LMFDB - Embedded newform 637.2.bb.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	637.227
Dual form			637.2.bb.a.362.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56744 + 1.56744i) q^{2} +(-0.959879 + 0.554186i) q^{3} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(0.635898 - 2.37321i) q^{6} +(1.43221 + 1.43221i) q^{8} +(-0.885755 + 1.53417i) q^{9} +O(q^{10})$	\(q+(-1.56744 + 1.56744i) q^{2} +(-0.959879 + 0.554186i) q^{3} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(0.635898 - 2.37321i) q^{6} +(1.43221 + 1.43221i) q^{8} +(-0.885755 + 1.53417i) q^{9} +(3.36131 + 5.82195i) q^{10} +(-0.188977 + 0.705270i) q^{11} +(1.61475 + 2.79683i) q^{12} +(2.65012 + 2.44476i) q^{13} +(0.869990 + 3.24685i) q^{15} +1.33764 q^{16} -3.24611 q^{17} +(-1.01635 - 3.79309i) q^{18} +(-3.85949 + 1.03415i) q^{19} +(-8.53543 - 2.28706i) q^{20} +(-0.809258 - 1.40168i) q^{22} -5.96750i q^{23} +(-2.16847 - 0.581039i) q^{24} +(-3.63505 - 2.09870i) q^{25} +(-7.98592 + 0.321882i) q^{26} -5.28861i q^{27} +(2.78094 - 4.81672i) q^{29} +(-6.45289 - 3.72558i) q^{30} +(-3.99535 + 1.07055i) q^{31} +(-4.96110 + 4.96110i) q^{32} +(-0.209456 - 0.781702i) q^{33} +(5.08807 - 5.08807i) q^{34} +(4.47016 + 2.58085i) q^{36} +(-6.97285 - 6.97285i) q^{37} +(4.42855 - 7.67048i) q^{38} +(-3.89865 - 0.878018i) q^{39} +(5.31969 - 3.07132i) q^{40} +(-2.46389 + 0.660198i) q^{41} +(-5.73009 + 3.30827i) q^{43} +(2.05497 + 0.550626i) q^{44} +(3.79893 + 3.79893i) q^{45} +(9.35370 + 9.35370i) q^{46} +(1.69510 + 0.454201i) q^{47} +(-1.28397 + 0.741302i) q^{48} +(8.98729 - 2.40814i) q^{50} +(3.11587 - 1.79895i) q^{51} +(7.12338 - 7.72173i) q^{52} +(3.37073 - 5.83828i) q^{53} +(8.28958 + 8.28958i) q^{54} +(1.91767 + 1.10717i) q^{55} +(3.13153 - 3.13153i) q^{57} +(3.19097 + 11.9089i) q^{58} +(2.33153 - 2.33153i) q^{59} +(9.46044 - 2.53492i) q^{60} +(-6.30371 - 3.63945i) q^{61} +(4.58444 - 7.94048i) q^{62} -12.8772i q^{64} +(9.24179 - 5.84425i) q^{65} +(1.55358 + 0.896960i) q^{66} +(-6.27534 - 1.68147i) q^{67} +9.45827i q^{68} +(3.30711 + 5.72808i) q^{69} +(-8.06938 - 2.16218i) q^{71} +(-3.46586 + 0.928673i) q^{72} +(-1.62921 - 6.08031i) q^{73} +21.8590 q^{74} +4.65227 q^{75} +(3.01323 + 11.2455i) q^{76} +(7.48713 - 4.73465i) q^{78} +(7.87501 + 13.6399i) q^{79} +(1.04995 - 3.91846i) q^{80} +(0.273613 + 0.473911i) q^{81} +(2.82718 - 4.89682i) q^{82} +(-10.4223 - 10.4223i) q^{83} +(-2.54795 + 9.50909i) q^{85} +(3.79606 - 14.1671i) q^{86} +6.16463i q^{87} +(-1.28075 + 0.739443i) q^{88} +(6.62546 - 6.62546i) q^{89} -11.9092 q^{90} -17.3877 q^{92} +(3.24176 - 3.24176i) q^{93} +(-3.36890 + 1.94504i) q^{94} +12.1177i q^{95} +(2.01268 - 7.51143i) q^{96} +(-2.37570 + 8.86623i) q^{97} +(-0.914619 - 0.914619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.56744	+	1.56744i	−1.10835	+	1.10835i	−0.114979	+	0.993368i	$0.536680\pi$
$2$	−1.56744	+	1.56744i	−1.10835	+	1.10835i	−0.993368	+	0.114979i	$0.963320\pi$
$3$	−0.959879	+	0.554186i	−0.554186	+	0.319960i	−0.750809	−	0.660520i	$-0.770336\pi$
$3$	−0.959879	+	0.554186i	−0.554186	+	0.319960i	0.196622	+	0.980479i	$0.437003\pi$
$4$		−	2.91373i		−	1.45686i
$5$	0.784926	−	2.92938i	0.351029	−	1.31006i	−0.534379	−	0.845245i	$-0.679454\pi$
$5$	0.784926	−	2.92938i	0.351029	−	1.31006i	0.885408	−	0.464815i	$-0.153879\pi$
$6$	0.635898	−	2.37321i	0.259604	−	0.968857i
$7$		0			0
$7$		0			0
$8$	1.43221	+	1.43221i	0.506364	+	0.506364i
$9$	−0.885755	+	1.53417i	−0.295252	+	0.511391i
$10$	3.36131	+	5.82195i	1.06294	+	1.84106i
$11$	−0.188977	+	0.705270i	−0.0569786	+	0.212647i	−0.988546	−	0.150923i	$-0.951775\pi$
$11$	−0.188977	+	0.705270i	−0.0569786	+	0.212647i	0.931567	+	0.363570i	$0.118442\pi$
$12$	1.61475	+	2.79683i	0.466138	+	0.807375i
$13$	2.65012	+	2.44476i	0.735011	+	0.678055i
$13$	2.65012	+	2.44476i	0.735011	+	0.678055i
$14$		0			0
$15$	0.869990	+	3.24685i	0.224631	+	0.838333i
$16$	1.33764			0.334410
$17$	−3.24611			−0.787296			−0.393648	−	0.919261i	$-0.628787\pi$
$17$	−3.24611			−0.787296			−0.393648	+	0.919261i	$0.628787\pi$
$18$	−1.01635	−	3.79309i	−0.239557	−	0.894039i
$19$	−3.85949	+	1.03415i	−0.885428	+	0.237250i	−0.672747	−	0.739872i	$-0.734886\pi$
$19$	−3.85949	+	1.03415i	−0.885428	+	0.237250i	−0.212680	+	0.977122i	$0.568219\pi$
$20$	−8.53543	−	2.28706i	−1.90858	−	0.511402i
$21$		0			0
$22$	−0.809258	−	1.40168i	−0.172534	−	0.298839i
$23$		−	5.96750i		−	1.24431i	−0.782894	−	0.622155i	$-0.786257\pi$
$23$		−	5.96750i		−	1.24431i	0.782894	−	0.622155i	$-0.213743\pi$
$24$	−2.16847	−	0.581039i	−0.442636	−	0.118604i
$25$	−3.63505	−	2.09870i	−0.727009	−	0.419739i
$26$	−7.98592	+	0.321882i	−1.56617	+	0.0631262i
$27$		−	5.28861i		−	1.01779i
$28$		0			0
$29$	2.78094	−	4.81672i	0.516407	−	0.894443i	−0.483412	−	0.875393i	$-0.660603\pi$
$29$	2.78094	−	4.81672i	0.516407	−	0.894443i	0.999819	−	0.0190499i	$-0.00606412\pi$
$30$	−6.45289	−	3.72558i	−1.17813	−	0.680195i
$31$	−3.99535	+	1.07055i	−0.717585	+	0.192276i	−0.599094	−	0.800679i	$-0.704472\pi$
$31$	−3.99535	+	1.07055i	−0.717585	+	0.192276i	−0.118491	+	0.992955i	$0.537806\pi$
$32$	−4.96110	+	4.96110i	−0.877007	+	0.877007i
$33$	−0.209456	−	0.781702i	−0.0364617	−	0.136077i
$34$	5.08807	−	5.08807i	0.872597	−	0.872597i
$35$		0			0
$36$	4.47016	+	2.58085i	0.745027	+	0.430142i
$37$	−6.97285	−	6.97285i	−1.14633	−	1.14633i	−0.987269	−	0.159061i	$-0.949153\pi$
$37$	−6.97285	−	6.97285i	−1.14633	−	1.14633i	−0.159061	−	0.987269i	$-0.550847\pi$
$38$	4.42855	−	7.67048i	0.718406	−	1.24432i
$39$	−3.89865	−	0.878018i	−0.624283	−	0.140595i
$40$	5.31969	−	3.07132i	0.841116	−	0.485619i
$41$	−2.46389	+	0.660198i	−0.384795	+	0.103106i	−0.446031	−	0.895018i	$-0.647163\pi$
$41$	−2.46389	+	0.660198i	−0.384795	+	0.103106i	0.0612351	+	0.998123i	$0.480496\pi$
$42$		0			0
$43$	−5.73009	+	3.30827i	−0.873831	+	0.504507i	−0.868619	−	0.495480i	$-0.834992\pi$
$43$	−5.73009	+	3.30827i	−0.873831	+	0.504507i	−0.00521150	+	0.999986i	$0.501659\pi$
$44$	2.05497	+	0.550626i	0.309798	+	0.0830101i
$45$	3.79893	+	3.79893i	0.566310	+	0.566310i
$46$	9.35370	+	9.35370i	1.37913	+	1.37913i
$47$	1.69510	+	0.454201i	0.247256	+	0.0662521i	0.380318	−	0.924856i	$-0.375814\pi$
$47$	1.69510	+	0.454201i	0.247256	+	0.0662521i	−0.133062	+	0.991108i	$0.542481\pi$
$48$	−1.28397	+	0.741302i	−0.185326	+	0.106998i
$49$		0			0
$50$	8.98729	−	2.40814i	1.27099	−	0.340562i
$51$	3.11587	−	1.79895i	0.436309	−	0.251903i
$52$	7.12338	−	7.72173i	0.987835	−	1.07081i
$53$	3.37073	−	5.83828i	0.463005	−	0.801949i	−0.536104	−	0.844152i	$-0.680104\pi$
$53$	3.37073	−	5.83828i	0.463005	−	0.801949i	0.999109	+	0.0422032i	$0.0134377\pi$
$54$	8.28958	+	8.28958i	1.12807	+	1.12807i
$55$	1.91767	+	1.10717i	0.258579	+	0.149291i
$56$		0			0
$57$	3.13153	−	3.13153i	0.414782	−	0.414782i
$58$	3.19097	+	11.9089i	0.418995	+	1.56371i
$59$	2.33153	−	2.33153i	0.303540	−	0.303540i	−0.538857	−	0.842397i	$-0.681144\pi$
$59$	2.33153	−	2.33153i	0.303540	−	0.303540i	0.842397	+	0.538857i	$0.181144\pi$
$60$	9.46044	−	2.53492i	1.22134	−	0.327256i
$61$	−6.30371	−	3.63945i	−0.807108	−	0.465984i	0.0388426	−	0.999245i	$-0.487633\pi$
$61$	−6.30371	−	3.63945i	−0.807108	−	0.465984i	−0.845951	+	0.533261i	$0.820966\pi$
$62$	4.58444	−	7.94048i	0.582224	−	1.00844i
$63$		0			0
$64$		−	12.8772i		−	1.60964i
$65$	9.24179	−	5.84425i	1.14630	−	0.724891i
$66$	1.55358	+	0.896960i	0.191233	+	0.110408i
$67$	−6.27534	−	1.68147i	−0.766655	−	0.205424i	−0.145762	−	0.989320i	$-0.546563\pi$
$67$	−6.27534	−	1.68147i	−0.766655	−	0.205424i	−0.620893	+	0.783895i	$0.713230\pi$
$68$			9.45827i			1.14698i
$69$	3.30711	+	5.72808i	0.398129	+	0.689580i
$70$		0			0
$71$	−8.06938	−	2.16218i	−0.957659	−	0.256604i	−0.254050	−	0.967191i	$-0.581763\pi$
$71$	−8.06938	−	2.16218i	−0.957659	−	0.256604i	−0.703609	+	0.710587i	$0.748429\pi$
$72$	−3.46586	+	0.928673i	−0.408455	+	0.109445i
$73$	−1.62921	−	6.08031i	−0.190685	−	0.711646i	−0.993342	−	0.115205i	$-0.963248\pi$
$73$	−1.62921	−	6.08031i	−0.190685	−	0.711646i	0.802657	−	0.596441i	$-0.203419\pi$
$74$	21.8590			2.54106
$75$	4.65227			0.537198
$76$	3.01323	+	11.2455i	0.345641	+	1.28995i
$77$		0			0
$78$	7.48713	−	4.73465i	0.847751	−	0.536094i
$79$	7.87501	+	13.6399i	0.886008	+	1.53461i	0.844554	+	0.535471i	$0.179866\pi$
$79$	7.87501	+	13.6399i	0.886008	+	1.53461i	0.0414546	+	0.999140i	$0.486801\pi$
$80$	1.04995	−	3.91846i	0.117388	−	0.438097i
$81$	0.273613	+	0.473911i	0.0304014	+	0.0526568i
$82$	2.82718	−	4.89682i	0.312210	−	0.540763i
$83$	−10.4223	−	10.4223i	−1.14399	−	1.14399i	−0.987713	−	0.156277i	$-0.950051\pi$
$83$	−10.4223	−	10.4223i	−1.14399	−	1.14399i	−0.156277	−	0.987713i	$-0.549949\pi$
$84$		0			0
$85$	−2.54795	+	9.50909i	−0.276364	+	1.03141i
$86$	3.79606	−	14.1671i	0.409339	−	1.52768i
$87$			6.16463i			0.660918i
$88$	−1.28075	+	0.739443i	−0.136529	+	0.0788249i
$89$	6.62546	−	6.62546i	0.702297	−	0.702297i	−0.262606	−	0.964903i	$-0.584582\pi$
$89$	6.62546	−	6.62546i	0.702297	−	0.702297i	0.964903	+	0.262606i	$0.0845820\pi$
$90$	−11.9092			−1.25534
$91$		0			0
$92$	−17.3877			−1.81279
$93$	3.24176	−	3.24176i	0.336155	−	0.336155i
$94$	−3.36890	+	1.94504i	−0.347476	+	0.200615i
$95$			12.1177i			1.24324i
$96$	2.01268	−	7.51143i	0.205418	−	0.766632i
$97$	−2.37570	+	8.86623i	−0.241216	+	0.900230i	0.734032	+	0.679115i	$0.237636\pi$
$97$	−2.37570	+	8.86623i	−0.241216	+	0.900230i	−0.975248	+	0.221115i	$0.929030\pi$
$98$		0			0
$99$	−0.914619	−	0.914619i	−0.0919227	−	0.0919227i
$100$	−6.11503	+	10.5915i	−0.611503	+	1.05915i
$101$	6.10920	+	10.5814i	0.607888	+	1.05289i	0.991588	+	0.129435i	$0.0413163\pi$
$101$	6.10920	+	10.5814i	0.607888	+	1.05289i	−0.383700	+	0.923458i	$0.625350\pi$
$102$	−2.06419	+	7.70367i	−0.204386	+	0.762777i
$103$	−0.347680	−	0.602200i	−0.0342580	−	0.0593366i	0.848388	−	0.529375i	$-0.177573\pi$
$103$	−0.347680	−	0.602200i	−0.0342580	−	0.0593366i	−0.882646	+	0.470038i	$0.844240\pi$
$104$	0.294113	+	7.29697i	0.0288401	+	0.715526i
$105$		0			0
$106$	3.86773	+	14.4346i	0.375667	+	1.40201i
$107$	−13.7976			−1.33386			−0.666930	−	0.745120i	$-0.732392\pi$
$107$	−13.7976			−1.33386			−0.666930	+	0.745120i	$0.732392\pi$
$108$	−15.4096			−1.48279
$109$	−3.39308	−	12.6631i	−0.324998	−	1.21291i	−0.914314	−	0.405006i	$-0.867269\pi$
$109$	−3.39308	−	12.6631i	−0.324998	−	1.21291i	0.589316	−	0.807903i	$-0.299397\pi$
$110$	−4.74126	+	1.27042i	−0.452061	+	0.121129i
$111$	10.5574	+	2.82883i	1.00206	+	0.268501i
$112$		0			0
$113$	−5.92811	−	10.2678i	−0.557670	−	0.965912i	−0.997690	−	0.0679248i	$-0.978362\pi$
$113$	−5.92811	−	10.2678i	−0.557670	−	0.965912i	0.440021	−	0.897988i	$-0.354971\pi$
$114$			9.81697i			0.919444i
$115$	−17.4811	−	4.68405i	−1.63012	−	0.436790i
$116$	−14.0346	−	8.10290i	−1.30308	−	0.752335i
$117$	−6.09804	+	1.90028i	−0.563764	+	0.175681i
$118$			7.30907i			0.672855i
$119$		0			0
$120$	−3.40417	+	5.89620i	−0.310757	+	0.538247i
$121$	9.06459	+	5.23344i	0.824053	+	0.475767i
$122$	15.5853	−	4.17607i	1.41103	−	0.378084i
$123$	1.99917	−	1.99917i	0.180259	−	0.180259i
$124$	3.11929	+	11.6414i	0.280121	+	1.04542i
$125$	1.72116	−	1.72116i	0.153945	−	0.153945i
$126$		0			0
$127$	−3.91434	−	2.25995i	−0.347342	−	0.200538i	0.316172	−	0.948702i	$-0.397602\pi$
$127$	−3.91434	−	2.25995i	−0.347342	−	0.200538i	−0.663514	+	0.748164i	$0.730936\pi$
$128$	10.2620	+	10.2620i	0.907038	+	0.907038i
$129$	3.66680	−	6.35108i	0.322843	−	0.559181i
$130$	−5.32544	+	23.6465i	−0.467072	+	2.07393i
$131$	−10.9818	+	6.34037i	−0.959488	+	0.553960i	−0.896015	−	0.444023i	$-0.853551\pi$
$131$	−10.9818	+	6.34037i	−0.959488	+	0.553960i	−0.0634723	+	0.997984i	$0.520217\pi$
$132$	−2.27767	+	0.610299i	−0.198246	+	0.0531197i
$133$		0			0
$134$	12.4718	−	7.20061i	1.07740	−	0.622038i
$135$	−15.4924	−	4.15117i	−1.33337	−	0.357276i
$136$	−4.64912	−	4.64912i	−0.398659	−	0.398659i
$137$	−7.16928	−	7.16928i	−0.612513	−	0.612513i	0.331087	−	0.943600i	$-0.392585\pi$
$137$	−7.16928	−	7.16928i	−0.612513	−	0.612513i	−0.943600	+	0.331087i	$0.892585\pi$
$138$	−14.1621	−	3.79473i	−1.20556	−	0.323029i
$139$	−0.0630104	+	0.0363791i	−0.00534447	+	0.00308563i	−0.502670	−	0.864478i	$-0.667649\pi$
$139$	−0.0630104	+	0.0363791i	−0.00534447	+	0.00308563i	0.497325	+	0.867564i	$0.334316\pi$
$140$		0			0
$141$	−1.87881	+	0.503424i	−0.158224	+	0.0423960i
$142$	16.0374	−	9.25917i	1.34582	−	0.777012i
$143$	−2.22503	+	1.40705i	−0.186066	+	0.117663i
$144$	−1.18482	+	2.05217i	−0.0987351	+	0.171014i
$145$	−11.9272	−	11.9272i	−0.990500	−	0.990500i
$146$	12.0842	+	6.97682i	1.00010	+	0.577406i
$147$		0			0
$148$	−20.3170	+	20.3170i	−1.67005	+	1.67005i
$149$	−0.322028	−	1.20183i	−0.0263816	−	0.0984574i	0.951480	−	0.307711i	$-0.0995631\pi$
$149$	−0.322028	−	1.20183i	−0.0263816	−	0.0984574i	−0.977861	+	0.209254i	$0.932896\pi$
$150$	−7.29216	+	7.29216i	−0.595402	+	0.595402i
$151$	−0.716844	+	0.192078i	−0.0583359	+	0.0156311i	−0.287869	−	0.957670i	$-0.592947\pi$
$151$	−0.716844	+	0.192078i	−0.0583359	+	0.0156311i	0.229533	+	0.973301i	$0.426280\pi$
$152$	−7.00874	−	4.04650i	−0.568484	−	0.328214i
$153$	2.87525	−	4.98009i	0.232450	−	0.402616i
$154$		0			0
$155$			12.5442i			1.00757i
$156$	−2.55831	+	11.3596i	−0.204828	+	0.909496i
$157$	7.82322	+	4.51674i	0.624361	+	0.360475i	0.778565	−	0.627564i	$-0.215948\pi$
$157$	7.82322	+	4.51674i	0.624361	+	0.360475i	−0.154204	+	0.988039i	$0.549281\pi$
$158$	−33.7233	−	9.03614i	−2.68289	−	0.718877i
$159$			7.47205i			0.592572i
$160$	10.6389	+	18.4271i	0.841076	+	1.45679i
$161$		0			0
$162$	−1.17170	−	0.313955i	−0.0920572	−	0.0246667i
$163$	−2.20381	+	0.590509i	−0.172616	+	0.0462523i	−0.344092	−	0.938936i	$-0.611813\pi$
$163$	−2.20381	+	0.590509i	−0.172616	+	0.0462523i	0.171476	+	0.985188i	$0.445146\pi$
$164$	1.92364	+	7.17912i	0.150211	+	0.560595i
$165$	−2.45431			−0.191068
$166$	32.6725			2.53588
$167$	0.729973	+	2.72430i	0.0564870	+	0.210812i	0.988401	−	0.151867i	$-0.0485286\pi$
$167$	0.729973	+	2.72430i	0.0564870	+	0.210812i	−0.931914	+	0.362680i	$0.881862\pi$
$168$		0			0
$169$	1.04626	+	12.9578i	0.0804816	+	0.996756i
$170$	−10.9112	−	18.8987i	−0.836847	−	1.44946i
$171$	1.83200	−	6.83712i	0.140097	−	0.522848i
$172$	9.63940	+	16.6959i	0.734998	+	1.27305i
$173$	2.31972	−	4.01787i	0.176365	−	0.305473i	−0.764268	−	0.644899i	$-0.776899\pi$
$173$	2.31972	−	4.01787i	0.176365	−	0.305473i	0.940633	+	0.339426i	$0.110233\pi$
$174$	−9.66268	−	9.66268i	−0.732526	−	0.732526i
$175$		0			0
$176$	−0.252783	+	0.943397i	−0.0190542	+	0.0711113i
$177$	−0.945886	+	3.53010i	−0.0710972	+	0.265338i
$178$			20.7700i			1.55678i
$179$	12.1991	−	7.04316i	0.911804	−	0.526430i	0.0307928	−	0.999526i	$-0.490197\pi$
$179$	12.1991	−	7.04316i	0.911804	−	0.526430i	0.881011	+	0.473096i	$0.156863\pi$
$180$	11.0690	−	11.0690i	0.825038	−	0.825038i
$181$	19.3214			1.43615			0.718075	−	0.695966i	$-0.245024\pi$
$181$	19.3214			1.43615			0.718075	+	0.695966i	$0.245024\pi$
$182$		0			0
$183$	8.06774			0.596384
$184$	8.54675	−	8.54675i	0.630075	−	0.630075i
$185$	−25.8993	+	14.9530i	−1.90416	+	1.09936i
$186$			10.1625i			0.745153i
$187$	0.613438	−	2.28938i	0.0448590	−	0.167416i
$188$	1.32342	−	4.93907i	0.0965203	−	0.360219i
$189$		0			0
$190$	−18.9937	−	18.9937i	−1.37795	−	1.37795i
$191$	−3.84651	+	6.66236i	−0.278324	+	0.482071i	−0.970968	−	0.239208i	$-0.923112\pi$
$191$	−3.84651	+	6.66236i	−0.278324	+	0.482071i	0.692644	+	0.721279i	$0.256446\pi$
$192$	7.13635	+	12.3605i	0.515021	+	0.892043i
$193$	2.07797	−	7.75507i	0.149575	−	0.558222i	−0.849934	−	0.526889i	$-0.823358\pi$
$193$	2.07797	−	7.75507i	0.149575	−	0.558222i	0.999509	−	0.0313328i	$-0.00997516\pi$
$194$	−10.1735	−	17.6210i	−0.730416	−	1.26512i
$195$	−5.63220	+	10.7315i	−0.403330	+	0.768495i
$196$		0			0
$197$	−1.52597	−	5.69500i	−0.108721	−	0.405752i	0.890020	−	0.455922i	$-0.150690\pi$
$197$	−1.52597	−	5.69500i	−0.108721	−	0.405752i	−0.998741	+	0.0501699i	$0.984024\pi$
$198$	2.86722			0.203764
$199$	−8.74035			−0.619587			−0.309794	−	0.950804i	$-0.600260\pi$
$199$	−8.74035			−0.619587			−0.309794	+	0.950804i	$0.600260\pi$
$200$	−2.20039	−	8.21195i	−0.155591	−	0.580673i
$201$	6.95542	−	1.86370i	0.490597	−	0.131455i
$202$	−26.1616	−	7.00997i	−1.84072	−	0.493220i
$203$		0			0
$204$	−5.24165	−	9.07880i	−0.366989	−	0.635643i
$205$			7.73589i			0.540298i
$206$	1.48888	+	0.398944i	0.103735	+	0.0277958i
$207$	9.15518	+	5.28575i	0.636329	+	0.367385i
$208$	3.54491	+	3.27021i	0.245795	+	0.226749i
$209$		−	2.91741i		−	0.201802i
$210$		0			0
$211$	−10.0859	+	17.4692i	−0.694340	+	1.20263i	0.276063	+	0.961140i	$0.410970\pi$
$211$	−10.0859	+	17.4692i	−0.694340	+	1.20263i	−0.970403	+	0.241492i	$0.922363\pi$
$212$	−17.0112	−	9.82140i	−1.16833	−	0.674536i
$213$	8.94388	−	2.39651i	0.612825	−	0.164206i
$214$	21.6268	−	21.6268i	1.47838	−	1.47838i
$215$	5.19349	+	19.3824i	0.354193	+	1.32187i
$216$	7.57443	−	7.57443i	0.515375	−	0.515375i
$217$		0			0
$218$	25.1671	+	14.5303i	1.70453	+	0.984113i
$219$	4.93347	+	4.93347i	0.333373	+	0.333373i
$220$	3.22599	−	5.58758i	0.217496	−	0.376715i
$221$	−8.60257	−	7.93596i	−0.578671	−	0.533831i
$222$	−20.9820	+	12.1140i	−1.40822	+	0.813037i
$223$	−12.7683	+	3.42126i	−0.855031	+	0.229105i	−0.659604	−	0.751613i	$-0.729276\pi$
$223$	−12.7683	+	3.42126i	−0.855031	+	0.229105i	−0.195427	+	0.980718i	$0.562609\pi$
$224$		0			0
$225$	6.43952	−	3.71786i	0.429301	−	0.247857i
$226$	25.3861	+	6.80218i	1.68866	+	0.452474i
$227$	−5.38732	−	5.38732i	−0.357569	−	0.357569i	0.505347	−	0.862916i	$-0.331364\pi$
$227$	−5.38732	−	5.38732i	−0.357569	−	0.357569i	−0.862916	+	0.505347i	$0.831364\pi$
$228$	−9.12444	−	9.12444i	−0.604281	−	0.604281i
$229$	28.2478	+	7.56897i	1.86667	+	0.500171i	0.999999	+	0.00128230i	$0.000408168\pi$
$229$	28.2478	+	7.56897i	1.86667	+	0.500171i	0.866666	+	0.498889i	$0.166258\pi$
$230$	34.7425	−	20.0586i	2.29085	−	1.32263i
$231$		0			0
$232$	10.8815	−	2.91568i	0.714404	−	0.191424i
$233$	−0.786647	+	0.454171i	−0.0515350	+	0.0297537i	−0.525546	−	0.850765i	$-0.676139\pi$
$233$	−0.786647	+	0.454171i	−0.0515350	+	0.0297537i	0.474011	+	0.880519i	$0.342806\pi$
$234$	6.57974	−	12.5369i	0.430131	−	0.819562i
$235$	2.66106	−	4.60909i	0.173588	−	0.300664i
$236$	−6.79346	−	6.79346i	−0.442216	−	0.442216i
$237$	−15.1181	−	8.72845i	−0.982027	−	0.566974i
$238$		0			0
$239$	7.05491	−	7.05491i	0.456344	−	0.456344i	−0.441109	−	0.897453i	$-0.645415\pi$
$239$	7.05491	−	7.05491i	0.456344	−	0.456344i	0.897453	+	0.441109i	$0.145415\pi$
$240$	1.16373	+	4.34311i	0.0751187	+	0.280347i
$241$	−5.10472	+	5.10472i	−0.328824	+	0.328824i	−0.852139	−	0.523315i	$-0.824695\pi$
$241$	−5.10472	+	5.10472i	−0.328824	+	0.328824i	0.523315	+	0.852139i	$0.324695\pi$
$242$	−22.4113	+	6.00509i	−1.44065	+	0.386021i
$243$	13.2149	+	7.62965i	0.847739	+	0.489442i
$244$	−10.6044	+	18.3673i	−0.678876	+	1.17585i
$245$		0			0
$246$			6.26714i			0.399578i
$247$	−12.7564	−	6.69493i	−0.811667	−	0.425988i
$248$	−7.25545	−	4.18894i	−0.460722	−	0.265998i
$249$	15.7800	+	4.22823i	1.00001	+	0.267953i
$250$			5.39563i			0.341249i
$251$	2.92724	+	5.07013i	0.184766	+	0.320023i	0.943498	−	0.331380i	$-0.107514\pi$
$251$	2.92724	+	5.07013i	0.184766	+	0.320023i	−0.758732	+	0.651403i	$0.774181\pi$
$252$		0			0
$253$	4.20870	+	1.12772i	0.264599	+	0.0708990i
$254$	9.67782	−	2.59316i	0.607240	−	0.162710i
$255$	−2.82408	−	10.5396i	−0.176851	−	0.660016i
$256$	−6.41568			−0.400980
$257$	−15.9760			−0.996558			−0.498279	−	0.867017i	$-0.666034\pi$
$257$	−15.9760			−0.996558			−0.498279	+	0.867017i	$0.666034\pi$
$258$	4.20745	+	15.7024i	0.261944	+	0.977589i
$259$		0			0
$260$	−17.0286	−	26.9281i	−1.05607	−	1.67001i
$261$	4.92646	+	8.53287i	0.304940	+	0.528171i
$262$	7.27522	−	27.1515i	0.449465	−	1.67743i
$263$	12.0727	+	20.9106i	0.744437	+	1.28940i	0.950457	+	0.310856i	$0.100616\pi$
$263$	12.0727	+	20.9106i	0.744437	+	1.28940i	−0.206020	+	0.978548i	$0.566051\pi$
$264$	0.819579	−	1.41955i	0.0504416	−	0.0873674i
$265$	−14.4568	−	14.4568i	−0.888073	−	0.888073i
$266$		0			0
$267$	−2.68790	+	10.0314i	−0.164497	+	0.613910i
$268$	−4.89935	+	18.2846i	−0.299276	+	1.11691i
$269$		−	29.4878i		−	1.79790i	−0.438047	−	0.898952i	$-0.644330\pi$
$269$		−	29.4878i		−	1.79790i	0.438047	−	0.898952i	$-0.355670\pi$
$270$	30.7900	−	17.7766i	1.87382	−	1.08185i
$271$	−0.604773	+	0.604773i	−0.0367374	+	0.0367374i	−0.725237	−	0.688499i	$-0.758270\pi$
$271$	−0.604773	+	0.604773i	−0.0367374	+	0.0367374i	0.688499	+	0.725237i	$0.258270\pi$
$272$	−4.34212			−0.263280
$273$		0			0
$274$	22.4748			1.35775
$275$	2.16709	−	2.16709i	0.130680	−	0.130680i
$276$	16.6901	−	9.63602i	1.00462	−	0.580020i
$277$			14.2038i			0.853426i	0.904387	+	0.426713i	$0.140329\pi$
$277$			14.2038i			0.853426i	−0.904387	+	0.426713i	$0.859671\pi$
$278$	0.0417430	−	0.155787i	0.00250358	−	0.00934348i
$279$	1.89649	−	7.07779i	0.113540	−	0.423736i
$280$		0			0
$281$	1.82178	+	1.82178i	0.108679	+	0.108679i	0.759355	−	0.650676i	$-0.225515\pi$
$281$	1.82178	+	1.82178i	0.108679	+	0.108679i	−0.650676	+	0.759355i	$0.725515\pi$
$282$	2.15583	−	3.73400i	0.128378	−	0.222356i
$283$	9.55836	+	16.5556i	0.568185	+	0.984126i	0.996746	+	0.0806125i	$0.0256876\pi$
$283$	9.55836	+	16.5556i	0.568185	+	0.984126i	−0.428560	+	0.903513i	$0.640979\pi$
$284$	−6.30002	+	23.5120i	−0.373837	+	1.39518i
$285$	−6.71544	−	11.6315i	−0.397788	−	0.688989i
$286$	1.28214	−	5.69306i	0.0758144	−	0.336637i
$287$		0			0
$288$	−3.21686	−	12.0055i	−0.189555	−	0.707431i
$289$	−6.46280			−0.380165
$290$	37.3903			2.19563
$291$	−2.63316	−	9.82709i	−0.154359	−	0.576074i
$292$	−17.7164	+	4.74709i	−1.03677	+	0.277802i
$293$	−0.0611926	−	0.0163965i	−0.00357491	−	0.000957894i	0.257031	−	0.966403i	$-0.417256\pi$
$293$	−0.0611926	−	0.0163965i	−0.00357491	−	0.000957894i	−0.260606	+	0.965445i	$0.583922\pi$
$294$		0			0
$295$	−4.99987	−	8.66004i	−0.291104	−	0.504207i
$296$		−	19.9732i		−	1.16092i
$297$	3.72990	+	0.999424i	0.216431	+	0.0579924i
$298$	2.38855	+	1.37903i	0.138365	+	0.0798850i
$299$	14.5891	−	15.8146i	0.843712	−	0.914582i
$300$		−	13.5555i		−	0.782625i
$301$		0			0
$302$	0.822539	−	1.42468i	0.0473318	−	0.0819810i
$303$	−11.7282	−	6.77127i	−0.673766	−	0.388999i
$304$	−5.16261	+	1.38332i	−0.296096	+	0.0793387i
$305$	−15.6093	+	15.6093i	−0.893785	+	0.893785i
$306$	3.29920	+	12.3128i	0.188602	+	0.703874i
$307$	4.12063	−	4.12063i	0.235177	−	0.235177i	−0.579673	−	0.814849i	$-0.696820\pi$
$307$	4.12063	−	4.12063i	0.235177	−	0.235177i	0.814849	+	0.579673i	$0.196820\pi$
$308$		0			0
$309$	0.667462	+	0.385360i	0.0379706	+	0.0219223i
$310$	−19.6623	−	19.6623i	−1.11674	−	1.11674i
$311$	−2.60731	+	4.51600i	−0.147847	+	0.256079i	−0.930432	−	0.366466i	$-0.880568\pi$
$311$	−2.60731	+	4.51600i	−0.147847	+	0.256079i	0.782584	+	0.622544i	$0.213901\pi$
$312$	−4.32619	−	6.84121i	−0.244922	−	0.387307i
$313$	14.7297	−	8.50419i	0.832571	−	0.480685i	−0.0221612	−	0.999754i	$-0.507055\pi$
$313$	14.7297	−	8.50419i	0.832571	−	0.480685i	0.854732	+	0.519069i	$0.173721\pi$
$314$	−19.3421	+	5.18271i	−1.09154	+	0.292477i
$315$		0			0
$316$	39.7430	−	22.9457i	2.23572	−	1.29079i
$317$	3.82263	+	1.02427i	0.214700	+	0.0575288i	0.364566	−	0.931178i	$-0.381217\pi$
$317$	3.82263	+	1.02427i	0.214700	+	0.0575288i	−0.149866	+	0.988706i	$0.547884\pi$
$318$	−11.7120	−	11.7120i	−0.656776	−	0.656776i
$319$	2.87156	+	2.87156i	0.160776	+	0.160776i
$320$	−37.7221	−	10.1076i	−2.10873	−	0.565033i
$321$	13.2440	−	7.64642i	0.739208	−	0.426782i
$322$		0			0
$323$	12.5283	−	3.35695i	0.697094	−	0.186786i
$324$	1.38085	−	0.797233i	0.0767138	−	0.0442907i
$325$	−4.50249	−	14.4486i	−0.249753	−	0.801465i
$326$	2.52875	−	4.37993i	0.140055	−	0.242582i
$327$	10.2747	+	10.2747i	0.568191	+	0.568191i
$328$	−4.47437	−	2.58328i	−0.247056	−	0.142638i
$329$		0			0
$330$	3.84698	−	3.84698i	0.211770	−	0.211770i
$331$	−3.47024	−	12.9511i	−0.190742	−	0.711858i	−0.993328	−	0.115322i	$-0.963210\pi$
$331$	−3.47024	−	12.9511i	−0.190742	−	0.711858i	0.802586	−	0.596536i	$-0.203457\pi$
$332$	−30.3676	+	30.3676i	−1.66664	+	1.66664i
$333$	16.8738	−	4.52132i	0.924678	−	0.247767i
$334$	−5.41436	−	3.12598i	−0.296260	−	0.171046i
$335$	−9.85135	+	17.0630i	−0.538237	+	0.932253i
$336$		0			0
$337$		−	15.2503i		−	0.830737i	−0.909653	−	0.415368i	$-0.863653\pi$
$337$		−	15.2503i		−	0.830737i	0.909653	−	0.415368i	$-0.136347\pi$
$338$	−21.9506	−	18.6707i	−1.19395	−	1.01555i
$339$	11.3805	+	6.57056i	0.618106	+	0.356864i
$340$	27.7069	+	7.42404i	1.50262	+	0.402625i
$341$		−	3.02011i		−	0.163548i
$342$	7.84522	+	13.5883i	0.424221	+	0.734772i
$343$		0			0
$344$	−12.9449	−	3.46857i	−0.697941	−	0.187013i
$345$	19.3756	−	5.19167i	1.04315	−	0.279510i
$346$	2.66175	+	9.93378i	0.143096	+	0.534043i
$347$	9.79224			0.525675			0.262838	−	0.964840i	$-0.415342\pi$
$347$	9.79224			0.525675			0.262838	+	0.964840i	$0.415342\pi$
$348$	17.9621			0.962867
$349$	1.16556	+	4.34994i	0.0623911	+	0.232847i	0.990079	−	0.140509i	$-0.0448738\pi$
$349$	1.16556	+	4.34994i	0.0623911	+	0.232847i	−0.927688	+	0.373356i	$0.878207\pi$
$350$		0			0
$351$	12.9294	−	14.0155i	0.690121	−	0.748089i
$352$	−2.56138	−	4.43645i	−0.136522	−	0.236463i
$353$	−4.38567	+	16.3675i	−0.233425	+	0.871156i	0.745427	+	0.666587i	$0.232246\pi$
$353$	−4.38567	+	16.3675i	−0.233425	+	0.871156i	−0.978852	+	0.204568i	$0.934421\pi$
$354$	−4.05059	−	7.01583i	−0.215286	−	0.372887i
$355$	−12.6677	+	21.9412i	−0.672333	+	1.16452i
$356$	−19.3048	−	19.3048i	−1.02315	−	1.02315i
$357$		0			0
$358$	−8.08163	+	30.1611i	−0.427128	+	1.59406i
$359$	−4.12643	+	15.4000i	−0.217784	+	0.812782i	0.767383	+	0.641189i	$0.221558\pi$
$359$	−4.12643	+	15.4000i	−0.217784	+	0.812782i	−0.985168	+	0.171594i	$0.945108\pi$
$360$			10.8818i			0.573519i
$361$	−2.62828	+	1.51744i	−0.138330	+	0.0798651i
$362$	−30.2851	+	30.2851i	−1.59175	+	1.59175i
$363$	−11.6012			−0.608906
$364$		0			0
$365$	−19.0904			−0.999235
$366$	−12.6457	+	12.6457i	−0.661001	+	0.661001i
$367$	20.7903	−	12.0033i	1.08524	−	0.626565i	0.152937	−	0.988236i	$-0.451127\pi$
$367$	20.7903	−	12.0033i	1.08524	−	0.626565i	0.932306	+	0.361671i	$0.117793\pi$
$368$		−	7.98237i		−	0.416110i
$369$	1.16955	−	4.36481i	0.0608842	−	0.227223i
$370$	17.1577	−	64.0335i	0.891987	−	3.32894i
$371$		0			0
$372$	−9.44563	−	9.44563i	−0.489733	−	0.489733i
$373$	7.17404	−	12.4258i	0.371458	−	0.643384i	−0.618332	−	0.785917i	$-0.712191\pi$
$373$	7.17404	−	12.4258i	0.371458	−	0.643384i	0.989790	+	0.142533i	$0.0455247\pi$
$374$	2.62694	+	4.54999i	0.135836	+	0.235274i
$375$	−0.698262	+	2.60595i	−0.0360581	+	0.134571i
$376$	1.77724	+	3.07826i	0.0916540	+	0.158749i
$377$	19.1456	−	5.96616i	0.986047	−	0.307273i
$378$		0			0
$379$	−2.18843	−	8.16732i	−0.112412	−	0.419527i	0.886668	−	0.462406i	$-0.153014\pi$
$379$	−2.18843	−	8.16732i	−0.112412	−	0.419527i	−0.999080	+	0.0428788i	$0.986347\pi$
$380$	35.3076			1.81124
$381$	5.00973			0.256656
$382$	−4.41366	−	16.4720i	−0.225823	−	0.842781i
$383$	−18.9731	+	5.08381i	−0.969478	+	0.259771i	−0.708607	−	0.705603i	$-0.750676\pi$
$383$	−18.9731	+	5.08381i	−0.969478	+	0.259771i	−0.260870	+	0.965374i	$0.584010\pi$
$384$	−15.5373	−	4.16320i	−0.792884	−	0.212453i
$385$		0			0
$386$	8.89852	+	15.4127i	0.452923	+	0.784485i
$387$		−	11.7213i		−	0.595825i
$388$	25.8338	+	6.92215i	1.31151	+	0.351419i
$389$	−4.88185	−	2.81854i	−0.247520	−	0.142906i	0.371108	−	0.928590i	$-0.378978\pi$
$389$	−4.88185	−	2.81854i	−0.247520	−	0.142906i	−0.618628	+	0.785684i	$0.712311\pi$
$390$	−7.99277	−	25.6490i	−0.404730	−	1.29879i
$391$			19.3712i			0.979641i
$392$		0			0
$393$	7.02749	−	12.1720i	0.354490	−	0.613995i
$394$	11.3184	+	6.53470i	0.570214	+	0.329213i
$395$	46.1379	−	12.3626i	2.32145	−	0.622030i
$396$	−2.66495	+	2.66495i	−0.133919	+	0.133919i
$397$	3.51692	+	13.1253i	0.176509	+	0.658740i	0.996290	+	0.0860629i	$0.0274286\pi$
$397$	3.51692	+	13.1253i	0.176509	+	0.658740i	−0.819781	+	0.572678i	$0.805905\pi$
$398$	13.7000	−	13.7000i	0.686717	−	0.686717i
$399$		0			0
$400$	−4.86238	−	2.80730i	−0.243119	−	0.140365i
$401$	5.57129	+	5.57129i	0.278217	+	0.278217i	0.832397	−	0.554180i	$-0.186968\pi$
$401$	5.57129	+	5.57129i	0.278217	+	0.278217i	−0.554180	+	0.832397i	$0.686968\pi$
$402$	−7.98096	+	13.8234i	−0.398054	+	0.689450i
$403$	−13.2054	−	6.93059i	−0.657807	−	0.345237i
$404$	30.8315	−	17.8005i	1.53392	−	0.885610i
$405$	1.60303	−	0.429531i	0.0796553	−	0.0213436i
$406$		0			0
$407$	6.23545	−	3.60004i	0.309080	−	0.178447i
$408$	7.03907	+	1.88611i	0.348486	+	0.0933766i
$409$	−2.68114	−	2.68114i	−0.132574	−	0.132574i	0.637706	−	0.770280i	$-0.279883\pi$
$409$	−2.68114	−	2.68114i	−0.132574	−	0.132574i	−0.770280	+	0.637706i	$0.779883\pi$
$410$	−12.1255	−	12.1255i	−0.598838	−	0.598838i
$411$	10.8548	+	2.90852i	0.535426	+	0.143467i
$412$	−1.75465	+	1.01305i	−0.0864453	+	0.0499092i
$413$		0			0
$414$	−22.6353	+	6.06510i	−1.11246	+	0.298084i
$415$	−38.7115	+	22.3501i	−1.90027	+	1.09712i
$416$	−25.2762	+	1.01879i	−1.23927	+	0.0499502i
$417$	0.0403216	−	0.0698390i	0.00197456	−	0.00342003i
$418$	4.57287	+	4.57287i	0.223666	+	0.223666i
$419$	3.07221	+	1.77374i	0.150087	+	0.0866528i	0.573163	−	0.819441i	$-0.305716\pi$
$419$	3.07221	+	1.77374i	0.150087	+	0.0866528i	−0.423076	+	0.906094i	$0.639050\pi$
$420$		0			0
$421$	−21.1170	+	21.1170i	−1.02918	+	1.02918i	−0.0296199	+	0.999561i	$0.509430\pi$
$421$	−21.1170	+	21.1170i	−1.02918	+	1.02918i	−0.999561	+	0.0296199i	$0.990570\pi$
$422$	−11.5730	−	43.1910i	−0.563364	−	2.10250i
$423$	−2.19827	+	2.19827i	−0.106883	+	0.106883i
$424$	13.1893	−	3.53406i	0.640528	−	0.171629i
$425$	11.7997	+	6.81259i	0.572372	+	0.330459i
$426$	−10.2626	+	17.7754i	−0.497225	+	0.861219i
$427$		0			0
$428$			40.2024i			1.94325i
$429$	1.35599	−	2.58368i	0.0654679	−	0.124741i
$430$	−38.5212	−	22.2402i	−1.85766	−	1.07252i
$431$	15.5793	+	4.17446i	0.750428	+	0.201077i	0.613708	−	0.789533i	$-0.289677\pi$
$431$	15.5793	+	4.17446i	0.750428	+	0.201077i	0.136720	+	0.990610i	$0.456344\pi$
$432$		−	7.07426i		−	0.340360i
$433$	−14.9794	−	25.9452i	−0.719866	−	1.24684i	−0.961052	−	0.276366i	$-0.910870\pi$
$433$	−14.9794	−	25.9452i	−0.719866	−	1.24684i	0.241186	−	0.970479i	$-0.422463\pi$
$434$		0			0
$435$	18.0586	+	4.83878i	0.865842	+	0.232002i
$436$	−36.8970	+	9.88651i	−1.76704	+	0.473478i
$437$	6.17128	+	23.0315i	0.295212	+	1.10175i
$438$	−15.4658			−0.738986
$439$	−4.51920			−0.215690			−0.107845	−	0.994168i	$-0.534395\pi$
$439$	−4.51920			−0.215690			−0.107845	+	0.994168i	$0.534395\pi$
$440$	1.16082	+	4.33222i	0.0553397	+	0.206531i
$441$		0			0
$442$	25.9231	−	1.04486i	1.23304	−	0.0496990i
$443$	16.8631	+	29.2078i	0.801191	+	1.38770i	0.918833	+	0.394648i	$0.129133\pi$
$443$	16.8631	+	29.2078i	0.801191	+	1.38770i	−0.117641	+	0.993056i	$0.537533\pi$
$444$	8.24246	−	30.7613i	0.391170	−	1.45987i
$445$	−14.2080	−	24.6090i	−0.673524	−	1.16658i
$446$	14.6510	−	25.3762i	0.693743	−	1.20160i
$447$	0.975144	+	0.975144i	0.0461227	+	0.0461227i
$448$		0			0
$449$	−0.999901	+	3.73168i	−0.0471882	+	0.176109i	−0.985498	−	0.169687i	$-0.945724\pi$
$449$	−0.999901	+	3.73168i	−0.0471882	+	0.176109i	0.938310	+	0.345796i	$0.112391\pi$
$450$	−4.26604	+	15.9211i	−0.201103	+	0.750527i
$451$		−	1.86247i		−	0.0877004i
$452$	−29.9176	+	17.2729i	−1.40720	+	0.812449i
$453$	0.581636	−	0.581636i	0.0273277	−	0.0273277i
$454$	16.8886			0.792620
$455$		0			0
$456$	8.97006			0.420061
$457$	0.367380	−	0.367380i	0.0171853	−	0.0171853i	−0.698462	−	0.715647i	$-0.746132\pi$
$457$	0.367380	−	0.367380i	0.0171853	−	0.0171853i	0.715647	+	0.698462i	$0.246132\pi$
$458$	−56.1405	+	32.4128i	−2.62328	+	1.51455i
$459$			17.1674i			0.801305i
$460$	−13.6480	+	50.9352i	−0.636343	+	2.37487i
$461$	−7.57790	+	28.2811i	−0.352938	+	1.31718i	0.530122	+	0.847922i	$0.322146\pi$
$461$	−7.57790	+	28.2811i	−0.352938	+	1.31718i	−0.883060	+	0.469261i	$0.844520\pi$
$462$		0			0
$463$	15.0661	+	15.0661i	0.700181	+	0.700181i	0.964449	−	0.264268i	$-0.0851303\pi$
$463$	15.0661	+	15.0661i	0.700181	+	0.700181i	−0.264268	+	0.964449i	$0.585130\pi$
$464$	3.71989	−	6.44304i	0.172692	−	0.299111i
$465$	−6.95182	−	12.0409i	−0.322383	−	0.558384i
$466$	0.521136	−	1.94491i	0.0241412	−	0.0900961i
$467$	−2.14169	−	3.70951i	−0.0991054	−	0.171656i	0.812209	−	0.583366i	$-0.198265\pi$
$467$	−2.14169	−	3.70951i	−0.0991054	−	0.171656i	−0.911315	+	0.411711i	$0.864931\pi$
$468$	5.53690	+	17.7681i	0.255943	+	0.821328i
$469$		0			0
$470$	3.05342	+	11.3955i	0.140844	+	0.525636i
$471$	−10.0125			−0.461350
$472$	6.67851			0.307404
$473$	−1.25037	−	4.66645i	−0.0574921	−	0.214564i
$474$	37.3780	−	10.0154i	1.71683	−	0.460023i
$475$	16.1998	+	4.34072i	0.743297	+	0.199166i
$476$		0			0
$477$	5.97128	+	10.3426i	0.273406	+	0.473553i
$478$			22.1163i			1.01158i
$479$	−10.8652	−	2.91131i	−0.496442	−	0.133021i	0.00190599	−	0.999998i	$-0.499393\pi$
$479$	−10.8652	−	2.91131i	−0.496442	−	0.133021i	−0.498348	+	0.866977i	$0.666060\pi$
$480$	−20.4240	−	11.7918i	−0.932226	−	0.538221i
$481$	−1.43191	−	35.5259i	−0.0652895	−	1.61984i
$482$		−	16.0027i		−	0.728902i
$483$		0			0
$484$	15.2488	−	26.4117i	0.693129	−	1.20053i
$485$	24.1078	+	13.9187i	1.09468	+	0.632014i
$486$	−32.6726	+	8.75461i	−1.48206	+	0.397117i
$487$	4.97171	−	4.97171i	0.225290	−	0.225290i	−0.585432	−	0.810722i	$-0.699075\pi$
$487$	4.97171	−	4.97171i	0.225290	−	0.225290i	0.810722	+	0.585432i	$0.199075\pi$
$488$	−3.81580	−	14.2407i	−0.172733	−	0.644648i
$489$	1.78814	−	1.78814i	0.0808625	−	0.0808625i
$490$		0			0
$491$	−0.343800	−	0.198493i	−0.0155155	−	0.00895787i	0.492222	−	0.870470i	$-0.336185\pi$
$491$	−0.343800	−	0.198493i	−0.0155155	−	0.00895787i	−0.507738	+	0.861512i	$0.669518\pi$
$492$	−5.82503	−	5.82503i	−0.262613	−	0.262613i
$493$	−9.02721	+	15.6356i	−0.406565	+	0.704192i
$494$	30.4887	−	9.50091i	1.37175	−	0.427466i
$495$	−3.39718	+	1.96136i	−0.152692	+	0.0881566i
$496$	−5.34434	+	1.43201i	−0.239968	+	0.0642992i
$497$		0			0
$498$	−31.3616	+	18.1066i	−1.40535	+	0.811378i
$499$	1.91022	+	0.511843i	0.0855133	+	0.0229132i	0.301322	−	0.953522i	$-0.402572\pi$
$499$	1.91022	+	0.511843i	0.0855133	+	0.0229132i	−0.215809	+	0.976436i	$0.569239\pi$
$500$	−5.01500	−	5.01500i	−0.224277	−	0.224277i
$501$	−2.21045	−	2.21045i	−0.0987558	−	0.0987558i
$502$	−12.5354	−	3.35884i	−0.559481	−	0.149913i
$503$	4.35557	−	2.51469i	0.194205	−	0.112124i	−0.399745	−	0.916627i	$-0.630901\pi$
$503$	4.35557	−	2.51469i	0.194205	−	0.112124i	0.593950	+	0.804502i	$0.297568\pi$
$504$		0			0
$505$	35.7924	−	9.59053i	1.59274	−	0.426773i
$506$	−8.36451	+	4.82925i	−0.371848	+	0.214687i
$507$	−8.18534	−	11.8581i	−0.363524	−	0.526638i
$508$	−6.58487	+	11.4053i	−0.292156	+	0.506030i
$509$	−4.21429	−	4.21429i	−0.186795	−	0.186795i	0.607514	−	0.794309i	$-0.292167\pi$
$509$	−4.21429	−	4.21429i	−0.186795	−	0.186795i	−0.794309	+	0.607514i	$0.792167\pi$
$510$	20.9468	+	12.0936i	0.927539	+	0.535515i
$511$		0			0
$512$	−10.4677	+	10.4677i	−0.462613	+	0.462613i
$513$	5.46920	+	20.4113i	0.241471	+	0.901183i
$514$	25.0415	−	25.0415i	1.10453	−	1.10453i
$515$	−2.03698	+	0.545807i	−0.0897600	+	0.0240511i
$516$	−18.5053	−	10.6841i	−0.814651	−	0.470339i
$517$	−0.640669	+	1.10967i	−0.0281766	+	0.0488033i
$518$		0			0
$519$			5.14222i			0.225719i
$520$	21.6065	+	4.86601i	0.947506	+	0.213389i
$521$	17.6087	+	10.1664i	0.771453	+	0.445399i	0.833393	−	0.552681i	$-0.186395\pi$
$521$	17.6087	+	10.1664i	0.771453	+	0.445399i	−0.0619398	+	0.998080i	$0.519729\pi$
$522$	−21.0967	−	5.65284i	−0.923376	−	0.247418i
$523$		−	27.0854i		−	1.18436i	−0.805806	−	0.592180i	$-0.798267\pi$
$523$		−	27.0854i		−	1.18436i	0.805806	−	0.592180i	$-0.201733\pi$
$524$	18.4741	+	31.9981i	0.807045	+	1.39784i
$525$		0			0
$526$	−51.6994	−	13.8528i	−2.25420	−	0.604011i
$527$	12.9693	−	3.47512i	0.564952	−	0.151379i
$528$	−0.280177	−	1.04564i	−0.0121932	−	0.0455055i
$529$	−12.6111			−0.548309
$530$	45.3202			1.96858
$531$	1.51181	+	5.64214i	0.0656069	+	0.244848i
$532$		0			0
$533$	−8.14364	−	4.27403i	−0.352740	−	0.185129i
$534$	−11.5105	−	19.9367i	−0.498106	−	0.862745i
$535$	−10.8301	+	40.4183i	−0.468224	+	1.74744i
$536$	−6.57940	−	11.3959i	−0.284187	−	0.492226i
$537$	−7.80644	+	13.5212i	−0.336873	+	0.583481i
$538$	46.2204	+	46.2204i	1.99270	+	1.99270i
$539$		0			0
$540$	−12.0954	+	45.1406i	−0.520502	+	1.94254i
$541$	8.82915	−	32.9508i	0.379595	−	1.41667i	−0.466919	−	0.884300i	$-0.654636\pi$
$541$	8.82915	−	32.9508i	0.379595	−	1.41667i	0.846513	−	0.532367i	$-0.178697\pi$
$542$		−	1.89589i		−	0.0814355i
$543$	−18.5462	+	10.7077i	−0.795894	+	0.459510i
$544$	16.1043	−	16.1043i	0.690464	−	0.690464i
$545$	−39.7585			−1.70307
$546$		0			0
$547$	−12.5750			−0.537669			−0.268834	−	0.963186i	$-0.586638\pi$
$547$	−12.5750			−0.537669			−0.268834	+	0.963186i	$0.586638\pi$
$548$	−20.8893	+	20.8893i	−0.892348	+	0.892348i
$549$	11.1671	−	6.44732i	0.476600	−	0.275165i
$550$			6.79355i			0.289678i
$551$	−5.75180	+	21.4660i	−0.245035	+	0.914482i
$552$	−3.46735	+	12.9403i	−0.147580	+	0.550777i
$553$		0			0
$554$	−22.2637	−	22.2637i	−0.945892	−	0.945892i
$555$	16.5735	−	28.7061i	0.703505	−	1.21851i
$556$	0.105999	+	0.183595i	0.00449535	+	0.00778617i
$557$	−7.89194	+	29.4531i	−0.334392	+	1.24797i	0.570134	+	0.821551i	$0.306891\pi$
$557$	−7.89194	+	29.4531i	−0.334392	+	1.24797i	−0.904527	+	0.426417i	$0.859776\pi$
$558$	8.12138	+	14.0666i	0.343805	+	0.595488i
$559$	−23.2734	−	5.24141i	−0.984358	−	0.221688i
$560$		0			0
$561$	0.679918	+	2.53749i	0.0287062	+	0.107133i
$562$	−5.71107			−0.240907
$563$	32.2270			1.35821			0.679104	−	0.734042i	$-0.262369\pi$
$563$	32.2270			1.35821			0.679104	+	0.734042i	$0.262369\pi$
$564$	1.46684	+	5.47433i	0.0617652	+	0.230511i
$565$	−34.7314	+	9.30625i	−1.46116	+	0.391517i
$566$	−40.9320	−	10.9677i	−1.72050	−	0.461006i
$567$		0			0
$568$	−8.46038	−	14.6538i	−0.354989	−	0.614860i
$569$			8.01324i			0.335932i	0.985793	+	0.167966i	$0.0537199\pi$
$569$			8.01324i			0.335932i	−0.985793	+	0.167966i	$0.946280\pi$
$570$	28.7577	+	7.70560i	1.20453	+	0.322752i
$571$	20.5058	+	11.8390i	0.858139	+	0.495447i	0.863389	−	0.504539i	$-0.168338\pi$
$571$	20.5058	+	11.8390i	0.858139	+	0.495447i	−0.00524963	+	0.999986i	$0.501671\pi$
$572$	4.09975	+	6.48313i	0.171419	+	0.271073i
$573$		−	8.52674i		−	0.356210i
$574$		0			0
$575$	−12.5240	+	21.6922i	−0.522286	+	0.904626i
$576$	19.7558	+	11.4060i	0.823157	+	0.475250i
$577$	−41.4172	+	11.0977i	−1.72422	+	0.462004i	−0.978839	−	0.204634i	$-0.934400\pi$
$577$	−41.4172	+	11.0977i	−1.72422	+	0.462004i	−0.745382	+	0.666638i	$0.767733\pi$
$578$	10.1300	−	10.1300i	0.421354	−	0.421354i
$579$	2.30316	+	8.59551i	0.0957161	+	0.357217i
$580$	−34.7526	+	34.7526i	−1.44302	+	1.44302i
$581$		0			0
$582$	19.5307	+	11.2760i	0.809573	+	0.467407i
$583$	3.48057	+	3.48057i	0.144151	+	0.144151i
$584$	6.37492	−	11.0417i	0.263796	−	0.456908i
$585$	0.780129	+	19.3551i	0.0322544	+	0.800234i
$586$	0.121616	−	0.0702151i	0.00502392	−	0.00290056i
$587$	31.0661	−	8.32414i	1.28224	−	0.343574i	0.447530	−	0.894269i	$-0.352304\pi$
$587$	31.0661	−	8.32414i	1.28224	−	0.343574i	0.834707	+	0.550695i	$0.185637\pi$
$588$		0			0
$589$	14.3129	−	8.26355i	0.589752	−	0.340494i
$590$	21.4111	+	5.73708i	0.881480	+	0.236192i
$591$	4.62084	+	4.62084i	0.190076	+	0.190076i
$592$	−9.32716	−	9.32716i	−0.383344	−	0.383344i
$593$	−33.1918	−	8.89371i	−1.36302	−	0.365221i	−0.498097	−	0.867121i	$-0.665968\pi$
$593$	−33.1918	−	8.89371i	−1.36302	−	0.365221i	−0.864926	+	0.501900i	$0.832634\pi$
$594$	−7.41292	+	4.27985i	−0.304156	+	0.175605i
$595$		0			0
$596$	−3.50180	+	0.938303i	−0.143439	+	0.0384344i
$597$	8.38968	−	4.84379i	0.343367	−	0.198243i
$598$	1.92083	+	47.6560i	0.0785486	+	1.94880i
$599$	−2.36262	+	4.09217i	−0.0965339	+	0.167202i	−0.910248	−	0.414064i	$-0.864109\pi$
$599$	−2.36262	+	4.09217i	−0.0965339	+	0.167202i	0.813714	+	0.581266i	$0.197442\pi$
$600$	6.66306	+	6.66306i	0.272018	+	0.272018i
$601$	−2.81859	−	1.62731i	−0.114973	−	0.0663794i	0.441411	−	0.897305i	$-0.354478\pi$
$601$	−2.81859	−	1.62731i	−0.114973	−	0.0663794i	−0.556383	+	0.830926i	$0.687811\pi$
$602$		0			0
$603$	8.13808	−	8.13808i	0.331408	−	0.331408i
$604$	0.559662	+	2.08869i	0.0227723	+	0.0849875i
$605$	22.4458	−	22.4458i	0.912551	−	0.912551i
$606$	28.9968	−	7.76966i	1.17791	−	0.315621i
$607$	13.6571	+	7.88495i	0.554326	+	0.320040i	0.750865	−	0.660456i	$-0.229637\pi$
$607$	13.6571	+	7.88495i	0.554326	+	0.320040i	−0.196539	+	0.980496i	$0.562970\pi$
$608$	14.0168	−	24.2778i	0.568457	−	0.984596i
$609$		0			0
$610$		−	48.9332i		−	1.98125i
$611$	3.38181	+	5.34781i	0.136813	+	0.216349i
$612$	−14.5106	−	8.37771i	−0.586557	−	0.338649i
$613$	−12.8002	−	3.42979i	−0.516993	−	0.138528i	−0.00911789	−	0.999958i	$-0.502902\pi$
$613$	−12.8002	−	3.42979i	−0.516993	−	0.138528i	−0.507876	+	0.861430i	$0.669569\pi$
$614$			12.9177i			0.521314i
$615$	−4.28713	−	7.42552i	−0.172874	−	0.299426i
$616$		0			0
$617$	−36.8780	−	9.88144i	−1.48465	−	0.397812i	−0.576726	−	0.816938i	$-0.695670\pi$
$617$	−36.8780	−	9.88144i	−1.48465	−	0.397812i	−0.907928	+	0.419126i	$0.862337\pi$
$618$	−1.65023	+	0.442179i	−0.0663822	+	0.0177870i
$619$	−4.73495	−	17.6711i	−0.190314	−	0.710261i	−0.993430	−	0.114439i	$-0.963493\pi$
$619$	−4.73495	−	17.6711i	−0.190314	−	0.710261i	0.803117	−	0.595822i	$-0.203174\pi$
$620$	36.5504			1.46790
$621$	−31.5598			−1.26645
$622$	−2.99175	−	11.1653i	−0.119958	−	0.447690i
$623$		0			0
$624$	−5.21499	−	1.17447i	−0.208767	−	0.0470165i
$625$	−14.1844	−	24.5682i	−0.567377	−	0.982726i
$626$	−9.75809	+	36.4177i	−0.390012	+	1.45554i
$627$	1.61679	+	2.80036i	0.0645684	+	0.111836i
$628$	13.1606	−	22.7948i	0.525163	−	0.909610i
$629$	22.6346	+	22.6346i	0.902501	+	0.902501i
$630$		0			0
$631$	8.97429	−	33.4925i	0.357261	−	1.33332i	−0.520354	−	0.853950i	$-0.674200\pi$
$631$	8.97429	−	33.4925i	0.357261	−	1.33332i	0.877615	−	0.479366i	$-0.159133\pi$
$632$	−8.25659	+	30.8140i	−0.328430	+	1.22572i
$633$		−	22.3578i		−	0.888643i
$634$	−7.59722	+	4.38626i	−0.301724	+	0.174201i
$635$	−9.69271	+	9.69271i	−0.384644	+	0.384644i
$636$	21.7715			0.863298
$637$		0			0
$638$	−9.00199			−0.356392
$639$	10.4647	−	10.4647i	0.413975	−	0.413975i
$640$	38.1161	−	22.0063i	1.50667	−	0.869877i
$641$		−	15.7583i		−	0.622414i	−0.950342	−	0.311207i	$-0.899267\pi$
$641$		−	15.7583i		−	0.622414i	0.950342	−	0.311207i	$-0.100733\pi$
$642$	−8.77385	+	32.7444i	−0.346276	+	1.29232i
$643$	7.83090	−	29.2253i	0.308821	−	1.15253i	−0.620786	−	0.783980i	$-0.713186\pi$
$643$	7.83090	−	29.2253i	0.308821	−	1.15253i	0.929606	−	0.368554i	$-0.120147\pi$
$644$		0			0
$645$	−15.7266	−	15.7266i	−0.619233	−	0.619233i
$646$	−14.3755	+	24.8992i	−0.565598	+	0.979645i
$647$	−22.4737	−	38.9255i	−0.883531	−	1.53032i	−0.847388	−	0.530974i	$-0.821826\pi$
$647$	−22.4737	−	38.9255i	−0.883531	−	1.53032i	−0.0361431	−	0.999347i	$-0.511507\pi$
$648$	−0.286870	+	1.07061i	−0.0112693	+	0.0420577i
$649$	1.20376	+	2.08497i	0.0472515	+	0.0818421i
$650$	29.7047	+	15.5900i	1.16511	+	0.611488i
$651$		0			0
$652$	1.72058	+	6.42131i	0.0673833	+	0.251478i
$653$	−4.80782			−0.188145			−0.0940723	−	0.995565i	$-0.529988\pi$
$653$	−4.80782			−0.188145			−0.0940723	+	0.995565i	$0.529988\pi$
$654$	−32.2099			−1.25951
$655$	9.95343	+	37.1467i	0.388913	+	1.45144i
$656$	−3.29580	+	0.883107i	−0.128679	+	0.0344796i
$657$	10.7713	+	2.88617i	0.420229	+	0.112600i
$658$		0			0
$659$	−1.29400	−	2.24128i	−0.0504072	−	0.0873078i	0.839721	−	0.543018i	$-0.182719\pi$
$659$	−1.29400	−	2.24128i	−0.0504072	−	0.0873078i	−0.890128	+	0.455710i	$0.849385\pi$
$660$			7.15120i			0.278360i
$661$	1.14316	+	0.306308i	0.0444637	+	0.0119140i	0.280982	−	0.959713i	$-0.409340\pi$
$661$	1.14316	+	0.306308i	0.0444637	+	0.0119140i	−0.236519	+	0.971627i	$0.576006\pi$
$662$	25.7395	+	14.8607i	1.00039	+	0.577577i
$663$	12.6554	+	2.85014i	0.491496	+	0.110690i
$664$		−	29.8538i		−	1.15855i
$665$		0			0
$666$	−19.3617	+	33.5355i	−0.750252	+	1.29948i
$667$	−28.7438	−	16.5953i	−1.11297	−	0.642571i
$668$	7.93786	−	2.12694i	0.307125	−	0.0822939i
$669$	10.3600	−	10.3600i	0.400542	−	0.400542i
$670$	−11.3039	−	42.1867i	−0.436707	−	1.62981i
$671$	3.75805	−	3.75805i	0.145078	−	0.145078i
$672$		0			0
$673$	28.3877	+	16.3896i	1.09426	+	0.631774i	0.934709	−	0.355415i	$-0.115660\pi$
$673$	28.3877	+	16.3896i	1.09426	+	0.631774i	0.159556	+	0.987189i	$0.448994\pi$
$674$	23.9039	+	23.9039i	0.920744	+	0.920744i
$675$	−11.0992	+	19.2244i	−0.427208	+	0.739946i
$676$	37.7556	−	3.04852i	1.45214	−	0.117251i
$677$	−6.57450	+	3.79579i	−0.252678	+	0.145884i	−0.620990	−	0.783818i	$-0.713269\pi$
$677$	−6.57450	+	3.79579i	−0.252678	+	0.145884i	0.368312	+	0.929702i	$0.379936\pi$
$678$	−28.1373	+	7.53935i	−1.08060	+	0.289547i
$679$		0			0
$680$	−17.2683	+	9.96984i	−0.662208	+	0.382326i
$681$	8.15675	+	2.18560i	0.312567	+	0.0837522i
$682$	4.73383	+	4.73383i	0.181268	+	0.181268i
$683$	16.7687	+	16.7687i	0.641635	+	0.641635i	0.950957	−	0.309322i	$-0.100102\pi$
$683$	16.7687	+	16.7687i	0.641635	+	0.641635i	−0.309322	+	0.950957i	$0.600102\pi$
$684$	−19.9215	−	5.33796i	−0.761719	−	0.204102i
$685$	−26.6289	+	15.3742i	−1.01744	+	0.587418i
$686$		0			0
$687$	−31.3091	+	8.38924i	−1.19452	+	0.320069i
$688$	−7.66480	+	4.42528i	−0.292218	+	0.168712i
$689$	23.2060	−	7.23149i	0.884080	−	0.275498i
$690$	−22.2324	+	38.5077i	−0.846373	+	1.46596i
$691$	−2.45150	−	2.45150i	−0.0932596	−	0.0932596i	0.658938	−	0.752197i	$-0.271006\pi$
$691$	−2.45150	−	2.45150i	−0.0932596	−	0.0932596i	−0.752197	+	0.658938i	$0.771006\pi$
$692$	−11.7070	−	6.75903i	−0.445033	−	0.256940i
$693$		0			0
$694$	−15.3487	+	15.3487i	−0.582630	+	0.582630i
$695$	0.0571097	+	0.213136i	0.00216630	+	0.00808473i
$696$	−8.82907	+	8.82907i	−0.334665	+	0.334665i
$697$	7.99806	−	2.14307i	0.302948	−	0.0811747i
$698$	−8.64521	−	4.99131i	−0.327226	−	0.188924i
$699$	0.503391	−	0.871899i	0.0190400	−	0.0329782i
$700$		0			0
$701$		−	40.4604i		−	1.52817i	−0.645116	−	0.764085i	$-0.723191\pi$
$701$		−	40.4604i		−	1.52817i	0.645116	−	0.764085i	$-0.276809\pi$
$702$	1.70231	+	42.2344i	0.0642494	+	1.59404i
$703$	34.1226	+	19.7007i	1.28696	+	0.743026i
$704$	9.08187	+	2.43348i	0.342286	+	0.0917153i
$705$			5.89889i			0.222165i
$706$	−18.7808	−	32.5294i	−0.706826	−	1.22426i
$707$		0			0
$708$	10.2857	+	2.75606i	0.386562	+	0.103579i
$709$	37.1048	−	9.94221i	1.39350	−	0.373388i	0.517495	−	0.855686i	$-0.326865\pi$
$709$	37.1048	−	9.94221i	1.39350	−	0.373388i	0.876007	+	0.482299i	$0.160198\pi$
$710$	−14.5355	−	54.2473i	−0.545508	−	2.03587i
$711$	−27.9013			−1.04638
$712$	18.9782			0.711237
$713$	6.38851	+	23.8422i	0.239252	+	0.892899i
$714$		0			0
$715$	2.37530	+	7.62239i	0.0888310	+	0.285061i
$716$	−20.5219	−	35.5449i	−0.766938	−	1.32837i
$717$	−2.86213	+	10.6816i	−0.106888	+	0.398912i
$718$	−17.6707	−	30.6065i	−0.659464	−	1.14223i
$719$	21.3049	−	36.9012i	0.794540	−	1.37618i	−0.128591	−	0.991698i	$-0.541045\pi$
$719$	21.3049	−	36.9012i	0.794540	−	1.37618i	0.923131	−	0.384486i	$-0.125621\pi$
$720$	5.08160	+	5.08160i	0.189380	+	0.189380i
$721$		0			0
$722$	1.74118	−	6.49816i	0.0647999	−	0.241836i
$723$	2.07095	−	7.72888i	0.0770193	−	0.287440i
$724$		−	56.2974i		−	2.09227i
$725$	−20.2177	+	11.6727i	−0.750865	+	0.433512i
$726$	18.1842	−	18.1842i	0.674878	−	0.674878i
$727$	23.6095			0.875628			0.437814	−	0.899066i	$-0.355753\pi$
$727$	23.6095			0.875628			0.437814	+	0.899066i	$0.355753\pi$
$728$		0			0
$729$	−18.5547			−0.687210
$730$	29.9230	−	29.9230i	1.10750	−	1.10750i
$731$	18.6005	−	10.7390i	0.687964	−	0.397196i
$732$		−	23.5072i		−	0.868851i
$733$	6.59668	−	24.6192i	0.243654	−	0.909329i	−0.730401	−	0.683018i	$-0.760667\pi$
$733$	6.59668	−	24.6192i	0.243654	−	0.909329i	0.974055	−	0.226311i	$-0.0726665\pi$
$734$	−13.7731	+	51.4019i	−0.508374	+	1.89728i
$735$		0			0
$736$	29.6054	+	29.6054i	1.09127	+	1.09127i
$737$	2.37178	−	4.10805i	0.0873658	−	0.151322i
$738$	5.00838	+	8.67477i	0.184361	+	0.319323i
$739$	7.03335	−	26.2488i	0.258726	−	0.965579i	−0.707253	−	0.706960i	$-0.750066\pi$
$739$	7.03335	−	26.2488i	0.258726	−	0.965579i	0.965979	−	0.258619i	$-0.0832673\pi$
$740$	43.5689	+	75.4636i	1.60163	+	2.77410i
$741$	15.9548	−	0.643077i	0.586114	−	0.0236240i
$742$		0			0
$743$	−7.41429	−	27.6705i	−0.272004	−	1.01513i	−0.957823	−	0.287360i	$-0.907222\pi$
$743$	−7.41429	−	27.6705i	−0.272004	−	1.01513i	0.685818	−	0.727773i	$-0.259444\pi$
$744$	9.28581			0.340434
$745$	−3.77338			−0.138246
$746$	8.23182	+	30.7216i	0.301388	+	1.12480i
$747$	25.2211	−	6.75797i	0.922791	−	0.247261i
$748$	−6.67064	−	1.78739i	−0.243903	−	0.0653535i
$749$		0			0
$750$	−2.99018	−	5.17915i	−0.109186	−	0.189116i
$751$			19.8037i			0.722648i	0.932440	+	0.361324i	$0.117675\pi$
$751$			19.8037i			0.722648i	−0.932440	+	0.361324i	$0.882325\pi$
$752$	2.26744	+	0.607558i	0.0826849	+	0.0221554i
$753$	−5.61959	−	3.24447i	−0.204789	−	0.118235i
$754$	−20.6579	+	39.3611i	−0.752317	+	1.43345i
$755$			2.25068i			0.0819105i
$756$		0			0
$757$	16.3218	−	28.2703i	0.593228	−	1.02750i	−0.400567	−	0.916268i	$-0.631187\pi$
$757$	16.3218	−	28.2703i	0.593228	−	1.02750i	0.993794	−	0.111233i	$-0.0354799\pi$
$758$	16.2320	+	9.37155i	0.589573	+	0.340390i
$759$	−4.66481	+	1.24993i	−0.169322	+	0.0453697i
$760$	−17.3551	+	17.3551i	−0.629535	+	0.629535i
$761$	6.44626	+	24.0578i	0.233677	+	0.872094i	0.978741	+	0.205101i	$0.0657522\pi$
$761$	6.44626	+	24.0578i	0.233677	+	0.872094i	−0.745064	+	0.666993i	$0.767581\pi$
$762$	−7.85244	+	7.85244i	−0.284464	+	0.284464i
$763$		0			0
$764$	19.4123	+	11.2077i	0.702312	+	0.405480i
$765$	−12.3317	−	12.3317i	−0.445854	−	0.445854i
$766$	21.7705	−	37.7077i	0.786601	−	1.36243i
$767$	11.8789	−	0.478793i	0.428922	−	0.0172882i
$768$	6.15827	−	3.55548i	0.222218	−	0.128297i
$769$	52.0116	−	13.9365i	1.87559	−	0.502562i	0.875783	−	0.482705i	$-0.160346\pi$
$769$	52.0116	−	13.9365i	1.87559	−	0.502562i	0.999803	−	0.0198562i	$-0.00632083\pi$
$770$		0			0
$771$	15.3351	−	8.85370i	0.552279	−	0.318858i
$772$	−22.5962	−	6.05463i	−0.813254	−	0.217911i
$773$	−23.3186	−	23.3186i	−0.838711	−	0.838711i	0.149979	−	0.988689i	$-0.452080\pi$
$773$	−23.3186	−	23.3186i	−0.838711	−	0.838711i	−0.988689	+	0.149979i	$0.952080\pi$
$774$	18.3724	+	18.3724i	0.660381	+	0.660381i
$775$	16.7700	+	4.49352i	0.602397	+	0.161412i
$776$	−16.1009	+	9.29584i	−0.577987	+	0.333701i
$777$		0			0
$778$	12.0699	−	3.23412i	0.432727	−	0.115949i
$779$	8.82663	−	5.09606i	0.316247	−	0.182585i
$780$	31.2686	+	16.4107i	1.11959	+	0.587597i
$781$	3.04985	−	5.28249i	0.109132	−	0.189022i
$782$	−30.3631	−	30.3631i	−1.08578	−	1.08578i
$783$	−25.4738	−	14.7073i	−0.910359	−	0.525596i
$784$		0			0
$785$	19.3719	−	19.3719i	0.691413	−	0.691413i
$786$	8.06366	+	30.0940i	0.287621	+	1.07342i
$787$	−1.78895	+	1.78895i	−0.0637690	+	0.0637690i	−0.738272	−	0.674503i	$-0.764358\pi$
$787$	−1.78895	+	1.78895i	−0.0637690	+	0.0637690i	0.674503	+	0.738272i	$0.264358\pi$
$788$	−16.5937	+	4.44627i	−0.591126	+	0.158392i
$789$	−23.1768	−	13.3811i	−0.825114	−	0.476380i
$790$	−52.9406	+	91.6959i	−1.88354	+	3.26239i
$791$		0			0
$792$		−	2.61986i		−	0.0930927i
$793$	−7.80799	−	25.0561i	−0.277270	−	0.889767i
$794$	−26.0857	−	15.0606i	−0.925746	−	0.534480i
$795$	21.8885	+	5.86501i	0.776305	+	0.208010i
$796$			25.4670i			0.902655i
$797$	15.5118	+	26.8672i	0.549456	+	0.951686i	0.998312	+	0.0580819i	$0.0184985\pi$
$797$	15.5118	+	26.8672i	0.549456	+	0.951686i	−0.448855	+	0.893604i	$0.648168\pi$
$798$		0			0
$799$	−5.50248	−	1.47439i	−0.194664	−	0.0521600i
$800$	28.4457	−	7.62199i	1.00571	−	0.269478i
$801$	4.29606	+	16.0331i	0.151794	+	0.566503i
$802$	−17.4653			−0.616722
$803$	4.59614			0.162194
$804$	−5.43031	−	20.2662i	−0.191512	−	0.714734i
$805$		0			0
$806$	31.5619	−	9.83535i	1.11172	−	0.346435i
$807$	16.3418	+	28.3047i	0.575257	+	0.996374i
$808$	−6.40521	+	23.9046i	−0.225335	+	0.840960i
$809$	−1.72648	−	2.99036i	−0.0607000	−	0.105135i	0.834079	−	0.551646i	$-0.186000\pi$
$809$	−1.72648	−	2.99036i	−0.0607000	−	0.105135i	−0.894778	+	0.446510i	$0.852667\pi$
$810$	−1.83939	+	3.18592i	−0.0646296	+	0.111942i
$811$	−27.5137	−	27.5137i	−0.966135	−	0.966135i	0.0333099	−	0.999445i	$-0.489395\pi$
$811$	−27.5137	−	27.5137i	−0.966135	−	0.966135i	−0.999445	+	0.0333099i	$0.989395\pi$
$812$		0			0
$813$	0.245352	−	0.915666i	0.00860487	−	0.0321138i
$814$	−4.13084	+	15.4165i	−0.144786	+	0.540349i
$815$			6.91931i			0.242373i
$816$	4.16791	−	2.40634i	0.145906	−	0.0842389i
$817$	18.6940	−	18.6940i	0.654020	−	0.654020i
$818$	8.40504			0.293875
$819$		0			0
$820$	22.5403			0.787141
$821$	−12.7874	+	12.7874i	−0.446284	+	0.446284i	−0.894117	−	0.447833i	$-0.852196\pi$
$821$	−12.7874	+	12.7874i	−0.446284	+	0.446284i	0.447833	+	0.894117i	$0.352196\pi$
$822$	−21.5731	+	12.4552i	−0.752448	+	0.434426i
$823$		−	51.6586i		−	1.80071i	−0.435159	−	0.900353i	$-0.643308\pi$
$823$		−	51.6586i		−	1.80071i	0.435159	−	0.900353i	$-0.356692\pi$
$824$	0.364527	−	1.36043i	0.0126989	−	0.0473929i
$825$	−0.879171	+	3.28111i	−0.0306088	+	0.114234i
$826$		0			0
$827$	34.2663	+	34.2663i	1.19156	+	1.19156i	0.976630	+	0.214927i	$0.0689514\pi$
$827$	34.2663	+	34.2663i	1.19156	+	1.19156i	0.214927	+	0.976630i	$0.431049\pi$
$828$	15.4012	−	26.6757i	0.535230	−	0.927045i
$829$	7.28433	+	12.6168i	0.252995	+	0.438201i	0.964349	−	0.264633i	$-0.0852510\pi$
$829$	7.28433	+	12.6168i	0.252995	+	0.438201i	−0.711354	+	0.702834i	$0.751918\pi$
$830$	25.6455	−	95.7102i	0.890167	−	3.32215i
$831$	−7.87158	−	13.6340i	−0.273062	−	0.472957i
$832$	31.4816	−	34.1260i	1.09143	−	1.18311i
$833$		0			0
$834$	0.0462668	+	0.172670i	0.00160209	+	0.00597907i
$835$	8.55348			0.296005
$836$	−8.50055			−0.293998
$837$	5.66172	+	21.1298i	0.195698	+	0.730354i
$838$	−7.59572	+	2.03527i	−0.262390	+	0.0703072i
$839$	−46.6633	−	12.5034i	−1.61100	−	0.431665i	−0.662658	−	0.748922i	$-0.730572\pi$
$839$	−46.6633	−	12.5034i	−1.61100	−	0.431665i	−0.948340	+	0.317257i	$0.897238\pi$
$840$		0			0
$841$	−0.967215	−	1.67527i	−0.0333522	−	0.0577678i
$842$		−	66.1993i		−	2.28138i
$843$	−2.75830	−	0.739085i	−0.0950010	−	0.0254554i
$844$	50.9006	+	29.3875i	1.75207	+	1.01156i
$845$	38.7797	+	7.10604i	1.33406	+	0.244455i
$846$		−	6.89130i		−	0.236928i
$847$		0			0
$848$	4.50882	−	7.80951i	0.154834	−	0.268180i
$849$	−18.3497	−	10.5942i	−0.629761	−	0.363593i
$850$	−29.1737	+	7.81707i	−1.00065	+	0.268123i
$851$	−41.6105	+	41.6105i	−1.42639	+	1.42639i
$852$	−6.98277	−	26.0601i	−0.239226	−	0.892803i
$853$	36.7362	−	36.7362i	1.25783	−	1.25783i	0.305696	−	0.952129i	$-0.401111\pi$
$853$	36.7362	−	36.7362i	1.25783	−	1.25783i	0.952129	−	0.305696i	$-0.0988891\pi$
$854$		0			0
$855$	−18.5906	−	10.7333i	−0.635784	−	0.367070i
$856$	−19.7611	−	19.7611i	−0.675420	−	0.675420i
$857$	3.64891	−	6.32009i	0.124644	−	0.215890i	−0.796950	−	0.604046i	$-0.793554\pi$
$857$	3.64891	−	6.32009i	0.124644	−	0.215890i	0.921594	+	0.388156i	$0.126888\pi$
$858$	1.92432	+	6.17519i	0.0656951	+	0.210817i
$859$	−35.5603	+	20.5307i	−1.21330	+	0.700500i	−0.963477	−	0.267791i	$-0.913706\pi$
$859$	−35.5603	+	20.5307i	−1.21330	+	0.700500i	−0.249825	+	0.968291i	$0.580373\pi$
$860$	56.4750	−	15.1324i	1.92578	−	0.516012i
$861$		0			0
$862$	−30.9628	+	17.8764i	−1.05460	+	0.608872i
$863$	−52.4930	−	14.0655i	−1.78688	−	0.478794i	−0.795073	−	0.606514i	$-0.792567\pi$
$863$	−52.4930	−	14.0655i	−1.78688	−	0.478794i	−0.991810	+	0.127720i	$0.959234\pi$
$864$	26.2373	+	26.2373i	0.892612	+	0.892612i
$865$	−9.94907	−	9.94907i	−0.338278	−	0.338278i
$866$	64.1468	+	17.1881i	2.17980	+	0.584075i
$867$	6.20350	−	3.58159i	0.210682	−	0.121637i
$868$		0			0
$869$	−11.1080	+	2.97639i	−0.376814	+	0.100967i
$870$	−35.8902	+	20.7212i	−1.21679	+	0.702514i
$871$	−12.5196	−	19.7978i	−0.424210	−	0.670824i
$872$	13.2767	−	22.9960i	0.449606	−	0.778741i
$873$	−11.4980	−	11.4980i	−0.389150	−	0.389150i
$874$	−45.7736	−	26.4274i	−1.54832	−	0.893920i
$875$		0			0
$876$	14.3748	−	14.3748i	0.485680	−	0.485680i
$877$	11.0381	+	41.1947i	0.372729	+	1.39105i	0.856634	+	0.515925i	$0.172552\pi$
$877$	11.0381	+	41.1947i	0.372729	+	1.39105i	−0.483905	+	0.875121i	$0.660782\pi$
$878$	7.08357	−	7.08357i	0.239059	−	0.239059i
$879$	0.0678242	−	0.0181734i	0.00228765	−	0.000612975i
$880$	2.56516	+	1.48099i	0.0864714	+	0.0499243i
$881$	−13.6175	+	23.5863i	−0.458786	+	0.794641i	−0.998897	−	0.0469528i	$-0.985049\pi$
$881$	−13.6175	+	23.5863i	−0.458786	+	0.794641i	0.540111	+	0.841594i	$0.318382\pi$
$882$		0			0
$883$			21.3903i			0.719842i	0.932983	+	0.359921i	$0.117196\pi$
$883$			21.3903i			0.719842i	−0.932983	+	0.359921i	$0.882804\pi$
$884$	−23.1232	+	25.0655i	−0.777719	+	0.843046i
$885$	9.59855	+	5.54172i	0.322652	+	0.186283i
$886$	−72.2133	−	19.3495i	−2.42605	−	0.650059i
$887$		−	15.8366i		−	0.531741i	−0.964009	−	0.265871i	$-0.914341\pi$
$887$		−	15.8366i		−	0.531741i	0.964009	−	0.265871i	$-0.0856594\pi$
$888$	11.0689	+	19.1719i	0.371448	+	0.643367i
$889$		0			0
$890$	60.8433	+	16.3029i	2.03947	+	0.546475i
$891$	−0.385941	+	0.103413i	−0.0129295	+	0.00346446i
$892$	9.96864	+	37.2035i	0.333775	+	1.24566i
$893$	−7.01194			−0.234646
$894$	−3.05696			−0.102240
$895$	−11.0567	−	41.2642i	−0.369585	−	1.37931i
$896$		0			0
$897$	−5.23957	+	23.2652i	−0.174944	+	0.776803i
$898$	−4.28190	−	7.41646i	−0.142889	−	0.247491i
$899$	−5.95426	+	22.2216i	−0.198586	+	0.741132i
$900$	−10.8328	−	18.7630i	−0.361095	−	0.625434i
$901$	−10.9417	+	18.9517i	−0.364523	+	0.631371i
$902$	2.91931	+	2.91931i	0.0972024	+	0.0972024i
$903$		0			0
$904$	6.21535	−	23.1960i	0.206720	−	0.771488i
$905$	15.1659	−	56.5998i	0.504131	−	1.88144i
$906$			1.82336i			0.0605770i
$907$	−22.5733	+	13.0327i	−0.749533	+	0.432743i	−0.825525	−	0.564365i	$-0.809121\pi$
$907$	−22.5733	+	13.0327i	−0.749533	+	0.432743i	0.0759921	+	0.997108i	$0.475788\pi$
$908$	−15.6972	+	15.6972i	−0.520929	+	0.520929i
$909$	−21.6450			−0.717919
$910$		0			0
$911$	−45.9225			−1.52148			−0.760739	−	0.649057i	$-0.775163\pi$
$911$	−45.9225			−1.52148			−0.760739	+	0.649057i	$0.775163\pi$
$912$	4.18886	−	4.18886i	0.138707	−	0.138707i
$913$	9.32006	−	5.38094i	0.308449	−	0.178083i
$914$			1.15169i			0.0380946i
$915$	6.33257	−	23.6335i	0.209348	−	0.781299i
$916$	22.0539	−	82.3063i	0.728682	−	2.71948i
$917$		0			0
$918$	−26.9088	−	26.9088i	−0.888124	−	0.888124i
$919$	−1.32248	+	2.29060i	−0.0436245	+	0.0755598i	−0.887013	−	0.461744i	$-0.847224\pi$
$919$	−1.32248	+	2.29060i	−0.0436245	+	0.0755598i	0.843389	+	0.537304i	$0.180557\pi$
$920$	−18.3281	−	31.7453i	−0.604261	−	1.04661i
$921$	−1.67171	+	6.23890i	−0.0550846	+	0.205579i
$922$	−32.4510	−	56.2068i	−1.06872	−	1.85107i
$923$	−16.0988	−	25.4578i	−0.529898	−	0.837953i
$924$		0			0
$925$	10.7128	+	39.9805i	0.352233	+	1.31455i
$926$	−47.2304			−1.55209
$927$	1.23184			0.0404589
$928$	10.0997	+	37.6927i	0.331540	+	1.23732i
$929$	15.8375	−	4.24365i	0.519612	−	0.139230i	0.0105250	−	0.999945i	$-0.496650\pi$
$929$	15.8375	−	4.24365i	0.519612	−	0.139230i	0.509087	+	0.860715i	$0.329983\pi$
$930$	29.7700	+	7.97684i	0.976195	+	0.261571i
$931$		0			0
$932$	1.32333	+	2.29208i	0.0433472	+	0.0750795i
$933$		−	5.77975i		−	0.189220i
$934$	9.17139	+	2.45747i	0.300097	+	0.0804108i
$935$	−6.22497	−	3.59399i	−0.203578	−	0.117536i
$936$	−11.4553	−	6.01210i	−0.374429	−	0.196512i
$937$			17.9634i			0.586840i	0.955984	+	0.293420i	$0.0947934\pi$
$937$			17.9634i			0.586840i	−0.955984	+	0.293420i	$0.905207\pi$
$938$		0			0
$939$	−9.42581	+	16.3260i	−0.307600	+	0.532778i
$940$	−13.4296	−	7.75361i	−0.438027	−	0.252895i
$941$	−50.6367	+	13.5681i	−1.65071	+	0.442307i	−0.959812	−	0.280645i	$-0.909452\pi$
$941$	−50.6367	+	13.5681i	−1.65071	+	0.442307i	−0.690899	+	0.722952i	$0.742785\pi$
$942$	15.6939	−	15.6939i	0.511336	−	0.511336i
$943$	3.93974	+	14.7033i	0.128295	+	0.478805i
$944$	3.11875	−	3.11875i	0.101507	−	0.101507i
$945$		0			0
$946$	9.27425	+	5.35449i	0.301532	+	0.174090i
$947$	6.25266	+	6.25266i	0.203184	+	0.203184i	0.801363	−	0.598179i	$-0.204109\pi$
$947$	6.25266	+	6.25266i	0.203184	+	0.203184i	−0.598179	+	0.801363i	$0.704109\pi$
$948$	−25.4323	+	44.0501i	−0.826004	+	1.43068i
$949$	10.5473	−	20.0966i	0.342380	−	0.652363i
$950$	−32.1960	+	18.5884i	−1.04458	+	0.603086i
$951$	−4.23690	+	1.13527i	−0.137391	+	0.0368138i
$952$		0			0
$953$	−21.4513	+	12.3849i	−0.694877	+	0.401188i	−0.805437	−	0.592682i	$-0.798069\pi$
$953$	−21.4513	+	12.3849i	−0.694877	+	0.401188i	0.110559	+	0.993870i	$0.464736\pi$
$954$	−25.5710	−	6.85172i	−0.827890	−	0.221833i
$955$	16.4974	+	16.4974i	0.533842	+	0.533842i
$956$	−20.5561	−	20.5561i	−0.664832	−	0.664832i
$957$	−4.34773	−	1.16497i	−0.140542	−	0.0376581i
$958$	21.5938	−	12.4672i	0.697664	−	0.402797i
$959$		0			0
$960$	41.8102	−	11.2030i	1.34942	−	0.361575i
$961$	−12.0301	+	6.94557i	−0.388067	+	0.224051i
$962$	57.9290	+	53.4402i	1.86771	+	1.72298i
$963$	12.2213	−	21.1678i	0.393825	−	0.682124i
$964$	14.8738	+	14.8738i	0.479052	+	0.479052i
$965$	−21.0865	−	12.1743i	−0.678799	−	0.391905i
$966$		0			0
$967$	0.370336	−	0.370336i	0.0119092	−	0.0119092i	−0.701127	−	0.713036i	$-0.747319\pi$
$967$	0.370336	−	0.370336i	0.0119092	−	0.0119092i	0.713036	+	0.701127i	$0.247319\pi$
$968$	5.48702	+	20.4778i	0.176360	+	0.658183i
$969$	−10.1653	+	10.1653i	−0.326556	+	0.326556i
$970$	−59.6042	+	15.9709i	−1.91378	+	0.512795i
$971$	−28.8662	−	16.6659i	−0.926359	−	0.534834i	−0.0407007	−	0.999171i	$-0.512959\pi$
$971$	−28.8662	−	16.6659i	−0.926359	−	0.534834i	−0.885658	+	0.464338i	$0.846292\pi$
$972$	22.2307	−	38.5048i	0.713051	−	1.23504i
$973$		0			0
$974$			15.5857i			0.499398i
$975$	12.3291	+	11.3737i	0.394847	+	0.364250i
$976$	−8.43210	−	4.86828i	−0.269905	−	0.155830i
$977$	30.7510	+	8.23970i	0.983811	+	0.263611i	0.714649	−	0.699484i	$-0.246587\pi$
$977$	30.7510	+	8.23970i	0.983811	+	0.263611i	0.269162	+	0.963095i	$0.413253\pi$
$978$			5.60560i			0.179247i
$979$	3.42068	+	5.92479i	0.109325	+	0.189357i
$980$		0			0
$981$	22.4329	+	6.01087i	0.716226	+	0.191912i
$982$	0.850011	−	0.227760i	0.0271250	−	0.00726811i
$983$	−12.7899	−	47.7326i	−0.407935	−	1.52243i	−0.798577	−	0.601892i	$-0.794414\pi$
$983$	−12.7899	−	47.7326i	−0.407935	−	1.52243i	0.390642	−	0.920543i	$-0.372253\pi$
$984$	5.72647			0.182553
$985$	−17.8806			−0.569724
$986$	−10.3582	−	38.6574i	−0.329873	−	1.23110i
$987$		0			0
$988$	−19.5072	+	37.1686i	−0.620607	+	1.18249i
$989$	19.7421	+	34.1944i	0.627763	+	1.08732i
$990$	2.25055	−	8.39918i	0.0715273	−	0.266943i
$991$	−21.3389	−	36.9601i	−0.677853	−	1.17408i	−0.975626	−	0.219439i	$-0.929577\pi$
$991$	−21.3389	−	36.9601i	−0.677853	−	1.17408i	0.297774	−	0.954637i	$-0.403756\pi$
$992$	14.5102	−	25.1324i	0.460699	−	0.797955i
$993$	10.5083	+	10.5083i	0.333472	+	0.333472i
$994$		0			0
$995$	−6.86053	+	25.6038i	−0.217493	+	0.811696i
$996$	12.3199	−	45.9786i	0.390372	−	1.45689i
$997$			5.47320i			0.173338i	0.996237	+	0.0866689i	$0.0276222\pi$
$997$			5.47320i			0.173338i	−0.996237	+	0.0866689i	$0.972378\pi$
$998$	−3.79644	+	2.19188i	−0.120174	+	0.0693826i
$999$	−36.8767	+	36.8767i	−1.16673	+	1.16673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.227.1		28
7.2	even	3		91.2.w.a.19.7	✓	28
7.3	odd	6		637.2.bd.b.97.1		28
7.4	even	3		637.2.bd.a.97.1		28
7.5	odd	6		637.2.x.a.19.7		28
7.6	odd	2		91.2.ba.a.45.1	yes	28
13.11	odd	12		637.2.x.a.570.7		28
21.2	odd	6		819.2.gh.b.19.1		28
21.20	even	2		819.2.et.b.136.7		28
91.11	odd	12		637.2.bd.b.440.1		28
91.24	even	12		637.2.bd.a.440.1		28
91.37	odd	12		91.2.ba.a.89.1	yes	28
91.76	even	12		91.2.w.a.24.7	yes	28
91.89	even	12	inner	637.2.bb.a.362.1		28
273.128	even	12		819.2.et.b.271.7		28
273.167	odd	12		819.2.gh.b.388.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.7	✓	28	7.2	even	3
91.2.w.a.24.7	yes	28	91.76	even	12
91.2.ba.a.45.1	yes	28	7.6	odd	2
91.2.ba.a.89.1	yes	28	91.37	odd	12
637.2.x.a.19.7		28	7.5	odd	6
637.2.x.a.570.7		28	13.11	odd	12
637.2.bb.a.227.1		28	1.1	even	1	trivial
637.2.bb.a.362.1		28	91.89	even	12	inner
637.2.bd.a.97.1		28	7.4	even	3
637.2.bd.a.440.1		28	91.24	even	12
637.2.bd.b.97.1		28	7.3	odd	6
637.2.bd.b.440.1		28	91.11	odd	12
819.2.et.b.136.7		28	21.20	even	2
819.2.et.b.271.7		28	273.128	even	12
819.2.gh.b.19.1		28	21.2	odd	6
819.2.gh.b.388.1		28	273.167	odd	12

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.56744 + 1.56744i) q^{2} +(-0.959879 + 0.554186i) q^{3} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(0.635898 - 2.37321i) q^{6} +(1.43221 + 1.43221i) q^{8} +(-0.885755 + 1.53417i) q^{9} +O(q^{10})\)	\(q+(-1.56744 + 1.56744i) q^{2} +(-0.959879 + 0.554186i) q^{3} -2.91373i q^{4} +(0.784926 - 2.92938i) q^{5} +(0.635898 - 2.37321i) q^{6} +(1.43221 + 1.43221i) q^{8} +(-0.885755 + 1.53417i) q^{9} +(3.36131 + 5.82195i) q^{10} +(-0.188977 + 0.705270i) q^{11} +(1.61475 + 2.79683i) q^{12} +(2.65012 + 2.44476i) q^{13} +(0.869990 + 3.24685i) q^{15} +1.33764 q^{16} -3.24611 q^{17} +(-1.01635 - 3.79309i) q^{18} +(-3.85949 + 1.03415i) q^{19} +(-8.53543 - 2.28706i) q^{20} +(-0.809258 - 1.40168i) q^{22} -5.96750i q^{23} +(-2.16847 - 0.581039i) q^{24} +(-3.63505 - 2.09870i) q^{25} +(-7.98592 + 0.321882i) q^{26} -5.28861i q^{27} +(2.78094 - 4.81672i) q^{29} +(-6.45289 - 3.72558i) q^{30} +(-3.99535 + 1.07055i) q^{31} +(-4.96110 + 4.96110i) q^{32} +(-0.209456 - 0.781702i) q^{33} +(5.08807 - 5.08807i) q^{34} +(4.47016 + 2.58085i) q^{36} +(-6.97285 - 6.97285i) q^{37} +(4.42855 - 7.67048i) q^{38} +(-3.89865 - 0.878018i) q^{39} +(5.31969 - 3.07132i) q^{40} +(-2.46389 + 0.660198i) q^{41} +(-5.73009 + 3.30827i) q^{43} +(2.05497 + 0.550626i) q^{44} +(3.79893 + 3.79893i) q^{45} +(9.35370 + 9.35370i) q^{46} +(1.69510 + 0.454201i) q^{47} +(-1.28397 + 0.741302i) q^{48} +(8.98729 - 2.40814i) q^{50} +(3.11587 - 1.79895i) q^{51} +(7.12338 - 7.72173i) q^{52} +(3.37073 - 5.83828i) q^{53} +(8.28958 + 8.28958i) q^{54} +(1.91767 + 1.10717i) q^{55} +(3.13153 - 3.13153i) q^{57} +(3.19097 + 11.9089i) q^{58} +(2.33153 - 2.33153i) q^{59} +(9.46044 - 2.53492i) q^{60} +(-6.30371 - 3.63945i) q^{61} +(4.58444 - 7.94048i) q^{62} -12.8772i q^{64} +(9.24179 - 5.84425i) q^{65} +(1.55358 + 0.896960i) q^{66} +(-6.27534 - 1.68147i) q^{67} +9.45827i q^{68} +(3.30711 + 5.72808i) q^{69} +(-8.06938 - 2.16218i) q^{71} +(-3.46586 + 0.928673i) q^{72} +(-1.62921 - 6.08031i) q^{73} +21.8590 q^{74} +4.65227 q^{75} +(3.01323 + 11.2455i) q^{76} +(7.48713 - 4.73465i) q^{78} +(7.87501 + 13.6399i) q^{79} +(1.04995 - 3.91846i) q^{80} +(0.273613 + 0.473911i) q^{81} +(2.82718 - 4.89682i) q^{82} +(-10.4223 - 10.4223i) q^{83} +(-2.54795 + 9.50909i) q^{85} +(3.79606 - 14.1671i) q^{86} +6.16463i q^{87} +(-1.28075 + 0.739443i) q^{88} +(6.62546 - 6.62546i) q^{89} -11.9092 q^{90} -17.3877 q^{92} +(3.24176 - 3.24176i) q^{93} +(-3.36890 + 1.94504i) q^{94} +12.1177i q^{95} +(2.01268 - 7.51143i) q^{96} +(-2.37570 + 8.86623i) q^{97} +(-0.914619 - 0.914619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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