LMFDB - Embedded newform 770.2.bd.a.527.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.46
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(2.51796 + 0.674686i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.550816 + 2.16716i) q^{5} +2.60679i q^{6} +(-2.23755 + 1.41186i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(3.28685 + 1.89767i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(2.51796 + 0.674686i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.550816 + 2.16716i) q^{5} +2.60679i q^{6} +(-2.23755 + 1.41186i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(3.28685 + 1.89767i) q^{9} +(-1.95076 + 1.09295i) q^{10} +(-3.21067 + 0.831617i) q^{11} +(-2.51796 + 0.674686i) q^{12} +(0.233580 + 0.233580i) q^{13} +(-1.94288 - 1.79589i) q^{14} +(-0.0752204 + 5.82846i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.03795 + 0.278118i) q^{17} +(-0.982304 + 3.66601i) q^{18} +(1.68776 - 2.92329i) q^{19} +(-1.56060 - 1.60141i) q^{20} +(-6.58664 + 2.04537i) q^{21} +(-1.63426 - 2.88603i) q^{22} +(0.270442 + 1.00930i) q^{23} +(-1.30339 - 2.25754i) q^{24} +(-4.39320 + 2.38742i) q^{25} +(-0.165166 + 0.286076i) q^{26} +(1.46601 + 1.46601i) q^{27} +(1.23185 - 2.34149i) q^{28} +6.63372 q^{29} +(-5.64933 + 1.43586i) q^{30} +(1.19225 + 2.06504i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-8.64543 - 0.0722152i) q^{33} +1.07457i q^{34} +(-4.29222 - 4.07147i) q^{35} -3.79533 q^{36} +(11.1730 - 2.99379i) q^{37} +(3.26051 + 0.873651i) q^{38} +(0.430553 + 0.745739i) q^{39} +(1.14293 - 1.92190i) q^{40} +2.15884i q^{41} +(-3.68042 - 5.83282i) q^{42} +(-0.522011 - 0.522011i) q^{43} +(2.36471 - 2.32554i) q^{44} +(-2.30210 + 8.16841i) q^{45} +(-0.904915 + 0.522453i) q^{46} +(-5.98529 + 1.60375i) q^{47} +(1.84328 - 1.84328i) q^{48} +(3.01329 - 6.31823i) q^{49} +(-3.44311 - 3.62560i) q^{50} +(2.42588 + 1.40058i) q^{51} +(-0.319077 - 0.0854963i) q^{52} +(5.89670 + 1.58002i) q^{53} +(-1.03663 + 1.79549i) q^{54} +(-3.57074 - 6.49999i) q^{55} +(2.58053 + 0.583852i) q^{56} +(6.22203 - 6.22203i) q^{57} +(1.71693 + 6.40768i) q^{58} +(1.71046 - 0.987536i) q^{59} +(-2.84909 - 5.08521i) q^{60} +(7.62508 + 4.40234i) q^{61} +(-1.68610 + 1.68610i) q^{62} +(-10.0337 + 0.394455i) q^{63} +1.00000i q^{64} +(-0.377547 + 0.634867i) q^{65} +(-2.16785 - 8.36953i) q^{66} +(-3.30161 + 12.3218i) q^{67} +(-1.03795 + 0.278118i) q^{68} +2.72385i q^{69} +(2.82183 - 5.19974i) q^{70} +5.48625 q^{71} +(-0.982304 - 3.66601i) q^{72} +(-1.14200 + 4.26200i) q^{73} +(5.78356 + 10.0174i) q^{74} +(-12.6727 + 3.04740i) q^{75} +3.37553i q^{76} +(6.00992 - 6.39381i) q^{77} +(-0.608894 + 0.608894i) q^{78} +(6.50015 - 11.2586i) q^{79} +(2.15223 + 0.606561i) q^{80} +(-2.99073 - 5.18010i) q^{81} +(-2.08528 + 0.558748i) q^{82} +(8.47152 + 8.47152i) q^{83} +(4.68151 - 5.06466i) q^{84} +(-0.0310072 + 2.40260i) q^{85} +(0.369118 - 0.639330i) q^{86} +(16.7034 + 4.47568i) q^{87} +(2.85833 + 1.68225i) q^{88} +(-13.1775 - 7.60804i) q^{89} +(-8.48591 - 0.109517i) q^{90} +(-0.852431 - 0.192865i) q^{91} +(-0.738860 - 0.738860i) q^{92} +(1.60879 + 6.00410i) q^{93} +(-3.09821 - 5.36626i) q^{94} +(7.26491 + 2.04747i) q^{95} +(2.25754 + 1.30339i) q^{96} +(-0.281451 - 0.281451i) q^{97} +(6.88284 + 1.27534i) q^{98} +(-12.1311 - 3.35938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	2.51796	+	0.674686i	1.45375	+	0.389530i	0.897325	−	0.441371i	$-0.145508\pi$
$3$	2.51796	+	0.674686i	1.45375	+	0.389530i	0.556421	+	0.830901i	$0.312174\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.550816	+	2.16716i	0.246333	+	0.969185i
$5$	0.550816	+	2.16716i	0.246333	+	0.969185i
$6$			2.60679i			1.06422i
$7$	−2.23755	+	1.41186i	−0.845716	+	0.533634i
$7$	−2.23755	+	1.41186i	−0.845716	+	0.533634i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	3.28685	+	1.89767i	1.09562	+	0.632555i
$10$	−1.95076	+	1.09295i	−0.616884	+	0.345622i
$11$	−3.21067	+	0.831617i	−0.968054	+	0.250742i
$11$	−3.21067	+	0.831617i	−0.968054	+	0.250742i
$12$	−2.51796	+	0.674686i	−0.726873	+	0.194765i
$13$	0.233580	+	0.233580i	0.0647835	+	0.0647835i	0.738756	−	0.673973i	$-0.235413\pi$
$13$	0.233580	+	0.233580i	0.0647835	+	0.0647835i	−0.673973	+	0.738756i	$0.735413\pi$
$14$	−1.94288	−	1.79589i	−0.519255	−	0.479973i
$15$	−0.0752204	+	5.82846i	−0.0194218	+	1.50490i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.03795	+	0.278118i	0.251740	+	0.0674535i	0.382482	−	0.923963i	$-0.375069\pi$
$17$	1.03795	+	0.278118i	0.251740	+	0.0674535i	−0.130742	+	0.991416i	$0.541736\pi$
$18$	−0.982304	+	3.66601i	−0.231531	+	0.864086i
$19$	1.68776	−	2.92329i	0.387200	−	0.670650i	−0.604872	−	0.796323i	$-0.706776\pi$
$19$	1.68776	−	2.92329i	0.387200	−	0.670650i	0.992072	+	0.125673i	$0.0401090\pi$
$20$	−1.56060	−	1.60141i	−0.348961	−	0.358086i
$21$	−6.58664	+	2.04537i	−1.43732	+	0.446336i
$22$	−1.63426	−	2.88603i	−0.348426	−	0.615304i
$23$	0.270442	+	1.00930i	0.0563910	+	0.210454i	0.988373	−	0.152052i	$-0.0485880\pi$
$23$	0.270442	+	1.00930i	0.0563910	+	0.210454i	−0.931982	+	0.362506i	$0.881921\pi$
$24$	−1.30339	−	2.25754i	−0.266054	−	0.460819i
$25$	−4.39320	+	2.38742i	−0.878641	+	0.477484i
$26$	−0.165166	+	0.286076i	−0.0323918	+	0.0561042i
$27$	1.46601	+	1.46601i	0.282134	+	0.282134i
$28$	1.23185	−	2.34149i	0.232797	−	0.442499i
$29$	6.63372			1.23185			0.615925	−	0.787805i	$-0.288782\pi$
$29$	6.63372			1.23185			0.615925	+	0.787805i	$0.288782\pi$
$30$	−5.64933	+	1.43586i	−1.03142	+	0.262151i
$31$	1.19225	+	2.06504i	0.214135	+	0.370893i	0.953005	−	0.302956i	$-0.0979734\pi$
$31$	1.19225	+	2.06504i	0.214135	+	0.370893i	−0.738870	+	0.673848i	$0.764640\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−8.64543	−	0.0722152i	−1.50498	−	0.0125711i
$34$			1.07457i			0.184286i
$35$	−4.29222	−	4.07147i	−0.725517	−	0.688204i
$36$	−3.79533			−0.632555
$37$	11.1730	−	2.99379i	1.83683	−	0.492176i	0.838237	−	0.545305i	$-0.183586\pi$
$37$	11.1730	−	2.99379i	1.83683	−	0.492176i	0.998588	+	0.0531297i	$0.0169197\pi$
$38$	3.26051	+	0.873651i	0.528925	+	0.141725i
$39$	0.430553	+	0.745739i	0.0689436	+	0.119414i
$40$	1.14293	−	1.92190i	0.180713	−	0.303879i
$41$			2.15884i			0.337154i	0.985688	+	0.168577i	$0.0539172\pi$
$41$			2.15884i			0.337154i	−0.985688	+	0.168577i	$0.946083\pi$
$42$	−3.68042	−	5.83282i	−0.567901	−	0.900024i
$43$	−0.522011	−	0.522011i	−0.0796059	−	0.0796059i	0.666183	−	0.745789i	$-0.267927\pi$
$43$	−0.522011	−	0.522011i	−0.0796059	−	0.0796059i	−0.745789	+	0.666183i	$0.767927\pi$
$44$	2.36471	−	2.32554i	0.356494	−	0.350588i
$45$	−2.30210	+	8.16841i	−0.343177	+	1.21768i
$46$	−0.904915	+	0.522453i	−0.133422	+	0.0770315i
$47$	−5.98529	+	1.60375i	−0.873044	+	0.233932i	−0.667404	−	0.744696i	$-0.732594\pi$
$47$	−5.98529	+	1.60375i	−0.873044	+	0.233932i	−0.205641	+	0.978628i	$0.565928\pi$
$48$	1.84328	−	1.84328i	0.266054	−	0.266054i
$49$	3.01329	−	6.31823i	0.430470	−	0.902605i
$50$	−3.44311	−	3.62560i	−0.486930	−	0.512737i
$51$	2.42588	+	1.40058i	0.339691	+	0.196121i
$52$	−0.319077	−	0.0854963i	−0.0442480	−	0.0118562i
$53$	5.89670	+	1.58002i	0.809975	+	0.217032i	0.639959	−	0.768409i	$-0.278951\pi$
$53$	5.89670	+	1.58002i	0.809975	+	0.217032i	0.170016	+	0.985441i	$0.445618\pi$
$54$	−1.03663	+	1.79549i	−0.141067	+	0.244335i
$55$	−3.57074	−	6.49999i	−0.481479	−	0.876458i
$56$	2.58053	+	0.583852i	0.344837	+	0.0780205i
$57$	6.22203	−	6.22203i	0.824128	−	0.824128i
$58$	1.71693	+	6.40768i	0.225444	+	0.841370i
$59$	1.71046	−	0.987536i	0.222683	−	0.128566i	−0.384509	−	0.923121i	$-0.625629\pi$
$59$	1.71046	−	0.987536i	0.222683	−	0.128566i	0.607192	+	0.794555i	$0.292296\pi$
$60$	−2.84909	−	5.08521i	−0.367816	−	0.656498i
$61$	7.62508	+	4.40234i	0.976291	+	0.563662i	0.901148	−	0.433511i	$-0.142725\pi$
$61$	7.62508	+	4.40234i	0.976291	+	0.563662i	0.0751426	+	0.997173i	$0.476059\pi$
$62$	−1.68610	+	1.68610i	−0.214135	+	0.214135i
$63$	−10.0337	+	0.394455i	−1.26413	+	0.0496966i
$64$			1.00000i			0.125000i
$65$	−0.377547	+	0.634867i	−0.0468289	+	0.0787455i
$66$	−2.16785	−	8.36953i	−0.266843	−	1.03022i
$67$	−3.30161	+	12.3218i	−0.403356	+	1.50535i	0.403712	+	0.914886i	$0.367720\pi$
$67$	−3.30161	+	12.3218i	−0.403356	+	1.50535i	−0.807068	+	0.590459i	$0.798947\pi$
$68$	−1.03795	+	0.278118i	−0.125870	+	0.0337268i
$69$			2.72385i			0.327913i
$70$	2.82183	−	5.19974i	0.337273	−	0.621488i
$71$	5.48625			0.651098			0.325549	−	0.945525i	$-0.394451\pi$
$71$	5.48625			0.651098			0.325549	+	0.945525i	$0.394451\pi$
$72$	−0.982304	−	3.66601i	−0.115766	−	0.432043i
$73$	−1.14200	+	4.26200i	−0.133661	+	0.498830i	−1.00000		0.000627169i	$-0.999800\pi$
$73$	−1.14200	+	4.26200i	−0.133661	+	0.498830i	0.866339	+	0.499457i	$0.166467\pi$
$74$	5.78356	+	10.0174i	0.672325	+	1.16450i
$75$	−12.6727	+	3.04740i	−1.46331	+	0.351883i
$76$			3.37553i			0.387200i
$77$	6.00992	−	6.39381i	0.684894	−	0.728643i
$78$	−0.608894	+	0.608894i	−0.0689436	+	0.0689436i
$79$	6.50015	−	11.2586i	0.731324	−	1.26669i	−0.224994	−	0.974360i	$-0.572236\pi$
$79$	6.50015	−	11.2586i	0.731324	−	1.26669i	0.956318	−	0.292330i	$-0.0944305\pi$
$80$	2.15223	+	0.606561i	0.240626	+	0.0678156i
$81$	−2.99073	−	5.18010i	−0.332303	−	0.575566i
$82$	−2.08528	+	0.558748i	−0.230280	+	0.0617034i
$83$	8.47152	+	8.47152i	0.929870	+	0.929870i	0.997697	−	0.0678273i	$-0.0216067\pi$
$83$	8.47152	+	8.47152i	0.929870	+	0.929870i	−0.0678273	+	0.997697i	$0.521607\pi$
$84$	4.68151	−	5.06466i	0.510795	−	0.552600i
$85$	−0.0310072	+	2.40260i	−0.00336321	+	0.260599i
$86$	0.369118	−	0.639330i	0.0398030	−	0.0689408i
$87$	16.7034	+	4.47568i	1.79080	+	0.479843i
$88$	2.85833	+	1.68225i	0.304699	+	0.179328i
$89$	−13.1775	−	7.60804i	−1.39681	−	0.806451i	−0.402756	−	0.915307i	$-0.631948\pi$
$89$	−13.1775	−	7.60804i	−1.39681	−	0.806451i	−0.994057	+	0.108856i	$0.965281\pi$
$90$	−8.48591	−	0.109517i	−0.894493	−	0.0115441i
$91$	−0.852431	−	0.192865i	−0.0893591	−	0.0202178i
$92$	−0.738860	−	0.738860i	−0.0770315	−	0.0770315i
$93$	1.60879	+	6.00410i	0.166824	+	0.622596i
$94$	−3.09821	−	5.36626i	−0.319556	−	0.553488i
$95$	7.26491	+	2.04747i	0.745364	+	0.210066i
$96$	2.25754	+	1.30339i	0.230409	+	0.133027i
$97$	−0.281451	−	0.281451i	−0.0285771	−	0.0285771i	0.692674	−	0.721251i	$-0.256433\pi$
$97$	−0.281451	−	0.281451i	−0.0285771	−	0.0285771i	−0.721251	+	0.692674i	$0.756433\pi$
$98$	6.88284	+	1.27534i	0.695272	+	0.128829i
$99$	−12.1311	−	3.35938i	−1.21922	−	0.337630i
$100$	2.61092	−	4.26417i	0.261092	−	0.426417i
$101$	−5.35459	+	3.09147i	−0.532802	+	0.307613i	−0.742157	−	0.670227i	$-0.766197\pi$
$101$	−5.35459	+	3.09147i	−0.532802	+	0.307613i	0.209355	+	0.977840i	$0.432864\pi$
$102$	−0.724994	+	2.70571i	−0.0717851	+	0.267906i
$103$	−4.93798	−	18.4288i	−0.486554	−	1.81584i	−0.572959	−	0.819584i	$-0.694204\pi$
$103$	−4.93798	−	18.4288i	−0.486554	−	1.81584i	0.0864045	−	0.996260i	$-0.472462\pi$
$104$		−	0.330332i		−	0.0323918i
$105$	−8.06068	−	13.1477i	−0.786642	−	1.28308i
$106$			6.10472i			0.592943i
$107$	−0.710514	−	2.65167i	−0.0686880	−	0.256347i	0.923040	−	0.384704i	$-0.125696\pi$
$107$	−0.710514	−	2.65167i	−0.0686880	−	0.256347i	−0.991728	+	0.128357i	$0.959030\pi$
$108$	−2.00261	−	0.536598i	−0.192701	−	0.0516342i
$109$	−7.34159	−	12.7160i	−0.703196	−	1.21797i	−0.967338	−	0.253488i	$-0.918422\pi$
$109$	−7.34159	−	12.7160i	−0.703196	−	1.21797i	0.264142	−	0.964484i	$-0.414911\pi$
$110$	5.35433	−	5.13139i	0.510515	−	0.489259i
$111$	30.1530			2.86199
$112$	0.103932	+	2.64371i	0.00982061	+	0.249807i
$113$	−9.52334	+	9.52334i	−0.895880	+	0.895880i	−0.995069	−	0.0991883i	$-0.968375\pi$
$113$	−9.52334	+	9.52334i	−0.895880	+	0.895880i	0.0991883	+	0.995069i	$0.468375\pi$
$114$	7.62040	+	4.39964i	0.713716	+	0.412064i
$115$	−2.03836	+	1.14203i	−0.190078	+	0.106495i
$116$	−5.74497	+	3.31686i	−0.533407	+	0.307963i
$117$	0.324487	+	1.21100i	0.0299988	+	0.111957i
$118$	1.39659	+	1.39659i	0.128566	+	0.128566i
$119$	−2.71513	+	0.843139i	−0.248896	+	0.0772904i
$120$	4.17454	−	4.06816i	0.381081	−	0.371370i
$121$	9.61683	−	5.34010i	0.874257	−	0.485463i
$122$	−2.27882	+	8.50467i	−0.206315	+	0.769976i
$123$	−1.45654	+	5.43587i	−0.131332	+	0.490136i
$124$	−2.06504	−	1.19225i	−0.185446	−	0.107068i
$125$	−7.59378	−	8.20576i	−0.679208	−	0.733946i
$126$	−2.97794	−	9.58976i	−0.265296	−	0.854324i
$127$	−8.14616	+	8.14616i	−0.722855	+	0.722855i	−0.969186	−	0.246331i	$-0.920775\pi$
$127$	−8.14616	+	8.14616i	−0.722855	+	0.722855i	0.246331	+	0.969186i	$0.420775\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−0.962210	−	1.66660i	−0.0847179	−	0.146736i
$130$	−0.710950	−	0.200367i	−0.0623545	−	0.0175733i
$131$	3.78477	+	2.18514i	0.330677	+	0.190917i	0.656142	−	0.754638i	$-0.272187\pi$
$131$	3.78477	+	2.18514i	0.330677	+	0.190917i	−0.325465	+	0.945554i	$0.605521\pi$
$132$	7.52327	−	4.26017i	0.654816	−	0.370801i
$133$	0.350824	+	8.92392i	0.0304203	+	0.773802i
$134$	−12.7564			−1.10199
$135$	−2.36959	+	3.98459i	−0.203942	+	0.342939i
$136$	−0.537283	−	0.930601i	−0.0460716	−	0.0797984i
$137$	−3.47575	+	12.9717i	−0.296953	+	1.10824i	0.642701	+	0.766117i	$0.277814\pi$
$137$	−3.47575	+	12.9717i	−0.296953	+	1.10824i	−0.939654	+	0.342127i	$0.888853\pi$
$138$	−2.63103	+	0.704983i	−0.223968	+	0.0600122i
$139$	−4.16294			−0.353096			−0.176548	−	0.984292i	$-0.556493\pi$
$139$	−4.16294			−0.353096			−0.176548	+	0.984292i	$0.556493\pi$
$140$	5.75290	+	1.37989i	0.486209	+	0.116622i
$141$	−16.1528			−1.36031
$142$	1.41995	+	5.29931i	0.119159	+	0.444708i
$143$	−0.944199	−	0.555700i	−0.0789579	−	0.0464700i
$144$	3.28685	−	1.89767i	0.273904	−	0.158139i
$145$	3.65396	+	14.3764i	0.303445	+	1.19389i
$146$	−4.41235			−0.365169
$147$	11.8502	−	13.8760i	0.977386	−	1.14448i
$148$	−8.17918	+	8.17918i	−0.672325	+	0.672325i
$149$	−2.65708	+	4.60220i	−0.217677	+	0.377027i	−0.954097	−	0.299497i	$-0.903181\pi$
$149$	−2.65708	+	4.60220i	−0.217677	+	0.377027i	0.736421	+	0.676524i	$0.236514\pi$
$150$	−6.22349	−	11.4521i	−0.508146	−	0.935063i
$151$	−9.14123	+	5.27769i	−0.743903	+	0.429492i	−0.823487	−	0.567336i	$-0.807974\pi$
$151$	−9.14123	+	5.27769i	−0.743903	+	0.429492i	0.0795839	+	0.996828i	$0.474641\pi$
$152$	−3.26051	+	0.873651i	−0.264462	+	0.0708625i
$153$	2.88381	+	2.88381i	0.233143	+	0.233143i
$154$	7.73143	+	4.15030i	0.623016	+	0.334441i
$155$	−3.81858	+	3.72127i	−0.306715	+	0.298900i
$156$	−0.745739	−	0.430553i	−0.0597069	−	0.0344718i
$157$	3.03914	−	11.3422i	0.242550	−	0.905208i	−0.732049	−	0.681252i	$-0.761436\pi$
$157$	3.03914	−	11.3422i	0.242550	−	0.905208i	0.974599	−	0.223956i	$-0.0718974\pi$
$158$	12.5573	+	3.36472i	0.999007	+	0.267683i
$159$	13.7817	+	7.95684i	1.09296	+	0.631019i
$160$	−0.0288556	+	2.23588i	−0.00228124	+	0.176762i
$161$	−2.03012	−	1.87654i	−0.159996	−	0.147892i
$162$	4.22953	−	4.22953i	0.332303	−	0.332303i
$163$	−3.69728	−	13.7984i	−0.289593	−	1.08078i	−0.945417	−	0.325863i	$-0.894345\pi$
$163$	−3.69728	−	13.7984i	−0.289593	−	1.08078i	0.655824	−	0.754914i	$-0.272322\pi$
$164$	−1.07942	−	1.86961i	−0.0842885	−	0.145992i
$165$	−4.60554	−	18.7758i	−0.358541	−	1.46170i
$166$	−5.99027	+	10.3754i	−0.464935	+	0.805291i
$167$	13.4380	−	13.4380i	1.03986	−	1.03986i	0.0406929	−	0.999172i	$-0.487043\pi$
$167$	13.4380	−	13.4380i	1.03986	−	1.03986i	0.999172	−	0.0406929i	$-0.0129565\pi$
$168$	6.10375	+	3.21116i	0.470914	+	0.247746i
$169$		−	12.8909i		−	0.991606i
$170$	−2.32876	+	0.591888i	−0.178608	+	0.0453958i
$171$	11.0949	−	6.40562i	0.848446	−	0.489850i
$172$	0.713080	+	0.191069i	0.0543719	+	0.0145689i
$173$	24.0020	−	6.43132i	1.82484	−	0.488964i	0.827473	−	0.561505i	$-0.189777\pi$
$173$	24.0020	−	6.43132i	1.82484	−	0.488964i	0.997365	+	0.0725409i	$0.0231108\pi$
$174$			17.2927i			1.31095i
$175$	6.45932	−	11.5446i	0.488279	−	0.872688i
$176$	−0.885135	+	3.19633i	−0.0667195	+	0.240933i
$177$	4.97315	−	1.33255i	0.373805	−	0.100161i
$178$	3.93821	−	14.6976i	0.295181	−	1.10163i
$179$	−4.18455	+	2.41595i	−0.312768	+	0.180577i	−0.648165	−	0.761500i	$-0.724463\pi$
$179$	−4.18455	+	2.41595i	−0.312768	+	0.180577i	0.335396	+	0.942077i	$0.391130\pi$
$180$	−2.09053	−	8.22510i	−0.155819	−	0.613063i
$181$	1.30829			0.0972441			0.0486221	−	0.998817i	$-0.484517\pi$
$181$	1.30829			0.0972441			0.0486221	+	0.998817i	$0.484517\pi$
$182$	−0.0343320	−	0.873303i	−0.00254485	−	0.0647335i
$183$	16.2294	+	16.2294i	1.19972	+	1.19972i
$184$	0.522453	−	0.904915i	0.0385158	−	0.0667112i
$185$	12.6423	+	22.5646i	0.929479	+	1.65898i
$186$	−5.38313	+	3.10795i	−0.394710	+	0.227886i
$187$	−3.56381	−	0.0297684i	−0.260611	−	0.00217688i
$188$	4.38154	−	4.38154i	0.319556	−	0.319556i
$189$	−5.35009	−	1.21047i	−0.389162	−	0.0880490i
$190$	−0.0974030	+	7.54729i	−0.00706636	+	0.547538i
$191$	6.41683	−	11.1143i	0.464306	−	0.804201i	−0.534864	−	0.844938i	$-0.679637\pi$
$191$	6.41683	−	11.1143i	0.464306	−	0.804201i	0.999170	+	0.0407370i	$0.0129706\pi$
$192$	−0.674686	+	2.51796i	−0.0486912	+	0.181718i
$193$	5.04600	−	18.8319i	0.363219	−	1.35555i	−0.506600	−	0.862181i	$-0.669098\pi$
$193$	5.04600	−	18.8319i	0.363219	−	1.35555i	0.869819	−	0.493370i	$-0.164235\pi$
$194$	0.199016	−	0.344706i	0.0142885	−	0.0247485i
$195$	−1.37898	+	1.34384i	−0.0987511	+	0.0962347i
$196$	0.549530	+	6.97840i	0.0392521	+	0.498457i
$197$	5.59017	−	5.59017i	0.398283	−	0.398283i	−0.479344	−	0.877627i	$-0.659125\pi$
$197$	5.59017	−	5.59017i	0.398283	−	0.398283i	0.877627	+	0.479344i	$0.159125\pi$
$198$	0.105141	−	12.5872i	0.00747206	−	0.894537i
$199$	2.47631	−	1.42970i	0.175541	−	0.101349i	−0.409655	−	0.912241i	$-0.634351\pi$
$199$	2.47631	−	1.42970i	0.175541	−	0.101349i	0.585196	+	0.810892i	$0.301018\pi$
$200$	4.79462	+	1.41830i	0.339031	+	0.100289i
$201$	−16.6267	+	28.7982i	−1.17275	+	2.03127i
$202$	−4.37200	−	4.37200i	−0.307613	−	0.307613i
$203$	−14.8433	+	9.36590i	−1.04180	+	0.657357i
$204$	−2.80116			−0.196121
$205$	−4.67856	+	1.18912i	−0.326765	+	0.0830520i
$206$	16.5228	−	9.53945i	1.15120	−	0.664645i
$207$	−1.02642	+	3.83063i	−0.0713408	+	0.266247i
$208$	0.319077	−	0.0854963i	0.0221240	−	0.00592810i
$209$	−2.98780	+	10.7893i	−0.206670	+	0.746312i
$210$	10.6134	−	11.1889i	0.732397	−	0.772107i
$211$		−	7.21109i		−	0.496432i	−0.968705	−	0.248216i	$-0.920156\pi$
$211$		−	7.21109i		−	0.496432i	0.968705	−	0.248216i	$-0.0798442\pi$
$212$	−5.89670	+	1.58002i	−0.404987	+	0.108516i
$213$	13.8142	+	3.70150i	0.946531	+	0.253622i
$214$	2.37743	−	1.37261i	0.162517	−	0.0938295i
$215$	0.843752	−	1.41882i	0.0575434	−	0.0967625i
$216$		−	2.07325i		−	0.141067i
$217$	−5.58329	−	2.93735i	−0.379018	−	0.199400i
$218$	10.3826	−	10.3826i	0.703196	−	0.703196i
$219$	−5.75102	+	9.96106i	−0.388618	+	0.673106i
$220$	6.34235	+	3.84378i	0.427601	+	0.259148i
$221$	0.177482	+	0.307408i	0.0119387	+	0.0206785i
$222$	7.80416	+	29.1255i	0.523781	+	1.95478i
$223$	−10.7374	+	10.7374i	−0.719032	+	0.719032i	−0.968407	−	0.249375i	$-0.919775\pi$
$223$	−10.7374	+	10.7374i	−0.719032	+	0.719032i	0.249375	+	0.968407i	$0.419775\pi$
$224$	−2.52673	+	0.784632i	−0.168824	+	0.0524255i
$225$	−18.9703	−	0.489732i	−1.26469	−	0.0326488i
$226$	−11.6637	−	6.73402i	−0.775855	−	0.447940i
$227$	25.3812	+	6.80087i	1.68461	+	0.451390i	0.968990	−	0.247101i	$-0.0794781\pi$
$227$	25.3812	+	6.80087i	1.68461	+	0.451390i	0.715619	+	0.698491i	$0.246145\pi$
$228$	−2.27742	+	8.49945i	−0.150826	+	0.562890i
$229$	19.6662	+	11.3543i	1.29958	+	0.750313i	0.980331	−	0.197358i	$-0.0632363\pi$
$229$	19.6662	+	11.3543i	1.29958	+	0.750313i	0.319248	+	0.947671i	$0.396570\pi$
$230$	−1.63068	−	1.67332i	−0.107524	−	0.110336i
$231$	19.4466	−	12.0446i	1.27949	−	0.792474i
$232$	−4.69075	−	4.69075i	−0.307963	−	0.307963i
$233$	16.1023	−	4.31459i	1.05489	−	0.282658i	0.310621	−	0.950534i	$-0.399463\pi$
$233$	16.1023	−	4.31459i	1.05489	−	0.282658i	0.744273	+	0.667876i	$0.232796\pi$
$234$	−1.08575	+	0.626860i	−0.0709779	+	0.0409791i
$235$	−6.77239	−	12.0877i	−0.441782	−	0.788517i
$236$	−0.987536	+	1.71046i	−0.0642831	+	0.111342i
$237$	23.9631	−	23.9631i	1.55657	−	1.55657i
$238$	−1.51714	−	2.40440i	−0.0983414	−	0.155854i
$239$	−11.3875			−0.736593			−0.368297	−	0.929708i	$-0.620059\pi$
$239$	−11.3875			−0.736593			−0.368297	+	0.929708i	$0.620059\pi$
$240$	5.00999	+	2.97937i	0.323393	+	0.192318i
$241$	−22.3225	+	12.8879i	−1.43792	+	0.830182i	−0.997705	−	0.0677110i	$-0.978430\pi$
$241$	−22.3225	+	12.8879i	−1.43792	+	0.830182i	−0.440213	+	0.897893i	$0.645097\pi$
$242$	7.64716	+	7.90702i	0.491578	+	0.508283i
$243$	−5.64540	−	21.0689i	−0.362153	−	1.35157i
$244$	−8.80468			−0.563662
$245$	15.3524	+	3.05011i	0.980830	+	0.194864i
$246$	−5.62763			−0.358804
$247$	1.07705	−	0.288595i	0.0685312	−	0.0183629i
$248$	0.617156	−	2.30326i	0.0391894	−	0.146257i
$249$	15.6153	+	27.0466i	0.989582	+	1.71401i
$250$	5.96074	−	9.45883i	0.376991	−	0.598229i
$251$	−13.7881			−0.870299			−0.435149	−	0.900358i	$-0.643304\pi$
$251$	−13.7881			−0.870299			−0.435149	+	0.900358i	$0.643304\pi$
$252$	8.49225	−	5.35848i	0.534962	−	0.337553i
$253$	−1.70765	−	3.01563i	−0.107359	−	0.189591i
$254$	−9.97697	−	5.76021i	−0.626011	−	0.361427i
$255$	−1.69908	+	6.02874i	−0.106400	+	0.377534i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	18.6893	−	5.00778i	1.16581	−	0.312377i	0.376523	−	0.926407i	$-0.377120\pi$
$257$	18.6893	−	5.00778i	1.16581	−	0.312377i	0.789282	+	0.614031i	$0.210453\pi$
$258$	1.36077	−	1.36077i	0.0847179	−	0.0847179i
$259$	−20.7733	+	22.4735i	−1.29079	+	1.39643i
$260$	0.00953195	−	0.738584i	0.000591146	−	0.0458050i
$261$	21.8041	+	12.5886i	1.34964	+	0.779213i
$262$	−1.13111	+	4.22137i	−0.0698803	+	0.260797i
$263$	3.38305	−	12.6257i	0.208608	−	0.778534i	−0.779712	−	0.626138i	$-0.784635\pi$
$263$	3.38305	−	12.6257i	0.208608	−	0.778534i	0.988320	−	0.152396i	$-0.0486988\pi$
$264$	6.06218	+	6.16430i	0.373101	+	0.379387i
$265$	−0.176155	+	13.6494i	−0.0108211	+	0.838478i
$266$	−8.52904	+	2.64855i	−0.522949	+	0.162393i
$267$	−28.0474	−	28.0474i	−1.71648	−	1.71648i
$268$	−3.30161	−	12.3218i	−0.201678	−	0.752673i
$269$	3.25841	−	1.88124i	0.198669	−	0.114701i	−0.397366	−	0.917660i	$-0.630076\pi$
$269$	3.25841	−	1.88124i	0.198669	−	0.114701i	0.596034	+	0.802959i	$0.296742\pi$
$270$	−4.46212	−	1.25756i	−0.271556	−	0.0765324i
$271$	−15.3171	−	8.84333i	−0.930448	−	0.537194i	−0.0434946	−	0.999054i	$-0.513849\pi$
$271$	−15.3171	−	8.84333i	−0.930448	−	0.537194i	−0.886953	+	0.461859i	$0.847182\pi$
$272$	0.759832	−	0.759832i	0.0460716	−	0.0460716i
$273$	−2.01627	−	1.06075i	−0.122030	−	0.0641995i
$274$	−13.4293			−0.811291
$275$	12.1197	−	11.3187i	0.730846	−	0.682542i
$276$	−1.36192	−	2.35892i	−0.0819781	−	0.141990i
$277$	−9.82150	−	2.63166i	−0.590116	−	0.158121i	−0.0486100	−	0.998818i	$-0.515479\pi$
$277$	−9.82150	−	2.63166i	−0.590116	−	0.158121i	−0.541506	+	0.840697i	$0.682146\pi$
$278$	−1.07745	−	4.02110i	−0.0646211	−	0.241169i
$279$			9.04999i			0.541809i
$280$	0.156093	+	5.91402i	0.00932833	+	0.353430i
$281$		−	18.0133i		−	1.07458i	−0.843397	−	0.537291i	$-0.819448\pi$
$281$		−	18.0133i		−	1.07458i	0.843397	−	0.537291i	$-0.180552\pi$
$282$	−4.18064	−	15.6024i	−0.248954	−	0.929107i
$283$	−3.10748	+	11.5973i	−0.184720	+	0.689385i	0.809970	+	0.586471i	$0.199483\pi$
$283$	−3.10748	+	11.5973i	−0.184720	+	0.689385i	−0.994690	+	0.102914i	$0.967183\pi$
$284$	−4.75123	+	2.74313i	−0.281934	+	0.162775i
$285$	16.9114	+	10.0570i	1.00174	+	0.595723i
$286$	0.292389	−	1.05585i	0.0172893	−	0.0624338i
$287$	−3.04798	−	4.83052i	−0.179917	−	0.285136i
$288$	2.68370	+	2.68370i	0.158139	+	0.158139i
$289$	−13.7224	−	7.92265i	−0.807202	−	0.466039i
$290$	−12.9408	+	7.25033i	−0.759909	+	0.425754i
$291$	−0.518793	−	0.898575i	−0.0304122	−	0.0526754i
$292$	−1.14200	−	4.26200i	−0.0668305	−	0.249415i
$293$	7.72627	+	7.72627i	0.451374	+	0.451374i	0.895810	−	0.444437i	$-0.146596\pi$
$293$	7.72627	+	7.72627i	0.451374	+	0.451374i	−0.444437	+	0.895810i	$0.646596\pi$
$294$	16.4703	+	7.85500i	0.960566	+	0.458113i
$295$	3.08230	+	3.16290i	0.179459	+	0.184151i
$296$	−10.0174	−	5.78356i	−0.582250	−	0.336162i
$297$	−5.92605	−	3.48772i	−0.343864	−	0.202378i
$298$	−5.13309	−	1.37541i	−0.297352	−	0.0796752i
$299$	−0.172583	+	0.298923i	−0.00998074	+	0.0172872i
$300$	9.45116	−	8.97546i	0.545663	−	0.518198i
$301$	1.90504	+	0.431020i	0.109804	+	0.0248436i
$302$	−7.46378	−	7.46378i	−0.429492	−	0.429492i
$303$	−15.5684	+	4.17155i	−0.894382	+	0.239649i
$304$	−1.68776	−	2.92329i	−0.0968000	−	0.167662i
$305$	−5.34058	+	18.9497i	−0.305801	+	1.08506i
$306$	−2.03916	+	3.53194i	−0.116571	+	0.201907i
$307$	2.76489	−	2.76489i	0.157800	−	0.157800i	−0.623791	−	0.781591i	$-0.714408\pi$
$307$	2.76489	−	2.76489i	0.157800	−	0.157800i	0.781591	+	0.623791i	$0.214408\pi$
$308$	−2.00784	+	8.54217i	−0.114407	+	0.486735i
$309$		−	49.7346i		−	2.82930i
$310$	−4.58279	−	2.72533i	−0.260285	−	0.154788i
$311$	1.54653	+	2.67867i	0.0876958	+	0.151894i	0.906537	−	0.422127i	$-0.138716\pi$
$311$	1.54653	+	2.67867i	0.0876958	+	0.151894i	−0.818841	+	0.574020i	$0.805383\pi$
$312$	0.222871	−	0.831764i	0.0126176	−	0.0470894i
$313$	2.56647	+	9.57819i	0.145065	+	0.541391i	0.999752	+	0.0222479i	$0.00708230\pi$
$313$	2.56647	+	9.57819i	0.145065	+	0.541391i	−0.854687	+	0.519143i	$0.826251\pi$
$314$	11.7423			0.662658
$315$	−6.38160	−	21.5275i	−0.359562	−	1.21294i
$316$			13.0003i			0.731324i
$317$	22.7472	−	6.09510i	1.27761	−	0.342335i	0.444669	−	0.895695i	$-0.353321\pi$
$317$	22.7472	−	6.09510i	1.27761	−	0.342335i	0.832942	+	0.553360i	$0.186655\pi$
$318$	−4.11877	+	15.3714i	−0.230969	+	0.861988i
$319$	−21.2987	+	5.51671i	−1.19250	+	0.308877i
$320$	−2.16716	+	0.550816i	−0.121148	+	0.0307916i
$321$		−	7.15619i		−	0.399419i
$322$	1.28716	−	2.44663i	0.0717309	−	0.136345i
$323$	2.56484	−	2.56484i	0.142711	−	0.142711i
$324$	5.18010	+	2.99073i	0.287783	+	0.166152i
$325$	−1.58382	−	0.468511i	−0.0878545	−	0.0259883i
$326$	12.3713	−	7.14260i	0.685185	−	0.395592i
$327$	−9.90653	−	36.9717i	−0.547832	−	2.04454i
$328$	1.52653	−	1.52653i	0.0842885	−	0.0842885i
$329$	11.1281	−	12.0389i	0.613514	−	0.663725i
$330$	16.9441	−	9.30816i	0.932740	−	0.512397i
$331$	3.89302	−	6.74291i	0.213980	−	0.370624i	−0.738977	−	0.673731i	$-0.764691\pi$
$331$	3.89302	−	6.74291i	0.213980	−	0.370624i	0.952957	+	0.303107i	$0.0980240\pi$
$332$	−11.5723	−	3.10079i	−0.635113	−	0.170178i
$333$	42.4051	+	11.3624i	2.32379	+	0.622657i
$334$	16.4581	+	9.50211i	0.900549	+	0.519932i
$335$	−28.5219	−	0.368095i	−1.55832	−	0.0201112i
$336$	−1.52198	+	6.72688i	−0.0830307	+	0.366981i
$337$	7.79520	−	7.79520i	0.424631	−	0.424631i	−0.462163	−	0.886795i	$-0.652927\pi$
$337$	7.79520	−	7.79520i	0.424631	−	0.424631i	0.886795	+	0.462163i	$0.152927\pi$
$338$	12.4516	−	3.33641i	0.677280	−	0.181477i
$339$	−30.4047	+	17.5541i	−1.65135	+	0.953410i
$340$	−1.17445	−	2.09622i	−0.0636934	−	0.113683i
$341$	−5.54526	−	5.63868i	−0.300293	−	0.305352i
$342$	9.05892	+	9.05892i	0.489850	+	0.489850i
$343$	2.17807	+	18.3917i	0.117605	+	0.993060i
$344$			0.738235i			0.0398030i
$345$	−5.90302	+	1.50034i	−0.317808	+	0.0807755i
$346$	12.4244	+	21.5196i	0.667937	+	1.15690i
$347$	−27.1227	−	7.26752i	−1.45602	−	0.390141i	−0.557910	−	0.829901i	$-0.688397\pi$
$347$	−27.1227	−	7.26752i	−1.45602	−	0.390141i	−0.898115	+	0.439761i	$0.855063\pi$
$348$	−16.7034	+	4.47568i	−0.895399	+	0.239921i
$349$	−37.0121			−1.98121			−0.990606	−	0.136744i	$-0.956336\pi$
$349$	−37.0121			−1.98121			−0.990606	+	0.136744i	$0.956336\pi$
$350$	12.8230	+	3.25127i	0.685418	+	0.173788i
$351$			0.684863i			0.0365553i
$352$	−3.31651	−	0.0277028i	−0.176771	−	0.00147656i
$353$	−3.91830	−	1.04991i	−0.208550	−	0.0558809i	0.153031	−	0.988221i	$-0.451096\pi$
$353$	−3.91830	−	1.04991i	−0.208550	−	0.0558809i	−0.361582	+	0.932340i	$0.617763\pi$
$354$	2.57429	+	4.45881i	0.136822	+	0.236983i
$355$	3.02192	+	11.8896i	0.160387	+	0.631035i
$356$	15.2161			0.806451
$357$	−7.40546	+	0.291129i	−0.391938	+	0.0154082i
$358$	−3.41667	−	3.41667i	−0.180577	−	0.180577i
$359$	−10.4232	+	18.0536i	−0.550117	+	0.952830i	0.448149	+	0.893959i	$0.352083\pi$
$359$	−10.4232	+	18.0536i	−0.550117	+	0.952830i	−0.998266	+	0.0588711i	$0.981250\pi$
$360$	7.40377	−	4.14811i	0.390213	−	0.218625i
$361$	3.80290	+	6.58681i	0.200153	+	0.346674i
$362$	0.338609	+	1.26371i	0.0177969	+	0.0664190i
$363$	27.8177	−	6.95782i	1.46005	−	0.365191i
$364$	0.834660	−	0.259190i	0.0437481	−	0.0135852i
$365$	−9.86549	−	0.127321i	−0.516383	−	0.00666429i
$366$	−11.4760	+	19.8769i	−0.599858	+	1.03898i
$367$	−6.87004	+	25.6393i	−0.358613	+	1.33836i	0.517263	+	0.855826i	$0.326951\pi$
$367$	−6.87004	+	25.6393i	−0.358613	+	1.33836i	−0.875876	+	0.482536i	$0.839716\pi$
$368$	1.00930	+	0.270442i	0.0526135	+	0.0140977i
$369$	−4.09675	+	7.09578i	−0.213268	+	0.369392i
$370$	−18.5237	+	18.0517i	−0.963001	+	0.938462i
$371$	−15.4250	+	4.78996i	−0.800824	+	0.248682i
$372$	−4.39530	−	4.39530i	−0.227886	−	0.227886i
$373$	−32.1654	+	8.61870i	−1.66546	+	0.446259i	−0.963882	−	0.266330i	$-0.914189\pi$
$373$	−32.1654	+	8.61870i	−1.66546	+	0.446259i	−0.701581	+	0.712590i	$0.747522\pi$
$374$	−0.893627	−	3.45008i	−0.0462083	−	0.178399i
$375$	−13.5845	−	25.7852i	−0.701502	−	1.33154i
$376$	5.36626	+	3.09821i	0.276744	+	0.159778i
$377$	1.54951	+	1.54951i	0.0798036	+	0.0798036i
$378$	−0.215477	−	5.48108i	−0.0110829	−	0.281916i
$379$		−	33.6853i		−	1.73030i	−0.501516	−	0.865148i	$-0.667224\pi$
$379$		−	33.6853i		−	1.73030i	0.501516	−	0.865148i	$-0.332776\pi$
$380$	−7.31533	+	1.85930i	−0.375268	+	0.0953799i
$381$	−26.0078	+	15.0156i	−1.33242	+	0.769274i
$382$	12.3964	+	3.32160i	0.634253	+	0.169948i
$383$	−0.861946	−	3.21683i	−0.0440434	−	0.164372i	0.940401	−	0.340067i	$-0.110450\pi$
$383$	−0.861946	−	3.21683i	−0.0440434	−	0.164372i	−0.984445	+	0.175694i	$0.943783\pi$
$384$	−2.60679			−0.133027
$385$	17.1668	+	9.50267i	0.874901	+	0.484301i
$386$	19.4962			0.992332
$387$	−0.725171	−	2.70638i	−0.0368625	−	0.137573i
$388$	0.384470	+	0.103018i	0.0195185	+	0.00522997i
$389$	−8.04652	+	4.64566i	−0.407975	+	0.235544i	−0.689919	−	0.723886i	$-0.742354\pi$
$389$	−8.04652	+	4.64566i	−0.407975	+	0.235544i	0.281945	+	0.959431i	$0.409021\pi$
$390$	−1.65496	−	0.984184i	−0.0838022	−	0.0498361i
$391$			1.12282i			0.0567834i
$392$	−6.59838	+	2.33695i	−0.333269	+	0.118034i
$393$	8.05563	+	8.05563i	0.406353	+	0.406353i
$394$	6.84654	+	3.95285i	0.344924	+	0.199142i
$395$	27.9796	+	7.88548i	1.40781	+	0.396761i
$396$	12.1856	−	3.15626i	0.612347	−	0.158608i
$397$	25.4848	−	6.82864i	1.27905	−	0.342720i	0.445557	−	0.895254i	$-0.353006\pi$
$397$	25.4848	−	6.82864i	1.27905	−	0.342720i	0.833490	+	0.552534i	$0.186339\pi$
$398$	2.02190	+	2.02190i	0.101349	+	0.101349i
$399$	−5.13748	+	22.7068i	−0.257196	+	1.13676i
$400$	−0.129036	+	4.99833i	−0.00645178	+	0.249917i
$401$	−10.8662	+	18.8209i	−0.542633	+	0.939869i	0.456118	+	0.889919i	$0.349239\pi$
$401$	−10.8662	+	18.8209i	−0.542633	+	0.939869i	−0.998752	+	0.0499494i	$0.984094\pi$
$402$	−32.1202	−	8.60659i	−1.60201	−	0.429258i
$403$	−0.203867	+	0.760840i	−0.0101553	+	0.0379002i
$404$	3.09147	−	5.35459i	0.153807	−	0.266401i
$405$	9.57878	−	9.33468i	0.475973	−	0.463844i
$406$	−12.8885	−	11.9135i	−0.639645	−	0.591255i
$407$	−33.3831	+	18.9037i	−1.65474	+	0.937022i
$408$	−0.724994	−	2.70571i	−0.0358925	−	0.133953i
$409$	−5.64481	−	9.77709i	−0.279118	−	0.483446i	0.692048	−	0.721851i	$-0.256709\pi$
$409$	−5.64481	−	9.77709i	−0.279118	−	0.483446i	−0.971166	+	0.238405i	$0.923375\pi$
$410$	−2.35950	−	4.21137i	−0.116528	−	0.207985i
$411$	−17.5036	+	30.3171i	−0.863389	+	1.49543i
$412$	13.4908	+	13.4908i	0.664645	+	0.664645i
$413$	−2.43299	+	4.62460i	−0.119719	+	0.227562i
$414$	−3.96576			−0.194907
$415$	−13.6929	+	23.0254i	−0.672159	+	1.13027i
$416$	0.165166	+	0.286076i	0.00809794	+	0.0140260i
$417$	−10.4821	−	2.80868i	−0.513312	−	0.137542i
$418$	−11.1950	−	0.0935116i	−0.547564	−	0.00457380i
$419$		−	6.06087i		−	0.296093i	−0.988980	−	0.148046i	$-0.952701\pi$
$419$		−	6.06087i		−	0.296093i	0.988980	−	0.148046i	$-0.0472985\pi$
$420$	13.5546	+	7.35590i	0.661397	+	0.358931i
$421$	−10.1921			−0.496730			−0.248365	−	0.968666i	$-0.579893\pi$
$421$	−10.1921			−0.496730			−0.248365	+	0.968666i	$0.579893\pi$
$422$	6.96537	−	1.86637i	0.339069	−	0.0908533i
$423$	−22.7162	−	6.08677i	−1.10450	−	0.295949i
$424$	−3.05236	−	5.28684i	−0.148236	−	0.256752i
$425$	−5.22391	+	1.25619i	−0.253397	+	0.0609344i
$426$			14.3015i			0.692909i
$427$	−23.2770	+	0.915084i	−1.12645	+	0.0442840i
$428$	1.94116	+	1.94116i	0.0938295	+	0.0938295i
$429$	−2.00253	−	2.03627i	−0.0966832	−	0.0983120i
$430$	1.58885	+	0.447785i	0.0766212	+	0.0215941i
$431$	−17.6482	+	10.1892i	−0.850082	+	0.490795i	−0.860678	−	0.509149i	$-0.829960\pi$
$431$	−17.6482	+	10.1892i	−0.850082	+	0.490795i	0.0105967	+	0.999944i	$0.496627\pi$
$432$	2.00261	−	0.536598i	0.0963506	−	0.0258171i
$433$	−0.0258776	+	0.0258776i	−0.00124360	+	0.00124360i	−0.707728	−	0.706485i	$-0.750280\pi$
$433$	−0.0258776	+	0.0258776i	−0.00124360	+	0.00124360i	0.706485	+	0.707728i	$0.250280\pi$
$434$	1.39220	−	6.15328i	0.0668277	−	0.295367i
$435$	−0.498991	+	38.6644i	−0.0239248	+	1.85382i
$436$	12.7160	+	7.34159i	0.608986	+	0.351598i
$437$	3.40693	+	0.912884i	0.162975	+	0.0436692i
$438$	−11.1101	−	2.97695i	−0.530862	−	0.142244i
$439$	10.4251	−	18.0568i	0.497562	−	0.861803i	−0.502434	−	0.864615i	$-0.667562\pi$
$439$	10.4251	−	18.0568i	0.497562	−	0.861803i	0.999996	+	0.00281297i	$0.000895398\pi$
$440$	−2.07129	+	7.12108i	−0.0987448	+	0.339484i
$441$	21.8941	−	15.0489i	1.04258	−	0.716613i
$442$	−0.250997	+	0.250997i	−0.0119387	+	0.0119387i
$443$	2.12580	+	7.93361i	0.101000	+	0.376937i	0.997861	−	0.0653759i	$-0.0208247\pi$
$443$	2.12580	+	7.93361i	0.101000	+	0.376937i	−0.896861	+	0.442313i	$0.854158\pi$
$444$	−26.1132	+	15.0765i	−1.23928	+	0.715498i
$445$	9.22949	−	32.7485i	0.437520	−	1.55243i
$446$	−13.1506	−	7.59251i	−0.622700	−	0.359516i
$447$	−9.79547	+	9.79547i	−0.463310	+	0.463310i
$448$	−1.41186	−	2.23755i	−0.0667042	−	0.105714i
$449$		−	9.10993i		−	0.429924i	−0.976622	−	0.214962i	$-0.931037\pi$
$449$		−	9.10993i		−	0.429924i	0.976622	−	0.214962i	$-0.0689628\pi$
$450$	−4.43684	−	18.4507i	−0.209155	−	0.869774i
$451$	−1.79533	−	6.93132i	−0.0845386	−	0.326383i
$452$	3.48578	−	13.0091i	0.163957	−	0.611898i
$453$	−26.5780	+	7.12157i	−1.24875	+	0.334600i
$454$			26.2765i			1.23322i
$455$	−0.0515625	−	1.95359i	−0.00241729	−	0.0915858i
$456$	−8.79928			−0.412064
$457$	3.44410	+	12.8535i	0.161108	+	0.601264i	0.998505	+	0.0546677i	$0.0174100\pi$
$457$	3.44410	+	12.8535i	0.161108	+	0.601264i	−0.837396	+	0.546596i	$0.815923\pi$
$458$	−5.87741	+	21.9348i	−0.274633	+	1.02495i
$459$	1.11392	+	1.92937i	0.0519935	+	0.0900554i
$460$	1.19426	−	2.00821i	0.0556824	−	0.0936332i
$461$			23.3632i			1.08813i	0.839042	+	0.544066i	$0.183116\pi$
$461$			23.3632i			1.08813i	−0.839042	+	0.544066i	$0.816884\pi$
$462$	16.6673	+	15.6666i	0.775433	+	0.728875i
$463$	−23.7551	+	23.7551i	−1.10399	+	1.10399i	−0.110070	+	0.993924i	$0.535108\pi$
$463$	−23.7551	+	23.7551i	−1.10399	+	1.10399i	−0.993924	+	0.110070i	$0.964892\pi$
$464$	3.31686	−	5.74497i	0.153981	−	0.266703i
$465$	−12.1257	+	6.79367i	−0.562317	+	0.315049i
$466$	8.33514	+	14.4369i	0.386118	+	0.668776i
$467$	−21.8592	+	5.85715i	−1.01152	+	0.271037i	−0.726266	−	0.687414i	$-0.758746\pi$
$467$	−21.8592	+	5.85715i	−1.01152	+	0.271037i	−0.285257	+	0.958451i	$0.592079\pi$
$468$	−0.886514	−	0.886514i	−0.0409791	−	0.0409791i
$469$	−10.0091	−	32.2321i	−0.462178	−	1.48834i
$470$	9.92303	−	9.67017i	0.457715	−	0.446052i
$471$	15.3049	−	26.5088i	0.705211	−	1.22146i
$472$	−1.90777	−	0.511186i	−0.0878124	−	0.0235293i
$473$	2.11012	+	1.24189i	0.0970234	+	0.0571023i
$474$	29.3487	+	16.9445i	1.34803	+	0.778286i
$475$	−0.435563	+	16.8720i	−0.0199850	+	0.774142i
$476$	1.92981	−	2.08775i	0.0884525	−	0.0956917i
$477$	16.3833	+	16.3833i	0.750138	+	0.750138i
$478$	−2.94729	−	10.9994i	−0.134806	−	0.503103i
$479$	8.65218	+	14.9860i	0.395328	+	0.684728i	0.993143	−	0.116906i	$-0.0372976\pi$
$479$	8.65218	+	14.9860i	0.395328	+	0.684728i	−0.597815	+	0.801634i	$0.703964\pi$
$480$	−1.58117	+	5.61040i	−0.0721704	+	0.256078i
$481$	3.30908	+	1.91050i	0.150881	+	0.0871111i
$482$	−18.2262	−	18.2262i	−0.830182	−	0.830182i
$483$	−3.84569	−	6.09475i	−0.174985	−	0.277321i
$484$	−5.65837	+	9.43307i	−0.257199	+	0.428776i
$485$	0.454923	−	0.764980i	0.0206570	−	0.0347359i
$486$	18.8899	−	10.9061i	0.856862	−	0.494710i
$487$	0.274754	−	1.02539i	0.0124503	−	0.0464651i	−0.959421	−	0.281977i	$-0.909010\pi$
$487$	0.274754	−	1.02539i	0.0124503	−	0.0464651i	0.971872	+	0.235512i	$0.0756766\pi$
$488$	−2.27882	−	8.50467i	−0.103157	−	0.384988i
$489$		−	37.2384i		−	1.68398i
$490$	1.02732	+	15.6187i	0.0464095	+	0.705582i
$491$		−	3.65008i		−	0.164726i	−0.996602	−	0.0823630i	$-0.973753\pi$
$491$		−	3.65008i		−	0.164726i	0.996602	−	0.0823630i	$-0.0262467\pi$
$492$	−1.45654	−	5.43587i	−0.0656658	−	0.245068i
$493$	6.88547	+	1.84496i	0.310106	+	0.0830927i
$494$	0.557523	+	0.965659i	0.0250842	+	0.0434470i
$495$	0.598296	−	28.1406i	0.0268914	−	1.26482i
$496$	2.38451			0.107068
$497$	−12.2758	+	7.74583i	−0.550644	+	0.347448i
$498$	−22.0834	+	22.0834i	−0.989582	+	0.989582i
$499$	−30.9223	−	17.8530i	−1.38427	−	0.799210i	−0.391610	−	0.920131i	$-0.628082\pi$
$499$	−30.9223	−	17.8530i	−1.38427	−	0.799210i	−0.992662	+	0.120922i	$0.961415\pi$
$500$	10.6793	+	3.30951i	0.477592	+	0.148006i
$501$	42.9028	−	24.7700i	1.91676	−	1.10664i
$502$	−3.56863	−	13.3183i	−0.159276	−	0.594425i
$503$	−22.9796	−	22.9796i	−1.02461	−	1.02461i	−0.999689	−	0.0249219i	$-0.992066\pi$
$503$	−22.9796	−	22.9796i	−1.02461	−	1.02461i	−0.0249219	−	0.999689i	$-0.507934\pi$
$504$	7.37385	+	6.81601i	0.328458	+	0.303609i
$505$	−9.64913	−	9.90144i	−0.429381	−	0.440608i
$506$	2.47091	−	2.42997i	0.109845	−	0.108025i
$507$	8.69729	−	32.4587i	0.386260	−	1.44154i
$508$	2.98170	−	11.1279i	0.132292	−	0.493719i
$509$	23.4448	+	13.5359i	1.03917	+	0.599967i	0.919599	−	0.392858i	$-0.128514\pi$
$509$	23.4448	+	13.5359i	1.03917	+	0.599967i	0.119574	+	0.992825i	$0.461847\pi$
$510$	−6.26307	−	0.0808292i	−0.277333	−	0.00357918i
$511$	−3.46207	−	11.1488i	−0.153153	−	0.493194i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	6.75987	−	1.81130i	0.298456	−	0.0799709i
$514$	9.67428	+	16.7563i	0.426714	+	0.739091i
$515$	37.2183	−	20.8523i	1.64004	−	0.918863i
$516$	1.66660	+	0.962210i	0.0733678	+	0.0423589i
$517$	17.8831	−	10.1266i	0.786498	−	0.445367i
$518$	−27.0842	−	14.2489i	−1.19001	−	0.626061i
$519$	64.7752			2.84332
$520$	0.715885	−	0.181952i	0.0313936	−	0.00797914i
$521$	17.7873	+	30.8085i	0.779275	+	1.34974i	0.932360	+	0.361531i	$0.117746\pi$
$521$	17.7873	+	30.8085i	0.779275	+	1.34974i	−0.153085	+	0.988213i	$0.548921\pi$
$522$	−6.51633	+	24.3193i	−0.285212	+	1.06443i
$523$	−4.19084	+	1.12293i	−0.183253	+	0.0491024i	−0.349278	−	0.937019i	$-0.613573\pi$
$523$	−4.19084	+	1.12293i	−0.183253	+	0.0491024i	0.166026	+	0.986121i	$0.446907\pi$
$524$	−4.37028			−0.190917
$525$	24.0533	−	24.7108i	1.04977	−	1.07847i
$526$	13.0711			0.569926
$527$	0.663174	+	2.47500i	0.0288883	+	0.107813i
$528$	−4.38525	+	7.45105i	−0.190844	+	0.324265i
$529$	18.9730	−	10.9541i	0.824914	−	0.476265i
$530$	−13.2299	+	3.36258i	−0.574671	+	0.146061i
$531$	7.49605			0.325301
$532$	−4.76578	−	7.55293i	−0.206623	−	0.327461i
$533$	−0.504262	+	0.504262i	−0.0218420	+	0.0218420i
$534$	19.8325	−	34.3510i	0.858238	−	1.48651i
$535$	5.35525	−	3.00039i	0.231528	−	0.129718i
$536$	11.0474	−	6.37822i	0.477175	−	0.275497i
$537$	−12.1666	+	3.26002i	−0.525026	+	0.140680i
$538$	2.66048	+	2.66048i	0.114701	+	0.114701i
$539$	−4.42034	+	22.7917i	−0.190398	+	0.981707i
$540$	0.0598251	−	4.63555i	0.00257446	−	0.199482i
$541$	−26.0491	−	15.0395i	−1.11994	−	0.646597i	−0.178553	−	0.983930i	$-0.557142\pi$
$541$	−26.0491	−	15.0395i	−1.11994	−	0.646597i	−0.941385	+	0.337334i	$0.890475\pi$
$542$	4.57765	−	17.0840i	0.196627	−	0.733821i
$543$	3.29421	+	0.882682i	0.141368	+	0.0378795i
$544$	0.930601	+	0.537283i	0.0398992	+	0.0230358i
$545$	23.5138	−	22.9146i	1.00722	−	0.981554i
$546$	0.502758	−	2.22211i	0.0215161	−	0.0950974i
$547$	−12.1692	+	12.1692i	−0.520319	+	0.520319i	−0.917668	−	0.397349i	$-0.869930\pi$
$547$	−12.1692	+	12.1692i	−0.520319	+	0.520319i	0.397349	+	0.917668i	$0.369930\pi$
$548$	−3.47575	−	12.9717i	−0.148477	−	0.554122i
$549$	16.7083	+	28.9397i	0.713094	+	1.23512i
$550$	14.0698	+	8.77725i	0.599939	+	0.374263i
$551$	11.1962	−	19.3923i	0.476972	−	0.826140i
$552$	1.92605	−	1.92605i	0.0819781	−	0.0819781i
$553$	1.35114	+	34.3690i	0.0574564	+	1.46152i
$554$		−	10.1680i		−	0.431995i
$555$	16.6088	+	65.3464i	0.705002	+	2.77380i
$556$	3.60522	−	2.08147i	0.152895	−	0.0882741i
$557$	37.6503	+	10.0884i	1.59529	+	0.427457i	0.943617	−	0.331040i	$-0.107399\pi$
$557$	37.6503	+	10.0884i	1.59529	+	0.427457i	0.651676	+	0.758497i	$0.274066\pi$
$558$	−8.74162	+	2.34231i	−0.370062	+	0.0991579i
$559$		−	0.243863i		−	0.0103143i
$560$	−5.67211	+	1.68144i	−0.239690	+	0.0710536i
$561$	−8.95344	−	2.47940i	−0.378015	−	0.104681i
$562$	17.3995	−	4.66218i	0.733953	−	0.196662i
$563$	9.11640	−	34.0229i	0.384211	−	1.43389i	−0.455197	−	0.890391i	$-0.650431\pi$
$563$	9.11640	−	34.0229i	0.384211	−	1.43389i	0.839408	−	0.543502i	$-0.182902\pi$
$564$	13.9887	−	8.07638i	0.589031	−	0.340077i
$565$	−25.8843	−	15.3930i	−1.08896	−	0.647590i
$566$	−12.0064			−0.504665
$567$	14.0055	+	7.36824i	0.588176	+	0.309437i
$568$	−3.87937	−	3.87937i	−0.162775	−	0.162775i
$569$	−6.12229	+	10.6041i	−0.256660	+	0.444548i	−0.965345	−	0.260977i	$-0.915955\pi$
$569$	−6.12229	+	10.6041i	−0.256660	+	0.444548i	0.708685	+	0.705525i	$0.249289\pi$
$570$	−5.33730	+	18.9381i	−0.223555	+	0.793228i
$571$	3.79952	−	2.19366i	0.159005	−	0.0918016i	−0.418386	−	0.908269i	$-0.637404\pi$
$571$	3.79952	−	2.19366i	0.159005	−	0.0918016i	0.577391	+	0.816468i	$0.304071\pi$
$572$	1.09555	+	0.00915113i	0.0458073	+	0.000382628i
$573$	23.6560	−	23.6560i	0.988243	−	0.988243i
$574$	3.87704	−	4.19435i	0.161825	−	0.175069i
$575$	−3.59773	−	3.78841i	−0.150036	−	0.157988i
$576$	−1.89767	+	3.28685i	−0.0790694	+	0.136952i
$577$	−11.2990	+	42.1685i	−0.470384	+	1.75550i	0.168007	+	0.985786i	$0.446267\pi$
$577$	−11.2990	+	42.1685i	−0.470384	+	1.75550i	−0.638391	+	0.769712i	$0.720400\pi$
$578$	4.10107	−	15.3054i	0.170582	−	0.636620i
$579$	25.4113	−	44.0136i	1.05606	−	1.82914i
$580$	−10.3526	−	10.6233i	−0.429868	−	0.441109i
$581$	−30.9161	−	6.99486i	−1.28262	−	0.290196i
$582$	0.733684	−	0.733684i	0.0304122	−	0.0304122i
$583$	−20.2464	−	0.169118i	−0.838518	−	0.00700414i
$584$	3.82121	−	2.20617i	0.158123	−	0.0912922i
$585$	−2.44571	+	1.37026i	−0.101117	+	0.0566531i
$586$	−5.46330	+	9.46271i	−0.225687	+	0.390901i
$587$	−5.97297	−	5.97297i	−0.246531	−	0.246531i	0.573014	−	0.819545i	$-0.305774\pi$
$587$	−5.97297	−	5.97297i	−0.246531	−	0.246531i	−0.819545	+	0.573014i	$0.805774\pi$
$588$	−3.32453	+	17.9421i	−0.137101	+	0.739919i
$589$	8.04897			0.331652
$590$	−2.25737	+	3.79590i	−0.0929344	+	0.156275i
$591$	17.8475	−	10.3042i	0.734146	−	0.423859i
$592$	2.99379	−	11.1730i	0.123044	−	0.459206i
$593$	−18.2550	+	4.89142i	−0.749644	+	0.200866i	−0.613360	−	0.789803i	$-0.710183\pi$
$593$	−18.2550	+	4.89142i	−0.749644	+	0.200866i	−0.136284	+	0.990670i	$0.543516\pi$
$594$	1.83511	−	6.62681i	0.0752955	−	0.271901i
$595$	−3.32276	−	5.41973i	−0.136220	−	0.222187i
$596$		−	5.31416i		−	0.217677i
$597$	7.19985	−	1.92919i	0.294670	−	0.0789567i
$598$	−0.333405	−	0.0893356i	−0.0136339	−	0.00365321i
$599$	−0.720090	+	0.415744i	−0.0294221	+	0.0169868i	−0.514639	−	0.857407i	$-0.672074\pi$
$599$	−0.720090	+	0.415744i	−0.0294221	+	0.0169868i	0.485217	+	0.874394i	$0.338741\pi$
$600$	11.1158	+	6.80610i	0.453799	+	0.277858i
$601$		−	17.8571i		−	0.728405i	−0.931320	−	0.364203i	$-0.881342\pi$
$601$		−	17.8571i		−	0.728405i	0.931320	−	0.364203i	$-0.118658\pi$
$602$	0.0767259	+	1.95168i	0.00312712	+	0.0795445i
$603$	−34.2345	+	34.2345i	−1.39414	+	1.39414i
$604$	5.27769	−	9.14123i	0.214746	−	0.371951i
$605$	16.8700	+	17.8998i	0.685862	+	0.727732i
$606$	−8.05881	−	13.9583i	−0.327367	−	0.567016i
$607$	5.05917	+	18.8811i	0.205345	+	0.766360i	0.989344	+	0.145597i	$0.0465103\pi$
$607$	5.05917	+	18.8811i	0.205345	+	0.766360i	−0.783998	+	0.620763i	$0.786823\pi$
$608$	2.38686	−	2.38686i	0.0968000	−	0.0968000i
$609$	−43.6939	+	13.5684i	−1.77057	+	0.549819i
$610$	−19.6862	−	0.254064i	−0.797072	−	0.0102868i
$611$	−1.77265	−	1.02344i	−0.0717138	−	0.0414040i
$612$	−3.93936	−	1.05555i	−0.159239	−	0.0426681i
$613$	11.6246	−	43.3836i	0.469513	−	1.75225i	−0.171963	−	0.985103i	$-0.555011\pi$
$613$	11.6246	−	43.3836i	0.469513	−	1.75225i	0.641476	−	0.767143i	$-0.278322\pi$
$614$	3.38628	+	1.95507i	0.136659	+	0.0789002i
$615$	−12.5827	−	0.162389i	−0.507384	−	0.00654814i
$616$	−8.77076	+	0.271452i	−0.353384	+	0.0109371i
$617$	23.9741	+	23.9741i	0.965162	+	0.965162i	0.999413	−	0.0342513i	$-0.0109047\pi$
$617$	23.9741	+	23.9741i	0.965162	+	0.965162i	−0.0342513	+	0.999413i	$0.510905\pi$
$618$	48.0399	−	12.8723i	1.93245	−	0.517798i
$619$	−29.9296	+	17.2799i	−1.20297	+	0.694537i	−0.961215	−	0.275800i	$-0.911057\pi$
$619$	−29.9296	+	17.2799i	−1.20297	+	0.694537i	−0.241758	+	0.970337i	$0.577724\pi$
$620$	1.44635	−	5.13200i	0.0580868	−	0.206106i
$621$	−1.08318	+	1.87612i	−0.0434665	+	0.0752861i
$622$	−2.18713	+	2.18713i	−0.0876958	+	0.0876958i
$623$	40.2269	−	1.58143i	1.61166	−	0.0633587i
$624$	0.861106			0.0344718
$625$	13.6005	−	20.9768i	0.544018	−	0.839073i
$626$	−8.58757	+	4.95804i	−0.343228	+	0.198163i
$627$	−14.8026	+	25.1512i	−0.591157	+	1.00444i
$628$	3.03914	+	11.3422i	0.121275	+	0.452604i
$629$	12.4296			0.495601
$630$	19.1423	−	11.7359i	0.762647	−	0.467569i
$631$	29.8505			1.18833			0.594166	−	0.804343i	$-0.297482\pi$
$631$	29.8505			1.18833			0.594166	+	0.804343i	$0.297482\pi$
$632$	−12.5573	+	3.36472i	−0.499504	+	0.133842i
$633$	4.86522	−	18.1572i	0.193375	−	0.721685i
$634$	11.7748	+	20.3946i	0.467638	+	0.809973i
$635$	−22.1411	−	13.1670i	−0.878643	−	0.522518i
$636$	−15.9137			−0.631019
$637$	2.17966	−	0.771969i	0.0863613	−	0.0305865i
$638$	−10.8412	−	19.1451i	−0.429209	−	0.757963i
$639$	18.0325	+	10.4111i	0.713355	+	0.411856i
$640$	−1.09295	−	1.95076i	−0.0432027	−	0.0771105i
$641$	−3.62166	−	6.27290i	−0.143047	−	0.247765i	0.785596	−	0.618740i	$-0.212357\pi$
$641$	−3.62166	−	6.27290i	−0.143047	−	0.247765i	−0.928643	+	0.370976i	$0.879023\pi$
$642$	6.91235	−	1.85216i	0.272809	−	0.0730988i
$643$	−2.14204	+	2.14204i	−0.0844738	+	0.0844738i	−0.748081	−	0.663607i	$-0.769025\pi$
$643$	−2.14204	+	2.14204i	−0.0844738	+	0.0844738i	0.663607	+	0.748081i	$0.269025\pi$
$644$	2.69641	+	0.610071i	0.106253	+	0.0240402i
$645$	3.08179	−	3.00326i	0.121345	−	0.118253i
$646$	3.14127	+	1.81361i	0.123592	+	0.0713557i
$647$	9.27420	−	34.6118i	0.364607	−	1.36073i	−0.503347	−	0.864084i	$-0.667898\pi$
$647$	9.27420	−	34.6118i	0.364607	−	1.36073i	0.867953	−	0.496646i	$-0.165435\pi$
$648$	−1.54812	+	5.77765i	−0.0608157	+	0.226967i
$649$	−4.67048	+	4.59310i	−0.183332	+	0.180295i
$650$	0.0426246	−	1.65111i	0.00167187	−	0.0647619i
$651$	−12.0767	−	11.1631i	−0.473324	−	0.437516i
$652$	10.1012	+	10.1012i	0.395592	+	0.395592i
$653$	8.44826	+	31.5293i	0.330606	+	1.23384i	0.908555	+	0.417766i	$0.137187\pi$
$653$	8.44826	+	31.5293i	0.330606	+	1.23384i	−0.577949	+	0.816073i	$0.696147\pi$
$654$	33.1479	−	19.1379i	1.29618	−	0.748353i
$655$	−2.65084	+	9.40584i	−0.103577	+	0.367516i
$656$	1.86961	+	1.07942i	0.0729960	+	0.0421442i
$657$	−11.8414	+	11.8414i	−0.461978	+	0.461978i
$658$	14.5088	+	7.63305i	0.565614	+	0.297567i
$659$	−14.3397			−0.558594			−0.279297	−	0.960205i	$-0.590101\pi$
$659$	−14.3397			−0.558594			−0.279297	+	0.960205i	$0.590101\pi$
$660$	13.3764	+	13.9576i	0.520677	+	0.543298i
$661$	−5.59619	−	9.69289i	−0.217667	−	0.377010i	0.736428	−	0.676516i	$-0.236511\pi$
$661$	−5.59619	−	9.69289i	−0.217667	−	0.377010i	−0.954094	+	0.299507i	$0.903178\pi$
$662$	7.52074	+	2.01518i	0.292302	+	0.0783221i
$663$	0.239489	+	0.893785i	0.00930098	+	0.0347117i
$664$		−	11.9805i		−	0.464935i
$665$	−19.1464	+	5.67573i	−0.742464	+	0.220096i
$666$			43.9010i			1.70113i
$667$	1.79403	+	6.69543i	0.0694653	+	0.259248i
$668$	−4.91865	+	18.3567i	−0.190308	+	0.710241i
$669$	−34.2808	+	19.7921i	−1.32537	+	0.765205i
$670$	−7.02646	−	27.6453i	−0.271456	−	1.06803i
$671$	−28.1427	−	7.79333i	−1.08644	−	0.300858i
$672$	−6.89158	+	0.270927i	−0.265849	+	0.0104512i
$673$	−7.94043	−	7.94043i	−0.306081	−	0.306081i	0.537306	−	0.843387i	$-0.319442\pi$
$673$	−7.94043	−	7.94043i	−0.306081	−	0.306081i	−0.843387	+	0.537306i	$0.819442\pi$
$674$	9.54713	+	5.51204i	0.367742	+	0.212316i
$675$	−9.94048	−	2.94050i	−0.382609	−	0.113180i
$676$	6.44544	+	11.1638i	0.247902	+	0.429378i
$677$	12.4058	+	46.2991i	0.476794	+	1.77942i	0.614468	+	0.788942i	$0.289371\pi$
$677$	12.4058	+	46.2991i	0.476794	+	1.77942i	−0.137674	+	0.990478i	$0.543963\pi$
$678$	−24.8253	−	24.8253i	−0.953410	−	0.953410i
$679$	1.02713	+	0.232392i	0.0394178	+	0.00891839i
$680$	1.72082	−	1.67697i	0.0659905	−	0.0643089i
$681$	59.3204	+	34.2486i	2.27316	+	1.31241i
$682$	4.01133	−	6.81571i	0.153602	−	0.260987i
$683$	−21.1454	−	5.66590i	−0.809108	−	0.216800i	−0.169529	−	0.985525i	$-0.554225\pi$
$683$	−21.1454	−	5.66590i	−0.809108	−	0.216800i	−0.639579	+	0.768725i	$0.720891\pi$
$684$	−6.40562	+	11.0949i	−0.244925	+	0.424223i
$685$	−30.0262	−	0.387510i	−1.14724	−	0.0148060i
$686$	−17.2013	+	6.86399i	−0.656750	+	0.262068i
$687$	41.8582	+	41.8582i	1.59699	+	1.59699i
$688$	−0.713080	+	0.191069i	−0.0271859	+	0.00728445i
$689$	1.00829	+	1.74641i	0.0384129	+	0.0665331i
$690$	−2.97703	−	5.31357i	−0.113334	−	0.202284i
$691$	4.39196	−	7.60709i	0.167078	−	0.289387i	−0.770313	−	0.637666i	$-0.779900\pi$
$691$	4.39196	−	7.60709i	0.167078	−	0.289387i	0.937391	+	0.348278i	$0.113234\pi$
$692$	−17.5707	+	17.5707i	−0.667937	+	0.667937i
$693$	31.8870	−	9.61070i	1.21129	−	0.365080i
$694$		−	28.0795i		−	1.06588i
$695$	−2.29302	−	9.02178i	−0.0869791	−	0.342216i
$696$	−8.64634	−	14.9759i	−0.327739	−	0.567660i
$697$	−0.600412	+	2.24077i	−0.0227422	+	0.0848751i
$698$	−9.57944	−	35.7510i	−0.362587	−	1.35319i
$699$	43.4559			1.64365
$700$	0.178352	+	13.2276i	0.00674108	+	0.499955i
$701$		−	21.5645i		−	0.814481i	−0.913321	−	0.407240i	$-0.866491\pi$
$701$		−	21.5645i		−	0.814481i	0.913321	−	0.407240i	$-0.133509\pi$
$702$	−0.661527	+	0.177256i	−0.0249677	+	0.00669008i
$703$	10.1056	−	37.7147i	0.381141	−	1.42244i
$704$	−0.831617	−	3.21067i	−0.0313427	−	0.121007i
$705$	−8.89721	−	35.0057i	−0.335088	−	1.31839i
$706$		−	4.05653i		−	0.152669i
$707$	7.61645	−	14.4773i	0.286446	−	0.544474i
$708$	−3.64060	+	3.64060i	−0.136822	+	0.136822i
$709$	−0.491298	−	0.283651i	−0.0184511	−	0.0106527i	0.490746	−	0.871303i	$-0.336724\pi$
$709$	−0.491298	−	0.283651i	−0.0184511	−	0.0106527i	−0.509197	+	0.860650i	$0.670058\pi$
$710$	−10.7024	+	5.99621i	−0.401652	+	0.225034i
$711$	42.7301	−	24.6702i	1.60250	−	0.925205i
$712$	3.93821	+	14.6976i	0.147591	+	0.550816i
$713$	−1.76182	+	1.76182i	−0.0659806	+	0.0659806i
$714$	−2.19788	−	7.07777i	−0.0822537	−	0.264879i
$715$	0.684214	−	2.35232i	0.0255881	−	0.0879719i
$716$	2.41595	−	4.18455i	0.0902884	−	0.156384i
$717$	−28.6732	−	7.68295i	−1.07082	−	0.286925i
$718$	−20.1361	−	5.39546i	−0.751473	−	0.201357i
$719$	12.6238	+	7.28836i	0.470788	+	0.271810i	0.716570	−	0.697515i	$-0.245711\pi$
$719$	12.6238	+	7.28836i	0.470788	+	0.271810i	−0.245781	+	0.969325i	$0.579044\pi$
$720$	5.92300	+	6.07788i	0.220737	+	0.226509i
$721$	37.0679	+	34.2637i	1.38048	+	1.27605i
$722$	−5.37811	+	5.37811i	−0.200153	+	0.200153i
$723$	−64.9024	+	17.3906i	−2.41375	+	0.646762i
$724$	−1.13301	+	0.654143i	−0.0421079	+	0.0243110i
$725$	−29.1433	+	15.8375i	−1.08235	+	0.588189i
$726$	13.9205	+	25.0690i	0.516638	+	0.930398i
$727$	19.9149	+	19.9149i	0.738604	+	0.738604i	0.972308	−	0.233704i	$-0.0750846\pi$
$727$	19.9149	+	19.9149i	0.738604	+	0.738604i	−0.233704	+	0.972308i	$0.575085\pi$
$728$	0.466384	+	0.739136i	0.0172853	+	0.0273942i
$729$		−	38.9152i		−	1.44130i
$730$	−2.43039	−	9.56229i	−0.0899529	−	0.353916i
$731$	−0.396641	−	0.687002i	−0.0146703	−	0.0254097i
$732$	−22.1698	−	5.94039i	−0.819421	−	0.219563i
$733$	11.6627	−	3.12501i	0.430772	−	0.115425i	−0.0369164	−	0.999318i	$-0.511754\pi$
$733$	11.6627	−	3.12501i	0.430772	−	0.115425i	0.467689	+	0.883893i	$0.345087\pi$
$734$	−26.5438			−0.979749
$735$	36.5989	+	18.0381i	1.34997	+	0.665346i
$736$			1.04491i			0.0385158i
$737$	0.353389	−	42.3069i	0.0130173	−	1.55839i
$738$	−7.91432	−	2.12063i	−0.291330	−	0.0780617i
$739$	−19.8968	−	34.4622i	−0.731915	−	1.26771i	−0.956064	−	0.293159i	$-0.905293\pi$
$739$	−19.8968	−	34.4622i	−0.731915	−	1.26771i	0.224148	−	0.974555i	$-0.428040\pi$
$740$	−22.2309	−	13.2204i	−0.817223	−	0.485992i
$741$	2.90669			0.106780
$742$	−8.61902	−	13.6596i	−0.316414	−	0.501461i
$743$	31.1550	+	31.1550i	1.14297	+	1.14297i	0.987905	+	0.155061i	$0.0495574\pi$
$743$	31.1550	+	31.1550i	1.14297	+	1.14297i	0.155061	+	0.987905i	$0.450443\pi$
$744$	3.10795	−	5.38313i	0.113943	−	0.197355i
$745$	−11.4373	−	3.22336i	−0.419030	−	0.118095i
$746$	−16.6501	−	28.8387i	−0.609602	−	1.05586i
$747$	11.7685	+	43.9207i	0.430588	+	1.60698i
$748$	3.10123	−	1.75612i	0.113392	−	0.0642102i
$749$	5.33361	+	4.93012i	0.194886	+	0.180142i
$750$	21.3907	−	19.7953i	0.781077	−	0.722824i
$751$	−5.58962	+	9.68151i	−0.203968	+	0.353283i	−0.949803	−	0.312847i	$-0.898717\pi$
$751$	−5.58962	+	9.68151i	−0.203968	+	0.353283i	0.745835	+	0.666130i	$0.232051\pi$
$752$	−1.60375	+	5.98529i	−0.0584829	+	0.218261i
$753$	−34.7180	−	9.30265i	−1.26519	−	0.339008i
$754$	−1.09567	+	1.89775i	−0.0399018	+	0.0691120i
$755$	−16.4728	−	16.9035i	−0.599505	−	0.615182i
$756$	5.23855	−	1.62674i	0.190524	−	0.0591641i
$757$	8.94506	+	8.94506i	0.325114	+	0.325114i	0.850725	−	0.525611i	$-0.176163\pi$
$757$	8.94506	+	8.94506i	0.325114	+	0.325114i	−0.525611	+	0.850725i	$0.676163\pi$
$758$	32.5375	−	8.71839i	1.18181	−	0.316666i
$759$	−2.26520	−	8.74538i	−0.0822214	−	0.317437i
$760$	−3.68929	−	6.58484i	−0.133825	−	0.238857i
$761$	12.0174	+	6.93823i	0.435629	+	0.251511i	0.701742	−	0.712431i	$-0.252406\pi$
$761$	12.0174	+	6.93823i	0.435629	+	0.251511i	−0.266113	+	0.963942i	$0.585739\pi$
$762$	−21.2353	−	21.2353i	−0.769274	−	0.769274i
$763$	34.3804	+	18.0874i	1.24466	+	0.654809i
$764$			12.8337i			0.464306i
$765$	−4.66125	+	7.83815i	−0.168528	+	0.283389i
$766$	2.88413	−	1.66515i	0.104208	−	0.0601644i
$767$	0.630199	+	0.168861i	0.0227552	+	0.00609723i
$768$	−0.674686	−	2.51796i	−0.0243456	−	0.0908591i
$769$	24.0164			0.866053			0.433026	−	0.901381i	$-0.357446\pi$
$769$	24.0164			0.866053			0.433026	+	0.901381i	$0.357446\pi$
$770$	−4.73578	+	19.0413i	−0.170666	+	0.686202i
$771$	50.4376			1.81646
$772$	5.04600	+	18.8319i	0.181609	+	0.677776i
$773$	9.44141	+	2.52982i	0.339584	+	0.0909912i	0.424581	−	0.905390i	$-0.360421\pi$
$773$	9.44141	+	2.52982i	0.339584	+	0.0909912i	−0.0849971	+	0.996381i	$0.527088\pi$
$774$	2.42647	−	1.40092i	0.0872177	−	0.0503551i
$775$	−10.1679	−	6.22575i	−0.365243	−	0.223635i
$776$			0.398032i			0.0142885i
$777$	−67.4689	+	42.5718i	−2.42043	+	1.52726i
$778$	−6.56995	−	6.56995i	−0.235544	−	0.235544i
$779$	6.31092	+	3.64361i	0.226112	+	0.130546i
$780$	0.522313	−	1.85330i	0.0187018	−	0.0663586i
$781$	−17.6146	+	4.56246i	−0.630298	+	0.163258i
$782$	−1.08456	+	0.290607i	−0.0387838	+	0.0103921i
$783$	9.72512	+	9.72512i	0.347547	+	0.347547i
$784$	−3.96510	−	5.76870i	−0.141611	−	0.206025i
$785$	26.2545	+	0.338832i	0.937062	+	0.0120934i
$786$	−5.69619	+	9.86609i	−0.203176	+	0.351912i
$787$	0.502115	+	0.134541i	0.0178985	+	0.00479588i	0.267757	−	0.963486i	$-0.413718\pi$
$787$	0.502115	+	0.134541i	0.0178985	+	0.00479588i	−0.249859	+	0.968282i	$0.580384\pi$
$788$	−2.04615	+	7.63632i	−0.0728909	+	0.272033i
$789$	17.0368	−	29.5085i	0.606525	−	1.05053i
$790$	−0.375132	+	29.0671i	−0.0133466	+	1.03416i
$791$	7.86334	−	34.7546i	0.279588	−	1.23573i
$792$	6.20257	+	10.9534i	0.220399	+	0.389214i
$793$	0.752768	+	2.80937i	0.0267316	+	0.0997635i
$794$	13.1919	+	22.8491i	0.468164	+	0.810884i
$795$	−9.65263	+	34.2499i	−0.342343	+	1.21472i
$796$	−1.42970	+	2.47631i	−0.0506743	+	0.0877705i
$797$	35.8399	+	35.8399i	1.26951	+	1.26951i	0.946339	+	0.323174i	$0.104750\pi$
$797$	35.8399	+	35.8399i	1.26951	+	1.26951i	0.323174	+	0.946339i	$0.395250\pi$
$798$	−23.2627	+	0.914523i	−0.823492	+	0.0323738i
$799$	−6.65847			−0.235560
$800$	−4.86142	+	1.16903i	−0.171877	+	0.0413313i
$801$	−28.8750	−	50.0130i	−1.02025	−	1.76712i
$802$	−20.9919	−	5.62477i	−0.741251	−	0.198618i
$803$	0.122234	−	14.6336i	0.00431356	−	0.516408i
$804$		−	33.2533i		−	1.17275i
$805$	2.94855	−	5.43324i	0.103923	−	0.191497i
$806$	−0.787680			−0.0277448
$807$	9.47379	−	2.53849i	0.333493	−	0.0893592i
$808$	5.97227	+	1.60026i	0.210104	+	0.0562971i
$809$	−21.8140	−	37.7830i	−0.766940	−	1.32838i	−0.939215	−	0.343330i	$-0.888445\pi$
$809$	−21.8140	−	37.7830i	−0.766940	−	1.32838i	0.172274	−	0.985049i	$-0.444888\pi$
$810$	11.4958	+	6.83639i	0.403921	+	0.240206i
$811$			27.1636i			0.953842i	0.878946	+	0.476921i	$0.158247\pi$
$811$			27.1636i			0.953842i	−0.878946	+	0.476921i	$0.841753\pi$
$812$	8.17173	−	15.5328i	0.286771	−	0.545093i
$813$	−32.6014	−	32.6014i	−1.14338	−	1.14338i
$814$	−26.8997	−	27.3529i	−0.942836	−	0.958719i
$815$	27.8670	−	15.6130i	0.976137	−	0.546900i
$816$	2.42588	−	1.40058i	0.0849227	−	0.0490301i
$817$	−2.40702	+	0.644960i	−0.0842111	+	0.0225643i
$818$	7.98296	−	7.98296i	0.279118	−	0.279118i
$819$	−2.43582	−	2.25155i	−0.0851145	−	0.0786755i
$820$	3.45719	−	3.36909i	0.120730	−	0.117654i
$821$	−9.95835	−	5.74945i	−0.347549	−	0.200657i	0.316056	−	0.948740i	$-0.397641\pi$
$821$	−9.95835	−	5.74945i	−0.347549	−	0.200657i	−0.663605	+	0.748083i	$0.730974\pi$
$822$	−33.8143	−	9.06053i	−1.17941	−	0.316022i
$823$	14.9446	+	4.00440i	0.520937	+	0.139585i	0.509700	−	0.860352i	$-0.329756\pi$
$823$	14.9446	+	4.00440i	0.520937	+	0.139585i	0.0112370	+	0.999937i	$0.496423\pi$
$824$	−9.53945	+	16.5228i	−0.332323	+	0.575600i
$825$	38.1535	−	20.3230i	1.32834	−	0.707556i
$826$	−5.09672	−	1.15315i	−0.177338	−	0.0401232i
$827$	−22.8782	+	22.8782i	−0.795554	+	0.795554i	−0.982391	−	0.186837i	$-0.940176\pi$
$827$	−22.8782	+	22.8782i	−0.795554	+	0.795554i	0.186837	+	0.982391i	$0.440176\pi$
$828$	−1.02642	−	3.83063i	−0.0356704	−	0.133124i
$829$	28.5026	−	16.4560i	0.989936	−	0.571540i	0.0846808	−	0.996408i	$-0.473013\pi$
$829$	28.5026	−	16.4560i	0.989936	−	0.571540i	0.905255	+	0.424868i	$0.139680\pi$
$830$	−25.7848	−	7.26693i	−0.895005	−	0.252239i
$831$	−22.9546	−	13.2528i	−0.796286	−	0.459736i
$832$	−0.233580	+	0.233580i	−0.00809794	+	0.00809794i
$833$	4.88486	−	5.71996i	0.169250	−	0.198185i
$834$		−	10.8519i		−	0.375771i
$835$	36.5243	+	21.7205i	1.26397	+	0.751669i
$836$	−2.80715	−	10.8377i	−0.0970872	−	0.374830i
$837$	−1.27952	+	4.77524i	−0.0442267	+	0.165056i
$838$	5.85435	−	1.56867i	0.202235	−	0.0541888i
$839$			15.3584i			0.530232i	0.964217	+	0.265116i	$0.0854103\pi$
$839$			15.3584i			0.530232i	−0.964217	+	0.265116i	$0.914590\pi$
$840$	−3.59707	+	14.9966i	−0.124111	+	0.517431i
$841$	15.0062			0.517456
$842$	−2.63790	−	9.84477i	−0.0909079	−	0.339273i
$843$	12.1533	−	45.3568i	0.418582	−	1.56217i
$844$	3.60554	+	6.24498i	0.124108	+	0.214961i
$845$	27.9367	−	7.10051i	0.961050	−	0.244265i
$846$		−	23.5175i		−	0.808548i
$847$	−13.9787	+	25.5264i	−0.480313	+	0.877097i
$848$	4.31669	−	4.31669i	0.148236	−	0.148236i
$849$	−15.6490	+	27.1049i	−0.537073	+	0.930237i
$850$	−2.56544	−	4.72078i	−0.0879938	−	0.161922i
$851$	6.04327	+	10.4673i	0.207161	+	0.358813i
$852$	−13.8142	+	3.70150i	−0.473266	+	0.126811i
$853$	17.5026	+	17.5026i	0.599277	+	0.599277i	0.940120	−	0.340843i	$-0.110713\pi$
$853$	17.5026	+	17.5026i	0.599277	+	0.599277i	−0.340843	+	0.940120i	$0.610713\pi$
$854$	−6.90844	−	22.2470i	−0.236402	−	0.761277i
$855$	19.9933	+	20.5161i	0.683756	+	0.701635i
$856$	−1.37261	+	2.37743i	−0.0469148	+	0.0812587i
$857$	−0.151368	−	0.0405589i	−0.00517062	−	0.00138546i	0.256233	−	0.966615i	$-0.417519\pi$
$857$	−0.151368	−	0.0405589i	−0.00517062	−	0.00138546i	−0.261403	+	0.965230i	$0.584185\pi$
$858$	1.44859	−	2.46132i	0.0494541	−	0.0840282i
$859$	−11.3113	−	6.53060i	−0.385938	−	0.222821i	0.294461	−	0.955664i	$-0.404860\pi$
$859$	−11.3113	−	6.53060i	−0.385938	−	0.222821i	−0.680398	+	0.732842i	$0.738193\pi$
$860$	−0.0213022	+	1.65061i	−0.000726400	+	0.0562852i
$861$	−4.41562	−	14.2195i	−0.150484	−	0.484599i
$862$	−14.4097	−	14.4097i	−0.490795	−	0.490795i
$863$	1.77748	+	6.63366i	0.0605063	+	0.225813i	0.989558	−	0.144139i	$-0.0460411\pi$
$863$	1.77748	+	6.63366i	0.0605063	+	0.225813i	−0.929051	+	0.369951i	$0.879374\pi$
$864$	1.03663	+	1.79549i	0.0352668	+	0.0610839i
$865$	27.1584	+	48.4738i	0.923414	+	1.64816i
$866$	−0.0316934	−	0.0182982i	−0.00107699	−	0.000621798i
$867$	−29.2073	−	29.2073i	−0.991931	−	0.991931i
$868$	6.30394	−	0.247825i	0.213970	−	0.00841175i
$869$	−11.5070	+	41.5533i	−0.390349	+	1.40960i
$870$	−37.4761	+	9.52509i	−1.27056	+	0.322931i
$871$	−3.64932	+	2.10693i	−0.123652	+	0.0713907i
$872$	−3.80028	+	14.1829i	−0.128694	+	0.480292i
$873$	−0.390989	−	1.45919i	−0.0132330	−	0.0493861i
$874$			3.52711i			0.119306i
$875$	28.5769	+	7.63947i	0.966075	+	0.258261i
$876$		−	11.5020i		−	0.388618i
$877$	−3.70190	−	13.8157i	−0.125004	−	0.466523i	0.874835	−	0.484420i	$-0.160969\pi$
$877$	−3.70190	−	13.8157i	−0.125004	−	0.466523i	−0.999840	+	0.0178976i	$0.994303\pi$
$878$	20.1397	+	5.39642i	0.679682	+	0.182120i
$879$	14.2417	+	24.6673i	0.480359	+	0.832006i
$880$	−7.41452	−	0.157640i	−0.249944	−	0.00531405i
$881$	−20.3475			−0.685523			−0.342762	−	0.939422i	$-0.611362\pi$
$881$	−20.3475			−0.685523			−0.342762	+	0.939422i	$0.611362\pi$
$882$	20.2027	+	17.2532i	0.680261	+	0.580945i
$883$	24.6962	−	24.6962i	0.831093	−	0.831093i	−0.156573	−	0.987666i	$-0.550045\pi$
$883$	24.6962	−	24.6962i	0.831093	−	0.831093i	0.987666	+	0.156573i	$0.0500447\pi$
$884$	−0.307408	−	0.177482i	−0.0103392	−	0.00596936i
$885$	5.62716	+	10.0437i	0.189155	+	0.337614i
$886$	−7.11308	+	4.10674i	−0.238969	+	0.137969i
$887$	−0.568036	−	2.11994i	−0.0190728	−	0.0711805i	0.955734	−	0.294234i	$-0.0950644\pi$
$887$	−0.568036	−	2.11994i	−0.0190728	−	0.0711805i	−0.974806	+	0.223053i	$0.928398\pi$
$888$	−21.3214	−	21.3214i	−0.715498	−	0.715498i
$889$	6.72622	−	29.7287i	0.225590	−	0.997069i
$890$	34.0214	+	0.439070i	1.14040	+	0.0147176i
$891$	13.9101	+	14.1444i	0.466006	+	0.473857i
$892$	3.93017	−	14.6676i	0.131592	−	0.491108i
$893$	−5.41352	+	20.2035i	−0.181156	+	0.676085i
$894$	−11.9969	−	6.92644i	−0.401238	−	0.231655i
$895$	−7.54069	−	7.73787i	−0.252057	−	0.258648i
$896$	1.79589	−	1.94288i	0.0599966	−	0.0649069i
$897$	−0.636237	+	0.636237i	−0.0212433	+	0.0212433i
$898$	8.79952	−	2.35782i	0.293644	−	0.0786816i
$899$	7.90907	+	13.6989i	0.263782	+	0.456885i
$900$	16.6737	−	9.06104i	0.555788	−	0.302035i
$901$	5.68106	+	3.27996i	0.189263	+	0.109271i
$902$	6.23048	−	3.52811i	0.207452	−	0.117473i
$903$	4.50600	+	2.37059i	0.149950	+	0.0788884i
$904$	13.4680			0.447940
$905$	0.720625	+	2.83527i	0.0239544	+	0.0942476i
$906$	−13.7578	−	23.8292i	−0.457073	−	0.791673i
$907$	−9.04267	+	33.7477i	−0.300257	+	1.12057i	0.636695	+	0.771116i	$0.280301\pi$
$907$	−9.04267	+	33.7477i	−0.300257	+	1.12057i	−0.936952	+	0.349459i	$0.886365\pi$
$908$	−25.3812	+	6.80087i	−0.842304	+	0.225695i
$909$	−23.4663			−0.778329
$910$	1.87368	−	0.555432i	0.0621119	−	0.0184124i
$911$	22.1668			0.734419			0.367210	−	0.930138i	$-0.380313\pi$
$911$	22.1668			0.734419			0.367210	+	0.930138i	$0.380313\pi$
$912$	−2.27742	−	8.49945i	−0.0754130	−	0.281445i
$913$	−34.2443	−	20.1542i	−1.13332	−	0.667007i
$914$	−11.5242	+	6.65349i	−0.381186	+	0.220078i
$915$	−26.2324	+	44.1113i	−0.867218	+	1.45828i
$916$	−22.7086			−0.750313
$917$	−11.5537	+	0.454210i	−0.381538	+	0.0149993i
$918$	−1.57533	+	1.57533i	−0.0519935	+	0.0519935i
$919$	−2.13392	+	3.69605i	−0.0703914	+	0.121921i	−0.899073	−	0.437799i	$-0.855758\pi$
$919$	−2.13392	+	3.69605i	−0.0703914	+	0.121921i	0.828681	+	0.559720i	$0.189091\pi$
$920$	2.24888	+	0.633800i	0.0741432	+	0.0208958i
$921$	8.82731	−	5.09645i	0.290870	−	0.167934i
$922$	−22.5671	+	6.04684i	−0.743208	+	0.199142i
$923$	1.28148	+	1.28148i	0.0421804	+	0.0421804i
$924$	−10.8189	+	20.1542i	−0.355917	+	0.663024i
$925$	−41.9377	+	39.8269i	−1.37890	+	1.30950i
$926$	−29.0940	−	16.7974i	−0.956087	−	0.551997i
$927$	18.7413	−	69.9434i	0.615544	−	2.29724i
$928$	6.40768	+	1.71693i	0.210342	+	0.0563611i
$929$	23.6707	+	13.6663i	0.776611	+	0.448377i	0.835228	−	0.549904i	$-0.185336\pi$
$929$	23.6707	+	13.6663i	0.776611	+	0.448377i	−0.0586167	+	0.998281i	$0.518669\pi$
$930$	−9.70055	−	9.95421i	−0.318094	−	0.326411i
$931$	−13.3843	−	19.4724i	−0.438654	−	0.638183i
$932$	−11.7877	+	11.7877i	−0.386118	+	0.386118i
$933$	2.08685	+	7.78822i	0.0683203	+	0.254975i
$934$	−11.3152	−	19.5984i	−0.370243	−	0.641280i
$935$	−1.89849	−	7.73975i	−0.0620872	−	0.253117i
$936$	0.626860	−	1.08575i	0.0204896	−	0.0354890i
$937$	35.6082	−	35.6082i	1.16327	−	1.16327i	0.179514	−	0.983755i	$-0.442547\pi$
$937$	35.6082	−	35.6082i	1.16327	−	1.16327i	0.983755	−	0.179514i	$-0.0574526\pi$
$938$	28.5432	−	18.0103i	0.931970	−	0.588059i
$939$			25.8491i			0.843553i
$940$	11.9089	+	7.08209i	0.388427	+	0.230992i
$941$	−19.5298	+	11.2755i	−0.636652	+	0.367571i	−0.783324	−	0.621614i	$-0.786477\pi$
$941$	−19.5298	+	11.2755i	−0.636652	+	0.367571i	0.146672	+	0.989185i	$0.453144\pi$
$942$	29.5667	+	7.92239i	0.963337	+	0.258125i
$943$	−2.17892	+	0.583840i	−0.0709554	+	0.0190124i
$944$		−	1.97507i		−	0.0642831i
$945$	−0.323620	−	12.2613i	−0.0105274	−	0.398859i
$946$	−0.653437	+	2.35964i	−0.0212451	+	0.0767187i
$947$	−22.6038	+	6.05667i	−0.734525	+	0.196815i	−0.606643	−	0.794974i	$-0.707484\pi$
$947$	−22.6038	+	6.05667i	−0.734525	+	0.196815i	−0.127881	+	0.991789i	$0.540818\pi$
$948$	−8.77112	+	32.7342i	−0.284873	+	1.06316i
$949$	−1.26227	+	0.728771i	−0.0409750	+	0.0236569i
$950$	−16.4099	+	3.94608i	−0.532406	+	0.128028i
$951$	61.3889			1.99067
$952$	2.51608	+	1.32370i	0.0815466	+	0.0429014i
$953$	−19.4667	−	19.4667i	−0.630588	−	0.630588i	0.317628	−	0.948216i	$-0.397114\pi$
$953$	−19.4667	−	19.4667i	−0.630588	−	0.630588i	−0.948216	+	0.317628i	$0.897114\pi$
$954$	−11.5847	+	20.0653i	−0.375069	+	0.649638i
$955$	27.6210	+	7.78440i	0.893793	+	0.251897i
$956$	9.86183	−	5.69373i	0.318954	−	0.184148i
$957$	−57.3513	−	0.479055i	−1.85391	−	0.0154857i
$958$	−12.2360	+	12.2360i	−0.395328	+	0.395328i
$959$	−10.5370	−	33.9321i	−0.340258	−	1.09572i
$960$	−5.82846	−	0.0752204i	−0.188113	−	0.00242773i
$961$	12.6571	−	21.9227i	0.408292	−	0.707183i
$962$	−0.988945	+	3.69079i	−0.0318849	+	0.118996i
$963$	2.69664	−	10.0640i	0.0868978	−	0.324307i
$964$	12.8879	−	22.3225i	0.415091	−	0.718959i
$965$	43.5913	+	0.562576i	1.40325	+	0.0181100i
$966$	4.89174	−	5.29209i	0.157389	−	0.170270i
$967$	32.2306	−	32.2306i	1.03647	−	1.03647i	0.0371584	−	0.999309i	$-0.488169\pi$
$967$	32.2306	−	32.2306i	1.03647	−	1.03647i	0.999309	−	0.0371584i	$-0.0118306\pi$
$968$	−10.5761	−	3.02410i	−0.339930	−	0.0971984i
$969$	8.18862	−	4.72770i	0.263056	−	0.151876i
$970$	0.856656	+	0.241431i	0.0275056	+	0.00775188i
$971$	−20.3754	+	35.2913i	−0.653878	+	1.13255i	0.328295	+	0.944575i	$0.393526\pi$
$971$	−20.3754	+	35.2913i	−0.653878	+	1.13255i	−0.982174	+	0.187975i	$0.939808\pi$
$972$	15.4235	+	15.4235i	0.494710	+	0.494710i
$973$	9.31481	−	5.87750i	0.298619	−	0.188424i
$974$	1.06157			0.0340148
$975$	−3.67190	−	2.24827i	−0.117595	−	0.0720024i
$976$	7.62508	−	4.40234i	0.244073	−	0.140915i
$977$	−3.05794	+	11.4124i	−0.0978323	+	0.365115i	−0.997434	−	0.0715970i	$-0.977190\pi$
$977$	−3.05794	+	11.4124i	−0.0978323	+	0.365115i	0.899601	+	0.436712i	$0.143857\pi$
$978$	35.9696	−	9.63802i	1.15018	−	0.308190i
$979$	48.6356	+	13.4683i	1.55440	+	0.430448i
$980$	−14.8206	+	5.03474i	−0.473428	+	0.160829i
$981$		−	55.7275i		−	1.77924i
$982$	3.52571	−	0.944711i	0.112510	−	0.0301469i
$983$	35.3920	+	9.48326i	1.12883	+	0.302469i	0.774452	−	0.632633i	$-0.218026\pi$
$983$	35.3920	+	9.48326i	1.12883	+	0.302469i	0.354378	+	0.935102i	$0.384693\pi$
$984$	4.87367	−	2.81381i	0.155367	−	0.0897011i
$985$	15.1940	+	9.03567i	0.484121	+	0.287900i
$986$			7.12836i			0.227013i
$987$	36.1427	−	22.8055i	1.15043	−	0.725906i
$988$	−0.788457	+	0.788457i	−0.0250842	+	0.0250842i
$989$	0.385693	−	0.668040i	0.0122643	−	0.0212424i
$990$	27.3365	−	6.70540i	0.868812	−	0.213112i
$991$	14.7340	+	25.5200i	0.468040	+	0.810669i	0.999333	−	0.0365190i	$-0.0116269\pi$
$991$	14.7340	+	25.5200i	0.468040	+	0.810669i	−0.531293	+	0.847188i	$0.678294\pi$
$992$	0.617156	+	2.30326i	0.0195947	+	0.0731285i
$993$	14.3518	−	14.3518i	0.455442	−	0.455442i
$994$	−10.6591	−	9.85273i	−0.338086	−	0.312510i
$995$	4.46238	+	4.57907i	0.141467	+	0.145166i
$996$	−27.0466	−	15.6153i	−0.857003	−	0.494791i
$997$	−58.0924	−	15.5658i	−1.83980	−	0.492974i	−0.840963	−	0.541093i	$-0.818011\pi$
$997$	−58.0924	−	15.5658i	−1.83980	−	0.492974i	−0.998842	+	0.0481184i	$0.984678\pi$
$998$	9.24139	−	34.4893i	0.292531	−	1.09174i
$999$	20.7686	+	11.9908i	0.657091	+	0.379372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.527.46	yes	192
5.3	odd	4	inner	770.2.bd.a.373.27	yes	192
7.4	even	3	inner	770.2.bd.a.417.3	yes	192
11.10	odd	2	inner	770.2.bd.a.527.22	yes	192
35.18	odd	12	inner	770.2.bd.a.263.22	✓	192
55.43	even	4	inner	770.2.bd.a.373.3	yes	192
77.32	odd	6	inner	770.2.bd.a.417.27	yes	192
385.263	even	12	inner	770.2.bd.a.263.46	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.22	✓	192	35.18	odd	12	inner
770.2.bd.a.263.46	yes	192	385.263	even	12	inner
770.2.bd.a.373.3	yes	192	55.43	even	4	inner
770.2.bd.a.373.27	yes	192	5.3	odd	4	inner
770.2.bd.a.417.3	yes	192	7.4	even	3	inner
770.2.bd.a.417.27	yes	192	77.32	odd	6	inner
770.2.bd.a.527.22	yes	192	11.10	odd	2	inner
770.2.bd.a.527.46	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(2.51796 + 0.674686i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.550816 + 2.16716i) q^{5} +2.60679i q^{6} +(-2.23755 + 1.41186i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(3.28685 + 1.89767i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(2.51796 + 0.674686i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.550816 + 2.16716i) q^{5} +2.60679i q^{6} +(-2.23755 + 1.41186i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(3.28685 + 1.89767i) q^{9} +(-1.95076 + 1.09295i) q^{10} +(-3.21067 + 0.831617i) q^{11} +(-2.51796 + 0.674686i) q^{12} +(0.233580 + 0.233580i) q^{13} +(-1.94288 - 1.79589i) q^{14} +(-0.0752204 + 5.82846i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.03795 + 0.278118i) q^{17} +(-0.982304 + 3.66601i) q^{18} +(1.68776 - 2.92329i) q^{19} +(-1.56060 - 1.60141i) q^{20} +(-6.58664 + 2.04537i) q^{21} +(-1.63426 - 2.88603i) q^{22} +(0.270442 + 1.00930i) q^{23} +(-1.30339 - 2.25754i) q^{24} +(-4.39320 + 2.38742i) q^{25} +(-0.165166 + 0.286076i) q^{26} +(1.46601 + 1.46601i) q^{27} +(1.23185 - 2.34149i) q^{28} +6.63372 q^{29} +(-5.64933 + 1.43586i) q^{30} +(1.19225 + 2.06504i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-8.64543 - 0.0722152i) q^{33} +1.07457i q^{34} +(-4.29222 - 4.07147i) q^{35} -3.79533 q^{36} +(11.1730 - 2.99379i) q^{37} +(3.26051 + 0.873651i) q^{38} +(0.430553 + 0.745739i) q^{39} +(1.14293 - 1.92190i) q^{40} +2.15884i q^{41} +(-3.68042 - 5.83282i) q^{42} +(-0.522011 - 0.522011i) q^{43} +(2.36471 - 2.32554i) q^{44} +(-2.30210 + 8.16841i) q^{45} +(-0.904915 + 0.522453i) q^{46} +(-5.98529 + 1.60375i) q^{47} +(1.84328 - 1.84328i) q^{48} +(3.01329 - 6.31823i) q^{49} +(-3.44311 - 3.62560i) q^{50} +(2.42588 + 1.40058i) q^{51} +(-0.319077 - 0.0854963i) q^{52} +(5.89670 + 1.58002i) q^{53} +(-1.03663 + 1.79549i) q^{54} +(-3.57074 - 6.49999i) q^{55} +(2.58053 + 0.583852i) q^{56} +(6.22203 - 6.22203i) q^{57} +(1.71693 + 6.40768i) q^{58} +(1.71046 - 0.987536i) q^{59} +(-2.84909 - 5.08521i) q^{60} +(7.62508 + 4.40234i) q^{61} +(-1.68610 + 1.68610i) q^{62} +(-10.0337 + 0.394455i) q^{63} +1.00000i q^{64} +(-0.377547 + 0.634867i) q^{65} +(-2.16785 - 8.36953i) q^{66} +(-3.30161 + 12.3218i) q^{67} +(-1.03795 + 0.278118i) q^{68} +2.72385i q^{69} +(2.82183 - 5.19974i) q^{70} +5.48625 q^{71} +(-0.982304 - 3.66601i) q^{72} +(-1.14200 + 4.26200i) q^{73} +(5.78356 + 10.0174i) q^{74} +(-12.6727 + 3.04740i) q^{75} +3.37553i q^{76} +(6.00992 - 6.39381i) q^{77} +(-0.608894 + 0.608894i) q^{78} +(6.50015 - 11.2586i) q^{79} +(2.15223 + 0.606561i) q^{80} +(-2.99073 - 5.18010i) q^{81} +(-2.08528 + 0.558748i) q^{82} +(8.47152 + 8.47152i) q^{83} +(4.68151 - 5.06466i) q^{84} +(-0.0310072 + 2.40260i) q^{85} +(0.369118 - 0.639330i) q^{86} +(16.7034 + 4.47568i) q^{87} +(2.85833 + 1.68225i) q^{88} +(-13.1775 - 7.60804i) q^{89} +(-8.48591 - 0.109517i) q^{90} +(-0.852431 - 0.192865i) q^{91} +(-0.738860 - 0.738860i) q^{92} +(1.60879 + 6.00410i) q^{93} +(-3.09821 - 5.36626i) q^{94} +(7.26491 + 2.04747i) q^{95} +(2.25754 + 1.30339i) q^{96} +(-0.281451 - 0.281451i) q^{97} +(6.88284 + 1.27534i) q^{98} +(-12.1311 - 3.35938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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