q^{38} +(3.53553 + 3.67423i) q^{39} +2.89949 q^{40} +(-0.0857864 - 0.148586i) q^{41} +(-1.70711 + 2.95680i) q^{43} -1.07107 q^{44} +(-0.914214 + 1.58346i) q^{45} +(0.292893 - 0.507306i) q^{46} -3.65685 q^{47} +(-2.12132 + 3.67423i) q^{48} +(0.343146 + 0.594346i) q^{50} -8.24264 q^{51} +(-1.82843 + 6.33386i) q^{52} -3.00000 q^{53} +(1.17157 + 2.02922i) q^{54} +(0.535534 + 0.927572i) q^{55} +8.48528 q^{57} +(-0.863961 + 1.49642i) q^{58} +(5.12132 - 8.87039i) q^{59} +4.72792 q^{60} +(-2.08579 + 3.61269i) q^{61} +(-0.535534 - 0.927572i) q^{62} -4.17157 q^{64} +(6.39949 - 1.58346i) q^{65} +0.343146 q^{66} +(-2.12132 - 3.67423i) q^{67} +(-5.32843 - 9.22911i) q^{68} +(1.00000 - 1.73205i) q^{69} +(5.82843 - 10.0951i) q^{71} +(-0.792893 + 1.37333i) q^{72} -10.6569 q^{73} +(1.96447 - 3.40256i) q^{74} +(1.17157 + 2.02922i) q^{75} +(5.48528 + 9.50079i) q^{76} +(0.585786 - 2.02922i) q^{78} +1.75736 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} +1.41421 q^{86} +(-2.94975 + 5.10911i) q^{87} +(0.464466 + 0.804479i) q^{88} +(-7.65685 - 13.2621i) q^{89} +0.757359 q^{90} +2.58579 q^{92} +(-1.82843 - 3.16693i) q^{93} +(0.757359 + 1.31178i) q^{94} +(5.48528 - 9.50079i) q^{95} +6.24264 q^{96} +(5.41421 - 9.37769i) q^{97} -0.585786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9} + 10 q^{10} - 4 q^{11} - 16 q^{12} - 14 q^{13} + 8 q^{15} - 6 q^{16} + 6 q^{17} + 4 q^{18} - 12 q^{19} - 18 q^{20} + 8 q^{22} - 4 q^{24} + 16 q^{25} - 10 q^{26} - 14 q^{29} - 12 q^{30} + 16 q^{31} - 6 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} + 2 q^{37} - 24 q^{38} - 28 q^{40} - 6 q^{41} - 4 q^{43} + 24 q^{44} + 2 q^{45} + 4 q^{46} + 8 q^{47} + 24 q^{50} - 16 q^{51} + 4 q^{52} - 12 q^{53} + 16 q^{54} - 12 q^{55} + 22 q^{58} + 12 q^{59} - 32 q^{60} - 14 q^{61} + 12 q^{62} - 28 q^{64} - 14 q^{65} + 24 q^{66} - 10 q^{68} + 4 q^{69} + 12 q^{71} - 6 q^{72} - 20 q^{73} + 22 q^{74} + 16 q^{75} - 12 q^{76} + 8 q^{78} + 24 q^{79} - 6 q^{80} + 10 q^{81} + 14 q^{82} - 24 q^{83} - 10 q^{85} + 8 q^{87} + 16 q^{88} - 8 q^{89} + 20 q^{90} + 16 q^{92} + 4 q^{93} + 20 q^{94} - 12 q^{95} + 8 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9 + 10 * q^10 - 4 * q^11 - 16 * q^12 - 14 * q^13 + 8 * q^15 - 6 * q^16 + 6 * q^17 + 4 * q^18 - 12 * q^19 - 18 * q^20 + 8 * q^22 - 4 * q^24 + 16 * q^25 - 10 * q^26 - 14 * q^29 - 12 * q^30 + 16 * q^31 - 6 * q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 + 2 * q^37 - 24 * q^38 - 28 * q^40 - 6 * q^41 - 4 * q^43 + 24 * q^44 + 2 * q^45 + 4 * q^46 + 8 * q^47 + 24 * q^50 - 16 * q^51 + 4 * q^52 - 12 * q^53 + 16 * q^54 - 12 * q^55 + 22 * q^58 + 12 * q^59 - 32 * q^60 - 14 * q^61 + 12 * q^62 - 28 * q^64 - 14 * q^65 + 24 * q^66 - 10 * q^68 + 4 * q^69 + 12 * q^71 - 6 * q^72 - 20 * q^73 + 22 * q^74 + 16 * q^75 - 12 * q^76 + 8 * q^78 + 24 * q^79 - 6 * q^80 + 10 * q^81 + 14 * q^82 - 24 * q^83 - 10 * q^85 + 8 * q^87 + 16 * q^88 - 8 * q^89 + 20 * q^90 + 16 * q^92 + 4 * q^93 + 20 * q^94 - 12 * q^95 + 8 * q^96 + 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.207107	−	0.358719i	−0.146447	−	0.253653i	0.783465	−	0.621436i	$-0.213450\pi$
$2$	−0.207107	−	0.358719i	−0.146447	−	0.253653i	−0.929912	+	0.367783i	$0.880117\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	0.586445	−	0.809989i	$-0.300527\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	−0.994694	+	0.102882i	$0.967194\pi$
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	−1.82843			−0.817697			−0.408849	−	0.912602i	$-0.634070\pi$
$5$	−1.82843			−0.817697			−0.408849	+	0.912602i	$0.634070\pi$
$6$	−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	0.818487	−	0.574526i	$-0.194813\pi$
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	−0.906797	+	0.421567i	$0.861480\pi$
$12$	−2.58579			−0.746452
$13$	−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
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	2.91421	−	5.04757i	0.706801	−	1.22421i	−0.259237	−	0.965814i	$-0.583471\pi$
$17$	2.91421	−	5.04757i	0.706801	−	1.22421i	0.966038	−	0.258401i	$-0.0831955\pi$
$18$	−0.414214			−0.0976311
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$	−1.67157	+	2.89525i	−0.373775	+	0.647397i
$21$		0			0
$22$	−0.121320	+	0.210133i	−0.0258656	+	0.0448005i
$23$	0.707107	+	1.22474i	0.147442	+	0.255377i	0.930281	−	0.366847i	$-0.119563\pi$
$23$	0.707107	+	1.22474i	0.147442	+	0.255377i	−0.782839	+	0.622224i	$0.786229\pi$
$24$	1.12132	+	1.94218i	0.228889	+	0.396447i
$25$	−1.65685			−0.331371
$26$	1.03553	+	1.07616i	0.203085	+	0.211052i
$27$	−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
$31$	2.58579			0.464421			0.232210	−	0.972666i	$-0.425404\pi$
$31$	2.58579			0.464421			0.232210	+	0.972666i	$0.425404\pi$
$32$	−2.20711	+	3.82282i	−0.390165	+	0.675786i
$33$	−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
$37$	4.74264	+	8.21449i	0.779685	+	1.35045i	0.932123	+	0.362142i	$0.117954\pi$
$37$	4.74264	+	8.21449i	0.779685	+	1.35045i	−0.152438	+	0.988313i	$0.548712\pi$
$38$	2.48528			0.403166
$39$	3.53553	+	3.67423i	0.566139	+	0.588348i
$40$	2.89949			0.458450
$41$	−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	$0.250498\pi$
$44$	−1.07107			−0.161470
$45$	−0.914214	+	1.58346i	−0.136283	+	0.236049i
$46$	0.292893	−	0.507306i	0.0431847	−	0.0747982i
$47$	−3.65685			−0.533407			−0.266704	−	0.963779i	$-0.585934\pi$
$47$	−3.65685			−0.533407			−0.266704	+	0.963779i	$0.585934\pi$
$48$	−2.12132	+	3.67423i	−0.306186	+	0.530330i
$49$		0			0
$50$	0.343146	+	0.594346i	0.0485281	+	0.0840532i
$51$	−8.24264			−1.15420
$52$	−1.82843	+	6.33386i	−0.253557	+	0.878348i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	1.17157	+	2.02922i	0.159431	+	0.276142i
$55$	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
$59$	5.12132	−	8.87039i	0.666739	−	1.15483i	−0.312072	−	0.950059i	$-0.601023\pi$
$59$	5.12132	−	8.87039i	0.666739	−	1.15483i	0.978811	−	0.204767i	$-0.0656438\pi$
$60$	4.72792			0.610372
$61$	−2.08579	+	3.61269i	−0.267058	+	0.462557i	−0.968101	−	0.250562i	$-0.919385\pi$
$61$	−2.08579	+	3.61269i	−0.267058	+	0.462557i	0.701043	+	0.713119i	$0.252718\pi$
$62$	−0.535534	−	0.927572i	−0.0680129	−	0.117802i
$63$		0			0
$64$	−4.17157			−0.521447
$65$	6.39949	−	1.58346i	0.793760	−	0.196405i
$66$	0.343146			0.0422383
$67$	−2.12132	−	3.67423i	−0.259161	−	0.448879i	0.706857	−	0.707357i	$-0.250113\pi$
$67$	−2.12132	−	3.67423i	−0.259161	−	0.448879i	−0.966017	+	0.258478i	$0.916779\pi$
$68$	−5.32843	−	9.22911i	−0.646167	−	1.11919i
$69$	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
$73$	−10.6569			−1.24729			−0.623645	−	0.781708i	$-0.714349\pi$
$73$	−10.6569			−1.24729			−0.623645	+	0.781708i	$0.714349\pi$
$74$	1.96447	−	3.40256i	0.228365	−	0.395539i
$75$	1.17157	+	2.02922i	0.135282	+	0.234315i
$76$	5.48528	+	9.50079i	0.629205	+	1.08981i
$77$		0			0
$78$	0.585786	−	2.02922i	0.0663273	−	0.229764i
$79$	1.75736			0.197718			0.0988592	−	0.995101i	$-0.468481\pi$
$79$	1.75736			0.197718			0.0988592	+	0.995101i	$0.468481\pi$
$80$	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
$86$	1.41421			0.152499
$87$	−2.94975	+	5.10911i	−0.316246	+	0.547754i
$88$	0.464466	+	0.804479i	0.0495123	+	0.0857577i
$89$	−7.65685	−	13.2621i	−0.811625	−	1.40578i	−0.911726	−	0.410798i	$-0.865250\pi$
$89$	−7.65685	−	13.2621i	−0.811625	−	1.40578i	0.100101	−	0.994977i	$-0.468083\pi$
$90$	0.757359			0.0798327
$91$		0			0
$92$	2.58579			0.269587
$93$	−1.82843	−	3.16693i	−0.189599	−	0.328395i
$94$	0.757359	+	1.31178i	0.0781156	+	0.135300i
$95$	5.48528	−	9.50079i	0.562778	−	0.974760i
$96$	6.24264			0.637137
$97$	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	−0.957219	−	0.289363i	$-0.906556\pi$
$101$	−7.32843	−	12.6932i	−0.729206	−	1.26302i	0.228014	−	0.973658i	$-0.426777\pi$
$102$	1.70711	+	2.95680i	0.169029	+	0.292766i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	5.55025	−	1.37333i	0.544247	−	0.134666i
$105$		0			0
$106$	0.621320	+	1.07616i	0.0603480	+	0.104526i
$107$	−8.65685	−	14.9941i	−0.836890	−	1.44954i	−0.892483	−	0.451082i	$-0.851038\pi$
$107$	−8.65685	−	14.9941i	−0.836890	−	1.44954i	0.0555929	−	0.998454i	$-0.482295\pi$
$108$	−5.17157	+	8.95743i	−0.497635	+	0.861929i
$109$	−13.6569			−1.30809			−0.654045	−	0.756456i	$-0.726929\pi$
$109$	−13.6569			−1.30809			−0.654045	+	0.756456i	$0.726929\pi$
$110$	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	$0.762009\pi$
$114$	−1.75736	−	3.04384i	−0.164592	−	0.285081i
$115$	−1.29289	−	2.23936i	−0.120563	−	0.208821i
$116$	−7.62742			−0.708188
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	−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
$122$	1.72792			0.156439
$123$	−0.121320	+	0.210133i	−0.0109391	+	0.0189471i
$124$	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	$-0.367815\pi$
$128$	5.27817	+	9.14207i	0.466529	+	0.808052i
$129$	4.82843			0.425119
$130$	−1.89340	−	1.96768i	−0.166062	−	0.172577i
$131$	21.3137			1.86219			0.931094	−	0.364780i	$-0.118856\pi$
$131$	21.3137			1.86219			0.931094	+	0.364780i	$0.118856\pi$
$132$	0.757359	+	1.31178i	0.0659197	+	0.114176i
$133$		0			0
$134$	−0.878680	+	1.52192i	−0.0759064	+	0.131474i
$135$	10.3431			0.890196
$136$	−4.62132	+	8.00436i	−0.396275	+	0.686368i
$137$	0.0857864	−	0.148586i	0.00732923	−	0.0126946i	−0.862338	−	0.506334i	$-0.831000\pi$
$137$	0.0857864	−	0.148586i	0.00732923	−	0.0126946i	0.869667	+	0.493639i	$0.164334\pi$
$138$	−0.828427			−0.0705204
$139$	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
$142$	−4.82843			−0.405193
$143$	1.46447	+	1.52192i	0.122465	+	0.127269i
$144$	−3.00000			−0.250000
$145$	3.81371	+	6.60554i	0.316711	+	0.548560i
$146$	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	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$	0.485281	−	0.840532i	0.0396231	−	0.0686292i
$151$	14.9706			1.21829			0.609144	−	0.793060i	$-0.291513\pi$
$151$	14.9706			1.21829			0.609144	+	0.793060i	$0.291513\pi$
$152$	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
$156$	9.05025	−	2.23936i	0.724600	−	0.179292i
$157$	5.48528			0.437773			0.218887	−	0.975750i	$-0.429758\pi$
$157$	5.48528			0.437773			0.218887	+	0.975750i	$0.429758\pi$
$158$	−0.363961	−	0.630399i	−0.0289552	−	0.0501519i
$159$	2.12132	+	3.67423i	0.168232	+	0.291386i
$160$	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	−0.999967	−	0.00818201i	$-0.997396\pi$
$163$	−6.29289	+	10.8996i	−0.492897	+	0.853723i	0.507069	+	0.861905i	$0.330729\pi$
$164$	−0.313708			−0.0244965
$165$	0.757359	−	1.31178i	0.0589603	−	0.102122i
$166$	−0.221825	−	0.384213i	−0.0172170	−	0.0298207i
$167$	−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
$170$	4.41421			0.338555
$171$	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	−0.606299	−	0.795237i	$-0.707346\pi$
$173$	5.07107	−	8.78335i	0.385546	−	0.667786i	0.991845	+	0.127452i	$0.0406797\pi$
$174$	2.44365			0.185253
$175$		0			0
$176$	−0.878680	+	1.52192i	−0.0662330	+	0.114719i
$177$	−14.4853			−1.08878
$178$	−3.17157	+	5.49333i	−0.237719	+	0.411742i
$179$	2.82843	+	4.89898i	0.211407	+	0.366167i	0.952155	−	0.305616i	$-0.0988623\pi$
$179$	2.82843	+	4.89898i	0.211407	+	0.366167i	−0.740748	+	0.671783i	$0.765529\pi$
$180$	1.67157	+	2.89525i	0.124592	+	0.215799i
$181$	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
$184$	−1.12132	−	1.94218i	−0.0826648	−	0.143180i
$185$	−8.67157	−	15.0196i	−0.637547	−	1.10426i
$186$	−0.757359	+	1.31178i	−0.0555323	+	0.0961847i
$187$	−3.41421			−0.249672
$188$	−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	0.406903	+	0.913471i	$0.366609\pi$
$191$	−8.12132	+	14.0665i	−0.587638	+	1.01782i	−0.994541	+	0.104348i	$0.966725\pi$
$192$	2.94975	+	5.10911i	0.212880	+	0.368718i
$193$	−3.57107	−	6.18527i	−0.257051	−	0.445226i	0.708400	−	0.705812i	$-0.249418\pi$
$193$	−3.57107	−	6.18527i	−0.257051	−	0.445226i	−0.965451	+	0.260586i	$0.916084\pi$
$194$	−4.48528			−0.322024
$195$	−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	$-0.343815\pi$
$198$	0.121320	+	0.210133i	0.00862186	+	0.0149335i
$199$	7.48528	−	12.9649i	0.530618	−	0.919057i	−0.468744	−	0.883334i	$-0.655293\pi$
$199$	7.48528	−	12.9649i	0.530618	−	0.919057i	0.999362	−	0.0357226i	$-0.0113733\pi$
$200$	2.62742			0.185786
$201$	−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
$205$	0.156854	+	0.271680i	0.0109552	+	0.0189749i
$206$	−2.89949	−	5.02207i	−0.202017	−	0.349904i
$207$	1.41421			0.0982946
$208$	7.50000	+	7.79423i	0.520031	+	0.540433i
$209$	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
$213$	−16.4853			−1.12955
$214$	−3.58579	+	6.21076i	−0.245119	+	0.424559i
$215$	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
$219$	7.53553	+	13.0519i	0.509204	+	0.881968i
$220$	1.95837			0.132033
$221$	−5.82843	+	20.1903i	−0.392062	+	1.35814i
$222$	−5.55635			−0.372918
$223$	−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
$226$	8.41421			0.559705
$227$	−2.94975	+	5.10911i	−0.195782	+	0.339104i	−0.947156	−	0.320772i	$-0.896058\pi$
$227$	−2.94975	+	5.10911i	−0.195782	+	0.339104i	0.751375	+	0.659876i	$0.229391\pi$
$228$	7.75736	−	13.4361i	0.513744	−	0.889830i
$229$	−12.4853			−0.825051			−0.412525	−	0.910946i	$-0.635353\pi$
$229$	−12.4853			−0.825051			−0.412525	+	0.910946i	$0.635353\pi$
$230$	−0.535534	+	0.927572i	−0.0353121	+	0.0611623i
$231$		0			0
$232$	3.30761	+	5.72895i	0.217155	+	0.376124i
$233$	2.82843			0.185296			0.0926482	−	0.995699i	$-0.470467\pi$
$233$	2.82843			0.185296			0.0926482	+	0.995699i	$0.470467\pi$
$234$	1.44975	−	0.358719i	0.0947730	−	0.0234502i
$235$	6.68629			0.436166
$236$	−9.36396	−	16.2189i	−0.609542	−	1.05576i
$237$	−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
$241$	−7.74264	+	13.4106i	−0.498747	+	0.863856i	−0.999999	−	0.00144585i	$-0.999540\pi$
$241$	−7.74264	+	13.4106i	−0.498747	+	0.863856i	0.501252	+	0.865302i	$0.332873\pi$
$242$	−4.41421			−0.283756
$243$	−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
$247$	6.00000	−	20.7846i	0.381771	−	1.32249i
$248$	−4.10051			−0.260382
$249$	−0.757359	−	1.31178i	−0.0479957	−	0.0831310i
$250$	−2.52082	−	4.36618i	−0.159430	−	0.276141i
$251$	−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
$255$	15.0711			0.943787
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	−1.00000	−	1.73205i	−0.0622573	−	0.107833i
$259$		0			0
$260$	3.34315	−	11.5810i	0.207333	−	0.718223i
$261$	−4.17157			−0.258214
$262$	−4.41421	−	7.64564i	−0.272711	−	0.472349i
$263$	3.36396	+	5.82655i	0.207431	+	0.359281i	0.950904	−	0.309485i	$-0.100157\pi$
$263$	3.36396	+	5.82655i	0.207431	+	0.359281i	−0.743474	+	0.668765i	$0.766823\pi$
$264$	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
$268$	−7.75736			−0.473856
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	−2.14214	−	3.71029i	−0.130366	−	0.225801i
$271$	10.5355	+	18.2481i	0.639988	+	1.10849i	0.985435	+	0.170054i	$0.0543941\pi$
$271$	10.5355	+	18.2481i	0.639988	+	1.10849i	−0.345447	+	0.938438i	$0.612273\pi$
$272$	−17.4853			−1.06020
$273$		0			0
$274$	−0.0710678			−0.00429336
$275$	0.485281	+	0.840532i	0.0292636	+	0.0506860i
$276$	−1.82843	−	3.16693i	−0.110058	−	0.190627i
$277$	−0.985281	+	1.70656i	−0.0591998	+	0.102537i	−0.894106	−	0.447855i	$-0.852188\pi$
$277$	−0.985281	+	1.70656i	−0.0591998	+	0.102537i	0.834907	+	0.550392i	$0.185522\pi$
$278$	−4.92893			−0.295618
$279$	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	0.994037	+	0.109041i	$0.0347781\pi$
$283$	9.94975	+	17.2335i	0.591451	+	1.02442i	−0.402586	+	0.915382i	$0.631889\pi$
$284$	−10.6569	−	18.4582i	−0.632368	−	1.09529i
$285$	−15.5147			−0.919013
$286$	0.242641	−	0.840532i	0.0143476	−	0.0497017i
$287$		0			0
$288$	2.20711	+	3.82282i	0.130055	+	0.225262i
$289$	−8.48528	−	14.6969i	−0.499134	−	0.864526i
$290$	1.57969	−	2.73610i	0.0927626	−	0.160669i
$291$	−15.3137			−0.897705
$292$	−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
$296$	−7.52082	−	13.0264i	−0.437139	−	0.757146i
$297$	1.65685	+	2.86976i	0.0961404	+	0.166520i
$298$	1.24264			0.0719842
$299$	−3.53553	−	3.67423i	−0.204465	−	0.212486i
$300$	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
$304$	18.0000			1.03237
$305$	3.81371	−	6.60554i	0.218372	−	0.378232i
$306$	−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
$310$	0.979185	+	1.69600i	0.0556140	+	0.0963262i
$311$	−12.9289			−0.733132			−0.366566	−	0.930392i	$-0.619467\pi$
$311$	−12.9289			−0.733132			−0.366566	+	0.930392i	$0.619467\pi$
$312$	−5.60660	−	5.82655i	−0.317411	−	0.329864i
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	−1.13604	−	1.96768i	−0.0641104	−	0.111042i
$315$		0			0
$316$	1.60660	−	2.78272i	0.0903784	−	0.156540i
$317$	32.6569			1.83419			0.917096	−	0.398667i	$-0.130527\pi$
$317$	32.6569			1.83419			0.917096	+	0.398667i	$0.130527\pi$
$318$	0.878680	−	1.52192i	0.0492739	−	0.0853449i
$319$	−1.22183	+	2.11626i	−0.0684091	+	0.118488i
$320$	7.62742			0.426386
$321$	−12.2426	+	21.2049i	−0.683318	+	1.18354i
$322$		0			0
$323$	17.4853	+	30.2854i	0.972907	+	1.68512i
$324$	9.14214			0.507896
$325$	5.79899	−	1.43488i	0.321670	−	0.0795927i
$326$	5.21320			0.288733
$327$	9.65685	+	16.7262i	0.534025	+	0.924959i
$328$	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	−0.290417	−	0.956900i	$-0.593794\pi$
$331$	12.4350	−	21.5381i	0.683491	−	1.18384i	0.973908	−	0.226941i	$-0.0728725\pi$
$332$	0.979185	−	1.69600i	0.0537397	−	0.0930800i
$333$	9.48528			0.519790
$334$	−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	$0.530262\pi$
$338$	−4.55635	−	2.86976i	−0.247833	−	0.156094i
$339$	28.7279			1.56029
$340$	9.74264	+	16.8747i	0.528369	+	0.915162i
$341$	−0.757359	−	1.31178i	−0.0410133	−	0.0710371i
$342$	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
$346$	−4.20101			−0.225848
$347$	3.05025	−	5.28319i	0.163746	−	0.283617i	−0.772463	−	0.635060i	$-0.780976\pi$
$347$	3.05025	−	5.28319i	0.163746	−	0.283617i	0.936209	+	0.351443i	$0.114309\pi$
$348$	5.39340	+	9.34164i	0.289116	+	0.500764i
$349$	−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
$352$	2.58579			0.137823
$353$	−2.91421	−	5.04757i	−0.155108	−	0.268655i	0.777990	−	0.628276i	$-0.216239\pi$
$353$	−2.91421	−	5.04757i	−0.155108	−	0.268655i	−0.933098	+	0.359621i	$0.882906\pi$
$354$	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
$359$	−16.9706			−0.895672			−0.447836	−	0.894116i	$-0.647805\pi$
$359$	−16.9706			−0.895672			−0.447836	+	0.894116i	$0.647805\pi$
$360$	1.44975	−	2.51104i	0.0764084	−	0.132343i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−1.89340	−	3.27946i	−0.0995148	−	0.172365i
$363$	−15.0711			−0.791026
$364$		0			0
$365$	19.4853			1.01991
$366$	−1.22183	−	2.11626i	−0.0638658	−	0.110619i
$367$	14.3640	+	24.8791i	0.749793	+	1.29868i	0.947922	+	0.318503i	$0.103180\pi$
$367$	14.3640	+	24.8791i	0.749793	+	1.29868i	−0.198129	+	0.980176i	$0.563487\pi$
$368$	2.12132	−	3.67423i	0.110581	−	0.191533i
$369$	−0.171573			−0.00893173
$370$	−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	0.288547	+	0.957466i	$0.406828\pi$
$373$	−13.2279	+	22.9114i	−0.684916	+	1.18631i	−0.973463	+	0.228843i	$0.926506\pi$
$374$	0.707107	+	1.22474i	0.0365636	+	0.0633300i
$375$	−8.60660	−	14.9071i	−0.444443	−	0.769798i
$376$	5.79899			0.299060
$377$	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	$0.831350\pi$
$380$	−10.0294	−	17.3715i	−0.514499	−	0.891139i
$381$	−9.41421	+	16.3059i	−0.482305	+	0.835376i
$382$	6.72792			0.344230
$383$	17.0208	−	29.4809i	0.869723	−	1.50640i	0.00744324	−	0.999972i	$-0.497631\pi$
$383$	17.0208	−	29.4809i	0.869723	−	1.50640i	0.862280	−	0.506432i	$-0.169036\pi$
$384$	7.46447	−	12.9288i	0.380919	−	0.659772i
$385$		0			0
$386$	−1.47918	+	2.56202i	−0.0752885	+	0.130404i
$387$	1.70711	+	2.95680i	0.0867771	+	0.150302i
$388$	−9.89949	−	17.1464i	−0.502571	−	0.870478i
$389$	27.1421			1.37616			0.688080	−	0.725634i	$-0.258454\pi$
$389$	27.1421			1.37616			0.688080	+	0.725634i	$0.258454\pi$
$390$	−1.07107	+	3.71029i	−0.0542356	+	0.187878i
$391$	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
$395$	−3.21320			−0.161674
$396$	−0.535534	+	0.927572i	−0.0269116	+	0.0466122i
$397$	−3.31371	+	5.73951i	−0.166310	+	0.288058i	−0.937120	−	0.349008i	$-0.886519\pi$
$397$	−3.31371	+	5.73951i	−0.166310	+	0.288058i	0.770810	+	0.637066i	$0.219852\pi$
$398$	−6.20101			−0.310829
$399$		0			0
$400$	2.48528	+	4.30463i	0.124264	+	0.215232i
$401$	−4.39949	−	7.62015i	−0.219700	−	0.380532i	0.735016	−	0.678050i	$-0.237175\pi$
$401$	−4.39949	−	7.62015i	−0.219700	−	0.380532i	−0.954716	+	0.297518i	$0.903841\pi$
$402$	2.48528			0.123955
$403$	−9.05025	+	2.23936i	−0.450825	+	0.111550i
$404$	−26.7990			−1.33330
$405$	−4.57107	−	7.91732i	−0.227138	−	0.393415i
$406$		0			0
$407$	2.77817	−	4.81194i	0.137709	−	0.238519i
$408$	13.0711			0.647114
$409$	10.9853	−	19.0271i	0.543187	−	0.940828i	−0.455531	−	0.890220i	$-0.650551\pi$
$409$	10.9853	−	19.0271i	0.543187	−	0.940828i	0.998719	−	0.0506081i	$-0.0161159\pi$
$410$	0.0649712	−	0.112533i	0.00320870	−	0.00555763i
$411$	−0.242641			−0.0119686
$412$	12.7990	−	22.1685i	0.630561	−	1.09216i
$413$		0			0
$414$	−0.292893	−	0.507306i	−0.0143949	−	0.0249327i
$415$	−1.95837			−0.0961326
$416$	4.41421	−	15.2913i	0.216425	−	0.749717i
$417$	−16.8284			−0.824092
$418$	−0.727922	−	1.26080i	−0.0356038	−	0.0616676i
$419$	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
$423$	−1.82843	+	3.16693i	−0.0889012	+	0.153981i
$424$	4.75736			0.231038
$425$	−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
$429$	0.828427	−	2.86976i	0.0399968	−	0.138553i
$430$	−2.58579			−0.124698
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	8.48528	+	14.6969i	0.408248	+	0.707107i
$433$	−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
$437$	−8.48528			−0.405906
$438$	3.12132	−	5.40629i	0.149142	−	0.258322i
$439$	0.636039	+	1.10165i	0.0303565	+	0.0525790i	0.880805	−	0.473480i	$-0.157002\pi$
$439$	0.636039	+	1.10165i	0.0303565	+	0.0525790i	−0.850448	+	0.526059i	$0.823669\pi$
$440$	−0.849242	−	1.47093i	−0.0404860	−	0.0701239i
$441$		0			0
$442$	8.44975	−	2.09077i	0.401914	−	0.0994478i
$443$	25.6569			1.21899			0.609497	−	0.792788i	$-0.291371\pi$
$443$	25.6569			1.21899			0.609497	+	0.792788i	$0.291371\pi$
$444$	−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	$0.888645\pi$
$450$	0.686292			0.0323521
$451$	−0.0502525	+	0.0870399i	−0.00236630	+	0.00409855i
$452$	18.5711	+	32.1660i	0.873510	+	1.51296i
$453$	−10.5858	−	18.3351i	−0.497364	−	0.861459i
$454$	2.44365			0.114686
$455$		0			0
$456$	−13.4558			−0.630128
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$	2.58579	+	4.47871i	0.120826	+	0.209277i
$459$	−16.4853	+	28.5533i	−0.769467	+	1.33276i
$460$	−4.72792			−0.220441
$461$	−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
$467$	11.4142			0.528187			0.264093	−	0.964497i	$-0.414927\pi$
$467$	11.4142			0.528187			0.264093	+	0.964497i	$0.414927\pi$
$468$	4.57107	+	4.75039i	0.211298	+	0.219587i
$469$		0			0
$470$	−1.38478	−	2.39850i	−0.0638750	−	0.110635i
$471$	−3.87868	−	6.71807i	−0.178720	−	0.309552i
$472$	−8.12132	+	14.0665i	−0.373814	+	0.647465i
$473$	2.00000			0.0919601
$474$	−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
$478$	−5.05025	−	8.74729i	−0.230993	−	0.400092i
$479$	0.807612	+	1.39882i	0.0369007	+	0.0639139i	0.883886	−	0.467703i	$-0.154918\pi$
$479$	0.807612	+	1.39882i	0.0369007	+	0.0639139i	−0.846985	+	0.531616i	$0.821585\pi$
$480$	−11.4142			−0.520985
$481$	−23.7132	−	24.6435i	−1.08123	−	1.12365i
$482$	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
$486$	4.10051			0.186003
$487$	6.48528	−	11.2328i	0.293876	−	0.509008i	−0.680847	−	0.732426i	$-0.738388\pi$
$487$	6.48528	−	11.2328i	0.293876	−	0.509008i	0.974723	+	0.223418i	$0.0717213\pi$
$488$	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	$0.925746\pi$
$492$	0.221825	+	0.384213i	0.0100007	+	0.0173217i
$493$	−24.3137			−1.09503
$494$	−8.69848	+	2.15232i	−0.391363	+	0.0968373i
$495$	1.07107			0.0481409
$496$	−3.87868	−	6.71807i	−0.174158	−	0.301650i
$497$		0			0
$498$	−0.313708	+	0.543359i	−0.0140576	+	0.0243485i
$499$	20.0416			0.897187			0.448593	−	0.893736i	$-0.351925\pi$
$499$	20.0416			0.897187			0.448593	+	0.893736i	$0.351925\pi$
$500$	11.1274	−	19.2733i	0.497633	−	0.861926i
$501$	−4.75736	+	8.23999i	−0.212543	+	0.368136i
$502$	9.51472			0.424663
$503$	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
$506$	−0.343146			−0.0152547
$507$	−15.5563	−	9.79796i	−0.690882	−	0.435143i
$508$	−24.3431			−1.08005
$509$	−2.32843	−	4.03295i	−0.103206	−	0.178758i	0.809798	−	0.586709i	$-0.199577\pi$
$509$	−2.32843	−	4.03295i	−0.103206	−	0.178758i	−0.913004	+	0.407951i	$0.866243\pi$
$510$	−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
$514$	−3.10660	+	5.38079i	−0.137026	+	0.237337i
$515$	−25.5980			−1.12798
$516$	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
$520$	−10.1482	+	2.51104i	−0.445029	+	0.110116i
$521$	−24.6569			−1.08024			−0.540118	−	0.841589i	$-0.681620\pi$
$521$	−24.6569			−1.08024			−0.540118	+	0.841589i	$0.681620\pi$
$522$	0.863961	+	1.49642i	0.0378145	+	0.0654967i
$523$	8.48528	+	14.6969i	0.371035	+	0.642652i	0.989725	−	0.142983i	$-0.0456695\pi$
$523$	8.48528	+	14.6969i	0.371035	+	0.642652i	−0.618690	+	0.785635i	$0.712336\pi$
$524$	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
$528$	2.48528			0.108158
$529$	10.5000	−	18.1865i	0.456522	−	0.790719i
$530$	−1.13604	−	1.96768i	−0.0493464	−	0.0854704i
$531$	−5.12132	−	8.87039i	−0.222246	−	0.384942i
$532$		0			0
$533$	0.428932	+	0.445759i	0.0185791	+	0.0193080i
$534$	8.97056			0.388194
$535$	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
$541$	−11.4853			−0.493791			−0.246895	−	0.969042i	$-0.579410\pi$
$541$	−11.4853			−0.493791			−0.246895	+	0.969042i	$0.579410\pi$
$542$	4.36396	−	7.55860i	0.187448	−	0.324670i
$543$	−6.46447	−	11.1968i	−0.277417	−	0.480500i
$544$	12.8640	+	22.2810i	0.551538	+	0.955291i
$545$	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	$0.493678\pi$
$548$	−0.156854	−	0.271680i	−0.00670048	−	0.0116056i
$549$	2.08579	+	3.61269i	0.0890192	+	0.154186i
$550$	0.201010	−	0.348160i	0.00857110	−	0.0148456i
$551$	25.0294			1.06629
$552$	−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	0.705600	−	0.708610i	$-0.250677\pi$
$557$	−6.15685	−	10.6640i	−0.260874	−	0.451848i	−0.966474	+	0.256763i	$0.917344\pi$
$558$	−1.07107			−0.0453419
$559$	3.41421	−	11.8272i	0.144406	−	0.500237i
$560$		0			0
$561$	2.41421	+	4.18154i	0.101928	+	0.176545i
$562$	3.62132	+	6.27231i	0.152756	+	0.264581i
$563$	−0.0502525	+	0.0870399i	−0.00211789	+	0.00366830i	−0.867082	−	0.498165i	$-0.834007\pi$
$563$	−0.0502525	+	0.0870399i	−0.00211789	+	0.00366830i	0.864965	+	0.501833i	$0.167341\pi$
$564$	9.45584			0.398163
$565$	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
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	0.598394	−	0.801202i	$-0.295806\pi$
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	−0.993058	+	0.117623i	$0.962472\pi$
$570$	3.21320	+	5.56543i	0.134586	+	0.233110i
$571$	28.9706			1.21238			0.606190	−	0.795320i	$-0.292697\pi$
$571$	28.9706			1.21238			0.606190	+	0.795320i	$0.292697\pi$
$572$	3.74874	−	0.927572i	0.156743	−	0.0387837i
$573$	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
$577$	−13.6863			−0.569768			−0.284884	−	0.958562i	$-0.591955\pi$
$577$	−13.6863			−0.569768			−0.284884	+	0.958562i	$0.591955\pi$
$578$	−3.51472	+	6.08767i	−0.146193	+	0.253214i
$579$	−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
$583$	0.878680	+	1.52192i	0.0363912	+	0.0630314i
$584$	16.8995			0.699306
$585$	1.82843	−	6.33386i	0.0755962	−	0.261873i
$586$	11.7868			0.486908
$587$	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
$590$	7.75736			0.319365
$591$	−10.4853	+	18.1610i	−0.431307	+	0.747045i
$592$	14.2279	−	24.6435i	0.584764	−	1.01284i
$593$	25.2843			1.03830			0.519150	−	0.854683i	$-0.326248\pi$
$593$	25.2843			1.03830			0.519150	+	0.854683i	$0.326248\pi$
$594$	0.686292	−	1.18869i	0.0281589	−	0.0487726i
$595$		0			0
$596$	2.74264	+	4.75039i	0.112343	+	0.194584i
$597$	−21.1716			−0.866495
$598$	−0.585786	+	2.02922i	−0.0239546	+	0.0829811i
$599$	28.3431			1.15807			0.579035	−	0.815303i	$-0.303430\pi$
$599$	28.3431			1.15807			0.579035	+	0.815303i	$0.303430\pi$
$600$	−1.85786	−	3.21792i	−0.0758470	−	0.131371i
$601$	−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
$605$	−9.74264	+	16.8747i	−0.396095	+	0.686056i
$606$	8.58579			0.348774
$607$	16.1716	−	28.0100i	0.656384	−	1.13689i	−0.325161	−	0.945659i	$-0.605419\pi$
$607$	16.1716	−	28.0100i	0.656384	−	1.13689i	0.981545	−	0.191232i	$-0.0612482\pi$
$608$	−13.2426	−	22.9369i	−0.537060	−	0.930215i
$609$		0			0
$610$	−3.15938			−0.127920
$611$	12.7990	−	3.16693i	0.517792	−	0.128120i
$612$	−10.6569			−0.430778
$613$	7.39949	+	12.8163i	0.298863	+	0.517646i	0.975876	−	0.218325i	$-0.0700594\pi$
$613$	7.39949	+	12.8163i	0.298863	+	0.517646i	−0.677013	+	0.735971i	$0.736726\pi$
$614$	6.77817	+	11.7401i	0.273545	+	0.473794i
$615$	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
$619$	41.5563			1.67029			0.835145	−	0.550029i	$-0.185383\pi$
$619$	41.5563			1.67029			0.835145	+	0.550029i	$0.185383\pi$
$620$	−4.32233	+	7.48650i	−0.173589	+	0.300665i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	2.67767	+	4.63786i	0.107365	+	0.185961i
$623$		0			0
$624$	4.24264	−	14.6969i	0.169842	−	0.588348i
$625$	−13.9706			−0.558823
$626$	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	$0.327254\pi$
$632$	−2.78680			−0.110853
$633$	−17.4853	+	30.2854i	−0.694978	+	1.20374i
$634$	−6.76346	−	11.7146i	−0.268611	−	0.465248i
$635$	12.1716	+	21.0818i	0.483014	+	0.836605i
$636$	7.75736			0.307599
$637$		0			0
$638$	1.01219			0.0400731
$639$	−5.82843	−	10.0951i	−0.230569	−	0.399357i
$640$	−9.65076	−	16.7156i	−0.381480	−	0.660742i
$641$	7.39949	−	12.8163i	0.292262	−	0.506213i	−0.682082	−	0.731276i	$-0.738925\pi$
$641$	7.39949	−	12.8163i	0.292262	−	0.506213i	0.974344	+	0.225062i	$0.0722586\pi$
$642$	10.1421			0.400278
$643$	−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	0.984495	−	0.175412i	$-0.0561258\pi$
$647$	8.65685	+	14.9941i	0.340336	+	0.589479i	−0.644159	+	0.764892i	$0.722793\pi$
$648$	−3.96447	−	6.86666i	−0.155739	−	0.269748i
$649$	−6.00000			−0.235521
$650$	−1.71573	−	1.78304i	−0.0672964	−	0.0699365i
$651$		0			0
$652$	11.5061	+	19.9291i	0.450614	+	0.780486i
$653$	−13.0711	−	22.6398i	−0.511510	−	0.885962i	−0.999911	−	0.0133425i	$-0.995753\pi$
$653$	−13.0711	−	22.6398i	−0.511510	−	0.885962i	0.488401	−	0.872620i	$-0.337580\pi$
$654$	4.00000	−	6.92820i	0.156412	−	0.270914i
$655$	−38.9706			−1.52271
$656$	−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	$0.0702575\pi$
$660$	−1.38478	−	2.39850i	−0.0539023	−	0.0933616i
$661$	16.5711	+	28.7019i	0.644540	+	1.11638i	0.984408	+	0.175903i	$0.0562843\pi$
$661$	16.5711	+	28.7019i	0.644540	+	1.11638i	−0.339868	+	0.940473i	$0.610382\pi$
$662$	−10.3015			−0.400380
$663$	28.8492	−	7.13834i	1.12041	−	0.277230i
$664$	−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
$668$	−12.3015			−0.475960
$669$	−1.41421	+	2.44949i	−0.0546767	+	0.0947027i
$670$	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	$0.923585\pi$
$674$	0.721825	+	1.25024i	0.0278037	+	0.0481574i
$675$	9.37258			0.360751
$676$	0.914214	−	23.7520i	0.0351621	−	0.913537i
$677$	−17.6569			−0.678608			−0.339304	−	0.940677i	$-0.610192\pi$
$677$	−17.6569			−0.678608			−0.339304	+	0.940677i	$0.610192\pi$
$678$	−5.94975	−	10.3053i	−0.228499	−	0.395771i
$679$		0			0
$680$	8.44975	−	14.6354i	0.324033	−	0.561242i
$681$	8.34315			0.319710
$682$	−0.313708	+	0.543359i	−0.0120125	+	0.0208063i
$683$	−2.65685	+	4.60181i	−0.101662	+	0.176083i	−0.912369	−	0.409368i	$-0.865749\pi$
$683$	−2.65685	+	4.60181i	−0.101662	+	0.176083i	0.810708	+	0.585451i	$0.199083\pi$
$684$	10.9706			0.419470
$685$	−0.156854	+	0.271680i	−0.00599309	+	0.0103803i
$686$		0			0
$687$	8.82843	+	15.2913i	0.336826	+	0.583399i
$688$	10.2426			0.390497
$689$	10.5000	−	2.59808i	0.400018	−	0.0989788i
$690$	1.51472			0.0576644
$691$	−14.9706	−	25.9298i	−0.569507	−	0.986415i	−0.996615	−	0.0822143i	$-0.973801\pi$
$691$	−14.9706	−	25.9298i	−0.569507	−	0.986415i	0.427108	−	0.904201i	$-0.359533\pi$
$692$	−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
$696$	4.67767	−	8.10196i	0.177307	−	0.307104i
$697$	−1.00000			−0.0378777
$698$	−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	$0.415716\pi$
$702$	−5.85786	−	6.08767i	−0.221091	−	0.229764i
$703$	−56.9117			−2.14646
$704$	1.22183	+	2.11626i	0.0460493	+	0.0797597i
$705$	−4.72792	−	8.18900i	−0.178064	−	0.308416i
$706$	−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	−0.982709	−	0.185155i	$-0.940721\pi$
$709$	−8.81371	+	15.2658i	−0.331006	+	0.573319i	0.651704	+	0.758474i	$0.274055\pi$
$710$	8.82843			0.331325
$711$	0.878680	−	1.52192i	0.0329531	−	0.0570764i
$712$	12.1421	+	21.0308i	0.455046	+	0.788162i
$713$	1.82843	+	3.16693i	0.0684751	+	0.118602i
$714$		0			0
$715$	−2.67767	−	2.78272i	−0.100139	−	0.104068i
$716$	10.3431			0.386542
$717$	−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	−0.869591	−	0.493774i	$-0.835617\pi$
$719$	−0.192388	+	0.333226i	−0.00717487	+	0.0124272i	0.862416	+	0.506201i	$0.168951\pi$
$720$	5.48528			0.204424
$721$		0			0
$722$	−3.52082	+	6.09823i	−0.131031	+	0.226953i
$723$	21.8995			0.814451
$724$	8.35786	−	14.4762i	0.310618	−	0.538005i
$725$	3.45584	+	5.98570i	0.128347	+	0.222303i
$726$	3.12132	+	5.40629i	0.115843	+	0.200646i
$727$	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
$730$	−4.03553	−	6.98975i	−0.149362	−	0.258702i
$731$	9.94975	+	17.2335i	0.368005	+	0.637403i
$732$	5.39340	−	9.34164i	0.199346	−	0.345277i
$733$	−21.0000			−0.775653			−0.387826	−	0.921732i	$-0.626774\pi$
$733$	−21.0000			−0.775653			−0.387826	+	0.921732i	$0.626774\pi$
$734$	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	0.990038	−	0.140798i	$-0.0449668\pi$
$739$	10.1421	+	17.5667i	0.373084	+	0.646201i	−0.616954	+	0.786999i	$0.711633\pi$
$740$	−31.7107			−1.16571
$741$	−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	$-0.363461\pi$
$744$	2.89949	+	5.02207i	0.106301	+	0.184118i
$745$	2.74264	−	4.75039i	0.100483	−	0.174041i
$746$	10.9584			0.401214
$747$	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
$751$	8.77817	+	15.2042i	0.320320	+	0.554811i	0.980554	−	0.196249i	$-0.0628762\pi$
$751$	8.77817	+	15.2042i	0.320320	+	0.554811i	−0.660234	+	0.751060i	$0.729543\pi$
$752$	5.48528	+	9.50079i	0.200028	+	0.346458i
$753$	32.4853			1.18383
$754$	1.72792	−	5.98570i	0.0629272	−	0.217986i
$755$	−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
$759$	−1.17157			−0.0425254
$760$	−8.69848	+	15.0662i	−0.315527	+	0.546509i
$761$	−8.92893	+	15.4654i	−0.323674	+	0.560619i	−0.981243	−	0.192775i	$-0.938251\pi$
$761$	−8.92893	+	15.4654i	−0.323674	+	0.560619i	0.657569	+	0.753394i	$0.271585\pi$
$762$	7.79899			0.282528
$763$		0			0
$764$	14.8492	+	25.7196i	0.537227	+	0.930504i
$765$	5.32843	+	9.22911i	0.192650	+	0.333679i
$766$	−14.1005			−0.509472
$767$	−10.2426	+	35.4815i	−0.369840	+	1.28116i
$768$	5.61522			0.202622
$769$	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
$772$	−13.0589			−0.469999
$773$	−3.17157	+	5.49333i	−0.114074	+	0.197581i	−0.917409	−	0.397946i	$-0.869723\pi$
$773$	−3.17157	+	5.49333i	−0.114074	+	0.197581i	0.803335	+	0.595527i	$0.203057\pi$
$774$	0.707107	−	1.22474i	0.0254164	−	0.0440225i
$775$	−4.28427			−0.153896
$776$	−8.58579	+	14.8710i	−0.308212	+	0.533838i
$777$		0			0
$778$	−5.62132	−	9.73641i	−0.201534	−	0.349067i
$779$	1.02944			0.0368834
$780$	−16.5477	+	4.09450i	−0.592504	+	0.146607i
$781$	−6.82843			−0.244340
$782$	−1.70711	−	2.95680i	−0.0610460	−	0.105735i
$783$	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
$787$	6.94975	−	12.0373i	0.247732	−	0.429084i	−0.715164	−	0.698956i	$-0.753648\pi$
$787$	6.94975	−	12.0373i	0.247732	−	0.429084i	0.962896	+	0.269872i	$0.0869815\pi$
$788$	−27.1127			−0.965850
$789$	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
$793$	4.17157	−	14.4508i	0.148137	−	0.513161i
$794$	2.74517			0.0974223
$795$	−3.87868	−	6.71807i	−0.137563	−	0.238265i
$796$	−13.6863	−	23.7054i	−0.485098	−	0.840214i
$797$	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
$801$	−15.3137			−0.541083
$802$	−1.82233	+	3.15637i	−0.0643487	+	0.111455i
$803$	3.12132	+	5.40629i	0.110149	+	0.190784i
$804$	5.48528	+	9.50079i	0.193451	+	0.335067i
$805$		0			0
$806$	2.67767	+	2.78272i	0.0943169	+	0.0980170i
$807$	−25.4558			−0.896088
$808$	11.6213	+	20.1287i	0.408837	+	0.708126i
$809$	−17.5711	−	30.4340i	−0.617766	−	1.07000i	−0.989892	−	0.141820i	$-0.954705\pi$
$809$	−17.5711	−	30.4340i	−0.617766	−	1.07000i	0.372127	−	0.928182i	$-0.378629\pi$
$810$	−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
$814$	−2.30152			−0.0806681
$815$	11.5061	−	19.9291i	0.403041	−	0.698087i
$816$	12.3640	+	21.4150i	0.432825	+	0.749675i
$817$	−10.2426	−	17.7408i	−0.358345	−	0.620671i
$818$	−9.10051			−0.318192
$819$		0			0
$820$	0.573593			0.0200307
$821$	19.9706	+	34.5900i	0.696977	+	1.20720i	0.969510	+	0.245054i	$0.0788056\pi$
$821$	19.9706	+	34.5900i	0.696977	+	1.20720i	−0.272532	+	0.962147i	$0.587861\pi$
$822$	0.0502525	+	0.0870399i	0.00175276	+	0.00303587i
$823$	−9.65685	+	16.7262i	−0.336617	+	0.583037i	−0.983794	−	0.179302i	$-0.942616\pi$
$823$	−9.65685	+	16.7262i	−0.336617	+	0.583037i	0.647177	+	0.762340i	$0.275949\pi$
$824$	−22.2010			−0.773409
$825$	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	−0.916782	−	0.399387i	$-0.869223\pi$
$829$	−23.1569	−	40.1088i	−0.804271	−	1.39304i	0.112511	−	0.993650i	$-0.464111\pi$
$830$	0.405592	+	0.702505i	0.0140783	+	0.0243843i
$831$	2.78680			0.0966729
$832$	14.6005	−	3.61269i	0.506181	−	0.125247i
$833$		0			0
$834$	3.48528	+	6.03668i	0.120685	+	0.209033i
$835$	6.15076	+	10.6534i	0.212856	+	0.368677i
$836$	3.21320	−	5.56543i	0.111131	−	0.192484i
$837$	−14.6274			−0.505597
$838$	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
$842$	−4.44975	−	7.70719i	−0.153348	−	0.265607i
$843$	12.3640	+	21.4150i	0.425837	+	0.737572i
$844$	−45.2132			−1.55630
$845$	−21.0269	+	11.0843i	−0.723348	+	0.381310i
$846$	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
$850$	4.00000			0.137199
$851$	−6.70711	+	11.6170i	−0.229917	+	0.398227i
$852$	−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
$856$	13.7279	+	23.7775i	0.469211	+	0.812697i
$857$	1.20101			0.0410257			0.0205129	−	0.999790i	$-0.493470\pi$
$857$	1.20101			0.0410257			0.0205129	+	0.999790i	$0.493470\pi$
$858$	−1.20101	+	0.297173i	−0.0410018	+	0.0101453i
$859$	−12.9289			−0.441129			−0.220565	−	0.975372i	$-0.570790\pi$
$859$	−12.9289			−0.441129			−0.220565	+	0.975372i	$0.570790\pi$
$860$	−5.70711	−	9.88500i	−0.194611	−	0.337076i
$861$		0			0
$862$	−2.48528	+	4.30463i	−0.0846490	+	0.146616i
$863$	−20.1838			−0.687063			−0.343532	−	0.939141i	$-0.611623\pi$
$863$	−20.1838			−0.687063			−0.343532	+	0.939141i	$0.611623\pi$
$864$	12.4853	−	21.6251i	0.424758	−	0.735702i
$865$	−9.27208	+	16.0597i	−0.315260	+	0.546047i
$866$	7.24264			0.246115
$867$	−12.0000	+	20.7846i	−0.407541	+	0.705882i
$868$		0			0
$869$	−0.514719	−	0.891519i	−0.0174606	−	0.0302427i
$870$	−4.46804			−0.151481
$871$	10.6066	+	11.0227i	0.359391	+	0.373490i
$872$	21.6569			0.733394
$873$	−5.41421	−	9.37769i	−0.183243	−	0.317387i
$874$	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	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$	0.263456	−	0.456319i	0.00889121	−	0.0154000i
$879$	40.2426			1.35735
$880$	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	$0.108014\pi$
$884$	26.6421	+	27.6873i	0.896072	+	0.931225i
$885$	26.4853			0.890293
$886$	−5.31371	−	9.20361i	−0.178518	−	0.309201i
$887$	17.3137	+	29.9882i	0.581337	+	1.00691i	0.995321	+	0.0966217i	$0.0308037\pi$
$887$	17.3137	+	29.9882i	0.581337	+	1.00691i	−0.413984	+	0.910284i	$0.635863\pi$
$888$	−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
$892$	−3.65685			−0.122441
$893$	10.9706	−	19.0016i	0.367116	−	0.635863i
$894$	−0.878680	−	1.52192i	−0.0293874	−	0.0509005i
$895$	−5.17157	−	8.95743i	−0.172867	−	0.299414i
$896$		0			0
$897$	−2.00000	+	6.92820i	−0.0667781	+	0.231326i
$898$	13.4558			0.449027
$899$	−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
$905$	−16.7157			−0.555650
$906$	−4.38478	+	7.59466i	−0.145674	+	0.252316i
$907$	3.36396	+	5.82655i	0.111698	+	0.193467i	0.916455	−	0.400137i	$-0.131038\pi$
$907$	3.36396	+	5.82655i	0.111698	+	0.193467i	−0.804757	+	0.593605i	$0.797704\pi$
$908$	5.39340	+	9.34164i	0.178986	+	0.310013i
$909$	−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	$0.663474\pi$
$912$	−12.7279	−	22.0454i	−0.421464	−	0.729996i
$913$	−0.313708	−	0.543359i	−0.0103822	−	0.0179826i
$914$	5.17767	−	8.96799i	0.171262	−	0.296635i
$915$	−10.7868			−0.356600
$916$	−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	−0.887328	−	0.461139i	$-0.847441\pi$
$919$	−1.34315	+	2.32640i	−0.0443063	+	0.0767407i	0.843022	+	0.537879i	$0.180774\pi$
$920$	2.05025	+	3.55114i	0.0675948	+	0.117078i
$921$	23.1421	+	40.0834i	0.762559	+	1.32079i
$922$	0.556349			0.0183224
$923$	−11.6569	+	40.3805i	−0.383690	+	1.32914i
$924$		0			0
$925$	−7.85786	−	13.6102i	−0.258365	−	0.447501i
$926$	−1.39340	−	2.41344i	−0.0457899	−	0.0793104i
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$	18.4142			0.604476
$929$	−24.4706	+	42.3843i	−0.802853	+	1.39058i	0.114878	+	0.993380i	$0.463352\pi$
$929$	−24.4706	+	42.3843i	−0.802853	+	1.39058i	−0.917731	+	0.397203i	$0.869981\pi$
$930$	1.38478	−	2.39850i	0.0454086	−	0.0786500i
$931$		0			0
$932$	2.58579	−	4.47871i	0.0847003	−	0.146705i
$933$	9.14214	+	15.8346i	0.299300	+	0.518403i
$934$	−2.36396	−	4.09450i	−0.0773512	−	0.133976i
$935$	6.24264			0.204156
$936$	1.58579	−	5.49333i	0.0518331	−	0.179555i
$937$	−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
$941$	52.9706			1.72679			0.863395	−	0.504528i	$-0.168333\pi$
$941$	52.9706			1.72679			0.863395	+	0.504528i	$0.168333\pi$
$942$	−1.60660	+	2.78272i	−0.0523459	+	0.0906658i
$943$	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
$947$	−10.7071	−	18.5453i	−0.347934	−	0.602640i	0.637948	−	0.770079i	$-0.279783\pi$
$947$	−10.7071	−	18.5453i	−0.347934	−	0.602640i	−0.985882	+	0.167440i	$0.946450\pi$
$948$	−4.54416			−0.147587
$949$	37.2990	−	9.22911i	1.21078	−	0.299589i
$950$	−4.11775			−0.133597
$951$	−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	$0.200900\pi$
$954$	1.24264			0.0402320
$955$	14.8492	−	25.7196i	0.480510	−	0.832268i
$956$	22.2929	−	38.6124i	0.721004	−	1.24882i
$957$	3.45584			0.111712
$958$	0.334524	−	0.579412i	0.0108080	−	0.0187200i
$959$		0			0
$960$	−5.39340	−	9.34164i	−0.174071	−	0.301500i
$961$	−24.3137			−0.784313
$962$	−3.92893	+	13.6102i	−0.126674	+	0.438811i
$963$	−17.3137			−0.557926
$964$	14.1569	+	24.5204i	0.455962	+	0.789749i
$965$	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
$969$	24.7279	−	42.8300i	0.794375	−	1.37590i
$970$	8.20101			0.263319
$971$	−25.8284	+	44.7361i	−0.828874	+	1.43565i	0.0700488	+	0.997544i	$0.477685\pi$
$971$	−25.8284	+	44.7361i	−0.828874	+	1.43565i	−0.898922	+	0.438108i	$0.855649\pi$
$972$	9.05025	+	15.6755i	0.290287	+	0.502792i
$973$		0			0
$974$	−5.37258			−0.172149
$975$	−5.85786	−	6.08767i	−0.187602	−	0.194962i
$976$	12.5147			0.400586
$977$	−15.2990	−	26.4986i	−0.489458	−	0.847766i	0.510468	−	0.859897i	$-0.329472\pi$
$977$	−15.2990	−	26.4986i	−0.489458	−	0.847766i	−0.999926	+	0.0121303i	$0.996139\pi$
$978$	−3.68629	−	6.38484i	−0.117875	−	0.204165i
$979$	−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
$983$	−42.0000			−1.33959			−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000			−1.33959			−0.669796	+	0.742545i	$0.733618\pi$
$984$	0.192388	−	0.333226i	0.00613311	−	0.0106229i
$985$	13.5563	+	23.4803i	0.431941	+	0.748144i
$986$	5.03553	+	8.72180i	0.160364	+	0.277759i
$987$		0			0
$988$	−27.4264	−	28.5024i	−0.872550	−	0.906781i
$989$	−4.82843			−0.153535
$990$	−0.221825	−	0.384213i	−0.00705007	−	0.0122111i
$991$	−9.87868	−	17.1104i	−0.313807	−	0.543529i	0.665376	−	0.746508i	$-0.268271\pi$
$991$	−9.87868	−	17.1104i	−0.313807	−	0.543529i	−0.979183	+	0.202979i	$0.934938\pi$
$992$	−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
$996$	−2.76955			−0.0877566
$997$	−6.98528	+	12.0989i	−0.221226	+	0.383175i	−0.955181	−	0.296024i	$-0.904339\pi$
$997$	−6.98528	+	12.0989i	−0.221226	+	0.383175i	0.733954	+	0.679199i	$0.237673\pi$
$998$	−4.15076	−	7.18932i	−0.131390	−	0.227574i
$999$	−26.8284	−	46.4682i	−0.848814	−	1.47019i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.e.295.1	✓	4	91.48	odd	6
637.2.f.e.393.1	yes	4	7.6	odd	2
637.2.f.f.295.1	yes	4	13.9	even	3	inner
637.2.f.f.393.1	yes	4	1.1	even	1	trivial
637.2.g.f.263.1		4	7.2	even	3
637.2.g.f.373.1		4	91.74	even	3
637.2.g.g.263.1		4	7.5	odd	6
637.2.g.g.373.1		4	91.87	odd	6
637.2.h.b.165.2		4	91.9	even	3
637.2.h.b.471.2		4	7.4	even	3
637.2.h.c.165.2		4	91.61	odd	6
637.2.h.c.471.2		4	7.3	odd	6
8281.2.a.o.1.2		2	91.55	odd	6
8281.2.a.p.1.2		2	13.3	even	3
8281.2.a.x.1.1		2	13.10	even	6
8281.2.a.y.1.1		2	91.62	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.82843 q^{5} +(-0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.82843 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} -2.58579 q^{12} +(-3.50000 + 0.866025i) q^{13} +(1.29289 + 2.23936i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.91421 - 5.04757i) q^{17} -0.414214 q^{18} +(-3.00000 + 5.19615i) q^{19} +(-1.67157 + 2.89525i) q^{20} +(-0.121320 + 0.210133i) q^{22} +(0.707107 + 1.22474i) q^{23} +(1.12132 + 1.94218i) q^{24} -1.65685 q^{25} +(1.03553 + 1.07616i) q^{26} -5.65685 q^{27} +(-2.08579 - 3.61269i) q^{29} +(0.535534 - 0.927572i) q^{30} +2.58579 q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.414214 + 0.717439i) q^{33} -2.41421 q^{34} +(-0.914214 - 1.58346i) q^{36} +(4.74264 + 8.21449i) q^{37} +2.48528 q^{38} +(3.53553 + 3.67423i) q^{39} +2.89949 q^{40} +(-0.0857864 - 0.148586i) q^{41} +(-1.70711 + 2.95680i) q^{43} -1.07107 q^{44} +(-0.914214 + 1.58346i) q^{45} +(0.292893 - 0.507306i) q^{46} -3.65685 q^{47} +(-2.12132 + 3.67423i) q^{48} +(0.343146 + 0.594346i) q^{50} -8.24264 q^{51} +(-1.82843 + 6.33386i) q^{52} -3.00000 q^{53} +(1.17157 + 2.02922i) q^{54} +(0.535534 + 0.927572i) q^{55} +8.48528 q^{57} +(-0.863961 + 1.49642i) q^{58} +(5.12132 - 8.87039i) q^{59} +4.72792 q^{60} +(-2.08579 + 3.61269i) q^{61} +(-0.535534 - 0.927572i) q^{62} -4.17157 q^{64} +(6.39949 - 1.58346i) q^{65} +0.343146 q^{66} +(-2.12132 - 3.67423i) q^{67} +(-5.32843 - 9.22911i) q^{68} +(1.00000 - 1.73205i) q^{69} +(5.82843 - 10.0951i) q^{71} +(-0.792893 + 1.37333i) q^{72} -10.6569 q^{73} +(1.96447 - 3.40256i) q^{74} +(1.17157 + 2.02922i) q^{75} +(5.48528 + 9.50079i) q^{76} +(0.585786 - 2.02922i) q^{78} +1.75736 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} +1.41421 q^{86} +(-2.94975 + 5.10911i) q^{87} +(0.464466 + 0.804479i) q^{88} +(-7.65685 - 13.2621i) q^{89} +0.757359 q^{90} +2.58579 q^{92} +(-1.82843 - 3.16693i) q^{93} +(0.757359 + 1.31178i) q^{94} +(5.48528 - 9.50079i) q^{95} +6.24264 q^{96} +(5.41421 - 9.37769i) q^{97} -0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{8} + 2 q^{9} + 10 q^{10} - 4 q^{11} - 16 q^{12} - 14 q^{13} + 8 q^{15} - 6 q^{16} + 6 q^{17} + 4 q^{18} - 12 q^{19} - 18 q^{20} + 8 q^{22} - 4 q^{24} + 16 q^{25} - 10 q^{26} - 14 q^{29} - 12 q^{30} + 16 q^{31} - 6 q^{32} + 4 q^{33} - 4 q^{34} + 2 q^{36} + 2 q^{37} - 24 q^{38} - 28 q^{40} - 6 q^{41} - 4 q^{43} + 24 q^{44} + 2 q^{45} + 4 q^{46} + 8 q^{47} + 24 q^{50} - 16 q^{51} + 4 q^{52} - 12 q^{53} + 16 q^{54} - 12 q^{55} + 22 q^{58} + 12 q^{59} - 32 q^{60} - 14 q^{61} + 12 q^{62} - 28 q^{64} - 14 q^{65} + 24 q^{66} - 10 q^{68} + 4 q^{69} + 12 q^{71} - 6 q^{72} - 20 q^{73} + 22 q^{74} + 16 q^{75} - 12 q^{76} + 8 q^{78} + 24 q^{79} - 6 q^{80} + 10 q^{81} + 14 q^{82} - 24 q^{83} - 10 q^{85} + 8 q^{87} + 16 q^{88} - 8 q^{89} + 20 q^{90} + 16 q^{92} + 4 q^{93} + 20 q^{94} - 12 q^{95} + 8 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 12 * q^8 + 2 * q^9 + 10 * q^10 - 4 * q^11 - 16 * q^12 - 14 * q^13 + 8 * q^15 - 6 * q^16 + 6 * q^17 + 4 * q^18 - 12 * q^19 - 18 * q^20 + 8 * q^22 - 4 * q^24 + 16 * q^25 - 10 * q^26 - 14 * q^29 - 12 * q^30 + 16 * q^31 - 6 * q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 + 2 * q^37 - 24 * q^38 - 28 * q^40 - 6 * q^41 - 4 * q^43 + 24 * q^44 + 2 * q^45 + 4 * q^46 + 8 * q^47 + 24 * q^50 - 16 * q^51 + 4 * q^52 - 12 * q^53 + 16 * q^54 - 12 * q^55 + 22 * q^58 + 12 * q^59 - 32 * q^60 - 14 * q^61 + 12 * q^62 - 28 * q^64 - 14 * q^65 + 24 * q^66 - 10 * q^68 + 4 * q^69 + 12 * q^71 - 6 * q^72 - 20 * q^73 + 22 * q^74 + 16 * q^75 - 12 * q^76 + 8 * q^78 + 24 * q^79 - 6 * q^80 + 10 * q^81 + 14 * q^82 - 24 * q^83 - 10 * q^85 + 8 * q^87 + 16 * q^88 - 8 * q^89 + 20 * q^90 + 16 * q^92 + 4 * q^93 + 20 * q^94 - 12 * q^95 + 8 * q^96 + 16 * q^97 - 8 * q^99

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