LMFDB - Embedded newform 570.2.s.a.521.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, degree $2$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.2
Character	$\chi$	$=$	570.521
Dual form			570.2.s.a.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.22385 - 1.22564i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.67336 - 0.447064i) q^{6} +3.20940 q^{7} +1.00000 q^{8} +(-0.00438801 + 3.00000i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.22385 - 1.22564i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.67336 - 0.447064i) q^{6} +3.20940 q^{7} +1.00000 q^{8} +(-0.00438801 + 3.00000i) q^{9} +(0.866025 - 0.500000i) q^{10} -2.81844i q^{11} +(-0.449511 + 1.67270i) q^{12} +(-1.17608 + 0.679010i) q^{13} +(-1.60470 + 2.77942i) q^{14} +(0.447064 + 1.67336i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48891 - 1.43697i) q^{17} +(-2.59588 - 1.50380i) q^{18} +(4.04290 - 1.62940i) q^{19} +1.00000i q^{20} +(-3.92782 - 3.93357i) q^{21} +(2.44084 + 1.40922i) q^{22} +(-3.23945 + 1.87030i) q^{23} +(-1.22385 - 1.22564i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.35802i q^{26} +(3.68229 - 3.66616i) q^{27} +(-1.60470 - 2.77942i) q^{28} +(-1.23451 - 2.13824i) q^{29} +(-1.67270 - 0.449511i) q^{30} -6.20471i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.45439 + 3.44934i) q^{33} +(2.48891 - 1.43697i) q^{34} +(-2.77942 - 1.60470i) q^{35} +(2.60027 - 1.49620i) q^{36} -11.8172i q^{37} +(-0.610351 + 4.31596i) q^{38} +(2.27156 + 0.610445i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(5.87998 - 10.1844i) q^{41} +(5.37049 - 1.43481i) q^{42} +(2.63866 - 4.57030i) q^{43} +(-2.44084 + 1.40922i) q^{44} +(1.50380 - 2.59588i) q^{45} -3.74059i q^{46} +(-8.22978 + 4.75146i) q^{47} +(1.67336 - 0.447064i) q^{48} +3.30026 q^{49} -1.00000 q^{50} +(1.28484 + 4.80914i) q^{51} +(1.17608 + 0.679010i) q^{52} +(-1.96402 - 3.40178i) q^{53} +(1.33385 + 5.02204i) q^{54} +(-1.40922 + 2.44084i) q^{55} +3.20940 q^{56} +(-6.94496 - 2.96101i) q^{57} +2.46903 q^{58} +(1.85319 - 3.20982i) q^{59} +(1.22564 - 1.22385i) q^{60} +(0.946137 + 1.63876i) q^{61} +(5.37344 + 3.10235i) q^{62} +(-0.0140829 + 9.62820i) q^{63} +1.00000 q^{64} +1.35802 q^{65} +(-1.26002 - 4.71626i) q^{66} +(-9.15518 + 5.28574i) q^{67} +2.87394i q^{68} +(6.25690 + 1.68144i) q^{69} +(2.77942 - 1.60470i) q^{70} +(0.825761 - 1.43026i) q^{71} +(-0.00438801 + 3.00000i) q^{72} +(-4.52170 + 7.83182i) q^{73} +(10.2340 + 5.90861i) q^{74} +(0.449511 - 1.67270i) q^{75} +(-3.43255 - 2.68656i) q^{76} -9.04550i q^{77} +(-1.66444 + 1.66201i) q^{78} +(7.55110 + 4.35963i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-8.99996 - 0.0263280i) q^{81} +(5.87998 + 10.1844i) q^{82} +8.01355i q^{83} +(-1.44266 + 5.36838i) q^{84} +(1.43697 + 2.48891i) q^{85} +(2.63866 + 4.57030i) q^{86} +(-1.10986 + 4.12995i) q^{87} -2.81844i q^{88} +(-1.31900 - 2.28458i) q^{89} +(1.49620 + 2.60027i) q^{90} +(-3.77451 + 2.17921i) q^{91} +(3.23945 + 1.87030i) q^{92} +(-7.60474 + 7.59363i) q^{93} -9.50293i q^{94} +(-4.31596 - 0.610351i) q^{95} +(-0.449511 + 1.67270i) q^{96} +(8.27383 + 4.77690i) q^{97} +(-1.65013 + 2.85811i) q^{98} +(8.45531 + 0.0123673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9 - 2 * q^12 + 18 * q^13 + 6 * q^14 - 12 * q^16 + 12 * q^17 + 2 * q^18 + 6 * q^19 - 6 * q^21 + 18 * q^22 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 + 40 * q^39 + 6 * q^41 - 6 * q^42 - 22 * q^43 - 18 * q^44 + 8 * q^45 + 12 * q^47 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.22385	−	1.22564i	−0.706589	−	0.707624i
$3$	−1.22385	−	1.22564i	−0.706589	−	0.707624i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.67336	−	0.447064i	0.683146	−	0.182513i
$7$	3.20940			1.21304			0.606520	−	0.795068i	$-0.292565\pi$
$7$	3.20940			1.21304			0.606520	+	0.795068i	$0.292565\pi$
$8$	1.00000			0.353553
$9$	−0.00438801	+	3.00000i	−0.00146267	+	0.999999i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$		−	2.81844i		−	0.849791i	−0.905242	−	0.424896i	$-0.860311\pi$
$11$		−	2.81844i		−	0.849791i	0.905242	−	0.424896i	$-0.139689\pi$
$12$	−0.449511	+	1.67270i	−0.129763	+	0.482868i
$13$	−1.17608	+	0.679010i	−0.326186	+	0.188323i	−0.654146	−	0.756368i	$-0.726972\pi$
$13$	−1.17608	+	0.679010i	−0.326186	+	0.188323i	0.327961	+	0.944691i	$0.393639\pi$
$14$	−1.60470	+	2.77942i	−0.428874	+	0.742832i
$15$	0.447064	+	1.67336i	0.115431	+	0.432060i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.48891	−	1.43697i	−0.603648	−	0.348516i	0.166827	−	0.985986i	$-0.446648\pi$
$17$	−2.48891	−	1.43697i	−0.603648	−	0.348516i	−0.770475	+	0.637470i	$0.779981\pi$
$18$	−2.59588	−	1.50380i	−0.611855	−	0.354449i
$19$	4.04290	−	1.62940i	0.927505	−	0.373810i
$19$	4.04290	−	1.62940i	0.927505	−	0.373810i
$20$			1.00000i			0.223607i
$21$	−3.92782	−	3.93357i	−0.857121	−	0.858376i
$22$	2.44084	+	1.40922i	0.520389	+	0.300447i
$23$	−3.23945	+	1.87030i	−0.675471	+	0.389984i	−0.798147	−	0.602463i	$-0.794186\pi$
$23$	−3.23945	+	1.87030i	−0.675471	+	0.389984i	0.122675	+	0.992447i	$0.460853\pi$
$24$	−1.22385	−	1.22564i	−0.249817	−	0.250183i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	1.35802i		−	0.266329i
$27$	3.68229	−	3.66616i	0.708656	−	0.705554i
$28$	−1.60470	−	2.77942i	−0.303260	−	0.525262i
$29$	−1.23451	−	2.13824i	−0.229243	−	0.397061i	0.728341	−	0.685215i	$-0.240292\pi$
$29$	−1.23451	−	2.13824i	−0.229243	−	0.397061i	−0.957584	+	0.288154i	$0.906959\pi$
$30$	−1.67270	−	0.449511i	−0.305393	−	0.0820691i
$31$		−	6.20471i		−	1.11440i	−0.830379	−	0.557199i	$-0.811876\pi$
$31$		−	6.20471i		−	1.11440i	0.830379	−	0.557199i	$-0.188124\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.45439	+	3.44934i	−0.601332	+	0.600454i
$34$	2.48891	−	1.43697i	0.426844	−	0.246438i
$35$	−2.77942	−	1.60470i	−0.469808	−	0.271244i
$36$	2.60027	−	1.49620i	0.433378	−	0.249366i
$37$		−	11.8172i		−	1.94274i	−0.237572	−	0.971370i	$-0.576351\pi$
$37$		−	11.8172i		−	1.94274i	0.237572	−	0.971370i	$-0.423649\pi$
$38$	−0.610351	+	4.31596i	−0.0990120	+	0.700140i
$39$	2.27156	+	0.610445i	0.363741	+	0.0977494i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	5.87998	−	10.1844i	0.918299	−	1.59054i	0.116301	−	0.993214i	$-0.462896\pi$
$41$	5.87998	−	10.1844i	0.918299	−	1.59054i	0.801998	−	0.597326i	$-0.203770\pi$
$42$	5.37049	−	1.43481i	0.828684	−	0.221396i
$43$	2.63866	−	4.57030i	0.402393	−	0.696964i	−0.591622	−	0.806216i	$-0.701512\pi$
$43$	2.63866	−	4.57030i	0.402393	−	0.696964i	0.994014	+	0.109251i	$0.0348453\pi$
$44$	−2.44084	+	1.40922i	−0.367970	+	0.212448i
$45$	1.50380	−	2.59588i	0.224173	−	0.386971i
$46$		−	3.74059i		−	0.551520i
$47$	−8.22978	+	4.75146i	−1.20044	+	0.693072i	−0.960652	−	0.277754i	$-0.910410\pi$
$47$	−8.22978	+	4.75146i	−1.20044	+	0.693072i	−0.239784	+	0.970826i	$0.577077\pi$
$48$	1.67336	−	0.447064i	0.241529	−	0.0645281i
$49$	3.30026			0.471466
$50$	−1.00000			−0.141421
$51$	1.28484	+	4.80914i	0.179913	+	0.673414i
$52$	1.17608	+	0.679010i	0.163093	+	0.0941617i
$53$	−1.96402	−	3.40178i	−0.269779	−	0.467271i	0.699026	−	0.715097i	$-0.253617\pi$
$53$	−1.96402	−	3.40178i	−0.269779	−	0.467271i	−0.968805	+	0.247826i	$0.920284\pi$
$54$	1.33385	+	5.02204i	0.181514	+	0.683413i
$55$	−1.40922	+	2.44084i	−0.190019	+	0.329123i
$56$	3.20940			0.428874
$57$	−6.94496	−	2.96101i	−0.919882	−	0.392195i
$58$	2.46903			0.324199
$59$	1.85319	−	3.20982i	0.241265	−	0.417883i	−0.719810	−	0.694171i	$-0.755771\pi$
$59$	1.85319	−	3.20982i	0.241265	−	0.417883i	0.961075	+	0.276288i	$0.0891044\pi$
$60$	1.22564	−	1.22385i	0.158229	−	0.157998i
$61$	0.946137	+	1.63876i	0.121140	+	0.209821i	0.920218	−	0.391407i	$-0.128012\pi$
$61$	0.946137	+	1.63876i	0.121140	+	0.209821i	−0.799077	+	0.601228i	$0.794678\pi$
$62$	5.37344	+	3.10235i	0.682427	+	0.393999i
$63$	−0.0140829	+	9.62820i	−0.00177428	+	1.21304i
$64$	1.00000			0.125000
$65$	1.35802			0.168442
$66$	−1.26002	−	4.71626i	−0.155098	−	0.580532i
$67$	−9.15518	+	5.28574i	−1.11848	+	0.645756i	−0.941013	−	0.338370i	$-0.890125\pi$
$67$	−9.15518	+	5.28574i	−1.11848	+	0.645756i	−0.177470	+	0.984126i	$0.556791\pi$
$68$			2.87394i			0.348516i
$69$	6.25690	+	1.68144i	0.753243	+	0.202421i
$70$	2.77942	−	1.60470i	0.332205	−	0.191798i
$71$	0.825761	−	1.43026i	0.0979999	−	0.169741i	−0.812857	−	0.582464i	$-0.802089\pi$
$71$	0.825761	−	1.43026i	0.0979999	−	0.169741i	0.910857	+	0.412723i	$0.135422\pi$
$72$	−0.00438801	+	3.00000i	−0.000517131	+	0.353553i
$73$	−4.52170	+	7.83182i	−0.529225	+	0.916645i	0.470194	+	0.882563i	$0.344184\pi$
$73$	−4.52170	+	7.83182i	−0.529225	+	0.916645i	−0.999419	+	0.0340817i	$0.989149\pi$
$74$	10.2340	+	5.90861i	1.18968	+	0.686862i
$75$	0.449511	−	1.67270i	0.0519051	−	0.193147i
$76$	−3.43255	−	2.68656i	−0.393741	−	0.308169i
$77$		−	9.04550i		−	1.03083i
$78$	−1.66444	+	1.66201i	−0.188461	+	0.188186i
$79$	7.55110	+	4.35963i	0.849565	+	0.490497i	0.860504	−	0.509443i	$-0.170149\pi$
$79$	7.55110	+	4.35963i	0.849565	+	0.490497i	−0.0109389	+	0.999940i	$0.503482\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−8.99996	−	0.0263280i	−0.999996	−	0.00292533i
$82$	5.87998	+	10.1844i	0.649335	+	1.12468i
$83$			8.01355i			0.879602i	0.898095	+	0.439801i	$0.144951\pi$
$83$			8.01355i			0.879602i	−0.898095	+	0.439801i	$0.855049\pi$
$84$	−1.44266	+	5.36838i	−0.157407	+	0.585738i
$85$	1.43697	+	2.48891i	0.155861	+	0.269960i
$86$	2.63866	+	4.57030i	0.284535	+	0.492828i
$87$	−1.10986	+	4.12995i	−0.118989	+	0.442777i
$88$		−	2.81844i		−	0.300447i
$89$	−1.31900	−	2.28458i	−0.139814	−	0.242165i	0.787612	−	0.616171i	$-0.211317\pi$
$89$	−1.31900	−	2.28458i	−0.139814	−	0.242165i	−0.927426	+	0.374006i	$0.877984\pi$
$90$	1.49620	+	2.60027i	0.157713	+	0.274092i
$91$	−3.77451	+	2.17921i	−0.395676	+	0.228444i
$92$	3.23945	+	1.87030i	0.337736	+	0.194992i
$93$	−7.60474	+	7.59363i	−0.788575	+	0.787422i
$94$		−	9.50293i		−	0.980152i
$95$	−4.31596	−	0.610351i	−0.442808	−	0.0626207i
$96$	−0.449511	+	1.67270i	−0.0458780	+	0.170720i
$97$	8.27383	+	4.77690i	0.840080	+	0.485021i	0.857291	−	0.514831i	$-0.172145\pi$
$97$	8.27383	+	4.77690i	0.840080	+	0.485021i	−0.0172113	+	0.999852i	$0.505479\pi$
$98$	−1.65013	+	2.85811i	−0.166688	+	0.288713i
$99$	8.45531	+	0.0123673i	0.849790	+	0.00124296i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	16.9742	−	9.80004i	1.68899	−	0.975140i	0.733701	−	0.679472i	$-0.237791\pi$
$101$	16.9742	−	9.80004i	1.68899	−	0.975140i	0.955291	−	0.295667i	$-0.0955420\pi$
$102$	−4.80725	−	1.29187i	−0.475989	−	0.127914i
$103$		−	1.41243i		−	0.139171i	−0.997576	−	0.0695853i	$-0.977832\pi$
$103$		−	1.41243i		−	0.139171i	0.997576	−	0.0695853i	$-0.0221676\pi$
$104$	−1.17608	+	0.679010i	−0.115324	+	0.0665824i
$105$	1.43481	+	5.37049i	0.140023	+	0.524106i
$106$	3.92804			0.381525
$107$	−0.133041			−0.0128615			−0.00643076	−	0.999979i	$-0.502047\pi$
$107$	−0.133041			−0.0128615			−0.00643076	+	0.999979i	$0.502047\pi$
$108$	−5.01614	−	1.35587i	−0.482678	−	0.130469i
$109$	−9.72530	−	5.61490i	−0.931514	−	0.537810i	−0.0442242	−	0.999022i	$-0.514082\pi$
$109$	−9.72530	−	5.61490i	−0.931514	−	0.537810i	−0.887290	+	0.461211i	$0.847415\pi$
$110$	−1.40922	−	2.44084i	−0.134364	−	0.232725i
$111$	−14.4837	+	14.4625i	−1.37473	+	1.37272i
$112$	−1.60470	+	2.77942i	−0.151630	+	0.262631i
$113$	−11.8510			−1.11485			−0.557423	−	0.830229i	$-0.688210\pi$
$113$	−11.8510			−1.11485			−0.557423	+	0.830229i	$0.688210\pi$
$114$	6.03679	−	4.53401i	0.565397	−	0.424649i
$115$	3.74059			0.348812
$116$	−1.23451	+	2.13824i	−0.114622	+	0.198531i
$117$	−2.03187	−	3.53121i	−0.187846	−	0.326461i
$118$	1.85319	+	3.20982i	0.170600	+	0.295488i
$119$	−7.98790	−	4.61182i	−0.732249	−	0.422764i
$120$	0.447064	+	1.67336i	0.0408112	+	0.152756i
$121$	3.05640			0.277855
$122$	−1.89227			−0.171319
$123$	−19.6787	+	5.25746i	−1.77436	+	0.474049i
$124$	−5.37344	+	3.10235i	−0.482549	+	0.278600i
$125$		−	1.00000i		−	0.0894427i
$126$	−8.33122	−	4.82629i	−0.742204	−	0.429960i
$127$	−1.19910	+	0.692300i	−0.106403	+	0.0614317i	−0.552257	−	0.833674i	$-0.686233\pi$
$127$	−1.19910	+	0.692300i	−0.106403	+	0.0614317i	0.445854	+	0.895106i	$0.352900\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−8.83087	+	2.35930i	−0.777515	+	0.207725i
$130$	−0.679010	+	1.17608i	−0.0595531	+	0.103149i
$131$	16.9209	+	9.76931i	1.47839	+	0.853549i	0.999701	−	0.0244360i	$-0.00777899\pi$
$131$	16.9209	+	9.76931i	1.47839	+	0.853549i	0.478689	+	0.877985i	$0.341112\pi$
$132$	4.71441	+	1.26692i	0.410337	+	0.110271i
$133$	12.9753	−	5.22939i	1.12510	−	0.453446i
$134$		−	10.5715i		−	0.913238i
$135$	−5.02204	+	1.33385i	−0.432228	+	0.114799i
$136$	−2.48891	−	1.43697i	−0.213422	−	0.123219i
$137$	4.09190	−	2.36246i	0.349595	−	0.201839i	−0.314912	−	0.949121i	$-0.601975\pi$
$137$	4.09190	−	2.36246i	0.349595	−	0.201839i	0.664507	+	0.747282i	$0.268642\pi$
$138$	−4.58462	+	4.57792i	−0.390269	+	0.389698i
$139$	1.29172	+	2.23732i	0.109562	+	0.189767i	0.915593	−	0.402106i	$-0.131722\pi$
$139$	1.29172	+	2.23732i	0.109562	+	0.189767i	−0.806031	+	0.591874i	$0.798388\pi$
$140$			3.20940i			0.271244i
$141$	15.8956	+	4.27167i	1.33865	+	0.359740i
$142$	0.825761	+	1.43026i	0.0692964	+	0.120025i
$143$	1.91375	+	3.31471i	0.160036	+	0.277190i
$144$	−2.59588	−	1.50380i	−0.216323	−	0.125317i
$145$			2.46903i			0.205042i
$146$	−4.52170	−	7.83182i	−0.374219	−	0.648166i
$147$	−4.03902	−	4.04493i	−0.333133	−	0.333621i
$148$	−10.2340	+	5.90861i	−0.841231	+	0.485685i
$149$	10.2414	+	5.91288i	0.839009	+	0.484402i	0.856927	−	0.515437i	$-0.172370\pi$
$149$	10.2414	+	5.91288i	0.839009	+	0.484402i	−0.0179181	+	0.999839i	$0.505704\pi$
$150$	1.22385	+	1.22564i	0.0999268	+	0.100073i
$151$		−	5.46814i		−	0.444991i	−0.974934	−	0.222495i	$-0.928580\pi$
$151$		−	5.46814i		−	0.444991i	0.974934	−	0.222495i	$-0.0714202\pi$
$152$	4.04290	−	1.62940i	0.327923	−	0.132162i
$153$	4.32183	−	7.46040i	0.349399	−	0.603138i
$154$	7.83364	+	4.52275i	0.631252	+	0.364454i
$155$	−3.10235	+	5.37344i	−0.249187	+	0.431605i
$156$	−0.607122	−	2.27245i	−0.0486086	−	0.181942i
$157$	8.57463	−	14.8517i	0.684330	−	1.18529i	−0.289317	−	0.957233i	$-0.593428\pi$
$157$	8.57463	−	14.8517i	0.684330	−	1.18529i	0.973647	−	0.228061i	$-0.0732384\pi$
$158$	−7.55110	+	4.35963i	−0.600733	+	0.346834i
$159$	−1.76570	+	6.57045i	−0.140029	+	0.521071i
$160$			1.00000i			0.0790569i
$161$	−10.3967	+	6.00253i	−0.819374	+	0.473066i
$162$	4.52278	−	7.78103i	0.355343	−	0.611336i
$163$	3.07053			0.240502			0.120251	−	0.992744i	$-0.461630\pi$
$163$	3.07053			0.240502			0.120251	+	0.992744i	$0.461630\pi$
$164$	−11.7600			−0.918299
$165$	4.71626	−	1.26002i	0.367161	−	0.0980926i
$166$	−6.93994	−	4.00678i	−0.538644	−	0.310986i
$167$	11.6737	+	20.2195i	0.903339	+	1.56463i	0.823131	+	0.567851i	$0.192225\pi$
$167$	11.6737	+	20.2195i	0.903339	+	1.56463i	0.0802078	+	0.996778i	$0.474442\pi$
$168$	−3.92782	−	3.93357i	−0.303038	−	0.303482i
$169$	−5.57789	+	9.66119i	−0.429069	+	0.743169i
$170$	−2.87394			−0.220421
$171$	4.87045	+	12.1358i	0.372453	+	0.928051i
$172$	−5.27733			−0.402393
$173$	4.79757	−	8.30963i	0.364752	−	0.631769i	−0.623984	−	0.781437i	$-0.714487\pi$
$173$	4.79757	−	8.30963i	0.364752	−	0.631769i	0.988736	+	0.149668i	$0.0478204\pi$
$174$	−3.02172	−	3.02614i	−0.229076	−	0.229411i
$175$	1.60470	+	2.77942i	0.121304	+	0.210105i
$176$	2.44084	+	1.40922i	0.183985	+	0.106224i
$177$	−6.20211	+	1.65699i	−0.466179	+	0.124547i
$178$	2.63801			0.197727
$179$	−18.3924			−1.37471			−0.687357	−	0.726320i	$-0.741229\pi$
$179$	−18.3924			−1.37471			−0.687357	+	0.726320i	$0.741229\pi$
$180$	−3.00000	−	0.00438801i	−0.223607	−	0.000327063i
$181$	−12.8805	+	7.43657i	−0.957402	+	0.552756i	−0.895372	−	0.445318i	$-0.853091\pi$
$181$	−12.8805	+	7.43657i	−0.957402	+	0.552756i	−0.0620293	+	0.998074i	$0.519757\pi$
$182$		−	4.35843i		−	0.323068i
$183$	0.850599	−	3.16522i	0.0628781	−	0.233980i
$184$	−3.23945	+	1.87030i	−0.238815	+	0.137880i
$185$	−5.90861	+	10.2340i	−0.434410	+	0.752420i
$186$	−2.77390	−	10.3827i	−0.203392	−	0.761297i
$187$	−4.05001	+	7.01483i	−0.296166	+	0.512975i
$188$	8.22978	+	4.75146i	0.600218	+	0.346536i
$189$	11.8179	−	11.7662i	0.859629	−	0.855865i
$190$	2.68656	−	3.43255i	0.194903	−	0.249023i
$191$		−	1.89205i		−	0.136904i	−0.997654	−	0.0684520i	$-0.978194\pi$
$191$		−	1.89205i		−	0.136904i	0.997654	−	0.0684520i	$-0.0218060\pi$
$192$	−1.22385	−	1.22564i	−0.0883237	−	0.0884530i
$193$	−17.5241	−	10.1175i	−1.26141	−	0.728277i	−0.288065	−	0.957611i	$-0.593012\pi$
$193$	−17.5241	−	10.1175i	−1.26141	−	0.728277i	−0.973348	+	0.229334i	$0.926345\pi$
$194$	−8.27383	+	4.77690i	−0.594026	+	0.342961i
$195$	−1.66201	−	1.66444i	−0.119019	−	0.119193i
$196$	−1.65013	−	2.85811i	−0.117867	−	0.204151i
$197$		−	8.39151i		−	0.597871i	−0.954273	−	0.298935i	$-0.903369\pi$
$197$		−	8.39151i		−	0.597871i	0.954273	−	0.298935i	$-0.0966315\pi$
$198$	−4.23836	+	7.31633i	−0.301207	+	0.519949i
$199$	−0.537524	−	0.931019i	−0.0381041	−	0.0659982i	0.846344	−	0.532636i	$-0.178799\pi$
$199$	−0.537524	−	0.931019i	−0.0381041	−	0.0659982i	−0.884449	+	0.466638i	$0.845465\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	17.6830	+	4.75200i	1.24726	+	0.335180i
$202$			19.6001i			1.37906i
$203$	−3.96205	−	6.86247i	−0.278081	−	0.481651i
$204$	3.52242	−	3.51727i	0.246619	−	0.246258i
$205$	−10.1844	+	5.87998i	−0.711311	+	0.410676i
$206$	1.22320	+	0.706213i	0.0852242	+	0.0492042i
$207$	−5.59667	−	9.72654i	−0.388995	−	0.676041i
$208$		−	1.35802i		−	0.0941617i
$209$	−4.59236	−	11.3947i	−0.317660	−	0.788186i
$210$	−5.36838	−	1.44266i	−0.370453	−	0.0995531i
$211$	21.4433	+	12.3803i	1.47622	+	0.852293i	0.999640	−	0.0268399i	$-0.00854442\pi$
$211$	21.4433	+	12.3803i	1.47622	+	0.852293i	0.476576	+	0.879133i	$0.341878\pi$
$212$	−1.96402	+	3.40178i	−0.134890	+	0.233636i
$213$	−2.76359	+	0.738337i	−0.189358	+	0.0505900i
$214$	0.0665203	−	0.115217i	0.00454724	−	0.00787604i
$215$	−4.57030	+	2.63866i	−0.311692	+	0.179955i
$216$	3.68229	−	3.66616i	0.250548	−	0.249451i
$217$		−	19.9134i		−	1.35181i
$218$	9.72530	−	5.61490i	0.658680	−	0.380289i
$219$	15.1329	−	4.04298i	1.02258	−	0.273199i
$220$	2.81844			0.190019
$221$	3.90287			0.262535
$222$	−5.28306	−	19.7745i	−0.354576	−	1.32718i
$223$	5.77968	+	3.33690i	0.387036	+	0.223455i	0.680875	−	0.732400i	$-0.261600\pi$
$223$	5.77968	+	3.33690i	0.387036	+	0.223455i	−0.293839	+	0.955855i	$0.594933\pi$
$224$	−1.60470	−	2.77942i	−0.107219	−	0.185708i
$225$	−2.60027	+	1.49620i	−0.173351	+	0.0997466i
$226$	5.92548	−	10.2632i	0.394157	−	0.682701i
$227$	24.0873			1.59873			0.799367	−	0.600843i	$-0.205168\pi$
$227$	24.0873			1.59873			0.799367	+	0.600843i	$0.205168\pi$
$228$	0.908172	+	7.49501i	0.0601451	+	0.496369i
$229$	−21.6662			−1.43174			−0.715872	−	0.698232i	$-0.753970\pi$
$229$	−21.6662			−1.43174			−0.715872	+	0.698232i	$0.753970\pi$
$230$	−1.87030	+	3.23945i	−0.123324	+	0.213603i
$231$	−11.0865	+	11.0703i	−0.729440	+	0.728374i
$232$	−1.23451	−	2.13824i	−0.0810498	−	0.140382i
$233$	15.3569	+	8.86633i	1.00607	+	0.580852i	0.910037	−	0.414526i	$-0.136053\pi$
$233$	15.3569	+	8.86633i	1.00607	+	0.580852i	0.0960285	+	0.995379i	$0.469386\pi$
$234$	4.07405	+	0.00595899i	0.266329	+	0.000389552i
$235$	9.50293			0.619903
$236$	−3.70638			−0.241265
$237$	−3.89807	−	14.5905i	−0.253207	−	0.947752i
$238$	7.98790	−	4.61182i	0.517779	−	0.298940i
$239$			10.0104i			0.647519i	0.946139	+	0.323759i	$0.104947\pi$
$239$			10.0104i			0.647519i	−0.946139	+	0.323759i	$0.895053\pi$
$240$	−1.67270	−	0.449511i	−0.107973	−	0.0290158i
$241$	4.57707	−	2.64257i	0.294835	−	0.170223i	−0.345285	−	0.938498i	$-0.612218\pi$
$241$	4.57707	−	2.64257i	0.294835	−	0.170223i	0.640120	+	0.768275i	$0.278884\pi$
$242$	−1.52820	+	2.64692i	−0.0982365	+	0.170151i
$243$	10.9823	+	11.0629i	0.704516	+	0.709688i
$244$	0.946137	−	1.63876i	0.0605702	−	0.104911i
$245$	−2.85811	−	1.65013i	−0.182598	−	0.105423i
$246$	5.28624	−	19.6709i	0.337038	−	1.25417i
$247$	−3.64840	+	4.66147i	−0.232142	+	0.296602i
$248$		−	6.20471i		−	0.393999i
$249$	9.82173	−	9.80738i	0.622427	−	0.621517i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	20.3061	−	11.7237i	1.28171	−	0.739996i	0.304549	−	0.952497i	$-0.401494\pi$
$251$	20.3061	−	11.7237i	1.28171	−	0.739996i	0.977161	+	0.212501i	$0.0681609\pi$
$252$	8.34530	−	4.80190i	0.525705	−	0.302491i
$253$	5.27131	+	9.13018i	0.331405	+	0.574010i
$254$		−	1.38460i		−	0.0868775i
$255$	1.29187	−	4.80725i	0.0808999	−	0.301042i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.54668	−	2.67892i	−0.0964790	−	0.167106i	0.813746	−	0.581221i	$-0.197425\pi$
$257$	−1.54668	−	2.67892i	−0.0964790	−	0.167106i	−0.910225	+	0.414114i	$0.864091\pi$
$258$	2.37222	−	8.82741i	0.147688	−	0.549571i
$259$		−	37.9262i		−	2.35662i
$260$	−0.679010	−	1.17608i	−0.0421104	−	0.0729373i
$261$	6.42013	−	3.69415i	0.397396	−	0.228662i
$262$	−16.9209	+	9.76931i	−1.04538	+	0.603550i
$263$	6.03680	+	3.48535i	0.372245	+	0.214916i	0.674439	−	0.738331i	$-0.264386\pi$
$263$	6.03680	+	3.48535i	0.372245	+	0.214916i	−0.302194	+	0.953247i	$0.597719\pi$
$264$	−3.45439	+	3.44934i	−0.212603	+	0.212292i
$265$			3.92804i			0.241298i
$266$	−1.95886	+	13.8516i	−0.120106	+	0.849298i
$267$	−1.18581	+	4.41260i	−0.0725706	+	0.270047i
$268$	9.15518	+	5.28574i	0.559241	+	0.322878i
$269$	−5.00015	+	8.66052i	−0.304865	+	0.528041i	−0.977231	−	0.212177i	$-0.931945\pi$
$269$	−5.00015	+	8.66052i	−0.304865	+	0.528041i	0.672366	+	0.740218i	$0.265278\pi$
$270$	1.35587	−	5.01614i	0.0825157	−	0.305272i
$271$	−8.30819	+	14.3902i	−0.504687	+	0.874143i	0.495298	+	0.868723i	$0.335059\pi$
$271$	−8.30819	+	14.3902i	−0.504687	+	0.874143i	−0.999985	+	0.00542045i	$0.998275\pi$
$272$	2.48891	−	1.43697i	0.150912	−	0.0871291i
$273$	7.29036	+	1.95916i	0.441233	+	0.118574i
$274$			4.72492i			0.285443i
$275$	2.44084	−	1.40922i	0.147188	−	0.0849791i
$276$	−1.67228	−	6.25936i	−0.100660	−	0.376769i
$277$	28.0673			1.68640			0.843199	−	0.537601i	$-0.180669\pi$
$277$	28.0673			1.68640			0.843199	+	0.537601i	$0.180669\pi$
$278$	−2.58344			−0.154944
$279$	18.6141	+	0.0272263i	1.11440	+	0.00163000i
$280$	−2.77942	−	1.60470i	−0.166102	−	0.0958992i
$281$	−2.46716	−	4.27325i	−0.147179	−	0.254921i	0.783005	−	0.622015i	$-0.213686\pi$
$281$	−2.46716	−	4.27325i	−0.147179	−	0.254921i	−0.930184	+	0.367094i	$0.880353\pi$
$282$	−11.6472	+	11.6301i	−0.693579	+	0.692565i
$283$	−4.00792	+	6.94192i	−0.238246	+	0.412654i	−0.960211	−	0.279275i	$-0.909906\pi$
$283$	−4.00792	+	6.94192i	−0.238246	+	0.412654i	0.721965	+	0.691929i	$0.243239\pi$
$284$	−1.65152			−0.0979999
$285$	4.53401	+	6.03679i	0.268571	+	0.357588i
$286$	−3.82749			−0.226324
$287$	18.8712	−	32.6859i	1.11393	−	1.92939i
$288$	2.60027	−	1.49620i	0.153222	−	0.0881643i
$289$	−4.37023	−	7.56947i	−0.257073	−	0.445263i
$290$	−2.13824	−	1.23451i	−0.125562	−	0.0724931i
$291$	−4.27116	−	15.9869i	−0.250380	−	0.937171i
$292$	9.04340			0.529225
$293$	18.1274			1.05902			0.529508	−	0.848305i	$-0.322376\pi$
$293$	18.1274			1.05902			0.529508	+	0.848305i	$0.322376\pi$
$294$	5.52253	−	1.47543i	0.322080	−	0.0860488i
$295$	−3.20982	+	1.85319i	−0.186883	+	0.107897i
$296$		−	11.8172i		−	0.686862i
$297$	−10.3329	−	10.3783i	−0.599573	−	0.602210i
$298$	−10.2414	+	5.91288i	−0.593269	+	0.342524i
$299$	2.53990	−	4.39923i	0.146886	−	0.254414i
$300$	−1.67336	+	0.447064i	−0.0966115	+	0.0258113i
$301$	8.46854	−	14.6679i	0.488118	−	0.845446i
$302$	4.73555	+	2.73407i	0.272500	+	0.157328i
$303$	−32.7851	−	8.81045i	−1.88346	−	0.506147i
$304$	−0.610351	+	4.31596i	−0.0350060	+	0.247537i
$305$		−	1.89227i		−	0.108351i
$306$	4.29998	+	7.47301i	0.245814	+	0.427204i
$307$	−18.4910	−	10.6758i	−1.05534	−	0.609300i	−0.131200	−	0.991356i	$-0.541883\pi$
$307$	−18.4910	−	10.6758i	−1.05534	−	0.609300i	−0.924139	+	0.382056i	$0.875216\pi$
$308$	−7.83364	+	4.52275i	−0.446363	+	0.257708i
$309$	−1.73113	+	1.72860i	−0.0984804	+	0.0983364i
$310$	−3.10235	−	5.37344i	−0.176202	−	0.305191i
$311$			11.1447i			0.631960i	0.948766	+	0.315980i	$0.102333\pi$
$311$			11.1447i			0.631960i	−0.948766	+	0.315980i	$0.897667\pi$
$312$	2.27156	+	0.610445i	0.128602	+	0.0345596i
$313$	0.759314	+	1.31517i	0.0429189	+	0.0743378i	0.886687	−	0.462370i	$-0.153001\pi$
$313$	0.759314	+	1.31517i	0.0429189	+	0.0743378i	−0.843768	+	0.536708i	$0.819668\pi$
$314$	8.57463	+	14.8517i	0.483894	+	0.838129i
$315$	4.82629	−	8.33122i	0.271931	−	0.469411i
$316$		−	8.71926i		−	0.490497i
$317$	−1.84677	−	3.19870i	−0.103725	−	0.179657i	0.809492	−	0.587131i	$-0.199743\pi$
$317$	−1.84677	−	3.19870i	−0.103725	−	0.179657i	−0.913217	+	0.407475i	$0.866409\pi$
$318$	−4.80733	−	4.81437i	−0.269582	−	0.269976i
$319$	−6.02650	+	3.47940i	−0.337419	+	0.194809i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	0.162822	+	0.163060i	0.00908782	+	0.00910112i
$322$		−	12.0051i		−	0.669016i
$323$	−12.4038	−	1.75411i	−0.690166	−	0.0976014i
$324$	4.47718	+	7.80736i	0.248732	+	0.433742i
$325$	−1.17608	−	0.679010i	−0.0652371	−	0.0376647i
$326$	−1.53526	+	2.65915i	−0.0850303	+	0.147277i
$327$	5.02044	+	18.7915i	0.277631	+	1.03917i
$328$	5.87998	−	10.1844i	0.324668	−	0.562341i
$329$	−26.4127	+	15.2494i	−1.45618	+	0.840725i
$330$	−1.26692	+	4.71441i	−0.0697416	+	0.259520i
$331$			30.9937i			1.70357i	0.523892	+	0.851784i	$0.324479\pi$
$331$			30.9937i			1.70357i	−0.523892	+	0.851784i	$0.675521\pi$
$332$	6.93994	−	4.00678i	0.380879	−	0.219900i
$333$	35.4516	+	0.0518541i	1.94274	+	0.00284158i
$334$	−23.3474			−1.27751
$335$	10.5715			0.577582
$336$	5.37049	−	1.43481i	0.292984	−	0.0782752i
$337$	11.8763	+	6.85679i	0.646944	+	0.373513i	0.787284	−	0.616590i	$-0.211486\pi$
$337$	11.8763	+	6.85679i	0.646944	+	0.373513i	−0.140340	+	0.990103i	$0.544820\pi$
$338$	−5.57789	−	9.66119i	−0.303397	−	0.525500i
$339$	14.5038	+	14.5250i	0.787738	+	0.788891i
$340$	1.43697	−	2.48891i	0.0779307	−	0.134980i
$341$	−17.4876			−0.947006
$342$	−12.9452	−	1.84999i	−0.699995	−	0.100036i
$343$	−11.8739			−0.641133
$344$	2.63866	−	4.57030i	0.142267	−	0.246414i
$345$	−4.57792	−	4.58462i	−0.246467	−	0.246828i
$346$	4.79757	+	8.30963i	0.257919	+	0.446728i
$347$	−16.3458	−	9.43723i	−0.877486	−	0.506617i	−0.00765736	−	0.999971i	$-0.502437\pi$
$347$	−16.3458	−	9.43723i	−0.877486	−	0.506617i	−0.869829	+	0.493354i	$0.835771\pi$
$348$	4.13157	−	1.10381i	0.221475	−	0.0591706i
$349$	−8.31293			−0.444981			−0.222491	−	0.974935i	$-0.571419\pi$
$349$	−8.31293			−0.444981			−0.222491	+	0.974935i	$0.571419\pi$
$350$	−3.20940			−0.171550
$351$	−1.84130	+	6.81201i	−0.0982813	+	0.363598i
$352$	−2.44084	+	1.40922i	−0.130097	+	0.0751116i
$353$			32.9930i			1.75604i	0.478623	+	0.878020i	$0.341136\pi$
$353$			32.9930i			1.75604i	−0.478623	+	0.878020i	$0.658864\pi$
$354$	1.66606	−	6.19968i	0.0885500	−	0.329509i
$355$	−1.43026	+	0.825761i	−0.0759104	+	0.0438269i
$356$	−1.31900	+	2.28458i	−0.0699070	+	0.121083i
$357$	4.12355	+	15.4345i	0.218242	+	0.816878i
$358$	9.19621	−	15.9283i	0.486035	−	0.841837i
$359$	−15.5156	−	8.95794i	−0.818882	−	0.472782i	0.0311486	−	0.999515i	$-0.490083\pi$
$359$	−15.5156	−	8.95794i	−0.818882	−	0.472782i	−0.850031	+	0.526733i	$0.823417\pi$
$360$	1.50380	−	2.59588i	0.0792571	−	0.136815i
$361$	13.6901	−	13.1750i	0.720533	−	0.693421i
$362$		−	14.8731i		−	0.781715i
$363$	−3.74057	−	3.74605i	−0.196329	−	0.196617i
$364$	3.77451	+	2.17921i	0.197838	+	0.114222i
$365$	7.83182	−	4.52170i	0.409936	−	0.236677i
$366$	2.31586	+	2.31925i	0.121052	+	0.121229i
$367$	−7.66209	−	13.2711i	−0.399958	−	0.692747i	0.593763	−	0.804640i	$-0.297642\pi$
$367$	−7.66209	−	13.2711i	−0.399958	−	0.692747i	−0.993720	+	0.111893i	$0.964308\pi$
$368$		−	3.74059i		−	0.194992i
$369$	30.5274	+	17.6846i	1.58920	+	0.920624i
$370$	−5.90861	−	10.2340i	−0.307174	−	0.532041i
$371$	−6.30333	−	10.9177i	−0.327253	−	0.566818i
$372$	10.3786	+	2.78909i	0.538108	+	0.144607i
$373$			8.21379i			0.425294i	0.977129	+	0.212647i	$0.0682084\pi$
$373$			8.21379i			0.425294i	−0.977129	+	0.212647i	$0.931792\pi$
$374$	−4.05001	−	7.01483i	−0.209421	−	0.362728i
$375$	−1.22564	+	1.22385i	−0.0632918	+	0.0631993i
$376$	−8.22978	+	4.75146i	−0.424418	+	0.245038i
$377$	2.90377	+	1.67649i	0.149552	+	0.0863438i
$378$	4.28085	+	16.1177i	0.220183	+	0.829007i
$379$		−	30.2639i		−	1.55455i	−0.629161	−	0.777275i	$-0.716601\pi$
$379$		−	30.2639i		−	1.55455i	0.629161	−	0.777275i	$-0.283399\pi$
$380$	1.62940	+	4.04290i	0.0835864	+	0.207397i
$381$	2.31603	+	0.622393i	0.118654	+	0.0318862i
$382$	1.63856	+	0.946026i	0.0838363	+	0.0484029i
$383$	10.9707	−	19.0019i	0.560578	−	0.970949i	−0.436868	−	0.899526i	$-0.643912\pi$
$383$	10.9707	−	19.0019i	0.560578	−	0.970949i	0.997446	−	0.0714239i	$-0.0227543\pi$
$384$	1.67336	−	0.447064i	0.0853933	−	0.0228141i
$385$	−4.52275	+	7.83364i	−0.230501	+	0.399239i
$386$	17.5241	−	10.1175i	0.891953	−	0.514970i
$387$	13.6993	+	7.93604i	0.696375	+	0.403412i
$388$		−	9.55380i		−	0.485021i
$389$	−20.5871	+	11.8860i	−1.04381	+	0.602643i	−0.920910	−	0.389776i	$-0.872553\pi$
$389$	−20.5871	+	11.8860i	−1.04381	+	0.602643i	−0.122899	+	0.992419i	$0.539219\pi$
$390$	2.27245	−	0.607122i	0.115070	−	0.0307428i
$391$	10.7502			0.543663
$392$	3.30026			0.166688
$393$	−8.73502	−	32.6952i	−0.440623	−	1.64925i
$394$	7.26726	+	4.19576i	0.366119	+	0.211379i
$395$	−4.35963	−	7.55110i	−0.219357	−	0.379937i
$396$	−4.21694	−	7.32869i	−0.211909	−	0.368281i
$397$	−15.7374	+	27.2581i	−0.789840	+	1.36804i	0.136225	+	0.990678i	$0.456503\pi$
$397$	−15.7374	+	27.2581i	−0.789840	+	1.36804i	−0.926065	+	0.377364i	$0.876830\pi$
$398$	1.07505			0.0538873
$399$	−22.2892	−	9.50306i	−1.11585	−	0.475748i
$400$	−1.00000			−0.0500000
$401$	−14.4572	+	25.0407i	−0.721960	+	1.25047i	0.238253	+	0.971203i	$0.423425\pi$
$401$	−14.4572	+	25.0407i	−0.721960	+	1.25047i	−0.960213	+	0.279268i	$0.909908\pi$
$402$	−12.9568	+	12.9379i	−0.646229	+	0.645284i
$403$	4.21306	+	7.29723i	0.209867	+	0.363501i
$404$	−16.9742	−	9.80004i	−0.844496	−	0.487570i
$405$	7.78103	+	4.52278i	0.386643	+	0.224739i
$406$	7.92410			0.393266
$407$	−33.3061			−1.65092
$408$	1.28484	+	4.80914i	0.0636088	+	0.238088i
$409$	28.2766	−	16.3255i	1.39819	−	0.807244i	0.403985	−	0.914766i	$-0.367625\pi$
$409$	28.2766	−	16.3255i	1.39819	−	0.807244i	0.994203	+	0.107522i	$0.0342916\pi$
$410$		−	11.7600i		−	0.580783i
$411$	−7.90339	−	2.12390i	−0.389846	−	0.104764i
$412$	−1.22320	+	0.706213i	−0.0602626	+	0.0347926i
$413$	5.94763	−	10.3016i	0.292664	−	0.506909i
$414$	11.2218	+	0.0164137i	0.551519	+	0.000806691i
$415$	4.00678	−	6.93994i	0.196685	−	0.340668i
$416$	1.17608	+	0.679010i	0.0576620	+	0.0332912i
$417$	1.16128	−	4.32133i	0.0568684	−	0.211616i
$418$	12.1643	+	1.72024i	0.594973	+	0.0841395i
$419$		−	6.89309i		−	0.336750i	−0.985723	−	0.168375i	$-0.946148\pi$
$419$		−	6.89309i		−	0.336750i	0.985723	−	0.168375i	$-0.0538519\pi$
$420$	3.93357	−	3.92782i	0.191939	−	0.191658i
$421$	−16.3349	−	9.43094i	−0.796113	−	0.459636i	0.0459975	−	0.998942i	$-0.485353\pi$
$421$	−16.3349	−	9.43094i	−0.796113	−	0.459636i	−0.842110	+	0.539306i	$0.818687\pi$
$422$	−21.4433	+	12.3803i	−1.04384	+	0.602662i
$423$	−14.2183	−	24.7102i	−0.691316	−	1.20145i
$424$	−1.96402	−	3.40178i	−0.0953813	−	0.165205i
$425$		−	2.87394i		−	0.139407i
$426$	0.742378	−	2.76251i	0.0359683	−	0.133844i
$427$	3.03654	+	5.25943i	0.146948	+	0.254522i
$428$	0.0665203	+	0.115217i	0.00321538	+	0.00556920i
$429$	1.72050	−	6.40227i	0.0830666	−	0.309104i
$430$		−	5.27733i		−	0.254495i
$431$	5.45320	+	9.44522i	0.262671	+	0.454960i	0.966951	−	0.254963i	$-0.0820632\pi$
$431$	5.45320	+	9.44522i	0.262671	+	0.454960i	−0.704280	+	0.709923i	$0.748730\pi$
$432$	1.33385	+	5.02204i	0.0641748	+	0.241623i
$433$	−16.5710	+	9.56729i	−0.796353	+	0.459774i	−0.842194	−	0.539174i	$-0.818736\pi$
$433$	−16.5710	+	9.56729i	−0.796353	+	0.459774i	0.0458415	+	0.998949i	$0.485403\pi$
$434$	17.2455	+	9.95670i	0.827811	+	0.477937i
$435$	3.02614	−	3.02172i	0.145092	−	0.144880i
$436$			11.2298i			0.537810i
$437$	−10.0493	+	12.8398i	−0.480724	+	0.614210i
$438$	−4.06511	+	15.1269i	−0.194239	+	0.722793i
$439$	16.7584	+	9.67549i	0.799837	+	0.461786i	0.843414	−	0.537264i	$-0.180542\pi$
$439$	16.7584	+	9.67549i	0.799837	+	0.461786i	−0.0435774	+	0.999050i	$0.513876\pi$
$440$	−1.40922	+	2.44084i	−0.0671819	+	0.116362i
$441$	−0.0144816	+	9.90078i	−0.000689599	+	0.471466i
$442$	−1.95143	+	3.37998i	−0.0928202	+	0.160769i
$443$	16.8746	−	9.74255i	0.801736	−	0.462882i	−0.0423420	−	0.999103i	$-0.513482\pi$
$443$	16.8746	−	9.74255i	0.801736	−	0.462882i	0.844078	+	0.536221i	$0.180149\pi$
$444$	19.7667	+	5.31197i	0.938087	+	0.252095i
$445$			2.63801i			0.125053i
$446$	−5.77968	+	3.33690i	−0.273676	+	0.158007i
$447$	−5.28687	−	19.7888i	−0.250061	−	0.935976i
$448$	3.20940			0.151630
$449$	10.3060			0.486372			0.243186	−	0.969980i	$-0.421807\pi$
$449$	10.3060			0.486372			0.243186	+	0.969980i	$0.421807\pi$
$450$	0.00438801	−	3.00000i	0.000206853	−	0.141421i
$451$	−28.7042	−	16.5724i	−1.35163	−	0.780362i
$452$	5.92548	+	10.2632i	0.278711	+	0.482742i
$453$	−6.70197	+	6.69218i	−0.314886	+	0.314426i
$454$	−12.0437	+	20.8603i	−0.565238	+	0.979020i
$455$	4.35843			0.204326
$456$	−6.94496	−	2.96101i	−0.325227	−	0.138662i
$457$	−3.18775			−0.149117			−0.0745583	−	0.997217i	$-0.523755\pi$
$457$	−3.18775			−0.149117			−0.0745583	+	0.997217i	$0.523755\pi$
$458$	10.8331	−	18.7635i	0.506198	−	0.876760i
$459$	−14.4330	+	3.83340i	−0.673676	+	0.178928i
$460$	−1.87030	−	3.23945i	−0.0872030	−	0.151040i
$461$	−28.6530	−	16.5428i	−1.33450	−	0.770477i	−0.348518	−	0.937302i	$-0.613315\pi$
$461$	−28.6530	−	16.5428i	−1.33450	−	0.770477i	−0.985986	+	0.166825i	$0.946648\pi$
$462$	−4.04392	−	15.1364i	−0.188140	−	0.704208i
$463$	−5.36206			−0.249196			−0.124598	−	0.992207i	$-0.539764\pi$
$463$	−5.36206			−0.249196			−0.124598	+	0.992207i	$0.539764\pi$
$464$	2.46903			0.114622
$465$	10.3827	−	2.77390i	0.481487	−	0.128637i
$466$	−15.3569	+	8.86633i	−0.711396	+	0.410725i
$467$			41.3216i			1.91213i	0.293148	+	0.956067i	$0.405297\pi$
$467$			41.3216i			1.91213i	−0.293148	+	0.956067i	$0.594703\pi$
$468$	−2.04219	+	3.52525i	−0.0944001	+	0.162955i
$469$	−29.3826	+	16.9641i	−1.35676	+	0.783328i
$470$	−4.75146	+	8.22978i	−0.219169	+	0.379611i
$471$	−28.6969	+	7.66681i	−1.32228	+	0.353268i
$472$	1.85319	−	3.20982i	0.0853000	−	0.147744i
$473$	−12.8811	−	7.43692i	−0.592274	−	0.341950i
$474$	14.5847	+	3.91940i	0.669899	+	0.180024i
$475$	3.43255	+	2.68656i	0.157496	+	0.123268i
$476$			9.22363i			0.422764i
$477$	10.2140	−	5.87713i	0.467665	−	0.269095i
$478$	−8.66926	−	5.00520i	−0.396523	−	0.228932i
$479$	−6.39802	+	3.69390i	−0.292333	+	0.168779i	−0.638994	−	0.769212i	$-0.720649\pi$
$479$	−6.39802	+	3.69390i	−0.292333	+	0.168779i	0.346660	+	0.937991i	$0.387316\pi$
$480$	1.22564	−	1.22385i	0.0559426	−	0.0558608i
$481$	8.02401	+	13.8980i	0.365863	+	0.633694i
$482$			5.28515i			0.240732i
$483$	20.0809	+	5.39641i	0.913713	+	0.245545i
$484$	−1.52820	−	2.64692i	−0.0694637	−	0.120315i
$485$	−4.77690	−	8.27383i	−0.216908	−	0.375695i
$486$	−15.0719	+	3.97950i	−0.683677	+	0.180514i
$487$			2.64014i			0.119636i	0.998209	+	0.0598180i	$0.0190520\pi$
$487$			2.64014i			0.119636i	−0.998209	+	0.0598180i	$0.980948\pi$
$488$	0.946137	+	1.63876i	0.0428296	+	0.0741831i
$489$	−3.75786	−	3.76336i	−0.169936	−	0.170185i
$490$	2.85811	−	1.65013i	0.129116	−	0.0745453i
$491$	14.1387	+	8.16297i	0.638070	+	0.368390i	0.783871	−	0.620924i	$-0.213243\pi$
$491$	14.1387	+	8.16297i	0.638070	+	0.368390i	−0.145801	+	0.989314i	$0.546576\pi$
$492$	14.3924	+	14.4135i	0.648860	+	0.649810i
$493$			7.09584i			0.319580i
$494$	−2.21275	−	5.49034i	−0.0995565	−	0.247022i
$495$	−7.31633	−	4.23836i	−0.328844	−	0.190500i
$496$	5.37344	+	3.10235i	0.241274	+	0.139300i
$497$	2.65020	−	4.59028i	0.118878	−	0.205902i
$498$	3.58257	+	13.4096i	0.160539	+	0.600897i
$499$	−6.98906	+	12.1054i	−0.312873	+	0.541912i	−0.978983	−	0.203941i	$-0.934625\pi$
$499$	−6.98906	+	12.1054i	−0.312873	+	0.541912i	0.666110	+	0.745854i	$0.267958\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	10.4949	−	39.0533i	0.468879	−	1.74477i
$502$			23.4475i			1.04651i
$503$	16.0900	−	9.28957i	0.717418	−	0.414201i	−0.0963836	−	0.995344i	$-0.530728\pi$
$503$	16.0900	−	9.28957i	0.717418	−	0.414201i	0.813802	+	0.581143i	$0.197394\pi$
$504$	−0.0140829	+	9.62820i	−0.000627301	+	0.428874i
$505$	−19.6001			−0.872192
$506$	−10.5426			−0.468677
$507$	18.6676	−	4.98735i	0.829059	−	0.221496i
$508$	1.19910	+	0.692300i	0.0532014	+	0.0307158i
$509$	−7.26580	−	12.5847i	−0.322051	−	0.557808i	0.658860	−	0.752265i	$-0.271039\pi$
$509$	−7.26580	−	12.5847i	−0.322051	−	0.557808i	−0.980911	+	0.194457i	$0.937706\pi$
$510$	3.51727	+	3.52242i	0.155747	+	0.155975i
$511$	−14.5120	+	25.1355i	−0.641971	+	1.11193i
$512$	1.00000			0.0441942
$513$	8.91349	−	20.8219i	0.393540	−	0.919307i
$514$	3.09335			0.136442
$515$	−0.706213	+	1.22320i	−0.0311195	+	0.0539005i
$516$	6.45865	+	6.46811i	0.284326	+	0.284743i
$517$	13.3917	+	23.1951i	0.588967	+	1.02012i
$518$	32.8451	+	18.9631i	1.44313	+	0.833191i
$519$	−16.0561	+	4.28964i	−0.704785	+	0.188294i
$520$	1.35802			0.0595531
$521$	36.4420			1.59655			0.798276	−	0.602291i	$-0.205745\pi$
$521$	36.4420			1.59655			0.798276	+	0.602291i	$0.205745\pi$
$522$	−0.0108341	+	7.40707i	−0.000474196	+	0.324199i
$523$	−17.8504	+	10.3060i	−0.780545	+	0.450648i	−0.836624	−	0.547778i	$-0.815474\pi$
$523$	−17.8504	+	10.3060i	−0.780545	+	0.450648i	0.0560782	+	0.998426i	$0.482140\pi$
$524$		−	19.5386i		−	0.853549i
$525$	1.44266	−	5.36838i	0.0629629	−	0.234295i
$526$	−6.03680	+	3.48535i	−0.263217	+	0.151968i
$527$	−8.91598	+	15.4429i	−0.388386	+	0.672705i
$528$	−1.26002	−	4.71626i	−0.0548355	−	0.205249i
$529$	−4.50399	+	7.80114i	−0.195826	+	0.339180i
$530$	−3.40178	−	1.96402i	−0.147764	−	0.0853116i
$531$	9.62131	+	5.57365i	0.417529	+	0.241876i
$532$	−11.0164	−	8.62224i	−0.477623	−	0.373822i
$533$			15.9703i			0.691749i
$534$	−3.22852	−	3.23325i	−0.139712	−	0.139916i
$535$	0.115217	+	0.0665203i	0.00498125	+	0.00287592i
$536$	−9.15518	+	5.28574i	−0.395443	+	0.228309i
$537$	22.5095	+	22.5425i	0.971358	+	0.972780i
$538$	−5.00015	−	8.66052i	−0.215572	−	0.373381i
$539$		−	9.30159i		−	0.400648i
$540$	3.66616	+	3.68229i	0.157767	+	0.158460i
$541$	−20.9329	−	36.2568i	−0.899975	−	1.55880i	−0.827524	−	0.561431i	$-0.810251\pi$
$541$	−20.9329	−	36.2568i	−0.899975	−	1.55880i	−0.0724514	−	0.997372i	$-0.523082\pi$
$542$	−8.30819	−	14.3902i	−0.356868	−	0.618113i
$543$	24.8784	+	6.68565i	1.06763	+	0.286909i
$544$			2.87394i			0.123219i
$545$	5.61490	+	9.72530i	0.240516	+	0.416586i
$546$	−5.34187	+	5.33406i	−0.228611	+	0.228277i
$547$	−0.131381	+	0.0758528i	−0.00561744	+	0.00324323i	−0.502806	−	0.864399i	$-0.667699\pi$
$547$	−0.131381	+	0.0758528i	−0.00561744	+	0.00324323i	0.497189	+	0.867642i	$0.334366\pi$
$548$	−4.09190	−	2.36246i	−0.174797	−	0.100919i
$549$	−4.92042	+	2.83122i	−0.209998	+	0.120833i
$550$			2.81844i			0.120179i
$551$	−8.47506	−	6.63318i	−0.361050	−	0.282583i
$552$	6.25690	+	1.68144i	0.266311	+	0.0715667i
$553$	24.2345	+	13.9918i	1.03056	+	0.594992i
$554$	−14.0336	+	24.3070i	−0.596232	+	1.03270i
$555$	19.7745	−	5.28306i	0.839380	−	0.224253i
$556$	1.29172	−	2.23732i	0.0547811	−	0.0948837i
$557$	−8.93906	+	5.16097i	−0.378760	+	0.218677i	−0.677279	−	0.735727i	$-0.736841\pi$
$557$	−8.93906	+	5.16097i	−0.378760	+	0.218677i	0.298518	+	0.954404i	$0.403508\pi$
$558$	−9.33063	+	16.1067i	−0.394997	+	0.681850i
$559$			7.16671i			0.303120i
$560$	2.77942	−	1.60470i	0.117452	−	0.0678110i
$561$	13.5543	−	3.62123i	0.572261	−	0.152888i
$562$	4.93433			0.208142
$563$	42.9116			1.80851			0.904255	−	0.426994i	$-0.140427\pi$
$563$	42.9116			1.80851			0.904255	+	0.426994i	$0.140427\pi$
$564$	−4.24842	−	15.9018i	−0.178891	−	0.669588i
$565$	10.2632	+	5.92548i	0.431778	+	0.249287i
$566$	−4.00792	−	6.94192i	−0.168465	−	0.291790i
$567$	−28.8845	−	0.0844972i	−1.21303	−	0.00354855i
$568$	0.825761	−	1.43026i	0.0346482	−	0.0600124i
$569$	−14.9370			−0.626192			−0.313096	−	0.949722i	$-0.601366\pi$
$569$	−14.9370			−0.626192			−0.313096	+	0.949722i	$0.601366\pi$
$570$	−7.49501	+	0.908172i	−0.313932	+	0.0380391i
$571$	−9.17120			−0.383803			−0.191901	−	0.981414i	$-0.561465\pi$
$571$	−9.17120			−0.383803			−0.191901	+	0.981414i	$0.561465\pi$
$572$	1.91375	−	3.31471i	0.0800178	−	0.138595i
$573$	−2.31897	+	2.31558i	−0.0968765	+	0.0967349i
$574$	18.8712	+	32.6859i	0.787670	+	1.36428i
$575$	−3.23945	−	1.87030i	−0.135094	−	0.0779967i
$576$	−0.00438801	+	3.00000i	−0.000182834	+	0.125000i
$577$	11.1217			0.463001			0.231500	−	0.972835i	$-0.425637\pi$
$577$	11.1217			0.463001			0.231500	+	0.972835i	$0.425637\pi$
$578$	8.74047			0.363555
$579$	9.04638	+	33.8606i	0.375955	+	1.40720i
$580$	2.13824	−	1.23451i	0.0887856	−	0.0512604i
$581$			25.7187i			1.06699i
$582$	15.9807	+	4.29454i	0.662420	+	0.178014i
$583$	−9.58772	+	5.53547i	−0.397083	+	0.229256i
$584$	−4.52170	+	7.83182i	−0.187109	+	0.324083i
$585$	−0.00595899	+	4.07405i	−0.000246374	+	0.168441i
$586$	−9.06372	+	15.6988i	−0.374419	+	0.648513i
$587$	−2.96690	−	1.71294i	−0.122457	−	0.0707005i	0.437520	−	0.899209i	$-0.355857\pi$
$587$	−2.96690	−	1.71294i	−0.122457	−	0.0707005i	−0.559977	+	0.828508i	$0.689190\pi$
$588$	−1.48350	+	5.52036i	−0.0611787	+	0.227656i
$589$	−10.1099	−	25.0850i	−0.416573	−	1.03361i
$590$		−	3.70638i		−	0.152589i
$591$	−10.2850	+	10.2699i	−0.423067	+	0.422449i
$592$	10.2340	+	5.90861i	0.420616	+	0.242842i
$593$	37.6958	−	21.7637i	1.54798	−	0.893727i	0.549685	−	0.835372i	$-0.314748\pi$
$593$	37.6958	−	21.7637i	1.54798	−	0.893727i	0.998296	−	0.0583555i	$-0.0185857\pi$
$594$	14.1543	−	3.75937i	0.580758	−	0.154249i
$595$	4.61182	+	7.98790i	0.189066	+	0.327472i
$596$		−	11.8258i		−	0.484402i
$597$	−0.483246	+	1.79824i	−0.0197780	+	0.0735970i
$598$	2.53990	+	4.39923i	0.103864	+	0.179898i
$599$	−8.31767	−	14.4066i	−0.339851	−	0.588639i	0.644554	−	0.764559i	$-0.277043\pi$
$599$	−8.31767	−	14.4066i	−0.339851	−	0.588639i	−0.984404	+	0.175920i	$0.943710\pi$
$600$	0.449511	−	1.67270i	0.0183512	−	0.0682879i
$601$			33.9509i			1.38489i	0.721472	+	0.692444i	$0.243466\pi$
$601$			33.9509i			1.38489i	−0.721472	+	0.692444i	$0.756534\pi$
$602$	8.46854	+	14.6679i	0.345152	+	0.597820i
$603$	−15.8170	−	27.4887i	−0.644120	−	1.11943i
$604$	−4.73555	+	2.73407i	−0.192687	+	0.111248i
$605$	−2.64692	−	1.52820i	−0.107613	−	0.0621302i
$606$	24.0226	−	23.9875i	0.975853	−	0.974427i
$607$		−	25.0735i		−	1.01770i	−0.860854	−	0.508852i	$-0.830070\pi$
$607$		−	25.0735i		−	1.01770i	0.860854	−	0.508852i	$-0.169930\pi$
$608$	−3.43255	−	2.68656i	−0.139208	−	0.108954i
$609$	−3.56197	+	13.2547i	−0.144338	+	0.537107i
$610$	1.63876	+	0.946137i	0.0663514	+	0.0383080i
$611$	6.45258	−	11.1762i	0.261043	−	0.452141i
$612$	−8.62181	−	0.0126109i	−0.348516	−	0.000509764i
$613$	−7.45511	+	12.9126i	−0.301109	+	0.521536i	−0.976387	−	0.216027i	$-0.930690\pi$
$613$	−7.45511	+	12.9126i	−0.301109	+	0.521536i	0.675278	+	0.737563i	$0.264024\pi$
$614$	18.4910	−	10.6758i	0.746238	−	0.430840i
$615$	19.6709	+	5.28624i	0.793209	+	0.213162i
$616$		−	9.04550i		−	0.364454i
$617$	5.34291	−	3.08473i	0.215097	−	0.124187i	−0.388581	−	0.921415i	$-0.627035\pi$
$617$	5.34291	−	3.08473i	0.215097	−	0.124187i	0.603678	+	0.797228i	$0.293701\pi$
$618$	−0.631445	−	2.36350i	−0.0254004	−	0.0950738i
$619$	30.6509			1.23196			0.615982	−	0.787760i	$-0.288759\pi$
$619$	30.6509			1.23196			0.615982	+	0.787760i	$0.288759\pi$
$620$	6.20471			0.249187
$621$	−5.07176	+	18.7633i	−0.203523	+	0.752946i
$622$	−9.65163	−	5.57237i	−0.386995	−	0.223432i
$623$	−4.23321	−	7.33214i	−0.169600	−	0.293756i
$624$	−1.66444	+	1.66201i	−0.0666310	+	0.0665337i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.51863			−0.0606965
$627$	−8.34542	+	19.5739i	−0.333284	+	0.781708i
$628$	−17.1493			−0.684330
$629$	−16.9810	+	29.4120i	−0.677077	+	1.17273i
$630$	4.80190	+	8.34530i	0.191312	+	0.332485i
$631$	−4.52634	−	7.83986i	−0.180191	−	0.312100i	0.761755	−	0.647866i	$-0.224338\pi$
$631$	−4.52634	−	7.83986i	−0.180191	−	0.312100i	−0.941945	+	0.335766i	$0.891005\pi$
$632$	7.55110	+	4.35963i	0.300367	+	0.173417i
$633$	−11.0696	−	41.4333i	−0.439975	−	1.64683i
$634$	3.69354			0.146689
$635$	1.38460			0.0549462
$636$	6.57303	−	1.75609i	0.260638	−	0.0696334i
$637$	−3.88137	+	2.24091i	−0.153785	+	0.0887881i
$638$		−	6.95880i		−	0.275502i
$639$	4.28715	+	2.48356i	0.169597	+	0.0982480i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	−7.29491	+	12.6352i	−0.288132	+	0.499059i	−0.973364	−	0.229266i	$-0.926367\pi$
$641$	−7.29491	+	12.6352i	−0.288132	+	0.499059i	0.685232	+	0.728325i	$0.259701\pi$
$642$	−0.222625	+	0.0594777i	−0.00878630	+	0.00234740i
$643$	−13.5090	+	23.3983i	−0.532743	+	0.922739i	0.466526	+	0.884508i	$0.345506\pi$
$643$	−13.5090	+	23.3983i	−0.532743	+	0.922739i	−0.999269	+	0.0382309i	$0.987828\pi$
$644$	10.3967	+	6.00253i	0.409687	+	0.236533i
$645$	8.82741	+	2.37222i	0.347579	+	0.0934060i
$646$	7.72101	−	9.86495i	0.303779	−	0.388131i
$647$		−	10.8293i		−	0.425743i	−0.977080	−	0.212872i	$-0.931718\pi$
$647$		−	10.8293i		−	0.425743i	0.977080	−	0.212872i	$-0.0682816\pi$
$648$	−8.99996	−	0.0263280i	−0.353552	−	0.00103426i
$649$	−9.04668	−	5.22310i	−0.355113	−	0.205025i
$650$	1.17608	−	0.679010i	0.0461296	−	0.0266329i
$651$	−24.4067	+	24.3710i	−0.956573	+	0.955175i
$652$	−1.53526	−	2.65915i	−0.0601255	−	0.104140i
$653$		−	39.3283i		−	1.53904i	−0.638625	−	0.769518i	$-0.720497\pi$
$653$		−	39.3283i		−	1.53904i	0.638625	−	0.769518i	$-0.279503\pi$
$654$	−18.7841	−	5.04792i	−0.734518	−	0.197389i
$655$	−9.76931	−	16.9209i	−0.381719	−	0.661156i
$656$	5.87998	+	10.1844i	0.229575	+	0.397635i
$657$	−23.4756	−	13.5995i	−0.915870	−	0.530565i
$658$		−	30.4987i		−	1.18896i
$659$	15.2330	+	26.3843i	0.593392	+	1.02779i	0.993772	+	0.111436i	$0.0355451\pi$
$659$	15.2330	+	26.3843i	0.593392	+	1.02779i	−0.400379	+	0.916350i	$0.631122\pi$
$660$	−3.44934	−	3.45439i	−0.134266	−	0.134462i
$661$	30.2120	−	17.4429i	1.17511	−	0.678450i	0.220231	−	0.975448i	$-0.429319\pi$
$661$	30.2120	−	17.4429i	1.17511	−	0.678450i	0.954878	+	0.296998i	$0.0959854\pi$
$662$	−26.8413	−	15.4969i	−1.04322	−	0.602303i
$663$	−4.77652	−	4.78351i	−0.185505	−	0.185776i
$664$			8.01355i			0.310986i
$665$	−13.8516	−	1.95886i	−0.537143	−	0.0759614i
$666$	−17.7707	+	30.6761i	−0.688602	+	1.18867i
$667$	7.99828	+	4.61781i	0.309695	+	0.178802i
$668$	11.6737	−	20.2195i	0.451670	−	0.782315i
$669$	−2.98362	−	11.1677i	−0.115353	−	0.431767i
$670$	−5.28574	+	9.15518i	−0.204206	+	0.353695i
$671$	4.61874	−	2.66663i	0.178304	−	0.102944i
$672$	−1.44266	+	5.36838i	−0.0556519	+	0.207090i
$673$		−	19.8592i		−	0.765516i	−0.923849	−	0.382758i	$-0.874974\pi$
$673$		−	19.8592i		−	0.765516i	0.923849	−	0.382758i	$-0.125026\pi$
$674$	−11.8763	+	6.85679i	−0.457458	+	0.264114i
$675$	5.01614	+	1.35587i	0.193071	+	0.0521875i
$676$	11.1558			0.429069
$677$	−31.0348			−1.19276			−0.596382	−	0.802701i	$-0.703395\pi$
$677$	−31.0348			−1.19276			−0.596382	+	0.802701i	$0.703395\pi$
$678$	−19.8309	+	5.29814i	−0.761603	+	0.203474i
$679$	26.5540	+	15.3310i	1.01905	+	0.588349i
$680$	1.43697	+	2.48891i	0.0551053	+	0.0954452i
$681$	−29.4793	−	29.5224i	−1.12965	−	1.13130i
$682$	8.74380	−	15.1447i	0.334817	−	0.579920i
$683$	−0.186788			−0.00714726			−0.00357363	−	0.999994i	$-0.501138\pi$
$683$	−0.186788			−0.00714726			−0.00357363	+	0.999994i	$0.501138\pi$
$684$	8.07473	−	10.2859i	0.308745	−	0.393289i
$685$	−4.72492			−0.180530
$686$	5.93697	−	10.2831i	0.226675	−	0.392612i
$687$	26.5162	+	26.5550i	1.01165	+	1.01314i
$688$	2.63866	+	4.57030i	0.100598	+	0.174241i
$689$	4.61969	+	2.66718i	0.175996	+	0.101611i
$690$	6.25936	−	1.67228i	0.238290	−	0.0636628i
$691$	45.2803			1.72254			0.861272	−	0.508144i	$-0.169668\pi$
$691$	45.2803			1.72254			0.861272	+	0.508144i	$0.169668\pi$
$692$	−9.59513			−0.364752
$693$	27.1365	+	0.0396917i	1.03083	+	0.00150776i
$694$	16.3458	−	9.43723i	0.620476	−	0.358232i
$695$		−	2.58344i		−	0.0979954i
$696$	−1.10986	+	4.12995i	−0.0420689	+	0.156545i
$697$	−29.2694	+	16.8987i	−1.10866	+	0.640085i
$698$	4.15647	−	7.19921i	0.157325	−	0.272494i
$699$	−7.92763	−	29.6731i	−0.299851	−	1.12234i
$700$	1.60470	−	2.77942i	0.0606520	−	0.105052i
$701$	−14.6766	−	8.47353i	−0.554327	−	0.320041i	0.196539	−	0.980496i	$-0.437030\pi$
$701$	−14.6766	−	8.47353i	−0.554327	−	0.320041i	−0.750865	+	0.660455i	$0.770363\pi$
$702$	−4.97872	−	5.00062i	−0.187910	−	0.188736i
$703$	−19.2550	−	47.7759i	−0.726215	−	1.80190i
$704$		−	2.81844i		−	0.106224i
$705$	−11.6301	−	11.6472i	−0.438017	−	0.438658i
$706$	−28.5728	−	16.4965i	−1.07535	−	0.620854i
$707$	54.4769	−	31.4523i	2.04881	−	1.18288i
$708$	4.53605	+	4.54269i	0.170475	+	0.170725i
$709$	12.7967	+	22.1645i	0.480589	+	0.832405i	0.999752	−	0.0222707i	$-0.00708956\pi$
$709$	12.7967	+	22.1645i	0.480589	+	0.832405i	−0.519163	+	0.854675i	$0.673756\pi$
$710$		−	1.65152i		−	0.0619806i
$711$	−13.1120	+	22.6341i	−0.491739	+	0.848847i
$712$	−1.31900	−	2.28458i	−0.0494317	−	0.0856183i
$713$	11.6046	+	20.0998i	0.434597	+	0.752744i
$714$	−15.4284	−	4.14613i	−0.577394	−	0.155165i
$715$		−	3.82749i		−	0.143140i
$716$	9.19621	+	15.9283i	0.343679	+	0.595269i
$717$	12.2691	−	12.2512i	0.458199	−	0.457530i
$718$	15.5156	−	8.95794i	0.579037	−	0.334307i
$719$	38.2562	+	22.0872i	1.42671	+	0.823714i	0.996860	−	0.0791847i	$-0.0252317\pi$
$719$	38.2562	+	22.0872i	1.42671	+	0.823714i	0.429854	+	0.902898i	$0.358565\pi$
$720$	1.49620	+	2.60027i	0.0557600	+	0.0969062i
$721$		−	4.53304i		−	0.168819i
$722$	4.56482	+	18.4435i	0.169885	+	0.686396i
$723$	−8.84049	−	2.37573i	−0.328781	−	0.0883544i
$724$	12.8805	+	7.43657i	0.478701	+	0.276378i
$725$	1.23451	−	2.13824i	0.0458487	−	0.0794122i
$726$	5.11446	−	1.36641i	0.189815	−	0.0507121i
$727$	−5.60464	+	9.70752i	−0.207865	+	0.360032i	−0.951042	−	0.309063i	$-0.899985\pi$
$727$	−5.60464	+	9.70752i	−0.207865	+	0.360032i	0.743177	+	0.669095i	$0.233318\pi$
$728$	−3.77451	+	2.17921i	−0.139893	+	0.0807671i
$729$	0.118476	−	26.9997i	0.00438799	−	0.999990i
$730$			9.04340i			0.334711i
$731$	−13.1348	+	7.58337i	−0.485807	+	0.280481i
$732$	−3.16646	+	0.845968i	−0.117036	+	0.0312679i
$733$	−4.73362			−0.174840			−0.0874202	−	0.996172i	$-0.527862\pi$
$733$	−4.73362			−0.174840			−0.0874202	+	0.996172i	$0.527862\pi$
$734$	15.3242			0.565625
$735$	1.47543	+	5.52253i	0.0544220	+	0.203701i
$736$	3.23945	+	1.87030i	0.119408	+	0.0689400i
$737$	14.8975	+	25.8033i	0.548758	+	0.950477i
$738$	−30.5791	+	17.5952i	−1.12563	+	0.647690i
$739$	3.93967	−	6.82371i	0.144923	−	0.251014i	−0.784421	−	0.620229i	$-0.787040\pi$
$739$	3.93967	−	6.82371i	0.144923	−	0.251014i	0.929344	+	0.369214i	$0.120373\pi$
$740$	11.8172			0.434410
$741$	10.1784	−	1.23331i	0.373912	−	0.0453069i
$742$	12.6067			0.462805
$743$	−6.72320	+	11.6449i	−0.246650	+	0.427211i	−0.962594	−	0.270947i	$-0.912663\pi$
$743$	−6.72320	+	11.6449i	−0.246650	+	0.427211i	0.715944	+	0.698158i	$0.245997\pi$
$744$	−7.60474	+	7.59363i	−0.278803	+	0.278396i
$745$	−5.91288	−	10.2414i	−0.216631	−	0.375216i
$746$	−7.11335	−	4.10690i	−0.260438	−	0.150364i
$747$	−24.0406	−	0.0351635i	−0.879601	−	0.00128657i
$748$	8.10003			0.296166
$749$	−0.426981			−0.0156015
$750$	−0.447064	−	1.67336i	−0.0163245	−	0.0611025i
$751$	28.4743	−	16.4397i	1.03904	−	0.599892i	0.119481	−	0.992836i	$-0.461877\pi$
$751$	28.4743	−	16.4397i	1.03904	−	0.599892i	0.919562	+	0.392944i	$0.128543\pi$
$752$		−	9.50293i		−	0.346536i
$753$	−39.2207	−	10.5399i	−1.42928	−	0.384095i
$754$	−2.90377	+	1.67649i	−0.105749	+	0.0610543i
$755$	−2.73407	+	4.73555i	−0.0995030	+	0.172344i
$756$	−16.0988	−	4.35154i	−0.585508	−	0.158264i
$757$	22.4848	−	38.9449i	0.817225	−	1.41548i	−0.0904939	−	0.995897i	$-0.528845\pi$
$757$	22.4848	−	38.9449i	0.817225	−	1.41548i	0.907719	−	0.419578i	$-0.137822\pi$
$758$	26.2093	+	15.1319i	0.951963	+	0.549616i
$759$	4.73903	−	17.6347i	0.172016	−	0.640099i
$760$	−4.31596	−	0.610351i	−0.156556	−	0.0221398i
$761$		−	9.71303i		−	0.352097i	−0.984381	−	0.176049i	$-0.943668\pi$
$761$		−	9.71303i		−	0.352097i	0.984381	−	0.176049i	$-0.0563316\pi$
$762$	−1.69702	+	1.69454i	−0.0614766	+	0.0613868i
$763$	−31.2124	−	18.0205i	−1.12996	−	0.652385i
$764$	−1.63856	+	0.946026i	−0.0592812	+	0.0342260i
$765$	−7.47301	+	4.29998i	−0.270187	+	0.155466i
$766$	10.9707	+	19.0019i	0.396388	+	0.686565i
$767$			5.03333i			0.181743i
$768$	−0.449511	+	1.67270i	−0.0162203	+	0.0603585i
$769$	13.8272	+	23.9494i	0.498621	+	0.863638i	0.999999	−	0.00159104i	$-0.000506444\pi$
$769$	13.8272	+	23.9494i	0.498621	+	0.863638i	−0.501377	+	0.865229i	$0.667173\pi$
$770$	−4.52275	−	7.83364i	−0.162989	−	0.282305i
$771$	−1.39050	+	5.17426i	−0.0500775	+	0.186346i
$772$			20.2351i			0.728277i
$773$	0.918990	+	1.59174i	0.0330538	+	0.0572508i	0.882079	−	0.471101i	$-0.156143\pi$
$773$	0.918990	+	1.59174i	0.0330538	+	0.0572508i	−0.849025	+	0.528352i	$0.822810\pi$
$774$	−13.7225	+	7.89593i	−0.493244	+	0.283813i
$775$	5.37344	−	3.10235i	0.193019	−	0.111440i
$776$	8.27383	+	4.77690i	0.297013	+	0.171481i
$777$	−46.4839	+	46.4160i	−1.66760	+	1.66516i
$778$		−	23.7720i		−	0.852267i
$779$	7.17771	−	50.7555i	0.257168	−	1.81850i
$780$	−0.610445	+	2.27156i	−0.0218574	+	0.0813351i
$781$	−4.03110	−	2.32736i	−0.144244	−	0.0832794i
$782$	−5.37512	+	9.30998i	−0.192214	+	0.332924i
$783$	−12.3850	−	3.34768i	−0.442603	−	0.119636i
$784$	−1.65013	+	2.85811i	−0.0589333	+	0.102075i
$785$	−14.8517	+	8.57463i	−0.530079	+	0.306042i
$786$	32.6823	+	8.78283i	1.16574	+	0.313273i
$787$		−	52.3955i		−	1.86770i	−0.357666	−	0.933850i	$-0.616427\pi$
$787$		−	52.3955i		−	1.86770i	0.357666	−	0.933850i	$-0.383573\pi$
$788$	−7.26726	+	4.19576i	−0.258886	+	0.149468i
$789$	−3.11635	−	11.6645i	−0.110945	−	0.415267i
$790$	8.71926			0.310217
$791$	−38.0345			−1.35235
$792$	8.45531	+	0.0123673i	0.300446	+	0.000439454i
$793$	−2.22546	−	1.28487i	−0.0790286	−	0.0456272i
$794$	−15.7374	−	27.2581i	−0.558501	−	0.967352i
$795$	4.81437	−	4.80733i	0.170748	−	0.170498i
$796$	−0.537524	+	0.931019i	−0.0190520	+	0.0329991i
$797$	−48.3530			−1.71275			−0.856375	−	0.516354i	$-0.827289\pi$
$797$	−48.3530			−1.71275			−0.856375	+	0.516354i	$0.827289\pi$
$798$	19.3745	−	14.5514i	0.685849	−	0.515116i
$799$	27.3109			0.966189
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	6.85952	−	3.94698i	0.242369	−	0.139460i
$802$	−14.4572	−	25.0407i	−0.510503	−	0.884217i
$803$	22.0735	+	12.7441i	0.778957	+	0.449731i
$804$	−4.72613	−	17.6899i	−0.166678	−	0.623875i
$805$	12.0051			0.423123
$806$	−8.42611			−0.296797
$807$	16.7341	−	4.47078i	0.589069	−	0.157379i
$808$	16.9742	−	9.80004i	0.597149	−	0.344764i
$809$		−	30.0431i		−	1.05626i	−0.849164	−	0.528129i	$-0.822894\pi$
$809$		−	30.0431i		−	1.05626i	0.849164	−	0.528129i	$-0.177106\pi$
$810$	−7.80736	+	4.47718i	−0.274323	+	0.157312i
$811$	5.51238	−	3.18257i	0.193566	−	0.111755i	−0.400085	−	0.916478i	$-0.631019\pi$
$811$	5.51238	−	3.18257i	0.193566	−	0.111755i	0.593651	+	0.804723i	$0.297686\pi$
$812$	−3.96205	+	6.86247i	−0.139041	+	0.240826i
$813$	27.8052	−	7.42859i	0.975171	−	0.260532i
$814$	16.6531	−	28.8440i	0.583690	−	1.01098i
$815$	−2.65915	−	1.53526i	−0.0931461	−	0.0537779i
$816$	−4.80725	−	1.29187i	−0.168288	−	0.0452244i
$817$	3.22102	−	22.7767i	0.112689	−	0.796857i
$818$			32.6510i			1.14162i
$819$	−6.52107	−	11.3331i	−0.227865	−	0.396010i
$820$	10.1844	+	5.87998i	0.355656	+	0.205338i
$821$	−44.8460	+	25.8919i	−1.56514	+	0.903632i	−0.568414	+	0.822743i	$0.692443\pi$
$821$	−44.8460	+	25.8919i	−1.56514	+	0.903632i	−0.996723	+	0.0808894i	$0.974224\pi$
$822$	5.79105	−	5.78259i	0.201986	−	0.201691i
$823$	12.4036	+	21.4836i	0.432361	+	0.748871i	0.997076	−	0.0764150i	$-0.0243474\pi$
$823$	12.4036	+	21.4836i	0.432361	+	0.748871i	−0.564715	+	0.825286i	$0.691014\pi$
$824$		−	1.41243i		−	0.0492042i
$825$	−4.71441	−	1.26692i	−0.164135	−	0.0441085i
$826$	5.94763	+	10.3016i	0.206945	+	0.358439i
$827$	−16.9483	−	29.3554i	−0.589352	−	1.02079i	−0.994317	−	0.106455i	$-0.966050\pi$
$827$	−16.9483	−	29.3554i	−0.589352	−	1.02079i	0.404966	−	0.914332i	$-0.367283\pi$
$828$	−5.62510	+	9.71012i	−0.195486	+	0.337450i
$829$			38.0529i			1.32163i	0.750548	+	0.660816i	$0.229790\pi$
$829$			38.0529i			1.32163i	−0.750548	+	0.660816i	$0.770210\pi$
$830$	4.00678	+	6.93994i	0.139077	+	0.240889i
$831$	−34.3501	−	34.4004i	−1.19159	−	1.19334i
$832$	−1.17608	+	0.679010i	−0.0407732	+	0.0235404i
$833$	−8.21404	−	4.74238i	−0.284600	−	0.164314i
$834$	3.16174	+	3.16637i	0.109482	+	0.109642i
$835$		−	23.3474i		−	0.807971i
$836$	−7.57190	+	9.67444i	−0.261880	+	0.334597i
$837$	−22.7475	−	22.8475i	−0.786268	−	0.789726i
$838$	5.96959	+	3.44655i	0.206216	+	0.119059i
$839$	−7.01424	+	12.1490i	−0.242158	+	0.419431i	−0.961329	−	0.275403i	$-0.911189\pi$
$839$	−7.01424	+	12.1490i	−0.242158	+	0.419431i	0.719170	+	0.694834i	$0.244522\pi$
$840$	1.43481	+	5.37049i	0.0495056	+	0.185299i
$841$	11.4520	−	19.8354i	0.394895	−	0.683978i
$842$	16.3349	−	9.43094i	0.562937	−	0.325012i
$843$	−2.21804	+	8.25367i	−0.0763932	+	0.284272i
$844$		−	24.7606i		−	0.852293i
$845$	9.66119	−	5.57789i	0.332355	−	0.191885i
$846$	28.5088	+	0.0416989i	0.980151	+	0.00143364i
$847$	9.80922			0.337049
$848$	3.92804			0.134890
$849$	13.4134	−	3.58359i	0.460346	−	0.122989i
$850$	2.48891	+	1.43697i	0.0853688	+	0.0492877i
$851$	22.1017	+	38.2813i	0.757637	+	1.31227i
$852$	2.02121	+	2.02417i	0.0692457	+	0.0693470i
$853$	24.0528	−	41.6607i	0.823553	−	1.42644i	−0.0794674	−	0.996837i	$-0.525322\pi$
$853$	24.0528	−	41.6607i	0.823553	−	1.42644i	0.903020	−	0.429598i	$-0.141345\pi$
$854$	−6.07307			−0.207816
$855$	1.84999	−	12.9452i	0.0632683	−	0.442716i
$856$	−0.133041			−0.00454724
$857$	−9.49407	+	16.4442i	−0.324311	+	0.561724i	−0.981373	−	0.192113i	$-0.938466\pi$
$857$	−9.49407	+	16.4442i	−0.324311	+	0.561724i	0.657061	+	0.753837i	$0.271799\pi$
$858$	4.68427	+	4.69113i	0.159918	+	0.160153i
$859$	−6.40982	−	11.1021i	−0.218700	−	0.378800i	0.735711	−	0.677296i	$-0.236848\pi$
$859$	−6.40982	−	11.1021i	−0.218700	−	0.378800i	−0.954411	+	0.298496i	$0.903515\pi$
$860$	4.57030	+	2.63866i	0.155846	+	0.0899777i
$861$	−63.1567	+	16.8733i	−2.15238	+	0.575040i
$862$	−10.9064			−0.371473
$863$	−35.5443			−1.20994			−0.604971	−	0.796247i	$-0.706815\pi$
$863$	−35.5443			−1.20994			−0.604971	+	0.796247i	$0.706815\pi$
$864$	−5.01614	−	1.35587i	−0.170652	−	0.0461277i
$865$	−8.30963	+	4.79757i	−0.282536	+	0.163122i
$866$		−	19.1346i		−	0.650219i
$867$	−3.92894	+	14.6202i	−0.133434	+	0.496529i
$868$	−17.2455	+	9.95670i	−0.585351	+	0.337953i
$869$	12.2874	−	21.2823i	0.416820	−	0.721953i
$870$	1.10381	+	4.13157i	0.0374228	+	0.140073i
$871$	7.17814	−	12.4329i	0.243222	−	0.421273i
$872$	−9.72530	−	5.61490i	−0.329340	−	0.190145i
$873$	−14.3670	+	24.8005i	−0.486249	+	0.839370i
$874$	−6.09491	−	15.1228i	−0.206163	−	0.511538i
$875$		−	3.20940i		−	0.108498i
$876$	−11.0678	−	11.0840i	−0.373945	−	0.374492i
$877$	−13.5878	−	7.84493i	−0.458828	−	0.264904i	0.252723	−	0.967539i	$-0.418674\pi$
$877$	−13.5878	−	7.84493i	−0.458828	−	0.264904i	−0.711551	+	0.702634i	$0.752007\pi$
$878$	−16.7584	+	9.67549i	−0.565570	+	0.326532i
$879$	−22.1853	−	22.2177i	−0.748290	−	0.749385i
$880$	−1.40922	−	2.44084i	−0.0475048	−	0.0822807i
$881$		−	3.34699i		−	0.112763i	−0.998409	−	0.0563814i	$-0.982044\pi$
$881$		−	3.34699i		−	0.112763i	0.998409	−	0.0563814i	$-0.0179563\pi$
$882$	−8.56708	−	4.96293i	−0.288469	−	0.167111i
$883$	−15.8500	−	27.4530i	−0.533396	−	0.923868i	−0.999239	−	0.0390012i	$-0.987582\pi$
$883$	−15.8500	−	27.4530i	−0.533396	−	0.923868i	0.465844	−	0.884867i	$-0.345751\pi$
$884$	−1.95143	−	3.37998i	−0.0656338	−	0.113681i
$885$	6.19968	+	1.66606i	0.208400	+	0.0560040i
$886$			19.4851i			0.654614i
$887$	14.2516	+	24.6845i	0.478521	+	0.828823i	0.999697	−	0.0246262i	$-0.00783956\pi$
$887$	14.2516	+	24.6845i	0.478521	+	0.828823i	−0.521175	+	0.853450i	$0.674506\pi$
$888$	−14.4837	+	14.4625i	−0.486040	+	0.485330i
$889$	−3.84839	+	2.22187i	−0.129071	+	0.0745191i
$890$	−2.28458	−	1.31900i	−0.0765793	−	0.0442131i
$891$	−0.0742039	+	25.3658i	−0.00248592	+	0.849788i
$892$		−	6.67380i		−	0.223455i
$893$	−25.5302	+	32.6193i	−0.854334	+	1.09156i
$894$	19.7810	+	5.31581i	0.661576	+	0.177787i
$895$	15.9283	+	9.19621i	0.532424	+	0.307395i
$896$	−1.60470	+	2.77942i	−0.0536093	+	0.0928540i
$897$	−8.50032	+	2.27099i	−0.283818	+	0.0758263i
$898$	−5.15302	+	8.92529i	−0.171958	+	0.297841i
$899$	−13.2672	+	7.65980i	−0.442484	+	0.255468i
$900$	2.59588	+	1.50380i	0.0865293	+	0.0501266i
$901$			11.2890i			0.376090i
$902$	28.7042	−	16.5724i	0.955745	−	0.551800i
$903$	−28.3418	+	7.57196i	−0.943157	+	0.251979i
$904$	−11.8510			−0.394157
$905$	14.8731			0.494400
$906$	−2.44461	−	9.15017i	−0.0812167	−	0.303994i
$907$	18.7055	+	10.7996i	0.621105	+	0.358595i	0.777299	−	0.629131i	$-0.216589\pi$
$907$	18.7055	+	10.7996i	0.621105	+	0.358595i	−0.156194	+	0.987726i	$0.549923\pi$
$908$	−12.0437	−	20.8603i	−0.399683	−	0.692272i
$909$	29.3256	+	50.9654i	0.972668	+	1.69042i
$910$	−2.17921	+	3.77451i	−0.0722403	+	0.125124i
$911$	−26.3839			−0.874137			−0.437068	−	0.899428i	$-0.643983\pi$
$911$	−26.3839			−0.874137			−0.437068	+	0.899428i	$0.643983\pi$
$912$	6.03679	−	4.53401i	0.199898	−	0.150136i
$913$	22.5857			0.747478
$914$	1.59387	−	2.76067i	0.0527207	−	0.0913149i
$915$	−2.31925	+	2.31586i	−0.0766720	+	0.0765599i
$916$	10.8331	+	18.7635i	0.357936	+	0.619963i
$917$	54.3061	+	31.3537i	1.79335	+	1.03539i
$918$	3.89670	−	14.4161i	0.128610	−	0.475801i
$919$	16.4871			0.543860			0.271930	−	0.962317i	$-0.412338\pi$
$919$	16.4871			0.543860			0.271930	+	0.962317i	$0.412338\pi$
$920$	3.74059			0.123324
$921$	9.54554	+	35.7289i	0.314536	+	1.17731i
$922$	28.6530	−	16.5428i	0.943637	−	0.544809i
$923$			2.24280i			0.0738226i
$924$	15.1305	+	4.06606i	0.497755	+	0.133763i
$925$	10.2340	−	5.90861i	0.336492	−	0.194274i
$926$	2.68103	−	4.64368i	0.0881041	−	0.152601i
$927$	4.23727	+	0.00619773i	0.139170	+	0.000203560i
$928$	−1.23451	+	2.13824i	−0.0405249	+	0.0701912i
$929$	6.99418	+	4.03809i	0.229472	+	0.132485i	0.610328	−	0.792149i	$-0.291038\pi$
$929$	6.99418	+	4.03809i	0.229472	+	0.132485i	−0.380857	+	0.924634i	$0.624371\pi$
$930$	−2.78909	+	10.3786i	−0.0914577	+	0.340329i
$931$	13.3426	−	5.37744i	0.437287	−	0.176239i
$932$		−	17.7327i		−	0.580852i
$933$	13.6594	−	13.6395i	0.447190	−	0.446536i
$934$	−35.7855	−	20.6608i	−1.17094	−	0.676042i
$935$	7.01483	−	4.05001i	0.229409	−	0.132450i
$936$	−2.03187	−	3.53121i	−0.0664136	−	0.115421i
$937$	−4.76274	−	8.24931i	−0.155592	−	0.269493i	0.777682	−	0.628657i	$-0.216395\pi$
$937$	−4.76274	−	8.24931i	−0.155592	−	0.269493i	−0.933274	+	0.359164i	$0.883062\pi$
$938$		−	33.9282i		−	1.10779i
$939$	0.682640	−	2.54021i	0.0222771	−	0.0828968i
$940$	−4.75146	−	8.22978i	−0.154976	−	0.268426i
$941$	14.0778	+	24.3835i	0.458925	+	0.794881i	0.998904	−	0.0467973i	$-0.0149015\pi$
$941$	14.0778	+	24.3835i	0.458925	+	0.794881i	−0.539980	+	0.841678i	$0.681568\pi$
$942$	7.70878	−	28.6856i	0.251166	−	0.934628i
$943$			43.9892i			1.43249i
$944$	1.85319	+	3.20982i	0.0603162	+	0.104471i
$945$	−16.1177	+	4.28085i	−0.524310	+	0.139256i
$946$	12.8811	−	7.43692i	0.418801	−	0.241795i
$947$	−8.11070	−	4.68272i	−0.263562	−	0.152168i	0.362396	−	0.932024i	$-0.381959\pi$
$947$	−8.11070	−	4.68272i	−0.263562	−	0.152168i	−0.625959	+	0.779856i	$0.715292\pi$
$948$	−10.6867	+	10.6711i	−0.347087	+	0.346580i
$949$		−	12.2811i		−	0.398662i
$950$	−4.04290	+	1.62940i	−0.131169	+	0.0528647i
$951$	−1.66029	+	6.17820i	−0.0538385	+	0.200342i
$952$	−7.98790	−	4.61182i	−0.258889	−	0.149470i
$953$	23.5528	−	40.7947i	0.762951	−	1.32147i	−0.178373	−	0.983963i	$-0.557083\pi$
$953$	23.5528	−	40.7947i	0.762951	−	1.32147i	0.941323	−	0.337506i	$-0.109583\pi$
$954$	−0.0172363	+	11.7841i	−0.000558045	+	0.381525i
$955$	−0.946026	+	1.63856i	−0.0306127	+	0.0530227i
$956$	8.66926	−	5.00520i	0.280384	−	0.161880i
$957$	11.6400	+	3.12806i	0.376268	+	0.101116i
$958$		−	7.38780i		−	0.238689i
$959$	13.1326	−	7.58208i	0.424072	−	0.244838i
$960$	0.447064	+	1.67336i	0.0144289	+	0.0540075i
$961$	−7.49841			−0.241884
$962$	−16.0480			−0.517409
$963$	0.000583783	−	0.399121i	1.88121e−5	−	0.0128615i
$964$	−4.57707	−	2.64257i	−0.147418	−	0.0851116i
$965$	10.1175	+	17.5241i	0.325695	+	0.564121i
$966$	−14.7139	+	14.6924i	−0.473412	+	0.472720i
$967$	−13.5335	+	23.4406i	−0.435206	+	0.753800i	−0.997312	−	0.0732655i	$-0.976658\pi$
$967$	−13.5335	+	23.4406i	−0.435206	+	0.753800i	0.562106	+	0.827065i	$0.309991\pi$
$968$	3.05640			0.0982365
$969$	13.0305	+	17.3494i	0.418599	+	0.557342i
$970$	9.55380			0.306754
$971$	−0.875674	+	1.51671i	−0.0281017	+	0.0486736i	−0.879734	−	0.475466i	$-0.842280\pi$
$971$	−0.875674	+	1.51671i	−0.0281017	+	0.0486736i	0.851633	+	0.524139i	$0.175613\pi$
$972$	4.08962	−	15.0424i	0.131175	−	0.482486i
$973$	4.14565	+	7.18047i	0.132903	+	0.230195i
$974$	−2.28643	−	1.32007i	−0.0732618	−	0.0422977i
$975$	0.607122	+	2.27245i	0.0194434	+	0.0727768i
$976$	−1.89227			−0.0605702
$977$	9.85378			0.315250			0.157625	−	0.987499i	$-0.449616\pi$
$977$	9.85378			0.315250			0.157625	+	0.987499i	$0.449616\pi$
$978$	5.13809	−	1.37272i	0.164298	−	0.0438948i
$979$	−6.43895	+	3.71753i	−0.205790	+	0.118813i
$980$			3.30026i			0.105423i
$981$	16.8874	−	29.1512i	0.539172	−	0.930727i
$982$	−14.1387	+	8.16297i	−0.451183	+	0.260491i
$983$	26.3520	−	45.6430i	0.840499	−	1.45579i	−0.0489751	−	0.998800i	$-0.515596\pi$
$983$	26.3520	−	45.6430i	0.840499	−	1.45579i	0.889474	−	0.456986i	$-0.151071\pi$
$984$	−19.6787	+	5.25746i	−0.627333	+	0.167602i
$985$	−4.19576	+	7.26726i	−0.133688	+	0.231554i
$986$	−6.14517	−	3.54792i	−0.195702	−	0.112989i
$987$	51.0153	+	13.7095i	1.62384	+	0.436379i
$988$	5.86115	+	0.828868i	0.186468	+	0.0263698i
$989$			19.7403i			0.627706i
$990$	7.32869	−	4.21694i	0.232921	−	0.134023i
$991$	−4.35746	−	2.51578i	−0.138419	−	0.0799164i	0.429191	−	0.903214i	$-0.358799\pi$
$991$	−4.35746	−	2.51578i	−0.138419	−	0.0799164i	−0.567610	+	0.823297i	$0.692132\pi$
$992$	−5.37344	+	3.10235i	−0.170607	+	0.0984998i
$993$	37.9871	−	37.9316i	1.20549	−	1.20372i
$994$	2.65020	+	4.59028i	0.0840593	+	0.145595i
$995$			1.07505i			0.0340813i
$996$	−13.4043	−	3.60218i	−0.424732	−	0.114140i
$997$	−8.30937	−	14.3922i	−0.263160	−	0.455807i	0.703920	−	0.710280i	$-0.251431\pi$
$997$	−8.30937	−	14.3922i	−0.263160	−	0.455807i	−0.967080	+	0.254473i	$0.918098\pi$
$998$	−6.98906	−	12.1054i	−0.221235	−	0.383190i
$999$	−43.3239	−	43.5144i	−1.37071	−	1.37674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.a.521.2	yes	24
3.2	odd	2		570.2.s.b.521.2	yes	24
19.12	odd	6		570.2.s.b.221.2	yes	24
57.50	even	6	inner	570.2.s.a.221.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.2	✓	24	57.50	even	6	inner
570.2.s.a.521.2	yes	24	1.1	even	1	trivial
570.2.s.b.221.2	yes	24	19.12	odd	6
570.2.s.b.521.2	yes	24	3.2	odd	2

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.22385 - 1.22564i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.67336 - 0.447064i) q^{6} +3.20940 q^{7} +1.00000 q^{8} +(-0.00438801 + 3.00000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.22385 - 1.22564i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.67336 - 0.447064i) q^{6} +3.20940 q^{7} +1.00000 q^{8} +(-0.00438801 + 3.00000i) q^{9} +(0.866025 - 0.500000i) q^{10} -2.81844i q^{11} +(-0.449511 + 1.67270i) q^{12} +(-1.17608 + 0.679010i) q^{13} +(-1.60470 + 2.77942i) q^{14} +(0.447064 + 1.67336i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48891 - 1.43697i) q^{17} +(-2.59588 - 1.50380i) q^{18} +(4.04290 - 1.62940i) q^{19} +1.00000i q^{20} +(-3.92782 - 3.93357i) q^{21} +(2.44084 + 1.40922i) q^{22} +(-3.23945 + 1.87030i) q^{23} +(-1.22385 - 1.22564i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.35802i q^{26} +(3.68229 - 3.66616i) q^{27} +(-1.60470 - 2.77942i) q^{28} +(-1.23451 - 2.13824i) q^{29} +(-1.67270 - 0.449511i) q^{30} -6.20471i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.45439 + 3.44934i) q^{33} +(2.48891 - 1.43697i) q^{34} +(-2.77942 - 1.60470i) q^{35} +(2.60027 - 1.49620i) q^{36} -11.8172i q^{37} +(-0.610351 + 4.31596i) q^{38} +(2.27156 + 0.610445i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(5.87998 - 10.1844i) q^{41} +(5.37049 - 1.43481i) q^{42} +(2.63866 - 4.57030i) q^{43} +(-2.44084 + 1.40922i) q^{44} +(1.50380 - 2.59588i) q^{45} -3.74059i q^{46} +(-8.22978 + 4.75146i) q^{47} +(1.67336 - 0.447064i) q^{48} +3.30026 q^{49} -1.00000 q^{50} +(1.28484 + 4.80914i) q^{51} +(1.17608 + 0.679010i) q^{52} +(-1.96402 - 3.40178i) q^{53} +(1.33385 + 5.02204i) q^{54} +(-1.40922 + 2.44084i) q^{55} +3.20940 q^{56} +(-6.94496 - 2.96101i) q^{57} +2.46903 q^{58} +(1.85319 - 3.20982i) q^{59} +(1.22564 - 1.22385i) q^{60} +(0.946137 + 1.63876i) q^{61} +(5.37344 + 3.10235i) q^{62} +(-0.0140829 + 9.62820i) q^{63} +1.00000 q^{64} +1.35802 q^{65} +(-1.26002 - 4.71626i) q^{66} +(-9.15518 + 5.28574i) q^{67} +2.87394i q^{68} +(6.25690 + 1.68144i) q^{69} +(2.77942 - 1.60470i) q^{70} +(0.825761 - 1.43026i) q^{71} +(-0.00438801 + 3.00000i) q^{72} +(-4.52170 + 7.83182i) q^{73} +(10.2340 + 5.90861i) q^{74} +(0.449511 - 1.67270i) q^{75} +(-3.43255 - 2.68656i) q^{76} -9.04550i q^{77} +(-1.66444 + 1.66201i) q^{78} +(7.55110 + 4.35963i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-8.99996 - 0.0263280i) q^{81} +(5.87998 + 10.1844i) q^{82} +8.01355i q^{83} +(-1.44266 + 5.36838i) q^{84} +(1.43697 + 2.48891i) q^{85} +(2.63866 + 4.57030i) q^{86} +(-1.10986 + 4.12995i) q^{87} -2.81844i q^{88} +(-1.31900 - 2.28458i) q^{89} +(1.49620 + 2.60027i) q^{90} +(-3.77451 + 2.17921i) q^{91} +(3.23945 + 1.87030i) q^{92} +(-7.60474 + 7.59363i) q^{93} -9.50293i q^{94} +(-4.31596 - 0.610351i) q^{95} +(-0.449511 + 1.67270i) q^{96} +(8.27383 + 4.77690i) q^{97} +(-1.65013 + 2.85811i) q^{98} +(8.45531 + 0.0123673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9 - 2 * q^12 + 18 * q^13 + 6 * q^14 - 12 * q^16 + 12 * q^17 + 2 * q^18 + 6 * q^19 - 6 * q^21 + 18 * q^22 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 + 40 * q^39 + 6 * q^41 - 6 * q^42 - 22 * q^43 - 18 * q^44 + 8 * q^45 + 12 * q^47 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

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