LMFDB - Embedded newform 483.2.v.a.41.14

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			41.14
Character	$\chi$	$=$	483.41
Dual form			483.2.v.a.377.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.493988 + 1.68237i) q^{2} +(0.151912 - 1.72538i) q^{3} +(-0.903836 - 0.580860i) q^{4} +(-0.558871 + 3.88703i) q^{5} +(2.82768 + 1.10789i) q^{6} +(-1.99258 - 1.74058i) q^{7} +(-1.22655 + 1.06281i) q^{8} +(-2.95385 - 0.524209i) q^{9} +(-6.26335 - 2.86037i) q^{10} +(-1.22718 - 4.17938i) q^{11} +(-1.13951 + 1.47122i) q^{12} +(-1.88613 - 0.861367i) q^{13} +(3.91261 - 2.49244i) q^{14} +(6.62169 + 1.55475i) q^{15} +(-2.07478 - 4.54313i) q^{16} +(-1.78108 + 1.14463i) q^{17} +(2.34108 - 4.71051i) q^{18} +(-1.42444 + 2.21647i) q^{19} +(2.76295 - 3.18861i) q^{20} +(-3.30585 + 3.17354i) q^{21} +7.63748 q^{22} +(4.27389 + 2.17574i) q^{23} +(1.64742 + 2.27771i) q^{24} +(-9.99921 - 2.93603i) q^{25} +(2.38086 - 2.74766i) q^{26} +(-1.35318 + 5.01686i) q^{27} +(0.789938 + 2.73061i) q^{28} +(-0.621661 - 0.967323i) q^{29} +(-5.88670 + 10.3721i) q^{30} +(0.602646 - 0.522195i) q^{31} +(5.45526 - 0.784348i) q^{32} +(-7.39743 + 1.48245i) q^{33} +(-1.04586 - 3.56187i) q^{34} +(7.87927 - 6.77248i) q^{35} +(2.36530 + 2.18957i) q^{36} +(-1.02173 - 7.10631i) q^{37} +(-3.02527 - 3.49135i) q^{38} +(-1.77271 + 3.12343i) q^{39} +(-3.44569 - 5.36161i) q^{40} +(0.650274 - 4.52275i) q^{41} +(-3.70602 - 7.12935i) q^{42} +(-5.13293 + 5.92372i) q^{43} +(-1.31847 + 4.49029i) q^{44} +(3.68844 - 11.1887i) q^{45} +(-5.77165 + 6.11548i) q^{46} -9.37202 q^{47} +(-8.15378 + 2.88962i) q^{48} +(0.940785 + 6.93649i) q^{49} +(9.87898 - 15.3720i) q^{50} +(1.70435 + 3.24691i) q^{51} +(1.20442 + 1.87411i) q^{52} +(-8.95765 + 4.09082i) q^{53} +(-7.77176 - 4.75482i) q^{54} +(16.9312 - 2.43434i) q^{55} +(4.29390 + 0.0171625i) q^{56} +(3.60786 + 2.79440i) q^{57} +(1.93449 - 0.568017i) q^{58} +(-4.97577 + 10.8954i) q^{59} +(-5.08183 - 5.25151i) q^{60} +(3.12603 - 2.70872i) q^{61} +(0.580826 + 1.27183i) q^{62} +(4.97336 + 6.18593i) q^{63} +(0.0463023 - 0.322040i) q^{64} +(4.40226 - 6.85005i) q^{65} +(1.16022 - 13.1775i) q^{66} +(7.89696 + 2.31876i) q^{67} +2.27467 q^{68} +(4.40322 - 7.04355i) q^{69} +(7.50155 + 16.6014i) q^{70} +(-0.509646 + 1.73569i) q^{71} +(4.18017 - 2.49641i) q^{72} +(0.202891 - 0.315705i) q^{73} +(12.4602 + 1.79150i) q^{74} +(-6.58476 + 16.8064i) q^{75} +(2.57492 - 1.17593i) q^{76} +(-4.82928 + 10.4638i) q^{77} +(-4.37907 - 4.52529i) q^{78} +(-0.623336 + 1.36491i) q^{79} +(18.8188 - 5.52570i) q^{80} +(8.45041 + 3.09687i) q^{81} +(7.28772 + 3.32819i) q^{82} +(2.36036 + 16.4166i) q^{83} +(4.83133 - 0.948129i) q^{84} +(-3.45382 - 7.56281i) q^{85} +(-7.43027 - 11.5617i) q^{86} +(-1.76343 + 0.925651i) q^{87} +(5.94708 + 3.82196i) q^{88} +(-6.73704 + 7.77495i) q^{89} +(17.0015 + 11.7324i) q^{90} +(2.25900 + 4.99930i) q^{91} +(-2.59910 - 4.44904i) q^{92} +(-0.809435 - 1.11912i) q^{93} +(4.62967 - 15.7672i) q^{94} +(-7.81942 - 6.77557i) q^{95} +(-0.524578 - 9.53152i) q^{96} +(-1.26788 - 0.182293i) q^{97} +(-12.1345 - 1.84380i) q^{98} +(1.43402 + 12.9885i) 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 $

$2$	−0.493988	+	1.68237i	−0.349302	+	1.18961i	0.578230	+	0.815873i	$0.303743\pi$
$2$	−0.493988	+	1.68237i	−0.349302	+	1.18961i	−0.927533	+	0.373741i	$0.878075\pi$
$3$	0.151912	−	1.72538i	0.0877062	−	0.996146i
$3$	0.151912	−	1.72538i	0.0877062	−	0.996146i
$4$	−0.903836	−	0.580860i	−0.451918	−	0.290430i
$5$	−0.558871	+	3.88703i	−0.249935	+	1.73833i	0.348632	+	0.937260i	$0.386646\pi$
$5$	−0.558871	+	3.88703i	−0.249935	+	1.73833i	−0.598566	+	0.801073i	$0.704263\pi$
$6$	2.82768	+	1.10789i	1.15439	+	0.452293i
$7$	−1.99258	−	1.74058i	−0.753126	−	0.657876i
$7$	−1.99258	−	1.74058i	−0.753126	−	0.657876i
$8$	−1.22655	+	1.06281i	−0.433650	+	0.375760i
$9$	−2.95385	−	0.524209i	−0.984615	−	0.174736i
$10$	−6.26335	−	2.86037i	−1.98064	−	0.904530i
$11$	−1.22718	−	4.17938i	−0.370008	−	1.26013i	−0.908637	−	0.417588i	$-0.862876\pi$
$11$	−1.22718	−	4.17938i	−0.370008	−	1.26013i	0.538629	−	0.842543i	$-0.318943\pi$
$12$	−1.13951	+	1.47122i	−0.328947	+	0.424704i
$13$	−1.88613	−	0.861367i	−0.523118	−	0.238900i	0.136312	−	0.990666i	$-0.456475\pi$
$13$	−1.88613	−	0.861367i	−0.523118	−	0.238900i	−0.659430	+	0.751766i	$0.729202\pi$
$14$	3.91261	−	2.49244i	1.04569	−	0.666132i
$15$	6.62169	+	1.55475i	1.70971	+	0.401434i
$16$	−2.07478	−	4.54313i	−0.518694	−	1.13578i
$17$	−1.78108	+	1.14463i	−0.431975	+	0.277613i	−0.738506	−	0.674247i	$-0.764468\pi$
$17$	−1.78108	+	1.14463i	−0.431975	+	0.277613i	0.306531	+	0.951861i	$0.400832\pi$
$18$	2.34108	−	4.71051i	0.551798	−	1.11028i
$19$	−1.42444	+	2.21647i	−0.326789	+	0.508494i	−0.965309	−	0.261112i	$-0.915911\pi$
$19$	−1.42444	+	2.21647i	−0.326789	+	0.508494i	0.638519	+	0.769606i	$0.279547\pi$
$20$	2.76295	−	3.18861i	0.617814	−	0.712995i
$21$	−3.30585	+	3.17354i	−0.721395	+	0.692524i
$22$	7.63748			1.62832
$23$	4.27389	+	2.17574i	0.891168	+	0.453673i
$23$	4.27389	+	2.17574i	0.891168	+	0.453673i
$24$	1.64742	+	2.27771i	0.336278	+	0.464936i
$25$	−9.99921	−	2.93603i	−1.99984	−	0.587206i
$26$	2.38086	−	2.74766i	0.466926	−	0.538861i
$27$	−1.35318	+	5.01686i	−0.260420	+	0.965495i
$28$	0.789938	+	2.73061i	0.149284	+	0.516036i
$29$	−0.621661	−	0.967323i	−0.115439	−	0.179627i	0.778726	−	0.627365i	$-0.215866\pi$
$29$	−0.621661	−	0.967323i	−0.115439	−	0.179627i	−0.894165	+	0.447737i	$0.852230\pi$
$30$	−5.88670	+	10.3721i	−1.07476	+	1.89368i
$31$	0.602646	−	0.522195i	0.108238	−	0.0937891i	−0.599060	−	0.800704i	$-0.704459\pi$
$31$	0.602646	−	0.522195i	0.108238	−	0.0937891i	0.707299	+	0.706915i	$0.249914\pi$
$32$	5.45526	−	0.784348i	0.964363	−	0.138654i
$33$	−7.39743	+	1.48245i	−1.28773	+	0.258061i
$34$	−1.04586	−	3.56187i	−0.179363	−	0.610855i
$35$	7.87927	−	6.77248i	1.33184	−	1.14476i
$36$	2.36530	+	2.18957i	0.394217	+	0.364928i
$37$	−1.02173	−	7.10631i	−0.167972	−	1.16827i	−0.883068	−	0.469245i	$-0.844526\pi$
$37$	−1.02173	−	7.10631i	−0.167972	−	1.16827i	0.715096	−	0.699026i	$-0.246383\pi$
$38$	−3.02527	−	3.49135i	−0.490764	−	0.566371i
$39$	−1.77271	+	3.12343i	−0.283860	+	0.500149i
$40$	−3.44569	−	5.36161i	−0.544812	−	0.847744i
$41$	0.650274	−	4.52275i	0.101556	−	0.706336i	−0.873895	−	0.486116i	$-0.838413\pi$
$41$	0.650274	−	4.52275i	0.101556	−	0.706336i	0.975450	−	0.220220i	$-0.0706775\pi$
$42$	−3.70602	−	7.12935i	−0.571852	−	1.10008i
$43$	−5.13293	+	5.92372i	−0.782764	+	0.903358i	−0.997306	−	0.0733566i	$-0.976629\pi$
$43$	−5.13293	+	5.92372i	−0.782764	+	0.903358i	0.214541	+	0.976715i	$0.431174\pi$
$44$	−1.31847	+	4.49029i	−0.198767	+	0.676937i
$45$	3.68844	−	11.1887i	0.549840	−	1.66792i
$46$	−5.77165	+	6.11548i	−0.850983	+	0.901678i
$47$	−9.37202			−1.36705			−0.683525	−	0.729927i	$-0.739554\pi$
$47$	−9.37202			−1.36705			−0.683525	+	0.729927i	$0.739554\pi$
$48$	−8.15378	+	2.88962i	−1.17690	+	0.417080i
$49$	0.940785	+	6.93649i	0.134398	+	0.990927i
$50$	9.87898	−	15.3720i	1.39710	−	2.17393i
$51$	1.70435	+	3.24691i	0.238657	+	0.454659i
$52$	1.20442	+	1.87411i	0.167023	+	0.259893i
$53$	−8.95765	+	4.09082i	−1.23043	+	0.561917i	−0.921207	−	0.389073i	$-0.872795\pi$
$53$	−8.95765	+	4.09082i	−1.23043	+	0.561917i	−0.309220	+	0.950990i	$0.600068\pi$
$54$	−7.77176	−	4.75482i	−1.05760	−	0.647049i
$55$	16.9312	−	2.43434i	2.28300	−	0.328247i
$56$	4.29390	+	0.0171625i	0.573797	+	0.00229344i
$57$	3.60786	+	2.79440i	0.477873	+	0.370128i
$58$	1.93449	−	0.568017i	0.254011	−	0.0745843i
$59$	−4.97577	+	10.8954i	−0.647790	+	1.41846i	0.245685	+	0.969350i	$0.420987\pi$
$59$	−4.97577	+	10.8954i	−0.647790	+	1.41846i	−0.893475	+	0.449113i	$0.851740\pi$
$60$	−5.08183	−	5.25151i	−0.656062	−	0.677967i
$61$	3.12603	−	2.70872i	0.400247	−	0.346816i	−0.431361	−	0.902180i	$-0.641966\pi$
$61$	3.12603	−	2.70872i	0.400247	−	0.346816i	0.831608	+	0.555363i	$0.187421\pi$
$62$	0.580826	+	1.27183i	0.0737650	+	0.161523i
$63$	4.97336	+	6.18593i	0.626584	+	0.779354i
$64$	0.0463023	−	0.322040i	0.00578779	−	0.0402550i
$65$	4.40226	−	6.85005i	0.546033	−	0.849644i
$66$	1.16022	−	13.1775i	0.142813	−	1.62204i
$67$	7.89696	+	2.31876i	0.964767	+	0.283281i	0.725922	−	0.687777i	$-0.241413\pi$
$67$	7.89696	+	2.31876i	0.964767	+	0.283281i	0.238845	+	0.971058i	$0.423231\pi$
$68$	2.27467			0.275845
$69$	4.40322	−	7.04355i	0.530086	−	0.847944i
$70$	7.50155	+	16.6014i	0.896606	+	1.98424i
$71$	−0.509646	+	1.73569i	−0.0604838	+	0.205989i	−0.984191	−	0.177110i	$-0.943325\pi$
$71$	−0.509646	+	1.73569i	−0.0604838	+	0.205989i	0.923707	+	0.383099i	$0.125143\pi$
$72$	4.18017	−	2.49641i	0.492638	−	0.294205i
$73$	0.202891	−	0.315705i	0.0237466	−	0.0369505i	−0.829177	−	0.558986i	$-0.811191\pi$
$73$	0.202891	−	0.315705i	0.0237466	−	0.0369505i	0.852924	+	0.522035i	$0.174827\pi$
$74$	12.4602	+	1.79150i	1.44847	+	0.208258i
$75$	−6.58476	+	16.8064i	−0.760342	+	1.94063i
$76$	2.57492	−	1.17593i	0.295364	−	0.134888i
$77$	−4.82928	+	10.4638i	−0.550348	+	1.19246i
$78$	−4.37907	−	4.52529i	−0.495832	−	0.512388i
$79$	−0.623336	+	1.36491i	−0.0701307	+	0.153565i	−0.941451	−	0.337150i	$-0.890537\pi$
$79$	−0.623336	+	1.36491i	−0.0701307	+	0.153565i	0.871320	+	0.490715i	$0.163264\pi$
$80$	18.8188	−	5.52570i	2.10401	−	0.617792i
$81$	8.45041	+	3.09687i	0.938934	+	0.344096i
$82$	7.28772	+	3.32819i	0.804794	+	0.367537i
$83$	2.36036	+	16.4166i	0.259083	+	1.80196i	0.539397	+	0.842052i	$0.318652\pi$
$83$	2.36036	+	16.4166i	0.259083	+	1.80196i	−0.280314	+	0.959908i	$0.590439\pi$
$84$	4.83133	−	0.948129i	0.527141	−	0.103449i
$85$	−3.45382	−	7.56281i	−0.374619	−	0.820302i
$86$	−7.43027	−	11.5617i	−0.801227	−	1.24673i
$87$	−1.76343	+	0.925651i	−0.189060	+	0.0992402i
$88$	5.94708	+	3.82196i	0.633961	+	0.407422i
$89$	−6.73704	+	7.77495i	−0.714124	+	0.824143i	−0.990587	−	0.136881i	$-0.956292\pi$
$89$	−6.73704	+	7.77495i	−0.714124	+	0.824143i	0.276463	+	0.961025i	$0.410838\pi$
$90$	17.0015	+	11.7324i	1.79212	+	1.23670i
$91$	2.25900	+	4.99930i	0.236807	+	0.524069i
$92$	−2.59910	−	4.44904i	−0.270975	−	0.463845i
$93$	−0.809435	−	1.11912i	−0.0839345	−	0.116047i
$94$	4.62967	−	15.7672i	0.477514	−	1.62626i
$95$	−7.81942	−	6.77557i	−0.802256	−	0.695158i
$96$	−0.524578	−	9.53152i	−0.0535395	−	0.972807i
$97$	−1.26788	−	0.182293i	−0.128734	−	0.0185091i	0.0776468	−	0.996981i	$-0.475259\pi$
$97$	−1.26788	−	0.182293i	−0.128734	−	0.0185091i	−0.206380	+	0.978472i	$0.566168\pi$
$98$	−12.1345	−	1.84380i	−1.22577	−	0.186252i
$99$	1.43402	+	12.9885i	0.144125	+	1.30540i
$100$	7.33222	+	8.46183i	0.733222	+	0.846183i
$101$	−2.57556	−	17.9134i	−0.256278	−	1.78245i	−0.558795	−	0.829306i	$-0.688736\pi$
$101$	−2.57556	−	17.9134i	−0.256278	−	1.78245i	0.302518	−	0.953144i	$-0.402173\pi$
$102$	−6.30444	+	1.26341i	−0.624232	+	0.125096i
$103$	0.229998	+	0.783301i	0.0226624	+	0.0771810i	0.970048	−	0.242914i	$-0.0781033\pi$
$103$	0.229998	+	0.783301i	0.0226624	+	0.0771810i	−0.947385	+	0.320095i	$0.896285\pi$
$104$	3.22890	−	0.948090i	0.316620	−	0.0929679i
$105$	−10.4881	−	14.6235i	−1.02354	−	1.42711i
$106$	−2.45730	−	17.0909i	−0.238674	−	1.66001i
$107$	11.0719	−	9.59384i	1.07036	−	0.927471i	0.0728033	−	0.997346i	$-0.476805\pi$
$107$	11.0719	−	9.59384i	1.07036	−	0.927471i	0.997556	+	0.0698749i	$0.0222600\pi$
$108$	4.13715	−	3.74841i	0.398097	−	0.360691i
$109$	−5.12509	+	3.29369i	−0.490894	+	0.315479i	−0.762565	−	0.646912i	$-0.776060\pi$
$109$	−5.12509	+	3.29369i	−0.490894	+	0.315479i	0.271671	+	0.962390i	$0.412424\pi$
$110$	−4.26836	+	29.6871i	−0.406972	+	2.83055i
$111$	−12.4163	+	0.683343i	−1.17850	+	0.0648601i
$112$	−3.77349	+	12.6639i	−0.356562	+	1.19662i
$113$	−1.53221	+	5.21824i	−0.144138	+	0.490890i	−0.999638	−	0.0269135i	$-0.991432\pi$
$113$	−1.53221	+	5.21824i	−0.144138	+	0.490890i	0.855499	+	0.517804i	$0.173250\pi$
$114$	−6.48346	+	4.68935i	−0.607232	+	0.439198i
$115$	−10.8457	+	15.3968i	−1.01137	+	1.43576i
$116$			1.23540i			0.114704i
$117$	5.11980	+	3.53307i	0.473326	+	0.326633i
$118$	−15.8721	−	13.7533i	−1.46115	−	1.26609i
$119$	5.54126	+	0.819333i	0.507967	+	0.0751081i
$120$	−9.77423	+	5.13063i	−0.892261	+	0.468360i
$121$	−6.70748	+	4.31063i	−0.609771	+	0.391876i
$122$	3.01285	+	6.59721i	0.272770	+	0.597284i
$123$	−7.70467	−	1.80903i	−0.694707	−	0.163114i
$124$	−0.848015	+	0.121926i	−0.0761540	+	0.0109493i
$125$	8.84403	−	19.3657i	0.791035	−	1.73212i
$126$	−12.8638	+	5.31125i	−1.14600	+	0.473164i
$127$	11.0189	−	3.23544i	0.977770	−	0.287099i	0.246467	−	0.969151i	$-0.420730\pi$
$127$	11.0189	−	3.23544i	0.977770	−	0.287099i	0.731304	+	0.682052i	$0.238912\pi$
$128$	10.5455	+	4.81598i	0.932102	+	0.425677i
$129$	9.44089	+	9.75612i	0.831224	+	0.858978i
$130$	9.34965	+	10.7901i	0.820019	+	0.946352i
$131$	−2.12230	−	4.64719i	−0.185426	−	0.406027i	0.793975	−	0.607950i	$-0.208008\pi$
$131$	−2.12230	−	4.64719i	−0.185426	−	0.406027i	−0.979401	+	0.201923i	$0.935281\pi$
$132$	7.54715	+	2.95698i	0.656895	+	0.257372i
$133$	6.69626	−	1.93716i	0.580639	−	0.167973i
$134$	−7.80201	+	12.1402i	−0.673991	+	1.04875i
$135$	−18.7444	−	8.06364i	−1.61326	−	0.694007i
$136$	0.968055	−	3.29689i	0.0830100	−	0.282706i
$137$			22.1754i			1.89457i	0.320390	+	0.947286i	$0.396186\pi$
$137$			22.1754i			1.89457i	−0.320390	+	0.947286i	$0.603814\pi$
$138$	9.67472	+	10.8873i	0.823567	+	0.926787i
$139$		−	13.0848i		−	1.10984i	−0.831904	−	0.554920i	$-0.812749\pi$
$139$		−	13.0848i		−	1.10984i	0.831904	−	0.554920i	$-0.187251\pi$
$140$	−11.0554	+	1.54446i	−0.934355	+	0.130530i
$141$	−1.42372	+	16.1703i	−0.119899	+	1.36178i
$142$	−2.66832	−	1.71483i	−0.223921	−	0.143905i
$143$	−1.28536	+	8.93991i	−0.107488	+	0.747592i
$144$	3.74702	+	14.5073i	0.312252	+	1.20894i
$145$	4.10744	−	1.87581i	0.341104	−	0.155777i
$146$	0.430906	+	0.497293i	0.0356621	+	0.0411562i
$147$	12.1110	−	0.569474i	0.998896	−	0.0469695i
$148$	−3.20429	+	7.01643i	−0.263391	+	0.576747i
$149$	1.76192	+	6.00055i	0.144342	+	0.491584i	0.999648	−	0.0265395i	$-0.00844877\pi$
$149$	1.76192	+	6.00055i	0.144342	+	0.491584i	−0.855306	+	0.518124i	$0.826631\pi$
$150$	−25.0217	−	19.3801i	−2.04302	−	1.58238i
$151$	3.59727	−	7.87693i	0.292742	−	0.641015i	−0.704925	−	0.709282i	$-0.749020\pi$
$151$	3.59727	−	7.87693i	0.292742	−	0.641015i	0.997667	+	0.0682664i	$0.0217468\pi$
$152$	−0.608545	−	4.23252i	−0.0493595	−	0.343303i
$153$	5.86106	−	2.44740i	0.473838	−	0.197861i
$154$	−15.2183	−	13.2936i	−1.22633	−	1.07123i
$155$	1.69299	+	2.63434i	0.135984	+	0.211595i
$156$	3.41651	−	1.79338i	0.273540	−	0.143585i
$157$	−7.69133	+	11.9679i	−0.613835	+	0.955145i	0.385637	+	0.922651i	$0.373982\pi$
$157$	−7.69133	+	11.9679i	−0.613835	+	0.955145i	−0.999472	+	0.0324950i	$0.989655\pi$
$158$	−1.98837	−	1.72293i	−0.158186	−	0.137069i
$159$	5.69743	+	16.0768i	0.451836	+	1.27497i
$160$			21.6431i			1.71104i
$161$	−4.72905	−	11.7744i	−0.372701	−	0.927951i
$162$	−9.38448	+	12.6869i	−0.737314	+	0.996777i
$163$	10.7895	+	3.16808i	0.845099	+	0.248144i	0.675491	−	0.737368i	$-0.263932\pi$
$163$	10.7895	+	3.16808i	0.845099	+	0.248144i	0.169608	+	0.985512i	$0.445750\pi$
$164$	−3.21483	+	3.71011i	−0.251036	+	0.289711i
$165$	−1.62811	−	29.5825i	−0.126748	−	2.30300i
$166$	−28.7848	−	4.13864i	−2.23414	−	0.321220i
$167$	−1.45120	+	0.932628i	−0.112297	+	0.0721689i	−0.595584	−	0.803293i	$-0.703079\pi$
$167$	−1.45120	+	0.932628i	−0.112297	+	0.0721689i	0.483287	+	0.875462i	$0.339443\pi$
$168$	0.681906	−	7.40599i	0.0526102	−	0.571385i
$169$	−5.69766	−	6.57545i	−0.438281	−	0.505804i
$170$	14.4296	−	2.07466i	1.10670	−	0.159119i
$171$	5.36947	−	5.80041i	0.410614	−	0.443569i
$172$	8.08018	−	2.37255i	0.616108	−	0.180906i
$173$	−5.13414	+	1.50752i	−0.390341	+	0.114615i	−0.471013	−	0.882126i	$-0.656112\pi$
$173$	−5.13414	+	1.50752i	−0.390341	+	0.114615i	0.0806719	+	0.996741i	$0.474293\pi$
$174$	−0.686172	−	3.42401i	−0.0520185	−	0.259573i
$175$	14.8139	+	23.2547i	1.11982	+	1.75789i
$176$	−16.4413	+	14.2465i	−1.23931	+	1.07387i
$177$	18.0428	+	10.2402i	1.35618	+	0.769702i
$178$	−9.75233	−	15.1749i	−0.730968	−	1.13741i
$179$	−12.1613	−	1.74853i	−0.908977	−	0.130691i	−0.328063	−	0.944656i	$-0.606396\pi$
$179$	−12.1613	−	1.74853i	−0.908977	−	0.130691i	−0.580914	+	0.813965i	$0.697305\pi$
$180$	−9.83282	+	7.97031i	−0.732895	+	0.594072i
$181$	−4.36980	−	3.78646i	−0.324805	−	0.281445i	0.477160	−	0.878817i	$-0.341666\pi$
$181$	−4.36980	−	3.78646i	−0.324805	−	0.281445i	−0.801965	+	0.597371i	$0.796212\pi$
$182$	−9.52659	+	1.33087i	−0.706158	+	0.0986510i
$183$	−4.19868	−	5.80506i	−0.310375	−	0.429123i
$184$	−7.55453	+	1.87369i	−0.556928	+	0.138130i
$185$	28.1935			2.07283
$186$	2.28262	−	0.808937i	0.167370	−	0.0593142i
$187$	6.96954	+	6.03914i	0.509663	+	0.441626i
$188$	8.47077	+	5.44383i	0.617794	+	0.397032i
$189$	11.4286	−	7.64120i	0.831306	−	0.555816i
$190$	15.2617	−	9.80810i	1.10720	−	0.711555i
$191$	16.5976	−	7.57986i	1.20096	−	0.548459i	0.288441	−	0.957498i	$-0.406863\pi$
$191$	16.5976	−	7.57986i	1.20096	−	0.548459i	0.912517	+	0.409039i	$0.134136\pi$
$192$	−0.548606	−	0.128810i	−0.0395922	−	0.00929610i
$193$	1.11914	+	7.78381i	0.0805577	+	0.560291i	0.989629	+	0.143650i	$0.0458839\pi$
$193$	1.11914	+	7.78381i	0.0805577	+	0.560291i	−0.909071	+	0.416641i	$0.863207\pi$
$194$	0.933002	−	2.04299i	0.0669857	−	0.146678i
$195$	−11.1502	−	8.63616i	−0.798480	−	0.618448i
$196$	3.17882	−	6.81592i	0.227058	−	0.486851i
$197$	−24.6341	−	11.2500i	−1.75511	−	0.801530i	−0.986901	−	0.161328i	$-0.948422\pi$
$197$	−24.6341	−	11.2500i	−1.75511	−	0.801530i	−0.768206	−	0.640203i	$-0.778850\pi$
$198$	−22.5599	−	4.00364i	−1.60326	−	0.284526i
$199$	19.5803	−	16.9664i	1.38801	−	1.20272i	0.434757	−	0.900548i	$-0.356834\pi$
$199$	19.5803	−	16.9664i	1.38801	−	1.20272i	0.953254	−	0.302171i	$-0.0977113\pi$
$200$	15.3850	−	7.02608i	1.08788	−	0.496819i
$201$	5.20037	−	13.2730i	0.366806	−	0.936204i
$202$	31.4092	+	4.51597i	2.20995	+	0.317742i
$203$	−0.444988	+	3.00952i	−0.0312321	+	0.211227i
$204$	0.345549	−	3.92466i	0.0241933	−	0.274782i
$205$	17.2167	+	5.05527i	1.20246	+	0.353075i
$206$	−1.43142			−0.0997317
$207$	−11.4839	−	8.66721i	−0.798185	−	0.602413i
$208$			10.3561i			0.718064i
$209$	11.0115	+	3.23328i	0.761683	+	0.223650i
$210$	29.7832	−	10.4210i	2.05524	−	0.719121i
$211$	3.28049	+	2.10825i	0.225839	+	0.145138i	0.648668	−	0.761072i	$-0.275327\pi$
$211$	3.28049	+	2.10825i	0.225839	+	0.145138i	−0.422829	+	0.906209i	$0.638963\pi$
$212$	10.4724	+	1.50571i	0.719250	+	0.103413i
$213$	2.91731	+	1.14300i	0.199890	+	0.0783173i
$214$	10.6710	+	23.3662i	0.729455	+	1.59728i
$215$	−20.1570	−	23.2624i	−1.37470	−	1.58649i
$216$	−3.67223	−	7.59160i	−0.249864	−	0.516543i
$217$	−2.10974	−	0.00843254i	−0.143219	−	0.000572438i
$218$	−3.00948	−	10.2493i	−0.203827	−	0.694173i
$219$	−0.513888	−	0.398023i	−0.0347253	−	0.0268959i
$220$	−16.7171	−	7.63442i	−1.12706	−	0.514713i
$221$	4.34529	−	0.624758i	0.292296	−	0.0420258i
$222$	4.98386	−	21.2263i	0.334495	−	1.42462i
$223$	−25.3693	+	11.5858i	−1.69886	+	0.775842i	−0.700811	+	0.713347i	$0.747179\pi$
$223$	−25.3693	+	11.5858i	−1.69886	+	0.775842i	−0.998045	+	0.0624952i	$0.980094\pi$
$224$	−12.2353	−	7.93242i	−0.817504	−	0.530007i
$225$	27.9970	+	13.9143i	1.86647	+	0.927618i
$226$	−8.02211	−	5.15549i	−0.533623	−	0.342938i
$227$	12.4325	−	14.3479i	0.825176	−	0.952304i	−0.174299	−	0.984693i	$-0.555766\pi$
$227$	12.4325	−	14.3479i	0.825176	−	0.952304i	0.999475	+	0.0323885i	$0.0103114\pi$
$228$	−1.63776	−	4.62134i	−0.108463	−	0.306056i
$229$			7.77742i			0.513946i	0.966419	+	0.256973i	$0.0827252\pi$
$229$			7.77742i			0.513946i	−0.966419	+	0.256973i	$0.917275\pi$
$230$	−20.5454	−	25.8523i	−1.35473	−	1.70465i
$231$	17.3203	+	9.92189i	1.13959	+	0.652813i
$232$	1.79058	+	0.525761i	0.117557	+	0.0345179i
$233$	−3.92459	−	3.40068i	−0.257108	−	0.222786i	0.516763	−	0.856129i	$-0.327137\pi$
$233$	−3.92459	−	3.40068i	−0.257108	−	0.222786i	−0.773871	+	0.633343i	$0.781682\pi$
$234$	−8.47305	+	6.86810i	−0.553901	+	0.448982i
$235$	5.23775	−	36.4293i	0.341673	−	2.37639i
$236$	10.8260	−	6.95744i	0.704712	−	0.452891i
$237$	2.26030	+	1.28283i	0.146822	+	0.0833291i
$238$	−4.11574	+	8.91771i	−0.266784	+	0.578050i
$239$	3.27363	−	0.470677i	0.211753	−	0.0304455i	−0.0356216	−	0.999365i	$-0.511341\pi$
$239$	3.27363	−	0.470677i	0.211753	−	0.0304455i	0.247375	+	0.968920i	$0.420432\pi$
$240$	−6.67511	−	33.3089i	−0.430877	−	2.15008i
$241$	−1.26913	−	4.32227i	−0.0817520	−	0.278422i	0.908464	−	0.417962i	$-0.137256\pi$
$241$	−1.26913	−	4.32227i	−0.0817520	−	0.278422i	−0.990216	+	0.139541i	$0.955437\pi$
$242$	−3.93866	−	13.4139i	−0.253187	−	0.862275i
$243$	6.62698	−	14.1097i	0.425121	−	0.905137i
$244$	−4.39881	+	0.632453i	−0.281605	+	0.0404886i
$245$	−27.4881	−	0.219741i	−1.75615	−	0.0140387i
$246$	6.84947	−	12.0685i	0.436706	−	0.769457i
$247$	4.59588	−	2.95359i	0.292429	−	0.187932i
$248$	−0.184179	+	1.28100i	−0.0116954	+	0.0813433i
$249$	28.6834	−	1.57862i	1.81774	−	0.100041i
$250$	28.2115	+	24.4454i	1.78425	+	1.54606i
$251$	−13.6253	−	4.00076i	−0.860023	−	0.252526i	−0.178157	−	0.984002i	$-0.557013\pi$
$251$	−13.6253	−	4.00076i	−0.860023	−	0.252526i	−0.681867	+	0.731477i	$0.738832\pi$
$252$	−0.901944	−	8.47989i	−0.0568171	−	0.534183i
$253$	3.84842	−	20.5322i	0.241948	−	1.29085i
$254$			20.1362i			1.26345i
$255$	−13.5734	+	4.81026i	−0.849997	+	0.301230i
$256$	−12.8855	+	14.8707i	−0.805344	+	0.929417i
$257$	−9.40755	−	6.04587i	−0.586827	−	0.377131i	0.213277	−	0.976992i	$-0.431586\pi$
$257$	−9.40755	−	6.04587i	−0.586827	−	0.377131i	−0.800104	+	0.599861i	$0.795223\pi$
$258$	−21.0771	+	11.0637i	−1.31220	+	0.688793i
$259$	−10.3332	+	15.9383i	−0.642073	+	0.990360i
$260$	−7.95784	+	3.63423i	−0.493525	+	0.225385i
$261$	1.32921	+	3.18320i	0.0822760	+	0.197035i
$262$	8.86669	−	1.27484i	0.547786	−	0.0787597i
$263$	−2.44888	−	1.11837i	−0.151004	−	0.0689613i	0.338479	−	0.940974i	$-0.390087\pi$
$263$	−2.44888	−	1.11837i	−0.151004	−	0.0689613i	−0.489484	+	0.872012i	$0.662815\pi$
$264$	7.49774	−	9.68035i	0.461454	−	0.595785i
$265$	−10.8950	−	37.1049i	−0.669273	−	2.27933i
$266$	−0.0488528	+	12.2225i	−0.00299536	+	0.749411i
$267$	12.3913	+	12.8050i	0.758334	+	0.783655i
$268$	−5.79068	−	6.68280i	−0.353722	−	0.408217i
$269$	−7.85971	−	17.2104i	−0.479215	−	1.04933i	−0.982679	−	0.185318i	$-0.940668\pi$
$269$	−7.85971	−	17.2104i	−0.479215	−	1.04933i	0.503463	−	0.864017i	$-0.332059\pi$
$270$	22.8256	−	27.5517i	1.38912	−	1.67675i
$271$	17.6181	+	2.53310i	1.07022	+	0.153875i	0.654838	−	0.755770i	$-0.272737\pi$
$271$	17.6181	+	2.53310i	1.07022	+	0.153875i	0.415387	+	0.909645i	$0.363646\pi$
$272$	8.89553	+	5.71681i	0.539371	+	0.346633i
$273$	8.96884	−	3.13817i	0.542819	−	0.189931i
$274$	−37.3072	−	10.9544i	−2.25381	−	0.661778i
$275$			45.3935i			2.73733i
$276$	−8.07111	+	3.80856i	−0.485824	+	0.229248i
$277$	1.25766			0.0755653			0.0377827	−	0.999286i	$-0.487971\pi$
$277$	1.25766			0.0755653			0.0377827	+	0.999286i	$0.487971\pi$
$278$	22.0135	+	6.46375i	1.32028	+	0.387670i
$279$	−2.05386	+	1.22657i	−0.122962	+	0.0734330i
$280$	−2.46645	+	16.6809i	−0.147398	+	0.996877i
$281$	11.0464	+	1.58824i	0.658975	+	0.0947463i	0.463686	−	0.886000i	$-0.346527\pi$
$281$	11.0464	+	1.58824i	0.658975	+	0.0947463i	0.195289	+	0.980746i	$0.437436\pi$
$282$	−26.5011	−	10.3831i	−1.57811	−	0.618307i
$283$	−23.8672	+	10.8998i	−1.41876	+	0.647926i	−0.969414	−	0.245432i	$-0.921070\pi$
$283$	−23.8672	+	10.8998i	−1.41876	+	0.647926i	−0.449346	+	0.893358i	$0.648343\pi$
$284$	1.46883	−	1.27275i	0.0871591	−	0.0755238i
$285$	−12.8783	+	12.4622i	−0.762842	+	0.738194i
$286$	−14.4053	−	6.57867i	−0.851801	−	0.389005i
$287$	−9.16793	+	7.88012i	−0.541166	+	0.465149i
$288$	−16.5252	−	0.542856i	−0.973754	−	0.0319881i
$289$	−5.19999	+	11.3864i	−0.305882	+	0.669788i
$290$	1.12677	+	7.83686i	0.0661662	+	0.460196i
$291$	−0.507130	+	2.15988i	−0.0297285	+	0.126614i
$292$	−0.366761	+	0.167494i	−0.0214630	+	0.00980185i
$293$	−9.74317	+	6.26156i	−0.569202	+	0.365804i	−0.793364	−	0.608748i	$-0.791672\pi$
$293$	−9.74317	+	6.26156i	−0.569202	+	0.365804i	0.224161	+	0.974552i	$0.428036\pi$
$294$	−5.02461	+	20.6564i	−0.293041	+	1.20471i
$295$	−39.5700	−	25.4301i	−2.30385	−	1.48060i
$296$	8.80587	+	7.63033i	0.511831	+	0.443504i
$297$	22.6280	−	0.501114i	1.31301	−	0.0290776i
$298$	−10.9655			−0.635215
$299$	−6.18701	−	7.78512i	−0.357804	−	0.450225i
$300$	15.7137	−	11.3654i	0.907230	−	0.656181i
$301$	20.5385	−	2.86925i	1.18382	−	0.165381i
$302$	11.4749	+	9.94305i	0.660306	+	0.572158i
$303$	−31.2986	+	1.72255i	−1.79806	+	0.0989580i
$304$	13.0251	+	1.87273i	0.747041	+	0.107408i
$305$	8.78183	+	13.6648i	0.502846	+	0.782444i
$306$	1.22214	+	11.0694i	0.0698651	+	0.632798i
$307$	9.17327	−	7.94868i	0.523546	−	0.453655i	−0.352549	−	0.935793i	$-0.614685\pi$
$307$	9.17327	−	7.94868i	0.523546	−	0.453655i	0.876095	+	0.482138i	$0.160140\pi$
$308$	10.4429	−	6.65239i	0.595037	−	0.379055i
$309$	1.38643	−	0.277841i	0.0788712	−	0.0158058i
$310$	−5.26825	+	1.54690i	−0.299217	+	0.0878580i
$311$	20.6264	−	6.05646i	1.16962	−	0.343431i	0.361454	−	0.932390i	$-0.382280\pi$
$311$	20.6264	−	6.05646i	1.16962	−	0.343431i	0.808163	+	0.588959i	$0.200462\pi$
$312$	−1.14531	−	5.71509i	−0.0648401	−	0.323553i
$313$	−11.0776	+	1.59272i	−0.626142	+	0.0900256i	−0.448080	−	0.893994i	$-0.647892\pi$
$313$	−11.0776	+	1.59272i	−0.626142	+	0.0900256i	−0.178062	+	0.984019i	$0.556983\pi$
$314$	−16.3351	−	18.8517i	−0.921841	−	1.06386i
$315$	−26.8244	+	15.8745i	−1.51138	+	0.894425i
$316$	1.35622	−	0.871588i	0.0762932	−	0.0490307i
$317$	−23.8175	−	3.42443i	−1.33772	−	0.192335i	−0.563955	−	0.825806i	$-0.690721\pi$
$317$	−23.8175	−	3.42443i	−1.33772	−	0.192335i	−0.773767	+	0.633470i	$0.781630\pi$
$318$	−29.8615	+	1.64346i	−1.67455	+	0.0921607i
$319$	−3.27992	+	3.78523i	−0.183640	+	0.211932i
$320$	1.22590	+	0.359957i	0.0685300	+	0.0201222i
$321$	−14.8710	−	20.5606i	−0.830020	−	1.14758i
$322$	22.1450	−	2.13960i	1.23409	−	0.119235i
$323$		−	5.57817i		−	0.310378i
$324$	−5.83894	−	7.70757i	−0.324385	−	0.428198i
$325$	16.3308	+	14.1507i	0.905870	+	0.784941i
$326$	−10.6598	+	16.5869i	−0.590391	+	0.918666i
$327$	4.90430	+	9.34305i	0.271208	+	0.516672i
$328$	4.00924	+	6.23850i	0.221373	+	0.344463i
$329$	18.6745	+	16.3127i	1.02956	+	0.899349i
$330$	50.5730	+	11.8743i	2.78395	+	0.653661i
$331$	−0.557892	−	3.88022i	−0.0306645	−	0.213276i	0.968728	−	0.248125i	$-0.0798143\pi$
$331$	−0.557892	−	3.88022i	−0.0306645	−	0.213276i	−0.999393	+	0.0348483i	$0.988905\pi$
$332$	7.40239	−	16.2090i	0.406259	−	0.889584i
$333$	−0.707153	+	21.5266i	−0.0387517	+	1.17965i
$334$	−0.852150	−	2.90216i	−0.0466276	−	0.158799i
$335$	−13.4265	+	29.3998i	−0.733566	+	1.60629i
$336$	21.2767	+	8.43448i	1.16074	+	0.460139i
$337$	−4.53815	−	5.23730i	−0.247209	−	0.285294i	0.618561	−	0.785737i	$-0.287716\pi$
$337$	−4.53815	−	5.23730i	−0.247209	−	0.285294i	−0.865770	+	0.500443i	$0.833171\pi$
$338$	13.8769	−	6.33737i	0.754804	−	0.344708i
$339$	8.77066	+	3.43635i	0.476357	+	0.186637i
$340$	−1.27125	+	8.84172i	−0.0689431	+	0.479510i
$341$	−2.92201	−	1.87786i	−0.158236	−	0.101692i
$342$	7.10598	+	11.8988i	0.384248	+	0.643412i
$343$	10.1989	−	15.4591i	0.550689	−	0.834711i
$344$		−	12.7211i		−	0.685873i
$345$	24.9177	+	21.0519i	1.34152	+	1.13340i
$346$		−	9.38221i		−	0.504391i
$347$	5.04853	−	17.1937i	0.271019	−	0.923006i	−0.705705	−	0.708506i	$-0.749369\pi$
$347$	5.04853	−	17.1937i	0.271019	−	0.923006i	0.976724	−	0.214500i	$-0.0688123\pi$
$348$	2.13153	+	0.187671i	0.114262	+	0.0100602i
$349$	−0.297783	+	0.463360i	−0.0159400	+	0.0248031i	−0.849132	−	0.528181i	$-0.822874\pi$
$349$	−0.297783	+	0.463360i	−0.0159400	+	0.0248031i	0.833192	+	0.552984i	$0.186511\pi$
$350$	−46.4408	+	13.4349i	−2.48237	+	0.718124i
$351$	6.87363	−	8.29687i	0.366887	−	0.442854i
$352$	−9.97266	−	21.8371i	−0.531544	−	1.16392i
$353$	4.78208	+	5.51881i	0.254524	+	0.293737i	0.868604	−	0.495508i	$-0.165018\pi$
$353$	4.78208	+	5.51881i	0.254524	+	0.293737i	−0.614079	+	0.789244i	$0.710472\pi$
$354$	−26.1408	+	25.2961i	−1.38937	+	1.34447i
$355$	−6.46187	−	2.95104i	−0.342961	−	0.156625i
$356$	10.6053	−	3.11401i	0.562082	−	0.165042i
$357$	2.25544	−	9.43630i	0.119371	−	0.499422i
$358$	8.94920	−	19.5960i	0.472980	−	1.03568i
$359$	−26.4331	+	3.80050i	−1.39509	+	0.200583i	−0.798513	−	0.601977i	$-0.794380\pi$
$359$	−26.4331	+	3.80050i	−1.39509	+	0.200583i	−0.596572	+	0.802560i	$0.703471\pi$
$360$	7.36745	+	17.6436i	0.388298	+	0.929900i
$361$	5.00916	+	10.9685i	0.263640	+	0.577292i
$362$	8.52885	−	5.48116i	0.448267	−	0.288083i
$363$	6.41852	+	12.2278i	0.336885	+	0.641791i
$364$	0.862130	−	5.83071i	0.0451879	−	0.305612i
$365$	1.11376	+	0.965083i	0.0582971	+	0.0505147i
$366$	11.8404	−	4.19610i	0.618906	−	0.219334i
$367$		−	15.3991i		−	0.803826i	−0.915678	−	0.401913i	$-0.868345\pi$
$367$		−	15.3991i		−	0.803826i	0.915678	−	0.401913i	$-0.131655\pi$
$368$	1.01729	−	23.9310i	0.0530298	−	1.24749i
$369$	−4.29168	+	13.0186i	−0.223416	+	0.677723i
$370$	−13.9272	+	47.4319i	−0.724043	+	2.46586i
$371$	24.9692	+	7.44017i	1.29634	+	0.386274i
$372$	0.0815452	+	1.48167i	0.00422792	+	0.0768209i
$373$	−0.615332	+	4.27973i	−0.0318607	+	0.221596i	−0.999531	−	0.0306224i	$-0.990251\pi$
$373$	−0.615332	+	4.27973i	−0.0318607	+	0.221596i	0.967670	+	0.252218i	$0.0811602\pi$
$374$	−13.6029	+	8.74208i	−0.703391	+	0.452042i
$375$	−32.0697	−	18.2012i	−1.65607	−	0.939904i
$376$	11.4952	−	9.96068i	0.592822	−	0.513683i
$377$	0.339313	+	2.35997i	0.0174755	+	0.121545i
$378$	7.20975	+	23.0017i	0.370830	+	1.18308i
$379$	2.97530	−	0.873626i	0.152831	−	0.0448751i	−0.204422	−	0.978883i	$-0.565532\pi$
$379$	2.97530	−	0.873626i	0.152831	−	0.0448751i	0.357253	+	0.934008i	$0.383713\pi$
$380$	3.13182	+	10.6660i	0.160659	+	0.547154i
$381$	−3.90846	−	19.5033i	−0.200236	−	0.999183i
$382$	4.55311	+	31.6676i	0.232958	+	1.62026i
$383$	5.13446	+	5.92548i	0.262359	+	0.302778i	0.871611	−	0.490198i	$-0.163076\pi$
$383$	5.13446	+	5.92548i	0.262359	+	0.302778i	−0.609252	+	0.792977i	$0.708530\pi$
$384$	9.91137	−	17.4634i	0.505787	−	0.891175i
$385$	−37.9740	−	24.6195i	−1.93534	−	1.25472i
$386$	−13.6481	−	1.96230i	−0.694670	−	0.0998784i
$387$	18.2671	−	14.8070i	0.928571	−	0.752683i
$388$	1.04007	+	0.901224i	0.0528014	+	0.0457527i
$389$	3.67734	−	12.5239i	0.186449	−	0.634986i	−0.812218	−	0.583355i	$-0.801740\pi$
$389$	3.67734	−	12.5239i	0.186449	−	0.634986i	0.998666	−	0.0516310i	$-0.0164420\pi$
$390$	20.0373	−	14.4925i	1.01463	−	0.733858i
$391$	−10.1026	+	1.01686i	−0.510908	+	0.0514249i
$392$	−8.52609	−	7.50807i	−0.430633	−	0.379215i
$393$	−8.34056	+	2.95581i	−0.420725	+	0.149101i
$394$	31.0956	−	35.8863i	1.56658	−	1.80792i
$395$	−4.95710	−	3.18574i	−0.249419	−	0.160292i
$396$	6.24841	−	12.5725i	0.313994	−	0.631791i
$397$	6.27655	+	9.76650i	0.315011	+	0.490166i	0.962267	−	0.272106i	$-0.0877201\pi$
$397$	6.27655	+	9.76650i	0.315011	+	0.490166i	−0.647256	+	0.762272i	$0.724084\pi$
$398$	18.8714	+	41.3225i	0.945936	+	2.07131i
$399$	−2.32509	−	11.8478i	−0.116400	−	0.593134i
$400$	7.40735	+	51.5193i	0.370368	+	2.57596i
$401$	−14.2020	−	6.48583i	−0.709213	−	0.323887i	0.0279428	−	0.999610i	$-0.491104\pi$
$401$	−14.2020	−	6.48583i	−0.709213	−	0.323887i	−0.737156	+	0.675723i	$0.763832\pi$
$402$	19.7611	+	15.3056i	0.985596	+	0.763376i
$403$	−1.58647	+	0.465830i	−0.0790277	+	0.0232046i
$404$	−8.07729	+	17.6868i	−0.401860	+	0.879951i
$405$	−16.7603	+	31.1163i	−0.832826	+	1.54618i
$406$	−4.84331	−	2.23530i	−0.240369	−	0.110936i
$407$	−28.4461	+	12.9909i	−1.41002	+	0.643936i
$408$	−5.54132	−	2.17109i	−0.274336	−	0.107485i
$409$	−28.4293	−	4.08751i	−1.40574	−	0.202114i	−0.602664	−	0.797995i	$-0.705894\pi$
$409$	−28.4293	−	4.08751i	−1.40574	−	0.202114i	−0.803073	+	0.595881i	$0.796803\pi$
$410$	−17.0097	+	26.4676i	−0.840047	+	1.30714i
$411$	38.2609	+	3.36870i	1.88727	+	0.166166i
$412$	0.247108	−	0.841573i	0.0121741	−	0.0414613i
$413$	28.8789	−	13.0493i	1.42104	−	0.642115i
$414$	20.2544	−	15.0386i	0.995447	−	0.739108i
$415$	−65.1311			−3.19716
$416$	−10.9649	−	3.21960i	−0.537600	−	0.157854i
$417$	−22.5762	−	1.98774i	−1.10556	−	0.0973399i
$418$	−10.8791	+	16.9283i	−0.532116	+	0.827988i
$419$	0.0885265	−	0.615715i	0.00432480	−	0.0300797i	−0.987545	−	0.157338i	$-0.949709\pi$
$419$	0.0885265	−	0.615715i	0.00432480	−	0.0300797i	0.991870	+	0.127259i	$0.0406178\pi$
$420$	0.985318	+	19.3094i	0.0480786	+	0.942202i
$421$	2.67110	+	5.84889i	0.130181	+	0.285057i	0.963487	−	0.267755i	$-0.0862818\pi$
$421$	2.67110	+	5.84889i	0.130181	+	0.285057i	−0.833306	+	0.552813i	$0.813555\pi$
$422$	−5.16737	+	4.47756i	−0.251544	+	0.217964i
$423$	27.6835	+	4.91290i	1.34602	+	0.238873i
$424$	6.63922	−	14.5379i	0.322429	−	0.706021i
$425$	21.1700	−	6.21609i	1.02690	−	0.301524i
$426$	−3.36407	+	4.34336i	−0.162990	+	0.210436i
$427$	−10.9436	−	0.0437411i	−0.529599	−	0.00211678i
$428$	−15.5798	+	2.24004i	−0.753080	+	0.108277i
$429$	15.2294	+	3.57581i	0.735284	+	0.172642i
$430$	49.0934	−	22.4202i	2.36749	−	1.08120i
$431$	12.6882	+	19.7432i	0.611168	+	0.950997i	0.999565	+	0.0295041i	$0.00939283\pi$
$431$	12.6882	+	19.7432i	0.611168	+	0.950997i	−0.388396	+	0.921492i	$0.626971\pi$
$432$	25.5998	−	4.26119i	1.23167	−	0.205017i
$433$	−1.58321	+	2.46352i	−0.0760842	+	0.118389i	−0.877210	−	0.480106i	$-0.840598\pi$
$433$	−1.58321	+	2.46352i	−0.0760842	+	0.118389i	0.801126	+	0.598495i	$0.204235\pi$
$434$	1.05638	−	3.54520i	0.0507076	−	0.170175i
$435$	−2.61250	−	7.37184i	−0.125260	−	0.353453i
$436$	6.54541			0.313468
$437$	−10.9104	+	6.37376i	−0.521914	+	0.304898i
$438$	0.923476	−	0.667931i	0.0441254	−	0.0319150i
$439$	2.49644	−	8.50209i	0.119148	−	0.405782i	−0.878222	−	0.478253i	$-0.841270\pi$
$439$	2.49644	−	8.50209i	0.119148	−	0.405782i	0.997371	+	0.0724706i	$0.0230884\pi$
$440$	−18.1797	+	20.9805i	−0.866684	+	1.00021i
$441$	0.857240	−	20.9825i	0.0408210	−	0.999166i
$442$	−1.09545	+	7.61901i	−0.0521051	+	0.362399i
$443$	−7.85509	−	12.2228i	−0.373206	−	0.580721i	0.602953	−	0.797777i	$-0.293991\pi$
$443$	−7.85509	−	12.2228i	−0.373206	−	0.580721i	−0.976159	+	0.217056i	$0.930354\pi$
$444$	11.6192	+	6.59449i	0.551423	+	0.312961i
$445$	−26.4564	−	30.5323i	−1.25415	−	1.44737i
$446$	−6.95942	−	48.4038i	−0.329538	−	2.29199i
$447$	10.6209	−	2.12842i	0.502350	−	0.100671i
$448$	−0.652796	+	0.561098i	−0.0308417	+	0.0265094i
$449$	−8.47484	−	28.8626i	−0.399952	−	1.36211i	−0.875838	−	0.482605i	$-0.839691\pi$
$449$	−8.47484	−	28.8626i	−0.399952	−	1.36211i	0.475886	−	0.879507i	$-0.342128\pi$
$450$	−37.2391	+	40.2279i	−1.75547	+	1.89636i
$451$	−19.7003	+	2.83248i	−0.927652	+	0.133376i
$452$	4.41593	−	3.82643i	0.207708	−	0.179980i
$453$	−13.0442	−	7.40324i	−0.612870	−	0.347835i
$454$	17.9970	+	28.0038i	0.844639	+	1.31428i
$455$	−20.6949	+	5.98683i	−0.970193	+	0.280667i
$456$	−7.39514	+	0.406999i	−0.346309	+	0.0190595i
$457$	11.6126	−	13.4017i	0.543215	−	0.626903i	−0.416074	−	0.909331i	$-0.636594\pi$
$457$	11.6126	−	13.4017i	0.543215	−	0.626903i	0.959289	+	0.282427i	$0.0911396\pi$
$458$	−13.0845	−	3.84195i	−0.611398	−	0.179523i
$459$	−3.33232	−	10.4843i	−0.155540	−	0.489366i
$460$	18.7461	−	7.61633i	0.874043	−	0.355113i
$461$	−11.0014			−0.512384			−0.256192	−	0.966626i	$-0.582468\pi$
$461$	−11.0014			−0.512384			−0.256192	+	0.966626i	$0.582468\pi$
$462$	−25.2483	+	24.2379i	−1.17466	+	1.12765i
$463$	−0.248210	+	0.286449i	−0.0115353	+	0.0133124i	−0.761488	−	0.648179i	$-0.775531\pi$
$463$	−0.248210	+	0.286449i	−0.0115353	+	0.0133124i	0.749953	+	0.661492i	$0.230076\pi$
$464$	−3.10486	+	4.83126i	−0.144140	+	0.224286i
$465$	4.80242	−	2.52086i	0.222707	−	0.116902i
$466$	7.65989	−	4.92271i	0.354838	−	0.228040i
$467$	4.74878	+	10.3984i	0.219747	+	0.481179i	0.987112	−	0.160032i	$-0.0511596\pi$
$467$	4.74878	+	10.3984i	0.219747	+	0.481179i	−0.767365	+	0.641211i	$0.778432\pi$
$468$	−2.57524	−	6.16720i	−0.119040	−	0.285079i
$469$	−11.6994	−	18.3656i	−0.540227	−	0.848044i
$470$	58.7002	+	26.8075i	2.70764	+	1.23654i
$471$	19.4808	+	15.0885i	0.897628	+	0.695241i
$472$	−5.47674	−	18.6521i	−0.252087	−	0.858530i
$473$	31.0565	+	14.1830i	1.42798	+	0.652136i
$474$	−3.27476	+	3.16895i	−0.150415	+	0.145555i
$475$	20.7509	−	17.9808i	0.952117	−	0.825014i
$476$	−4.53248	−	3.95924i	−0.207746	−	0.181472i
$477$	28.6039	−	7.38797i	1.30968	−	0.338272i
$478$	−0.825282	+	5.73996i	−0.0377475	+	0.262540i
$479$	−24.9843	−	16.0564i	−1.14156	−	0.733638i	−0.173621	−	0.984813i	$-0.555547\pi$
$479$	−24.9843	−	16.0564i	−1.14156	−	0.733638i	−0.967942	+	0.251175i	$0.919183\pi$
$480$	37.3425	+	3.28784i	1.70444	+	0.150069i
$481$	−4.19402	+	14.2835i	−0.191231	+	0.651272i
$482$	7.89859			0.359771
$483$	−21.0336	+	6.37073i	−0.957064	+	0.289878i
$484$	8.56633			0.389379
$485$	1.41716	−	4.82641i	0.0643500	−	0.219156i
$486$	20.4641	+	18.1190i	0.928268	+	0.821896i
$487$	10.5736	+	6.79527i	0.479137	+	0.307923i	0.757824	−	0.652459i	$-0.226263\pi$
$487$	10.5736	+	6.79527i	0.479137	+	0.307923i	−0.278686	+	0.960382i	$0.589899\pi$
$488$	−0.955371	+	6.64475i	−0.0432476	+	0.300794i
$489$	7.10519	−	18.1347i	0.321308	−	0.820079i
$490$	13.9485	−	46.1367i	0.630129	−	2.08424i
$491$	−6.94084	+	6.01427i	−0.313236	+	0.271420i	−0.797262	−	0.603633i	$-0.793719\pi$
$491$	−6.94084	+	6.01427i	−0.313236	+	0.271420i	0.484027	+	0.875053i	$0.339174\pi$
$492$	5.91297	+	6.11040i	0.266577	+	0.275478i
$493$	2.21445	+	1.01131i	0.0997339	+	0.0455470i
$494$	2.69872	+	9.19100i	0.121421	+	0.413523i
$495$	−51.2883	−	1.68483i	−2.30524	−	0.0757277i
$496$	−3.62275	−	1.65446i	−0.162666	−	0.0742873i
$497$	4.03662	−	2.57144i	0.181067	−	0.115345i
$498$	−11.5135	+	49.0360i	−0.515930	+	2.19735i
$499$	3.13363	+	6.86169i	0.140281	+	0.307171i	0.966712	−	0.255865i	$-0.0823603\pi$
$499$	3.13363	+	6.86169i	0.140281	+	0.307171i	−0.826432	+	0.563037i	$0.809633\pi$
$500$	−19.2423	+	12.3663i	−0.860544	+	0.553038i
$501$	1.38868	+	2.64554i	0.0620416	+	0.118194i
$502$	13.4615	−	20.9465i	0.600817	−	0.934889i
$503$	7.65259	−	8.83156i	0.341212	−	0.393780i	−0.559046	−	0.829137i	$-0.688832\pi$
$503$	7.65259	−	8.83156i	0.341212	−	0.393780i	0.900258	+	0.435357i	$0.143378\pi$
$504$	−12.6745	−	2.30160i	−0.564569	−	0.102521i
$505$	71.0693			3.16254
$506$	32.6417	+	16.6172i	1.45110	+	0.738723i
$507$	−12.2107	+	8.83171i	−0.542294	+	0.392230i
$508$	−11.8386	−	3.47614i	−0.525254	−	0.154229i
$509$	2.96390	−	3.42052i	0.131372	−	0.151612i	−0.686252	−	0.727364i	$-0.740745\pi$
$509$	2.96390	−	3.42052i	0.131372	−	0.151612i	0.817624	+	0.575752i	$0.195291\pi$
$510$	−1.38755	−	25.2116i	−0.0614417	−	1.11639i
$511$	−0.953786	+	0.275921i	−0.0421930	+	0.0122060i
$512$	−6.11718	−	9.51851i	−0.270344	−	0.420663i
$513$	−9.19221	−	10.1455i	−0.405846	−	0.447935i
$514$	14.8186	−	12.8404i	0.653620	−	0.566365i
$515$	−3.17326	+	0.456245i	−0.139830	+	0.0201046i
$516$	−2.86607	−	14.3018i	−0.126172	−	0.629600i
$517$	11.5011	+	39.1693i	0.505819	+	1.72266i
$518$	−21.7097	−	25.2576i	−0.953869	−	1.10976i
$519$	1.82110	+	9.08733i	0.0799375	+	0.398889i
$520$	1.88072	+	13.0807i	0.0824750	+	0.573626i
$521$	25.7972	+	29.7716i	1.13020	+	1.30432i	0.946998	+	0.321239i	$0.104099\pi$
$521$	25.7972	+	29.7716i	1.13020	+	1.30432i	0.183198	+	0.983076i	$0.441355\pi$
$522$	−6.01194	+	0.663757i	−0.263135	+	0.0290519i
$523$	−3.27180	−	5.09103i	−0.143066	−	0.222615i	0.762324	−	0.647195i	$-0.224058\pi$
$523$	−3.27180	−	5.09103i	−0.143066	−	0.222615i	−0.905390	+	0.424580i	$0.860422\pi$
$524$	−0.781156	+	5.43306i	−0.0341250	+	0.237344i
$525$	42.3735	−	22.0269i	1.84933	−	0.961331i
$526$	3.09122	−	3.56746i	0.134784	−	0.155549i
$527$	−0.475639	+	1.61988i	−0.0207192	+	0.0705630i
$528$	22.0829	+	30.5317i	0.961037	+	1.32872i
$529$	13.5323	+	18.5978i	0.588362	+	0.808598i
$530$	67.8061			2.94531
$531$	20.4091	−	29.5750i	0.885681	−	1.28345i
$532$	−7.17754	−	2.13871i	−0.311186	−	0.0927250i
$533$	−5.12225	+	7.97038i	−0.221869	+	0.345235i
$534$	−27.6639	+	14.5212i	−1.19714	+	0.628393i
$535$	31.1038	+	48.3985i	1.34473	+	2.09245i
$536$	−12.1504	+	5.54890i	−0.524817	+	0.239676i
$537$	−4.86431	+	20.7172i	−0.209911	+	0.894012i
$538$	32.8368	−	4.72122i	1.41570	−	0.203546i
$539$	27.8357	−	12.4442i	1.19897	−	0.536010i
$540$	12.2581	+	18.1761i	0.527503	+	0.782175i
$541$	23.0596	−	6.77089i	0.991407	−	0.291104i	0.254482	−	0.967078i	$-0.418095\pi$
$541$	23.0596	−	6.77089i	0.991407	−	0.291104i	0.736925	+	0.675974i	$0.236277\pi$
$542$	−12.9648	+	28.3889i	−0.556884	+	1.21941i
$543$	−7.19689	+	6.96435i	−0.308848	+	0.298869i
$544$	−8.81845	+	7.64123i	−0.378088	+	0.327615i
$545$	−9.93843	−	21.7621i	−0.425715	−	0.932187i
$546$	0.849060	+	16.6391i	0.0363364	+	0.712089i
$547$	−4.43844	+	30.8701i	−0.189774	+	1.31991i	0.642817	+	0.766020i	$0.277766\pi$
$547$	−4.43844	+	30.8701i	−0.189774	+	1.31991i	−0.832591	+	0.553888i	$0.813143\pi$
$548$	12.8808	−	20.0429i	0.550240	−	0.856191i
$549$	−10.6537	+	6.36245i	−0.454691	+	0.271543i
$550$	−76.3687	−	22.4239i	−3.25637	−	0.956157i
$551$	3.02956			0.129064
$552$	2.08519	+	13.3190i	0.0887517	+	0.566896i
$553$	3.61779	−	1.63474i	0.153844	−	0.0695164i
$554$	−0.621268	+	2.11585i	−0.0263952	+	0.0898937i
$555$	4.28292	−	48.6444i	0.181800	−	2.06484i
$556$	−7.60045	+	11.8265i	−0.322331	+	0.501557i
$557$	9.76400	+	1.40385i	0.413714	+	0.0594831i	0.346029	−	0.938224i	$-0.387530\pi$
$557$	9.76400	+	1.40385i	0.413714	+	0.0594831i	0.0676845	+	0.997707i	$0.478439\pi$
$558$	−1.04896	−	4.06127i	−0.0444062	−	0.171927i
$559$	14.7839	−	6.75156i	0.625291	−	0.285561i
$560$	−47.1160	−	21.7451i	−1.99101	−	0.918900i
$561$	11.4785	−	11.1077i	0.484625	−	0.468966i
$562$	−8.12881	+	17.7996i	−0.342893	+	0.750831i
$563$	−38.5829	+	11.3290i	−1.62608	+	0.477459i	−0.962642	−	0.270776i	$-0.912720\pi$
$563$	−38.5829	+	11.3290i	−1.62608	+	0.477459i	−0.663433	+	0.748235i	$0.730901\pi$
$564$	10.6795	−	13.7883i	0.449687	−	0.580591i
$565$	−19.4271	−	8.87208i	−0.817306	−	0.373251i
$566$	−6.54736	−	45.5379i	−0.275206	−	1.91410i
$567$	−11.4478	−	20.8794i	−0.480763	−	0.876850i
$568$	−1.21961	−	2.67057i	−0.0511736	−	0.112055i
$569$	5.27101	+	8.20185i	0.220972	+	0.343839i	0.933985	−	0.357311i	$-0.116306\pi$
$569$	5.27101	+	8.20185i	0.220972	+	0.343839i	−0.713013	+	0.701151i	$0.752670\pi$
$570$	−14.6042	−	27.8222i	−0.611704	−	1.16534i
$571$	21.8008	+	14.0105i	0.912335	+	0.586322i	0.910424	−	0.413676i	$-0.135755\pi$
$571$	21.8008	+	14.0105i	0.912335	+	0.586322i	0.00191087	+	0.999998i	$0.499392\pi$
$572$	6.35459	−	7.33359i	0.265699	−	0.306633i
$573$	−10.5567	−	29.7885i	−0.441014	−	1.24443i
$574$	−8.72842	−	19.3165i	−0.364317	−	0.806256i
$575$	−36.3475	−	34.3040i	−1.51580	−	1.43057i
$576$	−0.305586	+	0.926983i	−0.0127328	+	0.0386243i
$577$	3.19919	−	10.8954i	0.133184	−	0.453583i	−0.865713	−	0.500541i	$-0.833134\pi$
$577$	3.19919	−	10.8954i	0.133184	−	0.453583i	0.998897	+	0.0469579i	$0.0149527\pi$
$578$	−16.5874	−	14.3731i	−0.689944	−	0.597840i
$579$	13.6000	−	0.748492i	0.565197	−	0.0311062i
$580$	−4.80203	−	0.690428i	−0.199394	−	0.0286685i
$581$	23.8712	−	36.8199i	0.990345	−	1.52755i
$582$	−3.38319	−	1.92013i	−0.140238	−	0.0795921i
$583$	28.0897	+	32.4173i	1.16336	+	1.34259i
$584$	0.0866785	+	0.602862i	0.00358678	+	0.0249466i
$585$	−16.5945	+	17.9263i	−0.686097	+	0.741161i
$586$	−5.72124	−	19.4848i	−0.236342	−	0.804908i
$587$	−1.69326	+	0.497186i	−0.0698884	+	0.0205211i	−0.316490	−	0.948596i	$-0.602504\pi$
$587$	−1.69326	+	0.497186i	−0.0698884	+	0.0205211i	0.246601	+	0.969117i	$0.420686\pi$
$588$	−11.2771	−	6.52007i	−0.465061	−	0.268883i
$589$	0.298999	+	2.07958i	0.0123200	+	0.0856878i
$590$	62.3299	−	54.0092i	2.56608	−	2.22352i
$591$	−23.1527	+	40.7941i	−0.952376	+	1.67804i
$592$	−30.1650	+	19.3859i	−1.23977	+	0.796755i
$593$	4.26622	−	29.6722i	0.175192	−	1.21849i	−0.692511	−	0.721408i	$-0.743495\pi$
$593$	4.26622	−	29.6722i	0.175192	−	1.21849i	0.867703	−	0.497083i	$-0.165595\pi$
$594$	−10.3349	+	38.3162i	−0.424046	+	1.57213i
$595$	−6.28162	+	21.0812i	−0.257521	+	0.864243i
$596$	1.89299	−	6.44695i	0.0775401	−	0.264077i
$597$	−26.2990	−	36.3608i	−1.07635	−	1.48815i
$598$	16.1538	−	6.56308i	0.660576	−	0.268384i
$599$		−	7.98304i		−	0.326178i	−0.986611	−	0.163089i	$-0.947854\pi$
$599$		−	7.98304i		−	0.326178i	0.986611	−	0.163089i	$-0.0521458\pi$
$600$	−9.78547	−	27.6122i	−0.399490	−	1.12726i
$601$	−12.9208	−	11.1959i	−0.527049	−	0.456691i	0.350235	−	0.936662i	$-0.386102\pi$
$601$	−12.9208	−	11.1959i	−0.527049	−	0.456691i	−0.877284	+	0.479971i	$0.840647\pi$
$602$	−5.31863	+	35.9707i	−0.216771	+	1.46606i
$603$	−22.1109	−	10.9889i	−0.900425	−	0.447503i
$604$	−7.82673	+	5.02994i	−0.318465	+	0.204665i
$605$	−13.0070	−	28.4813i	−0.528808	−	1.15793i
$606$	12.5632	−	53.5067i	0.510344	−	2.17356i
$607$	−34.0039	+	4.88902i	−1.38017	+	0.198439i	−0.792112	−	0.610376i	$-0.791018\pi$
$607$	−34.0039	+	4.88902i	−1.38017	+	0.198439i	−0.588063	+	0.808815i	$0.700109\pi$
$608$	−6.03221	+	13.2087i	−0.244638	+	0.535683i
$609$	5.12496	+	1.22495i	0.207674	+	0.0496376i
$610$	−27.3274	+	8.02404i	−1.10645	+	0.324884i
$611$	17.6768	+	8.07275i	0.715129	+	0.326588i
$612$	−6.71903	−	1.19240i	−0.271601	−	0.0482001i
$613$	20.0784	+	23.1717i	0.810960	+	0.935898i	0.998929	−	0.0462772i	$-0.0147358\pi$
$613$	20.0784	+	23.1717i	0.810960	+	0.935898i	−0.187969	+	0.982175i	$0.560190\pi$
$614$	8.84113	+	19.3594i	0.356799	+	0.781281i
$615$	11.3377	−	28.9373i	0.457178	−	1.16686i
$616$	−5.19765	−	17.9669i	−0.209419	−	0.723908i
$617$	−21.6893	+	33.7491i	−0.873177	+	1.35869i	0.0595955	+	0.998223i	$0.481019\pi$
$617$	−21.6893	+	33.7491i	−0.873177	+	1.35869i	−0.932772	+	0.360467i	$0.882617\pi$
$618$	−0.217449	+	2.46974i	−0.00874709	+	0.0993473i
$619$	−7.07086	+	24.0812i	−0.284202	+	0.967903i	0.686402	+	0.727222i	$0.259189\pi$
$619$	−7.07086	+	24.0812i	−0.284202	+	0.967903i	−0.970604	+	0.240681i	$0.922629\pi$
$620$		−	3.36440i		−	0.135118i
$621$	−16.6987	+	18.4974i	−0.670097	+	0.742273i
$622$			37.6931i			1.51135i
$623$	26.9570	−	3.76592i	1.08001	−	0.150879i
$624$	17.8681	+	1.57321i	0.715297	+	0.0629787i
$625$	26.4976	+	17.0290i	1.05990	+	0.681158i
$626$	2.79266	−	19.4234i	0.111617	−	0.776314i
$627$	7.25140	−	18.5079i	0.289593	−	0.739132i
$628$	13.9034	−	6.34947i	0.554806	−	0.253371i
$629$	9.95388	+	11.4874i	0.396887	+	0.458032i
$630$	−13.4558	−	52.9703i	−0.536092	−	2.11039i
$631$	7.70840	−	16.8791i	0.306867	−	0.671944i	−0.691879	−	0.722013i	$-0.743217\pi$
$631$	7.70840	−	16.8791i	0.306867	−	0.671944i	0.998746	+	0.0500690i	$0.0159441\pi$
$632$	−0.686094	−	2.33662i	−0.0272914	−	0.0929458i
$633$	4.13586	−	5.33982i	0.164386	−	0.212239i
$634$	17.5267	−	38.3781i	0.696074	−	1.52419i
$635$	6.41813	+	44.6391i	0.254696	+	1.77145i
$636$	4.18880	−	17.8402i	0.166097	−	0.707408i
$637$	4.20042	−	13.8935i	0.166427	−	0.550480i
$638$	−4.74792	−	7.38790i	−0.187972	−	0.292490i
$639$	2.41528	−	4.85981i	0.0955471	−	0.192251i
$640$	−24.6135	+	38.2993i	−0.972932	+	1.51391i
$641$	17.4903	+	15.1554i	0.690826	+	0.598604i	0.927874	−	0.372894i	$-0.121634\pi$
$641$	17.4903	+	15.1554i	0.690826	+	0.598604i	−0.237048	+	0.971498i	$0.576180\pi$
$642$	41.9366	−	14.8619i	1.65511	−	0.586552i
$643$			26.5828i			1.04832i	0.851619	+	0.524162i	$0.175621\pi$
$643$			26.5828i			1.04832i	−0.851619	+	0.524162i	$0.824379\pi$
$644$	−2.56498	+	13.3890i	−0.101074	+	0.527602i
$645$	−43.1986	+	31.2446i	−1.70094	+	1.23026i
$646$	9.38454	+	2.75555i	0.369230	+	0.108416i
$647$	−14.4258	+	16.6483i	−0.567137	+	0.654511i	−0.964789	−	0.263025i	$-0.915280\pi$
$647$	−14.4258	+	16.6483i	−0.567137	+	0.654511i	0.397652	+	0.917536i	$0.369825\pi$
$648$	−13.6562	+	5.18272i	−0.536467	+	0.203597i
$649$	51.6422	+	7.42503i	2.02714	+	0.291458i
$650$	−31.8740	+	20.4842i	−1.25020	+	0.803455i
$651$	−0.335044	+	3.63882i	−0.0131314	+	0.142617i
$652$	−7.91173	−	9.13062i	−0.309847	−	0.357583i
$653$	20.6295	−	2.96607i	0.807293	−	0.116071i	0.273703	−	0.961814i	$-0.411752\pi$
$653$	20.6295	−	2.96607i	0.807293	−	0.116071i	0.533590	+	0.845743i	$0.320842\pi$
$654$	−18.1411	+	3.63549i	−0.709374	+	0.142159i
$655$	19.2499	−	5.65227i	0.752155	−	0.220853i
$656$	−21.8966	+	6.42943i	−0.854919	+	0.251027i
$657$	−0.764805	+	0.826186i	−0.0298379	+	0.0322326i
$658$	−36.6690	+	23.3592i	−1.42951	+	0.910636i
$659$	28.8363	−	24.9868i	1.12330	−	0.973347i	0.123483	−	0.992347i	$-0.460594\pi$
$659$	28.8363	−	24.9868i	1.12330	−	0.973347i	0.999819	+	0.0189995i	$0.00604810\pi$
$660$	−15.7118	+	27.6834i	−0.611580	+	1.07758i
$661$	12.1371	+	18.8857i	0.472078	+	0.734568i	0.992881	−	0.119109i	$-0.0380037\pi$
$661$	12.1371	+	18.8857i	0.472078	+	0.734568i	−0.520803	+	0.853677i	$0.674367\pi$
$662$	6.80356	+	0.978205i	0.264428	+	0.0380190i
$663$	−0.417843	−	7.59217i	−0.0162277	−	0.294855i
$664$	−20.3429	−	17.6272i	−0.789456	−	0.684068i
$665$	3.78746	+	27.1112i	0.146871	+	1.05133i
$666$	−35.8663	−	11.8236i	−1.38979	−	0.458154i
$667$	−0.552268	−	5.48681i	−0.0213839	−	0.212450i
$668$	1.85337			0.0717090
$669$	16.1359	+	45.5317i	0.623852	+	1.76036i
$670$	−42.8289	−	37.1114i	−1.65462	−	1.43374i
$671$	−15.1570	−	9.74079i	−0.585128	−	0.376039i
$672$	−15.5451	+	19.9054i	−0.599665	+	0.767869i
$673$	−0.390287	+	0.250822i	−0.0150445	+	0.00966849i	−0.548141	−	0.836386i	$-0.684664\pi$
$673$	−0.390287	+	0.250822i	−0.0150445	+	0.00966849i	0.533097	+	0.846054i	$0.321028\pi$
$674$	11.0529	−	5.04767i	0.425740	−	0.194429i
$675$	28.2604	−	46.1917i	1.08774	−	1.77792i
$676$	1.33033	+	9.25266i	0.0511666	+	0.355872i
$677$	−13.6329	+	29.8518i	−0.523954	+	1.14730i	0.443967	+	0.896043i	$0.353571\pi$
$677$	−13.6329	+	29.8518i	−0.523954	+	1.14730i	−0.967921	+	0.251256i	$0.919156\pi$
$678$	−10.1138	+	13.0580i	−0.388419	+	0.501488i
$679$	2.20906	+	2.57008i	0.0847760	+	0.0986305i
$680$	12.2741	+	5.60540i	0.470690	+	0.214957i
$681$	−22.8669	−	23.6304i	−0.876261	−	0.905519i
$682$	4.60269	−	3.98826i	0.176246	−	0.152718i
$683$	−17.3463	+	7.92179i	−0.663738	+	0.303119i	−0.718650	−	0.695372i	$-0.755239\pi$
$683$	−17.3463	+	7.92179i	−0.663738	+	0.303119i	0.0549120	+	0.998491i	$0.482512\pi$
$684$	−8.22235	+	2.12371i	−0.314389	+	0.0812021i
$685$	−86.1964	−	12.3932i	−3.29340	−	0.473519i
$686$	20.9697	+	24.7949i	0.800627	+	0.946674i
$687$	13.4190	+	1.18148i	0.511966	+	0.0450763i
$688$	37.5619	+	11.0292i	1.43203	+	0.420483i
$689$	20.4190			0.777901
$690$	−47.7261	+	31.5213i	−1.81690	+	1.20000i
$691$			38.1537i			1.45144i	0.687992	+	0.725718i	$0.258492\pi$
$691$			38.1537i			1.45144i	−0.687992	+	0.725718i	$0.741508\pi$
$692$	5.51608	+	1.61967i	0.209690	+	0.0615705i
$693$	19.7502	−	28.3768i	0.750246	−	1.07795i
$694$	26.4323	+	16.9870i	1.00335	+	0.644817i
$695$	50.8611	+	7.31272i	1.92927	+	0.277387i
$696$	1.17915	−	3.00955i	0.0446954	−	0.114077i
$697$	4.01869	+	8.79970i	0.152219	+	0.333313i
$698$	−0.632441	−	0.729876i	−0.0239382	−	0.0276262i
$699$	−6.46363	+	6.25479i	−0.244477	+	0.236578i
$700$	0.118402	−	29.6232i	0.00447519	−	1.11965i
$701$	−4.73080	−	16.1116i	−0.178680	−	0.608528i	−0.999313	−	0.0370718i	$-0.988197\pi$
$701$	−4.73080	−	16.1116i	−0.178680	−	0.608528i	0.820633	−	0.571456i	$-0.193621\pi$
$702$	10.5629	+	15.6625i	0.398671	+	0.591145i
$703$	17.2064	+	7.85788i	0.648950	+	0.296365i
$704$	−1.40275	+	0.201685i	−0.0528680	+	0.00760128i
$705$	−62.0586	−	14.5711i	−2.33726	−	0.548780i
$706$	−11.6470	+	5.31900i	−0.438340	+	0.200183i
$707$	−26.0476	+	40.1769i	−0.979622	+	1.51101i
$708$	−10.3596	−	19.7358i	−0.389338	−	0.741718i
$709$	−37.5606	−	24.1388i	−1.41062	−	0.906550i	−0.410633	−	0.911801i	$-0.634692\pi$
$709$	−37.5606	−	24.1388i	−1.41062	−	0.906550i	−0.999986	+	0.00525099i	$0.998329\pi$
$710$	8.15683	−	9.41348i	0.306120	−	0.353282i
$711$	2.55674	−	3.70499i	0.0958852	−	0.138948i
$712$		−	16.6965i		−	0.625730i
$713$	3.71180	−	0.920607i	0.139008	−	0.0344770i
$714$	14.7612	+	8.45590i	0.552423	+	0.316454i
$715$	−34.0313	−	9.99250i	−1.27270	−	0.373698i
$716$	9.97616	+	8.64439i	0.372826	+	0.323056i
$717$	−0.314792	−	5.71974i	−0.0117561	−	0.213608i
$718$	6.66378	−	46.3476i	0.248690	−	1.72968i
$719$	21.4250	−	13.7690i	0.799018	−	0.513498i	−0.0762773	−	0.997087i	$-0.524303\pi$
$719$	21.4250	−	13.7690i	0.799018	−	0.513498i	0.875295	+	0.483589i	$0.160667\pi$
$720$	−58.4845	+	6.45707i	−2.17959	+	0.240641i
$721$	0.905106	−	1.96112i	0.0337079	−	0.0730361i
$722$	−20.9276	+	3.00894i	−0.778845	+	0.111981i
$723$	−7.65034	+	1.53313i	−0.284519	+	0.0570177i
$724$	1.75018	+	5.96058i	0.0650451	+	0.221523i
$725$	3.37602	+	11.4977i	0.125382	+	0.427013i
$726$	−23.7423	+	4.75796i	−0.881159	+	0.176584i
$727$	25.0116	−	3.59613i	0.927630	−	0.133373i	0.338091	−	0.941113i	$-0.390219\pi$
$727$	25.0116	−	3.59613i	0.927630	−	0.133373i	0.589538	+	0.807740i	$0.299310\pi$
$728$	−8.08408	−	3.73100i	−0.299616	−	0.138280i
$729$	−23.3378	−	13.5775i	−0.864363	−	0.502869i
$730$	−2.17381	+	1.39702i	−0.0804564	+	0.0517062i
$731$	2.36169	−	16.4259i	0.0873502	−	0.607534i
$732$	0.422989	+	7.68567i	0.0156341	+	0.284071i
$733$	−14.2923	−	12.3844i	−0.527899	−	0.457427i	0.349673	−	0.936872i	$-0.386293\pi$
$733$	−14.2923	−	12.3844i	−0.527899	−	0.457427i	−0.877572	+	0.479445i	$0.840838\pi$
$734$	25.9070	+	7.60697i	0.956243	+	0.280778i
$735$	−4.55490	+	47.3940i	−0.168010	+	1.74815i
$736$	25.0217	+	8.51700i	0.922313	+	0.313941i
$737$		−	35.8499i		−	1.32055i
$738$	−19.7821	−	13.6512i	−0.728190	−	0.502509i
$739$	−25.1922	+	29.0734i	−0.926711	+	1.06948i	0.0706952	+	0.997498i	$0.477478\pi$
$739$	−25.1922	+	29.0734i	−0.926711	+	1.06948i	−0.997406	+	0.0719832i	$0.977067\pi$
$740$	−25.4823	−	16.3765i	−0.936747	−	0.602011i
$741$	−4.39789	−	8.37830i	−0.161560	−	0.307785i
$742$	−24.8516	+	38.3322i	−0.912332	+	1.40722i
$743$	46.1236	−	21.0639i	1.69211	−	0.772761i	0.693479	−	0.720477i	$-0.256077\pi$
$743$	46.1236	−	21.0639i	1.69211	−	0.772761i	0.998632	−	0.0522843i	$-0.0166502\pi$
$744$	2.18222	+	0.512377i	0.0800041	+	0.0187847i
$745$	−24.3090	+	3.49511i	−0.890614	+	0.128051i
$746$	−6.89612	−	3.14935i	−0.252485	−	0.115306i
$747$	1.63363	−	49.7295i	0.0597713	−	1.81951i
$748$	−2.79143	−	9.50672i	−0.102065	−	0.347600i
$749$	−38.7605	−	0.154924i	−1.41628	−	0.00566079i
$750$	46.4631	−	44.9619i	1.69659	−	1.64178i
$751$	−10.2690	−	11.8511i	−0.374721	−	0.432451i	0.536797	−	0.843711i	$-0.319634\pi$
$751$	−10.2690	−	11.8511i	−0.374721	−	0.432451i	−0.911518	+	0.411260i	$0.865089\pi$
$752$	19.4448	+	42.5783i	0.709081	+	1.55267i
$753$	−8.97266	+	22.9011i	−0.326982	+	0.834561i
$754$	−4.13797	−	0.594950i	−0.150696	−	0.0216668i
$755$	28.6074	+	18.3849i	1.04113	+	0.669095i
$756$	−14.7680	+	0.267998i	−0.537107	+	0.00974701i
$757$	7.43347	+	2.18266i	0.270174	+	0.0793303i	0.414013	−	0.910271i	$-0.364127\pi$
$757$	7.43347	+	2.18266i	0.270174	+	0.0793303i	−0.143839	+	0.989601i	$0.545945\pi$
$758$			5.43711i			0.197485i
$759$	−34.8412	−	9.75906i	−1.26466	−	0.354231i
$760$	16.7920			0.609111
$761$	−36.8409	−	10.8175i	−1.33548	−	0.392133i	−0.465427	−	0.885086i	$-0.654099\pi$
$761$	−36.8409	−	10.8175i	−1.33548	−	0.392133i	−0.870056	+	0.492953i	$0.835917\pi$
$762$	34.7424	+	3.05892i	1.25859	+	0.110813i
$763$	15.9451	+	2.35764i	0.577251	+	0.0853525i
$764$	−19.4043	−	2.78992i	−0.702023	−	0.100936i
$765$	6.23755	+	24.1499i	0.225519	+	0.873141i
$766$	−12.5052	+	5.71094i	−0.451832	+	0.206345i
$767$	18.7699	−	16.2642i	0.677742	−	0.587266i
$768$	23.7000	+	24.4914i	0.855202	+	0.883756i
$769$	40.9640	+	18.7076i	1.47720	+	0.674614i	0.981073	−	0.193637i	$-0.0620284\pi$
$769$	40.9640	+	18.7076i	1.47720	+	0.674614i	0.496125	+	0.868251i	$0.334756\pi$
$770$	60.1777	−	51.7246i	2.16866	−	1.86403i
$771$	−11.8605	+	15.3131i	−0.427146	+	0.551489i
$772$	3.50978	−	7.68536i	0.126320	−	0.276602i
$773$	1.71668	+	11.9398i	0.0617446	+	0.429443i	0.997123	+	0.0757956i	$0.0241496\pi$
$773$	1.71668	+	11.9398i	0.0617446	+	0.429443i	−0.935379	+	0.353647i	$0.884941\pi$
$774$	15.8871	+	38.0466i	0.571050	+	1.36756i
$775$	−7.55916	+	3.45215i	−0.271533	+	0.124005i
$776$	1.74886	−	1.12392i	0.0627804	−	0.0403465i
$777$	25.9299	+	20.2499i	0.930230	+	0.726460i
$778$	19.2532	+	12.3733i	0.690261	+	0.443604i
$779$	9.09829	+	7.88371i	0.325980	+	0.282463i
$780$	5.06152	+	14.2824i	0.181231	+	0.511390i
$781$	7.87956			0.281953
$782$	3.27981	−	17.4985i	0.117286	−	0.625747i
$783$	5.69414	−	1.80982i	0.203492	−	0.0646777i
$784$	29.5614	−	18.6658i	1.05577	−	0.666635i
$785$	−42.2213	−	36.5850i	−1.50694	−	1.30577i
$786$	−0.852621	−	15.4920i	−0.0304120	−	0.552582i
$787$	−49.9200	−	7.17741i	−1.77946	−	0.255847i	−0.827366	−	0.561664i	$-0.810161\pi$
$787$	−49.9200	−	7.17741i	−1.77946	−	0.255847i	−0.952090	+	0.305817i	$0.901071\pi$
$788$	15.7305	+	24.4771i	0.560376	+	0.871962i
$789$	−2.30161	+	4.05534i	−0.0819396	+	0.144374i
$790$	7.80834	−	6.76596i	0.277808	−	0.240722i
$791$	12.1358	−	7.73084i	0.431499	−	0.274877i
$792$	−15.5633	−	14.4070i	−0.553016	−	0.511930i
$793$	−8.22930	+	2.41634i	−0.292231	+	0.0858068i
$794$	−19.5314	+	5.73494i	−0.693143	+	0.203525i
$795$	−65.6750	+	13.1613i	−2.32925	+	0.466782i
$796$	−27.5525	+	3.96145i	−0.976573	+	0.140410i
$797$	−24.4018	−	28.1611i	−0.864355	−	0.997518i	−0.999977	−	0.00675771i	$-0.997849\pi$
$797$	−24.4018	−	28.1611i	−0.864355	−	0.997518i	0.135623	−	0.990761i	$-0.456697\pi$
$798$	21.0810	+	1.94103i	0.746260	+	0.0687118i
$799$	16.6923	−	10.7275i	0.590531	−	0.379511i
$800$	−56.8511	−	8.17396i	−2.00999	−	0.288993i
$801$	23.9759	−	19.4344i	0.847146	−	0.686681i
$802$	17.9272	−	20.6891i	0.633030	−	0.730556i
$803$	−1.56843	−	0.460534i	−0.0553489	−	0.0162519i
$804$	−12.4100	+	8.97591i	−0.437668	+	0.316556i
$805$	48.4103	−	11.8016i	1.70624	−	0.415952i
$806$		−	2.89914i		−	0.102118i
$807$	−30.8883	+	10.9465i	−1.08732	+	0.385335i
$808$	22.1976	+	19.2343i	0.780908	+	0.676661i
$809$	4.79537	−	7.46175i	0.168596	−	0.262341i	−0.746666	−	0.665199i	$-0.768347\pi$
$809$	4.79537	−	7.46175i	0.168596	−	0.262341i	0.915263	+	0.402858i	$0.131983\pi$
$810$	−44.0696	−	43.5681i	−1.54845	−	1.53083i
$811$	−14.3655	−	22.3532i	−0.504441	−	0.784926i	0.491877	−	0.870665i	$-0.336311\pi$
$811$	−14.3655	−	22.3532i	−0.504441	−	0.784926i	−0.996318	+	0.0857393i	$0.972675\pi$
$812$	2.15031	−	2.46164i	0.0754610	−	0.0863865i
$813$	7.04695	−	30.0131i	0.247147	−	1.05260i
$814$	−7.80347	−	54.2743i	−0.273511	−	1.90231i
$815$	−18.3444	+	40.1686i	−0.642576	+	1.40704i
$816$	11.2150	−	14.4797i	0.392603	−	0.506891i
$817$	−5.81820	−	19.8150i	−0.203553	−	0.693238i
$818$	20.9204	−	45.8093i	0.731465	−	1.60169i
$819$	−4.05205	−	15.9513i	−0.141590	−	0.557385i
$820$	−12.6246	−	14.5696i	−0.440872	−	0.508793i
$821$	−39.6203	+	18.0940i	−1.38276	+	0.631485i	−0.961336	−	0.275380i	$-0.911196\pi$
$821$	−39.6203	+	18.0940i	−1.38276	+	0.631485i	−0.421423	+	0.906864i	$0.638469\pi$
$822$	−24.5678	+	62.7049i	−0.856901	+	2.18708i
$823$	7.44774	−	51.8002i	0.259612	−	1.80564i	−0.275981	−	0.961163i	$-0.589003\pi$
$823$	7.44774	−	51.8002i	0.259612	−	1.80564i	0.535592	−	0.844477i	$-0.320088\pi$
$824$	−1.11460	−	0.716313i	−0.0388291	−	0.0249539i
$825$	78.3209	+	6.89581i	2.72678	+	0.240081i
$826$	7.68793	+	55.0313i	0.267497	+	1.91478i
$827$		−	1.94824i		−	0.0677468i	−0.999426	−	0.0338734i	$-0.989216\pi$
$827$		−	1.94824i		−	0.0677468i	0.999426	−	0.0338734i	$-0.0107843\pi$
$828$	5.34510	+	14.5043i	0.185755	+	0.504058i
$829$			3.09702i			0.107564i	0.998553	+	0.0537820i	$0.0171276\pi$
$829$			3.09702i			0.107564i	−0.998553	+	0.0537820i	$0.982872\pi$
$830$	32.1740	−	109.575i	1.11678	−	3.80339i
$831$	0.191053	−	2.16993i	0.00662755	−	0.0752741i
$832$	−0.364726	+	0.567525i	−0.0126446	+	0.0196754i
$833$	−9.61533	−	11.2776i	−0.333151	−	0.390745i
$834$	14.4965	−	36.9997i	0.501973	−	1.28119i
$835$	−2.81412	−	6.16207i	−0.0973867	−	0.213247i
$836$	−8.07453	−	9.31851i	−0.279264	−	0.322287i
$837$	1.80429	+	3.73002i	0.0623655	+	0.128928i
$838$	0.992130	+	0.453090i	0.0342725	+	0.0156517i
$839$	43.7662	−	12.8509i	1.51098	−	0.443663i	0.581812	−	0.813324i	$-0.302344\pi$
$839$	43.7662	−	12.8509i	1.51098	−	0.443663i	0.929167	+	0.369660i	$0.120526\pi$
$840$	28.4062	+	6.78958i	0.980108	+	0.234263i
$841$	11.4978	−	25.1766i	0.396475	−	0.868160i
$842$	−11.1595	+	1.60449i	−0.384581	+	0.0552944i
$843$	4.41839	−	18.8180i	0.152177	−	0.648126i
$844$	−1.74043	−	3.81102i	−0.0599082	−	0.131181i
$845$	28.7432	−	18.4721i	0.988797	−	0.635461i
$846$	−21.9406	+	44.1470i	−0.754335	+	1.51780i
$847$	20.8682	+	3.08558i	0.717040	+	0.106022i
$848$	37.1702	+	32.2082i	1.27643	+	1.10603i
$849$	15.1805	+	42.8357i	0.520995	+	1.47012i
$850$			38.6865i			1.32694i
$851$	11.0947	−	32.5946i	0.380322	−	1.11733i
$852$	−1.97284	−	2.72763i	−0.0675884	−	0.0934472i
$853$	−5.36448	+	18.2697i	−0.183676	+	0.625544i	0.815245	+	0.579116i	$0.196602\pi$
$853$	−5.36448	+	18.2697i	−0.183676	+	0.625544i	−0.998922	+	0.0464284i	$0.985216\pi$
$854$	5.47961	−	18.3896i	0.187508	−	0.629279i
$855$	19.5455	+	24.1130i	0.668444	+	0.824647i
$856$	−3.38377	+	23.5346i	−0.115655	+	0.804397i
$857$	17.2739	−	11.1013i	0.590065	−	0.379212i	−0.211270	−	0.977428i	$-0.567760\pi$
$857$	17.2739	−	11.1013i	0.590065	−	0.379212i	0.801335	+	0.598216i	$0.204124\pi$
$858$	−13.5390	+	23.8551i	−0.462214	+	0.814401i
$859$	−38.0162	+	32.9412i	−1.29710	+	1.12394i	−0.312346	+	0.949968i	$0.601115\pi$
$859$	−38.0162	+	32.9412i	−1.29710	+	1.12394i	−0.984751	+	0.173972i	$0.944340\pi$
$860$	4.70642	+	32.7338i	0.160487	+	1.11621i
$861$	12.2035	+	17.0152i	0.415893	+	0.579877i
$862$	−39.4832	+	11.5933i	−1.34480	+	0.394870i
$863$	12.4734	+	42.4804i	0.424598	+	1.44605i	0.843063	+	0.537815i	$0.180750\pi$
$863$	12.4734	+	42.4804i	0.424598	+	1.44605i	−0.418464	+	0.908233i	$0.637432\pi$
$864$	−3.44699	+	28.4296i	−0.117269	+	0.967196i
$865$	−2.99045	−	20.7991i	−0.101678	−	0.707189i
$866$	−3.36247	−	3.88049i	−0.114261	−	0.131865i
$867$	18.8559	+	10.7017i	0.640379	+	0.363448i
$868$	1.90196	+	1.23309i	0.0645569	+	0.0418537i
$869$	6.46944	+	0.930165i	0.219461	+	0.0315537i
$870$	13.6927	−	0.753593i	0.464226	−	0.0255492i
$871$	−12.8974	−	11.1757i	−0.437011	−	0.378673i
$872$	2.78560	−	9.48687i	0.0943322	−	0.321266i
$873$	3.64956	+	1.20310i	0.123519	+	0.0407188i
$874$	−5.33342	−	21.5038i	−0.180405	−	0.727378i
$875$	−51.3300	+	23.1941i	−1.73527	+	0.784105i
$876$	0.233275	+	0.658244i	0.00788163	+	0.0222400i
$877$	−32.1374	+	37.0886i	−1.08520	+	1.25239i	−0.119476	+	0.992837i	$0.538122\pi$
$877$	−32.1374	+	37.0886i	−1.08520	+	1.25239i	−0.965728	+	0.259556i	$0.916424\pi$
$878$	13.0704	+	8.39986i	0.441106	+	0.283482i
$879$	9.32344	+	17.7618i	0.314472	+	0.599092i
$880$	−46.1880	−	71.8699i	−1.55700	−	2.42274i
$881$	2.73515	+	5.98913i	0.0921494	+	0.201779i	0.950094	−	0.311962i	$-0.100986\pi$
$881$	2.73515	+	5.98913i	0.0921494	+	0.201779i	−0.857945	+	0.513741i	$0.828259\pi$
$882$	34.8768	+	11.8073i	1.17436	+	0.397573i
$883$	4.37601	+	30.4358i	0.147264	+	1.02425i	0.920672	+	0.390337i	$0.127642\pi$
$883$	4.37601	+	30.4358i	0.147264	+	1.02425i	−0.773407	+	0.633909i	$0.781449\pi$
$884$	−4.29033	−	1.95933i	−0.144299	−	0.0658993i
$885$	−49.8876	+	64.4100i	−1.67695	+	2.16512i
$886$	24.4435	−	7.17726i	0.821196	−	0.241125i
$887$	1.14580	−	2.50896i	0.0384724	−	0.0842427i	−0.889420	−	0.457091i	$-0.848891\pi$
$887$	1.14580	−	2.50896i	0.0384724	−	0.0842427i	0.927892	+	0.372848i	$0.121619\pi$
$888$	14.5029	−	14.0343i	0.486686	−	0.470960i
$889$	−27.5877	−	12.7324i	−0.925260	−	0.427030i
$890$	64.4357	−	29.4268i	2.15989	−	0.986388i
$891$	2.57284	−	39.1179i	0.0861934	−	1.31050i
$892$	29.6594	+	4.26438i	0.993072	+	0.142782i
$893$	13.3499	−	20.7728i	0.446737	−	0.695136i
$894$	−1.66579	+	18.9196i	−0.0557123	+	0.632767i
$895$	13.5932	−	46.2941i	0.454370	−	1.54744i
$896$	−12.6303	−	27.9516i	−0.421948	−	0.933796i
$897$	−14.3721	+	9.49226i	−0.479871	+	0.316938i
$898$	52.7441			1.76009
$899$	−0.879773	−	0.258325i	−0.0293421	−	0.00861561i
$900$	−17.2225	−	28.8386i	−0.574082	−	0.961286i
$901$	11.2718	−	17.5393i	0.375518	−	0.584317i
$902$	4.96645	−	34.5424i	0.165365	−	1.15014i
$903$	−1.83050	−	35.8725i	−0.0609151	−	1.19376i
$904$	−3.66666	−	8.02887i	−0.121951	−	0.267036i
$905$	17.1602	−	14.8694i	0.570425	−	0.494276i
$906$	18.8987	−	18.2880i	0.627866	−	0.607579i
$907$	−6.97995	+	15.2840i	−0.231766	+	0.507496i	−0.989406	−	0.145177i	$-0.953625\pi$
$907$	−6.97995	+	15.2840i	−0.231766	+	0.507496i	0.757640	+	0.652672i	$0.226352\pi$
$908$	−19.5711	+	5.74659i	−0.649490	+	0.190707i
$909$	−1.78257	+	54.2635i	−0.0591241	+	1.79981i
$910$	0.150981	−	37.7739i	0.00500496	−	1.25219i
$911$	−54.5086	+	7.83716i	−1.80595	+	0.259657i	−0.961269	−	0.275611i	$-0.911120\pi$
$911$	−54.5086	+	7.83716i	−1.80595	+	0.259657i	−0.844683	+	0.535267i	$0.820211\pi$
$912$	5.20983	−	22.1887i	0.172515	−	0.734742i
$913$	65.7148	−	30.0110i	2.17484	−	0.993218i
$914$	16.8101	+	26.1570i	0.556027	+	0.865196i
$915$	24.9110	−	13.0761i	0.823532	−	0.432283i
$916$	4.51759	−	7.02951i	0.149265	−	0.232261i
$917$	−3.85993	+	12.9540i	−0.127466	+	0.427777i
$918$	19.2846	−	0.427073i	0.636487	−	0.0140955i
$919$	−18.3790			−0.606268			−0.303134	−	0.952948i	$-0.598033\pi$
$919$	−18.3790			−0.606268			−0.303134	+	0.952948i	$0.598033\pi$
$920$	−3.06107	−	30.4119i	−0.100921	−	1.00265i
$921$	−12.3209	−	17.0348i	−0.405989	−	0.561317i
$922$	5.43454	−	18.5084i	0.178977	−	0.609540i
$923$	2.45633	−	2.83475i	0.0808510	−	0.0933070i
$924$	−9.89149	−	19.0284i	−0.325406	−	0.625990i
$925$	−10.6478	+	74.0574i	−0.350099	+	2.43499i
$926$	−0.359301	−	0.559083i	−0.0118074	−	0.0183726i
$927$	−0.268765	−	2.43432i	−0.00882739	−	0.0799535i
$928$	−4.15004	−	4.78940i	−0.136232	−	0.157220i
$929$	0.701550	+	4.87939i	0.0230171	+	0.160088i	0.998088	−	0.0618050i	$-0.0196857\pi$
$929$	0.701550	+	4.87939i	0.0230171	+	0.160088i	−0.975071	+	0.221893i	$0.928777\pi$
$930$	1.86867	+	9.32471i	0.0612762	+	0.305769i
$931$	−16.7146	−	7.79540i	−0.547800	−	0.255484i
$932$	1.57187	+	5.35329i	0.0514882	+	0.175353i
$933$	−7.31628	−	36.5084i	−0.239524	−	1.19523i
$934$	−19.8397	+	2.85252i	−0.649176	+	0.0933375i
$935$	−27.3694	+	23.7157i	−0.895075	+	0.775587i
$936$	−10.0347	+	1.10789i	−0.327993	+	0.0362126i
$937$	2.04590	+	3.18348i	0.0668367	+	0.104000i	0.873063	−	0.487607i	$-0.162130\pi$
$937$	2.04590	+	3.18348i	0.0668367	+	0.104000i	−0.806227	+	0.591607i	$0.798494\pi$
$938$	36.6771	−	10.6103i	1.19755	−	0.346439i
$939$	1.06522	+	19.3549i	0.0347621	+	0.631625i
$940$	−25.8944	+	29.8837i	−0.844583	+	0.974700i
$941$	−8.58808	−	2.52169i	−0.279964	−	0.0822047i	0.138736	−	0.990329i	$-0.455696\pi$
$941$	−8.58808	−	2.52169i	−0.279964	−	0.0822047i	−0.418700	+	0.908125i	$0.637514\pi$
$942$	−35.0077	+	25.3204i	−1.14061	+	0.824982i
$943$	12.6195	−	17.9149i	0.410949	−	0.583391i
$944$	59.8229			1.94707
$945$	23.3145	+	48.6936i	0.758421	+	1.58400i
$946$	−39.2026	+	45.2422i	−1.27459	+	1.47095i
$947$	6.50255	−	10.1182i	0.211304	−	0.328796i	−0.719382	−	0.694615i	$-0.755575\pi$
$947$	6.50255	−	10.1182i	0.211304	−	0.328796i	0.930686	+	0.365819i	$0.119211\pi$
$948$	−1.29779	−	2.47239i	−0.0421503	−	0.0802995i
$949$	−0.654617	+	0.420697i	−0.0212498	+	0.0136564i
$950$	19.9996	+	43.7930i	0.648872	+	1.42083i
$951$	−9.52658	+	40.5739i	−0.308921	+	1.31570i
$952$	−7.66742	+	4.88436i	−0.248503	+	0.158303i
$953$	−13.4021	−	6.12054i	−0.434137	−	0.198264i	0.186345	−	0.982484i	$-0.440336\pi$
$953$	−13.4021	−	6.12054i	−0.434137	−	0.198264i	−0.620482	+	0.784221i	$0.713063\pi$
$954$	−1.70072	+	51.7720i	−0.0550629	+	1.67618i
$955$	20.1872	+	68.7514i	0.653244	+	2.22474i
$956$	−3.23222	−	1.47611i	−0.104537	−	0.0477407i
$957$	6.03269	+	6.23412i	0.195009	+	0.201521i
$958$	39.3548	−	34.1012i	1.27150	−	1.10176i
$959$	38.5980	−	44.1863i	1.24639	−	1.42685i
$960$	0.807290	−	2.06046i	0.0260552	−	0.0665010i
$961$	−4.32127	+	30.0551i	−0.139396	+	0.969518i
$962$	−21.9584	−	14.1118i	−0.707966	−	0.454982i
$963$	−37.7338	+	22.5347i	−1.21595	+	0.726172i
$964$	−1.36355	+	4.64381i	−0.0439169	+	0.149567i
$965$	−30.8814			−0.994107
$966$	−0.327544	−	38.5334i	−0.0105386	−	1.23979i
$967$	22.5026			0.723634			0.361817	−	0.932249i	$-0.382156\pi$
$967$	22.5026			0.723634			0.361817	+	0.932249i	$0.382156\pi$
$968$	3.64566	−	12.4160i	0.117176	−	0.399065i
$969$	−9.62444	−	0.847389i	−0.309182	−	0.0272220i
$970$	7.41974	+	4.76838i	0.238233	+	0.153103i
$971$	−6.91398	+	48.0878i	−0.221880	+	1.54321i	0.509037	+	0.860745i	$0.330002\pi$
$971$	−6.91398	+	48.0878i	−0.221880	+	1.54321i	−0.730917	+	0.682466i	$0.760907\pi$
$972$	−14.1855	+	8.90349i	−0.454999	+	0.285580i
$973$	−22.7751	+	26.0726i	−0.730137	+	0.835850i
$974$	−16.6554	+	14.4320i	−0.533674	+	0.462431i
$975$	26.8962	−	26.0271i	0.861366	−	0.833535i
$976$	−18.7919	−	8.58196i	−0.601513	−	0.274702i
$977$	9.40825	+	32.0416i	0.300997	+	1.02510i	0.961620	+	0.274383i	$0.0884736\pi$
$977$	9.40825	+	32.0416i	0.300997	+	1.02510i	−0.660624	+	0.750717i	$0.729708\pi$
$978$	26.9994	+	20.9119i	0.863345	+	0.668688i
$979$	40.7620	+	18.6154i	1.30276	+	0.594951i
$980$	24.7171	+	16.1654i	0.789560	+	0.516384i
$981$	16.8653	−	7.04244i	0.538468	−	0.224848i
$982$	−6.68953	−	14.6480i	−0.213471	−	0.467437i
$983$	11.0831	−	7.12266i	0.353495	−	0.227178i	−0.351826	−	0.936065i	$-0.614439\pi$
$983$	11.0831	−	7.12266i	0.353495	−	0.227178i	0.705321	+	0.708888i	$0.250803\pi$
$984$	11.3728	−	5.96974i	0.362552	−	0.190308i
$985$	57.4964	−	89.4662i	1.83199	−	2.85063i
$986$	−2.79531	+	3.22595i	−0.0890207	+	0.102735i
$987$	30.9825	−	29.7425i	0.986183	−	0.946715i
$988$	−5.86954			−0.186735
$989$	−34.8261	+	14.1494i	−1.10740	+	0.449925i
$990$	28.1703	−	85.4536i	0.895312	−	2.71589i
$991$	−36.2824	−	10.6535i	−1.15255	−	0.338419i	−0.351016	−	0.936370i	$-0.614164\pi$
$991$	−36.2824	−	10.6535i	−1.15255	−	0.338419i	−0.801533	+	0.597951i	$0.795982\pi$
$992$	2.87801	−	3.32140i	0.0913768	−	0.105454i
$993$	−6.77960	+	0.373122i	−0.215144	+	0.0118407i
$994$	2.33207	+	8.06135i	0.0739687	+	0.255691i
$995$	55.0062	+	85.5913i	1.74381	+	2.71343i
$996$	−26.8421	−	15.2342i	−0.850524	−	0.482716i
$997$	40.7108	−	35.2761i	1.28932	−	1.11720i	0.302892	−	0.953025i	$-0.402048\pi$
$997$	40.7108	−	35.2761i	1.28932	−	1.11720i	0.986430	−	0.164179i	$-0.0524976\pi$
$998$	−13.0919	+	1.88233i	−0.414416	+	0.0595840i
$999$	37.0340	+	4.49024i	1.17170	+	0.142065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.14	yes	600
3.2	odd	2	inner	483.2.v.a.41.47	yes	600
7.6	odd	2	inner	483.2.v.a.41.13	✓	600
21.20	even	2	inner	483.2.v.a.41.48	yes	600
23.9	even	11	inner	483.2.v.a.377.48	yes	600
69.32	odd	22	inner	483.2.v.a.377.13	yes	600
161.55	odd	22	inner	483.2.v.a.377.47	yes	600
483.377	even	22	inner	483.2.v.a.377.14	yes	600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.13	✓	600	7.6	odd	2	inner
483.2.v.a.41.14	yes	600	1.1	even	1	trivial
483.2.v.a.41.47	yes	600	3.2	odd	2	inner
483.2.v.a.41.48	yes	600	21.20	even	2	inner
483.2.v.a.377.13	yes	600	69.32	odd	22	inner
483.2.v.a.377.14	yes	600	483.377	even	22	inner
483.2.v.a.377.47	yes	600	161.55	odd	22	inner
483.2.v.a.377.48	yes	600	23.9	even	11	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+(-0.493988 + 1.68237i) q^{2} +(0.151912 - 1.72538i) q^{3} +(-0.903836 - 0.580860i) q^{4} +(-0.558871 + 3.88703i) q^{5} +(2.82768 + 1.10789i) q^{6} +(-1.99258 - 1.74058i) q^{7} +(-1.22655 + 1.06281i) q^{8} +(-2.95385 - 0.524209i) q^{9} +(-6.26335 - 2.86037i) q^{10} +(-1.22718 - 4.17938i) q^{11} +(-1.13951 + 1.47122i) q^{12} +(-1.88613 - 0.861367i) q^{13} +(3.91261 - 2.49244i) q^{14} +(6.62169 + 1.55475i) q^{15} +(-2.07478 - 4.54313i) q^{16} +(-1.78108 + 1.14463i) q^{17} +(2.34108 - 4.71051i) q^{18} +(-1.42444 + 2.21647i) q^{19} +(2.76295 - 3.18861i) q^{20} +(-3.30585 + 3.17354i) q^{21} +7.63748 q^{22} +(4.27389 + 2.17574i) q^{23} +(1.64742 + 2.27771i) q^{24} +(-9.99921 - 2.93603i) q^{25} +(2.38086 - 2.74766i) q^{26} +(-1.35318 + 5.01686i) q^{27} +(0.789938 + 2.73061i) q^{28} +(-0.621661 - 0.967323i) q^{29} +(-5.88670 + 10.3721i) q^{30} +(0.602646 - 0.522195i) q^{31} +(5.45526 - 0.784348i) q^{32} +(-7.39743 + 1.48245i) q^{33} +(-1.04586 - 3.56187i) q^{34} +(7.87927 - 6.77248i) q^{35} +(2.36530 + 2.18957i) q^{36} +(-1.02173 - 7.10631i) q^{37} +(-3.02527 - 3.49135i) q^{38} +(-1.77271 + 3.12343i) q^{39} +(-3.44569 - 5.36161i) q^{40} +(0.650274 - 4.52275i) q^{41} +(-3.70602 - 7.12935i) q^{42} +(-5.13293 + 5.92372i) q^{43} +(-1.31847 + 4.49029i) q^{44} +(3.68844 - 11.1887i) q^{45} +(-5.77165 + 6.11548i) q^{46} -9.37202 q^{47} +(-8.15378 + 2.88962i) q^{48} +(0.940785 + 6.93649i) q^{49} +(9.87898 - 15.3720i) q^{50} +(1.70435 + 3.24691i) q^{51} +(1.20442 + 1.87411i) q^{52} +(-8.95765 + 4.09082i) q^{53} +(-7.77176 - 4.75482i) q^{54} +(16.9312 - 2.43434i) q^{55} +(4.29390 + 0.0171625i) q^{56} +(3.60786 + 2.79440i) q^{57} +(1.93449 - 0.568017i) q^{58} +(-4.97577 + 10.8954i) q^{59} +(-5.08183 - 5.25151i) q^{60} +(3.12603 - 2.70872i) q^{61} +(0.580826 + 1.27183i) q^{62} +(4.97336 + 6.18593i) q^{63} +(0.0463023 - 0.322040i) q^{64} +(4.40226 - 6.85005i) q^{65} +(1.16022 - 13.1775i) q^{66} +(7.89696 + 2.31876i) q^{67} +2.27467 q^{68} +(4.40322 - 7.04355i) q^{69} +(7.50155 + 16.6014i) q^{70} +(-0.509646 + 1.73569i) q^{71} +(4.18017 - 2.49641i) q^{72} +(0.202891 - 0.315705i) q^{73} +(12.4602 + 1.79150i) q^{74} +(-6.58476 + 16.8064i) q^{75} +(2.57492 - 1.17593i) q^{76} +(-4.82928 + 10.4638i) q^{77} +(-4.37907 - 4.52529i) q^{78} +(-0.623336 + 1.36491i) q^{79} +(18.8188 - 5.52570i) q^{80} +(8.45041 + 3.09687i) q^{81} +(7.28772 + 3.32819i) q^{82} +(2.36036 + 16.4166i) q^{83} +(4.83133 - 0.948129i) q^{84} +(-3.45382 - 7.56281i) q^{85} +(-7.43027 - 11.5617i) q^{86} +(-1.76343 + 0.925651i) q^{87} +(5.94708 + 3.82196i) q^{88} +(-6.73704 + 7.77495i) q^{89} +(17.0015 + 11.7324i) q^{90} +(2.25900 + 4.99930i) q^{91} +(-2.59910 - 4.44904i) q^{92} +(-0.809435 - 1.11912i) q^{93} +(4.62967 - 15.7672i) q^{94} +(-7.81942 - 6.77557i) q^{95} +(-0.524578 - 9.53152i) q^{96} +(-1.26788 - 0.182293i) q^{97} +(-12.1345 - 1.84380i) q^{98} +(1.43402 + 12.9885i) 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

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