LMFDB - Embedded newform 637.2.f.j.393.4

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.4
Root			$0.756174 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.j.295.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425563 + 0.737096i) q^{2} +(0.330612 + 0.572636i) q^{3} +(0.637793 - 1.10469i) q^{4} -3.44148 q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +O(q^{10})$	\(q+(0.425563 + 0.737096i) q^{2} +(0.330612 + 0.572636i) q^{3} +(0.637793 - 1.10469i) q^{4} -3.44148 q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(-1.46456 - 2.53670i) q^{10} +(0.448993 + 0.777679i) q^{11} +0.843447 q^{12} +(3.07517 - 1.88237i) q^{13} +(-1.13779 - 1.97071i) q^{15} +(-0.0891447 - 0.154403i) q^{16} +(0.968404 - 1.67733i) q^{17} +2.18125 q^{18} +(0.519020 - 0.898968i) q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} +(0.921723 + 1.59647i) q^{24} +6.84378 q^{25} +(2.69617 + 1.46563i) q^{26} +3.67824 q^{27} +(0.917969 + 1.58997i) q^{29} +(0.968404 - 1.67733i) q^{30} +9.13385 q^{31} +(2.86381 - 4.96026i) q^{32} +(-0.296885 + 0.514219i) q^{33} +1.64847 q^{34} +(-1.63452 - 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} +0.883501 q^{38} +(2.09460 + 1.13862i) q^{39} -9.59462 q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +1.14546 q^{44} +(-4.40988 + 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} -7.19129 q^{47} +(0.0589445 - 0.102095i) q^{48} +(2.91246 + 5.04452i) q^{50} +1.28066 q^{51} +(-0.118109 - 4.59767i) q^{52} -9.38648 q^{53} +(1.56532 + 2.71122i) q^{54} +(-1.54520 - 2.67637i) q^{55} +0.686375 q^{57} +(-0.781307 + 1.35326i) q^{58} +(-0.255259 + 0.442121i) q^{59} -2.90270 q^{60} +(0.718095 - 1.24378i) q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(-10.5831 + 6.47813i) q^{65} -0.505372 q^{66} +(4.22466 + 7.31732i) q^{67} +(-1.23528 - 2.13957i) q^{68} +(1.86800 - 3.23547i) q^{69} +(1.72419 - 2.98638i) q^{71} +(3.57244 - 6.18764i) q^{72} -10.9005 q^{73} +(-4.51097 + 7.81324i) q^{74} +(2.26263 + 3.91899i) q^{75} +(-0.662054 - 1.14671i) q^{76} +(0.0521095 + 2.02848i) q^{78} -12.0918 q^{79} +(0.306789 + 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(2.26886 - 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +3.33185 q^{86} +(-0.606982 + 1.05132i) q^{87} +(1.25176 + 2.16812i) q^{88} +(6.80391 + 11.7847i) q^{89} -7.50673 q^{90} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} +(-3.06035 - 5.30067i) q^{94} +(-1.78619 + 3.09378i) q^{95} +3.78723 q^{96} +(0.253120 - 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23} + 11 q^{24} - 14 q^{25} - 11 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} + 32 q^{31} + 8 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} - 34 q^{38} + 43 q^{39} - 10 q^{40} + 8 q^{41} - 11 q^{43} - 42 q^{44} + 7 q^{45} + 16 q^{46} - 2 q^{47} - 21 q^{48} + 6 q^{50} + 40 q^{51} + 16 q^{52} + 4 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} - 13 q^{59} - 40 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 14 q^{65} + 36 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 60 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} - 14 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} + 14 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} - 45 q^{94} - 6 q^{95} + 38 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * 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 $

$2$	0.425563	+	0.737096i	0.300918	+	0.521206i	0.976344	−	0.216222i	$-0.0693735\pi$
$2$	0.425563	+	0.737096i	0.300918	+	0.521206i	−0.675426	+	0.737428i	$0.736040\pi$
$3$	0.330612	+	0.572636i	0.190879	+	0.330612i	0.945542	−	0.325501i	$-0.105533\pi$
$3$	0.330612	+	0.572636i	0.190879	+	0.330612i	−0.754663	+	0.656113i	$0.772200\pi$
$4$	0.637793	−	1.10469i	0.318896	−	0.552345i
$5$	−3.44148			−1.53908			−0.769538	−	0.638601i	$-0.779513\pi$
$5$	−3.44148			−1.53908			−0.769538	+	0.638601i	$0.779513\pi$
$6$	−0.281392	+	0.487385i	−0.114878	+	0.198974i
$7$		0			0
$7$		0			0
$8$	2.78793			0.985684
$9$	1.28139	−	2.21944i	0.427131	−	0.739812i
$10$	−1.46456	−	2.53670i	−0.463136	−	0.802175i
$11$	0.448993	+	0.777679i	0.135377	+	0.234479i	0.925741	−	0.378158i	$-0.123442\pi$
$11$	0.448993	+	0.777679i	0.135377	+	0.234479i	−0.790365	+	0.612637i	$0.790109\pi$
$12$	0.843447			0.243482
$13$	3.07517	−	1.88237i	0.852900	−	0.522075i
$13$	3.07517	−	1.88237i	0.852900	−	0.522075i
$14$		0			0
$15$	−1.13779	−	1.97071i	−0.293777	−	0.508836i
$16$	−0.0891447	−	0.154403i	−0.0222862	−	0.0386008i
$17$	0.968404	−	1.67733i	0.234873	−	0.406811i	−0.724363	−	0.689419i	$-0.757866\pi$
$17$	0.968404	−	1.67733i	0.234873	−	0.406811i	0.959236	+	0.282607i	$0.0911994\pi$
$18$	2.18125			0.514126
$19$	0.519020	−	0.898968i	0.119071	−	0.206237i	−0.800329	−	0.599562i	$-0.795342\pi$
$19$	0.519020	−	0.898968i	0.119071	−	0.206237i	0.919400	+	0.393324i	$0.128675\pi$
$20$	−2.19495	+	3.80177i	−0.490806	+	0.850101i
$21$		0			0
$22$	−0.382150	+	0.661902i	−0.0814745	+	0.141118i
$23$	−2.82506	−	4.89315i	−0.589067	−	1.02029i	−0.994355	−	0.106104i	$-0.966162\pi$
$23$	−2.82506	−	4.89315i	−0.589067	−	1.02029i	0.405288	−	0.914189i	$-0.367171\pi$
$24$	0.921723	+	1.59647i	0.188146	+	0.325878i
$25$	6.84378			1.36876
$26$	2.69617	+	1.46563i	0.528762	+	0.287434i
$27$	3.67824			0.707878
$28$		0			0
$29$	0.917969	+	1.58997i	0.170463	+	0.295250i	0.938582	−	0.345057i	$-0.112140\pi$
$29$	0.917969	+	1.58997i	0.170463	+	0.295250i	−0.768119	+	0.640307i	$0.778807\pi$
$30$	0.968404	−	1.67733i	0.176806	−	0.306236i
$31$	9.13385			1.64049			0.820244	−	0.572014i	$-0.193838\pi$
$31$	9.13385			1.64049			0.820244	+	0.572014i	$0.193838\pi$
$32$	2.86381	−	4.96026i	0.506254	−	0.876858i
$33$	−0.296885	+	0.514219i	−0.0516810	+	0.0895141i
$34$	1.64847			0.282710
$35$		0			0
$36$	−1.63452	−	2.83108i	−0.272421	−	0.471847i
$37$	5.30001	+	9.17989i	0.871316	+	1.50916i	0.860636	+	0.509221i	$0.170067\pi$
$37$	5.30001	+	9.17989i	0.871316	+	1.50916i	0.0106808	+	0.999943i	$0.496600\pi$
$38$	0.883501			0.143323
$39$	2.09460	+	1.13862i	0.335404	+	0.182325i
$40$	−9.59462			−1.51704
$41$	−2.66571	−	4.61715i	−0.416314	−	0.721078i	0.579251	−	0.815149i	$-0.303345\pi$
$41$	−2.66571	−	4.61715i	−0.416314	−	0.721078i	−0.995565	+	0.0940715i	$0.970012\pi$
$42$		0			0
$43$	1.95732	−	3.39018i	0.298489	−	0.516998i	−0.677302	−	0.735706i	$-0.736851\pi$
$43$	1.95732	−	3.39018i	0.298489	−	0.516998i	0.975790	+	0.218708i	$0.0701841\pi$
$44$	1.14546			0.172684
$45$	−4.40988	+	7.63814i	−0.657387	+	1.13863i
$46$	2.40448	−	4.16469i	0.354522	−	0.614050i
$47$	−7.19129			−1.04896			−0.524479	−	0.851423i	$-0.675740\pi$
$47$	−7.19129			−1.04896			−0.524479	+	0.851423i	$0.675740\pi$
$48$	0.0589445	−	0.102095i	0.00850791	−	0.0147361i
$49$		0			0
$50$	2.91246	+	5.04452i	0.411883	+	0.713403i
$51$	1.28066			0.179329
$52$	−0.118109	−	4.59767i	−0.0163788	−	0.637582i
$53$	−9.38648			−1.28933			−0.644666	−	0.764464i	$-0.723004\pi$
$53$	−9.38648			−1.28933			−0.644666	+	0.764464i	$0.723004\pi$
$54$	1.56532	+	2.71122i	0.213013	+	0.368950i
$55$	−1.54520	−	2.67637i	−0.208355	−	0.360881i
$56$		0			0
$57$	0.686375			0.0909127
$58$	−0.781307	+	1.35326i	−0.102591	+	0.177692i
$59$	−0.255259	+	0.442121i	−0.0332318	+	0.0575592i	−0.882163	−	0.470944i	$-0.843913\pi$
$59$	−0.255259	+	0.442121i	−0.0332318	+	0.0575592i	0.848931	+	0.528503i	$0.177247\pi$
$60$	−2.90270			−0.374737
$61$	0.718095	−	1.24378i	0.0919426	−	0.159249i	−0.816386	−	0.577507i	$-0.804026\pi$
$61$	0.718095	−	1.24378i	0.0919426	−	0.159249i	0.908328	+	0.418258i	$0.137359\pi$
$62$	3.88702	+	6.73252i	0.493653	+	0.855031i
$63$		0			0
$64$	4.51834			0.564792
$65$	−10.5831	+	6.47813i	−1.31268	+	0.803513i
$66$	−0.505372			−0.0622070
$67$	4.22466	+	7.31732i	0.516124	+	0.893953i	0.999825	+	0.0187197i	$0.00595900\pi$
$67$	4.22466	+	7.31732i	0.516124	+	0.893953i	−0.483701	+	0.875233i	$0.660708\pi$
$68$	−1.23528	−	2.13957i	−0.149800	−	0.259461i
$69$	1.86800	−	3.23547i	0.224881	−	0.389504i
$70$		0			0
$71$	1.72419	−	2.98638i	0.204623	−	0.354418i	−0.745389	−	0.666629i	$-0.767736\pi$
$71$	1.72419	−	2.98638i	0.204623	−	0.354418i	0.950013	+	0.312211i	$0.101070\pi$
$72$	3.57244	−	6.18764i	0.421016	−	0.729221i
$73$	−10.9005			−1.27581			−0.637905	−	0.770115i	$-0.720199\pi$
$73$	−10.9005			−1.27581			−0.637905	+	0.770115i	$0.720199\pi$
$74$	−4.51097	+	7.81324i	−0.524390	+	0.908270i
$75$	2.26263	+	3.91899i	0.261266	+	0.452526i
$76$	−0.662054	−	1.14671i	−0.0759428	−	0.131537i
$77$		0			0
$78$	0.0521095	+	2.02848i	0.00590024	+	0.229680i
$79$	−12.0918			−1.36043			−0.680216	−	0.733012i	$-0.738114\pi$
$79$	−12.0918			−1.36043			−0.680216	+	0.733012i	$0.738114\pi$
$80$	0.306789	+	0.531375i	0.0343001	+	0.0594095i
$81$	−2.62811	−	4.55201i	−0.292012	−	0.505779i
$82$	2.26886	−	3.92977i	0.250553	−	0.433971i
$83$	−1.51669			−0.166479			−0.0832393	−	0.996530i	$-0.526527\pi$
$83$	−1.51669			−0.166479			−0.0832393	+	0.996530i	$0.526527\pi$
$84$		0			0
$85$	−3.33274	+	5.77248i	−0.361487	+	0.626113i
$86$	3.33185			0.359283
$87$	−0.606982	+	1.05132i	−0.0650754	+	0.112714i
$88$	1.25176	+	2.16812i	0.133438	+	0.231122i
$89$	6.80391	+	11.7847i	0.721213	+	1.24918i	0.960514	+	0.278232i	$0.0897484\pi$
$89$	6.80391	+	11.7847i	0.721213	+	1.24918i	−0.239301	+	0.970945i	$0.576918\pi$
$90$	−7.50673			−0.791279
$91$		0			0
$92$	−7.20722			−0.751405
$93$	3.01976	+	5.23037i	0.313134	+	0.542364i
$94$	−3.06035	−	5.30067i	−0.315651	−	0.546723i
$95$	−1.78619	+	3.09378i	−0.183260	+	0.317415i
$96$	3.78723			0.386533
$97$	0.253120	−	0.438417i	0.0257005	−	0.0445145i	−0.852889	−	0.522092i	$-0.825152\pi$
$97$	0.253120	−	0.438417i	0.0257005	−	0.0445145i	0.878590	+	0.477578i	$0.158485\pi$
$98$		0			0
$99$	2.30134			0.231294
$100$	4.36491	−	7.56025i	0.436491	−	0.756025i
$101$	−2.99327	−	5.18450i	−0.297842	−	0.515877i	0.677800	−	0.735246i	$-0.262933\pi$
$101$	−2.99327	−	5.18450i	−0.297842	−	0.515877i	−0.975642	+	0.219369i	$0.929600\pi$
$102$	0.545002	+	0.943972i	0.0539633	+	0.0934671i
$103$	4.13302			0.407239			0.203619	−	0.979050i	$-0.434730\pi$
$103$	4.13302			0.407239			0.203619	+	0.979050i	$0.434730\pi$
$104$	8.57338	−	5.24792i	0.840689	−	0.514601i
$105$		0			0
$106$	−3.99454	−	6.91874i	−0.387984	−	0.672008i
$107$	7.06169	+	12.2312i	0.682679	+	1.18243i	0.974160	+	0.225858i	$0.0725186\pi$
$107$	7.06169	+	12.2312i	0.682679	+	1.18243i	−0.291481	+	0.956577i	$0.594148\pi$
$108$	2.34596	−	4.06331i	0.225740	−	0.390993i
$109$	−4.20237			−0.402514			−0.201257	−	0.979538i	$-0.564503\pi$
$109$	−4.20237			−0.402514			−0.201257	+	0.979538i	$0.564503\pi$
$110$	1.31516	−	2.27792i	0.125396	−	0.217191i
$111$	−3.50449	+	6.06995i	−0.332631	+	0.576135i
$112$		0			0
$113$	−6.88472	+	11.9247i	−0.647660	+	1.12178i	0.336020	+	0.941855i	$0.390919\pi$
$113$	−6.88472	+	11.9247i	−0.647660	+	1.12178i	−0.983680	+	0.179926i	$0.942414\pi$
$114$	0.292096	+	0.505925i	0.0273573	+	0.0473842i
$115$	9.72240	+	16.8397i	0.906618	+	1.57031i
$116$	2.34190			0.217440
$117$	−0.237294	−	9.23720i	−0.0219379	−	0.853980i
$118$	−0.434514			−0.0400003
$119$		0			0
$120$	−3.17209	−	5.49422i	−0.289571	−	0.501552i
$121$	5.09681	−	8.82793i	0.463346	−	0.802539i
$122$	1.22238			0.110669
$123$	1.76263	−	3.05297i	0.158931	−	0.275277i
$124$	5.82550	−	10.0901i	0.523145	−	0.906114i
$125$	−6.34531			−0.567542
$126$		0			0
$127$	−0.972482	−	1.68439i	−0.0862938	−	0.149465i	0.819648	−	0.572868i	$-0.194169\pi$
$127$	−0.972482	−	1.68439i	−0.0862938	−	0.149465i	−0.905942	+	0.423402i	$0.860836\pi$
$128$	−3.80478	−	6.59007i	−0.336298	−	0.582485i
$129$	2.58845			0.227901
$130$	−9.27880	−	5.04394i	−0.813804	−	0.442383i
$131$	12.0354			1.05154			0.525769	−	0.850627i	$-0.323778\pi$
$131$	12.0354			1.05154			0.525769	+	0.850627i	$0.323778\pi$
$132$	0.378702	+	0.655931i	0.0329618	+	0.0570914i
$133$		0			0
$134$	−3.59571	+	6.22796i	−0.310622	+	0.538014i
$135$	−12.6586			−1.08948
$136$	2.69985	−	4.67627i	0.231510	−	0.400987i
$137$	−4.35857	+	7.54927i	−0.372378	+	0.644978i	−0.989931	−	0.141552i	$-0.954791\pi$
$137$	−4.35857	+	7.54927i	−0.372378	+	0.644978i	0.617553	+	0.786529i	$0.288124\pi$
$138$	3.17980			0.270683
$139$	2.10625	−	3.64813i	0.178650	−	0.309430i	−0.762769	−	0.646672i	$-0.776160\pi$
$139$	2.10625	−	3.64813i	0.178650	−	0.309430i	0.941418	+	0.337241i	$0.109494\pi$
$140$		0			0
$141$	−2.37752	−	4.11799i	−0.200224	−	0.346798i
$142$	2.93500			0.246300
$143$	2.84461	+	1.54633i	0.237878	+	0.129310i
$144$	−0.456917			−0.0380764
$145$	−3.15917	−	5.47184i	−0.262355	−	0.454412i
$146$	−4.63885	−	8.03473i	−0.383914	−	0.664959i
$147$		0			0
$148$	13.5212			1.11144
$149$	−2.93242	+	5.07910i	−0.240233	+	0.416096i	−0.960781	−	0.277310i	$-0.910557\pi$
$149$	−2.93242	+	5.07910i	−0.240233	+	0.416096i	0.720548	+	0.693406i	$0.243891\pi$
$150$	−1.92578	+	3.33555i	−0.157240	+	0.272347i
$151$	−16.8568			−1.37179			−0.685893	−	0.727702i	$-0.740588\pi$
$151$	−16.8568			−1.37179			−0.685893	+	0.727702i	$0.740588\pi$
$152$	1.44699	−	2.50626i	0.117367	−	0.203285i
$153$	−2.48181	−	4.29862i	−0.200643	−	0.347523i
$154$		0			0
$155$	−31.4339			−2.52483
$156$	2.59374	−	1.58768i	0.207666	−	0.127116i
$157$	1.93900			0.154749			0.0773746	−	0.997002i	$-0.475346\pi$
$157$	1.93900			0.154749			0.0773746	+	0.997002i	$0.475346\pi$
$158$	−5.14581	−	8.91280i	−0.409379	−	0.709065i
$159$	−3.10328	−	5.37504i	−0.246106	−	0.426268i
$160$	−9.85573	+	17.0706i	−0.779164	+	1.34955i
$161$		0			0
$162$	2.23685	−	3.87433i	0.175743	−	0.304396i
$163$	5.94797	−	10.3022i	0.465881	−	0.806929i	−0.533360	−	0.845888i	$-0.679071\pi$
$163$	5.94797	−	10.3022i	0.465881	−	0.806929i	0.999241	+	0.0389590i	$0.0124042\pi$
$164$	−6.80069			−0.531045
$165$	1.02172	−	1.76968i	0.0795410	−	0.137769i
$166$	−0.645448	−	1.11795i	−0.0500965	−	0.0867696i
$167$	8.28801	+	14.3553i	0.641346	+	1.11084i	0.985133	+	0.171796i	$0.0549569\pi$
$167$	8.28801	+	14.3553i	0.641346	+	1.11084i	−0.343787	+	0.939048i	$0.611710\pi$
$168$		0			0
$169$	5.91338	−	11.5772i	0.454875	−	0.890555i
$170$	−5.67316			−0.435112
$171$	−1.33013	−	2.30386i	−0.101718	−	0.176181i
$172$	−2.49673	−	4.32447i	−0.190374	−	0.329738i
$173$	−4.99328	+	8.64862i	−0.379632	+	0.657542i	−0.991009	−	0.133798i	$-0.957283\pi$
$173$	−4.99328	+	8.64862i	−0.379632	+	0.657542i	0.611377	+	0.791340i	$0.290616\pi$
$174$	−1.03324			−0.0783295
$175$		0			0
$176$	0.0800507	−	0.138652i	0.00603405	−	0.0104513i
$177$	−0.337566			−0.0253730
$178$	−5.79098	+	10.0303i	−0.434052	+	0.751801i
$179$	−4.58829	−	7.94715i	−0.342945	−	0.593998i	0.642033	−	0.766677i	$-0.278091\pi$
$179$	−4.58829	−	7.94715i	−0.342945	−	0.593998i	−0.984978	+	0.172679i	$0.944758\pi$
$180$	5.62518	+	9.74310i	0.419276	+	0.726208i
$181$	−6.00489			−0.446340			−0.223170	−	0.974780i	$-0.571640\pi$
$181$	−6.00489			−0.446340			−0.223170	+	0.974780i	$0.571640\pi$
$182$		0			0
$183$	0.949642			0.0701995
$184$	−7.87609	−	13.6418i	−0.580633	−	1.00569i
$185$	−18.2399	−	31.5924i	−1.34102	−	2.32272i
$186$	−2.57019	+	4.45170i	−0.188456	+	0.326415i
$187$	1.73923			0.127185
$188$	−4.58655	+	7.94415i	−0.334509	+	0.579386i
$189$		0			0
$190$	−3.04055			−0.220585
$191$	−0.658061	+	1.13980i	−0.0476156	+	0.0824727i	−0.888851	−	0.458197i	$-0.848496\pi$
$191$	−0.658061	+	1.13980i	−0.0476156	+	0.0824727i	0.841235	+	0.540669i	$0.181829\pi$
$192$	1.49382	+	2.58736i	0.107807	+	0.186727i
$193$	8.21270	+	14.2248i	0.591163	+	1.02392i	0.994076	+	0.108686i	$0.0346643\pi$
$193$	8.21270	+	14.2248i	0.591163	+	1.02392i	−0.402913	+	0.915238i	$0.632002\pi$
$194$	0.430874			0.0309350
$195$	−7.20852	−	3.91854i	−0.516213	−	0.280613i
$196$		0			0
$197$	12.7938	+	22.1594i	0.911517	+	1.57879i	0.811922	+	0.583766i	$0.198421\pi$
$197$	12.7938	+	22.1594i	0.911517	+	1.57879i	0.0995951	+	0.995028i	$0.468245\pi$
$198$	0.979367	+	1.69631i	0.0696006	+	0.120552i
$199$	−12.6894	+	21.9787i	−0.899528	+	1.55803i	−0.0714284	+	0.997446i	$0.522756\pi$
$199$	−12.6894	+	21.9787i	−0.899528	+	1.55803i	−0.828099	+	0.560582i	$0.810578\pi$
$200$	19.0800			1.34916
$201$	−2.79344	+	4.83838i	−0.197034	+	0.341273i
$202$	2.54765	−	4.41266i	0.179252	−	0.310473i
$203$		0			0
$204$	0.816797	−	1.41473i	0.0571873	−	0.0990512i
$205$	9.17399	+	15.8898i	0.640740	+	1.10979i
$206$	1.75886	+	3.04643i	0.122546	+	0.212255i
$207$	−14.4801			−1.00643
$208$	−0.564779	−	0.307013i	−0.0391604	−	0.0212875i
$209$	0.932145			0.0644778
$210$		0			0
$211$	2.84824	+	4.93330i	0.196081	+	0.339622i	0.947254	−	0.320483i	$-0.103845\pi$
$211$	2.84824	+	4.93330i	0.196081	+	0.339622i	−0.751173	+	0.660105i	$0.770512\pi$
$212$	−5.98663	+	10.3691i	−0.411164	+	0.712156i
$213$	2.28014			0.156233
$214$	−6.01038	+	10.4103i	−0.410861	+	0.711633i
$215$	−6.73608	+	11.6672i	−0.459397	+	0.795699i
$216$	10.2547			0.697744
$217$		0			0
$218$	−1.78837	−	3.09755i	−0.121124	−	0.209793i
$219$	−3.60384	−	6.24203i	−0.243525	−	0.421797i
$220$	−3.94207			−0.265774
$221$	−0.179334	−	6.98096i	−0.0120633	−	0.469590i
$222$	−5.96552			−0.400380
$223$	1.17906	+	2.04219i	0.0789558	+	0.136755i	0.902800	−	0.430061i	$-0.141508\pi$
$223$	1.17906	+	2.04219i	0.0789558	+	0.136755i	−0.823844	+	0.566817i	$0.808175\pi$
$224$		0			0
$225$	8.76956	−	15.1893i	0.584637	−	1.01262i
$226$	−11.7195			−0.779571
$227$	13.1463	−	22.7701i	0.872551	−	1.51130i	0.0132022	−	0.999913i	$-0.495797\pi$
$227$	13.1463	−	22.7701i	0.872551	−	1.51130i	0.859349	−	0.511390i	$-0.170869\pi$
$228$	0.437765	−	0.758232i	0.0289917	−	0.0502151i
$229$	−0.0685555			−0.00453027			−0.00226514	−	0.999997i	$-0.500721\pi$
$229$	−0.0685555			−0.00453027			−0.00226514	+	0.999997i	$0.500721\pi$
$230$	−8.27498	+	14.3327i	−0.545636	+	0.945069i
$231$		0			0
$232$	2.55924	+	4.43273i	0.168022	+	0.291023i
$233$	14.6703			0.961082			0.480541	−	0.876972i	$-0.340440\pi$
$233$	14.6703			0.961082			0.480541	+	0.876972i	$0.340440\pi$
$234$	6.70772	−	4.10592i	0.438498	−	0.268412i
$235$	24.7487			1.61443
$236$	0.325604	+	0.563963i	0.0211950	+	0.0367109i
$237$	−3.99768	−	6.92419i	−0.259677	−	0.449774i
$238$		0			0
$239$	3.35434			0.216974			0.108487	−	0.994098i	$-0.465399\pi$
$239$	3.35434			0.216974			0.108487	+	0.994098i	$0.465399\pi$
$240$	−0.202856	+	0.351357i	−0.0130943	+	0.0226800i
$241$	−4.28989	+	7.43031i	−0.276336	+	0.478628i	−0.970471	−	0.241216i	$-0.922454\pi$
$241$	−4.28989	+	7.43031i	−0.276336	+	0.478628i	0.694135	+	0.719845i	$0.255787\pi$
$242$	8.67605			0.557718
$243$	7.25513	−	12.5662i	0.465417	−	0.806125i
$244$	−0.915991	−	1.58654i	−0.0586403	−	0.101568i
$245$		0			0
$246$	3.00044			0.191301
$247$	−0.0961145	−	3.74147i	−0.00611562	−	0.238064i
$248$	25.4646			1.61700
$249$	−0.501436	−	0.868513i	−0.0317772	−	0.0550398i
$250$	−2.70033	−	4.67711i	−0.170784	−	0.295806i
$251$	10.7575	−	18.6326i	0.679010	−	1.17608i	−0.296270	−	0.955104i	$-0.595743\pi$
$251$	10.7575	−	18.6326i	0.679010	−	1.17608i	0.975280	−	0.220975i	$-0.0709238\pi$
$252$		0			0
$253$	2.53687	−	4.39399i	0.159492	−	0.276248i
$254$	0.827704	−	1.43363i	0.0519348	−	0.0899537i
$255$	−4.40737			−0.276000
$256$	7.75668	−	13.4350i	0.484793	−	0.839686i
$257$	2.46896	+	4.27636i	0.154010	+	0.266752i	0.932698	−	0.360659i	$-0.117448\pi$
$257$	2.46896	+	4.27636i	0.154010	+	0.266752i	−0.778688	+	0.627411i	$0.784115\pi$
$258$	1.10155	+	1.90794i	0.0685795	+	0.118783i
$259$		0			0
$260$	0.406471	+	15.8228i	0.0252083	+	0.981288i
$261$	4.70511			0.291239
$262$	5.12182	+	8.87125i	0.316427	+	0.548068i
$263$	4.47719	+	7.75473i	0.276076	+	0.478177i	0.970406	−	0.241480i	$-0.0776327\pi$
$263$	4.47719	+	7.75473i	0.276076	+	0.478177i	−0.694330	+	0.719656i	$0.744299\pi$
$264$	−0.827695	+	1.43361i	−0.0509411	+	0.0882326i
$265$	32.3034			1.98438
$266$		0			0
$267$	−4.49890	+	7.79233i	−0.275328	+	0.476883i
$268$	10.7778			0.658360
$269$	−2.41172	+	4.17723i	−0.147045	+	0.254690i	−0.930134	−	0.367220i	$-0.880310\pi$
$269$	−2.41172	+	4.17723i	−0.147045	+	0.254690i	0.783089	+	0.621910i	$0.213643\pi$
$270$	−5.38702	−	9.33060i	−0.327844	−	0.567842i
$271$	−3.71072	−	6.42715i	−0.225410	−	0.390422i	0.731032	−	0.682343i	$-0.239039\pi$
$271$	−3.71072	−	6.42715i	−0.225410	−	0.390422i	−0.956442	+	0.291921i	$0.905706\pi$
$272$	−0.345312			−0.0209376
$273$		0			0
$274$	−7.41938			−0.448221
$275$	3.07281	+	5.32226i	0.185297	+	0.320944i
$276$	−2.38279	−	4.12712i	−0.143427	−	0.248423i
$277$	−1.90816	+	3.30503i	−0.114650	+	0.198580i	−0.917640	−	0.397413i	$-0.869908\pi$
$277$	−1.90816	+	3.30503i	−0.114650	+	0.198580i	0.802990	+	0.595993i	$0.203241\pi$
$278$	3.58536			0.215036
$279$	11.7040	−	20.2720i	0.700702	−	1.21365i
$280$		0			0
$281$	8.54978			0.510037			0.255019	−	0.966936i	$-0.417918\pi$
$281$	8.54978			0.510037			0.255019	+	0.966936i	$0.417918\pi$
$282$	2.02357	−	3.50493i	0.120502	−	0.208715i
$283$	7.63217	+	13.2193i	0.453686	+	0.785807i	0.998612	−	0.0526775i	$-0.0167755\pi$
$283$	7.63217	+	13.2193i	0.453686	+	0.785807i	−0.544926	+	0.838484i	$0.683442\pi$
$284$	−2.19935	−	3.80938i	−0.130507	−	0.226045i
$285$	−2.36215			−0.139921
$286$	0.0707683	+	2.75481i	0.00418461	+	0.162895i
$287$		0			0
$288$	−7.33932	−	12.7121i	−0.432474	−	0.749066i
$289$	6.62439	+	11.4738i	0.389670	+	0.674928i
$290$	2.68885	−	4.65723i	0.157895	−	0.273482i
$291$	0.334738			0.0196227
$292$	−6.95227	+	12.0417i	−0.406851	+	0.704687i
$293$	−2.96982	+	5.14388i	−0.173499	+	0.300509i	−0.939641	−	0.342163i	$-0.888841\pi$
$293$	−2.96982	+	5.14388i	−0.173499	+	0.300509i	0.766142	+	0.642671i	$0.222174\pi$
$294$		0			0
$295$	0.878467	−	1.52155i	0.0511463	−	0.0885881i
$296$	14.7761	+	25.5929i	0.858842	+	1.48756i
$297$	1.65151	+	2.86049i	0.0958301	+	0.165983i
$298$	−4.99171			−0.289162
$299$	−17.8983	−	9.72949i	−1.03508	−	0.562671i
$300$	5.77236			0.333267
$301$		0			0
$302$	−7.17362	−	12.4251i	−0.412796	−	0.714983i
$303$	1.97922	−	3.42811i	0.113703	−	0.196940i
$304$	−0.185071			−0.0106146
$305$	−2.47131	+	4.28043i	−0.141507	+	0.245097i
$306$	2.11233	−	3.65867i	0.120754	−	0.209152i
$307$	−22.2133			−1.26778			−0.633891	−	0.773422i	$-0.718543\pi$
$307$	−22.2133			−1.26778			−0.633891	+	0.773422i	$0.718543\pi$
$308$		0			0
$309$	1.36642	+	2.36672i	0.0777332	+	0.134638i
$310$	−13.3771	−	23.1698i	−0.759769	−	1.31596i
$311$	−9.84259			−0.558122			−0.279061	−	0.960273i	$-0.590023\pi$
$311$	−9.84259			−0.558122			−0.279061	+	0.960273i	$0.590023\pi$
$312$	5.83961	+	3.17440i	0.330603	+	0.179715i
$313$	20.9125			1.18205			0.591023	−	0.806655i	$-0.298724\pi$
$313$	20.9125			1.18205			0.591023	+	0.806655i	$0.298724\pi$
$314$	0.825166	+	1.42923i	0.0465668	+	0.0806561i
$315$		0			0
$316$	−7.71205	+	13.3577i	−0.433837	+	0.751427i
$317$	−25.3603			−1.42438			−0.712188	−	0.701989i	$-0.752295\pi$
$317$	−25.3603			−1.42438			−0.712188	+	0.701989i	$0.752295\pi$
$318$	2.64128	−	4.57483i	0.148116	−	0.256544i
$319$	−0.824324	+	1.42777i	−0.0461533	+	0.0799398i
$320$	−15.5498			−0.869259
$321$	−4.66935	+	8.08755i	−0.260618	+	0.451403i
$322$		0			0
$323$	−1.00524	−	1.74113i	−0.0559331	−	0.0968790i
$324$	−6.70475			−0.372486
$325$	21.0458	−	12.8825i	1.16741	−	0.714593i
$326$	10.1249			0.560768
$327$	−1.38935	−	2.40643i	−0.0768314	−	0.133076i
$328$	−7.43183	−	12.8723i	−0.410354	−	0.710755i
$329$		0			0
$330$	1.73923			0.0957413
$331$	−0.891417	+	1.54398i	−0.0489967	+	0.0848648i	−0.889484	−	0.456967i	$-0.848936\pi$
$331$	−0.891417	+	1.54398i	−0.0489967	+	0.0848648i	0.840487	+	0.541832i	$0.182269\pi$
$332$	−0.967335	+	1.67547i	−0.0530894	+	0.0919536i
$333$	27.1656			1.48866
$334$	−7.05414	+	12.2181i	−0.385985	+	0.668546i
$335$	−14.5391	−	25.1824i	−0.794354	−	1.37586i
$336$		0			0
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$	11.0500	−	0.568103i	0.601043	−	0.0309007i
$339$	−9.10468			−0.494498
$340$	4.25120	+	7.36329i	0.230554	+	0.399331i
$341$	4.10103	+	7.10320i	0.222083	+	0.384660i
$342$	1.13211	−	1.96087i	0.0612176	−	0.106032i
$343$		0			0
$344$	5.45689	−	9.45160i	0.294216	−	0.509596i
$345$	−6.42867	+	11.1348i	−0.346108	+	0.599477i
$346$	−8.49982			−0.456953
$347$	−0.316694	+	0.548531i	−0.0170010	+	0.0294467i	−0.874401	−	0.485204i	$-0.838745\pi$
$347$	−0.316694	+	0.548531i	−0.0170010	+	0.0294467i	0.857400	+	0.514651i	$0.172079\pi$
$348$	0.774258	+	1.34105i	0.0415046	+	0.0718881i
$349$	15.2994	+	26.4994i	0.818960	+	1.41848i	0.906449	+	0.422315i	$0.138783\pi$
$349$	15.2994	+	26.4994i	0.818960	+	1.41848i	−0.0874885	+	0.996166i	$0.527884\pi$
$350$		0			0
$351$	11.3112	−	6.92381i	0.603749	−	0.369565i
$352$	5.14332			0.274140
$353$	−0.550173	−	0.952928i	−0.0292828	−	0.0507192i	0.851013	−	0.525145i	$-0.175989\pi$
$353$	−0.550173	−	0.952928i	−0.0292828	−	0.0507192i	−0.880295	+	0.474426i	$0.842656\pi$
$354$	−0.143655	−	0.248819i	−0.00763520	−	0.0132246i
$355$	−5.93375	+	10.2776i	−0.314931	+	0.545476i
$356$	17.3579			0.919969
$357$		0			0
$358$	3.90521	−	6.76402i	0.206397	−	0.357489i
$359$	−9.77386			−0.515845			−0.257922	−	0.966166i	$-0.583038\pi$
$359$	−9.77386			−0.515845			−0.257922	+	0.966166i	$0.583038\pi$
$360$	−12.2945	+	21.2946i	−0.647975	+	1.12233i
$361$	8.96124	+	15.5213i	0.471644	+	0.816912i
$362$	−2.55546	−	4.42618i	−0.134312	−	0.232635i
$363$	6.74026			0.353772
$364$		0			0
$365$	37.5139			1.96357
$366$	0.404132	+	0.699977i	0.0211243	+	0.0365884i
$367$	−5.57363	−	9.65381i	−0.290941	−	0.503925i	0.683092	−	0.730333i	$-0.260635\pi$
$367$	−5.57363	−	9.65381i	−0.290941	−	0.503925i	−0.974033	+	0.226408i	$0.927302\pi$
$368$	−0.503679	+	0.872397i	−0.0262561	+	0.0454769i
$369$	−13.6633			−0.711283
$370$	15.5244	−	26.8891i	0.807076	−	1.39790i
$371$		0			0
$372$	7.70391			0.399429
$373$	15.3651	−	26.6131i	0.795573	−	1.37797i	−0.126902	−	0.991915i	$-0.540504\pi$
$373$	15.3651	−	26.6131i	0.795573	−	1.37797i	0.922475	−	0.386057i	$-0.126163\pi$
$374$	0.740150	+	1.28198i	0.0382723	+	0.0662895i
$375$	−2.09783	−	3.63355i	−0.108332	−	0.187636i
$376$	−20.0489			−1.03394
$377$	5.81582	+	3.16147i	0.299530	+	0.162824i
$378$		0			0
$379$	−11.3286	−	19.6217i	−0.581912	−	1.00790i	−0.995253	−	0.0973246i	$-0.968972\pi$
$379$	−11.3286	−	19.6217i	−0.581912	−	1.00790i	0.413341	−	0.910576i	$-0.364362\pi$
$380$	2.27844	+	3.94638i	0.116882	+	0.202445i
$381$	0.643028	−	1.11376i	0.0329433	−	0.0570595i
$382$	−1.12019			−0.0573137
$383$	−0.294631	+	0.510317i	−0.0150550	+	0.0260760i	−0.873455	−	0.486905i	$-0.838126\pi$
$383$	−0.294631	+	0.510317i	−0.0150550	+	0.0260760i	0.858400	+	0.512981i	$0.171459\pi$
$384$	2.51581	−	4.35751i	0.128384	−	0.222368i
$385$		0			0
$386$	−6.99004	+	12.1071i	−0.355783	+	0.616235i
$387$	−5.01619	−	8.68830i	−0.254988	−	0.441651i
$388$	−0.322877	−	0.559239i	−0.0163916	−	0.0283910i
$389$	5.69945			0.288974			0.144487	−	0.989507i	$-0.453847\pi$
$389$	5.69945			0.288974			0.144487	+	0.989507i	$0.453847\pi$
$390$	−0.179334	−	6.98096i	−0.00908091	−	0.353495i
$391$	−10.9432			−0.553422
$392$		0			0
$393$	3.97904	+	6.89191i	0.200716	+	0.347651i
$394$	−10.8891	+	18.8605i	−0.548584	+	0.950176i
$395$	41.6136			2.09381
$396$	1.46778	−	2.54227i	0.0737588	−	0.127754i
$397$	−12.7641	+	22.1082i	−0.640614	+	1.10958i	0.344682	+	0.938720i	$0.387987\pi$
$397$	−12.7641	+	22.1082i	−0.640614	+	1.10958i	−0.985296	+	0.170857i	$0.945346\pi$
$398$	−21.6005			−1.08274
$399$		0			0
$400$	−0.610086	−	1.05670i	−0.0305043	−	0.0528350i
$401$	−12.7506	−	22.0846i	−0.636733	−	1.10285i	−0.986145	−	0.165884i	$-0.946952\pi$
$401$	−12.7506	−	22.0846i	−0.636733	−	1.10285i	0.349413	−	0.936969i	$-0.386381\pi$
$402$	−4.75514			−0.237165
$403$	28.0882	−	17.1933i	1.39917	−	0.856457i
$404$	−7.63635			−0.379922
$405$	9.04457	+	15.6657i	0.449428	+	0.778433i
$406$		0			0
$407$	−4.75934	+	8.24341i	−0.235912	+	0.408611i
$408$	3.57040			0.176761
$409$	0.0734938	−	0.127295i	0.00363403	−	0.00629433i	−0.864203	−	0.503144i	$-0.832177\pi$
$409$	0.0734938	−	0.127295i	0.00363403	−	0.00629433i	0.867837	+	0.496850i	$0.165510\pi$
$410$	−7.80822	+	13.5242i	−0.385621	+	0.667914i
$411$	−5.76398			−0.284316
$412$	2.63601	−	4.56570i	0.129867	−	0.224936i
$413$		0			0
$414$	−6.16217	−	10.6732i	−0.302854	−	0.524559i
$415$	5.21966			0.256223
$416$	−0.530333	−	20.6444i	−0.0260017	−	1.01217i
$417$	2.78540			0.136402
$418$	0.396686	+	0.687080i	0.0194026	+	0.0336062i
$419$	6.84795	+	11.8610i	0.334544	+	0.579447i	0.983397	−	0.181466i	$-0.0580844\pi$
$419$	6.84795	+	11.8610i	0.334544	+	0.579447i	−0.648853	+	0.760914i	$0.724751\pi$
$420$		0			0
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	−2.42421	+	4.19885i	−0.118009	+	0.204397i
$423$	−9.21486	+	15.9606i	−0.448042	+	0.776032i
$424$	−26.1689			−1.27087
$425$	6.62754	−	11.4792i	0.321483	−	0.556825i
$426$	0.970345	+	1.68069i	0.0470134	+	0.0814295i
$427$		0			0
$428$	18.0156			0.870816
$429$	0.0549785	+	2.14016i	0.00265439	+	0.103328i
$430$	−11.4665			−0.552964
$431$	−11.1455	−	19.3046i	−0.536861	−	0.929870i	−0.999071	−	0.0430997i	$-0.986277\pi$
$431$	−11.1455	−	19.3046i	−0.536861	−	0.929870i	0.462210	−	0.886771i	$-0.347057\pi$
$432$	−0.327896	−	0.567932i	−0.0157759	−	0.0273246i
$433$	−12.9481	+	22.4268i	−0.622247	+	1.07776i	0.366819	+	0.930292i	$0.380447\pi$
$433$	−12.9481	+	22.4268i	−0.622247	+	1.07776i	−0.989066	+	0.147472i	$0.952886\pi$
$434$		0			0
$435$	2.08892	−	3.61811i	0.100156	−	0.173475i
$436$	−2.68024	+	4.64232i	−0.128360	+	0.222327i
$437$	−5.86505			−0.280564
$438$	3.06732	−	5.31275i	0.146562	−	0.253853i
$439$	−13.9919	−	24.2347i	−0.667798	−	1.15666i	−0.978519	−	0.206159i	$-0.933904\pi$
$439$	−13.9919	−	24.2347i	−0.667798	−	1.15666i	0.310721	−	0.950501i	$-0.399430\pi$
$440$	−4.30792	−	7.46153i	−0.205372	−	0.355715i
$441$		0			0
$442$	5.06932	−	3.10302i	0.241123	−	0.147596i
$443$	33.2089			1.57780			0.788900	−	0.614521i	$-0.210651\pi$
$443$	33.2089			1.57780			0.788900	+	0.614521i	$0.210651\pi$
$444$	4.47028	+	7.74275i	0.212150	+	0.367454i
$445$	−23.4155	−	40.5568i	−1.11000	−	1.92258i
$446$	−1.00353	+	1.73816i	−0.0475185	+	0.0823044i
$447$	−3.87796			−0.183421
$448$		0			0
$449$	−9.84320	+	17.0489i	−0.464529	+	0.804589i	−0.999180	−	0.0404845i	$-0.987110\pi$
$449$	−9.84320	+	17.0489i	−0.464529	+	0.804589i	0.534651	+	0.845073i	$0.320443\pi$
$450$	14.9280			0.703712
$451$	2.39377	−	4.14614i	0.112718	−	0.195234i
$452$	8.78205	+	15.2110i	0.413073	+	0.715464i
$453$	−5.57305	−	9.65281i	−0.261845	−	0.453528i
$454$	22.3783			1.05027
$455$		0			0
$456$	1.91357			0.0896111
$457$	0.373471	+	0.646871i	0.0174702	+	0.0302593i	0.874628	−	0.484794i	$-0.161105\pi$
$457$	0.373471	+	0.646871i	0.0174702	+	0.0302593i	−0.857158	+	0.515053i	$0.827772\pi$
$458$	−0.0291746	−	0.0505320i	−0.00136324	−	0.00236120i
$459$	3.56203	−	6.16961i	0.166261	−	0.287973i
$460$	24.8035			1.15647
$461$	−16.5855	+	28.7269i	−0.772464	+	1.33795i	0.163744	+	0.986503i	$0.447643\pi$
$461$	−16.5855	+	28.7269i	−0.772464	+	1.33795i	−0.936209	+	0.351445i	$0.885691\pi$
$462$		0			0
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	0.163664	−	0.283475i	0.00759792	−	0.0131600i
$465$	−10.3924	−	18.0002i	−0.481937	−	0.834740i
$466$	6.24313	+	10.8134i	0.289207	+	0.500922i
$467$	29.6065			1.37003			0.685013	−	0.728531i	$-0.259797\pi$
$467$	29.6065			1.37003			0.685013	+	0.728531i	$0.259797\pi$
$468$	−10.3556	−	5.62928i	−0.478687	−	0.260214i
$469$		0			0
$470$	10.5321	+	18.2422i	0.485810	+	0.841448i
$471$	0.641056	+	1.11034i	0.0295383	+	0.0511618i
$472$	−0.711644	+	1.23260i	−0.0327561	+	0.0567352i
$473$	3.51530			0.161634
$474$	3.40253	−	5.89335i	0.156283	−	0.270691i
$475$	3.55205	−	6.15234i	0.162979	−	0.282289i
$476$		0			0
$477$	−12.0278	+	20.8327i	−0.550714	+	0.953864i
$478$	1.42748	+	2.47247i	0.0652915	+	0.113088i
$479$	7.04527	+	12.2028i	0.321907	+	0.557559i	0.980881	−	0.194606i	$-0.0623429\pi$
$479$	7.04527	+	12.2028i	0.321907	+	0.557559i	−0.658975	+	0.752165i	$0.729010\pi$
$480$	−13.0337			−0.594903
$481$	33.5784	+	18.2532i	1.53104	+	0.832273i
$482$	−7.30247			−0.332618
$483$		0			0
$484$	−6.50142	−	11.2608i	−0.295519	−	0.511854i
$485$	−0.871108	+	1.50880i	−0.0395550	+	0.0685112i
$486$	12.3500			0.560210
$487$	8.39773	−	14.5453i	0.380537	−	0.659110i	−0.610602	−	0.791938i	$-0.709072\pi$
$487$	8.39773	−	14.5453i	0.380537	−	0.659110i	0.991139	+	0.132828i	$0.0424057\pi$
$488$	2.00200	−	3.46757i	0.0906263	−	0.156969i
$489$	7.86587			0.355707
$490$		0			0
$491$	−10.8345	−	18.7659i	−0.488954	−	0.846893i	0.510965	−	0.859601i	$-0.329288\pi$
$491$	−10.8345	−	18.7659i	−0.488954	−	0.846893i	−0.999919	+	0.0127081i	$0.995955\pi$
$492$	−2.24839	−	3.89432i	−0.101365	−	0.175570i
$493$	3.55586			0.160148
$494$	2.71692	−	1.66308i	0.122240	−	0.0748253i
$495$	−7.92003			−0.355979
$496$	−0.814234	−	1.41029i	−0.0365602	−	0.0633241i
$497$		0			0
$498$	0.426785	−	0.739213i	0.0191247	−	0.0331249i
$499$	−23.3048			−1.04327			−0.521633	−	0.853170i	$-0.674677\pi$
$499$	−23.3048			−1.04327			−0.521633	+	0.853170i	$0.674677\pi$
$500$	−4.04699	+	7.00960i	−0.180987	+	0.313479i
$501$	−5.48023	+	9.49203i	−0.244838	+	0.424073i
$502$	18.3120			0.817306
$503$	−21.9415	+	38.0037i	−0.978322	+	1.69450i	−0.309816	+	0.950796i	$0.600268\pi$
$503$	−21.9415	+	38.0037i	−0.978322	+	1.69450i	−0.668506	+	0.743707i	$0.733066\pi$
$504$		0			0
$505$	10.3013	+	17.8423i	0.458401	+	0.793974i
$506$	4.31839			0.191976
$507$	8.58456	−	0.441349i	0.381254	−	0.0196010i
$508$	−2.48097			−0.110075
$509$	9.96210	+	17.2549i	0.441563	+	0.764809i	0.997806	−	0.0662109i	$-0.0210910\pi$
$509$	9.96210	+	17.2549i	0.441563	+	0.764809i	−0.556243	+	0.831020i	$0.687758\pi$
$510$	−1.87561	−	3.24866i	−0.0830536	−	0.143853i
$511$		0			0
$512$	−2.01529			−0.0890641
$513$	1.90908	−	3.30662i	0.0842879	−	0.145991i
$514$	−2.10139	+	3.63972i	−0.0926886	+	0.160541i
$515$	−14.2237			−0.626771
$516$	1.65090	−	2.85944i	0.0726767	−	0.125880i
$517$	−3.22884	−	5.59252i	−0.142004	−	0.245959i
$518$		0			0
$519$	−6.60335			−0.289855
$520$	−29.5051	+	18.0606i	−1.29388	+	0.792010i
$521$	16.5241			0.723933			0.361967	−	0.932191i	$-0.382105\pi$
$521$	16.5241			0.723933			0.361967	+	0.932191i	$0.382105\pi$
$522$	2.00232	+	3.46812i	0.0876392	+	0.151796i
$523$	−5.99809	−	10.3890i	−0.262278	−	0.454279i	0.704569	−	0.709636i	$-0.251140\pi$
$523$	−5.99809	−	10.3890i	−0.262278	−	0.454279i	−0.966847	+	0.255357i	$0.917807\pi$
$524$	7.67609	−	13.2954i	0.335332	−	0.580812i
$525$		0			0
$526$	−3.81065	+	6.60024i	−0.166152	+	0.287784i
$527$	8.84526	−	15.3204i	0.385305	−	0.667369i
$528$	0.105863			0.00460709
$529$	−4.46197	+	7.72837i	−0.193999	+	0.336016i
$530$	13.7471	+	23.8107i	0.597137	+	1.03427i
$531$	0.654173	+	1.13306i	0.0283887	+	0.0491706i
$532$		0			0
$533$	−16.8887	−	9.18068i	−0.731531	−	0.397660i
$534$	−7.65826			−0.331405
$535$	−24.3026	−	42.0934i	−1.05070	−	1.81986i
$536$	11.7781	+	20.4002i	0.508735	+	0.881155i
$537$	3.03388	−	5.25484i	0.130922	−	0.226763i
$538$	−4.10536			−0.176995
$539$		0			0
$540$	−8.07356	+	13.9838i	−0.347431	+	0.601767i
$541$	36.2317			1.55772			0.778860	−	0.627197i	$-0.215798\pi$
$541$	36.2317			1.55772			0.778860	+	0.627197i	$0.215798\pi$
$542$	3.15829	−	5.47031i	0.135660	−	0.234970i
$543$	−1.98529	−	3.43862i	−0.0851968	−	0.147565i
$544$	−5.54665	−	9.60707i	−0.237811	−	0.411900i
$545$	14.4624			0.619500
$546$		0			0
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	5.55973	+	9.62974i	0.237500	+	0.411362i
$549$	−1.84032	−	3.18753i	−0.0785430	−	0.136040i
$550$	−2.61535	+	4.52991i	−0.111519	+	0.193156i
$551$	1.90578			0.0811888
$552$	5.20786	−	9.02027i	0.221661	−	0.383928i
$553$		0			0
$554$	−3.24816			−0.138001
$555$	12.0606	−	20.8896i	0.511945	−	0.886715i
$556$	−2.68670	−	4.65350i	−0.113941	−	0.197352i
$557$	−5.41399	−	9.37731i	−0.229398	−	0.397329i	0.728232	−	0.685331i	$-0.240342\pi$
$557$	−5.41399	−	9.37731i	−0.229398	−	0.397329i	−0.957630	+	0.288002i	$0.907009\pi$
$558$	19.9232			0.843417
$559$	−0.362466	−	14.1098i	−0.0153307	−	0.596781i
$560$		0			0
$561$	0.575009	+	0.995945i	0.0242769	+	0.0420488i
$562$	3.63847	+	6.30201i	0.153480	+	0.265834i
$563$	−6.92997	+	12.0031i	−0.292064	+	0.505869i	−0.974298	−	0.225265i	$-0.927675\pi$
$563$	−6.92997	+	12.0031i	−0.292064	+	0.505869i	0.682234	+	0.731134i	$0.261009\pi$
$564$	−6.06547			−0.255402
$565$	23.6936	−	41.0386i	0.996798	−	1.72651i
$566$	−6.49594	+	11.2513i	−0.273045	+	0.472927i
$567$		0			0
$568$	4.80692	−	8.32583i	0.201694	−	0.349344i
$569$	−13.7060	−	23.7395i	−0.574586	−	0.995212i	−0.996086	−	0.0883842i	$-0.971830\pi$
$569$	−13.7060	−	23.7395i	−0.574586	−	0.995212i	0.421500	−	0.906828i	$-0.361504\pi$
$570$	−1.00524	−	1.74113i	−0.0421049	−	0.0729279i
$571$	−0.207758			−0.00869439			−0.00434719	−	0.999991i	$-0.501384\pi$
$571$	−0.207758			−0.00869439			−0.00434719	+	0.999991i	$0.501384\pi$
$572$	3.52248	−	2.15617i	0.147282	−	0.0901542i
$573$	−0.870251			−0.0363552
$574$		0			0
$575$	−19.3341	−	33.4876i	−0.806288	−	1.39653i
$576$	5.78976	−	10.0282i	0.241240	−	0.417840i
$577$	3.32656			0.138487			0.0692434	−	0.997600i	$-0.477942\pi$
$577$	3.32656			0.138487			0.0692434	+	0.997600i	$0.477942\pi$
$578$	−5.63818	+	9.76562i	−0.234518	+	0.406196i
$579$	−5.43043	+	9.40577i	−0.225681	+	0.390891i
$580$	−8.05959			−0.334656
$581$		0			0
$582$	0.142452	+	0.246734i	0.00590483	+	0.0102275i
$583$	−4.21447	−	7.29967i	−0.174545	−	0.302321i
$584$	−30.3899			−1.25754
$585$	0.816643	+	31.7896i	0.0337640	+	1.31434i
$586$	−5.05538			−0.208836
$587$	−7.54051	−	13.0606i	−0.311230	−	0.539067i	0.667399	−	0.744701i	$-0.267408\pi$
$587$	−7.54051	−	13.0606i	−0.311230	−	0.539067i	−0.978629	+	0.205634i	$0.934074\pi$
$588$		0			0
$589$	4.74064	−	8.21104i	0.195335	−	0.338330i
$590$	1.49537			0.0615635
$591$	−8.45953	+	14.6523i	−0.347978	+	0.602716i
$592$	0.944935	−	1.63668i	0.0388366	−	0.0672670i
$593$	−25.8491			−1.06149			−0.530747	−	0.847530i	$-0.678089\pi$
$593$	−25.8491			−1.06149			−0.530747	+	0.847530i	$0.678089\pi$
$594$	−1.40564	+	2.43464i	−0.0576740	+	0.0998944i
$595$		0			0
$596$	3.74055	+	6.47882i	0.153219	+	0.265383i
$597$	−16.7810			−0.686803
$598$	−0.445274	−	17.3333i	−0.0182086	−	0.708810i
$599$	−35.5469			−1.45241			−0.726203	−	0.687480i	$-0.758717\pi$
$599$	−35.5469			−1.45241			−0.726203	+	0.687480i	$0.758717\pi$
$600$	6.30807	+	10.9259i	0.257526	+	0.446048i
$601$	−13.6474	−	23.6379i	−0.556688	−	0.964212i	−0.997770	−	0.0667449i	$-0.978739\pi$
$601$	−13.6474	−	23.6379i	−0.556688	−	0.964212i	0.441082	−	0.897467i	$-0.354595\pi$
$602$		0			0
$603$	21.6538			0.881810
$604$	−10.7511	+	18.6215i	−0.437458	+	0.757699i
$605$	−17.5406	+	30.3811i	−0.713125	+	1.23517i
$606$	3.36913			0.136862
$607$	−19.4629	+	33.7108i	−0.789976	+	1.36828i	0.136006	+	0.990708i	$0.456574\pi$
$607$	−19.4629	+	33.7108i	−0.789976	+	1.36828i	−0.925981	+	0.377570i	$0.876760\pi$
$608$	−2.97274	−	5.14894i	−0.120561	−	0.208817i
$609$		0			0
$610$	−4.20679			−0.170328
$611$	−22.1145	+	13.5367i	−0.894656	+	0.547635i
$612$	−6.33152			−0.255937
$613$	−0.443322	−	0.767857i	−0.0179056	−	0.0310135i	0.856934	−	0.515427i	$-0.172367\pi$
$613$	−0.443322	−	0.767857i	−0.0179056	−	0.0310135i	−0.874839	+	0.484413i	$0.839033\pi$
$614$	−9.45317	−	16.3734i	−0.381499	−	0.660775i
$615$	−6.06606	+	10.5067i	−0.244607	+	0.423672i
$616$		0			0
$617$	−17.3944	+	30.1280i	−0.700272	+	1.21291i	0.268099	+	0.963391i	$0.413605\pi$
$617$	−17.3944	+	30.1280i	−0.700272	+	1.21291i	−0.968371	+	0.249515i	$0.919729\pi$
$618$	−1.16300	+	2.01437i	−0.0467827	+	0.0810300i
$619$	−2.05562			−0.0826221			−0.0413111	−	0.999146i	$-0.513153\pi$
$619$	−2.05562			−0.0826221			−0.0413111	+	0.999146i	$0.513153\pi$
$620$	−20.0483	+	34.7247i	−0.805161	+	1.39458i
$621$	−10.3913	−	17.9982i	−0.416987	−	0.722243i
$622$	−4.18864	−	7.25494i	−0.167949	−	0.290897i
$623$		0			0
$624$	−0.0109156	−	0.424915i	−0.000436975	−	0.0170102i
$625$	−12.3816			−0.495265
$626$	8.89959	+	15.4145i	0.355699	+	0.616089i
$627$	0.308178	+	0.533780i	0.0123074	+	0.0213171i
$628$	1.23668	−	2.14199i	0.0493489	−	0.0854749i
$629$	20.5302			0.818593
$630$		0			0
$631$	22.6169	−	39.1736i	0.900363	−	1.55947i	0.0733401	−	0.997307i	$-0.476634\pi$
$631$	22.6169	−	39.1736i	0.900363	−	1.55947i	0.827023	−	0.562168i	$-0.190033\pi$
$632$	−33.7111			−1.34095
$633$	−1.88332	+	3.26201i	−0.0748554	+	0.129653i
$634$	−10.7924	−	18.6930i	−0.428621	−	0.742393i
$635$	3.34678	+	5.79679i	0.132813	+	0.230038i
$636$	−7.91700			−0.313929
$637$		0			0
$638$	−1.40321			−0.0555534
$639$	−4.41872	−	7.65345i	−0.174802	−	0.302766i
$640$	13.0941	+	22.6796i	0.517588	+	0.896489i
$641$	9.53097	−	16.5081i	0.376451	−	0.652032i	−0.614092	−	0.789234i	$-0.710478\pi$
$641$	9.53097	−	16.5081i	0.376451	−	0.652032i	0.990543	+	0.137202i	$0.0438111\pi$
$642$	−7.94841			−0.313699
$643$	−5.26755	+	9.12367i	−0.207732	+	0.359802i	−0.951000	−	0.309192i	$-0.899942\pi$
$643$	−5.26755	+	9.12367i	−0.207732	+	0.359802i	0.743268	+	0.668994i	$0.233275\pi$
$644$		0			0
$645$	−8.90811			−0.350756
$646$	0.855587	−	1.48192i	0.0336626	−	0.0583053i
$647$	−12.0804	−	20.9239i	−0.474930	−	0.822603i	0.524658	−	0.851313i	$-0.324193\pi$
$647$	−12.0804	−	20.9239i	−0.474930	−	0.822603i	−0.999588	+	0.0287105i	$0.990860\pi$
$648$	−7.32699	−	12.6907i	−0.287831	−	0.498538i
$649$	−0.458438			−0.0179952
$650$	18.4520	+	10.0305i	0.723745	+	0.393427i
$651$		0			0
$652$	−7.58714	−	13.1413i	−0.297135	−	0.514654i
$653$	16.8445	+	29.1755i	0.659176	+	1.14173i	0.980829	+	0.194869i	$0.0624282\pi$
$653$	16.8445	+	29.1755i	0.659176	+	1.14173i	−0.321653	+	0.946858i	$0.604238\pi$
$654$	1.18251	−	2.04817i	0.0462400	−	0.0800900i
$655$	−41.4196			−1.61840
$656$	−0.475268	+	0.823189i	−0.0185561	+	0.0321401i
$657$	−13.9678	+	24.1930i	−0.544937	+	0.943859i
$658$		0			0
$659$	2.10030	−	3.63782i	0.0818159	−	0.141709i	−0.822214	−	0.569178i	$-0.807261\pi$
$659$	2.10030	−	3.63782i	0.0818159	−	0.141709i	0.904030	+	0.427469i	$0.140595\pi$
$660$	−1.30329	−	2.25737i	−0.0507307	−	0.0878681i
$661$	8.83631	+	15.3049i	0.343693	+	0.595293i	0.985115	−	0.171894i	$-0.0549888\pi$
$661$	8.83631	+	15.3049i	0.343693	+	0.595293i	−0.641423	+	0.767188i	$0.721655\pi$
$662$	−1.51742			−0.0589760
$663$	3.93826	−	2.41068i	0.152949	−	0.0936230i
$664$	−4.22844			−0.164095
$665$		0			0
$666$	11.5607	+	20.0236i	0.447966	+	0.775900i
$667$	5.18664	−	8.98353i	0.200828	−	0.347844i
$668$	21.1441			0.818091
$669$	−0.779623	+	1.35035i	−0.0301420	+	0.0522074i
$670$	12.3746	−	21.4334i	0.478071	−	0.828044i
$671$	1.28968			0.0497875
$672$		0			0
$673$	10.3052	+	17.8491i	0.397235	+	0.688031i	0.993384	−	0.114843i	$-0.0366366\pi$
$673$	10.3052	+	17.8491i	0.397235	+	0.688031i	−0.596149	+	0.802874i	$0.703303\pi$
$674$	4.06901	+	7.04774i	0.156733	+	0.271469i
$675$	25.1731			0.968911
$676$	−9.01772	−	13.9163i	−0.346835	−	0.535243i
$677$	21.3074			0.818909			0.409455	−	0.912330i	$-0.365719\pi$
$677$	21.3074			0.818909			0.409455	+	0.912330i	$0.365719\pi$
$678$	−3.87461	−	6.71102i	−0.148804	−	0.257735i
$679$		0			0
$680$	−9.29147	+	16.0933i	−0.356312	+	0.617150i
$681$	17.3853			0.666206
$682$	−3.49049	+	6.04571i	−0.133658	+	0.231502i
$683$	3.34878	−	5.80026i	0.128138	−	0.221941i	−0.794817	−	0.606849i	$-0.792433\pi$
$683$	3.34878	−	5.80026i	0.128138	−	0.221941i	0.922955	+	0.384908i	$0.125767\pi$
$684$	−3.39340			−0.129750
$685$	14.9999	−	25.9806i	0.573118	−	0.992670i
$686$		0			0
$687$	−0.0226652	−	0.0392573i	−0.000864732	−	0.00149776i
$688$	−0.697939			−0.0266087
$689$	−28.8651	+	17.6688i	−1.09967	+	0.673128i
$690$	−10.9432			−0.416601
$691$	−12.4632	−	21.5868i	−0.474121	−	0.821202i	0.525440	−	0.850831i	$-0.323901\pi$
$691$	−12.4632	−	21.5868i	−0.474121	−	0.821202i	−0.999561	+	0.0296291i	$0.990567\pi$
$692$	6.36936	+	11.0321i	0.242127	+	0.419376i
$693$		0			0
$694$	−0.539093			−0.0204637
$695$	−7.24861	+	12.5550i	−0.274955	+	0.476237i
$696$	−1.69223	+	2.93102i	−0.0641437	+	0.111100i
$697$	−10.3260			−0.391123
$698$	−13.0217	+	22.5543i	−0.492880	+	0.853694i
$699$	4.85017	+	8.40073i	0.183450	+	0.317745i
$700$		0			0
$701$	−4.94583			−0.186801			−0.0934007	−	0.995629i	$-0.529774\pi$
$701$	−4.94583			−0.186801			−0.0934007	+	0.995629i	$0.529774\pi$
$702$	9.91715	+	5.39095i	0.374299	+	0.203468i
$703$	11.0032			0.414995
$704$	2.02870	+	3.51382i	0.0764597	+	0.132432i
$705$	8.18220	+	14.1720i	0.308160	+	0.533748i
$706$	0.468266	−	0.811061i	0.0176234	−	0.0305247i
$707$		0			0
$708$	−0.215297	+	0.372905i	−0.00809136	+	0.0140146i
$709$	2.32249	−	4.02267i	0.0872228	−	0.151074i	−0.819113	−	0.573632i	$-0.805534\pi$
$709$	2.32249	−	4.02267i	0.0872228	−	0.151074i	0.906336	+	0.422557i	$0.138867\pi$
$710$	−10.1007			−0.379074
$711$	−15.4943	+	26.8369i	−0.581082	+	1.00646i
$712$	18.9688	+	32.8550i	0.710888	+	1.23129i
$713$	−25.8037	−	44.6933i	−0.966356	−	1.67378i
$714$		0			0
$715$	−9.78966	−	5.32165i	−0.366113	−	0.199018i
$716$	−11.7055			−0.437455
$717$	1.10898	+	1.92082i	0.0414157	+	0.0717342i
$718$	−4.15939	−	7.20427i	−0.155227	−	0.268861i
$719$	15.8706	−	27.4887i	0.591875	−	1.02516i	−0.402105	−	0.915594i	$-0.631721\pi$
$719$	15.8706	−	27.4887i	0.591875	−	1.02516i	0.993980	−	0.109564i	$-0.0349453\pi$
$720$	1.57247			0.0586025
$721$		0			0
$722$	−7.62714	+	13.2106i	−0.283853	+	0.491647i
$723$	−5.67315			−0.210987
$724$	−3.82987	+	6.63354i	−0.142336	+	0.246533i
$725$	6.28237	+	10.8814i	0.233322	+	0.404125i
$726$	2.86840	+	4.96822i	0.106456	+	0.184388i
$727$	−47.8755			−1.77560			−0.887801	−	0.460227i	$-0.847768\pi$
$727$	−47.8755			−1.77560			−0.887801	+	0.460227i	$0.847768\pi$
$728$		0			0
$729$	−6.17412			−0.228671
$730$	15.9645	+	27.6514i	0.590873	+	1.02342i
$731$	−3.79096	−	6.56613i	−0.140214	−	0.242857i
$732$	0.605675	−	1.04906i	0.0223864	−	0.0387743i
$733$	7.60208			0.280789			0.140395	−	0.990096i	$-0.455163\pi$
$733$	7.60208			0.280789			0.140395	+	0.990096i	$0.455163\pi$
$734$	4.74386	−	8.21660i	0.175099	−	0.303280i
$735$		0			0
$736$	−32.3618			−1.19287
$737$	−3.79368	+	6.57086i	−0.139742	+	0.242041i
$738$	−5.81459	−	10.0712i	−0.214038	−	0.370725i
$739$	16.7118	+	28.9457i	0.614754	+	1.06479i	0.990428	+	0.138033i	$0.0440781\pi$
$739$	16.7118	+	28.9457i	0.614754	+	1.06479i	−0.375673	+	0.926752i	$0.622589\pi$
$740$	−46.5330			−1.71059
$741$	2.11072	−	1.29201i	0.0775394	−	0.0474632i
$742$		0			0
$743$	1.46912	+	2.54458i	0.0538966	+	0.0933517i	0.891715	−	0.452597i	$-0.149503\pi$
$743$	1.46912	+	2.54458i	0.0538966	+	0.0933517i	−0.837818	+	0.545949i	$0.816169\pi$
$744$	8.41888	+	14.5819i	0.308651	+	0.534599i
$745$	10.0919	−	17.4796i	0.369737	−	0.640403i
$746$	26.1552			0.957609
$747$	−1.94348	+	3.36620i	−0.0711081	+	0.123163i
$748$	1.10927	−	1.92131i	0.0405588	−	0.0702499i
$749$		0			0
$750$	1.78552	−	3.09261i	0.0651980	−	0.112926i
$751$	−0.598389	−	1.03644i	−0.0218355	−	0.0378202i	0.854901	−	0.518791i	$-0.173618\pi$
$751$	−0.598389	−	1.03644i	−0.0218355	−	0.0378202i	−0.876737	+	0.480971i	$0.840284\pi$
$752$	0.641065	+	1.11036i	0.0233773	+	0.0404906i
$753$	14.2263			0.518434
$754$	0.144686	+	5.63223i	0.00526916	+	0.205114i
$755$	58.0123			2.11128
$756$		0			0
$757$	−5.77321	−	9.99950i	−0.209831	−	0.363438i	0.741830	−	0.670588i	$-0.233958\pi$
$757$	−5.77321	−	9.99950i	−0.209831	−	0.363438i	−0.951661	+	0.307150i	$0.900625\pi$
$758$	9.64207	−	16.7006i	0.350216	−	0.606592i
$759$	3.35487			0.121774
$760$	−4.97979	+	8.62525i	−0.180636	+	0.312871i
$761$	17.3249	−	30.0075i	0.628026	−	1.08777i	−0.359921	−	0.932983i	$-0.617197\pi$
$761$	17.3249	−	30.0075i	0.628026	−	1.08777i	0.987947	−	0.154790i	$-0.0494702\pi$
$762$	1.09459			0.0396530
$763$		0			0
$764$	0.839413	+	1.45391i	0.0303689	+	0.0526005i
$765$	8.54110	+	14.7936i	0.308804	+	0.534864i
$766$	−0.501537			−0.0181213
$767$	0.0472700	+	1.84009i	0.00170682	+	0.0664418i
$768$	10.2578			0.370146
$769$	−3.27437	−	5.67138i	−0.118077	−	0.204515i	0.800929	−	0.598760i	$-0.204340\pi$
$769$	−3.27437	−	5.67138i	−0.118077	−	0.204515i	−0.919006	+	0.394245i	$0.871006\pi$
$770$		0			0
$771$	−1.63253	+	2.82763i	−0.0587943	+	0.101835i
$772$	20.9520			0.754079
$773$	16.9637	−	29.3821i	0.610143	−	1.05680i	−0.381073	−	0.924545i	$-0.624445\pi$
$773$	16.9637	−	29.3821i	0.610143	−	1.05680i	0.991216	−	0.132254i	$-0.0422214\pi$
$774$	4.26941	−	7.39484i	0.153461	−	0.265802i
$775$	62.5100			2.24542
$776$	0.705683	−	1.22228i	0.0253325	−	0.0438772i
$777$		0			0
$778$	2.42547	+	4.20104i	0.0869575	+	0.150615i
$779$	−5.53423			−0.198284
$780$	−8.92632	+	5.46396i	−0.319613	+	0.195641i
$781$	3.09659			0.110805
$782$	−4.65703	−	8.06620i	−0.166535	−	0.288447i
$783$	3.37651	+	5.84829i	0.120667	+	0.209001i
$784$		0			0
$785$	−6.67303			−0.238171
$786$	−3.38667	+	5.86588i	−0.120798	+	0.209229i
$787$	6.48717	−	11.2361i	0.231243	−	0.400524i	−0.726932	−	0.686710i	$-0.759054\pi$
$787$	6.48717	−	11.2361i	0.231243	−	0.400524i	0.958174	+	0.286186i	$0.0923876\pi$
$788$	32.6390			1.16272
$789$	−2.96042	+	5.12760i	−0.105394	+	0.182548i
$790$	17.7092	+	30.6732i	0.630065	+	1.09130i
$791$		0			0
$792$	6.41600			0.227983
$793$	−0.132980	−	5.17655i	−0.00472226	−	0.183825i
$794$	−21.7278			−0.771090
$795$	10.6799	+	18.4981i	0.378776	+	0.656059i
$796$	16.1864	+	28.0357i	0.573712	+	0.993699i
$797$	2.20956	−	3.82707i	0.0782667	−	0.135562i	−0.824235	−	0.566247i	$-0.808395\pi$
$797$	2.20956	−	3.82707i	0.0782667	−	0.135562i	0.902502	+	0.430685i	$0.141728\pi$
$798$		0			0
$799$	−6.96408	+	12.0621i	−0.246371	+	0.426728i
$800$	19.5993	−	33.9469i	0.692938	−	1.20020i
$801$	34.8739			1.23221
$802$	10.8523	−	18.7968i	0.383209	−	0.663737i
$803$	−4.89426	−	8.47711i	−0.172715	−	0.299151i
$804$	3.56327	+	6.17177i	0.125667	+	0.217662i
$805$		0			0
$806$	24.6264	+	13.3869i	0.867427	+	0.471532i
$807$	−3.18937			−0.112271
$808$	−8.34504	−	14.4540i	−0.293578	−	0.508491i
$809$	−5.73580	−	9.93470i	−0.201660	−	0.349285i	0.747403	−	0.664371i	$-0.231300\pi$
$809$	−5.73580	−	9.93470i	−0.201660	−	0.349285i	−0.949063	+	0.315085i	$0.897967\pi$
$810$	−7.69807	+	13.3334i	−0.270482	+	0.468489i
$811$	−23.8664			−0.838063			−0.419032	−	0.907972i	$-0.637630\pi$
$811$	−23.8664			−0.838063			−0.419032	+	0.907972i	$0.637630\pi$
$812$		0			0
$813$	2.45361	−	4.24978i	0.0860520	−	0.149046i
$814$	−8.10159			−0.283960
$815$	−20.4698	+	35.4548i	−0.717026	+	1.24193i
$816$	−0.114164	−	0.197738i	−0.00399655	−	0.00692223i
$817$	−2.03178	−	3.51914i	−0.0710829	−	0.123119i
$818$	0.125105			0.00437419
$819$		0			0
$820$	23.4044			0.817318
$821$	−15.4847	−	26.8203i	−0.540420	−	0.936035i	−0.998880	−	0.0473197i	$-0.984932\pi$
$821$	−15.4847	−	26.8203i	−0.540420	−	0.936035i	0.458460	−	0.888715i	$-0.348401\pi$
$822$	−2.45293	−	4.24861i	−0.0855559	−	0.148187i
$823$	4.30678	−	7.45957i	0.150125	−	0.260024i	−0.781148	−	0.624346i	$-0.785366\pi$
$823$	4.30678	−	7.45957i	0.150125	−	0.260024i	0.931273	+	0.364321i	$0.118699\pi$
$824$	11.5226			0.401408
$825$	−2.03181	+	3.51920i	−0.0707386	+	0.122523i
$826$		0			0
$827$	22.9128			0.796756			0.398378	−	0.917221i	$-0.369573\pi$
$827$	22.9128			0.796756			0.398378	+	0.917221i	$0.369573\pi$
$828$	−9.23528	+	15.9960i	−0.320948	+	0.555898i
$829$	−21.2806	−	36.8590i	−0.739104	−	1.28017i	−0.952899	−	0.303287i	$-0.901916\pi$
$829$	−21.2806	−	36.8590i	−0.739104	−	1.28017i	0.213795	−	0.976879i	$-0.431418\pi$
$830$	2.22129	+	3.84739i	0.0771022	+	0.133545i
$831$	−2.52344			−0.0875370
$832$	13.8947	−	8.50518i	0.481711	−	0.294864i
$833$		0			0
$834$	1.18536	+	2.05311i	0.0410458	+	0.0710933i
$835$	−28.5230	−	49.4033i	−0.987080	−	1.70967i
$836$	0.594515	−	1.02973i	0.0205617	−	0.0356140i
$837$	33.5965			1.16126
$838$	−5.82846	+	10.0952i	−0.201341	+	0.348733i
$839$	0.920524	−	1.59439i	0.0317800	−	0.0550446i	−0.849698	−	0.527270i	$-0.823216\pi$
$839$	0.920524	−	1.59439i	0.0317800	−	0.0550446i	0.881478	+	0.472225i	$0.156549\pi$
$840$		0			0
$841$	12.8147	−	22.1957i	0.441885	−	0.765367i
$842$	1.46465	+	2.53686i	0.0504753	+	0.0874258i
$843$	2.82666	+	4.89591i	0.0973553	+	0.168624i
$844$	7.26635			0.250118
$845$	−20.3508	+	39.8427i	−0.700088	+	1.37063i
$846$	−15.6860			−0.539296
$847$		0			0
$848$	0.836755	+	1.44930i	0.0287343	+	0.0497692i
$849$	−5.04657	+	8.74092i	−0.173198	+	0.299988i
$850$	11.2817			0.386960
$851$	29.9457	−	51.8675i	1.02653	−	1.77800i
$852$	1.45426	−	2.51885i	0.0498221	−	0.0862944i
$853$	27.0293			0.925466			0.462733	−	0.886498i	$-0.346869\pi$
$853$	27.0293			0.925466			0.462733	+	0.886498i	$0.346869\pi$
$854$		0			0
$855$	4.57763	+	7.92869i	0.156552	+	0.271155i
$856$	19.6875	+	34.0998i	0.672906	+	1.16551i
$857$	−16.7854			−0.573377			−0.286688	−	0.958024i	$-0.592554\pi$
$857$	−16.7854			−0.573377			−0.286688	+	0.958024i	$0.592554\pi$
$858$	−1.55411	+	0.951297i	−0.0530563	+	0.0324767i
$859$	−51.6116			−1.76096			−0.880482	−	0.474079i	$-0.842781\pi$
$859$	−51.6116			−1.76096			−0.880482	+	0.474079i	$0.842781\pi$
$860$	8.59245	+	14.8826i	0.293000	+	0.507491i
$861$		0			0
$862$	9.48624	−	16.4306i	0.323102	−	0.559630i
$863$	21.9614			0.747573			0.373787	−	0.927515i	$-0.378059\pi$
$863$	21.9614			0.747573			0.373787	+	0.927515i	$0.378059\pi$
$864$	10.5338	−	18.2450i	0.358366	−	0.620709i
$865$	17.1843	−	29.7640i	0.584283	−	1.01201i
$866$	−22.0410			−0.748983
$867$	−4.38020	+	7.58673i	−0.148759	+	0.257659i
$868$		0			0
$869$	−5.42913	−	9.40352i	−0.184170	−	0.318993i
$870$	3.55586			0.120555
$871$	26.7654	+	14.5497i	0.906913	+	0.492997i
$872$	−11.7159			−0.396752
$873$	−0.648693	−	1.12357i	−0.0219549	−	0.0380270i
$874$	−2.49595	−	4.32311i	−0.0844267	−	0.146231i
$875$		0			0
$876$	−9.19401			−0.310637
$877$	4.80873	−	8.32896i	0.162379	−	0.281249i	−0.773342	−	0.633989i	$-0.781417\pi$
$877$	4.80873	−	8.32896i	0.162379	−	0.281249i	0.935721	+	0.352740i	$0.114750\pi$
$878$	11.9089	−	20.6268i	0.401905	−	0.696120i
$879$	−3.92743			−0.132469
$880$	−0.275493	+	0.477167i	−0.00928686	+	0.0160853i
$881$	14.4863	+	25.0910i	0.488055	+	0.845336i	0.999906	−	0.0137383i	$-0.00437318\pi$
$881$	14.4863	+	25.0910i	0.488055	+	0.845336i	−0.511851	+	0.859075i	$0.671040\pi$
$882$		0			0
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	−7.82617	−	4.25430i	−0.263223	−	0.143088i
$885$	1.16173			0.0390510
$886$	14.1325	+	24.4781i	0.474789	+	0.822359i
$887$	−15.7072	−	27.2057i	−0.527397	−	0.913478i	−0.999490	−	0.0319293i	$-0.989835\pi$
$887$	−15.7072	−	27.2057i	−0.527397	−	0.913478i	0.472094	−	0.881548i	$-0.343498\pi$
$888$	−9.77029	+	16.9226i	−0.327869	+	0.567886i
$889$		0			0
$890$	19.9295	−	34.5190i	0.668039	−	1.15708i
$891$	2.36000	−	4.08765i	0.0790631	−	0.136941i
$892$	3.00799			0.100715
$893$	−3.73242	+	6.46474i	−0.124901	+	0.216334i
$894$	−1.65032	−	2.85843i	−0.0551949	−	0.0956003i
$895$	15.7905	+	27.3499i	0.527818	+	0.914208i
$896$		0			0
$897$	−0.345925	−	13.4659i	−0.0115501	−	0.449613i
$898$	−16.7556			−0.559142
$899$	8.38459	+	14.5225i	0.279642	+	0.484354i
$900$	−11.1863	−	19.3753i	−0.372877	−	0.645843i
$901$	−9.08991	+	15.7442i	−0.302829	+	0.524515i
$902$	4.07480			0.135676
$903$		0			0
$904$	−19.1942	+	33.2453i	−0.638388	+	1.10572i
$905$	20.6657			0.686951
$906$	4.74337	−	8.21575i	0.157588	−	0.272950i
$907$	−4.86821	−	8.43198i	−0.161646	−	0.279979i	0.773813	−	0.633414i	$-0.218347\pi$
$907$	−4.86821	−	8.43198i	−0.161646	−	0.279979i	−0.935459	+	0.353435i	$0.885014\pi$
$908$	−16.7692	−	29.0452i	−0.556507	−	0.963898i
$909$	−15.3422			−0.508869
$910$		0			0
$911$	−38.4372			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$911$	−38.4372			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$912$	−0.0611867	−	0.105979i	−0.00202609	−	0.00350930i
$913$	−0.680984	−	1.17950i	−0.0225373	−	0.0390357i
$914$	−0.317871	+	0.550568i	−0.0105142	+	0.0182112i
$915$	−3.26817			−0.108042
$916$	−0.0437242	+	0.0757325i	−0.00144469	+	0.00250227i
$917$		0			0
$918$	6.06346			0.200124
$919$	−27.1402	+	47.0082i	−0.895273	+	1.55066i	−0.0618056	+	0.998088i	$0.519686\pi$
$919$	−27.1402	+	47.0082i	−0.895273	+	1.55066i	−0.833467	+	0.552569i	$0.813647\pi$
$920$	27.1054	+	46.9479i	0.893639	+	1.54783i
$921$	−7.34398	−	12.7202i	−0.241993	−	0.419143i
$922$	−28.2327			−0.929795
$923$	−0.319293	−	12.4292i	−0.0105097	−	0.409112i
$924$		0			0
$925$	36.2721	+	62.8251i	1.19262	+	2.06568i
$926$	−13.0869	−	22.6673i	−0.430064	−	0.744892i
$927$	5.29602	−	9.17297i	0.173944	−	0.301280i
$928$	10.5155			0.345190
$929$	−19.0960	+	33.0752i	−0.626519	+	1.08516i	0.361726	+	0.932284i	$0.382188\pi$
$929$	−19.0960	+	33.0752i	−0.626519	+	1.08516i	−0.988245	+	0.152878i	$0.951146\pi$
$930$	8.84526	−	15.3204i	0.290047	−	0.502377i
$931$		0			0
$932$	9.35660	−	16.2061i	0.306486	−	0.530849i
$933$	−3.25408	−	5.63622i	−0.106534	−	0.184522i
$934$	12.5994	+	21.8228i	0.412266	+	0.714065i
$935$	−5.98552			−0.195747
$936$	−0.661561	−	25.7527i	−0.0216238	−	0.841754i
$937$	19.0376			0.621931			0.310966	−	0.950421i	$-0.399348\pi$
$937$	19.0376			0.621931			0.310966	+	0.950421i	$0.399348\pi$
$938$		0			0
$939$	6.91392	+	11.9753i	0.225627	+	0.390798i
$940$	15.7845	−	27.3396i	0.514835	−	0.891720i
$941$	−46.1622			−1.50484			−0.752422	−	0.658682i	$-0.771114\pi$
$941$	−46.1622			−1.50484			−0.752422	+	0.658682i	$0.771114\pi$
$942$	−0.545619	+	0.945040i	−0.0177772	+	0.0307911i
$943$	−15.0616	+	26.0875i	−0.490474	+	0.849526i
$944$	0.0910198			0.00296244
$945$		0			0
$946$	1.49598	+	2.59111i	0.0486385	+	0.0842443i
$947$	4.59687	+	7.96201i	0.149378	+	0.258730i	0.930998	−	0.365025i	$-0.118940\pi$
$947$	4.59687	+	7.96201i	0.149378	+	0.258730i	−0.781620	+	0.623755i	$0.785606\pi$
$948$	−10.1988			−0.331241
$949$	−33.5210	+	20.5188i	−1.08814	+	0.666068i
$950$	6.04648			0.196174
$951$	−8.38440	−	14.5222i	−0.271883	−	0.470915i
$952$		0			0
$953$	22.3232	−	38.6648i	0.723118	−	1.25248i	−0.236626	−	0.971601i	$-0.576042\pi$
$953$	22.3232	−	38.6648i	0.723118	−	1.25248i	0.959744	−	0.280876i	$-0.0906250\pi$
$954$	−20.4743			−0.662879
$955$	2.26470	−	3.92258i	0.0732841	−	0.126932i
$956$	2.13937	−	3.70550i	0.0691923	−	0.119844i
$957$	−1.09012			−0.0352387
$958$	−5.99641	+	10.3861i	−0.193735	+	0.335559i
$959$		0			0
$960$	−5.14093	−	8.90436i	−0.165923	−	0.287387i
$961$	52.4271			1.69120
$962$	0.835363	+	32.5184i	0.0269332	+	1.04843i
$963$	36.1952			1.16637
$964$	5.47212	+	9.47799i	0.176245	+	0.305266i
$965$	−28.2638	−	48.9544i	−0.909845	−	1.57590i
$966$		0			0
$967$	13.8268			0.444639			0.222320	−	0.974974i	$-0.428637\pi$
$967$	13.8268			0.444639			0.222320	+	0.974974i	$0.428637\pi$
$968$	14.2096	−	24.6117i	0.456713	−	0.791050i
$969$	0.664689	−	1.15128i	0.0213529	−	0.0369843i
$970$	−1.48284			−0.0476113
$971$	3.63437	−	6.29491i	0.116632	−	0.202013i	−0.801799	−	0.597594i	$-0.796123\pi$
$971$	3.63437	−	6.29491i	0.116632	−	0.202013i	0.918431	+	0.395581i	$0.129457\pi$
$972$	−9.25454	−	16.0293i	−0.296839	−	0.514141i
$973$		0			0
$974$	14.2950			0.458043
$975$	14.3350	+	7.79247i	0.459086	+	0.249559i
$976$	−0.256057			−0.00819619
$977$	−21.4050	−	37.0746i	−0.684808	−	1.18612i	−0.973497	−	0.228699i	$-0.926553\pi$
$977$	−21.4050	−	37.0746i	−0.684808	−	1.18612i	0.288689	−	0.957423i	$-0.406781\pi$
$978$	3.34742	+	5.79790i	0.107039	+	0.185397i
$979$	−6.10982	+	10.5825i	−0.195271	+	0.338219i
$980$		0			0
$981$	−5.38489	+	9.32690i	−0.171926	+	0.297785i
$982$	9.22152	−	15.9721i	0.294270	−	0.509691i
$983$	46.3088			1.47702			0.738511	−	0.674242i	$-0.235529\pi$
$983$	46.3088			1.47702			0.738511	+	0.674242i	$0.235529\pi$
$984$	4.91410	−	8.51147i	0.156656	−	0.271336i
$985$	−44.0294	−	76.2612i	−1.40289	−	2.42988i
$986$	1.51324	+	2.62101i	0.0481914	+	0.0834700i
$987$		0			0
$988$	−4.19446	−	2.28010i	−0.133444	−	0.0725398i
$989$	−22.1182			−0.703319
$990$	−3.37047	−	5.83782i	−0.107121	−	0.185538i
$991$	29.1162	+	50.4307i	0.924907	+	1.60199i	0.791711	+	0.610896i	$0.209190\pi$
$991$	29.1162	+	50.4307i	0.924907	+	1.60199i	0.133195	+	0.991090i	$0.457476\pi$
$992$	26.1576	−	45.3062i	0.830504	−	1.43847i
$993$	−1.17885			−0.0374097
$994$		0			0
$995$	43.6703	−	75.6392i	1.38444	−	2.39792i
$996$	−1.27925			−0.0405346
$997$	−2.24739	+	3.89260i	−0.0711757	+	0.123280i	−0.899417	−	0.437092i	$-0.856008\pi$
$997$	−2.24739	+	3.89260i	−0.0711757	+	0.123280i	0.828241	+	0.560372i	$0.189342\pi$
$998$	−9.91765	−	17.1779i	−0.313938	−	0.543756i
$999$	19.4947	+	33.7658i	0.616786	+	1.06830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.j.393.4		12
7.2	even	3		637.2.g.l.263.4		12
7.3	odd	6		91.2.h.b.16.3	yes	12
7.4	even	3		637.2.h.l.471.3		12
7.5	odd	6		91.2.g.b.81.4	yes	12
7.6	odd	2		637.2.f.k.393.4		12
13.3	even	3		8281.2.a.ca.1.3		6
13.9	even	3	inner	637.2.f.j.295.4		12
13.10	even	6		8281.2.a.cf.1.4		6
21.5	even	6		819.2.n.d.172.3		12
21.17	even	6		819.2.s.d.289.4		12
91.3	odd	6		1183.2.e.h.170.4		12
91.9	even	3		637.2.h.l.165.3		12
91.10	odd	6		1183.2.e.g.170.3		12
91.48	odd	6		637.2.f.k.295.4		12
91.55	odd	6		8281.2.a.bz.1.3		6
91.61	odd	6		91.2.h.b.74.3	yes	12
91.62	odd	6		8281.2.a.ce.1.4		6
91.68	odd	6		1183.2.e.h.508.4		12
91.74	even	3		637.2.g.l.373.4		12
91.75	odd	6		1183.2.e.g.508.3		12
91.87	odd	6		91.2.g.b.9.4	✓	12
273.152	even	6		819.2.s.d.802.4		12
273.269	even	6		819.2.n.d.100.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	91.87	odd	6
91.2.g.b.81.4	yes	12	7.5	odd	6
91.2.h.b.16.3	yes	12	7.3	odd	6
91.2.h.b.74.3	yes	12	91.61	odd	6
637.2.f.j.295.4		12	13.9	even	3	inner
637.2.f.j.393.4		12	1.1	even	1	trivial
637.2.f.k.295.4		12	91.48	odd	6
637.2.f.k.393.4		12	7.6	odd	2
637.2.g.l.263.4		12	7.2	even	3
637.2.g.l.373.4		12	91.74	even	3
637.2.h.l.165.3		12	91.9	even	3
637.2.h.l.471.3		12	7.4	even	3
819.2.n.d.100.3		12	273.269	even	6
819.2.n.d.172.3		12	21.5	even	6
819.2.s.d.289.4		12	21.17	even	6
819.2.s.d.802.4		12	273.152	even	6
1183.2.e.g.170.3		12	91.10	odd	6
1183.2.e.g.508.3		12	91.75	odd	6
1183.2.e.h.170.4		12	91.3	odd	6
1183.2.e.h.508.4		12	91.68	odd	6
8281.2.a.bz.1.3		6	91.55	odd	6
8281.2.a.ca.1.3		6	13.3	even	3
8281.2.a.ce.1.4		6	91.62	odd	6
8281.2.a.cf.1.4		6	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)

\(f(q)\)	\(=\)	\(q+(0.425563 + 0.737096i) q^{2} +(0.330612 + 0.572636i) q^{3} +(0.637793 - 1.10469i) q^{4} -3.44148 q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +O(q^{10})\)	\(q+(0.425563 + 0.737096i) q^{2} +(0.330612 + 0.572636i) q^{3} +(0.637793 - 1.10469i) q^{4} -3.44148 q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(-1.46456 - 2.53670i) q^{10} +(0.448993 + 0.777679i) q^{11} +0.843447 q^{12} +(3.07517 - 1.88237i) q^{13} +(-1.13779 - 1.97071i) q^{15} +(-0.0891447 - 0.154403i) q^{16} +(0.968404 - 1.67733i) q^{17} +2.18125 q^{18} +(0.519020 - 0.898968i) q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} +(0.921723 + 1.59647i) q^{24} +6.84378 q^{25} +(2.69617 + 1.46563i) q^{26} +3.67824 q^{27} +(0.917969 + 1.58997i) q^{29} +(0.968404 - 1.67733i) q^{30} +9.13385 q^{31} +(2.86381 - 4.96026i) q^{32} +(-0.296885 + 0.514219i) q^{33} +1.64847 q^{34} +(-1.63452 - 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} +0.883501 q^{38} +(2.09460 + 1.13862i) q^{39} -9.59462 q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +1.14546 q^{44} +(-4.40988 + 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} -7.19129 q^{47} +(0.0589445 - 0.102095i) q^{48} +(2.91246 + 5.04452i) q^{50} +1.28066 q^{51} +(-0.118109 - 4.59767i) q^{52} -9.38648 q^{53} +(1.56532 + 2.71122i) q^{54} +(-1.54520 - 2.67637i) q^{55} +0.686375 q^{57} +(-0.781307 + 1.35326i) q^{58} +(-0.255259 + 0.442121i) q^{59} -2.90270 q^{60} +(0.718095 - 1.24378i) q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(-10.5831 + 6.47813i) q^{65} -0.505372 q^{66} +(4.22466 + 7.31732i) q^{67} +(-1.23528 - 2.13957i) q^{68} +(1.86800 - 3.23547i) q^{69} +(1.72419 - 2.98638i) q^{71} +(3.57244 - 6.18764i) q^{72} -10.9005 q^{73} +(-4.51097 + 7.81324i) q^{74} +(2.26263 + 3.91899i) q^{75} +(-0.662054 - 1.14671i) q^{76} +(0.0521095 + 2.02848i) q^{78} -12.0918 q^{79} +(0.306789 + 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(2.26886 - 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +3.33185 q^{86} +(-0.606982 + 1.05132i) q^{87} +(1.25176 + 2.16812i) q^{88} +(6.80391 + 11.7847i) q^{89} -7.50673 q^{90} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} +(-3.06035 - 5.30067i) q^{94} +(-1.78619 + 3.09378i) q^{95} +3.78723 q^{96} +(0.253120 - 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23} + 11 q^{24} - 14 q^{25} - 11 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} + 32 q^{31} + 8 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} - 34 q^{38} + 43 q^{39} - 10 q^{40} + 8 q^{41} - 11 q^{43} - 42 q^{44} + 7 q^{45} + 16 q^{46} - 2 q^{47} - 21 q^{48} + 6 q^{50} + 40 q^{51} + 16 q^{52} + 4 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} - 13 q^{59} - 40 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 14 q^{65} + 36 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 60 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} - 14 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} + 14 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} - 45 q^{94} - 6 q^{95} + 38 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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