LMFDB - Embedded newform 572.2.t.a.87.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(87,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, 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("572.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.t (of order $6$, degree $2$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			87.14
Character	$\chi$	$=$	572.87
Dual form			572.2.t.a.263.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19068 + 0.763078i) q^{2} +(-2.37620 - 1.37190i) q^{3} +(0.835423 - 1.81716i) q^{4} +1.57679 q^{5} +(3.87615 - 0.179738i) q^{6} +(0.286729 + 0.496630i) q^{7} +(0.391917 + 2.80114i) q^{8} +(2.26422 + 3.92174i) q^{9} +O(q^{10})$	\(q+(-1.19068 + 0.763078i) q^{2} +(-2.37620 - 1.37190i) q^{3} +(0.835423 - 1.81716i) q^{4} +1.57679 q^{5} +(3.87615 - 0.179738i) q^{6} +(0.286729 + 0.496630i) q^{7} +(0.391917 + 2.80114i) q^{8} +(2.26422 + 3.92174i) q^{9} +(-1.87745 + 1.20322i) q^{10} +(-3.25416 - 0.640664i) q^{11} +(-4.47809 + 3.17182i) q^{12} +(-1.32019 + 3.35516i) q^{13} +(-0.720370 - 0.372529i) q^{14} +(-3.74677 - 2.16320i) q^{15} +(-2.60414 - 3.03619i) q^{16} +(2.82829 - 1.63292i) q^{17} +(-5.68855 - 2.94175i) q^{18} +(0.446504 + 0.773368i) q^{19} +(1.31729 - 2.86528i) q^{20} -1.57346i q^{21} +(4.36353 - 1.72035i) q^{22} +(3.92787 + 2.26776i) q^{23} +(2.91162 - 7.19375i) q^{24} -2.51373 q^{25} +(-0.988327 - 5.00232i) q^{26} -4.19373i q^{27} +(1.14200 - 0.106137i) q^{28} +(-1.23606 - 0.713642i) q^{29} +(6.11189 - 0.283409i) q^{30} +2.13840i q^{31} +(5.41754 + 1.62796i) q^{32} +(6.85361 + 5.98673i) q^{33} +(-2.12154 + 4.10248i) q^{34} +(0.452113 + 0.783082i) q^{35} +(9.01801 - 0.838134i) q^{36} +(-1.03356 + 1.79018i) q^{37} +(-1.12178 - 0.580114i) q^{38} +(7.73998 - 6.16136i) q^{39} +(0.617971 + 4.41682i) q^{40} +(9.59598 + 5.54024i) q^{41} +(1.20067 + 1.87348i) q^{42} +(2.86577 + 4.96366i) q^{43} +(-3.88279 + 5.37810i) q^{44} +(3.57020 + 6.18377i) q^{45} +(-6.40730 + 0.297107i) q^{46} +6.60943i q^{47} +(2.02260 + 10.7872i) q^{48} +(3.33557 - 5.77738i) q^{49} +(2.99304 - 1.91817i) q^{50} -8.96079 q^{51} +(4.99394 + 5.20198i) q^{52} +8.91277 q^{53} +(3.20014 + 4.99338i) q^{54} +(-5.13113 - 1.01019i) q^{55} +(-1.27876 + 0.997808i) q^{56} -2.45024i q^{57} +(2.01632 - 0.0934968i) q^{58} +(4.96297 - 2.86537i) q^{59} +(-7.06102 + 5.00130i) q^{60} +(-9.42166 + 5.43960i) q^{61} +(-1.63177 - 2.54615i) q^{62} +(-1.29844 + 2.24896i) q^{63} +(-7.69280 + 2.19563i) q^{64} +(-2.08167 + 5.29039i) q^{65} +(-12.7288 - 1.89842i) q^{66} +(6.79453 + 3.92282i) q^{67} +(-0.604448 - 6.50363i) q^{68} +(-6.22228 - 10.7773i) q^{69} +(-1.13587 - 0.587400i) q^{70} +(14.1662 - 8.17885i) q^{71} +(-10.0980 + 7.87940i) q^{72} +2.80396i q^{73} +(-0.135410 - 2.92021i) q^{74} +(5.97313 + 3.44859i) q^{75} +(1.77835 - 0.165280i) q^{76} +(-0.614890 - 1.79981i) q^{77} +(-4.51422 + 13.2424i) q^{78} +0.297057 q^{79} +(-4.10618 - 4.78744i) q^{80} +(1.03928 - 1.80009i) q^{81} +(-15.6534 + 0.725848i) q^{82} +8.81958 q^{83} +(-2.85922 - 1.31450i) q^{84} +(4.45963 - 2.57477i) q^{85} +(-7.19987 - 3.72331i) q^{86} +(1.95809 + 3.39151i) q^{87} +(0.519234 - 9.36645i) q^{88} +(1.52380 - 2.63930i) q^{89} +(-8.96966 - 4.63853i) q^{90} +(-2.04481 + 0.306376i) q^{91} +(7.40231 - 5.24303i) q^{92} +(2.93368 - 5.08127i) q^{93} +(-5.04351 - 7.86970i) q^{94} +(0.704044 + 1.21944i) q^{95} +(-10.6398 - 11.3007i) q^{96} +(0.361220 + 0.625652i) q^{97} +(0.437005 + 9.42430i) q^{98} +(-4.85561 - 14.2126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) $ 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9	$ 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9} - 4 q^{12} + 8 q^{14} - 14 q^{16} - 26 q^{20} + 112 q^{25} - 14 q^{33} + 12 q^{34} - 6 q^{36} - 4 q^{37} + 40 q^{38} + 54 q^{42} - 16 q^{44} - 48 q^{45} - 40 q^{48} - 52 q^{49} - 32 q^{53} - 18 q^{56} - 6 q^{58} - 52 q^{60} + 16 q^{64} - 84 q^{66} - 12 q^{69} - 68 q^{70} - 4 q^{77} + 28 q^{78} - 44 q^{80} - 40 q^{81} - 38 q^{82} + 120 q^{86} - 14 q^{88} - 64 q^{92} - 8 q^{93}+O(q^{100}) $ 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9 - 4 * q^12 + 8 * q^14 - 14 * q^16 - 26 * q^20 + 112 * q^25 - 14 * q^33 + 12 * q^34 - 6 * q^36 - 4 * q^37 + 40 * q^38 + 54 * q^42 - 16 * q^44 - 48 * q^45 - 40 * q^48 - 52 * q^49 - 32 * q^53 - 18 * q^56 - 6 * q^58 - 52 * q^60 + 16 * q^64 - 84 * q^66 - 12 * q^69 - 68 * q^70 - 4 * q^77 + 28 * q^78 - 44 * q^80 - 40 * q^81 - 38 * q^82 + 120 * q^86 - 14 * q^88 - 64 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.19068	+	0.763078i	−0.841936	+	0.539578i
$2$	−1.19068	+	0.763078i	−0.841936	+	0.539578i
$3$	−2.37620	−	1.37190i	−1.37190	−	0.792067i	−0.380733	−	0.924685i	$-0.624328\pi$
$3$	−2.37620	−	1.37190i	−1.37190	−	0.792067i	−0.991167	+	0.132618i	$0.957662\pi$
$4$	0.835423	−	1.81716i	0.417711	−	0.908580i
$5$	1.57679			0.705162			0.352581	−	0.935781i	$-0.385304\pi$
$5$	1.57679			0.705162			0.352581	+	0.935781i	$0.385304\pi$
$6$	3.87615	−	0.179738i	1.58243	−	0.0733776i
$7$	0.286729	+	0.496630i	0.108374	+	0.187708i	0.915111	−	0.403201i	$-0.132102\pi$
$7$	0.286729	+	0.496630i	0.108374	+	0.187708i	−0.806738	+	0.590909i	$0.798769\pi$
$8$	0.391917	+	2.80114i	0.138563	+	0.990354i
$9$	2.26422	+	3.92174i	0.754740	+	1.30725i
$10$	−1.87745	+	1.20322i	−0.593701	+	0.380490i
$11$	−3.25416	−	0.640664i	−0.981166	−	0.193168i
$11$	−3.25416	−	0.640664i	−0.981166	−	0.193168i
$12$	−4.47809	+	3.17182i	−1.29271	+	0.915625i
$13$	−1.32019	+	3.35516i	−0.366155	+	0.930554i
$13$	−1.32019	+	3.35516i	−0.366155	+	0.930554i
$14$	−0.720370	−	0.372529i	−0.192527	−	0.0995625i
$15$	−3.74677	−	2.16320i	−0.967412	−	0.558536i
$16$	−2.60414	−	3.03619i	−0.651034	−	0.759048i
$17$	2.82829	−	1.63292i	0.685962	−	0.396040i	−0.116136	−	0.993233i	$-0.537051\pi$
$17$	2.82829	−	1.63292i	0.685962	−	0.396040i	0.802097	+	0.597193i	$0.203717\pi$
$18$	−5.68855	−	2.94175i	−1.34080	−	0.693377i
$19$	0.446504	+	0.773368i	0.102435	+	0.177423i	0.912687	−	0.408658i	$-0.134003\pi$
$19$	0.446504	+	0.773368i	0.102435	+	0.177423i	−0.810252	+	0.586081i	$0.800670\pi$
$20$	1.31729	−	2.86528i	0.294554	−	0.640696i
$21$		−	1.57346i		−	0.343356i
$22$	4.36353	−	1.72035i	0.930307	−	0.366781i
$23$	3.92787	+	2.26776i	0.819018	+	0.472860i	0.850078	−	0.526657i	$-0.176555\pi$
$23$	3.92787	+	2.26776i	0.819018	+	0.472860i	−0.0310597	+	0.999518i	$0.509888\pi$
$24$	2.91162	−	7.19375i	0.594331	−	1.46842i
$25$	−2.51373			−0.502746
$26$	−0.988327	−	5.00232i	−0.193827	−	0.981036i
$27$		−	4.19373i		−	0.807083i
$28$	1.14200	−	0.106137i	0.215817	−	0.0200580i
$29$	−1.23606	−	0.713642i	−0.229531	−	0.132520i	0.380825	−	0.924647i	$-0.375640\pi$
$29$	−1.23606	−	0.713642i	−0.229531	−	0.132520i	−0.610356	+	0.792127i	$0.708974\pi$
$30$	6.11189	−	0.283409i	1.11587	−	0.0517431i
$31$			2.13840i			0.384069i	0.981388	+	0.192034i	$0.0615085\pi$
$31$			2.13840i			0.384069i	−0.981388	+	0.192034i	$0.938492\pi$
$32$	5.41754	+	1.62796i	0.957695	+	0.287786i
$33$	6.85361	+	5.98673i	1.19306	+	1.04216i
$34$	−2.12154	+	4.10248i	−0.363841	+	0.703570i
$35$	0.452113	+	0.783082i	0.0764210	+	0.132365i
$36$	9.01801	−	0.838134i	1.50300	−	0.139689i
$37$	−1.03356	+	1.79018i	−0.169916	+	0.294303i	−0.938390	−	0.345578i	$-0.887683\pi$
$37$	−1.03356	+	1.79018i	−0.169916	+	0.294303i	0.768474	+	0.639881i	$0.221016\pi$
$38$	−1.12178	−	0.580114i	−0.181977	−	0.0941068i
$39$	7.73998	−	6.16136i	1.23939	−	0.986607i
$40$	0.617971	+	4.41682i	0.0977097	+	0.698360i
$41$	9.59598	+	5.54024i	1.49864	+	0.865241i	0.999999	−	0.00156704i	$-0.000498806\pi$
$41$	9.59598	+	5.54024i	1.49864	+	0.865241i	0.498642	+	0.866808i	$0.333832\pi$
$42$	1.20067	+	1.87348i	0.185268	+	0.289084i
$43$	2.86577	+	4.96366i	0.437026	+	0.756951i	0.997459	−	0.0712491i	$-0.0226985\pi$
$43$	2.86577	+	4.96366i	0.437026	+	0.756951i	−0.560433	+	0.828200i	$0.689365\pi$
$44$	−3.88279	+	5.37810i	−0.585352	+	0.810779i
$45$	3.57020	+	6.18377i	0.532214	+	0.921822i
$46$	−6.40730	+	0.297107i	−0.944706	+	0.0438061i
$47$			6.60943i			0.964085i	0.876148	+	0.482042i	$0.160105\pi$
$47$			6.60943i			0.964085i	−0.876148	+	0.482042i	$0.839895\pi$
$48$	2.02260	+	10.7872i	0.291937	+	1.55700i
$49$	3.33557	−	5.77738i	0.476510	−	0.825340i
$50$	2.99304	−	1.91817i	0.423280	−	0.271271i
$51$	−8.96079			−1.25476
$52$	4.99394	+	5.20198i	0.692535	+	0.721384i
$53$	8.91277			1.22426			0.612132	−	0.790756i	$-0.290312\pi$
$53$	8.91277			1.22426			0.612132	+	0.790756i	$0.290312\pi$
$54$	3.20014	+	4.99338i	0.435484	+	0.679512i
$55$	−5.13113	−	1.01019i	−0.691881	−	0.136215i
$56$	−1.27876	+	0.997808i	−0.170881	+	0.133338i
$57$		−	2.45024i		−	0.324542i
$58$	2.01632	−	0.0934968i	0.264755	−	0.0122767i
$59$	4.96297	−	2.86537i	0.646124	−	0.373040i	−0.140846	−	0.990032i	$-0.544982\pi$
$59$	4.96297	−	2.86537i	0.646124	−	0.373040i	0.786970	+	0.616992i	$0.211649\pi$
$60$	−7.06102	+	5.00130i	−0.911573	+	0.645665i
$61$	−9.42166	+	5.43960i	−1.20632	+	0.696469i	−0.961953	−	0.273214i	$-0.911913\pi$
$61$	−9.42166	+	5.43960i	−1.20632	+	0.696469i	−0.244367	+	0.969683i	$0.578580\pi$
$62$	−1.63177	−	2.54615i	−0.207235	−	0.323361i
$63$	−1.29844	+	2.24896i	−0.163588	+	0.283342i
$64$	−7.69280	+	2.19563i	−0.961600	+	0.274454i
$65$	−2.08167	+	5.29039i	−0.258199	+	0.656192i
$66$	−12.7288	−	1.89842i	−1.56680	−	0.233679i
$67$	6.79453	+	3.92282i	0.830084	+	0.479249i	0.853881	−	0.520468i	$-0.174242\pi$
$67$	6.79453	+	3.92282i	0.830084	+	0.479249i	−0.0237974	+	0.999717i	$0.507576\pi$
$68$	−0.604448	−	6.50363i	−0.0733001	−	0.788681i
$69$	−6.22228	−	10.7773i	−0.749074	−	1.29743i
$70$	−1.13587	−	0.587400i	−0.135763	−	0.0702077i
$71$	14.1662	−	8.17885i	1.68122	−	0.970651i	0.720361	−	0.693599i	$-0.243976\pi$
$71$	14.1662	−	8.17885i	1.68122	−	0.970651i	0.960855	−	0.277052i	$-0.0893574\pi$
$72$	−10.0980	+	7.87940i	−1.19006	+	0.928596i
$73$			2.80396i			0.328179i	0.986445	+	0.164089i	$0.0524685\pi$
$73$			2.80396i			0.328179i	−0.986445	+	0.164089i	$0.947531\pi$
$74$	−0.135410	−	2.92021i	−0.0157411	−	0.339467i
$75$	5.97313	+	3.44859i	0.689717	+	0.398208i
$76$	1.77835	−	0.165280i	0.203991	−	0.0189589i
$77$	−0.614890	−	1.79981i	−0.0700732	−	0.205107i
$78$	−4.51422	+	13.2424i	−0.511135	+	1.49941i
$79$	0.297057			0.0334215			0.0167108	−	0.999860i	$-0.494681\pi$
$79$	0.297057			0.0334215			0.0167108	+	0.999860i	$0.494681\pi$
$80$	−4.10618	−	4.78744i	−0.459085	−	0.535252i
$81$	1.03928	−	1.80009i	0.115476	−	0.200010i
$82$	−15.6534	+	0.725848i	−1.72862	+	0.0801565i
$83$	8.81958			0.968075			0.484037	−	0.875047i	$-0.339170\pi$
$83$	8.81958			0.968075			0.484037	+	0.875047i	$0.339170\pi$
$84$	−2.85922	−	1.31450i	−0.311967	−	0.143424i
$85$	4.45963	−	2.57477i	0.483714	−	0.279273i
$86$	−7.19987	−	3.72331i	−0.776381	−	0.401494i
$87$	1.95809	+	3.39151i	0.209929	+	0.363608i
$88$	0.519234	−	9.36645i	0.0553505	−	0.998467i
$89$	1.52380	−	2.63930i	0.161522	−	0.279765i	−0.773892	−	0.633317i	$-0.781693\pi$
$89$	1.52380	−	2.63930i	0.161522	−	0.279765i	0.935415	+	0.353552i	$0.115026\pi$
$90$	−8.96966	−	4.63853i	−0.945485	−	0.488944i
$91$	−2.04481	+	0.306376i	−0.214354	+	0.0321169i
$92$	7.40231	−	5.24303i	0.771744	−	0.546624i
$93$	2.93368	−	5.08127i	0.304208	−	0.526904i
$94$	−5.04351	−	7.86970i	−0.520199	−	0.811697i
$95$	0.704044	+	1.21944i	0.0722334	+	0.125112i
$96$	−10.6398	−	11.3007i	−1.08592	−	1.15337i
$97$	0.361220	+	0.625652i	0.0366763	+	0.0635253i	0.883781	−	0.467901i	$-0.154990\pi$
$97$	0.361220	+	0.625652i	0.0366763	+	0.0635253i	−0.847105	+	0.531426i	$0.821656\pi$
$98$	0.437005	+	9.42430i	0.0441442	+	0.951998i
$99$	−4.85561	−	14.2126i	−0.488007	−	1.42842i
$100$	−2.10003	+	4.56785i	−0.210003	+	0.456785i
$101$	−13.8751	−	8.01079i	−1.38062	−	0.797104i	−0.388391	−	0.921495i	$-0.626969\pi$
$101$	−13.8751	−	8.01079i	−1.38062	−	0.797104i	−0.992233	+	0.124391i	$0.960302\pi$
$102$	10.6694	−	6.83778i	1.05643	−	0.677041i
$103$			3.64727i			0.359376i	0.983724	+	0.179688i	$0.0575088\pi$
$103$			3.64727i			0.359376i	−0.983724	+	0.179688i	$0.942491\pi$
$104$	−9.91569	−	2.38310i	−0.972313	−	0.233683i
$105$		−	2.48101i		−	0.242122i
$106$	−10.6122	+	6.80114i	−1.03075	+	0.660586i
$107$	−7.30323	+	12.6496i	−0.706030	+	1.22288i	0.260289	+	0.965531i	$0.416182\pi$
$107$	−7.30323	+	12.6496i	−0.706030	+	1.22288i	−0.966319	+	0.257348i	$0.917151\pi$
$108$	−7.62067	−	3.50354i	−0.733300	−	0.337128i
$109$			7.61084i			0.728986i	0.931206	+	0.364493i	$0.118758\pi$
$109$			7.61084i			0.728986i	−0.931206	+	0.364493i	$0.881242\pi$
$110$	6.88037	−	2.71264i	0.656018	−	0.258640i
$111$	4.91188	−	2.83588i	0.466215	−	0.269170i
$112$	0.761182	−	2.16386i	0.0719249	−	0.204465i
$113$	−1.12062	−	1.94096i	−0.105419	−	0.182590i	0.808491	−	0.588509i	$-0.200285\pi$
$113$	−1.12062	−	1.94096i	−0.105419	−	0.182590i	−0.913909	+	0.405919i	$0.866952\pi$
$114$	1.86972	+	2.91744i	0.175116	+	0.273243i
$115$	6.19344	+	3.57578i	0.577541	+	0.333443i
$116$	−2.32944	+	1.64993i	−0.216283	+	0.153192i
$117$	−16.1473	+	2.41936i	−1.49282	+	0.223670i
$118$	−3.72279	+	7.19887i	−0.342711	+	0.662710i
$119$	1.62191	+	0.936410i	0.148680	+	0.0858406i
$120$	4.59101	−	11.3430i	0.419100	−	1.03547i
$121$	10.1791	+	4.16965i	0.925373	+	0.379059i
$122$	7.06731	−	13.6663i	0.639844	−	1.23729i
$123$	−15.2013	−	26.3295i	−1.37066	−	2.37405i
$124$	3.88582	+	1.78647i	0.348957	+	0.160430i
$125$	−11.8476			−1.05968
$126$	−0.170113	−	3.66859i	−0.0151549	−	0.326824i
$127$	−3.06048	+	5.30091i	−0.271574	+	0.470380i	−0.969265	−	0.246019i	$-0.920877\pi$
$127$	−3.06048	+	5.30091i	−0.271574	+	0.470380i	0.697691	+	0.716399i	$0.254211\pi$
$128$	7.48421	−	8.48450i	0.661517	−	0.749931i
$129$		−	15.7262i		−	1.38461i
$130$	−1.55839	−	7.88761i	−0.136679	−	0.691790i
$131$	14.3706			1.25557			0.627783	−	0.778388i	$-0.283962\pi$
$131$	14.3706			1.25557			0.627783	+	0.778388i	$0.283962\pi$
$132$	16.6045	−	7.45265i	1.44524	−	0.648670i
$133$	−0.256052	+	0.443495i	−0.0222025	+	0.0384559i
$134$	−11.0835	+	0.513943i	−0.957470	+	0.0443980i
$135$		−	6.61263i		−	0.569125i
$136$	5.68248	+	7.28248i	0.487269	+	0.624468i
$137$	10.0609	+	17.4260i	0.859560	+	1.48880i	0.872349	+	0.488884i	$0.162596\pi$
$137$	10.0609	+	17.4260i	0.859560	+	1.48880i	−0.0127885	+	0.999918i	$0.504071\pi$
$138$	15.6326	+	8.08419i	1.33074	+	0.688172i
$139$	−4.77323	−	8.26748i	−0.404860	−	0.701239i	0.589445	−	0.807809i	$-0.299347\pi$
$139$	−4.77323	−	8.26748i	−0.404860	−	0.701239i	−0.994305	+	0.106570i	$0.966013\pi$
$140$	1.80069	−	0.167356i	0.152186	−	0.0141442i
$141$	9.06748	−	15.7053i	0.763620	−	1.32263i
$142$	−10.6262	+	20.5483i	−0.891734	+	1.72437i
$143$	6.44565	−	10.0724i	0.539012	−	0.842298i
$144$	6.01083	−	17.0874i	0.500902	−	1.42395i
$145$	−1.94901	−	1.12526i	−0.161857	−	0.0934481i
$146$	−2.13964	−	3.33861i	−0.177078	−	0.276305i
$147$	−15.8520	+	9.15214i	−1.30745	+	0.754856i
$148$	2.38958	+	3.37369i	0.196422	+	0.277316i
$149$	−16.3808	+	9.45744i	−1.34197	+	0.774784i	−0.987096	−	0.160132i	$-0.948808\pi$
$149$	−16.3808	+	9.45744i	−1.34197	+	0.774784i	−0.354870	+	0.934916i	$0.615475\pi$
$150$	−9.74360	+	0.451812i	−0.795562	+	0.0368903i
$151$	−9.52035			−0.774755			−0.387378	−	0.921921i	$-0.626619\pi$
$151$	−9.52035			−0.774755			−0.387378	+	0.921921i	$0.626619\pi$
$152$	−1.99132	+	1.55382i	−0.161517	+	0.126031i
$153$	12.8077	+	7.39456i	1.03544	+	0.597814i
$154$	2.10553	+	1.67378i	0.169669	+	0.134877i
$155$			3.37182i			0.270831i
$156$	−4.73001	−	19.2121i	−0.378704	−	1.53820i
$157$	−9.08062			−0.724712			−0.362356	−	0.932040i	$-0.618028\pi$
$157$	−9.08062			−0.724712			−0.362356	+	0.932040i	$0.618028\pi$
$158$	−0.353699	+	0.226678i	−0.0281388	+	0.0180335i
$159$	−21.1785	−	12.2274i	−1.67957	−	0.969698i
$160$	8.54233	+	2.56696i	0.675330	+	0.202936i
$161$			2.60093i			0.204982i
$162$	0.136160	+	2.93638i	0.0106977	+	0.230703i
$163$	−3.68800	+	2.12927i	−0.288867	+	0.166777i	−0.637431	−	0.770508i	$-0.720003\pi$
$163$	−3.68800	+	2.12927i	−0.288867	+	0.166777i	0.348564	+	0.937285i	$0.386669\pi$
$164$	18.0842	−	12.8090i	1.41214	−	1.00021i
$165$	10.8067	+	9.43982i	0.841301	+	0.734889i
$166$	−10.5013	+	6.73003i	−0.815057	+	0.522352i
$167$	5.95936	−	10.3219i	0.461149	−	0.798734i	−0.537869	−	0.843028i	$-0.680771\pi$
$167$	5.95936	−	10.3219i	0.461149	−	0.798734i	0.999019	+	0.0442944i	$0.0141040\pi$
$168$	4.40748	−	0.616664i	0.340044	−	0.0475766i
$169$	−9.51419	−	8.85891i	−0.731860	−	0.681454i
$170$	−3.34523	+	6.46876i	−0.256567	+	0.496131i
$171$	−2.02197	+	3.50215i	−0.154624	+	0.267816i
$172$	11.4139	−	1.06081i	0.870301	−	0.0808858i
$173$	0.321438	−	0.185582i	0.0244384	−	0.0141095i	−0.487731	−	0.872994i	$-0.662175\pi$
$173$	0.321438	−	0.185582i	0.0244384	−	0.0141095i	0.512169	+	0.858884i	$0.328842\pi$
$174$	−4.91944	−	2.54402i	−0.372942	−	0.192862i
$175$	−0.720760	−	1.24839i	−0.0544844	−	0.0943697i
$176$	6.52910	+	11.5486i	0.492149	+	0.870511i
$177$	−15.7240			−1.18189
$178$	0.199639	+	4.30533i	0.0149635	+	0.322698i
$179$	−4.51236	−	2.60521i	−0.337269	−	0.194722i	0.321795	−	0.946810i	$-0.395714\pi$
$179$	−4.51236	−	2.60521i	−0.337269	−	0.194722i	−0.659064	+	0.752087i	$0.729047\pi$
$180$	14.2195	−	1.32156i	1.05986	−	0.0985035i
$181$	14.3513			1.06672			0.533362	−	0.845887i	$-0.320928\pi$
$181$	14.3513			1.06672			0.533362	+	0.845887i	$0.320928\pi$
$182$	2.20092	−	1.92515i	0.163143	−	0.142701i
$183$	29.8503			2.20660
$184$	−4.81292	+	11.8913i	−0.354813	+	0.876639i
$185$	−1.62971	+	2.82273i	−0.119818	+	0.207531i
$186$	0.384351	+	8.28878i	0.0281820	+	0.607763i
$187$	−10.2499	+	3.50178i	−0.749544	+	0.256075i
$188$	12.0104	+	5.52167i	0.875948	+	0.402709i
$189$	2.08273	−	1.20247i	0.151496	−	0.0874665i
$190$	−1.76882	−	0.914718i	−0.128323	−	0.0663606i
$191$	−4.34400	+	2.50801i	−0.314321	+	0.181473i	−0.648858	−	0.760909i	$-0.724753\pi$
$191$	−4.34400	+	2.50801i	−0.314321	+	0.181473i	0.334537	+	0.942382i	$0.391420\pi$
$192$	21.2918	+	5.33650i	1.53661	+	0.385129i
$193$	22.5040	+	12.9927i	1.61988	+	0.935236i	0.986951	+	0.161023i	$0.0514793\pi$
$193$	22.5040	+	12.9927i	1.61988	+	0.935236i	0.632925	+	0.774213i	$0.281854\pi$
$194$	−0.907518	−	0.469310i	−0.0651560	−	0.0336945i
$195$	12.2043	−	9.71518i	0.873971	−	0.695718i
$196$	−7.71181	−	10.8878i	−0.550844	−	0.777702i
$197$	−15.4725	−	8.93306i	−1.10237	−	0.636454i	−0.165528	−	0.986205i	$-0.552933\pi$
$197$	−15.4725	−	8.93306i	−1.10237	−	0.636454i	−0.936843	+	0.349751i	$0.886266\pi$
$198$	16.6268	+	13.2174i	1.18161	+	0.939318i
$199$	−16.7132	+	9.64936i	−1.18477	+	0.684025i	−0.957112	−	0.289717i	$-0.906439\pi$
$199$	−16.7132	+	9.64936i	−1.18477	+	0.684025i	−0.227654	+	0.973742i	$0.573106\pi$
$200$	−0.985172	−	7.04132i	−0.0696622	−	0.497896i
$201$	−10.7634	−	18.6428i	−0.759195	−	1.31496i
$202$	22.6336	−	1.04952i	1.59250	−	0.0738442i
$203$		−	0.818489i		−	0.0574466i
$204$	−7.48604	+	16.2832i	−0.524128	+	1.14005i
$205$	15.1309	+	8.73581i	1.05679	+	0.610135i
$206$	−2.78315	−	4.34272i	−0.193911	−	0.302572i
$207$			20.5388i			1.42755i
$208$	13.6249	−	4.72894i	0.944715	−	0.327893i
$209$	−0.957526	−	2.80272i	−0.0662335	−	0.193868i
$210$	1.89321	+	2.95408i	0.130644	+	0.203851i
$211$	−5.88988	+	10.2016i	−0.405476	+	0.702305i	−0.994377	−	0.105900i	$-0.966228\pi$
$211$	−5.88988	+	10.2016i	−0.405476	+	0.702305i	0.588901	+	0.808205i	$0.299561\pi$
$212$	7.44593	−	16.1959i	0.511389	−	1.11234i
$213$	−44.8822			−3.07528
$214$	−0.956822	−	20.6345i	−0.0654070	−	1.41054i
$215$	4.51872	+	7.82665i	0.308174	+	0.533773i
$216$	11.7472	−	1.64359i	0.799298	−	0.111832i
$217$	−1.06200	+	0.613143i	−0.0720929	+	0.0416229i
$218$	−5.80767	−	9.06205i	−0.393345	−	0.613759i
$219$	3.84675	−	6.66277i	0.259939	−	0.450228i
$220$	−6.12235	+	8.48014i	−0.412768	+	0.571731i
$221$	1.74480	+	11.6451i	0.117368	+	0.783336i
$222$	−3.68447	+	7.12477i	−0.247285	+	0.478183i
$223$	6.71515	+	3.87700i	0.449680	+	0.259623i	0.707695	−	0.706518i	$-0.249735\pi$
$223$	6.71515	+	3.87700i	0.449680	+	0.259623i	−0.258015	+	0.966141i	$0.583068\pi$
$224$	0.744873	+	3.15730i	0.0497689	+	0.210956i
$225$	−5.69163	−	9.85820i	−0.379442	−	0.657213i
$226$	2.81540	+	1.45594i	0.187277	+	0.0968478i
$227$	−7.81286	−	13.5323i	−0.518558	−	0.898168i	−0.999767	−	0.0215630i	$-0.993136\pi$
$227$	−7.81286	−	13.5323i	−0.518558	−	0.898168i	0.481210	−	0.876606i	$-0.340198\pi$
$228$	−4.45247	−	2.04698i	−0.294872	−	0.135565i
$229$	−4.40894			−0.291351			−0.145675	−	0.989332i	$-0.546536\pi$
$229$	−4.40894			−0.291351			−0.145675	+	0.989332i	$0.546536\pi$
$230$	−10.1030	+	0.468476i	−0.666171	+	0.0308904i
$231$	−1.00806	+	5.12028i	−0.0663253	+	0.336890i
$232$	1.51458	−	3.74208i	0.0994370	−	0.245680i
$233$		−	4.82310i		−	0.315972i	−0.987441	−	0.157986i	$-0.949500\pi$
$233$		−	4.82310i		−	0.315972i	0.987441	−	0.157986i	$-0.0505000\pi$
$234$	17.3800	−	15.2023i	1.13617	−	0.993806i
$235$			10.4217i			0.679836i
$236$	−1.06066	−	11.4123i	−0.0690431	−	0.742878i
$237$	−0.705867	−	0.407532i	−0.0458510	−	0.0264721i
$238$	−2.64572	+	0.122682i	−0.171497	+	0.00795232i
$239$	−16.1895			−1.04721			−0.523606	−	0.851961i	$-0.675413\pi$
$239$	−16.1895			−1.04721			−0.523606	+	0.851961i	$0.675413\pi$
$240$	3.18922	+	17.0092i	0.205863	+	1.09794i
$241$	7.79160	−	4.49848i	0.501901	−	0.289773i	−0.227597	−	0.973755i	$-0.573087\pi$
$241$	7.79160	−	4.49848i	0.501901	−	0.289773i	0.729498	+	0.683983i	$0.239754\pi$
$242$	−15.3018	+	2.80275i	−0.983636	+	0.180167i
$243$	−15.8347	+	9.14217i	−1.01580	+	0.586471i
$244$	2.01355	+	21.6650i	0.128904	+	1.38696i
$245$	5.25950	−	9.10972i	0.336017	−	0.581999i
$246$	38.1913	+	19.7501i	2.43499	+	1.25922i
$247$	−3.18424	+	0.477098i	−0.202609	+	0.0303570i
$248$	−5.98997	+	0.838075i	−0.380364	+	0.0532178i
$249$	−20.9571	−	12.0996i	−1.32810	−	0.766780i
$250$	14.1066	−	9.04063i	0.892182	−	0.571780i
$251$	22.9452	−	13.2474i	1.44829	−	0.836168i	0.449906	−	0.893076i	$-0.351457\pi$
$251$	22.9452	−	13.2474i	1.44829	−	0.836168i	0.998379	+	0.0569077i	$0.0181241\pi$
$252$	3.00197	+	4.23830i	0.189106	+	0.266988i
$253$	−11.3290	−	9.89609i	−0.712251	−	0.622162i
$254$	−0.400965	−	8.64706i	−0.0251588	−	0.542565i
$255$	−14.1293			−0.884810
$256$	−2.43694	+	15.8133i	−0.152308	+	0.988333i
$257$	−10.3740	+	17.9684i	−0.647115	+	1.12084i	0.336694	+	0.941614i	$0.390691\pi$
$257$	−10.3740	+	17.9684i	−0.647115	+	1.12084i	−0.983809	+	0.179222i	$0.942642\pi$
$258$	12.0003	+	18.7248i	0.747107	+	1.16576i
$259$	−1.18541			−0.0736576
$260$	7.87440	+	8.20243i	0.488350	+	0.508693i
$261$		−	6.46337i		−	0.400072i
$262$	−17.1108	+	10.9659i	−1.05711	+	0.677476i
$263$	−10.4378	+	18.0788i	−0.643623	+	1.11479i	0.340995	+	0.940065i	$0.389236\pi$
$263$	−10.4378	+	18.0788i	−0.643623	+	1.11479i	−0.984618	+	0.174722i	$0.944097\pi$
$264$	−14.0836	+	21.5442i	−0.866788	+	1.32596i
$265$	14.0536			0.863305
$266$	−0.0335463	−	0.723446i	−0.00205685	−	0.0443573i
$267$	−7.24171	+	4.18100i	−0.443185	+	0.255873i
$268$	12.8047	−	9.06953i	0.782172	−	0.554010i
$269$	6.20650	+	10.7500i	0.378417	+	0.655437i	0.990832	−	0.135099i	$-0.0431352\pi$
$269$	6.20650	+	10.7500i	0.378417	+	0.655437i	−0.612415	+	0.790536i	$0.709802\pi$
$270$	5.04596	+	7.87351i	0.307087	+	0.479167i
$271$	−12.3814	+	21.4452i	−0.752115	+	1.30270i	0.194680	+	0.980867i	$0.437633\pi$
$271$	−12.3814	+	21.4452i	−0.752115	+	1.30270i	−0.946796	+	0.321835i	$0.895700\pi$
$272$	−12.3231	−	4.33491i	−0.747198	−	0.262842i
$273$	5.27920	+	2.07726i	0.319512	+	0.125722i
$274$	−25.2767	−	13.0715i	−1.52702	−	0.789676i
$275$	8.18007	+	1.61046i	0.493277	+	0.0971142i
$276$	−24.7823	+	2.30327i	−1.49172	+	0.138640i
$277$	3.87541	−	2.23747i	0.232851	−	0.134436i	−0.379036	−	0.925382i	$-0.623744\pi$
$277$	3.87541	−	2.23747i	0.232851	−	0.134436i	0.611886	+	0.790946i	$0.290411\pi$
$278$	11.9921	+	6.20155i	0.719239	+	0.371944i
$279$	−8.38627	+	4.84181i	−0.502073	+	0.289872i
$280$	−2.01633	+	1.57333i	−0.120499	+	0.0940247i
$281$		−	19.5977i		−	1.16910i	−0.811357	−	0.584551i	$-0.801271\pi$
$281$		−	19.5977i		−	1.16910i	0.811357	−	0.584551i	$-0.198729\pi$
$282$	1.18796	+	25.6192i	0.0707422	+	1.52560i
$283$	6.18078	−	10.7054i	0.367409	−	0.636372i	−0.621750	−	0.783215i	$-0.713578\pi$
$283$	6.18078	−	10.7054i	0.367409	−	0.636372i	0.989160	+	0.146844i	$0.0469115\pi$
$284$	−3.02752	−	32.5750i	−0.179650	−	1.93297i
$285$		−	3.86351i		−	0.228855i
$286$	0.0113657	+	16.9115i	0.000672065	+	1.00000i
$287$			6.35421i			0.375077i
$288$	5.88204	+	24.9323i	0.346603	+	1.46915i
$289$	−3.16718	+	5.48571i	−0.186304	+	0.322689i
$290$	3.17931	−	0.147425i	0.186696	−	0.00865709i
$291$		−	1.98223i		−	0.116200i
$292$	5.09524	+	2.34249i	0.298176	+	0.137084i
$293$	25.1059	−	14.4949i	1.46670	−	0.846801i	0.467396	−	0.884048i	$-0.345192\pi$
$293$	25.1059	−	14.4949i	1.46670	−	0.846801i	0.999306	+	0.0372469i	$0.0118588\pi$
$294$	11.8908	−	22.9935i	0.693484	−	1.34101i
$295$	7.82557	−	4.51810i	0.455622	−	0.263054i
$296$	−5.41961	−	2.19355i	−0.315008	−	0.127497i
$297$	−2.68677	+	13.6471i	−0.155902	+	0.791883i
$298$	12.2874	−	23.7606i	0.711792	−	1.37641i
$299$	−12.7942	+	10.1848i	−0.739910	+	0.589000i
$300$	11.2567	−	7.97309i	0.649907	−	0.460327i
$301$	−1.64340	+	2.84645i	−0.0947241	+	0.164067i
$302$	11.3357	−	7.26477i	0.652294	−	0.418041i
$303$	21.9800	+	38.0705i	1.26272	+	2.18709i
$304$	1.18534	−	3.36963i	0.0679837	−	0.193261i
$305$	−14.8560	+	8.57711i	−0.850651	+	0.491124i
$306$	−20.8925	+	0.968788i	−1.19435	+	0.0553819i
$307$	−16.9695			−0.968502			−0.484251	−	0.874929i	$-0.660908\pi$
$307$	−16.9695			−0.968502			−0.484251	+	0.874929i	$0.660908\pi$
$308$	−3.78424	−	0.386249i	−0.215627	−	0.0220086i
$309$	5.00369	−	8.66664i	0.284650	−	0.493028i
$310$	−2.57296	−	4.01474i	−0.146134	−	0.228022i
$311$			18.4674i			1.04719i	0.851966	+	0.523596i	$0.175410\pi$
$311$			18.4674i			1.04719i	−0.851966	+	0.523596i	$0.824590\pi$
$312$	20.2923	+	19.2661i	1.14882	+	1.09073i
$313$	−10.8812			−0.615044			−0.307522	−	0.951541i	$-0.599500\pi$
$313$	−10.8812			−0.615044			−0.307522	+	0.951541i	$0.599500\pi$
$314$	10.8121	−	6.92922i	0.610161	−	0.391039i
$315$	−2.04736	+	3.54614i	−0.115356	+	0.199802i
$316$	0.248168	−	0.539800i	0.0139605	−	0.0303661i
$317$	7.54932			0.424012			0.212006	−	0.977268i	$-0.432000\pi$
$317$	7.54932			0.424012			0.212006	+	0.977268i	$0.432000\pi$
$318$	34.5473	−	1.60196i	1.93732	−	0.0898335i
$319$	3.56514	+	3.11421i	0.199610	+	0.174362i
$320$	−12.1299	+	3.46205i	−0.678084	+	0.193534i
$321$	34.7079	−	20.0386i	1.93720	−	1.11845i
$322$	−1.98472	−	3.09687i	−0.110604	−	0.172582i
$323$	2.52569	+	1.45821i	0.140533	+	0.0811368i
$324$	−2.40281	−	3.39237i	−0.133489	−	0.188465i
$325$	3.31861	−	8.43396i	0.184083	−	0.467832i
$326$	2.76642	−	5.34950i	0.153218	−	0.296282i
$327$	10.4413	−	18.0849i	0.577406	−	1.00010i
$328$	−11.7582	+	29.0510i	−0.649238	+	1.60408i
$329$	−3.28244	+	1.89512i	−0.180967	+	0.104481i
$330$	−20.0706	−	2.99341i	−1.10485	−	0.164782i
$331$	12.3895	−	7.15306i	0.680987	−	0.393168i	−0.119240	−	0.992865i	$-0.538046\pi$
$331$	12.3895	−	7.15306i	0.680987	−	0.393168i	0.800227	+	0.599697i	$0.204712\pi$
$332$	7.36808	−	16.0266i	0.404376	−	0.879573i
$333$	−9.36081			−0.512969
$334$	0.780758	+	16.8375i	0.0427212	+	0.921308i
$335$	10.7136	+	6.18547i	0.585344	+	0.337949i
$336$	−4.77732	+	4.09750i	−0.260624	+	0.223537i
$337$			11.8048i			0.643050i	0.946901	+	0.321525i	$0.104195\pi$
$337$			11.8048i			0.643050i	−0.946901	+	0.321525i	$0.895805\pi$
$338$	18.0884	+	3.28803i	0.983877	+	0.178845i
$339$			6.14949i			0.333994i
$340$	−0.953088	−	10.2549i	−0.0516884	−	0.556148i
$341$	1.37000	−	6.95870i	0.0741896	−	0.376835i
$342$	−0.264905	−	5.71285i	−0.0143244	−	0.308915i
$343$	7.83984			0.423312
$344$	−12.7808	+	9.97277i	−0.689093	+	0.537696i
$345$	−9.81123	−	16.9935i	−0.528219	−	0.914902i
$346$	−0.241115	+	0.466250i	−0.0129624	+	0.0250658i
$347$	−11.1386	−	19.2926i	−0.597951	−	1.03568i	−0.993123	−	0.117075i	$-0.962648\pi$
$347$	−11.1386	−	19.2926i	−0.597951	−	1.03568i	0.395172	−	0.918607i	$-0.370685\pi$
$348$	7.79875	−	0.724816i	0.418057	−	0.0388542i
$349$	25.1184	+	14.5021i	1.34456	+	0.776279i	0.987472	−	0.157793i	$-0.0504379\pi$
$349$	25.1184	+	14.5021i	1.34456	+	0.776279i	0.357083	+	0.934073i	$0.383771\pi$
$350$	1.81081	+	0.936437i	0.0967921	+	0.0500546i
$351$	14.0706	+	5.53653i	0.751035	+	0.295518i
$352$	−16.5866	−	8.76848i	−0.884066	−	0.467361i
$353$	5.63794	−	9.76519i	0.300077	−	0.519749i	−0.676076	−	0.736832i	$-0.736321\pi$
$353$	5.63794	−	9.76519i	0.300077	−	0.519749i	0.976153	+	0.217083i	$0.0696543\pi$
$354$	18.7222	−	11.9987i	0.995075	−	0.637722i
$355$	22.3371	−	12.8963i	1.18553	−	0.684466i
$356$	−3.52301	−	4.97392i	−0.186719	−	0.263617i
$357$	−2.56932	−	4.45020i	−0.135983	−	0.235529i
$358$	7.36074	−	0.341318i	0.389027	−	0.0180392i
$359$	25.1393			1.32680			0.663402	−	0.748263i	$-0.269112\pi$
$359$	25.1393			1.32680			0.663402	+	0.748263i	$0.269112\pi$
$360$	−15.9224	+	12.4242i	−0.839184	+	0.654811i
$361$	9.10127	−	15.7639i	0.479014	−	0.829677i
$362$	−17.0878	+	10.9512i	−0.898113	+	0.575581i
$363$	−18.4672	−	23.8726i	−0.969279	−	1.25299i
$364$	−1.15155	+	3.97170i	−0.0603575	+	0.208174i
$365$			4.42126i			0.231419i
$366$	−35.5421	+	22.7781i	−1.85782	+	1.19063i
$367$	−16.0132	−	9.24521i	−0.835881	−	0.482596i	0.0199811	−	0.999800i	$-0.493639\pi$
$367$	−16.0132	−	9.24521i	−0.835881	−	0.482596i	−0.855862	+	0.517204i	$0.826973\pi$
$368$	−3.34337	−	17.8313i	−0.174285	−	0.929523i
$369$			50.1773i			2.61213i
$370$	−0.213514	−	4.60456i	−0.0111000	−	0.239380i
$371$	2.55555	+	4.42635i	0.132678	+	0.229805i
$372$	−6.78263	−	9.57597i	−0.351663	−	0.496491i
$373$	4.88447	−	2.82005i	0.252909	−	0.146017i	−0.368187	−	0.929752i	$-0.620021\pi$
$373$	4.88447	−	2.82005i	0.252909	−	0.146017i	0.621095	+	0.783735i	$0.286688\pi$
$374$	9.53214	−	11.9909i	0.492895	−	0.620037i
$375$	28.1522	+	16.2537i	1.45377	+	0.839337i
$376$	−18.5140	+	2.59035i	−0.954785	+	0.133587i
$377$	4.02622	−	3.20505i	0.207361	−	0.165068i
$378$	−1.56228	+	3.02104i	−0.0803553	+	0.155385i
$379$	−25.0570	−	14.4667i	−1.28709	−	0.743103i	−0.308957	−	0.951076i	$-0.599980\pi$
$379$	−25.0570	−	14.4667i	−1.28709	−	0.743103i	−0.978135	+	0.207973i	$0.933313\pi$
$380$	2.80409	−	0.260612i	0.143847	−	0.0133691i
$381$	14.5446	−	8.39735i	0.745145	−	0.430209i
$382$	3.25849	−	6.30105i	0.166719	−	0.322390i
$383$	12.7708	−	7.37323i	0.652558	−	0.376755i	−0.136878	−	0.990588i	$-0.543707\pi$
$383$	12.7708	−	7.37323i	0.652558	−	0.376755i	0.789436	+	0.613833i	$0.210373\pi$
$384$	−29.4239	+	9.89328i	−1.50153	+	0.504864i
$385$	−0.969553	−	2.83792i	−0.0494130	−	0.144634i
$386$	−36.7095	+	1.70222i	−1.86846	+	0.0866408i
$387$	−12.9775	+	22.4776i	−0.659681	+	1.14260i
$388$	1.43868	−	0.133711i	0.0730379	−	0.00678815i
$389$	27.7405			1.40650			0.703250	−	0.710943i	$-0.251731\pi$
$389$	27.7405			1.40650			0.703250	+	0.710943i	$0.251731\pi$
$390$	−7.11798	+	20.8805i	−0.360433	+	1.05733i
$391$	14.8122			0.749087
$392$	17.4905	+	7.07916i	0.883405	+	0.357552i
$393$	−34.1475	−	19.7150i	−1.72251	−	0.994493i
$394$	25.2394	−	1.17035i	1.27154	−	0.0589615i
$395$	0.468397			0.0235676
$396$	−29.8830	−	3.05010i	−1.50168	−	0.153273i
$397$	−11.3857	−	19.7207i	−0.571433	−	0.989751i	−0.996419	−	0.0845515i	$-0.973054\pi$
$397$	−11.3857	−	19.7207i	−0.571433	−	0.989751i	0.424986	−	0.905200i	$-0.360279\pi$
$398$	12.5368	−	24.2427i	0.628412	−	1.21518i
$399$	1.21686	−	0.702555i	0.0609192	−	0.0351717i
$400$	6.54610	+	7.63217i	0.327305	+	0.381608i
$401$	−14.6922	+	25.4477i	−0.733694	+	1.27080i	0.221600	+	0.975138i	$0.428872\pi$
$401$	−14.6922	+	25.4477i	−0.733694	+	1.27080i	−0.955294	+	0.295658i	$0.904461\pi$
$402$	27.0417	+	13.9842i	1.34872	+	0.697470i
$403$	−7.17468	−	2.82310i	−0.357396	−	0.140629i
$404$	−26.1485	+	18.5209i	−1.30093	+	0.921448i
$405$	1.63873	−	2.83836i	0.0814291	−	0.141039i
$406$	0.624571	+	0.974555i	0.0309969	+	0.0483664i
$407$	4.51027	−	5.16335i	0.223566	−	0.255938i
$408$	−3.51188	−	25.1004i	−0.173864	−	1.24266i
$409$	11.6933	−	6.75113i	0.578196	−	0.333822i	−0.182220	−	0.983258i	$-0.558328\pi$
$409$	11.6933	−	6.75113i	0.578196	−	0.333822i	0.760416	+	0.649436i	$0.224995\pi$
$410$	−24.6821	+	1.14451i	−1.21896	+	0.0565233i
$411$		−	55.2102i		−	2.72332i
$412$	6.62767	+	3.04701i	0.326522	+	0.150116i
$413$	2.84606	+	1.64317i	0.140045	+	0.0808553i
$414$	−15.6727	−	24.4551i	−0.770272	−	1.20190i
$415$	13.9066			0.682650
$416$	−12.6143	+	16.0275i	−0.618465	+	0.785812i
$417$			26.1936i			1.28271i
$418$	3.27880	+	2.60647i	0.160371	+	0.127486i
$419$	17.2874	+	9.98091i	0.844546	+	0.487599i	0.858807	−	0.512299i	$-0.171206\pi$
$419$	17.2874	+	9.98091i	0.844546	+	0.487599i	−0.0142606	+	0.999898i	$0.504539\pi$
$420$	−4.50840	−	2.07269i	−0.219987	−	0.101137i
$421$	−13.7907			−0.672117			−0.336059	−	0.941841i	$-0.609094\pi$
$421$	−13.7907			−0.672117			−0.336059	+	0.941841i	$0.609094\pi$
$422$	−0.771655	−	16.6412i	−0.0375636	−	0.810082i
$423$	−25.9205	+	14.9652i	−1.26030	+	0.727633i
$424$	3.49306	+	24.9659i	0.169638	+	1.21245i
$425$	−7.10956	+	4.10471i	−0.344864	+	0.199108i
$426$	53.4403	−	34.2487i	2.58919	−	1.65935i
$427$	−5.40293	−	3.11939i	−0.261466	−	0.150958i
$428$	16.8850	+	23.8389i	0.816167	+	1.15229i
$429$	−29.1345	+	15.0913i	−1.40663	+	0.728615i
$430$	−11.3527	−	5.87088i	−0.547475	−	0.283119i
$431$	−4.65373	+	8.06049i	−0.224162	+	0.388260i	−0.956068	−	0.293146i	$-0.905298\pi$
$431$	−4.65373	+	8.06049i	−0.224162	+	0.388260i	0.731906	+	0.681406i	$0.238631\pi$
$432$	−12.7330	+	10.9210i	−0.612615	+	0.525439i
$433$	−4.83221	−	8.36963i	−0.232221	−	0.402219i	0.726240	−	0.687441i	$-0.241266\pi$
$433$	−4.83221	−	8.36963i	−0.232221	−	0.402219i	−0.958461	+	0.285222i	$0.907933\pi$
$434$	0.796617	−	1.54044i	0.0382388	−	0.0739435i
$435$	3.08750	+	5.34771i	0.148034	+	0.256403i
$436$	13.8301	+	6.35827i	0.662342	+	0.304506i
$437$			4.05025i			0.193750i
$438$	0.503977	+	10.8686i	0.0240809	+	0.519321i
$439$	17.0878	−	29.5969i	0.815555	−	1.41258i	−0.0933740	−	0.995631i	$-0.529765\pi$
$439$	17.0878	−	29.5969i	0.815555	−	1.41258i	0.908929	−	0.416951i	$-0.136901\pi$
$440$	0.818723	−	14.7689i	0.0390311	−	0.704081i
$441$	30.2099			1.43857
$442$	−10.9636	−	12.5342i	−0.521487	−	0.596190i
$443$			40.0594i			1.90328i	0.307218	+	0.951639i	$0.400602\pi$
$443$			40.0594i			1.90328i	−0.307218	+	0.951639i	$0.599398\pi$
$444$	−1.04974	−	11.2948i	−0.0498186	−	0.536029i
$445$	2.40271	−	4.16162i	0.113900	−	0.197280i
$446$	−10.9540	+	0.507939i	−0.518688	+	0.0240516i
$447$	51.8987			2.45472
$448$	−3.29617	−	3.19093i	−0.155729	−	0.150757i
$449$	3.26288	+	5.65148i	0.153985	+	0.266710i	0.932689	−	0.360682i	$-0.117456\pi$
$449$	3.26288	+	5.65148i	0.153985	+	0.266710i	−0.778704	+	0.627391i	$0.784123\pi$
$450$	14.2995	+	7.39477i	0.674084	+	0.348593i
$451$	−27.6774	−	24.1766i	−1.30328	−	1.13843i
$452$	−4.46323	+	0.414812i	−0.209932	+	0.0195111i
$453$	22.6223	+	13.0610i	1.06289	+	0.613658i
$454$	19.6288	+	10.1507i	0.921224	+	0.476398i
$455$	−3.22424	+	0.483091i	−0.151155	+	0.0226477i
$456$	6.86346	−	0.960288i	0.321411	−	0.0449696i
$457$	−15.5908	−	9.00137i	−0.729308	−	0.421066i	0.0888607	−	0.996044i	$-0.471677\pi$
$457$	−15.5908	−	9.00137i	−0.729308	−	0.421066i	−0.818169	+	0.574978i	$0.805011\pi$
$458$	5.24962	−	3.36437i	0.245299	−	0.157206i
$459$	−6.84800	−	11.8611i	−0.319637	−	0.553628i
$460$	11.6719	−	8.26717i	0.544205	−	0.385459i
$461$	−5.76812	+	3.33023i	−0.268648	+	0.155104i	−0.628273	−	0.777993i	$-0.716238\pi$
$461$	−5.76812	+	3.33023i	−0.268648	+	0.155104i	0.359625	+	0.933097i	$0.382905\pi$
$462$	−2.70690	−	6.86582i	−0.125936	−	0.319427i
$463$			11.8807i			0.552142i	0.961137	+	0.276071i	$0.0890324\pi$
$463$			11.8807i			0.552142i	−0.961137	+	0.276071i	$0.910968\pi$
$464$	1.05213	+	5.61135i	0.0488437	+	0.260500i
$465$	4.62579	−	8.01211i	0.214516	−	0.371553i
$466$	3.68040	+	5.74275i	0.170491	+	0.266028i
$467$		−	38.3213i		−	1.77330i	−0.462442	−	0.886650i	$-0.653027\pi$
$467$		−	38.3213i		−	1.77330i	0.462442	−	0.886650i	$-0.346973\pi$
$468$	−9.09343	+	31.3634i	−0.420344	+	1.44977i
$469$			4.49916i			0.207752i
$470$	−7.95257	−	12.4089i	−0.366825	−	0.572379i
$471$	21.5774	+	12.4577i	0.994233	+	0.574021i
$472$	9.97139	+	12.7790i	0.458970	+	0.588201i
$473$	−6.14563	−	17.9885i	−0.282576	−	0.827113i
$474$	1.15144	−	0.0533923i	0.0528873	−	0.00245239i
$475$	−1.12239	−	1.94404i	−0.0514988	−	0.0891986i
$476$	3.05659	−	2.16497i	0.140098	−	0.0992312i
$477$	20.1805	+	34.9536i	0.924000	+	1.60042i
$478$	19.2765	−	12.3539i	0.881684	−	0.565052i
$479$	11.8211	−	20.4747i	0.540119	−	0.935513i	−0.458778	−	0.888551i	$-0.651713\pi$
$479$	11.8211	−	20.4747i	0.540119	−	0.935513i	0.998897	−	0.0469622i	$-0.0149540\pi$
$480$	−16.7767	−	17.8188i	−0.765747	−	0.813315i
$481$	−4.64183	−	5.83113i	−0.211649	−	0.265877i
$482$	−5.84458	+	11.3018i	−0.266213	+	0.514785i
$483$	3.56822	−	6.18034i	0.162360	−	0.281215i
$484$	16.0808	−	15.0136i	0.730944	−	0.682438i
$485$	0.569569	+	0.986522i	0.0258628	+	0.0447956i
$486$	11.8778	−	22.9685i	0.538789	−	1.04187i
$487$	−14.8738	+	8.58739i	−0.673996	+	0.389132i	−0.797589	−	0.603201i	$-0.793892\pi$
$487$	−14.8738	+	8.58739i	−0.673996	+	0.389132i	0.123593	+	0.992333i	$0.460558\pi$
$488$	−18.9296	−	24.2595i	−0.856902	−	1.09818i
$489$	11.6846			0.528395
$490$	0.689066	+	14.8601i	0.0311288	+	0.671313i
$491$	−18.4020	+	31.8732i	−0.830470	+	1.43842i	0.0671963	+	0.997740i	$0.478595\pi$
$491$	−18.4020	+	31.8732i	−0.830470	+	1.43842i	−0.897666	+	0.440676i	$0.854739\pi$
$492$	−60.5444	+	5.62699i	−2.72955	+	0.253684i
$493$	−4.66127			−0.209933
$494$	3.42734	−	2.99790i	0.154203	−	0.134882i
$495$	−7.65628	−	22.4103i	−0.344124	−	1.00727i
$496$	6.49260	−	5.56870i	0.291527	−	0.250042i
$497$	8.12372	+	4.69023i	0.364399	+	0.210386i
$498$	34.1860	−	1.58521i	1.53191	−	0.0710350i
$499$		−	34.8688i		−	1.56094i	−0.625192	−	0.780471i	$-0.714979\pi$
$499$		−	34.8688i		−	1.56094i	0.625192	−	0.780471i	$-0.285021\pi$
$500$	−9.89774	+	21.5289i	−0.442640	+	0.962804i
$501$	−28.3213	+	16.3513i	−1.26530	+	0.730522i
$502$	−17.2115	+	33.2823i	−0.768186	+	1.48546i
$503$	−21.6307	−	37.4655i	−0.964466	−	1.67050i	−0.711042	−	0.703149i	$-0.751777\pi$
$503$	−21.6307	−	37.4655i	−0.964466	−	1.67050i	−0.253424	−	0.967355i	$-0.581557\pi$
$504$	−6.80853	−	2.75570i	−0.303276	−	0.122749i
$505$	−21.8781	−	12.6313i	−0.973564	−	0.562088i
$506$	21.0407	+	3.13810i	0.935375	+	0.139505i
$507$	10.4541	+	34.1031i	0.464282	+	1.51457i
$508$	7.07581	+	9.98989i	0.313938	+	0.443230i
$509$	−12.4858	+	21.6260i	−0.553423	+	0.958556i	0.444602	+	0.895728i	$0.353345\pi$
$509$	−12.4858	+	21.6260i	−0.553423	+	0.958556i	−0.998024	+	0.0628280i	$0.979988\pi$
$510$	16.8234	−	10.7818i	0.744953	−	0.477424i
$511$	−1.39253	+	0.803978i	−0.0616019	+	0.0355659i
$512$	−9.16521	−	20.6881i	−0.405049	−	0.914295i
$513$	3.24329	−	1.87252i	0.143195	−	0.0826737i
$514$	−1.35914	−	29.3107i	−0.0599491	−	1.29284i
$515$			5.75098i			0.253419i
$516$	−28.5770	−	13.1380i	−1.25803	−	0.578369i
$517$	4.23443	−	21.5081i	0.186230	−	0.945927i
$518$	1.41144	−	0.904558i	0.0620149	−	0.0397440i
$519$	−1.01840			−0.0447028
$520$	−15.6350	−	3.75766i	−0.685639	−	0.164784i
$521$	−0.376597			−0.0164990			−0.00824950	−	0.999966i	$-0.502626\pi$
$521$	−0.376597			−0.0164990			−0.00824950	+	0.999966i	$0.502626\pi$
$522$	4.93205	+	7.69578i	0.215870	+	0.336835i
$523$	−4.80639	+	8.32491i	−0.210169	+	0.364023i	−0.951767	−	0.306821i	$-0.900735\pi$
$523$	−4.80639	+	8.32491i	−0.210169	+	0.364023i	0.741598	+	0.670844i	$0.234068\pi$
$524$	12.0055	−	26.1137i	0.524464	−	1.14078i
$525$			3.95524i			0.172621i
$526$	−1.36750	−	29.4909i	−0.0596256	−	1.28586i
$527$	3.49183	+	6.04803i	0.152107	+	0.263456i
$528$	0.329127	−	36.3991i	0.0143234	−	1.58407i
$529$	−1.21454	−	2.10365i	−0.0528063	−	0.0914631i
$530$	−16.7333	+	10.7240i	−0.726847	+	0.465820i
$531$	22.4745	+	12.9757i	0.975311	+	0.563096i
$532$	0.591989	+	0.835793i	0.0256660	+	0.0362362i
$533$	−31.2569	+	24.8819i	−1.35389	+	1.07775i
$534$	5.43210	−	10.5042i	0.235070	−	0.454562i
$535$	−11.5157	+	19.9457i	−0.497866	+	0.862328i
$536$	−8.32550	+	20.5699i	−0.359607	+	0.888483i
$537$	7.14817	+	12.3810i	0.308466	+	0.534280i
$538$	−15.5930	−	8.06370i	−0.672262	−	0.347651i
$539$	−14.5558	+	16.6635i	−0.626965	+	0.717749i
$540$	−12.0162	−	5.52435i	−0.517095	−	0.237730i
$541$		−	15.2080i		−	0.653843i	−0.945052	−	0.326921i	$-0.893989\pi$
$541$		−	15.2080i		−	0.653843i	0.945052	−	0.326921i	$-0.106011\pi$
$542$	−1.62213	−	34.9822i	−0.0696764	−	1.50262i
$543$	−34.1016	−	19.6886i	−1.46344	−	0.844917i
$544$	17.9807	−	4.24203i	0.770917	−	0.181875i
$545$			12.0007i			0.514054i
$546$	−7.87093	+	1.55509i	−0.336845	+	0.0665517i
$547$	−26.4325			−1.13017			−0.565087	−	0.825031i	$-0.691157\pi$
$547$	−26.4325			−1.13017			−0.565087	+	0.825031i	$0.691157\pi$
$548$	40.0709	−	3.72419i	1.71174	−	0.159089i
$549$	−42.6654	−	24.6329i	−1.82091	−	1.05131i
$550$	−10.9687	+	4.32450i	−0.467708	+	0.184397i
$551$		−	1.27458i		−	0.0542988i
$552$	27.7501	−	21.6533i	1.18112	−	0.921625i
$553$	0.0851750	+	0.147527i	0.00362201	+	0.00627350i
$554$	−2.90699	+	5.62134i	−0.123506	+	0.238828i
$555$	7.74502	−	4.47159i	0.328758	−	0.189808i
$556$	−19.0110	+	1.76688i	−0.806246	+	0.0749325i
$557$	19.5208	+	11.2704i	0.827125	+	0.477541i	0.852867	−	0.522128i	$-0.174862\pi$
$557$	19.5208	+	11.2704i	0.827125	+	0.477541i	−0.0257424	+	0.999669i	$0.508195\pi$
$558$	6.29065	−	12.1644i	0.266304	−	0.514961i
$559$	−20.4372	+	3.06213i	−0.864403	+	0.129514i
$560$	1.20022	−	3.41195i	0.0507187	−	0.144181i
$561$	29.1598	+	5.74086i	1.23113	+	0.242379i
$562$	14.9546	+	23.3346i	0.630822	+	0.984309i
$563$	−0.374419	−	0.648512i	−0.0157799	−	0.0273315i	0.858028	−	0.513604i	$-0.171690\pi$
$563$	−0.374419	−	0.648512i	−0.0157799	−	0.0273315i	−0.873808	+	0.486272i	$0.838356\pi$
$564$	−20.9639	−	29.5977i	−0.882740	−	1.24629i
$565$	−1.76698	−	3.06049i	−0.0743373	−	0.128756i
$566$	0.809767	+	17.4631i	0.0340370	+	0.734030i
$567$	1.19197			0.0500580
$568$	28.4621	+	36.4761i	1.19424	+	1.53050i
$569$	−36.5451	−	21.0993i	−1.53205	−	0.884529i	−0.999267	−	0.0382770i	$-0.987813\pi$
$569$	−36.5451	−	21.0993i	−1.53205	−	0.884529i	−0.532782	−	0.846252i	$-0.678854\pi$
$570$	2.94816	+	4.60019i	0.123485	+	0.192681i
$571$	25.4757			1.06613			0.533063	−	0.846076i	$-0.321041\pi$
$571$	25.4757			1.06613			0.533063	+	0.846076i	$0.321041\pi$
$572$	−12.9184	−	20.1275i	−0.540144	−	0.841573i
$573$	13.7630			0.574956
$574$	−4.84876	−	7.56581i	−0.202383	−	0.315791i
$575$	−9.87361	−	5.70053i	−0.411758	−	0.237729i
$576$	−26.0289	−	25.1978i	−1.08454	−	1.04991i
$577$	24.2528			1.00966			0.504828	−	0.863220i	$-0.331556\pi$
$577$	24.2528			1.00966			0.504828	+	0.863220i	$0.331556\pi$
$578$	−0.414943	−	8.94851i	−0.0172594	−	0.372209i
$579$	−35.6494	−	61.7466i	−1.48154	−	2.56610i
$580$	−3.67304	+	2.60160i	−0.152515	+	0.108026i
$581$	2.52883	+	4.38007i	0.104914	+	0.181716i
$582$	1.51260	+	2.36020i	0.0626992	+	0.0978333i
$583$	−29.0036	−	5.71010i	−1.20121	−	0.236488i
$584$	−7.85429	+	1.09892i	−0.325013	+	0.0454735i
$585$	−25.4609	+	3.81483i	−1.05268	+	0.157724i
$586$	−18.8323	+	36.4165i	−0.777954	+	1.50435i
$587$	−31.4767	−	18.1731i	−1.29918	−	0.750084i	−0.318920	−	0.947782i	$-0.603320\pi$
$587$	−31.4767	−	18.1731i	−1.29918	−	0.750084i	−0.980263	+	0.197698i	$0.936653\pi$
$588$	3.38780	+	36.4515i	0.139711	+	1.50323i
$589$	−1.65377	+	0.954806i	−0.0681425	+	0.0393421i
$590$	−5.87007	+	11.3511i	−0.241667	+	0.467318i
$591$	24.5105	+	42.4535i	1.00823	+	1.74630i
$592$	8.12685	−	1.52378i	0.334011	−	0.0626270i
$593$			21.6628i			0.889584i	0.895634	+	0.444792i	$0.146722\pi$
$593$			21.6628i			0.889584i	−0.895634	+	0.444792i	$0.853278\pi$
$594$	−7.21470	−	18.2995i	−0.296023	−	0.750836i
$595$	2.55741	+	1.47652i	0.104844	+	0.0605315i
$596$	3.50081	+	37.6674i	0.143399	+	1.54292i
$597$	52.9519			2.16718
$598$	7.46203	−	21.8898i	0.305145	−	0.895139i
$599$		−	12.3899i		−	0.506238i	−0.967435	−	0.253119i	$-0.918544\pi$
$599$		−	12.3899i		−	0.506238i	0.967435	−	0.253119i	$-0.0814564\pi$
$600$	−7.31901	+	18.0831i	−0.298797	+	0.738241i
$601$	−14.3624	−	8.29215i	−0.585856	−	0.338244i	0.177601	−	0.984103i	$-0.443166\pi$
$601$	−14.3624	−	8.29215i	−0.585856	−	0.338244i	−0.763457	+	0.645858i	$0.776500\pi$
$602$	−0.215308	−	4.64325i	−0.00877530	−	0.189245i
$603$			35.5285i			1.44683i
$604$	−7.95352	+	17.3000i	−0.323624	+	0.703927i
$605$	16.0503	+	6.57466i	0.652538	+	0.267298i
$606$	−55.2219	−	28.5572i	−2.24324	−	1.16006i
$607$	10.9453	+	18.9579i	0.444258	+	0.769477i	0.998000	−	0.0632110i	$-0.0201341\pi$
$607$	10.9453	+	18.9579i	0.444258	+	0.769477i	−0.553742	+	0.832688i	$0.686801\pi$
$608$	1.15994	+	4.91664i	0.0470417	+	0.199396i
$609$	−1.12288	+	1.94489i	−0.0455016	+	0.0788110i
$610$	11.1437	−	21.5488i	0.451194	−	0.872487i
$611$	−22.1757	−	8.72572i	−0.897133	−	0.353005i
$612$	24.1370	−	17.0961i	0.975679	−	0.691070i
$613$	13.5533	+	7.82500i	0.547413	+	0.316049i	0.748078	−	0.663611i	$-0.230977\pi$
$613$	13.5533	+	7.82500i	0.547413	+	0.316049i	−0.200665	+	0.979660i	$0.564310\pi$
$614$	20.2052	−	12.9491i	0.815416	−	0.522582i
$615$	−23.9693	−	41.5161i	−0.966536	−	1.67409i
$616$	4.80054	−	2.42777i	0.193419	−	0.0978177i
$617$	1.13041	+	1.95793i	0.0455087	+	0.0788233i	0.887882	−	0.460070i	$-0.152176\pi$
$617$	1.13041	+	1.95793i	0.0455087	+	0.0788233i	−0.842374	+	0.538894i	$0.818842\pi$
$618$	0.655552	+	14.1374i	0.0263701	+	0.568689i
$619$		−	19.6284i		−	0.788930i	−0.918911	−	0.394465i	$-0.870930\pi$
$619$		−	19.6284i		−	0.788930i	0.918911	−	0.394465i	$-0.129070\pi$
$620$	6.12713	+	2.81689i	0.246071	+	0.113129i
$621$	9.51036	−	16.4724i	0.381638	−	0.661016i
$622$	−14.0921	−	21.9888i	−0.565042	−	0.881669i
$623$	1.74767			0.0700191
$624$	−38.8631	−	7.45506i	−1.55577	−	0.298441i
$625$	−6.11252			−0.244501
$626$	12.9560	−	8.30324i	0.517827	−	0.331864i
$627$	−1.56978	+	7.97346i	−0.0626909	+	0.318429i
$628$	−7.58616	+	16.5009i	−0.302721	+	0.658459i
$629$			6.75085i			0.269174i
$630$	−0.268233	−	5.78460i	−0.0106866	−	0.230464i
$631$	27.3133	−	15.7693i	1.08732	−	0.627767i	0.154462	−	0.987999i	$-0.450636\pi$
$631$	27.3133	−	15.7693i	1.08732	−	0.627767i	0.932863	+	0.360231i	$0.117302\pi$
$632$	0.116421	+	0.832099i	0.00463100	+	0.0330991i
$633$	27.9911	−	16.1607i	1.11255	−	0.642328i
$634$	−8.98880	+	5.76072i	−0.356991	+	0.228788i
$635$	−4.82574	+	8.35843i	−0.191504	+	0.331694i
$636$	−39.9122	+	28.2697i	−1.58262	+	1.12097i
$637$	14.9804	+	18.8186i	0.593547	+	0.745621i
$638$	−6.62132	−	0.987529i	−0.262140	−	0.0390967i
$639$	64.1507	+	37.0374i	2.53776	+	1.46518i
$640$	11.8010	−	13.3783i	0.466477	−	0.528823i
$641$	22.3477	+	38.7073i	0.882681	+	1.52885i	0.848349	+	0.529438i	$0.177597\pi$
$641$	22.3477	+	38.7073i	0.882681	+	1.52885i	0.0343320	+	0.999410i	$0.489070\pi$
$642$	−26.0348	+	50.3443i	−1.02751	+	1.98693i
$643$	−1.42178	+	0.820865i	−0.0560695	+	0.0323718i	−0.527773	−	0.849386i	$-0.676973\pi$
$643$	−1.42178	+	0.820865i	−0.0560695	+	0.0323718i	0.471703	+	0.881757i	$0.343639\pi$
$644$	4.72631	+	2.17288i	0.186243	+	0.0856234i
$645$		−	24.7969i		−	0.976378i
$646$	−4.12000	+	0.191045i	−0.162099	+	0.00751656i
$647$	−8.33900	−	4.81452i	−0.327840	−	0.189279i	0.327042	−	0.945010i	$-0.393948\pi$
$647$	−8.33900	−	4.81452i	−0.327840	−	0.189279i	−0.654882	+	0.755731i	$0.727282\pi$
$648$	5.44961	+	2.20569i	0.214081	+	0.0866477i
$649$	−17.9860	+	6.14478i	−0.706014	+	0.241204i
$650$	2.48439	+	12.5745i	0.0974457	+	0.493212i
$651$	3.36468			0.131872
$652$	0.788180	+	8.48053i	0.0308675	+	0.332123i
$653$	−5.42953	+	9.40422i	−0.212474	+	0.368016i	−0.952488	−	0.304576i	$-0.901485\pi$
$653$	−5.42953	+	9.40422i	−0.212474	+	0.368016i	0.740014	+	0.672591i	$0.234819\pi$
$654$	1.36795	+	29.5008i	0.0534912	+	1.15357i
$655$	22.6595			0.885378
$656$	−8.16801	−	43.5628i	−0.318907	−	1.70084i
$657$	−10.9964	+	6.34878i	−0.429011	+	0.247689i
$658$	2.46220	−	4.76124i	0.0959867	−	0.185612i
$659$	18.3386	+	31.7635i	0.714372	+	1.23733i	0.963201	+	0.268781i	$0.0866209\pi$
$659$	18.3386	+	31.7635i	0.714372	+	1.23733i	−0.248829	+	0.968547i	$0.580046\pi$
$660$	26.1818	−	11.7513i	1.01913	−	0.457418i
$661$	16.7443	−	29.0019i	0.651277	−	1.12804i	−0.331537	−	0.943442i	$-0.607567\pi$
$661$	16.7443	−	29.0019i	0.651277	−	1.12804i	0.982813	−	0.184602i	$-0.0590996\pi$
$662$	−9.29351	+	17.9711i	−0.361202	+	0.698468i
$663$	11.8300	−	30.0649i	0.459437	−	1.16762i
$664$	3.45654	+	24.7049i	0.134140	+	0.958736i
$665$	−0.403740	+	0.699299i	−0.0156564	+	0.0271176i
$666$	11.1457	−	7.14303i	0.431887	−	0.276787i
$667$	−3.23673	−	5.60619i	−0.125327	−	0.217072i
$668$	−13.7780	−	19.4523i	−0.533086	−	0.752631i
$669$	−10.6377	−	18.4250i	−0.411277	−	0.712353i
$670$	−17.4764	+	0.810382i	−0.675172	+	0.0313078i
$671$	34.1445	−	11.6652i	1.31813	−	0.450330i
$672$	2.56153	−	8.52426i	0.0988132	−	0.328831i
$673$	−33.9222	−	19.5850i	−1.30760	−	0.754946i	−0.325909	−	0.945401i	$-0.605670\pi$
$673$	−33.9222	−	19.5850i	−1.30760	−	0.754946i	−0.981696	+	0.190455i	$0.939004\pi$
$674$	−9.00801	−	14.0557i	−0.346976	−	0.541407i
$675$			10.5419i			0.405758i
$676$	−24.0464	+	9.88786i	−0.924862	+	0.380302i
$677$		−	47.6007i		−	1.82944i	−0.404083	−	0.914722i	$-0.632409\pi$
$677$		−	47.6007i		−	1.82944i	0.404083	−	0.914722i	$-0.367591\pi$
$678$	−4.69254	−	7.32205i	−0.180216	−	0.281202i
$679$	−0.207145	+	0.358785i	−0.00794949	+	0.0137689i
$680$	8.96009	+	11.4830i	0.343604	+	0.440351i
$681$			42.8739i			1.64293i
$682$	3.67881	+	9.33098i	0.140869	+	0.357302i
$683$	−8.40121	+	4.85044i	−0.321464	+	0.185597i	−0.652045	−	0.758180i	$-0.726089\pi$
$683$	−8.40121	+	4.85044i	−0.321464	+	0.185597i	0.330581	+	0.943778i	$0.392755\pi$
$684$	4.67477	+	6.60001i	0.178744	+	0.252358i
$685$	15.8639	+	27.4771i	0.606130	+	1.04985i
$686$	−9.33472	+	5.98241i	−0.356401	+	0.228410i
$687$	10.4765	+	6.04862i	0.399704	+	0.230769i
$688$	7.60777	−	21.6271i	0.290043	−	0.824525i
$689$	−11.7666	+	29.9038i	−0.448271	+	1.13924i
$690$	24.6494	+	12.7471i	0.938387	+	0.485273i
$691$	7.61102	+	4.39423i	0.289537	+	0.167164i	0.637733	−	0.770258i	$-0.279872\pi$
$691$	7.61102	+	4.39423i	0.289537	+	0.167164i	−0.348196	+	0.937422i	$0.613206\pi$
$692$	−0.0686960	−	0.739143i	−0.00261143	−	0.0280980i
$693$	5.66615	−	6.48661i	0.215239	−	0.246406i
$694$	27.9842	+	14.4716i	1.06227	+	0.549336i
$695$	−7.52639	−	13.0361i	−0.285492	−	0.494487i
$696$	−8.73270	+	6.81408i	−0.331012	+	0.258287i
$697$	36.1870			1.37068
$698$	−40.9741	+	1.89997i	−1.55089	+	0.0719150i
$699$	−6.61681	+	11.4606i	−0.250271	+	0.433481i
$700$	−2.87067	+	0.266800i	−0.108501	+	0.0100841i
$701$			42.7997i			1.61652i	0.588824	+	0.808261i	$0.299591\pi$
$701$			42.7997i			1.61652i	−0.588824	+	0.808261i	$0.700409\pi$
$702$	−20.9784	+	4.14478i	−0.791778	+	0.156435i
$703$	−1.84595			−0.0696214
$704$	26.4403	−	2.21642i	0.996505	−	0.0835344i
$705$	14.2975	−	24.7640i	0.538476	−	0.932668i
$706$	0.738647	+	15.9294i	0.0277993	+	0.599510i
$707$		−	9.18772i		−	0.345540i
$708$	−13.1362	+	28.5731i	−0.493689	+	1.07384i
$709$	12.3871	+	21.4550i	0.465206	+	0.805760i	0.999211	−	0.0397211i	$-0.0126469\pi$
$709$	12.3871	+	21.4550i	0.465206	+	0.805760i	−0.534005	+	0.845481i	$0.679314\pi$
$710$	−16.7554	+	32.4003i	−0.628818	+	1.21596i
$711$	0.672602	+	1.16498i	0.0252245	+	0.0436902i
$712$	7.99026	+	3.23400i	0.299448	+	0.121199i
$713$	−4.84938	+	8.39937i	−0.181611	+	0.314559i
$714$	6.45508	+	3.33815i	0.241575	+	0.124927i
$715$	10.1634	−	15.8821i	0.380091	−	0.593957i
$716$	−8.50381	+	6.02322i	−0.317802	+	0.225098i
$717$	38.4695	+	22.2104i	1.43667	+	0.829461i
$718$	−29.9328	+	19.1833i	−1.11708	+	0.715914i
$719$	14.7948	−	8.54180i	0.551754	−	0.318555i	−0.198075	−	0.980187i	$-0.563469\pi$
$719$	14.7948	−	8.54180i	0.551754	−	0.318555i	0.749829	+	0.661632i	$0.230136\pi$
$720$	9.47782	−	26.9432i	0.353218	−	1.00411i
$721$	−1.81134	+	1.04578i	−0.0674580	+	0.0389469i
$722$	1.19239	+	25.7146i	0.0443762	+	0.957000i
$723$	−24.6859			−0.918077
$724$	11.9894	−	26.0786i	0.445583	−	0.969204i
$725$	3.10713	+	1.79390i	0.115396	+	0.0666239i
$726$	40.2052	+	14.3326i	1.49215	+	0.531934i
$727$			7.58331i			0.281249i	0.990063	+	0.140625i	$0.0449111\pi$
$727$			7.58331i			0.281249i	−0.990063	+	0.140625i	$0.955089\pi$
$728$	−1.65960	−	5.60773i	−0.0615088	−	0.207836i
$729$	43.9329			1.62714
$730$	−3.37377	−	5.26429i	−0.124869	−	0.194840i
$731$	16.2105	+	9.35912i	0.599566	+	0.346159i
$732$	24.9376	−	54.2428i	0.921722	−	2.00487i
$733$			11.3308i			0.418512i	0.977861	+	0.209256i	$0.0671041\pi$
$733$			11.3308i			0.418512i	−0.977861	+	0.209256i	$0.932896\pi$
$734$	26.1213	−	1.21125i	0.964156	−	0.0447080i
$735$	−24.9953	+	14.4310i	−0.921964	+	0.532296i
$736$	17.5876	+	18.6801i	0.648287	+	0.688558i
$737$	−19.5973	−	17.1185i	−0.721875	−	0.630568i
$738$	−38.2892	−	59.7450i	−1.40945	−	2.19924i
$739$	22.4652	−	38.9108i	0.826395	−	1.43136i	−0.0744542	−	0.997224i	$-0.523721\pi$
$739$	22.4652	−	38.9108i	0.826395	−	1.43136i	0.900849	−	0.434133i	$-0.142945\pi$
$740$	3.76786	+	5.31961i	0.138509	+	0.195553i
$741$	8.22093	+	3.23478i	0.302003	+	0.118833i
$742$	−6.42049	−	3.32026i	−0.235704	−	0.121891i
$743$	5.51803	−	9.55751i	0.202437	−	0.350631i	−0.746876	−	0.664963i	$-0.768447\pi$
$743$	5.51803	−	9.55751i	0.202437	−	0.350631i	0.949313	+	0.314332i	$0.101781\pi$
$744$	15.3831	+	6.22621i	0.563973	+	0.228264i
$745$	−25.8291	+	14.9124i	−0.946303	+	0.546349i
$746$	−3.66391	+	7.08501i	−0.134145	+	0.259401i
$747$	19.9695	+	34.5881i	0.730644	+	1.26551i
$748$	−2.19968	+	21.5511i	−0.0804282	+	0.787986i
$749$	−8.37620			−0.306060
$750$	−45.9231	+	2.12946i	−1.67687	+	0.0777567i
$751$	8.71309	+	5.03051i	0.317945	+	0.183566i	0.650476	−	0.759527i	$-0.274569\pi$
$751$	8.71309	+	5.03051i	0.317945	+	0.183566i	−0.332531	+	0.943092i	$0.607903\pi$
$752$	20.0675	−	17.2119i	0.731787	−	0.627652i
$753$	−72.6964			−2.64920
$754$	−2.34823	+	6.88850i	−0.0855175	+	0.250864i
$755$	−15.0116			−0.546328
$756$	−0.445110	−	4.78922i	−0.0161885	−	0.174182i
$757$	−17.1268	+	29.6644i	−0.622483	+	1.07817i	0.366539	+	0.930403i	$0.380543\pi$
$757$	−17.1268	+	29.6644i	−0.622483	+	1.07817i	−0.989022	+	0.147769i	$0.952791\pi$
$758$	40.8740	−	1.89533i	1.48461	−	0.0688415i
$759$	13.3436	+	39.0574i	0.484343	+	1.41769i
$760$	−3.13990	+	2.45005i	−0.113896	+	0.0888725i
$761$	−1.54455	+	0.891744i	−0.0559898	+	0.0323257i	−0.527734	−	0.849410i	$-0.676958\pi$
$761$	−1.54455	+	0.891744i	−0.0559898	+	0.0323257i	0.471744	+	0.881736i	$0.343625\pi$
$762$	−10.9101	+	21.0972i	−0.395232	+	0.764272i
$763$	−3.77977	+	2.18225i	−0.136837	+	0.0790028i
$764$	0.928377	+	9.98900i	0.0335875	+	0.361389i
$765$	20.1951	+	11.6597i	0.730157	+	0.421556i
$766$	−9.57956	+	18.5243i	−0.346124	+	0.669309i
$767$	3.06171	+	20.4344i	0.110552	+	0.737844i
$768$	27.4850	−	34.2324i	0.991778	−	1.23526i
$769$	9.65971	+	5.57703i	0.348338	+	0.201113i	0.663953	−	0.747774i	$-0.268877\pi$
$769$	9.65971	+	5.57703i	0.348338	+	0.201113i	−0.315615	+	0.948887i	$0.602211\pi$
$770$	3.31998	+	2.63921i	0.119644	+	0.0951104i
$771$	49.3016	−	28.4643i	1.77555	−	1.02512i
$772$	42.4102	−	30.0390i	1.52638	−	1.08113i
$773$	24.5940	+	42.5980i	0.884584	+	1.53214i	0.846190	+	0.532881i	$0.178891\pi$
$773$	24.5940	+	42.5980i	0.884584	+	1.53214i	0.0383936	+	0.999263i	$0.487776\pi$
$774$	−1.70022	−	36.6664i	−0.0611133	−	1.31795i
$775$		−	5.37537i		−	0.193089i
$776$	−1.61097	+	1.25703i	−0.0578305	+	0.0451248i
$777$	2.81676	+	1.62626i	0.101051	+	0.0583417i
$778$	−33.0300	+	21.1682i	−1.18418	+	0.758916i
$779$			9.89497i			0.354524i
$780$	−7.45825	−	30.2935i	−0.267048	−	1.08468i
$781$	−51.3389	+	17.5395i	−1.83705	+	0.627613i
$782$	−17.6366	+	11.3029i	−0.630683	+	0.404191i
$783$	−2.99282	+	5.18372i	−0.106955	+	0.185251i
$784$	−26.2275	+	4.91765i	−0.936698	+	0.175630i
$785$	−14.3182			−0.511040
$786$	55.7027	−	2.58294i	1.98685	−	0.0921304i
$787$	−2.33016	−	4.03595i	−0.0830612	−	0.143866i	0.821502	−	0.570205i	$-0.193136\pi$
$787$	−2.33016	−	4.03595i	−0.0830612	−	0.143866i	−0.904563	+	0.426339i	$0.859803\pi$
$788$	−29.1589	+	20.6531i	−1.03874	+	0.735737i
$789$	49.6046	−	28.6393i	1.76597	−	1.01958i
$790$	−0.557709	+	0.357423i	−0.0198424	+	0.0127166i
$791$	0.642627	−	1.11306i	0.0228492	−	0.0395759i
$792$	37.9085	−	19.1714i	1.34702	−	0.681226i
$793$	−5.81232	−	38.7925i	−0.206401	−	1.37756i
$794$	28.6051	+	14.7927i	1.01516	+	0.524974i
$795$	−33.3941	−	19.2801i	−1.18437	−	0.683795i
$796$	3.57186	+	38.4318i	0.126601	+	1.36218i
$797$	−5.91107	−	10.2383i	−0.209381	−	0.362658i	0.742139	−	0.670246i	$-0.233812\pi$
$797$	−5.91107	−	10.2383i	−0.209381	−	0.362658i	−0.951520	+	0.307588i	$0.900478\pi$
$798$	−0.912783	+	1.76508i	−0.0323122	+	0.0624830i
$799$	10.7926	+	18.6934i	0.381816	+	0.661325i
$800$	−13.6182	−	4.09226i	−0.481477	−	0.144683i
$801$	13.8009			0.487630
$802$	−1.92488	−	41.5112i	−0.0679699	−	1.46581i
$803$	1.79640	−	9.12453i	0.0633935	−	0.321998i
$804$	−42.8690	+	3.98425i	−1.51187	+	0.140514i
$805$			4.10113i			0.144546i
$806$	10.6970	−	2.11344i	0.376785	−	0.0744428i
$807$		−	34.0588i		−	1.19893i
$808$	17.0015	−	42.0057i	0.598111	−	1.47776i
$809$	−21.4450	−	12.3813i	−0.753967	−	0.435303i	0.0731583	−	0.997320i	$-0.476692\pi$
$809$	−21.4450	−	12.3813i	−0.753967	−	0.435303i	−0.827126	+	0.562017i	$0.810026\pi$
$810$	0.214696	+	4.63005i	0.00754364	+	0.162683i
$811$	23.5278			0.826173			0.413087	−	0.910692i	$-0.364451\pi$
$811$	23.5278			0.826173			0.413087	+	0.910692i	$0.364451\pi$
$812$	−1.48732	−	0.683784i	−0.0521949	−	0.0239961i
$813$	58.8413	−	33.9720i	2.06365	−	1.19145i
$814$	−1.43023	+	9.58957i	−0.0501294	+	0.336114i
$815$	−5.81521	+	3.35741i	−0.203698	+	0.117605i
$816$	23.3351	+	27.2067i	0.816893	+	0.952424i
$817$	−2.55916	+	4.43259i	−0.0895335	+	0.155077i
$818$	−8.77130	+	16.9613i	−0.306681	+	0.593038i
$819$	−5.83143	−	7.32552i	−0.203767	−	0.255974i
$820$	28.5150	−	20.1971i	0.995788	−	0.705313i
$821$	16.3397	+	9.43371i	0.570258	+	0.329239i	0.757252	−	0.653122i	$-0.226541\pi$
$821$	16.3397	+	9.43371i	0.570258	+	0.329239i	−0.186994	+	0.982361i	$0.559875\pi$
$822$	42.1297	+	65.7375i	1.46944	+	2.29286i
$823$	−10.8042	+	6.23781i	−0.376611	+	0.217436i	−0.676343	−	0.736587i	$-0.736436\pi$
$823$	−10.8042	+	6.23781i	−0.376611	+	0.217436i	0.299732	+	0.954023i	$0.403103\pi$
$824$	−10.2165	+	1.42943i	−0.355909	+	0.0497964i
$825$	−17.2281	−	15.0490i	−0.599806	−	0.523939i
$826$	−4.64261	+	0.215278i	−0.161537	+	0.00749049i
$827$	32.2669			1.12203			0.561015	−	0.827805i	$-0.310411\pi$
$827$	32.2669			1.12203			0.561015	+	0.827805i	$0.310411\pi$
$828$	37.3223	+	17.1586i	1.29704	+	0.596302i
$829$	−9.00352	+	15.5946i	−0.312705	+	0.541621i	−0.978947	−	0.204114i	$-0.934569\pi$
$829$	−9.00352	+	15.5946i	−0.312705	+	0.541621i	0.666242	+	0.745736i	$0.267902\pi$
$830$	−16.5583	+	10.6119i	−0.574747	+	0.368343i
$831$	−12.2783			−0.425930
$832$	2.78929	−	28.7092i	0.0967014	−	0.995313i
$833$		−	21.7868i		−	0.754869i
$834$	−19.9878	−	31.1881i	−0.692120	−	1.07996i
$835$	9.39667	−	16.2755i	0.325185	−	0.563237i
$836$	−5.89293	−	0.601479i	−0.203811	−	0.0208026i
$837$	8.96788			0.309975
$838$	−28.2000	+	1.30763i	−0.974152	+	0.0451715i
$839$	21.4900	−	12.4073i	0.741918	−	0.428347i	−0.0808481	−	0.996726i	$-0.525763\pi$
$839$	21.4900	−	12.4073i	0.741918	−	0.428347i	0.822766	+	0.568380i	$0.192430\pi$
$840$	6.94967	−	0.972350i	0.239786	−	0.0335493i
$841$	−13.4814	−	23.3505i	−0.464877	−	0.805190i
$842$	16.4203	−	10.5234i	0.565880	−	0.362660i
$843$	−26.8861	+	46.5681i	−0.926007	+	1.60389i
$844$	13.6173	+	19.2255i	0.468728	+	0.661768i
$845$	−15.0019	−	13.9686i	−0.516081	−	0.480536i
$846$	19.4433	−	37.5981i	0.668475	−	1.29265i
$847$	0.847876	+	6.25081i	0.0291333	+	0.214780i
$848$	−23.2101	−	27.0609i	−0.797038	−	0.929275i
$849$	−29.3735	+	16.9588i	−1.00810	+	0.582025i
$850$	5.33298	−	10.3125i	0.182920	−	0.353717i
$851$	−8.11937	+	4.68772i	−0.278328	+	0.160693i
$852$	−37.4957	+	81.5582i	−1.28458	+	2.79414i
$853$		−	33.8607i		−	1.15937i	−0.814842	−	0.579684i	$-0.803176\pi$
$853$		−	33.8607i		−	1.15937i	0.814842	−	0.579684i	$-0.196824\pi$
$854$	8.81348	−	0.408682i	0.301591	−	0.0139848i
$855$	−3.18822	+	5.52216i	−0.109035	+	0.188854i
$856$	−38.2955	−	15.4998i	−1.30891	−	0.529773i
$857$		−	57.8874i		−	1.97739i	−0.149927	−	0.988697i	$-0.547904\pi$
$857$		−	57.8874i		−	1.97739i	0.149927	−	0.988697i	$-0.452096\pi$
$858$	23.1739	−	40.2008i	0.791145	−	1.37243i
$859$		−	13.5205i		−	0.461312i	−0.973035	−	0.230656i	$-0.925913\pi$
$859$		−	13.5205i		−	0.461312i	0.973035	−	0.230656i	$-0.0740873\pi$
$860$	17.9973	−	1.67267i	0.613703	−	0.0570376i
$861$	8.71733	−	15.0989i	0.297086	−	0.514568i
$862$	−0.609702	−	13.1486i	−0.0207665	−	0.447843i
$863$			25.5718i			0.870475i	0.900316	+	0.435238i	$0.143336\pi$
$863$			25.5718i			0.870475i	−0.900316	+	0.435238i	$0.856664\pi$
$864$	6.82724	−	22.7197i	0.232267	−	0.772940i
$865$	0.506840	−	0.292624i	0.0172331	−	0.00994952i
$866$	12.1403	+	6.27817i	0.412543	+	0.213341i
$867$	15.0517	−	8.69009i	0.511182	−	0.295131i
$868$	0.226964	+	2.44205i	0.00770366	+	0.0828885i
$869$	−0.966670	−	0.190314i	−0.0327920	−	0.00645595i
$870$	−7.75693	−	4.01139i	−0.262985	−	0.135999i
$871$	−22.1318	+	17.6179i	−0.749907	+	0.596958i
$872$	−21.3190	+	2.98281i	−0.721954	+	0.101011i
$873$	−1.63576	+	2.83322i	−0.0553622	+	0.0958901i
$874$	−3.09066	−	4.82254i	−0.104543	−	0.163125i
$875$	−3.39705	−	5.88387i	−0.114841	−	0.198911i
$876$	−8.89365	−	12.5564i	−0.300489	−	0.424241i
$877$	21.7632	−	12.5650i	0.734890	−	0.424289i	−0.0853182	−	0.996354i	$-0.527191\pi$
$877$	21.7632	−	12.5650i	0.734890	−	0.424289i	0.820209	+	0.572065i	$0.193857\pi$
$878$	2.23873	+	48.2796i	0.0755535	+	1.62936i
$879$	−79.5422			−2.68289
$880$	10.2950	+	18.2098i	0.347045	+	0.613852i
$881$	0.930290	−	1.61131i	0.0313423	−	0.0542864i	−0.849929	−	0.526898i	$-0.823355\pi$
$881$	0.930290	−	1.61131i	0.0313423	−	0.0542864i	0.881271	+	0.472611i	$0.156688\pi$
$882$	−35.9702	+	23.0525i	−1.21118	+	0.776218i
$883$		−	4.05615i		−	0.136500i	−0.997668	−	0.0682502i	$-0.978258\pi$
$883$		−	4.05615i		−	0.136500i	0.997668	−	0.0682502i	$-0.0217416\pi$
$884$	22.6187	+	6.55803i	0.760750	+	0.220570i
$885$	−24.7935			−0.833424
$886$	−30.5684	−	47.6978i	−1.02697	−	1.60244i
$887$	17.1751	−	29.7481i	0.576682	−	0.998843i	−0.419175	−	0.907906i	$-0.637681\pi$
$887$	17.1751	−	29.7481i	0.576682	−	0.998843i	0.995857	−	0.0909369i	$-0.0289862\pi$
$888$	9.86875	+	12.6475i	0.331173	+	0.424421i
$889$	−3.51012			−0.117726
$890$	0.314788	+	6.78861i	0.0105517	+	0.227555i
$891$	−4.53524	+	5.19194i	−0.151936	+	0.173937i
$892$	12.6551	−	8.96357i	0.423724	−	0.300123i
$893$	−5.11152	+	2.95114i	−0.171051	+	0.0987561i
$894$	−61.7945	+	39.6027i	−2.06672	+	1.32451i
$895$	−7.11504	−	4.10787i	−0.237830	−	0.137311i
$896$	6.35960	+	1.28413i	0.212459	+	0.0428997i
$897$	44.3741	−	6.64862i	1.48161	−	0.221991i
$898$	−8.19756	−	4.23925i	−0.273556	−	0.141466i
$899$	1.52605	−	2.64320i	0.0508967	−	0.0881558i
$900$	−22.6688	+	2.10684i	−0.755628	+	0.0702281i
$901$	25.2079	−	14.5538i	0.839798	−	0.484857i
$902$	51.4035	+	7.66653i	1.71155	+	0.255267i
$903$	7.81010	−	4.50916i	0.259904	−	0.150056i
$904$	4.99773	−	3.89970i	0.166222	−	0.129702i
$905$	22.6290			0.752214
$906$	−36.9023	+	1.71117i	−1.22600	+	0.0568497i
$907$	36.2908	+	20.9525i	1.20502	+	0.695716i	0.961666	−	0.274222i	$-0.0884204\pi$
$907$	36.2908	+	20.9525i	1.20502	+	0.695716i	0.243350	+	0.969939i	$0.421754\pi$
$908$	−31.1173	+	2.89205i	−1.03267	+	0.0959759i
$909$		−	72.5528i		−	2.40642i
$910$	3.47039	−	3.03555i	0.115042	−	0.100628i
$911$		−	18.1454i		−	0.601185i	−0.953753	−	0.300593i	$-0.902816\pi$
$911$		−	18.1454i		−	0.601185i	0.953753	−	0.300593i	$-0.0971844\pi$
$912$	−7.43939	+	6.38075i	−0.246343	+	0.211288i
$913$	−28.7003	−	5.65039i	−0.949842	−	0.187001i
$914$	25.4324	−	1.17930i	0.841229	−	0.0390079i
$915$	47.0677			1.55601
$916$	−3.68333	+	8.01174i	−0.121701	+	0.264715i
$917$	4.12048	+	7.13688i	0.136070	+	0.235681i
$918$	17.2047	+	8.89716i	0.567840	+	0.293650i
$919$	4.53290	+	7.85121i	0.149527	+	0.258988i	0.931053	−	0.364885i	$-0.118892\pi$
$919$	4.53290	+	7.85121i	0.149527	+	0.258988i	−0.781526	+	0.623873i	$0.785558\pi$
$920$	−7.58897	+	18.7501i	−0.250201	+	0.618173i
$921$	40.3230	+	23.2805i	1.32869	+	0.767118i
$922$	4.32675	−	8.36675i	0.142494	−	0.275544i
$923$	8.73926	+	58.3274i	0.287656	+	1.91987i
$924$	8.46221	+	6.10940i	0.278386	+	0.200984i
$925$	2.59809	−	4.50002i	0.0854246	−	0.147960i
$926$	−9.06588	−	14.1460i	−0.297923	−	0.464868i
$927$	−14.3037	+	8.25822i	−0.469794	+	0.271235i
$928$	−5.53464	−	5.87845i	−0.181684	−	0.192970i
$929$	−10.9423	−	18.9527i	−0.359006	−	0.621816i	0.628789	−	0.777576i	$-0.283551\pi$
$929$	−10.9423	−	18.9527i	−0.359006	−	0.621816i	−0.987795	+	0.155759i	$0.950218\pi$
$930$	0.606042	+	13.0697i	0.0198729	+	0.428572i
$931$	5.95739			0.195245
$932$	−8.76434	−	4.02932i	−0.287085	−	0.131985i
$933$	25.3355	−	43.8824i	0.829447	−	1.43664i
$934$	29.2422	+	45.6283i	0.956833	+	1.49300i
$935$	−16.1619	+	5.52158i	−0.528550	+	0.180575i
$936$	−13.1054	−	44.2826i	−0.428362	−	1.44742i
$937$			4.45613i			0.145576i	0.997347	+	0.0727878i	$0.0231896\pi$
$937$			4.45613i			0.145576i	−0.997347	+	0.0727878i	$0.976810\pi$
$938$	−3.43321	−	5.35704i	−0.112098	−	0.174914i
$939$	25.8560	+	14.9280i	0.843779	+	0.487156i
$940$	18.9379	+	8.70652i	0.617686	+	0.283975i
$941$			55.7038i			1.81589i	0.419086	+	0.907946i	$0.362350\pi$
$941$			55.7038i			1.81589i	−0.419086	+	0.907946i	$0.637650\pi$
$942$	−35.1979	+	1.63213i	−1.14681	+	0.0531776i
$943$	25.1279	+	43.5228i	0.818276	+	1.41730i
$944$	−21.6241	−	7.60672i	−0.703804	−	0.247578i
$945$	3.28403	−	1.89604i	0.106830	−	0.0616781i
$946$	21.0441	+	16.7289i	0.684203	+	0.543904i
$947$	−25.6319	−	14.7986i	−0.832925	−	0.480890i	0.0219279	−	0.999760i	$-0.493020\pi$
$947$	−25.6319	−	14.7986i	−0.832925	−	0.480890i	−0.854853	+	0.518870i	$0.826353\pi$
$948$	−1.33025	+	0.942211i	−0.0432045	+	0.0306016i
$949$	−9.40773	−	3.70176i	−0.305388	−	0.120164i
$950$	2.81986	+	1.45825i	0.0914883	+	0.0473118i
$951$	−17.9387	−	10.3569i	−0.581702	−	0.335846i
$952$	−1.98736	+	4.91019i	−0.0644109	+	0.159140i
$953$	9.30737	−	5.37361i	0.301495	−	0.174068i	−0.341619	−	0.939838i	$-0.610975\pi$
$953$	9.30737	−	5.37361i	0.301495	−	0.174068i	0.643114	+	0.765770i	$0.277642\pi$
$954$	−50.7008	−	26.2192i	−1.64150	−	0.848877i
$955$	−6.84959	+	3.95461i	−0.221647	+	0.127968i
$956$	−13.5251	+	29.4189i	−0.437432	+	0.951475i
$957$	−4.19912	−	12.2910i	−0.135738	−	0.397312i
$958$	1.54872	+	33.3992i	0.0500370	+	1.07908i
$959$	−5.76951	+	9.99309i	−0.186307	+	0.322694i
$960$	33.5728	+	8.41455i	1.08356	+	0.271578i
$961$	26.4272			0.852491
$962$	9.97653	+	3.40091i	0.321656	+	0.109650i
$963$	−66.1444			−2.13147
$964$	−1.66518	−	17.9167i	−0.0536318	−	0.577058i
$965$	35.4842	+	20.4868i	1.14228	+	0.659493i
$966$	0.467485	+	10.0816i	0.0150411	+	0.324371i
$967$	−44.0661			−1.41707			−0.708535	−	0.705676i	$-0.750644\pi$
$967$	−44.0661			−1.41707			−0.708535	+	0.705676i	$0.750644\pi$
$968$	−7.69042	+	30.1473i	−0.247179	+	0.968970i
$969$	−4.00103	−	6.92998i	−0.128532	−	0.222623i
$970$	−1.43097	−	0.740003i	−0.0459455	−	0.0237601i
$971$	18.3097	−	10.5711i	0.587588	−	0.339244i	−0.176555	−	0.984291i	$-0.556495\pi$
$971$	18.3097	−	10.5711i	0.587588	−	0.339244i	0.764143	+	0.645047i	$0.223162\pi$
$972$	3.38411	+	36.4118i	0.108545	+	1.16791i
$973$	2.73725	−	4.74106i	0.0877523	−	0.151991i
$974$	11.1570	−	21.5747i	0.357494	−	0.691297i
$975$	−19.4562	+	15.4880i	−0.623098	+	0.496013i
$976$	41.0510	+	14.4405i	1.31401	+	0.462230i
$977$	14.0227	−	24.2881i	0.448627	−	0.777045i	−0.549670	−	0.835382i	$-0.685247\pi$
$977$	14.0227	−	24.2881i	0.448627	−	0.777045i	0.998297	+	0.0583371i	$0.0185798\pi$
$978$	−13.9126	+	8.91625i	−0.444874	+	0.285110i
$979$	−6.64959	+	7.61245i	−0.212522	+	0.243295i
$980$	−12.1599	−	17.1678i	−0.388434	−	0.548406i
$981$	−29.8478	+	17.2326i	−0.952965	+	0.550195i
$982$	−2.41091	−	51.9928i	−0.0769353	−	1.65916i
$983$			2.75721i			0.0879415i	0.999033	+	0.0439707i	$0.0140008\pi$
$983$			2.75721i			0.0879415i	−0.999033	+	0.0439707i	$0.985999\pi$
$984$	67.7949	−	52.9000i	2.16122	−	1.68639i
$985$	−24.3969	−	14.0856i	−0.777350	−	0.448803i
$986$	5.55006	−	3.55691i	0.176750	−	0.113275i
$987$	10.3997			0.331025
$988$	−1.79323	+	6.18486i	−0.0570501	+	0.196767i
$989$			25.9955i			0.826609i
$990$	26.2169	+	20.8410i	0.833229	+	0.662372i
$991$	−31.1334	−	17.9749i	−0.988984	−	0.570990i	−0.0840134	−	0.996465i	$-0.526774\pi$
$991$	−31.1334	−	17.9749i	−0.988984	−	0.570990i	−0.904970	+	0.425475i	$0.860107\pi$
$992$	−3.48124	+	11.5849i	−0.110530	+	0.367820i
$993$	−39.2532			−1.24566
$994$	−13.2517	+	0.614485i	−0.420320	+	0.0194903i
$995$	−26.3532	+	15.2150i	−0.835453	+	0.482349i
$996$	−39.4949	+	27.9741i	−1.25144	+	0.886393i
$997$	−39.7511	+	22.9503i	−1.25893	+	0.726843i	−0.972866	−	0.231368i	$-0.925680\pi$
$997$	−39.7511	+	22.9503i	−1.25893	+	0.726843i	−0.286062	+	0.958211i	$0.592346\pi$
$998$	26.6076	+	41.5175i	0.842250	+	1.31421i
$999$	7.50751	+	4.33446i	0.237527	+	0.137136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.t.a.87.14	✓	160
4.3	odd	2	inner	572.2.t.a.87.42	yes	160
11.10	odd	2	inner	572.2.t.a.87.67	yes	160
13.3	even	3	inner	572.2.t.a.263.39	yes	160
44.43	even	2	inner	572.2.t.a.87.39	yes	160
52.3	odd	6	inner	572.2.t.a.263.67	yes	160
143.120	odd	6	inner	572.2.t.a.263.42	yes	160
572.263	even	6	inner	572.2.t.a.263.14	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.t.a.87.14	✓	160	1.1	even	1	trivial
572.2.t.a.87.39	yes	160	44.43	even	2	inner
572.2.t.a.87.42	yes	160	4.3	odd	2	inner
572.2.t.a.87.67	yes	160	11.10	odd	2	inner
572.2.t.a.263.14	yes	160	572.263	even	6	inner
572.2.t.a.263.39	yes	160	13.3	even	3	inner
572.2.t.a.263.42	yes	160	143.120	odd	6	inner
572.2.t.a.263.67	yes	160	52.3	odd	6	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19068 + 0.763078i) q^{2} +(-2.37620 - 1.37190i) q^{3} +(0.835423 - 1.81716i) q^{4} +1.57679 q^{5} +(3.87615 - 0.179738i) q^{6} +(0.286729 + 0.496630i) q^{7} +(0.391917 + 2.80114i) q^{8} +(2.26422 + 3.92174i) q^{9} +O(q^{10})\)	\(q+(-1.19068 + 0.763078i) q^{2} +(-2.37620 - 1.37190i) q^{3} +(0.835423 - 1.81716i) q^{4} +1.57679 q^{5} +(3.87615 - 0.179738i) q^{6} +(0.286729 + 0.496630i) q^{7} +(0.391917 + 2.80114i) q^{8} +(2.26422 + 3.92174i) q^{9} +(-1.87745 + 1.20322i) q^{10} +(-3.25416 - 0.640664i) q^{11} +(-4.47809 + 3.17182i) q^{12} +(-1.32019 + 3.35516i) q^{13} +(-0.720370 - 0.372529i) q^{14} +(-3.74677 - 2.16320i) q^{15} +(-2.60414 - 3.03619i) q^{16} +(2.82829 - 1.63292i) q^{17} +(-5.68855 - 2.94175i) q^{18} +(0.446504 + 0.773368i) q^{19} +(1.31729 - 2.86528i) q^{20} -1.57346i q^{21} +(4.36353 - 1.72035i) q^{22} +(3.92787 + 2.26776i) q^{23} +(2.91162 - 7.19375i) q^{24} -2.51373 q^{25} +(-0.988327 - 5.00232i) q^{26} -4.19373i q^{27} +(1.14200 - 0.106137i) q^{28} +(-1.23606 - 0.713642i) q^{29} +(6.11189 - 0.283409i) q^{30} +2.13840i q^{31} +(5.41754 + 1.62796i) q^{32} +(6.85361 + 5.98673i) q^{33} +(-2.12154 + 4.10248i) q^{34} +(0.452113 + 0.783082i) q^{35} +(9.01801 - 0.838134i) q^{36} +(-1.03356 + 1.79018i) q^{37} +(-1.12178 - 0.580114i) q^{38} +(7.73998 - 6.16136i) q^{39} +(0.617971 + 4.41682i) q^{40} +(9.59598 + 5.54024i) q^{41} +(1.20067 + 1.87348i) q^{42} +(2.86577 + 4.96366i) q^{43} +(-3.88279 + 5.37810i) q^{44} +(3.57020 + 6.18377i) q^{45} +(-6.40730 + 0.297107i) q^{46} +6.60943i q^{47} +(2.02260 + 10.7872i) q^{48} +(3.33557 - 5.77738i) q^{49} +(2.99304 - 1.91817i) q^{50} -8.96079 q^{51} +(4.99394 + 5.20198i) q^{52} +8.91277 q^{53} +(3.20014 + 4.99338i) q^{54} +(-5.13113 - 1.01019i) q^{55} +(-1.27876 + 0.997808i) q^{56} -2.45024i q^{57} +(2.01632 - 0.0934968i) q^{58} +(4.96297 - 2.86537i) q^{59} +(-7.06102 + 5.00130i) q^{60} +(-9.42166 + 5.43960i) q^{61} +(-1.63177 - 2.54615i) q^{62} +(-1.29844 + 2.24896i) q^{63} +(-7.69280 + 2.19563i) q^{64} +(-2.08167 + 5.29039i) q^{65} +(-12.7288 - 1.89842i) q^{66} +(6.79453 + 3.92282i) q^{67} +(-0.604448 - 6.50363i) q^{68} +(-6.22228 - 10.7773i) q^{69} +(-1.13587 - 0.587400i) q^{70} +(14.1662 - 8.17885i) q^{71} +(-10.0980 + 7.87940i) q^{72} +2.80396i q^{73} +(-0.135410 - 2.92021i) q^{74} +(5.97313 + 3.44859i) q^{75} +(1.77835 - 0.165280i) q^{76} +(-0.614890 - 1.79981i) q^{77} +(-4.51422 + 13.2424i) q^{78} +0.297057 q^{79} +(-4.10618 - 4.78744i) q^{80} +(1.03928 - 1.80009i) q^{81} +(-15.6534 + 0.725848i) q^{82} +8.81958 q^{83} +(-2.85922 - 1.31450i) q^{84} +(4.45963 - 2.57477i) q^{85} +(-7.19987 - 3.72331i) q^{86} +(1.95809 + 3.39151i) q^{87} +(0.519234 - 9.36645i) q^{88} +(1.52380 - 2.63930i) q^{89} +(-8.96966 - 4.63853i) q^{90} +(-2.04481 + 0.306376i) q^{91} +(7.40231 - 5.24303i) q^{92} +(2.93368 - 5.08127i) q^{93} +(-5.04351 - 7.86970i) q^{94} +(0.704044 + 1.21944i) q^{95} +(-10.6398 - 11.3007i) q^{96} +(0.361220 + 0.625652i) q^{97} +(0.437005 + 9.42430i) q^{98} +(-4.85561 - 14.2126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) \) 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9	\( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9} - 4 q^{12} + 8 q^{14} - 14 q^{16} - 26 q^{20} + 112 q^{25} - 14 q^{33} + 12 q^{34} - 6 q^{36} - 4 q^{37} + 40 q^{38} + 54 q^{42} - 16 q^{44} - 48 q^{45} - 40 q^{48} - 52 q^{49} - 32 q^{53} - 18 q^{56} - 6 q^{58} - 52 q^{60} + 16 q^{64} - 84 q^{66} - 12 q^{69} - 68 q^{70} - 4 q^{77} + 28 q^{78} - 44 q^{80} - 40 q^{81} - 38 q^{82} + 120 q^{86} - 14 q^{88} - 64 q^{92} - 8 q^{93}+O(q^{100}) \) 160 * q - 2 * q^4 - 16 * q^5 + 68 * q^9 - 4 * q^12 + 8 * q^14 - 14 * q^16 - 26 * q^20 + 112 * q^25 - 14 * q^33 + 12 * q^34 - 6 * q^36 - 4 * q^37 + 40 * q^38 + 54 * q^42 - 16 * q^44 - 48 * q^45 - 40 * q^48 - 52 * q^49 - 32 * q^53 - 18 * q^56 - 6 * q^58 - 52 * q^60 + 16 * q^64 - 84 * q^66 - 12 * q^69 - 68 * q^70 - 4 * q^77 + 28 * q^78 - 44 * q^80 - 40 * q^81 - 38 * q^82 + 120 * q^86 - 14 * q^88 - 64 * q^92 - 8 * q^93

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