LMFDB - Embedded newform 115.2.l.a.102.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$115 = 5 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	115.l (of order $44$ , degree $20$ , 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			102.2
Character	$\chi$	$=$	115.102
Dual form			115.2.l.a.53.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.130187 + 1.82025i) q^{2} +(2.18625 - 0.475590i) q^{3} +(-1.31673 - 0.189318i) q^{4} +(-2.19962 + 0.402068i) q^{5} +(0.581073 + 4.04145i) q^{6} +(1.27539 - 0.696418i) q^{7} +(-0.259794 + 1.19425i) q^{8} +(1.82462 - 0.833276i) q^{9} +(-0.445503 - 4.05622i) q^{10} +(-0.442394 - 0.383336i) q^{11} +(-2.96875 + 0.212329i) q^{12} +(2.04998 - 3.75425i) q^{13} +(1.10162 + 2.41221i) q^{14} +(-4.61771 + 1.92514i) q^{15} +(-4.69280 - 1.37793i) q^{16} +(-3.87794 - 2.90299i) q^{17} +(1.27923 + 3.42975i) q^{18} +(-0.557198 + 3.87540i) q^{19} +(2.97244 - 0.112989i) q^{20} +(2.45712 - 2.12911i) q^{21} +(0.755364 - 0.755364i) q^{22} +(-2.33424 - 4.18943i) q^{23} +2.73450i q^{24} +(4.67668 - 1.76880i) q^{25} +(6.56681 + 4.22023i) q^{26} +(-1.78057 + 1.33292i) q^{27} +(-1.81120 + 0.675542i) q^{28} +(7.18468 - 1.03300i) q^{29} +(-2.90308 - 8.65604i) q^{30} +(2.25101 - 1.44663i) q^{31} +(2.26491 - 6.07245i) q^{32} +(-1.14950 - 0.627672i) q^{33} +(5.78904 - 6.68091i) q^{34} +(-2.52538 + 2.04465i) q^{35} +(-2.56029 + 0.751770i) q^{36} +(-3.66931 - 1.36858i) q^{37} +(-6.98167 - 1.51877i) q^{38} +(2.69628 - 9.18269i) q^{39} +(0.0912780 - 2.73137i) q^{40} +(-4.72306 + 10.3421i) q^{41} +(3.55564 + 4.74977i) q^{42} +(0.517211 + 2.37758i) q^{43} +(0.509942 + 0.588505i) q^{44} +(-3.67844 + 2.56651i) q^{45} +(7.92971 - 3.70350i) q^{46} +(7.19735 + 7.19735i) q^{47} +(-10.9150 - 0.780655i) q^{48} +(-2.64285 + 4.11236i) q^{49} +(2.61081 + 8.74303i) q^{50} +(-9.85880 - 4.50236i) q^{51} +(-3.41002 + 4.55525i) q^{52} +(-1.84291 - 3.37504i) q^{53} +(-2.19445 - 3.41462i) q^{54} +(1.12723 + 0.665323i) q^{55} +(0.500360 + 1.70407i) q^{56} +(0.624925 + 8.73760i) q^{57} +(0.944971 + 13.2124i) q^{58} +(1.40944 + 4.80010i) q^{59} +(6.44476 - 1.66068i) q^{60} +(2.46982 + 3.84312i) q^{61} +(2.34019 + 4.28574i) q^{62} +(1.74680 - 2.33345i) q^{63} +(1.86067 + 0.849740i) q^{64} +(-2.99971 + 9.08216i) q^{65} +(1.29217 - 2.01066i) q^{66} +(-4.42912 - 0.316777i) q^{67} +(4.55663 + 4.55663i) q^{68} +(-7.09569 - 8.04901i) q^{69} +(-3.39301 - 4.86302i) q^{70} +(-4.81468 - 5.55644i) q^{71} +(0.521118 + 2.39554i) q^{72} +(-6.08761 - 8.13210i) q^{73} +(2.96886 - 6.50090i) q^{74} +(9.38319 - 6.09122i) q^{75} +(1.46736 - 4.99738i) q^{76} +(-0.831189 - 0.180814i) q^{77} +(16.3638 + 6.10338i) q^{78} +(-6.81598 + 2.00135i) q^{79} +(10.8764 + 1.14410i) q^{80} +(-7.19959 + 8.30877i) q^{81} +(-18.2103 - 9.94357i) q^{82} +(4.24103 - 11.3706i) q^{83} +(-3.63846 + 2.33829i) q^{84} +(9.69721 + 4.82629i) q^{85} +(-4.39514 + 0.631925i) q^{86} +(15.2162 - 5.67536i) q^{87} +(0.572733 - 0.428742i) q^{88} +(10.2977 + 6.61790i) q^{89} +(-4.19282 - 7.02983i) q^{90} -6.21579i q^{91} +(2.28044 + 5.95828i) q^{92} +(4.23327 - 4.23327i) q^{93} +(-14.0380 + 12.1640i) q^{94} +(-0.332547 - 8.74845i) q^{95} +(2.06366 - 14.3531i) q^{96} +(5.96510 + 15.9930i) q^{97} +(-7.14148 - 5.34604i) q^{98} +(-1.12663 - 0.330807i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100})$ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$ .

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.130187	+	1.82025i	−0.0920562	+	1.28711i	0.716038	+	0.698061i	$0.245954\pi$
$2$	−0.130187	+	1.82025i	−0.0920562	+	1.28711i	−0.808094	+	0.589053i	$0.799501\pi$
$3$	2.18625	−	0.475590i	1.26223	−	0.274582i	0.468836	−	0.883285i	$-0.344674\pi$
$3$	2.18625	−	0.475590i	1.26223	−	0.274582i	0.793398	+	0.608703i	$0.208310\pi$
$4$	−1.31673	−	0.189318i	−0.658367	−	0.0946589i
$5$	−2.19962	+	0.402068i	−0.983701	+	0.179810i
$5$	−2.19962	+	0.402068i	−0.983701	+	0.179810i
$6$	0.581073	+	4.04145i	0.237222	+	1.64992i
$7$	1.27539	−	0.696418i	0.482054	−	0.263221i	−0.219797	−	0.975546i	$-0.570539\pi$
$7$	1.27539	−	0.696418i	0.482054	−	0.263221i	0.701850	+	0.712325i	$0.252358\pi$
$8$	−0.259794	+	1.19425i	−0.0918511	+	0.422233i
$9$	1.82462	−	0.833276i	0.608207	−	0.277759i
$10$	−0.445503	−	4.05622i	−0.140880	−	1.28269i
$11$	−0.442394	−	0.383336i	−0.133387	−	0.115580i	0.585612	−	0.810591i	$-0.300854\pi$
$11$	−0.442394	−	0.383336i	−0.133387	−	0.115580i	−0.718999	+	0.695011i	$0.755400\pi$
$12$	−2.96875	+	0.212329i	−0.857004	+	0.0612942i
$13$	2.04998	−	3.75425i	0.568561	−	1.04124i	−0.422313	−	0.906450i	$-0.638782\pi$
$13$	2.04998	−	3.75425i	0.568561	−	1.04124i	0.990874	−	0.134792i	$-0.0430365\pi$
$14$	1.10162	+	2.41221i	0.294420	+	0.644689i
$15$	−4.61771	+	1.92514i	−1.19229	+	0.497069i
$16$	−4.69280	−	1.37793i	−1.17320	−	0.344483i
$17$	−3.87794	−	2.90299i	−0.940539	−	0.704079i	0.0147065	−	0.999892i	$-0.495319\pi$
$17$	−3.87794	−	2.90299i	−0.940539	−	0.704079i	−0.955246	+	0.295813i	$0.904410\pi$
$18$	1.27923	+	3.42975i	0.301518	+	0.808401i
$19$	−0.557198	+	3.87540i	−0.127830	+	0.889077i	0.820467	+	0.571694i	$0.193713\pi$
$19$	−0.557198	+	3.87540i	−0.127830	+	0.889077i	−0.948297	+	0.317384i	$0.897196\pi$
$20$	2.97244	−	0.112989i	0.664657	−	0.0252650i
$21$	2.45712	−	2.12911i	0.536188	−	0.464610i
$22$	0.755364	−	0.755364i	0.161044	−	0.161044i
$23$	−2.33424	−	4.18943i	−0.486723	−	0.873556i
$23$	−2.33424	−	4.18943i	−0.486723	−	0.873556i
$24$			2.73450i			0.558177i
$25$	4.67668	−	1.76880i	0.935337	−	0.353759i
$26$	6.56681	+	4.22023i	1.28786	+	0.827656i
$27$	−1.78057	+	1.33292i	−0.342671	+	0.256521i
$28$	−1.81120	+	0.675542i	−0.342284	+	0.127665i
$29$	7.18468	−	1.03300i	1.33416	−	0.191823i	0.561941	−	0.827178i	$-0.310055\pi$
$29$	7.18468	−	1.03300i	1.33416	−	0.191823i	0.772221	+	0.635354i	$0.219146\pi$
$30$	−2.90308	−	8.65604i	−0.530027	−	1.58037i
$31$	2.25101	−	1.44663i	0.404293	−	0.259823i	−0.322654	−	0.946517i	$-0.604575\pi$
$31$	2.25101	−	1.44663i	0.404293	−	0.259823i	0.726947	+	0.686694i	$0.240939\pi$
$32$	2.26491	−	6.07245i	0.400383	−	1.07347i
$33$	−1.14950	−	0.627672i	−0.200101	−	0.109264i
$34$	5.78904	−	6.68091i	0.992812	−	1.14577i
$35$	−2.52538	+	2.04465i	−0.426867	+	0.345609i
$36$	−2.56029	+	0.751770i	−0.426715	+	0.125295i
$37$	−3.66931	−	1.36858i	−0.603230	−	0.224993i	0.0292470	−	0.999572i	$-0.490689\pi$
$37$	−3.66931	−	1.36858i	−0.603230	−	0.224993i	−0.632477	+	0.774579i	$0.717962\pi$
$38$	−6.98167	−	1.51877i	−1.13258	−	0.246377i
$39$	2.69628	−	9.18269i	0.431750	−	1.47041i
$40$	0.0912780	−	2.73137i	0.0144323	−	0.431867i
$41$	−4.72306	+	10.3421i	−0.737617	+	1.61516i	0.0498168	+	0.998758i	$0.484136\pi$
$41$	−4.72306	+	10.3421i	−0.737617	+	1.61516i	−0.787434	+	0.616399i	$0.788591\pi$
$42$	3.55564	+	4.74977i	0.548647	+	0.732906i
$43$	0.517211	+	2.37758i	0.0788739	+	0.362578i	0.999619	−	0.0275861i	$-0.00878203\pi$
$43$	0.517211	+	2.37758i	0.0788739	+	0.362578i	−0.920745	+	0.390164i	$0.872418\pi$
$44$	0.509942	+	0.588505i	0.0768767	+	0.0887204i
$45$	−3.67844	+	2.56651i	−0.548350	+	0.382593i
$46$	7.92971	−	3.70350i	1.16917	−	0.546052i
$47$	7.19735	+	7.19735i	1.04984	+	1.04984i	0.998691	+	0.0511497i	$0.0162886\pi$
$47$	7.19735	+	7.19735i	1.04984	+	1.04984i	0.0511497	+	0.998691i	$0.483711\pi$
$48$	−10.9150	−	0.780655i	−1.57544	−	0.112678i
$49$	−2.64285	+	4.11236i	−0.377551	+	0.587480i
$50$	2.61081	+	8.74303i	0.369225	+	1.23645i
$51$	−9.85880	−	4.50236i	−1.38051	−	0.630457i
$52$	−3.41002	+	4.55525i	−0.472884	+	0.631700i
$53$	−1.84291	−	3.37504i	−0.253143	−	0.463597i	0.719945	−	0.694031i	$-0.244167\pi$
$53$	−1.84291	−	3.37504i	−0.253143	−	0.463597i	−0.973088	+	0.230435i	$0.925985\pi$
$54$	−2.19445	−	3.41462i	−0.298626	−	0.464671i
$55$	1.12723	+	0.665323i	0.151995	+	0.0897122i
$56$	0.500360	+	1.70407i	0.0668635	+	0.227716i
$57$	0.624925	+	8.73760i	0.0827734	+	1.15732i
$58$	0.944971	+	13.2124i	0.124081	+	1.73488i
$59$	1.40944	+	4.80010i	0.183493	+	0.624920i	0.998938	+	0.0460847i	$0.0146744\pi$
$59$	1.40944	+	4.80010i	0.183493	+	0.624920i	−0.815444	+	0.578835i	$0.803507\pi$
$60$	6.44476	−	1.66068i	0.832015	−	0.214393i
$61$	2.46982	+	3.84312i	0.316228	+	0.492061i	0.962587	−	0.270973i	$-0.0873453\pi$
$61$	2.46982	+	3.84312i	0.316228	+	0.492061i	−0.646359	+	0.763034i	$0.723709\pi$
$62$	2.34019	+	4.28574i	0.297204	+	0.544289i
$63$	1.74680	−	2.33345i	0.220076	−	0.293987i
$64$	1.86067	+	0.849740i	0.232584	+	0.106217i
$65$	−2.99971	+	9.08216i	−0.372068	+	1.12650i
$66$	1.29217	−	2.01066i	0.159055	−	0.247495i
$67$	−4.42912	−	0.316777i	−0.541103	−	0.0387005i	−0.201887	−	0.979409i	$-0.564707\pi$
$67$	−4.42912	−	0.316777i	−0.541103	−	0.0387005i	−0.339216	+	0.940708i	$0.610162\pi$
$68$	4.55663	+	4.55663i	0.552573	+	0.552573i
$69$	−7.09569	−	8.04901i	−0.854221	−	0.968987i
$70$	−3.39301	−	4.86302i	−0.405543	−	0.581242i
$71$	−4.81468	−	5.55644i	−0.571398	−	0.659428i	0.394335	−	0.918967i	$-0.370975\pi$
$71$	−4.81468	−	5.55644i	−0.571398	−	0.659428i	−0.965733	+	0.259539i	$0.916430\pi$
$72$	0.521118	+	2.39554i	0.0614144	+	0.282317i
$73$	−6.08761	−	8.13210i	−0.712501	−	0.951790i	0.287481	−	0.957786i	$-0.407182\pi$
$73$	−6.08761	−	8.13210i	−0.712501	−	0.951790i	−0.999982	+	0.00599601i	$0.998091\pi$
$74$	2.96886	−	6.50090i	0.345123	−	0.755714i
$75$	9.38319	−	6.09122i	1.08348	−	0.703353i
$76$	1.46736	−	4.99738i	0.168318	−	0.573239i
$77$	−0.831189	−	0.180814i	−0.0947227	−	0.0206057i
$78$	16.3638	+	6.10338i	1.85284	+	0.691072i
$79$	−6.81598	+	2.00135i	−0.766857	+	0.225170i	−0.641688	−	0.766966i	$-0.721766\pi$
$79$	−6.81598	+	2.00135i	−0.766857	+	0.225170i	−0.125169	+	0.992135i	$0.539947\pi$
$80$	10.8764	+	1.14410i	1.21602	+	0.127915i
$81$	−7.19959	+	8.30877i	−0.799954	+	0.923197i
$82$	−18.2103	−	9.94357i	−2.01099	−	1.09808i
$83$	4.24103	−	11.3706i	0.465513	−	1.24809i	−0.466130	−	0.884716i	$-0.654352\pi$
$83$	4.24103	−	11.3706i	0.465513	−	1.24809i	0.931643	−	0.363374i	$-0.118375\pi$
$84$	−3.63846	+	2.33829i	−0.396988	+	0.255129i
$85$	9.69721	+	4.82629i	1.05181	+	0.523485i
$86$	−4.39514	+	0.631925i	−0.473940	+	0.0681422i
$87$	15.2162	−	5.67536i	1.63135	−	0.608463i
$88$	0.572733	−	0.428742i	0.0610535	−	0.0457041i
$89$	10.2977	+	6.61790i	1.09155	+	0.701496i	0.957197	−	0.289437i	$-0.0934681\pi$
$89$	10.2977	+	6.61790i	1.09155	+	0.701496i	0.134353	+	0.990934i	$0.457104\pi$
$90$	−4.19282	−	7.02983i	−0.441962	−	0.741009i
$91$		−	6.21579i		−	0.651592i
$92$	2.28044	+	5.95828i	0.237752	+	0.621193i
$93$	4.23327	−	4.23327i	0.438969	−	0.438969i
$94$	−14.0380	+	12.1640i	−1.44791	+	1.25462i
$95$	−0.332547	−	8.74845i	−0.0341186	−	0.897572i
$96$	2.06366	−	14.3531i	0.210622	−	1.46491i
$97$	5.96510	+	15.9930i	0.605664	+	1.62385i	0.770437	+	0.637516i	$0.220038\pi$
$97$	5.96510	+	15.9930i	0.605664	+	1.62385i	−0.164774	+	0.986331i	$0.552689\pi$
$98$	−7.14148	−	5.34604i	−0.721398	−	0.540032i
$99$	−1.12663	−	0.330807i	−0.113230	−	0.0332474i
$100$	−6.49281	+	1.44365i	−0.649281	+	0.144365i
$101$	1.23783	+	2.71046i	0.123168	+	0.269701i	0.961165	−	0.275974i	$-0.0890005\pi$
$101$	1.23783	+	2.71046i	0.123168	+	0.269701i	−0.837997	+	0.545675i	$0.816273\pi$
$102$	9.47893	−	17.3594i	0.938554	−	1.71883i
$103$	10.4749	−	0.749178i	1.03212	−	0.0738187i	0.455011	−	0.890486i	$-0.349635\pi$
$103$	10.4749	−	0.749178i	1.03212	−	0.0738187i	0.577109	+	0.816667i	$0.304181\pi$
$104$	3.95096	+	3.42353i	0.387423	+	0.335704i
$105$	−4.54870	+	5.67117i	−0.443908	+	0.553450i
$106$	6.38335	−	2.91518i	0.620005	−	0.283147i
$107$	3.99765	−	18.3769i	0.386467	−	1.77656i	−0.213920	−	0.976851i	$-0.568623\pi$
$107$	3.99765	−	18.3769i	0.386467	−	1.77656i	0.600387	−	0.799710i	$-0.295013\pi$
$108$	2.59689	−	1.41801i	0.249885	−	0.136448i
$109$	0.0713274	+	0.496093i	0.00683192	+	0.0475171i	0.992952	−	0.118515i	$-0.0378135\pi$
$109$	0.0713274	+	0.496093i	0.00683192	+	0.0475171i	−0.986120	+	0.166032i	$0.946904\pi$
$110$	−1.35781	+	1.96522i	−0.129462	+	0.187377i
$111$	−8.67291	−	1.24698i	−0.823197	−	0.118358i
$112$	−6.94479	+	1.51075i	−0.656221	+	0.142752i
$113$	−1.30412	+	18.2339i	−0.122681	+	1.71530i	0.447917	+	0.894075i	$0.352166\pi$
$113$	−1.30412	+	18.2339i	−0.122681	+	1.71530i	−0.570598	+	0.821229i	$0.693289\pi$
$114$	−15.9860			−1.49723
$115$	6.81889	+	8.27664i	0.635864	+	0.771801i
$116$	−9.65587			−0.896525
$117$	0.612100	−	8.55827i	0.0565887	−	0.791213i
$118$	−8.92090	+	1.94062i	−0.821235	+	0.178649i
$119$	−6.96760	−	1.00179i	−0.638719	−	0.0918339i
$120$	−1.09945	−	6.01487i	−0.100366	−	0.549080i
$121$	−1.51670	−	10.5489i	−0.137882	−	0.958988i
$122$	−7.31699	+	3.99538i	−0.662449	+	0.361725i
$123$	−5.40722	+	24.8566i	−0.487552	+	2.24124i
$124$	−3.23785	+	1.47868i	−0.290768	+	0.132789i
$125$	−9.57576	+	5.77103i	−0.856482	+	0.516176i
$126$	4.02007	+	3.48341i	0.358136	+	0.310327i
$127$	−1.90638	+	0.136347i	−0.169164	+	0.0120989i	−0.155664	−	0.987810i	$-0.549752\pi$
$127$	−1.90638	+	0.136347i	−0.169164	+	0.0120989i	−0.0134998	+	0.999909i	$0.504297\pi$
$128$	4.42313	−	8.10036i	0.390953	−	0.715977i
$129$	2.26151	+	4.95201i	0.199115	+	0.436000i
$130$	−16.1413	−	6.64262i	−1.41569	−	0.582596i
$131$	−5.26786	−	1.54678i	−0.460255	−	0.135143i	0.0433819	−	0.999059i	$-0.486187\pi$
$131$	−5.26786	−	1.54678i	−0.460255	−	0.135143i	−0.503637	+	0.863916i	$0.668005\pi$
$132$	1.39475	+	1.04410i	0.121397	+	0.0908770i
$133$	1.98825	+	5.33070i	0.172403	+	0.462230i
$134$	1.15323	−	8.02089i	0.0996238	−	0.692899i
$135$	3.38066	−	3.64783i	0.290961	−	0.313955i
$136$	4.47438	−	3.87707i	0.383675	−	0.332456i
$137$	8.78965	−	8.78965i	0.750951	−	0.750951i	−0.223706	−	0.974657i	$-0.571816\pi$
$137$	8.78965	−	8.78965i	0.750951	−	0.750951i	0.974657	+	0.223706i	$0.0718156\pi$
$138$	15.5750	−	11.8681i	1.32583	−	1.01028i
$139$		−	0.874304i		−	0.0741575i	−0.999312	−	0.0370787i	$-0.988195\pi$
$139$		−	0.874304i		−	0.0741575i	0.999312	−	0.0370787i	$-0.0118052\pi$
$140$	3.71234	−	2.21416i	0.313750	−	0.187131i
$141$	19.1582	+	12.3122i	1.61341	+	1.03688i
$142$	10.7409	−	8.04057i	0.901360	−	0.674750i
$143$	−2.34604	+	0.875027i	−0.196185	+	0.0731734i
$144$	−9.71078	+	1.39620i	−0.809231	+	0.116350i
$145$	−15.3882	+	5.16094i	−1.27792	+	0.428593i
$146$	15.5950	−	10.0223i	1.29065	−	0.829452i
$147$	−3.82215	+	10.2476i	−0.315245	+	0.845206i
$148$	4.57240	+	2.49672i	0.375849	+	0.205229i
$149$	3.46392	−	3.99758i	0.283776	−	0.327495i	−0.595909	−	0.803052i	$-0.703208\pi$
$149$	3.46392	−	3.99758i	0.283776	−	0.327495i	0.879685	+	0.475557i	$0.157754\pi$
$150$	9.86599	+	17.8728i	0.805555	+	1.45931i
$151$	4.45916	−	1.30933i	0.362881	−	0.106552i	−0.0952087	−	0.995457i	$-0.530352\pi$
$151$	4.45916	−	1.30933i	0.362881	−	0.106552i	0.458090	+	0.888906i	$0.348534\pi$
$152$	−4.48346	−	1.67224i	−0.363656	−	0.135637i
$153$	−9.49476	−	2.06546i	−0.767606	−	0.166983i
$154$	0.437338	−	1.48943i	0.0352417	−	0.120022i
$155$	−4.36972	+	4.08711i	−0.350984	+	0.328284i
$156$	−5.28873	+	11.5807i	−0.423437	+	0.927198i
$157$	−2.81281	−	3.75748i	−0.224487	−	0.299879i	0.674131	−	0.738612i	$-0.264518\pi$
$157$	−2.81281	−	3.75748i	−0.224487	−	0.299879i	−0.898618	+	0.438733i	$0.855428\pi$
$158$	−2.75562	−	12.6674i	−0.219225	−	1.00776i
$159$	−5.63420	−	6.50221i	−0.446821	−	0.515659i
$160$	−2.54041	+	14.2678i	−0.200837	+	1.12796i
$161$	−5.89467	−	3.71757i	−0.464565	−	0.292985i
$162$	−14.1868	−	14.1868i	−1.11462	−	1.11462i
$163$	16.4156	+	1.17407i	1.28577	+	0.0919601i	0.697430	−	0.716653i	$-0.254327\pi$
$163$	16.4156	+	1.17407i	1.28577	+	0.0919601i	0.588341	+	0.808613i	$0.299781\pi$
$164$	8.17694	−	12.7236i	0.638512	−	0.993544i
$165$	2.78082	+	0.918467i	0.216487	+	0.0715025i
$166$	20.1453	+	9.20006i	1.56358	+	0.714063i
$167$	2.31674	−	3.09481i	0.179275	−	0.239483i	−0.701898	−	0.712278i	$-0.747664\pi$
$167$	2.31674	−	3.09481i	0.179275	−	0.239483i	0.881173	+	0.472794i	$0.156755\pi$
$168$	1.90435	+	3.48756i	0.146924	+	0.269071i
$169$	−2.86366	−	4.45595i	−0.220282	−	0.342765i
$170$	−10.0475	+	17.0231i	−0.770610	+	1.30561i
$171$	2.21260	+	7.53543i	0.169202	+	0.576248i
$172$	−0.230911	−	3.22856i	−0.0176068	−	0.246175i
$173$	−1.24642	−	17.4272i	−0.0947635	−	1.32497i	−0.793053	−	0.609152i	$-0.791510\pi$
$173$	−1.24642	−	17.4272i	−0.0947635	−	1.32497i	0.698290	−	0.715815i	$-0.253945\pi$
$174$	8.34965	+	28.4363i	0.632985	+	2.15575i
$175$	4.73279	−	5.51284i	0.357766	−	0.416731i
$176$	1.54786	+	2.40851i	0.116674	+	0.181548i
$177$	5.36427	+	9.82392i	0.403203	+	0.738411i
$178$	−13.3869	+	17.8828i	−1.00339	+	1.34037i
$179$	−5.56791	−	2.54278i	−0.416165	−	0.190056i	0.196317	−	0.980540i	$-0.437102\pi$
$179$	−5.56791	−	2.54278i	−0.416165	−	0.190056i	−0.612483	+	0.790484i	$0.709829\pi$
$180$	5.32941	−	2.68302i	0.397231	−	0.199981i
$181$	−7.97365	+	12.4072i	−0.592677	+	0.922223i	0.407283	+	0.913302i	$0.366476\pi$
$181$	−7.97365	+	12.4072i	−0.592677	+	0.922223i	−0.999960	+	0.00892124i	$0.997160\pi$
$182$	11.3143	+	0.809216i	0.838673	+	0.0599831i
$183$	7.22741	+	7.22741i	0.534265	+	0.534265i
$184$	5.60967	−	1.69929i	0.413550	−	0.125273i
$185$	8.62135	+	1.53505i	0.633854	+	0.112859i
$186$	7.15450	+	8.25674i	0.524594	+	0.605413i
$187$	0.602755	+	2.77082i	0.0440778	+	0.202623i
$188$	−8.11440	−	10.8396i	−0.591804	−	0.790557i
$189$	−1.34266	+	2.94002i	−0.0976643	+	0.213855i
$190$	15.9677	+	0.533616i	1.15842	+	0.0387125i
$191$	3.95682	−	13.4757i	0.286306	−	0.975067i	−0.683248	−	0.730187i	$-0.739433\pi$
$191$	3.95682	−	13.4757i	0.286306	−	0.975067i	0.969553	−	0.244880i	$-0.0787487\pi$
$192$	4.47202	+	0.972829i	0.322741	+	0.0702079i
$193$	3.30672	+	1.23334i	0.238023	+	0.0887779i	0.465645	−	0.884972i	$-0.345822\pi$
$193$	3.30672	+	1.23334i	0.238023	+	0.0887779i	−0.227622	+	0.973750i	$0.573095\pi$
$194$	−29.8880	+	8.77590i	−2.14583	+	0.630073i
$195$	−2.23874	+	21.2825i	−0.160319	+	1.52407i
$196$	4.25848	−	4.91454i	0.304177	−	0.351039i
$197$	−5.03603	−	2.74988i	−0.358802	−	0.195921i	0.289729	−	0.957109i	$-0.406435\pi$
$197$	−5.03603	−	2.74988i	−0.358802	−	0.195921i	−0.648532	+	0.761188i	$0.724617\pi$
$198$	0.748825	−	2.00768i	0.0532167	−	0.142679i
$199$	0.271547	−	0.174513i	0.0192494	−	0.0123709i	−0.530981	−	0.847384i	$-0.678176\pi$
$199$	0.271547	−	0.174513i	0.0192494	−	0.0123709i	0.550230	+	0.835013i	$0.314540\pi$
$200$	0.897417	+	6.04467i	0.0634569	+	0.427423i
$201$	−9.83383	+	1.41389i	−0.693625	+	0.0997283i
$202$	−5.09488	+	1.90029i	−0.358474	+	0.133704i
$203$	8.44390	−	6.32102i	0.592645	−	0.443649i
$204$	12.1290	+	7.79486i	0.849202	+	0.545749i
$205$	6.23074	−	24.6476i	0.435174	−	1.72146i
$206$			19.1645i			1.33525i
$207$	−7.75005	−	5.69905i	−0.538666	−	0.396111i
$208$	−14.7932	+	14.7932i	−1.02573	+	1.02573i
$209$	1.73208	−	1.50086i	0.119811	−	0.103816i
$210$	−9.73079	−	9.01810i	−0.671488	−	0.622308i
$211$	2.26649	−	15.7638i	0.156031	−	1.08522i	−0.749825	−	0.661636i	$-0.769862\pi$
$211$	2.26649	−	15.7638i	0.156031	−	1.08522i	0.905856	−	0.423585i	$-0.139229\pi$
$212$	1.78767	+	4.79292i	0.122777	+	0.329179i
$213$	−13.1687	−	9.85797i	−0.902305	−	0.675457i
$214$	32.9302	+	9.66917i	2.25106	+	0.660971i
$215$	−2.09362	−	5.02183i	−0.142784	−	0.342486i
$216$	−1.12926	−	2.47274i	−0.0768367	−	0.168249i
$217$	1.86346	−	3.41267i	0.126500	−	0.231667i
$218$	−0.912301	+	0.0652491i	−0.0617888	+	0.00441922i
$219$	−17.1766	−	14.8836i	−1.16069	−	1.00574i
$220$	−1.35830	−	1.08946i	−0.0915766	−	0.0734512i
$221$	−18.8482	+	8.60771i	−1.26787	+	0.579017i
$222$	3.39892	−	15.6246i	0.228120	−	1.04865i
$223$	−6.55607	+	3.57989i	−0.439027	+	0.239727i	−0.683531	−	0.729921i	$-0.739557\pi$
$223$	−6.55607	+	3.57989i	−0.439027	+	0.239727i	0.244504	+	0.969648i	$0.421375\pi$
$224$	−1.34031	−	9.32209i	−0.0895535	−	0.622858i
$225$	7.05927	−	7.12434i	0.470618	−	0.474956i
$226$	−33.0206	−	4.74765i	−2.19650	−	0.315809i
$227$	−23.2049	+	5.04792i	−1.54016	+	0.335042i	−0.900928	−	0.433969i	$-0.857113\pi$
$227$	−23.2049	+	5.04792i	−1.54016	+	0.335042i	−0.639236	+	0.769011i	$0.720749\pi$
$228$	0.831322	−	11.6234i	0.0550556	−	0.769778i
$229$	24.1061			1.59298			0.796489	−	0.604653i	$-0.206688\pi$
$229$	24.1061			1.59298			0.796489	+	0.604653i	$0.206688\pi$
$230$	−15.9533	+	11.3346i	−1.05193	+	0.747381i
$231$	−1.90318			−0.125220
$232$	−0.632872	+	8.84871i	−0.0415501	+	0.580946i
$233$	11.0526	−	2.40434i	0.724077	−	0.157513i	0.164601	−	0.986360i	$-0.447366\pi$
$233$	11.0526	−	2.40434i	0.724077	−	0.157513i	0.559476	+	0.828847i	$0.311003\pi$
$234$	15.4985	+	2.22835i	1.01317	+	0.145672i
$235$	−18.7253	−	12.9376i	−1.22150	−	0.843958i
$236$	−0.947109	−	6.58729i	−0.0616515	−	0.428796i
$237$	−13.9496	+	7.61707i	−0.906126	+	0.494782i
$238$	2.73060	−	12.5524i	0.176999	−	0.813650i
$239$	−6.57185	+	3.00126i	−0.425098	+	0.194136i	−0.616464	−	0.787383i	$-0.711435\pi$
$239$	−6.57185	+	3.00126i	−0.425098	+	0.194136i	0.191366	+	0.981519i	$0.438708\pi$
$240$	24.3227	−	2.67142i	1.57003	−	0.172439i
$241$	−5.85650	−	5.07469i	−0.377251	−	0.326889i	0.445511	−	0.895277i	$-0.353022\pi$
$241$	−5.85650	−	5.07469i	−0.377251	−	0.326889i	−0.822761	+	0.568387i	$0.807568\pi$
$242$	19.3991	−	1.38745i	1.24702	−	0.0891886i
$243$	−8.59070	+	15.7327i	−0.551094	+	1.00925i
$244$	−2.52453	−	5.52795i	−0.161616	−	0.353890i
$245$	4.15983	−	10.1082i	0.265762	−	0.645792i
$246$	−44.5413	−	13.0785i	−2.83985	−	0.833856i
$247$	13.4070	+	10.0363i	0.853065	+	0.638597i
$248$	1.14285	+	3.06410i	0.0725711	+	0.194571i
$249$	3.86420	−	26.8761i	0.244884	−	1.70320i
$250$	−9.25809	−	18.1816i	−0.585533	−	1.14991i
$251$	15.7180	−	13.6197i	0.992112	−	0.859670i	0.00200710	−	0.999998i	$-0.499361\pi$
$251$	15.7180	−	13.6197i	0.992112	−	0.859670i	0.990105	+	0.140328i	$0.0448157\pi$
$252$	−2.74184	+	2.74184i	−0.172719	+	0.172719i
$253$	−0.573307	+	2.74818i	−0.0360435	+	0.172776i
$254$		−	3.48785i		−	0.218847i
$255$	23.4959	+	5.93960i	1.47137	+	0.371952i
$256$	17.6105	+	11.3176i	1.10065	+	0.707348i
$257$	−7.51113	+	5.62276i	−0.468532	+	0.350738i	−0.807310	−	0.590128i	$-0.799077\pi$
$257$	−7.51113	+	5.62276i	−0.468532	+	0.350738i	0.338778	+	0.940866i	$0.389986\pi$
$258$	−9.30834	+	3.47183i	−0.579512	+	0.216147i
$259$	−5.63291	+	0.809891i	−0.350012	+	0.0503242i
$260$	5.66924	−	11.3909i	0.351591	−	0.706433i
$261$	12.2485	−	7.87165i	0.758165	−	0.487243i
$262$	3.50134	−	9.38747i	0.216314	−	0.579960i
$263$	−13.0497	−	7.12568i	−0.804679	−	0.439388i	0.0235878	−	0.999722i	$-0.492491\pi$
$263$	−13.0497	−	7.12568i	−0.804679	−	0.439388i	−0.828267	+	0.560334i	$0.810673\pi$
$264$	1.04823	−	1.20973i	0.0645143	−	0.0744534i
$265$	5.41070	+	6.68283i	0.332377	+	0.410523i
$266$	−9.96208	+	2.92513i	−0.610814	+	0.179351i
$267$	25.6607	+	9.57095i	1.57041	+	0.585732i
$268$	5.77200	+	1.25562i	0.352581	+	0.0766993i
$269$	0.125400	−	0.427073i	0.00764576	−	0.0260391i	−0.955582	−	0.294726i	$-0.904772\pi$
$269$	0.125400	−	0.427073i	0.00764576	−	0.0260391i	0.963228	+	0.268687i	$0.0865898\pi$
$270$	6.19986	+	6.62857i	0.377312	+	0.403402i
$271$	5.10177	−	11.1713i	0.309910	−	0.678609i	−0.689025	−	0.724737i	$-0.741961\pi$
$271$	5.10177	−	11.1713i	0.309910	−	0.678609i	0.998936	+	0.0461284i	$0.0146883\pi$
$272$	14.1983	+	18.9667i	0.860898	+	1.15003i
$273$	−2.95617	−	13.5893i	−0.178915	−	0.822461i
$274$	14.8551	+	17.1437i	0.897429	+	1.03569i
$275$	−2.74698	−	1.01024i	−0.165649	−	0.0609197i
$276$	7.81932	+	11.9417i	0.470668	+	0.718808i
$277$	−6.00568	−	6.00568i	−0.360846	−	0.360846i	0.503278	−	0.864124i	$-0.332127\pi$
$277$	−6.00568	−	6.00568i	−0.360846	−	0.360846i	−0.864124	+	0.503278i	$0.832127\pi$
$278$	1.59145	+	0.113823i	0.0954491	+	0.00682665i
$279$	2.90179	−	4.51527i	0.173725	−	0.270322i
$280$	−1.78576	−	3.54713i	−0.106719	−	0.211982i
$281$	9.07878	+	4.14614i	0.541594	+	0.247338i	0.667377	−	0.744720i	$-0.267417\pi$
$281$	9.07878	+	4.14614i	0.541594	+	0.247338i	−0.125783	+	0.992058i	$0.540144\pi$
$282$	−24.9055	+	33.2699i	−1.48310	+	1.98119i
$283$	7.94011	+	14.5412i	0.471991	+	0.864386i	0.999886	+	0.0150772i	$0.00479941\pi$
$283$	7.94011	+	14.5412i	0.471991	+	0.864386i	−0.527896	+	0.849309i	$0.677019\pi$
$284$	5.28772	+	8.22786i	0.313769	+	0.488234i
$285$	−4.88771	−	18.9682i	−0.289523	−	1.12358i
$286$	−1.28735	−	4.38430i	−0.0761224	−	0.259249i
$287$	1.17863	+	16.4794i	0.0695724	+	0.972749i
$288$	−0.927433	−	12.9672i	−0.0546495	−	0.764100i
$289$	1.82163	+	6.20390i	0.107155	+	0.364935i
$290$	−7.39087	−	28.6824i	−0.434007	−	1.68429i
$291$	20.6473	+	32.1279i	1.21037	+	1.88337i
$292$	6.47622	+	11.8603i	0.378992	+	0.694072i
$293$	−5.60193	+	7.48330i	−0.327268	+	0.437179i	−0.933754	−	0.357915i	$-0.883488\pi$
$293$	−5.60193	+	7.48330i	−0.327268	+	0.437179i	0.606486	+	0.795094i	$0.292579\pi$
$294$	−18.1556	−	8.29138i	−1.05886	−	0.483563i
$295$	−5.03020	−	9.99173i	−0.292869	−	0.581741i
$296$	2.58770	−	4.02654i	0.150407	−	0.234038i
$297$	1.29867	+	0.0928828i	0.0753565	+	0.00538961i
$298$	6.82566	+	6.82566i	0.395400	+	0.395400i
$299$	−20.5133	+	0.175098i	−1.18632	+	0.0101262i
$300$	−13.5083	+	6.24411i	−0.779904	+	0.360504i
$301$	2.31544	+	2.67216i	0.133460	+	0.154021i
$302$	1.80278	+	8.28727i	0.103739	+	0.476879i
$303$	3.99527	+	5.33706i	0.229522	+	0.306606i
$304$	7.95485	−	17.4187i	0.456242	−	0.999031i
$305$	−6.97787	−	7.46038i	−0.399552	−	0.427180i
$306$	4.99576	−	17.0140i	0.285588	−	0.972625i
$307$	−28.3815	−	6.17401i	−1.61982	−	0.352369i	−0.690984	−	0.722870i	$-0.742823\pi$
$307$	−28.3815	−	6.17401i	−1.61982	−	0.352369i	−0.928832	+	0.370501i	$0.879186\pi$
$308$	1.06022	+	0.395443i	0.0604118	+	0.0225324i
$309$	22.5444	−	6.61964i	1.28251	−	0.376578i
$310$	−6.87069	−	8.48609i	−0.390229	−	0.481978i
$311$	−17.2521	+	19.9100i	−0.978279	+	1.12899i	0.0133550	+	0.999911i	$0.495749\pi$
$311$	−17.2521	+	19.9100i	−0.978279	+	1.12899i	−0.991634	+	0.129083i	$0.958797\pi$
$312$	10.2660	+	5.60566i	0.581197	+	0.317358i
$313$	−8.33843	+	22.3562i	−0.471316	+	1.26365i	0.456205	+	0.889875i	$0.349208\pi$
$313$	−8.33843	+	22.3562i	−0.471316	+	1.26365i	−0.927521	+	0.373772i	$0.878064\pi$
$314$	7.20576	−	4.63086i	0.406644	−	0.261334i
$315$	−2.90410	+	5.83505i	−0.163627	+	0.328768i
$316$	9.35372	−	1.34486i	0.526188	−	0.0756544i
$317$	−10.9384	+	4.07979i	−0.614359	+	0.229144i	−0.637329	−	0.770592i	$-0.719961\pi$
$317$	−10.9384	+	4.07979i	−0.614359	+	0.229144i	0.0229696	+	0.999736i	$0.492688\pi$
$318$	12.5692	−	9.40917i	0.704844	−	0.527640i
$319$	−3.57444	−	2.29716i	−0.200130	−	0.128616i
$320$	−4.43443	−	1.12099i	−0.247892	−	0.0626653i
$321$		−	42.0778i		−	2.34855i
$322$	7.53432	−	10.2458i	0.419871	−	0.570977i
$323$	13.4110	−	13.4110i	0.746210	−	0.746210i
$324$	11.0529	−	9.57743i	0.614052	−	0.532079i
$325$	2.94659	−	21.1834i	0.163447	−	1.17505i
$326$	−4.27421	+	29.7278i	−0.236726	+	1.64647i
$327$	0.391877	+	1.05066i	0.0216708	+	0.0581017i
$328$	−11.1240	−	8.32734i	−0.614221	−	0.459800i
$329$	14.1918	+	4.16709i	0.782420	+	0.229739i
$330$	−2.03387	+	4.94223i	−0.111961	+	0.272061i
$331$	3.20239	+	7.01225i	0.176019	+	0.385428i	0.976993	−	0.213271i	$-0.0684118\pi$
$331$	3.20239	+	7.01225i	0.176019	+	0.385428i	−0.800974	+	0.598699i	$0.795685\pi$
$332$	−7.73697	+	14.1692i	−0.424621	+	0.777636i
$333$	−7.83549	+	0.560405i	−0.429382	+	0.0307100i
$334$	5.33172	+	4.61996i	0.291739	+	0.252793i
$335$	9.86976	−	1.08402i	0.539243	−	0.0592262i
$336$	−14.4646	+	6.60575i	−0.789107	+	0.360373i
$337$	−3.90567	+	17.9541i	−0.212755	+	0.978020i	0.739604	+	0.673042i	$0.235013\pi$
$337$	−3.90567	+	17.9541i	−0.212755	+	0.978020i	−0.952359	+	0.304978i	$0.901351\pi$
$338$	8.48377	−	4.63249i	0.461456	−	0.251974i
$339$	5.82075	+	40.4842i	0.316140	+	2.19880i
$340$	−11.8549	−	8.19080i	−0.642925	−	0.444208i
$341$	−1.55038	−	0.222911i	−0.0839577	−	0.0120713i
$342$	−14.0044	+	3.04648i	−0.757274	+	0.164735i
$343$	−1.23242	+	17.2315i	−0.0665445	+	0.930414i
$344$	−2.97381			−0.160337
$345$	18.8441	+	14.8518i	1.01453	+	0.799596i
$346$	31.8842			1.71411
$347$	2.28878	−	32.0013i	0.122868	−	1.71792i	−0.445616	−	0.895224i	$-0.647015\pi$
$347$	2.28878	−	32.0013i	0.122868	−	1.71792i	0.568484	−	0.822695i	$-0.307530\pi$
$348$	−21.1102	+	4.59224i	−1.13162	+	0.246170i
$349$	−4.71236	−	0.677535i	−0.252247	−	0.0362676i	0.0150314	−	0.999887i	$-0.495215\pi$
$349$	−4.71236	−	0.677535i	−0.252247	−	0.0362676i	−0.267278	+	0.963619i	$0.586124\pi$
$350$	9.41861	+	9.33259i	0.503446	+	0.498848i
$351$	1.35398	+	9.41717i	0.0722704	+	0.502651i
$352$	−3.32977	+	1.81819i	−0.177477	+	0.0969100i
$353$	−0.345979	+	1.59044i	−0.0184146	+	0.0846504i	−0.985437	−	0.170041i	$-0.945610\pi$
$353$	−0.345979	+	1.59044i	−0.0184146	+	0.0846504i	0.967022	+	0.254691i	$0.0819738\pi$
$354$	−18.5804	+	8.48538i	−0.987537	+	0.450993i
$355$	12.8246	+	10.2862i	0.680657	+	0.545937i
$356$	−12.3064	−	10.6635i	−0.652237	−	0.565167i
$357$	−15.7094	+	1.12356i	−0.831428	+	0.0594649i
$358$	5.35338	−	9.80398i	0.282935	−	0.518157i
$359$	1.76020	+	3.85431i	0.0929000	+	0.203423i	0.950378	−	0.311099i	$-0.100697\pi$
$359$	1.76020	+	3.85431i	0.0929000	+	0.203423i	−0.857478	+	0.514521i	$0.827970\pi$
$360$	−2.10943	−	5.05976i	−0.111177	−	0.266673i
$361$	3.52213	+	1.03419i	0.185375	+	0.0544311i
$362$	−21.5463	−	16.1293i	−1.13245	−	0.847739i
$363$	−8.33282	−	22.3412i	−0.437360	−	1.17261i
$364$	−1.17676	+	8.18454i	−0.0616789	+	0.428986i
$365$	16.6601	+	15.4399i	0.872030	+	0.808163i
$366$	−14.0966	+	12.2148i	−0.736843	+	0.638478i
$367$	6.68904	−	6.68904i	0.349165	−	0.349165i	−0.510633	−	0.859799i	$-0.670589\pi$
$367$	6.68904	−	6.68904i	0.349165	−	0.349165i	0.859799	+	0.510633i	$0.170589\pi$
$368$	5.18139	+	22.8766i	0.270099	+	1.19252i
$369$			22.8059i			1.18723i
$370$	−3.91657	+	15.4932i	−0.203613	+	0.805453i
$371$	−4.70087	−	3.02107i	−0.244057	−	0.156846i
$372$	−6.37552	+	4.77265i	−0.330555	+	0.247450i
$373$	14.4837	−	5.40215i	0.749939	−	0.279713i	0.0547110	−	0.998502i	$-0.482576\pi$
$373$	14.4837	−	5.40215i	0.749939	−	0.279713i	0.695228	+	0.718790i	$0.255304\pi$
$374$	−5.12207	+	0.736443i	−0.264856	+	0.0380805i
$375$	−18.1904	+	17.1711i	−0.939348	+	0.886710i
$376$	−10.4653	+	6.72564i	−0.539706	+	0.346848i
$377$	10.8503	−	29.0907i	0.558818	−	1.49825i
$378$	−5.17679	−	2.82674i	−0.266265	−	0.145392i
$379$	−3.74436	+	4.32123i	−0.192335	+	0.221966i	−0.843724	−	0.536778i	$-0.819641\pi$
$379$	−3.74436	+	4.32123i	−0.192335	+	0.221966i	0.651389	+	0.758744i	$0.274187\pi$
$380$	−1.21836	+	11.5823i	−0.0625006	+	0.594161i
$381$	−4.10299	+	1.20475i	−0.210203	+	0.0617210i
$382$	24.0141	+	8.95678i	1.22867	+	0.458269i
$383$	−2.70760	−	0.589002i	−0.138352	−	0.0300966i	0.142856	−	0.989743i	$-0.454371\pi$
$383$	−2.70760	−	0.589002i	−0.138352	−	0.0300966i	−0.281208	+	0.959647i	$0.590735\pi$
$384$	5.81763	−	19.8130i	0.296880	−	1.01108i
$385$	1.90100	+	0.0635285i	0.0968840	+	0.00323771i
$386$	−2.67549	+	5.85850i	−0.136179	+	0.298190i
$387$	2.92489	+	3.90720i	0.148681	+	0.198614i
$388$	−4.82668	−	22.1879i	−0.245037	−	1.12642i
$389$	−5.44294	−	6.28149i	−0.275968	−	0.318484i	0.600798	−	0.799401i	$-0.294849\pi$
$389$	−5.44294	−	6.28149i	−0.275968	−	0.318484i	−0.876766	+	0.480917i	$0.840304\pi$
$390$	−38.4482	−	6.84579i	−1.94690	−	0.346650i
$391$	−3.10982	+	23.0227i	−0.157271	+	1.16431i
$392$	−4.22461	−	4.22461i	−0.213375	−	0.213375i
$393$	−12.2525	−	0.876316i	−0.618057	−	0.0442043i
$394$	5.66111	−	8.80886i	0.285203	−	0.443784i
$395$	14.1879	−	7.14270i	0.713871	−	0.359388i
$396$	1.42084	+	0.648875i	0.0713998	+	0.0326072i
$397$	11.6373	−	15.5456i	0.584060	−	0.780213i	−0.407029	−	0.913415i	$-0.633435\pi$
$397$	11.6373	−	15.5456i	0.584060	−	0.780213i	0.991089	+	0.133203i	$0.0425261\pi$
$398$	0.282305	+	0.517004i	0.0141507	+	0.0259150i
$399$	6.88204	+	10.7087i	0.344533	+	0.536104i
$400$	−24.3840	+	1.85646i	−1.21920	+	0.0928229i
$401$	7.52475	+	25.6269i	0.375768	+	1.27975i	0.902858	+	0.429939i	$0.141465\pi$
$401$	7.52475	+	25.6269i	0.375768	+	1.27975i	−0.527090	+	0.849809i	$0.676717\pi$
$402$	−1.29340	−	18.0841i	−0.0645091	−	0.901955i
$403$	−0.816518	−	11.4164i	−0.0406736	−	0.568692i
$404$	−1.11675	−	3.80330i	−0.0555603	−	0.189221i
$405$	12.4957	−	21.1709i	0.620916	−	1.05199i
$406$	10.4066	+	16.1930i	0.516470	+	0.803643i
$407$	1.09865	+	2.01203i	0.0544581	+	0.0997326i
$408$	7.93823	−	10.6042i	0.393001	−	0.524988i
$409$	−7.68627	−	3.51020i	−0.380062	−	0.173568i	0.216218	−	0.976345i	$-0.430628\pi$
$409$	−7.68627	−	3.51020i	−0.380062	−	0.173568i	−0.596280	+	0.802777i	$0.703355\pi$
$410$	44.0537	+	14.5503i	2.17566	+	0.718589i
$411$	15.0361	−	23.3967i	0.741677	−	1.15407i
$412$	−13.9345	−	0.996612i	−0.686501	−	0.0490995i
$413$	5.14046	+	5.14046i	0.252946	+	0.252946i
$414$	11.3827	−	13.3651i	0.559428	−	0.656860i
$415$	−4.75690	+	26.7163i	−0.233507	+	1.31145i
$416$	−18.1545	−	20.9514i	−0.890098	−	1.02723i
$417$	−0.415810	−	1.91145i	−0.0203623	−	0.0936040i
$418$	2.50645	+	3.34822i	0.122594	+	0.163767i
$419$	10.2374	−	22.4167i	0.500128	−	1.09513i	−0.476299	−	0.879283i	$-0.658022\pi$
$419$	10.2374	−	22.4167i	0.500128	−	1.09513i	0.976428	−	0.215845i	$-0.0692507\pi$
$420$	7.06308	−	6.60627i	0.344643	−	0.322353i
$421$	2.97947	−	10.1471i	0.145210	−	0.494541i	−0.854478	−	0.519487i	$-0.826123\pi$
$421$	2.97947	−	10.1471i	0.145210	−	0.494541i	0.999689	+	0.0249456i	$0.00794125\pi$
$422$	28.3990	+	6.17782i	1.38244	+	0.300732i
$423$	19.1298	+	7.13504i	0.930122	+	0.346918i
$424$	4.50943	−	1.32409i	0.218997	−	0.0643034i
$425$	−23.2707	−	6.71709i	−1.12880	−	0.325827i
$426$	19.6584	−	22.6870i	0.952453	−	1.09919i
$427$	5.82641	+	3.18146i	0.281960	+	0.153962i
$428$	−8.74291	+	23.4406i	−0.422604	+	1.13305i
$429$	−4.71288	+	3.02878i	−0.227540	+	0.146231i
$430$	9.41357	−	3.15714i	0.453962	−	0.152251i
$431$	5.77493	−	0.830310i	0.278169	−	0.0399946i	−0.00181856	−	0.999998i	$-0.500579\pi$
$431$	5.77493	−	0.830310i	0.278169	−	0.0399946i	0.279987	+	0.960004i	$0.409670\pi$
$432$	10.1925	−	3.80162i	0.490389	−	0.182906i
$433$	−2.79423	+	2.09174i	−0.134282	+	0.100522i	−0.664307	−	0.747460i	$-0.731273\pi$
$433$	−2.79423	+	2.09174i	−0.134282	+	0.100522i	0.530025	+	0.847982i	$0.322182\pi$
$434$	5.96933	+	3.83625i	0.286537	+	0.184146i
$435$	−31.1881	+	18.6016i	−1.49536	+	0.891880i
$436$		−	0.666726i		−	0.0319304i
$437$	17.5363	−	6.71177i	0.838877	−	0.321068i
$438$	29.3281	−	29.3281i	1.40135	−	1.40135i
$439$	−23.8217	+	20.6416i	−1.13695	+	0.985169i	−0.999985	−	0.00540742i	$-0.998279\pi$
$439$	−23.8217	+	20.6416i	−1.13695	+	0.985169i	−0.136960	+	0.990577i	$0.543733\pi$
$440$	−1.08741	+	1.17335i	−0.0518404	+	0.0559372i
$441$	−1.39547	+	9.70572i	−0.0664510	+	0.462177i
$442$	−13.2144	−	35.4292i	−0.628546	−	1.68520i
$443$	−5.64575	−	4.22635i	−0.268238	−	0.200800i	0.456689	−	0.889627i	$-0.349035\pi$
$443$	−5.64575	−	4.22635i	−0.268238	−	0.200800i	−0.724926	+	0.688826i	$0.758126\pi$
$444$	11.1838	+	3.28387i	0.530762	+	0.155846i
$445$	−25.3118	−	10.4165i	−1.19990	−	0.493791i
$446$	−5.66279	−	12.3998i	−0.268141	−	0.587146i
$447$	5.67180	−	10.3871i	0.268267	−	0.491294i
$448$	2.96486	−	0.212051i	0.140077	−	0.0100185i
$449$	−0.839111	−	0.727094i	−0.0396001	−	0.0343137i	0.634836	−	0.772647i	$-0.281068\pi$
$449$	−0.839111	−	0.727094i	−0.0396001	−	0.0343137i	−0.674436	+	0.738333i	$0.735613\pi$
$450$	12.0491	+	13.7772i	0.568000	+	0.649462i
$451$	6.05393	−	2.76474i	0.285069	−	0.130186i
$452$	5.16918	−	23.7623i	0.243138	−	1.11769i
$453$	9.12615	−	4.98326i	0.428784	−	0.234134i
$454$	−6.16751	−	42.8960i	−0.289456	−	2.01321i
$455$	2.49917	+	13.6724i	0.117163	+	0.640972i
$456$	−10.5973	−	1.52366i	−0.496263	−	0.0713518i
$457$	−12.4915	+	2.71736i	−0.584329	+	0.127113i	−0.495006	−	0.868890i	$-0.664834\pi$
$457$	−12.4915	+	2.71736i	−0.584329	+	0.127113i	−0.0893231	+	0.996003i	$0.528470\pi$
$458$	−3.13831	+	43.8793i	−0.146644	+	2.05035i
$459$	10.7744			0.502907
$460$	−7.41174	−	12.1891i	−0.345574	−	0.568318i
$461$	42.2423			1.96742			0.983709	−	0.179768i	$-0.0575348\pi$
$461$	42.2423			1.96742			0.983709	+	0.179768i	$0.0575348\pi$
$462$	0.247770	−	3.46427i	0.0115273	−	0.161173i
$463$	−28.9973	+	6.30799i	−1.34762	+	0.293157i	−0.827754	−	0.561091i	$-0.810382\pi$
$463$	−28.9973	+	6.30799i	−1.34762	+	0.293157i	−0.519866	+	0.854248i	$0.674018\pi$
$464$	−35.1397	−	5.05232i	−1.63132	−	0.234548i
$465$	−7.60953	+	11.0136i	−0.352883	+	0.510746i
$466$	2.93760	+	20.4315i	0.136082	+	0.946470i
$467$	−15.3855	+	8.40112i	−0.711956	+	0.388758i	−0.794038	−	0.607868i	$-0.792025\pi$
$467$	−15.3855	+	8.40112i	−0.711956	+	0.388758i	0.0820817	+	0.996626i	$0.473843\pi$
$468$	−2.42621	+	11.1531i	−0.112151	+	0.515552i
$469$	−5.86948	+	2.68050i	−0.271028	+	0.123774i
$470$	25.9876	−	32.4004i	1.19872	−	1.49452i
$471$	−7.93654	−	6.87705i	−0.365696	−	0.316878i
$472$	−6.09871	+	0.436188i	−0.280716	+	0.0200772i
$473$	0.682602	−	1.25009i	0.0313861	−	0.0574793i
$474$	−12.0489	−	26.3835i	−0.553426	−	1.21183i
$475$	4.24895	+	19.1096i	0.194955	+	0.876807i
$476$	8.98482	+	2.63818i	0.411818	+	0.120921i
$477$	−6.17494	−	4.62250i	−0.282731	−	0.211650i
$478$	−4.60749	−	12.3532i	−0.210742	−	0.565020i
$479$	1.67430	−	11.6450i	0.0765006	−	0.532073i	−0.915149	−	0.403115i	$-0.867928\pi$
$479$	1.67430	−	11.6450i	0.0765006	−	0.532073i	0.991650	−	0.128958i	$-0.0411633\pi$
$480$	1.23163	+	32.4011i	0.0562161	+	1.47890i
$481$	−12.6600	+	10.9699i	−0.577245	+	0.500186i
$482$	9.99966	−	9.99966i	0.455472	−	0.455472i
$483$	−14.6553	−	5.32409i	−0.666838	−	0.242255i
$484$			14.1772i			0.644417i
$485$	−19.5512	−	32.7803i	−0.887776	−	1.48848i
$486$	−27.5191	−	17.6855i	−1.24829	−	0.802229i
$487$	−2.42446	+	1.81493i	−0.109863	+	0.0822421i	−0.652796	−	0.757533i	$-0.726404\pi$
$487$	−2.42446	+	1.81493i	−0.109863	+	0.0822421i	0.542934	+	0.839775i	$0.317313\pi$
$488$	−5.23131	+	1.95118i	−0.236810	+	0.0883257i
$489$	36.4471	−	5.24030i	1.64819	−	0.236974i
$490$	17.8580	+	8.88792i	0.806743	+	0.401515i
$491$	20.6052	−	13.2422i	0.929900	−	0.597611i	0.0143863	−	0.999897i	$-0.495421\pi$
$491$	20.6052	−	13.2422i	0.929900	−	0.597611i	0.915514	+	0.402286i	$0.131784\pi$
$492$	11.8257	−	31.7058i	0.533142	−	1.42941i
$493$	−30.8606	−	16.8511i	−1.38989	−	0.758937i
$494$	−20.0141	+	23.0975i	−0.900477	+	1.03921i
$495$	2.61116	+	0.274671i	0.117363	+	0.0123455i
$496$	−12.5569	+	3.68704i	−0.563821	+	0.165553i
$497$	−10.0102	−	3.73362i	−0.449020	−	0.167476i
$498$	48.4182	+	10.5327i	2.16967	+	0.471984i
$499$	−6.27104	+	21.3572i	−0.280730	+	0.956079i	0.691563	+	0.722316i	$0.256922\pi$
$499$	−6.27104	+	21.3572i	−0.280730	+	0.956079i	−0.972294	+	0.233763i	$0.924896\pi$
$500$	13.7013	−	5.78604i	0.612740	−	0.258760i
$501$	3.59313	−	7.86785i	0.160529	−	0.351510i
$502$	22.7451	+	30.3839i	1.01516	+	1.35610i
$503$	−0.217433	−	0.999522i	−0.00969485	−	0.0445665i	0.972045	−	0.234793i	$-0.0754413\pi$
$503$	−0.217433	−	0.999522i	−0.00969485	−	0.0445665i	−0.981740	+	0.190227i	$0.939078\pi$
$504$	2.33293	+	2.69234i	0.103917	+	0.119926i
$505$	−3.81254	−	5.46430i	−0.169656	−	0.243158i
$506$	−4.92774	−	1.40134i	−0.219065	−	0.0622972i
$507$	−8.37990	−	8.37990i	−0.372164	−	0.372164i
$508$	2.53601	+	0.181379i	0.112517	+	0.00804740i
$509$	−19.1407	+	29.7835i	−0.848396	+	1.32013i	0.0973584	+	0.995249i	$0.468961\pi$
$509$	−19.1407	+	29.7835i	−0.848396	+	1.32013i	−0.945755	+	0.324881i	$0.894676\pi$
$510$	−13.8704	+	41.9952i	−0.614193	+	1.85958i
$511$	−13.4274	−	6.13211i	−0.593995	−	0.271269i
$512$	−11.8317	+	15.8053i	−0.522892	+	0.698501i
$513$	−4.17346	−	7.64313i	−0.184263	−	0.337452i
$514$	−9.25701	−	14.4042i	−0.408309	−	0.635341i
$515$	−22.7396	+	5.85952i	−1.00202	+	0.258201i
$516$	−2.04030	−	6.94863i	−0.0898192	−	0.305896i
$517$	−0.425056	−	5.94306i	−0.0186940	−	0.261376i
$518$	−0.740874	−	10.3588i	−0.0325521	−	0.455138i
$519$	−11.0132	−	37.5075i	−0.483426	−	1.64640i
$520$	−10.0671	−	5.94191i	−0.441472	−	0.260570i
$521$	−7.87621	−	12.2556i	−0.345063	−	0.536929i	0.624735	−	0.780837i	$-0.285207\pi$
$521$	−7.87621	−	12.2556i	−0.345063	−	0.536929i	−0.969798	+	0.243908i	$0.921571\pi$
$522$	12.7338	+	23.3202i	0.557344	+	1.02070i
$523$	14.5082	−	19.3807i	0.634401	−	0.847460i	−0.362005	−	0.932176i	$-0.617908\pi$
$523$	14.5082	−	19.3807i	0.634401	−	0.847460i	0.996405	+	0.0847164i	$0.0269984\pi$
$524$	6.64353	+	3.03400i	0.290224	+	0.132541i
$525$	7.72523	−	14.3033i	0.337157	−	0.624248i
$526$	14.6694	−	22.8261i	0.639618	−	0.995265i
$527$	−12.9288	−	0.924689i	−0.563189	−	0.0402801i
$528$	4.52947	+	4.52947i	0.197120	+	0.197120i
$529$	−12.1026	+	19.5583i	−0.526201	+	0.850360i
$530$	−12.8689	+	8.97883i	−0.558987	+	0.390015i
$531$	6.57150	+	7.58391i	0.285179	+	0.329114i
$532$	−1.60880	−	7.39552i	−0.0697502	−	0.320637i
$533$	29.1445	+	38.9325i	1.26239	+	1.68635i
$534$	−20.7622	+	45.4630i	−0.898470	+	1.96738i
$535$	−1.40456	+	42.0296i	−0.0607246	+	1.81710i
$536$	1.52897	−	5.20720i	0.0660416	−	0.224917i
$537$	−13.3822	−	2.91112i	−0.577484	−	0.125624i
$538$	0.761055	+	0.283859i	0.0328114	+	0.0122380i
$539$	2.74560	−	0.806181i	0.118261	−	0.0347247i
$540$	−5.14203	+	4.16320i	−0.221278	+	0.179156i
$541$	−0.905294	+	1.04476i	−0.0389216	+	0.0449179i	−0.774877	−	0.632113i	$-0.782188\pi$
$541$	−0.905294	+	1.04476i	−0.0389216	+	0.0449179i	0.735955	+	0.677030i	$0.236733\pi$
$542$	19.6704	+	10.7409i	0.844918	+	0.461360i
$543$	−11.5317	+	30.9176i	−0.494871	+	1.32680i
$544$	−26.4115	+	16.9736i	−1.13238	+	0.727738i
$545$	−0.356356	−	1.06254i	−0.0152646	−	0.0455142i
$546$	25.1208	−	3.61183i	1.07507	−	0.154572i
$547$	38.0556	−	14.1940i	1.62714	−	0.606892i	0.640233	−	0.768181i	$-0.278838\pi$
$547$	38.0556	−	14.1940i	1.62714	−	0.606892i	0.986907	+	0.161289i	$0.0515650\pi$
$548$	−13.2377	+	9.90959i	−0.565485	+	0.423317i
$549$	7.70886	+	4.95419i	0.329006	+	0.211440i
$550$	2.19651	−	4.86868i	0.0936596	−	0.207601i
$551$			28.4191i			1.21069i
$552$	11.4560	−	6.38298i	0.487599	−	0.271678i
$553$	−7.29928	+	7.29928i	−0.310397	+	0.310397i
$554$	11.7137	−	10.1500i	0.497668	−	0.431232i
$555$	19.5785	−	0.744220i	0.831061	−	0.0315904i
$556$	−0.165521	+	1.15122i	−0.00701966	+	0.0488228i
$557$	8.09864	+	21.7133i	0.343150	+	0.920021i	0.987826	+	0.155565i	$0.0497198\pi$
$557$	8.09864	+	21.7133i	0.343150	+	0.920021i	−0.644675	+	0.764456i	$0.723007\pi$
$558$	7.84116	+	5.86982i	0.331943	+	0.248489i
$559$	9.98630	+	2.93224i	0.422376	+	0.124021i
$560$	14.6685	−	6.11535i	0.619857	−	0.258421i
$561$	2.63555	+	5.77105i	0.111273	+	0.243654i
$562$	−8.72897	+	15.9859i	−0.368209	+	0.674325i
$563$	40.6116	−	2.90460i	1.71158	−	0.122414i	0.819141	−	0.573592i	$-0.194451\pi$
$563$	40.6116	−	2.90460i	1.71158	−	0.122414i	0.892434	+	0.451178i	$0.148996\pi$
$564$	−22.8953	−	19.8389i	−0.964067	−	0.835369i
$565$	−4.46271	−	40.6321i	−0.187748	−	1.70941i
$566$	−27.5024	+	12.5599i	−1.15601	+	0.527934i
$567$	−3.39594	+	15.6109i	−0.142616	+	0.655595i
$568$	7.88663	−	4.30643i	0.330916	−	0.180694i
$569$	4.77705	+	33.2251i	0.200264	+	1.39287i	0.803499	+	0.595306i	$0.202969\pi$
$569$	4.77705	+	33.2251i	0.200264	+	1.39287i	−0.603234	+	0.797564i	$0.706122\pi$
$570$	35.1632	−	6.42746i	1.47282	−	0.269217i
$571$	−13.0044	−	1.86974i	−0.544215	−	0.0782464i	−0.135276	−	0.990808i	$-0.543192\pi$
$571$	−13.0044	−	1.86974i	−0.544215	−	0.0782464i	−0.408939	+	0.912562i	$0.634101\pi$
$572$	3.25476	−	0.708031i	0.136089	−	0.0296042i
$573$	2.24170	−	31.3431i	0.0936485	−	1.30938i
$574$	−30.1502			−1.25844
$575$	−18.3267	−	15.4638i	−0.764278	−	0.644887i
$576$	4.10308			0.170962
$577$	−0.856035	+	11.9689i	−0.0356372	+	0.498273i	0.948019	+	0.318215i	$0.103083\pi$
$577$	−0.856035	+	11.9689i	−0.0356372	+	0.498273i	−0.983656	+	0.180059i	$0.942371\pi$
$578$	−11.5298	+	2.50816i	−0.479577	+	0.104326i
$579$	7.81589	+	1.12376i	0.324817	+	0.0467017i
$580$	21.2393	−	3.88232i	0.881913	−	0.161204i
$581$	−2.50973	−	17.4556i	−0.104121	−	0.724179i
$582$	−61.1689	+	33.4008i	−2.53553	+	1.38451i
$583$	−0.478482	+	2.19955i	−0.0198167	+	0.0910960i
$584$	11.2933	−	5.15749i	0.467321	−	0.213418i
$585$	2.09462	+	19.0711i	0.0866018	+	0.788492i
$586$	−12.8922	−	11.1712i	−0.532573	−	0.461477i
$587$	−0.653652	+	0.0467501i	−0.0269791	+	0.00192958i	−0.0848222	−	0.996396i	$-0.527032\pi$
$587$	−0.653652	+	0.0467501i	−0.0269791	+	0.00192958i	0.0578431	+	0.998326i	$0.481578\pi$
$588$	6.97280	−	12.7697i	0.287553	−	0.526615i
$589$	4.35203	+	9.52961i	0.179322	+	0.392661i
$590$	18.8423	−	7.85544i	0.775727	−	0.323403i
$591$	−12.3179	−	3.61685i	−0.506689	−	0.148777i
$592$	15.3335	+	11.4785i	0.630204	+	0.471765i
$593$	9.06814	+	24.3126i	0.372384	+	0.998399i	0.979082	+	0.203467i	$0.0652210\pi$
$593$	9.06814	+	24.3126i	0.372384	+	0.998399i	−0.606698	+	0.794932i	$0.707506\pi$
$594$	−0.338141	+	2.35182i	−0.0138741	+	0.0964963i
$595$	15.7289	−	0.597888i	0.644821	−	0.0245110i
$596$	−5.31788	+	4.60797i	−0.217829	+	0.188750i
$597$	0.510674	−	0.510674i	0.0209005	−	0.0209005i
$598$	2.35185	−	37.3622i	0.0961741	−	1.52785i
$599$			5.35190i			0.218673i	0.994005	+	0.109336i	$0.0348726\pi$
$599$			5.35190i			0.218673i	−0.994005	+	0.109336i	$0.965127\pi$
$600$	4.83677	+	12.7884i	0.197460	+	0.522084i
$601$	−13.1311	−	8.43886i	−0.535629	−	0.344228i	0.244698	−	0.969599i	$-0.421311\pi$
$601$	−13.1311	−	8.43886i	−0.535629	−	0.344228i	−0.780327	+	0.625371i	$0.784948\pi$
$602$	−5.16545	+	3.86680i	−0.210528	+	0.157599i
$603$	−8.34542	+	3.11268i	−0.339852	+	0.126758i
$604$	−6.11941	+	0.879838i	−0.248995	+	0.0358001i
$605$	7.57752	+	22.5937i	0.308070	+	0.918565i
$606$	−10.2349	+	6.57759i	−0.415766	+	0.267196i
$607$	−0.151451	+	0.406055i	−0.00614719	+	0.0164813i	−0.939987	−	0.341210i	$-0.889163\pi$
$607$	−0.151451	+	0.406055i	−0.00614719	+	0.0164813i	0.933840	+	0.357691i	$0.116436\pi$
$608$	22.2712	+	12.1610i	0.903215	+	0.493193i
$609$	15.4543	−	17.8352i	0.626239	−	0.722718i
$610$	14.4882	−	11.7303i	0.586611	−	0.474944i
$611$	41.7750	−	12.2663i	1.69004	−	0.496239i
$612$	12.1110	+	4.51719i	0.489560	+	0.182596i
$613$	5.52699	+	1.20232i	0.223233	+	0.0485614i	0.322790	−	0.946470i	$-0.395379\pi$
$613$	5.52699	+	1.20232i	0.223233	+	0.0485614i	−0.0995575	+	0.995032i	$0.531743\pi$
$614$	14.9332	−	50.8577i	0.602654	−	2.05245i
$615$	1.89981	−	56.8492i	0.0766078	−	2.29238i
$616$	0.431876	−	0.945677i	0.0174008	−	0.0381024i
$617$	19.3225	+	25.8118i	0.777893	+	1.03914i	0.997972	+	0.0636615i	$0.0202778\pi$
$617$	19.3225	+	25.8118i	0.777893	+	1.03914i	−0.220078	+	0.975482i	$0.570631\pi$
$618$	9.11443	+	41.8984i	0.366636	+	1.68540i
$619$	−23.4793	−	27.0966i	−0.943713	−	1.08910i	−0.995900	−	0.0904658i	$-0.971164\pi$
$619$	−23.4793	−	27.0966i	−0.943713	−	1.08910i	0.0521863	−	0.998637i	$-0.483381\pi$
$620$	6.52752	−	4.55437i	0.262152	−	0.182908i
$621$	9.74046	+	4.34823i	0.390871	+	0.174488i
$622$	−33.9953	−	33.9953i	−1.36309	−	1.36309i
$623$	17.7424	+	1.26896i	0.710834	+	0.0508399i
$624$	−25.3062	+	39.3773i	−1.01306	+	1.57635i
$625$	18.7427	−	16.5442i	0.749709	−	0.661767i
$626$	−39.6084	−	18.0885i	−1.58307	−	0.722964i
$627$	3.07298	−	4.10502i	0.122723	−	0.163939i
$628$	2.99237	+	5.48011i	0.119408	+	0.218680i
$629$	10.2564	+	15.9592i	0.408949	+	0.636337i
$630$	−10.2432	−	6.04584i	−0.408099	−	0.240872i
$631$	−10.4688	−	35.6536i	−0.416758	−	1.41935i	−0.854127	−	0.520065i	$-0.825908\pi$
$631$	−10.4688	−	35.6536i	−0.416758	−	1.41935i	0.437368	−	0.899282i	$-0.355911\pi$
$632$	−0.619372	−	8.65995i	−0.0246373	−	0.344474i
$633$	−2.54198	−	35.5415i	−0.101035	−	1.41265i
$634$	−6.00223	−	20.4417i	−0.238379	−	0.811844i
$635$	4.13850	−	1.06641i	0.164231	−	0.0423191i
$636$	6.18775	+	9.62833i	0.245360	+	0.381788i
$637$	10.0210	+	18.3522i	0.397048	+	0.727140i
$638$	4.64675	−	6.20734i	0.183967	−	0.245751i
$639$	−13.4150	−	6.12643i	−0.530690	−	0.242358i
$640$	−6.47233	+	19.5961i	−0.255841	+	0.774605i
$641$	−12.2535	+	19.0667i	−0.483982	+	0.753091i	−0.994268	−	0.106914i	$-0.965903\pi$
$641$	−12.2535	+	19.0667i	−0.483982	+	0.753091i	0.510286	+	0.860005i	$0.329540\pi$
$642$	76.5922	+	5.47799i	3.02285	+	0.216199i
$643$	−10.6823	−	10.6823i	−0.421270	−	0.421270i	0.464371	−	0.885641i	$-0.346280\pi$
$643$	−10.6823	−	10.6823i	−0.421270	−	0.421270i	−0.885641	+	0.464371i	$0.846280\pi$
$644$	7.05791	+	6.01101i	0.278121	+	0.236867i
$645$	−6.96551	−	9.98328i	−0.274267	−	0.393091i
$646$	22.6655	+	26.1574i	0.891764	+	1.02915i
$647$	−2.07770	−	9.55104i	−0.0816829	−	0.375490i	0.918100	−	0.396350i	$-0.129723\pi$
$647$	−2.07770	−	9.55104i	−0.0816829	−	0.375490i	−0.999782	+	0.0208598i	$0.993360\pi$
$648$	−8.05238	−	10.7567i	−0.316327	−	0.422564i
$649$	1.21653	−	2.66382i	0.0477529	−	0.104564i
$650$	38.1756	+	8.12135i	1.49737	+	0.318545i
$651$	2.45096	−	8.34720i	0.0960607	−	0.327153i
$652$	−21.3927	−	4.65370i	−0.837804	−	0.182253i
$653$	−14.8711	−	5.54665i	−0.581953	−	0.217057i	0.0412086	−	0.999151i	$-0.486879\pi$
$653$	−14.8711	−	5.54665i	−0.581953	−	0.217057i	−0.623161	+	0.782093i	$0.714152\pi$
$654$	−1.96349	+	0.576532i	−0.0767785	+	0.0225442i
$655$	12.2092	+	1.28430i	0.477053	+	0.0501819i
$656$	36.4150	−	42.0252i	1.42177	−	1.64081i
$657$	−17.8839	−	9.76533i	−0.697716	−	0.380982i
$658$	−9.43276	+	25.2902i	−0.367727	+	0.985915i
$659$	−3.82362	+	2.45729i	−0.148947	+	0.0957224i	−0.612992	−	0.790089i	$-0.710034\pi$
$659$	−3.82362	+	2.45729i	−0.148947	+	0.0957224i	0.464045	+	0.885812i	$0.346398\pi$
$660$	−3.48772	−	1.73584i	−0.135759	−	0.0675673i
$661$	4.00499	−	0.575830i	0.155776	−	0.0223972i	−0.0639856	−	0.997951i	$-0.520381\pi$
$661$	4.00499	−	0.575830i	0.155776	−	0.0223972i	0.219761	+	0.975554i	$0.429472\pi$
$662$	−13.1810	+	4.91625i	−0.512293	+	0.191076i
$663$	−37.1133	+	27.7827i	−1.44136	+	1.07899i
$664$	12.4776	+	8.01890i	0.484227	+	0.311194i
$665$	−6.51670	−	10.9261i	−0.252707	−	0.423697i
$666$		−	14.3355i		−	0.555491i
$667$	−21.0985	−	27.6884i	−0.816936	−	1.07210i
$668$	−3.63643	+	3.63643i	−0.140698	+	0.140698i
$669$	−12.6307	+	10.9445i	−0.488330	+	0.423140i
$670$	0.688270	+	18.1066i	0.0265902	+	0.699519i
$671$	0.380573	−	2.64694i	0.0146919	−	0.102184i
$672$	−7.36376	−	19.7430i	−0.284063	−	0.761603i
$673$	15.1919	+	11.3725i	0.585606	+	0.438379i	0.850557	−	0.525883i	$-0.176265\pi$
$673$	15.1919	+	11.3725i	0.585606	+	0.438379i	−0.264951	+	0.964262i	$0.585356\pi$
$674$	−32.1725	−	9.44669i	−1.23924	−	0.363873i
$675$	−5.96951	+	9.38311i	−0.229767	+	0.361156i
$676$	2.92709	+	6.40944i	0.112581	+	0.246517i
$677$	−23.7990	+	43.5846i	−0.914669	+	1.67509i	−0.194966	+	0.980810i	$0.562459\pi$
$677$	−23.7990	+	43.5846i	−0.914669	+	1.67509i	−0.719704	+	0.694281i	$0.755722\pi$
$678$	−74.4494	+	5.32472i	−2.85921	+	0.204495i
$679$	18.7457	+	16.2432i	0.719393	+	0.623358i
$680$	−8.28310	+	10.3271i	−0.317642	+	0.396026i
$681$	−48.3311	+	22.0721i	−1.85205	+	0.845803i
$682$	0.607594	−	2.79306i	0.0232660	−	0.106952i
$683$	−19.5594	+	10.6802i	−0.748418	+	0.408667i	−0.807715	−	0.589573i	$-0.799296\pi$
$683$	−19.5594	+	10.6802i	−0.748418	+	0.408667i	0.0592966	+	0.998240i	$0.481114\pi$
$684$	−1.48682	−	10.3410i	−0.0568498	−	0.395399i
$685$	−15.7999	+	22.8680i	−0.603683	+	0.873740i
$686$	−31.2053	−	4.48664i	−1.19142	−	0.171301i
$687$	52.7021	−	11.4646i	2.01071	−	0.437403i
$688$	0.848973	−	11.8702i	0.0323668	−	0.452547i
$689$	−16.4486			−0.626644
$690$	−29.4874	+	32.3675i	−1.12257	+	1.23221i
$691$	−18.1911			−0.692022			−0.346011	−	0.938230i	$-0.612464\pi$
$691$	−18.1911			−0.692022			−0.346011	+	0.938230i	$0.612464\pi$
$692$	−1.65808	+	23.1830i	−0.0630307	+	0.881285i
$693$	−1.66727	+	0.362693i	−0.0633344	+	0.0137776i
$694$	57.9525	+	8.33231i	2.19985	+	0.316290i
$695$	0.351529	+	1.92314i	0.0133343	+	0.0729488i
$696$	2.82474	+	19.6465i	0.107071	+	0.744699i
$697$	48.3386	−	26.3949i	1.83096	−	0.999778i
$698$	1.84677	−	8.48949i	0.0699015	−	0.321332i
$699$	23.0202	−	10.5130i	0.870704	−	0.397637i
$700$	−7.27551	+	6.36293i	−0.274988	+	0.240496i
$701$	−13.6169	−	11.7991i	−0.514302	−	0.445645i	0.358635	−	0.933478i	$-0.383242\pi$
$701$	−13.6169	−	11.7991i	−0.514302	−	0.445645i	−0.872937	+	0.487833i	$0.837788\pi$
$702$	−17.3179	+	1.23860i	−0.653623	+	0.0467480i
$703$	7.34832	−	13.4574i	0.277147	−	0.507557i
$704$	−0.497413	−	1.08918i	−0.0187469	−	0.0410501i
$705$	−47.0912	−	19.3794i	−1.77356	−	0.729869i
$706$	−2.84996	−	0.836823i	−0.107260	−	0.0314943i
$707$	3.46633	+	2.59486i	0.130365	+	0.0975898i
$708$	−5.20347	−	13.9510i	−0.195558	−	0.524312i
$709$	6.23325	−	43.3532i	0.234095	−	1.62816i	−0.445995	−	0.895035i	$-0.647150\pi$
$709$	6.23325	−	43.3532i	0.234095	−	1.62816i	0.680090	−	0.733129i	$-0.261941\pi$
$710$	−20.3932	+	22.0048i	−0.765342	+	0.825826i
$711$	−10.7689	+	9.33129i	−0.403865	+	0.349951i
$712$	−10.5787	+	10.5787i	−0.396455	+	0.396455i
$713$	−11.3150	−	6.05364i	−0.423749	−	0.226711i
$714$		−	28.7413i		−	1.07562i
$715$	4.80858	−	2.86799i	0.179831	−	0.107257i
$716$	6.85007	+	4.40227i	0.255999	+	0.164521i
$717$	−12.9404	+	9.68703i	−0.483266	+	0.361769i
$718$	−7.24498	+	2.70224i	−0.270380	+	0.100847i
$719$	41.9439	−	6.03063i	1.56425	−	0.224905i	0.694899	−	0.719108i	$-0.255449\pi$
$719$	41.9439	−	6.03063i	1.56425	−	0.224905i	0.869346	+	0.494203i	$0.164540\pi$
$720$	20.7987	−	6.97550i	0.775121	−	0.259962i
$721$	12.8378	−	8.25038i	0.478106	−	0.307260i
$722$	−2.34102	+	6.27653i	−0.0871239	+	0.233588i
$723$	−15.2173	−	8.30926i	−0.565936	−	0.309025i
$724$	12.8481	−	14.8275i	0.477495	−	0.551059i
$725$	31.7733	−	17.5392i	1.18003	−	0.651391i
$726$	41.7514	−	12.2593i	1.54954	−	0.454986i
$727$	46.8844	+	17.4870i	1.73885	+	0.648556i	0.999688	−	0.0249749i	$-0.00795059\pi$
$727$	46.8844	+	17.4870i	1.73885	+	0.648556i	0.739159	+	0.673531i	$0.235223\pi$
$728$	7.42323	+	1.61483i	0.275123	+	0.0598494i
$729$	−2.00696	+	6.83508i	−0.0743319	+	0.253151i
$730$	−30.2735	+	28.3156i	−1.12047	+	1.04801i
$731$	4.89638	−	10.7216i	0.181099	−	0.396552i
$732$	−8.14829	−	10.8848i	−0.301170	−	0.402315i
$733$	2.71975	+	12.5025i	0.100456	+	0.461790i	0.999704	+	0.0243492i	$0.00775135\pi$
$733$	2.71975	+	12.5025i	0.100456	+	0.461790i	−0.899247	+	0.437441i	$0.855885\pi$
$734$	11.3049	+	13.0466i	0.417273	+	0.481558i
$735$	4.28707	−	24.0776i	0.158131	−	0.888114i
$736$	−30.7269	+	4.68590i	−1.13261	+	0.172725i
$737$	1.83798	+	1.83798i	0.0677030	+	0.0677030i
$738$	−41.5126	−	2.96904i	−1.52810	−	0.109292i
$739$	9.30098	−	14.4726i	0.342142	−	0.532384i	−0.626957	−	0.779054i	$-0.715700\pi$
$739$	9.30098	−	14.4726i	0.342142	−	0.532384i	0.969100	+	0.246670i	$0.0793364\pi$
$740$	−11.0614	−	3.65343i	−0.406626	−	0.134303i
$741$	34.0842	+	15.5657i	1.25211	+	0.571822i
$742$	6.11110	−	8.16347i	0.224346	−	0.299691i
$743$	−7.79489	−	14.2753i	−0.285967	−	0.523709i	0.694723	−	0.719277i	$-0.255527\pi$
$743$	−7.79489	−	14.2753i	−0.285967	−	0.523709i	−0.980690	+	0.195568i	$0.937345\pi$
$744$	3.95582	+	6.15538i	0.145027	+	0.225667i
$745$	−6.01203	+	10.1859i	−0.220264	+	0.373183i
$746$	7.94769	+	27.0673i	0.290986	+	0.991006i
$747$	−1.73661	−	24.2810i	−0.0635394	−	0.888397i
$748$	−0.269103	−	3.76255i	−0.00983937	−	0.137572i
$749$	−7.69942	−	26.2218i	−0.281331	−	0.958124i
$750$	−28.8875	−	35.3466i	−1.05482	−	1.29068i
$751$	3.63333	+	5.65356i	0.132582	+	0.206301i	0.901197	−	0.433411i	$-0.142690\pi$
$751$	3.63333	+	5.65356i	0.132582	+	0.206301i	−0.768615	+	0.639712i	$0.779054\pi$
$752$	−23.8583	−	43.6932i	−0.870022	−	1.59333i
$753$	27.8861	−	37.2515i	1.01623	−	1.35752i
$754$	51.5399	+	23.5375i	1.87697	+	0.857185i
$755$	−9.28204	+	4.67291i	−0.337808	+	0.170065i
$756$	2.32453	−	3.61703i	0.0845422	−	0.131550i
$757$	−2.17215	−	0.155355i	−0.0789482	−	0.00564649i	0.0318092	−	0.999494i	$-0.489873\pi$
$757$	−2.17215	−	0.155355i	−0.0789482	−	0.00564649i	−0.110757	+	0.993847i	$0.535328\pi$
$758$	−7.37826	−	7.37826i	−0.267990	−	0.267990i
$759$	0.0536124	+	6.28087i	0.00194601	+	0.227981i
$760$	10.5343	+	1.87565i	0.382118	+	0.0680370i
$761$	3.52878	+	4.07243i	0.127918	+	0.147625i	0.816095	−	0.577917i	$-0.196134\pi$
$761$	3.52878	+	4.07243i	0.127918	+	0.147625i	−0.688177	+	0.725543i	$0.741589\pi$
$762$	−1.65879	−	7.62533i	−0.0600916	−	0.276236i
$763$	0.436458	+	0.583040i	0.0158009	+	0.0211075i
$764$	−7.76127	+	16.9948i	−0.280793	+	0.614850i
$765$	21.7154	+	0.725694i	0.785120	+	0.0262375i
$766$	1.42463	−	4.85184i	0.0514739	−	0.175304i
$767$	20.9101	+	4.54871i	0.755020	+	0.164245i
$768$	43.8835	+	16.3677i	1.58351	+	0.590618i
$769$	0.800452	−	0.235034i	0.0288650	−	0.00847554i	−0.267268	−	0.963622i	$-0.586121\pi$
$769$	0.800452	−	0.235034i	0.0288650	−	0.00847554i	0.296133	+	0.955147i	$0.404303\pi$
$770$	−0.363124	+	3.45203i	−0.0130861	+	0.124403i
$771$	−13.7471	+	15.8650i	−0.495090	+	0.571364i
$772$	−4.12057	−	2.25000i	−0.148303	−	0.0809794i
$773$	2.50269	−	6.70998i	0.0900156	−	0.241341i	−0.884139	−	0.467224i	$-0.845254\pi$
$773$	2.50269	−	6.70998i	0.0900156	−	0.241341i	0.974154	+	0.225883i	$0.0725267\pi$
$774$	−7.49288	+	4.81538i	−0.269326	+	0.173085i
$775$	7.96845	−	10.7470i	0.286235	−	0.386044i
$776$	−20.6495	+	2.96894i	−0.741273	+	0.106579i
$777$	−11.9298	+	4.44958i	−0.427979	+	0.159628i
$778$	12.1425	−	9.08976i	0.435330	−	0.325884i
$779$	−37.4479	−	24.0663i	−1.34171	−	0.862264i
$780$	6.97698	−	27.5996i	0.249816	−	0.988224i
$781$			4.30378i			0.154001i
$782$	−41.5022	−	8.65792i	−1.48412	−	0.309607i
$783$	−11.4159	+	11.4159i	−0.407972	+	0.407972i
$784$	18.0689	−	15.6568i	0.645319	−	0.559172i
$785$	7.69789	+	7.13409i	0.274749	+	0.254627i
$786$	3.19024	−	22.1886i	0.113792	−	0.791441i
$787$	−1.81692	−	4.87134i	−0.0647661	−	0.173645i	0.900535	−	0.434783i	$-0.143175\pi$
$787$	−1.81692	−	4.87134i	−0.0647661	−	0.173645i	−0.965301	+	0.261138i	$0.915902\pi$
$788$	6.11051	+	4.57427i	0.217678	+	0.162952i
$789$	−31.9189	−	9.37222i	−1.13634	−	0.333660i
$790$	11.1545	+	26.7555i	0.396858	+	0.951917i
$791$	11.0352	+	24.1637i	0.392366	+	0.859161i
$792$	0.687759	−	1.25954i	0.0244384	−	0.0447557i
$793$	19.4911	−	1.39403i	0.692150	−	0.0495035i
$794$	26.7820	+	23.2067i	0.950456	+	0.823575i
$795$	15.0074	+	12.0371i	0.532259	+	0.426911i
$796$	−0.390593	+	0.178378i	−0.0138442	+	0.00632244i
$797$	6.20157	−	28.5081i	0.219671	−	1.00981i	−0.726757	−	0.686895i	$-0.758973\pi$
$797$	6.20157	−	28.5081i	0.219671	−	1.00981i	0.946428	−	0.322915i	$-0.104663\pi$
$798$	−20.3885	+	11.1329i	−0.721743	+	0.394102i
$799$	−7.01706	−	48.8047i	−0.248246	−	1.72659i
$800$	−0.148668	−	32.4051i	−0.00525622	−	1.14569i
$801$	24.3039	+	3.49437i	0.858734	+	0.123467i
$802$	−47.6272	+	10.3607i	−1.68177	+	0.365847i
$803$	−0.424207	+	5.93119i	−0.0149700	+	0.209307i
$804$	13.2162			0.466100
$805$	14.4608	+	5.80719i	0.509675	+	0.204676i
$806$	20.8871			0.735716
$807$	0.0710442	−	0.993328i	0.00250087	−	0.0349668i
$808$	−3.55856	+	0.774118i	−0.125190	+	0.0272334i
$809$	−2.93628	−	0.422173i	−0.103234	−	0.0148428i	0.0905042	−	0.995896i	$-0.471152\pi$
$809$	−2.93628	−	0.422173i	−0.103234	−	0.0148428i	−0.193738	+	0.981053i	$0.562061\pi$
$810$	36.9096	+	25.5015i	1.29687	+	0.896032i
$811$	−0.251637	−	1.75017i	−0.00883617	−	0.0614569i	0.984926	−	0.172975i	$-0.0553379\pi$
$811$	−0.251637	−	1.75017i	−0.00883617	−	0.0614569i	−0.993762	+	0.111518i	$0.964429\pi$
$812$	−12.3150	+	6.72452i	−0.432173	+	0.235984i
$813$	5.84079	−	26.8497i	0.204845	−	0.941659i
$814$	−3.80544	+	1.73788i	−0.133380	+	0.0609128i
$815$	−36.5802	+	4.01768i	−1.28135	+	0.140733i
$816$	40.0615	+	34.7134i	1.40243	+	1.21521i
$817$	−9.50226	+	0.679615i	−0.332442	+	0.0237767i
$818$	7.39012	−	13.5340i	0.258389	−	0.473205i
$819$	−5.17947	−	11.3414i	−0.180985	−	0.396302i
$820$	−12.8705	+	31.2747i	−0.449456	+	1.09216i
$821$	3.64863	+	1.07133i	0.127338	+	0.0373898i	0.344781	−	0.938683i	$-0.387953\pi$
$821$	3.64863	+	1.07133i	0.127338	+	0.0373898i	−0.217443	+	0.976073i	$0.569771\pi$
$822$	40.6304	+	30.4155i	1.41715	+	1.06086i
$823$	−0.691382	−	1.85367i	−0.0241001	−	0.0646148i	0.924343	−	0.381564i	$-0.124614\pi$
$823$	−0.691382	−	1.85367i	−0.0241001	−	0.0646148i	−0.948443	+	0.316949i	$0.897342\pi$
$824$	−1.82660	+	12.7043i	−0.0636327	+	0.442575i
$825$	−6.48605	−	0.902201i	−0.225815	−	0.0314106i
$826$	−10.0262	+	8.68773i	−0.348855	+	0.302285i
$827$	−18.2444	+	18.2444i	−0.634419	+	0.634419i	−0.949173	−	0.314754i	$-0.898078\pi$
$827$	−18.2444	+	18.2444i	−0.634419	+	0.634419i	0.314754	+	0.949173i	$0.398078\pi$
$828$	9.12582	+	8.97135i	0.317144	+	0.311776i
$829$			19.3318i			0.671421i	0.941965	+	0.335711i	$0.108976\pi$
$829$			19.3318i			0.671421i	−0.941965	+	0.335711i	$0.891024\pi$
$830$	−48.0112	−	12.1369i	−1.66649	−	0.421277i
$831$	−15.9862	−	10.2737i	−0.554554	−	0.356390i
$832$	7.00446	−	5.24348i	0.242836	−	0.181785i
$833$	22.1870	−	8.27532i	0.768734	−	0.286723i
$834$	3.53346	−	0.508034i	0.122354	−	0.0175918i
$835$	−3.85164	+	7.73889i	−0.133291	+	0.267815i
$836$	−2.56483	+	1.64832i	−0.0887065	+	0.0570082i
$837$	−2.07983	+	5.57625i	−0.0718896	+	0.192743i
$838$	39.4714	+	21.5530i	1.36352	+	0.744536i
$839$	−33.8719	+	39.0903i	−1.16939	+	1.34955i	−0.244343	+	0.969689i	$0.578572\pi$
$839$	−33.8719	+	39.0903i	−1.16939	+	1.34955i	−0.925045	+	0.379857i	$0.875973\pi$
$840$	−5.59110	−	6.90564i	−0.192911	−	0.238267i
$841$	22.7272	−	6.67332i	0.783698	−	0.230114i
$842$	18.0825	+	6.74442i	0.623164	+	0.232428i
$843$	21.8204	+	4.74673i	0.751533	+	0.163486i
$844$	−5.96872	+	20.3276i	−0.205452	+	0.699704i
$845$	8.09058	+	8.65002i	0.278324	+	0.297570i
$846$	−15.4780	+	33.8922i	−0.532146	+	1.16524i
$847$	−9.28080	−	12.3977i	−0.318892	−	0.425990i
$848$	3.99784	+	18.3778i	0.137286	+	0.631095i
$849$	24.2748	+	28.0146i	0.833108	+	0.961457i
$850$	15.2564	−	41.4841i	0.523289	−	1.42289i
$851$	2.83148	+	18.5669i	0.0970617	+	0.636465i
$852$	15.4734	+	15.4734i	0.530110	+	0.530110i
$853$	−25.1076	−	1.79573i	−0.859669	−	0.0614847i	−0.365459	−	0.930827i	$-0.619088\pi$
$853$	−25.1076	−	1.79573i	−0.859669	−	0.0614847i	−0.494210	+	0.869343i	$0.664542\pi$
$854$	−6.54959	+	10.1914i	−0.224123	+	0.348741i
$855$	−7.89664	−	15.6855i	−0.270059	−	0.536432i
$856$	20.9081	+	9.54842i	0.714625	+	0.326358i
$857$	−16.2698	+	21.7339i	−0.555764	+	0.742414i	−0.987158	−	0.159750i	$-0.948931\pi$
$857$	−16.2698	+	21.7339i	−0.555764	+	0.742414i	0.431393	+	0.902164i	$0.358022\pi$
$858$	−4.89960	−	8.97294i	−0.167269	−	0.306331i
$859$	27.0582	+	42.1035i	0.923216	+	1.43655i	0.899543	+	0.436832i	$0.143899\pi$
$859$	27.0582	+	42.1035i	0.923216	+	1.43655i	0.0236723	+	0.999720i	$0.492464\pi$
$860$	1.80602	+	7.00877i	0.0615846	+	0.238997i
$861$	10.4142	+	35.4676i	0.354916	+	1.20873i
$862$	0.759553	+	10.6199i	0.0258705	+	0.361717i
$863$	−0.584215	−	8.16839i	−0.0198869	−	0.278055i	−0.997659	−	0.0683848i	$-0.978215\pi$
$863$	−0.584215	−	8.16839i	−0.0198869	−	0.278055i	0.977772	−	0.209670i	$-0.0672391\pi$
$864$	4.06126	+	13.8314i	0.138167	+	0.470553i
$865$	9.74858	+	37.8322i	0.331462	+	1.28633i
$866$	−3.44372	−	5.35853i	−0.117022	−	0.182090i
$867$	6.93305	+	12.6969i	0.235459	+	0.431211i
$868$	−3.09976	+	4.14079i	−0.105213	+	0.140548i
$869$	3.78254	+	1.72743i	0.128314	+	0.0585989i
$870$	−29.7994	−	59.1920i	−1.01029	−	2.00680i
$871$	−10.2689	+	15.9786i	−0.347947	+	0.541416i
$872$	−0.610992	−	0.0436990i	−0.0206908	−	0.00147983i
$873$	24.2106	+	24.2106i	0.819406	+	0.819406i
$874$	9.93412	+	32.7944i	0.336027	+	1.10929i
$875$	−8.19383	+	14.0291i	−0.277002	+	0.474269i
$876$	19.7993	+	22.8496i	0.668956	+	0.772016i
$877$	−5.72006	−	26.2947i	−0.193153	−	0.887908i	−0.967048	−	0.254595i	$-0.918058\pi$
$877$	−5.72006	−	26.2947i	−0.193153	−	0.887908i	0.773895	−	0.633314i	$-0.218306\pi$
$878$	−34.4717	−	46.0487i	−1.16336	−	1.55407i
$879$	−8.68825	+	19.0246i	−0.293047	+	0.641685i
$880$	−4.37308	−	4.67547i	−0.147417	−	0.157610i
$881$	−2.64297	+	9.00112i	−0.0890439	+	0.303256i	−0.991958	−	0.126565i	$-0.959605\pi$
$881$	−2.64297	+	9.00112i	−0.0890439	+	0.303256i	0.902914	+	0.429820i	$0.141423\pi$
$882$	−17.4852	−	3.80367i	−0.588757	−	0.128076i
$883$	−28.3807	−	10.5855i	−0.955087	−	0.356229i	−0.176877	−	0.984233i	$-0.556599\pi$
$883$	−28.3807	−	10.5855i	−0.955087	−	0.356229i	−0.778210	+	0.628004i	$0.783872\pi$
$884$	26.4477	−	7.76575i	0.889533	−	0.261190i
$885$	−15.7492	−	19.4521i	−0.529405	−	0.653876i
$886$	8.42804	−	9.72648i	0.283146	−	0.326768i
$887$	−43.5701	−	23.7911i	−1.46294	−	0.798827i	−0.466615	−	0.884461i	$-0.654527\pi$
$887$	−43.5701	−	23.7911i	−1.46294	−	0.798827i	−0.996327	+	0.0856340i	$0.972708\pi$
$888$	3.74238	−	10.0337i	0.125586	−	0.336709i
$889$	−2.33643	+	1.50154i	−0.0783615	+	0.0503599i
$890$	22.2560	−	44.7178i	0.746023	−	1.49895i
$891$	6.37011	−	0.915883i	0.213407	−	0.0306832i
$892$	9.31034	−	3.47258i	0.311733	−	0.116270i
$893$	−31.9029	+	23.8822i	−1.06759	+	0.799188i
$894$	18.1688	+	11.6764i	0.607656	+	0.390517i
$895$	13.2697	+	3.35448i	0.443557	+	0.112128i
$896$		−	13.4115i		−	0.448047i
$897$	−44.7640	+	10.1387i	−1.49463	+	0.338523i
$898$	1.43274	−	1.43274i	0.0478111	−	0.0478111i
$899$	14.6784	−	12.7189i	0.489552	−	0.424199i
$900$	−10.6439	+	8.04442i	−0.354798	+	0.268147i
$901$	−2.65101	+	18.4381i	−0.0883178	+	0.614264i
$902$	4.24438	+	11.3796i	0.141323	+	0.378900i
$903$	6.33298	+	4.74081i	0.210748	+	0.157764i
$904$	−21.4372	−	6.29452i	−0.712989	−	0.209353i
$905$	12.5505	−	30.4972i	0.417192	−	1.01376i
$906$	7.88268	+	17.2607i	0.261885	+	0.573447i
$907$	12.4341	−	22.7713i	0.412867	−	0.756110i	−0.585649	−	0.810565i	$-0.699160\pi$
$907$	12.4341	−	22.7713i	0.412867	−	0.756110i	0.998516	+	0.0544551i	$0.0173422\pi$
$908$	31.5103	−	2.25366i	1.04571	−	0.0747905i
$909$	4.51712	+	3.91411i	0.149824	+	0.129823i
$910$	−25.2126	+	2.76915i	−0.835789	+	0.0917965i
$911$	46.0875	−	21.0474i	1.52695	−	0.697333i	0.537638	−	0.843176i	$-0.319317\pi$
$911$	46.0875	−	21.0474i	1.52695	−	0.697333i	0.989308	+	0.145843i	$0.0465893\pi$
$912$	9.10716	−	41.8649i	0.301568	−	1.38629i
$913$	−6.23499	+	3.40456i	−0.206348	+	0.112674i
$914$	−3.32006	−	23.0915i	−0.109818	−	0.763799i
$915$	−18.8035	−	12.9917i	−0.621624	−	0.429491i
$916$	−31.7414	−	4.56372i	−1.04876	−	0.150790i
$917$	−7.79580	+	1.69587i	−0.257440	+	0.0560026i
$918$	−1.40269	+	19.6122i	−0.0462957	+	0.647298i
$919$	−11.8208			−0.389933			−0.194966	−	0.980810i	$-0.562460\pi$
$919$	−11.8208			−0.389933			−0.194966	+	0.980810i	$0.562460\pi$
$920$	−11.6559	+	5.99326i	−0.384285	+	0.197592i
$921$	−64.9854			−2.14134
$922$	−5.49940	+	76.8916i	−0.181113	+	2.53229i
$923$	−30.7303	+	6.68496i	−1.01150	+	0.220038i
$924$	2.50598	+	0.360306i	0.0824408	+	0.0118532i
$925$	−19.5809	+	0.0898335i	−0.643817	+	0.00295371i
$926$	−7.70706	−	53.6038i	−0.253270	−	1.76153i
$927$	18.4884	−	10.0954i	0.607238	−	0.331577i
$928$	9.99978	−	45.9683i	0.328259	−	1.50898i
$929$	17.7516	−	8.10691i	0.582413	−	0.265979i	−0.102346	−	0.994749i	$-0.532635\pi$
$929$	17.7516	−	8.10691i	0.582413	−	0.265979i	0.684759	+	0.728770i	$0.259908\pi$
$930$	−19.0570	−	15.2851i	−0.624903	−	0.501219i
$931$	−14.4644	−	12.5335i	−0.474053	−	0.410769i
$932$	−15.0085	+	1.07343i	−0.491618	+	0.0351612i
$933$	−28.2485	+	51.7333i	−0.924815	+	1.69367i
$934$	−13.2892	−	29.0993i	−0.434835	−	0.952157i
$935$	−2.43989	−	5.85242i	−0.0797930	−	0.191394i
$936$	10.0617	+	2.95439i	0.328878	+	0.0965674i
$937$	−19.2666	−	14.4228i	−0.629414	−	0.471173i	0.236322	−	0.971675i	$-0.424058\pi$
$937$	−19.2666	−	14.4228i	−0.629414	−	0.471173i	−0.865736	+	0.500502i	$0.833149\pi$
$938$	−4.11507	−	11.0329i	−0.134362	−	0.360238i
$939$	−7.59753	+	52.8420i	−0.247936	+	1.72443i
$940$	22.2069	+	20.5804i	0.724308	+	0.671260i
$941$	9.30046	−	8.05890i	0.303186	−	0.262713i	−0.489958	−	0.871746i	$-0.662988\pi$
$941$	9.30046	−	8.05890i	0.303186	−	0.262713i	0.793145	+	0.609033i	$0.208442\pi$
$942$	13.5512	−	13.5512i	0.441522	−	0.441522i
$943$	54.3520	−	4.35393i	1.76995	−	0.141784i
$944$		−	24.4680i		−	0.796367i
$945$	1.77126	−	7.00678i	0.0576192	−	0.227931i
$946$	2.18662	+	1.40526i	0.0710932	+	0.0456888i
$947$	−18.3071	+	13.7045i	−0.594902	+	0.445338i	−0.853825	−	0.520560i	$-0.825723\pi$
$947$	−18.3071	+	13.7045i	−0.594902	+	0.445338i	0.258923	+	0.965898i	$0.416632\pi$
$948$	19.8100	−	7.38874i	0.643399	−	0.239975i
$949$	−43.0094	+	6.18382i	−1.39614	+	0.200735i
$950$	−35.3374	+	5.24634i	−1.14650	+	0.170214i
$951$	−21.9737	+	14.1216i	−0.712546	+	0.457925i
$952$	3.00653	−	8.06083i	0.0974423	−	0.261253i
$953$	45.8827	+	25.0539i	1.48629	+	0.811574i	0.998127	−	0.0611797i	$-0.0194863\pi$
$953$	45.8827	+	25.0539i	1.48629	+	0.811574i	0.488160	+	0.872754i	$0.337668\pi$
$954$	9.21803	−	10.6382i	0.298445	−	0.344424i
$955$	−3.28537	+	31.2324i	−0.106312	+	1.01066i
$956$	9.22157	−	2.70770i	0.298247	−	0.0875732i
$957$	−8.90714	−	3.32219i	−0.287927	−	0.107391i
$958$	20.9789	+	4.56367i	0.677796	+	0.147446i
$959$	5.08900	−	17.3315i	0.164332	−	0.559665i
$960$	−10.2279	−	0.341801i	−0.330104	−	0.0110316i
$961$	−9.90358	+	21.6858i	−0.319470	+	0.699543i
$962$	−18.3199	−	24.4725i	−0.590657	−	0.789026i
$963$	−8.01883	−	36.8620i	−0.258403	−	1.18786i
$964$	6.75073	+	7.79075i	0.217426	+	0.250923i
$965$	−7.76942	−	1.38336i	−0.250107	−	0.0445320i
$966$	11.5991	−	25.9832i	0.373196	−	0.835996i
$967$	5.44951	+	5.44951i	0.175244	+	0.175244i	0.789279	−	0.614035i	$-0.210454\pi$
$967$	5.44951	+	5.44951i	0.175244	+	0.175244i	−0.614035	+	0.789279i	$0.710454\pi$
$968$	12.9921	+	0.929211i	0.417581	+	0.0298660i
$969$	22.9418	−	35.6981i	0.736995	−	1.14679i
$970$	62.2138	−	31.3207i	1.99756	−	1.00565i
$971$	2.49673	+	1.14022i	0.0801237	+	0.0365913i	0.455074	−	0.890454i	$-0.349613\pi$
$971$	2.49673	+	1.14022i	0.0801237	+	0.0365913i	−0.374950	+	0.927045i	$0.622340\pi$
$972$	14.2901	−	19.0894i	0.458357	−	0.612293i
$973$	−0.608881	−	1.11508i	−0.0195198	−	0.0357479i
$974$	−2.98799	−	4.64941i	−0.0957415	−	0.148977i
$975$	−3.63264	−	47.7137i	−0.116338	−	1.52806i
$976$	−6.29484	−	21.4382i	−0.201493	−	0.686221i
$977$	3.46394	+	48.4322i	0.110821	+	1.54948i	0.683652	+	0.729808i	$0.260391\pi$
$977$	3.46394	+	48.4322i	0.110821	+	1.54948i	−0.572830	+	0.819674i	$0.694155\pi$
$978$	4.79373	+	67.0252i	0.153287	+	2.14323i
$979$	−2.01874	−	6.87519i	−0.0645191	−	0.219732i
$980$	−7.39106	+	12.5223i	−0.236099	+	0.400012i
$981$	0.543528	+	0.845745i	0.0173535	+	0.0270026i
$982$	21.4216	+	39.2307i	0.683590	+	1.25190i
$983$	−12.0316	+	16.0723i	−0.383747	+	0.512626i	−0.950273	−	0.311418i	$-0.899196\pi$
$983$	−12.0316	+	16.0723i	−0.383747	+	0.512626i	0.566526	+	0.824044i	$0.308287\pi$
$984$	−28.2803	−	12.9152i	−0.901544	−	0.411721i
$985$	12.1830	+	4.02388i	0.388183	+	0.128211i
$986$	34.6910	−	53.9803i	1.10479	−	1.71908i
$987$	33.0087	+	2.36083i	1.05068	+	0.0751460i
$988$	−15.7534	−	15.7534i	−0.501181	−	0.501181i
$989$	8.75341	−	7.71667i	0.278342	−	0.245376i
$990$	−0.839910	+	4.71721i	−0.0266941	+	0.149923i
$991$	−32.9694	−	38.0487i	−1.04731	−	1.20866i	−0.977465	−	0.211098i	$-0.932296\pi$
$991$	−32.9694	−	38.0487i	−1.04731	−	1.20866i	−0.0698417	−	0.997558i	$-0.522249\pi$
$992$	−3.68629	−	16.9456i	−0.117040	−	0.538024i
$993$	10.3362	+	13.8075i	0.328009	+	0.438168i
$994$	8.09934	−	17.7351i	0.256895	−	0.562523i
$995$	−0.527135	+	0.493042i	−0.0167113	+	0.0156305i
$996$	−10.1762	+	34.6571i	−0.322446	+	1.09815i
$997$	17.8860	+	3.89085i	0.566454	+	0.123225i	0.486667	−	0.873587i	$-0.338212\pi$
$997$	17.8860	+	3.89085i	0.566454	+	0.123225i	0.0797868	+	0.996812i	$0.474576\pi$
$998$	−38.0591	−	14.1953i	−1.20474	−	0.449345i
$999$	8.35767	−	2.45403i	0.264425	−	0.0776422i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.102.2	yes	200
5.2	odd	4		575.2.r.b.493.2		200
5.3	odd	4	inner	115.2.l.a.33.9	yes	200
5.4	even	2		575.2.r.b.332.9		200
23.7	odd	22	inner	115.2.l.a.7.9	✓	200
115.7	even	44		575.2.r.b.168.9		200
115.53	even	44	inner	115.2.l.a.53.2	yes	200
115.99	odd	22		575.2.r.b.7.2		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.9	✓	200	23.7	odd	22	inner
115.2.l.a.33.9	yes	200	5.3	odd	4	inner
115.2.l.a.53.2	yes	200	115.53	even	44	inner
115.2.l.a.102.2	yes	200	1.1	even	1	trivial
575.2.r.b.7.2		200	115.99	odd	22
575.2.r.b.168.9		200	115.7	even	44
575.2.r.b.332.9		200	5.4	even	2
575.2.r.b.493.2		200	5.2	odd	4

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Classical	Maass
Hilbert	Bianchi

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

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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	115.2.l.a.102.2

Level	$115$
Weight	$2$
Character	115.102
Analytic conductor	$0.918$
Analytic rank	$0$
Dimension	$200$
Inner twists	$4$