LMFDB - Embedded newform 570.2.bc.a.169.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.9
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.a.199.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.29893 + 1.82010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.19817 - 1.26911i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.29893 + 1.82010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.19817 - 1.26911i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.963141 + 2.01801i) q^{10} +(1.02048 - 1.76753i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(0.766336 + 0.913284i) q^{13} +(2.38515 - 0.868125i) q^{14} +(-2.22922 - 0.174899i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.04185 + 0.536361i) q^{17} -1.00000i q^{18} +(-4.26465 - 0.901550i) q^{19} +(0.598086 + 2.15460i) q^{20} +(-0.440758 + 2.49966i) q^{21} +(1.31191 - 1.56347i) q^{22} +(-1.95222 + 5.36369i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(-1.62555 + 4.72838i) q^{25} +(0.596104 + 1.03248i) q^{26} +(0.866025 + 0.500000i) q^{27} +(2.49966 - 0.440758i) q^{28} +(0.517837 + 2.93680i) q^{29} +(-2.16498 - 0.559342i) q^{30} +(-2.15058 - 3.72491i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.698051 + 1.91788i) q^{33} +(2.90250 + 1.05642i) q^{34} +(5.16519 + 2.35240i) q^{35} +(0.173648 - 0.984808i) q^{36} -5.86835i q^{37} +(-4.04330 - 1.62840i) q^{38} -1.19221 q^{39} +(0.214857 + 2.22572i) q^{40} +(-1.13532 - 0.952646i) q^{41} +(-0.868125 + 2.38515i) q^{42} +(0.681215 + 1.87162i) q^{43} +(1.56347 - 1.31191i) q^{44} +(1.56689 - 1.59526i) q^{45} +(-2.85396 + 4.94320i) q^{46} +(0.447606 - 0.0789250i) q^{47} +(-0.984808 + 0.173648i) q^{48} +(-0.278704 + 0.482729i) q^{49} +(-2.42193 + 4.37427i) q^{50} +(-2.36614 + 1.98543i) q^{51} +(0.407759 + 1.12031i) q^{52} +(-0.274401 + 0.753911i) q^{53} +(0.766044 + 0.642788i) q^{54} +(4.54262 - 0.438516i) q^{55} +2.53823 q^{56} +(3.43189 - 2.68740i) q^{57} +2.98211i q^{58} +(2.25009 - 12.7609i) q^{59} +(-2.03496 - 0.926789i) q^{60} +(-4.15561 - 1.51252i) q^{61} +(-1.47108 - 4.04176i) q^{62} +(-1.63154 - 1.94439i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.666851 + 2.58110i) q^{65} +(0.354410 + 2.00996i) q^{66} +(5.06877 - 0.893761i) q^{67} +(2.67496 + 1.54439i) q^{68} +(-2.85396 - 4.94320i) q^{69} +(4.67823 + 3.21359i) q^{70} +(3.33397 - 1.21346i) q^{71} +(0.342020 - 0.939693i) q^{72} +(-3.82239 + 4.55535i) q^{73} +(1.01903 - 5.77920i) q^{74} +(-2.57727 - 4.28459i) q^{75} +(-3.69911 - 2.30577i) q^{76} -5.18043i q^{77} +(-1.17410 - 0.207025i) q^{78} +(-11.6117 - 9.74336i) q^{79} +(-0.174899 + 2.22922i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.952646 - 1.13532i) q^{82} +(3.84806 - 2.22168i) q^{83} +(-1.26911 + 2.19817i) q^{84} +(2.97493 + 6.23318i) q^{85} +(0.345862 + 1.96148i) q^{86} +(-2.58258 - 1.49105i) q^{87} +(1.76753 - 1.02048i) q^{88} +(8.03388 - 6.74123i) q^{89} +(1.82010 - 1.29893i) q^{90} +(2.84360 + 1.03498i) q^{91} +(-3.66898 + 4.37252i) q^{92} +(4.23581 + 0.746887i) q^{93} +0.454511 q^{94} +(-3.89857 - 8.93315i) q^{95} -1.00000 q^{96} +(-17.9076 - 3.15760i) q^{97} +(-0.358294 + 0.426999i) q^{98} +(-1.91788 - 0.698051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{5}+O(q^{10}) $ 60 * q - 6 * q^5	$ 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.642788	+	0.766044i	−0.371114	+	0.442276i
$3$	−0.642788	+	0.766044i	−0.371114	+	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.29893	+	1.82010i	0.580900	+	0.813975i
$5$	1.29893	+	1.82010i	0.580900	+	0.813975i
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	2.19817	−	1.26911i	0.830830	−	0.479680i	−0.0233070	−	0.999728i	$-0.507420\pi$
$7$	2.19817	−	1.26911i	0.830830	−	0.479680i	0.854137	+	0.520049i	$0.174086\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	0.963141	+	2.01801i	0.304572	+	0.638150i
$11$	1.02048	−	1.76753i	0.307687	−	0.532930i	−0.670169	−	0.742209i	$-0.733778\pi$
$11$	1.02048	−	1.76753i	0.307687	−	0.532930i	0.977856	+	0.209279i	$0.0671116\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	0.766336	+	0.913284i	0.212543	+	0.253299i	0.861774	−	0.507292i	$-0.169353\pi$
$13$	0.766336	+	0.913284i	0.212543	+	0.253299i	−0.649231	+	0.760592i	$0.724909\pi$
$14$	2.38515	−	0.868125i	0.637459	−	0.232016i
$15$	−2.22922	−	0.174899i	−0.575581	−	0.0451588i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.04185	+	0.536361i	0.737758	+	0.130087i	0.529885	−	0.848069i	$-0.322235\pi$
$17$	3.04185	+	0.536361i	0.737758	+	0.130087i	0.207872	+	0.978156i	$0.433346\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−4.26465	−	0.901550i	−0.978377	−	0.206830i
$19$	−4.26465	−	0.901550i	−0.978377	−	0.206830i
$20$	0.598086	+	2.15460i	0.133736	+	0.481783i
$21$	−0.440758	+	2.49966i	−0.0961814	+	0.545472i
$22$	1.31191	−	1.56347i	0.279700	−	0.333333i
$23$	−1.95222	+	5.36369i	−0.407067	+	1.11841i	0.551658	+	0.834070i	$0.313995\pi$
$23$	−1.95222	+	5.36369i	−0.407067	+	1.11841i	−0.958725	+	0.284336i	$0.908227\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	−1.62555	+	4.72838i	−0.325110	+	0.945676i
$26$	0.596104	+	1.03248i	0.116906	+	0.202486i
$27$	0.866025	+	0.500000i	0.166667	+	0.0962250i
$28$	2.49966	−	0.440758i	0.472392	−	0.0832955i
$29$	0.517837	+	2.93680i	0.0961599	+	0.545350i	0.994386	+	0.105816i	$0.0337454\pi$
$29$	0.517837	+	2.93680i	0.0961599	+	0.545350i	−0.898226	+	0.439534i	$0.855143\pi$
$30$	−2.16498	−	0.559342i	−0.395269	−	0.102121i
$31$	−2.15058	−	3.72491i	−0.386255	−	0.669013i	0.605688	−	0.795702i	$-0.292898\pi$
$31$	−2.15058	−	3.72491i	−0.386255	−	0.669013i	−0.991942	+	0.126690i	$0.959565\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	0.698051	+	1.91788i	0.121515	+	0.333860i
$34$	2.90250	+	1.05642i	0.497775	+	0.181175i
$35$	5.16519	+	2.35240i	0.873076	+	0.397628i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$		−	5.86835i		−	0.964751i	−0.875964	−	0.482376i	$-0.839774\pi$
$37$		−	5.86835i		−	0.964751i	0.875964	−	0.482376i	$-0.160226\pi$
$38$	−4.04330	−	1.62840i	−0.655911	−	0.264162i
$39$	−1.19221			−0.190906
$40$	0.214857	+	2.22572i	0.0339719	+	0.351917i
$41$	−1.13532	−	0.952646i	−0.177307	−	0.148778i	0.549815	−	0.835286i	$-0.314698\pi$
$41$	−1.13532	−	0.952646i	−0.177307	−	0.148778i	−0.727122	+	0.686508i	$0.759143\pi$
$42$	−0.868125	+	2.38515i	−0.133955	+	0.368037i
$43$	0.681215	+	1.87162i	0.103884	+	0.285420i	0.980735	−	0.195343i	$-0.0625820\pi$
$43$	0.681215	+	1.87162i	0.103884	+	0.285420i	−0.876851	+	0.480763i	$0.840360\pi$
$44$	1.56347	−	1.31191i	0.235702	−	0.197778i
$45$	1.56689	−	1.59526i	0.233579	−	0.237807i
$46$	−2.85396	+	4.94320i	−0.420793	+	0.728835i
$47$	0.447606	−	0.0789250i	0.0652900	−	0.0115124i	−0.140908	−	0.990023i	$-0.545002\pi$
$47$	0.447606	−	0.0789250i	0.0652900	−	0.0115124i	0.206198	+	0.978510i	$0.433891\pi$
$48$	−0.984808	+	0.173648i	−0.142145	+	0.0250640i
$49$	−0.278704	+	0.482729i	−0.0398148	+	0.0689612i
$50$	−2.42193	+	4.37427i	−0.342512	+	0.618616i
$51$	−2.36614	+	1.98543i	−0.331326	+	0.278016i
$52$	0.407759	+	1.12031i	0.0565460	+	0.155359i
$53$	−0.274401	+	0.753911i	−0.0376919	+	0.103558i	−0.957111	−	0.289722i	$-0.906437\pi$
$53$	−0.274401	+	0.753911i	−0.0376919	+	0.103558i	0.919419	+	0.393279i	$0.128659\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	4.54262	−	0.438516i	0.612527	−	0.0591295i
$56$	2.53823			0.339185
$57$	3.43189	−	2.68740i	0.454565	−	0.355955i
$58$			2.98211i			0.391570i
$59$	2.25009	−	12.7609i	0.292937	−	1.66133i	−0.382534	−	0.923941i	$-0.624949\pi$
$59$	2.25009	−	12.7609i	0.292937	−	1.66133i	0.675471	−	0.737387i	$-0.263940\pi$
$60$	−2.03496	−	0.926789i	−0.262712	−	0.119648i
$61$	−4.15561	−	1.51252i	−0.532072	−	0.193658i	0.0619914	−	0.998077i	$-0.480255\pi$
$61$	−4.15561	−	1.51252i	−0.532072	−	0.193658i	−0.594063	+	0.804418i	$0.702477\pi$
$62$	−1.47108	−	4.04176i	−0.186827	−	0.513304i
$63$	−1.63154	−	1.94439i	−0.205555	−	0.244971i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.666851	+	2.58110i	−0.0827127	+	0.320147i
$66$	0.354410	+	2.00996i	0.0436249	+	0.247409i
$67$	5.06877	−	0.893761i	0.619249	−	0.109190i	0.144782	−	0.989464i	$-0.453752\pi$
$67$	5.06877	−	0.893761i	0.619249	−	0.109190i	0.474467	+	0.880273i	$0.342641\pi$
$68$	2.67496	+	1.54439i	0.324387	+	0.187285i
$69$	−2.85396	−	4.94320i	−0.343576	−	0.595092i
$70$	4.67823	+	3.21359i	0.559155	+	0.384097i
$71$	3.33397	−	1.21346i	0.395669	−	0.144012i	−0.136520	−	0.990637i	$-0.543592\pi$
$71$	3.33397	−	1.21346i	0.395669	−	0.144012i	0.532189	+	0.846626i	$0.321370\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	−3.82239	+	4.55535i	−0.447377	+	0.533164i	−0.941852	−	0.336029i	$-0.890916\pi$
$73$	−3.82239	+	4.55535i	−0.447377	+	0.533164i	0.494474	+	0.869192i	$0.335361\pi$
$74$	1.01903	−	5.77920i	0.118460	−	0.671818i
$75$	−2.57727	−	4.28459i	−0.297597	−	0.494742i
$76$	−3.69911	−	2.30577i	−0.424317	−	0.264491i
$77$		−	5.18043i		−	0.590365i
$78$	−1.17410	−	0.207025i	−0.132940	−	0.0234409i
$79$	−11.6117	−	9.74336i	−1.30642	−	1.09621i	−0.988998	−	0.147928i	$-0.952740\pi$
$79$	−11.6117	−	9.74336i	−1.30642	−	1.09621i	−0.317418	−	0.948286i	$-0.602816\pi$
$80$	−0.174899	+	2.22922i	−0.0195543	+	0.249234i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−0.952646	−	1.13532i	−0.105202	−	0.125375i
$83$	3.84806	−	2.22168i	0.422380	−	0.243861i	−0.273715	−	0.961811i	$-0.588253\pi$
$83$	3.84806	−	2.22168i	0.422380	−	0.243861i	0.696095	+	0.717950i	$0.254919\pi$
$84$	−1.26911	+	2.19817i	−0.138472	+	0.239840i
$85$	2.97493	+	6.23318i	0.322676	+	0.676083i
$86$	0.345862	+	1.96148i	0.0372952	+	0.211512i
$87$	−2.58258	−	1.49105i	−0.276882	−	0.159858i
$88$	1.76753	−	1.02048i	0.188419	−	0.108784i
$89$	8.03388	−	6.74123i	0.851590	−	0.714569i	−0.108550	−	0.994091i	$-0.534621\pi$
$89$	8.03388	−	6.74123i	0.851590	−	0.714569i	0.960139	+	0.279522i	$0.0901762\pi$
$90$	1.82010	−	1.29893i	0.191856	−	0.136920i
$91$	2.84360	+	1.03498i	0.298090	+	0.108496i
$92$	−3.66898	+	4.37252i	−0.382518	+	0.455867i
$93$	4.23581	+	0.746887i	0.439233	+	0.0774486i
$94$	0.454511			0.0468792
$95$	−3.89857	−	8.93315i	−0.399985	−	0.916522i
$96$	−1.00000			−0.102062
$97$	−17.9076	−	3.15760i	−1.81824	−	0.320605i	−0.842363	−	0.538911i	$-0.818836\pi$
$97$	−17.9076	−	3.15760i	−1.81824	−	0.320605i	−0.975880	+	0.218306i	$0.929947\pi$
$98$	−0.358294	+	0.426999i	−0.0361932	+	0.0431334i
$99$	−1.91788	−	0.698051i	−0.192754	−	0.0701568i
$100$	−3.14472	+	3.88726i	−0.314472	+	0.388726i
$101$	−4.39810	+	3.69045i	−0.437628	+	0.367213i	−0.834821	−	0.550522i	$-0.814429\pi$
$101$	−4.39810	+	3.69045i	−0.437628	+	0.367213i	0.397193	+	0.917735i	$0.369984\pi$
$102$	−2.67496	+	1.54439i	−0.264861	+	0.152917i
$103$	−15.5001	−	8.94900i	−1.52727	−	0.881771i	−0.999475	−	0.0324015i	$-0.989684\pi$
$103$	−15.5001	−	8.94900i	−1.52727	−	0.881771i	−0.527798	−	0.849370i	$-0.676982\pi$
$104$	0.207025	+	1.17410i	0.0203004	+	0.115130i
$105$	−5.12216	+	2.44467i	−0.499872	+	0.238575i
$106$	−0.401147	+	0.694808i	−0.0389629	+	0.0674857i
$107$	5.54774	−	3.20299i	0.536320	−	0.309644i	−0.207266	−	0.978285i	$-0.566457\pi$
$107$	5.54774	−	3.20299i	0.536320	−	0.309644i	0.743586	+	0.668640i	$0.233123\pi$
$108$	0.642788	+	0.766044i	0.0618523	+	0.0737127i
$109$	13.2805	−	4.83369i	1.27204	−	0.462984i	0.384246	−	0.923231i	$-0.374461\pi$
$109$	13.2805	−	4.83369i	1.27204	−	0.462984i	0.887791	+	0.460247i	$0.152239\pi$
$110$	4.54976	+	0.356964i	0.433802	+	0.0340351i
$111$	4.49542	+	3.77210i	0.426686	+	0.358032i
$112$	2.49966	+	0.440758i	0.236196	+	0.0416478i
$113$			6.06844i			0.570871i	0.958398	+	0.285436i	$0.0921383\pi$
$113$			6.06844i			0.570871i	−0.958398	+	0.285436i	$0.907862\pi$
$114$	3.84641	−	2.05063i	0.360250	−	0.192060i
$115$	−12.2983	+	3.41382i	−1.14682	+	0.318341i
$116$	−0.517837	+	2.93680i	−0.0480800	+	0.272675i
$117$	0.766336	−	0.913284i	0.0708478	−	0.0844331i
$118$	4.43181	−	12.1763i	0.407982	−	1.12092i
$119$	7.36721	−	2.68144i	0.675351	−	0.245808i
$120$	−1.84311	−	1.26608i	−0.168252	−	0.115576i
$121$	3.41723	+	5.91881i	0.310657	+	0.538074i
$122$	−3.82983	−	2.21116i	−0.346737	−	0.200189i
$123$	1.45954	−	0.257356i	0.131602	−	0.0232050i
$124$	−0.746887	−	4.23581i	−0.0670724	−	0.380387i
$125$	−10.7176	+	3.18319i	−0.958613	+	0.284713i
$126$	−1.26911	−	2.19817i	−0.113062	−	0.195828i
$127$	−10.1199	−	12.0604i	−0.897995	−	1.07019i	−0.997175	−	0.0751195i	$-0.976066\pi$
$127$	−10.1199	−	12.0604i	−0.897995	−	1.07019i	0.0991793	−	0.995070i	$-0.468378\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−1.87162	−	0.681215i	−0.164787	−	0.0599776i
$130$	−1.10492	+	2.42609i	−0.0969083	+	0.212783i
$131$	2.64819	−	15.0187i	0.231374	−	1.31219i	−0.618744	−	0.785593i	$-0.712358\pi$
$131$	2.64819	−	15.0187i	0.231374	−	1.31219i	0.850118	−	0.526593i	$-0.176531\pi$
$132$			2.04097i			0.177643i
$133$	−10.5186	+	3.43056i	−0.912077	+	0.297467i
$134$	5.14697			0.444630
$135$	0.214857	+	2.22572i	0.0184920	+	0.191560i
$136$	2.36614	+	1.98543i	0.202895	+	0.170249i
$137$	−6.60705	+	18.1527i	−0.564478	+	1.55089i	0.248521	+	0.968627i	$0.420056\pi$
$137$	−6.60705	+	18.1527i	−0.564478	+	1.55089i	−0.812999	+	0.582265i	$0.802167\pi$
$138$	−1.95222	−	5.36369i	−0.166184	−	0.456588i
$139$	5.89795	−	4.94897i	0.500257	−	0.419766i	−0.357428	−	0.933941i	$-0.616346\pi$
$139$	5.89795	−	4.94897i	0.500257	−	0.419766i	0.857685	+	0.514175i	$0.171902\pi$
$140$	4.04912	+	3.97713i	0.342213	+	0.336129i
$141$	−0.227256	+	0.393618i	−0.0191384	+	0.0331486i
$142$	3.49403	−	0.616092i	0.293213	−	0.0517013i
$143$	2.39629	−	0.422530i	0.200388	−	0.0353338i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−4.67264	+	4.75722i	−0.388042	+	0.395066i
$146$	−4.55535	+	3.82239i	−0.377004	+	0.316344i
$147$	−0.190644	−	0.523791i	−0.0157241	−	0.0432016i
$148$	2.00710	−	5.51445i	0.164982	−	0.453285i
$149$	10.7549	+	9.02443i	0.881075	+	0.739310i	0.966400	−	0.257043i	$-0.0827484\pi$
$149$	10.7549	+	9.02443i	0.881075	+	0.739310i	−0.0853248	+	0.996353i	$0.527193\pi$
$150$	−1.79410	−	4.66703i	−0.146488	−	0.381062i
$151$	1.45104			0.118084			0.0590419	−	0.998256i	$-0.481195\pi$
$151$	1.45104			0.118084			0.0590419	+	0.998256i	$0.481195\pi$
$152$	−3.24252	−	2.91309i	−0.263003	−	0.236283i
$153$		−	3.08878i		−	0.249713i
$154$	0.899573	−	5.10173i	0.0724896	−	0.411109i
$155$	3.98626	−	8.75267i	0.320184	−	0.703031i
$156$	−1.12031	−	0.407759i	−0.0896965	−	0.0326468i
$157$	−3.48523	−	9.57560i	−0.278152	−	0.764216i	−0.997572	−	0.0696410i	$-0.977815\pi$
$157$	−3.48523	−	9.57560i	−0.278152	−	0.764216i	0.719420	−	0.694575i	$-0.244408\pi$
$158$	−9.74336	−	11.6117i	−0.775140	−	0.923776i
$159$	−0.401147	−	0.694808i	−0.0318131	−	0.0551018i
$160$	−0.559342	+	2.16498i	−0.0442198	+	0.171157i
$161$	2.51581	+	14.2679i	0.198274	+	1.12447i
$162$	−0.984808	+	0.173648i	−0.0773738	+	0.0136431i
$163$	6.73520	+	3.88857i	0.527542	+	0.304576i	0.740015	−	0.672591i	$-0.234818\pi$
$163$	6.73520	+	3.88857i	0.527542	+	0.304576i	−0.212473	+	0.977167i	$0.568152\pi$
$164$	−0.741027	−	1.28350i	−0.0578645	−	0.100224i
$165$	−2.58402	+	3.76172i	−0.201166	+	0.292850i
$166$	4.17539	−	1.51972i	0.324073	−	0.117953i
$167$	−2.53286	+	6.95897i	−0.195998	+	0.538501i	−0.998292	−	0.0584290i	$-0.981391\pi$
$167$	−2.53286	+	6.95897i	−0.195998	+	0.538501i	0.802293	+	0.596930i	$0.203613\pi$
$168$	−1.63154	+	1.94439i	−0.125876	+	0.150013i
$169$	2.01061	−	11.4027i	0.154662	−	0.877134i
$170$	1.84735	+	6.65508i	0.141686	+	0.510421i
$171$	−0.147305	+	4.35641i	−0.0112647	+	0.333143i
$172$			1.99174i			0.151869i
$173$	0.471446	+	0.0831286i	0.0358434	+	0.00632015i	0.191541	−	0.981485i	$-0.438651\pi$
$173$	0.471446	+	0.0831286i	0.0358434	+	0.00632015i	−0.155698	+	0.987805i	$0.549763\pi$
$174$	−2.28443	−	1.91686i	−0.173182	−	0.145317i
$175$	2.42762	+	12.4568i	0.183511	+	0.941644i
$176$	1.91788	−	0.698051i	0.144566	−	0.0526176i
$177$	8.32909	+	9.92622i	0.626053	+	0.746100i
$178$	9.08243	−	5.24374i	0.680757	−	0.393035i
$179$	5.28891	−	9.16066i	0.395312	−	0.684700i	−0.597829	−	0.801624i	$-0.703970\pi$
$179$	5.28891	−	9.16066i	0.395312	−	0.684700i	0.993141	+	0.116923i	$0.0373032\pi$
$180$	2.01801	−	0.963141i	0.150413	−	0.0717883i
$181$	1.70412	+	9.66454i	0.126666	+	0.718360i	0.980304	+	0.197493i	$0.0632800\pi$
$181$	1.70412	+	9.66454i	0.126666	+	0.718360i	−0.853638	+	0.520867i	$0.825609\pi$
$182$	2.62067	+	1.51305i	0.194257	+	0.112154i
$183$	3.82983	−	2.21116i	0.283109	−	0.163453i
$184$	−4.37252	+	3.66898i	−0.322346	+	0.270481i
$185$	10.6810	−	7.62260i	0.785283	−	0.560424i
$186$	4.04176	+	1.47108i	0.296356	+	0.107865i
$187$	4.05219	−	4.82921i	0.296326	−	0.353147i
$188$	0.447606	+	0.0789250i	0.0326450	+	0.00575620i
$189$	2.53823			0.184629
$190$	−2.28812	−	9.47441i	−0.165998	−	0.687346i
$191$	6.03130			0.436410			0.218205	−	0.975903i	$-0.429980\pi$
$191$	6.03130			0.436410			0.218205	+	0.975903i	$0.429980\pi$
$192$	−0.984808	−	0.173648i	−0.0710724	−	0.0125320i
$193$	−15.2070	+	18.1230i	−1.09463	+	1.30452i	−0.145594	+	0.989344i	$0.546509\pi$
$193$	−15.2070	+	18.1230i	−1.09463	+	1.30452i	−0.949032	+	0.315180i	$0.897935\pi$
$194$	−17.0872	−	6.21925i	−1.22679	−	0.446516i
$195$	−1.54860	−	2.16994i	−0.110897	−	0.155393i
$196$	−0.426999	+	0.358294i	−0.0304999	+	0.0255925i
$197$	19.1080	−	11.0320i	1.36139	−	0.785999i	0.371581	−	0.928401i	$-0.378816\pi$
$197$	19.1080	−	11.0320i	1.36139	−	0.785999i	0.989809	+	0.142402i	$0.0454825\pi$
$198$	−1.76753	−	1.02048i	−0.125613	−	0.0725226i
$199$	−0.299524	−	1.69869i	−0.0212327	−	0.120417i	0.972349	−	0.233532i	$-0.0750283\pi$
$199$	−0.299524	−	1.69869i	−0.0212327	−	0.120417i	−0.993582	+	0.113115i	$0.963917\pi$
$200$	−3.77196	+	3.28212i	−0.266718	+	0.232081i
$201$	−2.57348	+	4.45740i	−0.181519	+	0.314401i
$202$	−4.97213	+	2.87066i	−0.349838	+	0.201979i
$203$	4.86543	+	5.79839i	0.341486	+	0.406967i
$204$	−2.90250	+	1.05642i	−0.203216	+	0.0739645i
$205$	0.259210	−	3.30382i	0.0181040	−	0.230749i
$206$	−13.7107	−	11.5046i	−0.955267	−	0.801565i
$207$	5.62120	+	0.991170i	0.390701	+	0.0688911i
$208$			1.19221i			0.0826647i
$209$	−5.94551	+	6.61787i	−0.411260	+	0.457767i
$210$	−5.46886	+	1.51808i	−0.377387	+	0.104757i
$211$	−4.26295	+	24.1764i	−0.293473	+	1.66437i	0.379870	+	0.925040i	$0.375969\pi$
$211$	−4.26295	+	24.1764i	−0.293473	+	1.66437i	−0.673343	+	0.739330i	$0.735142\pi$
$212$	−0.515705	+	0.614594i	−0.0354188	+	0.0422105i
$213$	−1.21346	+	3.33397i	−0.0831452	+	0.228440i
$214$	6.01965	−	2.19097i	0.411495	−	0.149772i
$215$	−2.52169	+	3.67099i	−0.171978	+	0.250360i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−9.45465	−	5.45865i	−0.641824	−	0.370557i
$218$	13.9181	−	2.45413i	0.942650	−	0.166215i
$219$	−1.03261	−	5.85625i	−0.0697776	−	0.395729i
$220$	4.41865	+	1.14160i	0.297905	+	0.0769665i
$221$	1.84123	+	3.18911i	0.123855	+	0.214523i
$222$	3.77210	+	4.49542i	0.253167	+	0.301713i
$223$	1.86623	+	5.12742i	0.124972	+	0.343357i	0.986363	−	0.164585i	$-0.0526285\pi$
$223$	1.86623	+	5.12742i	0.124972	+	0.343357i	−0.861391	+	0.507942i	$0.830406\pi$
$224$	2.38515	+	0.868125i	0.159365	+	0.0580040i
$225$	4.93882	+	0.779777i	0.329255	+	0.0519852i
$226$	−1.05377	+	5.97625i	−0.0700960	+	0.397534i
$227$			17.8078i			1.18195i	0.806691	+	0.590974i	$0.201256\pi$
$227$			17.8078i			1.18195i	−0.806691	+	0.590974i	$0.798744\pi$
$228$	4.14407	−	1.35156i	0.274448	−	0.0895091i
$229$	0.0303474			0.00200541			0.00100271	−	0.999999i	$-0.499681\pi$
$229$	0.0303474			0.00200541			0.00100271	+	0.999999i	$0.499681\pi$
$230$	−12.7042	+	1.22639i	−0.837693	+	0.0808656i
$231$	3.96844	+	3.32992i	0.261104	+	0.219093i
$232$	−1.01994	+	2.80226i	−0.0669624	+	0.183978i
$233$	−3.24520	−	8.91612i	−0.212600	−	0.584114i	0.786854	−	0.617139i	$-0.211708\pi$
$233$	−3.24520	−	8.91612i	−0.212600	−	0.584114i	−0.999455	+	0.0330245i	$0.989486\pi$
$234$	0.913284	−	0.766336i	0.0597032	−	0.0500970i
$235$	0.725062	+	0.712171i	0.0472978	+	0.0464569i
$236$	6.47888	−	11.2217i	0.421739	−	0.730474i
$237$	14.9277	−	2.63215i	0.969658	−	0.170977i
$238$	7.72091	−	1.36140i	0.500472	−	0.0882468i
$239$	−10.3442	+	17.9166i	−0.669109	+	1.15893i	0.309044	+	0.951048i	$0.399991\pi$
$239$	−10.3442	+	17.9166i	−0.669109	+	1.15893i	−0.978154	+	0.207884i	$0.933342\pi$
$240$	−1.59526	−	1.56689i	−0.102973	−	0.101143i
$241$	1.92536	−	1.61557i	0.124023	−	0.104068i	−0.578667	−	0.815564i	$-0.696427\pi$
$241$	1.92536	−	1.61557i	0.124023	−	0.104068i	0.702690	+	0.711497i	$0.251982\pi$
$242$	2.33752	+	6.42229i	0.150262	+	0.412840i
$243$	0.342020	−	0.939693i	0.0219406	−	0.0602813i
$244$	−3.38769	−	2.84261i	−0.216874	−	0.181979i
$245$	−1.24063	+	0.119763i	−0.0792611	+	0.00765138i
$246$	1.48205			0.0944923
$247$	−2.44478	−	4.58572i	−0.155558	−	0.291783i
$248$		−	4.30115i		−	0.273123i
$249$	−0.771581	+	4.37586i	−0.0488970	+	0.277309i
$250$	−11.1075	+	1.27373i	−0.702503	+	0.0805578i
$251$	−17.9421	−	6.53039i	−1.13250	−	0.412195i	−0.293298	−	0.956021i	$-0.594753\pi$
$251$	−17.9421	−	6.53039i	−1.13250	−	0.412195i	−0.839198	+	0.543827i	$0.816975\pi$
$252$	−0.868125	−	2.38515i	−0.0546867	−	0.150250i
$253$	7.48826	+	8.92416i	0.470783	+	0.561057i
$254$	−7.87188	−	13.6345i	−0.493926	−	0.855504i
$255$	−6.68714	−	1.72768i	−0.418765	−	0.108192i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	6.40834	−	1.12996i	0.399742	−	0.0704852i	0.0298365	−	0.999555i	$-0.490501\pi$
$257$	6.40834	−	1.12996i	0.399742	−	0.0704852i	0.369905	+	0.929070i	$0.379390\pi$
$258$	−1.72490	−	0.995869i	−0.107387	−	0.0620001i
$259$	−7.44760	−	12.8996i	−0.462772	−	0.801544i
$260$	−1.50943	+	2.19737i	−0.0936106	+	0.136275i
$261$	2.80226	−	1.01994i	0.173456	−	0.0631327i
$262$	5.21592	−	14.3306i	0.322241	−	0.885349i
$263$	2.55816	−	3.04869i	0.157743	−	0.187990i	−0.681385	−	0.731926i	$-0.738622\pi$
$263$	2.55816	−	3.04869i	0.157743	−	0.187990i	0.839127	+	0.543935i	$0.183066\pi$
$264$	−0.354410	+	2.00996i	−0.0218124	+	0.123704i
$265$	−1.72862	+	0.479841i	−0.106188	+	0.0294764i
$266$	−10.9545	+	1.55191i	−0.671663	+	0.0951537i
$267$			10.4875i			0.641824i
$268$	5.06877	+	0.893761i	0.309625	+	0.0545952i
$269$	11.1775	+	9.37900i	0.681502	+	0.571848i	0.916445	−	0.400161i	$-0.131046\pi$
$269$	11.1775	+	9.37900i	0.681502	+	0.571848i	−0.234943	+	0.972009i	$0.575490\pi$
$270$	−0.174899	+	2.22922i	−0.0106440	+	0.135666i
$271$	−0.712432	+	0.259304i	−0.0432772	+	0.0157516i	−0.363568	−	0.931568i	$-0.618442\pi$
$271$	−0.712432	+	0.259304i	−0.0432772	+	0.0157516i	0.320291	+	0.947319i	$0.396219\pi$
$272$	1.98543	+	2.36614i	0.120384	+	0.143468i
$273$	−2.62067	+	1.51305i	−0.158610	+	0.0915737i
$274$	−9.65886	+	16.7296i	−0.583513	+	1.01067i
$275$	6.69870	+	7.69843i	0.403947	+	0.464233i
$276$	−0.991170	−	5.62120i	−0.0596614	−	0.338357i
$277$	−4.03494	−	2.32958i	−0.242436	−	0.139971i	0.373860	−	0.927485i	$-0.378034\pi$
$277$	−4.03494	−	2.32958i	−0.242436	−	0.139971i	−0.616296	+	0.787515i	$0.711367\pi$
$278$	6.66772	−	3.84961i	0.399903	−	0.230884i
$279$	−3.29487	+	2.76473i	−0.197259	+	0.165520i
$280$	3.29699	+	4.61983i	0.197033	+	0.276088i
$281$	−23.0883	−	8.40345i	−1.37733	−	0.501308i	−0.455964	−	0.889998i	$-0.650705\pi$
$281$	−23.0883	−	8.40345i	−1.37733	−	0.501308i	−0.921368	+	0.388691i	$0.872928\pi$
$282$	−0.292154	+	0.348176i	−0.0173975	+	0.0207336i
$283$	27.5561	+	4.85888i	1.63804	+	0.288831i	0.915445	−	0.402442i	$-0.131839\pi$
$283$	27.5561	+	4.85888i	1.63804	+	0.288831i	0.722594	+	0.691273i	$0.242950\pi$
$284$	3.54793			0.210531
$285$	9.34914	+	2.75563i	0.553795	+	0.163230i
$286$	2.43325			0.143881
$287$	−3.70464	−	0.653228i	−0.218678	−	0.0385588i
$288$	0.642788	−	0.766044i	0.0378766	−	0.0451396i
$289$	−7.00959	−	2.55128i	−0.412329	−	0.150075i
$290$	−5.42774	+	3.87355i	−0.318728	+	0.227463i
$291$	13.9297	−	11.6884i	0.816571	−	0.685184i
$292$	−5.14990	+	2.97330i	−0.301375	+	0.173999i
$293$	−12.9400	−	7.47091i	−0.755963	−	0.436455i	0.0718815	−	0.997413i	$-0.477100\pi$
$293$	−12.9400	−	7.47091i	−0.755963	−	0.436455i	−0.827844	+	0.560958i	$0.810433\pi$
$294$	−0.0967927	−	0.548939i	−0.00564507	−	0.0320148i
$295$	26.1489	−	12.4802i	1.52245	−	0.726623i
$296$	2.93418	−	5.08214i	0.170546	−	0.295394i
$297$	1.76753	−	1.02048i	0.102562	−	0.0592144i
$298$	9.02443	+	10.7549i	0.522771	+	0.623014i
$299$	−6.39463	+	2.32745i	−0.369811	+	0.134600i
$300$	−0.956425	−	4.90767i	−0.0552192	−	0.283345i
$301$	3.87273	+	3.24960i	0.223220	+	0.187304i
$302$	1.42899	+	0.251970i	0.0822293	+	0.0144992i
$303$		−	5.74132i		−	0.329830i
$304$	−2.68740	−	3.43189i	−0.154133	−	0.196832i
$305$	−2.64492	−	9.52830i	−0.151448	−	0.545589i
$306$	0.536361	−	3.04185i	0.0306617	−	0.173891i
$307$	−18.4262	+	21.9595i	−1.05164	+	1.25329i	−0.0852092	+	0.996363i	$0.527156\pi$
$307$	−18.4262	+	21.9595i	−1.05164	+	1.25329i	−0.966430	+	0.256931i	$0.917289\pi$
$308$	1.77181	−	4.86802i	0.100958	−	0.277381i
$309$	16.8186	−	6.12148i	0.956778	−	0.348239i
$310$	5.44558	−	7.92749i	0.309288	−	0.450251i
$311$	−10.5969	−	18.3544i	−0.600897	−	1.04078i	−0.992685	−	0.120729i	$-0.961477\pi$
$311$	−10.5969	−	18.3544i	−0.600897	−	1.04078i	0.391788	−	0.920055i	$-0.371857\pi$
$312$	−1.03248	−	0.596104i	−0.0584528	−	0.0337477i
$313$	4.02888	−	0.710401i	0.227726	−	0.0401542i	−0.0586206	−	0.998280i	$-0.518670\pi$
$313$	4.02888	−	0.710401i	0.227726	−	0.0401542i	0.286347	+	0.958126i	$0.407559\pi$
$314$	−1.76950	−	10.0353i	−0.0998586	−	0.566326i
$315$	1.41974	−	5.49521i	0.0799931	−	0.309620i
$316$	−7.57899	−	13.1272i	−0.426351	−	0.738462i
$317$	15.9122	+	18.9634i	0.893716	+	1.06509i	0.997512	+	0.0704907i	$0.0224565\pi$
$317$	15.9122	+	18.9634i	0.893716	+	1.06509i	−0.103796	+	0.994599i	$0.533099\pi$
$318$	−0.274401	−	0.753911i	−0.0153876	−	0.0422772i
$319$	5.71932	+	2.08166i	0.320221	+	0.116551i
$320$	−0.926789	+	2.03496i	−0.0518091	+	0.113758i
$321$	−1.11239	+	6.30865i	−0.0620873	+	0.352115i
$322$			14.4880i			0.807384i
$323$	−12.4889	−	5.02977i	−0.694899	−	0.279864i
$324$	−1.00000			−0.0555556
$325$	−5.56407	+	2.13894i	−0.308639	+	0.118647i
$326$	5.95763	+	4.99905i	0.329963	+	0.276872i
$327$	−4.83369	+	13.2805i	−0.267304	+	0.734411i
$328$	−0.506893	−	1.39268i	−0.0279885	−	0.0768977i
$329$	0.883749	−	0.741553i	0.0487226	−	0.0408831i
$330$	−3.19798	+	3.25586i	−0.176043	+	0.179229i
$331$	14.8518	−	25.7242i	0.816331	−	1.41393i	−0.0920366	−	0.995756i	$-0.529338\pi$
$331$	14.8518	−	25.7242i	0.816331	−	1.41393i	0.908368	−	0.418172i	$-0.137329\pi$
$332$	4.37586	−	0.771581i	0.240156	−	0.0423460i
$333$	−5.77920	+	1.01903i	−0.316698	+	0.0558424i
$334$	−3.70279	+	6.41342i	−0.202608	+	0.350927i
$335$	8.21073	+	8.06475i	0.448600	+	0.440624i
$336$	−1.94439	+	1.63154i	−0.106075	+	0.0890078i
$337$	−6.90505	−	18.9715i	−0.376142	−	1.03344i	−0.972942	−	0.231052i	$-0.925783\pi$
$337$	−6.90505	−	18.9715i	−0.376142	−	1.03344i	0.596799	−	0.802390i	$-0.296439\pi$
$338$	3.96013	−	10.8804i	0.215403	−	0.591814i
$339$	−4.64870	−	3.90072i	−0.252483	−	0.211858i
$340$	0.663647	+	6.87476i	0.0359913	+	0.372836i
$341$	−8.77850			−0.475382
$342$	−0.901550	+	4.26465i	−0.0487502	+	0.230606i
$343$			19.1824i			1.03575i
$344$	−0.345862	+	1.96148i	−0.0186476	+	0.105756i
$345$	5.29004	−	11.6154i	0.284806	−	0.625351i
$346$	0.449848	+	0.163731i	0.0241840	+	0.00880226i
$347$	2.81330	+	7.72948i	0.151026	+	0.414940i	0.992016	−	0.126110i	$-0.0402492\pi$
$347$	2.81330	+	7.72948i	0.151026	+	0.414940i	−0.840990	+	0.541050i	$0.818027\pi$
$348$	−1.91686	−	2.28443i	−0.102755	−	0.122458i
$349$	−1.96736	−	3.40757i	−0.105310	−	0.182403i	0.808555	−	0.588421i	$-0.200250\pi$
$349$	−1.96736	−	3.40757i	−0.105310	−	0.182403i	−0.913865	+	0.406018i	$0.866917\pi$
$350$	0.227645	+	12.6891i	0.0121681	+	0.678260i
$351$	0.207025	+	1.17410i	0.0110502	+	0.0626686i
$352$	2.00996	−	0.354410i	0.107131	−	0.0188901i
$353$	24.0749	+	13.8997i	1.28138	+	0.739804i	0.977100	−	0.212779i	$-0.0682515\pi$
$353$	24.0749	+	13.8997i	1.28138	+	0.739804i	0.304278	+	0.952583i	$0.401585\pi$
$354$	6.47888	+	11.2217i	0.344349	+	0.596429i
$355$	6.53923	+	4.49195i	0.347066	+	0.238408i
$356$	9.85501	−	3.58693i	0.522315	−	0.190107i
$357$	−2.68144	+	7.36721i	−0.141917	+	0.389914i
$358$	6.79929	−	8.10308i	0.359354	−	0.428261i
$359$	−2.76864	+	15.7017i	−0.146123	+	0.828706i	0.820335	+	0.571883i	$0.193787\pi$
$359$	−2.76864	+	15.7017i	−0.146123	+	0.828706i	−0.966458	+	0.256823i	$0.917324\pi$
$360$	2.15460	−	0.598086i	0.113557	−	0.0315219i
$361$	17.3744	+	7.68958i	0.914443	+	0.404715i
$362$			9.81363i			0.515793i
$363$	−6.73063	−	1.18679i	−0.353266	−	0.0622904i
$364$	2.31812	+	1.94513i	0.121503	+	0.101953i
$365$	−13.2562	−	1.04005i	−0.693863	−	0.0544390i
$366$	4.15561	−	1.51252i	0.217217	−	0.0790607i
$367$	12.1115	+	14.4339i	0.632216	+	0.753445i	0.983119	−	0.182966i	$-0.0585699\pi$
$367$	12.1115	+	14.4339i	0.632216	+	0.753445i	−0.350903	+	0.936412i	$0.614125\pi$
$368$	−4.94320	+	2.85396i	−0.257682	+	0.148773i
$369$	−0.741027	+	1.28350i	−0.0385763	+	0.0668162i
$370$	11.8424	−	5.65205i	0.615656	−	0.293836i
$371$	0.353618	+	2.00547i	0.0183589	+	0.104119i
$372$	3.72491	+	2.15058i	0.193127	+	0.111502i
$373$	−13.5459	+	7.82076i	−0.701383	+	0.404943i	−0.807862	−	0.589371i	$-0.799375\pi$
$373$	−13.5459	+	7.82076i	−0.701383	+	0.404943i	0.106480	+	0.994315i	$0.466042\pi$
$374$	4.82921	−	4.05219i	0.249713	−	0.209534i
$375$	4.45069	−	10.2563i	0.229833	−	0.529632i
$376$	0.427101	+	0.155452i	0.0220260	+	0.00801682i
$377$	−2.28530	+	2.72351i	−0.117699	+	0.140268i
$378$	2.49966	+	0.440758i	0.128569	+	0.0226702i
$379$	10.0442			0.515938			0.257969	−	0.966153i	$-0.416947\pi$
$379$	10.0442			0.515938			0.257969	+	0.966153i	$0.416947\pi$
$380$	−0.608146	−	9.72780i	−0.0311972	−	0.499026i
$381$	15.7438			0.806577
$382$	5.93967	+	1.04732i	0.303900	+	0.0535858i
$383$	−20.9358	+	24.9503i	−1.06977	+	1.27490i	−0.110051	+	0.993926i	$0.535102\pi$
$383$	−20.9358	+	24.9503i	−1.06977	+	1.27490i	−0.959716	+	0.280973i	$0.909343\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	9.42892	−	6.72903i	0.480542	−	0.342943i
$386$	−18.1230	+	15.2070i	−0.922438	+	0.774017i
$387$	1.72490	−	0.995869i	0.0876814	−	0.0506229i
$388$	−15.7477	−	9.09194i	−0.799468	−	0.461573i
$389$	5.52930	+	31.3582i	0.280347	+	1.58992i	0.721449	+	0.692467i	$0.243476\pi$
$389$	5.52930	+	31.3582i	0.280347	+	1.58992i	−0.441103	+	0.897457i	$0.645413\pi$
$390$	−1.14826	−	2.40588i	−0.0581446	−	0.121827i
$391$	−8.81525	+	15.2685i	−0.445806	+	0.772159i
$392$	−0.482729	+	0.278704i	−0.0243815	+	0.0140767i
$393$	9.80273	+	11.6824i	0.494482	+	0.589301i
$394$	20.7334	−	7.54634i	1.04453	−	0.380179i
$395$	2.65112	−	33.7904i	0.133392	−	1.70018i
$396$	−1.56347	−	1.31191i	−0.0785674	−	0.0659258i
$397$	12.1488	+	2.14216i	0.609729	+	0.107512i	0.469983	−	0.882676i	$-0.344260\pi$
$397$	12.1488	+	2.14216i	0.609729	+	0.107512i	0.139746	+	0.990187i	$0.455371\pi$
$398$		−	1.72489i		−	0.0864610i
$399$	4.13325	−	10.2628i	0.206921	−	0.513784i
$400$	−4.28459	+	2.57727i	−0.214229	+	0.128863i
$401$	−3.57556	+	20.2780i	−0.178555	+	1.01264i	0.755405	+	0.655259i	$0.227440\pi$
$401$	−3.57556	+	20.2780i	−0.178555	+	1.01264i	−0.933960	+	0.357378i	$0.883671\pi$
$402$	−3.30841	+	3.94280i	−0.165008	+	0.196649i
$403$	1.75383	−	4.81862i	0.0873646	−	0.240032i
$404$	−5.39507	+	1.96365i	−0.268415	+	0.0976950i
$405$	−1.84311	−	1.26608i	−0.0915848	−	0.0629118i
$406$	3.78463	+	6.55517i	0.187828	+	0.325328i
$407$	−10.3725	−	5.98855i	−0.514145	−	0.296842i
$408$	−3.04185	+	0.536361i	−0.150594	+	0.0265538i
$409$	4.76661	+	27.0328i	0.235694	+	1.33669i	0.841148	+	0.540805i	$0.181880\pi$
$409$	4.76661	+	27.0328i	0.235694	+	1.33669i	−0.605454	+	0.795880i	$0.707009\pi$
$410$	0.828975	−	3.20862i	0.0409402	−	0.158462i
$411$	−9.65886	−	16.7296i	−0.476436	−	0.825212i
$412$	−11.5046	−	13.7107i	−0.566792	−	0.675476i
$413$	−11.2489	−	30.9062i	−0.553525	−	1.52080i
$414$	5.36369	+	1.95222i	0.263611	+	0.0959465i
$415$	9.04206	+	4.11806i	0.443857	+	0.202147i
$416$	−0.207025	+	1.17410i	−0.0101502	+	0.0575648i
$417$			7.69922i			0.377033i
$418$	−7.00437	+	5.48490i	−0.342595	+	0.268275i
$419$	−25.6411			−1.25265			−0.626325	−	0.779562i	$-0.715442\pi$
$419$	−25.6411			−1.25265			−0.626325	+	0.779562i	$0.715442\pi$
$420$	−5.64938	+	0.545357i	−0.275662	+	0.0266107i
$421$	−3.05442	−	2.56296i	−0.148863	−	0.124911i	0.565315	−	0.824875i	$-0.308755\pi$
$421$	−3.05442	−	2.56296i	−0.148863	−	0.124911i	−0.714178	+	0.699964i	$0.753199\pi$
$422$	−8.39637	+	23.0688i	−0.408729	+	1.12297i
$423$	−0.155452	−	0.427101i	−0.00755833	−	0.0207663i
$424$	−0.614594	+	0.515705i	−0.0298473	+	0.0250449i
$425$	−7.48080	+	13.5112i	−0.362872	+	0.655388i
$426$	−1.77397	+	3.07260i	−0.0859490	+	0.148868i
$427$	−11.0543	+	1.94917i	−0.534955	+	0.0943270i
$428$	6.30865	−	1.11239i	0.304940	−	0.0537692i
$429$	−1.21663	+	2.10726i	−0.0587393	+	0.101739i
$430$	−3.12084	+	3.17733i	−0.150500	+	0.153225i
$431$	4.99416	−	4.19060i	0.240560	−	0.201854i	−0.514535	−	0.857470i	$-0.672035\pi$
$431$	4.99416	−	4.19060i	0.240560	−	0.201854i	0.755095	+	0.655616i	$0.227591\pi$
$432$	0.342020	+	0.939693i	0.0164555	+	0.0452110i
$433$	3.63638	−	9.99087i	0.174753	−	0.480130i	−0.821134	−	0.570736i	$-0.806658\pi$
$433$	3.63638	−	9.99087i	0.174753	−	0.480130i	0.995887	+	0.0906055i	$0.0288802\pi$
$434$	−8.36313	−	7.01750i	−0.401443	−	0.336851i
$435$	−0.640727	−	6.63734i	−0.0307205	−	0.318236i
$436$	14.1328			0.676837
$437$	13.1612	−	21.1142i	0.629584	−	1.01003i
$438$		−	5.94659i		−	0.284139i
$439$	−1.11017	+	6.29608i	−0.0529854	+	0.300495i	−0.999772	−	0.0213677i	$-0.993198\pi$
$439$	−1.11017	+	6.29608i	−0.0529854	+	0.300495i	0.946786	+	0.321863i	$0.104309\pi$
$440$	4.15328	+	1.89154i	0.198000	+	0.0901758i
$441$	0.523791	+	0.190644i	0.0249424	+	0.00907831i
$442$	1.25948	+	3.46038i	0.0599072	+	0.164594i
$443$	2.09024	+	2.49105i	0.0993104	+	0.118353i	0.813411	−	0.581690i	$-0.197608\pi$
$443$	2.09024	+	2.49105i	0.0993104	+	0.118353i	−0.714100	+	0.700044i	$0.753164\pi$
$444$	2.93418	+	5.08214i	0.139250	+	0.241188i
$445$	22.7052	+	5.86609i	1.07633	+	0.278079i
$446$	0.947508	+	5.37359i	0.0448658	+	0.254447i
$447$	−13.8262	+	2.43794i	−0.653958	+	0.115310i
$448$	2.19817	+	1.26911i	0.103854	+	0.0599600i
$449$	12.0517	+	20.8741i	0.568754	+	0.985110i	0.996690	+	0.0813012i	$0.0259076\pi$
$449$	12.0517	+	20.8741i	0.568754	+	0.985110i	−0.427936	+	0.903809i	$0.640759\pi$
$450$	4.72838	+	1.62555i	0.222898	+	0.0766291i
$451$	−2.84240	+	1.03455i	−0.133844	+	0.0487151i
$452$	−2.07553	+	5.70247i	−0.0976247	+	0.268222i
$453$	−0.932709	+	1.11156i	−0.0438225	+	0.0522256i
$454$	−3.09230	+	17.5373i	−0.145129	+	0.823066i
$455$	1.80986	+	6.52001i	0.0848477	+	0.305663i
$456$	4.31580	−	0.611415i	0.202106	−	0.0286321i
$457$		−	41.1506i		−	1.92495i	−0.271377	−	0.962473i	$-0.587479\pi$
$457$		−	41.1506i		−	1.92495i	0.271377	−	0.962473i	$-0.412521\pi$
$458$	0.0298864	+	0.00526978i	0.00139650	+	0.000246240i
$459$	2.36614	+	1.98543i	0.110442	+	0.0926719i
$460$	−12.7242	−	0.998311i	−0.593268	−	0.0465465i
$461$	−17.0259	+	6.19692i	−0.792975	+	0.288619i	−0.706572	−	0.707641i	$-0.749759\pi$
$461$	−17.0259	+	6.19692i	−0.792975	+	0.288619i	−0.0864028	+	0.996260i	$0.527537\pi$
$462$	3.32992	+	3.96844i	0.154922	+	0.184629i
$463$	20.4806	−	11.8245i	0.951815	−	0.549531i	0.0581710	−	0.998307i	$-0.481473\pi$
$463$	20.4806	−	11.8245i	0.951815	−	0.549531i	0.893644	+	0.448776i	$0.148140\pi$
$464$	−1.49105	+	2.58258i	−0.0692204	+	0.119893i
$465$	4.14262	+	8.67976i	0.192109	+	0.402514i
$466$	−1.64763	−	9.34418i	−0.0763251	−	0.432861i
$467$	−30.3366	−	17.5148i	−1.40381	−	0.810489i	−0.409027	−	0.912522i	$-0.634132\pi$
$467$	−30.3366	−	17.5148i	−1.40381	−	0.810489i	−0.994781	+	0.102033i	$0.967465\pi$
$468$	1.03248	−	0.596104i	0.0477265	−	0.0275549i
$469$	10.0077	−	8.39748i	0.462114	−	0.387760i
$470$	0.590379	+	0.827257i	0.0272322	+	0.0381585i
$471$	9.57560	+	3.48523i	0.441220	+	0.160591i
$472$	8.32909	−	9.92622i	0.383377	−	0.456891i
$473$	4.00331	+	0.705892i	0.184073	+	0.0324570i
$474$	15.1580			0.696229
$475$	11.1953	−	18.6994i	0.513674	−	0.857986i
$476$	7.84002			0.359347
$477$	0.790106	+	0.139317i	0.0361765	+	0.00637889i
$478$	−13.2982	+	15.8482i	−0.608247	+	0.724880i
$479$	−17.4558	−	6.35341i	−0.797578	−	0.290295i	−0.0890954	−	0.996023i	$-0.528398\pi$
$479$	−17.4558	−	6.35341i	−0.797578	−	0.290295i	−0.708482	+	0.705729i	$0.750620\pi$
$480$	−1.29893	−	1.82010i	−0.0592879	−	0.0830759i
$481$	5.35947	−	4.49713i	0.244371	−	0.205052i
$482$	2.17664	−	1.25669i	0.0991435	−	0.0572405i
$483$	−12.5470	−	7.24399i	−0.570907	−	0.329613i
$484$	1.18679	+	6.73063i	0.0539451	+	0.305938i
$485$	−17.5136	−	36.6952i	−0.795253	−	1.66624i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−7.31948	+	4.22590i	−0.331677	+	0.191494i	−0.656585	−	0.754252i	$-0.728000\pi$
$487$	−7.31948	+	4.22590i	−0.331677	+	0.191494i	0.324908	+	0.945746i	$0.394667\pi$
$488$	−2.84261	−	3.38769i	−0.128679	−	0.153353i
$489$	−7.30812	+	2.65994i	−0.330485	+	0.120287i
$490$	−1.24258	−	0.0974901i	−0.0561341	−	0.00440416i
$491$	−6.73403	−	5.65052i	−0.303902	−	0.255004i	0.478064	−	0.878325i	$-0.341339\pi$
$491$	−6.73403	−	5.65052i	−0.303902	−	0.255004i	−0.781966	+	0.623321i	$0.785783\pi$
$492$	1.45954	+	0.257356i	0.0658011	+	0.0116025i
$493$			9.21106i			0.414845i
$494$	−1.61134	−	4.94059i	−0.0724975	−	0.222288i
$495$	−1.22067	−	4.39746i	−0.0548651	−	0.197651i
$496$	0.746887	−	4.23581i	0.0335362	−	0.190193i
$497$	5.78860	−	6.89858i	0.259654	−	0.309444i
$498$	−1.51972	+	4.17539i	−0.0681002	+	0.187104i
$499$	5.47311	−	1.99205i	0.245010	−	0.0891764i	−0.216596	−	0.976261i	$-0.569495\pi$
$499$	5.47311	−	1.99205i	0.245010	−	0.0891764i	0.461606	+	0.887085i	$0.347273\pi$
$500$	−11.1600	−	0.674425i	−0.499089	−	0.0301612i
$501$	−3.70279	−	6.41342i	−0.165428	−	0.286531i
$502$	−16.5355	−	9.54679i	−0.738017	−	0.426094i
$503$	−41.9612	+	7.39890i	−1.87096	+	0.329901i	−0.989748	−	0.142823i	$-0.954382\pi$
$503$	−41.9612	+	7.39890i	−1.87096	+	0.329901i	−0.881211	+	0.472724i	$0.843271\pi$
$504$	−0.440758	−	2.49966i	−0.0196329	−	0.111344i
$505$	−12.4298	−	3.21136i	−0.553120	−	0.142904i
$506$	5.82483	+	10.0889i	0.258945	+	0.448507i
$507$	7.44261	+	8.86975i	0.330538	+	0.393920i
$508$	−5.38468	−	14.7943i	−0.238907	−	0.656391i
$509$	−22.1016	−	8.04433i	−0.979637	−	0.356559i	−0.197938	−	0.980215i	$-0.563424\pi$
$509$	−22.1016	−	8.04433i	−0.979637	−	0.356559i	−0.781699	+	0.623656i	$0.785647\pi$
$510$	−6.28554	−	2.86265i	−0.278328	−	0.126760i
$511$	−2.62101	+	14.8645i	−0.115947	+	0.657566i
$512$			1.00000i			0.0441942i
$513$	−3.24252	−	2.91309i	−0.143161	−	0.128616i
$514$	6.50720			0.287020
$515$	−3.84552	−	39.8360i	−0.169454	−	1.75538i
$516$	−1.52576	−	1.28027i	−0.0671679	−	0.0563605i
$517$	0.317272	−	0.871698i	0.0139536	−	0.0383372i
$518$	−5.09446	−	13.9969i	−0.223838	−	0.614989i
$519$	−0.366720	+	0.307714i	−0.0160972	+	0.0135072i
$520$	−1.86806	+	1.90188i	−0.0819200	+	0.0834028i
$521$	21.2524	−	36.8102i	0.931084	−	1.61268i	0.149612	−	0.988745i	$-0.452198\pi$
$521$	21.2524	−	36.8102i	0.931084	−	1.61268i	0.781472	−	0.623940i	$-0.214469\pi$
$522$	2.93680	−	0.517837i	0.128540	−	0.0226651i
$523$	42.2164	−	7.44390i	1.84600	−	0.325499i	0.862448	−	0.506146i	$-0.168930\pi$
$523$	42.2164	−	7.44390i	1.84600	−	0.325499i	0.983548	+	0.180648i	$0.0578193\pi$
$524$	7.62517	−	13.2072i	0.333107	−	0.576958i
$525$	−11.1029	−	6.14740i	−0.484570	−	0.268294i
$526$	3.04869	−	2.55816i	0.132929	−	0.111541i
$527$	−4.54384	−	12.4841i	−0.197933	−	0.543816i
$528$	−0.698051	+	1.91788i	−0.0303788	+	0.0834650i
$529$	−7.33896	−	6.15812i	−0.319085	−	0.267744i
$530$	−1.78568	+	0.172379i	−0.0775652	+	0.00748766i
$531$	−12.9578			−0.562319
$532$	−11.0576	−	0.373894i	−0.479406	−	0.0162104i
$533$		−	1.76692i		−	0.0765336i
$534$	−1.82113	+	10.3282i	−0.0788081	+	0.446943i
$535$	13.0359	+	5.93699i	0.563591	+	0.256678i
$536$	4.83657	+	1.76037i	0.208908	+	0.0760362i
$537$	3.61783	+	9.93990i	0.156121	+	0.428938i
$538$	9.37900	+	11.1775i	0.404357	+	0.481894i
$539$	0.568824	+	0.985233i	0.0245010	+	0.0424370i
$540$	−0.559342	+	2.16498i	−0.0240702	+	0.0931659i
$541$	−6.23743	−	35.3742i	−0.268168	−	1.52086i	−0.759860	−	0.650087i	$-0.774732\pi$
$541$	−6.23743	−	35.3742i	−0.268168	−	1.52086i	0.491692	−	0.870769i	$-0.336379\pi$
$542$	−0.746636	+	0.131652i	−0.0320708	+	0.00565494i
$543$	−8.49886	−	4.90682i	−0.364721	−	0.210572i
$544$	1.54439	+	2.67496i	0.0662151	+	0.114688i
$545$	26.0482	+	17.8932i	1.11578	+	0.766459i
$546$	−2.84360	+	1.03498i	−0.121695	+	0.0442932i
$547$	10.4734	−	28.7753i	0.447808	−	1.23034i	−0.486438	−	0.873715i	$-0.661704\pi$
$547$	10.4734	−	28.7753i	0.447808	−	1.23034i	0.934246	−	0.356628i	$-0.116074\pi$
$548$	−12.4172	+	14.7982i	−0.530436	+	0.632149i
$549$	−0.767926	+	4.35513i	−0.0327743	+	0.185872i
$550$	5.26012	+	8.74470i	0.224292	+	0.372875i
$551$	0.439280	−	12.9913i	0.0187140	−	0.553447i
$552$		−	5.70792i		−	0.242945i
$553$	−37.8899	−	6.68100i	−1.61124	−	0.284105i
$554$	−3.56912	−	2.99485i	−0.151637	−	0.127239i
$555$	−1.02637	+	13.0818i	−0.0435670	+	0.555293i
$556$	7.23490	−	2.63329i	0.306828	−	0.111676i
$557$	4.08411	+	4.86726i	0.173049	+	0.206232i	0.845597	−	0.533821i	$-0.179245\pi$
$557$	4.08411	+	4.86726i	0.173049	+	0.206232i	−0.672548	+	0.740054i	$0.734800\pi$
$558$	−3.72491	+	2.15058i	−0.157688	+	0.0910411i
$559$	−1.18728	+	2.05643i	−0.0502167	+	0.0869779i
$560$	2.44467	+	5.12216i	0.103306	+	0.216451i
$561$	1.09469	+	6.20832i	0.0462180	+	0.262115i
$562$	−21.2783	−	12.2850i	−0.897570	−	0.518212i
$563$	−7.49985	+	4.33004i	−0.316081	+	0.182489i	−0.649644	−	0.760238i	$-0.725082\pi$
$563$	−7.49985	+	4.33004i	−0.316081	+	0.182489i	0.333563	+	0.942728i	$0.391749\pi$
$564$	−0.348176	+	0.292154i	−0.0146608	+	0.0123019i
$565$	−11.0452	+	7.88250i	−0.464675	+	0.331619i
$566$	26.2937	+	9.57013i	1.10521	+	0.402262i
$567$	−1.63154	+	1.94439i	−0.0685183	+	0.0816569i
$568$	3.49403	+	0.616092i	0.146606	+	0.0258507i
$569$	−5.60373			−0.234921			−0.117460	−	0.993078i	$-0.537475\pi$
$569$	−5.60373			−0.234921			−0.117460	+	0.993078i	$0.537475\pi$
$570$	8.72860	+	4.33723i	0.365601	+	0.181667i
$571$	3.84318			0.160832			0.0804161	−	0.996761i	$-0.474375\pi$
$571$	3.84318			0.160832			0.0804161	+	0.996761i	$0.474375\pi$
$572$	2.39629	+	0.422530i	0.100194	+	0.0176669i
$573$	−3.87684	+	4.62024i	−0.161958	+	0.193013i
$574$	−3.53493	−	1.28661i	−0.147545	−	0.0537020i
$575$	−22.1881	−	17.9498i	−0.925309	−	0.748558i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	21.6250	−	12.4852i	0.900262	−	0.519766i	0.0229766	−	0.999736i	$-0.492686\pi$
$577$	21.6250	−	12.4852i	0.900262	−	0.519766i	0.877285	+	0.479970i	$0.159352\pi$
$578$	−6.46007	−	3.72973i	−0.268704	−	0.155136i
$579$	−4.10816	−	23.2985i	−0.170729	−	0.968253i
$580$	−6.01791	+	2.87219i	−0.249880	+	0.119261i
$581$	5.63913	−	9.76725i	0.233950	−	0.405214i
$582$	15.7477	−	9.09194i	0.652763	−	0.376873i
$583$	1.05254	+	1.25436i	0.0435916	+	0.0519505i
$584$	−5.58797	+	2.03385i	−0.231232	+	0.0841615i
$585$	2.65769	+	0.208516i	0.109882	+	0.00862109i
$586$	−11.4461	−	9.60442i	−0.472834	−	0.396755i
$587$	8.82531	+	1.55614i	0.364260	+	0.0642288i	0.352783	−	0.935705i	$-0.385236\pi$
$587$	8.82531	+	1.55614i	0.364260	+	0.0642288i	0.0114771	+	0.999934i	$0.496347\pi$
$588$		−	0.557407i		−	0.0229871i
$589$	5.81325	+	17.8243i	0.239531	+	0.734436i
$590$	27.9188	−	7.74985i	1.14940	−	0.319056i
$591$	−3.83138	+	21.7288i	−0.157602	+	0.893805i
$592$	3.77210	−	4.49542i	0.155033	−	0.184761i
$593$	−12.0589	+	33.1316i	−0.495200	+	1.36055i	0.400666	+	0.916224i	$0.368779\pi$
$593$	−12.0589	+	33.1316i	−0.495200	+	1.36055i	−0.895865	+	0.444326i	$0.853443\pi$
$594$	1.91788	−	0.698051i	0.0786916	−	0.0286414i
$595$	14.4500	+	9.92606i	0.592393	+	0.406929i
$596$	7.01976	+	12.1586i	0.287540	+	0.498035i
$597$	1.49380	+	0.862446i	0.0611372	+	0.0352976i
$598$	−6.70164	+	1.18168i	−0.274050	+	0.0483225i
$599$	5.78203	+	32.7915i	0.236247	+	1.33983i	0.839971	+	0.542631i	$0.182572\pi$
$599$	5.78203	+	32.7915i	0.236247	+	1.33983i	−0.603724	+	0.797194i	$0.706317\pi$
$600$	−0.0896865	−	4.99920i	−0.00366143	−	0.204091i
$601$	−23.3322	−	40.4125i	−0.951739	−	1.64846i	−0.741660	−	0.670776i	$-0.765961\pi$
$601$	−23.3322	−	40.4125i	−0.951739	−	1.64846i	−0.210079	−	0.977684i	$-0.567372\pi$
$602$	3.24960	+	3.87273i	0.132444	+	0.157841i
$603$	−1.76037	−	4.83657i	−0.0716876	−	0.196960i
$604$	1.36353	+	0.496284i	0.0554812	+	0.0201935i
$605$	−6.33410	+	13.9078i	−0.257518	+	0.565434i
$606$	0.996969	−	5.65409i	0.0404991	−	0.229682i
$607$			6.90728i			0.280358i	0.990126	+	0.140179i	$0.0447678\pi$
$607$			6.90728i			0.280358i	−0.990126	+	0.140179i	$0.955232\pi$
$608$	−2.05063	−	3.84641i	−0.0831642	−	0.155993i
$609$	−7.56926			−0.306722
$610$	−0.950166	−	9.84283i	−0.0384711	−	0.398525i
$611$	0.415098	+	0.348308i	0.0167931	+	0.0140910i
$612$	1.05642	−	2.90250i	0.0427034	−	0.117327i
$613$	−2.07142	−	5.69119i	−0.0836640	−	0.229865i	0.890806	−	0.454385i	$-0.150141\pi$
$613$	−2.07142	−	5.69119i	−0.0836640	−	0.229865i	−0.974470	+	0.224520i	$0.927919\pi$
$614$	−21.9595	+	18.4262i	−0.886213	+	0.743621i
$615$	2.36426	+	2.32222i	0.0953360	+	0.0936410i
$616$	2.59022	−	4.48639i	0.104363	−	0.180762i
$617$	27.9435	−	4.92719i	1.12496	−	0.198361i	0.419944	−	0.907550i	$-0.362050\pi$
$617$	27.9435	−	4.92719i	1.12496	−	0.198361i	0.705018	+	0.709189i	$0.250939\pi$
$618$	17.6261	−	3.10796i	0.709025	−	0.125020i
$619$	−16.3613	+	28.3385i	−0.657614	+	1.13902i	0.323617	+	0.946188i	$0.395101\pi$
$619$	−16.3613	+	28.3385i	−0.657614	+	1.13902i	−0.981232	+	0.192833i	$0.938232\pi$
$620$	6.73945	−	6.86144i	0.270663	−	0.275562i
$621$	−4.37252	+	3.66898i	−0.175463	+	0.147231i
$622$	−7.24873	−	19.9157i	−0.290648	−	0.798548i
$623$	9.10444	−	25.0143i	0.364762	−	1.00217i
$624$	−0.913284	−	0.766336i	−0.0365606	−	0.0306780i
$625$	−19.7152	−	15.3724i	−0.788608	−	0.614897i
$626$	4.09104			0.163511
$627$	−1.24788	−	8.80841i	−0.0498354	−	0.351774i
$628$		−	10.1901i		−	0.406631i
$629$	3.14755	−	17.8507i	0.125501	−	0.711753i
$630$	2.35240	−	5.16519i	0.0937219	−	0.205786i
$631$	6.88231	+	2.50496i	0.273981	+	0.0997208i	0.475357	−	0.879793i	$-0.342319\pi$
$631$	6.88231	+	2.50496i	0.273981	+	0.0997208i	−0.201376	+	0.979514i	$0.564541\pi$
$632$	−5.18433	−	14.2438i	−0.206222	−	0.566589i
$633$	−15.7800	−	18.8059i	−0.627199	−	0.747467i
$634$	12.3775	+	21.4384i	0.491572	+	0.851427i
$635$	8.80614	−	34.0849i	0.349461	−	1.35262i
$636$	−0.139317	−	0.790106i	−0.00552428	−	0.0313297i
$637$	−0.654449	+	0.115397i	−0.0259302	+	0.00457220i
$638$	5.27096	+	3.04319i	0.208679	+	0.120481i
$639$	−1.77397	−	3.07260i	−0.0701770	−	0.121550i
$640$	−1.26608	+	1.84311i	−0.0500460	+	0.0728553i
$641$	−2.99981	+	1.09184i	−0.118485	+	0.0431251i	−0.400582	−	0.916261i	$-0.631192\pi$
$641$	−2.99981	+	1.09184i	−0.118485	+	0.0431251i	0.282097	+	0.959386i	$0.408970\pi$
$642$	−2.19097	+	6.01965i	−0.0864708	+	0.237577i
$643$	−22.5910	+	26.9229i	−0.890903	+	1.06174i	0.106819	+	0.994279i	$0.465934\pi$
$643$	−22.5910	+	26.9229i	−0.890903	+	1.06174i	−0.997722	+	0.0674586i	$0.978511\pi$
$644$	−2.51581	+	14.2679i	−0.0991369	+	0.562233i
$645$	−1.19123	−	4.29140i	−0.0469047	−	0.168974i
$646$	−11.4257	−	7.12203i	−0.449539	−	0.280212i
$647$			8.49871i			0.334119i	0.985947	+	0.167059i	$0.0534271\pi$
$647$			8.49871i			0.334119i	−0.985947	+	0.167059i	$0.946573\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	−20.2591	−	16.9994i	−0.795238	−	0.667284i
$650$	−5.85096	+	1.14026i	−0.229494	+	0.0447246i
$651$	10.2589	−	3.73393i	0.402078	−	0.146344i
$652$	4.99905	+	5.95763i	0.195778	+	0.233319i
$653$	2.53932	−	1.46608i	0.0993712	−	0.0573720i	−0.449491	−	0.893285i	$-0.648395\pi$
$653$	2.53932	−	1.46608i	0.0993712	−	0.0573720i	0.548862	+	0.835913i	$0.315061\pi$
$654$	−7.06638	+	12.2393i	−0.276317	+	0.478596i
$655$	30.7753	−	14.6882i	1.20249	−	0.573917i
$656$	−0.257356	−	1.45954i	−0.0100481	−	0.0569854i
$657$	5.14990	+	2.97330i	0.200917	+	0.115999i
$658$	0.999092	−	0.576826i	0.0389487	−	0.0224870i
$659$	−0.888827	+	0.745814i	−0.0346238	+	0.0290528i	−0.659935	−	0.751322i	$-0.729416\pi$
$659$	−0.888827	+	0.745814i	−0.0346238	+	0.0290528i	0.625312	+	0.780375i	$0.284972\pi$
$660$	−3.71477	+	2.65108i	−0.144597	+	0.103193i
$661$	30.7523	+	11.1929i	1.19613	+	0.435354i	0.861871	−	0.507128i	$-0.169293\pi$
$661$	30.7523	+	11.1929i	1.19613	+	0.435354i	0.334256	+	0.942482i	$0.391515\pi$
$662$	19.0932	−	22.7544i	0.742077	−	0.884373i
$663$	−3.62652	−	0.639453i	−0.140842	−	0.0248343i
$664$	4.44336			0.172436
$665$	−19.9069	−	14.6888i	−0.771956	−	0.569608i
$666$	−5.86835			−0.227394
$667$	−16.7630	−	2.95577i	−0.649067	−	0.114448i
$668$	−4.76022	+	5.67300i	−0.184178	+	0.219495i
$669$	−5.12742	−	1.86623i	−0.198237	−	0.0721525i
$670$	6.68556	+	9.36801i	0.258286	+	0.361918i
$671$	−6.91415	+	5.80166i	−0.266918	+	0.223971i
$672$	−2.19817	+	1.26911i	−0.0847962	+	0.0489571i
$673$	0.905622	+	0.522861i	0.0349092	+	0.0201548i	0.517353	−	0.855772i	$-0.326917\pi$
$673$	0.905622	+	0.522861i	0.0349092	+	0.0201548i	−0.482444	+	0.875927i	$0.660251\pi$
$674$	−3.50579	−	19.8823i	−0.135038	−	0.765838i
$675$	−3.77196	+	3.28212i	−0.145183	+	0.126329i
$676$	5.78932	−	10.0274i	0.222666	−	0.385669i
$677$	−26.8473	+	15.5003i	−1.03183	+	0.595725i	−0.917507	−	0.397719i	$-0.869802\pi$
$677$	−26.8473	+	15.5003i	−1.03183	+	0.595725i	−0.114318	+	0.993444i	$0.536468\pi$
$678$	−3.90072	−	4.64870i	−0.149806	−	0.178532i
$679$	−43.3713	+	15.7859i	−1.66444	+	0.605806i
$680$	−0.540225	+	6.88556i	−0.0207167	+	0.264049i
$681$	−13.6416	−	11.4467i	−0.522747	−	0.438637i
$682$	−8.64514	−	1.52437i	−0.331039	−	0.0583712i
$683$		−	33.6926i		−	1.28921i	−0.764514	−	0.644607i	$-0.777021\pi$
$683$		−	33.6926i		−	1.28921i	0.764514	−	0.644607i	$-0.222979\pi$
$684$	−1.62840	+	4.04330i	−0.0622635	+	0.154600i
$685$	−41.6219	+	11.5537i	−1.59029	+	0.441442i
$686$	−3.33099	+	18.8910i	−0.127178	+	0.721261i
$687$	−0.0195070	+	0.0232475i	−0.000744237	+	0.000886947i
$688$	−0.681215	+	1.87162i	−0.0259711	+	0.0713549i
$689$	−0.898818	+	0.327143i	−0.0342422	+	0.0124632i
$690$	7.22666	−	10.5203i	0.275114	−	0.400502i
$691$	−24.9883	−	43.2810i	−0.950601	−	1.64649i	−0.744129	−	0.668036i	$-0.767135\pi$
$691$	−24.9883	−	43.2810i	−0.950601	−	1.64649i	−0.206472	−	0.978453i	$-0.566198\pi$
$692$	0.414582	+	0.239359i	0.0157601	+	0.00909908i
$693$	−5.10173	+	0.899573i	−0.193799	+	0.0341719i
$694$	1.42835	+	8.10057i	0.0542194	+	0.307494i
$695$	16.6687	+	4.30650i	0.632278	+	0.163355i
$696$	−1.49105	−	2.58258i	−0.0565182	−	0.0978924i
$697$	−2.94251	−	3.50675i	−0.111456	−	0.132828i
$698$	−1.34575	−	3.69743i	−0.0509376	−	0.139950i
$699$	8.91612	+	3.24520i	0.337239	+	0.122745i
$700$	−1.97925	+	12.5358i	−0.0748087	+	0.473810i
$701$	−3.63745	+	20.6290i	−0.137385	+	0.779147i	0.835785	+	0.549057i	$0.185013\pi$
$701$	−3.63745	+	20.6290i	−0.137385	+	0.779147i	−0.973169	+	0.230090i	$0.926098\pi$
$702$			1.19221i			0.0449970i
$703$	−5.29061	+	25.0265i	−0.199539	+	0.943891i
$704$	2.04097			0.0769218
$705$	−1.01161	+	0.0976550i	−0.0380996	+	0.00367790i
$706$	21.2955	+	17.8691i	0.801467	+	0.672511i
$707$	−4.98418	+	13.6939i	−0.187449	+	0.515013i
$708$	4.43181	+	12.1763i	0.166558	+	0.457614i
$709$	−11.6400	+	9.76713i	−0.437150	+	0.366812i	−0.834642	−	0.550793i	$-0.814325\pi$
$709$	−11.6400	+	9.76713i	−0.437150	+	0.366812i	0.397492	+	0.917606i	$0.369881\pi$
$710$	5.65986	+	5.55924i	0.212411	+	0.208634i
$711$	−7.57899	+	13.1272i	−0.284234	+	0.492308i
$712$	10.3282	−	1.82113i	0.387064	−	0.0682498i
$713$	24.1776	−	4.26317i	0.905460	−	0.159657i
$714$	−3.92001	+	6.78965i	−0.146703	+	0.254096i
$715$	3.88167	+	3.81265i	0.145166	+	0.142585i
$716$	8.10308	−	6.79929i	0.302826	−	0.254102i
$717$	−7.07584	−	19.4407i	−0.264252	−	0.726026i
$718$	−5.45316	+	14.9824i	−0.203510	+	0.559139i
$719$	32.8511	+	27.5654i	1.22514	+	1.02801i	0.998539	+	0.0540268i	$0.0172056\pi$
$719$	32.8511	+	27.5654i	1.22514	+	1.02801i	0.226601	+	0.973988i	$0.427239\pi$
$720$	2.22572	−	0.214857i	0.0829477	−	0.00800726i
$721$	−45.4292			−1.69187
$722$	15.7752	+	10.5898i	0.587091	+	0.394111i
$723$			2.51337i			0.0934734i
$724$	−1.70412	+	9.66454i	−0.0633331	+	0.359180i
$725$	−14.7281	−	2.32538i	−0.546987	−	0.0863624i
$726$	−6.42229	−	2.33752i	−0.238354	−	0.0867536i
$727$	−5.28688	−	14.5256i	−0.196080	−	0.538724i	0.802219	−	0.597030i	$-0.203653\pi$
$727$	−5.28688	−	14.5256i	−0.196080	−	0.538724i	−0.998299	+	0.0583052i	$0.981430\pi$
$728$	1.94513	+	2.31812i	0.0720915	+	0.0859153i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	−12.8742	−	3.32618i	−0.476497	−	0.123107i
$731$	1.06829	+	6.05858i	0.0395121	+	0.224085i
$732$	4.35513	−	0.767926i	0.160970	−	0.0283834i
$733$	25.8705	+	14.9363i	0.955547	+	0.551685i	0.894800	−	0.446468i	$-0.147318\pi$
$733$	25.8705	+	14.9363i	0.955547	+	0.551685i	0.0607474	+	0.998153i	$0.480652\pi$
$734$	9.42108	+	16.3178i	0.347739	+	0.602301i
$735$	0.705720	−	1.02736i	0.0260309	−	0.0378948i
$736$	−5.36369	+	1.95222i	−0.197708	+	0.0719599i
$737$	3.59285	−	9.87127i	0.132344	−	0.363613i
$738$	−0.952646	+	1.13532i	−0.0350674	+	0.0417917i
$739$	5.87045	−	33.2930i	0.215948	−	1.22470i	−0.663305	−	0.748349i	$-0.730847\pi$
$739$	5.87045	−	33.2930i	0.215948	−	1.22470i	0.879254	−	0.476354i	$-0.158042\pi$
$740$	12.6439	−	3.50978i	0.464801	−	0.129022i
$741$	5.08434	+	1.07483i	0.186778	+	0.0394850i
$742$			2.03641i			0.0747588i
$743$	35.2448	+	6.21460i	1.29301	+	0.227992i	0.777493	−	0.628891i	$-0.216491\pi$
$743$	35.2448	+	6.21460i	1.29301	+	0.227992i	0.515512	+	0.856883i	$0.327602\pi$
$744$	3.29487	+	2.76473i	0.120796	+	0.101360i
$745$	−2.45550	+	31.2971i	−0.0899626	+	1.14664i
$746$	−14.6982	+	5.34971i	−0.538140	+	0.195867i
$747$	−2.85614	−	3.40381i	−0.104501	−	0.124539i
$748$	5.45950	−	3.15205i	0.199619	−	0.115250i
$749$	8.12991	−	14.0814i	0.297060	−	0.514524i
$750$	6.16406	−	9.32761i	0.225080	−	0.340596i
$751$	8.37817	+	47.5149i	0.305724	+	1.73385i	0.620079	+	0.784540i	$0.287101\pi$
$751$	8.37817	+	47.5149i	0.305724	+	1.73385i	−0.314355	+	0.949305i	$0.601788\pi$
$752$	0.393618	+	0.227256i	0.0143538	+	0.00828716i
$753$	16.5355	−	9.54679i	0.602588	−	0.347904i
$754$	−2.72351	+	2.28530i	−0.0991843	+	0.0832255i
$755$	1.88480	+	2.64104i	0.0685949	+	0.0961172i
$756$	2.38515	+	0.868125i	0.0867472	+	0.0315734i
$757$	10.9039	−	12.9947i	0.396308	−	0.472302i	−0.530582	−	0.847633i	$-0.678027\pi$
$757$	10.9039	−	12.9947i	0.396308	−	0.472302i	0.926891	+	0.375331i	$0.122471\pi$
$758$	9.89164	+	1.74416i	0.359281	+	0.0633509i
$759$	−11.6497			−0.422856
$760$	1.09031	−	9.68562i	0.0395497	−	0.351334i
$761$	51.0498			1.85056			0.925278	−	0.379291i	$-0.123832\pi$
$761$	51.0498			1.85056			0.925278	+	0.379291i	$0.123832\pi$
$762$	15.5046	+	2.73387i	0.561671	+	0.0990378i
$763$	23.0582	−	27.4797i	0.834762	−	0.994831i
$764$	5.66757	+	2.06283i	0.205045	+	0.0746304i
$765$	5.62189	−	4.01211i	0.203260	−	0.145058i
$766$	−24.9503	+	20.9358i	−0.901490	+	0.756440i
$767$	13.3787	−	7.72417i	0.483075	−	0.278904i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	7.31957	+	41.5114i	0.263951	+	1.49694i	0.772007	+	0.635614i	$0.219253\pi$
$769$	7.31957	+	41.5114i	0.263951	+	1.49694i	−0.508056	+	0.861324i	$0.669636\pi$
$770$	10.4542	−	4.98949i	0.376742	−	0.179809i
$771$	−3.25360	+	5.63540i	−0.117176	+	0.202954i
$772$	−20.4884	+	11.8290i	−0.737393	+	0.425734i
$773$	19.7297	+	23.5130i	0.709629	+	0.845703i	0.993580	−	0.113136i	$-0.0360895\pi$
$773$	19.7297	+	23.5130i	0.709629	+	0.845703i	−0.283950	+	0.958839i	$0.591645\pi$
$774$	1.87162	−	0.681215i	0.0672741	−	0.0244858i
$775$	21.1086	−	4.11373i	0.758245	−	0.147769i
$776$	−13.9297	−	11.6884i	−0.500045	−	0.419588i
$777$	14.6689	+	2.58653i	0.526244	+	0.0927911i
$778$			31.8420i			1.14159i
$779$	3.98288	+	5.08625i	0.142701	+	0.182234i
$780$	−0.713042	−	2.56873i	−0.0255310	−	0.0919752i
$781$	1.25742	−	7.13120i	0.0449941	−	0.255174i
$782$	−11.3327	+	13.5057i	−0.405255	+	0.482964i
$783$	−1.01994	+	2.80226i	−0.0364497	+	0.100145i
$784$	−0.523791	+	0.190644i	−0.0187068	+	0.00680873i
$785$	12.9015	−	18.7815i	0.460474	−	0.670342i
$786$	7.62517	+	13.2072i	0.271981	+	0.471085i
$787$	−2.82286	−	1.62978i	−0.100624	−	0.0580954i	0.448843	−	0.893610i	$-0.351836\pi$
$787$	−2.82286	−	1.62978i	−0.100624	−	0.0580954i	−0.549468	+	0.835515i	$0.685169\pi$
$788$	21.7288	−	3.83138i	0.774058	−	0.136487i
$789$	0.691082	+	3.91932i	0.0246032	+	0.139532i
$790$	8.47849	−	32.8167i	0.301651	−	1.16757i
$791$	7.70154	+	13.3395i	0.273835	+	0.474297i
$792$	−1.31191	−	1.56347i	−0.0466166	−	0.0555555i
$793$	−1.80324	−	4.95435i	−0.0640348	−	0.175934i
$794$	11.5922	+	4.21922i	0.411392	+	0.149735i
$795$	0.743558	−	1.63264i	0.0263713	−	0.0579037i
$796$	0.299524	−	1.69869i	0.0106164	−	0.0602083i
$797$			14.0250i			0.496790i	0.968659	+	0.248395i	$0.0799030\pi$
$797$			14.0250i			0.496790i	−0.968659	+	0.248395i	$0.920097\pi$
$798$	5.85258	−	9.38917i	0.207179	−	0.332373i
$799$	1.40388			0.0496658
$800$	−4.66703	+	1.79410i	−0.165005	+	0.0634311i
$801$	−8.03388	−	6.74123i	−0.283863	−	0.238190i
$802$	−7.04249	+	19.3491i	−0.248679	+	0.683240i
$803$	4.15103	+	11.4049i	0.146487	+	0.402468i
$804$	−3.94280	+	3.30841i	−0.139052	+	0.116678i
$805$	−22.7011	+	23.1121i	−0.800110	+	0.814593i
$806$	2.56393	−	4.44086i	0.0903106	−	0.156423i
$807$	−14.3695	+	2.53372i	−0.505829	+	0.0891913i
$808$	−5.65409	+	0.996969i	−0.198910	+	0.0350733i
$809$	22.2628	−	38.5604i	0.782719	−	1.35571i	−0.147633	−	0.989042i	$-0.547165\pi$
$809$	22.2628	−	38.5604i	0.782719	−	1.35571i	0.930352	−	0.366668i	$-0.119501\pi$
$810$	−1.59526	−	1.56689i	−0.0560516	−	0.0550550i
$811$	−18.4566	+	15.4869i	−0.648098	+	0.543819i	−0.906493	−	0.422220i	$-0.861251\pi$
$811$	−18.4566	+	15.4869i	−0.648098	+	0.543819i	0.258395	+	0.966039i	$0.416806\pi$
$812$	2.58884	+	7.11278i	0.0908504	+	0.249610i
$813$	0.259304	−	0.712432i	0.00909419	−	0.0249861i
$814$	−9.17500	−	7.69874i	−0.321584	−	0.269841i
$815$	1.67098	+	17.3097i	0.0585317	+	0.606334i
$816$	−3.08878			−0.108129
$817$	−1.21778	−	8.59596i	−0.0426047	−	0.300734i
$818$			27.4498i			0.959760i
$819$	0.525475	−	2.98012i	0.0183616	−	0.104134i
$820$	1.37355	−	3.01592i	0.0479665	−	0.105321i
$821$	36.6485	+	13.3390i	1.27904	+	0.465533i	0.890115	−	0.455736i	$-0.150624\pi$
$821$	36.6485	+	13.3390i	1.27904	+	0.465533i	0.388926	+	0.921269i	$0.372846\pi$
$822$	−6.60705	−	18.1527i	−0.230447	−	0.633149i
$823$	19.0874	+	22.7475i	0.665346	+	0.792928i	0.988142	−	0.153540i	$-0.0490674\pi$
$823$	19.0874	+	22.7475i	0.665346	+	0.792928i	−0.322796	+	0.946468i	$0.604623\pi$
$824$	−8.94900	−	15.5001i	−0.311753	−	0.539973i
$825$	−10.2032	+	0.183047i	−0.355229	+	0.00637288i
$826$	−5.71124	−	32.3901i	−0.198719	−	1.12699i
$827$	−7.08207	+	1.24876i	−0.246268	+	0.0434236i	−0.295419	−	0.955368i	$-0.595459\pi$
$827$	−7.08207	+	1.24876i	−0.246268	+	0.0434236i	0.0491517	+	0.998791i	$0.484348\pi$
$828$	4.94320	+	2.85396i	0.171788	+	0.0991819i
$829$	−5.31011	−	9.19739i	−0.184428	−	0.319439i	0.758956	−	0.651142i	$-0.225710\pi$
$829$	−5.31011	−	9.19739i	−0.184428	−	0.319439i	−0.943384	+	0.331704i	$0.892377\pi$
$830$	8.18960	+	5.62563i	0.284265	+	0.195269i
$831$	4.37817	−	1.59352i	0.151877	−	0.0552787i
$832$	−0.407759	+	1.12031i	−0.0141365	+	0.0388397i
$833$	−1.10669	+	1.31890i	−0.0383446	+	0.0456973i
$834$	−1.33696	+	7.58226i	−0.0462950	+	0.262552i
$835$	−15.9561	+	4.42917i	−0.552182	+	0.153278i
$836$	−7.85040	+	4.18527i	−0.271512	+	0.144751i
$837$		−	4.30115i		−	0.148670i
$838$	−25.2516	−	4.45253i	−0.872300	−	0.153810i
$839$	32.8608	+	27.5734i	1.13448	+	0.951941i	0.999244	−	0.0388725i	$-0.0123766\pi$
$839$	32.8608	+	27.5734i	1.13448	+	0.951941i	0.135235	+	0.990814i	$0.456821\pi$
$840$	−5.65826	−	0.443934i	−0.195228	−	0.0153172i
$841$	18.8944	−	6.87702i	0.651533	−	0.237138i
$842$	−2.56296	−	3.05442i	−0.0883255	−	0.105262i
$843$	21.2783	−	12.2850i	0.732863	−	0.423119i
$844$	−12.2747	+	21.2603i	−0.422511	+	0.731811i
$845$	23.3658	−	11.1519i	0.803808	−	0.383636i
$846$	−0.0789250	−	0.447606i	−0.00271350	−	0.0153890i
$847$	15.0233	+	8.67370i	0.516206	+	0.298032i
$848$	−0.694808	+	0.401147i	−0.0238598	+	0.0137755i
$849$	−21.4348	+	17.9860i	−0.735641	+	0.617276i
$850$	−9.71333	+	12.0069i	−0.333165	+	0.411832i
$851$	31.4760	+	11.4563i	1.07898	+	0.392718i
$852$	−2.28057	+	2.71787i	−0.0781310	+	0.0931129i
$853$	−20.1730	−	3.55704i	−0.690710	−	0.121791i	−0.182734	−	0.983162i	$-0.558495\pi$
$853$	−20.1730	−	3.55704i	−0.690710	−	0.121791i	−0.507976	+	0.861372i	$0.669606\pi$
$854$	−11.2248			−0.384106
$855$	−8.12045	+	5.39057i	−0.277714	+	0.184354i
$856$	6.40597			0.218952
$857$	19.9954	+	3.52573i	0.683029	+	0.120437i	0.504387	−	0.863478i	$-0.331718\pi$
$857$	19.9954	+	3.52573i	0.683029	+	0.120437i	0.178642	+	0.983914i	$0.442830\pi$
$858$	−1.56407	+	1.86398i	−0.0533963	+	0.0636353i
$859$	48.2772	+	17.5715i	1.64720	+	0.599531i	0.988275	−	0.152681i	$-0.0487908\pi$
$859$	48.2772	+	17.5715i	1.64720	+	0.599531i	0.658921	+	0.752212i	$0.271013\pi$
$860$	−3.62517	+	2.58713i	−0.123617	+	0.0882206i
$861$	2.88170	−	2.41803i	0.0982080	−	0.0824063i
$862$	5.64597	−	3.25971i	0.192303	−	0.111026i
$863$	−16.8474	−	9.72688i	−0.573494	−	0.331107i	0.185050	−	0.982729i	$-0.440755\pi$
$863$	−16.8474	−	9.72688i	−0.573494	−	0.331107i	−0.758544	+	0.651622i	$0.774089\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	0.461074	+	0.966058i	0.0156770	+	0.0328470i
$866$	5.31603	−	9.20763i	0.180646	−	0.312888i
$867$	6.46007	−	3.72973i	0.219396	−	0.126668i
$868$	−7.01750	−	8.36313i	−0.238189	−	0.283863i
$869$	−29.0712	+	10.5810i	−0.986172	+	0.358937i
$870$	0.521568	−	6.64776i	0.0176828	−	0.225380i
$871$	4.70064	+	3.94431i	0.159275	+	0.133648i
$872$	13.9181	+	2.45413i	0.471325	+	0.0831073i
$873$			18.1839i			0.615431i
$874$	16.6277	−	18.5080i	0.562439	−	0.626043i
$875$	−19.5193	+	20.5990i	−0.659873	+	0.696375i
$876$	1.03261	−	5.85625i	0.0348888	−	0.197864i
$877$	−14.4813	+	17.2581i	−0.488998	+	0.582765i	−0.952962	−	0.303089i	$-0.901982\pi$
$877$	−14.4813	+	17.2581i	−0.488998	+	0.582765i	0.463964	+	0.885854i	$0.346427\pi$
$878$	−2.18660	+	6.00765i	−0.0737943	+	0.202748i
$879$	14.0407	−	5.11041i	0.473582	−	0.172370i
$880$	3.76172	+	2.58402i	0.126808	+	0.0871072i
$881$	−13.8486	−	23.9865i	−0.466572	−	0.808127i	0.532699	−	0.846305i	$-0.321178\pi$
$881$	−13.8486	−	23.9865i	−0.466572	−	0.808127i	−0.999271	+	0.0381782i	$0.987845\pi$
$882$	0.482729	+	0.278704i	0.0162543	+	0.00938444i
$883$	20.5373	−	3.62128i	0.691136	−	0.121866i	0.182961	−	0.983120i	$-0.441432\pi$
$883$	20.5373	−	3.62128i	0.691136	−	0.121866i	0.508174	+	0.861254i	$0.330321\pi$
$884$	0.639453	+	3.62652i	0.0215071	+	0.121973i
$885$	−7.24782	+	28.0533i	−0.243633	+	0.943001i
$886$	1.62592	+	2.81617i	0.0546238	+	0.0946112i
$887$	2.78513	+	3.31919i	0.0935156	+	0.111448i	0.810773	−	0.585361i	$-0.199047\pi$
$887$	2.78513	+	3.31919i	0.0935156	+	0.111448i	−0.717257	+	0.696808i	$0.754603\pi$
$888$	2.00710	+	5.51445i	0.0673537	+	0.185053i
$889$	−37.5513	−	13.6675i	−1.25943	−	0.458395i
$890$	21.3416	+	9.71969i	0.715373	+	0.325805i
$891$	−0.354410	+	2.00996i	−0.0118732	+	0.0673362i
$892$			5.45648i			0.182697i
$893$	−1.98004	−	0.0669519i	−0.0662594	−	0.00224046i
$894$	−14.0395			−0.469552
$895$	23.5433	−	2.27272i	0.786965	−	0.0759687i
$896$	1.94439	+	1.63154i	0.0649577	+	0.0545059i
$897$	2.32745	−	6.39463i	0.0777115	−	0.213510i
$898$	8.24383	+	22.6497i	0.275100	+	0.755832i
$899$	9.82566	−	8.24470i	0.327704	−	0.274976i
$900$	4.37427	+	2.42193i	0.145809	+	0.0807309i
$901$	−1.23906	+	2.14611i	−0.0412789	+	0.0714972i
$902$	−2.97887	+	0.525255i	−0.0991855	+	0.0174891i
$903$	−4.97868	+	0.877876i	−0.165680	+	0.0292139i
$904$	−3.03422	+	5.25543i	−0.100917	+	0.174793i
$905$	−15.3769	+	15.6553i	−0.511146	+	0.520399i
$906$	−1.11156	+	0.932709i	−0.0369291	+	0.0309872i
$907$	14.7787	+	40.6041i	0.490718	+	1.34824i	0.900025	+	0.435839i	$0.143548\pi$
$907$	14.7787	+	40.6041i	0.490718	+	1.34824i	−0.409307	+	0.912397i	$0.634229\pi$
$908$	−6.09064	+	16.7339i	−0.202125	+	0.555333i
$909$	4.39810	+	3.69045i	0.145876	+	0.122404i
$910$	0.650178	+	6.73524i	0.0215532	+	0.223271i
$911$	2.30878			0.0764933			0.0382466	−	0.999268i	$-0.487823\pi$
$911$	2.30878			0.0764933			0.0382466	+	0.999268i	$0.487823\pi$
$912$	4.35641	+	0.147305i	0.144255	+	0.00487777i
$913$		−	9.06875i		−	0.300132i
$914$	7.14573	−	40.5255i	0.236360	−	1.34046i
$915$	8.99923	+	4.09855i	0.297505	+	0.135494i
$916$	0.0285173	+	0.0103794i	0.000942237	+	0.000342946i
$917$	−13.2392	−	36.3744i	−0.437197	−	1.20119i
$918$	1.98543	+	2.36614i	0.0655289	+	0.0780943i
$919$	14.1391	+	24.4897i	0.466406	+	0.807839i	0.999264	−	0.0383656i	$-0.0122152\pi$
$919$	14.1391	+	24.4897i	0.466406	+	0.807839i	−0.532857	+	0.846205i	$0.678882\pi$
$920$	−12.3575	−	3.19268i	−0.407416	−	0.105259i
$921$	−4.97781	−	28.2306i	−0.164025	−	0.930229i
$922$	−17.8433	+	3.14626i	−0.587638	+	0.103616i
$923$	3.66318	+	2.11494i	0.120575	+	0.0696140i
$924$	2.59022	+	4.48639i	0.0852119	+	0.147591i
$925$	27.7478	+	9.53929i	0.912343	+	0.313650i
$926$	22.2228	−	8.08843i	0.730286	−	0.265802i
$927$	−6.12148	+	16.8186i	−0.201056	+	0.552396i
$928$	−1.91686	+	2.28443i	−0.0629240	+	0.0749899i
$929$	0.546498	−	3.09934i	0.0179300	−	0.101686i	−0.974529	−	0.224260i	$-0.928004\pi$
$929$	0.546498	−	3.09934i	0.0179300	−	0.101686i	0.992459	+	0.122574i	$0.0391147\pi$
$930$	2.57246	+	9.26725i	0.0843542	+	0.303885i
$931$	1.62378	−	1.80740i	0.0532171	−	0.0592352i
$932$		−	9.48833i		−	0.310801i
$933$	20.8719	+	3.68028i	0.683315	+	0.120487i
$934$	−26.8343	−	22.5166i	−0.878044	−	0.736766i
$935$	14.0532	+	1.10258i	0.459588	+	0.0360583i
$936$	1.12031	−	0.407759i	0.0366184	−	0.0133280i
$937$	−10.3034	−	12.2791i	−0.336597	−	0.401141i	0.571022	−	0.820935i	$-0.306547\pi$
$937$	−10.3034	−	12.2791i	−0.336597	−	0.401141i	−0.907620	+	0.419793i	$0.862103\pi$
$938$	11.3139	−	6.53208i	0.369412	−	0.213280i
$939$	−2.04552	+	3.54294i	−0.0667530	+	0.115620i
$940$	0.437758	+	0.917207i	0.0142781	+	0.0299160i
$941$	−0.227729	−	1.29151i	−0.00742374	−	0.0421021i	0.980871	−	0.194660i	$-0.0623602\pi$
$941$	−0.227729	−	1.29151i	−0.00742374	−	0.0421021i	−0.988295	+	0.152557i	$0.951249\pi$
$942$	8.82492	+	5.09507i	0.287531	+	0.166006i
$943$	7.32610	−	4.22972i	0.238570	−	0.137739i
$944$	9.92622	−	8.32909i	0.323071	−	0.271089i
$945$	3.29699	+	4.61983i	0.107251	+	0.150283i
$946$	3.81992	+	1.39034i	0.124196	+	0.0452037i
$947$	−31.5426	+	37.5910i	−1.02500	+	1.22154i	−0.0501333	+	0.998743i	$0.515965\pi$
$947$	−31.5426	+	37.5910i	−1.02500	+	1.22154i	−0.974864	+	0.222802i	$0.928480\pi$
$948$	14.9277	+	2.63215i	0.484829	+	0.0854884i
$949$	−7.08957			−0.230137
$950$	14.2723	−	16.4712i	0.463054	−	0.534398i
$951$	−24.7549			−0.802734
$952$	7.72091	+	1.36140i	0.250236	+	0.0441234i
$953$	6.30845	−	7.51812i	0.204351	−	0.243536i	−0.654129	−	0.756383i	$-0.726965\pi$
$953$	6.30845	−	7.51812i	0.204351	−	0.243536i	0.858480	+	0.512847i	$0.171409\pi$
$954$	0.753911	+	0.274401i	0.0244088	+	0.00888406i
$955$	7.83425	+	10.9776i	0.253510	+	0.355226i
$956$	−15.8482	+	13.2982i	−0.512568	+	0.430095i
$957$	−5.27096	+	3.04319i	−0.170386	+	0.0983723i
$958$	−16.0874	−	9.28806i	−0.519760	−	0.300084i
$959$	8.51445	+	48.2878i	0.274946	+	1.55930i
$960$	−0.963141	−	2.01801i	−0.0310853	−	0.0651309i
$961$	6.25005	−	10.8254i	0.201615	−	0.349207i
$962$	6.05897	−	3.49815i	0.195349	−	0.112785i
$963$	−4.11768	−	4.90726i	−0.132690	−	0.158134i
$964$	2.36180	−	0.859624i	0.0760684	−	0.0276866i
$965$	−52.7387	−	4.13776i	−1.69772	−	0.133199i
$966$	−11.0984	−	9.31270i	−0.357087	−	0.299631i
$967$	7.08284	+	1.24890i	0.227769	+	0.0401618i	0.286368	−	0.958120i	$-0.407552\pi$
$967$	7.08284	+	1.24890i	0.227769	+	0.0401618i	−0.0585988	+	0.998282i	$0.518663\pi$
$968$			6.83446i			0.219668i
$969$	11.8807	−	6.33395i	0.381664	−	0.203476i
$970$	−10.8755	−	39.1789i	−0.349192	−	1.25796i
$971$	3.50146	−	19.8578i	0.112367	−	0.637266i	−0.875653	−	0.482941i	$-0.839569\pi$
$971$	3.50146	−	19.8578i	0.112367	−	0.637266i	0.988020	−	0.154325i	$-0.0493203\pi$
$972$	0.642788	−	0.766044i	0.0206174	−	0.0245709i
$973$	6.68389	−	18.3638i	0.214276	−	0.588717i
$974$	−7.94210	+	2.89069i	−0.254481	+	0.0926236i
$975$	1.93799	−	5.63721i	0.0620654	−	0.180535i
$976$	−2.21116	−	3.82983i	−0.0707774	−	0.122590i
$977$	8.27051	+	4.77498i	0.264597	+	0.152765i	0.626430	−	0.779478i	$-0.284516\pi$
$977$	8.27051	+	4.77498i	0.264597	+	0.152765i	−0.361833	+	0.932243i	$0.617849\pi$
$978$	−7.65899	+	1.35049i	−0.244907	+	0.0431838i
$979$	−3.71687	−	21.0794i	−0.118792	−	0.673701i
$980$	−1.20677	−	0.311781i	−0.0385490	−	0.00995948i
$981$	−7.06638	−	12.2393i	−0.225612	−	0.390772i
$982$	−5.65052	−	6.73403i	−0.180315	−	0.214891i
$983$	−10.8703	−	29.8659i	−0.346709	−	0.952576i	−0.983399	−	0.181456i	$-0.941919\pi$
$983$	−10.8703	−	29.8659i	−0.346709	−	0.952576i	0.636690	−	0.771120i	$-0.280303\pi$
$984$	1.39268	+	0.506893i	0.0443969	+	0.0161591i
$985$	44.8994	+	20.4487i	1.43061	+	0.651550i
$986$	−1.59948	+	9.07113i	−0.0509380	+	0.288883i
$987$			1.15365i			0.0367211i
$988$	−0.728934	−	5.14533i	−0.0231905	−	0.163695i
$989$	−11.3687			−0.361503
$990$	−0.438516	−	4.54262i	−0.0139370	−	0.144374i
$991$	2.71485	+	2.27803i	0.0862402	+	0.0723641i	0.684889	−	0.728648i	$-0.259851\pi$
$991$	2.71485	+	2.27803i	0.0862402	+	0.0723641i	−0.598648	+	0.801012i	$0.704295\pi$
$992$	1.47108	−	4.04176i	0.0467068	−	0.128326i
$993$	10.1593	+	27.9123i	0.322394	+	0.885771i
$994$	6.89858	−	5.78860i	0.218810	−	0.183603i
$995$	2.70272	−	2.75164i	0.0856820	−	0.0872330i
$996$	−2.22168	+	3.84806i	−0.0703966	+	0.121931i
$997$	32.7618	−	5.77678i	1.03758	−	0.182953i	0.371188	−	0.928558i	$-0.378951\pi$
$997$	32.7618	−	5.77678i	1.03758	−	0.182953i	0.666388	+	0.745605i	$0.267840\pi$
$998$	5.73588	−	1.01139i	0.181566	−	0.0320150i
$999$	2.93418	−	5.08214i	0.0928332	−	0.160792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.169.9	yes	60
5.4	even	2	inner	570.2.bc.a.169.3	✓	60
19.9	even	9	inner	570.2.bc.a.199.3	yes	60
95.9	even	18	inner	570.2.bc.a.199.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.169.3	✓	60	5.4	even	2	inner
570.2.bc.a.169.9	yes	60	1.1	even	1	trivial
570.2.bc.a.199.3	yes	60	19.9	even	9	inner
570.2.bc.a.199.9	yes	60	95.9	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.29893 + 1.82010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.19817 - 1.26911i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.29893 + 1.82010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.19817 - 1.26911i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.963141 + 2.01801i) q^{10} +(1.02048 - 1.76753i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(0.766336 + 0.913284i) q^{13} +(2.38515 - 0.868125i) q^{14} +(-2.22922 - 0.174899i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.04185 + 0.536361i) q^{17} -1.00000i q^{18} +(-4.26465 - 0.901550i) q^{19} +(0.598086 + 2.15460i) q^{20} +(-0.440758 + 2.49966i) q^{21} +(1.31191 - 1.56347i) q^{22} +(-1.95222 + 5.36369i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(-1.62555 + 4.72838i) q^{25} +(0.596104 + 1.03248i) q^{26} +(0.866025 + 0.500000i) q^{27} +(2.49966 - 0.440758i) q^{28} +(0.517837 + 2.93680i) q^{29} +(-2.16498 - 0.559342i) q^{30} +(-2.15058 - 3.72491i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.698051 + 1.91788i) q^{33} +(2.90250 + 1.05642i) q^{34} +(5.16519 + 2.35240i) q^{35} +(0.173648 - 0.984808i) q^{36} -5.86835i q^{37} +(-4.04330 - 1.62840i) q^{38} -1.19221 q^{39} +(0.214857 + 2.22572i) q^{40} +(-1.13532 - 0.952646i) q^{41} +(-0.868125 + 2.38515i) q^{42} +(0.681215 + 1.87162i) q^{43} +(1.56347 - 1.31191i) q^{44} +(1.56689 - 1.59526i) q^{45} +(-2.85396 + 4.94320i) q^{46} +(0.447606 - 0.0789250i) q^{47} +(-0.984808 + 0.173648i) q^{48} +(-0.278704 + 0.482729i) q^{49} +(-2.42193 + 4.37427i) q^{50} +(-2.36614 + 1.98543i) q^{51} +(0.407759 + 1.12031i) q^{52} +(-0.274401 + 0.753911i) q^{53} +(0.766044 + 0.642788i) q^{54} +(4.54262 - 0.438516i) q^{55} +2.53823 q^{56} +(3.43189 - 2.68740i) q^{57} +2.98211i q^{58} +(2.25009 - 12.7609i) q^{59} +(-2.03496 - 0.926789i) q^{60} +(-4.15561 - 1.51252i) q^{61} +(-1.47108 - 4.04176i) q^{62} +(-1.63154 - 1.94439i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.666851 + 2.58110i) q^{65} +(0.354410 + 2.00996i) q^{66} +(5.06877 - 0.893761i) q^{67} +(2.67496 + 1.54439i) q^{68} +(-2.85396 - 4.94320i) q^{69} +(4.67823 + 3.21359i) q^{70} +(3.33397 - 1.21346i) q^{71} +(0.342020 - 0.939693i) q^{72} +(-3.82239 + 4.55535i) q^{73} +(1.01903 - 5.77920i) q^{74} +(-2.57727 - 4.28459i) q^{75} +(-3.69911 - 2.30577i) q^{76} -5.18043i q^{77} +(-1.17410 - 0.207025i) q^{78} +(-11.6117 - 9.74336i) q^{79} +(-0.174899 + 2.22922i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.952646 - 1.13532i) q^{82} +(3.84806 - 2.22168i) q^{83} +(-1.26911 + 2.19817i) q^{84} +(2.97493 + 6.23318i) q^{85} +(0.345862 + 1.96148i) q^{86} +(-2.58258 - 1.49105i) q^{87} +(1.76753 - 1.02048i) q^{88} +(8.03388 - 6.74123i) q^{89} +(1.82010 - 1.29893i) q^{90} +(2.84360 + 1.03498i) q^{91} +(-3.66898 + 4.37252i) q^{92} +(4.23581 + 0.746887i) q^{93} +0.454511 q^{94} +(-3.89857 - 8.93315i) q^{95} -1.00000 q^{96} +(-17.9076 - 3.15760i) q^{97} +(-0.358294 + 0.426999i) q^{98} +(-1.91788 - 0.698051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{5}+O(q^{10}) \) 60 * q - 6 * q^5	\( 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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