LMFDB - Embedded newform 357.2.bl.a.10.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(10,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 8, 9]))

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

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

chi := DirichletCharacter("357.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, degree $16$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.22
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19456 - 0.288919i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(2.80077 - 0.750463i) q^{4} +(1.81750 - 1.59391i) q^{5} +(-1.22975 - 1.84045i) q^{6} +(-2.53809 + 0.747063i) q^{7} +(1.83962 - 0.761994i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(3.52811 - 4.02303i) q^{10} +(6.12220 - 0.401270i) q^{11} +(-1.91182 - 2.18001i) q^{12} +(-1.93919 - 1.93919i) q^{13} +(-5.35415 + 2.37278i) q^{14} +(-2.23339 - 0.925101i) q^{15} +(-1.20520 + 0.695825i) q^{16} +(-1.67081 + 3.76940i) q^{17} +(-1.10675 + 1.91694i) q^{18} +(-0.168515 - 1.28000i) q^{19} +(3.89423 - 5.82813i) q^{20} +(1.79259 + 1.94593i) q^{21} +(13.3196 - 2.64943i) q^{22} +(-1.19810 - 0.590837i) q^{23} +(-1.49705 - 1.31288i) q^{24} +(0.110144 - 0.836630i) q^{25} +(-4.81593 - 3.69540i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-6.54795 + 3.99709i) q^{28} +(0.988225 + 4.96814i) q^{29} +(-5.16859 - 1.38492i) q^{30} +(0.796154 - 0.392620i) q^{31} +(-5.60328 + 4.29955i) q^{32} +(-3.06767 - 5.31335i) q^{33} +(-2.57765 + 8.75490i) q^{34} +(-3.42223 + 5.40327i) q^{35} +(-1.10962 + 2.67885i) q^{36} +(-0.491054 + 7.49203i) q^{37} +(-0.739630 - 2.76034i) q^{38} +(-0.881524 + 2.59689i) q^{39} +(2.12896 - 4.31710i) q^{40} +(0.303942 - 1.52802i) q^{41} +(4.49616 + 3.75254i) q^{42} +(0.638340 + 1.54109i) q^{43} +(16.8457 - 5.71834i) q^{44} +(0.158106 + 2.41223i) q^{45} +(-2.80000 - 0.950473i) q^{46} +(1.49827 - 5.59161i) q^{47} +(1.15711 + 0.773159i) q^{48} +(5.88379 - 3.79223i) q^{49} -1.86786i q^{50} +(4.11965 - 0.168656i) q^{51} +(-6.88650 - 3.97592i) q^{52} +(0.274336 + 0.357522i) q^{53} +(2.20876 + 0.144770i) q^{54} +(10.4875 - 10.4875i) q^{55} +(-4.09985 + 3.30832i) q^{56} +(-1.07346 + 0.717263i) q^{57} +(3.60411 + 10.6174i) q^{58} +(-7.93991 - 1.04531i) q^{59} +(-6.94946 - 0.914914i) q^{60} +(2.55458 + 7.52555i) q^{61} +(1.63377 - 1.09165i) q^{62} +(0.952406 - 2.46838i) q^{63} +(-9.08642 + 9.08642i) q^{64} +(-6.61536 - 0.433594i) q^{65} +(-8.26731 - 10.7742i) q^{66} +(-11.9999 - 6.92817i) q^{67} +(-1.85076 + 11.8111i) q^{68} +1.33586i q^{69} +(-5.94919 + 12.8465i) q^{70} +(6.51440 + 4.35279i) q^{71} +(-0.515357 + 1.92334i) q^{72} +(-0.868463 - 0.294804i) q^{73} +(1.08695 + 16.5836i) q^{74} +(-0.799067 + 0.271247i) q^{75} +(-1.43256 - 3.45850i) q^{76} +(-15.2389 + 5.59213i) q^{77} +(-1.18427 + 5.95371i) q^{78} +(3.85365 - 7.81443i) q^{79} +(-1.08138 + 3.18564i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.225545 - 3.44115i) q^{82} +(5.67933 - 13.7111i) q^{83} +(6.48097 + 4.10481i) q^{84} +(2.97136 + 9.51401i) q^{85} +(1.84613 + 3.19759i) q^{86} +(4.01871 - 3.08367i) q^{87} +(10.9567 - 5.40326i) q^{88} +(-10.4953 - 2.81219i) q^{89} +(1.04391 + 5.24810i) q^{90} +(6.37053 + 3.47314i) q^{91} +(-3.79900 - 0.755667i) q^{92} +(-0.704260 - 0.540398i) q^{93} +(1.67251 - 12.7040i) q^{94} +(-2.34647 - 2.05780i) q^{95} +(6.33442 + 3.12379i) q^{96} +(8.60161 - 1.71097i) q^{97} +(11.8167 - 10.0222i) q^{98} +(-3.40861 + 5.10134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	2.19456	−	0.288919i	1.55179	−	0.204297i	0.694636	−	0.719361i	$-0.255565\pi$
$2$	2.19456	−	0.288919i	1.55179	−	0.204297i	0.857152	+	0.515064i	$0.172232\pi$
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$4$	2.80077	−	0.750463i	1.40038	−	0.375231i
$5$	1.81750	−	1.59391i	0.812811	−	0.712817i	−0.148310	−	0.988941i	$-0.547383\pi$
$5$	1.81750	−	1.59391i	0.812811	−	0.712817i	0.961122	+	0.276124i	$0.0890501\pi$
$6$	−1.22975	−	1.84045i	−0.502044	−	0.751363i
$7$	−2.53809	+	0.747063i	−0.959308	+	0.282363i
$7$	−2.53809	+	0.747063i	−0.959308	+	0.282363i
$8$	1.83962	−	0.761994i	0.650402	−	0.269406i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	3.52811	−	4.02303i	1.11568	−	1.27219i
$11$	6.12220	−	0.401270i	1.84591	−	0.120987i	0.898095	−	0.439802i	$-0.144952\pi$
$11$	6.12220	−	0.401270i	1.84591	−	0.120987i	0.947817	+	0.318815i	$0.103285\pi$
$12$	−1.91182	−	2.18001i	−0.551894	−	0.629314i
$13$	−1.93919	−	1.93919i	−0.537834	−	0.537834i	0.385058	−	0.922892i	$-0.374181\pi$
$13$	−1.93919	−	1.93919i	−0.537834	−	0.537834i	−0.922892	+	0.385058i	$0.874181\pi$
$14$	−5.35415	+	2.37278i	−1.43096	+	0.634152i
$15$	−2.23339	−	0.925101i	−0.576659	−	0.238860i
$16$	−1.20520	+	0.695825i	−0.301301	+	0.173956i
$17$	−1.67081	+	3.76940i	−0.405232	+	0.914214i
$17$	−1.67081	+	3.76940i	−0.405232	+	0.914214i
$18$	−1.10675	+	1.91694i	−0.260863	+	0.451828i
$19$	−0.168515	−	1.28000i	−0.0386599	−	0.293651i	−0.999843	−	0.0177386i	$-0.994353\pi$
$19$	−0.168515	−	1.28000i	−0.0386599	−	0.293651i	0.961183	−	0.275912i	$-0.0889800\pi$
$20$	3.89423	−	5.82813i	0.870776	−	1.30321i
$21$	1.79259	+	1.94593i	0.391175	+	0.424636i
$22$	13.3196	−	2.64943i	2.83975	−	0.564861i
$23$	−1.19810	−	0.590837i	−0.249821	−	0.123198i	0.313068	−	0.949731i	$-0.398643\pi$
$23$	−1.19810	−	0.590837i	−0.249821	−	0.123198i	−0.562889	+	0.826533i	$0.690310\pi$
$24$	−1.49705	−	1.31288i	−0.305585	−	0.267991i
$25$	0.110144	−	0.836630i	0.0220289	−	0.167326i
$26$	−4.81593	−	3.69540i	−0.944482	−	0.724727i
$27$	0.980785	+	0.195090i	0.188752	+	0.0375451i
$28$	−6.54795	+	3.99709i	−1.23745	+	0.755379i
$29$	0.988225	+	4.96814i	0.183509	+	0.922561i	0.957295	+	0.289114i	$0.0933606\pi$
$29$	0.988225	+	4.96814i	0.183509	+	0.922561i	−0.773786	+	0.633447i	$0.781639\pi$
$30$	−5.16859	−	1.38492i	−0.943651	−	0.252851i
$31$	0.796154	−	0.392620i	0.142994	−	0.0705166i	−0.369384	−	0.929277i	$-0.620431\pi$
$31$	0.796154	−	0.392620i	0.142994	−	0.0705166i	0.512378	+	0.858760i	$0.328765\pi$
$32$	−5.60328	+	4.29955i	−0.990530	+	0.760060i
$33$	−3.06767	−	5.31335i	−0.534012	−	0.924936i
$34$	−2.57765	+	8.75490i	−0.442063	+	1.50145i
$35$	−3.42223	+	5.40327i	−0.578463	+	0.913318i
$36$	−1.10962	+	2.67885i	−0.184936	+	0.446475i
$37$	−0.491054	+	7.49203i	−0.0807287	+	1.23168i	0.744787	+	0.667303i	$0.232551\pi$
$37$	−0.491054	+	7.49203i	−0.0807287	+	1.23168i	−0.825515	+	0.564380i	$0.809115\pi$
$38$	−0.739630	−	2.76034i	−0.119984	−	0.447786i
$39$	−0.881524	+	2.59689i	−0.141157	+	0.415835i
$40$	2.12896	−	4.31710i	0.336618	−	0.682594i
$41$	0.303942	−	1.52802i	0.0474678	−	0.238637i	−0.949766	−	0.312960i	$-0.898680\pi$
$41$	0.303942	−	1.52802i	0.0474678	−	0.238637i	0.997234	+	0.0743229i	$0.0236795\pi$
$42$	4.49616	+	3.75254i	0.693772	+	0.579029i
$43$	0.638340	+	1.54109i	0.0973460	+	0.235014i	0.965049	−	0.262068i	$-0.0844046\pi$
$43$	0.638340	+	1.54109i	0.0973460	+	0.235014i	−0.867703	+	0.497083i	$0.834405\pi$
$44$	16.8457	−	5.71834i	2.53958	−	0.862073i
$45$	0.158106	+	2.41223i	0.0235690	+	0.359594i
$46$	−2.80000	−	0.950473i	−0.412838	−	0.140140i
$47$	1.49827	−	5.59161i	0.218545	−	0.815620i	−0.766344	−	0.642431i	$-0.777926\pi$
$47$	1.49827	−	5.59161i	0.218545	−	0.815620i	0.984889	−	0.173189i	$-0.0554072\pi$
$48$	1.15711	+	0.773159i	0.167015	+	0.111596i
$49$	5.88379	−	3.79223i	0.840542	−	0.541747i
$50$		−	1.86786i		−	0.264155i
$51$	4.11965	−	0.168656i	0.576867	−	0.0236166i
$52$	−6.88650	−	3.97592i	−0.954986	−	0.551361i
$53$	0.274336	+	0.357522i	0.0376829	+	0.0491094i	0.811815	−	0.583915i	$-0.198480\pi$
$53$	0.274336	+	0.357522i	0.0376829	+	0.0491094i	−0.774132	+	0.633024i	$0.781813\pi$
$54$	2.20876	+	0.144770i	0.300574	+	0.0197006i
$55$	10.4875	−	10.4875i	1.41414	−	1.41414i
$56$	−4.09985	+	3.30832i	−0.547866	+	0.442093i
$57$	−1.07346	+	0.717263i	−0.142183	+	0.0950039i
$58$	3.60411	+	10.6174i	0.473243	+	1.39413i
$59$	−7.93991	−	1.04531i	−1.03369	−	0.136088i	−0.405457	−	0.914114i	$-0.632888\pi$
$59$	−7.93991	−	1.04531i	−1.03369	−	0.136088i	−0.628232	+	0.778026i	$0.716221\pi$
$60$	−6.94946	−	0.914914i	−0.897171	−	0.118115i
$61$	2.55458	+	7.52555i	0.327080	+	0.963548i	0.978752	+	0.205047i	$0.0657347\pi$
$61$	2.55458	+	7.52555i	0.327080	+	0.963548i	−0.651672	+	0.758501i	$0.725932\pi$
$62$	1.63377	−	1.09165i	0.207489	−	0.138640i
$63$	0.952406	−	2.46838i	0.119992	−	0.310987i
$64$	−9.08642	+	9.08642i	−1.13580	+	1.13580i
$65$	−6.61536	−	0.433594i	−0.820535	−	0.0537807i
$66$	−8.26731	−	10.7742i	−1.01764	−	1.32621i
$67$	−11.9999	−	6.92817i	−1.46603	−	0.846411i	−0.466749	−	0.884390i	$-0.654575\pi$
$67$	−11.9999	−	6.92817i	−1.46603	−	0.846411i	−0.999279	+	0.0379788i	$0.987908\pi$
$68$	−1.85076	+	11.8111i	−0.224438	+	1.43231i
$69$			1.33586i			0.160819i
$70$	−5.94919	+	12.8465i	−0.711064	+	1.53545i
$71$	6.51440	+	4.35279i	0.773118	+	0.516581i	0.878437	−	0.477858i	$-0.158587\pi$
$71$	6.51440	+	4.35279i	0.773118	+	0.516581i	−0.105320	+	0.994438i	$0.533587\pi$
$72$	−0.515357	+	1.92334i	−0.0607354	+	0.226668i
$73$	−0.868463	−	0.294804i	−0.101646	−	0.0345041i	0.270153	−	0.962817i	$-0.412926\pi$
$73$	−0.868463	−	0.294804i	−0.101646	−	0.0345041i	−0.371799	+	0.928313i	$0.621259\pi$
$74$	1.08695	+	16.5836i	0.126355	+	1.92780i
$75$	−0.799067	+	0.271247i	−0.0922683	+	0.0313209i
$76$	−1.43256	−	3.45850i	−0.164326	−	0.396717i
$77$	−15.2389	+	5.59213i	−1.73663	+	0.637282i
$78$	−1.18427	+	5.95371i	−0.134092	+	0.674125i
$79$	3.85365	−	7.81443i	0.433569	−	0.879192i	−0.564967	−	0.825113i	$-0.691111\pi$
$79$	3.85365	−	7.81443i	0.433569	−	0.879192i	0.998537	−	0.0540784i	$-0.0172221\pi$
$80$	−1.08138	+	3.18564i	−0.120902	+	0.356166i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	0.225545	−	3.44115i	0.0249072	−	0.380011i
$83$	5.67933	−	13.7111i	0.623387	−	1.50499i	−0.224314	−	0.974517i	$-0.572014\pi$
$83$	5.67933	−	13.7111i	0.623387	−	1.50499i	0.847702	−	0.530473i	$-0.177986\pi$
$84$	6.48097	+	4.10481i	0.707131	+	0.447871i
$85$	2.97136	+	9.51401i	0.322290	+	1.03194i
$86$	1.84613	+	3.19759i	0.199073	+	0.344805i
$87$	4.01871	−	3.08367i	0.430851	−	0.330604i
$88$	10.9567	−	5.40326i	1.16799	−	0.575989i
$89$	−10.4953	−	2.81219i	−1.11249	−	0.298092i	−0.344652	−	0.938731i	$-0.612003\pi$
$89$	−10.4953	−	2.81219i	−1.11249	−	0.298092i	−0.767843	+	0.640639i	$0.778670\pi$
$90$	1.04391	+	5.24810i	0.110038	+	0.553199i
$91$	6.37053	+	3.47314i	0.667813	+	0.364084i
$92$	−3.79900	−	0.755667i	−0.396073	−	0.0787838i
$93$	−0.704260	−	0.540398i	−0.0730284	−	0.0560366i
$94$	1.67251	−	12.7040i	0.172507	−	1.31032i
$95$	−2.34647	−	2.05780i	−0.240742	−	0.211126i
$96$	6.33442	+	3.12379i	0.646504	+	0.318820i
$97$	8.60161	−	1.71097i	0.873361	−	0.173722i	0.261994	−	0.965070i	$-0.415620\pi$
$97$	8.60161	−	1.71097i	0.873361	−	0.173722i	0.611367	+	0.791347i	$0.290620\pi$
$98$	11.8167	−	10.0222i	1.19367	−	1.01240i
$99$	−3.40861	+	5.10134i	−0.342578	+	0.512704i
$100$	−0.319371	−	2.42587i	−0.0319371	−	0.242587i
$101$	−9.08141	+	15.7295i	−0.903634	+	1.56514i	−0.0808933	+	0.996723i	$0.525777\pi$
$101$	−9.08141	+	15.7295i	−0.903634	+	1.56514i	−0.822741	+	0.568417i	$0.807556\pi$
$102$	8.99210	−	1.56037i	0.890351	−	0.154500i
$103$	−14.4466	+	8.34076i	−1.42347	+	0.821839i	−0.996593	−	0.0824722i	$-0.973718\pi$
$103$	−14.4466	+	8.34076i	−1.42347	+	0.821839i	−0.426874	+	0.904311i	$0.640385\pi$
$104$	−5.04501	−	2.08971i	−0.494704	−	0.204913i
$105$	6.35966	+	0.679504i	0.620639	+	0.0663128i
$106$	0.705342	+	0.705342i	0.0685088	+	0.0685088i
$107$	−10.2946	−	11.7388i	−0.995219	−	1.13483i	−0.990868	−	0.134839i	$-0.956948\pi$
$107$	−10.2946	−	11.7388i	−0.995219	−	1.13483i	−0.00435120	−	0.999991i	$-0.501385\pi$
$108$	2.89336	−	0.189641i	0.278413	−	0.0182482i
$109$	6.20867	−	7.07963i	0.594683	−	0.678106i	−0.373707	−	0.927547i	$-0.621914\pi$
$109$	6.20867	−	7.07963i	0.594683	−	0.678106i	0.968390	+	0.249441i	$0.0802469\pi$
$110$	19.9854	−	26.0455i	1.90554	−	2.48334i
$111$	6.93659	−	2.87323i	0.658392	−	0.272715i
$112$	2.53909	−	2.66643i	0.239921	−	0.251954i
$113$	−10.5293	−	15.7583i	−0.990518	−	1.48241i	−0.872026	−	0.489459i	$-0.837194\pi$
$113$	−10.5293	−	15.7583i	−0.990518	−	1.48241i	−0.118491	−	0.992955i	$-0.537806\pi$
$114$	−2.14854	+	1.88422i	−0.201229	+	0.176473i
$115$	−3.11929	+	0.835810i	−0.290875	+	0.0779397i
$116$	6.49620	+	13.1730i	0.603157	+	1.22308i
$117$	2.71897	−	0.357959i	0.251368	−	0.0330933i
$118$	−17.7266			−1.63187
$119$	1.42469	−	10.8153i	0.130601	−	0.991435i
$120$	−4.81350			−0.439411
$121$	26.4144	−	3.47752i	2.40131	−	0.316138i
$122$	7.78045	+	15.7772i	0.704409	+	1.42840i
$123$	−1.50487	+	0.403229i	−0.135690	+	0.0363579i
$124$	1.93520	−	1.69712i	0.173786	−	0.152406i
$125$	5.58187	+	8.35386i	0.499258	+	0.747192i
$126$	1.37695	−	5.69219i	0.122668	−	0.507100i
$127$	17.9361	−	7.42939i	1.59157	−	0.659252i	0.601382	−	0.798962i	$-0.294617\pi$
$127$	17.9361	−	7.42939i	1.59157	−	0.659252i	0.990192	+	0.139710i	$0.0446172\pi$
$128$	−8.71636	+	11.3594i	−0.770424	+	1.00404i
$129$	1.09983	−	1.25412i	0.0968347	−	0.110419i
$130$	−14.6431	+	0.959758i	−1.28428	+	0.0841764i
$131$	−5.61557	−	6.40333i	−0.490635	−	0.559462i	0.452546	−	0.891741i	$-0.350516\pi$
$131$	−5.61557	−	6.40333i	−0.490635	−	0.559462i	−0.943181	+	0.332279i	$0.892182\pi$
$132$	−12.5793	−	12.5793i	−1.09489	−	1.09489i
$133$	1.38394	+	3.12285i	0.120003	+	0.270785i
$134$	−28.3363	−	11.7373i	−2.44788	−	1.01395i
$135$	2.09353	−	1.20870i	0.180183	−	0.104029i
$136$	−0.201395	+	8.20740i	−0.0172695	+	0.703779i
$137$	0.365057	−	0.632298i	0.0311889	−	0.0540208i	−0.850010	−	0.526767i	$-0.823404\pi$
$137$	0.365057	−	0.632298i	0.0311889	−	0.0540208i	0.881199	+	0.472746i	$0.156737\pi$
$138$	0.385956	+	2.93163i	0.0328548	+	0.249557i
$139$	5.33575	−	7.98552i	0.452573	−	0.677323i	−0.533088	−	0.846060i	$-0.678969\pi$
$139$	5.33575	−	7.98552i	0.452573	−	0.677323i	0.985661	+	0.168736i	$0.0539687\pi$
$140$	−5.52992	+	17.7015i	−0.467364	+	1.49605i
$141$	−5.67763	+	1.12935i	−0.478142	+	0.0951084i
$142$	15.5539	+	7.67031i	1.30525	+	0.643678i
$143$	−12.6502	−	11.0940i	−1.05787	−	0.927723i
$144$	0.181647	−	1.37974i	0.0151372	−	0.114979i
$145$	9.71486	+	7.45447i	0.806775	+	0.619060i
$146$	−1.99107	−	0.396048i	−0.164782	−	0.0327772i
$147$	−6.00348	−	3.59975i	−0.495159	−	0.296903i
$148$	4.24717	+	21.3519i	0.349115	+	1.75512i
$149$	10.2246	+	2.73968i	0.837633	+	0.224443i	0.652041	−	0.758184i	$-0.273913\pi$
$149$	10.2246	+	2.73968i	0.837633	+	0.224443i	0.185592	+	0.982627i	$0.440580\pi$
$150$	−1.67523	+	0.826133i	−0.136782	+	0.0674534i
$151$	11.4191	−	8.76215i	0.929270	−	0.713054i	−0.0288011	−	0.999585i	$-0.509169\pi$
$151$	11.4191	−	8.76215i	0.929270	−	0.713054i	0.958071	+	0.286531i	$0.0925023\pi$
$152$	−1.28535	−	2.22629i	−0.104256	−	0.180576i
$153$	−1.97334	−	3.62021i	−0.159535	−	0.292677i
$154$	−31.8270	+	16.6751i	−2.56469	+	1.34372i
$155$	0.821213	−	1.98258i	0.0659614	−	0.159245i
$156$	−0.520076	+	7.93482i	−0.0416394	+	0.635294i
$157$	−0.679739	−	2.53682i	−0.0542490	−	0.202460i	0.933482	−	0.358624i	$-0.116754\pi$
$157$	−0.679739	−	2.53682i	−0.0542490	−	0.202460i	−0.987731	+	0.156164i	$0.950087\pi$
$158$	6.19932	−	18.2626i	0.493192	−	1.45290i
$159$	0.199316	−	0.404172i	0.0158068	−	0.0320529i
$160$	−3.33090	+	16.7455i	−0.263330	+	1.32385i
$161$	3.48227	+	0.604541i	0.274442	+	0.0476445i
$162$	−0.847068	−	2.04500i	−0.0665520	−	0.160671i
$163$	0.730010	−	0.247805i	0.0571788	−	0.0194096i	−0.292704	−	0.956203i	$-0.594555\pi$
$163$	0.730010	−	0.247805i	0.0571788	−	0.0194096i	0.349882	+	0.936794i	$0.386222\pi$
$164$	−0.295452	−	4.50772i	−0.0230709	−	0.351994i
$165$	−14.0445	−	4.76746i	−1.09336	−	0.371146i
$166$	8.50222	−	31.7307i	0.659900	−	2.46278i
$167$	7.64667	+	5.10934i	0.591717	+	0.395373i	0.815068	−	0.579365i	$-0.196700\pi$
$167$	7.64667	+	5.10934i	0.591717	+	0.395373i	−0.223351	+	0.974738i	$0.571700\pi$
$168$	4.78046	+	2.21381i	0.368820	+	0.170799i
$169$		−	5.47909i		−	0.421469i
$170$	9.26962	+	20.0206i	0.710947	+	1.53551i
$171$	1.11807	+	0.645520i	0.0855012	+	0.0493642i
$172$	2.94437	+	3.83718i	0.224506	+	0.292582i
$173$	9.52154	+	0.624074i	0.723909	+	0.0474475i	0.422903	−	0.906175i	$-0.361011\pi$
$173$	9.52154	+	0.624074i	0.723909	+	0.0474475i	0.301006	+	0.953622i	$0.402678\pi$
$174$	7.92837	−	7.92837i	0.601048	−	0.601048i
$175$	0.345459	+	2.20573i	0.0261143	+	0.166737i
$176$	−7.09928	+	4.74359i	−0.535128	+	0.357561i
$177$	2.57422	+	7.58342i	0.193491	+	0.570005i
$178$	−23.8450	−	3.13925i	−1.78725	−	0.235297i
$179$	−23.4319	−	3.08487i	−1.75138	−	0.230574i	−0.814487	−	0.580182i	$-0.802982\pi$
$179$	−23.4319	−	3.08487i	−1.75138	−	0.230574i	−0.936896	+	0.349608i	$0.886315\pi$
$180$	2.25311	+	6.63744i	0.167937	+	0.494725i
$181$	−5.57542	+	3.72538i	−0.414418	+	0.276905i	−0.745251	−	0.666784i	$-0.767670\pi$
$181$	−5.57542	+	3.72538i	−0.414418	+	0.276905i	0.330833	+	0.943689i	$0.392670\pi$
$182$	14.9840	+	5.78144i	1.11069	+	0.428549i
$183$	5.61960	−	5.61960i	0.415413	−	0.415413i
$184$	−2.65426	−	0.173969i	−0.195674	−	0.0128252i
$185$	11.0491	+	14.3995i	0.812346	+	1.05867i
$186$	−1.70167	−	0.982461i	−0.124773	−	0.0720375i
$187$	−8.71650	+	23.7475i	−0.637414	+	1.73659i
$188$		−	16.7852i		−	1.22418i
$189$	−2.63507	+	0.237552i	−0.191673	+	0.0172794i
$190$	−5.74400	−	3.83802i	−0.416714	−	0.278439i
$191$	−3.17607	+	11.8532i	−0.229812	+	0.857671i	0.750607	+	0.660749i	$0.229761\pi$
$191$	−3.17607	+	11.8532i	−0.229812	+	0.857671i	−0.980419	+	0.196922i	$0.936905\pi$
$192$	12.1682	+	4.13054i	0.878163	+	0.298096i
$193$	−1.02020	−	15.5652i	−0.0734356	−	1.12041i	−0.862486	−	0.506081i	$-0.831094\pi$
$193$	−1.02020	−	15.5652i	−0.0734356	−	1.12041i	0.789050	−	0.614329i	$-0.210573\pi$
$194$	18.3824	−	6.23999i	1.31978	−	0.448005i
$195$	2.53702	+	6.12491i	0.181680	+	0.438614i
$196$	13.6332	−	15.0367i	0.973800	−	1.07405i
$197$	1.04189	−	5.23793i	0.0742316	−	0.373187i	−0.925756	−	0.378121i	$-0.876570\pi$
$197$	1.04189	−	5.23793i	0.0742316	−	0.373187i	0.999988	+	0.00493346i	$0.00157037\pi$
$198$	−6.00652	+	12.1800i	−0.426865	+	0.865596i
$199$	−5.87505	+	17.3073i	−0.416471	+	1.22688i	0.513128	+	0.858312i	$0.328487\pi$
$199$	−5.87505	+	17.3073i	−0.416471	+	1.22688i	−0.929599	+	0.368572i	$0.879847\pi$
$200$	−0.434884	−	1.62301i	−0.0307509	−	0.114764i
$201$	−0.906249	+	13.8267i	−0.0639218	+	0.975259i
$202$	−15.3851	+	37.1430i	−1.08250	+	2.61337i
$203$	−6.21972	−	11.8713i	−0.436539	−	0.833204i
$204$	11.4116	−	3.56401i	0.798973	−	0.249531i
$205$	−1.88311	−	3.26164i	−0.131522	−	0.227802i
$206$	−29.2941	+	22.4782i	−2.04102	+	1.56613i
$207$	1.19810	−	0.590837i	0.0832736	−	0.0410660i
$208$	3.68645	+	0.987782i	0.255609	+	0.0684903i
$209$	−1.54530	−	7.76876i	−0.106891	−	0.537376i
$210$	14.1530	−	0.346215i	0.976647	−	0.0238911i
$211$	4.67480	+	0.929876i	0.321827	+	0.0640153i	0.353360	−	0.935487i	$-0.385039\pi$
$211$	4.67480	+	0.929876i	0.321827	+	0.0640153i	−0.0315333	+	0.999503i	$0.510039\pi$
$212$	1.03666	+	0.795455i	0.0711979	+	0.0546321i
$213$	1.02265	−	7.76778i	0.0700707	−	0.532239i
$214$	−25.9837	−	22.7871i	−1.77621	−	1.55769i
$215$	3.61654	+	1.78348i	0.246646	+	0.121632i
$216$	1.95293	−	0.388461i	0.132880	−	0.0264314i
$217$	−1.72740	+	1.59128i	−0.117263	+	0.108023i
$218$	11.5799	−	17.3305i	0.784287	−	1.17377i
$219$	0.119710	+	0.909289i	0.00808927	+	0.0614441i
$220$	21.5026	−	37.2436i	1.44970	−	2.51096i
$221$	10.5496	−	4.06956i	0.709643	−	0.273748i
$222$	14.3926	−	8.30958i	0.965969	−	0.557703i
$223$	−12.7830	−	5.29489i	−0.856013	−	0.354572i	−0.0888659	−	0.996044i	$-0.528324\pi$
$223$	−12.7830	−	5.29489i	−0.856013	−	0.354572i	−0.767147	+	0.641472i	$0.778324\pi$
$224$	11.0096	−	15.0986i	0.735609	−	1.00882i
$225$	0.596692	+	0.596692i	0.0397795	+	0.0397795i
$226$	−27.6601	−	31.5404i	−1.83993	−	2.09803i
$227$	14.4029	−	0.944014i	0.955953	−	0.0626564i	0.420565	−	0.907263i	$-0.361832\pi$
$227$	14.4029	−	0.944014i	0.955953	−	0.0626564i	0.535388	+	0.844606i	$0.320165\pi$
$228$	−2.46823	+	2.81448i	−0.163463	+	0.186393i
$229$	5.79133	−	7.54741i	0.382702	−	0.498747i	−0.561791	−	0.827279i	$-0.689887\pi$
$229$	5.79133	−	7.54741i	0.382702	−	0.498747i	0.944493	+	0.328532i	$0.106554\pi$
$230$	−6.60398	+	2.73546i	−0.435453	+	0.180371i
$231$	11.7554	+	11.1940i	0.773450	+	0.736513i
$232$	5.60365	+	8.38646i	0.367898	+	0.550598i
$233$	−7.90473	+	6.93226i	−0.517856	+	0.454147i	−0.877939	−	0.478773i	$-0.841082\pi$
$233$	−7.90473	+	6.93226i	−0.517856	+	0.454147i	0.360083	+	0.932920i	$0.382748\pi$
$234$	5.86351	−	1.57112i	0.383310	−	0.102708i
$235$	−6.18940	−	12.5509i	−0.403752	−	0.818727i
$236$	−23.0223	+	3.03094i	−1.49862	+	0.197298i
$237$	−8.71297			−0.565968
$238$	0.00183067	−	24.1464i	0.000118664	−	1.56518i
$239$	−2.10674			−0.136274			−0.0681368	−	0.997676i	$-0.521705\pi$
$239$	−2.10674			−0.136274			−0.0681368	+	0.997676i	$0.521705\pi$
$240$	3.33540	−	0.439114i	0.215299	−	0.0283447i
$241$	−0.128564	−	0.260702i	−0.00828153	−	0.0167933i	0.892693	−	0.450666i	$-0.148813\pi$
$241$	−0.128564	−	0.260702i	−0.00828153	−	0.0167933i	−0.900974	+	0.433873i	$0.857147\pi$
$242$	56.9632	−	15.2632i	3.66173	−	0.981158i
$243$	−0.751840	+	0.659346i	−0.0482305	+	0.0422971i
$244$	12.8024	+	19.1602i	0.819591	+	1.22661i
$245$	4.64935	−	16.2706i	0.297036	−	1.03949i
$246$	−3.18603	+	1.31970i	−0.203134	+	0.0841407i
$247$	−2.15537	+	2.80893i	−0.137143	+	0.178728i
$248$	1.16544	−	1.32893i	0.0740058	−	0.0843874i
$249$	−14.8090	+	0.970635i	−0.938484	+	0.0615115i
$250$	14.6633	+	16.7203i	0.927391	+	1.05749i
$251$	21.0814	+	21.0814i	1.33065	+	1.33065i	0.904791	+	0.425856i	$0.140027\pi$
$251$	21.0814	+	21.0814i	1.33065	+	1.33065i	0.425856	+	0.904791i	$0.359973\pi$
$252$	0.815034	−	7.62811i	0.0513423	−	0.480526i
$253$	−7.57208	−	3.13646i	−0.476053	−	0.197187i
$254$	37.2154	−	21.4863i	2.33510	−	1.34817i
$255$	7.21866	−	6.87288i	0.452050	−	0.430396i
$256$	−2.99648	+	5.19005i	−0.187280	+	0.324378i
$257$	3.03290	+	23.0372i	0.189187	+	1.43702i	0.777753	+	0.628570i	$0.216360\pi$
$257$	3.03290	+	23.0372i	0.189187	+	1.43702i	−0.588565	+	0.808450i	$0.700307\pi$
$258$	2.05131	−	3.07000i	0.127709	−	0.191130i
$259$	−4.35068	−	19.3823i	−0.270338	−	1.20436i
$260$	−18.8535	+	3.75019i	−1.16924	+	0.232577i
$261$	−4.54309	−	2.24040i	−0.281210	−	0.138677i
$262$	−14.1738	−	12.4301i	−0.875658	−	0.767931i
$263$	−3.02060	+	22.9437i	−0.186258	+	1.41477i	0.601542	+	0.798841i	$0.294553\pi$
$263$	−3.02060	+	22.9437i	−0.186258	+	1.41477i	−0.787801	+	0.615930i	$0.788780\pi$
$264$	−9.69207	−	7.43699i	−0.596506	−	0.457715i
$265$	1.06846	+	0.212530i	0.0656351	+	0.0130556i
$266$	3.93940	+	6.45343i	0.241540	+	0.395685i
$267$	2.11975	+	10.6567i	0.129727	+	0.652180i
$268$	−38.8084	−	10.3987i	−2.37060	−	0.635200i
$269$	13.8829	−	6.84630i	0.846457	−	0.417426i	0.0332820	−	0.999446i	$-0.489404\pi$
$269$	13.8829	−	6.84630i	0.846457	−	0.417426i	0.813175	+	0.582020i	$0.197737\pi$
$270$	4.24517	−	3.25743i	0.258353	−	0.198241i
$271$	−9.91021	−	17.1650i	−0.602003	−	1.04270i	−0.992517	−	0.122102i	$-0.961036\pi$
$271$	−9.91021	−	17.1650i	−0.602003	−	1.04270i	0.390515	−	0.920597i	$-0.372297\pi$
$272$	−0.609171	−	5.70549i	−0.0369364	−	0.345946i
$273$	0.297348	−	7.24968i	0.0179963	−	0.438771i
$274$	0.618457	−	1.49309i	0.0373624	−	0.0902007i
$275$	0.338612	−	5.16621i	0.0204190	−	0.311534i
$276$	1.00252	+	3.74144i	0.0603443	+	0.225208i
$277$	−10.0868	+	29.7149i	−0.606060	+	1.78539i	0.0128325	+	0.999918i	$0.495915\pi$
$277$	−10.0868	+	29.7149i	−0.606060	+	1.78539i	−0.618892	+	0.785476i	$0.712418\pi$
$278$	9.40246	−	19.0663i	0.563922	−	1.14352i
$279$	−0.173182	+	0.870644i	−0.0103681	+	0.0521241i
$280$	−2.17834	+	12.5477i	−0.130181	+	0.749866i
$281$	0.200758	+	0.484673i	0.0119762	+	0.0289131i	0.929755	−	0.368180i	$-0.120019\pi$
$281$	0.200758	+	0.484673i	0.0119762	+	0.0289131i	−0.917778	+	0.397093i	$0.870019\pi$
$282$	−12.1336	+	4.11880i	−0.722545	+	0.245271i
$283$	1.03056	+	15.7233i	0.0612603	+	0.934651i	0.912293	+	0.409538i	$0.134310\pi$
$283$	1.03056	+	15.7233i	0.0612603	+	0.934651i	−0.851033	+	0.525113i	$0.824023\pi$
$284$	21.5119	+	7.30231i	1.27650	+	0.433313i
$285$	−0.807766	+	3.01462i	−0.0478479	+	0.178571i
$286$	−30.9669	−	20.6915i	−1.83111	−	1.22351i
$287$	0.370096	+	4.10532i	0.0218461	+	0.242329i
$288$		−	7.06278i		−	0.416178i
$289$	−11.4168	−	12.5959i	−0.671574	−	0.740937i
$290$	23.4736	+	13.5525i	1.37842	+	0.795829i
$291$	−5.33891	−	6.95780i	−0.312973	−	0.407874i
$292$	−2.65360	−	0.173926i	−0.155290	−	0.0101783i
$293$	−7.59491	+	7.59491i	−0.443699	+	0.443699i	−0.893253	−	0.449554i	$-0.851583\pi$
$293$	−7.59491	+	7.59491i	−0.443699	+	0.443699i	0.449554	+	0.893253i	$0.351583\pi$
$294$	−14.2150	−	6.16535i	−0.829038	−	0.359571i
$295$	−16.0969	+	10.7556i	−0.937200	+	0.626217i
$296$	4.80553	+	14.1566i	0.279316	+	0.822838i
$297$	6.08284	+	0.800822i	0.352962	+	0.0464684i
$298$	23.2301	+	3.05830i	1.34568	+	0.177162i
$299$	1.17760	+	3.46908i	0.0681021	+	0.200622i
$300$	−2.03444	+	1.35937i	−0.117458	+	0.0784832i
$301$	−2.77146	−	3.43454i	−0.159744	−	0.197964i
$302$	22.5282	−	22.5282i	1.29636	−	1.29636i
$303$	18.1239	+	1.18791i	1.04119	+	0.0682434i
$304$	1.09375	+	1.42540i	0.0627306	+	0.0817522i
$305$	16.6380	+	9.60594i	0.952688	+	0.550035i
$306$	−5.37656	−	7.37463i	−0.307358	−	0.421580i
$307$			7.74112i			0.441809i	0.975295	+	0.220905i	$0.0709009\pi$
$307$			7.74112i			0.441809i	−0.975295	+	0.220905i	$0.929099\pi$
$308$	−38.4839	+	27.0985i	−2.19282	+	1.54408i
$309$	13.8702	+	9.26775i	0.789046	+	0.527224i
$310$	1.22939	−	4.58816i	0.0698249	−	0.260590i
$311$	−5.36537	−	1.82130i	−0.304242	−	0.103276i	0.165143	−	0.986270i	$-0.447191\pi$
$311$	−5.36537	−	1.82130i	−0.304242	−	0.103276i	−0.469386	+	0.882993i	$0.655525\pi$
$312$	0.357146	+	5.44899i	0.0202194	+	0.308488i
$313$	−3.01239	+	1.02257i	−0.170270	+	0.0577990i	−0.405273	−	0.914196i	$-0.632823\pi$
$313$	−3.01239	+	1.02257i	−0.170270	+	0.0577990i	0.235003	+	0.971995i	$0.424490\pi$
$314$	−2.22466	−	5.37081i	−0.125545	−	0.303092i
$315$	−2.20338	−	6.00434i	−0.124146	−	0.338306i
$316$	4.92873	−	24.7784i	0.277263	−	1.39389i
$317$	−1.35492	+	2.74751i	−0.0761001	+	0.154316i	−0.931598	−	0.363491i	$-0.881585\pi$
$317$	−1.35492	+	2.74751i	−0.0761001	+	0.154316i	0.855498	+	0.517807i	$0.173251\pi$
$318$	0.320637	−	0.944566i	0.0179804	−	0.0529686i
$319$	8.04368	+	30.0194i	0.450359	+	1.68076i
$320$	−2.03168	+	30.9975i	−0.113575	+	1.73281i
$321$	−5.97499	+	14.4249i	−0.333491	+	0.805119i
$322$	7.81672	+	0.320606i	0.435609	+	0.0178666i
$323$	5.10637	+	1.50343i	0.284126	+	0.0836533i
$324$	−1.44978	−	2.51110i	−0.0805435	−	0.139505i
$325$	−1.83598	+	1.40879i	−0.101842	+	0.0781458i
$326$	1.53046	−	0.754737i	0.0847641	−	0.0418010i
$327$	−9.09555	−	2.43715i	−0.502985	−	0.134774i
$328$	−0.605205	−	3.04257i	−0.0334169	−	0.167998i
$329$	0.374551	+	15.3113i	0.0206496	+	0.844139i
$330$	−32.1988	−	6.40475i	−1.77249	−	0.352570i
$331$	11.0981	+	8.51589i	0.610008	+	0.468076i	0.866980	−	0.498343i	$-0.166058\pi$
$331$	11.0981	+	8.51589i	0.610008	+	0.468076i	−0.256972	+	0.966419i	$0.582725\pi$
$332$	5.61679	−	42.6637i	0.308261	−	2.34148i
$333$	−5.64489	−	4.95044i	−0.309338	−	0.271282i
$334$	18.2573	+	9.00349i	0.998993	+	0.492649i
$335$	−32.8528	+	6.53483i	−1.79494	+	0.357036i
$336$	−3.51446	−	1.09791i	−0.191729	−	0.0598958i
$337$	8.72820	−	13.0627i	0.475455	−	0.711569i	−0.513777	−	0.857924i	$-0.671754\pi$
$337$	8.72820	−	13.0627i	0.475455	−	0.711569i	0.989232	+	0.146355i	$0.0467541\pi$
$338$	−1.58302	−	12.0242i	−0.0861047	−	0.654030i
$339$	−9.47616	+	16.4132i	−0.514674	+	0.891442i
$340$	15.4620	+	24.4166i	0.838545	+	1.32418i
$341$	4.71667	−	2.72317i	0.255422	−	0.147468i
$342$	2.64018	+	1.09360i	0.142765	+	0.0591351i
$343$	−12.1006	+	14.0206i	−0.653369	+	0.757040i
$344$	2.34860	+	2.34860i	0.126628	+	0.126628i
$345$	2.12924	+	2.42793i	0.114634	+	0.130716i
$346$	21.0759	−	1.38139i	1.13305	−	0.0742638i
$347$	4.80678	−	5.48109i	0.258042	−	0.294240i	−0.608284	−	0.793719i	$-0.708142\pi$
$347$	4.80678	−	5.48109i	0.258042	−	0.294240i	0.866326	+	0.499479i	$0.166475\pi$
$348$	8.94129	−	11.6525i	0.479304	−	0.624641i
$349$	−5.71825	+	2.36858i	−0.306091	+	0.126787i	−0.530442	−	0.847721i	$-0.677974\pi$
$349$	−5.71825	+	2.36858i	−0.306091	+	0.126787i	0.224351	+	0.974508i	$0.427974\pi$
$350$	1.39541	+	4.74079i	0.0745877	+	0.253406i
$351$	−1.52361	−	2.28024i	−0.0813243	−	0.121710i
$352$	−32.5791	+	28.5711i	−1.73647	+	1.52285i
$353$	−22.6638	+	6.07275i	−1.20627	+	0.323220i	−0.805299	−	0.592870i	$-0.797995\pi$
$353$	−22.6638	+	6.07275i	−1.20627	+	0.323220i	−0.400974	+	0.916089i	$0.631328\pi$
$354$	7.84029	+	15.8985i	0.416707	+	0.844997i
$355$	18.7779	−	2.47215i	0.996626	−	0.131208i
$356$	−31.5052			−1.66977
$357$	−10.3301	+	3.50571i	−0.546724	+	0.185542i
$358$	−52.3140			−2.76488
$359$	9.89847	−	1.30316i	0.522421	−	0.0687781i	0.135296	−	0.990805i	$-0.456801\pi$
$359$	9.89847	−	1.30316i	0.522421	−	0.0687781i	0.387125	+	0.922027i	$0.373468\pi$
$360$	2.12896	+	4.31710i	0.112206	+	0.227531i
$361$	16.7426	−	4.48617i	0.881189	−	0.236114i
$362$	−11.1593	+	9.78640i	−0.586517	+	0.514362i
$363$	−14.8017	−	22.1523i	−0.776886	−	1.16269i
$364$	20.4488	+	4.94660i	1.07181	+	0.259272i
$365$	−2.04832	+	0.848443i	−0.107214	+	0.0444095i
$366$	10.7089	−	13.9562i	0.559765	−	0.729500i
$367$	−5.08891	+	5.80280i	−0.265639	+	0.302903i	−0.869247	−	0.494378i	$-0.835396\pi$
$367$	−5.08891	+	5.80280i	−0.265639	+	0.302903i	0.603608	+	0.797281i	$0.293729\pi$
$368$	1.85507	−	0.121588i	0.0967023	−	0.00633820i
$369$	1.02723	+	1.17133i	0.0534756	+	0.0609772i
$370$	28.4082	+	28.4082i	1.47687	+	1.47687i
$371$	−0.963381	−	0.702475i	−0.0500162	−	0.0364707i
$372$	−2.37802	−	0.985007i	−0.123294	−	0.0510702i
$373$	−1.15826	+	0.668724i	−0.0599726	+	0.0346252i	−0.529686	−	0.848194i	$-0.677690\pi$
$373$	−1.15826	+	0.668724i	−0.0599726	+	0.0346252i	0.469714	+	0.882819i	$0.344357\pi$
$374$	−12.2678	+	54.6336i	−0.634352	+	2.82503i
$375$	5.02355	−	8.70104i	0.259415	−	0.449320i
$376$	−1.50454	−	11.4281i	−0.0775905	−	0.589358i
$377$	7.71781	−	11.5505i	0.397488	−	0.594882i
$378$	−5.71417	+	1.28264i	−0.293905	+	0.0659721i
$379$	14.9861	−	2.98092i	0.769783	−	0.153119i	0.205451	−	0.978667i	$-0.434134\pi$
$379$	14.9861	−	2.98092i	0.769783	−	0.153119i	0.564332	+	0.825548i	$0.309134\pi$
$380$	−8.11621	−	4.00247i	−0.416353	−	0.205322i
$381$	−14.5962	−	12.8005i	−0.747784	−	0.655789i
$382$	−3.54544	+	26.9303i	−0.181400	+	1.37787i
$383$	−21.5157	−	16.5096i	−1.09940	−	0.843600i	−0.110752	−	0.993848i	$-0.535326\pi$
$383$	−21.5157	−	16.5096i	−1.09940	−	0.843600i	−0.988648	+	0.150248i	$0.951993\pi$
$384$	14.0431	+	2.79334i	0.716632	+	0.142547i
$385$	−18.7834	+	34.4531i	−0.957291	+	1.75589i
$386$	−6.73598	−	33.8641i	−0.342853	−	1.72364i
$387$	−1.61123	−	0.431727i	−0.0819032	−	0.0219459i
$388$	22.8071	−	11.2472i	1.15785	−	0.570990i
$389$	−27.6697	+	21.2317i	−1.40291	+	1.07649i	−0.417058	+	0.908880i	$0.636939\pi$
$389$	−27.6697	+	21.2317i	−1.40291	+	1.07649i	−0.985853	+	0.167612i	$0.946394\pi$
$390$	7.33725	+	12.7085i	0.371536	+	0.643520i
$391$	4.22890	−	3.52894i	0.213865	−	0.178466i
$392$	7.93427	−	11.4597i	0.400741	−	0.578800i
$393$	−3.25927	+	7.86858i	−0.164408	+	0.396917i
$394$	0.773149	−	11.7960i	0.0389507	−	0.594273i
$395$	−5.45145	−	20.3451i	−0.274292	−	1.02367i
$396$	−5.71834	+	16.8457i	−0.287358	+	0.846528i
$397$	1.70170	−	3.45070i	0.0854056	−	0.173185i	−0.849980	−	0.526815i	$-0.823386\pi$
$397$	1.70170	−	3.45070i	0.0854056	−	0.173185i	0.935386	+	0.353630i	$0.115053\pi$
$398$	−7.89272	+	39.6794i	−0.395626	+	1.98895i
$399$	2.18870	−	2.62242i	0.109572	−	0.131285i
$400$	0.449401	+	1.08495i	0.0224701	+	0.0542476i
$401$	−25.4636	+	8.64372i	−1.27159	+	0.431647i	−0.874004	−	0.485918i	$-0.838485\pi$
$401$	−25.4636	+	8.64372i	−1.27159	+	0.431647i	−0.397586	+	0.917565i	$0.630152\pi$
$402$	2.00598	+	30.6053i	0.100049	+	1.52645i
$403$	−2.30526	−	0.782530i	−0.114833	−	0.0389806i
$404$	−13.6305	+	50.8698i	−0.678144	+	2.53087i
$405$	−2.01000	−	1.34304i	−0.0998777	−	0.0667361i
$406$	−17.0794	−	24.2553i	−0.847637	−	1.20377i
$407$			46.0647i			2.28334i
$408$	7.45007	−	3.44941i	0.368833	−	0.170771i
$409$	11.9304	+	6.88802i	0.589921	+	0.340591i	0.765066	−	0.643952i	$-0.222706\pi$
$409$	11.9304	+	6.88802i	0.589921	+	0.340591i	−0.175145	+	0.984543i	$0.556040\pi$
$410$	−5.07494	−	6.61379i	−0.250633	−	0.326632i
$411$	−0.728551	−	0.0477518i	−0.0359368	−	0.00235542i
$412$	−34.2021	+	34.2021i	−1.68502	+	1.68502i
$413$	20.9331	−	3.27853i	1.03005	−	0.161326i
$414$	2.45860	−	1.64278i	0.120833	−	0.0807383i
$415$	−11.5320	−	33.9723i	−0.566086	−	1.66763i
$416$	19.2035	+	2.52818i	0.941527	+	0.123954i
$417$	−9.52194	−	1.25359i	−0.466291	−	0.0613884i
$418$	−5.63580	−	16.6025i	−0.275656	−	0.812057i
$419$	23.7931	−	15.8981i	1.16237	−	0.776671i	0.183877	−	0.982949i	$-0.441135\pi$
$419$	23.7931	−	15.8981i	1.16237	−	0.776671i	0.978493	+	0.206278i	$0.0661352\pi$
$420$	18.3218	−	2.86955i	0.894015	−	0.140020i
$421$	−3.32865	+	3.32865i	−0.162229	+	0.162229i	−0.783553	−	0.621325i	$-0.786595\pi$
$421$	−3.32865	+	3.32865i	−0.162229	+	0.162229i	0.621325	+	0.783553i	$0.286595\pi$
$422$	10.5278	+	0.690028i	0.512485	+	0.0335900i
$423$	3.52403	+	4.59261i	0.171344	+	0.223300i
$424$	0.777102	+	0.448660i	0.0377394	+	0.0217889i
$425$	2.96956	+	1.81303i	0.144045	+	0.0879450i
$426$		−	17.3423i		−	0.840238i
$427$	−12.1058	−	17.1921i	−0.585841	−	0.831983i
$428$	−37.6423	−	25.1518i	−1.81951	−	1.21576i
$429$	−4.35481	+	16.2524i	−0.210252	+	0.784672i
$430$	8.45199	+	2.86906i	0.407591	+	0.138359i
$431$	−2.22364	−	33.9263i	−0.107109	−	1.63417i	−0.626350	−	0.779542i	$-0.715452\pi$
$431$	−2.22364	−	33.9263i	−0.107109	−	1.63417i	0.519241	−	0.854628i	$-0.326215\pi$
$432$	−1.31779	+	0.447331i	−0.0634024	+	0.0215222i
$433$	11.6445	+	28.1122i	0.559597	+	1.35099i	0.910086	+	0.414419i	$0.136015\pi$
$433$	11.6445	+	28.1122i	0.559597	+	1.35099i	−0.350489	+	0.936567i	$0.613985\pi$
$434$	−3.33113	+	3.99124i	−0.159899	+	0.191586i
$435$	2.38894	−	12.0100i	0.114541	−	0.575836i
$436$	12.0760	−	24.4878i	0.578337	−	1.17275i
$437$	−0.554371	+	1.63313i	−0.0265192	+	0.0781230i
$438$	0.525422	+	1.96090i	0.0251056	+	0.0936956i
$439$	−0.568357	+	8.67146i	−0.0271262	+	0.413866i	0.962603	+	0.270914i	$0.0873260\pi$
$439$	−0.568357	+	8.67146i	−0.0271262	+	0.413866i	−0.989730	+	0.142952i	$0.954341\pi$
$440$	11.3016	−	27.2844i	0.538782	−	1.30073i
$441$	−0.573250	+	6.97649i	−0.0272976	+	0.332214i
$442$	21.9760	−	11.9789i	1.04529	−	0.569777i
$443$	12.1961	+	21.1242i	0.579453	+	1.00364i	0.995542	+	0.0943176i	$0.0300669\pi$
$443$	12.1961	+	21.1242i	0.579453	+	1.00364i	−0.416090	+	0.909324i	$0.636600\pi$
$444$	17.2715	−	13.2529i	0.819669	−	0.628954i
$445$	−23.5575	+	11.6173i	−1.11673	+	0.550712i
$446$	−29.5828	−	7.92670i	−1.40079	−	0.375340i
$447$	−2.06509	−	10.3819i	−0.0976754	−	0.491047i
$448$	16.2740	−	29.8503i	0.768875	−	1.41029i
$449$	29.4309	+	5.85416i	1.38893	+	0.276275i	0.832226	−	0.554437i	$-0.187066\pi$
$449$	29.4309	+	5.85416i	1.38893	+	0.276275i	0.556703	+	0.830712i	$0.312066\pi$
$450$	1.48187	+	1.13708i	0.0698561	+	0.0536025i
$451$	1.24764	−	9.47680i	0.0587493	−	0.446245i
$452$	−41.3162	−	36.2334i	−1.94335	−	1.70427i
$453$	−12.9091	−	6.36604i	−0.606520	−	0.299103i
$454$	31.3352	−	6.23296i	1.47064	−	0.292528i
$455$	17.1143	−	3.84160i	0.802331	−	0.180097i
$456$	−1.42820	+	2.13746i	−0.0668818	+	0.100096i
$457$	0.264369	+	2.00808i	0.0123667	+	0.0939341i	0.996515	−	0.0834126i	$-0.0265819\pi$
$457$	0.264369	+	2.00808i	0.0123667	+	0.0939341i	−0.984148	+	0.177347i	$0.943249\pi$
$458$	10.5288	−	18.2365i	0.491980	−	0.852134i
$459$	−2.37408	+	3.37101i	−0.110813	+	0.157345i
$460$	−8.10914	+	4.68182i	−0.378091	+	0.218291i
$461$	−10.8365	−	4.48864i	−0.504708	−	0.209057i	0.115777	−	0.993275i	$-0.463064\pi$
$461$	−10.8365	−	4.48864i	−0.504708	−	0.209057i	−0.620485	+	0.784218i	$0.713064\pi$
$462$	29.0321	+	21.1696i	1.35070	+	0.984898i
$463$	8.73024	+	8.73024i	0.405729	+	0.405729i	0.880246	−	0.474517i	$-0.157377\pi$
$463$	8.73024	+	8.73024i	0.405729	+	0.405729i	−0.474517	+	0.880246i	$0.657377\pi$
$464$	−4.64797	−	5.29999i	−0.215777	−	0.246046i
$465$	−2.14134	+	0.140351i	−0.0993022	+	0.00650861i
$466$	−15.3445	+	17.4971i	−0.710822	+	0.810537i
$467$	4.70082	−	6.12623i	0.217528	−	0.283488i	−0.671824	−	0.740711i	$-0.734489\pi$
$467$	4.70082	−	6.12623i	0.217528	−	0.283488i	0.889352	+	0.457222i	$0.151156\pi$
$468$	7.34655	−	3.04304i	0.339594	−	0.140665i
$469$	35.6327	+	8.61960i	1.64537	+	0.398016i
$470$	−17.2092	−	25.7554i	−0.793800	−	1.18801i
$471$	−1.97456	+	1.73165i	−0.0909831	+	0.0797900i
$472$	−15.4029	+	4.12720i	−0.708977	+	0.189970i
$473$	4.52644	+	9.17871i	0.208126	+	0.422038i
$474$	−19.1211	+	2.51735i	−0.878263	+	0.115625i
$475$	−1.08944			−0.0499871
$476$	−4.12624	−	31.3602i	−0.189126	−	1.43739i
$477$	−0.450646			−0.0206337
$478$	−4.62337	+	0.608678i	−0.211468	+	0.0278403i
$479$	−14.6190	−	29.6445i	−0.667961	−	1.35449i	−0.921959	−	0.387286i	$-0.873412\pi$
$479$	−14.6190	−	29.6445i	−0.667961	−	1.35449i	0.253998	−	0.967205i	$-0.418254\pi$
$480$	16.4918	−	4.41898i	0.752746	−	0.201698i
$481$	15.4807	−	13.5762i	0.705860	−	0.619022i
$482$	−0.357463	−	0.534981i	−0.0162820	−	0.0243677i
$483$	−0.997974	−	3.39054i	−0.0454094	−	0.154275i
$484$	71.3707	−	29.5627i	3.24412	−	1.34376i
$485$	12.9063	−	16.8198i	0.586046	−	0.763749i
$486$	−1.45946	+	1.66419i	−0.0662024	+	0.0754894i
$487$	26.7011	−	1.75008i	1.20994	−	0.0793038i	0.552958	−	0.833209i	$-0.313499\pi$
$487$	26.7011	−	1.75008i	1.20994	−	0.0793038i	0.656983	+	0.753905i	$0.271832\pi$
$488$	10.4339	+	11.8975i	0.472319	+	0.538577i
$489$	−0.545125	−	0.545125i	−0.0246514	−	0.0246514i
$490$	5.50239	−	37.0501i	0.248573	−	1.67375i
$491$	5.39335	+	2.23400i	0.243398	+	0.100819i	0.501048	−	0.865419i	$-0.332948\pi$
$491$	5.39335	+	2.23400i	0.243398	+	0.100819i	−0.257650	+	0.966238i	$0.582948\pi$
$492$	−3.91218	+	2.25870i	−0.176375	+	0.101830i
$493$	−20.3781	−	4.57583i	−0.917782	−	0.206085i
$494$	−3.91853	+	6.78710i	−0.176303	+	0.305366i
$495$	1.93591	+	14.7047i	0.0870127	+	0.660927i
$496$	−0.686333	+	1.02717i	−0.0308173	+	0.0461213i
$497$	−19.7859	−	6.18109i	−0.887521	−	0.277260i
$498$	−32.2189	+	6.40873i	−1.44376	+	0.287182i
$499$	−26.8184	−	13.2254i	−1.20056	−	0.592049i	−0.271662	−	0.962393i	$-0.587573\pi$
$499$	−26.8184	−	13.2254i	−1.20056	−	0.592049i	−0.928895	+	0.370344i	$0.879240\pi$
$500$	21.9028	+	19.2082i	0.979522	+	0.859018i
$501$	1.20039	−	9.11790i	0.0536296	−	0.407358i
$502$	52.3552	+	40.1736i	2.33673	+	1.79304i
$503$	32.4711	+	6.45891i	1.44782	+	0.287988i	0.855536	−	0.517744i	$-0.173228\pi$
$503$	32.4711	+	6.45891i	1.44782	+	0.287988i	0.592280	+	0.805732i	$0.298228\pi$
$504$	−0.128834	−	5.26661i	−0.00573871	−	0.234593i
$505$	8.56581	+	43.0632i	0.381174	+	1.91629i
$506$	−17.5236	−	4.69543i	−0.779018	−	0.208737i
$507$	−4.91405	+	2.42334i	−0.218241	+	0.107624i
$508$	44.6594	−	34.2684i	1.98144	−	1.52041i
$509$	−4.81235	−	8.33523i	−0.213304	−	0.369453i	0.739443	−	0.673219i	$-0.235089\pi$
$509$	−4.81235	−	8.33523i	−0.213304	−	0.369453i	−0.952746	+	0.303767i	$0.901756\pi$
$510$	13.8561	−	17.1685i	0.613557	−	0.760236i
$511$	2.42447	+	0.0994406i	0.107252	+	0.00439899i
$512$	5.88222	−	14.2009i	0.259960	−	0.627598i
$513$	0.0844381	−	1.28828i	0.00372803	−	0.0568788i
$514$	13.3118	+	49.6802i	0.587157	+	2.19130i
$515$	−12.9624	+	38.1859i	−0.571190	+	1.68267i
$516$	2.13920	−	4.33787i	0.0941731	−	0.190964i
$517$	6.92894	−	34.8341i	0.304734	−	1.53200i
$518$	−15.1478	−	41.2786i	−0.665554	−	1.81368i
$519$	−3.65155	−	8.81563i	−0.160285	−	0.386963i
$520$	−12.5001	+	4.24322i	−0.548167	+	0.186078i
$521$	1.39297	+	21.2527i	0.0610273	+	0.931097i	0.913116	+	0.407699i	$0.133669\pi$
$521$	1.39297	+	21.2527i	0.0610273	+	0.931097i	−0.852089	+	0.523397i	$0.824664\pi$
$522$	−10.6174	−	3.60411i	−0.464710	−	0.157748i
$523$	6.33616	−	23.6469i	0.277061	−	1.03401i	−0.677387	−	0.735627i	$-0.736888\pi$
$523$	6.33616	−	23.6469i	0.277061	−	1.03401i	0.954448	−	0.298378i	$-0.0964457\pi$
$524$	−20.5334	−	13.7200i	−0.897004	−	0.599359i
$525$	1.82546	−	1.28540i	0.0796698	−	0.0560995i
$526$			51.2241i			2.23348i
$527$	0.149716	+	3.65702i	0.00652174	+	0.159302i
$528$	7.39432	+	4.26911i	0.321797	+	0.185789i
$529$	−12.9152	−	16.8314i	−0.561529	−	0.731798i
$530$	2.40621	+	0.157711i	0.104519	+	0.00685054i
$531$	5.66281	−	5.66281i	0.245745	−	0.245745i
$532$	6.21968	+	7.70778i	0.269657	+	0.334174i
$533$	−3.55252	+	2.37372i	−0.153877	+	0.102817i
$534$	7.73085	+	22.7743i	0.334546	+	0.985542i
$535$	−37.4210	−	4.92657i	−1.61785	−	0.212994i
$536$	−27.3545	−	3.60129i	−1.18154	−	0.155552i
$537$	7.59693	+	22.3798i	0.327832	+	0.965762i
$538$	28.4889	−	19.0357i	1.22824	−	0.820685i
$539$	34.5000	−	25.5777i	1.48602	−	1.10171i
$540$	4.95641	−	4.95641i	0.213290	−	0.213290i
$541$	4.31721	+	0.282965i	0.185611	+	0.0121656i	0.157925	−	0.987451i	$-0.449519\pi$
$541$	4.31721	+	0.282965i	0.185611	+	0.0121656i	0.0276860	+	0.999617i	$0.491186\pi$
$542$	−26.7079	−	34.8063i	−1.14720	−	1.49506i
$543$	5.80713	+	3.35275i	0.249208	+	0.143880i
$544$	−6.84469	−	28.3048i	−0.293463	−	1.21356i
$545$		−	22.7633i		−	0.975072i
$546$	−1.44202	−	15.9958i	−0.0617130	−	0.684556i
$547$	8.16676	+	5.45685i	0.349185	+	0.233318i	0.717777	−	0.696273i	$-0.245160\pi$
$547$	8.16676	+	5.45685i	0.349185	+	0.233318i	−0.368591	+	0.929591i	$0.620160\pi$
$548$	0.547924	−	2.04488i	0.0234061	−	0.0873529i
$549$	−7.52555	−	2.55458i	−0.321183	−	0.109027i
$550$	−0.749515	−	11.4354i	−0.0319594	−	0.487607i
$551$	6.19267	−	2.10213i	0.263817	−	0.0895537i
$552$	1.01792	+	2.45747i	0.0433255	+	0.104597i
$553$	−3.94303	+	22.7126i	−0.167675	+	0.965839i
$554$	−13.5510	+	68.1253i	−0.575726	+	2.89437i
$555$	8.02760	−	16.2784i	0.340753	−	0.690978i
$556$	8.95136	−	26.3699i	0.379622	−	1.11833i
$557$	−3.65411	−	13.6373i	−0.154829	−	0.577831i	−0.999120	−	0.0419455i	$-0.986644\pi$
$557$	−3.65411	−	13.6373i	−0.154829	−	0.577831i	0.844290	−	0.535886i	$-0.180022\pi$
$558$	−0.128512	+	1.96071i	−0.00544035	+	0.0830037i
$559$	1.75060	−	4.22633i	0.0740426	−	0.178755i
$560$	0.364762	−	8.89331i	0.0154140	−	0.375811i
$561$	25.1537	−	2.68564i	1.06199	−	0.113388i
$562$	0.580607	+	1.00564i	0.0244914	+	0.0424204i
$563$	1.88831	−	1.44895i	0.0795826	−	0.0610659i	−0.568204	−	0.822888i	$-0.692362\pi$
$563$	1.88831	−	1.44895i	0.0795826	−	0.0610659i	0.647787	+	0.761822i	$0.275695\pi$
$564$	−15.0542	+	7.42389i	−0.633895	+	0.312602i
$565$	−44.2543	−	11.8579i	−1.86179	−	0.498866i
$566$	6.80437	+	34.2079i	0.286009	+	1.43786i
$567$	1.37851	+	2.25825i	0.0578921	+	0.0948377i
$568$	15.3008	+	3.04352i	0.642007	+	0.127703i
$569$	9.88930	+	7.58833i	0.414581	+	0.318119i	0.794905	−	0.606734i	$-0.207521\pi$
$569$	9.88930	+	7.58833i	0.414581	+	0.318119i	−0.380324	+	0.924853i	$0.624187\pi$
$570$	−0.901708	+	6.84915i	−0.0377684	+	0.286879i
$571$	−15.2789	−	13.3992i	−0.639403	−	0.560741i	0.277064	−	0.960851i	$-0.410638\pi$
$571$	−15.2789	−	13.3992i	−0.639403	−	0.560741i	−0.916467	+	0.400110i	$0.868972\pi$
$572$	−43.7559	−	21.5780i	−1.82953	−	0.902223i
$573$	12.0356	−	2.39403i	0.502794	−	0.100012i
$574$	1.99830	+	8.90243i	0.0834075	+	0.371580i
$575$	−0.626276	+	0.937289i	−0.0261175	+	0.0390876i
$576$	−1.67728	−	12.7402i	−0.0698867	−	0.530842i
$577$	5.13838	−	8.89994i	0.213914	−	0.370509i	−0.739022	−	0.673681i	$-0.764712\pi$
$577$	5.13838	−	8.89994i	0.213914	−	0.370509i	0.952936	+	0.303172i	$0.0980455\pi$
$578$	−28.6940	−	24.3440i	−1.19351	−	1.01258i
$579$	−13.5088	+	7.79932i	−0.561407	+	0.324128i
$580$	32.8033	+	13.5876i	1.36208	+	0.564194i
$581$	−4.17157	+	39.0428i	−0.173066	+	1.61977i
$582$	−13.7268	−	13.7268i	−0.568994	−	0.568994i
$583$	1.82300	+	2.07873i	0.0755010	+	0.0860924i
$584$	−1.82228	+	0.119438i	−0.0754064	+	0.00494239i
$585$	4.37117	−	4.98437i	0.180726	−	0.206078i
$586$	−14.4732	+	18.8618i	−0.597881	+	0.779174i
$587$	22.1824	−	9.18825i	0.915566	−	0.379240i	0.125381	−	0.992109i	$-0.459985\pi$
$587$	22.1824	−	9.18825i	0.915566	−	0.379240i	0.790185	+	0.612869i	$0.209985\pi$
$588$	−19.5158	−	5.57668i	−0.804819	−	0.229978i
$589$	−0.636715	−	0.952912i	−0.0262354	−	0.0392640i
$590$	−32.2182	+	28.2546i	−1.32640	+	1.16322i
$591$	−5.15858	+	1.38224i	−0.212196	+	0.0568576i
$592$	−4.62132	−	9.37111i	−0.189935	−	0.385150i
$593$	−25.6893	+	3.38207i	−1.05493	+	0.138885i	−0.637988	−	0.770046i	$-0.720233\pi$
$593$	−25.6893	+	3.38207i	−1.05493	+	0.138885i	−0.416947	+	0.908931i	$0.636900\pi$
$594$	13.5805			0.557216
$595$	−14.6492	−	21.9276i	−0.600557	−	0.898945i
$596$	30.6928			1.25723
$597$	18.1209	−	2.38567i	0.741641	−	0.0976389i
$598$	3.58659	+	7.27288i	0.146667	+	0.297410i
$599$	22.8397	−	6.11987i	0.933204	−	0.250051i	0.239984	−	0.970777i	$-0.422858\pi$
$599$	22.8397	−	6.11987i	0.933204	−	0.250051i	0.693220	+	0.720726i	$0.256191\pi$
$600$	−1.26329	+	1.10787i	−0.0515735	+	0.0452287i
$601$	8.76475	+	13.1174i	0.357522	+	0.535069i	0.966014	−	0.258491i	$-0.0832252\pi$
$601$	8.76475	+	13.1174i	0.357522	+	0.535069i	−0.608492	+	0.793560i	$0.708225\pi$
$602$	−7.07443	−	6.73658i	−0.288332	−	0.274563i
$603$	12.8016	−	5.30259i	0.521321	−	0.215938i
$604$	25.4064	−	33.1103i	1.03377	−	1.34724i
$605$	42.4653	−	48.4224i	1.72646	−	1.96865i
$606$	40.1172	−	2.62942i	1.62965	−	0.106813i
$607$	29.5099	+	33.6496i	1.19777	+	1.36579i	0.913392	+	0.407081i	$0.133453\pi$
$607$	29.5099	+	33.6496i	1.19777	+	1.36579i	0.284377	+	0.958713i	$0.408213\pi$
$608$	6.44764	+	6.44764i	0.261486	+	0.261486i
$609$	−7.89616	+	10.8289i	−0.319968	+	0.438807i
$610$	39.2884	+	16.2738i	1.59074	+	0.658906i
$611$	−13.7486	+	7.93776i	−0.556209	+	0.321127i
$612$	−8.24370	−	8.65845i	−0.333232	−	0.349997i
$613$	14.8994	−	25.8065i	0.601781	−	1.04231i	−0.390771	−	0.920488i	$-0.627792\pi$
$613$	14.8994	−	25.8065i	0.601781	−	1.04231i	0.992551	−	0.121827i	$-0.0388752\pi$
$614$	2.23656	+	16.9884i	0.0902602	+	0.685594i
$615$	−2.09240	+	3.13149i	−0.0843735	+	0.126274i
$616$	−23.7726	+	21.8993i	−0.957824	+	0.882349i
$617$	−19.7096	+	3.92049i	−0.793479	+	0.157833i	−0.575156	−	0.818044i	$-0.695059\pi$
$617$	−19.7096	+	3.92049i	−0.793479	+	0.157833i	−0.218323	+	0.975877i	$0.570059\pi$
$618$	33.1165	+	16.3313i	1.33214	+	0.656940i
$619$	21.1897	+	18.5829i	0.851687	+	0.746910i	0.969230	−	0.246158i	$-0.0791683\pi$
$619$	21.1897	+	18.5829i	0.851687	+	0.746910i	−0.117543	+	0.993068i	$0.537502\pi$
$620$	0.812170	−	6.16904i	0.0326175	−	0.247755i
$621$	−1.05981	−	0.813222i	−0.0425288	−	0.0326335i
$622$	−12.3008	−	2.44679i	−0.493219	−	0.0981073i
$623$	28.7388	−	0.703018i	1.15139	−	0.0281658i
$624$	−0.744561	−	3.74316i	−0.0298063	−	0.149846i
$625$	27.5358	+	7.37820i	1.10143	+	0.295128i
$626$	−6.31543	+	3.11442i	−0.252415	+	0.124477i
$627$	−6.28412	+	4.82197i	−0.250964	+	0.192571i
$628$	−3.80758	−	6.59492i	−0.151939	−	0.263166i
$629$	−27.4200	−	14.3688i	−1.09331	−	0.572920i
$630$	−6.57021	−	12.5403i	−0.261763	−	0.499617i
$631$	7.69012	−	18.5656i	0.306139	−	0.739085i	−0.693684	−	0.720279i	$-0.744014\pi$
$631$	7.69012	−	18.5656i	0.306139	−	0.739085i	0.999823	−	0.0188054i	$-0.00598631\pi$
$632$	1.13469	−	17.3120i	0.0451355	−	0.688634i
$633$	−1.23363	−	4.60398i	−0.0490325	−	0.182992i
$634$	−2.17965	+	6.42105i	−0.0865650	+	0.255012i
$635$	20.7572	−	42.0914i	0.823724	−	1.67035i
$636$	0.254920	−	1.28157i	0.0101082	−	0.0508176i
$637$	−18.7636	−	4.05594i	−0.743442	−	0.160702i
$638$	26.3255	+	63.5554i	1.04224	+	2.51618i
$639$	−7.41901	+	2.51842i	−0.293492	+	0.0996270i
$640$	2.26379	+	34.5387i	0.0894841	+	1.36526i
$641$	−14.5441	−	4.93707i	−0.574458	−	0.195002i	0.0190661	−	0.999818i	$-0.493931\pi$
$641$	−14.5441	−	4.93707i	−0.574458	−	0.195002i	−0.593525	+	0.804816i	$0.702264\pi$
$642$	−8.94483	+	33.3826i	−0.353024	+	1.31750i
$643$	−14.7861	−	9.87978i	−0.583108	−	0.389620i	0.228741	−	0.973487i	$-0.426539\pi$
$643$	−14.7861	−	9.87978i	−0.583108	−	0.389620i	−0.811849	+	0.583867i	$0.801539\pi$
$644$	10.2067	−	0.920140i	0.402201	−	0.0362586i
$645$		−	4.03239i		−	0.158775i
$646$	11.6406	+	1.82405i	0.457994	+	0.0717662i
$647$	17.7812	+	10.2660i	0.699051	+	0.403598i	0.806994	−	0.590560i	$-0.201093\pi$
$647$	17.7812	+	10.2660i	0.699051	+	0.403598i	−0.107943	+	0.994157i	$0.534426\pi$
$648$	−1.21216	−	1.57971i	−0.0476180	−	0.0620570i
$649$	−49.0292	−	3.21354i	−1.92456	−	0.126143i
$650$	−3.62213	+	3.62213i	−0.142072	+	0.142072i
$651$	2.19119	+	0.845451i	0.0858794	+	0.0331358i
$652$	1.85862	−	1.24189i	0.0727891	−	0.0486361i
$653$	1.33338	+	3.92802i	0.0521793	+	0.153715i	0.969896	−	0.243521i	$-0.0783026\pi$
$653$	1.33338	+	3.92802i	0.0521793	+	0.153715i	−0.917716	+	0.397237i	$0.869969\pi$
$654$	−20.6649	−	2.72058i	−0.808060	−	0.106383i
$655$	−20.4126	−	2.68737i	−0.797587	−	0.105004i
$656$	0.696922	+	2.05307i	0.0272102	+	0.0801588i
$657$	0.762570	−	0.509533i	0.0297507	−	0.0198788i
$658$	5.24570	+	33.4933i	0.204499	+	1.30571i
$659$	−7.25275	+	7.25275i	−0.282527	+	0.282527i	−0.834116	−	0.551589i	$-0.814022\pi$
$659$	−7.25275	+	7.25275i	−0.282527	+	0.282527i	0.551589	+	0.834116i	$0.314022\pi$
$660$	−42.9131	−	2.81267i	−1.67039	−	0.109483i
$661$	−6.38627	−	8.32275i	−0.248397	−	0.323717i	0.652468	−	0.757816i	$-0.273734\pi$
$661$	−6.38627	−	8.32275i	−0.248397	−	0.323717i	−0.900865	+	0.434099i	$0.857067\pi$
$662$	26.8159	+	15.4822i	1.04223	+	0.601731i
$663$	−8.31584	−	7.66173i	−0.322961	−	0.297557i
$664$		−	29.5508i		−	1.14679i
$665$	7.49285	+	3.46991i	0.290560	+	0.134557i
$666$	−13.8183	−	9.23311i	−0.535450	−	0.357776i
$667$	1.75137	−	6.53621i	0.0678134	−	0.253083i
$668$	25.2509	+	8.57153i	0.976987	+	0.331642i
$669$	0.904932	+	13.8066i	0.0349867	+	0.533794i
$670$	−70.2094	+	23.8329i	−2.71242	+	0.920744i
$671$	18.6594	+	45.0478i	0.720339	+	1.73905i
$672$	−18.4110	−	3.19624i	−0.710219	−	0.123298i
$673$	6.71261	−	33.7466i	0.258752	−	1.30083i	−0.604720	−	0.796438i	$-0.706715\pi$
$673$	6.71261	−	33.7466i	0.258752	−	1.30083i	0.863472	−	0.504397i	$-0.168285\pi$
$674$	15.3805	−	31.1886i	0.592434	−	1.20134i
$675$	0.271247	−	0.799067i	0.0104403	−	0.0307561i
$676$	−4.11186	−	15.3457i	−0.158148	−	0.590218i
$677$	−2.18482	+	33.3338i	−0.0839693	+	1.28112i	0.723132	+	0.690710i	$0.242702\pi$
$677$	−2.18482	+	33.3338i	−0.0839693	+	1.28112i	−0.807101	+	0.590413i	$0.798965\pi$
$678$	−16.0539	+	38.7576i	−0.616547	+	1.48848i
$679$	−20.5534	+	10.7685i	−0.788769	+	0.413258i
$680$	12.7158	+	15.2380i	0.487628	+	0.584349i
$681$	−7.21689	−	12.5000i	−0.276552	−	0.479002i
$682$	9.56423	−	7.33889i	0.366233	−	0.281021i
$683$	−34.2769	+	16.9035i	−1.31157	+	0.646794i	−0.957502	−	0.288426i	$-0.906868\pi$
$683$	−34.2769	+	16.9035i	−1.31157	+	0.646794i	−0.354067	+	0.935220i	$0.615201\pi$
$684$	3.61590	+	0.968878i	0.138257	+	0.0370460i
$685$	−0.344331	−	1.73107i	−0.0131562	−	0.0661408i
$686$	−22.5046	+	34.2651i	−0.859229	+	1.30825i
$687$	−9.33051	−	1.85595i	−0.355981	−	0.0708090i
$688$	−1.84166	−	1.41315i	−0.0702126	−	0.0538760i
$689$	0.161313	−	1.22529i	0.00614552	−	0.0466799i
$690$	5.37422	+	4.71307i	0.204593	+	0.179423i
$691$	−31.4444	−	15.5067i	−1.19620	−	0.589902i	−0.268521	−	0.963274i	$-0.586535\pi$
$691$	−31.4444	−	15.5067i	−1.19620	−	0.589902i	−0.927682	+	0.373372i	$0.878202\pi$
$692$	27.1359	−	5.39767i	1.03155	−	0.205189i
$693$	4.84032	−	15.4941i	0.183869	−	0.588572i
$694$	8.96518	−	13.4173i	0.340314	−	0.509315i
$695$	−3.03043	−	23.0184i	−0.114951	−	0.873137i
$696$	5.04315	−	8.73500i	0.191160	−	0.331099i
$697$	5.25189	+	3.69872i	0.198930	+	0.140099i
$698$	−11.8647	+	6.85010i	−0.449086	+	0.259280i
$699$	9.71353	+	4.02347i	0.367399	+	0.152182i
$700$	2.62287	+	5.91847i	0.0991351	+	0.223697i
$701$	0.358450	+	0.358450i	0.0135385	+	0.0135385i	0.713844	−	0.700305i	$-0.246953\pi$
$701$	0.358450	+	0.358450i	0.0135385	+	0.0135385i	−0.700305	+	0.713844i	$0.746953\pi$
$702$	−4.00246	−	4.56393i	−0.151063	−	0.172255i
$703$	9.67251	−	0.633970i	0.364806	−	0.0239106i
$704$	−51.9828	+	59.2750i	−1.95917	+	2.23401i
$705$	−8.51902	+	11.1022i	−0.320845	+	0.418133i
$706$	−47.9825	+	19.8750i	−1.80585	+	0.748006i
$707$	11.2985	−	46.7072i	0.424925	−	1.75660i
$708$	12.9009	+	19.3075i	0.484845	+	0.725621i
$709$	1.40377	−	1.23107i	0.0527197	−	0.0462339i	−0.632581	−	0.774495i	$-0.718004\pi$
$709$	1.40377	−	1.23107i	0.0527197	−	0.0462339i	0.685300	+	0.728261i	$0.259671\pi$
$710$	40.4949	−	10.8506i	1.51975	−	0.407215i
$711$	3.85365	+	7.81443i	0.144523	+	0.293064i
$712$	−21.4501	+	2.82396i	−0.803877	+	0.105832i
$713$	−1.18585			−0.0444103
$714$	−21.6571	+	10.6780i	−0.810495	+	0.399615i
$715$	−40.6745			−1.52114
$716$	−67.9424	+	8.94478i	−2.53913	+	0.334282i
$717$	0.931787	+	1.88948i	0.0347982	+	0.0705638i
$718$	21.3463	−	5.71972i	0.796636	−	0.213458i
$719$	−2.08655	+	1.82985i	−0.0778151	+	0.0682420i	−0.697370	−	0.716711i	$-0.745646\pi$
$719$	−2.08655	+	1.82985i	−0.0778151	+	0.0682420i	0.619555	+	0.784953i	$0.287313\pi$
$720$	−1.86904	−	2.79721i	−0.0696549	−	0.104246i
$721$	30.4357	−	31.9621i	1.13349	−	1.19033i
$722$	35.4465	−	14.6824i	1.31918	−	0.546423i
$723$	−0.176954	+	0.230611i	−0.00658099	+	0.00857651i
$724$	−12.8197	+	14.6180i	−0.476440	+	0.543275i
$725$	4.26535	−	0.279566i	0.158411	−	0.0103828i
$726$	−38.8834	−	44.3380i	−1.44310	−	1.64554i
$727$	17.9107	+	17.9107i	0.664269	+	0.664269i	0.956383	−	0.292114i	$-0.0943587\pi$
$727$	17.9107	+	17.9107i	0.664269	+	0.664269i	−0.292114	+	0.956383i	$0.594359\pi$
$728$	14.3658	+	1.53493i	0.532433	+	0.0568884i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	−4.25003	+	2.45376i	−0.157301	+	0.0908177i
$731$	−6.87553	−	0.168713i	−0.254301	−	0.00624009i
$732$	11.5219	−	19.9565i	0.425861	−	0.737613i
$733$	0.0865168	+	0.657160i	0.00319557	+	0.0242728i	0.992968	−	0.118380i	$-0.0377701\pi$
$733$	0.0865168	+	0.657160i	0.00319557	+	0.0242728i	−0.989773	+	0.142653i	$0.954437\pi$
$734$	−9.49139	+	14.2049i	−0.350334	+	0.524311i
$735$	−16.6490	+	3.02642i	−0.614108	+	0.111631i
$736$	9.25362	−	1.84066i	0.341093	−	0.0678476i
$737$	−76.2461	−	37.6004i	−2.80856	−	1.38503i
$738$	2.59274	+	2.27377i	0.0954402	+	0.0836988i
$739$	−2.21995	+	16.8622i	−0.0816623	+	0.620287i	0.900856	+	0.434119i	$0.142940\pi$
$739$	−2.21995	+	16.8622i	−0.0816623	+	0.620287i	−0.982518	+	0.186168i	$0.940393\pi$
$740$	41.7522	+	32.0376i	1.53484	+	1.17773i
$741$	3.47255	+	0.690734i	0.127567	+	0.0253747i
$742$	−2.31715	−	1.26328i	−0.0850654	−	0.0463766i
$743$	1.89588	+	9.53123i	0.0695531	+	0.349667i	0.999853	−	0.0171323i	$-0.00545364\pi$
$743$	1.89588	+	9.53123i	0.0695531	+	0.349667i	−0.930300	+	0.366799i	$0.880454\pi$
$744$	−1.70735	−	0.457483i	−0.0625944	−	0.0167721i
$745$	22.9500	−	11.3177i	0.840825	−	0.414649i
$746$	−2.34867	+	1.80220i	−0.0859910	+	0.0659832i
$747$	7.42040	+	12.8525i	0.271498	+	0.470249i
$748$	−6.59129	+	73.0525i	−0.241001	+	2.67106i
$749$	34.8983	+	22.1033i	1.27516	+	0.807637i
$750$	8.51058	−	20.5464i	0.310762	−	0.750247i
$751$	−1.02621	+	15.6569i	−0.0374468	+	0.571328i	0.937372	+	0.348330i	$0.113251\pi$
$751$	−1.02621	+	15.6569i	−0.0374468	+	0.571328i	−0.974819	+	0.222998i	$0.928416\pi$
$752$	2.08506	+	7.78156i	0.0760344	+	0.283764i
$753$	9.58327	−	28.2314i	0.349234	−	1.02881i
$754$	13.6000	−	27.5781i	0.495284	−	1.00434i
$755$	6.78811	−	34.1261i	0.247045	−	1.24198i
$756$	−7.20193	+	2.64285i	−0.261932	+	0.0961194i
$757$	−0.673804	−	1.62671i	−0.0244898	−	0.0591236i	0.911162	−	0.412049i	$-0.135187\pi$
$757$	−0.673804	−	1.62671i	−0.0244898	−	0.0591236i	−0.935651	+	0.352926i	$0.885187\pi$
$758$	32.0266	−	10.8716i	1.16326	−	0.394873i
$759$	0.536042	+	8.17841i	0.0194571	+	0.296858i
$760$	−5.88463	−	1.99756i	−0.213458	−	0.0724592i
$761$	8.22575	−	30.6989i	0.298183	−	1.11283i	−0.640473	−	0.767981i	$-0.721262\pi$
$761$	8.22575	−	30.6989i	0.298183	−	1.11283i	0.938656	−	0.344854i	$-0.112072\pi$
$762$	−35.7305	−	23.8743i	−1.29438	−	0.864876i
$763$	−10.4692	+	22.6070i	−0.379011	+	0.818429i
$764$			35.5817i			1.28730i
$765$	−9.35683	−	3.43442i	−0.338297	−	0.124172i
$766$	−51.9874	−	30.0149i	−1.87838	−	1.08448i
$767$	13.3699	+	17.4240i	0.482761	+	0.629146i
$768$	5.98013	+	0.391958i	0.215789	+	0.0141436i
$769$	28.4755	−	28.4755i	1.02685	−	1.02685i	0.0272230	−	0.999629i	$-0.491334\pi$
$769$	28.4755	−	28.4755i	1.02685	−	1.02685i	0.999629	−	0.0272230i	$-0.00866641\pi$
$770$	−31.2672	+	81.0362i	−1.12679	+	2.92034i
$771$	19.3200	−	12.9092i	0.695793	−	0.464914i
$772$	−14.5385	−	42.8289i	−0.523251	−	1.54145i
$773$	−39.6351	−	5.21806i	−1.42558	−	0.187681i	−0.622063	−	0.782968i	$-0.713705\pi$
$773$	−39.6351	−	5.21806i	−1.42558	−	0.187681i	−0.803513	+	0.595287i	$0.797038\pi$
$774$	−3.66067	−	0.481936i	−0.131580	−	0.0173228i
$775$	−0.240786	−	0.709332i	−0.00864928	−	0.0254800i
$776$	14.5199	−	9.70189i	0.521234	−	0.348278i
$777$	−15.4592	+	12.4746i	−0.554595	+	0.447523i
$778$	−54.5886	+	54.5886i	−1.95710	+	1.95710i
$779$	−2.00708	−	0.131551i	−0.0719110	−	0.00471330i
$780$	11.7021	+	15.2505i	0.419003	+	0.546056i
$781$	41.6291	+	24.0346i	1.48961	+	0.860025i
$782$	8.26100	−	8.96627i	0.295413	−	0.320633i
$783$			5.06548i			0.181025i
$784$	−4.45244	+	8.66449i	−0.159016	+	0.309446i
$785$	−5.27888	−	3.52723i	−0.188411	−	0.125892i
$786$	−4.87928	+	18.2097i	−0.174038	+	0.649519i
$787$	23.0057	+	7.80937i	0.820064	+	0.278374i	0.699774	−	0.714365i	$-0.253284\pi$
$787$	23.0057	+	7.80937i	0.820064	+	0.278374i	0.120290	+	0.992739i	$0.461618\pi$
$788$	−1.01279	−	15.4521i	−0.0360790	−	0.550459i
$789$	21.9136	−	7.43866i	0.780144	−	0.264823i
$790$	−17.8416	−	43.0735i	−0.634776	−	1.53249i
$791$	38.4968	+	32.1298i	1.36879	+	1.14241i
$792$	−2.38334	+	11.9818i	−0.0846882	+	0.425756i
$793$	9.63965	−	19.5473i	0.342314	−	0.694144i
$794$	2.73750	−	8.06441i	0.0971502	−	0.286195i
$795$	−0.281956	−	1.05227i	−0.00999995	−	0.0373203i
$796$	−3.46612	+	52.8828i	−0.122853	+	1.87438i
$797$	18.5475	−	44.7776i	0.656985	−	1.58610i	−0.145451	−	0.989365i	$-0.546463\pi$
$797$	18.5475	−	44.7776i	0.656985	−	1.58610i	0.802436	−	0.596738i	$-0.203537\pi$
$798$	4.04556	−	6.38742i	0.143211	−	0.226112i
$799$	18.5737	+	14.9901i	0.657090	+	0.530312i
$800$	2.97996	+	5.16145i	0.105358	+	0.182485i
$801$	8.62017	−	6.61449i	0.304579	−	0.233711i
$802$	−53.3840	+	26.3261i	−1.88506	+	0.929606i
$803$	−5.43520	−	1.45636i	−0.191804	−	0.0513937i
$804$	7.83822	+	39.4054i	0.276433	+	1.38972i
$805$	7.29262	−	4.45166i	0.257031	−	0.156901i
$806$	−5.28511	−	1.05127i	−0.186160	−	0.0370296i
$807$	−12.2805	−	9.42317i	−0.432295	−	0.331711i
$808$	−4.72055	+	35.8561i	−0.166068	+	1.26141i
$809$	20.6855	+	18.1407i	0.727265	+	0.637794i	0.940730	−	0.339157i	$-0.110142\pi$
$809$	20.6855	+	18.1407i	0.727265	+	0.637794i	−0.213465	+	0.976951i	$0.568475\pi$
$810$	−4.79909	−	2.36665i	−0.168623	−	0.0831556i
$811$	9.94901	−	1.97898i	0.349357	−	0.0694914i	−0.0172928	−	0.999850i	$-0.505505\pi$
$811$	9.94901	−	1.97898i	0.349357	−	0.0694914i	0.366650	+	0.930359i	$0.380505\pi$
$812$	−26.3290	−	28.5811i	−0.923966	−	1.00300i
$813$	−11.0116	+	16.4801i	−0.386195	+	0.577982i
$814$	13.3090	+	101.092i	0.466480	+	3.54327i
$815$	0.931817	−	1.61395i	0.0326401	−	0.0565343i
$816$	−4.84767	+	3.06982i	−0.169702	+	0.107465i
$817$	1.86502	−	1.07677i	0.0652487	−	0.0376714i
$818$	28.1721	+	11.6693i	0.985014	+	0.408006i
$819$	−6.63356	+	2.93977i	−0.231795	+	0.102724i
$820$	−7.72188	−	7.72188i	−0.269660	−	0.269660i
$821$	−2.21950	−	2.53085i	−0.0774611	−	0.0883274i	0.711811	−	0.702371i	$-0.247875\pi$
$821$	−2.21950	−	2.53085i	−0.0774611	−	0.0883274i	−0.789272	+	0.614044i	$0.789542\pi$
$822$	−1.61265	+	0.105698i	−0.0562475	+	0.00368665i
$823$	0.796070	−	0.907743i	0.0277492	−	0.0316419i	−0.737799	−	0.675021i	$-0.764135\pi$
$823$	0.796070	−	0.907743i	0.0277492	−	0.0316419i	0.765548	+	0.643379i	$0.222468\pi$
$824$	−20.2206	+	26.3520i	−0.704418	+	0.918016i
$825$	−4.78320	+	1.98127i	−0.166530	+	0.0689788i
$826$	44.9918	−	13.2429i	1.56546	−	0.460780i
$827$	−1.21299	−	1.81537i	−0.0421799	−	0.0631267i	0.809780	−	0.586733i	$-0.199586\pi$
$827$	−1.21299	−	1.81537i	−0.0421799	−	0.0631267i	−0.851960	+	0.523606i	$0.824586\pi$
$828$	2.91219	−	2.55392i	0.101206	−	0.0887550i
$829$	−10.7372	+	2.87701i	−0.372917	+	0.0999227i	−0.440409	−	0.897797i	$-0.645167\pi$
$829$	−10.7372	+	2.87701i	−0.372917	+	0.0999227i	0.0674928	+	0.997720i	$0.478500\pi$
$830$	−35.1230	−	71.2224i	−1.21914	−	2.47217i
$831$	31.1118	−	4.09594i	1.07925	−	0.142087i
$832$	35.2406			1.22175
$833$	4.46370	+	28.5145i	0.154658	+	0.987968i
$834$	−21.2587			−0.736127
$835$	22.0417	−	2.90184i	0.762783	−	0.100422i
$836$	−10.1582	−	20.5988i	−0.351329	−	0.712424i
$837$	0.857453	−	0.229754i	0.0296379	−	0.00794145i
$838$	47.6222	−	41.7635i	1.64508	−	1.44270i
$839$	−5.51326	−	8.25118i	−0.190339	−	0.284862i	0.724010	−	0.689789i	$-0.242297\pi$
$839$	−5.51326	−	8.25118i	−0.190339	−	0.284862i	−0.914349	+	0.404927i	$0.867297\pi$
$840$	12.2171	−	3.59599i	0.421530	−	0.124074i
$841$	3.08664	−	1.27853i	0.106436	−	0.0440872i
$842$	−6.34321	+	8.26663i	−0.218602	+	0.284887i
$843$	0.345897	−	0.394420i	0.0119133	−	0.0135845i
$844$	13.7909	−	0.903901i	0.474701	−	0.0311136i
$845$	−8.73316	−	9.95826i	−0.300430	−	0.342575i
$846$	9.06060	+	9.06060i	0.311510	+	0.311510i
$847$	−64.4441	+	28.5595i	−2.21433	+	0.981315i
$848$	−0.579403	−	0.239997i	−0.0198968	−	0.00824152i
$849$	13.6460	−	7.87850i	0.468328	−	0.270389i
$850$	7.04071	+	3.12084i	0.241494	+	0.107044i
$851$	5.01490	−	8.68606i	0.171909	−	0.297754i
$852$	−2.96523	−	22.5232i	−0.101587	−	0.771632i
$853$	−10.2193	+	15.2943i	−0.349902	+	0.523665i	−0.964118	−	0.265472i	$-0.914472\pi$
$853$	−10.2193	+	15.2943i	−0.349902	+	0.523665i	0.614217	+	0.789137i	$0.289472\pi$
$854$	−31.5341	−	34.2314i	−1.07907	−	1.17138i
$855$	3.06100	−	0.608871i	0.104684	−	0.0208229i
$856$	−27.8830	−	13.7504i	−0.953022	−	0.469978i
$857$	−40.6704	−	35.6670i	−1.38927	−	1.21836i	−0.946900	−	0.321529i	$-0.895803\pi$
$857$	−40.6704	−	35.6670i	−1.38927	−	1.21836i	−0.442374	−	0.896831i	$-0.645863\pi$
$858$	−4.86127	+	36.9250i	−0.165961	+	1.26060i
$859$	6.43234	+	4.93571i	0.219469	+	0.168404i	0.712644	−	0.701526i	$-0.247497\pi$
$859$	6.43234	+	4.93571i	0.219469	+	0.168404i	−0.493176	+	0.869930i	$0.664164\pi$
$860$	11.4675	+	2.28103i	0.391039	+	0.0777825i
$861$	3.51826	−	2.14766i	0.119902	−	0.0731922i
$862$	−14.6819	−	73.8107i	−0.500066	−	2.51400i
$863$	−17.6724	−	4.73532i	−0.601577	−	0.161192i	−0.0548381	−	0.998495i	$-0.517464\pi$
$863$	−17.6724	−	4.73532i	−0.601577	−	0.161192i	−0.546739	+	0.837303i	$0.684131\pi$
$864$	−6.33442	+	3.12379i	−0.215501	+	0.106273i
$865$	18.3001	−	14.0422i	0.622223	−	0.477448i
$866$	33.6766	+	58.3296i	1.14438	+	1.98212i
$867$	−6.24744	+	15.8104i	−0.212174	+	0.536950i
$868$	−3.64384	+	5.75316i	−0.123680	+	0.195275i
$869$	20.4571	−	49.3878i	0.693960	−	1.67537i
$870$	1.77275	−	27.0469i	0.0601018	−	0.916976i
$871$	9.83513	+	36.7052i	0.333251	+	1.24371i
$872$	6.02693	−	17.7548i	0.204098	−	0.601252i
$873$	−3.87893	+	7.86568i	−0.131282	+	0.266213i
$874$	−0.744760	+	3.74416i	−0.0251919	+	0.126648i
$875$	−20.4081	−	17.0328i	−0.689921	−	0.575815i
$876$	1.01767	+	2.45687i	0.0343838	+	0.0830099i
$877$	7.69984	−	2.61374i	0.260005	−	0.0882598i	−0.188393	−	0.982094i	$-0.560328\pi$
$877$	7.69984	−	2.61374i	0.260005	−	0.0882598i	0.448398	+	0.893834i	$0.351995\pi$
$878$	1.25806	+	19.1942i	0.0424574	+	0.647774i
$879$	10.1708	+	3.45252i	0.343053	+	0.116451i
$880$	−5.34212	+	19.9371i	−0.180083	+	0.672078i
$881$	4.04042	+	2.69972i	0.136125	+	0.0909560i	0.621768	−	0.783201i	$-0.286415\pi$
$881$	4.04042	+	2.69972i	0.136125	+	0.0909560i	−0.485643	+	0.874157i	$0.661415\pi$
$882$	0.757610	+	15.4759i	0.0255100	+	0.521102i
$883$		−	44.7736i		−	1.50675i	−0.657590	−	0.753376i	$-0.728424\pi$
$883$		−	44.7736i		−	1.50675i	0.657590	−	0.753376i	$-0.271576\pi$
$884$	26.4929	−	19.3150i	0.891053	−	0.649632i
$885$	16.7659	+	9.67981i	0.563580	+	0.325383i
$886$	32.8682	+	42.8346i	1.10423	+	1.43906i
$887$	4.98685	+	0.326855i	0.167442	+	0.0109747i	0.148893	−	0.988853i	$-0.452429\pi$
$887$	4.98685	+	0.326855i	0.167442	+	0.0109747i	0.0185484	+	0.999828i	$0.494096\pi$
$888$	10.5713	−	10.5713i	0.354749	−	0.354749i
$889$	−39.9733	+	32.2559i	−1.34066	+	1.08183i
$890$	−48.3419	+	32.3010i	−1.62042	+	1.08273i
$891$	−1.97214	−	5.80973i	−0.0660691	−	0.194633i
$892$	−39.7758	−	5.23658i	−1.33179	−	0.175334i
$893$	−7.40971	−	0.975507i	−0.247956	−	0.0326441i
$894$	−7.53149	−	22.1871i	−0.251891	−	0.742047i
$895$	−47.5045	+	31.7415i	−1.58790	+	1.06100i
$896$	13.6367	−	35.3428i	0.455571	−	1.18072i
$897$	2.59049	−	2.59049i	0.0864940	−	0.0864940i
$898$	66.2792	+	4.34417i	2.21176	+	0.144967i
$899$	2.73737	+	3.56741i	0.0912965	+	0.118980i
$900$	2.11899	+	1.22340i	0.0706330	+	0.0407800i
$901$	−1.80601	+	0.436730i	−0.0601668	+	0.0145496i
$902$		−	21.1579i		−	0.704480i
$903$	−1.85456	+	4.00470i	−0.0617160	+	0.133268i
$904$	−31.3777	−	20.9659i	−1.04361	−	0.697315i
$905$	−4.19543	+	15.6576i	−0.139461	+	0.520475i
$906$	−30.1690	−	10.2410i	−1.00230	−	0.340234i
$907$	−2.11136	−	32.2131i	−0.0701064	−	1.06962i	−0.877491	−	0.479593i	$-0.840784\pi$
$907$	−2.11136	−	32.2131i	−0.0701064	−	1.06962i	0.807385	−	0.590025i	$-0.200882\pi$
$908$	39.6306	−	13.4528i	1.31519	−	0.446446i
$909$	−6.95061	−	16.7803i	−0.230537	−	0.556566i
$910$	36.4485	−	13.3753i	1.20825	−	0.443386i
$911$	−5.72126	+	28.7627i	−0.189554	+	0.952952i	0.762492	+	0.646997i	$0.223976\pi$
$911$	−5.72126	+	28.7627i	−0.189554	+	0.952952i	−0.952046	+	0.305954i	$0.901024\pi$
$912$	0.794649	−	1.61139i	0.0263135	−	0.0533584i
$913$	29.2681	−	86.2211i	0.968633	−	2.85350i
$914$	1.16035	+	4.33047i	0.0383809	+	0.143239i
$915$	1.25652	−	19.1707i	0.0415392	−	0.633765i
$916$	10.5561	−	25.4847i	0.348784	−	0.842039i
$917$	19.0365	+	12.0570i	0.628641	+	0.398159i
$918$	−4.23612	+	8.08381i	−0.139813	+	0.266805i
$919$	4.80832	+	8.32825i	0.158612	+	0.274724i	0.934368	−	0.356309i	$-0.115965\pi$
$919$	4.80832	+	8.32825i	0.158612	+	0.274724i	−0.775757	+	0.631032i	$0.782632\pi$
$920$	−5.10141	+	3.91445i	−0.168188	+	0.129055i
$921$	6.94280	−	3.42381i	0.228773	−	0.112818i
$922$	−25.0783	−	6.71971i	−0.825909	−	0.221302i
$923$	−4.19179	−	21.0735i	−0.137974	−	0.693644i
$924$	41.3249	+	22.5298i	1.35949	+	0.741177i
$925$	6.21397	+	1.23604i	0.204314	+	0.0406406i
$926$	21.6814	+	16.6367i	0.712494	+	0.546716i
$927$	2.17737	−	16.5388i	0.0715143	−	0.543205i
$928$	−26.8981	−	23.5890i	−0.882973	−	0.774346i
$929$	23.8373	+	11.7553i	0.782077	+	0.385677i	0.789074	−	0.614298i	$-0.210561\pi$
$929$	23.8373	+	11.7553i	0.782077	+	0.385677i	−0.00699754	+	0.999976i	$0.502227\pi$
$930$	−4.65874	+	0.926682i	−0.152766	+	0.0303871i
$931$	−5.84554	−	6.89218i	−0.191580	−	0.225882i
$932$	−16.9369	+	25.3478i	−0.554786	+	0.830296i
$933$	0.739570	+	5.61760i	0.0242125	+	0.183912i
$934$	8.54625	−	14.8025i	0.279642	−	0.484354i
$935$	22.0090	+	57.0543i	0.719770	+	1.86588i
$936$	4.72909	−	2.73034i	0.154575	−	0.0892440i
$937$	22.8080	+	9.44737i	0.745104	+	0.308632i	0.722742	−	0.691118i	$-0.242881\pi$
$937$	22.8080	+	9.44737i	0.745104	+	0.308632i	0.0223617	+	0.999750i	$0.492881\pi$
$938$	80.6885	+	8.62125i	2.63457	+	0.281494i
$939$	2.24946	+	2.24946i	0.0734083	+	0.0734083i
$940$	−26.7540	−	30.5071i	−0.872619	−	0.995032i
$941$	46.1010	−	3.02162i	1.50285	−	0.0985020i	0.708392	−	0.705820i	$-0.249421\pi$
$941$	46.1010	−	3.02162i	1.50285	−	0.0985020i	0.794459	+	0.607318i	$0.207754\pi$
$942$	−3.83299	+	4.37069i	−0.124886	+	0.142405i
$943$	−1.26696	+	1.65114i	−0.0412580	+	0.0537685i
$944$	10.2966	−	4.26498i	0.335125	−	0.138813i
$945$	−4.41060	+	4.63180i	−0.143477	+	0.150672i
$946$	12.5854	+	18.8355i	0.409188	+	0.612393i
$947$	−22.8570	+	20.0450i	−0.742752	+	0.651376i	−0.944668	−	0.328027i	$-0.893616\pi$
$947$	−22.8570	+	20.0450i	−0.742752	+	0.651376i	0.201916	+	0.979403i	$0.435283\pi$
$948$	−24.4030	+	6.53876i	−0.792572	+	0.212369i
$949$	1.11243	+	2.25579i	0.0361111	+	0.0732262i
$950$	−2.39085	+	0.314761i	−0.0775694	+	0.0102122i
$951$	3.06344			0.0993388
$952$	−5.62029	−	20.9816i	−0.182155	−	0.680016i
$953$	32.4072			1.04977			0.524886	−	0.851172i	$-0.324108\pi$
$953$	32.4072			1.04977			0.524886	+	0.851172i	$0.324108\pi$
$954$	−0.988970	+	0.130200i	−0.0320191	+	0.00421539i
$955$	13.1205	+	26.6056i	0.424568	+	0.860939i
$956$	−5.90048	+	1.58103i	−0.190835	+	0.0511342i
$957$	23.3660	−	20.4914i	0.755314	−	0.662393i
$958$	−40.6472	−	60.8329i	−1.31325	−	1.96542i
$959$	−0.454181	+	1.87755i	−0.0146663	+	0.0606292i
$960$	28.6994	−	11.8877i	0.926269	−	0.383673i
$961$	−18.3919	+	23.9688i	−0.593287	+	0.773186i
$962$	30.0509	−	34.2665i	0.968880	−	1.10480i
$963$	15.5800	−	1.02116i	0.502057	−	0.0329066i
$964$	−0.555724	−	0.633682i	−0.0178987	−	0.0204095i
$965$	−26.6637	−	26.6637i	−0.858336	−	0.858336i
$966$	−3.16971	−	7.15241i	−0.101984	−	0.230125i
$967$	−42.2140	−	17.4856i	−1.35751	−	0.562299i	−0.419136	−	0.907923i	$-0.637667\pi$
$967$	−42.2140	−	17.4856i	−1.35751	−	0.562299i	−0.938373	+	0.345625i	$0.887667\pi$
$968$	45.9425	−	26.5249i	1.47665	−	0.852542i
$969$	−0.910101	−	5.24472i	−0.0292367	−	0.168485i
$970$	23.4641	−	40.6410i	0.753387	−	1.30490i
$971$	3.34561	+	25.4124i	0.107366	+	0.815524i	0.957394	+	0.288786i	$0.0932517\pi$
$971$	3.34561	+	25.4124i	0.107366	+	0.815524i	−0.850028	+	0.526738i	$0.823415\pi$
$972$	−1.61091	+	2.41090i	−0.0516700	+	0.0773297i
$973$	−7.57693	+	24.2541i	−0.242905	+	0.777551i
$974$	58.0915	−	11.5551i	1.86137	−	0.370250i
$975$	2.07554	+	1.02354i	0.0664705	+	0.0327796i
$976$	−8.31525	−	7.29228i	−0.266165	−	0.233420i
$977$	−0.695190	+	5.28049i	−0.0222411	+	0.168938i	−0.998961	−	0.0455826i	$-0.985486\pi$
$977$	−0.695190	+	5.28049i	−0.0222411	+	0.168938i	0.976719	+	0.214521i	$0.0688189\pi$
$978$	−1.35381	−	1.03881i	−0.0432899	−	0.0332175i
$979$	−65.3824	−	13.0054i	−2.08963	−	0.415654i
$980$	0.811263	−	49.0593i	0.0259148	−	1.56714i
$981$	1.83705	+	9.23548i	0.0586525	+	0.294866i
$982$	12.4815	+	3.34440i	0.398300	+	0.106724i
$983$	17.7516	−	8.75414i	0.566189	−	0.279214i	−0.136583	−	0.990629i	$-0.543612\pi$
$983$	17.7516	−	8.75414i	0.566189	−	0.279214i	0.702772	+	0.711415i	$0.251945\pi$
$984$	−2.46113	+	1.88849i	−0.0784578	+	0.0602028i
$985$	−6.45514	−	11.1806i	−0.205678	−	0.356245i
$986$	−46.0429	−	4.15431i	−1.46631	−	0.132300i
$987$	13.5666	−	7.10794i	0.431831	−	0.226248i
$988$	−3.92869	+	9.48469i	−0.124988	+	0.301748i
$989$	0.145738	−	2.22353i	0.00463420	−	0.0707043i
$990$	8.49694	+	31.7110i	0.270051	+	1.00784i
$991$	7.61590	−	22.4357i	0.241927	−	0.712694i	−0.756358	−	0.654158i	$-0.773023\pi$
$991$	7.61590	−	22.4357i	0.241927	−	0.712694i	0.998285	−	0.0585365i	$-0.0186434\pi$
$992$	−2.77299	+	5.62307i	−0.0880425	+	0.178533i
$993$	2.72909	−	13.7201i	0.0866052	−	0.435394i
$994$	−45.2073	−	7.84822i	−1.43389	−	0.248930i
$995$	16.9084	+	40.8204i	0.536031	+	1.29409i
$996$	−40.7482	+	13.8321i	−1.29116	+	0.438288i
$997$	−1.29363	−	19.7369i	−0.0409696	−	0.625075i	−0.968136	−	0.250425i	$-0.919430\pi$
$997$	−1.29363	−	19.7369i	−0.0409696	−	0.625075i	0.927166	−	0.374650i	$-0.122237\pi$
$998$	−62.6756	−	21.2755i	−1.98396	−	0.673465i
$999$	−1.94324	+	7.25227i	−0.0614814	+	0.229452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.22	✓	384
7.5	odd	6	inner	357.2.bl.a.61.3	yes	384
17.12	odd	16	inner	357.2.bl.a.199.3	yes	384
119.12	even	48	inner	357.2.bl.a.250.22	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.22	✓	384	1.1	even	1	trivial
357.2.bl.a.61.3	yes	384	7.5	odd	6	inner
357.2.bl.a.199.3	yes	384	17.12	odd	16	inner
357.2.bl.a.250.22	yes	384	119.12	even	48	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19456 - 0.288919i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(2.80077 - 0.750463i) q^{4} +(1.81750 - 1.59391i) q^{5} +(-1.22975 - 1.84045i) q^{6} +(-2.53809 + 0.747063i) q^{7} +(1.83962 - 0.761994i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(3.52811 - 4.02303i) q^{10} +(6.12220 - 0.401270i) q^{11} +(-1.91182 - 2.18001i) q^{12} +(-1.93919 - 1.93919i) q^{13} +(-5.35415 + 2.37278i) q^{14} +(-2.23339 - 0.925101i) q^{15} +(-1.20520 + 0.695825i) q^{16} +(-1.67081 + 3.76940i) q^{17} +(-1.10675 + 1.91694i) q^{18} +(-0.168515 - 1.28000i) q^{19} +(3.89423 - 5.82813i) q^{20} +(1.79259 + 1.94593i) q^{21} +(13.3196 - 2.64943i) q^{22} +(-1.19810 - 0.590837i) q^{23} +(-1.49705 - 1.31288i) q^{24} +(0.110144 - 0.836630i) q^{25} +(-4.81593 - 3.69540i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-6.54795 + 3.99709i) q^{28} +(0.988225 + 4.96814i) q^{29} +(-5.16859 - 1.38492i) q^{30} +(0.796154 - 0.392620i) q^{31} +(-5.60328 + 4.29955i) q^{32} +(-3.06767 - 5.31335i) q^{33} +(-2.57765 + 8.75490i) q^{34} +(-3.42223 + 5.40327i) q^{35} +(-1.10962 + 2.67885i) q^{36} +(-0.491054 + 7.49203i) q^{37} +(-0.739630 - 2.76034i) q^{38} +(-0.881524 + 2.59689i) q^{39} +(2.12896 - 4.31710i) q^{40} +(0.303942 - 1.52802i) q^{41} +(4.49616 + 3.75254i) q^{42} +(0.638340 + 1.54109i) q^{43} +(16.8457 - 5.71834i) q^{44} +(0.158106 + 2.41223i) q^{45} +(-2.80000 - 0.950473i) q^{46} +(1.49827 - 5.59161i) q^{47} +(1.15711 + 0.773159i) q^{48} +(5.88379 - 3.79223i) q^{49} -1.86786i q^{50} +(4.11965 - 0.168656i) q^{51} +(-6.88650 - 3.97592i) q^{52} +(0.274336 + 0.357522i) q^{53} +(2.20876 + 0.144770i) q^{54} +(10.4875 - 10.4875i) q^{55} +(-4.09985 + 3.30832i) q^{56} +(-1.07346 + 0.717263i) q^{57} +(3.60411 + 10.6174i) q^{58} +(-7.93991 - 1.04531i) q^{59} +(-6.94946 - 0.914914i) q^{60} +(2.55458 + 7.52555i) q^{61} +(1.63377 - 1.09165i) q^{62} +(0.952406 - 2.46838i) q^{63} +(-9.08642 + 9.08642i) q^{64} +(-6.61536 - 0.433594i) q^{65} +(-8.26731 - 10.7742i) q^{66} +(-11.9999 - 6.92817i) q^{67} +(-1.85076 + 11.8111i) q^{68} +1.33586i q^{69} +(-5.94919 + 12.8465i) q^{70} +(6.51440 + 4.35279i) q^{71} +(-0.515357 + 1.92334i) q^{72} +(-0.868463 - 0.294804i) q^{73} +(1.08695 + 16.5836i) q^{74} +(-0.799067 + 0.271247i) q^{75} +(-1.43256 - 3.45850i) q^{76} +(-15.2389 + 5.59213i) q^{77} +(-1.18427 + 5.95371i) q^{78} +(3.85365 - 7.81443i) q^{79} +(-1.08138 + 3.18564i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.225545 - 3.44115i) q^{82} +(5.67933 - 13.7111i) q^{83} +(6.48097 + 4.10481i) q^{84} +(2.97136 + 9.51401i) q^{85} +(1.84613 + 3.19759i) q^{86} +(4.01871 - 3.08367i) q^{87} +(10.9567 - 5.40326i) q^{88} +(-10.4953 - 2.81219i) q^{89} +(1.04391 + 5.24810i) q^{90} +(6.37053 + 3.47314i) q^{91} +(-3.79900 - 0.755667i) q^{92} +(-0.704260 - 0.540398i) q^{93} +(1.67251 - 12.7040i) q^{94} +(-2.34647 - 2.05780i) q^{95} +(6.33442 + 3.12379i) q^{96} +(8.60161 - 1.71097i) q^{97} +(11.8167 - 10.0222i) q^{98} +(-3.40861 + 5.10134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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