LMFDB - Embedded newform 504.2.be.a.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(139,504)]

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, 2, 3]))

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

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

chi := DirichletCharacter("504.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.be (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:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.6
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38885 - 0.266643i) q^{2} +(0.855137 - 1.50623i) q^{3} +(1.85780 + 0.740655i) q^{4} +(1.56998 - 2.71929i) q^{5} +(-1.58928 + 1.86392i) q^{6} +(2.63479 + 0.240603i) q^{7} +(-2.38272 - 1.52403i) q^{8} +(-1.53748 - 2.57607i) q^{9} +O(q^{10})$	\(q+(-1.38885 - 0.266643i) q^{2} +(0.855137 - 1.50623i) q^{3} +(1.85780 + 0.740655i) q^{4} +(1.56998 - 2.71929i) q^{5} +(-1.58928 + 1.86392i) q^{6} +(2.63479 + 0.240603i) q^{7} +(-2.38272 - 1.52403i) q^{8} +(-1.53748 - 2.57607i) q^{9} +(-2.90555 + 3.35806i) q^{10} +(-2.45675 - 4.25522i) q^{11} +(2.70427 - 2.16492i) q^{12} +(-0.00152976 + 0.00264962i) q^{13} +(-3.59517 - 1.03671i) q^{14} +(-2.75334 - 4.69013i) q^{15} +(2.90286 + 2.75198i) q^{16} +4.75942i q^{17} +(1.44844 + 3.98773i) q^{18} -0.144762i q^{19} +(4.93077 - 3.88909i) q^{20} +(2.61551 - 3.76286i) q^{21} +(2.27743 + 6.56494i) q^{22} +(6.46589 + 3.73308i) q^{23} +(-4.33309 + 2.28568i) q^{24} +(-2.42969 - 4.20835i) q^{25} +(0.00283111 - 0.00327202i) q^{26} +(-5.19493 + 0.112914i) q^{27} +(4.71671 + 2.39846i) q^{28} +(-1.28018 + 0.739113i) q^{29} +(2.57338 + 7.24804i) q^{30} +(-2.61862 + 4.53559i) q^{31} +(-3.29784 - 4.59611i) q^{32} +(-8.51022 + 0.0616493i) q^{33} +(1.26907 - 6.61011i) q^{34} +(4.79084 - 6.78701i) q^{35} +(-0.948359 - 5.92458i) q^{36} +3.48471i q^{37} +(-0.0385998 + 0.201052i) q^{38} +(0.00268280 + 0.00456996i) q^{39} +(-7.88510 + 4.08660i) q^{40} +(3.64893 + 2.10671i) q^{41} +(-4.63589 + 4.52863i) q^{42} +(-2.84808 - 4.93302i) q^{43} +(-1.41251 - 9.72497i) q^{44} +(-9.41891 + 0.136471i) q^{45} +(-7.98474 - 6.90877i) q^{46} +(-1.34899 - 2.33652i) q^{47} +(6.62747 - 2.01907i) q^{48} +(6.88422 + 1.26788i) q^{49} +(2.25235 + 6.49262i) q^{50} +(7.16879 + 4.06995i) q^{51} +(-0.00480445 + 0.00378945i) q^{52} -1.20360i q^{53} +(7.24507 + 1.22837i) q^{54} -15.4282 q^{55} +(-5.91127 - 4.58878i) q^{56} +(-0.218045 - 0.123791i) q^{57} +(1.97506 - 0.685165i) q^{58} +(-7.52454 - 4.34429i) q^{59} +(-1.64139 - 10.7526i) q^{60} +(6.70053 + 11.6057i) q^{61} +(4.84626 - 5.60101i) q^{62} +(-3.43113 - 7.15733i) q^{63} +(3.35468 + 7.26265i) q^{64} +(0.00480339 + 0.00831972i) q^{65} +(11.8359 + 2.18357i) q^{66} +(7.04455 - 12.2015i) q^{67} +(-3.52508 + 8.84206i) q^{68} +(11.1521 - 6.54684i) q^{69} +(-8.46347 + 8.14868i) q^{70} -10.6004i q^{71} +(-0.262623 + 8.48122i) q^{72} -6.20735i q^{73} +(0.929176 - 4.83974i) q^{74} +(-8.41647 + 0.0609702i) q^{75} +(0.107218 - 0.268939i) q^{76} +(-5.44921 - 11.8027i) q^{77} +(-0.00250745 - 0.00706234i) q^{78} +(-5.81900 + 3.35960i) q^{79} +(12.0409 - 3.57316i) q^{80} +(-4.27230 + 7.92133i) q^{81} +(-4.50608 - 3.89887i) q^{82} +(-12.8073 + 7.39428i) q^{83} +(7.64608 - 5.05346i) q^{84} +(12.9422 + 7.47220i) q^{85} +(2.64020 + 7.61065i) q^{86} +(0.0185472 + 2.56030i) q^{87} +(-0.631332 + 13.8832i) q^{88} +4.25153i q^{89} +(13.1178 + 2.32195i) q^{90} +(-0.00466810 + 0.00661313i) q^{91} +(9.24742 + 11.7243i) q^{92} +(4.59238 + 7.82281i) q^{93} +(1.25053 + 3.60478i) q^{94} +(-0.393649 - 0.227273i) q^{95} +(-9.74293 + 1.03701i) q^{96} +(-3.32577 + 1.92013i) q^{97} +(-9.22307 - 3.59652i) q^{98} +(-7.18455 + 12.8711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38885	−	0.266643i	−0.982064	−	0.188545i
$2$	−1.38885	−	0.266643i	−0.982064	−	0.188545i
$3$	0.855137	−	1.50623i	0.493713	−	0.869625i
$3$	0.855137	−	1.50623i	0.493713	−	0.869625i
$4$	1.85780	+	0.740655i	0.928901	+	0.370327i
$5$	1.56998	−	2.71929i	0.702118	−	1.21610i	−0.265604	−	0.964082i	$-0.585571\pi$
$5$	1.56998	−	2.71929i	0.702118	−	1.21610i	0.967722	−	0.252021i	$-0.0810952\pi$
$6$	−1.58928	+	1.86392i	−0.648822	+	0.760940i
$7$	2.63479	+	0.240603i	0.995856	+	0.0909395i
$7$	2.63479	+	0.240603i	0.995856	+	0.0909395i
$8$	−2.38272	−	1.52403i	−0.842417	−	0.538825i
$9$	−1.53748	−	2.57607i	−0.512494	−	0.858691i
$10$	−2.90555	+	3.35806i	−0.918815	+	1.06191i
$11$	−2.45675	−	4.25522i	−0.740739	−	1.28300i	−0.952159	−	0.305603i	$-0.901142\pi$
$11$	−2.45675	−	4.25522i	−0.740739	−	1.28300i	0.211420	−	0.977395i	$-0.432191\pi$
$12$	2.70427	−	2.16492i	0.780657	−	0.624960i
$13$	−0.00152976	+	0.00264962i	−0.000424279	+	0.000734873i	−0.866237	−	0.499633i	$-0.833468\pi$
$13$	−0.00152976	+	0.00264962i	−0.000424279	+	0.000734873i	0.865813	+	0.500367i	$0.166802\pi$
$14$	−3.59517	−	1.03671i	−0.960849	−	0.277073i
$15$	−2.75334	−	4.69013i	−0.710909	−	1.21099i
$16$	2.90286	+	2.75198i	0.725715	+	0.687995i
$17$			4.75942i			1.15433i	0.816628	+	0.577164i	$0.195841\pi$
$17$			4.75942i			1.15433i	−0.816628	+	0.577164i	$0.804159\pi$
$18$	1.44844	+	3.98773i	0.341400	+	0.939918i
$19$		−	0.144762i		−	0.0332106i	−0.999862	−	0.0166053i	$-0.994714\pi$
$19$		−	0.144762i		−	0.0332106i	0.999862	−	0.0166053i	$-0.00528588\pi$
$20$	4.93077	−	3.88909i	1.10255	−	0.869627i
$21$	2.61551	−	3.76286i	0.570751	−	0.821123i
$22$	2.27743	+	6.56494i	0.485550	+	1.39965i
$23$	6.46589	+	3.73308i	1.34823	+	0.778401i	0.987999	−	0.154461i	$-0.0493642\pi$
$23$	6.46589	+	3.73308i	1.34823	+	0.778401i	0.360232	+	0.932863i	$0.382698\pi$
$24$	−4.33309	+	2.28568i	−0.884489	+	0.466562i
$25$	−2.42969	−	4.20835i	−0.485938	−	0.841670i
$26$	0.00283111	−	0.00327202i	0.000555226	−	0.000641697i
$27$	−5.19493	+	0.112914i	−0.999764	+	0.0217304i
$28$	4.71671	+	2.39846i	0.891375	+	0.453267i
$29$	−1.28018	+	0.739113i	−0.237724	+	0.137250i	−0.614130	−	0.789205i	$-0.710493\pi$
$29$	−1.28018	+	0.739113i	−0.237724	+	0.137250i	0.376406	+	0.926455i	$0.377160\pi$
$30$	2.57338	+	7.24804i	0.469832	+	1.32330i
$31$	−2.61862	+	4.53559i	−0.470319	+	0.814616i	−0.999424	−	0.0339402i	$-0.989194\pi$
$31$	−2.61862	+	4.53559i	−0.470319	+	0.814616i	0.529105	+	0.848556i	$0.322528\pi$
$32$	−3.29784	−	4.59611i	−0.582981	−	0.812486i
$33$	−8.51022	+	0.0616493i	−1.48144	+	0.0107318i
$34$	1.26907	−	6.61011i	0.217643	−	1.13362i
$35$	4.79084	−	6.78701i	0.809800	−	1.14721i
$36$	−0.948359	−	5.92458i	−0.158060	−	0.987430i
$37$			3.48471i			0.572883i	0.958098	+	0.286442i	$0.0924725\pi$
$37$			3.48471i			0.572883i	−0.958098	+	0.286442i	$0.907528\pi$
$38$	−0.0385998	+	0.201052i	−0.00626171	+	0.0326150i
$39$	0.00268280	+	0.00456996i	0.000429591	+	0.000731780i
$40$	−7.88510	+	4.08660i	−1.24674	+	0.646148i
$41$	3.64893	+	2.10671i	0.569868	+	0.329013i	0.757097	−	0.653303i	$-0.226617\pi$
$41$	3.64893	+	2.10671i	0.569868	+	0.329013i	−0.187229	+	0.982316i	$0.559951\pi$
$42$	−4.63589	+	4.52863i	−0.715333	+	0.698784i
$43$	−2.84808	−	4.93302i	−0.434329	−	0.752279i	0.562912	−	0.826517i	$-0.309681\pi$
$43$	−2.84808	−	4.93302i	−0.434329	−	0.752279i	−0.997241	+	0.0742376i	$0.976348\pi$
$44$	−1.41251	−	9.72497i	−0.212944	−	1.46609i
$45$	−9.41891	+	0.136471i	−1.40409	+	0.0203439i
$46$	−7.98474	−	6.90877i	−1.17729	−	1.01864i
$47$	−1.34899	−	2.33652i	−0.196771	−	0.340817i	0.750709	−	0.660633i	$-0.229712\pi$
$47$	−1.34899	−	2.33652i	−0.196771	−	0.340817i	−0.947480	+	0.319816i	$0.896379\pi$
$48$	6.62747	−	2.01907i	0.956593	−	0.291427i
$49$	6.88422	+	1.26788i	0.983460	+	0.181125i
$50$	2.25235	+	6.49262i	0.318530	+	0.918195i
$51$	7.16879	+	4.06995i	1.00383	+	0.569907i
$52$	−0.00480445	+	0.00378945i	−0.000666257	+	0.000525502i
$53$		−	1.20360i		−	0.165328i	−0.996577	−	0.0826639i	$-0.973657\pi$
$53$		−	1.20360i		−	0.165328i	0.996577	−	0.0826639i	$-0.0263428\pi$
$54$	7.24507	+	1.22837i	0.985930	+	0.167160i
$55$	−15.4282			−2.08034
$56$	−5.91127	−	4.58878i	−0.789926	−	0.613202i
$57$	−0.218045	−	0.123791i	−0.0288808	−	0.0163965i
$58$	1.97506	−	0.685165i	0.259338	−	0.0899665i
$59$	−7.52454	−	4.34429i	−0.979611	−	0.565579i	−0.0774586	−	0.996996i	$-0.524681\pi$
$59$	−7.52454	−	4.34429i	−0.979611	−	0.565579i	−0.902153	+	0.431417i	$0.858014\pi$
$60$	−1.64139	−	10.7526i	−0.211903	−	1.38815i
$61$	6.70053	+	11.6057i	0.857915	+	1.48595i	0.873914	+	0.486081i	$0.161574\pi$
$61$	6.70053	+	11.6057i	0.857915	+	1.48595i	−0.0159989	+	0.999872i	$0.505093\pi$
$62$	4.84626	−	5.60101i	0.615476	−	0.711329i
$63$	−3.43113	−	7.15733i	−0.432282	−	0.901739i
$64$	3.35468	+	7.26265i	0.419334	+	0.907832i
$65$	0.00480339	+	0.00831972i	0.000595787	+	0.00103193i
$66$	11.8359	+	2.18357i	1.45689	+	0.268779i
$67$	7.04455	−	12.2015i	0.860629	−	1.49065i	−0.0106932	−	0.999943i	$-0.503404\pi$
$67$	7.04455	−	12.2015i	0.860629	−	1.49065i	0.871322	−	0.490711i	$-0.163263\pi$
$68$	−3.52508	+	8.84206i	−0.427479	+	1.07226i
$69$	11.1521	−	6.54684i	1.34256	−	0.788148i
$70$	−8.46347	+	8.14868i	−1.01158	+	0.973954i
$71$		−	10.6004i		−	1.25803i	−0.777392	−	0.629017i	$-0.783458\pi$
$71$		−	10.6004i		−	1.25803i	0.777392	−	0.629017i	$-0.216542\pi$
$72$	−0.262623	+	8.48122i	−0.0309504	+	0.999521i
$73$		−	6.20735i		−	0.726515i	−0.931689	−	0.363257i	$-0.881665\pi$
$73$		−	6.20735i		−	0.726515i	0.931689	−	0.363257i	$-0.118335\pi$
$74$	0.929176	−	4.83974i	0.108015	−	0.562608i
$75$	−8.41647	+	0.0609702i	−0.971851	+	0.00704023i
$76$	0.107218	−	0.268939i	0.0122988	−	0.0308494i
$77$	−5.44921	−	11.8027i	−0.620995	−	1.34504i
$78$	−0.00250745	−	0.00706234i	−0.000283913	−	0.000799653i
$79$	−5.81900	+	3.35960i	−0.654688	+	0.377984i	−0.790250	−	0.612784i	$-0.790049\pi$
$79$	−5.81900	+	3.35960i	−0.654688	+	0.377984i	0.135562	+	0.990769i	$0.456716\pi$
$80$	12.0409	−	3.57316i	1.34621	−	0.399491i
$81$	−4.27230	+	7.92133i	−0.474700	+	0.880148i
$82$	−4.50608	−	3.89887i	−0.497613	−	0.430558i
$83$	−12.8073	+	7.39428i	−1.40578	+	0.811627i	−0.994978	−	0.100097i	$-0.968085\pi$
$83$	−12.8073	+	7.39428i	−1.40578	+	0.811627i	−0.410802	+	0.911725i	$0.634751\pi$
$84$	7.64608	−	5.05346i	0.834256	−	0.551378i
$85$	12.9422	+	7.47220i	1.40378	+	0.810474i
$86$	2.64020	+	7.61065i	0.284700	+	0.820677i
$87$	0.0185472	+	2.56030i	0.00198846	+	0.274493i
$88$	−0.631332	+	13.8832i	−0.0673002	+	1.47995i
$89$			4.25153i			0.450661i	0.974282	+	0.225331i	$0.0723462\pi$
$89$			4.25153i			0.450661i	−0.974282	+	0.225331i	$0.927654\pi$
$90$	13.1178	+	2.32195i	1.38274	+	0.244755i
$91$	−0.00466810	+	0.00661313i	−0.000489350	+	0.000693244i
$92$	9.24742	+	11.7243i	0.964110	+	1.22234i
$93$	4.59238	+	7.82281i	0.476208	+	0.811188i
$94$	1.25053	+	3.60478i	0.128982	+	0.371805i
$95$	−0.393649	−	0.227273i	−0.0403876	−	0.0233178i
$96$	−9.74293	+	1.03701i	−0.994383	+	0.105839i
$97$	−3.32577	+	1.92013i	−0.337681	+	0.194960i	−0.659246	−	0.751927i	$-0.729124\pi$
$97$	−3.32577	+	1.92013i	−0.337681	+	0.194960i	0.321565	+	0.946887i	$0.395791\pi$
$98$	−9.22307	−	3.59652i	−0.931671	−	0.363304i
$99$	−7.18455	+	12.8711i	−0.722074	+	1.29360i
$100$	−1.39695	−	9.61784i	−0.139695	−	0.961784i
$101$	7.56418	+	13.1016i	0.752664	+	1.30365i	0.946527	+	0.322624i	$0.104565\pi$
$101$	7.56418	+	13.1016i	0.752664	+	1.30365i	−0.193863	+	0.981029i	$0.562102\pi$
$102$	−8.87115	−	7.56406i	−0.878374	−	0.748953i
$103$	8.10641	−	14.0407i	0.798749	−	1.38347i	−0.121683	−	0.992569i	$-0.538829\pi$
$103$	8.10641	−	14.0407i	0.798749	−	1.38347i	0.920431	−	0.390904i	$-0.127838\pi$
$104$	0.00768308	−	0.00398190i	0.000753388	−	0.000390457i
$105$	−6.12600	−	13.0200i	−0.597836	−	1.27062i
$106$	−0.320933	+	1.67162i	−0.0311718	+	0.162363i
$107$	17.5870			1.70020			0.850102	−	0.526618i	$-0.176540\pi$
$107$	17.5870			1.70020			0.850102	+	0.526618i	$0.176540\pi$
$108$	−9.73478	−	3.63787i	−0.936729	−	0.350055i
$109$			1.36992i			0.131215i	0.997846	+	0.0656074i	$0.0208985\pi$
$109$			1.36992i			0.131215i	−0.997846	+	0.0656074i	$0.979102\pi$
$110$	21.4275	+	4.11384i	2.04303	+	0.392239i
$111$	5.24880	+	2.97991i	0.498194	+	0.282840i
$112$	6.98629	+	7.94932i	0.660142	+	0.751141i
$113$	−3.08882	+	5.35000i	−0.290572	+	0.503285i	−0.973945	−	0.226784i	$-0.927179\pi$
$113$	−3.08882	+	5.35000i	−0.290572	+	0.503285i	0.683373	+	0.730069i	$0.260512\pi$
$114$	0.269824	+	0.230067i	0.0252713	+	0.0215478i
$115$	20.3027	−	11.7217i	1.89323	−	1.09306i
$116$	−2.92575	+	0.424954i	−0.271649	+	0.0394560i
$117$	0.00917759		0.000132975i	0.000848469		1.22935e-5i
$118$	9.29207	+	8.03994i	0.855404	+	0.740136i
$119$	−1.14513	+	12.5401i	−0.104974	+	1.14954i
$120$	−0.587463	+	15.3714i	−0.0536278	+	1.40321i
$121$	−6.57129	+	11.3818i	−0.597390	+	1.03471i
$122$	−6.21145	−	17.9052i	−0.562359	−	1.62106i
$123$	6.29354	−	3.69462i	0.567470	−	0.333133i
$124$	−8.22419	+	6.48674i	−0.738554	+	0.582526i
$125$	0.441537			0.0394923
$126$	2.85687	+	10.8553i	0.254510	+	0.967070i
$127$		−	6.14240i		−	0.545050i	−0.962149	−	0.272525i	$-0.912141\pi$
$127$		−	6.14240i		−	0.545050i	0.962149	−	0.272525i	$-0.0878588\pi$
$128$	−2.72260	−	10.9812i	−0.240646	−	0.970613i
$129$	−9.86579	+	0.0714692i	−0.868634	+	0.00629252i
$130$	−0.00445279	−	0.0128356i	−0.000390535	−	0.00112576i
$131$	16.4174	+	9.47859i	1.43440	+	0.828149i	0.997452	−	0.0713403i	$-0.0227276\pi$
$131$	16.4174	+	9.47859i	1.43440	+	0.828149i	0.436944	+	0.899489i	$0.356061\pi$
$132$	−15.8560	−	6.18861i	−1.38009	−	0.538649i
$133$	0.0348302	−	0.381417i	0.00302016	−	0.0330730i
$134$	−13.0373	+	15.0677i	−1.12625	+	1.30165i
$135$	−7.84890	+	14.3038i	−0.675525	+	1.23107i
$136$	7.25348	−	11.3403i	0.621981	−	0.972426i
$137$	−4.61071	−	7.98599i	−0.393920	−	0.682289i	0.599043	−	0.800717i	$-0.295548\pi$
$137$	−4.61071	−	7.98599i	−0.393920	−	0.682289i	−0.992963	+	0.118428i	$0.962215\pi$
$138$	−17.2343	+	6.11894i	−1.46708	+	0.520879i
$139$	8.72124	+	5.03521i	0.739726	+	0.427081i	0.821970	−	0.569531i	$-0.192875\pi$
$139$	8.72124	+	5.03521i	0.739726	+	0.427081i	−0.0822437	+	0.996612i	$0.526209\pi$
$140$	13.9273	−	9.06056i	1.17707	−	0.765757i
$141$	−4.67293	+	0.0338514i	−0.393531	+	0.00285080i
$142$	−2.82652	+	14.7223i	−0.237196	+	1.23547i
$143$	0.0150330			0.00125712
$144$	2.62620	−	11.7091i	0.218850	−	0.975758i
$145$			4.64158i			0.385462i
$146$	−1.65515	+	8.62106i	−0.136981	+	0.713484i
$147$	7.79667	−	9.28504i	0.643059	−	0.765817i
$148$	−2.58097	+	6.47391i	−0.212154	+	0.532152i
$149$	6.89535	+	3.98103i	0.564889	+	0.326139i	0.755105	−	0.655603i	$-0.227586\pi$
$149$	6.89535	+	3.98103i	0.564889	+	0.326139i	−0.190216	+	0.981742i	$0.560919\pi$
$150$	11.7055	+	2.15952i	0.955748	+	0.176324i
$151$	5.17026	−	2.98505i	0.420750	−	0.242920i	−0.274648	−	0.961545i	$-0.588561\pi$
$151$	5.17026	−	2.98505i	0.420750	−	0.242920i	0.695398	+	0.718625i	$0.255228\pi$
$152$	−0.220621	+	0.344926i	−0.0178947	+	0.0279772i
$153$	12.2606	−	7.31752i	0.991211	−	0.591586i
$154$	4.42101	+	17.8452i	0.356255	+	1.43801i
$155$	8.22239	+	14.2416i	0.660438	+	1.14391i
$156$	0.00159934	+	0.0104771i	0.000128050	+	0.000838841i
$157$	0.560609	−	0.971003i	0.0447415	−	0.0774945i	−0.842787	−	0.538247i	$-0.819087\pi$
$157$	0.560609	−	0.971003i	0.0447415	−	0.0774945i	0.887529	+	0.460752i	$0.152420\pi$
$158$	8.97752	−	3.11438i	0.714213	−	0.247767i
$159$	−1.81291	−	1.02925i	−0.143773	−	0.0816246i
$160$	−17.6757	+	1.75196i	−1.39739	+	0.138504i
$161$	16.1381	+	11.3916i	1.27186	+	0.897784i
$162$	8.04574	−	9.86235i	0.632133	−	0.774860i
$163$	−11.9907			−0.939182			−0.469591	−	0.882884i	$-0.655599\pi$
$163$	−11.9907			−0.939182			−0.469591	+	0.882884i	$0.655599\pi$
$164$	5.21865	+	6.61646i	0.407508	+	0.516659i
$165$	−13.1933	+	23.2386i	−1.02709	+	1.80912i
$166$	19.7590	−	6.85456i	1.53359	−	0.532017i
$167$	−8.55886	+	14.8244i	−0.662304	+	1.14714i	0.317704	+	0.948190i	$0.397088\pi$
$167$	−8.55886	+	14.8244i	−0.662304	+	1.14714i	−0.980009	+	0.198955i	$0.936245\pi$
$168$	−11.9667	+	4.97972i	−0.923253	+	0.384193i
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$	−15.9824	−	13.8287i	−1.22579	−	1.06061i
$171$	−0.372917	+	0.222569i	−0.0285177	+	0.0170202i
$172$	−1.63751	−	11.2740i	−0.124859	−	0.859637i
$173$	−5.48146	−	9.49417i	−0.416748	−	0.721828i	0.578862	−	0.815425i	$-0.303497\pi$
$173$	−5.48146	−	9.49417i	−0.416748	−	0.721828i	−0.995610	+	0.0935970i	$0.970163\pi$
$174$	0.656927	−	3.56081i	0.0498015	−	0.269944i
$175$	−5.38918	−	11.6727i	−0.407384	−	0.882373i
$176$	4.57868	−	19.1133i	0.345131	−	1.44072i
$177$	−12.9780	+	7.61875i	−0.975489	+	0.572660i
$178$	1.13364	−	5.90473i	0.0849701	−	0.442578i
$179$	−22.3710			−1.67209			−0.836045	−	0.548661i	$-0.815138\pi$
$179$	−22.3710			−1.67209			−0.836045	+	0.548661i	$0.815138\pi$
$180$	−17.5995	−	6.72262i	−1.31179	−	0.501075i
$181$	−0.881686			−0.0655352			−0.0327676	−	0.999463i	$-0.510432\pi$
$181$	−0.881686			−0.0655352			−0.0327676	+	0.999463i	$0.510432\pi$
$182$	0.00824663	−	0.00793991i	0.000611281	−	0.000588546i
$183$	23.2107	−	0.168142i	1.71579	−	0.0124294i
$184$	−9.71705	−	18.7491i	−0.716351	−	1.38220i
$185$	9.47595	+	5.47094i	0.696685	+	0.402232i
$186$	−4.29222	−	12.0892i	−0.314721	−	0.886425i
$187$	20.2524	−	11.6927i	1.48100	−	0.855056i
$188$	−0.775605	−	5.33994i	−0.0565668	−	0.389455i
$189$	−13.7147	−	0.952412i	−0.997597	−	0.0692778i
$190$	0.486118	+	0.420612i	0.0352667	+	0.0305144i
$191$	−4.34800	+	2.51032i	−0.314610	+	0.181640i	−0.648988	−	0.760799i	$-0.724807\pi$
$191$	−4.34800	+	2.51032i	−0.314610	+	0.181640i	0.334377	+	0.942439i	$0.391474\pi$
$192$	13.8080	+	1.15764i	0.996504	+	0.0835452i
$193$	6.80704	−	11.7901i	0.489982	−	0.848673i	−0.509952	−	0.860203i	$-0.670337\pi$
$193$	6.80704	−	11.7901i	0.489982	−	0.848673i	0.999934	+	0.0115300i	$0.00367018\pi$
$194$	5.13098	−	1.77998i	0.368383	−	0.127795i
$195$	0.0166390		0.000120535i	0.00119154		8.63172e-6i
$196$	11.8505	+	7.45430i	0.846462	+	0.532450i
$197$			8.62330i			0.614385i	0.951647	+	0.307192i	$0.0993895\pi$
$197$			8.62330i			0.614385i	−0.951647	+	0.307192i	$0.900611\pi$
$198$	13.4102	−	15.9603i	0.953025	−	1.13425i
$199$	3.90133			0.276558			0.138279	−	0.990393i	$-0.455843\pi$
$199$	3.90133			0.276558			0.138279	+	0.990393i	$0.455843\pi$
$200$	−0.624377	+	13.7302i	−0.0441501	+	0.970873i
$201$	−12.3543	−	21.0447i	−0.871405	−	1.48438i
$202$	−7.01207	−	20.2130i	−0.493367	−	1.42218i
$203$	−3.55084	+	1.63939i	−0.249220	+	0.115063i
$204$	10.3038	+	12.8708i	0.721409	+	0.901134i
$205$	11.4575	−	6.61501i	0.800228	−	0.462012i
$206$	−15.0024	+	17.3389i	−1.04527	+	1.20806i
$207$	−0.324499	−	22.3961i	−0.0225542	−	1.55664i
$208$	−0.0117324	+	0.00348161i	−0.000813495	+	0.000241406i
$209$	−0.615994	+	0.355644i	−0.0426092	+	0.0246004i
$210$	5.03640	+	19.7162i	0.347545	+	1.36055i
$211$	8.53055	−	14.7753i	0.587267	−	1.01718i	−0.407322	−	0.913285i	$-0.633537\pi$
$211$	8.53055	−	14.7753i	0.587267	−	1.01718i	0.994589	−	0.103892i	$-0.0331295\pi$
$212$	0.891455	−	2.23606i	0.0612254	−	0.153573i
$213$	−15.9667	−	9.06478i	−1.09402	−	0.621108i
$214$	−24.4258	−	4.68947i	−1.66971	−	0.320566i
$215$	−17.8858			−1.21980
$216$	12.5501	+	7.64817i	0.853927	+	0.520392i
$217$	−7.99080	+	11.3203i	−0.542451	+	0.768470i
$218$	0.365281	−	1.90262i	0.0247399	−	0.128861i
$219$	−9.34971	−	5.30813i	−0.631795	−	0.358690i
$220$	−28.6626	−	11.4270i	−1.93243	−	0.770408i
$221$	−0.0126106	−	0.00728076i	−0.000848284	−	0.000489757i
$222$	−6.49521	−	5.53820i	−0.435930	−	0.371699i
$223$	−0.913925	−	1.58296i	−0.0612009	−	0.106003i	0.833802	−	0.552064i	$-0.186160\pi$
$223$	−0.913925	−	1.58296i	−0.0612009	−	0.106003i	−0.895002	+	0.446061i	$0.852826\pi$
$224$	−7.58326	−	12.9033i	−0.506678	−	0.862135i
$225$	−7.10540	+	12.7293i	−0.473693	+	0.848621i
$226$	5.71645	−	6.60672i	0.380252	−	0.439473i
$227$	−14.6610	+	8.46455i	−0.973087	+	0.561812i	−0.900176	−	0.435527i	$-0.856562\pi$
$227$	−14.6610	+	8.46455i	−0.973087	+	0.561812i	−0.0729107	+	0.997338i	$0.523229\pi$
$228$	−0.313398	−	0.391476i	−0.0207553	−	0.0259261i
$229$	−3.76642	+	6.52362i	−0.248892	+	0.431093i	−0.963219	−	0.268719i	$-0.913400\pi$
$229$	−3.76642	+	6.52362i	−0.248892	+	0.431093i	0.714327	+	0.699812i	$0.246733\pi$
$230$	−31.3229	+	10.8662i	−2.06537	+	0.716494i
$231$	−22.4375	−	1.88516i	−1.47628	−	0.124034i
$232$	4.17674	+	0.189936i	0.274216	+	0.0124699i
$233$	2.45313			0.160710			0.0803550	−	0.996766i	$-0.474395\pi$
$233$	2.45313			0.160710			0.0803550	+	0.996766i	$0.474395\pi$
$234$	−0.0127817	−	0.00226246i	−0.000835569	−	0.000147902i
$235$	−8.47158			−0.552625
$236$	−10.7615	−	13.6439i	−0.700513	−	0.888144i
$237$	0.0843051	+	11.6377i	0.00547621	+	0.755949i
$238$	4.93414	−	17.1109i	0.319833	−	1.10913i
$239$	4.04463	+	2.33517i	0.261625	+	0.151050i	0.625076	−	0.780564i	$-0.285068\pi$
$239$	4.04463	+	2.33517i	0.261625	+	0.151050i	−0.363450	+	0.931614i	$0.618401\pi$
$240$	4.91458	−	21.1919i	0.317235	−	1.36793i
$241$	−0.991611	+	0.572507i	−0.0638753	+	0.0368784i	−0.531598	−	0.846997i	$-0.678408\pi$
$241$	−0.991611	+	0.572507i	−0.0638753	+	0.0368784i	0.467722	+	0.883876i	$0.345075\pi$
$242$	12.1614	−	14.0554i	0.781765	−	0.903516i
$243$	8.27798	+	13.2089i	0.531033	+	0.847351i
$244$	3.85248	+	26.5238i	0.246630	+	1.69801i
$245$	14.2558	−	16.7296i	0.910772	−	1.06882i
$246$	−9.72592	+	3.45314i	−0.620102	+	0.220164i
$247$	0.000383564	0	0.000221451i	2.44056e−5	0	1.40906e-5i
$248$	13.1518	−	6.81617i	0.835141	−	0.432827i
$249$	0.185551	+	25.6138i	0.0117588	+	1.62321i
$250$	−0.613229	−	0.117733i	−0.0387840	−	0.00744609i
$251$		−	18.6944i		−	1.17998i	−0.807411	−	0.589990i	$-0.799132\pi$
$251$		−	18.6944i		−	1.17998i	0.807411	−	0.589990i	$-0.200868\pi$
$252$	−1.07325	−	15.8382i	−0.0676084	−	0.997712i
$253$		−	36.6851i		−	2.30637i
$254$	−1.63783	+	8.53087i	−0.102767	+	0.535275i
$255$	22.3223	−	13.1043i	1.39787	−	0.820622i
$256$	0.853205	+	15.9772i	0.0533253	+	0.998577i
$257$	17.1488	+	9.90088i	1.06971	+	0.617600i	0.928104	−	0.372322i	$-0.121438\pi$
$257$	17.1488	+	9.90088i	1.06971	+	0.617600i	0.141611	+	0.989922i	$0.454772\pi$
$258$	13.7211	+	2.53139i	0.854241	+	0.157597i
$259$	−0.838434	+	9.18148i	−0.0520978	+	0.570510i
$260$	0.00276171	+	0.0190140i	0.000171274	+	0.00117920i
$261$	3.87227	+	2.16147i	0.239687	+	0.133791i
$262$	−20.2739	−	17.5419i	−1.25253	−	1.08374i
$263$	8.66077	−	5.00030i	0.534046	−	0.308332i	−0.208616	−	0.977998i	$-0.566896\pi$
$263$	8.66077	−	5.00030i	0.534046	−	0.308332i	0.742663	+	0.669666i	$0.233563\pi$
$264$	20.3714	+	12.8229i	1.25377	+	0.789197i
$265$	−3.27295	−	1.88964i	−0.201056	−	0.116080i
$266$	−0.150076	+	0.520443i	−0.00920175	+	0.0319104i
$267$	6.40380	+	3.63564i	0.391906	+	0.222498i
$268$	22.1245	−	17.4504i	1.35147	−	1.06596i
$269$	−4.08064			−0.248801			−0.124401	−	0.992232i	$-0.539701\pi$
$269$	−4.08064			−0.248801			−0.124401	+	0.992232i	$0.539701\pi$
$270$	14.7149	−	17.7729i	0.895523	−	1.08163i
$271$	10.3084			0.626193			0.313096	−	0.949721i	$-0.398634\pi$
$271$	10.3084			0.626193			0.313096	+	0.949721i	$0.398634\pi$
$272$	−13.0978	+	13.8159i	−0.794172	+	0.837713i
$273$	0.00596905	+	0.0126864i	0.000361263	+	0.000767815i
$274$	4.27417	+	12.3207i	0.258212	+	0.744324i
$275$	−11.9383	+	20.6778i	−0.719907	+	1.24692i
$276$	25.5674	−	3.90288i	1.53898	−	0.234926i
$277$	−21.3726	+	12.3395i	−1.28415	+	0.741407i	−0.977605	−	0.210448i	$-0.932508\pi$
$277$	−21.3726	+	12.3395i	−1.28415	+	0.741407i	−0.306549	+	0.951855i	$0.599174\pi$
$278$	−10.7699	−	9.31861i	−0.645934	−	0.558893i
$279$	15.7101	−	0.227624i	0.940539	−	0.0136275i
$280$	−21.7588	+	8.87014i	−1.30034	+	0.530092i
$281$	−6.61103	−	11.4506i	−0.394381	−	0.683088i	0.598641	−	0.801017i	$-0.295708\pi$
$281$	−6.61103	−	11.4506i	−0.394381	−	0.683088i	−0.993022	+	0.117930i	$0.962374\pi$
$282$	6.49902	+	1.19899i	0.387011	+	0.0713988i
$283$	−3.85941	−	2.22823i	−0.229418	−	0.132455i	0.380885	−	0.924622i	$-0.375619\pi$
$283$	−3.85941	−	2.22823i	−0.229418	−	0.132455i	−0.610304	+	0.792168i	$0.708953\pi$
$284$	7.85122	−	19.6934i	0.465884	−	1.16859i
$285$	−0.678951	+	0.398578i	−0.0402176	+	0.0236097i
$286$	−0.0208785	−	0.00400844i	−0.00123457	−	0.000237024i
$287$	9.10729	+	6.42869i	0.537586	+	0.379474i
$288$	−6.76955	+	15.5619i	−0.398900	+	0.916995i
$289$	−5.65204			−0.332473
$290$	1.23765	−	6.44645i	0.0726771	−	0.378549i
$291$	0.0481834	+	6.65136i	0.00282456	+	0.389910i
$292$	4.59750	−	11.5320i	0.269048	−	0.674861i
$293$	10.8291	−	18.7565i	0.632642	−	1.09577i	−0.354367	−	0.935106i	$-0.615304\pi$
$293$	10.8291	−	18.7565i	0.632642	−	1.09577i	0.987009	−	0.160662i	$-0.0513629\pi$
$294$	−13.3042	+	10.8166i	−0.775916	+	0.630836i
$295$	−23.6268	+	13.6409i	−1.37560	+	0.794206i
$296$	5.31080	−	8.30309i	0.308684	−	0.482607i
$297$	13.2431	+	21.8282i	0.768444	+	1.26660i
$298$	−8.51508	−	7.36765i	−0.493265	−	0.426797i
$299$	−0.0197825	+	0.0114214i	−0.00114405	+	0.000660519i
$300$	−15.6813	−	6.12043i	−0.905361	−	0.353363i
$301$	−6.31719	−	13.6827i	−0.364117	−	0.788660i
$302$	−7.97665	+	2.76717i	−0.459005	+	0.159233i
$303$	26.2024	−	0.189814i	1.50529	−	0.0109045i
$304$	0.398382	−	0.420223i	0.0228487	−	0.0241015i
$305$	42.0789			2.40943
$306$	−18.9793	+	6.89372i	−1.08497	+	0.394088i
$307$			5.22129i			0.297994i	0.988838	+	0.148997i	$0.0476046\pi$
$307$			5.22129i			0.297994i	−0.988838	+	0.148997i	$0.952395\pi$
$308$	−1.38181	−	25.9631i	−0.0787361	−	1.47938i
$309$	−14.2165	−	24.2169i	−0.808749	−	1.37765i
$310$	−7.62223	−	21.9719i	−0.432914	−	1.24792i
$311$	−10.6562	+	18.4570i	−0.604256	+	1.04660i	0.387912	+	0.921696i	$0.373196\pi$
$311$	−10.6562	+	18.4570i	−0.604256	+	1.04660i	−0.992169	+	0.124906i	$0.960137\pi$
$312$	0.000572412	−	0.0149776i	3.24065e−5	−	0.000847939i
$313$	4.38992	−	2.53452i	0.248133	−	0.143260i	−0.370776	−	0.928722i	$-0.620908\pi$
$313$	4.38992	−	2.53452i	0.248133	−	0.143260i	0.618909	+	0.785463i	$0.287575\pi$
$314$	−1.03751	+	1.19909i	−0.0585502	+	0.0676688i
$315$	−24.8497	−	1.90665i	−1.40012	−	0.107427i
$316$	−13.2989	+	1.93160i	−0.748119	+	0.108661i
$317$	−3.35620	+	1.93770i	−0.188503	+	0.108832i	−0.591281	−	0.806465i	$-0.701378\pi$
$317$	−3.35620	+	1.93770i	−0.188503	+	0.108832i	0.402779	+	0.915297i	$0.368044\pi$
$318$	2.24342	+	1.91287i	0.125805	+	0.107268i
$319$	6.29018	+	3.63164i	0.352183	+	0.203333i
$320$	25.0160	+	2.27991i	1.39844	+	0.127451i
$321$	15.0393	−	26.4902i	0.839414	−	1.47854i
$322$	−19.3758	−	20.1243i	−1.07977	−	1.12148i
$323$	0.688981			0.0383360
$324$	−13.8041	+	11.5520i	−0.766892	+	0.641776i
$325$	0.0148674			0.000824693
$326$	16.6532	+	3.19723i	0.922337	+	0.177078i
$327$	2.06342	+	1.17147i	0.114108	+	0.0647825i
$328$	−5.48369	−	10.5808i	−0.302786	−	0.584226i
$329$	−2.99214	−	6.48082i	−0.164962	−	0.357299i
$330$	24.5199	−	28.7569i	1.34977	−	1.58302i
$331$	6.20448	+	10.7465i	0.341029	+	0.590679i	0.984624	−	0.174687i	$-0.0558913\pi$
$331$	6.20448	+	10.7465i	0.341029	+	0.590679i	−0.643595	+	0.765366i	$0.722558\pi$
$332$	−29.2700	+	4.25135i	−1.60640	+	0.233323i
$333$	8.97688	−	5.35769i	0.491930	−	0.293599i
$334$	15.8398	−	18.3067i	0.866714	−	1.00170i
$335$	−22.1197	−	38.3124i	−1.20853	−	2.09323i
$336$	17.9478	−	3.72523i	0.979131	−	0.203228i
$337$	−14.5440	+	25.1909i	−0.792261	+	1.37224i	0.132304	+	0.991209i	$0.457763\pi$
$337$	−14.5440	+	25.1909i	−0.792261	+	1.37224i	−0.924564	+	0.381026i	$0.875571\pi$
$338$	−6.02555	−	17.3693i	−0.327747	−	0.944765i
$339$	5.41698	+	9.22747i	0.294210	+	0.501167i
$340$	18.5098	+	23.4676i	1.00383	+	1.27271i
$341$	25.7333			1.39353
$342$	0.577271	−	0.209678i	0.0312153	−	0.0113381i
$343$	17.8334	+	4.99696i	0.962913	+	0.269810i
$344$	−0.731895	+	16.0946i	−0.0394611	+	0.867760i
$345$	−0.294143	−	40.6043i	−0.0158361	−	2.18606i
$346$	5.08136	+	14.6476i	0.273176	+	0.787458i
$347$	−9.48245	+	16.4241i	−0.509044	+	0.881691i	0.490901	+	0.871216i	$0.336668\pi$
$347$	−9.48245	+	16.4241i	−0.509044	+	0.881691i	−0.999945	+	0.0104754i	$0.996666\pi$
$348$	−1.86184	+	4.77026i	−0.0998050	+	0.255713i
$349$	9.63099	+	16.6814i	0.515535	+	0.892933i	0.999837	+	0.0180321i	$0.00574011\pi$
$349$	9.63099	+	16.6814i	0.515535	+	0.892933i	−0.484302	+	0.874901i	$0.660927\pi$
$350$	4.37231	+	17.6486i	0.233710	+	0.943357i
$351$	0.00764781	−	0.0139373i	0.000408210	−	0.000743919i
$352$	−11.4555	+	25.3246i	−0.610581	+	1.34980i
$353$	−25.0834	+	14.4819i	−1.33505	+	0.770794i	−0.986069	−	0.166334i	$-0.946807\pi$
$353$	−25.0834	+	14.4819i	−1.33505	+	0.770794i	−0.348985	+	0.937128i	$0.613474\pi$
$354$	20.0560	−	7.12079i	1.06597	−	0.378466i
$355$	−28.8255	−	16.6424i	−1.52990	−	0.883288i
$356$	−3.14892	+	7.89850i	−0.166892	+	0.418620i
$357$	17.9090	+	12.4483i	0.947845	+	0.658834i
$358$	31.0700	+	5.96509i	1.64210	+	0.315265i
$359$			36.1721i			1.90909i	0.298068	+	0.954545i	$0.403658\pi$
$359$			36.1721i			1.90909i	−0.298068	+	0.954545i	$0.596342\pi$
$360$	22.6506	+	14.0295i	1.19379	+	0.739420i
$361$	18.9790			0.998897
$362$	1.22453	+	0.235096i	0.0643598	+	0.0123564i
$363$	11.5243	+	19.6309i	0.604869	+	1.03035i
$364$	−0.0135705	+	0.00882843i	−0.000711285	+	0.000462736i
$365$	−16.8796	−	9.74542i	−0.883517	−	0.510099i
$366$	−32.2810	−	5.95546i	−1.68736	−	0.311297i
$367$	−12.8245	−	22.2126i	−0.669432	−	1.15949i	−0.978063	−	0.208309i	$-0.933204\pi$
$367$	−12.8245	−	22.2126i	−0.669432	−	1.15949i	0.308631	−	0.951182i	$-0.400129\pi$
$368$	8.49620	+	28.6306i	0.442895	+	1.49247i
$369$	−0.183126	−	12.6390i	−0.00953318	−	0.657958i
$370$	−11.7019	−	10.1250i	−0.608351	−	0.526374i
$371$	0.289591	−	3.17124i	0.0150348	−	0.164643i
$372$	2.73773	+	17.9346i	0.141945	+	0.929866i
$373$	20.6385	+	11.9156i	1.06862	+	0.616968i	0.927804	−	0.373068i	$-0.121694\pi$
$373$	20.6385	+	11.9156i	1.06862	+	0.616968i	0.140816	+	0.990036i	$0.455027\pi$
$374$	−31.2453	+	10.8393i	−1.61565	+	0.560484i
$375$	0.377575	−	0.665059i	0.0194979	−	0.0343435i
$376$	−0.346662	+	7.62318i	−0.0178777	+	0.393135i
$377$		−	0.00452266i		−	0.000232929i
$378$	18.7937	+	4.97969i	0.966643	+	0.256128i
$379$	−20.4309			−1.04947			−0.524734	−	0.851266i	$-0.675835\pi$
$379$	−20.4309			−1.04947			−0.524734	+	0.851266i	$0.675835\pi$
$380$	−0.562991	−	0.713787i	−0.0288808	−	0.0366165i
$381$	−9.25190	−	5.25260i	−0.473989	−	0.269099i
$382$	6.70808	−	2.32709i	0.343215	−	0.119064i
$383$	−3.21927	+	5.57593i	−0.164497	+	0.284917i	−0.936476	−	0.350730i	$-0.885933\pi$
$383$	−3.21927	+	5.57593i	−0.164497	+	0.284917i	0.771980	+	0.635647i	$0.219267\pi$
$384$	−18.8685	−	5.28958i	−0.962879	−	0.269933i
$385$	−40.6502	−	3.71209i	−2.07172	−	0.189186i
$386$	−12.5977	+	14.5597i	−0.641207	+	0.741068i
$387$	−8.32895	+	14.9213i	−0.423384	+	0.758493i
$388$	−7.60078	+	1.10398i	−0.385871	+	0.0560462i
$389$	−27.2581	+	15.7375i	−1.38204	+	0.797921i	−0.992401	−	0.123047i	$-0.960734\pi$
$389$	−27.2581	+	15.7375i	−1.38204	+	0.797921i	−0.389639	+	0.920968i	$0.627400\pi$
$390$	−0.0231412	−	0.00426927i	−0.00117180	−	0.000216183i
$391$	−17.7673	+	30.7738i	−0.898530	+	1.55630i
$392$	−14.4709	−	13.5127i	−0.730889	−	0.682496i
$393$	28.3161	−	16.6230i	1.42836	−	0.838518i
$394$	2.29935	−	11.9765i	0.115839	−	0.603365i
$395$			21.0981i			1.06156i
$396$	−22.8805	+	18.5907i	−1.14979	+	0.934218i
$397$	−19.9895			−1.00324			−0.501621	−	0.865088i	$-0.667263\pi$
$397$	−19.9895			−1.00324			−0.501621	+	0.865088i	$0.667263\pi$
$398$	−5.41836	−	1.04026i	−0.271598	−	0.0521437i
$399$	−0.544718	−	0.378626i	−0.0272700	−	0.0189550i
$400$	4.52824	−	18.9027i	0.226412	−	0.945136i
$401$	9.25181	−	16.0246i	0.462013	−	0.800231i	−0.537048	−	0.843552i	$-0.680460\pi$
$401$	9.25181	−	16.0246i	0.462013	−	0.800231i	0.999061	+	0.0433210i	$0.0137938\pi$
$402$	11.5468	+	32.5221i	0.575903	+	1.62206i
$403$	−0.00801173	−	0.0138767i	−0.000399093	−	0.000691249i
$404$	4.34903	+	29.9425i	0.216373	+	1.48970i
$405$	14.8330	+	24.0540i	0.737056	+	1.19525i
$406$	5.36871	−	1.33006i	0.266445	−	0.0660097i
$407$	14.8282	−	8.56109i	0.735008	−	0.424357i
$408$	−10.8785	−	20.6230i	−0.538565	−	1.02099i
$409$	−18.3066	−	10.5693i	−0.905205	−	0.522620i	−0.0263197	−	0.999654i	$-0.508379\pi$
$409$	−18.3066	−	10.5693i	−0.905205	−	0.522620i	−0.878885	+	0.477033i	$0.841712\pi$
$410$	−17.6766	+	6.13217i	−0.872986	+	0.302846i
$411$	−15.9716	+	0.115700i	−0.787819	+	0.00570708i
$412$	25.4594	−	20.0808i	1.25430	−	0.989312i
$413$	−18.7803	−	13.2567i	−0.924119	−	0.652321i
$414$	−5.52110	+	31.1914i	−0.271347	+	1.53297i
$415$			46.4355i			2.27943i
$416$	0.0172229	−	0.00170707i	0.000844420	−	8.36961e-5i
$417$	15.0421	−	8.83044i	0.736613	−	0.432428i
$418$	0.950352	−	0.329685i	0.0464832	−	0.0161254i
$419$	−4.51865	−	2.60884i	−0.220750	−	0.127450i	0.385547	−	0.922688i	$-0.374013\pi$
$419$	−4.51865	−	2.60884i	−0.220750	−	0.127450i	−0.606298	+	0.795238i	$0.707346\pi$
$420$	−1.73761	−	28.7258i	−0.0847867	−	1.40167i
$421$	−3.22988	+	1.86477i	−0.157415	+	0.0908834i	−0.576638	−	0.817000i	$-0.695636\pi$
$421$	−3.22988	+	1.86477i	−0.157415	+	0.0908834i	0.419223	+	0.907883i	$0.362302\pi$
$422$	−15.7874	+	18.2461i	−0.768518	+	0.888206i
$423$	−3.94500	+	7.06747i	−0.191813	+	0.343632i
$424$	−1.83433	+	2.86785i	−0.0890828	+	0.139275i
$425$	20.0293	−	11.5639i	0.971563	−	0.560932i
$426$	19.7582	+	16.8470i	0.957289	+	0.816240i
$427$	14.8621	+	32.1906i	0.719228	+	1.55781i
$428$	32.6733	+	13.0259i	1.57932	+	0.629632i
$429$	0.0128552	−	0.0226432i	0.000620657	−	0.00109322i
$430$	24.8406	+	4.76912i	1.19792	+	0.229987i
$431$			18.3303i			0.882938i	0.897277	+	0.441469i	$0.145542\pi$
$431$			18.3303i			0.882938i	−0.897277	+	0.441469i	$0.854458\pi$
$432$	−15.3909	−	13.9686i	−0.740494	−	0.672063i
$433$		−	35.0470i		−	1.68425i	−0.539281	−	0.842126i	$-0.681304\pi$
$433$		−	35.0470i		−	1.68425i	0.539281	−	0.842126i	$-0.318696\pi$
$434$	14.1165	−	13.5915i	0.677613	−	0.652411i
$435$	6.99130	+	3.96918i	0.335207	+	0.190308i
$436$	−1.01464	+	2.54505i	−0.0485924	+	0.121886i
$437$	0.540408	−	0.936013i	0.0258512	−	0.0447756i
$438$	11.5700	+	9.86523i	0.552834	+	0.471379i
$439$	−7.70657	−	13.3482i	−0.367815	−	0.637074i	0.621409	−	0.783486i	$-0.286561\pi$
$439$	−7.70657	−	13.3482i	−0.367815	−	0.637074i	−0.989224	+	0.146413i	$0.953227\pi$
$440$	36.7611	+	23.5131i	1.75252	+	1.12094i
$441$	−7.31822	−	19.6836i	−0.348487	−	0.937314i
$442$	0.0155729	+	0.0134744i	0.000740728	+	0.000640913i
$443$	−0.868291	−	1.50392i	−0.0412538	−	0.0714536i	0.844661	−	0.535301i	$-0.179802\pi$
$443$	−0.868291	−	1.50392i	−0.0412538	−	0.0714536i	−0.885915	+	0.463848i	$0.846469\pi$
$444$	7.54414	+	9.42362i	0.358029	+	0.447225i
$445$	11.5611	+	6.67483i	0.548051	+	0.316417i
$446$	0.847217	+	2.44219i	0.0401169	+	0.115641i
$447$	11.8928	−	6.98168i	0.562512	−	0.330222i
$448$	7.09144	+	19.9427i	0.335039	+	0.942204i
$449$	−9.10746			−0.429808			−0.214904	−	0.976635i	$-0.568944\pi$
$449$	−9.10746			−0.429808			−0.214904	+	0.976635i	$0.568944\pi$
$450$	13.2625	−	15.7845i	0.625201	−	0.744088i
$451$		−	20.7027i		−	0.974853i
$452$	−9.70092	+	7.65149i	−0.456293	+	0.359896i
$453$	−0.0749062	−	10.3402i	−0.00351940	−	0.485827i
$454$	22.6190	−	7.84671i	1.06156	−	0.368264i
$455$	0.0106542	+	0.0230764i	0.000499475	+	0.00108184i
$456$	0.330879	+	0.627266i	0.0154948	+	0.0293744i
$457$	−1.66030	−	2.87573i	−0.0776657	−	0.134521i	0.824577	−	0.565750i	$-0.191413\pi$
$457$	−1.66030	−	2.87573i	−0.0776657	−	0.134521i	−0.902242	+	0.431229i	$0.858080\pi$
$458$	6.97046	−	8.05604i	0.325708	−	0.376434i
$459$	−0.537406	−	24.7248i	−0.0250840	−	1.15406i
$460$	46.4001	−	6.73943i	2.16342	−	0.314228i
$461$	−17.4869	−	30.2883i	−0.814448	−	1.41067i	−0.909724	−	0.415214i	$-0.863707\pi$
$461$	−17.4869	−	30.2883i	−0.814448	−	1.41067i	0.0952755	−	0.995451i	$-0.469627\pi$
$462$	30.6596	+	8.60100i	1.42641	+	0.400155i
$463$	−8.21310	−	4.74183i	−0.381695	−	0.220372i	0.296861	−	0.954921i	$-0.404060\pi$
$463$	−8.21310	−	4.74183i	−0.381695	−	0.220372i	−0.678555	+	0.734549i	$0.737394\pi$
$464$	−5.75021	−	1.37749i	−0.266947	−	0.0639485i
$465$	28.4824	−	0.206331i	1.32084	−	0.00956837i
$466$	−3.40703	−	0.654112i	−0.157828	−	0.0303011i
$467$			1.77339i			0.0820626i	0.999158	+	0.0410313i	$0.0130643\pi$
$467$			1.77339i			0.0820626i	−0.999158	+	0.0410313i	$0.986936\pi$
$468$	0.0171486	+	0.00655039i	0.000792696	+	0.000302792i
$469$	21.4966	−	30.4535i	0.992623	−	1.40621i
$470$	11.7657	+	2.25889i	0.542713	+	0.104195i
$471$	−0.983161	−	1.67475i	−0.0453017	−	0.0771684i
$472$	11.3080	+	21.8188i	0.520494	+	1.00429i
$473$	−13.9941	+	24.2385i	−0.643449	+	1.11449i
$474$	2.98603	−	16.1855i	0.137153	−	0.743423i
$475$	−0.609208	+	0.351726i	−0.0279524	+	0.0161383i
$476$	−11.4153	+	22.4488i	−0.523218	+	1.02894i
$477$	−3.10057	+	1.85052i	−0.141965	+	0.0847295i
$478$	−4.99472	−	4.32167i	−0.228453	−	0.197669i
$479$	16.7023	+	28.9292i	0.763147	+	1.32181i	0.941221	+	0.337792i	$0.109680\pi$
$479$	16.7023	+	28.9292i	0.763147	+	1.32181i	−0.178074	+	0.984017i	$0.556987\pi$
$480$	−12.4763	+	28.1219i	−0.569462	+	1.28358i
$481$	−0.00923317	−	0.00533077i	−0.000420996	−	0.000243062i
$482$	1.52985	−	0.530719i	0.0696829	−	0.0241736i
$483$	30.9587	−	14.5663i	1.40867	−	0.662790i
$484$	−20.6381	+	16.2781i	−0.938097	+	0.739913i
$485$			12.0583i			0.547539i
$486$	−7.97480	−	20.5524i	−0.361744	−	0.932277i
$487$		−	9.64922i		−	0.437248i	−0.975809	−	0.218624i	$-0.929843\pi$
$487$		−	9.64922i		−	0.437248i	0.975809	−	0.218624i	$-0.0701568\pi$
$488$	1.72189	−	37.8648i	0.0779463	−	1.71406i
$489$	−10.2537	+	18.0608i	−0.463687	+	0.816735i
$490$	−24.2600	+	19.4337i	−1.09596	+	0.877926i
$491$	9.78296	−	16.9446i	0.441499	−	0.764698i	−0.556302	−	0.830980i	$-0.687780\pi$
$491$	9.78296	−	16.9446i	0.441499	−	0.764698i	0.997801	+	0.0662817i	$0.0211136\pi$
$492$	14.4286	−	2.20254i	0.650491	−	0.0992980i
$493$	−3.51775	−	6.09292i	−0.158431	−	0.274411i
$494$	−0.000473664	0	0.000409836i	−2.13111e−5	0	1.84394e-5i
$495$	23.7207	+	39.7443i	1.06616	+	1.78637i
$496$	−20.0834	+	5.95979i	−0.901770	+	0.267602i
$497$	2.55049	−	27.9298i	0.114405	−	1.25282i
$498$	6.57206	−	35.6232i	0.294501	−	1.59632i
$499$	13.3516	−	23.1257i	0.597700	−	1.03525i	−0.395459	−	0.918484i	$-0.629415\pi$
$499$	13.3516	−	23.1257i	0.597700	−	1.03525i	0.993160	−	0.116764i	$-0.0372521\pi$
$500$	0.820289	+	0.327027i	0.0366845	+	0.0146251i
$501$	15.0100	+	25.5685i	0.670597	+	1.14232i
$502$	−4.98473	+	25.9637i	−0.222480	+	1.15882i
$503$	22.2390			0.991586			0.495793	−	0.868441i	$-0.334877\pi$
$503$	22.2390			0.991586			0.495793	+	0.868441i	$0.334877\pi$
$504$	−2.73256	+	22.2830i	−0.121718	+	0.992565i
$505$	47.5025			2.11384
$506$	−9.78183	+	50.9500i	−0.434855	+	2.26500i
$507$	22.5161	−	0.163110i	0.999973	−	0.00724395i
$508$	4.54940	−	11.4114i	0.201847	−	0.506298i
$509$	−5.02744	+	8.70778i	−0.222837	+	0.385966i	−0.955668	−	0.294445i	$-0.904865\pi$
$509$	−5.02744	+	8.70778i	−0.222837	+	0.385966i	0.732831	+	0.680411i	$0.238199\pi$
$510$	−34.4964	+	12.2478i	−1.52753	+	0.542341i
$511$	1.49351	−	16.3550i	0.0660689	−	0.723504i
$512$	3.07525	−	22.4175i	0.135908	−	0.990721i
$513$	0.0163457	+	0.752027i	0.000721679	+	0.0332028i
$514$	−21.1771	−	18.3235i	−0.934083	−	0.808213i
$515$	−25.4539	−	44.0874i	−1.12163	−	1.94272i
$516$	−18.3816	−	7.17437i	−0.809206	−	0.315834i
$517$	−6.62829	+	11.4805i	−0.291512	+	0.504913i
$518$	3.61264	−	12.5281i	0.158730	−	0.550454i
$519$	−18.9878	+	0.137551i	−0.833473	+	0.00603780i
$520$	0.00123437	−	0.0271440i	5.41305e−5	−	0.00119034i
$521$		−	25.3692i		−	1.11145i	−0.831368	−	0.555723i	$-0.812442\pi$
$521$		−	25.3692i		−	1.11145i	0.831368	−	0.555723i	$-0.187558\pi$
$522$	−4.80165	−	4.03446i	−0.210163	−	0.176584i
$523$			27.5574i			1.20500i	0.798118	+	0.602501i	$0.205829\pi$
$523$			27.5574i			1.20500i	−0.798118	+	0.602501i	$0.794171\pi$
$524$	23.4799	+	29.7690i	1.02573	+	1.30046i
$525$	−22.1903	−	1.86439i	−0.968464	−	0.0813686i
$526$	−13.3618	+	4.63532i	−0.582602	+	0.202110i
$527$	−21.5868	−	12.4631i	−0.940334	−	0.542902i
$528$	−24.8737	−	23.2410i	−1.08249	−	1.01144i
$529$	16.3718	+	28.3568i	0.711817	+	1.23290i
$530$	4.04177	+	3.49713i	0.175563	+	0.151906i
$531$	0.377629	+	26.0630i	0.0163877	+	1.13104i
$532$	0.347206	−	0.682800i	0.0150533	−	0.0296031i
$533$	−0.0111640	+	0.00644553i	−0.000483566	+	0.000279187i
$534$	−7.92449	−	6.75688i	−0.342926	−	0.292399i
$535$	27.6114	−	47.8243i	1.19374	−	2.06762i
$536$	−35.3806	+	18.3367i	−1.52821	+	0.792024i
$537$	−19.1303	+	33.6960i	−0.825533	+	1.45409i
$538$	5.66739	+	1.08808i	0.244339	+	0.0469103i
$539$	−11.5177	−	32.4088i	−0.496104	−	1.39594i
$540$	−25.1759	+	20.7603i	−1.08340	+	0.893380i
$541$		−	4.43801i		−	0.190805i	−0.995439	−	0.0954025i	$-0.969586\pi$
$541$		−	4.43801i		−	0.190805i	0.995439	−	0.0954025i	$-0.0304138\pi$
$542$	−14.3169	−	2.74867i	−0.614961	−	0.118066i
$543$	−0.753962	+	1.32803i	−0.0323556	+	0.0569910i
$544$	21.8748	−	15.6958i	0.937875	−	0.672951i
$545$	3.72522	+	2.15076i	0.159571	+	0.0921282i
$546$	−0.00490737	−	0.0192111i	−0.000210016	−	0.000822158i
$547$	−10.8877	−	18.8580i	−0.465524	−	0.806311i	0.533701	−	0.845673i	$-0.320801\pi$
$547$	−10.8877	−	18.8580i	−0.465524	−	0.806311i	−0.999225	+	0.0393623i	$0.987467\pi$
$548$	−2.65093	−	18.2513i	−0.113242	−	0.779658i
$549$	19.5951	−	35.1045i	0.836297	−	1.49823i
$550$	22.0941	−	25.5350i	0.942095	−	1.08882i
$551$	0.106995	+	0.185321i	0.00455815	+	0.00789495i
$552$	−36.5499	−	1.39686i	−1.55567	−	0.0594544i
$553$	−16.1402	+	7.45176i	−0.686349	+	0.316881i
$554$	32.9735	−	11.4388i	1.40091	−	0.485988i
$555$	16.3437	−	9.59459i	0.693753	−	0.407268i
$556$	12.4730	+	15.8139i	0.528973	+	0.670657i
$557$		−	28.1042i		−	1.19081i	−0.803424	−	0.595407i	$-0.796991\pi$
$557$		−	28.1042i		−	1.19081i	0.803424	−	0.595407i	$-0.203009\pi$
$558$	−21.8796	−	3.87286i	−0.926239	−	0.163951i
$559$	0.0174275			0.000737106
$560$	32.5849	−	6.51744i	1.37696	−	0.275412i
$561$	−0.293415	−	40.5037i	−0.0123880	−	1.71007i
$562$	6.12849	+	17.6660i	0.258515	+	0.745195i
$563$	−26.4437	−	15.2673i	−1.11447	−	0.643439i	−0.174486	−	0.984660i	$-0.555826\pi$
$563$	−26.4437	−	15.2673i	−1.11447	−	0.643439i	−0.939983	+	0.341220i	$0.889160\pi$
$564$	−8.70645	−	3.39814i	−0.366608	−	0.143087i
$565$	9.69879	+	16.7988i	0.408031	+	0.706731i
$566$	4.76599	+	4.12376i	0.200330	+	0.173335i
$567$	−13.1625	+	19.8431i	−0.552773	+	0.833332i
$568$	−16.1553	+	25.2577i	−0.677861	+	1.05979i
$569$	−3.02111	−	5.23272i	−0.126652	−	0.219367i	0.795726	−	0.605657i	$-0.207090\pi$
$569$	−3.02111	−	5.23272i	−0.126652	−	0.219367i	−0.922377	+	0.386290i	$0.873756\pi$
$570$	1.04924	−	0.372527i	0.0439478	−	0.0156034i
$571$	−6.69435	+	11.5950i	−0.280150	+	0.485234i	−0.971421	−	0.237361i	$-0.923717\pi$
$571$	−6.69435	+	11.5950i	−0.280150	+	0.485234i	0.691272	+	0.722595i	$0.257051\pi$
$572$	0.0279283	+	0.0111342i	0.00116774	+	0.000465546i
$573$	0.0629935	+	8.69578i	0.00263159	+	0.363271i
$574$	−10.9345	−	11.3569i	−0.456396	−	0.474027i
$575$		−	36.2809i		−	1.51302i
$576$	13.5514	−	19.8081i	0.564640	−	0.825337i
$577$			0.599391i			0.0249530i	0.999922	+	0.0124765i	$0.00397149\pi$
$577$			0.599391i			0.0249530i	−0.999922	+	0.0124765i	$0.996029\pi$
$578$	7.84983	+	1.50708i	0.326510	+	0.0626862i
$579$	−11.9378	−	20.3352i	−0.496116	−	0.845101i
$580$	−3.43781	+	8.62314i	−0.142747	+	0.358056i
$581$	−35.5235	+	16.4009i	−1.47376	+	0.680423i
$582$	1.70662	−	9.25058i	0.0707418	−	0.383449i
$583$	−5.12161	+	2.95696i	−0.212115	+	0.122465i
$584$	−9.46017	+	14.7903i	−0.391465	+	0.612029i
$585$	0.0140471	−	0.0251653i	0.000580775	−	0.00104046i
$586$	−20.0413	+	23.1625i	−0.827897	+	0.956833i
$587$	19.0144	−	10.9780i	0.784810	−	0.453110i	−0.0533221	−	0.998577i	$-0.516981\pi$
$587$	19.0144	−	10.9780i	0.784810	−	0.453110i	0.838132	+	0.545467i	$0.183648\pi$
$588$	21.3617	−	11.4751i	0.880941	−	0.473226i
$589$	0.656580	+	0.379077i	0.0270539	+	0.0156196i
$590$	36.4513	−	12.6453i	1.50068	−	0.520597i
$591$	12.9887	+	7.37410i	0.534284	+	0.303330i
$592$	−9.58987	+	10.1156i	−0.394141	+	0.415750i
$593$		−	42.7301i		−	1.75471i	−0.479839	−	0.877357i	$-0.659305\pi$
$593$		−	42.7301i		−	1.75471i	0.479839	−	0.877357i	$-0.340695\pi$
$594$	−12.5724	−	33.8472i	−0.515851	−	1.38877i
$595$	32.3022	+	22.8016i	1.32426	+	0.934775i
$596$	9.86163	+	12.5030i	0.403948	+	0.512145i
$597$	3.33617	−	5.87631i	0.136540	−	0.240502i
$598$	0.0305204	−	0.0105878i	0.00124807	−	0.000432966i
$599$	28.6698	+	16.5525i	1.17142	+	0.676318i	0.954013	−	0.299764i	$-0.0969080\pi$
$599$	28.6698	+	16.5525i	1.17142	+	0.676318i	0.217403	+	0.976082i	$0.430241\pi$
$600$	20.1470	+	12.6817i	0.822498	+	0.517727i
$601$	−36.8155	+	21.2555i	−1.50174	+	0.867028i	−0.501739	+	0.865019i	$0.667306\pi$
$601$	−36.8155	+	21.2555i	−1.50174	+	0.867028i	−0.999998	+	0.00200931i	$0.999360\pi$
$602$	5.12522	+	20.6877i	0.208888	+	0.843167i
$603$	−42.2629	+	0.612349i	−1.72108	+	0.0249368i
$604$	11.8162	−	1.71626i	0.480795	−	0.0698335i
$605$	20.6336	+	35.7385i	0.838875	+	1.45297i
$606$	−36.4418	−	6.72308i	−1.48035	−	0.273106i
$607$	−17.4767	+	30.2705i	−0.709357	+	1.22864i	0.255739	+	0.966746i	$0.417681\pi$
$607$	−17.4767	+	30.2705i	−0.709357	+	1.22864i	−0.965096	+	0.261896i	$0.915652\pi$
$608$	−0.665342	+	0.477401i	−0.0269832	+	0.0193612i
$609$	−0.567148	+	6.75030i	−0.0229820	+	0.273536i
$610$	−58.4412	−	11.2201i	−2.36621	−	0.454287i
$611$	0.00825454			0.000333943
$612$	28.1975	−	4.51363i	1.13982	−	0.182453i
$613$			10.0649i			0.406516i	0.979125	+	0.203258i	$0.0651529\pi$
$613$			10.0649i			0.406516i	−0.979125	+	0.203258i	$0.934847\pi$
$614$	1.39222	−	7.25158i	0.0561855	−	0.292650i
$615$	−0.165996	−	22.9145i	−0.00669359	−	0.924000i
$616$	−5.00376	+	36.4273i	−0.201607	+	1.46770i
$617$	4.13298	−	7.15853i	0.166387	−	0.288191i	−0.770760	−	0.637126i	$-0.780123\pi$
$617$	4.13298	−	7.15853i	0.166387	−	0.288191i	0.937147	+	0.348934i	$0.113456\pi$
$618$	13.2873	+	37.4243i	0.534495	+	1.50543i
$619$	−13.0107	+	7.51172i	−0.522943	+	0.301921i	−0.738138	−	0.674650i	$-0.764295\pi$
$619$	−13.0107	+	7.51172i	−0.522943	+	0.301921i	0.215195	+	0.976571i	$0.430961\pi$
$620$	4.72747	+	32.5480i	0.189860	+	1.30716i
$621$	−34.0113	−	18.6630i	−1.36483	−	0.748920i
$622$	19.7213	−	22.7926i	0.790751	−	0.913902i
$623$	−1.02293	+	11.2019i	−0.0409829	+	0.448794i
$624$	−0.00478867	+	0.0206490i	−0.000191700	+	0.000826621i
$625$	12.8417	−	22.2424i	0.513666	−	0.889696i
$626$	−6.77275	+	2.34953i	−0.270694	+	0.0939059i
$627$	0.00892446	+	1.23195i	0.000356409	+	0.0491995i
$628$	1.76068	−	1.38871i	0.0702587	−	0.0554158i
$629$	−16.5852			−0.661295
$630$	34.0040	+	9.27405i	1.35475	+	0.369487i
$631$		−	26.7419i		−	1.06458i	−0.846563	−	0.532288i	$-0.821332\pi$
$631$		−	26.7419i		−	1.06458i	0.846563	−	0.532288i	$-0.178668\pi$
$632$	18.9851	+	0.863343i	0.755188	+	0.0343419i
$633$	−14.9603	−	25.4839i	−0.594620	−	1.01290i
$634$	5.17793	−	1.79627i	0.205642	−	0.0713389i
$635$	−16.7030	−	9.64347i	−0.662837	−	0.382689i
$636$	−2.60571	−	3.25488i	−0.103323	−	0.129064i
$637$	−0.0138906	+	0.0163010i	−0.000550366	+	0.000645870i
$638$	−7.76776	−	6.72103i	−0.307529	−	0.266088i
$639$	−27.3074	+	16.2979i	−1.08026	+	0.644735i
$640$	−34.1356	−	9.83681i	−1.34933	−	0.388834i
$641$	11.4636	+	19.8556i	0.452785	+	0.784247i	0.998558	−	0.0536860i	$-0.0170970\pi$
$641$	11.4636	+	19.8556i	0.452785	+	0.784247i	−0.545772	+	0.837933i	$0.683764\pi$
$642$	−27.9508	+	32.7808i	−1.10313	+	1.29375i
$643$	9.08174	+	5.24335i	0.358149	+	0.206777i	0.668268	−	0.743920i	$-0.267036\pi$
$643$	9.08174	+	5.24335i	0.358149	+	0.206777i	−0.310120	+	0.950698i	$0.600369\pi$
$644$	21.5441	+	33.1161i	0.848956	+	1.30496i
$645$	−15.2948	+	26.9401i	−0.602231	+	1.06077i
$646$	−0.956891	−	0.183712i	−0.0376484	−	0.00722806i
$647$	28.1895			1.10825			0.554123	−	0.832435i	$-0.313054\pi$
$647$	28.1895			1.10825			0.554123	+	0.832435i	$0.313054\pi$
$648$	22.2520	−	12.3632i	0.874141	−	0.485672i
$649$			42.6915i			1.67579i
$650$	−0.0206485	−	0.00396429i	−0.000809902	−	0.000155492i
$651$	10.2178	+	21.7164i	0.400465	+	0.851133i
$652$	−22.2763	−	8.88095i	−0.872407	−	0.347805i
$653$	−1.18235	−	0.682631i	−0.0462690	−	0.0267134i	0.476687	−	0.879073i	$-0.341837\pi$
$653$	−1.18235	−	0.682631i	−0.0462690	−	0.0267134i	−0.522956	+	0.852360i	$0.675171\pi$
$654$	−2.55342	−	2.17720i	−0.0998466	−	0.0851351i
$655$	51.5501	−	29.7625i	2.01423	−	1.16292i
$656$	4.79472	+	16.1573i	0.187202	+	0.630836i
$657$	−15.9906	+	9.54368i	−0.623852	+	0.372335i
$658$	2.42756	+	9.79871i	0.0946360	+	0.381994i
$659$	−4.20158	−	7.27736i	−0.163670	−	0.283486i	0.772512	−	0.635000i	$-0.219000\pi$
$659$	−4.20158	−	7.27736i	−0.163670	−	0.283486i	−0.936182	+	0.351515i	$0.885667\pi$
$660$	−41.7222	+	33.4010i	−1.62404	+	1.30013i
$661$	15.0631	−	26.0901i	0.585888	−	1.01479i	−0.408876	−	0.912590i	$-0.634079\pi$
$661$	15.0631	−	26.0901i	0.585888	−	1.01479i	0.994764	−	0.102198i	$-0.0325876\pi$
$662$	−5.75160	−	16.5796i	−0.223542	−	0.644384i
$663$	−0.0217504	+	0.0127685i	−0.000844714	+	0.000495889i
$664$	41.7852	+	1.90017i	1.62158	+	0.0737407i
$665$	−0.982499	−	0.693531i	−0.0380997	−	0.0268940i
$666$	−13.8961	+	5.04739i	−0.538464	+	0.195582i
$667$	−11.0367			−0.427342
$668$	−26.8804	+	21.2016i	−1.04003	+	0.820315i
$669$	−3.16585	+	0.0229339i	−0.122399	+	0.000886674i
$670$	20.5051	+	59.1081i	0.792182	+	2.28355i
$671$	32.9231	−	57.0245i	1.27098	−	2.20141i
$672$	−25.9201	+	0.388121i	−0.999888	+	0.0149721i
$673$	−8.76725	−	15.1853i	−0.337953	−	0.585351i	0.646095	−	0.763257i	$-0.276401\pi$
$673$	−8.76725	−	15.1853i	−0.337953	−	0.585351i	−0.984047	+	0.177906i	$0.943068\pi$
$674$	26.9164	−	31.1083i	1.03678	−	1.19825i
$675$	13.0972	+	21.5877i	0.504113	+	0.830911i
$676$	3.73718	+	25.7300i	0.143738	+	0.989615i
$677$	−8.44897	−	14.6341i	−0.324720	−	0.562432i	0.656735	−	0.754121i	$-0.271937\pi$
$677$	−8.44897	−	14.6341i	−0.324720	−	0.562432i	−0.981456	+	0.191689i	$0.938604\pi$
$678$	−5.06293	−	14.2600i	−0.194441	−	0.547650i
$679$	−9.22469	+	4.25895i	−0.354011	+	0.163444i
$680$	−19.4498	−	37.5285i	−0.745867	−	1.43915i
$681$	0.212408	+	29.3213i	0.00813948	+	1.12359i
$682$	−35.7396	−	6.86161i	−1.36854	−	0.262744i
$683$	35.6582			1.36442			0.682211	−	0.731155i	$-0.261018\pi$
$683$	35.6582			1.36442			0.682211	+	0.731155i	$0.261018\pi$
$684$	−0.857652	+	0.137286i	−0.0327932	+	0.00524926i
$685$	−28.9550			−1.10631
$686$	−23.4355	−	11.6952i	−0.894772	−	0.446524i
$687$	6.60530	+	11.2517i	0.252008	+	0.429279i
$688$	5.30800	−	22.1578i	0.202366	−	0.844757i
$689$	0.00318910	+	0.00184123i	0.000121495	+	7.01451e-5i
$690$	−10.4183	+	56.4716i	−0.396619	+	2.14984i
$691$	−29.9973	+	17.3190i	−1.14115	+	0.658844i	−0.946716	−	0.322071i	$-0.895621\pi$
$691$	−29.9973	+	17.3190i	−1.14115	+	0.658844i	−0.194436	+	0.980915i	$0.562288\pi$
$692$	−3.15157	−	21.6982i	−0.119805	−	0.824840i
$693$	−22.0266	+	32.1840i	−0.836721	+	1.22257i
$694$	17.5491	−	20.2821i	0.666153	−	0.769899i
$695$	27.3844	−	15.8104i	1.03875	−	0.599722i
$696$	3.85777	−	6.12873i	0.146228	−	0.232309i
$697$	−10.0267	+	17.3668i	−0.379789	+	0.657814i
$698$	−8.92801	−	25.7359i	−0.337930	−	0.974119i
$699$	2.09776	−	3.69499i	0.0793447	−	0.139757i
$700$	−1.36659	−	25.6771i	−0.0516523	−	0.970503i
$701$		−	1.07099i		−	0.0404508i	−0.999795	−	0.0202254i	$-0.993562\pi$
$701$		−	1.07099i		−	0.0404508i	0.999795	−	0.0202254i	$-0.00643838\pi$
$702$	−0.0143379	+	0.0173176i	−0.000541151	+	0.000653610i
$703$	0.504453			0.0190258
$704$	22.6626	−	32.1175i	0.854129	−	1.21047i
$705$	−7.24436	+	12.7602i	−0.272838	+	0.480576i
$706$	38.6985	−	13.4249i	1.45644	−	0.505251i
$707$	16.7777	+	36.3398i	0.630992	+	1.36670i
$708$	−29.7535	+	4.54189i	−1.11820	+	0.170695i
$709$	10.9338	−	6.31263i	0.410628	−	0.237076i	−0.280432	−	0.959874i	$-0.590478\pi$
$709$	10.9338	−	6.31263i	0.410628	−	0.237076i	0.691059	+	0.722798i	$0.257144\pi$
$710$	35.5967	+	30.7999i	1.33592	+	1.15590i
$711$	17.6012	+	9.82483i	0.660096	+	0.368460i
$712$	6.47945	−	10.1302i	0.242828	−	0.379645i
$713$	−33.8635	+	19.5511i	−1.26820	+	0.732194i
$714$	−21.5537	−	22.0641i	−0.806625	−	0.825729i
$715$	0.0236015	−	0.0408790i	0.000882646	−	0.00152879i
$716$	−41.5610	−	16.5692i	−1.55321	−	0.619221i
$717$	6.97602	−	4.09527i	0.260524	−	0.152941i
$718$	9.64505	−	50.2376i	0.359950	−	1.87485i
$719$	−51.3903			−1.91654			−0.958268	−	0.285871i	$-0.907717\pi$
$719$	−51.3903			−1.91654			−0.958268	+	0.285871i	$0.907717\pi$
$720$	−27.7173	−	25.5245i	−1.03296	−	0.951242i
$721$	24.7369	−	35.0439i	0.921251	−	1.30510i
$722$	−26.3590	−	5.06064i	−0.980981	−	0.188337i
$723$	0.0143664	+	1.98317i	0.000534291	+	0.0737549i
$724$	−1.63800	−	0.653025i	−0.0608757	−	0.0242695i
$725$	6.22089	+	3.59163i	0.231038	+	0.133390i
$726$	−10.7711	−	30.3372i	−0.399752	−	1.12592i
$727$	−2.42380	−	4.19814i	−0.0898936	−	0.155700i	0.817572	−	0.575826i	$-0.195319\pi$
$727$	−2.42380	−	4.19814i	−0.0898936	−	0.155700i	−0.907466	+	0.420126i	$0.861986\pi$
$728$	0.0212014	−	0.00864289i	0.000785774	−	0.000320327i
$729$	26.9745	−	1.17316i	0.999056	−	0.0434504i
$730$	20.8446	+	18.0357i	0.771494	+	0.667533i
$731$	23.4783	−	13.5552i	0.868377	−	0.501358i
$732$	43.2455	+	16.8787i	1.59840	+	0.623857i
$733$	−9.21675	+	15.9639i	−0.340429	+	0.589639i	−0.984512	−	0.175315i	$-0.943905\pi$
$733$	−9.21675	+	15.9639i	−0.340429	+	0.589639i	0.644084	+	0.764955i	$0.277239\pi$
$734$	11.8884	+	34.2696i	0.438809	+	1.26491i
$735$	−13.0081	−	35.7788i	−0.479810	−	1.31972i
$736$	−4.16578	−	42.0291i	−0.153553	−	1.54921i
$737$	−69.2270			−2.55001
$738$	−3.11576	+	17.6024i	−0.114693	+	0.647954i
$739$	−37.2220			−1.36923			−0.684617	−	0.728903i	$-0.740031\pi$
$739$	−37.2220			−1.36923			−0.684617	+	0.728903i	$0.740031\pi$
$740$	13.5524	+	17.1823i	0.498195	+	0.631635i
$741$	0.000661556	0	0.000388366i	2.43029e−5	0	1.42670e-5i
$742$	−1.24779	+	4.32716i	−0.0458078	+	0.158855i
$743$	0.203269	+	0.117357i	0.00745721	+	0.00430542i	0.503724	−	0.863865i	$-0.331963\pi$
$743$	0.203269	+	0.117357i	0.00745721	+	0.00430542i	−0.496267	+	0.868170i	$0.665296\pi$
$744$	0.979849	−	25.6385i	0.0359230	−	0.939951i
$745$	21.6512	−	12.5003i	0.793237	−	0.457976i
$746$	−25.4865	−	22.0521i	−0.933127	−	0.807386i
$747$	38.7391	+	21.6239i	1.41739	+	0.791176i
$748$	46.2852	−	6.72274i	1.69235	−	0.245808i
$749$	46.3382	+	4.23150i	1.69316	+	0.154616i
$750$	−0.701728	+	0.822988i	−0.0256235	+	0.0300513i
$751$	−21.3339	−	12.3171i	−0.778486	−	0.449459i	0.0574076	−	0.998351i	$-0.481717\pi$
$751$	−21.3339	−	12.3171i	−0.778486	−	0.449459i	−0.835893	+	0.548892i	$0.815050\pi$
$752$	2.51413	−	10.4950i	0.0916809	−	0.382714i
$753$	−28.1581	−	15.9863i	−1.02614	−	0.582572i
$754$	−0.00120594	+	0.00628129i	−4.39177e−5	+	0.000228751i
$755$		−	18.7459i		−	0.682233i
$756$	−24.7738	−	11.9272i	−0.901014	−	0.433790i
$757$			47.6057i			1.73026i	0.501549	+	0.865129i	$0.332764\pi$
$757$			47.6057i			1.73026i	−0.501549	+	0.865129i	$0.667236\pi$
$758$	28.3755	+	5.44778i	1.03064	+	0.197872i
$759$	−55.2563	−	31.3707i	−2.00568	−	1.13869i
$760$	0.591583	+	1.14146i	0.0214590	+	0.0414051i
$761$	−3.65849	−	2.11223i	−0.132620	−	0.0765683i	0.432222	−	0.901767i	$-0.357730\pi$
$761$	−3.65849	−	2.11223i	−0.132620	−	0.0765683i	−0.564842	+	0.825199i	$0.691063\pi$
$762$	11.4489	+	9.76202i	0.414751	+	0.353641i
$763$	−0.329608	+	3.60946i	−0.0119326	+	0.130671i
$764$	−9.93701	+	1.44331i	−0.359508	+	0.0522172i
$765$	−0.649523	−	44.8285i	−0.0234835	−	1.62078i
$766$	5.95786	−	6.88573i	0.215266	−	0.248792i
$767$	0.0230215	−	0.0132915i	0.000831257	−	0.000479926i
$768$	24.7951	+	12.3776i	0.894715	+	0.446638i
$769$	−0.0261786	−	0.0151142i	−0.000944026	−	0.000545033i	0.499528	−	0.866298i	$-0.333507\pi$
$769$	−0.0261786	−	0.0151142i	−0.000944026	−	0.000545033i	−0.500472	+	0.865753i	$0.666840\pi$
$770$	55.4671	+	15.9946i	1.99890	+	0.576406i
$771$	29.5776	−	17.3635i	1.06521	−	0.625333i
$772$	21.3786	−	16.8621i	0.769431	−	0.606880i
$773$	25.4101			0.913940			0.456970	−	0.889482i	$-0.348935\pi$
$773$	25.4101			0.913940			0.456970	+	0.889482i	$0.348935\pi$
$774$	15.5463	−	18.5026i	0.558801	−	0.665062i
$775$	25.4498			0.914183
$776$	10.8507	+	0.493432i	0.389517	+	0.0177132i
$777$	13.1125	+	9.11430i	0.470408	+	0.326974i
$778$	42.0537	−	14.5888i	1.50770	−	0.523033i
$779$	0.304972	−	0.528226i	0.0109267	−	0.0189257i
$780$	0.0310013	+	0.0120998i	0.00111002	+	0.000433243i
$781$	−45.1070	+	26.0425i	−1.61406	+	0.931875i
$782$	32.8817	−	38.0027i	1.17585	−	1.35897i
$783$	6.56699	−	3.98419i	0.234685	−	0.142383i
$784$	16.4948	+	22.6257i	0.589099	+	0.808061i
$785$	−1.76029	−	3.04892i	−0.0628275	−	0.108821i
$786$	−43.7592	+	15.5365i	−1.56084	+	0.554168i
$787$	−20.0897	−	11.5988i	−0.716121	−	0.413453i	0.0972022	−	0.995265i	$-0.469011\pi$
$787$	−20.0897	−	11.5988i	−0.716121	−	0.413453i	−0.813323	+	0.581812i	$0.802344\pi$
$788$	−6.38689	+	16.0204i	−0.227523	+	0.570703i
$789$	−0.125477	−	17.3211i	−0.00446708	−	0.616647i
$790$	5.62566	−	29.3020i	0.200152	−	1.04252i
$791$	−9.42562	+	13.3529i	−0.335136	+	0.474775i
$792$	36.7347	−	19.7187i	1.30531	−	0.700675i
$793$	−0.0410008			−0.00145598
$794$	27.7623	+	5.33005i	0.985248	+	0.189157i
$795$	−5.64506	+	3.31393i	−0.200210	+	0.117533i
$796$	7.24790	+	2.88954i	0.256895	+	0.102417i
$797$	−5.90785	+	10.2327i	−0.209267	+	0.362461i	−0.951484	−	0.307699i	$-0.900441\pi$
$797$	−5.90785	+	10.2327i	−0.209267	+	0.362461i	0.742217	+	0.670160i	$0.233774\pi$
$798$	0.655573	+	0.671099i	0.0232070	+	0.0237567i
$799$	11.1205	−	6.42042i	0.393415	−	0.227138i
$800$	−11.3293	+	25.0456i	−0.400552	+	0.885495i
$801$	10.9522	−	6.53665i	0.386979	−	0.230961i
$802$	−17.1222	+	19.7888i	−0.604607	+	0.698768i
$803$	−26.4136	+	15.2499i	−0.932117	+	0.538158i
$804$	−7.36497	−	48.2472i	−0.259743	−	1.70155i
$805$	56.3135	−	25.9994i	1.98479	−	0.916360i
$806$	0.00742695	+	0.0214090i	0.000261603	+	0.000754098i
$807$	−3.48951	+	6.14640i	−0.122836	+	0.216364i
$808$	1.94383	−	42.7453i	0.0683837	−	1.50377i
$809$	−0.692973			−0.0243636			−0.0121818	−	0.999926i	$-0.503878\pi$
$809$	−0.692973			−0.0243636			−0.0121818	+	0.999926i	$0.503878\pi$
$810$	−14.1869	−	37.3624i	−0.498477	−	1.31278i
$811$		−	8.99923i		−	0.316006i	−0.987439	−	0.158003i	$-0.949494\pi$
$811$		−	8.99923i		−	0.316006i	0.987439	−	0.158003i	$-0.0505055\pi$
$812$	−7.81098	+	0.415717i	−0.274112	+	0.0145888i
$813$	8.81512	−	15.5269i	0.309160	−	0.544552i
$814$	−22.8769	+	7.93620i	−0.801836	+	0.278164i
$815$	−18.8251	+	32.6061i	−0.659416	+	1.14214i
$816$	9.60959	+	31.5429i	0.336403	+	1.10422i
$817$	−0.714113	+	0.412294i	−0.0249837	+	0.0144243i
$818$	22.6069	+	19.5606i	0.790432	+	0.683919i
$819$	0.0242130	+	0.00185780i	0.000846071	+	6.49168e-5i
$820$	26.1853	−	3.80330i	0.914429	−	0.132817i
$821$	27.6582	−	15.9685i	0.965279	−	0.557304i	0.0674849	−	0.997720i	$-0.478503\pi$
$821$	27.6582	−	15.9685i	0.965279	−	0.557304i	0.897794	+	0.440416i	$0.145169\pi$
$822$	22.2129	+	4.09802i	0.774765	+	0.142935i
$823$	−21.0016	−	12.1253i	−0.732070	−	0.422661i	0.0871088	−	0.996199i	$-0.472237\pi$
$823$	−21.0016	−	12.1253i	−0.732070	−	0.422661i	−0.819179	+	0.573538i	$0.805571\pi$
$824$	−40.7137	+	21.1007i	−1.41833	+	0.735076i
$825$	20.9367	+	35.6642i	0.728921	+	1.24167i
$826$	22.5482	+	23.4192i	0.784552	+	0.814859i
$827$	−10.3468			−0.359795			−0.179897	−	0.983685i	$-0.557577\pi$
$827$	−10.3468			−0.359795			−0.179897	+	0.983685i	$0.557577\pi$
$828$	15.9850	−	41.8480i	0.555516	−	1.45432i
$829$	−33.5765			−1.16616			−0.583080	−	0.812415i	$-0.698153\pi$
$829$	−33.5765			−1.16616			−0.583080	+	0.812415i	$0.698153\pi$
$830$	12.3817	−	64.4919i	0.429776	−	2.23855i
$831$	0.309644	+	42.7440i	0.0107414	+	1.48277i
$832$	−0.0243751	−	0.00222150i	−0.000845056	−	7.70165e-5i
$833$	−6.03436	+	32.7649i	−0.209078	+	1.13524i
$834$	−23.2457	+	8.25328i	−0.804934	+	0.285788i
$835$	26.8745	+	46.5480i	0.930031	+	1.61086i
$836$	−1.40780	+	0.204478i	−0.0486899	+	0.00707202i
$837$	13.0914	−	23.8577i	0.452506	−	0.824644i
$838$	5.58009	+	4.82816i	0.192761	+	0.166786i
$839$	25.1393	+	43.5426i	0.867906	+	1.50326i	0.864132	+	0.503264i	$0.167868\pi$
$839$	25.1393	+	43.5426i	0.867906	+	1.50326i	0.00377355	+	0.999993i	$0.498799\pi$
$840$	−5.24625	+	40.3590i	−0.181013	+	1.39252i
$841$	−13.4074	+	23.2223i	−0.462325	+	0.800770i
$842$	4.98304	−	1.72866i	0.171727	−	0.0595736i
$843$	−22.9007	+	0.165896i	−0.788741	+	0.00571376i
$844$	26.7915	−	21.1315i	0.922201	−	0.727375i
$845$	40.8195			1.40423
$846$	7.36351	−	8.76374i	0.253163	−	0.301303i
$847$	−20.0524	+	28.4076i	−0.689010	+	0.976095i
$848$	3.31230	−	3.49390i	0.113745	−	0.119981i
$849$	−6.65656	+	3.90773i	−0.228453	+	0.134113i
$850$	−30.9011	+	10.7198i	−1.05990	+	0.367688i
$851$	−13.0087	+	22.5318i	−0.445933	+	0.772379i
$852$	−22.9490	−	28.6663i	−0.786221	−	0.982093i
$853$	−0.662275	−	1.14709i	−0.0226759	−	0.0392757i	0.854465	−	0.519509i	$-0.173885\pi$
$853$	−0.662275	−	1.14709i	−0.0226759	−	0.0392757i	−0.877141	+	0.480234i	$0.840552\pi$
$854$	−12.0578	−	48.6708i	−0.412610	−	1.66548i
$855$	0.0197558	+	1.36350i	0.000675634	+	0.0466306i
$856$	−41.9050	−	26.8032i	−1.43228	−	0.916113i
$857$	−14.2751	+	8.24171i	−0.487627	+	0.281532i	−0.723589	−	0.690231i	$-0.757509\pi$
$857$	−14.2751	+	8.24171i	−0.487627	+	0.281532i	0.235963	+	0.971762i	$0.424176\pi$
$858$	−0.0238917	+	0.0280202i	−0.000815648	+	0.000956593i
$859$	−24.5229	−	14.1583i	−0.836712	−	0.483076i	0.0194332	−	0.999811i	$-0.493814\pi$
$859$	−24.5229	−	14.1583i	−0.836712	−	0.483076i	−0.856145	+	0.516735i	$0.827147\pi$
$860$	−33.2282	−	13.2472i	−1.13307	−	0.451725i
$861$	17.4711	−	8.22030i	0.595413	−	0.280147i
$862$	4.88764	−	25.4580i	0.166474	−	0.867102i
$863$			28.0618i			0.955236i	0.878568	+	0.477618i	$0.158500\pi$
$863$			28.0618i			0.955236i	−0.878568	+	0.477618i	$0.841500\pi$
$864$	17.6510	+	23.5041i	0.600499	+	0.799626i
$865$	−34.4232			−1.17042
$866$	−9.34506	+	48.6750i	−0.317558	+	1.65404i
$867$	−4.83327	+	8.51329i	−0.164146	+	0.289127i
$868$	−23.2297	+	15.1124i	−0.788469	+	0.512948i
$869$	28.5917	+	16.5074i	0.969907	+	0.559976i
$870$	−8.65151	−	7.37678i	−0.293314	−	0.250096i
$871$	0.0215529	+	0.0373308i	0.000730294	+	0.00126491i
$872$	2.08780	−	3.26414i	0.0707019	−	0.110538i
$873$	10.0597	+	5.61525i	0.340470	+	0.190047i
$874$	−1.00013	+	1.15588i	−0.0338298	+	0.0390984i
$875$	1.16336	+	0.106235i	0.0393287	+	0.00359141i
$876$	−13.4384	−	16.7864i	−0.454043	−	0.567159i
$877$	−35.5941	−	20.5502i	−1.20193	−	0.693932i	−0.240943	−	0.970539i	$-0.577457\pi$
$877$	−35.5941	−	20.5502i	−1.20193	−	0.693932i	−0.960983	+	0.276607i	$0.910790\pi$
$878$	7.14406	+	20.5935i	0.241100	+	0.694997i
$879$	−18.9914	−	32.3505i	−0.640563	−	1.09116i
$880$	−44.7861	−	42.4582i	−1.50974	−	1.43127i
$881$		−	7.06690i		−	0.238090i	−0.992889	−	0.119045i	$-0.962017\pi$
$881$		−	7.06690i		−	0.238090i	0.992889	−	0.119045i	$-0.0379832\pi$
$882$	4.91540	+	29.2889i	0.165510	+	0.986208i
$883$	10.4659			0.352207			0.176103	−	0.984372i	$-0.443651\pi$
$883$	10.4659			0.352207			0.176103	+	0.984372i	$0.443651\pi$
$884$	−0.0180356	−	0.0228664i	−0.000606602	−	0.000769079i
$885$	0.342303	+	47.2523i	0.0115064	+	1.58837i
$886$	0.804914	+	2.32025i	0.0270416	+	0.0779502i
$887$	27.2108	−	47.1305i	0.913650	−	1.58249i	0.104784	−	0.994495i	$-0.466585\pi$
$887$	27.2108	−	47.1305i	0.913650	−	1.58249i	0.808866	−	0.587993i	$-0.200082\pi$
$888$	−7.96493	−	15.0996i	−0.267285	−	0.506709i
$889$	1.47788	−	16.1839i	0.0495666	−	0.542792i
$890$	−14.2769	−	12.3530i	−0.478562	−	0.414074i
$891$	44.2030	−	1.28119i	1.48086	−	0.0429214i
$892$	−0.525462	−	3.61774i	−0.0175938	−	0.121131i
$893$	−0.338239	+	0.195283i	−0.0113187	+	0.00653488i
$894$	−18.3790	+	6.52536i	−0.614685	+	0.218241i
$895$	−35.1221	+	60.8333i	−1.17400	+	2.03343i
$896$	−4.53135	−	29.5883i	−0.151382	−	0.988475i
$897$	0.000286607		0.0395640i	9.56954e−6		0.00132100i
$898$	12.6489	+	2.42844i	0.422099	+	0.0810382i
$899$		−	7.74184i		−	0.258205i
$900$	−22.6285	+	18.3859i	−0.754282	+	0.612864i
$901$	5.72845			0.190842
$902$	−5.52024	+	28.7529i	−0.183804	+	0.957368i
$903$	−26.0115	−	2.18544i	−0.865607	−	0.0727268i
$904$	15.5133	−	8.04007i	0.515966	−	0.267409i
$905$	−1.38423	+	2.39756i	−0.0460134	+	0.0796976i
$906$	−2.65312	+	14.3810i	−0.0881441	+	0.477777i
$907$	13.6754	+	23.6865i	0.454085	+	0.786498i	0.998635	−	0.0522304i	$-0.0166330\pi$
$907$	13.6754	+	23.6865i	0.454085	+	0.786498i	−0.544550	+	0.838728i	$0.683300\pi$
$908$	−33.5066	+	4.86670i	−1.11196	+	0.161507i
$909$	22.1207	−	39.6293i	0.733699	−	1.31442i
$910$	−0.00864386	−	0.0348905i	−0.000286541	−	0.00115661i
$911$	−38.3035	+	22.1145i	−1.26905	+	0.732688i	−0.974809	−	0.223043i	$-0.928401\pi$
$911$	−38.3035	+	22.1145i	−1.26905	+	0.732688i	−0.294244	+	0.955730i	$0.595068\pi$
$912$	−0.292284	−	0.959404i	−0.00967849	−	0.0317690i
$913$	62.9286	+	36.3318i	2.08263	+	1.20241i
$914$	1.53912	+	4.43666i	0.0509095	+	0.146752i
$915$	35.9832	−	63.3806i	1.18957	−	2.09530i
$916$	−11.8290	+	9.32999i	−0.390841	+	0.308272i
$917$	40.9758	+	28.9242i	1.35314	+	0.955160i
$918$	−5.84633	+	34.4823i	−0.192958	+	1.13809i
$919$			10.0059i			0.330063i	0.986288	+	0.165031i	$0.0527725\pi$
$919$			10.0059i			0.330063i	−0.986288	+	0.165031i	$0.947227\pi$
$920$	−66.2398	−	3.01223i	−2.18386	−	0.0993103i
$921$	7.86448	+	4.46491i	0.259143	+	0.147124i
$922$	16.2106	+	46.7286i	0.533866	+	1.53892i
$923$	0.0280870	+	0.0162160i	0.000924495	+	0.000533757i
$924$	−40.2881	−	20.1207i	−1.32538	−	0.661921i
$925$	14.6649	−	8.46678i	0.482179	−	0.278386i
$926$	10.1424	+	8.77566i	0.333299	+	0.288386i
$927$	−48.6334	+	0.704652i	−1.59733	+	0.0231438i
$928$	7.61888	+	3.44638i	0.250102	+	0.113133i
$929$	42.8279	−	24.7267i	1.40514	−	0.811258i	0.410225	−	0.911984i	$-0.365450\pi$
$929$	42.8279	−	24.7267i	1.40514	−	0.811258i	0.994914	+	0.100727i	$0.0321168\pi$
$930$	−39.6128	−	7.30809i	−1.29896	−	0.239642i
$931$	0.183540	−	0.996572i	0.00601529	−	0.0326613i
$932$	4.55744	+	1.81692i	0.149284	+	0.0595153i
$933$	18.6881	+	31.8340i	0.611822	+	1.04220i
$934$	0.472862	−	2.46297i	0.0154725	−	0.0805908i
$935$		−	73.4294i		−	2.40140i
$936$	−0.0220703	−	0.0136701i	−0.000721389	−	0.000446820i
$937$			5.07634i			0.165837i	0.996556	+	0.0829185i	$0.0264241\pi$
$937$			5.07634i			0.165837i	−0.996556	+	0.0829185i	$0.973576\pi$
$938$	−37.9758	+	36.5634i	−1.23995	+	1.19384i
$939$	−0.0636008	−	8.77962i	−0.00207553	−	0.286512i
$940$	−15.7385	−	6.27452i	−0.513334	−	0.204652i
$941$	−0.115462	+	0.199987i	−0.00376397	+	0.00651939i	−0.867901	−	0.496737i	$-0.834531\pi$
$941$	−0.115462	+	0.199987i	−0.00376397	+	0.00651939i	0.864137	+	0.503256i	$0.167865\pi$
$942$	0.918901	+	2.58813i	0.0299394	+	0.0843257i
$943$	15.7291	+	27.2435i	0.512209	+	0.887172i
$944$	−9.88728	−	33.3183i	−0.321803	−	1.08442i
$945$	−24.1217	+	35.7990i	−0.784680	+	1.16454i
$946$	25.8987	−	29.9321i	0.842039	−	0.973178i
$947$	1.96643	+	3.40595i	0.0639004	+	0.110679i	0.896206	−	0.443639i	$-0.146313\pi$
$947$	1.96643	+	3.40595i	0.0639004	+	0.110679i	−0.832305	+	0.554317i	$0.812979\pi$
$948$	−8.46289	+	21.6830i	−0.274862	+	0.704230i
$949$	0.0164471	+	0.00949575i	0.000533896	+	0.000308245i
$950$	0.939883	−	0.326053i	0.0304938	−	0.0105786i
$951$	0.0486243	+	6.71222i	0.00157675	+	0.217659i
$952$	21.8399	−	28.1342i	0.707836	−	0.911834i
$953$	−4.36766			−0.141482			−0.0707412	−	0.997495i	$-0.522536\pi$
$953$	−4.36766			−0.141482			−0.0707412	+	0.997495i	$0.522536\pi$
$954$	4.79966	−	1.74335i	0.155395	−	0.0564429i
$955$			15.7646i			0.510132i
$956$	5.78457	+	7.33396i	0.187086	+	0.237197i
$957$	10.8491	−	6.36894i	0.350700	−	0.205879i
$958$	−15.4832	−	44.6319i	−0.500239	−	1.44199i
$959$	−10.2268	−	22.1507i	−0.330240	−	0.715285i
$960$	24.8262	−	35.7304i	0.801263	−	1.15319i
$961$	1.78561	+	3.09277i	0.0576004	+	0.0997668i
$962$	0.0114021	+	0.00986560i	0.000367617	+	0.000318080i
$963$	−27.0398	−	45.3055i	−0.871345	−	1.45995i
$964$	−2.26625	+	0.329163i	−0.0729909	+	0.0106016i
$965$	−21.3739	−	37.0206i	−0.688049	−	1.19174i
$966$	−46.8809	+	11.9755i	−1.50837	+	0.385305i
$967$	−2.75518	−	1.59071i	−0.0886007	−	0.0511537i	0.455045	−	0.890468i	$-0.349623\pi$
$967$	−2.75518	−	1.59071i	−0.0886007	−	0.0511537i	−0.543646	+	0.839315i	$0.682956\pi$
$968$	33.0037	−	17.1048i	1.06078	−	0.549768i
$969$	0.589173	−	1.03777i	0.0189270	−	0.0333379i
$970$	3.21527	−	16.7472i	0.103236	−	0.537719i
$971$		−	7.63444i		−	0.245001i	−0.992468	−	0.122500i	$-0.960909\pi$
$971$		−	7.63444i		−	0.245001i	0.992468	−	0.122500i	$-0.0390913\pi$
$972$	5.59562	+	30.6707i	0.179480	+	0.983762i
$973$	21.7671	+	15.3651i	0.697822	+	0.492582i
$974$	−2.57290	+	13.4013i	−0.0824410	+	0.429405i
$975$	0.0127136	−	0.0223937i	0.000407162	−	0.000717174i
$976$	−12.4878	+	52.1294i	−0.399726	+	1.66862i
$977$	5.02726	−	8.70747i	0.160836	−	0.278577i	−0.774333	−	0.632779i	$-0.781914\pi$
$977$	5.02726	−	8.70747i	0.160836	−	0.278577i	0.935169	+	0.354202i	$0.115248\pi$
$978$	19.0566	−	22.3496i	0.609362	−	0.714661i
$979$	18.0912	−	10.4450i	0.578198	−	0.333823i
$980$	38.8754	−	20.5217i	1.24183	−	0.655542i
$981$	3.52902	−	2.10623i	0.112673	−	0.0672468i
$982$	−18.1052	+	20.9249i	−0.577761	+	0.667741i
$983$	−5.20615	−	9.01731i	−0.166050	−	0.287608i	0.770977	−	0.636862i	$-0.219768\pi$
$983$	−5.20615	−	9.01731i	−0.166050	−	0.287608i	−0.937028	+	0.349255i	$0.886435\pi$
$984$	−20.6264	−	0.788300i	−0.657547	−	0.0251301i
$985$	23.4492	+	13.5384i	0.747155	+	0.431370i
$986$	3.26098	+	9.40012i	0.103851	+	0.299361i
$987$	−12.3203	−	1.03513i	−0.392160	−	0.0329486i
$988$	0.000548567	0	0.000695500i	1.74523e−5	0	2.21268e-5i
$989$		−	42.5285i		−	1.35233i
$990$	−22.3469	−	61.5238i	−0.710230	−	1.95535i
$991$			21.8839i			0.695166i	0.937649	+	0.347583i	$0.112998\pi$
$991$			21.8839i			0.695166i	−0.937649	+	0.347583i	$0.887002\pi$
$992$	29.4819	−	2.92215i	0.936051	−	0.0927783i
$993$	21.4924	−	0.155694i	0.682040	−	0.00494080i
$994$	−10.9895	+	38.1102i	−0.348567	+	1.20878i
$995$	6.12502	−	10.6088i	0.194176	−	0.336323i
$996$	−18.6263	+	47.7229i	−0.590197	+	1.51216i
$997$	7.79631	+	13.5036i	0.246912	+	0.427663i	0.962667	−	0.270687i	$-0.0872510\pi$
$997$	7.79631	+	13.5036i	0.246912	+	0.427663i	−0.715756	+	0.698351i	$0.753918\pi$
$998$	−24.7097	+	28.5580i	−0.782171	+	0.903986i
$999$	−0.393474	−	18.1028i	−0.0124490	−	0.572748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.be.a.139.6	yes	184
7.6	odd	2	inner	504.2.be.a.139.5	✓	184
8.3	odd	2	inner	504.2.be.a.139.58	yes	184
9.7	even	3	inner	504.2.be.a.475.57	yes	184
56.27	even	2	inner	504.2.be.a.139.57	yes	184
63.34	odd	6	inner	504.2.be.a.475.58	yes	184
72.43	odd	6	inner	504.2.be.a.475.5	yes	184
504.475	even	6	inner	504.2.be.a.475.6	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.5	✓	184	7.6	odd	2	inner
504.2.be.a.139.6	yes	184	1.1	even	1	trivial
504.2.be.a.139.57	yes	184	56.27	even	2	inner
504.2.be.a.139.58	yes	184	8.3	odd	2	inner
504.2.be.a.475.5	yes	184	72.43	odd	6	inner
504.2.be.a.475.6	yes	184	504.475	even	6	inner
504.2.be.a.475.57	yes	184	9.7	even	3	inner
504.2.be.a.475.58	yes	184	63.34	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38885 - 0.266643i) q^{2} +(0.855137 - 1.50623i) q^{3} +(1.85780 + 0.740655i) q^{4} +(1.56998 - 2.71929i) q^{5} +(-1.58928 + 1.86392i) q^{6} +(2.63479 + 0.240603i) q^{7} +(-2.38272 - 1.52403i) q^{8} +(-1.53748 - 2.57607i) q^{9} +O(q^{10})\)	\(q+(-1.38885 - 0.266643i) q^{2} +(0.855137 - 1.50623i) q^{3} +(1.85780 + 0.740655i) q^{4} +(1.56998 - 2.71929i) q^{5} +(-1.58928 + 1.86392i) q^{6} +(2.63479 + 0.240603i) q^{7} +(-2.38272 - 1.52403i) q^{8} +(-1.53748 - 2.57607i) q^{9} +(-2.90555 + 3.35806i) q^{10} +(-2.45675 - 4.25522i) q^{11} +(2.70427 - 2.16492i) q^{12} +(-0.00152976 + 0.00264962i) q^{13} +(-3.59517 - 1.03671i) q^{14} +(-2.75334 - 4.69013i) q^{15} +(2.90286 + 2.75198i) q^{16} +4.75942i q^{17} +(1.44844 + 3.98773i) q^{18} -0.144762i q^{19} +(4.93077 - 3.88909i) q^{20} +(2.61551 - 3.76286i) q^{21} +(2.27743 + 6.56494i) q^{22} +(6.46589 + 3.73308i) q^{23} +(-4.33309 + 2.28568i) q^{24} +(-2.42969 - 4.20835i) q^{25} +(0.00283111 - 0.00327202i) q^{26} +(-5.19493 + 0.112914i) q^{27} +(4.71671 + 2.39846i) q^{28} +(-1.28018 + 0.739113i) q^{29} +(2.57338 + 7.24804i) q^{30} +(-2.61862 + 4.53559i) q^{31} +(-3.29784 - 4.59611i) q^{32} +(-8.51022 + 0.0616493i) q^{33} +(1.26907 - 6.61011i) q^{34} +(4.79084 - 6.78701i) q^{35} +(-0.948359 - 5.92458i) q^{36} +3.48471i q^{37} +(-0.0385998 + 0.201052i) q^{38} +(0.00268280 + 0.00456996i) q^{39} +(-7.88510 + 4.08660i) q^{40} +(3.64893 + 2.10671i) q^{41} +(-4.63589 + 4.52863i) q^{42} +(-2.84808 - 4.93302i) q^{43} +(-1.41251 - 9.72497i) q^{44} +(-9.41891 + 0.136471i) q^{45} +(-7.98474 - 6.90877i) q^{46} +(-1.34899 - 2.33652i) q^{47} +(6.62747 - 2.01907i) q^{48} +(6.88422 + 1.26788i) q^{49} +(2.25235 + 6.49262i) q^{50} +(7.16879 + 4.06995i) q^{51} +(-0.00480445 + 0.00378945i) q^{52} -1.20360i q^{53} +(7.24507 + 1.22837i) q^{54} -15.4282 q^{55} +(-5.91127 - 4.58878i) q^{56} +(-0.218045 - 0.123791i) q^{57} +(1.97506 - 0.685165i) q^{58} +(-7.52454 - 4.34429i) q^{59} +(-1.64139 - 10.7526i) q^{60} +(6.70053 + 11.6057i) q^{61} +(4.84626 - 5.60101i) q^{62} +(-3.43113 - 7.15733i) q^{63} +(3.35468 + 7.26265i) q^{64} +(0.00480339 + 0.00831972i) q^{65} +(11.8359 + 2.18357i) q^{66} +(7.04455 - 12.2015i) q^{67} +(-3.52508 + 8.84206i) q^{68} +(11.1521 - 6.54684i) q^{69} +(-8.46347 + 8.14868i) q^{70} -10.6004i q^{71} +(-0.262623 + 8.48122i) q^{72} -6.20735i q^{73} +(0.929176 - 4.83974i) q^{74} +(-8.41647 + 0.0609702i) q^{75} +(0.107218 - 0.268939i) q^{76} +(-5.44921 - 11.8027i) q^{77} +(-0.00250745 - 0.00706234i) q^{78} +(-5.81900 + 3.35960i) q^{79} +(12.0409 - 3.57316i) q^{80} +(-4.27230 + 7.92133i) q^{81} +(-4.50608 - 3.89887i) q^{82} +(-12.8073 + 7.39428i) q^{83} +(7.64608 - 5.05346i) q^{84} +(12.9422 + 7.47220i) q^{85} +(2.64020 + 7.61065i) q^{86} +(0.0185472 + 2.56030i) q^{87} +(-0.631332 + 13.8832i) q^{88} +4.25153i q^{89} +(13.1178 + 2.32195i) q^{90} +(-0.00466810 + 0.00661313i) q^{91} +(9.24742 + 11.7243i) q^{92} +(4.59238 + 7.82281i) q^{93} +(1.25053 + 3.60478i) q^{94} +(-0.393649 - 0.227273i) q^{95} +(-9.74293 + 1.03701i) q^{96} +(-3.32577 + 1.92013i) q^{97} +(-9.22307 - 3.59652i) q^{98} +(-7.18455 + 12.8711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

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