LMFDB - Embedded newform 132.2.j.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,2,Mod(7,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("132.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	132.19
Dual form			132.2.j.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38167 - 0.301665i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.81800 + 0.833600i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(1.40726 - 0.140058i) q^{6} +(-1.03321 + 3.17989i) q^{7} +(-2.26039 - 1.70018i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.38167 - 0.301665i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.81800 + 0.833600i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(1.40726 - 0.140058i) q^{6} +(-1.03321 + 3.17989i) q^{7} +(-2.26039 - 1.70018i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.248420 + 0.278981i) q^{10} +(1.85745 + 2.74771i) q^{11} +(-1.98661 - 0.231009i) q^{12} +(3.89823 + 5.36545i) q^{13} +(2.38681 - 4.08186i) q^{14} +(0.251215 + 0.0816246i) q^{15} +(2.61022 + 3.03096i) q^{16} +(-2.74676 + 3.78059i) q^{17} +(-1.29510 + 0.568070i) q^{18} +(-1.27559 - 3.92586i) q^{19} +(-0.259074 - 0.460397i) q^{20} -3.34353i q^{21} +(-1.73748 - 4.35674i) q^{22} -0.765361i q^{23} +(2.67515 + 0.918469i) q^{24} +(-1.52352 - 4.68893i) q^{25} +(-3.76748 - 8.58922i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-4.52913 + 4.91975i) q^{28} +(3.67765 + 1.19494i) q^{29} +(-0.322471 - 0.188560i) q^{30} +(-2.37677 - 3.27135i) q^{31} +(-2.69212 - 4.97519i) q^{32} +(-2.61562 - 2.03924i) q^{33} +(4.93558 - 4.39491i) q^{34} +(0.714499 - 0.519114i) q^{35} +(1.96077 - 0.394195i) q^{36} +(0.274094 - 0.843576i) q^{37} +(0.578143 + 5.80903i) q^{38} +(-5.36545 - 3.89823i) q^{39} +(0.219068 + 0.714269i) q^{40} +(-5.66025 + 1.83913i) q^{41} +(-1.00863 + 4.61964i) q^{42} +2.10908 q^{43} +(1.08634 + 6.54369i) q^{44} -0.264143 q^{45} +(-0.230883 + 1.05747i) q^{46} +(4.91501 - 1.59698i) q^{47} +(-3.41909 - 2.07601i) q^{48} +(-3.38106 - 2.45648i) q^{49} +(0.690516 + 6.93812i) q^{50} +(1.44406 - 4.44436i) q^{51} +(2.61433 + 13.0039i) q^{52} +(4.59637 - 3.33946i) q^{53} +(1.05617 - 0.940476i) q^{54} +(0.0296780 - 0.875559i) q^{55} +(7.74185 - 5.43116i) q^{56} +(2.42632 + 3.33954i) q^{57} +(-4.72080 - 2.76042i) q^{58} +(9.46770 + 3.07624i) q^{59} +(0.388665 + 0.357806i) q^{60} +(1.87298 - 2.57794i) q^{61} +(2.29705 + 5.23689i) q^{62} +(1.03321 + 3.17989i) q^{63} +(2.21876 + 7.68616i) q^{64} -1.75181i q^{65} +(2.99875 + 3.60659i) q^{66} +5.99397i q^{67} +(-8.14511 + 4.58341i) q^{68} +(0.236510 + 0.727902i) q^{69} +(-1.14380 + 0.501703i) q^{70} +(-2.69549 + 3.71003i) q^{71} +(-2.82804 - 0.0468496i) q^{72} +(-14.3347 - 4.65764i) q^{73} +(-0.633184 + 1.08285i) q^{74} +(2.89792 + 3.98864i) q^{75} +(0.953581 - 8.20054i) q^{76} +(-10.6565 + 3.06752i) q^{77} +(6.23730 + 7.00462i) q^{78} +(11.6701 - 8.47885i) q^{79} +(-0.0872089 - 1.05297i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.37537 - 0.833558i) q^{82} +(-0.496492 - 0.360722i) q^{83} +(2.78717 - 6.07853i) q^{84} +(1.17394 - 0.381437i) q^{85} +(-2.91404 - 0.636235i) q^{86} -3.86691 q^{87} +(0.473040 - 9.36890i) q^{88} +2.78024 q^{89} +(0.364957 + 0.0796826i) q^{90} +(-21.0892 + 6.85231i) q^{91} +(0.638005 - 1.39142i) q^{92} +(3.27135 + 2.37677i) q^{93} +(-7.27265 + 0.723810i) q^{94} +(-0.336938 + 1.03699i) q^{95} +(4.09777 + 3.89978i) q^{96} +(8.14034 - 5.91430i) q^{97} +(3.93046 + 4.41398i) q^{98} +(3.11777 + 1.13116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) $ 48 * q - 4 * q^4 + 12 * q^9	$ 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	−1.38167	−	0.301665i	−0.976985	−	0.213309i
$2$	−1.38167	−	0.301665i	−0.976985	−	0.213309i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	1.81800	+	0.833600i	0.908998	+	0.416800i
$5$	−0.213696	−	0.155259i	−0.0955677	−	0.0694340i	0.538975	−	0.842322i	$-0.318812\pi$
$5$	−0.213696	−	0.155259i	−0.0955677	−	0.0694340i	−0.634543	+	0.772888i	$0.718812\pi$
$6$	1.40726	−	0.140058i	0.574512	−	0.0571782i
$7$	−1.03321	+	3.17989i	−0.390516	+	1.20189i	0.541883	+	0.840454i	$0.317712\pi$
$7$	−1.03321	+	3.17989i	−0.390516	+	1.20189i	−0.932399	+	0.361431i	$0.882288\pi$
$8$	−2.26039	−	1.70018i	−0.799170	−	0.601105i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	0.248420	+	0.278981i	0.0785573	+	0.0882214i
$11$	1.85745	+	2.74771i	0.560041	+	0.828465i
$11$	1.85745	+	2.74771i	0.560041	+	0.828465i
$12$	−1.98661	−	0.231009i	−0.573486	−	0.0666865i
$13$	3.89823	+	5.36545i	1.08117	+	1.48811i	0.858221	+	0.513280i	$0.171570\pi$
$13$	3.89823	+	5.36545i	1.08117	+	1.48811i	0.222953	+	0.974829i	$0.428430\pi$
$14$	2.38681	−	4.08186i	0.637902	−	1.09092i
$15$	0.251215	+	0.0816246i	0.0648633	+	0.0210754i
$16$	2.61022	+	3.03096i	0.652556	+	0.757741i
$17$	−2.74676	+	3.78059i	−0.666188	+	0.916929i	−0.999666	−	0.0258289i	$-0.991777\pi$
$17$	−2.74676	+	3.78059i	−0.666188	+	0.916929i	0.333479	+	0.942758i	$0.391777\pi$
$18$	−1.29510	+	0.568070i	−0.305259	+	0.133895i
$19$	−1.27559	−	3.92586i	−0.292640	−	0.900655i	−0.984004	−	0.178147i	$-0.942990\pi$
$19$	−1.27559	−	3.92586i	−0.292640	−	0.900655i	0.691363	−	0.722507i	$-0.257010\pi$
$20$	−0.259074	−	0.460397i	−0.0579308	−	0.102948i
$21$		−	3.34353i		−	0.729619i
$22$	−1.73748	−	4.35674i	−0.370432	−	0.928859i
$23$		−	0.765361i		−	0.159589i	−0.996811	−	0.0797944i	$-0.974574\pi$
$23$		−	0.765361i		−	0.159589i	0.996811	−	0.0797944i	$-0.0254264\pi$
$24$	2.67515	+	0.918469i	0.546062	+	0.187482i
$25$	−1.52352	−	4.68893i	−0.304705	−	0.937785i
$26$	−3.76748	−	8.58922i	−0.738863	−	1.68448i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−4.52913	+	4.91975i	−0.855924	+	0.929745i
$29$	3.67765	+	1.19494i	0.682922	+	0.221895i	0.629874	−	0.776697i	$-0.283106\pi$
$29$	3.67765	+	1.19494i	0.682922	+	0.221895i	0.0530476	+	0.998592i	$0.483106\pi$
$30$	−0.322471	−	0.188560i	−0.0588749	−	0.0344263i
$31$	−2.37677	−	3.27135i	−0.426881	−	0.587551i	0.540353	−	0.841439i	$-0.318291\pi$
$31$	−2.37677	−	3.27135i	−0.426881	−	0.587551i	−0.967234	+	0.253887i	$0.918291\pi$
$32$	−2.69212	−	4.97519i	−0.475904	−	0.879497i
$33$	−2.61562	−	2.03924i	−0.455322	−	0.354986i
$34$	4.93558	−	4.39491i	0.846445	−	0.753721i
$35$	0.714499	−	0.519114i	0.120772	−	0.0877463i
$36$	1.96077	−	0.394195i	0.326795	−	0.0656992i
$37$	0.274094	−	0.843576i	0.0450608	−	0.138683i	−0.925995	−	0.377536i	$-0.876771\pi$
$37$	0.274094	−	0.843576i	0.0450608	−	0.138683i	0.971056	+	0.238853i	$0.0767714\pi$
$38$	0.578143	+	5.80903i	0.0937872	+	0.942349i
$39$	−5.36545	−	3.89823i	−0.859160	−	0.624216i
$40$	0.219068	+	0.714269i	0.0346377	+	0.112936i
$41$	−5.66025	+	1.83913i	−0.883983	+	0.287223i	−0.715610	−	0.698500i	$-0.753851\pi$
$41$	−5.66025	+	1.83913i	−0.883983	+	0.287223i	−0.168373	+	0.985723i	$0.553851\pi$
$42$	−1.00863	+	4.61964i	−0.155635	+	0.712827i
$43$	2.10908			0.321631			0.160816	−	0.986984i	$-0.448588\pi$
$43$	2.10908			0.321631			0.160816	+	0.986984i	$0.448588\pi$
$44$	1.08634	+	6.54369i	0.163772	+	0.986498i
$45$	−0.264143			−0.0393761
$46$	−0.230883	+	1.05747i	−0.0340418	+	0.155916i
$47$	4.91501	−	1.59698i	0.716928	−	0.232944i	0.0722371	−	0.997387i	$-0.476986\pi$
$47$	4.91501	−	1.59698i	0.716928	−	0.232944i	0.644691	+	0.764444i	$0.276986\pi$
$48$	−3.41909	−	2.07601i	−0.493503	−	0.299647i
$49$	−3.38106	−	2.45648i	−0.483008	−	0.350926i
$50$	0.690516	+	6.93812i	0.0976536	+	0.981198i
$51$	1.44406	−	4.44436i	0.202209	−	0.622334i
$52$	2.61433	+	13.0039i	0.362542	+	1.80332i
$53$	4.59637	−	3.33946i	0.631360	−	0.458710i	−0.225511	−	0.974241i	$-0.572405\pi$
$53$	4.59637	−	3.33946i	0.631360	−	0.458710i	0.856871	+	0.515531i	$0.172405\pi$
$54$	1.05617	−	0.940476i	0.143727	−	0.127983i
$55$	0.0296780	−	0.875559i	0.00400178	−	0.118060i
$56$	7.74185	−	5.43116i	1.03455	−	0.725769i
$57$	2.42632	+	3.33954i	0.321374	+	0.442333i
$58$	−4.72080	−	2.76042i	−0.619872	−	0.362461i
$59$	9.46770	+	3.07624i	1.23259	+	0.400493i	0.851652	−	0.524108i	$-0.175601\pi$
$59$	9.46770	+	3.07624i	1.23259	+	0.400493i	0.380938	+	0.924601i	$0.375601\pi$
$60$	0.388665	+	0.357806i	0.0501764	+	0.0461925i
$61$	1.87298	−	2.57794i	0.239811	−	0.330071i	−0.672100	−	0.740461i	$-0.734607\pi$
$61$	1.87298	−	2.57794i	0.239811	−	0.330071i	0.911910	+	0.410390i	$0.134607\pi$
$62$	2.29705	+	5.23689i	0.291726	+	0.665086i
$63$	1.03321	+	3.17989i	0.130172	+	0.400628i
$64$	2.21876	+	7.68616i	0.277345	+	0.960770i
$65$		−	1.75181i		−	0.217285i
$66$	2.99875	+	3.60659i	0.369120	+	0.443941i
$67$			5.99397i			0.732280i	0.930560	+	0.366140i	$0.119321\pi$
$67$			5.99397i			0.732280i	−0.930560	+	0.366140i	$0.880679\pi$
$68$	−8.14511	+	4.58341i	−0.987739	+	0.555820i
$69$	0.236510	+	0.727902i	0.0284724	+	0.0876291i
$70$	−1.14380	+	0.501703i	−0.136710	+	0.0599649i
$71$	−2.69549	+	3.71003i	−0.319896	+	0.440299i	−0.938435	−	0.345455i	$-0.887725\pi$
$71$	−2.69549	+	3.71003i	−0.319896	+	0.440299i	0.618539	+	0.785754i	$0.287725\pi$
$72$	−2.82804	−	0.0468496i	−0.333288	−	0.00552128i
$73$	−14.3347	−	4.65764i	−1.67775	−	0.545135i	−0.693280	−	0.720669i	$-0.743835\pi$
$73$	−14.3347	−	4.65764i	−1.67775	−	0.545135i	−0.984473	+	0.175534i	$0.943835\pi$
$74$	−0.633184	+	1.08285i	−0.0736062	+	0.125879i
$75$	2.89792	+	3.98864i	0.334622	+	0.460568i
$76$	0.953581	−	8.20054i	0.109383	−	0.940666i
$77$	−10.6565	+	3.06752i	−1.21442	+	0.349576i
$78$	6.23730	+	7.00462i	0.706235	+	0.793117i
$79$	11.6701	−	8.47885i	1.31299	−	0.953945i	0.313002	−	0.949753i	$-0.398665\pi$
$79$	11.6701	−	8.47885i	1.31299	−	0.953945i	0.999991	−	0.00419263i	$-0.00133456\pi$
$80$	−0.0872089	−	1.05297i	−0.00975026	−	0.117725i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	8.37537	−	0.833558i	0.924905	−	0.0920511i
$83$	−0.496492	−	0.360722i	−0.0544971	−	0.0395944i	0.560203	−	0.828355i	$-0.310723\pi$
$83$	−0.496492	−	0.360722i	−0.0544971	−	0.0395944i	−0.614700	+	0.788761i	$0.710723\pi$
$84$	2.78717	−	6.07853i	0.304105	−	0.663222i
$85$	1.17394	−	0.381437i	0.127332	−	0.0413727i
$86$	−2.91404	−	0.636235i	−0.314229	−	0.0686070i
$87$	−3.86691			−0.414576
$88$	0.473040	−	9.36890i	0.0504263	−	0.998728i
$89$	2.78024			0.294705			0.147353	−	0.989084i	$-0.452925\pi$
$89$	2.78024			0.294705			0.147353	+	0.989084i	$0.452925\pi$
$90$	0.364957	+	0.0796826i	0.0384698	+	0.00839928i
$91$	−21.0892	+	6.85231i	−2.21075	+	0.718317i
$92$	0.638005	−	1.39142i	0.0665166	−	0.145066i
$93$	3.27135	+	2.37677i	0.339223	+	0.246460i
$94$	−7.27265	+	0.723810i	−0.750117	+	0.0746553i
$95$	−0.336938	+	1.03699i	−0.0345691	+	0.106393i
$96$	4.09777	+	3.89978i	0.418227	+	0.398019i
$97$	8.14034	−	5.91430i	0.826526	−	0.600506i	−0.0920484	−	0.995755i	$-0.529341\pi$
$97$	8.14034	−	5.91430i	0.826526	−	0.600506i	0.918574	+	0.395248i	$0.129341\pi$
$98$	3.93046	+	4.41398i	0.397036	+	0.445880i
$99$	3.11777	+	1.13116i	0.313347	+	0.113686i
$100$	1.13893	−	9.79446i	0.113893	−	0.979446i
$101$	11.6323	+	16.0105i	1.15746	+	1.59310i	0.720198	+	0.693769i	$0.244051\pi$
$101$	11.6323	+	16.0105i	1.15746	+	1.59310i	0.437260	+	0.899335i	$0.355949\pi$
$102$	−3.33591	+	5.70499i	−0.330304	+	0.564878i
$103$	6.38362	+	2.07416i	0.628997	+	0.204373i	0.606131	−	0.795365i	$-0.292721\pi$
$103$	6.38362	+	2.07416i	0.628997	+	0.204373i	0.0228662	+	0.999739i	$0.492721\pi$
$104$	0.310710	−	18.7557i	0.0304676	−	1.83915i
$105$	−0.519114	+	0.714499i	−0.0506604	+	0.0697280i
$106$	−7.35804	+	3.22745i	−0.714676	+	0.313478i
$107$	−3.77667	−	11.6234i	−0.365104	−	1.12368i	−0.949916	−	0.312506i	$-0.898832\pi$
$107$	−3.77667	−	11.6234i	−0.365104	−	1.12368i	0.584811	−	0.811169i	$-0.301168\pi$
$108$	−1.74299	+	0.980812i	−0.167719	+	0.0943787i
$109$		−	2.09407i		−	0.200576i	−0.994958	−	0.100288i	$-0.968024\pi$
$109$		−	2.09407i		−	0.200576i	0.994958	−	0.100288i	$-0.0319764\pi$
$110$	−0.305131	+	1.20078i	−0.0290931	+	0.114490i
$111$			0.886988i			0.0841892i
$112$	−12.3350	+	5.16860i	−1.16555	+	0.488387i
$113$	−3.72590	−	11.4671i	−0.350503	−	1.07874i	−0.958571	−	0.284853i	$-0.908055\pi$
$113$	−3.72590	−	11.4671i	−0.350503	−	1.07874i	0.608068	−	0.793885i	$-0.291945\pi$
$114$	−2.34494	−	5.34606i	−0.219623	−	0.500704i
$115$	−0.118829	+	0.163555i	−0.0110809	+	0.0152515i
$116$	5.68985	+	5.23808i	0.528289	+	0.486344i
$117$	6.30747	+	2.04942i	0.583126	+	0.189469i
$118$	−12.1532	−	7.10641i	−1.11879	−	0.654198i
$119$	−9.18389	−	12.6405i	−0.841886	−	1.15876i
$120$	−0.429067	−	0.611614i	−0.0391683	−	0.0558325i
$121$	−4.09979	+	10.2074i	−0.372708	+	0.927949i
$122$	−3.36550	+	2.99683i	−0.304698	+	0.271320i
$123$	4.81490	−	3.49823i	0.434145	−	0.315425i
$124$	−1.59397	−	7.92857i	−0.143143	−	0.712007i
$125$	−0.810551	+	2.49462i	−0.0724979	+	0.223125i
$126$	−0.468287	−	4.70523i	−0.0417183	−	0.419175i
$127$	1.89867	+	1.37946i	0.168480	+	0.122408i	0.668830	−	0.743415i	$-0.266795\pi$
$127$	1.89867	+	1.37946i	0.168480	+	0.122408i	−0.500350	+	0.865823i	$0.666795\pi$
$128$	−0.746942	−	11.2890i	−0.0660210	−	0.997818i
$129$	−2.00585	+	0.651741i	−0.176605	+	0.0573826i
$130$	−0.528460	+	2.42042i	−0.0463490	+	0.212285i
$131$	−13.7656			−1.20271			−0.601353	−	0.798983i	$-0.705372\pi$
$131$	−13.7656			−1.20271			−0.601353	+	0.798983i	$0.705372\pi$
$132$	−3.05528	−	5.88772i	−0.265928	−	0.512460i
$133$	13.8018			1.19676
$134$	1.80817	−	8.28166i	0.156202	−	0.715427i
$135$	0.251215	−	0.0816246i	0.0216211	−	0.00702512i
$136$	12.6365	−	3.87564i	1.08357	−	0.332333i
$137$	−4.81224	−	3.49630i	−0.411138	−	0.298709i	0.362925	−	0.931819i	$-0.381778\pi$
$137$	−4.81224	−	3.49630i	−0.411138	−	0.298709i	−0.774062	+	0.633110i	$0.781778\pi$
$138$	−0.107195	−	1.07706i	−0.00912501	−	0.0916857i
$139$	2.33565	−	7.18840i	0.198107	−	0.609712i	−0.801819	−	0.597567i	$-0.796134\pi$
$139$	2.33565	−	7.18840i	0.198107	−	0.609712i	0.999926	−	0.0121448i	$-0.00386591\pi$
$140$	1.73169	−	0.348141i	0.146355	−	0.0294233i
$141$	−4.18096	+	3.03764i	−0.352100	+	0.255816i
$142$	4.84345	−	4.31288i	0.406453	−	0.361929i
$143$	−7.50194	+	20.6772i	−0.627344	+	1.72912i
$144$	3.89327	+	0.917851i	0.324439	+	0.0764876i
$145$	−0.600373	−	0.826342i	−0.0498582	−	0.0686240i
$146$	18.4007	+	10.7596i	1.52286	+	0.890469i
$147$	3.97467	+	1.29145i	0.327826	+	0.106517i
$148$	1.20151	−	1.30513i	0.0987633	−	0.107281i
$149$	10.4316	−	14.3578i	0.854588	−	1.17624i	−0.128245	−	0.991743i	$-0.540934\pi$
$149$	10.4316	−	14.3578i	0.854588	−	1.17624i	0.982833	−	0.184497i	$-0.0590656\pi$
$150$	−2.80072	−	6.38516i	−0.228678	−	0.521346i
$151$	4.19328	+	12.9056i	0.341245	+	1.05024i	0.963564	+	0.267479i	$0.0861906\pi$
$151$	4.19328	+	12.9056i	0.341245	+	1.05024i	−0.622319	+	0.782764i	$0.713809\pi$
$152$	−3.79134	+	11.0427i	−0.307519	+	0.895684i
$153$			4.67307i			0.377795i
$154$	15.6491	−	1.02358i	1.26104	−	0.0824825i
$155$			1.06809i			0.0857910i
$156$	−6.50481	−	11.5596i	−0.520802	−	0.925509i
$157$	4.46673	+	13.7472i	0.356484	+	1.09714i	0.955144	+	0.296141i	$0.0957000\pi$
$157$	4.46673	+	13.7472i	0.356484	+	1.09714i	−0.598660	+	0.801003i	$0.704300\pi$
$158$	−18.6820	+	8.19446i	−1.48626	+	0.651916i
$159$	−3.33946	+	4.59637i	−0.264836	+	0.364516i
$160$	−0.197149	+	1.48115i	−0.0155860	+	0.117095i
$161$	2.43376	+	0.790778i	0.191807	+	0.0623220i
$162$	−0.713858	+	1.22082i	−0.0560860	+	0.0959168i
$163$	−3.68738	−	5.07524i	−0.288818	−	0.397523i	0.639812	−	0.768531i	$-0.279012\pi$
$163$	−3.68738	−	5.07524i	−0.288818	−	0.397523i	−0.928630	+	0.371008i	$0.879012\pi$
$164$	−11.8234	−	1.37486i	−0.923254	−	0.107358i
$165$	0.242337	+	0.841877i	0.0188659	+	0.0655401i
$166$	0.577168	+	0.648172i	0.0447969	+	0.0503079i
$167$	−1.90114	+	1.38126i	−0.147115	+	0.106885i	−0.658908	−	0.752223i	$-0.728981\pi$
$167$	−1.90114	+	1.38126i	−0.147115	+	0.106885i	0.511793	+	0.859109i	$0.328981\pi$
$168$	−5.68462	+	7.55770i	−0.438578	+	0.583090i
$169$	−9.57467	+	29.4678i	−0.736513	+	2.26675i
$170$	−1.73706	+	0.172881i	−0.133227	+	0.0132594i
$171$	−3.33954	−	2.42632i	−0.255381	−	0.185545i
$172$	3.83429	+	1.75813i	0.292362	+	0.134056i
$173$	15.5257	−	5.04461i	1.18040	−	0.383534i	0.347883	−	0.937538i	$-0.386901\pi$
$173$	15.5257	−	5.04461i	1.18040	−	0.383534i	0.832514	+	0.554004i	$0.186901\pi$
$174$	5.34277	+	1.16651i	0.405034	+	0.0884329i
$175$	16.4844			1.24610
$176$	−3.47985	+	12.8020i	−0.262304	+	0.964985i
$177$	−9.95493			−0.748259
$178$	−3.84137	−	0.838702i	−0.287922	−	0.0628634i
$179$	23.3391	−	7.58332i	1.74444	−	0.566804i	0.749035	−	0.662530i	$-0.230517\pi$
$179$	23.3391	−	7.58332i	1.74444	−	0.566804i	0.995408	+	0.0957267i	$0.0305175\pi$
$180$	−0.480210	−	0.220189i	−0.0357928	−	0.0164119i
$181$	−10.6410	−	7.73114i	−0.790939	−	0.574651i	0.117303	−	0.993096i	$-0.462575\pi$
$181$	−10.6410	−	7.73114i	−0.790939	−	0.574651i	−0.908242	+	0.418445i	$0.862575\pi$
$182$	31.2054	−	3.10571i	2.31310	−	0.230211i
$183$	−0.984684	+	3.03055i	−0.0727899	+	0.224024i
$184$	−1.30125	+	1.73002i	−0.0959296	+	0.127539i
$185$	−0.189546	+	0.137713i	−0.0139357	+	0.0101249i
$186$	−3.80292	−	4.27075i	−0.278843	−	0.313147i
$187$	−15.4899	−	0.525047i	−1.13274	−	0.0383952i
$188$	10.2667	+	1.19384i	0.748777	+	0.0870698i
$189$	−1.96528	−	2.70498i	−0.142953	−	0.196758i
$190$	0.778358	−	1.33113i	0.0564680	−	0.0965701i
$191$	−10.5402	−	3.42473i	−0.762665	−	0.247805i	−0.0982428	−	0.995162i	$-0.531322\pi$
$191$	−10.5402	−	3.42473i	−0.762665	−	0.247805i	−0.664422	+	0.747358i	$0.731322\pi$
$192$	−4.48532	−	6.62434i	−0.323700	−	0.478070i
$193$	8.15394	−	11.2229i	0.586933	−	0.807844i	−0.407501	−	0.913205i	$-0.633600\pi$
$193$	8.15394	−	11.2229i	0.586933	−	0.807844i	0.994434	+	0.105361i	$0.0335997\pi$
$194$	−13.0314	+	5.71593i	−0.935597	+	0.410380i
$195$	0.541339	+	1.66607i	0.0387661	+	0.119310i
$196$	−4.09903	−	7.28433i	−0.292788	−	0.520309i
$197$		−	6.04339i		−	0.430574i	−0.976551	−	0.215287i	$-0.930931\pi$
$197$		−	6.04339i		−	0.430574i	0.976551	−	0.215287i	$-0.0690686\pi$
$198$	−3.96648	−	2.50341i	−0.281885	−	0.177909i
$199$			17.1475i			1.21556i	0.794107	+	0.607778i	$0.207939\pi$
$199$			17.1475i			1.21556i	−0.794107	+	0.607778i	$0.792061\pi$
$200$	−4.52826	+	13.1891i	−0.320196	+	0.932609i
$201$	−1.85224	−	5.70061i	−0.130647	−	0.402090i
$202$	−11.2421	−	25.6302i	−0.790995	−	1.80333i
$203$	−7.59955	+	10.4599i	−0.533384	+	0.734140i
$204$	6.33011	−	6.87605i	0.443196	−	0.481420i
$205$	1.49511	+	0.485792i	0.104423	+	0.0339292i
$206$	−8.19432	−	4.79152i	−0.570926	−	0.333841i
$207$	−0.449868	−	0.619190i	−0.0312680	−	0.0430367i
$208$	−6.08725	+	25.8204i	−0.422075	+	1.79032i
$209$	8.41778	−	10.7970i	0.582270	−	0.746846i
$210$	0.932781	−	0.830600i	0.0643680	−	0.0573169i
$211$	10.3629	−	7.52909i	0.713411	−	0.518324i	−0.170861	−	0.985295i	$-0.554655\pi$
$211$	10.3629	−	7.52909i	0.713411	−	0.518324i	0.884272	+	0.466972i	$0.154655\pi$
$212$	11.1400	−	2.23959i	0.765095	−	0.153816i
$213$	1.41710	−	4.36140i	0.0970983	−	0.298838i
$214$	1.71172	+	17.1989i	0.117011	+	1.17569i
$215$	−0.450701	−	0.327453i	−0.0307376	−	0.0223321i
$216$	2.70410	−	0.829356i	0.183991	−	0.0564305i
$217$	12.8582	−	4.17789i	0.872873	−	0.283614i
$218$	−0.631708	+	2.89330i	−0.0427847	+	0.195959i
$219$	15.0724			1.01850
$220$	0.783821	−	1.56702i	0.0528452	−	0.105649i
$221$	−30.9921			−2.08476
$222$	0.267573	−	1.22552i	0.0179583	−	0.0822516i
$223$	−1.94261	+	0.631192i	−0.130087	+	0.0422677i	−0.373337	−	0.927696i	$-0.621786\pi$
$223$	−1.94261	+	0.631192i	−0.130087	+	0.0422677i	0.243250	+	0.969964i	$0.421786\pi$
$224$	18.6021	−	3.42023i	1.24290	−	0.228524i
$225$	−3.98864	−	2.89792i	−0.265909	−	0.193194i
$226$	1.68871	+	16.9677i	0.112331	+	1.12868i
$227$	−5.65067	+	17.3910i	−0.375048	+	1.15428i	0.568398	+	0.822754i	$0.307564\pi$
$227$	−5.65067	+	17.3910i	−0.375048	+	1.15428i	−0.943446	+	0.331526i	$0.892436\pi$
$228$	1.62720	+	8.09385i	0.107764	+	0.536028i
$229$	−10.0961	+	7.33523i	−0.667168	+	0.484726i	−0.869076	−	0.494679i	$-0.835286\pi$
$229$	−10.0961	+	7.33523i	−0.667168	+	0.484726i	0.201908	+	0.979404i	$0.435286\pi$
$230$	0.213521	−	0.190131i	0.0140792	−	0.0125369i
$231$	9.18705	−	6.21044i	0.604464	−	0.408617i
$232$	−6.28132	−	8.95370i	−0.412389	−	0.587839i
$233$	−7.79576	−	10.7299i	−0.510717	−	0.702942i	0.473323	−	0.880889i	$-0.343054\pi$
$233$	−7.79576	−	10.7299i	−0.510717	−	0.702942i	−0.984040	+	0.177947i	$0.943054\pi$
$234$	−8.09657	−	4.73436i	−0.529289	−	0.309494i
$235$	−1.29826	−	0.421831i	−0.0846894	−	0.0275172i
$236$	14.6479	+	13.4849i	0.953497	+	0.877791i
$237$	−8.47885	+	11.6701i	−0.550761	+	0.758057i
$238$	8.87585	+	20.2355i	0.575336	+	1.31167i
$239$	−6.21895	−	19.1400i	−0.402271	−	1.23806i	−0.923153	−	0.384433i	$-0.874397\pi$
$239$	−6.21895	−	19.1400i	−0.402271	−	1.23806i	0.520882	−	0.853629i	$-0.325603\pi$
$240$	0.408325	+	0.974481i	0.0263573	+	0.0629024i
$241$			10.0285i			0.645994i	0.946400	+	0.322997i	$0.104690\pi$
$241$			10.0285i			0.645994i	−0.946400	+	0.322997i	$0.895310\pi$
$242$	8.74376	−	12.8665i	0.562070	−	0.827090i
$243$			1.00000i			0.0641500i
$244$	5.55404	−	3.12536i	0.355561	−	0.200081i
$245$	0.341127	+	1.04988i	0.0217938	+	0.0670744i
$246$	−7.70787	+	3.38089i	−0.491436	+	0.215558i
$247$	16.0915	−	22.1480i	1.02388	−	1.40925i
$248$	−0.189441	+	11.4355i	−0.0120295	+	0.726154i
$249$	0.583661	+	0.189643i	0.0369880	+	0.0120181i
$250$	1.87245	−	3.20221i	0.118424	−	0.202526i
$251$	−7.39146	−	10.1735i	−0.466545	−	0.642144i	0.509305	−	0.860586i	$-0.329902\pi$
$251$	−7.39146	−	10.1735i	−0.466545	−	0.642144i	−0.975850	+	0.218442i	$0.929902\pi$
$252$	−0.772386	+	6.64231i	−0.0486557	+	0.418426i
$253$	2.10299	−	1.42162i	0.132214	−	0.0893763i
$254$	−2.20719	−	2.47872i	−0.138491	−	0.155529i
$255$	−0.998616	+	0.725537i	−0.0625358	+	0.0454349i
$256$	−2.37348	+	15.8230i	−0.148342	+	0.988936i
$257$	0.311817	−	0.959673i	0.0194506	−	0.0598628i	−0.940860	−	0.338795i	$-0.889981\pi$
$257$	0.311817	−	0.959673i	0.0194506	−	0.0598628i	0.960311	+	0.278933i	$0.0899806\pi$
$258$	2.96802	−	0.295392i	0.184781	−	0.0183903i
$259$	2.39928	+	1.74318i	0.149084	+	0.108316i
$260$	1.46031	−	3.18479i	0.0905646	−	0.197512i
$261$	3.67765	−	1.19494i	0.227641	−	0.0739649i
$262$	19.0195	+	4.15260i	1.17503	+	0.256549i
$263$	14.7299			0.908282			0.454141	−	0.890930i	$-0.349946\pi$
$263$	14.7299			0.908282			0.454141	+	0.890930i	$0.349946\pi$
$264$	2.44526	+	9.05653i	0.150495	+	0.557391i
$265$	−1.50071			−0.0921877
$266$	−19.0694	−	4.16351i	−1.16922	−	0.255281i
$267$	−2.64417	+	0.859142i	−0.161820	+	0.0525787i
$268$	−4.99657	+	10.8970i	−0.305214	+	0.665641i
$269$	9.60330	+	6.97720i	0.585523	+	0.425408i	0.840711	−	0.541484i	$-0.182137\pi$
$269$	9.60330	+	6.97720i	0.585523	+	0.425408i	−0.255188	+	0.966892i	$0.582137\pi$
$270$	−0.371718	+	0.0369952i	−0.0226220	+	0.00225145i
$271$	4.35634	−	13.4074i	0.264629	−	0.814443i	−0.727150	−	0.686478i	$-0.759156\pi$
$271$	4.35634	−	13.4074i	0.264629	−	0.814443i	0.991779	−	0.127965i	$-0.0408444\pi$
$272$	−18.6285	+	1.54285i	−1.12952	+	0.0935493i
$273$	17.9396	−	13.0339i	1.08575	−	0.788845i
$274$	5.59420	+	6.28240i	0.337958	+	0.379534i
$275$	10.0539	−	12.8956i	0.606275	−	0.777636i
$276$	−0.176805	+	1.52048i	−0.0106424	+	0.0915220i
$277$	−12.0276	−	16.5545i	−0.722665	−	0.994664i	−0.999431	−	0.0337262i	$-0.989263\pi$
$277$	−12.0276	−	16.5545i	−0.722665	−	0.994664i	0.276766	−	0.960937i	$-0.410737\pi$
$278$	−5.39558	+	9.22738i	−0.323605	+	0.553421i
$279$	−3.84570	−	1.24954i	−0.230236	−	0.0748082i
$280$	−2.49764	−	0.0413762i	−0.149262	−	0.00247270i
$281$	−7.74854	+	10.6650i	−0.462239	+	0.636218i	−0.974971	−	0.222331i	$-0.928633\pi$
$281$	−7.74854	+	10.6650i	−0.462239	+	0.636218i	0.512732	+	0.858549i	$0.328633\pi$
$282$	6.69303	−	2.93576i	0.398564	−	0.174822i
$283$	1.28277	+	3.94797i	0.0762529	+	0.234682i	0.981916	−	0.189315i	$-0.0606267\pi$
$283$	1.28277	+	3.94797i	0.0762529	+	0.234682i	−0.905664	+	0.423997i	$0.860627\pi$
$284$	−7.99307	+	4.49785i	−0.474302	+	0.266898i
$285$		−	1.09035i		−	0.0645870i
$286$	16.6028	−	26.3059i	0.981742	−	1.55550i
$287$		−	19.8992i		−	1.17461i
$288$	−5.10231	−	2.44263i	−0.300657	−	0.143933i
$289$	−1.49490	−	4.60083i	−0.0879353	−	0.270637i
$290$	0.580235	+	1.32284i	0.0340726	+	0.0776798i
$291$	−5.91430	+	8.14034i	−0.346702	+	0.477195i
$292$	−22.1779	−	20.4170i	−1.29786	−	1.19481i
$293$	−7.59864	−	2.46895i	−0.443917	−	0.144237i	0.0785249	−	0.996912i	$-0.474979\pi$
$293$	−7.59864	−	2.46895i	−0.443917	−	0.144237i	−0.522442	+	0.852675i	$0.674979\pi$
$294$	−5.10208	−	2.98337i	−0.297559	−	0.173994i
$295$	−1.54559	−	2.12733i	−0.0899880	−	0.123858i
$296$	−2.05379	+	1.44080i	−0.119374	+	0.0837450i
$297$	−3.31472	−	0.112356i	−0.192340	−	0.00651955i
$298$	−18.7442	+	16.6909i	−1.08582	+	0.966876i
$299$	4.10651	−	2.98355i	0.237486	−	0.172543i
$300$	1.94347	+	9.66703i	0.112206	+	0.558126i
$301$	−2.17912	+	6.70663i	−0.125602	+	0.386564i
$302$	−1.90055	−	19.0962i	−0.109364	−	1.09886i
$303$	−16.0105	−	11.6323i	−0.919779	−	0.668259i
$304$	8.56957	−	14.1136i	0.491499	−	0.809473i
$305$	−0.800496	+	0.260097i	−0.0458363	+	0.0148931i
$306$	1.40970	−	6.45662i	0.0805873	−	0.369100i
$307$	−28.2669			−1.61328			−0.806639	−	0.591044i	$-0.798716\pi$
$307$	−28.2669			−1.61328			−0.806639	+	0.591044i	$0.798716\pi$
$308$	−21.9306	−	3.30655i	−1.24961	−	0.188408i
$309$	−6.71214			−0.381840
$310$	0.322205	−	1.47574i	0.0183000	−	0.0838165i
$311$	−12.2480	+	3.97962i	−0.694522	+	0.225664i	−0.634942	−	0.772560i	$-0.718976\pi$
$311$	−12.2480	+	3.97962i	−0.694522	+	0.225664i	−0.0595796	+	0.998224i	$0.518976\pi$
$312$	5.50034	+	17.9338i	0.311395	+	1.01530i
$313$	−7.79540	−	5.66369i	−0.440622	−	0.320131i	0.345260	−	0.938507i	$-0.387791\pi$
$313$	−7.79540	−	5.66369i	−0.440622	−	0.320131i	−0.785882	+	0.618376i	$0.787791\pi$
$314$	−2.02448	−	20.3415i	−0.114248	−	1.14793i
$315$	0.272915	−	0.839945i	0.0153770	−	0.0473255i
$316$	28.2842	−	5.68629i	1.59111	−	0.319879i
$317$	−5.37930	+	3.90829i	−0.302132	+	0.219512i	−0.728513	−	0.685032i	$-0.759788\pi$
$317$	−5.37930	+	3.90829i	−0.302132	+	0.219512i	0.426381	+	0.904544i	$0.359788\pi$
$318$	6.00058	−	5.34325i	0.336496	−	0.299634i
$319$	3.54769	+	12.3246i	0.198632	+	0.690047i
$320$	0.719206	−	1.98698i	0.0402049	−	0.111076i
$321$	7.18365	+	9.88744i	0.400952	+	0.551863i
$322$	−3.12410	−	1.82677i	−0.174099	−	0.101802i
$323$	18.3458	+	5.96092i	1.02079	+	0.331675i
$324$	1.35459	−	1.47142i	0.0752551	−	0.0817456i
$325$	19.2192	−	26.4529i	1.06609	−	1.46734i
$326$	3.56370	+	8.12463i	0.197375	+	0.449982i
$327$	0.647104	+	1.99158i	0.0357849	+	0.110135i
$328$	15.9213	+	5.46631i	0.879104	+	0.301826i
$329$			17.2792i			0.952633i
$330$	−0.0808640	−	1.23630i	−0.00445142	−	0.0680559i
$331$			4.25037i			0.233621i	0.993154	+	0.116811i	$0.0372671\pi$
$331$			4.25037i			0.233621i	−0.993154	+	0.116811i	$0.962733\pi$
$332$	−0.601922	−	1.06967i	−0.0330348	−	0.0587056i
$333$	−0.274094	−	0.843576i	−0.0150203	−	0.0462277i
$334$	3.04342	−	1.33493i	0.166529	−	0.0730442i
$335$	0.930619	−	1.28089i	0.0508451	−	0.0699823i
$336$	10.1341	−	8.72737i	0.552862	−	0.476117i
$337$	18.7683	+	6.09818i	1.02237	+	0.332189i	0.771770	−	0.635901i	$-0.219372\pi$
$337$	18.7683	+	6.09818i	1.02237	+	0.332189i	0.250602	+	0.968090i	$0.419372\pi$
$338$	22.1184	−	37.8263i	1.20308	−	2.05748i
$339$	7.08708	+	9.75454i	0.384918	+	0.529794i
$340$	2.45219	+	0.285148i	0.132989	+	0.0154643i
$341$	4.57397	−	12.6070i	0.247695	−	0.682709i
$342$	3.88219	+	4.35978i	0.209925	+	0.235750i
$343$	−7.63014	+	5.54362i	−0.411989	+	0.299328i
$344$	−4.76735	−	3.58581i	−0.257038	−	0.193334i
$345$	0.0624723	−	0.192270i	0.00336339	−	0.0103515i
$346$	−22.9731	+	2.28639i	−1.23504	+	0.122917i
$347$	7.87165	+	5.71909i	0.422572	+	0.307017i	0.778672	−	0.627431i	$-0.215894\pi$
$347$	7.87165	+	5.71909i	0.422572	+	0.307017i	−0.356100	+	0.934448i	$0.615894\pi$
$348$	−7.03002	−	3.22345i	−0.376849	−	0.172795i
$349$	−18.2493	+	5.92957i	−0.976865	+	0.317403i	−0.753584	−	0.657352i	$-0.771677\pi$
$349$	−18.2493	+	5.92957i	−0.976865	+	0.317403i	−0.223281	+	0.974754i	$0.571677\pi$
$350$	−22.7759	−	4.97276i	−1.21742	−	0.265805i
$351$	−6.63206			−0.353993
$352$	8.66990	−	16.6383i	0.462107	−	0.886824i
$353$	−2.30703			−0.122791			−0.0613955	−	0.998114i	$-0.519555\pi$
$353$	−2.30703			−0.122791			−0.0613955	+	0.998114i	$0.519555\pi$
$354$	13.7544	+	3.00305i	0.731037	+	0.159611i
$355$	1.15203	−	0.374318i	0.0611435	−	0.0198667i
$356$	5.05447	+	2.31761i	0.267887	+	0.122833i
$357$	12.6405	+	9.18389i	0.669009	+	0.486063i
$358$	−34.5344	+	3.43703i	−1.82520	+	0.181653i
$359$	−5.45434	+	16.7867i	−0.287869	+	0.885971i	0.697655	+	0.716434i	$0.254227\pi$
$359$	−5.45434	+	16.7867i	−0.287869	+	0.885971i	−0.985524	+	0.169536i	$0.945773\pi$
$360$	0.597067	+	0.449091i	0.0314682	+	0.0236691i
$361$	1.58605	−	1.15233i	0.0834765	−	0.0606492i
$362$	12.3701	+	13.8919i	0.650157	+	0.730140i
$363$	0.744857	−	10.9748i	0.0390948	−	0.576025i
$364$	−44.0522	−	5.12251i	−2.30896	−	0.268493i
$365$	2.34013	+	3.22092i	0.122488	+	0.168590i
$366$	2.27471	−	3.89015i	0.118901	−	0.203342i
$367$	−5.96243	−	1.93731i	−0.311236	−	0.101127i	0.149234	−	0.988802i	$-0.452319\pi$
$367$	−5.96243	−	1.93731i	−0.311236	−	0.101127i	−0.460470	+	0.887675i	$0.652319\pi$
$368$	2.31978	−	1.99776i	0.120927	−	0.104141i
$369$	−3.49823	+	4.81490i	−0.182111	+	0.250654i
$370$	0.303432	−	0.133094i	0.0157747	−	0.00691923i
$371$	5.87010	+	18.0663i	0.304760	+	0.937956i
$372$	3.96602	+	7.04796i	0.205629	+	0.365420i
$373$			0.0244567i			0.00126632i	1.00000		0.000633161i	$0.000201541\pi$
$373$			0.0244567i			0.00126632i	−1.00000		0.000633161i	$0.999798\pi$
$374$	21.2435	+	5.39821i	1.09848	+	0.279135i
$375$		−	2.62300i		−	0.135451i
$376$	−13.8250	−	4.74660i	−0.712971	−	0.244787i
$377$	7.92492	+	24.3904i	0.408154	+	1.25617i
$378$	1.89936	+	4.33023i	0.0976926	+	0.222723i
$379$	−18.8371	+	25.9270i	−0.967596	+	1.33178i	−0.0243438	+	0.999704i	$0.507750\pi$
$379$	−18.8371	+	25.9270i	−0.967596	+	1.33178i	−0.943252	+	0.332078i	$0.892250\pi$
$380$	−1.47698	+	1.60437i	−0.0757677	+	0.0823024i
$381$	−2.23202	−	0.725227i	−0.114350	−	0.0371545i
$382$	13.5300	+	7.91145i	0.692253	+	0.404785i
$383$	20.7395	+	28.5454i	1.05974	+	1.45860i	0.880052	+	0.474878i	$0.157508\pi$
$383$	20.7395	+	28.5454i	1.05974	+	1.45860i	0.179685	+	0.983724i	$0.442492\pi$
$384$	4.19888	+	10.5057i	0.214273	+	0.536116i
$385$	2.75352	+	0.999008i	0.140332	+	0.0509142i
$386$	−14.6516	+	13.0466i	−0.745745	+	0.664053i
$387$	1.70628	−	1.23968i	0.0867350	−	0.0630167i
$388$	19.7293	−	3.96639i	1.00160	−	0.201363i
$389$	2.94817	−	9.07354i	0.149478	−	0.460047i	−0.848081	−	0.529866i	$-0.822242\pi$
$389$	2.94817	−	9.07354i	0.149478	−	0.460047i	0.997560	+	0.0698193i	$0.0222423\pi$
$390$	−0.245354	−	2.46526i	−0.0124240	−	0.124833i
$391$	2.89352	+	2.10226i	0.146332	+	0.106316i
$392$	3.46606	+	11.3010i	0.175062	+	0.570789i
$393$	13.0919	−	4.25381i	0.660397	−	0.214576i
$394$	−1.82308	+	8.34994i	−0.0918454	+	0.420664i
$395$	−3.81028			−0.191716
$396$	4.72515	+	4.65542i	0.237448	+	0.233944i
$397$	−8.04088			−0.403560			−0.201780	−	0.979431i	$-0.564673\pi$
$397$	−8.04088			−0.403560			−0.201780	+	0.979431i	$0.564673\pi$
$398$	5.17281	−	23.6921i	0.259289	−	1.18758i
$399$	−13.1263	+	4.26498i	−0.657135	+	0.213516i
$400$	10.2352	−	16.8569i	0.511761	−	0.842844i
$401$	30.1047	+	21.8724i	1.50336	+	1.09225i	0.969020	+	0.246983i	$0.0794390\pi$
$401$	30.1047	+	21.8724i	1.50336	+	1.09225i	0.534338	+	0.845271i	$0.320561\pi$
$402$	0.839501	+	8.43508i	0.0418705	+	0.420704i
$403$	8.28705	−	25.5049i	0.412807	−	1.27049i
$404$	7.80114	+	38.8037i	0.388121	+	1.93056i
$405$	−0.213696	+	0.155259i	−0.0106186	+	0.00771489i
$406$	13.6554	−	12.1595i	0.677707	−	0.603468i
$407$	2.82702	−	0.813766i	0.140130	−	0.0403369i
$408$	−10.8204	+	7.59083i	−0.535687	+	0.375802i
$409$	−6.07530	−	8.36194i	−0.300404	−	0.413471i	0.631954	−	0.775006i	$-0.282253\pi$
$409$	−6.07530	−	8.36194i	−0.300404	−	0.413471i	−0.932359	+	0.361534i	$0.882253\pi$
$410$	−1.91920	−	1.12223i	−0.0947826	−	0.0554228i
$411$	5.65713	+	1.83811i	0.279046	+	0.0906674i
$412$	9.87638	+	9.09221i	0.486574	+	0.447941i
$413$	−19.5642	+	26.9279i	−0.962693	+	1.32503i
$414$	0.434779	+	0.991223i	0.0213682	+	0.0487159i
$415$	0.0500928	+	0.154170i	0.00245896	+	0.00756790i
$416$	16.1997	−	33.8389i	0.794253	−	1.65909i
$417$			7.55833i			0.370133i
$418$	−14.8876	+	12.3785i	−0.728178	+	0.605454i
$419$			2.33902i			0.114269i	0.998366	+	0.0571343i	$0.0181963\pi$
$419$			2.33902i			0.114269i	−0.998366	+	0.0571343i	$0.981804\pi$
$420$	−1.53935	+	0.866224i	−0.0751128	+	0.0422674i
$421$	4.01513	+	12.3573i	0.195686	+	0.602258i	0.999968	+	0.00801103i	$0.00255002\pi$
$421$	4.01513	+	12.3573i	0.195686	+	0.602258i	−0.804282	+	0.594247i	$0.797450\pi$
$422$	−16.5893	+	7.27655i	−0.807555	+	0.354217i
$423$	3.03764	−	4.18096i	0.147695	−	0.203285i
$424$	−16.0673	−	0.266173i	−0.780297	−	0.0129265i
$425$	21.9117	+	7.11954i	1.06287	+	0.345348i
$426$	−3.27364	+	5.59850i	−0.158609	+	0.271248i
$427$	6.26237	+	8.61942i	0.303057	+	0.417123i
$428$	2.82329	−	24.2795i	0.136469	−	1.17359i
$429$	0.745151	−	21.9834i	0.0359763	−	1.06137i
$430$	0.523937	+	0.588392i	0.0252665	+	0.0283748i
$431$	−22.6258	+	16.4386i	−1.08985	+	0.791821i	−0.979374	−	0.202058i	$-0.935237\pi$
$431$	−22.6258	+	16.4386i	−1.08985	+	0.791821i	−0.110474	+	0.993879i	$0.535237\pi$
$432$	−3.98635	+	0.330158i	−0.191793	+	0.0158848i
$433$	9.68478	−	29.8067i	0.465421	−	1.43242i	−0.393032	−	0.919525i	$-0.628574\pi$
$433$	9.68478	−	29.8067i	0.465421	−	1.43242i	0.858453	−	0.512893i	$-0.171426\pi$
$434$	−19.0261	+	1.89357i	−0.913281	+	0.0908942i
$435$	0.826342	+	0.600373i	0.0396201	+	0.0287857i
$436$	1.74562	−	3.80701i	0.0835999	−	0.182323i
$437$	−3.00470	+	0.976287i	−0.143734	+	0.0467021i
$438$	−20.8250	−	4.54682i	−0.995059	−	0.217256i
$439$	−1.92512			−0.0918811			−0.0459405	−	0.998944i	$-0.514628\pi$
$439$	−1.92512			−0.0918811			−0.0459405	+	0.998944i	$0.514628\pi$
$440$	−1.55569	+	1.92865i	−0.0741648	+	0.0919448i
$441$	−4.17922			−0.199010
$442$	42.8207	+	9.34924i	2.03677	+	0.444698i
$443$	25.8441	−	8.39727i	1.22789	−	0.398966i	0.377942	−	0.925829i	$-0.376632\pi$
$443$	25.8441	−	8.39727i	1.22789	−	0.398966i	0.849950	+	0.526863i	$0.176632\pi$
$444$	−0.739393	+	1.61254i	−0.0350901	+	0.0765278i
$445$	−0.594127	−	0.431658i	−0.0281643	−	0.0204626i
$446$	2.87444	−	0.286079i	0.136109	−	0.0135462i
$447$	−5.48420	+	16.8786i	−0.259394	+	0.798333i
$448$	−26.7336	−	0.885986i	−1.26304	−	0.0418589i
$449$	8.13130	−	5.90774i	0.383740	−	0.278803i	−0.379146	−	0.925337i	$-0.623782\pi$
$449$	8.13130	−	5.90774i	0.383740	−	0.278803i	0.762885	+	0.646534i	$0.223782\pi$
$450$	4.63676	+	5.20718i	0.218579	+	0.245469i
$451$	−15.5670	−	12.1366i	−0.733021	−	0.571492i
$452$	2.78534	−	23.9531i	0.131011	−	1.12666i
$453$	−7.97610	−	10.9782i	−0.374750	−	0.515799i
$454$	13.0536	−	22.3239i	0.612635	−	1.04771i
$455$	5.57057	+	1.80999i	0.261152	+	0.0848535i
$456$	0.193390	−	11.6739i	0.00905633	−	0.546678i
$457$	5.80668	−	7.99221i	0.271625	−	0.373860i	−0.651312	−	0.758810i	$-0.725781\pi$
$457$	5.80668	−	7.99221i	0.271625	−	0.373860i	0.922937	+	0.384950i	$0.125781\pi$
$458$	16.1622	−	7.08920i	0.755210	−	0.331257i
$459$	−1.44406	−	4.44436i	−0.0674029	−	0.207445i
$460$	−0.352370	+	0.198285i	−0.0164293	+	0.00924510i
$461$			23.0867i			1.07526i	0.843182	+	0.537628i	$0.180679\pi$
$461$			23.0867i			1.07526i	−0.843182	+	0.537628i	$0.819321\pi$
$462$	−14.5669	+	5.80933i	−0.677713	+	0.270274i
$463$			5.87663i			0.273110i	0.990632	+	0.136555i	$0.0436031\pi$
$463$			5.87663i			0.273110i	−0.990632	+	0.136555i	$0.956397\pi$
$464$	5.97765	+	14.2659i	0.277506	+	0.662276i
$465$	−0.330058	−	1.01581i	−0.0153061	−	0.0471072i
$466$	7.53428	+	17.1769i	0.349019	+	0.795704i
$467$	−2.22211	+	3.05847i	−0.102827	+	0.141529i	−0.857330	−	0.514768i	$-0.827878\pi$
$467$	−2.22211	+	3.05847i	−0.102827	+	0.141529i	0.754503	+	0.656297i	$0.227878\pi$
$468$	9.75856	+	8.98375i	0.451090	+	0.415274i
$469$	−19.0602	−	6.19302i	−0.880117	−	0.285967i
$470$	1.66651	+	0.974470i	0.0768705	+	0.0449490i
$471$	−8.49623	−	11.6941i	−0.391485	−	0.538833i
$472$	−16.1706	−	23.0503i	−0.744311	−	1.06098i
$473$	3.91750	+	5.79513i	0.180127	+	0.266460i
$474$	15.2354	−	13.5664i	0.699785	−	0.623128i
$475$	−16.4647	+	11.9623i	−0.755452	+	0.548868i
$476$	−6.15913	−	30.6362i	−0.282303	−	1.40421i
$477$	1.75566	−	5.40336i	0.0803860	−	0.247403i
$478$	2.81865	+	28.3211i	0.128922	+	1.29538i
$479$	−17.5590	−	12.7573i	−0.802290	−	0.582898i	0.109295	−	0.994009i	$-0.465141\pi$
$479$	−17.5590	−	12.7573i	−0.802290	−	0.582898i	−0.911585	+	0.411112i	$0.865141\pi$
$480$	−0.270201	−	1.46958i	−0.0123330	−	0.0670770i
$481$	5.59465	−	1.81781i	0.255094	−	0.0828851i
$482$	3.02526	−	13.8561i	0.137797	−	0.631127i
$483$	−2.55901			−0.116439
$484$	−15.9623	+	15.1395i	−0.725560	+	0.688159i
$485$	−2.65781			−0.120685
$486$	0.301665	−	1.38167i	0.0136838	−	0.0626736i
$487$	7.27475	−	2.36371i	0.329651	−	0.107110i	−0.139516	−	0.990220i	$-0.544555\pi$
$487$	7.27475	−	2.36371i	0.329651	−	0.107110i	0.469166	+	0.883110i	$0.344555\pi$
$488$	−8.61663	+	2.64275i	−0.390057	+	0.119631i
$489$	5.07524	+	3.68738i	0.229510	+	0.166749i
$490$	−0.154611	−	1.55349i	−0.00698461	−	0.0701795i
$491$	7.07668	−	21.7798i	0.319366	−	0.982908i	−0.654553	−	0.756016i	$-0.727143\pi$
$491$	7.07668	−	21.7798i	0.319366	−	0.982908i	0.973920	−	0.226893i	$-0.0728567\pi$
$492$	11.6696	−	2.34607i	0.526106	−	0.105769i
$493$	−14.6192	+	10.6215i	−0.658416	+	0.478367i
$494$	−28.9143	+	25.7469i	−1.30092	+	1.15841i
$495$	−0.490631	−	0.725787i	−0.0220522	−	0.0326217i
$496$	3.71143	−	15.7429i	0.166648	−	0.706875i
$497$	−9.01247	−	12.4046i	−0.404264	−	0.556422i
$498$	−0.749215	−	0.438093i	−0.0335731	−	0.0196314i
$499$	−36.2914	−	11.7918i	−1.62462	−	0.527873i	−0.651598	−	0.758564i	$-0.725901\pi$
$499$	−36.2914	−	11.7918i	−1.62462	−	0.527873i	−0.973027	+	0.230692i	$0.925901\pi$
$500$	−3.55309	+	3.85953i	−0.158899	+	0.172604i
$501$	1.38126	−	1.90114i	0.0617102	−	0.0849368i
$502$	7.14354	+	16.2861i	0.318832	+	0.726883i
$503$	−0.902960	−	2.77903i	−0.0402610	−	0.123911i	0.928906	−	0.370316i	$-0.120751\pi$
$503$	−0.902960	−	2.77903i	−0.0402610	−	0.123911i	−0.969167	+	0.246405i	$0.920751\pi$
$504$	3.07093	−	8.94445i	0.136790	−	0.398417i
$505$		−	5.22740i		−	0.232616i
$506$	−3.33448	+	1.32980i	−0.148236	+	0.0591169i
$507$		−	30.9843i		−	1.37606i
$508$	2.30185	+	4.09059i	0.102128	+	0.181491i
$509$	−9.59462	−	29.5292i	−0.425274	−	1.30886i	−0.902732	−	0.430204i	$-0.858442\pi$
$509$	−9.59462	−	29.5292i	−0.425274	−	1.30886i	0.477457	−	0.878655i	$-0.341558\pi$
$510$	1.59862	−	0.701202i	0.0707882	−	0.0310497i
$511$	29.6215	−	40.7705i	1.31038	−	1.80358i
$512$	8.05259	−	21.1461i	0.355878	−	0.934533i
$513$	3.92586	+	1.27559i	0.173331	+	0.0563187i
$514$	−0.720326	+	1.23188i	−0.0317722	+	0.0543360i
$515$	−1.04212	−	1.43436i	−0.0459213	−	0.0632053i
$516$	−4.18992	−	0.487215i	−0.184451	−	0.0214485i
$517$	13.5174	+	10.5387i	0.594495	+	0.463491i
$518$	−2.78915	−	3.13227i	−0.122548	−	0.137624i
$519$	−13.2069	+	9.59541i	−0.579721	+	0.421192i
$520$	−2.97840	+	3.95978i	−0.130611	+	0.173648i
$521$	0.962822	−	2.96326i	0.0421820	−	0.129823i	−0.927748	−	0.373208i	$-0.878258\pi$
$521$	0.962822	−	2.96326i	0.0421820	−	0.129823i	0.969930	+	0.243385i	$0.0782578\pi$
$522$	−5.44175	+	0.541589i	−0.238179	+	0.0237047i
$523$	31.4971	+	22.8840i	1.37727	+	1.00065i	0.997129	+	0.0757180i	$0.0241249\pi$
$523$	31.4971	+	22.8840i	1.37727	+	1.00065i	0.380142	+	0.924928i	$0.375875\pi$
$524$	−25.0258	−	11.4750i	−1.09326	−	0.501288i
$525$	−15.6776	+	5.09396i	−0.684226	+	0.222318i
$526$	−20.3517	−	4.44348i	−0.887378	−	0.193745i
$527$	18.8961			0.823126
$528$	−0.646493	−	13.2507i	−0.0281350	−	0.576664i
$529$	22.4142			0.974531
$530$	2.07347	+	0.452711i	0.0900660	+	0.0196645i
$531$	9.46770	−	3.07624i	0.410863	−	0.133498i
$532$	25.0916	+	11.5051i	1.08786	+	0.498811i
$533$	−31.9327	−	23.2005i	−1.38316	−	1.00492i
$534$	3.91253	−	0.389394i	0.169312	−	0.0168507i
$535$	−0.997579	+	3.07023i	−0.0431291	+	0.132738i
$536$	10.1908	−	13.5487i	0.440177	−	0.585216i
$537$	−19.8534	+	14.4243i	−0.856737	+	0.622456i
$538$	−11.1638	−	12.5371i	−0.481304	−	0.540514i
$539$	0.469560	−	13.8529i	0.0202254	−	0.596689i
$540$	0.524749	+	0.0610193i	0.0225816	+	0.00262585i
$541$	−3.61016	−	4.96896i	−0.155213	−	0.213632i	0.724328	−	0.689456i	$-0.242150\pi$
$541$	−3.61016	−	4.96896i	−0.155213	−	0.213632i	−0.879541	+	0.475823i	$0.842150\pi$
$542$	−10.0635	+	17.2104i	−0.432266	+	0.739251i
$543$	12.5092	+	4.06450i	0.536823	+	0.174424i
$544$	26.2038	+	3.48786i	1.12348	+	0.149541i
$545$	−0.325124	+	0.447494i	−0.0139268	+	0.0191686i
$546$	−28.7183	+	12.5967i	−1.22903	+	0.539089i
$547$	−7.06160	−	21.7334i	−0.301932	−	0.929252i	−0.980804	−	0.194996i	$-0.937531\pi$
$547$	−7.06160	−	21.7334i	−0.301932	−	0.929252i	0.678872	−	0.734257i	$-0.262469\pi$
$548$	−5.83412	−	10.3677i	−0.249221	−	0.442888i
$549$		−	3.18650i		−	0.135997i
$550$	−17.7813	+	14.7845i	−0.758198	+	0.630414i
$551$		−	15.9622i		−	0.680012i
$552$	0.702960	−	2.04745i	0.0299200	−	0.0871454i
$553$	14.9041	+	45.8702i	0.633788	+	1.95060i
$554$	11.6241	+	26.5011i	0.493862	+	1.12592i
$555$	0.137713	−	0.189546i	0.00584559	−	0.00804577i
$556$	10.2385	−	11.1215i	0.434207	−	0.471656i
$557$	−17.3847	−	5.64864i	−0.736615	−	0.239341i	−0.0834032	−	0.996516i	$-0.526579\pi$
$557$	−17.3847	−	5.64864i	−0.736615	−	0.239341i	−0.653212	+	0.757175i	$0.726579\pi$
$558$	4.93652	+	2.88656i	0.208980	+	0.122198i
$559$	8.22167	+	11.3162i	0.347739	+	0.478622i
$560$	3.43842	+	0.810618i	0.145300	+	0.0342549i
$561$	14.8940	−	4.28730i	0.628827	−	0.181010i
$562$	13.9231	−	12.3979i	0.587312	−	0.522975i
$563$	−13.4244	+	9.75341i	−0.565772	+	0.411057i	−0.833567	−	0.552419i	$-0.813705\pi$
$563$	−13.4244	+	9.75341i	−0.565772	+	0.411057i	0.267795	+	0.963476i	$0.413705\pi$
$564$	−10.1331	+	2.03718i	−0.426682	+	0.0857807i
$565$	−0.984169	+	3.02896i	−0.0414043	+	0.127429i
$566$	−0.581398	−	5.84173i	−0.0244380	−	0.245546i
$567$	2.70498	+	1.96528i	0.113598	+	0.0825340i
$568$	12.4006	−	3.80330i	0.520317	−	0.159583i
$569$	−39.2099	+	12.7401i	−1.64376	+	0.534091i	−0.977375	−	0.211513i	$-0.932161\pi$
$569$	−39.2099	+	12.7401i	−1.64376	+	0.534091i	−0.666389	+	0.745604i	$0.732161\pi$
$570$	−0.328922	+	1.50650i	−0.0137770	+	0.0631005i
$571$	8.89753			0.372350			0.186175	−	0.982517i	$-0.440391\pi$
$571$	8.89753			0.372350			0.186175	+	0.982517i	$0.440391\pi$
$572$	−30.8750	+	31.3375i	−1.29095	+	1.31029i
$573$	11.0827			0.462985
$574$	−6.00289	+	27.4940i	−0.250556	+	1.14758i
$575$	−3.58872	+	1.16605i	−0.149660	+	0.0486275i
$576$	6.31283	+	4.91408i	0.263035	+	0.204753i
$577$	−16.3150	−	11.8536i	−0.679204	−	0.493470i	0.193890	−	0.981023i	$-0.437890\pi$
$577$	−16.3150	−	11.8536i	−0.679204	−	0.493470i	−0.873093	+	0.487553i	$0.837890\pi$
$578$	0.677542	+	6.80776i	0.0281820	+	0.283166i
$579$	−4.28678	+	13.1933i	−0.178152	+	0.548297i
$580$	−0.402637	−	2.00276i	−0.0167186	−	0.0831600i
$581$	1.66004	−	1.20609i	0.0688699	−	0.0500369i
$582$	10.6272	−	9.46308i	0.440513	−	0.392257i
$583$	17.7134	+	6.42661i	0.733612	+	0.266163i
$584$	24.4833	+	34.8997i	1.01313	+	1.44416i
$585$	−1.02969	−	1.41725i	−0.0425724	−	0.0585959i
$586$	9.75398	+	5.70350i	0.402933	+	0.235610i
$587$	0.526749	+	0.171151i	0.0217413	+	0.00706417i	0.319867	−	0.947462i	$-0.396362\pi$
$587$	0.526749	+	0.171151i	0.0217413	+	0.00706417i	−0.298126	+	0.954526i	$0.596362\pi$
$588$	6.14939	+	5.66114i	0.253597	+	0.233461i
$589$	−9.81107	+	13.5038i	−0.404258	+	0.556414i
$590$	1.49375	+	3.40551i	0.0614969	+	0.140202i
$591$	1.86751	+	5.74760i	0.0768191	+	0.236425i
$592$	3.27230	−	1.37115i	0.134491	−	0.0563539i
$593$		−	34.6597i		−	1.42330i	−0.702533	−	0.711651i	$-0.747948\pi$
$593$		−	34.6597i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$594$	4.54594	+	1.15517i	0.186522	+	0.0473973i
$595$			4.12712i			0.169195i
$596$	30.9333	−	17.4067i	1.26708	−	0.713007i
$597$	−5.29887	−	16.3083i	−0.216868	−	0.667453i
$598$	−6.57385	+	2.88348i	−0.268825	+	0.117914i
$599$	19.4341	−	26.7488i	0.794057	−	1.09293i	−0.199535	−	0.979891i	$-0.563943\pi$
$599$	19.4341	−	26.7488i	0.794057	−	1.09293i	0.993591	−	0.113034i	$-0.0360570\pi$
$600$	0.230979	−	13.9429i	0.00942969	−	0.569216i
$601$	−10.1517	−	3.29847i	−0.414095	−	0.134548i	0.0945579	−	0.995519i	$-0.469856\pi$
$601$	−10.1517	−	3.29847i	−0.414095	−	0.134548i	−0.508653	+	0.860972i	$0.669856\pi$
$602$	5.03397	−	8.60896i	0.205169	−	0.350875i
$603$	3.52317	+	4.84923i	0.143475	+	0.197476i
$604$	−3.13473	+	26.9579i	−0.127550	+	1.09690i
$605$	2.46091	−	1.54476i	0.100050	−	0.0628033i
$606$	18.6121	+	20.9018i	0.756064	+	0.849076i
$607$	6.00393	−	4.36211i	0.243692	−	0.177053i	−0.459235	−	0.888315i	$-0.651876\pi$
$607$	6.00393	−	4.36211i	0.243692	−	0.177053i	0.702927	+	0.711262i	$0.251876\pi$
$608$	−16.0979	+	16.9152i	−0.652855	+	0.686001i
$609$	3.99532	−	12.2963i	0.161899	−	0.498273i
$610$	1.18448	−	0.117885i	0.0479582	−	0.00477303i
$611$	27.7284	+	20.1458i	1.12177	+	0.815014i
$612$	−3.89547	+	8.49563i	−0.157465	+	0.343415i
$613$	8.38874	−	2.72567i	0.338818	−	0.110089i	−0.134666	−	0.990891i	$-0.542996\pi$
$613$	8.38874	−	2.72567i	0.338818	−	0.110089i	0.473484	+	0.880802i	$0.342996\pi$
$614$	39.0554	+	8.52714i	1.57615	+	0.344127i
$615$	−1.57206			−0.0633914
$616$	29.3033	+	11.1842i	1.18066	+	0.450626i
$617$	30.1412			1.21344			0.606719	−	0.794917i	$-0.292485\pi$
$617$	30.1412			1.21344			0.606719	+	0.794917i	$0.292485\pi$
$618$	9.27392	+	2.02482i	0.373052	+	0.0814501i
$619$	−7.17057	+	2.32986i	−0.288210	+	0.0936450i	−0.449554	−	0.893253i	$-0.648417\pi$
$619$	−7.17057	+	2.32986i	−0.288210	+	0.0936450i	0.161344	+	0.986898i	$0.448417\pi$
$620$	−0.890359	+	1.94178i	−0.0357577	+	0.0779838i
$621$	0.619190	+	0.449868i	0.0248472	+	0.0180526i
$622$	18.1232	−	1.80371i	0.726673	−	0.0723221i
$623$	−2.87257	+	8.84087i	−0.115087	+	0.354202i
$624$	−2.18963	−	26.4377i	−0.0876555	−	1.05836i
$625$	−19.3827	+	14.0823i	−0.775307	+	0.563293i
$626$	9.06209	+	10.1769i	0.362194	+	0.406752i
$627$	−4.66932	+	12.8698i	−0.186475	+	0.513971i
$628$	−3.33915	+	28.7158i	−0.133247	+	1.14588i
$629$	2.43635	+	3.35334i	0.0971435	+	0.133707i
$630$	−0.630458	+	1.07819i	−0.0251181	+	0.0429562i
$631$	−39.5316	−	12.8446i	−1.57373	−	0.511336i	−0.613297	−	0.789852i	$-0.710157\pi$
$631$	−39.5316	−	12.8446i	−1.57373	−	0.511336i	−0.960431	+	0.278516i	$0.910157\pi$
$632$	−40.7947	−	0.675809i	−1.62273	−	0.0268823i
$633$	−7.52909	+	10.3629i	−0.299254	+	0.411888i
$634$	8.61139	−	3.77720i	0.342002	−	0.150012i
$635$	−0.191563	−	0.589571i	−0.00760196	−	0.0233964i
$636$	−9.90266	+	5.57241i	−0.392666	+	0.220960i
$637$		−	27.7169i		−	1.09818i
$638$	−1.18380	−	18.0987i	−0.0468673	−	0.716535i
$639$			4.58584i			0.181413i
$640$	−1.59311	+	2.52839i	−0.0629730	+	0.0999433i
$641$	−8.25277	−	25.3994i	−0.325965	−	1.00322i	−0.971003	−	0.239066i	$-0.923159\pi$
$641$	−8.25277	−	25.3994i	−0.325965	−	1.00322i	0.645039	−	0.764150i	$-0.276841\pi$
$642$	−6.94270	−	15.8282i	−0.274007	−	0.624689i
$643$	9.57732	−	13.1820i	0.377693	−	0.519849i	−0.577279	−	0.816547i	$-0.695885\pi$
$643$	9.57732	−	13.1820i	0.377693	−	0.519849i	0.954971	+	0.296698i	$0.0958854\pi$
$644$	3.76538	+	3.46642i	0.148377	+	0.136596i
$645$	0.529831	+	0.172152i	0.0208621	+	0.00677850i
$646$	−23.5496	−	13.7703i	−0.926547	−	0.541785i
$647$	−2.85269	−	3.92639i	−0.112151	−	0.154362i	0.749252	−	0.662285i	$-0.230413\pi$
$647$	−2.85269	−	3.92639i	−0.112151	−	0.154362i	−0.861402	+	0.507923i	$0.830413\pi$
$648$	−2.31547	+	1.62438i	−0.0909602	+	0.0638116i
$649$	9.13314	+	31.7284i	0.358507	+	1.24545i
$650$	−34.5344	+	30.7513i	−1.35455	+	1.20617i
$651$	−10.9379	+	7.94682i	−0.428688	+	0.311460i
$652$	−2.47292	−	12.3006i	−0.0968469	−	0.481727i
$653$	1.84727	−	5.68532i	0.0722893	−	0.222484i	−0.908384	−	0.418138i	$-0.862683\pi$
$653$	1.84727	−	5.68532i	0.0722893	−	0.222484i	0.980673	+	0.195654i	$0.0626830\pi$
$654$	−0.293290	−	2.94691i	−0.0114686	−	0.115233i
$655$	2.94165	+	2.13724i	0.114940	+	0.0835087i
$656$	−20.3488	−	12.3555i	−0.794489	−	0.482401i
$657$	−14.3347	+	4.65764i	−0.559251	+	0.181712i
$658$	5.21253	−	23.8741i	0.203206	−	0.930708i
$659$	−38.6071			−1.50392			−0.751959	−	0.659209i	$-0.770891\pi$
$659$	−38.6071			−1.50392			−0.751959	+	0.659209i	$0.770891\pi$
$660$	−0.261221	+	1.73254i	−0.0101680	+	0.0674391i
$661$	38.4608			1.49595			0.747975	−	0.663727i	$-0.231026\pi$
$661$	38.4608			1.49595			0.747975	+	0.663727i	$0.231026\pi$
$662$	1.28219	−	5.87259i	0.0498336	−	0.228245i
$663$	29.4753	−	9.57709i	1.14472	−	0.371943i
$664$	0.508973	+	1.65950i	0.0197520	+	0.0644011i
$665$	−2.94938	−	2.14285i	−0.114372	−	0.0830962i
$666$	0.124229	+	1.24822i	0.00481379	+	0.0483677i
$667$	0.914560	−	2.81473i	0.0354119	−	0.108987i
$668$	−4.60769	+	0.926335i	−0.178277	+	0.0358410i
$669$	1.65248	−	1.20060i	0.0638886	−	0.0464178i
$670$	−1.67220	+	1.48902i	−0.0646028	+	0.0575259i
$671$	10.5624	+	0.358023i	0.407756	+	0.0138213i
$672$	−16.6347	+	9.00119i	−0.641698	+	0.347228i
$673$	4.48381	+	6.17144i	0.172838	+	0.237891i	0.886644	−	0.462452i	$-0.153030\pi$
$673$	4.48381	+	6.17144i	0.172838	+	0.237891i	−0.713806	+	0.700343i	$0.753030\pi$
$674$	−24.0918	−	14.0874i	−0.927983	−	0.542625i
$675$	4.68893	+	1.52352i	0.180477	+	0.0586405i
$676$	−41.9711	+	45.5909i	−1.61427	+	1.75350i
$677$	−4.43491	+	6.10413i	−0.170448	+	0.234601i	−0.885692	−	0.464274i	$-0.846315\pi$
$677$	−4.43491	+	6.10413i	−0.170448	+	0.234601i	0.715244	+	0.698875i	$0.246315\pi$
$678$	−6.84937	−	15.6154i	−0.263049	−	0.599707i
$679$	10.3962	+	31.9961i	0.398968	+	1.22790i
$680$	−3.30209	−	1.13372i	−0.126629	−	0.0434761i
$681$		−	18.2860i		−	0.700720i
$682$	−10.1228	+	16.0389i	−0.387622	+	0.614160i
$683$		−	10.7849i		−	0.412674i	−0.978481	−	0.206337i	$-0.933846\pi$
$683$		−	10.7849i		−	0.412674i	0.978481	−	0.206337i	$-0.0661543\pi$
$684$	−4.04869	−	7.19487i	−0.154806	−	0.275103i
$685$	0.485524	+	1.49429i	0.0185509	+	0.0570939i
$686$	12.2146	−	5.35768i	0.466356	−	0.204557i
$687$	7.33523	−	10.0961i	0.279857	−	0.385190i
$688$	5.50516	+	6.39254i	0.209882	+	0.243713i
$689$	35.8354	+	11.6436i	1.36522	+	0.443587i
$690$	−0.144317	+	0.246807i	−0.00549405	+	0.00939578i
$691$	16.0497	+	22.0905i	0.610558	+	0.840361i	0.996623	−	0.0821106i	$-0.0261661\pi$
$691$	16.0497	+	22.0905i	0.610558	+	0.840361i	−0.386065	+	0.922471i	$0.626166\pi$
$692$	32.4308	+	3.77115i	1.23284	+	0.143358i
$693$	−6.81827	+	8.74543i	−0.259005	+	0.332211i
$694$	−9.15074	−	10.2765i	−0.347357	−	0.390089i
$695$	−1.61518	+	1.17350i	−0.0612674	+	0.0445134i
$696$	8.74073	+	6.57444i	0.331317	+	0.249204i
$697$	8.59437	−	26.4508i	0.325535	−	1.00189i
$698$	27.0032	−	2.68749i	1.02209	−	0.101723i
$699$	10.7299	+	7.79576i	0.405844	+	0.294863i
$700$	29.9686	+	13.7414i	1.13270	+	0.519376i
$701$	9.15601	−	2.97497i	0.345818	−	0.112363i	−0.130958	−	0.991388i	$-0.541805\pi$
$701$	9.15601	−	2.97497i	0.345818	−	0.112363i	0.476776	+	0.879025i	$0.341805\pi$
$702$	9.16329	+	2.00066i	0.345846	+	0.0755101i
$703$	−3.66140			−0.138092
$704$	−16.9981	+	20.3731i	−0.640639	+	0.767842i
$705$	1.36507			0.0514117
$706$	3.18755	+	0.695951i	0.119965	+	0.0261925i
$707$	−62.9302	+	20.4473i	−2.36673	+	0.768999i
$708$	−18.0980	−	8.29843i	−0.680166	−	0.311874i
$709$	14.5854	+	10.5969i	0.547765	+	0.397974i	0.826961	−	0.562260i	$-0.190068\pi$
$709$	14.5854	+	10.5969i	0.547765	+	0.397974i	−0.279196	+	0.960234i	$0.590068\pi$
$710$	−1.70464	+	0.169654i	−0.0639740	+	0.00636700i
$711$	4.45760	−	13.7191i	0.167173	−	0.514505i
$712$	−6.28445	−	4.72692i	−0.235520	−	0.177149i
$713$	−2.50376	+	1.81909i	−0.0937666	+	0.0681254i
$714$	−14.6945	−	16.5023i	−0.549929	−	0.617582i
$715$	4.81346	−	3.25390i	0.180013	−	0.121689i
$716$	48.7518	+	5.66899i	1.82194	+	0.211860i
$717$	11.8292	+	16.2814i	0.441768	+	0.608041i
$718$	12.6000	−	21.5483i	0.470230	−	0.804174i
$719$	−45.6978	−	14.8481i	−1.70424	−	0.553741i	−0.714882	−	0.699245i	$-0.753520\pi$
$719$	−45.6978	−	14.8481i	−1.70424	−	0.553741i	−0.989358	+	0.145504i	$0.953520\pi$
$720$	−0.689471	−	0.800607i	−0.0256951	−	0.0298369i
$721$	−13.1912	+	18.1562i	−0.491267	+	0.676171i
$722$	−2.53901	+	1.11368i	−0.0944923	+	0.0414470i
$723$	−3.09899	−	9.53770i	−0.115253	−	0.354711i
$724$	−12.9006	−	22.9255i	−0.479448	−	0.852020i
$725$		−	19.0647i		−	0.708046i
$726$	−4.33984	+	14.9387i	−0.161067	+	0.554428i
$727$			27.0238i			1.00226i	0.865373	+	0.501128i	$0.167081\pi$
$727$			27.0238i			1.00226i	−0.865373	+	0.501128i	$0.832919\pi$
$728$	59.3202	+	20.3666i	2.19855	+	0.754837i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−2.26164	−	5.15616i	−0.0837071	−	0.190838i
$731$	−5.79313	+	7.97356i	−0.214267	+	0.294913i
$732$	−4.31641	+	4.68869i	−0.159539	+	0.173299i
$733$	−32.7676	−	10.6468i	−1.21030	−	0.393250i	−0.366759	−	0.930316i	$-0.619532\pi$
$733$	−32.7676	−	10.6468i	−1.21030	−	0.393250i	−0.843540	+	0.537066i	$0.819532\pi$
$734$	7.65366	+	4.47537i	0.282502	+	0.165189i
$735$	−0.648862	−	0.893082i	−0.0239336	−	0.0329418i
$736$	−3.80782	+	2.06044i	−0.140358	+	0.0759489i
$737$	−16.4697	+	11.1335i	−0.606668	+	0.410107i
$738$	6.28587	−	5.59728i	0.231386	−	0.206039i
$739$	23.8296	−	17.3132i	0.876585	−	0.636876i	−0.0557608	−	0.998444i	$-0.517758\pi$
$739$	23.8296	−	17.3132i	0.876585	−	0.636876i	0.932346	+	0.361568i	$0.117758\pi$
$740$	−0.459391	+	0.0923565i	−0.0168876	+	0.00339509i
$741$	−8.45980	+	26.0366i	−0.310778	+	0.956478i
$742$	−2.66054	−	26.7324i	−0.0976714	−	0.981377i
$743$	−35.7350	−	25.9630i	−1.31099	−	0.952491i	−0.999998	−	0.00207936i	$-0.999338\pi$
$743$	−35.7350	−	25.9630i	−1.31099	−	0.952491i	−0.310994	−	0.950412i	$-0.600662\pi$
$744$	−3.35359	−	10.9343i	−0.122948	−	0.400872i
$745$	−4.45837	+	1.44861i	−0.163342	+	0.0530731i
$746$	0.00737774	−	0.0337910i	0.000270118	−	0.00123718i
$747$	−0.613698			−0.0224540
$748$	−27.7230	−	13.8669i	−1.01365	−	0.507025i
$749$	40.8632			1.49311
$750$	−0.791266	+	3.62410i	−0.0288930	+	0.132334i
$751$	11.6991	−	3.80126i	0.426905	−	0.138710i	−0.0876808	−	0.996149i	$-0.527946\pi$
$751$	11.6991	−	3.80126i	0.426905	−	0.138710i	0.514586	+	0.857439i	$0.327946\pi$
$752$	17.6697	+	10.7287i	0.644346	+	0.391237i
$753$	10.1735	+	7.39146i	0.370742	+	0.269360i
$754$	−3.59185	−	36.0900i	−0.130808	−	1.31432i
$755$	1.10762	−	3.40892i	0.0403106	−	0.124063i
$756$	−1.31800	−	6.55589i	−0.0479354	−	0.238436i
$757$	−9.30726	+	6.76212i	−0.338278	+	0.245773i	−0.743935	−	0.668252i	$-0.767043\pi$
$757$	−9.30726	+	6.76212i	−0.338278	+	0.245773i	0.405657	+	0.914025i	$0.367043\pi$
$758$	33.8478	−	30.1400i	1.22941	−	1.09473i
$759$	−1.56076	+	2.00190i	−0.0566519	+	0.0726643i
$760$	2.52468	−	1.77115i	0.0915798	−	0.0642462i
$761$	−7.53101	−	10.3655i	−0.272999	−	0.375751i	0.650400	−	0.759591i	$-0.274601\pi$
$761$	−7.53101	−	10.3655i	−0.272999	−	0.375751i	−0.923399	+	0.383841i	$0.874601\pi$
$762$	2.86513	+	1.67534i	0.103793	+	0.0606913i
$763$	6.65892	+	2.16361i	0.241069	+	0.0783280i
$764$	−16.3073	−	15.0125i	−0.589976	−	0.543133i
$765$	0.725537	−	0.998616i	0.0262319	−	0.0361050i
$766$	−20.0438	−	45.6966i	−0.724213	−	1.65108i
$767$	20.4018	+	62.7904i	0.736668	+	2.26723i
$768$	−2.63226	−	15.7820i	−0.0949833	−	0.569484i
$769$			6.41973i			0.231501i	0.993278	+	0.115751i	$0.0369274\pi$
$769$			6.41973i			0.231501i	−0.993278	+	0.115751i	$0.963073\pi$
$770$	−3.50307	−	2.21093i	−0.126242	−	0.0796766i
$771$			1.00906i			0.0363404i
$772$	24.1793	−	13.6061i	0.870231	−	0.489695i
$773$	8.70055	+	26.7775i	0.312937	+	0.963121i	0.976595	+	0.215085i	$0.0690028\pi$
$773$	8.70055	+	26.7775i	0.312937	+	0.963121i	−0.663658	+	0.748036i	$0.730997\pi$
$774$	−2.73148	+	1.19810i	−0.0981809	+	0.0430650i
$775$	−11.7180	+	16.1285i	−0.420924	+	0.579352i
$776$	−28.4558	−	0.471401i	−1.02150	−	0.0169223i
$777$	−2.82052	−	0.916444i	−0.101186	−	0.0328772i
$778$	−6.81055	+	11.6472i	−0.244170	+	0.417573i
$779$	14.4403	+	19.8754i	0.517378	+	0.712110i
$780$	−0.404684	+	3.48017i	−0.0144900	+	0.124610i
$781$	−15.2008	−	0.515247i	−0.543927	−	0.0184370i
$782$	−3.36369	−	3.77750i	−0.120285	−	0.135083i
$783$	−3.12839	+	2.27291i	−0.111800	+	0.0812272i
$784$	−1.37980	−	16.6598i	−0.0492787	−	0.594994i
$785$	1.17985	−	3.63122i	0.0421108	−	0.129604i
$786$	−19.3718	+	1.92798i	−0.690969	+	0.0687686i
$787$	10.3223	+	7.49956i	0.367949	+	0.267330i	0.756360	−	0.654156i	$-0.226976\pi$
$787$	10.3223	+	7.49956i	0.367949	+	0.267330i	−0.388411	+	0.921486i	$0.626976\pi$
$788$	5.03777	−	10.9869i	0.179463	−	0.391391i
$789$	−14.0089	+	4.55178i	−0.498731	+	0.162048i
$790$	5.26453	+	1.14943i	0.187304	+	0.0408948i
$791$	40.3139			1.43340
$792$	−5.12420	−	7.85764i	−0.182081	−	0.279209i
$793$	21.1331			0.750459
$794$	11.1098	+	2.42565i	0.394272	+	0.0860832i
$795$	1.42726	−	0.463744i	0.0506196	−	0.0164473i
$796$	−14.2942	+	31.1741i	−0.506643	+	1.10494i
$797$	32.4990	+	23.6119i	1.15117	+	0.836376i	0.988636	−	0.150327i	$-0.0480325\pi$
$797$	32.4990	+	23.6119i	1.15117	+	0.836376i	0.162536	+	0.986703i	$0.448033\pi$
$798$	19.4227	−	1.93304i	0.687556	−	0.0684289i
$799$	−7.46282	+	22.9682i	−0.264015	+	0.812556i
$800$	−19.2268	+	20.2030i	−0.679770	+	0.714283i
$801$	2.24926	−	1.63419i	0.0794738	−	0.0577411i
$802$	−34.9965	−	39.3018i	−1.23577	−	1.38780i
$803$	−13.8282	−	48.0389i	−0.487986	−	1.69526i
$804$	1.38466	−	11.9077i	0.0488332	−	0.419952i
$805$	−0.397310	−	0.546850i	−0.0140033	−	0.0192739i
$806$	−19.1439	+	32.7393i	−0.674314	+	1.15319i
$807$	−11.2894	−	3.66813i	−0.397404	−	0.129124i
$808$	0.927157	−	55.9671i	0.0326173	−	1.96891i
$809$	11.8866	−	16.3605i	0.417910	−	0.575204i	−0.547215	−	0.836992i	$-0.684312\pi$
$809$	11.8866	−	16.3605i	0.417910	−	0.575204i	0.965125	+	0.261788i	$0.0843121\pi$
$810$	0.342092	−	0.150052i	0.0120199	−	0.00527227i
$811$	−8.62836	−	26.5554i	−0.302983	−	0.932485i	−0.980422	−	0.196907i	$-0.936910\pi$
$811$	−8.62836	−	26.5554i	−0.302983	−	0.932485i	0.677439	−	0.735579i	$-0.263090\pi$
$812$	−22.5353	+	12.6811i	−0.790835	+	0.445018i
$813$			14.0974i			0.494417i
$814$	−4.15147	+	0.271540i	−0.145509	+	0.00951749i
$815$			1.65706i			0.0580441i
$816$	17.2400	−	7.22387i	0.603520	−	0.252886i
$817$	−2.69032	−	8.27995i	−0.0941223	−	0.289679i
$818$	5.87153	+	13.3861i	0.205293	+	0.468034i
$819$	−13.0339	+	17.9396i	−0.455440	+	0.626859i
$820$	2.31316	+	2.12950i	0.0807789	+	0.0743652i
$821$	−25.0864	−	8.15107i	−0.875522	−	0.284474i	−0.163425	−	0.986556i	$-0.552254\pi$
$821$	−25.0864	−	8.15107i	−0.875522	−	0.284474i	−0.712097	+	0.702081i	$0.752254\pi$
$822$	−7.26176	−	4.24621i	−0.253283	−	0.148104i
$823$	−25.1235	−	34.5796i	−0.875752	−	1.20537i	−0.977579	−	0.210567i	$-0.932469\pi$
$823$	−25.1235	−	34.5796i	−0.875752	−	1.20537i	0.101828	−	0.994802i	$-0.467531\pi$
$824$	−10.9030	−	15.5417i	−0.379826	−	0.541422i
$825$	−5.57689	+	15.3713i	−0.194162	+	0.535160i
$826$	35.1544	−	31.3034i	1.22318	−	1.08919i
$827$	10.1906	−	7.40391i	0.354362	−	0.257459i	−0.396334	−	0.918106i	$-0.629718\pi$
$827$	10.1906	−	7.40391i	0.354362	−	0.257459i	0.750697	+	0.660647i	$0.229718\pi$
$828$	−0.301701	−	1.50070i	−0.0104849	−	0.0521528i
$829$	−3.42053	+	10.5273i	−0.118800	+	0.365628i	−0.992721	−	0.120440i	$-0.961569\pi$
$829$	−3.42053	+	10.5273i	−0.118800	+	0.365628i	0.873921	+	0.486068i	$0.161569\pi$
$830$	−0.0227038	−	0.228122i	−0.000788062	−	0.00791824i
$831$	16.5545	+	12.0276i	0.574269	+	0.417231i
$832$	−32.5905	+	41.8671i	−1.12987	+	1.45148i
$833$	18.5739	−	6.03504i	0.643549	−	0.209102i
$834$	2.28008	−	10.4431i	0.0789528	−	0.361614i
$835$	0.620720			0.0214809
$836$	24.3039	−	12.6119i	0.840568	−	0.436192i
$837$	4.04361			0.139768
$838$	0.705601	−	3.23174i	0.0243746	−	0.111639i
$839$	0.759442	−	0.246758i	0.0262189	−	0.00851902i	−0.295878	−	0.955226i	$-0.595612\pi$
$839$	0.759442	−	0.246758i	0.0262189	−	0.00851902i	0.322097	+	0.946707i	$0.395612\pi$
$840$	2.38818	−	0.732462i	0.0824001	−	0.0252723i
$841$	−11.3643	−	8.25664i	−0.391872	−	0.284712i
$842$	−1.81980	−	18.2849i	−0.0627145	−	0.630139i
$843$	4.07365	−	12.5374i	0.140304	−	0.431811i
$844$	25.1160	−	5.04934i	0.864527	−	0.173805i
$845$	6.62121	−	4.81059i	0.227777	−	0.165489i
$846$	−5.45825	+	4.86033i	−0.187659	+	0.167102i
$847$	−28.2226	−	23.5833i	−0.969740	−	0.810331i
$848$	22.1193	+	5.21470i	0.759581	+	0.179074i
$849$	−2.43998	−	3.35834i	−0.0837398	−	0.115258i
$850$	−28.1269	−	16.4468i	−0.964745	−	0.564121i
$851$	−0.645640	−	0.209781i	−0.0221323	−	0.00719121i
$852$	6.21195	−	6.74771i	0.212818	−	0.231173i
$853$	9.71467	−	13.3711i	0.332624	−	0.457818i	−0.609645	−	0.792675i	$-0.708688\pi$
$853$	9.71467	−	13.3711i	0.332624	−	0.457818i	0.942269	+	0.334857i	$0.108688\pi$
$854$	−6.05233	−	13.7983i	−0.207106	−	0.472168i
$855$	0.336938	+	1.03699i	0.0115230	+	0.0354642i
$856$	−11.2251	+	32.6945i	−0.383667	+	1.11747i
$857$			4.04192i			0.138069i	0.997614	+	0.0690347i	$0.0219919\pi$
$857$			4.04192i			0.138069i	−0.997614	+	0.0690347i	$0.978008\pi$
$858$	−7.66119	+	30.1490i	−0.261549	+	1.02927i
$859$		−	13.5474i		−	0.462231i	−0.972926	−	0.231115i	$-0.925762\pi$
$859$		−	13.5474i		−	0.462231i	0.972926	−	0.231115i	$-0.0742375\pi$
$860$	−0.546408	−	0.971014i	−0.0186323	−	0.0331113i
$861$	6.14919	+	18.9252i	0.209564	+	0.644971i
$862$	36.2203	−	15.8873i	1.23367	−	0.541122i
$863$	−9.44467	+	12.9995i	−0.321500	+	0.442507i	−0.938925	−	0.344123i	$-0.888176\pi$
$863$	−9.44467	+	12.9995i	−0.321500	+	0.442507i	0.617424	+	0.786630i	$0.288176\pi$
$864$	5.60740	+	0.746374i	0.190768	+	0.0253922i
$865$	−4.10100	−	1.33250i	−0.139438	−	0.0453062i
$866$	−22.3728	+	38.2613i	−0.760257	+	1.30017i
$867$	2.84347	+	3.91370i	0.0965692	+	0.132916i
$868$	26.8589	+	3.12323i	0.911650	+	0.106009i
$869$	44.9740	+	16.3171i	1.52564	+	0.553520i
$870$	−0.960616	−	1.07879i	−0.0325679	−	0.0365745i
$871$	−32.1604	+	23.3659i	−1.08971	+	0.791723i
$872$	−3.56030	+	4.73343i	−0.120567	+	0.160294i
$873$	3.10933	−	9.56954i	0.105235	−	0.323880i
$874$	4.44600	−	0.442488i	0.150388	−	0.0149674i
$875$	−7.09514	−	5.15492i	−0.239860	−	0.174268i
$876$	27.4016	+	12.5644i	0.925815	+	0.424511i
$877$	−8.88213	+	2.88598i	−0.299928	+	0.0974526i	−0.455115	−	0.890432i	$-0.650402\pi$
$877$	−8.88213	+	2.88598i	−0.299928	+	0.0974526i	0.155187	+	0.987885i	$0.450402\pi$
$878$	2.65987	+	0.580742i	0.0897664	+	0.0195991i
$879$	7.98968			0.269485
$880$	2.73125	−	2.19545i	0.0920706	−	0.0740086i
$881$	−27.4351			−0.924312			−0.462156	−	0.886799i	$-0.652924\pi$
$881$	−27.4351			−0.924312			−0.462156	+	0.886799i	$0.652924\pi$
$882$	5.77428	+	1.26072i	0.194430	+	0.0424508i
$883$	24.6985	−	8.02501i	0.831169	−	0.270063i	0.137631	−	0.990484i	$-0.456051\pi$
$883$	24.6985	−	8.02501i	0.831169	−	0.270063i	0.693538	+	0.720420i	$0.256051\pi$
$884$	−56.3436	−	25.8350i	−1.89504	−	0.868926i
$885$	2.12733	+	1.54559i	0.0715094	+	0.0519546i
$886$	−38.2411	+	3.80594i	−1.28473	+	0.127863i
$887$	6.60250	−	20.3204i	0.221690	−	0.682292i	−0.776920	−	0.629599i	$-0.783219\pi$
$887$	6.60250	−	20.3204i	0.221690	−	0.682292i	0.998611	−	0.0526937i	$-0.0167807\pi$
$888$	1.50804	−	2.00494i	0.0506066	−	0.0672815i
$889$	−6.34826	+	4.61228i	−0.212914	+	0.154691i
$890$	0.690668	+	0.775634i	0.0231512	+	0.0259993i
$891$	3.18721	−	0.917448i	0.106775	−	0.0307357i
$892$	−4.05782	−	0.471854i	−0.135866	−	0.0157988i
$893$	−12.5391	−	17.2586i	−0.419604	−	0.577536i
$894$	12.6690	−	21.6662i	0.423716	−	0.724628i
$895$	−6.16484	−	2.00308i	−0.206068	−	0.0669555i
$896$	36.6696	+	9.28873i	1.22505	+	0.310315i
$897$	−2.98355	+	4.10651i	−0.0996179	+	0.137112i
$898$	−13.0169	+	5.70958i	−0.434379	+	0.190531i
$899$	−4.83187	−	14.8710i	−0.161152	−	0.495974i
$900$	−4.83563	−	8.59333i	−0.161188	−	0.286444i
$901$			26.5497i			0.884499i
$902$	17.8472	+	21.4648i	0.594246	+	0.714699i
$903$		−	7.05177i		−	0.234668i
$904$	−11.0742	+	32.2550i	−0.368323	+	1.07278i
$905$	1.07361	+	3.30422i	0.0356879	+	0.109836i
$906$	7.70857	+	17.5742i	0.256100	+	0.583865i
$907$	−11.6618	+	16.0511i	−0.387223	+	0.532967i	−0.957480	−	0.288499i	$-0.906844\pi$
$907$	−11.6618	+	16.0511i	−0.387223	+	0.532967i	0.570257	+	0.821467i	$0.306844\pi$
$908$	−24.7700	+	26.9063i	−0.822022	+	0.892918i
$909$	18.8215	+	6.11547i	0.624269	+	0.202837i
$910$	−7.15065	−	4.18124i	−0.237042	−	0.138607i
$911$	6.00261	+	8.26188i	0.198875	+	0.273728i	0.896794	−	0.442449i	$-0.145890\pi$
$911$	6.00261	+	8.26188i	0.198875	+	0.273728i	−0.697918	+	0.716177i	$0.745890\pi$
$912$	−3.78879	+	16.0710i	−0.125459	+	0.532165i
$913$	0.0689525	−	2.03424i	0.00228200	−	0.0673234i
$914$	−10.4339	+	9.29088i	−0.345121	+	0.307315i
$915$	0.680943	−	0.494734i	0.0225113	−	0.0163554i
$916$	−24.4693	+	4.91934i	−0.808488	+	0.162539i
$917$	14.2227	−	43.7731i	0.469676	−	1.44552i
$918$	0.654499	+	6.57623i	0.0216017	+	0.217048i
$919$	24.3478	+	17.6897i	0.803159	+	0.583529i	0.911839	−	0.410548i	$-0.134662\pi$
$919$	24.3478	+	17.6897i	0.803159	+	0.583529i	−0.108680	+	0.994077i	$0.534662\pi$
$920$	0.546673	−	0.167666i	0.0180233	−	0.00552779i
$921$	26.8834	−	8.73496i	0.885840	−	0.287827i
$922$	6.96446	−	31.8981i	0.229362	−	1.05051i
$923$	−30.4136			−1.00108
$924$	21.8790	−	3.63222i	0.719768	−	0.119491i
$925$	−4.37305			−0.143785
$926$	1.77277	−	8.11954i	0.0582570	−	0.266825i
$927$	6.38362	−	2.07416i	0.209666	−	0.0681245i
$928$	−3.95560	−	21.5139i	−0.129849	−	0.706228i
$929$	13.9833	+	10.1594i	0.458776	+	0.333321i	0.793051	−	0.609155i	$-0.208491\pi$
$929$	13.9833	+	10.1594i	0.458776	+	0.333321i	−0.334275	+	0.942476i	$0.608491\pi$
$930$	0.149594	+	1.50308i	0.00490538	+	0.0492879i
$931$	−5.33097	+	16.4070i	−0.174716	+	0.537719i
$932$	−5.22818	−	26.0055i	−0.171255	−	0.851840i
$933$	10.4188	−	7.56969i	0.341096	−	0.247821i
$934$	3.99285	−	3.55545i	0.130650	−	0.116338i
$935$	3.22862	+	2.51715i	0.105587	+	0.0823197i
$936$	−10.7730	−	15.3563i	−0.352126	−	0.501938i
$937$	−4.26015	−	5.86359i	−0.139173	−	0.191555i	0.733741	−	0.679429i	$-0.237773\pi$
$937$	−4.26015	−	5.86359i	−0.139173	−	0.191555i	−0.872914	+	0.487874i	$0.837773\pi$
$938$	24.4666	+	14.3065i	0.798861	+	0.467123i
$939$	9.16404	+	2.97758i	0.299057	+	0.0971696i
$940$	−2.00860	−	1.84912i	−0.0655133	−	0.0603117i
$941$	−22.6672	+	31.1987i	−0.738930	+	1.01705i	0.259750	+	0.965676i	$0.416360\pi$
$941$	−22.6672	+	31.1987i	−0.738930	+	1.01705i	−0.998680	+	0.0513733i	$0.983640\pi$
$942$	8.21125	+	18.7203i	0.267537	+	0.609940i
$943$	1.40760	+	4.33214i	0.0458377	+	0.141074i
$944$	15.3888	+	36.7259i	0.500864	+	1.19533i
$945$			0.883170i			0.0287295i
$946$	−3.66448	−	9.18869i	−0.119143	−	0.298750i
$947$			25.4572i			0.827247i	0.910448	+	0.413624i	$0.135737\pi$
$947$			25.4572i			0.827247i	−0.910448	+	0.413624i	$0.864263\pi$
$948$	−25.1427	+	14.1483i	−0.816598	+	0.459515i
$949$	−30.8897	−	95.0689i	−1.00272	−	3.08607i
$950$	26.3573	−	11.5611i	0.855143	−	0.375091i
$951$	3.90829	−	5.37930i	0.126735	−	0.174436i
$952$	−0.732005	+	44.1869i	−0.0237244	+	1.43211i
$953$	−28.3146	−	9.19996i	−0.917198	−	0.298016i	−0.187881	−	0.982192i	$-0.560162\pi$
$953$	−28.3146	−	9.19996i	−0.917198	−	0.298016i	−0.729317	+	0.684176i	$0.760162\pi$
$954$	−4.05573	+	6.93601i	−0.131309	+	0.224562i
$955$	1.72068	+	2.36832i	0.0556800	+	0.0766370i
$956$	4.64904	−	39.9805i	0.150361	−	1.29306i
$957$	−7.18257	−	10.6251i	−0.232180	−	0.343461i
$958$	20.4122	+	22.9233i	0.659488	+	0.740618i
$959$	16.0899	−	11.6900i	0.519570	−	0.377490i
$960$	−0.0699938	+	2.11198i	−0.00225904	+	0.0681639i
$961$	4.52686	−	13.9323i	0.146028	−	0.449428i
$962$	−8.27830	+	0.823897i	−0.266903	+	0.0265635i
$963$	−9.88744	−	7.18365i	−0.318618	−	0.231490i
$964$	−8.35978	+	18.2318i	−0.269250	+	0.587208i
$965$	−3.48493	+	1.13232i	−0.112184	+	0.0364507i
$966$	3.53570	+	0.771964i	0.113759	+	0.0248375i
$967$	27.0950			0.871316			0.435658	−	0.900112i	$-0.356516\pi$
$967$	27.0950			0.871316			0.435658	+	0.900112i	$0.356516\pi$
$968$	26.6216	−	16.1024i	0.855652	−	0.517552i
$969$	−19.2900			−0.619683
$970$	3.67220	+	0.801767i	0.117907	+	0.0257432i
$971$	−0.248827	+	0.0808487i	−0.00798523	+	0.00259456i	−0.313007	−	0.949751i	$-0.601336\pi$
$971$	−0.248827	+	0.0808487i	−0.00798523	+	0.00259456i	0.305022	+	0.952345i	$0.401336\pi$
$972$	−0.833600	+	1.81800i	−0.0267377	+	0.0583123i
$973$	20.4451	+	14.8542i	0.655440	+	0.476205i
$974$	−10.7643	+	1.07132i	−0.344911	+	0.0343272i
$975$	−10.1041	+	31.0973i	−0.323591	+	0.995909i
$976$	12.7025	−	1.05205i	0.406598	−	0.0336753i
$977$	−41.1035	+	29.8634i	−1.31502	+	0.955416i	−0.315037	+	0.949079i	$0.602017\pi$
$977$	−41.1035	+	29.8634i	−1.31502	+	0.955416i	−0.999980	+	0.00633607i	$0.997983\pi$
$978$	−5.89992	−	6.62574i	−0.188659	−	0.211868i
$979$	5.16415	+	7.63929i	0.165047	+	0.244153i
$980$	−0.255013	+	2.19304i	−0.00814609	+	0.0700542i
$981$	−1.23086	−	1.69414i	−0.0392985	−	0.0540897i
$982$	−16.3478	+	27.9576i	−0.521680	+	0.892163i
$983$	9.50959	+	3.08985i	0.303309	+	0.0985510i	0.456717	−	0.889612i	$-0.349025\pi$
$983$	9.50959	+	3.08985i	0.303309	+	0.0985510i	−0.153409	+	0.988163i	$0.549025\pi$
$984$	−16.8312	−	0.278827i	−0.536559	−	0.00888869i
$985$	−0.938291	+	1.29145i	−0.0298964	+	0.0411489i
$986$	23.4030	−	10.2652i	0.745302	−	0.326911i
$987$	−5.33957	−	16.4335i	−0.169960	−	0.523084i
$988$	47.7169	−	26.8512i	1.51808	−	0.854250i
$989$		−	1.61421i		−	0.0513287i
$990$	0.458943	+	1.15080i	0.0145862	+	0.0365748i
$991$		−	55.4443i		−	1.76125i	−0.473816	−	0.880624i	$-0.657124\pi$
$991$		−	55.4443i		−	1.76125i	0.473816	−	0.880624i	$-0.342876\pi$
$992$	−9.87702	+	20.6317i	−0.313596	+	0.655058i
$993$	−1.31344	−	4.04234i	−0.0416807	−	0.128280i
$994$	8.71018	+	19.8577i	0.276270	+	0.629849i
$995$	2.66231	−	3.66435i	0.0844009	−	0.116168i
$996$	0.903007	+	0.831310i	0.0286129	+	0.0263411i
$997$	53.9438	+	17.5274i	1.70842	+	0.555098i	0.990069	−	0.140585i	$-0.0448983\pi$
$997$	53.9438	+	17.5274i	1.70842	+	0.555098i	0.718349	+	0.695683i	$0.244898\pi$
$998$	46.5853	+	27.2401i	1.47463	+	0.862271i
$999$	0.521359	+	0.717589i	0.0164951	+	0.0227035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.19.1	yes	48
3.2	odd	2		396.2.r.b.19.12		48
4.3	odd	2	inner	132.2.j.a.19.8	yes	48
11.7	odd	10	inner	132.2.j.a.7.8	yes	48
12.11	even	2		396.2.r.b.19.5		48
33.29	even	10		396.2.r.b.271.5		48
44.7	even	10	inner	132.2.j.a.7.1	✓	48
132.95	odd	10		396.2.r.b.271.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.1	✓	48	44.7	even	10	inner
132.2.j.a.7.8	yes	48	11.7	odd	10	inner
132.2.j.a.19.1	yes	48	1.1	even	1	trivial
132.2.j.a.19.8	yes	48	4.3	odd	2	inner
396.2.r.b.19.5		48	12.11	even	2
396.2.r.b.19.12		48	3.2	odd	2
396.2.r.b.271.5		48	33.29	even	10
396.2.r.b.271.12		48	132.95	odd	10

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38167 - 0.301665i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.81800 + 0.833600i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(1.40726 - 0.140058i) q^{6} +(-1.03321 + 3.17989i) q^{7} +(-2.26039 - 1.70018i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.38167 - 0.301665i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.81800 + 0.833600i) q^{4} +(-0.213696 - 0.155259i) q^{5} +(1.40726 - 0.140058i) q^{6} +(-1.03321 + 3.17989i) q^{7} +(-2.26039 - 1.70018i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.248420 + 0.278981i) q^{10} +(1.85745 + 2.74771i) q^{11} +(-1.98661 - 0.231009i) q^{12} +(3.89823 + 5.36545i) q^{13} +(2.38681 - 4.08186i) q^{14} +(0.251215 + 0.0816246i) q^{15} +(2.61022 + 3.03096i) q^{16} +(-2.74676 + 3.78059i) q^{17} +(-1.29510 + 0.568070i) q^{18} +(-1.27559 - 3.92586i) q^{19} +(-0.259074 - 0.460397i) q^{20} -3.34353i q^{21} +(-1.73748 - 4.35674i) q^{22} -0.765361i q^{23} +(2.67515 + 0.918469i) q^{24} +(-1.52352 - 4.68893i) q^{25} +(-3.76748 - 8.58922i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-4.52913 + 4.91975i) q^{28} +(3.67765 + 1.19494i) q^{29} +(-0.322471 - 0.188560i) q^{30} +(-2.37677 - 3.27135i) q^{31} +(-2.69212 - 4.97519i) q^{32} +(-2.61562 - 2.03924i) q^{33} +(4.93558 - 4.39491i) q^{34} +(0.714499 - 0.519114i) q^{35} +(1.96077 - 0.394195i) q^{36} +(0.274094 - 0.843576i) q^{37} +(0.578143 + 5.80903i) q^{38} +(-5.36545 - 3.89823i) q^{39} +(0.219068 + 0.714269i) q^{40} +(-5.66025 + 1.83913i) q^{41} +(-1.00863 + 4.61964i) q^{42} +2.10908 q^{43} +(1.08634 + 6.54369i) q^{44} -0.264143 q^{45} +(-0.230883 + 1.05747i) q^{46} +(4.91501 - 1.59698i) q^{47} +(-3.41909 - 2.07601i) q^{48} +(-3.38106 - 2.45648i) q^{49} +(0.690516 + 6.93812i) q^{50} +(1.44406 - 4.44436i) q^{51} +(2.61433 + 13.0039i) q^{52} +(4.59637 - 3.33946i) q^{53} +(1.05617 - 0.940476i) q^{54} +(0.0296780 - 0.875559i) q^{55} +(7.74185 - 5.43116i) q^{56} +(2.42632 + 3.33954i) q^{57} +(-4.72080 - 2.76042i) q^{58} +(9.46770 + 3.07624i) q^{59} +(0.388665 + 0.357806i) q^{60} +(1.87298 - 2.57794i) q^{61} +(2.29705 + 5.23689i) q^{62} +(1.03321 + 3.17989i) q^{63} +(2.21876 + 7.68616i) q^{64} -1.75181i q^{65} +(2.99875 + 3.60659i) q^{66} +5.99397i q^{67} +(-8.14511 + 4.58341i) q^{68} +(0.236510 + 0.727902i) q^{69} +(-1.14380 + 0.501703i) q^{70} +(-2.69549 + 3.71003i) q^{71} +(-2.82804 - 0.0468496i) q^{72} +(-14.3347 - 4.65764i) q^{73} +(-0.633184 + 1.08285i) q^{74} +(2.89792 + 3.98864i) q^{75} +(0.953581 - 8.20054i) q^{76} +(-10.6565 + 3.06752i) q^{77} +(6.23730 + 7.00462i) q^{78} +(11.6701 - 8.47885i) q^{79} +(-0.0872089 - 1.05297i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.37537 - 0.833558i) q^{82} +(-0.496492 - 0.360722i) q^{83} +(2.78717 - 6.07853i) q^{84} +(1.17394 - 0.381437i) q^{85} +(-2.91404 - 0.636235i) q^{86} -3.86691 q^{87} +(0.473040 - 9.36890i) q^{88} +2.78024 q^{89} +(0.364957 + 0.0796826i) q^{90} +(-21.0892 + 6.85231i) q^{91} +(0.638005 - 1.39142i) q^{92} +(3.27135 + 2.37677i) q^{93} +(-7.27265 + 0.723810i) q^{94} +(-0.336938 + 1.03699i) q^{95} +(4.09777 + 3.89978i) q^{96} +(8.14034 - 5.91430i) q^{97} +(3.93046 + 4.41398i) q^{98} +(3.11777 + 1.13116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) \) 48 * q - 4 * q^4 + 12 * q^9	\( 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Introduction

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