LMFDB - Embedded newform 570.2.bf.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.12
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.438663 + 1.67558i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.09802 - 0.773495i) q^{5} +(-0.722960 - 1.57395i) q^{6} +(1.27073 + 0.733656i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.61515 + 1.47003i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(0.438663 + 1.67558i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.09802 - 0.773495i) q^{5} +(-0.722960 - 1.57395i) q^{6} +(1.27073 + 0.733656i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.61515 + 1.47003i) q^{9} +(-1.93183 + 1.12606i) q^{10} +(-3.45839 + 1.99670i) q^{11} +(0.985291 + 1.42450i) q^{12} +(0.858834 + 0.720648i) q^{13} +(-1.37882 - 0.501850i) q^{14} +(2.21638 + 3.17611i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.870724 + 4.93812i) q^{17} +(2.32015 - 1.90181i) q^{18} +(4.32194 - 0.566387i) q^{19} +(1.70695 - 1.44441i) q^{20} +(-0.671879 + 2.45104i) q^{21} +(3.05912 - 2.56691i) q^{22} +(-1.52355 + 0.554528i) q^{23} +(-1.21768 - 1.23177i) q^{24} +(3.80341 - 3.24562i) q^{25} +(-0.970926 - 0.560564i) q^{26} +(-3.61032 - 3.73705i) q^{27} +(1.44502 + 0.254796i) q^{28} +(-0.0965571 + 0.547602i) q^{29} +(-2.73423 - 2.74299i) q^{30} +(0.916441 + 0.529107i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-4.86270 - 4.91893i) q^{33} +(-1.71499 - 4.71190i) q^{34} +(3.23350 + 0.556325i) q^{35} +(-1.95466 + 2.27581i) q^{36} +9.18483 q^{37} +(-4.15793 + 1.30828i) q^{38} +(-0.830766 + 1.75517i) q^{39} +(-1.43019 + 1.71888i) q^{40} +(0.860741 - 0.722248i) q^{41} +(0.236054 - 2.53047i) q^{42} +(-3.98161 + 10.9394i) q^{43} +(-2.56691 + 3.05912i) q^{44} +(-4.34959 + 5.10696i) q^{45} +(1.40412 - 0.810666i) q^{46} +(-1.83264 + 10.3934i) q^{47} +(1.41308 + 1.00160i) q^{48} +(-2.42350 - 4.19762i) q^{49} +(-3.18203 + 3.85677i) q^{50} +(-7.89227 + 3.62514i) q^{51} +(1.05352 + 0.383449i) q^{52} +(-2.12846 - 5.84790i) q^{53} +(4.20441 + 3.05335i) q^{54} +(-5.71134 + 6.86417i) q^{55} -1.46731 q^{56} +(2.84490 + 6.99332i) q^{57} -0.556050i q^{58} +(-2.24523 - 12.7333i) q^{59} +(3.16901 + 2.22652i) q^{60} +(2.91236 - 1.06001i) q^{61} +(-0.994397 - 0.361931i) q^{62} +(-4.40165 - 0.0506101i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.35927 + 0.847632i) q^{65} +(5.64299 + 3.99980i) q^{66} +(-1.51906 + 8.61503i) q^{67} +(2.50715 + 4.34251i) q^{68} +(-1.59748 - 2.30959i) q^{69} +(-3.28098 + 0.0136184i) q^{70} +(3.90235 + 1.42034i) q^{71} +(1.52977 - 2.58066i) q^{72} +(-8.14026 - 9.70118i) q^{73} +(-9.04529 + 1.59493i) q^{74} +(7.10672 + 4.94919i) q^{75} +(3.86758 - 2.01042i) q^{76} -5.85956 q^{77} +(0.513363 - 1.87276i) q^{78} +(1.18523 + 1.41250i) q^{79} +(1.10999 - 1.94112i) q^{80} +(4.67802 - 7.68870i) q^{81} +(-0.722248 + 0.860741i) q^{82} +(3.61778 - 6.26618i) q^{83} +(0.206945 + 2.53302i) q^{84} +(5.64641 + 9.68679i) q^{85} +(2.02152 - 11.4646i) q^{86} +(-0.959909 + 0.0784234i) q^{87} +(1.99670 - 3.45839i) q^{88} +(5.85814 + 4.91556i) q^{89} +(3.39669 - 5.78468i) q^{90} +(0.562639 + 1.54584i) q^{91} +(-1.24201 + 1.04217i) q^{92} +(-0.484555 + 1.76767i) q^{93} -10.5537i q^{94} +(8.62945 - 4.53130i) q^{95} +(-1.56554 - 0.741008i) q^{96} +(0.183486 + 1.04060i) q^{97} +(3.11559 + 3.71301i) q^{98} +(6.10899 - 10.3056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	0.438663	+	1.67558i	0.253262	+	0.967398i
$3$	0.438663	+	1.67558i	0.253262	+	0.967398i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	2.09802	−	0.773495i	0.938265	−	0.345918i
$5$	2.09802	−	0.773495i	0.938265	−	0.345918i
$6$	−0.722960	−	1.57395i	−0.295147	−	0.642564i
$7$	1.27073	+	0.733656i	0.480291	+	0.277296i	0.720538	−	0.693416i	$-0.243895\pi$
$7$	1.27073	+	0.733656i	0.480291	+	0.277296i	−0.240247	+	0.970712i	$0.577228\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.61515	+	1.47003i	−0.871717	+	0.490010i
$10$	−1.93183	+	1.12606i	−0.610900	+	0.356092i
$11$	−3.45839	+	1.99670i	−1.04274	+	0.602028i	−0.920609	−	0.390486i	$-0.872307\pi$
$11$	−3.45839	+	1.99670i	−1.04274	+	0.602028i	−0.122134	+	0.992514i	$0.538974\pi$
$12$	0.985291	+	1.42450i	0.284429	+	0.411218i
$13$	0.858834	+	0.720648i	0.238198	+	0.199872i	0.754070	−	0.656794i	$-0.228088\pi$
$13$	0.858834	+	0.720648i	0.238198	+	0.199872i	−0.515873	+	0.856665i	$0.672532\pi$
$14$	−1.37882	−	0.501850i	−0.368506	−	0.134125i
$15$	2.21638	+	3.17611i	0.572267	+	0.820068i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.870724	+	4.93812i	0.211182	+	1.19767i	0.887411	+	0.460979i	$0.152502\pi$
$17$	0.870724	+	4.93812i	0.211182	+	1.19767i	−0.676230	+	0.736691i	$0.736387\pi$
$18$	2.32015	−	1.90181i	0.546865	−	0.448262i
$19$	4.32194	−	0.566387i	0.991522	−	0.129938i
$19$	4.32194	−	0.566387i	0.991522	−	0.129938i
$20$	1.70695	−	1.44441i	0.381685	−	0.322981i
$21$	−0.671879	+	2.45104i	−0.146616	+	0.534861i
$22$	3.05912	−	2.56691i	0.652207	−	0.547267i
$23$	−1.52355	+	0.554528i	−0.317683	+	0.115627i	−0.495940	−	0.868357i	$-0.665176\pi$
$23$	−1.52355	+	0.554528i	−0.317683	+	0.115627i	0.178257	+	0.983984i	$0.442954\pi$
$24$	−1.21768	−	1.23177i	−0.248559	−	0.251433i
$25$	3.80341	−	3.24562i	0.760682	−	0.649125i
$26$	−0.970926	−	0.560564i	−0.190414	−	0.109936i
$27$	−3.61032	−	3.73705i	−0.694807	−	0.719196i
$28$	1.44502	+	0.254796i	0.273083	+	0.0481519i
$29$	−0.0965571	+	0.547602i	−0.0179302	+	0.101687i	−0.992460	−	0.122573i	$-0.960885\pi$
$29$	−0.0965571	+	0.547602i	−0.0179302	+	0.101687i	0.974529	+	0.224260i	$0.0719966\pi$
$30$	−2.73423	−	2.74299i	−0.499200	−	0.500798i
$31$	0.916441	+	0.529107i	0.164598	+	0.0950305i	0.580036	−	0.814591i	$-0.303038\pi$
$31$	0.916441	+	0.529107i	0.164598	+	0.0950305i	−0.415438	+	0.909621i	$0.636372\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−4.86270	−	4.91893i	−0.846487	−	0.856276i
$34$	−1.71499	−	4.71190i	−0.294119	−	0.808084i
$35$	3.23350	+	0.556325i	0.546561	+	0.0940361i
$36$	−1.95466	+	2.27581i	−0.325776	+	0.379302i
$37$	9.18483			1.50998			0.754988	−	0.655739i	$-0.227643\pi$
$37$	9.18483			1.50998			0.754988	+	0.655739i	$0.227643\pi$
$38$	−4.15793	+	1.30828i	−0.674506	+	0.212231i
$39$	−0.830766	+	1.75517i	−0.133029	+	0.281052i
$40$	−1.43019	+	1.71888i	−0.226134	+	0.271779i
$41$	0.860741	−	0.722248i	0.134425	−	0.112796i	−0.573096	−	0.819488i	$-0.694258\pi$
$41$	0.860741	−	0.722248i	0.134425	−	0.112796i	0.707521	+	0.706692i	$0.249813\pi$
$42$	0.236054	−	2.53047i	0.0364239	−	0.390460i
$43$	−3.98161	+	10.9394i	−0.607190	+	1.66824i	0.129147	+	0.991625i	$0.458776\pi$
$43$	−3.98161	+	10.9394i	−0.607190	+	1.66824i	−0.736337	+	0.676615i	$0.763446\pi$
$44$	−2.56691	+	3.05912i	−0.386976	+	0.461180i
$45$	−4.34959	+	5.10696i	−0.648398	+	0.761301i
$46$	1.40412	−	0.810666i	0.207025	−	0.119526i
$47$	−1.83264	+	10.3934i	−0.267317	+	1.51603i	0.495037	+	0.868872i	$0.335155\pi$
$47$	−1.83264	+	10.3934i	−0.267317	+	1.51603i	−0.762354	+	0.647160i	$0.775956\pi$
$48$	1.41308	+	1.00160i	0.203960	+	0.144569i
$49$	−2.42350	−	4.19762i	−0.346214	−	0.599660i
$50$	−3.18203	+	3.85677i	−0.450007	+	0.545430i
$51$	−7.89227	+	3.62514i	−1.10514	+	0.507621i
$52$	1.05352	+	0.383449i	0.146096	+	0.0531748i
$53$	−2.12846	−	5.84790i	−0.292367	−	0.803271i	−0.995719	−	0.0924298i	$-0.970537\pi$
$53$	−2.12846	−	5.84790i	−0.292367	−	0.803271i	0.703352	−	0.710841i	$-0.251686\pi$
$54$	4.20441	+	3.05335i	0.572147	+	0.415508i
$55$	−5.71134	+	6.86417i	−0.770117	+	0.925564i
$56$	−1.46731			−0.196078
$57$	2.84490	+	6.99332i	0.376817	+	0.926288i
$58$		−	0.556050i		−	0.0730130i
$59$	−2.24523	−	12.7333i	−0.292304	−	1.65774i	−0.677962	−	0.735097i	$-0.737137\pi$
$59$	−2.24523	−	12.7333i	−0.292304	−	1.65774i	0.385659	−	0.922642i	$-0.373974\pi$
$60$	3.16901	+	2.22652i	0.409117	+	0.287442i
$61$	2.91236	−	1.06001i	0.372890	−	0.135721i	−0.148776	−	0.988871i	$-0.547533\pi$
$61$	2.91236	−	1.06001i	0.372890	−	0.135721i	0.521665	+	0.853150i	$0.325311\pi$
$62$	−0.994397	−	0.361931i	−0.126288	−	0.0459653i
$63$	−4.40165	−	0.0506101i	−0.554555	−	0.00637627i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	2.35927	+	0.847632i	0.292632	+	0.105136i
$66$	5.64299	+	3.99980i	0.694604	+	0.492342i
$67$	−1.51906	+	8.61503i	−0.185583	+	1.05249i	0.739621	+	0.673023i	$0.235005\pi$
$67$	−1.51906	+	8.61503i	−0.185583	+	1.05249i	−0.925204	+	0.379470i	$0.876106\pi$
$68$	2.50715	+	4.34251i	0.304036	+	0.526607i
$69$	−1.59748	−	2.30959i	−0.192314	−	0.278042i
$70$	−3.28098	+	0.0136184i	−0.392152	+	0.00162771i
$71$	3.90235	+	1.42034i	0.463124	+	0.168563i	0.563035	−	0.826433i	$-0.309634\pi$
$71$	3.90235	+	1.42034i	0.463124	+	0.168563i	−0.0999112	+	0.994996i	$0.531856\pi$
$72$	1.52977	−	2.58066i	0.180285	−	0.304134i
$73$	−8.14026	−	9.70118i	−0.952745	−	1.13544i	−0.990687	−	0.136157i	$-0.956525\pi$
$73$	−8.14026	−	9.70118i	−0.952745	−	1.13544i	0.0379421	−	0.999280i	$-0.487920\pi$
$74$	−9.04529	+	1.59493i	−1.05149	+	0.185407i
$75$	7.10672	+	4.94919i	0.820614	+	0.571484i
$76$	3.86758	−	2.01042i	0.443642	−	0.230611i
$77$	−5.85956			−0.667759
$78$	0.513363	−	1.87276i	0.0581269	−	0.212049i
$79$	1.18523	+	1.41250i	0.133349	+	0.158919i	0.828587	−	0.559861i	$-0.189145\pi$
$79$	1.18523	+	1.41250i	0.133349	+	0.158919i	−0.695238	+	0.718780i	$0.744701\pi$
$80$	1.10999	−	1.94112i	0.124100	−	0.217023i
$81$	4.67802	−	7.68870i	0.519780	−	0.854300i
$82$	−0.722248	+	0.860741i	−0.0797589	+	0.0950530i
$83$	3.61778	−	6.26618i	0.397103	−	0.687803i	−0.596264	−	0.802788i	$-0.703349\pi$
$83$	3.61778	−	6.26618i	0.397103	−	0.687803i	0.993367	+	0.114985i	$0.0366822\pi$
$84$	0.206945	+	2.53302i	0.0225795	+	0.276375i
$85$	5.64641	+	9.68679i	0.612439	+	1.05068i
$86$	2.02152	−	11.4646i	0.217986	−	1.23626i
$87$	−0.959909	+	0.0784234i	−0.102913	+	0.00840787i
$88$	1.99670	−	3.45839i	0.212849	−	0.368665i
$89$	5.85814	+	4.91556i	0.620962	+	0.521049i	0.898106	−	0.439780i	$-0.144943\pi$
$89$	5.85814	+	4.91556i	0.620962	+	0.521049i	−0.277144	+	0.960828i	$0.589388\pi$
$90$	3.39669	−	5.78468i	0.358043	−	0.609758i
$91$	0.562639	+	1.54584i	0.0589806	+	0.162048i
$92$	−1.24201	+	1.04217i	−0.129489	+	0.108654i
$93$	−0.484555	+	1.76767i	−0.0502460	+	0.183299i
$94$		−	10.5537i		−	1.08853i
$95$	8.62945	−	4.53130i	0.885363	−	0.464901i
$96$	−1.56554	−	0.741008i	−0.159782	−	0.0756288i
$97$	0.183486	+	1.04060i	0.0186302	+	0.105657i	0.992705	−	0.120570i	$-0.0384721\pi$
$97$	0.183486	+	1.04060i	0.0186302	+	0.105657i	−0.974075	+	0.226227i	$0.927361\pi$
$98$	3.11559	+	3.71301i	0.314722	+	0.375071i
$99$	6.10899	−	10.3056i	0.613977	−	1.03575i
$100$	2.46397	−	4.35073i	0.246397	−	0.435073i
$101$	−7.32895	+	8.73431i	−0.729258	+	0.869096i	−0.995495	−	0.0948116i	$-0.969775\pi$
$101$	−7.32895	+	8.73431i	−0.729258	+	0.869096i	0.266237	+	0.963908i	$0.414220\pi$
$102$	7.14287	−	4.94054i	0.707250	−	0.489187i
$103$	0.0380996	+	0.0659905i	0.00375407	+	0.00650224i	0.867896	−	0.496745i	$-0.165472\pi$
$103$	0.0380996	+	0.0659905i	0.00375407	+	0.00650224i	−0.864142	+	0.503248i	$0.832138\pi$
$104$	−1.10410	−	0.194682i	−0.108266	−	0.0190901i
$105$	0.486248	+	5.66203i	0.0474529	+	0.552558i
$106$	3.11160	+	5.38946i	0.302226	+	0.523470i
$107$	−3.43397	−	1.98261i	−0.331975	−	0.191666i	0.324743	−	0.945802i	$-0.394722\pi$
$107$	−3.43397	−	1.98261i	−0.331975	−	0.191666i	−0.656718	+	0.754137i	$0.728056\pi$
$108$	−4.67074	−	2.27688i	−0.449442	−	0.219093i
$109$	6.94615	−	19.0844i	0.665320	−	1.82795i	0.114326	−	0.993443i	$-0.463529\pi$
$109$	6.94615	−	19.0844i	0.665320	−	1.82795i	0.550995	−	0.834509i	$-0.314249\pi$
$110$	4.43262	−	7.75165i	0.422634	−	0.739091i
$111$	4.02904	+	15.3899i	0.382419	+	1.46075i
$112$	1.44502	−	0.254796i	0.136542	−	0.0240760i
$113$		−	18.8522i		−	1.77346i	−0.462286	−	0.886731i	$-0.652971\pi$
$113$		−	18.8522i		−	1.77346i	0.462286	−	0.886731i	$-0.347029\pi$
$114$	−4.01606	−	6.39306i	−0.376138	−	0.598765i
$115$	−2.76753	+	2.34188i	−0.258073	+	0.218381i
$116$	0.0965571	+	0.547602i	0.00896510	+	0.0508436i
$117$	−3.30536	−	0.622089i	−0.305580	−	0.0575122i
$118$	4.42224	+	12.1500i	0.407100	+	1.11850i
$119$	−2.51643	+	6.91383i	−0.230680	+	0.633789i
$120$	−3.50749	−	1.64240i	−0.320189	−	0.149930i
$121$	2.47362	−	4.28444i	0.224875	−	0.389494i
$122$	−2.68405	+	1.54964i	−0.243002	+	0.140297i
$123$	1.58776	+	1.12542i	0.143164	+	0.101476i
$124$	1.04214	+	0.183757i	0.0935868	+	0.0165019i
$125$	5.46917	−	9.75132i	0.489178	−	0.872184i
$126$	4.34356	−	0.714496i	0.386955	−	0.0636524i
$127$	−4.34388	−	3.64494i	−0.385457	−	0.323437i	0.429383	−	0.903122i	$-0.358731\pi$
$127$	−4.34388	−	3.64494i	−0.385457	−	0.323437i	−0.814840	+	0.579686i	$0.803175\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−20.0764	−	1.87282i	−1.76763	−	0.164892i
$130$	−2.47062	−	0.425071i	−0.216688	−	0.0372812i
$131$	22.4309	−	3.95517i	1.95980	−	0.345565i	0.962581	−	0.270993i	$-0.0873522\pi$
$131$	22.4309	−	3.95517i	1.95980	−	0.345565i	0.997216	−	0.0745716i	$-0.0237589\pi$
$132$	−6.25182	−	2.95914i	−0.544151	−	0.257560i
$133$	5.90756	+	2.45110i	0.512250	+	0.212537i
$134$		−	8.74793i		−	0.755706i
$135$	−10.4651	−	5.04786i	−0.900696	−	0.434450i
$136$	−3.22313	−	3.84118i	−0.276381	−	0.329378i
$137$	8.03552	−	2.92469i	0.686521	−	0.249873i	0.0248759	−	0.999691i	$-0.492081\pi$
$137$	8.03552	−	2.92469i	0.686521	−	0.249873i	0.661645	+	0.749817i	$0.269859\pi$
$138$	1.97427	+	1.99710i	0.168061	+	0.170005i
$139$	−5.62221	−	4.71760i	−0.476870	−	0.400141i	0.372423	−	0.928063i	$-0.378527\pi$
$139$	−5.62221	−	4.71760i	−0.476870	−	0.400141i	−0.849293	+	0.527922i	$0.822971\pi$
$140$	3.22877	−	0.583148i	0.272881	−	0.0492850i
$141$	−18.2189	+	1.48846i	−1.53431	+	0.125351i
$142$	−4.08970	−	0.721125i	−0.343200	−	0.0605155i
$143$	−4.40910	−	0.777443i	−0.368707	−	0.0650130i
$144$	−1.05840	+	2.80709i	−0.0882003	+	0.233925i
$145$	0.220989	+	1.22357i	0.0183521	+	0.101612i
$146$	9.70118	+	8.14026i	0.802875	+	0.673693i
$147$	5.97036	−	5.90211i	0.492427	−	0.486798i
$148$	8.63091	−	3.14140i	0.709457	−	0.258221i
$149$	5.50648	+	6.56237i	0.451109	+	0.537610i	0.942888	−	0.333109i	$-0.108098\pi$
$149$	5.50648	+	6.56237i	0.451109	+	0.537610i	−0.491780	+	0.870720i	$0.663653\pi$
$150$	−7.85817	−	3.63993i	−0.641617	−	0.297199i
$151$		−	7.10146i		−	0.577908i	−0.957343	−	0.288954i	$-0.906692\pi$
$151$		−	7.10146i		−	0.577908i	0.957343	−	0.288954i	$-0.0933075\pi$
$152$	−3.45972	+	2.65148i	−0.280620	+	0.215063i
$153$	−9.53626	−	11.6339i	−0.770961	−	0.940548i
$154$	5.77054	−	1.01750i	0.465004	−	0.0819927i
$155$	2.33198	+	0.401217i	0.187309	+	0.0322266i
$156$	−0.180361	+	1.93346i	−0.0144405	+	0.154801i
$157$	−1.66611	+	4.57761i	−0.132970	+	0.365333i	−0.988253	−	0.152830i	$-0.951161\pi$
$157$	−1.66611	+	4.57761i	−0.132970	+	0.365333i	0.855282	+	0.518162i	$0.173384\pi$
$158$	−1.41250	−	1.18523i	−0.112373	−	0.0942917i
$159$	8.86496	−	6.13167i	0.703037	−	0.486273i
$160$	−0.756052	+	2.10437i	−0.0597712	+	0.166365i
$161$	−2.34286	−	0.413109i	−0.184643	−	0.0325576i
$162$	−3.27182	+	8.38422i	−0.257059	+	0.658727i
$163$	−4.84877	+	2.79944i	−0.379785	+	0.219269i	−0.677725	−	0.735316i	$-0.737034\pi$
$163$	−4.84877	+	2.79944i	−0.379785	+	0.219269i	0.297940	+	0.954585i	$0.403701\pi$
$164$	0.561809	−	0.973082i	0.0438699	−	0.0759849i
$165$	−14.0068	−	6.55876i	−1.09043	−	0.510599i
$166$	−2.47471	+	6.79921i	−0.192075	+	0.527721i
$167$	−5.37104	−	14.7568i	−0.415624	−	1.14192i	−0.954155	−	0.299312i	$-0.903243\pi$
$167$	−5.37104	−	14.7568i	−0.415624	−	1.14192i	0.538531	−	0.842605i	$-0.318979\pi$
$168$	−0.643655	−	2.45860i	−0.0496590	−	0.189685i
$169$	−2.03916	−	11.5647i	−0.156859	−	0.889590i
$170$	−7.24272	−	8.55914i	−0.555492	−	0.656456i
$171$	−10.4699	+	7.83458i	−0.800655	+	0.599125i
$172$			11.6415i			0.887652i
$173$	11.0644	−	1.95095i	0.841209	−	0.148328i	0.263590	−	0.964635i	$-0.415093\pi$
$173$	11.0644	−	1.95095i	0.841209	−	0.148328i	0.577618	+	0.816307i	$0.303982\pi$
$174$	0.931708	−	0.243918i	0.0706326	−	0.0184914i
$175$	7.21428	−	1.33391i	0.545348	−	0.100834i
$176$	−1.36582	+	3.75257i	−0.102953	+	0.282860i
$177$	20.3508	−	9.34770i	1.52966	−	0.702616i
$178$	−6.62272	−	3.82363i	−0.496394	−	0.286593i
$179$	−4.11990	−	7.13587i	−0.307936	−	0.533360i	0.669975	−	0.742384i	$-0.266305\pi$
$179$	−4.11990	−	7.13587i	−0.307936	−	0.533360i	−0.977911	+	0.209024i	$0.932971\pi$
$180$	−2.34059	+	6.28662i	−0.174457	+	0.468577i
$181$	−2.83286	−	0.499510i	−0.210565	−	0.0371283i	0.0673706	−	0.997728i	$-0.478539\pi$
$181$	−2.83286	−	0.499510i	−0.210565	−	0.0371283i	−0.277935	+	0.960600i	$0.589650\pi$
$182$	−0.822523	−	1.42465i	−0.0609695	−	0.105602i
$183$	3.05368	+	4.41491i	0.225735	+	0.326360i
$184$	1.04217	−	1.24201i	0.0768300	−	0.0915624i
$185$	19.2700	−	7.10442i	1.41676	−	0.522327i
$186$	0.170240	−	1.82496i	0.0124826	−	0.133812i
$187$	−12.8712	−	15.3393i	−0.941238	−	1.12172i
$188$	1.83264	+	10.3934i	0.133659	+	0.758016i
$189$	−1.84604	−	7.39752i	−0.134279	−	0.538090i
$190$	−7.71149	+	5.96094i	−0.559451	+	0.432452i
$191$			13.4760i			0.975086i	0.873099	+	0.487543i	$0.162107\pi$
$191$			13.4760i			0.975086i	−0.873099	+	0.487543i	$0.837893\pi$
$192$	1.67043	+	0.457898i	0.120553	+	0.0330459i
$193$	13.7953	−	11.5756i	0.993007	−	0.833232i	0.00700665	−	0.999975i	$-0.497770\pi$
$193$	13.7953	−	11.5756i	0.993007	−	0.833232i	0.986000	+	0.166744i	$0.0533253\pi$
$194$	−0.361397	−	0.992931i	−0.0259468	−	0.0712883i
$195$	−0.385352	+	4.32498i	−0.0275956	+	0.309718i
$196$	−3.71301	−	3.11559i	−0.265215	−	0.222542i
$197$	−2.65351	+	4.59601i	−0.189055	+	0.327452i	−0.944935	−	0.327257i	$-0.893876\pi$
$197$	−2.65351	+	4.59601i	−0.189055	+	0.327452i	0.755881	+	0.654709i	$0.227209\pi$
$198$	−4.22663	+	11.2099i	−0.300374	+	0.796649i
$199$	−1.55006	+	8.79082i	−0.109881	+	0.623165i	0.879277	+	0.476310i	$0.158026\pi$
$199$	−1.55006	+	8.79082i	−0.109881	+	0.623165i	−0.989158	+	0.146854i	$0.953085\pi$
$200$	−1.67104	+	4.71250i	−0.118160	+	0.333224i
$201$	−15.1015	+	1.23378i	−1.06518	+	0.0870239i
$202$	5.70091	−	9.87427i	0.401115	−	0.694751i
$203$	−0.524450	+	0.625015i	−0.0368092	+	0.0438674i
$204$	−6.17644	+	6.10583i	−0.432437	+	0.427494i
$205$	1.24720	−	2.18107i	0.0871083	−	0.152333i
$206$	−0.0489800	−	0.0583720i	−0.00341260	−	0.00406697i
$207$	3.16915	−	3.68985i	0.220271	−	0.256462i
$208$	1.12113			0.0777363
$209$	−13.8160	+	10.5884i	−0.955676	+	0.732416i
$210$	−1.46206	−	5.49158i	−0.100892	−	0.378955i
$211$	13.1059	−	2.31092i	0.902246	−	0.159090i	0.296765	−	0.954950i	$-0.404092\pi$
$211$	13.1059	−	2.31092i	0.902246	−	0.159090i	0.605480	+	0.795860i	$0.292981\pi$
$212$	−4.00020	−	4.76725i	−0.274735	−	0.327416i
$213$	−0.668080	+	7.16176i	−0.0457761	+	0.490715i
$214$	3.72608	+	1.35618i	0.254710	+	0.0927067i
$215$	0.108047	+	26.0308i	0.00736872	+	1.77529i
$216$	4.99516	+	1.43122i	0.339878	+	0.0973821i
$217$	0.776366	+	1.34470i	0.0527031	+	0.0912845i
$218$	−3.52665	+	20.0006i	−0.238855	+	1.35461i
$219$	12.6843	−	17.8952i	0.857126	−	1.20925i
$220$	−3.01922	+	8.40360i	−0.203556	+	0.566571i
$221$	−2.81084	+	4.86851i	−0.189077	+	0.327492i
$222$	−6.64026	−	14.4565i	−0.445665	−	0.970256i
$223$	7.24422	+	2.63668i	0.485109	+	0.176565i	0.572984	−	0.819566i	$-0.305786\pi$
$223$	7.24422	+	2.63668i	0.485109	+	0.176565i	−0.0878757	+	0.996131i	$0.528008\pi$
$224$	−1.37882	+	0.501850i	−0.0921264	+	0.0335313i
$225$	−5.17533	+	14.0789i	−0.345022	+	0.938595i
$226$	3.27364	+	18.5658i	0.217760	+	1.23498i
$227$			8.01737i			0.532131i	0.963955	+	0.266066i	$0.0857238\pi$
$227$			8.01737i			0.532131i	−0.963955	+	0.266066i	$0.914276\pi$
$228$	5.06519	+	5.59856i	0.335450	+	0.370774i
$229$	−23.9108			−1.58007			−0.790034	−	0.613063i	$-0.789937\pi$
$229$	−23.9108			−1.58007			−0.790034	+	0.613063i	$0.789937\pi$
$230$	2.31882	−	2.78687i	0.152899	−	0.183761i
$231$	−2.57037	−	9.81818i	−0.169118	−	0.645989i
$232$	−0.190180	−	0.522516i	−0.0124860	−	0.0343049i
$233$	8.83895	+	3.21712i	0.579059	+	0.210760i	0.614910	−	0.788597i	$-0.289192\pi$
$233$	8.83895	+	3.21712i	0.579059	+	0.210760i	−0.0358516	+	0.999357i	$0.511414\pi$
$234$	3.36316	+	0.0386696i	0.219857	+	0.00252791i
$235$	4.19433	+	23.2231i	0.273608	+	1.51491i
$236$	−6.46488	−	11.1975i	−0.420828	−	0.728895i
$237$	−1.84685	+	2.60556i	−0.119965	+	0.169249i
$238$	1.27762	−	7.24576i	0.0828160	−	0.469673i
$239$	12.0004	−	6.92846i	0.776244	−	0.448165i	−0.0588536	−	0.998267i	$-0.518745\pi$
$239$	12.0004	−	6.92846i	0.776244	−	0.448165i	0.835097	+	0.550102i	$0.185411\pi$
$240$	3.73941	+	1.00838i	0.241378	+	0.0650906i
$241$	−4.56509	+	5.44046i	−0.294063	+	0.350451i	−0.892766	−	0.450520i	$-0.851239\pi$
$241$	−4.56509	+	5.44046i	−0.294063	+	0.350451i	0.598703	+	0.800971i	$0.295683\pi$
$242$	−1.69206	+	4.64889i	−0.108770	+	0.298842i
$243$	14.9351	+	4.46567i	0.958088	+	0.286473i
$244$	2.37418	−	1.99217i	0.151991	−	0.127536i
$245$	−8.33140	−	6.93215i	−0.532273	−	0.442879i
$246$	−1.75907	−	0.832610i	−0.112154	−	0.0530853i
$247$	4.12000	+	2.62817i	0.262149	+	0.167226i
$248$	−1.05821			−0.0671967
$249$	12.0865	+	3.31315i	0.765950	+	0.209962i
$250$	−3.69279	+	10.5529i	−0.233552	+	0.667423i
$251$	−4.92483	−	13.5309i	−0.310852	−	0.854060i	−0.992485	−	0.122366i	$-0.960952\pi$
$251$	−4.92483	−	13.5309i	−0.310852	−	0.854060i	0.681633	−	0.731695i	$-0.261270\pi$
$252$	−4.15350	+	1.45789i	−0.261646	+	0.0918386i
$253$	4.16181	−	4.95985i	0.261651	−	0.311823i
$254$	4.91082	+	2.83526i	0.308132	+	0.177900i
$255$	−13.7541	+	13.7103i	−0.861318	+	0.858570i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−19.8835	−	3.50600i	−1.24030	−	0.218698i	−0.485256	−	0.874372i	$-0.661274\pi$
$257$	−19.8835	−	3.50600i	−1.24030	−	0.218698i	−0.755044	+	0.655674i	$0.772385\pi$
$258$	20.0966	−	1.64187i	1.25116	−	0.102218i
$259$	11.6714	+	6.73850i	0.725227	+	0.418710i
$260$	2.50690	−	0.0104054i	0.155471	−	0.000645317i
$261$	−0.552481	−	1.57400i	−0.0341977	−	0.0974284i
$262$	−21.4033	+	7.79017i	−1.32230	+	0.481278i
$263$	15.5786	−	13.0720i	0.960620	−	0.806056i	−0.0204337	−	0.999791i	$-0.506505\pi$
$263$	15.5786	−	13.0720i	0.960620	−	0.806056i	0.981054	+	0.193735i	$0.0620603\pi$
$264$	6.67069	+	1.82857i	0.410552	+	0.112541i
$265$	−8.98889	−	10.6227i	−0.552183	−	0.652546i
$266$	−6.24343	−	1.38802i	−0.382810	−	0.0851051i
$267$	−5.66668	+	11.9721i	−0.346795	+	0.732679i
$268$	1.51906	+	8.61503i	0.0927914	+	0.526246i
$269$	4.16275	−	3.49296i	0.253807	−	0.212970i	−0.507002	−	0.861945i	$-0.669246\pi$
$269$	4.16275	−	3.49296i	0.253807	−	0.212970i	0.760810	+	0.648975i	$0.224802\pi$
$270$	11.1827	+	3.15392i	0.680558	+	0.191941i
$271$	26.1960	+	9.53457i	1.59129	+	0.579184i	0.977621	−	0.210375i	$-0.0674686\pi$
$271$	26.1960	+	9.53457i	1.59129	+	0.579184i	0.613674	+	0.789559i	$0.289691\pi$
$272$	3.84118	+	3.22313i	0.232905	+	0.195431i
$273$	−2.34337	+	1.62085i	−0.141827	+	0.0980982i
$274$	−7.40557	+	4.27561i	−0.447387	+	0.258299i
$275$	−6.67312	+	18.8189i	−0.402405	+	1.13482i
$276$	−2.29107	−	1.62393i	−0.137906	−	0.0977492i
$277$	9.90628	−	5.71940i	0.595211	−	0.343645i	−0.171944	−	0.985107i	$-0.555005\pi$
$277$	9.90628	−	5.71940i	0.595211	−	0.343645i	0.767155	+	0.641462i	$0.221672\pi$
$278$	6.35600	+	3.66964i	0.381208	+	0.220090i
$279$	−3.17443	−	0.0364996i	−0.190048	−	0.00218517i
$280$	−3.07846	+	1.13496i	−0.183973	+	0.0678268i
$281$	19.4818	−	7.09080i	1.16219	−	0.423002i	0.312309	−	0.949981i	$-0.398898\pi$
$281$	19.4818	−	7.09080i	1.16219	−	0.423002i	0.849878	+	0.526979i	$0.176675\pi$
$282$	17.6836	−	4.62953i	1.05305	−	0.275684i
$283$	−7.07203	+	1.24699i	−0.420388	+	0.0741258i	−0.379841	−	0.925052i	$-0.624021\pi$
$283$	−7.07203	+	1.24699i	−0.420388	+	0.0741258i	−0.0405474	+	0.999178i	$0.512910\pi$
$284$	4.15279			0.246423
$285$	11.3780	+	12.4716i	0.673973	+	0.738756i
$286$	4.47712			0.264737
$287$	1.62365	−	0.286293i	0.0958411	−	0.0168994i
$288$	0.554878	−	2.94824i	0.0326965	−	0.173727i
$289$	−7.65209	+	2.78513i	−0.450123	+	0.163831i
$290$	−0.430102	−	1.16661i	−0.0252565	−	0.0685055i
$291$	−1.66313	+	0.763919i	−0.0974941	+	0.0447817i
$292$	−10.9673	−	6.33200i	−0.641815	−	0.370552i
$293$	−2.56685	+	1.48197i	−0.149957	+	0.0865778i	−0.573101	−	0.819485i	$-0.694260\pi$
$293$	−2.56685	+	1.48197i	−0.149957	+	0.0865778i	0.423144	+	0.906062i	$0.360926\pi$
$294$	−4.85477	+	6.84918i	−0.283136	+	0.399453i
$295$	−14.5597	−	24.9782i	−0.847699	−	1.45428i
$296$	−7.95429	+	4.59241i	−0.462334	+	0.266929i
$297$	19.9477	+	5.71543i	1.15748	+	0.331643i
$298$	−6.56237	−	5.50648i	−0.380148	−	0.318982i
$299$	−1.70810	−	0.621698i	−0.0987820	−	0.0359537i
$300$	8.37086	+	2.22008i	0.483292	+	0.128176i
$301$	−13.0853	+	10.9799i	−0.754224	+	0.632869i
$302$	1.23315	+	6.99357i	0.0709601	+	0.402435i
$303$	−17.8500	−	8.44885i	−1.02545	−	0.485374i
$304$	2.94674	−	3.21197i	0.169007	−	0.184219i
$305$	5.29029	−	4.47663i	0.302921	−	0.256331i
$306$	11.4116	+	9.80124i	0.652357	+	0.560299i
$307$	−22.9484	+	19.2560i	−1.30973	+	1.09900i	−0.321357	+	0.946958i	$0.604139\pi$
$307$	−22.9484	+	19.2560i	−1.30973	+	1.09900i	−0.988375	+	0.152037i	$0.951417\pi$
$308$	−5.50619	+	2.00409i	−0.313744	+	0.114194i
$309$	−0.0938596	+	0.0927866i	−0.00533949	+	0.00527845i
$310$	−2.36622	+	0.00982150i	−0.134392	+	0.000557824i
$311$	−23.6033	−	13.6274i	−1.33842	−	0.772737i	−0.351847	−	0.936058i	$-0.614446\pi$
$311$	−23.6033	−	13.6274i	−1.33842	−	0.772737i	−0.986573	+	0.163320i	$0.947780\pi$
$312$	−0.158120	−	1.93540i	−0.00895179	−	0.109571i
$313$	−10.3529	−	1.82550i	−0.585181	−	0.103183i	−0.126783	−	0.991930i	$-0.540465\pi$
$313$	−10.3529	−	1.82550i	−0.585181	−	0.103183i	−0.458398	+	0.888747i	$0.651576\pi$
$314$	0.845907	−	4.79738i	0.0477373	−	0.270732i
$315$	−9.27390	+	3.29847i	−0.522525	+	0.185848i
$316$	1.59685	+	0.921944i	0.0898301	+	0.0518634i
$317$	−8.62947	+	10.2842i	−0.484679	+	0.577618i	−0.951856	−	0.306546i	$-0.900827\pi$
$317$	−8.62947	+	10.2842i	−0.484679	+	0.577618i	0.467177	+	0.884164i	$0.345271\pi$
$318$	−7.66553	+	7.57790i	−0.429862	+	0.424947i
$319$	−0.759466	−	2.08662i	−0.0425219	−	0.116828i
$320$	0.379146	−	2.20369i	0.0211949	−	0.123190i
$321$	1.81566	−	6.62360i	0.101340	−	0.369693i
$322$	2.37900			0.132577
$323$	6.56011	+	20.8491i	0.365014	+	1.16008i
$324$	1.76621	−	8.82499i	0.0981229	−	0.490277i
$325$	5.60545	−	0.0465340i	0.310934	−	0.00258124i
$326$	4.28899	−	3.59889i	0.237545	−	0.199324i
$327$	35.0245	+	3.26724i	1.93686	+	0.180679i
$328$	−0.384300	+	1.05586i	−0.0212194	+	0.0582999i
$329$	−9.95396	+	11.8627i	−0.548780	+	0.654010i
$330$	14.9330	+	4.02686i	0.822032	+	0.221671i
$331$	−3.51218	+	2.02776i	−0.193047	+	0.111456i	−0.593408	−	0.804902i	$-0.702218\pi$
$331$	−3.51218	+	2.02776i	−0.193047	+	0.111456i	0.400361	+	0.916357i	$0.368885\pi$
$332$	1.25644	−	7.12564i	0.0689563	−	0.391070i
$333$	−24.0197	+	13.5020i	−1.31627	+	0.739903i
$334$	7.85194	+	13.6000i	0.429639	+	0.744157i
$335$	3.47665	+	19.2495i	0.189950	+	1.05171i
$336$	1.06081	+	2.30948i	0.0578718	+	0.125992i
$337$	10.5775	+	3.84988i	0.576191	+	0.209716i	0.613645	−	0.789582i	$-0.289703\pi$
$337$	10.5775	+	3.84988i	0.576191	+	0.209716i	−0.0374540	+	0.999298i	$0.511925\pi$
$338$	4.01637	+	11.0349i	0.218462	+	0.600218i
$339$	31.5883	−	8.26974i	1.71564	−	0.449150i
$340$	8.61897	+	7.17142i	0.467429	+	0.388925i
$341$	−4.22587			−0.228844
$342$	8.95041	−	9.53364i	0.483983	−	0.515520i
$343$		−	17.3832i		−	0.938607i
$344$	−2.02152	−	11.4646i	−0.108993	−	0.618129i
$345$	−5.13802	−	3.60993i	−0.276621	−	0.194352i
$346$	−10.5575	+	3.84262i	−0.567575	+	0.206580i
$347$	6.60547	+	2.40420i	0.354600	+	0.129064i	0.513177	−	0.858283i	$-0.328468\pi$
$347$	6.60547	+	2.40420i	0.354600	+	0.129064i	−0.158577	+	0.987347i	$0.550691\pi$
$348$	−0.875197	+	0.402002i	−0.0469155	+	0.0215496i
$349$	−12.3586	+	21.4058i	−0.661543	+	1.14583i	0.318667	+	0.947867i	$0.396765\pi$
$349$	−12.3586	+	21.4058i	−0.661543	+	1.14583i	−0.980210	+	0.197959i	$0.936569\pi$
$350$	−6.87304	+	2.56639i	−0.367380	+	0.137180i
$351$	−0.407574	−	5.81128i	−0.0217547	−	0.310183i
$352$	0.693447	−	3.93273i	0.0369608	−	0.209615i
$353$	0.0536155	+	0.0928649i	0.00285367	+	0.00494270i	0.867449	−	0.497527i	$-0.165758\pi$
$353$	0.0536155	+	0.0928649i	0.00285367	+	0.00494270i	−0.864595	+	0.502469i	$0.832425\pi$
$354$	−18.4185	+	12.7396i	−0.978930	+	0.677101i
$355$	9.28585	−	0.0385429i	0.492842	−	0.00204564i
$356$	7.18607	+	2.61552i	0.380861	+	0.138622i
$357$	−12.6885	−	1.18364i	−0.671549	−	0.0626450i
$358$	5.29644	+	6.31205i	0.279925	+	0.333602i
$359$	−14.7117	+	2.59408i	−0.776456	+	0.136910i	−0.547814	−	0.836600i	$-0.684540\pi$
$359$	−14.7117	+	2.59408i	−0.776456	+	0.136910i	−0.228642	+	0.973511i	$0.573429\pi$
$360$	1.21337	−	6.59755i	0.0639502	−	0.347722i
$361$	18.3584	−	4.89579i	0.966232	−	0.257673i
$362$	2.87656			0.151189
$363$	8.26401	+	2.26533i	0.433748	+	0.118899i
$364$	1.05742	+	1.26018i	0.0554236	+	0.0660513i
$365$	−24.5823	−	14.0569i	−1.28670	−	0.735770i
$366$	−3.77393	−	3.81757i	−0.197267	−	0.199548i
$367$	20.3774	−	24.2848i	1.06369	−	1.26766i	0.101629	−	0.994822i	$-0.467595\pi$
$367$	20.3774	−	24.2848i	1.06369	−	1.26766i	0.962061	−	0.272834i	$-0.0879609\pi$
$368$	−0.810666	+	1.40412i	−0.0422589	+	0.0731946i
$369$	−1.18924	+	3.15410i	−0.0619095	+	0.164196i
$370$	−17.7436	+	10.3427i	−0.922444	+	0.537691i
$371$	1.58565	−	8.99266i	0.0823228	−	0.466876i
$372$	0.149247	+	1.82680i	0.00773809	+	0.0947149i
$373$	−2.38442	+	4.12993i	−0.123460	+	0.213840i	−0.921130	−	0.389255i	$-0.872733\pi$
$373$	−2.38442	+	4.12993i	−0.123460	+	0.213840i	0.797670	+	0.603095i	$0.206066\pi$
$374$	15.3393	+	12.8712i	0.793179	+	0.665556i
$375$	18.7382	+	4.88651i	0.967639	+	0.252338i
$376$	−3.60959	−	9.91726i	−0.186150	−	0.511444i
$377$	−0.477555	+	0.400716i	−0.0245953	+	0.0206379i
$378$	3.10256	+	6.96457i	0.159578	+	0.358219i
$379$			28.2186i			1.44949i	0.689017	+	0.724746i	$0.258043\pi$
$379$			28.2186i			1.44949i	−0.689017	+	0.724746i	$0.741957\pi$
$380$	6.55923	−	7.20947i	0.336482	−	0.369838i
$381$	4.20191	−	8.87742i	0.215270	−	0.454804i
$382$	−2.34008	−	13.2712i	−0.119729	−	0.679015i
$383$	−14.1575	−	16.8723i	−0.723415	−	0.862132i	0.271543	−	0.962426i	$-0.412466\pi$
$383$	−14.1575	−	16.8723i	−0.723415	−	0.862132i	−0.994958	+	0.100294i	$0.968022\pi$
$384$	−1.72456	−	0.160875i	−0.0880063	−	0.00820961i
$385$	−12.2935	+	4.53234i	−0.626535	+	0.230990i
$386$	−11.5756	+	13.7953i	−0.589184	+	0.702162i
$387$	−5.66872	−	34.4612i	−0.288157	−	1.75176i
$388$	0.528327	+	0.915090i	0.0268218	+	0.0464566i
$389$	−32.4527	−	5.72229i	−1.64542	−	0.290132i	−0.727265	−	0.686357i	$-0.759209\pi$
$389$	−32.4527	−	5.72229i	−1.64542	−	0.290132i	−0.918153	+	0.396225i	$0.870320\pi$
$390$	−0.371527	−	4.32619i	−0.0188130	−	0.219065i
$391$	−4.06492	−	7.04065i	−0.205572	−	0.356061i
$392$	4.19762	+	2.42350i	0.212012	+	0.122405i
$393$	16.4668	+	35.8498i	0.830641	+	1.80838i
$394$	1.81511	−	4.98696i	0.0914437	−	0.251240i
$395$	3.57920	+	2.04669i	0.180089	+	0.102980i
$396$	2.21585	−	11.7735i	0.111351	−	0.591640i
$397$	14.8216	−	2.61345i	0.743875	−	0.131165i	0.211150	−	0.977454i	$-0.432279\pi$
$397$	14.8216	−	2.61345i	0.743875	−	0.131165i	0.532725	+	0.846288i	$0.321168\pi$
$398$		−	8.92643i		−	0.447442i
$399$	−1.51559	+	10.9738i	−0.0758744	+	0.549377i
$400$	0.827335	−	4.93108i	0.0413668	−	0.246554i
$401$	1.72636	+	9.79066i	0.0862102	+	0.488922i	0.997089	+	0.0762481i	$0.0242941\pi$
$401$	1.72636	+	9.79066i	0.0862102	+	0.488922i	−0.910879	+	0.412674i	$0.864595\pi$
$402$	14.6579	−	3.83739i	0.731068	−	0.191392i
$403$	0.405771	+	1.11485i	0.0202129	+	0.0555345i
$404$	−3.89965	+	10.7142i	−0.194015	+	0.533052i
$405$	3.86743	−	19.7495i	0.192174	−	0.981361i
$406$	0.407950	−	0.706589i	0.0202462	−	0.0350674i
$407$	−31.7647	+	18.3393i	−1.57452	+	0.909047i
$408$	5.02234	−	7.08560i	0.248643	−	0.350789i
$409$	−15.1273	−	2.66734i	−0.747995	−	0.131892i	−0.213359	−	0.976974i	$-0.568440\pi$
$409$	−15.1273	−	2.66734i	−0.747995	−	0.131892i	−0.534636	+	0.845082i	$0.679551\pi$
$410$	−0.849514	+	2.36451i	−0.0419545	+	0.116775i
$411$	8.42544	+	12.1812i	0.415596	+	0.600855i
$412$	0.0583720	+	0.0489800i	0.00287578	+	0.00241307i
$413$	6.48880	−	17.8278i	0.319293	−	0.877251i
$414$	−2.48027	+	4.18411i	−0.121899	+	0.205638i
$415$	2.74333	−	15.9449i	0.134665	−	0.782706i
$416$	−1.10410	+	0.194682i	−0.0541328	+	0.00954507i
$417$	5.43847	−	11.4899i	0.266323	−	0.562663i
$418$	11.7675	−	12.8267i	0.575567	−	0.627373i
$419$			26.3192i			1.28578i	0.765959	+	0.642890i	$0.222265\pi$
$419$			26.3192i			1.28578i	−0.765959	+	0.642890i	$0.777735\pi$
$420$	2.39345	+	5.15427i	0.116789	+	0.251502i
$421$	−22.9933	−	27.4024i	−1.12063	−	1.33551i	−0.935716	−	0.352755i	$-0.885245\pi$
$421$	−22.9933	−	27.4024i	−1.12063	−	1.33551i	−0.184910	−	0.982755i	$-0.559199\pi$
$422$	−12.5055	+	4.55162i	−0.608757	+	0.221570i
$423$	−10.4860	−	29.8743i	−0.509846	−	1.45254i
$424$	4.76725	+	4.00020i	0.231518	+	0.194267i
$425$	19.3390	+	15.9557i	0.938079	+	0.773963i
$426$	−0.585696	−	7.16896i	−0.0283770	−	0.347337i
$427$	4.47851	+	0.789682i	0.216730	+	0.0382154i
$428$	−3.90497	−	0.688552i	−0.188754	−	0.0332824i
$429$	−0.631437	−	7.72884i	−0.0304861	−	0.373152i
$430$	−4.62661	−	25.6166i	−0.223115	−	1.23534i
$431$	1.99894	+	1.67731i	0.0962856	+	0.0807932i	0.689660	−	0.724134i	$-0.257760\pi$
$431$	1.99894	+	1.67731i	0.0962856	+	0.0807932i	−0.593374	+	0.804927i	$0.702205\pi$
$432$	−5.16780	−	0.542076i	−0.248636	−	0.0260806i
$433$	−21.5433	+	7.84111i	−1.03530	+	0.376820i	−0.803098	−	0.595847i	$-0.796817\pi$
$433$	−21.5433	+	7.84111i	−1.03530	+	0.376820i	−0.232206	+	0.972667i	$0.574594\pi$
$434$	−0.998076	−	1.18946i	−0.0479092	−	0.0570960i
$435$	−1.95325	+	0.907019i	−0.0936513	+	0.0434882i
$436$		−	20.3092i		−	0.972633i
$437$	−6.27064	+	3.25956i	−0.299965	+	0.155926i
$438$	−9.38412	+	19.8260i	−0.448391	+	0.947321i
$439$	−19.7286	+	3.47868i	−0.941593	+	0.166028i	−0.623316	−	0.781970i	$-0.714215\pi$
$439$	−19.7286	+	3.47868i	−0.941593	+	0.166028i	−0.318277	+	0.947998i	$0.603104\pi$
$440$	1.51408	−	8.80021i	0.0721809	−	0.419534i
$441$	12.5084	+	7.41480i	0.595640	+	0.353086i
$442$	1.92273	−	5.28265i	0.0914547	−	0.251270i
$443$	1.55549	+	1.30521i	0.0739034	+	0.0620123i	0.678991	−	0.734147i	$-0.262417\pi$
$443$	1.55549	+	1.30521i	0.0739034	+	0.0620123i	−0.605088	+	0.796159i	$0.706862\pi$
$444$	9.04972	+	13.0838i	0.429481	+	0.620929i
$445$	16.0927	+	5.78173i	0.762866	+	0.274080i
$446$	−7.59201	−	1.33868i	−0.359492	−	0.0633882i
$447$	−8.58030	+	12.1052i	−0.405834	+	0.572558i
$448$	1.27073	−	0.733656i	0.0600363	−	0.0346620i
$449$	7.37540	−	12.7746i	0.348067	−	0.602869i	−0.637839	−	0.770169i	$-0.720172\pi$
$449$	7.37540	−	12.7746i	0.348067	−	0.602869i	0.985906	+	0.167300i	$0.0535050\pi$
$450$	2.65192	−	14.7637i	0.125013	−	0.695968i
$451$	−1.53466	+	4.21645i	−0.0722645	+	0.198545i
$452$	−6.44782	−	17.7152i	−0.303280	−	0.833255i
$453$	11.8991	−	3.11514i	0.559067	−	0.146362i
$454$	−1.39220	−	7.89557i	−0.0653392	−	0.370557i
$455$	2.37613	+	2.80801i	0.111395	+	0.131641i
$456$	−5.96042	−	4.63394i	−0.279122	−	0.217004i
$457$		−	1.10156i		−	0.0515290i	−0.999668	−	0.0257645i	$-0.991798\pi$
$457$		−	1.10156i		−	0.0515290i	0.999668	−	0.0257645i	$-0.00820200\pi$
$458$	23.5475	−	4.15206i	1.10030	−	0.194013i
$459$	15.3104	−	21.0822i	0.714629	−	0.984031i
$460$	−1.79966	+	3.14719i	−0.0839095	+	0.146739i
$461$	9.51370	−	26.1387i	0.443097	−	1.21740i	−0.494347	−	0.869265i	$-0.664593\pi$
$461$	9.51370	−	26.1387i	0.443097	−	1.21740i	0.937444	−	0.348135i	$-0.113185\pi$
$462$	4.23623	+	9.22268i	0.197087	+	0.429078i
$463$	−27.6924	−	15.9882i	−1.28697	−	0.743034i	−0.308860	−	0.951108i	$-0.599947\pi$
$463$	−27.6924	−	15.9882i	−1.28697	−	0.743034i	−0.978113	+	0.208074i	$0.933281\pi$
$464$	0.278025	+	0.481554i	0.0129070	+	0.0223556i
$465$	0.350678	+	4.08342i	0.0162623	+	0.189364i
$466$	−9.26331	−	1.63337i	−0.429115	−	0.0756645i
$467$	−6.75998	−	11.7086i	−0.312815	−	0.541811i	0.666156	−	0.745813i	$-0.267939\pi$
$467$	−6.75998	−	11.7086i	−0.312815	−	0.541811i	−0.978971	+	0.204002i	$0.934605\pi$
$468$	−3.31878	+	0.545925i	−0.153411	+	0.0252354i
$469$	−8.25078	+	9.83290i	−0.380986	+	0.454041i
$470$	−8.16326	−	22.1420i	−0.376543	−	1.02133i
$471$	−8.40101	−	0.783684i	−0.387098	−	0.0361102i
$472$	8.31109	+	9.90477i	0.382549	+	0.455904i
$473$	−8.07272	−	45.7827i	−0.371184	−	2.10509i
$474$	1.36634	−	2.88668i	0.0627579	−	0.132589i
$475$	14.5999	−	16.1816i	0.669887	−	0.742463i
$476$			7.35754i			0.337232i
$477$	14.1628	+	12.1642i	0.648472	+	0.556962i
$478$	−10.6150	+	8.90705i	−0.485519	+	0.407399i
$479$	−5.47290	−	15.0367i	−0.250063	−	0.687043i	−0.999683	−	0.0251743i	$-0.991986\pi$
$479$	−5.47290	−	15.0367i	−0.250063	−	0.687043i	0.749620	−	0.661869i	$-0.230236\pi$
$480$	−3.85770	−	0.343718i	−0.176079	−	0.0156885i
$481$	7.88825	+	6.61902i	0.359673	+	0.301802i
$482$	3.55101	−	6.15053i	0.161744	−	0.280149i
$483$	−0.335526	−	4.10687i	−0.0152670	−	0.186869i
$484$	0.859080	−	4.87208i	0.0390491	−	0.221458i
$485$	1.18986	+	2.04128i	0.0540287	+	0.0926898i
$486$	−15.4837	−	1.80437i	−0.702354	−	0.0818477i
$487$	−13.7689	+	23.8483i	−0.623926	+	1.08067i	0.364821	+	0.931078i	$0.381130\pi$
$487$	−13.7689	+	23.8483i	−0.623926	+	1.08067i	−0.988747	+	0.149594i	$0.952203\pi$
$488$	−1.99217	+	2.37418i	−0.0901814	+	0.107474i
$489$	−6.81766	−	6.89650i	−0.308305	−	0.311871i
$490$	9.40858	+	5.38010i	0.425036	+	0.243048i
$491$	18.9101	+	22.5362i	0.853401	+	1.01704i	0.999614	+	0.0277906i	$0.00884715\pi$
$491$	18.9101	+	22.5362i	0.853401	+	1.01704i	−0.146213	+	0.989253i	$0.546708\pi$
$492$	1.87692	+	0.514503i	0.0846182	+	0.0231956i
$493$	−2.78820			−0.125574
$494$	−4.51378	−	1.87281i	−0.203085	−	0.0842616i
$495$	4.84547	−	26.3467i	0.217788	−	1.18419i
$496$	1.04214	−	0.183757i	0.0467934	−	0.00825094i
$497$	3.91679	+	4.66785i	0.175692	+	0.209382i
$498$	−12.4782	−	1.16402i	−0.559161	−	0.0521610i
$499$	16.9466	+	6.16804i	0.758632	+	0.276119i	0.692233	−	0.721674i	$-0.256627\pi$
$499$	16.9466	+	6.16804i	0.758632	+	0.276119i	0.0663986	+	0.997793i	$0.478849\pi$
$500$	1.80420	−	11.0338i	0.0806861	−	0.493447i
$501$	22.3702	−	15.4729i	0.999427	−	0.691278i
$502$	7.19962	+	12.4701i	0.321335	+	0.556568i
$503$	−1.87378	+	10.6267i	−0.0835478	+	0.473823i	0.914113	+	0.405460i	$0.132889\pi$
$503$	−1.87378	+	10.6267i	−0.0835478	+	0.473823i	−0.997661	+	0.0683630i	$0.978222\pi$
$504$	3.83724	−	2.15699i	0.170924	−	0.0960801i
$505$	−8.62038	+	23.9937i	−0.383602	+	1.06771i
$506$	−3.23731	+	5.60719i	−0.143916	+	0.249270i
$507$	18.4830	−	8.48977i	0.820861	−	0.377044i
$508$	−5.32855	−	1.93943i	−0.236416	−	0.0860485i
$509$	39.2916	−	14.3010i	1.74157	−	0.633880i	0.742228	−	0.670147i	$-0.233769\pi$
$509$	39.2916	−	14.3010i	1.74157	−	0.633880i	0.999342	+	0.0362677i	$0.0115469\pi$
$510$	11.1644	−	15.8904i	0.494369	−	0.703637i
$511$	−3.22674	−	18.2997i	−0.142742	−	0.809532i
$512$			1.00000i			0.0441942i
$513$	−17.7202	−	14.1065i	−0.782368	−	0.622817i
$514$	20.1903			0.890554
$515$	0.130977	+	0.108980i	0.00577155	+	0.00480222i
$516$	−19.5062	+	5.10667i	−0.858713	+	0.224809i
$517$	−14.4145	−	39.6036i	−0.633950	−	1.74176i
$518$	−12.6642	−	4.60941i	−0.556435	−	0.202526i
$519$	8.12250	+	17.6835i	0.356538	+	0.776218i
$520$	−2.46701	+	0.445566i	−0.108185	+	0.0195393i
$521$	−3.15857	−	5.47081i	−0.138380	−	0.239680i	0.788504	−	0.615030i	$-0.210856\pi$
$521$	−3.15857	−	5.47081i	−0.138380	−	0.239680i	−0.926883	+	0.375349i	$0.877523\pi$
$522$	0.817410	+	1.45415i	0.0357771	+	0.0636466i
$523$	−5.75986	+	32.6658i	−0.251861	+	1.42837i	0.552142	+	0.833750i	$0.313811\pi$
$523$	−5.75986	+	32.6658i	−0.251861	+	1.42837i	−0.804003	+	0.594625i	$0.797301\pi$
$524$	19.7254	−	11.3885i	0.861708	−	0.497507i
$525$	5.39972	+	11.5030i	0.235663	+	0.502031i
$526$	−13.0720	+	15.5786i	−0.569968	+	0.679261i
$527$	−1.81483	+	4.98620i	−0.0790552	+	0.217202i
$528$	−6.88687	−	0.642438i	−0.299713	−	0.0279585i
$529$	−15.6053	+	13.0944i	−0.678492	+	0.569322i
$530$	10.6969	+	8.90040i	0.464645	+	0.386609i
$531$	24.5900	+	29.9990i	1.06711	+	1.30185i
$532$	6.38961	+	0.282774i	0.277025	+	0.0122598i
$533$	1.25972			0.0545645
$534$	3.50167	−	12.7742i	0.151532	−	0.552793i
$535$	−8.73810	−	1.50339i	−0.377781	−	0.0649973i
$536$	−2.99197	−	8.22036i	−0.129233	−	0.355066i
$537$	10.1495	−	10.0335i	0.437983	−	0.432976i
$538$	−3.49296	+	4.16275i	−0.150592	+	0.179469i
$539$	16.7628	+	9.67800i	0.722024	+	0.416861i
$540$	−11.5605	−	1.16414i	−0.497484	−	0.0500968i
$541$	−2.75508	+	15.6248i	−0.118450	+	0.671763i	0.866534	+	0.499118i	$0.166343\pi$
$541$	−2.75508	+	15.6248i	−0.118450	+	0.671763i	−0.984984	+	0.172645i	$0.944769\pi$
$542$	−27.4537	−	4.84083i	−1.17924	−	0.207931i
$543$	−0.405700	−	4.96581i	−0.0174103	−	0.213103i
$544$	−4.34251	−	2.50715i	−0.186184	−	0.107493i
$545$	−0.188493	−	45.4123i	−0.00807417	−	1.94525i
$546$	2.02631	−	2.00315i	0.0867181	−	0.0857267i
$547$	−7.52637	+	2.73937i	−0.321804	+	0.117127i	−0.497871	−	0.867251i	$-0.665885\pi$
$547$	−7.52637	+	2.73937i	−0.321804	+	0.117127i	0.176067	+	0.984378i	$0.443663\pi$
$548$	6.55061	−	5.49662i	0.279828	−	0.234804i
$549$	−6.05801	+	7.05335i	−0.258550	+	0.301030i
$550$	3.30388	−	19.6918i	0.140878	−	0.839659i
$551$	−0.107160	+	2.42140i	−0.00456515	+	0.103155i
$552$	2.53826	+	1.20142i	0.108035	+	0.0511359i
$553$	0.469816	+	2.66446i	0.0199786	+	0.113304i
$554$	−8.76262	+	7.35271i	−0.372288	+	0.312387i
$555$	20.3571	+	29.1720i	0.864109	+	1.23828i
$556$	−6.89666	−	2.51018i	−0.292484	−	0.106455i
$557$	15.8846	+	13.3288i	0.673053	+	0.564759i	0.913967	−	0.405788i	$-0.133003\pi$
$557$	15.8846	+	13.3288i	0.673053	+	0.564759i	−0.240914	+	0.970546i	$0.577447\pi$
$558$	3.13255	−	0.515290i	0.132611	−	0.0218139i
$559$	−11.3030	+	6.52578i	−0.478065	+	0.276011i
$560$	2.83460	−	1.65228i	0.119784	−	0.0698218i
$561$	20.0562	−	28.2956i	0.846774	−	1.19464i
$562$	−17.9545	+	10.3661i	−0.757366	+	0.437266i
$563$	6.66675	+	3.84905i	0.280970	+	0.162218i	0.633862	−	0.773446i	$-0.281469\pi$
$563$	6.66675	+	3.84905i	0.280970	+	0.162218i	−0.352892	+	0.935664i	$0.614802\pi$
$564$	−16.6111	+	7.62992i	−0.699453	+	0.321278i
$565$	−14.5821	−	39.5523i	−0.613472	−	1.66398i
$566$	6.74805	−	2.45609i	0.283642	−	0.103237i
$567$	11.5854	−	6.33820i	0.486539	−	0.266179i
$568$	−4.08970	+	0.721125i	−0.171600	+	0.0302577i
$569$	42.6669			1.78869			0.894345	−	0.447378i	$-0.147642\pi$
$569$	42.6669			1.78869			0.894345	+	0.447378i	$0.147642\pi$
$570$	−13.3708	−	10.3064i	−0.560041	−	0.431688i
$571$	16.4950			0.690295			0.345148	−	0.938548i	$-0.387829\pi$
$571$	16.4950			0.690295			0.345148	+	0.938548i	$0.387829\pi$
$572$	−4.40910	+	0.777443i	−0.184354	+	0.0325065i
$573$	−22.5801	+	5.91140i	−0.943296	+	0.246952i
$574$	−1.54927	+	0.563888i	−0.0646653	+	0.0235362i
$575$	−3.99491	+	7.05398i	−0.166599	+	0.294171i
$576$	−0.0344917	+	2.99980i	−0.00143715	+	0.124992i
$577$	−20.0050	−	11.5499i	−0.832820	−	0.480829i	0.0219973	−	0.999758i	$-0.492997\pi$
$577$	−20.0050	−	11.5499i	−0.832820	−	0.480829i	−0.854817	+	0.518929i	$0.826331\pi$
$578$	7.05221	−	4.07159i	0.293333	−	0.169356i
$579$	25.4474	+	18.0374i	1.05756	+	0.749607i
$580$	0.626147	+	1.07420i	0.0259993	+	0.0446036i
$581$	9.19445	−	5.30842i	0.381450	−	0.220230i
$582$	1.50521	−	1.04111i	0.0623928	−	0.0431555i
$583$	19.0375	+	15.9744i	0.788455	+	0.661592i
$584$	11.9003	+	4.33134i	0.492436	+	0.179232i
$585$	−7.41590	+	1.25152i	−0.306610	+	0.0517439i
$586$	2.27052	−	1.90519i	0.0937941	−	0.0787026i
$587$	2.46572	+	13.9838i	0.101771	+	0.577173i	0.992461	+	0.122561i	$0.0391109\pi$
$587$	2.46572	+	13.9838i	0.101771	+	0.577173i	−0.890690	+	0.454612i	$0.849778\pi$
$588$	3.59166	−	7.58815i	0.148118	−	0.312930i
$589$	4.26049	+	1.76771i	0.175550	+	0.0728373i
$590$	18.6759	+	22.0704i	0.768876	+	0.908625i
$591$	−8.86499	−	2.43007i	−0.364657	−	0.0999598i
$592$	7.03598	−	5.90389i	0.289177	−	0.242648i
$593$	−18.9374	+	6.89266i	−0.777667	+	0.283048i	−0.700199	−	0.713947i	$-0.746906\pi$
$593$	−18.9374	+	6.89266i	−0.777667	+	0.283048i	−0.0774673	+	0.996995i	$0.524683\pi$
$594$	−20.6371	−	2.16473i	−0.846750	−	0.0888198i
$595$	0.0682868	+	16.4518i	0.00279949	+	0.674459i
$596$	7.41886	+	4.28328i	0.303888	+	0.175450i
$597$	−15.4097	+	1.25895i	−0.630677	+	0.0515255i
$598$	1.79011	+	0.315644i	0.0732029	+	0.0129077i
$599$	6.07921	−	34.4769i	0.248390	−	1.40869i	−0.564096	−	0.825709i	$-0.690775\pi$
$599$	6.07921	−	34.4769i	0.248390	−	1.40869i	0.812486	−	0.582980i	$-0.198114\pi$
$600$	−8.62920	−	0.732766i	−0.352286	−	0.0299150i
$601$	31.1103	+	17.9615i	1.26901	+	0.732665i	0.974801	−	0.223075i	$-0.0716094\pi$
$601$	31.1103	+	17.9615i	1.26901	+	0.732665i	0.294212	+	0.955740i	$0.404943\pi$
$602$	10.9799	−	13.0853i	0.447506	−	0.533317i
$603$	−8.69177	−	24.7627i	−0.353956	−	1.00841i
$604$	−2.42884	−	6.67318i	−0.0988281	−	0.271528i
$605$	1.87573	−	10.9022i	0.0762591	−	0.443237i
$606$	19.0459	+	5.22088i	0.773688	+	0.212084i
$607$	−4.02159			−0.163231			−0.0816156	−	0.996664i	$-0.526008\pi$
$607$	−4.02159			−0.163231			−0.0816156	+	0.996664i	$0.526008\pi$
$608$	−2.34421	+	3.67487i	−0.0950705	+	0.149036i
$609$	−1.27732	−	0.604588i	−0.0517596	−	0.0244991i
$610$	−4.43256	+	5.32727i	−0.179469	+	0.215695i
$611$	−9.06391	+	7.60552i	−0.366686	+	0.307686i
$612$	−12.9402	−	7.67073i	−0.523076	−	0.310071i
$613$	−14.3908	+	39.5385i	−0.581241	+	1.59695i	0.204822	+	0.978799i	$0.434339\pi$
$613$	−14.3908	+	39.5385i	−0.581241	+	1.59695i	−0.786063	+	0.618147i	$0.787884\pi$
$614$	19.2560	−	22.9484i	0.777107	−	0.926120i
$615$	4.20167	+	1.13303i	0.169428	+	0.0456883i
$616$	5.07453	−	2.92978i	0.204459	−	0.118044i
$617$	−7.04118	+	39.9325i	−0.283467	+	1.60762i	0.427242	+	0.904137i	$0.359485\pi$
$617$	−7.04118	+	39.9325i	−0.283467	+	1.60762i	−0.710709	+	0.703486i	$0.751626\pi$
$618$	0.0763215	−	0.107676i	0.00307010	−	0.00433135i
$619$	17.3444	+	30.0414i	0.697130	+	1.20747i	0.969457	+	0.245261i	$0.0788735\pi$
$619$	17.3444	+	30.0414i	0.697130	+	1.20747i	−0.272327	+	0.962205i	$0.587793\pi$
$620$	2.32857	−	0.420562i	0.0935175	−	0.0168902i
$621$	7.57283	+	3.69157i	0.303887	+	0.148138i
$622$	25.6111	+	9.32167i	1.02691	+	0.373765i
$623$	3.83778	+	10.5442i	0.153757	+	0.422445i
$624$	0.491797	+	1.87854i	0.0196876	+	0.0752019i
$625$	3.93186	−	24.6889i	0.157274	−	0.987555i
$626$	10.5126			0.420169
$627$	−23.8023	−	18.5052i	−0.950574	−	0.739026i
$628$			4.87139i			0.194389i
$629$	7.99745	+	45.3558i	0.318879	+	1.80845i
$630$	8.56024	−	4.85876i	0.341048	−	0.193577i
$631$	−41.0327	+	14.9347i	−1.63349	+	0.594540i	−0.985883	−	0.167438i	$-0.946450\pi$
$631$	−41.0327	+	14.9347i	−1.63349	+	0.594540i	−0.647602	+	0.761978i	$0.724228\pi$
$632$	−1.73269	−	0.630647i	−0.0689226	−	0.0250858i
$633$	9.62119	+	20.9463i	0.382408	+	0.832539i
$634$	6.71253	−	11.6264i	0.266589	−	0.461745i
$635$	−11.9329	−	4.28721i	−0.473543	−	0.170133i
$636$	6.23319	−	8.79388i	0.247162	−	0.348700i
$637$	0.943623	−	5.35155i	0.0373877	−	0.212036i
$638$	1.11027	+	1.92304i	0.0439558	+	0.0761337i
$639$	−12.2932	+	2.02217i	−0.486310	+	0.0799959i
$640$	0.00928120	+	2.23605i	0.000366872	+	0.0883876i
$641$	−1.92159	−	0.699400i	−0.0758981	−	0.0276246i	0.303792	−	0.952738i	$-0.401747\pi$
$641$	−1.92159	−	0.699400i	−0.0758981	−	0.0276246i	−0.379690	+	0.925114i	$0.623969\pi$
$642$	−0.637903	+	6.83826i	−0.0251760	+	0.269885i
$643$	−13.7195	−	16.3503i	−0.541044	−	0.644791i	0.424377	−	0.905485i	$-0.360493\pi$
$643$	−13.7195	−	16.3503i	−0.541044	−	0.644791i	−0.965421	+	0.260694i	$0.916049\pi$
$644$	−2.34286	+	0.413109i	−0.0923215	+	0.0162788i
$645$	−43.5694	+	11.5998i	−1.71554	+	0.456742i
$646$	−10.0809	−	19.3932i	−0.396626	−	0.763016i
$647$	−26.0265			−1.02321			−0.511604	−	0.859222i	$-0.670948\pi$
$647$	−26.0265			−1.02321			−0.511604	+	0.859222i	$0.670948\pi$
$648$	−0.206936	+	8.99762i	−0.00812923	+	0.353460i
$649$	33.1895	+	39.5537i	1.30280	+	1.55262i
$650$	−5.51221	+	1.01920i	−0.216207	+	0.0399764i
$651$	−1.91260	+	1.89074i	−0.0749607	+	0.0741038i
$652$	−3.59889	+	4.28899i	−0.140943	+	0.167970i
$653$	17.5382	−	30.3770i	0.686321	−	1.18874i	−0.286698	−	0.958021i	$-0.592558\pi$
$653$	17.5382	−	30.3770i	0.686321	−	1.18874i	0.973020	−	0.230722i	$-0.0741089\pi$
$654$	−35.0597	+	2.86434i	−1.37094	+	0.112004i
$655$	44.0013	−	25.6482i	1.71927	−	1.00216i
$656$	0.195114	−	1.10655i	0.00761793	−	0.0432034i
$657$	35.5490	+	13.4036i	1.38690	+	0.522925i
$658$	7.74281	−	13.4109i	0.301846	−	0.522813i
$659$	−15.2457	−	12.7926i	−0.593887	−	0.498330i	0.295587	−	0.955316i	$-0.404485\pi$
$659$	−15.2457	−	12.7926i	−0.593887	−	0.498330i	−0.889474	+	0.456986i	$0.848929\pi$
$660$	−15.4053	−	1.37260i	−0.599652	−	0.0534285i
$661$	4.29627	+	11.8039i	0.167106	+	0.459119i	0.994774	−	0.102098i	$-0.0325556\pi$
$661$	4.29627	+	11.8039i	0.167106	+	0.459119i	−0.827669	+	0.561217i	$0.810333\pi$
$662$	3.10670	−	2.60683i	0.120745	−	0.101317i
$663$	−9.39060	−	2.57415i	−0.364701	−	0.0999719i
$664$			7.23557i			0.280794i
$665$	14.2901	+	0.572993i	0.554147	+	0.0222197i
$666$	21.3102	−	17.4678i	0.825753	−	0.676864i
$667$	−0.156551	−	0.887846i	−0.00606168	−	0.0343775i
$668$	−10.0943	−	12.0299i	−0.390559	−	0.465450i
$669$	−1.24021	+	13.2949i	−0.0479491	+	0.514010i
$670$	−6.76648	−	18.3534i	−0.261412	−	0.709052i
$671$	−7.95554	+	9.48105i	−0.307120	+	0.366012i
$672$	−1.44573	−	2.09019i	−0.0557702	−	0.0806307i
$673$	−15.4249	−	26.7167i	−0.594585	−	1.02985i	−0.993605	−	0.112910i	$-0.963983\pi$
$673$	−15.4249	−	26.7167i	−0.594585	−	1.02985i	0.399020	−	0.916942i	$-0.369350\pi$
$674$	−11.0853	−	1.95464i	−0.426989	−	0.0752898i
$675$	−25.8606	−	2.49579i	−0.995375	−	0.0960629i
$676$	−5.87154	−	10.1698i	−0.225828	−	0.391146i
$677$	22.0540	+	12.7329i	0.847605	+	0.489365i	0.859842	−	0.510560i	$-0.170562\pi$
$677$	22.0540	+	12.7329i	0.847605	+	0.489365i	−0.0122372	+	0.999925i	$0.503895\pi$
$678$	−29.6724	+	13.6294i	−1.13956	+	0.523432i
$679$	−0.530282	+	1.45694i	−0.0203504	+	0.0559122i
$680$	−9.73333	−	5.56580i	−0.373256	−	0.213439i
$681$	−13.4338	+	3.51692i	−0.514783	+	0.134769i
$682$	4.16167	−	0.733815i	0.159359	−	0.0280992i
$683$			36.9796i			1.41499i	0.706720	+	0.707493i	$0.250174\pi$
$683$			36.9796i			1.41499i	−0.706720	+	0.707493i	$0.749826\pi$
$684$	−7.15893	+	10.9430i	−0.273729	+	0.418417i
$685$	14.5965	−	12.3515i	0.557703	−	0.471927i
$686$	3.01857	+	17.1191i	0.115249	+	0.653612i
$687$	−10.4888	−	40.0645i	−0.400171	−	1.52855i
$688$	3.98161	+	10.9394i	0.151797	+	0.417060i
$689$	2.38628	−	6.55625i	0.0909100	−	0.249773i
$690$	5.68682	+	2.66288i	0.216493	+	0.101374i
$691$	20.9577	−	36.2997i	0.797267	−	1.38091i	−0.124123	−	0.992267i	$-0.539612\pi$
$691$	20.9577	−	36.2997i	0.797267	−	1.38091i	0.921390	−	0.388640i	$-0.127055\pi$
$692$	9.72985	−	5.61753i	0.369873	−	0.213546i
$693$	15.3236	−	8.61374i	0.582097	−	0.327209i
$694$	−6.92260	−	1.22064i	−0.262778	−	0.0463349i
$695$	−15.4446	−	5.54888i	−0.585846	−	0.210481i
$696$	0.792094	−	0.547871i	0.0300242	−	0.0207670i
$697$	4.31601	+	3.62157i	0.163481	+	0.137177i
$698$	8.45381	−	23.2267i	0.319981	−	0.879142i
$699$	−1.51322	+	16.2216i	−0.0572354	+	0.613558i
$700$	6.32298	−	3.72090i	0.238986	−	0.140637i
$701$	−29.4596	+	5.19453i	−1.11267	+	0.196195i	−0.699622	−	0.714513i	$-0.746648\pi$
$701$	−29.4596	+	5.19453i	−1.11267	+	0.196195i	−0.413052	+	0.910707i	$0.635537\pi$
$702$	1.41050	+	5.65222i	0.0532359	+	0.213329i
$703$	39.6963	−	5.20217i	1.49717	−	0.196203i
$704$			3.99340i			0.150507i
$705$	−37.0724	+	17.2151i	−1.39623	+	0.648356i
$706$	−0.0689268	−	0.0821438i	−0.00259410	−	0.00309152i
$707$	−15.7211	+	5.72201i	−0.591253	+	0.215198i
$708$	15.9264	−	15.7444i	0.598552	−	0.591709i
$709$	12.4127	+	10.4155i	0.466170	+	0.391163i	0.845395	−	0.534141i	$-0.179365\pi$
$709$	12.4127	+	10.4155i	0.466170	+	0.391163i	−0.379225	+	0.925304i	$0.623809\pi$
$710$	−9.13808	+	1.65043i	−0.342946	+	0.0619395i
$711$	−5.17597	−	1.95158i	−0.194114	−	0.0731899i
$712$	−7.53108	−	1.32793i	−0.282239	−	0.0497664i
$713$	−1.68965	−	0.297931i	−0.0632780	−	0.0111576i
$714$	12.7013	−	1.03768i	0.475335	−	0.0388343i
$715$	−9.85174	+	1.77932i	−0.368434	+	0.0665429i
$716$	−6.31205	−	5.29644i	−0.235892	−	0.197937i
$717$	16.8733	+	17.0685i	0.630146	+	0.637433i
$718$	14.0378	−	5.10933i	0.523885	−	0.190679i
$719$	−2.12568	−	2.53328i	−0.0792744	−	0.0944755i	0.724949	−	0.688802i	$-0.241863\pi$
$719$	−2.12568	−	2.53328i	−0.0792744	−	0.0944755i	−0.804224	+	0.594327i	$0.797419\pi$
$720$	−0.0492833	+	6.70802i	−0.00183668	+	0.249993i
$721$			0.111808i			0.00416395i
$722$	−17.2294	+	8.00931i	−0.641210	+	0.298076i
$723$	−11.1185	−	5.26265i	−0.413500	−	0.195720i
$724$	−2.83286	+	0.499510i	−0.105282	+	0.0185641i
$725$	1.41007	+	2.39614i	0.0523685	+	0.0889906i
$726$	−8.53183	−	0.795887i	−0.316646	−	0.0295381i
$727$	3.84103	−	10.5531i	0.142456	−	0.391394i	−0.847861	−	0.530218i	$-0.822110\pi$
$727$	3.84103	−	10.5531i	0.142456	−	0.391394i	0.990317	+	0.138824i	$0.0443323\pi$
$728$	−1.26018	−	1.05742i	−0.0467053	−	0.0391904i
$729$	−0.931111	+	26.9839i	−0.0344856	+	0.999405i
$730$	26.6498	+	9.57464i	0.986352	+	0.354373i
$731$	−57.4869	−	10.1365i	−2.12623	−	0.374912i
$732$	4.37951	+	3.10424i	0.161871	+	0.114736i
$733$	−3.05112	+	1.76156i	−0.112696	+	0.0650648i	−0.555288	−	0.831658i	$-0.687392\pi$
$733$	−3.05112	+	1.76156i	−0.112696	+	0.0650648i	0.442593	+	0.896723i	$0.354059\pi$
$734$	−15.8508	+	27.4544i	−0.585063	+	1.01336i
$735$	7.96071	−	17.0008i	0.293635	−	0.627084i
$736$	0.554528	−	1.52355i	0.0204402	−	0.0561590i
$737$	−11.9481	−	32.8272i	−0.440115	−	1.20921i
$738$	0.623471	−	3.31269i	0.0229503	−	0.121942i
$739$	−2.09177	−	11.8630i	−0.0769471	−	0.436389i	−0.998806	−	0.0488620i	$-0.984441\pi$
$739$	−2.09177	−	11.8630i	−0.0769471	−	0.436389i	0.921858	−	0.387527i	$-0.126671\pi$
$740$	15.6780	−	13.2667i	0.576335	−	0.487693i
$741$	−2.59642	+	8.05628i	−0.0953818	+	0.295955i
$742$			9.13139i			0.335224i
$743$	−12.7130	+	2.24165i	−0.466396	+	0.0822383i	−0.401908	−	0.915680i	$-0.631653\pi$
$743$	−12.7130	+	2.24165i	−0.466396	+	0.0822383i	−0.0644887	+	0.997918i	$0.520542\pi$
$744$	−0.464199	−	1.77313i	−0.0170184	−	0.0650059i
$745$	16.6287	+	9.50877i	0.609228	+	0.348374i
$746$	1.63104	−	4.48124i	0.0597165	−	0.164070i
$747$	−0.249567	+	21.7053i	−0.00913117	+	0.794154i
$748$	−17.3414	−	10.0120i	−0.634064	−	0.366077i
$749$	−2.90910	−	5.03871i	−0.106296	−	0.184110i
$750$	−19.3021	−	1.55841i	−0.704813	−	0.0569051i
$751$	−45.5479	−	8.03132i	−1.66207	−	0.293067i	−0.737857	−	0.674957i	$-0.764162\pi$
$751$	−45.5479	−	8.03132i	−1.66207	−	0.293067i	−0.924208	+	0.381890i	$0.875273\pi$
$752$	5.27686	+	9.13980i	0.192427	+	0.333294i
$753$	20.5117	−	14.1874i	0.747489	−	0.517019i
$754$	0.400716	−	0.477555i	0.0145932	−	0.0173915i
$755$	−5.49294	−	14.8990i	−0.199909	−	0.542231i
$756$	−4.26481	−	6.32001i	−0.155110	−	0.229857i
$757$	8.43375	+	10.0509i	0.306530	+	0.365308i	0.897215	−	0.441594i	$-0.145587\pi$
$757$	8.43375	+	10.0509i	0.306530	+	0.365308i	−0.590685	+	0.806902i	$0.701142\pi$
$758$	−4.90010	−	27.7899i	−0.177980	−	1.00937i
$759$	10.1363	+	4.79775i	0.367923	+	0.174147i
$760$	−5.20767	+	8.23894i	−0.188902	+	0.298858i
$761$		−	23.9917i		−	0.869698i	−0.900503	−	0.434849i	$-0.856802\pi$
$761$		−	23.9917i		−	0.869698i	0.900503	−	0.434849i	$-0.143198\pi$
$762$	−2.59652	+	9.47221i	−0.0940621	+	0.343142i
$763$	22.8280	−	19.1550i	0.826431	−	0.693458i
$764$	4.60905	+	12.6633i	0.166750	+	0.458141i
$765$	−29.0061	−	17.0320i	−1.04872	−	0.615794i
$766$	16.8723	+	14.1575i	0.609619	+	0.511531i
$767$	7.24796	−	12.5538i	0.261709	−	0.453293i
$768$	1.72630	−	0.141037i	0.0622925	−	0.00508922i
$769$	−0.108949	+	0.617881i	−0.00392880	+	0.0222813i	−0.986709	−	0.162496i	$-0.948045\pi$
$769$	−0.108949	+	0.617881i	−0.00392880	+	0.0222813i	0.982780	+	0.184778i	$0.0591565\pi$
$770$	11.3197	−	6.59823i	0.407934	−	0.237784i
$771$	−2.84756	−	34.8544i	−0.102553	−	1.25525i
$772$	9.00424	−	15.5958i	0.324070	−	0.561305i
$773$	−24.6949	+	29.4302i	−0.888214	+	1.05853i	0.109699	+	0.993965i	$0.465011\pi$
$773$	−24.6949	+	29.4302i	−0.888214	+	1.05853i	−0.997913	+	0.0645674i	$0.979433\pi$
$774$	11.5667	+	32.9533i	0.415757	+	1.18448i
$775$	5.20288	−	0.962009i	0.186893	−	0.0345564i
$776$	−0.679205	−	0.809444i	−0.0243820	−	0.0290574i
$777$	−6.17110	+	22.5124i	−0.221387	+	0.807627i
$778$	32.9534			1.18144
$779$	3.31100	−	3.60903i	0.118629	−	0.129307i
$780$	1.11712	+	4.19595i	0.0399992	+	0.150239i
$781$	−16.3318	+	2.87974i	−0.584398	+	0.103045i
$782$	5.22576	+	6.22782i	0.186873	+	0.222706i
$783$	2.39502	−	1.61618i	0.0855911	−	0.0577577i
$784$	−4.55469	−	1.65777i	−0.162667	−	0.0592061i
$785$	0.0452123	+	10.8927i	0.00161370	+	0.388776i
$786$	−22.4419	−	32.4458i	−0.800476	−	1.15730i
$787$	18.4113	+	31.8892i	0.656290	+	1.13673i	0.981569	+	0.191110i	$0.0612087\pi$
$787$	18.4113	+	31.8892i	0.656290	+	1.13673i	−0.325278	+	0.945618i	$0.605458\pi$
$788$	−0.921553	+	5.22639i	−0.0328290	+	0.186182i
$789$	28.7370	+	20.3691i	1.02307	+	0.725158i
$790$	−3.88023	−	1.39408i	−0.138052	−	0.0495990i
$791$	13.8310	−	23.9560i	0.491774	−	0.851777i
$792$	−0.137739	+	11.9794i	−0.00489435	+	0.425670i
$793$	3.26513	+	1.18841i	0.115948	+	0.0422017i
$794$	−14.1426	+	5.14749i	−0.501902	+	0.182678i
$795$	13.8561	−	19.7214i	0.491425	−	0.699446i
$796$	1.55006	+	8.79082i	0.0549404	+	0.311582i
$797$			42.0662i			1.49006i	0.667031	+	0.745030i	$0.267565\pi$
$797$			42.0662i			1.49006i	−0.667031	+	0.745030i	$0.732435\pi$
$798$	−0.413016	−	11.0703i	−0.0146206	−	0.391883i
$799$	−52.9195			−1.87216
$800$	0.0415064	+	4.99983i	0.00146747	+	0.176771i
$801$	−22.5459	−	4.24329i	−0.796622	−	0.149929i
$802$	−3.40026	−	9.34214i	−0.120067	−	0.329882i
$803$	47.5225	+	17.2968i	1.67703	+	0.610390i
$804$	−13.7688	+	6.32440i	−0.485589	+	0.223044i
$805$	−5.23491	+	0.945477i	−0.184506	+	0.0333237i
$806$	−0.593197	−	1.02745i	−0.0208945	−	0.0361903i
$807$	7.67879	+	5.44280i	0.270306	+	0.191596i
$808$	1.97991	−	11.2286i	0.0696529	−	0.395021i
$809$	−28.9062	+	16.6890i	−1.01629	+	0.586755i	−0.913027	−	0.407899i	$-0.866262\pi$
$809$	−28.9062	+	16.6890i	−1.01629	+	0.586755i	−0.103262	+	0.994654i	$0.532928\pi$
$810$	−0.379211	+	20.1210i	−0.0133241	+	0.706981i
$811$	17.3716	−	20.7026i	0.609998	−	0.726968i	−0.369318	−	0.929303i	$-0.620409\pi$
$811$	17.3716	−	20.7026i	0.609998	−	0.726968i	0.979316	+	0.202335i	$0.0648531\pi$
$812$	−0.279054	+	0.766694i	−0.00979287	+	0.0269057i
$813$	−4.48474	+	48.0760i	−0.157287	+	1.68610i
$814$	28.0975	−	23.5766i	0.984817	−	0.826360i
$815$	−8.00748	+	9.62379i	−0.280490	+	0.337107i
$816$	−3.71564	+	7.85007i	−0.130073	+	0.274807i
$817$	−11.0124	+	49.5345i	−0.385274	+	1.73299i
$818$	15.3606			0.537072
$819$	−3.74381	−	3.21550i	−0.130819	−	0.112359i
$820$	0.426015	−	2.47611i	0.0148771	−	0.0864694i
$821$	18.7241	+	51.4441i	0.653476	+	1.79541i	0.604493	+	0.796611i	$0.293376\pi$
$821$	18.7241	+	51.4441i	0.653476	+	1.79541i	0.0489832	+	0.998800i	$0.484402\pi$
$822$	−10.4127	−	10.5331i	−0.363184	−	0.367384i
$823$	−4.99713	+	5.95535i	−0.174189	+	0.207590i	−0.846075	−	0.533065i	$-0.821040\pi$
$823$	−4.99713	+	5.95535i	−0.174189	+	0.207590i	0.671885	+	0.740655i	$0.265485\pi$
$824$	−0.0659905	−	0.0380996i	−0.00229889	−	0.00132726i
$825$	−34.4598	−	2.92623i	−1.19974	−	0.101878i
$826$	−3.29445	+	18.6838i	−0.114629	+	0.650091i
$827$	−51.8725	−	9.14651i	−1.80378	−	0.318055i	−0.832149	−	0.554551i	$-0.812890\pi$
$827$	−51.8725	−	9.14651i	−1.80378	−	0.318055i	−0.971632	+	0.236496i	$0.924001\pi$
$828$	1.71603	−	4.55123i	0.0596360	−	0.158166i
$829$	24.5606	+	14.1801i	0.853026	+	0.492495i	0.861671	−	0.507468i	$-0.169418\pi$
$829$	24.5606	+	14.1801i	0.853026	+	0.492495i	−0.00864497	+	0.999963i	$0.502752\pi$
$830$	0.0671547	+	16.1791i	0.00233097	+	0.561584i
$831$	13.9288	+	14.0899i	0.483186	+	0.488773i
$832$	1.05352	−	0.383449i	0.0365241	−	0.0132937i
$833$	18.6182	−	15.6225i	0.645081	−	0.541287i
$834$	−3.36064	+	12.2597i	−0.116369	+	0.424520i
$835$	−22.6829	−	26.8057i	−0.784975	−	0.927649i
$836$	−9.36139	+	14.6752i	−0.323770	+	0.507553i
$837$	−1.33135	−	5.33504i	−0.0460181	−	0.184406i
$838$	−4.57029	−	25.9194i	−0.157878	−	0.895371i
$839$	−4.36062	+	3.65900i	−0.150545	+	0.126323i	−0.714950	−	0.699176i	$-0.753550\pi$
$839$	−4.36062	+	3.65900i	−0.150545	+	0.126323i	0.564404	+	0.825499i	$0.309106\pi$
$840$	−3.25212	−	4.66034i	−0.112209	−	0.160797i
$841$	26.9605	+	9.81283i	0.929674	+	0.338374i
$842$	27.4024	+	22.9933i	0.944348	+	0.792402i
$843$	20.4272	+	29.5329i	0.703549	+	1.01717i
$844$	11.5251	−	6.65403i	0.396711	−	0.229041i
$845$	−13.2234	−	22.6857i	−0.454900	−	0.780411i
$846$	15.5143	+	27.5996i	0.533393	+	0.948893i
$847$	6.28661	−	3.62957i	0.216010	−	0.124714i
$848$	−5.38946	−	3.11160i	−0.185075	−	0.106853i
$849$	−5.19167	−	11.3028i	−0.178178	−	0.387910i
$850$	−21.8159	−	12.3551i	−0.748278	−	0.423775i
$851$	−13.9936	+	5.09325i	−0.479694	+	0.174594i
$852$	1.82167	+	6.95835i	0.0624096	+	0.238389i
$853$	35.8870	−	6.32784i	1.22875	−	0.216661i	0.478660	−	0.878001i	$-0.341123\pi$
$853$	35.8870	−	6.32784i	1.22875	−	0.216661i	0.750087	+	0.661339i	$0.230012\pi$
$854$	−4.54760			−0.155616
$855$	−15.9062	+	24.5356i	−0.543979	+	0.839099i
$856$	3.96521			0.135528
$857$	−7.95711	+	1.40305i	−0.271810	+	0.0479274i	−0.307892	−	0.951421i	$-0.599623\pi$
$857$	−7.95711	+	1.40305i	−0.271810	+	0.0479274i	0.0360819	+	0.999349i	$0.488512\pi$
$858$	1.96394	+	7.50177i	0.0670479	+	0.256106i
$859$	−2.80987	+	1.02271i	−0.0958715	+	0.0348944i	−0.389511	−	0.921022i	$-0.627356\pi$
$859$	−2.80987	+	1.02271i	−0.0958715	+	0.0348944i	0.293639	+	0.955916i	$0.405134\pi$
$860$	9.00461	+	24.4240i	0.307054	+	0.832853i
$861$	1.19194	+	2.59497i	0.0406213	+	0.0884365i
$862$	−2.25983	−	1.30472i	−0.0769703	−	0.0444388i
$863$	20.8445	−	12.0346i	0.709554	−	0.409661i	−0.101342	−	0.994852i	$-0.532314\pi$
$863$	20.8445	−	12.0346i	0.709554	−	0.409661i	0.810896	+	0.585190i	$0.198980\pi$
$864$	5.18342	−	0.363539i	0.176344	−	0.0123678i
$865$	21.7043	−	12.6514i	0.737967	−	0.430160i
$866$	19.8544	−	11.4629i	0.674680	−	0.389527i
$867$	−8.02341	−	11.6000i	−0.272489	−	0.393956i
$868$	1.18946	+	0.998076i	0.0403729	+	0.0338769i
$869$	−6.91932	−	2.51843i	−0.234722	−	0.0854317i
$870$	1.76608	−	1.23242i	0.0598756	−	0.0417829i
$871$	−7.51302	+	6.30417i	−0.254569	+	0.213609i
$872$	3.52665	+	20.0006i	0.119427	+	0.677307i
$873$	−2.00956	−	2.45160i	−0.0680133	−	0.0829741i
$874$	5.60936	−	4.29893i	0.189739	−	0.145413i
$875$	14.1040	−	8.37879i	0.476801	−	0.283255i
$876$	5.79882	−	21.1543i	0.195924	−	0.714737i
$877$	−2.53783	+	2.12949i	−0.0856963	+	0.0719077i	−0.684629	−	0.728891i	$-0.740036\pi$
$877$	−2.53783	+	2.12949i	−0.0856963	+	0.0719077i	0.598933	+	0.800799i	$0.295592\pi$
$878$	18.8248	−	6.85166i	0.635305	−	0.231232i
$879$	−3.60915	−	3.65089i	−0.121734	−	0.123141i
$880$	0.0370635	+	8.92944i	0.00124941	+	0.301011i
$881$	32.0253	+	18.4898i	1.07896	+	0.622938i	0.930616	−	0.365998i	$-0.119272\pi$
$881$	32.0253	+	18.4898i	1.07896	+	0.622938i	0.148344	+	0.988936i	$0.452606\pi$
$882$	−13.6060	−	5.13008i	−0.458137	−	0.172739i
$883$	9.67887	+	1.70665i	0.325720	+	0.0574332i	0.334117	−	0.942532i	$-0.391562\pi$
$883$	9.67887	+	1.70665i	0.325720	+	0.0574332i	−0.00839736	+	0.999965i	$0.502673\pi$
$884$	−0.976193	+	5.53627i	−0.0328329	+	0.186205i
$885$	35.4661	−	35.3530i	1.19218	−	1.18838i
$886$	−1.75850	−	1.01527i	−0.0590780	−	0.0341087i
$887$	15.5521	−	18.5342i	0.522187	−	0.622318i	−0.438909	−	0.898531i	$-0.644635\pi$
$887$	15.5521	−	18.5342i	0.522187	−	0.622318i	0.961096	+	0.276213i	$0.0890795\pi$
$888$	−11.1842	−	11.3136i	−0.375318	−	0.379658i
$889$	−2.84576	−	7.81865i	−0.0954436	−	0.262229i
$890$	−16.8522	−	2.89942i	−0.564887	−	0.0971889i
$891$	−0.826380	+	35.9311i	−0.0276848	+	1.20374i
$892$	7.70913			0.258121
$893$	−2.03387	+	45.9577i	−0.0680608	+	1.53791i
$894$	6.34790	−	13.4113i	0.212305	−	0.448540i
$895$	−14.1632	−	11.7845i	−0.473424	−	0.393913i
$896$	−1.12403	+	0.943170i	−0.0375511	+	0.0315091i
$897$	0.292426	−	3.13478i	0.00976381	−	0.104667i
$898$	−5.04507	+	13.8612i	−0.168356	+	0.462555i
$899$	−0.378229	+	0.450756i	−0.0126147	+	0.0150336i
$900$	−0.0479415	+	14.9999i	−0.00159805	+	0.499997i
$901$	27.0243	−	15.6025i	0.900311	−	0.519795i
$902$	0.779169	−	4.41889i	0.0259435	−	0.147133i
$903$	−24.1377	−	17.1090i	−0.803252	−	0.569353i
$904$	9.42608	+	16.3264i	0.313507	+	0.543010i
$905$	−6.32978	+	1.14322i	−0.210409	+	0.0380019i
$906$	−11.1774	+	5.13407i	−0.371343	+	0.170568i
$907$	−12.6566	−	4.60662i	−0.420255	−	0.152960i	0.123232	−	0.992378i	$-0.460674\pi$
$907$	−12.6566	−	4.60662i	−0.420255	−	0.152960i	−0.543487	+	0.839417i	$0.682896\pi$
$908$	2.74210	+	7.53386i	0.0909998	+	0.250020i
$909$	6.32662	−	33.6153i	0.209841	−	1.11495i
$910$	−2.82763	−	2.35274i	−0.0937351	−	0.0779924i
$911$	−15.2281			−0.504529			−0.252264	−	0.967658i	$-0.581175\pi$
$911$	−15.2281			−0.504529			−0.252264	+	0.967658i	$0.581175\pi$
$912$	6.67454	+	3.52853i	0.221016	+	0.116841i
$913$			28.8945i			0.956269i
$914$	0.191285	+	1.08483i	0.00632713	+	0.0358830i
$915$	9.82162	+	6.90059i	0.324693	+	0.228126i
$916$	−22.4688	+	8.17797i	−0.742389	+	0.270208i
$917$	31.4053	+	11.4306i	1.03710	+	0.377472i
$918$	−11.4169	+	23.4205i	−0.376815	+	0.772992i
$919$	10.3478	−	17.9229i	0.341342	−	0.591222i	−0.643340	−	0.765581i	$-0.722452\pi$
$919$	10.3478	−	17.9229i	0.341342	−	0.591222i	0.984682	+	0.174359i	$0.0557852\pi$
$920$	1.22581	−	3.41189i	0.0404138	−	0.112487i
$921$	−42.3315	−	30.0050i	−1.39487	−	0.988698i
$922$	−4.83023	+	27.3936i	−0.159075	+	0.902161i
$923$	2.32791	+	4.03206i	0.0766240	+	0.132717i
$924$	−5.77337	−	8.34695i	−0.189930	−	0.274595i
$925$	34.9337	−	29.8105i	1.14861	−	0.980163i
$926$	30.0480	+	10.9366i	0.987437	+	0.359398i
$927$	−0.196644	−	0.116568i	−0.00645865	−	0.00382858i
$928$	−0.357422	−	0.425959i	−0.0117330	−	0.0139828i
$929$	34.8234	−	6.14030i	1.14252	−	0.201457i	0.429812	−	0.902919i	$-0.358580\pi$
$929$	34.8234	−	6.14030i	1.14252	−	0.201457i	0.712707	+	0.701462i	$0.247469\pi$
$930$	−1.05443	−	3.96049i	−0.0345761	−	0.129869i
$931$	−12.8517	−	16.7692i	−0.421197	−	0.549590i
$932$	9.40622			0.308111
$933$	12.4799	−	45.5271i	0.408573	−	1.49049i
$934$	8.69047	+	10.3569i	0.284361	+	0.338888i
$935$	−38.8691	−	22.2265i	−1.27116	−	0.726884i
$936$	3.17357	−	1.11393i	0.103731	−	0.0364100i
$937$	−0.315237	+	0.375684i	−0.0102983	+	0.0122731i	−0.771169	−	0.636630i	$-0.780328\pi$
$937$	−0.315237	+	0.375684i	−0.0102983	+	0.0122731i	0.760871	+	0.648904i	$0.224772\pi$
$938$	6.41797	−	11.1162i	0.209554	−	0.362958i
$939$	−1.48266	−	18.1479i	−0.0483849	−	0.592235i
$940$	11.8842	+	20.3881i	0.387618	+	0.664985i
$941$	−4.07266	+	23.0972i	−0.132765	+	0.752947i	0.843625	+	0.536932i	$0.180417\pi$
$941$	−4.07266	+	23.0972i	−0.132765	+	0.752947i	−0.976390	+	0.216015i	$0.930694\pi$
$942$	8.40947	−	0.687043i	0.273995	−	0.0223851i
$943$	−0.910879	+	1.57769i	−0.0296623	+	0.0513766i
$944$	−9.90477	−	8.31109i	−0.322373	−	0.270503i
$945$	−9.59497	−	14.0923i	−0.312124	−	0.458422i
$946$	15.9002	+	43.6853i	0.516959	+	1.42033i
$947$	8.22333	−	6.90020i	0.267222	−	0.224226i	−0.499324	−	0.866416i	$-0.666418\pi$
$947$	8.22333	−	6.90020i	0.267222	−	0.224226i	0.766546	+	0.642189i	$0.221974\pi$
$948$	−0.844313	+	3.08008i	−0.0274220	+	0.100036i
$949$		−	14.1980i		−	0.460886i
$950$	−11.5681	+	18.4710i	−0.375320	+	0.599279i
$951$	−21.0174	−	9.94809i	−0.681537	−	0.322589i
$952$	−1.27762	−	7.24576i	−0.0414080	−	0.234837i
$953$	12.6100	+	15.0280i	0.408476	+	0.486803i	0.930585	−	0.366076i	$-0.119299\pi$
$953$	12.6100	+	15.0280i	0.408476	+	0.486803i	−0.522109	+	0.852879i	$0.674854\pi$
$954$	−16.0600	−	9.52008i	−0.519961	−	0.308224i
$955$	10.4236	+	28.2729i	0.337299	+	0.914889i
$956$	8.90705	−	10.6150i	0.288075	−	0.343314i
$957$	3.16315	−	2.18787i	0.102250	−	0.0707237i
$958$	8.00084	+	13.8579i	0.258496	+	0.447727i
$959$	12.3567	+	2.17882i	0.399018	+	0.0703577i
$960$	3.85878	−	0.331387i	0.124542	−	0.0106955i
$961$	−14.9401	−	25.8770i	−0.481938	−	0.834742i
$962$	−8.91779	−	5.14869i	−0.287521	−	0.166000i
$963$	11.8948	+	0.136767i	0.383306	+	0.00440725i
$964$	−2.42903	+	6.67371i	−0.0782339	+	0.214946i
$965$	19.9892	−	34.9565i	0.643474	−	1.12529i
$966$	1.04358	+	3.98621i	0.0335766	+	0.128254i
$967$	41.1045	−	7.24783i	1.32183	−	0.233075i	0.532181	−	0.846631i	$-0.321373\pi$
$967$	41.1045	−	7.24783i	1.32183	−	0.233075i	0.789651	+	0.613556i	$0.210262\pi$
$968$			4.94724i			0.159010i
$969$	−32.0567	+	20.1377i	−1.02981	+	0.646917i
$970$	−1.52625	−	1.80365i	−0.0490048	−	0.0579118i
$971$	−9.62504	−	54.5863i	−0.308882	−	1.75176i	−0.604643	−	0.796497i	$-0.706684\pi$
$971$	−9.62504	−	54.5863i	−0.308882	−	1.75176i	0.295760	−	0.955262i	$-0.404427\pi$
$972$	15.5618	−	0.911759i	0.499144	−	0.0292447i
$973$	−3.68322	−	10.1196i	−0.118079	−	0.324418i
$974$	9.41845	−	25.8770i	0.301787	−	0.829152i
$975$	2.53687	+	9.37198i	0.0812450	+	0.300144i
$976$	1.54964	−	2.68405i	0.0496026	−	0.0859143i
$977$	5.92005	−	3.41794i	0.189399	−	0.109350i	−0.402302	−	0.915507i	$-0.631790\pi$
$977$	5.92005	−	3.41794i	0.189399	−	0.109350i	0.591701	+	0.806157i	$0.298456\pi$
$978$	7.91165	+	5.60785i	0.252987	+	0.179319i
$979$	−30.0746	−	5.30297i	−0.961189	−	0.169484i
$980$	−10.1999	−	3.66458i	−0.325823	−	0.117061i
$981$	9.88940	+	60.1196i	0.315744	+	1.91947i
$982$	−22.5362	−	18.9101i	−0.719159	−	0.603446i
$983$	−15.9126	+	43.7195i	−0.507533	+	1.39443i	0.376242	+	0.926521i	$0.377216\pi$
$983$	−15.9126	+	43.7195i	−0.507533	+	1.39443i	−0.883775	+	0.467913i	$0.845006\pi$
$984$	−1.93775	−	0.180762i	−0.0617732	−	0.00576248i
$985$	−2.01213	+	11.6950i	−0.0641118	+	0.372634i
$986$	2.74584	−	0.484166i	0.0874454	−	0.0154190i
$987$	−24.2433	−	11.4750i	−0.771673	−	0.365252i
$988$	4.77042	+	1.06055i	0.151767	+	0.0337405i
$989$		−	18.8747i		−	0.600179i
$990$	−0.196808	+	26.7878i	−0.00625497	+	0.851373i
$991$	−12.9115	−	15.3873i	−0.410146	−	0.488793i	0.520940	−	0.853594i	$-0.325582\pi$
$991$	−12.9115	−	15.3873i	−0.410146	−	0.488793i	−0.931086	+	0.364800i	$0.881137\pi$
$992$	−0.994397	+	0.361931i	−0.0315721	+	0.0114913i
$993$	−4.93833	−	4.99544i	−0.156713	−	0.158525i
$994$	−4.66785	−	3.91679i	−0.148055	−	0.124233i
$995$	3.54760	+	19.6423i	0.112466	+	0.622703i
$996$	12.4907	−	1.02048i	0.395785	−	0.0323351i
$997$	49.1491	+	8.66632i	1.55657	+	0.274465i	0.884684	−	0.466191i	$-0.154374\pi$
$997$	49.1491	+	8.66632i	1.55657	+	0.274465i	0.671885	+	0.740656i	$0.265485\pi$
$998$	−17.7602	−	3.13160i	−0.562188	−	0.0991290i
$999$	−33.1602	−	34.3242i	−1.04914	−	1.08597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.29.12	✓	240
3.2	odd	2	inner	570.2.bf.a.29.22	yes	240
5.4	even	2	inner	570.2.bf.a.29.29	yes	240
15.14	odd	2	inner	570.2.bf.a.29.19	yes	240
19.2	odd	18	inner	570.2.bf.a.59.19	yes	240
57.2	even	18	inner	570.2.bf.a.59.29	yes	240
95.59	odd	18	inner	570.2.bf.a.59.22	yes	240
285.59	even	18	inner	570.2.bf.a.59.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.12	✓	240	1.1	even	1	trivial
570.2.bf.a.29.19	yes	240	15.14	odd	2	inner
570.2.bf.a.29.22	yes	240	3.2	odd	2	inner
570.2.bf.a.29.29	yes	240	5.4	even	2	inner
570.2.bf.a.59.12	yes	240	285.59	even	18	inner
570.2.bf.a.59.19	yes	240	19.2	odd	18	inner
570.2.bf.a.59.22	yes	240	95.59	odd	18	inner
570.2.bf.a.59.29	yes	240	57.2	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.438663 + 1.67558i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.09802 - 0.773495i) q^{5} +(-0.722960 - 1.57395i) q^{6} +(1.27073 + 0.733656i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.61515 + 1.47003i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.438663 + 1.67558i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.09802 - 0.773495i) q^{5} +(-0.722960 - 1.57395i) q^{6} +(1.27073 + 0.733656i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.61515 + 1.47003i) q^{9} +(-1.93183 + 1.12606i) q^{10} +(-3.45839 + 1.99670i) q^{11} +(0.985291 + 1.42450i) q^{12} +(0.858834 + 0.720648i) q^{13} +(-1.37882 - 0.501850i) q^{14} +(2.21638 + 3.17611i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.870724 + 4.93812i) q^{17} +(2.32015 - 1.90181i) q^{18} +(4.32194 - 0.566387i) q^{19} +(1.70695 - 1.44441i) q^{20} +(-0.671879 + 2.45104i) q^{21} +(3.05912 - 2.56691i) q^{22} +(-1.52355 + 0.554528i) q^{23} +(-1.21768 - 1.23177i) q^{24} +(3.80341 - 3.24562i) q^{25} +(-0.970926 - 0.560564i) q^{26} +(-3.61032 - 3.73705i) q^{27} +(1.44502 + 0.254796i) q^{28} +(-0.0965571 + 0.547602i) q^{29} +(-2.73423 - 2.74299i) q^{30} +(0.916441 + 0.529107i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-4.86270 - 4.91893i) q^{33} +(-1.71499 - 4.71190i) q^{34} +(3.23350 + 0.556325i) q^{35} +(-1.95466 + 2.27581i) q^{36} +9.18483 q^{37} +(-4.15793 + 1.30828i) q^{38} +(-0.830766 + 1.75517i) q^{39} +(-1.43019 + 1.71888i) q^{40} +(0.860741 - 0.722248i) q^{41} +(0.236054 - 2.53047i) q^{42} +(-3.98161 + 10.9394i) q^{43} +(-2.56691 + 3.05912i) q^{44} +(-4.34959 + 5.10696i) q^{45} +(1.40412 - 0.810666i) q^{46} +(-1.83264 + 10.3934i) q^{47} +(1.41308 + 1.00160i) q^{48} +(-2.42350 - 4.19762i) q^{49} +(-3.18203 + 3.85677i) q^{50} +(-7.89227 + 3.62514i) q^{51} +(1.05352 + 0.383449i) q^{52} +(-2.12846 - 5.84790i) q^{53} +(4.20441 + 3.05335i) q^{54} +(-5.71134 + 6.86417i) q^{55} -1.46731 q^{56} +(2.84490 + 6.99332i) q^{57} -0.556050i q^{58} +(-2.24523 - 12.7333i) q^{59} +(3.16901 + 2.22652i) q^{60} +(2.91236 - 1.06001i) q^{61} +(-0.994397 - 0.361931i) q^{62} +(-4.40165 - 0.0506101i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.35927 + 0.847632i) q^{65} +(5.64299 + 3.99980i) q^{66} +(-1.51906 + 8.61503i) q^{67} +(2.50715 + 4.34251i) q^{68} +(-1.59748 - 2.30959i) q^{69} +(-3.28098 + 0.0136184i) q^{70} +(3.90235 + 1.42034i) q^{71} +(1.52977 - 2.58066i) q^{72} +(-8.14026 - 9.70118i) q^{73} +(-9.04529 + 1.59493i) q^{74} +(7.10672 + 4.94919i) q^{75} +(3.86758 - 2.01042i) q^{76} -5.85956 q^{77} +(0.513363 - 1.87276i) q^{78} +(1.18523 + 1.41250i) q^{79} +(1.10999 - 1.94112i) q^{80} +(4.67802 - 7.68870i) q^{81} +(-0.722248 + 0.860741i) q^{82} +(3.61778 - 6.26618i) q^{83} +(0.206945 + 2.53302i) q^{84} +(5.64641 + 9.68679i) q^{85} +(2.02152 - 11.4646i) q^{86} +(-0.959909 + 0.0784234i) q^{87} +(1.99670 - 3.45839i) q^{88} +(5.85814 + 4.91556i) q^{89} +(3.39669 - 5.78468i) q^{90} +(0.562639 + 1.54584i) q^{91} +(-1.24201 + 1.04217i) q^{92} +(-0.484555 + 1.76767i) q^{93} -10.5537i q^{94} +(8.62945 - 4.53130i) q^{95} +(-1.56554 - 0.741008i) q^{96} +(0.183486 + 1.04060i) q^{97} +(3.11559 + 3.71301i) q^{98} +(6.10899 - 10.3056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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