LMFDB - Embedded newform 507.2.s.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$507 = 3 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	507.s (of order $52$ , degree $24$ , 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.436480 + 2.38179i) q^{2} +(1.15819 + 1.28787i) q^{3} +(-3.61239 - 1.37000i) q^{4} +(-0.777816 - 0.0470492i) q^{5} +(-3.57296 + 2.19643i) q^{6} +(3.90248 + 2.35913i) q^{7} +(2.33436 - 3.86150i) q^{8} +(-0.317208 + 2.98318i) q^{9} +(0.451562 - 1.83206i) q^{10} +(0.401992 + 2.19360i) q^{11} +(-2.41944 - 6.23899i) q^{12} +(-3.07952 + 1.87524i) q^{13} +(-7.32231 + 8.26518i) q^{14} +(-0.840263 - 1.05622i) q^{15} +(2.39473 + 2.12155i) q^{16} +(2.71123 - 0.668259i) q^{17} +(-6.96687 - 2.05762i) q^{18} +(4.51732 - 4.51732i) q^{19} +(2.74531 + 1.23557i) q^{20} +(1.48155 + 7.75819i) q^{21} -5.40016 q^{22} -4.33705 q^{23} +(7.67673 - 1.46599i) q^{24} +(-4.36076 - 0.529492i) q^{25} +(-3.12228 - 8.15329i) q^{26} +(-4.20933 + 3.04656i) q^{27} +(-10.8653 - 13.8685i) q^{28} +(7.82506 - 5.40125i) q^{29} +(2.88244 - 1.54031i) q^{30} +(-4.42063 - 3.46334i) q^{31} +(1.00561 - 0.787843i) q^{32} +(-2.35948 + 3.05831i) q^{33} +(0.408256 + 6.74927i) q^{34} +(-2.92442 - 2.01858i) q^{35} +(5.23283 - 10.3418i) q^{36} +(-2.61638 + 3.33957i) q^{37} +(8.78760 + 12.7310i) q^{38} +(-5.98173 - 1.79414i) q^{39} +(-1.99738 + 2.89371i) q^{40} +(-1.28150 - 4.11248i) q^{41} +(-19.1251 + 0.142450i) q^{42} +(0.00737244 + 0.000895177i) q^{43} +(1.55307 - 8.47485i) q^{44} +(0.387086 - 2.30544i) q^{45} +(1.89303 - 10.3300i) q^{46} +(6.36565 + 2.86494i) q^{47} +(0.0412730 + 5.54125i) q^{48} +(6.41079 + 12.2147i) q^{49} +(3.16452 - 10.1553i) q^{50} +(4.00074 + 2.71774i) q^{51} +(13.6935 - 2.55515i) q^{52} +(3.30070 + 13.3915i) q^{53} +(-5.41898 - 11.3555i) q^{54} +(-0.209469 - 1.72513i) q^{55} +(18.2196 - 9.56238i) q^{56} +(11.0496 + 0.585813i) q^{57} +(9.44917 + 20.9952i) q^{58} +(0.641459 - 10.6046i) q^{59} +(1.58834 + 4.96662i) q^{60} +(1.86851 + 0.460545i) q^{61} +(10.1785 - 9.01733i) q^{62} +(-8.27562 + 10.8935i) q^{63} +(4.41116 + 8.40476i) q^{64} +(2.48353 - 1.31370i) q^{65} +(-6.25439 - 6.95469i) q^{66} +(1.95632 + 0.880468i) q^{67} +(-10.7095 - 1.30037i) q^{68} +(-5.02312 - 5.58555i) q^{69} +(6.08428 - 6.08428i) q^{70} +(2.12637 + 6.82375i) q^{71} +(10.7791 + 8.18872i) q^{72} +(6.69984 - 1.22779i) q^{73} +(-6.81216 - 7.68933i) q^{74} +(-4.36866 - 6.22933i) q^{75} +(-22.5070 + 10.1296i) q^{76} +(-3.60622 + 9.50883i) q^{77} +(6.88417 - 13.4641i) q^{78} +(-2.40538 - 6.34245i) q^{79} +(-1.76284 - 1.76284i) q^{80} +(-8.79876 - 1.89258i) q^{81} +(10.3544 - 1.25726i) q^{82} +(-11.1001 - 3.45892i) q^{83} +(5.27677 - 30.0553i) q^{84} +(-2.14028 + 0.392221i) q^{85} +(-0.00535005 + 0.0171689i) q^{86} +(16.0190 + 3.82199i) q^{87} +(9.40898 + 3.56836i) q^{88} +(2.69839 - 2.69839i) q^{89} +(5.32213 + 1.92824i) q^{90} +(-16.4417 + 0.0530881i) q^{91} +(15.6671 + 5.94175i) q^{92} +(-0.659585 - 9.70438i) q^{93} +(-9.60218 + 13.9112i) q^{94} +(-3.72618 + 3.30111i) q^{95} +(2.17932 + 0.382621i) q^{96} +(-2.22639 + 0.134671i) q^{97} +(-31.8911 + 9.93768i) q^{98} +(-6.67142 + 0.503388i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100})$ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$ .

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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

)

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

$2$	−0.436480	+	2.38179i	−0.308638	+	1.68418i	0.354003	+	0.935244i	$0.384820\pi$
$2$	−0.436480	+	2.38179i	−0.308638	+	1.68418i	−0.662641	+	0.748937i	$0.730565\pi$
$3$	1.15819	+	1.28787i	0.668679	+	0.743551i
$3$	1.15819	+	1.28787i	0.668679	+	0.743551i
$4$	−3.61239	−	1.37000i	−1.80619	−	0.684999i
$5$	−0.777816	−	0.0470492i	−0.347850	−	0.0210410i	−0.114470	−	0.993427i	$-0.536517\pi$
$5$	−0.777816	−	0.0470492i	−0.347850	−	0.0210410i	−0.233380	+	0.972386i	$0.574979\pi$
$6$	−3.57296	+	2.19643i	−1.45865	+	0.896689i
$7$	3.90248	+	2.35913i	1.47500	+	0.891668i	0.999931	+	0.0117186i	$0.00373022\pi$
$7$	3.90248	+	2.35913i	1.47500	+	0.891668i	0.475068	+	0.879949i	$0.342424\pi$
$8$	2.33436	−	3.86150i	0.825321	−	1.36525i
$9$	−0.317208	+	2.98318i	−0.105736	+	0.994394i
$10$	0.451562	−	1.83206i	0.142796	−	0.579348i
$11$	0.401992	+	2.19360i	0.121205	+	0.661395i	0.986965	+	0.160935i	$0.0514510\pi$
$11$	0.401992	+	2.19360i	0.121205	+	0.661395i	−0.865760	+	0.500460i	$0.833164\pi$
$12$	−2.41944	−	6.23899i	−0.698432	−	1.80104i
$13$	−3.07952	+	1.87524i	−0.854106	+	0.520098i
$13$	−3.07952	+	1.87524i	−0.854106	+	0.520098i
$14$	−7.32231	+	8.26518i	−1.95697	+	2.20896i
$15$	−0.840263	−	1.05622i	−0.216955	−	0.272714i
$16$	2.39473	+	2.12155i	0.598683	+	0.530387i
$17$	2.71123	−	0.668259i	0.657570	−	0.162077i	0.103608	−	0.994618i	$-0.466961\pi$
$17$	2.71123	−	0.668259i	0.657570	−	0.162077i	0.553962	+	0.832542i	$0.313115\pi$
$18$	−6.96687	−	2.05762i	−1.64211	−	0.484986i
$19$	4.51732	−	4.51732i	1.03634	−	1.03634i	0.0370302	−	0.999314i	$-0.488210\pi$
$19$	4.51732	−	4.51732i	1.03634	−	1.03634i	0.999314	−	0.0370302i	$-0.0117898\pi$
$20$	2.74531	+	1.23557i	0.613871	+	0.276281i
$21$	1.48155	+	7.75819i	0.323301	+	1.69298i
$22$	−5.40016			−1.15132
$23$	−4.33705			−0.904338			−0.452169	−	0.891932i	$-0.649350\pi$
$23$	−4.33705			−0.904338			−0.452169	+	0.891932i	$0.649350\pi$
$24$	7.67673	−	1.46599i	1.56701	−	0.299245i
$25$	−4.36076	−	0.529492i	−0.872152	−	0.105898i
$26$	−3.12228	−	8.15329i	−0.612330	−	1.59899i
$27$	−4.20933	+	3.04656i	−0.810086	+	0.586311i
$28$	−10.8653	−	13.8685i	−2.05334	−	2.62090i
$29$	7.82506	−	5.40125i	1.45308	−	1.00299i	0.459701	−	0.888074i	$-0.347957\pi$
$29$	7.82506	−	5.40125i	1.45308	−	1.00299i	0.993376	−	0.114912i	$-0.0366587\pi$
$30$	2.88244	−	1.54031i	0.526260	−	0.281222i
$31$	−4.42063	−	3.46334i	−0.793968	−	0.622034i	0.135567	−	0.990768i	$-0.456714\pi$
$31$	−4.42063	−	3.46334i	−0.793968	−	0.622034i	−0.929535	+	0.368734i	$0.879791\pi$
$32$	1.00561	−	0.787843i	0.177768	−	0.139272i
$33$	−2.35948	+	3.05831i	−0.410734	+	0.532383i
$34$	0.408256	+	6.74927i	0.0700153	+	1.15749i
$35$	−2.92442	−	2.01858i	−0.494316	−	0.341202i
$36$	5.23283	−	10.3418i	0.872138	−	1.72364i
$37$	−2.61638	+	3.33957i	−0.430131	+	0.549021i	−0.952833	−	0.303494i	$-0.901847\pi$
$37$	−2.61638	+	3.33957i	−0.430131	+	0.549021i	0.522703	+	0.852515i	$0.324924\pi$
$38$	8.78760	+	12.7310i	1.42554	+	2.06525i
$39$	−5.98173	−	1.79414i	−0.957843	−	0.287293i
$40$	−1.99738	+	2.89371i	−0.315814	+	0.457535i
$41$	−1.28150	−	4.11248i	−0.200137	−	0.642262i	−0.999161	−	0.0409626i	$-0.986958\pi$
$41$	−1.28150	−	4.11248i	−0.200137	−	0.642262i	0.799024	−	0.601300i	$-0.205350\pi$
$42$	−19.1251	+	0.142450i	−2.95106	+	0.0219805i
$43$	0.00737244		0.000895177i	0.00112429		0.000136513i	0.121099	−	0.992640i	$-0.461358\pi$
$43$	0.00737244		0.000895177i	0.00112429		0.000136513i	−0.119975	+	0.992777i	$0.538281\pi$
$44$	1.55307	−	8.47485i	0.234135	−	1.27763i
$45$	0.387086	−	2.30544i	0.0577034	−	0.343675i
$46$	1.89303	−	10.3300i	0.279113	−	1.52307i
$47$	6.36565	+	2.86494i	0.928525	+	0.417895i	0.817504	−	0.575923i	$-0.195357\pi$
$47$	6.36565	+	2.86494i	0.928525	+	0.417895i	0.111021	+	0.993818i	$0.464588\pi$
$48$	0.0412730	+	5.54125i	0.00595725	+	0.799810i
$49$	6.41079	+	12.2147i	0.915827	+	1.74496i
$50$	3.16452	−	10.1553i	0.447531	−	1.43618i
$51$	4.00074	+	2.71774i	0.560216	+	0.380560i
$52$	13.6935	−	2.55515i	1.89895	−	0.354336i
$53$	3.30070	+	13.3915i	0.453386	+	1.83946i	0.537863	+	0.843032i	$0.319232\pi$
$53$	3.30070	+	13.3915i	0.453386	+	1.83946i	−0.0844771	+	0.996425i	$0.526922\pi$
$54$	−5.41898	−	11.3555i	−0.737430	−	1.54529i
$55$	−0.209469	−	1.72513i	−0.0282447	−	0.232616i
$56$	18.2196	−	9.56238i	2.43469	−	1.27783i
$57$	11.0496	+	0.585813i	1.46356	+	0.0775929i
$58$	9.44917	+	20.9952i	1.24074	+	2.75680i
$59$	0.641459	−	10.6046i	0.0835109	−	1.38060i	−0.679245	−	0.733912i	$-0.737692\pi$
$59$	0.641459	−	10.6046i	0.0835109	−	1.38060i	0.762755	−	0.646687i	$-0.223846\pi$
$60$	1.58834	+	4.96662i	0.205054	+	0.641187i
$61$	1.86851	+	0.460545i	0.239238	+	0.0589668i	0.357111	−	0.934062i	$-0.383762\pi$
$61$	1.86851	+	0.460545i	0.239238	+	0.0589668i	−0.117874	+	0.993029i	$0.537608\pi$
$62$	10.1785	−	9.01733i	1.29267	−	1.14520i
$63$	−8.27562	+	10.8935i	−1.04263	+	1.37245i
$64$	4.41116	+	8.40476i	0.551395	+	1.05059i
$65$	2.48353	−	1.31370i	0.308044	−	0.162945i
$66$	−6.25439	−	6.95469i	−0.769862	−	0.856063i
$67$	1.95632	+	0.880468i	0.239003	+	0.107566i	0.526375	−	0.850253i	$-0.323551\pi$
$67$	1.95632	+	0.880468i	0.239003	+	0.107566i	−0.287372	+	0.957819i	$0.592782\pi$
$68$	−10.7095	−	1.30037i	−1.29872	−	0.157693i
$69$	−5.02312	−	5.58555i	−0.604712	−	0.672421i
$70$	6.08428	−	6.08428i	0.727211	−	0.727211i
$71$	2.12637	+	6.82375i	0.252353	+	0.809830i	0.990778	+	0.135494i	$0.0432623\pi$
$71$	2.12637	+	6.82375i	0.252353	+	0.809830i	−0.738425	+	0.674336i	$0.764430\pi$
$72$	10.7791	+	8.18872i	1.27033	+	0.965050i
$73$	6.69984	−	1.22779i	0.784157	−	0.143702i	0.226763	−	0.973950i	$-0.427186\pi$
$73$	6.69984	−	1.22779i	0.784157	−	0.143702i	0.557394	+	0.830248i	$0.311801\pi$
$74$	−6.81216	−	7.68933i	−0.791897	−	0.893867i
$75$	−4.36866	−	6.22933i	−0.504449	−	0.719302i
$76$	−22.5070	+	10.1296i	−2.58173	+	1.16194i
$77$	−3.60622	+	9.50883i	−0.410967	+	1.08363i
$78$	6.88417	−	13.4641i	0.779479	−	1.52451i
$79$	−2.40538	−	6.34245i	−0.270626	−	0.713582i	−0.999579	−	0.0290180i	$-0.990762\pi$
$79$	−2.40538	−	6.34245i	−0.270626	−	0.713582i	0.728953	−	0.684564i	$-0.240007\pi$
$80$	−1.76284	−	1.76284i	−0.197092	−	0.197092i
$81$	−8.79876	−	1.89258i	−0.977640	−	0.210287i
$82$	10.3544	−	1.25726i	1.14346	−	0.138841i
$83$	−11.1001	−	3.45892i	−1.21839	−	0.379665i	−0.380128	−	0.924934i	$-0.624120\pi$
$83$	−11.1001	−	3.45892i	−1.21839	−	0.379665i	−0.838261	+	0.545268i	$0.816428\pi$
$84$	5.27677	−	30.0553i	0.575743	−	3.27930i
$85$	−2.14028	+	0.392221i	−0.232146	+	0.0425423i
$86$	−0.00535005	+	0.0171689i	−0.000576910	+	0.00185137i
$87$	16.0190	+	3.82199i	1.71741	+	0.409760i
$88$	9.40898	+	3.56836i	1.00300	+	0.380388i
$89$	2.69839	−	2.69839i	0.286029	−	0.286029i	−0.549479	−	0.835508i	$-0.685174\pi$
$89$	2.69839	−	2.69839i	0.286029	−	0.286029i	0.835508	+	0.549479i	$0.185174\pi$
$90$	5.32213	+	1.92824i	0.561002	+	0.203254i
$91$	−16.4417	+	0.0530881i	−1.72356	+	0.00556515i
$92$	15.6671	+	5.94175i	1.63341	+	0.619470i
$93$	−0.659585	−	9.70438i	−0.0683958	−	1.00630i
$94$	−9.60218	+	13.9112i	−0.990389	+	1.43483i
$95$	−3.72618	+	3.30111i	−0.382298	+	0.338686i
$96$	2.17932	+	0.382621i	0.222426	+	0.0390511i
$97$	−2.22639	+	0.134671i	−0.226055	+	0.0136738i	−0.173018	−	0.984919i	$-0.555352\pi$
$97$	−2.22639	+	0.134671i	−0.226055	+	0.0136738i	−0.0530374	+	0.998593i	$0.516890\pi$
$98$	−31.8911	+	9.93768i	−3.22149	+	1.00386i
$99$	−6.67142	+	0.503388i	−0.670503	+	0.0505924i
$100$	15.0273	+	7.88696i	1.50273	+	0.788696i
$101$	0.617578	−	5.08622i	0.0614513	−	0.506097i	−0.929190	−	0.369603i	$-0.879494\pi$
$101$	0.617578	−	5.08622i	0.0614513	−	0.506097i	0.990641	−	0.136494i	$-0.0435834\pi$
$102$	−8.21933	+	8.34269i	−0.813835	+	0.826050i
$103$	−0.648914	+	1.23640i	−0.0639394	+	0.121826i	−0.915328	−	0.402709i	$-0.868069\pi$
$103$	−0.648914	+	1.23640i	−0.0639394	+	0.121826i	0.851389	+	0.524535i	$0.175761\pi$
$104$	0.0525307	+	16.2691i	0.00515106	+	1.59531i
$105$	−0.787356	−	6.10415i	−0.0768381	−	0.595704i
$106$	−33.3363	+	2.01648i	−3.23791	+	0.195858i
$107$	2.34965	+	2.65221i	0.227150	+	0.256399i	0.851025	−	0.525125i	$-0.175981\pi$
$107$	2.34965	+	2.65221i	0.227150	+	0.256399i	−0.623876	+	0.781524i	$0.714443\pi$
$108$	19.3795	−	5.23857i	1.86479	−	0.504082i
$109$	2.84502	+	3.63140i	0.272503	+	0.347825i	0.903984	−	0.427567i	$-0.140629\pi$
$109$	2.84502	+	3.63140i	0.272503	+	0.347825i	−0.631480	+	0.775392i	$0.717552\pi$
$110$	4.20033	+	0.254073i	0.400486	+	0.0242249i
$111$	−7.33118	+	0.498284i	−0.695845	+	0.0472951i
$112$	4.34038	+	13.9288i	0.410128	+	1.31615i
$113$	6.49706	+	12.3791i	0.611192	+	1.16453i	0.972680	+	0.232152i	$0.0745766\pi$
$113$	6.49706	+	12.3791i	0.611192	+	1.16453i	−0.361488	+	0.932377i	$0.617731\pi$
$114$	−6.21821	+	26.0622i	−0.582389	+	2.44095i
$115$	3.37343	+	0.204055i	0.314574	+	0.0190282i
$116$	−35.6668	+	8.79108i	−3.31158	+	0.816231i
$117$	−4.61734	−	9.78163i	−0.426873	−	0.904312i
$118$	24.9779	+	6.15651i	2.29940	+	0.566752i
$119$	12.1570	+	3.78829i	1.11443	+	0.347272i
$120$	−6.04006	+	0.779088i	−0.551379	+	0.0711207i
$121$	5.63490	−	2.13704i	0.512264	−	0.194276i
$122$	−1.91249	+	4.24937i	−0.173148	+	0.384720i
$123$	3.81212	−	6.41343i	0.343727	−	0.578279i
$124$	11.2242	+	18.5672i	1.00797	+	1.66738i
$125$	7.19932	+	1.31933i	0.643927	+	0.118004i
$126$	−22.3339	−	24.4656i	−1.98966	−	2.17957i
$127$	11.5432	−	4.37777i	1.02430	−	0.388464i	0.215468	−	0.976511i	$-0.430872\pi$
$127$	11.5432	−	4.37777i	1.02430	−	0.388464i	0.808827	+	0.588047i	$0.200103\pi$
$128$	−19.5045	+	6.07785i	−1.72397	+	0.537211i
$129$	0.00738579	+	0.0105315i	0.000650283	+	0.000927248i
$130$	2.04496	+	6.48866i	0.179355	+	0.569093i
$131$	−7.37384	+	5.08979i	−0.644255	+	0.444697i	−0.844869	−	0.534973i	$-0.820322\pi$
$131$	−7.37384	+	5.08979i	−0.644255	+	0.444697i	0.200614	+	0.979670i	$0.435706\pi$
$132$	12.7132	−	7.81531i	1.10655	−	0.680235i
$133$	28.2857	−	6.97180i	2.45268	−	0.604532i
$134$	−2.95099	+	4.27524i	−0.254926	+	0.369325i
$135$	3.41742	−	2.17162i	0.294125	−	0.186903i
$136$	3.74851	−	12.0294i	0.321432	−	1.03151i
$137$	−7.66794	−	9.78740i	−0.655116	−	0.836194i	0.339415	−	0.940637i	$-0.389771\pi$
$137$	−7.66794	−	9.78740i	−0.655116	−	0.836194i	−0.994531	+	0.104443i	$0.966694\pi$
$138$	15.4961	−	9.52604i	1.31912	−	0.810910i
$139$	11.6677	+	10.3366i	0.989638	+	0.876743i	0.992375	−	0.123253i	$-0.0393327\pi$
$139$	11.6677	+	10.3366i	0.989638	+	0.876743i	−0.00273690	+	0.999996i	$0.500871\pi$
$140$	7.79867	+	11.2983i	0.659108	+	0.954883i
$141$	3.68293	+	11.5163i	0.310159	+	0.969843i
$142$	−17.1809	+	2.08614i	−1.44179	+	0.175065i
$143$	−5.35147	−	6.00141i	−0.447512	−	0.501863i
$144$	−7.08859	+	6.47095i	−0.590716	+	0.539246i
$145$	−6.34058	+	3.83301i	−0.526556	+	0.318314i
$146$			16.4935i			1.36501i
$147$	−8.30608	+	22.4032i	−0.685074	+	1.84778i
$148$	14.0266	−	8.47937i	1.15298	−	0.697000i
$149$	7.01194	−	15.5799i	0.574441	−	1.27636i	−0.364156	−	0.931338i	$-0.618642\pi$
$149$	7.01194	−	15.5799i	0.574441	−	1.27636i	0.938596	−	0.345017i	$-0.112127\pi$
$150$	16.7438	−	7.68626i	1.36713	−	0.627580i
$151$	−3.07229	+	1.38273i	−0.250020	+	0.112525i	−0.531548	−	0.847028i	$-0.678389\pi$
$151$	−3.07229	+	1.38273i	−0.250020	+	0.112525i	0.281528	+	0.959553i	$0.409159\pi$
$152$	−6.89859	−	27.9887i	−0.559550	−	2.27018i
$153$	1.13351	+	8.30008i	0.0916391	+	0.671021i
$154$	−21.0740	−	12.7397i	−1.69819	−	1.02659i
$155$	3.27549	+	2.90183i	0.263093	+	0.233080i
$156$	19.1503	+	14.6761i	1.53325	+	1.17503i
$157$	−11.0034	+	9.74818i	−0.878169	+	0.777990i	−0.976127	−	0.217201i	$-0.930307\pi$
$157$	−11.0034	+	9.74818i	−0.878169	+	0.777990i	0.0979582	+	0.995191i	$0.468769\pi$
$158$	16.1563	−	2.96075i	1.28533	−	0.235545i
$159$	−13.4236	+	19.7607i	−1.06456	+	1.56712i
$160$	−0.819245	+	0.565484i	−0.0647670	+	0.0447054i
$161$	−16.9253	−	10.2317i	−1.33390	−	0.806369i
$162$	8.34821	−	20.1307i	0.655897	−	1.58162i
$163$	−8.90574	+	11.3673i	−0.697551	+	0.890359i	−0.997985	−	0.0634440i	$-0.979792\pi$
$163$	−8.90574	+	11.3673i	−0.697551	+	0.890359i	0.300434	+	0.953803i	$0.402869\pi$
$164$	−1.00481	+	16.6115i	−0.0784627	+	1.29714i
$165$	1.97914	−	2.26779i	0.154075	−	0.176547i
$166$	13.0834	−	24.9283i	1.01547	−	1.93481i
$167$	11.8623	+	2.17384i	0.917929	+	0.168217i	0.618394	−	0.785868i	$-0.287784\pi$
$167$	11.8623	+	2.17384i	0.917929	+	0.168217i	0.299536	+	0.954085i	$0.403168\pi$
$168$	33.4168	+	12.3894i	2.57816	+	0.955864i
$169$	5.96694	−	11.5497i	0.458996	−	0.888439i
$170$		−	5.26890i		−	0.404106i
$171$	12.0431	+	14.9089i	0.920956	+	1.14011i
$172$	−0.0254057	−	0.0133340i	−0.00193717	−	0.00101670i
$173$	−5.24179	+	13.8215i	−0.398526	+	1.05083i	0.574168	+	0.818737i	$0.305326\pi$
$173$	−5.24179	+	13.8215i	−0.398526	+	1.05083i	−0.972694	+	0.232090i	$0.925444\pi$
$174$	−16.0951	+	36.4856i	−1.22017	+	2.76597i
$175$	−15.7686	−	12.3539i	−1.19200	−	0.933870i
$176$	−3.69116	+	6.10593i	−0.278232	+	0.460252i
$177$	14.4002	−	11.4560i	1.08239	−	0.861083i
$178$	5.24922	+	7.60481i	0.393446	+	0.570004i
$179$	−0.327612	−	0.0807490i	−0.0244869	−	0.00603547i	0.227053	−	0.973882i	$-0.427091\pi$
$179$	−0.327612	−	0.0807490i	−0.0244869	−	0.00603547i	−0.251540	+	0.967847i	$0.580937\pi$
$180$	−4.55675	+	7.79784i	−0.339640	+	0.581217i
$181$	2.49914	+	2.82094i	0.185760	+	0.209679i	0.834012	−	0.551746i	$-0.186038\pi$
$181$	2.49914	+	2.82094i	0.185760	+	0.209679i	−0.648252	+	0.761425i	$0.724500\pi$
$182$	7.05003	−	39.1839i	0.522583	−	2.90451i
$183$	1.57096	+	2.93979i	0.116128	+	0.217315i
$184$	−10.1242	+	16.7475i	−0.746369	+	1.23464i
$185$	2.19219	−	2.47447i	0.161173	−	0.181927i
$186$	23.4017	+	2.66477i	1.71590	+	0.195390i
$187$	2.55578	+	5.67872i	0.186897	+	0.415269i
$188$	−19.0702	−	19.0702i	−1.39084	−	1.39084i
$189$	−23.6141	+	1.95877i	−1.71767	+	0.142480i
$190$	−6.23615	−	10.3158i	−0.452418	−	0.748390i
$191$		−	4.22327i		−	0.305585i	−0.988258	−	0.152793i	$-0.951173\pi$
$191$		−	4.22327i		−	0.305585i	0.988258	−	0.152793i	$-0.0488266\pi$
$192$	−5.71528	+	15.4153i	−0.412464	+	1.11250i
$193$	−6.51748	−	10.7812i	−0.469138	−	0.776050i	0.528188	−	0.849128i	$-0.322872\pi$
$193$	−6.51748	−	10.7812i	−0.469138	−	0.776050i	−0.997326	+	0.0730779i	$0.976718\pi$
$194$	0.651012	−	5.36157i	0.0467399	−	0.384938i
$195$	4.56827	+	1.67695i	0.327141	+	0.120089i
$196$	−6.42408	−	52.9071i	−0.458863	−	3.77908i
$197$	10.5286	−	8.24867i	0.750135	−	0.587693i	−0.167147	−	0.985932i	$-0.553455\pi$
$197$	10.5286	−	8.24867i	0.750135	−	0.587693i	0.917282	+	0.398239i	$0.130378\pi$
$198$	1.71297	−	16.1097i	0.121736	−	1.14486i
$199$	15.8089	−	17.8446i	1.12066	−	1.26497i	0.160041	−	0.987110i	$-0.448837\pi$
$199$	15.8089	−	17.8446i	1.12066	−	1.26497i	0.960623	−	0.277857i	$-0.0896241\pi$
$200$	−12.2242	+	15.6031i	−0.864383	+	1.10330i
$201$	1.13186	+	3.53923i	0.0798350	+	0.249638i
$202$	11.8447	+	3.69097i	0.833393	+	0.259696i
$203$	43.2794	−	2.61792i	3.03762	−	0.183742i
$204$	−10.7289	−	15.2985i	−0.751175	−	1.07111i
$205$	0.803283	+	3.25905i	0.0561037	+	0.227622i
$206$	−2.66162	−	2.08524i	−0.185444	−	0.145286i
$207$	1.37575	−	12.9382i	0.0956211	−	0.899268i
$208$	−11.3530	−	2.04266i	−0.787192	−	0.141633i
$209$	11.7251	+	8.09326i	0.811043	+	0.559823i
$210$	14.8825	+	0.789019i	1.02699	+	0.0544475i
$211$	1.12037	+	2.95417i	0.0771293	+	0.203373i	0.968035	−	0.250815i	$-0.0806986\pi$
$211$	1.12037	+	2.95417i	0.0771293	+	0.203373i	−0.890906	+	0.454188i	$0.849929\pi$
$212$	6.42286	−	52.8970i	0.441124	−	3.63298i
$213$	−6.32536	+	10.6417i	−0.433407	+	0.729154i
$214$	−7.34259	+	4.43875i	−0.501929	+	0.303427i
$215$	−0.00569229	−	0.00104315i	−0.000388211	−	7.11422e-5i
$216$	1.93820	+	23.3661i	0.131878	+	1.58986i
$217$	−9.08093	−	23.9444i	−0.616454	−	1.62546i
$218$	−9.89102	+	5.19121i	−0.669905	+	0.351593i
$219$	9.34090	+	7.20650i	0.631200	+	0.486970i
$220$	−1.60674	+	6.51880i	−0.108326	+	0.439498i
$221$	−7.09616	+	7.14213i	−0.477339	+	0.480432i
$222$	2.01310	−	17.6788i	0.135111	−	1.18653i
$223$	−0.434202	+	7.17821i	−0.0290763	+	0.480688i	0.954270	+	0.298946i	$0.0966351\pi$
$223$	−0.434202	+	7.17821i	−0.0290763	+	0.480688i	−0.983346	+	0.181742i	$0.941826\pi$
$224$	5.78299	−	0.702182i	0.386392	−	0.0469165i
$225$	2.96284	−	12.8410i	0.197523	−	0.856066i
$226$	−32.3203	+	10.0714i	−2.14991	+	0.669940i
$227$	−2.07039	+	0.931806i	−0.137416	+	0.0618461i	−0.477954	−	0.878385i	$-0.658622\pi$
$227$	−2.07039	+	0.931806i	−0.137416	+	0.0618461i	0.340538	+	0.940231i	$0.389391\pi$
$228$	−39.1129	−	17.2541i	−2.59031	−	1.14268i
$229$	−10.3955	+	8.14438i	−0.686956	+	0.538196i	−0.898391	−	0.439196i	$-0.855263\pi$
$229$	−10.3955	+	8.14438i	−0.686956	+	0.538196i	0.211435	+	0.977392i	$0.432186\pi$
$230$	−1.95845	+	7.94574i	−0.129136	+	0.523926i
$231$	−16.4228	+	6.36866i	−1.08054	+	0.419027i
$232$	−2.59043	−	42.8249i	−0.170070	−	2.81159i
$233$	−13.4891	+	7.07963i	−0.883700	+	0.463802i	−0.844578	−	0.535433i	$-0.820149\pi$
$233$	−13.4891	+	7.07963i	−0.883700	+	0.463802i	−0.0391224	+	0.999234i	$0.512456\pi$
$234$	25.3132	−	6.72805i	1.65477	−	0.439827i
$235$	−4.81651	−	2.52790i	−0.314194	−	0.164902i
$236$	−16.8454	+	37.4290i	−1.09655	+	2.43642i
$237$	5.38237	−	10.4435i	0.349622	−	0.678381i
$238$	−14.3292	+	27.3020i	−0.928825	+	1.76973i
$239$	−0.481599	−	0.481599i	−0.0311521	−	0.0311521i	0.691359	−	0.722511i	$-0.257012\pi$
$239$	−0.481599	−	0.481599i	−0.0311521	−	0.0311521i	−0.722511	+	0.691359i	$0.757012\pi$
$240$	0.228608	−	4.31201i	0.0147566	−	0.278339i
$241$	−1.80359	−	29.8168i	−0.116179	−	1.92067i	−0.330322	−	0.943868i	$-0.607157\pi$
$241$	−1.80359	−	29.8168i	−0.116179	−	1.92067i	0.214143	−	0.976802i	$-0.431304\pi$
$242$	2.63046	+	14.3539i	0.169092	+	0.922706i
$243$	−7.75321	−	13.5236i	−0.497369	−	0.867539i
$244$	−6.11882	−	4.22351i	−0.391717	−	0.270383i
$245$	−4.41172	−	9.80244i	−0.281854	−	0.626255i
$246$	13.6115	+	11.8790i	0.867840	+	0.757378i
$247$	−5.44013	+	22.3823i	−0.346147	+	1.42415i
$248$	−23.6930	+	8.98558i	−1.50451	+	0.570585i
$249$	−8.40130	−	18.3015i	−0.532411	−	1.15981i
$250$	−6.28472	+	16.5714i	−0.397480	+	1.04807i
$251$	−1.43304	−	11.8022i	−0.0904528	−	0.744946i	−0.965408	−	0.260743i	$-0.916033\pi$
$251$	−1.43304	−	11.8022i	−0.0904528	−	0.744946i	0.874955	−	0.484203i	$-0.160891\pi$
$252$	44.8188	−	28.0139i	2.82332	−	1.76471i
$253$	−1.74346	−	9.51375i	−0.109610	−	0.598125i
$254$	5.38855	+	29.4044i	0.338108	+	1.84499i
$255$	−2.98397	−	2.30213i	−0.186864	−	0.144165i
$256$	−3.67458	−	30.2629i	−0.229661	−	1.89143i
$257$	−3.04748	+	8.03555i	−0.190097	+	0.501244i	−0.995850	−	0.0910071i	$-0.970991\pi$
$257$	−3.04748	+	8.03555i	−0.190097	+	0.501244i	0.805753	+	0.592251i	$0.201761\pi$
$258$	−0.0283076	+	0.0129946i	−0.00176236	+	0.000809011i
$259$	−18.0889	+	6.86020i	−1.12399	+	0.426272i
$260$	−10.7712	+	1.34317i	−0.668004	+	0.0832999i
$261$	13.6307	+	25.0569i	0.843721	+	1.55098i
$262$	−8.90430	−	19.7845i	−0.550109	−	1.22229i
$263$	10.7980	+	7.45334i	0.665835	+	0.459592i	0.852428	−	0.522845i	$-0.175129\pi$
$263$	10.7980	+	7.45334i	0.665835	+	0.459592i	−0.186593	+	0.982437i	$0.559745\pi$
$264$	6.30178	+	16.2503i	0.387848	+	1.00014i
$265$	−1.93728	−	10.5714i	−0.119006	−	0.649395i
$266$	4.25924	+	70.4137i	0.261151	+	4.31734i
$267$	6.60042	+	0.349932i	0.403939	+	0.0214155i
$268$	−5.86074	−	5.86074i	−0.358002	−	0.358002i
$269$	−7.58551	+	14.4530i	−0.462497	+	0.881214i	0.536800	+	0.843710i	$0.319633\pi$
$269$	−7.58551	+	14.4530i	−0.462497	+	0.881214i	−0.999296	+	0.0375042i	$0.988059\pi$
$270$	3.68070	+	9.08746i	0.224000	+	0.553045i
$271$	6.74553	−	14.9880i	0.409762	−	0.910454i	−0.585265	−	0.810842i	$-0.699009\pi$
$271$	6.74553	−	14.9880i	0.409762	−	0.910454i	0.995026	−	0.0996112i	$-0.0317599\pi$
$272$	7.91042	+	4.15171i	0.479639	+	0.251734i
$273$	−19.1110	−	21.1133i	−1.15665	−	1.27783i
$274$	26.6584	−	13.9914i	1.61050	−	0.845253i
$275$	−0.591497	−	9.77861i	−0.0356686	−	0.589672i
$276$	10.4932	+	27.0588i	0.631619	+	1.62875i
$277$	−3.15274	+	12.7912i	−0.189430	+	0.768546i	0.796948	+	0.604048i	$0.206447\pi$
$277$	−3.15274	+	12.7912i	−0.189430	+	0.768546i	−0.986377	+	0.164498i	$0.947400\pi$
$278$	−29.7124	+	23.2782i	−1.78203	+	1.39613i
$279$	11.7340	−	12.0889i	0.702498	−	0.723746i
$280$	−14.6214	+	6.58055i	−0.873795	+	0.393263i
$281$	22.9302	−	7.14533i	1.36790	−	0.426255i	0.476381	−	0.879239i	$-0.341948\pi$
$281$	22.9302	−	7.14533i	1.36790	−	0.426255i	0.891519	+	0.452984i	$0.149641\pi$
$282$	−29.0368	+	3.74537i	−1.72912	+	0.223034i
$283$	−7.01684	+	0.851998i	−0.417108	+	0.0506461i	−0.326401	−	0.945232i	$-0.605836\pi$
$283$	−7.01684	+	0.851998i	−0.417108	+	0.0506461i	−0.0907072	+	0.995878i	$0.528913\pi$
$284$	1.66726	−	27.5631i	0.0989338	−	1.63557i
$285$	−8.56700	−	0.975530i	−0.507465	−	0.0577854i
$286$	16.6299	−	10.1266i	0.983348	−	0.598798i
$287$	4.70086	−	19.0721i	0.277483	−	1.12579i
$288$	2.03129	+	3.24982i	0.119695	+	0.191498i
$289$	−8.14854	+	4.27669i	−0.479326	+	0.251570i
$290$	−6.36191	−	16.7750i	−0.373584	−	0.985060i
$291$	−2.75201	−	2.71132i	−0.161326	−	0.158940i
$292$	−25.8845	−	4.74351i	−1.51478	−	0.277593i
$293$	16.7771	−	10.1421i	0.980129	−	0.592509i	0.0659518	−	0.997823i	$-0.478992\pi$
$293$	16.7771	−	10.1421i	0.980129	−	0.592509i	0.914178	+	0.405314i	$0.132838\pi$
$294$	−49.7343	−	29.5619i	−2.90056	−	1.72408i
$295$	−0.997874	+	8.21823i	−0.0580985	+	0.478484i
$296$	6.78817	+	17.8989i	0.394554	+	1.04035i
$297$	−8.37505	−	8.00889i	−0.485970	−	0.464723i
$298$	34.0475	+	23.5013i	1.97232	+	1.36139i
$299$	13.3561	−	8.13302i	0.772401	−	0.470345i
$300$	7.24711	+	28.4878i	0.418412	+	1.64474i
$301$	0.0266590	+	0.0208860i	0.00153660	+	0.00120385i
$302$	−1.95238	−	7.92110i	−0.112347	−	0.455808i
$303$	7.26565	−	5.09543i	0.417400	−	0.292725i
$304$	20.4015	−	1.23406i	1.17011	−	0.0707783i
$305$	−1.43168	−	0.446131i	−0.0819780	−	0.0255454i
$306$	−20.2638	−	0.923023i	−1.15840	−	0.0527657i
$307$	8.77394	−	11.1991i	0.500755	−	0.639167i	−0.469014	−	0.883191i	$-0.655391\pi$
$307$	8.77394	−	11.1991i	0.500755	−	0.639167i	0.969769	+	0.244024i	$0.0784675\pi$
$308$	26.0541	−	29.4090i	1.48457	−	1.67574i
$309$	−2.34389	+	0.596269i	−0.133339	+	0.0339206i
$310$	−8.34123	+	6.53494i	−0.473750	+	0.371159i
$311$	−2.86084	−	23.5611i	−0.162223	−	1.33603i	−0.815433	−	0.578851i	$-0.803501\pi$
$311$	−2.86084	−	23.5611i	−0.162223	−	1.33603i	0.653210	−	0.757177i	$-0.273422\pi$
$312$	−20.8916	+	18.9103i	−1.18275	+	1.07058i
$313$	3.66452	−	30.1801i	0.207131	−	1.70588i	−0.404337	−	0.914610i	$-0.632498\pi$
$313$	3.66452	−	30.1801i	0.207131	−	1.70588i	0.611469	−	0.791269i	$-0.290579\pi$
$314$	−18.4154	−	30.4627i	−1.03924	−	1.71911i
$315$	6.94944	−	8.08376i	0.391556	−	0.455468i
$316$			26.2067i			1.47424i
$317$	−14.2557	−	23.5818i	−0.800679	−	1.32448i	−0.942370	−	0.334574i	$-0.891408\pi$
$317$	−14.2557	−	23.5818i	−0.800679	−	1.32448i	0.141690	−	0.989911i	$-0.454746\pi$
$318$	−41.2067	−	40.5974i	−2.31075	−	2.27659i
$319$	14.9938	+	14.9938i	0.839490	+	0.839490i
$320$	−3.03563	−	6.74489i	−0.169697	−	0.377051i
$321$	−0.694361	+	6.09780i	−0.0387554	+	0.340346i
$322$	31.7573	−	35.8465i	1.76976	−	1.99765i
$323$	9.22876	−	15.2662i	0.513502	−	0.849436i
$324$	29.1917	+	18.8910i	1.62176	+	1.04950i
$325$	14.4220	−	6.54689i	0.799988	−	0.363156i
$326$	−23.1875	−	26.1732i	−1.28423	−	1.44960i
$327$	−1.38170	+	7.86984i	−0.0764081	+	0.435203i
$328$	−18.8719	−	4.65149i	−1.04202	−	0.256836i
$329$	18.0830	+	26.1978i	0.996949	+	1.44433i
$330$	4.53755	+	5.70373i	0.249784	+	0.313980i
$331$	−6.06153	+	10.0270i	−0.333172	+	0.551133i	−0.976786	−	0.214216i	$-0.931280\pi$
$331$	−6.06153	+	10.0270i	−0.333172	+	0.551133i	0.643614	+	0.765350i	$0.277434\pi$
$332$	35.3590	+	27.7020i	1.94058	+	1.52034i
$333$	−9.13260	−	8.86449i	−0.500463	−	0.485771i
$334$	−10.3553	+	27.3046i	−0.566615	+	1.49404i
$335$	−1.48023	−	0.776885i	−0.0808737	−	0.0424458i
$336$	−12.9115	+	21.7220i	−0.704378	+	1.18503i
$337$			6.58216i			0.358553i	0.983799	+	0.179277i	$0.0573757\pi$
$337$			6.58216i			0.358553i	−0.983799	+	0.179277i	$0.942624\pi$
$338$	24.9045	+	19.2532i	1.35463	+	1.04724i
$339$	−8.41785	+	22.7047i	−0.457195	+	1.23315i
$340$	8.26886	+	1.51532i	0.448442	+	0.0821800i
$341$	5.82012	−	11.0893i	0.315177	−	0.600520i
$342$	−40.7665	+	22.1766i	−2.20440	+	1.19917i
$343$	−1.87086	+	30.9289i	−0.101017	+	1.67001i
$344$	0.0206667	−	0.0263790i	0.00111427	−	0.00142226i
$345$	3.64426	+	4.58086i	0.196201	+	0.246625i
$346$	−30.6319	−	18.5177i	−1.64678	−	0.995515i
$347$	−5.58785	+	3.85702i	−0.299972	+	0.207056i	−0.708537	−	0.705674i	$-0.750645\pi$
$347$	−5.58785	+	3.85702i	−0.299972	+	0.207056i	0.408565	+	0.912729i	$0.366029\pi$
$348$	−52.6306	−	35.7524i	−2.82129	−	1.91653i
$349$	17.6749	−	3.23905i	0.946116	−	0.173382i	0.315018	−	0.949086i	$-0.397989\pi$
$349$	17.6749	−	3.23905i	0.946116	−	0.173382i	0.631097	+	0.775704i	$0.282605\pi$
$350$	36.3072	−	32.1654i	1.94070	−	1.71931i
$351$	7.24971	−	17.2755i	0.386961	−	0.922096i
$352$	2.13246	+	1.88919i	0.113660	+	0.100694i
$353$	−29.4576	−	17.8078i	−1.56787	−	0.947812i	−0.991425	−	0.130677i	$-0.958285\pi$
$353$	−29.4576	−	17.8078i	−1.56787	−	0.947812i	−0.576447	−	0.817134i	$-0.695561\pi$
$354$	21.0003	+	39.2987i	1.11615	+	2.08870i
$355$	−1.33287	−	5.40766i	−0.0707414	−	0.287009i
$356$	−13.4444	+	6.05085i	−0.712554	+	0.320694i
$357$	9.20130	+	20.0442i	0.486985	+	1.06085i
$358$	0.335323	−	0.745058i	0.0177224	−	0.0393775i
$359$	−16.7977	+	10.1546i	−0.886550	+	0.535938i	−0.885803	−	0.464061i	$-0.846392\pi$
$359$	−16.7977	+	10.1546i	−0.886550	+	0.535938i	−0.000747172		1.00000i	$0.500238\pi$
$360$	−7.99887	−	6.87646i	−0.421578	−	0.362422i
$361$		−	21.8124i		−	1.14802i
$362$	−7.80973	+	4.72114i	−0.410470	+	0.248138i
$363$	9.27848	+	4.78192i	0.486994	+	0.250986i
$364$	59.4666	+	22.3333i	3.11690	+	1.17059i
$365$	−5.26901	+	0.639774i	−0.275793	+	0.0334873i
$366$	−7.68765	+	2.45853i	−0.401840	+	0.128510i
$367$	−4.20796	−	6.09628i	−0.219654	−	0.318223i	0.697630	−	0.716459i	$-0.254238\pi$
$367$	−4.20796	−	6.09628i	−0.219654	−	0.318223i	−0.917283	+	0.398235i	$0.869623\pi$
$368$	−10.3861	−	9.20126i	−0.541412	−	0.479649i
$369$	12.6748	−	2.51844i	0.659823	−	0.131105i
$370$	4.93683	+	6.30139i	0.256653	+	0.327594i
$371$	−18.7113	+	60.0467i	−0.971442	+	3.11747i
$372$	−10.9123	+	35.9596i	−0.565776	+	1.86442i
$373$	1.79721	−	2.60371i	0.0930562	−	0.134815i	−0.773691	−	0.633564i	$-0.781591\pi$
$373$	1.79721	−	2.60371i	0.0930562	−	0.134815i	0.866747	+	0.498748i	$0.166207\pi$
$374$	−14.6411	+	3.60870i	−0.757072	+	0.186602i
$375$	6.63904	+	10.7998i	0.342839	+	0.557699i
$376$	25.9227	−	17.8931i	1.33686	−	0.922768i
$377$	−13.9688	+	31.3071i	−0.719430	+	1.61240i
$378$	5.64168	−	57.0988i	0.290176	−	2.93684i
$379$	−13.7050	+	4.27064i	−0.703977	+	0.219368i	−0.628534	−	0.777782i	$-0.716345\pi$
$379$	−13.7050	+	4.27064i	−0.703977	+	0.219368i	−0.0754431	+	0.997150i	$0.524037\pi$
$380$	17.9829	−	6.82002i	0.922504	−	0.349859i
$381$	19.0072	+	9.79587i	0.973768	+	0.501858i
$382$	10.0590	+	1.84337i	0.514661	+	0.0943151i
$383$	1.48893	+	2.46299i	0.0760808	+	0.125853i	0.891505	−	0.453011i	$-0.149650\pi$
$383$	1.48893	+	2.46299i	0.0760808	+	0.125853i	−0.815424	+	0.578864i	$0.803496\pi$
$384$	−30.4173	−	18.0799i	−1.55223	−	0.922638i
$385$	3.25236	−	7.22645i	0.165756	−	0.368294i
$386$	28.5234	−	10.8175i	1.45180	−	0.550596i
$387$	−0.00500908	+	0.0217094i	−0.000254626	+	0.00110355i
$388$	8.22706	+	2.56366i	0.417666	+	0.130150i
$389$	−9.67413	−	2.38446i	−0.490498	−	0.120897i	−0.0136933	−	0.999906i	$-0.504359\pi$
$389$	−9.67413	−	2.38446i	−0.490498	−	0.120897i	−0.476804	+	0.879009i	$0.658205\pi$
$390$	−5.98810	+	10.1487i	−0.303219	+	0.513900i
$391$	−11.7588	+	2.89827i	−0.594666	+	0.146572i
$392$	62.1323	+	3.75831i	3.13816	+	0.189823i
$393$	−15.0953	−	3.60160i	−0.761455	−	0.181677i
$394$	15.0511	+	28.6774i	0.758262	+	1.44475i
$395$	1.57253	+	5.04643i	0.0791226	+	0.253913i
$396$	24.7894	+	7.32140i	1.24571	+	0.367914i
$397$	−13.9199	−	0.842000i	−0.698621	−	0.0422588i	−0.292750	−	0.956189i	$-0.594570\pi$
$397$	−13.9199	−	0.842000i	−0.698621	−	0.0422588i	−0.405871	+	0.913930i	$0.633032\pi$
$398$	35.6018	+	45.4423i	1.78456	+	2.27782i
$399$	41.7389	+	28.3536i	2.08956	+	1.41946i
$400$	−9.31951	−	10.5196i	−0.465976	−	0.525978i
$401$	−5.21242	+	0.315293i	−0.260296	+	0.0157450i	−0.190011	−	0.981782i	$-0.560852\pi$
$401$	−5.21242	+	0.315293i	−0.260296	+	0.0157450i	−0.0702848	+	0.997527i	$0.522391\pi$
$402$	−8.92374	+	1.15105i	−0.445076	+	0.0574090i
$403$	20.1080	+	2.37570i	1.00165	+	0.118342i
$404$	−9.19903	+	17.5273i	−0.457669	+	0.872015i
$405$	6.75477	+	1.88605i	0.335647	+	0.0937187i
$406$	−12.6552	+	104.225i	−0.628068	+	5.17261i
$407$	−8.37743	−	4.39682i	−0.415254	−	0.217942i
$408$	19.8337	−	9.10469i	0.981916	−	0.450749i
$409$	22.3151	−	6.95368i	1.10341	−	0.343837i	0.308906	−	0.951093i	$-0.400037\pi$
$409$	22.3151	−	6.95368i	1.10341	−	0.343837i	0.794507	+	0.607255i	$0.207729\pi$
$410$	−8.11299	+	0.490746i	−0.400672	+	0.0242362i
$411$	3.72398	−	21.2109i	0.183690	−	1.04626i
$412$	4.03800	−	3.57735i	0.198938	−	0.176243i
$413$	27.5209	−	39.8709i	1.35421	−	1.96192i
$414$	30.2157	+	8.92402i	1.48502	+	0.438591i
$415$	8.47106	+	3.21265i	0.415828	+	0.157703i
$416$	−1.61940	+	4.31194i	−0.0793975	+	0.211410i
$417$	0.201091	+	26.9982i	0.00984749	+	1.32211i
$418$	−24.3942	+	24.3942i	−1.19316	+	1.19316i
$419$	−7.33405	−	2.78144i	−0.358292	−	0.135882i	0.168890	−	0.985635i	$-0.445982\pi$
$419$	−7.33405	−	2.78144i	−0.358292	−	0.135882i	−0.527181	+	0.849753i	$0.676751\pi$
$420$	−5.51844	+	23.1292i	−0.269272	+	1.12859i
$421$	4.64621	−	14.9102i	0.226442	−	0.726679i	−0.769659	−	0.638456i	$-0.779574\pi$
$421$	4.64621	−	14.9102i	0.226442	−	0.726679i	0.996101	−	0.0882229i	$-0.0281188\pi$
$422$	−7.52523	+	1.37905i	−0.366323	+	0.0671311i
$423$	−10.5659	+	18.0811i	−0.513731	+	0.879133i
$424$	59.4162	+	18.5148i	2.88550	+	0.899159i
$425$	−12.1769	+	1.47854i	−0.590665	+	0.0717197i
$426$	−22.5853	−	19.7106i	−1.09426	−	0.954980i
$427$	6.20532	+	6.20532i	0.300296	+	0.300296i
$428$	−4.85434	−	12.7998i	−0.234643	−	0.618703i
$429$	1.53102	−	13.8427i	0.0739185	−	0.668334i
$430$	0.00496913	−	0.0131025i	0.000239633	−	0.000631860i
$431$	−0.581138	+	0.261549i	−0.0279924	+	0.0125984i	−0.424361	−	0.905493i	$-0.639501\pi$
$431$	−0.581138	+	0.261549i	−0.0279924	+	0.0125984i	0.396368	+	0.918092i	$0.370270\pi$
$432$	−16.5436	−	1.63460i	−0.795956	−	0.0786449i
$433$	−12.3751	−	13.9686i	−0.594707	−	0.671286i	0.371685	−	0.928359i	$-0.378780\pi$
$433$	−12.3751	−	13.9686i	−0.594707	−	0.671286i	−0.966392	+	0.257073i	$0.917242\pi$
$434$	60.9943	−	11.1776i	2.92782	−	0.536543i
$435$	−12.2800	−	3.72648i	−0.588780	−	0.178671i
$436$	−5.30230	−	17.0157i	−0.253934	−	0.814903i
$437$	−19.5919	+	19.5919i	−0.937205	+	0.937205i
$438$	−21.2415	+	19.1026i	−1.01496	+	0.912757i
$439$	−23.7829	−	2.88776i	−1.13509	−	0.137825i	−0.468653	−	0.883382i	$-0.655260\pi$
$439$	−23.7829	−	2.88776i	−1.13509	−	0.137825i	−0.666442	+	0.745557i	$0.732184\pi$
$440$	−7.15057	−	3.21821i	−0.340890	−	0.153422i
$441$	−38.4723	+	15.2499i	−1.83202	+	0.726187i
$442$	−13.9137	−	20.0190i	−0.661809	−	0.952205i
$443$	3.17932	+	6.05769i	0.151054	+	0.287809i	0.949211	−	0.314640i	$-0.101884\pi$
$443$	3.17932	+	6.05769i	0.151054	+	0.287809i	−0.798157	+	0.602449i	$0.794191\pi$
$444$	27.1657	+	8.24370i	1.28923	+	0.391229i
$445$	−2.22581	+	1.97190i	−0.105514	+	0.0934769i
$446$	−16.9075	−	4.16732i	−0.800592	−	0.197328i
$447$	28.1860	−	9.01397i	1.33315	−	0.426346i
$448$	−2.61347	+	43.2059i	−0.123475	+	2.04129i
$449$	−5.56113	−	12.3563i	−0.262446	−	0.583131i	0.732809	−	0.680435i	$-0.238209\pi$
$449$	−5.56113	−	12.3563i	−0.262446	−	0.583131i	−0.995255	+	0.0973034i	$0.968978\pi$
$450$	29.2913	+	12.6617i	1.38081	+	0.596878i
$451$	8.50599	−	4.46429i	0.400531	−	0.210215i
$452$	−6.51053	−	53.6191i	−0.306230	−	2.52203i
$453$	−5.33906	−	2.35525i	−0.250851	−	0.110659i
$454$	−1.31569	−	5.33795i	−0.0617482	−	0.250522i
$455$	12.7911	+	0.732277i	0.599657	+	0.0343297i
$456$	28.0559	−	41.3006i	1.31384	−	1.93408i
$457$	10.5895	−	33.9829i	0.495355	−	1.58965i	−0.281231	−	0.959640i	$-0.590743\pi$
$457$	10.5895	−	33.9829i	0.495355	−	1.58965i	0.776586	−	0.630011i	$-0.216950\pi$
$458$	−14.8608	−	28.3149i	−0.694399	−	1.32307i
$459$	−9.37659	+	11.0729i	−0.437662	+	0.516836i
$460$	−11.9066	−	5.35871i	−0.555147	−	0.249851i
$461$	−2.11353	+	11.5332i	−0.0984371	+	0.537154i	0.897024	+	0.441982i	$0.145725\pi$
$461$	−2.11353	+	11.5332i	−0.0984371	+	0.537154i	−0.995461	+	0.0951716i	$0.969660\pi$
$462$	−8.00060	−	41.8955i	−0.372222	−	1.94915i
$463$	0.233745	−	1.27550i	0.0108630	−	0.0592777i	−0.977742	−	0.209812i	$-0.932715\pi$
$463$	0.233745	−	1.27550i	0.0108630	−	0.0592777i	0.988605	+	0.150534i	$0.0480994\pi$
$464$	30.1979	+	3.66669i	1.40190	+	0.170222i
$465$	0.0564528	+	7.57925i	0.00261793	+	0.351479i
$466$	−10.9745	−	35.2183i	−0.508383	−	1.63146i
$467$	−19.6025	+	28.3991i	−0.907094	+	1.31415i	0.0419869	+	0.999118i	$0.486631\pi$
$467$	−19.6025	+	28.3991i	−0.907094	+	1.31415i	−0.949080	+	0.315034i	$0.897984\pi$
$468$	3.27880	+	41.6607i	0.151563	+	1.92577i
$469$	5.55736	+	8.05123i	0.256615	+	0.371771i
$470$	8.12323	−	10.3685i	0.374697	−	0.478265i
$471$	−25.2984	−	2.88074i	−1.16569	−	0.132738i
$472$	−39.4522	−	27.2319i	−1.81594	−	1.25345i
$473$	0.00100000	+	0.0165320i	4.59802e−5	+	0.000760144i
$474$	22.5251	+	17.3781i	1.03461	+	0.798202i
$475$	−22.0908	+	17.3071i	−1.01360	+	0.794103i
$476$	−38.7260	−	30.3399i	−1.77500	−	1.39063i
$477$	−40.9962	+	5.59870i	−1.87709	+	0.256347i
$478$	1.35728	−	0.936861i	0.0620804	−	0.0428510i
$479$	−2.98492	−	3.80996i	−0.136384	−	0.174082i	0.714164	−	0.699978i	$-0.246807\pi$
$479$	−2.98492	−	3.80996i	−0.136384	−	0.174082i	−0.850549	+	0.525896i	$0.823730\pi$
$480$	−1.67711	−	0.400144i	−0.0765491	−	0.0182640i
$481$	1.79472	−	15.1906i	0.0818324	−	0.692633i
$482$	71.8047	+	8.71867i	3.27061	+	0.397125i
$483$	−6.42556	−	33.6477i	−0.292373	−	1.53102i
$484$	−23.2832			−1.05833
$485$	1.73805			0.0789210
$486$	35.5945	−	12.5638i	1.61460	−	0.569903i
$487$	17.3542	+	7.81050i	0.786395	+	0.353927i	0.763498	−	0.645810i	$-0.223480\pi$
$487$	17.3542	+	7.81050i	0.786395	+	0.353927i	0.0228967	+	0.999738i	$0.492711\pi$
$488$	6.14016	−	6.14016i	0.277952	−	0.277952i
$489$	−24.9541	+	1.69608i	−1.12847	+	0.0766993i
$490$	25.2730	−	6.22923i	1.14172	−	0.281408i
$491$	−8.70556	−	7.71246i	−0.392877	−	0.348058i	0.443441	−	0.896304i	$-0.353758\pi$
$491$	−8.70556	−	7.71246i	−0.392877	−	0.348058i	−0.836318	+	0.548245i	$0.815296\pi$
$492$	−22.5572	+	17.9452i	−1.01696	+	0.809032i
$493$	17.6061	−	19.8732i	0.792939	−	0.895044i
$494$	−50.9354	−	22.7267i	−2.29169	−	1.02252i
$495$	5.21282	−	0.0776579i	0.234299	−	0.00349047i
$496$	−3.23858	−	17.6723i	−0.145416	−	0.793511i
$497$	−7.80002	+	31.6459i	−0.349879	+	1.41951i
$498$	47.2573	−	12.0219i	2.11765	−	0.538716i
$499$	−7.33300	+	12.1303i	−0.328270	+	0.543025i	−0.975703	−	0.219098i	$-0.929689\pi$
$499$	−7.33300	+	12.1303i	−0.328270	+	0.543025i	0.647433	+	0.762122i	$0.275843\pi$
$500$	−24.1993	−	14.6290i	−1.08222	−	0.654227i
$501$	10.9391	+	17.7947i	0.488723	+	0.795010i
$502$	28.7358	+	1.73820i	1.28254	+	0.0775795i
$503$	31.1202	+	11.8023i	1.38758	+	0.526240i	0.931514	−	0.363705i	$-0.118488\pi$
$503$	31.1202	+	11.8023i	1.38758	+	0.526240i	0.456068	+	0.889945i	$0.349257\pi$
$504$	22.7469	+	57.3856i	1.01323	+	2.55616i
$505$	−0.719665	+	3.92708i	−0.0320247	+	0.174753i
$506$	23.4208			1.04118
$507$	21.7853	−	5.69207i	0.967520	−	0.252794i
$508$	−47.6961			−2.11617
$509$	−5.83811	+	31.8575i	−0.258770	+	1.41206i	0.555473	+	0.831535i	$0.312537\pi$
$509$	−5.83811	+	31.8575i	−0.258770	+	1.41206i	−0.814242	+	0.580525i	$0.802847\pi$
$510$	6.78565	−	6.10237i	0.300473	−	0.270217i
$511$	29.0425	+	11.0144i	1.28477	+	0.487247i
$512$	32.8993	+	1.99004i	1.45396	+	0.0879482i
$513$	−5.25262	+	32.7772i	−0.231909	+	1.44715i
$514$	−17.8089	−	10.7658i	−0.785515	−	0.474860i
$515$	0.562907	−	0.931162i	0.0248047	−	0.0410319i
$516$	−0.0122522	−	0.0481624i	−0.000539373	−	0.00212023i
$517$	−3.72560	+	15.1154i	−0.163852	+	0.664773i
$518$	−8.44415	−	46.0782i	−0.371015	−	2.02456i
$519$	−23.8712	+	9.25711i	−1.04783	+	0.406342i
$520$	0.724588	−	12.6568i	0.0317753	−	0.555038i
$521$	2.20753	−	2.49179i	0.0967136	−	0.109167i	−0.698161	−	0.715941i	$-0.745998\pi$
$521$	2.20753	−	2.49179i	0.0967136	−	0.109167i	0.794875	+	0.606774i	$0.207537\pi$
$522$	−65.6298	+	21.5287i	−2.87254	+	0.942288i
$523$	−20.9541	−	18.5637i	−0.916259	−	0.811734i	0.0662784	−	0.997801i	$-0.478887\pi$
$523$	−20.9541	−	18.5637i	−0.916259	−	0.811734i	−0.982537	+	0.186067i	$0.940426\pi$
$524$	33.6101	−	8.28416i	1.46827	−	0.361895i
$525$	−2.35278	−	34.6161i	−0.102684	−	1.51077i
$526$	−22.4654	+	22.4654i	−0.979539	+	0.979539i
$527$	−14.2997	−	6.43579i	−0.622907	−	0.280348i
$528$	−12.1387	+	2.31807i	−0.528268	+	0.100881i
$529$	−4.18998			−0.182173
$530$	26.0244			1.13043
$531$	31.4319	+	5.27745i	1.36403	+	0.229022i
$532$	−111.730	−	13.5665i	−4.84412	−	0.588183i
$533$	11.6583	+	10.2614i	0.504978	+	0.444469i
$534$	−3.71441	+	15.5681i	−0.160738	+	0.673697i
$535$	−1.70281	−	2.17348i	−0.0736191	−	0.0939678i
$536$	7.96669	−	5.49901i	0.344108	−	0.237521i
$537$	−0.275441	−	0.515443i	−0.0118862	−	0.0222430i
$538$	−31.1131	−	24.3755i	−1.34138	−	1.05090i
$539$	−24.2171	+	18.9729i	−1.04311	+	0.817222i
$540$	−15.3202	+	3.16286i	−0.659275	+	0.136108i
$541$	0.00439185	+	0.0726060i	0.000188821	+	0.00312158i	0.998269	−	0.0588176i	$-0.0187330\pi$
$541$	0.00439185	+	0.0726060i	0.000188821	+	0.00312158i	−0.998080	+	0.0619392i	$0.980272\pi$
$542$	32.7539	+	22.6084i	1.40690	+	0.971114i
$543$	−0.738536	+	6.48574i	−0.0316936	+	0.278330i
$544$	2.19995	−	2.80803i	0.0943222	−	0.120393i
$545$	−2.04205	−	2.95841i	−0.0874716	−	0.126725i
$546$	58.6290	−	36.3028i	2.50909	−	1.55362i
$547$	10.8983	−	15.7889i	0.465976	−	0.675083i	−0.517590	−	0.855629i	$-0.673171\pi$
$547$	10.8983	−	15.7889i	0.465976	−	0.675083i	0.983567	+	0.180545i	$0.0577863\pi$
$548$	14.2908	+	45.8609i	0.610474	+	1.95908i
$549$	−1.96660	+	5.42800i	−0.0839322	+	0.231662i
$550$	23.5488	+	2.85934i	1.00412	+	0.121923i
$551$	10.9491	−	59.7474i	0.466448	−	2.54533i
$552$	−33.2944	+	6.35809i	−1.41710	+	0.270618i
$553$	5.57575	−	30.4259i	0.237105	−	1.29384i
$554$	−29.0898	−	13.0922i	−1.23591	−	0.556236i
$555$	5.72575	−	0.0426473i	0.243045	−	0.00181028i
$556$	−27.9869	−	53.3246i	−1.18691	−	2.26147i
$557$	−6.64802	+	21.3343i	−0.281686	+	0.903961i	0.700112	+	0.714033i	$0.253133\pi$
$557$	−6.64802	+	21.3343i	−0.281686	+	0.903961i	−0.981798	+	0.189929i	$0.939174\pi$
$558$	23.6717	+	33.2246i	1.00210	+	1.40651i
$559$	−0.0243823	+	0.0110684i	−0.00103126	+	0.000468143i
$560$	−2.72068	−	11.0382i	−0.114970	−	0.466451i
$561$	−4.35337	+	9.86853i	−0.183799	+	0.416650i
$562$	7.01014	+	57.7337i	0.295705	+	2.43535i
$563$	−26.0825	+	13.6892i	−1.09925	+	0.576930i	−0.913980	−	0.405758i	$-0.867007\pi$
$563$	−26.0825	+	13.6892i	−1.09925	+	0.576930i	−0.185268	+	0.982688i	$0.559315\pi$
$564$	2.47305	−	46.6467i	0.104134	−	1.96418i
$565$	−4.47109	−	9.93435i	−0.188100	−	0.417941i
$566$	1.03342	−	17.0845i	0.0434380	−	0.718116i
$567$	−29.8721	−	28.1432i	−1.25451	−	1.18190i
$568$	31.3136	+	7.71812i	1.31389	+	0.323845i
$569$	1.96045	−	1.73680i	0.0821862	−	0.0728106i	−0.621029	−	0.783787i	$-0.713285\pi$
$569$	1.96045	−	1.73680i	0.0821862	−	0.0728106i	0.703216	+	0.710977i	$0.251747\pi$
$570$	6.06283	−	19.9790i	0.253944	−	0.836829i
$571$	−14.4060	−	27.4484i	−0.602874	−	1.14868i	−0.975355	−	0.220641i	$-0.929185\pi$
$571$	−14.4060	−	27.4484i	−0.602874	−	1.14868i	0.372481	−	0.928040i	$-0.378507\pi$
$572$	11.1097	+	29.0109i	0.464518	+	1.21301i
$573$	5.43902	−	4.89134i	0.227218	−	0.204338i
$574$	43.3740	+	19.5211i	1.81040	+	0.814793i
$575$	18.9128	+	2.29644i	0.788720	+	0.0957680i
$576$	−26.4722	+	10.4932i	−1.10301	+	0.437218i
$577$	−7.44346	+	7.44346i	−0.309875	+	0.309875i	−0.844861	−	0.534986i	$-0.820317\pi$
$577$	−7.44346	+	7.44346i	−0.309875	+	0.309875i	0.534986	+	0.844861i	$0.320317\pi$
$578$	−6.62950	−	21.2748i	−0.275751	−	0.884916i
$579$	6.33634	−	20.8803i	0.263329	−	0.867757i
$580$	28.1558	−	5.15975i	1.16911	−	0.214247i
$581$	−35.1577	−	39.6848i	−1.45859	−	1.64640i
$582$	7.65898	−	5.37128i	0.317475	−	0.222647i
$583$	−28.0486	+	12.6237i	−1.16166	+	0.522819i
$584$	10.8987	−	28.7376i	0.450992	−	1.18917i
$585$	3.13122	+	7.82555i	0.129460	+	0.323546i
$586$	16.8335	+	44.3864i	0.695387	+	1.83359i
$587$	8.62425	+	8.62425i	0.355961	+	0.355961i	0.862322	−	0.506361i	$-0.169010\pi$
$587$	8.62425	+	8.62425i	0.355961	+	0.355961i	−0.506361	+	0.862322i	$0.669010\pi$
$588$	60.6971	−	69.5497i	2.50311	−	2.86818i
$589$	−35.6144	+	4.32437i	−1.46747	+	0.178183i
$590$	−19.1386	−	5.96382i	−0.787922	−	0.245527i
$591$	22.8173	+	4.00601i	0.938580	+	0.164785i
$592$	−13.3506	+	2.44659i	−0.548706	+	0.100554i
$593$	11.4044	−	36.5981i	0.468324	−	1.50290i	−0.354745	−	0.934963i	$-0.615432\pi$
$593$	11.4044	−	36.5981i	0.468324	−	1.50290i	0.823069	−	0.567942i	$-0.192260\pi$
$594$	22.7311	−	16.4519i	0.932666	−	0.675030i
$595$	−9.27770	−	3.51857i	−0.380349	−	0.144247i
$596$	−46.6743	+	46.6743i	−1.91185	+	1.91185i
$597$	41.2911	−	0.307550i	1.68993	−	0.0125872i
$598$	13.5415	+	35.3612i	0.553754	+	1.44603i
$599$	−7.43209	−	2.81862i	−0.303667	−	0.115166i	0.198065	−	0.980189i	$-0.436534\pi$
$599$	−7.43209	−	2.81862i	−0.303667	−	0.115166i	−0.501732	+	0.865023i	$0.667304\pi$
$600$	−34.2526	+	2.32807i	−1.39836	+	0.0950433i
$601$	24.4017	−	35.3519i	0.995365	−	1.44204i	0.100901	−	0.994896i	$-0.467827\pi$
$601$	24.4017	−	35.3519i	0.995365	−	1.44204i	0.894464	−	0.447139i	$-0.147557\pi$
$602$	−0.0613821	+	0.0543798i	−0.00250175	+	0.00221636i
$603$	−3.24716	+	5.55677i	−0.132235	+	0.226289i
$604$	12.9926	−	0.785910i	0.528663	−	0.0319782i
$605$	−4.48346	+	1.39710i	−0.182279	+	0.0568003i
$606$	8.96494	+	19.5293i	0.364176	+	0.793324i
$607$	3.55286	+	1.86469i	0.144206	+	0.0756852i	0.535283	−	0.844673i	$-0.320205\pi$
$607$	3.55286	+	1.86469i	0.144206	+	0.0756852i	−0.391077	+	0.920358i	$0.627897\pi$
$608$	0.983712	−	8.10159i	0.0398948	−	0.328563i
$609$	53.4971	+	52.7061i	2.16781	+	2.13576i
$610$	1.68749	−	3.21525i	0.0683246	−	0.130182i
$611$	−24.9756	+	3.11445i	−1.01041	+	0.125997i
$612$	7.27640	−	31.5360i	0.294131	−	1.27477i
$613$	−15.3671	+	0.929536i	−0.620670	+	0.0375436i	−0.367721	−	0.929936i	$-0.619862\pi$
$613$	−15.3671	+	0.929536i	−0.620670	+	0.0375436i	−0.252949	+	0.967480i	$0.581400\pi$
$614$	22.8443	+	25.7859i	0.921921	+	1.04063i
$615$	−3.26687	+	4.80911i	−0.131733	+	0.193922i
$616$	28.3001	+	36.1225i	1.14025	+	1.45542i
$617$	−27.3936	−	1.65701i	−1.10283	−	0.0667087i	−0.501084	−	0.865399i	$-0.667065\pi$
$617$	−27.3936	−	1.65701i	−1.10283	−	0.0667087i	−0.601742	+	0.798690i	$0.705527\pi$
$618$	−0.397130	−	5.84291i	−0.0159749	−	0.235036i
$619$	12.2561	+	39.3313i	0.492615	+	1.58086i	0.781764	+	0.623574i	$0.214320\pi$
$619$	12.2561	+	39.3313i	0.492615	+	1.58086i	−0.289149	+	0.957284i	$0.593372\pi$
$620$	−7.85682	−	14.9699i	−0.315538	−	0.601207i
$621$	18.2561	−	13.2131i	0.732592	−	0.530223i
$622$	57.3663	+	3.47002i	2.30018	+	0.139135i
$623$	16.8963	−	4.16456i	0.676936	−	0.166850i
$624$	−10.5183	−	16.9870i	−0.421068	−	0.680025i
$625$	15.7880	+	3.89140i	0.631521	+	0.155656i
$626$	70.2832	+	21.9011i	2.80908	+	0.875345i
$627$	3.15682	+	24.4739i	0.126071	+	0.977394i
$628$	53.1036	−	20.1395i	2.11906	−	0.803655i
$629$	−4.86193	+	10.8028i	−0.193858	+	0.430734i
$630$	16.2205	+	20.0805i	0.646242	+	0.800027i
$631$	21.0616	+	34.8401i	0.838448	+	1.38696i	0.920667	+	0.390348i	$0.127645\pi$
$631$	21.0616	+	34.8401i	0.838448	+	1.38696i	−0.0822192	+	0.996614i	$0.526201\pi$
$632$	−30.1064	−	5.51720i	−1.19757	−	0.219463i
$633$	−2.50698	+	4.86436i	−0.0996436	+	0.193341i
$634$	62.3892	−	23.6611i	2.47779	−	0.939703i
$635$	−9.18447	+	2.86200i	−0.364475	+	0.113575i
$636$	75.5633	−	52.9928i	2.99628	−	2.10130i
$637$	−42.6478	−	25.5938i	−1.68977	−	1.01406i
$638$	−42.2565	+	29.1676i	−1.67295	+	1.15476i
$639$	−21.0310	+	4.17879i	−0.831973	+	0.165310i
$640$	15.4569	−	3.80977i	0.610986	−	0.150595i
$641$	−16.8740	+	24.4462i	−0.666482	+	0.965566i	0.333259	+	0.942835i	$0.391852\pi$
$641$	−16.8740	+	24.4462i	−0.666482	+	0.965566i	−0.999742	+	0.0227310i	$0.992764\pi$
$642$	−14.2206	−	4.31539i	−0.561243	−	0.170315i
$643$	14.7961	−	47.4825i	0.583503	−	1.87253i	0.104928	−	0.994480i	$-0.466539\pi$
$643$	14.7961	−	47.4825i	0.583503	−	1.87253i	0.478575	−	0.878047i	$-0.341153\pi$
$644$	47.1232	+	60.1483i	1.85691	+	2.37018i
$645$	−0.00524929	−	0.00853908i	−0.000206691	−	0.000336226i
$646$	32.3328	+	28.6444i	1.27212	+	1.12700i
$647$	9.21271	+	13.3469i	0.362189	+	0.524722i	0.961139	−	0.276065i	$-0.0890305\pi$
$647$	9.21271	+	13.3469i	0.362189	+	0.524722i	−0.598950	+	0.800787i	$0.704415\pi$
$648$	−27.8477	+	29.5585i	−1.09396	+	1.16117i
$649$	23.5201	−	2.85585i	0.923243	−	0.112102i
$650$	9.29843	+	37.2078i	0.364714	+	1.45941i
$651$	20.3199	−	39.4272i	0.796399	−	1.54527i
$652$	47.7442	−	28.8624i	1.86981	−	1.13034i
$653$		−	49.5872i		−	1.94050i	−0.242108	−	0.970249i	$-0.577839\pi$
$653$		−	49.5872i		−	1.94050i	0.242108	−	0.970249i	$-0.422161\pi$
$654$	−18.1412	−	6.72595i	−0.709379	−	0.263005i
$655$	5.97496	−	3.61199i	0.233461	−	0.141132i
$656$	5.65598	−	12.5671i	0.220829	−	0.490661i
$657$	1.53748	+	20.3763i	0.0599829	+	0.794956i
$658$	−70.2905	+	31.6352i	−2.74021	+	1.23327i
$659$	5.68292	+	23.0565i	0.221375	+	0.898154i	0.971535	+	0.236897i	$0.0761304\pi$
$659$	5.68292	+	23.0565i	0.221375	+	0.898154i	−0.750160	+	0.661257i	$0.770023\pi$
$660$	−10.2563	+	5.48072i	−0.399225	+	0.213337i
$661$	−5.43992	−	3.28855i	−0.211588	−	0.127910i	0.407575	−	0.913172i	$-0.366374\pi$
$661$	−5.43992	−	3.28855i	−0.211588	−	0.127910i	−0.619164	+	0.785262i	$0.712528\pi$
$662$	−21.2365	−	18.8139i	−0.825379	−	0.731222i
$663$	−17.4168	−	0.866995i	−0.676412	−	0.0336713i
$664$	−39.2681	+	34.7885i	−1.52390	+	1.35006i
$665$	−22.3291	+	4.09196i	−0.865885	+	0.158679i
$666$	25.0996	−	17.8828i	0.972588	−	0.692944i
$667$	−33.9377	+	23.4255i	−1.31407	+	0.907038i
$668$	−39.8729	−	24.1040i	−1.54273	−	0.932612i
$669$	−9.74747	+	7.75451i	−0.376859	+	0.299807i
$670$	2.49647	−	3.18651i	0.0964471	−	0.123106i
$671$	−0.259127	+	4.28389i	−0.0100035	+	0.165378i
$672$	7.60210	+	6.63447i	0.293257	+	0.255930i
$673$	−18.9351	+	36.0779i	−0.729896	+	1.39070i	0.183249	+	0.983067i	$0.441339\pi$
$673$	−18.9351	+	36.0779i	−0.729896	+	1.39070i	−0.913145	+	0.407635i	$0.866354\pi$
$674$	−15.6773	−	2.87298i	−0.603869	−	0.110663i
$675$	19.9690	−	11.0565i	0.768608	−	0.425565i
$676$	−37.3780	+	33.5473i	−1.43761	+	1.29028i
$677$			4.41038i			0.169505i	0.996402	+	0.0847524i	$0.0270099\pi$
$677$			4.41038i			0.169505i	−0.996402	+	0.0847524i	$0.972990\pi$
$678$	−50.4036	−	29.9597i	−1.93574	−	1.15060i
$679$	−9.00613	−	4.72678i	−0.345624	−	0.181397i
$680$	−3.48162	+	9.18028i	−0.133514	+	0.352048i
$681$	−3.59794	−	1.58718i	−0.137873	−	0.0608209i
$682$	23.8721	+	18.7026i	0.914109	+	0.716159i
$683$	22.8261	−	37.7590i	0.873417	−	1.44481i	−0.0220882	−	0.999756i	$-0.507031\pi$
$683$	22.8261	−	37.7590i	0.873417	−	1.44481i	0.895505	−	0.445052i	$-0.146815\pi$
$684$	−23.0790	−	70.3557i	−0.882448	−	2.69012i
$685$	5.50375	+	7.97356i	0.210288	+	0.304654i
$686$	−72.8497	−	17.9558i	−2.78141	−	0.685557i
$687$	−22.5289	−	3.95536i	−0.859529	−	0.150907i
$688$	0.0157559	+	0.0177847i	0.000600687	+	0.000678035i
$689$	−35.2768	−	35.0497i	−1.34394	−	1.33529i
$690$	−12.5013	+	6.68042i	−0.475917	+	0.254319i
$691$	−10.7301	+	17.7498i	−0.408192	+	0.675233i	−0.990466	−	0.137761i	$-0.956010\pi$
$691$	−10.7301	+	17.7498i	−0.408192	+	0.675233i	0.582273	+	0.812993i	$0.302163\pi$
$692$	37.8708	−	42.7473i	1.43963	−	1.62501i
$693$	−27.2226	−	13.7743i	−1.03410	−	0.523242i
$694$	−6.74763	−	14.9926i	−0.256136	−	0.569112i
$695$	−8.58896	−	8.58896i	−0.325798	−	0.325798i
$696$	52.1527	−	52.9354i	1.97684	−	2.00651i
$697$	−6.22265	−	10.2935i	−0.235700	−	0.389895i
$698$			43.5117i			1.64694i
$699$	−24.7405	−	9.17265i	−0.935772	−	0.346942i
$700$	40.0375	+	66.2302i	1.51328	+	2.50327i
$701$	−2.52920	+	20.8298i	−0.0955264	+	0.786731i	0.863683	+	0.504035i	$0.168152\pi$
$701$	−2.52920	+	20.8298i	−0.0955264	+	0.786731i	−0.959210	+	0.282696i	$0.908771\pi$
$702$	37.9822	+	24.8077i	1.43355	+	0.936306i
$703$	3.26685	+	26.9049i	0.123212	+	1.01474i
$704$	−16.6634	+	13.0550i	−0.628026	+	0.492027i
$705$	−2.32281	−	9.13080i	−0.0874822	−	0.343886i
$706$	55.2721	−	62.3893i	2.08019	−	2.34805i
$707$	14.4091	−	18.3919i	0.541911	−	0.691699i
$708$	−67.7138	+	21.6551i	−2.54484	+	0.813849i
$709$	22.2592	+	6.93625i	0.835962	+	0.260496i	0.685457	−	0.728113i	$-0.259602\pi$
$709$	22.2592	+	6.93625i	0.835962	+	0.260496i	0.150505	+	0.988609i	$0.451910\pi$
$710$	13.4617	−	0.814283i	0.505209	−	0.0305595i
$711$	19.6837	−	5.16379i	0.738196	−	0.193657i
$712$	−4.12083	−	16.7189i	−0.154435	−	0.626566i
$713$	19.1725	+	15.0207i	0.718015	+	0.562529i
$714$	−51.7573	+	13.1667i	−1.93697	+	0.492752i
$715$	3.88010	+	4.91977i	0.145107	+	0.183989i
$716$	1.07283	+	0.740524i	0.0400937	+	0.0276747i
$717$	0.0624546	−	1.17802i	0.00233241	−	0.0439939i
$718$	−16.8542	−	44.4410i	−0.628994	−	1.65852i
$719$	−0.400206	+	3.29599i	−0.0149252	+	0.122920i	−0.998267	−	0.0588456i	$-0.981258\pi$
$719$	−0.400206	+	3.29599i	−0.0149252	+	0.122920i	0.983342	+	0.181765i	$0.0581811\pi$
$720$	5.81807	−	4.69970i	0.216827	−	0.175147i
$721$	−5.44921	+	3.29416i	−0.202939	+	0.122681i
$722$	51.9525	+	9.52065i	1.93347	+	0.354322i
$723$	36.3113	−	36.8562i	1.35043	−	1.37070i
$724$	−5.16317	−	13.6142i	−0.191888	−	0.505966i
$725$	−36.9831	+	19.4102i	−1.37352	+	0.720878i
$726$	−15.4394	+	20.0122i	−0.573010	+	0.742723i
$727$	−2.41721	+	9.80702i	−0.0896494	+	0.363722i	−0.998583	−	0.0532192i	$-0.983052\pi$
$727$	−2.41721	+	9.80702i	−0.0896494	+	0.363722i	0.908933	+	0.416941i	$0.136898\pi$
$728$	−38.1759	+	63.6137i	−1.41489	+	2.35768i
$729$	8.43695	−	25.6480i	0.312480	−	0.949924i
$730$	0.776008	−	12.8289i	0.0287213	−	0.474820i
$731$	0.0205866	−	0.00249967i	0.000761423	−	9.24535e-5i
$732$	−1.64740	−	12.7718i	−0.0608897	−	0.472061i
$733$	−5.94042	+	1.85111i	−0.219415	+	0.0683723i	−0.405240	−	0.914211i	$-0.632812\pi$
$733$	−5.94042	+	1.85111i	−0.219415	+	0.0683723i	0.185825	+	0.982583i	$0.440504\pi$
$734$	16.3568	−	7.36158i	0.603739	−	0.271721i
$735$	7.51465	−	17.0348i	0.277182	−	0.628337i
$736$	−4.36137	+	3.41692i	−0.160762	+	0.125949i
$737$	−1.14497	+	4.64532i	−0.0421755	+	0.171113i
$738$	0.466112	+	31.2880i	0.0171578	+	1.15173i
$739$	−0.699966	−	11.5718i	−0.0257487	−	0.425676i	−0.988095	−	0.153848i	$-0.950833\pi$
$739$	−0.699966	−	11.5718i	−0.0257487	−	0.425676i	0.962346	−	0.271828i	$-0.0876282\pi$
$740$	−11.3090	+	5.93545i	−0.415729	+	0.218191i
$741$	−35.1261	+	18.9167i	−1.29039	+	0.694921i
$742$	−134.852	−	70.7756i	−4.95056	−	2.59825i
$743$	−1.03976	+	2.31025i	−0.0381451	+	0.0847548i	−0.929987	−	0.367592i	$-0.880182\pi$
$743$	−1.03976	+	2.31025i	−0.0381451	+	0.0847548i	0.891842	+	0.452347i	$0.149413\pi$
$744$	−39.0132	−	20.1065i	−1.43029	−	0.737141i
$745$	−6.18702	+	11.7884i	−0.226675	+	0.431893i
$746$	5.41706	+	5.41706i	0.198333	+	0.198333i
$747$	13.8396	−	32.0163i	0.506365	−	1.17141i
$748$	−1.45265	−	24.0151i	−0.0531141	−	0.878081i
$749$	2.91256	+	15.8933i	0.106423	+	0.580730i
$750$	−28.6207	+	11.0989i	−1.04508	+	0.405275i
$751$	−4.23061	−	2.92018i	−0.154377	−	0.106559i	0.488372	−	0.872635i	$-0.337591\pi$
$751$	−4.23061	−	2.92018i	−0.154377	−	0.106559i	−0.642749	+	0.766077i	$0.722206\pi$
$752$	9.16590	+	20.3658i	0.334246	+	0.742664i
$753$	13.5399	−	15.5147i	0.493421	−	0.565386i
$754$	−68.4700	−	46.9357i	−2.49353	−	1.70930i
$755$	2.45473	−	0.930958i	0.0893370	−	0.0338810i
$756$	87.9866	+	25.2754i	3.20004	+	0.919256i
$757$	15.6197	−	41.1857i	0.567707	−	1.49692i	−0.276560	−	0.960997i	$-0.589194\pi$
$757$	15.6197	−	41.1857i	0.567707	−	1.49692i	0.844267	−	0.535923i	$-0.180036\pi$
$758$	−4.18984	−	34.5064i	−0.152182	−	1.25333i
$759$	10.2332	−	13.2640i	0.371442	−	0.481454i
$760$	4.04899	+	22.0946i	0.146872	+	0.801456i
$761$	−2.65026	−	14.4620i	−0.0960718	−	0.524247i	−0.996086	−	0.0883867i	$-0.971829\pi$
$761$	−2.65026	−	14.4620i	−0.0960718	−	0.524247i	0.900014	−	0.435860i	$-0.143556\pi$
$762$	−31.6280	+	40.9955i	−1.14576	+	1.48511i
$763$	2.53568	+	20.8832i	0.0917979	+	0.756024i
$764$	−5.78587	+	15.2561i	−0.209325	+	0.551946i
$765$	−0.491152	−	6.50926i	−0.0177576	−	0.235343i
$766$	−6.51622	+	2.47128i	−0.235441	+	0.0892909i
$767$	17.9108	+	33.8600i	0.646720	+	1.22261i
$768$	34.7188	−	39.7825i	1.25281	−	1.43553i
$769$	7.70299	+	17.1153i	0.277777	+	0.617195i	0.996985	−	0.0776001i	$-0.0247257\pi$
$769$	7.70299	+	17.1153i	0.277777	+	0.617195i	−0.719208	+	0.694795i	$0.755495\pi$
$770$	15.7923	+	10.9006i	0.569115	+	0.392832i
$771$	−13.8783	+	5.38191i	−0.499814	+	0.193825i
$772$	8.77340	+	47.8749i	0.315761	+	1.72305i
$773$	2.48426	+	41.0697i	0.0893527	+	1.47718i	0.716124	+	0.697973i	$0.245914\pi$
$773$	2.48426	+	41.0697i	0.0893527	+	1.47718i	−0.626772	+	0.779203i	$0.715624\pi$
$774$	−0.0495209	−	0.0214063i	−0.00177999	−	0.000769433i
$775$	17.4435	+	17.4435i	0.626588	+	0.626588i
$776$	−4.67715	+	8.91156i	−0.167900	+	0.319906i
$777$	−29.7853	−	15.3507i	−1.06854	−	0.550702i
$778$	9.90184	−	22.0010i	0.354998	−	0.788774i
$779$	−24.3664	−	12.7885i	−0.873016	−	0.458194i
$780$	−14.2049	−	12.3163i	−0.508618	−	0.440994i
$781$	−14.1138	+	7.40749i	−0.505031	+	0.265061i
$782$	−1.77063	−	29.2719i	−0.0633175	−	1.04676i
$783$	−16.4830	+	46.5751i	−0.589056	+	1.66446i
$784$	−10.5620	+	42.8518i	−0.377215	+	1.53042i
$785$	9.01728	−	7.06459i	0.321841	−	0.252146i
$786$	15.1670	−	34.3817i	0.540990	−	1.22636i
$787$	−23.0508	+	10.3743i	−0.821671	+	0.369804i	−0.777237	−	0.629208i	$-0.783379\pi$
$787$	−23.0508	+	10.3743i	−0.821671	+	0.369804i	−0.0444339	+	0.999012i	$0.514148\pi$
$788$	−49.3342	+	15.3732i	−1.75746	+	0.547646i
$789$	2.90721	+	22.5388i	0.103499	+	0.802402i
$790$	−12.7059	+	1.54278i	−0.452057	+	0.0548896i
$791$	−3.84931	+	63.6366i	−0.136866	+	2.26266i
$792$	−13.6297	+	26.9368i	−0.484309	+	0.957157i
$793$	−6.61774	+	2.08564i	−0.235003	+	0.0740632i
$794$	8.08123	−	32.7869i	0.286792	−	1.16356i
$795$	11.3708	−	14.7386i	0.403281	−	0.522724i
$796$	−81.5548	+	42.8033i	−2.89063	+	1.51712i
$797$	−10.6857	−	28.1759i	−0.378507	−	0.998041i	−0.979971	−	0.199141i	$-0.936185\pi$
$797$	−10.6857	−	28.1759i	−0.378507	−	0.998041i	0.601464	−	0.798900i	$-0.294584\pi$
$798$	−85.7506	+	87.0376i	−3.03554	+	3.08110i
$799$	19.1733	+	3.51363i	0.678301	+	0.124303i
$800$	−4.80237	+	2.90313i	−0.169789	+	0.102641i
$801$	7.19385	+	8.90576i	0.254182	+	0.314669i
$802$	1.52415	−	12.5525i	0.0538196	−	0.443245i
$803$	5.38657	+	14.2032i	0.190088	+	0.501220i
$804$	0.760031	−	14.3357i	0.0268042	−	0.505581i
$805$	12.6833	+	8.75468i	0.447029	+	0.308562i
$806$	−14.4352	+	46.8562i	−0.508457	+	1.65044i
$807$	−27.3990	+	6.97011i	−0.964489	+	0.245360i
$808$	−18.1988	−	14.2578i	−0.640231	−	0.501589i
$809$	−5.75057	−	23.3310i	−0.202179	−	0.820274i	−0.981155	−	0.193220i	$-0.938107\pi$
$809$	−5.75057	−	23.3310i	−0.202179	−	0.820274i	0.778976	−	0.627054i	$-0.215739\pi$
$810$	−7.44050	+	15.2652i	−0.261433	+	0.536365i
$811$	30.4831	−	1.84389i	1.07041	−	0.0647477i	0.484238	−	0.874936i	$-0.339097\pi$
$811$	30.4831	−	1.84389i	1.07041	−	0.0647477i	0.586169	+	0.810189i	$0.300635\pi$
$812$	−159.928	−	49.8357i	−5.61238	−	1.74889i
$813$	27.1151	−	8.67149i	0.950968	−	0.304123i
$814$	14.1289	−	18.0342i	0.495217	−	0.632098i
$815$	7.46185	−	8.42269i	0.261377	−	0.295034i
$816$	3.81489	+	14.9960i	0.133548	+	0.524966i
$817$	0.0373475	−	0.0292599i	0.00130662	−	0.00102367i
$818$	6.82212	+	56.1852i	0.238530	+	1.96447i
$819$	5.05708	−	49.0655i	0.176709	−	1.71449i
$820$	1.56312	−	12.8734i	0.0545865	−	0.449560i
$821$	17.8309	+	29.4959i	0.622302	+	1.02941i	0.994846	+	0.101398i	$0.0323316\pi$
$821$	17.8309	+	29.4959i	0.622302	+	1.02941i	−0.372544	+	0.928014i	$0.621515\pi$
$822$	48.8946	+	18.1279i	1.70539	+	0.632282i
$823$			16.8529i			0.587456i	0.955889	+	0.293728i	$0.0948961\pi$
$823$			16.8529i			0.587456i	−0.955889	+	0.293728i	$0.905104\pi$
$824$	3.25957	+	5.39199i	0.113553	+	0.187839i
$825$	11.9085	−	12.0872i	0.414601	−	0.420823i
$826$	82.9519	+	82.9519i	2.88626	+	2.88626i
$827$	−18.8106	−	41.7955i	−0.654110	−	1.45337i	−0.877952	−	0.478748i	$-0.841091\pi$
$827$	−18.8106	−	41.7955i	−0.654110	−	1.45337i	0.223842	−	0.974625i	$-0.428140\pi$
$828$	−22.6951	+	44.8531i	−0.788708	+	1.55875i
$829$	−34.2429	+	38.6523i	−1.18931	+	1.34245i	−0.263404	+	0.964686i	$0.584845\pi$
$829$	−34.2429	+	38.6523i	−1.18931	+	1.34245i	−0.925902	+	0.377763i	$0.876693\pi$
$830$	−11.3493	+	18.7740i	−0.393940	+	0.651657i
$831$	−20.1248	+	10.7542i	−0.698121	+	0.373060i
$832$	−29.3452	−	17.6107i	−1.01736	−	0.610540i
$833$	25.5437	+	28.8329i	0.885038	+	0.999001i
$834$	−64.3918	−	11.3052i	−2.22971	−	0.391467i
$835$	−9.12438	−	2.24896i	−0.315762	−	0.0778284i
$836$	−31.2679	−	45.2994i	−1.08142	−	1.56671i
$837$	29.1591	+	1.11064i	1.00789	+	0.0383895i
$838$	9.82597	−	16.2541i	0.339432	−	0.561490i
$839$	−16.0302	−	12.5589i	−0.553425	−	0.433581i	0.300647	−	0.953735i	$-0.402797\pi$
$839$	−16.0302	−	12.5589i	−0.553425	−	0.433581i	−0.854072	+	0.520155i	$0.825874\pi$
$840$	−25.4092	−	11.2089i	−0.876700	−	0.386744i
$841$	21.7745	−	57.4146i	0.750845	−	1.97982i
$842$	33.4850	+	17.5743i	1.15397	+	0.605650i
$843$	35.7597	+	21.2554i	1.23163	+	0.732075i
$844$		−	12.2065i		−	0.420165i
$845$	−5.18459	+	8.70280i	−0.178355	+	0.299385i
$846$	−38.4536	−	33.0578i	−1.32206	−	1.13655i
$847$	27.0316	+	4.95373i	0.928818	+	0.170212i
$848$	−20.5063	+	39.0715i	−0.704190	+	1.34172i
$849$	−9.22407	−	8.04999i	−0.316569	−	0.276275i
$850$	1.79338	−	29.6481i	0.0615125	−	1.01692i
$851$	11.3474	−	14.4839i	0.388984	−	0.496501i
$852$	37.4287	−	29.7760i	1.28229	−	1.02011i
$853$	−18.8757	−	11.4107i	−0.646290	−	0.390696i	0.155893	−	0.987774i	$-0.450175\pi$
$853$	−18.8757	−	11.4107i	−0.646290	−	0.390696i	−0.802183	+	0.597078i	$0.796328\pi$
$854$	−17.4883	+	12.0713i	−0.598436	+	0.413071i
$855$	−8.66583	−	12.1630i	−0.296365	−	0.415966i
$856$	15.7265	−	2.88198i	0.537519	−	0.0985041i
$857$	37.9405	−	33.6124i	1.29602	−	1.14818i	0.316117	−	0.948720i	$-0.397621\pi$
$857$	37.9405	−	33.6124i	1.29602	−	1.14818i	0.979907	−	0.199456i	$-0.0639175\pi$
$858$	32.3023	+	9.68865i	1.10278	+	0.330765i
$859$	5.53331	+	4.90209i	0.188794	+	0.167257i	0.752225	−	0.658906i	$-0.228981\pi$
$859$	5.53331	+	4.90209i	0.188794	+	0.167257i	−0.563431	+	0.826163i	$0.690519\pi$
$860$	0.0191336	+	0.0115667i	0.000652451	+	0.000394420i
$861$	30.0068	−	16.0350i	1.02263	−	0.546471i
$862$	−0.369300	−	1.49831i	−0.0125784	−	0.0510326i
$863$	−9.81125	+	4.41569i	−0.333979	+	0.150312i	−0.570462	−	0.821324i	$-0.693236\pi$
$863$	−9.81125	+	4.41569i	−0.333979	+	0.150312i	0.236483	+	0.971636i	$0.424005\pi$
$864$	−1.83273	+	6.37994i	−0.0623506	+	0.217050i
$865$	4.72744	−	10.5039i	0.160738	−	0.357145i
$866$	38.6717	−	23.3778i	1.31412	−	0.794411i
$867$	−14.9453	−	5.54105i	−0.507570	−	0.188184i
$868$			98.9374i			3.35816i
$869$	12.9459	−	7.82604i	0.439158	−	0.265480i
$870$	14.2357	−	27.6218i	0.482634	−	0.936468i
$871$	−7.67563	+	0.957149i	−0.260079	+	0.0324317i
$872$	20.6639	−	2.50906i	0.699769	−	0.0849674i
$873$	0.304478	−	6.68443i	0.0103050	−	0.226234i
$874$	−38.1123	−	55.2152i	−1.28917	−	1.86768i
$875$	24.9828	+	22.1328i	0.844571	+	0.748225i
$876$	−23.8701	−	38.8297i	−0.806494	−	1.31193i
$877$	3.90162	+	4.98005i	0.131748	+	0.168164i	0.848554	−	0.529108i	$-0.177474\pi$
$877$	3.90162	+	4.98005i	0.131748	+	0.168164i	−0.716806	+	0.697273i	$0.754397\pi$
$878$	17.2588	−	55.3854i	0.582456	−	1.86917i
$879$	32.4927	+	9.86024i	1.09595	+	0.332578i
$880$	3.15832	−	4.57562i	0.106467	−	0.154244i
$881$	36.2676	−	8.93916i	1.22189	−	0.301168i	0.424942	−	0.905221i	$-0.360295\pi$
$881$	36.2676	−	8.93916i	1.22189	−	0.301168i	0.796944	+	0.604053i	$0.206448\pi$
$882$	−19.5298	−	98.2894i	−0.657602	−	3.30958i
$883$	−40.3506	+	27.8520i	−1.35791	+	0.937295i	−0.357913	+	0.933755i	$0.616511\pi$
$883$	−40.3506	+	27.8520i	−1.35791	+	0.937295i	−0.999994	+	0.00354009i	$0.998873\pi$
$884$	35.4188	−	16.0784i	1.19126	−	0.540776i
$885$	−11.7397	+	8.23312i	−0.394626	+	0.276753i
$886$	−15.8159	+	4.92842i	−0.531344	+	0.165574i
$887$	1.87256	−	0.710170i	0.0628746	−	0.0238452i	−0.322967	−	0.946410i	$-0.604680\pi$
$887$	1.87256	−	0.710170i	0.0628746	−	0.0238452i	0.385842	+	0.922565i	$0.373911\pi$
$888$	−15.1895	+	29.4726i	−0.509726	+	0.989034i
$889$	55.3749	+	10.1478i	1.85721	+	0.340347i
$890$	−3.72513	−	6.16211i	−0.124867	−	0.206554i
$891$	0.614532	−	20.0617i	0.0205876	−	0.672094i
$892$	11.4026	−	25.3356i	0.381788	−	0.848298i
$893$	41.6975	−	15.8138i	1.39535	−	0.529188i
$894$	9.16679	+	71.0676i	0.306583	+	2.37686i
$895$	0.251022	+	0.0782217i	0.00839075	+	0.00261466i
$896$	−90.4543	−	22.2950i	−3.02187	−	0.744823i
$897$	25.9431	+	7.78129i	0.866214	+	0.259810i
$898$	31.8575	−	7.85218i	1.06310	−	0.262031i
$899$	−53.2980	−	3.22393i	−1.77759	−	0.107524i
$900$	−28.2950	+	42.3275i	−0.943168	+	1.41092i
$901$	17.8979	+	34.1016i	0.596266	+	1.13609i
$902$	6.92031	+	22.2081i	0.230421	+	0.739448i
$903$	0.00397769	+	0.0585231i	0.000132369	+	0.00194753i
$904$	62.9684	+	3.80889i	2.09430	+	0.126682i
$905$	−1.81115	−	2.31176i	−0.0602046	−	0.0768454i
$906$	7.94011	−	11.6885i	0.263793	−	0.388325i
$907$	−9.35042	−	10.5544i	−0.310475	−	0.350454i	0.572474	−	0.819923i	$-0.305984\pi$
$907$	−9.35042	−	10.5544i	−0.310475	−	0.350454i	−0.882949	+	0.469469i	$0.844445\pi$
$908$	8.75561	−	0.529617i	0.290565	−	0.0175760i
$909$	14.9772	+	3.45574i	0.496763	+	0.114620i
$910$	−7.32720	+	30.1462i	−0.242894	+	0.999336i
$911$	−14.6627	+	27.9374i	−0.485796	+	0.925607i	0.511983	+	0.858996i	$0.328911\pi$
$911$	−14.6627	+	27.9374i	−0.485796	+	0.925607i	−0.997779	+	0.0666116i	$0.978781\pi$
$912$	25.2180	+	24.8451i	0.835052	+	0.822705i
$913$	3.12534	−	25.7395i	0.103434	−	0.851854i
$914$	76.3180	+	40.0548i	2.52437	+	1.32489i
$915$	−1.08360	−	2.36052i	−0.0358227	−	0.0780365i
$916$	48.7105	−	15.1788i	1.60944	−	0.501521i
$917$	−40.7837	+	2.46696i	−1.34680	+	0.0814662i
$918$	−22.2805	−	27.1661i	−0.735367	−	0.896616i
$919$	−31.0417	+	27.5005i	−1.02397	+	0.907159i	−0.995718	−	0.0924421i	$-0.970533\pi$
$919$	−31.0417	+	27.5005i	−1.02397	+	0.907159i	−0.0282524	+	0.999601i	$0.508994\pi$
$920$	8.66275	−	12.5502i	0.285602	−	0.413767i
$921$	24.5848	−	1.67098i	0.810098	−	0.0550606i
$922$	−26.5471	−	10.0680i	−0.874283	−	0.331572i
$923$	−19.3444	−	17.0265i	−0.636728	−	0.560433i
$924$	68.0505	−	0.506863i	2.23870	−	0.0166746i
$925$	13.1777	−	13.1777i	0.433280	−	0.433280i
$926$	2.93596	+	1.11346i	0.0964816	+	0.0365906i
$927$	−3.48257	−	2.32803i	−0.114383	−	0.0764624i
$928$	3.61360	−	11.5965i	0.118622	−	0.380672i
$929$	44.8173	−	8.21307i	1.47041	−	0.269462i	0.615457	−	0.788171i	$-0.288972\pi$
$929$	44.8173	−	8.21307i	1.47041	−	0.269462i	0.854951	+	0.518709i	$0.173587\pi$
$930$	−18.0768	−	3.17373i	−0.592763	−	0.104071i
$931$	84.1375	+	26.2183i	2.75749	+	0.859270i
$932$	58.4269	−	7.09431i	1.91384	−	0.232382i
$933$	27.0302	−	30.9725i	0.884929	−	1.01400i
$934$	−59.0846	−	59.0846i	−1.93331	−	1.93331i
$935$	−1.72075	−	4.53725i	−0.0562746	−	0.148384i
$936$	−48.5503	−	5.00398i	−1.58692	−	0.163560i
$937$	9.04468	−	23.8489i	0.295477	−	0.779109i	−0.702263	−	0.711917i	$-0.747827\pi$
$937$	9.04468	−	23.8489i	0.295477	−	0.779109i	0.997740	−	0.0671913i	$-0.0214038\pi$
$938$	−21.6020	+	9.72228i	−0.705331	+	0.317444i
$939$	43.1122	−	30.2347i	1.40691	−	0.986673i
$940$	13.9359	+	15.7303i	0.454538	+	0.513067i
$941$	5.85989	−	1.07386i	0.191027	−	0.0350070i	−0.0838897	−	0.996475i	$-0.526734\pi$
$941$	5.85989	−	1.07386i	0.191027	−	0.0350070i	0.274917	+	0.961468i	$0.411350\pi$
$942$	17.9036	−	58.9981i	0.583330	−	1.92226i
$943$	5.55794	+	17.8361i	0.180991	+	0.580822i
$944$	24.0342	−	24.0342i	0.782248	−	0.782248i
$945$	18.4596	−	0.412540i	0.600489	−	0.0134199i
$946$	−0.0398124	−	0.00483410i	−0.00129441	−	0.000157170i
$947$	−37.2721	−	16.7748i	−1.21118	−	0.545108i	−0.298747	−	0.954332i	$-0.596569\pi$
$947$	−37.2721	−	16.7748i	−1.21118	−	0.545108i	−0.912434	+	0.409224i	$0.865799\pi$
$948$	−33.7508	+	30.3523i	−1.09618	+	0.985797i
$949$	−18.3299	+	16.3448i	−0.595015	+	0.530576i
$950$	−31.5796	−	60.1700i	−1.02458	−	1.95217i
$951$	13.8595	−	45.6715i	0.449425	−	1.48100i
$952$	43.0074	−	38.1012i	1.39388	−	1.23487i
$953$	−32.1202	−	7.91691i	−1.04047	−	0.256454i	−0.318173	−	0.948033i	$-0.603069\pi$
$953$	−32.1202	−	7.91691i	−1.04047	−	0.256454i	−0.722301	+	0.691579i	$0.756915\pi$
$954$	4.55904	−	100.088i	0.147604	−	3.24047i
$955$	−0.198701	+	3.28493i	−0.00642983	+	0.106298i
$956$	1.07993	+	2.39951i	0.0349275	+	0.0776058i
$957$	−1.94442	+	36.6756i	−0.0628541	+	1.18555i
$958$	10.3774	−	5.44648i	0.335278	−	0.175968i
$959$	−6.83421	−	56.2848i	−0.220688	−	1.81753i
$960$	5.17071	−	11.7213i	0.166884	−	0.378304i
$961$	0.128429	+	0.521056i	0.00414286	+	0.0168083i
$962$	35.3976	+	10.9051i	1.14126	+	0.351593i
$963$	−8.65736	+	6.16815i	−0.278980	+	0.198766i
$964$	−34.3337	+	110.181i	−1.10581	+	3.54868i
$965$	4.56215	+	8.69245i	0.146861	+	0.279820i
$966$	82.9464	−	0.617812i	2.66876	−	0.0198778i
$967$	0.458023	+	0.206140i	0.0147290	+	0.00662900i	0.417764	−	0.908556i	$-0.362814\pi$
$967$	0.458023	+	0.206140i	0.0147290	+	0.00662900i	−0.403035	+	0.915185i	$0.632045\pi$
$968$	4.90171	−	26.7478i	0.157547	−	0.859707i
$969$	30.3495	−	5.79572i	0.974967	−	0.186185i
$970$	−0.758625	+	4.13968i	−0.0243580	+	0.132917i
$971$	−11.5884	−	1.40708i	−0.371888	−	0.0451554i	−0.0675409	−	0.997717i	$-0.521515\pi$
$971$	−11.5884	−	1.40708i	−0.371888	−	0.0451554i	−0.304347	+	0.952561i	$0.598438\pi$
$972$	9.48029	+	59.4743i	0.304080	+	1.90764i
$973$	21.1473	+	67.8641i	0.677952	+	2.17562i
$974$	−26.1777	+	37.9250i	−0.838789	+	1.21520i
$975$	25.1349	+	10.9911i	0.804961	+	0.351997i
$976$	3.49750	+	5.06700i	0.111952	+	0.162191i
$977$	17.2920	−	22.0716i	0.553219	−	0.706132i	−0.426954	−	0.904273i	$-0.640413\pi$
$977$	17.2920	−	22.0716i	0.553219	−	0.706132i	0.980174	+	0.198141i	$0.0634904\pi$
$978$	6.85227	−	60.1759i	0.219111	−	1.92421i
$979$	7.00393	+	4.83446i	0.223846	+	0.154510i
$980$	2.50752	+	41.4542i	0.0800997	+	1.32421i
$981$	−11.7356	+	7.33530i	−0.374688	+	0.234198i
$982$	22.1693	−	17.3685i	0.707450	−	0.554251i
$983$	27.7502	+	21.7409i	0.885094	+	0.693427i	0.952578	−	0.304294i	$-0.0984204\pi$
$983$	27.7502	+	21.7409i	0.885094	+	0.693427i	−0.0674845	+	0.997720i	$0.521497\pi$
$984$	−15.8666	−	29.6918i	−0.505809	−	0.946539i
$985$	−8.57744	+	5.92058i	−0.273300	+	0.188645i
$986$	39.6491	+	50.6083i	1.26268	+	1.61170i
$987$	−12.7958	+	53.6305i	−0.407294	+	1.70708i
$988$	50.3155	−	73.4004i	1.60075	−	2.33518i
$989$	−0.0319747	−	0.00388243i	−0.00101674	−	0.000123454i
$990$	−2.09032	+	12.4498i	−0.0664349	+	0.395679i
$991$	−56.0707			−1.78114			−0.890572	−	0.454842i	$-0.849696\pi$
$991$	−56.0707			−1.78114			−0.890572	+	0.454842i	$0.849696\pi$
$992$	−7.17398			−0.227774
$993$	−19.9338	+	3.80668i	−0.632581	+	0.120801i
$994$	−71.9695	−	32.3908i	−2.28273	−	1.02737i
$995$	−13.1360	+	13.1360i	−0.416439	+	0.416439i
$996$	5.27578	+	77.6218i	0.167170	+	2.45954i
$997$	0.938109	−	0.231223i	0.0297102	−	0.00732291i	−0.224433	−	0.974490i	$-0.572053\pi$
$997$	0.938109	−	0.231223i	0.0297102	−	0.00732291i	0.254143	+	0.967167i	$0.418207\pi$
$998$	−25.6910	−	22.7603i	−0.813236	−	0.720464i
$999$	0.839038	−	22.0283i	0.0265460	−	0.696945i

Display

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instead) (See

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.s.a.5.5	✓	1392
3.2	odd	2	inner	507.2.s.a.5.54	yes	1392
169.34	odd	52	inner	507.2.s.a.203.54	yes	1392
507.203	even	52	inner	507.2.s.a.203.5	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.s.a.5.5	✓	1392	1.1	even	1	trivial
507.2.s.a.5.54	yes	1392	3.2	odd	2	inner
507.2.s.a.203.5	yes	1392	507.203	even	52	inner
507.2.s.a.203.54	yes	1392	169.34	odd	52	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	507.2.s.a.5.5

Level	$507$
Weight	$2$
Character	507.5
Analytic conductor	$4.048$
Analytic rank	$0$
Dimension	$1392$
Inner twists	$4$