LMFDB - Embedded newform 128.2.k.a.117.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

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

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$128 = 2^{7}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	128.k (of order $32$ , degree $16$ , 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			117.4
Character	$\chi$	$=$	128.117
Dual form			128.2.k.a.93.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.783932 - 1.17705i) q^{2} +(0.0366493 - 0.00360964i) q^{3} +(-0.770901 + 1.84546i) q^{4} +(0.689249 - 1.28949i) q^{5} +(-0.0329793 - 0.0403084i) q^{6} +(0.803771 - 4.04083i) q^{7} +(2.77653 - 0.539322i) q^{8} +(-2.94103 + 0.585006i) q^{9} +(-2.05813 + 0.199594i) q^{10} +(3.56453 - 2.92534i) q^{11} +(-0.0215916 + 0.0704174i) q^{12} +(-1.10639 + 0.591377i) q^{13} +(-5.38637 + 2.22166i) q^{14} +(0.0206059 - 0.0497470i) q^{15} +(-2.81142 - 2.84533i) q^{16} +(1.79587 + 4.33561i) q^{17} +(2.99415 + 3.00313i) q^{18} +(-5.26472 - 1.59704i) q^{19} +(1.84836 + 2.26605i) q^{20} +(0.0148717 - 0.150995i) q^{21} +(-6.23762 - 1.90237i) q^{22} +(5.52259 + 3.69008i) q^{23} +(0.0998112 - 0.0297880i) q^{24} +(1.59012 + 2.37978i) q^{25} +(1.56341 + 0.838677i) q^{26} +(-0.211398 + 0.0641267i) q^{27} +(6.83755 + 4.59841i) q^{28} +(3.77234 - 4.59660i) q^{29} +(-0.0747084 + 0.0147441i) q^{30} +(2.71245 + 2.71245i) q^{31} +(-1.14514 + 5.53973i) q^{32} +(0.120078 - 0.120078i) q^{33} +(3.69540 - 5.51265i) q^{34} +(-4.65663 - 3.82160i) q^{35} +(1.18764 - 5.87852i) q^{36} +(2.06513 + 6.80782i) q^{37} +(2.24739 + 7.44882i) q^{38} +(-0.0384137 + 0.0256672i) q^{39} +(1.21827 - 3.95205i) q^{40} +(-4.97984 + 7.45286i) q^{41} +(-0.189387 + 0.100865i) q^{42} +(-7.73927 - 0.762251i) q^{43} +(2.65068 + 8.83334i) q^{44} +(-1.27274 + 4.19565i) q^{45} +(0.0140763 - 9.39314i) q^{46} +(3.13888 - 1.30017i) q^{47} +(-0.113307 - 0.0941311i) q^{48} +(-9.21512 - 3.81703i) q^{49} +(1.55458 - 3.73724i) q^{50} +(0.0814673 + 0.152415i) q^{51} +(-0.238444 - 2.49769i) q^{52} +(-1.10537 - 1.34690i) q^{53} +(0.241202 + 0.198555i) q^{54} +(-1.31535 - 6.61273i) q^{55} +(0.0523889 - 11.6530i) q^{56} +(-0.198713 - 0.0395265i) q^{57} +(-8.36769 - 0.836809i) q^{58} +(5.59887 + 2.99266i) q^{59} +(0.0759209 + 0.0763773i) q^{60} +(-0.746510 - 7.57944i) q^{61} +(1.06632 - 5.31906i) q^{62} +12.3544i q^{63} +(7.41826 - 2.99489i) q^{64} +1.83429i q^{65} +(-0.235471 - 0.0472051i) q^{66} +(-0.0403179 - 0.409354i) q^{67} +(-9.38561 - 0.0281301i) q^{68} +(0.215719 + 0.115304i) q^{69} +(-0.847737 + 8.47697i) q^{70} +(-5.65925 - 1.12569i) q^{71} +(-7.85035 + 3.21045i) q^{72} +(0.124112 + 0.623951i) q^{73} +(6.39424 - 7.76764i) q^{74} +(0.0668669 + 0.0814776i) q^{75} +(7.00584 - 8.48466i) q^{76} +(-8.95572 - 16.7550i) q^{77} +(0.0603254 + 0.0250936i) q^{78} +(-0.538125 - 0.222899i) q^{79} +(-5.60681 + 1.66417i) q^{80} +(8.30364 - 3.43948i) q^{81} +(12.6763 + 0.0189963i) q^{82} +(1.28484 - 4.23554i) q^{83} +(0.267190 + 0.143847i) q^{84} +(6.82854 + 0.672553i) q^{85} +(5.16985 + 9.70707i) q^{86} +(0.121661 - 0.182079i) q^{87} +(8.31934 - 10.0447i) q^{88} +(-7.19626 + 4.80839i) q^{89} +(5.93624 - 1.79103i) q^{90} +(1.50037 + 4.94606i) q^{91} +(-11.0672 + 7.34702i) q^{92} +(0.109200 + 0.0896183i) q^{93} +(-3.99103 - 2.67538i) q^{94} +(-5.68807 + 5.68807i) q^{95} +(-0.0219720 + 0.207161i) q^{96} +(9.96703 + 9.96703i) q^{97} +(2.73119 + 13.8390i) q^{98} +(-8.77204 + 10.6888i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100})$ 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$ .

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{21}{32}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.783932	−	1.17705i	−0.554324	−	0.832301i
$2$	−0.783932	−	1.17705i	−0.554324	−	0.832301i
$3$	0.0366493	−	0.00360964i	0.0211595	−	0.00208403i	−0.0874319	−	0.996171i	$-0.527866\pi$
$3$	0.0366493	−	0.00360964i	0.0211595	−	0.00208403i	0.108591	+	0.994086i	$0.465366\pi$
$4$	−0.770901	+	1.84546i	−0.385451	+	0.922728i
$5$	0.689249	−	1.28949i	0.308242	−	0.576680i	−0.679333	−	0.733830i	$-0.737731\pi$
$5$	0.689249	−	1.28949i	0.308242	−	0.576680i	0.987575	+	0.157151i	$0.0502308\pi$
$6$	−0.0329793	−	0.0403084i	−0.0134637	−	0.0164558i
$7$	0.803771	−	4.04083i	0.303797	−	1.52729i	−0.463557	−	0.886067i	$-0.653427\pi$
$7$	0.803771	−	4.04083i	0.303797	−	1.52729i	0.767354	−	0.641224i	$-0.221573\pi$
$8$	2.77653	−	0.539322i	0.981652	−	0.190679i
$9$	−2.94103	+	0.585006i	−0.980342	+	0.195002i
$10$	−2.05813	+	0.199594i	−0.650837	+	0.0631172i
$11$	3.56453	−	2.92534i	1.07475	−	0.882022i	0.0813426	−	0.996686i	$-0.474079\pi$
$11$	3.56453	−	2.92534i	1.07475	−	0.882022i	0.993404	+	0.114664i	$0.0365792\pi$
$12$	−0.0215916	+	0.0704174i	−0.00623295	+	0.0203277i
$13$	−1.10639	+	0.591377i	−0.306857	+	0.164018i	−0.617637	−	0.786463i	$-0.711910\pi$
$13$	−1.10639	+	0.591377i	−0.306857	+	0.164018i	0.310780	+	0.950482i	$0.399410\pi$
$14$	−5.38637	+	2.22166i	−1.43957	+	0.593763i
$15$	0.0206059	−	0.0497470i	0.00532042	−	0.0128446i
$16$	−2.81142	−	2.84533i	−0.702856	−	0.711333i
$17$	1.79587	+	4.33561i	0.435562	+	1.05154i	0.977465	+	0.211098i	$0.0677040\pi$
$17$	1.79587	+	4.33561i	0.435562	+	1.05154i	−0.541903	+	0.840441i	$0.682296\pi$
$18$	2.99415	+	3.00313i	0.705727	+	0.707845i
$19$	−5.26472	−	1.59704i	−1.20781	−	0.366385i	−0.378726	−	0.925509i	$-0.623638\pi$
$19$	−5.26472	−	1.59704i	−1.20781	−	0.366385i	−0.829084	+	0.559124i	$0.811138\pi$
$20$	1.84836	+	2.26605i	0.413307	+	0.506705i
$21$	0.0148717	−	0.150995i	0.00324527	−	0.0329498i
$22$	−6.23762	−	1.90237i	−1.32987	−	0.405588i
$23$	5.52259	+	3.69008i	1.15154	+	0.769434i	0.976583	−	0.215142i	$-0.0690214\pi$
$23$	5.52259	+	3.69008i	1.15154	+	0.769434i	0.174957	+	0.984576i	$0.444021\pi$
$24$	0.0998112	−	0.0297880i	0.0203739	−	0.00608046i
$25$	1.59012	+	2.37978i	0.318024	+	0.475956i
$26$	1.56341	+	0.838677i	0.306611	+	0.164478i
$27$	−0.211398	+	0.0641267i	−0.0406835	+	0.0123412i
$28$	6.83755	+	4.59841i	1.29218	+	0.869018i
$29$	3.77234	−	4.59660i	0.700505	−	0.853568i	−0.294263	−	0.955724i	$-0.595074\pi$
$29$	3.77234	−	4.59660i	0.700505	−	0.853568i	0.994768	+	0.102156i	$0.0325742\pi$
$30$	−0.0747084	+	0.0147441i	−0.0136398	+	0.00269189i
$31$	2.71245	+	2.71245i	0.487170	+	0.487170i	0.907412	−	0.420242i	$-0.138055\pi$
$31$	2.71245	+	2.71245i	0.487170	+	0.487170i	−0.420242	+	0.907412i	$0.638055\pi$
$32$	−1.14514	+	5.53973i	−0.202434	+	0.979296i
$33$	0.120078	−	0.120078i	0.0209029	−	0.0209029i
$34$	3.69540	−	5.51265i	0.633755	−	0.945412i
$35$	−4.65663	−	3.82160i	−0.787115	−	0.645968i
$36$	1.18764	−	5.87852i	0.197939	−	0.979753i
$37$	2.06513	+	6.80782i	0.339505	+	1.11920i	0.946015	+	0.324123i	$0.105069\pi$
$37$	2.06513	+	6.80782i	0.339505	+	1.11920i	−0.606510	+	0.795076i	$0.707431\pi$
$38$	2.24739	+	7.44882i	0.364575	+	1.20836i
$39$	−0.0384137	+	0.0256672i	−0.00615112	+	0.00411004i
$40$	1.21827	−	3.95205i	0.192625	−	0.624874i
$41$	−4.97984	+	7.45286i	−0.777721	+	1.16394i	0.204985	+	0.978765i	$0.434286\pi$
$41$	−4.97984	+	7.45286i	−0.777721	+	1.16394i	−0.982705	+	0.185176i	$0.940714\pi$
$42$	−0.189387	+	0.100865i	−0.0292231	+	0.0155638i
$43$	−7.73927	−	0.762251i	−1.18023	−	0.116242i	−0.511188	−	0.859469i	$-0.670794\pi$
$43$	−7.73927	−	0.762251i	−1.18023	−	0.116242i	−0.669039	+	0.743227i	$0.733294\pi$
$44$	2.65068	+	8.83334i	0.399605	+	1.33168i
$45$	−1.27274	+	4.19565i	−0.189728	+	0.625451i
$46$	0.0140763	−	9.39314i	0.00207544	−	1.38494i
$47$	3.13888	−	1.30017i	0.457853	−	0.189649i	−0.141823	−	0.989892i	$-0.545296\pi$
$47$	3.13888	−	1.30017i	0.457853	−	0.189649i	0.599675	+	0.800243i	$0.295296\pi$
$48$	−0.113307	−	0.0941311i	−0.0163545	−	0.0135867i
$49$	−9.21512	−	3.81703i	−1.31645	−	0.545290i
$50$	1.55458	−	3.73724i	0.219851	−	0.528525i
$51$	0.0814673	+	0.152415i	0.0114077	+	0.0213423i
$52$	−0.238444	−	2.49769i	−0.0330663	−	0.346367i
$53$	−1.10537	−	1.34690i	−0.151834	−	0.185010i	0.691538	−	0.722340i	$-0.256933\pi$
$53$	−1.10537	−	1.34690i	−0.151834	−	0.185010i	−0.843373	+	0.537329i	$0.819433\pi$
$54$	0.241202	+	0.198555i	0.0328234	+	0.0270199i
$55$	−1.31535	−	6.61273i	−0.177362	−	0.891660i
$56$	0.0523889	−	11.6530i	0.00700076	−	1.55720i
$57$	−0.198713	−	0.0395265i	−0.0263202	−	0.00523541i
$58$	−8.36769	−	0.836809i	−1.09873	−	0.109878i
$59$	5.59887	+	2.99266i	0.728911	+	0.389611i	0.793717	−	0.608287i	$-0.208143\pi$
$59$	5.59887	+	2.99266i	0.728911	+	0.389611i	−0.0648061	+	0.997898i	$0.520643\pi$
$60$	0.0759209	+	0.0763773i	0.00980134	+	0.00986027i
$61$	−0.746510	−	7.57944i	−0.0955808	−	0.970448i	−0.916669	−	0.399647i	$-0.869133\pi$
$61$	−0.746510	−	7.57944i	−0.0955808	−	0.970448i	0.821088	−	0.570801i	$-0.193367\pi$
$62$	1.06632	−	5.31906i	0.135422	−	0.675522i
$63$			12.3544i			1.55651i
$64$	7.41826	−	2.99489i	0.927283	−	0.374361i
$65$			1.83429i			0.227515i
$66$	−0.235471	−	0.0472051i	−0.0289845	−	0.00581055i
$67$	−0.0403179	−	0.409354i	−0.00492561	−	0.0500106i	0.992408	−	0.122991i	$-0.0392488\pi$
$67$	−0.0403179	−	0.409354i	−0.00492561	−	0.0500106i	−0.997333	+	0.0729809i	$0.976749\pi$
$68$	−9.38561	−	0.0281301i	−1.13817	−	0.00341128i
$69$	0.215719	+	0.115304i	0.0259695	+	0.0138810i
$70$	−0.847737	+	8.47697i	−0.101324	+	1.01319i
$71$	−5.65925	−	1.12569i	−0.671629	−	0.133595i	−0.152516	−	0.988301i	$-0.548738\pi$
$71$	−5.65925	−	1.12569i	−0.671629	−	0.133595i	−0.519113	+	0.854706i	$0.673738\pi$
$72$	−7.85035	+	3.21045i	−0.925172	+	0.378355i
$73$	0.124112	+	0.623951i	0.0145262	+	0.0730280i	0.987368	−	0.158441i	$-0.0506468\pi$
$73$	0.124112	+	0.623951i	0.0145262	+	0.0730280i	−0.972842	+	0.231469i	$0.925647\pi$
$74$	6.39424	−	7.76764i	0.743315	−	0.902969i
$75$	0.0668669	+	0.0814776i	0.00772113	+	0.00940822i
$76$	7.00584	−	8.48466i	0.803625	−	0.973257i
$77$	−8.95572	−	16.7550i	−1.02060	−	1.90941i
$78$	0.0603254	+	0.0250936i	0.00683050	+	0.00284129i
$79$	−0.538125	−	0.222899i	−0.0605438	−	0.0250780i	0.352206	−	0.935922i	$-0.385432\pi$
$79$	−0.538125	−	0.222899i	−0.0605438	−	0.0250780i	−0.412750	+	0.910844i	$0.635432\pi$
$80$	−5.60681	+	1.66417i	−0.626860	+	0.186060i
$81$	8.30364	−	3.43948i	0.922627	−	0.382165i
$82$	12.6763	+	0.0189963i	1.39986	+	0.00209779i
$83$	1.28484	−	4.23554i	0.141029	−	0.464911i	−0.857763	−	0.514045i	$-0.828146\pi$
$83$	1.28484	−	4.23554i	0.141029	−	0.464911i	0.998792	+	0.0491346i	$0.0156463\pi$
$84$	0.267190	+	0.143847i	0.0291528	+	0.0156950i
$85$	6.82854	+	0.672553i	0.740659	+	0.0729486i
$86$	5.16985	+	9.70707i	0.557479	+	1.04674i
$87$	0.121661	−	0.182079i	0.0130435	−	0.0195209i
$88$	8.31934	−	10.0447i	0.886845	−	1.07077i
$89$	−7.19626	+	4.80839i	−0.762802	+	0.509688i	−0.875074	−	0.483989i	$-0.839187\pi$
$89$	−7.19626	+	4.80839i	−0.762802	+	0.509688i	0.112272	+	0.993678i	$0.464187\pi$
$90$	5.93624	−	1.79103i	0.625735	−	0.188791i
$91$	1.50037	+	4.94606i	0.157282	+	0.518488i
$92$	−11.0672	+	7.34702i	−1.15384	+	0.765979i
$93$	0.109200	+	0.0896183i	0.0113235	+	0.00929299i
$94$	−3.99103	−	2.67538i	−0.411643	−	0.275944i
$95$	−5.68807	+	5.68807i	−0.583584	+	0.583584i
$96$	−0.0219720	+	0.207161i	−0.00224251	+	0.0211433i
$97$	9.96703	+	9.96703i	1.01200	+	1.01200i	0.999927	+	0.0120718i	$0.00384267\pi$
$97$	9.96703	+	9.96703i	1.01200	+	1.01200i	0.0120718	+	0.999927i	$0.496157\pi$
$98$	2.73119	+	13.8390i	0.275892	+	1.39795i
$99$	−8.77204	+	10.6888i	−0.881623	+	1.07426i
$100$	−5.61761	+	1.09992i	−0.561761	+	0.109992i
$101$	9.96775	−	3.02368i	0.991828	−	0.300868i	0.247650	−	0.968849i	$-0.420342\pi$
$101$	9.96775	−	3.02368i	0.991828	−	0.300868i	0.744178	+	0.667982i	$0.232842\pi$
$102$	0.115535	−	0.215374i	0.0114397	−	0.0213252i
$103$	1.10205	+	1.64934i	0.108589	+	0.162514i	0.881784	−	0.471654i	$-0.156343\pi$
$103$	1.10205	+	1.64934i	0.108589	+	0.162514i	−0.773195	+	0.634168i	$0.781343\pi$
$104$	−2.75298	+	2.23868i	−0.269952	+	0.219520i
$105$	−0.184457	−	0.123250i	−0.0180011	−	0.0120280i
$106$	−0.718832	+	2.35695i	−0.0698192	+	0.228927i
$107$	−0.566058	+	5.74729i	−0.0547229	+	0.555611i	0.928262	+	0.371926i	$0.121303\pi$
$107$	−0.566058	+	5.74729i	−0.0547229	+	0.555611i	−0.982985	+	0.183685i	$0.941197\pi$
$108$	0.0446235	−	0.439560i	0.00429390	−	0.0422967i
$109$	−3.87468	−	1.17537i	−0.371127	−	0.112580i	0.0992112	−	0.995066i	$-0.468368\pi$
$109$	−3.87468	−	1.17537i	−0.371127	−	0.112580i	−0.470338	+	0.882486i	$0.655868\pi$
$110$	−6.75238	+	6.73217i	−0.643814	+	0.641887i
$111$	0.100259	+	0.242048i	0.00951620	+	0.0229741i
$112$	−13.7572	+	9.07349i	−1.29994	+	0.857364i
$113$	6.68005	−	16.1271i	0.628407	−	1.51711i	−0.213195	−	0.977010i	$-0.568387\pi$
$113$	6.68005	−	16.1271i	0.628407	−	1.51711i	0.841602	−	0.540098i	$-0.181613\pi$
$114$	0.109253	+	0.264882i	0.0102325	+	0.0248084i
$115$	8.56477	−	4.57797i	0.798669	−	0.426898i
$116$	5.57474	+	10.5052i	0.517601	+	0.975384i
$117$	2.90796	−	2.38650i	0.268841	−	0.220632i
$118$	−0.866620	−	8.93621i	−0.0797788	−	0.822645i
$119$	18.9629	−	3.77196i	1.73833	−	0.345775i
$120$	0.0303833	−	0.149237i	0.00277360	−	0.0136234i
$121$	2.00231	−	10.0663i	0.182028	−	0.915115i
$122$	−8.33618	+	6.82044i	−0.754722	+	0.617494i
$123$	−0.155606	+	0.291118i	−0.0140305	+	0.0262492i
$124$	−7.09673	+	2.91467i	−0.637305	+	0.261745i
$125$	11.4402	−	1.12676i	1.02324	−	0.100781i
$126$	14.5418	−	9.68501i	1.29548	−	0.862809i
$127$	−4.06138			−0.360389			−0.180194	−	0.983631i	$-0.557673\pi$
$127$	−4.06138			−0.360389			−0.180194	+	0.983631i	$0.557673\pi$
$128$	−9.34055	−	6.38389i	−0.825596	−	0.564262i
$129$	−0.286390			−0.0252152
$130$	2.15905	−	1.43796i	0.189361	−	0.126117i
$131$	−16.4789	+	1.62303i	−1.43977	+	0.141805i	−0.787562	−	0.616236i	$-0.788657\pi$
$131$	−16.4789	+	1.62303i	−1.43977	+	0.141805i	−0.652207	+	0.758041i	$0.726157\pi$
$132$	0.129031	+	0.314168i	0.0112307	+	0.0273448i
$133$	−10.6850	+	19.9902i	−0.926506	+	1.73337i
$134$	−0.450225	+	0.368362i	−0.0388935	+	0.0318216i
$135$	−0.0630145	+	0.316795i	−0.00542342	+	0.0272654i
$136$	7.32457	+	11.0694i	0.628077	+	0.949194i
$137$	−2.82514	+	0.561955i	−0.241368	+	0.0480110i	−0.314292	−	0.949326i	$-0.601767\pi$
$137$	−2.82514	+	0.561955i	−0.241368	+	0.0480110i	0.0729239	+	0.997338i	$0.476767\pi$
$138$	−0.0333900	−	0.344303i	−0.00284234	−	0.0293090i
$139$	5.74628	−	4.71585i	0.487393	−	0.399993i	−0.358347	−	0.933589i	$-0.616659\pi$
$139$	5.74628	−	4.71585i	0.487393	−	0.399993i	0.845740	+	0.533595i	$0.179159\pi$
$140$	10.6424	−	5.64754i	0.899447	−	0.477304i
$141$	0.110345	−	0.0589804i	0.00929269	−	0.00496705i
$142$	3.11147	+	7.54370i	0.261108	+	0.633053i
$143$	−2.21378	+	5.34454i	−0.185126	+	0.446933i
$144$	9.93300	+	6.72349i	0.827750	+	0.560291i
$145$	−3.32722	−	8.03261i	−0.276310	−	0.667072i
$146$	0.637128	−	0.635221i	0.0527291	−	0.0525713i
$147$	−0.351506	−	0.106628i	−0.0289917	−	0.00879454i
$148$	−14.1556	−	1.43705i	−1.16358	−	0.118125i
$149$	0.643929	−	6.53793i	0.0527528	−	0.535608i	−0.932098	−	0.362205i	$-0.882024\pi$
$149$	0.643929	−	6.53793i	0.0527528	−	0.535608i	0.984851	−	0.173402i	$-0.0554761\pi$
$150$	0.0434842	−	0.142579i	0.00355047	−	0.0116415i
$151$	−4.36438	−	2.91619i	−0.355168	−	0.237316i	0.365167	−	0.930942i	$-0.381012\pi$
$151$	−4.36438	−	2.91619i	−0.355168	−	0.237316i	−0.720335	+	0.693626i	$0.756012\pi$
$152$	−15.4790	−	1.59484i	−1.25551	−	0.129359i
$153$	−7.81805	−	11.7005i	−0.632052	−	0.945933i
$154$	−12.7008	+	23.6761i	−1.02346	+	1.90788i
$155$	5.36724	−	1.62813i	0.431107	−	0.130775i
$156$	−0.0177546	−	0.0906777i	−0.00142150	−	0.00726003i
$157$	−13.1319	+	16.0012i	−1.04804	+	1.27704i	−0.0883131	+	0.996093i	$0.528148\pi$
$157$	−13.1319	+	16.0012i	−1.04804	+	1.27704i	−0.959724	+	0.280944i	$0.909352\pi$
$158$	0.159490	+	0.808138i	0.0126883	+	0.0642920i
$159$	−0.0453728	−	0.0453728i	−0.00359830	−	0.00359830i
$160$	6.35417	+	5.29491i	0.502341	+	0.418599i
$161$	19.3499	−	19.3499i	1.52498	−	1.52498i
$162$	−10.5579	−	7.07750i	−0.829510	−	0.556061i
$163$	1.26066	+	1.03460i	0.0987424	+	0.0810358i	0.682469	−	0.730914i	$-0.260906\pi$
$163$	1.26066	+	1.03460i	0.0987424	+	0.0810358i	−0.583727	+	0.811950i	$0.698406\pi$
$164$	−9.91496	−	14.9355i	−0.774229	−	1.16627i
$165$	−0.0720764	−	0.237604i	−0.00561114	−	0.0184974i
$166$	−5.99267	+	1.80805i	−0.465122	+	0.140332i
$167$	−0.615305	+	0.411134i	−0.0476137	+	0.0318145i	−0.579149	−	0.815221i	$-0.696615\pi$
$167$	−0.615305	+	0.411134i	−0.0476137	+	0.0318145i	0.531536	+	0.847036i	$0.321615\pi$
$168$	−0.0401431	−	0.427263i	−0.00309711	−	0.0329641i
$169$	−6.34804	+	9.50052i	−0.488311	+	0.730809i
$170$	−4.56148	−	8.56478i	−0.349850	−	0.656889i
$171$	16.4180	+	1.61703i	1.25551	+	0.123657i
$172$	7.37291	−	13.6949i	0.562179	−	1.04422i
$173$	0.921635	−	3.03822i	0.0700706	−	0.230992i	−0.914910	−	0.403659i	$-0.867738\pi$
$173$	0.921635	−	3.03822i	0.0700706	−	0.230992i	0.984980	+	0.172667i	$0.0552384\pi$
$174$	−0.309691		0.000464094i	−0.0234776		3.51829e-5i
$175$	10.8944	−	4.51260i	0.823538	−	0.341121i
$176$	−18.3450	−	1.91792i	−1.38280	−	0.144569i
$177$	0.215997	+	0.0894690i	0.0162353	+	0.00672490i
$178$	11.3011	+	4.70092i	0.847053	+	0.352349i
$179$	5.22776	+	9.78045i	0.390741	+	0.731025i	0.997982	−	0.0634924i	$-0.0202239\pi$
$179$	5.22776	+	9.78045i	0.390741	+	0.731025i	−0.607241	+	0.794518i	$0.707724\pi$
$180$	−6.76174	−	5.58322i	−0.503990	−	0.416148i
$181$	−10.8362	−	13.2039i	−0.805446	−	0.981438i	−1.00000		0.000546504i	$-0.999826\pi$
$181$	−10.8362	−	13.2039i	−0.805446	−	0.981438i	0.194554	−	0.980892i	$-0.437674\pi$
$182$	4.64558	−	5.64339i	0.344353	−	0.418316i
$183$	−0.0547181	−	0.275086i	−0.00404488	−	0.0203350i
$184$	17.3238	+	7.26716i	1.27713	+	0.535742i
$185$	10.2020	+	2.02931i	0.750069	+	0.149198i
$186$	0.0198798	−	0.198789i	0.00145766	−	0.0145759i
$187$	19.0845	+	10.2009i	1.39560	+	0.745963i
$188$	−0.0203655	+	6.79497i	−0.00148531	+	0.495574i
$189$	0.0892101	+	0.905765i	0.00648908	+	0.0658847i
$190$	11.1542	+	2.23609i	0.809212	+	0.162223i
$191$		−	16.5498i		−	1.19750i	−0.800937	−	0.598749i	$-0.795665\pi$
$191$		−	16.5498i		−	1.19750i	0.800937	−	0.598749i	$-0.204335\pi$
$192$	0.261064	−	0.136538i	0.0188406	−	0.00985377i
$193$			13.9894i			1.00698i	0.864001	+	0.503490i	$0.167951\pi$
$193$			13.9894i			1.00698i	−0.864001	+	0.503490i	$0.832049\pi$
$194$	3.91824	−	19.5452i	0.281313	−	1.40326i
$195$	0.00662112	+	0.0672254i	0.000474148	+	0.00481411i
$196$	14.1481	−	14.0636i	1.01058	−	1.00454i
$197$	14.3346	+	7.66201i	1.02130	+	0.545895i	0.894986	−	0.446095i	$-0.147186\pi$
$197$	14.3346	+	7.66201i	1.02130	+	0.545895i	0.126313	+	0.991990i	$0.459686\pi$
$198$	19.4579	+	1.94588i	1.38281	+	0.138288i
$199$	−27.0230	−	5.37522i	−1.91561	−	0.381039i	−0.915823	−	0.401582i	$-0.868461\pi$
$199$	−27.0230	−	5.37522i	−1.91561	−	0.381039i	−0.999789	+	0.0205426i	$0.993461\pi$
$200$	5.69849	+	5.74995i	0.402944	+	0.406583i
$201$	−0.00295524	−	0.0148570i	−0.000208447	−	0.00104793i
$202$	−11.3731	−	9.36219i	−0.800206	−	0.658722i
$203$	−15.5420	−	18.9380i	−1.09084	−	1.32919i
$204$	−0.344078	+	0.0328477i	−0.0240903	+	0.00229980i
$205$	6.17807	+	11.5584i	0.431495	+	0.807271i
$206$	1.07742	−	2.59014i	0.0750676	−	0.180464i
$207$	−18.4008	−	7.62186i	−1.27894	−	0.529756i
$208$	4.79319	+	1.48543i	0.332348	+	0.102996i
$209$	−23.4381	+	9.70839i	−1.62125	+	0.671544i
$210$	−0.000470155		0.313735i	−3.24438e−5		0.0216498i
$211$	5.45700	−	17.9893i	0.375676	−	1.23844i	−0.541754	−	0.840537i	$-0.682239\pi$
$211$	5.45700	−	17.9893i	0.375676	−	1.23844i	0.917429	−	0.397899i	$-0.130261\pi$
$212$	3.33777	−	1.00159i	0.229239	−	0.0687893i
$213$	−0.211471	−	0.0208281i	−0.0144897	−	0.00142712i
$214$	7.20860	−	3.83920i	0.492770	−	0.262442i
$215$	−6.31720	+	9.45436i	−0.430830	+	0.644782i
$216$	−0.552367	+	0.292061i	−0.0375838	+	0.0198722i
$217$	13.1407	−	8.78035i	0.892051	−	0.596049i
$218$	1.65401	+	5.48211i	0.112024	+	0.371295i
$219$	0.00680085	+	0.0224194i	0.000459559	+	0.00151496i
$220$	13.2175	+	2.67033i	0.891125	+	0.180034i
$221$	−4.55091	−	3.73483i	−0.306127	−	0.251232i
$222$	0.206306	−	0.307759i	0.0138464	−	0.0206555i
$223$	−15.9192	+	15.9192i	−1.06603	+	1.06603i	−0.0683694	+	0.997660i	$0.521780\pi$
$223$	−15.9192	+	15.9192i	−1.06603	+	1.06603i	−0.997660	+	0.0683694i	$0.978220\pi$
$224$	21.4647	+	9.07999i	1.43417	+	0.606682i
$225$	−6.06877	−	6.06877i	−0.404585	−	0.404585i
$226$	−24.2191	+	4.77976i	−1.61103	+	0.317945i
$227$	−9.70495	+	11.8255i	−0.644140	+	0.784887i	−0.988053	−	0.154114i	$-0.950748\pi$
$227$	−9.70495	+	11.8255i	−0.644140	+	0.784887i	0.343913	+	0.939002i	$0.388248\pi$
$228$	0.226133	−	0.336245i	0.0149760	−	0.0222684i
$229$	−8.35745	+	2.53520i	−0.552276	+	0.167531i	−0.554074	−	0.832467i	$-0.686928\pi$
$229$	−8.35745	+	2.53520i	−0.552276	+	0.167531i	0.00179841	+	0.999998i	$0.499428\pi$
$230$	−12.1027	−	6.49237i	−0.798029	−	0.428094i
$231$	−0.388700	−	0.581731i	−0.0255746	−	0.0382751i
$232$	7.99496	−	14.7971i	0.524895	−	0.971479i
$233$	6.08316	+	4.06464i	0.398521	+	0.266283i	0.738641	−	0.674099i	$-0.235468\pi$
$233$	6.08316	+	4.06464i	0.398521	+	0.266283i	−0.340120	+	0.940382i	$0.610468\pi$
$234$	−5.08867	−	1.55196i	−0.332657	−	0.101455i
$235$	0.486913	−	4.94371i	0.0317627	−	0.322492i
$236$	−9.83901	+	8.02543i	−0.640465	+	0.522411i
$237$	−0.0205265	−	0.00622664i	−0.00133334	−	0.000404464i
$238$	−19.3054	−	19.3634i	−1.25139	−	1.25514i
$239$	0.698274	+	1.68578i	0.0451676	+	0.109044i	0.944853	−	0.327494i	$-0.106204\pi$
$239$	0.698274	+	1.68578i	0.0451676	+	0.109044i	−0.899686	+	0.436539i	$0.856204\pi$
$240$	−0.199479	+	0.0812293i	−0.0128763	+	0.00524333i
$241$	−7.95850	+	19.2135i	−0.512652	+	1.23765i	0.429682	+	0.902980i	$0.358626\pi$
$241$	−7.95850	+	19.2135i	−0.512652	+	1.23765i	−0.942335	+	0.334672i	$0.891374\pi$
$242$	−13.4182	+	5.53445i	−0.862554	+	0.355768i
$243$	0.876382	−	0.468436i	0.0562200	−	0.0300502i
$244$	14.5630	+	4.46535i	0.932301	+	0.285865i
$245$	−11.2735	+	9.25196i	−0.720241	+	0.591086i
$246$	0.464645	−	0.0450605i	0.0296247	−	0.00287295i
$247$	6.76928	−	1.34649i	0.430719	−	0.0856753i
$248$	8.99408	+	6.06831i	0.571125	+	0.385338i
$249$	0.0317996	−	0.159867i	0.00201522	−	0.0101312i
$250$	−10.2946	−	12.5824i	−0.651088	−	0.795782i
$251$	−6.47552	+	12.1148i	−0.408731	+	0.764682i	−0.999098	−	0.0424525i	$-0.986483\pi$
$251$	−6.47552	+	12.1148i	−0.408731	+	0.764682i	0.590367	+	0.807135i	$0.298983\pi$
$252$	−22.7995	−	9.52403i	−1.43623	−	0.599957i
$253$	30.4802	−	3.00203i	1.91627	−	0.188736i
$254$	3.18384	+	4.78045i	0.199772	+	0.299952i
$255$	0.252689			0.0158240
$256$	−0.191813	+	15.9989i	−0.0119883	+	0.999928i
$257$	6.66776			0.415924			0.207962	−	0.978137i	$-0.433317\pi$
$257$	6.66776			0.415924			0.207962	+	0.978137i	$0.433317\pi$
$258$	0.224510	+	0.337096i	0.0139774	+	0.0209867i
$259$	29.1692	−	2.87291i	1.81248	−	0.178514i
$260$	−3.38510	−	1.41406i	−0.209935	−	0.0876960i
$261$	−8.40549	+	15.7256i	−0.520287	+	0.973388i
$262$	14.8287	+	18.1242i	0.916122	+	1.11972i
$263$	3.35988	−	16.8912i	0.207179	−	1.04156i	−0.727512	−	0.686095i	$-0.759323\pi$
$263$	3.35988	−	16.8912i	0.207179	−	1.04156i	0.934690	−	0.355463i	$-0.115677\pi$
$264$	0.268640	−	0.398162i	0.0165337	−	0.0245052i
$265$	−2.49869	+	0.497020i	−0.153493	+	0.0305317i
$266$	31.9058	−	3.09418i	1.95627	−	0.189716i
$267$	−0.246381	+	0.202200i	−0.0150783	+	0.0123744i
$268$	0.786527	+	0.241167i	0.0480448	+	0.0147316i
$269$	−28.0681	+	15.0027i	−1.71134	+	0.914733i	−0.741520	+	0.670931i	$0.765895\pi$
$269$	−28.0681	+	15.0027i	−1.71134	+	0.914733i	−0.969825	+	0.243802i	$0.921605\pi$
$270$	0.422283	−	0.174175i	0.0256994	−	0.0105999i
$271$	6.44511	−	15.5599i	0.391512	−	0.945194i	−0.598098	−	0.801423i	$-0.704077\pi$
$271$	6.44511	−	15.5599i	0.391512	−	0.945194i	0.989611	−	0.143772i	$-0.0459231\pi$
$272$	7.28730	−	17.2991i	0.441857	−	1.04891i
$273$	0.0728411	+	0.175854i	0.00440854	+	0.0106432i
$274$	2.87616	+	2.88480i	0.173755	+	0.174277i
$275$	12.6297	+	3.83118i	0.761599	+	0.231029i
$276$	−0.379087	+	0.309212i	−0.0228183	+	0.0186124i
$277$	−1.53021	+	15.5365i	−0.0919415	+	0.933497i	0.832971	+	0.553317i	$0.186638\pi$
$277$	−1.53021	+	15.5365i	−0.0919415	+	0.933497i	−0.924912	+	0.380180i	$0.875862\pi$
$278$	−10.0555	−	3.06676i	−0.603089	−	0.183932i
$279$	−9.56417	−	6.39058i	−0.572592	−	0.382594i
$280$	−14.9904	−	8.09937i	−0.895845	−	0.484030i
$281$	−6.81310	−	10.1965i	−0.406435	−	0.608274i	0.570631	−	0.821206i	$-0.306698\pi$
$281$	−6.81310	−	10.1965i	−0.406435	−	0.608274i	−0.977067	+	0.212933i	$0.931698\pi$
$282$	−0.155926	−	0.0836446i	−0.00928524	−	0.00498097i
$283$	−25.5875	+	7.76187i	−1.52102	+	0.461395i	−0.936701	−	0.350131i	$-0.886137\pi$
$283$	−25.5875	+	7.76187i	−1.52102	+	0.461395i	−0.584316	+	0.811526i	$0.698637\pi$
$284$	6.44015	−	9.57610i	0.382152	−	0.568237i
$285$	−0.187932	+	0.228996i	−0.0111321	+	0.0135645i
$286$	8.02625	−	1.58402i	0.474602	−	0.0936651i
$287$	26.1131	+	26.1131i	1.54141	+	1.54141i
$288$	0.127099	−	16.9624i	0.00748940	−	0.999520i
$289$	−3.55154	+	3.55154i	−0.208914	+	0.208914i
$290$	−6.84649	+	10.2133i	−0.402040	+	0.599747i
$291$	0.401262	+	0.329307i	0.0235224	+	0.0193043i
$292$	−1.24715	−	0.251962i	−0.0729841	−	0.0147450i
$293$	−4.09507	−	13.4996i	−0.239237	−	0.788657i	−0.991536	−	0.129835i	$-0.958555\pi$
$293$	−4.09507	−	13.4996i	−0.239237	−	0.788657i	0.752299	−	0.658822i	$-0.228945\pi$
$294$	0.150050	+	0.497330i	0.00875108	+	0.0290048i
$295$	7.71804	−	5.15703i	0.449362	−	0.300254i
$296$	9.40551	+	17.7884i	0.546684	+	1.03393i
$297$	−0.565941	+	0.846991i	−0.0328392	+	0.0491474i
$298$	−8.20027	+	4.36735i	−0.475029	+	0.252994i
$299$	−8.29236	−	0.816726i	−0.479559	−	0.0472325i
$300$	−0.201911	+	0.0605888i	−0.0116573	+	0.00349810i
$301$	−9.30073	+	30.6604i	−0.536085	+	1.76724i
$302$	−0.0111242	+	7.42320i	−0.000640126	+	0.427157i
$303$	0.354397	−	0.146796i	0.0203595	−	0.00843320i
$304$	10.2573	+	19.4698i	0.588294	+	1.11667i
$305$	−10.2882	−	4.26150i	−0.589099	−	0.244013i
$306$	−7.64332	+	18.3747i	−0.436940	+	1.05041i
$307$	4.45987	+	8.34384i	0.254538	+	0.476208i	0.976440	−	0.215788i	$-0.0692319\pi$
$307$	4.45987	+	8.34384i	0.254538	+	0.476208i	−0.721902	+	0.691995i	$0.756732\pi$
$308$	37.8246	−	3.61096i	2.15525	−	0.205754i
$309$	0.0463430	+	0.0564691i	0.00263636	+	0.00321242i
$310$	−6.12395	−	5.04117i	−0.347817	−	0.286319i
$311$	0.396062	+	1.99114i	0.0224586	+	0.112907i	0.990389	−	0.138313i	$-0.0441681\pi$
$311$	0.396062	+	1.99114i	0.0224586	+	0.112907i	−0.967930	+	0.251220i	$0.919168\pi$
$312$	−0.0928140	+	0.0919832i	−0.00525456	+	0.00520752i
$313$	22.6817	+	4.51167i	1.28205	+	0.255015i	0.788678	−	0.614806i	$-0.210766\pi$
$313$	22.6817	+	4.51167i	1.28205	+	0.255015i	0.493368	+	0.869821i	$0.335766\pi$
$314$	29.1288	+	2.91301i	1.64383	+	0.164391i
$315$	15.9309	+	8.51526i	0.897607	+	0.479781i
$316$	0.826191	−	0.821253i	0.0464769	−	0.0461991i
$317$	0.535210	+	5.43408i	0.0300604	+	0.305208i	0.998445	+	0.0557462i	$0.0177538\pi$
$317$	0.535210	+	5.43408i	0.0300604	+	0.305208i	−0.968385	+	0.249462i	$0.919746\pi$
$318$	−0.0178370	+	0.0889754i	−0.00100025	+	0.00498949i
$319$		−	27.4201i		−	1.53523i
$320$	1.25114	−	11.6300i	0.0699409	−	0.650139i
$321$			0.212677i			0.0118705i
$322$	−37.9448	−	7.60682i	−2.11458	−	0.423911i
$323$	−2.53062	−	25.6938i	−0.140808	−	1.42964i
$324$	−0.0538754	+	17.9755i	−0.00299308	+	0.998640i
$325$	−3.16664	−	1.69260i	−0.175653	−	0.0938887i
$326$	0.229502	−	2.29491i	0.0127110	−	0.127104i
$327$	−0.146247	−	0.0290903i	−0.00808748	−	0.00160870i
$328$	−9.80720	+	23.3788i	−0.541512	+	1.29088i
$329$	−2.73081	−	13.7287i	−0.150555	−	0.756889i
$330$	−0.223169	+	0.271103i	−0.0122851	+	0.0149237i
$331$	−3.02365	−	3.68432i	−0.166195	−	0.202509i	0.683253	−	0.730182i	$-0.260565\pi$
$331$	−3.02365	−	3.68432i	−0.166195	−	0.202509i	−0.849448	+	0.527673i	$0.823065\pi$
$332$	6.82602	+	5.63629i	0.374627	+	0.309332i
$333$	−10.0562	−	18.8139i	−0.551078	−	1.03099i
$334$	0.966283	+	0.401945i	0.0528726	+	0.0219934i
$335$	−0.555649	−	0.230157i	−0.0303584	−	0.0125748i
$336$	−0.471441	+	0.382196i	−0.0257192	+	0.0208505i
$337$	22.1659	−	9.18143i	1.20746	−	0.500144i	0.314055	−	0.949405i	$-0.398312\pi$
$337$	22.1659	−	9.18143i	1.20746	−	0.500144i	0.893401	+	0.449261i	$0.148312\pi$
$338$	16.1590	+	0.0242155i	0.878936	+	0.00131715i
$339$	0.186606	−	0.615159i	0.0101351	−	0.0334108i
$340$	−6.50530	+	12.0833i	−0.352799	+	0.655309i
$341$	17.6034	+	1.73379i	0.953279	+	0.0938898i
$342$	−10.9672	−	20.5924i	−0.593040	−	1.11351i
$343$	−6.80818	+	10.1892i	−0.367607	+	0.550163i
$344$	−21.8994	+	2.05754i	−1.18074	+	0.110935i
$345$	0.297368	−	0.198695i	0.0160098	−	0.0106974i
$346$	−4.29865	+	1.29695i	−0.231097	+	0.0697244i
$347$	−1.34451	−	4.43226i	−0.0721772	−	0.237936i	0.913428	−	0.407001i	$-0.133425\pi$
$347$	−1.34451	−	4.43226i	−0.0721772	−	0.237936i	−0.985605	+	0.169065i	$0.945925\pi$
$348$	0.242230	+	0.364886i	0.0129849	+	0.0195599i
$349$	−0.686993	−	0.563801i	−0.0367739	−	0.0301796i	0.615827	−	0.787882i	$-0.288822\pi$
$349$	−0.686993	−	0.563801i	−0.0367739	−	0.0301796i	−0.652601	+	0.757702i	$0.726322\pi$
$350$	−13.8520	−	9.28569i	−0.740422	−	0.496341i
$351$	0.195965	−	0.195965i	0.0104598	−	0.0104598i
$352$	12.1237	+	23.0965i	0.646196	+	1.23105i
$353$	4.09854	+	4.09854i	0.218143	+	0.218143i	0.807716	−	0.589572i	$-0.200704\pi$
$353$	4.09854	+	4.09854i	0.218143	+	0.218143i	−0.589572	+	0.807716i	$0.700704\pi$
$354$	−0.0640175	−	0.324378i	−0.00340249	−	0.0172405i
$355$	−5.35221	+	6.52169i	−0.284066	+	0.346135i
$356$	−3.32606	−	16.9872i	−0.176281	−	0.900319i
$357$	0.681363	−	0.206689i	0.0360615	−	0.0109391i
$358$	7.41389	−	13.8206i	0.391836	−	0.730439i
$359$	−0.341789	−	0.511524i	−0.0180390	−	0.0269972i	0.822341	−	0.568996i	$-0.192668\pi$
$359$	−0.341789	−	0.511524i	−0.0180390	−	0.0269972i	−0.840380	+	0.541998i	$0.817668\pi$
$360$	−1.27099	+	12.3358i	−0.0669870	+	0.650153i
$361$	9.36884	+	6.26006i	0.493097	+	0.329477i
$362$	−7.04686	+	23.1057i	−0.370375	+	1.21441i
$363$	0.0370475	−	0.376149i	0.00194449	−	0.0197427i
$364$	−10.2844	−	1.04406i	−0.539048	−	0.0547234i
$365$	0.890126	+	0.270017i	0.0465913	+	0.0141333i
$366$	−0.280896	+	0.280055i	−0.0146827	+	0.0146387i
$367$	−11.5332	−	27.8436i	−0.602028	−	1.45342i	−0.871490	−	0.490413i	$-0.836846\pi$
$367$	−11.5332	−	27.8436i	−0.602028	−	1.45342i	0.269463	−	0.963011i	$-0.413154\pi$
$368$	−5.02684	−	26.0880i	−0.262042	−	1.35993i
$369$	10.2859	−	24.8323i	0.535461	−	1.29272i
$370$	−5.60910	−	13.5992i	−0.291603	−	0.706987i
$371$	−6.33105	+	3.38401i	−0.328692	+	0.175689i
$372$	−0.249569	+	0.132437i	−0.0129396	+	0.00686656i
$373$	11.1415	−	9.14355i	0.576883	−	0.473435i	−0.300133	−	0.953897i	$-0.597031\pi$
$373$	11.1415	−	9.14355i	0.576883	−	0.473435i	0.877015	+	0.480462i	$0.159531\pi$
$374$	−2.95399	−	30.4603i	−0.152747	−	1.57506i
$375$	0.415209	−	0.0825901i	0.0214413	−	0.00426494i
$376$	8.01399	−	5.30282i	0.413290	−	0.273472i
$377$	−1.45534	+	7.31650i	−0.0749540	+	0.376819i
$378$	0.996198	−	0.815063i	0.0512389	−	0.0419223i
$379$	12.9442	−	24.2169i	0.664898	−	1.24394i	−0.292803	−	0.956173i	$-0.594588\pi$
$379$	12.9442	−	24.2169i	0.664898	−	1.24394i	0.957701	−	0.287765i	$-0.0929121\pi$
$380$	−6.11215	−	14.8820i	−0.313547	−	0.763432i
$381$	−0.148847	+	0.0146601i	−0.00762564	+	0.000751060i
$382$	−19.4799	+	12.9739i	−0.996679	+	0.663801i
$383$	−9.55775			−0.488378			−0.244189	−	0.969728i	$-0.578522\pi$
$383$	−9.55775			−0.488378			−0.244189	+	0.969728i	$0.578522\pi$
$384$	−0.365368	−	0.200249i	−0.0186451	−	0.0102189i
$385$	−27.7782			−1.41571
$386$	16.4663	−	10.9667i	0.838110	−	0.558192i
$387$	23.2073	−	2.28572i	1.17969	−	0.116190i
$388$	−26.0773	+	10.7101i	−1.32388	+	0.543724i
$389$	1.39647	−	2.61262i	0.0708039	−	0.132465i	−0.844029	−	0.536298i	$-0.819822\pi$
$389$	1.39647	−	2.61262i	0.0708039	−	0.132465i	0.914833	+	0.403833i	$0.132322\pi$
$390$	0.0739372	−	0.0604935i	0.00374396	−	0.00306321i
$391$	−6.08088	+	30.5707i	−0.307524	+	1.54603i
$392$	−27.6447	−	5.62818i	−1.39627	−	0.284266i
$393$	−0.598082	+	0.118966i	−0.0301692	+	0.00600103i
$394$	−2.21878	−	22.8791i	−0.111780	−	1.15263i
$395$	−0.658328	+	0.540276i	−0.0331241	+	0.0271842i
$396$	−12.9633	−	24.4284i	−0.651429	−	1.22757i
$397$	32.5659	−	17.4068i	1.63443	−	0.873623i	0.639987	−	0.768386i	$-0.278940\pi$
$397$	32.5659	−	17.4068i	1.63443	−	0.873623i	0.994447	−	0.105237i	$-0.0335601\pi$
$398$	14.8573	+	36.0213i	0.744730	+	1.80559i
$399$	−0.319440	+	0.771196i	−0.0159920	+	0.0386081i
$400$	2.30077	−	11.2150i	0.115038	−	0.560749i
$401$	7.96736	+	19.2349i	0.397871	+	0.960546i	0.988170	+	0.153361i	$0.0490099\pi$
$401$	7.96736	+	19.2349i	0.397871	+	0.960546i	−0.590299	+	0.807185i	$0.700990\pi$
$402$	−0.0151708	+	0.0151254i	−0.000756649	+	0.000754385i
$403$	−4.60510	−	1.39694i	−0.229396	−	0.0695866i
$404$	−2.10407	+	20.7260i	−0.104682	+	1.03116i
$405$	1.28809	−	13.0782i	0.0640055	−	0.649859i
$406$	−10.1071	+	33.1398i	−0.501608	+	1.64470i
$407$	27.2764	+	18.2255i	1.35204	+	0.903405i
$408$	0.308397	+	0.379247i	0.0152679	+	0.0187755i
$409$	−4.32153	−	6.46763i	−0.213686	−	0.319804i	0.709106	−	0.705102i	$-0.249099\pi$
$409$	−4.32153	−	6.46763i	−0.213686	−	0.319804i	−0.922792	+	0.385298i	$0.874099\pi$
$410$	8.76160	−	16.3329i	0.432704	−	0.806623i
$411$	−0.101511	+	0.0307930i	−0.00500716	+	0.00151890i
$412$	−3.89336	+	0.762314i	−0.191812	+	0.0375565i
$413$	16.5931	−	20.2187i	0.816491	−	0.994897i
$414$	5.45365	+	27.6337i	0.268032	+	1.35812i
$415$	−4.57613	−	4.57613i	−0.224633	−	0.224633i
$416$	−2.00910	−	6.80631i	−0.0985044	−	0.333707i
$417$	0.193575	−	0.193575i	0.00947939	−	0.00947939i
$418$	29.8012	+	19.9772i	1.45762	+	0.977116i
$419$	−9.13549	−	7.49730i	−0.446298	−	0.366267i	0.384236	−	0.923235i	$-0.374465\pi$
$419$	−9.13549	−	7.49730i	−0.446298	−	0.366267i	−0.830534	+	0.556968i	$0.811965\pi$
$420$	0.369651	−	0.245394i	0.0180371	−	0.0119740i
$421$	−10.1911	−	33.5955i	−0.496683	−	1.63735i	−0.743831	−	0.668368i	$-0.766993\pi$
$421$	−10.1911	−	33.5955i	−0.496683	−	1.63735i	0.247147	−	0.968978i	$-0.420507\pi$
$422$	−25.4523	+	7.67923i	−1.23900	+	0.373819i
$423$	−8.47092	+	5.66009i	−0.411870	+	0.275203i
$424$	−3.79550	−	3.14355i	−0.184326	−	0.152664i
$425$	−7.46216	+	11.1679i	−0.361968	+	0.541723i
$426$	0.141263	+	0.265240i	0.00684422	+	0.0128509i
$427$	−31.2273	−	3.07562i	−1.51119	−	0.148840i
$428$	−10.1700	−	5.47523i	−0.491585	−	0.264655i
$429$	−0.0618416	+	0.203865i	−0.00298574	+	0.00984268i
$430$	16.0805	+	0.0240978i	0.775472	+	0.00116210i
$431$	28.5880	−	11.8415i	1.37704	−	0.570387i	0.433349	−	0.901226i	$-0.357332\pi$
$431$	28.5880	−	11.8415i	1.37704	−	0.570387i	0.943687	+	0.330839i	$0.107332\pi$
$432$	0.776789	+	0.421209i	0.0373733	+	0.0202654i
$433$	−30.1527	−	12.4897i	−1.44905	−	0.600216i	−0.487076	−	0.873360i	$-0.661936\pi$
$433$	−30.1527	−	12.4897i	−1.44905	−	0.600216i	−0.961973	+	0.273144i	$0.911936\pi$
$434$	−20.6364	−	8.58412i	−0.990577	−	0.412051i
$435$	−0.150935	−	0.282380i	−0.00723678	−	0.0135391i
$436$	5.15609	−	6.24446i	0.246932	−	0.299055i
$437$	−23.1817	−	28.2470i	−1.10893	−	1.35124i
$438$	0.0210574	−	0.0255802i	0.00100616	−	0.00122227i
$439$	3.45004	+	17.3445i	0.164661	+	0.827808i	0.971501	+	0.237037i	$0.0761764\pi$
$439$	3.45004	+	17.3445i	0.164661	+	0.827808i	−0.806839	+	0.590771i	$0.798824\pi$
$440$	−7.21851	−	17.6511i	−0.344129	−	0.841481i
$441$	29.3349	+	5.83507i	1.39690	+	0.277861i
$442$	−0.828490	+	8.28451i	−0.0394072	+	0.394054i
$443$	−8.74870	−	4.67627i	−0.415663	−	0.222177i	0.250289	−	0.968171i	$-0.419474\pi$
$443$	−8.74870	−	4.67627i	−0.415663	−	0.222177i	−0.665952	+	0.745995i	$0.731974\pi$
$444$	−0.523978	−	0.00157044i	−0.0248669	−	7.45299e-5i
$445$	1.24037	+	12.5937i	0.0587993	+	0.597000i
$446$	31.2173	+	6.25816i	1.47818	+	0.296332i
$447$		−	0.241935i		−	0.0114431i
$448$	−6.13925	−	32.3832i	−0.290052	−	1.52996i
$449$			30.4620i			1.43759i	0.695221	+	0.718796i	$0.255306\pi$
$449$			30.4620i			1.43759i	−0.695221	+	0.718796i	$0.744694\pi$
$450$	−2.38575	+	11.9008i	−0.112465	+	0.561007i
$451$	4.05131	+	41.1337i	0.190769	+	1.93691i
$452$	24.6122	+	24.7601i	1.15766	+	1.16462i
$453$	−0.170478	−	0.0911223i	−0.00800975	−	0.00428130i
$454$	21.5273	+	2.15283i	1.01032	+	0.101037i
$455$	7.41205	+	1.47435i	0.347482	+	0.0691185i
$456$	−0.573051	−	0.00257629i	−0.0268356	−	0.000120646i
$457$	−6.06747	−	30.5032i	−0.283824	−	1.42688i	−0.814922	−	0.579571i	$-0.803220\pi$
$457$	−6.06747	−	30.5032i	−0.283824	−	1.42688i	0.531098	−	0.847311i	$-0.321780\pi$
$458$	9.53574	+	7.84972i	0.445576	+	0.366793i
$459$	−0.657670	−	0.801374i	−0.0306974	−	0.0374049i
$460$	1.84584	+	19.3351i	0.0860629	+	0.901503i
$461$	5.51400	+	10.3160i	0.256813	+	0.480463i	0.976978	−	0.213340i	$-0.0684341\pi$
$461$	5.51400	+	10.3160i	0.256813	+	0.480463i	−0.720165	+	0.693802i	$0.755934\pi$
$462$	−0.380013	+	0.913558i	−0.0176798	+	0.0425026i
$463$	−6.22097	−	2.57681i	−0.289113	−	0.119755i	0.233414	−	0.972378i	$-0.425010\pi$
$463$	−6.22097	−	2.57681i	−0.289113	−	0.119755i	−0.522526	+	0.852623i	$0.675010\pi$
$464$	−23.6845	+	2.18945i	−1.09952	+	0.101643i
$465$	0.190828	−	0.0790438i	0.00884946	−	0.00366557i
$466$	0.0155051	−	10.3466i	0.000718261	−	0.479297i
$467$	−1.52727	+	5.03474i	−0.0706737	+	0.232980i	−0.985160	−	0.171636i	$-0.945095\pi$
$467$	−1.52727	+	5.03474i	−0.0706737	+	0.232980i	0.914487	+	0.404616i	$0.132595\pi$
$468$	2.16243	+	7.20627i	0.0999585	+	0.333110i
$469$	−1.68654	−	0.166110i	−0.0778771	−	0.00767023i
$470$	−6.20070	+	3.30241i	−0.286017	+	0.152329i
$471$	−0.423515	+	0.633835i	−0.0195145	+	0.0292056i
$472$	17.1595	+	5.28962i	0.789828	+	0.243475i
$473$	−29.8167	+	19.9229i	−1.37097	+	0.916055i
$474$	0.00876228	+	0.0290420i	0.000402465	+	0.00133394i
$475$	−4.57094	−	15.0684i	−0.209729	−	0.691384i
$476$	−7.65756	+	37.9031i	−0.350984	+	1.73728i
$477$	4.03886	+	3.31461i	0.184927	+	0.151766i
$478$	1.43685	−	2.14344i	0.0657202	−	0.0980389i
$479$	6.11672	−	6.11672i	0.279480	−	0.279480i	−0.553421	−	0.832901i	$-0.686678\pi$
$479$	6.11672	−	6.11672i	0.279480	−	0.279480i	0.832901	+	0.553421i	$0.186678\pi$
$480$	0.251989	+	0.171118i	0.0115017	+	0.00781045i
$481$	−6.31083	−	6.31083i	−0.287749	−	0.287749i
$482$	28.8542	−	5.69453i	1.31427	−	0.259379i
$483$	0.639313	−	0.779006i	0.0290898	−	0.0354460i
$484$	17.0333	+	11.4553i	0.774240	+	0.520694i
$485$	19.7222	−	5.98267i	0.895539	−	0.271659i
$486$	−1.23840	−	0.664325i	−0.0561749	−	0.0301344i
$487$	21.6739	+	32.4372i	0.982136	+	1.46987i	0.879927	+	0.475108i	$0.157591\pi$
$487$	21.6739	+	32.4372i	0.982136	+	1.46987i	0.102209	+	0.994763i	$0.467409\pi$
$488$	−6.16046	−	20.6419i	−0.278871	−	0.934417i
$489$	0.0499368	+	0.0333667i	0.00225822	+	0.00150889i
$490$	19.7277	+	6.01664i	0.891208	+	0.271804i
$491$	−3.46641	+	35.1950i	−0.156437	+	1.58833i	0.521527	+	0.853235i	$0.325363\pi$
$491$	−3.46641	+	35.1950i	−0.156437	+	1.58833i	−0.677964	+	0.735095i	$0.737137\pi$
$492$	−0.417288	−	0.511586i	−0.0188128	−	0.0230641i
$493$	26.7037	+	8.10047i	1.20267	+	0.364827i
$494$	−6.89154	−	6.91223i	−0.310065	−	0.310996i
$495$	7.73698	+	18.6787i	0.347751	+	0.839546i
$496$	0.0919753	−	15.3436i	0.00412981	−	0.688950i
$497$	−9.09749	+	21.9633i	−0.408078	+	0.985188i
$498$	−0.213101	+	0.0878953i	−0.00954927	+	0.00393868i
$499$	8.99901	−	4.81007i	0.402851	−	0.215328i	−0.257512	−	0.966275i	$-0.582903\pi$
$499$	8.99901	−	4.81007i	0.402851	−	0.215328i	0.660363	+	0.750947i	$0.270403\pi$
$500$	−6.73989	+	21.9810i	−0.301417	+	0.983022i
$501$	−0.0210664	+	0.0172888i	−0.000941179	+	0.000772406i
$502$	19.3362	−	1.87519i	0.863015	−	0.0836939i
$503$	−9.40636	+	1.87104i	−0.419409	+	0.0834256i	−0.400283	−	0.916392i	$-0.631088\pi$
$503$	−9.40636	+	1.87104i	−0.419409	+	0.0834256i	−0.0191255	+	0.999817i	$0.506088\pi$
$504$	6.66300	+	34.3024i	0.296794	+	1.52795i
$505$	2.97124	−	14.9374i	0.132218	−	0.664707i
$506$	−27.4279	−	33.5233i	−1.21932	−	1.49029i
$507$	−0.198358	+	0.371102i	−0.00880938	+	0.0164812i
$508$	3.13092	−	7.49509i	0.138912	−	0.332541i
$509$	−14.2059	+	1.39916i	−0.629666	+	0.0620167i	−0.407816	−	0.913064i	$-0.633710\pi$
$509$	−14.2059	+	1.39916i	−0.629666	+	0.0620167i	−0.221850	+	0.975081i	$0.571210\pi$
$510$	−0.198091	−	0.297428i	−0.00877162	−	0.0131703i
$511$	2.62104			0.115948
$512$	18.9818	−	12.3162i	0.838887	−	0.544306i
$513$	1.21536			0.0536595
$514$	−5.22707	−	7.84830i	−0.230556	−	0.346174i
$515$	2.88640	−	0.284286i	0.127190	−	0.0125271i
$516$	0.220779	−	0.528521i	0.00971923	−	0.0232668i
$517$	7.38521	−	13.8168i	0.324801	−	0.607660i
$518$	−26.2482	−	32.0814i	−1.15328	−	1.40958i
$519$	0.0228104	−	0.114676i	0.00100126	−	0.00503370i
$520$	0.989272	+	5.09296i	0.0433824	+	0.223341i
$521$	23.7996	−	4.73403i	1.04268	−	0.207402i	0.356093	−	0.934450i	$-0.384109\pi$
$521$	23.7996	−	4.73403i	1.04268	−	0.207402i	0.686586	+	0.727049i	$0.259109\pi$
$522$	25.0991	−	2.43408i	1.09856	−	0.106537i
$523$	8.82290	−	7.24077i	0.385799	−	0.316617i	−0.421424	−	0.906864i	$-0.638470\pi$
$523$	8.82290	−	7.24077i	0.385799	−	0.316617i	0.807223	+	0.590247i	$0.200970\pi$
$524$	9.70838	−	31.6623i	0.424113	−	1.38317i
$525$	0.382983	−	0.204709i	0.0167147	−	0.00893422i
$526$	−22.5158	+	9.28683i	−0.981734	+	0.404925i
$527$	−6.88891	+	16.6313i	−0.300086	+	0.724471i
$528$	−0.679253	−	0.00407168i	−0.0295607	−	0.000177197i
$529$	8.08061	+	19.5083i	0.351331	+	0.848188i
$530$	2.54382	+	2.55146i	0.110497	+	0.110828i
$531$	−18.2172	−	5.52611i	−0.790557	−	0.239813i
$532$	−28.6540	−	35.1292i	−1.24231	−	1.52304i
$533$	1.10219	−	11.1907i	0.0477411	−	0.484724i
$534$	0.431146	+	0.131493i	0.0186575	+	0.00569024i
$535$	7.02094	+	4.69124i	0.303542	+	0.202820i
$536$	−0.332718	−	1.11484i	−0.0143712	−	0.0481538i
$537$	0.226898	+	0.339576i	0.00979135	+	0.0146538i
$538$	39.6625	+	21.2765i	1.70997	+	0.917296i
$539$	−44.0137	+	13.3514i	−1.89580	+	0.575086i
$540$	−0.536054	−	0.360508i	−0.0230681	−	0.0155138i
$541$	−24.7539	+	30.1627i	−1.06425	+	1.29680i	−0.111265	+	0.993791i	$0.535490\pi$
$541$	−24.7539	+	30.1627i	−1.06425	+	1.29680i	−0.952989	+	0.303006i	$0.902010\pi$
$542$	−23.3673	+	4.61165i	−1.00371	+	0.198087i
$543$	−0.444799	−	0.444799i	−0.0190882	−	0.0190882i
$544$	−26.0746	+	4.98376i	−1.11794	+	0.213677i
$545$	−4.18626	+	4.18626i	−0.179319	+	0.179319i
$546$	0.149887	−	0.223595i	0.00641456	−	0.00956899i
$547$	−2.48007	−	2.03534i	−0.106040	−	0.0870250i	0.579879	−	0.814703i	$-0.303100\pi$
$547$	−2.48007	−	2.03534i	−0.106040	−	0.0870250i	−0.685919	+	0.727678i	$0.740600\pi$
$548$	1.14084	−	5.64688i	0.0487342	−	0.241223i
$549$	6.62952	+	21.8546i	0.282941	+	0.932732i
$550$	−5.39133	−	17.8692i	−0.229887	−	0.761944i
$551$	−27.2012	+	18.1753i	−1.15881	+	0.774293i
$552$	0.661136	+	0.203804i	0.0281398	+	0.00867447i
$553$	−1.33322	+	1.99531i	−0.0566945	+	0.0848493i
$554$	19.4868	−	10.3784i	0.827916	−	0.440937i
$555$	0.381223	+	0.0375472i	0.0161820	+	0.00159379i
$556$	4.27308	+	14.2400i	0.181219	+	0.603909i
$557$	1.59983	−	5.27393i	0.0677869	−	0.223464i	−0.916502	−	0.400031i	$-0.868999\pi$
$557$	1.59983	−	5.27393i	0.0677869	−	0.223464i	0.984289	+	0.176567i	$0.0564994\pi$
$558$	−0.0243777	+	16.2673i	−0.00103199	+	0.688650i
$559$	9.01341	−	3.73348i	0.381227	−	0.157909i
$560$	2.21804	+	23.9938i	0.0937295	+	1.01392i
$561$	0.736256	+	0.304967i	0.0310848	+	0.0128757i
$562$	−6.66083	+	16.0128i	−0.280970	+	0.675457i
$563$	10.5560	+	19.7488i	0.444881	+	0.832313i	1.00000		0.000542432i	$0.000172662\pi$
$563$	10.5560	+	19.7488i	0.444881	+	0.832313i	−0.555119	+	0.831771i	$0.687327\pi$
$564$	0.0237810	+	0.249104i	0.00100136	+	0.0104892i
$565$	−16.1916	−	19.7295i	−0.681184	−	0.830025i
$566$	29.1950	+	24.0330i	1.22716	+	1.01018i
$567$	−7.22413	−	36.3182i	−0.303385	−	1.52522i
$568$	−16.3202	−	0.0733715i	−0.684781	−	0.00307860i
$569$	−10.1866	−	2.02625i	−0.427047	−	0.0849448i	−0.0231123	−	0.999733i	$-0.507358\pi$
$569$	−10.1866	−	2.02625i	−0.427047	−	0.0849448i	−0.403934	+	0.914788i	$0.632358\pi$
$570$	0.416866	+	0.0416886i	0.0174606	+	0.00174614i
$571$	−35.7824	−	19.1261i	−1.49745	−	0.800402i	−0.499617	−	0.866247i	$-0.666526\pi$
$571$	−35.7824	−	19.1261i	−1.49745	−	0.800402i	−0.997830	+	0.0658447i	$0.979026\pi$
$572$	−8.15651	−	8.20555i	−0.341041	−	0.343091i
$573$	−0.0597387	−	0.606537i	−0.00249562	−	0.0253384i
$574$	10.2656	−	51.2074i	0.428477	−	2.13735i
$575$			19.0102i			0.792781i
$576$	−20.0653	+	13.1478i	−0.836053	+	0.547824i
$577$		−	10.9847i		−	0.457300i	−0.973509	−	0.228650i	$-0.926569\pi$
$577$		−	10.9847i		−	0.457300i	0.973509	−	0.228650i	$-0.0734311\pi$
$578$	6.96451	+	1.39618i	0.289685	+	0.0580734i
$579$	0.0504967	+	0.512702i	0.00209857	+	0.0213072i
$580$	17.3888	+	0.0521169i	0.722030	+	0.00216404i
$581$	−16.0824	−	8.59621i	−0.667210	−	0.356631i
$582$	0.0730495	−	0.730461i	0.00302800	−	0.0302786i
$583$	−7.88025	−	1.56748i	−0.326367	−	0.0649183i
$584$	0.681111	+	1.66549i	0.0281846	+	0.0689183i
$585$	−1.07307	−	5.39469i	−0.0443660	−	0.223043i
$586$	−12.6795	+	15.4029i	−0.523786	+	0.636288i
$587$	−3.40000	−	4.14291i	−0.140333	−	0.170996i	0.698101	−	0.715999i	$-0.254029\pi$
$587$	−3.40000	−	4.14291i	−0.140333	−	0.170996i	−0.838434	+	0.545003i	$0.816529\pi$
$588$	0.467754	−	0.566489i	0.0192898	−	0.0233616i
$589$	−9.94840	−	18.6121i	−0.409917	−	0.766900i
$590$	−12.1205	−	5.04177i	−0.498993	−	0.207566i
$591$	0.553010	+	0.229064i	0.0227478	+	0.00942245i
$592$	13.5646	−	25.0156i	0.557500	−	1.02814i
$593$	−7.53473	+	3.12099i	−0.309414	+	0.128164i	−0.531987	−	0.846753i	$-0.678554\pi$
$593$	−7.53473	+	3.12099i	−0.309414	+	0.128164i	0.222573	+	0.974916i	$0.428554\pi$
$594$	1.44061	+	0.00215886i	0.0591090	+	8.85791e-5i
$595$	8.20626	−	27.0524i	0.336424	−	1.10904i
$596$	11.5691	+	6.22844i	0.473887	+	0.255127i
$597$	−1.00978	−	0.0994544i	−0.0413275	−	0.00407040i
$598$	5.53931	+	10.4008i	0.226519	+	0.425320i
$599$	−1.89809	+	2.84069i	−0.0775539	+	0.116068i	−0.868219	−	0.496182i	$-0.834735\pi$
$599$	−1.89809	+	2.84069i	−0.0775539	+	0.116068i	0.790665	+	0.612249i	$0.209735\pi$
$600$	0.229601	+	0.190162i	0.00937341	+	0.00776334i
$601$	7.39859	−	4.94358i	0.301795	−	0.201653i	−0.395447	−	0.918489i	$-0.629410\pi$
$601$	7.39859	−	4.94358i	0.301795	−	0.201653i	0.697242	+	0.716836i	$0.254410\pi$
$602$	43.3800	−	13.0882i	1.76804	−	0.533436i
$603$	0.358051	+	1.18034i	0.0145810	+	0.0480670i
$604$	8.74621	−	5.80619i	0.355878	−	0.236250i
$605$	−11.6003	−	9.52013i	−0.471620	−	0.387048i
$606$	−0.450609	−	0.302065i	−0.0183047	−	0.0122706i
$607$	18.5682	−	18.5682i	0.753658	−	0.753658i	−0.221502	−	0.975160i	$-0.571096\pi$
$607$	18.5682	−	18.5682i	0.753658	−	0.753658i	0.975160	+	0.221502i	$0.0710958\pi$
$608$	14.8760	−	27.3363i	0.603301	−	1.10863i
$609$	−0.637963	−	0.637963i	−0.0258516	−	0.0258516i
$610$	3.04922	+	15.4504i	0.123459	+	0.625570i
$611$	−2.70393	+	3.29475i	−0.109389	+	0.133291i
$612$	27.6198	−	5.40791i	1.11646	−	0.218602i
$613$	14.0986	−	4.27676i	0.569437	−	0.172737i	0.00757992	−	0.999971i	$-0.497587\pi$
$613$	14.0986	−	4.27676i	0.569437	−	0.172737i	0.561857	+	0.827235i	$0.310087\pi$
$614$	6.32489	−	11.7905i	0.255252	−	0.475826i
$615$	0.268143	+	0.401305i	0.0108126	+	0.0161822i
$616$	−33.9022	−	41.6907i	−1.36596	−	1.67977i
$617$	12.6257	+	8.43625i	0.508293	+	0.339631i	0.783128	−	0.621861i	$-0.213623\pi$
$617$	12.6257	+	8.43625i	0.508293	+	0.339631i	−0.274835	+	0.961492i	$0.588623\pi$
$618$	0.0301373	−	0.0988161i	0.00121230	−	0.00397497i
$619$	−1.46662	+	14.8908i	−0.0589484	+	0.598513i	0.919651	+	0.392737i	$0.128472\pi$
$619$	−1.46662	+	14.8908i	−0.0589484	+	0.598513i	−0.978599	+	0.205776i	$0.934028\pi$
$620$	−1.13296	+	11.1601i	−0.0455008	+	0.448202i
$621$	−1.40409	−	0.425927i	−0.0563444	−	0.0170919i
$622$	2.03319	−	2.02710i	0.0815234	−	0.0812794i
$623$	13.6457	+	32.9437i	0.546705	+	1.31986i
$624$	0.181029	+	0.0371383i	0.00724695	+	0.00148672i
$625$	0.955738	−	2.30736i	0.0382295	−	0.0922943i
$626$	−12.4704	−	30.2344i	−0.498419	−	1.20841i
$627$	−0.823947	+	0.440409i	−0.0329053	+	0.0175882i
$628$	−19.4062	−	36.5697i	−0.774392	−	1.45929i
$629$	−25.8074	+	21.1795i	−1.02901	+	0.844484i
$630$	−2.46587	−	25.4269i	−0.0982424	−	1.01303i
$631$	1.74029	−	0.346165i	0.0692798	−	0.0137806i	−0.160329	−	0.987064i	$-0.551255\pi$
$631$	1.74029	−	0.346165i	0.0692798	−	0.0137806i	0.229609	+	0.973283i	$0.426255\pi$
$632$	−1.61433	−	0.328663i	−0.0642148	−	0.0130735i
$633$	0.135060	−	0.678994i	0.00536817	−	0.0269876i
$634$	5.97662	−	4.88992i	0.237362	−	0.194203i
$635$	−2.79930	+	5.23712i	−0.111087	+	0.207829i
$636$	0.118712	−	0.0487556i	0.00470722	−	0.00193329i
$637$	12.4528	−	1.22649i	0.493398	−	0.0485955i
$638$	−32.2749	+	21.4955i	−1.27777	+	0.851014i
$639$	17.3025			0.684478
$640$	−14.6700	+	7.64450i	−0.579881	+	0.302175i
$641$	−29.2868			−1.15676			−0.578379	−	0.815768i	$-0.696314\pi$
$641$	−29.2868			−1.15676			−0.578379	+	0.815768i	$0.696314\pi$
$642$	0.250332	−	0.166724i	0.00987982	−	0.00658009i
$643$	−13.7849	+	1.35770i	−0.543625	+	0.0535424i	−0.366103	−	0.930574i	$-0.619308\pi$
$643$	−13.7849	+	1.35770i	−0.543625	+	0.0535424i	−0.177522	+	0.984117i	$0.556808\pi$
$644$	20.7925	+	50.6262i	0.819340	+	1.99495i
$645$	−0.197394	+	0.369299i	−0.00777239	+	0.0145411i
$646$	−28.2591	+	23.1209i	−1.11184	+	0.909679i
$647$	7.47571	−	37.5829i	0.293900	−	1.47754i	−0.498155	−	0.867088i	$-0.665989\pi$
$647$	7.47571	−	37.5829i	0.293900	−	1.47754i	0.792055	−	0.610449i	$-0.209011\pi$
$648$	21.2003	−	14.0282i	0.832828	−	0.551078i
$649$	28.7119	−	5.71115i	1.12704	−	0.224182i
$650$	0.490147	+	5.05418i	0.0192251	+	0.198241i
$651$	0.449905	−	0.369227i	0.0176331	−	0.0144712i
$652$	−2.88115	+	1.52892i	−0.112834	+	0.0598771i
$653$	34.0910	−	18.2220i	1.33409	−	0.713083i	0.358671	−	0.933464i	$-0.383230\pi$
$653$	34.0910	−	18.2220i	1.33409	−	0.713083i	0.975414	+	0.220381i	$0.0707299\pi$
$654$	0.0804068	+	0.194945i	0.00314416	+	0.00762296i
$655$	−9.26518	+	22.3681i	−0.362021	+	0.873995i
$656$	35.2063	−	6.78384i	1.37457	−	0.264864i
$657$	−0.730031	−	1.76245i	−0.0284812	−	0.0687598i
$658$	−14.0186	+	13.9767i	−0.546504	+	0.544868i
$659$	−28.5921	−	8.67331i	−1.11379	−	0.337864i	−0.320828	−	0.947137i	$-0.603961\pi$
$659$	−28.5921	−	8.67331i	−1.11379	−	0.337864i	−0.792960	+	0.609273i	$0.791461\pi$
$660$	0.494052	+	0.0501554i	0.0192309	+	0.00195230i
$661$	−0.474420	+	4.81687i	−0.0184528	+	0.187354i	−0.999992	−	0.00390476i	$-0.998757\pi$
$661$	−0.474420	+	4.81687i	−0.0184528	+	0.187354i	0.981540	+	0.191259i	$0.0612571\pi$
$662$	−1.96631	+	6.44724i	−0.0764226	+	0.250579i
$663$	−0.180269	−	0.120452i	−0.00700106	−	0.00467796i
$664$	1.28307	−	12.4530i	0.0497929	−	0.483272i
$665$	18.4126	+	27.5565i	0.714012	+	1.06859i
$666$	−14.2615	+	26.5855i	−0.552622	+	1.03017i
$667$	37.7949	−	11.4650i	1.46342	−	0.443925i
$668$	−0.284390	−	1.45246i	−0.0110034	−	0.0561974i
$669$	−0.525965	+	0.640891i	−0.0203350	+	0.0247783i
$670$	0.164684	+	0.834456i	0.00636230	+	0.0322378i
$671$	−24.8334	−	24.8334i	−0.958681	−	0.958681i
$672$	0.819442	+	0.255295i	0.0316107	+	0.00984823i
$673$	−12.6838	+	12.6838i	−0.488923	+	0.488923i	−0.907966	−	0.419043i	$-0.862366\pi$
$673$	−12.6838	+	12.6838i	−0.488923	+	0.488923i	0.419043	+	0.907966i	$0.362366\pi$
$674$	−28.1836	−	18.8928i	−1.08559	−	0.727725i
$675$	−0.488755	−	0.401111i	−0.0188122	−	0.0154388i
$676$	−12.6391	−	19.0390i	−0.486119	−	0.732269i
$677$	2.87578	+	9.48019i	0.110525	+	0.364353i	0.994702	−	0.102799i	$-0.0327799\pi$
$677$	2.87578	+	9.48019i	0.110525	+	0.364353i	−0.884177	+	0.467153i	$0.845280\pi$
$678$	−0.870360	+	0.262597i	−0.0334260	+	0.0100850i
$679$	48.2863	−	32.2639i	1.85306	−	1.23817i
$680$	19.3224	−	1.81542i	0.740980	−	0.0696181i
$681$	−0.312994	+	0.468428i	−0.0119939	+	0.0179502i
$682$	−11.7591	−	22.0793i	−0.450280	−	0.845460i
$683$	28.6573	+	2.82250i	1.09654	+	0.108000i	0.630071	−	0.776537i	$-0.283026\pi$
$683$	28.6573	+	2.82250i	1.09654	+	0.108000i	0.466470	+	0.884537i	$0.345526\pi$
$684$	−15.6408	+	29.0521i	−0.598040	+	1.11083i
$685$	−1.22259	+	4.03032i	−0.0467126	+	0.153991i
$686$	17.3303	+	0.0259707i	0.661675	+	0.000991568i
$687$	−0.297143	+	0.123081i	−0.0113367	+	0.00469583i
$688$	19.5895	+	24.1638i	0.746842	+	0.921236i
$689$	2.01949	+	0.836501i	0.0769365	+	0.0318681i
$690$	−0.466991	−	0.194254i	−0.0177780	−	0.00739513i
$691$	15.7704	+	29.5043i	0.599934	+	1.12240i	0.980291	+	0.197558i	$0.0633010\pi$
$691$	15.7704	+	29.5043i	0.599934	+	1.12240i	−0.380357	+	0.924840i	$0.624199\pi$
$692$	4.89642	+	4.04301i	0.186134	+	0.153692i
$693$	36.1408	+	44.0377i	1.37287	+	1.67285i
$694$	−4.16299	+	5.05715i	−0.158025	+	0.191967i
$695$	−2.12045	−	10.6602i	−0.0804331	−	0.404364i
$696$	0.239597	−	0.571163i	0.00908192	−	0.0216499i
$697$	−41.2558	−	8.20629i	−1.56268	−	0.310835i
$698$	−0.125067	+	1.25061i	−0.00473384	+	0.0473362i
$699$	0.237616	+	0.127008i	0.00898744	+	0.00480389i
$700$	−0.0706845	+	23.5839i	−0.00267162	+	0.891388i
$701$	−4.23637	−	43.0126i	−0.160006	−	1.62456i	−0.654973	−	0.755653i	$-0.727320\pi$
$701$	−4.23637	−	43.0126i	−0.160006	−	1.62456i	0.494967	−	0.868912i	$-0.335180\pi$
$702$	−0.384284	−	0.0770376i	−0.0145038	−	0.00290760i
$703$		−	39.1394i		−	1.47617i
$704$	17.6816	−	32.3763i	0.666400	−	1.22023i
$705$		−	0.182941i		−	0.00688995i
$706$	1.61122	−	8.03717i	0.0606390	−	0.302483i
$707$	−4.20640	−	42.7083i	−0.158198	−	1.60621i
$708$	−0.331624	+	0.329642i	−0.0124632	+	0.0123887i
$709$	−27.6144	−	14.7602i	−1.03708	−	0.554332i	−0.137236	−	0.990538i	$-0.543822\pi$
$709$	−27.6144	−	14.7602i	−1.03708	−	0.554332i	−0.899847	+	0.436206i	$0.856322\pi$
$710$	11.8721	+	1.18727i	0.445553	+	0.0445574i
$711$	1.71304	+	0.340744i	0.0642438	+	0.0127789i
$712$	−17.3874	+	17.2317i	−0.651620	+	0.645787i
$713$	4.97059	+	24.9889i	0.186150	+	0.935840i
$714$	−0.777426	−	0.639969i	−0.0290944	−	0.0239502i
$715$	5.36591	+	6.53838i	0.200674	+	0.244522i
$716$	−22.0795	+	2.10784i	−0.825149	+	0.0787737i
$717$	0.0316763	+	0.0592623i	0.00118297	+	0.00221319i
$718$	−0.334151	+	0.803304i	−0.0124704	+	0.0299790i
$719$	6.58340	+	2.72694i	0.245520	+	0.101698i	0.502050	−	0.864839i	$-0.332579\pi$
$719$	6.58340	+	2.72694i	0.245520	+	0.101698i	−0.256530	+	0.966536i	$0.582579\pi$
$720$	15.5162	−	8.17439i	0.578255	−	0.304642i
$721$	7.55051	−	3.12752i	0.281196	−	0.116475i
$722$	0.0238799	−	15.9351i	0.000888717	−	0.593042i
$723$	−0.222320	+	0.732890i	−0.00826816	+	0.0272565i
$724$	32.7208	−	9.81876i	1.21606	−	0.364911i
$725$	16.9374	+	1.66819i	0.629038	+	0.0619549i
$726$	−0.471790	+	0.251269i	−0.0175098	+	0.00932546i
$727$	−25.1421	+	37.6278i	−0.932469	+	1.39554i	−0.0140614	+	0.999901i	$0.504476\pi$
$727$	−25.1421	+	37.6278i	−0.932469	+	1.39554i	−0.918407	+	0.395637i	$0.870524\pi$
$728$	6.83335	+	12.9237i	0.253261	+	0.478985i
$729$	−22.3888	+	14.9597i	−0.829215	+	0.554064i
$730$	−0.379974	−	1.25940i	−0.0140635	−	0.0466124i
$731$	−10.5939	−	34.9233i	−0.391829	−	1.29169i
$732$	0.549842	+	0.111085i	0.0203228	+	0.00410581i
$733$	14.1244	+	11.5916i	0.521696	+	0.428145i	0.858031	−	0.513597i	$-0.171688\pi$
$733$	14.1244	+	11.5916i	0.521696	+	0.428145i	−0.336335	+	0.941742i	$0.609188\pi$
$734$	−23.7321	+	35.4026i	−0.875968	+	1.30674i
$735$	−0.379771	+	0.379771i	−0.0140081	+	0.0140081i
$736$	−26.7662	+	26.3680i	−0.986614	+	0.971939i
$737$	−1.34121	−	1.34121i	−0.0494042	−	0.0494042i
$738$	−37.2923	+	7.35982i	−1.37275	+	0.270919i
$739$	32.0860	−	39.0969i	1.18030	−	1.43820i	0.306533	−	0.951860i	$-0.400831\pi$
$739$	32.0860	−	39.0969i	1.18030	−	1.43820i	0.873769	−	0.486342i	$-0.161669\pi$
$740$	−11.6098	+	17.2630i	−0.426784	+	0.634602i
$741$	0.243229	−	0.0737827i	0.00893524	−	0.00271047i
$742$	8.94627	+	4.79913i	0.328428	+	0.176182i
$743$	11.1144	+	16.6338i	0.407747	+	0.610236i	0.977336	−	0.211693i	$-0.0678977\pi$
$743$	11.1144	+	16.6338i	0.407747	+	0.610236i	−0.569589	+	0.821929i	$0.692898\pi$
$744$	0.351531	+	0.189934i	0.0128878	+	0.00696332i
$745$	−7.98679	−	5.33660i	−0.292613	−	0.195518i
$746$	−19.4966	−	5.94614i	−0.713820	−	0.217704i
$747$	−1.30092	+	13.2085i	−0.0475982	+	0.483272i
$748$	−33.5376	+	27.3558i	−1.22626	+	1.00023i
$749$	22.7688	+	6.90685i	0.831955	+	0.252371i
$750$	−0.422708	−	0.423977i	−0.0154351	−	0.0154814i
$751$	−4.58067	−	11.0587i	−0.167151	−	0.403538i	0.818002	−	0.575215i	$-0.195082\pi$
$751$	−4.58067	−	11.0587i	−0.167151	−	0.403538i	−0.985153	+	0.171677i	$0.945082\pi$
$752$	−12.5241	−	5.27583i	−0.456708	−	0.192390i
$753$	−0.193593	+	0.467375i	−0.00705492	+	0.0170321i
$754$	9.75279	−	4.02263i	0.355176	−	0.146495i
$755$	−6.76855	+	3.61787i	−0.246333	+	0.131668i
$756$	−1.74032	−	0.533622i	−0.0632949	−	0.0194077i
$757$	−7.67831	+	6.30143i	−0.279073	+	0.229029i	−0.763509	−	0.645798i	$-0.776525\pi$
$757$	−7.67831	+	6.30143i	−0.279073	+	0.229029i	0.484436	+	0.874827i	$0.339025\pi$
$758$	−38.6519	+	3.74840i	−1.40390	+	0.136148i
$759$	1.10624	−	0.220045i	0.0401540	−	0.00798712i
$760$	−12.7254	+	18.8608i	−0.461599	+	0.684154i
$761$	0.964534	−	4.84904i	0.0349643	−	0.175778i	−0.959357	−	0.282194i	$-0.908938\pi$
$761$	0.964534	−	4.84904i	0.0349643	−	0.175778i	0.994322	+	0.106417i	$0.0339377\pi$
$762$	0.133941	+	0.163708i	0.00485218	+	0.00593050i
$763$	−7.86384	+	14.7122i	−0.284690	+	0.532617i
$764$	30.5419	+	12.7582i	1.10497	+	0.461576i
$765$	−20.4764	+	2.01675i	−0.740325	+	0.0729156i
$766$	7.49263	+	11.2500i	0.270720	+	0.406478i
$767$	−7.96432			−0.287575
$768$	0.0507203	+	0.587039i	0.00183021	+	0.0211829i
$769$	15.1231			0.545352			0.272676	−	0.962106i	$-0.412091\pi$
$769$	15.1231			0.545352			0.272676	+	0.962106i	$0.412091\pi$
$770$	21.7762	+	32.6964i	0.784760	+	1.17829i
$771$	0.244369	−	0.0240682i	0.00880073	−	0.000866796i
$772$	−25.8168	−	10.7845i	−0.929168	−	0.388141i
$773$	−3.39052	+	6.34322i	−0.121949	+	0.228150i	−0.935487	−	0.353362i	$-0.885038\pi$
$773$	−3.39052	+	6.34322i	−0.121949	+	0.228150i	0.813538	+	0.581511i	$0.197538\pi$
$774$	−20.8834	−	25.5243i	−0.750637	−	0.917454i
$775$	−2.14192	+	10.7681i	−0.0769399	+	0.386803i
$776$	33.0492	+	22.2984i	1.18640	+	0.800464i
$777$	1.05866	−	0.210580i	0.0379792	−	0.00755453i
$778$	−4.16992	+	0.404393i	−0.149499	+	0.0144982i
$779$	38.1200	−	31.2842i	1.36579	−	1.12087i
$780$	−0.129166	−	0.0396051i	−0.00462488	−	0.00141809i
$781$	−23.4656	+	12.5426i	−0.839666	+	0.448811i
$782$	40.7503	−	16.8078i	1.45723	−	0.601046i
$783$	−0.502697	+	1.21362i	−0.0179649	+	0.0433712i
$784$	15.0469	+	36.9513i	0.537389	+	1.31969i
$785$	11.5824	+	27.9623i	0.413392	+	0.998018i
$786$	0.608884	+	0.610712i	0.0217182	+	0.0217834i
$787$	6.49153	+	1.96918i	0.231398	+	0.0701938i	0.403854	−	0.914823i	$-0.367670\pi$
$787$	6.49153	+	1.96918i	0.231398	+	0.0701938i	−0.172456	+	0.985017i	$0.555170\pi$
$788$	−25.1905	+	20.5473i	−0.897374	+	0.731965i
$789$	0.0621658	−	0.631180i	0.00221316	−	0.0224706i
$790$	1.15202	+	0.351347i	0.0409870	+	0.0125004i
$791$	−59.7976	−	39.9555i	−2.12616	−	1.42065i
$792$	−18.5912	+	34.4086i	−0.660609	+	1.22266i
$793$	5.30824	+	7.94434i	0.188501	+	0.282112i
$794$	−46.0181	−	24.6859i	−1.63312	−	0.876071i
$795$	−0.0897812	+	0.0272348i	−0.00318421	+	0.000965920i
$796$	30.7518	−	45.7261i	1.08997	−	1.62072i
$797$	−8.96855	+	10.9282i	−0.317682	+	0.387097i	−0.907229	−	0.420637i	$-0.861806\pi$
$797$	−8.96855	+	10.9282i	−0.317682	+	0.387097i	0.589546	+	0.807734i	$0.299306\pi$
$798$	1.15816	−	0.228568i	0.0409983	−	0.00809122i
$799$	11.2740	+	11.2740i	0.398846	+	0.398846i
$800$	−15.0043	+	6.08366i	−0.530481	+	0.215090i
$801$	18.3515	−	18.3515i	0.648417	−	0.648417i
$802$	16.3946	−	24.4569i	0.578914	−	0.863602i
$803$	2.26767	+	1.86103i	0.0800242	+	0.0656742i
$804$	0.0296962	+	0.00599952i	0.00104730	+	0.000211587i
$805$	−11.6147	−	38.2885i	−0.409364	−	1.34949i
$806$	1.96581	+	6.51555i	0.0692428	+	0.229500i
$807$	−0.974523	+	0.651156i	−0.0343048	+	0.0229218i
$808$	26.0450	−	13.7712i	0.916261	−	0.484468i
$809$	3.68268	−	5.51152i	0.129476	−	0.193775i	−0.761067	−	0.648673i	$-0.775324\pi$
$809$	3.68268	−	5.51152i	0.129476	−	0.193775i	0.890543	+	0.454898i	$0.150324\pi$
$810$	−16.4034	+	8.73624i	−0.576358	+	0.306960i
$811$	−10.3923	−	1.02355i	−0.364922	−	0.0359417i	−0.0861056	−	0.996286i	$-0.527442\pi$
$811$	−10.3923	−	1.02355i	−0.364922	−	0.0359417i	−0.278817	+	0.960344i	$0.589942\pi$
$812$	46.9306	−	14.0828i	1.64694	−	0.494209i
$813$	0.180043	−	0.593523i	0.00631439	−	0.0208157i
$814$	0.0695237	−	46.3933i	0.00243681	−	1.62608i
$815$	2.20301	−	0.912518i	0.0771682	−	0.0319641i
$816$	0.204631	−	0.660303i	0.00716351	−	0.0231152i
$817$	39.5277	+	16.3729i	1.38290	+	0.572816i
$818$	−4.22495	+	10.1568i	−0.147722	+	0.355126i
$819$	−7.30611	−	13.6688i	−0.255296	−	0.477625i
$820$	−26.0931	+	2.49101i	−0.911212	+	0.0869898i
$821$	22.0551	+	26.8742i	0.769729	+	0.937917i	0.999375	−	0.0353570i	$-0.0112568\pi$
$821$	22.0551	+	26.8742i	0.769729	+	0.937917i	−0.229646	+	0.973274i	$0.573757\pi$
$822$	0.115822	+	0.0953439i	0.00403977	+	0.00332550i
$823$	0.0833099	+	0.418827i	0.00290400	+	0.0145994i	0.982210	−	0.187785i	$-0.0601309\pi$
$823$	0.0833099	+	0.418827i	0.00290400	+	0.0145994i	−0.979306	+	0.202385i	$0.935131\pi$
$824$	3.94941	+	3.98508i	0.137584	+	0.138827i
$825$	0.476699	+	0.0948212i	0.0165965	+	0.00330125i
$826$	−36.8063	−	3.68080i	−1.28065	−	0.128071i
$827$	44.0310	+	23.5351i	1.53111	+	0.818395i	0.999589	−	0.0286512i	$-0.00912122\pi$
$827$	44.0310	+	23.5351i	1.53111	+	0.818395i	0.531520	+	0.847046i	$0.321621\pi$
$828$	28.2510	−	28.0822i	0.981791	−	0.975923i
$829$	2.49627	+	25.3450i	0.0866989	+	0.880269i	0.935916	+	0.352224i	$0.114575\pi$
$829$	2.49627	+	25.3450i	0.0866989	+	0.880269i	−0.849217	+	0.528044i	$0.822925\pi$
$830$	−1.79897	+	8.97372i	−0.0624431	+	0.311482i
$831$			0.574925i			0.0199439i
$832$	−6.43637	+	7.70050i	−0.223141	+	0.266967i
$833$		−	46.8080i		−	1.62180i
$834$	−0.379597	−	0.0760980i	−0.0131444	−	0.00263506i
$835$	0.106056	+	1.07681i	0.00367022	+	0.0372644i
$836$	0.152070	−	50.7383i	0.00525946	−	1.75482i
$837$	−0.747345	−	0.399464i	−0.0258320	−	0.0138075i
$838$	−1.66311	+	16.6303i	−0.0574512	+	0.574485i
$839$	41.2437	+	8.20388i	1.42389	+	0.283229i	0.846130	−	0.532977i	$-0.178927\pi$
$839$	41.2437	+	8.20388i	1.42389	+	0.283229i	0.577761	+	0.816206i	$0.303927\pi$
$840$	−0.578622	−	0.242726i	−0.0199644	−	0.00837486i
$841$	−1.24063	−	6.23709i	−0.0427805	−	0.215072i
$842$	−31.5546	+	38.3321i	−1.08744	+	1.32101i
$843$	−0.286501	−	0.349103i	−0.00986762	−	0.0120237i
$844$	28.9917	+	23.9387i	0.997936	+	0.824003i
$845$	7.87548	+	14.7340i	0.270925	+	0.506865i
$846$	13.3028	+	5.53359i	0.457361	+	0.190249i
$847$	−39.0667	−	16.1820i	−1.34235	−	0.556019i
$848$	−0.724706	+	6.93184i	−0.0248865	+	0.238040i
$849$	−0.909745	+	0.376829i	−0.0312224	+	0.0129327i
$850$	18.9950	+	0.0284654i	0.651524	+	0.000976356i
$851$	−13.7165	+	45.2173i	−0.470196	+	1.55003i
$852$	0.201461	−	0.374204i	0.00690192	−	0.0128200i
$853$	13.3262	+	1.31251i	0.456280	+	0.0449396i	0.323547	−	0.946212i	$-0.395125\pi$
$853$	13.3262	+	1.31251i	0.456280	+	0.0449396i	0.132733	+	0.991152i	$0.457625\pi$
$854$	20.8599	+	39.1672i	0.713811	+	1.34027i
$855$	13.4012	−	20.0563i	0.458312	−	0.685912i
$856$	1.52796	+	16.2628i	0.0522245	+	0.555851i
$857$	−5.67506	+	3.79196i	−0.193856	+	0.129531i	−0.648711	−	0.761035i	$-0.724691\pi$
$857$	−5.67506	+	3.79196i	−0.193856	+	0.129531i	0.454854	+	0.890566i	$0.349691\pi$
$858$	0.288439	−	0.0870252i	0.00984714	−	0.00297099i
$859$	7.54947	+	24.8873i	0.257585	+	0.849143i	0.986390	+	0.164422i	$0.0525759\pi$
$859$	7.54947	+	24.8873i	0.257585	+	0.849143i	−0.728805	+	0.684721i	$0.759924\pi$
$860$	−12.5777	−	18.9465i	−0.428895	−	0.646070i
$861$	1.05129	+	0.862768i	0.0358277	+	0.0294030i
$862$	−36.3492	−	24.3666i	−1.23806	−	0.829930i
$863$	−6.48415	+	6.48415i	−0.220723	+	0.220723i	−0.808803	−	0.588080i	$-0.799884\pi$
$863$	−6.48415	+	6.48415i	−0.220723	+	0.220723i	0.588080	+	0.808803i	$0.299884\pi$
$864$	−0.113166	−	1.24452i	−0.00384998	−	0.0423394i
$865$	−3.28254	−	3.28254i	−0.111610	−	0.111610i
$866$	8.93671	+	45.2824i	0.303682	+	1.53876i
$867$	−0.117342	+	0.142981i	−0.00398513	+	0.00485589i
$868$	6.07356	+	31.0194i	0.206150	+	1.05287i
$869$	−2.57022	+	0.779666i	−0.0871886	+	0.0264484i
$870$	−0.214053	+	0.399025i	−0.00725706	+	0.0135282i
$871$	0.286690	+	0.429062i	0.00971412	+	0.0145382i
$872$	−11.3921	−	1.17376i	−0.385784	−	0.0397484i
$873$	−35.1441	−	23.4825i	−1.18945	−	0.794763i
$874$	−15.0753	+	49.4298i	−0.509929	+	1.67199i
$875$	4.64226	−	47.1336i	0.156937	−	1.59341i
$876$	−0.0466168	−	0.00473247i	−0.00157504	−	0.000159895i
$877$	−8.61441	−	2.61315i	−0.290888	−	0.0882399i	0.141468	−	0.989943i	$-0.454818\pi$
$877$	−8.61441	−	2.61315i	−0.290888	−	0.0882399i	−0.432356	+	0.901703i	$0.642318\pi$
$878$	17.7108	−	17.6578i	0.597710	−	0.595922i
$879$	−0.198810	−	0.479971i	−0.00670571	−	0.0161890i
$880$	−15.1174	+	22.3338i	−0.509607	+	0.752872i
$881$	−2.60377	+	6.28607i	−0.0877234	+	0.211783i	−0.961653	−	0.274270i	$-0.911564\pi$
$881$	−2.60377	+	6.28607i	−0.0877234	+	0.211783i	0.873929	+	0.486053i	$0.161564\pi$
$882$	−16.1284	−	39.1030i	−0.543071	−	1.31667i
$883$	−15.3984	+	8.23060i	−0.518196	+	0.276982i	−0.709692	−	0.704512i	$-0.751166\pi$
$883$	−15.3984	+	8.23060i	−0.518196	+	0.276982i	0.191496	+	0.981493i	$0.438666\pi$
$884$	10.4008	−	5.51931i	0.349816	−	0.185635i
$885$	0.264246	−	0.216861i	0.00888252	−	0.00728970i
$886$	1.35416	+	13.9635i	0.0454940	+	0.469115i
$887$	4.15051	−	0.825587i	0.139360	−	0.0277205i	−0.124917	−	0.992167i	$-0.539867\pi$
$887$	4.15051	−	0.825587i	0.139360	−	0.0277205i	0.264278	+	0.964447i	$0.414867\pi$
$888$	0.408915	+	0.617981i	0.0137223	+	0.0207381i
$889$	−3.26442	+	16.4113i	−0.109485	+	0.550419i
$890$	13.8511	−	11.3326i	0.464290	−	0.379870i
$891$	19.5370	−	36.5511i	0.654513	−	1.22451i
$892$	−17.1061	−	41.6504i	−0.572754	−	1.39456i
$893$	−18.6017	+	1.83211i	−0.622483	+	0.0613093i
$894$	−0.284770	+	0.189660i	−0.00952412	+	0.00634319i
$895$	16.2151			0.542010
$896$	−33.3039	+	32.6124i	−1.11261	+	1.08950i
$897$	−0.306857			−0.0102457
$898$	35.8554	−	23.8802i	1.19651	−	0.796891i
$899$	22.7003	−	2.23578i	0.757097	−	0.0745676i
$900$	15.8781	−	6.52123i	0.529269	−	0.217374i
$901$	3.85452	−	7.21130i	0.128413	−	0.240243i
$902$	45.2405	−	37.0146i	1.50634	−	1.23245i
$903$	−0.230192	+	1.15725i	−0.00766032	+	0.0385110i
$904$	9.84970	−	48.3800i	0.327596	−	1.60910i
$905$	−24.4952	+	4.87239i	−0.814247	+	0.161964i
$906$	0.0263874	+	0.272095i	0.000876662	+	0.00903975i
$907$	−39.5891	+	32.4899i	−1.31453	+	1.07881i	−0.323354	+	0.946278i	$0.604811\pi$
$907$	−39.5891	+	32.4899i	−1.31453	+	1.07881i	−0.991179	+	0.132532i	$0.957689\pi$
$908$	−14.3419	−	27.0264i	−0.475953	−	0.896902i
$909$	−27.5465	+	14.7239i	−0.913661	+	0.488362i
$910$	−4.07516	−	9.88016i	−0.135090	−	0.327524i
$911$	6.88722	−	16.6272i	0.228184	−	0.550884i	−0.767773	−	0.640722i	$-0.778635\pi$
$911$	6.88722	−	16.6272i	0.228184	−	0.550884i	0.995956	+	0.0898381i	$0.0286350\pi$
$912$	0.446200	+	0.676530i	0.0147752	+	0.0224021i
$913$	−7.81053	−	18.8563i	−0.258491	−	0.624052i
$914$	−31.1474	+	31.0542i	−1.03026	+	1.02718i
$915$	−0.392437	−	0.119044i	−0.0129736	−	0.00393549i
$916$	1.76416	−	17.3777i	0.0582894	−	0.574175i
$917$	−6.68688	+	67.8930i	−0.220820	+	2.24203i
$918$	−0.427689	+	1.40233i	−0.0141159	+	0.0462839i
$919$	−6.13433	−	4.09883i	−0.202353	−	0.135208i	0.450265	−	0.892895i	$-0.351329\pi$
$919$	−6.13433	−	4.09883i	−0.202353	−	0.135208i	−0.652618	+	0.757687i	$0.726329\pi$
$920$	21.3114	−	17.3300i	0.702615	−	0.571355i
$921$	0.193569	+	0.289697i	0.00637833	+	0.00954585i
$922$	7.81983	−	14.5773i	0.257532	−	0.480077i
$923$	6.92704	−	2.10129i	0.228006	−	0.0691650i
$924$	1.37321	−	0.268872i	0.0451753	−	0.00884525i
$925$	−12.9173	+	15.7398i	−0.424719	+	0.517522i
$926$	1.84378	+	9.34245i	0.0605903	+	0.307012i
$927$	−4.20604	−	4.20604i	−0.138145	−	0.138145i
$928$	21.1441	+	26.1615i	0.694090	+	0.858793i
$929$	32.3233	−	32.3233i	1.06049	−	1.06049i	0.0624437	−	0.998048i	$-0.480111\pi$
$929$	32.3233	−	32.3233i	1.06049	−	1.06049i	0.998048	−	0.0624437i	$-0.0198894\pi$
$930$	−0.242635	−	0.162650i	−0.00795632	−	0.00533351i
$931$	42.4191	+	34.8125i	1.39023	+	1.14093i
$932$	−12.1906	+	8.09278i	−0.399318	+	0.265088i
$933$	0.0217027	+	0.0715442i	0.000710514	+	0.00234225i
$934$	7.12343	−	2.14922i	0.233086	−	0.0703245i
$935$	26.3080	−	17.5784i	0.860364	−	0.574877i
$936$	6.78695	−	8.19452i	0.221838	−	0.267846i
$937$	26.5714	−	39.7669i	0.868050	−	1.29913i	−0.0850202	−	0.996379i	$-0.527095\pi$
$937$	26.5714	−	39.7669i	0.868050	−	1.29913i	0.953070	−	0.302749i	$-0.0979045\pi$
$938$	1.12661	+	2.11536i	0.0367852	+	0.0690690i
$939$	0.847554	+	0.0834768i	0.0276589	+	0.00272416i
$940$	8.74803	+	4.70969i	0.285329	+	0.153613i
$941$	−6.11264	+	20.1507i	−0.199266	+	0.656893i	0.799176	+	0.601097i	$0.205270\pi$
$941$	−6.11264	+	20.1507i	−0.199266	+	0.656893i	−0.998442	+	0.0557960i	$0.982230\pi$
$942$	1.07806	+	0.00161556i	0.0351252	+	5.26377e-5i
$943$	−55.0032	+	22.7831i	−1.79115	+	0.741919i
$944$	−7.22569	−	24.3443i	−0.235176	−	0.792339i
$945$	1.22947	+	0.509262i	0.0399946	+	0.0165663i
$946$	46.8245	+	19.4776i	1.52240	+	0.633272i
$947$	−25.4082	−	47.5355i	−0.825657	−	1.54470i	−0.838580	−	0.544779i	$-0.816614\pi$
$947$	−25.4082	−	47.5355i	−0.825657	−	1.54470i	0.0129232	−	0.999916i	$-0.495886\pi$
$948$	0.0273149	−	0.0330806i	0.000887146	−	0.00107441i
$949$	−0.506306	−	0.616936i	−0.0164354	−	0.0200266i
$950$	−14.1529	+	17.1928i	−0.459182	+	0.557808i
$951$	0.0392301	+	0.197223i	0.00127212	+	0.00639540i
$952$	50.6169	−	20.7001i	1.64050	−	0.670894i
$953$	−11.1394	−	2.21576i	−0.360840	−	0.0717755i	0.0113410	−	0.999936i	$-0.496390\pi$
$953$	−11.1394	−	2.21576i	−0.360840	−	0.0717755i	−0.372181	+	0.928160i	$0.621390\pi$
$954$	0.735273	−	7.35238i	0.0238053	−	0.238042i
$955$	−21.3408	−	11.4069i	−0.690573	−	0.369119i
$956$	−3.64934	−	0.0109376i	−0.118028	−	0.000353748i
$957$	−0.0989767	−	1.00493i	−0.00319946	−	0.0324847i
$958$	−11.9948	−	2.40460i	−0.387534	−	0.0776892i
$959$			11.8676i			0.383224i
$960$	0.00387315	−	0.430749i	0.000125005	−	0.0139024i
$961$		−	16.2853i		−	0.525331i
$962$	−2.48091	+	12.3754i	−0.0799878	+	0.399000i
$963$	−1.69741	−	17.2341i	−0.0546982	−	0.555360i
$964$	−29.3225	−	29.4988i	−0.944415	−	0.950093i
$965$	18.0393	+	9.64219i	0.580704	+	0.310393i
$966$	−1.41811	−	0.141818i	−0.0456269	−	0.00456290i
$967$	−26.1443	−	5.20042i	−0.840744	−	0.167234i	−0.244110	−	0.969748i	$-0.578496\pi$
$967$	−26.1443	−	5.20042i	−0.840744	−	0.167234i	−0.596634	+	0.802513i	$0.703496\pi$
$968$	0.130508	−	29.0292i	0.00419468	−	0.933034i
$969$	−0.185491	−	0.932526i	−0.00595883	−	0.0299571i
$970$	−22.5028	−	18.5241i	−0.722521	−	0.594772i
$971$	18.3143	+	22.3160i	0.587733	+	0.716155i	0.978940	−	0.204148i	$-0.0654424\pi$
$971$	18.3143	+	22.3160i	0.587733	+	0.716155i	−0.391207	+	0.920303i	$0.627942\pi$
$972$	0.188874	+	1.97844i	0.00605815	+	0.0634586i
$973$	−14.4373	−	27.0102i	−0.462838	−	0.865908i
$974$	21.1895	−	50.9398i	0.678954	−	1.63222i
$975$	−0.122165	−	0.0506023i	−0.00391240	−	0.00162057i
$976$	−19.4673	+	23.4331i	−0.623132	+	0.750074i
$977$	30.5357	−	12.6483i	0.976925	−	0.404655i	0.163639	−	0.986520i	$-0.447677\pi$
$977$	30.5357	−	12.6483i	0.976925	−	0.404655i	0.813285	+	0.581865i	$0.197677\pi$
$978$	0.000127282	−	0.0849354i	4.07003e−6	−	0.00271593i
$979$	−11.5852	+	38.1911i	−0.370263	+	1.22059i
$980$	−8.38330	−	27.9372i	−0.267795	−	0.892421i
$981$	12.0831	+	1.19008i	0.385785	+	0.0379965i
$982$	44.1438	−	23.5104i	1.40869	−	0.750246i
$983$	−5.32883	+	7.97516i	−0.169963	+	0.254368i	−0.906666	−	0.421848i	$-0.861382\pi$
$983$	−5.32883	+	7.97516i	−0.169963	+	0.254368i	0.736703	+	0.676216i	$0.236382\pi$
$984$	−0.275038	+	0.892219i	−0.00876789	+	0.0284429i
$985$	19.7602	−	13.2034i	0.629614	−	0.420694i
$986$	−11.3992	−	37.7818i	−0.363024	−	1.20322i
$987$	−0.149638	−	0.493291i	−0.00476303	−	0.0157016i
$988$	−2.73355	+	13.5304i	−0.0869658	+	0.430460i
$989$	−39.9280	−	32.7681i	−1.26964	−	1.04196i
$990$	15.9206	−	23.7497i	0.505988	−	0.754814i
$991$	5.56401	−	5.56401i	0.176747	−	0.176747i	−0.613189	−	0.789936i	$-0.710114\pi$
$991$	5.56401	−	5.56401i	0.176747	−	0.176747i	0.789936	+	0.613189i	$0.210114\pi$
$992$	−18.1324	+	11.9201i	−0.575703	+	0.378464i
$993$	−0.124114	−	0.124114i	−0.00393862	−	0.00393862i
$994$	32.9837	−	6.50950i	1.04618	−	0.206469i
$995$	−25.5569	+	31.1412i	−0.810209	+	0.987242i
$996$	0.270514	+	0.181927i	0.00857156	+	0.00576457i
$997$	−27.1669	+	8.24099i	−0.860385	+	0.260995i	−0.689491	−	0.724295i	$-0.742166\pi$
$997$	−27.1669	+	8.24099i	−0.860385	+	0.260995i	−0.170894	+	0.985289i	$0.554666\pi$
$998$	−12.7163	−	6.82153i	−0.402528	−	0.215932i
$999$	−0.873127	−	1.30673i	−0.0276245	−	0.0413430i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.k.a.117.4	yes	240
4.3	odd	2		512.2.k.a.305.8		240
128.35	odd	32		512.2.k.a.465.8		240
128.93	even	32	inner	128.2.k.a.93.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.93.4	✓	240	128.93	even	32	inner
128.2.k.a.117.4	yes	240	1.1	even	1	trivial
512.2.k.a.305.8		240	4.3	odd	2
512.2.k.a.465.8		240	128.35	odd	32

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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

Character values

Coefficient data

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	128.2.k.a.117.4

Level	$128$
Weight	$2$
Character	128.117
Analytic conductor	$1.022$
Analytic rank	$0$
Dimension	$240$
Inner twists	$2$