LMFDB - Embedded newform 570.2.k.a.533.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			533.5
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.274986 + 1.71008i) q^{3} +1.00000i q^{4} +(2.05001 - 0.893014i) q^{5} +(1.40366 - 1.01477i) q^{6} +(2.76585 - 2.76585i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.84877 - 0.940499i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.274986 + 1.71008i) q^{3} +1.00000i q^{4} +(2.05001 - 0.893014i) q^{5} +(1.40366 - 1.01477i) q^{6} +(2.76585 - 2.76585i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.84877 - 0.940499i) q^{9} +(-2.08103 - 0.818117i) q^{10} -4.37906i q^{11} +(-1.71008 - 0.274986i) q^{12} +(-0.0858524 - 0.0858524i) q^{13} -3.91150 q^{14} +(0.963404 + 3.75125i) q^{15} -1.00000 q^{16} +(-4.90493 - 4.90493i) q^{17} +(1.34935 + 2.67941i) q^{18} -1.00000i q^{19} +(0.893014 + 2.05001i) q^{20} +(3.96926 + 5.49040i) q^{21} +(-3.09646 + 3.09646i) q^{22} +(-4.04057 + 4.04057i) q^{23} +(1.01477 + 1.40366i) q^{24} +(3.40505 - 3.66137i) q^{25} +0.121414i q^{26} +(2.39170 - 4.61300i) q^{27} +(2.76585 + 2.76585i) q^{28} +7.73552 q^{29} +(1.97130 - 3.33376i) q^{30} -4.80009 q^{31} +(0.707107 + 0.707107i) q^{32} +(7.48856 + 1.20418i) q^{33} +6.93661i q^{34} +(3.20007 - 8.13995i) q^{35} +(0.940499 - 2.84877i) q^{36} +(-1.15860 + 1.15860i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(0.170423 - 0.123206i) q^{39} +(0.818117 - 2.08103i) q^{40} -3.99475i q^{41} +(1.07561 - 6.68899i) q^{42} +(-2.22743 - 2.22743i) q^{43} +4.37906 q^{44} +(-6.67986 + 0.615959i) q^{45} +5.71423 q^{46} +(9.37516 + 9.37516i) q^{47} +(0.274986 - 1.71008i) q^{48} -8.29985i q^{49} +(-4.99671 + 0.181243i) q^{50} +(9.73662 - 7.03904i) q^{51} +(0.0858524 - 0.0858524i) q^{52} +(-1.61864 + 1.61864i) q^{53} +(-4.95307 + 1.57069i) q^{54} +(-3.91056 - 8.97711i) q^{55} -3.91150i q^{56} +(1.71008 + 0.274986i) q^{57} +(-5.46984 - 5.46984i) q^{58} +13.6615 q^{59} +(-3.75125 + 0.963404i) q^{60} +13.0690 q^{61} +(3.39418 + 3.39418i) q^{62} +(-10.4805 + 5.27798i) q^{63} -1.00000i q^{64} +(-0.252665 - 0.0993306i) q^{65} +(-4.44373 - 6.14670i) q^{66} +(-9.57951 + 9.57951i) q^{67} +(4.90493 - 4.90493i) q^{68} +(-5.79861 - 8.02081i) q^{69} +(-8.01860 + 3.49303i) q^{70} +10.1120i q^{71} +(-2.67941 + 1.34935i) q^{72} +(-3.04806 - 3.04806i) q^{73} +1.63851 q^{74} +(5.32490 + 6.82975i) q^{75} +1.00000 q^{76} +(-12.1118 - 12.1118i) q^{77} +(-0.207627 - 0.0333871i) q^{78} -1.24732i q^{79} +(-2.05001 + 0.893014i) q^{80} +(7.23092 + 5.35852i) q^{81} +(-2.82471 + 2.82471i) q^{82} +(-9.27133 + 9.27133i) q^{83} +(-5.49040 + 3.96926i) q^{84} +(-14.4353 - 5.67496i) q^{85} +3.15007i q^{86} +(-2.12716 + 13.2284i) q^{87} +(-3.09646 - 3.09646i) q^{88} +4.47665 q^{89} +(5.15893 + 4.28783i) q^{90} -0.474910 q^{91} +(-4.04057 - 4.04057i) q^{92} +(1.31996 - 8.20856i) q^{93} -13.2585i q^{94} +(-0.893014 - 2.05001i) q^{95} +(-1.40366 + 1.01477i) q^{96} +(-1.05430 + 1.05430i) q^{97} +(-5.86888 + 5.86888i) q^{98} +(-4.11850 + 12.4749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.274986	+	1.71008i	−0.158763	+	0.987317i
$3$	−0.274986	+	1.71008i	−0.158763	+	0.987317i
$4$			1.00000i			0.500000i
$5$	2.05001	−	0.893014i	0.916791	−	0.399368i
$5$	2.05001	−	0.893014i	0.916791	−	0.399368i
$6$	1.40366	−	1.01477i	0.573040	−	0.414277i
$7$	2.76585	−	2.76585i	1.04539	−	1.04539i	0.0464734	−	0.998920i	$-0.485202\pi$
$7$	2.76585	−	2.76585i	1.04539	−	1.04539i	0.998920	−	0.0464734i	$-0.0147983\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.84877	−	0.940499i	−0.949588	−	0.313500i
$10$	−2.08103	−	0.818117i	−0.658079	−	0.258711i
$11$		−	4.37906i		−	1.32034i	−0.751117	−	0.660169i	$-0.770485\pi$
$11$		−	4.37906i		−	1.32034i	0.751117	−	0.660169i	$-0.229515\pi$
$12$	−1.71008	−	0.274986i	−0.493658	−	0.0793817i
$13$	−0.0858524	−	0.0858524i	−0.0238112	−	0.0238112i	0.695101	−	0.718912i	$-0.255360\pi$
$13$	−0.0858524	−	0.0858524i	−0.0238112	−	0.0238112i	−0.718912	+	0.695101i	$0.755360\pi$
$14$	−3.91150			−1.04539
$15$	0.963404	+	3.75125i	0.248750	+	0.968568i
$16$	−1.00000			−0.250000
$17$	−4.90493	−	4.90493i	−1.18962	−	1.18962i	−0.977173	−	0.212447i	$-0.931857\pi$
$17$	−4.90493	−	4.90493i	−1.18962	−	1.18962i	−0.212447	−	0.977173i	$-0.568143\pi$
$18$	1.34935	+	2.67941i	0.318044	+	0.631544i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	0.893014	+	2.05001i	0.199684	+	0.458395i
$21$	3.96926	+	5.49040i	0.866164	+	1.19810i
$22$	−3.09646	+	3.09646i	−0.660169	+	0.660169i
$23$	−4.04057	+	4.04057i	−0.842517	+	0.842517i	−0.989186	−	0.146669i	$-0.953145\pi$
$23$	−4.04057	+	4.04057i	−0.842517	+	0.842517i	0.146669	+	0.989186i	$0.453145\pi$
$24$	1.01477	+	1.40366i	0.207138	+	0.286520i
$25$	3.40505	−	3.66137i	0.681010	−	0.732274i
$26$			0.121414i			0.0238112i
$27$	2.39170	−	4.61300i	0.460283	−	0.887772i
$28$	2.76585	+	2.76585i	0.522696	+	0.522696i
$29$	7.73552			1.43645			0.718225	−	0.695811i	$-0.244955\pi$
$29$	7.73552			1.43645			0.718225	+	0.695811i	$0.244955\pi$
$30$	1.97130	−	3.33376i	0.359909	−	0.608659i
$31$	−4.80009			−0.862122			−0.431061	−	0.902323i	$-0.641861\pi$
$31$	−4.80009			−0.862122			−0.431061	+	0.902323i	$0.641861\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	7.48856	+	1.20418i	1.30359	+	0.209621i
$34$			6.93661i			1.18962i
$35$	3.20007	−	8.13995i	0.540910	−	1.37590i
$36$	0.940499	−	2.84877i	0.156750	−	0.474794i
$37$	−1.15860	+	1.15860i	−0.190473	+	0.190473i	−0.795901	−	0.605427i	$-0.793002\pi$
$37$	−1.15860	+	1.15860i	−0.190473	+	0.190473i	0.605427	+	0.795901i	$0.293002\pi$
$38$	−0.707107	+	0.707107i	−0.114708	+	0.114708i
$39$	0.170423	−	0.123206i	0.0272895	−	0.0197288i
$40$	0.818117	−	2.08103i	0.129356	−	0.329040i
$41$		−	3.99475i		−	0.623874i	−0.950103	−	0.311937i	$-0.899022\pi$
$41$		−	3.99475i		−	0.623874i	0.950103	−	0.311937i	$-0.100978\pi$
$42$	1.07561	−	6.68899i	0.165970	−	1.03213i
$43$	−2.22743	−	2.22743i	−0.339680	−	0.339680i	0.516567	−	0.856247i	$-0.327210\pi$
$43$	−2.22743	−	2.22743i	−0.339680	−	0.339680i	−0.856247	+	0.516567i	$0.827210\pi$
$44$	4.37906			0.660169
$45$	−6.67986	+	0.615959i	−0.995775	+	0.0918217i
$46$	5.71423			0.842517
$47$	9.37516	+	9.37516i	1.36751	+	1.36751i	0.863979	+	0.503528i	$0.167965\pi$
$47$	9.37516	+	9.37516i	1.36751	+	1.36751i	0.503528	+	0.863979i	$0.332035\pi$
$48$	0.274986	−	1.71008i	0.0396909	−	0.246829i
$49$		−	8.29985i		−	1.18569i
$50$	−4.99671	+	0.181243i	−0.706642	+	0.0256317i
$51$	9.73662	−	7.03904i	1.36340	−	0.985663i
$52$	0.0858524	−	0.0858524i	0.0119056	−	0.0119056i
$53$	−1.61864	+	1.61864i	−0.222337	+	0.222337i	−0.809482	−	0.587145i	$-0.800252\pi$
$53$	−1.61864	+	1.61864i	−0.222337	+	0.222337i	0.587145	+	0.809482i	$0.300252\pi$
$54$	−4.95307	+	1.57069i	−0.674028	+	0.213744i
$55$	−3.91056	−	8.97711i	−0.527300	−	1.21047i
$56$		−	3.91150i		−	0.522696i
$57$	1.71008	+	0.274986i	0.226506	+	0.0364228i
$58$	−5.46984	−	5.46984i	−0.718225	−	0.718225i
$59$	13.6615			1.77857			0.889286	−	0.457351i	$-0.151202\pi$
$59$	13.6615			1.77857			0.889286	+	0.457351i	$0.151202\pi$
$60$	−3.75125	+	0.963404i	−0.484284	+	0.124375i
$61$	13.0690			1.67331			0.836655	−	0.547730i	$-0.184508\pi$
$61$	13.0690			1.67331			0.836655	+	0.547730i	$0.184508\pi$
$62$	3.39418	+	3.39418i	0.431061	+	0.431061i
$63$	−10.4805	+	5.27798i	−1.32042	+	0.664963i
$64$		−	1.00000i		−	0.125000i
$65$	−0.252665	−	0.0993306i	−0.0313393	−	0.0123204i
$66$	−4.44373	−	6.14670i	−0.546985	−	0.756606i
$67$	−9.57951	+	9.57951i	−1.17032	+	1.17032i	−0.188191	+	0.982132i	$0.560262\pi$
$67$	−9.57951	+	9.57951i	−1.17032	+	1.17032i	−0.982132	+	0.188191i	$0.939738\pi$
$68$	4.90493	−	4.90493i	0.594810	−	0.594810i
$69$	−5.79861	−	8.02081i	−0.698070	−	0.965592i
$70$	−8.01860	+	3.49303i	−0.958407	+	0.417496i
$71$			10.1120i			1.20007i	0.799973	+	0.600036i	$0.204847\pi$
$71$			10.1120i			1.20007i	−0.799973	+	0.600036i	$0.795153\pi$
$72$	−2.67941	+	1.34935i	−0.315772	+	0.159022i
$73$	−3.04806	−	3.04806i	−0.356748	−	0.356748i	0.505865	−	0.862613i	$-0.331174\pi$
$73$	−3.04806	−	3.04806i	−0.356748	−	0.356748i	−0.862613	+	0.505865i	$0.831174\pi$
$74$	1.63851			0.190473
$75$	5.32490	+	6.82975i	0.614867	+	0.788631i
$76$	1.00000			0.114708
$77$	−12.1118	−	12.1118i	−1.38027	−	1.38027i
$78$	−0.207627	−	0.0333871i	−0.0235092	−	0.00378034i
$79$		−	1.24732i		−	0.140334i	−0.997535	−	0.0701671i	$-0.977647\pi$
$79$		−	1.24732i		−	0.140334i	0.997535	−	0.0701671i	$-0.0223532\pi$
$80$	−2.05001	+	0.893014i	−0.229198	+	0.0998420i
$81$	7.23092	+	5.35852i	0.803436	+	0.595391i
$82$	−2.82471	+	2.82471i	−0.311937	+	0.311937i
$83$	−9.27133	+	9.27133i	−1.01766	+	1.01766i	−0.0178196	+	0.999841i	$0.505672\pi$
$83$	−9.27133	+	9.27133i	−1.01766	+	1.01766i	−0.999841	+	0.0178196i	$0.994328\pi$
$84$	−5.49040	+	3.96926i	−0.599052	+	0.433082i
$85$	−14.4353	−	5.67496i	−1.56573	−	0.615536i
$86$			3.15007i			0.339680i
$87$	−2.12716	+	13.2284i	−0.228056	+	1.41823i
$88$	−3.09646	−	3.09646i	−0.330084	−	0.330084i
$89$	4.47665			0.474524			0.237262	−	0.971446i	$-0.423750\pi$
$89$	4.47665			0.474524			0.237262	+	0.971446i	$0.423750\pi$
$90$	5.15893	+	4.28783i	0.543799	+	0.451977i
$91$	−0.474910			−0.0497841
$92$	−4.04057	−	4.04057i	−0.421258	−	0.421258i
$93$	1.31996	−	8.20856i	0.136874	−	0.851188i
$94$		−	13.2585i		−	1.36751i
$95$	−0.893014	−	2.05001i	−0.0916213	−	0.210326i
$96$	−1.40366	+	1.01477i	−0.143260	+	0.103569i
$97$	−1.05430	+	1.05430i	−0.107048	+	0.107048i	−0.758602	−	0.651554i	$-0.774117\pi$
$97$	−1.05430	+	1.05430i	−0.107048	+	0.107048i	0.651554	+	0.758602i	$0.274117\pi$
$98$	−5.86888	+	5.86888i	−0.592846	+	0.592846i
$99$	−4.11850	+	12.4749i	−0.413925	+	1.25378i
$100$	3.66137	+	3.40505i	0.366137	+	0.340505i
$101$		−	1.32352i		−	0.131695i	−0.997830	−	0.0658476i	$-0.979025\pi$
$101$		−	1.32352i		−	0.131695i	0.997830	−	0.0658476i	$-0.0209751\pi$
$102$	−11.8622	−	1.90747i	−1.17453	−	0.188868i
$103$	8.88033	+	8.88033i	0.875005	+	0.875005i	0.993013	−	0.118008i	$-0.0376508\pi$
$103$	8.88033	+	8.88033i	0.875005	+	0.875005i	−0.118008	+	0.993013i	$0.537651\pi$
$104$	−0.121414			−0.0119056
$105$	13.0400	+	7.71075i	1.27258	+	0.752493i
$106$	2.28910			0.222337
$107$	7.02479	+	7.02479i	0.679112	+	0.679112i	0.959799	−	0.280687i	$-0.0905623\pi$
$107$	7.02479	+	7.02479i	0.679112	+	0.679112i	−0.280687	+	0.959799i	$0.590562\pi$
$108$	4.61300	+	2.39170i	0.443886	+	0.230142i
$109$			0.223709i			0.0214274i	0.999943	+	0.0107137i	$0.00341035\pi$
$109$			0.223709i			0.0214274i	−0.999943	+	0.0107137i	$0.996590\pi$
$110$	−3.58259	+	9.11296i	−0.341586	+	0.868887i
$111$	−1.66271	−	2.29991i	−0.157817	−	0.218298i
$112$	−2.76585	+	2.76585i	−0.261348	+	0.261348i
$113$	4.90305	−	4.90305i	0.461240	−	0.461240i	−0.437822	−	0.899062i	$-0.644250\pi$
$113$	4.90305	−	4.90305i	0.461240	−	0.461240i	0.899062	+	0.437822i	$0.144250\pi$
$114$	−1.01477	−	1.40366i	−0.0950416	−	0.131464i
$115$	−4.67491	+	11.8915i	−0.435937	+	1.10889i
$116$			7.73552i			0.718225i
$117$	0.163829	+	0.325317i	0.0151460	+	0.0300756i
$118$	−9.66012	−	9.66012i	−0.889286	−	0.889286i
$119$	−27.1326			−2.48724
$120$	3.33376	+	1.97130i	0.304329	+	0.179954i
$121$	−8.17619			−0.743290
$122$	−9.24116	−	9.24116i	−0.836655	−	0.836655i
$123$	6.83135	+	1.09850i	0.615962	+	0.0990484i
$124$		−	4.80009i		−	0.431061i
$125$	3.71073	−	10.5466i	0.331897	−	0.943316i
$126$	11.1430	+	3.67876i	0.992693	+	0.327730i
$127$	1.71446	−	1.71446i	0.152134	−	0.152134i	−0.626936	−	0.779070i	$-0.715691\pi$
$127$	1.71446	−	1.71446i	0.152134	−	0.152134i	0.779070	+	0.626936i	$0.215691\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	4.42161	−	3.19658i	0.389301	−	0.281443i
$130$	0.108424	+	0.248899i	0.00950942	+	0.0218299i
$131$			1.03462i			0.0903948i	0.998978	+	0.0451974i	$0.0143917\pi$
$131$			1.03462i			0.0903948i	−0.998978	+	0.0451974i	$0.985608\pi$
$132$	−1.20418	+	7.48856i	−0.104811	+	0.651795i
$133$	−2.76585	−	2.76585i	−0.239830	−	0.239830i
$134$	13.5475			1.17032
$135$	0.783531	−	11.5925i	0.0674356	−	0.997724i
$136$	−6.93661			−0.594810
$137$	3.90513	+	3.90513i	0.333638	+	0.333638i	0.853966	−	0.520328i	$-0.174190\pi$
$137$	3.90513	+	3.90513i	0.333638	+	0.333638i	−0.520328	+	0.853966i	$0.674190\pi$
$138$	−1.57133	+	9.77180i	−0.133761	+	0.831831i
$139$			0.884659i			0.0750358i	0.999296	+	0.0375179i	$0.0119451\pi$
$139$			0.884659i			0.0750358i	−0.999296	+	0.0375179i	$0.988055\pi$
$140$	8.13995	+	3.20007i	0.687952	+	0.270455i
$141$	−18.6103	+	13.4543i	−1.56727	+	1.13305i
$142$	7.15026	−	7.15026i	0.600036	−	0.600036i
$143$	−0.375953	+	0.375953i	−0.0314388	+	0.0314388i
$144$	2.84877	+	0.940499i	0.237397	+	0.0783749i
$145$	15.8579	−	6.90793i	1.31692	−	0.573672i
$146$			4.31060i			0.356748i
$147$	14.1934	+	2.28234i	1.17065	+	0.188245i
$148$	−1.15860	−	1.15860i	−0.0952366	−	0.0952366i
$149$	14.4191			1.18126			0.590629	−	0.806943i	$-0.298880\pi$
$149$	14.4191			1.18126			0.590629	+	0.806943i	$0.298880\pi$
$150$	1.06409	−	8.59463i	0.0868823	−	0.701749i
$151$	12.5541			1.02164			0.510820	−	0.859687i	$-0.329342\pi$
$151$	12.5541			1.02164			0.510820	+	0.859687i	$0.329342\pi$
$152$	−0.707107	−	0.707107i	−0.0573539	−	0.0573539i
$153$	9.35991	+	18.5861i	0.756704	+	1.50259i
$154$			17.1287i			1.38027i
$155$	−9.84022	+	4.28655i	−0.790386	+	0.344304i
$156$	0.123206	+	0.170423i	0.00986441	+	0.0136448i
$157$	−9.08703	+	9.08703i	−0.725224	+	0.725224i	−0.969664	−	0.244440i	$-0.921396\pi$
$157$	−9.08703	+	9.08703i	−0.725224	+	0.725224i	0.244440	+	0.969664i	$0.421396\pi$
$158$	−0.881987	+	0.881987i	−0.0701671	+	0.0701671i
$159$	−2.32290	−	3.21311i	−0.184218	−	0.254816i
$160$	2.08103	+	0.818117i	0.164520	+	0.0646778i
$161$			22.3512i			1.76152i
$162$	−1.32399	−	8.90208i	−0.104023	−	0.699414i
$163$	−2.97919	−	2.97919i	−0.233348	−	0.233348i	0.580740	−	0.814089i	$-0.302763\pi$
$163$	−2.97919	−	2.97919i	−0.233348	−	0.233348i	−0.814089	+	0.580740i	$0.802763\pi$
$164$	3.99475			0.311937
$165$	16.4269	−	4.21881i	1.27884	−	0.328434i
$166$	13.1116			1.01766
$167$	−6.66427	−	6.66427i	−0.515697	−	0.515697i	0.400569	−	0.916266i	$-0.368812\pi$
$167$	−6.66427	−	6.66427i	−0.515697	−	0.515697i	−0.916266	+	0.400569i	$0.868812\pi$
$168$	6.68899	+	1.07561i	0.516067	+	0.0829851i
$169$		−	12.9853i		−	0.998866i
$170$	6.19449	+	14.2201i	0.475096	+	1.09063i
$171$	−0.940499	+	2.84877i	−0.0719217	+	0.217851i
$172$	2.22743	−	2.22743i	0.169840	−	0.169840i
$173$	3.33173	−	3.33173i	0.253307	−	0.253307i	−0.569018	−	0.822325i	$-0.692677\pi$
$173$	3.33173	−	3.33173i	0.253307	−	0.253307i	0.822325	+	0.569018i	$0.192677\pi$
$174$	10.8580	−	7.84975i	0.823144	−	0.595088i
$175$	−0.708933	−	19.5447i	−0.0535903	−	1.47744i
$176$			4.37906i			0.330084i
$177$	−3.75672	+	23.3622i	−0.282372	+	1.75601i
$178$	−3.16547	−	3.16547i	−0.237262	−	0.237262i
$179$	−20.3926			−1.52421			−0.762105	−	0.647453i	$-0.775834\pi$
$179$	−20.3926			−1.52421			−0.762105	+	0.647453i	$0.775834\pi$
$180$	−0.615959	−	6.67986i	−0.0459109	−	0.497888i
$181$	−19.7998			−1.47171			−0.735855	−	0.677139i	$-0.763220\pi$
$181$	−19.7998			−1.47171			−0.735855	+	0.677139i	$0.763220\pi$
$182$	0.335812	+	0.335812i	0.0248920	+	0.0248920i
$183$	−3.59379	+	22.3490i	−0.265661	+	1.65209i
$184$			5.71423i			0.421258i
$185$	−1.34050	+	3.40979i	−0.0985552	+	0.250693i
$186$	−6.73768	+	4.87097i	−0.494031	+	0.357157i
$187$	−21.4790	+	21.4790i	−1.57070	+	1.57070i
$188$	−9.37516	+	9.37516i	−0.683754	+	0.683754i
$189$	−6.14378	−	19.3740i	−0.446894	−	1.40925i
$190$	−0.818117	+	2.08103i	−0.0593525	+	0.150974i
$191$			16.0949i			1.16458i	0.812979	+	0.582292i	$0.197844\pi$
$191$			16.0949i			1.16458i	−0.812979	+	0.582292i	$0.802156\pi$
$192$	1.71008	+	0.274986i	0.123415	+	0.0198454i
$193$	−2.75631	−	2.75631i	−0.198404	−	0.198404i	0.600912	−	0.799315i	$-0.294804\pi$
$193$	−2.75631	−	2.75631i	−0.198404	−	0.198404i	−0.799315	+	0.600912i	$0.794804\pi$
$194$	1.49100			0.107048
$195$	0.239343	−	0.404764i	0.0171397	−	0.0289858i
$196$	8.29985			0.592846
$197$	−9.52900	−	9.52900i	−0.678913	−	0.678913i	0.280841	−	0.959754i	$-0.409387\pi$
$197$	−9.52900	−	9.52900i	−0.678913	−	0.678913i	−0.959754	+	0.280841i	$0.909387\pi$
$198$	11.7333	−	5.90888i	0.833851	−	0.419926i
$199$			7.61755i			0.539994i	0.962861	+	0.269997i	$0.0870227\pi$
$199$			7.61755i			0.539994i	−0.962861	+	0.269997i	$0.912977\pi$
$200$	−0.181243	−	4.99671i	−0.0128158	−	0.353321i
$201$	−13.7475	−	19.0160i	−0.969675	−	1.34128i
$202$	−0.935870	+	0.935870i	−0.0658476	+	0.0658476i
$203$	21.3953	−	21.3953i	1.50166	−	1.50166i
$204$	7.03904	+	9.73662i	0.492831	+	0.681700i
$205$	−3.56736	−	8.18925i	−0.249155	−	0.571962i
$206$		−	12.5587i		−	0.875005i
$207$	15.3108	−	7.71048i	1.06417	−	0.535916i
$208$	0.0858524	+	0.0858524i	0.00595279	+	0.00595279i
$209$	−4.37906			−0.302906
$210$	−3.76836	−	14.6730i	−0.260041	−	1.01253i
$211$	5.54199			0.381526			0.190763	−	0.981636i	$-0.438904\pi$
$211$	5.54199			0.381526			0.190763	+	0.981636i	$0.438904\pi$
$212$	−1.61864	−	1.61864i	−0.111168	−	0.111168i
$213$	−17.2923	−	2.78066i	−1.18485	−	0.190528i
$214$		−	9.93455i		−	0.679112i
$215$	−6.55538	−	2.57712i	−0.447073	−	0.175758i
$216$	−1.57069	−	4.95307i	−0.106872	−	0.337014i
$217$	−13.2763	+	13.2763i	−0.901257	+	0.901257i
$218$	0.158186	−	0.158186i	0.0107137	−	0.0107137i
$219$	6.05060	−	4.37426i	0.408862	−	0.295585i
$220$	8.97711	−	3.91056i	0.605236	−	0.263650i
$221$			0.842199i			0.0566525i
$222$	−0.450568	+	2.80199i	−0.0302402	+	0.188057i
$223$	9.53065	+	9.53065i	0.638219	+	0.638219i	0.950116	−	0.311897i	$-0.100964\pi$
$223$	9.53065	+	9.53065i	0.638219	+	0.638219i	−0.311897	+	0.950116i	$0.600964\pi$
$224$	3.91150			0.261348
$225$	−13.1437	+	7.22793i	−0.876247	+	0.481862i
$226$	−6.93395			−0.461240
$227$	−13.7533	−	13.7533i	−0.912836	−	0.912836i	0.0836582	−	0.996495i	$-0.473340\pi$
$227$	−13.7533	−	13.7533i	−0.912836	−	0.912836i	−0.996495	+	0.0836582i	$0.973340\pi$
$228$	−0.274986	+	1.71008i	−0.0182114	+	0.113253i
$229$		−	6.49460i		−	0.429175i	−0.976705	−	0.214588i	$-0.931159\pi$
$229$		−	6.49460i		−	0.429175i	0.976705	−	0.214588i	$-0.0688407\pi$
$230$	11.7142	−	5.10289i	0.772412	−	0.336474i
$231$	24.0428	−	17.3816i	1.58190	−	1.14363i
$232$	5.46984	−	5.46984i	0.359113	−	0.359113i
$233$	7.94673	−	7.94673i	0.520608	−	0.520608i	−0.397147	−	0.917755i	$-0.630000\pi$
$233$	7.94673	−	7.94673i	0.520608	−	0.520608i	0.917755	+	0.397147i	$0.130000\pi$
$234$	0.114189	−	0.345879i	0.00746479	−	0.0226108i
$235$	27.5913	+	10.8470i	1.79986	+	0.707579i
$236$			13.6615i			0.889286i
$237$	2.13302	+	0.342995i	0.138554	+	0.0222799i
$238$	19.1856	+	19.1856i	1.24362	+	1.24362i
$239$	−7.51189			−0.485903			−0.242952	−	0.970038i	$-0.578116\pi$
$239$	−7.51189			−0.485903			−0.242952	+	0.970038i	$0.578116\pi$
$240$	−0.963404	−	3.75125i	−0.0621875	−	0.242142i
$241$	11.2111			0.722170			0.361085	−	0.932533i	$-0.382406\pi$
$241$	11.2111			0.722170			0.361085	+	0.932533i	$0.382406\pi$
$242$	5.78144	+	5.78144i	0.371645	+	0.371645i
$243$	−11.1519	+	10.8920i	−0.715396	+	0.698720i
$244$			13.0690i			0.836655i
$245$	−7.41188	−	17.0147i	−0.473528	−	1.08703i
$246$	−4.05373	−	5.60725i	−0.258457	−	0.357505i
$247$	−0.0858524	+	0.0858524i	−0.00546266	+	0.00546266i
$248$	−3.39418	+	3.39418i	−0.215531	+	0.215531i
$249$	−13.3053	−	18.4042i	−0.843186	−	1.16632i
$250$	−10.0814	+	4.83369i	−0.637606	+	0.305709i
$251$		−	10.7576i		−	0.679015i	−0.940603	−	0.339508i	$-0.889740\pi$
$251$		−	10.7576i		−	0.679015i	0.940603	−	0.339508i	$-0.110260\pi$
$252$	−5.27798	−	10.4805i	−0.332481	−	0.660212i
$253$	17.6939	+	17.6939i	1.11241	+	1.11241i
$254$	−2.42462			−0.152134
$255$	13.6742	−	23.1250i	0.856309	−	1.44814i
$256$	1.00000			0.0625000
$257$	−2.67697	−	2.67697i	−0.166985	−	0.166985i	0.618668	−	0.785653i	$-0.287673\pi$
$257$	−2.67697	−	2.67697i	−0.166985	−	0.166985i	−0.785653	+	0.618668i	$0.787673\pi$
$258$	−5.38688	−	0.866225i	−0.335372	−	0.0539288i
$259$			6.40905i			0.398239i
$260$	0.0993306	−	0.252665i	0.00616022	−	0.0156696i
$261$	−22.0367	−	7.27525i	−1.36404	−	0.450327i
$262$	0.731584	−	0.731584i	0.0451974	−	0.0451974i
$263$	16.7660	−	16.7660i	1.03384	−	1.03384i	0.0344303	−	0.999407i	$-0.489038\pi$
$263$	16.7660	−	16.7660i	1.03384	−	1.03384i	0.999407	−	0.0344303i	$-0.0109617\pi$
$264$	6.14670	−	4.44373i	0.378303	−	0.273492i
$265$	−1.87275	+	4.76368i	−0.115042	+	0.292631i
$266$			3.91150i			0.239830i
$267$	−1.23102	+	7.65545i	−0.0753371	+	0.468506i
$268$	−9.57951	−	9.57951i	−0.585162	−	0.585162i
$269$	−12.5500			−0.765186			−0.382593	−	0.923917i	$-0.624969\pi$
$269$	−12.5500			−0.765186			−0.382593	+	0.923917i	$0.624969\pi$
$270$	−8.75118	+	7.64310i	−0.532580	+	0.465144i
$271$	−12.9702			−0.787886			−0.393943	−	0.919135i	$-0.628889\pi$
$271$	−12.9702			−0.787886			−0.393943	+	0.919135i	$0.628889\pi$
$272$	4.90493	+	4.90493i	0.297405	+	0.297405i
$273$	0.130594	−	0.812135i	0.00790389	−	0.0491526i
$274$		−	5.52269i		−	0.333638i
$275$	−16.0334	−	14.9109i	−0.966848	−	0.899163i
$276$	8.02081	−	5.79861i	0.482796	−	0.349035i
$277$	10.2241	−	10.2241i	0.614306	−	0.614306i	−0.329759	−	0.944065i	$-0.606967\pi$
$277$	10.2241	−	10.2241i	0.614306	−	0.614306i	0.944065	+	0.329759i	$0.106967\pi$
$278$	0.625548	−	0.625548i	0.0375179	−	0.0375179i
$279$	13.6743	+	4.51448i	0.818661	+	0.270275i
$280$	−3.49303	−	8.01860i	−0.208748	−	0.479203i
$281$		−	3.48157i		−	0.207693i	−0.994593	−	0.103846i	$-0.966885\pi$
$281$		−	3.48157i		−	0.207693i	0.994593	−	0.103846i	$-0.0331150\pi$
$282$	22.6731	+	3.64590i	1.35016	+	0.217110i
$283$	−3.43456	−	3.43456i	−0.204164	−	0.204164i	0.597618	−	0.801781i	$-0.296114\pi$
$283$	−3.43456	−	3.43456i	−0.204164	−	0.204164i	−0.801781	+	0.597618i	$0.796114\pi$
$284$	−10.1120			−0.600036
$285$	3.75125	−	0.963404i	0.222205	−	0.0570671i
$286$	0.531678			0.0314388
$287$	−11.0489	−	11.0489i	−0.652194	−	0.652194i
$288$	−1.34935	−	2.67941i	−0.0795111	−	0.157886i
$289$			31.1166i			1.83039i
$290$	−16.0979	−	6.32856i	−0.945299	−	0.371626i
$291$	−1.51302	−	2.09286i	−0.0886949	−	0.122685i
$292$	3.04806	−	3.04806i	0.178374	−	0.178374i
$293$	4.27164	−	4.27164i	0.249552	−	0.249552i	−0.571235	−	0.820787i	$-0.693535\pi$
$293$	4.27164	−	4.27164i	0.249552	−	0.249552i	0.820787	+	0.571235i	$0.193535\pi$
$294$	−8.42241	−	11.6501i	−0.491205	−	0.679449i
$295$	28.0061	−	12.1999i	1.63058	−	0.710305i
$296$			1.63851i			0.0952366i
$297$	−20.2006	−	10.4734i	−1.17216	−	0.607729i
$298$	−10.1958	−	10.1958i	−0.590629	−	0.590629i
$299$	0.693785			0.0401226
$300$	−6.82975	+	5.32490i	−0.394316	+	0.307433i
$301$	−12.3215			−0.710199
$302$	−8.87711	−	8.87711i	−0.510820	−	0.510820i
$303$	2.26333	+	0.363950i	0.130025	+	0.0209084i
$304$			1.00000i			0.0573539i
$305$	26.7915	−	11.6708i	1.53408	−	0.668267i
$306$	6.52387	−	19.7608i	0.372945	−	1.12965i
$307$	−12.5877	+	12.5877i	−0.718417	+	0.718417i	−0.968281	−	0.249864i	$-0.919614\pi$
$307$	−12.5877	+	12.5877i	−0.718417	+	0.718417i	0.249864	+	0.968281i	$0.419614\pi$
$308$	12.1118	−	12.1118i	0.690136	−	0.690136i
$309$	−17.6281	+	12.7441i	−1.00283	+	0.724988i
$310$	9.98914	+	3.92704i	0.567345	+	0.223041i
$311$		−	2.19199i		−	0.124296i	−0.998067	−	0.0621481i	$-0.980205\pi$
$311$		−	2.19199i		−	0.124296i	0.998067	−	0.0621481i	$-0.0197951\pi$
$312$	0.0333871	−	0.207627i	0.00189017	−	0.0117546i
$313$	12.2938	+	12.2938i	0.694888	+	0.694888i	0.963303	−	0.268416i	$-0.0865001\pi$
$313$	12.2938	+	12.2938i	0.694888	+	0.694888i	−0.268416	+	0.963303i	$0.586500\pi$
$314$	12.8510			0.725224
$315$	−16.7719	+	20.1792i	−0.944987	+	1.13697i
$316$	1.24732			0.0701671
$317$	5.00014	+	5.00014i	0.280836	+	0.280836i	0.833442	−	0.552606i	$-0.186367\pi$
$317$	5.00014	+	5.00014i	0.280836	+	0.280836i	−0.552606	+	0.833442i	$0.686367\pi$
$318$	−0.629471	+	3.91455i	−0.0352990	+	0.219517i
$319$		−	33.8743i		−	1.89660i
$320$	−0.893014	−	2.05001i	−0.0499210	−	0.114599i
$321$	−13.9447	+	10.0813i	−0.778317	+	0.562681i
$322$	15.8047	−	15.8047i	0.880761	−	0.880761i
$323$	−4.90493	+	4.90493i	−0.272917	+	0.272917i
$324$	−5.35852	+	7.23092i	−0.297695	+	0.401718i
$325$	−0.606669	+	0.0220054i	−0.0336520	+	0.00122064i
$326$			4.21322i			0.233348i
$327$	−0.382561	−	0.0615169i	−0.0211557	−	0.00340189i
$328$	−2.82471	−	2.82471i	−0.155969	−	0.155969i
$329$	51.8605			2.85916
$330$	−14.5988	−	8.63246i	−0.803635	−	0.475201i
$331$	15.5843			0.856592			0.428296	−	0.903639i	$-0.359114\pi$
$331$	15.5843			0.856592			0.428296	+	0.903639i	$0.359114\pi$
$332$	−9.27133	−	9.27133i	−0.508830	−	0.508830i
$333$	4.39025	−	2.21092i	0.240584	−	0.121158i
$334$			9.42471i			0.515697i
$335$	−11.0834	+	28.1927i	−0.605552	+	1.54033i
$336$	−3.96926	−	5.49040i	−0.216541	−	0.299526i
$337$	−12.8769	+	12.8769i	−0.701449	+	0.701449i	−0.964722	−	0.263272i	$-0.915198\pi$
$337$	−12.8769	+	12.8769i	−0.701449	+	0.701449i	0.263272	+	0.964722i	$0.415198\pi$
$338$	−9.18196	+	9.18196i	−0.499433	+	0.499433i
$339$	7.03634	+	9.73288i	0.382162	+	0.528618i
$340$	5.67496	−	14.4353i	0.307768	−	0.782864i
$341$			21.0199i			1.13829i
$342$	2.67941	−	1.34935i	0.144886	−	0.0729644i
$343$	−3.59519	−	3.59519i	−0.194122	−	0.194122i
$344$	−3.15007			−0.169840
$345$	−19.0499	−	11.2645i	−1.02561	−	0.606459i
$346$	−4.71178			−0.253307
$347$	−5.40671	−	5.40671i	−0.290247	−	0.290247i	0.546931	−	0.837178i	$-0.315796\pi$
$347$	−5.40671	−	5.40671i	−0.290247	−	0.290247i	−0.837178	+	0.546931i	$0.815796\pi$
$348$	−13.2284	−	2.12716i	−0.709116	−	0.114028i
$349$		−	4.70970i		−	0.252104i	−0.992024	−	0.126052i	$-0.959769\pi$
$349$		−	4.70970i		−	0.252104i	0.992024	−	0.126052i	$-0.0402307\pi$
$350$	−13.3189	+	14.3215i	−0.711923	+	0.765514i
$351$	−0.601370	+	0.190704i	−0.0320988	+	0.0101790i
$352$	3.09646	−	3.09646i	0.165042	−	0.165042i
$353$	−1.82994	+	1.82994i	−0.0973976	+	0.0973976i	−0.754127	−	0.656729i	$-0.771940\pi$
$353$	−1.82994	+	1.82994i	−0.0973976	+	0.0973976i	0.656729	+	0.754127i	$0.271940\pi$
$354$	19.1760	−	13.8632i	1.01919	−	0.736821i
$355$	9.03015	+	20.7296i	0.479271	+	1.10022i
$356$			4.47665i			0.237262i
$357$	7.46109	−	46.3990i	0.394883	−	2.45569i
$358$	14.4197	+	14.4197i	0.762105	+	0.762105i
$359$	9.20818			0.485989			0.242995	−	0.970028i	$-0.421870\pi$
$359$	9.20818			0.485989			0.242995	+	0.970028i	$0.421870\pi$
$360$	−4.28783	+	5.15893i	−0.225988	+	0.271899i
$361$	−1.00000			−0.0526316
$362$	14.0006	+	14.0006i	0.735855	+	0.735855i
$363$	2.24834	−	13.9820i	0.118007	−	0.733863i
$364$		−	0.474910i		−	0.0248920i
$365$	−8.97050	−	3.52658i	−0.469537	−	0.184590i
$366$	18.3443	−	13.2620i	0.958874	−	0.693214i
$367$	14.0925	−	14.0925i	0.735621	−	0.735621i	−0.236107	−	0.971727i	$-0.575871\pi$
$367$	14.0925	−	14.0925i	0.735621	−	0.735621i	0.971727	+	0.236107i	$0.0758715\pi$
$368$	4.04057	−	4.04057i	0.210629	−	0.210629i
$369$	−3.75705	+	11.3801i	−0.195584	+	0.592424i
$370$	3.35896	−	1.46321i	0.174624	−	0.0760689i
$371$			8.95381i			0.464859i
$372$	8.20856	+	1.31996i	0.425594	+	0.0684368i
$373$	−6.94081	−	6.94081i	−0.359382	−	0.359382i	0.504203	−	0.863585i	$-0.331786\pi$
$373$	−6.94081	−	6.94081i	−0.359382	−	0.359382i	−0.863585	+	0.504203i	$0.831786\pi$
$374$	30.3759			1.57070
$375$	17.0151	+	9.24581i	0.878658	+	0.477452i
$376$	13.2585			0.683754
$377$	−0.664113	−	0.664113i	−0.0342036	−	0.0342036i
$378$	−9.35515	+	18.0438i	−0.481177	+	0.928071i
$379$		−	34.8937i		−	1.79237i	−0.443683	−	0.896184i	$-0.646329\pi$
$379$		−	34.8937i		−	1.79237i	0.443683	−	0.896184i	$-0.353671\pi$
$380$	2.05001	−	0.893014i	0.105163	−	0.0458107i
$381$	2.46042	+	3.40333i	0.126051	+	0.174358i
$382$	11.3808	−	11.3808i	0.582292	−	0.582292i
$383$	−3.00238	+	3.00238i	−0.153415	+	0.153415i	−0.779641	−	0.626227i	$-0.784599\pi$
$383$	−3.00238	+	3.00238i	−0.153415	+	0.153415i	0.626227	+	0.779641i	$0.284599\pi$
$384$	−1.01477	−	1.40366i	−0.0517846	−	0.0716300i
$385$	−35.6454	−	14.0133i	−1.81666	−	0.714184i
$386$			3.89801i			0.198404i
$387$	4.25054	+	8.44033i	0.216067	+	0.429046i
$388$	−1.05430	−	1.05430i	−0.0535239	−	0.0535239i
$389$	4.18737			0.212308			0.106154	−	0.994350i	$-0.466146\pi$
$389$	4.18737			0.212308			0.106154	+	0.994350i	$0.466146\pi$
$390$	−0.455453	+	0.116970i	−0.0230627	+	0.00592303i
$391$	39.6374			2.00455
$392$	−5.86888	−	5.86888i	−0.296423	−	0.296423i
$393$	−1.76928	−	0.284505i	−0.0892483	−	0.0143514i
$394$			13.4760i			0.678913i
$395$	−1.11387	−	2.55701i	−0.0560450	−	0.128657i
$396$	−12.4749	−	4.11850i	−0.626888	−	0.206963i
$397$	−6.47953	+	6.47953i	−0.325198	+	0.325198i	−0.850757	−	0.525559i	$-0.823856\pi$
$397$	−6.47953	+	6.47953i	−0.325198	+	0.325198i	0.525559	+	0.850757i	$0.323856\pi$
$398$	5.38642	−	5.38642i	0.269997	−	0.269997i
$399$	5.49040	−	3.96926i	0.274864	−	0.198712i
$400$	−3.40505	+	3.66137i	−0.170253	+	0.183068i
$401$			12.0856i			0.603528i	0.953383	+	0.301764i	$0.0975754\pi$
$401$			12.0856i			0.603528i	−0.953383	+	0.301764i	$0.902425\pi$
$402$	−3.72537	+	23.1673i	−0.185805	+	1.15548i
$403$	0.412100	+	0.412100i	0.0205281	+	0.0205281i
$404$	1.32352			0.0658476
$405$	19.6087	+	4.52768i	0.974363	+	0.224982i
$406$	−30.2575			−1.50166
$407$	5.07360	+	5.07360i	0.251489	+	0.251489i
$408$	1.90747	−	11.8622i	0.0944340	−	0.587266i
$409$			14.2278i			0.703521i	0.936090	+	0.351760i	$0.114417\pi$
$409$			14.2278i			0.703521i	−0.936090	+	0.351760i	$0.885583\pi$
$410$	−3.26817	+	8.31318i	−0.161403	+	0.410559i
$411$	−7.75196	+	5.60424i	−0.382376	+	0.276437i
$412$	−8.88033	+	8.88033i	−0.437502	+	0.437502i
$413$	37.7856	−	37.7856i	1.85931	−	1.85931i
$414$	−16.2785	−	5.37422i	−0.800044	−	0.264129i
$415$	−10.7269	+	27.2857i	−0.526561	+	1.33940i
$416$		−	0.121414i		−	0.00595279i
$417$	−1.51284	−	0.243269i	−0.0740841	−	0.0119129i
$418$	3.09646	+	3.09646i	0.151453	+	0.151453i
$419$	−27.8666			−1.36137			−0.680686	−	0.732576i	$-0.738318\pi$
$419$	−27.8666			−1.36137			−0.680686	+	0.732576i	$0.738318\pi$
$420$	−7.71075	+	13.0400i	−0.376246	+	0.636288i
$421$	30.3012			1.47679			0.738396	−	0.674368i	$-0.235584\pi$
$421$	30.3012			1.47679			0.738396	+	0.674368i	$0.235584\pi$
$422$	−3.91878	−	3.91878i	−0.190763	−	0.190763i
$423$	−17.8903	−	35.5249i	−0.869856	−	1.72728i
$424$			2.28910i			0.111168i
$425$	−34.6603	+	1.25721i	−1.68127	+	0.0609838i
$426$	10.2613	+	14.1938i	0.497162	+	0.687690i
$427$	36.1468	−	36.1468i	1.74927	−	1.74927i
$428$	−7.02479	+	7.02479i	−0.339556	+	0.339556i
$429$	−0.539529	−	0.746293i	−0.0260487	−	0.0360314i
$430$	2.81305	+	6.45766i	0.135658	+	0.311416i
$431$			23.2155i			1.11825i	0.829082	+	0.559126i	$0.188863\pi$
$431$			23.2155i			1.11825i	−0.829082	+	0.559126i	$0.811137\pi$
$432$	−2.39170	+	4.61300i	−0.115071	+	0.221943i
$433$	20.5816	+	20.5816i	0.989090	+	0.989090i	0.999941	−	0.0108515i	$-0.00345420\pi$
$433$	20.5816	+	20.5816i	0.989090	+	0.989090i	−0.0108515	+	0.999941i	$0.503454\pi$
$434$	18.7756			0.901257
$435$	7.45243	+	29.0179i	0.357317	+	1.39130i
$436$	−0.223709			−0.0107137
$437$	4.04057	+	4.04057i	0.193287	+	0.193287i
$438$	−7.37149	−	1.18536i	−0.352223	−	0.0566386i
$439$			29.7544i			1.42010i	0.704151	+	0.710050i	$0.251328\pi$
$439$			29.7544i			1.42010i	−0.704151	+	0.710050i	$0.748672\pi$
$440$	−9.11296	−	3.58259i	−0.434443	−	0.170793i
$441$	−7.80600	+	23.6443i	−0.371714	+	1.12592i
$442$	0.595525	−	0.595525i	0.0283262	−	0.0283262i
$443$	12.8988	−	12.8988i	0.612842	−	0.612842i	−0.330844	−	0.943686i	$-0.607333\pi$
$443$	12.8988	−	12.8988i	0.612842	−	0.612842i	0.943686	+	0.330844i	$0.107333\pi$
$444$	2.29991	−	1.66271i	0.109149	−	0.0789086i
$445$	9.17717	−	3.99771i	0.435040	−	0.189510i
$446$		−	13.4784i		−	0.638219i
$447$	−3.96505	+	24.6578i	−0.187541	+	1.16628i
$448$	−2.76585	−	2.76585i	−0.130674	−	0.130674i
$449$	−6.08743			−0.287284			−0.143642	−	0.989630i	$-0.545881\pi$
$449$	−6.08743			−0.287284			−0.143642	+	0.989630i	$0.545881\pi$
$450$	14.4049	+	4.18308i	0.679055	+	0.197192i
$451$	−17.4932			−0.823725
$452$	4.90305	+	4.90305i	0.230620	+	0.230620i
$453$	−3.45221	+	21.4686i	−0.162199	+	1.00868i
$454$			19.4501i			0.912836i
$455$	−0.973568	+	0.424101i	−0.0456416	+	0.0198822i
$456$	1.40366	−	1.01477i	0.0657322	−	0.0475208i
$457$	13.6315	−	13.6315i	0.637656	−	0.637656i	−0.312321	−	0.949977i	$-0.601106\pi$
$457$	13.6315	−	13.6315i	0.637656	−	0.637656i	0.949977	+	0.312321i	$0.101106\pi$
$458$	−4.59237	+	4.59237i	−0.214588	+	0.214588i
$459$	−34.3575	+	10.8953i	−1.60367	+	0.508549i
$460$	−11.8915	−	4.67491i	−0.554443	−	0.217969i
$461$			20.6355i			0.961091i	0.876970	+	0.480546i	$0.159561\pi$
$461$			20.6355i			0.961091i	−0.876970	+	0.480546i	$0.840439\pi$
$462$	−29.2915	−	4.71016i	−1.36276	−	0.219137i
$463$	1.47081	+	1.47081i	0.0683543	+	0.0683543i	0.740458	−	0.672103i	$-0.234609\pi$
$463$	1.47081	+	1.47081i	0.0683543	+	0.0683543i	−0.672103	+	0.740458i	$0.734609\pi$
$464$	−7.73552			−0.359113
$465$	−4.62443	−	18.0063i	−0.214453	−	0.835024i
$466$	−11.2384			−0.520608
$467$	24.9074	+	24.9074i	1.15258	+	1.15258i	0.986035	+	0.166541i	$0.0532597\pi$
$467$	24.9074	+	24.9074i	1.15258	+	1.15258i	0.166541	+	0.986035i	$0.446740\pi$
$468$	−0.325317	+	0.163829i	−0.0150378	+	0.00757301i
$469$			52.9910i			2.44690i
$470$	−11.8400	−	27.1800i	−0.546139	−	1.25372i
$471$	−13.0408	−	18.0384i	−0.600887	−	0.831165i
$472$	9.66012	−	9.66012i	0.444643	−	0.444643i
$473$	−9.75407	+	9.75407i	−0.448493	+	0.448493i
$474$	−1.26574	−	1.75080i	−0.0581372	−	0.0804171i
$475$	−3.66137	−	3.40505i	−0.167995	−	0.156235i
$476$		−	27.1326i		−	1.24362i
$477$	6.13344	−	3.08879i	0.280831	−	0.141426i
$478$	5.31171	+	5.31171i	0.242952	+	0.242952i
$479$	−11.4278			−0.522150			−0.261075	−	0.965318i	$-0.584077\pi$
$479$	−11.4278			−0.522150			−0.261075	+	0.965318i	$0.584077\pi$
$480$	−1.97130	+	3.33376i	−0.0899772	+	0.152165i
$481$	0.198938			0.00907078
$482$	−7.92744	−	7.92744i	−0.361085	−	0.361085i
$483$	−38.2224	−	6.14628i	−1.73918	−	0.279665i
$484$		−	8.17619i		−	0.371645i
$485$	−1.21982	+	3.10282i	−0.0553890	+	0.140892i
$486$	15.5874	+	0.183816i	0.707058	+	0.00833808i
$487$	−6.40458	+	6.40458i	−0.290219	+	0.290219i	−0.837167	−	0.546948i	$-0.815790\pi$
$487$	−6.40458	+	6.40458i	−0.290219	+	0.290219i	0.546948	+	0.837167i	$0.315790\pi$
$488$	9.24116	−	9.24116i	0.418328	−	0.418328i
$489$	5.91390	−	4.27543i	0.267436	−	0.193342i
$490$	−6.79025	+	17.2722i	−0.306752	+	0.780280i
$491$		−	8.15301i		−	0.367940i	−0.982932	−	0.183970i	$-0.941105\pi$
$491$		−	8.15301i		−	0.367940i	0.982932	−	0.183970i	$-0.0588950\pi$
$492$	−1.09850	+	6.83135i	−0.0495242	+	0.307981i
$493$	−37.9422	−	37.9422i	−1.70883	−	1.70883i
$494$	0.121414			0.00546266
$495$	2.69732	+	29.2515i	0.121236	+	1.31476i
$496$	4.80009			0.215531
$497$	27.9683	+	27.9683i	1.25455	+	1.25455i
$498$	−3.60552	+	22.4220i	−0.161567	+	1.00475i
$499$		−	1.46257i		−	0.0654738i	−0.999464	−	0.0327369i	$-0.989578\pi$
$499$		−	1.46257i		−	0.0654738i	0.999464	−	0.0327369i	$-0.0104223\pi$
$500$	10.5466	+	3.71073i	0.471658	+	0.165949i
$501$	13.2290	−	9.56387i	0.591030	−	0.427282i
$502$	−7.60679	+	7.60679i	−0.339508	+	0.339508i
$503$	−27.1555	+	27.1555i	−1.21081	+	1.21081i	−0.240043	+	0.970762i	$0.577161\pi$
$503$	−27.1555	+	27.1555i	−1.21081	+	1.21081i	−0.970762	+	0.240043i	$0.922839\pi$
$504$	−3.67876	+	11.1430i	−0.163865	+	0.496346i
$505$	−1.18192	−	2.71323i	−0.0525949	−	0.120737i
$506$		−	25.0230i		−	1.11241i
$507$	22.2059	+	3.57077i	0.986197	+	0.158583i
$508$	1.71446	+	1.71446i	0.0760670	+	0.0760670i
$509$	3.41038			0.151162			0.0755812	−	0.997140i	$-0.475919\pi$
$509$	3.41038			0.151162			0.0755812	+	0.997140i	$0.475919\pi$
$510$	−26.0209	+	6.68276i	−1.15223	+	0.295918i
$511$	−16.8609			−0.745884
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.61300	−	2.39170i	−0.203669	−	0.105596i
$514$			3.78581i			0.166985i
$515$	26.1350	+	10.2745i	1.15165	+	0.452747i
$516$	3.19658	+	4.42161i	0.140722	+	0.194651i
$517$	41.0544	−	41.0544i	1.80557	−	1.80557i
$518$	4.53188	−	4.53188i	0.199119	−	0.199119i
$519$	4.78135	+	6.61371i	0.209878	+	0.290310i
$520$	−0.248899	+	0.108424i	−0.0109149	+	0.00475471i
$521$		−	26.3131i		−	1.15280i	−0.817169	−	0.576399i	$-0.804457\pi$
$521$		−	26.3131i		−	1.15280i	0.817169	−	0.576399i	$-0.195543\pi$
$522$	10.4379	+	20.7267i	0.456855	+	0.907182i
$523$	1.67071	+	1.67071i	0.0730549	+	0.0730549i	0.742690	−	0.669635i	$-0.233550\pi$
$523$	1.67071	+	1.67071i	0.0730549	+	0.0730549i	−0.669635	+	0.742690i	$0.733550\pi$
$524$	−1.03462			−0.0451974
$525$	33.6179	+	4.16218i	1.46721	+	0.181652i
$526$	−23.7107			−1.03384
$527$	23.5441	+	23.5441i	1.02560	+	1.02560i
$528$	−7.48856	−	1.20418i	−0.325898	−	0.0524053i
$529$		−	9.65240i		−	0.419669i
$530$	4.69267	−	2.04420i	0.203836	−	0.0887942i
$531$	−38.9183	−	12.8486i	−1.68891	−	0.557582i
$532$	2.76585	−	2.76585i	0.119915	−	0.119915i
$533$	−0.342959	+	0.342959i	−0.0148552	+	0.0148552i
$534$	6.28368	−	4.54276i	0.271921	−	0.196584i
$535$	20.6741	+	8.12763i	0.893819	+	0.351388i
$536$			13.5475i			0.585162i
$537$	5.60767	−	34.8729i	0.241989	−	1.50488i
$538$	8.87418	+	8.87418i	0.382593	+	0.382593i
$539$	−36.3456			−1.56551
$540$	11.5925	+	0.783531i	0.498862	+	0.0337178i
$541$	−23.9511			−1.02974			−0.514870	−	0.857269i	$-0.672160\pi$
$541$	−23.9511			−1.02974			−0.514870	+	0.857269i	$0.672160\pi$
$542$	9.17134	+	9.17134i	0.393943	+	0.393943i
$543$	5.44469	−	33.8594i	0.233654	−	1.45304i
$544$		−	6.93661i		−	0.297405i
$545$	0.199775	+	0.458605i	0.00855743	+	0.0196445i
$546$	−0.666610	+	0.481922i	−0.0285283	+	0.0206244i
$547$	−18.6458	+	18.6458i	−0.797236	+	0.797236i	−0.982659	−	0.185423i	$-0.940634\pi$
$547$	−18.6458	+	18.6458i	−0.797236	+	0.797236i	0.185423	+	0.982659i	$0.440634\pi$
$548$	−3.90513	+	3.90513i	−0.166819	+	0.166819i
$549$	−37.2304	−	12.2914i	−1.58896	−	0.524582i
$550$	0.793675	+	21.8809i	0.0338424	+	0.933006i
$551$		−	7.73552i		−	0.329544i
$552$	−9.77180	−	1.57133i	−0.415915	−	0.0668804i
$553$	−3.44989	−	3.44989i	−0.146704	−	0.146704i
$554$	−14.4590			−0.614306
$555$	−5.46241	−	3.23000i	−0.231866	−	0.137106i
$556$	−0.884659			−0.0375179
$557$	−4.22121	−	4.22121i	−0.178859	−	0.178859i	0.612000	−	0.790858i	$-0.290365\pi$
$557$	−4.22121	−	4.22121i	−0.178859	−	0.178859i	−0.790858	+	0.612000i	$0.790365\pi$
$558$	−6.47700	−	12.8614i	−0.274193	−	0.544468i
$559$			0.382461i			0.0161764i
$560$	−3.20007	+	8.13995i	−0.135228	+	0.343976i
$561$	−30.8244	−	42.6373i	−1.30141	−	1.80015i
$562$	−2.46184	+	2.46184i	−0.103846	+	0.103846i
$563$	11.0358	−	11.0358i	0.465105	−	0.465105i	−0.435219	−	0.900325i	$-0.643329\pi$
$563$	11.0358	−	11.0358i	0.465105	−	0.465105i	0.900325	+	0.435219i	$0.143329\pi$
$564$	−13.4543	−	18.6103i	−0.566526	−	0.783636i
$565$	5.67279	−	14.4298i	0.238656	−	0.607065i
$566$			4.85720i			0.204164i
$567$	34.8205	−	5.17879i	1.46232	−	0.217489i
$568$	7.15026	+	7.15026i	0.300018	+	0.300018i
$569$	16.3299			0.684585			0.342293	−	0.939593i	$-0.388797\pi$
$569$	16.3299			0.684585			0.342293	+	0.939593i	$0.388797\pi$
$570$	−3.33376	−	1.97130i	−0.139636	−	0.0825688i
$571$	28.8841			1.20876			0.604381	−	0.796695i	$-0.293421\pi$
$571$	28.8841			1.20876			0.604381	+	0.796695i	$0.293421\pi$
$572$	−0.375953	−	0.375953i	−0.0157194	−	0.0157194i
$573$	−27.5236	−	4.42587i	−1.14981	−	0.184893i
$574$			15.6255i			0.652194i
$575$	1.03566	+	28.5524i	0.0431902	+	1.19072i
$576$	−0.940499	+	2.84877i	−0.0391874	+	0.118699i
$577$	−10.6942	+	10.6942i	−0.445205	+	0.445205i	−0.893757	−	0.448552i	$-0.851940\pi$
$577$	−10.6942	+	10.6942i	−0.445205	+	0.445205i	0.448552	+	0.893757i	$0.351940\pi$
$578$	22.0028	−	22.0028i	0.915194	−	0.915194i
$579$	5.47147	−	3.95557i	0.227386	−	0.164388i
$580$	6.90793	+	15.8579i	0.286836	+	0.658462i
$581$			51.2862i			2.12771i
$582$	−0.410006	+	2.54974i	−0.0169953	+	0.105690i
$583$	7.08811	+	7.08811i	0.293560	+	0.293560i
$584$	−4.31060			−0.178374
$585$	0.626364	+	0.520601i	0.0258970	+	0.0215242i
$586$	−6.04102			−0.249552
$587$	−26.1994	−	26.1994i	−1.08136	−	1.08136i	−0.996383	−	0.0849807i	$-0.972917\pi$
$587$	−26.1994	−	26.1994i	−1.08136	−	1.08136i	−0.0849807	−	0.996383i	$-0.527083\pi$
$588$	−2.28234	+	14.1934i	−0.0941223	+	0.585327i
$589$			4.80009i			0.197784i
$590$	−28.4299	−	11.1767i	−1.17044	−	0.460137i
$591$	18.9157	−	13.6750i	0.778089	−	0.562516i
$592$	1.15860	−	1.15860i	0.0476183	−	0.0476183i
$593$	13.6587	−	13.6587i	0.560897	−	0.560897i	−0.368665	−	0.929562i	$-0.620185\pi$
$593$	13.6587	−	13.6587i	0.560897	−	0.560897i	0.929562	+	0.368665i	$0.120185\pi$
$594$	6.87817	+	21.6898i	0.282215	+	0.889944i
$595$	−55.6220	+	24.2298i	−2.28028	+	0.993324i
$596$			14.4191i			0.590629i
$597$	−13.0266	−	2.09472i	−0.533145	−	0.0857313i
$598$	−0.490580	−	0.490580i	−0.0200613	−	0.0200613i
$599$	29.0472			1.18684			0.593418	−	0.804894i	$-0.297778\pi$
$599$	29.0472			1.18684			0.593418	+	0.804894i	$0.297778\pi$
$600$	8.59463	+	1.06409i	0.350874	+	0.0434412i
$601$	−14.9410			−0.609458			−0.304729	−	0.952439i	$-0.598566\pi$
$601$	−14.9410			−0.609458			−0.304729	+	0.952439i	$0.598566\pi$
$602$	8.71261	+	8.71261i	0.355100	+	0.355100i
$603$	36.2993	−	18.2803i	1.47822	−	0.744430i
$604$			12.5541i			0.510820i
$605$	−16.7612	+	7.30145i	−0.681441	+	0.296846i
$606$	−1.34306	−	1.85777i	−0.0545583	−	0.0754666i
$607$	8.68114	−	8.68114i	0.352357	−	0.352357i	−0.508629	−	0.860986i	$-0.669848\pi$
$607$	8.68114	−	8.68114i	0.352357	−	0.352357i	0.860986	+	0.508629i	$0.169848\pi$
$608$	0.707107	−	0.707107i	0.0286770	−	0.0286770i
$609$	30.7043	+	42.4711i	1.24420	+	1.72102i
$610$	−27.1969	−	10.6920i	−1.10117	−	0.432905i
$611$		−	1.60976i		−	0.0651239i
$612$	−18.5861	+	9.35991i	−0.751297	+	0.378352i
$613$	−5.07536	−	5.07536i	−0.204992	−	0.204992i	0.597143	−	0.802135i	$-0.296303\pi$
$613$	−5.07536	−	5.07536i	−0.204992	−	0.204992i	−0.802135	+	0.597143i	$0.796303\pi$
$614$	17.8017			0.718417
$615$	14.9853	−	3.84855i	0.604265	−	0.155189i
$616$	−17.1287			−0.690136
$617$	−4.31435	−	4.31435i	−0.173689	−	0.173689i	0.614909	−	0.788598i	$-0.289193\pi$
$617$	−4.31435	−	4.31435i	−0.173689	−	0.173689i	−0.788598	+	0.614909i	$0.789193\pi$
$618$	21.4764	+	3.45346i	0.863907	+	0.138919i
$619$			6.95816i			0.279672i	0.990175	+	0.139836i	$0.0446575\pi$
$619$			6.95816i			0.279672i	−0.990175	+	0.139836i	$0.955342\pi$
$620$	−4.28655	−	9.84022i	−0.172152	−	0.395193i
$621$	8.97531	+	28.3030i	0.360167	+	1.13576i
$622$	−1.54997	+	1.54997i	−0.0621481	+	0.0621481i
$623$	12.3818	−	12.3818i	0.496064	−	0.496064i
$624$	−0.170423	+	0.123206i	−0.00682238	+	0.00493221i
$625$	−1.81124	−	24.9343i	−0.0724496	−	0.997372i
$626$		−	17.3861i		−	0.694888i
$627$	1.20418	−	7.48856i	0.0480904	−	0.299064i
$628$	−9.08703	−	9.08703i	−0.362612	−	0.362612i
$629$	11.3657			0.453181
$630$	26.1283	−	2.40932i	1.04098	−	0.0959898i
$631$	−16.5313			−0.658102			−0.329051	−	0.944312i	$-0.606729\pi$
$631$	−16.5313			−0.658102			−0.329051	+	0.944312i	$0.606729\pi$
$632$	−0.881987	−	0.881987i	−0.0350835	−	0.0350835i
$633$	−1.52397	+	9.47726i	−0.0605724	+	0.376687i
$634$		−	7.07127i		−	0.280836i
$635$	1.98362	−	5.04570i	0.0787176	−	0.200233i
$636$	3.21311	−	2.32290i	0.127408	−	0.0921090i
$637$	−0.712562	+	0.712562i	−0.0282327	+	0.0282327i
$638$	−23.9528	+	23.9528i	−0.948300	+	0.948300i
$639$	9.51031	−	28.8067i	0.376222	−	1.13958i
$640$	−0.818117	+	2.08103i	−0.0323389	+	0.0822599i
$641$		−	16.7295i		−	0.660775i	−0.943845	−	0.330388i	$-0.892820\pi$
$641$		−	16.7295i		−	0.660775i	0.943845	−	0.330388i	$-0.107180\pi$
$642$	16.9889	+	2.73187i	0.670499	+	0.107818i
$643$	21.5217	+	21.5217i	0.848733	+	0.848733i	0.989975	−	0.141242i	$-0.0451095\pi$
$643$	21.5217	+	21.5217i	0.848733	+	0.848733i	−0.141242	+	0.989975i	$0.545110\pi$
$644$	−22.3512			−0.880761
$645$	6.20974	−	10.5016i	0.244508	−	0.413499i
$646$	6.93661			0.272917
$647$	7.41491	+	7.41491i	0.291510	+	0.291510i	0.837677	−	0.546166i	$-0.183913\pi$
$647$	7.41491	+	7.41491i	0.291510	+	0.291510i	−0.546166	+	0.837677i	$0.683913\pi$
$648$	8.90208	−	1.32399i	0.349707	−	0.0520113i
$649$		−	59.8244i		−	2.34831i
$650$	0.444540	+	0.413420i	0.0174363	+	0.0162157i
$651$	−19.0528	−	26.3545i	−0.746739	−	1.03291i
$652$	2.97919	−	2.97919i	0.116674	−	0.116674i
$653$	−19.0621	+	19.0621i	−0.745959	+	0.745959i	−0.973718	−	0.227758i	$-0.926860\pi$
$653$	−19.0621	+	19.0621i	−0.745959	+	0.745959i	0.227758	+	0.973718i	$0.426860\pi$
$654$	0.227012	+	0.314010i	0.00887688	+	0.0122788i
$655$	0.923926	+	2.12097i	0.0361008	+	0.0828731i
$656$			3.99475i			0.155969i
$657$	5.81651	+	11.5499i	0.226924	+	0.450604i
$658$	−36.6709	−	36.6709i	−1.42958	−	1.42958i
$659$	−43.8126			−1.70670			−0.853349	−	0.521341i	$-0.825432\pi$
$659$	−43.8126			−1.70670			−0.853349	+	0.521341i	$0.825432\pi$
$660$	4.21881	+	16.4269i	0.164217	+	0.639418i
$661$	−16.9162			−0.657963			−0.328982	−	0.944336i	$-0.606705\pi$
$661$	−16.9162			−0.657963			−0.328982	+	0.944336i	$0.606705\pi$
$662$	−11.0198	−	11.0198i	−0.428296	−	0.428296i
$663$	−1.44023	−	0.231593i	−0.0559339	−	0.00899434i
$664$			13.1116i			0.508830i
$665$	−8.13995	−	3.20007i	−0.315654	−	0.124093i
$666$	−4.66774	−	1.54102i	−0.180871	−	0.0597133i
$667$	−31.2559	+	31.2559i	−1.21023	+	1.21023i
$668$	6.66427	−	6.66427i	0.257848	−	0.257848i
$669$	−18.9190	+	13.6774i	−0.731451	+	0.528799i
$670$	27.7724	−	12.0981i	1.07294	−	0.467390i
$671$		−	57.2299i		−	2.20933i
$672$	−1.07561	+	6.68899i	−0.0414925	+	0.258033i
$673$	−29.1932	−	29.1932i	−1.12532	−	1.12532i	−0.990929	−	0.134386i	$-0.957094\pi$
$673$	−29.1932	−	29.1932i	−1.12532	−	1.12532i	−0.134386	−	0.990929i	$-0.542906\pi$
$674$	18.2107			0.701449
$675$	−8.74602	−	24.4644i	−0.336635	−	0.941635i
$676$	12.9853			0.499433
$677$	10.7238	+	10.7238i	0.412148	+	0.412148i	0.882486	−	0.470338i	$-0.155868\pi$
$677$	10.7238	+	10.7238i	0.412148	+	0.412148i	−0.470338	+	0.882486i	$0.655868\pi$
$678$	1.90674	−	11.8576i	0.0732280	−	0.455390i
$679$			5.83207i			0.223814i
$680$	−14.2201	+	6.19449i	−0.545316	+	0.237548i
$681$	27.3012	−	19.7373i	1.04618	−	0.756333i
$682$	14.8633	−	14.8633i	0.569146	−	0.569146i
$683$	−35.6719	+	35.6719i	−1.36495	+	1.36495i	−0.497459	+	0.867488i	$0.665733\pi$
$683$	−35.6719	+	35.6719i	−1.36495	+	1.36495i	−0.867488	+	0.497459i	$0.834267\pi$
$684$	−2.84877	−	0.940499i	−0.108925	−	0.0359609i
$685$	11.4929	+	4.51821i	0.439121	+	0.172632i
$686$			5.08436i			0.194122i
$687$	11.1063	+	1.78593i	0.423732	+	0.0681373i
$688$	2.22743	+	2.22743i	0.0849201	+	0.0849201i
$689$	0.277928			0.0105882
$690$	5.50511	+	21.4355i	0.209576	+	0.816035i
$691$	−26.9995			−1.02711			−0.513554	−	0.858057i	$-0.671671\pi$
$691$	−26.9995			−1.02711			−0.513554	+	0.858057i	$0.671671\pi$
$692$	3.33173	+	3.33173i	0.126653	+	0.126653i
$693$	23.1126	+	45.8949i	0.877975	+	1.74340i
$694$			7.64624i			0.290247i
$695$	0.790013	+	1.81356i	0.0299669	+	0.0687921i
$696$	7.84975	+	10.8580i	0.297544	+	0.411572i
$697$	−19.5939	+	19.5939i	−0.742173	+	0.742173i
$698$	−3.33026	+	3.33026i	−0.126052	+	0.126052i
$699$	11.4043	+	15.7748i	0.431351	+	0.596658i
$700$	19.5447	−	0.708933i	0.738719	−	0.0267951i
$701$			43.3103i			1.63581i	0.575354	+	0.817905i	$0.304864\pi$
$701$			43.3103i			1.63581i	−0.575354	+	0.817905i	$0.695136\pi$
$702$	0.560081	+	0.290385i	0.0211389	+	0.0109599i
$703$	1.15860	+	1.15860i	0.0436975	+	0.0436975i
$704$	−4.37906			−0.165042
$705$	−26.1365	+	44.2006i	−0.984356	+	1.66469i
$706$	2.58792			0.0973976
$707$	−3.66066	−	3.66066i	−0.137673	−	0.137673i
$708$	−23.3622	−	3.75672i	−0.878007	−	0.141186i
$709$			5.62201i			0.211139i	0.994412	+	0.105569i	$0.0336665\pi$
$709$			5.62201i			0.211139i	−0.994412	+	0.105569i	$0.966333\pi$
$710$	8.27279	−	21.0434i	0.310472	−	0.789743i
$711$	−1.17310	+	3.55331i	−0.0439947	+	0.133260i
$712$	3.16547	−	3.16547i	0.118631	−	0.118631i
$713$	19.3951	−	19.3951i	0.726353	−	0.726353i
$714$	−38.0848	+	27.5332i	−1.42529	+	1.03041i
$715$	−0.434975	+	1.10644i	−0.0162671	+	0.0413784i
$716$		−	20.3926i		−	0.762105i
$717$	2.06567	−	12.8459i	0.0771437	−	0.479741i
$718$	−6.51117	−	6.51117i	−0.242995	−	0.242995i
$719$	36.9146			1.37668			0.688340	−	0.725388i	$-0.258340\pi$
$719$	36.9146			1.37668			0.688340	+	0.725388i	$0.258340\pi$
$720$	6.67986	−	0.615959i	0.248944	−	0.0229554i
$721$	49.1233			1.82945
$722$	0.707107	+	0.707107i	0.0263158	+	0.0263158i
$723$	−3.08290	+	19.1719i	−0.114654	+	0.713010i
$724$		−	19.7998i		−	0.735855i
$725$	26.3399	−	28.3226i	0.978238	−	1.05188i
$726$	−11.4766	+	8.29692i	−0.425935	+	0.307928i
$727$	23.0361	−	23.0361i	0.854362	−	0.854362i	−0.136305	−	0.990667i	$-0.543523\pi$
$727$	23.0361	−	23.0361i	0.854362	−	0.854362i	0.990667	+	0.136305i	$0.0435227\pi$
$728$	−0.335812	+	0.335812i	−0.0124460	+	0.0124460i
$729$	−15.5595	−	22.0658i	−0.576279	−	0.817253i
$730$	3.84943	+	8.83677i	0.142474	+	0.327063i
$731$			21.8508i			0.808181i
$732$	−22.3490	−	3.59379i	−0.826044	−	0.132830i
$733$	−32.4240	−	32.4240i	−1.19761	−	1.19761i	−0.974881	−	0.222726i	$-0.928505\pi$
$733$	−32.4240	−	32.4240i	−1.19761	−	1.19761i	−0.222726	−	0.974881i	$-0.571495\pi$
$734$	−19.9298			−0.735621
$735$	31.1348	−	7.99611i	1.14842	−	0.294941i
$736$	−5.71423			−0.210629
$737$	41.9493	+	41.9493i	1.54522	+	1.54522i
$738$	10.7036	−	5.39030i	0.394004	−	0.198420i
$739$		−	36.8773i		−	1.35655i	−0.734806	−	0.678277i	$-0.762727\pi$
$739$		−	36.8773i		−	1.35655i	0.734806	−	0.678277i	$-0.237273\pi$
$740$	−3.40979	−	1.34050i	−0.125346	−	0.0492776i
$741$	−0.123206	−	0.170423i	−0.00452610	−	0.00626064i
$742$	6.33130	−	6.33130i	0.232429	−	0.232429i
$743$	−25.4177	+	25.4177i	−0.932483	+	0.932483i	−0.997861	−	0.0653772i	$-0.979175\pi$
$743$	−25.4177	+	25.4177i	−0.932483	+	0.932483i	0.0653772	+	0.997861i	$0.479175\pi$
$744$	−4.87097	−	6.73768i	−0.178579	−	0.247015i
$745$	29.5592	−	12.8765i	1.08297	−	0.471757i
$746$			9.81579i			0.359382i
$747$	35.1315	−	17.6922i	1.28540	−	0.647323i
$748$	−21.4790	−	21.4790i	−0.785349	−	0.785349i
$749$	38.8590			1.41988
$750$	−5.49374	−	18.5693i	−0.200603	−	0.678055i
$751$	4.92408			0.179682			0.0898412	−	0.995956i	$-0.471364\pi$
$751$	4.92408			0.179682			0.0898412	+	0.995956i	$0.471364\pi$
$752$	−9.37516	−	9.37516i	−0.341877	−	0.341877i
$753$	18.3964	+	2.95820i	0.670403	+	0.107803i
$754$			0.939198i			0.0342036i
$755$	25.7361	−	11.2110i	0.936631	−	0.408011i
$756$	19.3740	−	6.14378i	0.704624	−	0.223447i
$757$	13.6895	−	13.6895i	0.497555	−	0.497555i	−0.413121	−	0.910676i	$-0.635561\pi$
$757$	13.6895	−	13.6895i	0.497555	−	0.497555i	0.910676	+	0.413121i	$0.135561\pi$
$758$	−24.6735	+	24.6735i	−0.896184	+	0.896184i
$759$	−35.1236	+	25.3925i	−1.27491	+	0.921688i
$760$	−2.08103	−	0.818117i	−0.0754869	−	0.0296762i
$761$		−	20.7833i		−	0.753394i	−0.926337	−	0.376697i	$-0.877060\pi$
$761$		−	20.7833i		−	0.753394i	0.926337	−	0.376697i	$-0.122940\pi$
$762$	0.666737	−	4.14630i	0.0241533	−	0.150204i
$763$	0.618745	+	0.618745i	0.0224001	+	0.0224001i
$764$	−16.0949			−0.582292
$765$	35.7855	+	29.7430i	1.29383	+	1.07536i
$766$	4.24601			0.153415
$767$	−1.17287	−	1.17287i	−0.0423499	−	0.0423499i
$768$	−0.274986	+	1.71008i	−0.00992271	+	0.0617073i
$769$			41.2077i			1.48599i	0.669297	+	0.742995i	$0.266595\pi$
$769$			41.2077i			1.48599i	−0.669297	+	0.742995i	$0.733405\pi$
$770$	15.2962	+	35.1140i	0.551236	+	1.26542i
$771$	5.31397	−	3.84171i	0.191378	−	0.138356i
$772$	2.75631	−	2.75631i	0.0992018	−	0.0992018i
$773$	12.8806	−	12.8806i	0.463282	−	0.463282i	−0.436448	−	0.899729i	$-0.643764\pi$
$773$	12.8806	−	12.8806i	0.463282	−	0.463282i	0.899729	+	0.436448i	$0.143764\pi$
$774$	2.96263	−	8.97380i	0.106490	−	0.322557i
$775$	−16.3446	+	17.5749i	−0.587114	+	0.631310i
$776$			1.49100i			0.0535239i
$777$	−10.9600	−	1.76240i	−0.393188	−	0.0632257i
$778$	−2.96092	−	2.96092i	−0.106154	−	0.106154i
$779$	−3.99475			−0.143127
$780$	0.404764	+	0.239343i	0.0144929	+	0.00856985i
$781$	44.2811			1.58450
$782$	−28.0279	−	28.0279i	−1.00227	−	1.00227i
$783$	18.5011	−	35.6840i	0.661174	−	1.27524i
$784$			8.29985i			0.296423i
$785$	−10.5136	+	26.7433i	−0.375247	+	0.954510i
$786$	1.04989	+	1.45224i	0.0374484	+	0.0517998i
$787$	−20.6001	+	20.6001i	−0.734316	+	0.734316i	−0.971472	−	0.237156i	$-0.923785\pi$
$787$	−20.6001	+	20.6001i	−0.734316	+	0.734316i	0.237156	+	0.971472i	$0.423785\pi$
$788$	9.52900	−	9.52900i	0.339457	−	0.339457i
$789$	24.0609	+	33.2817i	0.856589	+	1.18486i
$790$	−1.02045	+	2.59570i	−0.0363061	+	0.0923510i
$791$		−	27.1222i		−	0.964354i
$792$	5.90888	+	11.7333i	0.209963	+	0.416925i
$793$	−1.12200	−	1.12200i	−0.0398435	−	0.0398435i
$794$	9.16344			0.325198
$795$	−7.63131	−	4.51250i	−0.270655	−	0.160042i
$796$	−7.61755			−0.269997
$797$	−29.3132	−	29.3132i	−1.03833	−	1.03833i	−0.999236	−	0.0390930i	$-0.987553\pi$
$797$	−29.3132	−	29.3132i	−1.03833	−	1.03833i	−0.0390930	−	0.999236i	$-0.512447\pi$
$798$	−6.68899	−	1.07561i	−0.236788	−	0.0380762i
$799$		−	91.9689i		−	3.25363i
$800$	4.99671	−	0.181243i	0.176661	−	0.00640791i
$801$	−12.7529	−	4.21029i	−0.450603	−	0.148763i
$802$	8.54583	−	8.54583i	0.301764	−	0.301764i
$803$	−13.3476	+	13.3476i	−0.471028	+	0.471028i
$804$	19.0160	−	13.7475i	0.670642	−	0.484838i
$805$	19.9599	+	45.8201i	0.703496	+	1.61495i
$806$		−	0.582797i		−	0.0205281i
$807$	3.45107	−	21.4615i	0.121484	−	0.755481i
$808$	−0.935870	−	0.935870i	−0.0329238	−	0.0329238i
$809$	3.65445			0.128483			0.0642417	−	0.997934i	$-0.479537\pi$
$809$	3.65445			0.128483			0.0642417	+	0.997934i	$0.479537\pi$
$810$	−10.6639	−	17.0670i	−0.374690	−	0.599673i
$811$	5.62337			0.197463			0.0987316	−	0.995114i	$-0.468521\pi$
$811$	5.62337			0.197463			0.0987316	+	0.995114i	$0.468521\pi$
$812$	21.3953	+	21.3953i	0.750828	+	0.750828i
$813$	3.56664	−	22.1802i	0.125087	−	0.777893i
$814$		−	7.17515i		−	0.251489i
$815$	−8.76783	−	3.44690i	−0.307124	−	0.120740i
$816$	−9.73662	+	7.03904i	−0.340850	+	0.246416i
$817$	−2.22743	+	2.22743i	−0.0779280	+	0.0779280i
$818$	10.0606	−	10.0606i	0.351760	−	0.351760i
$819$	1.35291	+	0.446652i	0.0472744	+	0.0156073i
$820$	8.18925	−	3.56736i	0.285981	−	0.124578i
$821$		−	29.9356i		−	1.04476i	−0.852713	−	0.522379i	$-0.825045\pi$
$821$		−	29.9356i		−	1.04476i	0.852713	−	0.522379i	$-0.174955\pi$
$822$	9.44426	+	1.51867i	0.329406	+	0.0529695i
$823$	−25.9697	−	25.9697i	−0.905246	−	0.905246i	0.0906383	−	0.995884i	$-0.471109\pi$
$823$	−25.9697	−	25.9697i	−0.905246	−	0.905246i	−0.995884	+	0.0906383i	$0.971109\pi$
$824$	12.5587			0.437502
$825$	29.9079	−	23.3181i	1.04126	−	0.811831i
$826$	−53.4369			−1.85931
$827$	20.1949	+	20.1949i	0.702247	+	0.702247i	0.964892	−	0.262645i	$-0.0845949\pi$
$827$	20.1949	+	20.1949i	0.702247	+	0.702247i	−0.262645	+	0.964892i	$0.584595\pi$
$828$	7.71048	+	15.3108i	0.267958	+	0.532086i
$829$			54.6415i			1.89778i	0.315613	+	0.948888i	$0.397790\pi$
$829$			54.6415i			1.89778i	−0.315613	+	0.948888i	$0.602210\pi$
$830$	26.8789	−	11.7089i	0.932982	−	0.406421i
$831$	14.6726	+	20.2955i	0.508985	+	0.704044i
$832$	−0.0858524	+	0.0858524i	−0.00297640	+	0.00297640i
$833$	−40.7102	+	40.7102i	−1.41052	+	1.41052i
$834$	0.897722	+	1.24176i	0.0310856	+	0.0429985i
$835$	−19.6131	−	7.71051i	−0.678739	−	0.266833i
$836$		−	4.37906i		−	0.151453i
$837$	−11.4804	+	22.1428i	−0.396820	+	0.765368i
$838$	19.7046	+	19.7046i	0.680686	+	0.680686i
$839$	16.3986			0.566144			0.283072	−	0.959099i	$-0.408646\pi$
$839$	16.3986			0.566144			0.283072	+	0.959099i	$0.408646\pi$
$840$	14.6730	−	3.76836i	0.506267	−	0.130021i
$841$	30.8383			1.06339
$842$	−21.4262	−	21.4262i	−0.738396	−	0.738396i
$843$	5.95377	+	0.957383i	0.205059	+	0.0329740i
$844$			5.54199i			0.190763i
$845$	−11.5960	−	26.6199i	−0.398915	−	0.915751i
$846$	−12.4696	+	37.7703i	−0.428713	+	1.29857i
$847$	−22.6141	+	22.6141i	−0.777030	+	0.777030i
$848$	1.61864	−	1.61864i	0.0555842	−	0.0555842i
$849$	6.81784	−	4.92893i	0.233988	−	0.169160i
$850$	25.3975	+	23.6195i	0.871127	+	0.810143i
$851$		−	9.36283i		−	0.320954i
$852$	2.78066	−	17.2923i	0.0952638	−	0.592426i
$853$	26.5007	+	26.5007i	0.907366	+	0.907366i	0.996059	−	0.0886927i	$-0.0282689\pi$
$853$	26.5007	+	26.5007i	0.907366	+	0.907366i	−0.0886927	+	0.996059i	$0.528269\pi$
$854$	−51.1193			−1.74927
$855$	0.615959	+	6.67986i	0.0210654	+	0.228447i
$856$	9.93455			0.339556
$857$	22.7533	+	22.7533i	0.777239	+	0.777239i	0.979360	−	0.202121i	$-0.0647836\pi$
$857$	22.7533	+	22.7533i	0.777239	+	0.777239i	−0.202121	+	0.979360i	$0.564784\pi$
$858$	−0.146204	+	0.909213i	−0.00499133	+	0.0310400i
$859$		−	41.5266i		−	1.41687i	−0.705776	−	0.708435i	$-0.749402\pi$
$859$		−	41.5266i		−	1.41687i	0.705776	−	0.708435i	$-0.250598\pi$
$860$	2.57712	−	6.55538i	0.0878792	−	0.223537i
$861$	21.9328	−	15.8562i	0.747467	−	0.540377i
$862$	16.4159	−	16.4159i	0.559126	−	0.559126i
$863$	7.36244	−	7.36244i	0.250620	−	0.250620i	−0.570605	−	0.821225i	$-0.693291\pi$
$863$	7.36244	−	7.36244i	0.250620	−	0.250620i	0.821225	+	0.570605i	$0.193291\pi$
$864$	4.95307	−	1.57069i	0.168507	−	0.0534361i
$865$	3.85478	−	9.80534i	0.131067	−	0.333392i
$866$		−	29.1068i		−	0.989090i
$867$	−53.2120	−	8.55664i	−1.80717	−	0.290599i
$868$	−13.2763	−	13.2763i	−0.450628	−	0.450628i
$869$	−5.46208			−0.185288
$870$	15.2491	−	25.7884i	0.516991	−	0.874308i
$871$	1.64485			0.0557335
$872$	0.158186	+	0.158186i	0.00535686	+	0.00535686i
$873$	3.99502	−	2.01188i	0.135211	−	0.0680920i
$874$		−	5.71423i		−	0.193287i
$875$	−18.9070	−	39.4336i	−0.639172	−	1.33310i
$876$	4.37426	+	6.05060i	0.147792	+	0.204431i
$877$	−1.47878	+	1.47878i	−0.0499350	+	0.0499350i	−0.731633	−	0.681698i	$-0.761242\pi$
$877$	−1.47878	+	1.47878i	−0.0499350	+	0.0499350i	0.681698	+	0.731633i	$0.261242\pi$
$878$	21.0395	−	21.0395i	0.710050	−	0.710050i
$879$	6.13022	+	8.47951i	0.206767	+	0.286007i
$880$	3.91056	+	8.97711i	0.131825	+	0.302618i
$881$			21.9350i			0.739009i	0.929229	+	0.369504i	$0.120473\pi$
$881$			21.9350i			0.739009i	−0.929229	+	0.369504i	$0.879527\pi$
$882$	22.2387	−	11.1994i	0.748817	−	0.377103i
$883$	16.2095	+	16.2095i	0.545493	+	0.545493i	0.925134	−	0.379641i	$-0.123952\pi$
$883$	16.2095	+	16.2095i	0.545493	+	0.545493i	−0.379641	+	0.925134i	$0.623952\pi$
$884$	−0.842199			−0.0283262
$885$	13.1615	+	51.2476i	0.442420	+	1.72267i
$886$	−18.2417			−0.612842
$887$	−10.8840	−	10.8840i	−0.365449	−	0.365449i	0.500366	−	0.865814i	$-0.333199\pi$
$887$	−10.8840	−	10.8840i	−0.365449	−	0.365449i	−0.865814	+	0.500366i	$0.833199\pi$
$888$	−2.80199	−	0.450568i	−0.0940287	−	0.0151201i
$889$		−	9.48390i		−	0.318080i
$890$	−9.31605	−	3.66243i	−0.312275	−	0.122765i
$891$	23.4653	−	31.6647i	0.786117	−	1.06081i
$892$	−9.53065	+	9.53065i	−0.319110	+	0.319110i
$893$	9.37516	−	9.37516i	0.313728	−	0.313728i
$894$	20.2394	−	14.6320i	0.676908	−	0.489368i
$895$	−41.8049	+	18.2108i	−1.39738	+	0.608721i
$896$			3.91150i			0.130674i
$897$	−0.190781	+	1.18643i	−0.00637001	+	0.0396137i
$898$	4.30447	+	4.30447i	0.143642	+	0.143642i
$899$	−37.1312			−1.23840
$900$	−7.22793	−	13.1437i	−0.240931	−	0.438124i
$901$	15.8786			0.528992
$902$	12.3696	+	12.3696i	0.411862	+	0.411862i
$903$	3.38824	−	21.0708i	0.112754	−	0.701191i
$904$		−	6.93395i		−	0.230620i
$905$	−40.5898	+	17.6815i	−1.34925	+	0.587754i
$906$	17.6217	−	12.7395i	0.585441	−	0.423242i
$907$	10.1424	−	10.1424i	0.336773	−	0.336773i	−0.518379	−	0.855151i	$-0.673464\pi$
$907$	10.1424	−	10.1424i	0.336773	−	0.336773i	0.855151	+	0.518379i	$0.173464\pi$
$908$	13.7533	−	13.7533i	0.456418	−	0.456418i
$909$	−1.24477	+	3.77040i	−0.0412864	+	0.125056i
$910$	0.988301	+	0.388532i	0.0327619	+	0.0128797i
$911$		−	33.7497i		−	1.11818i	−0.829108	−	0.559088i	$-0.811151\pi$
$911$		−	33.7497i		−	1.11818i	0.829108	−	0.559088i	$-0.188849\pi$
$912$	−1.71008	−	0.274986i	−0.0566265	−	0.00910571i
$913$	40.5997	+	40.5997i	1.34366	+	1.34366i
$914$	−19.2779			−0.637656
$915$	12.5907	+	49.0250i	0.416236	+	1.62071i
$916$	6.49460			0.214588
$917$	2.86159	+	2.86159i	0.0944980	+	0.0944980i
$918$	31.9986	+	16.5903i	1.05611	+	0.547562i
$919$		−	43.6233i		−	1.43900i	−0.694493	−	0.719499i	$-0.744371\pi$
$919$		−	43.6233i		−	1.43900i	0.694493	−	0.719499i	$-0.255629\pi$
$920$	5.10289	+	11.7142i	0.168237	+	0.386206i
$921$	−18.0645	−	24.9874i	−0.595246	−	0.823363i
$922$	14.5915	−	14.5915i	0.480546	−	0.480546i
$923$	0.868139	−	0.868139i	0.0285751	−	0.0285751i
$924$	17.3816	+	24.0428i	0.571814	+	0.790951i
$925$	0.296969	+	8.18718i	0.00976429	+	0.269193i
$926$		−	2.08004i		−	0.0683543i
$927$	−16.9460	−	33.6499i	−0.556581	−	1.10521i
$928$	5.46984	+	5.46984i	0.179556	+	0.179556i
$929$	−50.9123			−1.67038			−0.835190	−	0.549962i	$-0.814642\pi$
$929$	−50.9123			−1.67038			−0.835190	+	0.549962i	$0.814642\pi$
$930$	−9.46244	+	16.0024i	−0.310286	+	0.524738i
$931$	−8.29985			−0.272017
$932$	7.94673	+	7.94673i	0.260304	+	0.260304i
$933$	3.74848	+	0.602766i	0.122720	+	0.0197337i
$934$		−	35.2243i		−	1.15258i
$935$	−24.8510	+	63.2131i	−0.812715	+	2.06729i
$936$	0.345879	+	0.114189i	0.0113054	+	0.00373240i
$937$	11.7524	−	11.7524i	0.383934	−	0.383934i	−0.488583	−	0.872517i	$-0.662486\pi$
$937$	11.7524	−	11.7524i	0.383934	−	0.383934i	0.872517	+	0.488583i	$0.162486\pi$
$938$	37.4703	−	37.4703i	1.22345	−	1.22345i
$939$	−24.4041	+	17.6428i	−0.796397	+	0.575751i
$940$	−10.8470	+	27.5913i	−0.353790	+	0.899928i
$941$			35.7875i			1.16664i	0.812242	+	0.583320i	$0.198247\pi$
$941$			35.7875i			1.16664i	−0.812242	+	0.583320i	$0.801753\pi$
$942$	−3.53385	+	21.9763i	−0.115139	+	0.716026i
$943$	16.1410	+	16.1410i	0.525625	+	0.525625i
$944$	−13.6615			−0.444643
$945$	−29.8960	−	34.2302i	−0.972517	−	1.11351i
$946$	13.7943			0.448493
$947$	−35.8866	−	35.8866i	−1.16616	−	1.16616i	−0.983103	−	0.183055i	$-0.941401\pi$
$947$	−35.8866	−	35.8866i	−1.16616	−	1.16616i	−0.183055	−	0.983103i	$-0.558599\pi$
$948$	−0.342995	+	2.13302i	−0.0111400	+	0.0692771i
$949$			0.523366i			0.0169892i
$950$	0.181243	+	4.99671i	0.00588030	+	0.162115i
$951$	−9.92562	+	7.17568i	−0.321860	+	0.232687i
$952$	−19.1856	+	19.1856i	−0.621810	+	0.621810i
$953$	−7.52954	+	7.52954i	−0.243906	+	0.243906i	−0.818464	−	0.574558i	$-0.805174\pi$
$953$	−7.52954	+	7.52954i	−0.243906	+	0.243906i	0.574558	+	0.818464i	$0.305174\pi$
$954$	−6.52110	−	2.15289i	−0.211128	−	0.0697025i
$955$	14.3730	+	32.9946i	0.465098	+	1.06768i
$956$		−	7.51189i		−	0.242952i
$957$	57.9279	+	9.31498i	1.87254	+	0.301111i
$958$	8.08069	+	8.08069i	0.261075	+	0.261075i
$959$	21.6020			0.697566
$960$	3.75125	−	0.963404i	0.121071	−	0.0310937i
$961$	−7.95909			−0.256745
$962$	−0.140670	−	0.140670i	−0.00453539	−	0.00453539i
$963$	−13.4052	−	26.6188i	−0.431976	−	0.857778i
$964$			11.2111i			0.361085i
$965$	−8.11188	−	3.18903i	−0.261131	−	0.102659i
$966$	22.6813	+	31.3734i	0.729758	+	1.00942i
$967$	26.9948	−	26.9948i	0.868094	−	0.868094i	−0.124167	−	0.992261i	$-0.539626\pi$
$967$	26.9948	−	26.9948i	0.868094	−	0.868094i	0.992261	+	0.124167i	$0.0396259\pi$
$968$	−5.78144	+	5.78144i	−0.185823	+	0.185823i
$969$	−7.03904	−	9.73662i	−0.226127	−	0.312785i
$970$	3.05657	−	1.33149i	0.0981405	−	0.0427515i
$971$			5.51830i			0.177091i	0.996072	+	0.0885453i	$0.0282218\pi$
$971$			5.51830i			0.177091i	−0.996072	+	0.0885453i	$0.971778\pi$
$972$	−10.8920	−	11.1519i	−0.349360	−	0.357698i
$973$	2.44683	+	2.44683i	0.0784419	+	0.0784419i
$974$	9.05744			0.290219
$975$	0.129195	−	1.04351i	0.00413754	−	0.0334189i
$976$	−13.0690			−0.418328
$977$	−24.9913	−	24.9913i	−0.799542	−	0.799542i	0.183482	−	0.983023i	$-0.441263\pi$
$977$	−24.9913	−	24.9913i	−0.799542	−	0.799542i	−0.983023	+	0.183482i	$0.941263\pi$
$978$	−7.20495	−	1.15858i	−0.230389	−	0.0370472i
$979$		−	19.6036i		−	0.626532i
$980$	17.0147	−	7.41188i	0.543516	−	0.236764i
$981$	0.210398	−	0.637294i	0.00671749	−	0.0203472i
$982$	−5.76505	+	5.76505i	−0.183970	+	0.183970i
$983$	−5.21812	+	5.21812i	−0.166432	+	0.166432i	−0.785409	−	0.618977i	$-0.787547\pi$
$983$	−5.21812	+	5.21812i	−0.166432	+	0.166432i	0.618977	+	0.785409i	$0.287547\pi$
$984$	5.60725	−	4.05373i	0.178753	−	0.129228i
$985$	−28.0440	−	11.0250i	−0.893558	−	0.351285i
$986$			53.6583i			1.70883i
$987$	−14.2609	+	88.6858i	−0.453931	+	2.82290i
$988$	−0.0858524	−	0.0858524i	−0.00273133	−	0.00273133i
$989$	18.0002			0.572373
$990$	18.7767	−	22.5913i	0.596762	−	0.717997i
$991$	−34.4931			−1.09571			−0.547855	−	0.836574i	$-0.684555\pi$
$991$	−34.4931			−1.09571			−0.547855	+	0.836574i	$0.684555\pi$
$992$	−3.39418	−	3.39418i	−0.107765	−	0.107765i
$993$	−4.28547	+	26.6505i	−0.135995	+	0.845727i
$994$		−	39.5531i		−	1.25455i
$995$	6.80258	+	15.6160i	0.215656	+	0.495062i
$996$	18.4042	−	13.3053i	0.583160	−	0.421593i
$997$	−26.5745	+	26.5745i	−0.841623	+	0.841623i	−0.989070	−	0.147447i	$-0.952894\pi$
$997$	−26.5745	+	26.5745i	−0.841623	+	0.841623i	0.147447	+	0.989070i	$0.452894\pi$
$998$	−1.03420	+	1.03420i	−0.0327369	+	0.0327369i
$999$	2.57360	+	8.11567i	0.0814252	+	0.256768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.533.5	yes	36
3.2	odd	2	inner	570.2.k.a.533.18	yes	36
5.2	odd	4	inner	570.2.k.a.77.18	yes	36
15.2	even	4	inner	570.2.k.a.77.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.5	✓	36	15.2	even	4	inner
570.2.k.a.77.18	yes	36	5.2	odd	4	inner
570.2.k.a.533.5	yes	36	1.1	even	1	trivial
570.2.k.a.533.18	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.274986 + 1.71008i) q^{3} +1.00000i q^{4} +(2.05001 - 0.893014i) q^{5} +(1.40366 - 1.01477i) q^{6} +(2.76585 - 2.76585i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.84877 - 0.940499i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.274986 + 1.71008i) q^{3} +1.00000i q^{4} +(2.05001 - 0.893014i) q^{5} +(1.40366 - 1.01477i) q^{6} +(2.76585 - 2.76585i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.84877 - 0.940499i) q^{9} +(-2.08103 - 0.818117i) q^{10} -4.37906i q^{11} +(-1.71008 - 0.274986i) q^{12} +(-0.0858524 - 0.0858524i) q^{13} -3.91150 q^{14} +(0.963404 + 3.75125i) q^{15} -1.00000 q^{16} +(-4.90493 - 4.90493i) q^{17} +(1.34935 + 2.67941i) q^{18} -1.00000i q^{19} +(0.893014 + 2.05001i) q^{20} +(3.96926 + 5.49040i) q^{21} +(-3.09646 + 3.09646i) q^{22} +(-4.04057 + 4.04057i) q^{23} +(1.01477 + 1.40366i) q^{24} +(3.40505 - 3.66137i) q^{25} +0.121414i q^{26} +(2.39170 - 4.61300i) q^{27} +(2.76585 + 2.76585i) q^{28} +7.73552 q^{29} +(1.97130 - 3.33376i) q^{30} -4.80009 q^{31} +(0.707107 + 0.707107i) q^{32} +(7.48856 + 1.20418i) q^{33} +6.93661i q^{34} +(3.20007 - 8.13995i) q^{35} +(0.940499 - 2.84877i) q^{36} +(-1.15860 + 1.15860i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(0.170423 - 0.123206i) q^{39} +(0.818117 - 2.08103i) q^{40} -3.99475i q^{41} +(1.07561 - 6.68899i) q^{42} +(-2.22743 - 2.22743i) q^{43} +4.37906 q^{44} +(-6.67986 + 0.615959i) q^{45} +5.71423 q^{46} +(9.37516 + 9.37516i) q^{47} +(0.274986 - 1.71008i) q^{48} -8.29985i q^{49} +(-4.99671 + 0.181243i) q^{50} +(9.73662 - 7.03904i) q^{51} +(0.0858524 - 0.0858524i) q^{52} +(-1.61864 + 1.61864i) q^{53} +(-4.95307 + 1.57069i) q^{54} +(-3.91056 - 8.97711i) q^{55} -3.91150i q^{56} +(1.71008 + 0.274986i) q^{57} +(-5.46984 - 5.46984i) q^{58} +13.6615 q^{59} +(-3.75125 + 0.963404i) q^{60} +13.0690 q^{61} +(3.39418 + 3.39418i) q^{62} +(-10.4805 + 5.27798i) q^{63} -1.00000i q^{64} +(-0.252665 - 0.0993306i) q^{65} +(-4.44373 - 6.14670i) q^{66} +(-9.57951 + 9.57951i) q^{67} +(4.90493 - 4.90493i) q^{68} +(-5.79861 - 8.02081i) q^{69} +(-8.01860 + 3.49303i) q^{70} +10.1120i q^{71} +(-2.67941 + 1.34935i) q^{72} +(-3.04806 - 3.04806i) q^{73} +1.63851 q^{74} +(5.32490 + 6.82975i) q^{75} +1.00000 q^{76} +(-12.1118 - 12.1118i) q^{77} +(-0.207627 - 0.0333871i) q^{78} -1.24732i q^{79} +(-2.05001 + 0.893014i) q^{80} +(7.23092 + 5.35852i) q^{81} +(-2.82471 + 2.82471i) q^{82} +(-9.27133 + 9.27133i) q^{83} +(-5.49040 + 3.96926i) q^{84} +(-14.4353 - 5.67496i) q^{85} +3.15007i q^{86} +(-2.12716 + 13.2284i) q^{87} +(-3.09646 - 3.09646i) q^{88} +4.47665 q^{89} +(5.15893 + 4.28783i) q^{90} -0.474910 q^{91} +(-4.04057 - 4.04057i) q^{92} +(1.31996 - 8.20856i) q^{93} -13.2585i q^{94} +(-0.893014 - 2.05001i) q^{95} +(-1.40366 + 1.01477i) q^{96} +(-1.05430 + 1.05430i) q^{97} +(-5.86888 + 5.86888i) q^{98} +(-4.11850 + 12.4749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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