LMFDB - Embedded newform 507.2.s.a.5.6

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			5.6
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422557 + 2.30582i) q^{2} +(1.72797 + 0.118863i) q^{3} +(-3.26821 - 1.23947i) q^{4} +(-4.34895 - 0.263063i) q^{5} +(-1.00424 + 3.93415i) q^{6} +(-1.68324 - 1.01756i) q^{7} +(1.81349 - 2.99989i) q^{8} +(2.97174 + 0.410783i) q^{9} +(2.44426 - 9.91674i) q^{10} +(-0.442448 - 2.41436i) q^{11} +(-5.50004 - 2.53023i) q^{12} +(1.44563 - 3.30305i) q^{13} +(3.05757 - 3.45128i) q^{14} +(-7.48358 - 0.971495i) q^{15} +(0.918268 + 0.813515i) q^{16} +(1.89290 - 0.466559i) q^{17} +(-2.20292 + 6.67872i) q^{18} +(-0.970755 + 0.970755i) q^{19} +(13.8872 + 6.25014i) q^{20} +(-2.78764 - 1.95838i) q^{21} +5.75404 q^{22} -7.33820 q^{23} +(3.49024 - 4.96815i) q^{24} +(13.8806 + 1.68541i) q^{25} +(7.00538 + 4.72909i) q^{26} +(5.08625 + 1.06305i) q^{27} +(4.23997 + 5.41192i) q^{28} +(-1.67516 + 1.15628i) q^{29} +(5.40233 - 16.8453i) q^{30} +(-8.16452 - 6.39650i) q^{31} +(3.25500 - 2.55013i) q^{32} +(-0.477557 - 4.22453i) q^{33} +(0.275941 + 4.56184i) q^{34} +(7.05267 + 4.86811i) q^{35} +(-9.20314 - 5.02591i) q^{36} +(-3.09840 + 3.95481i) q^{37} +(-1.82819 - 2.64858i) q^{38} +(2.89061 - 5.53573i) q^{39} +(-8.67596 + 12.5693i) q^{40} +(-0.343490 - 1.10230i) q^{41} +(5.69361 - 5.60027i) q^{42} +(-11.9763 - 1.45418i) q^{43} +(-1.54651 + 8.43905i) q^{44} +(-12.8159 - 2.56823i) q^{45} +(3.10081 - 16.9206i) q^{46} +(3.16861 + 1.42607i) q^{47} +(1.49004 + 1.51488i) q^{48} +(-1.45517 - 2.77260i) q^{49} +(-9.75162 + 31.2941i) q^{50} +(3.32633 - 0.581202i) q^{51} +(-8.81866 + 9.00326i) q^{52} +(-2.45032 - 9.94132i) q^{53} +(-4.60043 + 11.2788i) q^{54} +(1.28906 + 10.6163i) q^{55} +(-6.10511 + 3.20421i) q^{56} +(-1.79282 + 1.56205i) q^{57} +(-1.95832 - 4.35122i) q^{58} +(0.0999412 - 1.65222i) q^{59} +(23.2538 + 12.4507i) q^{60} +(2.62241 + 0.646367i) q^{61} +(18.1991 - 16.1230i) q^{62} +(-4.58418 - 3.71537i) q^{63} +(5.64496 + 10.7556i) q^{64} +(-7.15589 + 13.9845i) q^{65} +(9.94280 + 0.683944i) q^{66} +(-0.663626 - 0.298674i) q^{67} +(-6.76470 - 0.821383i) q^{68} +(-12.6802 - 0.872242i) q^{69} +(-14.2051 + 14.2051i) q^{70} +(-0.110106 - 0.353342i) q^{71} +(6.62154 - 8.16994i) q^{72} +(-3.92021 + 0.718406i) q^{73} +(-7.80983 - 8.81548i) q^{74} +(23.7850 + 4.56224i) q^{75} +(4.37586 - 1.96941i) q^{76} +(-1.71200 + 4.51418i) q^{77} +(11.5430 + 9.00439i) q^{78} +(2.65066 + 6.98923i) q^{79} +(-3.77950 - 3.77950i) q^{80} +(8.66251 + 2.44149i) q^{81} +(2.68684 - 0.326241i) q^{82} +(9.96854 + 3.10632i) q^{83} +(6.68326 + 9.85561i) q^{84} +(-8.35488 + 1.53109i) q^{85} +(8.41373 - 27.0006i) q^{86} +(-3.03207 + 1.79890i) q^{87} +(-8.04519 - 3.05114i) q^{88} +(-0.936073 + 0.936073i) q^{89} +(11.3373 - 28.4659i) q^{90} +(-5.79439 + 4.08883i) q^{91} +(23.9828 + 9.09548i) q^{92} +(-13.3477 - 12.0234i) q^{93} +(-4.62719 + 6.70364i) q^{94} +(4.47714 - 3.96640i) q^{95} +(5.92766 - 4.01965i) q^{96} +(-3.59479 + 0.217445i) q^{97} +(7.00800 - 2.18378i) q^{98} +(-0.323063 - 7.35662i) 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

)

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

$2$	−0.422557	+	2.30582i	−0.298793	+	1.63046i	0.400974	+	0.916089i	$0.368672\pi$
$2$	−0.422557	+	2.30582i	−0.298793	+	1.63046i	−0.699767	+	0.714371i	$0.746713\pi$
$3$	1.72797	+	0.118863i	0.997642	+	0.0686257i
$3$	1.72797	+	0.118863i	0.997642	+	0.0686257i
$4$	−3.26821	−	1.23947i	−1.63411	−	0.619735i
$5$	−4.34895	−	0.263063i	−1.94491	−	0.117645i	−0.958837	−	0.283956i	$-0.908353\pi$
$5$	−4.34895	−	0.263063i	−1.94491	−	0.117645i	−0.986073	+	0.166311i	$0.946814\pi$
$6$	−1.00424	+	3.93415i	−0.409980	+	1.60611i
$7$	−1.68324	−	1.01756i	−0.636207	−	0.384600i	0.162166	−	0.986763i	$-0.448152\pi$
$7$	−1.68324	−	1.01756i	−0.636207	−	0.384600i	−0.798373	+	0.602163i	$0.794306\pi$
$8$	1.81349	−	2.99989i	0.641167	−	1.06062i
$9$	2.97174	+	0.410783i	0.990581	+	0.136928i
$10$	2.44426	−	9.91674i	0.772942	−	3.13595i
$11$	−0.442448	−	2.41436i	−0.133403	−	0.727958i	−0.980500	−	0.196519i	$-0.937036\pi$
$11$	−0.442448	−	2.41436i	−0.133403	−	0.727958i	0.847097	−	0.531439i	$-0.178348\pi$
$12$	−5.50004	−	2.53023i	−1.58772	−	0.730416i
$13$	1.44563	−	3.30305i	0.400946	−	0.916102i
$13$	1.44563	−	3.30305i	0.400946	−	0.916102i
$14$	3.05757	−	3.45128i	0.817170	−	0.922394i
$15$	−7.48358	−	0.971495i	−1.93225	−	0.250839i
$16$	0.918268	+	0.813515i	0.229567	+	0.203379i
$17$	1.89290	−	0.466559i	0.459097	−	0.113157i	−0.00298304	−	0.999996i	$-0.500950\pi$
$17$	1.89290	−	0.466559i	0.459097	−	0.113157i	0.462080	+	0.886838i	$0.347103\pi$
$18$	−2.20292	+	6.67872i	−0.519234	+	1.57419i
$19$	−0.970755	+	0.970755i	−0.222706	+	0.222706i	−0.809637	−	0.586931i	$-0.800336\pi$
$19$	−0.970755	+	0.970755i	−0.222706	+	0.222706i	0.586931	+	0.809637i	$0.300336\pi$
$20$	13.8872	+	6.25014i	3.10528	+	1.39757i
$21$	−2.78764	−	1.95838i	−0.608313	−	0.427354i
$22$	5.75404			1.22677
$23$	−7.33820			−1.53012			−0.765060	−	0.643958i	$-0.777291\pi$
$23$	−7.33820			−1.53012			−0.765060	+	0.643958i	$0.777291\pi$
$24$	3.49024	−	4.96815i	0.712441	−	1.01412i
$25$	13.8806	+	1.68541i	2.77613	+	0.337083i
$26$	7.00538	+	4.72909i	1.37387	+	0.927451i
$27$	5.08625	+	1.06305i	0.978849	+	0.204584i
$28$	4.23997	+	5.41192i	0.801279	+	1.02276i
$29$	−1.67516	+	1.15628i	−0.311070	+	0.214716i	−0.713363	−	0.700795i	$-0.752829\pi$
$29$	−1.67516	+	1.15628i	−0.311070	+	0.214716i	0.402293	+	0.915511i	$0.368213\pi$
$30$	5.40233	−	16.8453i	0.986326	−	3.07551i
$31$	−8.16452	−	6.39650i	−1.46639	−	1.14884i	−0.957653	−	0.287924i	$-0.907035\pi$
$31$	−8.16452	−	6.39650i	−1.46639	−	1.14884i	−0.508738	−	0.860921i	$-0.669888\pi$
$32$	3.25500	−	2.55013i	0.575409	−	0.450804i
$33$	−0.477557	−	4.22453i	−0.0831321	−	0.735396i
$34$	0.275941	+	4.56184i	0.0473234	+	0.782349i
$35$	7.05267	+	4.86811i	1.19212	+	0.822860i
$36$	−9.20314	−	5.02591i	−1.53386	−	0.837652i
$37$	−3.09840	+	3.95481i	−0.509373	+	0.650167i	−0.971610	−	0.236590i	$-0.923970\pi$
$37$	−3.09840	+	3.95481i	−0.509373	+	0.650167i	0.462236	+	0.886757i	$0.347047\pi$
$38$	−1.82819	−	2.64858i	−0.296571	−	0.429657i
$39$	2.89061	−	5.53573i	0.462869	−	0.886427i
$40$	−8.67596	+	12.5693i	−1.37179	+	1.98738i
$41$	−0.343490	−	1.10230i	−0.0536440	−	0.172150i	0.924011	−	0.382366i	$-0.124891\pi$
$41$	−0.343490	−	1.10230i	−0.0536440	−	0.172150i	−0.977655	+	0.210217i	$0.932583\pi$
$42$	5.69361	−	5.60027i	0.878543	−	0.864140i
$43$	−11.9763	−	1.45418i	−1.82636	−	0.221761i	−0.865909	−	0.500201i	$-0.833259\pi$
$43$	−11.9763	−	1.45418i	−1.82636	−	0.221761i	−0.960454	+	0.278440i	$0.910183\pi$
$44$	−1.54651	+	8.43905i	−0.233146	+	1.27224i
$45$	−12.8159	−	2.56823i	−1.91048	−	0.382850i
$46$	3.10081	−	16.9206i	0.457189	−	2.49480i
$47$	3.16861	+	1.42607i	0.462189	+	0.208014i	0.628110	−	0.778125i	$-0.283829\pi$
$47$	3.16861	+	1.42607i	0.462189	+	0.208014i	−0.165921	+	0.986139i	$0.553060\pi$
$48$	1.49004	+	1.51488i	0.215069	+	0.218653i
$49$	−1.45517	−	2.77260i	−0.207882	−	0.396085i
$50$	−9.75162	+	31.2941i	−1.37909	+	4.42565i
$51$	3.32633	−	0.581202i	0.465780	−	0.0813846i
$52$	−8.81866	+	9.00326i	−1.22293	+	1.24853i
$53$	−2.45032	−	9.94132i	−0.336577	−	1.36555i	−0.858614	−	0.512623i	$-0.828674\pi$
$53$	−2.45032	−	9.94132i	−0.336577	−	1.36555i	0.522037	−	0.852923i	$-0.325172\pi$
$54$	−4.60043	+	11.2788i	−0.626040	+	1.53485i
$55$	1.28906	+	10.6163i	0.173816	+	1.43151i
$56$	−6.10511	+	3.20421i	−0.815830	+	0.428180i
$57$	−1.79282	+	1.56205i	−0.237465	+	0.206898i
$58$	−1.95832	−	4.35122i	−0.257140	−	0.571343i
$59$	0.0999412	−	1.65222i	0.0130112	−	0.215101i	−0.985859	−	0.167578i	$-0.946406\pi$
$59$	0.0999412	−	1.65222i	0.0130112	−	0.215101i	0.998870	−	0.0475237i	$-0.0151329\pi$
$60$	23.2538	+	12.4507i	3.00205	+	1.60738i
$61$	2.62241	+	0.646367i	0.335765	+	0.0827588i	0.403594	−	0.914938i	$-0.367761\pi$
$61$	2.62241	+	0.646367i	0.335765	+	0.0827588i	−0.0678284	+	0.997697i	$0.521607\pi$
$62$	18.1991	−	16.1230i	2.31129	−	2.04763i
$63$	−4.58418	−	3.71537i	−0.577552	−	0.468092i
$64$	5.64496	+	10.7556i	0.705620	+	1.34445i
$65$	−7.15589	+	13.9845i	−0.887579	+	1.73457i
$66$	9.94280	+	0.683944i	1.22387	+	0.0841877i
$67$	−0.663626	−	0.298674i	−0.0810748	−	0.0364888i	0.369470	−	0.929243i	$-0.379539\pi$
$67$	−0.663626	−	0.298674i	−0.0810748	−	0.0364888i	−0.450544	+	0.892754i	$0.648770\pi$
$68$	−6.76470	−	0.821383i	−0.820340	−	0.0996074i
$69$	−12.6802	−	0.872242i	−1.52651	−	0.105006i
$70$	−14.2051	+	14.2051i	−1.69784	+	1.69784i
$71$	−0.110106	−	0.353342i	−0.0130672	−	0.0419340i	0.947957	−	0.318398i	$-0.103145\pi$
$71$	−0.110106	−	0.353342i	−0.0130672	−	0.0419340i	−0.961024	+	0.276464i	$0.910837\pi$
$72$	6.62154	−	8.16994i	0.780356	−	0.962836i
$73$	−3.92021	+	0.718406i	−0.458826	+	0.0840831i	−0.404697	−	0.914451i	$-0.632623\pi$
$73$	−3.92021	+	0.718406i	−0.458826	+	0.0840831i	−0.0541295	+	0.998534i	$0.517238\pi$
$74$	−7.80983	−	8.81548i	−0.907874	−	1.02478i
$75$	23.7850	+	4.56224i	2.74645	+	0.526802i
$76$	4.37586	−	1.96941i	0.501945	−	0.225907i
$77$	−1.71200	+	4.51418i	−0.195101	+	0.514439i
$78$	11.5430	+	9.00439i	1.30698	+	1.01955i
$79$	2.65066	+	6.98923i	0.298223	+	0.786349i	0.997445	+	0.0714443i	$0.0227608\pi$
$79$	2.65066	+	6.98923i	0.298223	+	0.786349i	−0.699222	+	0.714905i	$0.746470\pi$
$80$	−3.77950	−	3.77950i	−0.422561	−	0.422561i
$81$	8.66251	+	2.44149i	0.962502	+	0.271276i
$82$	2.68684	−	0.326241i	0.296712	−	0.0360273i
$83$	9.96854	+	3.10632i	1.09419	+	0.340963i	0.790906	−	0.611937i	$-0.209609\pi$
$83$	9.96854	+	3.10632i	1.09419	+	0.340963i	0.303283	+	0.952900i	$0.401917\pi$
$84$	6.68326	+	9.85561i	0.729203	+	1.07533i
$85$	−8.35488	+	1.53109i	−0.906214	+	0.166070i
$86$	8.41373	−	27.0006i	0.907276	−	2.91155i
$87$	−3.03207	+	1.79890i	−0.325072	+	0.192862i
$88$	−8.04519	−	3.05114i	−0.857620	−	0.325252i
$89$	−0.936073	+	0.936073i	−0.0992235	+	0.0992235i	−0.754976	−	0.655752i	$-0.772351\pi$
$89$	−0.936073	+	0.936073i	−0.0992235	+	0.0992235i	0.655752	+	0.754976i	$0.272351\pi$
$90$	11.3373	−	28.4659i	1.19506	−	3.00057i
$91$	−5.79439	+	4.08883i	−0.607418	+	0.428626i
$92$	23.9828	+	9.09548i	2.50038	+	0.948269i
$93$	−13.3477	−	12.0234i	−1.38409	−	1.24677i
$94$	−4.62719	+	6.70364i	−0.477258	+	0.691427i
$95$	4.47714	−	3.96640i	0.459345	−	0.406944i
$96$	5.92766	−	4.01965i	0.604989	−	0.410253i
$97$	−3.59479	+	0.217445i	−0.364995	+	0.0220782i	−0.241859	−	0.970312i	$-0.577757\pi$
$97$	−3.59479	+	0.217445i	−0.364995	+	0.0220782i	−0.123137	+	0.992390i	$0.539295\pi$
$98$	7.00800	−	2.18378i	0.707915	−	0.220595i
$99$	−0.323063	−	7.35662i	−0.0324690	−	0.739368i
$100$	−43.2759	−	22.7129i	−4.32759	−	2.27129i
$101$	−1.41909	+	11.6873i	−0.141205	+	1.16293i	0.733990	+	0.679160i	$0.237656\pi$
$101$	−1.41909	+	11.6873i	−0.141205	+	1.16293i	−0.875196	+	0.483769i	$0.839267\pi$
$102$	−0.0654187	+	7.91551i	−0.00647742	+	0.783753i
$103$	−4.61145	+	8.78638i	−0.454379	+	0.865747i	0.545243	+	0.838278i	$0.316437\pi$
$103$	−4.61145	+	8.78638i	−0.454379	+	0.865747i	−0.999623	+	0.0274696i	$0.991255\pi$
$104$	−7.28714	−	10.3268i	−0.714563	−	1.01263i
$105$	11.6081	+	9.25023i	1.13284	+	0.902730i
$106$	23.9583	−	1.44921i	2.32703	−	0.140760i
$107$	−7.40200	−	8.35513i	−0.715578	−	0.807721i	0.272421	−	0.962178i	$-0.412176\pi$
$107$	−7.40200	−	8.35513i	−0.715578	−	0.807721i	−0.987999	+	0.154457i	$0.950637\pi$
$108$	−15.3053	−	9.77853i	−1.47276	−	0.940939i
$109$	0.773804	+	0.987687i	0.0741169	+	0.0946033i	0.822819	−	0.568303i	$-0.192400\pi$
$109$	0.773804	+	0.987687i	0.0741169	+	0.0946033i	−0.748703	+	0.662906i	$0.769323\pi$
$110$	−25.0241	−	1.51368i	−2.38595	−	0.144323i
$111$	−5.82401	+	6.46550i	−0.552791	+	0.613678i
$112$	−0.717873	−	2.30374i	−0.0678326	−	0.217683i
$113$	−2.03177	−	3.87121i	−0.191132	−	0.364173i	0.770965	−	0.636877i	$-0.219774\pi$
$113$	−2.03177	−	3.87121i	−0.191132	−	0.364173i	−0.962098	+	0.272705i	$0.912082\pi$
$114$	−2.84423	−	4.79397i	−0.266386	−	0.448997i
$115$	31.9135	+	1.93041i	2.97595	+	0.180012i
$116$	6.90797	−	1.70266i	0.641388	−	0.158088i
$117$	5.65288	−	9.22198i	0.522609	−	0.852572i
$118$	3.76750	+	0.928605i	0.346826	+	0.0854850i
$119$	−3.66097	−	1.14080i	−0.335601	−	0.104577i
$120$	−16.4858	+	20.6881i	−1.50494	+	1.88856i
$121$	4.65179	−	1.76419i	0.422890	−	0.160381i
$122$	−2.59852	+	5.77368i	−0.235259	+	0.522724i
$123$	−0.462516	−	1.94556i	−0.0417037	−	0.175425i
$124$	18.7551	+	31.0248i	1.68426	+	2.78611i
$125$	−38.4952	−	7.05451i	−3.44311	−	0.630974i
$126$	10.5040	−	9.00032i	0.935774	−	0.801813i
$127$	1.08853	−	0.412825i	0.0965915	−	0.0366323i	−0.305836	−	0.952084i	$-0.598936\pi$
$127$	1.08853	−	0.412825i	0.0965915	−	0.0366323i	0.402427	+	0.915452i	$0.368167\pi$
$128$	−19.2902	+	6.01106i	−1.70503	+	0.531308i
$129$	−20.5217	−	3.93632i	−1.80684	−	0.346573i
$130$	−29.2220	−	22.4094i	−2.56294	−	1.96544i
$131$	−7.03971	+	4.85916i	−0.615062	+	0.424547i	−0.834444	−	0.551092i	$-0.814211\pi$
$131$	−7.03971	+	4.85916i	−0.615062	+	0.424547i	0.219382	+	0.975639i	$0.429596\pi$
$132$	−3.67542	+	14.3986i	−0.319904	+	1.25324i
$133$	2.62182	−	0.646220i	0.227340	−	0.0560344i
$134$	0.969107	−	1.40399i	0.0837181	−	0.121287i
$135$	−21.8402	−	5.96116i	−1.87971	−	0.513055i
$136$	2.03315	−	6.52460i	0.174341	−	0.559480i
$137$	2.10037	+	2.68093i	0.179447	+	0.229047i	0.868532	−	0.495634i	$-0.165064\pi$
$137$	2.10037	+	2.68093i	0.179447	+	0.229047i	−0.689085	+	0.724681i	$0.741987\pi$
$138$	7.36933	−	28.8696i	0.627319	−	2.45754i
$139$	−1.10698	−	0.980698i	−0.0938928	−	0.0831817i	0.614871	−	0.788628i	$-0.289208\pi$
$139$	−1.10698	−	0.980698i	−0.0938928	−	0.0831817i	−0.708763	+	0.705446i	$0.750747\pi$
$140$	−17.0158	−	24.6516i	−1.43809	−	2.08344i
$141$	5.30574	+	2.84084i	0.446824	+	0.239242i
$142$	0.861269	−	0.104577i	0.0722761	−	0.00877591i
$143$	−8.61438	−	2.02885i	−0.720371	−	0.169661i
$144$	2.39468	+	2.79477i	0.199557	+	0.232897i
$145$	7.58938	−	4.58794i	0.630264	−	0.381008i
$146$		−	9.34287i		−	0.773222i
$147$	−2.18493	−	4.96392i	−0.180210	−	0.409417i
$148$	15.0281	−	9.08480i	1.23530	−	0.746766i
$149$	5.66703	−	12.5916i	0.464262	−	1.03155i	−0.519893	−	0.854232i	$-0.674028\pi$
$149$	5.66703	−	12.5916i	0.464262	−	1.03155i	0.984154	−	0.177315i	$-0.0567412\pi$
$150$	−20.5702	+	52.9160i	−1.67955	+	4.32057i
$151$	16.3797	−	7.37191i	1.33296	−	0.599917i	0.386368	−	0.922345i	$-0.373730\pi$
$151$	16.3797	−	7.37191i	1.33296	−	0.599917i	0.946594	+	0.322427i	$0.104499\pi$
$152$	1.15170	+	4.67261i	0.0934149	+	0.378999i
$153$	5.81688	−	0.608920i	0.470267	−	0.0492282i
$154$	−9.68546	−	5.85507i	−0.780477	−	0.471815i
$155$	33.8244	+	29.9658i	2.71684	+	2.40691i
$156$	−16.3085	+	14.5091i	−1.30573	+	1.16166i
$157$	7.37495	−	6.53364i	0.588585	−	0.521441i	−0.315426	−	0.948950i	$-0.602147\pi$
$157$	7.37495	−	6.53364i	0.588585	−	0.521441i	0.904011	+	0.427509i	$0.140609\pi$
$158$	−17.2359	+	3.15860i	−1.37122	+	0.251285i
$159$	−3.05241	−	17.4695i	−0.242072	−	1.38542i
$160$	−14.8267	+	10.2341i	−1.17215	+	0.809079i
$161$	12.3520	+	7.46704i	0.973473	+	0.588485i
$162$	−9.29003	+	18.9425i	−0.729894	+	1.48826i
$163$	−7.89916	+	10.0825i	−0.618710	+	0.789725i	−0.990341	−	0.138656i	$-0.955722\pi$
$163$	−7.89916	+	10.0825i	−0.618710	+	0.789725i	0.371631	+	0.928381i	$0.378799\pi$
$164$	−0.243666	+	4.02829i	−0.0190271	+	0.314556i
$165$	0.965556	+	18.4979i	0.0751685	+	1.44006i
$166$	−11.3749	+	21.6731i	−0.882863	+	1.68216i
$167$	14.4568	+	2.64931i	1.11870	+	0.205010i	0.707624	−	0.706589i	$-0.249767\pi$
$167$	14.4568	+	2.64931i	1.11870	+	0.205010i	0.411080	+	0.911599i	$0.365152\pi$
$168$	−10.9303	+	4.81110i	−0.843291	+	0.371184i
$169$	−8.82031	−	9.54999i	−0.678485	−	0.734614i
$170$		−	19.9118i		−	1.52717i
$171$	−3.28360	+	2.48606i	−0.251104	+	0.190114i
$172$	37.3386	+	19.5968i	2.84704	+	1.49424i
$173$	−4.83595	+	12.7514i	−0.367670	+	0.969467i	0.615720	+	0.787965i	$0.288865\pi$
$173$	−4.83595	+	12.7514i	−0.367670	+	0.969467i	−0.983391	+	0.181502i	$0.941904\pi$
$174$	−2.86672	−	7.75153i	−0.217325	−	0.587642i
$175$	−21.6495	−	16.9613i	−1.63655	−	1.28215i
$176$	1.55783	−	2.57697i	0.117426	−	0.194247i
$177$	0.369084	−	2.84311i	0.0277420	−	0.213701i
$178$	−1.76287	−	2.55396i	−0.132133	−	0.191427i
$179$	−2.07066	−	0.510372i	−0.154768	−	0.0381470i	0.161170	−	0.986927i	$-0.448473\pi$
$179$	−2.07066	−	0.510372i	−0.154768	−	0.0381470i	−0.315939	+	0.948780i	$0.602319\pi$
$180$	38.7019	+	24.2785i	2.88467	+	1.80961i
$181$	4.35249	+	4.91295i	0.323518	+	0.365177i	0.887658	−	0.460502i	$-0.152331\pi$
$181$	4.35249	+	4.91295i	0.323518	+	0.365177i	−0.564140	+	0.825679i	$0.690792\pi$
$182$	−6.97965	−	15.0886i	−0.517366	−	1.11844i
$183$	4.45461	+	1.42861i	0.329295	+	0.105606i
$184$	−13.3078	+	22.0138i	−0.981063	+	1.62288i
$185$	14.5151	−	16.3842i	1.06718	−	1.20459i
$186$	33.3640	−	25.6969i	2.44636	−	1.88419i
$187$	−1.96395	−	4.36373i	−0.143619	−	0.319107i
$188$	−8.58811	−	8.58811i	−0.626352	−	0.626352i
$189$	−7.47969	−	6.96492i	−0.544067	−	0.506624i
$190$	7.25395	+	11.9995i	0.526257	+	0.870535i
$191$		−	20.9170i		−	1.51350i	−0.653703	−	0.756751i	$-0.726785\pi$
$191$		−	20.9170i		−	1.51350i	0.653703	−	0.756751i	$-0.273215\pi$
$192$	8.47586	+	19.2563i	0.611693	+	1.38970i
$193$	5.87404	+	9.71685i	0.422823	+	0.699434i	0.992474	−	0.122452i	$-0.0390758\pi$
$193$	5.87404	+	9.71685i	0.422823	+	0.699434i	−0.569652	+	0.821886i	$0.692922\pi$
$194$	1.01762	−	8.38081i	0.0730605	−	0.601707i
$195$	−14.0274	+	23.3142i	−1.00452	+	1.66957i
$196$	1.31926	+	10.8651i	0.0942328	+	0.776077i
$197$	−5.50117	+	4.30989i	−0.391942	+	0.307067i	−0.793273	−	0.608866i	$-0.791625\pi$
$197$	−5.50117	+	4.30989i	−0.391942	+	0.307067i	0.401331	+	0.915933i	$0.368548\pi$
$198$	17.0995	+	2.36367i	1.21521	+	0.167978i
$199$	6.02589	−	6.80183i	0.427164	−	0.482169i	−0.495041	−	0.868870i	$-0.664847\pi$
$199$	6.02589	−	6.80183i	0.427164	−	0.482169i	0.922205	+	0.386701i	$0.126385\pi$
$200$	30.2285	−	38.5838i	2.13748	−	2.72829i
$201$	−1.11122	−	0.594979i	−0.0783796	−	0.0419666i
$202$	−26.3491	−	8.21072i	−1.85392	−	0.577704i
$203$	3.99629	−	0.241731i	0.280485	−	0.0169662i
$204$	−11.5915	−	2.22340i	−0.811571	−	0.155669i
$205$	1.20385	+	4.88419i	0.0840802	+	0.341127i
$206$	−18.3112	−	14.3459i	−1.27580	−	0.999526i
$207$	−21.8073	−	3.01441i	−1.51571	−	0.209516i
$208$	4.01456	−	1.85705i	0.278360	−	0.128763i
$209$	2.77326	+	1.91425i	0.191831	+	0.132411i
$210$	−26.2345	+	22.8575i	−1.81035	+	1.57732i
$211$	−7.65858	−	20.1940i	−0.527238	−	1.39021i	−0.888985	−	0.457937i	$-0.848589\pi$
$211$	−7.65858	−	20.1940i	−0.527238	−	1.39021i	0.361747	−	0.932276i	$-0.382181\pi$
$212$	−4.31381	+	35.5275i	−0.296274	+	2.44004i
$213$	−0.148260	−	0.623651i	−0.0101586	−	0.0427319i
$214$	22.3932	−	13.5371i	1.53077	−	0.925380i
$215$	51.7017	+	9.47468i	3.52602	+	0.646168i
$216$	12.4129	−	13.3303i	0.844592	−	0.907014i
$217$	7.23409	+	19.0747i	0.491082	+	1.29488i
$218$	−2.60440	+	1.36690i	−0.176392	+	0.0925779i
$219$	−6.85940	+	0.775413i	−0.463515	+	0.0523976i
$220$	8.94572	−	36.2942i	0.603120	−	2.44695i
$221$	1.19537	−	6.92683i	0.0804094	−	0.465949i
$222$	−12.4473	−	16.1612i	−0.835408	−	1.08467i
$223$	−0.617695	+	10.2117i	−0.0413639	+	0.683827i	0.917108	+	0.398639i	$0.130517\pi$
$223$	−0.617695	+	10.2117i	−0.0413639	+	0.683827i	−0.958472	+	0.285188i	$0.907944\pi$
$224$	−8.07387	+	0.980346i	−0.539458	+	0.0655021i
$225$	40.5574	+	10.7106i	2.70382	+	0.714037i
$226$	9.78484	−	3.04908i	0.650878	−	0.202822i
$227$	−12.9813	+	5.84239i	−0.861596	+	0.387773i	−0.792526	−	0.609839i	$-0.791234\pi$
$227$	−12.9813	+	5.84239i	−0.861596	+	0.387773i	−0.0690709	+	0.997612i	$0.522003\pi$
$228$	7.79543	−	2.88295i	0.516265	−	0.190928i
$229$	3.31094	−	2.59395i	0.218793	−	0.171413i	−0.501338	−	0.865252i	$-0.667159\pi$
$229$	3.31094	−	2.59395i	0.218793	−	0.171413i	0.720131	+	0.693838i	$0.244082\pi$
$230$	−17.9364	+	72.7710i	−1.18269	+	4.79838i
$231$	−3.49485	+	7.59686i	−0.229945	+	0.499837i
$232$	0.430814	+	7.12221i	0.0282843	+	0.467596i
$233$	19.8193	−	10.4020i	1.29840	−	0.681455i	0.333175	−	0.942865i	$-0.391880\pi$
$233$	19.8193	−	10.4020i	1.29840	−	0.681455i	0.965228	+	0.261410i	$0.0841876\pi$
$234$	18.8756	+	16.9313i	1.23393	+	1.10684i
$235$	−13.4050	−	7.03547i	−0.874444	−	0.458944i
$236$	−2.37451	+	5.27595i	−0.154568	+	0.343435i
$237$	3.74950	+	12.3922i	0.243556	+	0.804961i
$238$	4.17746	−	7.95948i	0.270784	−	0.515937i
$239$	−0.658839	−	0.658839i	−0.0426167	−	0.0426167i	0.685477	−	0.728094i	$-0.259594\pi$
$239$	−0.658839	−	0.658839i	−0.0426167	−	0.0426167i	−0.728094	+	0.685477i	$0.759594\pi$
$240$	−6.08161	−	6.98010i	−0.392566	−	0.450563i
$241$	−1.41937	−	23.4650i	−0.0914296	−	1.51151i	−0.697779	−	0.716313i	$-0.745828\pi$
$241$	−1.41937	−	23.4650i	−0.0914296	−	1.51151i	0.606350	−	0.795198i	$-0.292633\pi$
$242$	2.10226	+	11.4717i	0.135138	+	0.737426i
$243$	14.6783	+	5.24846i	0.941616	+	0.336689i
$244$	−7.76945	−	5.36286i	−0.497388	−	0.343322i
$245$	5.59910	+	12.4407i	0.357713	+	0.794807i
$246$	4.68155	−	0.244368i	0.298485	−	0.0155803i
$247$	1.80310	+	4.60981i	0.114729	+	0.293315i
$248$	−33.9951	+	12.8926i	−2.15869	+	0.818683i
$249$	16.8561	+	6.55252i	1.06821	+	0.415249i
$250$	32.5328	−	85.7820i	2.05756	−	5.42533i
$251$	−1.36633	−	11.2527i	−0.0862420	−	0.710267i	−0.970133	−	0.242574i	$-0.922008\pi$
$251$	−1.36633	−	11.2527i	−0.0862420	−	0.710267i	0.883891	−	0.467693i	$-0.154915\pi$
$252$	10.3770	+	17.8246i	0.653688	+	1.12284i
$253$	3.24678	+	17.7171i	0.204123	+	1.11386i
$254$	0.491934	+	2.68440i	0.0308667	+	0.168434i
$255$	−14.6190	+	1.65258i	−0.915475	+	0.103489i
$256$	−2.78092	−	22.9029i	−0.173807	−	1.43143i
$257$	−0.680730	+	1.79494i	−0.0424628	+	0.111965i	−0.954570	−	0.297986i	$-0.903685\pi$
$257$	−0.680730	+	1.79494i	−0.0424628	+	0.111965i	0.912107	+	0.409951i	$0.134454\pi$
$258$	17.7480	−	45.6561i	1.10494	−	2.84242i
$259$	9.23961	−	3.50412i	0.574121	−	0.217736i
$260$	40.7204	−	36.8349i	2.52537	−	2.28440i
$261$	−5.45313	+	2.74804i	−0.337541	+	0.170100i
$262$	−8.22967	−	18.2856i	−0.508431	−	1.12969i
$263$	12.5830	+	8.68543i	0.775902	+	0.535567i	0.888940	−	0.458024i	$-0.151443\pi$
$263$	12.5830	+	8.68543i	0.775902	+	0.535567i	−0.113038	+	0.993591i	$0.536058\pi$
$264$	−13.5392	−	6.22854i	−0.833278	−	0.383340i
$265$	8.04111	+	43.8789i	0.493962	+	2.69546i
$266$	0.382199	+	6.31850i	0.0234341	+	0.387412i
$267$	−1.72877	+	1.50624i	−0.105799	+	0.0921803i
$268$	1.79867	+	1.79867i	0.109871	+	0.109871i
$269$	7.40227	−	14.1038i	0.451324	−	0.859927i	−0.548395	−	0.836220i	$-0.684761\pi$
$269$	7.40227	−	14.1038i	0.451324	−	0.859927i	0.999719	−	0.0237070i	$-0.00754689\pi$
$270$	22.9741	−	47.8406i	1.39816	−	2.91149i
$271$	4.40896	−	9.79631i	0.267825	−	0.595083i	−0.728079	−	0.685493i	$-0.759587\pi$
$271$	4.40896	−	9.79631i	0.267825	−	0.595083i	0.995905	+	0.0904094i	$0.0288176\pi$
$272$	2.11775	+	1.11148i	0.128407	+	0.0673933i
$273$	−10.4985	+	6.37663i	−0.635400	+	0.385931i
$274$	−7.06926	+	3.71024i	−0.427070	+	0.224144i
$275$	−2.07226	−	34.2586i	−0.124962	−	2.06587i
$276$	40.3604	+	18.5674i	2.42941	+	1.11762i
$277$	5.77353	−	23.4241i	0.346898	−	1.40742i	−0.495521	−	0.868596i	$-0.665023\pi$
$277$	5.77353	−	23.4241i	0.346898	−	1.40742i	0.842419	−	0.538823i	$-0.181131\pi$
$278$	2.72907	−	2.13809i	0.163679	−	0.128234i
$279$	−21.6353	−	22.3626i	−1.29527	−	1.33881i
$280$	27.3937	−	12.3289i	1.63709	−	0.736794i
$281$	−9.45525	+	2.94637i	−0.564053	+	0.175766i	−0.566253	−	0.824232i	$-0.691607\pi$
$281$	−9.45525	+	2.94637i	−0.564053	+	0.175766i	0.00220004	+	0.999998i	$0.499300\pi$
$282$	−8.79244	+	11.0337i	−0.523582	+	0.657045i
$283$	−13.0237	+	1.58137i	−0.774180	+	0.0940024i	−0.498085	−	0.867128i	$-0.665963\pi$
$283$	−13.0237	+	1.58137i	−0.774180	+	0.0940024i	−0.276094	+	0.961131i	$0.589040\pi$
$284$	−0.0781075	+	1.29127i	−0.00463483	+	0.0766228i
$285$	8.20781	−	6.32164i	0.486188	−	0.374462i
$286$	8.31822	−	19.0059i	0.491867	−	1.12384i
$287$	−0.543473	+	2.20496i	−0.0320802	+	0.130154i
$288$	10.7206	−	6.24124i	0.631717	−	0.367768i
$289$	−11.6873	+	6.13399i	−0.687491	+	0.360823i
$290$	7.37201	+	19.4384i	0.432899	+	1.14146i
$291$	−6.23752	−	0.0515508i	−0.365650	−	0.00302196i
$292$	13.7025	+	2.51108i	0.801881	+	0.146950i
$293$	−8.36665	+	5.05781i	−0.488785	+	0.295481i	−0.740186	−	0.672402i	$-0.765263\pi$
$293$	−8.36665	+	5.05781i	−0.488785	+	0.295481i	0.251401	+	0.967883i	$0.419109\pi$
$294$	12.3692	−	2.94051i	0.721384	−	0.171494i
$295$	−0.869279	+	7.15915i	−0.0506114	+	0.416822i
$296$	6.24506	+	16.4669i	0.362987	+	0.957117i
$297$	0.316189	−	12.7504i	0.0183472	−	0.739853i
$298$	26.6394	+	18.3878i	1.54318	+	1.06518i
$299$	−10.6083	+	24.2385i	−0.613495	+	1.40175i
$300$	−72.0796	−	44.3911i	−4.16152	−	2.56292i
$301$	18.6793	+	14.6343i	1.07666	+	0.843505i
$302$	10.0769	+	40.8837i	0.579862	+	2.35259i
$303$	−3.84134	+	20.0266i	−0.220679	+	1.15050i
$304$	−1.68114	+	0.101690i	−0.0964198	+	0.00583233i
$305$	−11.2347	−	3.50088i	−0.643298	−	0.200460i
$306$	−1.05390	+	13.6700i	−0.0602477	+	0.781460i
$307$	8.36702	−	10.6797i	0.477531	−	0.609524i	−0.487029	−	0.873386i	$-0.661919\pi$
$307$	8.36702	−	10.6797i	0.477531	−	0.609524i	0.964560	+	0.263862i	$0.0849964\pi$
$308$	11.1904	−	12.6313i	0.637631	−	0.719737i
$309$	−9.01281	+	14.6344i	−0.512721	+	0.832524i
$310$	−83.3886	+	65.3308i	−4.73615	+	3.71054i
$311$	2.31304	+	19.0496i	0.131161	+	1.08020i	0.898503	+	0.438967i	$0.144656\pi$
$311$	2.31304	+	19.0496i	0.131161	+	1.08020i	−0.767342	+	0.641237i	$0.778421\pi$
$312$	−11.3645	−	18.7105i	−0.643386	−	1.05928i
$313$	1.49263	−	12.2929i	0.0843682	−	0.694834i	−0.887747	−	0.460331i	$-0.847731\pi$
$313$	1.49263	−	12.2929i	0.0843682	−	0.694834i	0.972115	−	0.234503i	$-0.0753463\pi$
$314$	11.9490	+	19.7661i	0.674323	+	1.11547i
$315$	18.9590	+	17.3639i	1.06822	+	0.978344i
$316$		−	26.1277i		−	1.46980i
$317$	17.2232	+	28.4907i	0.967354	+	1.60020i	0.787326	+	0.616537i	$0.211465\pi$
$317$	17.2232	+	28.4907i	0.967354	+	1.60020i	0.180028	+	0.983662i	$0.442381\pi$
$318$	41.5714	+	0.343572i	2.33121	+	0.0192666i
$319$	3.53286	+	3.53286i	0.197802	+	0.197802i
$320$	−21.7203	−	48.2604i	−1.21420	−	2.69784i
$321$	−11.7973	−	15.3172i	−0.658461	−	0.854923i
$322$	−22.4371	+	25.3262i	−1.25037	+	1.41137i
$323$	−1.38463	+	2.29046i	−0.0770430	+	0.127445i
$324$	−25.2848	−	18.7162i	−1.40471	−	1.03979i
$325$	25.6333	−	43.4120i	1.42188	−	2.40806i
$326$	−19.9106	−	22.4745i	−1.10275	−	1.24475i
$327$	1.21971	+	1.79867i	0.0674500	+	0.0994666i
$328$	−3.92968	−	0.968579i	−0.216980	−	0.0534808i
$329$	−3.88243	−	5.62467i	−0.214045	−	0.310098i
$330$	−43.0608	−	5.59002i	−2.37042	−	0.307721i
$331$	0.755606	−	1.24993i	0.0415319	−	0.0687021i	−0.834326	−	0.551272i	$-0.814143\pi$
$331$	0.755606	−	1.24993i	0.0415319	−	0.0687021i	0.875858	+	0.482570i	$0.160297\pi$
$332$	−28.7291	−	22.5078i	−1.57672	−	1.23528i
$333$	−10.8322	+	10.4799i	−0.593602	+	0.574296i
$334$	−12.2177	+	32.2154i	−0.668521	+	1.76275i
$335$	2.80751	+	1.47349i	0.153390	+	0.0805055i
$336$	−0.966632	−	4.06611i	−0.0527341	−	0.221824i
$337$			18.8037i			1.02430i	0.858896	+	0.512150i	$0.171151\pi$
$337$			18.8037i			1.02430i	−0.858896	+	0.512150i	$0.828849\pi$
$338$	25.7476	−	16.3026i	1.40049	−	0.886745i
$339$	−3.05068	−	6.93082i	−0.165690	−	0.376431i
$340$	29.2033	+	5.35170i	1.58377	+	0.290237i
$341$	−11.8311	+	22.5422i	−0.640689	+	1.22073i
$342$	−4.34490	−	8.62190i	−0.234946	−	0.466219i
$343$	−1.20318	+	19.8909i	−0.0649656	+	1.07401i
$344$	−26.0813	+	33.2903i	−1.40621	+	1.79489i
$345$	54.9160	+	7.12903i	2.95658	+	0.383814i
$346$	−27.3588	−	16.5390i	−1.47082	−	0.889142i
$347$	−22.5856	+	15.5897i	−1.21246	+	0.836899i	−0.990413	−	0.138138i	$-0.955888\pi$
$347$	−22.5856	+	15.5897i	−1.21246	+	0.836899i	−0.222044	+	0.975037i	$0.571273\pi$
$348$	12.1391	−	2.12104i	0.650725	−	0.113700i
$349$	−6.05000	+	1.10870i	−0.323849	+	0.0593475i	−0.339720	−	0.940527i	$-0.610332\pi$
$349$	−6.05000	+	1.10870i	−0.323849	+	0.0593475i	0.0158713	+	0.999874i	$0.494948\pi$
$350$	48.2579	−	42.7527i	2.57949	−	2.28523i
$351$	10.8641	−	15.2634i	0.579885	−	0.814698i
$352$	−7.59712	−	6.73046i	−0.404928	−	0.358735i
$353$	−14.5580	−	8.80064i	−0.774846	−	0.468411i	0.0738644	−	0.997268i	$-0.476467\pi$
$353$	−14.5580	−	8.80064i	−0.774846	−	0.468411i	−0.848711	+	0.528857i	$0.822621\pi$
$354$	6.39974	+	2.05242i	0.340142	+	0.109085i
$355$	0.385894	+	1.56563i	0.0204811	+	0.0830952i
$356$	4.21952	−	1.89905i	0.223634	−	0.100650i
$357$	−6.19044	−	2.40643i	−0.327633	−	0.127362i
$358$	2.05180	−	4.55890i	0.108441	−	0.240945i
$359$	−7.98358	+	4.82624i	−0.421357	+	0.254719i	−0.712095	−	0.702084i	$-0.752253\pi$
$359$	−7.98358	+	4.82624i	−0.421357	+	0.254719i	0.290737	+	0.956803i	$0.406099\pi$
$360$	−30.9460	+	33.7888i	−1.63100	+	1.78083i
$361$			17.1153i			0.900804i
$362$	−13.1675	+	7.96006i	−0.692071	+	0.418371i
$363$	8.24784	−	2.49554i	0.432900	−	0.130982i
$364$	24.0053	−	6.18121i	1.25822	−	0.323983i
$365$	17.2378	−	2.09305i	0.902268	−	0.109555i
$366$	−5.17644	+	9.66786i	−0.270577	+	0.505347i
$367$	8.75992	+	12.6909i	0.457264	+	0.662461i	0.982017	−	0.188793i	$-0.0604577\pi$
$367$	8.75992	+	12.6909i	0.457264	+	0.662461i	−0.524753	+	0.851255i	$0.675842\pi$
$368$	−6.73844	−	5.96974i	−0.351265	−	0.311194i
$369$	−0.567957	−	3.41684i	−0.0295667	−	0.177874i
$370$	31.6456	+	40.3926i	1.64517	+	2.09991i
$371$	−5.99138	+	19.2270i	−0.311057	+	0.998217i
$372$	28.7206	+	55.8391i	1.48909	+	2.89512i
$373$	15.9916	−	23.1678i	0.828012	−	1.19958i	−0.149513	−	0.988760i	$-0.547771\pi$
$373$	15.9916	−	23.1678i	0.828012	−	1.19958i	0.977524	−	0.210822i	$-0.0676141\pi$
$374$	10.8919	−	2.68460i	0.563204	−	0.138817i
$375$	−65.6799	−	16.7656i	−3.39170	−	0.865773i
$376$	10.0243	−	6.91928i	0.516964	−	0.356835i
$377$	1.39759	+	7.20471i	0.0719796	+	0.371061i
$378$	19.2204	−	14.3037i	0.988593	−	0.735704i
$379$	−24.0151	+	7.48340i	−1.23357	+	0.384396i	−0.843871	−	0.536546i	$-0.819729\pi$
$379$	−24.0151	+	7.48340i	−1.23357	+	0.384396i	−0.389700	+	0.920942i	$0.627421\pi$
$380$	−19.5485	+	7.41376i	−1.00282	+	0.380318i
$381$	1.93002	−	0.583962i	0.0988777	−	0.0299173i
$382$	48.2309	+	8.83863i	2.46771	+	0.452224i
$383$	1.66427	+	2.75305i	0.0850404	+	0.140674i	0.895406	−	0.445250i	$-0.146885\pi$
$383$	1.66427	+	2.75305i	0.0850404	+	0.140674i	−0.810366	+	0.585924i	$0.800732\pi$
$384$	−34.0473	+	8.09402i	−1.73747	+	0.413046i
$385$	8.63293	−	19.1816i	0.439975	−	0.977584i
$386$	−24.8874	+	9.43855i	−1.26674	+	0.480409i
$387$	−34.9930	−	9.24110i	−1.77880	−	0.469752i
$388$	12.0181	+	3.74498i	0.610124	+	0.190122i
$389$	−32.7414	−	8.07002i	−1.66005	−	0.409166i	−0.705858	−	0.708353i	$-0.749438\pi$
$389$	−32.7414	−	8.07002i	−1.66005	−	0.409166i	−0.954194	+	0.299187i	$0.903285\pi$
$390$	−47.8310	−	42.1962i	−2.42202	−	2.13669i
$391$	−13.8905	+	3.42370i	−0.702473	+	0.173144i
$392$	−10.9564	−	0.662741i	−0.553383	−	0.0334735i
$393$	−12.7420	+	7.55971i	−0.642747	+	0.381337i
$394$	−7.61327	−	14.5059i	−0.383551	−	0.730795i
$395$	−9.68900	−	31.0931i	−0.487507	−	1.56446i
$396$	−8.06246	+	24.4434i	−0.405154	+	1.22833i
$397$	6.85383	+	0.414580i	0.343984	+	0.0208072i	0.231467	−	0.972843i	$-0.425647\pi$
$397$	6.85383	+	0.414580i	0.343984	+	0.0208072i	0.112517	+	0.993650i	$0.464109\pi$
$398$	13.1375	+	16.7688i	0.658523	+	0.840543i
$399$	4.60723	−	0.805009i	0.230650	−	0.0403009i
$400$	11.3750	+	12.8398i	0.568752	+	0.641988i
$401$	23.1872	−	1.40257i	1.15791	−	0.0700408i	0.529771	−	0.848140i	$-0.322278\pi$
$401$	23.1872	−	1.40257i	1.15791	−	0.0700408i	0.628141	+	0.778100i	$0.283816\pi$
$402$	1.84147	−	2.31086i	0.0918441	−	0.115255i
$403$	−32.9308	+	17.7209i	−1.64040	+	0.882740i
$404$	19.1239	−	36.4376i	0.951452	−	1.81284i
$405$	−37.0306	−	12.8967i	−1.84007	−	0.640842i
$406$	−1.13127	+	9.31687i	−0.0561441	+	0.462388i
$407$	10.9192	+	5.73085i	0.541246	+	0.284068i
$408$	4.28875	−	11.0326i	0.212325	−	0.546197i
$409$	36.4134	−	11.3469i	1.80053	−	0.561066i	0.801221	−	0.598368i	$-0.204184\pi$
$409$	36.4134	−	11.3469i	1.80053	−	0.561066i	0.999304	+	0.0373021i	$0.0118764\pi$
$410$	−11.7708	+	0.712000i	−0.581316	+	0.0351632i
$411$	3.31071	+	4.88221i	0.163305	+	0.240822i
$412$	25.9616	−	23.0000i	1.27904	−	1.13313i
$413$	−1.84946	+	2.67940i	−0.0910059	+	0.131845i
$414$	16.1655	−	49.0098i	0.794491	−	2.40870i
$415$	−42.5356	−	16.1316i	−2.08799	−	0.791870i
$416$	−3.71769	−	14.4380i	−0.182275	−	0.707881i
$417$	−1.79626	−	1.82619i	−0.0879630	−	0.0894291i
$418$	−5.58577	+	5.58577i	−0.273209	+	0.273209i
$419$	−20.8427	−	7.90459i	−1.01823	−	0.386164i	−0.211687	−	0.977338i	$-0.567896\pi$
$419$	−20.8427	−	7.90459i	−1.01823	−	0.386164i	−0.806545	+	0.591173i	$0.798665\pi$
$420$	−26.4725	−	44.6197i	−1.29173	−	2.17722i
$421$	10.3329	−	33.1595i	0.503596	−	1.61610i	−0.256680	−	0.966496i	$-0.582629\pi$
$421$	10.3329	−	33.1595i	0.503596	−	1.61610i	0.760276	−	0.649600i	$-0.225064\pi$
$422$	49.7999	−	9.12617i	2.42422	−	0.444255i
$423$	8.83048	+	5.53954i	0.429353	+	0.269342i
$424$	−34.2665	−	10.6779i	−1.66413	−	0.518563i
$425$	27.0611	−	3.28581i	1.31265	−	0.159385i
$426$	1.50068	−	0.0783324i	0.0727079	−	0.00379522i
$427$	−3.75645	−	3.75645i	−0.181787	−	0.181787i
$428$	13.8354	+	36.4809i	0.668758	+	1.76337i
$429$	−14.6442	−	4.52971i	−0.707029	−	0.218697i
$430$	−43.6938	+	115.211i	−2.10710	+	5.55597i
$431$	−0.733352	+	0.330055i	−0.0353243	+	0.0158982i	−0.427998	−	0.903780i	$-0.640781\pi$
$431$	−0.733352	+	0.330055i	−0.0353243	+	0.0158982i	0.392674	+	0.919678i	$0.371550\pi$
$432$	3.80573	+	5.11390i	0.183103	+	0.246043i
$433$	0.911314	+	1.02866i	0.0437950	+	0.0494343i	0.770000	−	0.638044i	$-0.220256\pi$
$433$	0.911314	+	1.02866i	0.0437950	+	0.0494343i	−0.726205	+	0.687478i	$0.758718\pi$
$434$	−47.0397	+	8.62035i	−2.25798	+	0.413790i
$435$	13.6595	−	7.02571i	0.654925	−	0.336857i
$436$	−1.30475	−	4.18708i	−0.0624860	−	0.200525i
$437$	7.12360	−	7.12360i	0.340768	−	0.340768i
$438$	1.11052	−	16.1442i	0.0530629	−	0.771399i
$439$	−16.7666	−	2.03584i	−0.800228	−	0.0971653i	−0.289802	−	0.957087i	$-0.593589\pi$
$439$	−16.7666	−	2.03584i	−0.800228	−	0.0971653i	−0.510427	+	0.859921i	$0.670512\pi$
$440$	34.1855	+	15.3856i	1.62973	+	0.733482i
$441$	−3.18546	−	8.83721i	−0.151688	−	0.420819i
$442$	15.4669	+	5.68329i	0.735686	+	0.270327i
$443$	−14.7361	−	28.0772i	−0.700131	−	1.33399i	−0.932433	−	0.361344i	$-0.882318\pi$
$443$	−14.7361	−	28.0772i	−0.700131	−	1.33399i	0.232302	−	0.972644i	$-0.425374\pi$
$444$	27.0479	−	13.9120i	1.28364	−	0.660232i
$445$	4.31718	−	3.82469i	0.204654	−	0.181308i
$446$	−23.2853	−	5.73932i	−1.10259	−	0.271765i
$447$	11.2891	−	21.0843i	0.533958	−	0.997255i
$448$	1.44256	−	23.8483i	0.0681544	−	1.12673i
$449$	5.83177	+	12.9577i	0.275218	+	0.611510i	0.996722	−	0.0809004i	$-0.0257796\pi$
$449$	5.83177	+	12.9577i	0.275218	+	0.611510i	−0.721504	+	0.692410i	$0.756549\pi$
$450$	−41.8344	+	88.9921i	−1.97209	+	4.19513i
$451$	−2.50937	+	1.31702i	−0.118161	+	0.0620159i
$452$	1.84200	+	15.1702i	0.0866404	+	0.713548i
$453$	29.1799	−	10.7915i	1.37099	−	0.507028i
$454$	−7.98617	−	32.4012i	−0.374810	−	1.52066i
$455$	26.2752	−	16.2579i	1.23180	−	0.762180i
$456$	1.43469	+	8.21102i	0.0671856	+	0.384516i
$457$	4.34806	−	13.9534i	0.203394	−	0.652714i	−0.795512	−	0.605938i	$-0.792798\pi$
$457$	4.34806	−	13.9534i	0.203394	−	0.652714i	0.998905	−	0.0467754i	$-0.0148945\pi$
$458$	4.58213	+	8.73052i	0.214109	+	0.407950i
$459$	10.1238	−	0.360780i	0.472537	−	0.0168398i
$460$	−101.907	−	45.8648i	−4.75146	−	2.13846i
$461$	5.41728	−	29.5611i	0.252308	−	1.37680i	−0.576423	−	0.817152i	$-0.695552\pi$
$461$	5.41728	−	29.5611i	0.252308	−	1.37680i	0.828731	−	0.559648i	$-0.189064\pi$
$462$	−16.0402	−	11.2686i	−0.746258	−	0.524263i
$463$	4.77056	−	26.0321i	0.221707	−	1.20981i	−0.664773	−	0.747046i	$-0.731472\pi$
$463$	4.77056	−	26.0321i	0.221707	−	1.20981i	0.886479	−	0.462768i	$-0.153144\pi$
$464$	−2.47890	−	0.300993i	−0.115080	−	0.0139733i
$465$	54.8857	+	55.8005i	2.54526	+	2.58769i
$466$	15.6102	+	50.0950i	0.723131	+	2.32061i
$467$	−0.467380	+	0.677117i	−0.0216278	+	0.0313333i	−0.833649	−	0.552295i	$-0.813752\pi$
$467$	−0.467380	+	0.677117i	−0.0216278	+	0.0313333i	0.812021	+	0.583628i	$0.198368\pi$
$468$	−29.9052	+	23.1328i	−1.38237	+	1.06932i
$469$	0.813127	+	1.17802i	0.0375467	+	0.0543958i
$470$	21.8869	−	27.9366i	1.00957	−	1.28862i
$471$	13.5203	−	10.4133i	0.622982	−	0.479819i
$472$	−4.77524	−	3.29611i	−0.219798	−	0.151716i
$473$	1.78796	+	29.5584i	0.0822103	+	1.35910i
$474$	−30.1586	+	3.40925i	−1.38523	+	0.156592i
$475$	−15.1108	+	11.8386i	−0.693332	+	0.543191i
$476$	10.5508	+	8.26606i	0.483597	+	0.378874i
$477$	−3.19798	−	30.5496i	−0.146425	−	1.39877i
$478$	1.79756	−	1.24077i	0.0822185	−	0.0567513i
$479$	−20.6495	−	26.3571i	−0.943498	−	1.20429i	−0.978781	−	0.204909i	$-0.934310\pi$
$479$	−20.6495	−	26.3571i	−0.943498	−	1.20429i	0.0352830	−	0.999377i	$-0.488767\pi$
$480$	−26.8365	+	15.9219i	−1.22491	+	0.726732i
$481$	8.58381	+	15.9514i	0.391388	+	0.727320i
$482$	54.7057	+	6.64248i	2.49178	+	0.302557i
$483$	20.4563	+	14.3710i	0.930793	+	0.653903i
$484$	−17.3897			−0.790442
$485$	15.6908			0.712481
$486$	−18.3044	+	31.6278i	−0.830306	+	1.43467i
$487$	−7.61571	−	3.42755i	−0.345101	−	0.155317i	0.230448	−	0.973085i	$-0.425981\pi$
$487$	−7.61571	−	3.42755i	−0.345101	−	0.155317i	−0.575549	+	0.817767i	$0.695212\pi$
$488$	6.69476	−	6.69476i	0.303057	−	0.303057i
$489$	−14.8479	+	16.4834i	−0.671447	+	0.745404i
$490$	−31.0519	+	7.65361i	−1.40278	+	0.345755i
$491$	−0.523923	−	0.464156i	−0.0236443	−	0.0209471i	0.651218	−	0.758891i	$-0.274258\pi$
$491$	−0.523923	−	0.464156i	−0.0236443	−	0.0209471i	−0.674862	+	0.737944i	$0.735797\pi$
$492$	−0.899862	+	6.93178i	−0.0405689	+	0.312509i
$493$	−2.63145	+	2.97029i	−0.118515	+	0.133775i
$494$	−11.3913	+	2.20972i	−0.512519	+	0.0994199i
$495$	−0.530271	+	32.0786i	−0.0238339	+	1.44182i
$496$	−2.29358	−	12.5157i	−0.102985	−	0.561970i
$497$	−0.174211	+	0.706800i	−0.00781442	+	0.0317043i
$498$	−22.2316	+	36.0983i	−0.996221	+	1.61760i
$499$	21.7703	−	36.0125i	0.974572	−	1.61214i	0.199861	−	0.979824i	$-0.435951\pi$
$499$	21.7703	−	36.0125i	0.974572	−	1.61214i	0.774712	−	0.632315i	$-0.217895\pi$
$500$	117.067	+	70.7693i	5.23538	+	3.16490i
$501$	24.6660	+	6.29631i	1.10200	+	0.281299i
$502$	26.5241	+	1.60441i	1.18383	+	0.0716085i
$503$	5.09330	+	1.93164i	0.227099	+	0.0861274i	0.465530	−	0.885032i	$-0.345864\pi$
$503$	5.09330	+	1.93164i	0.227099	+	0.0861274i	−0.238431	+	0.971160i	$0.576633\pi$
$504$	−19.4591	+	7.01421i	−0.866775	+	0.312438i
$505$	9.24607	−	50.4542i	0.411445	−	2.24518i
$506$	−42.2243			−1.87710
$507$	−14.1061	−	17.5505i	−0.626472	−	0.779444i
$508$	−4.06923			−0.180543
$509$	−2.46372	+	13.4441i	−0.109202	+	0.595898i	0.882807	+	0.469735i	$0.155651\pi$
$509$	−2.46372	+	13.4441i	−0.109202	+	0.595898i	−0.992010	+	0.126162i	$0.959734\pi$
$510$	2.36678	−	34.4070i	0.104803	−	1.52357i
$511$	7.32970	+	2.77979i	0.324247	+	0.122971i
$512$	13.6487	+	0.825597i	0.603195	+	0.0364866i
$513$	−5.96946	+	3.90554i	−0.263558	+	0.172434i
$514$	−3.85115	−	2.32810i	−0.169867	−	0.102688i
$515$	22.3663	−	36.9984i	0.985578	−	1.63035i
$516$	62.1905	+	38.3008i	2.73778	+	1.68610i
$517$	2.04112	−	8.28113i	0.0897682	−	0.364204i
$518$	4.17561	+	22.7856i	0.183466	+	1.00114i
$519$	−9.87203	+	21.4591i	−0.433334	+	0.941950i
$520$	28.9748	+	46.8277i	1.27063	+	2.05353i
$521$	−9.44140	+	10.6571i	−0.413635	+	0.466897i	−0.917993	−	0.396597i	$-0.870191\pi$
$521$	−9.44140	+	10.6571i	−0.413635	+	0.466897i	0.504358	+	0.863495i	$0.331729\pi$
$522$	−4.03223	−	13.7351i	−0.176486	−	0.601171i
$523$	9.24835	+	8.19333i	0.404402	+	0.358269i	0.840670	−	0.541548i	$-0.182161\pi$
$523$	9.24835	+	8.19333i	0.404402	+	0.358269i	−0.436268	+	0.899817i	$0.643700\pi$
$524$	29.0301	−	7.15527i	1.26818	−	0.312579i
$525$	−35.3936	−	31.8819i	−1.54470	−	1.39144i
$526$	−25.3441	+	25.3441i	−1.10505	+	1.10505i
$527$	−18.4390	−	8.29872i	−0.803216	−	0.361498i
$528$	2.99819	−	4.26775i	0.130480	−	0.185730i
$529$	30.8492			1.34127
$530$	−104.575			−4.54243
$531$	0.975706	−	4.86893i	0.0423420	−	0.211294i
$532$	−9.36963	−	1.13768i	−0.406225	−	0.0493246i
$533$	−4.13750	−	0.458950i	−0.179215	−	0.0198793i
$534$	−2.74261	−	4.62270i	−0.118684	−	0.200044i
$535$	29.9930	+	38.2832i	1.29671	+	1.65513i
$536$	−2.09947	+	1.44916i	−0.0906832	+	0.0625941i
$537$	−3.51737	−	1.12803i	−0.151786	−	0.0486781i
$538$	29.3930	+	23.0280i	1.26722	+	0.992806i
$539$	−6.05022	+	4.74004i	−0.260601	+	0.204168i
$540$	63.9898	+	46.5526i	2.75368	+	2.00331i
$541$	0.481949	+	7.96756i	0.0207206	+	0.342552i	0.993732	+	0.111793i	$0.0356594\pi$
$541$	0.481949	+	7.96756i	0.0207206	+	0.342552i	−0.973011	+	0.230759i	$0.925879\pi$
$542$	20.7255	+	14.3058i	0.890236	+	0.614485i
$543$	6.93700	+	9.00677i	0.297695	+	0.386517i
$544$	4.97162	−	6.34581i	0.213157	−	0.272074i
$545$	−3.10541	−	4.49896i	−0.133021	−	0.192714i
$546$	−10.2671	−	26.9022i	−0.439393	−	1.15131i
$547$	13.4286	−	19.4547i	0.574166	−	0.831823i	−0.423072	−	0.906096i	$-0.639048\pi$
$547$	13.4286	−	19.4547i	0.574166	−	0.831823i	0.997238	+	0.0742730i	$0.0236636\pi$
$548$	−3.54154	−	11.3652i	−0.151287	−	0.485497i
$549$	7.52762	+	2.99808i	0.321271	+	0.127955i
$550$	79.8698	+	9.69795i	3.40566	+	0.413522i
$551$	0.503707	−	2.74864i	0.0214586	−	0.117096i
$552$	−25.6121	+	36.4573i	−1.09012	+	1.55172i
$553$	2.65022	−	14.4618i	0.112699	−	0.614977i
$554$	51.5721	+	23.2107i	2.19109	+	0.986130i
$555$	27.0292	−	26.5861i	1.14733	−	1.12852i
$556$	2.40230	+	4.57720i	0.101880	+	0.194116i
$557$	8.25612	−	26.4948i	0.349823	−	1.12262i	−0.597372	−	0.801964i	$-0.703788\pi$
$557$	8.25612	−	26.4948i	0.349823	−	1.12262i	0.947195	−	0.320658i	$-0.103904\pi$
$558$	60.7062	−	40.4376i	2.56990	−	1.71186i
$559$	−22.1165	+	37.4560i	−0.935428	+	1.58422i
$560$	2.51597	+	10.2077i	0.106319	+	0.431353i
$561$	−2.87496	−	7.77382i	−0.121381	−	0.328211i
$562$	−2.79842	−	23.0471i	−0.118044	−	0.972183i
$563$	−19.0833	+	10.0157i	−0.804267	+	0.422112i	−0.816166	−	0.577817i	$-0.803905\pi$
$563$	−19.0833	+	10.0157i	−0.804267	+	0.422112i	0.0118992	+	0.999929i	$0.496212\pi$
$564$	−13.8192	−	15.8608i	−0.581892	−	0.667859i
$565$	7.81768	+	17.3702i	0.328892	+	0.730769i
$566$	1.85692	−	30.6985i	0.0780522	−	1.29036i
$567$	−12.0968	−	12.9242i	−0.508017	−	0.542766i
$568$	−1.25966	−	0.310479i	−0.0528543	−	0.0130274i
$569$	4.72014	−	4.18168i	0.197879	−	0.175305i	−0.558365	−	0.829596i	$-0.688571\pi$
$569$	4.72014	−	4.18168i	0.197879	−	0.175305i	0.756243	+	0.654290i	$0.227033\pi$
$570$	11.1083	+	21.5970i	0.465275	+	0.904597i
$571$	−4.20333	−	8.00878i	−0.175904	−	0.335157i	0.781502	−	0.623903i	$-0.214454\pi$
$571$	−4.20333	−	8.00878i	−0.175904	−	0.335157i	−0.957406	+	0.288746i	$0.906762\pi$
$572$	25.6389	+	17.3080i	1.07202	+	0.723682i
$573$	2.48626	−	36.1439i	0.103865	−	1.50993i
$574$	−4.85458	−	2.18487i	−0.202626	−	0.0911947i
$575$	−101.859	−	12.3679i	−4.24781	−	0.515778i
$576$	12.3572	+	34.2816i	0.514881	+	1.42840i
$577$	6.80621	−	6.80621i	0.283346	−	0.283346i	−0.551096	−	0.834442i	$-0.685790\pi$
$577$	6.80621	−	6.80621i	0.283346	−	0.283346i	0.834442	+	0.551096i	$0.185790\pi$
$578$	−9.20530	−	29.5409i	−0.382890	−	1.22874i
$579$	8.99517	+	17.4886i	0.373827	+	0.726802i
$580$	−30.4903	+	5.58756i	−1.26604	+	0.232011i
$581$	−13.6186	−	15.3723i	−0.564996	−	0.637749i
$582$	2.75458	−	14.3608i	0.114181	−	0.595275i
$583$	−22.9178	+	10.3145i	−0.949159	+	0.427182i
$584$	−4.95415	+	13.0630i	−0.205004	+	0.540552i
$585$	−27.0101	+	38.6189i	−1.11673	+	1.59669i
$586$	−8.12702	−	21.4292i	−0.335724	−	0.885231i
$587$	22.3359	+	22.3359i	0.921901	+	0.921901i	0.997164	−	0.0752625i	$-0.0239795\pi$
$587$	22.3359	+	22.3359i	0.921901	+	0.921901i	−0.0752625	+	0.997164i	$0.523979\pi$
$588$	0.988179	+	18.9313i	0.0407518	+	0.780714i
$589$	14.1352	−	1.71632i	0.582430	−	0.0707198i
$590$	−16.1404	−	5.02955i	−0.664489	−	0.207063i
$591$	−10.0181	+	6.79347i	−0.412091	+	0.279446i
$592$	−6.06246	+	1.11099i	−0.249166	+	0.0456613i
$593$	−5.37195	+	17.2392i	−0.220599	+	0.707929i	0.776380	+	0.630265i	$0.217054\pi$
$593$	−5.37195	+	17.2392i	−0.220599	+	0.707929i	−0.996980	+	0.0776637i	$0.975254\pi$
$594$	29.2665	+	6.11684i	1.20082	+	0.250977i
$595$	15.6213	+	5.92437i	0.640410	+	0.242876i
$596$	−34.1280	+	34.1280i	−1.39794	+	1.39794i
$597$	11.2210	−	11.0371i	0.459246	−	0.451717i
$598$	−51.4069	−	34.7030i	−2.10218	−	1.41911i
$599$	−12.0823	−	4.58222i	−0.493671	−	0.187225i	0.0951901	−	0.995459i	$-0.469654\pi$
$599$	−12.0823	−	4.58222i	−0.493671	−	0.187225i	−0.588861	+	0.808235i	$0.700423\pi$
$600$	56.8201	−	63.0786i	2.31967	−	2.57517i
$601$	−17.6232	+	25.5316i	−0.718864	+	1.04145i	0.277863	+	0.960621i	$0.410374\pi$
$601$	−17.6232	+	25.5316i	−0.718864	+	1.04145i	−0.996728	+	0.0808341i	$0.974242\pi$
$602$	−41.6370	+	36.8872i	−1.69700	+	1.50341i
$603$	−1.84943	−	1.16019i	−0.0753148	−	0.0472465i
$604$	−62.6696	+	3.79082i	−2.54999	+	0.154246i
$605$	−20.6945	+	6.44867i	−0.841352	+	0.262176i
$606$	−44.5545	−	17.3198i	−1.80990	−	0.703569i
$607$	−13.5456	−	7.10928i	−0.549799	−	0.288557i	0.166860	−	0.985981i	$-0.446637\pi$
$607$	−13.5456	−	7.10928i	−0.549799	−	0.288557i	−0.716659	+	0.697424i	$0.754330\pi$
$608$	−0.684257	+	5.63537i	−0.0277503	+	0.228544i
$609$	6.93419	+	0.0573085i	0.280988	+	0.00232226i
$610$	12.8197	−	24.4259i	0.519054	−	0.988975i
$611$	9.29103	−	8.40450i	0.375875	−	0.340010i
$612$	−19.7655	−	5.21977i	−0.798975	−	0.210997i
$613$	−32.0559	+	1.93903i	−1.29473	+	0.0783165i	−0.693322	−	0.720628i	$-0.743854\pi$
$613$	−32.0559	+	1.93903i	−1.29473	+	0.0783165i	−0.601405	+	0.798945i	$0.705392\pi$
$614$	21.0899	+	23.8056i	0.851121	+	0.960717i
$615$	1.49966	+	8.58282i	0.0604719	+	0.346093i
$616$	10.4373	+	13.3223i	0.420532	+	0.536769i
$617$	44.2074	+	2.67406i	1.77972	+	0.107653i	0.917216	−	0.398390i	$-0.130431\pi$
$617$	44.2074	+	2.67406i	1.77972	+	0.107653i	0.862508	+	0.506044i	$0.168893\pi$
$618$	−29.9359	−	26.9658i	−1.20420	−	1.08472i
$619$	10.3960	+	33.3619i	0.417849	+	1.34093i	0.888609	+	0.458665i	$0.151672\pi$
$619$	10.3960	+	33.3619i	0.417849	+	1.34093i	−0.470760	+	0.882261i	$0.656020\pi$
$620$	−73.4037	−	139.859i	−2.94797	−	5.61688i
$621$	−37.3239	−	7.80089i	−1.49776	−	0.313039i
$622$	−44.9024	−	2.71609i	−1.80042	−	0.108905i
$623$	2.52815	−	0.623132i	0.101288	−	0.0249653i
$624$	7.15776	−	2.73173i	0.286540	−	0.109357i
$625$	97.6766	+	24.0751i	3.90706	+	0.963005i
$626$	27.7144	+	8.63616i	1.10769	+	0.345170i
$627$	4.56458	+	3.63739i	0.182292	+	0.145263i
$628$	−32.2012	+	12.2123i	−1.28497	+	0.487323i
$629$	−4.01982	+	8.93167i	−0.160281	+	0.356129i
$630$	−48.0492	+	36.3788i	−1.91433	+	1.44936i
$631$	6.13979	+	10.1565i	0.244421	+	0.404322i	0.953771	−	0.300535i	$-0.0971651\pi$
$631$	6.13979	+	10.1565i	0.244421	+	0.404322i	−0.709350	+	0.704857i	$0.751011\pi$
$632$	25.7738	+	4.72323i	1.02523	+	0.187880i
$633$	−10.8334	−	35.8049i	−0.430591	−	1.42312i
$634$	−72.9723	+	27.6747i	−2.89810	+	1.09910i
$635$	−4.84257	+	1.50900i	−0.192171	+	0.0598830i
$636$	−11.6770	+	60.8775i	−0.463025	+	2.41395i
$637$	−11.2617	+	0.798355i	−0.446204	+	0.0316320i
$638$	−9.63896	+	6.65329i	−0.381610	+	0.263406i
$639$	−0.182059	−	1.09527i	−0.00720215	−	0.0433283i
$640$	85.4733	−	21.0673i	3.37863	−	0.832757i
$641$	19.2036	−	27.8213i	0.758498	−	1.09887i	−0.233467	−	0.972365i	$-0.575007\pi$
$641$	19.2036	−	27.8213i	0.758498	−	1.09887i	0.991965	−	0.126510i	$-0.0403775\pi$
$642$	40.3037	−	20.7300i	1.59066	−	0.818149i
$643$	−9.74925	+	31.2865i	−0.384473	+	1.23382i	0.536403	+	0.843962i	$0.319783\pi$
$643$	−9.74925	+	31.2865i	−0.384473	+	1.23382i	−0.920876	+	0.389855i	$0.872525\pi$
$644$	−31.1138	−	39.7138i	−1.22605	−	1.56494i
$645$	88.2126	+	22.5174i	3.47337	+	0.886620i
$646$	−4.69630	−	4.16056i	−0.184774	−	0.163695i
$647$	2.44391	+	3.54061i	0.0960799	+	0.139196i	0.868076	−	0.496432i	$-0.165357\pi$
$647$	2.44391	+	3.54061i	0.0960799	+	0.139196i	−0.771996	+	0.635628i	$0.780741\pi$
$648$	23.0336	−	21.5589i	0.904845	−	0.846915i
$649$	−4.03329	+	0.489730i	−0.158320	+	0.0192236i
$650$	89.2686	+	77.4498i	3.50140	+	3.03783i
$651$	10.2330	+	33.8204i	0.401063	+	1.32553i
$652$	38.3131	−	23.1611i	1.50046	−	0.907058i
$653$		−	7.28486i		−	0.285079i	−0.989789	−	0.142539i	$-0.954473\pi$
$653$		−	7.28486i		−	0.285079i	0.989789	−	0.142539i	$-0.0455268\pi$
$654$	−4.66280	+	2.05239i	−0.182330	+	0.0802546i
$655$	31.8936	−	19.2804i	1.24619	−	0.753347i
$656$	0.581319	−	1.29164i	0.0226967	−	0.0504300i
$657$	−11.9450	+	0.524559i	−0.466018	+	0.0204650i
$658$	14.6100	−	6.57544i	0.569558	−	0.256337i
$659$	−5.85812	−	23.7673i	−0.228200	−	0.925844i	−0.967582	−	0.252558i	$-0.918728\pi$
$659$	−5.85812	−	23.7673i	−0.228200	−	0.925844i	0.739382	−	0.673286i	$-0.235118\pi$
$660$	19.7720	−	61.6519i	0.769622	−	2.39980i
$661$	19.9705	+	12.0726i	0.776763	+	0.469570i	0.849375	−	0.527791i	$-0.176979\pi$
$661$	19.9705	+	12.0726i	0.776763	+	0.469570i	−0.0726114	+	0.997360i	$0.523133\pi$
$662$	2.56281	+	2.27046i	0.0996066	+	0.0882438i
$663$	2.88891	−	11.8273i	0.112196	−	0.459333i
$664$	27.3965	−	24.2712i	1.06319	−	0.941905i
$665$	−11.5722	+	2.12068i	−0.448749	+	0.0822363i
$666$	−19.5876	−	29.4055i	−0.759003	−	1.13944i
$667$	12.2927	−	8.48503i	0.475975	−	0.328542i
$668$	−43.9643	−	26.5773i	−1.70103	−	1.02831i
$669$	−2.28115	+	17.5721i	−0.0881945	+	0.679376i
$670$	−4.58394	+	5.85097i	−0.177093	+	0.226043i
$671$	0.400281	−	6.61744i	0.0154527	−	0.255463i
$672$	−14.0679	+	0.734319i	−0.542682	+	0.0283270i
$673$	3.27509	−	6.24017i	0.126246	−	0.240541i	−0.814127	−	0.580687i	$-0.802784\pi$
$673$	3.27509	−	6.24017i	0.126246	−	0.240541i	0.940373	+	0.340146i	$0.110476\pi$
$674$	−43.3578	−	7.94562i	−1.67008	−	0.306054i
$675$	68.8087	+	23.3283i	2.64845	+	0.897906i
$676$	16.9897	+	42.1439i	0.653451	+	1.62092i
$677$		−	22.4525i		−	0.862918i	−0.902132	−	0.431459i	$-0.857999\pi$
$677$		−	22.4525i		−	0.862918i	0.902132	−	0.431459i	$-0.142001\pi$
$678$	17.2703	−	4.10565i	0.663262	−	0.157677i
$679$	6.27217	+	3.29189i	0.240704	+	0.126331i
$680$	−10.5584	+	27.8403i	−0.404898	+	1.06763i
$681$	−23.1256	+	8.55247i	−0.886176	+	0.327731i
$682$	−46.9790	−	36.8057i	−1.79892	−	1.40936i
$683$	6.36215	−	10.5243i	0.243441	−	0.402700i	−0.710037	−	0.704165i	$-0.751322\pi$
$683$	6.36215	−	10.5243i	0.243441	−	0.402700i	0.953477	+	0.301464i	$0.0974754\pi$
$684$	13.8129	−	4.05506i	0.528150	−	0.155049i
$685$	−8.42917	−	12.2118i	−0.322062	−	0.466587i
$686$	−45.3565	−	11.1794i	−1.73172	−	0.426830i
$687$	6.02952	−	4.08872i	0.230040	−	0.155994i
$688$	−9.81442	−	11.0782i	−0.374171	−	0.422352i
$689$	−36.3790	−	6.27796i	−1.38593	−	0.239171i
$690$	−39.6434	+	123.614i	−1.50920	+	4.70590i
$691$	9.30544	−	15.3931i	0.353996	−	0.585580i	−0.627139	−	0.778908i	$-0.715774\pi$
$691$	9.30544	−	15.3931i	0.353996	−	0.585580i	0.981134	+	0.193327i	$0.0619279\pi$
$692$	31.6098	−	35.6801i	1.20163	−	1.35635i
$693$	−6.94198	+	12.7117i	−0.263704	+	0.482878i
$694$	−26.4033	−	58.6658i	−1.00226	−	2.22692i
$695$	4.55622	+	4.55622i	0.172827	+	0.172827i
$696$	−0.102135	+	12.3582i	−0.00387143	+	0.468435i
$697$	−1.16448	−	1.92628i	−0.0441078	−	0.0729632i
$698$		−	14.4187i		−	0.545755i
$699$	35.4835	−	15.6185i	1.34211	−	0.590744i
$700$	49.7322	+	82.2671i	1.87970	+	3.10940i
$701$	1.92825	−	15.8806i	0.0728290	−	0.599801i	−0.909910	−	0.414805i	$-0.863850\pi$
$701$	1.92825	−	15.8806i	0.0728290	−	0.599801i	0.982739	−	0.184996i	$-0.0592272\pi$
$702$	30.6038	+	31.5004i	1.15507	+	1.18891i
$703$	−0.831369	−	6.84694i	−0.0313557	−	0.258237i
$704$	23.4702	−	18.3878i	0.884568	−	0.693015i
$705$	−22.3271	−	13.7504i	−0.840887	−	0.517871i
$706$	26.4443	−	29.8494i	0.995244	−	1.12340i
$707$	14.2812	−	18.2286i	0.537099	−	0.685556i
$708$	−4.73019	+	8.83442i	−0.177772	+	0.332018i
$709$	−16.5053	−	5.14325i	−0.619868	−	0.193159i	−0.0285438	−	0.999593i	$-0.509087\pi$
$709$	−16.5053	−	5.14325i	−0.619868	−	0.193159i	−0.591324	+	0.806434i	$0.701395\pi$
$710$	−3.77313	+	0.228232i	−0.141603	+	0.00856540i
$711$	5.00603	+	21.8590i	0.187741	+	0.819778i
$712$	1.11055	+	4.50567i	0.0416196	+	0.168857i
$713$	59.9129	+	46.9388i	2.24376	+	1.75787i
$714$	8.16460	−	13.2572i	0.305553	−	0.496138i
$715$	36.9298	+	11.0895i	1.38110	+	0.414723i
$716$	6.13476	+	4.23452i	0.229267	+	0.158252i
$717$	−1.06014	−	1.21676i	−0.0395917	−	0.0454409i
$718$	−7.75492	−	20.4480i	−0.289411	−	0.763114i
$719$	3.85381	−	31.7390i	0.143723	−	1.18367i	−0.725136	−	0.688606i	$-0.758223\pi$
$719$	3.85381	−	31.7390i	0.143723	−	1.18367i	0.868859	−	0.495060i	$-0.164854\pi$
$720$	−9.67915	−	12.7843i	−0.360720	−	0.476441i
$721$	16.7028	−	10.0972i	0.622046	−	0.376040i
$722$	−39.4647	−	7.23218i	−1.46872	−	0.269154i
$723$	0.336498	−	40.7154i	0.0125145	−	1.51422i
$724$	−8.13542	−	21.4513i	−0.302351	−	0.797233i
$725$	−25.2011	+	13.2266i	−0.935947	+	0.491223i
$726$	2.26908	+	20.0725i	0.0842134	+	0.744962i
$727$	−1.58126	+	6.41544i	−0.0586458	+	0.237935i	−0.992949	−	0.118545i	$-0.962177\pi$
$727$	−1.58126	+	6.41544i	−0.0586458	+	0.237935i	0.934303	+	0.356480i	$0.116023\pi$
$728$	1.75794	+	24.7976i	0.0651534	+	0.919060i
$729$	24.7398	+	10.8139i	0.916291	+	0.400514i
$730$	−2.45777	+	40.6317i	−0.0909660	+	1.50385i
$731$	−23.3484	+	2.83501i	−0.863571	+	0.104857i
$732$	−12.7879	−	10.1904i	−0.472655	−	0.376646i
$733$	−38.2966	+	11.9337i	−1.41452	+	0.440782i	−0.907099	−	0.420918i	$-0.861708\pi$
$733$	−38.2966	+	11.9337i	−1.41452	+	0.440782i	−0.507419	+	0.861699i	$0.669400\pi$
$734$	−32.9645	+	14.8361i	−1.21674	+	0.547612i
$735$	8.19632	+	22.1626i	0.302326	+	0.817481i
$736$	−23.8859	+	18.7134i	−0.880445	+	0.689785i
$737$	−0.427486	+	1.73438i	−0.0157467	+	0.0638867i
$738$	8.11861	+	0.134204i	0.298850	+	0.00494011i
$739$	−1.95050	−	32.2456i	−0.0717504	−	1.18618i	−0.838746	−	0.544523i	$-0.816711\pi$
$739$	−1.95050	−	32.2456i	−0.0717504	−	1.18618i	0.766996	−	0.641652i	$-0.221751\pi$
$740$	−67.7463	+	35.5560i	−2.49041	+	1.30707i
$741$	2.56776	+	8.17992i	0.0943292	+	0.300497i
$742$	−41.8023	−	21.9396i	−1.53461	−	0.805426i
$743$	7.52697	−	16.7242i	0.276138	−	0.613553i	−0.720680	−	0.693268i	$-0.756170\pi$
$743$	7.52697	−	16.7242i	0.276138	−	0.613553i	0.996818	+	0.0797149i	$0.0254010\pi$
$744$	−60.2749	+	18.2373i	−2.20978	+	0.668611i
$745$	−27.9581	+	53.2696i	−1.02430	+	1.95165i
$746$	46.6633	+	46.6633i	1.70847	+	1.70847i
$747$	28.3479	+	13.3261i	1.03720	+	0.487577i
$748$	1.00991	+	16.6959i	0.0369261	+	0.610461i
$749$	3.95755	+	21.5957i	0.144606	+	0.789089i
$750$	66.4120	−	144.362i	2.42502	−	5.27134i
$751$	−13.2120	−	9.11957i	−0.482112	−	0.332778i	0.302094	−	0.953278i	$-0.402314\pi$
$751$	−13.2120	−	9.11957i	−0.482112	−	0.332778i	−0.784206	+	0.620500i	$0.786930\pi$
$752$	1.74950	+	3.88723i	0.0637977	+	0.141753i
$753$	−1.02344	−	19.6068i	−0.0372961	−	0.714511i
$754$	−17.2033	+	0.178194i	−0.626508	+	0.00648943i
$755$	−73.1739	+	27.7512i	−2.66307	+	1.00997i
$756$	15.8124	+	32.0337i	0.575091	+	1.16505i
$757$	−13.4574	+	35.4844i	−0.489119	+	1.28970i	0.432510	+	0.901629i	$0.357628\pi$
$757$	−13.4574	+	35.4844i	−0.489119	+	1.28970i	−0.921629	+	0.388072i	$0.873141\pi$
$758$	−7.10762	−	58.5366i	−0.258161	−	2.12614i
$759$	3.50441	+	31.0005i	0.127202	+	1.12525i
$760$	−3.77948	−	20.6239i	−0.137096	−	0.748109i
$761$	−3.16236	−	17.2565i	−0.114636	−	0.625546i	−0.989885	−	0.141874i	$-0.954687\pi$
$761$	−3.16236	−	17.2565i	−0.114636	−	0.625546i	0.875249	−	0.483672i	$-0.160697\pi$
$762$	0.530970	+	4.69702i	0.0192350	+	0.170155i
$763$	−0.297473	−	2.44991i	−0.0107692	−	0.0886927i
$764$	−25.9260	+	68.3613i	−0.937970	+	2.47322i
$765$	−25.4575	+	1.11796i	−0.920418	+	0.0404198i
$766$	−7.05127	+	2.67420i	−0.254773	+	0.0966226i
$767$	−5.31291	−	2.71862i	−0.191838	−	0.0981636i
$768$	−2.08302	−	39.9061i	−0.0751646	−	1.43999i
$769$	−10.1268	−	22.5009i	−0.365183	−	0.811404i	−0.999272	−	0.0381437i	$-0.987856\pi$
$769$	−10.1268	−	22.5009i	−0.365183	−	0.811404i	0.634089	−	0.773260i	$-0.281375\pi$
$770$	40.5814	+	28.0113i	1.46245	+	1.00946i
$771$	−1.38963	+	3.02068i	−0.0500463	+	0.108787i
$772$	−7.15387	−	39.0374i	−0.257474	−	1.40499i
$773$	2.19468	+	36.2824i	0.0789372	+	1.30499i	0.794853	+	0.606802i	$0.207548\pi$
$773$	2.19468	+	36.2824i	0.0789372	+	1.30499i	−0.715916	+	0.698186i	$0.753991\pi$
$774$	36.0949	−	76.7827i	1.29740	−	2.75990i
$775$	−102.548	−	102.548i	−3.68364	−	3.68364i
$776$	−5.86682	+	11.1783i	−0.210607	+	0.401277i
$777$	16.3823	−	4.95676i	0.587710	−	0.177823i
$778$	32.4431	−	72.0856i	1.16314	−	2.58439i
$779$	1.40350	+	0.736616i	0.0502858	+	0.0263920i
$780$	74.7418	−	58.8093i	2.67619	−	2.10571i
$781$	−0.804380	+	0.422171i	−0.0287830	+	0.0151065i
$782$	−2.02491	−	33.4757i	−0.0724106	−	1.19709i
$783$	−9.74948	+	4.10035i	−0.348418	+	0.146535i
$784$	0.919311	−	3.72979i	0.0328325	−	0.133207i
$785$	−33.7921	+	26.4744i	−1.20609	+	0.944912i
$786$	−12.0471	−	32.5751i	−0.429706	−	1.16191i
$787$	5.08279	−	2.28758i	0.181182	−	0.0815434i	−0.317792	−	0.948161i	$-0.602941\pi$
$787$	5.08279	−	2.28758i	0.181182	−	0.0815434i	0.498974	+	0.866617i	$0.333710\pi$
$788$	23.3210	−	7.26711i	0.830775	−	0.258880i
$789$	20.7107	+	16.5038i	0.737319	+	0.587551i
$790$	75.7892	−	9.20248i	2.69646	−	0.327409i
$791$	−0.519214	+	8.58363i	−0.0184611	+	0.305199i
$792$	−22.6549	−	12.3720i	−0.805006	−	0.439621i
$793$	5.92602	−	7.72756i	0.210439	−	0.274414i
$794$	−3.85208	+	15.6285i	−0.136705	+	0.554635i
$795$	8.67919	+	76.7772i	0.307819	+	2.72301i
$796$	−28.1246	+	14.7609i	−0.996848	+	0.523186i
$797$	−3.68326	−	9.71196i	−0.130468	−	0.344015i	0.853825	−	0.520561i	$-0.174277\pi$
$797$	−3.68326	−	9.71196i	−0.130468	−	0.344015i	−0.984293	+	0.176545i	$0.943508\pi$
$798$	−0.0906100	+	10.9636i	−0.00320756	+	0.388107i
$799$	6.66322	+	1.22108i	0.235728	+	0.0431987i
$800$	49.4796	−	29.9114i	1.74937	−	1.05753i
$801$	−3.16629	+	2.39724i	−0.111875	+	0.0847025i
$802$	−6.56384	+	54.0581i	−0.231777	+	1.90886i
$803$	3.46899	+	9.14696i	0.122418	+	0.322789i
$804$	2.89425	+	3.32184i	0.102072	+	0.117152i
$805$	−51.7539	−	35.7232i	−1.82409	−	1.25908i
$806$	−26.9460	−	83.4206i	−0.949132	−	2.93837i
$807$	14.4673	−	23.4911i	0.509273	−	0.826927i
$808$	32.4870	+	25.4520i	1.14289	+	0.895397i
$809$	−8.88153	−	36.0338i	−0.312258	−	1.26688i	−0.891983	−	0.452068i	$-0.850686\pi$
$809$	−8.88153	−	36.0338i	−0.312258	−	1.26688i	0.579725	−	0.814812i	$-0.303160\pi$
$810$	45.3850	−	79.9363i	1.59467	−	2.80867i
$811$	−28.7465	+	1.73884i	−1.00943	+	0.0610591i	−0.556805	−	0.830643i	$-0.687973\pi$
$811$	−28.7465	+	1.73884i	−1.00943	+	0.0610591i	−0.452622	+	0.891702i	$0.649511\pi$
$812$	−13.3604	−	4.16325i	−0.468856	−	0.146102i
$813$	8.78296	−	16.4036i	0.308032	−	0.575301i
$814$	−17.8283	+	22.7562i	−0.624882	+	0.797603i
$815$	37.0054	−	41.7705i	1.29624	−	1.46316i
$816$	3.52728	+	2.17232i	0.123480	+	0.0760465i
$817$	13.0377	−	10.2144i	0.456130	−	0.357355i
$818$	10.7771	+	88.7573i	0.376812	+	3.10333i
$819$	−18.8991	+	9.77072i	−0.660387	+	0.341417i
$820$	2.11939	−	17.4547i	0.0740122	−	0.609545i
$821$	−11.2898	−	18.6757i	−0.394018	−	0.651785i	0.594291	−	0.804250i	$-0.297433\pi$
$821$	−11.2898	−	18.6757i	−0.394018	−	0.651785i	−0.988309	+	0.152465i	$0.951279\pi$
$822$	−12.6565	+	5.57089i	−0.441445	+	0.194307i
$823$			29.2212i			1.01859i	0.860593	+	0.509293i	$0.170093\pi$
$823$			29.2212i			1.01859i	−0.860593	+	0.509293i	$0.829907\pi$
$824$	17.9953	+	29.7679i	0.626896	+	1.03701i
$825$	0.491283	−	59.4441i	0.0171043	−	2.06958i
$826$	−5.39672	−	5.39672i	−0.187776	−	0.187776i
$827$	−6.77388	−	15.0509i	−0.235551	−	0.523373i	0.755770	−	0.654837i	$-0.227263\pi$
$827$	−6.77388	−	15.0509i	−0.235551	−	0.523373i	−0.991321	+	0.131465i	$0.958032\pi$
$828$	67.5345	+	36.8812i	2.34699	+	1.28171i
$829$	−0.242034	+	0.273200i	−0.00840621	+	0.00948864i	−0.752699	−	0.658365i	$-0.771248\pi$
$829$	−0.242034	+	0.273200i	−0.00840621	+	0.00948864i	0.744293	+	0.667854i	$0.232787\pi$
$830$	55.1703	−	91.2628i	1.91499	−	3.16778i
$831$	12.7607	−	39.7899i	0.442665	−	1.38030i
$832$	43.6867	−	3.09701i	1.51456	−	0.107370i
$833$	−4.04808	−	4.56934i	−0.140258	−	0.158318i
$834$	4.96989	−	3.37017i	0.172093	−	0.116699i
$835$	−62.1752	−	15.3248i	−2.15166	−	0.530337i
$836$	−6.69097	−	9.69354i	−0.231412	−	0.335258i
$837$	−34.7270	−	41.2135i	−1.20034	−	1.42455i
$838$	27.0338	−	44.7193i	0.933866	−	1.54480i
$839$	18.9147	+	14.8187i	0.653007	+	0.511598i	0.887671	−	0.460478i	$-0.152322\pi$
$839$	18.9147	+	14.8187i	0.653007	+	0.511598i	−0.234664	+	0.972077i	$0.575399\pi$
$840$	48.8010	−	18.0479i	1.68379	−	0.622711i
$841$	−8.81436	+	23.2416i	−0.303943	+	0.801433i
$842$	72.0936	+	37.8376i	2.48451	+	1.30397i
$843$	−16.6886	+	3.96736i	−0.574785	+	0.136643i
$844$			75.4909i			2.59850i
$845$	35.8468	+	43.8527i	1.23317	+	1.50858i
$846$	−16.5046	+	18.0207i	−0.567438	+	0.619565i
$847$	−9.62527	−	1.76390i	−0.330728	−	0.0606082i
$848$	5.83737	−	11.1222i	0.200456	−	0.381937i
$849$	−22.6925	+	1.18451i	−0.778805	+	0.0406522i
$850$	−3.85836	+	63.7864i	−0.132341	+	2.18785i
$851$	22.7367	−	29.0212i	0.779403	−	0.994834i
$852$	−0.288452	+	2.22199i	−0.00988219	+	0.0761241i
$853$	41.3817	+	25.0161i	1.41688	+	0.856535i	0.998657	−	0.0518089i	$-0.0164987\pi$
$853$	41.3817	+	25.0161i	1.41688	+	0.856535i	0.418225	+	0.908344i	$0.362653\pi$
$854$	10.2490	−	7.07437i	0.350714	−	0.242080i
$855$	14.9342	−	9.94798i	0.510740	−	0.340214i
$856$	−38.4879	+	7.05317i	−1.31549	+	0.241072i
$857$	−34.1971	+	30.2960i	−1.16815	+	1.03489i	−0.169368	+	0.985553i	$0.554173\pi$
$857$	−34.1971	+	30.2960i	−1.16815	+	1.03489i	−0.998782	+	0.0493378i	$0.984289\pi$
$858$	16.6327	−	31.8528i	0.567831	−	1.08744i
$859$	26.5198	+	23.4945i	0.904845	+	0.801623i	0.980705	−	0.195496i	$-0.0626316\pi$
$859$	26.5198	+	23.4945i	0.904845	+	0.801623i	−0.0758597	+	0.997119i	$0.524170\pi$
$860$	−157.228	−	95.0479i	−5.36145	−	3.24111i
$861$	−1.20119	+	3.74549i	−0.0409365	+	0.127646i
$862$	−0.451164	−	1.83044i	−0.0153667	−	0.0623452i
$863$	−1.50895	+	0.679124i	−0.0513653	+	0.0231177i	−0.435933	−	0.899979i	$-0.643581\pi$
$863$	−1.50895	+	0.679124i	−0.0513653	+	0.0231177i	0.384567	+	0.923097i	$0.374351\pi$
$864$	19.2667	−	9.51037i	0.655466	−	0.323549i
$865$	24.3857	−	54.1829i	0.829139	−	1.84227i
$866$	−2.75699	+	1.66666i	−0.0936863	+	0.0566353i
$867$	−20.9245	+	9.21014i	−0.710632	+	0.312793i
$868$		−	71.3068i		−	2.42031i
$869$	15.7017	−	9.49203i	0.532645	−	0.321995i
$870$	10.4281	+	34.4652i	0.353545	+	1.16848i
$871$	−1.94589	+	1.76022i	−0.0659340	+	0.0596427i
$872$	4.36624	−	0.530157i	0.147859	−	0.0179534i
$873$	−10.7721	−	0.830490i	−0.364581	−	0.0281078i
$874$	13.4156	+	19.4358i	0.453789	+	0.657427i
$875$	57.6185	+	51.0455i	1.94786	+	1.72565i
$876$	23.3791	+	5.96780i	0.789906	+	0.201633i
$877$	−23.2509	−	29.6776i	−0.785128	−	1.00214i	−0.999677	−	0.0254284i	$-0.991905\pi$
$877$	−23.2509	−	29.6776i	−0.785128	−	1.00214i	0.214549	−	0.976713i	$-0.431172\pi$
$878$	11.7791	−	37.8006i	0.397527	−	1.27571i
$879$	−15.0585	+	7.74525i	−0.507910	+	0.261241i
$880$	−7.45285	+	10.7973i	−0.251235	+	0.363977i
$881$	−53.1015	+	13.0883i	−1.78903	+	0.440957i	−0.987582	−	0.157103i	$-0.949785\pi$
$881$	−53.1015	+	13.0883i	−1.78903	+	0.440957i	−0.801451	+	0.598060i	$0.795938\pi$
$882$	21.7230	−	3.61087i	0.731453	−	0.121584i
$883$	−19.8417	+	13.6958i	−0.667727	+	0.460899i	−0.853085	−	0.521772i	$-0.825271\pi$
$883$	−19.8417	+	13.6958i	−0.667727	+	0.460899i	0.185357	+	0.982671i	$0.440656\pi$
$884$	−12.4923	+	21.1567i	−0.420162	+	0.711578i
$885$	−2.35305	+	12.2675i	−0.0790968	+	0.412366i
$886$	70.9678	−	22.1144i	2.38421	−	0.742949i
$887$	31.7855	−	12.0546i	1.06725	−	0.404755i	0.242442	−	0.970166i	$-0.422052\pi$
$887$	31.7855	−	12.0546i	1.06725	−	0.404755i	0.824810	+	0.565411i	$0.191282\pi$
$888$	8.83396	+	29.1965i	0.296448	+	0.979771i
$889$	−2.25234	−	0.412756i	−0.0755410	−	0.0138434i
$890$	6.99478	+	11.5708i	0.234466	+	0.387854i
$891$	2.06192	−	21.9947i	0.0690768	−	0.736849i
$892$	14.6759	−	32.6084i	0.491384	−	1.09181i
$893$	−4.46031	+	1.69157i	−0.149259	+	0.0566063i
$894$	43.8463	+	34.9400i	1.46644	+	1.16857i
$895$	8.87094	+	2.76430i	0.296523	+	0.0924002i
$896$	38.5867	+	9.51076i	1.28909	+	0.317732i
$897$	−21.2119	+	40.6223i	−0.708245	+	1.35634i
$898$	−32.3423	+	7.97166i	−1.07928	+	0.266018i
$899$	21.0731	+	1.27469i	0.702826	+	0.0425131i
$900$	−119.275	−	85.2740i	−3.97582	−	2.84247i
$901$	−9.27643	−	17.6748i	−0.309043	−	0.588832i
$902$	−1.97645	−	6.34266i	−0.0658087	−	0.211187i
$903$	30.5377	+	27.5078i	1.01623	+	0.915403i
$904$	−15.2978	−	0.925345i	−0.508797	−	0.0307765i
$905$	−17.6364	−	22.5112i	−0.586253	−	0.748296i
$906$	12.5530	+	71.8435i	0.417047	+	2.38684i
$907$	5.84551	+	6.59822i	0.194097	+	0.219090i	0.837500	−	0.546437i	$-0.184016\pi$
$907$	5.84551	+	6.59822i	0.194097	+	0.219090i	−0.643403	+	0.765528i	$0.722478\pi$
$908$	49.6670	−	3.00430i	1.64826	−	0.0997012i
$909$	−9.01813	+	34.1487i	−0.299112	+	1.13264i
$910$	26.3849	+	67.4556i	0.874651	+	2.23613i
$911$	−9.71372	+	18.5079i	−0.321830	+	0.613195i	−0.991595	−	0.129377i	$-0.958702\pi$
$911$	−9.71372	+	18.5079i	−0.321830	+	0.613195i	0.669766	+	0.742573i	$0.266395\pi$
$912$	−2.91704	−	0.0241082i	−0.0965928	−	0.000798303i
$913$	3.08923	−	25.4421i	0.102238	−	0.842009i
$914$	30.3368	+	15.9220i	1.00345	+	0.526652i
$915$	−18.9971	−	7.38480i	−0.628024	−	0.244134i
$916$	−14.0360	+	4.37379i	−0.463762	+	0.144514i
$917$	16.7940	−	1.01585i	0.554588	−	0.0335464i
$918$	−3.44597	+	23.4960i	−0.113734	+	0.775484i
$919$	−18.9045	+	16.7479i	−0.623601	+	0.552462i	−0.914650	−	0.404246i	$-0.867534\pi$
$919$	−18.9045	+	16.7479i	−0.623601	+	0.552462i	0.291050	+	0.956708i	$0.405996\pi$
$920$	63.6660	−	92.2361i	2.09900	−	3.04093i
$921$	15.7274	−	17.4597i	0.518235	−	0.575316i
$922$	65.8735	+	24.9825i	2.16943	+	0.822756i
$923$	−1.32628	−	0.147117i	−0.0436550	−	0.00484241i
$924$	20.8380	−	20.4964i	0.685520	−	0.674282i
$925$	−49.6732	+	49.6732i	−1.63325	+	1.63325i
$926$	58.0095	+	22.0001i	1.90631	+	0.722968i
$927$	−17.3133	+	24.2165i	−0.568644	+	0.795376i
$928$	−2.50399	+	8.03559i	−0.0821975	+	0.263781i
$929$	20.2916	−	3.71857i	0.665744	−	0.122002i	0.163253	−	0.986584i	$-0.447801\pi$
$929$	20.2916	−	3.71857i	0.665744	−	0.122002i	0.502492	+	0.864582i	$0.332417\pi$
$930$	−151.858	+	102.978i	−4.97962	+	3.37677i
$931$	4.10413	+	1.27890i	0.134507	+	0.0419142i
$932$	−77.6665	+	9.43042i	−2.54405	+	0.308904i
$933$	1.73256	+	33.1921i	0.0567216	+	1.08666i
$934$	−1.36382	−	1.36382i	−0.0446254	−	0.0446254i
$935$	7.39321	+	19.4943i	0.241784	+	0.637532i
$936$	−17.4134	−	33.6820i	−0.569176	−	1.10093i
$937$	−1.92184	+	5.06748i	−0.0627838	+	0.165547i	−0.962737	−	0.270439i	$-0.912831\pi$
$937$	−1.92184	+	5.06748i	−0.0627838	+	0.165547i	0.899953	+	0.435986i	$0.143600\pi$
$938$	−3.05989	+	1.37714i	−0.0999089	+	0.0449653i
$939$	4.04038	−	21.0643i	0.131853	−	0.687406i
$940$	35.0901	+	39.6085i	1.14451	+	1.29189i
$941$	−43.7502	+	8.01753i	−1.42622	+	0.261364i	−0.837262	−	0.546802i	$-0.815845\pi$
$941$	−43.7502	+	8.01753i	−1.42622	+	0.261364i	−0.588955	+	0.808166i	$0.700460\pi$
$942$	18.2981	+	35.5755i	0.596184	+	1.15911i
$943$	2.52060	+	8.08888i	0.0820819	+	0.263410i
$944$	1.43588	−	1.43588i	0.0467340	−	0.0467340i
$945$	30.6966	+	32.2577i	0.998560	+	1.04934i
$946$	−68.9119	−	8.36742i	−2.24052	−	0.272048i
$947$	−46.6749	−	21.0067i	−1.51673	−	0.682625i	−0.530451	−	0.847715i	$-0.677978\pi$
$947$	−46.6749	−	21.0067i	−1.51673	−	0.682625i	−0.986278	+	0.165091i	$0.947208\pi$
$948$	3.10562	−	45.1478i	0.100866	−	1.46633i
$949$	−3.29425	+	13.9872i	−0.106936	+	0.454044i
$950$	−20.9124	−	39.8453i	−0.678489	−	1.29275i
$951$	26.3747	+	51.2783i	0.855258	+	1.66281i
$952$	−10.0614	+	8.91366i	−0.326093	+	0.288893i
$953$	29.9831	+	7.39016i	0.971246	+	0.239391i	0.692855	−	0.721077i	$-0.256353\pi$
$953$	29.9831	+	7.39016i	0.971246	+	0.239391i	0.278391	+	0.960468i	$0.410199\pi$
$954$	71.7932	+	5.53499i	2.32439	+	0.179202i
$955$	−5.50250	+	90.9671i	−0.178057	+	2.94363i
$956$	1.33662	+	2.96984i	0.0432292	+	0.0960514i
$957$	5.68473	+	6.52459i	0.183761	+	0.210910i
$958$	69.5002	−	36.4765i	2.24545	−	1.17850i
$959$	−0.807445	−	6.64991i	−0.0260738	−	0.214737i
$960$	−31.7955	−	85.9742i	−1.02620	−	2.77481i
$961$	18.3255	+	74.3495i	0.591145	+	2.39837i
$962$	−40.4081	+	13.0524i	−1.30281	+	0.420825i
$963$	−18.5647	−	27.8699i	−0.598239	−	0.898095i
$964$	−24.4453	+	78.4478i	−0.787331	+	2.52663i
$965$	−22.9898	−	43.8033i	−0.740067	−	1.41008i
$966$	−41.7809	+	41.0959i	−1.34428	+	1.32224i
$967$	−15.0885	−	6.79078i	−0.485213	−	0.218377i	0.153015	−	0.988224i	$-0.451102\pi$
$967$	−15.0885	−	6.79078i	−0.485213	−	0.218377i	−0.638228	+	0.769847i	$0.720332\pi$
$968$	3.14362	−	17.1542i	0.101040	−	0.551357i
$969$	−2.66485	+	3.79326i	−0.0856073	+	0.121857i
$970$	−6.63024	+	36.1801i	−0.212884	+	1.16167i
$971$	4.07812	+	0.495174i	0.130873	+	0.0158909i	0.185711	−	0.982604i	$-0.440541\pi$
$971$	4.07812	+	0.495174i	0.130873	+	0.0158909i	−0.0548380	+	0.998495i	$0.517464\pi$
$972$	−41.4666	−	35.3465i	−1.33004	−	1.13374i
$973$	0.865401	+	2.77717i	0.0277435	+	0.0890320i
$974$	11.1214	−	16.1121i	0.356352	−	0.516265i
$975$	49.4536	−	71.9676i	1.58378	−	2.30481i
$976$	1.88225	+	2.72691i	0.0602493	+	0.0872862i
$977$	−7.94039	+	10.1352i	−0.254036	+	0.324252i	−0.897325	−	0.441371i	$-0.854492\pi$
$977$	−7.94039	+	10.1352i	−0.254036	+	0.324252i	0.643289	+	0.765623i	$0.277569\pi$
$978$	−31.7336	−	41.2018i	−1.01473	−	1.31749i
$979$	2.67418	+	1.84585i	0.0854672	+	0.0589938i
$980$	−2.87919	−	47.5988i	−0.0919725	−	1.52049i
$981$	1.89382	+	3.25302i	0.0604650	+	0.103861i
$982$	1.29165	−	1.01194i	0.0412181	−	0.0322923i
$983$	−1.59240	−	1.24756i	−0.0507896	−	0.0397911i	0.591003	−	0.806669i	$-0.298732\pi$
$983$	−1.59240	−	1.24756i	−0.0507896	−	0.0397911i	−0.641793	+	0.766878i	$0.721809\pi$
$984$	−6.67523	−	2.14077i	−0.212799	−	0.0682452i
$985$	25.0581	−	17.2964i	0.798417	−	0.551108i
$986$	−5.73702	−	7.32276i	−0.182704	−	0.233204i
$987$	−6.04015	−	10.1807i	−0.192260	−	0.324056i
$988$	−0.179203	−	17.3007i	−0.00570119	−	0.550409i
$989$	87.8842	+	10.6711i	2.79456	+	0.339321i
$990$	−73.7433	−	14.7777i	−2.34371	−	0.469667i
$991$	57.9597			1.84115			0.920575	−	0.390565i	$-0.127720\pi$
$991$	57.9597			1.84115			0.920575	+	0.390565i	$0.127720\pi$
$992$	−42.8875			−1.36168
$993$	1.45423	−	2.07002i	0.0461487	−	0.0656900i
$994$	−1.55614	−	0.700362i	−0.0493578	−	0.0222141i
$995$	−27.9956	+	27.9956i	−0.887521	+	0.887521i
$996$	−46.9677	−	42.3076i	−1.48823	−	1.34057i
$997$	−16.4809	+	4.06217i	−0.521954	+	0.128650i	−0.491486	−	0.870886i	$-0.663546\pi$
$997$	−16.4809	+	4.06217i	−0.521954	+	0.128650i	−0.0304682	+	0.999536i	$0.509700\pi$
$998$	73.8390	+	65.4157i	2.33733	+	2.07070i
$999$	−19.9634	+	16.8214i	−0.631614	+	0.532206i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.s.a.5.6	✓	1392
3.2	odd	2	inner	507.2.s.a.5.53	yes	1392
169.34	odd	52	inner	507.2.s.a.203.53	yes	1392
507.203	even	52	inner	507.2.s.a.203.6	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.s.a.5.6	✓	1392	1.1	even	1	trivial
507.2.s.a.5.53	yes	1392	3.2	odd	2	inner
507.2.s.a.203.6	yes	1392	507.203	even	52	inner
507.2.s.a.203.53	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.5.6

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