LMFDB - Embedded newform 504.2.br.a.155.11

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			155.11
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27467 - 0.612543i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(1.24958 + 1.56158i) q^{4} +(-1.17058 - 2.02750i) q^{5} +(2.36114 - 0.651926i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +O(q^{10})$	\(q+(-1.27467 - 0.612543i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(1.24958 + 1.56158i) q^{4} +(-1.17058 - 2.02750i) q^{5} +(2.36114 - 0.651926i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +(0.250172 + 3.30142i) q^{10} +(3.74998 + 2.16505i) q^{11} +(-3.40902 - 0.615309i) q^{12} +(-4.95064 + 2.85826i) q^{13} +(-0.797628 - 1.16781i) q^{14} +(3.83641 + 1.31337i) q^{15} +(-0.877090 + 3.90265i) q^{16} -0.835037i q^{17} +(-2.33939 + 3.53938i) q^{18} -2.79658 q^{19} +(1.70338 - 4.36148i) q^{20} +(-1.69964 + 0.333509i) q^{21} +(-3.45381 - 5.05676i) q^{22} +(-4.32248 - 7.48676i) q^{23} +(3.96848 + 2.87249i) q^{24} +(-0.240497 + 0.416553i) q^{25} +(8.06126 - 0.610858i) q^{26} +(2.85320 + 4.34272i) q^{27} +(0.301378 + 1.97716i) q^{28} +(3.19193 - 5.52858i) q^{29} +(-4.08567 - 4.02408i) q^{30} +(7.02846 - 4.05788i) q^{31} +(3.50855 - 4.43735i) q^{32} +(-7.35962 + 1.44413i) q^{33} +(-0.511496 + 1.06440i) q^{34} -2.34115i q^{35} +(5.14999 - 3.07858i) q^{36} -2.91840i q^{37} +(3.56473 + 1.71303i) q^{38} +(3.20692 - 9.36756i) q^{39} +(-4.84284 + 4.51607i) q^{40} +(0.387918 - 0.223964i) q^{41} +(2.37077 + 0.615987i) q^{42} +(6.48309 - 11.2290i) q^{43} +(1.30500 + 8.56133i) q^{44} +(-6.50265 + 2.65414i) q^{45} +(0.923789 + 12.1909i) q^{46} +(4.13514 - 7.16227i) q^{47} +(-3.29899 - 6.09235i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.561712 - 0.383654i) q^{50} +(0.950812 + 1.08987i) q^{51} +(-10.6496 - 4.15922i) q^{52} -9.10223 q^{53} +(-0.976789 - 7.28326i) q^{54} -10.1374i q^{55} +(0.826939 - 2.70484i) q^{56} +(3.65003 - 3.18432i) q^{57} +(-7.45515 + 5.09194i) q^{58} +(-8.38108 + 4.83882i) q^{59} +(2.74298 + 7.63204i) q^{60} +(-3.82374 - 2.20764i) q^{61} +(-11.4446 + 0.867240i) q^{62} +(1.83858 - 2.37058i) q^{63} +(-7.19032 + 3.50704i) q^{64} +(11.5902 + 6.69161i) q^{65} +(10.2657 + 2.66729i) q^{66} +(1.10041 + 1.90597i) q^{67} +(1.30398 - 1.04345i) q^{68} +(14.1664 + 4.84976i) q^{69} +(-1.43406 + 2.98420i) q^{70} -4.50393 q^{71} +(-8.45031 + 0.769592i) q^{72} +2.85366 q^{73} +(-1.78764 + 3.72000i) q^{74} +(-0.160416 - 0.817516i) q^{75} +(-3.49456 - 4.36710i) q^{76} +(2.16505 + 3.74998i) q^{77} +(-9.82580 + 9.97620i) q^{78} +(6.46798 + 3.73429i) q^{79} +(8.93932 - 2.79006i) q^{80} +(-8.66875 - 2.41923i) q^{81} +(-0.631656 + 0.0478650i) q^{82} +(-4.89442 - 2.82579i) q^{83} +(-2.64464 - 2.23738i) q^{84} +(-1.69304 + 0.977475i) q^{85} +(-15.1421 + 10.3422i) q^{86} +(2.12907 + 10.8502i) q^{87} +(3.58074 - 11.7123i) q^{88} -8.68661i q^{89} +(9.91453 + 0.599994i) q^{90} -5.71651 q^{91} +(6.28991 - 16.1052i) q^{92} +(-4.55288 + 13.2992i) q^{93} +(-9.65814 + 6.59660i) q^{94} +(3.27361 + 5.67006i) q^{95} +(0.473307 + 9.78652i) q^{96} +(-3.64813 + 6.31875i) q^{97} +(-0.106859 - 1.41017i) q^{98} +(7.96124 - 10.2649i) 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 $

$2$	−1.27467	−	0.612543i	−0.901330	−	0.433133i
$2$	−1.27467	−	0.612543i	−0.901330	−	0.433133i
$3$	−1.30518	+	1.13865i	−0.753544	+	0.657398i
$3$	−1.30518	+	1.13865i	−0.753544	+	0.657398i
$4$	1.24958	+	1.56158i	0.624791	+	0.780792i
$5$	−1.17058	−	2.02750i	−0.523498	−	0.906724i	−0.999626	−	0.0273486i	$-0.991294\pi$
$5$	−1.17058	−	2.02750i	−0.523498	−	0.906724i	0.476128	−	0.879376i	$-0.342040\pi$
$6$	2.36114	−	0.651926i	0.963932	−	0.266148i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	−0.636271	−	2.75593i	−0.224956	−	0.974369i
$9$	0.406968	−	2.97227i	0.135656	−	0.990756i
$10$	0.250172	+	3.30142i	0.0791114	+	1.04400i
$11$	3.74998	+	2.16505i	1.13066	+	0.652788i	0.944102	−	0.329655i	$-0.106932\pi$
$11$	3.74998	+	2.16505i	1.13066	+	0.652788i	0.186561	+	0.982443i	$0.440266\pi$
$12$	−3.40902	−	0.615309i	−0.984098	−	0.177625i
$13$	−4.95064	+	2.85826i	−1.37306	+	0.792737i	−0.991312	−	0.131529i	$-0.958011\pi$
$13$	−4.95064	+	2.85826i	−1.37306	+	0.792737i	−0.381749	+	0.924266i	$0.624678\pi$
$14$	−0.797628	−	1.16781i	−0.213175	−	0.312112i
$15$	3.83641	+	1.31337i	0.990557	+	0.339110i
$16$	−0.877090	+	3.90265i	−0.219272	+	0.975664i
$17$		−	0.835037i		−	0.202526i	−0.994860	−	0.101263i	$-0.967712\pi$
$17$		−	0.835037i		−	0.202526i	0.994860	−	0.101263i	$-0.0322884\pi$
$18$	−2.33939	+	3.53938i	−0.551400	+	0.834241i
$19$	−2.79658			−0.641580			−0.320790	−	0.947150i	$-0.603948\pi$
$19$	−2.79658			−0.641580			−0.320790	+	0.947150i	$0.603948\pi$
$20$	1.70338	−	4.36148i	0.380887	−	0.975256i
$21$	−1.69964	+	0.333509i	−0.370892	+	0.0727776i
$22$	−3.45381	−	5.05676i	−0.736356	−	1.07811i
$23$	−4.32248	−	7.48676i	−0.901300	−	1.56110i	−0.825808	−	0.563951i	$-0.809281\pi$
$23$	−4.32248	−	7.48676i	−0.901300	−	1.56110i	−0.0754919	−	0.997146i	$-0.524053\pi$
$24$	3.96848	+	2.87249i	0.810062	+	0.586344i
$25$	−0.240497	+	0.416553i	−0.0480994	+	0.0833106i
$26$	8.06126	−	0.610858i	1.58094	−	0.119799i
$27$	2.85320	+	4.34272i	0.549098	+	0.835758i
$28$	0.301378	+	1.97716i	0.0569550	+	0.373649i
$29$	3.19193	−	5.52858i	0.592726	−	1.02663i	−0.401138	−	0.916018i	$-0.631385\pi$
$29$	3.19193	−	5.52858i	0.592726	−	1.02663i	0.993864	−	0.110613i	$-0.0352815\pi$
$30$	−4.08567	−	4.02408i	−0.745939	−	0.734693i
$31$	7.02846	−	4.05788i	1.26235	−	0.728818i	0.288821	−	0.957383i	$-0.406737\pi$
$31$	7.02846	−	4.05788i	1.26235	−	0.728818i	0.973529	+	0.228566i	$0.0734035\pi$
$32$	3.50855	−	4.43735i	0.620229	−	0.784421i
$33$	−7.35962	+	1.44413i	−1.28115	+	0.251391i
$34$	−0.511496	+	1.06440i	−0.0877209	+	0.182543i
$35$		−	2.34115i		−	0.395727i
$36$	5.14999	−	3.07858i	0.858331	−	0.513096i
$37$		−	2.91840i		−	0.479781i	−0.970800	−	0.239891i	$-0.922888\pi$
$37$		−	2.91840i		−	0.479781i	0.970800	−	0.239891i	$-0.0771116\pi$
$38$	3.56473	+	1.71303i	0.578275	+	0.277890i
$39$	3.20692	−	9.36756i	0.513518	−	1.50001i
$40$	−4.84284	+	4.51607i	−0.765720	+	0.714053i
$41$	0.387918	−	0.223964i	0.0605825	−	0.0349773i	−0.469403	−	0.882984i	$-0.655531\pi$
$41$	0.387918	−	0.223964i	0.0605825	−	0.0349773i	0.529985	+	0.848007i	$0.322197\pi$
$42$	2.37077	+	0.615987i	0.365818	+	0.0950489i
$43$	6.48309	−	11.2290i	0.988662	−	1.71241i	0.364292	−	0.931285i	$-0.381311\pi$
$43$	6.48309	−	11.2290i	0.988662	−	1.71241i	0.624371	−	0.781128i	$-0.285355\pi$
$44$	1.30500	+	8.56133i	0.196736	+	1.29067i
$45$	−6.50265	+	2.65414i	−0.969358	+	0.395656i
$46$	0.923789	+	12.1909i	0.136205	+	1.79745i
$47$	4.13514	−	7.16227i	0.603172	−	1.04472i	−0.389166	−	0.921168i	$-0.627237\pi$
$47$	4.13514	−	7.16227i	0.603172	−	1.04472i	0.992338	−	0.123556i	$-0.0394299\pi$
$48$	−3.29899	−	6.09235i	−0.476168	−	0.879354i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.561712	−	0.383654i	0.0794380	−	0.0542569i
$51$	0.950812	+	1.08987i	0.133140	+	0.152612i
$52$	−10.6496	−	4.15922i	−1.47684	−	0.576780i
$53$	−9.10223			−1.25029			−0.625144	−	0.780510i	$-0.714960\pi$
$53$	−9.10223			−1.25029			−0.625144	+	0.780510i	$0.714960\pi$
$54$	−0.976789	−	7.28326i	−0.132924	−	0.991126i
$55$		−	10.1374i		−	1.36693i
$56$	0.826939	−	2.70484i	0.110504	−	0.361450i
$57$	3.65003	−	3.18432i	0.483459	−	0.421773i
$58$	−7.45515	+	5.09194i	−0.978910	+	0.668604i
$59$	−8.38108	+	4.83882i	−1.09112	+	0.629961i	−0.933876	−	0.357598i	$-0.883596\pi$
$59$	−8.38108	+	4.83882i	−1.09112	+	0.629961i	−0.157249	+	0.987559i	$0.550262\pi$
$60$	2.74298	+	7.63204i	0.354117	+	0.985292i
$61$	−3.82374	−	2.20764i	−0.489580	−	0.282659i	0.234820	−	0.972039i	$-0.424550\pi$
$61$	−3.82374	−	2.20764i	−0.489580	−	0.282659i	−0.724400	+	0.689380i	$0.757883\pi$
$62$	−11.4446	+	0.867240i	−1.45347	+	0.110140i
$63$	1.83858	−	2.37058i	0.231639	−	0.298664i
$64$	−7.19032	+	3.50704i	−0.898790	+	0.438380i
$65$	11.5902	+	6.69161i	1.43759	+	0.829992i
$66$	10.2657	+	2.66729i	1.26362	+	0.328321i
$67$	1.10041	+	1.90597i	0.134437	+	0.232851i	0.925382	−	0.379036i	$-0.123744\pi$
$67$	1.10041	+	1.90597i	0.134437	+	0.232851i	−0.790945	+	0.611887i	$0.790411\pi$
$68$	1.30398	−	1.04345i	0.158131	−	0.126537i
$69$	14.1664	+	4.84976i	1.70543	+	0.583842i
$70$	−1.43406	+	2.98420i	−0.171403	+	0.356681i
$71$	−4.50393			−0.534518			−0.267259	−	0.963625i	$-0.586118\pi$
$71$	−4.50393			−0.534518			−0.267259	+	0.963625i	$0.586118\pi$
$72$	−8.45031	+	0.769592i	−0.995879	+	0.0906973i
$73$	2.85366			0.333995			0.166998	−	0.985957i	$-0.446593\pi$
$73$	2.85366			0.333995			0.166998	+	0.985957i	$0.446593\pi$
$74$	−1.78764	+	3.72000i	−0.207809	+	0.432441i
$75$	−0.160416	−	0.817516i	−0.0185232	−	0.0943986i
$76$	−3.49456	−	4.36710i	−0.400853	−	0.500941i
$77$	2.16505	+	3.74998i	0.246731	+	0.427350i
$78$	−9.82580	+	9.97620i	−1.11255	+	1.12958i
$79$	6.46798	+	3.73429i	0.727704	+	0.420140i	0.817582	−	0.575813i	$-0.195314\pi$
$79$	6.46798	+	3.73429i	0.727704	+	0.420140i	−0.0898776	+	0.995953i	$0.528648\pi$
$80$	8.93932	−	2.79006i	0.999447	−	0.311938i
$81$	−8.66875	−	2.41923i	−0.963195	−	0.268804i
$82$	−0.631656	+	0.0478650i	−0.0697547	+	0.00528581i
$83$	−4.89442	−	2.82579i	−0.537232	−	0.310171i	0.206724	−	0.978399i	$-0.433720\pi$
$83$	−4.89442	−	2.82579i	−0.537232	−	0.310171i	−0.743957	+	0.668228i	$0.767053\pi$
$84$	−2.64464	−	2.23738i	−0.288554	−	0.244118i
$85$	−1.69304	+	0.977475i	−0.183636	+	0.106022i
$86$	−15.1421	+	10.3422i	−1.63281	+	1.11523i
$87$	2.12907	+	10.8502i	0.228260	+	1.16327i
$88$	3.58074	−	11.7123i	0.381708	−	1.24853i
$89$		−	8.68661i		−	0.920779i	−0.887717	−	0.460389i	$-0.847710\pi$
$89$		−	8.68661i		−	0.920779i	0.887717	−	0.460389i	$-0.152290\pi$
$90$	9.91453	+	0.599994i	1.04508	+	0.0632450i
$91$	−5.71651			−0.599253
$92$	6.28991	−	16.1052i	0.655768	−	1.67909i
$93$	−4.55288	+	13.2992i	−0.472112	+	1.37906i
$94$	−9.65814	+	6.59660i	−0.996161	+	0.680387i
$95$	3.27361	+	5.67006i	0.335866	+	0.581736i
$96$	0.473307	+	9.78652i	0.0483067	+	0.998833i
$97$	−3.64813	+	6.31875i	−0.370411	+	0.641571i	−0.989629	−	0.143648i	$-0.954117\pi$
$97$	−3.64813	+	6.31875i	−0.370411	+	0.641571i	0.619217	+	0.785220i	$0.287450\pi$
$98$	−0.106859	−	1.41017i	−0.0107943	−	0.142449i
$99$	7.96124	−	10.2649i	0.800135	−	1.03166i
$100$	−0.951003	+	0.144961i	−0.0951003	+	0.0144961i
$101$	3.40502	−	5.89767i	0.338812	−	0.586840i	−0.645397	−	0.763847i	$-0.723308\pi$
$101$	3.40502	−	5.89767i	0.338812	−	0.586840i	0.984210	+	0.177007i	$0.0566416\pi$
$102$	−0.544382	−	1.97164i	−0.0539019	−	0.195222i
$103$	2.86229	−	1.65255i	0.282030	−	0.162830i	−0.352312	−	0.935883i	$-0.614604\pi$
$103$	2.86229	−	1.65255i	0.282030	−	0.162830i	0.634342	+	0.773052i	$0.281271\pi$
$104$	11.0271	+	11.8250i	1.08130	+	1.15954i
$105$	2.66575	+	3.05562i	0.260150	+	0.298198i
$106$	11.6024	+	5.57551i	1.12692	+	0.541541i
$107$			2.36937i			0.229055i	0.993420	+	0.114528i	$0.0365354\pi$
$107$			2.36937i			0.229055i	−0.993420	+	0.114528i	$0.963465\pi$
$108$	−3.21622	+	9.88210i	−0.309481	+	0.950906i
$109$		−	15.8120i		−	1.51452i	−0.653115	−	0.757258i	$-0.726538\pi$
$109$		−	15.8120i		−	1.51452i	0.653115	−	0.757258i	$-0.273462\pi$
$110$	−6.20962	+	12.9219i	−0.592064	+	1.23206i
$111$	3.32302	+	3.80902i	0.315407	+	0.361536i
$112$	−2.71091	+	2.94125i	−0.256157	+	0.277922i
$113$	−2.41824	+	1.39617i	−0.227489	+	0.131341i	−0.609413	−	0.792853i	$-0.708595\pi$
$113$	−2.41824	+	1.39617i	−0.227489	+	0.131341i	0.381924	+	0.924194i	$0.375262\pi$
$114$	−6.60313	+	1.82316i	−0.618440	+	0.170755i
$115$	−10.1196	+	17.5276i	−0.943657	+	1.63446i
$116$	12.6219	−	1.92395i	1.17192	−	0.178634i
$117$	6.48075	+	15.8779i	0.599145	+	1.46791i
$118$	13.6471	−	1.03414i	1.25632	−	0.0952002i
$119$	0.417519	−	0.723163i	0.0382739	−	0.0662923i
$120$	1.17856	−	11.4085i	0.107587	−	1.04145i
$121$	3.87492	+	6.71156i	0.352266	+	0.610142i
$122$	3.52175	+	5.15622i	0.318844	+	0.466822i
$123$	−0.251284	+	0.734014i	−0.0226576	+	0.0661838i
$124$	15.1194	+	5.90488i	1.35776	+	0.530273i
$125$	−10.5797			−0.946275
$126$	−3.79567	+	1.89550i	−0.338145	+	0.168865i
$127$			13.0937i			1.16188i	0.813947	+	0.580939i	$0.197314\pi$
$127$			13.0937i			1.16188i	−0.813947	+	0.580939i	$0.802686\pi$
$128$	11.3135	−	0.0659460i	0.999983	−	0.00582886i
$129$	4.32434	+	22.0378i	0.380737	+	1.94032i
$130$	−10.6748	−	15.6291i	−0.936244	−	1.37076i
$131$	19.3616	−	11.1784i	1.69163	−	0.976665i	0.738431	−	0.674329i	$-0.235567\pi$
$131$	19.3616	−	11.1784i	1.69163	−	0.976665i	0.953201	−	0.302336i	$-0.0977665\pi$
$132$	−11.4516	−	9.68811i	−0.996732	−	0.843241i
$133$	−2.42191	−	1.39829i	−0.210006	−	0.121247i
$134$	−0.235177	−	3.10354i	−0.0203162	−	0.268105i
$135$	5.46498	−	10.8683i	0.470350	−	0.935398i
$136$	−2.30131	+	0.531310i	−0.197335	+	0.0455594i
$137$	−3.02705	−	1.74767i	−0.258618	−	0.149313i	0.365086	−	0.930974i	$-0.381040\pi$
$137$	−3.02705	−	1.74767i	−0.258618	−	0.149313i	−0.623704	+	0.781661i	$0.714373\pi$
$138$	−15.0868	−	14.8594i	−1.28427	−	1.26491i
$139$	0.250284	+	0.433505i	0.0212288	+	0.0367694i	0.876445	−	0.481503i	$-0.159909\pi$
$139$	0.250284	+	0.433505i	0.0212288	+	0.0367694i	−0.855216	+	0.518272i	$0.826575\pi$
$140$	3.65591	−	2.92546i	0.308980	−	0.247247i
$141$	2.75821	+	14.0565i	0.232283	+	1.18377i
$142$	5.74103	+	2.75885i	0.481777	+	0.231517i
$143$	−24.7531			−2.06996
$144$	11.2428	+	4.19520i	0.936899	+	0.349600i
$145$	−14.9456			−1.24116
$146$	−3.63748	−	1.74799i	−0.301040	−	0.144664i
$147$	−1.63868	−	0.560992i	−0.135156	−	0.0462698i
$148$	4.55732	−	3.64678i	0.374609	−	0.299763i
$149$	5.56925	+	9.64622i	0.456251	+	0.790249i	0.998759	−	0.0498011i	$-0.0158588\pi$
$149$	5.56925	+	9.64622i	0.456251	+	0.790249i	−0.542509	+	0.840050i	$0.682525\pi$
$150$	−0.296286	+	1.14033i	−0.0241917	+	0.0931073i
$151$	0.0993683	+	0.0573703i	0.00808648	+	0.00466873i	0.504038	−	0.863682i	$-0.331847\pi$
$151$	0.0993683	+	0.0573703i	0.00808648	+	0.00466873i	−0.495951	+	0.868350i	$0.665181\pi$
$152$	1.77938	+	7.70719i	0.144327	+	0.625136i
$153$	−2.48195	−	0.339833i	−0.200654	−	0.0274739i
$154$	−0.462709	−	6.10619i	−0.0372862	−	0.492051i
$155$	−16.4547	−	9.50013i	−1.32167	−	0.763069i
$156$	18.6355	−	6.69766i	1.49204	−	0.536242i
$157$	−8.04897	+	4.64707i	−0.642378	+	0.370877i	−0.785530	−	0.618824i	$-0.787609\pi$
$157$	−8.04897	+	4.64707i	−0.642378	+	0.370877i	0.143152	+	0.989701i	$0.454276\pi$
$158$	−5.95714	−	8.72191i	−0.473925	−	0.693878i
$159$	11.8800	−	10.3642i	0.942146	−	0.821937i
$160$	−13.1037	−	1.91931i	−1.03594	−	0.151735i
$161$		−	8.64497i		−	0.681319i
$162$	9.56794	+	8.39372i	0.751728	+	0.659473i
$163$	23.1230			1.81113			0.905566	−	0.424205i	$-0.139446\pi$
$163$	23.1230			1.81113			0.905566	+	0.424205i	$0.139446\pi$
$164$	0.834474	+	0.325904i	0.0651615	+	0.0254488i
$165$	11.5430	+	13.2311i	0.898619	+	1.03004i
$166$	4.50786	+	6.60001i	0.349878	+	0.512260i
$167$	3.29049	+	5.69930i	0.254626	+	0.441025i	0.964794	−	0.263007i	$-0.0847143\pi$
$167$	3.29049	+	5.69930i	0.254626	+	0.441025i	−0.710168	+	0.704032i	$0.751381\pi$
$168$	2.00056	+	4.47189i	0.154346	+	0.345014i
$169$	9.83925	−	17.0421i	0.756865	−	1.31093i
$170$	2.75681	−	0.208903i	0.211438	−	0.0160221i
$171$	−1.13812	+	8.31219i	−0.0870341	+	0.635649i
$172$	25.6363	−	3.90772i	1.95475	−	0.297961i
$173$	0.420646	−	0.728581i	0.0319811	−	0.0553930i	−0.849592	−	0.527441i	$-0.823152\pi$
$173$	0.420646	−	0.728581i	0.0319811	−	0.0553930i	0.881573	+	0.472048i	$0.156485\pi$
$174$	3.93237	−	15.1347i	0.298112	−	1.14736i
$175$	−0.416553	+	0.240497i	−0.0314885	+	0.0181799i
$176$	−11.7385	+	12.7359i	−0.884825	+	0.960008i
$177$	5.42908	−	15.8586i	0.408075	−	1.19201i
$178$	−5.32092	+	11.0726i	−0.398820	+	0.829925i
$179$			14.3811i			1.07489i	0.843298	+	0.537446i	$0.180611\pi$
$179$			14.3811i			1.07489i	−0.843298	+	0.537446i	$0.819389\pi$
$180$	−12.2703	−	6.83787i	−0.914571	−	0.509665i
$181$			0.791999i			0.0588688i	0.999567	+	0.0294344i	$0.00937062\pi$
$181$			0.791999i			0.0588688i	−0.999567	+	0.0294344i	$0.990629\pi$
$182$	7.28668	+	3.50161i	0.540125	+	0.259557i
$183$	7.50437	−	1.47253i	0.554739	−	0.108853i
$184$	−17.8827	+	16.6761i	−1.31833	+	1.22938i
$185$	−5.91704	+	3.41621i	−0.435029	+	0.251164i
$186$	13.9498	−	14.1633i	1.02285	−	1.03850i
$187$	1.80790	−	3.13138i	0.132207	−	0.228989i
$188$	16.3517	−	2.49248i	1.19257	−	0.181782i
$189$	0.299580	+	5.18751i	0.0217912	+	0.377336i
$190$	−0.699627	−	9.23271i	−0.0507563	−	0.669811i
$191$	−11.7531	+	20.3569i	−0.850423	+	1.47298i	0.0304034	+	0.999538i	$0.490321\pi$
$191$	−11.7531	+	20.3569i	−0.850423	+	1.47298i	−0.880827	+	0.473439i	$0.843013\pi$
$192$	5.39135	−	12.7645i	0.389087	−	0.921201i
$193$	−9.00647	−	15.5997i	−0.648300	−	1.12289i	−0.983529	−	0.180752i	$-0.942147\pi$
$193$	−9.00647	−	15.5997i	−0.648300	−	1.12289i	0.335228	−	0.942137i	$-0.391186\pi$
$194$	8.52068	−	5.81970i	0.611749	−	0.417830i
$195$	−22.7466	+	4.46343i	−1.62892	+	0.319633i
$196$	−0.727580	+	1.86296i	−0.0519700	+	0.133069i
$197$	−4.47512			−0.318839			−0.159419	−	0.987211i	$-0.550962\pi$
$197$	−4.47512			−0.318839			−0.159419	+	0.987211i	$0.550962\pi$
$198$	−16.4356	+	8.20772i	−1.16803	+	0.583297i
$199$		−	13.7687i		−	0.976037i	−0.872833	−	0.488019i	$-0.837720\pi$
$199$		−	13.7687i		−	0.976037i	0.872833	−	0.488019i	$-0.162280\pi$
$200$	1.30101	+	0.397753i	0.0919955	+	0.0281254i
$201$	−3.60645	−	1.23464i	−0.254380	−	0.0870851i
$202$	−7.95286	+	5.43188i	−0.559561	+	0.382185i
$203$	5.52858	−	3.19193i	0.388030	−	0.224029i
$204$	−0.513806	+	2.84666i	−0.0359736	+	0.199306i
$205$	−0.908174	−	0.524335i	−0.0634296	−	0.0366211i
$206$	−4.66074	+	0.353178i	−0.324729	+	0.0246070i
$207$	−24.0118	+	9.80071i	−1.66893	+	0.681196i
$208$	−6.81263	−	21.8276i	−0.472371	−	1.51347i
$209$	−10.4871	−	6.05475i	−0.725411	−	0.418816i
$210$	−1.52626	−	5.52779i	−0.105322	−	0.381454i
$211$	3.78741	+	6.55998i	0.260736	+	0.451608i	0.966438	−	0.256901i	$-0.0827015\pi$
$211$	3.78741	+	6.55998i	0.260736	+	0.451608i	−0.705702	+	0.708509i	$0.749368\pi$
$212$	−11.3740	−	14.2139i	−0.781169	−	0.976215i
$213$	5.87842	−	5.12838i	0.402782	−	0.351391i
$214$	1.45134	−	3.02017i	0.0992114	−	0.206454i
$215$	−30.3558			−2.07025
$216$	10.1528	−	10.6264i	0.690814	−	0.723033i
$217$	8.11577			0.550934
$218$	−9.68554	+	20.1552i	−0.655988	+	1.36508i
$219$	−3.72452	+	3.24931i	−0.251680	+	0.219568i
$220$	15.8305	−	12.6676i	1.06729	−	0.854047i
$221$	2.38675	+	4.13397i	0.160550	+	0.278081i
$222$	−1.90258	−	6.89075i	−0.127693	−	0.462477i
$223$	6.65936	+	3.84478i	0.445944	+	0.257466i	0.706116	−	0.708097i	$-0.250446\pi$
$223$	6.65936	+	3.84478i	0.445944	+	0.257466i	−0.260172	+	0.965562i	$0.583779\pi$
$224$	5.25717	−	2.08859i	0.351259	−	0.139550i
$225$	1.14023	+	0.884345i	0.0760155	+	0.0589564i
$226$	3.93768	−	0.298386i	0.261931	−	0.0198483i
$227$	−9.72042	−	5.61209i	−0.645167	−	0.372487i	0.141435	−	0.989948i	$-0.454828\pi$
$227$	−9.72042	−	5.61209i	−0.645167	−	0.372487i	−0.786602	+	0.617460i	$0.788162\pi$
$228$	9.53360	+	1.72076i	0.631378	+	0.113960i
$229$	−14.8980	+	8.60134i	−0.984484	+	0.568392i	−0.903621	−	0.428333i	$-0.859101\pi$
$229$	−14.8980	+	8.60134i	−0.984484	+	0.568392i	−0.0808633	+	0.996725i	$0.525768\pi$
$230$	23.6356	−	16.1433i	1.55849	−	1.06446i
$231$	−7.09568	−	2.42916i	−0.466862	−	0.159827i
$232$	−17.2673	−	5.27906i	−1.13365	−	0.346587i
$233$		−	0.825385i		−	0.0540728i	−0.999634	−	0.0270364i	$-0.991393\pi$
$233$		−	0.825385i		−	0.0540728i	0.999634	−	0.0270364i	$-0.00860700\pi$
$234$	1.46504	−	24.2088i	0.0957724	−	1.58258i
$235$	−19.3620			−1.26304
$236$	−18.0291	−	7.04126i	−1.17359	−	0.458347i
$237$	−12.6939	+	2.49084i	−0.824556	+	0.161797i
$238$	−0.975168	+	0.666049i	−0.0632108	+	0.0431735i
$239$	−1.11213	−	1.92626i	−0.0719375	−	0.124599i	0.827813	−	0.561004i	$-0.189585\pi$
$239$	−1.11213	−	1.92626i	−0.0719375	−	0.124599i	−0.899750	+	0.436405i	$0.856252\pi$
$240$	−8.49050	+	13.8202i	−0.548059	+	0.892093i
$241$	0.657377	−	1.13861i	0.0423454	−	0.0733443i	−0.844076	−	0.536224i	$-0.819850\pi$
$241$	0.657377	−	1.13861i	0.0423454	−	0.0733443i	0.886421	+	0.462879i	$0.153184\pi$
$242$	−0.828137	−	10.9286i	−0.0532347	−	0.702517i
$243$	14.0689	−	6.71312i	0.902520	−	0.430647i
$244$	−1.33067	−	8.72972i	−0.0851871	−	0.558863i
$245$	1.17058	−	2.02750i	0.0747854	−	0.129532i
$246$	0.769920	−	0.781705i	0.0490883	−	0.0498397i
$247$	13.8449	−	7.99335i	0.880929	−	0.508605i
$248$	−15.6553	−	16.7880i	−0.994110	−	1.06604i
$249$	9.60566	−	1.88486i	0.608734	−	0.119448i
$250$	13.4856	+	6.48051i	0.852906	+	0.409863i
$251$		−	5.45242i		−	0.344153i	−0.985084	−	0.172077i	$-0.944952\pi$
$251$		−	5.45242i		−	0.344153i	0.985084	−	0.172077i	$-0.0550477\pi$
$252$	5.99931	−	0.0911339i	0.377921	−	0.00574090i
$253$		−	37.4336i		−	2.35343i
$254$	8.02045	−	16.6902i	0.503248	−	1.04723i
$255$	1.09671	−	3.20355i	0.0686787	−	0.200614i
$256$	−14.4614	−	6.84596i	−0.903839	−	0.427872i
$257$	−14.7701	+	8.52754i	−0.921336	+	0.531933i	−0.884061	−	0.467372i	$-0.845201\pi$
$257$	−14.7701	+	8.52754i	−0.921336	+	0.531933i	−0.0372747	+	0.999305i	$0.511868\pi$
$258$	7.98700	−	30.7399i	0.497249	−	1.91378i
$259$	1.45920	−	2.52741i	0.0906702	−	0.157045i
$260$	4.03341	+	26.4608i	0.250141	+	1.64103i
$261$	−15.1334	−	11.7372i	−0.936734	−	0.726515i
$262$	−31.5270	+	2.38902i	−1.94775	+	0.147594i
$263$	−7.72261	+	13.3760i	−0.476197	+	0.824797i	−0.999628	−	0.0272708i	$-0.991318\pi$
$263$	−7.72261	+	13.3760i	−0.476197	+	0.824797i	0.523431	+	0.852068i	$0.324652\pi$
$264$	8.66264	+	19.3638i	0.533148	+	1.19176i
$265$	10.6549	+	18.4548i	0.654523	+	1.13367i
$266$	2.23063	+	3.26589i	0.136769	+	0.200245i
$267$	9.89098	+	11.3376i	0.605318	+	0.693847i
$268$	−1.60128	+	4.10005i	−0.0978135	+	0.250450i
$269$	13.0114			0.793319			0.396659	−	0.917966i	$-0.370169\pi$
$269$	13.0114			0.793319			0.396659	+	0.917966i	$0.370169\pi$
$270$	−13.6234	+	10.5060i	−0.829093	+	0.639378i
$271$			12.0923i			0.734553i	0.930112	+	0.367276i	$0.119710\pi$
$271$			12.0923i			0.734553i	−0.930112	+	0.367276i	$0.880290\pi$
$272$	3.25886	+	0.732403i	0.197598	+	0.0444084i
$273$	7.46105	−	6.50909i	0.451563	−	0.393948i
$274$	2.78797	+	4.08190i	0.168428	+	0.246596i
$275$	−1.80372	+	1.04138i	−0.108768	+	0.0627975i
$276$	10.1287	+	28.1822i	0.609679	+	1.69637i
$277$	15.5250	+	8.96334i	0.932805	+	0.538555i	0.887697	−	0.460427i	$-0.152304\pi$
$277$	15.5250	+	8.96334i	0.932805	+	0.538555i	0.0451071	+	0.998982i	$0.485637\pi$
$278$	−0.0534901	−	0.705887i	−0.00320812	−	0.0423363i
$279$	−9.20076	−	22.5419i	−0.550835	−	1.34955i
$280$	−6.45206	+	1.48961i	−0.385584	+	0.0890210i
$281$	6.64341	+	3.83557i	0.396312	+	0.228811i	0.684892	−	0.728645i	$-0.259850\pi$
$281$	6.64341	+	3.83557i	0.396312	+	0.228811i	−0.288579	+	0.957456i	$0.593183\pi$
$282$	5.09438	−	19.6069i	0.303366	−	1.16758i
$283$	−10.0205	−	17.3559i	−0.595654	−	1.03170i	−0.993454	−	0.114231i	$-0.963559\pi$
$283$	−10.0205	−	17.3559i	−0.595654	−	1.03170i	0.397800	−	0.917472i	$-0.369774\pi$
$284$	−5.62803	−	7.03326i	−0.333962	−	0.417347i
$285$	−10.7288	−	3.67294i	−0.635522	−	0.217566i
$286$	31.5521	+	15.1623i	1.86572	+	0.896568i
$287$	0.447929			0.0264404
$288$	−11.7611	−	12.2342i	−0.693032	−	0.720907i
$289$	16.3027			0.958983
$290$	19.0507	+	9.15480i	1.11870	+	0.537589i
$291$	−2.43337	−	12.4010i	−0.142647	−	0.726960i
$292$	3.56588	+	4.45622i	0.208677	+	0.260781i
$293$	−2.38032	−	4.12283i	−0.139060	−	0.240858i	0.788081	−	0.615571i	$-0.211075\pi$
$293$	−2.38032	−	4.12283i	−0.139060	−	0.240858i	−0.927141	+	0.374713i	$0.877741\pi$
$294$	1.74516	+	1.71885i	0.101780	+	0.100245i
$295$	19.6214	+	11.3284i	1.14240	+	0.659566i
$296$	−8.04290	+	1.85689i	−0.467484	+	0.107930i
$297$	1.29721	+	22.4625i	0.0752720	+	1.30341i
$298$	−1.19024	−	15.7072i	−0.0689490	−	0.909892i
$299$	42.7982	+	24.7095i	2.47508	+	1.42899i
$300$	1.07617	−	1.27206i	0.0621326	−	0.0734422i
$301$	11.2290	−	6.48309i	0.647231	−	0.373679i
$302$	−0.0915203	−	0.133996i	−0.00526640	−	0.00771059i
$303$	2.27121	+	11.5746i	0.130478	+	0.664944i
$304$	2.45285	−	10.9141i	0.140681	−	0.625966i
$305$			10.3368i			0.591885i
$306$	2.95552	+	1.95348i	0.168956	+	0.111673i
$307$	9.22752			0.526642			0.263321	−	0.964708i	$-0.415182\pi$
$307$	9.22752			0.526642			0.263321	+	0.964708i	$0.415182\pi$
$308$	−3.15050	+	8.06683i	−0.179517	+	0.459650i
$309$	−1.85413	+	5.41600i	−0.105478	+	0.308106i
$310$	15.1551	+	22.1888i	0.860753	+	1.26024i
$311$	8.65935	+	14.9984i	0.491027	+	0.850483i	0.999947	−	0.0103307i	$-0.00328843\pi$
$311$	8.65935	+	14.9984i	0.491027	+	0.850483i	−0.508920	+	0.860814i	$0.669955\pi$
$312$	−27.8568	−	2.87774i	−1.57708	−	0.162920i
$313$	−9.21315	+	15.9576i	−0.520758	+	0.901979i	0.478951	+	0.877842i	$0.341017\pi$
$313$	−9.21315	+	15.9576i	−0.520758	+	0.901979i	−0.999709	+	0.0241373i	$0.992316\pi$
$314$	13.1063	−	0.993160i	0.739633	−	0.0560472i
$315$	−6.95853	−	0.952774i	−0.392069	−	0.0536827i
$316$	2.25086	+	14.7666i	0.126621	+	0.830685i
$317$	4.47969	−	7.75904i	0.251604	−	0.435791i	−0.712363	−	0.701811i	$-0.752375\pi$
$317$	4.47969	−	7.75904i	0.251604	−	0.435791i	0.963968	+	0.266019i	$0.0857085\pi$
$318$	−21.4917	+	5.93398i	−1.20519	+	0.332761i
$319$	23.9393	−	13.8214i	1.34035	−	0.773849i
$320$	15.5273	+	10.4731i	0.868004	+	0.585464i
$321$	−2.69787	−	3.09244i	−0.150580	−	0.172603i
$322$	−5.29541	+	11.0195i	−0.295102	+	0.614093i
$323$			2.33525i			0.129937i
$324$	−7.05448	−	16.5600i	−0.391916	−	0.920001i
$325$		−	2.74961i		−	0.152521i
$326$	−29.4742	−	14.1638i	−1.63243	−	0.784462i
$327$	18.0043	+	20.6375i	0.995640	+	1.14125i
$328$	−0.864051	−	0.926572i	−0.0477092	−	0.0511614i
$329$	7.16227	−	4.13514i	0.394869	−	0.227977i
$330$	−6.60886	−	23.9359i	−0.363806	−	1.31763i
$331$	−1.08539	+	1.87995i	−0.0596585	+	0.103332i	−0.894312	−	0.447444i	$-0.852335\pi$
$331$	−1.08539	+	1.87995i	−0.0596585	+	0.103332i	0.834654	+	0.550775i	$0.185668\pi$
$332$	−1.70326	−	11.1741i	−0.0934787	−	0.613259i
$333$	−8.67426	−	1.18769i	−0.475346	−	0.0650852i
$334$	−0.703235	−	9.28031i	−0.0384793	−	0.507796i
$335$	2.57623	−	4.46216i	0.140755	−	0.243794i
$336$	0.189165	−	6.92562i	0.0103198	−	0.377824i
$337$	−10.6654	−	18.4730i	−0.580982	−	1.00629i	−0.995363	−	0.0961865i	$-0.969335\pi$
$337$	−10.6654	−	18.4730i	−0.580982	−	1.00629i	0.414382	−	0.910103i	$-0.363998\pi$
$338$	−22.9808	+	15.6961i	−1.24999	+	0.853756i
$339$	1.56648	−	4.57577i	0.0850796	−	0.248522i
$340$	−3.64200	−	1.42238i	−0.197515	−	0.0771395i
$341$	35.1422			1.90305
$342$	6.54231	−	9.89818i	0.353767	−	0.535232i
$343$			1.00000i			0.0539949i
$344$	−35.0715	−	10.7222i	−1.89093	−	0.578105i
$345$	−6.74995	−	34.3993i	−0.363405	−	1.85200i
$346$	−0.982474	+	0.671038i	−0.0528181	+	0.0360752i
$347$	7.66832	−	4.42730i	0.411657	−	0.237670i	−0.279845	−	0.960045i	$-0.590283\pi$
$347$	7.66832	−	4.42730i	0.411657	−	0.237670i	0.691501	+	0.722375i	$0.256950\pi$
$348$	−14.2831	+	16.8830i	−0.765655	+	0.905023i
$349$	−11.4473	−	6.60908i	−0.612757	−	0.353776i	0.161286	−	0.986908i	$-0.448436\pi$
$349$	−11.4473	−	6.60908i	−0.612757	−	0.353776i	−0.774044	+	0.633132i	$0.781769\pi$
$350$	0.678284	−	0.0513983i	0.0362558	−	0.00274736i
$351$	−26.5378	−	13.3441i	−1.41648	−	0.712256i
$352$	22.7641	−	9.04381i	1.21333	−	0.482037i
$353$	6.35201	+	3.66734i	0.338083	+	0.195193i	0.659424	−	0.751771i	$-0.270800\pi$
$353$	6.35201	+	3.66734i	0.338083	+	0.195193i	−0.321341	+	0.946964i	$0.604133\pi$
$354$	−16.6344	+	16.8890i	−0.884107	+	0.897640i
$355$	5.27219	+	9.13170i	0.279819	+	0.484660i
$356$	13.5649	−	10.8546i	0.718937	−	0.575294i
$357$	0.278492	+	1.41926i	0.0147394	+	0.0751153i
$358$	8.80902	−	18.3312i	0.465571	−	0.968831i
$359$	−7.37152			−0.389054			−0.194527	−	0.980897i	$-0.562317\pi$
$359$	−7.37152			−0.389054			−0.194527	+	0.980897i	$0.562317\pi$
$360$	11.4521	+	16.2321i	0.603577	+	0.855508i
$361$	−11.1791			−0.588375
$362$	0.485134	−	1.00954i	0.0254981	−	0.0530602i
$363$	−12.6995	−	4.34760i	−0.666553	−	0.228190i
$364$	−7.14325	−	8.92681i	−0.374408	−	0.467892i
$365$	−3.34042	−	5.78578i	−0.174846	−	0.302842i
$366$	−10.4676	−	2.71975i	−0.547151	−	0.142164i
$367$	12.2740	+	7.08642i	0.640700	+	0.369908i	0.784884	−	0.619643i	$-0.212723\pi$
$367$	12.2740	+	7.08642i	0.640700	+	0.369908i	−0.144184	+	0.989551i	$0.546056\pi$
$368$	33.0094	−	10.3026i	1.72074	−	0.537060i
$369$	−0.507812	−	1.24414i	−0.0264356	−	0.0647674i
$370$	9.63486	−	0.730102i	0.500893	−	0.0379562i
$371$	−7.88276	−	4.55112i	−0.409253	−	0.236282i
$372$	−26.4570	+	9.50872i	−1.37173	+	0.493004i
$373$	−16.2925	+	9.40645i	−0.843591	+	0.487048i	−0.858483	−	0.512841i	$-0.828593\pi$
$373$	−16.2925	+	9.40645i	−0.843591	+	0.487048i	0.0148920	+	0.999889i	$0.495260\pi$
$374$	−4.22259	+	2.88406i	−0.218345	+	0.149131i
$375$	13.8083	−	12.0465i	0.713060	−	0.622080i
$376$	−22.3698	−	6.83901i	−1.15363	−	0.352695i
$377$			36.4934i			1.87950i
$378$	2.79571	−	6.79588i	0.143796	−	0.349543i
$379$	17.7706			0.912816			0.456408	−	0.889771i	$-0.349136\pi$
$379$	17.7706			0.912816			0.456408	+	0.889771i	$0.349136\pi$
$380$	−4.76363	+	12.1972i	−0.244369	+	0.625705i
$381$	−14.9091	−	17.0896i	−0.763816	−	0.875525i
$382$	27.4508	−	18.7492i	1.40451	−	0.959291i
$383$	11.7247	+	20.3078i	0.599106	+	1.03768i	0.992953	+	0.118506i	$0.0378103\pi$
$383$	11.7247	+	20.3078i	0.599106	+	1.03768i	−0.393848	+	0.919176i	$0.628856\pi$
$384$	−14.6910	+	12.9682i	−0.749699	+	0.661779i
$385$	5.06872	−	8.77928i	0.258326	−	0.447434i
$386$	1.92484	+	25.4013i	0.0979717	+	1.29289i
$387$	−30.7373	−	23.8393i	−1.56247	−	1.21182i
$388$	−14.4259	+	2.19893i	−0.732364	+	0.111634i
$389$	4.35082	−	7.53584i	0.220595	−	0.382082i	−0.734394	−	0.678724i	$-0.762533\pi$
$389$	4.35082	−	7.53584i	0.220595	−	0.382082i	0.954989	+	0.296642i	$0.0958666\pi$
$390$	31.7286	+	8.24389i	1.60664	+	0.417446i
$391$	−6.25172	+	3.60943i	−0.316163	+	0.182537i
$392$	2.06857	−	1.92899i	0.104479	−	0.0974288i
$393$	−12.5420	+	36.6359i	−0.632662	+	1.84804i
$394$	5.70431	+	2.74120i	0.287379	+	0.138100i
$395$		−	17.4851i		−	0.879769i
$396$	25.9777	−	0.394620i	1.30543	−	0.0198304i
$397$		−	19.7436i		−	0.990904i	−0.868635	−	0.495452i	$-0.835002\pi$
$397$		−	19.7436i		−	0.990904i	0.868635	−	0.495452i	$-0.164998\pi$
$398$	−8.43392	+	17.5506i	−0.422754	+	0.879732i
$399$	4.75318	−	0.932685i	0.237957	−	0.0466927i
$400$	−1.41473	−	1.30393i	−0.0707363	−	0.0651966i
$401$	−11.0421	+	6.37514i	−0.551415	+	0.318359i	−0.749692	−	0.661787i	$-0.769799\pi$
$401$	−11.0421	+	6.37514i	−0.551415	+	0.318359i	0.198278	+	0.980146i	$0.436465\pi$
$402$	3.84078	+	3.78288i	0.191561	+	0.188673i
$403$	−23.1969	+	40.1783i	−1.15552	+	2.00142i
$404$	13.4646	−	2.05239i	0.669887	−	0.102110i
$405$	5.24245	+	20.4078i	0.260499	+	1.01407i
$406$	−9.00232	+	0.682169i	−0.446778	+	0.0338555i
$407$	6.31849	−	10.9439i	0.313196	−	0.542471i
$408$	2.39863	−	3.31383i	0.118750	−	0.164059i
$409$	−11.1934	−	19.3875i	−0.553478	−	0.958652i	−0.998020	−	0.0628939i	$-0.979967\pi$
$409$	−11.1934	−	19.3875i	−0.553478	−	0.958652i	0.444542	−	0.895758i	$-0.353366\pi$
$410$	0.836447	+	1.22465i	0.0413092	+	0.0604812i
$411$	5.94080	−	1.16572i	0.293038	−	0.0575009i
$412$	6.15726	+	2.40472i	0.303346	+	0.118472i
$413$	−9.67764			−0.476206
$414$	36.6105	+	2.21555i	1.79931	+	0.108888i
$415$			13.2312i			0.649496i
$416$	−4.68648	+	31.9961i	−0.229773	+	1.56874i
$417$	−0.820274	−	0.280815i	−0.0401690	−	0.0137516i
$418$	9.65888	+	14.1417i	0.472431	+	0.691691i
$419$	−30.3014	+	17.4945i	−1.48032	+	0.854664i	−0.999751	−	0.0222925i	$-0.992903\pi$
$419$	−30.3014	+	17.4945i	−1.48032	+	0.854664i	−0.480570	+	0.876956i	$0.659570\pi$
$420$	−1.44053	+	7.98103i	−0.0702908	+	0.389434i
$421$	21.2669	+	12.2785i	1.03649	+	0.598415i	0.918836	−	0.394640i	$-0.129131\pi$
$421$	21.2669	+	12.2785i	1.03649	+	0.598415i	0.117650	+	0.993055i	$0.462464\pi$
$422$	−0.809434	−	10.6818i	−0.0394026	−	0.519981i
$423$	−19.6053	−	15.2055i	−0.953243	−	0.739319i
$424$	5.79148	+	25.0851i	0.281259	+	1.21824i
$425$	0.347837	+	0.200824i	0.0168726	+	0.00974139i
$426$	−10.6344	+	2.93622i	−0.515239	+	0.142261i
$427$	−2.20764	−	3.82374i	−0.106835	−	0.185044i
$428$	−3.69996	+	2.96072i	−0.178844	+	0.143112i
$429$	32.3072	−	28.1850i	1.55980	−	1.36079i
$430$	38.6937	+	18.5942i	1.86598	+	0.896694i
$431$	0.195268			0.00940573			0.00470286	−	0.999989i	$-0.498503\pi$
$431$	0.195268			0.00940573			0.00470286	+	0.999989i	$0.498503\pi$
$432$	−19.4507	+	7.32609i	−0.935821	+	0.352477i
$433$	22.6156			1.08684			0.543419	−	0.839462i	$-0.317130\pi$
$433$	22.6156			1.08684			0.543419	+	0.839462i	$0.317130\pi$
$434$	−10.3450	−	4.97126i	−0.496574	−	0.238628i
$435$	19.5066	−	17.0177i	0.935270	−	0.815937i
$436$	24.6918	−	19.7584i	1.18252	−	0.946257i
$437$	12.0882	+	20.9373i	0.578256	+	1.00157i
$438$	6.73789	−	1.86037i	0.321949	−	0.0888920i
$439$	−13.0274	−	7.52139i	−0.621765	−	0.358976i	0.155791	−	0.987790i	$-0.450207\pi$
$439$	−13.0274	−	7.52139i	−0.621765	−	0.358976i	−0.777556	+	0.628814i	$0.783541\pi$
$440$	−27.9381	+	6.45016i	−1.33190	+	0.307499i
$441$	2.77754	−	1.13369i	0.132264	−	0.0539852i
$442$	−0.510089	−	6.73145i	−0.0242625	−	0.320182i
$443$	−11.8077	−	6.81716i	−0.561000	−	0.323893i	0.192547	−	0.981288i	$-0.438325\pi$
$443$	−11.8077	−	6.81716i	−0.561000	−	0.323893i	−0.753547	+	0.657395i	$0.771659\pi$
$444$	−1.79572	+	9.94886i	−0.0852210	+	0.472152i
$445$	−17.6121	+	10.1683i	−0.834893	+	0.482025i
$446$	−6.13341	−	8.97999i	−0.290425	−	0.425215i
$447$	−18.2525	−	6.24861i	−0.863313	−	0.295549i
$448$	−7.98052	−	0.557976i	−0.377044	−	0.0263619i
$449$		−	14.8982i		−	0.703092i	−0.936171	−	0.351546i	$-0.885656\pi$
$449$		−	14.8982i		−	0.703092i	0.936171	−	0.351546i	$-0.114344\pi$
$450$	−0.911724	−	1.82569i	−0.0429791	−	0.0860640i
$451$	1.93958			0.0913312
$452$	−5.20203	−	2.03165i	−0.244683	−	0.0955610i
$453$	−0.195018	+	0.0382670i	−0.00916273	+	0.00179794i
$454$	8.95271	+	13.1078i	0.420172	+	0.615177i
$455$	6.69161	+	11.5902i	0.313708	+	0.543357i
$456$	−11.0982	−	8.03315i	−0.519720	−	0.376187i
$457$	9.68726	−	16.7788i	0.453151	−	0.784880i	−0.545429	−	0.838157i	$-0.683633\pi$
$457$	9.68726	−	16.7788i	0.453151	−	0.784880i	0.998580	+	0.0532768i	$0.0169666\pi$
$458$	24.2587	−	1.83825i	1.13353	−	0.0858959i
$459$	3.62634	−	2.38253i	0.169263	−	0.111207i
$460$	−40.0162	+	6.09964i	−1.86576	+	0.284397i
$461$	19.4767	−	33.7346i	0.907119	−	1.57118i	0.0890717	−	0.996025i	$-0.471610\pi$
$461$	19.4767	−	33.7346i	0.907119	−	1.57118i	0.818047	−	0.575151i	$-0.195057\pi$
$462$	7.55671	+	7.44279i	0.351570	+	0.346270i
$463$	−27.0116	+	15.5951i	−1.25533	+	0.724767i	−0.972164	−	0.234303i	$-0.924719\pi$
$463$	−27.0116	+	15.5951i	−1.25533	+	0.724767i	−0.283170	+	0.959070i	$0.591386\pi$
$464$	18.7765	+	17.3060i	0.871678	+	0.803413i
$465$	32.2936	−	6.33676i	1.49758	−	0.293860i
$466$	−0.505584	+	1.05210i	−0.0234207	+	0.0487374i
$467$		−	36.3880i		−	1.68384i	−0.539605	−	0.841918i	$-0.681426\pi$
$467$		−	36.3880i		−	1.68384i	0.539605	−	0.841918i	$-0.318574\pi$
$468$	−16.6964	+	29.9609i	−0.771791	+	1.38494i
$469$			2.20082i			0.101625i
$470$	24.6802	+	11.8600i	1.13841	+	0.547063i
$471$	5.21394	−	15.2302i	0.240246	−	0.701770i
$472$	18.6681	+	20.0189i	0.859269	+	0.921444i
$473$	48.6230	−	28.0725i	2.23569	−	1.29077i
$474$	17.7063	+	4.60054i	0.813277	+	0.211310i
$475$	0.672570	−	1.16493i	0.0308596	−	0.0534504i
$476$	1.65100	−	0.251662i	0.0756737	−	0.0115349i
$477$	−3.70432	+	27.0543i	−0.169609	+	1.23873i
$478$	0.237681	+	3.13658i	0.0108713	+	0.143464i
$479$	2.78534	−	4.82435i	0.127265	−	0.220430i	−0.795351	−	0.606149i	$-0.792713\pi$
$479$	2.78534	−	4.82435i	0.127265	−	0.220430i	0.922616	+	0.385719i	$0.126047\pi$
$480$	19.2881	−	12.4155i	0.880377	−	0.566687i
$481$	8.34152	+	14.4479i	0.380341	+	0.658769i
$482$	−1.53539	+	1.04868i	−0.0699350	+	0.0477662i
$483$	9.84356	+	11.2832i	0.447898	+	0.513403i
$484$	−5.63863	+	14.4377i	−0.256302	+	0.656257i
$485$	17.0817			0.775638
$486$	−22.0453	−	0.0607745i	−0.999996	−	0.00275679i
$487$			39.2739i			1.77967i	0.456283	+	0.889835i	$0.349181\pi$
$487$			39.2739i			1.77967i	−0.456283	+	0.889835i	$0.650819\pi$
$488$	−3.65116	+	11.9426i	−0.165280	+	0.540617i
$489$	−30.1796	+	26.3289i	−1.36477	+	1.19063i
$490$	−2.73403	+	1.86737i	−0.123511	+	0.0843591i
$491$	−7.69485	+	4.44263i	−0.347264	+	0.200493i	−0.663479	−	0.748194i	$-0.730921\pi$
$491$	−7.69485	+	4.44263i	−0.347264	+	0.200493i	0.316216	+	0.948687i	$0.397588\pi$
$492$	−1.46022	+	0.524809i	−0.0658320	+	0.0236602i
$493$	−4.61657	−	2.66538i	−0.207920	−	0.120043i
$494$	−22.5440	+	1.70832i	−1.01430	+	0.0768608i
$495$	−30.1312	−	4.12561i	−1.35430	−	0.185433i
$496$	9.67193	+	30.9888i	0.434283	+	1.39144i
$497$	−3.90051	−	2.25196i	−0.174962	−	0.101014i
$498$	−13.3986	−	3.48131i	−0.600407	−	0.156001i
$499$	−4.10241	−	7.10559i	−0.183649	−	0.318090i	0.759471	−	0.650541i	$-0.225458\pi$
$499$	−4.10241	−	7.10559i	−0.183649	−	0.318090i	−0.943121	+	0.332451i	$0.892124\pi$
$500$	−13.2202	−	16.5211i	−0.591224	−	0.738844i
$501$	−10.7842	−	3.69188i	−0.481801	−	0.164941i
$502$	−3.33984	+	6.95005i	−0.149064	+	0.310196i
$503$	−7.90162			−0.352316			−0.176158	−	0.984362i	$-0.556367\pi$
$503$	−7.90162			−0.352316			−0.176158	+	0.984362i	$0.556367\pi$
$504$	−7.70298	−	3.55867i	−0.343118	−	0.158516i
$505$	−15.9433			−0.709469
$506$	−22.9297	+	47.7157i	−1.01935	+	2.12122i
$507$	6.56296	+	33.4463i	0.291471	+	1.48540i
$508$	−20.4469	+	16.3616i	−0.907184	+	0.725930i
$509$	−7.27823	−	12.6063i	−0.322602	−	0.558763i	0.658422	−	0.752649i	$-0.271224\pi$
$509$	−7.27823	−	12.6063i	−0.322602	−	0.558763i	−0.981024	+	0.193886i	$0.937891\pi$
$510$	−3.36026	+	3.41169i	−0.148795	+	0.151072i
$511$	2.47134	+	1.42683i	0.109326	+	0.0631192i
$512$	14.2401	+	17.5846i	0.629332	+	0.777137i
$513$	−7.97921	−	12.1448i	−0.352291	−	0.536206i
$514$	24.0506	−	1.82248i	1.06083	−	0.0803862i
$515$	−6.70107	−	3.86886i	−0.295284	−	0.170482i
$516$	−29.0103	+	34.2909i	−1.27711	+	1.50957i
$517$	31.0134	−	17.9056i	1.36397	−	0.787487i
$518$	−3.40814	+	2.32779i	−0.149745	+	0.102277i
$519$	0.280579	+	1.42989i	0.0123160	+	0.0627654i
$520$	11.0671	−	36.1995i	0.485325	−	1.58745i
$521$		−	29.0795i		−	1.27400i	−0.770865	−	0.636999i	$-0.780176\pi$
$521$		−	29.0795i		−	1.27400i	0.770865	−	0.636999i	$-0.219824\pi$
$522$	12.1006	+	24.2310i	0.529628	+	1.06056i
$523$	−4.73922			−0.207231			−0.103616	−	0.994617i	$-0.533041\pi$
$523$	−4.73922			−0.207231			−0.103616	+	0.994617i	$0.533041\pi$
$524$	41.6500	+	16.2664i	1.81949	+	0.710602i
$525$	0.269834	−	0.788198i	0.0117765	−	0.0343998i
$526$	18.0372	−	12.3195i	0.786458	−	0.537158i
$527$	−3.38848	−	5.86903i	−0.147605	−	0.255659i
$528$	0.819106	−	29.9887i	0.0356470	−	1.30509i
$529$	−25.8677	+	44.8042i	−1.12468	+	1.94801i
$530$	−2.27713	−	30.0503i	−0.0989120	−	1.30530i
$531$	10.9714	+	26.8801i	0.476120	+	1.16650i
$532$	−0.842828	−	5.52930i	−0.0365412	−	0.239725i
$533$	−1.28029	+	2.21753i	−0.0554557	+	0.0960521i
$534$	−5.66302	−	20.5103i	−0.245063	−	0.887568i
$535$	4.80388	−	2.77352i	0.207690	−	0.119910i
$536$	4.55256	−	4.24537i	0.196641	−	0.183372i
$537$	−16.3749	−	18.7698i	−0.706631	−	0.809977i
$538$	−16.5853	−	7.97004i	−0.715042	−	0.343613i
$539$			4.33011i			0.186511i
$540$	23.8008	−	5.04686i	1.02422	−	0.217182i
$541$			1.32007i			0.0567541i	0.999597	+	0.0283771i	$0.00903391\pi$
$541$			1.32007i			0.0567541i	−0.999597	+	0.0283771i	$0.990966\pi$
$542$	7.40703	−	15.4137i	0.318159	−	0.662074i
$543$	−0.901807	−	1.03370i	−0.0387002	−	0.0443602i
$544$	−3.70535	−	2.92977i	−0.158866	−	0.125613i
$545$	−32.0588	+	18.5092i	−1.37325	+	0.792846i
$546$	−13.4975	+	3.72674i	−0.577639	+	0.159490i
$547$	12.7108	−	22.0157i	0.543473	−	0.941322i	−0.455229	−	0.890375i	$-0.650443\pi$
$547$	12.7108	−	22.0157i	0.543473	−	0.941322i	0.998701	−	0.0509476i	$-0.0162242\pi$
$548$	−1.05341	−	6.91084i	−0.0449997	−	0.295216i
$549$	−8.11783	+	10.4667i	−0.346461	+	0.446710i
$550$	2.93704	−	0.222560i	0.125236	−	0.00949001i
$551$	−8.92648	+	15.4611i	−0.380281	+	0.658666i
$552$	4.35195	−	42.1273i	0.185231	−	1.79306i
$553$	3.73429	+	6.46798i	0.158798	+	0.275046i
$554$	−14.2988	−	20.9350i	−0.607499	−	0.889444i
$555$	3.83293	−	11.1962i	0.162699	−	0.475251i
$556$	−0.364204	+	0.932540i	−0.0154457	+	0.0395485i
$557$	20.8986			0.885501			0.442750	−	0.896645i	$-0.354003\pi$
$557$	20.8986			0.885501			0.442750	+	0.896645i	$0.354003\pi$
$558$	−2.07992	+	34.3694i	−0.0880502	+	1.45497i
$559$			74.1213i			3.13500i
$560$	9.13671	+	2.05340i	0.386096	+	0.0867720i
$561$	1.20590	+	6.14556i	0.0509132	+	0.259466i
$562$	−6.11872	−	8.95847i	−0.258103	−	0.377890i
$563$	−17.8861	+	10.3265i	−0.753809	+	0.435212i	−0.827069	−	0.562101i	$-0.809993\pi$
$563$	−17.8861	+	10.3265i	−0.753809	+	0.435212i	0.0732593	+	0.997313i	$0.476660\pi$
$564$	−18.5038	+	21.8719i	−0.779149	+	0.920973i
$565$	5.66147	+	3.26865i	0.238180	+	0.137513i
$566$	2.14154	+	28.2611i	0.0900158	+	1.18790i
$567$	−6.29774	−	6.42950i	−0.264480	−	0.270013i
$568$	2.86572	+	12.4125i	0.120243	+	0.520817i
$569$	−3.99918	−	2.30893i	−0.167654	−	0.0967954i	0.413825	−	0.910356i	$-0.364193\pi$
$569$	−3.99918	−	2.30893i	−0.167654	−	0.0967954i	−0.581479	+	0.813561i	$0.697526\pi$
$570$	11.4259	+	11.2537i	0.478579	+	0.471365i
$571$	−1.93031	−	3.34340i	−0.0807810	−	0.139917i	0.822805	−	0.568324i	$-0.192408\pi$
$571$	−1.93031	−	3.34340i	−0.0807810	−	0.139917i	−0.903586	+	0.428408i	$0.859075\pi$
$572$	−30.9310	−	38.6541i	−1.29329	−	1.61621i
$573$	−7.83952	−	39.9520i	−0.327501	−	1.66902i
$574$	−0.570962	−	0.274376i	−0.0238315	−	0.0114522i
$575$	4.15818			0.173408
$576$	7.49763	+	22.7988i	0.312401	+	0.949950i
$577$	22.4523			0.934700			0.467350	−	0.884073i	$-0.345209\pi$
$577$	22.4523			0.934700			0.467350	+	0.884073i	$0.345209\pi$
$578$	−20.7806	−	9.98611i	−0.864360	−	0.415368i
$579$	29.5175	+	10.1051i	1.22671	+	0.419955i
$580$	−18.6757	−	23.3388i	−0.775467	−	0.969089i
$581$	−2.82579	−	4.89442i	−0.117234	−	0.203055i
$582$	−4.49440	+	17.2978i	−0.186299	+	0.717015i
$583$	−34.1332	−	19.7068i	−1.41365	−	0.816173i
$584$	−1.81570	−	7.86448i	−0.0751341	−	0.325435i
$585$	24.6061	−	31.7259i	1.01734	−	1.31171i
$586$	0.508714	+	6.71330i	0.0210148	+	0.277324i
$587$	25.9071	+	14.9575i	1.06930	+	0.617362i	0.927991	−	0.372603i	$-0.121535\pi$
$587$	25.9071	+	14.9575i	1.06930	+	0.617362i	0.141311	+	0.989965i	$0.454868\pi$
$588$	−1.17163	−	3.25995i	−0.0483174	−	0.134438i
$589$	−19.6557	+	11.3482i	−0.809898	+	0.467595i
$590$	−18.0717	−	26.4590i	−0.744001	−	1.08930i
$591$	5.84082	−	5.09558i	0.240259	−	0.209604i
$592$	11.3895	+	2.55970i	0.468105	+	0.105203i
$593$		−	5.47387i		−	0.224785i	−0.993664	−	0.112392i	$-0.964149\pi$
$593$		−	5.47387i		−	0.224785i	0.993664	−	0.112392i	$-0.0358514\pi$
$594$	12.1057	−	29.4269i	0.496703	−	1.20740i
$595$	−1.95495			−0.0801451
$596$	−8.10415	+	20.7506i	−0.331959	+	0.849977i
$597$	15.6777	+	17.9706i	0.641645	+	0.735487i
$598$	−39.4180	−	57.7123i	−1.61192	−	2.36003i
$599$	−6.54755	−	11.3407i	−0.267526	−	0.463368i	0.700696	−	0.713460i	$-0.252873\pi$
$599$	−6.54755	−	11.3407i	−0.267526	−	0.463368i	−0.968222	+	0.250091i	$0.919539\pi$
$600$	−2.15095	+	0.962257i	−0.0878122	+	0.0392840i
$601$	−5.72592	+	9.91758i	−0.233565	+	0.404546i	−0.958855	−	0.283897i	$-0.908372\pi$
$601$	−5.72592	+	9.91758i	−0.233565	+	0.404546i	0.725290	+	0.688444i	$0.241706\pi$
$602$	−18.2845	+	1.38555i	−0.745222	+	0.0564707i
$603$	6.11288	−	2.49505i	0.248936	−	0.101606i
$604$	0.0345803	+	0.226861i	0.00140705	+	0.00923084i
$605$	9.07178	−	15.7128i	0.368820	−	0.638816i
$606$	4.19490	−	16.1451i	0.170406	−	0.655848i
$607$	21.9000	−	12.6440i	0.888894	−	0.513203i	0.0153137	−	0.999883i	$-0.495125\pi$
$607$	21.9000	−	12.6440i	0.888894	−	0.513203i	0.873581	+	0.486679i	$0.161792\pi$
$608$	−9.81194	+	12.4094i	−0.397927	+	0.503269i
$609$	−3.58129	+	10.4611i	−0.145121	+	0.423906i
$610$	6.33175	−	13.1761i	0.256365	−	0.533484i
$611$			47.2771i			1.91263i
$612$	−2.57073	−	4.30043i	−0.103915	−	0.173835i
$613$		−	38.0928i		−	1.53855i	−0.638917	−	0.769276i	$-0.720617\pi$
$613$		−	38.0928i		−	1.53855i	0.638917	−	0.769276i	$-0.279383\pi$
$614$	−11.7621	−	5.65225i	−0.474678	−	0.228106i
$615$	1.78236	−	0.349741i	0.0718716	−	0.0141029i
$616$	8.95714	−	8.35275i	0.360893	−	0.336542i
$617$	−5.31999	+	3.07150i	−0.214175	+	0.123654i	−0.603250	−	0.797552i	$-0.706128\pi$
$617$	−5.31999	+	3.07150i	−0.214175	+	0.123654i	0.389075	+	0.921206i	$0.372795\pi$
$618$	5.68095	−	5.76790i	0.228521	−	0.232019i
$619$	10.5904	−	18.3431i	0.425663	−	0.737270i	−0.570819	−	0.821076i	$-0.693374\pi$
$619$	10.5904	−	18.3431i	0.425663	−	0.737270i	0.996482	+	0.0838060i	$0.0267076\pi$
$620$	−5.72625	−	37.5666i	−0.229972	−	1.50871i
$621$	20.1800	−	40.1326i	0.809797	−	1.61046i
$622$	−1.85065	−	24.4223i	−0.0742044	−	0.979246i
$623$	4.34331	−	7.52283i	0.174011	−	0.301396i
$624$	33.7456	+	20.7317i	1.35090	+	0.829931i
$625$	13.5868	+	23.5330i	0.543472	+	0.941322i
$626$	21.5185	−	14.6973i	0.860052	−	0.587423i
$627$	20.5818	−	4.03863i	0.821957	−	0.161287i
$628$	−17.3146	−	6.76224i	−0.690929	−	0.269843i
$629$	−2.43697			−0.0971683
$630$	8.28624	+	5.47688i	0.330132	+	0.218204i
$631$		−	40.4632i		−	1.61082i	−0.592721	−	0.805408i	$-0.701946\pi$
$631$		−	40.4632i		−	1.61082i	0.592721	−	0.805408i	$-0.298054\pi$
$632$	6.17606	−	20.2013i	0.245670	−	0.803565i
$633$	−12.4127	−	4.24941i	−0.493362	−	0.168899i
$634$	−10.4629	+	7.14624i	−0.415534	+	0.283814i
$635$	26.5474	−	15.3272i	1.05350	−	0.608240i
$636$	31.0297	+	5.60069i	1.23041	+	0.222082i
$637$	−4.95064	−	2.85826i	−0.196152	−	0.113248i
$638$	−38.9810	+	2.95387i	−1.54327	+	0.116945i
$639$	−1.83295	+	13.3869i	−0.0725105	+	0.529577i
$640$	−13.3770	−	22.8609i	−0.528774	−	0.903658i
$641$	32.4846	+	18.7550i	1.28306	+	0.740777i	0.977407	−	0.211365i	$-0.0677908\pi$
$641$	32.4846	+	18.7550i	1.28306	+	0.740777i	0.305656	+	0.952142i	$0.401124\pi$
$642$	1.54465	+	5.59441i	0.0609625	+	0.220794i
$643$	−9.91973	−	17.1815i	−0.391196	−	0.677571i	0.601412	−	0.798939i	$-0.294605\pi$
$643$	−9.91973	−	17.1815i	−0.391196	−	0.677571i	−0.992608	+	0.121368i	$0.961272\pi$
$644$	13.4998	−	10.8026i	0.531968	−	0.425682i
$645$	39.6197	−	34.5645i	1.56002	−	1.36098i
$646$	1.43044	−	2.97668i	0.0562800	−	0.117116i
$647$	−0.939565			−0.0369381			−0.0184691	−	0.999829i	$-0.505879\pi$
$647$	−0.939565			−0.0369381			−0.0184691	+	0.999829i	$0.505879\pi$
$648$	−1.15157	+	25.4298i	−0.0452379	+	0.998976i
$649$	−41.9052			−1.64492
$650$	−1.68425	+	3.50485i	−0.0660618	+	0.137472i
$651$	−10.5925	+	9.24099i	−0.415153	+	0.362183i
$652$	28.8941	+	36.1085i	1.13158	+	1.41412i
$653$	−2.47055	−	4.27911i	−0.0966799	−	0.167454i	0.813629	−	0.581385i	$-0.197489\pi$
$653$	−2.47055	−	4.27911i	−0.0966799	−	0.167454i	−0.910308	+	0.413931i	$0.864156\pi$
$654$	−10.3083	−	37.3344i	−0.403085	−	1.45989i
$655$	−45.3285	−	26.1704i	−1.77113	−	1.02256i
$656$	0.533817	+	1.71035i	0.0208420	+	0.0667778i
$657$	1.16135	−	8.48183i	0.0453084	−	0.330908i
$658$	−11.6625	+	0.883750i	−0.454651	+	0.0344522i
$659$	−17.3320	−	10.0066i	−0.675157	−	0.389802i	0.122871	−	0.992423i	$-0.460790\pi$
$659$	−17.3320	−	10.0066i	−0.675157	−	0.389802i	−0.798028	+	0.602621i	$0.794123\pi$
$660$	−6.23767	+	34.5587i	−0.242801	+	1.34520i
$661$	−13.2404	+	7.64434i	−0.514991	+	0.297330i	−0.734883	−	0.678194i	$-0.762763\pi$
$661$	−13.2404	+	7.64434i	−0.514991	+	0.297330i	0.219892	+	0.975524i	$0.429430\pi$
$662$	2.53507	−	1.73148i	0.0985284	−	0.0672957i
$663$	−7.82226	−	2.67790i	−0.303791	−	0.104001i
$664$	−4.67352	+	15.2867i	−0.181368	+	0.593237i
$665$			6.54723i			0.253891i
$666$	10.3293	+	6.82728i	0.400253	+	0.264552i
$667$	−55.1882			−2.13689
$668$	−4.78820	+	12.2601i	−0.185261	+	0.474359i
$669$	−13.0695	+	2.56454i	−0.505296	+	0.0991509i
$670$	−6.01712	+	4.10975i	−0.232462	+	0.158773i
$671$	−9.55931	−	16.5572i	−0.369033	−	0.639184i
$672$	−4.48336	+	8.71203i	−0.172950	+	0.336074i
$673$	7.32206	−	12.6822i	0.282245	−	0.488862i	−0.689693	−	0.724102i	$-0.742254\pi$
$673$	7.32206	−	12.6822i	0.282245	−	0.488862i	0.971937	+	0.235240i	$0.0755877\pi$
$674$	2.27938	+	30.0801i	0.0877984	+	1.15864i
$675$	−2.49516	+	0.144096i	−0.0960388	+	0.00554626i
$676$	38.9076	−	5.93066i	1.49645	−	0.228102i
$677$	−2.01058	+	3.48243i	−0.0772730	+	0.133841i	−0.902072	−	0.431585i	$-0.857955\pi$
$677$	−2.01058	+	3.48243i	−0.0772730	+	0.133841i	0.824799	+	0.565425i	$0.191288\pi$
$678$	−4.79961	+	4.87307i	−0.184328	+	0.187149i
$679$	−6.31875	+	3.64813i	−0.242491	+	0.140002i
$680$	3.77108	+	4.04395i	0.144614	+	0.155078i
$681$	19.0770	−	3.74336i	0.731034	−	0.143446i
$682$	−44.7948	−	21.5261i	−1.71528	−	0.824277i
$683$			12.0520i			0.461157i	0.973054	+	0.230578i	$0.0740618\pi$
$683$			12.0520i			0.461157i	−0.973054	+	0.230578i	$0.925938\pi$
$684$	−14.4024	+	8.60950i	−0.550688	+	0.329192i
$685$			8.18310i			0.312660i
$686$	0.612543	−	1.27467i	0.0233870	−	0.0486672i
$687$	9.65056	−	28.1898i	0.368192	−	1.07551i
$688$	38.1368	+	35.1501i	1.45395	+	1.34009i
$689$	45.0619	−	26.0165i	1.71672	−	0.991150i
$690$	−12.4671	+	47.9825i	−0.474613	+	1.82666i
$691$	22.5281	−	39.0198i	0.857009	−	1.48438i	−0.0177593	−	0.999842i	$-0.505653\pi$
$691$	22.5281	−	39.0198i	0.857009	−	1.48438i	0.874768	−	0.484541i	$-0.161013\pi$
$692$	1.66337	−	0.253547i	0.0632319	−	0.00963840i
$693$	12.0271	−	4.90900i	0.456870	−	0.186477i
$694$	−12.4865	+	0.946191i	−0.473981	+	0.0359169i
$695$	0.585954	−	1.01490i	0.0222265	−	0.0384974i
$696$	28.5479	−	12.7713i	1.08210	−	0.484094i
$697$	−0.187019	−	0.323926i	−0.00708383	−	0.0122696i
$698$	10.5432	+	15.4363i	0.399065	+	0.584274i
$699$	0.939822	+	1.07727i	0.0355473	+	0.0407462i
$700$	−0.896073	−	0.349962i	−0.0338684	−	0.0132273i
$701$	−19.9659			−0.754100			−0.377050	−	0.926193i	$-0.623061\pi$
$701$	−19.9659			−0.754100			−0.377050	+	0.926193i	$0.623061\pi$
$702$	25.6532	+	33.2649i	0.968216	+	1.25550i
$703$			8.16154i			0.307818i
$704$	−34.5565	−	2.41610i	−1.30240	−	0.0910600i
$705$	25.2708	−	22.0464i	0.951752	−	0.830317i
$706$	−5.85034	−	8.56553i	−0.220180	−	0.322368i
$707$	5.89767	−	3.40502i	0.221805	−	0.128059i
$708$	31.5486	−	11.3387i	1.18567	−	0.426133i
$709$	12.6541	+	7.30585i	0.475235	+	0.274377i	0.718429	−	0.695601i	$-0.244862\pi$
$709$	12.6541	+	7.30585i	0.475235	+	0.274377i	−0.243194	+	0.969978i	$0.578195\pi$
$710$	−1.12676	−	14.8694i	−0.0422865	−	0.558038i
$711$	13.7316	−	17.7048i	0.514974	−	0.663983i
$712$	−23.9397	+	5.52704i	−0.897178	+	0.207134i
$713$	−60.7608	−	35.0803i	−2.27551	−	1.31377i
$714$	0.514372	−	1.97968i	0.0192499	−	0.0740878i
$715$	28.9754	+	50.1869i	1.08362	+	1.87688i
$716$	−22.4572	+	17.9703i	−0.839266	+	0.671582i
$717$	3.64485	+	1.24779i	0.136120	+	0.0465995i
$718$	9.39628	+	4.51538i	0.350666	+	0.168512i
$719$	44.7348			1.66833			0.834163	−	0.551518i	$-0.185951\pi$
$719$	44.7348			1.66833			0.834163	+	0.551518i	$0.185951\pi$
$720$	−4.65478	−	27.7055i	−0.173473	−	1.03252i
$721$	3.30509			0.123088
$722$	14.2497	+	6.84770i	0.530320	+	0.254845i
$723$	0.438482	+	2.23461i	0.0163073	+	0.0831059i
$724$	−1.23677	+	0.989668i	−0.0459643	+	0.0367807i
$725$	1.53530	+	2.65921i	0.0570195	+	0.0987607i
$726$	13.5247	+	13.3208i	0.501948	+	0.494381i
$727$	−18.1033	−	10.4520i	−0.671415	−	0.387642i	0.125198	−	0.992132i	$-0.460043\pi$
$727$	−18.1033	−	10.4520i	−0.671415	−	0.387642i	−0.796613	+	0.604490i	$0.793377\pi$
$728$	3.63725	+	15.7543i	0.134805	+	0.583894i
$729$	−10.7185	+	24.7813i	−0.396982	+	0.917826i
$730$	0.713906	+	9.42113i	0.0264228	+	0.348692i
$731$	−9.37667	−	5.41362i	−0.346809	−	0.200230i
$732$	11.6768	+	9.87866i	0.431587	+	0.365126i
$733$	−9.70754	+	5.60465i	−0.358556	+	0.207012i	−0.668447	−	0.743760i	$-0.733041\pi$
$733$	−9.70754	+	5.60465i	−0.358556	+	0.207012i	0.309891	+	0.950772i	$0.399707\pi$
$734$	−11.3046	−	16.5512i	−0.417262	−	0.610917i
$735$	0.780795	+	3.97911i	0.0288001	+	0.146772i
$736$	−48.3870	−	7.08726i	−1.78357	−	0.261240i
$737$			9.52980i			0.351035i
$738$	−0.114796	+	1.89693i	−0.00422569	+	0.0698269i
$739$	−47.2936			−1.73972			−0.869862	−	0.493295i	$-0.835792\pi$
$739$	−47.2936			−1.73972			−0.869862	+	0.493295i	$0.835792\pi$
$740$	−12.7285	−	4.97113i	−0.467910	−	0.182742i
$741$	−8.96841	+	26.1972i	−0.329463	+	0.962377i
$742$	7.26019	+	10.6297i	0.266530	+	0.390229i
$743$	22.1430	+	38.3527i	0.812346	+	1.40703i	0.911218	+	0.411925i	$0.135143\pi$
$743$	22.1430	+	38.3527i	0.812346	+	1.40703i	−0.0988715	+	0.995100i	$0.531523\pi$
$744$	39.5485	+	4.08555i	1.44992	+	0.149783i
$745$	13.0385	−	22.5833i	0.477692	−	0.827387i
$746$	26.5294	−	2.01032i	0.971311	−	0.0736031i
$747$	−10.3909	+	13.3975i	−0.380183	+	0.490190i
$748$	7.14903	−	1.08972i	0.261394	−	0.0398442i
$749$	−1.18468	+	2.05193i	−0.0432874	+	0.0749759i
$750$	−24.9801	+	6.89716i	−0.912145	+	0.251849i
$751$	14.6361	−	8.45016i	0.534079	−	0.308351i	−0.208597	−	0.978002i	$-0.566890\pi$
$751$	14.6361	−	8.45016i	0.534079	−	0.308351i	0.742676	+	0.669651i	$0.233556\pi$
$752$	24.3250	+	22.4200i	0.887040	+	0.817572i
$753$	6.20838	+	7.11636i	0.226246	+	0.259335i
$754$	22.3538	−	46.5171i	0.814076	−	1.69405i
$755$		−	0.268625i		−	0.00977628i
$756$	−7.72638	+	6.95004i	−0.281006	+	0.252770i
$757$			50.5884i			1.83867i	0.393478	+	0.919334i	$0.371272\pi$
$757$			50.5884i			1.83867i	−0.393478	+	0.919334i	$0.628728\pi$
$758$	−22.6517	−	10.8853i	−0.822748	−	0.395371i
$759$	42.6237	+	48.8575i	1.54714	+	1.77341i
$760$	13.5434	−	12.6296i	0.491271	−	0.458122i
$761$	−23.8383	+	13.7630i	−0.864137	+	0.498910i	−0.865396	−	0.501089i	$-0.832933\pi$
$761$	−23.8383	+	13.7630i	−0.864137	+	0.498910i	0.00125832	+	0.999999i	$0.499599\pi$
$762$	8.53611	+	30.9161i	0.309231	+	1.11997i
$763$	7.90601	−	13.6936i	0.286217	−	0.495742i
$764$	−46.4755	+	7.08424i	−1.68143	+	0.256299i
$765$	2.21631	+	5.42996i	0.0801307	+	0.196320i
$766$	−2.50578	−	33.0677i	−0.0905374	−	1.19479i
$767$	27.6612	−	47.9106i	0.998787	−	1.72995i
$768$	26.6698	−	7.53128i	0.962365	−	0.271762i
$769$	−15.1192	−	26.1872i	−0.545212	−	0.944334i	−0.998594	−	0.0530180i	$-0.983116\pi$
$769$	−15.1192	−	26.1872i	−0.545212	−	0.944334i	0.453382	−	0.891316i	$-0.350217\pi$
$770$	−11.8387	+	8.08590i	−0.426635	+	0.291396i
$771$	9.56777	−	27.9479i	0.344575	−	1.00652i
$772$	13.1059	−	33.5574i	0.471691	−	1.20776i
$773$	37.6667			1.35478			0.677389	−	0.735625i	$-0.263111\pi$
$773$	37.6667			1.35478			0.677389	+	0.735625i	$0.263111\pi$
$774$	24.5774	+	49.2153i	0.883416	+	1.76901i
$775$			3.90364i			0.140223i
$776$	19.7352	+	6.03356i	0.708453	+	0.216592i
$777$	0.973311	+	4.96022i	0.0349174	+	0.177947i
$778$	−10.1619	+	6.94067i	−0.364322	+	0.248835i
$779$	−1.08484	+	0.626335i	−0.0388686	+	0.0224408i
$780$	−35.3938	−	29.9434i	−1.26730	−	1.07215i
$781$	−16.8897	−	9.75125i	−0.604359	−	0.348927i
$782$	10.1798	−	0.771398i	0.364030	−	0.0275851i
$783$	33.1163	−	1.91247i	1.18348	−	0.0683462i
$784$	−3.81834	+	1.19175i	−0.136369	+	0.0425623i
$785$	18.8439	+	10.8795i	0.672566	+	0.388306i
$786$	38.4280	−	39.0162i	1.37068	−	1.39166i
$787$	11.8139	+	20.4623i	0.421121	+	0.729403i	0.996049	−	0.0888005i	$-0.0283034\pi$
$787$	11.8139	+	20.4623i	0.421121	+	0.729403i	−0.574928	+	0.818204i	$0.694970\pi$
$788$	−5.59203	−	6.98827i	−0.199208	−	0.248947i
$789$	−5.15112	−	26.2513i	−0.183385	−	0.934571i
$790$	−10.7104	+	22.2877i	−0.381057	+	0.792962i
$791$	−2.79234			−0.0992843
$792$	−33.3547	−	15.4094i	−1.18521	−	0.547550i
$793$	25.2400			0.896298
$794$	−12.0938	+	25.1667i	−0.429194	+	0.893131i
$795$	−34.9199	−	11.9546i	−1.23848	−	0.423985i
$796$	21.5010	−	17.2051i	0.762082	−	0.609819i
$797$	24.4454	+	42.3407i	0.865900	+	1.49978i	0.866150	+	0.499784i	$0.166587\pi$
$797$	24.4454	+	42.3407i	0.865900	+	1.49978i	−0.000249782		1.00000i	$0.500080\pi$
$798$	−6.63006	−	1.72266i	−0.234702	−	0.0609815i
$799$	−5.98076	−	3.45299i	−0.211584	−	0.122158i
$800$	1.00460	+	2.52867i	0.0355179	+	0.0894018i
$801$	−25.8189	−	3.53517i	−0.912267	−	0.124909i
$802$	17.9801	−	1.36248i	0.634898	−	0.0481107i
$803$	10.7012	+	6.17832i	0.377636	+	0.218028i
$804$	−2.57856	−	7.17457i	−0.0909388	−	0.253028i
$805$	−17.5276	+	10.1196i	−0.617768	+	0.356669i
$806$	54.1794	−	37.0050i	1.90839	−	1.30345i
$807$	−16.9822	+	14.8154i	−0.597800	+	0.521526i
$808$	−18.4201	−	5.63149i	−0.648016	−	0.198115i
$809$			42.2224i			1.48446i	0.670144	+	0.742231i	$0.266232\pi$
$809$			42.2224i			1.48446i	−0.670144	+	0.742231i	$0.733768\pi$
$810$	5.81824	−	29.2245i	0.204432	−	1.02684i
$811$	27.8380			0.977525			0.488763	−	0.872417i	$-0.337448\pi$
$811$	27.8380			0.977525			0.488763	+	0.872417i	$0.337448\pi$
$812$	11.8929	+	4.64477i	0.417358	+	0.162999i
$813$	−13.7688	−	15.7825i	−0.482893	−	0.553518i
$814$	−14.7576	+	10.0796i	−0.517255	+	0.353290i
$815$	−27.0672	−	46.8818i	−0.948123	−	1.64220i
$816$	−5.08734	+	2.75478i	−0.178092	+	0.0964365i
$817$	−18.1305	+	31.4030i	−0.634306	+	1.09865i
$818$	2.39222	+	31.5692i	0.0836421	+	1.10379i
$819$	−2.32644	+	16.9910i	−0.0812922	+	0.593714i
$820$	−0.316045	−	2.07339i	−0.0110368	−	0.0724059i
$821$	22.0371	−	38.1693i	0.769099	−	1.33212i	−0.168954	−	0.985624i	$-0.554039\pi$
$821$	22.0371	−	38.1693i	0.769099	−	1.33212i	0.938052	−	0.346494i	$-0.112628\pi$
$822$	−8.28663	−	2.15308i	−0.289030	−	0.0750972i
$823$	−33.1369	+	19.1316i	−1.15508	+	0.666886i	−0.950120	−	0.311884i	$-0.899040\pi$
$823$	−33.1369	+	19.1316i	−1.15508	+	0.666886i	−0.204960	+	0.978770i	$0.565707\pi$
$824$	−6.37550	−	6.83682i	−0.222101	−	0.238172i
$825$	1.16841	−	3.41298i	0.0406788	−	0.118825i
$826$	12.3358	+	5.92797i	0.429218	+	0.206261i
$827$			2.31948i			0.0806562i	0.999186	+	0.0403281i	$0.0128403\pi$
$827$			2.31948i			0.0806562i	−0.999186	+	0.0403281i	$0.987160\pi$
$828$	−45.3093	−	25.2496i	−1.57461	−	0.877485i
$829$			42.7497i			1.48476i	0.669979	+	0.742380i	$0.266303\pi$
$829$			42.7497i			1.48476i	−0.669979	+	0.742380i	$0.733697\pi$
$830$	8.10470	−	16.8655i	0.281318	−	0.585410i
$831$	−30.4689	+	5.97871i	−1.05695	+	0.207399i
$832$	25.5727	−	37.9139i	0.886574	−	1.31443i
$833$	0.723163	−	0.417519i	0.0250561	−	0.0144662i
$834$	0.873570	+	0.860401i	0.0302493	+	0.0297932i
$835$	7.70355	−	13.3429i	0.266592	−	0.461751i
$836$	−3.64954	−	23.9425i	−0.126222	−	0.828067i
$837$	37.6759	+	18.9447i	1.30227	+	0.654826i
$838$	49.3406	−	3.73888i	1.70444	−	0.129158i
$839$	−8.06418	+	13.9676i	−0.278406	+	0.482214i	−0.970989	−	0.239125i	$-0.923140\pi$
$839$	−8.06418	+	13.9676i	−0.278406	+	0.482214i	0.692582	+	0.721339i	$0.256473\pi$
$840$	6.72493	−	9.29081i	0.232032	−	0.320563i
$841$	−5.87678	−	10.1789i	−0.202648	−	0.350996i
$842$	−19.5873	−	28.6779i	−0.675022	−	0.988306i
$843$	−13.0382	+	2.55840i	−0.449059	+	0.0881158i
$844$	−5.51128	+	14.1116i	−0.189706	+	0.485741i
$845$	−46.0704			−1.58487
$846$	15.6763	+	31.3912i	0.538962	+	1.07925i
$847$			7.74984i			0.266288i
$848$	7.98347	−	35.5229i	0.274154	−	1.21986i
$849$	32.8407	+	11.2428i	1.12709	+	0.385852i
$850$	−0.320365	−	0.469050i	−0.0109884	−	0.0160883i
$851$	−21.8493	+	12.6147i	−0.748986	+	0.432427i
$852$	15.3540	+	2.77131i	0.526018	+	0.0949435i
$853$	−19.0349	−	10.9898i	−0.651744	−	0.376284i	0.137380	−	0.990518i	$-0.456132\pi$
$853$	−19.0349	−	10.9898i	−0.651744	−	0.376284i	−0.789124	+	0.614234i	$0.789465\pi$
$854$	0.471810	+	6.22629i	0.0161450	+	0.213059i
$855$	18.1852	−	7.42252i	0.621921	−	0.253845i
$856$	6.52981	−	1.50756i	0.223184	−	0.0515273i
$857$	12.1589	+	7.01997i	0.415342	+	0.239798i	0.693082	−	0.720859i	$-0.256252\pi$
$857$	12.1589	+	7.01997i	0.415342	+	0.239798i	−0.277741	+	0.960656i	$0.589586\pi$
$858$	−58.4456	+	16.1372i	−1.99530	+	0.550915i
$859$	−17.3533	−	30.0567i	−0.592085	−	1.02552i	−0.993951	−	0.109823i	$-0.964972\pi$
$859$	−17.3533	−	30.0567i	−0.592085	−	1.02552i	0.401866	−	0.915699i	$-0.368362\pi$
$860$	−37.9321	−	47.4031i	−1.29347	−	1.61643i
$861$	−0.584626	+	0.510032i	−0.0199240	+	0.0173819i
$862$	−0.248903	−	0.119610i	−0.00847766	−	0.00407393i
$863$	25.5333			0.869163			0.434581	−	0.900633i	$-0.356896\pi$
$863$	25.5333			0.869163			0.434581	+	0.900633i	$0.356896\pi$
$864$	29.2808	+	2.57600i	0.996152	+	0.0876374i
$865$	−1.96959			−0.0669682
$866$	−28.8275	−	13.8530i	−0.979599	−	0.470746i
$867$	−21.2779	+	18.5630i	−0.722636	+	0.630434i
$868$	10.1413	+	12.6735i	0.344219	+	0.430165i
$869$	16.1699	+	28.0070i	0.548525	+	0.950074i
$870$	−35.2886	+	9.74340i	−1.19640	+	0.330332i
$871$	−10.8955	−	6.29051i	−0.369180	−	0.213146i
$872$	−43.5769	+	10.0607i	−1.47570	+	0.340699i
$873$	17.2963	+	13.4147i	0.585392	+	0.454020i
$874$	−2.58345	−	34.0928i	−0.0873866	−	1.15321i
$875$	−9.16227	−	5.28984i	−0.309741	−	0.178829i
$876$	−9.72816	−	1.75588i	−0.328684	−	0.0593257i
$877$	−15.5078	+	8.95342i	−0.523661	+	0.302336i	−0.738431	−	0.674329i	$-0.764433\pi$
$877$	−15.5078	+	8.95342i	−0.523661	+	0.302336i	0.214770	+	0.976665i	$0.431100\pi$
$878$	11.9985	+	17.5672i	0.404931	+	0.592863i
$879$	7.80118	+	2.67068i	0.263127	+	0.0900797i
$880$	39.5629	+	8.89145i	1.33367	+	0.299731i
$881$		−	30.2200i		−	1.01814i	−0.860726	−	0.509069i	$-0.829990\pi$
$881$		−	30.2200i		−	1.01814i	0.860726	−	0.509069i	$-0.170010\pi$
$882$	−4.23489	−	0.256282i	−0.142596	−	0.00862945i
$883$	30.6286			1.03073			0.515367	−	0.856970i	$-0.327656\pi$
$883$	30.6286			1.03073			0.515367	+	0.856970i	$0.327656\pi$
$884$	−3.47310	+	8.89285i	−0.116813	+	0.299099i
$885$	−38.5084	+	7.55626i	−1.29445	+	0.254001i
$886$	10.8751	+	15.9224i	0.365357	+	0.534922i
$887$	−0.740240	−	1.28213i	−0.0248548	−	0.0430498i	0.853330	−	0.521370i	$-0.174579\pi$
$887$	−0.740240	−	1.28213i	−0.0248548	−	0.0430498i	−0.878185	+	0.478321i	$0.841246\pi$
$888$	8.38306	−	11.5816i	0.281317	−	0.388653i
$889$	−6.54684	+	11.3395i	−0.219574	+	0.380314i
$890$	28.6782	−	2.17315i	0.961295	−	0.0728441i
$891$	−27.2699	−	27.8404i	−0.913577	−	0.932689i
$892$	2.31746	+	15.2035i	0.0775945	+	0.509052i
$893$	−11.5643	+	20.0299i	−0.386983	+	0.670274i
$894$	19.4384	+	19.1454i	0.650117	+	0.640317i
$895$	29.1576	−	16.8341i	0.974630	−	0.562703i
$896$	9.83077	+	5.59965i	0.328423	+	0.187071i
$897$	−83.9945	+	16.4817i	−2.80450	+	0.550308i
$898$	−9.12582	+	18.9904i	−0.304533	+	0.633718i
$899$		−	51.8099i		−	1.72796i
$900$	0.0438349	+	2.88563i	0.00146116	+	0.0961877i
$901$			7.60070i			0.253216i
$902$	−2.47233	−	1.18808i	−0.0823196	−	0.0395586i
$903$	−7.27393	+	21.2475i	−0.242061	+	0.707072i
$904$	5.38641	+	5.77616i	0.179149	+	0.192112i
$905$	1.60578	−	0.927095i	0.0533778	−	0.0308177i
$906$	0.272024	+	0.0706788i	0.00903739	+	0.00234814i
$907$	−14.2045	+	24.6029i	−0.471653	+	0.816927i	−0.999474	−	0.0324289i	$-0.989676\pi$
$907$	−14.2045	+	24.6029i	−0.471653	+	0.816927i	0.527821	+	0.849355i	$0.323009\pi$
$908$	−3.38272	−	22.1920i	−0.112259	−	0.736468i
$909$	−16.1437	−	12.5208i	−0.535453	−	0.415288i
$910$	−1.43011	−	18.8726i	−0.0474078	−	0.625622i
$911$	5.37955	−	9.31766i	0.178233	−	0.308708i	−0.763043	−	0.646348i	$-0.776295\pi$
$911$	5.37955	−	9.31766i	0.178233	−	0.308708i	0.941275	+	0.337640i	$0.109629\pi$
$912$	9.22589	+	17.0377i	0.305500	+	0.564176i
$913$	−12.2360	−	21.1934i	−0.404952	−	0.701398i
$914$	−22.6258	+	15.4536i	−0.748396	+	0.511161i
$915$	−11.7700	−	13.4914i	−0.389104	−	0.446011i
$916$	−32.0479	−	12.5163i	−1.05889	−	0.413551i
$917$	22.3569			0.738289
$918$	−6.08179	+	0.815655i	−0.200729	+	0.0269206i
$919$			27.2186i			0.897860i	0.893567	+	0.448930i	$0.148195\pi$
$919$			27.2186i			0.897860i	−0.893567	+	0.448930i	$0.851805\pi$
$920$	54.7438	+	16.7366i	1.80485	+	0.551788i
$921$	−12.0435	+	10.5069i	−0.396848	+	0.346213i
$922$	−45.4903	+	31.0703i	−1.49814	+	1.02324i
$923$	22.2973	−	12.8734i	0.733926	−	0.423732i
$924$	−5.07331	−	14.1159i	−0.166900	−	0.464380i
$925$	1.21567	+	0.701866i	0.0399709	+	0.0230772i
$926$	43.9836	−	3.33295i	1.44539	−	0.109527i
$927$	−3.74695	−	9.18004i	−0.123066	−	0.301512i
$928$	−13.3332	−	33.5610i	−0.437685	−	1.10169i
$929$	4.70377	+	2.71572i	0.154326	+	0.0891000i	0.575174	−	0.818031i	$-0.304934\pi$
$929$	4.70377	+	2.71572i	0.154326	+	0.0891000i	−0.420848	+	0.907131i	$0.638268\pi$
$930$	−45.0453	−	11.7039i	−1.47709	−	0.383786i
$931$	−1.39829	−	2.42191i	−0.0458271	−	0.0793750i
$932$	1.28891	−	1.03139i	0.0422196	−	0.0337842i
$933$	−28.3799	−	9.71565i	−0.929116	−	0.318076i
$934$	−22.2892	+	46.3828i	−0.729326	+	1.51769i
$935$	−8.46514			−0.276840
$936$	39.6348	−	27.9631i	1.29550	−	0.914003i
$937$	39.5722			1.29277			0.646383	−	0.763013i	$-0.276281\pi$
$937$	39.5722			1.29277			0.646383	+	0.763013i	$0.276281\pi$
$938$	1.34810	−	2.80533i	0.0440170	−	0.0915972i
$939$	−6.14533	−	31.3180i	−0.200545	−	1.02203i
$940$	−24.1944	−	30.2353i	−0.789133	−	0.986168i
$941$	−18.9698	−	32.8567i	−0.618399	−	1.07110i	−0.989778	−	0.142618i	$-0.954448\pi$
$941$	−18.9698	−	32.8567i	−0.618399	−	1.07110i	0.371378	−	0.928482i	$-0.378885\pi$
$942$	−15.9752	+	16.2197i	−0.520501	+	0.528467i
$943$	−3.35353	−	1.93616i	−0.109206	−	0.0630502i
$944$	−11.5333	−	36.9526i	−0.375377	−	1.20270i
$945$	10.1670	−	6.67977i	0.330732	−	0.217293i
$946$	−79.1740	+	5.99957i	−2.57417	+	0.195063i
$947$	37.8999	+	21.8815i	1.23158	+	0.711054i	0.967359	−	0.253408i	$-0.0815516\pi$
$947$	37.8999	+	21.8815i	1.23158	+	0.711054i	0.264222	+	0.964462i	$0.414885\pi$
$948$	−19.7517	−	16.7101i	−0.641505	−	0.542717i
$949$	−14.1274	+	8.15648i	−0.458596	+	0.264770i
$950$	−1.57087	+	1.07292i	−0.0509659	+	0.0348101i
$951$	2.98803	+	15.2277i	0.0968935	+	0.493792i
$952$	−2.25864	−	0.690525i	−0.0732031	−	0.0223800i
$953$			31.3940i			1.01695i	0.861077	+	0.508475i	$0.169791\pi$
$953$			31.3940i			1.01695i	−0.861077	+	0.508475i	$0.830209\pi$
$954$	21.2937	−	32.2163i	0.689409	−	1.04304i
$955$	55.0315			1.78078
$956$	1.61832	−	4.14370i	0.0523403	−	0.134017i
$957$	−15.5074	+	45.2978i	−0.501282	+	1.46427i
$958$	−6.50551	+	4.44332i	−0.210184	+	0.143557i
$959$	−1.74767	−	3.02705i	−0.0564351	−	0.0977484i
$960$	−32.1910	+	4.01090i	−1.03896	+	0.129451i
$961$	17.4329	−	30.1946i	0.562350	−	0.974019i
$962$	−1.78273	−	23.5259i	−0.0574774	−	0.758507i
$963$	7.04239	+	0.964255i	0.226938	+	0.0310727i
$964$	2.59948	−	0.396238i	0.0837237	−	0.0127620i
$965$	−21.0855	+	36.5212i	−0.678767	+	1.17566i
$966$	−5.63588	−	20.4120i	−0.181331	−	0.656745i
$967$	11.4126	−	6.58908i	0.367005	−	0.211891i	−0.305144	−	0.952306i	$-0.598705\pi$
$967$	11.4126	−	6.58908i	0.367005	−	0.211891i	0.672149	+	0.740416i	$0.265371\pi$
$968$	16.0311	−	14.9494i	0.515259	−	0.480492i
$969$	−2.65903	−	3.04791i	−0.0854202	−	0.0979131i
$970$	−21.7735	−	10.4632i	−0.699106	−	0.335955i
$971$			1.71689i			0.0550975i	0.999620	+	0.0275488i	$0.00877015\pi$
$971$			1.71689i			0.0550975i	−0.999620	+	0.0275488i	$0.991230\pi$
$972$	28.0633	+	13.5812i	0.900132	+	0.435616i
$973$			0.500569i			0.0160475i
$974$	24.0569	−	50.0614i	0.770834	−	1.60407i
$975$	3.13083	+	3.58872i	0.100267	+	0.114931i
$976$	11.9694	−	12.9864i	0.383131	−	0.415686i
$977$	41.3893	−	23.8961i	1.32416	−	0.764505i	0.339772	−	0.940508i	$-0.389650\pi$
$977$	41.3893	−	23.8961i	1.32416	−	0.764505i	0.984390	+	0.176003i	$0.0563167\pi$
$978$	54.5967	−	15.0745i	1.74581	−	0.482028i
$979$	18.8070	−	32.5747i	0.601074	−	1.04109i
$980$	4.62884	−	0.705571i	0.147863	−	0.0225386i
$981$	−46.9976	−	6.43498i	−1.50052	−	0.205453i
$982$	12.5297	−	0.949465i	0.399839	−	0.0302987i
$983$	1.26090	−	2.18395i	0.0402166	−	0.0696572i	−0.845216	−	0.534424i	$-0.820529\pi$
$983$	1.26090	−	2.18395i	0.0402166	−	0.0696572i	0.885433	+	0.464767i	$0.153862\pi$
$984$	2.18278	+	0.225491i	0.0695844	+	0.00718839i
$985$	5.23847	+	9.07329i	0.166911	+	0.289099i
$986$	4.25196	+	6.22533i	0.135410	+	0.198255i
$987$	−4.63956	+	13.5524i	−0.147679	+	0.431377i
$988$	29.7826	+	11.6316i	0.947511	+	0.370051i
$989$	−112.092			−3.56433
$990$	35.8803	+	23.7155i	1.14035	+	0.753727i
$991$			6.56996i			0.208702i	0.994541	+	0.104351i	$0.0332765\pi$
$991$			6.56996i			0.208702i	−0.994541	+	0.104351i	$0.966724\pi$
$992$	6.65342	−	45.4250i	0.211246	−	1.44225i
$993$	−0.723976	−	3.68955i	−0.0229747	−	0.117084i
$994$	3.59246	+	5.25975i	0.113946	+	0.166829i
$995$	−27.9160	+	16.1173i	−0.884997	+	0.510953i
$996$	14.9464	+	12.6448i	0.473596	+	0.400665i
$997$	36.4440	+	21.0410i	1.15419	+	0.666374i	0.949906	−	0.312537i	$-0.101179\pi$
$997$	36.4440	+	21.0410i	1.15419	+	0.666374i	0.204288	+	0.978911i	$0.434512\pi$
$998$	0.876757	+	11.5702i	0.0277532	+	0.366249i
$999$	12.6738	−	8.32676i	0.400981	−	0.263447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.11	✓	144
8.3	odd	2	inner	504.2.br.a.155.14	yes	144
9.5	odd	6	inner	504.2.br.a.491.14	yes	144
72.59	even	6	inner	504.2.br.a.491.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.11	✓	144	1.1	even	1	trivial
504.2.br.a.155.14	yes	144	8.3	odd	2	inner
504.2.br.a.491.11	yes	144	72.59	even	6	inner
504.2.br.a.491.14	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)

\(f(q)\)	\(=\)	\(q+(-1.27467 - 0.612543i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(1.24958 + 1.56158i) q^{4} +(-1.17058 - 2.02750i) q^{5} +(2.36114 - 0.651926i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +O(q^{10})\)	\(q+(-1.27467 - 0.612543i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(1.24958 + 1.56158i) q^{4} +(-1.17058 - 2.02750i) q^{5} +(2.36114 - 0.651926i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +(0.250172 + 3.30142i) q^{10} +(3.74998 + 2.16505i) q^{11} +(-3.40902 - 0.615309i) q^{12} +(-4.95064 + 2.85826i) q^{13} +(-0.797628 - 1.16781i) q^{14} +(3.83641 + 1.31337i) q^{15} +(-0.877090 + 3.90265i) q^{16} -0.835037i q^{17} +(-2.33939 + 3.53938i) q^{18} -2.79658 q^{19} +(1.70338 - 4.36148i) q^{20} +(-1.69964 + 0.333509i) q^{21} +(-3.45381 - 5.05676i) q^{22} +(-4.32248 - 7.48676i) q^{23} +(3.96848 + 2.87249i) q^{24} +(-0.240497 + 0.416553i) q^{25} +(8.06126 - 0.610858i) q^{26} +(2.85320 + 4.34272i) q^{27} +(0.301378 + 1.97716i) q^{28} +(3.19193 - 5.52858i) q^{29} +(-4.08567 - 4.02408i) q^{30} +(7.02846 - 4.05788i) q^{31} +(3.50855 - 4.43735i) q^{32} +(-7.35962 + 1.44413i) q^{33} +(-0.511496 + 1.06440i) q^{34} -2.34115i q^{35} +(5.14999 - 3.07858i) q^{36} -2.91840i q^{37} +(3.56473 + 1.71303i) q^{38} +(3.20692 - 9.36756i) q^{39} +(-4.84284 + 4.51607i) q^{40} +(0.387918 - 0.223964i) q^{41} +(2.37077 + 0.615987i) q^{42} +(6.48309 - 11.2290i) q^{43} +(1.30500 + 8.56133i) q^{44} +(-6.50265 + 2.65414i) q^{45} +(0.923789 + 12.1909i) q^{46} +(4.13514 - 7.16227i) q^{47} +(-3.29899 - 6.09235i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.561712 - 0.383654i) q^{50} +(0.950812 + 1.08987i) q^{51} +(-10.6496 - 4.15922i) q^{52} -9.10223 q^{53} +(-0.976789 - 7.28326i) q^{54} -10.1374i q^{55} +(0.826939 - 2.70484i) q^{56} +(3.65003 - 3.18432i) q^{57} +(-7.45515 + 5.09194i) q^{58} +(-8.38108 + 4.83882i) q^{59} +(2.74298 + 7.63204i) q^{60} +(-3.82374 - 2.20764i) q^{61} +(-11.4446 + 0.867240i) q^{62} +(1.83858 - 2.37058i) q^{63} +(-7.19032 + 3.50704i) q^{64} +(11.5902 + 6.69161i) q^{65} +(10.2657 + 2.66729i) q^{66} +(1.10041 + 1.90597i) q^{67} +(1.30398 - 1.04345i) q^{68} +(14.1664 + 4.84976i) q^{69} +(-1.43406 + 2.98420i) q^{70} -4.50393 q^{71} +(-8.45031 + 0.769592i) q^{72} +2.85366 q^{73} +(-1.78764 + 3.72000i) q^{74} +(-0.160416 - 0.817516i) q^{75} +(-3.49456 - 4.36710i) q^{76} +(2.16505 + 3.74998i) q^{77} +(-9.82580 + 9.97620i) q^{78} +(6.46798 + 3.73429i) q^{79} +(8.93932 - 2.79006i) q^{80} +(-8.66875 - 2.41923i) q^{81} +(-0.631656 + 0.0478650i) q^{82} +(-4.89442 - 2.82579i) q^{83} +(-2.64464 - 2.23738i) q^{84} +(-1.69304 + 0.977475i) q^{85} +(-15.1421 + 10.3422i) q^{86} +(2.12907 + 10.8502i) q^{87} +(3.58074 - 11.7123i) q^{88} -8.68661i q^{89} +(9.91453 + 0.599994i) q^{90} -5.71651 q^{91} +(6.28991 - 16.1052i) q^{92} +(-4.55288 + 13.2992i) q^{93} +(-9.65814 + 6.59660i) q^{94} +(3.27361 + 5.67006i) q^{95} +(0.473307 + 9.78652i) q^{96} +(-3.64813 + 6.31875i) q^{97} +(-0.106859 - 1.41017i) q^{98} +(7.96124 - 10.2649i) 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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