LMFDB - Embedded newform 637.2.f.e.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.e.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	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	1.82843			0.817697			0.408849	−	0.912602i	$-0.365930\pi$
$5$	1.82843			0.817697			0.408849	+	0.912602i	$0.365930\pi$
$6$	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	$0.416529\pi$
$17$	−2.91421	+	5.04757i	−0.706801	+	1.22421i	−0.966038	+	0.258401i	$0.916804\pi$
$18$	−0.414214			−0.0976311
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	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	$-0.574596\pi$
$31$	−2.58579			−0.464421			−0.232210	+	0.972666i	$0.574596\pi$
$32$	−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	0.872646	−	0.488352i	$-0.162402\pi$
$41$	0.0857864	+	0.148586i	0.0133976	+	0.0232053i	−0.859249	+	0.511558i	$0.829069\pi$
$42$		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	$-0.414066\pi$
$47$	3.65685			0.533407			0.266704	+	0.963779i	$0.414066\pi$
$48$	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	$0.398977\pi$
$59$	−5.12132	+	8.87039i	−0.666739	+	1.15483i	−0.978811	+	0.204767i	$0.934356\pi$
$60$	4.72792			0.610372
$61$	2.08579	−	3.61269i	0.267058	−	0.462557i	−0.701043	−	0.713119i	$-0.747282\pi$
$61$	2.08579	−	3.61269i	0.267058	−	0.462557i	0.968101	+	0.250562i	$0.0806153\pi$
$62$	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	$-0.285651\pi$
$73$	10.6569			1.24729			0.623645	+	0.781708i	$0.285651\pi$
$74$	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	$-0.518722\pi$
$83$	−1.07107			−0.117565			−0.0587825	+	0.998271i	$0.518722\pi$
$84$		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	$0.134750\pi$
$89$	7.65685	+	13.2621i	0.811625	+	1.40578i	−0.100101	+	0.994977i	$0.531917\pi$
$90$	−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	$0.351936\pi$
$97$	−5.41421	+	9.37769i	−0.549730	+	0.952160i	−0.998293	+	0.0584091i	$0.981397\pi$
$98$		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	$0.0934436\pi$
$101$	7.32843	+	12.6932i	0.729206	+	1.26302i	−0.228014	+	0.973658i	$0.573223\pi$
$102$	1.70711	+	2.95680i	0.169029	+	0.292766i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−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	$-0.881144\pi$
$131$	−21.3137			−1.86219			−0.931094	+	0.364780i	$0.881144\pi$
$132$	−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	$0.335045\pi$
$139$	−5.94975	+	10.3053i	−0.504651	+	0.874081i	−0.999986	+	0.00537886i	$0.998288\pi$
$140$		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	$-0.570242\pi$
$157$	−5.48528			−0.437773			−0.218887	+	0.975750i	$0.570242\pi$
$158$	−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	0.966325	−	0.257326i	$-0.0828415\pi$
$167$	3.36396	+	5.82655i	0.260311	+	0.450872i	−0.706013	+	0.708198i	$0.749508\pi$
$168$		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	−0.991845	−	0.127452i	$-0.959320\pi$
$173$	−5.07107	+	8.78335i	−0.385546	+	0.667786i	0.606299	+	0.795237i	$0.292654\pi$
$174$	−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	$-0.610347\pi$
$181$	−9.14214			−0.679530			−0.339765	+	0.940510i	$0.610347\pi$
$182$		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	$0.344707\pi$
$199$	−7.48528	+	12.9649i	−0.530618	+	0.919057i	−0.999362	+	0.0357226i	$0.988627\pi$
$200$	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	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$		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	−0.751375	−	0.659876i	$-0.770609\pi$
$227$	2.94975	−	5.10911i	0.195782	−	0.339104i	0.947156	+	0.320772i	$0.103942\pi$
$228$	7.75736	−	13.4361i	0.513744	−	0.889830i
$229$	12.4853			0.825051			0.412525	−	0.910946i	$-0.364647\pi$
$229$	12.4853			0.825051			0.412525	+	0.910946i	$0.364647\pi$
$230$	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	−0.501252	−	0.865302i	$-0.667127\pi$
$241$	7.74264	−	13.4106i	0.498747	−	0.863856i	0.999999	+	0.00144585i	$0.000460230\pi$
$242$	−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	$-0.575199\pi$
$251$	11.4853	−	19.8931i	0.724945	−	1.25564i	0.958997	−	0.283417i	$-0.0914680\pi$
$252$		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	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	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	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−2.14214	−	3.71029i	−0.130366	−	0.225801i
$271$	−10.5355	−	18.2481i	−0.639988	−	1.10849i	−0.985435	−	0.170054i	$-0.945606\pi$
$271$	−10.5355	−	18.2481i	−0.639988	−	1.10849i	0.345447	−	0.938438i	$-0.387727\pi$
$272$	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	$-0.965222\pi$
$283$	−9.94975	−	17.2335i	−0.591451	−	1.02442i	0.402586	−	0.915382i	$-0.368111\pi$
$284$	−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	$-0.520985\pi$
$293$	14.2279	−	24.6435i	0.831204	−	1.43969i	0.897084	−	0.441860i	$-0.145681\pi$
$294$		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	$-0.116346\pi$
$307$	32.7279			1.86788			0.933941	+	0.357428i	$0.116346\pi$
$308$		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	$-0.380533\pi$
$311$	12.9289			0.733132			0.366566	+	0.930392i	$0.380533\pi$
$312$	−5.60660	−	5.82655i	−0.317411	−	0.329864i
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	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	0.963325	−	0.268337i	$-0.0864741\pi$
$349$	4.65685	+	8.06591i	0.249276	+	0.431758i	−0.714049	+	0.700095i	$0.753141\pi$
$350$		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	0.933098	−	0.359621i	$-0.117094\pi$
$353$	2.91421	+	5.04757i	0.155108	+	0.268655i	−0.777990	+	0.628276i	$0.783761\pi$
$354$	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	$-0.896820\pi$
$367$	−14.3640	−	24.8791i	−0.749793	−	1.29868i	0.198129	−	0.980176i	$-0.436513\pi$
$368$	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	$0.502369\pi$
$383$	−17.0208	+	29.4809i	−0.869723	+	1.50640i	−0.862280	+	0.506432i	$0.830964\pi$
$384$	−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	−0.770810	−	0.637066i	$-0.780148\pi$
$397$	3.31371	−	5.73951i	0.166310	−	0.288058i	0.937120	+	0.349008i	$0.113481\pi$
$398$	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	$0.349449\pi$
$409$	−10.9853	+	19.0271i	−0.543187	+	0.940828i	−0.998719	+	0.0506081i	$0.983884\pi$
$410$	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	0.689664	−	0.724129i	$-0.257758\pi$
$419$	−5.77817	−	10.0081i	−0.282282	−	0.488927i	−0.971946	+	0.235202i	$0.924425\pi$
$420$		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	−0.575809	−	0.817584i	$-0.695313\pi$
$433$	8.74264	−	15.1427i	0.420144	−	0.727712i	0.995953	+	0.0898728i	$0.0286461\pi$
$434$		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	0.850448	−	0.526059i	$-0.176331\pi$
$439$	−0.636039	−	1.10165i	−0.0303565	−	0.0525790i	−0.880805	+	0.473480i	$0.842998\pi$
$440$	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	−0.849963	−	0.526843i	$-0.823376\pi$
$461$	0.671573	−	1.16320i	0.0312783	−	0.0541755i	0.881241	+	0.472668i	$0.156709\pi$
$462$		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	$-0.585073\pi$
$467$	−11.4142			−0.528187			−0.264093	+	0.964497i	$0.585073\pi$
$468$	−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	0.846985	−	0.531616i	$-0.178415\pi$
$479$	−0.807612	−	1.39882i	−0.0369007	−	0.0639139i	−0.883886	+	0.467703i	$0.845082\pi$
$480$	−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	−0.891979	−	0.452078i	$-0.850683\pi$
$503$	−1.22183	+	2.11626i	−0.0544785	+	0.0943595i	0.837500	+	0.546437i	$0.184016\pi$
$504$		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	0.913004	−	0.407951i	$-0.133757\pi$
$509$	2.32843	+	4.03295i	0.103206	+	0.178758i	−0.809798	+	0.586709i	$0.800423\pi$
$510$	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	$-0.318380\pi$
$521$	24.6569			1.08024			0.540118	+	0.841589i	$0.318380\pi$
$522$	0.863961	+	1.49642i	0.0378145	+	0.0654967i
$523$	−8.48528	−	14.6969i	−0.371035	−	0.642652i	0.618690	−	0.785635i	$-0.287664\pi$
$523$	−8.48528	−	14.6969i	−0.371035	−	0.642652i	−0.989725	+	0.142983i	$0.954331\pi$
$524$	−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	−0.864965	−	0.501833i	$-0.832659\pi$
$563$	0.0502525	−	0.0870399i	0.00211789	−	0.00366830i	0.867082	+	0.498165i	$0.165993\pi$
$564$	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	$-0.408045\pi$
$577$	13.6863			0.569768			0.284884	+	0.958562i	$0.408045\pi$
$578$	−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	$-0.957018\pi$
$587$	−14.8284	−	25.6836i	−0.612035	−	1.06008i	0.378862	−	0.925453i	$-0.376315\pi$
$588$		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	$-0.673752\pi$
$593$	−25.2843			−1.03830			−0.519150	+	0.854683i	$0.673752\pi$
$594$	−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	$0.0507121\pi$
$601$	15.4706	+	26.7958i	0.631057	+	1.09302i	−0.356278	+	0.934380i	$0.615955\pi$
$602$		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	$0.394581\pi$
$607$	−16.1716	+	28.0100i	−0.656384	+	1.13689i	−0.981545	+	0.191232i	$0.938752\pi$
$608$	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	$-0.814617\pi$
$619$	−41.5563			−1.67029			−0.835145	+	0.550029i	$0.814617\pi$
$620$	−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	−0.678947	−	0.734187i	$-0.737563\pi$
$643$	7.51472	−	13.0159i	0.296352	−	0.513296i	0.975298	+	0.220891i	$0.0708967\pi$
$644$		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	$-0.277207\pi$
$647$	−8.65685	−	14.9941i	−0.340336	−	0.589479i	−0.984495	+	0.175412i	$0.943874\pi$
$648$	−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	$-0.943716\pi$
$661$	−16.5711	−	28.7019i	−0.644540	−	1.11638i	0.339868	−	0.940473i	$-0.389618\pi$
$662$	−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	$-0.389808\pi$
$677$	17.6569			0.678608			0.339304	+	0.940677i	$0.389808\pi$
$678$	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	$0.0261992\pi$
$691$	14.9706	+	25.9298i	0.569507	+	0.986415i	−0.427108	+	0.904201i	$0.640467\pi$
$692$	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	−0.862416	−	0.506201i	$-0.831049\pi$
$719$	0.192388	−	0.333226i	0.00717487	−	0.0124272i	0.869591	+	0.493774i	$0.164383\pi$
$720$	−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	$-0.653246\pi$
$727$	−24.9706			−0.926107			−0.463053	+	0.886330i	$0.653246\pi$
$728$		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	$-0.373226\pi$
$733$	21.0000			0.775653			0.387826	+	0.921732i	$0.373226\pi$
$734$	−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	−0.657569	−	0.753394i	$-0.728415\pi$
$761$	8.92893	−	15.4654i	0.323674	−	0.560619i	0.981243	+	0.192775i	$0.0617487\pi$
$762$	−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	$-0.816172\pi$
$769$	−24.7279	−	42.8300i	−0.891712	−	1.54449i	−0.0538894	−	0.998547i	$-0.517162\pi$
$770$		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	−0.803335	−	0.595527i	$-0.796943\pi$
$773$	3.17157	−	5.49333i	0.114074	−	0.197581i	0.917409	+	0.397946i	$0.130277\pi$
$774$	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	−0.962896	−	0.269872i	$-0.913018\pi$
$787$	−6.94975	+	12.0373i	−0.247732	+	0.429084i	0.715164	+	0.698956i	$0.246352\pi$
$788$	−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	−0.980759	−	0.195221i	$-0.937458\pi$
$797$	−9.07107	+	15.7116i	−0.321314	+	0.556532i	0.659446	+	0.751752i	$0.270791\pi$
$798$		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	$-0.234524\pi$
$811$	42.1838			1.48127			0.740636	+	0.671906i	$0.234524\pi$
$812$		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	$0.130777\pi$
$829$	23.1569	+	40.1088i	0.804271	+	1.39304i	−0.112511	+	0.993650i	$0.535889\pi$
$830$	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	$0.421637\pi$
$839$	−20.7990	+	36.0249i	−0.718061	+	1.24372i	−0.961767	+	0.273869i	$0.911697\pi$
$840$		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	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$		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	$-0.506530\pi$
$857$	−1.20101			−0.0410257			−0.0205129	+	0.999790i	$0.506530\pi$
$858$	−1.20101	+	0.297173i	−0.0410018	+	0.0101453i
$859$	12.9289			0.441129			0.220565	−	0.975372i	$-0.429210\pi$
$859$	12.9289			0.441129			0.220565	+	0.975372i	$0.429210\pi$
$860$	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	0.901113	−	0.433585i	$-0.142752\pi$
$881$	2.22792	+	3.85887i	0.0750606	+	0.130009i	−0.826052	+	0.563594i	$0.809418\pi$
$882$		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	$-0.969196\pi$
$887$	−17.3137	−	29.9882i	−0.581337	−	1.00691i	0.413984	−	0.910284i	$-0.364137\pi$
$888$	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	$-0.536648\pi$
$929$	24.4706	−	42.3843i	0.802853	−	1.39058i	0.917731	−	0.397203i	$-0.130019\pi$
$930$	−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	$-0.292497\pi$
$937$	37.1421			1.21338			0.606690	+	0.794938i	$0.292497\pi$
$938$		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	$-0.831667\pi$
$941$	−52.9706			−1.72679			−0.863395	+	0.504528i	$0.831667\pi$
$942$	−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	$-0.522315\pi$
$971$	25.8284	−	44.7361i	0.828874	−	1.43565i	0.898922	−	0.438108i	$-0.144351\pi$
$972$	−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	$-0.266382\pi$
$983$	42.0000			1.33959			0.669796	+	0.742545i	$0.266382\pi$
$984$	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	−0.733954	−	0.679199i	$-0.762327\pi$
$997$	6.98528	−	12.0989i	0.221226	−	0.383175i	0.955181	+	0.296024i	$0.0956608\pi$
$998$	−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.e.393.1	yes	4
7.2	even	3		637.2.g.g.263.1		4
7.3	odd	6		637.2.h.b.471.2		4
7.4	even	3		637.2.h.c.471.2		4
7.5	odd	6		637.2.g.f.263.1		4
7.6	odd	2		637.2.f.f.393.1	yes	4
13.3	even	3		8281.2.a.o.1.2		2
13.9	even	3	inner	637.2.f.e.295.1	✓	4
13.10	even	6		8281.2.a.y.1.1		2
91.9	even	3		637.2.h.c.165.2		4
91.48	odd	6		637.2.f.f.295.1	yes	4
91.55	odd	6		8281.2.a.p.1.2		2
91.61	odd	6		637.2.h.b.165.2		4
91.62	odd	6		8281.2.a.x.1.1		2
91.74	even	3		637.2.g.g.373.1		4
91.87	odd	6		637.2.g.f.373.1		4

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