LMFDB - Embedded newform 770.2.w.b.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.4
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.732958 + 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.464104 + 2.18737i) q^{5} +(-1.91891 + 1.39417i) q^{6} +(-2.63063 - 0.282464i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.732958 + 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.464104 + 2.18737i) q^{5} +(-1.91891 + 1.39417i) q^{6} +(-2.63063 - 0.282464i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +(-0.910238 + 2.04242i) q^{10} +(-2.63315 - 2.01656i) q^{11} -2.37190 q^{12} +(0.478040 - 0.657965i) q^{13} +(-1.96220 - 1.77476i) q^{14} +(-5.27447 - 0.556321i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.374125 + 0.514939i) q^{17} +(-0.811453 - 2.49739i) q^{18} +(-0.231172 + 0.711476i) q^{19} +(-1.93690 + 1.11733i) q^{20} +(2.56533 - 5.72717i) q^{21} +(-0.944954 - 3.17916i) q^{22} +5.84039i q^{23} +(-1.91891 - 1.39417i) q^{24} +(-4.56921 + 2.03034i) q^{25} +(0.773484 - 0.251320i) q^{26} +(-0.717833 + 0.521536i) q^{27} +(-0.544270 - 2.58916i) q^{28} +(8.07009 - 2.62213i) q^{29} +(-3.94014 - 3.55033i) q^{30} +(2.72989 - 3.75737i) q^{31} -1.00000 q^{32} +(6.47898 - 4.46183i) q^{33} +0.636500i q^{34} +(-0.603032 - 5.88527i) q^{35} +(0.811453 - 2.49739i) q^{36} +(-3.85636 + 1.25301i) q^{37} +(-0.605217 + 0.439716i) q^{38} +(1.13386 + 1.56063i) q^{39} +(-2.22373 - 0.234546i) q^{40} +(-0.693842 + 2.13543i) q^{41} +(5.44174 - 3.12552i) q^{42} +1.78702 q^{43} +(1.10418 - 3.12743i) q^{44} +(2.39021 - 5.36321i) q^{45} +(-3.43289 + 4.72497i) q^{46} +(-1.40295 + 4.31784i) q^{47} +(-0.732958 - 2.25581i) q^{48} +(6.84043 + 1.48612i) q^{49} +(-4.88998 - 1.04314i) q^{50} +(-1.43582 + 0.466527i) q^{51} +(0.773484 + 0.251320i) q^{52} +(1.23908 - 1.70545i) q^{53} -0.887291 q^{54} +(3.18893 - 6.69558i) q^{55} +(1.08155 - 2.41459i) q^{56} +(-1.43552 - 1.04296i) q^{57} +(8.07009 + 2.62213i) q^{58} +(-11.4455 + 3.71887i) q^{59} +(-1.10081 - 5.18824i) q^{60} +(-9.48273 + 6.88961i) q^{61} +(4.41705 - 1.43519i) q^{62} +(5.15256 + 4.66038i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.66108 + 0.740287i) q^{65} +(7.86420 + 0.198551i) q^{66} +7.11959i q^{67} +(-0.374125 + 0.514939i) q^{68} +(-13.1748 - 4.28076i) q^{69} +(2.97141 - 5.11573i) q^{70} +(6.16231 - 4.47718i) q^{71} +(2.12441 - 1.54347i) q^{72} +(9.50651 - 3.08885i) q^{73} +(-3.85636 - 1.25301i) q^{74} +(-1.23103 - 11.7954i) q^{75} -0.748090 q^{76} +(6.35723 + 6.04861i) q^{77} +1.92904i q^{78} +(-9.15919 + 12.6065i) q^{79} +(-1.66117 - 1.49683i) q^{80} +(-3.08470 - 9.49374i) q^{81} +(-1.81650 + 1.31977i) q^{82} +(-4.36182 - 6.00353i) q^{83} +(6.23959 + 0.669978i) q^{84} +(-0.952731 + 1.05734i) q^{85} +(1.44573 + 1.05039i) q^{86} +20.1265i q^{87} +(2.73155 - 1.88112i) q^{88} +10.1872i q^{89} +(5.08614 - 2.93400i) q^{90} +(-1.44340 + 1.59583i) q^{91} +(-5.55454 + 1.80478i) q^{92} +(6.47503 + 8.91211i) q^{93} +(-3.67298 + 2.66857i) q^{94} +(-1.66355 - 0.175462i) q^{95} +(0.732958 - 2.25581i) q^{96} +(-9.78252 - 7.10742i) q^{97} +(4.66050 + 5.22300i) q^{98} +(2.48137 + 8.34821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.732958	+	2.25581i	−0.423173	+	1.30239i	0.481559	+	0.876414i	$0.340071\pi$
$3$	−0.732958	+	2.25581i	−0.423173	+	1.30239i	−0.904733	+	0.425980i	$0.859929\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.464104	+	2.18737i	0.207554	+	0.978224i
$5$	0.464104	+	2.18737i	0.207554	+	0.978224i
$6$	−1.91891	+	1.39417i	−0.783391	+	0.569167i
$7$	−2.63063	−	0.282464i	−0.994285	−	0.106761i
$7$	−2.63063	−	0.282464i	−0.994285	−	0.106761i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.12441	−	1.54347i	−0.708137	−	0.514492i
$10$	−0.910238	+	2.04242i	−0.287843	+	0.645869i
$11$	−2.63315	−	2.01656i	−0.793924	−	0.608017i
$11$	−2.63315	−	2.01656i	−0.793924	−	0.608017i
$12$	−2.37190			−0.684709
$13$	0.478040	−	0.657965i	0.132584	−	0.182487i	−0.737563	−	0.675278i	$-0.764024\pi$
$13$	0.478040	−	0.657965i	0.132584	−	0.182487i	0.870147	+	0.492792i	$0.164024\pi$
$14$	−1.96220	−	1.77476i	−0.524419	−	0.474326i
$15$	−5.27447	−	0.556321i	−1.36186	−	0.143641i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.374125	+	0.514939i	0.0907387	+	0.124891i	0.851973	−	0.523586i	$-0.175406\pi$
$17$	0.374125	+	0.514939i	0.0907387	+	0.124891i	−0.761234	+	0.648477i	$0.775406\pi$
$18$	−0.811453	−	2.49739i	−0.191261	−	0.588641i
$19$	−0.231172	+	0.711476i	−0.0530346	+	0.163224i	−0.974066	−	0.226265i	$-0.927348\pi$
$19$	−0.231172	+	0.711476i	−0.0530346	+	0.163224i	0.921031	+	0.389489i	$0.127348\pi$
$20$	−1.93690	+	1.11733i	−0.433104	+	0.249842i
$21$	2.56533	−	5.72717i	0.559800	−	1.24977i
$22$	−0.944954	−	3.17916i	−0.201465	−	0.677799i
$23$			5.84039i			1.21781i	0.793245	+	0.608903i	$0.208390\pi$
$23$			5.84039i			1.21781i	−0.793245	+	0.608903i	$0.791610\pi$
$24$	−1.91891	−	1.39417i	−0.391696	−	0.284583i
$25$	−4.56921	+	2.03034i	−0.913843	+	0.406068i
$26$	0.773484	−	0.251320i	0.151693	−	0.0492880i
$27$	−0.717833	+	0.521536i	−0.138147	+	0.100370i
$28$	−0.544270	−	2.58916i	−0.102857	−	0.489306i
$29$	8.07009	−	2.62213i	1.49858	−	0.486918i	0.558975	−	0.829184i	$-0.311195\pi$
$29$	8.07009	−	2.62213i	1.49858	−	0.486918i	0.939603	+	0.342267i	$0.111195\pi$
$30$	−3.94014	−	3.55033i	−0.719368	−	0.648199i
$31$	2.72989	−	3.75737i	0.490303	−	0.674844i	−0.490141	−	0.871643i	$-0.663055\pi$
$31$	2.72989	−	3.75737i	0.490303	−	0.674844i	0.980444	+	0.196799i	$0.0630548\pi$
$32$	−1.00000			−0.176777
$33$	6.47898	−	4.46183i	1.12785	−	0.776705i
$34$			0.636500i			0.109159i
$35$	−0.603032	−	5.88527i	−0.101931	−	0.994791i
$36$	0.811453	−	2.49739i	0.135242	−	0.416232i
$37$	−3.85636	+	1.25301i	−0.633982	+	0.205993i	−0.608338	−	0.793678i	$-0.708164\pi$
$37$	−3.85636	+	1.25301i	−0.633982	+	0.205993i	−0.0256440	+	0.999671i	$0.508164\pi$
$38$	−0.605217	+	0.439716i	−0.0981792	+	0.0713314i
$39$	1.13386	+	1.56063i	0.181563	+	0.249900i
$40$	−2.22373	−	0.234546i	−0.351603	−	0.0370850i
$41$	−0.693842	+	2.13543i	−0.108360	+	0.333498i	−0.990504	−	0.137481i	$-0.956099\pi$
$41$	−0.693842	+	2.13543i	−0.108360	+	0.333498i	0.882144	+	0.470979i	$0.156099\pi$
$42$	5.44174	−	3.12552i	0.839679	−	0.482278i
$43$	1.78702			0.272519			0.136259	−	0.990673i	$-0.456492\pi$
$43$	1.78702			0.272519			0.136259	+	0.990673i	$0.456492\pi$
$44$	1.10418	−	3.12743i	0.166461	−	0.471477i
$45$	2.39021	−	5.36321i	0.356311	−	0.799501i
$46$	−3.43289	+	4.72497i	−0.506153	+	0.696659i
$47$	−1.40295	+	4.31784i	−0.204642	+	0.629822i	0.795086	+	0.606496i	$0.207426\pi$
$47$	−1.40295	+	4.31784i	−0.204642	+	0.629822i	−0.999728	+	0.0233258i	$0.992574\pi$
$48$	−0.732958	−	2.25581i	−0.105793	−	0.325598i
$49$	6.84043	+	1.48612i	0.977204	+	0.212303i
$50$	−4.88998	−	1.04314i	−0.691547	−	0.147522i
$51$	−1.43582	+	0.466527i	−0.201056	+	0.0653269i
$52$	0.773484	+	0.251320i	0.107263	+	0.0348518i
$53$	1.23908	−	1.70545i	0.170201	−	0.234262i	−0.715392	−	0.698723i	$-0.753752\pi$
$53$	1.23908	−	1.70545i	0.170201	−	0.234262i	0.885594	+	0.464461i	$0.153752\pi$
$54$	−0.887291			−0.120745
$55$	3.18893	−	6.69558i	0.429995	−	0.902831i
$56$	1.08155	−	2.41459i	0.144528	−	0.322663i
$57$	−1.43552	−	1.04296i	−0.190139	−	0.138144i
$58$	8.07009	+	2.62213i	1.05965	+	0.344303i
$59$	−11.4455	+	3.71887i	−1.49008	+	0.484155i	−0.937106	−	0.349046i	$-0.886506\pi$
$59$	−11.4455	+	3.71887i	−1.49008	+	0.484155i	−0.552970	+	0.833201i	$0.686506\pi$
$60$	−1.10081	−	5.18824i	−0.142114	−	0.669798i
$61$	−9.48273	+	6.88961i	−1.21414	+	0.882124i	−0.995600	−	0.0937040i	$-0.970129\pi$
$61$	−9.48273	+	6.88961i	−1.21414	+	0.882124i	−0.218540	+	0.975828i	$0.570129\pi$
$62$	4.41705	−	1.43519i	0.560966	−	0.182269i
$63$	5.15256	+	4.66038i	0.649162	+	0.587153i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.66108	+	0.740287i	0.206031	+	0.0918213i
$66$	7.86420	+	0.198551i	0.968016	+	0.0244400i
$67$			7.11959i			0.869796i	0.900480	+	0.434898i	$0.143216\pi$
$67$			7.11959i			0.869796i	−0.900480	+	0.434898i	$0.856784\pi$
$68$	−0.374125	+	0.514939i	−0.0453693	+	0.0624455i
$69$	−13.1748	−	4.28076i	−1.58606	−	0.515343i
$70$	2.97141	−	5.11573i	0.355151	−	0.611447i
$71$	6.16231	−	4.47718i	0.731331	−	0.531343i	−0.158653	−	0.987334i	$-0.550715\pi$
$71$	6.16231	−	4.47718i	0.731331	−	0.531343i	0.889984	+	0.455991i	$0.150715\pi$
$72$	2.12441	−	1.54347i	0.250364	−	0.181900i
$73$	9.50651	−	3.08885i	1.11265	−	0.361523i	0.305693	−	0.952130i	$-0.401112\pi$
$73$	9.50651	−	3.08885i	1.11265	−	0.361523i	0.806959	+	0.590607i	$0.201112\pi$
$74$	−3.85636	−	1.25301i	−0.448293	−	0.145659i
$75$	−1.23103	−	11.7954i	−0.142147	−	1.36202i
$76$	−0.748090			−0.0858118
$77$	6.35723	+	6.04861i	0.724474	+	0.689303i
$78$			1.92904i			0.218421i
$79$	−9.15919	+	12.6065i	−1.03049	+	1.41835i	−0.125910	+	0.992042i	$0.540185\pi$
$79$	−9.15919	+	12.6065i	−1.03049	+	1.41835i	−0.904580	+	0.426305i	$0.859815\pi$
$80$	−1.66117	−	1.49683i	−0.185725	−	0.167351i
$81$	−3.08470	−	9.49374i	−0.342745	−	1.05486i
$82$	−1.81650	+	1.31977i	−0.200599	+	0.145744i
$83$	−4.36182	−	6.00353i	−0.478772	−	0.658973i	0.499496	−	0.866316i	$-0.333518\pi$
$83$	−4.36182	−	6.00353i	−0.478772	−	0.658973i	−0.978268	+	0.207343i	$0.933518\pi$
$84$	6.23959	+	0.669978i	0.680796	+	0.0731005i
$85$	−0.952731	+	1.05734i	−0.103338	+	0.114684i
$86$	1.44573	+	1.05039i	0.155897	+	0.113266i
$87$			20.1265i			2.15779i
$88$	2.73155	−	1.88112i	0.291185	−	0.200528i
$89$			10.1872i			1.07984i	0.841717	+	0.539919i	$0.181545\pi$
$89$			10.1872i			1.07984i	−0.841717	+	0.539919i	$0.818455\pi$
$90$	5.08614	−	2.93400i	0.536126	−	0.309271i
$91$	−1.44340	+	1.59583i	−0.151309	+	0.167289i
$92$	−5.55454	+	1.80478i	−0.579101	+	0.188161i
$93$	6.47503	+	8.91211i	0.671429	+	0.924143i
$94$	−3.67298	+	2.66857i	−0.378839	+	0.275242i
$95$	−1.66355	−	0.175462i	−0.170677	−	0.0180020i
$96$	0.732958	−	2.25581i	0.0748072	−	0.230233i
$97$	−9.78252	−	7.10742i	−0.993264	−	0.721649i	−0.0326308	−	0.999467i	$-0.510389\pi$
$97$	−9.78252	−	7.10742i	−0.993264	−	0.721649i	−0.960634	+	0.277819i	$0.910389\pi$
$98$	4.66050	+	5.22300i	0.470782	+	0.527602i
$99$	2.48137	+	8.34821i	0.249387	+	0.839026i
$100$	−3.34293	−	3.71817i	−0.334293	−	0.371817i
$101$	1.69439	+	1.23104i	0.168598	+	0.122493i	0.668884	−	0.743366i	$-0.266772\pi$
$101$	1.69439	+	1.23104i	0.168598	+	0.122493i	−0.500287	+	0.865860i	$0.666772\pi$
$102$	−1.43582	−	0.466527i	−0.142168	−	0.0461931i
$103$	−3.03083	−	9.32794i	−0.298637	−	0.919110i	−0.981976	−	0.189008i	$-0.939473\pi$
$103$	−3.03083	−	9.32794i	−0.298637	−	0.919110i	0.683339	−	0.730101i	$-0.260527\pi$
$104$	0.478040	+	0.657965i	0.0468756	+	0.0645188i
$105$	13.7181	+	2.95333i	1.33874	+	0.288215i
$106$	2.00488	−	0.651425i	0.194731	−	0.0632720i
$107$	−0.172623	+	0.531279i	−0.0166881	+	0.0513607i	−0.959054	−	0.283224i	$-0.908596\pi$
$107$	−0.172623	+	0.531279i	−0.0166881	+	0.0513607i	0.942366	+	0.334585i	$0.108596\pi$
$108$	−0.717833	−	0.521536i	−0.0690735	−	0.0501849i
$109$			2.34499i			0.224609i	0.993674	+	0.112305i	$0.0358232\pi$
$109$			2.34499i			0.224609i	−0.993674	+	0.112305i	$0.964177\pi$
$110$	6.51546	−	3.54243i	0.621224	−	0.337758i
$111$		−	9.61764i		−	0.912866i
$112$	2.29425	−	1.31773i	0.216787	−	0.124514i
$113$	8.21206	+	2.66826i	0.772526	+	0.251009i	0.668646	−	0.743581i	$-0.266874\pi$
$113$	8.21206	+	2.66826i	0.772526	+	0.251009i	0.103880	+	0.994590i	$0.466874\pi$
$114$	−0.548318	−	1.68755i	−0.0513547	−	0.158054i
$115$	−12.7751	+	2.71055i	−1.19129	+	0.252760i
$116$	4.98759	+	6.86483i	0.463086	+	0.637383i
$117$	−2.03110	+	0.659946i	−0.187776	+	0.0610120i
$118$	−11.4455	−	3.71887i	−1.05364	−	0.342349i
$119$	−0.838733	−	1.46029i	−0.0768865	−	0.133865i
$120$	2.15899	−	4.84441i	0.197088	−	0.442232i
$121$	2.86693	+	10.6198i	0.260630	+	0.965439i
$122$	−11.7213			−1.06120
$123$	−4.30856	−	3.13036i	−0.388490	−	0.282255i
$124$	4.41705	+	1.43519i	0.396663	+	0.128884i
$125$	−6.56171	−	9.05229i	−0.586897	−	0.809662i
$126$	1.42921	+	6.79893i	0.127324	+	0.605697i
$127$	3.94559	−	2.86664i	0.350115	−	0.254373i	−0.398802	−	0.917037i	$-0.630574\pi$
$127$	3.94559	−	2.86664i	0.350115	−	0.254373i	0.748917	+	0.662664i	$0.230574\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−1.30981	+	4.03119i	−0.115323	+	0.354927i
$130$	0.908709	+	1.57526i	0.0796990	+	0.138160i
$131$	12.5690			1.09816			0.549081	−	0.835769i	$-0.314978\pi$
$131$	12.5690			1.09816			0.549081	+	0.835769i	$0.314978\pi$
$132$	6.24557	+	4.78309i	0.543607	+	0.416315i
$133$	0.809096	−	1.80633i	0.0701575	−	0.156629i
$134$	−4.18479	+	5.75987i	−0.361511	+	0.497577i
$135$	−1.47395	−	1.32812i	−0.126857	−	0.114307i
$136$	−0.605347	+	0.196689i	−0.0519081	+	0.0168660i
$137$	12.0558	+	16.5933i	1.02999	+	1.41766i	0.904953	+	0.425511i	$0.139906\pi$
$137$	12.0558	+	16.5933i	1.02999	+	1.41766i	0.125039	+	0.992152i	$0.460094\pi$
$138$	−8.14249	−	11.2072i	−0.693135	−	0.954018i
$139$	1.58657	+	4.88296i	0.134571	+	0.414168i	0.995523	−	0.0945189i	$-0.0301313\pi$
$139$	1.58657	+	4.88296i	0.134571	+	0.414168i	−0.860952	+	0.508686i	$0.830131\pi$
$140$	5.41087	−	2.39216i	0.457302	−	0.202175i
$141$	−8.71194	−	6.32959i	−0.733678	−	0.533048i
$142$	7.61703			0.639207
$143$	−2.58558	+	0.768521i	−0.216217	+	0.0642670i
$144$	2.62592			0.218826
$145$	9.48095	+	16.4354i	0.787350	+	1.36488i
$146$	9.50651	+	3.08885i	0.786764	+	0.255635i
$147$	−8.36615	+	14.3415i	−0.690028	+	1.18286i
$148$	−2.38336	−	3.28042i	−0.195911	−	0.269649i
$149$	6.72048	+	9.24994i	0.550563	+	0.757785i	0.990088	−	0.140445i	$-0.0448534\pi$
$149$	6.72048	+	9.24994i	0.550563	+	0.757785i	−0.439526	+	0.898230i	$0.644853\pi$
$150$	5.93727	−	10.2663i	0.484776	−	0.838239i
$151$	1.93498	+	0.628714i	0.157467	+	0.0511640i	0.386690	−	0.922210i	$-0.373618\pi$
$151$	1.93498	+	0.628714i	0.157467	+	0.0511640i	−0.229223	+	0.973374i	$0.573618\pi$
$152$	−0.605217	−	0.439716i	−0.0490896	−	0.0356657i
$153$		−	1.67139i		−	0.135124i
$154$	1.58783	+	8.63011i	0.127951	+	0.695434i
$155$	9.48573	+	4.22748i	0.761912	+	0.339559i
$156$	−1.13386	+	1.56063i	−0.0907817	+	0.124950i
$157$	−1.25232	+	3.85425i	−0.0999461	+	0.307602i	−0.988511	−	0.151148i	$-0.951703\pi$
$157$	−1.25232	+	3.85425i	−0.0999461	+	0.307602i	0.888565	+	0.458751i	$0.151703\pi$
$158$	−14.8199	+	4.81527i	−1.17901	+	0.383082i
$159$	2.93899	+	4.04517i	0.233077	+	0.320803i
$160$	−0.464104	−	2.18737i	−0.0366907	−	0.172927i
$161$	1.64970	−	15.3639i	0.130015	−	1.21085i
$162$	3.08470	−	9.49374i	0.242357	−	0.745899i
$163$	−9.76479	+	13.4401i	−0.764837	+	1.05271i	0.231959	+	0.972726i	$0.425487\pi$
$163$	−9.76479	+	13.4401i	−0.764837	+	1.05271i	−0.996796	+	0.0799827i	$0.974513\pi$
$164$	−2.24532			−0.175330
$165$	12.7666	+	12.1012i	0.993880	+	0.942077i
$166$		−	7.42077i		−	0.575964i
$167$	1.66365	−	2.28982i	0.128737	−	0.177192i	−0.739783	−	0.672846i	$-0.765072\pi$
$167$	1.66365	−	2.28982i	0.128737	−	0.177192i	0.868520	+	0.495654i	$0.165072\pi$
$168$	4.65414	+	4.20956i	0.359074	+	0.324775i
$169$	3.81282	+	11.7347i	0.293294	+	0.902667i
$170$	−1.39226	+	0.295402i	−0.106782	+	0.0226563i
$171$	1.58925	−	1.15466i	0.121533	−	0.0882989i
$172$	0.552221	+	1.69956i	0.0421065	+	0.129590i
$173$	19.9440	+	6.48021i	1.51632	+	0.492681i	0.944727	−	0.327859i	$-0.106327\pi$
$173$	19.9440	+	6.48021i	1.51632	+	0.492681i	0.571589	+	0.820540i	$0.306327\pi$
$174$	−11.8301	+	16.2827i	−0.896835	+	1.23439i
$175$	12.5934	−	4.05043i	0.951972	−	0.306184i
$176$	3.31557	+	0.0837098i	0.249920	+	0.00630987i
$177$		−	28.5447i		−	2.14555i
$178$	−5.98787	+	8.24159i	−0.448809	+	0.617733i
$179$	0.393228	−	1.21023i	0.0293912	−	0.0904570i	−0.935285	−	0.353896i	$-0.884857\pi$
$179$	0.393228	−	1.21023i	0.0293912	−	0.0904570i	0.964676	+	0.263439i	$0.0848567\pi$
$180$	5.83934	+	0.615899i	0.435238	+	0.0459064i
$181$	3.21681	+	4.42756i	0.239103	+	0.329098i	0.911658	−	0.410950i	$-0.134803\pi$
$181$	3.21681	+	4.42756i	0.239103	+	0.329098i	−0.672554	+	0.740048i	$0.734803\pi$
$182$	−2.10574	+	0.442649i	−0.156088	+	0.0328113i
$183$	−8.59122	−	26.4411i	−0.635081	−	1.95458i
$184$	−5.55454	−	1.80478i	−0.409486	−	0.133050i
$185$	−4.53056	−	7.85379i	−0.333093	−	0.577422i
$186$			11.0160i			0.807731i
$187$	0.0532813	−	2.11036i	0.00389631	−	0.154325i
$188$	−4.54005			−0.331117
$189$	2.03567	−	1.16921i	0.148073	−	0.0850473i
$190$	−1.24271	−	1.11976i	−0.0901555	−	0.0812361i
$191$	−2.75958	−	8.49313i	−0.199676	−	0.614541i	−0.999890	−	0.0148259i	$-0.995281\pi$
$191$	−2.75958	−	8.49313i	−0.199676	−	0.614541i	0.800214	−	0.599715i	$-0.204719\pi$
$192$	1.91891	−	1.39417i	0.138485	−	0.100615i
$193$	17.0889	−	12.4158i	1.23008	−	0.893709i	0.233188	−	0.972432i	$-0.425084\pi$
$193$	17.0889	−	12.4158i	1.23008	−	0.893709i	0.996897	+	0.0787231i	$0.0250843\pi$
$194$	−3.73659	−	11.5000i	−0.268272	−	0.825655i
$195$	−2.88745	+	3.20448i	−0.206774	+	0.229477i
$196$	0.700426	+	6.96487i	0.0500304	+	0.497491i
$197$	13.6474			0.972338			0.486169	−	0.873865i	$-0.338394\pi$
$197$	13.6474			0.972338			0.486169	+	0.873865i	$0.338394\pi$
$198$	−2.89948	+	8.21235i	−0.206057	+	0.583627i
$199$			5.76658i			0.408782i	0.978889	+	0.204391i	$0.0655214\pi$
$199$			5.76658i			0.408782i	−0.978889	+	0.204391i	$0.934479\pi$
$200$	−0.519004	−	4.97299i	−0.0366991	−	0.351644i
$201$	−16.0605	−	5.21836i	−1.13282	−	0.368075i
$202$	0.647198	+	1.99187i	0.0455367	+	0.140147i
$203$	−21.9701	+	4.61834i	−1.54200	+	0.324144i
$204$	−0.887388	−	1.22138i	−0.0621296	−	0.0855140i
$205$	−4.99299	−	0.526632i	−0.348726	−	0.0367816i
$206$	3.03083	−	9.32794i	0.211168	−	0.649909i
$207$	9.01449	−	12.4074i	0.626551	−	0.862373i
$208$			0.813289i			0.0563915i
$209$	2.04345	−	1.40725i	0.141348	−	0.0973413i
$210$	9.36222	+	10.4526i	0.646054	+	0.721295i
$211$	−12.6807	+	17.4535i	−0.872974	+	1.20155i	0.105343	+	0.994436i	$0.466406\pi$
$211$	−12.6807	+	17.4535i	−0.872974	+	1.20155i	−0.978318	+	0.207110i	$0.933594\pi$
$212$	2.00488	+	0.651425i	0.137696	+	0.0447401i
$213$	5.58296	+	17.1826i	0.382538	+	1.17733i
$214$	−0.451933	+	0.328349i	−0.0308935	+	0.0224455i
$215$	0.829366	+	3.90889i	0.0565623	+	0.266584i
$216$	−0.274188	−	0.843864i	−0.0186561	−	0.0574177i
$217$	−8.24265	+	9.11316i	−0.559548	+	0.618641i
$218$	−1.37835	+	1.89714i	−0.0933537	+	0.128490i
$219$			23.7089i			1.60210i
$220$	7.35330	+	0.963803i	0.495760	+	0.0649796i
$221$	0.517658			0.0348215
$222$	5.65311	−	7.78083i	0.379412	−	0.522215i
$223$	4.89906	−	15.0778i	0.328065	−	1.00968i	−0.641972	−	0.766728i	$-0.721884\pi$
$223$	4.89906	−	15.0778i	0.328065	−	1.00968i	0.970038	−	0.242954i	$-0.0781163\pi$
$224$	2.63063	+	0.282464i	0.175766	+	0.0188729i
$225$	12.8407	+	2.73919i	0.856044	+	0.182613i
$226$	5.07533	+	6.98560i	0.337606	+	0.464675i
$227$	14.1957	−	4.61246i	0.942201	−	0.306140i	0.202658	−	0.979250i	$-0.435042\pi$
$227$	14.1957	−	4.61246i	0.942201	−	0.306140i	0.739542	+	0.673110i	$0.235042\pi$
$228$	0.548318	−	1.68755i	0.0363133	−	0.111761i
$229$	−12.7501	+	17.5490i	−0.842548	+	1.15967i	0.142907	+	0.989736i	$0.454355\pi$
$229$	−12.7501	+	17.5490i	−0.842548	+	1.15967i	−0.985456	+	0.169932i	$0.945645\pi$
$230$	−11.9285	−	5.31615i	−0.786543	−	0.350536i
$231$	−18.3041	+	9.90734i	−1.20432	+	0.651855i
$232$			8.48540i			0.557094i
$233$	−20.8110	−	15.1201i	−1.36338	−	0.990550i	−0.998222	−	0.0596025i	$-0.981017\pi$
$233$	−20.8110	−	15.1201i	−1.36338	−	0.990550i	−0.365153	−	0.930948i	$-0.618983\pi$
$234$	−2.03110	−	0.659946i	−0.132777	−	0.0431420i
$235$	−10.0959	−	1.06485i	−0.658581	−	0.0694633i
$236$	−7.07370	−	9.73612i	−0.460459	−	0.633767i
$237$	−21.7247	−	29.9015i	−1.41117	−	1.94231i
$238$	0.179788	−	1.67439i	0.0116540	−	0.108535i
$239$	−7.45527	−	2.42237i	−0.482242	−	0.156690i	0.0577999	−	0.998328i	$-0.481591\pi$
$239$	−7.45527	−	2.42237i	−0.482242	−	0.156690i	−0.540041	+	0.841638i	$0.681591\pi$
$240$	4.59414	−	2.65019i	0.296550	−	0.171069i
$241$	30.5782			1.96971			0.984856	−	0.173373i	$-0.0554665\pi$
$241$	30.5782			1.96971			0.984856	+	0.173373i	$0.0554665\pi$
$242$	−3.92278	+	10.2768i	−0.252166	+	0.660615i
$243$	21.0152			1.34813
$244$	−9.48273	−	6.88961i	−0.607070	−	0.441062i
$245$	−0.0760244	+	15.6523i	−0.00485702	+	0.999988i
$246$	−1.64573	−	5.06502i	−0.104928	−	0.322934i
$247$	0.357616	+	0.492217i	0.0227546	+	0.0313190i
$248$	2.72989	+	3.75737i	0.173348	+	0.238593i
$249$	16.7399	−	5.43911i	1.06085	−	0.344690i
$250$	0.0122717	−	11.1803i	0.000776128	−	0.707106i
$251$	2.29582	−	3.15992i	0.144911	−	0.199452i	−0.730392	−	0.683029i	$-0.760662\pi$
$251$	2.29582	−	3.15992i	0.144911	−	0.199452i	0.875302	+	0.483576i	$0.160662\pi$
$252$	−2.84006	+	6.34051i	−0.178907	+	0.399415i
$253$	11.7775	−	15.3786i	0.740447	−	0.966845i
$254$	4.87702			0.306012
$255$	−1.68684	−	2.92417i	−0.105634	−	0.183118i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.06728	−	18.6732i	−0.378466	−	1.16480i	−0.941110	−	0.338100i	$-0.890216\pi$
$257$	−6.06728	−	18.6732i	−0.378466	−	1.16480i	0.562644	−	0.826699i	$-0.309784\pi$
$258$	−3.42914	+	2.49141i	−0.213489	+	0.155109i
$259$	10.4986	−	2.20692i	0.652351	−	0.137131i
$260$	−0.190754	+	1.80854i	−0.0118301	+	0.112161i
$261$	−21.1914	−	6.88550i	−1.31171	−	0.426202i
$262$	10.1686	+	7.38790i	0.628216	+	0.456426i
$263$	−19.3898			−1.19563			−0.597814	−	0.801634i	$-0.703964\pi$
$263$	−19.3898			−1.19563			−0.597814	+	0.801634i	$0.703964\pi$
$264$	2.24134	+	7.54065i	0.137945	+	0.464095i
$265$	4.30553	+	1.91883i	0.264487	+	0.117873i
$266$	1.71631	−	0.985778i	0.105234	−	0.0604419i
$267$	−22.9803	−	7.46676i	−1.40637	−	0.456958i
$268$	−6.77113	+	2.20007i	−0.413613	+	0.134391i
$269$	−17.4834	−	24.0639i	−1.06598	−	1.46720i	−0.874076	−	0.485789i	$-0.838532\pi$
$269$	−17.4834	−	24.0639i	−1.06598	−	1.46720i	−0.191909	−	0.981413i	$-0.561468\pi$
$270$	−0.411796	−	1.94084i	−0.0250611	−	0.118116i
$271$	−0.613137	−	1.88704i	−0.0372454	−	0.114630i	0.930705	−	0.365770i	$-0.119194\pi$
$271$	−0.613137	−	1.88704i	−0.0372454	−	0.114630i	−0.967951	+	0.251141i	$0.919194\pi$
$272$	−0.605347	−	0.196689i	−0.0367046	−	0.0119260i
$273$	−2.54195	−	4.42571i	−0.153846	−	0.267856i
$274$			20.5105i			1.23908i
$275$	16.1257	+	3.86793i	0.972418	+	0.233245i
$276$		−	13.8528i		−	0.833842i
$277$	17.8717	+	12.9845i	1.07380	+	0.780165i	0.976592	−	0.215099i	$-0.0690073\pi$
$277$	17.8717	+	12.9845i	1.07380	+	0.780165i	0.0972125	+	0.995264i	$0.469007\pi$
$278$	−1.58657	+	4.88296i	−0.0951562	+	0.292861i
$279$	−11.5988	+	3.76868i	−0.694403	+	0.225625i
$280$	5.78357	+	1.24513i	0.345634	+	0.0744107i
$281$	−14.5120	−	19.9741i	−0.865716	−	1.19156i	−0.980176	−	0.198128i	$-0.936514\pi$
$281$	−14.5120	−	19.9741i	−0.865716	−	1.19156i	0.114460	−	0.993428i	$-0.463486\pi$
$282$	−3.32766	−	10.2415i	−0.198160	−	0.609872i
$283$	19.4605	+	6.32311i	1.15681	+	0.375870i	0.823704	−	0.567020i	$-0.191904\pi$
$283$	19.4605	+	6.32311i	1.15681	+	0.375870i	0.333105	+	0.942890i	$0.391904\pi$
$284$	6.16231	+	4.47718i	0.365666	+	0.265672i
$285$	1.61512	−	3.62405i	0.0956716	−	0.214670i
$286$	−2.54350	−	0.898018i	−0.150400	−	0.0531009i
$287$	2.42842	−	5.42153i	0.143345	−	0.320023i
$288$	2.12441	+	1.54347i	0.125182	+	0.0909501i
$289$	5.12810	−	15.7827i	0.301653	−	0.928392i
$290$	−1.99022	+	18.8693i	−0.116870	+	1.10804i
$291$	23.2032	−	16.8581i	1.36019	−	0.988239i
$292$	5.87534	+	8.08672i	0.343829	+	0.473239i
$293$	−13.3177	+	4.32720i	−0.778031	+	0.252798i	−0.670999	−	0.741458i	$-0.734135\pi$
$293$	−13.3177	+	4.32720i	−0.778031	+	0.252798i	−0.107032	+	0.994256i	$0.534135\pi$
$294$	−15.1981	+	6.68498i	−0.886369	+	0.389876i
$295$	−13.4465	−	23.3096i	−0.782883	−	1.35714i
$296$		−	4.05482i		−	0.235682i
$297$	2.94187	+	0.0742750i	0.170705	+	0.00430987i
$298$			11.4336i			0.662328i
$299$	3.84277	+	2.79194i	0.222233	+	0.161462i
$300$	10.8377	−	4.81577i	0.625716	−	0.278038i
$301$	−4.70100	−	0.504771i	−0.270961	−	0.0290945i
$302$	1.19589	+	1.64599i	0.0688155	+	0.0947164i
$303$	−4.01892	+	2.91991i	−0.230881	+	0.167745i
$304$	−0.231172	−	0.711476i	−0.0132586	−	0.0408059i
$305$	−19.4711	−	17.5448i	−1.11491	−	1.00461i
$306$	0.982421	−	1.35219i	0.0561613	−	0.0772993i
$307$		−	19.9751i		−	1.14004i	−0.821630	−	0.570021i	$-0.806935\pi$
$307$		−	19.9751i		−	1.14004i	0.821630	−	0.570021i	$-0.193065\pi$
$308$	−3.78807	+	7.91521i	−0.215846	+	0.451011i
$309$	23.2636			1.32342
$310$	5.18927	+	8.99567i	0.294731	+	0.510920i
$311$	29.0709	+	9.44572i	1.64846	+	0.535618i	0.978406	−	0.206693i	$-0.0662700\pi$
$311$	29.0709	+	9.44572i	1.64846	+	0.535618i	0.670056	+	0.742310i	$0.266270\pi$
$312$	−1.83463	+	0.596107i	−0.103865	+	0.0337479i
$313$	8.35933	−	6.07341i	0.472497	−	0.343289i	−0.325917	−	0.945399i	$-0.605673\pi$
$313$	8.35933	−	6.07341i	0.472497	−	0.343289i	0.798414	+	0.602109i	$0.205673\pi$
$314$	−3.27862	+	2.38206i	−0.185023	+	0.134427i
$315$	−7.80267	+	13.4335i	−0.439631	+	0.756891i
$316$	−14.8199	−	4.81527i	−0.833683	−	0.270880i
$317$	−1.53946	+	2.11889i	−0.0864649	+	0.119009i	−0.850058	−	0.526689i	$-0.823433\pi$
$317$	−1.53946	+	2.11889i	−0.0864649	+	0.119009i	0.763593	+	0.645698i	$0.223433\pi$
$318$			5.00010i			0.280392i
$319$	−26.5374	−	9.36940i	−1.48581	−	0.524586i
$320$	0.910238	−	2.04242i	0.0508839	−	0.114175i
$321$	−1.07194	−	0.778811i	−0.0598299	−	0.0434690i
$322$	10.3653	−	11.4600i	0.577636	−	0.638640i
$323$	−0.452854	+	0.147141i	−0.0251975	+	0.00818715i
$324$	8.07586	−	5.86746i	0.448659	−	0.325970i
$325$	−0.848372	+	3.97697i	−0.0470592	+	0.220602i
$326$	−15.7998	+	5.13365i	−0.875068	+	0.284327i
$327$	−5.28986	−	1.71878i	−0.292530	−	0.0950487i
$328$	−1.81650	−	1.31977i	−0.100300	−	0.0728719i
$329$	4.91028	−	10.9624i	0.270713	−	0.604375i
$330$	3.21550	+	17.2941i	0.177008	+	0.952009i
$331$	9.65619			0.530752			0.265376	−	0.964145i	$-0.414504\pi$
$331$	9.65619			0.530752			0.265376	+	0.964145i	$0.414504\pi$
$332$	4.36182	−	6.00353i	0.239386	−	0.329487i
$333$	10.1265	+	3.29030i	0.554928	+	0.180307i
$334$	2.69185	−	0.874634i	0.147291	−	0.0478578i
$335$	−15.5732	+	3.30423i	−0.850855	+	0.180530i
$336$	1.29095	+	6.14124i	0.0704273	+	0.335032i
$337$	6.71481	+	20.6661i	0.365779	+	1.12575i	0.949492	+	0.313792i	$0.101599\pi$
$337$	6.71481	+	20.6661i	0.365779	+	1.12575i	−0.583713	+	0.811960i	$0.698401\pi$
$338$	−3.81282	+	11.7347i	−0.207390	+	0.638282i
$339$	−12.0382	+	16.5691i	−0.653825	+	0.899913i
$340$	−1.30000	−	0.579366i	−0.0705023	−	0.0314205i
$341$	−14.7652	+	4.38871i	−0.799580	+	0.237662i
$342$	1.96442			0.106224
$343$	−17.5749	−	5.84160i	−0.948953	−	0.315417i
$344$	−0.552221	+	1.69956i	−0.0297738	+	0.0916342i
$345$	3.24913	−	30.8050i	0.174927	−	1.65848i
$346$	12.3261	+	16.9654i	0.662654	+	0.912066i
$347$	5.89044	−	4.27966i	0.316216	−	0.229744i	−0.418343	−	0.908289i	$-0.637389\pi$
$347$	5.89044	−	4.27966i	0.316216	−	0.229744i	0.734559	+	0.678545i	$0.237389\pi$
$348$	−19.1415	+	6.21944i	−1.02609	+	0.333397i
$349$	−3.04276	+	9.36466i	−0.162875	+	0.501279i	−0.998873	−	0.0474536i	$-0.984889\pi$
$349$	−3.04276	+	9.36466i	−0.162875	+	0.501279i	0.835998	+	0.548732i	$0.184889\pi$
$350$	12.5691	+	4.12535i	0.671845	+	0.220509i
$351$			0.721624i			0.0385175i
$352$	2.63315	+	2.01656i	0.140347	+	0.107483i
$353$	−7.84044			−0.417305			−0.208652	−	0.977990i	$-0.566908\pi$
$353$	−7.84044			−0.417305			−0.208652	+	0.977990i	$0.566908\pi$
$354$	16.7781	−	23.0931i	0.891747	−	1.22738i
$355$	12.6532	+	11.4014i	0.671563	+	0.605123i
$356$	−9.68857	+	3.14801i	−0.513493	+	0.166844i
$357$	3.90890	−	0.821692i	0.206881	−	0.0434885i
$358$	1.02948	−	0.747964i	0.0544099	−	0.0395311i
$359$	32.5863	−	10.5879i	1.71984	−	0.558809i	0.727917	−	0.685665i	$-0.240488\pi$
$359$	32.5863	−	10.5879i	1.71984	−	0.558809i	0.991921	+	0.126855i	$0.0404884\pi$
$360$	4.36211	+	3.93055i	0.229903	+	0.207158i
$361$	14.9186	+	10.8390i	0.785188	+	0.570472i
$362$			5.47276i			0.287642i
$363$	−26.0577	−	1.31662i	−1.36767	−	0.0691047i
$364$	−1.96376	−	0.879612i	−0.102929	−	0.0461042i
$365$	11.1685	+	19.3607i	0.584585	+	1.01339i
$366$	8.59122	−	26.4411i	0.449070	−	1.38210i
$367$	8.93956	+	27.5131i	0.466641	+	1.43617i	0.856907	+	0.515472i	$0.172383\pi$
$367$	8.93956	+	27.5131i	0.466641	+	1.43617i	−0.390266	+	0.920702i	$0.627617\pi$
$368$	−3.43289	−	4.72497i	−0.178952	−	0.246306i
$369$	4.76998	−	3.46559i	0.248315	−	0.180412i
$370$	0.951044	−	9.01684i	0.0494424	−	0.468763i
$371$	−3.74130	+	4.13642i	−0.194239	+	0.214752i
$372$	−6.47503	+	8.91211i	−0.335715	+	0.462072i
$373$	−25.7514			−1.33336			−0.666678	−	0.745346i	$-0.732285\pi$
$373$	−25.7514			−1.33336			−0.666678	+	0.745346i	$0.732285\pi$
$374$	1.28354	−	1.67600i	0.0663704	−	0.0866638i
$375$	25.2297	−	8.16703i	1.30286	−	0.421744i
$376$	−3.67298	−	2.66857i	−0.189419	−	0.137621i
$377$	2.13255	−	6.56332i	0.109832	−	0.338028i
$378$	2.33413	+	0.250628i	0.120055	+	0.0128909i
$379$	−9.34352	+	6.78846i	−0.479944	+	0.348700i	−0.801304	−	0.598257i	$-0.795860\pi$
$379$	−9.34352	+	6.78846i	−0.479944	+	0.348700i	0.321360	+	0.946957i	$0.395860\pi$
$380$	−0.347192	−	1.63635i	−0.0178106	−	0.0839431i
$381$	3.57465	+	11.0016i	0.183135	+	0.563631i
$382$	2.75958	−	8.49313i	0.141193	−	0.434546i
$383$	−7.03306	−	5.10982i	−0.359373	−	0.261100i	0.393418	−	0.919360i	$-0.371293\pi$
$383$	−7.03306	−	5.10982i	−0.359373	−	0.261100i	−0.752790	+	0.658260i	$0.771293\pi$
$384$	2.37190			0.121041
$385$	−10.2801	+	16.7128i	−0.523925	+	0.851764i
$386$	21.1230			1.07513
$387$	−3.79637	−	2.75823i	−0.192981	−	0.140209i
$388$	3.73659	−	11.5000i	0.189697	−	0.583826i
$389$	−8.02071	−	24.6852i	−0.406666	−	1.25159i	−0.919496	−	0.393100i	$-0.871403\pi$
$389$	−8.02071	−	24.6852i	−0.406666	−	1.25159i	0.512830	−	0.858490i	$-0.328597\pi$
$390$	−4.21954	+	0.895277i	−0.213665	+	0.0453341i
$391$	−3.00744	+	2.18504i	−0.152093	+	0.110502i
$392$	−3.52719	+	6.04640i	−0.178150	+	0.305389i
$393$	−9.21258	+	28.3534i	−0.464713	+	1.43024i
$394$	11.0410	+	8.02175i	0.556237	+	0.404130i
$395$	−31.8260	−	14.1838i	−1.60134	−	0.713666i
$396$	−7.17283	+	4.93966i	−0.360448	+	0.248227i
$397$	−16.6671			−0.836496			−0.418248	−	0.908333i	$-0.637356\pi$
$397$	−16.6671			−0.836496			−0.418248	+	0.908333i	$0.637356\pi$
$398$	−3.38951	+	4.66526i	−0.169901	+	0.233848i
$399$	3.48171	+	3.14913i	0.174304	+	0.157654i
$400$	2.50317	−	4.32830i	0.125158	−	0.216415i
$401$	17.5610	−	12.7588i	0.876956	−	0.637146i	−0.0554885	−	0.998459i	$-0.517672\pi$
$401$	17.5610	−	12.7588i	0.876956	−	0.637146i	0.932444	+	0.361314i	$0.117672\pi$
$402$	−9.92591	−	13.6618i	−0.495059	−	0.681391i
$403$	−1.16722	−	3.59234i	−0.0581435	−	0.178947i
$404$	−0.647198	+	1.99187i	−0.0321993	+	0.0990992i
$405$	19.3347	−	11.1535i	0.960751	−	0.554222i
$406$	−20.4888	−	9.17737i	−1.01684	−	0.455465i
$407$	12.6812	+	4.47725i	0.628581	+	0.221929i
$408$		−	1.50971i		−	0.0747420i
$409$	0.708496	+	0.514752i	0.0350329	+	0.0254529i	0.605164	−	0.796101i	$-0.293108\pi$
$409$	0.708496	+	0.514752i	0.0350329	+	0.0254529i	−0.570131	+	0.821554i	$0.693108\pi$
$410$	−3.72987	−	3.36086i	−0.184205	−	0.165981i
$411$	−46.2678	+	15.0333i	−2.28222	+	0.741539i
$412$	7.93482	−	5.76499i	0.390921	−	0.284020i
$413$	31.1593	−	6.55002i	1.53325	−	0.322305i
$414$	14.5858	−	4.73920i	0.716851	−	0.232919i
$415$	11.1076	−	12.3272i	0.545252	−	0.605119i
$416$	−0.478040	+	0.657965i	−0.0234378	+	0.0322594i
$417$	−12.1779			−0.596356
$418$	2.48034	+	0.0626225i	0.121318	+	0.00306297i
$419$			13.9264i			0.680349i	0.940362	+	0.340174i	$0.110486\pi$
$419$			13.9264i			0.680349i	−0.940362	+	0.340174i	$0.889514\pi$
$420$	1.43033	+	13.9593i	0.0697930	+	0.681143i
$421$	−5.40865	+	16.6461i	−0.263601	+	0.811282i	0.728411	+	0.685140i	$0.240259\pi$
$421$	−5.40865	+	16.6461i	−0.263601	+	0.811282i	−0.992012	+	0.126141i	$0.959741\pi$
$422$	−20.5178	+	6.66663i	−0.998790	+	0.324526i
$423$	9.64493	−	7.00745i	0.468952	−	0.340714i
$424$	1.23908	+	1.70545i	0.0601753	+	0.0828242i
$425$	−2.75496	−	1.59327i	−0.133635	−	0.0772847i
$426$	−5.58296	+	17.1826i	−0.270495	+	0.832499i
$427$	26.8916	−	15.4455i	1.30138	−	0.747459i
$428$	−0.558620			−0.0270019
$429$	0.161480	−	6.39587i	0.00779632	−	0.308796i
$430$	−1.62662	+	3.64985i	−0.0784425	+	0.176011i
$431$	2.46504	−	3.39284i	0.118737	−	0.163427i	−0.745511	−	0.666493i	$-0.767795\pi$
$431$	2.46504	−	3.39284i	0.118737	−	0.163427i	0.864248	+	0.503066i	$0.167795\pi$
$432$	0.274188	−	0.843864i	0.0131919	−	0.0406004i
$433$	3.34165	+	10.2845i	0.160589	+	0.494243i	0.998684	−	0.0512812i	$-0.0163305\pi$
$433$	3.34165	+	10.2845i	0.160589	+	0.494243i	−0.838095	+	0.545525i	$0.816330\pi$
$434$	−12.0250	+	2.52779i	−0.577220	+	0.121338i
$435$	−44.0242	+	9.34081i	−2.11080	+	0.447857i
$436$	−2.23022	+	0.724642i	−0.106808	+	0.0347040i
$437$	−4.15530	−	1.35014i	−0.198775	−	0.0645858i
$438$	−13.9357	+	19.1809i	−0.665875	+	0.916499i
$439$	6.91580			0.330073			0.165037	−	0.986287i	$-0.447226\pi$
$439$	6.91580			0.330073			0.165037	+	0.986287i	$0.447226\pi$
$440$	5.38244	+	5.10190i	0.256598	+	0.243223i
$441$	−12.2381	−	13.7152i	−0.582766	−	0.653102i
$442$	0.418794	+	0.304272i	0.0199200	+	0.0144727i
$443$	20.7098	+	6.72901i	0.983950	+	0.319705i	0.756434	−	0.654069i	$-0.226940\pi$
$443$	20.7098	+	6.72901i	0.983950	+	0.319705i	0.227516	+	0.973774i	$0.426940\pi$
$444$	9.14692	−	2.97201i	0.434093	−	0.141046i
$445$	−22.2831	+	4.72791i	−1.05632	+	0.224124i
$446$	12.8259	−	9.31857i	0.607324	−	0.441247i
$447$	−25.7920	+	8.38032i	−1.21992	+	0.396375i
$448$	1.96220	+	1.77476i	0.0927050	+	0.0838497i
$449$	−17.2079	−	12.5023i	−0.812091	−	0.590018i	0.102345	−	0.994749i	$-0.467365\pi$
$449$	−17.2079	−	12.5023i	−0.812091	−	0.590018i	−0.914436	+	0.404730i	$0.867365\pi$
$450$	8.77826	+	9.76360i	0.413811	+	0.460261i
$451$	6.13321	−	4.22372i	0.288802	−	0.198887i
$452$			8.63467i			0.406141i
$453$	−2.83652	+	3.90414i	−0.133271	+	0.183432i
$454$	14.1957	+	4.61246i	0.666236	+	0.216473i
$455$	−4.16057	−	2.41662i	−0.195051	−	0.113293i
$456$	1.43552	−	1.04296i	0.0672242	−	0.0488412i
$457$	−6.90983	+	5.02029i	−0.323228	+	0.234839i	−0.737552	−	0.675291i	$-0.764018\pi$
$457$	−6.90983	+	5.02029i	−0.323228	+	0.234839i	0.414323	+	0.910130i	$0.364018\pi$
$458$	−20.6300	+	6.70311i	−0.963979	+	0.313216i
$459$	−0.537119	−	0.174521i	−0.0250706	−	0.00814592i
$460$	−6.52562	−	11.3123i	−0.304258	−	0.527437i
$461$	−13.2900			−0.618978			−0.309489	−	0.950903i	$-0.600158\pi$
$461$	−13.2900			−0.618978			−0.309489	+	0.950903i	$0.600158\pi$
$462$	−20.6317	−	2.74367i	−0.959874	−	0.127647i
$463$		−	22.8521i		−	1.06203i	−0.847363	−	0.531015i	$-0.821811\pi$
$463$		−	22.8521i		−	1.06203i	0.847363	−	0.531015i	$-0.178189\pi$
$464$	−4.98759	+	6.86483i	−0.231543	+	0.318692i
$465$	−16.4890	+	18.2995i	−0.764661	+	0.848617i
$466$	−7.94910	−	24.4648i	−0.368235	−	1.13331i
$467$	21.1191	−	15.3439i	0.977275	−	0.710032i	0.0201767	−	0.999796i	$-0.493577\pi$
$467$	21.1191	−	15.3439i	0.977275	−	0.710032i	0.957098	+	0.289765i	$0.0935771\pi$
$468$	−1.25529	−	1.72776i	−0.0580259	−	0.0798658i
$469$	2.01103	−	18.7290i	0.0928607	−	0.864825i
$470$	−7.54181	−	6.79568i	−0.347878	−	0.313461i
$471$	−7.77656	−	5.65000i	−0.358325	−	0.260338i
$472$		−	12.0345i		−	0.553933i
$473$	−4.70550	−	3.60365i	−0.216359	−	0.165696i
$474$		−	36.9603i		−	1.69764i
$475$	−0.388261	−	3.72024i	−0.0178146	−	0.170696i
$476$	1.12964	−	1.24894i	0.0517768	−	0.0572449i
$477$	−5.26465	+	1.71059i	−0.241052	+	0.0783225i
$478$	−4.60761	−	6.34184i	−0.210747	−	0.290069i
$479$	10.9775	−	7.97561i	0.501574	−	0.364415i	−0.308044	−	0.951372i	$-0.599674\pi$
$479$	10.9775	−	7.97561i	0.501574	−	0.364415i	0.809618	+	0.586957i	$0.199674\pi$
$480$	5.27447	+	0.556321i	0.240746	+	0.0253925i
$481$	−1.01906	+	3.13634i	−0.0464651	+	0.143005i
$482$	24.7383	+	17.9734i	1.12680	+	0.818666i
$483$	33.4489	+	14.9825i	1.52198	+	0.681728i
$484$	−9.21412	+	6.00832i	−0.418824	+	0.273106i
$485$	11.0065	−	24.6966i	0.499778	−	1.12142i
$486$	17.0016	+	12.3524i	0.771210	+	0.560317i
$487$	−25.0477	−	8.13850i	−1.13502	−	0.368791i	−0.319539	−	0.947573i	$-0.603528\pi$
$487$	−25.0477	−	8.13850i	−1.13502	−	0.368791i	−0.815482	+	0.578782i	$0.803528\pi$
$488$	−3.62208	−	11.1476i	−0.163964	−	0.504629i
$489$	−23.1611	−	31.8785i	−1.04738	−	1.44160i
$490$	−9.26169	+	12.6183i	−0.418401	+	0.570036i
$491$	28.3233	−	9.20280i	1.27821	−	0.415317i	0.410262	−	0.911967i	$-0.365437\pi$
$491$	28.3233	−	9.20280i	1.27821	−	0.415317i	0.867950	+	0.496651i	$0.165437\pi$
$492$	1.64573	−	5.06502i	0.0741950	−	0.228349i
$493$	4.36946	+	3.17460i	0.196791	+	0.142977i
$494$			0.608413i			0.0273738i
$495$	−17.1090	+	9.30213i	−0.768994	+	0.418099i
$496$			4.64437i			0.208538i
$497$	−17.4754	+	10.0372i	−0.783879	+	0.450229i
$498$	16.7399	+	5.43911i	0.750132	+	0.243733i
$499$	−4.08584	−	12.5749i	−0.182907	−	0.562931i	0.816999	−	0.576639i	$-0.195636\pi$
$499$	−4.08584	−	12.5749i	−0.182907	−	0.562931i	−0.999906	+	0.0137088i	$0.995636\pi$
$500$	6.58156	−	9.03787i	0.294336	−	0.404186i
$501$	3.94602	+	5.43123i	0.176295	+	0.242649i
$502$	3.71471	−	1.20698i	0.165796	−	0.0538703i
$503$	15.6041	+	5.07007i	0.695752	+	0.226063i	0.635479	−	0.772119i	$-0.280803\pi$
$503$	15.6041	+	5.07007i	0.695752	+	0.226063i	0.0602731	+	0.998182i	$0.480803\pi$
$504$	−6.02451	+	3.46024i	−0.268353	+	0.154131i
$505$	−1.90638	+	4.27759i	−0.0848328	+	0.190350i
$506$	18.5675	−	5.51890i	0.825428	−	0.245345i
$507$	−29.2658			−1.29974
$508$	3.94559	+	2.86664i	0.175057	+	0.127187i
$509$	−39.3139	−	12.7738i	−1.74256	−	0.566191i	−0.747389	−	0.664386i	$-0.768693\pi$
$509$	−39.3139	−	12.7738i	−1.74256	−	0.566191i	−0.995167	+	0.0981955i	$0.968693\pi$
$510$	0.354098	−	3.35720i	0.0156797	−	0.148659i
$511$	−25.8806	+	5.44038i	−1.14489	+	0.240668i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−0.205117	−	0.631286i	−0.00905615	−	0.0278720i
$514$	6.06728	−	18.6732i	0.267616	−	0.823638i
$515$	18.9971	−	10.9587i	0.837111	−	0.482898i
$516$	−4.23865			−0.186596
$517$	12.4014	−	8.54037i	0.545413	−	0.375605i
$518$	9.79074	+	4.38549i	0.430180	+	0.192687i
$519$	−29.2363	+	40.2403i	−1.28333	+	1.76635i
$520$	−1.21736	+	1.35102i	−0.0533846	+	0.0592460i
$521$	40.5006	−	13.1594i	1.77436	−	0.576526i	0.775845	−	0.630924i	$-0.217324\pi$
$521$	40.5006	−	13.1594i	1.77436	−	0.576526i	0.998519	+	0.0543984i	$0.0173241\pi$
$522$	−13.0970	−	18.0265i	−0.573240	−	0.788997i
$523$	20.4047	+	28.0847i	0.892236	+	1.22806i	0.972879	+	0.231315i	$0.0743027\pi$
$523$	20.4047	+	28.0847i	0.892236	+	1.22806i	−0.0806429	+	0.996743i	$0.525697\pi$
$524$	3.88405	+	11.9539i	0.169675	+	0.522207i
$525$	−0.0934203	+	31.3772i	−0.00407720	+	1.36941i
$526$	−15.6867	−	11.3971i	−0.683973	−	0.496936i
$527$	2.95614			0.128771
$528$	−2.61901	+	7.41794i	−0.113978	+	0.322825i
$529$	−11.1101			−0.483050
$530$	2.35539	+	4.08310i	0.102311	+	0.177358i
$531$	30.0549	+	9.76543i	1.30427	+	0.423783i
$532$	1.96795	+	0.211309i	0.0853213	+	0.00916139i
$533$	1.07335	+	1.47734i	0.0464920	+	0.0639908i
$534$	−14.2026	−	19.5482i	−0.614608	−	0.845935i
$535$	−1.24222	−	0.131022i	−0.0537060	−	0.00566459i
$536$	−6.77113	−	2.20007i	−0.292468	−	0.0950287i
$537$	2.44184	+	1.77410i	0.105373	+	0.0765580i
$538$		−	29.7446i		−	1.28238i
$539$	−15.0150	−	17.7073i	−0.646742	−	0.762709i
$540$	0.807646	−	1.81222i	0.0347555	−	0.0779854i
$541$	2.63962	−	3.63313i	0.113486	−	0.156200i	−0.748495	−	0.663140i	$-0.769223\pi$
$541$	2.63962	−	3.63313i	0.113486	−	0.156200i	0.861981	+	0.506940i	$0.169223\pi$
$542$	0.613137	−	1.88704i	0.0263365	−	0.0810553i
$543$	−12.3455	+	4.01130i	−0.529797	+	0.172141i
$544$	−0.374125	−	0.514939i	−0.0160405	−	0.0220778i
$545$	−5.12937	+	1.08832i	−0.219718	+	0.0466185i
$546$	0.544886	−	5.07460i	0.0233190	−	0.217173i
$547$	−11.0877	+	34.1243i	−0.474074	+	1.45905i	0.373128	+	0.927780i	$0.378285\pi$
$547$	−11.0877	+	34.1243i	−0.474074	+	1.45905i	−0.847202	+	0.531270i	$0.821715\pi$
$548$	−12.0558	+	16.5933i	−0.514996	+	0.708832i
$549$	30.7792			1.31362
$550$	10.7725	+	12.6077i	0.459340	+	0.537594i
$551$			6.34784i			0.270427i
$552$	8.14249	−	11.2072i	0.346567	−	0.477009i
$553$	27.6553	−	30.5760i	1.17602	−	1.30022i
$554$	6.82637	+	21.0094i	0.290025	+	0.892604i
$555$	21.0374	−	4.46359i	0.892987	−	0.189469i
$556$	−4.15370	+	3.01784i	−0.176156	+	0.127985i
$557$	−14.1950	−	43.6878i	−0.601463	−	1.85111i	−0.519487	−	0.854479i	$-0.673877\pi$
$557$	−14.1950	−	43.6878i	−0.601463	−	1.85111i	−0.0819763	−	0.996634i	$-0.526123\pi$
$558$	−11.5988	−	3.76868i	−0.491017	−	0.159541i
$559$	0.854269	−	1.17580i	0.0361317	−	0.0497310i
$560$	3.94714	+	4.40683i	0.166797	+	0.186222i
$561$	4.72152	+	1.66700i	0.199343	+	0.0703806i
$562$		−	24.6894i		−	1.04146i
$563$	1.67074	−	2.29958i	0.0704135	−	0.0969158i	−0.772358	−	0.635188i	$-0.780923\pi$
$563$	1.67074	−	2.29958i	0.0704135	−	0.0969158i	0.842771	+	0.538272i	$0.180923\pi$
$564$	3.32766	−	10.2415i	0.140120	−	0.431245i
$565$	−2.02523	+	19.2012i	−0.0852021	+	0.807801i
$566$	12.0273	+	16.5541i	0.505544	+	0.695822i
$567$	5.43307	+	25.8458i	0.228168	+	1.08542i
$568$	2.35379	+	7.24423i	0.0987629	+	0.303961i
$569$	−16.9563	−	5.50944i	−0.710846	−	0.230968i	−0.0687963	−	0.997631i	$-0.521916\pi$
$569$	−16.9563	−	5.50944i	−0.710846	−	0.230968i	−0.642050	+	0.766663i	$0.721916\pi$
$570$	3.43683	−	1.98258i	0.143953	−	0.0830410i
$571$			21.8949i			0.916274i	0.888882	+	0.458137i	$0.151483\pi$
$571$			21.8949i			0.916274i	−0.888882	+	0.458137i	$0.848517\pi$
$572$	−1.52989	−	2.22154i	−0.0639681	−	0.0928874i
$573$	21.1816			0.884872
$574$	5.15133	−	2.95872i	0.215012	−	0.123495i
$575$	−11.8580	−	26.6860i	−0.494512	−	1.11288i
$576$	0.811453	+	2.49739i	0.0338105	+	0.104058i
$577$	31.6951	−	23.0279i	1.31949	−	0.958663i	0.319547	−	0.947570i	$-0.396469\pi$
$577$	31.6951	−	23.0279i	1.31949	−	0.958663i	0.999938	−	0.0110923i	$-0.00353088\pi$
$578$	13.4255	−	9.75422i	0.558428	−	0.405722i
$579$	15.4823	+	47.6496i	0.643422	+	1.98025i
$580$	−12.7012	+	14.0957i	−0.527388	+	0.585293i
$581$	9.77855	+	17.0251i	0.405683	+	0.706321i
$582$	28.6807			1.18885
$583$	−6.70185	+	1.99202i	−0.277562	+	0.0825009i
$584$			9.99573i			0.413626i
$585$	−2.38619	−	4.13650i	−0.0986569	−	0.171023i
$586$	−13.3177	−	4.32720i	−0.550151	−	0.178755i
$587$	−4.57871	−	14.0918i	−0.188983	−	0.581631i	0.811011	−	0.585031i	$-0.198918\pi$
$587$	−4.57871	−	14.0918i	−0.188983	−	0.581631i	−0.999994	+	0.00340007i	$0.998918\pi$
$588$	−16.2248	−	3.52493i	−0.669100	−	0.145365i
$589$	2.04220	+	2.81085i	0.0841475	+	0.115819i
$590$	2.82265	−	26.7615i	0.116207	−	1.10175i
$591$	−10.0030	+	30.7860i	−0.411468	+	1.26637i
$592$	2.38336	−	3.28042i	0.0979557	−	0.134824i
$593$		−	18.0520i		−	0.741306i	−0.928771	−	0.370653i	$-0.879134\pi$
$593$		−	18.0520i		−	0.741306i	0.928771	−	0.370653i	$-0.120866\pi$
$594$	2.33637	+	1.78928i	0.0958623	+	0.0734150i
$595$	2.80494	−	2.51235i	0.114991	−	0.102996i
$596$	−6.72048	+	9.24994i	−0.275281	+	0.378892i
$597$	−13.0083	−	4.22666i	−0.532395	−	0.172986i
$598$	1.46781	+	4.51745i	0.0600231	+	0.184732i
$599$	−31.0302	+	22.5447i	−1.26786	+	0.921153i	−0.999115	−	0.0420585i	$-0.986608\pi$
$599$	−31.0302	+	22.5447i	−1.26786	+	0.921153i	−0.268744	+	0.963212i	$0.586608\pi$
$600$	11.5985	+	2.47422i	0.473508	+	0.101010i
$601$	−13.0875	−	40.2791i	−0.533849	−	1.64302i	−0.746122	−	0.665809i	$-0.768087\pi$
$601$	−13.0875	−	40.2791i	−0.533849	−	1.64302i	0.212273	−	0.977210i	$-0.431913\pi$
$602$	−3.50649	−	3.17155i	−0.142914	−	0.129263i
$603$	10.9889	−	15.1249i	0.447503	−	0.615935i
$604$			2.03456i			0.0827851i
$605$	−21.8990	+	11.1998i	−0.890320	+	0.455335i
$606$	−4.96765			−0.201797
$607$	−14.1598	+	19.4893i	−0.574728	+	0.791046i	−0.993105	−	0.117228i	$-0.962599\pi$
$607$	−14.1598	+	19.4893i	−0.574728	+	0.791046i	0.418377	+	0.908274i	$0.362599\pi$
$608$	0.231172	−	0.711476i	0.00937528	−	0.0288541i
$609$	5.68502	−	52.9454i	0.230369	−	2.14546i
$610$	−5.43991	−	25.6389i	−0.220255	−	1.03809i
$611$	2.17032	+	2.98719i	0.0878019	+	0.120849i
$612$	1.58959	−	0.516489i	0.0642554	−	0.0208778i
$613$	−7.73309	+	23.8000i	−0.312337	+	0.961273i	0.664500	+	0.747288i	$0.268644\pi$
$613$	−7.73309	+	23.8000i	−0.312337	+	0.961273i	−0.976837	+	0.213985i	$0.931356\pi$
$614$	11.7411	−	16.1602i	0.473832	−	0.652174i
$615$	4.84764	−	10.8773i	0.195476	−	0.438613i
$616$	−7.71706	+	4.17696i	−0.310929	+	0.168295i
$617$			9.96719i			0.401264i	0.979667	+	0.200632i	$0.0642995\pi$
$617$			9.96719i			0.401264i	−0.979667	+	0.200632i	$0.935700\pi$
$618$	18.8206	+	13.6740i	0.757076	+	0.550048i
$619$	−17.5478	−	5.70164i	−0.705307	−	0.229168i	−0.0656656	−	0.997842i	$-0.520917\pi$
$619$	−17.5478	−	5.70164i	−0.705307	−	0.229168i	−0.639641	+	0.768674i	$0.720917\pi$
$620$	−1.08932	+	10.3278i	−0.0437481	+	0.414776i
$621$	−3.04598	−	4.19243i	−0.122231	−	0.168236i
$622$	17.9668	+	24.7292i	0.720404	+	0.991552i
$623$	2.87751	−	26.7987i	0.115285	−	1.07367i
$624$	−1.83463	−	0.596107i	−0.0734439	−	0.0238634i
$625$	16.7554	−	18.5541i	0.670217	−	0.742165i
$626$	10.3327			0.412978
$627$	1.67672	+	5.64109i	0.0669618	+	0.225283i
$628$	−4.05259			−0.161716
$629$	−2.08799	−	1.51701i	−0.0832534	−	0.0604872i
$630$	−14.2085	+	6.28162i	−0.566080	+	0.250266i
$631$	7.41037	+	22.8068i	0.295002	+	0.907924i	0.983221	+	0.182420i	$0.0583931\pi$
$631$	7.41037	+	22.8068i	0.295002	+	0.907924i	−0.688218	+	0.725504i	$0.741607\pi$
$632$	−9.15919	−	12.6065i	−0.364333	−	0.501461i
$633$	−30.0773	−	41.3979i	−1.19547	−	1.64542i
$634$	−2.49090	+	0.809344i	−0.0989264	+	0.0321431i
$635$	8.10159	+	7.30007i	0.321502	+	0.289694i
$636$	−2.93899	+	4.04517i	−0.116538	+	0.160401i
$637$	4.24781	−	3.79034i	0.168304	−	0.150179i
$638$	−15.9620	−	23.1783i	−0.631943	−	0.917638i
$639$	−20.0017			−0.791254
$640$	1.93690	−	1.11733i	0.0765627	−	0.0441662i
$641$	−13.5051	+	41.5643i	−0.533417	+	1.64169i	0.213627	+	0.976915i	$0.431472\pi$
$641$	−13.5051	+	41.5643i	−0.533417	+	1.64169i	−0.747044	+	0.664775i	$0.768528\pi$
$642$	−0.409445	−	1.26014i	−0.0161595	−	0.0497339i
$643$	31.0256	−	22.5414i	1.22353	−	0.888947i	0.227142	−	0.973862i	$-0.427062\pi$
$643$	31.0256	−	22.5414i	1.22353	−	0.888947i	0.996388	+	0.0849146i	$0.0270617\pi$
$644$	15.1217	−	3.17875i	0.595879	−	0.125260i
$645$	−9.42562	−	0.994159i	−0.371133	−	0.0391450i
$646$	−0.452854	−	0.147141i	−0.0178173	−	0.00578919i
$647$	10.9257	+	7.93796i	0.429532	+	0.312073i	0.781462	−	0.623953i	$-0.214474\pi$
$647$	10.9257	+	7.93796i	0.429532	+	0.312073i	−0.351930	+	0.936026i	$0.614474\pi$
$648$	9.98231			0.392142
$649$	37.6370	+	13.2883i	1.47738	+	0.521610i
$650$	−3.02395	+	2.71877i	−0.118609	+	0.106639i
$651$	−14.5161	−	25.2734i	−0.568929	−	0.990544i
$652$	−15.7998	−	5.13365i	−0.618766	−	0.201049i
$653$	31.7819	−	10.3266i	1.24372	−	0.404109i	0.388054	−	0.921637i	$-0.373147\pi$
$653$	31.7819	−	10.3266i	1.24372	−	0.404109i	0.855667	+	0.517527i	$0.173147\pi$
$654$	−3.26931	−	4.49982i	−0.127840	−	0.175957i
$655$	5.83335	+	27.4932i	0.227928	+	1.07425i
$656$	−0.693842	−	2.13543i	−0.0270900	−	0.0833744i
$657$	−24.9633	−	8.11106i	−0.973911	−	0.316443i
$658$	10.4160	−	5.98254i	0.406059	−	0.233224i
$659$		−	5.15933i		−	0.200979i	−0.994938	−	0.100489i	$-0.967959\pi$
$659$		−	5.15933i		−	0.200979i	0.994938	−	0.100489i	$-0.0320409\pi$
$660$	−7.56382	+	15.8812i	−0.294421	+	0.618177i
$661$			33.9879i			1.32198i	0.750396	+	0.660989i	$0.229863\pi$
$661$			33.9879i			1.32198i	−0.750396	+	0.660989i	$0.770137\pi$
$662$	7.81203	+	5.67577i	0.303623	+	0.220595i
$663$	−0.379422	+	1.16774i	−0.0147355	+	0.0453513i
$664$	7.05758	−	2.29315i	0.273887	−	0.0889913i
$665$	4.32663	+	0.931469i	0.167779	+	0.0361208i
$666$	6.25851	+	8.61411i	0.242512	+	0.333790i
$667$	15.3143	+	47.1325i	0.592971	+	1.82498i
$668$	2.69185	+	0.874634i	0.104151	+	0.0338406i
$669$	30.4218	+	22.1027i	1.17617	+	0.854541i
$670$	−14.5412	−	6.48052i	−0.561774	−	0.250364i
$671$	38.8628	+	0.981188i	1.50028	+	0.0378784i
$672$	−2.56533	+	5.72717i	−0.0989596	+	0.220930i
$673$	13.2169	+	9.60262i	0.509473	+	0.370154i	0.812624	−	0.582789i	$-0.198039\pi$
$673$	13.2169	+	9.60262i	0.509473	+	0.370154i	−0.303151	+	0.952943i	$0.598039\pi$
$674$	−6.71481	+	20.6661i	−0.258645	+	0.796027i
$675$	2.22104	−	3.84046i	0.0854878	−	0.147819i
$676$	−9.98211	+	7.25242i	−0.383927	+	0.278939i
$677$	11.3366	+	15.6036i	0.435703	+	0.599693i	0.969250	−	0.246077i	$-0.0791415\pi$
$677$	11.3366	+	15.6036i	0.435703	+	0.599693i	−0.533548	+	0.845770i	$0.679142\pi$
$678$	−19.4782	+	6.32885i	−0.748056	+	0.243058i
$679$	23.7266	+	21.4602i	0.910543	+	0.823567i
$680$	−0.711177	−	1.23284i	−0.0272724	−	0.0472771i
$681$			35.4035i			1.35667i
$682$	−14.5249	−	5.12821i	−0.556187	−	0.196369i
$683$			42.7262i			1.63487i	0.576020	+	0.817435i	$0.304605\pi$
$683$			42.7262i			1.63487i	−0.576020	+	0.817435i	$0.695395\pi$
$684$	1.58925	+	1.15466i	0.0607665	+	0.0441494i
$685$	−30.7007	+	34.0715i	−1.17301	+	1.30180i
$686$	−10.7848	−	15.0562i	−0.411764	−	0.574848i
$687$	−30.2419	−	41.6244i	−1.15380	−	1.58807i
$688$	−1.44573	+	1.05039i	−0.0551181	+	0.0400456i
$689$	−0.529797	−	1.63055i	−0.0201837	−	0.0621190i
$690$	20.7353	−	23.0120i	0.789380	−	0.876051i
$691$	22.0867	−	30.3997i	0.840216	−	1.15646i	−0.145718	−	0.989326i	$-0.546549\pi$
$691$	22.0867	−	30.3997i	0.840216	−	1.15646i	0.985934	−	0.167132i	$-0.0534508\pi$
$692$			20.9704i			0.797175i
$693$	−4.16950	−	22.6619i	−0.158386	−	0.860856i
$694$	7.28099			0.276382
$695$	−9.94453	+	5.73663i	−0.377218	+	0.217603i
$696$	−19.1415	−	6.21944i	−0.725555	−	0.235747i
$697$	−1.35920	+	0.441630i	−0.0514833	+	0.0167279i
$698$	−7.96605	+	5.78768i	−0.301520	+	0.219067i
$699$	49.3617	−	35.8634i	1.86703	−	1.35648i
$700$	7.74377	+	10.7254i	0.292687	+	0.405382i
$701$	−9.48040	−	3.08037i	−0.358070	−	0.116344i	0.124457	−	0.992225i	$-0.460281\pi$
$701$	−9.48040	−	3.08037i	−0.358070	−	0.116344i	−0.482527	+	0.875881i	$0.660281\pi$
$702$	−0.424160	+	0.583806i	−0.0160089	+	0.0220343i
$703$		−	3.03337i		−	0.114406i
$704$	0.944954	+	3.17916i	0.0356143	+	0.119819i
$705$	9.80194	−	21.9939i	0.369163	−	0.828337i
$706$	−6.34305	−	4.60850i	−0.238724	−	0.173443i
$707$	−4.10958	−	3.71702i	−0.154557	−	0.139793i
$708$	27.1476	−	8.82078i	1.02027	−	0.331505i
$709$	14.2703	−	10.3680i	0.535932	−	0.389377i	−0.286640	−	0.958038i	$-0.592538\pi$
$709$	14.2703	−	10.3680i	0.535932	−	0.389377i	0.822572	+	0.568661i	$0.192538\pi$
$710$	3.53510	+	16.6613i	0.132670	+	0.625288i
$711$	38.9158	−	12.6445i	1.45945	−	0.474206i
$712$	−9.68857	−	3.14801i	−0.363094	−	0.117977i
$713$	21.9445	+	15.9436i	0.821828	+	0.597093i
$714$	3.64534	+	1.63283i	0.136424	+	0.0611071i
$715$	−2.88102	−	5.29895i	−0.107744	−	0.198170i
$716$	1.27251			0.0475560
$717$	10.9288	−	15.0422i	0.408144	−	0.561762i
$718$	32.5863	+	10.5879i	1.21611	+	0.395138i
$719$	−6.31619	+	2.05225i	−0.235554	+	0.0765361i	−0.424415	−	0.905468i	$-0.639520\pi$
$719$	−6.31619	+	2.05225i	−0.235554	+	0.0765361i	0.188861	+	0.982004i	$0.439520\pi$
$720$	1.21870	+	5.74386i	0.0454182	+	0.214061i
$721$	5.33819	+	25.3945i	0.198804	+	0.945739i
$722$	5.69839	+	17.5378i	0.212072	+	0.652690i
$723$	−22.4125	+	68.9786i	−0.833530	+	2.56534i
$724$	−3.21681	+	4.42756i	−0.119552	+	0.164549i
$725$	−31.5502	+	28.3661i	−1.17174	+	1.05349i
$726$	−20.3072	−	16.3815i	−0.753671	−	0.607974i
$727$	−40.8132			−1.51368			−0.756839	−	0.653601i	$-0.773258\pi$
$727$	−40.8132			−1.51368			−0.756839	+	0.653601i	$0.773258\pi$
$728$	−1.07169	−	1.86589i	−0.0397196	−	0.0691545i
$729$	−6.14913	+	18.9251i	−0.227746	+	0.700929i
$730$	−2.34446	+	22.2278i	−0.0867725	+	0.822689i
$731$	0.668571	+	0.920209i	0.0247280	+	0.0340352i
$732$	22.4921	−	16.3415i	0.831332	−	0.603998i
$733$	−20.9481	+	6.80646i	−0.773737	+	0.251402i	−0.669164	−	0.743115i	$-0.733348\pi$
$733$	−20.9481	+	6.80646i	−0.773737	+	0.251402i	−0.104573	+	0.994517i	$0.533348\pi$
$734$	−8.93956	+	27.5131i	−0.329965	+	1.01553i
$735$	−35.2529	−	11.6440i	−1.30032	−	0.429494i
$736$		−	5.84039i		−	0.215280i
$737$	14.3571	−	18.7469i	0.528851	−	0.690552i
$738$	5.89602			0.217036
$739$	15.4581	−	21.2762i	0.568635	−	0.782659i	−0.423757	−	0.905776i	$-0.639289\pi$
$739$	15.4581	−	21.2762i	0.568635	−	0.782659i	0.992392	+	0.123117i	$0.0392891\pi$
$740$	6.06938	−	6.73577i	0.223115	−	0.247612i
$741$	−1.37247	+	0.445941i	−0.0504188	+	0.0163821i
$742$	−5.45811	+	1.14735i	−0.200373	+	0.0421206i
$743$	42.4776	−	30.8618i	1.55835	−	1.13221i	0.621005	−	0.783806i	$-0.286725\pi$
$743$	42.4776	−	30.8618i	1.55835	−	1.13221i	0.937345	−	0.348402i	$-0.113275\pi$
$744$	−10.4768	+	3.40412i	−0.384099	+	0.124801i
$745$	−17.1141	+	18.9931i	−0.627012	+	0.695855i
$746$	−20.8333	−	15.1363i	−0.762762	−	0.554179i
$747$			19.4863i			0.712967i
$748$	2.02353	−	0.601463i	0.0739877	−	0.0219917i
$749$	0.604175	−	1.34884i	0.0220761	−	0.0492855i
$750$	25.2117	+	8.22240i	0.920602	+	0.300239i
$751$	−0.953302	+	2.93396i	−0.0347865	+	0.107062i	−0.966942	−	0.254996i	$-0.917926\pi$
$751$	−0.953302	+	2.93396i	−0.0347865	+	0.107062i	0.932156	+	0.362058i	$0.117926\pi$
$752$	−1.40295	−	4.31784i	−0.0511604	−	0.157456i
$753$	5.44545	+	7.49502i	0.198443	+	0.273134i
$754$	5.58309	−	4.05635i	0.203324	−	0.147724i
$755$	−0.477199	+	4.52432i	−0.0173670	+	0.164657i
$756$	1.74104	+	1.57473i	0.0633210	+	0.0572724i
$757$	−18.8592	+	25.9575i	−0.685450	+	0.943440i	−0.999983	−	0.00580602i	$-0.998152\pi$
$757$	−18.8592	+	25.9575i	−0.685450	+	0.943440i	0.314534	+	0.949246i	$0.398152\pi$
$758$	−11.5492			−0.419487
$759$	26.0588	+	37.8398i	0.945875	+	1.37350i
$760$	0.680940	−	1.52791i	0.0247003	−	0.0554232i
$761$	20.1886	+	14.6679i	0.731836	+	0.531710i	0.890144	−	0.455680i	$-0.150604\pi$
$761$	20.1886	+	14.6679i	0.731836	+	0.531710i	−0.158308	+	0.987390i	$0.550604\pi$
$762$	−3.57465	+	11.0016i	−0.129496	+	0.398548i
$763$	0.662376	−	6.16880i	0.0239796	−	0.223326i
$764$	7.22468	−	5.24904i	0.261380	−	0.189904i
$765$	3.65597	−	0.775701i	0.132182	−	0.0280455i
$766$	−2.68639	−	8.26786i	−0.0970633	−	0.298730i
$767$	−3.02451	+	9.30850i	−0.109209	+	0.336110i
$768$	1.91891	+	1.39417i	0.0692426	+	0.0503077i
$769$	4.84628			0.174761			0.0873807	−	0.996175i	$-0.472150\pi$
$769$	4.84628			0.174761			0.0873807	+	0.996175i	$0.472150\pi$
$770$	−18.1404	+	7.47844i	−0.653733	+	0.269504i
$771$	46.5702			1.67718
$772$	17.0889	+	12.4158i	0.615042	+	0.446854i
$773$	−4.04957	+	12.4633i	−0.145653	+	0.448274i	−0.997094	−	0.0761761i	$-0.975729\pi$
$773$	−4.04957	+	12.4633i	−0.145653	+	0.448274i	0.851441	+	0.524450i	$0.175729\pi$
$774$	−1.45009	−	4.46291i	−0.0521223	−	0.160416i
$775$	−4.84471	+	22.7108i	−0.174027	+	0.815797i
$776$	9.78252	−	7.10742i	0.351172	−	0.255141i
$777$	−2.71664	+	25.3004i	−0.0974589	+	0.907648i
$778$	8.02071	−	24.6852i	0.287556	−	0.885008i
$779$	−1.35891	−	0.987304i	−0.0486879	−	0.0353738i
$780$	−3.93991	−	1.75589i	−0.141071	−	0.0628709i
$781$	−25.2548	−	0.637620i	−0.903687	−	0.0228159i
$782$	−3.71741			−0.132934
$783$	−4.42544	+	6.09110i	−0.158152	+	0.217678i
$784$	−6.40754	+	2.81841i	−0.228841	+	0.100657i
$785$	−9.01189	−	0.950521i	−0.321648	−	0.0339256i
$786$	−24.1188	+	17.5234i	−0.860291	+	0.625038i
$787$	6.18071	+	8.50701i	0.220318	+	0.303242i	0.904841	−	0.425749i	$-0.139989\pi$
$787$	6.18071	+	8.50701i	0.220318	+	0.303242i	−0.684523	+	0.728991i	$0.739989\pi$
$788$	4.21728	+	12.9795i	0.150235	+	0.462374i
$789$	14.2119	−	43.7398i	0.505958	−	1.55718i
$790$	−17.4108	−	30.1818i	−0.619447	−	1.07382i
$791$	−20.8492	−	9.33882i	−0.741313	−	0.332050i
$792$	−8.70640	−	0.219815i	−0.309369	−	0.00781078i
$793$			9.53281i			0.338520i
$794$	−13.4839	−	9.79665i	−0.478527	−	0.347670i
$795$	−7.48430	+	8.30605i	−0.265441	+	0.294585i
$796$	−5.48434	+	1.78197i	−0.194387	+	0.0631603i
$797$	11.5044	−	8.35841i	0.407505	−	0.296070i	−0.365086	−	0.930974i	$-0.618960\pi$
$797$	11.5044	−	8.35841i	0.407505	−	0.296070i	0.772591	+	0.634904i	$0.218960\pi$
$798$	0.965750	+	4.59420i	0.0341872	+	0.162633i
$799$	−2.74831	+	0.892978i	−0.0972280	+	0.0315913i
$800$	4.56921	−	2.03034i	0.161546	−	0.0717834i
$801$	15.7236	−	21.6417i	0.555567	−	0.764673i
$802$	21.7066			0.766488
$803$	−31.2609	−	11.0371i	−1.10317	−	0.389490i
$804$		−	16.8870i		−	0.595557i
$805$	34.3722	−	3.52194i	1.21146	−	0.124132i
$806$	1.16722	−	3.59234i	0.0411137	−	0.126535i
$807$	67.0983	−	21.8016i	2.36197	−	0.767451i
$808$	−1.69439	+	1.23104i	−0.0596083	+	0.0433080i
$809$	−2.58009	−	3.55118i	−0.0907110	−	0.124853i	0.761249	−	0.648459i	$-0.224586\pi$
$809$	−2.58009	−	3.55118i	−0.0907110	−	0.124853i	−0.851960	+	0.523606i	$0.824586\pi$
$810$	22.1980	+	2.34132i	0.779958	+	0.0822654i
$811$	7.15686	−	22.0265i	0.251311	−	0.773457i	−0.743223	−	0.669044i	$-0.766704\pi$
$811$	7.15686	−	22.0265i	0.251311	−	0.773457i	0.994534	−	0.104413i	$-0.0332962\pi$
$812$	−11.1814	−	19.4676i	−0.392391	−	0.683180i
$813$	4.70621			0.165054
$814$	7.62760	+	11.0760i	0.267347	+	0.388212i
$815$	−33.9304	−	15.1217i	−1.18853	−	0.529688i
$816$	0.887388	−	1.22138i	0.0310648	−	0.0427570i
$817$	−0.413111	+	1.27142i	−0.0144529	+	0.0444815i
$818$	0.270621	+	0.832887i	0.00946206	+	0.0291212i
$819$	5.52949	−	1.16236i	0.193216	−	0.0406161i
$820$	−1.04206	−	4.91136i	−0.0363904	−	0.171512i
$821$	−38.6154	+	12.5469i	−1.34769	+	0.437889i	−0.891913	−	0.452207i	$-0.850637\pi$
$821$	−38.6154	+	12.5469i	−1.34769	+	0.437889i	−0.455772	+	0.890096i	$0.650637\pi$
$822$	−46.2678	−	15.0333i	−1.61377	−	0.524347i
$823$	−8.28599	+	11.4047i	−0.288832	+	0.397543i	−0.928634	−	0.370997i	$-0.879016\pi$
$823$	−8.28599	+	11.4047i	−0.288832	+	0.397543i	0.639803	+	0.768539i	$0.279016\pi$
$824$	9.80798			0.341677
$825$	−20.5448	+	33.5416i	−0.715278	+	1.16777i
$826$	29.0584	+	13.0159i	1.01107	+	0.452881i
$827$	21.2902	+	15.4682i	0.740333	+	0.537883i	0.892815	−	0.450423i	$-0.148727\pi$
$827$	21.2902	+	15.4682i	0.740333	+	0.537883i	−0.152482	+	0.988306i	$0.548727\pi$
$828$	14.5858	+	4.73920i	0.506890	+	0.164699i
$829$	18.8039	−	6.10975i	0.653086	−	0.212201i	0.0363117	−	0.999341i	$-0.488439\pi$
$829$	18.8039	−	6.10975i	0.653086	−	0.212201i	0.616774	+	0.787140i	$0.288439\pi$
$830$	16.2320	−	3.44401i	0.563421	−	0.119543i
$831$	−42.3898	+	30.7980i	−1.47049	+	1.06837i
$832$	−0.773484	+	0.251320i	−0.0268157	+	0.00871296i
$833$	1.79392	+	4.07840i	0.0621555	+	0.141308i
$834$	−9.85216	−	7.15801i	−0.341152	−	0.247862i
$835$	5.78080	+	2.57631i	0.200053	+	0.0891570i
$836$	1.96983	+	1.50857i	0.0681280	+	0.0521750i
$837$			4.12090i			0.142439i
$838$	−8.18572	+	11.2667i	−0.282771	+	0.389201i
$839$	31.2076	+	10.1400i	1.07741	+	0.350071i	0.793368	−	0.608742i	$-0.208325\pi$
$839$	31.2076	+	10.1400i	1.07741	+	0.350071i	0.284039	+	0.958813i	$0.408325\pi$
$840$	−7.04789	+	12.1340i	−0.243175	+	0.418663i
$841$	34.7893	−	25.2759i	1.19963	−	0.871583i
$842$	−14.1600	+	10.2879i	−0.487987	+	0.354543i
$843$	55.6946	−	18.0963i	1.91822	−	0.623268i
$844$	−20.5178	−	6.66663i	−0.706251	−	0.229475i
$845$	−23.8986	+	13.7862i	−0.822136	+	0.474259i
$846$	11.9218			0.409879
$847$	−4.54212	−	28.7466i	−0.156069	−	0.987746i
$848$			2.10806i			0.0723910i
$849$	−28.5275	+	39.2648i	−0.979062	+	1.34756i
$850$	−1.29231	−	2.90830i	−0.0443259	−	0.0997540i
$851$	−7.31806	−	22.5227i	−0.250860	−	0.772067i
$852$	−14.6164	+	10.6194i	−0.500749	+	0.363816i
$853$	12.0566	+	16.5945i	0.412811	+	0.568185i	0.963901	−	0.266260i	$-0.0857881\pi$
$853$	12.0566	+	16.5945i	0.412811	+	0.568185i	−0.551090	+	0.834445i	$0.685788\pi$
$854$	30.8344	+	3.31085i	1.05513	+	0.113295i
$855$	3.26325	+	2.94040i	0.111601	+	0.100560i
$856$	−0.451933	−	0.328349i	−0.0154468	−	0.0112227i
$857$		−	5.95852i		−	0.203539i	−0.994808	−	0.101770i	$-0.967550\pi$
$857$		−	5.95852i		−	0.203539i	0.994808	−	0.101770i	$-0.0324504\pi$
$858$	3.89004	−	5.07945i	0.132804	−	0.173410i
$859$		−	44.9124i		−	1.53239i	−0.642607	−	0.766196i	$-0.722147\pi$
$859$		−	44.9124i		−	1.53239i	0.642607	−	0.766196i	$-0.277853\pi$
$860$	−3.46129	+	1.99669i	−0.118029	+	0.0680865i
$861$	10.4500	+	9.45182i	0.356136	+	0.322117i
$862$	3.98852	−	1.29595i	0.135849	−	0.0441402i
$863$	15.0350	+	20.6939i	0.511798	+	0.704430i	0.984221	−	0.176942i	$-0.0566205\pi$
$863$	15.0350	+	20.6939i	0.511798	+	0.704430i	−0.472423	+	0.881372i	$0.656620\pi$
$864$	0.717833	−	0.521536i	0.0244212	−	0.0177430i
$865$	−4.91853	+	46.6325i	−0.167235	+	1.58555i
$866$	−3.34165	+	10.2845i	−0.113554	+	0.349483i
$867$	31.8440	+	23.1360i	1.08148	+	0.785741i
$868$	−11.2142	−	5.02311i	−0.380636	−	0.170495i
$869$	49.5394	−	14.7248i	1.68051	−	0.499504i
$870$	−41.1067	−	18.3199i	−1.39365	−	0.621104i
$871$	4.68444	+	3.40344i	0.158726	+	0.115321i
$872$	−2.23022	−	0.724642i	−0.0755247	−	0.0245395i
$873$	9.81197	+	30.1981i	0.332085	+	1.02205i
$874$	−2.56811	−	3.53471i	−0.0868677	−	0.119563i
$875$	14.7045	+	25.6667i	0.497102	+	0.867692i
$876$	−22.5485	+	7.32645i	−0.761843	+	0.247538i
$877$	10.5701	−	32.5315i	0.356928	−	1.09851i	−0.597955	−	0.801529i	$-0.704020\pi$
$877$	10.5701	−	32.5315i	0.356928	−	1.09851i	0.954883	−	0.296982i	$-0.0959800\pi$
$878$	5.59500	+	4.06500i	0.188822	+	0.137187i
$879$		−	33.2140i		−	1.12028i
$880$	1.35567	+	7.29124i	0.0456995	+	0.245788i
$881$			9.77926i			0.329472i	0.986338	+	0.164736i	$0.0526772\pi$
$881$			9.77926i			0.329472i	−0.986338	+	0.164736i	$0.947323\pi$
$882$	−1.83926	−	18.2892i	−0.0619311	−	0.615828i
$883$	−18.7762	−	6.10076i	−0.631870	−	0.205307i	−0.0244668	−	0.999701i	$-0.507789\pi$
$883$	−18.7762	−	6.10076i	−0.631870	−	0.205307i	−0.607403	+	0.794394i	$0.707789\pi$
$884$	0.159965	+	0.492322i	0.00538021	+	0.0165586i
$885$	62.4378	−	13.2477i	2.09883	−	0.445317i
$886$	12.7993	+	17.6168i	0.430002	+	0.591847i
$887$	6.27723	−	2.03960i	0.210769	−	0.0684829i	−0.201730	−	0.979441i	$-0.564656\pi$
$887$	6.27723	−	2.03960i	0.210769	−	0.0684829i	0.412498	+	0.910958i	$0.364656\pi$
$888$	9.14692	+	2.97201i	0.306950	+	0.0997342i
$889$	−11.1891	+	6.42658i	−0.375271	+	0.215541i
$890$	−20.8064	−	9.27275i	−0.697433	−	0.310823i
$891$	−11.0223	+	31.2189i	−0.369260	+	1.04587i
$892$	15.8537			0.530821
$893$	−2.74772	−	1.99633i	−0.0919488	−	0.0668047i
$894$	−25.7920	−	8.38032i	−0.862612	−	0.280280i
$895$	2.82973	+	0.298463i	0.0945874	+	0.00997653i
$896$	0.544270	+	2.58916i	0.0181828	+	0.0864979i
$897$	−9.11467	+	6.62220i	−0.304330	+	0.221109i
$898$	−6.57283	−	20.2291i	−0.219338	−	0.675054i
$899$	12.1781	−	37.4805i	0.406164	−	1.25004i
$900$	1.36286	+	13.0587i	0.0454287	+	0.435288i
$901$	1.34178			0.0447011
$902$	7.44451	+	0.187955i	0.247875	+	0.00625823i
$903$	4.58430	−	10.2346i	0.152556	−	0.340586i
$904$	−5.07533	+	6.98560i	−0.168803	+	0.232338i
$905$	−8.19179	+	9.09121i	−0.272304	+	0.302202i
$906$	−4.58959	+	1.49125i	−0.152479	+	0.0495434i
$907$	13.9955	+	19.2631i	0.464712	+	0.639621i	0.975477	−	0.220099i	$-0.0706381\pi$
$907$	13.9955	+	19.2631i	0.464712	+	0.639621i	−0.510766	+	0.859720i	$0.670638\pi$
$908$	8.77341	+	12.0756i	0.291156	+	0.400742i
$909$	−1.69949	−	5.23048i	−0.0563684	−	0.173484i
$910$	−1.94552	−	4.40061i	−0.0644934	−	0.145879i
$911$	−27.3592	−	19.8776i	−0.906450	−	0.658575i	0.0336643	−	0.999433i	$-0.489282\pi$
$911$	−27.3592	−	19.8776i	−0.906450	−	0.658575i	−0.940115	+	0.340858i	$0.889282\pi$
$912$	1.77440			0.0587561
$913$	−0.621192	+	24.6041i	−0.0205584	+	0.814276i
$914$	−8.54102			−0.282512
$915$	53.8493	−	31.0636i	1.78020	−	1.02693i
$916$	−20.6300	−	6.70311i	−0.681636	−	0.221477i
$917$	−33.0645	−	3.55031i	−1.09189	−	0.117241i
$918$	−0.331958	−	0.456901i	−0.0109562	−	0.0150800i
$919$	0.912890	+	1.25649i	0.0301135	+	0.0414476i	0.823808	−	0.566869i	$-0.191845\pi$
$919$	0.912890	+	1.25649i	0.0301135	+	0.0414476i	−0.793695	+	0.608316i	$0.791845\pi$
$920$	1.36984	−	12.9875i	0.0451624	−	0.428184i
$921$	45.0602	+	14.6409i	1.48478	+	0.482435i
$922$	−10.7519	−	7.81168i	−0.354093	−	0.257264i
$923$		−	6.19485i		−	0.203906i
$924$	−15.0787	−	14.3467i	−0.496053	−	0.471972i
$925$	15.0765	−	13.5550i	0.495713	−	0.445686i
$926$	13.4322	−	18.4878i	0.441408	−	0.607546i
$927$	−7.95871	+	24.4944i	−0.261398	+	0.804501i
$928$	−8.07009	+	2.62213i	−0.264914	+	0.0860757i
$929$	11.0375	+	15.1919i	0.362130	+	0.498430i	0.950741	−	0.309987i	$-0.100325\pi$
$929$	11.0375	+	15.1919i	0.362130	+	0.498430i	−0.588610	+	0.808417i	$0.700325\pi$
$930$	−24.0961	+	5.11256i	−0.790141	+	0.167648i
$931$	−2.63866	+	4.52325i	−0.0864784	+	0.148243i
$932$	7.94910	−	24.4648i	0.260381	−	0.801372i
$933$	−42.6156	+	58.6553i	−1.39517	+	1.92029i
$934$	26.1046			0.854169
$935$	4.64087	−	0.862880i	0.151773	−	0.0282192i
$936$		−	2.13563i		−	0.0698052i
$937$	−0.385609	+	0.530745i	−0.0125973	+	0.0173387i	−0.815269	−	0.579082i	$-0.803411\pi$
$937$	−0.385609	+	0.530745i	−0.0125973	+	0.0173387i	0.802672	+	0.596421i	$0.203411\pi$
$938$	12.6356	−	13.9700i	0.412567	−	0.456138i
$939$	7.57343	+	23.3086i	0.247150	+	0.760648i
$940$	−2.10706	−	9.93079i	−0.0687246	−	0.323907i
$941$	−11.9922	+	8.71286i	−0.390935	+	0.284031i	−0.765839	−	0.643033i	$-0.777676\pi$
$941$	−11.9922	+	8.71286i	−0.390935	+	0.284031i	0.374903	+	0.927064i	$0.377676\pi$
$942$	−2.97038	−	9.14189i	−0.0967802	−	0.297859i
$943$	−12.4717	−	4.05231i	−0.406135	−	0.131961i
$944$	7.07370	−	9.73612i	0.230229	−	0.316884i
$945$	3.50226	+	3.91014i	0.113928	+	0.127197i
$946$	−1.68866	−	5.68124i	−0.0549030	−	0.184713i
$947$			5.22856i			0.169905i	0.996385	+	0.0849527i	$0.0270739\pi$
$947$			5.22856i			0.169905i	−0.996385	+	0.0849527i	$0.972926\pi$
$948$	21.7247	−	29.9015i	0.705585	−	0.971155i
$949$	2.51213	−	7.73154i	0.0815472	−	0.250976i
$950$	1.87259	−	3.23795i	0.0607550	−	0.105053i
$951$	−3.65145	−	5.02580i	−0.118407	−	0.162973i
$952$	1.64800	−	0.346428i	0.0534120	−	0.0112278i
$953$	−15.8323	−	48.7268i	−0.512859	−	1.57842i	−0.787144	−	0.616769i	$-0.788441\pi$
$953$	−15.8323	−	48.7268i	−0.512859	−	1.57842i	0.274286	−	0.961648i	$-0.411559\pi$
$954$	−5.26465	−	1.71059i	−0.170449	−	0.0553823i
$955$	17.2969	−	9.97794i	0.559715	−	0.322879i
$956$		−	7.83894i		−	0.253529i
$957$	40.5864	−	52.9961i	1.31197	−	1.71312i
$958$	13.5689			0.438392
$959$	−27.0272	−	47.0562i	−0.872754	−	1.51952i
$960$	3.94014	+	3.55033i	0.127168	+	0.114586i
$961$	2.91399	+	8.96834i	0.0939996	+	0.289301i
$962$	−2.66793	+	1.93836i	−0.0860175	+	0.0624954i
$963$	1.18674	−	0.862216i	0.0382421	−	0.0277845i
$964$	9.44917	+	29.0816i	0.304337	+	0.936654i
$965$	35.0890	+	31.6175i	1.12956	+	1.01780i
$966$	18.2542	+	31.7819i	0.587321	+	1.02257i
$967$	7.57412			0.243567			0.121784	−	0.992557i	$-0.461139\pi$
$967$	7.57412			0.243567			0.121784	+	0.992557i	$0.461139\pi$
$968$	−10.9860	−	0.555091i	−0.353103	−	0.0178413i
$969$		−	1.12940i		−	0.0362816i
$970$	23.4207	−	13.5105i	0.751994	−	0.433797i
$971$	−16.2356	−	5.27526i	−0.521025	−	0.169291i	0.0366854	−	0.999327i	$-0.488320\pi$
$971$	−16.2356	−	5.27526i	−0.521025	−	0.169291i	−0.557710	+	0.830036i	$0.688320\pi$
$972$	6.49405	+	19.9866i	0.208297	+	0.641072i
$973$	−2.79442	−	13.2934i	−0.0895849	−	0.426167i
$974$	−15.4804	−	21.3069i	−0.496023	−	0.682717i
$975$	−8.34947	−	4.82872i	−0.267397	−	0.154643i
$976$	3.62208	−	11.1476i	0.115940	−	0.356827i
$977$	5.94436	−	8.18171i	0.190177	−	0.261756i	−0.703272	−	0.710921i	$-0.748278\pi$
$977$	5.94436	−	8.18171i	0.190177	−	0.261756i	0.893449	+	0.449165i	$0.148278\pi$
$978$		−	39.4040i		−	1.26000i
$979$	20.5431	−	26.8243i	0.656560	−	0.857309i
$980$	−14.9097	+	4.76452i	−0.476273	+	0.152197i
$981$	3.61943	−	4.98172i	0.115560	−	0.159054i
$982$	28.3233	+	9.20280i	0.903833	+	0.293673i
$983$	−14.0688	−	43.2993i	−0.448725	−	1.38103i	−0.878347	−	0.478023i	$-0.841353\pi$
$983$	−14.0688	−	43.2993i	−0.448725	−	1.38103i	0.429623	−	0.903009i	$-0.358647\pi$
$984$	4.30856	−	3.13036i	0.137352	−	0.0997921i
$985$	6.33383	+	29.8520i	0.201812	+	0.951164i
$986$	1.66899	+	5.13661i	0.0531513	+	0.163583i
$987$	21.1300	+	19.1116i	0.672575	+	0.608330i
$988$	−0.357616	+	0.492217i	−0.0113773	+	0.0156595i
$989$			10.4369i			0.331875i
$990$	−19.3092	−	2.53086i	−0.613685	−	0.0804362i
$991$	−39.4532			−1.25327			−0.626635	−	0.779313i	$-0.715568\pi$
$991$	−39.4532			−1.25327			−0.626635	+	0.779313i	$0.715568\pi$
$992$	−2.72989	+	3.75737i	−0.0866741	+	0.119297i
$993$	−7.07758	+	21.7826i	−0.224600	+	0.691249i
$994$	−20.0376	−	2.15154i	−0.635554	−	0.0682427i
$995$	−12.6137	+	2.67629i	−0.399880	+	0.0848442i
$996$	10.3458	+	14.2398i	0.327820	+	0.451205i
$997$	−12.6405	+	4.10714i	−0.400328	+	0.130074i	−0.502259	−	0.864717i	$-0.667498\pi$
$997$	−12.6405	+	4.10714i	−0.400328	+	0.130074i	0.101932	+	0.994791i	$0.467498\pi$
$998$	4.08584	−	12.5749i	0.129335	−	0.398052i
$999$	2.11474	−	2.91069i	0.0669073	−	0.0920900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.4	yes	96
5.4	even	2		770.2.w.a.139.21	yes	96
7.6	odd	2	inner	770.2.w.b.139.21	yes	96
11.8	odd	10		770.2.w.a.349.4	yes	96
35.34	odd	2		770.2.w.a.139.4	✓	96
55.19	odd	10	inner	770.2.w.b.349.21	yes	96
77.41	even	10		770.2.w.a.349.21	yes	96
385.349	even	10	inner	770.2.w.b.349.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.4	✓	96	35.34	odd	2
770.2.w.a.139.21	yes	96	5.4	even	2
770.2.w.a.349.4	yes	96	11.8	odd	10
770.2.w.a.349.21	yes	96	77.41	even	10
770.2.w.b.139.4	yes	96	1.1	even	1	trivial
770.2.w.b.139.21	yes	96	7.6	odd	2	inner
770.2.w.b.349.4	yes	96	385.349	even	10	inner
770.2.w.b.349.21	yes	96	55.19	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.732958 + 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.464104 + 2.18737i) q^{5} +(-1.91891 + 1.39417i) q^{6} +(-2.63063 - 0.282464i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.732958 + 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.464104 + 2.18737i) q^{5} +(-1.91891 + 1.39417i) q^{6} +(-2.63063 - 0.282464i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +(-0.910238 + 2.04242i) q^{10} +(-2.63315 - 2.01656i) q^{11} -2.37190 q^{12} +(0.478040 - 0.657965i) q^{13} +(-1.96220 - 1.77476i) q^{14} +(-5.27447 - 0.556321i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.374125 + 0.514939i) q^{17} +(-0.811453 - 2.49739i) q^{18} +(-0.231172 + 0.711476i) q^{19} +(-1.93690 + 1.11733i) q^{20} +(2.56533 - 5.72717i) q^{21} +(-0.944954 - 3.17916i) q^{22} +5.84039i q^{23} +(-1.91891 - 1.39417i) q^{24} +(-4.56921 + 2.03034i) q^{25} +(0.773484 - 0.251320i) q^{26} +(-0.717833 + 0.521536i) q^{27} +(-0.544270 - 2.58916i) q^{28} +(8.07009 - 2.62213i) q^{29} +(-3.94014 - 3.55033i) q^{30} +(2.72989 - 3.75737i) q^{31} -1.00000 q^{32} +(6.47898 - 4.46183i) q^{33} +0.636500i q^{34} +(-0.603032 - 5.88527i) q^{35} +(0.811453 - 2.49739i) q^{36} +(-3.85636 + 1.25301i) q^{37} +(-0.605217 + 0.439716i) q^{38} +(1.13386 + 1.56063i) q^{39} +(-2.22373 - 0.234546i) q^{40} +(-0.693842 + 2.13543i) q^{41} +(5.44174 - 3.12552i) q^{42} +1.78702 q^{43} +(1.10418 - 3.12743i) q^{44} +(2.39021 - 5.36321i) q^{45} +(-3.43289 + 4.72497i) q^{46} +(-1.40295 + 4.31784i) q^{47} +(-0.732958 - 2.25581i) q^{48} +(6.84043 + 1.48612i) q^{49} +(-4.88998 - 1.04314i) q^{50} +(-1.43582 + 0.466527i) q^{51} +(0.773484 + 0.251320i) q^{52} +(1.23908 - 1.70545i) q^{53} -0.887291 q^{54} +(3.18893 - 6.69558i) q^{55} +(1.08155 - 2.41459i) q^{56} +(-1.43552 - 1.04296i) q^{57} +(8.07009 + 2.62213i) q^{58} +(-11.4455 + 3.71887i) q^{59} +(-1.10081 - 5.18824i) q^{60} +(-9.48273 + 6.88961i) q^{61} +(4.41705 - 1.43519i) q^{62} +(5.15256 + 4.66038i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.66108 + 0.740287i) q^{65} +(7.86420 + 0.198551i) q^{66} +7.11959i q^{67} +(-0.374125 + 0.514939i) q^{68} +(-13.1748 - 4.28076i) q^{69} +(2.97141 - 5.11573i) q^{70} +(6.16231 - 4.47718i) q^{71} +(2.12441 - 1.54347i) q^{72} +(9.50651 - 3.08885i) q^{73} +(-3.85636 - 1.25301i) q^{74} +(-1.23103 - 11.7954i) q^{75} -0.748090 q^{76} +(6.35723 + 6.04861i) q^{77} +1.92904i q^{78} +(-9.15919 + 12.6065i) q^{79} +(-1.66117 - 1.49683i) q^{80} +(-3.08470 - 9.49374i) q^{81} +(-1.81650 + 1.31977i) q^{82} +(-4.36182 - 6.00353i) q^{83} +(6.23959 + 0.669978i) q^{84} +(-0.952731 + 1.05734i) q^{85} +(1.44573 + 1.05039i) q^{86} +20.1265i q^{87} +(2.73155 - 1.88112i) q^{88} +10.1872i q^{89} +(5.08614 - 2.93400i) q^{90} +(-1.44340 + 1.59583i) q^{91} +(-5.55454 + 1.80478i) q^{92} +(6.47503 + 8.91211i) q^{93} +(-3.67298 + 2.66857i) q^{94} +(-1.66355 - 0.175462i) q^{95} +(0.732958 - 2.25581i) q^{96} +(-9.78252 - 7.10742i) q^{97} +(4.66050 + 5.22300i) q^{98} +(2.48137 + 8.34821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

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