LMFDB - Embedded newform 87.2.i.a.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(4,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

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("87.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$87 = 3 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	87.i (of order $14$ , degree $6$ , 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			22.1
Character	$\chi$	$=$	87.22
Dual form			87.2.i.a.4.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39841 + 0.319179i) q^{2} +(0.433884 - 0.900969i) q^{3} +(0.0517506 - 0.0249218i) q^{4} +(-0.831893 - 3.64476i) q^{5} +(-0.319179 + 1.39841i) q^{6} +(0.406749 + 0.195880i) q^{7} +(2.17847 - 1.73727i) q^{8} +(-0.623490 - 0.781831i) q^{9} +(2.32666 + 4.83137i) q^{10} +(-1.11035 - 0.885471i) q^{11} -0.0574388i q^{12} +(2.64255 - 3.31365i) q^{13} +(-0.631324 - 0.144096i) q^{14} +(-3.64476 - 0.831893i) q^{15} +(-2.56353 + 3.21456i) q^{16} +5.53520i q^{17} +(1.12144 + 0.894320i) q^{18} +(0.116412 + 0.241732i) q^{19} +(-0.133885 - 0.167886i) q^{20} +(0.352963 - 0.281479i) q^{21} +(1.83535 + 0.883856i) q^{22} +(-1.27940 + 5.60540i) q^{23} +(-0.620025 - 2.71651i) q^{24} +(-8.08741 + 3.89469i) q^{25} +(-2.63773 + 5.47730i) q^{26} +(-0.974928 + 0.222521i) q^{27} +0.0259312 q^{28} +(3.70484 - 3.90822i) q^{29} +5.36241 q^{30} +(8.01515 - 1.82941i) q^{31} +(0.140936 - 0.292656i) q^{32} +(-1.27954 + 0.616195i) q^{33} +(-1.76672 - 7.74051i) q^{34} +(0.375564 - 1.64545i) q^{35} +(-0.0517506 - 0.0249218i) q^{36} +(0.228457 - 0.182189i) q^{37} +(-0.239948 - 0.300886i) q^{38} +(-1.83894 - 3.81859i) q^{39} +(-8.14420 - 6.49478i) q^{40} -7.51870i q^{41} +(-0.403747 + 0.506283i) q^{42} +(6.27204 + 1.43155i) q^{43} +(-0.0795285 - 0.0181519i) q^{44} +(-2.33091 + 2.92287i) q^{45} -8.24704i q^{46} +(9.65726 + 7.70141i) q^{47} +(1.78395 + 3.70440i) q^{48} +(-4.23735 - 5.31347i) q^{49} +(10.0664 - 8.02772i) q^{50} +(4.98704 + 2.40163i) q^{51} +(0.0541714 - 0.237340i) q^{52} +(-0.454240 - 1.99016i) q^{53} +(1.29233 - 0.622353i) q^{54} +(-2.30364 + 4.78356i) q^{55} +(1.22639 - 0.279914i) q^{56} +0.268303 q^{57} +(-3.93348 + 6.64782i) q^{58} +1.99228 q^{59} +(-0.209351 + 0.0477830i) q^{60} +(-5.47355 + 11.3659i) q^{61} +(-10.6246 + 5.11653i) q^{62} +(-0.100459 - 0.440138i) q^{63} +(1.72615 - 7.56275i) q^{64} +(-14.2758 - 6.87486i) q^{65} +(1.59265 - 1.27010i) q^{66} +(-1.58651 - 1.98943i) q^{67} +(0.137947 + 0.286450i) q^{68} +(4.49519 + 3.58479i) q^{69} +2.42090i q^{70} +(-7.40161 + 9.28132i) q^{71} +(-2.71651 - 0.620025i) q^{72} +(-5.00461 - 1.14227i) q^{73} +(-0.261327 + 0.327694i) q^{74} +8.97635i q^{75} +(0.0120488 + 0.00960859i) q^{76} +(-0.278185 - 0.577658i) q^{77} +(3.79041 + 4.75302i) q^{78} +(6.30549 - 5.02846i) q^{79} +(13.8489 + 6.66928i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(2.39981 + 10.5143i) q^{82} +(-2.33602 + 1.12497i) q^{83} +(0.0112511 - 0.0233632i) q^{84} +(20.1745 - 4.60470i) q^{85} -9.22783 q^{86} +(-1.91372 - 5.03366i) q^{87} -3.95715 q^{88} +(2.72252 - 0.621397i) q^{89} +(2.32666 - 4.83137i) q^{90} +(1.72393 - 0.830201i) q^{91} +(0.0734871 + 0.321968i) q^{92} +(1.82941 - 8.01515i) q^{93} +(-15.9630 - 7.68737i) q^{94} +(0.784214 - 0.625390i) q^{95} +(-0.202524 - 0.253957i) q^{96} +(5.62184 + 11.6739i) q^{97} +(7.62153 + 6.07796i) q^{98} +1.42018i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 2 q^{4} - 4 q^{5} - 2 q^{6} + 8 q^{7} + 4 q^{9} - 28 q^{11} - 10 q^{13} - 14 q^{15} - 22 q^{16} - 20 q^{20} + 4 q^{22} + 18 q^{23} - 18 q^{25} + 28 q^{26} + 8 q^{28} + 28 q^{29} - 40 q^{30} + 28 q^{31}+ \cdots - 42 q^{98}+O(q^{100})$ 24 * q - 2 * q^4 - 4 * q^5 - 2 * q^6 + 8 * q^7 + 4 * q^9 - 28 * q^11 - 10 * q^13 - 14 * q^15 - 22 * q^16 - 20 * q^20 + 4 * q^22 + 18 * q^23 - 18 * q^25 + 28 * q^26 + 8 * q^28 + 28 * q^29 - 40 * q^30 + 28 * q^31 - 14 * q^32 + 34 * q^34 + 2 * q^36 - 28 * q^37 - 4 * q^38 + 14 * q^42 - 14 * q^43 + 14 * q^44 - 10 * q^45 + 56 * q^48 + 20 * q^49 + 42 * q^50 + 2 * q^51 - 68 * q^52 + 6 * q^53 + 2 * q^54 - 14 * q^55 + 32 * q^57 + 50 * q^58 + 28 * q^59 + 42 * q^60 - 8 * q^62 + 6 * q^63 - 20 * q^64 + 18 * q^65 - 28 * q^66 + 8 * q^67 + 14 * q^68 + 28 * q^69 - 42 * q^71 + 14 * q^72 - 84 * q^73 + 10 * q^74 - 14 * q^76 - 70 * q^77 + 2 * q^78 - 14 * q^79 + 36 * q^80 - 4 * q^81 - 50 * q^82 - 32 * q^83 + 14 * q^85 - 128 * q^86 - 44 * q^87 - 20 * q^88 - 14 * q^89 + 34 * q^91 - 58 * q^92 - 20 * q^93 - 44 * q^94 - 52 * q^96 + 56 * q^97 - 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$ .

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$1$

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

)

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

$2$	−1.39841	+	0.319179i	−0.988828	+	0.225694i	−0.686198	−	0.727414i	$-0.740722\pi$
$2$	−1.39841	+	0.319179i	−0.988828	+	0.225694i	−0.302630	+	0.953108i	$0.597865\pi$
$3$	0.433884	−	0.900969i	0.250503	−	0.520175i
$3$	0.433884	−	0.900969i	0.250503	−	0.520175i
$4$	0.0517506	−	0.0249218i	0.0258753	−	0.0124609i
$5$	−0.831893	−	3.64476i	−0.372034	−	1.62999i	−0.721059	−	0.692874i	$-0.756344\pi$
$5$	−0.831893	−	3.64476i	−0.372034	−	1.62999i	0.349024	−	0.937114i	$-0.386513\pi$
$6$	−0.319179	+	1.39841i	−0.130304	+	0.570900i
$7$	0.406749	+	0.195880i	0.153737	+	0.0740356i	0.509170	−	0.860666i	$-0.329952\pi$
$7$	0.406749	+	0.195880i	0.153737	+	0.0740356i	−0.355433	+	0.934702i	$0.615667\pi$
$8$	2.17847	−	1.73727i	0.770205	−	0.614218i
$9$	−0.623490	−	0.781831i	−0.207830	−	0.260610i
$10$	2.32666	+	4.83137i	0.735756	+	1.52781i
$11$	−1.11035	−	0.885471i	−0.334782	−	0.266979i	0.441641	−	0.897192i	$-0.354396\pi$
$11$	−1.11035	−	0.885471i	−0.334782	−	0.266979i	−0.776423	+	0.630212i	$0.782968\pi$
$12$		−	0.0574388i		−	0.0165812i
$13$	2.64255	−	3.31365i	0.732911	−	0.919041i	−0.266080	−	0.963951i	$-0.585729\pi$
$13$	2.64255	−	3.31365i	0.732911	−	0.919041i	0.998991	+	0.0449099i	$0.0143001\pi$
$14$	−0.631324	−	0.144096i	−0.168728	−	0.0385112i
$15$	−3.64476	−	0.831893i	−0.941074	−	0.214794i
$16$	−2.56353	+	3.21456i	−0.640882	+	0.803640i
$17$			5.53520i			1.34248i	0.741238	+	0.671242i	$0.234239\pi$
$17$			5.53520i			1.34248i	−0.741238	+	0.671242i	$0.765761\pi$
$18$	1.12144	+	0.894320i	0.264326	+	0.210793i
$19$	0.116412	+	0.241732i	0.0267068	+	0.0554572i	0.913895	−	0.405950i	$-0.133059\pi$
$19$	0.116412	+	0.241732i	0.0267068	+	0.0554572i	−0.887189	+	0.461407i	$0.847345\pi$
$20$	−0.133885	−	0.167886i	−0.0299376	−	0.0375405i
$21$	0.352963	−	0.281479i	0.0770229	−	0.0614237i
$22$	1.83535	+	0.883856i	0.391297	+	0.188439i
$23$	−1.27940	+	5.60540i	−0.266773	+	1.16881i	0.646970	+	0.762515i	$0.276036\pi$
$23$	−1.27940	+	5.60540i	−0.266773	+	1.16881i	−0.913743	+	0.406292i	$0.866821\pi$
$24$	−0.620025	−	2.71651i	−0.126562	−	0.554504i
$25$	−8.08741	+	3.89469i	−1.61748	+	0.778938i
$26$	−2.63773	+	5.47730i	−0.517301	+	1.07419i
$27$	−0.974928	+	0.222521i	−0.187625	+	0.0428242i
$28$	0.0259312			0.00490053
$29$	3.70484	−	3.90822i	0.687971	−	0.725738i
$29$	3.70484	−	3.90822i	0.687971	−	0.725738i
$30$	5.36241			0.979038
$31$	8.01515	−	1.82941i	1.43956	−	0.328571i	0.569695	−	0.821856i	$-0.307061\pi$
$31$	8.01515	−	1.82941i	1.43956	−	0.328571i	0.869868	+	0.493285i	$0.164204\pi$
$32$	0.140936	−	0.292656i	0.0249141	−	0.0517347i
$33$	−1.27954	+	0.616195i	−0.222740	+	0.107266i
$34$	−1.76672	−	7.74051i	−0.302990	−	1.32749i
$35$	0.375564	−	1.64545i	0.0634819	−	0.278132i
$36$	−0.0517506	−	0.0249218i	−0.00862510	−	0.00415363i
$37$	0.228457	−	0.182189i	0.0375582	−	0.0299516i	−0.604531	−	0.796582i	$-0.706639\pi$
$37$	0.228457	−	0.182189i	0.0375582	−	0.0299516i	0.642089	+	0.766630i	$0.278068\pi$
$38$	−0.239948	−	0.300886i	−0.0389247	−	0.0488101i
$39$	−1.83894	−	3.81859i	−0.294466	−	0.611464i
$40$	−8.14420	−	6.49478i	−1.28771	−	1.02691i
$41$		−	7.51870i		−	1.17422i	−0.809506	−	0.587112i	$-0.800265\pi$
$41$		−	7.51870i		−	1.17422i	0.809506	−	0.587112i	$-0.199735\pi$
$42$	−0.403747	+	0.506283i	−0.0622995	+	0.0781211i
$43$	6.27204	+	1.43155i	0.956477	+	0.218310i	0.672148	−	0.740417i	$-0.265372\pi$
$43$	6.27204	+	1.43155i	0.956477	+	0.218310i	0.284329	+	0.958727i	$0.408229\pi$
$44$	−0.0795285	−	0.0181519i	−0.0119894	−	0.00273650i
$45$	−2.33091	+	2.92287i	−0.347472	+	0.435716i
$46$		−	8.24704i		−	1.21596i
$47$	9.65726	+	7.70141i	1.40866	+	1.12337i	0.974979	+	0.222297i	$0.0713556\pi$
$47$	9.65726	+	7.70141i	1.40866	+	1.12337i	0.433677	+	0.901068i	$0.357216\pi$
$48$	1.78395	+	3.70440i	0.257491	+	0.534685i
$49$	−4.23735	−	5.31347i	−0.605336	−	0.759068i
$50$	10.0664	−	8.02772i	1.42361	−	1.13529i
$51$	4.98704	+	2.40163i	0.698326	+	0.336296i
$52$	0.0541714	−	0.237340i	0.00751222	−	0.0329132i
$53$	−0.454240	−	1.99016i	−0.0623947	−	0.273369i	0.934101	−	0.357008i	$-0.116203\pi$
$53$	−0.454240	−	1.99016i	−0.0623947	−	0.273369i	−0.996496	+	0.0836386i	$0.973346\pi$
$54$	1.29233	−	0.622353i	0.175864	−	0.0846915i
$55$	−2.30364	+	4.78356i	−0.310623	+	0.645015i
$56$	1.22639	−	0.279914i	0.163883	−	0.0374051i
$57$	0.268303			0.0355375
$58$	−3.93348	+	6.64782i	−0.516491	+	0.872901i
$59$	1.99228			0.259373			0.129686	−	0.991555i	$-0.458603\pi$
$59$	1.99228			0.259373			0.129686	+	0.991555i	$0.458603\pi$
$60$	−0.209351	+	0.0477830i	−0.0270271	+	0.00616876i
$61$	−5.47355	+	11.3659i	−0.700816	+	1.45526i	0.180912	+	0.983499i	$0.442095\pi$
$61$	−5.47355	+	11.3659i	−0.700816	+	1.45526i	−0.881727	+	0.471759i	$0.843619\pi$
$62$	−10.6246	+	5.11653i	−1.34932	+	0.649801i
$63$	−0.100459	−	0.440138i	−0.0126566	−	0.0554522i
$64$	1.72615	−	7.56275i	0.215768	−	0.945343i
$65$	−14.2758	−	6.87486i	−1.77069	−	0.852721i
$66$	1.59265	−	1.27010i	0.196042	−	0.156338i
$67$	−1.58651	−	1.98943i	−0.193824	−	0.243047i	0.675417	−	0.737436i	$-0.263963\pi$
$67$	−1.58651	−	1.98943i	−0.193824	−	0.243047i	−0.869241	+	0.494389i	$0.835392\pi$
$68$	0.137947	+	0.286450i	0.0167285	+	0.0347372i
$69$	4.49519	+	3.58479i	0.541157	+	0.431558i
$70$			2.42090i			0.289353i
$71$	−7.40161	+	9.28132i	−0.878409	+	1.10149i	0.115719	+	0.993282i	$0.463083\pi$
$71$	−7.40161	+	9.28132i	−0.878409	+	1.10149i	−0.994128	+	0.108209i	$0.965489\pi$
$72$	−2.71651	−	0.620025i	−0.320143	−	0.0730706i
$73$	−5.00461	−	1.14227i	−0.585745	−	0.133693i	−0.0806296	−	0.996744i	$-0.525693\pi$
$73$	−5.00461	−	1.14227i	−0.585745	−	0.133693i	−0.505116	+	0.863052i	$0.668550\pi$
$74$	−0.261327	+	0.327694i	−0.0303787	+	0.0380937i
$75$			8.97635i			1.03650i
$76$	0.0120488	+	0.00960859i	0.00138209	+	0.00110218i
$77$	−0.278185	−	0.577658i	−0.0317022	−	0.0658303i
$78$	3.79041	+	4.75302i	0.429179	+	0.538174i
$79$	6.30549	−	5.02846i	0.709423	−	0.565746i	−0.200917	−	0.979608i	$-0.564392\pi$
$79$	6.30549	−	5.02846i	0.709423	−	0.565746i	0.910339	+	0.413863i	$0.135821\pi$
$80$	13.8489	+	6.66928i	1.54835	+	0.745648i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	2.39981	+	10.5143i	0.265015	+	1.16111i
$83$	−2.33602	+	1.12497i	−0.256412	+	0.123481i	−0.557674	−	0.830060i	$-0.688306\pi$
$83$	−2.33602	+	1.12497i	−0.256412	+	0.123481i	0.301263	+	0.953541i	$0.402592\pi$
$84$	0.0112511	−	0.0233632i	0.00122760	−	0.00254913i
$85$	20.1745	−	4.60470i	2.18823	−	0.499450i
$86$	−9.22783			−0.995063
$87$	−1.91372	−	5.03366i	−0.205172	−	0.539665i
$88$	−3.95715			−0.421834
$89$	2.72252	−	0.621397i	0.288587	−	0.0658680i	−0.0757770	−	0.997125i	$-0.524144\pi$
$89$	2.72252	−	0.621397i	0.288587	−	0.0658680i	0.364364	+	0.931257i	$0.381287\pi$
$90$	2.32666	−	4.83137i	0.245252	−	0.509271i
$91$	1.72393	−	0.830201i	0.180717	−	0.0870287i
$92$	0.0734871	+	0.321968i	0.00766156	+	0.0335675i
$93$	1.82941	−	8.01515i	0.189701	−	0.831132i
$94$	−15.9630	−	7.68737i	−1.64646	−	0.792891i
$95$	0.784214	−	0.625390i	0.0804587	−	0.0641637i
$96$	−0.202524	−	0.253957i	−0.0206700	−	0.0259194i
$97$	5.62184	+	11.6739i	0.570812	+	1.18530i	0.964014	+	0.265851i	$0.0856529\pi$
$97$	5.62184	+	11.6739i	0.570812	+	1.18530i	−0.393202	+	0.919452i	$0.628633\pi$
$98$	7.62153	+	6.07796i	0.769890	+	0.613967i
$99$			1.42018i			0.142734i
$100$	−0.321466	+	0.403105i	−0.0321466	+	0.0403105i
$101$	3.21585	+	0.733997i	0.319989	+	0.0730354i	0.379499	−	0.925192i	$-0.376096\pi$
$101$	3.21585	+	0.733997i	0.319989	+	0.0730354i	−0.0595094	+	0.998228i	$0.518954\pi$
$102$	−7.74051	−	1.76672i	−0.766424	−	0.174931i
$103$	−5.22918	+	6.55718i	−0.515246	+	0.646098i	−0.969592	−	0.244727i	$-0.921302\pi$
$103$	−5.22918	+	6.55718i	−0.515246	+	0.646098i	0.454346	+	0.890825i	$0.349873\pi$
$104$		−	11.8095i		−	1.15802i
$105$	−1.31955	−	1.05231i	−0.128775	−	0.102695i
$106$	1.27043	+	2.63808i	0.123395	+	0.256233i
$107$	−0.954509	−	1.19692i	−0.0922759	−	0.115710i	0.733550	−	0.679636i	$-0.237862\pi$
$107$	−0.954509	−	1.19692i	−0.0922759	−	0.115710i	−0.825826	+	0.563925i	$0.809291\pi$
$108$	−0.0449075	+	0.0358125i	−0.00432123	+	0.00344606i
$109$	−17.6468	−	8.49823i	−1.69025	−	0.813983i	−0.995503	−	0.0947310i	$-0.969801\pi$
$109$	−17.6468	−	8.49823i	−1.69025	−	0.813983i	−0.694750	−	0.719252i	$-0.744485\pi$
$110$	1.69463	−	7.42468i	0.161577	−	0.707915i
$111$	−0.0650224	−	0.284882i	−0.00617165	−	0.0270398i
$112$	−1.67238	+	0.805375i	−0.158025	+	0.0761008i
$113$	−0.395048	+	0.820325i	−0.0371629	+	0.0771697i	−0.918724	−	0.394901i	$-0.870779\pi$
$113$	−0.395048	+	0.820325i	−0.0371629	+	0.0771697i	0.881561	+	0.472070i	$0.156493\pi$
$114$	−0.375198	+	0.0856365i	−0.0351405	+	0.00802060i
$115$	21.4947			2.00439
$116$	0.0943278	−	0.294584i	0.00875812	−	0.0273514i
$117$	−4.23832			−0.391832
$118$	−2.78603	+	0.635893i	−0.256475	+	0.0585387i
$119$	−1.08423	+	2.25144i	−0.0993916	+	0.206389i
$120$	−9.38523	+	4.51969i	−0.856750	+	0.412589i
$121$	−1.99892	−	8.75785i	−0.181720	−	0.796168i
$122$	4.02652	−	17.6413i	0.364544	−	1.59717i
$123$	−6.77412	−	3.26224i	−0.610801	−	0.294146i
$124$	0.369197	−	0.294425i	0.0331548	−	0.0264401i
$125$	9.26852	+	11.6224i	0.829002	+	1.03954i
$126$	0.280966	+	0.583431i	0.0250304	+	0.0519762i
$127$	1.89206	+	1.50886i	0.167893	+	0.133890i	0.703832	−	0.710367i	$-0.251471\pi$
$127$	1.89206	+	1.50886i	0.167893	+	0.133890i	−0.535939	+	0.844257i	$0.680042\pi$
$128$			11.7765i			1.04090i
$129$	4.01112	−	5.02979i	0.353159	−	0.442848i
$130$	22.1578	+	5.05737i	1.94337	+	0.443561i
$131$	−16.3901	−	3.74093i	−1.43201	−	0.326847i	−0.564980	−	0.825104i	$-0.691116\pi$
$131$	−16.3901	−	3.74093i	−1.43201	−	0.326847i	−0.867029	+	0.498258i	$0.833973\pi$
$132$	−0.0508604	+	0.0637769i	−0.00442683	+	0.00555107i
$133$			0.121127i			0.0105030i
$134$	2.85359	+	2.27566i	0.246512	+	0.196587i
$135$	1.62207	+	3.36827i	0.139606	+	0.289894i
$136$	9.61614	+	12.0583i	0.824578	+	1.03399i
$137$	−0.586620	+	0.467814i	−0.0501183	+	0.0399680i	−0.648229	−	0.761446i	$-0.724490\pi$
$137$	−0.586620	+	0.467814i	−0.0501183	+	0.0399680i	0.598110	+	0.801414i	$0.295918\pi$
$138$	−7.43032	−	3.57825i	−0.632511	−	0.304601i
$139$	−1.68368	+	7.37666i	−0.142807	+	0.625680i	0.851968	+	0.523594i	$0.175409\pi$
$139$	−1.68368	+	7.37666i	−0.142807	+	0.625680i	−0.994776	+	0.102087i	$0.967448\pi$
$140$	−0.0215720	−	0.0945129i	−0.00182316	−	0.00798780i
$141$	11.1289	−	5.35937i	0.937219	−	0.451341i
$142$	7.38811	−	15.3416i	0.619997	−	1.28744i
$143$	−5.86828	+	1.33940i	−0.490730	+	0.112006i
$144$	4.11158			0.342632
$145$	−17.3266	−	10.2520i	−1.43889	−	0.851385i
$146$	7.36311			0.609375
$147$	−6.62579	+	1.51229i	−0.546486	+	0.124732i
$148$	0.00728234	−	0.0151219i	0.000598605	−	0.00124302i
$149$	4.15387	−	2.00040i	0.340298	−	0.163879i	−0.255927	−	0.966696i	$-0.582381\pi$
$149$	4.15387	−	2.00040i	0.340298	−	0.163879i	0.596225	+	0.802817i	$0.296666\pi$
$150$	−2.86506	−	12.5527i	−0.233931	−	1.02492i
$151$	−1.84121	+	8.06687i	−0.149836	+	0.656473i	0.843094	+	0.537767i	$0.180732\pi$
$151$	−1.84121	+	8.06687i	−0.149836	+	0.656473i	−0.992929	+	0.118706i	$0.962125\pi$
$152$	0.673555	+	0.324367i	0.0546325	+	0.0263096i
$153$	4.32759	−	3.45114i	0.349865	−	0.279008i
$154$	0.573395	+	0.719015i	0.0462055	+	0.0579399i
$155$	−13.3355	−	27.6915i	−1.07113	−	2.22423i
$156$	−0.190332	−	0.151785i	−0.0152388	−	0.0121525i
$157$		−	0.0489743i		−	0.00390857i	−0.999998	−	0.00195429i	$-0.999378\pi$
$157$		−	0.0489743i		−	0.00390857i	0.999998	−	0.00195429i	$-0.000622069\pi$
$158$	−7.21271	+	9.04445i	−0.573812	+	0.719538i
$159$	−1.99016	−	0.454240i	−0.157830	−	0.0360236i
$160$	−1.18391	−	0.270219i	−0.0935959	−	0.0213627i
$161$	−1.61838	+	2.02938i	−0.127546	+	0.159938i
$162$		−	1.43438i		−	0.112695i
$163$	6.52760	+	5.20559i	0.511281	+	0.407733i	0.844859	−	0.534990i	$-0.179684\pi$
$163$	6.52760	+	5.20559i	0.511281	+	0.407733i	−0.333577	+	0.942723i	$0.608256\pi$
$164$	−0.187379	−	0.389097i	−0.0146319	−	0.0303834i
$165$	3.31033	+	4.15102i	0.257709	+	0.323156i
$166$	2.90766	−	2.31878i	0.225678	−	0.179972i
$167$	11.6992	+	5.63403i	0.905311	+	0.435975i	0.827804	−	0.561017i	$-0.189590\pi$
$167$	11.6992	+	5.63403i	0.905311	+	0.435975i	0.0775066	+	0.996992i	$0.475304\pi$
$168$	0.279914	−	1.22639i	0.0215959	−	0.0946177i
$169$	−1.10444	−	4.83888i	−0.0849572	−	0.372222i
$170$	−26.7426	+	12.8786i	−2.05106	+	0.987740i
$171$	0.116412	−	0.241732i	0.00890226	−	0.0184857i
$172$	0.360259	−	0.0822267i	0.0274695	−	0.00626973i
$173$	13.7120			1.04250			0.521251	−	0.853403i	$-0.325465\pi$
$173$	13.7120			1.04250			0.521251	+	0.853403i	$0.325465\pi$
$174$	4.28281	+	6.42832i	0.324679	+	0.487330i
$175$	−4.05243			−0.306335
$176$	5.69280	−	1.29934i	0.429111	−	0.0979418i
$177$	0.864417	−	1.79498i	0.0649736	−	0.134919i
$178$	−3.60887	+	1.73794i	−0.270497	+	0.130264i
$179$	1.53880	+	6.74193i	0.115015	+	0.503916i	0.999315	+	0.0369964i	$0.0117790\pi$
$179$	1.53880	+	6.74193i	0.115015	+	0.503916i	−0.884300	+	0.466919i	$0.845364\pi$
$180$	−0.0477830	+	0.209351i	−0.00356153	+	0.0156041i
$181$	12.2810	+	5.91424i	0.912843	+	0.439602i	0.830511	−	0.557003i	$-0.188049\pi$
$181$	12.2810	+	5.91424i	0.912843	+	0.439602i	0.0823325	+	0.996605i	$0.473763\pi$
$182$	−2.14579	+	1.71121i	−0.159056	+	0.126843i
$183$	7.86547	+	9.86299i	0.581432	+	0.729093i
$184$	6.95098	+	14.4339i	0.512433	+	1.06408i
$185$	−0.854087	−	0.681111i	−0.0627937	−	0.0500763i
$186$			11.7924i			0.864661i
$187$	4.90126	−	6.14598i	0.358416	−	0.449439i
$188$	0.691702	+	0.157876i	0.0504475	+	0.0115143i
$189$	−0.440138	−	0.100459i	−0.0320153	−	0.00730729i
$190$	−0.897045	+	1.12486i	−0.0650785	+	0.0816059i
$191$		−	20.0672i		−	1.45201i	−0.687689	−	0.726006i	$-0.741375\pi$
$191$		−	20.0672i		−	1.45201i	0.687689	−	0.726006i	$-0.258625\pi$
$192$	−6.06485	−	4.83656i	−0.437693	−	0.349049i
$193$	0.349953	+	0.726686i	0.0251902	+	0.0523080i	0.913184	−	0.407547i	$-0.133616\pi$
$193$	0.349953	+	0.726686i	0.0251902	+	0.0523080i	−0.887994	+	0.459855i	$0.847901\pi$
$194$	−11.5877	−	14.5305i	−0.831950	−	1.04323i
$195$	−12.3881	+	9.87915i	−0.887128	+	0.707461i
$196$	−0.351707	−	0.169373i	−0.0251219	−	0.0120981i
$197$	−0.260340	+	1.14063i	−0.0185485	+	0.0812662i	−0.983355	−	0.181694i	$-0.941842\pi$
$197$	−0.260340	+	1.14063i	−0.0185485	+	0.0812662i	0.964807	+	0.262961i	$0.0846990\pi$
$198$	−0.453293	−	1.98601i	−0.0322141	−	0.141139i
$199$	−3.84524	+	1.85177i	−0.272582	+	0.131268i	−0.565182	−	0.824967i	$-0.691194\pi$
$199$	−3.84524	+	1.85177i	−0.272582	+	0.131268i	0.292600	+	0.956235i	$0.405480\pi$
$200$	−10.8520	+	22.5345i	−0.767355	+	1.59343i
$201$	−2.48077	+	0.566220i	−0.174980	+	0.0399381i
$202$	−4.73137			−0.332898
$203$	2.27248	−	0.863960i	0.159497	−	0.0606381i
$204$	0.317936			0.0222599
$205$	−27.4039	+	6.25476i	−1.91397	+	0.436851i
$206$	5.21964	−	10.8387i	0.363670	−	0.755168i
$207$	5.18017	−	2.49464i	0.360047	−	0.173389i
$208$	3.87769	+	16.9893i	0.268869	+	1.17799i
$209$	0.0847892	−	0.371486i	0.00586499	−	0.0256962i
$210$	2.18115	+	1.05039i	0.150514	+	0.0724837i
$211$	−11.4959	+	9.16769i	−0.791412	+	0.631130i	−0.933440	−	0.358733i	$-0.883209\pi$
$211$	−11.4959	+	9.16769i	−0.791412	+	0.631130i	0.142029	+	0.989863i	$0.454637\pi$
$212$	−0.0731055	−	0.0916714i	−0.00502091	−	0.00629602i
$213$	5.15075	+	10.6956i	0.352923	+	0.732853i
$214$	1.71683	+	1.36913i	0.117360	+	0.0935915i
$215$		−	24.0510i		−	1.64026i
$216$	−1.73727	+	2.17847i	−0.118206	+	0.148226i
$217$	3.61849	+	0.825898i	0.245639	+	0.0560656i
$218$	27.3899	+	6.25157i	1.85508	+	0.423410i
$219$	−3.20057	+	4.01339i	−0.216274	+	0.271200i
$220$			0.304963i			0.0205606i
$221$	18.3417	+	14.6270i	1.23380	+	0.983921i
$222$	0.181856	+	0.377629i	0.0122054	+	0.0253448i
$223$	−14.1683	−	17.7665i	−0.948779	−	1.18973i	−0.981731	−	0.190275i	$-0.939062\pi$
$223$	−14.1683	−	17.7665i	−0.948779	−	1.18973i	0.0329515	−	0.999457i	$-0.489509\pi$
$224$	0.114651	−	0.0914309i	0.00766043	−	0.00610899i
$225$	8.08741	+	3.89469i	0.539161	+	0.259646i
$226$	0.290610	−	1.27324i	0.0193311	−	0.0846950i
$227$	−0.00888084	−	0.0389095i	−0.000589442	−	0.00258251i	0.974632	−	0.223812i	$-0.0718502\pi$
$227$	−0.00888084	−	0.0389095i	−0.000589442	−	0.00258251i	−0.975222	+	0.221229i	$0.928993\pi$
$228$	0.0138848	−	0.00668658i	0.000919545	−	0.000442829i
$229$	−9.90589	+	20.5698i	−0.654600	+	1.35929i	0.264162	+	0.964478i	$0.414905\pi$
$229$	−9.90589	+	20.5698i	−0.654600	+	1.35929i	−0.918762	+	0.394812i	$0.870810\pi$
$230$	−30.0585	+	6.86066i	−1.98200	+	0.452378i
$231$	−0.641152			−0.0421847
$232$	1.28124	−	14.9502i	0.0841173	−	0.981531i
$233$	−10.4551			−0.684938			−0.342469	−	0.939529i	$-0.611263\pi$
$233$	−10.4551			−0.684938			−0.342469	+	0.939529i	$0.611263\pi$
$234$	5.92692	−	1.35278i	0.387455	−	0.0884341i
$235$	20.0360	−	41.6052i	1.30700	−	2.71402i
$236$	0.103102	−	0.0496511i	0.00671134	−	0.00323201i
$237$	−1.79464	−	7.86281i	−0.116574	−	0.510745i
$238$	0.797598	−	3.49451i	0.0517006	−	0.226515i
$239$	27.4232	+	13.2063i	1.77386	+	0.854246i	0.963226	+	0.268691i	$0.0865910\pi$
$239$	27.4232	+	13.2063i	1.77386	+	0.854246i	0.810633	+	0.585555i	$0.199123\pi$
$240$	12.0176	−	9.58373i	0.775734	−	0.618627i
$241$	−10.8189	−	13.5665i	−0.696906	−	0.873892i	0.299883	−	0.953976i	$-0.403053\pi$
$241$	−10.8189	−	13.5665i	−0.696906	−	0.873892i	−0.996788	+	0.0800842i	$0.974481\pi$
$242$	5.59064	+	11.6091i	0.359380	+	0.746261i
$243$	0.781831	+	0.623490i	0.0501545	+	0.0399969i
$244$			0.724604i			0.0463880i
$245$	−15.8413	+	19.8644i	−1.01207	+	1.26909i
$246$	10.5143	+	2.39981i	0.670365	+	0.153006i
$247$	1.10864	+	0.253040i	0.0705411	+	0.0161005i
$248$	14.2826	−	17.9098i	0.906945	−	1.13727i
$249$			2.59279i			0.164311i
$250$	−16.6709	−	13.2946i	−1.05436	−	0.840822i
$251$	−0.465408	−	0.966431i	−0.0293763	−	0.0610006i	0.885764	−	0.464135i	$-0.153635\pi$
$251$	−0.465408	−	0.966431i	−0.0293763	−	0.0610006i	−0.915141	+	0.403135i	$0.867921\pi$
$252$	−0.0161678	−	0.0202738i	−0.00101848	−	0.00127713i
$253$	6.38399	−	5.09106i	0.401358	−	0.320072i
$254$	−3.12748	−	1.50611i	−0.196235	−	0.0945020i
$255$	4.60470	−	20.1745i	0.288357	−	1.26338i
$256$	−0.306502	−	1.34287i	−0.0191564	−	0.0839295i
$257$	10.5231	−	5.06765i	0.656412	−	0.316111i	−0.0758651	−	0.997118i	$-0.524172\pi$
$257$	10.5231	−	5.06765i	0.656412	−	0.316111i	0.732277	+	0.681007i	$0.238458\pi$
$258$	−4.00381	+	8.31399i	−0.249266	+	0.517606i
$259$	0.128612	−	0.0293548i	0.00799155	−	0.00182402i
$260$	−0.910114			−0.0564429
$261$	−5.36550	−	0.459823i	−0.332116	−	0.0284624i
$262$	24.1142			1.48978
$263$	−12.3694	+	2.82322i	−0.762727	+	0.174087i	−0.586153	−	0.810200i	$-0.699358\pi$
$263$	−12.3694	+	2.82322i	−0.762727	+	0.174087i	−0.176573	+	0.984287i	$0.556501\pi$
$264$	−1.71694	+	3.56527i	−0.105671	+	0.219427i
$265$	−6.87577	+	3.31120i	−0.422375	+	0.203405i
$266$	−0.0386612	−	0.169386i	−0.00237047	−	0.0103857i
$267$	0.621397	−	2.72252i	0.0380289	−	0.166616i
$268$	−0.131683	−	0.0634152i	−0.00804382	−	0.00387370i
$269$	−2.52030	+	2.00987i	−0.153665	+	0.122544i	−0.697305	−	0.716775i	$-0.745617\pi$
$269$	−2.52030	+	2.00987i	−0.153665	+	0.122544i	0.543639	+	0.839319i	$0.317046\pi$
$270$	−3.34341	−	4.19250i	−0.203473	−	0.255148i
$271$	−6.04156	−	12.5454i	−0.366999	−	0.762080i	0.632928	−	0.774211i	$-0.281853\pi$
$271$	−6.04156	−	12.5454i	−0.366999	−	0.762080i	−0.999926	+	0.0121303i	$0.996139\pi$
$272$	−17.7932	−	14.1896i	−1.07887	−	0.860373i
$273$		−	1.91342i		−	0.115805i
$274$	0.671022	−	0.841434i	0.0405379	−	0.0508329i
$275$	12.4284	+	2.83671i	0.749464	+	0.171060i
$276$	0.321968	+	0.0734871i	0.0193802	+	0.00442340i
$277$	11.0970	−	13.9152i	0.666753	−	0.836081i	−0.327307	−	0.944918i	$-0.606141\pi$
$277$	11.0970	−	13.9152i	0.666753	−	0.836081i	0.994060	+	0.108837i	$0.0347125\pi$
$278$		−	10.8530i		−	0.650921i
$279$	−6.42765	−	5.12588i	−0.384813	−	0.306878i
$280$	−2.04044	−	4.23703i	−0.121940	−	0.253211i
$281$	−6.41212	−	8.04055i	−0.382515	−	0.479659i	0.552881	−	0.833260i	$-0.313528\pi$
$281$	−6.41212	−	8.04055i	−0.382515	−	0.479659i	−0.935396	+	0.353601i	$0.884957\pi$
$282$	−13.8522	+	11.0467i	−0.824884	+	0.657823i
$283$	−18.0066	−	8.67153i	−1.07038	−	0.515469i	−0.186152	−	0.982521i	$-0.559602\pi$
$283$	−18.0066	−	8.67153i	−1.07038	−	0.515469i	−0.884230	+	0.467052i	$0.845316\pi$
$284$	−0.151731	+	0.664775i	−0.00900356	+	0.0394472i
$285$	−0.223199	−	0.977899i	−0.0132212	−	0.0579258i
$286$	7.77878	−	3.74606i	0.459969	−	0.221509i
$287$	1.47276	−	3.05822i	0.0869344	−	0.180521i
$288$	−0.316680	+	0.0722800i	−0.0186605	+	0.00425914i
$289$	−13.6385			−0.802262
$290$	27.5020	+	8.80632i	1.61497	+	0.517125i
$291$	12.9570			0.759554
$292$	−0.287459	+	0.0656106i	−0.0168223	+	0.00383957i
$293$	−5.81989	+	12.0851i	−0.340001	+	0.706020i	−0.998933	−	0.0461827i	$-0.985294\pi$
$293$	−5.81989	+	12.0851i	−0.340001	+	0.706020i	0.658932	+	0.752203i	$0.271009\pi$
$294$	8.78291	−	4.22963i	0.512230	−	0.246677i
$295$	−1.65736	−	7.26138i	−0.0964954	−	0.422774i
$296$	0.181176	−	0.793784i	0.0105306	−	0.0461378i
$297$	1.27954	+	0.616195i	0.0742466	+	0.0357553i
$298$	−5.17034	+	4.12321i	−0.299510	+	0.238851i
$299$	15.1935	+	19.0520i	0.878661	+	1.10181i
$300$	0.223707	+	0.464531i	0.0129157	+	0.0268197i
$301$	2.27073	+	1.81085i	0.130883	+	0.104376i
$302$		−	11.8685i		−	0.682956i
$303$	2.05661	−	2.57891i	0.118149	−	0.148155i
$304$	−1.07549	−	0.245473i	−0.0616835	−	0.0140789i
$305$	45.9795	+	10.4945i	2.63278	+	0.600915i
$306$	−4.95024	+	6.20740i	−0.282986	+	0.354854i
$307$			2.01324i			0.114902i	0.998348	+	0.0574508i	$0.0182972\pi$
$307$			2.01324i			0.114902i	−0.998348	+	0.0574508i	$0.981703\pi$
$308$	−0.0287925	−	0.0229613i	−0.00164061	−	0.00130834i
$309$	3.63896	+	7.55638i	0.207013	+	0.429867i
$310$	27.4871	+	34.4677i	1.56116	+	1.95763i
$311$	−15.7884	+	12.5909i	−0.895280	+	0.713962i	−0.958819	−	0.284017i	$-0.908333\pi$
$311$	−15.7884	+	12.5909i	−0.895280	+	0.713962i	0.0635390	+	0.997979i	$0.479761\pi$
$312$	−10.6400	−	5.12395i	−0.602371	−	0.290087i
$313$	−6.14242	+	26.9117i	−0.347190	+	1.52114i	0.436338	+	0.899783i	$0.356275\pi$
$313$	−6.14242	+	26.9117i	−0.347190	+	1.52114i	−0.783528	+	0.621356i	$0.786582\pi$
$314$	0.0156316	+	0.0684864i	0.000882141	+	0.00386491i
$315$	−1.52063	+	0.732296i	−0.0856777	+	0.0412602i
$316$	0.200995	−	0.417370i	0.0113068	−	0.0234789i
$317$	12.4987	−	2.85274i	0.701995	−	0.160226i	0.143398	−	0.989665i	$-0.454197\pi$
$317$	12.4987	−	2.85274i	0.701995	−	0.160226i	0.558597	+	0.829439i	$0.311340\pi$
$318$	2.92805			0.164197
$319$	−7.57426	+	1.05895i	−0.424077	+	0.0592897i
$320$	−29.0004			−1.62117
$321$	−1.49253	+	0.340660i	−0.0833049	+	0.0190138i
$322$	1.61543	−	3.35447i	0.0900243	−	0.186937i
$323$	−1.33804	+	0.644365i	−0.0744504	+	0.0358534i
$324$	0.0127813	+	0.0559987i	0.000710075	+	0.00311104i
$325$	−8.46572	+	37.0907i	−0.469594	+	2.05742i
$326$	−10.7898	−	5.19610i	−0.597592	−	0.287785i
$327$	−15.3133	+	12.2119i	−0.846826	+	0.675321i
$328$	−13.0620	−	16.3793i	−0.721229	−	0.904393i
$329$	2.41953	+	5.02420i	0.133393	+	0.276993i
$330$	−5.95413	−	4.74826i	−0.327764	−	0.261383i
$331$			15.4642i			0.849991i	0.905195	+	0.424996i	$0.139724\pi$
$331$			15.4642i			0.849991i	−0.905195	+	0.424996i	$0.860276\pi$
$332$	−0.0928543	+	0.116436i	−0.00509604	+	0.00639023i
$333$	−0.284882	−	0.0650224i	−0.0156114	−	0.00356320i
$334$	−18.1586	−	4.14458i	−0.993594	−	0.226781i
$335$	−5.93118	+	7.43746i	−0.324055	+	0.406352i
$336$			1.85620i			0.101264i
$337$	−3.43185	−	2.73681i	−0.186945	−	0.149083i	0.525545	−	0.850766i	$-0.323861\pi$
$337$	−3.43185	−	2.73681i	−0.186945	−	0.149083i	−0.712490	+	0.701682i	$0.752433\pi$
$338$	3.08894	+	6.41425i	0.168016	+	0.348889i
$339$	0.567682	+	0.711851i	0.0308323	+	0.0386624i
$340$	0.929285	−	0.741080i	0.0503976	−	0.0401907i
$341$	−10.5195	−	5.06591i	−0.569661	−	0.274334i
$342$	−0.0856365	+	0.375198i	−0.00463069	+	0.0202884i
$343$	−1.38595	−	6.07223i	−0.0748340	−	0.327869i
$344$	16.1504	−	7.77764i	0.870773	−	0.419342i
$345$	9.32620	−	19.3661i	0.502106	−	1.04263i
$346$	−19.1750	+	4.37658i	−1.03086	+	0.235286i
$347$	−36.3060			−1.94901			−0.974505	−	0.224367i	$-0.927969\pi$
$347$	−36.3060			−1.94901			−0.974505	+	0.224367i	$0.927969\pi$
$348$	−0.224484	−	0.212802i	−0.0120336	−	0.0114074i
$349$	11.1100			0.594703			0.297352	−	0.954768i	$-0.403897\pi$
$349$	11.1100			0.594703			0.297352	+	0.954768i	$0.403897\pi$
$350$	5.66698	−	1.29345i	0.302913	−	0.0691379i
$351$	−1.83894	+	3.81859i	−0.0981552	+	0.203821i
$352$	−0.415625	+	0.200155i	−0.0221529	+	0.0106683i
$353$	−0.0966037	−	0.423248i	−0.00514169	−	0.0225272i	0.972292	−	0.233770i	$-0.0751062\pi$
$353$	−0.0966037	−	0.423248i	−0.00514169	−	0.0225272i	−0.977434	+	0.211242i	$0.932249\pi$
$354$	−0.635893	+	2.78603i	−0.0337974	+	0.148076i
$355$	39.9856	+	19.2560i	2.12221	+	1.02200i
$356$	0.125406	−	0.100008i	0.00664649	−	0.00530040i
$357$	1.55804	+	1.95372i	0.0824603	+	0.103402i
$358$	−4.30377	−	8.93686i	−0.227461	−	0.472328i
$359$	6.54981	+	5.22330i	0.345686	+	0.275675i	0.780906	−	0.624649i	$-0.214758\pi$
$359$	6.54981	+	5.22330i	0.345686	+	0.275675i	−0.435220	+	0.900324i	$0.643329\pi$
$360$			10.4168i			0.549014i
$361$	11.8014	−	14.7985i	0.621128	−	0.778869i
$362$	−19.0617	−	4.35071i	−1.00186	−	0.228668i
$363$	−8.75785	−	1.99892i	−0.459668	−	0.104916i
$364$	0.0685243	−	0.0859268i	0.00359165	−	0.00450379i
$365$			19.1909i			1.00450i
$366$	−14.1472	−	11.2821i	−0.739489	−	0.589722i
$367$	14.4700	+	30.0473i	0.755329	+	1.56846i	0.821208	+	0.570630i	$0.193301\pi$
$367$	14.4700	+	30.0473i	0.755329	+	1.56846i	−0.0658785	+	0.997828i	$0.520985\pi$
$368$	−14.7391	−	18.4823i	−0.768331	−	0.963457i
$369$	−5.87836	+	4.68783i	−0.306015	+	0.244039i
$370$	1.41176	+	0.679870i	0.0733941	+	0.0353447i
$371$	0.205070	−	0.898470i	0.0106467	−	0.0466463i
$372$	−0.105079	−	0.460381i	−0.00544809	−	0.0238696i
$373$	22.5458	−	10.8575i	1.16738	−	0.562179i	0.253168	−	0.967422i	$-0.418527\pi$
$373$	22.5458	−	10.8575i	1.16738	−	0.562179i	0.914209	+	0.405243i	$0.132813\pi$
$374$	−4.89232	+	10.1590i	−0.252976	+	0.525310i
$375$	14.4928	−	3.30790i	0.748407	−	0.170819i
$376$	34.4175			1.77495
$377$	−3.16026	−	22.6042i	−0.162762	−	1.16417i
$378$	0.647560			0.0333069
$379$	3.08535	−	0.704210i	0.158484	−	0.0361729i	−0.142543	−	0.989789i	$-0.545528\pi$
$379$	3.08535	−	0.704210i	0.158484	−	0.0361729i	0.301026	+	0.953616i	$0.402671\pi$
$380$	0.0249977	−	0.0519083i	0.00128236	−	0.00266284i
$381$	2.18037	−	1.05001i	0.111704	−	0.0537938i
$382$	6.40503	+	28.0623i	0.327710	+	1.43579i
$383$	6.76874	−	29.6558i	0.345867	−	1.51534i	−0.440597	−	0.897705i	$-0.645233\pi$
$383$	6.76874	−	29.6558i	0.345867	−	1.51534i	0.786464	−	0.617636i	$-0.211910\pi$
$384$	10.6102	+	5.10961i	0.541450	+	0.260749i
$385$	−1.87401	+	1.49447i	−0.0955082	+	0.0761653i
$386$	−0.721323	−	0.904510i	−0.0367144	−	0.0460383i
$387$	−2.79132	−	5.79624i	−0.141891	−	0.294639i
$388$	0.581868	+	0.464024i	0.0295399	+	0.0235572i
$389$			4.88678i			0.247770i	0.992297	+	0.123885i	$0.0395354\pi$
$389$			4.88678i			0.247770i	−0.992297	+	0.123885i	$0.960465\pi$
$390$	14.1704	−	17.7692i	0.717548	−	0.899776i
$391$	−31.0270	−	7.08172i	−1.56911	−	0.358138i
$392$	−18.4619	−	4.21380i	−0.932466	−	0.212829i
$393$	−10.4819	+	13.1438i	−0.528740	+	0.663019i
$394$		−	1.67816i		−	0.0845446i
$395$	−23.5730	−	18.7989i	−1.18609	−	0.945874i
$396$	0.0353935	+	0.0734954i	0.00177859	+	0.00369328i
$397$	18.2813	+	22.9240i	0.917512	+	1.15052i	0.988222	+	0.153027i	$0.0489021\pi$
$397$	18.2813	+	22.9240i	0.917512	+	1.15052i	−0.0707099	+	0.997497i	$0.522526\pi$
$398$	4.78619	−	3.81686i	0.239910	−	0.191322i
$399$	0.109132	+	0.0525551i	0.00546342	+	0.00263104i
$400$	8.21257	−	35.9816i	0.410629	−	1.79908i
$401$	3.08899	+	13.5337i	0.154257	+	0.675843i	0.991619	+	0.129195i	$0.0412393\pi$
$401$	3.08899	+	13.5337i	0.154257	+	0.675843i	−0.837363	+	0.546648i	$0.815904\pi$
$402$	3.28842	−	1.58362i	0.164012	−	0.0789839i
$403$	15.1184	−	31.3937i	0.753101	−	1.56383i
$404$	0.184715	−	0.0421599i	0.00918990	−	0.00209754i
$405$	3.73850			0.185767
$406$	−2.90211	+	1.93350i	−0.144029	+	0.0959581i
$407$	−0.414989			−0.0205702
$408$	15.0364	−	3.43196i	0.744413	−	0.169907i
$409$	−2.96559	+	6.15810i	−0.146639	+	0.304499i	−0.961331	−	0.275395i	$-0.911191\pi$
$409$	−2.96559	+	6.15810i	−0.146639	+	0.304499i	0.814692	+	0.579893i	$0.196906\pi$
$410$	36.3256	−	17.4935i	1.79399	−	0.863942i
$411$	0.166961	+	0.731503i	0.00823557	+	0.0360824i
$412$	−0.107196	+	0.469658i	−0.00528119	+	0.0231384i
$413$	0.810357	+	0.390247i	0.0398750	+	0.0192028i
$414$	−6.44779	+	5.14194i	−0.316892	+	0.252713i
$415$	6.04357	+	7.57839i	0.296667	+	0.372009i
$416$	−0.597330	−	1.24037i	−0.0292865	−	0.0608141i
$417$	5.91562	+	4.71755i	0.289689	+	0.231020i
$418$			0.546554i			0.0267328i
$419$	−11.0875	+	13.9032i	−0.541658	+	0.679217i	−0.975049	−	0.221988i	$-0.928745\pi$
$419$	−11.0875	+	13.9032i	−0.541658	+	0.679217i	0.433391	+	0.901206i	$0.357317\pi$
$420$	−0.0945129	−	0.0215720i	−0.00461176	−	0.00105260i
$421$	−7.28420	−	1.66257i	−0.355010	−	0.0810287i	0.0412966	−	0.999147i	$-0.486851\pi$
$421$	−7.28420	−	1.66257i	−0.355010	−	0.0810287i	−0.396307	+	0.918118i	$0.629708\pi$
$422$	13.1499	−	16.4895i	0.640128	−	0.802695i
$423$		−	12.3521i		−	0.600580i
$424$	−4.44699	−	3.54636i	−0.215965	−	0.172226i
$425$	−21.5579	−	44.7654i	−1.04571	−	2.17144i
$426$	−10.6167	−	13.3129i	−0.514381	−	0.645013i
$427$	−4.45271	+	3.55092i	−0.215482	+	0.171841i
$428$	−0.0792257	−	0.0381531i	−0.00382952	−	0.00184420i
$429$	−1.33940	+	5.86828i	−0.0646667	+	0.283323i
$430$	7.67657	+	33.6333i	0.370197	+	1.62194i
$431$	−3.28480	+	1.58188i	−0.158223	+	0.0761964i	−0.511320	−	0.859391i	$-0.670843\pi$
$431$	−3.28480	+	1.58188i	−0.158223	+	0.0761964i	0.353096	+	0.935587i	$0.385129\pi$
$432$	1.78395	−	3.70440i	0.0858302	−	0.178228i
$433$	16.6964	−	3.81084i	0.802378	−	0.183137i	0.198382	−	0.980125i	$-0.436431\pi$
$433$	16.6964	−	3.81084i	0.802378	−	0.183137i	0.603996	+	0.796987i	$0.293574\pi$
$434$	−5.32377			−0.255549
$435$	−16.7545	+	11.1625i	−0.803316	+	0.535201i
$436$	−1.12502			−0.0538787
$437$	−1.50394	+	0.343265i	−0.0719434	+	0.0164206i
$438$	3.19473	−	6.63393i	0.152650	−	0.316982i
$439$	−10.0700	+	4.84944i	−0.480613	+	0.231451i	−0.658472	−	0.752605i	$-0.728797\pi$
$439$	−10.0700	+	4.84944i	−0.480613	+	0.231451i	0.177859	+	0.984056i	$0.443083\pi$
$440$	3.29193	+	14.4229i	0.156937	+	0.687584i
$441$	−1.51229	+	6.62579i	−0.0720140	+	0.315514i
$442$	−30.3180	−	14.6004i	−1.44208	−	0.694468i
$443$	−1.73244	+	1.38158i	−0.0823109	+	0.0656407i	−0.663781	−	0.747927i	$-0.731049\pi$
$443$	−1.73244	+	1.38158i	−0.0823109	+	0.0656407i	0.581470	+	0.813568i	$0.302478\pi$
$444$	−0.0104647	−	0.0131223i	−0.000496633	−	0.000622758i
$445$	−4.52969	−	9.40600i	−0.214728	−	0.445887i
$446$	25.4838	+	20.3227i	1.20669	+	0.962307i
$447$		−	4.61044i		−	0.218067i
$448$	2.18350	−	2.73802i	0.103161	−	0.129359i
$449$	−10.0704	−	2.29850i	−0.475251	−	0.108473i	−0.0218153	−	0.999762i	$-0.506945\pi$
$449$	−10.0704	−	2.29850i	−0.475251	−	0.108473i	−0.453435	+	0.891289i	$0.649802\pi$
$450$	−12.5527	−	2.86506i	−0.591738	−	0.135060i
$451$	−6.65759	+	8.34835i	−0.313494	+	0.393109i
$452$			0.0522976i			0.00245987i
$453$	6.46913	+	5.15896i	0.303946	+	0.242389i
$454$	0.0248382	+	0.0515770i	0.00116571	+	0.00242063i
$455$	−4.46001	−	5.59268i	−0.209089	−	0.262189i
$456$	0.584489	−	0.466114i	0.0273712	−	0.0218278i
$457$	9.40274	+	4.52812i	0.439841	+	0.211816i	0.640680	−	0.767808i	$-0.278652\pi$
$457$	9.40274	+	4.52812i	0.439841	+	0.211816i	−0.200839	+	0.979624i	$0.564367\pi$
$458$	7.28710	−	31.9269i	0.340504	−	1.49184i
$459$	−1.23170	−	5.39642i	−0.0574908	−	0.251883i
$460$	1.11236	−	0.535686i	0.0518642	−	0.0249765i
$461$	15.1808	−	31.5232i	0.707039	−	1.46818i	−0.168837	−	0.985644i	$-0.554001\pi$
$461$	15.1808	−	31.5232i	0.707039	−	1.46818i	0.875876	−	0.482537i	$-0.160285\pi$
$462$	0.896597	−	0.204642i	0.0417134	−	0.00952082i
$463$	−1.96604			−0.0913694			−0.0456847	−	0.998956i	$-0.514547\pi$
$463$	−1.96604			−0.0913694			−0.0456847	+	0.998956i	$0.514547\pi$
$464$	3.06576	+	21.9283i	0.142324	+	1.01799i
$465$	−30.7352			−1.42531
$466$	14.6206	−	3.33705i	0.677286	−	0.154586i
$467$	−15.2959	+	31.7623i	−0.707811	+	1.46978i	0.167323	+	0.985902i	$0.446488\pi$
$467$	−15.2959	+	31.7623i	−0.707811	+	1.46978i	−0.875134	+	0.483882i	$0.839227\pi$
$468$	−0.219335	+	0.105626i	−0.0101388	+	0.00488258i
$469$	−0.255624	−	1.11996i	−0.0118036	−	0.0517151i
$470$	−14.7391	+	64.5764i	−0.679865	+	2.97869i
$471$	−0.0441243	−	0.0212492i	−0.00203314	−	0.000979109i
$472$	4.34012	−	3.46113i	0.199770	−	0.159311i
$473$	−5.69653	−	7.14322i	−0.261927	−	0.328446i
$474$	5.01929	+	10.4227i	0.230544	+	0.478729i
$475$	−1.88294	−	1.50160i	−0.0863954	−	0.0688981i
$476$			0.143534i			0.00657888i
$477$	−1.27275	+	1.59598i	−0.0582754	+	0.0730750i
$478$	−42.5642	−	9.71500i	−1.94684	−	0.444354i
$479$	16.6729	+	3.80547i	0.761802	+	0.173876i	0.585736	−	0.810502i	$-0.300806\pi$
$479$	16.6729	+	3.80547i	0.761802	+	0.173876i	0.176066	+	0.984378i	$0.443663\pi$
$480$	−0.757136	+	0.949418i	−0.0345584	+	0.0433348i
$481$		−	1.23847i		−	0.0564693i
$482$	19.4594	+	15.5184i	0.886352	+	0.706842i
$483$	1.12622	+	2.33862i	0.0512449	+	0.106411i
$484$	−0.321707	−	0.403407i	−0.0146230	−	0.0183367i
$485$	37.8718	−	30.2017i	1.71967	−	1.37139i
$486$	−1.29233	−	0.622353i	−0.0586213	−	0.0282305i
$487$	0.776839	−	3.40355i	0.0352019	−	0.154230i	−0.954272	−	0.298939i	$-0.903367\pi$
$487$	0.776839	−	3.40355i	0.0352019	−	0.154230i	0.989474	+	0.144709i	$0.0462246\pi$
$488$	7.82176	+	34.2694i	0.354074	+	1.55130i
$489$	7.52229	−	3.62255i	0.340170	−	0.163817i
$490$	15.8124	−	32.8349i	0.714333	−	1.48333i
$491$	1.22196	−	0.278905i	0.0551464	−	0.0125868i	−0.194859	−	0.980831i	$-0.562425\pi$
$491$	1.22196	−	0.278905i	0.0551464	−	0.0125868i	0.250005	+	0.968245i	$0.419568\pi$
$492$	−0.431865			−0.0194700
$493$	21.6328	+	20.5070i	0.974292	+	0.923590i
$494$	−1.63110			−0.0733868
$495$	5.17624	−	1.18144i	0.232655	−	0.0531019i
$496$	−14.6663	+	30.4549i	−0.658537	+	1.36747i
$497$	−4.82862	+	2.32534i	−0.216593	+	0.104306i
$498$	−0.827564	−	3.62579i	−0.0370840	−	0.162476i
$499$	0.768702	−	3.36791i	0.0344118	−	0.150768i	−0.954803	−	0.297239i	$-0.903934\pi$
$499$	0.768702	−	3.36791i	0.0344118	−	0.150768i	0.989215	+	0.146471i	$0.0467914\pi$
$500$	0.769301	+	0.370476i	0.0344042	+	0.0165682i
$501$	10.1522	−	8.09609i	0.453566	−	0.361707i
$502$	0.959298	+	1.20292i	0.0428156	+	0.0536890i
$503$	−11.8365	−	24.5787i	−0.527762	−	1.09591i	−0.979067	−	0.203539i	$-0.934756\pi$
$503$	−11.8365	−	24.5787i	−0.527762	−	1.09591i	0.451305	−	0.892370i	$-0.350959\pi$
$504$	−0.983485	−	0.784303i	−0.0438079	−	0.0349356i
$505$		−	12.3316i		−	0.548750i
$506$	−7.30251	+	9.15706i	−0.324636	+	0.407081i
$507$	−4.83888	−	1.10444i	−0.214902	−	0.0490501i
$508$	0.135519	+	0.0309313i	0.00601267	+	0.00137235i
$509$	24.6614	−	30.9244i	1.09310	−	1.37070i	0.170307	−	0.985391i	$-0.445524\pi$
$509$	24.6614	−	30.9244i	1.09310	−	1.37070i	0.922788	−	0.385307i	$-0.125905\pi$
$510$			29.6820i			1.31434i
$511$	−1.81187	−	1.44492i	−0.0801525	−	0.0639195i
$512$	−9.36199	−	19.4404i	−0.413745	−	0.859151i
$513$	−0.167284	−	0.209767i	−0.00738576	−	0.00926146i
$514$	−13.0982	+	10.4454i	−0.577735	+	0.460728i
$515$	28.2495	+	13.6042i	1.24482	+	0.599474i
$516$	0.0822267	−	0.360259i	0.00361983	−	0.0158595i
$517$	−3.90352	−	17.1024i	−0.171677	−	0.752164i
$518$	−0.170483	+	0.0821004i	−0.00749060	+	0.00360728i
$519$	5.94941	−	12.3541i	0.261150	−	0.542283i
$520$	−43.0428	+	9.82425i	−1.88755	+	0.430822i
$521$	−33.5980			−1.47195			−0.735977	−	0.677006i	$-0.763277\pi$
$521$	−33.5980			−1.47195			−0.735977	+	0.677006i	$0.763277\pi$
$522$	7.64996	−	1.06953i	0.334829	−	0.0468121i
$523$	−8.65052			−0.378261			−0.189130	−	0.981952i	$-0.560567\pi$
$523$	−8.65052			−0.378261			−0.189130	+	0.981952i	$0.560567\pi$
$524$	−0.941428	+	0.214875i	−0.0411265	+	0.00938685i
$525$	−1.75829	+	3.65112i	−0.0767379	+	0.159348i
$526$	16.3964	−	7.89607i	0.714916	−	0.344285i
$527$	10.1261	+	44.3655i	0.441101	+	1.93259i
$528$	1.29934	−	5.69280i	0.0565467	−	0.247747i
$529$	−9.06142	−	4.36375i	−0.393975	−	0.189728i
$530$	8.55832	−	6.82503i	0.371750	−	0.296460i
$531$	−1.24217	−	1.55763i	−0.0539054	−	0.0675952i
$532$	0.00301870	+	0.00626840i	0.000130877	+	0.000271769i
$533$	−24.9143	−	19.8685i	−1.07916	−	0.860601i
$534$			4.00555i			0.173337i
$535$	−3.56843	+	4.47467i	−0.154277	+	0.193457i
$536$	−6.91234	−	1.57770i	−0.298568	−	0.0681461i
$537$	6.74193	+	1.53880i	0.290936	+	0.0664042i
$538$	2.88292	−	3.61506i	0.124291	−	0.155856i
$539$			9.65184i			0.415734i
$540$	0.167886	+	0.133885i	0.00722468	+	0.00576149i
$541$	−17.3909	−	36.1125i	−0.747691	−	1.55260i	−0.831126	−	0.556084i	$-0.812303\pi$
$541$	−17.3909	−	36.1125i	−0.747691	−	1.55260i	0.0834350	−	0.996513i	$-0.473411\pi$
$542$	12.4528	+	15.6154i	0.534895	+	0.670738i
$543$	10.6571	−	8.49875i	0.457340	−	0.364716i
$544$	1.61991	+	0.780107i	0.0694530	+	0.0334468i
$545$	−16.2938	+	71.3879i	−0.697950	+	3.05792i
$546$	0.610723	+	2.67575i	0.0261365	+	0.114512i
$547$	21.9974	−	10.5934i	0.940543	−	0.452941i	0.100182	−	0.994969i	$-0.468058\pi$
$547$	21.9974	−	10.5934i	0.940543	−	0.452941i	0.840361	+	0.542028i	$0.182343\pi$
$548$	−0.0186992	+	0.0388293i	−0.000798789	+	0.00165870i
$549$	12.2989	−	2.80715i	0.524906	−	0.119806i
$550$	−18.2855			−0.779698
$551$	1.37603	+	0.440615i	0.0586209	+	0.0187708i
$552$	16.0204			0.681872
$553$	3.54972	−	0.810201i	0.150950	−	0.0344532i
$554$	−11.0767	+	23.0011i	−0.470606	+	0.977223i
$555$	−0.984234	+	0.473982i	−0.0417784	+	0.0201194i
$556$	0.0967083	+	0.423707i	0.00410135	+	0.0179692i
$557$	−1.87302	+	8.20623i	−0.0793624	+	0.347709i	−0.998982	−	0.0450996i	$-0.985639\pi$
$557$	−1.87302	+	8.20623i	−0.0793624	+	0.347709i	0.919620	+	0.392809i	$0.128497\pi$
$558$	10.6246	+	5.11653i	0.449775	+	0.216600i
$559$	21.3178	−	17.0004i	0.901648	−	0.719040i
$560$	4.32664	+	5.42544i	0.182834	+	0.229267i
$561$	−3.41076	−	7.08252i	−0.144003	−	0.299024i
$562$	11.5332	+	9.19741i	0.486498	+	0.387969i
$563$			5.32771i			0.224536i	0.993678	+	0.112268i	$0.0358116\pi$
$563$			5.32771i			0.224536i	−0.993678	+	0.112268i	$0.964188\pi$
$564$	0.442360	−	0.554702i	0.0186267	−	0.0233572i
$565$	3.31853	+	0.757432i	0.139611	+	0.0318654i
$566$	27.9485	+	6.37906i	1.17476	+	0.268132i
$567$	−0.281479	+	0.352963i	−0.0118210	+	0.0148231i
$568$			33.0777i			1.38791i
$569$	−4.70014	−	3.74823i	−0.197040	−	0.157134i	0.520000	−	0.854166i	$-0.325932\pi$
$569$	−4.70014	−	3.74823i	−0.197040	−	0.157134i	−0.717040	+	0.697032i	$0.754503\pi$
$570$	0.624250	+	1.29627i	0.0261470	+	0.0542947i
$571$	−12.9032	−	16.1801i	−0.539983	−	0.677117i	0.434734	−	0.900559i	$-0.356842\pi$
$571$	−12.9032	−	16.1801i	−0.539983	−	0.677117i	−0.974717	+	0.223441i	$0.928271\pi$
$572$	−0.270307	+	0.215562i	−0.0113021	+	0.00901312i
$573$	−18.0799	−	8.70683i	−0.755299	−	0.363733i
$574$	−1.08341	+	4.74674i	−0.0452207	+	0.198125i
$575$	−11.4843	−	50.3161i	−0.478929	−	2.09832i
$576$	−6.98903	+	3.36574i	−0.291210	+	0.140239i
$577$	−11.5056	+	23.8917i	−0.478985	+	0.994623i	0.511790	+	0.859110i	$0.328982\pi$
$577$	−11.5056	+	23.8917i	−0.478985	+	0.994623i	−0.990776	+	0.135513i	$0.956732\pi$
$578$	19.0722	−	4.35311i	0.793300	−	0.181065i
$579$	0.806560			0.0335195
$580$	−1.15216	−	0.0987401i	−0.0478408	−	0.00409996i
$581$	−1.17053			−0.0485619
$582$	−18.1193	+	4.13561i	−0.751069	+	0.171427i
$583$	−1.25786	+	2.61198i	−0.0520953	+	0.108177i
$584$	−12.8868	+	6.20597i	−0.533260	+	0.256805i
$585$	3.52583	+	15.4477i	0.145775	+	0.638682i
$586$	4.28130	−	18.7576i	0.176859	−	0.774869i
$587$	−0.282262	−	0.135930i	−0.0116502	−	0.00561044i	0.428050	−	0.903755i	$-0.359201\pi$
$587$	−0.282262	−	0.135930i	−0.0116502	−	0.00561044i	−0.439700	+	0.898145i	$0.644915\pi$
$588$	−0.305200	+	0.243389i	−0.0125862	+	0.0100372i
$589$	1.37529	+	1.72456i	0.0566677	+	0.0710591i
$590$	4.63536	+	9.62543i	0.190835	+	0.396273i
$591$	0.914711	+	0.729457i	0.0376262	+	0.0300059i
$592$			1.20144i			0.0493787i
$593$	5.47251	−	6.86231i	0.224729	−	0.281801i	−0.656666	−	0.754182i	$-0.728034\pi$
$593$	5.47251	−	6.86231i	0.224729	−	0.281801i	0.881395	+	0.472380i	$0.156605\pi$
$594$	−1.98601	−	0.453293i	−0.0814869	−	0.0185988i
$595$	9.10792	+	2.07882i	0.373388	+	0.0852234i
$596$	0.165112	−	0.207044i	0.00676324	−	0.00848083i
$597$			4.26789i			0.174673i
$598$	−27.3278	−	21.7932i	−1.11752	−	0.891189i
$599$	−1.84626	−	3.83380i	−0.0754362	−	0.156645i	0.859840	−	0.510564i	$-0.170563\pi$
$599$	−1.84626	−	3.83380i	−0.0754362	−	0.156645i	−0.935276	+	0.353919i	$0.884849\pi$
$600$	15.5943	+	19.5547i	0.636637	+	0.798317i
$601$	−10.9634	+	8.74299i	−0.447205	+	0.356634i	−0.821049	−	0.570857i	$-0.806611\pi$
$601$	−10.9634	+	8.74299i	−0.447205	+	0.356634i	0.373844	+	0.927491i	$0.378039\pi$
$602$	−3.75341	−	1.80755i	−0.152978	−	0.0736701i
$603$	−0.566220	+	2.48077i	−0.0230583	+	0.101025i
$604$	0.105757	+	0.463352i	0.00430319	+	0.0188535i
$605$	−30.2574	+	14.5712i	−1.23014	+	0.592403i
$606$	−2.05286	+	4.26282i	−0.0833919	+	0.173165i
$607$	−3.87184	+	0.883722i	−0.157153	+	0.0358692i	−0.300374	−	0.953822i	$-0.597111\pi$
$607$	−3.87184	+	0.883722i	−0.157153	+	0.0358692i	0.143221	+	0.989691i	$0.454254\pi$
$608$	0.0871510			0.00353444
$609$	0.207590	−	2.42229i	0.00841199	−	0.0981562i
$610$	−67.6481			−2.73899
$611$	51.0395	−	11.6494i	2.06484	−	0.471286i
$612$	0.137947	−	0.286450i	0.00557618	−	0.0115791i
$613$	21.0025	−	10.1143i	0.848283	−	0.408511i	0.0413429	−	0.999145i	$-0.486836\pi$
$613$	21.0025	−	10.1143i	0.848283	−	0.408511i	0.806940	+	0.590634i	$0.201122\pi$
$614$	−0.642584	−	2.81534i	−0.0259326	−	0.113618i
$615$	−6.25476	+	27.4039i	−0.252216	+	1.10503i
$616$	−1.60957	−	0.775127i	−0.0648513	−	0.0312307i
$617$	−22.4100	+	17.8714i	−0.902192	+	0.719474i	−0.960339	−	0.278834i	$-0.910052\pi$
$617$	−22.4100	+	17.8714i	−0.902192	+	0.719474i	0.0581471	+	0.998308i	$0.481481\pi$
$618$	−7.50061	−	9.40547i	−0.301719	−	0.378344i
$619$	0.882084	+	1.83167i	0.0354540	+	0.0736209i	0.917944	−	0.396711i	$-0.129848\pi$
$619$	0.882084	+	1.83167i	0.0354540	+	0.0736209i	−0.882490	+	0.470332i	$0.844134\pi$
$620$	−1.38024	−	1.10070i	−0.0554318	−	0.0442054i
$621$		−	5.74956i		−	0.230722i
$622$	18.0600	−	22.6466i	0.724142	−	0.908045i
$623$	1.22910	+	0.280534i	0.0492429	+	0.0112394i
$624$	16.9893	+	3.87769i	0.680115	+	0.155232i
$625$	6.66702	−	8.36018i	0.266681	−	0.334407i
$626$		−	39.5942i		−	1.58250i
$627$	−0.297908	−	0.237574i	−0.0118973	−	0.00948779i
$628$	−0.00122053	−	0.00253445i	−4.87043e−5	−	0.000101136i
$629$	1.00845	+	1.26456i	0.0402096	+	0.0504212i
$630$	1.89273	−	1.50941i	0.0754084	−	0.0601362i
$631$	27.6702	+	13.3253i	1.10153	+	0.530470i	0.894140	−	0.447787i	$-0.147788\pi$
$631$	27.6702	+	13.3253i	1.10153	+	0.530470i	0.207393	+	0.978258i	$0.433502\pi$
$632$	5.00051	−	21.9087i	0.198910	−	0.871480i
$633$	3.27191	+	14.3352i	0.130047	+	0.569772i
$634$	−16.5678	+	7.97862i	−0.657990	+	0.316871i
$635$	3.92547	−	8.15131i	0.155777	−	0.323475i
$636$	−0.114312	+	0.0260910i	−0.00453278	+	0.00103458i
$637$	−28.8044			−1.14127
$638$	10.2540	−	3.89839i	0.405958	−	0.154339i
$639$	11.8713			0.469620
$640$	42.9224	−	9.79676i	1.69666	−	0.387251i
$641$	9.88794	−	20.5325i	0.390550	−	0.810986i	−0.609287	−	0.792950i	$-0.708544\pi$
$641$	9.88794	−	20.5325i	0.390550	−	0.810986i	0.999837	−	0.0180363i	$-0.00574146\pi$
$642$	1.97844	−	0.952769i	0.0780830	−	0.0376028i
$643$	−6.15658	−	26.9737i	−0.242792	−	1.06374i	−0.938463	−	0.345380i	$-0.887750\pi$
$643$	−6.15658	−	26.9737i	−0.242792	−	1.06374i	0.695671	−	0.718360i	$-0.255107\pi$
$644$	−0.0331762	+	0.145355i	−0.00130733	+	0.00572777i
$645$	−21.6692	−	10.4353i	−0.853224	−	0.410891i
$646$	1.66546	−	1.32816i	0.0655267	−	0.0522558i
$647$	−11.4275	−	14.3296i	−0.449261	−	0.563356i	0.504696	−	0.863297i	$-0.331604\pi$
$647$	−11.4275	−	14.3296i	−0.449261	−	0.563356i	−0.953958	+	0.299941i	$0.903033\pi$
$648$	1.20896	+	2.51043i	0.0474924	+	0.0986190i
$649$	−2.21212	−	1.76410i	−0.0868332	−	0.0692471i
$650$		−	54.5703i		−	2.14042i
$651$	2.31411	−	2.90181i	0.0906973	−	0.113731i
$652$	0.467540	+	0.106713i	0.0183103	+	0.00417920i
$653$	−17.2172	−	3.92971i	−0.673760	−	0.153781i	−0.128066	−	0.991766i	$-0.540877\pi$
$653$	−17.2172	−	3.92971i	−0.673760	−	0.153781i	−0.545694	+	0.837984i	$0.683734\pi$
$654$	17.5165	−	21.9650i	0.684950	−	0.858900i
$655$			62.8501i			2.45576i
$656$	24.1693	+	19.2744i	0.943654	+	0.752539i
$657$	2.22726	+	4.62496i	0.0868937	+	0.180437i
$658$	−4.98712	−	6.25365i	−0.194418	−	0.243793i
$659$	−8.15019	+	6.49956i	−0.317486	+	0.253187i	−0.769246	−	0.638953i	$-0.779368\pi$
$659$	−8.15019	+	6.49956i	−0.317486	+	0.253187i	0.451760	+	0.892140i	$0.350797\pi$
$660$	0.274762	+	0.132319i	0.0106951	+	0.00515049i
$661$	1.32334	−	5.79792i	0.0514718	−	0.225513i	−0.942650	−	0.333784i	$-0.891674\pi$
$661$	1.32334	−	5.79792i	0.0514718	−	0.225513i	0.994121	+	0.108271i	$0.0345315\pi$
$662$	−4.93586	−	21.6254i	−0.191838	−	0.840496i
$663$	21.1367	−	10.1789i	0.820880	−	0.395315i
$664$	−3.13457	+	6.50901i	−0.121645	+	0.252599i
$665$	0.441479	−	0.100765i	0.0171198	−	0.00390749i
$666$	0.419136			0.0162412
$667$	17.1672	+	25.7673i	0.664716	+	0.997713i
$668$	0.745850			0.0288578
$669$	−22.1544	+	5.05661i	−0.856540	+	0.195500i
$670$	5.92036	−	12.2938i	0.228724	−	0.474949i
$671$	16.1417	−	7.77344i	0.623144	−	0.300091i
$672$	−0.0326313	−	0.142967i	−0.00125878	−	0.00551508i
$673$	−0.421936	+	1.84862i	−0.0162644	+	0.0712592i	−0.982409	−	0.186743i	$-0.940207\pi$
$673$	−0.421936	+	1.84862i	−0.0162644	+	0.0712592i	0.966144	+	0.258002i	$0.0830641\pi$
$674$	5.67268	+	2.73182i	0.218503	+	0.105226i
$675$	7.01799	−	5.59666i	0.270123	−	0.215416i
$676$	−0.177749	−	0.222890i	−0.00683651	−	0.00857271i
$677$	−13.3689	−	27.7608i	−0.513808	−	1.06693i	−0.982961	−	0.183816i	$-0.941155\pi$
$677$	−13.3689	−	27.7608i	−0.513808	−	1.06693i	0.469153	−	0.883117i	$-0.344559\pi$
$678$	−1.02106	−	0.814271i	−0.0392137	−	0.0312719i
$679$			5.84954i			0.224485i
$680$	35.9499	−	45.0798i	1.37862	−	1.72873i
$681$	−0.0389095	−	0.00888084i	−0.00149102	−	0.000340314i
$682$	16.3275	+	3.72665i	0.625213	+	0.142701i
$683$	−24.6040	+	30.8524i	−0.941446	+	1.18054i	0.0419604	+	0.999119i	$0.486640\pi$
$683$	−24.6040	+	30.8524i	−0.941446	+	1.18054i	−0.983406	+	0.181417i	$0.941932\pi$
$684$		−	0.0154110i		−	0.000589254i
$685$	2.19308	+	1.74892i	0.0837931	+	0.0668228i
$686$	3.87625	+	8.04912i	0.147996	+	0.307317i
$687$	14.2347	+	17.8498i	0.543089	+	0.681013i
$688$	−20.6804	+	16.4920i	−0.788431	+	0.628753i
$689$	−7.79504	−	3.75389i	−0.296967	−	0.143012i
$690$	−6.86066	+	30.0585i	−0.261181	+	1.14431i
$691$	−10.1734	−	44.5726i	−0.387014	−	1.69562i	−0.674861	−	0.737945i	$-0.735797\pi$
$691$	−10.1734	−	44.5726i	−0.387014	−	1.69562i	0.287847	−	0.957676i	$-0.407061\pi$
$692$	0.709603	−	0.341727i	0.0269751	−	0.0129905i
$693$	−0.278185	+	0.577658i	−0.0105674	+	0.0219434i
$694$	50.7709	−	11.5881i	1.92724	−	0.439879i
$695$	28.2868			1.07298
$696$	−12.9138	−	7.64102i	−0.489496	−	0.289632i
$697$	41.6175			1.57638
$698$	−15.5364	+	3.54607i	−0.588060	+	0.134221i
$699$	−4.53631	+	9.41974i	−0.171579	+	0.356287i
$700$	−0.209716	+	0.100994i	−0.00792652	+	0.00381721i
$701$	2.74347	+	12.0199i	0.103619	+	0.453987i	0.999944	+	0.0105879i	$0.00337030\pi$
$701$	2.74347	+	12.0199i	0.103619	+	0.453987i	−0.896324	+	0.443399i	$0.853773\pi$
$702$	1.35278	−	5.92692i	0.0510575	−	0.223697i
$703$	0.0706361	+	0.0340165i	0.00266409	+	0.00128296i
$704$	−8.61321	+	6.86881i	−0.324623	+	0.258878i
$705$	−28.7917	−	36.1036i	−1.08436	−	1.35974i
$706$	0.270184	+	0.561043i	0.0101685	+	0.0211151i
$707$	1.16427	+	0.928473i	0.0437868	+	0.0349188i
$708$		−	0.114434i		−	0.00430070i
$709$	12.5325	−	15.7152i	0.470667	−	0.590197i	−0.488668	−	0.872470i	$-0.662517\pi$
$709$	12.5325	−	15.7152i	0.470667	−	0.590197i	0.959334	+	0.282273i	$0.0910883\pi$
$710$	−62.0625	−	14.1654i	−2.32917	−	0.531617i
$711$	−7.86281	−	1.79464i	−0.294879	−	0.0673041i
$712$	4.85139	−	6.08345i	0.181813	−	0.227987i
$713$			47.2687i			1.77023i
$714$	−2.80238	−	2.23482i	−0.104876	−	0.0836360i
$715$	9.76356	+	20.2742i	0.365137	+	0.758214i
$716$	0.247655	+	0.310549i	0.00925530	+	0.0116058i
$717$	23.7970	−	18.9774i	0.888714	−	0.708726i
$718$	−10.8265	−	5.21377i	−0.404042	−	0.194576i
$719$	4.06595	−	17.8141i	0.151634	−	0.664353i	−0.840776	−	0.541383i	$-0.817901\pi$
$719$	4.06595	−	17.8141i	0.151634	−	0.664353i	0.992410	−	0.122970i	$-0.0392419\pi$
$720$	−3.42040	−	14.9857i	−0.127471	−	0.558485i
$721$	−3.41138	+	1.64283i	−0.127046	+	0.0611823i
$722$	−11.7799	+	24.4612i	−0.438403	+	0.910353i
$723$	−16.9171	+	3.86121i	−0.629153	+	0.143600i
$724$	0.782945			0.0290979
$725$	−14.7412	+	46.0366i	−0.547475	+	1.70976i
$726$	12.8851			0.478212
$727$	−28.5817	+	6.52358i	−1.06004	+	0.241946i	−0.716783	−	0.697297i	$-0.754386\pi$
$727$	−28.5817	+	6.52358i	−1.06004	+	0.241946i	−0.343253	+	0.939243i	$0.611529\pi$
$728$	2.31324	−	4.80350i	0.0857345	−	0.178029i
$729$	0.900969	−	0.433884i	0.0333692	−	0.0160698i
$730$	−6.12532	−	26.8368i	−0.226708	−	0.993274i
$731$	−7.92393	+	34.7170i	−0.293077	+	1.28405i
$732$	0.652846	+	0.314394i	0.0241299	+	0.0116203i
$733$	17.8909	−	14.2675i	0.660815	−	0.526983i	−0.234669	−	0.972075i	$-0.575401\pi$
$733$	17.8909	−	14.2675i	0.660815	−	0.526983i	0.895485	+	0.445093i	$0.146829\pi$
$734$	−29.8256	−	37.4001i	−1.10088	−	1.38046i
$735$	11.0239	+	22.8914i	0.406623	+	0.844361i
$736$	1.46014	+	1.16442i	0.0538216	+	0.0429213i
$737$			3.61376i			0.133115i
$738$	6.72412	−	8.43178i	0.247518	−	0.310378i
$739$	13.1536	+	3.00222i	0.483863	+	0.110439i	0.457492	−	0.889214i	$-0.348748\pi$
$739$	13.1536	+	3.00222i	0.483863	+	0.110439i	0.0263709	+	0.999652i	$0.491605\pi$
$740$	−0.0611740	−	0.0139626i	−0.00224880	−	0.000513274i
$741$	0.709002	−	0.889061i	0.0260458	−	0.0326605i
$742$			1.32189i			0.0485280i
$743$	8.50302	+	6.78093i	0.311945	+	0.248768i	0.766929	−	0.641731i	$-0.221784\pi$
$743$	8.50302	+	6.78093i	0.311945	+	0.248768i	−0.454984	+	0.890500i	$0.650355\pi$
$744$	−9.93918	−	20.6389i	−0.364388	−	0.756660i
$745$	−10.7465	−	13.4757i	−0.393723	−	0.493713i
$746$	−28.0629	+	22.3794i	−1.02746	+	0.819369i
$747$	2.33602	+	1.12497i	0.0854706	+	0.0411605i
$748$	0.100474	−	0.440206i	0.00367370	−	0.0160955i
$749$	−0.153793	−	0.673813i	−0.00561949	−	0.0246206i
$750$	−19.2112	+	9.25162i	−0.701494	+	0.337822i
$751$	−10.1785	+	21.1358i	−0.371418	+	0.771257i	−0.999979	−	0.00650335i	$-0.997930\pi$
$751$	−10.1785	+	21.1358i	−0.371418	+	0.771257i	0.628561	+	0.777760i	$0.283644\pi$
$752$	−49.5133	+	11.3011i	−1.80556	+	0.412108i
$753$	−1.07266			−0.0390898
$754$	11.6341	+	30.6013i	0.423690	+	1.11443i
$755$	30.9335			1.12579
$756$	−0.0252810	+	0.00577023i	−0.000919461	+	0.000209861i
$757$	−16.1202	+	33.4740i	−0.585899	+	1.21663i	0.371653	+	0.928372i	$0.378791\pi$
$757$	−16.1202	+	33.4740i	−0.585899	+	1.21663i	−0.957552	+	0.288260i	$0.906923\pi$
$758$	−4.08983	+	1.96956i	−0.148549	+	0.0715375i
$759$	−1.81698	−	7.96071i	−0.0659522	−	0.288955i
$760$	0.621914	−	2.72479i	0.0225592	−	0.0988384i
$761$	12.6718	+	6.10244i	0.459354	+	0.221213i	0.649226	−	0.760596i	$-0.275093\pi$
$761$	12.6718	+	6.10244i	0.459354	+	0.221213i	−0.189872	+	0.981809i	$0.560807\pi$
$762$	−2.71392	+	2.16428i	−0.0983151	+	0.0784037i
$763$	−5.51316	−	6.91329i	−0.199590	−	0.250278i
$764$	−0.500110	−	1.03849i	−0.0180933	−	0.0375712i
$765$	−16.1787	−	12.9021i	−0.584942	−	0.466476i
$766$			43.6316i			1.57647i
$767$	5.26469	−	6.60171i	0.190097	−	0.238374i
$768$	−1.34287	−	0.306502i	−0.0484567	−	0.0110599i
$769$	8.10907	+	1.85084i	0.292421	+	0.0667431i	0.366215	−	0.930530i	$-0.380654\pi$
$769$	8.10907	+	1.85084i	0.292421	+	0.0667431i	−0.0737940	+	0.997274i	$0.523511\pi$
$770$	2.14363	−	2.68803i	0.0772512	−	0.0968700i
$771$		−	11.6797i		−	0.420636i
$772$	0.0362206	+	0.0288850i	0.00130361	+	0.00103959i
$773$	12.9574	+	26.9063i	0.466044	+	0.967751i	0.993028	+	0.117876i	$0.0376085\pi$
$773$	12.9574	+	26.9063i	0.466044	+	0.967751i	−0.526984	+	0.849875i	$0.676677\pi$
$774$	5.75346	+	7.21461i	0.206804	+	0.259324i
$775$	−57.6968	+	46.0117i	−2.07253	+	1.65279i
$776$	32.5277	+	15.6645i	1.16768	+	0.562323i
$777$	0.0293548	−	0.128612i	0.00105310	−	0.00461392i
$778$	−1.55976	−	6.83375i	−0.0559201	−	0.245002i
$779$	1.81751	−	0.875268i	0.0651191	−	0.0313597i
$780$	−0.394884	+	0.819984i	−0.0141391	+	0.0293602i
$781$	16.4367	−	3.75156i	0.588151	−	0.134242i
$782$	45.6490			1.63241
$783$	−2.74229	+	4.63464i	−0.0980014	+	0.165628i
$784$	27.9431			0.997966
$785$	−0.178500	+	0.0407414i	−0.00637093	+	0.00145412i
$786$	10.4628	−	21.7261i	0.373194	−	0.774945i
$787$	8.48387	−	4.08562i	0.302417	−	0.145637i	−0.276521	−	0.961008i	$-0.589182\pi$
$787$	8.48387	−	4.08562i	0.302417	−	0.145637i	0.578938	+	0.815371i	$0.303467\pi$
$788$	0.0149536	+	0.0655162i	0.000532702	+	0.00233392i
$789$	−2.82322	+	12.3694i	−0.100509	+	0.440361i
$790$	38.9651	+	18.7646i	1.38632	+	0.667614i
$791$	−0.321370	+	0.256284i	−0.0114266	+	0.00911241i
$792$	2.46725	+	3.09383i	0.0876697	+	0.109934i
$793$	23.1986	+	48.1724i	0.823807	+	1.71065i
$794$	−32.8817	−	26.2223i	−1.16693	−	0.930594i
$795$			7.63153i			0.270663i
$796$	−0.152844	+	0.191660i	−0.00541741	+	0.00679322i
$797$	30.0377	+	6.85591i	1.06399	+	0.242849i	0.718467	−	0.695561i	$-0.244844\pi$
$797$	30.0377	+	6.85591i	1.06399	+	0.242849i	0.345523	+	0.938410i	$0.387701\pi$
$798$	−0.169386	−	0.0386612i	−0.00599619	−	0.00136859i
$799$	−42.6288	+	53.4549i	−1.50810	+	1.89110i
$800$			2.91573i			0.103087i
$801$	−2.18329	−	1.74112i	−0.0771428	−	0.0615193i
$802$	−8.63937	−	17.9398i	−0.305067	−	0.633478i
$803$	4.54540	+	5.69975i	0.160404	+	0.201140i
$804$	−0.114270	+	0.0911275i	−0.00403000	+	0.00321382i
$805$	8.74294	+	4.21038i	0.308148	+	0.148396i
$806$	−11.1216	+	48.7269i	−0.391741	+	1.71633i
$807$	0.717315	+	3.14276i	0.0252507	+	0.110631i
$808$	8.28078	−	3.98782i	0.291317	−	0.140291i
$809$	12.2271	−	25.3898i	0.429881	−	0.892657i	−0.567706	−	0.823231i	$-0.692169\pi$
$809$	12.2271	−	25.3898i	0.429881	−	0.892657i	0.997587	−	0.0694260i	$-0.0221168\pi$
$810$	−5.22797	+	1.19325i	−0.183692	+	0.0419265i
$811$	−35.2846			−1.23901			−0.619505	−	0.784993i	$-0.712667\pi$
$811$	−35.2846			−1.23901			−0.619505	+	0.784993i	$0.712667\pi$
$812$	0.0960707	−	0.101345i	0.00337142	−	0.00355650i
$813$	−13.9244			−0.488349
$814$	0.580327	−	0.132456i	0.0203404	−	0.00464257i
$815$	13.5429	−	28.1221i	0.474386	−	0.985073i
$816$	−20.5046	+	9.87451i	−0.717805	+	0.345677i
$817$	0.384089	+	1.68280i	0.0134376	+	0.0588739i
$818$	2.18158	−	9.55813i	0.0762772	−	0.334192i
$819$	−1.72393	−	0.830201i	−0.0602390	−	0.0290096i
$820$	−1.26229	+	1.00664i	−0.0440810	+	0.0351534i
$821$	−24.3117	−	30.4859i	−0.848485	−	1.06397i	−0.997177	−	0.0750827i	$-0.976078\pi$
$821$	−24.3117	−	30.4859i	−0.848485	−	1.06397i	0.148693	−	0.988883i	$-0.452493\pi$
$822$	−0.466961	−	0.969654i	−0.0162871	−	0.0338206i
$823$	5.86605	+	4.67802i	0.204478	+	0.163066i	0.720375	−	0.693585i	$-0.243970\pi$
$823$	5.86605	+	4.67802i	0.204478	+	0.163066i	−0.515897	+	0.856651i	$0.672541\pi$
$824$			23.3691i			0.814101i
$825$	7.94829	−	9.96684i	0.276724	−	0.347001i
$826$	−1.25777	−	0.287079i	−0.0437635	−	0.00998874i
$827$	0.383277	+	0.0874805i	0.0133278	+	0.00304199i	0.229180	−	0.973384i	$-0.426396\pi$
$827$	0.383277	+	0.0874805i	0.0133278	+	0.00304199i	−0.215852	+	0.976426i	$0.569253\pi$
$828$	0.205906	−	0.258198i	0.00715573	−	0.00897301i
$829$		−	29.1169i		−	1.01127i	−0.862747	−	0.505635i	$-0.831258\pi$
$829$		−	29.1169i		−	1.01127i	0.862747	−	0.505635i	$-0.168742\pi$
$830$	−10.8703	−	8.66875i	−0.377313	−	0.300897i
$831$	−7.72234	−	16.0356i	−0.267885	−	0.556269i
$832$	−20.4989	−	25.7048i	−0.710670	−	0.891152i
$833$	29.4111	−	23.4546i	1.01904	−	0.812654i
$834$	−9.77824	−	4.70895i	−0.338593	−	0.163058i
$835$	10.8022	−	47.3277i	0.373827	−	1.63784i
$836$	−0.00487019	−	0.0213377i	−0.000168439	−	0.000737980i
$837$	−7.40711	+	3.56708i	−0.256027	+	0.123296i
$838$	11.0672	−	22.9814i	0.382312	−	0.793878i
$839$	22.2439	−	5.07703i	0.767946	−	0.175279i	0.179437	−	0.983769i	$-0.442572\pi$
$839$	22.2439	−	5.07703i	0.767946	−	0.175279i	0.588509	+	0.808491i	$0.299715\pi$
$840$	−4.70274			−0.162260
$841$	−1.54836	−	28.9586i	−0.0533917	−	0.998574i
$842$	10.7170			0.369332
$843$	−10.0264	+	2.28846i	−0.345328	+	0.0788188i
$844$	−0.366446	+	0.760932i	−0.0126136	+	0.0261924i
$845$	−16.7178	+	8.05087i	−0.575110	+	0.276958i
$846$	3.94253	+	17.2734i	0.135547	+	0.593870i
$847$	0.902427	−	3.95379i	0.0310078	−	0.135854i
$848$	7.56194	+	3.64164i	0.259678	+	0.125054i
$849$	−15.6256	+	12.4610i	−0.536268	+	0.427659i
$850$	44.4351	+	55.7198i	1.52411	+	1.91117i
$851$	0.728953	+	1.51369i	0.0249882	+	0.0518885i
$852$	0.533108	+	0.425140i	0.0182640	+	0.0145650i
$853$		−	25.8152i		−	0.883896i	−0.897041	−	0.441948i	$-0.854288\pi$
$853$		−	25.8152i		−	0.883896i	0.897041	−	0.441948i	$-0.145712\pi$
$854$	5.09336	−	6.38687i	0.174291	−	0.218554i
$855$	−0.977899	−	0.223199i	−0.0334435	−	0.00763325i
$856$	−4.15874	−	0.949204i	−0.142143	−	0.0324431i
$857$	13.9233	−	17.4593i	0.475612	−	0.596399i	−0.484923	−	0.874557i	$-0.661152\pi$
$857$	13.9233	−	17.4593i	0.475612	−	0.596399i	0.960535	+	0.278158i	$0.0897238\pi$
$858$		−	8.63379i		−	0.294753i
$859$	27.7488	+	22.1290i	0.946778	+	0.755030i	0.969596	−	0.244709i	$-0.0786925\pi$
$859$	27.7488	+	22.1290i	0.946778	+	0.755030i	−0.0228184	+	0.999740i	$0.507264\pi$
$860$	−0.599394	−	1.24465i	−0.0204392	−	0.0424423i
$861$	−2.11636	−	2.65383i	−0.0721252	−	0.0904421i
$862$	4.08862	−	3.26056i	0.139259	−	0.111055i
$863$	−39.0362	−	18.7988i	−1.32881	−	0.639919i	−0.371349	−	0.928493i	$-0.621105\pi$
$863$	−39.0362	−	18.7988i	−1.32881	−	0.639919i	−0.957458	+	0.288574i	$0.906819\pi$
$864$	−0.0722800	+	0.316680i	−0.00245902	+	0.0107737i
$865$	−11.4069	−	49.9769i	−0.387846	−	1.69927i
$866$	−22.1321	+	10.6583i	−0.752081	+	0.362183i
$867$	−5.91751	+	12.2878i	−0.200969	+	0.417316i
$868$	0.207842	−	0.0474386i	0.00705462	−	0.00161017i
$869$	−11.4538			−0.388544
$870$	19.8669	−	20.9575i	0.673550	−	0.710525i
$871$	−10.7847			−0.365426
$872$	−53.2066	+	12.1441i	−1.80180	+	0.411250i
$873$	5.62184	−	11.6739i	0.190271	−	0.395101i
$874$	1.99357	−	0.960055i	0.0674337	−	0.0324743i
$875$	1.49337	+	6.54290i	0.0504852	+	0.221190i
$876$	−0.0656106	+	0.287459i	−0.00221678	+	0.00971234i
$877$	−33.2450	−	16.0099i	−1.12260	−	0.540617i	−0.221908	−	0.975068i	$-0.571228\pi$
$877$	−33.2450	−	16.0099i	−1.12260	−	0.540617i	−0.900696	+	0.434450i	$0.856943\pi$
$878$	12.5341	−	9.99564i	0.423007	−	0.337337i
$879$	8.36316	+	10.4871i	0.282082	+	0.353720i
$880$	−9.47161	−	19.6680i	−0.319288	−	0.663008i
$881$	31.3000	+	24.9609i	1.05452	+	0.840955i	0.987630	−	0.156805i	$-0.0501194\pi$
$881$	31.3000	+	24.9609i	1.05452	+	0.840955i	0.0668946	+	0.997760i	$0.478691\pi$
$882$		−	9.74830i		−	0.328242i
$883$	−21.3281	+	26.7446i	−0.717749	+	0.900028i	−0.998208	−	0.0598376i	$-0.980942\pi$
$883$	−21.3281	+	26.7446i	−0.717749	+	0.900028i	0.280460	+	0.959866i	$0.409513\pi$
$884$	1.31373	+	0.299849i	0.0441854	+	0.0100850i
$885$	−7.26138	−	1.65736i	−0.244089	−	0.0557117i
$886$	1.98170	−	2.48498i	0.0665766	−	0.0834845i
$887$		−	14.3987i		−	0.483462i	−0.970343	−	0.241731i	$-0.922285\pi$
$887$		−	14.3987i		−	0.483462i	0.970343	−	0.241731i	$-0.0777151\pi$
$888$	−0.636566	−	0.507644i	−0.0213617	−	0.0170354i
$889$	0.474035	+	0.984345i	0.0158986	+	0.0330139i
$890$	9.33659	+	11.7077i	0.312963	+	0.392443i
$891$	1.11035	−	0.885471i	0.0371980	−	0.0296644i
$892$	−1.17599	−	0.566327i	−0.0393751	−	0.0189620i
$893$	−0.737456	+	3.23101i	−0.0246780	+	0.108122i
$894$	1.47156	+	6.44731i	0.0492162	+	0.215630i
$895$	23.2926	−	11.2171i	0.778587	−	0.374948i
$896$	−2.30677	+	4.79006i	−0.0770638	+	0.160025i
$897$	23.7575	−	5.42249i	0.793239	−	0.181052i
$898$	14.8162			0.494423
$899$	22.5451	−	38.1026i	0.751921	−	1.27079i
$900$	0.515591			0.0171864
$901$	11.0159	−	2.51431i	0.366994	−	0.0837639i
$902$	6.64545	−	13.7994i	0.221269	−	0.459470i
$903$	2.61675	−	1.26016i	0.0870800	−	0.0419355i
$904$	0.564527	+	2.47336i	0.0187759	+	0.0822626i
$905$	11.3395	−	49.6815i	0.376937	−	1.65147i
$906$	−10.6932	−	5.14955i	−0.355256	−	0.171082i
$907$	25.2733	−	20.1548i	0.839185	−	0.669228i	−0.106500	−	0.994313i	$-0.533964\pi$
$907$	25.2733	−	20.1548i	0.839185	−	0.669228i	0.945685	+	0.325085i	$0.105393\pi$
$908$	−0.00142928	−	0.00179226i	−4.74324e−5	−	5.94784e-5i
$909$	−1.43119	−	2.97189i	−0.0474695	−	0.0985715i
$910$	8.02201	+	6.39734i	0.265927	+	0.212070i
$911$			45.1351i			1.49539i	0.664040	+	0.747697i	$0.268840\pi$
$911$			45.1351i			1.49539i	−0.664040	+	0.747697i	$0.731160\pi$
$912$	−0.687801	+	0.862475i	−0.0227754	+	0.0285594i
$913$	3.58992	+	0.819375i	0.118809	+	0.0271174i
$914$	−14.5942	−	3.33103i	−0.482733	−	0.110181i
$915$	29.4050	−	36.8727i	0.972100	−	1.21898i
$916$			1.31137i			0.0433290i
$917$	−5.93388	−	4.73211i	−0.195954	−	0.156268i
$918$	3.44485	+	7.15330i	0.113697	+	0.236094i
$919$	−23.4814	−	29.4447i	−0.774580	−	0.971292i	0.225416	−	0.974263i	$-0.427626\pi$
$919$	−23.4814	−	29.4447i	−0.774580	−	0.971292i	−0.999996	+	0.00297027i	$0.999055\pi$
$920$	46.8255	−	37.3421i	1.54379	−	1.23113i
$921$	1.81387	+	0.873512i	0.0597689	+	0.0287832i
$922$	−11.1675	+	48.9279i	−0.367781	+	1.61135i
$923$	11.1960	+	49.0527i	0.368519	+	1.61459i
$924$	−0.0331800	+	0.0159787i	−0.00109154	+	0.000525659i
$925$	−1.13806	+	2.36320i	−0.0374192	+	0.0777017i
$926$	2.74933	−	0.627517i	0.0903487	−	0.0206215i
$927$	8.38695			0.275464
$928$	−0.621620	−	1.63505i	−0.0204057	−	0.0536731i
$929$	−27.4584			−0.900881			−0.450440	−	0.892807i	$-0.648733\pi$
$929$	−27.4584			−0.900881			−0.450440	+	0.892807i	$0.648733\pi$
$930$	42.9805	−	9.81003i	1.40939	−	0.321684i
$931$	0.791158	−	1.64286i	0.0259292	−	0.0538425i
$932$	−0.541059	+	0.260560i	−0.0177230	+	0.00853493i
$933$	4.49363	+	19.6879i	0.147115	+	0.644552i
$934$	11.2522	−	49.2990i	0.368182	−	1.61311i
$935$	−26.4780	−	12.7511i	−0.865923	−	0.417006i
$936$	−9.23304	+	7.36310i	−0.301791	+	0.240671i
$937$	12.8698	+	16.1382i	0.420437	+	0.527212i	0.946271	−	0.323376i	$-0.104818\pi$
$937$	12.8698	+	16.1382i	0.420437	+	0.527212i	−0.525833	+	0.850588i	$0.676246\pi$
$938$	0.714937	+	1.48458i	0.0233435	+	0.0484733i
$939$	21.5815	+	17.2107i	0.704286	+	0.561649i
$940$		−	2.65243i		−	0.0865126i
$941$	2.01927	−	2.53209i	0.0658264	−	0.0825437i	−0.747828	−	0.663892i	$-0.768903\pi$
$941$	2.01927	−	2.53209i	0.0658264	−	0.0825437i	0.813655	+	0.581349i	$0.197475\pi$
$942$	0.0684864	+	0.0156316i	0.00223141	+	0.000509304i
$943$	42.1454	+	9.61940i	1.37244	+	0.313251i
$944$	−5.10726	+	6.40430i	−0.166227	+	0.208442i
$945$			1.68777i			0.0549031i
$946$	10.2461	+	8.17097i	0.333129	+	0.265661i
$947$	−8.78374	−	18.2396i	−0.285433	−	0.592708i	0.708118	−	0.706094i	$-0.249545\pi$
$947$	−8.78374	−	18.2396i	−0.285433	−	0.592708i	−0.993551	+	0.113386i	$0.963830\pi$
$948$	−0.288829	−	0.362180i	−0.00938072	−	0.0117631i
$949$	−17.0100	+	13.5650i	−0.552168	+	0.440339i
$950$	3.11242	+	1.49886i	0.100980	+	0.0486295i
$951$	2.85274	−	12.4987i	0.0925063	−	0.405297i
$952$	1.54938	+	6.78829i	0.0502158	+	0.220010i
$953$	−30.3563	+	14.6188i	−0.983338	+	0.473551i	−0.855252	−	0.518212i	$-0.826598\pi$
$953$	−30.3563	+	14.6188i	−0.983338	+	0.473551i	−0.128086	+	0.991763i	$0.540883\pi$
$954$	1.27043	−	2.63808i	0.0411318	−	0.0854110i
$955$	−73.1402	+	16.6938i	−2.36676	+	0.540198i
$956$	1.74829			0.0565438
$957$	−2.33227	+	7.28363i	−0.0753916	+	0.235446i
$958$	−24.5302			−0.792535
$959$	−0.330242	+	0.0753756i	−0.0106641	+	0.00243401i
$960$	−12.5828	+	26.1285i	−0.406108	+	0.843292i
$961$	32.9659	−	15.8755i	1.06341	−	0.512114i
$962$	0.395293	+	1.73189i	0.0127448	+	0.0558385i
$963$	−0.340660	+	1.49253i	−0.0109776	+	0.0480961i
$964$	−0.897984	−	0.432446i	−0.0289221	−	0.0139282i
$965$	2.35747	−	1.88002i	0.0758897	−	0.0605200i
$966$	−2.32137	−	2.91090i	−0.0746887	−	0.0936567i
$967$	−21.5474	−	44.7436i	−0.692917	−	1.43886i	−0.888831	−	0.458235i	$-0.848482\pi$
$967$	−21.5474	−	44.7436i	−0.692917	−	1.43886i	0.195914	−	0.980621i	$-0.437233\pi$
$968$	−19.5693	−	15.6060i	−0.628983	−	0.501597i
$969$			1.48511i			0.0477086i
$970$	−43.3207	+	54.3224i	−1.39094	+	1.74419i
$971$	7.54053	+	1.72108i	0.241987	+	0.0552320i	0.341794	−	0.939775i	$-0.388965\pi$
$971$	7.54053	+	1.72108i	0.241987	+	0.0552320i	−0.0998070	+	0.995007i	$0.531823\pi$
$972$	0.0559987	+	0.0127813i	0.00179616	+	0.000409962i
$973$	−2.12977	+	2.67065i	−0.0682774	+	0.0856171i
$974$			5.00753i			0.160452i
$975$	29.7445	+	23.7204i	0.952585	+	0.759661i
$976$	−22.5049	−	46.7319i	−0.720365	−	1.49585i
$977$	−7.20499	−	9.03477i	−0.230508	−	0.289048i	0.653104	−	0.757269i	$-0.273467\pi$
$977$	−7.20499	−	9.03477i	−0.230508	−	0.289048i	−0.883611	+	0.468221i	$0.844895\pi$
$978$	−9.36304	+	7.46678i	−0.299397	+	0.238761i
$979$	−3.57317	−	1.72075i	−0.114199	−	0.0549953i
$980$	−0.324742	+	1.42279i	−0.0103735	+	0.0454493i
$981$	4.35839	+	19.0953i	0.139153	+	0.609668i
$982$	−1.61979	+	0.780050i	−0.0516896	+	0.0248924i
$983$	−5.39675	+	11.2065i	−0.172130	+	0.357431i	−0.969131	−	0.246547i	$-0.920704\pi$
$983$	−5.39675	+	11.2065i	−0.172130	+	0.357431i	0.797001	+	0.603978i	$0.206418\pi$
$984$	−20.4246	+	4.66178i	−0.651112	+	0.148612i
$985$	4.37389			0.139364
$986$	−36.7970	−	21.7726i	−1.17186	−	0.693381i
$987$	5.57644			0.177500
$988$	0.0636790	−	0.0145343i	0.00202590	−	0.000462398i
$989$	−16.0489	+	33.3258i	−0.510324	+	1.05970i
$990$	−6.86143	+	3.30429i	−0.218071	+	0.105017i
$991$	−6.11595	−	26.7957i	−0.194279	−	0.851194i	−0.974267	−	0.225398i	$-0.927632\pi$
$991$	−6.11595	−	26.7957i	−0.194279	−	0.851194i	0.779987	−	0.625795i	$-0.215225\pi$
$992$	0.594234	−	2.60351i	0.0188669	−	0.0826615i
$993$	13.9328	+	6.70968i	0.442144	+	0.212925i
$994$	6.01021	−	4.79298i	0.190632	−	0.152024i
$995$	9.94809	+	12.4745i	0.315376	+	0.395468i
$996$	0.0646169	+	0.134178i	0.00204746	+	0.00425160i
$997$	−21.5382	−	17.1761i	−0.682120	−	0.543973i	0.219977	−	0.975505i	$-0.429402\pi$
$997$	−21.5382	−	17.1761i	−0.682120	−	0.543973i	−0.902097	+	0.431532i	$0.857973\pi$
$998$			4.95508i			0.156850i
$999$	−0.182189	+	0.228457i	−0.00576419	+	0.00722807i

Display

a_p

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up to: 50 250 1000 (See

a_n

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.i.a.22.1	yes	24
3.2	odd	2		261.2.o.b.109.4		24
29.2	odd	28		2523.2.a.s.1.4		12
29.4	even	14	inner	87.2.i.a.4.1	✓	24
29.27	odd	28		2523.2.a.v.1.9		12
87.2	even	28		7569.2.a.bt.1.9		12
87.56	even	28		7569.2.a.bn.1.4		12
87.62	odd	14		261.2.o.b.91.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.i.a.4.1	✓	24	29.4	even	14	inner
87.2.i.a.22.1	yes	24	1.1	even	1	trivial
261.2.o.b.91.4		24	87.62	odd	14
261.2.o.b.109.4		24	3.2	odd	2
2523.2.a.s.1.4		12	29.2	odd	28
2523.2.a.v.1.9		12	29.27	odd	28
7569.2.a.bn.1.4		12	87.56	even	28
7569.2.a.bt.1.9		12	87.2	even	28

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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

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$q$ -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	87.2.i.a.22.1

Level	$87$
Weight	$2$
Character	87.22
Analytic conductor	$0.695$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$