LMFDB - Embedded newform 637.2.g.l.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.4
Root			$0.756174 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.l.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425563 + 0.737096i) q^{2} -0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 - 0.487385i) q^{6} +2.78793 q^{8} -2.56278 q^{9} +O(q^{10})$	\(q+(0.425563 + 0.737096i) q^{2} -0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 - 0.487385i) q^{6} +2.78793 q^{8} -2.56278 q^{9} +2.92913 q^{10} -0.897986 q^{11} +(-0.421723 + 0.730446i) 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} +(-1.09063 - 1.88902i) q^{18} -1.03804 q^{19} +(-2.19495 - 3.80177i) q^{20} +(-0.382150 - 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} -1.84345 q^{24} +(-3.42189 - 5.92688i) q^{25} +(-0.0788077 + 3.06776i) q^{26} +3.67824 q^{27} +(0.917969 - 1.58997i) q^{29} -1.93681 q^{30} +(-4.56692 - 7.91014i) q^{31} +(2.86381 - 4.96026i) q^{32} +0.593769 q^{33} +1.64847 q^{34} +(-1.63452 + 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} +(-0.441751 - 0.765135i) q^{38} +(-2.03338 - 1.24467i) q^{39} +(4.79731 - 8.30918i) q^{40} +(-2.66571 + 4.61715i) q^{41} +(1.95732 + 3.39018i) q^{43} +(-0.572729 + 0.991996i) q^{44} +(-4.40988 + 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} +(3.59565 - 6.22784i) q^{47} +(0.0589445 + 0.102095i) q^{48} +(2.91246 - 5.04452i) q^{50} +(-0.640331 + 1.10909i) q^{51} +(4.04076 - 2.19655i) q^{52} +(4.69324 + 8.12893i) q^{53} +(1.56532 + 2.71122i) q^{54} +(-1.54520 + 2.67637i) q^{55} +0.686375 q^{57} +1.56261 q^{58} +(-0.255259 + 0.442121i) q^{59} +(1.45135 + 2.51382i) q^{60} -1.43619 q^{61} +(3.88702 - 6.73252i) q^{62} +4.51834 q^{64} +(10.9018 - 5.92620i) q^{65} +(0.252686 + 0.437665i) q^{66} -8.44932 q^{67} +(-1.23528 - 2.13957i) q^{68} +(1.86800 + 3.23547i) q^{69} +(1.72419 + 2.98638i) q^{71} -7.14487 q^{72} +(5.45026 + 9.44013i) 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} +(6.04589 - 10.4718i) q^{79} -0.613579 q^{80} +5.25621 q^{81} -4.53771 q^{82} -1.51669 q^{83} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 + 2.88547i) q^{86} +(-0.606982 + 1.05132i) q^{87} -2.50353 q^{88} +(6.80391 + 11.7847i) q^{89} -7.50673 q^{90} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} +6.12069 q^{94} +(-1.78619 + 3.09378i) q^{95} +(-1.89362 + 3.27984i) q^{96} +(0.253120 + 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} - 22 q^{24} + 7 q^{25} - 5 q^{26} + 8 q^{27} + 3 q^{29} + 10 q^{30} - 16 q^{31} + 8 q^{32} + 32 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} + 17 q^{38} - 23 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} + 7 q^{45} + 16 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} + 25 q^{52} - 2 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} + 16 q^{58} - 13 q^{59} + 20 q^{60} - 10 q^{61} - 5 q^{62} - 30 q^{64} + 19 q^{65} - 18 q^{66} + 22 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} - 50 q^{72} + 30 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} - 14 q^{80} + 12 q^{81} + 2 q^{82} + 54 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} + 90 q^{94} - 6 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.425563	+	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	$0.736040\pi$
$3$	−0.661223			−0.381757			−0.190879	−	0.981614i	$-0.561134\pi$
$3$	−0.661223			−0.381757			−0.190879	+	0.981614i	$0.561134\pi$
$4$	0.637793	−	1.10469i	0.318896	−	0.552345i
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	−0.168276	−	0.985740i	$-0.553820\pi$
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	0.937814	−	0.347139i	$-0.112847\pi$
$6$	−0.281392	−	0.487385i	−0.114878	−	0.198974i
$7$		0			0
$7$		0			0
$8$	2.78793			0.985684
$9$	−2.56278			−0.854261
$10$	2.92913			0.926272
$11$	−0.897986			−0.270753			−0.135377	−	0.990794i	$-0.543224\pi$
$11$	−0.897986			−0.270753			−0.135377	+	0.990794i	$0.543224\pi$
$12$	−0.421723	+	0.730446i	−0.121741	+	0.210862i
$13$	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	$0.0911994\pi$
$18$	−1.09063	−	1.88902i	−0.257063	−	0.445246i
$19$	−1.03804			−0.238142			−0.119071	−	0.992886i	$-0.537992\pi$
$19$	−1.03804			−0.238142			−0.119071	+	0.992886i	$0.537992\pi$
$20$	−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	$-0.367171\pi$
$24$	−1.84345			−0.376292
$25$	−3.42189	−	5.92688i	−0.684378	−	1.18538i
$26$	−0.0788077	+	3.06776i	−0.0154555	+	0.601638i
$27$	3.67824			0.707878
$28$		0			0
$29$	0.917969	−	1.58997i	0.170463	−	0.295250i	−0.768119	−	0.640307i	$-0.778807\pi$
$29$	0.917969	−	1.58997i	0.170463	−	0.295250i	0.938582	+	0.345057i	$0.112140\pi$
$30$	−1.93681			−0.353611
$31$	−4.56692	−	7.91014i	−0.820244	−	1.42070i	−0.905501	−	0.424345i	$-0.860505\pi$
$31$	−4.56692	−	7.91014i	−0.820244	−	1.42070i	0.0852573	−	0.996359i	$-0.472829\pi$
$32$	2.86381	−	4.96026i	0.506254	−	0.876858i
$33$	0.593769			0.103362
$34$	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	$0.496600\pi$
$38$	−0.441751	−	0.765135i	−0.0716614	−	0.124121i
$39$	−2.03338	−	1.24467i	−0.325601	−	0.199306i
$40$	4.79731	−	8.30918i	0.758521	−	1.31380i
$41$	−2.66571	+	4.61715i	−0.416314	+	0.721078i	−0.995565	−	0.0940715i	$-0.970012\pi$
$41$	−2.66571	+	4.61715i	−0.416314	+	0.721078i	0.579251	+	0.815149i	$0.303345\pi$
$42$		0			0
$43$	1.95732	+	3.39018i	0.298489	+	0.516998i	0.975790	−	0.218708i	$-0.0701841\pi$
$43$	1.95732	+	3.39018i	0.298489	+	0.516998i	−0.677302	+	0.735706i	$0.736851\pi$
$44$	−0.572729	+	0.991996i	−0.0863422	+	0.149549i
$45$	−4.40988	+	7.63814i	−0.657387	+	1.13863i
$46$	2.40448	−	4.16469i	0.354522	−	0.614050i
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	−0.475115	−	0.879924i	$-0.657593\pi$
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	0.999594	−	0.0285004i	$-0.00907317\pi$
$48$	0.0589445	+	0.102095i	0.00850791	+	0.0147361i
$49$		0			0
$50$	2.91246	−	5.04452i	0.411883	−	0.713403i
$51$	−0.640331	+	1.10909i	−0.0896643	+	0.155303i
$52$	4.04076	−	2.19655i	0.560352	−	0.304607i
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	0.984378	+	0.176065i	$0.0563370\pi$
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	−0.339712	+	0.940529i	$0.610330\pi$
$54$	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
$58$	1.56261			0.205181
$59$	−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	$0.177247\pi$
$60$	1.45135	+	2.51382i	0.187369	+	0.324532i
$61$	−1.43619			−0.183885			−0.0919426	−	0.995764i	$-0.529308\pi$
$61$	−1.43619			−0.183885			−0.0919426	+	0.995764i	$0.529308\pi$
$62$	3.88702	−	6.73252i	0.493653	−	0.855031i
$63$		0			0
$64$	4.51834			0.564792
$65$	10.9018	−	5.92620i	1.35220	−	0.735055i
$66$	0.252686	+	0.437665i	0.0311035	+	0.0538729i
$67$	−8.44932			−1.03225			−0.516124	−	0.856514i	$-0.672626\pi$
$67$	−8.44932			−1.03225			−0.516124	+	0.856514i	$0.672626\pi$
$68$	−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	0.950013	−	0.312211i	$-0.101070\pi$
$71$	1.72419	+	2.98638i	0.204623	+	0.354418i	−0.745389	+	0.666629i	$0.767736\pi$
$72$	−7.14487			−0.842031
$73$	5.45026	+	9.44013i	0.637905	+	1.10488i	0.985892	+	0.167384i	$0.0535320\pi$
$73$	5.45026	+	9.44013i	0.637905	+	1.10488i	−0.347987	+	0.937499i	$0.613135\pi$
$74$	−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
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	−0.294699	−	0.955590i	$-0.595219\pi$
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	0.974915	−	0.222578i	$-0.0714472\pi$
$80$	−0.613579			−0.0686002
$81$	5.25621			0.584024
$82$	−4.53771			−0.501107
$83$	−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
$86$	−1.66593	+	2.88547i	−0.179642	+	0.311148i
$87$	−0.606982	+	1.05132i	−0.0650754	+	0.112714i
$88$	−2.50353			−0.266877
$89$	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
$94$	6.12069			0.631301
$95$	−1.78619	+	3.09378i	−0.183260	+	0.317415i
$96$	−1.89362	+	3.27984i	−0.193266	+	0.334747i
$97$	0.253120	+	0.438417i	0.0257005	+	0.0445145i	0.878590	−	0.477578i	$-0.158485\pi$
$97$	0.253120	+	0.438417i	0.0257005	+	0.0445145i	−0.852889	+	0.522092i	$0.825152\pi$
$98$		0			0
$99$	2.30134			0.231294
$100$	−8.72982			−0.872982
$101$	5.98654			0.595683			0.297842	−	0.954615i	$-0.403733\pi$
$101$	5.98654			0.595683			0.297842	+	0.954615i	$0.403733\pi$
$102$	−1.09000			−0.107927
$103$	−2.06651	+	3.57930i	−0.203619	+	0.352679i	−0.949692	−	0.313186i	$-0.898604\pi$
$103$	−2.06651	+	3.57930i	−0.203619	+	0.352679i	0.746073	+	0.665865i	$0.231937\pi$
$104$	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
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	0.948934	−	0.315475i	$-0.102164\pi$
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	−0.747677	+	0.664063i	$0.768831\pi$
$110$	−2.63032			−0.250791
$111$	−3.50449	−	6.06995i	−0.332631	−	0.576135i
$112$		0			0
$113$	−6.88472	−	11.9247i	−0.647660	−	1.12178i	−0.983680	−	0.179926i	$-0.942414\pi$
$113$	−6.88472	−	11.9247i	−0.647660	−	1.12178i	0.336020	−	0.941855i	$-0.390919\pi$
$114$	0.292096	+	0.505925i	0.0273573	+	0.0473842i
$115$	−19.4448			−1.81324
$116$	−1.17095	−	2.02814i	−0.108720	−	0.188308i
$117$	−7.88100	−	4.82410i	−0.728599	−	0.445989i
$118$	−0.434514			−0.0400003
$119$		0			0
$120$	−3.17209	+	5.49422i	−0.289571	+	0.501552i
$121$	−10.1936			−0.926693
$122$	−0.611189	−	1.05861i	−0.0553344	−	0.0958420i
$123$	1.76263	−	3.05297i	0.158931	−	0.275277i
$124$	−11.6510			−1.04629
$125$	−6.34531			−0.567542
$126$		0			0
$127$	−0.972482	+	1.68439i	−0.0862938	+	0.149465i	−0.905942	−	0.423402i	$-0.860836\pi$
$127$	−0.972482	+	1.68439i	−0.0862938	+	0.149465i	0.819648	+	0.572868i	$0.194169\pi$
$128$	−3.80478	−	6.59007i	−0.336298	−	0.582485i
$129$	−1.29423	−	2.24167i	−0.113950	−	0.197368i
$130$	9.00758	+	5.51370i	0.790017	+	0.483584i
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	0.473780	+	0.880643i	$0.342889\pi$
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	−0.999549	+	0.0300158i	$0.990444\pi$
$132$	0.378702	−	0.655931i	0.0329618	−	0.0570914i
$133$		0			0
$134$	−3.59571	−	6.22796i	−0.310622	−	0.538014i
$135$	6.32930	−	10.9627i	0.544739	−	0.943516i
$136$	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	$0.288124\pi$
$138$	−1.58990	+	2.75379i	−0.135341	+	0.234418i
$139$	2.10625	+	3.64813i	0.178650	+	0.309430i	0.941418	−	0.337241i	$-0.109494\pi$
$139$	2.10625	+	3.64813i	0.178650	+	0.309430i	−0.762769	+	0.646672i	$0.776160\pi$
$140$		0			0
$141$	−2.37752	+	4.11799i	−0.200224	+	0.346798i
$142$	−1.46750	+	2.54178i	−0.123150	+	0.213302i
$143$	−2.76146	−	1.69034i	−0.230925	−	0.141353i
$144$	0.228459	+	0.395702i	0.0190382	+	0.0329751i
$145$	−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
$149$	5.86484			0.480466			0.240233	−	0.970715i	$-0.422776\pi$
$149$	5.86484			0.480466			0.240233	+	0.970715i	$0.422776\pi$
$150$	−1.92578	+	3.33555i	−0.157240	+	0.272347i
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	0.973155	+	0.230150i	$0.0739216\pi$
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	−0.287262	+	0.957852i	$0.592745\pi$
$152$	−2.89398			−0.234733
$153$	−2.48181	+	4.29862i	−0.200643	+	0.347523i
$154$		0			0
$155$	−31.4339			−2.52483
$156$	−2.67184	+	1.45241i	−0.213919	+	0.116286i
$157$	−0.969500	−	1.67922i	−0.0773746	−	0.134017i	0.824742	−	0.565509i	$-0.191320\pi$
$157$	−0.969500	−	1.67922i	−0.0773746	−	0.134017i	−0.902116	+	0.431493i	$0.857987\pi$
$158$	10.2916			0.818757
$159$	−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
$163$	−11.8959			−0.931762			−0.465881	−	0.884847i	$-0.654262\pi$
$163$	−11.8959			−0.931762			−0.465881	+	0.884847i	$0.654262\pi$
$164$	3.40035	+	5.88957i	0.265522	+	0.459898i
$165$	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	−0.343787	−	0.939048i	$-0.611710\pi$
$167$	8.28801	−	14.3553i	0.641346	−	1.11084i	0.985133	−	0.171796i	$-0.0549569\pi$
$168$		0			0
$169$	5.91338	+	11.5772i	0.454875	+	0.890555i
$170$	2.83658	−	4.91310i	0.217556	−	0.376818i
$171$	2.66027			0.203436
$172$	4.99346			0.380748
$173$	9.98656			0.759264			0.379632	−	0.925138i	$-0.376051\pi$
$173$	9.98656			0.759264			0.379632	+	0.925138i	$0.376051\pi$
$174$	−1.03324			−0.0783295
$175$		0			0
$176$	0.0800507	+	0.138652i	0.00603405	+	0.0104513i
$177$	0.168783	−	0.292341i	0.0126865	−	0.0219737i
$178$	−5.79098	+	10.0303i	−0.434052	+	0.751801i
$179$	9.17657			0.685889			0.342945	−	0.939356i	$-0.388576\pi$
$179$	9.17657			0.685889			0.342945	+	0.939356i	$0.388576\pi$
$180$	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
$185$	36.4797			2.68204
$186$	−2.57019	+	4.45170i	−0.188456	+	0.326415i
$187$	−0.869614	+	1.50622i	−0.0635925	+	0.110145i
$188$	−4.58655	−	7.94415i	−0.334509	−	0.579386i
$189$		0			0
$190$	−3.04055			−0.220585
$191$	1.31612			0.0952313			0.0476156	−	0.998866i	$-0.484838\pi$
$191$	1.31612			0.0952313			0.0476156	+	0.998866i	$0.484838\pi$
$192$	−2.98763			−0.215614
$193$	−16.4254			−1.18233			−0.591163	−	0.806552i	$-0.701331\pi$
$193$	−16.4254			−1.18233			−0.591163	+	0.806552i	$0.701331\pi$
$194$	−0.215437	+	0.373148i	−0.0154675	+	0.0267905i
$195$	−7.20852	+	3.91854i	−0.516213	+	0.280613i
$196$		0			0
$197$	12.7938	−	22.1594i	0.911517	−	1.57879i	0.0995951	−	0.995028i	$-0.468245\pi$
$197$	12.7938	−	22.1594i	0.911517	−	1.57879i	0.811922	−	0.583766i	$-0.198421\pi$
$198$	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	$0.810578\pi$
$200$	−9.54000	−	16.5238i	−0.674580	−	1.16841i
$201$	5.58688			0.394068
$202$	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
$206$	−3.51772			−0.245091
$207$	7.24003	+	12.5401i	0.503217	+	0.871597i
$208$	0.0165082	−	0.642619i	0.00114464	−	0.0445576i
$209$	0.932145			0.0644778
$210$		0			0
$211$	2.84824	−	4.93330i	0.196081	−	0.339622i	−0.751173	−	0.660105i	$-0.770512\pi$
$211$	2.84824	−	4.93330i	0.196081	−	0.339622i	0.947254	+	0.320483i	$0.103845\pi$
$212$	11.9733			0.822327
$213$	−1.14007	−	1.97466i	−0.0781165	−	0.135302i
$214$	−6.01038	+	10.4103i	−0.410861	+	0.711633i
$215$	13.4722			0.918794
$216$	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
$220$	1.97104	+	3.41393i	0.132887	+	0.230167i
$221$	6.13536	−	3.33517i	0.412709	−	0.224348i
$222$	2.98276	−	5.16629i	0.200190	−	0.346739i
$223$	1.17906	−	2.04219i	0.0789558	−	0.136755i	−0.823844	−	0.566817i	$-0.808175\pi$
$223$	1.17906	−	2.04219i	0.0789558	−	0.136755i	0.902800	+	0.430061i	$0.141508\pi$
$224$		0			0
$225$	8.76956	+	15.1893i	0.584637	+	1.01262i
$226$	5.85976	−	10.1494i	0.389786	−	0.675129i
$227$	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
$229$	0.0342777	−	0.0593708i	0.00226514	−	0.00392333i	−0.864891	−	0.501960i	$-0.832612\pi$
$229$	0.0342777	−	0.0593708i	0.00226514	−	0.00392333i	0.867156	+	0.498037i	$0.165946\pi$
$230$	−8.27498	−	14.3327i	−0.545636	−	0.945069i
$231$		0			0
$232$	2.55924	−	4.43273i	0.168022	−	0.291023i
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	−0.999751	−	0.0223253i	$-0.992893\pi$
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	0.519210	+	0.854647i	$0.326226\pi$
$234$	0.201967	−	7.86202i	0.0132030	−	0.513956i
$235$	−12.3743	−	21.4330i	−0.807213	−	1.39813i
$236$	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	$0.465399\pi$
$240$	0.405713			0.0261886
$241$	−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	$0.255787\pi$
$242$	−4.33802	−	7.51368i	−0.278859	−	0.482998i
$243$	−14.5103			−0.930833
$244$	−0.915991	+	1.58654i	−0.0586403	+	0.101568i
$245$		0			0
$246$	3.00044			0.191301
$247$	−3.19215	−	1.95397i	−0.203112	−	0.124328i
$248$	−12.7323	−	22.0530i	−0.808501	−	1.40036i
$249$	1.00287			0.0635544
$250$	−2.70033	−	4.67711i	−0.170784	−	0.295806i
$251$	10.7575	+	18.6326i	0.679010	+	1.17608i	0.975280	+	0.220975i	$0.0709238\pi$
$251$	10.7575	+	18.6326i	0.679010	+	1.17608i	−0.296270	+	0.955104i	$0.595743\pi$
$252$		0			0
$253$	2.53687	+	4.39399i	0.159492	+	0.276248i
$254$	−1.65541			−0.103870
$255$	2.20369	+	3.81690i	0.138000	+	0.239023i
$256$	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
$261$	−2.35256	+	4.07475i	−0.145620	+	0.252221i
$262$	−10.2436			−0.632854
$263$	−8.95439			−0.552151			−0.276076	−	0.961136i	$-0.589034\pi$
$263$	−8.95439			−0.552151			−0.276076	+	0.961136i	$0.589034\pi$
$264$	1.65539			0.101882
$265$	32.3034			1.98438
$266$		0			0
$267$	−4.49890	−	7.79233i	−0.275328	−	0.476883i
$268$	−5.38891	+	9.33387i	−0.329180	+	0.570157i
$269$	−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	$0.213643\pi$
$270$	10.7740			0.655688
$271$	−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
$276$	4.76558			0.286854
$277$	−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	$0.203241\pi$
$278$	−1.79268	+	3.10502i	−0.107518	+	0.186226i
$279$	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	$0.417918\pi$
$282$	−4.04714			−0.241004
$283$	−15.2643			−0.907371			−0.453686	−	0.891162i	$-0.649891\pi$
$283$	−15.2643			−0.907371			−0.453686	+	0.891162i	$0.649891\pi$
$284$	4.39870			0.261015
$285$	1.18107	−	2.04568i	0.0699607	−	0.121176i
$286$	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
$291$	−0.167369	−	0.289892i	−0.00981135	−	0.0169938i
$292$	13.9045			0.813702
$293$	−2.96982	−	5.14388i	−0.173499	−	0.300509i	0.766142	−	0.642671i	$-0.222174\pi$
$293$	−2.96982	−	5.14388i	−0.173499	−	0.300509i	−0.939641	+	0.342163i	$0.888841\pi$
$294$		0			0
$295$	0.878467	+	1.52155i	0.0511463	+	0.0885881i
$296$	14.7761	+	25.5929i	0.858842	+	1.48756i
$297$	−3.30301			−0.191660
$298$	2.49586	+	4.32295i	0.144581	+	0.250422i
$299$	0.523159	−	20.3651i	0.0302551	−	1.17774i
$300$	5.77236			0.333267
$301$		0			0
$302$	−7.17362	+	12.4251i	−0.412796	+	0.714983i
$303$	−3.95844			−0.227406
$304$	0.0925356	+	0.160276i	0.00530728	+	0.00919248i
$305$	−2.47131	+	4.28043i	−0.141507	+	0.245097i
$306$	−4.22467			−0.241508
$307$	−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
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	0.971152	−	0.238463i	$-0.0766435\pi$
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	−0.692091	+	0.721811i	$0.743310\pi$
$312$	−5.66892	−	3.47005i	−0.320939	−	0.196453i
$313$	−10.4563	+	18.1108i	−0.591023	+	1.02368i	0.403072	+	0.915168i	$0.367942\pi$
$313$	−10.4563	+	18.1108i	−0.591023	+	1.02368i	−0.994095	+	0.108513i	$0.965391\pi$
$314$	0.825166	−	1.42923i	0.0465668	−	0.0806561i
$315$		0			0
$316$	−7.71205	−	13.3577i	−0.433837	−	0.751427i
$317$	12.6801	−	21.9626i	0.712188	−	1.23355i	−0.251847	−	0.967767i	$-0.581038\pi$
$317$	12.6801	−	21.9626i	0.712188	−	1.23355i	0.964034	−	0.265778i	$-0.0856288\pi$
$318$	2.64128	−	4.57483i	0.148116	−	0.256544i
$319$	−0.824324	+	1.42777i	−0.0461533	+	0.0799398i
$320$	7.77489	−	13.4665i	0.434629	−	0.752800i
$321$	−4.66935	−	8.08755i	−0.260618	−	0.451403i
$322$		0			0
$323$	−1.00524	+	1.74113i	−0.0559331	+	0.0968790i
$324$	3.35237	−	5.80648i	0.186243	−	0.322582i
$325$	0.633681	−	24.6674i	0.0351503	−	1.36830i
$326$	−5.06247	−	8.76845i	−0.280384	−	0.485640i
$327$	−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
$331$	1.78283			0.0979935			0.0489967	−	0.998799i	$-0.484398\pi$
$331$	1.78283			0.0979935			0.0489967	+	0.998799i	$0.484398\pi$
$332$	−0.967335	+	1.67547i	−0.0530894	+	0.0919536i
$333$	−13.5828	−	23.5261i	−0.744332	−	1.28922i
$334$	14.1083			0.771971
$335$	−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	$0.416138\pi$
$338$	−6.01701	+	9.28556i	−0.327282	+	0.505068i
$339$	4.55234	+	7.88488i	0.247249	+	0.428248i
$340$	−8.50240			−0.461107
$341$	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
$345$	12.8573			0.692216
$346$	4.24991	+	7.36106i	0.228477	+	0.395733i
$347$	−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	−0.0874885	−	0.996166i	$-0.527884\pi$
$349$	15.2994	−	26.4994i	0.818960	−	1.41848i	0.906449	−	0.422315i	$-0.138783\pi$
$350$		0			0
$351$	11.3112	+	6.92381i	0.603749	+	0.369565i
$352$	−2.57166	+	4.45425i	−0.137070	+	0.237412i
$353$	1.10035			0.0585655			0.0292828	−	0.999571i	$-0.490678\pi$
$353$	1.10035			0.0585655			0.0292828	+	0.999571i	$0.490678\pi$
$354$	0.287311			0.0152704
$355$	11.8675			0.629862
$356$	17.3579			0.919969
$357$		0			0
$358$	3.90521	+	6.76402i	0.206397	+	0.357489i
$359$	4.88693	−	8.46441i	0.257922	−	0.446734i	−0.707763	−	0.706450i	$-0.750295\pi$
$359$	4.88693	−	8.46441i	0.257922	−	0.446734i	0.965685	+	0.259716i	$0.0836288\pi$
$360$	−12.2945	+	21.2946i	−0.647975	+	1.12233i
$361$	−17.9225			−0.943288
$362$	−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
$367$	11.1473			0.581882			0.290941	−	0.956741i	$-0.406032\pi$
$367$	11.1473			0.581882			0.290941	+	0.956741i	$0.406032\pi$
$368$	−0.503679	+	0.872397i	−0.0262561	+	0.0454769i
$369$	6.83165	−	11.8328i	0.355641	−	0.615989i
$370$	15.5244	+	26.8891i	0.807076	+	1.39790i
$371$		0			0
$372$	7.70391			0.399429
$373$	−30.7301			−1.59115			−0.795573	−	0.605858i	$-0.792830\pi$
$373$	−30.7301			−1.59115			−0.795573	+	0.605858i	$0.792830\pi$
$374$	−1.48030			−0.0765445
$375$	4.19567			0.216663
$376$	10.0244	−	17.3628i	0.516970	−	0.895419i
$377$	5.81582	−	3.16147i	0.299530	−	0.162824i
$378$		0			0
$379$	−11.3286	+	19.6217i	−0.581912	+	1.00790i	0.413341	+	0.910576i	$0.364362\pi$
$379$	−11.3286	+	19.6217i	−0.581912	+	1.00790i	−0.995253	+	0.0973246i	$0.968972\pi$
$380$	2.27844	+	3.94638i	0.116882	+	0.202445i
$381$	0.643028	−	1.11376i	0.0329433	−	0.0570595i
$382$	0.560093	+	0.970109i	0.0286568	+	0.0496351i
$383$	0.589263			0.0301099			0.0150550	−	0.999887i	$-0.495208\pi$
$383$	0.589263			0.0301099			0.0150550	+	0.999887i	$0.495208\pi$
$384$	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
$388$	0.645753			0.0327832
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	0.784695	−	0.619883i	$-0.212820\pi$
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	−0.929181	+	0.369624i	$0.879486\pi$
$390$	−5.95602	−	3.64579i	−0.301595	−	0.184612i
$391$	−10.9432			−0.553422
$392$		0			0
$393$	3.97904	−	6.89191i	0.200716	−	0.347651i
$394$	21.7782			1.09717
$395$	−20.8068	−	36.0384i	−1.04690	−	1.81329i
$396$	1.46778	−	2.54227i	0.0737588	−	0.127754i
$397$	25.5283			1.28123			0.640614	−	0.767863i	$-0.278680\pi$
$397$	25.5283			1.28123			0.640614	+	0.767863i	$0.278680\pi$
$398$	−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	$-0.386381\pi$
$402$	2.37757	+	4.11807i	0.118582	+	0.205391i
$403$	0.845724	−	32.9217i	0.0421285	−	1.63995i
$404$	3.81817	−	6.61327i	0.189961	−	0.329022i
$405$	9.04457	−	15.6657i	0.449428	−	0.778433i
$406$		0			0
$407$	−4.75934	−	8.24341i	−0.235912	−	0.408611i
$408$	−1.78520	+	3.09206i	−0.0883807	+	0.153080i
$409$	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
$411$	2.88199	−	4.99175i	0.142158	−	0.246225i
$412$	2.63601	+	4.56570i	0.129867	+	0.224936i
$413$		0			0
$414$	−6.16217	+	10.6732i	−0.302854	+	0.524559i
$415$	−2.60983	+	4.52036i	−0.128112	+	0.221896i
$416$	18.1437	−	9.86292i	0.889570	−	0.483569i
$417$	−1.39270	−	2.41223i	−0.0682008	−	0.118127i
$418$	0.396686	+	0.687080i	0.0194026	+	0.0336062i
$419$	6.84795	−	11.8610i	0.334544	−	0.579447i	−0.648853	−	0.760914i	$-0.724751\pi$
$419$	6.84795	−	11.8610i	0.334544	−	0.579447i	0.983397	+	0.181466i	$0.0580844\pi$
$420$		0			0
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	4.84842			0.236017
$423$	−9.21486	+	15.9606i	−0.448042	+	0.776032i
$424$	13.0844	+	22.6629i	0.635437	+	1.10061i
$425$	−13.2551			−0.642966
$426$	0.970345	−	1.68069i	0.0470134	−	0.0814295i
$427$		0			0
$428$	18.0156			0.870816
$429$	1.82594	+	1.11769i	0.0881574	+	0.0539627i
$430$	5.73325	+	9.93028i	0.276482	+	0.478881i
$431$	22.2910			1.07372			0.536861	−	0.843671i	$-0.319610\pi$
$431$	22.2910			1.07372			0.536861	+	0.843671i	$0.319610\pi$
$432$	−0.327896	−	0.567932i	−0.0157759	−	0.0273246i
$433$	−12.9481	−	22.4268i	−0.622247	−	1.07776i	−0.989066	−	0.147472i	$-0.952886\pi$
$433$	−12.9481	−	22.4268i	−0.622247	−	1.07776i	0.366819	−	0.930292i	$-0.380447\pi$
$434$		0			0
$435$	2.08892	+	3.61811i	0.100156	+	0.173475i
$436$	5.36049			0.256721
$437$	2.93253	+	5.07929i	0.140282	+	0.242975i
$438$	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
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	0.137741	+	0.990468i	$0.456016\pi$
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	−0.926641	+	0.375947i	$0.877317\pi$
$444$	−8.94055			−0.424300
$445$	46.8310			2.22000
$446$	2.00706			0.0950370
$447$	−3.87796			−0.183421
$448$		0			0
$449$	−9.84320	−	17.0489i	−0.464529	−	0.804589i	0.534651	−	0.845073i	$-0.320443\pi$
$449$	−9.84320	−	17.0489i	−0.464529	−	0.804589i	−0.999180	+	0.0404845i	$0.987110\pi$
$450$	−7.46399	+	12.9280i	−0.351856	+	0.609433i
$451$	2.39377	−	4.14614i	0.112718	−	0.195234i
$452$	−17.5641			−0.826146
$453$	−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	$0.827772\pi$
$458$	0.0583493			0.00272648
$459$	3.56203	−	6.16961i	0.166261	−	0.287973i
$460$	−12.4017	+	21.4805i	−0.578235	+	1.00153i
$461$	−16.5855	−	28.7269i	−0.772464	−	1.33795i	−0.936209	−	0.351445i	$-0.885691\pi$
$461$	−16.5855	−	28.7269i	−0.772464	−	1.33795i	0.163744	−	0.986503i	$-0.447643\pi$
$462$		0			0
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	−0.327328			−0.0151958
$465$	20.7848			0.963874
$466$	−12.4863			−0.578414
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	0.288420	+	0.957504i	$0.406870\pi$
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	−0.973433	+	0.228973i	$0.926463\pi$
$468$	−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
$473$	−1.75765	−	3.04434i	−0.0808168	−	0.139979i
$474$	−6.80506			−0.312567
$475$	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
$479$	−14.0905			−0.643813			−0.321907	−	0.946771i	$-0.604324\pi$
$479$	−14.0905			−0.643813			−0.321907	+	0.946771i	$0.604324\pi$
$480$	6.51684	+	11.2875i	0.297452	+	0.515201i
$481$	−0.981481	+	38.2063i	−0.0447517	+	1.74206i
$482$	−7.30247			−0.332618
$483$		0			0
$484$	−6.50142	+	11.2608i	−0.295519	+	0.511854i
$485$	1.74222			0.0791100
$486$	−6.17502	−	10.6955i	−0.280105	−	0.485156i
$487$	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	$0.0424057\pi$
$488$	−4.00400			−0.181253
$489$	7.86587			0.355707
$490$		0			0
$491$	−10.8345	+	18.7659i	−0.488954	+	0.846893i	−0.999919	−	0.0127081i	$-0.995955\pi$
$491$	−10.8345	+	18.7659i	−0.488954	+	0.846893i	0.510965	+	0.859601i	$0.329288\pi$
$492$	−2.24839	−	3.89432i	−0.101365	−	0.175570i
$493$	−1.77793	−	3.07947i	−0.0800740	−	0.138692i
$494$	0.0818055	−	3.18446i	0.00368060	−	0.143276i
$495$	3.96001	−	6.85895i	0.177989	−	0.308287i
$496$	−0.814234	+	1.41029i	−0.0365602	+	0.0633241i
$497$		0			0
$498$	0.426785	+	0.739213i	0.0191247	+	0.0331249i
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	−0.478051	−	0.878332i	$-0.658656\pi$
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	0.999683	−	0.0251622i	$-0.00801023\pi$
$500$	−4.04699	+	7.00960i	−0.180987	+	0.313479i
$501$	−5.48023	+	9.49203i	−0.244838	+	0.424073i
$502$	−9.15601	+	15.8587i	−0.408653	+	0.707807i
$503$	−21.9415	−	38.0037i	−0.978322	−	1.69450i	−0.668506	−	0.743707i	$-0.733066\pi$
$503$	−21.9415	−	38.0037i	−0.978322	−	1.69450i	−0.309816	−	0.950796i	$-0.600268\pi$
$504$		0			0
$505$	10.3013	−	17.8423i	0.458401	−	0.793974i
$506$	−2.15919	+	3.73983i	−0.0959879	+	0.166256i
$507$	−3.91006	−	7.65512i	−0.173652	−	0.339976i
$508$	1.24048	+	2.14858i	0.0550376	+	0.0953279i
$509$	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
$513$	−3.81816			−0.168576
$514$	−2.10139	+	3.63972i	−0.0926886	+	0.160541i
$515$	7.11185	+	12.3181i	0.313386	+	0.542800i
$516$	−3.30179			−0.145353
$517$	−3.22884	+	5.59252i	−0.142004	+	0.245959i
$518$		0			0
$519$	−6.60335			−0.289855
$520$	30.3935	−	16.5219i	1.33284	−	0.724532i
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	0.626318	−	0.779568i	$-0.284561\pi$
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	−0.988284	+	0.152623i	$0.951228\pi$
$522$	−4.00464			−0.175278
$523$	−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
$527$	−17.6905			−0.770611
$528$	−0.0529314	−	0.0916798i	−0.00230354	−	0.00398985i
$529$	−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
$534$	3.82913	−	6.63225i	0.165703	−	0.287005i
$535$	48.6053			2.10139
$536$	−23.5561			−1.01747
$537$	−6.06776			−0.261843
$538$	−4.10536			−0.176995
$539$		0			0
$540$	−8.07356	−	13.9838i	−0.347431	−	0.601767i
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	0.153739	+	0.988112i	$0.450869\pi$
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	−0.932599	+	0.360914i	$0.882465\pi$
$542$	3.15829	−	5.47031i	0.135660	−	0.234970i
$543$	3.97057			0.170394
$544$	−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
$549$	3.68064			0.157086
$550$	−2.61535	+	4.52991i	−0.111519	+	0.193156i
$551$	−0.952888	+	1.65045i	−0.0405944	+	0.0703115i
$552$	5.20786	+	9.02027i	0.221661	+	0.383928i
$553$		0			0
$554$	−3.24816			−0.138001
$555$	−24.1213			−1.02389
$556$	5.37340			0.227883
$557$	10.8280			0.458796			0.229398	−	0.973333i	$-0.426324\pi$
$557$	10.8280			0.458796			0.229398	+	0.973333i	$0.426324\pi$
$558$	−9.96160	+	17.2540i	−0.421708	+	0.730420i
$559$	−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	$0.261009\pi$
$564$	3.03274	+	5.25285i	0.127701	+	0.221185i
$565$	−47.3873			−1.99360
$566$	−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	$-0.361504\pi$
$570$	2.01048			0.0842099
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	0.868191	−	0.496230i	$-0.165283\pi$
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	−0.863844	+	0.503760i	$0.831950\pi$
$572$	−3.62854	+	1.97247i	−0.151717	+	0.0824732i
$573$	−0.870251			−0.0363552
$574$		0			0
$575$	−19.3341	+	33.4876i	−0.806288	+	1.39653i
$576$	−11.5795			−0.482480
$577$	−1.66328	−	2.88089i	−0.0692434	−	0.119933i	0.829325	−	0.558766i	$-0.188725\pi$
$577$	−1.66328	−	2.88089i	−0.0692434	−	0.119933i	−0.898568	+	0.438833i	$0.855392\pi$
$578$	−5.63818	+	9.76562i	−0.234518	+	0.406196i
$579$	10.8609			0.451362
$580$	−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
$584$	15.1950	+	26.3185i	0.628772	+	1.08907i
$585$	−27.9389	+	15.1876i	−1.15513	+	0.627929i
$586$	2.52769	−	4.37809i	0.104418	−	0.180857i
$587$	−7.54051	+	13.0606i	−0.311230	+	0.539067i	−0.978629	−	0.205634i	$-0.934074\pi$
$587$	−7.54051	+	13.0606i	−0.311230	+	0.539067i	0.667399	+	0.744701i	$0.267408\pi$
$588$		0			0
$589$	4.74064	+	8.21104i	0.195335	+	0.338330i
$590$	−0.747686	+	1.29503i	−0.0307817	+	0.0533155i
$591$	−8.45953	+	14.6523i	−0.347978	+	0.602716i
$592$	0.944935	−	1.63668i	0.0388366	−	0.0672670i
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	−0.468609	−	0.883405i	$-0.655245\pi$
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	0.999356	−	0.0358751i	$-0.0114218\pi$
$594$	−1.40564	−	2.43464i	−0.0576740	−	0.0998944i
$595$		0			0
$596$	3.74055	−	6.47882i	0.153219	−	0.265383i
$597$	8.39052	−	14.5328i	0.343401	−	0.594788i
$598$	15.2337	−	8.28101i	0.622952	−	0.338636i
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	0.958477	+	0.285170i	$0.0920501\pi$
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	−0.232274	+	0.972650i	$0.574617\pi$
$600$	6.30807	+	10.9259i	0.257526	+	0.446048i
$601$	−13.6474	+	23.6379i	−0.556688	+	0.964212i	0.441082	+	0.897467i	$0.354595\pi$
$601$	−13.6474	+	23.6379i	−0.556688	+	0.964212i	−0.997770	+	0.0667449i	$0.978739\pi$
$602$		0			0
$603$	21.6538			0.881810
$604$	21.5023			0.874915
$605$	−17.5406	+	30.3811i	−0.713125	+	1.23517i
$606$	−1.68456	−	2.91775i	−0.0684308	−	0.118526i
$607$	38.9258			1.57995			0.789976	−	0.613138i	$-0.210093\pi$
$607$	38.9258			1.57995			0.789976	+	0.613138i	$0.210093\pi$
$608$	−2.97274	+	5.14894i	−0.120561	+	0.208817i
$609$		0			0
$610$	−4.20679			−0.170328
$611$	22.7803	−	12.3834i	0.921593	−	0.500977i
$612$	3.16576	+	5.48326i	0.127968	+	0.221648i
$613$	0.886645			0.0358113			0.0179056	−	0.999840i	$-0.494300\pi$
$613$	0.886645			0.0358113			0.0179056	+	0.999840i	$0.494300\pi$
$614$	−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	−0.968371	−	0.249515i	$-0.919729\pi$
$617$	−17.3944	−	30.1280i	−0.700272	−	1.21291i	0.268099	−	0.963391i	$-0.413605\pi$
$618$	2.32600			0.0935653
$619$	1.02781	+	1.78021i	0.0413111	+	0.0715529i	0.885942	−	0.463797i	$-0.153513\pi$
$619$	1.02781	+	1.78021i	0.0413111	+	0.0715529i	−0.844631	+	0.535350i	$0.820180\pi$
$620$	−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
$625$	6.19081	−	10.7228i	0.247632	−	0.428912i
$626$	−17.7992			−0.711398
$627$	−0.616356			−0.0246149
$628$	−2.47336			−0.0986979
$629$	20.5302			0.818593
$630$		0			0
$631$	22.6169	+	39.1736i	0.900363	+	1.55947i	0.827023	+	0.562168i	$0.190033\pi$
$631$	22.6169	+	39.1736i	0.900363	+	1.55947i	0.0733401	+	0.997307i	$0.476634\pi$
$632$	16.8555	−	29.1946i	0.670477	−	1.16130i
$633$	−1.88332	+	3.26201i	−0.0748554	+	0.129653i
$634$	21.5848			0.857241
$635$	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
$640$	−26.1881			−1.03518
$641$	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	$0.0438111\pi$
$642$	3.97420	−	6.88352i	0.156849	−	0.271671i
$643$	−5.26755	−	9.12367i	−0.207732	−	0.359802i	0.743268	−	0.668994i	$-0.233275\pi$
$643$	−5.26755	−	9.12367i	−0.207732	−	0.359802i	−0.951000	+	0.309192i	$0.899942\pi$
$644$		0			0
$645$	−8.90811			−0.350756
$646$	−1.71117			−0.0673252
$647$	24.1608			0.949860			0.474930	−	0.880024i	$-0.342473\pi$
$647$	24.1608			0.949860			0.474930	+	0.880024i	$0.342473\pi$
$648$	14.6540			0.575663
$649$	0.229219	−	0.397019i	0.00899762	−	0.0155843i
$650$	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
$655$	20.7098	+	35.8704i	0.809199	+	1.40157i
$656$	0.950537			0.0371122
$657$	−13.9678	−	24.1930i	−0.544937	−	0.943859i
$658$		0			0
$659$	2.10030	+	3.63782i	0.0818159	+	0.141709i	0.904030	−	0.427469i	$-0.140595\pi$
$659$	2.10030	+	3.63782i	0.0818159	+	0.141709i	−0.822214	+	0.569178i	$0.807261\pi$
$660$	−1.30329	−	2.25737i	−0.0507307	−	0.0878681i
$661$	−17.6726			−0.687385			−0.343693	−	0.939082i	$-0.611678\pi$
$661$	−17.6726			−0.687385			−0.343693	+	0.939082i	$0.611678\pi$
$662$	0.758708	+	1.31412i	0.0294880	+	0.0510748i
$663$	−4.05684	+	2.20529i	−0.157555	+	0.0856465i
$664$	−4.22844			−0.164095
$665$		0			0
$666$	11.5607	−	20.0236i	0.447966	−	0.775900i
$667$	−10.3733			−0.401655
$668$	−10.5721	−	18.3114i	−0.409046	−	0.708488i
$669$	−0.779623	+	1.35035i	−0.0301420	+	0.0522074i
$670$	−24.7491			−0.956143
$671$	1.28968			0.0497875
$672$		0			0
$673$	10.3052	−	17.8491i	0.397235	−	0.688031i	−0.596149	−	0.802874i	$-0.703303\pi$
$673$	10.3052	−	17.8491i	0.397235	−	0.688031i	0.993384	+	0.114843i	$0.0366366\pi$
$674$	4.06901	+	7.04774i	0.156733	+	0.271469i
$675$	−12.5865	−	21.8005i	−0.484456	−	0.839102i
$676$	16.5607	+	0.851419i	0.636952	+	0.0327469i
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	−0.994829	−	0.101567i	$-0.967614\pi$
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	0.585374	+	0.810763i	$0.300948\pi$
$678$	−3.87461	+	6.71102i	−0.148804	+	0.257735i
$679$		0			0
$680$	−9.29147	−	16.0933i	−0.356312	−	0.617150i
$681$	−8.69264	+	15.0561i	−0.333103	+	0.576951i
$682$	−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	$0.125767\pi$
$684$	1.69670	−	2.93877i	0.0648750	−	0.112367i
$685$	14.9999	+	25.9806i	0.573118	+	0.992670i
$686$		0			0
$687$	−0.0226652	+	0.0392573i	−0.000864732	+	0.00149776i
$688$	0.348970	−	0.604433i	0.0133043	−	0.0230438i
$689$	−0.869117	+	33.8323i	−0.0331107	+	1.28891i
$690$	5.47161	+	9.47710i	0.208301	+	0.360787i
$691$	−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
$695$	14.4972			0.549911
$696$	−1.69223	+	2.93102i	−0.0641437	+	0.111100i
$697$	5.16298	+	8.94254i	0.195562	+	0.338723i
$698$	26.0435			0.985761
$699$	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	$0.529774\pi$
$702$	−0.289874	+	11.2840i	−0.0109406	+	0.425886i
$703$	−5.50162	−	9.52908i	−0.207497	−	0.359396i
$704$	−4.05741			−0.152919
$705$	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
$709$	−4.64497			−0.174446			−0.0872228	−	0.996189i	$-0.527799\pi$
$709$	−4.64497			−0.174446			−0.0872228	+	0.996189i	$0.527799\pi$
$710$	5.05037	+	8.74749i	0.189537	+	0.328288i
$711$	−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
$716$	5.85275	−	10.1373i	0.218728	−	0.378847i
$717$	−2.21797			−0.0828315
$718$	8.31878			0.310454
$719$	−31.7413			−1.18375			−0.591875	−	0.806030i	$-0.701612\pi$
$719$	−31.7413			−1.18375			−0.591875	+	0.806030i	$0.701612\pi$
$720$	1.57247			0.0586025
$721$		0			0
$722$	−7.62714	−	13.2106i	−0.283853	−	0.491647i
$723$	2.83658	−	4.91309i	0.105493	−	0.182720i
$724$	−3.82987	+	6.63354i	−0.142336	+	0.246533i
$725$	−12.5647			−0.466643
$726$	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
$731$	7.58192			0.280427
$732$	0.605675	−	1.04906i	0.0223864	−	0.0387743i
$733$	−3.80104	+	6.58359i	−0.140395	+	0.243171i	−0.927645	−	0.373463i	$-0.878170\pi$
$733$	−3.80104	+	6.58359i	−0.140395	+	0.243171i	0.787251	+	0.616633i	$0.211504\pi$
$734$	4.74386	+	8.21660i	0.175099	+	0.303280i
$735$		0			0
$736$	−32.3618			−1.19287
$737$	7.58737			0.279484
$738$	11.6292			0.428076
$739$	−33.4236			−1.22951			−0.614754	−	0.788719i	$-0.710745\pi$
$739$	−33.4236			−1.22951			−0.614754	+	0.788719i	$0.710745\pi$
$740$	23.2665	−	40.2988i	0.855294	−	1.48141i
$741$	2.11072	+	1.29201i	0.0775394	+	0.0474632i
$742$		0			0
$743$	1.46912	−	2.54458i	0.0538966	−	0.0933517i	−0.837818	−	0.545949i	$-0.816169\pi$
$743$	1.46912	−	2.54458i	0.0538966	−	0.0933517i	0.891715	+	0.452597i	$0.149503\pi$
$744$	8.41888	+	14.5819i	0.308651	+	0.534599i
$745$	10.0919	−	17.4796i	0.369737	−	0.640403i
$746$	−13.0776	−	22.6511i	−0.478805	−	0.829314i
$747$	3.88695			0.142216
$748$	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	$0.840284\pi$
$752$	−1.28213			−0.0467545
$753$	−7.11313	−	12.3203i	−0.259217	−	0.448977i
$754$	4.80531	+	2.94141i	0.174999	+	0.107120i
$755$	58.0123			2.11128
$756$		0			0
$757$	−5.77321	+	9.99950i	−0.209831	+	0.363438i	−0.951661	−	0.307150i	$-0.900625\pi$
$757$	−5.77321	+	9.99950i	−0.209831	+	0.363438i	0.741830	+	0.670588i	$0.233958\pi$
$758$	−19.2841			−0.700432
$759$	−1.67744	−	2.90541i	−0.0608871	−	0.105460i
$760$	−4.97979	+	8.62525i	−0.180636	+	0.312871i
$761$	−34.6497			−1.25605			−0.628026	−	0.778192i	$-0.716137\pi$
$761$	−34.6497			−1.25605			−0.628026	+	0.778192i	$0.716137\pi$
$762$	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
$766$	0.250768	+	0.434344i	0.00906063	+	0.0156935i
$767$	−1.61720	+	0.879108i	−0.0583937	+	0.0317427i
$768$	−5.12890	+	8.88351i	−0.185073	+	0.320556i
$769$	−3.27437	+	5.67138i	−0.118077	+	0.204515i	−0.919006	−	0.394245i	$-0.871006\pi$
$769$	−3.27437	+	5.67138i	−0.118077	+	0.204515i	0.800929	+	0.598760i	$0.204340\pi$
$770$		0			0
$771$	−1.63253	−	2.82763i	−0.0587943	−	0.101835i
$772$	−10.4760	+	18.1450i	−0.377039	+	0.653051i
$773$	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
$775$	−31.2550	+	54.1352i	−1.12271	+	1.94459i
$776$	0.705683	+	1.22228i	0.0253325	+	0.0438772i
$777$		0			0
$778$	2.42547	−	4.20104i	0.0869575	−	0.150615i
$779$	2.76711	−	4.79278i	0.0991422	−	0.171719i
$780$	−0.268768	+	10.4624i	−0.00962345	+	0.374614i
$781$	−1.54830	−	2.68173i	−0.0554024	−	0.0959598i
$782$	−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
$786$	6.77333			0.241597
$787$	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	$0.0923876\pi$
$788$	−16.3195	−	28.2662i	−0.581359	−	1.00694i
$789$	5.92085			0.210788
$790$	17.7092	−	30.6732i	0.630065	−	1.09130i
$791$		0			0
$792$	6.41600			0.227983
$793$	−4.41653	−	2.70344i	−0.156836	−	0.0960019i
$794$	10.8639	+	18.8168i	0.385545	+	0.667784i
$795$	−21.3597			−0.757552
$796$	16.1864	+	28.0357i	0.573712	+	0.993699i
$797$	2.20956	+	3.82707i	0.0782667	+	0.135562i	0.902502	−	0.430685i	$-0.141728\pi$
$797$	2.20956	+	3.82707i	0.0782667	+	0.135562i	−0.824235	+	0.566247i	$0.808395\pi$
$798$		0			0
$799$	−6.96408	−	12.0621i	−0.246371	−	0.426728i
$800$	−39.1985			−1.38588
$801$	−17.4369	−	30.2017i	−0.616104	−	1.06712i
$802$	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
$807$	1.59469	−	2.76208i	0.0561356	−	0.0972298i
$808$	16.6901			0.587155
$809$	11.4716			0.403320			0.201660	−	0.979456i	$-0.435366\pi$
$809$	11.4716			0.403320			0.201660	+	0.979456i	$0.435366\pi$
$810$	15.3961			0.540965
$811$	−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
$814$	4.05079	−	7.01618i	0.141980	−	0.245917i
$815$	−20.4698	+	35.4548i	−0.717026	+	1.24193i
$816$	0.228329			0.00799310
$817$	−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	$-0.348401\pi$
$822$	4.90587			0.171112
$823$	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	$0.118699\pi$
$824$	−5.76129	+	9.97885i	−0.200704	+	0.347630i
$825$	−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	$0.369573\pi$
$828$	18.4706			0.641896
$829$	42.5611			1.47821			0.739104	−	0.673591i	$-0.235249\pi$
$829$	42.5611			1.47821			0.739104	+	0.673591i	$0.235249\pi$
$830$	−4.44259			−0.154204
$831$	1.26172	−	2.18536i	0.0437685	−	0.0758093i
$832$	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
$837$	−16.7982	−	29.0954i	−0.580632	−	1.00568i
$838$	11.6569			0.402682
$839$	0.920524	+	1.59439i	0.0317800	+	0.0550446i	0.881478	−	0.472225i	$-0.156549\pi$
$839$	0.920524	+	1.59439i	0.0317800	+	0.0550446i	−0.849698	+	0.527270i	$0.823216\pi$
$840$		0			0
$841$	12.8147	+	22.1957i	0.441885	+	0.765367i
$842$	1.46465	+	2.53686i	0.0504753	+	0.0874258i
$843$	−5.65332			−0.194711
$844$	−3.63317	−	6.29284i	−0.125059	−	0.216609i
$845$	44.6802	+	2.29709i	1.53705	+	0.0790224i
$846$	−15.6860			−0.539296
$847$		0			0
$848$	0.836755	−	1.44930i	0.0287343	−	0.0497692i
$849$	10.0931			0.346396
$850$	−5.64087	−	9.77027i	−0.193480	−	0.335118i
$851$	29.9457	−	51.8675i	1.02653	−	1.77800i
$852$	−2.90852			−0.0996442
$853$	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
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	0.973017	−	0.230732i	$-0.0741122\pi$
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	−0.686329	+	0.727291i	$0.740779\pi$
$858$	−0.0467936	+	1.82154i	−0.00159751	+	0.0621865i
$859$	25.8058	−	44.6969i	0.880482	−	1.52504i	0.0296769	−	0.999560i	$-0.490552\pi$
$859$	25.8058	−	44.6969i	0.880482	−	1.52504i	0.850806	−	0.525481i	$-0.176114\pi$
$860$	8.59245	−	14.8826i	0.293000	−	0.507491i
$861$		0			0
$862$	9.48624	+	16.4306i	0.323102	+	0.559630i
$863$	−10.9807	+	19.0191i	−0.373787	+	0.647417i	−0.990145	−	0.140049i	$-0.955274\pi$
$863$	−10.9807	+	19.0191i	−0.373787	+	0.647417i	0.616358	+	0.787466i	$0.288607\pi$
$864$	10.5338	−	18.2450i	0.358366	−	0.620709i
$865$	17.1843	−	29.7640i	0.584283	−	1.01201i
$866$	11.0205	−	19.0880i	0.374491	−	0.648638i
$867$	−4.38020	−	7.58673i	−0.148759	−	0.257659i
$868$		0			0
$869$	−5.42913	+	9.40352i	−0.184170	+	0.318993i
$870$	−1.77793	+	3.07947i	−0.0602775	+	0.104404i
$871$	−25.9831	−	15.9047i	−0.880404	−	0.538911i
$872$	5.85797	+	10.1463i	0.198376	+	0.343597i
$873$	−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
$877$	−9.61745			−0.324758			−0.162379	−	0.986728i	$-0.551917\pi$
$877$	−9.61745			−0.324758			−0.162379	+	0.986728i	$0.551917\pi$
$878$	11.9089	−	20.6268i	0.401905	−	0.696120i
$879$	1.96371	+	3.40125i	0.0662344	+	0.114721i
$880$	0.550986			0.0185737
$881$	14.4863	−	25.0910i	0.488055	−	0.845336i	−0.511851	−	0.859075i	$-0.671040\pi$
$881$	14.4863	−	25.0910i	0.488055	−	0.845336i	0.999906	+	0.0137383i	$0.00437318\pi$
$882$		0			0
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	0.228755	−	8.90481i	0.00769388	−	0.299501i
$885$	−0.580863	−	1.00608i	−0.0195255	−	0.0338191i
$886$	−28.2649			−0.949578
$887$	−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
$891$	−4.72001			−0.158126
$892$	−1.50399	−	2.60499i	−0.0503574	−	0.0872216i
$893$	−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
$898$	8.37780	−	14.5108i	0.279571	−	0.484231i
$899$	−16.7692			−0.559283
$900$	22.3726			0.745755
$901$	18.1798			0.605658
$902$	4.07480			0.135676
$903$		0			0
$904$	−19.1942	−	33.2453i	−0.638388	−	1.10572i
$905$	−10.3328	+	17.8970i	−0.343475	+	0.594917i
$906$	4.74337	−	8.21575i	0.157588	−	0.272950i
$907$	9.73642			0.323292			0.161646	−	0.986849i	$-0.448320\pi$
$907$	9.73642			0.323292			0.161646	+	0.986849i	$0.448320\pi$
$908$	−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
$913$	1.36197			0.0450746
$914$	−0.317871	+	0.550568i	−0.0105142	+	0.0182112i
$915$	1.63409	−	2.83032i	0.0540212	−	0.0935675i
$916$	−0.0437242	−	0.0757325i	−0.00144469	−	0.00250227i
$917$		0			0
$918$	6.06346			0.200124
$919$	54.2804			1.79055			0.895273	−	0.445519i	$-0.146981\pi$
$919$	54.2804			1.79055			0.895273	+	0.445519i	$0.146981\pi$
$920$	−54.2108			−1.78728
$921$	14.6880			0.483985
$922$	14.1164	−	24.4502i	0.464897	−	0.805226i
$923$	−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
$928$	−5.25777	−	9.10673i	−0.172595	−	0.298943i
$929$	38.1920			1.25304			0.626519	−	0.779406i	$-0.284479\pi$
$929$	38.1920			1.25304			0.626519	+	0.779406i	$0.284479\pi$
$930$	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
$934$	−25.1988			−0.824531
$935$	2.99276	+	5.18361i	0.0978736	+	0.169522i
$936$	−21.9717	−	13.4493i	−0.718168	−	0.439604i
$937$	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
$940$	−31.5691			−1.02967
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	0.946646	+	0.322275i	$0.104448\pi$
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	−0.194224	+	0.980957i	$0.562219\pi$
$942$	−0.545619	+	0.945040i	−0.0177772	+	0.0307911i
$943$	30.1232			0.980948
$944$	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	$0.785606\pi$
$948$	5.09938	+	8.83239i	0.165620	+	0.286863i
$949$	−1.00930	+	39.2894i	−0.0327634	+	1.27539i
$950$	−3.02324	+	5.23641i	−0.0980869	+	0.169892i
$951$	−8.38440	+	14.5222i	−0.271883	+	0.470915i
$952$		0			0
$953$	22.3232	+	38.6648i	0.723118	+	1.25248i	0.959744	+	0.280876i	$0.0906250\pi$
$953$	22.3232	+	38.6648i	0.723118	+	1.25248i	−0.236626	+	0.971601i	$0.576042\pi$
$954$	10.2371	−	17.7312i	0.331440	−	0.574070i
$955$	2.26470	−	3.92258i	0.0732841	−	0.126932i
$956$	2.13937	−	3.70550i	0.0691923	−	0.119844i
$957$	0.545062	−	0.944075i	0.0176194	−	0.0305176i
$958$	−5.99641	−	10.3861i	−0.193735	−	0.335559i
$959$		0			0
$960$	−5.14093	+	8.90436i	−0.165923	+	0.287387i
$961$	−26.2136	+	45.4032i	−0.845599	+	1.46462i
$962$	−28.5794	+	15.5357i	−0.921437	+	0.500892i
$963$	−18.0976	−	31.3459i	−0.583186	−	1.01011i
$964$	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	$0.428637\pi$
$968$	−28.4191			−0.913426
$969$	0.664689	−	1.15128i	0.0213529	−	0.0369843i
$970$	0.741422	+	1.28418i	0.0238056	+	0.0412326i
$971$	−7.26873			−0.233265			−0.116632	−	0.993175i	$-0.537210\pi$
$971$	−7.26873			−0.233265			−0.116632	+	0.993175i	$0.537210\pi$
$972$	−9.25454	+	16.0293i	−0.296839	+	0.514141i
$973$		0			0
$974$	14.2950			0.458043
$975$	−0.419005	+	16.3107i	−0.0134189	+	0.522360i
$976$	0.128029	+	0.221752i	0.00409810	+	0.00709811i
$977$	42.8101			1.36962			0.684808	−	0.728723i	$-0.259886\pi$
$977$	42.8101			1.36962			0.684808	+	0.728723i	$0.259886\pi$
$978$	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
$982$	−18.4430			−0.588541
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	−0.953166	−	0.302448i	$-0.902196\pi$
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	0.214655	−	0.976690i	$-0.431137\pi$
$984$	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
$989$	11.0591	−	19.1550i	0.351660	−	0.609092i
$990$	6.74094			0.214241
$991$	−58.2324			−1.84981			−0.924907	−	0.380194i	$-0.875857\pi$
$991$	−58.2324			−1.84981			−0.924907	+	0.380194i	$0.875857\pi$
$992$	−52.3151			−1.66101
$993$	−1.17885			−0.0374097
$994$		0			0
$995$	43.6703	+	75.6392i	1.38444	+	2.39792i
$996$	0.639625	−	1.10786i	0.0202673	−	0.0351040i
$997$	−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	$0.189342\pi$
$998$	19.8353			0.627875
$999$	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.g.l.373.4		12
7.2	even	3		637.2.f.j.295.4		12
7.3	odd	6		91.2.h.b.74.3	yes	12
7.4	even	3		637.2.h.l.165.3		12
7.5	odd	6		637.2.f.k.295.4		12
7.6	odd	2		91.2.g.b.9.4	✓	12
13.3	even	3		637.2.h.l.471.3		12
21.17	even	6		819.2.s.d.802.4		12
21.20	even	2		819.2.n.d.100.3		12
91.3	odd	6		91.2.g.b.81.4	yes	12
91.9	even	3		8281.2.a.ca.1.3		6
91.16	even	3		637.2.f.j.393.4		12
91.17	odd	6		1183.2.e.g.508.3		12
91.30	even	6		8281.2.a.cf.1.4		6
91.48	odd	6		1183.2.e.h.170.4		12
91.55	odd	6		91.2.h.b.16.3	yes	12
91.61	odd	6		8281.2.a.bz.1.3		6
91.68	odd	6		637.2.f.k.393.4		12
91.69	odd	6		1183.2.e.g.170.3		12
91.81	even	3	inner	637.2.g.l.263.4		12
91.82	odd	6		8281.2.a.ce.1.4		6
91.87	odd	6		1183.2.e.h.508.4		12
273.146	even	6		819.2.s.d.289.4		12
273.185	even	6		819.2.n.d.172.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	7.6	odd	2
91.2.g.b.81.4	yes	12	91.3	odd	6
91.2.h.b.16.3	yes	12	91.55	odd	6
91.2.h.b.74.3	yes	12	7.3	odd	6
637.2.f.j.295.4		12	7.2	even	3
637.2.f.j.393.4		12	91.16	even	3
637.2.f.k.295.4		12	7.5	odd	6
637.2.f.k.393.4		12	91.68	odd	6
637.2.g.l.263.4		12	91.81	even	3	inner
637.2.g.l.373.4		12	1.1	even	1	trivial
637.2.h.l.165.3		12	7.4	even	3
637.2.h.l.471.3		12	13.3	even	3
819.2.n.d.100.3		12	21.20	even	2
819.2.n.d.172.3		12	273.185	even	6
819.2.s.d.289.4		12	273.146	even	6
819.2.s.d.802.4		12	21.17	even	6
1183.2.e.g.170.3		12	91.69	odd	6
1183.2.e.g.508.3		12	91.17	odd	6
1183.2.e.h.170.4		12	91.48	odd	6
1183.2.e.h.508.4		12	91.87	odd	6
8281.2.a.bz.1.3		6	91.61	odd	6
8281.2.a.ca.1.3		6	91.9	even	3
8281.2.a.ce.1.4		6	91.82	odd	6
8281.2.a.cf.1.4		6	91.30	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.425563 + 0.737096i) q^{2} -0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 - 0.487385i) q^{6} +2.78793 q^{8} -2.56278 q^{9} +O(q^{10})\)	\(q+(0.425563 + 0.737096i) q^{2} -0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 - 0.487385i) q^{6} +2.78793 q^{8} -2.56278 q^{9} +2.92913 q^{10} -0.897986 q^{11} +(-0.421723 + 0.730446i) 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} +(-1.09063 - 1.88902i) q^{18} -1.03804 q^{19} +(-2.19495 - 3.80177i) q^{20} +(-0.382150 - 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} -1.84345 q^{24} +(-3.42189 - 5.92688i) q^{25} +(-0.0788077 + 3.06776i) q^{26} +3.67824 q^{27} +(0.917969 - 1.58997i) q^{29} -1.93681 q^{30} +(-4.56692 - 7.91014i) q^{31} +(2.86381 - 4.96026i) q^{32} +0.593769 q^{33} +1.64847 q^{34} +(-1.63452 + 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} +(-0.441751 - 0.765135i) q^{38} +(-2.03338 - 1.24467i) q^{39} +(4.79731 - 8.30918i) q^{40} +(-2.66571 + 4.61715i) q^{41} +(1.95732 + 3.39018i) q^{43} +(-0.572729 + 0.991996i) q^{44} +(-4.40988 + 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} +(3.59565 - 6.22784i) q^{47} +(0.0589445 + 0.102095i) q^{48} +(2.91246 - 5.04452i) q^{50} +(-0.640331 + 1.10909i) q^{51} +(4.04076 - 2.19655i) q^{52} +(4.69324 + 8.12893i) q^{53} +(1.56532 + 2.71122i) q^{54} +(-1.54520 + 2.67637i) q^{55} +0.686375 q^{57} +1.56261 q^{58} +(-0.255259 + 0.442121i) q^{59} +(1.45135 + 2.51382i) q^{60} -1.43619 q^{61} +(3.88702 - 6.73252i) q^{62} +4.51834 q^{64} +(10.9018 - 5.92620i) q^{65} +(0.252686 + 0.437665i) q^{66} -8.44932 q^{67} +(-1.23528 - 2.13957i) q^{68} +(1.86800 + 3.23547i) q^{69} +(1.72419 + 2.98638i) q^{71} -7.14487 q^{72} +(5.45026 + 9.44013i) 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} +(6.04589 - 10.4718i) q^{79} -0.613579 q^{80} +5.25621 q^{81} -4.53771 q^{82} -1.51669 q^{83} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 + 2.88547i) q^{86} +(-0.606982 + 1.05132i) q^{87} -2.50353 q^{88} +(6.80391 + 11.7847i) q^{89} -7.50673 q^{90} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} +6.12069 q^{94} +(-1.78619 + 3.09378i) q^{95} +(-1.89362 + 3.27984i) q^{96} +(0.253120 + 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} - 22 q^{24} + 7 q^{25} - 5 q^{26} + 8 q^{27} + 3 q^{29} + 10 q^{30} - 16 q^{31} + 8 q^{32} + 32 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} + 17 q^{38} - 23 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} + 7 q^{45} + 16 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} + 25 q^{52} - 2 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} + 16 q^{58} - 13 q^{59} + 20 q^{60} - 10 q^{61} - 5 q^{62} - 30 q^{64} + 19 q^{65} - 18 q^{66} + 22 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} - 50 q^{72} + 30 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} - 14 q^{80} + 12 q^{81} + 2 q^{82} + 54 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} + 90 q^{94} - 6 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

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