LMFDB - Embedded newform 504.2.br.a.155.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(155,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("504.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.br (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.5
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38704 - 0.275894i) q^{2} +(-0.942212 - 1.45335i) q^{3} +(1.84776 + 0.765353i) q^{4} +(-1.23804 - 2.14435i) q^{5} +(0.905915 + 2.27581i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.35177 - 1.57136i) q^{8} +(-1.22447 + 2.73873i) q^{9} +O(q^{10})$	\(q+(-1.38704 - 0.275894i) q^{2} +(-0.942212 - 1.45335i) q^{3} +(1.84776 + 0.765353i) q^{4} +(-1.23804 - 2.14435i) q^{5} +(0.905915 + 2.27581i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.35177 - 1.57136i) q^{8} +(-1.22447 + 2.73873i) q^{9} +(1.12560 + 3.31587i) q^{10} +(-2.37543 - 1.37145i) q^{11} +(-0.628658 - 3.40658i) q^{12} +(-1.24416 + 0.718319i) q^{13} +(-1.06327 - 0.932452i) q^{14} +(-1.95000 + 3.81974i) q^{15} +(2.82847 + 2.82838i) q^{16} -5.92119i q^{17} +(2.45400 - 3.46091i) q^{18} -6.77878 q^{19} +(-0.646425 - 4.90979i) q^{20} +(-0.0893025 - 1.72975i) q^{21} +(2.91644 + 2.55763i) q^{22} +(4.36696 + 7.56380i) q^{23} +(-0.0678810 + 4.89851i) q^{24} +(-0.565491 + 0.979458i) q^{25} +(1.92389 - 0.653080i) q^{26} +(5.13406 - 0.800874i) q^{27} +(1.21754 + 1.58670i) q^{28} +(-3.02501 + 5.23947i) q^{29} +(3.75858 - 4.76015i) q^{30} +(0.272404 - 0.157273i) q^{31} +(-3.14287 - 4.70344i) q^{32} +(0.244948 + 4.74453i) q^{33} +(-1.63362 + 8.21293i) q^{34} -2.47608i q^{35} +(-4.35864 + 4.12338i) q^{36} -4.10136i q^{37} +(9.40245 + 1.87023i) q^{38} +(2.21624 + 1.13140i) q^{39} +(-0.457965 + 6.98843i) q^{40} +(-4.41313 + 2.54792i) q^{41} +(-0.353361 + 2.42387i) q^{42} +(-3.34638 + 5.79610i) q^{43} +(-3.33958 - 4.35216i) q^{44} +(7.38875 - 0.764964i) q^{45} +(-3.97035 - 11.6961i) q^{46} +(-4.80524 + 8.32292i) q^{47} +(1.44562 - 6.77570i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.05459 - 1.20253i) q^{50} +(-8.60558 + 5.57902i) q^{51} +(-2.84869 + 0.375060i) q^{52} +5.72907 q^{53} +(-7.34211 - 0.305613i) q^{54} +6.79166i q^{55} +(-1.25101 - 2.53672i) q^{56} +(6.38705 + 9.85197i) q^{57} +(5.64135 - 6.43278i) q^{58} +(-3.61623 + 2.08783i) q^{59} +(-6.52660 + 5.56555i) q^{60} +(7.61956 + 4.39916i) q^{61} +(-0.421226 + 0.142989i) q^{62} +(-2.42979 + 1.75958i) q^{63} +(3.06164 + 7.39097i) q^{64} +(3.08065 + 1.77862i) q^{65} +(0.969235 - 6.64844i) q^{66} +(1.88584 + 3.26637i) q^{67} +(4.53180 - 10.9410i) q^{68} +(6.87828 - 13.4734i) q^{69} +(-0.683136 + 3.43443i) q^{70} -13.4166 q^{71} +(7.18322 - 4.51678i) q^{72} -6.42473 q^{73} +(-1.13154 + 5.68876i) q^{74} +(1.95631 - 0.100999i) q^{75} +(-12.5256 - 5.18816i) q^{76} +(-1.37145 - 2.37543i) q^{77} +(-2.76187 - 2.18075i) q^{78} +(-3.05016 - 1.76101i) q^{79} +(2.56328 - 9.56688i) q^{80} +(-6.00133 - 6.70702i) q^{81} +(6.82414 - 2.31651i) q^{82} +(1.11167 + 0.641825i) q^{83} +(1.15886 - 3.26451i) q^{84} +(-12.6971 + 7.33068i) q^{85} +(6.24068 - 7.11619i) q^{86} +(10.4650 - 0.540282i) q^{87} +(3.43140 + 6.95799i) q^{88} -17.1676i q^{89} +(-10.4596 - 0.977476i) q^{90} -1.43664 q^{91} +(2.28015 + 17.3184i) q^{92} +(-0.485235 - 0.247716i) q^{93} +(8.96131 - 10.2185i) q^{94} +(8.39241 + 14.5361i) q^{95} +(-3.87451 + 8.99934i) q^{96} +(5.92450 - 10.2615i) q^{97} +(-0.454589 - 1.33916i) q^{98} +(6.66469 - 4.82635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{6}+O(q^{10}) $ 144 * q + 6 * q^6	$ 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.38704	−	0.275894i	−0.980786	−	0.195087i
$2$	−1.38704	−	0.275894i	−0.980786	−	0.195087i
$3$	−0.942212	−	1.45335i	−0.543986	−	0.839094i
$3$	−0.942212	−	1.45335i	−0.543986	−	0.839094i
$4$	1.84776	+	0.765353i	0.923882	+	0.382676i
$5$	−1.23804	−	2.14435i	−0.553669	−	0.958982i	−0.998006	−	0.0631227i	$-0.979894\pi$
$5$	−1.23804	−	2.14435i	−0.553669	−	0.958982i	0.444337	−	0.895860i	$-0.353439\pi$
$6$	0.905915	+	2.27581i	0.369838	+	0.929096i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	−2.35177	−	1.57136i	−0.831476	−	0.555561i
$9$	−1.22447	+	2.73873i	−0.408158	+	0.912911i
$10$	1.12560	+	3.31587i	0.355946	+	1.04857i
$11$	−2.37543	−	1.37145i	−0.716218	−	0.413508i	0.0971413	−	0.995271i	$-0.469030\pi$
$11$	−2.37543	−	1.37145i	−0.716218	−	0.413508i	−0.813359	+	0.581762i	$0.802363\pi$
$12$	−0.628658	−	3.40658i	−0.181478	−	0.983395i
$13$	−1.24416	+	0.718319i	−0.345069	+	0.199226i	−0.662511	−	0.749052i	$-0.730509\pi$
$13$	−1.24416	+	0.718319i	−0.345069	+	0.199226i	0.317442	+	0.948278i	$0.397176\pi$
$14$	−1.06327	−	0.932452i	−0.284170	−	0.249208i
$15$	−1.95000	+	3.81974i	−0.503488	+	0.986253i
$16$	2.82847	+	2.82838i	0.707118	+	0.707096i
$17$		−	5.92119i		−	1.43610i	−0.695992	−	0.718050i	$-0.745035\pi$
$17$		−	5.92119i		−	1.43610i	0.695992	−	0.718050i	$-0.254965\pi$
$18$	2.45400	−	3.46091i	0.578412	−	0.815745i
$19$	−6.77878			−1.55516			−0.777580	−	0.628784i	$-0.783553\pi$
$19$	−6.77878			−1.55516			−0.777580	+	0.628784i	$0.783553\pi$
$20$	−0.646425	−	4.90979i	−0.144545	−	1.09786i
$21$	−0.0893025	−	1.72975i	−0.0194874	−	0.377462i
$22$	2.91644	+	2.55763i	0.621786	+	0.545288i
$23$	4.36696	+	7.56380i	0.910575	+	1.57716i	0.813254	+	0.581909i	$0.197694\pi$
$23$	4.36696	+	7.56380i	0.910575	+	1.57716i	0.0973207	+	0.995253i	$0.468973\pi$
$24$	−0.0678810	+	4.89851i	−0.0138562	+	0.999904i
$25$	−0.565491	+	0.979458i	−0.113098	+	0.195892i
$26$	1.92389	−	0.653080i	0.377305	−	0.128080i
$27$	5.13406	−	0.800874i	0.988051	−	0.154128i
$28$	1.21754	+	1.58670i	0.230093	+	0.299858i
$29$	−3.02501	+	5.23947i	−0.561730	+	0.972945i	0.435616	+	0.900133i	$0.356531\pi$
$29$	−3.02501	+	5.23947i	−0.561730	+	0.972945i	−0.997346	+	0.0728121i	$0.976803\pi$
$30$	3.75858	−	4.76015i	0.686219	−	0.869080i
$31$	0.272404	−	0.157273i	0.0489252	−	0.0282470i	−0.475338	−	0.879803i	$-0.657674\pi$
$31$	0.272404	−	0.157273i	0.0489252	−	0.0282470i	0.524263	+	0.851556i	$0.324341\pi$
$32$	−3.14287	−	4.70344i	−0.555586	−	0.831459i
$33$	0.244948	+	4.74453i	0.0426400	+	0.825917i
$34$	−1.63362	+	8.21293i	−0.280164	+	1.40851i
$35$		−	2.47608i		−	0.418534i
$36$	−4.35864	+	4.12338i	−0.726440	+	0.687230i
$37$		−	4.10136i		−	0.674260i	−0.941458	−	0.337130i	$-0.890544\pi$
$37$		−	4.10136i		−	0.674260i	0.941458	−	0.337130i	$-0.109456\pi$
$38$	9.40245	+	1.87023i	1.52528	+	0.303391i
$39$	2.21624	+	1.13140i	0.354882	+	0.181170i
$40$	−0.457965	+	6.98843i	−0.0724106	+	1.10497i
$41$	−4.41313	+	2.54792i	−0.689215	+	0.397918i	−0.803318	−	0.595551i	$-0.796934\pi$
$41$	−4.41313	+	2.54792i	−0.689215	+	0.397918i	0.114103	+	0.993469i	$0.463601\pi$
$42$	−0.353361	+	2.42387i	−0.0545247	+	0.374011i
$43$	−3.34638	+	5.79610i	−0.510319	+	0.883898i	0.489610	+	0.871942i	$0.337139\pi$
$43$	−3.34638	+	5.79610i	−0.510319	+	0.883898i	−0.999929	+	0.0119561i	$0.996194\pi$
$44$	−3.33958	−	4.35216i	−0.503461	−	0.656113i
$45$	7.38875	−	0.764964i	1.10145	−	0.114034i
$46$	−3.97035	−	11.6961i	−0.585396	−	1.72450i
$47$	−4.80524	+	8.32292i	−0.700916	+	1.21402i	0.267229	+	0.963633i	$0.413892\pi$
$47$	−4.80524	+	8.32292i	−0.700916	+	1.21402i	−0.968145	+	0.250389i	$0.919441\pi$
$48$	1.44562	−	6.77570i	0.208658	−	0.977989i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	1.05459	−	1.20253i	0.149141	−	0.170064i
$51$	−8.60558	+	5.57902i	−1.20502	+	0.781218i
$52$	−2.84869	+	0.375060i	−0.395042	+	0.0520114i
$53$	5.72907			0.786948			0.393474	−	0.919336i	$-0.371273\pi$
$53$	5.72907			0.786948			0.393474	+	0.919336i	$0.371273\pi$
$54$	−7.34211	−	0.305613i	−0.999135	−	0.0415886i
$55$			6.79166i			0.915787i
$56$	−1.25101	−	2.53672i	−0.167173	−	0.338984i
$57$	6.38705	+	9.85197i	0.845985	+	1.30493i
$58$	5.64135	−	6.43278i	0.740745	−	0.844665i
$59$	−3.61623	+	2.08783i	−0.470793	+	0.271813i	−0.716572	−	0.697513i	$-0.754290\pi$
$59$	−3.61623	+	2.08783i	−0.470793	+	0.271813i	0.245778	+	0.969326i	$0.420956\pi$
$60$	−6.52660	+	5.56555i	−0.842580	+	0.718509i
$61$	7.61956	+	4.39916i	0.975585	+	0.563254i	0.900934	−	0.433955i	$-0.142882\pi$
$61$	7.61956	+	4.39916i	0.975585	+	0.563254i	0.0746507	+	0.997210i	$0.476216\pi$
$62$	−0.421226	+	0.142989i	−0.0534958	+	0.0181596i
$63$	−2.42979	+	1.75958i	−0.306125	+	0.221686i
$64$	3.06164	+	7.39097i	0.382705	+	0.923871i
$65$	3.08065	+	1.77862i	0.382108	+	0.220610i
$66$	0.969235	−	6.64844i	0.119305	−	0.818366i
$67$	1.88584	+	3.26637i	0.230392	+	0.399050i	0.957923	−	0.287024i	$-0.0926659\pi$
$67$	1.88584	+	3.26637i	0.230392	+	0.399050i	−0.727532	+	0.686074i	$0.759333\pi$
$68$	4.53180	−	10.9410i	0.549561	−	1.32679i
$69$	6.87828	−	13.4734i	0.828047	−	1.62201i
$70$	−0.683136	+	3.43443i	−0.0816504	+	0.410493i
$71$	−13.4166			−1.59225			−0.796127	−	0.605130i	$-0.793121\pi$
$71$	−13.4166			−1.59225			−0.796127	+	0.605130i	$0.793121\pi$
$72$	7.18322	−	4.51678i	0.846551	−	0.532307i
$73$	−6.42473			−0.751958			−0.375979	−	0.926628i	$-0.622694\pi$
$73$	−6.42473			−0.751958			−0.375979	+	0.926628i	$0.622694\pi$
$74$	−1.13154	+	5.68876i	−0.131539	+	0.661305i
$75$	1.95631	−	0.100999i	0.225895	−	0.0116624i
$76$	−12.5256	−	5.18816i	−1.43678	−	0.595123i
$77$	−1.37145	−	2.37543i	−0.156292	−	0.270705i
$78$	−2.76187	−	2.18075i	−0.312720	−	0.246921i
$79$	−3.05016	−	1.76101i	−0.343170	−	0.198129i	0.318503	−	0.947922i	$-0.396820\pi$
$79$	−3.05016	−	1.76101i	−0.343170	−	0.198129i	−0.661673	+	0.749793i	$0.730153\pi$
$80$	2.56328	−	9.56688i	0.286584	−	1.06961i
$81$	−6.00133	−	6.70702i	−0.666814	−	0.745224i
$82$	6.82414	−	2.31651i	0.753601	−	0.255816i
$83$	1.11167	+	0.641825i	0.122022	+	0.0704494i	0.559769	−	0.828649i	$-0.310890\pi$
$83$	1.11167	+	0.641825i	0.122022	+	0.0704494i	−0.437747	+	0.899098i	$0.644223\pi$
$84$	1.15886	−	3.26451i	0.126442	−	0.356188i
$85$	−12.6971	+	7.33068i	−1.37719	+	0.795123i
$86$	6.24068	−	7.11619i	0.672950	−	0.767358i
$87$	10.4650	−	0.540282i	1.12197	−	0.0579243i
$88$	3.43140	+	6.95799i	0.365789	+	0.741725i
$89$		−	17.1676i		−	1.81976i	−0.414868	−	0.909881i	$-0.636172\pi$
$89$		−	17.1676i		−	1.81976i	0.414868	−	0.909881i	$-0.363828\pi$
$90$	−10.4596	−	0.977476i	−1.10253	−	0.103035i
$91$	−1.43664			−0.150601
$92$	2.28015	+	17.3184i	0.237722	+	1.80557i
$93$	−0.485235	−	0.247716i	−0.0503166	−	0.0256869i
$94$	8.96131	−	10.2185i	0.924288	−	1.05396i
$95$	8.39241	+	14.5361i	0.861043	+	1.49137i
$96$	−3.87451	+	8.99934i	−0.395441	+	0.918491i
$97$	5.92450	−	10.2615i	0.601542	−	1.04190i	−0.391046	−	0.920371i	$-0.627887\pi$
$97$	5.92450	−	10.2615i	0.601542	−	1.04190i	0.992588	−	0.121530i	$-0.0387800\pi$
$98$	−0.454589	−	1.33916i	−0.0459204	−	0.135276i
$99$	6.66469	−	4.82635i	0.669827	−	0.485066i
$100$	−1.79452	+	1.37701i	−0.179452	+	0.137701i
$101$	5.20261	−	9.01119i	0.517679	−	0.896646i	−0.482110	−	0.876111i	$-0.660129\pi$
$101$	5.20261	−	9.01119i	0.517679	−	0.896646i	0.999789	−	0.0205358i	$-0.00653721\pi$
$102$	13.4755	−	5.36409i	1.33427	−	0.531124i
$103$	−3.89721	+	2.25006i	−0.384004	+	0.221705i	−0.679559	−	0.733621i	$-0.737829\pi$
$103$	−3.89721	+	2.25006i	−0.384004	+	0.221705i	0.295555	+	0.955326i	$0.404495\pi$
$104$	4.05473	+	0.265714i	0.397599	+	0.0260554i
$105$	−3.59862	+	2.33299i	−0.351190	+	0.227677i
$106$	−7.94645	−	1.58062i	−0.771828	−	0.153523i
$107$		−	1.65425i		−	0.159922i	−0.996798	−	0.0799610i	$-0.974520\pi$
$107$		−	1.65425i		−	0.159922i	0.996798	−	0.0799610i	$-0.0254796\pi$
$108$	10.0995	+	2.44954i	0.971824	+	0.235707i
$109$			0.115532i			0.0110660i	0.999985	+	0.00553299i	$0.00176121\pi$
$109$			0.115532i			0.0110660i	−0.999985	+	0.00553299i	$0.998239\pi$
$110$	1.87378	−	9.42031i	0.178658	−	0.898191i
$111$	−5.96073	+	3.86435i	−0.565768	+	0.366788i
$112$	1.03534	+	3.86369i	0.0978300	+	0.365084i
$113$	−5.47062	+	3.15846i	−0.514633	+	0.297123i	−0.734736	−	0.678353i	$-0.762694\pi$
$113$	−5.47062	+	3.15846i	−0.514633	+	0.297123i	0.220103	+	0.975477i	$0.429361\pi$
$114$	−6.14100	−	15.4272i	−0.575157	−	1.44489i
$115$	10.8130	−	18.7286i	1.00831	−	1.74645i
$116$	−9.59955	+	7.36611i	−0.891295	+	0.683926i
$117$	−0.443837	−	4.28700i	−0.0410327	−	0.396333i
$118$	5.59188	−	1.89821i	0.514775	−	0.174745i
$119$	2.96060	−	5.12790i	0.271397	−	0.470074i
$120$	10.5882	−	5.91899i	0.966562	−	0.540328i
$121$	−1.73824	−	3.01071i	−0.158021	−	0.273701i
$122$	−9.35494	−	8.20400i	−0.846957	−	0.742755i
$123$	7.86113	+	4.01315i	0.708814	+	0.361854i
$124$	0.623708	−	0.0821176i	0.0560106	−	0.00737438i
$125$	−9.58001			−0.856862
$126$	3.85568	−	1.77024i	0.343491	−	0.157705i
$127$		−	15.6193i		−	1.38599i	−0.720942	−	0.692995i	$-0.756291\pi$
$127$		−	15.6193i		−	1.38599i	0.720942	−	0.692995i	$-0.243709\pi$
$128$	−2.20749	−	11.0963i	−0.195117	−	0.980780i
$129$	11.5768	−	0.597681i	1.01928	−	0.0526228i
$130$	−3.78228	−	3.31695i	−0.331728	−	0.290916i
$131$	−13.0397	+	7.52850i	−1.13929	+	0.657768i	−0.946254	−	0.323424i	$-0.895166\pi$
$131$	−13.0397	+	7.52850i	−1.13929	+	0.657768i	−0.193034	+	0.981192i	$0.561833\pi$
$132$	−3.17863	+	8.95425i	−0.276665	+	0.779368i
$133$	−5.87060	−	3.38939i	−0.509045	−	0.293898i
$134$	−1.71456	−	5.05088i	−0.148116	−	0.436329i
$135$	−8.07353	−	10.0177i	−0.694859	−	0.862187i
$136$	−9.30434	+	13.9253i	−0.797840	+	1.19408i
$137$	−3.47868	−	2.00842i	−0.297204	−	0.171591i	0.343982	−	0.938976i	$-0.388224\pi$
$137$	−3.47868	−	2.00842i	−0.297204	−	0.171591i	−0.641186	+	0.767386i	$0.721557\pi$
$138$	−13.2577	+	16.7905i	−1.12857	+	1.42931i
$139$	−6.05157	−	10.4816i	−0.513287	−	0.889040i	−0.999881	−	0.0154114i	$-0.995094\pi$
$139$	−6.05157	−	10.4816i	−0.513287	−	0.889040i	0.486594	−	0.873628i	$-0.338239\pi$
$140$	1.89508	−	4.57522i	0.160163	−	0.386676i
$141$	16.6237	−	0.858240i	1.39997	−	0.0722768i
$142$	18.6093	+	3.70155i	1.56166	+	0.310627i
$143$	3.94056			0.329526
$144$	−11.2096	+	4.28315i	−0.934132	+	0.356929i
$145$	14.9803			1.24405
$146$	8.91137	+	1.77255i	0.737510	+	0.146697i
$147$	0.787535	−	1.54266i	0.0649548	−	0.127236i
$148$	3.13899	−	7.57836i	0.258023	−	0.622937i
$149$	−3.97112	−	6.87818i	−0.325327	−	0.563482i	0.656252	−	0.754542i	$-0.272141\pi$
$149$	−3.97112	−	6.87818i	−0.325327	−	0.563482i	−0.981578	+	0.191060i	$0.938808\pi$
$150$	−2.74135	−	0.399644i	−0.223830	−	0.0326308i
$151$	−14.2049	−	8.20120i	−1.15598	−	0.667404i	−0.205641	−	0.978627i	$-0.565928\pi$
$151$	−14.2049	−	8.20120i	−1.15598	−	0.667404i	−0.950337	+	0.311223i	$0.899261\pi$
$152$	15.9421	+	10.6519i	1.29308	+	0.863985i
$153$	16.2166	+	7.25034i	1.31103	+	0.586156i
$154$	1.24690	+	3.67319i	0.100478	+	0.295994i
$155$	−0.674495	−	0.389420i	−0.0541768	−	0.0312790i
$156$	3.22917	+	3.78677i	0.258540	+	0.303184i
$157$	0.210889	−	0.121757i	0.0168308	−	0.00971727i	−0.491561	−	0.870843i	$-0.663574\pi$
$157$	0.210889	−	0.121757i	0.0168308	−	0.00971727i	0.508392	+	0.861126i	$0.330240\pi$
$158$	3.74485	+	3.28412i	0.297924	+	0.261270i
$159$	−5.39800	−	8.32636i	−0.428089	−	0.660324i
$160$	−6.19482	+	12.5625i	−0.489744	+	0.993150i
$161$			8.73393i			0.688330i
$162$	6.47366	+	10.9586i	0.508619	+	0.860992i
$163$	18.5188			1.45051			0.725253	−	0.688483i	$-0.241723\pi$
$163$	18.5188			1.45051			0.725253	+	0.688483i	$0.241723\pi$
$164$	−10.1045	+	1.33036i	−0.789027	+	0.103884i
$165$	9.87068	−	6.39918i	0.768431	−	0.498175i
$166$	−1.36486	−	1.19694i	−0.105934	−	0.0929007i
$167$	5.87871	+	10.1822i	0.454908	+	0.787924i	0.998683	−	0.0513070i	$-0.0163387\pi$
$167$	5.87871	+	10.1822i	0.454908	+	0.787924i	−0.543775	+	0.839231i	$0.683005\pi$
$168$	−2.50804	+	4.20829i	−0.193500	+	0.324677i
$169$	−5.46804	+	9.47092i	−0.420618	+	0.728532i
$170$	19.6339	−	6.66489i	1.50585	−	0.511174i
$171$	8.30044	−	18.5653i	0.634751	−	1.41972i
$172$	−10.6194	+	8.14868i	−0.809721	+	0.621331i
$173$	6.24178	−	10.8111i	0.474554	−	0.821951i	−0.525022	−	0.851089i	$-0.675943\pi$
$173$	6.24178	−	10.8111i	0.474554	−	0.821951i	0.999575	+	0.0291377i	$0.00927613\pi$
$174$	−14.6644	−	2.13784i	−1.11171	−	0.162069i
$175$	−0.979458	+	0.565491i	−0.0740401	+	0.0427471i
$176$	−2.83983	−	10.5977i	−0.214060	−	0.798834i
$177$	6.44162	+	3.28848i	0.484182	+	0.247178i
$178$	−4.73644	+	23.8122i	−0.355011	+	1.78480i
$179$			7.96916i			0.595643i	0.954622	+	0.297822i	$0.0962601\pi$
$179$			7.96916i			0.595643i	−0.954622	+	0.297822i	$0.903740\pi$
$180$	14.2381	+	4.24153i	1.06125	+	0.316145i
$181$			9.30143i			0.691370i	0.938351	+	0.345685i	$0.112353\pi$
$181$			9.30143i			0.691370i	−0.938351	+	0.345685i	$0.887647\pi$
$182$	1.99268	+	0.396360i	0.147707	+	0.0293801i
$183$	−0.785711	−	15.2189i	−0.0580815	−	1.12501i
$184$	1.61539	−	24.6504i	0.119088	−	1.81725i
$185$	−8.79476	+	5.07766i	−0.646604	+	0.373317i
$186$	0.604698	+	0.477465i	0.0443386	+	0.0350094i
$187$	−8.12063	+	14.0653i	−0.593839	+	1.02856i
$188$	−15.2489	+	11.7011i	−1.11214	+	0.853390i
$189$	4.84667	+	1.87345i	0.352543	+	0.136274i
$190$	−7.63020	−	22.4776i	−0.553553	−	1.63069i
$191$	−8.66949	+	15.0160i	−0.627302	+	1.08652i	0.360789	+	0.932648i	$0.382508\pi$
$191$	−8.66949	+	15.0160i	−0.627302	+	1.08652i	−0.988091	+	0.153872i	$0.950826\pi$
$192$	7.85698	−	11.4135i	0.567028	−	0.823698i
$193$	−5.64861	−	9.78368i	−0.406596	−	0.704245i	0.587910	−	0.808927i	$-0.299951\pi$
$193$	−5.64861	−	9.78368i	−0.406596	−	0.704245i	−0.994506	+	0.104682i	$0.966618\pi$
$194$	−11.0486	+	12.5986i	−0.793245	+	0.904529i
$195$	−0.317670	−	6.15311i	−0.0227488	−	0.440634i
$196$	0.261068	+	1.98289i	0.0186477	+	0.141635i
$197$	−24.2124			−1.72506			−0.862531	−	0.506004i	$-0.831122\pi$
$197$	−24.2124			−1.72506			−0.862531	+	0.506004i	$0.831122\pi$
$198$	−10.5758	+	4.85560i	−0.751586	+	0.345072i
$199$		−	17.7091i		−	1.25537i	−0.778468	−	0.627684i	$-0.784003\pi$
$199$		−	17.7091i		−	1.25537i	0.778468	−	0.627684i	$-0.215997\pi$
$200$	2.86899	−	1.41487i	0.202868	−	0.100046i
$201$	2.97033	−	5.81840i	0.209511	−	0.410398i
$202$	−9.70237	+	11.0635i	−0.682656	+	0.778426i
$203$	−5.23947	+	3.02501i	−0.367739	+	0.212314i
$204$	−20.1710	+	3.72240i	−1.41225	+	0.260620i
$205$	10.9273	+	6.30886i	0.763193	+	0.440630i
$206$	6.02637	−	2.04570i	0.419877	−	0.142531i
$207$	−26.0625	+	2.69827i	−1.81147	+	0.187543i
$208$	−5.55077	−	1.48723i	−0.384876	−	0.103121i
$209$	16.1025	+	9.29678i	1.11383	+	0.643072i
$210$	5.63510	−	2.24312i	0.388859	−	0.154790i
$211$	−2.66241	−	4.61143i	−0.183288	−	0.317464i	0.759710	−	0.650262i	$-0.225341\pi$
$211$	−2.66241	−	4.61143i	−0.183288	−	0.317464i	−0.942998	+	0.332798i	$0.892007\pi$
$212$	10.5860	+	4.38476i	0.727048	+	0.301146i
$213$	12.6412	+	19.4990i	0.866164	+	1.33605i
$214$	−0.456397	+	2.29451i	−0.0311986	+	0.156849i
$215$	16.5718			1.13019
$216$	−13.3326	−	6.18400i	−0.907168	−	0.420768i
$217$	0.314545			0.0213527
$218$	0.0318747	−	0.160248i	0.00215882	−	0.0108534i
$219$	6.05346	+	9.33741i	0.409055	+	0.630964i
$220$	−5.19801	+	12.5494i	−0.350450	+	0.846079i
$221$	4.25330	+	7.36694i	0.286108	+	0.495554i
$222$	9.33393	−	3.71549i	0.626453	−	0.249367i
$223$	4.93561	+	2.84957i	0.330513	+	0.190822i	0.656069	−	0.754701i	$-0.272218\pi$
$223$	4.93561	+	2.84957i	0.330513	+	0.190822i	−0.325556	+	0.945523i	$0.605551\pi$
$224$	−0.370085	−	5.64474i	−0.0247273	−	0.377155i
$225$	−1.99005	−	2.74805i	−0.132670	−	0.183203i
$226$	8.45938	−	2.87161i	0.562709	−	0.191017i
$227$	−7.05079	−	4.07078i	−0.467978	−	0.270187i	0.247415	−	0.968910i	$-0.420419\pi$
$227$	−7.05079	−	4.07078i	−0.467978	−	0.270187i	−0.715393	+	0.698723i	$0.753752\pi$
$228$	4.26154	+	23.0925i	0.282227	+	1.52934i
$229$	−20.7549	+	11.9829i	−1.37153	+	0.791851i	−0.991120	−	0.132969i	$-0.957549\pi$
$229$	−20.7549	+	11.9829i	−1.37153	+	0.791851i	−0.380405	+	0.924820i	$0.624215\pi$
$230$	−20.1651	+	22.9941i	−1.32965	+	1.51619i
$231$	−2.16013	+	4.23136i	−0.142126	+	0.278403i
$232$	15.3472	−	7.56864i	1.00759	−	0.496905i
$233$			20.2965i			1.32967i	0.746991	+	0.664834i	$0.231498\pi$
$233$			20.2965i			1.32967i	−0.746991	+	0.664834i	$0.768502\pi$
$234$	−0.567138	+	6.06870i	−0.0370749	+	0.396723i
$235$	23.7963			1.55230
$236$	−8.27988	+	1.09013i	−0.538974	+	0.0709615i
$237$	0.314526	+	6.09221i	0.0204306	+	0.395732i
$238$	−5.52122	+	6.29580i	−0.357888	+	0.408096i
$239$	−0.853659	−	1.47858i	−0.0552186	−	0.0956415i	0.837095	−	0.547058i	$-0.184252\pi$
$239$	−0.853659	−	1.47858i	−0.0552186	−	0.0956415i	−0.892313	+	0.451416i	$0.850919\pi$
$240$	−16.3192	+	5.28868i	−1.05340	+	0.341383i
$241$	−7.65491	+	13.2587i	−0.493096	+	0.854067i	−0.999968	−	0.00795372i	$-0.997468\pi$
$241$	−7.65491	+	13.2587i	−0.493096	+	0.854067i	0.506872	+	0.862021i	$0.330802\pi$
$242$	1.58037	+	4.65555i	0.101590	+	0.299270i
$243$	−4.09315	+	15.0415i	−0.262575	+	0.964911i
$244$	10.7123	+	13.9603i	0.685782	+	0.893714i
$245$	1.23804	−	2.14435i	0.0790955	−	0.136997i
$246$	−9.79650	−	7.73525i	−0.624602	−	0.493181i
$247$	8.43392	−	4.86933i	0.536638	−	0.309828i
$248$	−0.887764	−	0.0581768i	−0.0563731	−	0.00369423i
$249$	−0.114633	−	2.22039i	−0.00726458	−	0.140711i
$250$	13.2879	+	2.64307i	0.840398	+	0.167162i
$251$		−	18.7484i		−	1.18339i	−0.806163	−	0.591694i	$-0.798459\pi$
$251$		−	18.7484i		−	1.18339i	0.806163	−	0.591694i	$-0.201541\pi$
$252$	−5.83638	+	1.39164i	−0.367657	+	0.0876648i
$253$		−	23.9563i		−	1.50612i
$254$	−4.30928	+	21.6646i	−0.270388	+	1.35936i
$255$	22.6174	+	11.5463i	1.41636	+	0.723059i
$256$	0.000493426		16.0000i	3.08391e−5		1.00000i
$257$	10.2048	−	5.89176i	0.636559	−	0.367518i	−0.146729	−	0.989177i	$-0.546874\pi$
$257$	10.2048	−	5.89176i	0.636559	−	0.367518i	0.783288	+	0.621659i	$0.213541\pi$
$258$	−16.2224	−	2.36496i	−1.00996	−	0.147236i
$259$	2.05068	−	3.55189i	0.127423	−	0.220703i
$260$	4.33106	+	5.64425i	0.268601	+	0.350042i
$261$	−10.6455	−	14.7003i	−0.658938	−	0.909925i
$262$	20.1637	−	6.84475i	1.24572	−	0.422870i
$263$	13.2014	−	22.8655i	0.814032	−	1.40995i	−0.0959885	−	0.995382i	$-0.530601\pi$
$263$	13.2014	−	22.8655i	0.814032	−	1.40995i	0.910021	−	0.414563i	$-0.136065\pi$
$264$	6.87932	−	11.5429i	0.423393	−	0.710419i
$265$	−7.09282	−	12.2851i	−0.435709	−	0.754669i
$266$	7.20765	+	6.32089i	0.441929	+	0.387558i
$267$	−24.9506	+	16.1755i	−1.52695	+	0.989926i
$268$	0.984663	+	7.47881i	0.0601479	+	0.456841i
$269$	−0.779333			−0.0475168			−0.0237584	−	0.999718i	$-0.507563\pi$
$269$	−0.779333			−0.0475168			−0.0237584	+	0.999718i	$0.507563\pi$
$270$	8.43449	+	16.1224i	0.513307	+	0.981179i
$271$		−	3.26037i		−	0.198053i	−0.995085	−	0.0990265i	$-0.968427\pi$
$271$		−	3.26037i		−	0.198053i	0.995085	−	0.0990265i	$-0.0315729\pi$
$272$	16.7474	−	16.7479i	1.01546	−	1.01549i
$273$	1.35362	+	2.08794i	0.0819246	+	0.126368i
$274$	4.27096	+	3.74550i	0.258018	+	0.226274i
$275$	2.68656	−	1.55109i	0.162006	−	0.0935341i
$276$	23.0214	−	19.6315i	1.38572	−	1.18167i
$277$	−23.5438	−	13.5930i	−1.41461	−	0.816726i	−0.418793	−	0.908082i	$-0.637547\pi$
$277$	−23.5438	−	13.5930i	−1.41461	−	0.816726i	−0.995818	+	0.0913550i	$0.970880\pi$
$278$	5.50195	+	16.2080i	0.329985	+	0.972093i
$279$	0.0971761	+	0.938619i	0.00581778	+	0.0561936i
$280$	−3.89082	+	5.82317i	−0.232521	+	0.348001i
$281$	8.95111	+	5.16793i	0.533979	+	0.308293i	0.742635	−	0.669696i	$-0.233576\pi$
$281$	8.95111	+	5.16793i	0.533979	+	0.308293i	−0.208656	+	0.977989i	$0.566909\pi$
$282$	−23.2945	−	3.39596i	−1.38717	−	0.202227i
$283$	−6.30816	−	10.9260i	−0.374981	−	0.649486i	0.615343	−	0.788259i	$-0.289017\pi$
$283$	−6.30816	−	10.9260i	−0.374981	−	0.649486i	−0.990324	+	0.138773i	$0.955684\pi$
$284$	−24.7907	−	10.2684i	−1.47106	−	0.609318i
$285$	13.2186	−	25.8932i	0.783005	−	1.53378i
$286$	−5.46572	−	1.08718i	−0.323195	−	0.0642861i
$287$	−5.09584			−0.300798
$288$	16.7298	−	2.84824i	0.985815	−	0.167834i
$289$	−18.0605			−1.06238
$290$	−20.7783	−	4.13299i	−1.22015	−	0.242697i
$291$	−20.4958	+	1.05815i	−1.20148	+	0.0620296i
$292$	−11.8714	−	4.91719i	−0.694721	−	0.287757i
$293$	7.42929	+	12.8679i	0.434024	+	0.751751i	0.997215	−	0.0745751i	$-0.0237600\pi$
$293$	7.42929	+	12.8679i	0.434024	+	0.751751i	−0.563192	+	0.826326i	$0.690427\pi$
$294$	−1.51795	+	1.92245i	−0.0885288	+	0.112120i
$295$	8.95409	+	5.16965i	0.521327	+	0.300988i
$296$	−6.44473	+	9.64546i	−0.374592	+	0.560631i
$297$	−13.2939	−	5.13871i	−0.771393	−	0.298178i
$298$	3.61045	+	10.6359i	0.209148	+	0.616122i
$299$	−10.8664	−	6.27375i	−0.628423	−	0.362820i
$300$	3.69210	+	1.31064i	0.213164	+	0.0756701i
$301$	−5.79610	+	3.34638i	−0.334082	+	0.192882i
$302$	17.4401	+	15.2944i	1.00357	+	0.880097i
$303$	−17.9984	+	0.929212i	−1.03398	+	0.0533818i
$304$	−19.1736	−	19.1730i	−1.09968	−	1.09965i
$305$		−	21.7853i		−	1.24743i
$306$	−20.4927	−	14.5306i	−1.17149	−	0.830658i
$307$	1.31337			0.0749579			0.0374789	−	0.999297i	$-0.488067\pi$
$307$	1.31337			0.0749579			0.0374789	+	0.999297i	$0.488067\pi$
$308$	−0.716084	−	5.43887i	−0.0408027	−	0.309909i
$309$	6.94212	+	3.54400i	0.394924	+	0.201611i
$310$	0.828114	+	0.726231i	0.0470337	+	0.0412471i
$311$	16.9036	+	29.2779i	0.958515	+	1.66020i	0.726111	+	0.687578i	$0.241326\pi$
$311$	16.9036	+	29.2779i	0.958515	+	1.66020i	0.232404	+	0.972619i	$0.425341\pi$
$312$	−3.43424	−	6.14331i	−0.194425	−	0.347797i
$313$	2.71174	−	4.69687i	0.153277	−	0.265483i	−0.779153	−	0.626833i	$-0.784351\pi$
$313$	2.71174	−	4.69687i	0.153277	−	0.265483i	0.932430	+	0.361350i	$0.117684\pi$
$314$	−0.326104	+	0.110699i	−0.0184031	+	0.00624710i
$315$	6.78133	+	3.03190i	0.382085	+	0.170828i
$316$	−4.28819	−	5.58839i	−0.241229	−	0.314371i
$317$	2.38945	−	4.13865i	0.134205	−	0.232450i	−0.791089	−	0.611702i	$-0.790485\pi$
$317$	2.38945	−	4.13865i	0.134205	−	0.232450i	0.925293	+	0.379252i	$0.123819\pi$
$318$	5.19005	+	13.0383i	0.291043	+	0.731151i
$319$	14.3714	−	8.29731i	0.804642	−	0.464560i
$320$	12.0584	−	15.7155i	0.674084	−	0.878525i
$321$	−2.40420	+	1.55865i	−0.134190	+	0.0869954i
$322$	2.40964	−	12.1143i	0.134284	−	0.675104i
$323$			40.1385i			2.23336i
$324$	−5.95581	−	16.9861i	−0.330878	−	0.943673i
$325$		−	1.62481i		−	0.0901283i
$326$	−25.6864	−	5.10923i	−1.42264	−	0.282974i
$327$	0.167909	−	0.108856i	0.00928540	−	0.00601974i
$328$	14.3824	+	0.942503i	0.794133	+	0.0520410i
$329$	−8.32292	+	4.80524i	−0.458857	+	0.264921i
$330$	−15.4565	+	6.15266i	−0.850854	+	0.338693i
$331$	−1.18337	+	2.04965i	−0.0650436	+	0.112659i	−0.896713	−	0.442612i	$-0.854052\pi$
$331$	−1.18337	+	2.04965i	−0.0650436	+	0.112659i	0.831670	+	0.555271i	$0.187385\pi$
$332$	1.56289	+	2.03676i	0.0857747	+	0.111782i
$333$	11.2325	+	5.02201i	0.615540	+	0.275205i
$334$	−5.34480	−	15.7451i	−0.292454	−	0.861532i
$335$	4.66949	−	8.08779i	0.255121	−	0.441883i
$336$	4.63980	−	5.14512i	0.253122	−	0.280689i
$337$	−9.36092	−	16.2136i	−0.509922	−	0.883210i	−0.999934	−	0.0114946i	$-0.996341\pi$
$337$	−9.36092	−	16.2136i	−0.509922	−	0.883210i	0.490012	−	0.871715i	$-0.336992\pi$
$338$	10.1974	−	11.6279i	0.554663	−	0.632477i
$339$	9.74485	+	4.97480i	0.529268	+	0.270194i
$340$	−29.0718	+	3.82761i	−1.57664	+	0.207581i
$341$	−0.862768			−0.0467215
$342$	−16.6351	+	23.4608i	−0.899523	+	1.26861i
$343$			1.00000i			0.0539949i
$344$	16.9777	−	8.37272i	0.915376	−	0.451427i
$345$	−37.4074	+	1.93125i	−2.01394	+	0.103975i
$346$	−11.6403	+	13.2733i	−0.625787	+	0.713579i
$347$	27.0437	−	15.6137i	1.45178	−	0.838186i	0.453198	−	0.891410i	$-0.350283\pi$
$347$	27.0437	−	15.6137i	1.45178	−	0.838186i	0.998583	+	0.0532240i	$0.0169497\pi$
$348$	19.7504	+	7.01110i	1.05873	+	0.375834i
$349$	16.6971	+	9.64005i	0.893773	+	0.516020i	0.875175	−	0.483807i	$-0.160746\pi$
$349$	16.6971	+	9.64005i	0.893773	+	0.516020i	0.0185983	+	0.999827i	$0.494080\pi$
$350$	1.51456	−	0.514132i	0.0809569	−	0.0274815i
$351$	−5.81234	+	4.68431i	−0.310240	+	0.250030i
$352$	1.01511	+	15.4830i	0.0541054	+	0.825245i
$353$	11.0506	+	6.38005i	0.588163	+	0.339576i	0.764371	−	0.644777i	$-0.223050\pi$
$353$	11.0506	+	6.38005i	0.588163	+	0.339576i	−0.176208	+	0.984353i	$0.556383\pi$
$354$	−8.02751	−	6.33847i	−0.426658	−	0.336886i
$355$	16.6103	+	28.7698i	0.881581	+	1.52694i
$356$	13.1393	−	31.7217i	0.696380	−	1.68125i
$357$	−10.2422	+	0.528777i	−0.542073	+	0.0279859i
$358$	2.19864	−	11.0536i	0.116202	−	0.584199i
$359$	27.2190			1.43656			0.718281	−	0.695753i	$-0.244929\pi$
$359$	27.2190			1.43656			0.718281	+	0.695753i	$0.244929\pi$
$360$	−18.5787	−	9.81139i	−0.979182	−	0.517106i
$361$	26.9519			1.41852
$362$	2.56621	−	12.9015i	0.134877	−	0.678086i
$363$	−2.73784	+	5.36300i	−0.143700	+	0.281485i
$364$	−2.65457	−	1.09953i	−0.139137	−	0.0576313i
$365$	7.95408	+	13.7769i	0.416336	+	0.721115i
$366$	−3.10898	+	21.3260i	−0.162509	+	1.11473i
$367$	−19.4721	−	11.2422i	−1.01644	−	0.586840i	−0.103366	−	0.994643i	$-0.532961\pi$
$367$	−19.4721	−	11.2422i	−1.01644	−	0.586840i	−0.913070	+	0.407804i	$0.866295\pi$
$368$	−9.04151	+	33.7454i	−0.471321	+	1.75910i
$369$	−1.57432	−	15.2062i	−0.0819556	−	0.791605i
$370$	13.5996	−	4.61650i	0.707009	−	0.240000i
$371$	4.96152	+	2.86453i	0.257589	+	0.148719i
$372$	−0.707011	−	0.829096i	−0.0366568	−	0.0429866i
$373$	−6.12679	+	3.53731i	−0.317233	+	0.183155i	−0.650159	−	0.759798i	$-0.725298\pi$
$373$	−6.12679	+	3.53731i	−0.317233	+	0.183155i	0.332925	+	0.942953i	$0.391964\pi$
$374$	15.1442	−	17.2688i	0.783088	−	0.892947i
$375$	9.02640	+	13.9231i	0.466121	+	0.718988i
$376$	24.3791	−	12.0228i	1.25726	−	0.620029i
$377$		−	8.69168i		−	0.447645i
$378$	−6.20565	−	3.93572i	−0.319184	−	0.202432i
$379$	6.79398			0.348984			0.174492	−	0.984659i	$-0.444172\pi$
$379$	6.79398			0.348984			0.174492	+	0.984659i	$0.444172\pi$
$380$	4.38197	+	33.2824i	0.224791	+	1.70735i
$381$	−22.7004	+	14.7167i	−1.16298	+	0.753960i
$382$	16.1678	−	18.4359i	0.827215	−	0.943265i
$383$	−9.33591	−	16.1703i	−0.477043	−	0.826262i	0.522611	−	0.852571i	$-0.324958\pi$
$383$	−9.33591	−	16.1703i	−0.477043	−	0.826262i	−0.999654	+	0.0263088i	$0.991625\pi$
$384$	−14.0469	+	13.6633i	−0.716826	+	0.697252i
$385$	−3.39583	+	5.88175i	−0.173067	+	0.299762i
$386$	5.13560	+	15.1288i	0.261395	+	0.770035i
$387$	−11.7764	−	16.2620i	−0.598630	−	0.826645i
$388$	18.8008	−	14.4266i	0.954465	−	0.732398i
$389$	−2.91649	+	5.05152i	−0.147872	+	0.256122i	−0.930441	−	0.366442i	$-0.880576\pi$
$389$	−2.91649	+	5.05152i	−0.147872	+	0.256122i	0.782569	+	0.622564i	$0.213909\pi$
$390$	−1.25699	+	8.62226i	−0.0636500	+	0.436605i
$391$	44.7867	−	25.8576i	2.26496	−	1.30768i
$392$	0.184955	−	2.82237i	0.00934166	−	0.142551i
$393$	23.2278	+	11.8579i	1.17169	+	0.598153i
$394$	33.5836	+	6.68006i	1.69192	+	0.336536i
$395$			8.72082i			0.438792i
$396$	16.0086	−	3.81712i	0.804464	−	0.191818i
$397$			23.6528i			1.18710i	0.804796	+	0.593551i	$0.202275\pi$
$397$			23.6528i			1.18710i	−0.804796	+	0.593551i	$0.797725\pi$
$398$	−4.88585	+	24.5633i	−0.244905	+	1.23125i
$399$	0.605362	+	11.7256i	0.0303060	+	0.587013i
$400$	−4.36976	+	1.17095i	−0.218488	+	0.0585473i
$401$	−4.01114	+	2.31583i	−0.200307	+	0.115647i	−0.596799	−	0.802391i	$-0.703561\pi$
$401$	−4.01114	+	2.31583i	−0.200307	+	0.115647i	0.396492	+	0.918038i	$0.370228\pi$
$402$	−5.72523	+	7.25086i	−0.285548	+	0.361640i
$403$	−0.225944	+	0.391346i	−0.0112551	+	0.0194943i
$404$	16.5099	−	12.6687i	0.821400	−	0.630292i
$405$	−6.95230	+	21.1725i	−0.345463	+	1.05207i
$406$	8.10194	−	2.75027i	0.402092	−	0.136494i
$407$	−5.62483	+	9.74249i	−0.278812	+	0.482917i
$408$	29.0050	+	0.401936i	1.43596	+	0.0198988i
$409$	−0.869796	−	1.50653i	−0.0430086	−	0.0744931i	0.843720	−	0.536784i	$-0.180361\pi$
$409$	−0.869796	−	1.50653i	−0.0430086	−	0.0744931i	−0.886728	+	0.462291i	$0.847028\pi$
$410$	−13.4160	−	11.7654i	−0.662568	−	0.581052i
$411$	0.358713	+	6.94811i	0.0176940	+	0.342725i
$412$	−8.92322	+	1.17483i	−0.439615	+	0.0578799i
$413$	−4.17567			−0.205471
$414$	36.8942	+	3.44787i	1.81325	+	0.169453i
$415$		−	3.17842i		−	0.156023i
$416$	7.28882	+	3.59427i	0.357364	+	0.176224i
$417$	−9.53165	+	18.6710i	−0.466767	+	0.914322i
$418$	−19.7699	−	17.3376i	−0.966977	−	0.848009i
$419$	−0.814802	+	0.470426i	−0.0398057	+	0.0229818i	−0.519771	−	0.854306i	$-0.673983\pi$
$419$	−0.814802	+	0.470426i	−0.0398057	+	0.0229818i	0.479965	+	0.877288i	$0.340649\pi$
$420$	−8.43497	+	1.55661i	−0.411584	+	0.0759547i
$421$	6.79938	+	3.92562i	0.331381	+	0.191323i	0.656454	−	0.754366i	$-0.272055\pi$
$421$	6.79938	+	3.92562i	0.331381	+	0.191323i	−0.325073	+	0.945689i	$0.605389\pi$
$422$	2.42061	+	7.13079i	0.117833	+	0.347121i
$423$	−16.9104	−	23.3515i	−0.822210	−	1.13539i
$424$	−13.4735	−	9.00245i	−0.654329	−	0.437197i
$425$	5.79956	+	3.34838i	0.281320	+	0.162420i
$426$	−12.1543	−	30.5336i	−0.588876	−	1.47936i
$427$	4.39916	+	7.61956i	0.212890	+	0.368736i
$428$	1.26608	−	3.05666i	0.0611984	−	0.147749i
$429$	−3.71284	−	5.72703i	−0.179258	−	0.276504i
$430$	−22.9858	−	4.57207i	−1.10847	−	0.220485i
$431$	−12.8305			−0.618021			−0.309011	−	0.951059i	$-0.599998\pi$
$431$	−12.8305			−0.618021			−0.309011	+	0.951059i	$0.599998\pi$
$432$	16.7867	+	12.2559i	0.807652	+	0.589660i
$433$	14.1477			0.679893			0.339947	−	0.940445i	$-0.389591\pi$
$433$	14.1477			0.679893			0.339947	+	0.940445i	$0.389591\pi$
$434$	−0.436287	−	0.0867812i	−0.0209425	−	0.00416563i
$435$	−14.1146	−	21.7717i	−0.676746	−	1.04387i
$436$	−0.0884229	+	0.213476i	−0.00423469	+	0.0102237i
$437$	−29.6027	−	51.2734i	−1.41609	−	2.45274i
$438$	−5.82026	−	14.6215i	−0.278103	−	0.698642i
$439$	−22.5359	−	13.0111i	−1.07558	−	0.620985i	−0.145878	−	0.989303i	$-0.546601\pi$
$439$	−22.5359	−	13.0111i	−1.07558	−	0.620985i	−0.929700	+	0.368317i	$0.879934\pi$
$440$	10.6722	−	15.9724i	0.508775	−	0.761455i
$441$	−2.98405	+	0.308941i	−0.142098	+	0.0147115i
$442$	−3.86701	−	11.3917i	−0.183935	−	0.541848i
$443$	17.8379	+	10.2987i	0.847504	+	0.489307i	0.859808	−	0.510618i	$-0.170583\pi$
$443$	17.8379	+	10.2987i	0.847504	+	0.489307i	−0.0123038	+	0.999924i	$0.503917\pi$
$444$	−13.9716	+	2.57836i	−0.663064	+	0.122363i
$445$	−36.8134	+	21.2542i	−1.74512	+	1.00755i
$446$	−6.05971	−	5.31418i	−0.286935	−	0.251634i
$447$	−6.25479	+	12.2521i	−0.295841	+	0.579506i
$448$	−1.04403	+	7.93158i	−0.0493256	+	0.374732i
$449$		−	28.5153i		−	1.34572i	−0.739770	−	0.672860i	$-0.765066\pi$
$449$		−	28.5153i		−	1.34572i	0.739770	−	0.672860i	$-0.234934\pi$
$450$	2.00211	+	4.36070i	0.0943802	+	0.205565i
$451$	13.9774			0.658170
$452$	−12.5258	+	1.64915i	−0.589162	+	0.0775693i
$453$	1.46478	+	28.3720i	0.0688212	+	1.33303i
$454$	8.65664	+	7.59161i	0.406276	+	0.356292i
$455$	1.77862	+	3.08065i	0.0833828	+	0.144423i
$456$	0.460151	−	33.2059i	0.0215485	−	1.55501i
$457$	12.9748	−	22.4730i	0.606935	−	1.05124i	−0.384808	−	0.922997i	$-0.625732\pi$
$457$	12.9748	−	22.4730i	0.606935	−	1.05124i	0.991742	−	0.128245i	$-0.0409345\pi$
$458$	32.0940	−	10.8946i	1.49965	−	0.509070i
$459$	−4.74213	−	30.3998i	−0.221343	−	1.41894i
$460$	34.3138	−	26.3303i	1.59989	−	1.22766i
$461$	5.24916	−	9.09181i	0.244478	−	0.423448i	−0.717507	−	0.696551i	$-0.754717\pi$
$461$	5.24916	−	9.09181i	0.244478	−	0.423448i	0.961985	+	0.273104i	$0.0880502\pi$
$462$	4.16360	−	5.27310i	0.193708	−	0.245327i
$463$	18.1567	−	10.4828i	0.843815	−	0.487177i	−0.0147444	−	0.999891i	$-0.504693\pi$
$463$	18.1567	−	10.4828i	0.843815	−	0.487177i	0.858559	+	0.512715i	$0.171360\pi$
$464$	−23.3754	+	6.26380i	−1.08517	+	0.290790i
$465$	0.0695523	+	1.34720i	0.00322541	+	0.0624747i
$466$	5.59968	−	28.1521i	0.259400	−	1.30412i
$467$		−	26.9213i		−	1.24577i	−0.782315	−	0.622884i	$-0.785961\pi$
$467$		−	26.9213i		−	1.24577i	0.782315	−	0.622884i	$-0.214039\pi$
$468$	2.46096	−	8.26106i	0.113758	−	0.381868i
$469$			3.77168i			0.174160i
$470$	−33.0065	−	6.56526i	−1.52248	−	0.302833i
$471$	−0.375659	−	0.191776i	−0.0173094	−	0.00883657i
$472$	11.7853	+	0.772312i	0.542462	+	0.0355485i
$473$	15.8982	−	9.17881i	0.730998	−	0.422042i
$474$	1.24455	−	8.53692i	0.0571639	−	0.392114i
$475$	3.83334	−	6.63954i	0.175886	−	0.304643i
$476$	9.39514	−	7.20926i	0.430625	−	0.330436i
$477$	−7.01510	+	15.6904i	−0.321199	+	0.718414i
$478$	0.776128	+	2.28637i	0.0354993	+	0.104576i
$479$	−1.76317	+	3.05391i	−0.0805614	+	0.139537i	−0.903491	−	0.428607i	$-0.859005\pi$
$479$	−1.76317	+	3.05391i	−0.0805614	+	0.139537i	0.822930	+	0.568143i	$0.192338\pi$
$480$	24.0945	−	2.83324i	1.09976	−	0.129319i
$481$	2.94609	+	5.10277i	0.134330	+	0.232666i
$482$	14.2757	−	16.2784i	0.650239	−	0.741461i
$483$	12.6935	−	8.22921i	0.577574	−	0.374442i
$484$	−0.907595	−	6.89345i	−0.0412543	−	0.313339i
$485$	−29.3391			−1.33222
$486$	9.82722	−	19.7339i	0.445772	−	0.895147i
$487$			39.8913i			1.80765i	0.427903	+	0.903825i	$0.359252\pi$
$487$			39.8913i			1.80765i	−0.427903	+	0.903825i	$0.640748\pi$
$488$	−11.0068	−	22.3189i	−0.498254	−	1.01033i
$489$	−17.4486	−	26.9144i	−0.789055	−	1.21711i
$490$	−2.30883	+	2.63273i	−0.104302	+	0.118935i
$491$	−23.9763	+	13.8427i	−1.08203	+	0.624713i	−0.931444	−	0.363884i	$-0.881451\pi$
$491$	−23.9763	+	13.8427i	−1.08203	+	0.624713i	−0.150590	+	0.988596i	$0.548117\pi$
$492$	11.4540	+	13.4319i	0.516388	+	0.605557i
$493$	31.0239	+	17.9117i	1.39725	+	0.806700i
$494$	−13.0416	+	4.42709i	−0.586770	+	0.199184i
$495$	−18.6005	−	8.31621i	−0.836032	−	0.373786i
$496$	1.21531	+	0.325623i	0.0545692	+	0.0146209i
$497$	−11.6191	−	6.70828i	−0.521187	−	0.300908i
$498$	−0.453591	+	3.11140i	−0.0203259	+	0.139425i
$499$	−3.81590	−	6.60933i	−0.170823	−	0.295874i	0.767885	−	0.640588i	$-0.221309\pi$
$499$	−3.81590	−	6.60933i	−0.170823	−	0.295874i	−0.938708	+	0.344714i	$0.887976\pi$
$500$	−17.7016	−	7.33208i	−0.791640	−	0.327901i
$501$	9.25939	−	18.1377i	0.413679	−	0.810331i
$502$	−5.17257	+	26.0048i	−0.230863	+	1.16065i
$503$	8.13674			0.362799			0.181400	−	0.983409i	$-0.441937\pi$
$503$	8.13674			0.362799			0.181400	+	0.983409i	$0.441937\pi$
$504$	8.47924	−	0.320032i	0.377696	−	0.0142554i
$505$	−25.7642			−1.14649
$506$	−6.60941	+	33.2284i	−0.293824	+	1.47718i
$507$	18.9166	−	0.976618i	0.840117	−	0.0433731i
$508$	11.9543	−	28.8608i	0.530386	−	1.28049i
$509$	−1.38964	−	2.40692i	−0.0615946	−	0.106685i	0.833584	−	0.552393i	$-0.186285\pi$
$509$	−1.38964	−	2.40692i	−0.0615946	−	0.106685i	−0.895178	+	0.445708i	$0.852952\pi$
$510$	−28.1857	−	22.2552i	−1.24809	−	0.985479i
$511$	−5.56398	−	3.21237i	−0.246136	−	0.142107i
$512$	4.41362	−	22.1928i	0.195056	−	0.980792i
$513$	−34.8027	+	5.42895i	−1.53658	+	0.239694i
$514$	−15.7800	+	5.35666i	−0.696026	+	0.236272i
$515$	9.64981	+	5.57132i	0.425222	+	0.245502i
$516$	21.8486	+	7.75595i	0.961832	+	0.341437i
$517$	22.8290	−	13.1803i	1.00402	−	0.579669i
$518$	−3.82432	+	4.36084i	−0.168031	+	0.191604i
$519$	−21.5934	+	1.11481i	−0.947845	+	0.0489349i
$520$	−4.45014	−	9.02372i	−0.195151	−	0.395716i
$521$			3.80032i			0.166495i	0.996529	+	0.0832475i	$0.0265292\pi$
$521$			3.80032i			0.166495i	−0.996529	+	0.0832475i	$0.973471\pi$
$522$	10.7100	+	23.3269i	0.468763	+	1.02099i
$523$	−35.0380			−1.53210			−0.766052	−	0.642779i	$-0.777781\pi$
$523$	−35.0380			−1.53210			−0.766052	+	0.642779i	$0.777781\pi$
$524$	−29.8563	+	3.93090i	−1.30428	+	0.171722i
$525$	1.74471	+	0.890688i	0.0761456	+	0.0388728i
$526$	−24.6193	+	28.0732i	−1.07345	+	1.22405i
$527$	−0.931241	−	1.61296i	−0.0405655	−	0.0702615i
$528$	−12.7265	+	14.1126i	−0.553851	+	0.614171i
$529$	−26.6407	+	46.1431i	−1.15829	+	2.00622i
$530$	6.44864	+	18.9968i	0.280111	+	0.825170i
$531$	−1.29004	−	12.4604i	−0.0559828	−	0.540735i
$532$	−8.25341	−	10.7559i	−0.357831	−	0.466326i
$533$	3.66044	−	6.34007i	0.158551	−	0.274619i
$534$	39.0702	−	15.5524i	1.69073	−	0.673018i
$535$	−3.54728	+	2.04802i	−0.153362	+	0.0885438i
$536$	0.697592	−	10.6451i	0.0301314	−	0.459797i
$537$	11.5820	−	7.50864i	0.499801	−	0.324022i
$538$	1.08097	+	0.215013i	0.0466038	+	0.00926988i
$539$		−	2.74290i		−	0.118145i
$540$	−7.25091	−	24.6895i	−0.312029	−	1.06247i
$541$			13.2988i			0.571759i	0.958266	+	0.285879i	$0.0922857\pi$
$541$			13.2988i			0.571759i	−0.958266	+	0.285879i	$0.907714\pi$
$542$	−0.899515	+	4.52226i	−0.0386375	+	0.194248i
$543$	13.5183	−	8.76392i	0.580124	−	0.376096i
$544$	−27.8500	+	18.6095i	−1.19406	+	0.797877i
$545$	0.247742	−	0.143034i	0.0106121	−	0.00612689i
$546$	−1.30147	−	3.26952i	−0.0556978	−	0.139922i
$547$	13.1118	−	22.7104i	0.560621	−	0.971025i	−0.436821	−	0.899549i	$-0.643896\pi$
$547$	13.1118	−	22.7104i	0.560621	−	0.971025i	0.997442	−	0.0714763i	$-0.0227710\pi$
$548$	−4.89064	−	6.37350i	−0.208918	−	0.272262i
$549$	−21.3781	+	15.4813i	−0.912394	+	0.660726i
$550$	−4.15431	+	1.41021i	−0.177140	+	0.0601318i
$551$	20.5059	−	35.5172i	0.873580	−	1.51308i
$552$	−37.3478	+	20.8782i	−1.58963	+	0.888634i
$553$	−1.76101	−	3.05016i	−0.0748859	−	0.129706i
$554$	28.9060	+	25.3497i	1.22810	+	1.07701i
$555$	15.6662	+	7.99767i	0.664991	+	0.339482i
$556$	−3.15974	−	23.9992i	−0.134003	−	1.01779i
$557$	15.2311			0.645363			0.322682	−	0.946508i	$-0.395416\pi$
$557$	15.2311			0.645363			0.322682	+	0.946508i	$0.395416\pi$
$558$	0.124172	−	1.32871i	0.00525663	−	0.0562489i
$559$		−	9.61508i		−	0.406675i
$560$	7.00331	−	7.00352i	0.295944	−	0.295953i
$561$	28.0933	−	1.45039i	1.18610	−	0.0612353i
$562$	−10.9898	−	9.63769i	−0.463575	−	0.406541i
$563$	−8.07835	+	4.66404i	−0.340462	+	0.196566i	−0.660476	−	0.750847i	$-0.729646\pi$
$563$	−8.07835	+	4.66404i	−0.340462	+	0.196566i	0.320014	+	0.947413i	$0.396312\pi$
$564$	31.3735	+	11.1372i	1.32106	+	0.468959i
$565$	13.5457	+	7.82062i	0.569872	+	0.329016i
$566$	5.73524	+	16.8953i	0.241070	+	0.710161i
$567$	−1.84379	−	8.80911i	−0.0774321	−	0.369948i
$568$	31.5527	+	21.0823i	1.32392	+	0.884593i
$569$	−3.15096	−	1.81921i	−0.132095	−	0.0762651i	0.432496	−	0.901636i	$-0.357633\pi$
$569$	−3.15096	−	1.81921i	−0.132095	−	0.0762651i	−0.564591	+	0.825371i	$0.690966\pi$
$570$	−25.4786	+	32.2680i	−1.06718	+	1.35156i
$571$	21.5459	+	37.3186i	0.901667	+	1.56173i	0.825330	+	0.564651i	$0.190989\pi$
$571$	21.5459	+	37.3186i	0.901667	+	1.56173i	0.0763372	+	0.997082i	$0.475677\pi$
$572$	7.28123	+	3.01592i	0.304444	+	0.126102i
$573$	29.9920	−	1.54841i	1.25294	−	0.0646859i
$574$	7.06814	+	1.40591i	0.295018	+	0.0586816i
$575$	−9.87791			−0.411937
$576$	−23.9908	−	0.665031i	−0.999616	−	0.0277096i
$577$	−0.957969			−0.0398808			−0.0199404	−	0.999801i	$-0.506348\pi$
$577$	−0.957969			−0.0398808			−0.0199404	+	0.999801i	$0.506348\pi$
$578$	25.0507	+	4.98278i	1.04197	+	0.207256i
$579$	−8.89696	+	17.4277i	−0.369745	+	0.724272i
$580$	27.6801	+	11.4652i	1.14936	+	0.476068i
$581$	0.641825	+	1.11167i	0.0266274	+	0.0461200i
$582$	28.7204	+	4.18697i	1.19050	+	0.173556i
$583$	−13.6090	−	7.85715i	−0.563626	−	0.325410i
$584$	15.1095	+	10.0956i	0.625235	+	0.417758i
$585$	−8.64334	+	6.25922i	−0.357358	+	0.258787i
$586$	−6.75455	−	19.8980i	−0.279028	−	0.821979i
$587$	−11.9397	−	6.89339i	−0.492804	−	0.284521i	0.232933	−	0.972493i	$-0.425168\pi$
$587$	−11.9397	−	6.89339i	−0.492804	−	0.284521i	−0.725737	+	0.687972i	$0.758501\pi$
$588$	2.63586	−	2.24772i	0.108701	−	0.0926946i
$589$	−1.84657	+	1.06612i	−0.0760866	+	0.0439286i
$590$	−10.9934	−	9.64089i	−0.452592	−	0.396909i
$591$	22.8132	+	35.1892i	0.938410	+	1.44749i
$592$	11.6002	−	11.6006i	0.476767	−	0.476781i
$593$			35.3495i			1.45163i	0.687889	+	0.725816i	$0.258538\pi$
$593$			35.3495i			1.45163i	−0.687889	+	0.725816i	$0.741462\pi$
$594$	17.0215	+	10.7953i	0.698401	+	0.442937i
$595$	−14.6614			−0.601057
$596$	−2.07346	−	15.7486i	−0.0849323	−	0.645086i
$597$	−25.7376	+	16.6858i	−1.05337	+	0.682903i
$598$	13.3413	+	11.6999i	0.545567	+	0.478446i
$599$	5.24145	+	9.07845i	0.214160	+	0.370936i	0.953012	−	0.302932i	$-0.0979653\pi$
$599$	5.24145	+	9.07845i	0.214160	+	0.370936i	−0.738853	+	0.673867i	$0.764632\pi$
$600$	−4.75950	−	2.83655i	−0.194306	−	0.115802i
$601$	6.69581	−	11.5975i	0.273128	−	0.473071i	−0.696533	−	0.717524i	$-0.745275\pi$
$601$	6.69581	−	11.5975i	0.273128	−	0.473071i	0.969661	+	0.244453i	$0.0786085\pi$
$602$	8.96268	−	3.04246i	0.365292	−	0.124001i
$603$	−11.2549	+	1.16523i	−0.458334	+	0.0474517i
$604$	−19.9705	−	26.0256i	−0.812588	−	1.05897i
$605$	−4.30401	+	7.45477i	−0.174983	+	0.303080i
$606$	25.2209	+	3.67680i	1.02453	+	0.149360i
$607$	−8.15719	+	4.70955i	−0.331090	+	0.191155i	−0.656325	−	0.754478i	$-0.727890\pi$
$607$	−8.15719	+	4.70955i	−0.331090	+	0.191155i	0.325235	+	0.945633i	$0.394557\pi$
$608$	21.3048	+	31.8836i	0.864025	+	1.29305i
$609$	9.33310	+	4.76460i	0.378196	+	0.193071i
$610$	−6.01045	+	30.2172i	−0.243356	+	1.22346i
$611$		−	13.8068i		−	0.558562i
$612$	24.4153	+	25.8083i	0.986931	+	1.04324i
$613$			16.8678i			0.681286i	0.940193	+	0.340643i	$0.110645\pi$
$613$			16.8678i			0.681286i	−0.940193	+	0.340643i	$0.889355\pi$
$614$	−1.82170	−	0.362350i	−0.0735176	−	0.0146233i
$615$	−1.12679	−	21.8255i	−0.0454367	−	0.880087i
$616$	−0.507315	+	7.74150i	−0.0204403	+	0.311914i
$617$	6.32173	−	3.64985i	0.254503	−	0.146938i	−0.367321	−	0.930094i	$-0.619725\pi$
$617$	6.32173	−	3.64985i	0.254503	−	0.146938i	0.621825	+	0.783157i	$0.286392\pi$
$618$	−8.65124	−	6.83096i	−0.348004	−	0.274781i
$619$	−16.4695	+	28.5260i	−0.661965	+	1.14656i	0.318133	+	0.948046i	$0.396944\pi$
$619$	−16.4695	+	28.5260i	−0.661965	+	1.14656i	−0.980099	+	0.198512i	$0.936389\pi$
$620$	−0.948265	−	1.23578i	−0.0380832	−	0.0496302i
$621$	28.4779	+	35.3356i	1.14278	+	1.41797i
$622$	−15.3684	−	45.2732i	−0.616216	−	1.81529i
$623$	8.58380	−	14.8676i	0.343903	−	0.595657i
$624$	3.06852	+	9.46851i	0.122839	+	0.379044i
$625$	14.6879	+	25.4402i	0.587516	+	1.01761i
$626$	−5.05714	+	5.76660i	−0.202124	+	0.230480i
$627$	−1.66045	−	32.1622i	−0.0663120	−	1.28443i
$628$	0.482861	−	0.0635737i	0.0192683	−	0.00253687i
$629$	−24.2850			−0.968305
$630$	−8.56950	−	6.07629i	−0.341417	−	0.242085i
$631$			4.04934i			0.161202i	0.996746	+	0.0806008i	$0.0256839\pi$
$631$			4.04934i			0.161202i	−0.996746	+	0.0806008i	$0.974316\pi$
$632$	4.40609	+	8.93441i	0.175265	+	0.355392i
$633$	−4.19348	+	8.21437i	−0.166676	+	0.326492i
$634$	−4.45609	+	5.08124i	−0.176974	+	0.201802i
$635$	−33.4933	+	19.3374i	−1.32914	+	0.767379i
$636$	−3.60162	−	19.5165i	−0.142814	−	0.773881i
$637$	−1.24416	−	0.718319i	−0.0492956	−	0.0284608i
$638$	−22.2228	+	7.54374i	−0.879811	+	0.298659i
$639$	16.4282	−	36.7444i	0.649891	−	1.45359i
$640$	−21.0613	+	18.4713i	−0.832521	+	0.730141i
$641$	−43.4334	−	25.0763i	−1.71551	−	0.990453i	−0.926684	−	0.375842i	$-0.877354\pi$
$641$	−43.4334	−	25.0763i	−1.71551	−	0.990453i	−0.788830	−	0.614611i	$-0.789313\pi$
$642$	3.76475	−	1.49861i	0.148583	−	0.0591452i
$643$	−4.72901	−	8.19089i	−0.186494	−	0.323017i	0.757585	−	0.652737i	$-0.226379\pi$
$643$	−4.72901	−	8.19089i	−0.186494	−	0.323017i	−0.944079	+	0.329719i	$0.893046\pi$
$644$	−6.68453	+	16.1382i	−0.263408	+	0.635936i
$645$	−15.6142	−	24.0847i	−0.614808	−	0.948336i
$646$	11.0740	−	55.6737i	0.435699	−	2.19045i
$647$	−31.2520			−1.22864			−0.614322	−	0.789055i	$-0.710570\pi$
$647$	−31.2520			−1.22864			−0.614322	+	0.789055i	$0.710570\pi$
$648$	3.57458	+	25.2036i	0.140423	+	0.990092i
$649$	11.4535			0.449587
$650$	−0.448275	+	2.25368i	−0.0175828	+	0.0883965i
$651$	−0.296368	−	0.457146i	−0.0116156	−	0.0179169i
$652$	34.2184	+	14.1734i	1.34010	+	0.555074i
$653$	19.1340	+	33.1411i	0.748773	+	1.29691i	0.948411	+	0.317043i	$0.102690\pi$
$653$	19.1340	+	33.1411i	0.748773	+	1.29691i	−0.199638	+	0.979870i	$0.563977\pi$
$654$	−0.262930	+	0.104662i	−0.0102814	+	0.00409262i
$655$	32.2875	+	18.6412i	1.26158	+	0.728371i
$656$	−19.6889	−	5.27530i	−0.768722	−	0.205966i
$657$	7.86692	−	17.5956i	0.306918	−	0.686471i
$658$	12.8700	−	4.36882i	0.501723	−	0.170314i
$659$	30.2600	+	17.4706i	1.17876	+	0.680558i	0.955728	−	0.294252i	$-0.0950707\pi$
$659$	30.2600	+	17.4706i	1.17876	+	0.680558i	0.223034	+	0.974811i	$0.428404\pi$
$660$	23.1363	−	4.26963i	0.900580	−	0.166195i
$661$	−17.1104	+	9.87869i	−0.665517	+	0.384237i	−0.794376	−	0.607426i	$-0.792202\pi$
$661$	−17.1104	+	9.87869i	−0.665517	+	0.384237i	0.128859	+	0.991663i	$0.458869\pi$
$662$	2.20686	−	2.51646i	0.0857721	−	0.0978051i
$663$	6.69925	−	13.1228i	0.260177	−	0.509646i
$664$	−1.60586	−	3.25627i	−0.0623194	−	0.126368i
$665$			16.7848i			0.650887i
$666$	−14.1945	−	10.0647i	−0.550024	−	0.390000i
$667$	−52.8404			−2.04599
$668$	3.06948	+	23.3136i	0.118762	+	0.902032i
$669$	−0.508948	−	9.85808i	−0.0196771	−	0.381135i
$670$	−8.70815	+	9.92982i	−0.336425	+	0.383622i
$671$	−12.0665	−	20.8997i	−0.465821	−	0.806825i
$672$	−7.85510	+	5.85640i	−0.303017	+	0.225916i
$673$	−10.8106	+	18.7245i	−0.416718	+	0.721776i	−0.995607	−	0.0936300i	$-0.970153\pi$
$673$	−10.8106	+	18.7245i	−0.416718	+	0.721776i	0.578889	+	0.815406i	$0.303486\pi$
$674$	8.51074	+	25.0715i	0.327822	+	0.965719i
$675$	−2.11884	+	5.48149i	−0.0815542	+	0.210983i
$676$	−17.3522	+	13.3151i	−0.667394	+	0.512117i
$677$	−8.47152	+	14.6731i	−0.325587	+	0.563933i	−0.981631	−	0.190789i	$-0.938895\pi$
$677$	−8.47152	+	14.6731i	−0.325587	+	0.563933i	0.656044	+	0.754723i	$0.272229\pi$
$678$	−12.1440	−	9.58880i	−0.466387	−	0.368256i
$679$	10.2615	−	5.92450i	0.393802	−	0.227361i
$680$	41.3798	+	2.71170i	1.58684	+	0.103989i
$681$	0.727061	+	14.0828i	0.0278610	+	0.539655i
$682$	1.19669	+	0.238033i	0.0458238	+	0.00911474i
$683$		−	39.0952i		−	1.49594i	−0.663734	−	0.747969i	$-0.731029\pi$
$683$		−	39.0952i		−	1.49594i	0.663734	−	0.747969i	$-0.268971\pi$
$684$	29.5463	−	27.9515i	1.12973	−	1.06875i
$685$			9.94601i			0.380017i
$686$	0.275894	−	1.38704i	0.0105337	−	0.0529575i
$687$	36.9709	+	18.8739i	1.41053	+	0.720083i
$688$	−25.8588	+	6.92926i	−0.985856	+	0.264176i
$689$	−7.12791	+	4.11530i	−0.271552	+	0.156780i
$690$	52.4184	+	7.64175i	1.99553	+	0.290916i
$691$	−13.6515	+	23.6450i	−0.519327	+	0.899500i	0.480421	+	0.877038i	$0.340484\pi$
$691$	−13.6515	+	23.6450i	−0.519327	+	0.899500i	−0.999748	+	0.0224621i	$0.992849\pi$
$692$	19.8076	−	15.1992i	0.752973	−	0.577786i
$693$	8.18497	−	0.847397i	0.310921	−	0.0321900i
$694$	−41.8184	+	14.1956i	−1.58740	+	0.538858i
$695$	−14.9842	+	25.9534i	−0.568382	+	0.984467i
$696$	−25.4602	−	15.1737i	−0.965068	−	0.575157i
$697$	15.0867	+	26.1310i	0.571450	+	0.989781i
$698$	−20.4999	−	17.9778i	−0.775932	−	0.680468i
$699$	29.4980	−	19.1236i	1.11572	−	0.723321i
$700$	−2.24261	+	0.295263i	−0.0847626	+	0.0111599i
$701$	21.3653			0.806958			0.403479	−	0.914989i	$-0.367801\pi$
$701$	21.3653			0.806958			0.403479	+	0.914989i	$0.367801\pi$
$702$	9.35433	−	4.89375i	0.353056	−	0.184703i
$703$			27.8023i			1.04858i
$704$	2.86366	−	21.7556i	0.107928	−	0.819944i
$705$	−22.4212	−	34.5845i	−0.844430	−	1.30253i
$706$	−13.5674	−	11.8982i	−0.510615	−	0.447794i
$707$	9.01119	−	5.20261i	0.338901	−	0.195664i
$708$	9.38574	+	11.0065i	0.352738	+	0.413648i
$709$	28.3142	+	16.3472i	1.06336	+	0.613933i	0.926361	−	0.376638i	$-0.122920\pi$
$709$	28.3142	+	16.3472i	1.06336	+	0.613933i	0.137002	+	0.990571i	$0.456253\pi$
$710$	−15.1017	−	44.4876i	−0.566756	−	1.66959i
$711$	8.55779	−	6.19727i	0.320942	−	0.232416i
$712$	−26.9765	+	40.3743i	−1.01099	+	1.51309i
$713$	2.37916	+	1.37361i	0.0891002	+	0.0514420i
$714$	14.3522	+	2.09232i	0.537117	+	0.0783030i
$715$	−4.87858	−	8.44994i	−0.182448	−	0.316010i
$716$	−6.09922	+	14.7251i	−0.227939	+	0.550304i
$717$	−1.34457	+	2.63381i	−0.0502140	+	0.0983613i
$718$	−37.7538	−	7.50955i	−1.40896	−	0.280254i
$719$	−2.40631			−0.0897402			−0.0448701	−	0.998993i	$-0.514287\pi$
$719$	−2.40631			−0.0897402			−0.0448701	+	0.998993i	$0.514287\pi$
$720$	23.0625	+	18.7345i	0.859488	+	0.698195i
$721$	−4.50011			−0.167593
$722$	−37.3834	−	7.43587i	−1.39127	−	0.276734i
$723$	26.4821	−	1.36720i	0.984880	−	0.0508469i
$724$	−7.11887	+	17.1869i	−0.264571	+	0.638744i
$725$	−3.42123	−	5.92574i	−0.127061	−	0.220076i
$726$	5.27712	−	6.68335i	0.195852	−	0.248042i
$727$	−9.28073	−	5.35823i	−0.344203	−	0.198726i	0.317926	−	0.948116i	$-0.397014\pi$
$727$	−9.28073	−	5.35823i	−0.344203	−	0.198726i	−0.662129	+	0.749390i	$0.730347\pi$
$728$	3.37864	+	2.25748i	0.125221	+	0.0836678i
$729$	25.7172	−	8.22347i	0.952489	−	0.304573i
$730$	−7.23168	−	21.3036i	−0.267657	−	0.788481i
$731$	34.3198	+	19.8146i	1.26937	+	0.732868i
$732$	10.1960	−	28.7222i	0.376854	−	1.06160i
$733$	−8.93606	+	5.15924i	−0.330061	+	0.190561i	−0.655868	−	0.754875i	$-0.727697\pi$
$733$	−8.93606	+	5.15924i	−0.330061	+	0.190561i	0.325807	+	0.945436i	$0.394364\pi$
$734$	23.9070	+	20.9657i	0.882422	+	0.773857i
$735$	−4.28300	+	0.221120i	−0.157981	+	0.00815614i
$736$	21.8511	−	44.3118i	0.805442	−	1.63335i
$737$		−	10.3453i		−	0.381076i
$738$	−2.01167	+	21.5260i	−0.0740506	+	0.792384i
$739$	−5.46825			−0.201153			−0.100576	−	0.994929i	$-0.532069\pi$
$739$	−5.46825			−0.201153			−0.100576	+	0.994929i	$0.532069\pi$
$740$	−20.1368	+	2.65122i	−0.740245	+	0.0974609i
$741$	−15.0234	−	7.66954i	−0.551898	−	0.281747i
$742$	−6.09152	−	5.34208i	−0.223627	−	0.196114i
$743$	−7.02897	−	12.1745i	−0.257868	−	0.446641i	0.707803	−	0.706410i	$-0.249687\pi$
$743$	−7.02897	−	12.1745i	−0.257868	−	0.446641i	−0.965671	+	0.259770i	$0.916353\pi$
$744$	0.751910	+	1.34505i	0.0275664	+	0.0493119i
$745$	−9.83281	+	17.0309i	−0.360246	+	0.623965i
$746$	9.47404	−	3.21604i	0.346869	−	0.117748i
$747$	−3.11900	+	2.25868i	−0.114118	+	0.0826408i
$748$	−25.7700	+	19.7743i	−0.942243	+	0.723020i
$749$	0.827123	−	1.43262i	0.0302224	−	0.0523468i
$750$	−8.67867	−	21.8023i	−0.316900	−	0.796107i
$751$	28.1404	−	16.2469i	1.02686	−	0.592857i	0.110776	−	0.993845i	$-0.464666\pi$
$751$	28.1404	−	16.2469i	1.02686	−	0.592857i	0.916083	+	0.400988i	$0.131333\pi$
$752$	−37.1319	+	9.95007i	−1.35406	+	0.362842i
$753$	−27.2480	+	17.6650i	−0.992974	+	0.643747i
$754$	−2.39798	+	12.0557i	−0.0873294	+	0.439043i
$755$			40.6137i			1.47808i
$756$	7.52165	+	7.17111i	0.273560	+	0.260811i
$757$		−	31.4009i		−	1.14128i	−0.821199	−	0.570642i	$-0.806694\pi$
$757$		−	31.4009i		−	1.14128i	0.821199	−	0.570642i	$-0.193306\pi$
$758$	−9.42353	−	1.87442i	−0.342278	−	0.0680820i
$759$	−34.8170	+	22.5719i	−1.26378	+	0.819309i
$760$	3.10444	−	47.3730i	0.112610	−	1.71840i
$761$	26.8440	−	15.4984i	0.973096	−	0.561817i	0.0729171	−	0.997338i	$-0.476769\pi$
$761$	26.8440	−	15.4984i	0.973096	−	0.561817i	0.900179	+	0.435521i	$0.143436\pi$
$762$	35.5466	−	14.1498i	1.28772	−	0.512592i
$763$	−0.0577661	+	0.100054i	−0.00209127	+	0.00362219i
$764$	−27.5117	+	21.1108i	−0.995339	+	0.763762i
$765$	−4.52950	−	43.7502i	−0.163764	−	1.58179i
$766$	8.48801	+	25.0046i	0.306684	+	0.903451i
$767$	2.99946	−	5.19522i	0.108304	−	0.187588i
$768$	23.2532	−	15.0761i	0.839077	−	0.544012i
$769$	−21.5442	−	37.3156i	−0.776904	−	1.34564i	−0.933718	−	0.358009i	$-0.883456\pi$
$769$	−21.5442	−	37.3156i	−0.776904	−	1.34564i	0.156815	−	0.987628i	$-0.449877\pi$
$770$	6.33289	−	7.22134i	0.228222	−	0.260239i
$771$	−18.1779	−	9.27993i	−0.654661	−	0.334209i
$772$	−2.94934	−	22.4011i	−0.106149	−	0.806234i
$773$	20.4361			0.735034			0.367517	−	0.930017i	$-0.380208\pi$
$773$	20.4361			0.735034			0.367517	+	0.930017i	$0.380208\pi$
$774$	11.8478	+	25.8051i	0.425860	+	0.927547i
$775$			0.355745i			0.0127787i
$776$	−30.0577	+	14.8232i	−1.07901	+	0.532123i
$777$	−7.09432	+	0.366262i	−0.254507	+	0.0131396i
$778$	5.43898	−	6.20202i	0.194997	−	0.222353i
$779$	29.9156	−	17.2718i	1.07184	−	0.618826i
$780$	4.12232	−	11.6126i	0.147603	−	0.415799i
$781$	31.8701	+	18.4002i	1.14040	+	0.658410i
$782$	−69.2550	+	23.5092i	−2.47655	+	0.840687i
$783$	−11.3344	+	29.3224i	−0.405060	+	1.04790i
$784$	−1.03522	+	3.86372i	−0.0369720	+	0.137990i
$785$	−0.522179	−	0.301480i	−0.0186374	−	0.0107603i
$786$	−28.9463	−	22.8558i	−1.03248	−	0.815240i
$787$	−2.06970	−	3.58483i	−0.0737770	−	0.127785i	0.826777	−	0.562530i	$-0.190172\pi$
$787$	−2.06970	−	3.58483i	−0.0737770	−	0.127785i	−0.900554	+	0.434745i	$0.856839\pi$
$788$	−44.7388	−	18.5310i	−1.59375	−	0.660140i
$789$	−45.6701	+	2.35783i	−1.62590	+	0.0839411i
$790$	2.40602	−	12.0961i	0.0856025	−	0.430361i
$791$	−6.31693			−0.224604
$792$	−23.2578	+	0.877818i	−0.826429	+	0.0311919i
$793$	−12.6400			−0.448859
$794$	6.52568	−	32.8075i	0.231588	−	1.16429i
$795$	−11.1717	+	21.8836i	−0.396219	+	0.776130i
$796$	13.5537	−	32.7223i	0.480399	−	1.15981i
$797$	3.35270	+	5.80704i	0.118759	+	0.205696i	0.919276	−	0.393614i	$-0.128775\pi$
$797$	3.35270	+	5.80704i	0.118759	+	0.205696i	−0.800517	+	0.599310i	$0.795442\pi$
$798$	2.39536	−	16.4309i	0.0847947	−	0.581647i
$799$	49.2816	+	28.4527i	1.74346	+	1.00659i
$800$	6.38409	−	0.418559i	0.225712	−	0.0147983i
$801$	47.0175	+	21.0213i	1.66128	+	0.742751i
$802$	6.20254	−	2.10551i	0.219019	−	0.0743480i
$803$	15.2615	+	8.81122i	0.538566	+	0.310941i
$804$	9.94160	−	8.47769i	0.350613	−	0.298985i
$805$	18.7286	−	10.8130i	0.660096	−	0.381107i
$806$	0.421364	−	0.480477i	0.0148419	−	0.0169241i
$807$	0.734297	+	1.13265i	0.0258485	+	0.0398710i
$808$	−26.3952	+	13.0170i	−0.928579	+	0.457938i
$809$			0.225879i			0.00794149i	0.999992	+	0.00397075i	$0.00126393\pi$
$809$			0.225879i			0.00794149i	−0.999992	+	0.00397075i	$0.998736\pi$
$810$	15.4845	−	27.4490i	0.544070	−	0.964461i
$811$	−38.7775			−1.36166			−0.680830	−	0.732441i	$-0.738381\pi$
$811$	−38.7775			−1.36166			−0.680830	+	0.732441i	$0.738381\pi$
$812$	−11.9965	+	1.57946i	−0.420995	+	0.0554283i
$813$	−4.73846	+	3.07195i	−0.166185	+	0.107738i
$814$	10.4898	−	11.9614i	0.367666	−	0.419246i
$815$	−22.9270	−	39.7108i	−0.803099	−	1.39101i
$816$	−40.1202	−	8.55981i	−1.40449	−	0.299653i
$817$	22.6844	−	39.2905i	0.793627	−	1.37460i
$818$	0.790799	+	2.32959i	0.0276497	+	0.0814522i
$819$	1.75913	−	3.93457i	0.0614688	−	0.137485i
$820$	15.3625	+	20.0205i	0.536482	+	0.699146i
$821$	10.5479	−	18.2696i	0.368126	−	0.637612i	−0.621147	−	0.783694i	$-0.713333\pi$
$821$	10.5479	−	18.2696i	0.368126	−	0.637612i	0.989272	+	0.146082i	$0.0466663\pi$
$822$	1.41939	−	9.73627i	0.0495069	−	0.339592i
$823$	−38.4175	+	22.1804i	−1.33915	+	0.773159i	−0.986682	−	0.162664i	$-0.947991\pi$
$823$	−38.4175	+	22.1804i	−1.33915	+	0.773159i	−0.352470	+	0.935823i	$0.614658\pi$
$824$	12.7010	+	0.832320i	0.442460	+	0.0289952i
$825$	−4.78559	−	2.44307i	−0.166613	−	0.0850568i
$826$	5.79182	+	1.15204i	0.201523	+	0.0400846i
$827$		−	1.56277i		−	0.0543427i	−0.999631	−	0.0271713i	$-0.991350\pi$
$827$		−	1.56277i		−	0.0543427i	0.999631	−	0.0271713i	$-0.00864997\pi$
$828$	−50.2225	−	14.9612i	−1.74535	−	0.519938i
$829$		−	32.8826i		−	1.14206i	−0.820929	−	0.571030i	$-0.806544\pi$
$829$		−	32.8826i		−	1.14206i	0.820929	−	0.571030i	$-0.193456\pi$
$830$	−0.876908	+	4.40860i	−0.0304379	+	0.153025i
$831$	2.42778	+	47.0250i	0.0842189	+	1.63128i
$832$	−9.11825	−	6.99635i	−0.316119	−	0.242555i
$833$	5.12790	−	2.96060i	0.177671	−	0.102579i
$834$	18.3720	−	23.2677i	0.636170	−	0.805694i
$835$	14.5562	−	25.2120i	0.503737	−	0.872498i
$836$	22.6383	+	29.5023i	0.782962	+	1.02036i
$837$	1.27258	−	1.02561i	0.0439870	−	0.0354502i
$838$	1.25995	−	0.427701i	0.0435243	−	0.0147747i
$839$	−8.04626	+	13.9365i	−0.277788	+	0.481142i	−0.970835	−	0.239750i	$-0.922935\pi$
$839$	−8.04626	+	13.9365i	−0.277788	+	0.481142i	0.693047	+	0.720892i	$0.256268\pi$
$840$	12.1291	+	0.168079i	0.418494	+	0.00579927i
$841$	−3.80135	−	6.58414i	−0.131081	−	0.227039i
$842$	−8.34796	−	7.32091i	−0.287690	−	0.252295i
$843$	−0.923018	−	17.8784i	−0.0317904	−	0.615765i
$844$	−1.39014	−	10.5585i	−0.0478505	−	0.363439i
$845$	27.0786			0.931532
$846$	17.0128	+	37.0549i	0.584913	+	1.27397i
$847$		−	3.47647i		−	0.119453i
$848$	16.2045	+	16.2040i	0.556465	+	0.556448i
$849$	−9.93579	+	19.4626i	−0.340996	+	0.667956i
$850$	−7.12043	−	6.24440i	−0.244229	−	0.214181i
$851$	31.0219	−	17.9105i	1.06342	−	0.613964i
$852$	8.43443	+	45.7046i	0.288959	+	1.56581i
$853$	−18.0987	−	10.4493i	−0.619689	−	0.357778i	0.157059	−	0.987589i	$-0.449799\pi$
$853$	−18.0987	−	10.4493i	−0.619689	−	0.357778i	−0.776748	+	0.629812i	$0.783132\pi$
$854$	−3.99962	−	11.7823i	−0.136864	−	0.403184i
$855$	−50.0867	+	5.18553i	−1.71293	+	0.177341i
$856$	−2.59942	+	3.89040i	−0.0888464	+	0.132971i
$857$	−30.6078	−	17.6714i	−1.04554	−	0.603643i	−0.124143	−	0.992264i	$-0.539618\pi$
$857$	−30.6078	−	17.6714i	−1.04554	−	0.603643i	−0.921398	+	0.388621i	$0.872952\pi$
$858$	3.56981	+	8.96798i	0.121871	+	0.306162i
$859$	11.8114	+	20.4580i	0.403001	+	0.698018i	0.994087	−	0.108591i	$-0.0346338\pi$
$859$	11.8114	+	20.4580i	0.403001	+	0.698018i	−0.591086	+	0.806609i	$0.701300\pi$
$860$	30.6209	+	12.6833i	1.04416	+	0.432497i
$861$	4.80136	+	7.40606i	0.163630	+	0.252398i
$862$	17.7964	+	3.53984i	0.606146	+	0.120568i
$863$	−28.0196			−0.953799			−0.476899	−	0.878958i	$-0.658239\pi$
$863$	−28.0196			−0.953799			−0.476899	+	0.878958i	$0.658239\pi$
$864$	−19.9026	−	21.6307i	−0.677099	−	0.735892i
$865$	−30.9103			−1.05098
$866$	−19.6234	−	3.90326i	−0.666830	−	0.132638i
$867$	17.0168	+	26.2483i	0.577921	+	0.891439i
$868$	0.581206	+	0.240738i	0.0197274	+	0.00817118i
$869$	4.83029	+	8.36631i	0.163856	+	0.283808i
$870$	13.5709	+	34.0924i	0.460097	+	1.15584i
$871$	−4.69259	−	2.70927i	−0.159002	−	0.0918000i
$872$	0.181543	−	0.271705i	0.00614782	−	0.00920110i
$873$	20.8492	+	28.7906i	0.705639	+	0.974415i
$874$	26.9141	+	79.2855i	0.910384	+	2.68187i
$875$	−8.29653	−	4.79000i	−0.280474	−	0.161932i
$876$	4.03896	+	21.8864i	0.136464	+	0.739472i
$877$	13.5807	−	7.84081i	0.458587	−	0.264765i	−0.252863	−	0.967502i	$-0.581372\pi$
$877$	13.5807	−	7.84081i	0.458587	−	0.264765i	0.711450	+	0.702737i	$0.248039\pi$
$878$	27.6685	+	24.2644i	0.933766	+	0.818884i
$879$	11.7017	−	22.9217i	0.394687	−	0.773129i
$880$	−19.2094	+	19.2100i	−0.647549	+	0.647569i
$881$			30.0959i			1.01396i	0.861959	+	0.506978i	$0.169237\pi$
$881$			30.0959i			1.01396i	−0.861959	+	0.506978i	$0.830763\pi$
$882$	4.22423	+	0.394767i	0.142237	+	0.0132925i
$883$	−22.4847			−0.756671			−0.378335	−	0.925669i	$-0.623503\pi$
$883$	−22.4847			−0.756671			−0.378335	+	0.925669i	$0.623503\pi$
$884$	2.22080	+	16.8676i	0.0746936	+	0.567320i
$885$	−0.923324	−	17.8844i	−0.0310372	−	0.601176i
$886$	−21.9005	−	19.2061i	−0.735763	−	0.645242i
$887$	17.9854	+	31.1516i	0.603890	+	1.04597i	0.992226	+	0.124450i	$0.0397166\pi$
$887$	17.9854	+	31.1516i	0.603890	+	1.04597i	−0.388336	+	0.921518i	$0.626950\pi$
$888$	20.0906	+	0.278405i	0.674195	+	0.00934265i
$889$	7.80966	−	13.5267i	0.261928	−	0.453672i
$890$	56.9255	−	19.3239i	1.90815	−	0.647737i
$891$	5.05735	+	24.1626i	0.169428	+	0.809476i
$892$	6.93891	+	9.04282i	0.232332	+	0.302776i
$893$	32.5737	−	56.4192i	1.09004	−	1.88800i
$894$	12.0559	−	15.2686i	0.403211	−	0.510657i
$895$	17.0887	−	9.86615i	0.571211	−	0.329789i
$896$	3.63638	−	10.7134i	0.121483	−	0.357909i
$897$	1.12052	+	21.7040i	0.0374131	+	0.724675i
$898$	−7.86719	+	39.5519i	−0.262532	+	1.31986i
$899$			1.90300i			0.0634688i
$900$	−1.57391	−	6.60084i	−0.0524638	−	0.220028i
$901$		−	33.9229i		−	1.13014i
$902$	−19.3872	−	3.85628i	−0.645524	−	0.128400i
$903$	10.3246	+	5.27079i	0.343582	+	0.175401i
$904$	17.8287	+	1.16835i	0.592975	+	0.0388587i
$905$	19.9455	−	11.5155i	0.663011	−	0.382790i
$906$	5.79596	−	39.7573i	0.192558	−	1.32085i
$907$	19.9447	−	34.5452i	0.662252	−	1.14705i	−0.317771	−	0.948167i	$-0.602934\pi$
$907$	19.9447	−	34.5452i	0.662252	−	1.14705i	0.980023	−	0.198886i	$-0.0637323\pi$
$908$	−9.91263	−	12.9182i	−0.328962	−	0.428705i
$909$	18.3088	+	25.2825i	0.607264	+	0.838569i
$910$	−1.61708	−	4.76370i	−0.0536057	−	0.157915i
$911$	16.7665	−	29.0404i	0.555498	−	0.962150i	−0.442367	−	0.896834i	$-0.645861\pi$
$911$	16.7665	−	29.0404i	0.555498	−	0.962150i	0.997865	−	0.0653162i	$-0.0208056\pi$
$912$	−9.79957	+	45.9310i	−0.324496	+	1.52093i
$913$	−1.76047	−	3.04921i	−0.0582629	−	0.100914i
$914$	−24.1967	+	27.5913i	−0.800357	+	0.912639i
$915$	−31.6618	+	20.5264i	−1.04671	+	0.678582i
$916$	−47.5214	+	6.25668i	−1.57015	+	0.206727i
$917$	−15.0570			−0.497226
$918$	−1.80959	+	43.4740i	−0.0597254	+	1.43486i
$919$			38.6463i			1.27482i	0.770523	+	0.637412i	$0.219995\pi$
$919$			38.6463i			1.27482i	−0.770523	+	0.637412i	$0.780005\pi$
$920$	−54.8590	+	27.0543i	−1.80865	+	0.891952i
$921$	−1.23747	−	1.90879i	−0.0407760	−	0.0628967i
$922$	−9.78918	+	11.1625i	−0.322389	+	0.367617i
$923$	16.6924	−	9.63738i	0.549438	−	0.317218i
$924$	−7.22990	+	6.16529i	−0.237846	+	0.202823i
$925$	4.01712	+	2.31928i	0.132082	+	0.0762576i
$926$	−28.0763	+	9.53073i	−0.922643	+	0.313199i
$927$	−1.39027	−	13.4286i	−0.0456625	−	0.441052i
$928$	34.1507	−	2.23902i	1.12105	−	0.0734994i
$929$	37.9248	+	21.8959i	1.24427	+	0.718381i	0.969961	−	0.243260i	$-0.0782168\pi$
$929$	37.9248	+	21.8959i	1.24427	+	0.718381i	0.274311	+	0.961641i	$0.411550\pi$
$930$	0.275211	−	1.88781i	0.00902454	−	0.0619036i
$931$	−3.38939	−	5.87060i	−0.111083	−	0.192401i
$932$	−15.5340	+	37.5032i	−0.508832	+	1.22846i
$933$	26.6244	−	52.1529i	0.871643	−	1.70741i
$934$	−7.42741	+	37.3409i	−0.243032	+	1.22183i
$935$	40.2147			1.31516
$936$	−5.69263	+	10.7795i	−0.186069	+	0.352338i
$937$	19.5173			0.637601			0.318801	−	0.947822i	$-0.396720\pi$
$937$	19.5173			0.637601			0.318801	+	0.947822i	$0.396720\pi$
$938$	1.04058	−	5.23147i	0.0339762	−	0.170814i
$939$	−9.38125	+	0.484331i	−0.306146	+	0.0158055i
$940$	43.9700	+	18.2126i	1.43414	+	0.594029i
$941$	−5.82108	−	10.0824i	−0.189762	−	0.328677i	0.755409	−	0.655254i	$-0.227438\pi$
$941$	−5.82108	−	10.0824i	−0.189762	−	0.328677i	−0.945171	+	0.326576i	$0.894105\pi$
$942$	0.468144	+	0.369643i	0.0152530	+	0.0120436i
$943$	−38.5439	−	22.2533i	−1.25516	−	0.724669i
$944$	−16.1336	−	4.32272i	−0.525104	−	0.140693i
$945$	−1.98303	−	12.7124i	−0.0645079	−	0.413533i
$946$	−24.5838	+	8.34518i	−0.799288	+	0.271325i
$947$	−26.8266	−	15.4883i	−0.871747	−	0.503303i	−0.00381876	−	0.999993i	$-0.501216\pi$
$947$	−26.8266	−	15.4883i	−0.871747	−	0.503303i	−0.867928	+	0.496689i	$0.834549\pi$
$948$	−4.08152	+	11.4977i	−0.132562	+	0.373428i
$949$	7.99343	−	4.61501i	0.259478	−	0.149810i
$950$	−7.14880	+	8.15171i	−0.231938	+	0.264476i
$951$	−8.26628	+	0.426767i	−0.268053	+	0.0138389i
$952$	−15.0204	+	7.40747i	−0.486815	+	0.240078i
$953$		−	44.2845i		−	1.43452i	−0.696807	−	0.717259i	$-0.745397\pi$
$953$		−	44.2845i		−	1.43452i	0.696807	−	0.717259i	$-0.254603\pi$
$954$	14.0591	−	19.8278i	0.455181	−	0.641949i
$955$	42.9327			1.38927
$956$	−0.445726	−	3.38542i	−0.0144158	−	0.109492i
$957$	−25.5998	−	13.0689i	−0.827524	−	0.422456i
$958$	3.28815	−	3.74944i	0.106235	−	0.121139i
$959$	−2.00842	−	3.47868i	−0.0648552	−	0.112332i
$960$	−34.2018	−	2.71773i	−1.10386	−	0.0877142i
$961$	−15.4505	+	26.7611i	−0.498404	+	0.863261i
$962$	−2.67852	−	7.89056i	−0.0863589	−	0.254402i
$963$	4.53054	+	2.02558i	0.145995	+	0.0652734i
$964$	−24.2920	+	18.6402i	−0.782394	+	0.600362i
$965$	−13.9864	+	24.2252i	−0.450239	+	0.779837i
$966$	−19.8768	+	7.91219i	−0.639525	+	0.254571i
$967$	−32.3924	+	18.7017i	−1.04167	+	0.601407i	−0.920305	−	0.391201i	$-0.872060\pi$
$967$	−32.3924	+	18.7017i	−1.04167	+	0.601407i	−0.121363	+	0.992608i	$0.538726\pi$
$968$	−0.642992	+	9.81190i	−0.0206665	+	0.315367i
$969$	58.3354	−	37.8189i	1.87400	−	1.21492i
$970$	40.6945	+	8.09448i	1.30662	+	0.259898i
$971$		−	57.7057i		−	1.85186i	−0.377691	−	0.925932i	$-0.623282\pi$
$971$		−	57.7057i		−	1.85186i	0.377691	−	0.925932i	$-0.376718\pi$
$972$	−19.0752	+	24.6604i	−0.611838	+	0.790983i
$973$		−	12.1031i		−	0.388009i
$974$	11.0058	−	55.3309i	0.352648	−	1.77292i
$975$	−2.36142	+	1.53092i	−0.0756261	+	0.0490285i
$976$	9.10921	+	33.9939i	0.291579	+	1.08812i
$977$	0.194687	−	0.112403i	0.00622859	−	0.00359608i	−0.496882	−	0.867818i	$-0.665522\pi$
$977$	0.194687	−	0.112403i	0.00622859	−	0.00359608i	0.503111	+	0.864222i	$0.332189\pi$
$978$	16.7765	+	42.1453i	0.536452	+	1.34766i
$979$	−23.5446	+	40.7804i	−0.752487	+	1.30335i
$980$	3.92879	−	3.01472i	0.125501	−	0.0963016i
$981$	−0.316412	−	0.141466i	−0.0101023	−	0.00451667i
$982$	37.0752	−	12.5855i	1.18312	−	0.401619i
$983$	−3.00934	+	5.21233i	−0.0959830	+	0.166247i	−0.910018	−	0.414568i	$-0.863933\pi$
$983$	−3.00934	+	5.21233i	−0.0959830	+	0.166247i	0.814035	+	0.580815i	$0.197266\pi$
$984$	−12.1814	−	21.7907i	−0.388330	−	0.694662i
$985$	29.9759	+	51.9199i	0.955113	+	1.65430i
$986$	−38.0897	−	33.4035i	−1.21302	−	1.06378i
$987$	14.8257	+	7.56859i	0.471906	+	0.240911i
$988$	19.3107	−	2.54245i	0.614354	−	0.0808861i
$989$	−58.4541			−1.85873
$990$	23.5053	+	16.6667i	0.747048	+	0.529702i
$991$			14.9342i			0.474399i	0.971461	+	0.237200i	$0.0762296\pi$
$991$			14.9342i			0.474399i	−0.971461	+	0.237200i	$0.923770\pi$
$992$	−1.59585	−	0.786950i	−0.0506684	−	0.0249857i
$993$	4.09385	−	0.211355i	0.129914	−	0.00670715i
$994$	14.2654	+	12.5103i	0.452470	+	0.396803i
$995$	−37.9746	+	21.9246i	−1.20388	+	0.695058i
$996$	1.48757	−	4.19049i	0.0471353	−	0.132781i
$997$	−46.7707	−	27.0031i	−1.48124	−	0.855197i	−0.481470	−	0.876463i	$-0.659897\pi$
$997$	−46.7707	−	27.0031i	−1.48124	−	0.855197i	−0.999774	+	0.0212660i	$0.993230\pi$
$998$	3.46933	+	10.2202i	0.109820	+	0.323515i
$999$	−3.28468	−	21.0567i	−0.103923	−	0.666203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.5	✓	144
8.3	odd	2	inner	504.2.br.a.155.21	yes	144
9.5	odd	6	inner	504.2.br.a.491.21	yes	144
72.59	even	6	inner	504.2.br.a.491.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.5	✓	144	1.1	even	1	trivial
504.2.br.a.155.21	yes	144	8.3	odd	2	inner
504.2.br.a.491.5	yes	144	72.59	even	6	inner
504.2.br.a.491.21	yes	144	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38704 - 0.275894i) q^{2} +(-0.942212 - 1.45335i) q^{3} +(1.84776 + 0.765353i) q^{4} +(-1.23804 - 2.14435i) q^{5} +(0.905915 + 2.27581i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.35177 - 1.57136i) q^{8} +(-1.22447 + 2.73873i) q^{9} +O(q^{10})\)	\(q+(-1.38704 - 0.275894i) q^{2} +(-0.942212 - 1.45335i) q^{3} +(1.84776 + 0.765353i) q^{4} +(-1.23804 - 2.14435i) q^{5} +(0.905915 + 2.27581i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.35177 - 1.57136i) q^{8} +(-1.22447 + 2.73873i) q^{9} +(1.12560 + 3.31587i) q^{10} +(-2.37543 - 1.37145i) q^{11} +(-0.628658 - 3.40658i) q^{12} +(-1.24416 + 0.718319i) q^{13} +(-1.06327 - 0.932452i) q^{14} +(-1.95000 + 3.81974i) q^{15} +(2.82847 + 2.82838i) q^{16} -5.92119i q^{17} +(2.45400 - 3.46091i) q^{18} -6.77878 q^{19} +(-0.646425 - 4.90979i) q^{20} +(-0.0893025 - 1.72975i) q^{21} +(2.91644 + 2.55763i) q^{22} +(4.36696 + 7.56380i) q^{23} +(-0.0678810 + 4.89851i) q^{24} +(-0.565491 + 0.979458i) q^{25} +(1.92389 - 0.653080i) q^{26} +(5.13406 - 0.800874i) q^{27} +(1.21754 + 1.58670i) q^{28} +(-3.02501 + 5.23947i) q^{29} +(3.75858 - 4.76015i) q^{30} +(0.272404 - 0.157273i) q^{31} +(-3.14287 - 4.70344i) q^{32} +(0.244948 + 4.74453i) q^{33} +(-1.63362 + 8.21293i) q^{34} -2.47608i q^{35} +(-4.35864 + 4.12338i) q^{36} -4.10136i q^{37} +(9.40245 + 1.87023i) q^{38} +(2.21624 + 1.13140i) q^{39} +(-0.457965 + 6.98843i) q^{40} +(-4.41313 + 2.54792i) q^{41} +(-0.353361 + 2.42387i) q^{42} +(-3.34638 + 5.79610i) q^{43} +(-3.33958 - 4.35216i) q^{44} +(7.38875 - 0.764964i) q^{45} +(-3.97035 - 11.6961i) q^{46} +(-4.80524 + 8.32292i) q^{47} +(1.44562 - 6.77570i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.05459 - 1.20253i) q^{50} +(-8.60558 + 5.57902i) q^{51} +(-2.84869 + 0.375060i) q^{52} +5.72907 q^{53} +(-7.34211 - 0.305613i) q^{54} +6.79166i q^{55} +(-1.25101 - 2.53672i) q^{56} +(6.38705 + 9.85197i) q^{57} +(5.64135 - 6.43278i) q^{58} +(-3.61623 + 2.08783i) q^{59} +(-6.52660 + 5.56555i) q^{60} +(7.61956 + 4.39916i) q^{61} +(-0.421226 + 0.142989i) q^{62} +(-2.42979 + 1.75958i) q^{63} +(3.06164 + 7.39097i) q^{64} +(3.08065 + 1.77862i) q^{65} +(0.969235 - 6.64844i) q^{66} +(1.88584 + 3.26637i) q^{67} +(4.53180 - 10.9410i) q^{68} +(6.87828 - 13.4734i) q^{69} +(-0.683136 + 3.43443i) q^{70} -13.4166 q^{71} +(7.18322 - 4.51678i) q^{72} -6.42473 q^{73} +(-1.13154 + 5.68876i) q^{74} +(1.95631 - 0.100999i) q^{75} +(-12.5256 - 5.18816i) q^{76} +(-1.37145 - 2.37543i) q^{77} +(-2.76187 - 2.18075i) q^{78} +(-3.05016 - 1.76101i) q^{79} +(2.56328 - 9.56688i) q^{80} +(-6.00133 - 6.70702i) q^{81} +(6.82414 - 2.31651i) q^{82} +(1.11167 + 0.641825i) q^{83} +(1.15886 - 3.26451i) q^{84} +(-12.6971 + 7.33068i) q^{85} +(6.24068 - 7.11619i) q^{86} +(10.4650 - 0.540282i) q^{87} +(3.43140 + 6.95799i) q^{88} -17.1676i q^{89} +(-10.4596 - 0.977476i) q^{90} -1.43664 q^{91} +(2.28015 + 17.3184i) q^{92} +(-0.485235 - 0.247716i) q^{93} +(8.96131 - 10.2185i) q^{94} +(8.39241 + 14.5361i) q^{95} +(-3.87451 + 8.99934i) q^{96} +(5.92450 - 10.2615i) q^{97} +(-0.454589 - 1.33916i) q^{98} +(6.66469 - 4.82635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{6}+O(q^{10}) \) 144 * q + 6 * q^6	\( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

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