LMFDB - Embedded newform 588.2.n.g.263.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("588.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.3
Character	$\chi$	$=$	588.263
Dual form			588.2.n.g.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04635 - 0.951394i) q^{2} +(0.814407 + 1.52864i) q^{3} +(0.189699 + 1.99098i) q^{4} +(0.301907 - 0.174306i) q^{5} +(0.602184 - 2.37432i) q^{6} +(1.69572 - 2.26374i) q^{8} +(-1.67348 + 2.48987i) q^{9} +(-0.481734 - 0.104847i) q^{10} +(1.95188 - 3.38076i) q^{11} +(-2.88901 + 1.91145i) q^{12} +2.93923 q^{13} +(0.512326 + 0.319551i) q^{15} +(-3.92803 + 0.755373i) q^{16} +(3.38076 + 1.95188i) q^{17} +(4.11990 - 1.01314i) q^{18} +(4.83098 - 2.78917i) q^{19} +(0.404312 + 0.568026i) q^{20} +(-5.25879 + 1.68045i) q^{22} +(-1.09094 - 1.88957i) q^{23} +(4.84146 + 0.748534i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(-3.07547 - 2.79637i) q^{26} +(-5.16901 - 0.530383i) q^{27} +9.75220i q^{29} +(-0.232054 - 0.821786i) q^{30} +(2.28553 + 1.31955i) q^{31} +(4.82875 + 2.94672i) q^{32} +(6.75759 + 0.230411i) q^{33} +(-1.68045 - 5.25879i) q^{34} +(-5.27475 - 2.85955i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(-7.70850 - 1.67772i) q^{38} +(2.39373 + 4.49303i) q^{39} +(0.117365 - 0.979014i) q^{40} +7.57031i q^{41} +2.51757i q^{43} +(7.10130 + 3.24484i) q^{44} +(-0.0712361 + 1.04341i) q^{45} +(-0.656216 + 3.01507i) q^{46} +(2.18189 + 3.77914i) q^{47} +(-4.35371 - 5.38936i) q^{48} +(6.57182 - 2.10003i) q^{50} +(-0.230411 + 6.75759i) q^{51} +(0.557569 + 5.85197i) q^{52} +(1.49119 + 0.860938i) q^{53} +(4.90400 + 5.47273i) q^{54} -1.36090i q^{55} +(8.19802 + 5.11331i) q^{57} +(9.27819 - 10.2042i) q^{58} +(4.12318 - 7.14155i) q^{59} +(-0.539033 + 1.08065i) q^{60} +(-7.04795 - 12.2074i) q^{61} +(-1.13605 - 3.55515i) q^{62} +(-2.24908 - 7.67735i) q^{64} +(0.887375 - 0.512326i) q^{65} +(-6.85160 - 6.67022i) q^{66} +(-0.553478 - 0.319551i) q^{67} +(-3.24484 + 7.10130i) q^{68} +(2.00000 - 3.20654i) q^{69} -11.9341 q^{71} +(2.79868 + 8.01046i) q^{72} +(3.93923 - 6.82295i) q^{73} +(-0.192214 + 0.883151i) q^{74} +(-8.44485 - 0.287941i) q^{75} +(6.46962 + 9.08930i) q^{76} +(1.76996 - 6.97867i) q^{78} +(3.46410 - 2.00000i) q^{79} +(-1.05423 + 0.912731i) q^{80} +(-3.39892 - 8.33351i) q^{81} +(7.20235 - 7.92120i) q^{82} +8.94358 q^{83} +1.36090 q^{85} +(2.39520 - 2.63426i) q^{86} +(-14.9076 + 7.94226i) q^{87} +(-4.34333 - 10.1514i) q^{88} +(9.12760 - 5.26982i) q^{89} +(1.06723 - 1.02400i) q^{90} +(3.55515 - 2.53050i) q^{92} +(-0.155767 + 4.56840i) q^{93} +(1.31243 - 6.03014i) q^{94} +(0.972337 - 1.68414i) q^{95} +(-0.571901 + 9.78125i) q^{96} +2.00000 q^{97} +(5.15121 + 10.5176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} + 2 q^{24} + 12 q^{25} - 20 q^{30} - 16 q^{33} - 64 q^{34} - 40 q^{36} + 16 q^{37} + 20 q^{40} + 24 q^{45} - 92 q^{48}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 4 * q^4 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 + 2 * q^24 + 12 * q^25 - 20 * q^30 - 16 * q^33 - 64 * q^34 - 40 * q^36 + 16 * q^37 + 20 * q^40 + 24 * q^45 - 92 * q^48 - 28 * q^52 + 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 - 16 * q^61 + 40 * q^64 - 12 * q^66 + 48 * q^69 + 32 * q^72 + 24 * q^73 + 120 * q^76 + 40 * q^78 - 28 * q^81 + 8 * q^82 + 80 * q^85 + 56 * q^88 + 160 * q^90 - 24 * q^93 - 34 * q^96 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.04635	−	0.951394i	−0.739882	−	0.672737i
$2$	−1.04635	−	0.951394i	−0.739882	−	0.672737i
$3$	0.814407	+	1.52864i	0.470198	+	0.882561i
$3$	0.814407	+	1.52864i	0.470198	+	0.882561i
$4$	0.189699	+	1.99098i	0.0948493	+	0.995492i
$5$	0.301907	−	0.174306i	0.135017	−	0.0779520i	−0.430970	−	0.902366i	$-0.641829\pi$
$5$	0.301907	−	0.174306i	0.135017	−	0.0779520i	0.565987	+	0.824414i	$0.308495\pi$
$6$	0.602184	−	2.37432i	0.245841	−	0.969310i
$7$		0			0
$7$		0			0
$8$	1.69572	−	2.26374i	0.599527	−	0.800354i
$9$	−1.67348	+	2.48987i	−0.557827	+	0.829957i
$10$	−0.481734	−	0.104847i	−0.152338	−	0.0331556i
$11$	1.95188	−	3.38076i	0.588514	−	1.01934i	−0.405913	−	0.913912i	$-0.633046\pi$
$11$	1.95188	−	3.38076i	0.588514	−	1.01934i	0.994427	−	0.105425i	$-0.0336203\pi$
$12$	−2.88901	+	1.91145i	−0.833984	+	0.551789i
$13$	2.93923			0.815197			0.407599	−	0.913161i	$-0.366366\pi$
$13$	2.93923			0.815197			0.407599	+	0.913161i	$0.366366\pi$
$14$		0			0
$15$	0.512326	+	0.319551i	0.132282	+	0.0825077i
$16$	−3.92803	+	0.755373i	−0.982007	+	0.188843i
$17$	3.38076	+	1.95188i	0.819954	+	0.473401i	0.850401	−	0.526136i	$-0.176360\pi$
$17$	3.38076	+	1.95188i	0.819954	+	0.473401i	−0.0304464	+	0.999536i	$0.509693\pi$
$18$	4.11990	−	1.01314i	0.971069	−	0.238799i
$19$	4.83098	−	2.78917i	1.10830	−	0.639879i	0.169914	−	0.985459i	$-0.445651\pi$
$19$	4.83098	−	2.78917i	1.10830	−	0.639879i	0.938389	+	0.345580i	$0.112318\pi$
$20$	0.404312	+	0.568026i	0.0904068	+	0.127014i
$21$		0			0
$22$	−5.25879	+	1.68045i	−1.12118	+	0.358273i
$23$	−1.09094	−	1.88957i	−0.227477	−	0.394003i	0.729582	−	0.683893i	$-0.239714\pi$
$23$	−1.09094	−	1.88957i	−0.227477	−	0.394003i	−0.957060	+	0.289890i	$0.906381\pi$
$24$	4.84146	+	0.748534i	0.988258	+	0.152794i
$25$	−2.43923	+	4.22488i	−0.487847	+	0.844976i
$26$	−3.07547	−	2.79637i	−0.603149	−	0.548413i
$27$	−5.16901	−	0.530383i	−0.994777	−	0.102072i
$28$		0			0
$29$			9.75220i			1.81094i	0.424412	+	0.905469i	$0.360481\pi$
$29$			9.75220i			1.81094i	−0.424412	+	0.905469i	$0.639519\pi$
$30$	−0.232054	−	0.821786i	−0.0423671	−	0.150037i
$31$	2.28553	+	1.31955i	0.410493	+	0.236998i	0.691002	−	0.722853i	$-0.257170\pi$
$31$	2.28553	+	1.31955i	0.410493	+	0.236998i	−0.280508	+	0.959852i	$0.590503\pi$
$32$	4.82875	+	2.94672i	0.853611	+	0.520911i
$33$	6.75759	+	0.230411i	1.17635	+	0.0401094i
$34$	−1.68045	−	5.25879i	−0.288195	−	0.901874i
$35$		0			0
$36$	−5.27475	−	2.85955i	−0.879125	−	0.476592i
$37$	−0.319551	−	0.553478i	−0.0525338	−	0.0909913i	0.838563	−	0.544805i	$-0.183396\pi$
$37$	−0.319551	−	0.553478i	−0.0525338	−	0.0909913i	−0.891096	+	0.453814i	$0.850063\pi$
$38$	−7.70850	−	1.67772i	−1.25048	−	0.272162i
$39$	2.39373	+	4.49303i	0.383304	+	0.719461i
$40$	0.117365	−	0.979014i	0.0185570	−	0.154796i
$41$			7.57031i			1.18228i	0.806567	+	0.591142i	$0.201323\pi$
$41$			7.57031i			1.18228i	−0.806567	+	0.591142i	$0.798677\pi$
$42$		0			0
$43$			2.51757i			0.383926i	0.981402	+	0.191963i	$0.0614854\pi$
$43$			2.51757i			0.383926i	−0.981402	+	0.191963i	$0.938515\pi$
$44$	7.10130	+	3.24484i	1.07056	+	0.489178i
$45$	−0.0712361	+	1.04341i	−0.0106193	+	0.155542i
$46$	−0.656216	+	3.01507i	−0.0967538	+	0.444548i
$47$	2.18189	+	3.77914i	0.318261	+	0.551244i	0.980125	−	0.198379i	$-0.0635678\pi$
$47$	2.18189	+	3.77914i	0.318261	+	0.551244i	−0.661864	+	0.749624i	$0.730235\pi$
$48$	−4.35371	−	5.38936i	−0.628404	−	0.777887i
$49$		0			0
$50$	6.57182	−	2.10003i	0.929396	−	0.296989i
$51$	−0.230411	+	6.75759i	−0.0322640	+	0.946252i
$52$	0.557569	+	5.85197i	0.0773208	+	0.811522i
$53$	1.49119	+	0.860938i	0.204830	+	0.118259i	0.598907	−	0.800819i	$-0.295602\pi$
$53$	1.49119	+	0.860938i	0.204830	+	0.118259i	−0.394076	+	0.919078i	$0.628935\pi$
$54$	4.90400	+	5.47273i	0.667349	+	0.744745i
$55$		−	1.36090i		−	0.183504i
$56$		0			0
$57$	8.19802	+	5.11331i	1.08585	+	0.677275i
$58$	9.27819	−	10.2042i	1.21829	−	1.33988i
$59$	4.12318	−	7.14155i	0.536792	−	0.929751i	−0.462282	−	0.886733i	$-0.652969\pi$
$59$	4.12318	−	7.14155i	0.536792	−	0.929751i	0.999074	−	0.0430181i	$-0.0136973\pi$
$60$	−0.539033	+	1.08065i	−0.0695888	+	0.139511i
$61$	−7.04795	−	12.2074i	−0.902398	−	1.56300i	−0.824372	−	0.566048i	$-0.808472\pi$
$61$	−7.04795	−	12.2074i	−0.902398	−	1.56300i	−0.0780257	−	0.996951i	$-0.524862\pi$
$62$	−1.13605	−	3.55515i	−0.144279	−	0.451505i
$63$		0			0
$64$	−2.24908	−	7.67735i	−0.281135	−	0.959668i
$65$	0.887375	−	0.512326i	0.110065	−	0.0635462i
$66$	−6.85160	−	6.67022i	−0.843373	−	0.821047i
$67$	−0.553478	−	0.319551i	−0.0676181	−	0.0390393i	0.465810	−	0.884885i	$-0.345763\pi$
$67$	−0.553478	−	0.319551i	−0.0676181	−	0.0390393i	−0.533428	+	0.845846i	$0.679096\pi$
$68$	−3.24484	+	7.10130i	−0.393495	+	0.861159i
$69$	2.00000	−	3.20654i	0.240772	−	0.386022i
$70$		0			0
$71$	−11.9341			−1.41632			−0.708158	−	0.706054i	$-0.750474\pi$
$71$	−11.9341			−1.41632			−0.708158	+	0.706054i	$0.750474\pi$
$72$	2.79868	+	8.01046i	0.329827	+	0.944041i
$73$	3.93923	−	6.82295i	0.461053	−	0.798566i	−0.537961	−	0.842970i	$-0.680805\pi$
$73$	3.93923	−	6.82295i	0.461053	−	0.798566i	0.999014	+	0.0444032i	$0.0141386\pi$
$74$	−0.192214	+	0.883151i	−0.0223444	+	0.102664i
$75$	−8.44485	−	0.287941i	−0.975127	−	0.0332485i
$76$	6.46962	+	9.08930i	0.742116	+	1.04261i
$77$		0			0
$78$	1.76996	−	6.97867i	0.200409	−	0.790179i
$79$	3.46410	−	2.00000i	0.389742	−	0.225018i	−0.292306	−	0.956325i	$-0.594423\pi$
$79$	3.46410	−	2.00000i	0.389742	−	0.225018i	0.682048	+	0.731307i	$0.261089\pi$
$80$	−1.05423	+	0.912731i	−0.117867	+	0.102046i
$81$	−3.39892	−	8.33351i	−0.377657	−	0.925945i
$82$	7.20235	−	7.92120i	0.795367	−	0.874750i
$83$	8.94358			0.981685			0.490843	−	0.871248i	$-0.336689\pi$
$83$	8.94358			0.981685			0.490843	+	0.871248i	$0.336689\pi$
$84$		0			0
$85$	1.36090			0.147610
$86$	2.39520	−	2.63426i	0.258281	−	0.284060i
$87$	−14.9076	+	7.94226i	−1.59826	+	0.851500i
$88$	−4.34333	−	10.1514i	−0.463001	−	1.08214i
$89$	9.12760	−	5.26982i	0.967523	−	0.558600i	0.0690430	−	0.997614i	$-0.478005\pi$
$89$	9.12760	−	5.26982i	0.967523	−	0.558600i	0.898480	+	0.439014i	$0.144672\pi$
$90$	1.06723	−	1.02400i	0.112496	−	0.107939i
$91$		0			0
$92$	3.55515	−	2.53050i	0.370650	−	0.263823i
$93$	−0.155767	+	4.56840i	−0.0161523	+	0.473721i
$94$	1.31243	−	6.03014i	0.135367	−	0.621961i
$95$	0.972337	−	1.68414i	0.0997597	−	0.172789i
$96$	−0.571901	+	9.78125i	−0.0583694	+	0.998295i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	5.15121	+	10.5176i	0.517716	+	1.05706i
$100$	−8.87438	−	4.05502i	−0.887438	−	0.405502i
$101$	2.68047	+	1.54757i	0.266717	+	0.153989i	0.627395	−	0.778701i	$-0.284121\pi$
$101$	2.68047	+	1.54757i	0.266717	+	0.153989i	−0.360678	+	0.932690i	$0.617455\pi$
$102$	6.67022	−	6.85160i	0.660450	−	0.678409i
$103$	−6.26948	+	3.61968i	−0.617750	+	0.356658i	−0.775992	−	0.630742i	$-0.782751\pi$
$103$	−6.26948	+	3.61968i	−0.617750	+	0.356658i	0.158243	+	0.987400i	$0.449417\pi$
$104$	4.98412	−	6.65368i	0.488733	−	0.652447i
$105$		0			0
$106$	−0.741214	−	2.31955i	−0.0719931	−	0.225295i
$107$	−5.50703	−	9.53846i	−0.532385	−	0.922118i	−0.999285	−	0.0378077i	$-0.987963\pi$
$107$	−5.50703	−	9.53846i	−0.532385	−	0.922118i	0.466900	−	0.884310i	$-0.345371\pi$
$108$	0.0754286	−	10.3920i	0.00725812	−	0.999974i
$109$	−0.699867	+	1.21220i	−0.0670351	+	0.116108i	−0.897595	−	0.440821i	$-0.854687\pi$
$109$	−0.699867	+	1.21220i	−0.0670351	+	0.116108i	0.830560	+	0.556929i	$0.188021\pi$
$110$	−1.29475	+	1.42398i	−0.123450	+	0.135771i
$111$	0.585825	−	0.939235i	0.0556040	−	0.0891482i
$112$		0			0
$113$		−	8.83218i		−	0.830862i	−0.909625	−	0.415431i	$-0.863631\pi$
$113$		−	8.83218i		−	0.830862i	0.909625	−	0.415431i	$-0.136369\pi$
$114$	−3.71323	−	13.1499i	−0.347776	−	1.23160i
$115$	−0.658727	−	0.380316i	−0.0614266	−	0.0354646i
$116$	−19.4165	+	1.84998i	−1.80277	+	0.171766i
$117$	−4.91876	+	7.31832i	−0.454739	+	0.676579i
$118$	−11.1087	+	3.54980i	−1.02264	+	0.326786i
$119$		0			0
$120$	1.59214	−	0.617907i	0.145342	−	0.0564069i
$121$	−2.11968	−	3.67140i	−0.192699	−	0.333764i
$122$	−4.23943	+	19.4786i	−0.383820	+	1.76351i
$123$	−11.5723	+	6.16532i	−1.04344	+	0.555908i
$124$	−2.19364	+	4.80077i	−0.196995	+	0.431122i
$125$			3.44375i			0.308019i
$126$		0			0
$127$		−	12.3960i		−	1.09997i	−0.835174	−	0.549985i	$-0.814633\pi$
$127$		−	12.3960i		−	1.09997i	0.835174	−	0.549985i	$-0.185367\pi$
$128$	−4.95086	+	10.1730i	−0.437598	+	0.899171i
$129$	−3.84846	+	2.05033i	−0.338838	+	0.180521i
$130$	−1.41593	−	0.308171i	−0.124185	−	0.0270283i
$131$	0.805238	+	1.39471i	0.0703540	+	0.121857i	0.899056	−	0.437833i	$-0.144254\pi$
$131$	0.805238	+	1.39471i	0.0703540	+	0.121857i	−0.828702	+	0.559689i	$0.810920\pi$
$132$	0.823160	+	13.4980i	0.0716469	+	1.17485i
$133$		0			0
$134$	0.275113	+	0.860938i	0.0237662	+	0.0743737i
$135$	−1.65301	+	0.740864i	−0.142268	+	0.0637634i
$136$	10.1514	−	4.34333i	0.870473	−	0.372437i
$137$	−3.77914	−	2.18189i	−0.322874	−	0.186411i	0.329799	−	0.944051i	$-0.393019\pi$
$137$	−3.77914	−	2.18189i	−0.322874	−	0.186411i	−0.652673	+	0.757640i	$0.726352\pi$
$138$	−5.14338	+	1.45238i	−0.437834	+	0.123634i
$139$			16.8177i			1.42646i	0.700931	+	0.713230i	$0.252768\pi$
$139$			16.8177i			1.42646i	−0.700931	+	0.713230i	$0.747232\pi$
$140$		0			0
$141$	−4.00000	+	6.41308i	−0.336861	+	0.540079i
$142$	12.4872	+	11.3540i	1.04791	+	0.952808i
$143$	5.73704	−	9.93684i	0.479755	−	0.830961i
$144$	4.69270	−	11.0444i	0.391059	−	0.920366i
$145$	1.69987	+	2.94426i	0.141166	+	0.244507i
$146$	−10.6131	+	3.39144i	−0.878350	+	0.280677i
$147$		0			0
$148$	1.04135	−	0.741214i	0.0855982	−	0.0609274i
$149$	−6.63421	+	3.83026i	−0.543496	+	0.313788i	−0.746495	−	0.665391i	$-0.768265\pi$
$149$	−6.63421	+	3.83026i	−0.543496	+	0.313788i	0.202999	+	0.979179i	$0.434931\pi$
$150$	8.56233	+	8.33567i	0.699111	+	0.680604i
$151$	−10.9458	−	6.31955i	−0.890755	−	0.514278i	−0.0165658	−	0.999863i	$-0.505273\pi$
$151$	−10.9458	−	6.31955i	−0.890755	−	0.514278i	−0.874189	+	0.485585i	$0.838607\pi$
$152$	1.87802	−	15.6658i	0.152328	−	1.27066i
$153$	−10.5176	+	5.15121i	−0.850295	+	0.416451i
$154$		0			0
$155$	0.920022			0.0738980
$156$	−8.49147	+	5.61821i	−0.679861	+	0.449816i
$157$	0.108719	−	0.188307i	0.00867672	−	0.0150285i	−0.861654	−	0.507495i	$-0.830571\pi$
$157$	0.108719	−	0.188307i	0.00867672	−	0.0150285i	0.870331	+	0.492467i	$0.163905\pi$
$158$	−5.52745	−	1.20302i	−0.439741	−	0.0957075i
$159$	−0.101630	+	2.98064i	−0.00805978	+	0.236381i
$160$	1.97146	+	0.0479539i	0.155858	+	0.00379109i
$161$		0			0
$162$	−4.37199	+	11.9535i	−0.343496	+	0.939154i
$163$	−4.53743	+	2.61968i	−0.355399	+	0.205189i	−0.667060	−	0.745004i	$-0.732448\pi$
$163$	−4.53743	+	2.61968i	−0.355399	+	0.205189i	0.311662	+	0.950193i	$0.399114\pi$
$164$	−15.0724	+	1.43608i	−1.17695	+	0.112139i
$165$	2.08032	−	1.10833i	0.161953	−	0.0862830i
$166$	−9.35812	−	8.50887i	−0.726331	−	0.660416i
$167$	−11.4741			−0.887891			−0.443945	−	0.896054i	$-0.646422\pi$
$167$	−11.4741			−0.887891			−0.443945	+	0.896054i	$0.646422\pi$
$168$		0			0
$169$	−4.36090			−0.335454
$170$	−1.42398	−	1.29475i	−0.109214	−	0.0993028i
$171$	−1.13989	+	16.6961i	−0.0871695	+	1.27679i
$172$	−5.01244	+	0.477580i	−0.382195	+	0.0364151i
$173$	−18.3642	+	10.6025i	−1.39620	+	0.806097i	−0.993992	−	0.109451i	$-0.965091\pi$
$173$	−18.3642	+	10.6025i	−1.39620	+	0.806097i	−0.402208	+	0.915548i	$0.631757\pi$
$174$	23.1548	+	5.87262i	1.75536	+	0.445202i
$175$		0			0
$176$	−5.11331	+	14.7541i	−0.385430	+	1.11213i
$177$	14.2748	+	0.486723i	1.07296	+	0.0365843i
$178$	−14.5643	−	3.16986i	−1.09164	−	0.237591i
$179$	0.906046	−	1.56932i	0.0677211	−	0.117296i	−0.830177	−	0.557500i	$-0.811761\pi$
$179$	0.906046	−	1.56932i	0.0677211	−	0.117296i	0.897898	+	0.440204i	$0.145094\pi$
$180$	−2.09092	+	0.0561028i	−0.155848	+	0.00418166i
$181$	−7.53950			−0.560407			−0.280203	−	0.959941i	$-0.590402\pi$
$181$	−7.53950			−0.560407			−0.280203	+	0.959941i	$0.590402\pi$
$182$		0			0
$183$	12.9208	−	20.7156i	0.955136	−	1.53134i
$184$	−6.12744	−	0.734561i	−0.451721	−	0.0541526i
$185$	−0.192949	−	0.111399i	−0.0141859	−	0.00819023i
$186$	4.50934	−	4.63195i	0.330641	−	0.339631i
$187$	13.1977	−	7.61968i	0.965110	−	0.557206i
$188$	−7.11030	+	5.06100i	−0.518572	+	0.369111i
$189$		0			0
$190$	−2.61968	+	0.837122i	−0.190052	+	0.0607312i
$191$	0.815830	+	1.41306i	0.0590314	+	0.102245i	0.894031	−	0.448005i	$-0.147865\pi$
$191$	0.815830	+	1.41306i	0.0590314	+	0.102245i	−0.834999	+	0.550251i	$0.814532\pi$
$192$	9.90424	−	9.69052i	0.714777	−	0.699353i
$193$	7.57834	−	13.1261i	0.545501	−	0.944835i	−0.453075	−	0.891473i	$-0.649673\pi$
$193$	7.57834	−	13.1261i	0.545501	−	0.944835i	0.998575	−	0.0533622i	$-0.0169938\pi$
$194$	−2.09270	−	1.90279i	−0.150247	−	0.136612i
$195$	1.50585	+	0.939235i	0.107836	+	0.0672600i
$196$		0			0
$197$		−	21.2263i		−	1.51231i	−0.654393	−	0.756155i	$-0.727076\pi$
$197$		−	21.2263i		−	1.51231i	0.654393	−	0.756155i	$-0.272924\pi$
$198$	4.61638	−	15.9059i	0.328072	−	1.13038i
$199$	−3.25361	−	1.87847i	−0.230642	−	0.133161i	0.380226	−	0.924894i	$-0.375846\pi$
$199$	−3.25361	−	1.87847i	−0.230642	−	0.133161i	−0.610868	+	0.791732i	$0.709179\pi$
$200$	5.42779	+	12.6860i	0.383803	+	0.897036i
$201$	0.0377216	−	1.10631i	0.00266067	−	0.0780333i
$202$	−1.33236	−	4.16948i	−0.0937447	−	0.293364i
$203$		0			0
$204$	−13.4980	+	0.823160i	−0.945046	+	0.0576328i
$205$	1.31955	+	2.28553i	0.0921614	+	0.159628i
$206$	10.0038	+	2.17729i	0.696999	+	0.151699i
$207$	6.53046	+	0.445852i	0.453898	+	0.0309888i
$208$	−11.5454	+	2.22022i	−0.800529	+	0.153945i
$209$		−	21.7765i		−	1.50631i
$210$		0			0
$211$			9.83963i			0.677388i	0.940897	+	0.338694i	$0.109985\pi$
$211$			9.83963i			0.677388i	−0.940897	+	0.338694i	$0.890015\pi$
$212$	−1.43124	+	3.13225i	−0.0982978	+	0.215124i
$213$	−9.71921	−	18.2429i	−0.665949	−	1.24998i
$214$	−3.31255	+	15.2199i	−0.226441	+	1.04041i
$215$	0.438828	+	0.760072i	0.0299278	+	0.0518365i
$216$	−9.96584	+	10.8019i	−0.678090	+	0.734979i
$217$		0			0
$218$	1.88559	−	0.602542i	0.127708	−	0.0408093i
$219$	13.6380	+	0.465009i	0.921570	+	0.0314224i
$220$	2.70953	−	0.258160i	0.182676	−	0.0174052i
$221$	9.93684	+	5.73704i	0.668424	+	0.385915i
$222$	−1.50656	+	0.425419i	−0.101114	+	0.0285522i
$223$		−	22.9136i		−	1.53441i	−0.641403	−	0.767204i	$-0.721647\pi$
$223$		−	22.9136i		−	1.53441i	0.641403	−	0.767204i	$-0.278353\pi$
$224$		0			0
$225$	−6.43739	−	13.1436i	−0.429159	−	0.876243i
$226$	−8.40288	+	9.24155i	−0.558951	+	0.614739i
$227$	6.76508	−	11.7175i	0.449014	−	0.777715i	−0.549308	−	0.835620i	$-0.685109\pi$
$227$	6.76508	−	11.7175i	0.449014	−	0.777715i	0.998322	+	0.0579050i	$0.0184421\pi$
$228$	−8.62537	+	17.2921i	−0.571229	+	1.14520i
$229$	7.34809	+	12.7273i	0.485575	+	0.841041i	0.999863	−	0.0165769i	$-0.00527684\pi$
$229$	7.34809	+	12.7273i	0.485575	+	0.841041i	−0.514287	+	0.857618i	$0.671944\pi$
$230$	0.327428	+	1.02465i	0.0215900	+	0.0675636i
$231$		0			0
$232$	22.0765	+	16.5370i	1.44939	+	1.08571i
$233$	14.8869	−	8.59497i	0.975274	−	0.563075i	0.0744343	−	0.997226i	$-0.476285\pi$
$233$	14.8869	−	8.59497i	0.975274	−	0.563075i	0.900840	+	0.434151i	$0.142952\pi$
$234$	12.1093	−	2.97785i	0.791613	−	0.194668i
$235$	1.31745	+	0.760632i	0.0859412	+	0.0496182i
$236$	15.0009	+	6.85443i	0.976474	+	0.446186i
$237$	5.87847	+	3.66655i	0.381848	+	0.238168i
$238$		0			0
$239$	−14.5336			−0.940102			−0.470051	−	0.882639i	$-0.655764\pi$
$239$	−14.5336			−0.940102			−0.470051	+	0.882639i	$0.655764\pi$
$240$	−2.25381	−	0.868207i	−0.145483	−	0.0560425i
$241$	−9.39604	+	16.2744i	−0.605252	+	1.04833i	0.386759	+	0.922181i	$0.373594\pi$
$241$	−9.39604	+	16.2744i	−0.605252	+	1.04833i	−0.992012	+	0.126147i	$0.959739\pi$
$242$	−1.27502	+	5.85823i	−0.0819612	+	0.376581i
$243$	9.97083	−	11.9826i	0.639629	−	0.768684i
$244$	22.9678	−	16.3481i	1.47036	−	1.04658i
$245$		0			0
$246$	17.9743	+	4.55872i	1.14600	+	0.290653i
$247$	14.1994	−	8.19802i	0.903485	−	0.521628i
$248$	6.86274	−	2.93627i	0.435784	−	0.186453i
$249$	7.28371	+	13.6715i	0.461587	+	0.866397i
$250$	3.27637	−	3.60337i	0.207216	−	0.227897i
$251$	20.6405			1.30281			0.651407	−	0.758729i	$-0.274179\pi$
$251$	20.6405			1.30281			0.651407	+	0.758729i	$0.274179\pi$
$252$		0			0
$253$	−8.51757			−0.535495
$254$	−11.7935	+	12.9706i	−0.739991	+	0.813848i
$255$	1.10833	+	2.08032i	0.0694060	+	0.130275i
$256$	14.8588	−	5.93426i	0.928676	−	0.370891i
$257$	−4.17752	+	2.41189i	−0.260587	+	0.150450i	−0.624602	−	0.780943i	$-0.714739\pi$
$257$	−4.17752	+	2.41189i	−0.260587	+	0.150450i	0.364016	+	0.931393i	$0.381406\pi$
$258$	5.97751	+	1.51604i	0.372143	+	0.0943846i
$259$		0			0
$260$	1.18837	+	1.66956i	0.0736994	+	0.103542i
$261$	−24.2817	−	16.3201i	−1.50300	−	1.01019i
$262$	0.484361	−	2.22546i	0.0299239	−	0.137489i
$263$	7.22891	−	12.5208i	0.445754	−	0.772068i	−0.552351	−	0.833612i	$-0.686269\pi$
$263$	7.22891	−	12.5208i	0.445754	−	0.772068i	0.998104	+	0.0615439i	$0.0196024\pi$
$264$	11.9806	−	14.9067i	0.737353	−	0.917447i
$265$	0.600267			0.0368741
$266$		0			0
$267$	15.4892	+	9.66103i	0.947926	+	0.591246i
$268$	0.531226	−	1.16258i	0.0324498	−	0.0710161i
$269$	−4.08105	−	2.35619i	−0.248826	−	0.143660i	0.370401	−	0.928872i	$-0.379220\pi$
$269$	−4.08105	−	2.35619i	−0.248826	−	0.143660i	−0.619226	+	0.785212i	$0.712554\pi$
$270$	2.43448	+	0.797460i	0.148158	+	0.0485319i
$271$	−13.5743	+	7.83712i	−0.824580	+	0.476071i	−0.851993	−	0.523553i	$-0.824606\pi$
$271$	−13.5743	+	7.83712i	−0.824580	+	0.476071i	0.0274135	+	0.999624i	$0.491273\pi$
$272$	−14.7541	−	5.11331i	−0.894600	−	0.310040i
$273$		0			0
$274$	1.87847	+	5.87847i	0.113483	+	0.355131i
$275$	9.52220	+	16.4929i	0.574210	+	0.994561i
$276$	6.76356	+	3.37369i	0.407119	+	0.203072i
$277$	−8.49815	+	14.7192i	−0.510605	+	0.884393i	0.489320	+	0.872104i	$0.337245\pi$
$277$	−8.49815	+	14.7192i	−0.510605	+	0.884393i	−0.999924	+	0.0122887i	$0.996088\pi$
$278$	16.0003	−	17.5972i	0.959632	−	1.05541i
$279$	−7.11030	+	3.48243i	−0.425683	+	0.208488i
$280$		0			0
$281$		−	5.75822i		−	0.343507i	−0.985140	−	0.171753i	$-0.945057\pi$
$281$		−	5.75822i		−	0.343507i	0.985140	−	0.171753i	$-0.0549432\pi$
$282$	10.2868	−	2.90475i	0.612568	−	0.172975i
$283$	4.83098	+	2.78917i	0.287172	+	0.165799i	0.636666	−	0.771140i	$-0.280313\pi$
$283$	4.83098	+	2.78917i	0.287172	+	0.165799i	−0.349494	+	0.936939i	$0.613646\pi$
$284$	−2.26388	−	23.7606i	−0.134337	−	1.40993i
$285$	3.36632	+	0.114780i	0.199404	+	0.00679899i
$286$	−15.4568	+	4.93923i	−0.913980	+	0.292063i
$287$		0			0
$288$	−15.4178	+	7.09169i	−0.908501	+	0.417882i
$289$	−0.880316	−	1.52475i	−0.0517833	−	0.0896913i
$290$	1.02249	−	4.69797i	0.0600427	−	0.275874i
$291$	1.62881	+	3.05728i	0.0954828	+	0.179221i
$292$	14.3317	+	6.54865i	0.838697	+	0.383231i
$293$		−	23.7712i		−	1.38873i	−0.719624	−	0.694364i	$-0.755686\pi$
$293$		−	23.7712i		−	1.38873i	0.719624	−	0.694364i	$-0.244314\pi$
$294$		0			0
$295$		−	2.87478i		−	0.167376i
$296$	−1.79480	−	0.215162i	−0.104321	−	0.0125060i
$297$	−11.8824	+	16.4399i	−0.689487	+	0.953942i
$298$	10.5858	+	2.30395i	0.613219	+	0.133464i
$299$	−3.20654	−	5.55389i	−0.185439	−	0.321190i
$300$	−1.02869	−	16.8682i	−0.0593915	−	0.973885i
$301$		0			0
$302$	5.44074	+	17.0262i	0.313080	+	0.979749i
$303$	−0.182684	+	5.35783i	−0.0104949	+	0.307799i
$304$	−16.8694	+	14.6051i	−0.967525	+	0.837662i
$305$	−4.25565	−	2.45700i	−0.243678	−	0.140687i
$306$	15.9059	+	4.61638i	0.909280	+	0.263901i
$307$		−	3.69987i		−	0.211163i	−0.994411	−	0.105581i	$-0.966330\pi$
$307$		−	3.69987i		−	0.211163i	0.994411	−	0.105581i	$-0.0336703\pi$
$308$		0			0
$309$	−10.6391	−	6.63588i	−0.605237	−	0.377502i
$310$	−0.962666	−	0.875304i	−0.0546757	−	0.0497139i
$311$	3.79236	−	6.56857i	0.215045	−	0.372469i	−0.738241	−	0.674537i	$-0.764343\pi$
$311$	3.79236	−	6.56857i	0.215045	−	0.372469i	0.953287	+	0.302067i	$0.0976768\pi$
$312$	14.2302	+	2.20012i	0.805625	+	0.124557i
$313$	7.81770	+	13.5407i	0.441883	+	0.765363i	0.997829	−	0.0658547i	$-0.0209774\pi$
$313$	7.81770	+	13.5407i	0.441883	+	0.765363i	−0.555946	+	0.831218i	$0.687644\pi$
$314$	−0.292912	+	0.0936004i	−0.0165300	+	0.00528217i
$315$		0			0
$316$	4.63910	+	6.51757i	0.260970	+	0.366642i
$317$	12.0318	−	6.94659i	0.675776	−	0.390159i	−0.122486	−	0.992470i	$-0.539087\pi$
$317$	12.0318	−	6.94659i	0.675776	−	0.390159i	0.798262	+	0.602311i	$0.205753\pi$
$318$	2.94211	−	3.02211i	0.164985	−	0.169471i
$319$	32.9698	+	19.0351i	1.84596	+	1.06576i
$320$	−2.01722	−	1.92582i	−0.112766	−	0.107656i
$321$	10.0959	−	16.1865i	0.563499	−	0.903440i
$322$		0			0
$323$	21.7765			1.21168
$324$	15.9471	−	8.34804i	0.885950	−	0.463780i
$325$	−7.16948	+	12.4179i	−0.397691	+	0.688822i
$326$	7.24009	+	1.57577i	0.400991	+	0.0872740i
$327$	−2.42300	−	0.0826162i	−0.133992	−	0.00456868i
$328$	17.1373	+	12.8371i	0.946247	+	0.708811i
$329$		0			0
$330$	−3.23120	−	0.819511i	−0.177872	−	0.0451126i
$331$	−27.5359	+	15.8979i	−1.51351	+	0.873827i	−0.513638	+	0.858007i	$0.671702\pi$
$331$	−27.5359	+	15.8979i	−1.51351	+	0.873827i	−0.999875	+	0.0158198i	$0.994964\pi$
$332$	1.69658	+	17.8065i	0.0931121	+	0.977259i
$333$	1.91285	+	0.130595i	0.104824	+	0.00715658i
$334$	12.0059	+	10.9164i	0.656934	+	0.597317i
$335$	−0.222798			−0.0121728
$336$		0			0
$337$	−17.1178			−0.932468			−0.466234	−	0.884661i	$-0.654390\pi$
$337$	−17.1178			−0.932468			−0.466234	+	0.884661i	$0.654390\pi$
$338$	4.56303	+	4.14893i	0.248196	+	0.225672i
$339$	13.5012	−	7.19299i	0.733286	−	0.390670i
$340$	0.258160	+	2.70953i	0.0140007	+	0.146945i
$341$	8.92216	−	5.15121i	0.483162	−	0.278954i
$342$	17.0773	−	16.3855i	0.923437	−	0.886028i
$343$		0			0
$344$	5.69914	+	4.26909i	0.307277	+	0.230174i
$345$	0.0448946	−	1.31669i	0.00241704	−	0.0708881i
$346$	29.3025	+	6.37756i	1.57531	+	0.342860i
$347$	−4.22398	+	7.31616i	−0.226755	+	0.392752i	−0.956845	−	0.290600i	$-0.906145\pi$
$347$	−4.22398	+	7.31616i	−0.226755	+	0.392752i	0.730089	+	0.683352i	$0.239478\pi$
$348$	−18.6409	−	28.1742i	−0.999255	−	1.51029i
$349$	−17.4956			−0.936520			−0.468260	−	0.883591i	$-0.655119\pi$
$349$	−17.4956			−0.936520			−0.468260	+	0.883591i	$0.655119\pi$
$350$		0			0
$351$	−15.1929	−	1.55892i	−0.810939	−	0.0832089i
$352$	19.3873	−	10.5732i	1.03335	−	0.563553i
$353$	7.15990	+	4.13377i	0.381083	+	0.220018i	0.678289	−	0.734795i	$-0.262722\pi$
$353$	7.15990	+	4.13377i	0.381083	+	0.220018i	−0.297206	+	0.954813i	$0.596055\pi$
$354$	−14.4734	−	14.0903i	−0.769252	−	0.748888i
$355$	−3.60298	+	2.08018i	−0.191226	+	0.110405i
$356$	12.2236	+	17.1732i	0.647850	+	0.910179i
$357$		0			0
$358$	−2.44108	+	0.780049i	−0.129015	+	0.0412269i
$359$	−12.5650	−	21.7633i	−0.663156	−	1.14862i	−0.979782	−	0.200070i	$-0.935883\pi$
$359$	−12.5650	−	21.7633i	−0.663156	−	1.14862i	0.316625	−	0.948551i	$-0.397450\pi$
$360$	2.24121	+	1.93058i	0.118122	+	0.101751i
$361$	6.05892	−	10.4944i	0.318890	−	0.552334i
$362$	7.88896	+	7.17304i	0.414635	+	0.377006i
$363$	3.88596	−	6.23025i	0.203960	−	0.327003i
$364$		0			0
$365$		−	2.74653i		−	0.143760i
$366$	−33.2284	+	9.38296i	−1.73688	+	0.490455i
$367$	−18.8041	−	10.8565i	−0.981565	−	0.566707i	−0.0788227	−	0.996889i	$-0.525116\pi$
$367$	−18.8041	−	10.8565i	−0.981565	−	0.566707i	−0.902742	+	0.430182i	$0.858449\pi$
$368$	5.71259	+	6.59822i	0.297789	+	0.343956i
$369$	−18.8491	−	12.6688i	−0.981245	−	0.659510i
$370$	0.0959078	+	0.300133i	0.00498601	+	0.0156032i
$371$		0			0
$372$	−9.12516	+	0.556490i	−0.473118	+	0.0288526i
$373$	0.360898	+	0.625094i	0.0186866	+	0.0323662i	0.875217	−	0.483730i	$-0.160718\pi$
$373$	0.360898	+	0.625094i	0.0186866	+	0.0323662i	−0.856531	+	0.516096i	$0.827385\pi$
$374$	−21.0587	−	4.58333i	−1.08892	−	0.236999i
$375$	−5.26426	+	2.80462i	−0.271845	+	0.144830i
$376$	12.2549	+	1.46912i	0.631997	+	0.0757642i
$377$			28.6640i			1.47627i
$378$		0			0
$379$			18.2745i			0.938699i	0.883013	+	0.469349i	$0.155511\pi$
$379$			18.2745i			0.938699i	−0.883013	+	0.469349i	$0.844489\pi$
$380$	3.53754	+	1.61643i	0.181472	+	0.0829210i
$381$	18.9491	−	10.0954i	0.970791	−	0.517204i
$382$	0.490732	−	2.25473i	0.0251080	−	0.115362i
$383$	−1.02465	−	1.77475i	−0.0523573	−	0.0906855i	0.838659	−	0.544657i	$-0.183340\pi$
$383$	−1.02465	−	1.77475i	−0.0523573	−	0.0906855i	−0.891016	+	0.453971i	$0.850007\pi$
$384$	−19.5828	+	0.716843i	−0.999331	+	0.0365813i
$385$		0			0
$386$	−20.4177	+	6.52448i	−1.03923	+	0.332087i
$387$	−6.26843	−	4.21311i	−0.318642	−	0.214164i
$388$	0.379397	+	3.98197i	0.0192610	+	0.202154i
$389$	9.65328	+	5.57332i	0.489441	+	0.282579i	0.724342	−	0.689440i	$-0.242143\pi$
$389$	9.65328	+	5.57332i	0.489441	+	0.282579i	−0.234902	+	0.972019i	$0.575477\pi$
$390$	−0.682061	−	2.41542i	−0.0345375	−	0.122310i
$391$		−	8.51757i		−	0.430752i
$392$		0			0
$393$	−1.47622	+	2.36678i	−0.0744656	+	0.119389i
$394$	−20.1946	+	22.2101i	−1.01739	+	1.11893i
$395$	0.697224	−	1.20763i	0.0350811	−	0.0607623i
$396$	−19.9631	+	12.2511i	−1.00319	+	0.615643i
$397$	3.98719	+	6.90601i	0.200111	+	0.346603i	0.948564	−	0.316585i	$-0.102536\pi$
$397$	3.98719	+	6.90601i	0.200111	+	0.346603i	−0.748453	+	0.663188i	$0.769203\pi$
$398$	1.61725	+	5.06100i	0.0810652	+	0.253685i
$399$		0			0
$400$	6.39002	−	18.4380i	0.319501	−	0.921899i
$401$	−18.6004	+	10.7390i	−0.928860	+	0.536278i	−0.886451	−	0.462823i	$-0.846837\pi$
$401$	−18.6004	+	10.7390i	−0.928860	+	0.536278i	−0.0424093	+	0.999100i	$0.513503\pi$
$402$	−1.09201	+	1.12170i	−0.0544645	+	0.0559455i
$403$	6.71771	+	3.87847i	0.334633	+	0.193200i
$404$	−2.57271	+	5.63034i	−0.127997	+	0.280120i
$405$	−2.47874	−	1.92349i	−0.123169	−	0.0955790i
$406$		0			0
$407$	−2.49490			−0.123668
$408$	14.9067	+	11.9806i	0.737994	+	0.593126i
$409$	18.4568	−	31.9681i	0.912630	−	1.58072i	0.102296	−	0.994754i	$-0.467381\pi$
$409$	18.4568	−	31.9681i	0.912630	−	1.58072i	0.810334	−	0.585968i	$-0.199286\pi$
$410$	0.793726	−	3.64688i	0.0391993	−	0.180106i
$411$	0.257562	−	7.55389i	0.0127046	−	0.372606i
$412$	−8.39604	−	11.7958i	−0.413643	−	0.581136i
$413$		0			0
$414$	−6.40897	−	6.67956i	−0.314984	−	0.328282i
$415$	2.70013	−	1.55892i	0.132544	−	0.0765243i
$416$	14.1928	+	8.66110i	0.695861	+	0.424645i
$417$	−25.7082	+	13.6965i	−1.25894	+	0.670719i
$418$	−20.7180	+	22.7859i	−1.01335	+	1.11449i
$419$	−29.5773			−1.44494			−0.722472	−	0.691400i	$-0.756994\pi$
$419$	−29.5773			−1.44494			−0.722472	+	0.691400i	$0.756994\pi$
$420$		0			0
$421$	36.8309			1.79503			0.897515	−	0.440985i	$-0.145371\pi$
$421$	36.8309			1.79503			0.897515	+	0.440985i	$0.145371\pi$
$422$	9.36137	−	10.2957i	0.455704	−	0.501187i
$423$	−13.0609	−	0.891703i	−0.635044	−	0.0433561i
$424$	4.47758	−	1.91576i	0.217450	−	0.0930376i
$425$	−16.4929	+	9.52220i	−0.800024	+	0.461894i
$426$	−7.18652	+	28.3353i	−0.348188	+	1.37285i
$427$		0			0
$428$	17.9462	−	12.7738i	0.867464	−	0.617447i
$429$	19.8621	+	0.677232i	0.958953	+	0.0326971i
$430$	0.263960	−	1.21280i	0.0127293	−	0.0584864i
$431$	2.33839	−	4.05022i	0.112636	−	0.195092i	−0.804196	−	0.594364i	$-0.797404\pi$
$431$	2.33839	−	4.05022i	0.112636	−	0.195092i	0.916832	+	0.399272i	$0.130737\pi$
$432$	20.7047	−	1.82118i	0.996154	−	0.0876214i
$433$	16.5564			0.795650			0.397825	−	0.917461i	$-0.369765\pi$
$433$	16.5564			0.795650			0.397825	+	0.917461i	$0.369765\pi$
$434$		0			0
$435$	−3.11632	+	4.99631i	−0.149416	+	0.239555i
$436$	−2.54624	−	1.16347i	−0.121943	−	0.0557201i
$437$	−10.5407	−	6.08565i	−0.504228	−	0.291116i
$438$	−13.8277	−	13.4617i	−0.660713	−	0.643223i
$439$	−22.9313	+	13.2394i	−1.09445	+	0.631881i	−0.934758	−	0.355286i	$-0.884383\pi$
$439$	−22.9313	+	13.2394i	−1.09445	+	0.631881i	−0.159692	+	0.987167i	$0.551050\pi$
$440$	−3.08073	−	2.30770i	−0.146868	−	0.110015i
$441$		0			0
$442$	−4.93923	−	15.4568i	−0.234935	−	0.735205i
$443$	−2.30049	−	3.98457i	−0.109300	−	0.189313i	0.806187	−	0.591661i	$-0.201528\pi$
$443$	−2.30049	−	3.98457i	−0.109300	−	0.189313i	−0.915487	+	0.402348i	$0.868194\pi$
$444$	1.98113	+	0.988196i	0.0940203	+	0.0468977i
$445$	1.83712	−	3.18199i	0.0870879	−	0.150841i
$446$	−21.7999	+	23.9757i	−1.03225	+	1.13528i
$447$	−11.2580	−	7.02193i	−0.532487	−	0.332126i
$448$		0			0
$449$			17.0095i			0.802728i	0.915919	+	0.401364i	$0.131464\pi$
$449$			17.0095i			0.802728i	−0.915919	+	0.401364i	$0.868536\pi$
$450$	−5.76902	+	19.8773i	−0.271954	+	0.937027i
$451$	25.5934	+	14.7764i	1.20515	+	0.695791i
$452$	17.5847	−	1.67545i	0.827116	−	0.0788066i
$453$	0.745995	−	21.8789i	0.0350499	−	1.02796i
$454$	−18.2266	+	5.82431i	−0.855415	+	0.273348i
$455$		0			0
$456$	25.4768	−	9.88748i	1.19306	−	0.463024i
$457$	7.71559	+	13.3638i	0.360920	+	0.625132i	0.988113	−	0.153732i	$-0.0491293\pi$
$457$	7.71559	+	13.3638i	0.360920	+	0.625132i	−0.627192	+	0.778864i	$0.715796\pi$
$458$	4.41997	−	20.3081i	0.206531	−	0.948935i
$459$	−16.4399	−	11.8824i	−0.767351	−	0.554623i
$460$	0.632243	−	1.38366i	0.0294785	−	0.0645134i
$461$			33.3764i			1.55449i	0.629196	+	0.777247i	$0.283384\pi$
$461$			33.3764i			1.55449i	−0.629196	+	0.777247i	$0.716616\pi$
$462$		0			0
$463$		−	26.4787i		−	1.23057i	−0.788304	−	0.615286i	$-0.789041\pi$
$463$		−	26.4787i		−	1.23057i	0.788304	−	0.615286i	$-0.210959\pi$
$464$	−7.36655	−	38.3069i	−0.341984	−	1.77835i
$465$	0.749273	+	1.40638i	0.0347467	+	0.0652195i
$466$	−23.7541	−	5.16998i	−1.10039	−	0.239495i
$467$	−9.29557	−	16.1004i	−0.430148	−	0.745038i	0.566738	−	0.823898i	$-0.308205\pi$
$467$	−9.29557	−	16.1004i	−0.430148	−	0.745038i	−0.996886	+	0.0788602i	$0.974872\pi$
$468$	−15.5037	−	8.40489i	−0.716660	−	0.388516i
$469$		0			0
$470$	−0.654857	−	2.04930i	−0.0302063	−	0.0945274i
$471$	0.376395	+	0.0128338i	0.0173434	+	0.000591350i
$472$	−9.17490	−	21.4439i	−0.422309	−	0.987035i
$473$	8.51130	+	4.91400i	0.391350	+	0.225946i
$474$	−2.66260	−	9.42924i	−0.122297	−	0.433099i
$475$			27.2137i			1.24865i
$476$		0			0
$477$	−4.63910	+	2.27210i	−0.212410	+	0.104032i
$478$	15.2073	+	13.8272i	0.695564	+	0.632441i
$479$	−20.4388	+	35.4011i	−0.933874	+	1.61752i	−0.157245	+	0.987560i	$0.550261\pi$
$479$	−20.4388	+	35.4011i	−0.933874	+	1.61752i	−0.776629	+	0.629958i	$0.783072\pi$
$480$	1.53227	+	3.05271i	0.0699382	+	0.139337i
$481$	−0.939235	−	1.62680i	−0.0428254	−	0.0741758i
$482$	25.3149	−	8.08941i	1.15306	−	0.368462i
$483$		0			0
$484$	6.90760	−	4.91671i	0.313982	−	0.223487i
$485$	0.603814	−	0.348612i	0.0274178	−	0.0158297i
$486$	−21.8332	+	3.05180i	−0.990372	+	0.138432i
$487$	−18.5599	−	10.7156i	−0.841032	−	0.485570i	0.0165831	−	0.999862i	$-0.494721\pi$
$487$	−18.5599	−	10.7156i	−0.841032	−	0.485570i	−0.857615	+	0.514293i	$0.828055\pi$
$488$	−39.5858	−	4.74557i	−1.79197	−	0.214822i
$489$	−7.69987	−	4.80260i	−0.348200	−	0.217181i
$490$		0			0
$491$	−1.63166			−0.0736358			−0.0368179	−	0.999322i	$-0.511722\pi$
$491$	−1.63166			−0.0736358			−0.0368179	+	0.999322i	$0.511722\pi$
$492$	−14.4703	−	21.8707i	−0.652371	−	0.986006i
$493$	−19.0351	+	32.9698i	−0.857300	+	1.48489i
$494$	−22.6571	−	4.93121i	−1.01939	−	0.221866i
$495$	3.38846	+	2.27744i	0.152300	+	0.102363i
$496$	−9.97438	−	3.45681i	−0.447863	−	0.155215i
$497$		0			0
$498$	5.38568	−	21.2349i	0.241338	−	0.951558i
$499$	7.69218	−	4.44108i	0.344349	−	0.198810i	−0.317844	−	0.948143i	$-0.602959\pi$
$499$	7.69218	−	4.44108i	0.344349	−	0.198810i	0.662194	+	0.749333i	$0.269626\pi$
$500$	−6.85645	+	0.653275i	−0.306630	+	0.0292153i
$501$	−9.34457	−	17.5397i	−0.417485	−	0.783618i
$502$	−21.5971	−	19.6372i	−0.963928	−	0.876451i
$503$	34.8967			1.55597			0.777983	−	0.628286i	$-0.216243\pi$
$503$	34.8967			1.55597			0.777983	+	0.628286i	$0.216243\pi$
$504$		0			0
$505$	1.07900			0.0480150
$506$	8.91236	+	8.10357i	0.396203	+	0.360247i
$507$	−3.55155	−	6.66624i	−0.157730	−	0.296058i
$508$	24.6803	−	2.35151i	1.09501	−	0.104331i
$509$	20.5865	−	11.8856i	0.912479	−	0.526820i	0.0312508	−	0.999512i	$-0.490051\pi$
$509$	20.5865	−	11.8856i	0.912479	−	0.526820i	0.881228	+	0.472692i	$0.156718\pi$
$510$	0.819511	−	3.23120i	0.0362886	−	0.143080i
$511$		0			0
$512$	−21.1934	−	7.92728i	−0.936623	−	0.350340i
$513$	−26.4507	+	11.8550i	−1.16783	+	0.523410i
$514$	6.66581	+	1.45078i	0.294016	+	0.0639913i
$515$	−1.26186	+	2.18561i	−0.0556044	+	0.0963097i
$516$	−4.81222	−	7.27328i	−0.211846	−	0.320188i
$517$	17.0351			0.749205
$518$		0			0
$519$	−31.1634	−	19.4374i	−1.36792	−	0.853207i
$520$	0.344963	−	2.87755i	0.0151276	−	0.126189i
$521$	−4.96256	−	2.86513i	−0.217414	−	0.125524i	0.387338	−	0.921938i	$-0.373394\pi$
$521$	−4.96256	−	2.86513i	−0.217414	−	0.125524i	−0.604752	+	0.796414i	$0.706728\pi$
$522$	9.88032	+	40.1781i	0.432450	+	1.75855i
$523$	4.17225	−	2.40885i	0.182440	−	0.105332i	−0.405999	−	0.913874i	$-0.633076\pi$
$523$	4.17225	−	2.40885i	0.182440	−	0.105332i	0.588439	+	0.808542i	$0.299743\pi$
$524$	−2.62410	+	1.86779i	−0.114634	+	0.0815948i
$525$		0			0
$526$	−19.4762	+	6.22364i	−0.849204	+	0.271364i
$527$	5.15121	+	8.92216i	0.224390	+	0.388656i
$528$	−26.7181	+	4.19944i	−1.16275	+	0.182757i
$529$	9.11968	−	15.7958i	0.396508	−	0.686772i
$530$	−0.628089	−	0.571090i	−0.0272824	−	0.0248066i
$531$	10.8815	+	22.2174i	0.472216	+	0.964155i
$532$		0			0
$533$			22.2509i			0.963795i
$534$	−7.01572	−	24.8452i	−0.303600	−	1.07516i
$535$	−3.32522	−	1.91982i	−0.143762	−	0.0830009i
$536$	−1.66192	+	0.711065i	−0.0717842	+	0.0307133i
$537$	3.13681	+	0.106955i	0.135363	+	0.00461544i
$538$	2.02854	+	6.34809i	0.0874564	+	0.273685i
$539$		0			0
$540$	−1.78862	−	3.15057i	−0.0769700	−	0.135579i
$541$	6.01942	+	10.4259i	0.258795	+	0.448246i	0.965919	−	0.258843i	$-0.0833413\pi$
$541$	6.01942	+	10.4259i	0.258795	+	0.448246i	−0.707124	+	0.707089i	$0.750008\pi$
$542$	21.6597	+	4.71413i	0.930362	+	0.202489i
$543$	−6.14022	−	11.5252i	−0.263502	−	0.494593i
$544$	10.5732	+	19.3873i	0.453322	+	0.831223i
$545$			0.487964i			0.0209021i
$546$		0			0
$547$			35.3097i			1.50973i	0.655879	+	0.754866i	$0.272298\pi$
$547$			35.3097i			1.50973i	−0.655879	+	0.754866i	$0.727702\pi$
$548$	3.62720	−	7.93810i	0.154946	−	0.339099i
$549$	42.1895	+	2.88039i	1.80060	+	0.122932i
$550$	5.72772	−	26.3167i	0.244231	−	1.12215i
$551$	27.2005	+	47.1127i	1.15878	+	2.00707i
$552$	−3.86735	−	9.96488i	−0.164605	−	0.424133i
$553$		0			0
$554$	22.8958	−	7.31638i	0.972751	−	0.310843i
$555$	0.0131502	−	0.385674i	0.000558194	−	0.0163710i
$556$	−33.4838	+	3.19029i	−1.42003	+	0.135299i
$557$	−30.1308	−	17.3960i	−1.27668	−	0.737093i	−0.300445	−	0.953799i	$-0.597135\pi$
$557$	−30.1308	−	17.3960i	−1.27668	−	0.737093i	−0.976237	+	0.216706i	$0.930469\pi$
$558$	10.7530	+	3.12086i	0.455212	+	0.132117i
$559$			7.39973i			0.312975i
$560$		0			0
$561$	22.3960	+	13.9690i	0.945562	+	0.589771i
$562$	−5.47834	+	6.02512i	−0.231090	+	0.254154i
$563$	−6.43088	+	11.1386i	−0.271029	+	0.469436i	−0.969126	−	0.246567i	$-0.920697\pi$
$563$	−6.43088	+	11.1386i	−0.271029	+	0.469436i	0.698096	+	0.716004i	$0.254031\pi$
$564$	−13.5271	−	6.74738i	−0.569595	−	0.284116i
$565$	−1.53950	−	2.66649i	−0.0647673	−	0.112180i
$566$	−2.40130	−	7.51461i	−0.100934	−	0.315863i
$567$		0			0
$568$	−20.2369	+	27.0157i	−0.849120	+	1.13355i
$569$	−13.5887	+	7.84543i	−0.569667	+	0.328897i	−0.757016	−	0.653396i	$-0.773344\pi$
$569$	−13.5887	+	7.84543i	−0.569667	+	0.328897i	0.187349	+	0.982293i	$0.440010\pi$
$570$	−3.41315	−	3.32280i	−0.142961	−	0.139177i
$571$	−36.4003	−	21.0157i	−1.52331	−	0.879481i	−0.999620	−	0.0275690i	$-0.991223\pi$
$571$	−36.4003	−	21.0157i	−1.52331	−	0.879481i	−0.523685	−	0.851912i	$-0.675443\pi$
$572$	20.8724	+	9.53734i	0.872719	+	0.398776i
$573$	−1.49564	+	2.39792i	−0.0624813	+	0.100174i
$574$		0			0
$575$	10.6443			0.443897
$576$	22.8794	+	7.24799i	0.953308	+	0.302000i
$577$	19.3960	−	33.5949i	0.807468	−	1.39858i	−0.107145	−	0.994243i	$-0.534171\pi$
$577$	19.3960	−	33.5949i	0.807468	−	1.39858i	0.914612	−	0.404332i	$-0.132496\pi$
$578$	−0.529521	+	2.43295i	−0.0220252	+	0.101197i
$579$	26.2369	+	0.894589i	1.09037	+	0.0371778i
$580$	−5.53950	+	3.94293i	−0.230015	+	0.163721i
$581$		0			0
$582$	1.20437	−	4.74863i	0.0499227	−	0.196837i
$583$	5.82125	−	3.36090i	0.241091	−	0.139194i
$584$	−8.76559	−	20.4872i	−0.362723	−	0.847768i
$585$	−0.209380	+	3.06682i	−0.00865678	+	0.126797i
$586$	−22.6158	+	24.8730i	−0.934249	+	1.02749i
$587$	7.07471			0.292004			0.146002	−	0.989284i	$-0.453359\pi$
$587$	7.07471			0.292004			0.146002	+	0.989284i	$0.453359\pi$
$588$		0			0
$589$	14.7218			0.606601
$590$	−2.73505	+	3.00802i	−0.112600	+	0.123838i
$591$	32.4473	−	17.2868i	1.33471	−	0.711085i
$592$	1.67329	+	1.93270i	0.0687717	+	0.0794334i
$593$	15.9258	−	9.19477i	0.653994	−	0.377584i	−0.135991	−	0.990710i	$-0.543422\pi$
$593$	15.9258	−	9.19477i	0.653994	−	0.377584i	0.789985	+	0.613126i	$0.210088\pi$
$594$	28.0740	−	5.89710i	1.15189	−	0.241961i
$595$		0			0
$596$	−8.88449	−	12.4820i	−0.363923	−	0.511283i
$597$	0.221745	−	6.50343i	0.00907542	−	0.266168i
$598$	−1.92877	+	8.86200i	−0.0788734	+	0.362394i
$599$	−18.9258	+	32.7804i	−0.773287	+	1.33937i	0.162466	+	0.986714i	$0.448055\pi$
$599$	−18.9258	+	32.7804i	−0.773287	+	1.33937i	−0.935752	+	0.352658i	$0.885278\pi$
$600$	−14.9719	+	18.6287i	−0.611226	+	0.760514i
$601$	−21.9488			−0.895308			−0.447654	−	0.894207i	$-0.647740\pi$
$601$	−21.9488			−0.895308			−0.447654	+	0.894207i	$0.647740\pi$
$602$		0			0
$603$	1.72188	−	0.843327i	0.0701202	−	0.0343429i
$604$	10.5057	−	22.9917i	0.427472	−	0.935518i
$605$	−1.27989	−	0.738947i	−0.0520351	−	0.0300425i
$606$	5.28856	−	5.43236i	0.214833	−	0.220675i
$607$	22.4114	−	12.9392i	0.909651	−	0.525187i	0.0293323	−	0.999570i	$-0.490662\pi$
$607$	22.4114	−	12.9392i	0.909651	−	0.525187i	0.880319	+	0.474382i	$0.157329\pi$
$608$	31.5465	+	0.767338i	1.27938	+	0.0311197i
$609$		0			0
$610$	2.11533	+	6.61968i	0.0856470	+	0.268023i
$611$	6.41308	+	11.1078i	0.259445	+	0.449373i
$612$	−12.2511	−	19.9631i	−0.495223	−	0.806962i
$613$	6.45681	−	11.1835i	0.260788	−	0.451698i	−0.705664	−	0.708547i	$-0.749351\pi$
$613$	6.45681	−	11.1835i	0.260788	−	0.451698i	0.966452	+	0.256849i	$0.0826843\pi$
$614$	−3.52003	+	3.87136i	−0.142057	+	0.156235i
$615$	−2.41910	+	3.87847i	−0.0975475	+	0.156395i
$616$		0			0
$617$			26.4677i			1.06555i	0.846257	+	0.532775i	$0.178851\pi$
$617$			26.4677i			1.06555i	−0.846257	+	0.532775i	$0.821149\pi$
$618$	4.81889	+	17.0654i	0.193844	+	0.686472i
$619$	−29.7384	−	17.1695i	−1.19529	−	0.690100i	−0.235787	−	0.971805i	$-0.575767\pi$
$619$	−29.7384	−	17.1695i	−1.19529	−	0.690100i	−0.959501	+	0.281705i	$0.909100\pi$
$620$	0.174527	+	1.83175i	0.00700917	+	0.0735648i
$621$	4.63691	+	10.3458i	0.186073	+	0.415164i
$622$	−10.2174	+	3.26499i	−0.409682	+	0.130914i
$623$		0			0
$624$	−12.7966	−	15.8406i	−0.512273	−	0.634131i
$625$	−11.5959	−	20.0847i	−0.463836	−	0.803388i
$626$	4.70245	−	21.6060i	0.187948	−	0.863549i
$627$	33.2884	−	17.7349i	1.32941	−	0.708265i
$628$	0.395540	+	0.180736i	0.0157838	+	0.00721216i
$629$		−	2.49490i		−	0.0994782i
$630$		0			0
$631$		−	27.7569i		−	1.10499i	−0.833517	−	0.552493i	$-0.813677\pi$
$631$		−	27.7569i		−	1.10499i	0.833517	−	0.552493i	$-0.186323\pi$
$632$	1.34665	−	11.2333i	0.0535670	−	0.446836i
$633$	−15.0413	+	8.01347i	−0.597836	+	0.318507i
$634$	−19.1985	−	4.17846i	−0.762469	−	0.165948i
$635$	−2.16070	−	3.74245i	−0.0857449	−	0.148515i
$636$	−5.95369	+	0.363081i	−0.236079	+	0.0143971i
$637$		0			0
$638$	−16.3881	−	51.2847i	−0.648810	−	2.03038i
$639$	19.9715	−	29.7143i	0.790060	−	1.17548i
$640$	0.278508	+	3.93425i	0.0110090	+	0.155515i
$641$	6.03040	+	3.48165i	0.238186	+	0.137517i	0.614343	−	0.789039i	$-0.289421\pi$
$641$	6.03040	+	3.48165i	0.238186	+	0.137517i	−0.376156	+	0.926556i	$0.622754\pi$
$642$	−25.9636	+	7.33153i	−1.02470	+	0.289352i
$643$		−	9.74373i		−	0.384255i	−0.981370	−	0.192128i	$-0.938461\pi$
$643$		−	9.74373i		−	0.384255i	0.981370	−	0.192128i	$-0.0615387\pi$
$644$		0			0
$645$	−0.804492	+	1.28982i	−0.0316768	+	0.0507865i
$646$	−22.7859	−	20.7180i	−0.896498	−	0.815140i
$647$	−14.0948	+	24.4129i	−0.554123	+	0.959770i	0.443848	+	0.896102i	$0.353613\pi$
$647$	−14.0948	+	24.4129i	−0.554123	+	0.959770i	−0.997971	+	0.0636677i	$0.979720\pi$
$648$	−24.6285	−	6.43701i	−0.967500	−	0.252869i
$649$	−16.0959	−	27.8789i	−0.631820	−	1.09434i
$650$	19.3161	−	6.17248i	0.757641	−	0.242105i
$651$		0			0
$652$	−6.07649	−	8.53699i	−0.237974	−	0.334334i
$653$	9.39867	−	5.42633i	0.367799	−	0.212349i	−0.304698	−	0.952449i	$-0.598555\pi$
$653$	9.39867	−	5.42633i	0.367799	−	0.212349i	0.672496	+	0.740101i	$0.265222\pi$
$654$	2.45671	+	2.39167i	0.0960649	+	0.0935219i
$655$	0.486214	+	0.280716i	0.0189979	+	0.0109685i
$656$	−5.71841	−	29.7364i	−0.223267	−	1.16101i
$657$	10.3960	+	21.2263i	0.405588	+	0.828116i
$658$		0			0
$659$	19.2248			0.748893			0.374446	−	0.927249i	$-0.377833\pi$
$659$	19.2248			0.748893			0.374446	+	0.927249i	$0.377833\pi$
$660$	2.60129	+	3.93164i	0.101255	+	0.153039i
$661$	−1.37371	+	2.37933i	−0.0534311	+	0.0925454i	−0.891504	−	0.453013i	$-0.850349\pi$
$661$	−1.37371	+	2.37933i	−0.0534311	+	0.0925454i	0.838073	+	0.545558i	$0.183682\pi$
$662$	43.9374	+	9.56278i	1.70768	+	0.371668i
$663$	−0.677232	+	19.8621i	−0.0263015	+	0.771382i
$664$	15.1658	−	20.2460i	0.588547	−	0.785696i
$665$		0			0
$666$	−1.87727	−	1.95652i	−0.0727426	−	0.0758138i
$667$	18.4275	−	10.6391i	0.713514	−	0.411948i
$668$	−2.17662	−	22.8447i	−0.0842158	−	0.883888i
$669$	35.0267	−	18.6610i	1.35421	−	0.721476i
$670$	0.233125	+	0.211969i	0.00900641	+	0.00818908i
$671$	−55.0271			−2.12430
$672$		0			0
$673$	31.3097			1.20690			0.603449	−	0.797401i	$-0.293793\pi$
$673$	31.3097			1.20690			0.603449	+	0.797401i	$0.293793\pi$
$674$	17.9113	+	16.2858i	0.689916	+	0.627306i
$675$	14.8492	−	20.5447i	0.571547	−	0.790767i
$676$	−0.827256	−	8.68248i	−0.0318175	−	0.333941i
$677$	18.1712	−	10.4911i	0.698376	−	0.403208i	−0.108366	−	0.994111i	$-0.534562\pi$
$677$	18.1712	−	10.4911i	0.698376	−	0.403208i	0.806742	+	0.590903i	$0.201229\pi$
$678$	−20.9704	−	5.31860i	−0.805363	−	0.204259i
$679$		0			0
$680$	2.30770	−	3.08073i	0.0884963	−	0.118140i
$681$	23.4213	+	0.798587i	0.897506	+	0.0306019i
$682$	−14.2365	−	3.09852i	−0.545145	−	0.118648i
$683$	−7.91172	+	13.7035i	−0.302734	+	0.524350i	−0.976754	−	0.214363i	$-0.931233\pi$
$683$	−7.91172	+	13.7035i	−0.302734	+	0.524350i	0.674021	+	0.738713i	$0.264566\pi$
$684$	−33.4580	+	0.897733i	−1.27930	+	0.0343257i
$685$	−1.52126			−0.0581245
$686$		0			0
$687$	−13.4711	+	21.5978i	−0.513953	+	0.824006i
$688$	−1.90171	−	9.88909i	−0.0725019	−	0.377018i
$689$	4.38295	+	2.53050i	0.166977	+	0.0964043i
$690$	−1.29966	+	1.33500i	−0.0494774	+	0.0508228i
$691$	21.1390	−	12.2046i	0.804167	−	0.464286i	−0.0407593	−	0.999169i	$-0.512978\pi$
$691$	21.1390	−	12.2046i	0.804167	−	0.464286i	0.844926	+	0.534883i	$0.179644\pi$
$692$	−24.5931	−	34.5514i	−0.934891	−	1.31345i
$693$		0			0
$694$	11.3803	−	3.63659i	0.431991	−	0.138043i
$695$	2.93143	+	5.07738i	0.111195	+	0.192596i
$696$	−7.29985	+	47.2149i	−0.276700	+	1.78967i
$697$	−14.7764	+	25.5934i	−0.559694	+	0.969419i
$698$	18.3066	+	16.6452i	0.692914	+	0.630032i
$699$	25.2626	+	15.7569i	0.955520	+	0.595982i
$700$		0			0
$701$			21.4779i			0.811209i	0.914049	+	0.405605i	$0.132939\pi$
$701$			21.4779i			0.811209i	−0.914049	+	0.405605i	$0.867061\pi$
$702$	14.4140	+	16.0857i	0.544021	+	0.607114i
$703$	−3.08749	−	1.78256i	−0.116447	−	0.0672306i
$704$	−30.3452	−	7.38169i	−1.14368	−	0.278208i
$705$	−0.0897892	+	2.63338i	−0.00338166	+	0.0991787i
$706$	−3.55892	−	11.1373i	−0.133942	−	0.419156i
$707$		0			0
$708$	1.73885	+	28.5132i	0.0653501	+	1.07159i
$709$	21.0959	+	36.5392i	0.792273	+	1.37226i	0.924556	+	0.381046i	$0.124436\pi$
$709$	21.0959	+	36.5392i	0.792273	+	1.37226i	−0.132283	+	0.991212i	$0.542231\pi$
$710$	5.74906	+	1.25126i	0.215758	+	0.0469588i
$711$	−0.817369	+	11.9721i	−0.0306537	+	0.448990i
$712$	3.54831	−	29.5987i	0.132979	−	1.10926i
$713$		−	5.75822i		−	0.215647i
$714$		0			0
$715$		−	4.00000i		−	0.149592i
$716$	3.29636	+	1.50623i	0.123191	+	0.0562903i
$717$	−11.8363	−	22.2167i	−0.442034	−	0.829697i
$718$	−7.55802	+	34.7263i	−0.282063	+	1.29597i
$719$	−9.52940	−	16.5054i	−0.355387	−	0.615548i	0.631797	−	0.775134i	$-0.282317\pi$
$719$	−9.52940	−	16.5054i	−0.355387	−	0.615548i	−0.987184	+	0.159586i	$0.948984\pi$
$720$	−0.508344	−	4.15234i	−0.0189449	−	0.154749i
$721$		0			0
$722$	−16.3240	+	5.21635i	−0.607517	+	0.194133i
$723$	−32.5299	−	1.10916i	−1.20980	−	0.0412501i
$724$	−1.43023	−	15.0110i	−0.0531542	−	0.557880i
$725$	−41.2019	−	23.7879i	−1.53020	−	0.883461i
$726$	−9.99350	+	2.82194i	−0.370894	+	0.104732i
$727$		−	3.72549i		−	0.138171i	−0.997611	−	0.0690854i	$-0.977992\pi$
$727$		−	3.72549i		−	0.138171i	0.997611	−	0.0690854i	$-0.0220081\pi$
$728$		0			0
$729$	26.4374	+	5.48311i	0.979163	+	0.203078i
$730$	−2.61303	+	2.87383i	−0.0967126	+	0.106365i
$731$	−4.91400	+	8.51130i	−0.181751	+	0.314802i
$732$	43.6955	+	21.7955i	1.61503	+	0.805583i
$733$	−12.7090	−	22.0126i	−0.469417	−	0.813054i	0.529972	−	0.848015i	$-0.322203\pi$
$733$	−12.7090	−	22.0126i	−0.469417	−	0.813054i	−0.999389	+	0.0349611i	$0.988869\pi$
$734$	9.34681	+	29.2498i	0.344997	+	1.07963i
$735$		0			0
$736$	0.300133	−	12.3390i	0.0110631	−	0.454820i
$737$	−2.16065	+	1.24745i	−0.0795885	+	0.0459504i
$738$	7.66977	+	31.1889i	0.282328	+	1.14808i
$739$	20.1868	+	11.6548i	0.742582	+	0.428730i	0.823007	−	0.568031i	$-0.192295\pi$
$739$	20.1868	+	11.6548i	0.742582	+	0.428730i	−0.0804256	+	0.996761i	$0.525628\pi$
$740$	0.185192	−	0.405291i	0.00680779	−	0.0148988i
$741$	24.0959	+	15.0292i	0.885185	+	0.552113i
$742$		0			0
$743$	−33.8576			−1.24211			−0.621057	−	0.783765i	$-0.713297\pi$
$743$	−33.8576			−1.24211			−0.621057	+	0.783765i	$0.713297\pi$
$744$	10.0776	+	8.09934i	0.369461	+	0.296936i
$745$	−1.33528	+	2.31277i	−0.0489207	+	0.0847332i
$746$	0.217085	−	0.997424i	0.00794804	−	0.0365183i
$747$	−14.9669	+	22.2684i	−0.547611	+	0.814757i
$748$	17.6742	+	24.8309i	0.646234	+	0.907908i
$749$		0			0
$750$	8.17655	+	2.07377i	0.298566	+	0.0757235i
$751$	−41.7017	+	24.0765i	−1.52172	+	0.878564i	−0.522046	+	0.852918i	$0.674831\pi$
$751$	−41.7017	+	24.0765i	−1.52172	+	0.878564i	−0.999671	+	0.0256461i	$0.991836\pi$
$752$	−11.4252	−	13.1964i	−0.416633	−	0.481224i
$753$	16.8097	+	31.5518i	0.612581	+	1.14981i
$754$	27.2708	−	29.9926i	0.993143	−	1.09227i
$755$	−4.40614			−0.160356
$756$		0			0
$757$	−11.3923			−0.414062			−0.207031	−	0.978334i	$-0.566380\pi$
$757$	−11.3923			−0.414062			−0.207031	+	0.978334i	$0.566380\pi$
$758$	17.3863	−	19.1215i	0.631497	−	0.694526i
$759$	−6.93677	−	13.0203i	−0.251789	−	0.472607i
$760$	−2.16365	−	5.05695i	−0.0784837	−	0.183435i
$761$	−23.8583	+	13.7746i	−0.864861	+	0.499328i	−0.865637	−	0.500672i	$-0.833086\pi$
$761$	−23.8583	+	13.7746i	−0.864861	+	0.499328i	0.000776011		1.00000i	$0.499753\pi$
$762$	−29.4321	−	7.46470i	−1.06621	−	0.270417i
$763$		0			0
$764$	−2.65862	+	1.89236i	−0.0961853	+	0.0684632i
$765$	−2.27744	+	3.38846i	−0.0823410	+	0.122510i
$766$	−0.616341	+	2.83186i	−0.0222693	+	0.102319i
$767$	12.1190	−	20.9907i	0.437591	−	0.757930i
$768$	21.1725	+	17.8809i	0.763996	+	0.645221i
$769$	5.83461			0.210401			0.105201	−	0.994451i	$-0.466451\pi$
$769$	5.83461			0.210401			0.105201	+	0.994451i	$0.466451\pi$
$770$		0			0
$771$	−7.08912	−	4.42166i	−0.255308	−	0.159242i
$772$	27.5714	+	12.5983i	0.992315	+	0.453424i
$773$	41.1952	+	23.7841i	1.48169	+	0.855454i	0.999784	−	0.0207689i	$-0.00661143\pi$
$773$	41.1952	+	23.7841i	1.48169	+	0.855454i	0.481906	+	0.876223i	$0.339945\pi$
$774$	2.55065	+	10.3721i	0.0916810	+	0.372819i
$775$	−11.1499	+	6.43739i	−0.400516	+	0.231238i
$776$	3.39144	−	4.52749i	0.121745	−	0.162527i
$777$		0			0
$778$	−4.79829	−	15.0157i	−0.172027	−	0.538340i
$779$	21.1149	+	36.5720i	0.756519	+	1.31033i
$780$	−1.58434	+	3.17629i	−0.0567286	+	0.113729i
$781$	−23.2939	+	40.3463i	−0.833522	+	1.44370i
$782$	−8.10357	+	8.91236i	−0.289783	+	0.318706i
$783$	5.17240	−	50.4093i	0.184846	−	1.80148i
$784$		0			0
$785$		−	0.0758015i		−	0.00270547i
$786$	3.79639	−	1.07202i	0.135413	−	0.0382375i
$787$	42.2774	+	24.4089i	1.50703	+	0.870082i	0.999967	+	0.00817024i	$0.00260070\pi$
$787$	42.2774	+	24.4089i	1.50703	+	0.870082i	0.507059	+	0.861911i	$0.330733\pi$
$788$	42.2612	−	4.02659i	1.50549	−	0.143441i
$789$	25.0271	+	0.853341i	0.890989	+	0.0303797i
$790$	−1.87847	+	0.600267i	−0.0668330	+	0.0213565i
$791$		0			0
$792$	32.5441	+	6.17381i	1.15640	+	0.219377i
$793$	−20.7156	−	35.8805i	−0.735632	−	1.27415i
$794$	2.39834	−	11.0195i	0.0851140	−	0.391067i
$795$	0.488861	+	0.917592i	0.0173381	+	0.0325436i
$796$	3.12280	−	6.83422i	0.110685	−	0.242232i
$797$		−	12.7292i		−	0.450890i	−0.974256	−	0.225445i	$-0.927616\pi$
$797$		−	12.7292i		−	0.450890i	0.974256	−	0.225445i	$-0.0723837\pi$
$798$		0			0
$799$			17.0351i			0.602660i
$800$	−24.2280	+	13.2132i	−0.856589	+	0.467156i
$801$	−2.15369	+	31.5455i	−0.0760970	+	1.11461i
$802$	29.6795	+	6.45961i	1.04802	+	0.228097i
$803$	−15.3778	−	26.6352i	−0.542672	−	0.939936i
$804$	2.20981	−	0.134763i	0.0779339	−	0.00475273i
$805$		0			0
$806$	−3.33912	−	10.4494i	−0.117616	−	0.368065i
$807$	0.278138	−	8.15735i	0.00979093	−	0.287152i
$808$	8.04863	−	3.44366i	0.283150	−	0.121147i
$809$	23.0201	+	13.2906i	0.809342	+	0.467274i	0.846727	−	0.532027i	$-0.178570\pi$
$809$	23.0201	+	13.2906i	0.809342	+	0.467274i	−0.0373853	+	0.999301i	$0.511903\pi$
$810$	0.763629	+	4.37090i	0.0268312	+	0.153578i
$811$			4.13977i			0.145367i	0.997355	+	0.0726835i	$0.0231563\pi$
$811$			4.13977i			0.145367i	−0.997355	+	0.0726835i	$0.976844\pi$
$812$		0			0
$813$	−23.0351	−	14.3676i	−0.807878	−	0.503894i
$814$	2.61054	+	2.37363i	0.0914994	+	0.0831958i
$815$	−0.913253	+	1.58180i	−0.0319899	+	0.0554081i
$816$	−4.19944	−	26.7181i	−0.147010	−	0.935319i
$817$	7.02193	+	12.1623i	0.245666	+	0.425506i
$818$	−49.7266	+	15.8902i	−1.73865	+	0.555587i
$819$		0			0
$820$	−4.30013	+	3.06077i	−0.150167	+	0.106887i
$821$	−25.5549	+	14.7541i	−0.891871	+	0.514922i	−0.874554	−	0.484928i	$-0.838846\pi$
$821$	−25.5549	+	14.7541i	−0.891871	+	0.514922i	−0.0173172	+	0.999850i	$0.505513\pi$
$822$	−7.45623	+	7.65897i	−0.260066	+	0.267137i
$823$	10.4596	+	6.03884i	0.364598	+	0.210501i	0.671096	−	0.741371i	$-0.265824\pi$
$823$	10.4596	+	6.03884i	0.364598	+	0.210501i	−0.306498	+	0.951871i	$0.599157\pi$
$824$	−2.43723	+	20.3305i	−0.0849049	+	0.708245i
$825$	−17.4568	+	27.9880i	−0.607768	+	0.974416i
$826$		0			0
$827$	11.9341			0.414989			0.207494	−	0.978236i	$-0.433469\pi$
$827$	11.9341			0.414989			0.207494	+	0.978236i	$0.433469\pi$
$828$	0.351136	+	13.0866i	0.0122028	+	0.454791i
$829$	−1.25218	+	2.16884i	−0.0434900	+	0.0753269i	−0.886951	−	0.461863i	$-0.847181\pi$
$829$	−1.25218	+	2.16884i	−0.0434900	+	0.0753269i	0.843461	+	0.537190i	$0.180514\pi$
$830$	−4.30843	−	0.937709i	−0.149548	−	0.0325484i
$831$	−29.4214	−	1.00317i	−1.02062	−	0.0347996i
$832$	−6.61057	−	22.5655i	−0.229180	−	0.782319i
$833$		0			0
$834$	39.9305	+	10.1274i	1.38268	+	0.350682i
$835$	−3.46410	+	2.00000i	−0.119880	+	0.0692129i
$836$	43.3567	−	4.13097i	1.49952	−	0.142873i
$837$	−11.1141	−	8.03298i	−0.384158	−	0.277660i
$838$	30.9482	+	28.1396i	1.06909	+	0.972068i
$839$	−1.64607			−0.0568288			−0.0284144	−	0.999596i	$-0.509046\pi$
$839$	−1.64607			−0.0568288			−0.0284144	+	0.999596i	$0.509046\pi$
$840$		0			0
$841$	−66.1054			−2.27950
$842$	−38.5380	−	35.0407i	−1.32811	−	1.20758i
$843$	8.80225	−	4.68954i	0.303166	−	0.161516i
$844$	−19.5905	+	1.86656i	−0.674334	+	0.0642498i
$845$	−1.31658	+	0.760131i	−0.0452919	+	0.0261493i
$846$	12.8179	+	13.3591i	0.440690	+	0.459296i
$847$		0			0
$848$	−6.50776	−	2.25539i	−0.223477	−	0.0774503i
$849$	−0.329249	+	9.65635i	−0.0112998	+	0.331405i
$850$	26.3167	+	5.72772i	0.902657	+	0.196459i
$851$	−0.697224	+	1.20763i	−0.0239005	+	0.0413969i
$852$	34.4776	−	22.8114i	1.18118	−	0.781507i
$853$	15.1311			0.518077			0.259039	−	0.965867i	$-0.416594\pi$
$853$	15.1311			0.518077			0.259039	+	0.965867i	$0.416594\pi$
$854$		0			0
$855$	2.56610	+	5.23937i	0.0877587	+	0.179183i
$856$	−30.9310	−	3.70803i	−1.05720	−	0.126738i
$857$	−42.3681	−	24.4612i	−1.44727	−	0.835579i	−0.448947	−	0.893558i	$-0.648201\pi$
$857$	−42.3681	−	24.4612i	−1.44727	−	0.835579i	−0.998318	+	0.0579792i	$0.981534\pi$
$858$	−20.1384	−	19.6053i	−0.687515	−	0.669316i
$859$	−13.9058	+	8.02854i	−0.474461	+	0.273930i	−0.718105	−	0.695935i	$-0.754990\pi$
$859$	−13.9058	+	8.02854i	−0.474461	+	0.273930i	0.243644	+	0.969865i	$0.421657\pi$
$860$	−1.43005	+	1.01788i	−0.0487641	+	0.0347095i
$861$		0			0
$862$	−6.30013	+	2.01321i	−0.214583	+	0.0685703i
$863$	−7.45171	−	12.9067i	−0.253659	−	0.439350i	0.710871	−	0.703322i	$-0.248301\pi$
$863$	−7.45171	−	12.9067i	−0.253659	−	0.439350i	−0.964530	+	0.263972i	$0.914967\pi$
$864$	−23.3970	−	17.7927i	−0.795982	−	0.605320i
$865$	−3.69617	+	6.40196i	−0.125674	+	0.217673i
$866$	−17.3238	−	15.7517i	−0.588687	−	0.535263i
$867$	1.61386	−	2.58746i	0.0548096	−	0.0878746i
$868$		0			0
$869$		−	15.6151i		−	0.529704i
$870$	8.01422	−	2.26304i	0.271708	−	0.0767241i
$871$	−1.62680	−	0.939235i	−0.0551221	−	0.0318248i
$872$	1.55734	+	3.63988i	0.0527383	+	0.123262i
$873$	−3.34696	+	4.97974i	−0.113278	+	0.168539i
$874$	5.23937	+	16.3960i	0.177224	+	0.554604i
$875$		0			0
$876$	1.66128	+	27.2412i	0.0561295	+	0.920395i
$877$	−5.93923	−	10.2871i	−0.200554	−	0.347369i	0.748153	−	0.663526i	$-0.230941\pi$
$877$	−5.93923	−	10.2871i	−0.200554	−	0.347369i	−0.948707	+	0.316157i	$0.897607\pi$
$878$	36.5900	+	7.96364i	1.23485	+	0.268760i
$879$	36.3376	−	19.3594i	1.22564	−	0.652977i
$880$	1.02799	+	5.34565i	0.0346534	+	0.180202i
$881$		−	36.4995i		−	1.22970i	−0.788644	−	0.614850i	$-0.789217\pi$
$881$		−	36.4995i		−	1.22970i	0.788644	−	0.614850i	$-0.210783\pi$
$882$		0			0
$883$			31.1178i			1.04720i	0.851965	+	0.523599i	$0.175411\pi$
$883$			31.1178i			1.04720i	−0.851965	+	0.523599i	$0.824589\pi$
$884$	−9.53734	+	20.8724i	−0.320776	+	0.702015i
$885$	4.39450	−	2.34124i	0.147720	−	0.0786999i
$886$	−1.38378	+	6.35793i	−0.0464888	+	0.213599i
$887$	−28.4624	−	49.2983i	−0.955674	−	1.65528i	−0.732819	−	0.680424i	$-0.761796\pi$
$887$	−28.4624	−	49.2983i	−0.955674	−	1.65528i	−0.222855	−	0.974852i	$-0.571538\pi$
$888$	−1.13279	−	2.91884i	−0.0380141	−	0.0979497i
$889$		0			0
$890$	−4.94960	+	1.58165i	−0.165911	+	0.0530170i
$891$	−34.8079	−	4.77510i	−1.16611	−	0.159972i
$892$	45.6206	−	4.34668i	1.52749	−	0.145538i
$893$	21.0813	+	12.1713i	0.705459	+	0.407297i
$894$	5.09924	+	18.0582i	0.170544	+	0.603958i
$895$		−	0.631717i		−	0.0211160i
$896$		0			0
$897$	5.87847	−	9.42477i	0.196276	−	0.314684i
$898$	16.1827	−	17.7979i	0.540025	−	0.593924i
$899$	−12.8685	+	22.2889i	−0.429189	+	0.743378i
$900$	24.9476	−	15.3101i	0.831587	−	0.510335i
$901$	3.36090	+	5.82125i	0.111968	+	0.193934i
$902$	−12.7215	−	39.8107i	−0.423581	−	1.32555i
$903$		0			0
$904$	−19.9938	−	14.9769i	−0.664984	−	0.498124i
$905$	−2.27623	+	1.31418i	−0.0756643	+	0.0436848i
$906$	−21.5960	+	22.1832i	−0.717478	+	0.736988i
$907$	−5.81050	−	3.35469i	−0.192934	−	0.111391i	0.400421	−	0.916331i	$-0.368864\pi$
$907$	−5.81050	−	3.35469i	−0.192934	−	0.111391i	−0.593356	+	0.804940i	$0.702197\pi$
$908$	24.6126	+	11.2464i	0.816797	+	0.373224i
$909$	−8.33897	+	4.08419i	−0.276586	+	0.135464i
$910$		0			0
$911$	50.1275			1.66080			0.830399	−	0.557169i	$-0.188112\pi$
$911$	50.1275			1.66080			0.830399	+	0.557169i	$0.188112\pi$
$912$	−36.0645	−	13.8927i	−1.19422	−	0.460033i
$913$	17.4568	−	30.2361i	0.577736	−	1.00067i
$914$	4.64102	−	21.3238i	0.153511	−	0.705328i
$915$	0.290038	−	8.50636i	0.00958836	−	0.281211i
$916$	−23.9458	+	17.0443i	−0.791193	+	0.563158i
$917$		0			0
$918$	5.89710	+	28.0740i	0.194633	+	0.926580i
$919$	14.7529	−	8.51757i	0.486652	−	0.280969i	−0.236532	−	0.971624i	$-0.576011\pi$
$919$	14.7529	−	8.51757i	0.486652	−	0.280969i	0.723185	+	0.690655i	$0.242678\pi$
$920$	−1.97795	+	0.846280i	−0.0652112	+	0.0279010i
$921$	5.65577	−	3.01320i	0.186364	−	0.0992883i
$922$	31.7541	−	34.9234i	1.04577	−	1.15014i
$923$	−35.0771			−1.15458
$924$		0			0
$925$	3.11784			0.102514
$926$	−25.1917	+	27.7060i	−0.827851	+	0.910477i
$927$	1.47931	−	21.6677i	0.0485869	−	0.711659i
$928$	−28.7370	+	47.0910i	−0.943338	+	1.54584i
$929$	20.2721	−	11.7041i	0.665105	−	0.383999i	−0.129114	−	0.991630i	$-0.541213\pi$
$929$	20.2721	−	11.7041i	0.665105	−	0.383999i	0.794219	+	0.607631i	$0.207880\pi$
$930$	0.554023	−	2.18442i	0.0181671	−	0.0716301i
$931$		0			0
$932$	19.9365	+	28.0092i	0.653040	+	0.917470i
$933$	13.1295	+	0.447672i	0.429841	+	0.0146561i
$934$	−5.59140	+	25.6904i	−0.182956	+	0.840616i
$935$	2.65631	−	4.60087i	0.0868707	−	0.150464i
$936$	8.22597	+	23.5446i	0.268874	+	0.769580i
$937$	48.5929			1.58746			0.793730	−	0.608270i	$-0.208136\pi$
$937$	48.5929			1.58746			0.793730	+	0.608270i	$0.208136\pi$
$938$		0			0
$939$	−14.3320	+	22.9781i	−0.467707	+	0.749861i
$940$	−1.26449	+	2.76732i	−0.0412430	+	0.0902600i
$941$	12.6540	+	7.30579i	0.412509	+	0.238162i	0.691867	−	0.722025i	$-0.256788\pi$
$941$	12.6540	+	7.30579i	0.412509	+	0.238162i	−0.279358	+	0.960187i	$0.590122\pi$
$942$	−0.381631	−	0.371529i	−0.0124342	−	0.0121051i
$943$	14.3046	−	8.25879i	0.465823	−	0.268943i
$944$	−10.8014	+	31.1668i	−0.351556	+	1.01439i
$945$		0			0
$946$	−4.23065	−	13.2394i	−0.137550	−	0.430449i
$947$	−15.7125	−	27.2148i	−0.510587	−	0.884362i	−0.999925	−	0.0122681i	$-0.996095\pi$
$947$	−15.7125	−	27.2148i	−0.510587	−	0.884362i	0.489338	−	0.872094i	$-0.337238\pi$
$948$	−6.18490	+	12.3995i	−0.200876	+	0.402716i
$949$	11.5783	−	20.0543i	0.375849	−	0.650989i
$950$	25.8910	−	28.4751i	0.840015	−	0.923855i
$951$	20.4177	+	12.7350i	0.662088	+	0.412961i
$952$		0			0
$953$		−	14.0113i		−	0.453872i	−0.973910	−	0.226936i	$-0.927129\pi$
$953$		−	14.0113i		−	0.453872i	0.973910	−	0.226936i	$-0.0728708\pi$
$954$	7.01579	+	2.03620i	0.227145	+	0.0659243i
$955$	0.492609	+	0.284408i	0.0159405	+	0.00920323i
$956$	−2.75701	−	28.9362i	−0.0891680	−	0.935863i
$957$	−2.24701	+	65.9014i	−0.0726357	+	2.13029i
$958$	55.0666	−	17.5966i	1.77912	−	0.568520i
$959$		0			0
$960$	1.30104	−	4.65200i	0.0419909	−	0.150143i
$961$	−12.0176	−	20.8150i	−0.387664	−	0.671453i
$962$	−0.564961	+	2.59579i	−0.0182151	+	0.0836916i
$963$	32.9655	+	2.25064i	1.06230	+	0.0725258i
$964$	−34.1845	−	15.6201i	−1.10101	−	0.503090i
$965$		−	5.28380i		−	0.170091i
$966$		0			0
$967$		−	35.9876i		−	1.15728i	−0.815582	−	0.578641i	$-0.803583\pi$
$967$		−	35.9876i		−	1.15728i	0.815582	−	0.578641i	$-0.196417\pi$
$968$	−11.9055	−	1.42724i	−0.382657	−	0.0458732i
$969$	17.7349	+	33.2884i	0.569728	+	1.06938i
$970$	−0.963468	−	0.209694i	−0.0309351	−	0.00673288i
$971$	24.1922	+	41.9022i	0.776365	+	1.34470i	0.934024	+	0.357210i	$0.116272\pi$
$971$	24.1922	+	41.9022i	0.776365	+	1.34470i	−0.157659	+	0.987494i	$0.550395\pi$
$972$	25.7486	+	17.5787i	0.825886	+	0.563837i
$973$		0			0
$974$	9.22546	+	28.8701i	0.295603	+	0.925057i
$975$	−24.8214	−	0.846326i	−0.794921	−	0.0271041i
$976$	36.9057	+	42.6272i	1.18132	+	1.36446i
$977$	−32.6000	−	18.8216i	−1.04296	−	0.602156i	−0.122293	−	0.992494i	$-0.539025\pi$
$977$	−32.6000	−	18.8216i	−1.04296	−	0.602156i	−0.920672	+	0.390338i	$0.872358\pi$
$978$	3.48759	+	12.3508i	0.111521	+	0.394935i
$979$		−	41.1443i		−	1.31498i
$980$		0			0
$981$	−1.84702	−	3.77118i	−0.0589708	−	0.120405i
$982$	1.70729	+	1.55235i	0.0544818	+	0.0495375i
$983$	2.67750	−	4.63756i	0.0853989	−	0.147915i	−0.820162	−	0.572131i	$-0.806117\pi$
$983$	2.67750	−	4.63756i	0.0853989	−	0.147915i	0.905561	+	0.424216i	$0.139450\pi$
$984$	−5.66664	+	36.6513i	−0.180646	+	1.16840i
$985$	−3.69987	−	6.40836i	−0.117888	−	0.204187i
$986$	51.2847	−	16.3881i	1.63324	−	0.521903i
$987$		0			0
$988$	19.0157	+	26.7156i	0.604971	+	0.849936i
$989$	4.75713	−	2.74653i	0.151268	−	0.0873345i
$990$	−1.37878	−	5.60676i	−0.0438204	−	0.178195i
$991$	44.1913	+	25.5139i	1.40378	+	0.810475i	0.994779	−	0.102057i	$-0.0325424\pi$
$991$	44.1913	+	25.5139i	1.40378	+	0.810475i	0.409005	+	0.912532i	$0.365876\pi$
$992$	7.14791	+	13.1066i	0.226946	+	0.416135i
$993$	−46.7276	−	29.1452i	−1.48286	−	0.924895i
$994$		0			0
$995$	−1.30971			−0.0415207
$996$	−25.8380	+	17.0952i	−0.818710	+	0.541683i
$997$	−26.9653	+	46.7052i	−0.853998	+	1.47917i	0.0235729	+	0.999722i	$0.492496\pi$
$997$	−26.9653	+	46.7052i	−0.853998	+	1.47917i	−0.877571	+	0.479446i	$0.840838\pi$
$998$	−12.2739	−	2.67137i	−0.388525	−	0.0845606i
$999$	1.35821	+	3.03042i	0.0429718	+	0.0958783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.g.263.3		24
3.2	odd	2	inner	588.2.n.g.263.10		24
4.3	odd	2	inner	588.2.n.g.263.7		24
7.2	even	3	inner	588.2.n.g.275.6		24
7.3	odd	6		84.2.e.a.71.11	yes	12
7.4	even	3		588.2.e.c.491.11		12
7.5	odd	6		588.2.n.f.275.6		24
7.6	odd	2		588.2.n.f.263.3		24
12.11	even	2	inner	588.2.n.g.263.6		24
21.2	odd	6	inner	588.2.n.g.275.7		24
21.5	even	6		588.2.n.f.275.7		24
21.11	odd	6		588.2.e.c.491.2		12
21.17	even	6		84.2.e.a.71.2	yes	12
21.20	even	2		588.2.n.f.263.10		24
28.3	even	6		84.2.e.a.71.1	✓	12
28.11	odd	6		588.2.e.c.491.1		12
28.19	even	6		588.2.n.f.275.10		24
28.23	odd	6	inner	588.2.n.g.275.10		24
28.27	even	2		588.2.n.f.263.7		24
56.3	even	6		1344.2.h.h.575.4		12
56.45	odd	6		1344.2.h.h.575.9		12
84.11	even	6		588.2.e.c.491.12		12
84.23	even	6	inner	588.2.n.g.275.3		24
84.47	odd	6		588.2.n.f.275.3		24
84.59	odd	6		84.2.e.a.71.12	yes	12
84.83	odd	2		588.2.n.f.263.6		24
168.59	odd	6		1344.2.h.h.575.10		12
168.101	even	6		1344.2.h.h.575.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	28.3	even	6
84.2.e.a.71.2	yes	12	21.17	even	6
84.2.e.a.71.11	yes	12	7.3	odd	6
84.2.e.a.71.12	yes	12	84.59	odd	6
588.2.e.c.491.1		12	28.11	odd	6
588.2.e.c.491.2		12	21.11	odd	6
588.2.e.c.491.11		12	7.4	even	3
588.2.e.c.491.12		12	84.11	even	6
588.2.n.f.263.3		24	7.6	odd	2
588.2.n.f.263.6		24	84.83	odd	2
588.2.n.f.263.7		24	28.27	even	2
588.2.n.f.263.10		24	21.20	even	2
588.2.n.f.275.3		24	84.47	odd	6
588.2.n.f.275.6		24	7.5	odd	6
588.2.n.f.275.7		24	21.5	even	6
588.2.n.f.275.10		24	28.19	even	6
588.2.n.g.263.3		24	1.1	even	1	trivial
588.2.n.g.263.6		24	12.11	even	2	inner
588.2.n.g.263.7		24	4.3	odd	2	inner
588.2.n.g.263.10		24	3.2	odd	2	inner
588.2.n.g.275.3		24	84.23	even	6	inner
588.2.n.g.275.6		24	7.2	even	3	inner
588.2.n.g.275.7		24	21.2	odd	6	inner
588.2.n.g.275.10		24	28.23	odd	6	inner
1344.2.h.h.575.3		12	168.101	even	6
1344.2.h.h.575.4		12	56.3	even	6
1344.2.h.h.575.9		12	56.45	odd	6
1344.2.h.h.575.10		12	168.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.04635 - 0.951394i) q^{2} +(0.814407 + 1.52864i) q^{3} +(0.189699 + 1.99098i) q^{4} +(0.301907 - 0.174306i) q^{5} +(0.602184 - 2.37432i) q^{6} +(1.69572 - 2.26374i) q^{8} +(-1.67348 + 2.48987i) q^{9} +(-0.481734 - 0.104847i) q^{10} +(1.95188 - 3.38076i) q^{11} +(-2.88901 + 1.91145i) q^{12} +2.93923 q^{13} +(0.512326 + 0.319551i) q^{15} +(-3.92803 + 0.755373i) q^{16} +(3.38076 + 1.95188i) q^{17} +(4.11990 - 1.01314i) q^{18} +(4.83098 - 2.78917i) q^{19} +(0.404312 + 0.568026i) q^{20} +(-5.25879 + 1.68045i) q^{22} +(-1.09094 - 1.88957i) q^{23} +(4.84146 + 0.748534i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(-3.07547 - 2.79637i) q^{26} +(-5.16901 - 0.530383i) q^{27} +9.75220i q^{29} +(-0.232054 - 0.821786i) q^{30} +(2.28553 + 1.31955i) q^{31} +(4.82875 + 2.94672i) q^{32} +(6.75759 + 0.230411i) q^{33} +(-1.68045 - 5.25879i) q^{34} +(-5.27475 - 2.85955i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(-7.70850 - 1.67772i) q^{38} +(2.39373 + 4.49303i) q^{39} +(0.117365 - 0.979014i) q^{40} +7.57031i q^{41} +2.51757i q^{43} +(7.10130 + 3.24484i) q^{44} +(-0.0712361 + 1.04341i) q^{45} +(-0.656216 + 3.01507i) q^{46} +(2.18189 + 3.77914i) q^{47} +(-4.35371 - 5.38936i) q^{48} +(6.57182 - 2.10003i) q^{50} +(-0.230411 + 6.75759i) q^{51} +(0.557569 + 5.85197i) q^{52} +(1.49119 + 0.860938i) q^{53} +(4.90400 + 5.47273i) q^{54} -1.36090i q^{55} +(8.19802 + 5.11331i) q^{57} +(9.27819 - 10.2042i) q^{58} +(4.12318 - 7.14155i) q^{59} +(-0.539033 + 1.08065i) q^{60} +(-7.04795 - 12.2074i) q^{61} +(-1.13605 - 3.55515i) q^{62} +(-2.24908 - 7.67735i) q^{64} +(0.887375 - 0.512326i) q^{65} +(-6.85160 - 6.67022i) q^{66} +(-0.553478 - 0.319551i) q^{67} +(-3.24484 + 7.10130i) q^{68} +(2.00000 - 3.20654i) q^{69} -11.9341 q^{71} +(2.79868 + 8.01046i) q^{72} +(3.93923 - 6.82295i) q^{73} +(-0.192214 + 0.883151i) q^{74} +(-8.44485 - 0.287941i) q^{75} +(6.46962 + 9.08930i) q^{76} +(1.76996 - 6.97867i) q^{78} +(3.46410 - 2.00000i) q^{79} +(-1.05423 + 0.912731i) q^{80} +(-3.39892 - 8.33351i) q^{81} +(7.20235 - 7.92120i) q^{82} +8.94358 q^{83} +1.36090 q^{85} +(2.39520 - 2.63426i) q^{86} +(-14.9076 + 7.94226i) q^{87} +(-4.34333 - 10.1514i) q^{88} +(9.12760 - 5.26982i) q^{89} +(1.06723 - 1.02400i) q^{90} +(3.55515 - 2.53050i) q^{92} +(-0.155767 + 4.56840i) q^{93} +(1.31243 - 6.03014i) q^{94} +(0.972337 - 1.68414i) q^{95} +(-0.571901 + 9.78125i) q^{96} +2.00000 q^{97} +(5.15121 + 10.5176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} + 2 q^{24} + 12 q^{25} - 20 q^{30} - 16 q^{33} - 64 q^{34} - 40 q^{36} + 16 q^{37} + 20 q^{40} + 24 q^{45} - 92 q^{48}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 4 * q^4 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 + 2 * q^24 + 12 * q^25 - 20 * q^30 - 16 * q^33 - 64 * q^34 - 40 * q^36 + 16 * q^37 + 20 * q^40 + 24 * q^45 - 92 * q^48 - 28 * q^52 + 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 - 16 * q^61 + 40 * q^64 - 12 * q^66 + 48 * q^69 + 32 * q^72 + 24 * q^73 + 120 * q^76 + 40 * q^78 - 28 * q^81 + 8 * q^82 + 80 * q^85 + 56 * q^88 + 160 * q^90 - 24 * q^93 - 34 * q^96 + 48 * q^97

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