LMFDB - Embedded newform 570.2.s.b.521.2

Newspace parameters

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

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.b.221.2

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.67336 - 0.447064i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.22385 + 1.22564i) q^{6} +3.20940 q^{7} -1.00000 q^{8} +(2.60027 + 1.49620i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.67336 - 0.447064i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.22385 + 1.22564i) q^{6} +3.20940 q^{7} -1.00000 q^{8} +(2.60027 + 1.49620i) 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} +(-1.22564 - 1.22385i) 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} +(-5.37049 - 1.43481i) q^{21} +(2.44084 + 1.40922i) q^{22} +(3.23945 - 1.87030i) q^{23} +(1.67336 + 0.447064i) 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} +(1.26002 - 4.71626i) q^{33} +(2.48891 - 1.43697i) q^{34} +(2.77942 + 1.60470i) q^{35} +(-0.00438801 - 3.00000i) 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} +(-3.92782 + 3.93357i) 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} +(1.22385 - 1.22564i) q^{48} +3.30026 q^{49} +1.00000 q^{50} +(-3.52242 - 3.51727i) q^{51} +(1.17608 + 0.679010i) q^{52} +(1.96402 + 3.40178i) q^{53} +(-5.01614 + 1.35587i) q^{54} +(-1.40922 + 2.44084i) q^{55} -3.20940 q^{56} +(-7.49368 + 0.919133i) q^{57} +2.46903 q^{58} +(-1.85319 + 3.20982i) q^{59} +(-0.447064 + 1.67336i) q^{60} +(0.946137 + 1.63876i) q^{61} +(-5.37344 - 3.10235i) q^{62} +(8.34530 + 4.80190i) q^{63} +1.00000 q^{64} -1.35802 q^{65} +(-3.45439 - 3.44934i) 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} +(-2.60027 - 1.49620i) 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} +(0.607122 - 2.27245i) q^{78} +(7.55110 + 4.35963i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(4.52278 + 7.78103i) 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} +(3.00000 - 0.00438801i) q^{90} +(-3.77451 + 2.17921i) q^{91} +(-3.23945 - 1.87030i) q^{92} +(-2.77390 + 10.3827i) 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} +(-4.21694 + 7.32869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24q + 12q^{2} + 2q^{3} - 12q^{4} + 4q^{6} - 12q^{7} - 24q^{8} + 2q^{9} + O(q^{10}) $	$ 24q + 12q^{2} + 2q^{3} - 12q^{4} + 4q^{6} - 12q^{7} - 24q^{8} + 2q^{9} + 2q^{12} + 18q^{13} - 6q^{14} - 12q^{16} - 12q^{17} - 2q^{18} + 6q^{19} + 6q^{21} + 18q^{22} - 2q^{24} + 12q^{25} - 28q^{27} + 6q^{28} + 12q^{32} - 8q^{33} - 12q^{34} - 4q^{36} - 6q^{38} + 40q^{39} - 6q^{41} - 6q^{42} - 22q^{43} + 18q^{44} + 8q^{45} - 12q^{47} - 4q^{48} + 12q^{49} + 24q^{50} - 4q^{51} - 18q^{52} - 8q^{53} - 32q^{54} + 12q^{56} - 20q^{57} - 26q^{59} + 22q^{61} + 18q^{62} + 30q^{63} + 24q^{64} - 8q^{65} - 22q^{66} - 48q^{67} + 64q^{69} - 24q^{71} - 2q^{72} - 8q^{73} - 30q^{74} - 2q^{75} - 12q^{76} + 2q^{78} + 18q^{79} - 6q^{81} + 6q^{82} - 12q^{84} + 22q^{86} - 24q^{87} - 28q^{89} + 16q^{90} + 18q^{91} + 14q^{93} - 2q^{96} + 6q^{97} + 6q^{98} - 52q^{99} + O(q^{100}) $

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
$3$	−1.67336	−	0.447064i	−0.966115	−	0.258113i
$3$	−1.67336	−	0.447064i	−0.966115	−	0.258113i
$4$	−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
$6$	−1.22385	+	1.22564i	−0.499634	+	0.500366i
$7$	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
$9$	2.60027	+	1.49620i	0.866756	+	0.498733i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$			2.81844i			0.849791i	0.905242	+	0.424896i	$0.139689\pi$
$11$			2.81844i			0.849791i	−0.905242	+	0.424896i	$0.860311\pi$
$12$	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
$15$	−1.22564	−	1.22385i	−0.316459	−	0.315996i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.48891	+	1.43697i	0.603648	+	0.348516i	0.770475	−	0.637470i	$-0.220019\pi$
$17$	2.48891	+	1.43697i	0.603648	+	0.348516i	−0.166827	+	0.985986i	$0.553352\pi$
$18$	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
$21$	−5.37049	−	1.43481i	−1.17194	−	0.313101i
$22$	2.44084	+	1.40922i	0.520389	+	0.300447i
$23$	3.23945	−	1.87030i	0.675471	−	0.389984i	−0.122675	−	0.992447i	$-0.539147\pi$
$23$	3.23945	−	1.87030i	0.675471	−	0.389984i	0.798147	+	0.602463i	$0.205814\pi$
$24$	1.67336	+	0.447064i	0.341573	+	0.0912566i
$25$	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	0.957584	−	0.288154i	$-0.0930415\pi$
$29$	1.23451	+	2.13824i	0.229243	+	0.397061i	−0.728341	+	0.685215i	$0.759708\pi$
$30$	−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
$33$	1.26002	−	4.71626i	0.219342	−	0.820996i
$34$	2.48891	−	1.43697i	0.426844	−	0.246438i
$35$	2.77942	+	1.60470i	0.469808	+	0.271244i
$36$	−0.00438801	−	3.00000i	−0.000731334	−	0.499999i
$37$		−	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	$0.537104\pi$
$41$	−5.87998	+	10.1844i	−0.918299	+	1.59054i	−0.801998	+	0.597326i	$0.796230\pi$
$42$	−3.92782	+	3.93357i	−0.606076	+	0.606963i
$43$	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	0.239784	−	0.970826i	$-0.422923\pi$
$47$	8.22978	−	4.75146i	1.20044	−	0.693072i	0.960652	+	0.277754i	$0.0895899\pi$
$48$	1.22385	−	1.22564i	0.176647	−	0.176906i
$49$	3.30026			0.471466
$50$	1.00000			0.141421
$51$	−3.52242	−	3.51727i	−0.493237	−	0.492516i
$52$	1.17608	+	0.679010i	0.163093	+	0.0941617i
$53$	1.96402	+	3.40178i	0.269779	+	0.467271i	0.968805	−	0.247826i	$-0.0797160\pi$
$53$	1.96402	+	3.40178i	0.269779	+	0.467271i	−0.699026	+	0.715097i	$0.746383\pi$
$54$	−5.01614	+	1.35587i	−0.682610	+	0.184511i
$55$	−1.40922	+	2.44084i	−0.190019	+	0.329123i
$56$	−3.20940			−0.428874
$57$	−7.49368	+	0.919133i	−0.992562	+	0.121742i
$58$	2.46903			0.324199
$59$	−1.85319	+	3.20982i	−0.241265	+	0.417883i	−0.961075	−	0.276288i	$-0.910896\pi$
$59$	−1.85319	+	3.20982i	−0.241265	+	0.417883i	0.719810	+	0.694171i	$0.244229\pi$
$60$	−0.447064	+	1.67336i	−0.0577157	+	0.216030i
$61$	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
$63$	8.34530	+	4.80190i	1.05141	+	0.604983i
$64$	1.00000			0.125000
$65$	−1.35802			−0.168442
$66$	−3.45439	−	3.44934i	−0.425206	−	0.424585i
$67$	−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	−0.910857	−	0.412723i	$-0.864578\pi$
$71$	−0.825761	+	1.43026i	−0.0979999	+	0.169741i	0.812857	+	0.582464i	$0.197911\pi$
$72$	−2.60027	−	1.49620i	−0.306444	−	0.176329i
$73$	−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
$78$	0.607122	−	2.27245i	0.0687430	−	0.257305i
$79$	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
$81$	4.52278	+	7.78103i	0.502531	+	0.864559i
$82$	5.87998	+	10.1844i	0.649335	+	1.12468i
$83$		−	8.01355i		−	0.879602i	−0.898095	−	0.439801i	$-0.855049\pi$
$83$		−	8.01355i		−	0.879602i	0.898095	−	0.439801i	$-0.144951\pi$
$84$	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	0.927426	−	0.374006i	$-0.122016\pi$
$89$	1.31900	+	2.28458i	0.139814	+	0.242165i	−0.787612	+	0.616171i	$0.788683\pi$
$90$	3.00000	−	0.00438801i	0.316227	−	0.000462536i
$91$	−3.77451	+	2.17921i	−0.395676	+	0.228444i
$92$	−3.23945	−	1.87030i	−0.337736	−	0.194992i
$93$	−2.77390	+	10.3827i	−0.287640	+	1.07664i
$94$		−	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
$99$	−4.21694	+	7.32869i	−0.423819	+	0.736562i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−16.9742	+	9.80004i	−1.68899	+	0.975140i	−0.733701	+	0.679472i	$0.762209\pi$
$101$	−16.9742	+	9.80004i	−1.68899	+	0.975140i	−0.955291	+	0.295667i	$0.904458\pi$
$102$	−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
$105$	−3.93357	−	3.92782i	−0.383877	−	0.383316i
$106$	3.92804			0.381525
$107$	0.133041			0.0128615			0.00643076	−	0.999979i	$-0.497953\pi$
$107$	0.133041			0.0128615			0.00643076	+	0.999979i	$0.497953\pi$
$108$	−1.33385	+	5.02204i	−0.128350	+	0.483246i
$109$	−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
$111$	−5.28306	+	19.7745i	−0.501446	+	1.87691i
$112$	−1.60470	+	2.77942i	−0.151630	+	0.262631i
$113$	11.8510			1.11485			0.557423	−	0.830229i	$-0.311790\pi$
$113$	11.8510			1.11485			0.557423	+	0.830229i	$0.311790\pi$
$114$	−2.95085	+	6.94928i	−0.276372	+	0.650860i
$115$	3.74059			0.348812
$116$	1.23451	−	2.13824i	0.114622	−	0.198531i
$117$	−4.07405	+	0.00595899i	−0.376646	+	0.000550909i
$118$	1.85319	+	3.20982i	0.170600	+	0.295488i
$119$	7.98790	+	4.61182i	0.732249	+	0.422764i
$120$	1.22564	+	1.22385i	0.111885	+	0.111722i
$121$	3.05640			0.277855
$122$	1.89227			0.171319
$123$	14.3924	−	14.4135i	1.29772	−	1.29962i
$124$	−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
$129$	−6.45865	+	6.46811i	−0.568653	+	0.569485i
$130$	−0.679010	+	1.17608i	−0.0595531	+	0.103149i
$131$	−16.9209	−	9.76931i	−1.47839	−	0.853549i	−0.478689	−	0.877985i	$-0.658888\pi$
$131$	−16.9209	−	9.76931i	−1.47839	−	0.853549i	−0.999701	+	0.0244360i	$0.992221\pi$
$132$	−4.71441	+	1.26692i	−0.410337	+	0.110271i
$133$	12.9753	−	5.22939i	1.12510	−	0.453446i
$134$			10.5715i			0.913238i
$135$	−1.35587	−	5.01614i	−0.116695	−	0.431720i
$136$	−2.48891	−	1.43697i	−0.213422	−	0.123219i
$137$	−4.09190	+	2.36246i	−0.349595	+	0.201839i	−0.664507	−	0.747282i	$-0.731358\pi$
$137$	−4.09190	+	2.36246i	−0.349595	+	0.201839i	0.314912	+	0.949121i	$0.398025\pi$
$138$	−1.67228	+	6.25936i	−0.142354	+	0.532832i
$139$	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
$147$	−5.52253	−	1.47543i	−0.455490	−	0.121691i
$148$	−10.2340	+	5.90861i	−0.841231	+	0.485685i
$149$	−10.2414	−	5.91288i	−0.839009	−	0.484402i	0.0179181	−	0.999839i	$-0.494296\pi$
$149$	−10.2414	−	5.91288i	−0.839009	−	0.484402i	−0.856927	+	0.515437i	$0.827630\pi$
$150$	−1.67336	−	0.447064i	−0.136629	−	0.0365026i
$151$		−	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
$156$	−1.66444	−	1.66201i	−0.133262	−	0.133067i
$157$	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
$162$	8.99996	−	0.0263280i	0.707104	−	0.00206852i
$163$	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
$165$	3.44934	−	3.45439i	0.268531	−	0.268924i
$166$	−6.93994	−	4.00678i	−0.538644	−	0.310986i
$167$	−11.6737	−	20.2195i	−0.903339	−	1.56463i	−0.823131	−	0.567851i	$-0.807775\pi$
$167$	−11.6737	−	20.2195i	−0.903339	−	1.56463i	−0.0802078	−	0.996778i	$-0.525558\pi$
$168$	5.37049	+	1.43481i	0.414342	+	0.110698i
$169$	−5.57789	+	9.66119i	−0.429069	+	0.743169i
$170$	2.87394			0.220421
$171$	12.9505	+	1.81211i	0.990352	+	0.138576i
$172$	−5.27733			−0.402393
$173$	−4.79757	+	8.30963i	−0.364752	+	0.631769i	−0.988736	−	0.149668i	$-0.952180\pi$
$173$	−4.79757	+	8.30963i	−0.364752	+	0.631769i	0.623984	+	0.781437i	$0.285513\pi$
$174$	−4.13157	−	1.10381i	−0.313214	−	0.0836799i
$175$	1.60470	+	2.77942i	0.121304	+	0.210105i
$176$	−2.44084	−	1.40922i	−0.183985	−	0.106224i
$177$	4.53605	−	4.54269i	0.340950	−	0.341449i
$178$	2.63801			0.197727
$179$	18.3924			1.37471			0.687357	−	0.726320i	$-0.258771\pi$
$179$	18.3924			1.37471			0.687357	+	0.726320i	$0.258771\pi$
$180$	1.49620	−	2.60027i	0.111520	−	0.193812i
$181$	−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
$186$	7.60474	+	7.59363i	0.557607	+	0.556792i
$187$	−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	$0.0218060\pi$
$191$			1.89205i			0.136904i	−0.997654	+	0.0684520i	$0.978194\pi$
$192$	−1.67336	−	0.447064i	−0.120764	−	0.0322641i
$193$	−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
$195$	2.27245	+	0.607122i	0.162734	+	0.0434769i
$196$	−1.65013	−	2.85811i	−0.117867	−	0.204151i
$197$			8.39151i			0.597871i	0.954273	+	0.298935i	$0.0966315\pi$
$197$			8.39151i			0.597871i	−0.954273	+	0.298935i	$0.903369\pi$
$198$	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
$204$	−1.28484	+	4.80914i	−0.0899565	+	0.336707i
$205$	−10.1844	+	5.87998i	−0.711311	+	0.410676i
$206$	−1.22320	−	0.706213i	−0.0852242	−	0.0492042i
$207$	11.2218	−	0.0164137i	0.779966	−	0.00114083i
$208$		−	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
$213$	2.02121	−	2.02417i	0.138491	−	0.138694i
$214$	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
$219$	11.0678	−	11.0840i	0.747890	−	0.748985i
$220$	2.81844			0.190019
$221$	−3.90287			−0.262535
$222$	14.4837	+	14.4625i	0.972080	+	0.970659i
$223$	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
$225$	0.00438801	+	3.00000i	0.000292534	+	0.200000i
$226$	5.92548	−	10.2632i	0.394157	−	0.682701i
$227$	−24.0873			−1.59873			−0.799367	−	0.600843i	$-0.794832\pi$
$227$	−24.0873			−1.59873			−0.799367	+	0.600843i	$0.794832\pi$
$228$	4.54283	+	6.03015i	0.300856	+	0.399356i
$229$	−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
$231$	4.04392	−	15.1364i	0.266070	−	0.995901i
$232$	−1.23451	−	2.13824i	−0.0810498	−	0.140382i
$233$	−15.3569	−	8.86633i	−1.00607	−	0.580852i	−0.0960285	−	0.995379i	$-0.530614\pi$
$233$	−15.3569	−	8.86633i	−1.00607	−	0.580852i	−0.910037	+	0.414526i	$0.863947\pi$
$234$	−2.03187	+	3.53121i	−0.132827	+	0.230843i
$235$	9.50293			0.619903
$236$	3.70638			0.241265
$237$	−10.6867	−	10.6711i	−0.694174	−	0.693160i
$238$	7.98790	−	4.61182i	0.517779	−	0.298940i
$239$		−	10.0104i		−	0.647519i	−0.946139	−	0.323759i	$-0.895053\pi$
$239$		−	10.0104i		−	0.647519i	0.946139	−	0.323759i	$-0.104947\pi$
$240$	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
$243$	−4.08962	−	15.0424i	−0.262349	−	0.964973i
$244$	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
$249$	−3.58257	+	13.4096i	−0.227036	+	0.849796i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−20.3061	+	11.7237i	−1.28171	+	0.739996i	−0.977161	−	0.212501i	$-0.931839\pi$
$251$	−20.3061	+	11.7237i	−1.28171	+	0.739996i	−0.304549	+	0.952497i	$0.598506\pi$
$252$	−0.0140829	−	9.62820i	−0.000887138	−	0.606519i
$253$	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	0.910225	−	0.414114i	$-0.135909\pi$
$257$	1.54668	+	2.67892i	0.0964790	+	0.167106i	−0.813746	+	0.581221i	$0.802575\pi$
$258$	2.37222	+	8.82741i	0.147688	+	0.549571i
$259$		−	37.9262i		−	2.35662i
$260$	0.679010	+	1.17608i	0.0421104	+	0.0729373i
$261$	0.0108341	+	7.40707i	0.000670614	+	0.458486i
$262$	−16.9209	+	9.76931i	−1.04538	+	0.603550i
$263$	−6.03680	−	3.48535i	−0.372245	−	0.214916i	0.302194	−	0.953247i	$-0.402281\pi$
$263$	−6.03680	−	3.48535i	−0.372245	−	0.214916i	−0.674439	+	0.738331i	$0.735614\pi$
$264$	−1.26002	+	4.71626i	−0.0775490	+	0.290266i
$265$			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	−0.672366	−	0.740218i	$-0.734722\pi$
$269$	5.00015	−	8.66052i	0.304865	−	0.528041i	0.977231	+	0.212177i	$0.0680554\pi$
$270$	−5.02204	−	1.33385i	−0.305631	−	0.0811754i
$271$	−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
$276$	4.58462	+	4.57792i	0.275962	+	0.275558i
$277$	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
$279$	9.28347	−	16.1339i	0.555787	−	0.965911i
$280$	−2.77942	−	1.60470i	−0.166102	−	0.0958992i
$281$	2.46716	+	4.27325i	0.147179	+	0.254921i	0.930184	−	0.367094i	$-0.119647\pi$
$281$	2.46716	+	4.27325i	0.147179	+	0.254921i	−0.783005	+	0.622015i	$0.786314\pi$
$282$	−4.24842	+	15.9018i	−0.252990	+	0.946940i
$283$	−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
$285$	−6.94928	−	2.95085i	−0.411640	−	0.174793i
$286$	−3.82749			−0.226324
$287$	−18.8712	+	32.6859i	−1.11393	+	1.92939i
$288$	0.00438801	+	3.00000i	0.000258566	+	0.176777i
$289$	−4.37023	−	7.56947i	−0.257073	−	0.445263i
$290$	2.13824	+	1.23451i	0.125562	+	0.0724931i
$291$	−11.7095	−	11.6924i	−0.686424	−	0.685421i
$292$	9.04340			0.529225
$293$	−18.1274			−1.05902			−0.529508	−	0.848305i	$-0.677624\pi$
$293$	−18.1274			−1.05902			−0.529508	+	0.848305i	$0.677624\pi$
$294$	−4.03902	+	4.04493i	−0.235561	+	0.235905i
$295$	−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
$300$	−1.22385	+	1.22564i	−0.0706589	+	0.0707624i
$301$	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
$306$	8.62181	−	0.0126109i	0.492876	−	0.000720915i
$307$	−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
$309$	−0.631445	+	2.36350i	−0.0359217	+	0.134455i
$310$	−3.10235	−	5.37344i	−0.176202	−	0.305191i
$311$		−	11.1447i		−	0.631960i	−0.948766	−	0.315980i	$-0.897667\pi$
$311$		−	11.1447i		−	0.631960i	0.948766	−	0.315980i	$-0.102333\pi$
$312$	−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	0.913217	−	0.407475i	$-0.133591\pi$
$317$	1.84677	+	3.19870i	0.103725	+	0.179657i	−0.809492	+	0.587131i	$0.800257\pi$
$318$	−6.57303	−	1.75609i	−0.368597	−	0.0984764i
$319$	−6.02650	+	3.47940i	−0.337419	+	0.194809i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−0.222625	−	0.0594777i	−0.0124257	−	0.00331972i
$322$		−	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
$327$	13.7637	+	13.7436i	0.761134	+	0.760022i
$328$	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
$333$	17.6809	−	30.7279i	0.968908	−	1.68388i
$334$	−23.3474			−1.27751
$335$	−10.5715			−0.577582
$336$	3.92782	−	3.93357i	0.214280	−	0.214594i
$337$	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
$339$	−19.8309	−	5.29814i	−1.07707	−	0.287756i
$340$	1.43697	−	2.48891i	0.0779307	−	0.134980i
$341$	17.4876			0.947006
$342$	8.04460	−	10.3094i	0.435002	−	0.557470i
$343$	−11.8739			−0.641133
$344$	−2.63866	+	4.57030i	−0.142267	+	0.246414i
$345$	−6.25936	−	1.67228i	−0.336992	−	0.0900327i
$346$	4.79757	+	8.30963i	0.257919	+	0.446728i
$347$	16.3458	+	9.43723i	0.877486	+	0.506617i	0.869829	−	0.493354i	$-0.164229\pi$
$347$	16.3458	+	9.43723i	0.877486	+	0.506617i	0.00765736	+	0.999971i	$0.497563\pi$
$348$	−3.02172	+	3.02614i	−0.161981	+	0.162218i
$349$	−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
$351$	6.82002	+	1.81139i	0.364026	+	0.0966849i
$352$	−2.44084	+	1.40922i	−0.130097	+	0.0751116i
$353$		−	32.9930i		−	1.75604i	−0.478623	−	0.878020i	$-0.658864\pi$
$353$		−	32.9930i		−	1.75604i	0.478623	−	0.878020i	$-0.341136\pi$
$354$	−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
$357$	−11.3049	−	11.2883i	−0.598316	−	0.597442i
$358$	9.19621	−	15.9283i	0.486035	−	0.841837i
$359$	15.5156	+	8.95794i	0.818882	+	0.472782i	0.850031	−	0.526733i	$-0.176583\pi$
$359$	15.5156	+	8.95794i	0.818882	+	0.472782i	−0.0311486	+	0.999515i	$0.509917\pi$
$360$	−1.50380	−	2.59588i	−0.0792571	−	0.136815i
$361$	13.6901	−	13.1750i	0.720533	−	0.693421i
$362$			14.8731i			0.781715i
$363$	−5.11446	−	1.36641i	−0.268440	−	0.0717178i
$364$	3.77451	+	2.17921i	0.197838	+	0.114222i
$365$	−7.83182	+	4.52170i	−0.409936	+	0.236677i
$366$	−3.16646	−	0.845968i	−0.165513	−	0.0442195i
$367$	−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
$375$	0.447064	−	1.67336i	0.0230863	−	0.0864119i
$376$	−8.22978	+	4.75146i	−0.424418	+	0.245038i
$377$	−2.90377	−	1.67649i	−0.149552	−	0.0863438i
$378$	−16.0988	+	4.35154i	−0.828033	+	0.223819i
$379$		−	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	$0.356088\pi$
$383$	−10.9707	+	19.0019i	−0.560578	+	0.970949i	−0.997446	+	0.0714239i	$0.977246\pi$
$384$	−1.22385	+	1.22564i	−0.0624543	+	0.0625457i
$385$	−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	0.122899	−	0.992419i	$-0.460781\pi$
$389$	20.5871	−	11.8860i	1.04381	−	0.602643i	0.920910	+	0.389776i	$0.127447\pi$
$390$	1.66201	−	1.66444i	0.0841592	−	0.0842823i
$391$	10.7502			0.543663
$392$	−3.30026			−0.166688
$393$	23.9473	+	23.9123i	1.20798	+	1.20622i
$394$	7.26726	+	4.19576i	0.366119	+	0.211379i
$395$	4.35963	+	7.55110i	0.219357	+	0.379937i
$396$	8.45531	−	0.0123673i	0.424895	−	0.000621481i
$397$	−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
$399$	−24.0502	+	2.94987i	−1.20402	+	0.147678i
$400$	−1.00000			−0.0500000
$401$	14.4572	−	25.0407i	0.721960	−	1.25047i	−0.238253	−	0.971203i	$-0.576575\pi$
$401$	14.4572	−	25.0407i	0.721960	−	1.25047i	0.960213	−	0.279268i	$-0.0900918\pi$
$402$	4.72613	−	17.6899i	0.235718	−	0.882292i
$403$	4.21306	+	7.29723i	0.209867	+	0.363501i
$404$	16.9742	+	9.80004i	0.844496	+	0.487570i
$405$	0.0263280	+	8.99996i	0.00130825	+	0.447212i
$406$	7.92410			0.393266
$407$	33.3061			1.65092
$408$	3.52242	+	3.51727i	0.174386	+	0.174131i
$409$	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
$414$	5.59667	−	9.72654i	0.275061	−	0.478033i
$415$	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	$0.0538519\pi$
$419$			6.89309i			0.336750i	−0.985723	+	0.168375i	$0.946148\pi$
$420$	−1.43481	+	5.37049i	−0.0700115	+	0.262053i
$421$	−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
$423$	28.5088	−	0.0416989i	1.38614	−	0.00202747i
$424$	−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	0.704280	−	0.709923i	$-0.251270\pi$
$431$	−5.45320	−	9.44522i	−0.262671	−	0.454960i	−0.966951	+	0.254963i	$0.917937\pi$
$432$	5.01614	−	1.35587i	0.241339	−	0.0652344i
$433$	−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
$435$	1.10381	−	4.13157i	0.0529238	−	0.198094i
$436$			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
$441$	8.58157	+	4.93785i	0.408646	+	0.235136i
$442$	−1.95143	+	3.37998i	−0.0928202	+	0.160769i
$443$	−16.8746	+	9.74255i	−0.801736	+	0.462882i	−0.844078	−	0.536221i	$-0.819851\pi$
$443$	−16.8746	+	9.74255i	−0.801736	+	0.462882i	0.0423420	+	0.999103i	$0.486518\pi$
$444$	19.7667	−	5.31197i	0.938087	−	0.252095i
$445$			2.63801i			0.125053i
$446$	5.77968	−	3.33690i	0.273676	−	0.158007i
$447$	14.4941	+	14.4729i	0.685549	+	0.684547i
$448$	3.20940			0.151630
$449$	−10.3060			−0.486372			−0.243186	−	0.969980i	$-0.578193\pi$
$449$	−10.3060			−0.486372			−0.243186	+	0.969980i	$0.578193\pi$
$450$	2.60027	+	1.49620i	0.122578	+	0.0705315i
$451$	−28.7042	−	16.5724i	−1.35163	−	0.780362i
$452$	−5.92548	−	10.2632i	−0.278711	−	0.482742i
$453$	−2.44461	+	9.15017i	−0.114858	+	0.429912i
$454$	−12.0437	+	20.8603i	−0.565238	+	0.979020i
$455$	−4.35843			−0.204326
$456$	7.49368	−	0.919133i	0.350924	−	0.0430424i
$457$	−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
$459$	−3.89670	−	14.4161i	−0.181882	−	0.672885i
$460$	−1.87030	−	3.23945i	−0.0872030	−	0.151040i
$461$	28.6530	+	16.5428i	1.33450	+	0.770477i	0.985986	−	0.166825i	$-0.0533516\pi$
$461$	28.6530	+	16.5428i	1.33450	+	0.770477i	0.348518	+	0.937302i	$0.386685\pi$
$462$	−11.0865	−	11.0703i	−0.515792	−	0.515038i
$463$	−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
$465$	−7.59363	+	7.60474i	−0.352146	+	0.352661i
$466$	−15.3569	+	8.86633i	−0.711396	+	0.410725i
$467$		−	41.3216i		−	1.91213i	−0.293148	−	0.956067i	$-0.594703\pi$
$467$		−	41.3216i		−	1.91213i	0.293148	−	0.956067i	$-0.405297\pi$
$468$	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
$471$	−20.9881	+	21.0188i	−0.967080	+	0.968496i
$472$	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
$477$	0.0172363	+	11.7841i	0.000789195	+	0.539558i
$478$	−8.66926	−	5.00520i	−0.396523	−	0.228932i
$479$	6.39802	−	3.69390i	0.292333	−	0.168779i	−0.346660	−	0.937991i	$-0.612684\pi$
$479$	6.39802	−	3.69390i	0.292333	−	0.168779i	0.638994	+	0.769212i	$0.279351\pi$
$480$	0.447064	−	1.67336i	0.0204056	−	0.0763781i
$481$	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
$489$	−5.13809	−	1.37272i	−0.232353	−	0.0620766i
$490$	2.85811	−	1.65013i	0.129116	−	0.0745453i
$491$	−14.1387	−	8.16297i	−0.638070	−	0.368390i	0.145801	−	0.989314i	$-0.453424\pi$
$491$	−14.1387	−	8.16297i	−0.638070	−	0.368390i	−0.783871	+	0.620924i	$0.786757\pi$
$492$	−19.6787	−	5.25746i	−0.887182	−	0.237024i
$493$			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
$498$	9.82173	+	9.80738i	0.440122	+	0.439479i
$499$	−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	−0.813802	−	0.581143i	$-0.802606\pi$
$503$	−16.0900	+	9.28957i	−0.717418	+	0.414201i	0.0963836	+	0.995344i	$0.469272\pi$
$504$	−8.34530	−	4.80190i	−0.371729	−	0.213894i
$505$	−19.6001			−0.872192
$506$	10.5426			0.468677
$507$	13.6530	−	13.6730i	0.606351	−	0.607238i
$508$	1.19910	+	0.692300i	0.0532014	+	0.0307158i
$509$	7.26580	+	12.5847i	0.322051	+	0.557808i	0.980911	−	0.194457i	$-0.0622945\pi$
$509$	7.26580	+	12.5847i	0.322051	+	0.557808i	−0.658860	+	0.752265i	$0.728961\pi$
$510$	−4.80914	−	1.28484i	−0.212952	−	0.0568935i
$511$	−14.5120	+	25.1355i	−0.641971	+	1.11193i
$512$	−1.00000			−0.0441942
$513$	−20.8608	−	8.82203i	−0.921025	−	0.389502i
$514$	3.09335			0.136442
$515$	0.706213	−	1.22320i	0.0311195	−	0.0539005i
$516$	8.83087	+	2.35930i	0.388758	+	0.103863i
$517$	13.3917	+	23.1951i	0.588967	+	1.02012i
$518$	−32.8451	−	18.9631i	−1.44313	−	0.833191i
$519$	11.7430	−	11.7602i	0.515460	−	0.516215i
$520$	1.35802			0.0595531
$521$	−36.4420			−1.59655			−0.798276	−	0.602291i	$-0.794255\pi$
$521$	−36.4420			−1.59655			−0.798276	+	0.602291i	$0.794255\pi$
$522$	6.42013	+	3.69415i	0.281001	+	0.161689i
$523$	−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
$528$	3.45439	+	3.44934i	0.150333	+	0.150113i
$529$	−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
$534$	−4.41433	−	1.17936i	−0.191027	−	0.0510358i
$535$	0.115217	+	0.0665203i	0.00498125	+	0.00287592i
$536$	9.15518	−	5.28574i	0.395443	−	0.228309i
$537$	−30.7771	−	8.22259i	−1.32813	−	0.354831i
$538$	−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
$546$	1.94850	−	7.29322i	0.0833880	−	0.312121i
$547$	−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
$549$	0.00830331	+	5.67682i	0.000354377	+	0.242281i
$550$			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
$555$	−14.4625	+	14.4837i	−0.613899	+	0.614797i
$556$	1.29172	−	2.23732i	0.0547811	−	0.0948837i
$557$	8.93906	−	5.16097i	0.378760	−	0.218677i	−0.298518	−	0.954404i	$-0.596492\pi$
$557$	8.93906	−	5.16097i	0.378760	−	0.218677i	0.677279	+	0.735727i	$0.263159\pi$
$558$	−9.33063	−	16.1067i	−0.394997	−	0.681850i
$559$			7.16671i			0.303120i
$560$	−2.77942	+	1.60470i	−0.117452	+	0.0678110i
$561$	9.91321	−	9.92772i	0.418536	−	0.419149i
$562$	4.93433			0.208142
$563$	−42.9116			−1.80851			−0.904255	−	0.426994i	$-0.859573\pi$
$563$	−42.9116			−1.80851			−0.904255	+	0.426994i	$0.859573\pi$
$564$	11.6472	+	11.6301i	0.490434	+	0.489718i
$565$	10.2632	+	5.92548i	0.431778	+	0.249287i
$566$	4.00792	+	6.94192i	0.168465	+	0.291790i
$567$	14.5154	+	24.9725i	0.609591	+	1.04874i
$568$	0.825761	−	1.43026i	0.0346482	−	0.0600124i
$569$	14.9370			0.626192			0.313096	−	0.949722i	$-0.398634\pi$
$569$	14.9370			0.626192			0.313096	+	0.949722i	$0.398634\pi$
$570$	−6.03015	+	4.54283i	−0.252575	+	0.190278i
$571$	−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
$573$	0.845868	−	3.16608i	0.0353366	−	0.132265i
$574$	18.8712	+	32.6859i	0.787670	+	1.36428i
$575$	3.23945	+	1.87030i	0.135094	+	0.0779967i
$576$	2.60027	+	1.49620i	0.108344	+	0.0623416i
$577$	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
$579$	24.8009	+	24.7647i	1.03069	+	1.02919i
$580$	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
$585$	−3.53121	−	2.03187i	−0.145998	−	0.0840073i
$586$	−9.06372	+	15.6988i	−0.374419	+	0.648513i
$587$	2.96690	+	1.71294i	0.122457	+	0.0707005i	0.559977	−	0.828508i	$-0.310810\pi$
$587$	2.96690	+	1.71294i	0.122457	+	0.0707005i	−0.437520	+	0.899209i	$0.644143\pi$
$588$	1.48350	+	5.52036i	0.0611787	+	0.227656i
$589$	−10.1099	−	25.0850i	−0.416573	−	1.03361i
$590$			3.70638i			0.152589i
$591$	3.75154	−	14.0420i	0.154318	−	0.577612i
$592$	10.2340	+	5.90861i	0.420616	+	0.242842i
$593$	−37.6958	+	21.7637i	−1.54798	+	0.893727i	−0.549685	+	0.835372i	$0.685252\pi$
$593$	−37.6958	+	21.7637i	−1.54798	+	0.893727i	−0.998296	+	0.0583555i	$0.981414\pi$
$594$	−3.82144	−	14.1377i	−0.156796	−	0.580076i
$595$	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	0.984404	−	0.175920i	$-0.0562901\pi$
$599$	8.31767	+	14.4066i	0.339851	+	0.588639i	−0.644554	+	0.764559i	$0.722957\pi$
$600$	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
$603$	−31.7144	+	0.0463877i	−1.29151	+	0.00188906i
$604$	−4.73555	+	2.73407i	−0.192687	+	0.111248i
$605$	2.64692	+	1.52820i	0.107613	+	0.0621302i
$606$	8.76249	−	32.7980i	0.355952	−	1.33233i
$607$		−	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
$612$	4.29998	−	7.47301i	0.173817	−	0.302079i
$613$	−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	−0.603678	−	0.797228i	$-0.706299\pi$
$617$	−5.34291	+	3.08473i	−0.215097	+	0.124187i	0.388581	+	0.921415i	$0.372965\pi$
$618$	1.73113	+	1.72860i	0.0696361	+	0.0695343i
$619$	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
$621$	−18.7854	−	4.98938i	−0.753832	−	0.200217i
$622$	−9.65163	−	5.57237i	−0.386995	−	0.223432i
$623$	4.23321	+	7.33214i	0.169600	+	0.293756i
$624$	−0.607122	+	2.27245i	−0.0243043	+	0.0909710i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.51863			0.0606965
$627$	−2.59052	−	21.1205i	−0.103455	−	0.843470i
$628$	−17.1493			−0.684330
$629$	16.9810	−	29.4120i	0.677077	−	1.17273i
$630$	9.62820	−	0.0140829i	0.383597	−	0.000561075i
$631$	−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
$633$	−30.3475	−	30.3032i	−1.20621	−	1.20444i
$634$	3.69354			0.146689
$635$	−1.38460			−0.0549462
$636$	−4.80733	+	4.81437i	−0.190623	+	0.190902i
$637$	−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	−0.685232	−	0.728325i	$-0.740299\pi$
$641$	7.29491	−	12.6352i	0.288132	−	0.499059i	0.973364	+	0.229266i	$0.0736325\pi$
$642$	−0.162822	+	0.163060i	−0.00642606	+	0.00643546i
$643$	−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	$0.0682816\pi$
$647$			10.8293i			0.425743i	−0.977080	+	0.212872i	$0.931718\pi$
$648$	−4.52278	−	7.78103i	−0.177672	−	0.305668i
$649$	−9.04668	−	5.22310i	−0.355113	−	0.205025i
$650$	−1.17608	+	0.679010i	−0.0461296	+	0.0266329i
$651$	−8.90257	+	33.3223i	−0.348919	+	1.30600i
$652$	−1.53526	−	2.65915i	−0.0601255	−	0.104140i
$653$			39.3283i			1.53904i	0.638625	+	0.769518i	$0.279503\pi$
$653$			39.3283i			1.53904i	−0.638625	+	0.769518i	$0.720497\pi$
$654$	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	$-0.964455\pi$
$659$	−15.2330	−	26.3843i	−0.593392	−	1.02779i	0.400379	−	0.916350i	$-0.368878\pi$
$660$	−4.71626	−	1.26002i	−0.183580	−	0.0490463i
$661$	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
$663$	6.53090	+	1.74483i	0.253639	+	0.0677636i
$664$			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
$669$	−8.17968	−	8.16772i	−0.316245	−	0.315782i
$670$	−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
$675$	1.33385	−	5.02204i	0.0513398	−	0.193298i
$676$	11.1558			0.429069
$677$	31.0348			1.19276			0.596382	−	0.802701i	$-0.296605\pi$
$677$	31.0348			1.19276			0.596382	+	0.802701i	$0.296605\pi$
$678$	−14.5038	+	14.5250i	−0.557015	+	0.557830i
$679$	26.5540	+	15.3310i	1.01905	+	0.588349i
$680$	−1.43697	−	2.48891i	−0.0551053	−	0.0954452i
$681$	40.3068	+	10.7686i	1.54456	+	0.412653i
$682$	8.74380	−	15.1447i	0.334817	−	0.579920i
$683$	0.186788			0.00714726			0.00357363	−	0.999994i	$-0.498862\pi$
$683$	0.186788			0.00714726			0.00357363	+	0.999994i	$0.498862\pi$
$684$	−4.90593	−	12.1215i	−0.187583	−	0.463479i
$685$	−4.72492			−0.180530
$686$	−5.93697	+	10.2831i	−0.226675	+	0.392612i
$687$	36.2554	+	9.68618i	1.38323	+	0.369551i
$688$	2.63866	+	4.57030i	0.100598	+	0.174241i
$689$	−4.61969	−	2.66718i	−0.175996	−	0.101611i
$690$	−4.57792	+	4.58462i	−0.174278	+	0.174533i
$691$	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
$693$	−13.5339	+	23.5207i	−0.514109	+	0.893479i
$694$	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
$699$	21.7339	+	21.7021i	0.822050	+	0.820848i
$700$	1.60470	−	2.77942i	0.0606520	−	0.105052i
$701$	14.6766	+	8.47353i	0.554327	+	0.320041i	0.750865	−	0.660455i	$-0.229637\pi$
$701$	14.6766	+	8.47353i	0.554327	+	0.320041i	−0.196539	+	0.980496i	$0.562970\pi$
$702$	4.97872	−	5.00062i	0.187910	−	0.188736i
$703$	−19.2550	−	47.7759i	−0.726215	−	1.80190i
$704$			2.81844i			0.106224i
$705$	−15.9018	−	4.24842i	−0.598897	−	0.160005i
$706$	−28.5728	−	16.4965i	−1.07535	−	0.620854i
$707$	−54.4769	+	31.4523i	−2.04881	+	1.18288i
$708$	−6.20211	−	1.65699i	−0.233089	−	0.0622735i
$709$	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
$717$	−4.47529	+	16.7510i	−0.167133	+	0.625577i
$718$	15.5156	−	8.95794i	0.579037	−	0.334307i
$719$	−38.2562	−	22.0872i	−1.42671	−	0.823714i	−0.429854	−	0.902898i	$-0.641435\pi$
$719$	−38.2562	−	22.0872i	−1.42671	−	0.823714i	−0.996860	+	0.0791847i	$0.974768\pi$
$720$	−3.00000	+	0.00438801i	−0.111803	+	0.000163531i
$721$		−	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
$726$	−3.74057	+	3.74605i	−0.138826	+	0.139029i
$727$	−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
$732$	−2.31586	+	2.31925i	−0.0855966	+	0.0857219i
$733$	−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
$735$	−4.04493	−	4.03902i	−0.149200	−	0.148982i
$736$	3.23945	+	1.87030i	0.119408	+	0.0689400i
$737$	−14.8975	−	25.8033i	−0.548758	−	0.950477i
$738$	0.0516028	+	35.2799i	0.00189952	+	1.29867i
$739$	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
$741$	8.18906	−	6.16925i	0.300832	−	0.226633i
$742$	12.6067			0.462805
$743$	6.72320	−	11.6449i	0.246650	−	0.427211i	−0.715944	−	0.698158i	$-0.754003\pi$
$743$	6.72320	−	11.6449i	0.246650	−	0.427211i	0.962594	+	0.270947i	$0.0873368\pi$
$744$	2.77390	−	10.3827i	0.101696	−	0.380649i
$745$	−5.91288	−	10.2414i	−0.216631	−	0.375216i
$746$	7.11335	+	4.10690i	0.260438	+	0.150364i
$747$	11.9899	−	20.8374i	0.438686	−	0.762400i
$748$	8.10003			0.296166
$749$	0.426981			0.0156015
$750$	−1.22564	−	1.22385i	−0.0447541	−	0.0446886i
$751$	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
$756$	−4.28085	+	16.1177i	−0.155693	+	0.586196i
$757$	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	$0.0563316\pi$
$761$			9.71303i			0.352097i	−0.984381	+	0.176049i	$0.943668\pi$
$762$	0.619005	−	2.31693i	0.0224242	−	0.0839337i
$763$	−31.2124	−	18.0205i	−1.12996	−	0.652385i
$764$	1.63856	−	0.946026i	0.0592812	−	0.0342260i
$765$	0.0126109	+	8.62181i	0.000455947	+	0.311722i
$766$	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	0.849025	−	0.528352i	$-0.177190\pi$
$773$	−0.918990	−	1.59174i	−0.0330538	−	0.0572508i	−0.882079	+	0.471101i	$0.843857\pi$
$774$	−0.0231570	−	15.8320i	−0.000832359	−	0.569069i
$775$	5.37344	−	3.10235i	0.193019	−	0.111440i

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.67336 - 0.447064i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.22385 + 1.22564i) q^{6} +3.20940 q^{7} -1.00000 q^{8} +(2.60027 + 1.49620i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.67336 - 0.447064i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.22385 + 1.22564i) q^{6} +3.20940 q^{7} -1.00000 q^{8} +(2.60027 + 1.49620i) 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} +(-1.22564 - 1.22385i) 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} +(-5.37049 - 1.43481i) q^{21} +(2.44084 + 1.40922i) q^{22} +(3.23945 - 1.87030i) q^{23} +(1.67336 + 0.447064i) 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} +(1.26002 - 4.71626i) q^{33} +(2.48891 - 1.43697i) q^{34} +(2.77942 + 1.60470i) q^{35} +(-0.00438801 - 3.00000i) 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} +(-3.92782 + 3.93357i) 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} +(1.22385 - 1.22564i) q^{48} +3.30026 q^{49} +1.00000 q^{50} +(-3.52242 - 3.51727i) q^{51} +(1.17608 + 0.679010i) q^{52} +(1.96402 + 3.40178i) q^{53} +(-5.01614 + 1.35587i) q^{54} +(-1.40922 + 2.44084i) q^{55} -3.20940 q^{56} +(-7.49368 + 0.919133i) q^{57} +2.46903 q^{58} +(-1.85319 + 3.20982i) q^{59} +(-0.447064 + 1.67336i) q^{60} +(0.946137 + 1.63876i) q^{61} +(-5.37344 - 3.10235i) q^{62} +(8.34530 + 4.80190i) q^{63} +1.00000 q^{64} -1.35802 q^{65} +(-3.45439 - 3.44934i) 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} +(-2.60027 - 1.49620i) 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} +(0.607122 - 2.27245i) q^{78} +(7.55110 + 4.35963i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(4.52278 + 7.78103i) 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} +(3.00000 - 0.00438801i) q^{90} +(-3.77451 + 2.17921i) q^{91} +(-3.23945 - 1.87030i) q^{92} +(-2.77390 + 10.3827i) 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} +(-4.21694 + 7.32869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24q + 12q^{2} + 2q^{3} - 12q^{4} + 4q^{6} - 12q^{7} - 24q^{8} + 2q^{9} + O(q^{10}) \)	\( 24q + 12q^{2} + 2q^{3} - 12q^{4} + 4q^{6} - 12q^{7} - 24q^{8} + 2q^{9} + 2q^{12} + 18q^{13} - 6q^{14} - 12q^{16} - 12q^{17} - 2q^{18} + 6q^{19} + 6q^{21} + 18q^{22} - 2q^{24} + 12q^{25} - 28q^{27} + 6q^{28} + 12q^{32} - 8q^{33} - 12q^{34} - 4q^{36} - 6q^{38} + 40q^{39} - 6q^{41} - 6q^{42} - 22q^{43} + 18q^{44} + 8q^{45} - 12q^{47} - 4q^{48} + 12q^{49} + 24q^{50} - 4q^{51} - 18q^{52} - 8q^{53} - 32q^{54} + 12q^{56} - 20q^{57} - 26q^{59} + 22q^{61} + 18q^{62} + 30q^{63} + 24q^{64} - 8q^{65} - 22q^{66} - 48q^{67} + 64q^{69} - 24q^{71} - 2q^{72} - 8q^{73} - 30q^{74} - 2q^{75} - 12q^{76} + 2q^{78} + 18q^{79} - 6q^{81} + 6q^{82} - 12q^{84} + 22q^{86} - 24q^{87} - 28q^{89} + 16q^{90} + 18q^{91} + 14q^{93} - 2q^{96} + 6q^{97} + 6q^{98} - 52q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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