LMFDB - Embedded newform 637.2.i.a.489.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (of order $4$, 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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			489.6
Character	$\chi$	$=$	637.489
Dual form			637.2.i.a.538.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.577557 - 0.577557i) q^{2} +3.00778i q^{3} -1.33286i q^{4} +(-2.22392 + 2.22392i) q^{5} +(1.73717 - 1.73717i) q^{6} +(-1.92491 + 1.92491i) q^{8} -6.04677 q^{9} +O(q^{10})$	\(q+(-0.577557 - 0.577557i) q^{2} +3.00778i q^{3} -1.33286i q^{4} +(-2.22392 + 2.22392i) q^{5} +(1.73717 - 1.73717i) q^{6} +(-1.92491 + 1.92491i) q^{8} -6.04677 q^{9} +2.56888 q^{10} +(-0.359592 + 0.359592i) q^{11} +4.00894 q^{12} +(-1.73717 - 3.15947i) q^{13} +(-6.68907 - 6.68907i) q^{15} -0.442215 q^{16} +1.21331 q^{17} +(3.49235 + 3.49235i) q^{18} +(1.26036 - 1.26036i) q^{19} +(2.96417 + 2.96417i) q^{20} +0.415370 q^{22} -5.20963i q^{23} +(-5.78973 - 5.78973i) q^{24} -4.89165i q^{25} +(-0.821461 + 2.82809i) q^{26} -9.16401i q^{27} +1.64443 q^{29} +7.72665i q^{30} +(-2.66706 + 2.66706i) q^{31} +(4.10523 + 4.10523i) q^{32} +(-1.08158 - 1.08158i) q^{33} +(-0.700755 - 0.700755i) q^{34} +8.05946i q^{36} +(1.95377 - 1.95377i) q^{37} -1.45586 q^{38} +(9.50300 - 5.22502i) q^{39} -8.56172i q^{40} +(-5.55629 + 5.55629i) q^{41} -7.46499i q^{43} +(0.479284 + 0.479284i) q^{44} +(13.4475 - 13.4475i) q^{45} +(-3.00886 + 3.00886i) q^{46} +(-3.46629 - 3.46629i) q^{47} -1.33009i q^{48} +(-2.82521 + 2.82521i) q^{50} +3.64937i q^{51} +(-4.21112 + 2.31539i) q^{52} -8.61964 q^{53} +(-5.29274 + 5.29274i) q^{54} -1.59941i q^{55} +(3.79090 + 3.79090i) q^{57} +(-0.949749 - 0.949749i) q^{58} +(1.77084 + 1.77084i) q^{59} +(-8.91557 + 8.91557i) q^{60} -10.5050i q^{61} +3.08076 q^{62} -3.85758i q^{64} +(10.8897 + 3.16309i) q^{65} +1.24934i q^{66} +(-5.23514 - 5.23514i) q^{67} -1.61716i q^{68} +15.6695 q^{69} +(0.840390 + 0.840390i) q^{71} +(11.6395 - 11.6395i) q^{72} +(-1.72851 - 1.72851i) q^{73} -2.25682 q^{74} +14.7130 q^{75} +(-1.67988 - 1.67988i) q^{76} +(-8.50628 - 2.47078i) q^{78} -12.4114 q^{79} +(0.983450 - 0.983450i) q^{80} +9.42307 q^{81} +6.41815 q^{82} +(-7.31472 + 7.31472i) q^{83} +(-2.69830 + 2.69830i) q^{85} +(-4.31146 + 4.31146i) q^{86} +4.94608i q^{87} -1.38437i q^{88} +(6.90114 + 6.90114i) q^{89} -15.5334 q^{90} -6.94369 q^{92} +(-8.02193 - 8.02193i) q^{93} +4.00396i q^{94} +5.60589i q^{95} +(-12.3477 + 12.3477i) q^{96} +(-2.93184 + 2.93184i) q^{97} +(2.17437 - 2.17437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.577557	−	0.577557i	−0.408395	−	0.408395i	0.472784	−	0.881178i	$-0.343249\pi$
$2$	−0.577557	−	0.577557i	−0.408395	−	0.408395i	−0.881178	+	0.472784i	$0.843249\pi$
$3$			3.00778i			1.73654i	0.496088	+	0.868272i	$0.334769\pi$
$3$			3.00778i			1.73654i	−0.496088	+	0.868272i	$0.665231\pi$
$4$		−	1.33286i		−	0.666428i
$5$	−2.22392	+	2.22392i	−0.994568	+	0.994568i	−0.999985	−	0.00541754i	$-0.998276\pi$
$5$	−2.22392	+	2.22392i	−0.994568	+	0.994568i	0.00541754	+	0.999985i	$0.498276\pi$
$6$	1.73717	−	1.73717i	0.709196	−	0.709196i
$7$		0			0
$7$		0			0
$8$	−1.92491	+	1.92491i	−0.680560	+	0.680560i
$9$	−6.04677			−2.01559
$10$	2.56888			0.812352
$11$	−0.359592	+	0.359592i	−0.108421	+	0.108421i	−0.759236	−	0.650815i	$-0.774427\pi$
$11$	−0.359592	+	0.359592i	−0.108421	+	0.108421i	0.650815	+	0.759236i	$0.274427\pi$
$12$	4.00894			1.15728
$13$	−1.73717	−	3.15947i	−0.481804	−	0.876279i
$13$	−1.73717	−	3.15947i	−0.481804	−	0.876279i
$14$		0			0
$15$	−6.68907	−	6.68907i	−1.72711	−	1.72711i
$16$	−0.442215			−0.110554
$17$	1.21331			0.294270			0.147135	−	0.989116i	$-0.452995\pi$
$17$	1.21331			0.294270			0.147135	+	0.989116i	$0.452995\pi$
$18$	3.49235	+	3.49235i	0.823155	+	0.823155i
$19$	1.26036	−	1.26036i	0.289147	−	0.289147i	−0.547596	−	0.836743i	$-0.684457\pi$
$19$	1.26036	−	1.26036i	0.289147	−	0.289147i	0.836743	+	0.547596i	$0.184457\pi$
$20$	2.96417	+	2.96417i	0.662808	+	0.662808i
$21$		0			0
$22$	0.415370			0.0885572
$23$		−	5.20963i		−	1.08628i	−0.839641	−	0.543142i	$-0.817235\pi$
$23$		−	5.20963i		−	1.08628i	0.839641	−	0.543142i	$-0.182765\pi$
$24$	−5.78973	−	5.78973i	−1.18182	−	1.18182i
$25$		−	4.89165i		−	0.978330i
$26$	−0.821461	+	2.82809i	−0.161102	+	0.554634i
$27$		−	9.16401i		−	1.76361i
$28$		0			0
$29$	1.64443			0.305362			0.152681	−	0.988276i	$-0.451209\pi$
$29$	1.64443			0.305362			0.152681	+	0.988276i	$0.451209\pi$
$30$			7.72665i			1.41069i
$31$	−2.66706	+	2.66706i	−0.479017	+	0.479017i	−0.904817	−	0.425800i	$-0.859993\pi$
$31$	−2.66706	+	2.66706i	−0.479017	+	0.479017i	0.425800	+	0.904817i	$0.359993\pi$
$32$	4.10523	+	4.10523i	0.725710	+	0.725710i
$33$	−1.08158	−	1.08158i	−0.188278	−	0.188278i
$34$	−0.700755	−	0.700755i	−0.120178	−	0.120178i
$35$		0			0
$36$			8.05946i			1.34324i
$37$	1.95377	−	1.95377i	0.321197	−	0.321197i	−0.528029	−	0.849226i	$-0.677069\pi$
$37$	1.95377	−	1.95377i	0.321197	−	0.321197i	0.849226	+	0.528029i	$0.177069\pi$
$38$	−1.45586			−0.236172
$39$	9.50300	−	5.22502i	1.52170	−	0.836673i
$40$		−	8.56172i		−	1.35373i
$41$	−5.55629	+	5.55629i	−0.867747	+	0.867747i	−0.992223	−	0.124476i	$-0.960275\pi$
$41$	−5.55629	+	5.55629i	−0.867747	+	0.867747i	0.124476	+	0.992223i	$0.460275\pi$
$42$		0			0
$43$		−	7.46499i		−	1.13840i	−0.822199	−	0.569200i	$-0.807253\pi$
$43$		−	7.46499i		−	1.13840i	0.822199	−	0.569200i	$-0.192747\pi$
$44$	0.479284	+	0.479284i	0.0722548	+	0.0722548i
$45$	13.4475	−	13.4475i	2.00464	−	2.00464i
$46$	−3.00886	+	3.00886i	−0.443632	+	0.443632i
$47$	−3.46629	−	3.46629i	−0.505610	−	0.505610i	0.407566	−	0.913176i	$-0.366378\pi$
$47$	−3.46629	−	3.46629i	−0.505610	−	0.505610i	−0.913176	+	0.407566i	$0.866378\pi$
$48$		−	1.33009i		−	0.191981i
$49$		0			0
$50$	−2.82521	+	2.82521i	−0.399545	+	0.399545i
$51$			3.64937i			0.511014i
$52$	−4.21112	+	2.31539i	−0.583977	+	0.321087i
$53$	−8.61964			−1.18400			−0.591999	−	0.805939i	$-0.701661\pi$
$53$	−8.61964			−1.18400			−0.591999	+	0.805939i	$0.701661\pi$
$54$	−5.29274	+	5.29274i	−0.720251	+	0.720251i
$55$		−	1.59941i		−	0.215664i
$56$		0			0
$57$	3.79090	+	3.79090i	0.502117	+	0.502117i
$58$	−0.949749	−	0.949749i	−0.124708	−	0.124708i
$59$	1.77084	+	1.77084i	0.230543	+	0.230543i	0.812919	−	0.582376i	$-0.197877\pi$
$59$	1.77084	+	1.77084i	0.230543	+	0.230543i	−0.582376	+	0.812919i	$0.697877\pi$
$60$	−8.91557	+	8.91557i	−1.15100	+	1.15100i
$61$		−	10.5050i		−	1.34503i	−0.740085	−	0.672513i	$-0.765215\pi$
$61$		−	10.5050i		−	1.34503i	0.740085	−	0.672513i	$-0.234785\pi$
$62$	3.08076			0.391256
$63$		0			0
$64$		−	3.85758i		−	0.482198i
$65$	10.8897	+	3.16309i	1.35071	+	0.392333i
$66$			1.24934i			0.153783i
$67$	−5.23514	−	5.23514i	−0.639575	−	0.639575i	0.310876	−	0.950450i	$-0.399378\pi$
$67$	−5.23514	−	5.23514i	−0.639575	−	0.639575i	−0.950450	+	0.310876i	$0.899378\pi$
$68$		−	1.61716i		−	0.196110i
$69$	15.6695			1.88638
$70$		0			0
$71$	0.840390	+	0.840390i	0.0997360	+	0.0997360i	0.755214	−	0.655478i	$-0.227533\pi$
$71$	0.840390	+	0.840390i	0.0997360	+	0.0997360i	−0.655478	+	0.755214i	$0.727533\pi$
$72$	11.6395	−	11.6395i	1.37173	−	1.37173i
$73$	−1.72851	−	1.72851i	−0.202306	−	0.202306i	0.598681	−	0.800987i	$-0.295692\pi$
$73$	−1.72851	−	1.72851i	−0.202306	−	0.202306i	−0.800987	+	0.598681i	$0.795692\pi$
$74$	−2.25682			−0.262350
$75$	14.7130			1.69891
$76$	−1.67988	−	1.67988i	−0.192695	−	0.192695i
$77$		0			0
$78$	−8.50628	−	2.47078i	−0.963146	−	0.279760i
$79$	−12.4114			−1.39639			−0.698197	−	0.715906i	$-0.746014\pi$
$79$	−12.4114			−1.39639			−0.698197	+	0.715906i	$0.746014\pi$
$80$	0.983450	−	0.983450i	0.109953	−	0.109953i
$81$	9.42307			1.04701
$82$	6.41815			0.708766
$83$	−7.31472	+	7.31472i	−0.802894	+	0.802894i	−0.983547	−	0.180653i	$-0.942179\pi$
$83$	−7.31472	+	7.31472i	−0.802894	+	0.802894i	0.180653	+	0.983547i	$0.442179\pi$
$84$		0			0
$85$	−2.69830	+	2.69830i	−0.292672	+	0.292672i
$86$	−4.31146	+	4.31146i	−0.464916	+	0.464916i
$87$			4.94608i			0.530275i
$88$		−	1.38437i		−	0.147574i
$89$	6.90114	+	6.90114i	0.731519	+	0.731519i	0.970921	−	0.239402i	$-0.0769513\pi$
$89$	6.90114	+	6.90114i	0.731519	+	0.731519i	−0.239402	+	0.970921i	$0.576951\pi$
$90$	−15.5334			−1.63737
$91$		0			0
$92$	−6.94369			−0.723930
$93$	−8.02193	−	8.02193i	−0.831835	−	0.831835i
$94$			4.00396i			0.412977i
$95$			5.60589i			0.575152i
$96$	−12.3477	+	12.3477i	−1.26023	+	1.26023i
$97$	−2.93184	+	2.93184i	−0.297683	+	0.297683i	−0.840106	−	0.542423i	$-0.817507\pi$
$97$	−2.93184	+	2.93184i	−0.297683	+	0.297683i	0.542423	+	0.840106i	$0.317507\pi$
$98$		0			0
$99$	2.17437	−	2.17437i	0.218532	−	0.218532i
$100$	−6.51986			−0.651986
$101$	−15.4517			−1.53751			−0.768753	−	0.639546i	$-0.779122\pi$
$101$	−15.4517			−1.53751			−0.768753	+	0.639546i	$0.779122\pi$
$102$	2.10772	−	2.10772i	0.208695	−	0.208695i
$103$	−17.5006			−1.72438			−0.862192	−	0.506581i	$-0.830909\pi$
$103$	−17.5006			−1.72438			−0.862192	+	0.506581i	$0.830909\pi$
$104$	9.42561	+	2.73781i	0.924257	+	0.268464i
$105$		0			0
$106$	4.97833	+	4.97833i	0.483538	+	0.483538i
$107$	2.12416			0.205351			0.102675	−	0.994715i	$-0.467260\pi$
$107$	2.12416			0.205351			0.102675	+	0.994715i	$0.467260\pi$
$108$	−12.2143			−1.17532
$109$	7.57249	+	7.57249i	0.725313	+	0.725313i	0.969682	−	0.244369i	$-0.0785810\pi$
$109$	7.57249	+	7.57249i	0.725313	+	0.725313i	−0.244369	+	0.969682i	$0.578581\pi$
$110$	−0.923750	+	0.923750i	−0.0880761	+	0.0880761i
$111$	5.87651	+	5.87651i	0.557773	+	0.557773i
$112$		0			0
$113$	5.21100			0.490210			0.245105	−	0.969497i	$-0.421178\pi$
$113$	5.21100			0.490210			0.245105	+	0.969497i	$0.421178\pi$
$114$		−	4.37892i		−	0.410123i
$115$	11.5858	+	11.5858i	1.08038	+	1.08038i
$116$		−	2.19178i		−	0.203502i
$117$	10.5042	+	19.1046i	0.971118	+	1.76622i
$118$		−	2.04552i		−	0.188305i
$119$		0			0
$120$	25.7518			2.35081
$121$			10.7414i			0.976490i
$122$	−6.06723	+	6.06723i	−0.549301	+	0.549301i
$123$	−16.7121	−	16.7121i	−1.50688	−	1.50688i
$124$	3.55480	+	3.55480i	0.319231	+	0.319231i
$125$	−0.240960	−	0.240960i	−0.0215521	−	0.0215521i
$126$		0			0
$127$			11.4359i			1.01477i	0.861720	+	0.507384i	$0.169387\pi$
$127$			11.4359i			1.01477i	−0.861720	+	0.507384i	$0.830613\pi$
$128$	5.98249	−	5.98249i	0.528782	−	0.528782i
$129$	22.4531			1.97688
$130$	−4.46258	−	8.11631i	−0.391394	−	0.711847i
$131$			7.02026i			0.613363i	0.951812	+	0.306681i	$0.0992186\pi$
$131$			7.02026i			0.613363i	−0.951812	+	0.306681i	$0.900781\pi$
$132$	−1.44158	+	1.44158i	−0.125474	+	0.125474i
$133$		0			0
$134$			6.04719i			0.522398i
$135$	20.3800	+	20.3800i	1.75403	+	1.75403i
$136$	−2.33551	+	2.33551i	−0.200269	+	0.200269i
$137$	4.39804	−	4.39804i	0.375750	−	0.375750i	−0.493816	−	0.869566i	$-0.664398\pi$
$137$	4.39804	−	4.39804i	0.375750	−	0.375750i	0.869566	+	0.493816i	$0.164398\pi$
$138$	−9.05001	−	9.05001i	−0.770388	−	0.770388i
$139$		−	1.91666i		−	0.162569i	−0.996691	−	0.0812847i	$-0.974098\pi$
$139$		−	1.91666i		−	0.162569i	0.996691	−	0.0812847i	$-0.0259023\pi$
$140$		0			0
$141$	10.4259	−	10.4259i	0.878015	−	0.878015i
$142$		−	0.970747i		−	0.0814633i
$143$	1.76079	+	0.511449i	0.147245	+	0.0427695i
$144$	2.67397			0.222831
$145$	−3.65707	+	3.65707i	−0.303703	+	0.303703i
$146$			1.99662i			0.165242i
$147$		0			0
$148$	−2.60409	−	2.60409i	−0.214055	−	0.214055i
$149$	0.789668	+	0.789668i	0.0646922	+	0.0646922i	0.738713	−	0.674020i	$-0.235434\pi$
$149$	0.789668	+	0.789668i	0.0646922	+	0.0646922i	−0.674020	+	0.738713i	$0.735434\pi$
$150$	−8.49762	−	8.49762i	−0.693827	−	0.693827i
$151$	−9.31908	+	9.31908i	−0.758376	+	0.758376i	−0.976027	−	0.217651i	$-0.930161\pi$
$151$	−9.31908	+	9.31908i	−0.758376	+	0.758376i	0.217651	+	0.976027i	$0.430161\pi$
$152$			4.85218i			0.393564i
$153$	−7.33659			−0.593128
$154$		0			0
$155$		−	11.8626i		−	0.952831i
$156$	−6.96420	−	12.6661i	−0.557582	−	1.01410i
$157$		−	13.9041i		−	1.10967i	−0.831962	−	0.554833i	$-0.812782\pi$
$157$		−	13.9041i		−	1.10967i	0.831962	−	0.554833i	$-0.187218\pi$
$158$	7.16831	+	7.16831i	0.570280	+	0.570280i
$159$		−	25.9260i		−	2.05607i
$160$	−18.2594			−1.44353
$161$		0			0
$162$	−5.44236	−	5.44236i	−0.427592	−	0.427592i
$163$	−5.78900	+	5.78900i	−0.453429	+	0.453429i	−0.896491	−	0.443062i	$-0.853892\pi$
$163$	−5.78900	+	5.78900i	−0.453429	+	0.453429i	0.443062	+	0.896491i	$0.353892\pi$
$164$	7.40573	+	7.40573i	0.578290	+	0.578290i
$165$	4.81068			0.374511
$166$	8.44933			0.655795
$167$	1.97146	+	1.97146i	0.152556	+	0.152556i	0.779259	−	0.626702i	$-0.215596\pi$
$167$	1.97146	+	1.97146i	0.152556	+	0.152556i	−0.626702	+	0.779259i	$0.715596\pi$
$168$		0			0
$169$	−6.96450	+	10.9771i	−0.535731	+	0.844389i
$170$	3.11685			0.239051
$171$	−7.62111	+	7.62111i	−0.582801	+	0.582801i
$172$	−9.94975			−0.758661
$173$	−1.80377			−0.137138			−0.0685690	−	0.997646i	$-0.521843\pi$
$173$	−1.80377			−0.137138			−0.0685690	+	0.997646i	$0.521843\pi$
$174$	2.85664	−	2.85664i	0.216561	−	0.216561i
$175$		0			0
$176$	0.159017	−	0.159017i	0.0119863	−	0.0119863i
$177$	−5.32630	+	5.32630i	−0.400349	+	0.400349i
$178$		−	7.97160i		−	0.597497i
$179$		−	17.1126i		−	1.27905i	−0.768769	−	0.639527i	$-0.779130\pi$
$179$		−	17.1126i		−	1.27905i	0.768769	−	0.639527i	$-0.220870\pi$
$180$	−17.9236	−	17.9236i	−1.33595	−	1.33595i
$181$	23.4682			1.74438			0.872190	−	0.489168i	$-0.162699\pi$
$181$	23.4682			1.74438			0.872190	+	0.489168i	$0.162699\pi$
$182$		0			0
$183$	31.5967			2.33570
$184$	10.0281	+	10.0281i	0.739281	+	0.739281i
$185$			8.69005i			0.638905i
$186$			9.26625i			0.679434i
$187$	−0.436296	+	0.436296i	−0.0319051	+	0.0319051i
$188$	−4.62006	+	4.62006i	−0.336953	+	0.336953i
$189$		0			0
$190$	3.23772	−	3.23772i	0.234889	−	0.234889i
$191$	25.2469			1.82680			0.913400	−	0.407063i	$-0.133447\pi$
$191$	25.2469			1.82680			0.913400	+	0.407063i	$0.133447\pi$
$192$	11.6028			0.837359
$193$	3.77593	−	3.77593i	0.271798	−	0.271798i	−0.558026	−	0.829824i	$-0.688441\pi$
$193$	3.77593	−	3.77593i	0.271798	−	0.271798i	0.829824	+	0.558026i	$0.188441\pi$
$194$	3.38661			0.243144
$195$	−9.51389	+	32.7540i	−0.681304	+	2.34556i
$196$		0			0
$197$	−10.7141	−	10.7141i	−0.763345	−	0.763345i	0.213580	−	0.976926i	$-0.431487\pi$
$197$	−10.7141	−	10.7141i	−0.763345	−	0.763345i	−0.976926	+	0.213580i	$0.931487\pi$
$198$	−2.51164			−0.178495
$199$	7.18030			0.508998			0.254499	−	0.967073i	$-0.418089\pi$
$199$	7.18030			0.508998			0.254499	+	0.967073i	$0.418089\pi$
$200$	9.41601	+	9.41601i	0.665812	+	0.665812i
$201$	15.7462	−	15.7462i	1.11065	−	1.11065i
$202$	8.92426	+	8.92426i	0.627909	+	0.627909i
$203$		0			0
$204$	4.86408			0.340554
$205$		−	24.7135i		−	1.72607i
$206$	10.1076	+	10.1076i	0.704229	+	0.704229i
$207$			31.5014i			2.18950i
$208$	0.768201	+	1.39716i	0.0532651	+	0.0968759i
$209$			0.906432i			0.0626992i
$210$		0			0
$211$	−2.72556			−0.187636			−0.0938178	−	0.995589i	$-0.529907\pi$
$211$	−2.72556			−0.187636			−0.0938178	+	0.995589i	$0.529907\pi$
$212$			11.4887i			0.789049i
$213$	−2.52771	+	2.52771i	−0.173196	+	0.173196i
$214$	−1.22683	−	1.22683i	−0.0838640	−	0.0838640i
$215$	16.6015	+	16.6015i	1.13222	+	1.13222i
$216$	17.6399	+	17.6399i	1.20025	+	1.20025i
$217$		0			0
$218$		−	8.74709i		−	0.592428i
$219$	5.19897	−	5.19897i	0.351314	−	0.351314i
$220$	−2.13178			−0.143725
$221$	−2.10772	−	3.83341i	−0.141781	−	0.257863i
$222$		−	6.78804i		−	0.455583i
$223$	−15.3311	+	15.3311i	−1.02665	+	1.02665i	−0.0270132	+	0.999635i	$0.508600\pi$
$223$	−15.3311	+	15.3311i	−1.02665	+	1.02665i	−0.999635	+	0.0270132i	$0.991400\pi$
$224$		0			0
$225$			29.5787i			1.97191i
$226$	−3.00965	−	3.00965i	−0.200199	−	0.200199i
$227$	−12.7981	+	12.7981i	−0.849440	+	0.849440i	−0.990063	−	0.140624i	$-0.955089\pi$
$227$	−12.7981	+	12.7981i	−0.849440	+	0.849440i	0.140624	+	0.990063i	$0.455089\pi$
$228$	5.05272	−	5.05272i	0.334624	−	0.334624i
$229$	3.05665	+	3.05665i	0.201989	+	0.201989i	0.800852	−	0.598863i	$-0.204381\pi$
$229$	3.05665	+	3.05665i	0.201989	+	0.201989i	−0.598863	+	0.800852i	$0.704381\pi$
$230$		−	13.3829i		−	0.882445i
$231$		0			0
$232$	−3.16538	+	3.16538i	−0.207817	+	0.207817i
$233$			9.88801i			0.647785i	0.946094	+	0.323892i	$0.104992\pi$
$233$			9.88801i			0.647785i	−0.946094	+	0.323892i	$0.895008\pi$
$234$	4.96718	−	17.1008i	0.324715	−	1.11791i
$235$	15.4175			1.00573
$236$	2.36027	−	2.36027i	0.153640	−	0.153640i
$237$		−	37.3309i		−	2.42490i
$238$		0			0
$239$	−8.13735	−	8.13735i	−0.526361	−	0.526361i	0.393124	−	0.919485i	$-0.371394\pi$
$239$	−8.13735	−	8.13735i	−0.526361	−	0.526361i	−0.919485	+	0.393124i	$0.871394\pi$
$240$	2.95801	+	2.95801i	0.190939	+	0.190939i
$241$	−10.3056	−	10.3056i	−0.663840	−	0.663840i	0.292443	−	0.956283i	$-0.405532\pi$
$241$	−10.3056	−	10.3056i	−0.663840	−	0.663840i	−0.956283	+	0.292443i	$0.905532\pi$
$242$	6.20377	−	6.20377i	0.398793	−	0.398793i
$243$			0.850534i			0.0545618i
$244$	−14.0016			−0.896362
$245$		0			0
$246$			19.3044i			1.23080i
$247$	−6.17154	−	1.79262i	−0.392685	−	0.114061i
$248$		−	10.2677i		−	0.652000i
$249$	−22.0011	−	22.0011i	−1.39426	−	1.39426i
$250$			0.278336i			0.0176035i
$251$	2.29786			0.145040			0.0725198	−	0.997367i	$-0.476896\pi$
$251$	2.29786			0.145040			0.0725198	+	0.997367i	$0.476896\pi$
$252$		0			0
$253$	1.87334	+	1.87334i	0.117776	+	0.117776i
$254$	6.60486	−	6.60486i	0.414426	−	0.414426i
$255$	−8.11591	−	8.11591i	−0.508238	−	0.508238i
$256$	−14.6256			−0.914102
$257$	−18.0503			−1.12595			−0.562974	−	0.826474i	$-0.690343\pi$
$257$	−18.0503			−1.12595			−0.562974	+	0.826474i	$0.690343\pi$
$258$	−12.9679	−	12.9679i	−0.807348	−	0.807348i
$259$		0			0
$260$	4.21594	−	14.5144i	0.261462	−	0.900148i
$261$	−9.94345			−0.615484
$262$	4.05460	−	4.05460i	0.250494	−	0.250494i
$263$	7.96336			0.491042			0.245521	−	0.969391i	$-0.421041\pi$
$263$	7.96336			0.491042			0.245521	+	0.969391i	$0.421041\pi$
$264$	4.16388			0.256269
$265$	19.1694	−	19.1694i	1.17757	−	1.17757i
$266$		0			0
$267$	−20.7571	+	20.7571i	−1.27032	+	1.27032i
$268$	−6.97769	+	6.97769i	−0.426230	+	0.426230i
$269$		−	8.04889i		−	0.490750i	−0.969428	−	0.245375i	$-0.921089\pi$
$269$		−	8.04889i		−	0.490750i	0.969428	−	0.245375i	$-0.0789110\pi$
$270$		−	23.5413i		−	1.43268i
$271$	15.7041	+	15.7041i	0.953953	+	0.953953i	0.998986	−	0.0450322i	$-0.0143390\pi$
$271$	15.7041	+	15.7041i	0.953953	+	0.953953i	−0.0450322	+	0.998986i	$0.514339\pi$
$272$	−0.536543			−0.0325327
$273$		0			0
$274$	−5.08024			−0.306909
$275$	1.75900	+	1.75900i	0.106072	+	0.106072i
$276$		−	20.8851i		−	1.25714i
$277$			1.47020i			0.0883356i	0.999024	+	0.0441678i	$0.0140636\pi$
$277$			1.47020i			0.0883356i	−0.999024	+	0.0441678i	$0.985936\pi$
$278$	−1.10698	+	1.10698i	−0.0663925	+	0.0663925i
$279$	16.1271	−	16.1271i	0.965502	−	0.965502i
$280$		0			0
$281$	−13.2274	+	13.2274i	−0.789081	+	0.789081i	−0.981343	−	0.192263i	$-0.938417\pi$
$281$	−13.2274	+	13.2274i	−0.789081	+	0.789081i	0.192263	+	0.981343i	$0.438417\pi$
$282$	−12.0431			−0.717153
$283$	−4.78654			−0.284530			−0.142265	−	0.989829i	$-0.545439\pi$
$283$	−4.78654			−0.284530			−0.142265	+	0.989829i	$0.545439\pi$
$284$	1.12012	−	1.12012i	0.0664668	−	0.0664668i
$285$	−16.8613			−0.998778
$286$	−0.721567	−	1.31235i	−0.0426671	−	0.0776008i
$287$		0			0
$288$	−24.8234	−	24.8234i	−1.46273	−	1.46273i
$289$	−15.5279			−0.913405
$290$	4.22434			0.248062
$291$	−8.81833	−	8.81833i	−0.516940	−	0.516940i
$292$	−2.30385	+	2.30385i	−0.134822	+	0.134822i
$293$	−15.3136	−	15.3136i	−0.894628	−	0.894628i	0.100326	−	0.994955i	$-0.468011\pi$
$293$	−15.3136	−	15.3136i	−0.894628	−	0.894628i	−0.994955	+	0.100326i	$0.968011\pi$
$294$		0			0
$295$	−7.87640			−0.458582
$296$			7.52167i			0.437188i
$297$	3.29531	+	3.29531i	0.191213	+	0.191213i
$298$		−	0.912157i		−	0.0528399i
$299$	−16.4597	+	9.05001i	−0.951888	+	0.523375i
$300$		−	19.6103i		−	1.13220i
$301$		0			0
$302$	10.7646			0.619433
$303$		−	46.4755i		−	2.66995i
$304$	−0.557350	+	0.557350i	−0.0319662	+	0.0319662i
$305$	23.3623	+	23.3623i	1.33772	+	1.33772i
$306$	4.23730	+	4.23730i	0.242230	+	0.242230i
$307$	9.36619	+	9.36619i	0.534556	+	0.534556i	0.921925	−	0.387369i	$-0.126616\pi$
$307$	9.36619	+	9.36619i	0.534556	+	0.534556i	−0.387369	+	0.921925i	$0.626616\pi$
$308$		0			0
$309$		−	52.6380i		−	2.99447i
$310$	−6.85136	+	6.85136i	−0.389131	+	0.389131i
$311$	5.42164			0.307433			0.153716	−	0.988115i	$-0.450876\pi$
$311$	5.42164			0.307433			0.153716	+	0.988115i	$0.450876\pi$
$312$	−8.23474	+	28.3502i	−0.466201	+	1.60501i
$313$		−	21.0929i		−	1.19224i	−0.802895	−	0.596120i	$-0.796708\pi$
$313$		−	21.0929i		−	1.19224i	0.802895	−	0.596120i	$-0.203292\pi$
$314$	−8.03039	+	8.03039i	−0.453181	+	0.453181i
$315$		0			0
$316$			16.5426i			0.930596i
$317$	−10.8958	−	10.8958i	−0.611971	−	0.611971i	0.331488	−	0.943459i	$-0.392449\pi$
$317$	−10.8958	−	10.8958i	−0.611971	−	0.611971i	−0.943459	+	0.331488i	$0.892449\pi$
$318$	−14.9738	+	14.9738i	−0.839686	+	0.839686i
$319$	−0.591322	+	0.591322i	−0.0331077	+	0.0331077i
$320$	8.57896	+	8.57896i	0.479579	+	0.479579i
$321$			6.38902i			0.356600i
$322$		0			0
$323$	1.52921	−	1.52921i	0.0850874	−	0.0850874i
$324$		−	12.5596i		−	0.697755i
$325$	−15.4550	+	8.49762i	−0.857290	+	0.471363i
$326$	6.68695			0.370356
$327$	−22.7764	+	22.7764i	−1.25954	+	1.25954i
$328$		−	21.3908i		−	1.18111i
$329$		0			0
$330$	−2.77844	−	2.77844i	−0.152948	−	0.152948i
$331$	−6.68797	−	6.68797i	−0.367604	−	0.367604i	0.498999	−	0.866603i	$-0.333701\pi$
$331$	−6.68797	−	6.68797i	−0.367604	−	0.367604i	−0.866603	+	0.498999i	$0.833701\pi$
$332$	9.74946	+	9.74946i	0.535071	+	0.535071i
$333$	−11.8140	+	11.8140i	−0.647401	+	0.647401i
$334$		−	2.27726i		−	0.124606i
$335$	23.2851			1.27220
$336$		0			0
$337$		−	30.8890i		−	1.68263i	−0.540545	−	0.841315i	$-0.681782\pi$
$337$		−	30.8890i		−	1.68263i	0.540545	−	0.841315i	$-0.318218\pi$
$338$	10.3623	−	2.31748i	0.563633	−	0.126054i
$339$			15.6736i			0.851271i
$340$	3.59645	+	3.59645i	0.195045	+	0.195045i
$341$		−	1.91810i		−	0.103871i
$342$	8.80326			0.476026
$343$		0			0
$344$	14.3695	+	14.3695i	0.774750	+	0.774750i
$345$	−34.8476	+	34.8476i	−1.87613	+	1.87613i
$346$	1.04178	+	1.04178i	0.0560064	+	0.0560064i
$347$	10.9743			0.589130			0.294565	−	0.955631i	$-0.404825\pi$
$347$	10.9743			0.589130			0.294565	+	0.955631i	$0.404825\pi$
$348$	6.59240			0.353390
$349$	−14.1593	−	14.1593i	−0.757930	−	0.757930i	0.218015	−	0.975945i	$-0.430042\pi$
$349$	−14.1593	−	14.1593i	−0.757930	−	0.757930i	−0.975945	+	0.218015i	$0.930042\pi$
$350$		0			0
$351$	−28.9534	+	15.9194i	−1.54542	+	0.849716i
$352$	−2.95242			−0.157364
$353$	13.4884	−	13.4884i	0.717914	−	0.717914i	−0.250264	−	0.968178i	$-0.580517\pi$
$353$	13.4884	−	13.4884i	0.717914	−	0.717914i	0.968178	+	0.250264i	$0.0805174\pi$
$354$	6.15248			0.327001
$355$	−3.73792			−0.198388
$356$	9.19822	−	9.19822i	0.487504	−	0.487504i
$357$		0			0
$358$	−9.88349	+	9.88349i	−0.522359	+	0.522359i
$359$	−19.8187	+	19.8187i	−1.04599	+	1.04599i	−0.0470981	+	0.998890i	$0.514997\pi$
$359$	−19.8187	+	19.8187i	−1.04599	+	1.04599i	−0.998890	+	0.0470981i	$0.985003\pi$
$360$			51.7707i			2.72855i
$361$			15.8230i			0.832788i
$362$	−13.5542	−	13.5542i	−0.712395	−	0.712395i
$363$	−32.3078			−1.69572
$364$		0			0
$365$	7.68812			0.402414
$366$	−18.2489	−	18.2489i	−0.953886	−	0.953886i
$367$		−	16.7244i		−	0.873004i	−0.899703	−	0.436502i	$-0.856217\pi$
$367$		−	16.7244i		−	0.873004i	0.899703	−	0.436502i	$-0.143783\pi$
$368$			2.30378i			0.120093i
$369$	33.5976	−	33.5976i	1.74902	−	1.74902i
$370$	5.01900	−	5.01900i	0.260925	−	0.260925i
$371$		0			0
$372$	−10.6921	+	10.6921i	−0.554358	+	0.554358i
$373$	16.3898			0.848632			0.424316	−	0.905514i	$-0.360515\pi$
$373$	16.3898			0.848632			0.424316	+	0.905514i	$0.360515\pi$
$374$	0.503972			0.0260597
$375$	0.724756	−	0.724756i	0.0374262	−	0.0374262i
$376$	13.3446			0.688197
$377$	−2.85664	−	5.19551i	−0.147125	−	0.267582i
$378$		0			0
$379$	2.80924	+	2.80924i	0.144301	+	0.144301i	0.775567	−	0.631266i	$-0.217464\pi$
$379$	2.80924	+	2.80924i	0.144301	+	0.144301i	−0.631266	+	0.775567i	$0.717464\pi$
$380$	7.47184			0.383297
$381$	−34.3966			−1.76219
$382$	−14.5815	−	14.5815i	−0.746055	−	0.746055i
$383$	−27.4207	+	27.4207i	−1.40113	+	1.40113i	−0.604606	+	0.796525i	$0.706669\pi$
$383$	−27.4207	+	27.4207i	−1.40113	+	1.40113i	−0.796525	+	0.604606i	$0.793331\pi$
$384$	17.9940	+	17.9940i	0.918255	+	0.918255i
$385$		0			0
$386$	−4.36163			−0.222001
$387$			45.1390i			2.29455i
$388$	3.90772	+	3.90772i	0.198384	+	0.198384i
$389$		−	4.88013i		−	0.247432i	−0.992318	−	0.123716i	$-0.960519\pi$
$389$		−	4.88013i		−	0.247432i	0.992318	−	0.123716i	$-0.0394812\pi$
$390$	24.4121	−	13.4225i	1.23616	−	0.679673i
$391$		−	6.32089i		−	0.319661i
$392$		0			0
$393$	−21.1154			−1.06513
$394$			12.3760i			0.623492i
$395$	27.6020	−	27.6020i	1.38881	−	1.38881i
$396$	−2.89812	−	2.89812i	−0.145636	−	0.145636i
$397$	−22.3845	−	22.3845i	−1.12345	−	1.12345i	−0.991220	−	0.132226i	$-0.957787\pi$
$397$	−22.3845	−	22.3845i	−1.12345	−	1.12345i	−0.132226	−	0.991220i	$-0.542213\pi$
$398$	−4.14703	−	4.14703i	−0.207872	−	0.207872i
$399$		0			0
$400$			2.16316i			0.108158i
$401$	6.84055	−	6.84055i	0.341601	−	0.341601i	−0.515368	−	0.856969i	$-0.672345\pi$
$401$	6.84055	−	6.84055i	0.341601	−	0.341601i	0.856969	+	0.515368i	$0.172345\pi$
$402$	−18.1886			−0.907167
$403$	13.0596	+	3.79336i	0.650545	+	0.188961i
$404$			20.5949i			1.02464i
$405$	−20.9562	+	20.9562i	−1.04132	+	1.04132i
$406$		0			0
$407$			1.40512i			0.0696491i
$408$	−7.02472	−	7.02472i	−0.347776	−	0.347776i
$409$	8.45738	−	8.45738i	0.418191	−	0.418191i	−0.466389	−	0.884580i	$-0.654445\pi$
$409$	8.45738	−	8.45738i	0.418191	−	0.418191i	0.884580	+	0.466389i	$0.154445\pi$
$410$	−14.2735	+	14.2735i	−0.704916	+	0.704916i
$411$	13.2284	+	13.2284i	0.652507	+	0.652507i
$412$			23.3258i			1.14918i
$413$		0			0
$414$	18.1939	−	18.1939i	0.894180	−	0.894180i
$415$		−	32.5347i		−	1.59707i
$416$	5.83888	−	20.1018i	0.286275	−	0.985574i
$417$	5.76491			0.282309
$418$	0.523516	−	0.523516i	0.0256060	−	0.0256060i
$419$			18.5355i			0.905516i	0.891633	+	0.452758i	$0.149560\pi$
$419$			18.5355i			0.905516i	−0.891633	+	0.452758i	$0.850440\pi$
$420$		0			0
$421$	19.2884	+	19.2884i	0.940060	+	0.940060i	0.998302	−	0.0582422i	$-0.0185496\pi$
$421$	19.2884	+	19.2884i	0.940060	+	0.940060i	−0.0582422	+	0.998302i	$0.518550\pi$
$422$	1.57417	+	1.57417i	0.0766294	+	0.0766294i
$423$	20.9598	+	20.9598i	1.01910	+	1.01910i
$424$	16.5921	−	16.5921i	0.805782	−	0.805782i
$425$		−	5.93508i		−	0.287894i
$426$	2.91980			0.141465
$427$		0			0
$428$		−	2.83120i		−	0.136851i
$429$	−1.53833	+	5.29608i	−0.0742711	+	0.255697i
$430$		−	19.1767i		−	0.924782i
$431$	−6.47809	−	6.47809i	−0.312039	−	0.312039i	0.533660	−	0.845699i	$-0.320816\pi$
$431$	−6.47809	−	6.47809i	−0.312039	−	0.312039i	−0.845699	+	0.533660i	$0.820816\pi$
$432$			4.05246i			0.194974i
$433$	23.6700			1.13751			0.568755	−	0.822507i	$-0.307425\pi$
$433$	23.6700			1.13751			0.568755	+	0.822507i	$0.307425\pi$
$434$		0			0
$435$	−10.9997	−	10.9997i	−0.527394	−	0.527394i
$436$	10.0930	−	10.0930i	0.483368	−	0.483368i
$437$	−6.56603	−	6.56603i	−0.314096	−	0.314096i
$438$	−6.00540			−0.286949
$439$	11.2981			0.539230			0.269615	−	0.962968i	$-0.413104\pi$
$439$	11.2981			0.539230			0.269615	+	0.962968i	$0.413104\pi$
$440$	3.07872	+	3.07872i	0.146772	+	0.146772i
$441$		0			0
$442$	−0.996685	+	3.43134i	−0.0474075	+	0.163212i
$443$	39.0288			1.85431			0.927157	−	0.374672i	$-0.122245\pi$
$443$	39.0288			1.85431			0.927157	+	0.374672i	$0.122245\pi$
$444$	7.83254	−	7.83254i	0.371716	−	0.371716i
$445$	−30.6952			−1.45509
$446$	17.7092			0.838555
$447$	−2.37515	+	2.37515i	−0.112341	+	0.112341i
$448$		0			0
$449$	−8.82288	+	8.82288i	−0.416378	+	0.416378i	−0.883953	−	0.467576i	$-0.845128\pi$
$449$	−8.82288	+	8.82288i	−0.416378	+	0.416378i	0.467576	+	0.883953i	$0.345128\pi$
$450$	17.0834	−	17.0834i	0.805318	−	0.805318i
$451$		−	3.99599i		−	0.188164i
$452$		−	6.94551i		−	0.326689i
$453$	−28.0298	−	28.0298i	−1.31695	−	1.31695i
$454$	14.7833			0.693813
$455$		0			0
$456$	−14.5943			−0.683441
$457$	16.1655	+	16.1655i	0.756192	+	0.756192i	0.975627	−	0.219435i	$-0.0704213\pi$
$457$	16.1655	+	16.1655i	0.756192	+	0.756192i	−0.219435	+	0.975627i	$0.570421\pi$
$458$		−	3.53078i		−	0.164982i
$459$		−	11.1188i		−	0.518980i
$460$	15.4422	−	15.4422i	0.719997	−	0.719997i
$461$	−7.67189	+	7.67189i	−0.357316	+	0.357316i	−0.862823	−	0.505507i	$-0.831306\pi$
$461$	−7.67189	+	7.67189i	−0.357316	+	0.357316i	0.505507	+	0.862823i	$0.331306\pi$
$462$		0			0
$463$	14.0571	−	14.0571i	0.653289	−	0.653289i	−0.300495	−	0.953783i	$-0.597152\pi$
$463$	14.0571	−	14.0571i	0.653289	−	0.653289i	0.953783	+	0.300495i	$0.0971518\pi$
$464$	−0.727189			−0.0337589
$465$	35.6803			1.65463
$466$	5.71089	−	5.71089i	0.264552	−	0.264552i
$467$	−9.92551			−0.459298			−0.229649	−	0.973274i	$-0.573758\pi$
$467$	−9.92551			−0.459298			−0.229649	+	0.973274i	$0.573758\pi$
$468$	25.4636	−	14.0006i	1.17706	−	0.647180i
$469$		0			0
$470$	−8.90450	−	8.90450i	−0.410734	−	0.410734i
$471$	41.8204			1.92698
$472$	−6.81742			−0.313797
$473$	2.68435	+	2.68435i	0.123427	+	0.123427i
$474$	−21.5607	+	21.5607i	−0.990316	+	0.990316i
$475$	−6.16525	−	6.16525i	−0.282881	−	0.282881i
$476$		0			0
$477$	52.1209			2.38645
$478$			9.39957i			0.429926i
$479$	−14.9168	−	14.9168i	−0.681564	−	0.681564i	0.278789	−	0.960352i	$-0.410067\pi$
$479$	−14.9168	−	14.9168i	−0.681564	−	0.681564i	−0.960352	+	0.278789i	$0.910067\pi$
$480$		−	54.9204i		−	2.50676i
$481$	−9.56689	−	2.77885i	−0.436212	−	0.126705i
$482$			11.9041i			0.542217i
$483$		0			0
$484$	14.3167			0.650760
$485$		−	13.0404i		−	0.592132i
$486$	0.491232	−	0.491232i	0.0222827	−	0.0222827i
$487$	31.0005	+	31.0005i	1.40477	+	1.40477i	0.783974	+	0.620794i	$0.213190\pi$
$487$	31.0005	+	31.0005i	1.40477	+	1.40477i	0.620794	+	0.783974i	$0.286810\pi$
$488$	20.2212	+	20.2212i	0.915371	+	0.915371i
$489$	−17.4120	−	17.4120i	−0.787400	−	0.787400i
$490$		0			0
$491$			37.1276i			1.67554i	0.546021	+	0.837772i	$0.316142\pi$
$491$			37.1276i			1.67554i	−0.546021	+	0.837772i	$0.683858\pi$
$492$	−22.2748	+	22.2748i	−1.00423	+	1.00423i
$493$	1.99519			0.0898590
$494$	2.52908	+	4.59975i	0.113789	+	0.206953i
$495$			9.67125i			0.434690i
$496$	1.17941	−	1.17941i	0.0529571	−	0.0529571i
$497$		0			0
$498$			25.4138i			1.13882i
$499$	−3.78711	−	3.78711i	−0.169534	−	0.169534i	0.617240	−	0.786775i	$-0.288251\pi$
$499$	−3.78711	−	3.78711i	−0.169534	−	0.169534i	−0.786775	+	0.617240i	$0.788251\pi$
$500$	−0.321165	+	0.321165i	−0.0143629	+	0.0143629i
$501$	−5.92973	+	5.92973i	−0.264921	+	0.264921i
$502$	−1.32715	−	1.32715i	−0.0592334	−	0.0592334i
$503$		−	27.7355i		−	1.23666i	−0.785917	−	0.618332i	$-0.787809\pi$
$503$		−	27.7355i		−	1.23666i	0.785917	−	0.618332i	$-0.212191\pi$
$504$		0			0
$505$	34.3634	−	34.3634i	1.52915	−	1.52915i
$506$		−	2.16393i		−	0.0961982i
$507$	−33.0166	−	20.9477i	−1.46632	−	0.930321i
$508$	15.2423			0.676269
$509$	21.4038	−	21.4038i	0.948709	−	0.948709i	−0.0500385	−	0.998747i	$-0.515934\pi$
$509$	21.4038	−	21.4038i	0.948709	−	0.948709i	0.998747	+	0.0500385i	$0.0159344\pi$
$510$			9.37480i			0.415123i
$511$		0			0
$512$	−3.51784	−	3.51784i	−0.155468	−	0.155468i
$513$	−11.5500	−	11.5500i	−0.509944	−	0.509944i
$514$	10.4251	+	10.4251i	0.459831	+	0.459831i
$515$	38.9199	−	38.9199i	1.71502	−	1.71502i
$516$		−	29.9267i		−	1.31745i
$517$	2.49290			0.109638
$518$		0			0
$519$		−	5.42535i		−	0.238146i
$520$	−27.0505	+	14.8731i	−1.18624	+	0.652230i
$521$			42.4001i			1.85758i	0.370601	+	0.928792i	$0.379152\pi$
$521$			42.4001i			1.85758i	−0.370601	+	0.928792i	$0.620848\pi$
$522$	5.74291	+	5.74291i	0.251360	+	0.251360i
$523$		−	4.15954i		−	0.181884i	−0.995856	−	0.0909420i	$-0.971012\pi$
$523$		−	4.15954i		−	0.181884i	0.995856	−	0.0909420i	$-0.0289878\pi$
$524$	9.35699			0.408762
$525$		0			0
$526$	−4.59929	−	4.59929i	−0.200539	−	0.200539i
$527$	−3.23596	+	3.23596i	−0.140961	+	0.140961i
$528$	0.478288	+	0.478288i	0.0208148	+	0.0208148i
$529$	−4.14030			−0.180013
$530$	−22.1428			−0.961824
$531$	−10.7078	−	10.7078i	−0.464681	−	0.464681i
$532$		0			0
$533$	27.2071	+	7.90273i	1.17847	+	0.342305i
$534$	23.9769			1.03758
$535$	−4.72397	+	4.72397i	−0.204235	+	0.204235i
$536$	20.1544			0.870538
$537$	51.4709			2.22113
$538$	−4.64870	+	4.64870i	−0.200420	+	0.200420i
$539$		0			0
$540$	27.1636	−	27.1636i	1.16894	−	1.16894i
$541$	29.6049	−	29.6049i	1.27281	−	1.27281i	0.328206	−	0.944606i	$-0.393556\pi$
$541$	29.6049	−	29.6049i	1.27281	−	1.27281i	0.944606	−	0.328206i	$-0.106444\pi$
$542$		−	18.1400i		−	0.779179i
$543$			70.5874i			3.02919i
$544$	4.98091	+	4.98091i	0.213555	+	0.213555i
$545$	−33.6812			−1.44275
$546$		0			0
$547$	−13.4403			−0.574667			−0.287334	−	0.957831i	$-0.592769\pi$
$547$	−13.4403			−0.574667			−0.287334	+	0.957831i	$0.592769\pi$
$548$	−5.86195	−	5.86195i	−0.250410	−	0.250410i
$549$			63.5212i			2.71102i
$550$		−	2.03184i		−	0.0866381i
$551$	2.07257	−	2.07257i	0.0882945	−	0.0882945i
$552$	−30.1624	+	30.1624i	−1.28380	+	1.28380i
$553$		0			0
$554$	0.849123	−	0.849123i	0.0360758	−	0.0360758i
$555$	−26.1378			−1.10949
$556$	−2.55464			−0.108341
$557$	14.7617	−	14.7617i	0.625475	−	0.625475i	−0.321451	−	0.946926i	$-0.604171\pi$
$557$	14.7617	−	14.7617i	0.625475	−	0.625475i	0.946926	+	0.321451i	$0.104171\pi$
$558$	−18.6286			−0.788612
$559$	−23.5854	+	12.9679i	−0.997556	+	0.548485i
$560$		0			0
$561$	−1.31228	−	1.31228i	−0.0554047	−	0.0554047i
$562$	15.2792			0.644513
$563$	−27.1576			−1.14456			−0.572278	−	0.820059i	$-0.693940\pi$
$563$	−27.1576			−1.14456			−0.572278	+	0.820059i	$0.693940\pi$
$564$	−13.8962	−	13.8962i	−0.585134	−	0.585134i
$565$	−11.5889	+	11.5889i	−0.487547	+	0.487547i
$566$	2.76450	+	2.76450i	0.116201	+	0.116201i
$567$		0			0
$568$	−3.23536			−0.135753
$569$		−	12.2474i		−	0.513438i	−0.966486	−	0.256719i	$-0.917359\pi$
$569$		−	12.2474i		−	0.513438i	0.966486	−	0.256719i	$-0.0826414\pi$
$570$	9.73837	+	9.73837i	0.407895	+	0.407895i
$571$			4.69218i			0.196362i	0.995169	+	0.0981809i	$0.0313024\pi$
$571$			4.69218i			0.196362i	−0.995169	+	0.0981809i	$0.968698\pi$
$572$	0.681687	−	2.34688i	0.0285028	−	0.0981280i
$573$			75.9372i			3.17232i
$574$		0			0
$575$	−25.4837			−1.06274
$576$			23.3259i			0.971913i
$577$	−12.0686	+	12.0686i	−0.502422	+	0.502422i	−0.912190	−	0.409768i	$-0.865610\pi$
$577$	−12.0686	+	12.0686i	−0.502422	+	0.502422i	0.409768	+	0.912190i	$0.365610\pi$
$578$	8.96824	+	8.96824i	0.373030	+	0.373030i
$579$	11.3572	+	11.3572i	0.471989	+	0.471989i
$580$	4.87435	+	4.87435i	0.202396	+	0.202396i
$581$		0			0
$582$			10.1862i			0.422231i
$583$	3.09955	−	3.09955i	0.128370	−	0.128370i
$584$	6.65445			0.275363
$585$	−65.8477	−	19.1265i	−2.72247	−	0.790782i
$586$			17.6889i			0.730723i
$587$	−6.21734	+	6.21734i	−0.256617	+	0.256617i	−0.823677	−	0.567060i	$-0.808081\pi$
$587$	−6.21734	+	6.21734i	−0.256617	+	0.256617i	0.567060	+	0.823677i	$0.308081\pi$
$588$		0			0
$589$			6.72291i			0.277013i
$590$	4.54907	+	4.54907i	0.187282	+	0.187282i
$591$	32.2256	−	32.2256i	1.32558	−	1.32558i
$592$	−0.863984	+	0.863984i	−0.0355095	+	0.0355095i
$593$	27.5126	+	27.5126i	1.12981	+	1.12981i	0.990208	+	0.139598i	$0.0445810\pi$
$593$	27.5126	+	27.5126i	1.12981	+	1.12981i	0.139598	+	0.990208i	$0.455419\pi$
$594$		−	3.80645i		−	0.156181i
$595$		0			0
$596$	1.05251	−	1.05251i	0.0431127	−	0.0431127i
$597$			21.5968i			0.883898i
$598$	14.7333	+	4.27951i	0.602490	+	0.175002i
$599$	−34.9803			−1.42926			−0.714629	−	0.699504i	$-0.753404\pi$
$599$	−34.9803			−1.42926			−0.714629	+	0.699504i	$0.753404\pi$
$600$	−28.3213	+	28.3213i	−1.15621	+	1.15621i
$601$		−	11.7882i		−	0.480852i	−0.970667	−	0.240426i	$-0.922713\pi$
$601$		−	11.7882i		−	0.480852i	0.970667	−	0.240426i	$-0.0772872\pi$
$602$		0			0
$603$	31.6557	+	31.6557i	1.28912	+	1.28912i
$604$	12.4210	+	12.4210i	0.505403	+	0.505403i
$605$	−23.8880	−	23.8880i	−0.971185	−	0.971185i
$606$	−26.8422	+	26.8422i	−1.09039	+	1.09039i
$607$			19.0996i			0.775227i	0.921822	+	0.387614i	$0.126701\pi$
$607$			19.0996i			0.775227i	−0.921822	+	0.387614i	$0.873299\pi$
$608$	10.3482			0.419673
$609$		0			0
$610$		−	26.9861i		−	1.09263i
$611$	−4.93011	+	16.9732i	−0.199451	+	0.686661i
$612$			9.77861i			0.395277i
$613$	−17.9731	−	17.9731i	−0.725925	−	0.725925i	0.243880	−	0.969805i	$-0.421580\pi$
$613$	−17.9731	−	17.9731i	−0.725925	−	0.725925i	−0.969805	+	0.243880i	$0.921580\pi$
$614$		−	10.8190i		−	0.436620i
$615$	74.3329			2.99739
$616$		0			0
$617$	−10.4089	−	10.4089i	−0.419046	−	0.419046i	0.465829	−	0.884875i	$-0.345756\pi$
$617$	−10.4089	−	10.4089i	−0.419046	−	0.419046i	−0.884875	+	0.465829i	$0.845756\pi$
$618$	−30.4015	+	30.4015i	−1.22293	+	1.22293i
$619$	22.4817	+	22.4817i	0.903616	+	0.903616i	0.995747	−	0.0921312i	$-0.0293679\pi$
$619$	22.4817	+	22.4817i	0.903616	+	0.903616i	−0.0921312	+	0.995747i	$0.529368\pi$
$620$	−15.8112			−0.634993
$621$	−47.7412			−1.91579
$622$	−3.13131	−	3.13131i	−0.125554	−	0.125554i
$623$		0			0
$624$	−4.20237	+	2.31058i	−0.168229	+	0.0924973i
$625$	25.5300			1.02120
$626$	−12.1823	+	12.1823i	−0.486904	+	0.486904i
$627$	−2.72635			−0.108880
$628$	−18.5321			−0.739512
$629$	2.37052	−	2.37052i	0.0945188	−	0.0945188i
$630$		0			0
$631$	26.3103	−	26.3103i	1.04739	−	1.04739i	0.0485754	−	0.998820i	$-0.484532\pi$
$631$	26.3103	−	26.3103i	1.04739	−	1.04739i	0.998820	−	0.0485754i	$-0.0154681\pi$
$632$	23.8909	−	23.8909i	0.950330	−	0.950330i
$633$		−	8.19791i		−	0.325838i
$634$			12.5859i			0.499851i
$635$	−25.4324	−	25.4324i	−1.00926	−	1.00926i
$636$	−34.5556			−1.37022
$637$		0			0
$638$	0.683045			0.0270420
$639$	−5.08164	−	5.08164i	−0.201027	−	0.201027i
$640$			26.6092i			1.05182i
$641$			23.1416i			0.914036i	0.889457	+	0.457018i	$0.151083\pi$
$641$			23.1416i			0.914036i	−0.889457	+	0.457018i	$0.848917\pi$
$642$	3.69003	−	3.69003i	0.145634	−	0.145634i
$643$	11.9385	−	11.9385i	0.470808	−	0.470808i	−0.431368	−	0.902176i	$-0.641969\pi$
$643$	11.9385	−	11.9385i	0.470808	−	0.470808i	0.902176	+	0.431368i	$0.141969\pi$
$644$		0			0
$645$	−49.9339	+	49.9339i	−1.96614	+	1.96614i
$646$	−1.76641			−0.0694984
$647$	−20.4734			−0.804891			−0.402446	−	0.915444i	$-0.631840\pi$
$647$	−20.4734			−0.804891			−0.402446	+	0.915444i	$0.631840\pi$
$648$	−18.1386	+	18.1386i	−0.712552	+	0.712552i
$649$	−1.27356			−0.0499915
$650$	13.8340	+	4.01830i	0.542615	+	0.157611i
$651$		0			0
$652$	7.71589	+	7.71589i	0.302178	+	0.302178i
$653$	−41.8639			−1.63826			−0.819130	−	0.573607i	$-0.805544\pi$
$653$	−41.8639			−1.63826			−0.819130	+	0.573607i	$0.805544\pi$
$654$	26.3094			1.02878
$655$	−15.6125	−	15.6125i	−0.610031	−	0.610031i
$656$	2.45707	−	2.45707i	0.0959326	−	0.0959326i
$657$	10.4519	+	10.4519i	0.407766	+	0.407766i
$658$		0			0
$659$	−36.8332			−1.43482			−0.717410	−	0.696651i	$-0.754672\pi$
$659$	−36.8332			−1.43482			−0.717410	+	0.696651i	$0.754672\pi$
$660$		−	6.41194i		−	0.249584i
$661$	−5.13448	−	5.13448i	−0.199708	−	0.199708i	0.600167	−	0.799875i	$-0.295101\pi$
$661$	−5.13448	−	5.13448i	−0.199708	−	0.199708i	−0.799875	+	0.600167i	$0.795101\pi$
$662$			7.72537i			0.300255i
$663$	11.5301	−	6.33956i	0.447791	−	0.246208i
$664$		−	28.1604i		−	1.09284i
$665$		0			0
$666$	13.6465			0.528790
$667$		−	8.56685i		−	0.331710i
$668$	2.62767	−	2.62767i	0.101668	−	0.101668i
$669$	−46.1127	−	46.1127i	−1.78282	−	1.78282i
$670$	−13.4485	−	13.4485i	−0.519560	−	0.519560i
$671$	3.77751	+	3.77751i	0.145829	+	0.145829i
$672$		0			0
$673$			28.4985i			1.09854i	0.835646	+	0.549269i	$0.185094\pi$
$673$			28.4985i			1.09854i	−0.835646	+	0.549269i	$0.814906\pi$
$674$	−17.8402	+	17.8402i	−0.687177	+	0.687177i
$675$	−44.8271			−1.72540
$676$	14.6308	+	9.28267i	0.562724	+	0.357026i
$677$			15.2264i			0.585196i	0.956236	+	0.292598i	$0.0945198\pi$
$677$			15.2264i			0.585196i	−0.956236	+	0.292598i	$0.905480\pi$
$678$	9.05238	−	9.05238i	0.347655	−	0.347655i
$679$		0			0
$680$		−	10.3880i		−	0.398362i
$681$	−38.4939	−	38.4939i	−1.47509	−	1.47509i
$682$	−1.10781	+	1.10781i	−0.0424204	+	0.0424204i
$683$	−30.5561	+	30.5561i	−1.16920	+	1.16920i	−0.186800	+	0.982398i	$0.559812\pi$
$683$	−30.5561	+	30.5561i	−1.16920	+	1.16920i	−0.982398	+	0.186800i	$0.940188\pi$
$684$	10.1578	+	10.1578i	0.388395	+	0.388395i
$685$			19.5618i			0.747418i
$686$		0			0
$687$	−9.19373	+	9.19373i	−0.350763	+	0.350763i
$688$			3.30113i			0.125854i
$689$	14.9738	+	27.2335i	0.570455	+	1.03751i
$690$	40.2530			1.53241
$691$	−7.09792	+	7.09792i	−0.270017	+	0.270017i	−0.829107	−	0.559090i	$-0.811151\pi$
$691$	−7.09792	+	7.09792i	−0.270017	+	0.270017i	0.559090	+	0.829107i	$0.311151\pi$
$692$			2.40416i			0.0913926i
$693$		0			0
$694$	−6.33827	−	6.33827i	−0.240597	−	0.240597i
$695$	4.26251	+	4.26251i	0.161686	+	0.161686i
$696$	−9.52077	−	9.52077i	−0.360884	−	0.360884i
$697$	−6.74149	+	6.74149i	−0.255352	+	0.255352i
$698$			16.3556i			0.619069i
$699$	−29.7410			−1.12491
$700$		0			0
$701$			24.4239i			0.922479i	0.887276	+	0.461239i	$0.152595\pi$
$701$			24.4239i			0.922479i	−0.887276	+	0.461239i	$0.847405\pi$
$702$	25.9166	+	7.52788i	0.978160	+	0.284121i
$703$		−	4.92491i		−	0.185746i
$704$	1.38716	+	1.38716i	0.0522804	+	0.0522804i
$705$			46.3726i			1.74649i
$706$	−15.5806			−0.586384
$707$		0			0
$708$	7.09918	+	7.09918i	0.266804	+	0.266804i
$709$	19.6765	−	19.6765i	0.738965	−	0.738965i	−0.233413	−	0.972378i	$-0.574989\pi$
$709$	19.6765	−	19.6765i	0.738965	−	0.738965i	0.972378	+	0.233413i	$0.0749894\pi$
$710$	2.15886	+	2.15886i	0.0810207	+	0.0810207i
$711$	75.0490			2.81456
$712$	−26.5682			−0.995685
$713$	13.8944	+	13.8944i	0.520349	+	0.520349i
$714$		0			0
$715$	−5.05328	+	2.77844i	−0.188982	+	0.103908i
$716$	−22.8086			−0.852397
$717$	24.4754	−	24.4754i	0.914050	−	0.914050i
$718$	22.8928			0.854352
$719$	13.8961			0.518235			0.259118	−	0.965846i	$-0.416568\pi$
$719$	13.8961			0.518235			0.259118	+	0.965846i	$0.416568\pi$
$720$	−5.94669	+	5.94669i	−0.221620	+	0.221620i
$721$		0			0
$722$	9.13867	−	9.13867i	0.340106	−	0.340106i
$723$	30.9969	−	30.9969i	1.15279	−	1.15279i
$724$		−	31.2798i		−	1.16250i
$725$		−	8.04395i		−	0.298745i
$726$	18.6596	+	18.6596i	0.692522	+	0.692522i
$727$	14.0631			0.521572			0.260786	−	0.965397i	$-0.416018\pi$
$727$	14.0631			0.521572			0.260786	+	0.965397i	$0.416018\pi$
$728$		0			0
$729$	25.7110			0.952259
$730$	−4.44033	−	4.44033i	−0.164344	−	0.164344i
$731$		−	9.05733i		−	0.334997i
$732$		−	42.1139i		−	1.55657i
$733$	16.0125	−	16.0125i	0.591436	−	0.591436i	−0.346583	−	0.938019i	$-0.612658\pi$
$733$	16.0125	−	16.0125i	0.591436	−	0.591436i	0.938019	+	0.346583i	$0.112658\pi$
$734$	−9.65927	+	9.65927i	−0.356530	+	0.356530i
$735$		0			0
$736$	21.3868	−	21.3868i	0.788327	−	0.788327i
$737$	3.76503			0.138687
$738$	−38.8090			−1.42858
$739$	0.706373	−	0.706373i	0.0259843	−	0.0259843i	−0.693995	−	0.719980i	$-0.744151\pi$
$739$	0.706373	−	0.706373i	0.0259843	−	0.0259843i	0.719980	+	0.693995i	$0.244151\pi$
$740$	11.5826			0.425784
$741$	5.39180	−	18.5626i	0.198073	−	0.681916i
$742$		0			0
$743$	−7.54553	−	7.54553i	−0.276819	−	0.276819i	0.555019	−	0.831838i	$-0.312711\pi$
$743$	−7.54553	−	7.54553i	−0.276819	−	0.276819i	−0.831838	+	0.555019i	$0.812711\pi$
$744$	30.8831			1.13223
$745$	−3.51232			−0.128681
$746$	−9.46605	−	9.46605i	−0.346577	−	0.346577i
$747$	44.2304	−	44.2304i	1.61830	−	1.61830i
$748$	0.581519	+	0.581519i	0.0212625	+	0.0212625i
$749$		0			0
$750$	−0.837176			−0.0305693
$751$			42.5323i			1.55203i	0.630717	+	0.776013i	$0.282761\pi$
$751$			42.5323i			1.55203i	−0.630717	+	0.776013i	$0.717239\pi$
$752$	1.53284	+	1.53284i	0.0558971	+	0.0558971i
$753$			6.91147i			0.251868i
$754$	−1.35083	+	4.65058i	−0.0491944	+	0.169364i
$755$		−	41.4498i		−	1.50851i
$756$		0			0
$757$	44.6260			1.62196			0.810979	−	0.585075i	$-0.198935\pi$
$757$	44.6260			1.62196			0.810979	+	0.585075i	$0.198935\pi$
$758$		−	3.24499i		−	0.117863i
$759$	−5.63461	+	5.63461i	−0.204523	+	0.204523i
$760$	−10.7909	−	10.7909i	−0.391426	−	0.391426i
$761$	−33.4735	−	33.4735i	−1.21342	−	1.21342i	−0.969896	−	0.243519i	$-0.921698\pi$
$761$	−33.4735	−	33.4735i	−1.21342	−	1.21342i	−0.243519	−	0.969896i	$-0.578302\pi$
$762$	19.8660	+	19.8660i	0.719669	+	0.719669i
$763$		0			0
$764$		−	33.6504i		−	1.21743i
$765$	16.3160	−	16.3160i	0.589906	−	0.589906i
$766$	31.6740			1.14443
$767$	2.51867	−	8.67115i	0.0909438	−	0.313097i
$768$		−	43.9907i		−	1.58738i
$769$	−17.0724	+	17.0724i	−0.615648	+	0.615648i	−0.944412	−	0.328764i	$-0.893368\pi$
$769$	−17.0724	+	17.0724i	−0.615648	+	0.615648i	0.328764	+	0.944412i	$0.393368\pi$
$770$		0			0
$771$		−	54.2915i		−	1.95526i
$772$	−5.03277	−	5.03277i	−0.181133	−	0.181133i
$773$	−27.8631	+	27.8631i	−1.00217	+	1.00217i	−0.00216786	+	0.999998i	$0.500690\pi$
$773$	−27.8631	+	27.8631i	−1.00217	+	1.00217i	−0.999998	+	0.00216786i	$0.999310\pi$
$774$	26.0704	−	26.0704i	0.937080	−	0.937080i
$775$	13.0463	+	13.0463i	0.468637	+	0.468637i
$776$		−	11.2871i		−	0.405182i
$777$		0			0
$778$	−2.81855	+	2.81855i	−0.101050	+	0.101050i
$779$			14.0059i			0.501812i
$780$	43.6563	+	12.6806i	1.56315	+	0.454040i
$781$	−0.604395			−0.0216270
$782$	−3.65068	+	3.65068i	−0.130548	+	0.130548i
$783$		−	15.0695i		−	0.538541i
$784$		0			0
$785$	30.9215	+	30.9215i	1.10364	+	1.10364i
$786$	12.1954	+	12.1954i	0.434994	+	0.434994i
$787$	−10.2855	−	10.2855i	−0.366638	−	0.366638i	0.499612	−	0.866250i	$-0.333476\pi$
$787$	−10.2855	−	10.2855i	−0.366638	−	0.366638i	−0.866250	+	0.499612i	$0.833476\pi$
$788$	−14.2803	+	14.2803i	−0.508714	+	0.508714i
$789$			23.9521i			0.852716i
$790$	−31.8835			−1.13436
$791$		0			0
$792$			8.37095i			0.297449i
$793$	−33.1902	+	18.2489i	−1.17862	+	0.648038i
$794$			25.8567i			0.917618i
$795$	57.6574	+	57.6574i	2.04490	+	2.04490i
$796$		−	9.57030i		−	0.339210i
$797$	−2.90737			−0.102984			−0.0514922	−	0.998673i	$-0.516398\pi$
$797$	−2.90737			−0.102984			−0.0514922	+	0.998673i	$0.516398\pi$
$798$		0			0
$799$	−4.20568	−	4.20568i	−0.148786	−	0.148786i
$800$	20.0814	−	20.0814i	0.709984	−	0.709984i
$801$	−41.7295	−	41.7295i	−1.47444	−	1.47444i
$802$	−7.90161			−0.279016
$803$	1.24311			0.0438685
$804$	−20.9874	−	20.9874i	−0.740168	−	0.740168i
$805$		0			0
$806$	−5.35179	−	9.73355i	−0.188509	−	0.342850i
$807$	24.2093			0.852209
$808$	29.7433	−	29.7433i	1.04636	−	1.04636i
$809$	1.86353			0.0655183			0.0327591	−	0.999463i	$-0.489571\pi$
$809$	1.86353			0.0655183			0.0327591	+	0.999463i	$0.489571\pi$
$810$	24.2068			0.850539
$811$	−12.4905	+	12.4905i	−0.438602	+	0.438602i	−0.891541	−	0.452940i	$-0.850375\pi$
$811$	−12.4905	+	12.4905i	−0.438602	+	0.438602i	0.452940	+	0.891541i	$0.350375\pi$
$812$		0			0
$813$	−47.2344	+	47.2344i	−1.65658	+	1.65658i
$814$	0.811536	−	0.811536i	0.0284443	−	0.0284443i
$815$		−	25.7485i		−	0.901932i
$816$		−	1.61380i		−	0.0564944i
$817$	−9.40859	−	9.40859i	−0.329165	−	0.329165i
$818$	−9.76924			−0.341574
$819$		0			0
$820$	−32.9395			−1.15030
$821$	−18.1889	−	18.1889i	−0.634795	−	0.634795i	0.314472	−	0.949267i	$-0.398173\pi$
$821$	−18.1889	−	18.1889i	−0.634795	−	0.634795i	−0.949267	+	0.314472i	$0.898173\pi$
$822$		−	15.2803i		−	0.532960i
$823$		−	16.9862i		−	0.592100i	−0.955172	−	0.296050i	$-0.904330\pi$
$823$		−	16.9862i		−	0.592100i	0.955172	−	0.296050i	$-0.0956696\pi$
$824$	33.6871	−	33.6871i	1.17355	−	1.17355i
$825$	−5.29069	+	5.29069i	−0.184198	+	0.184198i
$826$		0			0
$827$	−10.3024	+	10.3024i	−0.358251	+	0.358251i	−0.863168	−	0.504917i	$-0.831523\pi$
$827$	−10.3024	+	10.3024i	−0.358251	+	0.358251i	0.504917	+	0.863168i	$0.331523\pi$
$828$	41.9869			1.45914
$829$	−4.48598			−0.155805			−0.0779023	−	0.996961i	$-0.524822\pi$
$829$	−4.48598			−0.155805			−0.0779023	+	0.996961i	$0.524822\pi$
$830$	−18.7907	+	18.7907i	−0.652233	+	0.652233i
$831$	−4.42203			−0.153399
$832$	−12.1879	+	6.70127i	−0.422540	+	0.232325i
$833$		0			0
$834$	−3.32957	−	3.32957i	−0.115293	−	0.115293i
$835$	−8.76874			−0.303455
$836$	1.20814			0.0417845
$837$	24.4409	+	24.4409i	0.844802	+	0.844802i
$838$	10.7053	−	10.7053i	0.369808	−	0.369808i
$839$	3.77561	+	3.77561i	0.130348	+	0.130348i	0.769271	−	0.638923i	$-0.220620\pi$
$839$	3.77561	+	3.77561i	0.130348	+	0.130348i	−0.638923	+	0.769271i	$0.720620\pi$
$840$		0			0
$841$	−26.2959			−0.906754
$842$		−	22.2803i		−	0.767831i
$843$	−39.7852	−	39.7852i	−1.37027	−	1.37027i
$844$			3.63278i			0.125046i
$845$	−8.92361	−	39.9006i	−0.306981	−	1.37262i
$846$		−	24.2110i		−	0.832392i
$847$		0			0
$848$	3.81173			0.130895
$849$		−	14.3969i		−	0.494100i
$850$	−3.42785	+	3.42785i	−0.117574	+	0.117574i
$851$	−10.1784	−	10.1784i	−0.348911	−	0.348911i
$852$	3.36908	+	3.36908i	0.115423	+	0.115423i
$853$	18.5441	+	18.5441i	0.634938	+	0.634938i	0.949302	−	0.314364i	$-0.101791\pi$
$853$	18.5441	+	18.5441i	0.634938	+	0.634938i	−0.314364	+	0.949302i	$0.601791\pi$
$854$		0			0
$855$		−	33.8975i		−	1.15927i
$856$	−4.08883	+	4.08883i	−0.139753	+	0.139753i
$857$	46.6481			1.59347			0.796734	−	0.604329i	$-0.206559\pi$
$857$	46.6481			1.59347			0.796734	+	0.604329i	$0.206559\pi$
$858$	3.94726	−	2.17032i	0.134757	−	0.0740934i
$859$			2.41693i			0.0824647i	0.999150	+	0.0412323i	$0.0131284\pi$
$859$			2.41693i			0.0824647i	−0.999150	+	0.0412323i	$0.986872\pi$
$860$	22.1275	−	22.1275i	0.754540	−	0.754540i
$861$		0			0
$862$			7.48294i			0.254870i
$863$	39.0550	+	39.0550i	1.32945	+	1.32945i	0.905850	+	0.423598i	$0.139233\pi$
$863$	39.0550	+	39.0550i	1.32945	+	1.32945i	0.423598	+	0.905850i	$0.360767\pi$
$864$	37.6204	−	37.6204i	1.27987	−	1.27987i
$865$	4.01144	−	4.01144i	0.136393	−	0.136393i
$866$	−13.6708	−	13.6708i	−0.464553	−	0.464553i
$867$		−	46.7045i		−	1.58617i
$868$		0			0
$869$	4.46305	−	4.46305i	0.151399	−	0.151399i
$870$			12.7059i			0.430770i
$871$	−7.44596	+	25.6346i	−0.252297	+	0.868595i
$872$	−29.1528			−0.987238
$873$	17.7281	−	17.7281i	0.600006	−	0.600006i
$874$			7.58451i			0.256550i
$875$		0			0
$876$	−6.92948	−	6.92948i	−0.234125	−	0.234125i
$877$	−18.1716	−	18.1716i	−0.613611	−	0.613611i	0.330274	−	0.943885i	$-0.392859\pi$
$877$	−18.1716	−	18.1716i	−0.613611	−	0.613611i	−0.943885	+	0.330274i	$0.892859\pi$
$878$	−6.52531	−	6.52531i	−0.220219	−	0.220219i
$879$	46.0599	−	46.0599i	1.55356	−	1.55356i
$880$			0.707282i			0.0238425i
$881$	−14.0101			−0.472014			−0.236007	−	0.971751i	$-0.575839\pi$
$881$	−14.0101			−0.472014			−0.236007	+	0.971751i	$0.575839\pi$
$882$		0			0
$883$			26.0607i			0.877012i	0.898728	+	0.438506i	$0.144492\pi$
$883$			26.0607i			0.877012i	−0.898728	+	0.438506i	$0.855508\pi$
$884$	−5.10938	+	2.80928i	−0.171847	+	0.0944865i
$885$		−	23.6905i		−	0.796348i
$886$	−22.5414	−	22.5414i	−0.757292	−	0.757292i
$887$		−	22.8944i		−	0.768719i	−0.923183	−	0.384360i	$-0.874422\pi$
$887$		−	22.8944i		−	0.768719i	0.923183	−	0.384360i	$-0.125578\pi$
$888$	−22.6236			−0.759197
$889$		0			0
$890$	17.7282	+	17.7282i	0.594251	+	0.594251i
$891$	−3.38846	+	3.38846i	−0.113518	+	0.113518i
$892$	20.4342	+	20.4342i	0.684187	+	0.684187i
$893$	−8.73756			−0.292391
$894$	2.74357			0.0917588
$895$	38.0570	+	38.0570i	1.27211	+	1.27211i
$896$		0			0
$897$	−27.2205	−	49.5072i	−0.908865	−	1.65300i
$898$	10.1914			0.340093
$899$	−4.38577	+	4.38577i	−0.146274	+	0.146274i
$900$	39.4241			1.31414
$901$	−10.4583			−0.348416
$902$	−2.30792	+	2.30792i	−0.0768452	+	0.0768452i
$903$		0			0
$904$	−10.0307	+	10.0307i	−0.333617	+	0.333617i
$905$	−52.1915	+	52.1915i	−1.73490	+	1.73490i
$906$			32.3776i			1.07567i
$907$			22.6646i			0.752567i	0.926505	+	0.376284i	$0.122798\pi$
$907$			22.6646i			0.752567i	−0.926505	+	0.376284i	$0.877202\pi$
$908$	17.0580	+	17.0580i	0.566090	+	0.566090i
$909$	93.4330			3.09898
$910$		0			0
$911$	−5.46179			−0.180957			−0.0904786	−	0.995898i	$-0.528840\pi$
$911$	−5.46179			−0.180957			−0.0904786	+	0.995898i	$0.528840\pi$
$912$	−1.67639	−	1.67639i	−0.0555108	−	0.0555108i
$913$		−	5.26063i		−	0.174101i
$914$		−	18.6731i		−	0.617650i
$915$	−70.2686	+	70.2686i	−2.32301	+	2.32301i
$916$	4.07407	−	4.07407i	0.134611	−	0.134611i
$917$		0			0
$918$	−6.42172	+	6.42172i	−0.211948	+	0.211948i
$919$	−21.9291			−0.723375			−0.361688	−	0.932299i	$-0.617799\pi$
$919$	−21.9291			−0.723375			−0.361688	+	0.932299i	$0.617799\pi$
$920$	−44.6034			−1.47053
$921$	−28.1715	+	28.1715i	−0.928281	+	0.928281i
$922$	8.86191			0.291852
$923$	1.19529	−	4.11509i	0.0393434	−	0.135450i
$924$		0			0
$925$	−9.55714	−	9.55714i	−0.314237	−	0.314237i
$926$	−16.2376			−0.533599
$927$	105.822			3.47565
$928$	6.75075	+	6.75075i	0.221604	+	0.221604i
$929$	6.57227	−	6.57227i	0.215629	−	0.215629i	−0.591025	−	0.806654i	$-0.701276\pi$
$929$	6.57227	−	6.57227i	0.215629	−	0.215629i	0.806654	+	0.591025i	$0.201276\pi$
$930$	−20.6074	−	20.6074i	−0.675743	−	0.675743i
$931$		0			0
$932$	13.1793			0.431702
$933$			16.3071i			0.533871i
$934$	5.73255	+	5.73255i	0.187575	+	0.187575i
$935$		−	1.94058i		−	0.0634636i
$936$	−56.9944	−	16.5549i	−1.86292	−	0.541114i
$937$			3.37326i			0.110200i	0.998481	+	0.0550998i	$0.0175477\pi$
$937$			3.37326i			0.110200i	−0.998481	+	0.0550998i	$0.982452\pi$
$938$		0			0
$939$	63.4428			2.07038
$940$		−	20.5493i		−	0.670245i
$941$	−0.790206	+	0.790206i	−0.0257600	+	0.0257600i	−0.719869	−	0.694109i	$-0.755798\pi$
$941$	−0.790206	+	0.790206i	−0.0257600	+	0.0257600i	0.694109	+	0.719869i	$0.255798\pi$
$942$	−24.1537	−	24.1537i	−0.786970	−	0.786970i
$943$	28.9462	+	28.9462i	0.942619	+	0.942619i
$944$	−0.783090	−	0.783090i	−0.0254874	−	0.0254874i
$945$		0			0
$946$		−	3.10073i		−	0.100813i
$947$	8.40187	−	8.40187i	0.273024	−	0.273024i	−0.557292	−	0.830316i	$-0.688160\pi$
$947$	8.40187	−	8.40187i	0.273024	−	0.273024i	0.830316	+	0.557292i	$0.188160\pi$
$948$	−49.7567			−1.61602
$949$	−2.45846	+	8.46386i	−0.0798049	+	0.274749i
$950$			7.12157i			0.231054i
$951$	32.7723	−	32.7723i	1.06272	−	1.06272i
$952$		0			0
$953$			27.4279i			0.888478i	0.895908	+	0.444239i	$0.146526\pi$
$953$			27.4279i			0.888478i	−0.895908	+	0.444239i	$0.853474\pi$
$954$	−30.1028	−	30.1028i	−0.974615	−	0.974615i
$955$	−56.1471	+	56.1471i	−1.81688	+	1.81688i
$956$	−10.8459	+	10.8459i	−0.350782	+	0.350782i
$957$	−1.77857	−	1.77857i	−0.0574930	−	0.0574930i
$958$			17.2306i			0.556694i
$959$		0			0
$960$	−25.8037	+	25.8037i	−0.832810	+	0.832810i
$961$			16.7736i			0.541084i
$962$	3.92048	+	7.13037i	0.126401	+	0.229892i
$963$	−12.8443			−0.413902
$964$	−13.7358	+	13.7358i	−0.442401	+	0.442401i
$965$			16.7948i			0.540642i
$966$		0			0
$967$	−1.22569	−	1.22569i	−0.0394155	−	0.0394155i	0.687124	−	0.726540i	$-0.258873\pi$
$967$	−1.22569	−	1.22569i	−0.0394155	−	0.0394155i	−0.726540	+	0.687124i	$0.758873\pi$
$968$	−20.6763	−	20.6763i	−0.664560	−	0.664560i
$969$	4.59953	+	4.59953i	0.147758	+	0.147758i
$970$	−7.53155	+	7.53155i	−0.241823	+	0.241823i
$971$		−	12.3617i		−	0.396707i	−0.980131	−	0.198354i	$-0.936441\pi$
$971$		−	12.3617i		−	0.396707i	0.980131	−	0.198354i	$-0.0635595\pi$
$972$	1.13364			0.0363615
$973$		0			0
$974$		−	35.8091i		−	1.14740i
$975$	−25.5590	−	46.4854i	−0.818543	−	1.48872i
$976$			4.64546i			0.148698i
$977$	−0.118541	−	0.118541i	−0.00379245	−	0.00379245i	0.705208	−	0.709000i	$-0.250854\pi$
$977$	−0.118541	−	0.118541i	−0.00379245	−	0.00379245i	−0.709000	+	0.705208i	$0.750854\pi$
$978$			20.1129i			0.643140i
$979$	−4.96319			−0.158624
$980$		0			0
$981$	−45.7890	−	45.7890i	−1.46193	−	1.46193i
$982$	21.4433	−	21.4433i	0.684283	−	0.684283i
$983$	8.22071	+	8.22071i	0.262200	+	0.262200i	0.825947	−	0.563747i	$-0.190641\pi$
$983$	8.22071	+	8.22071i	0.262200	+	0.262200i	−0.563747	+	0.825947i	$0.690641\pi$
$984$	64.3388			2.05105
$985$	47.6544			1.51840
$986$	−1.15234	−	1.15234i	−0.0366979	−	0.0366979i
$987$		0			0
$988$	−2.38930	+	8.22576i	−0.0760137	+	0.261696i
$989$	−38.8899			−1.23663
$990$	5.58570	−	5.58570i	0.177525	−	0.177525i
$991$	9.19612			0.292124			0.146062	−	0.989275i	$-0.453340\pi$
$991$	9.19612			0.292124			0.146062	+	0.989275i	$0.453340\pi$
$992$	−21.8978			−0.695255
$993$	20.1160	−	20.1160i	0.638361	−	0.638361i
$994$		0			0
$995$	−15.9684	+	15.9684i	−0.506233	+	0.506233i
$996$	−29.3243	+	29.3243i	−0.929175	+	0.929175i
$997$			29.9824i			0.949553i	0.880106	+	0.474776i	$0.157471\pi$
$997$			29.9824i			0.949553i	−0.880106	+	0.474776i	$0.842529\pi$
$998$			4.37454i			0.138474i
$999$	−17.9043	−	17.9043i	−0.566468	−	0.566468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.489.6		32
7.2	even	3		91.2.bb.a.73.3	yes	32
7.3	odd	6		91.2.bb.a.47.6	yes	32
7.4	even	3		637.2.bc.b.411.6		32
7.5	odd	6		637.2.bc.b.619.3		32
7.6	odd	2	inner	637.2.i.a.489.5		32
13.5	odd	4	inner	637.2.i.a.538.6		32
21.2	odd	6		819.2.fn.e.73.6		32
21.17	even	6		819.2.fn.e.775.3		32
91.5	even	12		637.2.bc.b.31.6		32
91.18	odd	12		637.2.bc.b.460.3		32
91.31	even	12		91.2.bb.a.5.3	✓	32
91.44	odd	12		91.2.bb.a.31.6	yes	32
91.83	even	4	inner	637.2.i.a.538.5		32
273.44	even	12		819.2.fn.e.577.3		32
273.122	odd	12		819.2.fn.e.460.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.3	✓	32	91.31	even	12
91.2.bb.a.31.6	yes	32	91.44	odd	12
91.2.bb.a.47.6	yes	32	7.3	odd	6
91.2.bb.a.73.3	yes	32	7.2	even	3
637.2.i.a.489.5		32	7.6	odd	2	inner
637.2.i.a.489.6		32	1.1	even	1	trivial
637.2.i.a.538.5		32	91.83	even	4	inner
637.2.i.a.538.6		32	13.5	odd	4	inner
637.2.bc.b.31.6		32	91.5	even	12
637.2.bc.b.411.6		32	7.4	even	3
637.2.bc.b.460.3		32	91.18	odd	12
637.2.bc.b.619.3		32	7.5	odd	6
819.2.fn.e.73.6		32	21.2	odd	6
819.2.fn.e.460.6		32	273.122	odd	12
819.2.fn.e.577.3		32	273.44	even	12
819.2.fn.e.775.3		32	21.17	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.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.577557 - 0.577557i) q^{2} +3.00778i q^{3} -1.33286i q^{4} +(-2.22392 + 2.22392i) q^{5} +(1.73717 - 1.73717i) q^{6} +(-1.92491 + 1.92491i) q^{8} -6.04677 q^{9} +O(q^{10})\)	\(q+(-0.577557 - 0.577557i) q^{2} +3.00778i q^{3} -1.33286i q^{4} +(-2.22392 + 2.22392i) q^{5} +(1.73717 - 1.73717i) q^{6} +(-1.92491 + 1.92491i) q^{8} -6.04677 q^{9} +2.56888 q^{10} +(-0.359592 + 0.359592i) q^{11} +4.00894 q^{12} +(-1.73717 - 3.15947i) q^{13} +(-6.68907 - 6.68907i) q^{15} -0.442215 q^{16} +1.21331 q^{17} +(3.49235 + 3.49235i) q^{18} +(1.26036 - 1.26036i) q^{19} +(2.96417 + 2.96417i) q^{20} +0.415370 q^{22} -5.20963i q^{23} +(-5.78973 - 5.78973i) q^{24} -4.89165i q^{25} +(-0.821461 + 2.82809i) q^{26} -9.16401i q^{27} +1.64443 q^{29} +7.72665i q^{30} +(-2.66706 + 2.66706i) q^{31} +(4.10523 + 4.10523i) q^{32} +(-1.08158 - 1.08158i) q^{33} +(-0.700755 - 0.700755i) q^{34} +8.05946i q^{36} +(1.95377 - 1.95377i) q^{37} -1.45586 q^{38} +(9.50300 - 5.22502i) q^{39} -8.56172i q^{40} +(-5.55629 + 5.55629i) q^{41} -7.46499i q^{43} +(0.479284 + 0.479284i) q^{44} +(13.4475 - 13.4475i) q^{45} +(-3.00886 + 3.00886i) q^{46} +(-3.46629 - 3.46629i) q^{47} -1.33009i q^{48} +(-2.82521 + 2.82521i) q^{50} +3.64937i q^{51} +(-4.21112 + 2.31539i) q^{52} -8.61964 q^{53} +(-5.29274 + 5.29274i) q^{54} -1.59941i q^{55} +(3.79090 + 3.79090i) q^{57} +(-0.949749 - 0.949749i) q^{58} +(1.77084 + 1.77084i) q^{59} +(-8.91557 + 8.91557i) q^{60} -10.5050i q^{61} +3.08076 q^{62} -3.85758i q^{64} +(10.8897 + 3.16309i) q^{65} +1.24934i q^{66} +(-5.23514 - 5.23514i) q^{67} -1.61716i q^{68} +15.6695 q^{69} +(0.840390 + 0.840390i) q^{71} +(11.6395 - 11.6395i) q^{72} +(-1.72851 - 1.72851i) q^{73} -2.25682 q^{74} +14.7130 q^{75} +(-1.67988 - 1.67988i) q^{76} +(-8.50628 - 2.47078i) q^{78} -12.4114 q^{79} +(0.983450 - 0.983450i) q^{80} +9.42307 q^{81} +6.41815 q^{82} +(-7.31472 + 7.31472i) q^{83} +(-2.69830 + 2.69830i) q^{85} +(-4.31146 + 4.31146i) q^{86} +4.94608i q^{87} -1.38437i q^{88} +(6.90114 + 6.90114i) q^{89} -15.5334 q^{90} -6.94369 q^{92} +(-8.02193 - 8.02193i) q^{93} +4.00396i q^{94} +5.60589i q^{95} +(-12.3477 + 12.3477i) q^{96} +(-2.93184 + 2.93184i) q^{97} +(2.17437 - 2.17437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

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