LMFDB - Embedded newform 570.2.n.a.449.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.6
Character	$\chi$	$=$	570.449
Dual form			570.2.n.a.179.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.15831 + 1.28775i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.01208 + 0.975465i) q^{5} +(0.359253 - 1.69438i) q^{6} +1.18214i q^{7} +1.00000i q^{8} +(-0.316615 - 2.98325i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.15831 + 1.28775i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.01208 + 0.975465i) q^{5} +(0.359253 - 1.69438i) q^{6} +1.18214i q^{7} +1.00000i q^{8} +(-0.316615 - 2.98325i) q^{9} +(-2.23025 + 0.161263i) q^{10} +4.89120i q^{11} +(0.536070 + 1.64701i) q^{12} +(0.622803 - 1.07873i) q^{13} +(-0.591070 - 1.02376i) q^{14} +(-3.58678 + 1.46117i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.318854 + 0.552271i) q^{17} +(1.76582 + 2.42526i) q^{18} +(4.35888 - 0.0120744i) q^{19} +(1.85082 - 1.25478i) q^{20} +(-1.52230 - 1.36929i) q^{21} +(-2.44560 - 4.23590i) q^{22} +(0.859976 - 1.48952i) q^{23} +(-1.28775 - 1.15831i) q^{24} +(3.09694 + 3.92543i) q^{25} +1.24561i q^{26} +(4.20842 + 3.04781i) q^{27} +(1.02376 + 0.591070i) q^{28} +(-1.94156 + 3.36289i) q^{29} +(2.37566 - 3.05880i) q^{30} +6.45549i q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.29865 - 5.66554i) q^{33} +(-0.552271 - 0.318854i) q^{34} +(-1.15313 + 2.37856i) q^{35} +(-2.74187 - 1.21743i) q^{36} -9.66844 q^{37} +(-3.76887 + 2.18990i) q^{38} +(0.667731 + 2.05152i) q^{39} +(-0.975465 + 2.01208i) q^{40} +(-6.08673 - 10.5425i) q^{41} +(2.00300 + 0.424687i) q^{42} +(-9.32139 + 5.38171i) q^{43} +(4.23590 + 2.44560i) q^{44} +(2.27299 - 6.31138i) q^{45} +1.71995i q^{46} +(0.0980180 - 0.169772i) q^{47} +(1.69438 + 0.359253i) q^{48} +5.60255 q^{49} +(-4.64474 - 1.85105i) q^{50} +(-1.08052 - 0.229098i) q^{51} +(-0.622803 - 1.07873i) q^{52} +(-1.57394 - 0.908716i) q^{53} +(-5.16851 - 0.535272i) q^{54} +(-4.77119 + 9.84148i) q^{55} -1.18214 q^{56} +(-5.03341 + 5.62715i) q^{57} -3.88313i q^{58} +(1.25875 + 2.18022i) q^{59} +(-0.527981 + 3.83683i) q^{60} +(-5.71356 + 9.89618i) q^{61} +(-3.22774 - 5.59061i) q^{62} +(3.52661 - 0.374284i) q^{63} -1.00000 q^{64} +(2.30539 - 1.56296i) q^{65} +(8.28757 + 1.75718i) q^{66} +(-2.67262 + 4.62912i) q^{67} +0.637707 q^{68} +(0.922014 + 2.83277i) q^{69} +(-0.190636 - 2.63646i) q^{70} +(-2.99286 - 5.18379i) q^{71} +(2.98325 - 0.316615i) q^{72} +(8.20341 - 4.73624i) q^{73} +(8.37312 - 4.83422i) q^{74} +(-8.64221 - 0.558787i) q^{75} +(2.16898 - 3.78094i) q^{76} -5.78208 q^{77} +(-1.60403 - 1.44280i) q^{78} +(6.74355 - 3.89339i) q^{79} +(-0.161263 - 2.23025i) q^{80} +(-8.79951 + 1.88908i) q^{81} +(10.5425 + 6.08673i) q^{82} +8.21126 q^{83} +(-1.94699 + 0.633709i) q^{84} +(0.102839 + 1.42224i) q^{85} +(5.38171 - 9.32139i) q^{86} +(-2.08163 - 6.39553i) q^{87} -4.89120 q^{88} +(-2.46445 + 4.26855i) q^{89} +(1.18722 + 6.60231i) q^{90} +(1.27520 + 0.736240i) q^{91} +(-0.859976 - 1.48952i) q^{92} +(-8.31307 - 7.47748i) q^{93} +0.196036i q^{94} +(8.78220 + 4.22764i) q^{95} +(-1.64701 + 0.536070i) q^{96} +(0.141542 + 0.245159i) q^{97} +(-4.85195 + 2.80127i) q^{98} +(14.5916 - 1.54863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.15831	+	1.28775i	−0.668753	+	0.743485i
$3$	−1.15831	+	1.28775i	−0.668753	+	0.743485i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.01208	+	0.975465i	0.899830	+	0.436241i
$5$	2.01208	+	0.975465i	0.899830	+	0.436241i
$6$	0.359253	−	1.69438i	0.146665	−	0.691729i
$7$			1.18214i			0.446807i	0.974726	+	0.223403i	$0.0717167\pi$
$7$			1.18214i			0.446807i	−0.974726	+	0.223403i	$0.928283\pi$
$8$			1.00000i			0.353553i
$9$	−0.316615	−	2.98325i	−0.105538	−	0.994415i
$10$	−2.23025	+	0.161263i	−0.705265	+	0.0509959i
$11$			4.89120i			1.47475i	0.675483	+	0.737376i	$0.263935\pi$
$11$			4.89120i			1.47475i	−0.675483	+	0.737376i	$0.736065\pi$
$12$	0.536070	+	1.64701i	0.154750	+	0.475450i
$13$	0.622803	−	1.07873i	0.172734	−	0.299185i	−0.766640	−	0.642077i	$-0.778073\pi$
$13$	0.622803	−	1.07873i	0.172734	−	0.299185i	0.939375	+	0.342892i	$0.111406\pi$
$14$	−0.591070	−	1.02376i	−0.157970	−	0.273612i
$15$	−3.58678	+	1.46117i	−0.926102	+	0.377272i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.318854	+	0.552271i	0.0773334	+	0.133945i	0.902099	−	0.431530i	$-0.142026\pi$
$17$	0.318854	+	0.552271i	0.0773334	+	0.133945i	−0.824765	+	0.565475i	$0.808693\pi$
$18$	1.76582	+	2.42526i	0.416208	+	0.571639i
$19$	4.35888	−	0.0120744i	0.999996	−	0.00277005i
$19$	4.35888	−	0.0120744i	0.999996	−	0.00277005i
$20$	1.85082	−	1.25478i	0.413855	−	0.280578i
$21$	−1.52230	−	1.36929i	−0.332194	−	0.298803i
$22$	−2.44560	−	4.23590i	−0.521403	−	0.903097i
$23$	0.859976	−	1.48952i	0.179317	−	0.310587i	−0.762329	−	0.647189i	$-0.775944\pi$
$23$	0.859976	−	1.48952i	0.179317	−	0.310587i	0.941647	+	0.336602i	$0.109278\pi$
$24$	−1.28775	−	1.15831i	−0.262861	−	0.236440i
$25$	3.09694	+	3.92543i	0.619388	+	0.785085i
$26$			1.24561i			0.244283i
$27$	4.20842	+	3.04781i	0.809912	+	0.586552i
$28$	1.02376	+	0.591070i	0.193473	+	0.111702i
$29$	−1.94156	+	3.36289i	−0.360539	+	0.624472i	−0.988050	−	0.154136i	$-0.950741\pi$
$29$	−1.94156	+	3.36289i	−0.360539	+	0.624472i	0.627511	+	0.778608i	$0.284074\pi$
$30$	2.37566	−	3.05880i	0.433734	−	0.558458i
$31$			6.45549i			1.15944i	0.814816	+	0.579720i	$0.196838\pi$
$31$			6.45549i			1.15944i	−0.814816	+	0.579720i	$0.803162\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−6.29865	−	5.66554i	−1.09646	−	0.986245i
$34$	−0.552271	−	0.318854i	−0.0947137	−	0.0546830i
$35$	−1.15313	+	2.37856i	−0.194915	+	0.402050i
$36$	−2.74187	−	1.21743i	−0.456979	−	0.202904i
$37$	−9.66844			−1.58948			−0.794741	−	0.606949i	$-0.792393\pi$
$37$	−9.66844			−1.58948			−0.794741	+	0.606949i	$0.792393\pi$
$38$	−3.76887	+	2.18990i	−0.611391	+	0.355248i
$39$	0.667731	+	2.05152i	0.106923	+	0.328506i
$40$	−0.975465	+	2.01208i	−0.154234	+	0.318138i
$41$	−6.08673	−	10.5425i	−0.950588	−	1.64647i	−0.744156	−	0.668006i	$-0.767148\pi$
$41$	−6.08673	−	10.5425i	−0.950588	−	1.64647i	−0.206432	−	0.978461i	$-0.566185\pi$
$42$	2.00300	+	0.424687i	0.309069	+	0.0655307i
$43$	−9.32139	+	5.38171i	−1.42150	+	0.820703i	−0.996427	−	0.0844573i	$-0.973084\pi$
$43$	−9.32139	+	5.38171i	−1.42150	+	0.820703i	−0.425071	+	0.905160i	$0.639751\pi$
$44$	4.23590	+	2.44560i	0.638586	+	0.368688i
$45$	2.27299	−	6.31138i	0.338838	−	0.940845i
$46$			1.71995i			0.253593i
$47$	0.0980180	−	0.169772i	0.0142974	−	0.0247638i	−0.858788	−	0.512331i	$-0.828782\pi$
$47$	0.0980180	−	0.169772i	0.0142974	−	0.0247638i	0.873086	+	0.487567i	$0.162116\pi$
$48$	1.69438	+	0.359253i	0.244563	+	0.0518537i
$49$	5.60255			0.800364
$50$	−4.64474	−	1.85105i	−0.656865	−	0.261778i
$51$	−1.08052	−	0.229098i	−0.151303	−	0.0320802i
$52$	−0.622803	−	1.07873i	−0.0863672	−	0.149592i
$53$	−1.57394	−	0.908716i	−0.216198	−	0.124822i	0.387991	−	0.921663i	$-0.373169\pi$
$53$	−1.57394	−	0.908716i	−0.216198	−	0.124822i	−0.604188	+	0.796841i	$0.706503\pi$
$54$	−5.16851	−	0.535272i	−0.703345	−	0.0728413i
$55$	−4.77119	+	9.84148i	−0.643347	+	1.32703i
$56$	−1.18214			−0.157970
$57$	−5.03341	+	5.62715i	−0.666691	+	0.745334i
$58$		−	3.88313i		−	0.509879i
$59$	1.25875	+	2.18022i	0.163876	+	0.283841i	0.936255	−	0.351320i	$-0.114267\pi$
$59$	1.25875	+	2.18022i	0.163876	+	0.283841i	−0.772380	+	0.635161i	$0.780934\pi$
$60$	−0.527981	+	3.83683i	−0.0681620	+	0.495332i
$61$	−5.71356	+	9.89618i	−0.731547	+	1.26708i	0.224675	+	0.974434i	$0.427868\pi$
$61$	−5.71356	+	9.89618i	−0.731547	+	1.26708i	−0.956222	+	0.292642i	$0.905466\pi$
$62$	−3.22774	−	5.59061i	−0.409924	−	0.710009i
$63$	3.52661	−	0.374284i	0.444311	−	0.0471553i
$64$	−1.00000			−0.125000
$65$	2.30539	−	1.56296i	0.285948	−	0.193862i
$66$	8.28757	+	1.75718i	1.02013	+	0.216294i
$67$	−2.67262	+	4.62912i	−0.326513	+	0.565537i	−0.981817	−	0.189828i	$-0.939207\pi$
$67$	−2.67262	+	4.62912i	−0.326513	+	0.565537i	0.655305	+	0.755365i	$0.272540\pi$
$68$	0.637707			0.0773334
$69$	0.922014	+	2.83277i	0.110997	+	0.341026i
$70$	−0.190636	−	2.63646i	−0.0227853	−	0.315117i
$71$	−2.99286	−	5.18379i	−0.355188	−	0.615203i	0.631962	−	0.774999i	$-0.282250\pi$
$71$	−2.99286	−	5.18379i	−0.355188	−	0.615203i	−0.987150	+	0.159796i	$0.948916\pi$
$72$	2.98325	−	0.316615i	0.351579	−	0.0373135i
$73$	8.20341	−	4.73624i	0.960136	−	0.554335i	0.0639213	−	0.997955i	$-0.479639\pi$
$73$	8.20341	−	4.73624i	0.960136	−	0.554335i	0.896215	+	0.443620i	$0.146306\pi$
$74$	8.37312	−	4.83422i	0.973355	−	0.561967i
$75$	−8.64221	−	0.558787i	−0.997916	−	0.0645232i
$76$	2.16898	−	3.78094i	0.248800	−	0.433704i
$77$	−5.78208			−0.658929
$78$	−1.60403	−	1.44280i	−0.181621	−	0.163365i
$79$	6.74355	−	3.89339i	0.758708	−	0.438040i	−0.0701234	−	0.997538i	$-0.522339\pi$
$79$	6.74355	−	3.89339i	0.758708	−	0.438040i	0.828832	+	0.559498i	$0.189006\pi$
$80$	−0.161263	−	2.23025i	−0.0180298	−	0.249349i
$81$	−8.79951	+	1.88908i	−0.977723	+	0.209898i
$82$	10.5425	+	6.08673i	1.16423	+	0.672167i
$83$	8.21126			0.901303			0.450652	−	0.892700i	$-0.351192\pi$
$83$	8.21126			0.901303			0.450652	+	0.892700i	$0.351192\pi$
$84$	−1.94699	+	0.633709i	−0.212434	+	0.0691433i
$85$	0.102839	+	1.42224i	0.0111544	+	0.154264i
$86$	5.38171	−	9.32139i	0.580324	−	1.00515i
$87$	−2.08163	−	6.39553i	−0.223174	−	0.685673i
$88$	−4.89120			−0.521403
$89$	−2.46445	+	4.26855i	−0.261231	+	0.452465i	−0.966569	−	0.256406i	$-0.917462\pi$
$89$	−2.46445	+	4.26855i	−0.261231	+	0.452465i	0.705338	+	0.708871i	$0.250795\pi$
$90$	1.18722	+	6.60231i	0.125144	+	0.695945i
$91$	1.27520	+	0.736240i	0.133678	+	0.0771789i
$92$	−0.859976	−	1.48952i	−0.0896587	−	0.155294i
$93$	−8.31307	−	7.47748i	−0.862025	−	0.775379i
$94$			0.196036i			0.0202196i
$95$	8.78220	+	4.22764i	0.901035	+	0.433747i
$96$	−1.64701	+	0.536070i	−0.168097	+	0.0547124i
$97$	0.141542	+	0.245159i	0.0143715	+	0.0248921i	0.873122	−	0.487502i	$-0.162092\pi$
$97$	0.141542	+	0.245159i	0.0143715	+	0.0248921i	−0.858750	+	0.512394i	$0.828759\pi$
$98$	−4.85195	+	2.80127i	−0.490121	+	0.282971i
$99$	14.5916	−	1.54863i	1.46652	−	0.155643i
$100$	4.94799	−	0.719314i	0.494799	−	0.0719314i
$101$	14.0883	+	8.13386i	1.40183	+	0.809349i	0.994581	−	0.103966i	$-0.0331532\pi$
$101$	14.0883	+	8.13386i	1.40183	+	0.809349i	0.407254	+	0.913315i	$0.366487\pi$
$102$	1.05031	−	0.341856i	0.103996	−	0.0338487i
$103$	4.88946			0.481772			0.240886	−	0.970553i	$-0.422562\pi$
$103$	4.88946			0.481772			0.240886	+	0.970553i	$0.422562\pi$
$104$	1.07873	+	0.622803i	0.105778	+	0.0610708i
$105$	−1.72730	−	4.24007i	−0.168568	−	0.413789i
$106$	1.81743			0.176525
$107$		−	4.22366i		−	0.408317i	−0.978938	−	0.204158i	$-0.934554\pi$
$107$		−	4.22366i		−	0.408317i	0.978938	−	0.204158i	$-0.0654458\pi$
$108$	4.74370	−	2.12069i	0.456462	−	0.204064i
$109$	6.04292	−	3.48888i	0.578807	−	0.334174i	−0.181852	−	0.983326i	$-0.558209\pi$
$109$	6.04292	−	3.48888i	0.578807	−	0.334174i	0.760659	+	0.649151i	$0.224876\pi$
$110$	−0.788771	−	10.9086i	−0.0752063	−	1.04009i
$111$	11.1991	−	12.4506i	1.06297	−	1.18176i
$112$	1.02376	−	0.591070i	0.0967365	−	0.0558508i
$113$		−	2.46652i		−	0.232031i	−0.993247	−	0.116016i	$-0.962988\pi$
$113$		−	2.46652i		−	0.232031i	0.993247	−	0.116016i	$-0.0370122\pi$
$114$	1.54548	−	7.38996i	0.144748	−	0.692133i
$115$	3.18332	−	2.15816i	0.296846	−	0.201250i
$116$	1.94156	+	3.36289i	0.180270	+	0.312236i
$117$	−3.41529	−	1.51643i	−0.315744	−	0.140194i
$118$	−2.18022	−	1.25875i	−0.200706	−	0.115878i
$119$	−0.652861	+	0.376930i	−0.0598477	+	0.0345531i
$120$	−1.46117	−	3.58678i	−0.133386	−	0.327427i
$121$	−12.9238			−1.17489
$122$		−	11.4271i		−	1.03456i
$123$	20.6265	+	4.37336i	1.85983	+	0.394332i
$124$	5.59061	+	3.22774i	0.502052	+	0.289860i
$125$	2.40217	+	10.9192i	0.214857	+	0.976646i
$126$	−2.86699	+	2.08744i	−0.255412	+	0.185964i
$127$	3.48711	−	6.03986i	0.309431	−	0.535951i	−0.668807	−	0.743436i	$-0.733195\pi$
$127$	3.48711	−	6.03986i	0.309431	−	0.535951i	0.978238	+	0.207485i	$0.0665280\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	3.86679	−	18.2374i	0.340452	−	1.60571i
$130$	−1.21504	+	2.50626i	−0.106566	+	0.219813i
$131$	−12.2589	+	7.07770i	−1.07107	+	0.618382i	−0.928473	−	0.371399i	$-0.878878\pi$
$131$	−12.2589	+	7.07770i	−1.07107	+	0.618382i	−0.142596	+	0.989781i	$0.545545\pi$
$132$	−8.05583	+	2.62202i	−0.701170	+	0.228218i
$133$	0.0142736	+	5.15281i	0.00123768	+	0.446805i
$134$		−	5.34524i		−	0.461759i
$135$	5.49465	+	10.2376i	0.472905	+	0.881114i
$136$	−0.552271	+	0.318854i	−0.0473568	+	0.0273415i
$137$	6.51986	−	11.2927i	0.557029	−	0.964803i	−0.440714	−	0.897648i	$-0.645275\pi$
$137$	6.51986	−	11.2927i	0.557029	−	0.964803i	0.997743	−	0.0671547i	$-0.0213921\pi$
$138$	−2.21487	−	1.99225i	−0.188543	−	0.169591i
$139$	11.0177	−	19.0832i	0.934507	−	1.61861i	0.158995	−	0.987279i	$-0.449175\pi$
$139$	11.0177	−	19.0832i	0.934507	−	1.61861i	0.775511	−	0.631334i	$-0.217492\pi$
$140$	1.48333	+	2.18792i	0.125364	+	0.184913i
$141$	0.105089	+	0.322872i	0.00885008	+	0.0271908i
$142$	5.18379	+	2.99286i	0.435014	+	0.251156i
$143$	5.27626	+	3.04625i	0.441223	+	0.254740i
$144$	−2.42526	+	1.76582i	−0.202105	+	0.147152i
$145$	−7.18696	+	4.87247i	−0.596844	+	0.404637i
$146$	−4.73624	+	8.20341i	−0.391974	+	0.678919i
$147$	−6.48951	+	7.21470i	−0.535246	+	0.595058i
$148$	−4.83422	+	8.37312i	−0.397371	+	0.688266i
$149$	4.59319	−	2.65188i	0.376289	−	0.217251i	−0.299913	−	0.953966i	$-0.596958\pi$
$149$	4.59319	−	2.65188i	0.376289	−	0.217251i	0.676203	+	0.736716i	$0.263624\pi$
$150$	7.76377	−	3.83718i	0.633909	−	0.313304i
$151$			19.6711i			1.60081i	0.599460	+	0.800405i	$0.295382\pi$
$151$			19.6711i			1.60081i	−0.599460	+	0.800405i	$0.704618\pi$
$152$	0.0120744	+	4.35888i	0.000979359	+	0.353552i
$153$	1.54661	−	1.12608i	0.125036	−	0.0910379i
$154$	5.00743	−	2.89104i	0.403510	−	0.232966i
$155$	−6.29710	+	12.9890i	−0.505795	+	1.04330i
$156$	2.11053	+	0.447488i	0.168978	+	0.0358277i
$157$	12.6818	−	7.32182i	1.01211	−	0.584345i	0.100304	−	0.994957i	$-0.468018\pi$
$157$	12.6818	−	7.32182i	1.01211	−	0.584345i	0.911810	+	0.410612i	$0.134685\pi$
$158$	−3.89339	+	6.74355i	−0.309741	+	0.536488i
$159$	2.99332	−	0.974270i	0.237386	−	0.0772647i
$160$	1.25478	+	1.85082i	0.0991991	+	0.146320i
$161$	1.76082	+	1.01661i	0.138772	+	0.0801202i
$162$	6.67606	−	6.03575i	0.524521	−	0.474213i
$163$			10.9889i			0.860718i	0.902658	+	0.430359i	$0.141613\pi$
$163$			10.9889i			0.860718i	−0.902658	+	0.430359i	$0.858387\pi$
$164$	−12.1735			−0.950588
$165$	−7.14686	−	17.5436i	−0.556383	−	1.36577i
$166$	−7.11116	+	4.10563i	−0.551933	+	0.318659i
$167$	−13.1964	−	7.61896i	−1.02117	−	0.589573i	−0.106728	−	0.994288i	$-0.534037\pi$
$167$	−13.1964	−	7.61896i	−1.02117	−	0.589573i	−0.914443	+	0.404715i	$0.867371\pi$
$168$	1.36929	−	1.52230i	0.105643	−	0.117448i
$169$	5.72423	+	9.91466i	0.440326	+	0.762666i
$170$	−0.800183	−	1.18028i	−0.0613712	−	0.0905234i
$171$	−1.41611	−	12.9998i	−0.108293	−	0.994119i
$172$			10.7634i			0.820703i
$173$	20.3554	−	11.7522i	1.54759	−	0.893501i	0.549265	−	0.835648i	$-0.314908\pi$
$173$	20.3554	−	11.7522i	1.54759	−	0.893501i	0.998325	−	0.0578530i	$-0.0184255\pi$
$174$	5.00051	+	4.49788i	0.379087	+	0.340983i
$175$	−4.64040	+	3.66101i	−0.350781	+	0.276746i
$176$	4.23590	−	2.44560i	0.319293	−	0.184344i
$177$	−4.26562	−	0.904422i	−0.320624	−	0.0679805i
$178$		−	4.92889i		−	0.369436i
$179$	7.26697			0.543159			0.271579	−	0.962416i	$-0.412454\pi$
$179$	7.26697			0.543159			0.271579	+	0.962416i	$0.412454\pi$
$180$	−4.32932	−	5.12416i	−0.322688	−	0.381932i
$181$	−6.11788	−	3.53216i	−0.454738	−	0.262543i	0.255091	−	0.966917i	$-0.417895\pi$
$181$	−6.11788	−	3.53216i	−0.454738	−	0.262543i	−0.709829	+	0.704374i	$0.751228\pi$
$182$	−1.47248			−0.109147
$183$	−6.12573	−	18.8205i	−0.452827	−	1.39125i
$184$	1.48952	+	0.859976i	0.109809	+	0.0633983i
$185$	−19.4537	−	9.43122i	−1.43026	−	0.693397i
$186$	10.9381	+	2.31915i	0.802018	+	0.170049i
$187$	−2.70127	+	1.55958i	−0.197536	+	0.114048i
$188$	−0.0980180	−	0.169772i	−0.00714870	−	0.0123819i
$189$	−3.60294	+	4.97494i	−0.262075	+	0.361874i
$190$	−9.71943	+	0.729857i	−0.705122	+	0.0529494i
$191$		−	7.51033i		−	0.543429i	−0.962378	−	0.271714i	$-0.912409\pi$
$191$		−	7.51033i		−	0.543429i	0.962378	−	0.271714i	$-0.0875906\pi$
$192$	1.15831	−	1.28775i	0.0835941	−	0.0929356i
$193$	−5.20366	−	9.01300i	−0.374568	−	0.648770i	0.615695	−	0.787985i	$-0.288875\pi$
$193$	−5.20366	−	9.01300i	−0.374568	−	0.648770i	−0.990262	+	0.139215i	$0.955542\pi$
$194$	−0.245159	−	0.141542i	−0.0176014	−	0.0101622i
$195$	−0.657656	+	4.77917i	−0.0470957	+	0.342244i
$196$	2.80127	−	4.85195i	0.200091	−	0.346568i
$197$	20.8294			1.48403			0.742017	−	0.670381i	$-0.233869\pi$
$197$	20.8294			1.48403			0.742017	+	0.670381i	$0.233869\pi$
$198$	−11.8624	+	8.63697i	−0.843026	+	0.613803i
$199$	5.37464	−	9.30915i	0.380998	−	0.659908i	−0.610207	−	0.792242i	$-0.708914\pi$
$199$	5.37464	−	9.30915i	0.380998	−	0.659908i	0.991205	+	0.132334i	$0.0422470\pi$
$200$	−3.92543	+	3.09694i	−0.277570	+	0.218987i
$201$	−2.86542	−	8.80365i	−0.202111	−	0.620962i
$202$	−16.2677			−1.14459
$203$	−3.97540	−	2.29520i	−0.279018	−	0.161091i
$204$	−0.738666	+	0.821210i	−0.0517169	+	0.0574962i
$205$	−1.96313	−	27.1498i	−0.137111	−	1.89623i
$206$	−4.23439	+	2.44473i	−0.295024	+	0.170332i
$207$	−4.71589	−	2.09392i	−0.327777	−	0.145537i
$208$	−1.24561			−0.0863672
$209$	0.0590580	+	21.3202i	0.00408513	+	1.47475i
$210$	3.61593	+	2.80836i	0.249523	+	0.193795i
$211$	−3.29761	+	1.90388i	−0.227017	+	0.131068i	−0.609195	−	0.793020i	$-0.708507\pi$
$211$	−3.29761	+	1.90388i	−0.227017	+	0.131068i	0.382178	+	0.924089i	$0.375174\pi$
$212$	−1.57394	+	0.908716i	−0.108099	+	0.0624109i
$213$	10.1421	+	2.15039i	0.694927	+	0.147342i
$214$	2.11183	+	3.65780i	0.144362	+	0.250042i
$215$	−24.0051	+	1.73574i	−1.63713	+	0.118377i
$216$	−3.04781	+	4.20842i	−0.207377	+	0.286347i
$217$	−7.63128			−0.518045
$218$	−3.48888	+	6.04292i	−0.236297	+	0.409278i
$219$	−3.40302	+	16.0500i	−0.229955	+	1.08456i
$220$	6.13738	+	9.05271i	0.413782	+	0.610334i
$221$	0.794332			0.0534326
$222$	−3.47342	+	16.3821i	−0.233121	+	1.09949i
$223$	1.73860	+	3.01134i	0.116425	+	0.201654i	0.918349	−	0.395773i	$-0.129523\pi$
$223$	1.73860	+	3.01134i	0.116425	+	0.201654i	−0.801923	+	0.597427i	$0.796190\pi$
$224$	−0.591070	+	1.02376i	−0.0394925	+	0.0684030i
$225$	10.7300	−	10.4818i	0.715332	−	0.698785i
$226$	1.23326	+	2.13607i	0.0820354	+	0.142089i
$227$			19.6305i			1.30292i	0.758682	+	0.651461i	$0.225844\pi$
$227$			19.6305i			1.30292i	−0.758682	+	0.651461i	$0.774156\pi$
$228$	2.35655	+	7.17263i	0.156066	+	0.475019i
$229$	−10.1213			−0.668834			−0.334417	−	0.942425i	$-0.608539\pi$
$229$	−10.1213			−0.668834			−0.334417	+	0.942425i	$0.608539\pi$
$230$	−1.67775	+	3.46068i	−0.110628	+	0.228191i
$231$	6.69746	−	7.44589i	0.440661	−	0.489903i
$232$	−3.36289	−	1.94156i	−0.220784	−	0.127470i
$233$	6.21846	+	10.7707i	0.407385	+	0.705611i	0.994596	−	0.103823i	$-0.0331075\pi$
$233$	6.21846	+	10.7707i	0.407385	+	0.705611i	−0.587211	+	0.809434i	$0.699774\pi$
$234$	3.71595	−	0.394378i	0.242919	−	0.0257813i
$235$	0.362827	−	0.245982i	0.0236682	−	0.0160461i
$236$	2.51751			0.163876
$237$	−2.79742	+	13.1938i	−0.181712	+	0.857029i
$238$	0.376930	−	0.652861i	0.0244327	−	0.0423187i
$239$			2.35924i			0.152607i	0.997085	+	0.0763033i	$0.0243117\pi$
$239$			2.35924i			0.152607i	−0.997085	+	0.0763033i	$0.975688\pi$
$240$	3.05880	+	2.37566i	0.197445	+	0.153348i
$241$	−21.7637	−	12.5653i	−1.40193	−	0.809402i	−0.407335	−	0.913279i	$-0.633542\pi$
$241$	−21.7637	−	12.5653i	−1.40193	−	0.809402i	−0.994590	+	0.103877i	$0.966875\pi$
$242$	11.1924	−	6.46191i	0.719472	−	0.415387i
$243$	7.75993	−	13.5197i	0.497799	−	0.867292i
$244$	5.71356	+	9.89618i	0.365773	+	0.633538i
$245$	11.2728	+	5.46509i	0.720191	+	0.349152i
$246$	−20.0498	+	6.52583i	−1.27833	+	0.416071i
$247$	2.70170	−	4.70956i	0.171905	−	0.299662i
$248$	−6.45549			−0.409924
$249$	−9.51122	+	10.5741i	−0.602749	+	0.670105i
$250$	−7.53996	−	8.25524i	−0.476869	−	0.522107i
$251$	0.386534	+	0.223165i	0.0243978	+	0.0140861i	0.512149	−	0.858896i	$-0.328849\pi$
$251$	0.386534	+	0.223165i	0.0243978	+	0.0140861i	−0.487752	+	0.872983i	$0.662183\pi$
$252$	1.43917	−	3.24128i	0.0906590	−	0.204181i
$253$	7.28555	+	4.20632i	0.458039	+	0.264449i
$254$			6.97423i			0.437602i
$255$	−1.95062	−	1.51497i	−0.122152	−	0.0948714i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.2017	+	8.77669i	0.948254	+	0.547475i	0.892538	−	0.450972i	$-0.148922\pi$
$257$	15.2017	+	8.77669i	0.948254	+	0.547475i	0.0557162	+	0.998447i	$0.482256\pi$
$258$	5.76994	+	17.7274i	0.359221	+	1.10366i
$259$		−	11.4294i		−	0.710191i
$260$	−0.200871	−	2.77801i	−0.0124575	−	0.172285i
$261$	10.6470	+	4.72742i	0.659035	+	0.292620i
$262$	7.07770	−	12.2589i	0.437262	−	0.757360i
$263$	−3.13559	−	5.43101i	−0.193349	−	0.334890i	0.753009	−	0.658010i	$-0.228602\pi$
$263$	−3.13559	−	5.43101i	−0.193349	−	0.334890i	−0.946358	+	0.323120i	$0.895268\pi$
$264$	5.66554	−	6.29865i	0.348690	−	0.387655i
$265$	−2.28048	−	3.36374i	−0.140089	−	0.206633i
$266$	−2.58876	−	4.45532i	−0.158727	−	0.273173i
$267$	−2.64223	−	8.11792i	−0.161702	−	0.496809i
$268$	2.67262	+	4.62912i	0.163256	+	0.282768i
$269$	−5.87519	−	10.1761i	−0.358217	−	0.620450i	0.629446	−	0.777044i	$-0.283282\pi$
$269$	−5.87519	−	10.1761i	−0.358217	−	0.620450i	−0.987663	+	0.156594i	$0.949948\pi$
$270$	−9.87732	−	6.11871i	−0.601114	−	0.372373i
$271$	4.03454	+	6.98803i	0.245081	+	0.424493i	0.962154	−	0.272505i	$-0.0878521\pi$
$271$	4.03454	+	6.98803i	0.245081	+	0.424493i	−0.717073	+	0.696998i	$0.754519\pi$
$272$	0.318854	−	0.552271i	0.0193333	−	0.0334863i
$273$	−2.42518	+	0.789351i	−0.146779	+	0.0477737i
$274$			13.0397i			0.787758i
$275$	−19.2000	+	15.1477i	−1.15781	+	0.913443i
$276$	2.91426	+	0.617899i	0.175418	+	0.0371931i
$277$		−	6.18038i		−	0.371343i	−0.982612	−	0.185671i	$-0.940554\pi$
$277$		−	6.18038i		−	0.371343i	0.982612	−	0.185671i	$-0.0594460\pi$
$278$			22.0353i			1.32159i
$279$	19.2583	−	2.04391i	1.15296	−	0.122365i
$280$	−2.37856	−	1.15313i	−0.142146	−	0.0689130i
$281$	10.3319	−	17.8954i	0.616352	−	1.06755i	−0.373794	−	0.927512i	$-0.621943\pi$
$281$	10.3319	−	17.8954i	0.616352	−	1.06755i	0.990146	−	0.140041i	$-0.0447234\pi$
$282$	−0.252446	−	0.227071i	−0.0150329	−	0.0135219i
$283$	14.3170	−	8.26590i	0.851055	−	0.491357i	−0.00995159	−	0.999950i	$-0.503168\pi$
$283$	14.3170	−	8.26590i	0.851055	−	0.491357i	0.861007	+	0.508594i	$0.169834\pi$
$284$	−5.98573			−0.355188
$285$	−15.6167	+	6.41237i	−0.925054	+	0.379836i
$286$	−6.09250			−0.360257
$287$	12.4627	−	7.19537i	0.735652	−	0.424729i
$288$	1.21743	−	2.74187i	0.0717375	−	0.161566i
$289$	8.29666	−	14.3702i	0.488039	−	0.845309i
$290$	3.78785	−	7.81316i	0.222430	−	0.458805i
$291$	−0.479655	−	0.101699i	−0.0281178	−	0.00596171i
$292$		−	9.47248i		−	0.554335i
$293$		−	0.128937i		−	0.00753260i	−0.999993	−	0.00376630i	$-0.998801\pi$
$293$		−	0.128937i		−	0.00753260i	0.999993	−	0.00376630i	$-0.00119885\pi$
$294$	2.01273	−	9.49287i	0.117385	−	0.553635i
$295$	0.405981	+	5.61466i	0.0236371	+	0.326898i
$296$		−	9.66844i		−	0.561967i
$297$	−14.9075	+	20.5842i	−0.865019	+	1.19442i
$298$	−2.65188	+	4.59319i	−0.153619	+	0.266077i
$299$	−1.07119	−	1.85536i	−0.0619486	−	0.107298i
$300$	−4.80503	+	7.20498i	−0.277418	+	0.415980i
$301$	−6.36193	−	11.0192i	−0.366695	−	0.635135i
$302$	−9.83554	−	17.0356i	−0.565971	−	0.980291i
$303$	−26.7930	+	8.72063i	−1.53922	+	0.500987i
$304$	−2.18990	−	3.76887i	−0.125599	−	0.216159i
$305$	−21.1495	+	14.3385i	−1.21102	+	0.821022i
$306$	−0.776362	+	1.74851i	−0.0443816	+	0.0999559i
$307$	10.9073	+	18.8920i	0.622514	+	1.07823i	0.989016	+	0.147808i	$0.0472218\pi$
$307$	10.9073	+	18.8920i	0.622514	+	1.07823i	−0.366502	+	0.930417i	$0.619445\pi$
$308$	−2.89104	+	5.00743i	−0.164732	+	0.285325i
$309$	−5.66353	+	6.29641i	−0.322187	+	0.358190i
$310$	−1.04103	−	14.3973i	−0.0591267	−	0.817713i
$311$			26.0604i			1.47775i	0.673844	+	0.738874i	$0.264642\pi$
$311$			26.0604i			1.47775i	−0.673844	+	0.738874i	$0.735358\pi$
$312$	−2.05152	+	0.667731i	−0.116144	+	0.0378028i
$313$	−29.2035	−	16.8606i	−1.65068	−	0.953019i	−0.976794	−	0.214182i	$-0.931291\pi$
$313$	−29.2035	−	16.8606i	−1.65068	−	0.953019i	−0.673884	−	0.738837i	$-0.735375\pi$
$314$	−7.32182	+	12.6818i	−0.413194	+	0.715673i
$315$	7.46093	+	2.68700i	0.420376	+	0.151395i
$316$		−	7.78678i		−	0.438040i
$317$	17.9461	+	10.3612i	1.00795	+	0.581941i	0.910591	−	0.413308i	$-0.135627\pi$
$317$	17.9461	+	10.3612i	1.00795	+	0.581941i	0.0973601	+	0.995249i	$0.468960\pi$
$318$	−2.10516	+	2.34040i	−0.118051	+	0.131243i
$319$	−16.4485	−	9.49657i	−0.920941	−	0.531706i
$320$	−2.01208	−	0.975465i	−0.112479	−	0.0545301i
$321$	5.43904	+	4.89233i	0.303577	+	0.273063i
$322$	−2.03322			−0.113307
$323$	1.39651	+	2.40343i	0.0777041	+	0.133731i
$324$	−2.76376	+	8.56514i	−0.153542	+	0.475841i
$325$	6.16324	−	0.895981i	0.341875	−	0.0497001i
$326$	−5.49446	−	9.51668i	−0.304310	−	0.527080i
$327$	−2.50679	+	11.8230i	−0.138626	+	0.653814i
$328$	10.5425	−	6.08673i	0.582114	−	0.336084i
$329$	0.200694	+	0.115871i	0.0110646	+	0.00638817i
$330$	14.9612	+	11.6198i	0.823586	+	0.639650i
$331$		−	13.3818i		−	0.735532i	−0.929918	−	0.367766i	$-0.880123\pi$
$331$		−	13.3818i		−	0.735532i	0.929918	−	0.367766i	$-0.119877\pi$
$332$	4.10563	−	7.11116i	0.225326	−	0.390276i
$333$	3.06118	+	28.8433i	0.167752	+	1.58061i
$334$	15.2379			0.833782
$335$	−9.89307	+	6.70711i	−0.540516	+	0.366449i
$336$	−0.424687	+	2.00300i	−0.0231686	+	0.109272i
$337$	9.45399	+	16.3748i	0.514992	+	0.891992i	0.999849	+	0.0173983i	$0.00553834\pi$
$337$	9.45399	+	16.3748i	0.514992	+	0.891992i	−0.484857	+	0.874593i	$0.661128\pi$
$338$	−9.91466	−	5.72423i	−0.539287	−	0.311357i
$339$	3.17627	+	2.85701i	0.172512	+	0.155172i
$340$	1.28312	+	0.622061i	0.0695869	+	0.0337360i
$341$	−31.5751			−1.70989
$342$	7.72628	+	10.5501i	0.417790	+	0.570484i
$343$			14.8980i			0.804414i
$344$	−5.38171	−	9.32139i	−0.290162	−	0.502576i
$345$	−0.908102	+	6.59916i	−0.0488906	+	0.355287i
$346$	−11.7522	+	20.3554i	−0.631801	+	1.09431i
$347$	−10.2528	−	17.7584i	−0.550401	−	0.953323i	−0.998245	−	0.0592114i	$-0.981141\pi$
$347$	−10.2528	−	17.7584i	−0.550401	−	0.953323i	0.447844	−	0.894112i	$-0.352192\pi$
$348$	−6.57951	−	1.39503i	−0.352699	−	0.0747812i
$349$	−18.3965			−0.984740			−0.492370	−	0.870386i	$-0.663869\pi$
$349$	−18.3965			−0.984740			−0.492370	+	0.870386i	$0.663869\pi$
$350$	2.18820	−	5.49073i	0.116964	−	0.293492i
$351$	5.90878	−	2.64155i	0.315387	−	0.140996i
$352$	−2.44560	+	4.23590i	−0.130351	+	0.225774i
$353$	6.64568			0.353714			0.176857	−	0.984237i	$-0.443407\pi$
$353$	6.64568			0.353714			0.176857	+	0.984237i	$0.443407\pi$
$354$	4.14635	−	1.34956i	0.220376	−	0.0717282i
$355$	−0.965278	−	13.3496i	−0.0512317	−	0.708525i
$356$	2.46445	+	4.26855i	0.130615	+	0.226233i
$357$	0.270826	−	1.27733i	0.0143336	−	0.0676033i
$358$	−6.29338	+	3.63348i	−0.332615	+	0.192036i
$359$	5.49798	−	3.17426i	0.290172	−	0.167531i	−0.347847	−	0.937551i	$-0.613087\pi$
$359$	5.49798	−	3.17426i	0.290172	−	0.167531i	0.638020	+	0.770020i	$0.279754\pi$
$360$	6.31138	+	2.27299i	0.332639	+	0.119797i
$361$	18.9997	−	0.105261i	0.999985	−	0.00554007i
$362$	7.06431			0.371292
$363$	14.9698	−	16.6427i	0.785713	−	0.873514i
$364$	1.27520	−	0.736240i	0.0668389	−	0.0385894i
$365$	21.1260	−	1.52756i	1.10578	−	0.0799563i
$366$	14.7153	+	13.2362i	0.769182	+	0.691867i
$367$	−7.41907	−	4.28340i	−0.387272	−	0.223592i	0.293705	−	0.955896i	$-0.405112\pi$
$367$	−7.41907	−	4.28340i	−0.387272	−	0.223592i	−0.680978	+	0.732304i	$0.738445\pi$
$368$	−1.71995			−0.0896587
$369$	−29.5238	+	21.4961i	−1.53695	+	1.11904i
$370$	21.5630	−	1.55917i	1.12101	−	0.0810571i
$371$	1.07423	−	1.86062i	0.0557712	−	0.0965985i
$372$	−10.6322	+	3.46059i	−0.551255	+	0.179423i
$373$	33.4428			1.73160			0.865800	−	0.500390i	$-0.166810\pi$
$373$	33.4428			1.73160			0.865800	+	0.500390i	$0.166810\pi$
$374$	1.55958	−	2.70127i	0.0806438	−	0.139679i
$375$	−16.8437	−	9.55449i	−0.869807	−	0.493392i
$376$	0.169772	+	0.0980180i	0.00875533	+	0.00505489i
$377$	2.41842	+	4.18883i	0.124555	+	0.215736i
$378$	0.632766	−	6.10990i	0.0325460	−	0.314259i
$379$		−	6.73402i		−	0.345903i	−0.984930	−	0.172952i	$-0.944670\pi$
$379$		−	6.73402i		−	0.345903i	0.984930	−	0.172952i	$-0.0553305\pi$
$380$	8.05234	−	5.49179i	0.413077	−	0.281723i
$381$	3.73867	+	11.4866i	0.191538	+	0.588476i
$382$	3.75517	+	6.50414i	0.192131	+	0.332781i
$383$	−31.1110	+	17.9619i	−1.58970	+	0.917811i	−0.596339	+	0.802733i	$0.703379\pi$
$383$	−31.1110	+	17.9619i	−1.58970	+	0.917811i	−0.993356	+	0.115079i	$0.963288\pi$
$384$	−0.359253	+	1.69438i	−0.0183331	+	0.0864662i
$385$	−11.6340	−	5.64021i	−0.592924	−	0.287452i
$386$	9.01300	+	5.20366i	0.458750	+	0.264859i
$387$	19.0062	+	26.1041i	0.966142	+	1.32694i
$388$	0.283085			0.0143715
$389$	−13.1534	−	7.59410i	−0.666903	−	0.385036i	0.127999	−	0.991774i	$-0.459144\pi$
$389$	−13.1534	−	7.59410i	−0.666903	−	0.385036i	−0.794902	+	0.606738i	$0.792478\pi$
$390$	−1.82004	−	4.46771i	−0.0921613	−	0.226231i
$391$	1.09683			0.0554689
$392$			5.60255i			0.282971i
$393$	5.08538	−	23.9847i	0.256523	−	1.20987i
$394$	−18.0388	+	10.4147i	−0.908781	+	0.524685i
$395$	17.3664	−	1.25572i	0.873800	−	0.0631822i
$396$	5.95467	−	13.4110i	0.299233	−	0.673931i
$397$	−10.6507	+	6.14920i	−0.534545	+	0.308620i	−0.742865	−	0.669441i	$-0.766534\pi$
$397$	−10.6507	+	6.14920i	−0.534545	+	0.308620i	0.208320	+	0.978061i	$0.433200\pi$
$398$			10.7493i			0.538813i
$399$	−6.65207	−	5.95019i	−0.333020	−	0.297882i
$400$	1.85105	−	4.64474i	0.0925525	−	0.232237i
$401$	11.5605	+	20.0234i	0.577304	+	0.999920i	0.995787	+	0.0916957i	$0.0292287\pi$
$401$	11.5605	+	20.0234i	0.577304	+	0.999920i	−0.418483	+	0.908225i	$0.637438\pi$
$402$	6.88335	+	6.19147i	0.343310	+	0.308803i
$403$	6.96370	+	4.02050i	0.346887	+	0.200275i
$404$	14.0883	−	8.13386i	0.700917	−	0.404675i
$405$	−19.5481	−	4.78262i	−0.971351	−	0.237650i
$406$	4.59039			0.227817
$407$		−	47.2903i		−	2.34409i
$408$	0.229098	−	1.08052i	0.0113421	−	0.0534938i
$409$	−11.6788	−	6.74274i	−0.577478	−	0.333407i	0.182653	−	0.983178i	$-0.441532\pi$
$409$	−11.6788	−	6.74274i	−0.577478	−	0.333407i	−0.760130	+	0.649770i	$0.774865\pi$
$410$	15.2750	+	22.5309i	0.754380	+	1.11272i
$411$	6.99019	+	21.4765i	0.344801	+	1.05936i
$412$	2.44473	−	4.23439i	0.120443	−	0.208614i
$413$	−2.57733	+	1.48802i	−0.126822	+	0.0732207i
$414$	5.13104	−	0.544564i	0.252177	−	0.0267638i
$415$	16.5217	+	8.00980i	0.811020	+	0.393185i
$416$	1.07873	−	0.622803i	0.0528889	−	0.0305354i
$417$	11.8125	+	36.2923i	0.578459	+	1.77724i
$418$	−10.7112	−	18.4343i	−0.523903	−	0.901649i
$419$		−	38.3735i		−	1.87467i	−0.348433	−	0.937334i	$-0.613286\pi$
$419$		−	38.3735i		−	1.87467i	0.348433	−	0.937334i	$-0.386714\pi$
$420$	−4.53566	−	0.624147i	−0.221318	−	0.0304552i
$421$	1.13642	−	0.656111i	0.0553856	−	0.0319769i	−0.472052	−	0.881571i	$-0.656486\pi$
$421$	1.13642	−	0.656111i	0.0553856	−	0.0319769i	0.527437	+	0.849594i	$0.323153\pi$
$422$	1.90388	−	3.29761i	0.0926793	−	0.160525i
$423$	−0.537506	−	0.238659i	−0.0261344	−	0.0116040i
$424$	0.908716	−	1.57394i	0.0441312	−	0.0764374i
$425$	−1.18043	+	2.96199i	−0.0572592	+	0.143677i
$426$	−9.85853	+	3.20877i	−0.477647	+	0.155465i
$427$	−11.6987	−	6.75422i	−0.566138	−	0.326860i
$428$	−3.65780	−	2.11183i	−0.176806	−	0.102079i
$429$	−10.0344	+	3.26601i	−0.484465	+	0.157684i
$430$	19.9211	−	13.5057i	0.960681	−	0.651304i
$431$	2.29056	−	3.96737i	0.110333	−	0.191102i	−0.805572	−	0.592498i	$-0.798142\pi$
$431$	2.29056	−	3.96737i	0.110333	−	0.191102i	0.915904	+	0.401397i	$0.131475\pi$
$432$	0.535272	−	5.16851i	0.0257533	−	0.248670i
$433$	2.72960	−	4.72781i	0.131176	−	0.227204i	−0.792954	−	0.609282i	$-0.791458\pi$
$433$	2.72960	−	4.72781i	0.131176	−	0.227204i	0.924130	+	0.382077i	$0.124791\pi$
$434$	6.60888	−	3.81564i	0.317237	−	0.183157i
$435$	2.05022	−	14.8989i	0.0983003	−	0.714346i
$436$		−	6.97777i		−	0.334174i
$437$	3.73055	−	6.50304i	0.178456	−	0.311083i
$438$	−5.07791	−	15.6012i	−0.242632	−	0.745456i
$439$	−20.9417	+	12.0907i	−0.999491	+	0.577057i	−0.908098	−	0.418758i	$-0.862465\pi$
$439$	−20.9417	+	12.0907i	−0.999491	+	0.577057i	−0.0913936	+	0.995815i	$0.529132\pi$
$440$	−9.84148	−	4.77119i	−0.469174	−	0.227458i
$441$	−1.77385	−	16.7138i	−0.0844692	−	0.795894i
$442$	−0.687912	+	0.397166i	−0.0327206	+	0.0188913i
$443$	−8.90395	+	15.4221i	−0.423039	+	0.732726i	−0.996235	−	0.0866929i	$-0.972370\pi$
$443$	−8.90395	+	15.4221i	−0.423039	+	0.732726i	0.573196	+	0.819418i	$0.305703\pi$
$444$	−5.18296	−	15.9240i	−0.245972	−	0.755719i
$445$	−9.12248	+	6.18468i	−0.432447	+	0.293182i
$446$	−3.01134	−	1.73860i	−0.142591	−	0.0823249i
$447$	−1.90539	+	8.98661i	−0.0901221	+	0.425052i
$448$		−	1.18214i		−	0.0558508i
$449$	5.69376			0.268705			0.134352	−	0.990934i	$-0.457105\pi$
$449$	5.69376			0.268705			0.134352	+	0.990934i	$0.457105\pi$
$450$	−4.05154	+	14.4425i	−0.190991	+	0.680825i
$451$	51.5656	−	29.7714i	2.42813	−	1.40188i
$452$	−2.13607	−	1.23326i	−0.100472	−	0.0580078i
$453$	−25.3315	−	22.7853i	−1.19018	−	1.07055i
$454$	−9.81525	−	17.0005i	−0.460653	−	0.797874i
$455$	1.84764	+	2.72529i	0.0866186	+	0.127764i
$456$	−5.62715	−	5.03341i	−0.263515	−	0.235711i
$457$		−	39.4920i		−	1.84736i	−0.383166	−	0.923680i	$-0.625166\pi$
$457$		−	39.4920i		−	1.84736i	0.383166	−	0.923680i	$-0.374834\pi$
$458$	8.76529	−	5.06064i	0.409575	−	0.236468i
$459$	−0.341347	+	3.29600i	−0.0159327	+	0.153844i
$460$	−0.277365	−	3.83592i	−0.0129322	−	0.178851i
$461$	−12.3322	+	7.12002i	−0.574370	+	0.331612i	−0.758893	−	0.651216i	$-0.774259\pi$
$461$	−12.3322	+	7.12002i	−0.574370	+	0.331612i	0.184523	+	0.982828i	$0.440926\pi$
$462$	−2.07723	+	9.79706i	−0.0966415	+	0.455800i
$463$		−	6.96999i		−	0.323923i	−0.986797	−	0.161961i	$-0.948218\pi$
$463$		−	6.96999i		−	0.323923i	0.986797	−	0.161961i	$-0.0517820\pi$
$464$	3.88313			0.180270
$465$	−9.43255	−	23.1544i	−0.437424	−	1.07376i
$466$	−10.7707	−	6.21846i	−0.498942	−	0.288064i
$467$	−0.964919			−0.0446511			−0.0223256	−	0.999751i	$-0.507107\pi$
$467$	−0.964919			−0.0446511			−0.0223256	+	0.999751i	$0.507107\pi$
$468$	−3.02092	+	2.19952i	−0.139642	+	0.101673i
$469$	−5.47226	−	3.15941i	−0.252685	−	0.145888i
$470$	−0.191226	+	0.394440i	−0.00882060	+	0.0181942i
$471$	−5.26077	+	24.8119i	−0.242404	+	1.14327i
$472$	−2.18022	+	1.25875i	−0.100353	+	0.0579388i
$473$	−26.3230	−	45.5928i	−1.21033	−	2.09636i
$474$	−4.17425	−	12.8249i	−0.191730	−	0.589066i
$475$	13.5466	+	17.0731i	0.621560	+	0.783367i
$476$			0.753859i			0.0345531i
$477$	−2.21259	+	4.98317i	−0.101307	+	0.228164i
$478$	−1.17962	−	2.04316i	−0.0539546	−	0.0934521i
$479$	17.0678	+	9.85408i	0.779846	+	0.450244i	0.836376	−	0.548156i	$-0.184670\pi$
$479$	17.0678	+	9.85408i	0.779846	+	0.450244i	−0.0565295	+	0.998401i	$0.518004\pi$
$480$	−3.83683	−	0.527981i	−0.175126	−	0.0240989i
$481$	−6.02153	+	10.4296i	−0.274558	+	0.475549i
$482$	25.1306			1.14467
$483$	−3.34873	+	1.08995i	−0.152373	+	0.0495944i
$484$	−6.46191	+	11.1924i	−0.293723	+	0.508743i
$485$	0.0456512	+	0.631349i	0.00207291	+	0.0286681i
$486$	0.0395809	+	15.5884i	0.00179543	+	0.707105i
$487$	24.8549			1.12628			0.563141	−	0.826361i	$-0.309593\pi$
$487$	24.8549			1.12628			0.563141	+	0.826361i	$0.309593\pi$
$488$	−9.89618	−	5.71356i	−0.447979	−	0.258641i
$489$	−14.1510	−	12.7286i	−0.639931	−	0.575608i
$490$	−12.4951	+	0.903485i	−0.564469	+	0.0408153i
$491$	30.4914	−	17.6042i	1.37606	−	0.794466i	0.384374	−	0.923178i	$-0.374417\pi$
$491$	30.4914	−	17.6042i	1.37606	−	0.794466i	0.991682	+	0.128711i	$0.0410840\pi$
$492$	14.1007	−	15.6764i	0.635709	−	0.706747i
$493$	−2.47630			−0.111527
$494$	0.0150399	+	5.42945i	0.000676676	+	0.244282i
$495$	30.8702	+	11.1177i	1.38751	+	0.499702i
$496$	5.59061	−	3.22774i	0.251026	−	0.144930i
$497$	6.12796	−	3.53798i	0.274877	−	0.158700i
$498$	2.94992	−	13.9130i	0.132189	−	0.623458i
$499$	−8.51263	−	14.7443i	−0.381078	−	0.660046i	0.610139	−	0.792294i	$-0.291114\pi$
$499$	−8.51263	−	14.7443i	−0.381078	−	0.660046i	−0.991217	+	0.132249i	$0.957780\pi$
$500$	10.6574	+	3.37927i	0.476614	+	0.151126i
$501$	25.0970	−	8.16859i	1.12125	−	0.364946i
$502$	−0.446330			−0.0199207
$503$	−1.07048	+	1.85412i	−0.0477302	+	0.0826711i	−0.888903	−	0.458095i	$-0.848532\pi$
$503$	−1.07048	+	1.85412i	−0.0477302	+	0.0826711i	0.841173	+	0.540766i	$0.181865\pi$
$504$	0.374284	+	3.52661i	0.0166719	+	0.157088i
$505$	20.4124	+	30.1086i	0.908341	+	1.33981i
$506$	−8.41263			−0.373987
$507$	−19.3981	−	4.11290i	−0.861500	−	0.182660i
$508$	−3.48711	−	6.03986i	−0.154716	−	0.267975i
$509$	3.12831	−	5.41839i	0.138660	−	0.240166i	−0.788330	−	0.615253i	$-0.789054\pi$
$509$	3.12831	−	5.41839i	0.138660	−	0.240166i	0.926990	+	0.375087i	$0.122387\pi$
$510$	2.44677	+	0.336697i	0.108345	+	0.0149092i
$511$	5.59889	+	9.69757i	0.247681	+	0.428995i
$512$		−	1.00000i		−	0.0441942i
$513$	18.3808	+	13.2342i	0.811533	+	0.584306i
$514$	−17.5534			−0.774246
$515$	9.83798	+	4.76949i	0.433513	+	0.210169i
$516$	−13.8606	−	12.4674i	−0.610180	−	0.548847i
$517$	0.830389	+	0.479425i	0.0365205	+	0.0210851i
$518$	5.71472	+	9.89819i	0.251091	+	0.434902i
$519$	−8.44401	+	39.8254i	−0.370651	+	1.74814i
$520$	1.56296	+	2.30539i	0.0685404	+	0.101098i
$521$	37.8562			1.65851			0.829254	−	0.558872i	$-0.188766\pi$
$521$	37.8562			1.65851			0.829254	+	0.558872i	$0.188766\pi$
$522$	−11.5843	+	1.22946i	−0.507032	+	0.0538119i
$523$	11.1609	−	19.3312i	0.488030	−	0.845293i	−0.511875	−	0.859060i	$-0.671049\pi$
$523$	11.1609	−	19.3312i	0.488030	−	0.845293i	0.999905	+	0.0137667i	$0.00438221\pi$
$524$			14.1554i			0.618382i
$525$	0.660564	−	10.2163i	0.0288294	−	0.445876i
$526$	5.43101	+	3.13559i	0.236803	+	0.136718i
$527$	−3.56518	+	2.05836i	−0.155302	+	0.0896634i
$528$	−1.75718	+	8.28757i	−0.0764714	+	0.360670i
$529$	10.0209	+	17.3567i	0.435690	+	0.754638i
$530$	3.65682	+	1.77284i	0.158842	+	0.0770073i
$531$	6.10560	−	4.44546i	0.264961	−	0.192917i
$532$	4.46960	+	2.56404i	0.193782	+	0.111165i
$533$	−15.1633			−0.656797
$534$	6.34720	+	5.70921i	0.274670	+	0.247062i
$535$	4.12003	−	8.49835i	0.178125	−	0.367416i
$536$	−4.62912	−	2.67262i	−0.199947	−	0.115440i
$537$	−8.41743	+	9.35806i	−0.363239	+	0.403830i
$538$	10.1761	+	5.87519i	0.438724	+	0.253298i
$539$			27.4032i			1.18034i
$540$	11.6134	+	0.360298i	0.499760	+	0.0155047i
$541$	−9.42086	+	16.3174i	−0.405034	+	0.701540i	−0.994325	−	0.106381i	$-0.966074\pi$
$541$	−9.42086	+	16.3174i	−0.405034	+	0.701540i	0.589291	+	0.807921i	$0.299407\pi$
$542$	−6.98803	−	4.03454i	−0.300162	−	0.173298i
$543$	11.6350	−	3.78696i	0.499304	−	0.162514i
$544$			0.637707i			0.0273415i
$545$	15.5621	−	1.12526i	0.666609	−	0.0482008i
$546$	1.70559	−	1.89619i	0.0729927	−	0.0811494i
$547$	7.03497	−	12.1849i	0.300794	−	0.520990i	−0.675522	−	0.737340i	$-0.736082\pi$
$547$	7.03497	−	12.1849i	0.300794	−	0.520990i	0.976316	+	0.216350i	$0.0694151\pi$
$548$	−6.51986	−	11.2927i	−0.278515	−	0.482401i
$549$	31.3317	+	13.9117i	1.33721	+	0.593736i
$550$	9.05385	−	22.7183i	0.386058	−	0.968713i
$551$	−8.42244	+	14.6819i	−0.358808	+	0.625468i
$552$	−2.83277	+	0.922014i	−0.120571	+	0.0392435i
$553$	4.60253	+	7.97181i	0.195719	+	0.338996i
$554$	3.09019	+	5.35236i	0.131290	+	0.227400i
$555$	34.6786	−	14.1272i	1.47202	−	0.599667i
$556$	−11.0177	−	19.0832i	−0.467253	−	0.809306i
$557$	19.5014	−	33.7775i	0.826303	−	1.43120i	−0.0746166	−	0.997212i	$-0.523773\pi$
$557$	19.5014	−	33.7775i	0.826303	−	1.43120i	0.900919	−	0.433986i	$-0.142893\pi$
$558$	−15.6562	+	11.3992i	−0.662781	+	0.482568i
$559$			13.4070i			0.567054i
$560$	2.63646	−	0.190636i	0.111411	−	0.00805583i
$561$	1.12057	−	5.28504i	0.0473103	−	0.223135i
$562$			20.6639i			0.871653i
$563$		−	24.1695i		−	1.01862i	−0.860582	−	0.509311i	$-0.829900\pi$
$563$		−	24.1695i		−	1.01862i	0.860582	−	0.509311i	$-0.170100\pi$
$564$	0.332160	+	0.0704266i	0.0139865	+	0.00296549i
$565$	2.40601	−	4.96285i	0.101221	−	0.208789i
$566$	−8.26590	+	14.3170i	−0.347442	+	0.601787i
$567$	−2.23316	−	10.4022i	−0.0937839	−	0.436853i
$568$	5.18379	−	2.99286i	0.217507	−	0.125578i
$569$	−7.88191			−0.330427			−0.165213	−	0.986258i	$-0.552831\pi$
$569$	−7.88191			−0.330427			−0.165213	+	0.986258i	$0.552831\pi$
$570$	10.3183	−	13.3616i	0.432185	−	0.559657i
$571$	−5.31046			−0.222236			−0.111118	−	0.993807i	$-0.535443\pi$
$571$	−5.31046			−0.222236			−0.111118	+	0.993807i	$0.535443\pi$
$572$	5.27626	−	3.04625i	0.220612	−	0.127370i
$573$	9.67146	+	8.69933i	0.404031	+	0.363420i
$574$	−7.19537	+	12.4627i	−0.300329	+	0.520185i
$575$	8.51031	−	1.23719i	0.354904	−	0.0515942i
$576$	0.316615	+	2.98325i	0.0131923	+	0.124302i
$577$			41.8771i			1.74337i	0.490070	+	0.871683i	$0.336971\pi$
$577$			41.8771i			1.74337i	−0.490070	+	0.871683i	$0.663029\pi$
$578$			16.5933i			0.690192i
$579$	17.6340	+	3.73886i	0.732844	+	0.155382i
$580$	0.626206	+	8.66032i	0.0260018	+	0.359600i
$581$			9.70686i			0.402708i
$582$	0.466243	−	0.151753i	0.0193264	−	0.00629037i
$583$	4.44471	−	7.69846i	0.184081	−	0.318838i
$584$	4.73624	+	8.20341i	0.195987	+	0.339459i
$585$	−5.39262	−	6.38268i	−0.222957	−	0.263891i
$586$	0.0644687	+	0.111663i	0.00266318	+	0.00461276i
$587$	−16.3582	−	28.3333i	−0.675176	−	1.16944i	−0.976417	−	0.215892i	$-0.930734\pi$
$587$	−16.3582	−	28.3333i	−0.675176	−	1.16944i	0.301241	−	0.953548i	$-0.402599\pi$
$588$	3.00336	+	9.22743i	0.123856	+	0.380533i
$589$	0.0779458	+	28.1387i	0.00321170	+	1.15944i
$590$	−3.15892	−	4.65944i	−0.130051	−	0.191826i
$591$	−24.1270	+	26.8231i	−0.992452	+	1.10336i
$592$	4.83422	+	8.37312i	0.198685	+	0.344133i
$593$	11.4339	−	19.8041i	0.469535	−	0.813259i	−0.529858	−	0.848086i	$-0.677755\pi$
$593$	11.4339	−	19.8041i	0.469535	−	0.813259i	0.999393	+	0.0348277i	$0.0110882\pi$
$594$	2.61812	−	25.2802i	0.107423	−	1.03726i
$595$	−1.68129	+	0.121570i	−0.0689262	+	0.00498388i
$596$		−	5.30376i		−	0.217251i
$597$	5.76236	+	17.7041i	0.235838	+	0.724582i
$598$	1.85536	+	1.07119i	0.0758712	+	0.0438043i
$599$	8.59070	−	14.8795i	0.351007	−	0.607961i	−0.635419	−	0.772167i	$-0.719173\pi$
$599$	8.59070	−	14.8795i	0.351007	−	0.607961i	0.986426	+	0.164206i	$0.0525061\pi$
$600$	0.558787	−	8.64221i	0.0228124	−	0.352817i
$601$		−	25.0284i		−	1.02093i	−0.859898	−	0.510466i	$-0.829473\pi$
$601$		−	25.0284i		−	1.02093i	0.859898	−	0.510466i	$-0.170527\pi$
$602$	11.0192	+	6.36193i	0.449108	+	0.259293i
$603$	14.6560	+	6.50744i	0.596838	+	0.265003i
$604$	17.0356	+	9.83554i	0.693171	+	0.400202i
$605$	−26.0038	−	12.6067i	−1.05720	−	0.512536i
$606$	18.8431	−	20.9488i	0.765450	−	0.850987i
$607$	−42.2621			−1.71537			−0.857683	−	0.514179i	$-0.828097\pi$
$607$	−42.2621			−1.71537			−0.857683	+	0.514179i	$0.828097\pi$
$608$	3.78094	+	2.16898i	0.153337	+	0.0879639i
$609$	7.56041	−	2.46077i	0.306363	−	0.0997155i
$610$	11.1468	−	22.9923i	0.451319	−	0.930931i
$611$	−0.122092	−	0.211469i	−0.00493930	−	0.00855513i
$612$	−0.201908	−	1.90244i	−0.00816165	−	0.0769015i
$613$	−23.5979	+	13.6243i	−0.953111	+	0.550279i	−0.894046	−	0.447976i	$-0.852145\pi$
$613$	−23.5979	+	13.6243i	−0.953111	+	0.550279i	−0.0590647	+	0.998254i	$0.518812\pi$
$614$	−18.8920	−	10.9073i	−0.762420	−	0.440184i
$615$	37.2362	+	28.9200i	1.50151	+	1.16617i
$616$		−	5.78208i		−	0.232966i
$617$	3.86739	−	6.69852i	0.155695	−	0.269672i	−0.777617	−	0.628739i	$-0.783572\pi$
$617$	3.86739	−	6.69852i	0.155695	−	0.269672i	0.933312	+	0.359066i	$0.116905\pi$
$618$	1.75655	−	8.28462i	0.0706589	−	0.333256i
$619$	−28.3765			−1.14055			−0.570273	−	0.821455i	$-0.693163\pi$
$619$	−28.3765			−1.14055			−0.570273	+	0.821455i	$0.693163\pi$
$620$	8.10022	+	11.9479i	0.325313	+	0.479840i
$621$	8.15893	−	3.64750i	0.327407	−	0.146369i
$622$	−13.0302	−	22.5689i	−0.522463	−	0.904932i
$623$	−5.04602	−	2.91332i	−0.202164	−	0.116720i
$624$	1.44280	−	1.60403i	0.0577584	−	0.0642127i
$625$	−5.81795	+	24.3136i	−0.232718	+	0.972544i
$626$	33.7213			1.34777
$627$	−27.5235	−	24.6194i	−1.09918	−	0.983204i
$628$		−	14.6436i		−	0.584345i
$629$	−3.08282	−	5.33960i	−0.122920	−	0.212904i
$630$	−7.80485	+	1.40346i	−0.310953	+	0.0559151i
$631$	−10.6479	+	18.4427i	−0.423886	+	0.734191i	−0.996316	−	0.0857623i	$-0.972667\pi$
$631$	−10.6479	+	18.4427i	−0.423886	+	0.734191i	0.572430	+	0.819954i	$0.306001\pi$
$632$	3.89339	+	6.74355i	0.154871	+	0.268244i
$633$	1.36795	−	6.45180i	0.0543710	−	0.256436i
$634$	−20.7223			−0.822989
$635$	12.9080	−	8.75113i	0.512239	−	0.347278i
$636$	0.652918	−	3.07943i	0.0258899	−	0.122107i
$637$	3.48928	−	6.04361i	0.138250	−	0.239457i
$638$	18.9931			0.751945
$639$	−14.5169	+	10.5697i	−0.574281	+	0.418132i
$640$	2.23025	−	0.161263i	0.0881582	−	0.00637449i
$641$	1.93279	+	3.34770i	0.0763407	+	0.132226i	0.901669	−	0.432428i	$-0.142343\pi$
$641$	1.93279	+	3.34770i	0.0763407	+	0.132226i	−0.825328	+	0.564654i	$0.809010\pi$
$642$	−7.15651	−	1.51736i	−0.282445	−	0.0598856i
$643$	−21.2850	+	12.2889i	−0.839399	+	0.484628i	−0.857060	−	0.515217i	$-0.827712\pi$
$643$	−21.2850	+	12.2889i	−0.839399	+	0.484628i	0.0176606	+	0.999844i	$0.494378\pi$
$644$	1.76082	−	1.01661i	0.0693862	−	0.0400601i
$645$	25.5702	−	32.9231i	1.00683	−	1.29635i
$646$	−2.41113	−	1.38318i	−0.0948648	−	0.0544204i
$647$	−43.4177			−1.70693			−0.853464	−	0.521152i	$-0.825502\pi$
$647$	−43.4177			−1.70693			−0.853464	+	0.521152i	$0.825502\pi$
$648$	−1.88908	−	8.79951i	−0.0742102	−	0.345677i
$649$	−10.6639	+	6.15681i	−0.418595	+	0.241676i
$650$	−4.88953	+	3.85756i	−0.191783	+	0.151306i
$651$	8.83942	−	9.82721i	0.346444	−	0.385159i
$652$	9.51668	+	5.49446i	0.372702	+	0.215180i
$653$	−14.7907			−0.578804			−0.289402	−	0.957208i	$-0.593456\pi$
$653$	−14.7907			−0.578804			−0.289402	+	0.957208i	$0.593456\pi$
$654$	−3.74057	−	11.4924i	−0.146268	−	0.449389i
$655$	−31.5700	+	2.28275i	−1.23354	+	0.0891944i
$656$	−6.08673	+	10.5425i	−0.237647	+	0.411617i
$657$	−16.7267	−	22.9732i	−0.652570	−	0.896271i
$658$	−0.231742			−0.00903424
$659$	−3.94515	+	6.83320i	−0.153681	+	0.266184i	−0.932578	−	0.360968i	$-0.882446\pi$
$659$	−3.94515	+	6.83320i	−0.153681	+	0.266184i	0.778897	+	0.627152i	$0.215780\pi$
$660$	−18.7667	−	2.58246i	−0.730492	−	0.100522i
$661$	33.7114	+	19.4633i	1.31122	+	0.757035i	0.982299	−	0.187322i	$-0.0599807\pi$
$661$	33.7114	+	19.4633i	1.31122	+	0.757035i	0.328924	+	0.944356i	$0.393314\pi$
$662$	6.69092	+	11.5890i	0.260050	+	0.450420i
$663$	−0.920086	+	1.02290i	−0.0357332	+	0.0397263i
$664$			8.21126i			0.318659i
$665$	−4.99766	+	10.3818i	−0.193801	+	0.402588i
$666$	−17.0727	−	23.4485i	−0.661555	−	0.908610i
$667$	3.33940	+	5.78400i	0.129302	+	0.223958i
$668$	−13.1964	+	7.61896i	−0.510585	+	0.294786i
$669$	−5.89170	−	1.24919i	−0.227786	−	0.0482966i
$670$	5.21410	−	10.7551i	0.201438	−	0.415504i
$671$	−48.4042	−	27.9462i	−1.86862	−	1.07885i
$672$	−0.633709	−	1.94699i	−0.0244459	−	0.0751068i
$673$	7.79388			0.300432			0.150216	−	0.988653i	$-0.452003\pi$
$673$	7.79388			0.300432			0.150216	+	0.988653i	$0.452003\pi$
$674$	−16.3748	−	9.45399i	−0.630733	−	0.364154i
$675$	1.06926	+	25.9587i	0.0411557	+	0.999153i
$676$	11.4485			0.440326
$677$			31.7619i			1.22071i	0.792128	+	0.610355i	$0.208973\pi$
$677$			31.7619i			1.22071i	−0.792128	+	0.610355i	$0.791027\pi$
$678$	−4.17924	−	0.886107i	−0.160503	−	0.0340307i
$679$	−0.289812	+	0.167323i	−0.0111220	+	0.00642126i
$680$	−1.42224	+	0.102839i	−0.0545406	+	0.00394369i
$681$	−25.2792	−	22.7383i	−0.968703	−	0.871333i
$682$	27.3448	−	15.7875i	1.04709	−	0.604536i
$683$			40.8203i			1.56194i	0.624566	+	0.780972i	$0.285276\pi$
$683$			40.8203i			1.56194i	−0.624566	+	0.780972i	$0.714724\pi$
$684$	−11.9662	−	5.27351i	−0.457539	−	0.201638i
$685$	24.1341	−	16.3620i	0.922118	−	0.625159i
$686$	−7.44898	−	12.9020i	−0.284403	−	0.492601i
$687$	11.7236	−	13.0337i	0.447285	−	0.497267i
$688$	9.32139	+	5.38171i	0.355375	+	0.205176i
$689$	−1.96051	+	1.13190i	−0.0746896	+	0.0431220i
$690$	−2.51314	−	6.16909i	−0.0956736	−	0.234853i
$691$	−0.368227			−0.0140080			−0.00700400	−	0.999975i	$-0.502229\pi$
$691$	−0.368227			−0.0140080			−0.00700400	+	0.999975i	$0.502229\pi$
$692$		−	23.5044i		−	0.893501i
$693$	1.83069	+	17.2494i	0.0695423	+	0.655249i
$694$	17.7584	+	10.2528i	0.674101	+	0.389193i
$695$	40.7834	−	27.6495i	1.54700	−	1.04881i
$696$	6.39553	−	2.08163i	0.242422	−	0.0789038i
$697$	3.88156	−	6.72305i	0.147024	−	0.254654i
$698$	15.9318	−	9.19823i	0.603028	−	0.348158i
$699$	−21.0729	−	4.46800i	−0.797051	−	0.168995i
$700$	0.850329	+	5.84921i	0.0321394	+	0.221079i
$701$	22.0697	−	12.7420i	0.833563	−	0.481258i	−0.0215082	−	0.999769i	$-0.506847\pi$
$701$	22.0697	−	12.7420i	0.833563	−	0.481258i	0.855071	+	0.518511i	$0.173513\pi$
$702$	−3.79637	+	5.24204i	−0.143285	+	0.197848i
$703$	−42.1436	+	0.116740i	−1.58948	+	0.00440294i
$704$		−	4.89120i		−	0.184344i
$705$	−0.103503	+	0.752156i	−0.00389816	+	0.0283278i
$706$	−5.75533	+	3.32284i	−0.216605	+	0.125057i
$707$	−9.61536	+	16.6543i	−0.361623	+	0.626349i
$708$	−2.91606	+	3.24193i	−0.109592	+	0.121839i
$709$	−10.9886	+	19.0328i	−0.412685	+	0.714792i	−0.995182	−	0.0980411i	$-0.968742\pi$
$709$	−10.9886	+	19.0328i	−0.412685	+	0.714792i	0.582497	+	0.812833i	$0.302076\pi$
$710$	7.51078	+	11.0785i	0.281874	+	0.415768i
$711$	−13.7500	−	18.8850i	−0.515667	−	0.708241i
$712$	−4.26855	−	2.46445i	−0.159971	−	0.0923591i
$713$	9.61559	+	5.55157i	0.360107	+	0.207908i
$714$	0.404121	+	1.24161i	0.0151238	+	0.0464661i
$715$	7.64476	+	11.2761i	0.285898	+	0.421703i
$716$	3.63348	−	6.29338i	0.135790	−	0.235195i
$717$	−3.03812	−	2.73274i	−0.113461	−	0.102056i
$718$	−3.17426	+	5.49798i	−0.118462	+	0.205183i
$719$	−32.4837	+	18.7545i	−1.21144	+	0.699424i	−0.963072	−	0.269242i	$-0.913227\pi$
$719$	−32.4837	+	18.7545i	−1.21144	+	0.699424i	−0.248365	+	0.968666i	$0.579893\pi$
$720$	−6.60231	+	1.18722i	−0.246054	+	0.0442450i
$721$			5.78002i			0.215259i
$722$	−16.4016	+	9.59101i	−0.610404	+	0.356941i
$723$	41.3902	−	13.4717i	1.53932	−	0.501020i
$724$	−6.11788	+	3.53216i	−0.227369	+	0.131272i
$725$	−19.2137	+	2.79318i	−0.713577	+	0.103736i
$726$	−4.64292	+	21.8979i	−0.172315	+	0.812708i
$727$	33.2590	−	19.2021i	1.23351	−	0.712166i	0.265749	−	0.964042i	$-0.414381\pi$
$727$	33.2590	−	19.2021i	1.23351	−	0.712166i	0.967760	+	0.251876i	$0.0810475\pi$
$728$	−0.736240	+	1.27520i	−0.0272869	+	0.0472622i
$729$	8.42166	+	25.6530i	0.311913	+	0.950111i
$730$	−17.5318	+	11.8859i	−0.648882	+	0.439916i
$731$	−5.94432	−	3.43195i	−0.219859	−	0.126935i
$732$	−19.3619	−	4.10523i	−0.715638	−	0.151734i
$733$		−	11.6754i		−	0.431241i	−0.976477	−	0.215621i	$-0.930823\pi$
$733$		−	11.6754i		−	0.431241i	0.976477	−	0.215621i	$-0.0691775\pi$
$734$	8.56680			0.316206
$735$	−20.0951	+	8.18626i	−0.741219	+	0.301955i
$736$	1.48952	−	0.859976i	0.0549045	−	0.0316992i
$737$	−22.6419	−	13.0723i	−0.834026	−	0.481525i
$738$	14.8203	−	33.3781i	0.545542	−	1.22867i
$739$	14.3124	+	24.7898i	0.526491	+	0.911909i	0.999524	+	0.0308638i	$0.00982581\pi$
$739$	14.3124	+	24.7898i	0.526491	+	0.911909i	−0.473033	+	0.881045i	$0.656841\pi$
$740$	−17.8945	+	12.1318i	−0.657816	+	0.445973i
$741$	2.93533	+	8.93427i	0.107832	+	0.328209i
$742$			2.14846i			0.0788724i
$743$	11.3898	−	6.57588i	0.417850	−	0.241246i	−0.276307	−	0.961069i	$-0.589111\pi$
$743$	11.3898	−	6.57588i	0.417850	−	0.241246i	0.694157	+	0.719824i	$0.255777\pi$
$744$	7.47748	−	8.31307i	0.274138	−	0.304772i
$745$	11.8287	−	0.855303i	0.433370	−	0.0313359i
$746$	−28.9623	+	16.7214i	−1.06038	+	0.612213i
$747$	−2.59981	−	24.4962i	−0.0951222	−	0.896270i
$748$			3.11915i			0.114048i
$749$	4.99296			0.182439
$750$	19.3644	−	0.147439i	0.707086	−	0.00538370i
$751$	−28.1156	−	16.2326i	−1.02595	−	0.592335i	−0.110131	−	0.993917i	$-0.535127\pi$
$751$	−28.1156	−	16.2326i	−1.02595	−	0.592335i	−0.915823	+	0.401582i	$0.868461\pi$
$752$	−0.196036			−0.00714870
$753$	−0.735109	+	0.239264i	−0.0267889	+	0.00871927i
$754$	−4.18883	−	2.41842i	−0.152548	−	0.0880737i
$755$	−19.1884	+	39.5798i	−0.698339	+	1.44046i
$756$	2.50696	+	5.60771i	0.0911771	+	0.203950i
$757$	−20.7846	+	12.0000i	−0.755430	+	0.436148i	−0.827653	−	0.561241i	$-0.810324\pi$
$757$	−20.7846	+	12.0000i	−0.755430	+	0.436148i	0.0722226	+	0.997389i	$0.476991\pi$
$758$	3.36701	+	5.83183i	0.122295	+	0.211822i
$759$	−13.8557	+	4.50976i	−0.502928	+	0.163694i
$760$	−4.22764	+	8.78220i	−0.153353	+	0.318564i
$761$		−	37.9550i		−	1.37587i	−0.725773	−	0.687935i	$-0.758518\pi$
$761$		−	37.9550i		−	1.37587i	0.725773	−	0.687935i	$-0.241482\pi$
$762$	−8.98108	−	8.07835i	−0.325350	−	0.292648i
$763$	4.12435	+	7.14358i	0.149311	+	0.258615i
$764$	−6.50414	−	3.75517i	−0.235312	−	0.135857i
$765$	4.21034	−	0.757098i	0.152225	−	0.0273729i
$766$	17.9619	−	31.1110i	0.648990	−	1.12408i
$767$	3.13582			0.113228
$768$	−0.536070	−	1.64701i	−0.0193437	−	0.0594312i
$769$	−5.02601	+	8.70531i	−0.181243	+	0.313922i	−0.942304	−	0.334758i	$-0.891345\pi$
$769$	−5.02601	+	8.70531i	−0.181243	+	0.313922i	0.761061	+	0.648680i	$0.224679\pi$
$770$	12.8954	−	0.932437i	0.464720	−	0.0336027i
$771$	−28.9105	+	9.40983i	−1.04119	+	0.338887i
$772$	−10.4073			−0.374568
$773$	11.5762	+	6.68354i	0.416368	+	0.240390i	0.693522	−	0.720435i	$-0.256058\pi$
$773$	11.5762	+	6.68354i	0.416368	+	0.240390i	−0.277154	+	0.960826i	$0.589391\pi$
$774$	−29.5119	−	13.1037i	−1.06078	−	0.471001i
$775$	−25.3405	+	19.9922i	−0.910259	+	0.718142i
$776$	−0.245159	+	0.141542i	−0.00880069	+	0.00508108i
$777$	14.7183	+	13.2389i	0.528016	+	0.474943i
$778$	15.1882			0.544524
$779$	−26.6586	−	45.8802i	−0.955145	−	1.64383i
$780$	3.81006	+	2.95913i	0.136422	+	0.105954i
$781$	25.3550	−	14.6387i	0.907271	−	0.523813i
$782$	−0.949880	+	0.548413i	−0.0339676	+	0.0196112i
$783$	−18.4204	+	8.23492i	−0.658290	+	0.294292i
$784$	−2.80127	−	4.85195i	−0.100045	−	0.173284i
$785$	32.6589	−	2.36148i	1.16565	−	0.0842849i
$786$	7.58828	+	23.3140i	0.270665	+	0.831584i
$787$	31.7937			1.13332			0.566661	−	0.823951i	$-0.308235\pi$
$787$	31.7937			1.13332			0.566661	+	0.823951i	$0.308235\pi$
$788$	10.4147	−	18.0388i	0.371008	−	0.642605i
$789$	10.6258	+	2.25294i	0.378288	+	0.0802069i
$790$	−14.4119	+	9.77070i	−0.512753	+	0.347626i
$791$	2.91578			0.103673
$792$	1.54863	+	14.5916i	0.0550281	+	0.518492i
$793$	7.11684	+	12.3267i	0.252727	+	0.437735i
$794$	6.14920	−	10.6507i	0.218227	−	0.377980i
$795$	6.97317	+	0.959569i	0.247313	+	0.0340324i
$796$	−5.37464	−	9.30915i	−0.190499	−	0.329954i
$797$			50.5779i			1.79156i	0.444495	+	0.895781i	$0.353383\pi$
$797$			50.5779i			1.79156i	−0.444495	+	0.895781i	$0.646617\pi$
$798$	8.73596	+	1.82698i	0.309250	+	0.0646743i
$799$	0.125014			0.00442266
$800$	0.719314	+	4.94799i	0.0254316	+	0.174938i
$801$	13.5144	+	6.00056i	0.477508	+	0.212019i
$802$	−20.0234	−	11.5605i	−0.707051	−	0.408216i
$803$	23.1659	+	40.1245i	0.817506	+	1.41596i
$804$	−9.05690	−	1.92030i	−0.319412	−	0.0677236i
$805$	2.55125	+	3.76313i	0.0899198	+	0.132633i
$806$	−8.04099			−0.283232
$807$	19.9097	+	4.22136i	0.700853	+	0.148599i
$808$	−8.13386	+	14.0883i	−0.286148	+	0.495623i
$809$		−	15.8783i		−	0.558253i	−0.960254	−	0.279126i	$-0.909955\pi$
$809$		−	15.8783i		−	0.558253i	0.960254	−	0.279126i	$-0.0900449\pi$
$810$	19.3204	−	5.63216i	0.678851	−	0.197894i
$811$	17.3837	+	10.0365i	0.610425	+	0.352429i	0.773132	−	0.634245i	$-0.218689\pi$
$811$	17.3837	+	10.0365i	0.610425	+	0.352429i	−0.162707	+	0.986674i	$0.552022\pi$
$812$	−3.97540	+	2.29520i	−0.139509	+	0.0805456i
$813$	−13.6721	−	2.89884i	−0.479502	−	0.101667i
$814$	23.6451	+	40.9546i	0.828762	+	1.43546i
$815$	−10.7193	+	22.1106i	−0.375481	+	0.774500i
$816$	0.341856	+	1.05031i	0.0119673	+	0.0367681i
$817$	−40.5659	+	23.5708i	−1.41922	+	0.824637i
$818$	13.4855			0.471509
$819$	1.79263	−	4.03735i	0.0626397	−	0.141077i
$820$	−24.4940	−	11.8748i	−0.855367	−	0.414685i
$821$	15.4958	+	8.94651i	0.540807	+	0.312235i	0.745406	−	0.666611i	$-0.232256\pi$
$821$	15.4958	+	8.94651i	0.540807	+	0.312235i	−0.204599	+	0.978846i	$0.565589\pi$
$822$	−16.7919	−	15.1041i	−0.585686	−	0.526816i
$823$	−37.3229	−	21.5484i	−1.30099	−	0.751129i	−0.320419	−	0.947276i	$-0.603824\pi$
$823$	−37.3229	−	21.5484i	−1.30099	−	0.751129i	−0.980575	+	0.196146i	$0.937157\pi$
$824$			4.88946i			0.170332i
$825$	2.73314	−	42.2707i	0.0951557	−	1.47168i
$826$	1.48802	−	2.57733i	0.0517749	−	0.0896767i
$827$	−22.5954	−	13.0454i	−0.785717	−	0.453634i	0.0527352	−	0.998609i	$-0.483206\pi$
$827$	−22.5954	−	13.0454i	−0.785717	−	0.453634i	−0.838453	+	0.544974i	$0.816539\pi$
$828$	−4.17133	+	3.03713i	−0.144964	+	0.105547i
$829$		−	47.8942i		−	1.66343i	−0.555199	−	0.831717i	$-0.687358\pi$
$829$		−	47.8942i		−	1.66343i	0.555199	−	0.831717i	$-0.312642\pi$
$830$	−18.3131	+	1.32418i	−0.635658	+	0.0459628i
$831$	7.95880	+	7.15882i	0.276088	+	0.248337i
$832$	−0.622803	+	1.07873i	−0.0215918	+	0.0373981i
$833$	1.78639	+	3.09412i	0.0618949	+	0.107205i
$834$	−28.3761	−	25.5239i	−0.982583	−	0.883819i
$835$	−19.1203	−	28.2026i	−0.661684	−	0.975992i
$836$	18.4933	+	10.6089i	0.639605	+	0.366918i
$837$	−19.6751	+	27.1674i	−0.680072	+	0.939043i
$838$	19.1867	+	33.2324i	0.662795	+	1.14799i
$839$	−13.4667	−	23.3250i	−0.464921	−	0.805268i	0.534277	−	0.845310i	$-0.320584\pi$
$839$	−13.4667	−	23.3250i	−0.464921	−	0.805268i	−0.999198	+	0.0400421i	$0.987251\pi$
$840$	4.24007	−	1.72730i	0.146296	−	0.0595977i
$841$	6.96067	+	12.0562i	0.240023	+	0.415732i
$842$	−0.656111	+	1.13642i	−0.0226111	+	0.0391635i
$843$	11.0773	+	34.0335i	0.381522	+	1.17218i
$844$			3.80775i			0.131068i
$845$	1.84622	+	25.5329i	0.0635118	+	0.878358i
$846$	0.584824	−	0.0620680i	0.0201066	−	0.00213394i
$847$		−	15.2777i		−	0.524950i
$848$			1.81743i			0.0624109i
$849$	−5.93910	+	28.0112i	−0.203830	+	0.961343i
$850$	−0.458712	−	3.15537i	−0.0157337	−	0.108228i
$851$	−8.31463	+	14.4014i	−0.285022	+	0.493673i
$852$	6.93335	−	7.70814i	0.237533	−	0.264076i
$853$	0.722987	−	0.417417i	0.0247546	−	0.0142921i	−0.487572	−	0.873083i	$-0.662117\pi$
$853$	0.722987	−	0.417417i	0.0247546	−	0.0142921i	0.512326	+	0.858791i	$0.328784\pi$
$854$	13.5084			0.462250
$855$	9.83151	−	27.5380i	0.336231	−	0.941780i
$856$	4.22366			0.144362
$857$	4.53118	−	2.61608i	0.154782	−	0.0893634i	−0.420609	−	0.907242i	$-0.638183\pi$
$857$	4.53118	−	2.61608i	0.154782	−	0.0893634i	0.575391	+	0.817879i	$0.304850\pi$
$858$	7.05704	−	7.84564i	0.240923	−	0.267846i
$859$	12.7448	−	22.0746i	0.434847	−	0.753177i	−0.562436	−	0.826841i	$-0.690136\pi$
$859$	12.7448	−	22.0746i	0.434847	−	0.753177i	0.997283	+	0.0736639i	$0.0234692\pi$
$860$	−10.4993	+	21.6569i	−0.358024	+	0.738493i
$861$	−5.16992	+	24.3834i	−0.176190	+	0.830985i
$862$			4.58113i			0.156034i
$863$			38.1439i			1.29843i	0.760603	+	0.649217i	$0.224903\pi$
$863$			38.1439i			1.29843i	−0.760603	+	0.649217i	$0.775097\pi$
$864$	2.12069	+	4.74370i	0.0721475	+	0.161384i
$865$	52.4205	−	3.79039i	1.78235	−	0.128877i
$866$			5.45921i			0.185511i
$867$	8.89518	+	27.3293i	0.302096	+	0.928152i
$868$	−3.81564	+	6.60888i	−0.129511	+	0.224320i
$869$	19.0433	+	32.9840i	0.646001	+	1.11891i
$870$	5.67390	+	13.9279i	0.192363	+	0.472201i
$871$	3.32903	+	5.76605i	0.112800	+	0.195375i
$872$	3.48888	+	6.04292i	0.118149	+	0.204639i
$873$	0.686554	−	0.499877i	0.0232363	−	0.0169183i
$874$	0.0207673	+	7.49707i	0.000702465	+	0.253592i
$875$	−12.9080	+	2.83970i	−0.436372	+	0.0959995i
$876$	12.1982	+	10.9721i	0.412139	+	0.370713i
$877$	−10.6375	−	18.4247i	−0.359203	−	0.622158i	0.628625	−	0.777709i	$-0.283618\pi$
$877$	−10.6375	−	18.4247i	−0.359203	−	0.622158i	−0.987828	+	0.155551i	$0.950285\pi$
$878$	12.0907	−	20.9417i	0.408041	−	0.706747i
$879$	0.166039	+	0.149350i	0.00560037	+	0.00503745i
$880$	10.9086	−	0.788771i	0.367728	−	0.0265895i
$881$		−	13.0328i		−	0.439085i	−0.975603	−	0.219543i	$-0.929543\pi$
$881$		−	13.0328i		−	0.439085i	0.975603	−	0.219543i	$-0.0704565\pi$
$882$	9.89309	+	13.5876i	0.333118	+	0.457519i
$883$	15.1209	+	8.73004i	0.508858	+	0.293789i	0.732364	−	0.680913i	$-0.238417\pi$
$883$	15.1209	+	8.73004i	0.508858	+	0.293789i	−0.223506	+	0.974703i	$0.571750\pi$
$884$	0.397166	−	0.687912i	0.0133581	−	0.0231370i
$885$	−7.70054	−	5.98073i	−0.258851	−	0.201040i
$886$		−	17.8079i		−	0.598268i
$887$	12.8025	+	7.39156i	0.429868	+	0.248184i	0.699290	−	0.714838i	$-0.253500\pi$
$887$	12.8025	+	7.39156i	0.429868	+	0.248184i	−0.269423	+	0.963022i	$0.586833\pi$
$888$	12.4506	+	11.1991i	0.417814	+	0.375817i
$889$	7.13995	+	4.12225i	0.239466	+	0.138256i
$890$	4.80796	−	9.91733i	0.161163	−	0.332430i
$891$	−9.23988	−	43.0401i	−0.309548	−	1.44190i
$892$	3.47719			0.116425
$893$	0.425199	−	0.741200i	0.0142287	−	0.0248033i
$894$	−2.84319	−	8.73533i	−0.0950904	−	0.292153i
$895$	14.6217	+	7.08867i	0.488750	+	0.236948i
$896$	0.591070	+	1.02376i	0.0197462	+	0.0342015i
$897$	3.63002	+	0.769658i	0.121203	+	0.0256981i
$898$	−4.93094	+	2.84688i	−0.164548	+	0.0950015i
$899$	−21.7091	−	12.5337i	−0.724038	−	0.418023i
$900$	−3.71250	−	14.5333i	−0.123750	−	0.484444i
$901$		−	1.15899i		−	0.0386116i
$902$	−29.7714	+	51.5656i	−0.991280	+	1.71695i
$903$	21.5591	+	4.57108i	0.717442	+	0.152116i
$904$	2.46652			0.0820354
$905$	−8.86417	−	13.0748i	−0.294655	−	0.434620i
$906$	33.3303	+	7.06690i	1.10733	+	0.234782i
$907$	23.0208	+	39.8732i	0.764393	+	1.32397i	0.940567	+	0.339609i	$0.110295\pi$
$907$	23.0208	+	39.8732i	0.764393	+	1.32397i	−0.176174	+	0.984359i	$0.556372\pi$
$908$	17.0005	+	9.81525i	0.564182	+	0.325731i
$909$	19.8047	−	44.6041i	0.656882	−	1.47942i
$910$	−2.96275	−	1.43635i	−0.0982141	−	0.0476146i
$911$	−54.8805			−1.81827			−0.909137	−	0.416498i	$-0.863257\pi$
$911$	−54.8805			−1.81827			−0.909137	+	0.416498i	$0.863257\pi$
$912$	7.38996	+	1.54548i	0.244706	+	0.0511761i
$913$			40.1629i			1.32920i
$914$	19.7460	+	34.2011i	0.653140	+	1.13127i
$915$	6.03330	−	43.8439i	0.199455	−	1.44943i
$916$	−5.06064	+	8.76529i	−0.167208	+	0.289613i
$917$	−8.36683	−	14.4918i	−0.276297	−	0.478561i
$918$	−1.35238	−	3.02509i	−0.0446353	−	0.0998429i
$919$	−11.6421			−0.384037			−0.192018	−	0.981391i	$-0.561503\pi$
$919$	−11.6421			−0.384037			−0.192018	+	0.981391i	$0.561503\pi$
$920$	2.15816	+	3.18332i	0.0711526	+	0.104951i
$921$	−36.9624	−	7.83698i	−1.21795	−	0.258237i
$922$	7.12002	−	12.3322i	0.234485	−	0.406141i
$923$	−7.45586			−0.245413
$924$	−3.09960	−	9.52312i	−0.101969	−	0.313288i
$925$	−29.9426	−	37.9528i	−0.984506	−	1.24788i
$926$	3.48499	+	6.03619i	0.114524	+	0.198361i
$927$	−1.54808	−	14.5864i	−0.0508455	−	0.479082i
$928$	−3.36289	+	1.94156i	−0.110392	+	0.0637349i
$929$	−32.3182	+	18.6589i	−1.06033	+	0.612180i	−0.925523	−	0.378692i	$-0.876374\pi$
$929$	−32.3182	+	18.6589i	−1.06033	+	0.612180i	−0.134804	+	0.990872i	$0.543041\pi$
$930$	19.7460	+	15.3360i	0.647498	+	0.502888i
$931$	24.4208	−	0.0676471i	0.800361	−	0.00221705i
$932$	12.4369			0.407385
$933$	−33.5593	−	30.1861i	−1.09868	−	0.988248i
$934$	0.835644	−	0.482459i	0.0273431	−	0.0157866i
$935$	−6.95648	+	0.503005i	−0.227501	+	0.0164500i
$936$	1.51643	−	3.41529i	0.0495662	−	0.111632i
$937$	19.6425	+	11.3406i	0.641693	+	0.370482i	0.785266	−	0.619158i	$-0.212526\pi$
$937$	19.6425	+	11.3406i	0.641693	+	0.370482i	−0.143573	+	0.989640i	$0.545859\pi$
$938$	6.31882			0.206317
$939$	55.5391	−	18.0769i	1.81245	−	0.589919i
$940$	−0.0316134	−	0.437208i	−0.00103112	−	0.0142602i
$941$	−22.5937	+	39.1335i	−0.736535	+	1.27572i	0.217512	+	0.976058i	$0.430206\pi$
$941$	−22.5937	+	39.1335i	−0.736535	+	1.27572i	−0.954047	+	0.299658i	$0.903127\pi$
$942$	−7.85001	−	24.1182i	−0.255767	−	0.785812i
$943$	−20.9378			−0.681828
$944$	1.25875	−	2.18022i	0.0409689	−	0.0709602i
$945$	−12.1023	+	6.49545i	−0.393687	+	0.211297i
$946$	45.5928	+	26.3230i	1.48235	+	0.855834i
$947$	5.98265	+	10.3623i	0.194410	+	0.336728i	0.946707	−	0.322096i	$-0.104387\pi$
$947$	5.98265	+	10.3623i	0.194410	+	0.336728i	−0.752297	+	0.658824i	$0.771054\pi$
$948$	10.0274	+	9.01954i	0.325676	+	0.292941i
$949$		−	11.7990i		−	0.383011i
$950$	−20.2682	−	8.01243i	−0.657588	−	0.259957i
$951$	−34.1298	+	11.1086i	−1.10673	+	0.360221i
$952$	−0.376930	−	0.652861i	−0.0122164	−	0.0211593i
$953$	−10.2018	+	5.89002i	−0.330469	+	0.190796i	−0.656049	−	0.754718i	$-0.727774\pi$
$953$	−10.2018	+	5.89002i	−0.330469	+	0.190796i	0.325580	+	0.945514i	$0.394440\pi$
$954$	−0.575427	−	5.42185i	−0.0186301	−	0.175539i
$955$	7.32607	−	15.1114i	0.237066	−	0.488993i
$956$	2.04316	+	1.17962i	0.0660806	+	0.0381517i
$957$	31.2818	−	10.1816i	1.01120	−	0.329126i
$958$	−19.7082			−0.636742
$959$	13.3496	+	7.70738i	0.431080	+	0.248884i
$960$	3.58678	−	1.46117i	0.115763	−	0.0471590i
$961$	−10.6733			−0.344300
$962$		−	12.0431i		−	0.388284i
$963$	−12.6002	+	1.33728i	−0.406037	+	0.0430932i
$964$	−21.7637	+	12.5653i	−0.700963	+	0.404701i
$965$	−1.67832	−	23.2109i	−0.0540270	−	0.747184i
$966$	2.35511	−	2.61829i	0.0757745	−	0.0842421i
$967$	−4.32752	+	2.49850i	−0.139164	+	0.0803462i	−0.567965	−	0.823052i	$-0.692269\pi$
$967$	−4.32752	+	2.49850i	−0.139164	+	0.0803462i	0.428802	+	0.903399i	$0.358936\pi$
$968$		−	12.9238i		−	0.415387i
$969$	−4.71263	−	0.985567i	−0.151392	−	0.0316610i
$970$	−0.355210	−	0.523938i	−0.0114051	−	0.0168227i
$971$	−3.89219	−	6.74148i	−0.124906	−	0.216344i	0.796790	−	0.604256i	$-0.206530\pi$
$971$	−3.89219	−	6.74148i	−0.124906	−	0.216344i	−0.921696	+	0.387912i	$0.873196\pi$
$972$	−7.82848	−	13.4802i	−0.251099	−	0.432377i
$973$	22.5590	+	13.0244i	0.723207	+	0.417544i
$974$	−21.5250	+	12.4274i	−0.689704	+	0.398201i
$975$	−5.98517	+	8.97456i	−0.191679	+	0.287416i
$976$	11.4271			0.365773
$977$			15.3430i			0.490866i	0.969414	+	0.245433i	$0.0789302\pi$
$977$			15.3430i			0.490866i	−0.969414	+	0.245433i	$0.921070\pi$
$978$	18.6194	+	3.94780i	0.595384	+	0.126237i
$979$	−20.8783	−	12.0541i	−0.667274	−	0.385251i
$980$	10.3693	−	7.02997i	0.331235	−	0.224564i
$981$	−12.3215	−	16.9229i	−0.393395	−	0.540306i
$982$	−17.6042	+	30.4914i	−0.561772	+	0.973019i
$983$	10.3778	−	5.99164i	0.331001	−	0.191104i	−0.325284	−	0.945616i	$-0.605460\pi$
$983$	10.3778	−	5.99164i	0.331001	−	0.191104i	0.656286	+	0.754513i	$0.272127\pi$
$984$	−4.37336	+	20.6265i	−0.139418	+	0.657550i
$985$	41.9104	+	20.3183i	1.33538	+	0.647396i
$986$	2.14454	−	1.23815i	0.0682960	−	0.0394307i
$987$	−0.381680	+	0.124230i	−0.0121490	+	0.00395428i
$988$	−2.72775	−	4.69452i	−0.0867813	−	0.149353i
$989$			18.5126i			0.588665i
$990$	−32.2932	+	5.80692i	−1.02635	+	0.184556i
$991$	4.07300	−	2.35155i	0.129383	−	0.0746995i	−0.433911	−	0.900956i	$-0.642867\pi$
$991$	4.07300	−	2.35155i	0.129383	−	0.0746995i	0.563295	+	0.826256i	$0.309534\pi$
$992$	−3.22774	+	5.59061i	−0.102481	+	0.177502i
$993$	17.2325	+	15.5004i	0.546857	+	0.491889i
$994$	−3.53798	+	6.12796i	−0.112218	+	0.194367i
$995$	19.8950	−	13.4880i	0.630713	−	0.427598i
$996$	4.40181	+	13.5240i	0.139477	+	0.428524i
$997$	8.70143	+	5.02377i	0.275577	+	0.159105i	0.631419	−	0.775441i	$-0.282473\pi$
$997$	8.70143	+	5.02377i	0.275577	+	0.159105i	−0.355842	+	0.934546i	$0.615806\pi$
$998$	14.7443	+	8.51263i	0.466723	+	0.269463i
$999$	−40.6889	−	29.4676i	−1.28734	−	0.932314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.449.6	yes	80
3.2	odd	2	inner	570.2.n.a.449.40	yes	80
5.4	even	2	inner	570.2.n.a.449.35	yes	80
15.14	odd	2	inner	570.2.n.a.449.1	yes	80
19.8	odd	6	inner	570.2.n.a.179.1	✓	80
57.8	even	6	inner	570.2.n.a.179.35	yes	80
95.84	odd	6	inner	570.2.n.a.179.40	yes	80
285.179	even	6	inner	570.2.n.a.179.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.1	✓	80	19.8	odd	6	inner
570.2.n.a.179.6	yes	80	285.179	even	6	inner
570.2.n.a.179.35	yes	80	57.8	even	6	inner
570.2.n.a.179.40	yes	80	95.84	odd	6	inner
570.2.n.a.449.1	yes	80	15.14	odd	2	inner
570.2.n.a.449.6	yes	80	1.1	even	1	trivial
570.2.n.a.449.35	yes	80	5.4	even	2	inner
570.2.n.a.449.40	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.15831 + 1.28775i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.01208 + 0.975465i) q^{5} +(0.359253 - 1.69438i) q^{6} +1.18214i q^{7} +1.00000i q^{8} +(-0.316615 - 2.98325i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.15831 + 1.28775i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.01208 + 0.975465i) q^{5} +(0.359253 - 1.69438i) q^{6} +1.18214i q^{7} +1.00000i q^{8} +(-0.316615 - 2.98325i) q^{9} +(-2.23025 + 0.161263i) q^{10} +4.89120i q^{11} +(0.536070 + 1.64701i) q^{12} +(0.622803 - 1.07873i) q^{13} +(-0.591070 - 1.02376i) q^{14} +(-3.58678 + 1.46117i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.318854 + 0.552271i) q^{17} +(1.76582 + 2.42526i) q^{18} +(4.35888 - 0.0120744i) q^{19} +(1.85082 - 1.25478i) q^{20} +(-1.52230 - 1.36929i) q^{21} +(-2.44560 - 4.23590i) q^{22} +(0.859976 - 1.48952i) q^{23} +(-1.28775 - 1.15831i) q^{24} +(3.09694 + 3.92543i) q^{25} +1.24561i q^{26} +(4.20842 + 3.04781i) q^{27} +(1.02376 + 0.591070i) q^{28} +(-1.94156 + 3.36289i) q^{29} +(2.37566 - 3.05880i) q^{30} +6.45549i q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.29865 - 5.66554i) q^{33} +(-0.552271 - 0.318854i) q^{34} +(-1.15313 + 2.37856i) q^{35} +(-2.74187 - 1.21743i) q^{36} -9.66844 q^{37} +(-3.76887 + 2.18990i) q^{38} +(0.667731 + 2.05152i) q^{39} +(-0.975465 + 2.01208i) q^{40} +(-6.08673 - 10.5425i) q^{41} +(2.00300 + 0.424687i) q^{42} +(-9.32139 + 5.38171i) q^{43} +(4.23590 + 2.44560i) q^{44} +(2.27299 - 6.31138i) q^{45} +1.71995i q^{46} +(0.0980180 - 0.169772i) q^{47} +(1.69438 + 0.359253i) q^{48} +5.60255 q^{49} +(-4.64474 - 1.85105i) q^{50} +(-1.08052 - 0.229098i) q^{51} +(-0.622803 - 1.07873i) q^{52} +(-1.57394 - 0.908716i) q^{53} +(-5.16851 - 0.535272i) q^{54} +(-4.77119 + 9.84148i) q^{55} -1.18214 q^{56} +(-5.03341 + 5.62715i) q^{57} -3.88313i q^{58} +(1.25875 + 2.18022i) q^{59} +(-0.527981 + 3.83683i) q^{60} +(-5.71356 + 9.89618i) q^{61} +(-3.22774 - 5.59061i) q^{62} +(3.52661 - 0.374284i) q^{63} -1.00000 q^{64} +(2.30539 - 1.56296i) q^{65} +(8.28757 + 1.75718i) q^{66} +(-2.67262 + 4.62912i) q^{67} +0.637707 q^{68} +(0.922014 + 2.83277i) q^{69} +(-0.190636 - 2.63646i) q^{70} +(-2.99286 - 5.18379i) q^{71} +(2.98325 - 0.316615i) q^{72} +(8.20341 - 4.73624i) q^{73} +(8.37312 - 4.83422i) q^{74} +(-8.64221 - 0.558787i) q^{75} +(2.16898 - 3.78094i) q^{76} -5.78208 q^{77} +(-1.60403 - 1.44280i) q^{78} +(6.74355 - 3.89339i) q^{79} +(-0.161263 - 2.23025i) q^{80} +(-8.79951 + 1.88908i) q^{81} +(10.5425 + 6.08673i) q^{82} +8.21126 q^{83} +(-1.94699 + 0.633709i) q^{84} +(0.102839 + 1.42224i) q^{85} +(5.38171 - 9.32139i) q^{86} +(-2.08163 - 6.39553i) q^{87} -4.89120 q^{88} +(-2.46445 + 4.26855i) q^{89} +(1.18722 + 6.60231i) q^{90} +(1.27520 + 0.736240i) q^{91} +(-0.859976 - 1.48952i) q^{92} +(-8.31307 - 7.47748i) q^{93} +0.196036i q^{94} +(8.78220 + 4.22764i) q^{95} +(-1.64701 + 0.536070i) q^{96} +(0.141542 + 0.245159i) q^{97} +(-4.85195 + 2.80127i) q^{98} +(14.5916 - 1.54863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

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