LMFDB - Embedded newform 630.2.bf.e.209.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(209,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 3]))

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

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

chi := DirichletCharacter("630.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bf (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.12
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.e.419.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.979752 - 1.42832i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.452503 - 2.18980i) q^{5} +(0.747081 + 1.56265i) q^{6} +(2.02132 + 1.70712i) q^{7} +1.00000 q^{8} +(-1.08017 - 2.79879i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.979752 - 1.42832i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.452503 - 2.18980i) q^{5} +(0.747081 + 1.56265i) q^{6} +(2.02132 + 1.70712i) q^{7} +1.00000 q^{8} +(-1.08017 - 2.79879i) q^{9} +(1.67017 + 1.48678i) q^{10} +(5.48007 + 3.16392i) q^{11} +(-1.72683 - 0.134333i) q^{12} +(-2.28203 - 3.95259i) q^{13} +(-2.48907 + 0.896960i) q^{14} +(-2.68439 - 2.79178i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.72847i q^{17} +(2.96391 + 0.463940i) q^{18} +4.11761i q^{19} +(-2.12268 + 0.703023i) q^{20} +(4.41870 - 1.21454i) q^{21} +(-5.48007 + 3.16392i) q^{22} +(1.15619 + 2.00258i) q^{23} +(0.979752 - 1.42832i) q^{24} +(-4.59048 - 1.98179i) q^{25} +4.56405 q^{26} +(-5.05586 - 1.19930i) q^{27} +(0.467745 - 2.60408i) q^{28} +(-0.173539 - 0.100193i) q^{29} +(3.75995 - 0.928859i) q^{30} +(2.10971 - 1.21804i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(9.88818 - 4.72741i) q^{33} +(2.36292 + 1.36423i) q^{34} +(4.65291 - 3.65383i) q^{35} +(-1.88374 + 2.33485i) q^{36} -10.4673i q^{37} +(-3.56595 - 2.05880i) q^{38} +(-7.88136 - 0.613102i) q^{39} +(0.452503 - 2.18980i) q^{40} +(-1.03090 - 1.78558i) q^{41} +(-1.15753 + 4.43397i) q^{42} +(-7.26144 - 4.19239i) q^{43} -6.32783i q^{44} +(-6.61758 + 1.09890i) q^{45} -2.31238 q^{46} +(7.86014 + 4.53806i) q^{47} +(0.747081 + 1.56265i) q^{48} +(1.17150 + 6.90127i) q^{49} +(4.01152 - 2.98458i) q^{50} +(-3.89711 - 2.67322i) q^{51} +(-2.28203 + 3.95259i) q^{52} +6.77638 q^{53} +(3.56655 - 3.77885i) q^{54} +(9.40810 - 10.5686i) q^{55} +(2.02132 + 1.70712i) q^{56} +(5.88124 + 4.03424i) q^{57} +(0.173539 - 0.100193i) q^{58} +(-0.616709 - 1.06817i) q^{59} +(-1.07556 + 3.72064i) q^{60} +(1.66558 + 0.961623i) q^{61} +2.43609i q^{62} +(2.59449 - 7.50124i) q^{63} +1.00000 q^{64} +(-9.68801 + 3.20863i) q^{65} +(-0.850035 + 10.9271i) q^{66} +(-7.07376 + 4.08404i) q^{67} +(-2.36292 + 1.36423i) q^{68} +(3.99310 + 0.310629i) q^{69} +(0.837855 + 5.85645i) q^{70} +8.31846i q^{71} +(-1.08017 - 2.79879i) q^{72} -13.9450 q^{73} +(9.06497 + 5.23366i) q^{74} +(-7.32815 + 4.61500i) q^{75} +(3.56595 - 2.05880i) q^{76} +(5.67581 + 15.7504i) q^{77} +(4.47164 - 6.51891i) q^{78} +(1.01691 - 1.76135i) q^{79} +(1.67017 + 1.48678i) q^{80} +(-6.66646 + 6.04634i) q^{81} +2.06181 q^{82} +(3.64421 + 2.10398i) q^{83} +(-3.26117 - 3.21944i) q^{84} +(-5.97481 - 1.23464i) q^{85} +(7.26144 - 4.19239i) q^{86} +(-0.313132 + 0.149704i) q^{87} +(5.48007 + 3.16392i) q^{88} +9.48716 q^{89} +(2.35712 - 6.28045i) q^{90} +(2.13481 - 11.8851i) q^{91} +(1.15619 - 2.00258i) q^{92} +(0.327246 - 4.20671i) q^{93} +(-7.86014 + 4.53806i) q^{94} +(9.01675 + 1.86323i) q^{95} +(-1.72683 - 0.134333i) q^{96} +(2.42587 - 4.20173i) q^{97} +(-6.56243 - 2.43609i) q^{98} +(2.93574 - 18.7551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39} + 2 q^{42} - 54 q^{43} + 48 q^{46} + 32 q^{49} + 50 q^{50} - 26 q^{51} - 24 q^{53} + 110 q^{57} + 36 q^{58} + 26 q^{60} + 20 q^{63} + 32 q^{64} - 90 q^{65} - 66 q^{67} + 36 q^{70} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} + 4 q^{85} + 54 q^{86} - 24 q^{88} + 16 q^{91} - 24 q^{92} + 28 q^{93} + 12 q^{95} - 64 q^{98} + 58 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.979752	−	1.42832i	0.565660	−	0.824638i
$3$	0.979752	−	1.42832i	0.565660	−	0.824638i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.452503	−	2.18980i	0.202365	−	0.979310i
$5$	0.452503	−	2.18980i	0.202365	−	0.979310i
$6$	0.747081	+	1.56265i	0.304995	+	0.637948i
$7$	2.02132	+	1.70712i	0.763989	+	0.645230i
$7$	2.02132	+	1.70712i	0.763989	+	0.645230i
$8$	1.00000			0.353553
$9$	−1.08017	−	2.79879i	−0.360057	−	0.932930i
$10$	1.67017	+	1.48678i	0.528155	+	0.470161i
$11$	5.48007	+	3.16392i	1.65230	+	0.953957i	0.976123	+	0.217220i	$0.0696988\pi$
$11$	5.48007	+	3.16392i	1.65230	+	0.953957i	0.676179	+	0.736737i	$0.263634\pi$
$12$	−1.72683	−	0.134333i	−0.498494	−	0.0387785i
$13$	−2.28203	−	3.95259i	−0.632920	−	1.09625i	−0.986952	−	0.161017i	$-0.948523\pi$
$13$	−2.28203	−	3.95259i	−0.632920	−	1.09625i	0.354031	−	0.935234i	$-0.384811\pi$
$14$	−2.48907	+	0.896960i	−0.665232	+	0.239723i
$15$	−2.68439	−	2.79178i	−0.693107	−	0.720835i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	2.72847i		−	0.661751i	−0.943674	−	0.330875i	$-0.892656\pi$
$17$		−	2.72847i		−	0.661751i	0.943674	−	0.330875i	$-0.107344\pi$
$18$	2.96391	+	0.463940i	0.698600	+	0.109352i
$19$			4.11761i			0.944644i	0.881426	+	0.472322i	$0.156584\pi$
$19$			4.11761i			0.944644i	−0.881426	+	0.472322i	$0.843416\pi$
$20$	−2.12268	+	0.703023i	−0.474645	+	0.157201i
$21$	4.41870	−	1.21454i	0.964239	−	0.265034i
$22$	−5.48007	+	3.16392i	−1.16835	+	0.674549i
$23$	1.15619	+	2.00258i	0.241083	+	0.417568i	0.961023	−	0.276468i	$-0.0891641\pi$
$23$	1.15619	+	2.00258i	0.241083	+	0.417568i	−0.719940	+	0.694036i	$0.755831\pi$
$24$	0.979752	−	1.42832i	0.199991	−	0.291554i
$25$	−4.59048	−	1.98179i	−0.918096	−	0.396357i
$26$	4.56405			0.895085
$27$	−5.05586	−	1.19930i	−0.973000	−	0.230805i
$28$	0.467745	−	2.60408i	0.0883954	−	0.492124i
$29$	−0.173539	−	0.100193i	−0.0322254	−	0.0186054i	0.483801	−	0.875178i	$-0.339256\pi$
$29$	−0.173539	−	0.100193i	−0.0322254	−	0.0186054i	−0.516026	+	0.856573i	$0.672589\pi$
$30$	3.75995	−	0.928859i	0.686470	−	0.169586i
$31$	2.10971	−	1.21804i	0.378915	−	0.218767i	−0.298431	−	0.954431i	$-0.596463\pi$
$31$	2.10971	−	1.21804i	0.378915	−	0.218767i	0.677346	+	0.735664i	$0.263130\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	9.88818	−	4.72741i	1.72131	−	0.822936i
$34$	2.36292	+	1.36423i	0.405238	+	0.233964i
$35$	4.65291	−	3.65383i	0.786485	−	0.617610i
$36$	−1.88374	+	2.33485i	−0.313956	+	0.389142i
$37$		−	10.4673i		−	1.72082i	−0.509605	−	0.860409i	$-0.670208\pi$
$37$		−	10.4673i		−	1.72082i	0.509605	−	0.860409i	$-0.329792\pi$
$38$	−3.56595	−	2.05880i	−0.578474	−	0.333982i
$39$	−7.88136	−	0.613102i	−1.26203	−	0.0981748i
$40$	0.452503	−	2.18980i	0.0715470	−	0.346238i
$41$	−1.03090	−	1.78558i	−0.161000	−	0.278860i	0.774228	−	0.632907i	$-0.218139\pi$
$41$	−1.03090	−	1.78558i	−0.161000	−	0.278860i	−0.935228	+	0.354047i	$0.884805\pi$
$42$	−1.15753	+	4.43397i	−0.178611	+	0.684177i
$43$	−7.26144	−	4.19239i	−1.10736	−	0.639334i	−0.169215	−	0.985579i	$-0.554123\pi$
$43$	−7.26144	−	4.19239i	−1.10736	−	0.639334i	−0.938144	+	0.346245i	$0.887457\pi$
$44$		−	6.32783i		−	0.953957i
$45$	−6.61758	+	1.09890i	−0.986491	+	0.163814i
$46$	−2.31238			−0.340943
$47$	7.86014	+	4.53806i	1.14652	+	0.661943i	0.948037	−	0.318161i	$-0.103065\pi$
$47$	7.86014	+	4.53806i	1.14652	+	0.661943i	0.198483	+	0.980104i	$0.436399\pi$
$48$	0.747081	+	1.56265i	0.107832	+	0.225549i
$49$	1.17150	+	6.90127i	0.167358	+	0.985896i
$50$	4.01152	−	2.98458i	0.567314	−	0.422084i
$51$	−3.89711	−	2.67322i	−0.545705	−	0.374326i
$52$	−2.28203	+	3.95259i	−0.316460	+	0.548125i
$53$	6.77638			0.930808			0.465404	−	0.885098i	$-0.345909\pi$
$53$	6.77638			0.930808			0.465404	+	0.885098i	$0.345909\pi$
$54$	3.56655	−	3.77885i	0.485346	−	0.514237i
$55$	9.40810	−	10.5686i	1.26859	−	1.42507i
$56$	2.02132	+	1.70712i	0.270111	+	0.228123i
$57$	5.88124	+	4.03424i	0.778990	+	0.534348i
$58$	0.173539	−	0.100193i	0.0227868	−	0.0131560i
$59$	−0.616709	−	1.06817i	−0.0802887	−	0.139064i	0.823085	−	0.567918i	$-0.192251\pi$
$59$	−0.616709	−	1.06817i	−0.0802887	−	0.139064i	−0.903374	+	0.428854i	$0.858918\pi$
$60$	−1.07556	+	3.72064i	−0.138854	+	0.480333i
$61$	1.66558	+	0.961623i	0.213256	+	0.123123i	0.602824	−	0.797875i	$-0.294042\pi$
$61$	1.66558	+	0.961623i	0.213256	+	0.123123i	−0.389568	+	0.920998i	$0.627376\pi$
$62$			2.43609i			0.309383i
$63$	2.59449	−	7.50124i	0.326875	−	0.945068i
$64$	1.00000			0.125000
$65$	−9.68801	+	3.20863i	−1.20165	+	0.397982i
$66$	−0.850035	+	10.9271i	−0.104632	+	1.34504i
$67$	−7.07376	+	4.08404i	−0.864198	+	0.498945i	−0.865416	−	0.501054i	$-0.832946\pi$
$67$	−7.07376	+	4.08404i	−0.864198	+	0.498945i	0.00121797	+	0.999999i	$0.499612\pi$
$68$	−2.36292	+	1.36423i	−0.286546	+	0.165438i
$69$	3.99310	+	0.310629i	0.480713	+	0.0373953i
$70$	0.837855	+	5.85645i	0.100143	+	0.699980i
$71$			8.31846i			0.987220i	0.869684	+	0.493610i	$0.164323\pi$
$71$			8.31846i			0.987220i	−0.869684	+	0.493610i	$0.835677\pi$
$72$	−1.08017	−	2.79879i	−0.127299	−	0.329841i
$73$	−13.9450			−1.63214			−0.816072	−	0.577951i	$-0.803852\pi$
$73$	−13.9450			−1.63214			−0.816072	+	0.577951i	$0.803852\pi$
$74$	9.06497	+	5.23366i	1.05378	+	0.608401i
$75$	−7.32815	+	4.61500i	−0.846182	+	0.532894i
$76$	3.56595	−	2.05880i	0.409043	−	0.236161i
$77$	5.67581	+	15.7504i	0.646819	+	1.79493i
$78$	4.47164	−	6.51891i	0.506314	−	0.738121i
$79$	1.01691	−	1.76135i	0.114412	−	0.198167i	−0.803133	−	0.595800i	$-0.796835\pi$
$79$	1.01691	−	1.76135i	0.114412	−	0.198167i	0.917544	+	0.397633i	$0.130168\pi$
$80$	1.67017	+	1.48678i	0.186731	+	0.166227i
$81$	−6.66646	+	6.04634i	−0.740718	+	0.671816i
$82$	2.06181			0.227688
$83$	3.64421	+	2.10398i	0.400004	+	0.230942i	0.686486	−	0.727143i	$-0.259153\pi$
$83$	3.64421	+	2.10398i	0.400004	+	0.230942i	−0.286482	+	0.958086i	$0.592486\pi$
$84$	−3.26117	−	3.21944i	−0.355823	−	0.351269i
$85$	−5.97481	−	1.23464i	−0.648059	−	0.133915i
$86$	7.26144	−	4.19239i	0.783021	−	0.452078i
$87$	−0.313132	+	0.149704i	−0.0335713	+	0.0160500i
$88$	5.48007	+	3.16392i	0.584177	+	0.337275i
$89$	9.48716			1.00564			0.502819	−	0.864392i	$-0.332296\pi$
$89$	9.48716			1.00564			0.502819	+	0.864392i	$0.332296\pi$
$90$	2.35712	−	6.28045i	0.248462	−	0.662017i
$91$	2.13481	−	11.8851i	0.223789	−	1.24590i
$92$	1.15619	−	2.00258i	0.120541	−	0.208784i
$93$	0.327246	−	4.20671i	0.0339338	−	0.436216i
$94$	−7.86014	+	4.53806i	−0.810712	+	0.468065i
$95$	9.01675	+	1.86323i	0.925099	+	0.191163i
$96$	−1.72683	−	0.134333i	−0.176244	−	0.0137103i
$97$	2.42587	−	4.20173i	0.246310	−	0.426622i	−0.716189	−	0.697906i	$-0.754115\pi$
$97$	2.42587	−	4.20173i	0.246310	−	0.426622i	0.962499	+	0.271285i	$0.0874485\pi$
$98$	−6.56243	−	2.43609i	−0.662906	−	0.246082i
$99$	2.93574	−	18.7551i	0.295053	−	1.88496i
$100$	0.578965	+	4.96637i	0.0578965	+	0.496637i
$101$	−8.61527	+	14.9221i	−0.857252	+	1.48480i	0.0172883	+	0.999851i	$0.494497\pi$
$101$	−8.61527	+	14.9221i	−0.857252	+	1.48480i	−0.874540	+	0.484953i	$0.838837\pi$
$102$	4.26363	−	2.03839i	0.422163	−	0.201830i
$103$	9.19697	+	15.9296i	0.906204	+	1.56959i	0.819293	+	0.573375i	$0.194366\pi$
$103$	9.19697	+	15.9296i	0.906204	+	1.56959i	0.0869114	+	0.996216i	$0.472300\pi$
$104$	−2.28203	−	3.95259i	−0.223771	−	0.387583i
$105$	−0.660123	−	10.2257i	−0.0644214	−	0.997923i
$106$	−3.38819	+	5.86852i	−0.329090	+	0.570001i
$107$	−1.73454			−0.167685			−0.0838423	−	0.996479i	$-0.526719\pi$
$107$	−1.73454			−0.167685			−0.0838423	+	0.996479i	$0.526719\pi$
$108$	1.48931	+	4.97815i	0.143309	+	0.479023i
$109$	0.400269			0.0383388			0.0191694	−	0.999816i	$-0.493898\pi$
$109$	0.400269			0.0383388			0.0191694	+	0.999816i	$0.493898\pi$
$110$	4.44861	+	13.4320i	0.424159	+	1.28069i
$111$	−14.9506	−	10.2554i	−1.41905	−	0.973398i
$112$	−2.48907	+	0.896960i	−0.235195	+	0.0847547i
$113$	1.32959	+	2.30292i	0.125077	+	0.216640i	0.921763	−	0.387753i	$-0.126749\pi$
$113$	1.32959	+	2.30292i	0.125077	+	0.216640i	−0.796686	+	0.604394i	$0.793415\pi$
$114$	−6.43437	+	3.07619i	−0.602634	+	0.288111i
$115$	4.90845	−	1.62566i	0.457715	−	0.151594i
$116$			0.200386i			0.0186054i
$117$	−8.59749	+	10.6564i	−0.794838	+	0.985183i
$118$	1.23342			0.113545
$119$	4.65781	−	5.51512i	0.426981	−	0.505570i
$120$	−2.68439	−	2.79178i	−0.245050	−	0.254854i
$121$	14.5207	+	25.1507i	1.32007	+	2.28642i
$122$	−1.66558	+	0.961623i	−0.150795	+	0.0870613i
$123$	−3.56040	−	0.276968i	−0.321030	−	0.0249734i
$124$	−2.10971	−	1.21804i	−0.189458	−	0.109383i
$125$	−6.41693	+	9.15549i	−0.573948	+	0.818892i
$126$	5.19902	+	5.99751i	0.463166	+	0.534301i
$127$		−	0.955970i		−	0.0848287i	−0.999100	−	0.0424143i	$-0.986495\pi$
$127$		−	0.955970i		−	0.0848287i	0.999100	−	0.0424143i	$-0.0135050\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−13.1025	+	6.26412i	−1.15361	+	0.551525i
$130$	2.06525	−	9.99438i	0.181134	−	0.876565i
$131$	−5.64033	−	9.76935i	−0.492798	−	0.853552i	0.507167	−	0.861848i	$-0.330693\pi$
$131$	−5.64033	−	9.76935i	−0.492798	−	0.853552i	−0.999966	+	0.00829593i	$0.997359\pi$
$132$	−9.03814	−	6.19971i	−0.786670	−	0.539616i
$133$	−7.02924	+	8.32302i	−0.609512	+	0.721697i
$134$		−	8.16808i		−	0.705615i
$135$	−4.91402	+	10.5286i	−0.422931	+	0.906162i
$136$		−	2.72847i		−	0.233964i
$137$	0.913329	−	1.58193i	0.0780310	−	0.135154i	−0.824369	−	0.566052i	$-0.808470\pi$
$137$	0.913329	−	1.58193i	0.0780310	−	0.135154i	0.902400	+	0.430899i	$0.141803\pi$
$138$	−2.26556	+	3.30282i	−0.192858	+	0.281154i
$139$	−15.2206	+	8.78760i	−1.29099	+	0.745355i	−0.978830	−	0.204674i	$-0.934387\pi$
$139$	−15.2206	+	8.78760i	−1.29099	+	0.745355i	−0.312162	+	0.950029i	$0.601053\pi$
$140$	−5.49076	−	2.20262i	−0.464054	−	0.186155i
$141$	14.1828	−	6.78059i	1.19440	−	0.571029i
$142$	−7.20400	−	4.15923i	−0.604546	−	0.349035i
$143$		−	28.8806i		−	2.41512i
$144$	2.96391	+	0.463940i	0.246992	+	0.0386617i
$145$	−0.297930	+	0.334679i	−0.0247417	+	0.0277936i
$146$	6.97252	−	12.0768i	0.577050	−	0.999479i
$147$	11.0050	+	5.08826i	0.907675	+	0.419673i
$148$	−9.06497	+	5.23366i	−0.745136	+	0.430204i
$149$	5.26078	−	3.03731i	0.430980	−	0.248826i	−0.268784	−	0.963200i	$-0.586622\pi$
$149$	5.26078	−	3.03731i	0.430980	−	0.248826i	0.699764	+	0.714374i	$0.253288\pi$
$150$	−0.332630	−	8.65386i	−0.0271591	−	0.706585i
$151$	−8.97909	+	15.5522i	−0.730708	+	1.26562i	0.225873	+	0.974157i	$0.427477\pi$
$151$	−8.97909	+	15.5522i	−0.730708	+	1.26562i	−0.956581	+	0.291467i	$0.905857\pi$
$152$			4.11761i			0.333982i
$153$	−7.63641	+	2.94721i	−0.617367	+	0.238268i
$154$	−16.4782	−	2.95981i	−1.32785	−	0.238508i
$155$	−1.71262	−	5.17102i	−0.137561	−	0.415347i
$156$	3.40972	+	7.13201i	0.272996	+	0.571018i
$157$	−3.74566	−	6.48767i	−0.298936	−	0.517772i	0.676957	−	0.736023i	$-0.263298\pi$
$157$	−3.74566	−	6.48767i	−0.298936	−	0.517772i	−0.975893	+	0.218250i	$0.929965\pi$
$158$	1.01691	+	1.76135i	0.0809013	+	0.140125i
$159$	6.63918	−	9.67881i	0.526521	−	0.767580i
$160$	−2.12268	+	0.703023i	−0.167812	+	0.0555788i
$161$	−1.08161	+	6.02163i	−0.0852424	+	0.474571i
$162$	−1.90306	−	8.79650i	−0.149518	−	0.691118i
$163$		−	0.216711i		−	0.0169741i	−0.999964	−	0.00848704i	$-0.997298\pi$
$163$		−	0.216711i		−	0.0169741i	0.999964	−	0.00848704i	$-0.00270154\pi$
$164$	−1.03090	+	1.78558i	−0.0805000	+	0.139430i
$165$	−5.87766	−	23.7923i	−0.457576	−	1.85223i
$166$	−3.64421	+	2.10398i	−0.282845	+	0.163301i
$167$	−6.59580	+	3.80809i	−0.510398	+	0.294679i	−0.732997	−	0.680231i	$-0.761879\pi$
$167$	−6.59580	+	3.80809i	−0.510398	+	0.294679i	0.222599	+	0.974910i	$0.428546\pi$
$168$	4.41870	−	1.21454i	0.340910	−	0.0937036i
$169$	−3.91530	+	6.78149i	−0.301177	+	0.521653i
$170$	4.05663	−	4.55702i	0.311130	−	0.349507i
$171$	11.5243	−	4.44772i	0.881287	−	0.340126i
$172$			8.38479i			0.639334i
$173$	−6.39337	−	3.69121i	−0.486079	−	0.280638i	0.236868	−	0.971542i	$-0.423879\pi$
$173$	−6.39337	−	3.69121i	−0.486079	−	0.280638i	−0.722946	+	0.690904i	$0.757213\pi$
$174$	0.0269184	−	0.346033i	0.00204068	−	0.0262327i
$175$	−5.89571	−	11.8423i	−0.445674	−	0.895195i
$176$	−5.48007	+	3.16392i	−0.413075	+	0.238489i
$177$	−2.12991	−	0.165688i	−0.160094	−	0.0124539i
$178$	−4.74358	+	8.21613i	−0.355547	+	0.615825i
$179$		−	8.41037i		−	0.628620i	−0.949320	−	0.314310i	$-0.898227\pi$
$179$		−	8.41037i		−	0.628620i	0.949320	−	0.314310i	$-0.101773\pi$
$180$	4.26047	+	5.18155i	0.317557	+	0.386210i
$181$			19.8492i			1.47538i	0.675138	+	0.737691i	$0.264084\pi$
$181$			19.8492i			1.47538i	−0.675138	+	0.737691i	$0.735916\pi$
$182$	9.22543	+	7.79137i	0.683835	+	0.577535i
$183$	3.00536	−	1.43682i	0.222162	−	0.106213i
$184$	1.15619	+	2.00258i	0.0852356	+	0.147632i
$185$	−22.9214	−	4.73649i	−1.68521	−	0.348234i
$186$	3.47950	+	2.38676i	0.255129	+	0.175006i
$187$	8.63265	−	14.9522i	0.631282	−	1.09341i
$188$		−	9.07611i		−	0.661943i
$189$	−8.17218	−	11.0551i	−0.594439	−	0.804141i
$190$	−6.12198	+	6.87712i	−0.444135	+	0.498919i
$191$	2.20596	+	1.27361i	0.159618	+	0.0921553i	0.577681	−	0.816262i	$-0.303958\pi$
$191$	2.20596	+	1.27361i	0.159618	+	0.0921553i	−0.418063	+	0.908418i	$0.637291\pi$
$192$	0.979752	−	1.42832i	0.0707075	−	0.103080i
$193$	19.4328	−	11.2196i	1.39881	−	0.807601i	0.404539	−	0.914521i	$-0.367432\pi$
$193$	19.4328	−	11.2196i	1.39881	−	0.807601i	0.994268	+	0.106920i	$0.0340988\pi$
$194$	2.42587	+	4.20173i	0.174168	+	0.301667i
$195$	−4.90891	+	16.9812i	−0.351534	+	1.21605i
$196$	5.39093	−	4.46519i	0.385066	−	0.318942i
$197$	10.3672			0.738631			0.369315	−	0.929304i	$-0.379592\pi$
$197$	10.3672			0.738631			0.369315	+	0.929304i	$0.379592\pi$
$198$	14.7745	+	11.9200i	1.04998	+	0.847117i
$199$			11.5505i			0.818791i	0.912357	+	0.409395i	$0.134260\pi$
$199$			11.5505i			0.818791i	−0.912357	+	0.409395i	$0.865740\pi$
$200$	−4.59048	−	1.98179i	−0.324596	−	0.140133i
$201$	−1.09724	+	14.1049i	−0.0773933	+	0.994884i
$202$	−8.61527	−	14.9221i	−0.606169	−	1.04991i
$203$	−0.179738	−	0.498774i	−0.0126151	−	0.0350071i
$204$	−0.366522	+	4.71161i	−0.0256617	+	0.329879i
$205$	−4.37655	+	1.44950i	−0.305671	+	0.101237i
$206$	−18.3939			−1.28157
$207$	4.35593	−	5.39907i	0.302758	−	0.375262i
$208$	4.56405			0.316460
$209$	−13.0278	+	22.5648i	−0.901150	+	1.56084i
$210$	9.18575	+	4.54115i	0.633877	+	0.313369i
$211$	−0.154076	−	0.266868i	−0.0106071	−	0.0183720i	0.860673	−	0.509158i	$-0.170043\pi$
$211$	−0.154076	−	0.266868i	−0.0106071	−	0.0183720i	−0.871280	+	0.490786i	$0.836710\pi$
$212$	−3.38819	−	5.86852i	−0.232702	−	0.403051i
$213$	11.8814	+	8.15003i	0.814099	+	0.558431i
$214$	0.867271	−	1.50216i	0.0592854	−	0.102685i
$215$	−12.4663	+	14.0041i	−0.850198	+	0.955069i
$216$	−5.05586	−	1.19930i	−0.344007	−	0.0816019i
$217$	6.34375	+	1.13947i	0.430642	+	0.0773520i
$218$	−0.200135	+	0.346643i	−0.0135548	+	0.0234776i
$219$	−13.6627	+	19.9179i	−0.923239	+	1.34593i
$220$	−13.8567	−	2.86336i	−0.934220	−	0.193048i
$221$	−10.7845	+	6.22644i	−0.725444	+	0.418835i
$222$	16.3567	−	7.81994i	1.09779	−	0.524840i
$223$	−12.0678	+	20.9020i	−0.808118	+	1.39970i	0.106049	+	0.994361i	$0.466180\pi$
$223$	−12.0678	+	20.9020i	−0.808118	+	1.39970i	−0.914166	+	0.405340i	$0.867153\pi$
$224$	0.467745	−	2.60408i	0.0312525	−	0.173992i
$225$	−0.588099	+	14.9885i	−0.0392066	+	0.999231i
$226$	−2.65918			−0.176886
$227$	8.32843	+	4.80842i	0.552777	+	0.319146i	0.750241	−	0.661164i	$-0.229937\pi$
$227$	8.32843	+	4.80842i	0.552777	+	0.319146i	−0.197464	+	0.980310i	$0.563271\pi$
$228$	0.553129	−	7.11042i	0.0366319	−	0.470899i
$229$	19.7785	−	11.4191i	1.30700	−	0.754597i	0.325406	−	0.945574i	$-0.394499\pi$
$229$	19.7785	−	11.4191i	1.30700	−	0.754597i	0.981595	+	0.190977i	$0.0611656\pi$
$230$	−1.04636	+	5.06367i	−0.0689950	+	0.333888i
$231$	28.0575	+	7.32466i	1.84604	+	0.481927i
$232$	−0.173539	−	0.100193i	−0.0113934	−	0.00657799i
$233$	−24.1221			−1.58029			−0.790147	−	0.612918i	$-0.789996\pi$
$233$	−24.1221			−1.58029			−0.790147	+	0.612918i	$0.789996\pi$
$234$	−4.92996	−	12.7738i	−0.322281	−	0.835052i
$235$	13.4942	−	15.1587i	0.880264	−	0.988844i
$236$	−0.616709	+	1.06817i	−0.0401444	+	0.0695321i
$237$	−1.51943	−	3.17816i	−0.0986979	−	0.206443i
$238$	2.44732	+	6.79134i	0.158637	+	0.440217i
$239$	−13.7371	+	7.93114i	−0.888582	+	0.513023i	−0.873478	−	0.486863i	$-0.838141\pi$
$239$	−13.7371	+	7.93114i	−0.888582	+	0.513023i	−0.0151034	+	0.999886i	$0.504808\pi$
$240$	3.75995	−	0.928859i	0.242704	−	0.0599576i
$241$	−11.8605	−	6.84765i	−0.764000	−	0.441096i	0.0667298	−	0.997771i	$-0.478743\pi$
$241$	−11.8605	−	6.84765i	−0.764000	−	0.441096i	−0.830730	+	0.556675i	$0.812077\pi$
$242$	−29.0415			−1.86686
$243$	2.10460	+	15.4457i	0.135010	+	0.990844i
$244$		−	1.92325i		−	0.123123i
$245$	15.6425	+	0.557485i	0.999366	+	0.0356164i
$246$	2.02006	−	2.94491i	0.128794	−	0.187761i
$247$	16.2752	−	9.39649i	1.03557	−	0.597884i
$248$	2.10971	−	1.21804i	0.133967	−	0.0773458i
$249$	6.57557	−	3.14369i	0.416710	−	0.199223i
$250$	−4.72042	−	10.1350i	−0.298546	−	0.640992i
$251$	24.1645			1.52525			0.762624	−	0.646842i	$-0.223911\pi$
$251$	24.1645			1.52525			0.762624	+	0.646842i	$0.223911\pi$
$252$	−7.79351	+	1.50373i	−0.490945	+	0.0947259i
$253$			14.6324i			0.919930i
$254$	0.827895	+	0.477985i	0.0519467	+	0.0299915i
$255$	−7.61729	+	7.32427i	−0.477013	+	0.458664i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.37439	−	4.25760i	0.460002	−	0.265582i	−0.252043	−	0.967716i	$-0.581103\pi$
$257$	7.37439	−	4.25760i	0.460002	−	0.265582i	0.712045	+	0.702134i	$0.247769\pi$
$258$	1.12635	−	14.4791i	0.0701236	−	0.901432i
$259$	17.8689	−	21.1579i	1.11032	−	1.31468i
$260$	7.62277	+	6.78575i	0.472744	+	0.420834i
$261$	−0.0929670	+	0.593925i	−0.00575452	+	0.0367631i
$262$	11.2807			0.696922
$263$	−9.99743	+	17.3161i	−0.616468	+	1.06775i	0.373657	+	0.927567i	$0.378104\pi$
$263$	−9.99743	+	17.3161i	−0.616468	+	1.06775i	−0.990125	+	0.140187i	$0.955230\pi$
$264$	9.88818	−	4.72741i	0.608575	−	0.290952i
$265$	3.06633	−	14.8389i	0.188363	−	0.911549i
$266$	−3.69333	−	10.2490i	−0.226452	−	0.628407i
$267$	9.29507	−	13.5507i	0.568849	−	0.829287i
$268$	7.07376	+	4.08404i	0.432099	+	0.249472i
$269$	28.0807			1.71211			0.856055	−	0.516884i	$-0.172908\pi$
$269$	28.0807			1.71211			0.856055	+	0.516884i	$0.172908\pi$
$270$	−6.66107	−	9.51999i	−0.405380	−	0.579368i
$271$		−	11.3996i		−	0.692475i	−0.938147	−	0.346237i	$-0.887459\pi$
$271$		−	11.3996i		−	0.692475i	0.938147	−	0.346237i	$-0.112541\pi$
$272$	2.36292	+	1.36423i	0.143273	+	0.0827188i
$273$	−14.8842	−	14.6937i	−0.900830	−	0.889302i
$274$	0.913329	+	1.58193i	0.0551762	+	0.0955681i
$275$	−18.8859	−	25.3842i	−1.13886	−	1.53073i
$276$	−1.72754	−	3.61344i	−0.103986	−	0.217504i
$277$	17.2040	+	9.93273i	1.03369	+	0.596800i	0.918039	−	0.396490i	$-0.129772\pi$
$277$	17.2040	+	9.93273i	1.03369	+	0.596800i	0.115649	+	0.993290i	$0.463105\pi$
$278$		−	17.5752i		−	1.05409i
$279$	−5.68790	−	4.58895i	−0.340525	−	0.274733i
$280$	4.65291	−	3.65383i	0.278064	−	0.218358i
$281$	−9.44238	−	5.45156i	−0.563285	−	0.325213i	0.191178	−	0.981555i	$-0.438769\pi$
$281$	−9.44238	−	5.45156i	−0.563285	−	0.325213i	−0.754463	+	0.656343i	$0.772103\pi$
$282$	−1.21922	+	15.6729i	−0.0726034	+	0.933310i
$283$	−4.79927	−	8.31258i	−0.285287	−	0.494132i	0.687392	−	0.726287i	$-0.258756\pi$
$283$	−4.79927	−	8.31258i	−0.285287	−	0.494132i	−0.972679	+	0.232155i	$0.925422\pi$
$284$	7.20400	−	4.15923i	0.427479	−	0.246805i
$285$	11.4955	−	11.0533i	0.680932	−	0.654739i
$286$	25.0113	+	14.4403i	1.47895	+	0.853872i
$287$	0.964399	−	5.36910i	0.0569267	−	0.316928i
$288$	−1.88374	+	2.33485i	−0.111000	+	0.137582i
$289$	9.55547			0.562086
$290$	−0.140876	−	0.425354i	−0.00827251	−	0.0249777i
$291$	−3.62465	−	7.58157i	−0.212481	−	0.444440i
$292$	6.97252	+	12.0768i	0.408036	+	0.706739i
$293$	−1.70013	+	0.981568i	−0.0993224	+	0.0573438i	−0.548838	−	0.835928i	$-0.684930\pi$
$293$	−1.70013	+	0.981568i	−0.0993224	+	0.0573438i	0.449516	+	0.893272i	$0.351596\pi$
$294$	−9.90906	+	6.98646i	−0.577908	+	0.407459i
$295$	−2.61815	+	0.867122i	−0.152435	+	0.0504858i
$296$		−	10.4673i		−	0.608401i
$297$	−23.9119	−	22.5685i	−1.38751	−	1.30956i
$298$			6.07463i			0.351894i
$299$	5.27692	−	9.13990i	0.305172	−	0.528574i
$300$	7.66078	+	4.03887i	0.442295	+	0.233184i
$301$	−7.52082	−	20.8703i	−0.433493	−	1.20295i
$302$	−8.97909	−	15.5522i	−0.516689	−	0.894931i
$303$	12.8726	+	26.9253i	0.739513	+	1.54682i
$304$	−3.56595	−	2.05880i	−0.204521	−	0.118080i
$305$	2.85945	−	3.21216i	0.163731	−	0.183928i
$306$	1.26585	−	8.08693i	0.0723636	−	0.462299i
$307$	3.13370			0.178850			0.0894248	−	0.995994i	$-0.471497\pi$
$307$	3.13370			0.178850			0.0894248	+	0.995994i	$0.471497\pi$
$308$	10.8024	−	12.7906i	0.615521	−	0.728812i
$309$	31.7633	+	2.47091i	1.80695	+	0.140565i
$310$	5.33455	+	1.10234i	0.302982	+	0.0626085i
$311$	9.01232	+	15.6098i	0.511042	+	0.885150i	0.999918	+	0.0127972i	$0.00407359\pi$
$311$	9.01232	+	15.6098i	0.511042	+	0.885150i	−0.488876	+	0.872353i	$0.662593\pi$
$312$	−7.88136	−	0.613102i	−0.446194	−	0.0347100i
$313$	−2.49357	+	4.31899i	−0.140945	+	0.244124i	−0.927853	−	0.372947i	$-0.878347\pi$
$313$	−2.49357	+	4.31899i	−0.140945	+	0.244124i	0.786908	+	0.617070i	$0.211681\pi$
$314$	7.49132			0.422759
$315$	−15.2522	−	9.07576i	−0.859366	−	0.511361i
$316$	−2.03383			−0.114412
$317$	1.58024	−	2.73705i	0.0887550	−	0.153728i	−0.818230	−	0.574891i	$-0.805045\pi$
$317$	1.58024	−	2.73705i	0.0887550	−	0.153728i	0.906985	+	0.421163i	$0.138378\pi$
$318$	5.06251	+	10.5891i	0.283891	+	0.593807i
$319$	−0.634004	−	1.09813i	−0.0354974	−	0.0614833i
$320$	0.452503	−	2.18980i	0.0252957	−	0.122414i
$321$	−1.69942	+	2.47747i	−0.0948525	+	0.138279i
$322$	−4.67408	−	3.94751i	−0.260476	−	0.219986i
$323$	11.2348			0.625119
$324$	8.56952	+	2.75015i	0.476084	+	0.152786i
$325$	2.64243	+	22.6668i	0.146575	+	1.25733i
$326$	0.187677	+	0.108355i	0.0103945	+	0.00600124i
$327$	0.392165	−	0.571711i	0.0216867	−	0.0316157i
$328$	−1.03090	−	1.78558i	−0.0569221	−	0.0985920i
$329$	8.14091	+	22.5911i	0.448823	+	1.24549i
$330$	23.5436	+	6.80596i	1.29603	+	0.374656i
$331$	13.7475	−	23.8113i	0.755630	−	1.30879i	−0.189431	−	0.981894i	$-0.560664\pi$
$331$	13.7475	−	23.8113i	0.755630	−	1.30879i	0.945061	−	0.326895i	$-0.106002\pi$
$332$		−	4.20797i		−	0.230942i
$333$	−29.2958	+	11.3065i	−1.60540	+	0.619592i
$334$		−	7.61617i		−	0.416739i
$335$	5.74235	+	17.3382i	0.313738	+	0.947287i
$336$	−1.15753	+	4.43397i	−0.0631484	+	0.241893i
$337$	1.95439	−	1.12837i	0.106462	−	0.0614661i	−0.445823	−	0.895121i	$-0.647089\pi$
$337$	1.95439	−	1.12837i	0.106462	−	0.0614661i	0.552286	+	0.833655i	$0.313756\pi$
$338$	−3.91530	−	6.78149i	−0.212964	−	0.368864i
$339$	4.59197	+	0.357215i	0.249401	+	0.0194013i
$340$	1.91817	+	5.79166i	0.104028	+	0.314097i
$341$	15.4151			0.834777
$342$	−1.91032	+	12.2042i	−0.103298	+	0.659928i
$343$	−9.41329	+	15.9496i	−0.508270	+	0.861198i
$344$	−7.26144	−	4.19239i	−0.391511	−	0.226039i
$345$	2.48711	−	8.60355i	0.133901	−	0.463200i
$346$	6.39337	−	3.69121i	0.343709	−	0.198441i
$347$	9.66391	+	16.7384i	0.518786	+	0.898563i	0.999762	+	0.0218295i	$0.00694909\pi$
$347$	9.66391	+	16.7384i	0.518786	+	0.898563i	−0.480976	+	0.876734i	$0.659718\pi$
$348$	0.286214	+	0.196328i	0.0153427	+	0.0105243i
$349$	−25.1498	−	14.5202i	−1.34624	−	0.777250i	−0.358523	−	0.933521i	$-0.616719\pi$
$349$	−25.1498	−	14.5202i	−1.34624	−	0.777250i	−0.987714	+	0.156271i	$0.950053\pi$
$350$	13.2036	+	0.815323i	0.705763	+	0.0435809i
$351$	6.79727	+	22.7205i	0.362812	+	1.21273i
$352$		−	6.32783i		−	0.337275i
$353$	−18.9251	−	10.9264i	−1.00728	−	0.581554i	−0.0968865	−	0.995295i	$-0.530888\pi$
$353$	−18.9251	−	10.9264i	−1.00728	−	0.581554i	−0.910394	+	0.413742i	$0.864222\pi$
$354$	1.20845	−	1.76171i	0.0642281	−	0.0936339i
$355$	18.2158	+	3.76413i	0.966794	+	0.199779i
$356$	−4.74358	−	8.21613i	−0.251409	−	0.435454i
$357$	−3.31382	−	12.0563i	−0.175386	−	0.638086i
$358$	7.28359	+	4.20518i	0.384950	+	0.222251i
$359$		−	11.6743i		−	0.616144i	−0.951363	−	0.308072i	$-0.900316\pi$
$359$		−	11.6743i		−	0.616144i	0.951363	−	0.308072i	$-0.0996838\pi$
$360$	−6.61758	+	1.09890i	−0.348777	+	0.0579171i
$361$	2.04531			0.107648
$362$	−17.1900	−	9.92462i	−0.903484	−	0.521627i
$363$	50.1498	+	3.90122i	2.63218	+	0.204761i
$364$	−11.3602	+	4.09377i	−0.595439	+	0.214572i
$365$	−6.31017	+	30.5369i	−0.330289	+	1.59837i
$366$	−0.258355	+	3.32113i	−0.0135044	+	0.173598i
$367$	1.49120	−	2.58283i	0.0778398	−	0.134822i	−0.824478	−	0.565894i	$-0.808531\pi$
$367$	1.49120	−	2.58283i	0.0778398	−	0.134822i	0.902318	+	0.431072i	$0.141864\pi$
$368$	−2.31238			−0.120541
$369$	−3.88390	+	4.81401i	−0.202188	+	0.250607i
$370$	15.5626	−	17.4823i	0.809062	−	0.908859i
$371$	13.6973	+	11.5681i	0.711126	+	0.600585i
$372$	−3.80674	+	1.81995i	−0.197371	+	0.0943602i
$373$	5.10400	−	2.94680i	0.264275	−	0.152579i	−0.362008	−	0.932175i	$-0.617909\pi$
$373$	5.10400	−	2.94680i	0.264275	−	0.152579i	0.626283	+	0.779596i	$0.284575\pi$
$374$	8.63265	+	14.9522i	0.446383	+	0.773159i
$375$	6.78993	+	18.1355i	0.350631	+	0.936514i
$376$	7.86014	+	4.53806i	0.405356	+	0.234032i
$377$			0.914572i			0.0471028i
$378$	13.6601	−	1.54976i	0.702600	−	0.0797113i
$379$	−15.0087			−0.770948			−0.385474	−	0.922719i	$-0.625962\pi$
$379$	−15.0087			−0.770948			−0.385474	+	0.922719i	$0.625962\pi$
$380$	−2.89477	−	8.74035i	−0.148499	−	0.448371i
$381$	−1.36543	−	0.936614i	−0.0699530	−	0.0479842i
$382$	−2.20596	+	1.27361i	−0.112867	+	0.0651637i
$383$	1.74800	−	1.00921i	0.0893184	−	0.0515680i	−0.454676	−	0.890657i	$-0.650245\pi$
$383$	1.74800	−	1.00921i	0.0893184	−	0.0515680i	0.543994	+	0.839089i	$0.316911\pi$
$384$	0.747081	+	1.56265i	0.0381243	+	0.0797436i
$385$	37.0586	−	5.30181i	1.88868	−	0.270205i
$386$			22.4391i			1.14212i
$387$	−3.89004	+	24.8518i	−0.197742	+	1.26329i
$388$	−4.85175			−0.246310
$389$	−17.3287	−	10.0047i	−0.878601	−	0.507260i	−0.00840401	−	0.999965i	$-0.502675\pi$
$389$	−17.3287	−	10.0047i	−0.878601	−	0.507260i	−0.870197	+	0.492704i	$0.836008\pi$
$390$	−12.2517	−	12.7418i	−0.620389	−	0.645208i
$391$	5.46398	−	3.15463i	0.276326	−	0.159537i
$392$	1.17150	+	6.90127i	0.0591698	+	0.348567i
$393$	−19.4798	−	1.51536i	−0.982628	−	0.0764399i
$394$	−5.18359	+	8.97824i	−0.261145	+	0.452317i
$395$	−3.39685	−	3.02386i	−0.170914	−	0.152147i
$396$	−17.7103	+	6.83514i	−0.889975	+	0.343479i
$397$	−15.3842			−0.772110			−0.386055	−	0.922476i	$-0.626163\pi$
$397$	−15.3842			−0.772110			−0.386055	+	0.922476i	$0.626163\pi$
$398$	−10.0030	−	5.77523i	−0.501405	−	0.289486i
$399$	5.00099	+	18.1945i	0.250362	+	0.910863i
$400$	4.01152	−	2.98458i	0.200576	−	0.149229i
$401$	5.76625	−	3.32914i	0.287953	−	0.166250i	−0.349066	−	0.937098i	$-0.613501\pi$
$401$	5.76625	−	3.32914i	0.287953	−	0.166250i	0.637018	+	0.770849i	$0.280168\pi$
$402$	−11.6666	−	8.00269i	−0.581877	−	0.399138i
$403$	−9.62884	−	5.55921i	−0.479647	−	0.276924i
$404$	17.2305			0.857252
$405$	10.2237	+	17.3342i	0.508020	+	0.861345i
$406$	0.521820	+	0.0937294i	0.0258975	+	0.00465171i
$407$	33.1177	−	57.3616i	1.64159	−	2.84331i
$408$	−3.89711	−	2.67322i	−0.192936	−	0.132344i
$409$	11.3648	−	6.56146i	0.561952	−	0.324443i	−0.191976	−	0.981400i	$-0.561490\pi$
$409$	11.3648	−	6.56146i	0.561952	−	0.324443i	0.753929	+	0.656956i	$0.228156\pi$
$410$	0.932973	−	4.51495i	0.0460763	−	0.222978i
$411$	−1.36466	−	2.85443i	−0.0673139	−	0.140798i
$412$	9.19697	−	15.9296i	0.453102	−	0.784796i
$413$	0.576925	−	3.21192i	0.0283886	−	0.158048i
$414$	2.49777	+	6.47188i	0.122759	+	0.318076i
$415$	6.25632	−	7.02804i	0.307111	−	0.344993i
$416$	−2.28203	+	3.95259i	−0.111886	+	0.193792i
$417$	−2.36092	+	30.3495i	−0.115615	+	1.48622i
$418$	−13.0278	−	22.5648i	−0.637209	−	1.10368i
$419$	−13.6846	−	23.7023i	−0.668534	−	1.15794i	−0.978314	−	0.207127i	$-0.933589\pi$
$419$	−13.6846	−	23.7023i	−0.668534	−	1.15794i	0.309780	−	0.950808i	$-0.399745\pi$
$420$	−8.52562	+	5.68452i	−0.416008	+	0.277376i
$421$	−0.808320	+	1.40005i	−0.0393951	+	0.0682343i	−0.885051	−	0.465495i	$-0.845876\pi$
$421$	−0.808320	+	1.40005i	−0.0393951	+	0.0682343i	0.845656	+	0.533729i	$0.179210\pi$
$422$	0.308153			0.0150006
$423$	4.21077	−	26.9008i	0.204735	−	1.30796i
$424$	6.77638			0.329090
$425$	−5.40724	+	12.5250i	−0.262290	+	0.607551i
$426$	−12.9988	+	6.21457i	−0.629795	+	0.301097i
$427$	1.72507	+	4.78709i	0.0834822	+	0.231664i
$428$	0.867271	+	1.50216i	0.0419211	+	0.0726095i
$429$	−41.2506	−	28.2958i	−1.99160	−	1.36613i
$430$	−5.89470	−	17.7982i	−0.284268	−	0.858306i
$431$		−	6.18722i		−	0.298028i	−0.988835	−	0.149014i	$-0.952390\pi$
$431$		−	6.18722i		−	0.298028i	0.988835	−	0.149014i	$-0.0476099\pi$
$432$	3.56655	−	3.77885i	0.171596	−	0.181810i
$433$	−21.5398			−1.03514			−0.517568	−	0.855642i	$-0.673162\pi$
$433$	−21.5398			−1.03514			−0.517568	+	0.855642i	$0.673162\pi$
$434$	−4.15868	+	4.92412i	−0.199623	+	0.236365i
$435$	0.186130	+	0.753440i	0.00892425	+	0.0361247i
$436$	−0.200135	−	0.346643i	−0.00958471	−	0.0166012i
$437$	−8.24585	+	4.76075i	−0.394453	+	0.227737i
$438$	−10.4181	−	21.7912i	−0.497795	−	1.04122i
$439$	12.8703	+	7.43067i	0.614266	+	0.354646i	0.774633	−	0.632411i	$-0.217935\pi$
$439$	12.8703	+	7.43067i	0.614266	+	0.354646i	−0.160367	+	0.987057i	$0.551268\pi$
$440$	9.40810	−	10.5686i	0.448514	−	0.503838i
$441$	18.0498	−	10.7333i	0.859514	−	0.511112i
$442$		−	12.4529i		−	0.592323i
$443$	2.05313	−	3.55613i	0.0975472	−	0.168957i	−0.813122	−	0.582094i	$-0.802234\pi$
$443$	2.05313	−	3.55613i	0.0975472	−	0.168957i	0.910669	+	0.413137i	$0.135567\pi$
$444$	−1.40610	+	18.0753i	−0.0667307	+	0.857817i
$445$	4.29297	−	20.7750i	0.203506	−	0.984831i
$446$	−12.0678	−	20.9020i	−0.571425	−	0.989738i
$447$	0.816021	−	10.4899i	0.0385965	−	0.496154i
$448$	2.02132	+	1.70712i	0.0954986	+	0.0806537i
$449$			23.7106i			1.11897i	0.828839	+	0.559487i	$0.189002\pi$
$449$			23.7106i			1.11897i	−0.828839	+	0.559487i	$0.810998\pi$
$450$	−12.6863	−	8.00354i	−0.598040	−	0.377291i
$451$		−	13.0468i		−	0.614348i
$452$	1.32959	−	2.30292i	0.0625387	−	0.108320i
$453$	13.4162	+	28.0623i	0.630349	+	1.31848i
$454$	−8.32843	+	4.80842i	−0.390872	+	0.225670i
$455$	−25.0601	−	10.0529i	−1.17484	−	0.471286i
$456$	5.88124	+	4.03424i	0.275414	+	0.188920i
$457$	19.1410	+	11.0510i	0.895377	+	0.516946i	0.875698	−	0.482860i	$-0.160402\pi$
$457$	19.1410	+	11.0510i	0.895377	+	0.516946i	0.0196797	+	0.999806i	$0.493735\pi$
$458$			22.8383i			1.06716i
$459$	−3.27224	+	13.7947i	−0.152735	+	0.643883i
$460$	−3.86209	−	3.43801i	−0.180071	−	0.160298i
$461$	−9.53685	+	16.5183i	−0.444175	+	0.769334i	−0.997994	−	0.0633028i	$-0.979837\pi$
$461$	−9.53685	+	16.5183i	−0.444175	+	0.769334i	0.553819	+	0.832637i	$0.313170\pi$
$462$	−20.3721	+	20.6361i	−0.947794	+	0.960080i
$463$	−22.9165	+	13.2308i	−1.06502	+	0.614889i	−0.926816	−	0.375515i	$-0.877466\pi$
$463$	−22.9165	+	13.2308i	−1.06502	+	0.614889i	−0.138203	+	0.990404i	$0.544133\pi$
$464$	0.173539	−	0.100193i	0.00805635	−	0.00465134i
$465$	−9.06380	−	2.62015i	−0.420324	−	0.121507i
$466$	12.0611	−	20.8904i	0.558718	−	0.967728i
$467$			25.0308i			1.15829i	0.815225	+	0.579144i	$0.196613\pi$
$467$			25.0308i			1.15829i	−0.815225	+	0.579144i	$0.803387\pi$
$468$	13.5274	+	2.11745i	0.625306	+	0.0978791i
$469$	−21.2703	−	3.82057i	−0.982171	−	0.176418i
$470$	6.38071	+	19.2657i	0.294320	+	0.888658i
$471$	−12.9363	−	1.00633i	−0.596071	−	0.0463692i
$472$	−0.616709	−	1.06817i	−0.0283864	−	0.0491666i
$473$	−26.5288	−	45.9492i	−1.21979	−	2.11275i
$474$	3.51208	+	0.273209i	0.161315	+	0.0125489i
$475$	8.16021	−	18.9018i	0.374416	−	0.867274i
$476$	−7.10514	−	1.27623i	−0.325663	−	0.0584957i
$477$	−7.31965	−	18.9657i	−0.335144	−	0.868379i
$478$		−	15.8623i		−	0.725524i
$479$	3.86939	−	6.70198i	0.176797	−	0.306221i	−0.763985	−	0.645234i	$-0.776760\pi$
$479$	3.86939	−	6.70198i	0.176797	−	0.306221i	0.940782	+	0.339013i	$0.110093\pi$
$480$	−1.07556	+	3.72064i	−0.0490924	+	0.169823i
$481$	−41.3730	+	23.8867i	−1.88645	+	1.08914i
$482$	11.8605	−	6.84765i	0.540230	−	0.311902i
$483$	7.54108	+	7.44458i	0.343131	+	0.338740i
$484$	14.5207	−	25.1507i	0.660034	−	1.14321i
$485$	−8.10326	−	7.21348i	−0.367950	−	0.327547i
$486$	−14.4287	−	5.90023i	−0.654499	−	0.267640i
$487$			5.56297i			0.252082i	0.992025	+	0.126041i	$0.0402271\pi$
$487$			5.56297i			0.252082i	−0.992025	+	0.126041i	$0.959773\pi$
$488$	1.66558	+	0.961623i	0.0753973	+	0.0435306i
$489$	−0.309531	−	0.212323i	−0.0139975	−	0.00960156i
$490$	−8.30407	+	13.2681i	−0.375140	+	0.599392i
$491$	−7.49049	+	4.32464i	−0.338041	+	0.195168i	−0.659405	−	0.751788i	$-0.729192\pi$
$491$	−7.49049	+	4.32464i	−0.338041	+	0.195168i	0.321364	+	0.946956i	$0.395859\pi$
$492$	1.54034	+	3.22188i	0.0694438	+	0.145253i
$493$	−0.273373	+	0.473496i	−0.0123121	+	0.0213252i
$494$			18.7930i			0.845536i
$495$	−39.7416	−	14.9154i	−1.78625	−	0.670399i
$496$			2.43609i			0.109383i
$497$	−14.2006	+	16.8143i	−0.636983	+	0.754225i
$498$	−0.565267	+	7.26646i	−0.0253302	+	0.325618i
$499$	9.61871	+	16.6601i	0.430592	+	0.745808i	0.996924	−	0.0783693i	$-0.0249713\pi$
$499$	9.61871	+	16.6601i	0.430592	+	0.745808i	−0.566332	+	0.824177i	$0.691638\pi$
$500$	11.1374	+	0.979477i	0.498078	+	0.0438035i
$501$	−1.02310	+	13.1519i	−0.0457088	+	0.587582i
$502$	−12.0822	+	20.9270i	−0.539256	+	0.934019i
$503$		−	24.3743i		−	1.08680i	−0.839475	−	0.543398i	$-0.817137\pi$
$503$		−	24.3743i		−	1.08680i	0.839475	−	0.543398i	$-0.182863\pi$
$504$	2.59449	−	7.50124i	0.115568	−	0.334132i
$505$	28.7780	+	25.6181i	1.28061	+	1.13999i
$506$	−12.6720	−	7.31619i	−0.563340	−	0.325244i
$507$	5.85009	+	12.2365i	0.259812	+	0.543440i
$508$	−0.827895	+	0.477985i	−0.0367319	+	0.0212072i
$509$	−11.0101	−	19.0700i	−0.488013	−	0.845264i	0.511891	−	0.859050i	$-0.328945\pi$
$509$	−11.0101	−	19.0700i	−0.488013	−	0.845264i	−0.999905	+	0.0137860i	$0.995612\pi$
$510$	−2.53436	−	10.2589i	−0.112223	−	0.454272i
$511$	−28.1874	−	23.8058i	−1.24694	−	1.05311i
$512$	1.00000			0.0441942
$513$	4.93824	−	20.8180i	0.218028	−	0.919139i
$514$			8.51521i			0.375590i
$515$	39.0444	−	12.9314i	1.72050	−	0.569824i
$516$	11.9761	+	8.21502i	0.527220	+	0.361646i
$517$	28.7161	+	49.7377i	1.26293	+	2.18746i
$518$	9.38877	+	26.0539i	0.412519	+	1.14474i
$519$	−11.5361	+	5.51527i	−0.506380	+	0.242094i
$520$	−9.68801	+	3.20863i	−0.424848	+	0.140708i
$521$	−23.9844			−1.05078			−0.525388	−	0.850863i	$-0.676080\pi$
$521$	−23.9844			−1.05078			−0.525388	+	0.850863i	$0.676080\pi$
$522$	−0.467871	−	0.377474i	−0.0204782	−	0.0165216i
$523$	−23.3213			−1.01977			−0.509885	−	0.860242i	$-0.670312\pi$
$523$	−23.3213			−1.01977			−0.509885	+	0.860242i	$0.670312\pi$
$524$	−5.64033	+	9.76935i	−0.246399	+	0.426776i
$525$	−22.6909	−	3.18160i	−0.990313	−	0.138857i
$526$	−9.99743	−	17.3161i	−0.435909	−	0.755016i
$527$	−3.32339	−	5.75628i	−0.144769	−	0.250747i
$528$	−0.850035	+	10.9271i	−0.0369930	+	0.475542i
$529$	8.82644	−	15.2878i	0.383758	−	0.664689i
$530$	11.3177	+	10.0750i	0.491611	+	0.437630i
$531$	−2.32344	+	2.87985i	−0.100829	+	0.124975i
$532$	10.7226	+	1.92599i	0.464882	+	0.0835022i
$533$	−4.70510	+	8.14947i	−0.203800	+	0.352993i
$534$	7.08768	+	14.8251i	0.306714	+	0.641545i
$535$	−0.784886	+	3.79831i	−0.0339336	+	0.164215i
$536$	−7.07376	+	4.08404i	−0.305540	+	0.176404i
$537$	−12.0127	−	8.24008i	−0.518384	−	0.355586i
$538$	−14.0404	+	24.3186i	−0.605323	+	1.04845i
$539$	−15.4151	+	41.5260i	−0.663977	+	1.78865i
$540$	11.5751	−	1.00866i	0.498112	−	0.0434059i
$541$	29.4801			1.26745			0.633723	−	0.773560i	$-0.281526\pi$
$541$	29.4801			1.26745			0.633723	+	0.773560i	$0.281526\pi$
$542$	9.87232	+	5.69979i	0.424052	+	0.244827i
$543$	28.3510	+	19.4473i	1.21666	+	0.834565i
$544$	−2.36292	+	1.36423i	−0.101309	+	0.0584910i
$545$	0.181123	−	0.876511i	0.00775845	−	0.0375456i
$546$	20.1672	−	5.54321i	0.863076	−	0.237228i
$547$	−25.2017	−	14.5502i	−1.07755	−	0.622121i	−0.147313	−	0.989090i	$-0.547062\pi$
$547$	−25.2017	−	14.5502i	−1.07755	−	0.622121i	−0.930233	+	0.366969i	$0.880396\pi$
$548$	−1.82666			−0.0780310
$549$	0.892271	−	5.70033i	0.0380812	−	0.243284i
$550$	31.4263	−	3.66359i	1.34002	−	0.156216i
$551$	0.412555	−	0.714566i	0.0175754	−	0.0304415i
$552$	3.99310	+	0.310629i	0.169958	+	0.0132212i
$553$	5.06234	−	1.82426i	0.215272	−	0.0775755i
$554$	−17.2040	+	9.93273i	−0.730928	+	0.422001i
$555$	−29.2225	+	28.0984i	−1.24043	+	1.19271i
$556$	15.2206	+	8.78760i	0.645496	+	0.372677i
$557$	−11.3404			−0.480509			−0.240255	−	0.970710i	$-0.577231\pi$
$557$	−11.3404			−0.480509			−0.240255	+	0.970710i	$0.577231\pi$
$558$	6.81809	−	2.63139i	0.288633	−	0.111396i
$559$			38.2686i			1.61859i
$560$	0.837855	+	5.85645i	0.0354058	+	0.247480i
$561$	−12.8986	−	26.9796i	−0.544578	−	1.13908i
$562$	9.44238	−	5.45156i	0.398303	−	0.229960i
$563$	−12.0632	+	6.96467i	−0.508402	+	0.293526i	−0.732176	−	0.681115i	$-0.761495\pi$
$563$	−12.0632	+	6.96467i	−0.508402	+	0.293526i	0.223775	+	0.974641i	$0.428162\pi$
$564$	−12.9636	−	8.89234i	−0.545864	−	0.374435i
$565$	5.64459	−	1.86947i	0.237470	−	0.0786490i
$566$	9.59854			0.403457
$567$	−23.7969	+	0.841189i	−0.999376	+	0.0353266i
$568$			8.31846i			0.349035i
$569$	−24.0673	−	13.8953i	−1.00895	−	0.582519i	−0.0980680	−	0.995180i	$-0.531266\pi$
$569$	−24.0673	−	13.8953i	−1.00895	−	0.582519i	−0.910885	+	0.412660i	$0.864600\pi$
$570$	3.82468	+	15.4820i	0.160198	+	0.648469i
$571$	−17.6064	−	30.4952i	−0.736806	−	1.27619i	−0.953926	−	0.300041i	$-0.903000\pi$
$571$	−17.6064	−	30.4952i	−0.736806	−	1.27619i	0.217120	−	0.976145i	$-0.430334\pi$
$572$	−25.0113	+	14.4403i	−1.04578	+	0.603779i
$573$	3.98041	−	1.90298i	0.166284	−	0.0794983i
$574$	4.16758	+	3.51974i	0.173951	+	0.146911i
$575$	−1.33879	−	11.4842i	−0.0558313	−	0.478922i
$576$	−1.08017	−	2.79879i	−0.0450071	−	0.116616i
$577$	−3.29407			−0.137134			−0.0685670	−	0.997647i	$-0.521843\pi$
$577$	−3.29407			−0.137134			−0.0685670	+	0.997647i	$0.521843\pi$
$578$	−4.77773	+	8.27528i	−0.198727	+	0.344206i
$579$	3.01431	−	38.7486i	0.125270	−	1.61034i
$580$	0.438806	+	0.0906752i	0.0182204	+	0.00376508i
$581$	3.77438	+	10.4739i	0.156588	+	0.434531i
$582$	8.37816	+	0.651748i	0.347286	+	0.0270158i
$583$	37.1350	+	21.4399i	1.53798	+	0.887950i
$584$	−13.9450			−0.577050
$585$	19.4450	+	23.6489i	0.803952	+	0.977760i
$586$		−	1.96314i		−	0.0810964i
$587$	−24.4065	−	14.0911i	−1.00736	−	0.581602i	−0.0969457	−	0.995290i	$-0.530907\pi$
$587$	−24.4065	−	14.0911i	−1.00736	−	0.581602i	−0.910419	+	0.413687i	$0.864241\pi$
$588$	−1.09592	−	12.0747i	−0.0451952	−	0.497953i
$589$	5.01542	+	8.68696i	0.206657	+	0.357940i
$590$	0.558126	−	2.70095i	0.0229777	−	0.111196i
$591$	10.1573	−	14.8076i	0.417814	−	0.609103i
$592$	9.06497	+	5.23366i	0.372568	+	0.215102i
$593$		−	36.9570i		−	1.51764i	−0.651298	−	0.758822i	$-0.725775\pi$
$593$		−	36.9570i		−	1.51764i	0.651298	−	0.758822i	$-0.274225\pi$
$594$	31.5009	−	9.42408i	1.29250	−	0.386675i
$595$	−9.96935	−	12.6953i	−0.408704	−	0.520457i
$596$	−5.26078	−	3.03731i	−0.215490	−	0.124413i
$597$	16.4977	+	11.3166i	0.675206	+	0.463158i
$598$	5.27692	+	9.13990i	0.215789	+	0.373758i
$599$	31.2435	−	18.0385i	1.27658	−	0.737032i	0.300359	−	0.953826i	$-0.402893\pi$
$599$	31.2435	−	18.0385i	1.27658	−	0.737032i	0.976217	+	0.216794i	$0.0695601\pi$
$600$	−7.32815	+	4.61500i	−0.299170	+	0.188407i
$601$	−37.1333	−	21.4389i	−1.51470	−	0.874513i	−0.999852	−	0.0172319i	$-0.994515\pi$
$601$	−37.1333	−	21.4389i	−1.51470	−	0.874513i	−0.514849	−	0.857281i	$-0.672152\pi$
$602$	21.8346	+	3.92194i	0.889913	+	0.159846i
$603$	19.0712	+	15.3865i	0.776641	+	0.626588i
$604$	17.9582			0.730708
$605$	61.6457	−	20.4168i	2.50625	−	0.830062i
$606$	−29.7543	−	2.31463i	−1.20869	−	0.0940252i
$607$	−9.71483	−	16.8266i	−0.394313	−	0.682970i	0.598700	−	0.800973i	$-0.295684\pi$
$607$	−9.71483	−	16.8266i	−0.394313	−	0.682970i	−0.993013	+	0.118003i	$0.962351\pi$
$608$	3.56595	−	2.05880i	0.144618	−	0.0834955i
$609$	−0.888505	−	0.231952i	−0.0360041	−	0.00939919i
$610$	1.35209	+	4.08243i	0.0547444	+	0.165293i
$611$		−	41.4239i		−	1.67583i
$612$	6.37056	+	5.13972i	0.257515	+	0.207761i
$613$		−	32.1273i		−	1.29761i	−0.760955	−	0.648805i	$-0.775269\pi$
$613$		−	32.1273i		−	1.29761i	0.760955	−	0.648805i	$-0.224731\pi$
$614$	−1.56685	+	2.71386i	−0.0632329	+	0.109523i
$615$	−2.21760	+	7.67124i	−0.0894221	+	0.309334i
$616$	5.67581	+	15.7504i	0.228685	+	0.634602i
$617$	8.54944	+	14.8081i	0.344187	+	0.596150i	0.985206	−	0.171375i	$-0.0548211\pi$
$617$	8.54944	+	14.8081i	0.344187	+	0.596150i	−0.641018	+	0.767526i	$0.721488\pi$
$618$	−18.0215	+	26.2723i	−0.724931	+	1.05683i
$619$	−16.4455	−	9.49482i	−0.661001	−	0.381629i	0.131657	−	0.991295i	$-0.457970\pi$
$619$	−16.4455	−	9.49482i	−0.661001	−	0.381629i	−0.792658	+	0.609666i	$0.791303\pi$
$620$	−3.62193	+	4.06869i	−0.145460	+	0.163402i
$621$	−3.44385	−	11.5114i	−0.138197	−	0.461936i
$622$	−18.0246			−0.722722
$623$	19.1766	+	16.1957i	0.768296	+	0.648867i
$624$	4.47164	−	6.51891i	0.179009	−	0.260965i
$625$	17.1451	+	18.1947i	0.685802	+	0.727788i
$626$	−2.49357	−	4.31899i	−0.0996630	−	0.172621i
$627$	19.4656	+	40.7156i	0.777381	+	1.62603i
$628$	−3.74566	+	6.48767i	−0.149468	+	0.258886i
$629$	−28.5597			−1.13875
$630$	15.4860	−	8.67094i	0.616975	−	0.345459i
$631$	−32.7042			−1.30193			−0.650967	−	0.759106i	$-0.725636\pi$
$631$	−32.7042			−1.30193			−0.650967	+	0.759106i	$0.725636\pi$
$632$	1.01691	−	1.76135i	0.0404507	−	0.0700626i
$633$	−0.532129	−	0.0413950i	−0.0211502	−	0.00164530i
$634$	1.58024	+	2.73705i	0.0627593	+	0.108702i
$635$	−2.09339	−	0.432579i	−0.0830736	−	0.0171664i
$636$	−11.7017	−	0.910289i	−0.464002	−	0.0360953i
$637$	24.6045	−	20.3794i	0.974865	−	0.807460i
$638$	1.26801			0.0502009
$639$	23.2816	−	8.98536i	0.921007	−	0.355455i
$640$	1.67017	+	1.48678i	0.0660194	+	0.0587702i
$641$	−30.0032	−	17.3224i	−1.18506	−	0.684193i	−0.227877	−	0.973690i	$-0.573179\pi$
$641$	−30.0032	−	17.3224i	−1.18506	−	0.684193i	−0.957179	+	0.289497i	$0.906512\pi$
$642$	−1.29584	−	2.71048i	−0.0511429	−	0.106974i
$643$	4.50753	+	7.80727i	0.177760	+	0.307889i	0.941113	−	0.338093i	$-0.109782\pi$
$643$	4.50753	+	7.80727i	0.177760	+	0.307889i	−0.763353	+	0.645981i	$0.776448\pi$
$644$	5.75568	−	2.07412i	0.226806	−	0.0817316i
$645$	7.78829	+	31.5264i	0.306663	+	1.24135i
$646$	−5.61738	+	9.72958i	−0.221013	+	0.382805i
$647$			19.3322i			0.760028i	0.924981	+	0.380014i	$0.124081\pi$
$647$			19.3322i			0.760028i	−0.924981	+	0.380014i	$0.875919\pi$
$648$	−6.66646	+	6.04634i	−0.261883	+	0.237523i
$649$		−	7.80487i		−	0.306368i
$650$	−20.9512	−	9.04498i	−0.821774	−	0.354773i
$651$	7.84282	−	7.94449i	0.307385	−	0.311369i
$652$	−0.187677	+	0.108355i	−0.00734999	+	0.00424352i
$653$	−0.172113	−	0.298108i	−0.00673529	−	0.0116659i	0.862638	−	0.505822i	$-0.168811\pi$
$653$	−0.172113	−	0.298108i	−0.00673529	−	0.0116659i	−0.869373	+	0.494156i	$0.835477\pi$
$654$	0.299034	+	0.625480i	0.0116931	+	0.0244582i
$655$	−23.9452	+	7.93057i	−0.935617	+	0.309873i
$656$	2.06181			0.0805000
$657$	15.0630	+	39.0292i	0.587664	+	1.52268i
$658$	−23.6349	−	4.24530i	−0.921384	−	0.165499i
$659$	32.8621	+	18.9730i	1.28013	+	0.739082i	0.976871	−	0.213828i	$-0.0685931\pi$
$659$	32.8621	+	18.9730i	1.28013	+	0.739082i	0.303256	+	0.952909i	$0.401926\pi$
$660$	−17.6659	+	16.9864i	−0.687646	+	0.661194i
$661$	32.3820	−	18.6958i	1.25952	−	0.727182i	0.286535	−	0.958070i	$-0.407497\pi$
$661$	32.3820	−	18.6958i	1.25952	−	0.727182i	0.972980	+	0.230888i	$0.0741632\pi$
$662$	13.7475	+	23.8113i	0.534311	+	0.925454i
$663$	−1.67283	+	21.5040i	−0.0649672	+	0.835148i
$664$	3.64421	+	2.10398i	0.141423	+	0.0816504i
$665$	15.0450	+	19.1588i	0.583421	+	0.742948i
$666$	4.85621	−	31.0242i	0.188174	−	1.20216i
$667$		−	0.463369i		−	0.0179417i
$668$	6.59580	+	3.80809i	0.255199	+	0.147339i
$669$	18.0312	+	37.7154i	0.697127	+	1.45816i
$670$	−17.8865	−	3.69608i	−0.691015	−	0.142792i
$671$	6.08499	+	10.5395i	0.234909	+	0.406873i
$672$	−3.26117	−	3.21944i	−0.125802	−	0.124192i
$673$	−7.53903	−	4.35266i	−0.290608	−	0.167783i	0.347608	−	0.937640i	$-0.386994\pi$
$673$	−7.53903	−	4.35266i	−0.290608	−	0.167783i	−0.638216	+	0.769857i	$0.720327\pi$
$674$			2.25674i			0.0869262i
$675$	20.8321	+	15.5250i	0.801827	+	0.597557i
$676$	7.83059			0.301177
$677$	14.8248	+	8.55913i	0.569765	+	0.328954i	0.757055	−	0.653351i	$-0.226637\pi$
$677$	14.8248	+	8.55913i	0.569765	+	0.328954i	−0.187291	+	0.982305i	$0.559971\pi$
$678$	−2.60534	+	3.79815i	−0.100057	+	0.145867i
$679$	12.0763	−	4.35182i	0.463447	−	0.167008i
$680$	−5.97481	−	1.23464i	−0.229123	−	0.0473463i
$681$	15.0277	−	7.18456i	0.575864	−	0.275313i
$682$	−7.70757	+	13.3499i	−0.295138	+	0.511194i
$683$	42.3497			1.62046			0.810232	−	0.586109i	$-0.199341\pi$
$683$	42.3497			1.62046			0.810232	+	0.586109i	$0.199341\pi$
$684$	−9.61400	−	7.75650i	−0.367600	−	0.296577i
$685$	−3.05084	−	2.71584i	−0.116567	−	0.103767i
$686$	−9.10612	−	16.1270i	−0.347673	−	0.615730i
$687$	3.06792	−	39.4379i	0.117049	−	1.50465i
$688$	7.26144	−	4.19239i	0.276840	−	0.159834i
$689$	−15.4639	−	26.7842i	−0.589127	−	1.02040i
$690$	6.20734	+	6.45568i	0.236309	+	0.245763i
$691$	−6.66895	−	3.85032i	−0.253699	−	0.146473i	0.367758	−	0.929922i	$-0.380125\pi$
$691$	−6.66895	−	3.85032i	−0.253699	−	0.146473i	−0.621457	+	0.783449i	$0.713459\pi$
$692$			7.38242i			0.280638i
$693$	37.9513	−	32.8985i	1.44165	−	1.24971i
$694$	−19.3278			−0.733674
$695$	12.3558	+	37.3065i	0.468681	+	1.41512i
$696$	−0.313132	+	0.149704i	−0.0118693	+	0.00567453i
$697$	−4.87189	+	2.81279i	−0.184536	+	0.106542i
$698$	25.1498	−	14.5202i	0.951933	−	0.549599i
$699$	−23.6337	+	34.4540i	−0.893909	+	1.30317i
$700$	−7.30789	+	11.0270i	−0.276212	+	0.416781i
$701$		−	28.9809i		−	1.09459i	−0.836939	−	0.547297i	$-0.815657\pi$
$701$		−	28.9809i		−	1.09459i	0.836939	−	0.547297i	$-0.184343\pi$
$702$	−23.0752	−	5.47366i	−0.870917	−	0.206590i
$703$	43.1003			1.62556
$704$	5.48007	+	3.16392i	0.206538	+	0.119245i
$705$	−8.43043	−	34.1257i	−0.317508	−	1.28525i
$706$	18.9251	−	10.9264i	0.712255	−	0.411221i
$707$	−42.8880	+	15.4551i	−1.61297	+	0.581249i
$708$	0.921464	+	1.92740i	0.0346308	+	0.0724361i
$709$	−3.82844	+	6.63105i	−0.143780	+	0.249034i	−0.928917	−	0.370288i	$-0.879259\pi$
$709$	−3.82844	+	6.63105i	−0.143780	+	0.249034i	0.785137	+	0.619322i	$0.212592\pi$
$710$	−12.3677	+	13.8933i	−0.464153	+	0.521405i
$711$	−6.02808	−	0.943575i	−0.226071	−	0.0353868i
$712$	9.48716			0.355547
$713$	4.87847	+	2.81658i	0.182700	+	0.105482i
$714$	12.0980	+	3.15828i	0.452755	+	0.118196i
$715$	−63.2428	−	13.0685i	−2.36515	−	0.488736i
$716$	−7.28359	+	4.20518i	−0.272201	+	0.157155i
$717$	−2.13082	+	27.3915i	−0.0795770	+	1.02296i
$718$	10.1102	+	5.83713i	0.377310	+	0.217840i
$719$	−3.74789			−0.139773			−0.0698863	−	0.997555i	$-0.522264\pi$
$719$	−3.74789			−0.139773			−0.0698863	+	0.997555i	$0.522264\pi$
$720$	2.35712	−	6.28045i	0.0878445	−	0.234058i
$721$	−8.60366	+	47.8992i	−0.320417	+	1.78386i
$722$	−1.02266	+	1.77129i	−0.0380593	+	0.0659207i
$723$	−21.4009	+	10.2315i	−0.795909	+	0.380514i
$724$	17.1900	−	9.92462i	0.638860	−	0.368846i
$725$	0.598068	+	0.803851i	0.0222117	+	0.0298543i
$726$	−28.4535	+	41.4804i	−1.05601	+	1.53948i
$727$	−7.99237	+	13.8432i	−0.296420	+	0.513415i	−0.975314	−	0.220821i	$-0.929126\pi$
$727$	−7.99237	+	13.8432i	−0.296420	+	0.513415i	0.678894	+	0.734236i	$0.262460\pi$
$728$	2.13481	−	11.8851i	0.0791214	−	0.440493i
$729$	24.1234	+	12.1270i	0.893458	+	0.449146i
$730$	−23.2906	−	20.7332i	−0.862025	−	0.767371i
$731$	−11.4388	+	19.8126i	−0.423080	+	0.732796i
$732$	−2.74700	−	1.88431i	−0.101532	−	0.0696459i
$733$	17.2764	+	29.9236i	0.638118	+	1.10525i	0.985845	+	0.167657i	$0.0536201\pi$
$733$	17.2764	+	29.9236i	0.638118	+	1.10525i	−0.347728	+	0.937596i	$0.613047\pi$
$734$	1.49120	+	2.58283i	0.0550410	+	0.0953339i
$735$	16.1221	−	21.7963i	0.594672	−	0.803968i
$736$	1.15619	−	2.00258i	0.0426178	−	0.0738162i
$737$	−51.6863			−1.90389
$738$	−2.22710	−	5.77056i	−0.0819808	−	0.212417i
$739$	−2.42908			−0.0893552			−0.0446776	−	0.999001i	$-0.514226\pi$
$739$	−2.42908			−0.0893552			−0.0446776	+	0.999001i	$0.514226\pi$
$740$	7.35877	+	22.2187i	0.270514	+	0.816777i
$741$	2.52451	−	32.4524i	0.0927402	−	1.19217i
$742$	−16.8669	+	6.07814i	−0.619203	+	0.223136i
$743$	−7.44072	−	12.8877i	−0.272973	−	0.472804i	0.696648	−	0.717413i	$-0.254674\pi$
$743$	−7.44072	−	12.8877i	−0.272973	−	0.472804i	−0.969622	+	0.244609i	$0.921340\pi$
$744$	0.327246	−	4.20671i	0.0119974	−	0.154226i
$745$	−4.27060	−	12.8945i	−0.156463	−	0.472417i
$746$			5.89359i			0.215780i
$747$	1.95225	−	12.4720i	0.0714289	−	0.456328i
$748$	−17.2653			−0.631282
$749$	−3.50607	−	2.96107i	−0.128109	−	0.108195i
$750$	−19.1008	−	3.18750i	−0.697462	−	0.116391i
$751$	−2.50116	−	4.33213i	−0.0912685	−	0.158082i	0.816777	−	0.576954i	$-0.195759\pi$
$751$	−2.50116	−	4.33213i	−0.0912685	−	0.158082i	−0.908045	+	0.418872i	$0.862425\pi$
$752$	−7.86014	+	4.53806i	−0.286630	+	0.165486i
$753$	23.6752	−	34.5145i	0.862772	−	1.25778i
$754$	−0.792042	−	0.457286i	−0.0288445	−	0.0166534i
$755$	29.9933	+	26.6999i	1.09157	+	0.971708i
$756$	−5.48791	+	12.6049i	−0.199593	+	0.458435i
$757$		−	23.0241i		−	0.836826i	−0.908257	−	0.418413i	$-0.862586\pi$
$757$		−	23.0241i		−	0.836826i	0.908257	−	0.418413i	$-0.137414\pi$
$758$	7.50437	−	12.9980i	0.272571	−	0.472107i
$759$	20.8997	+	14.3361i	0.758610	+	0.520368i
$760$	9.01675	+	1.86323i	0.327072	+	0.0675864i
$761$	10.4160	+	18.0411i	0.377580	+	0.653988i	0.990710	−	0.135994i	$-0.0434228\pi$
$761$	10.4160	+	18.0411i	0.377580	+	0.653988i	−0.613129	+	0.789983i	$0.710090\pi$
$762$	1.49385	−	0.714188i	0.0541163	−	0.0258723i
$763$	0.809074	+	0.683306i	0.0292904	+	0.0247373i
$764$		−	2.54722i		−	0.0921553i
$765$	2.99831	+	18.0559i	0.108404	+	0.652811i
$766$			2.01841i			0.0729282i
$767$	−2.81470	+	4.87520i	−0.101633	+	0.176033i
$768$	−1.72683	−	0.134333i	−0.0623117	−	0.00484731i
$769$	24.3363	−	14.0506i	0.877590	−	0.506677i	0.00772702	−	0.999970i	$-0.497540\pi$
$769$	24.3363	−	14.0506i	0.877590	−	0.506677i	0.869863	+	0.493293i	$0.164207\pi$
$770$	−13.9378	+	34.7446i	−0.502284	+	1.25211i
$771$	1.14387	−	14.7044i	0.0411955	−	0.529564i
$772$	−19.4328	−	11.2196i	−0.699403	−	0.403801i
$773$		−	30.5269i		−	1.09798i	−0.835830	−	0.548989i	$-0.815013\pi$
$773$		−	30.5269i		−	1.09798i	0.835830	−	0.548989i	$-0.184987\pi$
$774$	−19.5772	−	15.7948i	−0.703689	−	0.567731i
$775$	−12.0985	+	1.41041i	−0.434591	+	0.0506633i
$776$	2.42587	−	4.20173i	0.0870838	−	0.150833i
$777$	−12.7129	−	46.2519i	−0.456075	−	1.65928i
$778$	17.3287	−	10.0047i	0.621265	−	0.358687i
$779$	7.35230	−	4.24485i	0.263424	−	0.152088i
$780$	17.1606	−	4.23936i	0.614449	−	0.151794i
$781$	−26.3189	+	45.5857i	−0.941765	+	1.63118i
$782$			6.30927i			0.225619i
$783$	0.757228	+	0.714686i	0.0270611	+	0.0255408i
$784$	−6.56243	−	2.43609i	−0.234373	−	0.0870031i
$785$	−15.9016	+	5.26657i	−0.567554	+	0.187972i
$786$	11.0523	−	16.1124i	0.394221	−	0.574709i
$787$	−10.7974	−	18.7017i	−0.384887	−	0.666644i	0.606867	−	0.794804i	$-0.292426\pi$
$787$	−10.7974	−	18.7017i	−0.384887	−	0.666644i	−0.991754	+	0.128160i	$0.959093\pi$
$788$	−5.18359	−	8.97824i	−0.184658	−	0.319837i
$789$	14.9378	+	31.2449i	0.531799	+	1.11235i
$790$	4.31716	−	1.42983i	0.153598	−	0.0508710i
$791$	−1.24382	+	6.92471i	−0.0442251	+	0.246215i
$792$	2.93574	−	18.7551i	0.104317	−	0.666434i
$793$		−	8.77780i		−	0.311709i
$794$	7.69209	−	13.3231i	0.272982	−	0.472819i
$795$	−18.1905	−	18.9182i	−0.645149	−	0.670959i
$796$	10.0030	−	5.77523i	0.354547	−	0.204698i
$797$	34.2994	−	19.8028i	1.21495	−	0.701450i	0.251114	−	0.967957i	$-0.419203\pi$
$797$	34.2994	−	19.8028i	1.21495	−	0.701450i	0.963833	+	0.266507i	$0.0858697\pi$
$798$	−18.2574	−	4.76625i	−0.646304	−	0.168724i
$799$	12.3819	−	21.4461i	0.438041	−	0.758710i
$800$	0.578965	+	4.96637i	0.0204695	+	0.175588i
$801$	−10.2478	−	26.5526i	−0.362087	−	0.938190i
$802$			6.65829i			0.235112i
$803$	−76.4197	−	44.1209i	−2.69679	−	1.55699i
$804$	12.7638	−	6.10222i	0.450146	−	0.215209i
$805$	12.6968	+	5.09331i	0.447502	+	0.179516i
$806$	9.62884	−	5.55921i	0.339161	−	0.195815i
$807$	27.5121	−	40.1081i	0.968473	−	1.41187i
$808$	−8.61527	+	14.9221i	−0.303084	+	0.524957i
$809$		−	7.18884i		−	0.252746i	−0.991983	−	0.126373i	$-0.959666\pi$
$809$		−	7.18884i		−	0.252746i	0.991983	−	0.126373i	$-0.0403337\pi$
$810$	−20.1237	+	0.186878i	−0.707076	+	0.00656623i
$811$			0.343005i			0.0120445i	0.999982	+	0.00602227i	$0.00191696\pi$
$811$			0.343005i			0.0120445i	−0.999982	+	0.00602227i	$0.998083\pi$
$812$	−0.342082	+	0.405045i	−0.0120047	+	0.0142143i
$813$	−16.2822	−	11.1688i	−0.571041	−	0.391705i
$814$	33.1177	+	57.3616i	1.16078	+	2.01052i
$815$	−0.474554	−	0.0980622i	−0.0166229	−	0.00343497i
$816$	4.26363	−	2.03839i	0.149257	−	0.0713578i
$817$	17.2626	−	29.8998i	0.603943	−	1.04606i
$818$			13.1229i			0.458832i
$819$	−35.5700	+	6.86309i	−1.24292	+	0.239816i
$820$	3.44358	+	3.06545i	0.120255	+	0.107050i
$821$	33.2366	+	19.1892i	1.15997	+	0.669707i	0.951296	−	0.308279i	$-0.0997532\pi$
$821$	33.2366	+	19.1892i	1.15997	+	0.669707i	0.208670	+	0.977986i	$0.433087\pi$
$822$	3.15434	+	0.245380i	0.110020	+	0.00855861i
$823$	−16.0577	+	9.27092i	−0.559737	+	0.323164i	−0.753040	−	0.657975i	$-0.771413\pi$
$823$	−16.0577	+	9.27092i	−0.559737	+	0.323164i	0.193303	+	0.981139i	$0.438080\pi$
$824$	9.19697	+	15.9296i	0.320392	+	0.554934i
$825$	−54.7602	+	2.10483i	−1.90651	+	0.0732807i
$826$	2.49314	+	2.10559i	0.0867474	+	0.0732629i
$827$	−26.9688			−0.937797			−0.468899	−	0.883252i	$-0.655349\pi$
$827$	−26.9688			−0.937797			−0.468899	+	0.883252i	$0.655349\pi$
$828$	−6.85370	−	1.07281i	−0.238183	−	0.0372827i
$829$		−	12.5804i		−	0.436937i	−0.975844	−	0.218468i	$-0.929894\pi$
$829$		−	12.5804i		−	0.436937i	0.975844	−	0.218468i	$-0.0701061\pi$
$830$	2.95830	+	8.93215i	0.102684	+	0.310040i
$831$	31.0427	−	14.8411i	1.07686	−	0.514833i
$832$	−2.28203	−	3.95259i	−0.0791151	−	0.137031i
$833$	18.8299	−	3.19641i	0.652417	−	0.110749i
$834$	−25.1029	−	17.2194i	−0.869244	−	0.596257i
$835$	5.35435	+	16.1667i	0.185295	+	0.559471i
$836$	26.0555			0.901150
$837$	−12.1272	+	3.62808i	−0.419177	+	0.125405i
$838$	27.3691			0.945450
$839$	24.8006	−	42.9559i	0.856213	−	1.48300i	−0.0193027	−	0.999814i	$-0.506145\pi$
$839$	24.8006	−	42.9559i	0.856213	−	1.48300i	0.875515	−	0.483190i	$-0.160522\pi$
$840$	−0.660123	−	10.2257i	−0.0227764	−	0.352819i
$841$	−14.4799	−	25.0800i	−0.499308	−	0.864826i
$842$	−0.808320	−	1.40005i	−0.0278565	−	0.0482489i
$843$	−17.0377	+	8.14552i	−0.586811	+	0.280547i
$844$	−0.154076	+	0.266868i	−0.00530353	+	0.00918598i
$845$	13.0785	+	11.6424i	0.449912	+	0.400510i
$846$	21.1914	+	17.0970i	0.728574	+	0.587808i
$847$	−13.5840	+	75.6263i	−0.466752	+	2.59855i
$848$	−3.38819	+	5.86852i	−0.116351	+	0.201526i
$849$	−16.5751	−	1.28940i	−0.568855	−	0.0442520i
$850$	−8.14333	−	10.9453i	−0.279314	−	0.375421i
$851$	20.9617	−	12.1022i	0.718558	−	0.414859i
$852$	1.11744	−	14.3646i	0.0382829	−	0.492123i
$853$	9.04430	−	15.6652i	0.309671	−	0.536366i	−0.668619	−	0.743605i	$-0.733114\pi$
$853$	9.04430	−	15.6652i	0.309671	−	0.536366i	0.978290	+	0.207239i	$0.0664478\pi$
$854$	−5.00828	−	0.899588i	−0.171380	−	0.0307833i
$855$	−4.52484	−	27.2486i	−0.154746	−	0.931883i
$856$	−1.73454			−0.0592854
$857$	18.2726	+	10.5497i	0.624179	+	0.360370i	0.778494	−	0.627652i	$-0.215984\pi$
$857$	18.2726	+	10.5497i	0.624179	+	0.360370i	−0.154315	+	0.988022i	$0.549317\pi$
$858$	45.1302	−	21.5761i	1.54072	−	0.736597i
$859$	−21.7021	+	12.5297i	−0.740466	+	0.427508i	−0.822239	−	0.569143i	$-0.807275\pi$
$859$	−21.7021	+	12.5297i	−0.740466	+	0.427508i	0.0817725	+	0.996651i	$0.473942\pi$
$860$	18.3610	+	3.79414i	0.626106	+	0.129379i
$861$	−6.72390	−	6.63786i	−0.229150	−	0.226217i
$862$	5.35829	+	3.09361i	0.182504	+	0.105369i
$863$	−36.1751			−1.23141			−0.615707	−	0.787975i	$-0.711130\pi$
$863$	−36.1751			−1.23141			−0.615707	+	0.787975i	$0.711130\pi$
$864$	1.48931	+	4.97815i	0.0506672	+	0.169360i
$865$	−10.9760	+	12.3299i	−0.373197	+	0.419230i
$866$	10.7699	−	18.6540i	0.365976	−	0.633889i
$867$	9.36199	−	13.6482i	0.317950	−	0.463518i
$868$	−2.18507	−	6.06358i	−0.0741661	−	0.205811i
$869$	11.1455	−	6.43486i	0.378085	−	0.218288i
$870$	−0.745564	−	0.215527i	−0.0252770	−	0.00730704i
$871$	32.2850	+	18.6398i	1.09394	+	0.631585i
$872$	0.400269			0.0135548
$873$	−14.3801	−	2.25092i	−0.486694	−	0.0761821i
$874$		−	9.52149i		−	0.322069i
$875$	−28.6002	+	7.55177i	−0.966863	+	0.255296i
$876$	24.0808	+	1.87327i	0.813613	+	0.0632921i
$877$	24.8553	−	14.3502i	0.839302	−	0.484571i	−0.0177247	−	0.999843i	$-0.505642\pi$
$877$	24.8553	−	14.3502i	0.839302	−	0.484571i	0.857027	+	0.515271i	$0.172309\pi$
$878$	−12.8703	+	7.43067i	−0.434351	+	0.250773i
$879$	−0.263713	+	3.39001i	−0.00889483	+	0.114342i
$880$	4.44861	+	13.4320i	0.149963	+	0.452791i
$881$	−13.5132			−0.455271			−0.227636	−	0.973746i	$-0.573099\pi$
$881$	−13.5132			−0.455271			−0.227636	+	0.973746i	$0.573099\pi$
$882$	0.270450	+	20.9983i	0.00910652	+	0.707048i
$883$			28.0874i			0.945218i	0.881272	+	0.472609i	$0.156688\pi$
$883$			28.0874i			0.945218i	−0.881272	+	0.472609i	$0.843312\pi$
$884$	10.7845	+	6.22644i	0.362722	+	0.209418i
$885$	−1.32662	+	4.58911i	−0.0445937	+	0.154261i
$886$	2.05313	+	3.55613i	0.0689763	+	0.119470i
$887$	25.4215	−	14.6771i	0.853569	−	0.492809i	−0.00828416	−	0.999966i	$-0.502637\pi$
$887$	25.4215	−	14.6771i	0.853569	−	0.492809i	0.861854	+	0.507157i	$0.169304\pi$
$888$	−14.9506	−	10.2554i	−0.501711	−	0.344148i
$889$	1.63195	−	1.93233i	0.0547340	−	0.0648081i
$890$	15.8452	+	14.1053i	0.531133	+	0.472812i
$891$	−55.6628	+	12.0422i	−1.86477	+	0.403430i
$892$	24.1355			0.808118
$893$	−18.6859	+	32.3650i	−0.625301	+	1.08305i
$894$	8.67648	+	5.95163i	0.290185	+	0.199052i
$895$	−18.4171	−	3.80572i	−0.615614	−	0.127211i
$896$	−2.48907	+	0.896960i	−0.0831540	+	0.0299653i
$897$	−7.88458	−	16.4920i	−0.263259	−	0.550650i
$898$	−20.5340	−	11.8553i	−0.685229	−	0.395617i
$899$	−0.488157			−0.0162809
$900$	13.2744	−	6.98492i	0.442481	−	0.232831i
$901$		−	18.4891i		−	0.615962i
$902$	11.2988	+	6.52338i	0.376210	+	0.217205i
$903$	−37.1779	−	9.70564i	−1.23720	−	0.322984i
$904$	1.32959	+	2.30292i	0.0442215	+	0.0765940i
$905$	43.4660	+	8.98184i	1.44486	+	0.298567i
$906$	−31.0108	−	2.41237i	−1.03026	−	0.0801457i
$907$	−39.8069	−	22.9825i	−1.32177	−	0.763122i	−0.337756	−	0.941234i	$-0.609668\pi$
$907$	−39.8069	−	22.9825i	−1.32177	−	0.763122i	−0.984010	+	0.178112i	$0.943001\pi$
$908$		−	9.61684i		−	0.319146i
$909$	51.0698	+	7.99395i	1.69388	+	0.265142i
$910$	21.2361	−	16.6763i	0.703970	−	0.552813i
$911$	−11.3878	−	6.57475i	−0.377295	−	0.217831i	0.299346	−	0.954145i	$-0.403232\pi$
$911$	−11.3878	−	6.57475i	−0.377295	−	0.217831i	−0.676641	+	0.736314i	$0.736565\pi$
$912$	−6.43437	+	3.07619i	−0.213063	+	0.101863i
$913$	13.3137	+	23.0599i	0.440618	+	0.763172i
$914$	−19.1410	+	11.0510i	−0.633127	+	0.365536i
$915$	−1.78642	−	7.23131i	−0.0590574	−	0.239060i
$916$	−19.7785	−	11.4191i	−0.653500	−	0.377299i
$917$	5.27647	−	29.3757i	0.174244	−	0.970072i
$918$	−10.3105	−	9.73122i	−0.340296	−	0.321178i
$919$	−53.8086			−1.77498			−0.887492	−	0.460824i	$-0.847554\pi$
$919$	−53.8086			−1.77498			−0.887492	+	0.460824i	$0.847554\pi$
$920$	4.90845	−	1.62566i	0.161827	−	0.0535964i
$921$	3.07025	−	4.47591i	0.101168	−	0.147486i
$922$	−9.53685	−	16.5183i	−0.314079	−	0.544001i
$923$	32.8794	−	18.9830i	1.08224	−	0.624831i
$924$	−7.68539	−	27.9608i	−0.252831	−	0.919843i
$925$	−20.7440	+	48.0501i	−0.682058	+	1.57988i
$926$		−	26.4617i		−	0.869585i
$927$	34.6494	−	42.9471i	1.13803	−	1.41057i
$928$			0.200386i			0.00657799i
$929$	−25.6490	+	44.4253i	−0.841515	+	1.45755i	0.0470989	+	0.998890i	$0.485002\pi$
$929$	−25.6490	+	44.4253i	−0.841515	+	1.45755i	−0.888614	+	0.458656i	$0.848331\pi$
$930$	6.80102	−	6.53940i	0.223014	−	0.214435i
$931$	−28.4167	+	4.82379i	−0.931321	+	0.158093i
$932$	12.0611	+	20.8904i	0.395073	+	0.684287i
$933$	31.1256	+	2.42130i	1.01900	+	0.0792697i
$934$	−21.6773	−	12.5154i	−0.709303	−	0.409516i
$935$	−28.8360	−	25.6697i	−0.943039	−	0.839489i
$936$	−8.59749	+	10.6564i	−0.281018	+	0.348315i
$937$	26.4979			0.865650			0.432825	−	0.901478i	$-0.357517\pi$
$937$	26.4979			0.865650			0.432825	+	0.901478i	$0.357517\pi$
$938$	13.9439	−	16.5103i	0.455283	−	0.539082i
$939$	3.72580	+	7.79314i	0.121587	+	0.254319i
$940$	−19.8749	−	4.10697i	−0.648248	−	0.133954i
$941$	27.4639	+	47.5689i	0.895298	+	1.55070i	0.833435	+	0.552617i	$0.186371\pi$
$941$	27.4639	+	47.5689i	0.895298	+	1.55070i	0.0618625	+	0.998085i	$0.480296\pi$
$942$	7.33964	−	10.7000i	0.239138	−	0.348624i
$943$	2.38384	−	4.12894i	0.0776287	−	0.134457i
$944$	1.23342			0.0401444
$945$	−27.9065	+	12.8930i	−0.907797	+	0.419410i
$946$	53.0576			1.72505
$947$	6.38577	−	11.0605i	0.207510	−	0.359417i	−0.743420	−	0.668825i	$-0.766797\pi$
$947$	6.38577	−	11.0605i	0.207510	−	0.359417i	0.950929	+	0.309408i	$0.100131\pi$
$948$	−1.99265	+	2.90495i	−0.0647182	+	0.0943483i
$949$	31.8230	+	55.1190i	1.03302	+	1.78924i
$950$	12.2893	+	16.5179i	0.398719	+	0.535910i
$951$	−2.36113	−	4.93871i	−0.0765650	−	0.160149i
$952$	4.65781	−	5.51512i	0.150961	−	0.178746i
$953$	27.4326			0.888629			0.444315	−	0.895871i	$-0.353447\pi$
$953$	27.4326			0.888629			0.444315	+	0.895871i	$0.353447\pi$
$954$	20.0846	+	3.14384i	0.650262	+	0.101785i
$955$	3.78716	−	4.25431i	0.122550	−	0.137666i
$956$	13.7371	+	7.93114i	0.444291	+	0.256511i
$957$	−2.18964	−	0.170335i	−0.0707810	−	0.00550615i
$958$	3.86939	+	6.70198i	0.125014	+	0.216531i
$959$	4.54668	−	1.63844i	0.146820	−	0.0529080i
$960$	−2.68439	−	2.79178i	−0.0866383	−	0.0901044i
$961$	−12.5327	+	21.7073i	−0.404282	+	0.700237i
$962$		−	47.7734i		−	1.54028i
$963$	1.87360	+	4.85462i	0.0603760	+	0.156438i
$964$			13.6953i			0.441096i
$965$	−15.7752	−	47.6310i	−0.507822	−	1.53330i
$966$	−10.2177	+	2.80848i	−0.328750	+	0.0903613i
$967$	3.69352	−	2.13245i	0.118776	−	0.0685751i	−0.439435	−	0.898274i	$-0.644821\pi$
$967$	3.69352	−	2.13245i	0.118776	−	0.0685751i	0.558211	+	0.829699i	$0.311488\pi$
$968$	14.5207	+	25.1507i	0.466714	+	0.808373i
$969$	11.0073	−	16.0468i	0.353605	−	0.515497i
$970$	10.2987	−	3.41089i	0.330671	−	0.109517i
$971$	−21.6336			−0.694255			−0.347127	−	0.937818i	$-0.612843\pi$
$971$	−21.6336			−0.694255			−0.347127	+	0.937818i	$0.612843\pi$
$972$	12.3241	−	9.54551i	0.395296	−	0.306172i
$973$	−45.7672	−	8.22071i	−1.46723	−	0.263544i
$974$	−4.81767	−	2.78148i	−0.154368	−	0.0891245i
$975$	34.9642	+	18.4336i	1.11975	+	0.590348i
$976$	−1.66558	+	0.961623i	−0.0533139	+	0.0307808i
$977$	20.6630	+	35.7893i	0.661067	+	1.14500i	0.980336	+	0.197337i	$0.0632293\pi$
$977$	20.6630	+	35.7893i	0.661067	+	1.14500i	−0.319269	+	0.947664i	$0.603437\pi$
$978$	0.338642	−	0.161900i	0.0108286	−	0.00517701i
$979$	51.9903	+	30.0166i	1.66162	+	0.959335i
$980$	−7.33848	−	13.8256i	−0.234419	−	0.441642i
$981$	−0.432359	−	1.12027i	−0.0138042	−	0.0357675i
$982$		−	8.64927i		−	0.276009i
$983$	32.8450	+	18.9631i	1.04759	+	0.604828i	0.921975	−	0.387250i	$-0.126575\pi$
$983$	32.8450	+	18.9631i	1.04759	+	0.604828i	0.125619	+	0.992079i	$0.459908\pi$
$984$	−3.56040	−	0.276968i	−0.113501	−	0.00882941i
$985$	4.69118	−	22.7021i	0.149473	−	0.723349i
$986$	−0.273373	−	0.473496i	−0.00870597	−	0.0150792i
$987$	40.2432	+	10.5059i	1.28096	+	0.334405i
$988$	−16.2752	−	9.39649i	−0.517783	−	0.298942i
$989$		−	19.3889i		−	0.616530i
$990$	32.7880	−	26.9595i	1.04207	−	0.856830i
$991$	−10.0234			−0.318404			−0.159202	−	0.987246i	$-0.550892\pi$
$991$	−10.0234			−0.318404			−0.159202	+	0.987246i	$0.550892\pi$
$992$	−2.10971	−	1.21804i	−0.0669834	−	0.0386729i
$993$	−20.5410	−	42.9649i	−0.651848	−	1.36345i
$994$	−7.46132	−	20.7052i	−0.236659	−	0.656730i
$995$	25.2933	+	5.22662i	0.801850	+	0.165695i
$996$	−6.01030	−	4.12277i	−0.190444	−	0.130635i
$997$	−11.8913	+	20.5963i	−0.376601	+	0.652292i	−0.990565	−	0.137042i	$-0.956241\pi$
$997$	−11.8913	+	20.5963i	−0.376601	+	0.652292i	0.613964	+	0.789334i	$0.289574\pi$
$998$	−19.2374			−0.608950
$999$	−12.5534	+	52.9213i	−0.397173	+	1.67436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.e.209.12	yes	32
3.2	odd	2		1890.2.bf.f.629.7		32
5.4	even	2		630.2.bf.f.209.5	yes	32
7.6	odd	2	inner	630.2.bf.e.209.5	✓	32
9.4	even	3		1890.2.bf.e.1259.4		32
9.5	odd	6		630.2.bf.f.419.12	yes	32
15.14	odd	2		1890.2.bf.e.629.13		32
21.20	even	2		1890.2.bf.f.629.10		32
35.34	odd	2		630.2.bf.f.209.12	yes	32
45.4	even	6		1890.2.bf.f.1259.10		32
45.14	odd	6	inner	630.2.bf.e.419.5	yes	32
63.13	odd	6		1890.2.bf.e.1259.13		32
63.41	even	6		630.2.bf.f.419.5	yes	32
105.104	even	2		1890.2.bf.e.629.4		32
315.104	even	6	inner	630.2.bf.e.419.12	yes	32
315.139	odd	6		1890.2.bf.f.1259.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.5	✓	32	7.6	odd	2	inner
630.2.bf.e.209.12	yes	32	1.1	even	1	trivial
630.2.bf.e.419.5	yes	32	45.14	odd	6	inner
630.2.bf.e.419.12	yes	32	315.104	even	6	inner
630.2.bf.f.209.5	yes	32	5.4	even	2
630.2.bf.f.209.12	yes	32	35.34	odd	2
630.2.bf.f.419.5	yes	32	63.41	even	6
630.2.bf.f.419.12	yes	32	9.5	odd	6
1890.2.bf.e.629.4		32	105.104	even	2
1890.2.bf.e.629.13		32	15.14	odd	2
1890.2.bf.e.1259.4		32	9.4	even	3
1890.2.bf.e.1259.13		32	63.13	odd	6
1890.2.bf.f.629.7		32	3.2	odd	2
1890.2.bf.f.629.10		32	21.20	even	2
1890.2.bf.f.1259.7		32	315.139	odd	6
1890.2.bf.f.1259.10		32	45.4	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.979752 - 1.42832i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.452503 - 2.18980i) q^{5} +(0.747081 + 1.56265i) q^{6} +(2.02132 + 1.70712i) q^{7} +1.00000 q^{8} +(-1.08017 - 2.79879i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.979752 - 1.42832i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.452503 - 2.18980i) q^{5} +(0.747081 + 1.56265i) q^{6} +(2.02132 + 1.70712i) q^{7} +1.00000 q^{8} +(-1.08017 - 2.79879i) q^{9} +(1.67017 + 1.48678i) q^{10} +(5.48007 + 3.16392i) q^{11} +(-1.72683 - 0.134333i) q^{12} +(-2.28203 - 3.95259i) q^{13} +(-2.48907 + 0.896960i) q^{14} +(-2.68439 - 2.79178i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.72847i q^{17} +(2.96391 + 0.463940i) q^{18} +4.11761i q^{19} +(-2.12268 + 0.703023i) q^{20} +(4.41870 - 1.21454i) q^{21} +(-5.48007 + 3.16392i) q^{22} +(1.15619 + 2.00258i) q^{23} +(0.979752 - 1.42832i) q^{24} +(-4.59048 - 1.98179i) q^{25} +4.56405 q^{26} +(-5.05586 - 1.19930i) q^{27} +(0.467745 - 2.60408i) q^{28} +(-0.173539 - 0.100193i) q^{29} +(3.75995 - 0.928859i) q^{30} +(2.10971 - 1.21804i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(9.88818 - 4.72741i) q^{33} +(2.36292 + 1.36423i) q^{34} +(4.65291 - 3.65383i) q^{35} +(-1.88374 + 2.33485i) q^{36} -10.4673i q^{37} +(-3.56595 - 2.05880i) q^{38} +(-7.88136 - 0.613102i) q^{39} +(0.452503 - 2.18980i) q^{40} +(-1.03090 - 1.78558i) q^{41} +(-1.15753 + 4.43397i) q^{42} +(-7.26144 - 4.19239i) q^{43} -6.32783i q^{44} +(-6.61758 + 1.09890i) q^{45} -2.31238 q^{46} +(7.86014 + 4.53806i) q^{47} +(0.747081 + 1.56265i) q^{48} +(1.17150 + 6.90127i) q^{49} +(4.01152 - 2.98458i) q^{50} +(-3.89711 - 2.67322i) q^{51} +(-2.28203 + 3.95259i) q^{52} +6.77638 q^{53} +(3.56655 - 3.77885i) q^{54} +(9.40810 - 10.5686i) q^{55} +(2.02132 + 1.70712i) q^{56} +(5.88124 + 4.03424i) q^{57} +(0.173539 - 0.100193i) q^{58} +(-0.616709 - 1.06817i) q^{59} +(-1.07556 + 3.72064i) q^{60} +(1.66558 + 0.961623i) q^{61} +2.43609i q^{62} +(2.59449 - 7.50124i) q^{63} +1.00000 q^{64} +(-9.68801 + 3.20863i) q^{65} +(-0.850035 + 10.9271i) q^{66} +(-7.07376 + 4.08404i) q^{67} +(-2.36292 + 1.36423i) q^{68} +(3.99310 + 0.310629i) q^{69} +(0.837855 + 5.85645i) q^{70} +8.31846i q^{71} +(-1.08017 - 2.79879i) q^{72} -13.9450 q^{73} +(9.06497 + 5.23366i) q^{74} +(-7.32815 + 4.61500i) q^{75} +(3.56595 - 2.05880i) q^{76} +(5.67581 + 15.7504i) q^{77} +(4.47164 - 6.51891i) q^{78} +(1.01691 - 1.76135i) q^{79} +(1.67017 + 1.48678i) q^{80} +(-6.66646 + 6.04634i) q^{81} +2.06181 q^{82} +(3.64421 + 2.10398i) q^{83} +(-3.26117 - 3.21944i) q^{84} +(-5.97481 - 1.23464i) q^{85} +(7.26144 - 4.19239i) q^{86} +(-0.313132 + 0.149704i) q^{87} +(5.48007 + 3.16392i) q^{88} +9.48716 q^{89} +(2.35712 - 6.28045i) q^{90} +(2.13481 - 11.8851i) q^{91} +(1.15619 - 2.00258i) q^{92} +(0.327246 - 4.20671i) q^{93} +(-7.86014 + 4.53806i) q^{94} +(9.01675 + 1.86323i) q^{95} +(-1.72683 - 0.134333i) q^{96} +(2.42587 - 4.20173i) q^{97} +(-6.56243 - 2.43609i) q^{98} +(2.93574 - 18.7551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39} + 2 q^{42} - 54 q^{43} + 48 q^{46} + 32 q^{49} + 50 q^{50} - 26 q^{51} - 24 q^{53} + 110 q^{57} + 36 q^{58} + 26 q^{60} + 20 q^{63} + 32 q^{64} - 90 q^{65} - 66 q^{67} + 36 q^{70} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} + 4 q^{85} + 54 q^{86} - 24 q^{88} + 16 q^{91} - 24 q^{92} + 28 q^{93} + 12 q^{95} - 64 q^{98} + 58 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Introduction

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