LMFDB - Embedded newform 650.2.l.c.391.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (of order $5$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			391.3
Character	$\chi$	$=$	650.391
Dual form			650.2.l.c.261.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.102252 - 0.314699i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.08823 - 0.799566i) q^{5} +(-0.102252 + 0.314699i) q^{6} +4.37811 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.33847 - 1.69900i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.102252 - 0.314699i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.08823 - 0.799566i) q^{5} +(-0.102252 + 0.314699i) q^{6} +4.37811 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.33847 - 1.69900i) q^{9} +(-2.15938 - 0.580567i) q^{10} +(1.51720 + 1.10231i) q^{11} +(0.267699 - 0.194495i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(-3.54196 - 2.57339i) q^{14} +(-0.465148 - 0.575407i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.34596 + 4.14245i) q^{17} -2.89051 q^{18} +(-1.89158 + 5.82170i) q^{19} +(1.40573 + 1.73894i) q^{20} +(-0.447670 - 1.37779i) q^{21} +(-0.579519 - 1.78358i) q^{22} +(-3.00849 - 2.18580i) q^{23} -0.330894 q^{24} +(3.72139 - 3.33935i) q^{25} +1.00000 q^{26} +(-1.57688 - 1.14567i) q^{27} +(1.35291 + 4.16383i) q^{28} +(0.545397 + 1.67856i) q^{29} +(0.0380974 + 0.738921i) q^{30} +(-0.796389 + 2.45103i) q^{31} +1.00000 q^{32} +(0.191760 - 0.590176i) q^{33} +(3.52378 - 2.56017i) q^{34} +(9.14249 - 3.50059i) q^{35} +(2.33847 + 1.69900i) q^{36} +(1.42615 - 1.03616i) q^{37} +(4.95223 - 3.59801i) q^{38} +(0.267699 + 0.194495i) q^{39} +(-0.115135 - 2.23310i) q^{40} +(-3.91563 + 2.84487i) q^{41} +(-0.447670 + 1.37779i) q^{42} +0.0361818 q^{43} +(-0.579519 + 1.78358i) q^{44} +(3.52480 - 5.41766i) q^{45} +(1.14914 + 3.53669i) q^{46} +(-2.97527 - 9.15694i) q^{47} +(0.267699 + 0.194495i) q^{48} +12.1678 q^{49} +(-4.97349 + 0.514214i) q^{50} +1.44125 q^{51} +(-0.809017 - 0.587785i) q^{52} +(-3.60908 - 11.1076i) q^{53} +(0.602316 + 1.85374i) q^{54} +(4.04963 + 1.08877i) q^{55} +(1.35291 - 4.16383i) q^{56} +2.02550 q^{57} +(0.545397 - 1.67856i) q^{58} +(-1.63532 + 1.18813i) q^{59} +(0.403506 - 0.620193i) q^{60} +(-7.90062 - 5.74014i) q^{61} +(2.08497 - 1.51482i) q^{62} +(10.2381 - 7.43840i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.21944 + 1.87429i) q^{65} +(-0.502034 + 0.364749i) q^{66} +(-3.19527 + 9.83404i) q^{67} -4.35563 q^{68} +(-0.380245 + 1.17027i) q^{69} +(-9.45402 - 2.54178i) q^{70} +(0.130275 + 0.400945i) q^{71} +(-0.893216 - 2.74904i) q^{72} +(-0.159106 - 0.115597i) q^{73} -1.76282 q^{74} +(-1.43141 - 0.829663i) q^{75} -6.12130 q^{76} +(6.64247 + 4.82604i) q^{77} +(-0.102252 - 0.314699i) q^{78} +(5.21071 + 16.0369i) q^{79} +(-1.21944 + 1.87429i) q^{80} +(2.48035 - 7.63372i) q^{81} +4.83998 q^{82} +(4.27681 - 13.1627i) q^{83} +(1.17202 - 0.851520i) q^{84} +(0.501483 + 9.72656i) q^{85} +(-0.0292717 - 0.0212671i) q^{86} +(0.472473 - 0.343272i) q^{87} +(1.51720 - 1.10231i) q^{88} +(-0.610578 - 0.443611i) q^{89} +(-6.03604 + 2.31115i) q^{90} +(-3.54196 + 2.57339i) q^{91} +(1.14914 - 3.53669i) q^{92} +0.852771 q^{93} +(-2.97527 + 9.15694i) q^{94} +(0.704773 + 13.6695i) q^{95} +(-0.102252 - 0.314699i) q^{96} +(-5.22153 - 16.0702i) q^{97} +(-9.84398 - 7.15207i) q^{98} +5.42076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.102252	−	0.314699i	−0.0590352	−	0.181692i	0.917190	−	0.398450i	$-0.130452\pi$
$3$	−0.102252	−	0.314699i	−0.0590352	−	0.181692i	−0.976225	+	0.216758i	$0.930452\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	2.08823	−	0.799566i	0.933884	−	0.357577i
$5$	2.08823	−	0.799566i	0.933884	−	0.357577i
$6$	−0.102252	+	0.314699i	−0.0417442	+	0.128475i
$7$	4.37811			1.65477			0.827385	−	0.561636i	$-0.189828\pi$
$7$	4.37811			1.65477			0.827385	+	0.561636i	$0.189828\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.33847	−	1.69900i	0.779490	−	0.566333i
$10$	−2.15938	−	0.580567i	−0.682857	−	0.183591i
$11$	1.51720	+	1.10231i	0.457453	+	0.332359i	0.792531	−	0.609831i	$-0.208763\pi$
$11$	1.51720	+	1.10231i	0.457453	+	0.332359i	−0.335078	+	0.942190i	$0.608763\pi$
$12$	0.267699	−	0.194495i	0.0772781	−	0.0561458i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−3.54196	−	2.57339i	−0.946630	−	0.687767i
$15$	−0.465148	−	0.575407i	−0.120101	−	0.148569i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.34596	+	4.14245i	−0.326444	+	1.00469i	0.644341	+	0.764739i	$0.277132\pi$
$17$	−1.34596	+	4.14245i	−0.326444	+	1.00469i	−0.970785	+	0.239953i	$0.922868\pi$
$18$	−2.89051			−0.681299
$19$	−1.89158	+	5.82170i	−0.433959	+	1.33559i	0.460190	+	0.887820i	$0.347781\pi$
$19$	−1.89158	+	5.82170i	−0.433959	+	1.33559i	−0.894149	+	0.447769i	$0.852219\pi$
$20$	1.40573	+	1.73894i	0.314331	+	0.388839i
$21$	−0.447670	−	1.37779i	−0.0976897	−	0.300658i
$22$	−0.579519	−	1.78358i	−0.123554	−	0.380260i
$23$	−3.00849	−	2.18580i	−0.627314	−	0.455770i	0.228155	−	0.973625i	$-0.426731\pi$
$23$	−3.00849	−	2.18580i	−0.627314	−	0.455770i	−0.855469	+	0.517855i	$0.826731\pi$
$24$	−0.330894			−0.0675436
$25$	3.72139	−	3.33935i	0.744278	−	0.667870i
$26$	1.00000			0.196116
$27$	−1.57688	−	1.14567i	−0.303472	−	0.220485i
$28$	1.35291	+	4.16383i	0.255676	+	0.786890i
$29$	0.545397	+	1.67856i	0.101278	+	0.311701i	0.988839	−	0.148989i	$-0.0476020\pi$
$29$	0.545397	+	1.67856i	0.101278	+	0.311701i	−0.887561	+	0.460690i	$0.847602\pi$
$30$	0.0380974	+	0.738921i	0.00695560	+	0.134908i
$31$	−0.796389	+	2.45103i	−0.143036	+	0.440219i	−0.996753	−	0.0805178i	$-0.974343\pi$
$31$	−0.796389	+	2.45103i	−0.143036	+	0.440219i	0.853717	+	0.520737i	$0.174343\pi$
$32$	1.00000			0.176777
$33$	0.191760	−	0.590176i	0.0333811	−	0.102736i
$34$	3.52378	−	2.56017i	0.604323	−	0.439066i
$35$	9.14249	−	3.50059i	1.54536	−	0.591707i
$36$	2.33847	+	1.69900i	0.389745	+	0.283166i
$37$	1.42615	−	1.03616i	0.234457	−	0.170343i	−0.464353	−	0.885650i	$-0.653713\pi$
$37$	1.42615	−	1.03616i	0.234457	−	0.170343i	0.698810	+	0.715307i	$0.253713\pi$
$38$	4.95223	−	3.59801i	0.803358	−	0.583674i
$39$	0.267699	+	0.194495i	0.0428662	+	0.0311441i
$40$	−0.115135	−	2.23310i	−0.0182044	−	0.353084i
$41$	−3.91563	+	2.84487i	−0.611518	+	0.444294i	−0.849949	−	0.526866i	$-0.823367\pi$
$41$	−3.91563	+	2.84487i	−0.611518	+	0.444294i	0.238431	+	0.971160i	$0.423367\pi$
$42$	−0.447670	+	1.37779i	−0.0690770	+	0.212597i
$43$	0.0361818			0.00551767			0.00275884	−	0.999996i	$-0.499122\pi$
$43$	0.0361818			0.00551767			0.00275884	+	0.999996i	$0.499122\pi$
$44$	−0.579519	+	1.78358i	−0.0873658	+	0.268884i
$45$	3.52480	−	5.41766i	0.525446	−	0.807617i
$46$	1.14914	+	3.53669i	0.169432	+	0.521457i
$47$	−2.97527	−	9.15694i	−0.433988	−	1.33568i	−0.894120	−	0.447827i	$-0.852198\pi$
$47$	−2.97527	−	9.15694i	−0.433988	−	1.33568i	0.460133	−	0.887850i	$-0.347802\pi$
$48$	0.267699	+	0.194495i	0.0386391	+	0.0280729i
$49$	12.1678			1.73826
$50$	−4.97349	+	0.514214i	−0.703357	+	0.0727209i
$51$	1.44125			0.201816
$52$	−0.809017	−	0.587785i	−0.112190	−	0.0815111i
$53$	−3.60908	−	11.1076i	−0.495745	−	1.52575i	−0.815792	−	0.578345i	$-0.803699\pi$
$53$	−3.60908	−	11.1076i	−0.495745	−	1.52575i	0.320047	−	0.947402i	$-0.396301\pi$
$54$	0.602316	+	1.85374i	0.0819649	+	0.252262i
$55$	4.04963	+	1.08877i	0.546052	+	0.146810i
$56$	1.35291	−	4.16383i	0.180790	−	0.556415i
$57$	2.02550			0.268284
$58$	0.545397	−	1.67856i	0.0716141	−	0.220406i
$59$	−1.63532	+	1.18813i	−0.212900	+	0.154681i	−0.689125	−	0.724643i	$-0.742005\pi$
$59$	−1.63532	+	1.18813i	−0.212900	+	0.154681i	0.476225	+	0.879324i	$0.342005\pi$
$60$	0.403506	−	0.620193i	0.0520923	−	0.0800665i
$61$	−7.90062	−	5.74014i	−1.01157	−	0.734949i	−0.0470329	−	0.998893i	$-0.514977\pi$
$61$	−7.90062	−	5.74014i	−1.01157	−	0.734949i	−0.964538	+	0.263944i	$0.914977\pi$
$62$	2.08497	−	1.51482i	0.264792	−	0.192383i
$63$	10.2381	−	7.43840i	1.28988	−	0.937150i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.21944	+	1.87429i	−0.151253	+	0.232477i
$66$	−0.502034	+	0.364749i	−0.0617961	+	0.0448975i
$67$	−3.19527	+	9.83404i	−0.390365	+	1.20142i	0.542148	+	0.840283i	$0.317611\pi$
$67$	−3.19527	+	9.83404i	−0.390365	+	1.20142i	−0.932513	+	0.361136i	$0.882389\pi$
$68$	−4.35563			−0.528197
$69$	−0.380245	+	1.17027i	−0.0457761	+	0.140884i
$70$	−9.45402	−	2.54178i	−1.12997	−	0.303801i
$71$	0.130275	+	0.400945i	0.0154608	+	0.0475834i	0.958489	−	0.285129i	$-0.0920363\pi$
$71$	0.130275	+	0.400945i	0.0154608	+	0.0475834i	−0.943028	+	0.332712i	$0.892036\pi$
$72$	−0.893216	−	2.74904i	−0.105267	−	0.323977i
$73$	−0.159106	−	0.115597i	−0.0186219	−	0.0135296i	0.578435	−	0.815728i	$-0.303664\pi$
$73$	−0.159106	−	0.115597i	−0.0186219	−	0.0135296i	−0.597057	+	0.802199i	$0.703664\pi$
$74$	−1.76282			−0.204923
$75$	−1.43141	−	0.829663i	−0.165285	−	0.0958013i
$76$	−6.12130			−0.702161
$77$	6.64247	+	4.82604i	0.756980	+	0.549978i
$78$	−0.102252	−	0.314699i	−0.0115778	−	0.0356327i
$79$	5.21071	+	16.0369i	0.586251	+	1.80429i	0.594189	+	0.804325i	$0.297473\pi$
$79$	5.21071	+	16.0369i	0.586251	+	1.80429i	−0.00793845	+	0.999968i	$0.502527\pi$
$80$	−1.21944	+	1.87429i	−0.136337	+	0.209552i
$81$	2.48035	−	7.63372i	0.275594	−	0.848191i
$82$	4.83998			0.534486
$83$	4.27681	−	13.1627i	0.469441	−	1.44479i	−0.383870	−	0.923387i	$-0.625409\pi$
$83$	4.27681	−	13.1627i	0.469441	−	1.44479i	0.853311	−	0.521403i	$-0.174591\pi$
$84$	1.17202	−	0.851520i	0.127877	−	0.0929084i
$85$	0.501483	+	9.72656i	0.0543935	+	1.05499i
$86$	−0.0292717	−	0.0212671i	−0.00315645	−	0.00229329i
$87$	0.472473	−	0.343272i	0.0506545	−	0.0368026i
$88$	1.51720	−	1.10231i	0.161734	−	0.117507i
$89$	−0.610578	−	0.443611i	−0.0647211	−	0.0470226i	0.554954	−	0.831881i	$-0.312736\pi$
$89$	−0.610578	−	0.443611i	−0.0647211	−	0.0470226i	−0.619675	+	0.784858i	$0.712736\pi$
$90$	−6.03604	+	2.31115i	−0.636255	+	0.243617i
$91$	−3.54196	+	2.57339i	−0.371299	+	0.269764i
$92$	1.14914	−	3.53669i	0.119806	−	0.368726i
$93$	0.852771			0.0884283
$94$	−2.97527	+	9.15694i	−0.306876	+	0.944466i
$95$	0.704773	+	13.6695i	0.0723081	+	1.40246i
$96$	−0.102252	−	0.314699i	−0.0104361	−	0.0321189i
$97$	−5.22153	−	16.0702i	−0.530166	−	1.63168i	−0.753868	−	0.657026i	$-0.771814\pi$
$97$	−5.22153	−	16.0702i	−0.530166	−	1.63168i	0.223702	−	0.974658i	$-0.428186\pi$
$98$	−9.84398	−	7.15207i	−0.994392	−	0.722468i
$99$	5.42076			0.544806
$100$	4.32588	+	2.50733i	0.432588	+	0.250733i
$101$	−16.0072			−1.59278			−0.796389	−	0.604784i	$-0.793259\pi$
$101$	−16.0072			−1.59278			−0.796389	+	0.604784i	$0.793259\pi$
$102$	−1.16600	−	0.847147i	−0.115451	−	0.0838801i
$103$	−1.88031	−	5.78700i	−0.185272	−	0.570210i	0.814681	−	0.579910i	$-0.196912\pi$
$103$	−1.88031	−	5.78700i	−0.185272	−	0.570210i	−0.999953	+	0.00970009i	$0.996912\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$	−2.03647	−	2.51919i	−0.198739	−	0.245848i
$106$	−3.60908	+	11.1076i	−0.350545	+	1.07887i
$107$	2.13169			0.206079			0.103039	−	0.994677i	$-0.467143\pi$
$107$	2.13169			0.206079			0.103039	+	0.994677i	$0.467143\pi$
$108$	0.602316	−	1.85374i	0.0579579	−	0.178376i
$109$	6.36309	−	4.62306i	0.609474	−	0.442809i	−0.239755	−	0.970833i	$-0.577067\pi$
$109$	6.36309	−	4.62306i	0.609474	−	0.442809i	0.849229	+	0.528025i	$0.177067\pi$
$110$	−2.63626	−	3.26115i	−0.251357	−	0.310939i
$111$	−0.471905	−	0.342859i	−0.0447912	−	0.0325427i
$112$	−3.54196	+	2.57339i	−0.334684	+	0.243162i
$113$	−5.99453	+	4.35528i	−0.563918	+	0.409710i	−0.832891	−	0.553438i	$-0.813316\pi$
$113$	−5.99453	+	4.35528i	−0.563918	+	0.409710i	0.268973	+	0.963148i	$0.413316\pi$
$114$	−1.63867	−	1.19056i	−0.153475	−	0.111506i
$115$	−8.03010	−	2.15895i	−0.748811	−	0.201324i
$116$	−1.42787	+	1.03741i	−0.132574	+	0.0963208i
$117$	−0.893216	+	2.74904i	−0.0825779	+	0.254149i
$118$	2.02136			0.186081
$119$	−5.89277	+	18.1361i	−0.540189	+	1.66253i
$120$	−0.690983	+	0.264572i	−0.0630778	+	0.0241520i
$121$	−2.31238	−	7.11677i	−0.210216	−	0.646979i
$122$	3.01777	+	9.28774i	0.273216	+	0.840872i
$123$	1.29566	+	0.941351i	0.116826	+	0.0848788i
$124$	−2.57717			−0.231437
$125$	5.10108	−	9.94882i	0.456254	−	0.889850i
$126$	−12.6550			−1.12739
$127$	15.4181	+	11.2019i	1.36814	+	0.994011i	0.997880	+	0.0650820i	$0.0207309\pi$
$127$	15.4181	+	11.2019i	1.36814	+	0.994011i	0.370258	+	0.928929i	$0.379269\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.00369966	−	0.0113864i	−0.000325737	−	0.00100252i
$130$	2.08823	−	0.799566i	0.183150	−	0.0701266i
$131$	−2.80183	+	8.62315i	−0.244797	+	0.753408i	0.750873	+	0.660447i	$0.229633\pi$
$131$	−2.80183	+	8.62315i	−0.244797	+	0.753408i	−0.995670	+	0.0929612i	$0.970367\pi$
$132$	0.620548			0.0540117
$133$	−8.28156	+	25.4880i	−0.718102	+	2.21009i
$134$	8.36533	−	6.07777i	0.722655	−	0.525039i
$135$	−4.20894	−	1.13160i	−0.362248	−	0.0973930i
$136$	3.52378	+	2.56017i	0.302161	+	0.219533i
$137$	16.8571	−	12.2474i	1.44020	−	1.04637i	0.452200	−	0.891916i	$-0.350639\pi$
$137$	16.8571	−	12.2474i	1.44020	−	1.04637i	0.988001	−	0.154451i	$-0.0493608\pi$
$138$	0.995493	−	0.723268i	0.0847420	−	0.0615687i
$139$	11.5950	+	8.42424i	0.983473	+	0.714535i	0.958482	−	0.285153i	$-0.0920444\pi$
$139$	11.5950	+	8.42424i	0.983473	+	0.714535i	0.0249908	+	0.999688i	$0.492044\pi$
$140$	6.15444	+	7.61328i	0.520145	+	0.643440i
$141$	−2.57746	+	1.87263i	−0.217061	+	0.157704i
$142$	0.130275	−	0.400945i	0.0109324	−	0.0336466i
$143$	−1.87536			−0.156826
$144$	−0.893216	+	2.74904i	−0.0744347	+	0.229086i
$145$	2.48103	+	3.06913i	0.206038	+	0.254878i
$146$	0.0607730	+	0.187040i	0.00502961	+	0.0154795i
$147$	−1.24419	−	3.82921i	−0.102619	−	0.315828i
$148$	1.42615	+	1.03616i	0.117229	+	0.0851716i
$149$	−10.4897			−0.859353			−0.429676	−	0.902983i	$-0.641372\pi$
$149$	−10.4897			−0.859353			−0.429676	+	0.902983i	$0.641372\pi$
$150$	0.670372	+	1.51257i	0.0547357	+	0.123501i
$151$	−16.3972			−1.33438			−0.667192	−	0.744885i	$-0.732504\pi$
$151$	−16.3972			−1.33438			−0.667192	+	0.744885i	$0.732504\pi$
$152$	4.95223	+	3.59801i	0.401679	+	0.291837i
$153$	3.89052	+	11.9738i	0.314530	+	0.968023i
$154$	−2.53720	−	7.80869i	−0.204453	−	0.629242i
$155$	0.296721	+	5.75508i	0.0238332	+	0.462259i
$156$	−0.102252	+	0.314699i	−0.00818671	+	0.0251961i
$157$	−13.5841			−1.08413			−0.542065	−	0.840336i	$-0.682357\pi$
$157$	−13.5841			−1.08413			−0.542065	+	0.840336i	$0.682357\pi$
$158$	5.21071	−	16.0369i	0.414542	−	1.27583i
$159$	−3.12652	+	2.27155i	−0.247949	+	0.180146i
$160$	2.08823	−	0.799566i	0.165089	−	0.0632112i
$161$	−13.1715	−	9.56966i	−1.03806	−	0.754195i
$162$	−6.49363	+	4.71790i	−0.510188	+	0.370673i
$163$	−16.3038	+	11.8454i	−1.27701	+	0.927804i	−0.999458	−	0.0329055i	$-0.989524\pi$
$163$	−16.3038	+	11.8454i	−1.27701	+	0.927804i	−0.277555	+	0.960710i	$0.589524\pi$
$164$	−3.91563	−	2.84487i	−0.305759	−	0.222147i
$165$	−0.0714465	−	1.38575i	−0.00556210	−	0.107880i
$166$	−11.1968	+	8.13497i	−0.869042	+	0.631396i
$167$	1.88683	−	5.80706i	0.146007	−	0.449364i	−0.851132	−	0.524952i	$-0.824083\pi$
$167$	1.88683	−	5.80706i	0.146007	−	0.449364i	0.997139	+	0.0755879i	$0.0240834\pi$
$168$	−1.44869			−0.111769
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	5.31142	−	8.16372i	0.407367	−	0.626128i
$171$	5.46764	+	16.8277i	0.418121	+	1.28684i
$172$	0.0111808	+	0.0344109i	0.000852527	+	0.00262381i
$173$	−20.9452	−	15.2175i	−1.59243	−	1.15697i	−0.900366	−	0.435133i	$-0.856701\pi$
$173$	−20.9452	−	15.2175i	−1.59243	−	1.15697i	−0.692064	−	0.721836i	$-0.743299\pi$
$174$	−0.584009			−0.0442736
$175$	16.2926	−	14.6200i	1.23161	−	1.10517i
$176$	−1.87536			−0.141361
$177$	0.541117	+	0.393144i	0.0406728	+	0.0295505i
$178$	0.233220	+	0.717777i	0.0174806	+	0.0537997i
$179$	−0.400974	−	1.23407i	−0.0299702	−	0.0922388i	0.934953	−	0.354773i	$-0.115442\pi$
$179$	−0.400974	−	1.23407i	−0.0299702	−	0.0922388i	−0.964923	+	0.262534i	$0.915442\pi$
$180$	6.24172	+	1.67813i	0.465230	+	0.125081i
$181$	−4.38426	+	13.4934i	−0.325880	+	1.00295i	0.645163	+	0.764045i	$0.276790\pi$
$181$	−4.38426	+	13.4934i	−0.325880	+	1.00295i	−0.971042	+	0.238909i	$0.923210\pi$
$182$	4.37811			0.324527
$183$	−0.998563	+	3.07326i	−0.0738159	+	0.227182i
$184$	−3.00849	+	2.18580i	−0.221789	+	0.161139i
$185$	2.14965	−	3.30403i	0.158045	−	0.242917i
$186$	−0.689906	−	0.501246i	−0.0505864	−	0.0367532i
$187$	−6.60836	+	4.80126i	−0.483251	+	0.351103i
$188$	7.78936	−	5.65930i	0.568097	−	0.412747i
$189$	−6.90377	−	5.01588i	−0.502176	−	0.364852i
$190$	7.46454	−	11.4731i	0.541535	−	0.832346i
$191$	9.14956	−	6.64755i	0.662039	−	0.481000i	−0.205312	−	0.978697i	$-0.565821\pi$
$191$	9.14956	−	6.64755i	0.662039	−	0.481000i	0.867351	+	0.497697i	$0.165821\pi$
$192$	−0.102252	+	0.314699i	−0.00737940	+	0.0227115i
$193$	6.52838			0.469923			0.234961	−	0.972005i	$-0.424504\pi$
$193$	6.52838			0.469923			0.234961	+	0.972005i	$0.424504\pi$
$194$	−5.22153	+	16.0702i	−0.374884	+	1.15377i
$195$	0.714528	+	0.192106i	0.0511684	+	0.0137570i
$196$	3.76007	+	11.5723i	0.268576	+	0.826592i
$197$	1.81586	+	5.58863i	0.129374	+	0.398174i	0.994673	−	0.103084i	$-0.0328710\pi$
$197$	1.81586	+	5.58863i	0.129374	+	0.398174i	−0.865298	+	0.501257i	$0.832871\pi$
$198$	−4.38548	−	3.18624i	−0.311663	−	0.226436i
$199$	0.626721			0.0444271			0.0222135	−	0.999753i	$-0.492929\pi$
$199$	0.626721			0.0444271			0.0222135	+	0.999753i	$0.492929\pi$
$200$	−2.02594	−	4.57117i	−0.143256	−	0.323230i
$201$	3.42149			0.241333
$202$	12.9501	+	9.40881i	0.911167	+	0.662002i
$203$	2.38781	+	7.34891i	0.167591	+	0.515793i
$204$	0.445372	+	1.37071i	0.0311823	+	0.0959691i
$205$	−5.90206	+	9.07153i	−0.412218	+	0.633583i
$206$	−1.88031	+	5.78700i	−0.131007	+	0.403199i
$207$	−10.7489			−0.747103
$208$	0.309017	−	0.951057i	0.0214265	−	0.0659439i
$209$	−9.28724	+	6.74757i	−0.642412	+	0.466739i
$210$	0.166794	+	3.23508i	0.0115099	+	0.223241i
$211$	5.41510	+	3.93430i	0.372791	+	0.270849i	0.758367	−	0.651827i	$-0.225997\pi$
$211$	5.41510	+	3.93430i	0.372791	+	0.270849i	−0.385576	+	0.922676i	$0.625997\pi$
$212$	9.44869	−	6.86488i	0.648939	−	0.471482i
$213$	0.112856	−	0.0819949i	0.00773278	−	0.00561820i
$214$	−1.72458	−	1.25298i	−0.117890	−	0.0856518i
$215$	0.0755558	−	0.0289297i	0.00515287	−	0.00197299i
$216$	−1.57688	+	1.14567i	−0.107293	+	0.0779532i
$217$	−3.48668	+	10.7309i	−0.236691	+	0.728460i
$218$	−7.86522			−0.532700
$219$	−0.0201095	+	0.0618905i	−0.00135887	+	0.00418218i
$220$	0.215919	+	4.18788i	0.0145573	+	0.282347i
$221$	−1.34596	−	4.14245i	−0.0905393	−	0.278651i
$222$	0.180252	+	0.554757i	0.0120977	+	0.0372329i
$223$	−6.41770	−	4.66273i	−0.429761	−	0.312240i	0.351792	−	0.936078i	$-0.385572\pi$
$223$	−6.41770	−	4.66273i	−0.429761	−	0.312240i	−0.781553	+	0.623838i	$0.785572\pi$
$224$	4.37811			0.292525
$225$	3.02881	−	14.1316i	0.201920	−	0.942107i
$226$	7.40964			0.492882
$227$	−4.53043	−	3.29155i	−0.300695	−	0.218468i	0.427198	−	0.904158i	$-0.359501\pi$
$227$	−4.53043	−	3.29155i	−0.300695	−	0.218468i	−0.727894	+	0.685690i	$0.759501\pi$
$228$	0.625915	+	1.92637i	0.0414522	+	0.127577i
$229$	0.641927	+	1.97565i	0.0424197	+	0.130554i	0.970024	−	0.243011i	$-0.0781351\pi$
$229$	0.641927	+	1.97565i	0.0424197	+	0.130554i	−0.927604	+	0.373565i	$0.878135\pi$
$230$	5.22749	+	6.46661i	0.344690	+	0.426395i
$231$	0.839545	−	2.58385i	0.0552380	−	0.170005i
$232$	1.76494			0.115874
$233$	−6.14734	+	18.9196i	−0.402726	+	1.23946i	0.520054	+	0.854134i	$0.325912\pi$
$233$	−6.14734	+	18.9196i	−0.402726	+	1.23946i	−0.922779	+	0.385329i	$0.874088\pi$
$234$	2.33847	−	1.69900i	0.152871	−	0.111067i
$235$	−13.5346	−	16.7428i	−0.882901	−	1.09218i
$236$	−1.63532	−	1.18813i	−0.106450	−	0.0773404i
$237$	4.51400	−	3.27961i	0.293216	−	0.213034i
$238$	15.4275	−	11.2087i	1.00001	−	0.726553i
$239$	1.05997	+	0.770113i	0.0685637	+	0.0498145i	0.621539	−	0.783383i	$-0.286508\pi$
$239$	1.05997	+	0.770113i	0.0685637	+	0.0498145i	−0.552975	+	0.833198i	$0.686508\pi$
$240$	0.714528	+	0.192106i	0.0461226	+	0.0124004i
$241$	4.50927	−	3.27618i	0.290468	−	0.211037i	−0.433002	−	0.901393i	$-0.642546\pi$
$241$	4.50927	−	3.27618i	0.290468	−	0.211037i	0.723470	+	0.690356i	$0.242546\pi$
$242$	−2.31238	+	7.11677i	−0.148645	+	0.457483i
$243$	−8.50336			−0.545491
$244$	3.01777	−	9.28774i	0.193193	−	0.594586i
$245$	25.4092	−	9.72898i	1.62333	−	0.621562i
$246$	−0.494898	−	1.52314i	−0.0315535	−	0.0971118i
$247$	−1.89158	−	5.82170i	−0.120359	−	0.370426i
$248$	2.08497	+	1.51482i	0.132396	+	0.0961913i
$249$	−4.57959			−0.290220
$250$	−9.97463	+	5.05043i	−0.630851	+	0.319417i
$251$	22.2328			1.40332			0.701660	−	0.712512i	$-0.252443\pi$
$251$	22.2328			1.40332			0.701660	+	0.712512i	$0.252443\pi$
$252$	10.2381	+	7.43840i	0.644938	+	0.468575i
$253$	−2.15506	−	6.63259i	−0.135487	−	0.416987i
$254$	−5.88920	−	18.1251i	−0.369522	−	1.13727i
$255$	3.00966	−	1.15238i	0.188473	−	0.0721646i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.58877			−0.410996			−0.205498	−	0.978658i	$-0.565881\pi$
$257$	−6.58877			−0.410996			−0.205498	+	0.978658i	$0.565881\pi$
$258$	−0.00369966	+	0.0113864i	−0.000230331	+	0.000708886i
$259$	6.24383	−	4.53641i	0.387973	−	0.281879i
$260$	−2.15938	−	0.580567i	−0.133919	−	0.0360052i
$261$	4.12726	+	2.99863i	0.255471	+	0.185611i
$262$	7.33529	−	5.32940i	0.453176	−	0.329252i
$263$	−3.45971	+	2.51363i	−0.213335	+	0.154997i	−0.689321	−	0.724456i	$-0.742091\pi$
$263$	−3.45971	+	2.51363i	−0.213335	+	0.154997i	0.475986	+	0.879453i	$0.342091\pi$
$264$	−0.502034	−	0.364749i	−0.0308980	−	0.0224487i
$265$	−16.4178	−	20.3095i	−1.00854	−	1.24760i
$266$	21.6814	−	15.7525i	1.32937	−	0.965845i
$267$	−0.0771712	+	0.237508i	−0.00472280	+	0.0145353i
$268$	−10.3401			−0.631623
$269$	−0.410048	+	1.26200i	−0.0250011	+	0.0769454i	−0.962779	−	0.270291i	$-0.912880\pi$
$269$	−0.410048	+	1.26200i	−0.0250011	+	0.0769454i	0.937777	+	0.347237i	$0.112880\pi$
$270$	2.73996	+	3.38944i	0.166749	+	0.206275i
$271$	−9.06684	−	27.9049i	−0.550772	−	1.69510i	−0.706856	−	0.707357i	$-0.749887\pi$
$271$	−9.06684	−	27.9049i	−0.550772	−	1.69510i	0.156085	−	0.987744i	$-0.450113\pi$
$272$	−1.34596	−	4.14245i	−0.0816110	−	0.251173i
$273$	1.17202	+	0.851520i	0.0709337	+	0.0515363i
$274$	−20.8365			−1.25878
$275$	9.32710	−	0.964339i	0.562445	−	0.0581518i
$276$	−1.23050			−0.0740672
$277$	21.2638	+	15.4491i	1.27762	+	0.928245i	0.999478	−	0.0322948i	$-0.0102815\pi$
$277$	21.2638	+	15.4491i	1.27762	+	0.928245i	0.278142	+	0.960540i	$0.410282\pi$
$278$	−4.42889	−	13.6307i	−0.265627	−	0.817516i
$279$	2.30197	+	7.08474i	0.137815	+	0.424152i
$280$	−0.504071	−	9.77676i	−0.0301240	−	0.584273i
$281$	8.28790	−	25.5075i	0.494415	−	1.52165i	−0.323452	−	0.946245i	$-0.604843\pi$
$281$	8.28790	−	25.5075i	0.494415	−	1.52165i	0.817867	−	0.575408i	$-0.195157\pi$
$282$	3.18591			0.189718
$283$	−3.40341	+	10.4746i	−0.202312	+	0.622651i	0.797502	+	0.603317i	$0.206155\pi$
$283$	−3.40341	+	10.4746i	−0.202312	+	0.622651i	−0.999813	+	0.0193340i	$0.993845\pi$
$284$	−0.341064	+	0.247798i	−0.0202384	+	0.0147041i
$285$	4.22971	−	1.61952i	0.250546	−	0.0959323i
$286$	1.51720	+	1.10231i	0.0897140	+	0.0651810i
$287$	−17.1430	+	12.4551i	−1.01192	+	0.735204i
$288$	2.33847	−	1.69900i	0.137796	−	0.100114i
$289$	−1.59497	−	1.15881i	−0.0938217	−	0.0681655i
$290$	−0.203206	−	3.94129i	−0.0119327	−	0.231441i
$291$	−4.52338	+	3.28643i	−0.265165	+	0.192654i
$292$	0.0607730	−	0.187040i	0.00355647	−	0.0109457i
$293$	−4.29176			−0.250727			−0.125364	−	0.992111i	$-0.540010\pi$
$293$	−4.29176			−0.250727			−0.125364	+	0.992111i	$0.540010\pi$
$294$	−1.24419	+	3.82921i	−0.0725623	+	0.223324i
$295$	−2.46493	+	3.78862i	−0.143514	+	0.220582i
$296$	−0.544740	−	1.67654i	−0.0316624	−	0.0974468i
$297$	−1.12956	−	3.47644i	−0.0655439	−	0.201723i
$298$	8.48637	+	6.16571i	0.491602	+	0.357170i
$299$	3.71870			0.215058
$300$	0.346726	−	1.61773i	0.0200183	−	0.0933999i
$301$	0.158408			0.00913048
$302$	13.2656	+	9.63803i	0.763350	+	0.554606i
$303$	1.63677	+	5.03746i	0.0940301	+	0.289395i
$304$	−1.89158	−	5.82170i	−0.108490	−	0.333897i
$305$	−21.0879	−	5.66965i	−1.20749	−	0.324643i
$306$	3.89052	−	11.9738i	0.222406	−	0.684496i
$307$	−2.37153			−0.135351			−0.0676753	−	0.997707i	$-0.521558\pi$
$307$	−2.37153			−0.135351			−0.0676753	+	0.997707i	$0.521558\pi$
$308$	−2.53720	+	7.80869i	−0.144570	+	0.444942i
$309$	−1.62890	+	1.18346i	−0.0926649	+	0.0673250i
$310$	3.14270	−	4.83037i	0.178493	−	0.274346i
$311$	14.1480	+	10.2791i	0.802257	+	0.582874i	0.911575	−	0.411133i	$-0.134867\pi$
$311$	14.1480	+	10.2791i	0.802257	+	0.582874i	−0.109318	+	0.994007i	$0.534867\pi$
$312$	0.267699	−	0.194495i	0.0151555	−	0.0110111i
$313$	19.7485	−	14.3481i	1.11625	−	0.811004i	0.132614	−	0.991168i	$-0.457663\pi$
$313$	19.7485	−	14.3481i	1.11625	−	0.811004i	0.983637	+	0.180164i	$0.0576628\pi$
$314$	10.9898	+	7.98454i	0.620189	+	0.450594i
$315$	15.4319	−	23.7191i	0.869492	−	1.33642i
$316$	−13.6418	+	9.91136i	−0.767412	+	0.557557i
$317$	9.30731	−	28.6450i	0.522751	−	1.60886i	−0.245971	−	0.969277i	$-0.579107\pi$
$317$	9.30731	−	28.6450i	0.522751	−	1.60886i	0.768721	−	0.639584i	$-0.220893\pi$
$318$	3.86459			0.216716
$319$	−1.02282	+	3.14791i	−0.0572668	+	0.176249i
$320$	−2.15938	−	0.580567i	−0.120713	−	0.0324547i
$321$	−0.217970	−	0.670842i	−0.0121659	−	0.0374428i
$322$	5.03107	+	15.4840i	0.280370	+	0.862891i
$323$	−21.5701	−	15.6716i	−1.20019	−	0.871990i
$324$	8.02657			0.445920
$325$	−1.04785	+	4.88897i	−0.0581240	+	0.271191i
$326$	20.1526			1.11615
$327$	−2.10551	−	1.52974i	−0.116435	−	0.0845951i
$328$	1.49564	+	4.60309i	0.0825827	+	0.254163i
$329$	−13.0261	−	40.0901i	−0.718149	−	2.21024i
$330$	−0.756720	+	1.16309i	−0.0416560	+	0.0640258i
$331$	−8.98068	+	27.6397i	−0.493623	+	1.51921i	0.325470	+	0.945553i	$0.394478\pi$
$331$	−8.98068	+	27.6397i	−0.493623	+	1.51921i	−0.819092	+	0.573662i	$0.805522\pi$
$332$	13.8400			0.759571
$333$	1.57458	−	4.84605i	0.0862863	−	0.265562i
$334$	−4.93978	+	3.58896i	−0.270293	+	0.196379i
$335$	1.19051	+	23.0905i	0.0650442	+	1.26157i
$336$	1.17202	+	0.851520i	0.0639387	+	0.0464542i
$337$	−7.39063	+	5.36961i	−0.402593	+	0.292501i	−0.770597	−	0.637323i	$-0.780042\pi$
$337$	−7.39063	+	5.36961i	−0.402593	+	0.292501i	0.368003	+	0.929825i	$0.380042\pi$
$338$	−0.809017	+	0.587785i	−0.0440047	+	0.0319713i
$339$	1.98356	+	1.44114i	0.107732	+	0.0782718i
$340$	−9.09554	+	3.48261i	−0.493275	+	0.188871i
$341$	−3.91009	+	2.84084i	−0.211743	+	0.153840i
$342$	5.46764	−	16.8277i	0.295656	−	0.909936i
$343$	22.6253			1.22165
$344$	0.0111808	−	0.0344109i	0.000602828	−	0.00185531i
$345$	0.141673	+	2.74783i	0.00762740	+	0.147938i
$346$	8.00034	+	24.6225i	0.430101	+	1.32371i
$347$	1.82016	+	5.60189i	0.0977116	+	0.300725i	0.987951	−	0.154768i	$-0.0494630\pi$
$347$	1.82016	+	5.60189i	0.0977116	+	0.300725i	−0.890239	+	0.455493i	$0.849463\pi$
$348$	0.472473	+	0.343272i	0.0253272	+	0.0184013i
$349$	26.0491			1.39438			0.697189	−	0.716887i	$-0.254434\pi$
$349$	26.0491			1.39438			0.697189	+	0.716887i	$0.254434\pi$
$350$	−21.7745	+	2.25129i	−1.16389	+	0.120336i
$351$	1.94914			0.104037
$352$	1.51720	+	1.10231i	0.0808671	+	0.0587534i
$353$	6.93554	+	21.3454i	0.369141	+	1.13610i	0.947347	+	0.320209i	$0.103753\pi$
$353$	6.93554	+	21.3454i	0.369141	+	1.13610i	−0.578205	+	0.815891i	$0.696247\pi$
$354$	−0.206688	−	0.636121i	−0.0109854	−	0.0338095i
$355$	0.592626	+	0.733101i	0.0314533	+	0.0389090i
$356$	0.233220	−	0.717777i	0.0123606	−	0.0380421i
$357$	6.30996			0.333959
$358$	−0.400974	+	1.23407i	−0.0211921	+	0.0652227i
$359$	21.7120	−	15.7747i	1.14592	−	0.832558i	0.157985	−	0.987442i	$-0.449500\pi$
$359$	21.7120	−	15.7747i	1.14592	−	0.832558i	0.987933	+	0.154884i	$0.0495004\pi$
$360$	−4.06328	−	5.02643i	−0.214153	−	0.264916i
$361$	−14.9427	−	10.8565i	−0.786460	−	0.571397i
$362$	11.4781	−	8.33936i	0.603278	−	0.438307i
$363$	−2.00320	+	1.45541i	−0.105141	+	0.0763891i
$364$	−3.54196	−	2.57339i	−0.185649	−	0.134882i
$365$	−0.424677	−	0.114178i	−0.0222286	−	0.00597633i
$366$	2.61427	−	1.89938i	0.136650	−	0.0992822i
$367$	−10.3544	+	31.8676i	−0.540496	+	1.66348i	0.190967	+	0.981596i	$0.438838\pi$
$367$	−10.3544	+	31.8676i	−0.540496	+	1.66348i	−0.731463	+	0.681881i	$0.761162\pi$
$368$	3.71870			0.193851
$369$	−4.32315	+	13.3053i	−0.225054	+	0.692645i
$370$	−3.68116	+	1.40949i	−0.191374	+	0.0732758i
$371$	−15.8009	−	48.6303i	−0.820344	−	2.52476i
$372$	0.263521	+	0.811034i	0.0136629	+	0.0420501i
$373$	−11.6791	−	8.48534i	−0.604719	−	0.439354i	0.242831	−	0.970068i	$-0.421924\pi$
$373$	−11.6791	−	8.48534i	−0.604719	−	0.439354i	−0.847551	+	0.530714i	$0.821924\pi$
$374$	8.16839			0.422377
$375$	−3.65248	−	0.588018i	−0.188613	−	0.0303651i
$376$	−9.62817			−0.496535
$377$	−1.42787	−	1.03741i	−0.0735389	−	0.0534292i
$378$	2.63701	+	8.11587i	0.135633	+	0.417435i
$379$	−0.538744	−	1.65808i	−0.0276734	−	0.0851700i	0.936266	−	0.351292i	$-0.114258\pi$
$379$	−0.538744	−	1.65808i	−0.0276734	−	0.0851700i	−0.963939	+	0.266122i	$0.914258\pi$
$380$	−12.7827	+	4.89438i	−0.655736	+	0.251076i
$381$	1.94871	−	5.99750i	0.0998352	−	0.307261i
$382$	−11.3095			−0.578643
$383$	−2.00840	+	6.18123i	−0.102625	+	0.315846i	−0.989166	−	0.146804i	$-0.953101\pi$
$383$	−2.00840	+	6.18123i	−0.102625	+	0.315846i	0.886541	+	0.462650i	$0.153101\pi$
$384$	0.267699	−	0.194495i	0.0136610	−	0.00992528i
$385$	17.7297	+	4.76677i	0.903591	+	0.242937i
$386$	−5.28157	−	3.83728i	−0.268825	−	0.195313i
$387$	0.0846101	−	0.0614728i	0.00430097	−	0.00312484i
$388$	13.6701	−	9.93194i	0.693997	−	0.504218i
$389$	18.9391	+	13.7601i	0.960253	+	0.697664i	0.953209	−	0.302311i	$-0.0977581\pi$
$389$	18.9391	+	13.7601i	0.960253	+	0.697664i	0.00704314	+	0.999975i	$0.497758\pi$
$390$	−0.465148	−	0.575407i	−0.0235537	−	0.0291368i
$391$	13.1039	−	9.52052i	0.662691	−	0.481473i
$392$	3.76007	−	11.5723i	0.189912	−	0.584489i
$393$	3.00019			0.151340
$394$	1.81586	−	5.58863i	0.0914816	−	0.281551i
$395$	23.7037	+	29.3224i	1.19266	+	1.47537i
$396$	1.67511	+	5.15545i	0.0841772	+	0.259071i
$397$	6.76376	+	20.8167i	0.339463	+	1.04476i	0.964482	+	0.264150i	$0.0850915\pi$
$397$	6.76376	+	20.8167i	0.339463	+	1.04476i	−0.625018	+	0.780610i	$0.714908\pi$
$398$	−0.507028	−	0.368377i	−0.0254150	−	0.0184651i
$399$	8.86787			0.443949
$400$	−1.04785	+	4.88897i	−0.0523923	+	0.244448i
$401$	17.7876			0.888270			0.444135	−	0.895960i	$-0.353511\pi$
$401$	17.7876			0.888270			0.444135	+	0.895960i	$0.353511\pi$
$402$	−2.76804	−	2.01110i	−0.138057	−	0.100305i
$403$	−0.796389	−	2.45103i	−0.0396710	−	0.122095i
$404$	−4.94651	−	15.2238i	−0.246098	−	0.757411i
$405$	−0.924135	−	17.9241i	−0.0459206	−	0.890658i
$406$	2.38781	−	7.34891i	0.118505	−	0.364720i
$407$	3.30592			0.163868
$408$	0.445372	−	1.37071i	0.0220492	−	0.0678604i
$409$	−17.0522	+	12.3891i	−0.843176	+	0.612603i	−0.923256	−	0.384185i	$-0.874482\pi$
$409$	−17.0522	+	12.3891i	−0.843176	+	0.612603i	0.0800803	+	0.996788i	$0.474482\pi$
$410$	10.1070	−	3.86988i	0.499148	−	0.191120i
$411$	−5.57793	−	4.05260i	−0.275139	−	0.199900i
$412$	4.92272	−	3.57656i	0.242525	−	0.176205i
$413$	−7.15959	+	5.20174i	−0.352300	+	0.255961i
$414$	8.69607	+	6.31807i	0.427389	+	0.310516i
$415$	−1.59347	−	30.9062i	−0.0782202	−	1.51713i
$416$	−0.809017	+	0.587785i	−0.0396653	+	0.0288185i
$417$	1.46549	−	4.51033i	0.0717656	−	0.220872i
$418$	11.4797			0.561488
$419$	−0.685285	+	2.10909i	−0.0334784	+	0.103036i	−0.966399	−	0.257045i	$-0.917251\pi$
$419$	−0.685285	+	2.10909i	−0.0334784	+	0.103036i	0.932921	+	0.360081i	$0.117251\pi$
$420$	1.76659	−	2.71527i	0.0862008	−	0.132492i
$421$	7.17634	+	22.0865i	0.349753	+	1.07643i	0.958990	+	0.283441i	$0.0914761\pi$
$421$	7.17634	+	22.0865i	0.349753	+	1.07643i	−0.609236	+	0.792989i	$0.708524\pi$
$422$	−2.06839	−	6.36583i	−0.100687	−	0.309884i
$423$	−22.5152	−	16.3583i	−1.09473	−	0.795366i
$424$	−11.6792			−0.567193
$425$	8.82424	+	19.9103i	0.428038	+	0.965791i
$426$	−0.139498			−0.00675870
$427$	−34.5898	−	25.1309i	−1.67392	−	1.21617i
$428$	0.658729	+	2.02736i	0.0318409	+	0.0979962i
$429$	0.191760	+	0.590176i	0.00925825	+	0.0284940i
$430$	−0.0781304	−	0.0210060i	−0.00376778	−	0.00101300i
$431$	−4.30571	+	13.2516i	−0.207399	+	0.638307i	0.792208	+	0.610252i	$0.208932\pi$
$431$	−4.30571	+	13.2516i	−0.207399	+	0.638307i	−0.999606	+	0.0280558i	$0.991068\pi$
$432$	1.94914			0.0937779
$433$	0.198679	−	0.611470i	0.00954789	−	0.0293854i	−0.946169	−	0.323673i	$-0.895082\pi$
$433$	0.198679	−	0.611470i	0.00954789	−	0.0293854i	0.955717	+	0.294287i	$0.0950823\pi$
$434$	9.12824	−	6.63206i	0.438170	−	0.318349i
$435$	0.712164	−	1.09460i	0.0341456	−	0.0524822i
$436$	6.36309	+	4.62306i	0.304737	+	0.221404i
$437$	18.4159	−	13.3799i	0.880950	−	0.640048i
$438$	0.0526472	−	0.0382505i	0.00251558	−	0.00182768i
$439$	−9.65983	−	7.01827i	−0.461038	−	0.334964i	0.332900	−	0.942962i	$-0.391973\pi$
$439$	−9.65983	−	7.01827i	−0.461038	−	0.334964i	−0.793938	+	0.607998i	$0.791973\pi$
$440$	2.28689	−	3.51498i	0.109023	−	0.167570i
$441$	28.4541	−	20.6731i	1.35496	−	0.984434i
$442$	−1.34596	+	4.14245i	−0.0640209	+	0.197036i
$443$	17.8931			0.850125			0.425063	−	0.905164i	$-0.360252\pi$
$443$	17.8931			0.850125			0.425063	+	0.905164i	$0.360252\pi$
$444$	0.180252	−	0.554757i	0.00855436	−	0.0263276i
$445$	−1.62972	−	0.438163i	−0.0772562	−	0.0207709i
$446$	2.45134	+	7.54446i	0.116075	+	0.357241i
$447$	1.07260	+	3.30111i	0.0507321	+	0.156137i
$448$	−3.54196	−	2.57339i	−0.167342	−	0.121581i
$449$	−22.6720			−1.06996			−0.534978	−	0.844866i	$-0.679680\pi$
$449$	−22.6720			−1.06996			−0.534978	+	0.844866i	$0.679680\pi$
$450$	−10.7567	+	9.65242i	−0.507076	+	0.455020i
$451$	−9.07672			−0.427406
$452$	−5.99453	−	4.35528i	−0.281959	−	0.204855i
$453$	1.67665	+	5.16019i	0.0787757	+	0.242447i
$454$	1.73047	+	5.32584i	0.0812151	+	0.249954i
$455$	−5.33883	+	8.20585i	−0.250288	+	0.384696i
$456$	0.625915	−	1.92637i	0.0293111	−	0.0902104i
$457$	−6.19454			−0.289769			−0.144884	−	0.989449i	$-0.546281\pi$
$457$	−6.19454			−0.289769			−0.144884	+	0.989449i	$0.546281\pi$
$458$	0.641927	−	1.97565i	0.0299953	−	0.0923160i
$459$	6.86832	−	4.99013i	0.320586	−	0.232919i
$460$	−0.428151	−	8.30424i	−0.0199626	−	0.387187i
$461$	4.90750	+	3.56551i	0.228565	+	0.166062i	0.696174	−	0.717873i	$-0.254884\pi$
$461$	4.90750	+	3.56551i	0.228565	+	0.166062i	−0.467609	+	0.883936i	$0.654884\pi$
$462$	−2.19796	+	1.59691i	−0.102258	+	0.0742949i
$463$	33.3682	−	24.2434i	1.55075	−	1.12669i	0.607642	−	0.794211i	$-0.292116\pi$
$463$	33.3682	−	24.2434i	1.55075	−	1.12669i	0.943111	−	0.332477i	$-0.107884\pi$
$464$	−1.42787	−	1.03741i	−0.0662871	−	0.0481604i
$465$	1.78078	−	0.681847i	0.0825817	−	0.0316199i
$466$	16.0939	−	11.6929i	0.745538	−	0.541665i
$467$	−4.30339	+	13.2445i	−0.199137	+	0.612881i	0.800766	+	0.598977i	$0.204426\pi$
$467$	−4.30339	+	13.2445i	−0.199137	+	0.612881i	−0.999903	+	0.0139042i	$0.995574\pi$
$468$	−2.89051			−0.133614
$469$	−13.9892	+	43.0545i	−0.645964	+	1.98807i
$470$	1.10854	+	21.5007i	0.0511329	+	0.991753i
$471$	1.38900	+	4.27491i	0.0640019	+	0.196978i
$472$	0.624635	+	1.92243i	0.0287512	+	0.0884870i
$473$	0.0548951	+	0.0398836i	0.00252408	+	0.00183385i
$474$	−5.57961			−0.256280
$475$	12.4014	+	27.9815i	0.569014	+	1.28388i
$476$	−19.0694			−0.874045
$477$	−27.3115	−	19.8430i	−1.25051	−	0.908548i
$478$	−0.404872	−	1.24607i	−0.0185184	−	0.0569939i
$479$	1.29636	+	3.98978i	0.0592321	+	0.182298i	0.976295	−	0.216446i	$-0.0694464\pi$
$479$	1.29636	+	3.98978i	0.0592321	+	0.182298i	−0.917063	+	0.398743i	$0.869446\pi$
$480$	−0.465148	−	0.575407i	−0.0212310	−	0.0262636i
$481$	−0.544740	+	1.67654i	−0.0248380	+	0.0764436i
$482$	−5.57377			−0.253878
$483$	−1.66475	+	5.12358i	−0.0757488	+	0.233131i
$484$	6.05388	−	4.39840i	0.275176	−	0.199927i
$485$	−23.7529	−	29.3833i	−1.07857	−	1.33423i
$486$	6.87936	+	4.99815i	0.312054	+	0.226721i
$487$	3.37553	−	2.45247i	0.152960	−	0.111132i	−0.508673	−	0.860960i	$-0.669864\pi$
$487$	3.37553	−	2.45247i	0.152960	−	0.111132i	0.661633	+	0.749828i	$0.269864\pi$
$488$	−7.90062	+	5.74014i	−0.357644	+	0.259844i
$489$	5.39484	+	3.91958i	0.243963	+	0.177250i
$490$	−26.2750	−	7.06424i	−1.18698	−	0.319130i
$491$	−34.9265	+	25.3756i	−1.57621	+	1.14519i	−0.655332	+	0.755341i	$0.727471\pi$
$491$	−34.9265	+	25.3756i	−1.57621	+	1.14519i	−0.920881	+	0.389845i	$0.872529\pi$
$492$	−0.494898	+	1.52314i	−0.0223117	+	0.0686684i
$493$	−7.68743			−0.346224
$494$	−1.89158	+	5.82170i	−0.0851064	+	0.261931i
$495$	11.3198	−	4.33425i	0.508786	−	0.194810i
$496$	−0.796389	−	2.45103i	−0.0357589	−	0.110055i
$497$	0.570358	+	1.75538i	0.0255840	+	0.0787396i
$498$	3.70497	+	2.69182i	0.166024	+	0.120623i
$499$	−4.93623			−0.220976			−0.110488	−	0.993877i	$-0.535241\pi$
$499$	−4.93623			−0.220976			−0.110488	+	0.993877i	$0.535241\pi$
$500$	11.0382	+	1.77706i	0.493644	+	0.0794724i
$501$	−2.02041			−0.0902653
$502$	−17.9867	−	13.0681i	−0.802785	−	0.583257i
$503$	−0.703528	−	2.16524i	−0.0313688	−	0.0965431i	0.934146	−	0.356890i	$-0.116163\pi$
$503$	−0.703528	−	2.16524i	−0.0313688	−	0.0965431i	−0.965515	+	0.260347i	$0.916163\pi$
$504$	−3.91060	−	12.0356i	−0.174192	−	0.536107i
$505$	−33.4267	+	12.7988i	−1.48747	+	0.569541i
$506$	−2.15506	+	6.63259i	−0.0958040	+	0.294855i
$507$	−0.330894			−0.0146955
$508$	−5.88920	+	18.1251i	−0.261291	+	0.804172i
$509$	−18.0062	+	13.0823i	−0.798113	+	0.579863i	−0.910360	−	0.413818i	$-0.864195\pi$
$509$	−18.0062	+	13.0823i	−0.798113	+	0.579863i	0.112247	+	0.993680i	$0.464195\pi$
$510$	−3.11222	−	0.836744i	−0.137811	−	0.0370516i
$511$	−0.696582	−	0.506097i	−0.0308150	−	0.0223884i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	9.65258	−	7.01301i	0.426172	−	0.309632i
$514$	5.33043	+	3.87278i	0.235115	+	0.170821i
$515$	−8.55360	−	10.5811i	−0.376917	−	0.466261i
$516$	0.00968584	−	0.00703718i	0.000426395	−	0.000309794i
$517$	5.57971	−	17.1726i	0.245396	−	0.755250i
$518$	−7.71780			−0.339101
$519$	−2.64727	+	8.14745i	−0.116202	+	0.357633i
$520$	1.40573	+	1.73894i	0.0616453	+	0.0762577i
$521$	5.32386	+	16.3852i	0.233243	+	0.717847i	0.997350	+	0.0727574i	$0.0231799\pi$
$521$	5.32386	+	16.3852i	0.233243	+	0.717847i	−0.764107	+	0.645089i	$0.776820\pi$
$522$	−1.57647	−	4.85189i	−0.0690004	−	0.212361i
$523$	13.7804	+	10.0121i	0.602575	+	0.437797i	0.846792	−	0.531924i	$-0.178531\pi$
$523$	13.7804	+	10.0121i	0.602575	+	0.437797i	−0.244217	+	0.969721i	$0.578531\pi$
$524$	−9.06692			−0.396090
$525$	−6.26687	−	3.63236i	−0.273509	−	0.158529i
$526$	4.27643			0.186461
$527$	−9.08137	−	6.59800i	−0.395591	−	0.287413i
$528$	0.191760	+	0.590176i	0.00834527	+	0.0256841i
$529$	−2.83408	−	8.72240i	−0.123221	−	0.379235i
$530$	1.34468	+	26.0809i	0.0584093	+	1.13288i
$531$	−1.80551	+	5.55680i	−0.0783526	+	0.241144i
$532$	−26.7997			−1.16191
$533$	1.49564	−	4.60309i	0.0647832	−	0.199382i
$534$	0.202037	−	0.146788i	0.00874299	−	0.00635215i
$535$	4.45146	−	1.70443i	0.192453	−	0.0736889i
$536$	8.36533	+	6.07777i	0.361327	+	0.262520i
$537$	−0.347361	+	0.252372i	−0.0149897	+	0.0108907i
$538$	1.07352	−	0.779958i	0.0462828	−	0.0336264i
$539$	18.4610	+	13.4127i	0.795174	+	0.577727i
$540$	−0.224413	−	4.35262i	−0.00965720	−	0.187307i
$541$	21.2444	−	15.4350i	0.913369	−	0.663602i	−0.0284953	−	0.999594i	$-0.509072\pi$
$541$	21.2444	−	15.4350i	0.913369	−	0.663602i	0.941865	+	0.335992i	$0.109072\pi$
$542$	−9.06684	+	27.9049i	−0.389454	+	1.19862i
$543$	4.69465			0.201467
$544$	−1.34596	+	4.14245i	−0.0577077	+	0.177606i
$545$	9.59115	−	14.7417i	0.410840	−	0.631465i
$546$	−0.447670	−	1.37779i	−0.0191585	−	0.0589639i
$547$	10.4570	+	32.1832i	0.447108	+	1.37606i	0.880156	+	0.474685i	$0.157438\pi$
$547$	10.4570	+	32.1832i	0.447108	+	1.37606i	−0.433048	+	0.901371i	$0.642562\pi$
$548$	16.8571	+	12.2474i	0.720100	+	0.523184i
$549$	−28.2279			−1.20474
$550$	−8.11261	−	4.70217i	−0.345923	−	0.200501i
$551$	−10.8037			−0.460254
$552$	0.995493	+	0.723268i	0.0423710	+	0.0307843i
$553$	22.8130	+	70.2113i	0.970110	+	2.98569i
$554$	−8.12206	−	24.9971i	−0.345073	−	1.06203i
$555$	−1.25958	−	0.338648i	−0.0534663	−	0.0143748i
$556$	−4.42889	+	13.6307i	−0.187827	+	0.578071i
$557$	−5.97635			−0.253226			−0.126613	−	0.991952i	$-0.540411\pi$
$557$	−5.97635			−0.253226			−0.126613	+	0.991952i	$0.540411\pi$
$558$	2.30197	−	7.08474i	0.0974502	−	0.299921i
$559$	−0.0292717	+	0.0212671i	−0.00123806	+	0.000899504i
$560$	−5.33883	+	8.20585i	−0.225607	+	0.346761i
$561$	2.18667	+	1.58871i	0.0923213	+	0.0670754i
$562$	−21.6980	+	15.7645i	−0.915276	+	0.664987i
$563$	−13.6156	+	9.89235i	−0.573831	+	0.416913i	−0.836495	−	0.547975i	$-0.815399\pi$
$563$	−13.6156	+	9.89235i	−0.573831	+	0.416913i	0.262664	+	0.964887i	$0.415399\pi$
$564$	−2.57746	−	1.87263i	−0.108530	−	0.0788520i
$565$	−9.03560	+	13.8878i	−0.380131	+	0.584265i
$566$	8.91024	−	6.47366i	0.374525	−	0.272108i
$567$	10.8592	−	33.4212i	0.456044	−	1.40356i
$568$	0.421579			0.0176890
$569$	3.83132	−	11.7916i	0.160617	−	0.494330i	−0.838069	−	0.545564i	$-0.816316\pi$
$569$	3.83132	−	11.7916i	0.160617	−	0.494330i	0.998687	+	0.0512343i	$0.0163155\pi$
$570$	−4.37384	−	1.17594i	−0.183200	−	0.0492547i
$571$	−5.45665	−	16.7938i	−0.228354	−	0.702800i	−0.997934	−	0.0642501i	$-0.979534\pi$
$571$	−5.45665	−	16.7938i	−0.228354	−	0.702800i	0.769580	−	0.638550i	$-0.220466\pi$
$572$	−0.579519	−	1.78358i	−0.0242309	−	0.0745751i
$573$	−3.02754	−	2.19964i	−0.126477	−	0.0918911i
$574$	21.1900			0.884452
$575$	−18.4949	+	1.91221i	−0.771291	+	0.0797446i
$576$	−2.89051			−0.120438
$577$	−19.4652	−	14.1423i	−0.810346	−	0.588751i	0.103585	−	0.994621i	$-0.466969\pi$
$577$	−19.4652	−	14.1423i	−0.810346	−	0.588751i	−0.913931	+	0.405870i	$0.866969\pi$
$578$	0.609224	+	1.87500i	0.0253404	+	0.0779897i
$579$	−0.667540	−	2.05448i	−0.0277420	−	0.0853811i
$580$	−2.15224	+	3.30801i	−0.0893668	+	0.137358i
$581$	18.7243	−	57.6276i	0.776816	−	2.39079i
$582$	5.59120			0.231763
$583$	6.76834	−	20.8308i	0.280316	−	0.862724i
$584$	−0.159106	+	0.115597i	−0.00658385	+	0.00478344i
$585$	0.332797	+	6.45480i	0.0137595	+	0.266873i
$586$	3.47211	+	2.52263i	0.143431	+	0.104209i
$587$	−23.4360	+	17.0272i	−0.967306	+	0.702789i	−0.954836	−	0.297133i	$-0.903969\pi$
$587$	−23.4360	+	17.0272i	−0.967306	+	0.702789i	−0.0124700	+	0.999922i	$0.503969\pi$
$588$	3.25732	−	2.36658i	0.134330	−	0.0975961i
$589$	−12.7627	−	9.27267i	−0.525880	−	0.382074i
$590$	4.22106	−	1.61621i	0.173778	−	0.0665384i
$591$	1.57306	−	1.14290i	0.0647072	−	0.0470125i
$592$	−0.544740	+	1.67654i	−0.0223887	+	0.0689053i
$593$	−19.1230			−0.785289			−0.392645	−	0.919690i	$-0.628440\pi$
$593$	−19.1230			−0.785289			−0.392645	+	0.919690i	$0.628440\pi$
$594$	−1.12956	+	3.47644i	−0.0463465	+	0.142640i
$595$	2.19555	+	42.5839i	0.0900087	+	1.74577i
$596$	−3.24151	−	9.97633i	−0.132777	−	0.408646i
$597$	−0.0640835	−	0.197229i	−0.00262276	−	0.00807203i
$598$	−3.00849	−	2.18580i	−0.123026	−	0.0893839i
$599$	−2.47213			−0.101008			−0.0505042	−	0.998724i	$-0.516083\pi$
$599$	−2.47213			−0.101008			−0.0505042	+	0.998724i	$0.516083\pi$
$600$	−1.23139	+	1.10497i	−0.0502712	+	0.0451103i
$601$	41.9772			1.71228			0.856142	−	0.516740i	$-0.172855\pi$
$601$	41.9772			1.71228			0.856142	+	0.516740i	$0.172855\pi$
$602$	−0.128155	−	0.0931098i	−0.00522319	−	0.00379487i
$603$	9.23596	+	28.4254i	0.376118	+	1.15757i
$604$	−5.06701	−	15.5947i	−0.206174	−	0.634538i
$605$	−10.5191	−	13.0125i	−0.427662	−	0.529034i
$606$	1.63677	−	5.03746i	0.0664893	−	0.204633i
$607$	40.8566			1.65832			0.829159	−	0.559013i	$-0.188820\pi$
$607$	40.8566			1.65832			0.829159	+	0.559013i	$0.188820\pi$
$608$	−1.89158	+	5.82170i	−0.0767139	+	0.236101i
$609$	2.06854	−	1.50288i	0.0838215	−	0.0608999i
$610$	13.7279	+	16.9820i	0.555828	+	0.687581i
$611$	7.78936	+	5.65930i	0.315124	+	0.228951i
$612$	−10.1855	+	7.40020i	−0.411725	+	0.299136i
$613$	−11.5724	+	8.40787i	−0.467406	+	0.339591i	−0.796430	−	0.604731i	$-0.793281\pi$
$613$	−11.5724	+	8.40787i	−0.467406	+	0.339591i	0.329023	+	0.944322i	$0.393281\pi$
$614$	1.91861	+	1.39395i	0.0774288	+	0.0562553i
$615$	3.45830	+	0.929791i	0.139452	+	0.0374928i
$616$	6.64247	−	4.82604i	0.267633	−	0.194447i
$617$	−10.4844	+	32.2676i	−0.422085	+	1.29904i	0.483673	+	0.875249i	$0.339302\pi$
$617$	−10.4844	+	32.2676i	−0.422085	+	1.29904i	−0.905758	+	0.423795i	$0.860698\pi$
$618$	2.01343			0.0809921
$619$	5.43201	−	16.7180i	0.218331	−	0.671954i	−0.780569	−	0.625069i	$-0.785071\pi$
$619$	5.43201	−	16.7180i	0.218331	−	0.671954i	0.998900	−	0.0468846i	$-0.0149293\pi$
$620$	−5.38172	+	2.06062i	−0.216135	+	0.0827564i
$621$	2.23983	+	6.89350i	0.0898814	+	0.276627i
$622$	−5.40404	−	16.6319i	−0.216682	−	0.666879i
$623$	−2.67317	−	1.94218i	−0.107098	−	0.0778116i
$624$	−0.330894			−0.0132464
$625$	2.69747	−	24.8540i	0.107899	−	0.994162i
$626$	−24.4105			−0.975639
$627$	3.07310	+	2.23273i	0.122728	+	0.0891668i
$628$	−4.19772	−	12.9193i	−0.167507	−	0.515535i
$629$	2.37269	+	7.30237i	0.0946052	+	0.291165i
$630$	−26.4264	+	10.1185i	−1.05285	+	0.403130i
$631$	−9.11684	+	28.0587i	−0.362936	+	1.11700i	0.588328	+	0.808622i	$0.299786\pi$
$631$	−9.11684	+	28.0587i	−0.362936	+	1.11700i	−0.951264	+	0.308379i	$0.900214\pi$
$632$	16.8622			0.670743
$633$	0.684417	−	2.10642i	0.0272031	−	0.0837227i
$634$	−24.3669	+	17.7036i	−0.967731	+	0.703098i
$635$	41.1533	+	11.0644i	1.63312	+	0.439076i
$636$	−3.12652	−	2.27155i	−0.123975	−	0.0900728i
$637$	−9.84398	+	7.15207i	−0.390033	+	0.283375i
$638$	2.67777	−	1.94551i	0.106014	−	0.0770237i
$639$	0.985849	+	0.716261i	0.0389996	+	0.0283349i
$640$	1.40573	+	1.73894i	0.0555664	+	0.0687378i
$641$	−25.4427	+	18.4852i	−1.00493	+	0.730121i	−0.963139	−	0.269005i	$-0.913305\pi$
$641$	−25.4427	+	18.4852i	−1.00493	+	0.730121i	−0.0417871	+	0.999127i	$0.513305\pi$
$642$	−0.217970	+	0.670842i	−0.00860259	+	0.0264760i
$643$	−16.6943			−0.658360			−0.329180	−	0.944267i	$-0.606772\pi$
$643$	−16.6943			−0.658360			−0.329180	+	0.944267i	$0.606772\pi$
$644$	5.03107	−	15.4840i	0.198252	−	0.610156i
$645$	−0.0168299	−	0.0208193i	−0.000662677	−	0.000819757i
$646$	8.23904	+	25.3571i	0.324161	+	0.997664i
$647$	−8.33751	−	25.6602i	−0.327781	−	1.00881i	−0.970169	−	0.242428i	$-0.922056\pi$
$647$	−8.33751	−	25.6602i	−0.327781	−	1.00881i	0.642388	−	0.766380i	$-0.277944\pi$
$648$	−6.49363	−	4.71790i	−0.255094	−	0.185337i
$649$	−3.79079			−0.148801
$650$	3.72139	−	3.33935i	0.145965	−	0.130980i
$651$	3.73352			0.146328
$652$	−16.3038	−	11.8454i	−0.638507	−	0.463902i
$653$	6.44534	+	19.8367i	0.252226	+	0.776271i	0.994364	+	0.106024i	$0.0338119\pi$
$653$	6.44534	+	19.8367i	0.252226	+	0.776271i	−0.742138	+	0.670247i	$0.766188\pi$
$654$	0.804234	+	2.47518i	0.0314480	+	0.0967871i
$655$	1.04392	+	20.2474i	0.0407892	+	0.791130i
$656$	1.49564	−	4.60309i	0.0583948	−	0.179721i
$657$	−0.568464			−0.0221779
$658$	−13.0261	+	40.0901i	−0.507808	+	1.56287i
$659$	7.18257	−	5.21845i	0.279793	−	0.203282i	−0.439034	−	0.898470i	$-0.644679\pi$
$659$	7.18257	−	5.21845i	0.279793	−	0.203282i	0.718827	+	0.695189i	$0.244679\pi$
$660$	1.29584	−	0.496169i	0.0504407	−	0.0193133i
$661$	−10.4687	−	7.60596i	−0.407185	−	0.295837i	0.365276	−	0.930899i	$-0.380975\pi$
$661$	−10.4687	−	7.60596i	−0.407185	−	0.295837i	−0.772461	+	0.635062i	$0.780975\pi$
$662$	23.5117	−	17.0823i	0.913809	−	0.663921i
$663$	−1.16600	+	0.847147i	−0.0452836	+	0.0329005i
$664$	−11.1968	−	8.13497i	−0.434521	−	0.315698i
$665$	3.08557	+	59.8464i	0.119653	+	2.32075i
$666$	−4.12229	+	2.99502i	−0.159736	+	0.116055i
$667$	2.02817	−	6.24206i	0.0785310	−	0.241693i
$668$	6.10590			0.236245
$669$	−0.811136	+	2.49642i	−0.0313603	+	0.0965172i
$670$	12.6091	−	19.3804i	0.487134	−	0.748730i
$671$	−5.65941	−	17.4179i	−0.218479	−	0.672410i
$672$	−0.447670	−	1.37779i	−0.0172693	−	0.0531493i
$673$	0.195124	+	0.141766i	0.00752148	+	0.00546468i	0.591540	−	0.806276i	$-0.298520\pi$
$673$	0.195124	+	0.141766i	0.00752148	+	0.00546468i	−0.584018	+	0.811741i	$0.698520\pi$
$674$	9.13533			0.351880
$675$	−9.69401	+	1.00227i	−0.373123	+	0.0385776i
$676$	1.00000			0.0384615
$677$	26.4489	+	19.2162i	1.01651	+	0.738540i	0.965565	−	0.260162i	$-0.0837759\pi$
$677$	26.4489	+	19.2162i	1.01651	+	0.738540i	0.0509475	+	0.998701i	$0.483776\pi$
$678$	−0.757651	−	2.33181i	−0.0290974	−	0.0895526i
$679$	−22.8604	−	70.3572i	−0.877303	−	2.70006i
$680$	9.40548	+	2.52873i	0.360684	+	0.0969725i
$681$	−0.572604	+	1.76229i	−0.0219422	+	0.0675312i
$682$	4.83313			0.185070
$683$	−14.3182	+	44.0670i	−0.547872	+	1.68618i	0.166188	+	0.986094i	$0.446854\pi$
$683$	−14.3182	+	44.0670i	−0.547872	+	1.68618i	−0.714061	+	0.700084i	$0.753146\pi$
$684$	−14.3145	+	10.4001i	−0.547327	+	0.397657i
$685$	25.4089	−	39.0538i	0.970824	−	1.49217i
$686$	−18.3043	−	13.2988i	−0.698860	−	0.507752i
$687$	0.556097	−	0.404028i	0.0212164	−	0.0154146i
$688$	−0.0292717	+	0.0212671i	−0.00111597	+	0.000810802i
$689$	9.44869	+	6.86488i	0.359967	+	0.261531i
$690$	1.50052	−	2.30631i	0.0571237	−	0.0877998i
$691$	16.1002	−	11.6975i	0.612480	−	0.444993i	−0.237807	−	0.971312i	$-0.576429\pi$
$691$	16.1002	−	11.6975i	0.612480	−	0.444993i	0.850287	+	0.526320i	$0.176429\pi$
$692$	8.00034	−	24.6225i	0.304127	−	0.936007i
$693$	23.7327			0.901529
$694$	1.82016	−	5.60189i	0.0690925	−	0.212645i
$695$	30.9487	+	8.32079i	1.17395	+	0.315625i
$696$	−0.180469	−	0.555426i	−0.00684065	−	0.0210534i
$697$	−6.51443	−	20.0494i	−0.246752	−	0.759424i
$698$	−21.0742	−	15.3113i	−0.797670	−	0.579541i
$699$	6.58256			0.248975
$700$	18.9392	+	10.9774i	0.715834	+	0.414906i
$701$	25.3255			0.956530			0.478265	−	0.878216i	$-0.341266\pi$
$701$	25.3255			0.956530			0.478265	+	0.878216i	$0.341266\pi$
$702$	−1.57688	−	1.14567i	−0.0595157	−	0.0432407i
$703$	3.33452	+	10.2626i	0.125764	+	0.387061i
$704$	−0.579519	−	1.78358i	−0.0218415	−	0.0672211i
$705$	−3.88502	+	5.97133i	−0.146318	+	0.224893i
$706$	6.93554	−	21.3454i	0.261022	−	0.803344i
$707$	−70.0814			−2.63568
$708$	−0.206688	+	0.636121i	−0.00776782	+	0.0239069i
$709$	34.1916	−	24.8416i	1.28409	−	0.932947i	0.284423	−	0.958699i	$-0.408198\pi$
$709$	34.1916	−	24.8416i	1.28409	−	0.932947i	0.999668	+	0.0257516i	$0.00819788\pi$
$710$	−0.0485383	−	0.941428i	−0.00182161	−	0.0353312i
$711$	39.4318	+	28.6489i	1.47881	+	1.07442i
$712$	−0.610578	+	0.443611i	−0.0228824	+	0.0166250i
$713$	7.75339	−	5.63317i	0.290367	−	0.210964i
$714$	−5.10487	−	3.70890i	−0.191045	−	0.138802i
$715$	−3.91619	+	1.49948i	−0.146457	+	0.0560773i
$716$	1.04976	−	0.762698i	0.0392315	−	0.0285034i
$717$	0.133970	−	0.412317i	0.00500320	−	0.0153983i
$718$	−26.8375			−1.00157
$719$	1.41803	−	4.36425i	0.0528837	−	0.162759i	−0.921127	−	0.389263i	$-0.872730\pi$
$719$	1.41803	−	4.36425i	0.0528837	−	0.162759i	0.974010	+	0.226504i	$0.0727296\pi$
$720$	0.332797	+	6.45480i	0.0124026	+	0.240556i
$721$	−8.23220	−	25.3361i	−0.306583	−	0.943566i
$722$	5.70762	+	17.5663i	0.212416	+	0.653748i
$723$	−1.49209	−	1.08407i	−0.0554916	−	0.0403170i
$724$	−14.1878			−0.527284
$725$	7.63493	+	4.42530i	0.283554	+	0.164351i
$726$	2.47609			0.0918962
$727$	−0.489817	−	0.355873i	−0.0181663	−	0.0131986i	0.578665	−	0.815565i	$-0.303574\pi$
$727$	−0.489817	−	0.355873i	−0.0181663	−	0.0131986i	−0.596831	+	0.802367i	$0.703574\pi$
$728$	1.35291	+	4.16383i	0.0501422	+	0.154322i
$729$	−6.57155	−	20.2252i	−0.243391	−	0.749080i
$730$	0.276459	+	0.341990i	0.0102322	+	0.0126576i
$731$	−0.0486994	+	0.149881i	−0.00180121	+	0.00554356i
$732$	−3.23142			−0.119437
$733$	13.3958	−	41.2280i	0.494784	−	1.52279i	−0.322508	−	0.946567i	$-0.604526\pi$
$733$	13.3958	−	41.2280i	0.494784	−	1.52279i	0.817292	−	0.576223i	$-0.195474\pi$
$734$	27.1082	−	19.6953i	1.00058	−	0.726966i
$735$	−5.65985	−	7.00145i	−0.208767	−	0.258252i
$736$	−3.00849	−	2.18580i	−0.110894	−	0.0805695i
$737$	−15.6880	+	11.3980i	−0.577877	+	0.419852i
$738$	11.3182	−	8.22312i	0.416627	−	0.302697i
$739$	−5.96098	−	4.33091i	−0.219278	−	0.159315i	0.472723	−	0.881211i	$-0.343271\pi$
$739$	−5.96098	−	4.33091i	−0.219278	−	0.159315i	−0.692002	+	0.721896i	$0.743271\pi$
$740$	3.80660	+	1.02343i	0.139933	+	0.0376221i
$741$	−1.63867	+	1.19056i	−0.0601979	+	0.0437363i
$742$	−15.8009	+	48.6303i	−0.580071	+	1.78527i
$743$	−23.6586			−0.867951			−0.433975	−	0.900925i	$-0.642890\pi$
$743$	−23.6586			−0.867951			−0.433975	+	0.900925i	$0.642890\pi$
$744$	0.263521	−	0.811034i	0.00966114	−	0.0297339i
$745$	−21.9050	+	8.38723i	−0.802535	+	0.307285i
$746$	4.46101	+	13.7296i	0.163329	+	0.502675i
$747$	−12.3622	−	38.0468i	−0.452307	−	1.39206i
$748$	−6.60836	−	4.80126i	−0.241626	−	0.175551i
$749$	9.33278			0.341012
$750$	2.60929	+	2.62259i	0.0952779	+	0.0957635i
$751$	21.7469			0.793557			0.396779	−	0.917914i	$-0.370128\pi$
$751$	21.7469			0.793557			0.396779	+	0.917914i	$0.370128\pi$
$752$	7.78936	+	5.65930i	0.284049	+	0.206373i
$753$	−2.27334	−	6.99664i	−0.0828453	−	0.254972i
$754$	0.545397	+	1.67856i	0.0198622	+	0.0611295i
$755$	−34.2411	+	13.1106i	−1.24616	+	0.477145i
$756$	2.63701	−	8.11587i	0.0959070	−	0.295171i
$757$	20.5772			0.747893			0.373946	−	0.927450i	$-0.378004\pi$
$757$	20.5772			0.747893			0.373946	+	0.927450i	$0.378004\pi$
$758$	−0.538744	+	1.65808i	−0.0195680	+	0.0602243i
$759$	−1.86691	+	1.35639i	−0.0677646	+	0.0492339i
$760$	13.2182	+	3.55382i	0.479476	+	0.128911i
$761$	7.98619	+	5.80230i	0.289499	+	0.210333i	0.723050	−	0.690796i	$-0.242740\pi$
$761$	7.98619	+	5.80230i	0.289499	+	0.210333i	−0.433551	+	0.901129i	$0.642740\pi$
$762$	−5.10178	+	3.70666i	−0.184818	+	0.134278i
$763$	27.8583	−	20.2402i	1.00854	−	0.732746i
$764$	9.14956	+	6.64755i	0.331020	+	0.240500i
$765$	17.6981	+	21.8933i	0.639877	+	0.791552i
$766$	5.25807	−	3.82021i	0.189982	−	0.138030i
$767$	0.624635	−	1.92243i	0.0225543	−	0.0694149i
$768$	−0.330894			−0.0119401
$769$	8.36741	−	25.7522i	0.301737	−	0.928650i	−0.679138	−	0.734010i	$-0.737646\pi$
$769$	8.36741	−	25.7522i	0.301737	−	0.928650i	0.980875	−	0.194639i	$-0.0623537\pi$
$770$	−11.5418	−	14.2777i	−0.415938	−	0.514532i
$771$	0.673715	+	2.07348i	0.0242633	+	0.0746746i
$772$	2.01738	+	6.20886i	0.0726071	+	0.223462i
$773$	−5.57138	−	4.04784i	−0.200388	−	0.145591i	0.483066	−	0.875584i	$-0.339523\pi$
$773$	−5.57138	−	4.04784i	−0.200388	−	0.145591i	−0.683454	+	0.729993i	$0.739523\pi$
$774$	−0.104584			−0.00375919
$775$	5.22119	+	11.7807i	0.187551	+	0.423174i
$776$	−16.8972			−0.606575
$777$	−2.06605	−	1.50107i	−0.0741191	−	0.0538507i
$778$	−7.23411	−	22.2643i	−0.259355	−	0.798214i
$779$	−9.15523	−	28.1769i	−0.328020	−	1.00954i
$780$	0.0380974	+	0.738921i	0.00136411	+	0.0264576i
$781$	−0.244313	+	0.751918i	−0.00874220	+	0.0269057i
$782$	−16.1973			−0.579213
$783$	1.06305	−	3.27174i	0.0379904	−	0.116922i
$784$	−9.84398	+	7.15207i	−0.351571	+	0.255431i
$785$	−28.3667	+	10.8614i	−1.01245	+	0.387660i
$786$	−2.42721	−	1.76347i	−0.0865756	−	0.0629009i
$787$	−15.6695	+	11.3845i	−0.558556	+	0.405815i	−0.830930	−	0.556377i	$-0.812191\pi$
$787$	−15.6695	+	11.3845i	−0.558556	+	0.405815i	0.272374	+	0.962191i	$0.412191\pi$
$788$	−4.75398	+	3.45397i	−0.169353	+	0.123042i
$789$	1.14480	+	0.831745i	0.0407559	+	0.0296109i
$790$	−1.94142	−	37.6550i	−0.0690727	−	1.33971i
$791$	−26.2447	+	19.0679i	−0.933153	+	0.677976i
$792$	1.67511	−	5.15545i	0.0595223	−	0.183191i
$793$	9.76571			0.346790
$794$	6.76376	−	20.8167i	0.240037	−	0.738757i
$795$	−4.71263	+	7.24337i	−0.167140	+	0.256896i
$796$	0.193667	+	0.596047i	0.00686436	+	0.0211263i
$797$	9.79499	+	30.1459i	0.346956	+	1.06782i	0.960528	+	0.278183i	$0.0897320\pi$
$797$	9.79499	+	30.1459i	0.346956	+	1.06782i	−0.613572	+	0.789639i	$0.710268\pi$
$798$	−7.17426	−	5.21240i	−0.253966	−	0.184517i
$799$	41.9367			1.48362
$800$	3.72139	−	3.33935i	0.131571	−	0.118064i
$801$	−2.18151			−0.0770799
$802$	−14.3905	−	10.4553i	−0.508145	−	0.369189i
$803$	−0.113972	−	0.350768i	−0.00402197	−	0.0123783i
$804$	1.05730	+	3.25403i	0.0372880	+	0.114761i
$805$	−35.1567	−	9.45214i	−1.23911	−	0.333144i
$806$	−0.796389	+	2.45103i	−0.0280516	+	0.0863340i
$807$	0.439079			0.0154563
$808$	−4.94651	+	15.2238i	−0.174017	+	0.535571i
$809$	14.0492	−	10.2074i	0.493945	−	0.358872i	−0.312754	−	0.949834i	$-0.601252\pi$
$809$	14.0492	−	10.2074i	0.493945	−	0.358872i	0.806699	+	0.590962i	$0.201252\pi$
$810$	−9.78791	+	15.0441i	−0.343912	+	0.528597i
$811$	−6.43185	−	4.67301i	−0.225853	−	0.164092i	0.469105	−	0.883143i	$-0.344577\pi$
$811$	−6.43185	−	4.67301i	−0.225853	−	0.164092i	−0.694957	+	0.719051i	$0.744577\pi$
$812$	−6.25136	+	4.54188i	−0.219380	+	0.159389i
$813$	−7.85454	+	5.70666i	−0.275471	+	0.200141i
$814$	−2.67455	−	1.94317i	−0.0937428	−	0.0681082i
$815$	−24.5749	+	37.7719i	−0.860821	+	1.32309i
$816$	−1.16600	+	0.847147i	−0.0408181	+	0.0296561i
$817$	−0.0684409	+	0.210640i	−0.00239445	+	0.00736934i
$818$	21.0776			0.736963
$819$	−3.91060	+	12.0356i	−0.136647	+	0.420557i
$820$	−10.4514	−	2.80993i	−0.364978	−	0.0981271i
$821$	−3.30530	−	10.1727i	−0.115356	−	0.355029i	0.876665	−	0.481101i	$-0.159763\pi$
$821$	−3.30530	−	10.1727i	−0.115356	−	0.355029i	−0.992021	+	0.126072i	$0.959763\pi$
$822$	2.13058	+	6.55725i	0.0743125	+	0.228710i
$823$	14.9414	+	10.8555i	0.520823	+	0.378400i	0.816914	−	0.576760i	$-0.195683\pi$
$823$	14.9414	+	10.8555i	0.520823	+	0.378400i	−0.296091	+	0.955160i	$0.595683\pi$
$824$	−6.08481			−0.211974
$825$	−1.25719	−	2.83663i	−0.0437698	−	0.0987587i
$826$	8.84974			0.307922
$827$	38.1015	+	27.6824i	1.32492	+	0.962611i	0.999857	+	0.0169187i	$0.00538564\pi$
$827$	38.1015	+	27.6824i	1.32492	+	0.962611i	0.325063	+	0.945692i	$0.394614\pi$
$828$	−3.32160	−	10.2228i	−0.115434	−	0.355268i
$829$	−0.195734	−	0.602408i	−0.00679814	−	0.0209225i	0.947600	−	0.319460i	$-0.103501\pi$
$829$	−0.195734	−	0.602408i	−0.00679814	−	0.0209225i	−0.954398	+	0.298537i	$0.903501\pi$
$830$	−16.8771	+	25.9403i	−0.585812	+	0.900400i
$831$	2.68755	−	8.27141i	0.0932299	−	0.286932i
$832$	1.00000			0.0346688
$833$	−16.3774	+	50.4046i	−0.567445	+	1.74642i
$834$	−3.83671	+	2.78754i	−0.132855	+	0.0965245i
$835$	−0.703001	−	13.6351i	−0.0243283	−	0.471862i
$836$	−9.28724	−	6.74757i	−0.321206	−	0.233370i
$837$	4.06390	−	2.95260i	0.140469	−	0.102057i
$838$	1.79410	−	1.30349i	0.0619761	−	0.0450283i
$839$	−16.8466	−	12.2398i	−0.581609	−	0.422563i	0.257695	−	0.966226i	$-0.417037\pi$
$839$	−16.8466	−	12.2398i	−0.581609	−	0.422563i	−0.839304	+	0.543663i	$0.817037\pi$
$840$	−3.02520	+	1.15832i	−0.104379	+	0.0399660i
$841$	20.9414	−	15.2148i	0.722117	−	0.524649i
$842$	7.17634	−	22.0865i	0.247313	−	0.761151i
$843$	−8.87466			−0.305660
$844$	−2.06839	+	6.36583i	−0.0711968	+	0.219121i
$845$	−0.115135	−	2.23310i	−0.00396075	−	0.0768210i
$846$	8.60004	+	26.4682i	0.295676	+	0.909996i
$847$	−10.1238	−	31.1580i	−0.347859	−	1.07060i
$848$	9.44869	+	6.86488i	0.324469	+	0.235741i
$849$	3.64436			0.125074
$850$	4.56402	−	21.2945i	0.156545	−	0.730396i
$851$	−6.55539			−0.224716
$852$	0.112856	+	0.0819949i	0.00386639	+	0.00280910i
$853$	0.154358	+	0.475064i	0.00528510	+	0.0162659i	0.953664	−	0.300873i	$-0.0972779\pi$
$853$	0.154358	+	0.475064i	0.00528510	+	0.0162659i	−0.948379	+	0.317139i	$0.897278\pi$
$854$	13.2121	+	40.6627i	0.452109	+	1.39145i
$855$	24.8725	+	30.7683i	0.850622	+	1.05225i
$856$	0.658729	−	2.02736i	0.0225149	−	0.0692938i
$857$	−3.77219			−0.128855			−0.0644277	−	0.997922i	$-0.520522\pi$
$857$	−3.77219			−0.128855			−0.0644277	+	0.997922i	$0.520522\pi$
$858$	0.191760	−	0.590176i	0.00654657	−	0.0201483i
$859$	16.4889	−	11.9799i	0.562594	−	0.408749i	−0.269813	−	0.962913i	$-0.586962\pi$
$859$	16.4889	−	11.9799i	0.562594	−	0.408749i	0.832407	+	0.554164i	$0.186962\pi$
$860$	0.0508619	+	0.0629181i	0.00173437	+	0.00214549i
$861$	5.67253	+	4.12134i	0.193319	+	0.140455i
$862$	11.2725	−	8.18994i	0.383942	−	0.278951i
$863$	39.7449	−	28.8764i	1.35293	−	0.982962i	0.354072	−	0.935218i	$-0.384797\pi$
$863$	39.7449	−	28.8764i	1.35293	−	0.982962i	0.998860	−	0.0477443i	$-0.0152033\pi$
$864$	−1.57688	−	1.14567i	−0.0536467	−	0.0389766i
$865$	−55.9057	−	15.0307i	−1.90085	−	0.511058i
$866$	−0.520147	+	0.377909i	−0.0176753	+	0.0128419i
$867$	−0.201589	+	0.620427i	−0.00684632	+	0.0210708i
$868$	−11.2831			−0.382974
$869$	−9.77198	+	30.0751i	−0.331492	+	1.02023i
$870$	−1.21954	+	0.466954i	−0.0413464	+	0.0158312i
$871$	−3.19527	−	9.83404i	−0.108268	−	0.333214i
$872$	−2.43049	−	7.48026i	−0.0823066	−	0.253314i
$873$	−39.5137	−	28.7084i	−1.33734	−	0.971631i
$874$	−22.7633			−0.769979
$875$	22.3331	−	43.5570i	0.754995	−	1.47250i
$876$	−0.0650756			−0.00219870
$877$	−26.0790	−	18.9475i	−0.880625	−	0.639811i	0.0527921	−	0.998606i	$-0.483188\pi$
$877$	−26.0790	−	18.9475i	−0.880625	−	0.639811i	−0.933417	+	0.358794i	$0.883188\pi$
$878$	3.68973	+	11.3558i	0.124522	+	0.383240i
$879$	0.438841	+	1.35061i	0.0148017	+	0.0455551i
$880$	−3.91619	+	1.49948i	−0.132015	+	0.0505474i
$881$	4.65812	−	14.3362i	0.156936	−	0.482999i	−0.841416	−	0.540388i	$-0.818277\pi$
$881$	4.65812	−	14.3362i	0.156936	−	0.482999i	0.998352	+	0.0573887i	$0.0182774\pi$
$882$	−35.1712			−1.18428
$883$	12.0717	−	37.1529i	0.406245	−	1.25029i	−0.513607	−	0.858026i	$-0.671691\pi$
$883$	12.0717	−	37.1529i	0.406245	−	1.25029i	0.919851	−	0.392267i	$-0.128309\pi$
$884$	3.52378	−	2.56017i	0.118517	−	0.0861080i
$885$	1.44432	+	0.388316i	0.0485503	+	0.0130531i
$886$	−14.4758	−	10.5173i	−0.486324	−	0.353335i
$887$	14.1113	−	10.2524i	0.473810	−	0.344243i	−0.325114	−	0.945675i	$-0.605403\pi$
$887$	14.1113	−	10.2524i	0.473810	−	0.344243i	0.798924	+	0.601431i	$0.205403\pi$
$888$	−0.471905	+	0.342859i	−0.0158361	+	0.0115056i
$889$	67.5023	+	49.0433i	2.26395	+	1.64486i
$890$	1.06093	+	1.31241i	0.0355623	+	0.0439920i
$891$	12.1779	−	8.84778i	0.407976	−	0.296412i
$892$	2.45134	−	7.54446i	0.0820771	−	0.252607i
$893$	58.9369			1.97225
$894$	1.07260	−	3.30111i	0.0358730	−	0.110406i
$895$	−1.82405	−	2.25642i	−0.0609711	−	0.0754237i
$896$	1.35291	+	4.16383i	0.0451975	+	0.139104i
$897$	−0.380245	−	1.17027i	−0.0126960	−	0.0390743i
$898$	18.3420	+	13.3262i	0.612081	+	0.444703i
$899$	−4.54855			−0.151703
$900$	14.3759	−	1.48634i	0.479197	−	0.0495447i
$901$	50.8704			1.69474
$902$	7.34322	+	5.33516i	0.244503	+	0.177642i
$903$	−0.0161975	−	0.0498508i	−0.000539020	−	0.00165893i
$904$	2.28971	+	7.04699i	0.0761545	+	0.234379i
$905$	1.63350	+	31.6827i	0.0542994	+	1.05317i
$906$	1.67665	−	5.16019i	0.0557028	−	0.171436i
$907$	−36.2440			−1.20346			−0.601731	−	0.798699i	$-0.705522\pi$
$907$	−36.2440			−1.20346			−0.601731	+	0.798699i	$0.705522\pi$
$908$	1.73047	−	5.32584i	0.0574277	−	0.176744i
$909$	−37.4324	+	27.1963i	−1.24156	+	0.902043i
$910$	9.14249	−	3.50059i	0.303070	−	0.116043i
$911$	−35.4619	−	25.7645i	−1.17490	−	0.853617i	−0.183316	−	0.983054i	$-0.558683\pi$
$911$	−35.4619	−	25.7645i	−1.17490	−	0.853617i	−0.991588	+	0.129437i	$0.958683\pi$
$912$	−1.63867	+	1.19056i	−0.0542617	+	0.0394234i
$913$	20.9981	−	15.2560i	0.694937	−	0.504901i
$914$	5.01149	+	3.64106i	0.165765	+	0.120436i
$915$	0.372048	+	7.21609i	0.0122995	+	0.238556i
$916$	−1.68059	+	1.22102i	−0.0555281	+	0.0403436i
$917$	−12.2667	+	37.7531i	−0.405083	+	1.24672i
$918$	−8.48971			−0.280202
$919$	5.10188	−	15.7020i	0.168295	−	0.517960i	−0.830969	−	0.556319i	$-0.812213\pi$
$919$	5.10188	−	15.7020i	0.168295	−	0.517960i	0.999264	+	0.0383594i	$0.0122132\pi$
$920$	−4.53473	+	6.96993i	−0.149505	+	0.229792i
$921$	0.242494	+	0.746320i	0.00799045	+	0.0245921i
$922$	−1.87450	−	5.76911i	−0.0617333	−	0.189996i
$923$	−0.341064	−	0.247798i	−0.0112263	−	0.00815636i
$924$	2.71682			0.0893770
$925$	1.84716	−	8.61835i	0.0607342	−	0.283370i
$926$	−41.2454			−1.35541
$927$	−14.2292	−	10.3381i	−0.467347	−	0.339547i
$928$	0.545397	+	1.67856i	0.0179035	+	0.0551014i
$929$	−7.11680	−	21.9033i	−0.233495	−	0.718623i	−0.997318	−	0.0731968i	$-0.976680\pi$
$929$	−7.11680	−	21.9033i	−0.233495	−	0.718623i	0.763823	−	0.645426i	$-0.223320\pi$
$930$	−1.84146	−	0.495091i	−0.0603839	−	0.0162347i
$931$	−23.0165	+	70.8374i	−0.754334	+	2.32160i
$932$	−19.8932			−0.651624
$933$	1.78817	−	5.50341i	0.0585419	−	0.180174i
$934$	11.2664	−	8.18554i	0.368649	−	0.267839i
$935$	−9.96085	+	15.3099i	−0.325754	+	0.500689i
$936$	2.33847	+	1.69900i	0.0764353	+	0.0555335i
$937$	40.4327	−	29.3761i	1.32088	−	0.959674i	0.320957	−	0.947094i	$-0.395995\pi$
$937$	40.4327	−	29.3761i	1.32088	−	0.959674i	0.999921	−	0.0125805i	$-0.00400459\pi$
$938$	36.6243	−	26.6091i	1.19583	−	0.868819i
$939$	−6.53467	−	4.74771i	−0.213251	−	0.154936i
$940$	11.7410	−	18.0460i	0.382948	−	0.588596i
$941$	−22.3409	+	16.2316i	−0.728294	+	0.529136i	−0.889023	−	0.457862i	$-0.848615\pi$
$941$	−22.3409	+	16.2316i	−0.728294	+	0.529136i	0.160729	+	0.986998i	$0.448615\pi$
$942$	1.38900	−	4.27491i	0.0452562	−	0.139284i
$943$	17.9984			0.586110
$944$	0.624635	−	1.92243i	0.0203301	−	0.0625697i
$945$	−18.4272	−	4.95429i	−0.599436	−	0.161163i
$946$	−0.0209681	−	0.0645330i	−0.000681730	−	0.00209815i
$947$	−5.48401	−	16.8781i	−0.178207	−	0.548463i	0.821559	−	0.570124i	$-0.193105\pi$
$947$	−5.48401	−	16.8781i	−0.178207	−	0.548463i	−0.999765	+	0.0216604i	$0.993105\pi$
$948$	4.51400	+	3.27961i	0.146608	+	0.106517i
$949$	0.196666			0.00638404
$950$	6.41417	−	29.9268i	0.208103	−	0.970954i
$951$	−9.96624			−0.323177
$952$	15.4275	+	11.2087i	0.500007	+	0.363277i
$953$	11.6881	+	35.9722i	0.378614	+	1.16526i	0.941008	+	0.338385i	$0.109881\pi$
$953$	11.6881	+	35.9722i	0.378614	+	1.16526i	−0.562393	+	0.826870i	$0.690119\pi$
$954$	10.4321	+	32.1066i	0.337751	+	1.03949i
$955$	13.7912	−	21.1973i	0.446273	−	0.685927i
$956$	−0.404872	+	1.24607i	−0.0130945	+	0.0403007i
$957$	1.09523			0.0354038
$958$	1.29636	−	3.98978i	0.0418834	−	0.128904i
$959$	73.8023	−	53.6205i	2.38320	−	1.73150i
$960$	0.0380974	+	0.738921i	0.00122959	+	0.0238486i
$961$	19.7062	+	14.3174i	0.635684	+	0.461851i
$962$	1.42615	−	1.03616i	0.0459809	−	0.0334071i
$963$	4.98490	−	3.62174i	0.160636	−	0.116709i
$964$	4.50927	+	3.27618i	0.145234	+	0.105519i
$965$	13.6327	−	5.21987i	0.438853	−	0.168034i
$966$	4.35838	−	3.16655i	0.140228	−	0.101882i
$967$	16.2582	−	50.0376i	0.522829	−	1.60910i	−0.245740	−	0.969336i	$-0.579031\pi$
$967$	16.2582	−	50.0376i	0.522829	−	1.60910i	0.768569	−	0.639766i	$-0.220969\pi$
$968$	−7.48301			−0.240513
$969$	−2.72625	+	8.39054i	−0.0875798	+	0.269543i
$970$	1.94546	+	37.7332i	0.0624648	+	1.21154i
$971$	8.30288	+	25.5536i	0.266452	+	0.820056i	0.991355	+	0.131205i	$0.0418845\pi$
$971$	8.30288	+	25.5536i	0.266452	+	0.820056i	−0.724903	+	0.688851i	$0.758115\pi$
$972$	−2.62768	−	8.08717i	−0.0842829	−	0.259396i
$973$	50.7640	+	36.8822i	1.62742	+	1.18239i
$974$	−4.17239			−0.133692
$975$	1.64570	−	0.170151i	0.0527046	−	0.00544918i
$976$	9.76571			0.312593
$977$	17.4253	+	12.6603i	0.557486	+	0.405037i	0.830538	−	0.556962i	$-0.188033\pi$
$977$	17.4253	+	12.6603i	0.557486	+	0.405037i	−0.273052	+	0.961999i	$0.588033\pi$
$978$	−2.06065	−	6.34202i	−0.0658922	−	0.202795i
$979$	−0.437372	−	1.34609i	−0.0139785	−	0.0430213i
$980$	17.1047	+	21.1592i	0.546389	+	0.675905i
$981$	7.02534	−	21.6218i	0.224302	−	0.690330i
$982$	43.1716			1.37766
$983$	−4.65015	+	14.3117i	−0.148317	+	0.456472i	−0.997423	−	0.0717508i	$-0.977141\pi$
$983$	−4.65015	+	14.3117i	−0.148317	+	0.456472i	0.849106	+	0.528223i	$0.177141\pi$
$984$	1.29566	−	0.941351i	0.0413041	−	0.0300092i
$985$	8.26040	+	10.2184i	0.263198	+	0.325587i
$986$	6.21926	+	4.51856i	0.198062	+	0.143900i
$987$	−11.2844	+	8.19858i	−0.359186	+	0.260964i
$988$	4.95223	−	3.59801i	0.157551	−	0.114468i
$989$	−0.108853	−	0.0790861i	−0.00346131	−	0.00251479i
$990$	−11.7055	−	3.14711i	−0.372025	−	0.100022i
$991$	−7.47226	+	5.42892i	−0.237364	+	0.172455i	−0.700108	−	0.714037i	$-0.746865\pi$
$991$	−7.47226	+	5.42892i	−0.237364	+	0.172455i	0.462744	+	0.886492i	$0.346865\pi$
$992$	−0.796389	+	2.45103i	−0.0252854	+	0.0778204i
$993$	9.61648			0.305170
$994$	0.570358	−	1.75538i	0.0180906	−	0.0556773i
$995$	1.30874	−	0.501105i	0.0414897	−	0.0158861i
$996$	−1.41517	−	4.35545i	−0.0448414	−	0.138008i
$997$	−14.1497	−	43.5483i	−0.448126	−	1.37919i	−0.879019	−	0.476786i	$-0.841802\pi$
$997$	−14.1497	−	43.5483i	−0.448126	−	1.37919i	0.430894	−	0.902403i	$-0.358198\pi$
$998$	3.99350	+	2.90144i	0.126412	+	0.0918436i
$999$	−3.43597			−0.108709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.391.3	yes	24
25.11	even	5	inner	650.2.l.c.261.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.261.3	✓	24	25.11	even	5	inner
650.2.l.c.391.3	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.102252 - 0.314699i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.08823 - 0.799566i) q^{5} +(-0.102252 + 0.314699i) q^{6} +4.37811 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.33847 - 1.69900i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.102252 - 0.314699i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.08823 - 0.799566i) q^{5} +(-0.102252 + 0.314699i) q^{6} +4.37811 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.33847 - 1.69900i) q^{9} +(-2.15938 - 0.580567i) q^{10} +(1.51720 + 1.10231i) q^{11} +(0.267699 - 0.194495i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(-3.54196 - 2.57339i) q^{14} +(-0.465148 - 0.575407i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.34596 + 4.14245i) q^{17} -2.89051 q^{18} +(-1.89158 + 5.82170i) q^{19} +(1.40573 + 1.73894i) q^{20} +(-0.447670 - 1.37779i) q^{21} +(-0.579519 - 1.78358i) q^{22} +(-3.00849 - 2.18580i) q^{23} -0.330894 q^{24} +(3.72139 - 3.33935i) q^{25} +1.00000 q^{26} +(-1.57688 - 1.14567i) q^{27} +(1.35291 + 4.16383i) q^{28} +(0.545397 + 1.67856i) q^{29} +(0.0380974 + 0.738921i) q^{30} +(-0.796389 + 2.45103i) q^{31} +1.00000 q^{32} +(0.191760 - 0.590176i) q^{33} +(3.52378 - 2.56017i) q^{34} +(9.14249 - 3.50059i) q^{35} +(2.33847 + 1.69900i) q^{36} +(1.42615 - 1.03616i) q^{37} +(4.95223 - 3.59801i) q^{38} +(0.267699 + 0.194495i) q^{39} +(-0.115135 - 2.23310i) q^{40} +(-3.91563 + 2.84487i) q^{41} +(-0.447670 + 1.37779i) q^{42} +0.0361818 q^{43} +(-0.579519 + 1.78358i) q^{44} +(3.52480 - 5.41766i) q^{45} +(1.14914 + 3.53669i) q^{46} +(-2.97527 - 9.15694i) q^{47} +(0.267699 + 0.194495i) q^{48} +12.1678 q^{49} +(-4.97349 + 0.514214i) q^{50} +1.44125 q^{51} +(-0.809017 - 0.587785i) q^{52} +(-3.60908 - 11.1076i) q^{53} +(0.602316 + 1.85374i) q^{54} +(4.04963 + 1.08877i) q^{55} +(1.35291 - 4.16383i) q^{56} +2.02550 q^{57} +(0.545397 - 1.67856i) q^{58} +(-1.63532 + 1.18813i) q^{59} +(0.403506 - 0.620193i) q^{60} +(-7.90062 - 5.74014i) q^{61} +(2.08497 - 1.51482i) q^{62} +(10.2381 - 7.43840i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.21944 + 1.87429i) q^{65} +(-0.502034 + 0.364749i) q^{66} +(-3.19527 + 9.83404i) q^{67} -4.35563 q^{68} +(-0.380245 + 1.17027i) q^{69} +(-9.45402 - 2.54178i) q^{70} +(0.130275 + 0.400945i) q^{71} +(-0.893216 - 2.74904i) q^{72} +(-0.159106 - 0.115597i) q^{73} -1.76282 q^{74} +(-1.43141 - 0.829663i) q^{75} -6.12130 q^{76} +(6.64247 + 4.82604i) q^{77} +(-0.102252 - 0.314699i) q^{78} +(5.21071 + 16.0369i) q^{79} +(-1.21944 + 1.87429i) q^{80} +(2.48035 - 7.63372i) q^{81} +4.83998 q^{82} +(4.27681 - 13.1627i) q^{83} +(1.17202 - 0.851520i) q^{84} +(0.501483 + 9.72656i) q^{85} +(-0.0292717 - 0.0212671i) q^{86} +(0.472473 - 0.343272i) q^{87} +(1.51720 - 1.10231i) q^{88} +(-0.610578 - 0.443611i) q^{89} +(-6.03604 + 2.31115i) q^{90} +(-3.54196 + 2.57339i) q^{91} +(1.14914 - 3.53669i) q^{92} +0.852771 q^{93} +(-2.97527 + 9.15694i) q^{94} +(0.704773 + 13.6695i) q^{95} +(-0.102252 - 0.314699i) q^{96} +(-5.22153 - 16.0702i) q^{97} +(-9.84398 - 7.15207i) q^{98} +5.42076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

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