LMFDB - Embedded newform 483.2.v.a.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(41,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("483.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.v (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$600$
Relative dimension:	$60$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	483.41
Dual form			483.2.v.a.377.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.601323 + 2.04792i) q^{2} +(-0.160145 + 1.72463i) q^{3} +(-2.14987 - 1.38164i) q^{4} +(-0.358395 + 2.49269i) q^{5} +(-3.43560 - 1.36502i) q^{6} +(-2.54603 + 0.719520i) q^{7} +(0.896135 - 0.776505i) q^{8} +(-2.94871 - 0.552383i) q^{9} +(-4.88932 - 2.23288i) q^{10} +(0.357014 + 1.21588i) q^{11} +(2.72710 - 3.48647i) q^{12} +(6.26424 + 2.86078i) q^{13} +(0.0574705 - 5.64673i) q^{14} +(-4.24158 - 1.01729i) q^{15} +(-1.07188 - 2.34708i) q^{16} +(4.94927 - 3.18070i) q^{17} +(2.90436 - 5.70655i) q^{18} +(-2.59233 + 4.03374i) q^{19} +(4.21450 - 4.86379i) q^{20} +(-0.833172 - 4.50620i) q^{21} -2.70470 q^{22} +(-3.20197 - 3.57035i) q^{23} +(1.19567 + 1.66986i) q^{24} +(-1.28761 - 0.378075i) q^{25} +(-9.62548 + 11.1084i) q^{26} +(1.42488 - 4.99697i) q^{27} +(6.46775 + 1.97082i) q^{28} +(2.68457 + 4.17728i) q^{29} +(4.63389 - 8.07468i) q^{30} +(-1.68716 + 1.46193i) q^{31} +(7.79855 - 1.12126i) q^{32} +(-2.15411 + 0.421000i) q^{33} +(3.53771 + 12.0483i) q^{34} +(-0.881057 - 6.60435i) q^{35} +(5.57614 + 5.26159i) q^{36} +(-0.484998 - 3.37323i) q^{37} +(-6.70194 - 7.73445i) q^{38} +(-5.93699 + 10.3454i) q^{39} +(1.61442 + 2.51208i) q^{40} +(-0.362478 + 2.52109i) q^{41} +(9.72932 + 1.00341i) q^{42} +(0.810224 - 0.935049i) q^{43} +(0.912367 - 3.10724i) q^{44} +(2.43372 - 7.15225i) q^{45} +(9.23719 - 4.41044i) q^{46} -4.02234 q^{47} +(4.21951 - 1.47272i) q^{48} +(5.96458 - 3.66385i) q^{49} +(1.54853 - 2.40956i) q^{50} +(4.69294 + 9.04505i) q^{51} +(-9.51473 - 14.8052i) q^{52} +(-5.33728 + 2.43745i) q^{53} +(9.37657 + 5.92282i) q^{54} +(-3.15876 + 0.454161i) q^{55} +(-1.72288 + 2.62180i) q^{56} +(-6.54157 - 5.11679i) q^{57} +(-10.1690 + 2.98589i) q^{58} +(-1.15440 + 2.52779i) q^{59} +(7.71331 + 8.04736i) q^{60} +(2.90140 - 2.51408i) q^{61} +(-1.97939 - 4.33425i) q^{62} +(7.90496 - 0.715268i) q^{63} +(-1.65878 + 11.5370i) q^{64} +(-9.37613 + 14.5895i) q^{65} +(0.433144 - 4.66460i) q^{66} +(10.4727 + 3.07507i) q^{67} -15.0349 q^{68} +(6.67031 - 4.95045i) q^{69} +(14.0550 + 2.16702i) q^{70} +(4.05783 - 13.8197i) q^{71} +(-3.07137 + 1.79468i) q^{72} +(-8.37846 + 13.0371i) q^{73} +(7.19974 + 1.03517i) q^{74} +(0.858244 - 2.16010i) q^{75} +(11.1463 - 5.09035i) q^{76} +(-1.78382 - 2.83879i) q^{77} +(-17.6164 - 18.3794i) q^{78} +(-1.68209 + 3.68326i) q^{79} +(6.23472 - 1.83068i) q^{80} +(8.38975 + 3.25763i) q^{81} +(-4.94501 - 2.25831i) q^{82} +(-0.734004 - 5.10511i) q^{83} +(-4.43472 + 10.8389i) q^{84} +(6.15472 + 13.4770i) q^{85} +(1.42770 + 2.22154i) q^{86} +(-7.63419 + 3.96093i) q^{87} +(1.26407 + 0.812367i) q^{88} +(-8.18741 + 9.44878i) q^{89} +(13.1838 + 9.28487i) q^{90} +(-18.0074 - 2.77640i) q^{91} +(1.95089 + 12.0997i) q^{92} +(-2.25110 - 3.14385i) q^{93} +(2.41873 - 8.23742i) q^{94} +(-9.12580 - 7.90755i) q^{95} +(0.684863 + 13.6292i) q^{96} +(-10.8781 - 1.56404i) q^{97} +(3.91661 + 14.4181i) q^{98} +(-0.381099 - 3.78247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) $ 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$	−0.601323	+	2.04792i	−0.425199	+	1.44810i	0.416989	+	0.908912i	$0.363086\pi$
$2$	−0.601323	+	2.04792i	−0.425199	+	1.44810i	−0.842188	+	0.539184i	$0.818733\pi$
$3$	−0.160145	+	1.72463i	−0.0924599	+	0.995716i
$3$	−0.160145	+	1.72463i	−0.0924599	+	0.995716i
$4$	−2.14987	−	1.38164i	−1.07493	−	0.690818i
$5$	−0.358395	+	2.49269i	−0.160279	+	1.11477i	0.737828	+	0.674989i	$0.235852\pi$
$5$	−0.358395	+	2.49269i	−0.160279	+	1.11477i	−0.898107	+	0.439777i	$0.855057\pi$
$6$	−3.43560	−	1.36502i	−1.40258	−	0.557269i
$7$	−2.54603	+	0.719520i	−0.962311	+	0.271953i
$7$	−2.54603	+	0.719520i	−0.962311	+	0.271953i
$8$	0.896135	−	0.776505i	0.316832	−	0.274536i
$9$	−2.94871	−	0.552383i	−0.982902	−	0.184128i
$10$	−4.88932	−	2.23288i	−1.54614	−	0.706097i
$11$	0.357014	+	1.21588i	0.107644	+	0.366601i	0.995643	−	0.0932434i	$-0.0297235\pi$
$11$	0.357014	+	1.21588i	0.107644	+	0.366601i	−0.888000	+	0.459844i	$0.847905\pi$
$12$	2.72710	−	3.48647i	0.787247	−	1.00646i
$13$	6.26424	+	2.86078i	1.73739	+	0.793439i	0.991915	+	0.126903i	$0.0405036\pi$
$13$	6.26424	+	2.86078i	1.73739	+	0.793439i	0.745473	+	0.666536i	$0.232224\pi$
$14$	0.0574705	−	5.64673i	0.0153596	−	1.50915i
$15$	−4.24158	−	1.01729i	−1.09517	−	0.262664i
$16$	−1.07188	−	2.34708i	−0.267969	−	0.586771i
$17$	4.94927	−	3.18070i	1.20037	−	0.771434i	0.221354	−	0.975194i	$-0.428952\pi$
$17$	4.94927	−	3.18070i	1.20037	−	0.771434i	0.979021	+	0.203759i	$0.0653160\pi$
$18$	2.90436	−	5.70655i	0.684564	−	1.34505i
$19$	−2.59233	+	4.03374i	−0.594721	+	0.925403i	0.405217	+	0.914221i	$0.367196\pi$
$19$	−2.59233	+	4.03374i	−0.594721	+	0.925403i	−0.999937	+	0.0111828i	$0.996440\pi$
$20$	4.21450	−	4.86379i	0.942390	−	1.08758i
$21$	−0.833172	−	4.50620i	−0.181813	−	0.983333i
$22$	−2.70470			−0.576643
$23$	−3.20197	−	3.57035i	−0.667657	−	0.744469i
$23$	−3.20197	−	3.57035i	−0.667657	−	0.744469i
$24$	1.19567	+	1.66986i	0.244066	+	0.340858i
$25$	−1.28761	−	0.378075i	−0.257521	−	0.0756150i
$26$	−9.62548	+	11.1084i	−1.88771	+	2.17854i
$27$	1.42488	−	4.99697i	0.274218	−	0.961668i
$28$	6.46775	+	1.97082i	1.22229	+	0.372450i
$29$	2.68457	+	4.17728i	0.498513	+	0.775701i	0.995768	−	0.0919032i	$-0.0292950\pi$
$29$	2.68457	+	4.17728i	0.498513	+	0.775701i	−0.497255	+	0.867604i	$0.665659\pi$
$30$	4.63389	−	8.07468i	0.846029	−	1.47423i
$31$	−1.68716	+	1.46193i	−0.303022	+	0.262570i	−0.793077	−	0.609121i	$-0.791522\pi$
$31$	−1.68716	+	1.46193i	−0.303022	+	0.262570i	0.490055	+	0.871692i	$0.336977\pi$
$32$	7.79855	−	1.12126i	1.37860	−	0.198213i
$33$	−2.15411	+	0.421000i	−0.374983	+	0.0732867i
$34$	3.53771	+	12.0483i	0.606712	+	2.06627i
$35$	−0.881057	−	6.60435i	−0.148926	−	1.11634i
$36$	5.57614	+	5.26159i	0.929356	+	0.876932i
$37$	−0.484998	−	3.37323i	−0.0797331	−	0.554556i	−0.990058	−	0.140661i	$-0.955077\pi$
$37$	−0.484998	−	3.37323i	−0.0797331	−	0.554556i	0.910325	−	0.413895i	$-0.135832\pi$
$38$	−6.70194	−	7.73445i	−1.08720	−	1.25469i
$39$	−5.93699	+	10.3454i	−0.950679	+	1.65658i
$40$	1.61442	+	2.51208i	0.255262	+	0.397195i
$41$	−0.362478	+	2.52109i	−0.0566095	+	0.393728i	0.941742	+	0.336336i	$0.109188\pi$
$41$	−0.362478	+	2.52109i	−0.0566095	+	0.393728i	−0.998352	+	0.0573923i	$0.981721\pi$
$42$	9.72932	+	1.00341i	1.50127	+	0.154830i
$43$	0.810224	−	0.935049i	0.123558	−	0.142594i	−0.690600	−	0.723237i	$-0.742653\pi$
$43$	0.810224	−	0.935049i	0.123558	−	0.142594i	0.814158	+	0.580643i	$0.197199\pi$
$44$	0.912367	−	3.10724i	0.137545	−	0.468434i
$45$	2.43372	−	7.15225i	0.362798	−	1.06619i
$46$	9.23719	−	4.41044i	1.36195	−	0.650284i
$47$	−4.02234			−0.586719			−0.293359	−	0.956002i	$-0.594773\pi$
$47$	−4.02234			−0.586719			−0.293359	+	0.956002i	$0.594773\pi$
$48$	4.21951	−	1.47272i	0.609034	−	0.212569i
$49$	5.96458	−	3.66385i	0.852083	−	0.523407i
$50$	1.54853	−	2.40956i	0.218996	−	0.340764i
$51$	4.69294	+	9.04505i	0.657143	+	1.26656i
$52$	−9.51473	−	14.8052i	−1.31946	−	2.05311i
$53$	−5.33728	+	2.43745i	−0.733132	+	0.334810i	−0.746757	−	0.665097i	$-0.768390\pi$
$53$	−5.33728	+	2.43745i	−0.733132	+	0.334810i	0.0136253	+	0.999907i	$0.495663\pi$
$54$	9.37657	+	5.92282i	1.27599	+	0.805994i
$55$	−3.15876	+	0.454161i	−0.425927	+	0.0612391i
$56$	−1.72288	+	2.62180i	−0.230229	+	0.350352i
$57$	−6.54157	−	5.11679i	−0.866452	−	0.677736i
$58$	−10.1690	+	2.98589i	−1.33526	+	0.392067i
$59$	−1.15440	+	2.52779i	−0.150290	+	0.329090i	−0.969771	−	0.244017i	$-0.921535\pi$
$59$	−1.15440	+	2.52779i	−0.150290	+	0.329090i	0.819481	+	0.573107i	$0.194262\pi$
$60$	7.71331	+	8.04736i	0.995784	+	1.03891i
$61$	2.90140	−	2.51408i	0.371486	−	0.321894i	−0.449031	−	0.893516i	$-0.648231\pi$
$61$	2.90140	−	2.51408i	0.371486	−	0.321894i	0.820517	+	0.571622i	$0.193685\pi$
$62$	−1.97939	−	4.33425i	−0.251382	−	0.550450i
$63$	7.90496	−	0.715268i	0.995931	−	0.0901153i
$64$	−1.65878	+	11.5370i	−0.207347	+	1.44213i
$65$	−9.37613	+	14.5895i	−1.16297	+	1.80961i
$66$	0.433144	−	4.66460i	0.0533164	−	0.574173i
$67$	10.4727	+	3.07507i	1.27945	+	0.375679i	0.849698	−	0.527270i	$-0.176784\pi$
$67$	10.4727	+	3.07507i	1.27945	+	0.375679i	0.429748	+	0.902949i	$0.358603\pi$
$68$	−15.0349			−1.82324
$69$	6.67031	−	4.95045i	0.803011	−	0.595964i
$70$	14.0550	+	2.16702i	1.67989	+	0.259008i
$71$	4.05783	−	13.8197i	0.481575	−	1.64010i	−0.257357	−	0.966316i	$-0.582852\pi$
$71$	4.05783	−	13.8197i	0.481575	−	1.64010i	0.738933	−	0.673779i	$-0.235330\pi$
$72$	−3.07137	+	1.79468i	−0.361964	+	0.211505i
$73$	−8.37846	+	13.0371i	−0.980624	+	1.52588i	−0.135870	+	0.990727i	$0.543383\pi$
$73$	−8.37846	+	13.0371i	−0.980624	+	1.52588i	−0.844754	+	0.535154i	$0.820254\pi$
$74$	7.19974	+	1.03517i	0.836953	+	0.120336i
$75$	0.858244	−	2.16010i	0.0991015	−	0.249427i
$76$	11.1463	−	5.09035i	1.27857	−	0.583904i
$77$	−1.78382	−	2.83879i	−0.203285	−	0.323510i
$78$	−17.6164	−	18.3794i	−1.99467	−	2.08105i
$79$	−1.68209	+	3.68326i	−0.189250	+	0.414399i	−0.980344	−	0.197295i	$-0.936784\pi$
$79$	−1.68209	+	3.68326i	−0.189250	+	0.414399i	0.791095	+	0.611694i	$0.209512\pi$
$80$	6.23472	−	1.83068i	0.697062	−	0.204676i
$81$	8.38975	+	3.25763i	0.932194	+	0.361959i
$82$	−4.94501	−	2.25831i	−0.546086	−	0.249389i
$83$	−0.734004	−	5.10511i	−0.0805675	−	0.560359i	−0.989623	−	0.143685i	$-0.954105\pi$
$83$	−0.734004	−	5.10511i	−0.0805675	−	0.560359i	0.909056	−	0.416674i	$-0.136804\pi$
$84$	−4.43472	+	10.8389i	−0.483867	+	1.18262i
$85$	6.15472	+	13.4770i	0.667574	+	1.46178i
$86$	1.42770	+	2.22154i	0.153952	+	0.239555i
$87$	−7.63419	+	3.96093i	−0.818471	+	0.424656i
$88$	1.26407	+	0.812367i	0.134750	+	0.0865986i
$89$	−8.18741	+	9.44878i	−0.867864	+	1.00157i	0.132083	+	0.991239i	$0.457834\pi$
$89$	−8.18741	+	9.44878i	−0.867864	+	1.00157i	−0.999947	+	0.0103299i	$0.996712\pi$
$90$	13.1838	+	9.28487i	1.38969	+	0.978712i
$91$	−18.0074	−	2.77640i	−1.88768	−	0.291046i
$92$	1.95089	+	12.0997i	0.203395	+	1.26148i
$93$	−2.25110	−	3.14385i	−0.233428	−	0.326002i
$94$	2.41873	−	8.23742i	0.249472	−	0.849625i
$95$	−9.12580	−	7.90755i	−0.936287	−	0.811297i
$96$	0.684863	+	13.6292i	0.0698986	+	1.39102i
$97$	−10.8781	−	1.56404i	−1.10451	−	0.158804i	−0.434147	−	0.900842i	$-0.642950\pi$
$97$	−10.8781	−	1.56404i	−1.10451	−	0.158804i	−0.670358	+	0.742038i	$0.733859\pi$
$98$	3.91661	+	14.4181i	0.395638	+	1.45645i
$99$	−0.381099	−	3.78247i	−0.0383019	−	0.380153i
$100$	2.24582	+	2.59181i	0.224582	+	0.259181i
$101$	−0.861847	−	5.99428i	−0.0857570	−	0.596453i	−0.986704	−	0.162525i	$-0.948036\pi$
$101$	−0.861847	−	5.99428i	−0.0857570	−	0.596453i	0.900947	−	0.433928i	$-0.142873\pi$
$102$	−21.3455	+	4.17176i	−2.11352	+	0.413066i
$103$	0.247305	+	0.842244i	0.0243677	+	0.0829888i	0.970779	−	0.239975i	$-0.0771391\pi$
$103$	0.247305	+	0.842244i	0.0243677	+	0.0829888i	−0.946411	+	0.322963i	$0.895321\pi$
$104$	7.83502	−	2.30057i	0.768287	−	0.225589i
$105$	11.5312	−	0.461842i	1.12533	−	0.0450712i
$106$	−1.78228	−	12.3960i	−0.173110	−	1.20401i
$107$	−4.62518	+	4.00774i	−0.447133	+	0.387443i	−0.849118	−	0.528203i	$-0.822866\pi$
$107$	−4.62518	+	4.00774i	−0.447133	+	0.387443i	0.401985	+	0.915646i	$0.368320\pi$
$108$	−9.96729	+	8.77416i	−0.959103	+	0.844294i
$109$	−6.71675	+	4.31659i	−0.643348	+	0.413454i	−0.821230	−	0.570597i	$-0.806712\pi$
$109$	−6.71675	+	4.31659i	−0.643348	+	0.413454i	0.177882	+	0.984052i	$0.443075\pi$
$110$	0.969350	−	6.74198i	0.0924239	−	0.642822i
$111$	5.89525	−	0.296235i	0.559553	−	0.0281174i
$112$	4.41781	+	5.20452i	0.417444	+	0.491781i
$113$	1.16224	−	3.95824i	0.109335	−	0.372359i	−0.886589	−	0.462558i	$-0.846932\pi$
$113$	1.16224	−	3.95824i	0.109335	−	0.372359i	0.995924	+	0.0901981i	$0.0287500\pi$
$114$	14.4124	−	10.3197i	1.34984	−	0.966532i
$115$	10.0473	−	6.70194i	0.936920	−	0.624959i
$116$		−	12.6897i		−	1.17821i
$117$	−16.8912	−	11.8959i	−1.56159	−	1.09977i
$118$	−4.48253	−	3.88413i	−0.412650	−	0.357564i
$119$	−10.3124	+	11.6593i	−0.945340	+	1.06880i
$120$	−4.59096	+	2.38198i	−0.419096	+	0.217444i
$121$	7.90289	−	5.07888i	0.718445	−	0.461716i
$122$	3.40394	+	7.45359i	0.308178	+	0.674817i
$123$	−4.28990	−	1.02888i	−0.386807	−	0.0927711i
$124$	5.64702	−	0.811919i	0.507117	−	0.0729125i
$125$	−3.82685	+	8.37964i	−0.342284	+	0.749498i
$126$	−3.28862	+	16.6188i	−0.292974	+	1.48052i
$127$	−18.8926	+	5.54738i	−1.67645	+	0.492250i	−0.975323	−	0.220785i	$-0.929138\pi$
$127$	−18.8926	+	5.54738i	−1.67645	+	0.492250i	−0.701128	+	0.713035i	$0.747320\pi$
$128$	−8.29592	−	3.78862i	−0.733262	−	0.334870i
$129$	1.48286	+	1.54708i	0.130559	+	0.136213i
$130$	−24.2401	−	27.9746i	−2.12600	−	2.45353i
$131$	7.08538	+	15.5148i	0.619052	+	1.35554i	0.916207	+	0.400706i	$0.131235\pi$
$131$	7.08538	+	15.5148i	0.619052	+	1.35554i	−0.297154	+	0.954829i	$0.596038\pi$
$132$	5.21273	+	2.07111i	0.453710	+	0.180267i
$133$	3.69780	−	12.1353i	0.320640	−	1.05226i
$134$	−12.5950	+	19.5981i	−1.08804	+	1.69302i
$135$	11.9452	+	5.34267i	1.02808	+	0.459824i
$136$	1.96538	−	6.69348i	0.168530	−	0.573961i
$137$		−	8.44773i		−	0.721738i	−0.932617	−	0.360869i	$-0.882480\pi$
$137$		−	8.44773i		−	0.721738i	0.932617	−	0.360869i	$-0.117520\pi$
$138$	6.12709	+	16.6371i	0.521573	+	1.41624i
$139$		−	13.3917i		−	1.13587i	−0.823072	−	0.567937i	$-0.807742\pi$
$139$		−	13.3917i		−	1.13587i	0.823072	−	0.567937i	$-0.192258\pi$
$140$	−7.23066	+	15.4158i	−0.611102	+	1.30287i
$141$	0.644159	−	6.93706i	0.0542480	−	0.584206i
$142$	25.8615	+	16.6202i	2.17025	+	1.39473i
$143$	−1.24194	+	8.63789i	−0.103856	+	0.722336i
$144$	1.86416	+	7.51295i	0.155347	+	0.626079i
$145$	−11.3748	+	5.19470i	−0.944627	+	0.431397i
$146$	−21.6608	−	24.9979i	−1.79266	−	2.06884i
$147$	5.36359	+	10.8735i	0.442381	+	0.896827i
$148$	−3.61790	+	7.92209i	−0.297389	+	0.651192i
$149$	0.801905	+	2.73104i	0.0656946	+	0.223735i	0.985797	−	0.167943i	$-0.0537126\pi$
$149$	0.801905	+	2.73104i	0.0656946	+	0.223735i	−0.920102	+	0.391679i	$0.871894\pi$
$150$	3.90762	+	3.05653i	0.319056	+	0.249565i
$151$	−6.69083	+	14.6509i	−0.544492	+	1.19227i	0.414815	+	0.909906i	$0.363846\pi$
$151$	−6.69083	+	14.6509i	−0.544492	+	1.19227i	−0.959307	+	0.282366i	$0.908881\pi$
$152$	0.809146	+	5.62773i	0.0656304	+	0.456469i
$153$	−16.3509	+	6.64507i	−1.32189	+	0.537222i
$154$	6.88625	−	1.94608i	0.554910	−	0.156820i
$155$	−3.03947	−	4.72951i	−0.244136	−	0.379884i
$156$	27.0573	−	14.0384i	2.16631	−	1.12397i
$157$	7.81767	−	12.1645i	0.623918	−	0.970835i	−0.375120	−	0.926976i	$-0.622398\pi$
$157$	7.81767	−	12.1645i	0.623918	−	0.970835i	0.999038	−	0.0438589i	$-0.0139652\pi$
$158$	−6.53153	−	5.65960i	−0.519620	−	0.450254i
$159$	−3.34897	−	9.59518i	−0.265590	−	0.760948i
$160$			19.8412i			1.56859i
$161$	10.7213	+	6.78634i	0.844954	+	0.534839i
$162$	−11.7163	+	15.2226i	−0.920520	+	1.19600i
$163$	7.65207	+	2.24685i	0.599357	+	0.175987i	0.567317	−	0.823500i	$-0.307982\pi$
$163$	7.65207	+	2.24685i	0.599357	+	0.175987i	0.0320397	+	0.999487i	$0.489800\pi$
$164$	4.26251	−	4.91919i	0.332846	−	0.384125i
$165$	−0.277400	−	5.52043i	−0.0215956	−	0.429765i
$166$	10.8962	+	1.56664i	0.845711	+	0.121595i
$167$	13.0536	−	8.38903i	1.01012	−	0.649163i	0.0726937	−	0.997354i	$-0.476840\pi$
$167$	13.0536	−	8.38903i	1.01012	−	0.649163i	0.937423	+	0.348191i	$0.113204\pi$
$168$	−4.24572	−	3.39120i	−0.327565	−	0.261637i
$169$	22.5435	+	26.0165i	1.73411	+	2.00127i
$170$	−31.3007	+	4.50036i	−2.40065	+	0.345162i
$171$	9.87218	−	10.4624i	0.754945	−	0.800077i
$172$	−3.03377	+	0.890796i	−0.231323	+	0.0679225i
$173$	14.6649	−	4.30600i	1.11495	−	0.327379i	0.328175	−	0.944617i	$-0.393566\pi$
$173$	14.6649	−	4.30600i	1.11495	−	0.327379i	0.786777	+	0.617237i	$0.211748\pi$
$174$	−3.52104	−	18.0160i	−0.266930	−	1.36579i
$175$	3.55032	+	0.0361339i	0.268379	+	0.00273147i
$176$	2.47109	−	2.14121i	0.186265	−	0.161400i
$177$	−4.17463	−	2.39573i	−0.313784	−	0.180074i
$178$	−14.4270	−	22.4489i	−1.08135	−	1.68262i
$179$	9.05931	+	1.30253i	0.677125	+	0.0973558i	0.472293	−	0.881441i	$-0.343426\pi$
$179$	9.05931	+	1.30253i	0.677125	+	0.0973558i	0.204831	+	0.978797i	$0.434335\pi$
$180$	−15.1140	+	12.0139i	−1.12653	+	0.895461i
$181$	−7.58342	−	6.57107i	−0.563671	−	0.488424i	0.325785	−	0.945444i	$-0.394371\pi$
$181$	−7.58342	−	6.57107i	−0.563671	−	0.488424i	−0.889456	+	0.457020i	$0.848917\pi$
$182$	16.5141	−	35.2081i	1.22411	−	2.60980i
$183$	3.87121	+	5.40646i	0.286168	+	0.399657i
$184$	−5.64179	−	0.713165i	−0.415918	−	0.0525752i
$185$	8.58225			0.630980
$186$	7.79197	−	2.71960i	0.571335	−	0.199411i
$187$	5.63430	+	4.88215i	0.412021	+	0.357018i
$188$	8.64750	+	5.55741i	0.630684	+	0.405316i
$189$	−0.0323679	+	13.7477i	−0.00235442	+	0.999997i
$190$	21.6816	−	13.9339i	1.57294	−	1.01087i
$191$	9.06504	−	4.13986i	0.655923	−	0.299550i	−0.0595138	−	0.998227i	$-0.518955\pi$
$191$	9.06504	−	4.13986i	0.655923	−	0.299550i	0.715437	+	0.698678i	$0.246228\pi$
$192$	−19.6315	−	4.70838i	−1.41678	−	0.339798i
$193$	−1.59302	−	11.0797i	−0.114668	−	0.797532i	−0.963277	−	0.268511i	$-0.913468\pi$
$193$	−1.59302	−	11.0797i	−0.114668	−	0.797532i	0.848609	−	0.529021i	$-0.177441\pi$
$194$	9.74427	−	21.3370i	0.699598	−	1.53191i
$195$	−23.6600	−	18.5068i	−1.69433	−	1.32530i
$196$	−17.8852	−	0.364096i	−1.27751	−	0.0260068i
$197$	16.0732	+	7.34038i	1.14517	+	0.522981i	0.895372	−	0.445318i	$-0.146909\pi$
$197$	16.0732	+	7.34038i	1.14517	+	0.522981i	0.249795	+	0.968299i	$0.419637\pi$
$198$	7.97535	+	1.49403i	0.566784	+	0.106176i
$199$	−8.62106	+	7.47019i	−0.611131	+	0.529548i	−0.904512	−	0.426448i	$-0.859765\pi$
$199$	−8.62106	+	7.47019i	−0.611131	+	0.529548i	0.293382	+	0.955995i	$0.405219\pi$
$200$	−1.44745	+	0.661026i	−0.102350	+	0.0467416i
$201$	−6.98051	+	17.5691i	−0.492367	+	1.23923i
$202$	12.7940	+	1.83950i	0.900185	+	0.129427i
$203$	−9.84065	−	8.70389i	−0.690679	−	0.610893i
$204$	2.40776	−	25.9296i	0.168577	−	1.81543i
$205$	−6.15439	−	1.80709i	−0.429841	−	0.126213i
$206$	−1.87356			−0.130537
$207$	7.46948	+	12.2966i	0.519164	+	0.854674i
$208$		−	17.7691i		−	1.23207i
$209$	−5.83003	−	1.71185i	−0.403271	−	0.118411i
$210$	−5.98814	+	23.8926i	−0.413221	+	1.64875i
$211$	6.83431	+	4.39214i	0.470493	+	0.302368i	0.754319	−	0.656508i	$-0.227967\pi$
$211$	6.83431	+	4.39214i	0.470493	+	0.302368i	−0.283826	+	0.958876i	$0.591604\pi$
$212$	14.8421	+	2.13397i	1.01936	+	0.146562i
$213$	23.1840	+	9.21141i	1.58854	+	0.631156i
$214$	−5.42629	−	11.8819i	−0.370934	−	0.812232i
$215$	2.04041	+	2.35476i	0.139155	+	0.160593i
$216$	−2.60329	−	5.58439i	−0.177132	−	0.379969i
$217$	3.24367	−	4.93607i	0.220195	−	0.335082i
$218$	−4.80109	−	16.3510i	−0.325171	−	1.10743i
$219$	−21.1425	−	16.5376i	−1.42868	−	1.11751i
$220$	7.41840	+	3.38787i	0.500148	+	0.228410i
$221$	40.1027	−	5.76590i	2.69760	−	0.387857i
$222$	−2.93828	+	12.2511i	−0.197205	+	0.822241i
$223$	−6.22503	+	2.84288i	−0.416859	+	0.190373i	−0.612792	−	0.790244i	$-0.709954\pi$
$223$	−6.22503	+	2.84288i	−0.416859	+	0.190373i	0.195933	+	0.980617i	$0.437226\pi$
$224$	−19.0486	+	8.46599i	−1.27274	+	0.565658i
$225$	3.58793	+	1.82608i	0.239195	+	0.121739i
$226$	7.40725	+	4.76035i	0.492723	+	0.316654i
$227$	−0.286968	+	0.331179i	−0.0190468	+	0.0219811i	−0.765193	−	0.643801i	$-0.777356\pi$
$227$	−0.286968	+	0.331179i	−0.0190468	+	0.0219811i	0.746146	+	0.665782i	$0.231902\pi$
$228$	6.99395	+	20.0385i	0.463186	+	1.32708i
$229$			28.2606i			1.86751i	0.357907	+	0.933757i	$0.383490\pi$
$229$			28.2606i			1.86751i	−0.357907	+	0.933757i	$0.616510\pi$
$230$	7.68331	+	24.6062i	0.506622	+	1.62248i
$231$	5.18153	−	2.62181i	0.340920	−	0.172502i
$232$	5.64942	+	1.65882i	0.370903	+	0.108907i
$233$	7.21014	+	6.24762i	0.472352	+	0.409295i	0.858239	−	0.513251i	$-0.171559\pi$
$233$	7.21014	+	6.24762i	0.472352	+	0.409295i	−0.385887	+	0.922546i	$0.626104\pi$
$234$	34.5188	−	27.4384i	2.25656	−	1.79371i
$235$	1.44159	−	10.0265i	0.0940388	−	0.654054i
$236$	5.97429	−	3.83944i	0.388893	−	0.249927i
$237$	−6.08288	−	3.49084i	−0.395126	−	0.226754i
$238$	−17.6761	−	28.1300i	−1.14577	−	1.82340i
$239$	7.30407	−	1.05017i	0.472461	−	0.0679297i	0.0980282	−	0.995184i	$-0.468746\pi$
$239$	7.30407	−	1.05017i	0.472461	−	0.0679297i	0.374433	+	0.927254i	$0.377837\pi$
$240$	2.15878	+	11.0458i	0.139349	+	0.713001i
$241$	1.21393	+	4.13428i	0.0781964	+	0.266313i	0.989307	−	0.145850i	$-0.0465917\pi$
$241$	1.21393	+	4.13428i	0.0781964	+	0.266313i	−0.911110	+	0.412163i	$0.864774\pi$
$242$	5.64894	+	19.2385i	0.363127	+	1.23670i
$243$	−6.96179	+	13.9475i	−0.446599	+	0.894734i
$244$	−9.71116	+	1.39625i	−0.621693	+	0.0893860i
$245$	6.99517	+	16.1810i	0.446905	+	1.03376i
$246$	4.68668	−	8.16667i	0.298812	−	0.520688i
$247$	−27.7786	+	17.8522i	−1.76751	+	1.13591i
$248$	−0.376724	+	2.62017i	−0.0239220	+	0.166381i
$249$	8.92199	−	0.448327i	0.565408	−	0.0284116i
$250$	−14.8596	−	12.8759i	−0.939806	−	0.814347i
$251$	0.402299	+	0.118126i	0.0253929	+	0.00745603i	0.294404	−	0.955681i	$-0.404879\pi$
$251$	0.402299	+	0.118126i	0.0253929	+	0.00745603i	−0.269011	+	0.963137i	$0.586697\pi$
$252$	−17.9829	−	9.38404i	−1.13281	−	0.591139i
$253$	3.19796	−	5.16787i	0.201054	−	0.324901i
$254$		−	42.0263i		−	2.63697i
$255$	−24.2284	+	8.45636i	−1.51724	+	0.529558i
$256$	−2.51839	+	2.90638i	−0.157399	+	0.181649i
$257$	12.9438	+	8.31850i	0.807415	+	0.518894i	0.878028	−	0.478610i	$-0.158859\pi$
$257$	12.9438	+	8.31850i	0.807415	+	0.518894i	−0.0706130	+	0.997504i	$0.522496\pi$
$258$	−4.05997	+	2.10648i	−0.252763	+	0.131144i
$259$	3.66193	+	8.23940i	0.227541	+	0.511971i
$260$	40.3149	−	18.4112i	2.50022	−	1.14181i
$261$	−5.60856	−	13.8005i	−0.347161	−	0.854229i
$262$	−36.0336	+	5.18086i	−2.22617	+	0.320074i
$263$	−18.2933	−	8.35426i	−1.12801	−	0.515146i	−0.238083	−	0.971245i	$-0.576519\pi$
$263$	−18.2933	−	8.35426i	−1.12801	−	0.515146i	−0.889929	+	0.456099i	$0.849246\pi$
$264$	−1.60347	+	2.04995i	−0.0986866	+	0.126166i
$265$	−4.16297	−	14.1778i	−0.255729	−	0.870933i
$266$	22.6285	+	14.8700i	1.38744	+	0.911738i
$267$	−14.9845	−	15.6334i	−0.917036	−	0.956752i
$268$	−18.2663	−	21.0805i	−1.11579	−	1.28769i
$269$	−3.20847	−	7.02556i	−0.195624	−	0.428356i	0.786246	−	0.617914i	$-0.212022\pi$
$269$	−3.20847	−	7.02556i	−0.195624	−	0.428356i	−0.981870	+	0.189558i	$0.939295\pi$
$270$	−18.1243	+	21.2502i	−1.10301	+	1.29325i
$271$	−0.530838	−	0.0763230i	−0.0322461	−	0.00463629i	0.126173	−	0.992008i	$-0.459731\pi$
$271$	−0.530838	−	0.0763230i	−0.0322461	−	0.00463629i	−0.158419	+	0.987372i	$0.550640\pi$
$272$	−12.7704	−	8.20703i	−0.774319	−	0.497625i
$273$	7.67207	−	30.6114i	0.464335	−	1.85269i
$274$	17.3002	+	5.07981i	1.04515	+	0.306882i
$275$		−	1.70055i		−	0.102547i
$276$	−21.1800	+	1.42686i	−1.27489	+	0.0858868i
$277$	23.1962			1.39373			0.696863	−	0.717205i	$-0.254579\pi$
$277$	23.1962			1.39373			0.696863	+	0.717205i	$0.254579\pi$
$278$	27.4252	+	8.05276i	1.64485	+	0.482972i
$279$	5.78248	−	3.37885i	0.346188	−	0.202286i
$280$	−5.91786	−	5.23425i	−0.353660	−	0.312806i
$281$	19.0311	+	2.73626i	1.13530	+	0.163232i	0.684237	−	0.729260i	$-0.260135\pi$
$281$	19.0311	+	2.73626i	1.13530	+	0.163232i	0.451064	+	0.892491i	$0.351044\pi$
$282$	13.8192	+	5.49059i	0.822920	+	0.326960i
$283$	7.57829	−	3.46089i	0.450482	−	0.205728i	−0.177237	−	0.984168i	$-0.556716\pi$
$283$	7.57829	−	3.46089i	0.450482	−	0.205728i	0.627719	+	0.778440i	$0.283989\pi$
$284$	−27.8176	+	24.1041i	−1.65067	+	1.43031i
$285$	15.0991	−	14.4723i	0.894391	−	0.857264i
$286$	−16.9429	−	7.73755i	−1.00185	−	0.457531i
$287$	−0.891094	−	6.67959i	−0.0525996	−	0.394284i
$288$	−23.6150	−	1.00151i	−1.39153	−	0.0590147i
$289$	7.31636	−	16.0206i	0.430374	−	0.942388i
$290$	−3.79839	−	26.4184i	−0.223049	−	1.55134i
$291$	4.43947	−	18.5103i	0.260246	−	1.08509i
$292$	36.0251	−	16.4521i	2.10821	−	0.962788i
$293$	−2.75419	+	1.77001i	−0.160901	+	0.103405i	−0.618614	−	0.785695i	$-0.712305\pi$
$293$	−2.75419	+	1.77001i	−0.160901	+	0.103405i	0.457712	+	0.889100i	$0.348669\pi$
$294$	−25.4932	+	4.44572i	−1.48679	+	0.259280i
$295$	−5.88727	−	3.78352i	−0.342770	−	0.220285i
$296$	−3.05396	−	2.64627i	−0.177508	−	0.153811i
$297$	6.58440	−	0.0515101i	0.382066	−	0.00298892i
$298$	−6.07514			−0.351924
$299$	−9.84393	−	31.5257i	−0.569289	−	1.82318i
$300$	−4.82958	+	3.45814i	−0.278836	+	0.199656i
$301$	−1.39007	+	2.96364i	−0.0801224	+	0.170821i
$302$	−25.9804	−	22.5122i	−1.49501	−	1.29543i
$303$	10.4759	−	0.526413i	0.601827	−	0.0302417i
$304$	12.2462	+	1.76074i	0.702367	+	0.100985i
$305$	5.22697	+	8.13333i	0.299296	+	0.465713i
$306$	−3.77637	−	37.4812i	−0.215881	−	2.14266i
$307$	10.9651	−	9.50135i	0.625813	−	0.542270i	−0.283187	−	0.959065i	$-0.591392\pi$
$307$	10.9651	−	9.50135i	0.625813	−	0.542270i	0.909001	+	0.416794i	$0.136846\pi$
$308$	−0.0871980	+	8.56760i	−0.00496857	+	0.488184i
$309$	−1.49217	+	0.291629i	−0.0848864	+	0.0165902i
$310$	11.5134	−	3.38063i	0.653915	−	0.192007i
$311$	8.81232	−	2.58753i	0.499701	−	0.146725i	−0.0221628	−	0.999754i	$-0.507055\pi$
$311$	8.81232	−	2.58753i	0.499701	−	0.146725i	0.521863	+	0.853029i	$0.325237\pi$
$312$	2.71289	+	13.8809i	0.153587	+	0.785854i
$313$	−6.78278	+	0.975216i	−0.383385	+	0.0551225i	−0.331313	−	0.943521i	$-0.607492\pi$
$313$	−6.78278	+	0.975216i	−0.383385	+	0.0551225i	−0.0520720	+	0.998643i	$0.516583\pi$
$314$	20.2110	+	23.3247i	1.14057	+	1.31629i
$315$	−1.05016	+	19.9610i	−0.0591695	+	1.12467i
$316$	8.70519	−	5.59448i	0.489705	−	0.314714i
$317$	−17.8072	−	2.56029i	−1.00015	−	0.143800i	−0.377261	−	0.926107i	$-0.623134\pi$
$317$	−17.8072	−	2.56029i	−1.00015	−	0.143800i	−0.622894	+	0.782307i	$0.714043\pi$
$318$	21.6639	−	1.08861i	1.21485	−	0.0610461i
$319$	−4.12063	+	4.75546i	−0.230711	+	0.266255i
$320$	−28.1638	−	8.26964i	−1.57440	−	0.462287i
$321$	−6.17118	−	8.61855i	−0.344441	−	0.481041i
$322$	−20.3448	+	17.8755i	−1.13377	+	0.996162i
$323$			28.2095i			1.56962i
$324$	−13.5360	−	18.5951i	−0.751999	−	1.03306i
$325$	−6.98428	−	6.05192i	−0.387418	−	0.335700i
$326$	−9.20273	+	14.3197i	−0.509692	+	0.793096i
$327$	−6.36887	−	12.2752i	−0.352200	−	0.678820i
$328$	1.63281	+	2.54070i	0.0901569	+	0.140287i
$329$	10.2410	−	2.89416i	0.564606	−	0.159560i
$330$	11.4722	+	2.75147i	0.631523	+	0.151463i
$331$	1.07487	+	7.47587i	0.0590801	+	0.410911i	0.997804	+	0.0662403i	$0.0211004\pi$
$331$	1.07487	+	7.47587i	0.0590801	+	0.410911i	−0.938724	+	0.344671i	$0.887991\pi$
$332$	−5.47540	+	11.9894i	−0.300501	+	0.658006i
$333$	−0.433201	+	10.2146i	−0.0237392	+	0.559755i
$334$	9.33062	+	31.7772i	0.510549	+	1.73877i
$335$	−11.4186	+	25.0032i	−0.623863	+	1.36607i
$336$	−9.68337	+	6.78562i	−0.528271	+	0.370186i
$337$	−8.07758	−	9.32202i	−0.440014	−	0.507803i	0.491816	−	0.870699i	$-0.336333\pi$
$337$	−8.07758	−	9.32202i	−0.440014	−	0.507803i	−0.931830	+	0.362896i	$0.881788\pi$
$338$	−66.8356	+	30.5228i	−3.63538	+	1.66022i
$339$	6.64037	+	2.63833i	0.360655	+	0.143295i
$340$	5.38842	−	37.4773i	0.292228	−	2.03249i
$341$	−2.37987	−	1.52945i	−0.128877	−	0.0828242i
$342$	15.4897	+	26.5087i	0.837586	+	1.43342i
$343$	−12.5498	+	13.6199i	−0.677626	+	0.735406i
$344$		−	1.46707i		−	0.0790993i
$345$	9.94933	+	18.4013i	0.535654	+	0.990690i
$346$			32.6218i			1.75376i
$347$	−4.88468	+	16.6357i	−0.262223	+	0.893051i	0.718148	+	0.695890i	$0.244990\pi$
$347$	−4.88468	+	16.6357i	−0.262223	+	0.893051i	−0.980371	+	0.197160i	$0.936828\pi$
$348$	21.8851	+	2.03220i	1.17316	+	0.108937i
$349$	−3.61437	+	5.62407i	−0.193473	+	0.301049i	−0.924414	−	0.381391i	$-0.875445\pi$
$349$	−3.61437	+	5.62407i	−0.193473	+	0.301049i	0.730941	+	0.682441i	$0.239081\pi$
$350$	−2.20889	+	7.24903i	−0.118070	+	0.387477i
$351$	23.2210	−	27.2260i	1.23945	−	1.45321i
$352$	4.14751	+	9.08177i	0.221063	+	0.484060i
$353$	7.01282	+	8.09323i	0.373255	+	0.430759i	0.911037	−	0.412325i	$-0.135283\pi$
$353$	7.01282	+	8.09323i	0.373255	+	0.430759i	−0.537782	+	0.843084i	$0.680738\pi$
$354$	7.41656	−	7.10869i	0.394186	−	0.377822i
$355$	32.9939	+	15.0678i	1.75114	+	0.799717i
$356$	30.6566	−	9.00160i	1.62480	−	0.477084i
$357$	−18.4565	−	19.6523i	−0.976821	−	1.04011i
$358$	−8.11505	+	17.7695i	−0.428894	+	0.939146i
$359$	24.0120	−	3.45240i	1.26730	−	0.182211i	0.524320	−	0.851521i	$-0.324320\pi$
$359$	24.0120	−	3.45240i	1.26730	−	0.182211i	0.742983	+	0.669311i	$0.233410\pi$
$360$	−3.37282	−	8.29918i	−0.177763	−	0.437405i
$361$	−1.65801	−	3.63054i	−0.0872638	−	0.191081i
$362$	18.0171	−	11.5789i	0.946957	−	0.608573i
$363$	7.49358	+	14.4429i	0.393311	+	0.758057i
$364$	34.8775	+	30.8485i	1.82808	+	1.61690i
$365$	−29.4948	−	25.5574i	−1.54383	−	1.33773i
$366$	−13.3998	+	4.67689i	−0.700420	+	0.244465i
$367$		−	1.38981i		−	0.0725475i	−0.999342	−	0.0362738i	$-0.988451\pi$
$367$		−	1.38981i		−	0.0725475i	0.999342	−	0.0362738i	$-0.0115488\pi$
$368$	−4.94778	+	11.3423i	−0.257921	+	0.591257i
$369$	2.46145	−	7.23373i	0.128138	−	0.376573i
$370$	−5.16070	+	17.5757i	−0.268292	+	0.913719i
$371$	11.8351	−	10.0461i	0.614448	−	0.521569i
$372$	0.495917	+	9.86905i	0.0257121	+	0.511687i
$373$	3.64719	−	25.3667i	0.188844	−	1.31344i	−0.646162	−	0.763200i	$-0.723627\pi$
$373$	3.64719	−	25.3667i	0.188844	−	1.31344i	0.835007	−	0.550240i	$-0.185464\pi$
$374$	−13.3863	+	8.60284i	−0.692188	+	0.444842i
$375$	−13.8389	−	7.94187i	−0.714640	−	0.410117i
$376$	−3.60456	+	3.12337i	−0.185891	+	0.161076i
$377$	4.86653	+	33.8475i	0.250639	+	1.74323i
$378$	−28.1347	−	8.33308i	−1.44709	−	0.428608i
$379$	−11.5660	+	3.39608i	−0.594104	+	0.174445i	−0.564943	−	0.825130i	$-0.691102\pi$
$379$	−11.5660	+	3.39608i	−0.594104	+	0.174445i	−0.0291612	+	0.999575i	$0.509284\pi$
$380$	8.69390	+	29.6087i	0.445988	+	1.51889i
$381$	−6.54162	−	33.4712i	−0.335137	−	1.71478i
$382$	3.02708	+	21.0538i	0.154879	+	1.07721i
$383$	−11.7429	−	13.5520i	−0.600035	−	0.692477i	0.371754	−	0.928331i	$-0.378757\pi$
$383$	−11.7429	−	13.5520i	−0.600035	−	0.692477i	−0.971788	+	0.235854i	$0.924211\pi$
$384$	7.86252	−	13.7007i	0.401233	−	0.699159i
$385$	7.71553	−	3.42910i	0.393220	−	0.174763i
$386$	23.6482	+	3.40009i	1.20366	+	0.173060i
$387$	−2.90562	+	2.30963i	−0.147701	+	0.117405i
$388$	21.2256	+	18.3921i	1.07757	+	0.933716i
$389$	−4.55101	+	15.4993i	−0.230745	+	0.785846i	0.759978	+	0.649949i	$0.225210\pi$
$389$	−4.55101	+	15.4993i	−0.230745	+	0.785846i	−0.990723	+	0.135897i	$0.956608\pi$
$390$	52.1277	−	37.3252i	2.63959	−	1.89004i
$391$	−27.2036	−	7.48610i	−1.37575	−	0.378588i
$392$	2.50007	−	7.91483i	0.126273	−	0.399759i
$393$	−27.8920	+	9.73504i	−1.40697	+	0.491068i
$394$	−24.6977	+	28.5026i	−1.24425	+	1.43594i
$395$	−8.57838	−	5.51299i	−0.431625	−	0.277389i
$396$	−4.40669	+	8.65836i	−0.221444	+	0.435099i
$397$	6.01887	+	9.36554i	0.302078	+	0.470043i	0.958797	−	0.284093i	$-0.0916924\pi$
$397$	6.01887	+	9.36554i	0.302078	+	0.470043i	−0.656719	+	0.754136i	$0.728056\pi$
$398$	−10.1143	−	22.1472i	−0.506983	−	1.11014i
$399$	20.3367	+	8.32074i	1.01811	+	0.416558i
$400$	0.492781	+	3.42737i	0.0246391	+	0.171368i
$401$	−9.27852	−	4.23736i	−0.463347	−	0.211604i	0.170042	−	0.985437i	$-0.445610\pi$
$401$	−9.27852	−	4.23736i	−0.463347	−	0.211604i	−0.633389	+	0.773833i	$0.718337\pi$
$402$	−31.7825	−	24.8602i	−1.58517	−	1.23991i
$403$	−14.7510	+	4.33129i	−0.734801	+	0.215757i
$404$	−6.42905	+	14.0777i	−0.319857	+	0.700390i
$405$	−11.1271	+	19.7455i	−0.552911	+	0.981164i
$406$	23.7423	−	14.9190i	1.17831	−	0.740417i
$407$	3.92828	−	1.79399i	0.194718	−	0.0889247i
$408$	11.2290	+	4.46149i	0.555920	+	0.220877i
$409$	12.2173	+	1.75658i	0.604106	+	0.0868574i	0.437580	−	0.899180i	$-0.355836\pi$
$409$	12.2173	+	1.75658i	0.604106	+	0.0868574i	0.166527	+	0.986037i	$0.446745\pi$
$410$	7.40155	−	11.5170i	0.365536	−	0.568786i
$411$	14.5692	+	1.35286i	0.718646	+	0.0667318i
$412$	0.632002	−	2.15240i	0.0311365	−	0.106041i
$413$	1.12035	−	7.26645i	0.0551289	−	0.357559i
$414$	−29.6740	+	7.90263i	−1.45840	+	0.388393i
$415$	12.9885			0.637582
$416$	52.0597	+	15.2861i	2.55244	+	0.749463i
$417$	23.0958	+	2.14462i	1.13101	+	0.105023i
$418$	7.01146	−	10.9100i	0.342942	−	0.533627i
$419$	−3.45273	+	24.0142i	−0.168677	+	1.17317i	0.712946	+	0.701219i	$0.247360\pi$
$419$	−3.45273	+	24.0142i	−0.168677	+	1.17317i	−0.881623	+	0.471954i	$0.843549\pi$
$420$	−25.4286	−	14.9390i	−1.24079	−	0.728948i
$421$	4.84187	+	10.6022i	0.235978	+	0.516720i	0.990159	−	0.139946i	$-0.0446930\pi$
$421$	4.84187	+	10.6022i	0.235978	+	0.516720i	−0.754181	+	0.656667i	$0.771966\pi$
$422$	−13.1044	+	11.3550i	−0.637911	+	0.552753i
$423$	11.8607	+	2.22187i	0.576687	+	0.108031i
$424$	−2.89023	+	6.32871i	−0.140362	+	0.307349i
$425$	−7.57526	+	2.22430i	−0.367454	+	0.107894i
$426$	−32.8053	+	41.9399i	−1.58942	+	2.03200i
$427$	−5.57813	+	8.48854i	−0.269945	+	0.410789i
$428$	15.4808	−	2.22580i	0.748291	−	0.107588i
$429$	−14.6983	−	3.52521i	−0.709640	−	0.170199i
$430$	−6.04929	+	2.76262i	−0.291723	+	0.133225i
$431$	−21.0530	−	32.7591i	−1.01409	−	1.57795i	−0.798980	−	0.601357i	$-0.794627\pi$
$431$	−21.0530	−	32.7591i	−1.01409	−	1.57795i	−0.215105	−	0.976591i	$-0.569010\pi$
$432$	−13.2556	+	2.01183i	−0.637761	+	0.0967943i
$433$	18.8143	−	29.2757i	0.904158	−	1.40690i	−0.00929588	−	0.999957i	$-0.502959\pi$
$433$	18.8143	−	29.2757i	0.904158	−	1.40690i	0.913454	−	0.406941i	$-0.133405\pi$
$434$	8.15816	+	9.61094i	0.391604	+	0.461340i
$435$	−7.13733	−	20.4493i	−0.342209	−	0.980467i
$436$	20.4041			0.977178
$437$	22.7024	−	3.66041i	1.08600	−	0.175101i
$438$	46.5810	−	33.3536i	2.22573	−	1.59370i
$439$	−9.68052	+	32.9688i	−0.462026	+	1.57352i	0.318203	+	0.948022i	$0.396921\pi$
$439$	−9.68052	+	32.9688i	−0.462026	+	1.57352i	−0.780229	+	0.625494i	$0.784898\pi$
$440$	−2.47802	+	2.85978i	−0.118135	+	0.136335i
$441$	−19.6116	+	7.50888i	−0.933888	+	0.357566i
$442$	−12.3066	+	85.5943i	−0.585365	+	4.07130i
$443$	−10.4714	−	16.2938i	−0.497512	−	0.774143i	0.498160	−	0.867085i	$-0.334009\pi$
$443$	−10.4714	−	16.2938i	−0.497512	−	0.774143i	−0.995672	+	0.0929418i	$0.970373\pi$
$444$	−13.0833	−	7.50823i	−0.620906	−	0.356325i
$445$	−20.6186	−	23.7951i	−0.977414	−	1.12800i
$446$	−2.07872	−	14.4578i	−0.0984303	−	0.684598i
$447$	−4.83846	+	0.945628i	−0.228851	+	0.0447267i
$448$	−4.07783	−	30.5672i	−0.192660	−	1.44417i
$449$	6.20626	+	21.1366i	0.292891	+	0.997496i	0.966127	+	0.258068i	$0.0830859\pi$
$449$	6.20626	+	21.1366i	0.292891	+	0.997496i	−0.673235	+	0.739428i	$0.735096\pi$
$450$	−5.89717	+	6.24972i	−0.277995	+	0.294614i
$451$	−3.19474	+	0.459335i	−0.150435	+	0.0216292i
$452$	−7.96751	+	6.90388i	−0.374760	+	0.324731i
$453$	−24.1959	−	13.8855i	−1.13682	−	0.652397i
$454$	−0.505667	−	0.786833i	−0.0237321	−	0.0369279i
$455$	13.3745	−	43.8918i	0.627005	−	2.05768i
$456$	−9.83534	+	0.494223i	−0.460582	+	0.0231441i
$457$	23.5440	−	27.1712i	1.10134	−	1.27101i	0.141661	−	0.989915i	$-0.454756\pi$
$457$	23.5440	−	27.1712i	1.10134	−	1.27101i	0.959679	−	0.281098i	$-0.0906987\pi$
$458$	−57.8754	−	16.9938i	−2.70434	−	0.794066i
$459$	−8.84178	−	29.2635i	−0.412699	−	1.36590i
$460$	−30.8601	+	0.526495i	−1.43886	+	0.0245479i
$461$	−14.6972			−0.684518			−0.342259	−	0.939606i	$-0.611192\pi$
$461$	−14.6972			−0.684518			−0.342259	+	0.939606i	$0.611192\pi$
$462$	2.25348	+	12.1879i	0.104841	+	0.567032i
$463$	4.50501	−	5.19906i	0.209366	−	0.241621i	−0.641348	−	0.767250i	$-0.721625\pi$
$463$	4.50501	−	5.19906i	0.209366	−	0.241621i	0.850714	+	0.525629i	$0.176170\pi$
$464$	6.92689	−	10.7785i	0.321573	−	0.500377i
$465$	8.64343	−	4.48456i	0.400829	−	0.207967i
$466$	−17.1302	+	11.0089i	−0.793542	+	0.509979i
$467$	12.1919	+	26.6966i	0.564175	+	1.23537i	0.949841	+	0.312733i	$0.101244\pi$
$467$	12.1919	+	26.6966i	0.564175	+	1.23537i	−0.385666	+	0.922638i	$0.626028\pi$
$468$	19.8780	+	48.9120i	0.918861	+	2.26096i
$469$	−28.8765	−	0.293894i	−1.33339	−	0.0135708i
$470$	19.6665	+	8.98139i	0.907148	+	0.414281i
$471$	19.7274	+	15.4307i	0.908989	+	0.711009i
$472$	0.928341	+	3.16164i	0.0427303	+	0.145526i
$473$	1.42617	+	0.651308i	0.0655752	+	0.0299472i
$474$	10.8067	−	10.3581i	0.496369	−	0.475764i
$475$	4.86295	−	4.21377i	0.223128	−	0.193341i
$476$	38.2793	−	10.8179i	1.75453	−	0.495837i
$477$	17.0845	−	4.23911i	0.782244	−	0.194096i
$478$	−2.24145	+	15.5896i	−0.102522	+	0.713053i
$479$	22.5547	+	14.4950i	1.03055	+	0.662294i	0.942632	−	0.333833i	$-0.108342\pi$
$479$	22.5547	+	14.4950i	1.03055	+	0.662294i	0.0879180	+	0.996128i	$0.471979\pi$
$480$	−34.2188	−	3.17748i	−1.56187	−	0.145032i
$481$	6.61194	−	22.5182i	0.301479	−	1.02674i
$482$	−9.19663			−0.418895
$483$	−13.4209	+	17.4034i	−0.610672	+	0.791884i
$484$	−24.0073			−1.09124
$485$	7.79733	−	26.5553i	0.354058	−	1.20581i
$486$	−24.3771	−	22.6441i	−1.10577	−	1.02716i
$487$	3.09805	+	1.99100i	0.140386	+	0.0902208i	0.608949	−	0.793210i	$-0.291592\pi$
$487$	3.09805	+	1.99100i	0.140386	+	0.0902208i	−0.468562	+	0.883430i	$0.655228\pi$
$488$	0.647851	−	4.50590i	0.0293268	−	0.203973i
$489$	−5.10043	+	12.8372i	−0.230650	+	0.580517i
$490$	−37.3436	+	4.59553i	−1.68701	+	0.207605i
$491$	−6.52090	+	5.65039i	−0.294284	+	0.254999i	−0.789471	−	0.613788i	$-0.789645\pi$
$491$	−6.52090	+	5.65039i	−0.294284	+	0.254999i	0.495187	+	0.868786i	$0.335100\pi$
$492$	7.80118	+	8.13904i	0.351704	+	0.366936i
$493$	26.5734	+	12.1357i	1.19680	+	0.546562i
$494$	−19.8560	−	67.6233i	−0.893363	−	3.04251i
$495$	9.56513	+	0.405657i	0.429921	+	0.0182329i
$496$	5.23970	+	2.39289i	0.235269	+	0.107444i
$497$	−0.387820	+	38.1051i	−0.0173961	+	1.70925i
$498$	−4.44685	+	18.5411i	−0.199268	+	0.830845i
$499$	6.69537	+	14.6608i	0.299726	+	0.656308i	0.998241	−	0.0592871i	$-0.0188828\pi$
$499$	6.69537	+	14.6608i	0.299726	+	0.656308i	−0.698515	+	0.715595i	$0.746155\pi$
$500$	19.8048	−	12.7278i	0.885700	−	0.569205i
$501$	12.3775	+	23.8561i	0.552987	+	1.06581i
$502$	−0.483823	+	0.752844i	−0.0215941	+	0.0336011i
$503$	−0.811173	+	0.936144i	−0.0361684	+	0.0417406i	−0.773546	−	0.633741i	$-0.781519\pi$
$503$	−0.811173	+	0.936144i	−0.0361684	+	0.0417406i	0.737377	+	0.675481i	$0.236064\pi$
$504$	6.52850	−	6.77922i	0.290803	−	0.301970i
$505$	15.2508			0.678651
$506$	8.66036	+	9.65670i	0.385000	+	0.429293i
$507$	−48.4792	+	34.7127i	−2.15304	+	1.54165i
$508$	48.2811	+	14.1766i	2.14213	+	0.628986i
$509$	−10.9942	+	12.6879i	−0.487308	+	0.562383i	−0.945144	−	0.326653i	$-0.894079\pi$
$509$	−10.9942	+	12.6879i	−0.487308	+	0.562383i	0.457836	+	0.889036i	$0.348625\pi$
$510$	−2.74880	−	54.7028i	−0.121719	−	2.42228i
$511$	11.9514	−	39.2215i	0.528697	−	1.73505i
$512$	−14.2990	−	22.2497i	−0.631934	−	0.983308i
$513$	16.4627	+	18.7014i	0.726847	+	0.825686i
$514$	−24.8190	+	21.5058i	−1.09472	+	0.948581i
$515$	−2.18809	+	0.314600i	−0.0964188	+	0.0138629i
$516$	−1.05045	−	5.37479i	−0.0462435	−	0.236612i
$517$	−1.43603	−	4.89067i	−0.0631566	−	0.215092i
$518$	−19.0756	+	2.54479i	−0.838134	+	0.111812i
$519$	5.07776	+	25.9811i	0.222889	+	1.14045i
$520$	2.92658	+	20.3548i	0.128339	+	0.892617i
$521$	−20.5810	−	23.7517i	−0.901669	−	1.04058i	−0.998972	−	0.0453268i	$-0.985567\pi$
$521$	−20.5810	−	23.7517i	−0.901669	−	1.04058i	0.0973032	−	0.995255i	$-0.468978\pi$
$522$	31.6348	−	3.18733i	1.38462	−	0.139506i
$523$	−17.9684	−	27.9594i	−0.785703	−	1.22258i	−0.970808	−	0.239859i	$-0.922899\pi$
$523$	−17.9684	−	27.9594i	−0.785703	−	1.22258i	0.185104	−	0.982719i	$-0.440738\pi$
$524$	6.20320	−	43.1442i	0.270988	−	1.88476i
$525$	−0.630885	+	6.11721i	−0.0275341	+	0.266977i
$526$	28.1090	−	32.4395i	1.22561	−	1.41443i
$527$	−3.70023	+	12.6018i	−0.161185	+	0.548945i
$528$	3.29707	+	4.60463i	0.143487	+	0.200391i
$529$	−2.49476	+	22.8643i	−0.108468	+	0.994100i
$530$	31.5382			1.36993
$531$	4.80030	−	6.81603i	0.208315	−	0.295791i
$532$	−24.7163	+	20.9802i	−1.07159	+	0.909608i
$533$	−9.48294	+	14.7557i	−0.410752	+	0.639142i
$534$	41.0265	−	21.2862i	1.77539	−	0.921145i
$535$	−8.33242	−	12.9655i	−0.360242	−	0.560548i
$536$	11.7728	−	5.37644i	0.508506	−	0.232227i
$537$	−3.69719	+	15.4154i	−0.159546	+	0.665223i
$538$	16.3171	−	2.34604i	0.703480	−	0.101145i
$539$	6.58422	+	5.94415i	0.283603	+	0.256033i
$540$	−18.2991	−	27.9900i	−0.787466	−	1.20450i
$541$	−19.6392	+	5.76660i	−0.844356	+	0.247925i	−0.675173	−	0.737659i	$-0.735931\pi$
$541$	−19.6392	+	5.76660i	−0.844356	+	0.247925i	−0.169183	+	0.985585i	$0.554113\pi$
$542$	0.475508	−	1.04122i	0.0204248	−	0.0447241i
$543$	12.5471	−	12.0263i	0.538449	−	0.516097i
$544$	35.0308	−	30.3543i	1.50193	−	1.30143i
$545$	−8.35269	−	18.2898i	−0.357790	−	0.783450i
$546$	58.0763	+	34.1191i	2.48544	+	1.46016i
$547$	3.64794	−	25.3720i	0.155975	−	1.08483i	−0.749982	−	0.661458i	$-0.769938\pi$
$547$	3.64794	−	25.3720i	0.155975	−	1.08483i	0.905957	−	0.423370i	$-0.139153\pi$
$548$	−11.6717	+	18.1615i	−0.498589	+	0.775820i
$549$	−9.94411	+	5.81059i	−0.424404	+	0.247990i
$550$	3.48258	+	1.02258i	0.148498	+	0.0436029i
$551$	−23.8094			−1.01431
$552$	2.13345	−	9.61580i	0.0908058	−	0.409276i
$553$	1.63247	−	10.5880i	0.0694198	−	0.450247i
$554$	−13.9484	+	47.5039i	−0.592611	+	2.01825i
$555$	−1.37441	+	14.8012i	−0.0583403	+	0.628277i
$556$	−18.5025	+	28.7905i	−0.784681	+	1.22099i
$557$	−44.4516	−	6.39118i	−1.88348	−	0.270803i	−0.897921	−	0.440156i	$-0.854923\pi$
$557$	−44.4516	−	6.39118i	−1.88348	−	0.270803i	−0.985555	+	0.169353i	$0.945832\pi$
$558$	3.44246	+	13.8738i	0.145731	+	0.587325i
$559$	7.75041	−	3.53949i	0.327808	−	0.149705i
$560$	−14.5566	+	9.14697i	−0.615128	+	0.386530i
$561$	−9.32222	+	8.93524i	−0.393584	+	0.377246i
$562$	−17.0475	+	37.3288i	−0.719104	+	1.57462i
$563$	16.1969	−	4.75584i	0.682619	−	0.200435i	0.0780040	−	0.996953i	$-0.475145\pi$
$563$	16.1969	−	4.75584i	0.682619	−	0.200435i	0.604615	+	0.796518i	$0.293327\pi$
$564$	−10.9693	+	14.0238i	−0.461893	+	0.590507i
$565$	9.45012	+	4.31573i	0.397570	+	0.181564i
$566$	2.53061	+	17.6008i	0.106370	+	0.739817i
$567$	−23.7045	−	2.25745i	−0.995496	−	0.0948040i
$568$	−7.09470	−	15.5352i	−0.297687	−	0.651844i
$569$	0.0424114	+	0.0659934i	0.00177798	+	0.00276659i	0.842141	−	0.539257i	$-0.181295\pi$
$569$	0.0424114	+	0.0659934i	0.00177798	+	0.00276659i	−0.840363	+	0.542023i	$0.817658\pi$
$570$	20.5586	+	39.6241i	0.861106	+	1.65967i
$571$	31.1517	+	20.0200i	1.30366	+	0.837810i	0.993605	−	0.112909i	$-0.0360168\pi$
$571$	31.1517	+	20.0200i	1.30366	+	0.837810i	0.310053	+	0.950719i	$0.399653\pi$
$572$	14.6044	−	16.8544i	0.610642	−	0.704718i
$573$	5.68802	+	16.2968i	0.237620	+	0.680810i
$574$	14.2151	+	2.19170i	0.593326	+	0.0914799i
$575$	2.77302	+	5.80779i	0.115643	+	0.242201i
$576$	11.2641	−	33.1031i	0.469338	−	1.37929i
$577$	3.78660	−	12.8960i	0.157638	−	0.536866i	−0.842360	−	0.538916i	$-0.818834\pi$
$577$	3.78660	−	12.8960i	0.157638	−	0.536866i	0.999998	+	0.00204930i	$0.000652313\pi$
$578$	28.4094	+	24.6169i	1.18167	+	1.02393i
$579$	19.3635	−	0.973009i	0.804718	−	0.0404369i
$580$	31.6315	+	4.54793i	1.31343	+	0.188842i
$581$	5.54203	+	12.4697i	0.229922	+	0.517329i
$582$	35.2379	+	20.2223i	1.46066	+	0.838241i
$583$	−4.86912	−	5.61927i	−0.201659	−	0.232726i
$584$	2.61518	+	18.1889i	0.108217	+	0.752664i
$585$	35.7065	−	37.8411i	1.47628	−	1.56454i
$586$	−1.96867	−	6.70469i	−0.0813252	−	0.276968i
$587$	24.2949	−	7.13362i	1.00276	−	0.294436i	0.261170	−	0.965293i	$-0.415892\pi$
$587$	24.2949	−	7.13362i	1.00276	−	0.294436i	0.741587	+	0.670857i	$0.234074\pi$
$588$	3.49215	−	30.7870i	0.144014	−	1.26963i
$589$	−1.52338	−	10.5954i	−0.0627699	−	0.436574i
$590$	11.2885	−	9.78152i	0.464739	−	0.402699i
$591$	−15.2335	+	26.5448i	−0.626622	+	1.09191i
$592$	−7.39740	+	4.75402i	−0.304031	+	0.195389i
$593$	−1.70235	+	11.8401i	−0.0699073	+	0.486216i	0.924549	+	0.381063i	$0.124442\pi$
$593$	−1.70235	+	11.8401i	−0.0699073	+	0.486216i	−0.994456	+	0.105152i	$0.966467\pi$
$594$	−3.85386	+	13.5153i	−0.158126	+	0.554539i
$595$	−25.3671	−	29.8844i	−1.03995	−	1.22514i
$596$	2.04931	−	6.97931i	0.0839430	−	0.285884i
$597$	−11.5027	−	16.0645i	−0.470774	−	0.657475i
$598$	70.4813	−	1.20246i	2.88220	−	0.0491722i
$599$			14.4284i			0.589527i	0.955570	+	0.294764i	$0.0952409\pi$
$599$			14.4284i			0.589527i	−0.955570	+	0.294764i	$0.904759\pi$
$600$	−0.908225	−	2.60217i	−0.0370781	−	0.106233i
$601$	−13.0757	−	11.3302i	−0.533369	−	0.462167i	0.346050	−	0.938216i	$-0.387523\pi$
$601$	−13.0757	−	11.3302i	−0.533369	−	0.462167i	−0.879418	+	0.476050i	$0.842068\pi$
$602$	−5.23340	−	4.62886i	−0.213298	−	0.188658i
$603$	−29.1823	−	14.8524i	−1.18840	−	0.604837i
$604$	34.6266	−	22.2532i	1.40894	−	0.905468i
$605$	9.82773	+	21.5197i	0.399554	+	0.874901i
$606$	−5.22137	+	21.7704i	−0.212104	+	0.884362i
$607$	5.90600	−	0.849154i	0.239717	−	0.0344661i	−0.0214091	−	0.999771i	$-0.506815\pi$
$607$	5.90600	−	0.849154i	0.239717	−	0.0344661i	0.261126	+	0.965305i	$0.415906\pi$
$608$	−15.6935	+	34.3640i	−0.636456	+	1.39364i
$609$	16.5869	−	15.5776i	0.672137	−	0.631237i
$610$	−19.7995	+	5.81365i	−0.801657	+	0.235388i
$611$	−25.1969	−	11.5071i	−1.01936	−	0.465525i
$612$	44.3334	+	8.30500i	1.79207	+	0.335710i
$613$	18.3810	+	21.2128i	0.742400	+	0.856775i	0.993809	−	0.111106i	$-0.0354393\pi$
$613$	18.3810	+	21.2128i	0.742400	+	0.856775i	−0.251409	+	0.967881i	$0.580894\pi$
$614$	12.8644	+	28.1691i	0.519164	+	1.13681i
$615$	4.10216	−	10.3247i	0.165415	−	0.416330i
$616$	−3.80287	−	1.15879i	−0.153222	−	0.0466890i
$617$	20.0674	−	31.2255i	0.807884	−	1.25709i	−0.155199	−	0.987883i	$-0.549602\pi$
$617$	20.0674	−	31.2255i	0.807884	−	1.25709i	0.963082	−	0.269208i	$-0.0867619\pi$
$618$	0.300041	−	3.23120i	0.0120694	−	0.129978i
$619$	−3.38411	+	11.5252i	−0.136019	+	0.463238i	−0.999127	−	0.0417816i	$-0.986697\pi$
$619$	−3.38411	+	11.5252i	−0.136019	+	0.463238i	0.863108	+	0.505020i	$0.168515\pi$
$620$			14.3673i			0.577004i
$621$	−22.4033	+	10.9128i	−0.899015	+	0.437917i
$622$			19.6028i			0.786002i
$623$	14.0468	−	29.9479i	0.562775	−	1.19984i
$624$	30.6452	+	2.84564i	1.22679	+	0.113917i
$625$	−25.1610	−	16.1700i	−1.00644	−	0.646800i
$626$	2.08148	−	14.4770i	0.0831925	−	0.578616i
$627$	3.88596	−	9.78051i	0.155190	−	0.390596i
$628$	−33.6139	+	15.3510i	−1.34134	+	0.612570i
$629$	−13.1296	−	15.1524i	−0.523513	−	0.604166i
$630$	−40.2470	−	14.1536i	−1.60348	−	0.563894i
$631$	1.36111	−	2.98042i	0.0541850	−	0.118649i	−0.880603	−	0.473855i	$-0.842862\pi$
$631$	1.36111	−	2.98042i	0.0541850	−	0.118649i	0.934788	+	0.355206i	$0.115589\pi$
$632$	1.35269	+	4.60685i	0.0538072	+	0.183250i
$633$	−8.66931	+	11.0833i	−0.344574	+	0.440521i
$634$	15.9512	−	34.9282i	0.633502	−	1.38718i
$635$	−7.05688	−	49.0817i	−0.280044	−	1.94775i
$636$	−6.05721	+	25.2554i	−0.240184	+	1.00144i
$637$	47.8451	−	5.88784i	1.89569	−	0.233285i
$638$	−7.26096	−	11.2983i	−0.287464	−	0.447303i
$639$	−19.5991	+	38.5087i	−0.775329	+	1.52338i
$640$	12.4171	−	19.3214i	0.490828	−	0.763744i
$641$	14.5112	+	12.5740i	0.573158	+	0.496644i	0.892532	−	0.450985i	$-0.148927\pi$
$641$	14.5112	+	12.5740i	0.573158	+	0.496644i	−0.319374	+	0.947629i	$0.603473\pi$
$642$	21.3609	−	7.45552i	0.843049	−	0.294246i
$643$			23.1350i			0.912356i	0.889889	+	0.456178i	$0.150782\pi$
$643$			23.1350i			0.912356i	−0.889889	+	0.456178i	$0.849218\pi$
$644$	−13.6730	−	29.4026i	−0.538793	−	1.15863i
$645$	−4.38785	+	3.14185i	−0.172771	+	0.123710i
$646$	−57.7707	−	16.9630i	−2.27296	−	0.667401i
$647$	16.3457	−	18.8639i	0.642615	−	0.741617i	−0.337220	−	0.941426i	$-0.609487\pi$
$647$	16.3457	−	18.8639i	0.642615	−	0.741617i	0.979835	+	0.199809i	$0.0640322\pi$
$648$	10.0479	−	3.59540i	0.394719	−	0.141241i
$649$	−3.48562	−	0.501156i	−0.136822	−	0.0196721i
$650$	16.5936	−	10.6641i	0.650856	−	0.418279i
$651$	7.99344	+	6.38463i	0.313288	+	0.250233i
$652$	−13.3466	−	15.4028i	−0.522694	−	0.603221i
$653$	24.1741	−	3.47572i	0.946007	−	0.136015i	0.347990	−	0.937498i	$-0.386864\pi$
$653$	24.1741	−	3.47572i	0.946007	−	0.136015i	0.598017	+	0.801483i	$0.295955\pi$
$654$	28.9683	−	5.66157i	1.13275	−	0.221385i
$655$	−41.2130	+	12.1012i	−1.61033	+	0.472834i
$656$	6.30574	−	1.85153i	0.246198	−	0.0722902i
$657$	31.9071	−	33.8146i	1.24481	−	1.31923i
$658$	−0.231166	+	22.7131i	−0.00901178	+	0.885448i
$659$	−9.16945	+	7.94538i	−0.357191	+	0.309508i	−0.814908	−	0.579590i	$-0.803213\pi$
$659$	−9.16945	+	7.94538i	−0.357191	+	0.309508i	0.457717	+	0.889098i	$0.348667\pi$
$660$	−7.03085	+	12.2515i	−0.273675	+	0.476887i
$661$	−6.99517	−	10.8847i	−0.272081	−	0.423366i	0.678145	−	0.734928i	$-0.262784\pi$
$661$	−6.99517	−	10.8847i	−0.272081	−	0.423366i	−0.950226	+	0.311562i	$0.899148\pi$
$662$	−15.9563	−	2.29417i	−0.620160	−	0.0891655i
$663$	3.52180	+	70.0858i	0.136775	+	2.72191i
$664$	−4.62191	−	4.00491i	−0.179365	−	0.155421i
$665$	28.9242	+	13.5667i	1.12163	+	0.526094i
$666$	−20.6581	−	7.02942i	−0.800486	−	0.272384i
$667$	6.31841	−	22.9604i	0.244650	−	0.889030i
$668$	−39.6541			−1.53426
$669$	−3.90600	−	11.1912i	−0.151015	−	0.432675i
$670$	−44.3382	−	38.4192i	−1.71293	−	1.48426i
$671$	4.09265	+	2.63018i	0.157995	+	0.101537i
$672$	−11.5502	−	34.2076i	−0.445557	−	1.31959i
$673$	19.7762	−	12.7094i	0.762318	−	0.489912i	−0.100805	−	0.994906i	$-0.532142\pi$
$673$	19.7762	−	12.7094i	0.762318	−	0.489912i	0.863123	+	0.504994i	$0.168505\pi$
$674$	23.9480	−	10.9367i	0.922441	−	0.421265i
$675$	−3.72391	+	5.89542i	−0.143333	+	0.226915i
$676$	−12.5201	−	87.0789i	−0.481541	−	3.34919i
$677$	3.08996	−	6.76606i	0.118757	−	0.260041i	−0.840913	−	0.541170i	$-0.817982\pi$
$677$	3.08996	−	6.76606i	0.118757	−	0.260041i	0.959670	+	0.281129i	$0.0907089\pi$
$678$	−9.39609	+	12.0124i	−0.360855	+	0.461335i
$679$	28.8214	−	3.84493i	1.10606	−	0.147555i
$680$	15.9804	+	7.29800i	0.612820	+	0.279866i
$681$	−0.525205	−	0.547952i	−0.0201259	−	0.0209975i
$682$	4.56325	−	3.95408i	0.174736	−	0.151409i
$683$	−8.46877	+	3.86756i	−0.324048	+	0.147988i	−0.570796	−	0.821092i	$-0.693365\pi$
$683$	−8.46877	+	3.86756i	−0.324048	+	0.147988i	0.246748	+	0.969080i	$0.420638\pi$
$684$	−35.6791	+	8.85292i	−1.36422	+	0.338500i
$685$	21.0576	+	3.02762i	0.804569	+	0.115680i
$686$	−20.3460	−	33.8909i	−0.776813	−	1.29396i
$687$	−48.7392	−	4.52580i	−1.85951	−	0.172670i
$688$	−3.06310	−	0.899407i	−0.116780	−	0.0342896i
$689$	−40.4070			−1.53939
$690$	−43.6670	+	9.31032i	−1.66237	+	0.354438i
$691$		−	18.3579i		−	0.698366i	−0.937054	−	0.349183i	$-0.886459\pi$
$691$		−	18.3579i		−	0.698366i	0.937054	−	0.349183i	$-0.113541\pi$
$692$	−37.4769	−	11.0042i	−1.42466	−	0.418318i
$693$	3.69186	+	9.35610i	0.140242	+	0.355409i
$694$	−31.1312	−	20.0068i	−1.18173	−	0.759449i
$695$	33.3815	+	4.79954i	1.26623	+	0.182057i
$696$	−3.76558	+	9.47752i	−0.142734	+	0.359244i
$697$	6.22484	+	13.6305i	0.235783	+	0.516292i
$698$	−9.34422	−	10.7838i	−0.353684	−	0.408173i
$699$	−11.9295	+	11.4343i	−0.451215	+	0.432485i
$700$	−7.58280	−	4.98293i	−0.286603	−	0.188337i
$701$	7.74298	+	26.3702i	0.292448	+	0.995987i	0.966364	+	0.257179i	$0.0827930\pi$
$701$	7.74298	+	26.3702i	0.292448	+	0.995987i	−0.673915	+	0.738808i	$0.735389\pi$
$702$	41.7932	+	63.9263i	1.57738	+	2.41274i
$703$	14.8640	+	6.78817i	0.560607	+	0.256021i
$704$	−14.6198	+	2.10201i	−0.551005	+	0.0792226i
$705$	17.0611	+	4.09190i	0.642558	+	0.154110i
$706$	−20.7912	+	9.49503i	−0.782488	+	0.357350i
$707$	6.50730	+	14.6415i	0.244732	+	0.550651i
$708$	5.66487	+	10.9183i	0.212899	+	0.410336i
$709$	−42.0006	−	26.9922i	−1.57737	−	1.01371i	−0.976804	−	0.214134i	$-0.931307\pi$
$709$	−42.0006	−	26.9922i	−1.57737	−	1.01371i	−0.600563	−	0.799578i	$-0.705057\pi$
$710$	−50.6977	+	58.5082i	−1.90265	+	2.19577i
$711$	6.99455	−	9.93169i	0.262316	−	0.372468i
$712$			14.8250i			0.555589i
$713$	10.6218	+	1.34268i	0.397791	+	0.0502837i
$714$	51.3446	−	25.9799i	1.92152	−	0.972275i
$715$	−21.0865	−	6.19155i	−0.788590	−	0.231551i
$716$	−17.6767	−	15.3169i	−0.660609	−	0.572421i
$717$	0.641439	+	12.7650i	0.0239550	+	0.476718i
$718$	−7.36871	+	51.2505i	−0.274998	+	1.91265i
$719$	−20.3109	+	13.0530i	−0.757468	+	0.486795i	−0.861487	−	0.507780i	$-0.830466\pi$
$719$	−20.3109	+	13.0530i	−0.757468	+	0.486795i	0.104019	+	0.994575i	$0.466830\pi$
$720$	−19.3956	+	1.95418i	−0.722831	+	0.0728280i
$721$	−1.23566	−	1.96644i	−0.0460184	−	0.0732341i
$722$	8.43205	−	1.21235i	0.313808	−	0.0451188i
$723$	−7.32452	+	1.43150i	−0.272402	+	0.0532382i
$724$	7.22452	+	24.6045i	0.268497	+	0.914418i
$725$	−1.87735	−	6.39366i	−0.0697229	−	0.237455i
$726$	−34.0840	+	6.66138i	−1.26498	+	0.247227i
$727$	16.0375	−	2.30584i	0.594797	−	0.0855189i	0.161659	−	0.986847i	$-0.448315\pi$
$727$	16.0375	−	2.30584i	0.594797	−	0.0855189i	0.433138	+	0.901328i	$0.357406\pi$
$728$	−18.2929	+	11.4948i	−0.677981	+	0.426025i
$729$	−22.9394	−	14.2402i	−0.849609	−	0.527413i
$730$	70.0752	−	45.0346i	2.59360	−	1.66681i
$731$	1.03591	−	7.20489i	0.0383144	−	0.266483i
$732$	−0.852827	−	16.9718i	−0.0315214	−	0.627295i
$733$	−35.4496	−	30.7172i	−1.30936	−	1.13457i	−0.981838	−	0.189723i	$-0.939241\pi$
$733$	−35.4496	−	30.7172i	−1.30936	−	1.13457i	−0.327522	−	0.944843i	$-0.606214\pi$
$734$	2.84622	+	0.835725i	0.105056	+	0.0308472i
$735$	−29.0265	+	9.47278i	−1.07066	+	0.349409i
$736$	−28.9740	−	24.2533i	−1.06800	−	0.893988i
$737$			13.8314i			0.509485i
$738$	13.3339	+	9.39064i	0.490829	+	0.345674i
$739$	13.4817	−	15.5587i	0.495933	−	0.572337i	−0.451508	−	0.892267i	$-0.649114\pi$
$739$	13.4817	−	15.5587i	0.495933	−	0.572337i	0.947441	+	0.319930i	$0.103659\pi$
$740$	−18.4507	−	11.8575i	−0.678261	−	0.435892i
$741$	−26.3399	−	50.7668i	−0.967621	−	1.86497i
$742$	13.4569	+	30.2783i	0.494019	+	1.11155i
$743$	−22.5344	+	10.2911i	−0.826708	+	0.377545i	−0.783401	−	0.621517i	$-0.786517\pi$
$743$	−22.5344	+	10.2911i	−0.826708	+	0.377545i	−0.0433072	+	0.999062i	$0.513789\pi$
$744$	−4.45850	−	1.06932i	−0.163457	−	0.0392031i
$745$	−7.09504	+	1.02011i	−0.259942	+	0.0373740i
$746$	49.7558	+	22.7227i	1.82169	+	0.831938i
$747$	−0.655614	+	15.4589i	−0.0239877	+	0.565613i
$748$	−5.36765	−	18.2805i	−0.196261	−	0.668403i
$749$	8.89221	−	13.5318i	0.324914	−	0.494440i
$750$	24.5860	−	23.5654i	0.897753	−	0.860486i
$751$	1.49547	+	1.72587i	0.0545706	+	0.0629778i	0.782379	−	0.622803i	$-0.214006\pi$
$751$	1.49547	+	1.72587i	0.0545706	+	0.0629778i	−0.727808	+	0.685781i	$0.759461\pi$
$752$	4.31146	+	9.44078i	0.157223	+	0.344270i
$753$	−0.268150	+	0.674901i	−0.00977192	+	0.0245947i
$754$	−72.2432	−	10.3870i	−2.63094	−	0.378272i
$755$	−34.1222	−	21.9290i	−1.24183	−	0.798078i
$756$	19.0639	−	29.5110i	0.693347	−	1.07330i
$757$	−45.4160	−	13.3353i	−1.65067	−	0.484681i	−0.681654	−	0.731675i	$-0.738739\pi$
$757$	−45.4160	−	13.3353i	−1.65067	−	0.484681i	−0.969017	+	0.246994i	$0.920557\pi$
$758$		−	25.7283i		−	0.934493i
$759$	8.40053	+	6.34290i	0.304920	+	0.230233i
$760$	−14.3182			−0.519376
$761$	24.0464	+	7.06067i	0.871682	+	0.255949i	0.686831	−	0.726818i	$-0.259001\pi$
$761$	24.0464	+	7.06067i	0.871682	+	0.255949i	0.184851	+	0.982766i	$0.440820\pi$
$762$	72.4799	+	6.73032i	2.62567	+	0.243814i
$763$	13.9952	−	15.8230i	0.506660	−	0.572832i
$764$	−25.2084	−	3.62442i	−0.912008	−	0.131127i
$765$	−10.7040	−	43.1394i	−0.387005	−	1.55971i
$766$	34.8147	−	15.8994i	1.25791	−	0.574467i
$767$	−14.4629	+	12.5322i	−0.522225	+	0.452511i
$768$	−4.60912	−	4.80874i	−0.166317	−	0.173520i
$769$	−19.7377	−	9.01388i	−0.711758	−	0.325049i	0.0264238	−	0.999651i	$-0.491588\pi$
$769$	−19.7377	−	9.01388i	−0.711758	−	0.325049i	−0.738182	+	0.674602i	$0.764315\pi$
$770$	2.38299	+	17.8628i	0.0858770	+	0.643729i
$771$	−16.4192	+	20.9912i	−0.591325	+	0.755979i
$772$	−11.8833	+	26.0208i	−0.427689	+	0.936508i
$773$	4.13501	+	28.7596i	0.148726	+	1.03441i	0.918309	+	0.395864i	$0.129555\pi$
$773$	4.13501	+	28.7596i	0.148726	+	1.03441i	−0.769583	+	0.638547i	$0.779536\pi$
$774$	−2.98272	−	7.33930i	−0.107212	−	0.263806i
$775$	2.72511	−	1.24452i	0.0978890	−	0.0447044i
$776$	−10.9627	+	7.04533i	−0.393540	+	0.252912i
$777$	−14.7964	+	4.99598i	−0.530817	+	0.179230i
$778$	−29.0047	−	18.6402i	−1.03987	−	0.668282i
$779$	−9.22976	−	7.99763i	−0.330690	−	0.286545i
$780$	25.2963	+	72.4767i	0.905752	+	2.59508i
$781$	18.2517			0.653099
$782$	31.6891	−	51.2092i	1.13320	−	1.83124i
$783$	24.6989	−	7.46262i	0.882668	−	0.266692i
$784$	−14.9927	−	10.0722i	−0.535452	−	0.359721i
$785$	27.5206	+	23.8468i	0.982253	+	0.851127i
$786$	−3.16445	−	62.9744i	−0.112872	−	2.24622i
$787$	−20.4521	−	2.94057i	−0.729039	−	0.104820i	−0.232207	−	0.972666i	$-0.574595\pi$
$787$	−20.4521	−	2.94057i	−0.729039	−	0.104820i	−0.496832	+	0.867846i	$0.665504\pi$
$788$	−24.4135	−	37.9881i	−0.869695	−	1.35327i
$789$	17.3376	−	30.2113i	0.617235	−	1.07555i
$790$	16.4485	−	14.2527i	0.585212	−	0.507089i
$791$	−0.111080	+	10.9141i	−0.00394953	+	0.388059i
$792$	−3.27863	−	3.09368i	−0.116501	−	0.109929i
$793$	25.3673	−	7.44851i	0.900819	−	0.264504i
$794$	−22.7991	+	6.69443i	−0.809111	+	0.237576i
$795$	25.1181	−	4.90908i	0.890847	−	0.174107i
$796$	28.8552	−	4.14875i	1.02275	−	0.147049i
$797$	−14.5270	−	16.7650i	−0.514572	−	0.593848i	0.437691	−	0.899125i	$-0.355796\pi$
$797$	−14.5270	−	16.7650i	−0.514572	−	0.593848i	−0.952264	+	0.305277i	$0.901251\pi$
$798$	−29.2691	+	36.6444i	−1.03611	+	1.29720i
$799$	−19.9077	+	12.7939i	−0.704283	+	0.452615i
$800$	−10.4654	−	1.50469i	−0.370007	−	0.0531990i
$801$	29.3616	−	23.3391i	1.03744	−	0.824646i
$802$	14.2571	−	16.4536i	0.503437	−	0.580997i
$803$	−18.8428	−	5.53274i	−0.664947	−	0.195246i
$804$	39.2813	−	28.1267i	1.38534	−	0.991953i
$805$	−20.7587	+	24.2926i	−0.731649	+	0.856203i
$806$		−	32.8134i		−	1.15580i
$807$	12.6303	−	4.40831i	0.444609	−	0.155180i
$808$	−5.42692	−	4.70245i	−0.190918	−	0.165432i
$809$	12.3888	−	19.2774i	0.435568	−	0.677757i	−0.552196	−	0.833715i	$-0.686210\pi$
$809$	12.3888	−	19.2774i	0.435568	−	0.677757i	0.987764	+	0.155957i	$0.0498462\pi$
$810$	−33.7462	−	34.6609i	−1.18572	−	1.21786i
$811$	−18.7386	−	29.1578i	−0.658000	−	1.02387i	−0.996556	−	0.0829222i	$-0.973575\pi$
$811$	−18.7386	−	29.1578i	−0.658000	−	1.02387i	0.338556	−	0.940946i	$-0.390062\pi$
$812$	9.13050	+	32.3084i	0.320418	+	1.13380i
$813$	0.216640	−	0.903277i	0.00759790	−	0.0316793i
$814$	1.31177	+	9.12357i	0.0459775	+	0.319781i
$815$	−8.34317	+	18.2690i	−0.292249	+	0.639935i
$816$	16.1992	−	20.7099i	0.567086	−	0.724992i
$817$	1.67138	+	5.69219i	0.0584741	+	0.199144i
$818$	−10.9439	+	23.9637i	−0.382643	+	0.837872i
$819$	51.5648	+	18.1338i	1.80182	+	0.633645i
$820$	10.7344	+	12.3881i	0.374861	+	0.432612i
$821$	−5.10760	+	2.33256i	−0.178256	+	0.0814070i	−0.502544	−	0.864551i	$-0.667603\pi$
$821$	−5.10760	+	2.33256i	−0.178256	+	0.0814070i	0.324288	+	0.945958i	$0.394875\pi$
$822$	−11.5313	+	29.0230i	−0.402202	+	1.01229i
$823$	−2.66120	+	18.5090i	−0.0927635	+	0.645185i	0.889396	+	0.457137i	$0.151125\pi$
$823$	−2.66120	+	18.5090i	−0.0927635	+	0.645185i	−0.982160	+	0.188048i	$0.939784\pi$
$824$	0.875626	+	0.562731i	0.0305039	+	0.0196037i
$825$	2.93282	+	0.272335i	0.102108	+	0.00948148i
$826$	14.2074	+	6.66387i	0.494338	+	0.231866i
$827$		−	13.3909i		−	0.465648i	−0.972519	−	0.232824i	$-0.925203\pi$
$827$		−	13.3909i		−	0.465648i	0.972519	−	0.232824i	$-0.0747966\pi$
$828$	0.931072	−	36.7562i	0.0323570	−	1.27737i
$829$		−	22.2503i		−	0.772786i	−0.922334	−	0.386393i	$-0.873721\pi$
$829$		−	22.2503i		−	0.772786i	0.922334	−	0.386393i	$-0.126279\pi$
$830$	−7.81030	+	26.5995i	−0.271100	+	0.923281i
$831$	−3.71476	+	40.0049i	−0.128864	+	1.38775i
$832$	−43.3959	+	67.5254i	−1.50448	+	2.34102i
$833$	17.8667	−	37.1049i	0.619045	−	1.28561i
$834$	−18.2801	+	46.0087i	−0.632987	+	1.59315i
$835$	16.2329	+	35.5452i	0.561764	+	1.23009i
$836$	10.1686	+	11.7352i	0.351690	+	0.405871i
$837$	4.90123	+	10.5138i	0.169411	+	0.363408i
$838$	−47.1030	−	21.5112i	−1.62715	−	0.743092i
$839$	12.1567	−	3.56952i	0.419695	−	0.123234i	−0.0650644	−	0.997881i	$-0.520725\pi$
$839$	12.1567	−	3.56952i	0.419695	−	0.123234i	0.484760	+	0.874647i	$0.338907\pi$
$840$	9.97486	−	9.36789i	0.344166	−	0.323223i
$841$	1.80431	−	3.95090i	0.0622177	−	0.136238i
$842$	−24.6240	+	3.54039i	−0.848598	+	0.122010i
$843$	−7.76679	+	32.3835i	−0.267502	+	1.11535i
$844$	−8.62451	−	18.8851i	−0.296868	−	0.650050i
$845$	−72.9307	+	46.8697i	−2.50889	+	1.61237i
$846$	−11.6823	+	22.9537i	−0.401647	+	0.789164i
$847$	−16.4667	+	18.6173i	−0.565802	+	0.639698i
$848$	11.4418	+	9.91439i	0.392914	+	0.340462i
$849$	4.75513	+	13.6240i	0.163196	+	0.467574i
$850$		−	16.8510i		−	0.577985i
$851$	−10.4907	+	12.5326i	−0.359615	+	0.429612i
$852$	−37.1158	−	51.8352i	−1.27157	−	1.77584i
$853$	10.0046	−	34.0727i	0.342553	−	1.16663i	−0.590545	−	0.807005i	$-0.701087\pi$
$853$	10.0046	−	34.0727i	0.342553	−	1.16663i	0.933098	−	0.359623i	$-0.117095\pi$
$854$	−14.0296	−	16.5279i	−0.480082	−	0.565573i
$855$	22.5413	+	28.3580i	0.770896	+	0.969822i
$856$	−1.03275	+	7.18295i	−0.0352988	+	0.245508i
$857$	−22.7407	+	14.6145i	−0.776807	+	0.499223i	−0.867972	−	0.496612i	$-0.834577\pi$
$857$	−22.7407	+	14.6145i	−0.776807	+	0.499223i	0.0911656	+	0.995836i	$0.470941\pi$
$858$	16.0577	−	27.9811i	0.548202	−	0.955258i
$859$	32.2287	−	27.9264i	1.09963	−	0.952835i	0.100517	−	0.994935i	$-0.467950\pi$
$859$	32.2287	−	27.9264i	1.09963	−	0.952835i	0.999113	+	0.0421004i	$0.0134049\pi$
$860$	−1.13319	−	7.88152i	−0.0386415	−	0.268758i
$861$	11.6625	−	0.467103i	0.397458	−	0.0159188i
$862$	79.7474	−	23.4160i	2.71621	−	0.797551i
$863$	10.6627	+	36.3137i	0.362961	+	1.23613i	0.915389	+	0.402571i	$0.131883\pi$
$863$	10.6627	+	36.3137i	0.362961	+	1.23613i	−0.552428	+	0.833561i	$0.686299\pi$
$864$	5.50907	−	40.5668i	0.187422	−	1.38011i
$865$	5.47772	+	38.0984i	0.186248	+	1.29538i
$866$	48.6406	+	56.1343i	1.65288	+	1.90752i
$867$	26.4580	+	15.1837i	0.898559	+	0.515664i
$868$	−13.7933	+	6.13032i	−0.468176	+	0.208077i
$869$	−5.07892	−	0.730238i	−0.172290	−	0.0247716i
$870$	46.1702	−	2.32004i	1.56532	−	0.0786568i
$871$	56.8065	+	49.2231i	1.92481	+	1.66786i
$872$	−2.66726	+	9.08384i	−0.0903247	+	0.307618i
$873$	31.2124	+	10.6208i	1.05638	+	0.359459i
$874$	−6.15526	+	48.6937i	−0.208205	+	1.64709i
$875$	3.71398	−	24.0884i	0.125555	−	0.814335i
$876$	22.6046	+	64.7648i	0.763739	+	2.18820i
$877$	1.29618	−	1.49587i	0.0437689	−	0.0505121i	−0.733443	−	0.679751i	$-0.762088\pi$
$877$	1.29618	−	1.49587i	0.0437689	−	0.0505121i	0.777212	+	0.629239i	$0.216633\pi$
$878$	−61.6963	−	39.6498i	−2.08215	−	1.33812i
$879$	−2.61154	−	5.03341i	−0.0880851	−	0.169773i
$880$	4.45176	+	6.92707i	0.150069	+	0.233512i
$881$	3.85589	+	8.44323i	0.129908	+	0.284460i	0.963398	−	0.268076i	$-0.0863877\pi$
$881$	3.85589	+	8.44323i	0.129908	+	0.284460i	−0.833490	+	0.552535i	$0.813660\pi$
$882$	−3.58462	−	44.6783i	−0.120701	−	1.50440i
$883$	5.40868	+	37.6182i	0.182017	+	1.26595i	0.851986	+	0.523565i	$0.175398\pi$
$883$	5.40868	+	37.6182i	0.182017	+	1.26595i	−0.669969	+	0.742389i	$0.733693\pi$
$884$	−94.1820	−	43.0115i	−3.16768	−	1.44663i
$885$	7.46799	−	9.54745i	0.251034	−	0.320934i
$886$	39.6651	−	11.6467i	1.33258	−	0.391280i
$887$	−14.5286	+	31.8133i	−0.487824	+	1.06818i	0.492414	+	0.870361i	$0.336115\pi$
$887$	−14.5286	+	31.8133i	−0.487824	+	1.06818i	−0.980238	+	0.197823i	$0.936613\pi$
$888$	5.05291	−	4.84316i	0.169565	−	0.162526i
$889$	44.1099	−	27.7175i	1.47940	−	0.929614i
$890$	61.1288	−	27.9166i	2.04904	−	0.935766i
$891$	−0.965625	+	11.3639i	−0.0323497	+	0.380706i
$892$	17.3108	+	2.48892i	0.579609	+	0.0833351i
$893$	10.4272	−	16.2251i	0.348934	−	0.542952i
$894$	0.972905	−	10.4774i	0.0325388	−	0.350416i
$895$	−6.49363	+	22.1153i	−0.217058	+	0.739232i
$896$	23.8477	+	3.67687i	0.796695	+	0.122836i
$897$	55.9466	−	11.9285i	1.86800	−	0.398280i
$898$	−47.0179			−1.56901
$899$	−10.6362	−	3.12307i	−0.354737	−	0.104160i
$900$	−5.19059	−	8.88305i	−0.173020	−	0.296102i
$901$	−18.6628	+	29.0399i	−0.621749	+	0.967460i
$902$	0.980392	−	6.81878i	0.0326435	−	0.227040i
$903$	−4.88857	−	2.87198i	−0.162681	−	0.0955733i
$904$	−2.03206	−	4.44960i	−0.0675855	−	0.147992i
$905$	19.0975	−	16.5481i	0.634823	−	0.550077i
$906$	42.9858	−	41.2015i	1.42811	−	1.36883i
$907$	11.4456	−	25.0623i	0.380043	−	0.832179i	−0.618866	−	0.785496i	$-0.712408\pi$
$907$	11.4456	−	25.0623i	0.380043	−	0.832179i	0.998910	−	0.0466825i	$-0.0148649\pi$
$908$	1.07451	−	0.315506i	0.0356590	−	0.0104704i
$909$	−0.769803	+	18.1514i	−0.0255328	+	0.602045i
$910$	81.8443	+	53.7829i	2.71311	+	1.78289i
$911$	−15.1499	+	2.17823i	−0.501940	+	0.0721680i	−0.388634	−	0.921392i	$-0.627053\pi$
$911$	−15.1499	+	2.17823i	−0.501940	+	0.0721680i	−0.113305	+	0.993560i	$0.536144\pi$
$912$	−4.99779	+	20.8382i	−0.165493	+	0.690021i
$913$	5.94514	−	2.71505i	0.196755	−	0.0898552i
$914$	41.4868	+	64.5547i	1.37226	+	2.13528i
$915$	−14.8641	+	7.71209i	−0.491391	+	0.254954i
$916$	39.0459	−	60.7566i	1.29011	−	2.00745i
$917$	−29.2028	−	34.4032i	−0.964363	−	1.13609i
$918$	65.2460	−	0.510422i	2.15344	−	0.0168464i
$919$	11.6886			0.385572			0.192786	−	0.981241i	$-0.438248\pi$
$919$	11.6886			0.385572			0.192786	+	0.981241i	$0.438248\pi$
$920$	3.79969	−	13.8077i	0.125272	−	0.455225i
$921$	14.6303	+	20.4324i	0.482085	+	0.673271i
$922$	8.83778	−	30.0987i	0.291057	−	0.991248i
$923$	64.9543	−	74.9613i	2.13800	−	2.46738i
$924$	−14.7620	−	1.52244i	−0.485634	−	0.0500848i
$925$	−0.650850	+	4.52676i	−0.0213998	+	0.148839i
$926$	7.93828	+	12.3522i	0.260868	+	0.405919i
$927$	−0.263989	−	2.62014i	−0.00867055	−	0.0860567i
$928$	25.6196	+	29.5666i	0.841005	+	0.970572i
$929$	−6.21685	−	43.2391i	−0.203968	−	1.41863i	−0.792360	−	0.610054i	$-0.791148\pi$
$929$	−6.21685	−	43.2391i	−0.203968	−	1.41863i	0.588392	−	0.808576i	$-0.299761\pi$
$930$	3.98653	+	20.3977i	0.130723	+	0.668867i
$931$	−0.683143	+	33.5575i	−0.0223891	+	1.09980i
$932$	−6.86890	−	23.3933i	−0.224998	−	0.766274i
$933$	3.05128	+	15.6124i	0.0998946	+	0.511126i
$934$	−62.0037	+	8.91478i	−2.02882	+	0.291701i
$935$	−14.1890	+	12.2948i	−0.464030	+	0.402085i
$936$	−24.3740	+	2.45577i	−0.796688	+	0.0802694i
$937$	19.0796	+	29.6884i	0.623303	+	0.969879i	0.999068	+	0.0431636i	$0.0137437\pi$
$937$	19.0796	+	29.6884i	0.623303	+	0.969879i	−0.375765	+	0.926715i	$0.622620\pi$
$938$	17.9659	−	58.9598i	0.586609	−	1.92511i
$939$	−0.595659	−	11.8540i	−0.0194386	−	0.386840i
$940$	−16.9521	+	19.5638i	−0.552918	+	0.638101i
$941$	−19.5279	−	5.73390i	−0.636590	−	0.186920i	−0.0525160	−	0.998620i	$-0.516724\pi$
$941$	−19.5279	−	5.73390i	−0.636590	−	0.186920i	−0.584074	+	0.811700i	$0.698542\pi$
$942$	−43.4633	+	31.1212i	−1.41611	+	1.01398i
$943$	10.1618	−	6.77828i	0.330914	−	0.220731i
$944$	7.17031			0.233374
$945$	−34.2572	−	5.00779i	−1.11439	−	0.162903i
$946$	−2.19141	+	2.52902i	−0.0712489	+	0.0822256i
$947$	−4.01692	+	6.25045i	−0.130532	+	0.203112i	−0.900367	−	0.435131i	$-0.856702\pi$
$947$	−4.01692	+	6.25045i	−0.130532	+	0.203112i	0.769835	+	0.638243i	$0.220339\pi$
$948$	8.25433	+	15.9092i	0.268088	+	0.516706i
$949$	−89.7811	+	57.6988i	−2.91442	+	1.87298i
$950$	5.70525	+	12.4928i	0.185103	+	0.405319i
$951$	7.26731	−	30.3009i	0.235659	−	0.982574i
$952$	−0.187838	+	18.4560i	−0.00608787	+	0.598161i
$953$	51.9232	+	23.7125i	1.68196	+	0.768124i	0.999301	+	0.0373840i	$0.0119025\pi$
$953$	51.9232	+	23.7125i	1.68196	+	0.768124i	0.682656	+	0.730740i	$0.260825\pi$
$954$	−1.59193	+	37.5367i	−0.0515407	+	1.21529i
$955$	7.07054	+	24.0801i	0.228797	+	0.779212i
$956$	−17.1537	−	7.83385i	−0.554792	−	0.253365i
$957$	−7.54151	−	7.86813i	−0.243783	−	0.254340i
$958$	−43.2472	+	37.4739i	−1.39725	+	1.21073i
$959$	6.07831	+	21.5082i	0.196279	+	0.694536i
$960$	18.7724	−	47.2478i	0.605876	−	1.52492i
$961$	−3.70250	+	25.7515i	−0.119435	+	0.830692i
$962$	42.1395	+	27.0814i	1.35863	+	0.873140i
$963$	15.8521	−	9.26278i	0.510827	−	0.298489i
$964$	3.10227	−	10.5654i	0.0999175	−	0.340288i
$965$	28.1891			0.907440
$966$	−27.5705	−	37.9500i	−0.887066	−	1.22102i
$967$	46.0986			1.48243			0.741215	−	0.671267i	$-0.234250\pi$
$967$	46.0986			1.48243			0.741215	+	0.671267i	$0.234250\pi$
$968$	3.13828	−	10.6880i	0.100868	−	0.343525i
$969$	−48.6510	−	4.51762i	−1.56290	−	0.145127i
$970$	49.6943	+	31.9366i	1.59559	+	1.02542i
$971$	1.20279	−	8.36562i	0.0385995	−	0.268465i	−0.961378	−	0.275233i	$-0.911245\pi$
$971$	1.20279	−	8.36562i	0.0385995	−	0.268465i	0.999977	+	0.00676741i	$0.00215415\pi$
$972$	34.2373	−	20.3667i	1.09816	−	0.653261i
$973$	9.63563	+	34.0958i	0.308904	+	1.09306i
$974$	−5.94033	+	5.14733i	−0.190340	+	0.164931i
$975$	11.5558	−	11.0761i	0.370083	−	0.354720i
$976$	−9.01069	−	4.11505i	−0.288425	−	0.131719i
$977$	6.04114	+	20.5742i	0.193273	+	0.658228i	0.997919	+	0.0644735i	$0.0205368\pi$
$977$	6.04114	+	20.5742i	0.193273	+	0.658228i	−0.804646	+	0.593755i	$0.797645\pi$
$978$	−23.2225	−	18.1645i	−0.742573	−	0.580838i
$979$	−14.4116	−	6.58154i	−0.460596	−	0.210347i
$980$	7.31753	−	44.4517i	0.233750	−	1.41996i
$981$	22.1901	−	9.01815i	0.708476	−	0.287927i
$982$	−7.65037	−	16.7520i	−0.244133	−	0.534577i
$983$	−38.6215	+	24.8205i	−1.23183	+	0.791652i	−0.984176	−	0.177195i	$-0.943298\pi$
$983$	−38.6215	+	24.8205i	−1.23183	+	0.791652i	−0.247659	+	0.968847i	$0.579661\pi$
$984$	−4.64326	+	2.40911i	−0.148022	+	0.0767998i
$985$	−24.0579	+	37.4348i	−0.766547	+	1.19277i
$986$	−40.8320	+	47.1226i	−1.30036	+	1.50069i
$987$	3.35130	+	18.1255i	0.106673	+	0.576940i
$988$	84.3856			2.68466
$989$	−5.93276	+	0.101217i	−0.188651	+	0.00321851i
$990$	−6.58248	+	19.3447i	−0.209205	+	0.614814i
$991$	−33.8354	−	9.93496i	−1.07482	−	0.315594i	−0.304013	−	0.952668i	$-0.598327\pi$
$991$	−33.8354	−	9.93496i	−1.07482	−	0.315594i	−0.770803	+	0.637074i	$0.780145\pi$
$992$	−11.5182	+	13.2927i	−0.365703	+	0.422043i
$993$	−13.0653	+	0.656526i	−0.414613	+	0.0208342i
$994$	−77.8029	−	23.7077i	−2.46776	−	0.751962i
$995$	−15.5311	−	24.1669i	−0.492370	−	0.766143i
$996$	−19.8005	−	11.3631i	−0.627403	−	0.360053i
$997$	−2.14132	+	1.85546i	−0.0678163	+	0.0587631i	−0.688109	−	0.725607i	$-0.741559\pi$
$997$	−2.14132	+	1.85546i	−0.0678163	+	0.0587631i	0.620293	+	0.784370i	$0.287014\pi$
$998$	−34.0502	+	4.89568i	−1.07784	+	0.154970i
$999$	−17.5470	−	2.38293i	−0.555163	−	0.0753925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.9	✓	600
3.2	odd	2	inner	483.2.v.a.41.52	yes	600
7.6	odd	2	inner	483.2.v.a.41.10	yes	600
21.20	even	2	inner	483.2.v.a.41.51	yes	600
23.9	even	11	inner	483.2.v.a.377.51	yes	600
69.32	odd	22	inner	483.2.v.a.377.10	yes	600
161.55	odd	22	inner	483.2.v.a.377.52	yes	600
483.377	even	22	inner	483.2.v.a.377.9	yes	600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.9	✓	600	1.1	even	1	trivial
483.2.v.a.41.10	yes	600	7.6	odd	2	inner
483.2.v.a.41.51	yes	600	21.20	even	2	inner
483.2.v.a.41.52	yes	600	3.2	odd	2	inner
483.2.v.a.377.9	yes	600	483.377	even	22	inner
483.2.v.a.377.10	yes	600	69.32	odd	22	inner
483.2.v.a.377.51	yes	600	23.9	even	11	inner
483.2.v.a.377.52	yes	600	161.55	odd	22	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.601323 + 2.04792i) q^{2} +(-0.160145 + 1.72463i) q^{3} +(-2.14987 - 1.38164i) q^{4} +(-0.358395 + 2.49269i) q^{5} +(-3.43560 - 1.36502i) q^{6} +(-2.54603 + 0.719520i) q^{7} +(0.896135 - 0.776505i) q^{8} +(-2.94871 - 0.552383i) q^{9} +(-4.88932 - 2.23288i) q^{10} +(0.357014 + 1.21588i) q^{11} +(2.72710 - 3.48647i) q^{12} +(6.26424 + 2.86078i) q^{13} +(0.0574705 - 5.64673i) q^{14} +(-4.24158 - 1.01729i) q^{15} +(-1.07188 - 2.34708i) q^{16} +(4.94927 - 3.18070i) q^{17} +(2.90436 - 5.70655i) q^{18} +(-2.59233 + 4.03374i) q^{19} +(4.21450 - 4.86379i) q^{20} +(-0.833172 - 4.50620i) q^{21} -2.70470 q^{22} +(-3.20197 - 3.57035i) q^{23} +(1.19567 + 1.66986i) q^{24} +(-1.28761 - 0.378075i) q^{25} +(-9.62548 + 11.1084i) q^{26} +(1.42488 - 4.99697i) q^{27} +(6.46775 + 1.97082i) q^{28} +(2.68457 + 4.17728i) q^{29} +(4.63389 - 8.07468i) q^{30} +(-1.68716 + 1.46193i) q^{31} +(7.79855 - 1.12126i) q^{32} +(-2.15411 + 0.421000i) q^{33} +(3.53771 + 12.0483i) q^{34} +(-0.881057 - 6.60435i) q^{35} +(5.57614 + 5.26159i) q^{36} +(-0.484998 - 3.37323i) q^{37} +(-6.70194 - 7.73445i) q^{38} +(-5.93699 + 10.3454i) q^{39} +(1.61442 + 2.51208i) q^{40} +(-0.362478 + 2.52109i) q^{41} +(9.72932 + 1.00341i) q^{42} +(0.810224 - 0.935049i) q^{43} +(0.912367 - 3.10724i) q^{44} +(2.43372 - 7.15225i) q^{45} +(9.23719 - 4.41044i) q^{46} -4.02234 q^{47} +(4.21951 - 1.47272i) q^{48} +(5.96458 - 3.66385i) q^{49} +(1.54853 - 2.40956i) q^{50} +(4.69294 + 9.04505i) q^{51} +(-9.51473 - 14.8052i) q^{52} +(-5.33728 + 2.43745i) q^{53} +(9.37657 + 5.92282i) q^{54} +(-3.15876 + 0.454161i) q^{55} +(-1.72288 + 2.62180i) q^{56} +(-6.54157 - 5.11679i) q^{57} +(-10.1690 + 2.98589i) q^{58} +(-1.15440 + 2.52779i) q^{59} +(7.71331 + 8.04736i) q^{60} +(2.90140 - 2.51408i) q^{61} +(-1.97939 - 4.33425i) q^{62} +(7.90496 - 0.715268i) q^{63} +(-1.65878 + 11.5370i) q^{64} +(-9.37613 + 14.5895i) q^{65} +(0.433144 - 4.66460i) q^{66} +(10.4727 + 3.07507i) q^{67} -15.0349 q^{68} +(6.67031 - 4.95045i) q^{69} +(14.0550 + 2.16702i) q^{70} +(4.05783 - 13.8197i) q^{71} +(-3.07137 + 1.79468i) q^{72} +(-8.37846 + 13.0371i) q^{73} +(7.19974 + 1.03517i) q^{74} +(0.858244 - 2.16010i) q^{75} +(11.1463 - 5.09035i) q^{76} +(-1.78382 - 2.83879i) q^{77} +(-17.6164 - 18.3794i) q^{78} +(-1.68209 + 3.68326i) q^{79} +(6.23472 - 1.83068i) q^{80} +(8.38975 + 3.25763i) q^{81} +(-4.94501 - 2.25831i) q^{82} +(-0.734004 - 5.10511i) q^{83} +(-4.43472 + 10.8389i) q^{84} +(6.15472 + 13.4770i) q^{85} +(1.42770 + 2.22154i) q^{86} +(-7.63419 + 3.96093i) q^{87} +(1.26407 + 0.812367i) q^{88} +(-8.18741 + 9.44878i) q^{89} +(13.1838 + 9.28487i) q^{90} +(-18.0074 - 2.77640i) q^{91} +(1.95089 + 12.0997i) q^{92} +(-2.25110 - 3.14385i) q^{93} +(2.41873 - 8.23742i) q^{94} +(-9.12580 - 7.90755i) q^{95} +(0.684863 + 13.6292i) q^{96} +(-10.8781 - 1.56404i) q^{97} +(3.91661 + 14.4181i) q^{98} +(-0.381099 - 3.78247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) \) 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Introduction

L-functions

Modular forms

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