LMFDB - Embedded newform 525.2.bh.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(13,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19, 10]))

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

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

chi := DirichletCharacter("525.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bh (of order $20$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	525.13
Dual form			525.2.bh.a.202.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65246 + 0.420109i) q^{2} +(0.891007 + 0.453990i) q^{3} +(4.95695 - 1.61061i) q^{4} +(-1.94004 + 1.11186i) q^{5} +(-2.55409 - 0.829873i) q^{6} +(-2.46059 + 0.972375i) q^{7} +(-7.68586 + 3.91614i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-2.65246 + 0.420109i) q^{2} +(0.891007 + 0.453990i) q^{3} +(4.95695 - 1.61061i) q^{4} +(-1.94004 + 1.11186i) q^{5} +(-2.55409 - 0.829873i) q^{6} +(-2.46059 + 0.972375i) q^{7} +(-7.68586 + 3.91614i) q^{8} +(0.587785 + 0.809017i) q^{9} +(4.67879 - 3.76420i) q^{10} +(-3.60516 - 2.61930i) q^{11} +(5.14788 + 0.815344i) q^{12} +(-0.326126 + 2.05908i) q^{13} +(6.11811 - 3.61290i) q^{14} +(-2.23336 + 0.109913i) q^{15} +(10.3080 - 7.48918i) q^{16} +(4.25761 - 2.16936i) q^{17} +(-1.89895 - 1.89895i) q^{18} +(1.86550 - 5.74141i) q^{19} +(-7.82593 + 8.63609i) q^{20} +(-2.63385 - 0.250691i) q^{21} +(10.6629 + 5.43304i) q^{22} +(-0.108703 - 0.686327i) q^{23} -8.62604 q^{24} +(2.52754 - 4.31411i) q^{25} -5.59864i q^{26} +(0.156434 + 0.987688i) q^{27} +(-10.6309 + 8.78306i) q^{28} +(-0.0613571 + 0.0199361i) q^{29} +(5.87774 - 1.22980i) q^{30} +(-1.45023 - 0.471210i) q^{31} +(-11.9962 + 11.9962i) q^{32} +(-2.02308 - 3.97053i) q^{33} +(-10.3818 + 7.54281i) q^{34} +(3.69250 - 4.62228i) q^{35} +(4.21664 + 3.06357i) q^{36} +(-0.676894 + 4.27374i) q^{37} +(-2.53615 + 16.0126i) q^{38} +(-1.22538 + 1.68660i) q^{39} +(10.5567 - 16.1431i) q^{40} +(3.39721 + 4.67586i) q^{41} +(7.09150 - 0.441554i) q^{42} +(-8.13411 - 8.13411i) q^{43} +(-22.0893 - 7.17725i) q^{44} +(-2.03984 - 0.915993i) q^{45} +(0.576664 + 1.77479i) q^{46} +(4.29458 - 8.42859i) q^{47} +(12.5845 - 1.99319i) q^{48} +(5.10898 - 4.78522i) q^{49} +(-4.89180 + 12.5049i) q^{50} +4.77843 q^{51} +(1.69979 + 10.7320i) q^{52} +(1.31152 - 2.57400i) q^{53} +(-0.829873 - 2.55409i) q^{54} +(9.90647 + 1.07313i) q^{55} +(15.1038 - 17.1095i) q^{56} +(4.26872 - 4.26872i) q^{57} +(0.154372 - 0.0786565i) q^{58} +(6.69600 - 4.86493i) q^{59} +(-10.8937 + 4.14192i) q^{60} +(6.37614 - 8.77600i) q^{61} +(4.04465 + 0.640610i) q^{62} +(-2.23296 - 1.41911i) q^{63} +(11.8014 - 16.2432i) q^{64} +(-1.65671 - 4.35731i) q^{65} +(7.03421 + 9.68175i) q^{66} +(-1.27232 - 2.49707i) q^{67} +(17.6108 - 17.6108i) q^{68} +(0.214730 - 0.660872i) q^{69} +(-7.85236 + 13.8117i) q^{70} +(2.02691 + 6.23819i) q^{71} +(-7.68586 - 3.91614i) q^{72} +(-7.03260 + 1.11385i) q^{73} -11.6203i q^{74} +(4.21062 - 2.69642i) q^{75} -31.4645i q^{76} +(11.4178 + 2.93946i) q^{77} +(2.54173 - 4.98843i) q^{78} +(-13.3233 + 4.32900i) q^{79} +(-11.6710 + 25.9904i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-10.9753 - 10.9753i) q^{82} +(-6.02741 - 11.8295i) q^{83} +(-13.4596 + 2.99944i) q^{84} +(-5.84793 + 8.94252i) q^{85} +(24.9926 + 18.1582i) q^{86} +(-0.0637204 - 0.0100923i) q^{87} +(37.9663 + 6.01327i) q^{88} +(0.632817 + 0.459768i) q^{89} +(5.79542 + 1.57268i) q^{90} +(-1.19974 - 5.38367i) q^{91} +(-1.64424 - 3.22701i) q^{92} +(-1.07824 - 1.07824i) q^{93} +(-7.85029 + 24.1607i) q^{94} +(2.76450 + 13.2128i) q^{95} +(-16.1348 + 5.24252i) q^{96} +(-0.735571 + 1.44364i) q^{97} +(-11.5411 + 14.8390i) q^{98} -4.45622i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 8 q^{7} - 24 q^{8}+O(q^{10}) $ 320 * q + 8 * q^7 - 24 * q^8	$ 320 q + 8 q^{7} - 24 q^{8} - 8 q^{15} + 80 q^{16} - 24 q^{22} + 36 q^{28} - 40 q^{29} - 32 q^{30} - 48 q^{32} + 28 q^{35} + 80 q^{36} - 32 q^{37} + 16 q^{42} - 144 q^{43} - 288 q^{50} + 136 q^{53} - 8 q^{57} - 32 q^{58} - 40 q^{60} - 8 q^{63} - 120 q^{64} - 40 q^{65} + 32 q^{67} - 40 q^{70} - 24 q^{72} + 24 q^{77} + 8 q^{78} + 80 q^{81} - 80 q^{84} - 48 q^{85} - 56 q^{88} + 40 q^{92} + 96 q^{93} - 88 q^{95} - 184 q^{98}+O(q^{100}) $ 320 * q + 8 * q^7 - 24 * q^8 - 8 * q^15 + 80 * q^16 - 24 * q^22 + 36 * q^28 - 40 * q^29 - 32 * q^30 - 48 * q^32 + 28 * q^35 + 80 * q^36 - 32 * q^37 + 16 * q^42 - 144 * q^43 - 288 * q^50 + 136 * q^53 - 8 * q^57 - 32 * q^58 - 40 * q^60 - 8 * q^63 - 120 * q^64 - 40 * q^65 + 32 * q^67 - 40 * q^70 - 24 * q^72 + 24 * q^77 + 8 * q^78 + 80 * q^81 - 80 * q^84 - 48 * q^85 - 56 * q^88 + 40 * q^92 + 96 * q^93 - 88 * q^95 - 184 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.65246	+	0.420109i	−1.87557	+	0.297062i	−0.986882	−	0.161443i	$-0.948385\pi$
$2$	−2.65246	+	0.420109i	−1.87557	+	0.297062i	−0.888692	+	0.458504i	$0.848385\pi$
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$4$	4.95695	−	1.61061i	2.47848	−	0.805306i
$5$	−1.94004	+	1.11186i	−0.867614	+	0.497239i
$5$	−1.94004	+	1.11186i	−0.867614	+	0.497239i
$6$	−2.55409	−	0.829873i	−1.04270	−	0.338794i
$7$	−2.46059	+	0.972375i	−0.930014	+	0.367523i
$7$	−2.46059	+	0.972375i	−0.930014	+	0.367523i
$8$	−7.68586	+	3.91614i	−2.71736	+	1.38456i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	4.67879	−	3.76420i	1.47956	−	1.19034i
$11$	−3.60516	−	2.61930i	−1.08700	−	0.789750i	−0.108107	−	0.994139i	$-0.534479\pi$
$11$	−3.60516	−	2.61930i	−1.08700	−	0.789750i	−0.978890	+	0.204390i	$0.934479\pi$
$12$	5.14788	+	0.815344i	1.48606	+	0.235370i
$13$	−0.326126	+	2.05908i	−0.0904512	+	0.571086i	0.900287	+	0.435298i	$0.143357\pi$
$13$	−0.326126	+	2.05908i	−0.0904512	+	0.571086i	−0.990738	+	0.135789i	$0.956643\pi$
$14$	6.11811	−	3.61290i	1.63513	−	0.965588i
$15$	−2.23336	+	0.109913i	−0.576652	+	0.0283794i
$16$	10.3080	−	7.48918i	2.57699	−	1.87230i
$17$	4.25761	−	2.16936i	1.03262	−	0.526148i	0.146312	−	0.989238i	$-0.453260\pi$
$17$	4.25761	−	2.16936i	1.03262	−	0.526148i	0.886311	+	0.463091i	$0.153260\pi$
$18$	−1.89895	−	1.89895i	−0.447588	−	0.447588i
$19$	1.86550	−	5.74141i	0.427975	−	1.31717i	−0.472143	−	0.881522i	$-0.656519\pi$
$19$	1.86550	−	5.74141i	0.427975	−	1.31717i	0.900117	−	0.435648i	$-0.143481\pi$
$20$	−7.82593	+	8.63609i	−1.74993	+	1.93109i
$21$	−2.63385	−	0.250691i	−0.574753	−	0.0547053i
$22$	10.6629	+	5.43304i	2.27335	+	1.15833i
$23$	−0.108703	−	0.686327i	−0.0226662	−	0.143109i	0.973760	−	0.227578i	$-0.0730806\pi$
$23$	−0.108703	−	0.686327i	−0.0226662	−	0.143109i	−0.996426	+	0.0844689i	$0.973081\pi$
$24$	−8.62604			−1.76078
$25$	2.52754	−	4.31411i	0.505507	−	0.862822i
$26$		−	5.59864i		−	1.09798i
$27$	0.156434	+	0.987688i	0.0301058	+	0.190081i
$28$	−10.6309	+	8.78306i	−2.00905	+	1.65984i
$29$	−0.0613571	+	0.0199361i	−0.0113937	+	0.00370205i	−0.314708	−	0.949188i	$-0.601907\pi$
$29$	−0.0613571	+	0.0199361i	−0.0113937	+	0.00370205i	0.303315	+	0.952890i	$0.401907\pi$
$30$	5.87774	−	1.22980i	1.07312	−	0.224529i
$31$	−1.45023	−	0.471210i	−0.260470	−	0.0846318i	0.175871	−	0.984413i	$-0.443726\pi$
$31$	−1.45023	−	0.471210i	−0.260470	−	0.0846318i	−0.436341	+	0.899781i	$0.643726\pi$
$32$	−11.9962	+	11.9962i	−2.12064	+	2.12064i
$33$	−2.02308	−	3.97053i	−0.352174	−	0.691180i
$34$	−10.3818	+	7.54281i	−1.78046	+	1.29358i
$35$	3.69250	−	4.62228i	0.624147	−	0.781307i
$36$	4.21664	+	3.06357i	0.702773	+	0.510594i
$37$	−0.676894	+	4.27374i	−0.111281	+	0.702598i	0.867462	+	0.497504i	$0.165750\pi$
$37$	−0.676894	+	4.27374i	−0.111281	+	0.702598i	−0.978742	+	0.205094i	$0.934250\pi$
$38$	−2.53615	+	16.0126i	−0.411417	+	2.59759i
$39$	−1.22538	+	1.68660i	−0.196219	+	0.270072i
$40$	10.5567	−	16.1431i	1.66916	−	2.55244i
$41$	3.39721	+	4.67586i	0.530555	+	0.730247i	0.987215	−	0.159395i	$-0.0509543\pi$
$41$	3.39721	+	4.67586i	0.530555	+	0.730247i	−0.456660	+	0.889641i	$0.650954\pi$
$42$	7.09150	−	0.441554i	1.09424	−	0.0681333i
$43$	−8.13411	−	8.13411i	−1.24044	−	1.24044i	−0.959818	−	0.280623i	$-0.909459\pi$
$43$	−8.13411	−	8.13411i	−1.24044	−	1.24044i	−0.280623	−	0.959818i	$-0.590541\pi$
$44$	−22.0893	−	7.17725i	−3.33009	−	1.08201i
$45$	−2.03984	−	0.915993i	−0.304082	−	0.136548i
$46$	0.576664	+	1.77479i	0.0850244	+	0.261678i
$47$	4.29458	−	8.42859i	0.626429	−	1.22944i	−0.331777	−	0.943358i	$-0.607648\pi$
$47$	4.29458	−	8.42859i	0.626429	−	1.22944i	0.958206	−	0.286079i	$-0.0923518\pi$
$48$	12.5845	−	1.99319i	1.81641	−	0.287692i
$49$	5.10898	−	4.78522i	0.729854	−	0.683603i
$50$	−4.89180	+	12.5049i	−0.691805	+	1.76845i
$51$	4.77843			0.669114
$52$	1.69979	+	10.7320i	0.235718	+	1.48827i
$53$	1.31152	−	2.57400i	0.180151	−	0.353566i	−0.783217	−	0.621748i	$-0.786423\pi$
$53$	1.31152	−	2.57400i	0.180151	−	0.353566i	0.963368	+	0.268182i	$0.0864228\pi$
$54$	−0.829873	−	2.55409i	−0.112931	−	0.347567i
$55$	9.90647	+	1.07313i	1.33579	+	0.144701i
$56$	15.1038	−	17.1095i	2.01833	−	2.28636i
$57$	4.26872	−	4.26872i	0.565405	−	0.565405i
$58$	0.154372	−	0.0786565i	0.0202700	−	0.0103281i
$59$	6.69600	−	4.86493i	0.871745	−	0.633360i	−0.0593096	−	0.998240i	$-0.518890\pi$
$59$	6.69600	−	4.86493i	0.871745	−	0.633360i	0.931055	+	0.364880i	$0.118890\pi$
$60$	−10.8937	+	4.14192i	−1.40637	+	0.534719i
$61$	6.37614	−	8.77600i	0.816381	−	1.12365i	−0.173926	−	0.984759i	$-0.555645\pi$
$61$	6.37614	−	8.77600i	0.816381	−	1.12365i	0.990307	−	0.138893i	$-0.0443545\pi$
$62$	4.04465	+	0.640610i	0.513671	+	0.0813576i
$63$	−2.23296	−	1.41911i	−0.281327	−	0.178791i
$64$	11.8014	−	16.2432i	1.47517	−	2.03040i
$65$	−1.65671	−	4.35731i	−0.205490	−	0.540458i
$66$	7.03421	+	9.68175i	0.865851	+	1.19174i
$67$	−1.27232	−	2.49707i	−0.155439	−	0.305065i	0.800134	−	0.599821i	$-0.204762\pi$
$67$	−1.27232	−	2.49707i	−0.155439	−	0.305065i	−0.955573	+	0.294756i	$0.904762\pi$
$68$	17.6108	−	17.6108i	2.13562	−	2.13562i
$69$	0.214730	−	0.660872i	0.0258505	−	0.0795596i
$70$	−7.85236	+	13.8117i	−0.938537	+	1.65081i
$71$	2.02691	+	6.23819i	0.240550	+	0.740337i	0.996337	+	0.0855190i	$0.0272548\pi$
$71$	2.02691	+	6.23819i	0.240550	+	0.740337i	−0.755786	+	0.654818i	$0.772745\pi$
$72$	−7.68586	−	3.91614i	−0.905787	−	0.461522i
$73$	−7.03260	+	1.11385i	−0.823103	+	0.130367i	−0.553759	−	0.832677i	$-0.686807\pi$
$73$	−7.03260	+	1.11385i	−0.823103	+	0.130367i	−0.269345	+	0.963044i	$0.586807\pi$
$74$		−	11.6203i		−	1.35083i
$75$	4.21062	−	2.69642i	0.486200	−	0.311356i
$76$		−	31.4645i		−	3.60923i
$77$	11.4178	+	2.93946i	1.30117	+	0.334982i
$78$	2.54173	−	4.98843i	0.287794	−	0.564828i
$79$	−13.3233	+	4.32900i	−1.49899	+	0.487050i	−0.939722	−	0.341939i	$-0.888916\pi$
$79$	−13.3233	+	4.32900i	−1.49899	+	0.487050i	−0.559265	+	0.828989i	$0.688916\pi$
$80$	−11.6710	+	25.9904i	−1.30486	+	2.90581i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	−10.9753	−	10.9753i	−1.21202	−	1.21202i
$83$	−6.02741	−	11.8295i	−0.661594	−	1.29845i	−0.941042	−	0.338291i	$-0.890151\pi$
$83$	−6.02741	−	11.8295i	−0.661594	−	1.29845i	0.279447	−	0.960161i	$-0.409849\pi$
$84$	−13.4596	+	2.99944i	−1.46857	+	0.327266i
$85$	−5.84793	+	8.94252i	−0.634297	+	0.969953i
$86$	24.9926	+	18.1582i	2.69503	+	1.95805i
$87$	−0.0637204	−	0.0100923i	−0.00683154	−	0.00108201i
$88$	37.9663	+	6.01327i	4.04722	+	0.641017i
$89$	0.632817	+	0.459768i	0.0670784	+	0.0487353i	0.620819	−	0.783954i	$-0.286800\pi$
$89$	0.632817	+	0.459768i	0.0670784	+	0.0487353i	−0.553741	+	0.832689i	$0.686800\pi$
$90$	5.79542	+	1.57268i	0.610891	+	0.165775i
$91$	−1.19974	−	5.38367i	−0.125766	−	0.564362i
$92$	−1.64424	−	3.22701i	−0.171424	−	0.336439i
$93$	−1.07824	−	1.07824i	−0.111809	−	0.111809i
$94$	−7.85029	+	24.1607i	−0.809696	+	2.49199i
$95$	2.76450	+	13.2128i	0.283631	+	1.35560i
$96$	−16.1348	+	5.24252i	−1.64675	+	0.535063i
$97$	−0.735571	+	1.44364i	−0.0746860	+	0.146579i	−0.925330	−	0.379162i	$-0.876212\pi$
$97$	−0.735571	+	1.44364i	−0.0746860	+	0.146579i	0.850644	+	0.525742i	$0.176212\pi$
$98$	−11.5411	+	14.8390i	−1.16582	+	1.49896i
$99$		−	4.45622i		−	0.447867i
$100$	5.58052	−	25.4557i	0.558052	−	2.54557i
$101$		−	10.5654i		−	1.05130i	−0.850702	−	0.525648i	$-0.823823\pi$
$101$		−	10.5654i		−	1.05130i	0.850702	−	0.525648i	$-0.176177\pi$
$102$	−12.6746	+	2.00746i	−1.25497	+	0.198768i
$103$	14.9072	+	7.59562i	1.46885	+	0.748419i	0.991477	−	0.130280i	$-0.0415875\pi$
$103$	14.9072	+	7.59562i	1.46885	+	0.748419i	0.477377	+	0.878698i	$0.341587\pi$
$104$	−5.55709	−	17.1030i	−0.544917	−	1.67708i
$105$	5.38851	−	2.44212i	0.525865	−	0.238326i
$106$	−2.39739	+	7.37842i	−0.232855	+	0.716655i
$107$	1.07877	−	1.07877i	0.104289	−	0.104289i	−0.653037	−	0.757326i	$-0.726506\pi$
$107$	1.07877	−	1.07877i	0.104289	−	0.104289i	0.757326	+	0.653037i	$0.226506\pi$
$108$	2.36622	+	4.64397i	0.227690	+	0.446866i
$109$	−5.62633	−	7.74399i	−0.538905	−	0.741739i	0.449550	−	0.893255i	$-0.351584\pi$
$109$	−5.62633	−	7.74399i	−0.538905	−	0.741739i	−0.988455	+	0.151516i	$0.951584\pi$
$110$	−26.7274	+	1.31536i	−2.54835	+	0.125415i
$111$	−2.54335	+	3.50063i	−0.241404	+	0.332265i
$112$	−18.0814	+	28.4510i	−1.70853	+	2.68837i
$113$	−16.8708	−	2.67207i	−1.58707	−	0.251367i	−0.700394	−	0.713756i	$-0.746992\pi$
$113$	−16.8708	−	2.67207i	−1.58707	−	0.251367i	−0.886677	+	0.462389i	$0.846992\pi$
$114$	−9.52929	+	13.1159i	−0.892499	+	1.22842i
$115$	0.973988	+	1.21064i	0.0908249	+	0.112893i
$116$	−0.272035	+	0.197645i	−0.0252578	+	0.0183509i
$117$	−1.85752	+	0.946456i	−0.171728	+	0.0874999i
$118$	−15.7171	+	15.7171i	−1.44688	+	1.44688i
$119$	−8.36679	+	9.47790i	−0.766983	+	0.868838i
$120$	16.7349	−	9.59094i	1.52768	−	0.875529i
$121$	2.73725	+	8.42440i	0.248841	+	0.765854i
$122$	−13.2256	+	25.9567i	−1.19739	+	2.35001i
$123$	0.904141	+	5.70852i	0.0815237	+	0.514720i
$124$	−7.94768			−0.713723
$125$	−0.106845	+	11.1798i	−0.00955648	+	0.999954i
$126$	6.51903	+	2.82605i	0.580762	+	0.251764i
$127$	−2.09409	+	0.331672i	−0.185821	+	0.0294311i	−0.248651	−	0.968593i	$-0.579987\pi$
$127$	−2.09409	+	0.331672i	−0.185821	+	0.0294311i	0.0628304	+	0.998024i	$0.479987\pi$
$128$	−9.07471	+	17.8101i	−0.802098	+	1.57421i
$129$	−3.55474	−	10.9404i	−0.312977	−	0.963245i
$130$	6.22491	+	10.8616i	0.545960	+	0.952627i
$131$	−15.9391	−	5.17891i	−1.39260	−	0.452484i	−0.485810	−	0.874064i	$-0.661475\pi$
$131$	−15.9391	−	5.17891i	−1.39260	−	0.452484i	−0.906791	+	0.421581i	$0.861475\pi$
$132$	−16.4233	−	16.4233i	−1.42947	−	1.42947i
$133$	0.992584	+	15.9412i	0.0860679	+	1.38228i
$134$	4.42382	+	6.08887i	0.382160	+	0.525998i
$135$	−1.40166	−	1.74223i	−0.120636	−	0.149947i
$136$	−24.2279	+	33.3468i	−2.07752	+	2.85947i
$137$	2.68846	−	16.9742i	0.229690	−	1.45021i	−0.555791	−	0.831322i	$-0.687585\pi$
$137$	2.68846	−	16.9742i	0.229690	−	1.45021i	0.785481	−	0.618885i	$-0.212415\pi$
$138$	−0.291926	+	1.84315i	−0.0248504	+	0.156899i
$139$	10.9515	+	7.95672i	0.928893	+	0.674880i	0.945722	−	0.324978i	$-0.105357\pi$
$139$	10.9515	+	7.95672i	0.928893	+	0.674880i	−0.0168285	+	0.999858i	$0.505357\pi$
$140$	10.8589	−	28.8596i	0.917742	−	2.43908i
$141$	7.65300	−	5.56023i	0.644499	−	0.468256i
$142$	−7.99703	−	15.6950i	−0.671096	−	1.31710i
$143$	6.56910	−	6.56910i	0.549335	−	0.549335i
$144$	12.1177	+	3.93730i	1.00981	+	0.328108i
$145$	0.0968692	−	0.106897i	0.00804455	−	0.00887735i
$146$	18.1858	−	5.90891i	1.50506	−	0.489025i
$147$	6.72458	−	1.94424i	0.554634	−	0.160358i
$148$	3.52800	+	22.2749i	0.290000	+	1.83099i
$149$			14.6542i			1.20052i	0.799805	+	0.600260i	$0.204936\pi$
$149$			14.6542i			1.20052i	−0.799805	+	0.600260i	$0.795064\pi$
$150$	−10.0357	+	8.92108i	−0.819413	+	0.728403i
$151$	−10.7290			−0.873116			−0.436558	−	0.899676i	$-0.643803\pi$
$151$	−10.7290			−0.873116			−0.436558	+	0.899676i	$0.643803\pi$
$152$	8.14622	+	51.4332i	0.660746	+	4.17179i
$153$	4.25761	+	2.16936i	0.344208	+	0.175383i
$154$	−31.5201	−	3.00010i	−2.53996	−	0.241755i
$155$	3.33744	−	0.698290i	0.268069	−	0.0560880i
$156$	−3.35772	+	10.3340i	−0.268833	+	0.827382i
$157$	−11.2050	−	11.2050i	−0.894259	−	0.894259i	0.100662	−	0.994921i	$-0.467904\pi$
$157$	−11.2050	−	11.2050i	−0.894259	−	0.894259i	−0.994921	+	0.100662i	$0.967904\pi$
$158$	33.5209	−	17.0797i	2.66678	−	1.35879i
$159$	2.33714	−	1.69803i	0.185347	−	0.134663i
$160$	9.93504	−	36.6112i	0.785434	−	2.89437i
$161$	0.934841	+	1.58307i	0.0736758	+	0.124763i
$162$	0.420109	−	2.65246i	0.0330069	−	0.208397i
$163$	14.9243	+	2.36378i	1.16896	+	0.185146i	0.710585	−	0.703612i	$-0.248430\pi$
$163$	14.9243	+	2.36378i	1.16896	+	0.185146i	0.458378	+	0.888757i	$0.348430\pi$
$164$	24.3708	+	17.7064i	1.90304	+	1.38264i
$165$	8.33954	+	5.45361i	0.649232	+	0.424563i
$166$	20.9571	+	28.8450i	1.62659	+	2.23881i
$167$	8.44741	−	4.30417i	0.653680	−	0.333067i	−0.0955032	−	0.995429i	$-0.530446\pi$
$167$	8.44741	−	4.30417i	0.653680	−	0.333067i	0.749184	+	0.662362i	$0.230446\pi$
$168$	21.2251	−	8.38774i	1.63755	−	0.647128i
$169$	8.23028	+	2.67418i	0.633098	+	0.205706i
$170$	11.7546	−	26.1765i	0.901535	−	2.00764i
$171$	5.74141	−	1.86550i	0.439057	−	0.142658i
$172$	−53.4213	−	27.2195i	−4.07334	−	2.07547i
$173$	−17.1419	+	2.71501i	−1.30328	+	0.206419i	−0.769194	−	0.639015i	$-0.779342\pi$
$173$	−17.1419	+	2.71501i	−1.30328	+	0.206419i	−0.534081	+	0.845433i	$0.679342\pi$
$174$	0.173256			0.0131345
$175$	−2.02429	+	13.0730i	−0.153022	+	0.988223i
$176$	−56.7783			−4.27983
$177$	8.17481	−	1.29476i	0.614456	−	0.0973203i
$178$	−1.87167	−	0.953666i	−0.140288	−	0.0714803i
$179$	1.55692	−	0.505873i	0.116369	−	0.0378107i	−0.250253	−	0.968180i	$-0.580514\pi$
$179$	1.55692	−	0.505873i	0.116369	−	0.0378107i	0.366623	+	0.930370i	$0.380514\pi$
$180$	−11.5867	−	1.25514i	−0.863622	−	0.0935528i
$181$	−0.402918	−	0.130916i	−0.0299487	−	0.00973091i	0.294004	−	0.955804i	$-0.405012\pi$
$181$	−0.402918	−	0.130916i	−0.0299487	−	0.00973091i	−0.323953	+	0.946073i	$0.605012\pi$
$182$	5.44398	+	13.7760i	0.403535	+	1.02114i
$183$	9.66540	−	4.92477i	0.714487	−	0.364049i
$184$	3.52323	+	4.84931i	0.259736	+	0.357496i
$185$	−3.43859	−	9.04385i	−0.252810	−	0.664917i
$186$	3.31298	+	2.40702i	0.242920	+	0.176491i
$187$	−21.0316	−	3.33108i	−1.53798	−	0.243593i
$188$	7.71285	−	48.6970i	0.562518	−	3.55160i
$189$	−1.34532	−	2.27818i	−0.0978579	−	0.165713i
$190$	−12.8835	−	33.8850i	−0.934669	−	2.45827i
$191$	1.87358	−	1.36124i	0.135568	−	0.0984956i	−0.517935	−	0.855420i	$-0.673299\pi$
$191$	1.87358	−	1.36124i	0.135568	−	0.0984956i	0.653502	+	0.756925i	$0.273299\pi$
$192$	17.8893	−	9.11507i	1.29105	−	0.657823i
$193$	−7.41480	−	7.41480i	−0.533729	−	0.533729i	0.387951	−	0.921680i	$-0.373183\pi$
$193$	−7.41480	−	7.41480i	−0.533729	−	0.533729i	−0.921680	+	0.387951i	$0.873183\pi$
$194$	1.34459	−	4.13822i	0.0965359	−	0.297107i
$195$	0.502040	−	4.63453i	0.0359518	−	0.331885i
$196$	17.6178	−	31.9487i	1.25842	−	2.28205i
$197$	−2.12668	−	1.08360i	−0.151519	−	0.0772030i	0.376587	−	0.926381i	$-0.377098\pi$
$197$	−2.12668	−	1.08360i	−0.151519	−	0.0772030i	−0.528106	+	0.849178i	$0.677098\pi$
$198$	1.87210	+	11.8200i	0.133044	+	0.840009i
$199$	−6.70024			−0.474967			−0.237484	−	0.971392i	$-0.576323\pi$
$199$	−6.70024			−0.474967			−0.237484	+	0.971392i	$0.576323\pi$
$200$	−2.53162	+	43.0558i	−0.179013	+	3.04451i
$201$		−	2.80252i		−	0.197675i
$202$	4.43862	+	28.0243i	0.312300	+	1.97178i
$203$	0.131589	−	0.108717i	0.00923574	−	0.00763041i
$204$	23.6865	−	7.69620i	1.65838	−	0.538842i
$205$	−11.7896	−	5.29415i	−0.823424	−	0.369759i
$206$	−42.7319	−	13.8844i	−2.97727	−	0.967375i
$207$	0.491356	−	0.491356i	0.0341516	−	0.0341516i
$208$	12.0591	+	23.6674i	0.836150	+	1.64104i
$209$	−21.7639	+	15.8124i	−1.50544	+	1.09377i
$210$	−13.2669	+	8.74139i	−0.915501	+	0.603213i
$211$	−7.49474	−	5.44525i	−0.515959	−	0.374866i	0.299120	−	0.954215i	$-0.403307\pi$
$211$	−7.49474	−	5.44525i	−0.515959	−	0.374866i	−0.815080	+	0.579349i	$0.803307\pi$
$212$	2.35542	−	14.8715i	0.161771	−	1.02138i
$213$	−1.02609	+	6.47847i	−0.0703064	+	0.443897i
$214$	−2.40819	+	3.31459i	−0.164621	+	0.226581i
$215$	24.8245	+	6.73654i	1.69302	+	0.459428i
$216$	−5.07026	−	6.97861i	−0.344987	−	0.474834i
$217$	4.02662	−	0.250719i	0.273345	−	0.0170199i
$218$	18.1770	+	18.1770i	1.23110	+	1.23110i
$219$	−6.77177	−	2.20028i	−0.457594	−	0.148681i
$220$	50.8343	−	10.6360i	3.42725	−	0.717081i
$221$	3.07837	+	9.47426i	0.207074	+	0.637308i
$222$	5.27551	−	10.3538i	0.354069	−	0.694899i
$223$	−10.6125	+	1.68086i	−0.710667	+	0.112559i	−0.501294	−	0.865277i	$-0.667142\pi$
$223$	−10.6125	+	1.68086i	−0.710667	+	0.112559i	−0.209373	+	0.977836i	$0.567142\pi$
$224$	17.8529	−	41.1824i	1.19284	−	2.75162i
$225$	4.97584	−	0.490951i	0.331723	−	0.0327301i
$226$	45.8717			3.05134
$227$	0.384133	+	2.42532i	0.0254958	+	0.160974i	0.997151	−	0.0754271i	$-0.0240320\pi$
$227$	0.384133	+	2.42532i	0.0254958	+	0.160974i	−0.971656	+	0.236401i	$0.924032\pi$
$228$	14.2846	−	28.0351i	0.946020	−	1.85667i
$229$	−1.65445	−	5.09188i	−0.109329	−	0.336481i	0.881393	−	0.472384i	$-0.156606\pi$
$229$	−1.65445	−	5.09188i	−0.109329	−	0.336481i	−0.990722	+	0.135903i	$0.956606\pi$
$230$	−3.09207	−	2.80200i	−0.203885	−	0.184758i
$231$	8.83881	+	7.80263i	0.581551	+	0.513375i
$232$	0.393509	−	0.393509i	0.0258351	−	0.0258351i
$233$	−18.4661	+	9.40896i	−1.20976	+	0.616402i	−0.938224	−	0.346028i	$-0.887530\pi$
$233$	−18.4661	+	9.40896i	−1.20976	+	0.616402i	−0.271532	+	0.962429i	$0.587530\pi$
$234$	4.52940	−	3.29080i	0.296096	−	0.215126i
$235$	1.03973	+	21.1268i	0.0678248	+	1.37816i
$236$	25.3562	−	34.8999i	1.65055	−	2.27179i
$237$	−13.8365	−	2.19148i	−0.898775	−	0.142352i
$238$	18.2109	−	28.6547i	1.18043	−	1.85741i
$239$	11.3224	−	15.5840i	0.732388	−	1.00805i	−0.266633	−	0.963798i	$-0.585911\pi$
$239$	11.3224	−	15.5840i	0.732388	−	1.00805i	0.999021	−	0.0442471i	$-0.0140889\pi$
$240$	−22.1983	+	17.8591i	−1.43289	+	1.15280i
$241$	9.23625	+	12.7126i	0.594959	+	0.818891i	0.995235	−	0.0975034i	$-0.0310857\pi$
$241$	9.23625	+	12.7126i	0.594959	+	0.818891i	−0.400276	+	0.916395i	$0.631086\pi$
$242$	−10.7996	−	21.1955i	−0.694226	−	1.36250i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	17.4715	−	53.7717i	1.11850	−	3.44238i
$245$	−4.59114	+	14.9640i	−0.293317	+	0.956015i
$246$	−4.79640	−	14.7618i	−0.305807	−	0.941178i
$247$	11.2136	+	5.71364i	0.713507	+	0.363550i
$248$	12.9916	−	2.05767i	0.824969	−	0.130662i
$249$		−	13.2765i		−	0.841365i
$250$	−4.41334	−	29.6990i	−0.279124	−	1.87833i
$251$			23.2322i			1.46640i	0.680012	+	0.733201i	$0.261974\pi$
$251$			23.2322i			1.46640i	−0.680012	+	0.733201i	$0.738026\pi$
$252$	−13.3543	−	3.43802i	−0.841244	−	0.216575i
$253$	−1.40580	+	2.75905i	−0.0883821	+	0.173460i
$254$	5.41517	−	1.75949i	0.339778	−	0.110401i
$255$	−9.27036	+	5.31294i	−0.580533	+	0.332709i
$256$	4.17946	−	12.8630i	0.261216	−	0.803940i
$257$	17.5954	+	17.5954i	1.09757	+	1.09757i	0.994694	+	0.102879i	$0.0328053\pi$
$257$	17.5954	+	17.5954i	1.09757	+	1.09757i	0.102879	+	0.994694i	$0.467195\pi$
$258$	14.0250	+	27.5255i	0.873155	+	1.71366i
$259$	−2.49012	−	11.1741i	−0.154728	−	0.694325i
$260$	−15.2302	−	18.9307i	−0.944535	−	1.17403i
$261$	−0.0521935	−	0.0379208i	−0.00323069	−	0.00234724i
$262$	44.4534	+	7.04073i	2.74634	+	0.434978i
$263$	−13.7364	−	2.17564i	−0.847024	−	0.134155i	−0.282189	−	0.959359i	$-0.591060\pi$
$263$	−13.7364	−	2.17564i	−0.847024	−	0.134155i	−0.564835	+	0.825204i	$0.691060\pi$
$264$	31.0983	+	22.5942i	1.91397	+	1.39058i
$265$	0.317524	+	6.45189i	0.0195053	+	0.396337i
$266$	−9.32983	−	41.8665i	−0.572049	−	2.56700i
$267$	0.355113	+	0.696949i	0.0217326	+	0.0426526i
$268$	−10.3286	−	10.3286i	−0.630922	−	0.630922i
$269$	−2.68334	+	8.25847i	−0.163606	+	0.503528i	−0.998931	−	0.0462288i	$-0.985280\pi$
$269$	−2.68334	+	8.25847i	−0.163606	+	0.503528i	0.835325	+	0.549757i	$0.185280\pi$
$270$	4.44978	+	4.03234i	0.270805	+	0.245400i
$271$	−19.2697	+	6.26111i	−1.17055	+	0.380335i	−0.828849	−	0.559473i	$-0.811004\pi$
$271$	−19.2697	+	6.26111i	−1.17055	+	0.380335i	−0.341703	+	0.939808i	$0.611004\pi$
$272$	27.6406	−	54.2478i	1.67596	−	3.28925i
$273$	1.37516	−	5.34155i	0.0832285	−	0.323285i
$274$			46.1530i			2.78820i
$275$	−20.4121	+	8.93268i	−1.23090	+	0.538661i
$276$		−	3.62176i		−	0.218004i
$277$	31.0086	−	4.91128i	1.86313	−	0.295090i	0.879580	−	0.475751i	$-0.157824\pi$
$277$	31.0086	−	4.91128i	1.86313	−	0.295090i	0.983545	+	0.180661i	$0.0578236\pi$
$278$	−32.3911	−	16.5041i	−1.94269	−	0.989849i
$279$	−0.471210	−	1.45023i	−0.0282106	−	0.0868233i
$280$	−10.2786	+	49.9865i	−0.614261	+	2.98727i
$281$	−2.33330	+	7.18116i	−0.139193	+	0.428392i	−0.996219	−	0.0868818i	$-0.972310\pi$
$281$	−2.33330	+	7.18116i	−0.139193	+	0.428392i	0.857026	+	0.515274i	$0.172310\pi$
$282$	−17.9634	+	17.9634i	−1.06970	+	1.06970i
$283$	−6.38279	−	12.5269i	−0.379417	−	0.744649i	0.619777	−	0.784778i	$-0.287223\pi$
$283$	−6.38279	−	12.5269i	−0.379417	−	0.744649i	−0.999194	+	0.0401294i	$0.987223\pi$
$284$	20.0946	+	27.6579i	1.19240	+	1.64119i
$285$	−3.53528	+	13.0277i	−0.209412	+	0.771695i
$286$	−14.6645	+	20.1840i	−0.867133	+	1.19351i
$287$	−12.9058	−	8.20200i	−0.761807	−	0.484149i
$288$	−16.7563	−	2.65394i	−0.987374	−	0.156385i
$289$	3.42879	−	4.71932i	0.201693	−	0.277607i
$290$	−0.212033	+	0.324237i	−0.0124510	+	0.0190399i
$291$	−1.31080	+	0.952350i	−0.0768403	+	0.0558278i
$292$	−33.0663	+	16.8481i	−1.93506	+	0.985961i
$293$	−1.22651	+	1.22651i	−0.0716537	+	0.0716537i	−0.742025	−	0.670372i	$-0.766135\pi$
$293$	−1.22651	+	1.22651i	−0.0716537	+	0.0716537i	0.670372	+	0.742025i	$0.266135\pi$
$294$	−17.0199	+	7.98208i	−0.992620	+	0.465524i
$295$	−7.58141	+	16.8832i	−0.441407	+	0.982977i
$296$	−11.5341	−	35.4982i	−0.670403	−	2.06329i
$297$	2.02308	−	3.97053i	0.117391	−	0.230393i
$298$	−6.15637	−	38.8698i	−0.356629	−	2.25166i
$299$	1.44865			0.0837778
$300$	16.5289	−	20.1477i	0.954299	−	1.16323i
$301$	27.9241	+	12.1053i	1.60952	+	0.697737i
$302$	28.4583	−	4.50736i	1.63759	−	0.259369i
$303$	4.79659	−	9.41384i	0.275557	−	0.540811i
$304$	−23.7690	−	73.1534i	−1.36324	−	4.19563i
$305$	−2.61230	+	24.1152i	−0.149580	+	1.38083i
$306$	−12.2045	−	3.96549i	−0.697686	−	0.226692i
$307$	−13.4790	−	13.4790i	−0.769284	−	0.769284i	0.208696	−	0.977981i	$-0.433078\pi$
$307$	−13.4790	−	13.4790i	−0.769284	−	0.769284i	−0.977981	+	0.208696i	$0.933078\pi$
$308$	61.3316	−	3.81883i	3.49469	−	0.217598i
$309$	9.83411	+	13.5355i	0.559443	+	0.770008i
$310$	−8.55907	+	3.25427i	−0.486122	+	0.184830i
$311$	6.24311	−	8.59290i	0.354014	−	0.487259i	−0.594455	−	0.804129i	$-0.702632\pi$
$311$	6.24311	−	8.59290i	0.354014	−	0.487259i	0.948469	+	0.316870i	$0.102632\pi$
$312$	2.81318	−	17.7617i	0.159265	−	1.00556i
$313$	−0.391349	+	2.47088i	−0.0221204	+	0.139662i	−0.996277	−	0.0862118i	$-0.972524\pi$
$313$	−0.391349	+	2.47088i	−0.0221204	+	0.139662i	0.974156	+	0.225874i	$0.0725238\pi$
$314$	34.4283	+	25.0136i	1.94290	+	1.41160i
$315$	5.90990	+	0.270391i	0.332985	+	0.0152348i
$316$	−59.0706	+	42.9173i	−3.32298	+	2.41429i
$317$	8.46585	+	16.6152i	0.475489	+	0.933200i	0.996808	+	0.0798382i	$0.0254404\pi$
$317$	8.46585	+	16.6152i	0.475489	+	0.933200i	−0.521318	+	0.853362i	$0.674560\pi$
$318$	−5.48582	+	5.48582i	−0.307630	+	0.307630i
$319$	0.273421	+	0.0888399i	0.0153086	+	0.00497408i
$320$	−4.83501	+	44.6339i	−0.270286	+	2.49511i
$321$	1.45094	−	0.471439i	0.0809836	−	0.0263132i
$322$	−3.14469	−	3.80629i	−0.175247	−	0.212116i
$323$	−4.51263	−	28.4916i	−0.251090	−	1.58532i
$324$			5.21205i			0.289558i
$325$	8.05881	+	6.61135i	0.447022	+	0.366732i
$326$	−40.5793			−2.24748
$327$	−1.49741	−	9.45424i	−0.0828067	−	0.522821i
$328$	−44.4218	−	22.6340i	−2.45278	−	1.24976i
$329$	−2.37144	+	24.9152i	−0.130742	+	1.37362i
$330$	−24.4114	−	10.9620i	−1.34380	−	0.603437i
$331$	5.86152	−	18.0399i	0.322178	−	0.991563i	−0.650520	−	0.759489i	$-0.725449\pi$
$331$	5.86152	−	18.0399i	0.322178	−	0.991563i	0.972698	−	0.232074i	$-0.0745511\pi$
$332$	−48.9303	−	48.9303i	−2.68540	−	2.68540i
$333$	−3.85540	+	1.96442i	−0.211274	+	0.107650i
$334$	−20.5982	+	14.9655i	−1.12708	+	0.818875i
$335$	5.24474	+	3.42978i	0.286551	+	0.187389i
$336$	−29.0271	+	17.1412i	−1.58356	+	0.935132i
$337$	0.605059	−	3.82019i	0.0329597	−	0.208099i	−0.965713	−	0.259614i	$-0.916405\pi$
$337$	0.605059	−	3.82019i	0.0329597	−	0.208099i	0.998672	+	0.0515144i	$0.0164048\pi$
$338$	−22.9539	−	3.63555i	−1.24853	−	0.197748i
$339$	−13.8189	−	10.0400i	−0.750540	−	0.545299i
$340$	−14.5850	+	53.7464i	−0.790981	+	2.91481i
$341$	3.99409	+	5.49739i	0.216292	+	0.297700i
$342$	−14.4452	+	7.36018i	−0.781105	+	0.397993i
$343$	−7.91805	+	16.7423i	−0.427534	+	0.903999i
$344$	94.3720	+	30.6633i	5.08820	+	1.65326i
$345$	0.318211	+	1.52087i	0.0171319	+	0.0818809i
$346$	44.3277	−	14.4029i	2.38307	−	0.774307i
$347$	20.0489	+	10.2154i	1.07628	+	0.548392i	0.899974	−	0.435943i	$-0.143585\pi$
$347$	20.0489	+	10.2154i	1.07628	+	0.548392i	0.176306	+	0.984335i	$0.443585\pi$
$348$	−0.332114	+	0.0526016i	−0.0178032	+	0.00281974i
$349$	11.2541			0.602420			0.301210	−	0.953558i	$-0.402610\pi$
$349$	11.2541			0.602420			0.301210	+	0.953558i	$0.402610\pi$
$350$	−0.122708	−	35.5260i	−0.00655903	−	1.89894i
$351$	−2.08475			−0.111276
$352$	74.6698	−	11.8265i	3.97991	−	0.630356i
$353$	0.829643	+	0.422724i	0.0441574	+	0.0224993i	0.475930	−	0.879483i	$-0.342112\pi$
$353$	0.829643	+	0.422724i	0.0441574	+	0.0224993i	−0.431772	+	0.901983i	$0.642112\pi$
$354$	−21.1394	+	6.86862i	−1.12355	+	0.365063i
$355$	−10.8683	−	9.84872i	−0.576829	−	0.522716i
$356$	3.87735	+	1.25983i	0.205499	+	0.0667707i
$357$	−11.7577	+	4.64642i	−0.622286	+	0.245915i
$358$	−3.91714	+	1.99588i	−0.207027	+	0.105486i
$359$	−3.48402	−	4.79534i	−0.183880	−	0.253089i	0.707119	−	0.707095i	$-0.249994\pi$
$359$	−3.48402	−	4.79534i	−0.183880	−	0.253089i	−0.890999	+	0.454006i	$0.849994\pi$
$360$	19.2651	−	0.948113i	1.01536	−	0.0499699i
$361$	−14.1124	−	10.2533i	−0.742758	−	0.539645i
$362$	1.12372	+	0.177980i	0.0590616	+	0.00935444i
$363$	−1.38569	+	8.74888i	−0.0727297	+	0.459197i
$364$	−14.6180	−	24.7543i	−0.766193	−	1.29748i
$365$	12.4051	−	9.98019i	0.649312	−	0.522387i
$366$	−23.5682	+	17.1233i	−1.23193	+	0.895048i
$367$	14.9759	−	7.63058i	0.781733	−	0.398313i	−0.0171090	−	0.999854i	$-0.505446\pi$
$367$	14.9759	−	7.63058i	0.781733	−	0.398313i	0.798842	+	0.601541i	$0.205446\pi$
$368$	−6.26054	−	6.26054i	−0.326353	−	0.326353i
$369$	−1.78602	+	5.49680i	−0.0929765	+	0.286152i
$370$	12.9201	+	22.5439i	0.671686	+	1.17200i
$371$	−0.724213	+	7.60883i	−0.0375993	+	0.395031i
$372$	−7.08144	−	3.60817i	−0.367155	−	0.187075i
$373$	−4.66922	−	29.4803i	−0.241763	−	1.52643i	−0.747803	−	0.663921i	$-0.768891\pi$
$373$	−4.66922	−	29.4803i	−0.241763	−	1.52643i	0.506040	−	0.862510i	$-0.331109\pi$
$374$	57.1849			2.95696
$375$	−5.17074	+	9.91279i	−0.267016	+	0.511895i
$376$			81.5991i			4.20815i
$377$	−0.0210399	−	0.132841i	−0.00108361	−	0.00684166i
$378$	4.52550	+	5.47760i	0.232767	+	0.281738i
$379$	−9.13547	+	2.96829i	−0.469258	+	0.152471i	−0.534094	−	0.845425i	$-0.679347\pi$
$379$	−9.13547	+	2.96829i	−0.469258	+	0.152471i	0.0648369	+	0.997896i	$0.479347\pi$
$380$	34.9841	+	61.0425i	1.79465	+	3.13141i
$381$	−2.01643	−	0.655177i	−0.103305	−	0.0335657i
$382$	−4.39774	+	4.39774i	−0.225008	+	0.225008i
$383$	−13.1491	−	25.8066i	−0.671889	−	1.31866i	−0.935260	−	0.353963i	$-0.884834\pi$
$383$	−13.1491	−	25.8066i	−0.671889	−	1.31866i	0.263370	−	0.964695i	$-0.415166\pi$
$384$	−16.1712	+	11.7491i	−0.825235	+	0.599569i
$385$	−25.4192	+	6.99227i	−1.29548	+	0.356359i
$386$	22.7825	+	16.5524i	1.15960	+	0.842497i
$387$	1.79952	−	11.3618i	0.0914750	−	0.577550i
$388$	−1.32105	+	8.34078i	−0.0670661	+	0.423439i
$389$	−2.53878	+	3.49433i	−0.128721	+	0.177170i	−0.868513	−	0.495666i	$-0.834924\pi$
$389$	−2.53878	+	3.49433i	−0.128721	+	0.177170i	0.739792	+	0.672836i	$0.234924\pi$
$390$	0.615363	+	12.5038i	0.0311601	+	0.633155i
$391$	−1.95171	−	2.68630i	−0.0987021	−	0.135852i
$392$	−20.5273	+	56.7860i	−1.03678	+	2.86813i
$393$	−11.8506	−	11.8506i	−0.597785	−	0.597785i
$394$	6.09616	+	1.98076i	0.307120	+	0.0997893i
$395$	21.0345	−	23.2121i	1.05836	−	1.16793i
$396$	−7.17725	−	22.0893i	−0.360670	−	1.11003i
$397$	15.5655	−	30.5489i	0.781208	−	1.53321i	−0.0635010	−	0.997982i	$-0.520227\pi$
$397$	15.5655	−	30.5489i	0.781208	−	1.53321i	0.844709	−	0.535226i	$-0.179773\pi$
$398$	17.7721	−	2.81483i	0.890836	−	0.141095i
$399$	−6.35276	+	14.6543i	−0.318036	+	0.733635i
$400$	−6.25538	−	63.3989i	−0.312769	−	3.16995i
$401$	−6.21102			−0.310163			−0.155082	−	0.987902i	$-0.549564\pi$
$401$	−6.21102			−0.310163			−0.155082	+	0.987902i	$0.549564\pi$
$402$	1.17737	+	7.43359i	0.0587216	+	0.370754i
$403$	1.44322	−	2.83248i	0.0718919	−	0.141096i
$404$	−17.0168	−	52.3722i	−0.846615	−	2.60561i
$405$	−0.457935	−	2.18867i	−0.0227550	−	0.108756i
$406$	−0.303362	+	0.343649i	−0.0150556	+	0.0170550i
$407$	13.6345	−	13.6345i	0.675839	−	0.675839i
$408$	−36.7263	+	18.7130i	−1.81822	+	0.926432i
$409$	−23.3874	+	16.9920i	−1.15643	+	0.840199i	−0.989323	−	0.145739i	$-0.953444\pi$
$409$	−23.3874	+	16.9920i	−1.15643	+	0.840199i	−0.167111	+	0.985938i	$0.553444\pi$
$410$	33.4957	+	9.08960i	1.65423	+	0.448904i
$411$	10.1016	−	13.9036i	0.498274	−	0.685815i
$412$	86.1281	+	13.6414i	4.24323	+	0.672061i
$413$	−11.7456	+	18.4816i	−0.577961	+	0.909420i
$414$	−1.09688	+	1.50973i	−0.0539087	+	0.0741989i
$415$	24.8461	+	16.2480i	1.21965	+	0.797585i
$416$	−20.7888	−	28.6134i	−1.01926	−	1.40289i
$417$	6.14557	+	12.0614i	0.300950	+	0.590647i
$418$	51.0850	−	51.0850i	2.49865	−	2.49865i
$419$	6.69610	−	20.6085i	0.327126	−	1.00679i	−0.643346	−	0.765576i	$-0.722454\pi$
$419$	6.69610	−	20.6085i	0.327126	−	1.00679i	0.970472	−	0.241214i	$-0.0775457\pi$
$420$	22.7773	−	20.7843i	1.11142	−	1.01417i
$421$	7.76256	+	23.8907i	0.378324	+	1.16436i	0.941209	+	0.337826i	$0.109692\pi$
$421$	7.76256	+	23.8907i	0.378324	+	1.16436i	−0.562885	+	0.826535i	$0.690308\pi$
$422$	22.1671	+	11.2947i	1.07908	+	0.549818i
$423$	9.34317	−	1.47981i	0.454280	−	0.0719509i
$424$			24.9195i			1.21020i
$425$	1.40240	−	23.8510i	0.0680265	−	1.15694i
$426$		−	17.6150i		−	0.853448i
$427$	−7.15548	+	27.7941i	−0.346278	+	1.34505i
$428$	3.60993	−	7.08489i	0.174493	−	0.342461i
$429$	8.83542	−	2.87080i	0.426578	−	0.138604i
$430$	−68.6762	−	7.43942i	−3.31186	−	0.358761i
$431$	10.8465	−	33.3822i	0.522459	−	1.60796i	−0.246827	−	0.969059i	$-0.579388\pi$
$431$	10.8465	−	33.3822i	0.522459	−	1.60796i	0.769286	−	0.638904i	$-0.220612\pi$
$432$	9.00950	+	9.00950i	0.433470	+	0.433470i
$433$	10.1085	+	19.8390i	0.485783	+	0.953403i	0.995652	+	0.0931507i	$0.0296938\pi$
$433$	10.1085	+	19.8390i	0.485783	+	0.953403i	−0.509869	+	0.860252i	$0.670306\pi$
$434$	−10.5751	+	2.35664i	−0.507623	+	0.113122i
$435$	0.134842	−	0.0512686i	0.00646516	−	0.00245814i
$436$	−40.3620	−	29.3247i	−1.93299	−	1.40440i
$437$	−4.14327	−	0.656229i	−0.198199	−	0.0313917i
$438$	18.8862	+	2.99128i	0.902419	+	0.142929i
$439$	8.51349	+	6.18541i	0.406327	+	0.295214i	0.772113	−	0.635485i	$-0.219200\pi$
$439$	8.51349	+	6.18541i	0.406327	+	0.295214i	−0.365786	+	0.930699i	$0.619200\pi$
$440$	−80.3422	+	30.5472i	−3.83016	+	1.45628i
$441$	6.87431	+	1.32056i	0.327348	+	0.0628840i
$442$	−12.1455	−	23.8369i	−0.577702	−	1.13380i
$443$	1.24168	+	1.24168i	0.0589941	+	0.0589941i	0.735988	−	0.676994i	$-0.236718\pi$
$443$	1.24168	+	1.24168i	0.0589941	+	0.0589941i	−0.676994	+	0.735988i	$0.736718\pi$
$444$	−6.96914	+	21.4488i	−0.330741	+	1.01791i
$445$	−1.73889	−	0.188367i	−0.0824313	−	0.00892945i
$446$	27.4432	−	8.91683i	1.29947	−	0.422224i
$447$	−6.65288	+	13.0570i	−0.314670	+	0.617575i
$448$	−13.2438	+	51.4431i	−0.625711	+	2.43046i
$449$		−	9.06922i		−	0.428003i	−0.976833	−	0.214001i	$-0.931350\pi$
$449$		−	9.06922i		−	0.428003i	0.976833	−	0.214001i	$-0.0686497\pi$
$450$	−12.9920	+	3.39262i	−0.612447	+	0.159930i
$451$		−	25.7556i		−	1.21278i
$452$	−87.9314	+	13.9270i	−4.13595	+	0.655070i
$453$	−9.55963	−	4.87088i	−0.449151	−	0.228854i
$454$	−2.03780	−	6.27169i	−0.0956385	−	0.294345i
$455$	8.31342	+	9.11061i	0.389739	+	0.427112i
$456$	−16.0919	+	49.5256i	−0.753570	+	2.31925i
$457$	5.98346	−	5.98346i	0.279894	−	0.279894i	−0.553172	−	0.833067i	$-0.686583\pi$
$457$	5.98346	−	5.98346i	0.279894	−	0.279894i	0.833067	+	0.553172i	$0.186583\pi$
$458$	6.52752	+	12.8110i	0.305011	+	0.598617i
$459$	2.80869	+	3.86583i	0.131098	+	0.180442i
$460$	6.77789	+	4.43237i	0.316021	+	0.206660i
$461$	−5.28667	+	7.27648i	−0.246225	+	0.338900i	−0.914185	−	0.405298i	$-0.867168\pi$
$461$	−5.28667	+	7.27648i	−0.246225	+	0.338900i	0.667960	+	0.744197i	$0.267168\pi$
$462$	−26.7226	−	16.9829i	−1.24325	−	0.790117i
$463$	−7.32645	−	1.16040i	−0.340489	−	0.0539282i	−0.0161514	−	0.999870i	$-0.505141\pi$
$463$	−7.32645	−	1.16040i	−0.340489	−	0.0539282i	−0.324338	+	0.945941i	$0.605141\pi$
$464$	−0.483162	+	0.665015i	−0.0224302	+	0.0308726i
$465$	3.29070	+	0.892984i	0.152602	+	0.0414111i
$466$	45.0279	−	32.7147i	2.08588	−	1.51548i
$467$	−20.5725	+	10.4822i	−0.951983	+	0.485060i	−0.859771	−	0.510680i	$-0.829394\pi$
$467$	−20.5725	+	10.4822i	−0.951983	+	0.485060i	−0.0922122	+	0.995739i	$0.529394\pi$
$468$	−7.68329	+	7.68329i	−0.355160	+	0.355160i
$469$	5.55874	+	4.90708i	0.256679	+	0.226588i
$470$	−11.6334	−	55.6013i	−0.536609	−	2.56469i
$471$	−4.89678	−	15.0707i	−0.225632	−	0.694423i
$472$	−32.4128	+	63.6136i	−1.49192	+	2.92805i
$473$	8.01908	+	50.6305i	0.368718	+	2.32799i
$474$	37.6214			1.72801
$475$	−20.0540	−	22.5596i	−0.920140	−	1.03511i
$476$	−26.2086	+	60.4572i	−1.20127	+	2.77105i
$477$	2.85330	−	0.451918i	0.130644	−	0.0206919i
$478$	−23.4854	+	46.0926i	−1.07420	+	2.10823i
$479$	2.15663	+	6.63742i	0.0985389	+	0.303271i	0.988160	−	0.153428i	$-0.0490314\pi$
$479$	2.15663	+	6.63742i	0.0985389	+	0.303271i	−0.889621	+	0.456700i	$0.849031\pi$
$480$	25.4733	−	28.1104i	1.16269	−	1.28306i
$481$	−8.57922	−	2.78756i	−0.391179	−	0.127102i
$482$	−29.8395	−	29.8395i	−1.35915	−	1.35915i
$483$	0.114252	+	1.83493i	0.00519867	+	0.0834922i
$484$	27.1369	+	37.3507i	1.23349	+	1.69776i
$485$	−0.178085	−	3.61858i	−0.00808641	−	0.164311i
$486$	1.57851	−	2.17264i	0.0716028	−	0.0985528i
$487$	0.271105	−	1.71169i	0.0122849	−	0.0775640i	−0.980784	−	0.195096i	$-0.937498\pi$
$487$	0.271105	−	1.71169i	0.0122849	−	0.0775640i	0.993069	+	0.117532i	$0.0374982\pi$
$488$	−14.6380	+	92.4210i	−0.662633	+	4.18370i
$489$	12.2245	+	8.88164i	0.552813	+	0.401642i
$490$	5.89131	−	41.6202i	0.266142	−	1.88021i
$491$	4.58431	−	3.33070i	0.206887	−	0.150312i	−0.479517	−	0.877533i	$-0.659188\pi$
$491$	4.58431	−	3.33070i	0.206887	−	0.150312i	0.686404	+	0.727220i	$0.259188\pi$
$492$	13.6760	+	26.8407i	0.616562	+	1.21007i
$493$	−0.217986	+	0.217986i	−0.00981760	+	0.00981760i
$494$	−32.1441	−	10.4443i	−1.44623	−	0.469909i
$495$	4.95470	+	8.64527i	0.222697	+	0.388576i
$496$	−18.4780	+	6.00385i	−0.829685	+	0.269581i
$497$	−11.0533	−	13.3787i	−0.495806	−	0.600117i
$498$	5.57758	+	35.2155i	0.249937	+	1.57804i
$499$		−	14.8529i		−	0.664908i	−0.943119	−	0.332454i	$-0.892123\pi$
$499$		−	14.8529i		−	0.664908i	0.943119	−	0.332454i	$-0.107877\pi$
$500$	17.4767	+	55.5900i	0.781584	+	2.48606i
$501$	9.48075			0.423569
$502$	−9.76004	−	61.6225i	−0.435612	−	2.75035i
$503$	−7.76006	−	3.95395i	−0.346004	−	0.176298i	0.272349	−	0.962199i	$-0.412200\pi$
$503$	−7.76006	−	3.95395i	−0.346004	−	0.176298i	−0.618353	+	0.785901i	$0.712200\pi$
$504$	22.7197	+	2.16247i	1.01201	+	0.0963241i
$505$	11.7472	+	20.4973i	0.522745	+	0.912119i
$506$	2.56974	−	7.90886i	0.114239	−	0.351592i
$507$	6.11918	+	6.11918i	0.271762	+	0.271762i
$508$	−9.84613	+	5.01686i	−0.436851	+	0.222587i
$509$	0.453567	−	0.329536i	0.0201040	−	0.0146064i	−0.577688	−	0.816258i	$-0.696045\pi$
$509$	0.453567	−	0.329536i	0.0201040	−	0.0146064i	0.597792	+	0.801651i	$0.296045\pi$
$510$	22.3573	−	17.9869i	0.989997	−	0.796475i
$511$	16.2212	−	9.57905i	0.717585	−	0.423752i
$512$	0.571888	−	3.61076i	0.0252741	−	0.159575i
$513$	5.96255	+	0.944376i	0.263253	+	0.0416952i
$514$	−54.0632	−	39.2792i	−2.38463	−	1.73253i
$515$	−37.3660	+	1.83893i	−1.64654	+	0.0810329i
$516$	−35.2413	−	48.5055i	−1.55141	−	2.13534i
$517$	−37.5597	+	19.1376i	−1.65187	+	0.841672i
$518$	11.2993	+	28.5928i	0.496462	+	1.25629i
$519$	−16.5061	−	5.36317i	−0.724539	−	0.235417i
$520$	29.7971	+	27.0018i	1.30669	+	1.18411i
$521$	−24.4336	+	7.93894i	−1.07045	+	0.347811i	−0.790664	−	0.612250i	$-0.790265\pi$
$521$	−24.4336	+	7.93894i	−1.07045	+	0.347811i	−0.279789	+	0.960061i	$0.590265\pi$
$522$	0.154372	+	0.0786565i	0.00675668	+	0.00344270i
$523$	25.5786	−	4.05125i	1.11847	−	0.177149i	0.430294	−	0.902689i	$-0.358410\pi$
$523$	25.5786	−	4.05125i	1.11847	−	0.177149i	0.688180	+	0.725540i	$0.258410\pi$
$524$	−87.3503			−3.81592
$525$	−7.73866	+	10.7291i	−0.337743	+	0.468256i
$526$	37.3493			1.62851
$527$	−7.19676	+	1.13986i	−0.313496	+	0.0496529i
$528$	−50.5899	−	25.7768i	−2.20164	−	1.12179i
$529$	21.4151	−	6.95818i	0.931090	−	0.302530i
$530$	−3.55272	−	16.9800i	−0.154320	−	0.737565i
$531$	7.87162	+	2.55764i	0.341599	+	0.110992i
$532$	30.5953	+	77.4211i	1.32647	+	3.35663i
$533$	−10.7359	+	5.47021i	−0.465023	+	0.236941i
$534$	−1.23472	−	1.69945i	−0.0534315	−	0.0735422i
$535$	−0.893419	+	3.29230i	−0.0386259	+	0.142338i
$536$	19.5577	+	14.2095i	0.844765	+	0.613758i
$537$	1.61688	+	0.256089i	0.0697737	+	0.0110511i
$538$	3.64800	−	23.0326i	0.157277	−	0.993005i
$539$	−30.9526	+	3.86955i	−1.33322	+	0.166673i
$540$	−9.75401	−	6.37860i	−0.419746	−	0.274491i
$541$	7.35471	−	5.34351i	0.316204	−	0.229735i	−0.418350	−	0.908286i	$-0.637392\pi$
$541$	7.35471	−	5.34351i	0.316204	−	0.229735i	0.734554	+	0.678550i	$0.237392\pi$
$542$	48.4819	−	24.7027i	2.08247	−	1.06107i
$543$	−0.299568	−	0.299568i	−0.0128557	−	0.0128557i
$544$	−25.0510	+	77.0991i	−1.07405	+	3.30560i
$545$	19.5256	+	8.76797i	0.836383	+	0.375579i
$546$	−1.40353	+	14.7460i	−0.0600655	+	0.631070i
$547$	5.09915	+	2.59815i	0.218024	+	0.111089i	0.559592	−	0.828768i	$-0.310958\pi$
$547$	5.09915	+	2.59815i	0.218024	+	0.111089i	−0.341568	+	0.939857i	$0.610958\pi$
$548$	−14.0124	−	88.4706i	−0.598578	−	3.77928i
$549$	10.8477			0.462970
$550$	50.3897	−	32.2689i	2.14863	−	1.37595i
$551$			0.389467i			0.0165919i
$552$	0.937680	+	5.92028i	0.0399103	+	0.251984i
$553$	28.5737	−	23.6071i	1.21508	−	1.00388i
$554$	−80.1858	+	26.0540i	−3.40677	+	1.10693i
$555$	1.04201	−	9.61922i	0.0442309	−	0.408313i
$556$	67.1012	+	21.8025i	2.84572	+	0.924632i
$557$	−5.54182	+	5.54182i	−0.234814	+	0.234814i	−0.814699	−	0.579884i	$-0.803098\pi$
$557$	−5.54182	+	5.54182i	−0.234814	+	0.234814i	0.579884	+	0.814699i	$0.303098\pi$
$558$	1.85912	+	3.64873i	0.0787029	+	0.154463i
$559$	19.4016	−	14.0961i	0.820598	−	0.596200i
$560$	3.44514	−	75.3001i	0.145584	−	3.18201i
$561$	−17.2270	−	12.5162i	−0.727325	−	0.528433i
$562$	3.17212	−	20.0280i	0.133808	−	0.844830i
$563$	2.32621	−	14.6871i	0.0980380	−	0.618987i	−0.888927	−	0.458050i	$-0.848548\pi$
$563$	2.32621	−	14.6871i	0.0980380	−	0.618987i	0.986965	−	0.160938i	$-0.0514518\pi$
$564$	28.9802	−	39.8878i	1.22029	−	1.67958i
$565$	35.7011	−	13.5740i	1.50195	−	0.571064i
$566$	22.1928	+	30.5457i	0.932832	+	1.28393i
$567$	−0.164420	−	2.64064i	−0.00690499	−	0.110896i
$568$	−40.0082	−	40.0082i	−1.67871	−	1.67871i
$569$	11.1066	+	3.60875i	0.465612	+	0.151287i	0.532422	−	0.846479i	$-0.321282\pi$
$569$	11.1066	+	3.60875i	0.465612	+	0.151287i	−0.0668096	+	0.997766i	$0.521282\pi$
$570$	3.90415	−	36.0407i	0.163527	−	1.50958i
$571$	−8.33559	−	25.6543i	−0.348834	−	1.07360i	−0.959499	−	0.281711i	$-0.909098\pi$
$571$	−8.33559	−	25.6543i	−0.348834	−	1.07360i	0.610666	−	0.791888i	$-0.290902\pi$
$572$	21.9824	−	43.1430i	0.919132	−	1.80390i
$573$	2.28736	−	0.362283i	0.0955559	−	0.0151346i
$574$	37.6779	+	16.3336i	1.57265	+	0.681753i
$575$	−3.23564	−	1.26576i	−0.134936	−	0.0527857i
$576$	20.0777			0.836569
$577$	−6.42153	−	40.5439i	−0.267332	−	1.68787i	−0.646799	−	0.762661i	$-0.723893\pi$
$577$	−6.42153	−	40.5439i	−0.267332	−	1.68787i	0.379467	−	0.925205i	$-0.376107\pi$
$578$	−7.11210	+	13.9583i	−0.295824	+	0.580588i
$579$	−3.24038	−	9.97288i	−0.134666	−	0.414459i
$580$	0.308006	−	0.685904i	0.0127893	−	0.0284806i
$581$	26.3336	+	23.2465i	1.09250	+	0.964428i
$582$	3.07675	−	3.07675i	0.127535	−	0.127535i
$583$	−11.4703	+	5.84442i	−0.475052	+	0.242051i
$584$	49.6895	−	36.1016i	2.05617	−	1.49389i
$585$	2.55135	−	3.90147i	0.105485	−	0.161306i
$586$	2.73801	−	3.76855i	0.113106	−	0.155677i
$587$	41.6346	+	6.59428i	1.71845	+	0.272175i	0.936371	−	0.351011i	$-0.114162\pi$
$587$	41.6346	+	6.59428i	1.71845	+	0.272175i	0.782074	+	0.623186i	$0.214162\pi$
$588$	30.2020	−	20.4682i	1.24551	−	0.844094i
$589$	−5.41082	+	7.44735i	−0.222949	+	0.306863i
$590$	13.0166	−	47.9670i	0.535887	−	1.97477i
$591$	−1.40294	−	1.93098i	−0.0577092	−	0.0794300i
$592$	25.0294	+	49.1230i	1.02870	+	2.01894i
$593$	1.33872	−	1.33872i	0.0549748	−	0.0549748i	−0.679085	−	0.734060i	$-0.737623\pi$
$593$	1.33872	−	1.33872i	0.0549748	−	0.0549748i	0.734060	+	0.679085i	$0.237623\pi$
$594$	−3.69810	+	11.3816i	−0.151735	+	0.466992i
$595$	5.69385	−	27.6902i	0.233425	−	1.13519i
$596$	23.6023	+	72.6403i	0.966786	+	2.97546i
$597$	−5.96996	−	3.04184i	−0.244334	−	0.124494i
$598$	−3.84250	+	0.608592i	−0.157131	+	0.0248872i
$599$		−	28.0135i		−	1.14460i	−0.820044	−	0.572301i	$-0.806051\pi$
$599$		−	28.0135i		−	1.14460i	0.820044	−	0.572301i	$-0.193949\pi$
$600$	−21.8026	+	37.2137i	−0.890089	+	1.51924i
$601$		−	6.80756i		−	0.277686i	−0.990314	−	0.138843i	$-0.955662\pi$
$601$		−	6.80756i		−	0.277686i	0.990314	−	0.138843i	$-0.0443384\pi$
$602$	−79.1532	−	20.3777i	−3.22604	−	0.830532i
$603$	1.27232	−	2.49707i	0.0518129	−	0.101688i
$604$	−53.1833	+	17.2803i	−2.16400	+	0.703125i
$605$	−14.6771	−	13.3003i	−0.596711	−	0.540732i
$606$	−8.76794	+	26.9849i	−0.356173	+	1.09619i
$607$	26.1679	+	26.1679i	1.06212	+	1.06212i	0.997938	+	0.0641853i	$0.0204449\pi$
$607$	26.1679	+	26.1679i	1.06212	+	1.06212i	0.0641853	+	0.997938i	$0.479555\pi$
$608$	46.4962	+	91.2538i	1.88567	+	3.70083i
$609$	0.166603	−	0.0371271i	0.00675110	−	0.00150446i
$610$	−3.20197	−	65.0621i	−0.129644	−	2.63429i
$611$	15.9546	+	11.5917i	0.645453	+	0.468949i
$612$	24.5988	+	3.89607i	0.994347	+	0.157489i
$613$	13.0732	+	2.07059i	0.528022	+	0.0836305i	0.414753	−	0.909934i	$-0.363868\pi$
$613$	13.0732	+	2.07059i	0.528022	+	0.0836305i	0.113269	+	0.993564i	$0.463868\pi$
$614$	41.4150	+	30.0898i	1.67138	+	1.21433i
$615$	−8.10115	−	10.0695i	−0.326670	−	0.406042i
$616$	−99.2666	+	22.1213i	−3.99956	+	0.891293i
$617$	−2.88682	−	5.66571i	−0.116219	−	0.228093i	0.825568	−	0.564303i	$-0.190855\pi$
$617$	−2.88682	−	5.66571i	−0.116219	−	0.228093i	−0.941787	+	0.336210i	$0.890855\pi$
$618$	−31.7710	−	31.7710i	−1.27802	−	1.27802i
$619$	4.41697	−	13.5940i	0.177533	−	0.546390i	−0.822207	−	0.569188i	$-0.807258\pi$
$619$	4.41697	−	13.5940i	0.177533	−	0.546390i	0.999740	+	0.0227983i	$0.00725757\pi$
$620$	15.4188	−	8.83670i	0.619236	−	0.354891i
$621$	0.660872	−	0.214730i	0.0265199	−	0.00861683i
$622$	−12.9497	+	25.4151i	−0.519234	+	1.01905i
$623$	−2.00417	−	0.515965i	−0.0802953	−	0.0206717i
$624$			26.5625i			1.06335i
$625$	−12.2231	−	21.8082i	−0.488925	−	0.872326i
$626$		−	6.71833i		−	0.268518i
$627$	−26.5705	+	4.20835i	−1.06112	+	0.168065i
$628$	−73.5898	−	37.4959i	−2.93655	−	1.49625i
$629$	6.38934	+	19.6644i	0.254760	+	0.784069i
$630$	−15.7894	+	1.76560i	−0.629064	+	0.0703431i
$631$	−6.43547	+	19.8063i	−0.256192	+	0.788478i	0.737400	+	0.675456i	$0.236053\pi$
$631$	−6.43547	+	19.8063i	−0.256192	+	0.788478i	−0.993592	+	0.113022i	$0.963947\pi$
$632$	85.4479	−	85.4479i	3.39894	−	3.39894i
$633$	−4.20577	−	8.25430i	−0.167164	−	0.328079i
$634$	−29.4355	−	40.5145i	−1.16903	−	1.60904i
$635$	3.69386	−	2.97180i	0.146586	−	0.117932i
$636$	8.85023	−	12.1813i	0.350935	−	0.483020i
$637$	8.18699	+	12.0804i	0.324381	+	0.478642i
$638$	−0.762561	−	0.120778i	−0.0301901	−	0.00478164i
$639$	−3.85541	+	5.30652i	−0.152518	+	0.209923i
$640$	−2.19702	−	44.6422i	−0.0868449	−	1.76464i
$641$	−21.0956	+	15.3269i	−0.833227	+	0.605375i	−0.920471	−	0.390812i	$-0.872194\pi$
$641$	−21.0956	+	15.3269i	−0.833227	+	0.605375i	0.0872431	+	0.996187i	$0.472194\pi$
$642$	−3.65051	+	1.86003i	−0.144074	+	0.0734095i
$643$	11.3182	−	11.3182i	0.446344	−	0.446344i	−0.447793	−	0.894137i	$-0.647790\pi$
$643$	11.3182	−	11.3182i	0.446344	−	0.446344i	0.894137	+	0.447793i	$0.147790\pi$
$644$	7.18367	+	6.34152i	0.283076	+	0.249891i
$645$	19.0605	+	17.2724i	0.750506	+	0.680100i
$646$	23.9392	+	73.6772i	0.941875	+	2.89879i
$647$	−0.306752	+	0.602034i	−0.0120596	+	0.0236684i	−0.896958	−	0.442116i	$-0.854228\pi$
$647$	−0.306752	+	0.602034i	−0.0120596	+	0.0236684i	0.884898	+	0.465785i	$0.154228\pi$
$648$	−1.34941	−	8.51984i	−0.0530098	−	0.334691i
$649$	−36.8829			−1.44778
$650$	−24.1532	−	14.1508i	−0.947366	−	0.555039i
$651$	3.70157	+	1.60466i	0.145076	+	0.0628914i
$652$	77.7863	−	12.3201i	3.04635	−	0.482494i
$653$	−0.720103	+	1.41328i	−0.0281798	+	0.0553060i	−0.904667	−	0.426119i	$-0.859881\pi$
$653$	−0.720103	+	1.41328i	−0.0281798	+	0.0553060i	0.876487	+	0.481425i	$0.159881\pi$
$654$	7.94362	+	24.4480i	0.310620	+	0.955991i
$655$	36.6807	−	7.67467i	1.43323	−	0.299874i
$656$	70.0367	+	22.7563i	2.73447	+	0.888485i
$657$	−5.03478	−	5.03478i	−0.196426	−	0.196426i
$658$	−4.17694	−	67.0830i	−0.162834	−	2.61517i
$659$	−12.2267	−	16.8287i	−0.476286	−	0.655552i	0.501500	−	0.865158i	$-0.332782\pi$
$659$	−12.2267	−	16.8287i	−0.476286	−	0.655552i	−0.977786	+	0.209606i	$0.932782\pi$
$660$	50.1223	+	13.6015i	1.95101	+	0.529438i
$661$	20.8417	−	28.6861i	0.810647	−	1.11576i	−0.180577	−	0.983561i	$-0.557796\pi$
$661$	20.8417	−	28.6861i	0.810647	−	1.11576i	0.991223	−	0.132198i	$-0.0422036\pi$
$662$	−7.96874	+	50.3127i	−0.309714	+	1.95546i
$663$	−1.55837	+	9.83918i	−0.0605222	+	0.382122i
$664$	92.6517	+	67.3154i	3.59558	+	2.61234i
$665$	−19.6500	−	29.8230i	−0.761996	−	1.15649i
$666$	9.40102	−	6.83024i	0.364282	−	0.264667i
$667$	0.0203524	+	0.0399439i	0.000788049	+	0.00154663i
$668$	34.9411	−	34.9411i	1.35191	−	1.35191i
$669$	−10.2189	−	3.32033i	−0.395086	−	0.128371i
$670$	−15.3524	−	6.89400i	−0.593114	−	0.266338i
$671$	−45.9740	+	14.9379i	−1.77481	+	0.576670i
$672$	34.6034	−	28.5888i	1.33486	−	1.10284i
$673$	5.94335	+	37.5248i	0.229099	+	1.44648i	0.787198	+	0.616701i	$0.211531\pi$
$673$	5.94335	+	37.5248i	0.229099	+	1.44648i	−0.558098	+	0.829775i	$0.688469\pi$
$674$			10.3871i			0.400097i
$675$	4.65639	+	1.82154i	0.179225	+	0.0701112i
$676$	45.1042			1.73478
$677$	2.26844	+	14.3224i	0.0871832	+	0.550453i	0.992158	+	0.124988i	$0.0398894\pi$
$677$	2.26844	+	14.3224i	0.0871832	+	0.550453i	−0.904975	+	0.425465i	$0.860111\pi$
$678$	40.8720	+	20.8253i	1.56968	+	0.799792i
$679$	0.406178	−	4.26745i	0.0155877	−	0.163770i
$680$	9.92616	−	91.6323i	0.380651	−	3.51394i
$681$	−0.758807	+	2.33537i	−0.0290775	+	0.0894915i
$682$	−12.9037	−	12.9037i	−0.494107	−	0.494107i
$683$	−23.6287	+	12.0394i	−0.904127	+	0.460676i	−0.843282	−	0.537471i	$-0.819380\pi$
$683$	−23.6287	+	12.0394i	−0.904127	+	0.460676i	−0.0608451	+	0.998147i	$0.519380\pi$
$684$	25.4553	−	18.4944i	0.973308	−	0.707150i
$685$	13.6573	+	35.9199i	0.521817	+	1.37243i
$686$	13.9687	−	47.7348i	0.533329	−	1.82252i
$687$	0.837538	−	5.28800i	0.0319541	−	0.201750i
$688$	−144.764	−	22.9284i	−5.51908	−	0.874136i
$689$	4.87235	+	3.53997i	0.185622	+	0.134862i
$690$	−1.48297	−	3.90037i	−0.0564558	−	0.148484i
$691$	15.3516	+	21.1297i	0.584003	+	0.803811i	0.994127	−	0.108219i	$-0.0345147\pi$
$691$	15.3516	+	21.1297i	0.584003	+	0.803811i	−0.410124	+	0.912030i	$0.634515\pi$
$692$	−80.5988	+	41.0671i	−3.06391	+	1.56114i
$693$	4.33312	+	10.9649i	0.164602	+	0.416523i
$694$	−57.4705	−	18.6733i	−2.18155	−	0.708829i
$695$	−30.0931	−	3.25987i	−1.14150	−	0.123654i
$696$	0.529269	−	0.171970i	0.0200619	−	0.00651850i
$697$	24.6076	+	12.5382i	0.932081	+	0.474919i
$698$	−29.8512	+	4.72796i	−1.12988	+	0.178956i
$699$	−20.7250			−0.783892
$700$	11.0211	+	68.0624i	0.416560	+	2.57252i
$701$	−4.48122			−0.169253			−0.0846267	−	0.996413i	$-0.526970\pi$
$701$	−4.48122			−0.169253			−0.0846267	+	0.996413i	$0.526970\pi$
$702$	5.52972	−	0.875821i	0.208706	−	0.0330557i
$703$	23.2746	+	11.8590i	0.877816	+	0.447270i
$704$	−85.0916	+	27.6479i	−3.20701	+	1.04202i
$705$	−8.66496	+	19.2961i	−0.326341	+	0.726735i
$706$	−2.37819	−	0.772720i	−0.0895043	−	0.0290817i
$707$	10.2735	+	25.9971i	0.386376	+	0.977721i
$708$	38.4368	−	19.5845i	1.44454	−	0.736032i
$709$	4.47598	+	6.16066i	0.168099	+	0.231368i	0.884753	−	0.466061i	$-0.154327\pi$
$709$	4.47598	+	6.16066i	0.168099	+	0.231368i	−0.716654	+	0.697429i	$0.754327\pi$
$710$	32.9653	+	21.5575i	1.23716	+	0.809039i
$711$	−11.3335	−	8.23424i	−0.425038	−	0.308808i
$712$	−6.66426	−	1.05551i	−0.249754	−	0.0395571i
$713$	−0.165758	+	1.04656i	−0.00620770	+	0.0391939i
$714$	29.2350	−	17.2640i	1.09409	−	0.646089i
$715$	−5.44042	+	20.0482i	−0.203460	+	0.749762i
$716$	6.90280	−	5.01518i	0.257970	−	0.187426i
$717$	17.1634	−	8.74517i	0.640977	−	0.326594i
$718$	11.2558	+	11.2558i	0.420063	+	0.420063i
$719$	−8.08985	+	24.8980i	−0.301701	+	0.928539i	0.679187	+	0.733965i	$0.262332\pi$
$719$	−8.08985	+	24.8980i	−0.301701	+	0.928539i	−0.980888	+	0.194574i	$0.937668\pi$
$720$	−27.8867	+	5.83471i	−1.03928	+	0.217447i
$721$	−44.0664	−	4.19426i	−1.64112	−	0.156202i
$722$	41.7401	+	21.2676i	1.55341	+	0.791500i
$723$	2.45816	+	15.5202i	0.0914198	+	0.577202i
$724$	−2.20810			−0.0820634
$725$	−0.0690756	+	0.315091i	−0.00256540	+	0.0117022i
$726$		−	23.7882i		−	0.882864i
$727$	1.00630	+	6.35352i	0.0373216	+	0.235639i	0.999297	−	0.0374979i	$-0.0119388\pi$
$727$	1.00630	+	6.35352i	0.0373216	+	0.235639i	−0.961975	+	0.273137i	$0.911939\pi$
$728$	30.3042	+	36.6798i	1.12315	+	1.35944i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	−28.7113	+	31.6836i	−1.06265	+	1.17266i
$731$	−52.2778	−	16.9861i	−1.93356	−	0.628253i
$732$	39.9791	−	39.9791i	1.47767	−	1.47767i
$733$	1.40426	+	2.75602i	0.0518676	+	0.101796i	0.915485	−	0.402351i	$-0.131807\pi$
$733$	1.40426	+	2.75602i	0.0518676	+	0.101796i	−0.863618	+	0.504147i	$0.831807\pi$
$734$	−36.5172	+	26.5313i	−1.34788	+	0.979289i
$735$	−10.8842	+	11.2487i	−0.401472	+	0.414914i
$736$	9.53732	+	6.92927i	0.351550	+	0.255416i
$737$	−1.95366	+	12.3349i	−0.0719640	+	0.454363i
$738$	2.42809	−	15.3304i	0.0893794	−	0.564319i
$739$	11.4745	−	15.7933i	0.422097	−	0.580967i	−0.544020	−	0.839072i	$-0.683098\pi$
$739$	11.4745	−	15.7933i	0.422097	−	0.580967i	0.966117	+	0.258106i	$0.0830983\pi$
$740$	−31.6111	−	39.2917i	−1.16205	−	1.44439i
$741$	7.39749	+	10.1818i	0.271754	+	0.374037i
$742$	−1.27559	−	20.4864i	−0.0468284	−	0.752079i
$743$	15.5913	+	15.5913i	0.571990	+	0.571990i	0.932684	−	0.360694i	$-0.117460\pi$
$743$	15.5913	+	15.5913i	0.571990	+	0.571990i	−0.360694	+	0.932684i	$0.617460\pi$
$744$	12.5098	+	4.06467i	0.458631	+	0.149018i
$745$	−16.2934	−	28.4298i	−0.596945	−	1.04159i
$746$	24.7698	+	76.2338i	0.906889	+	2.79112i
$747$	6.02741	−	11.8295i	0.220531	−	0.432817i
$748$	−109.618	+	17.3617i	−4.00802	+	0.634808i
$749$	−1.60544	+	3.70337i	−0.0586614	+	0.135318i
$750$	9.55073	−	28.4656i	0.348743	−	1.03942i
$751$	−35.5013			−1.29546			−0.647731	−	0.761869i	$-0.724282\pi$
$751$	−35.5013			−1.29546			−0.647731	+	0.761869i	$0.724282\pi$
$752$	−18.8548	−	119.045i	−0.687564	−	4.34111i
$753$	−10.5472	+	20.7000i	−0.384361	+	0.754351i
$754$	0.111615	+	0.343517i	0.00406479	+	0.0125101i
$755$	20.8148	−	11.9292i	0.757527	−	0.434147i
$756$	−10.3380	−	9.12604i	−0.375988	−	0.331911i
$757$	−7.40012	+	7.40012i	−0.268962	+	0.268962i	−0.828682	−	0.559720i	$-0.810909\pi$
$757$	−7.40012	+	7.40012i	−0.268962	+	0.268962i	0.559720	+	0.828682i	$0.310909\pi$
$758$	22.9845	−	11.7112i	0.834834	−	0.425369i
$759$	−2.50516	+	1.82011i	−0.0909316	+	0.0660657i
$760$	−72.9905	−	90.7252i	−2.64765	−	3.29095i
$761$	6.21925	−	8.56006i	0.225447	−	0.310302i	−0.681277	−	0.732026i	$-0.738575\pi$
$761$	6.21925	−	8.56006i	0.225447	−	0.310302i	0.906724	+	0.421724i	$0.138575\pi$
$762$	5.62374	+	0.890714i	0.203727	+	0.0322671i
$763$	21.3741	+	13.5838i	0.773796	+	0.491768i
$764$	7.09483	−	9.76520i	0.256682	−	0.353292i
$765$	−10.6720	+	0.525211i	−0.385846	+	0.0189890i
$766$	45.7192	+	62.9271i	1.65190	+	2.27365i
$767$	7.83354	+	15.3742i	0.282853	+	0.555130i
$768$	9.56362	−	9.56362i	0.345097	−	0.345097i
$769$	12.7683	−	39.2969i	0.460437	−	1.41708i	−0.404194	−	0.914673i	$-0.632448\pi$
$769$	12.7683	−	39.2969i	0.460437	−	1.41708i	0.864631	−	0.502407i	$-0.167552\pi$
$770$	64.4860	−	29.2256i	2.32391	−	1.05322i
$771$	7.68948	+	23.6658i	0.276930	+	0.852303i
$772$	−48.6971	−	24.8124i	−1.75265	−	0.893019i
$773$	−7.73181	+	1.22460i	−0.278094	+	0.0440457i	−0.293923	−	0.955829i	$-0.594961\pi$
$773$	−7.73181	+	1.22460i	−0.278094	+	0.0440457i	0.0158297	+	0.999875i	$0.494961\pi$
$774$			30.8926i			1.11041i
$775$	−5.69837	+	5.06547i	−0.204692	+	0.181957i
$776$		−	13.9762i		−	0.501717i
$777$	2.85422	−	11.0867i	0.102395	−	0.397733i
$778$	5.26602	−	10.3351i	0.188796	−	0.370533i
$779$	33.1835	−	10.7820i	1.18892	−	0.386305i
$780$	−4.97583	−	23.7817i	−0.178163	−	0.851522i
$781$	9.03237	−	27.7988i	0.323204	−	0.994719i
$782$	6.30537	+	6.30537i	0.225480	+	0.225480i
$783$	−0.0292890	−	0.0574830i	−0.00104670	−	0.00205427i
$784$	16.8258	−	87.5880i	0.600920	−	3.12814i
$785$	34.1967	+	9.27982i	1.22053	+	0.331211i
$786$	36.4119	+	26.4548i	1.29877	+	0.943611i
$787$	−28.5279	−	4.51838i	−1.01691	−	0.161063i	−0.374341	−	0.927291i	$-0.622131\pi$
$787$	−28.5279	−	4.51838i	−1.01691	−	0.161063i	−0.642569	+	0.766228i	$0.722131\pi$
$788$	−12.2871	−	1.94608i	−0.437709	−	0.0693263i
$789$	−11.2515	−	8.17471i	−0.400565	−	0.291027i
$790$	−46.0417	+	70.4059i	−1.63809	+	2.50493i
$791$	44.1103	−	9.82987i	1.56838	−	0.349510i
$792$	17.4512	+	34.2499i	0.620101	+	1.21702i
$793$	15.9911	+	15.9911i	0.567860	+	0.567860i
$794$	−28.4529	+	87.5691i	−1.00976	+	3.10771i
$795$	−2.64618	+	5.89283i	−0.0938504	+	0.208997i
$796$	−33.2128	+	10.7915i	−1.17720	+	0.382494i
$797$	12.8875	−	25.2931i	0.456498	−	0.895928i	−0.541959	−	0.840405i	$-0.682317\pi$
$797$	12.8875	−	25.2931i	0.456498	−	0.895928i	0.998457	−	0.0555236i	$-0.0176828\pi$
$798$	10.6940	−	41.5389i	0.378565	−	1.47046i
$799$		−	45.2022i		−	1.59914i
$800$	21.4321	+	82.0736i	0.757738	+	2.90174i
$801$			0.782204i			0.0276378i
$802$	16.4745	−	2.60930i	0.581734	−	0.0921377i
$803$	28.2712	+	14.4049i	0.997668	+	0.508337i
$804$	−4.51378	−	13.8920i	−0.159189	−	0.489932i
$805$	−3.57378	−	2.03180i	−0.125959	−	0.0716117i
$806$	−2.63814	+	8.11935i	−0.0929244	+	0.285992i
$807$	−6.14014	+	6.14014i	−0.216143	+	0.216143i
$808$	41.3756	+	81.2042i	1.45559	+	2.85675i
$809$	4.22423	+	5.81416i	0.148516	+	0.204415i	0.876793	−	0.480868i	$-0.159678\pi$
$809$	4.22423	+	5.81416i	0.148516	+	0.204415i	−0.728277	+	0.685283i	$0.759678\pi$
$810$	2.13414	+	5.61299i	0.0749859	+	0.197221i
$811$	29.0324	−	39.9597i	1.01947	−	1.40317i	0.106889	−	0.994271i	$-0.465911\pi$
$811$	29.0324	−	39.9597i	1.01947	−	1.40317i	0.912578	−	0.408904i	$-0.134089\pi$
$812$	0.477180	−	0.750842i	0.0167458	−	0.0263494i
$813$	−20.0119	−	3.16958i	−0.701849	−	0.111162i
$814$	−30.4371	+	41.8931i	−1.06682	+	1.46835i
$815$	−31.5820	+	12.0079i	−1.10627	+	0.420619i
$816$	49.2559	−	35.7865i	1.72430	−	1.25278i
$817$	−61.8755	+	31.5271i	−2.16475	+	1.10299i
$818$	54.8958	−	54.8958i	1.91939	−	1.91939i
$819$	3.65029	−	4.13505i	0.127551	−	0.144490i
$820$	−66.9675	−	7.25433i	−2.33861	−	0.253332i
$821$	1.67878	+	5.16675i	0.0585898	+	0.180321i	0.976068	−	0.217465i	$-0.0697788\pi$
$821$	1.67878	+	5.16675i	0.0585898	+	0.180321i	−0.917478	+	0.397786i	$0.869779\pi$
$822$	−20.9530	+	41.1226i	−0.730820	+	1.43432i
$823$	3.44638	+	21.7596i	0.120133	+	0.758493i	0.972043	+	0.234803i	$0.0754446\pi$
$823$	3.44638	+	21.7596i	0.120133	+	0.758493i	−0.851909	+	0.523689i	$0.824555\pi$
$824$	−144.321			−5.02764
$825$	−22.2427	−	1.30784i	−0.774392	−	0.0455331i
$826$	23.3904	−	53.9562i	0.813855	−	1.87738i
$827$	−7.15583	+	1.13337i	−0.248832	+	0.0394112i	−0.279605	−	0.960115i	$-0.590203\pi$
$827$	−7.15583	+	1.13337i	−0.248832	+	0.0394112i	0.0307721	+	0.999526i	$0.490203\pi$
$828$	1.64424	−	3.22701i	0.0571414	−	0.112146i
$829$	−1.37874	−	4.24331i	−0.0478855	−	0.147376i	0.924255	−	0.381776i	$-0.124688\pi$
$829$	−1.37874	−	4.24331i	−0.0478855	−	0.147376i	−0.972140	+	0.234400i	$0.924688\pi$
$830$	−72.7294	−	32.6592i	−2.52447	−	1.13362i
$831$	29.8585	+	9.70162i	1.03578	+	0.336546i
$832$	29.5973	+	29.5973i	1.02610	+	1.02610i
$833$	11.3712	−	31.4568i	0.393987	−	1.08992i
$834$	−21.3680	−	29.4105i	−0.739913	−	1.01840i
$835$	−11.6027	+	17.7426i	−0.401528	+	0.614009i
$836$	−82.4151	+	113.435i	−2.85038	+	3.92322i
$837$	0.238542	−	1.50609i	0.00824521	−	0.0520582i
$838$	−9.10335	+	57.4763i	−0.314470	+	1.98549i
$839$	−20.8262	−	15.1311i	−0.719002	−	0.522385i	0.167064	−	0.985946i	$-0.446572\pi$
$839$	−20.8262	−	15.1311i	−0.719002	−	0.522385i	−0.886065	+	0.463561i	$0.846572\pi$
$840$	−31.8517	+	39.8719i	−1.09899	+	1.37571i
$841$	−23.4581	+	17.0433i	−0.808901	+	0.587701i
$842$	−30.6266	−	60.1081i	−1.05546	−	2.07146i
$843$	−5.33916	+	5.33916i	−0.183891	+	0.183891i
$844$	−45.9213	−	14.9207i	−1.58068	−	0.513593i
$845$	−18.9404	+	3.96289i	−0.651570	+	0.136328i
$846$	−24.1607	+	7.85029i	−0.830662	+	0.269899i
$847$	−14.9269	−	18.0673i	−0.512895	−	0.620801i
$848$	−5.75805	−	36.3549i	−0.197732	−	1.24843i
$849$		−	14.0593i		−	0.482514i
$850$	6.30018	+	63.8529i	0.216094	+	2.19014i
$851$	3.00676			0.103070
$852$	5.34802	+	33.7661i	0.183220	+	1.15681i
$853$	1.03383	+	0.526761i	0.0353975	+	0.0180360i	0.471600	−	0.881813i	$-0.343677\pi$
$853$	1.03383	+	0.526761i	0.0353975	+	0.0180360i	−0.436202	+	0.899849i	$0.643677\pi$
$854$	7.30310	−	76.7289i	0.249907	−	2.62561i
$855$	−9.06442	+	10.0028i	−0.309997	+	0.342088i
$856$	−4.06665	+	12.5159i	−0.138995	+	0.427784i
$857$	27.2866	+	27.2866i	0.932094	+	0.932094i	0.997837	−	0.0657430i	$-0.0209417\pi$
$857$	27.2866	+	27.2866i	0.932094	+	0.932094i	−0.0657430	+	0.997837i	$0.520942\pi$
$858$	−22.2296	+	11.3265i	−0.758905	+	0.386681i
$859$	2.03842	−	1.48100i	0.0695499	−	0.0505309i	−0.552467	−	0.833535i	$-0.686313\pi$
$859$	2.03842	−	1.48100i	0.0695499	−	0.0505309i	0.622017	+	0.783004i	$0.286313\pi$
$860$	133.904	−	6.58995i	4.56609	−	0.224715i
$861$	−7.77554	−	13.1672i	−0.264990	−	0.448735i
$862$	−14.7459	+	93.1017i	−0.502246	+	3.17106i
$863$	32.2786	+	5.11243i	1.09878	+	0.174029i	0.679389	−	0.733778i	$-0.262245\pi$
$863$	32.2786	+	5.11243i	1.09878	+	0.174029i	0.419387	+	0.907807i	$0.362245\pi$
$864$	−13.7251	−	9.97187i	−0.466937	−	0.339250i
$865$	30.2373	−	24.3266i	1.02810	−	0.827131i
$866$	−35.1469	−	48.3756i	−1.19434	−	1.64387i
$867$	5.19760	−	2.64831i	0.176520	−	0.0899413i
$868$	19.5560	−	7.72812i	0.663773	−	0.262310i
$869$	59.3716	+	19.2910i	2.01404	+	0.654402i
$870$	−0.336124	+	0.192636i	−0.0113957	+	0.00653098i
$871$	5.55660	−	1.80545i	0.188278	−	0.0611753i
$872$	73.5697	+	37.4857i	2.49139	+	1.26942i
$873$	−1.60029	+	0.253461i	−0.0541615	+	0.00857834i
$874$	11.2656			0.381063
$875$	−10.6081	−	27.6128i	−0.358619	−	0.933484i
$876$	−37.1111			−1.25387
$877$	−28.5874	+	4.52780i	−0.965328	+	0.152893i	−0.619147	−	0.785275i	$-0.712522\pi$
$877$	−28.5874	+	4.52780i	−0.965328	+	0.152893i	−0.346180	+	0.938168i	$0.612522\pi$
$878$	−25.1803	−	12.8300i	−0.849792	−	0.432991i
$879$	−1.64966	+	0.536006i	−0.0556416	+	0.0180790i
$880$	110.152	−	63.1295i	3.71324	−	2.12810i
$881$	−12.5260	−	4.06994i	−0.422011	−	0.137120i	0.0903099	−	0.995914i	$-0.471214\pi$
$881$	−12.5260	−	4.06994i	−0.422011	−	0.137120i	−0.512321	+	0.858794i	$0.671214\pi$
$882$	−18.7886	−	0.614789i	−0.632646	−	0.0207010i
$883$	−30.0236	+	15.2978i	−1.01038	+	0.514812i	−0.879152	−	0.476541i	$-0.841890\pi$
$883$	−30.0236	+	15.2978i	−1.01038	+	0.514812i	−0.131223	+	0.991353i	$0.541890\pi$
$884$	30.5187	+	42.0054i	1.02645	+	1.41279i
$885$	−14.4199	+	11.6011i	−0.484719	+	0.389968i
$886$	−3.81516	−	2.77188i	−0.128173	−	0.0931230i
$887$	28.3541	+	4.49085i	0.952038	+	0.150788i	0.613086	−	0.790016i	$-0.289928\pi$
$887$	28.3541	+	4.49085i	0.952038	+	0.150788i	0.338952	+	0.940804i	$0.389928\pi$
$888$	5.83891	−	36.8654i	0.195941	−	1.23712i
$889$	4.83019	−	2.85235i	0.161999	−	0.0956648i
$890$	4.69147	−	0.230886i	0.157259	−	0.00773932i
$891$	3.60516	−	2.61930i	0.120777	−	0.0877500i
$892$	−49.8986	+	25.4246i	−1.67073	+	0.851279i
$893$	−40.3805	−	40.3805i	−1.35128	−	1.35128i
$894$	12.1611	−	37.4281i	0.406729	−	1.25178i
$895$	−2.45803	+	2.71249i	−0.0821628	+	0.0906685i
$896$	5.01100	−	52.6473i	0.167406	−	1.75882i
$897$	1.29076	+	0.657675i	0.0430972	+	0.0219591i
$898$	3.81006	+	24.0558i	0.127143	+	0.802751i
$899$	0.0983763			0.00328103
$900$	23.8743	−	10.4478i	0.795809	−	0.348259i
$901$		−	13.8042i		−	0.459886i
$902$	10.8201	+	68.3157i	0.360271	+	2.27466i
$903$	19.3849	+	23.4632i	0.645088	+	0.780805i
$904$	140.131	−	45.5313i	4.66068	−	1.51435i
$905$	0.927239	−	0.194006i	0.0308225	−	0.00644896i
$906$	27.4029	+	8.90373i	0.910399	+	0.295807i
$907$	12.4022	−	12.4022i	0.411810	−	0.411810i	−0.470559	−	0.882369i	$-0.655948\pi$
$907$	12.4022	−	12.4022i	0.411810	−	0.411810i	0.882369	+	0.470559i	$0.155948\pi$
$908$	5.81038	+	11.4035i	0.192824	+	0.378439i
$909$	8.54759	−	6.21019i	0.283506	−	0.205979i
$910$	−25.8785	−	20.6730i	−0.857863	−	0.685303i
$911$	−40.1396	−	29.1631i	−1.32988	−	0.966218i	−0.999752	−	0.0222829i	$-0.992907\pi$
$911$	−40.1396	−	29.1631i	−1.32988	−	0.966218i	−0.330133	−	0.943935i	$-0.607093\pi$
$912$	12.0326	−	75.9710i	0.398440	−	2.51565i
$913$	−9.25515	+	58.4347i	−0.306301	+	1.93391i
$914$	−13.3572	+	18.3846i	−0.441817	+	0.608108i
$915$	−13.2757	+	20.3008i	−0.438879	+	0.671125i
$916$	−16.4021	−	22.5755i	−0.541940	−	0.745917i
$917$	44.2553	−	2.75557i	1.46144	−	0.0909968i
$918$	−9.07402	−	9.07402i	−0.299487	−	0.299487i
$919$	42.3307	+	13.7541i	1.39636	+	0.453705i	0.908012	−	0.418944i	$-0.137600\pi$
$919$	42.3307	+	13.7541i	1.39636	+	0.453705i	0.488348	+	0.872649i	$0.337600\pi$
$920$	−12.2270	−	5.49054i	−0.403111	−	0.181018i
$921$	−5.89052	−	18.1292i	−0.194099	−	0.597376i
$922$	10.9658	−	21.5216i	0.361139	−	0.708775i
$923$	−13.5060	+	2.13914i	−0.444555	+	0.0704105i
$924$	56.3806	+	24.4414i	1.85478	+	0.804062i
$925$	16.7265	+	13.7222i	0.549964	+	0.451184i
$926$	19.9206			0.654633
$927$	2.61727	+	16.5248i	0.0859625	+	0.542746i
$928$	0.496893	−	0.975208i	0.0163113	−	0.0320128i
$929$	−7.95551	−	24.4845i	−0.261012	−	0.803312i	−0.992585	−	0.121549i	$-0.961214\pi$
$929$	−7.95551	−	24.4845i	−0.261012	−	0.803312i	0.731574	−	0.681762i	$-0.238786\pi$
$930$	−9.10360	−	0.986157i	−0.298519	−	0.0323374i
$931$	−17.9432	−	38.2596i	−0.588063	−	1.25391i
$932$	−76.3815	+	76.3815i	−2.50196	+	2.50196i
$933$	9.46374	−	4.82202i	0.309829	−	0.157866i
$934$	50.1642	−	36.4464i	1.64142	−	1.19256i
$935$	44.5059	−	16.9217i	1.45550	−	0.553400i
$936$	10.5702	−	14.5487i	0.345498	−	0.475538i
$937$	16.9708	+	2.68791i	0.554412	+	0.0878103i	0.427353	−	0.904085i	$-0.359446\pi$
$937$	16.9708	+	2.68791i	0.554412	+	0.0878103i	0.127059	+	0.991895i	$0.459446\pi$
$938$	−16.8059	−	10.6806i	−0.548730	−	0.348733i
$939$	−1.47045	+	2.02390i	−0.0479864	+	0.0660475i
$940$	39.1810	+	103.050i	1.27794	+	3.36112i
$941$	5.92053	+	8.14891i	0.193004	+	0.265647i	0.894541	−	0.446986i	$-0.147503\pi$
$941$	5.92053	+	8.14891i	0.193004	+	0.265647i	−0.701537	+	0.712633i	$0.747503\pi$
$942$	19.3199	+	37.9174i	0.629475	+	1.23541i
$943$	2.83988	−	2.83988i	0.0924792	−	0.0924792i
$944$	32.5879	−	100.295i	1.06064	−	3.26433i
$945$	5.14300	+	2.92396i	0.167302	+	0.0951163i
$946$	−42.5406	−	130.927i	−1.38312	−	4.25679i
$947$	−47.9961	−	24.4552i	−1.55966	−	0.794689i	−0.560231	−	0.828337i	$-0.689288\pi$
$947$	−47.9961	−	24.4552i	−1.55966	−	0.794689i	−0.999434	+	0.0336478i	$0.989288\pi$
$948$	−72.1163	+	11.4221i	−2.34223	+	0.370973i
$949$		−	14.8439i		−	0.481855i
$950$	62.6699	+	51.4136i	2.03328	+	1.66808i
$951$			18.6476i			0.604691i
$952$	27.1892	−	105.611i	0.881207	−	3.42288i
$953$	−20.8124	+	40.8467i	−0.674181	+	1.32316i	0.259741	+	0.965678i	$0.416363\pi$
$953$	−20.8124	+	40.8467i	−0.674181	+	1.32316i	−0.933922	+	0.357477i	$0.883637\pi$
$954$	−7.37842	+	2.39739i	−0.238885	+	0.0776185i
$955$	−2.12133	+	4.72402i	−0.0686445	+	0.152866i
$956$	31.0250	−	95.4852i	1.00342	−	3.08821i
$957$	0.203287	+	0.203287i	0.00657135	+	0.00657135i
$958$	−8.50881	−	16.6995i	−0.274907	−	0.539536i
$959$	9.89014	+	44.3808i	0.319369	+	1.43313i
$960$	−24.5714	+	37.5740i	−0.793038	+	1.21270i
$961$	−23.1984	−	16.8546i	−0.748335	−	0.543697i
$962$	23.9271	+	3.78969i	0.771442	+	0.122184i
$963$	1.50683	+	0.238658i	0.0485568	+	0.00769065i
$964$	66.2587	+	48.1398i	2.13405	+	1.55048i
$965$	22.6292	+	6.14081i	0.728461	+	0.197680i
$966$	−1.07392	−	4.81909i	−0.0345528	−	0.155052i
$967$	13.4796	+	26.4553i	0.433476	+	0.850744i	0.999650	+	0.0264584i	$0.00842295\pi$
$967$	13.4796	+	26.4553i	0.433476	+	0.850744i	−0.566174	+	0.824286i	$0.691577\pi$
$968$	−54.0293	−	54.0293i	−1.73657	−	1.73657i
$969$	8.91415	−	27.4349i	0.286364	−	0.881337i
$970$	1.99256	+	9.52332i	0.0639772	+	0.305775i
$971$	−28.8799	+	9.38363i	−0.926799	+	0.301135i	−0.733253	−	0.679956i	$-0.761999\pi$
$971$	−28.8799	+	9.38363i	−0.926799	+	0.301135i	−0.193546	+	0.981091i	$0.561999\pi$
$972$	−2.36622	+	4.64397i	−0.0758966	+	0.148955i
$973$	−34.6840	−	8.92926i	−1.11192	−	0.286259i
$974$			4.65408i			0.149126i
$975$	4.17896	+	9.54938i	0.133834	+	0.305825i
$976$		−	138.215i		−	4.42415i
$977$	50.4163	−	7.98516i	1.61296	−	0.255468i	0.716172	−	0.697924i	$-0.245893\pi$
$977$	50.4163	−	7.98516i	1.61296	−	0.255468i	0.896790	+	0.442456i	$0.145893\pi$
$978$	−36.1564	−	18.4226i	−1.15615	−	0.589090i
$979$	−1.07713	−	3.31508i	−0.0344253	−	0.105950i
$980$	1.34315	+	81.5704i	0.0429054	+	2.60567i
$981$	2.95794	−	9.10360i	0.0944397	−	0.290656i
$982$	−10.7605	+	10.7605i	−0.343380	+	0.343380i
$983$	−1.36512	−	2.67920i	−0.0435406	−	0.0854532i	0.868211	−	0.496195i	$-0.165270\pi$
$983$	−1.36512	−	2.67920i	−0.0435406	−	0.0854532i	−0.911752	+	0.410742i	$0.865270\pi$
$984$	−29.3045	−	40.3342i	−0.934193	−	1.28581i
$985$	5.33065	−	0.262343i	0.169849	−	0.00835893i
$986$	0.486622	−	0.669778i	0.0154972	−	0.0213301i
$987$	−13.4242	+	21.1230i	−0.427298	+	0.672353i
$988$	64.7880	+	10.2614i	2.06118	+	0.326459i
$989$	−4.69845	+	6.46687i	−0.149402	+	0.205634i
$990$	−16.7741	−	20.8497i	−0.533116	−	0.662648i
$991$	7.33724	−	5.33081i	0.233075	−	0.169339i	−0.465118	−	0.885249i	$-0.653988\pi$
$991$	7.33724	−	5.33081i	0.233075	−	0.169339i	0.698193	+	0.715910i	$0.253988\pi$
$992$	23.0500	−	11.7446i	0.731838	−	0.372890i
$993$	13.4126	−	13.4126i	0.425636	−	0.425636i
$994$	34.9388	+	30.8429i	1.10819	+	0.978278i
$995$	12.9988	−	7.44972i	0.412088	−	0.236172i
$996$	−21.3833	−	65.8111i	−0.677556	−	2.08530i
$997$	−16.5754	+	32.5311i	−0.524949	+	1.03027i	0.464525	+	0.885560i	$0.346225\pi$
$997$	−16.5754	+	32.5311i	−0.524949	+	1.03027i	−0.989474	+	0.144711i	$0.953775\pi$
$998$	6.23984	+	39.3968i	0.197519	+	1.24708i
$999$	−4.32701			−0.136901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bh.a.13.4	yes	320
7.6	odd	2	inner	525.2.bh.a.13.3	✓	320
25.2	odd	20	inner	525.2.bh.a.202.3	yes	320
175.27	even	20	inner	525.2.bh.a.202.4	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bh.a.13.3	✓	320	7.6	odd	2	inner
525.2.bh.a.13.4	yes	320	1.1	even	1	trivial
525.2.bh.a.202.3	yes	320	25.2	odd	20	inner
525.2.bh.a.202.4	yes	320	175.27	even	20	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65246 + 0.420109i) q^{2} +(0.891007 + 0.453990i) q^{3} +(4.95695 - 1.61061i) q^{4} +(-1.94004 + 1.11186i) q^{5} +(-2.55409 - 0.829873i) q^{6} +(-2.46059 + 0.972375i) q^{7} +(-7.68586 + 3.91614i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-2.65246 + 0.420109i) q^{2} +(0.891007 + 0.453990i) q^{3} +(4.95695 - 1.61061i) q^{4} +(-1.94004 + 1.11186i) q^{5} +(-2.55409 - 0.829873i) q^{6} +(-2.46059 + 0.972375i) q^{7} +(-7.68586 + 3.91614i) q^{8} +(0.587785 + 0.809017i) q^{9} +(4.67879 - 3.76420i) q^{10} +(-3.60516 - 2.61930i) q^{11} +(5.14788 + 0.815344i) q^{12} +(-0.326126 + 2.05908i) q^{13} +(6.11811 - 3.61290i) q^{14} +(-2.23336 + 0.109913i) q^{15} +(10.3080 - 7.48918i) q^{16} +(4.25761 - 2.16936i) q^{17} +(-1.89895 - 1.89895i) q^{18} +(1.86550 - 5.74141i) q^{19} +(-7.82593 + 8.63609i) q^{20} +(-2.63385 - 0.250691i) q^{21} +(10.6629 + 5.43304i) q^{22} +(-0.108703 - 0.686327i) q^{23} -8.62604 q^{24} +(2.52754 - 4.31411i) q^{25} -5.59864i q^{26} +(0.156434 + 0.987688i) q^{27} +(-10.6309 + 8.78306i) q^{28} +(-0.0613571 + 0.0199361i) q^{29} +(5.87774 - 1.22980i) q^{30} +(-1.45023 - 0.471210i) q^{31} +(-11.9962 + 11.9962i) q^{32} +(-2.02308 - 3.97053i) q^{33} +(-10.3818 + 7.54281i) q^{34} +(3.69250 - 4.62228i) q^{35} +(4.21664 + 3.06357i) q^{36} +(-0.676894 + 4.27374i) q^{37} +(-2.53615 + 16.0126i) q^{38} +(-1.22538 + 1.68660i) q^{39} +(10.5567 - 16.1431i) q^{40} +(3.39721 + 4.67586i) q^{41} +(7.09150 - 0.441554i) q^{42} +(-8.13411 - 8.13411i) q^{43} +(-22.0893 - 7.17725i) q^{44} +(-2.03984 - 0.915993i) q^{45} +(0.576664 + 1.77479i) q^{46} +(4.29458 - 8.42859i) q^{47} +(12.5845 - 1.99319i) q^{48} +(5.10898 - 4.78522i) q^{49} +(-4.89180 + 12.5049i) q^{50} +4.77843 q^{51} +(1.69979 + 10.7320i) q^{52} +(1.31152 - 2.57400i) q^{53} +(-0.829873 - 2.55409i) q^{54} +(9.90647 + 1.07313i) q^{55} +(15.1038 - 17.1095i) q^{56} +(4.26872 - 4.26872i) q^{57} +(0.154372 - 0.0786565i) q^{58} +(6.69600 - 4.86493i) q^{59} +(-10.8937 + 4.14192i) q^{60} +(6.37614 - 8.77600i) q^{61} +(4.04465 + 0.640610i) q^{62} +(-2.23296 - 1.41911i) q^{63} +(11.8014 - 16.2432i) q^{64} +(-1.65671 - 4.35731i) q^{65} +(7.03421 + 9.68175i) q^{66} +(-1.27232 - 2.49707i) q^{67} +(17.6108 - 17.6108i) q^{68} +(0.214730 - 0.660872i) q^{69} +(-7.85236 + 13.8117i) q^{70} +(2.02691 + 6.23819i) q^{71} +(-7.68586 - 3.91614i) q^{72} +(-7.03260 + 1.11385i) q^{73} -11.6203i q^{74} +(4.21062 - 2.69642i) q^{75} -31.4645i q^{76} +(11.4178 + 2.93946i) q^{77} +(2.54173 - 4.98843i) q^{78} +(-13.3233 + 4.32900i) q^{79} +(-11.6710 + 25.9904i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-10.9753 - 10.9753i) q^{82} +(-6.02741 - 11.8295i) q^{83} +(-13.4596 + 2.99944i) q^{84} +(-5.84793 + 8.94252i) q^{85} +(24.9926 + 18.1582i) q^{86} +(-0.0637204 - 0.0100923i) q^{87} +(37.9663 + 6.01327i) q^{88} +(0.632817 + 0.459768i) q^{89} +(5.79542 + 1.57268i) q^{90} +(-1.19974 - 5.38367i) q^{91} +(-1.64424 - 3.22701i) q^{92} +(-1.07824 - 1.07824i) q^{93} +(-7.85029 + 24.1607i) q^{94} +(2.76450 + 13.2128i) q^{95} +(-16.1348 + 5.24252i) q^{96} +(-0.735571 + 1.44364i) q^{97} +(-11.5411 + 14.8390i) q^{98} -4.45622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \) 320 * q + 8 * q^7 - 24 * q^8	\( 320 q + 8 q^{7} - 24 q^{8} - 8 q^{15} + 80 q^{16} - 24 q^{22} + 36 q^{28} - 40 q^{29} - 32 q^{30} - 48 q^{32} + 28 q^{35} + 80 q^{36} - 32 q^{37} + 16 q^{42} - 144 q^{43} - 288 q^{50} + 136 q^{53} - 8 q^{57} - 32 q^{58} - 40 q^{60} - 8 q^{63} - 120 q^{64} - 40 q^{65} + 32 q^{67} - 40 q^{70} - 24 q^{72} + 24 q^{77} + 8 q^{78} + 80 q^{81} - 80 q^{84} - 48 q^{85} - 56 q^{88} + 40 q^{92} + 96 q^{93} - 88 q^{95} - 184 q^{98}+O(q^{100}) \) 320 * q + 8 * q^7 - 24 * q^8 - 8 * q^15 + 80 * q^16 - 24 * q^22 + 36 * q^28 - 40 * q^29 - 32 * q^30 - 48 * q^32 + 28 * q^35 + 80 * q^36 - 32 * q^37 + 16 * q^42 - 144 * q^43 - 288 * q^50 + 136 * q^53 - 8 * q^57 - 32 * q^58 - 40 * q^60 - 8 * q^63 - 120 * q^64 - 40 * q^65 + 32 * q^67 - 40 * q^70 - 24 * q^72 + 24 * q^77 + 8 * q^78 + 80 * q^81 - 80 * q^84 - 48 * q^85 - 56 * q^88 + 40 * q^92 + 96 * q^93 - 88 * q^95 - 184 * q^98

Introduction

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