LMFDB - Embedded newform 273.2.bh.a.131.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.7
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61355 - 0.931585i) q^{2} +(-1.54166 - 0.789478i) q^{3} +(0.735702 + 1.27427i) q^{4} +(0.650945 - 1.12747i) q^{5} +(1.75209 + 2.71005i) q^{6} +(-0.953821 + 2.46784i) q^{7} +0.984865i q^{8} +(1.75345 + 2.43422i) q^{9} +O(q^{10})$	\(q+(-1.61355 - 0.931585i) q^{2} +(-1.54166 - 0.789478i) q^{3} +(0.735702 + 1.27427i) q^{4} +(0.650945 - 1.12747i) q^{5} +(1.75209 + 2.71005i) q^{6} +(-0.953821 + 2.46784i) q^{7} +0.984865i q^{8} +(1.75345 + 2.43422i) q^{9} +(-2.10067 + 1.21282i) q^{10} +(-3.00907 + 1.73729i) q^{11} +(-0.128193 - 2.54532i) q^{12} -1.00000i q^{13} +(3.83804 - 3.09342i) q^{14} +(-1.89365 + 1.22427i) q^{15} +(2.38889 - 4.13768i) q^{16} +(-0.478360 - 0.828544i) q^{17} +(-0.561600 - 5.56123i) q^{18} +(6.70949 + 3.87373i) q^{19} +1.91561 q^{20} +(3.41877 - 3.05155i) q^{21} +6.47373 q^{22} +(2.28181 + 1.31741i) q^{23} +(0.777530 - 1.51833i) q^{24} +(1.65254 + 2.86228i) q^{25} +(-0.931585 + 1.61355i) q^{26} +(-0.781464 - 5.13705i) q^{27} +(-3.84643 + 0.600165i) q^{28} +1.37565i q^{29} +(4.19602 - 0.211330i) q^{30} +(-0.469556 + 0.271098i) q^{31} +(-6.00336 + 3.46604i) q^{32} +(6.01053 - 0.302717i) q^{33} +1.78253i q^{34} +(2.16153 + 2.68183i) q^{35} +(-1.81184 + 4.02523i) q^{36} +(1.83050 - 3.17052i) q^{37} +(-7.21741 - 12.5009i) q^{38} +(-0.789478 + 1.54166i) q^{39} +(1.11041 + 0.641093i) q^{40} +9.40663 q^{41} +(-8.35916 + 1.73896i) q^{42} -6.05484 q^{43} +(-4.42756 - 2.55625i) q^{44} +(3.88591 - 0.392418i) q^{45} +(-2.45455 - 4.25141i) q^{46} +(-5.18925 + 8.98805i) q^{47} +(-6.94947 + 4.49293i) q^{48} +(-5.18045 - 4.70775i) q^{49} -6.15793i q^{50} +(0.0833526 + 1.65499i) q^{51} +(1.27427 - 0.735702i) q^{52} +(-3.90354 + 2.25371i) q^{53} +(-3.52467 + 9.01691i) q^{54} +4.52352i q^{55} +(-2.43049 - 0.939385i) q^{56} +(-7.28555 - 11.2690i) q^{57} +(1.28154 - 2.21969i) q^{58} +(1.58070 + 2.73786i) q^{59} +(-2.95322 - 1.51233i) q^{60} +(9.76740 + 5.63921i) q^{61} +1.01020 q^{62} +(-7.67973 + 2.00542i) q^{63} +3.36010 q^{64} +(-1.12747 - 0.650945i) q^{65} +(-9.98032 - 5.11087i) q^{66} +(1.90946 + 3.30728i) q^{67} +(0.703861 - 1.21912i) q^{68} +(-2.47773 - 3.83244i) q^{69} +(-0.989386 - 6.34093i) q^{70} +16.4877i q^{71} +(-2.39738 + 1.72691i) q^{72} +(-7.30665 + 4.21850i) q^{73} +(-5.90723 + 3.41054i) q^{74} +(-0.287949 - 5.71732i) q^{75} +11.3996i q^{76} +(-1.41723 - 9.08297i) q^{77} +(2.71005 - 1.75209i) q^{78} +(-0.00970735 + 0.0168136i) q^{79} +(-3.11007 - 5.38680i) q^{80} +(-2.85084 + 8.53655i) q^{81} +(-15.1781 - 8.76308i) q^{82} +13.7006 q^{83} +(6.40371 + 2.11142i) q^{84} -1.24555 q^{85} +(9.76980 + 5.64060i) q^{86} +(1.08605 - 2.12079i) q^{87} +(-1.71100 - 2.96353i) q^{88} +(0.846721 - 1.46656i) q^{89} +(-6.63569 - 2.98687i) q^{90} +(2.46784 + 0.953821i) q^{91} +3.87687i q^{92} +(0.937923 - 0.0472379i) q^{93} +(16.7463 - 9.66846i) q^{94} +(8.73502 - 5.04317i) q^{95} +(11.9915 - 0.603946i) q^{96} +13.4723i q^{97} +(3.97326 + 12.4222i) q^{98} +(-9.50520 - 4.27850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.61355	−	0.931585i	−1.14095	−	0.658730i	−0.194287	−	0.980945i	$-0.562239\pi$
$2$	−1.61355	−	0.931585i	−1.14095	−	0.658730i	−0.946667	+	0.322214i	$0.895573\pi$
$3$	−1.54166	−	0.789478i	−0.890079	−	0.455805i
$3$	−1.54166	−	0.789478i	−0.890079	−	0.455805i
$4$	0.735702	+	1.27427i	0.367851	+	0.637136i
$5$	0.650945	−	1.12747i	0.291112	−	0.504220i	−0.682961	−	0.730455i	$-0.739308\pi$
$5$	0.650945	−	1.12747i	0.291112	−	0.504220i	0.974073	+	0.226235i	$0.0726416\pi$
$6$	1.75209	+	2.71005i	0.715287	+	1.10638i
$7$	−0.953821	+	2.46784i	−0.360510	+	0.932755i
$7$	−0.953821	+	2.46784i	−0.360510	+	0.932755i
$8$			0.984865i			0.348202i
$9$	1.75345	+	2.43422i	0.584483	+	0.811406i
$10$	−2.10067	+	1.21282i	−0.664290	+	0.383528i
$11$	−3.00907	+	1.73729i	−0.907270	+	0.523813i	−0.879552	−	0.475803i	$-0.842157\pi$
$11$	−3.00907	+	1.73729i	−0.907270	+	0.523813i	−0.0277183	+	0.999616i	$0.508824\pi$
$12$	−0.128193	−	2.54532i	−0.0370063	−	0.734770i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	3.83804	−	3.09342i	1.02576	−	0.826752i
$15$	−1.89365	+	1.22427i	−0.488939	+	0.316106i
$16$	2.38889	−	4.13768i	0.597222	−	1.03442i
$17$	−0.478360	−	0.828544i	−0.116019	−	0.200951i	0.802167	−	0.597099i	$-0.203680\pi$
$17$	−0.478360	−	0.828544i	−0.116019	−	0.200951i	−0.918187	+	0.396148i	$0.870347\pi$
$18$	−0.561600	−	5.56123i	−0.132370	−	1.31079i
$19$	6.70949	+	3.87373i	1.53926	+	0.888694i	0.998882	+	0.0472727i	$0.0150530\pi$
$19$	6.70949	+	3.87373i	1.53926	+	0.888694i	0.540380	+	0.841421i	$0.318280\pi$
$20$	1.91561			0.428343
$21$	3.41877	−	3.05155i	0.746038	−	0.665904i
$22$	6.47373			1.38020
$23$	2.28181	+	1.31741i	0.475791	+	0.274698i	0.718661	−	0.695361i	$-0.244755\pi$
$23$	2.28181	+	1.31741i	0.475791	+	0.274698i	−0.242870	+	0.970059i	$0.578089\pi$
$24$	0.777530	−	1.51833i	0.158713	−	0.309928i
$25$	1.65254	+	2.86228i	0.330508	+	0.572457i
$26$	−0.931585	+	1.61355i	−0.182699	+	0.316444i
$27$	−0.781464	−	5.13705i	−0.150393	−	0.988626i
$28$	−3.84643	+	0.600165i	−0.726906	+	0.113420i
$29$			1.37565i			0.255452i	0.991809	+	0.127726i	$0.0407679\pi$
$29$			1.37565i			0.255452i	−0.991809	+	0.127726i	$0.959232\pi$
$30$	4.19602	−	0.211330i	0.766085	−	0.0385834i
$31$	−0.469556	+	0.271098i	−0.0843347	+	0.0486907i	−0.541574	−	0.840653i	$-0.682172\pi$
$31$	−0.469556	+	0.271098i	−0.0843347	+	0.0486907i	0.457240	+	0.889344i	$0.348838\pi$
$32$	−6.00336	+	3.46604i	−1.06125	+	0.612716i
$33$	6.01053	−	0.302717i	1.04630	−	0.0526962i
$34$			1.78253i			0.305702i
$35$	2.16153	+	2.68183i	0.365365	+	0.453312i
$36$	−1.81184	+	4.02523i	−0.301974	+	0.670872i
$37$	1.83050	−	3.17052i	0.300933	−	0.521231i	−0.675415	−	0.737438i	$-0.736035\pi$
$37$	1.83050	−	3.17052i	0.300933	−	0.521231i	0.976348	+	0.216207i	$0.0693687\pi$
$38$	−7.21741	−	12.5009i	−1.17082	−	2.02792i
$39$	−0.789478	+	1.54166i	−0.126418	+	0.246864i
$40$	1.11041	+	0.641093i	0.175571	+	0.101366i
$41$	9.40663			1.46907			0.734534	−	0.678571i	$-0.237401\pi$
$41$	9.40663			1.46907			0.734534	+	0.678571i	$0.237401\pi$
$42$	−8.35916	+	1.73896i	−1.28985	+	0.268328i
$43$	−6.05484			−0.923354			−0.461677	−	0.887048i	$-0.652752\pi$
$43$	−6.05484			−0.923354			−0.461677	+	0.887048i	$0.652752\pi$
$44$	−4.42756	−	2.55625i	−0.667480	−	0.385370i
$45$	3.88591	−	0.392418i	0.579277	−	0.0584982i
$46$	−2.45455	−	4.25141i	−0.361904	−	0.626836i
$47$	−5.18925	+	8.98805i	−0.756930	+	1.31104i	0.187479	+	0.982269i	$0.439968\pi$
$47$	−5.18925	+	8.98805i	−0.756930	+	1.31104i	−0.944409	+	0.328773i	$0.893365\pi$
$48$	−6.94947	+	4.49293i	−1.00307	+	0.648498i
$49$	−5.18045	−	4.70775i	−0.740064	−	0.672536i
$50$		−	6.15793i		−	0.870863i
$51$	0.0833526	+	1.65499i	0.0116717	+	0.231745i
$52$	1.27427	−	0.735702i	0.176710	−	0.102023i
$53$	−3.90354	+	2.25371i	−0.536192	+	0.309571i	−0.743534	−	0.668698i	$-0.766852\pi$
$53$	−3.90354	+	2.25371i	−0.536192	+	0.309571i	0.207342	+	0.978268i	$0.433519\pi$
$54$	−3.52467	+	9.01691i	−0.479647	+	1.22705i
$55$			4.52352i			0.609952i
$56$	−2.43049	−	0.939385i	−0.324788	−	0.125531i
$57$	−7.28555	−	11.2690i	−0.964994	−	1.49261i
$58$	1.28154	−	2.21969i	0.168274	−	0.291460i
$59$	1.58070	+	2.73786i	0.205790	+	0.356438i	0.950384	−	0.311079i	$-0.100690\pi$
$59$	1.58070	+	2.73786i	0.205790	+	0.356438i	−0.744594	+	0.667517i	$0.767357\pi$
$60$	−2.95322	−	1.51233i	−0.381259	−	0.195241i
$61$	9.76740	+	5.63921i	1.25059	+	0.722027i	0.971226	−	0.238160i	$-0.0765441\pi$
$61$	9.76740	+	5.63921i	1.25059	+	0.722027i	0.279361	+	0.960186i	$0.409877\pi$
$62$	1.01020			0.128296
$63$	−7.67973	+	2.00542i	−0.967555	+	0.252659i
$64$	3.36010			0.420012
$65$	−1.12747	−	0.650945i	−0.139845	−	0.0807398i
$66$	−9.98032	−	5.11087i	−1.22849	−	0.629105i
$67$	1.90946	+	3.30728i	0.233277	+	0.404048i	0.958771	−	0.284181i	$-0.0917217\pi$
$67$	1.90946	+	3.30728i	0.233277	+	0.404048i	−0.725493	+	0.688229i	$0.758388\pi$
$68$	0.703861	−	1.21912i	0.0853557	−	0.147840i
$69$	−2.47773	−	3.83244i	−0.298283	−	0.461371i
$70$	−0.989386	−	6.34093i	−0.118254	−	0.757886i
$71$			16.4877i			1.95673i	0.206894	+	0.978363i	$0.433664\pi$
$71$			16.4877i			1.95673i	−0.206894	+	0.978363i	$0.566336\pi$
$72$	−2.39738	+	1.72691i	−0.282534	+	0.203518i
$73$	−7.30665	+	4.21850i	−0.855179	+	0.493738i	−0.862395	−	0.506236i	$-0.831036\pi$
$73$	−7.30665	+	4.21850i	−0.855179	+	0.493738i	0.00721618	+	0.999974i	$0.497703\pi$
$74$	−5.90723	+	3.41054i	−0.686701	+	0.396467i
$75$	−0.287949	−	5.71732i	−0.0332495	−	0.660179i
$76$			11.3996i			1.30763i
$77$	−1.41723	−	9.08297i	−0.161509	−	1.03510i
$78$	2.71005	−	1.75209i	0.306853	−	0.198385i
$79$	−0.00970735	+	0.0168136i	−0.00109216	+	0.00189168i	−0.866571	−	0.499054i	$-0.833681\pi$
$79$	−0.00970735	+	0.0168136i	−0.00109216	+	0.00189168i	0.865479	+	0.500946i	$0.167014\pi$
$80$	−3.11007	−	5.38680i	−0.347717	−	0.602263i
$81$	−2.85084	+	8.53655i	−0.316760	+	0.948506i
$82$	−15.1781	−	8.76308i	−1.67614	−	0.967720i
$83$	13.7006			1.50384			0.751918	−	0.659257i	$-0.229129\pi$
$83$	13.7006			1.50384			0.751918	+	0.659257i	$0.229129\pi$
$84$	6.40371	+	2.11142i	0.698702	+	0.230375i
$85$	−1.24555			−0.135098
$86$	9.76980	+	5.64060i	1.05350	+	0.608241i
$87$	1.08605	−	2.12079i	0.116437	−	0.227373i
$88$	−1.71100	−	2.96353i	−0.182393	−	0.315914i
$89$	0.846721	−	1.46656i	0.0897523	−	0.155455i	−0.817654	−	0.575710i	$-0.804726\pi$
$89$	0.846721	−	1.46656i	0.0897523	−	0.155455i	0.907406	+	0.420254i	$0.138059\pi$
$90$	−6.63569	−	2.98687i	−0.699463	−	0.314843i
$91$	2.46784	+	0.953821i	0.258700	+	0.0999876i
$92$			3.87687i			0.404192i
$93$	0.937923	−	0.0472379i	0.0972581	−	0.00489834i
$94$	16.7463	−	9.66846i	1.72724	−	0.997225i
$95$	8.73502	−	5.04317i	0.896194	−	0.517418i
$96$	11.9915	−	0.603946i	1.22388	−	0.0616399i
$97$			13.4723i			1.36791i	0.729526	+	0.683953i	$0.239741\pi$
$97$			13.4723i			1.36791i	−0.729526	+	0.683953i	$0.760259\pi$
$98$	3.97326	+	12.4222i	0.401360	+	1.25484i
$99$	−9.50520	−	4.27850i	−0.955309	−	0.430005i
$100$	−2.43155	+	4.21157i	−0.243155	+	0.421157i
$101$	3.29692	+	5.71044i	0.328056	+	0.568210i	0.982126	−	0.188224i	$-0.0602731\pi$
$101$	3.29692	+	5.71044i	0.328056	+	0.568210i	−0.654070	+	0.756434i	$0.726940\pi$
$102$	1.40727	−	2.74806i	0.139341	−	0.272099i
$103$	−5.90774	−	3.41084i	−0.582107	−	0.336080i	0.179863	−	0.983692i	$-0.442434\pi$
$103$	−5.90774	−	3.41084i	−0.582107	−	0.336080i	−0.761970	+	0.647612i	$0.775768\pi$
$104$	0.984865			0.0965740
$105$	−1.21510	−	5.84096i	−0.118582	−	0.570019i
$106$	8.39808			0.815694
$107$	−1.96525	−	1.13464i	−0.189988	−	0.109690i	0.401989	−	0.915645i	$-0.368319\pi$
$107$	−1.96525	−	1.13464i	−0.189988	−	0.109690i	−0.591977	+	0.805955i	$0.701652\pi$
$108$	5.97108	−	4.77514i	0.574568	−	0.459488i
$109$	−8.52317	−	14.7626i	−0.816372	−	1.41400i	−0.908339	−	0.418235i	$-0.862649\pi$
$109$	−8.52317	−	14.7626i	−0.816372	−	1.41400i	0.0919669	−	0.995762i	$-0.470685\pi$
$110$	4.21405	−	7.29894i	0.401794	−	0.695927i
$111$	−5.32508	+	3.44274i	−0.505434	+	0.326770i
$112$	7.93255	+	9.84200i	0.749555	+	0.929981i
$113$		−	14.9166i		−	1.40324i	−0.712552	−	0.701619i	$-0.752461\pi$
$113$		−	14.9166i		−	1.40324i	0.712552	−	0.701619i	$-0.247539\pi$
$114$	1.25761	+	24.9702i	0.117786	+	2.33867i
$115$	2.97067	−	1.71512i	0.277017	−	0.159936i
$116$	−1.75296	+	1.01207i	−0.162758	+	0.0939684i
$117$	2.43422	−	1.75345i	0.225044	−	0.162106i
$118$		−	5.89023i		−	0.542240i
$119$	2.50098	−	0.390233i	0.229265	−	0.0357726i
$120$	−1.20574	−	1.86499i	−0.110069	−	0.170250i
$121$	0.536353	−	0.928991i	0.0487594	−	0.0844537i
$122$	−10.5068	−	18.1983i	−0.951242	−	1.64760i
$123$	−14.5019	−	7.42633i	−1.30759	−	0.669610i
$124$	−0.690906	−	0.398895i	−0.0620452	−	0.0358218i
$125$	10.8123			0.967082
$126$	14.2599	+	3.91848i	1.27037	+	0.349086i
$127$	2.91301			0.258488			0.129244	−	0.991613i	$-0.458745\pi$
$127$	2.91301			0.258488			0.129244	+	0.991613i	$0.458745\pi$
$128$	6.58503	+	3.80187i	0.582040	+	0.336041i
$129$	9.33452	+	4.78016i	0.821859	+	0.420870i
$130$	1.21282	+	2.10067i	0.106372	+	0.184241i
$131$	0.334792	−	0.579878i	0.0292510	−	0.0506641i	−0.851029	−	0.525118i	$-0.824021\pi$
$131$	0.334792	−	0.579878i	0.0292510	−	0.0506641i	0.880280	+	0.474454i	$0.157354\pi$
$132$	4.80770	+	7.43635i	0.418457	+	0.647251i
$133$	−15.9594	+	12.8631i	−1.38385	+	1.11537i
$134$		−	7.11529i		−	0.614667i
$135$	−6.30057	−	2.46286i	−0.542266	−	0.211970i
$136$	0.816004	−	0.471120i	0.0699718	−	0.0403982i
$137$	−7.40485	+	4.27519i	−0.632639	+	0.365254i	−0.781773	−	0.623563i	$-0.785685\pi$
$137$	−7.40485	+	4.27519i	−0.632639	+	0.365254i	0.149135	+	0.988817i	$0.452351\pi$
$138$	0.427697	+	8.49205i	0.0364080	+	0.722892i
$139$		−	19.3339i		−	1.63988i	−0.572447	−	0.819942i	$-0.694006\pi$
$139$		−	19.3339i		−	1.63988i	0.572447	−	0.819942i	$-0.305994\pi$
$140$	−1.82715	+	4.72741i	−0.154422	+	0.399539i
$141$	15.0959	−	9.75974i	1.27131	−	0.821918i
$142$	15.3597	−	26.6037i	1.28895	−	2.23254i
$143$	1.73729	+	3.00907i	0.145279	+	0.251631i
$144$	14.2608	−	1.44013i	1.18840	−	0.120011i
$145$	1.55101	+	0.895475i	0.128804	+	0.0743652i
$146$	15.7196			1.30096
$147$	4.26984	+	11.3476i	0.352171	+	0.935936i
$148$	5.38682			0.442794
$149$	−5.10781	−	2.94900i	−0.418448	−	0.241591i	0.275965	−	0.961168i	$-0.411003\pi$
$149$	−5.10781	−	2.94900i	−0.418448	−	0.241591i	−0.694413	+	0.719576i	$0.744336\pi$
$150$	−4.86155	+	9.49345i	−0.396944	+	0.775137i
$151$	4.43493	+	7.68152i	0.360909	+	0.625113i	0.988111	−	0.153744i	$-0.0491331\pi$
$151$	4.43493	+	7.68152i	0.360909	+	0.625113i	−0.627201	+	0.778857i	$0.715800\pi$
$152$	−3.81510	+	6.60794i	−0.309445	+	0.535975i
$153$	1.17808	−	2.61724i	0.0952419	−	0.211592i
$154$	−6.17478	+	15.9761i	−0.497578	+	1.28739i
$155$			0.705880i			0.0566977i
$156$	−2.54532	+	0.128193i	−0.203789	+	0.0102637i
$157$	1.15525	−	0.666985i	0.0921992	−	0.0532312i	−0.453192	−	0.891413i	$-0.649715\pi$
$157$	1.15525	−	0.666985i	0.0921992	−	0.0532312i	0.545391	+	0.838182i	$0.316381\pi$
$158$	0.0313266	−	0.0180864i	0.00249221	−	0.00143888i
$159$	7.79719	−	0.392701i	0.618357	−	0.0311432i
$160$			9.02482i			0.713474i
$161$	−5.42759	+	4.37458i	−0.427754	+	0.344765i
$162$	12.5525	−	11.1184i	0.986218	−	0.873542i
$163$	−10.0912	+	17.4785i	−0.790406	+	1.36902i	0.135310	+	0.990803i	$0.456797\pi$
$163$	−10.0912	+	17.4785i	−0.790406	+	1.36902i	−0.925716	+	0.378220i	$0.876536\pi$
$164$	6.92047	+	11.9866i	0.540398	+	0.935997i
$165$	3.57122	−	6.97375i	0.278019	−	0.542905i
$166$	−22.1066	−	12.7633i	−1.71581	−	0.990622i
$167$	1.90725			0.147587			0.0737936	−	0.997274i	$-0.476489\pi$
$167$	1.90725			0.147587			0.0737936	+	0.997274i	$0.476489\pi$
$168$	3.00537	+	3.36703i	0.231869	+	0.259772i
$169$	−1.00000			−0.0769231
$170$	2.00975	+	1.16033i	0.154141	+	0.0889934i
$171$	2.33525	+	23.1247i	0.178581	+	1.76839i
$172$	−4.45456	−	7.71552i	−0.339657	−	0.588303i
$173$	8.22131	−	14.2397i	0.625055	−	1.08263i	−0.363475	−	0.931604i	$-0.618410\pi$
$173$	8.22131	−	14.2397i	0.625055	−	1.08263i	0.988530	−	0.151023i	$-0.0482568\pi$
$174$	−3.72810	+	2.41027i	−0.282626	+	0.182722i
$175$	−8.63988	+	1.34810i	−0.653114	+	0.101906i
$176$			16.6008i			1.25133i
$177$	−0.275432	−	5.46878i	−0.0207027	−	0.411059i
$178$	−2.73246	+	1.57759i	−0.204806	+	0.118245i
$179$	3.54889	−	2.04895i	0.265256	−	0.153146i	−0.361474	−	0.932382i	$-0.617726\pi$
$179$	3.54889	−	2.04895i	0.265256	−	0.153146i	0.626730	+	0.779237i	$0.284393\pi$
$180$	3.35892	+	4.66300i	0.250359	+	0.347560i
$181$			9.88890i			0.735036i	0.930016	+	0.367518i	$0.119792\pi$
$181$			9.88890i			0.735036i	−0.930016	+	0.367518i	$0.880208\pi$
$182$	−3.09342	−	3.83804i	−0.229300	−	0.284495i
$183$	−10.6060	−	16.4049i	−0.784018	−	1.21269i
$184$	−1.29747	+	2.24728i	−0.0956506	+	0.165672i
$185$	−2.38311	−	4.12768i	−0.175210	−	0.303473i
$186$	−1.55739	−	0.797534i	−0.114194	−	0.0584780i
$187$	2.87884	+	1.66210i	0.210522	+	0.121545i
$188$	−15.2710			−1.11375
$189$	13.4228	+	2.97130i	0.976364	+	0.216130i
$190$	−18.7926			−1.36336
$191$	−18.8494	−	10.8827i	−1.36389	−	0.787444i	−0.373754	−	0.927528i	$-0.621929\pi$
$191$	−18.8494	−	10.8827i	−1.36389	−	0.787444i	−0.990140	+	0.140084i	$0.955263\pi$
$192$	−5.18014	−	2.65272i	−0.373844	−	0.191444i
$193$	4.11469	+	7.12685i	0.296182	+	0.513002i	0.975259	−	0.221065i	$-0.0709532\pi$
$193$	4.11469	+	7.12685i	0.296182	+	0.513002i	−0.679077	+	0.734067i	$0.737620\pi$
$194$	12.5506	−	21.7383i	0.901082	−	1.56072i
$195$	1.22427	+	1.89365i	0.0876719	+	0.135607i
$196$	2.18769	−	10.0648i	0.156264	−	0.718915i
$197$		−	15.9358i		−	1.13538i	−0.823243	−	0.567688i	$-0.807838\pi$
$197$		−	15.9358i		−	1.13538i	0.823243	−	0.567688i	$-0.192162\pi$
$198$	11.3514	+	15.7585i	0.806706	+	1.11991i
$199$	−0.341956	+	0.197429i	−0.0242406	+	0.0139953i	−0.512071	−	0.858943i	$-0.671122\pi$
$199$	−0.341956	+	0.197429i	−0.0242406	+	0.0139953i	0.487831	+	0.872938i	$0.337788\pi$
$200$	−2.81896	+	1.62753i	−0.199331	+	0.115084i
$201$	−0.332716	−	6.60618i	−0.0234680	−	0.465964i
$202$		−	12.2855i		−	0.864402i
$203$	−3.39489	−	1.31213i	−0.238275	−	0.0920933i
$204$	−2.04759	+	1.32379i	−0.143360	+	0.0926841i
$205$	6.12320	−	10.6057i	0.427663	−	0.740734i
$206$	6.35497	+	11.0071i	0.442772	+	0.766903i
$207$	0.794190	+	7.86444i	0.0552000	+	0.546616i
$208$	−4.13768	−	2.38889i	−0.286896	−	0.165640i
$209$	−26.9191			−1.86204
$210$	−3.48072	+	10.5567i	−0.240193	+	0.728479i
$211$	7.31164			0.503354			0.251677	−	0.967811i	$-0.419018\pi$
$211$	7.31164			0.503354			0.251677	+	0.967811i	$0.419018\pi$
$212$	−5.74368	−	3.31611i	−0.394477	−	0.227752i
$213$	13.0167	−	25.4184i	0.891887	−	1.74164i
$214$	2.11403	+	3.66160i	0.144512	+	0.250302i
$215$	−3.94137	+	6.82665i	−0.268799	+	0.465574i
$216$	5.05930	−	0.769637i	0.344242	−	0.0523671i
$217$	−0.221154	−	1.41737i	−0.0150129	−	0.0962171i
$218$			31.7602i			2.15107i
$219$	14.5948	−	0.735058i	0.986225	−	0.0496706i
$220$	−5.76420	+	3.32796i	−0.388622	+	0.224371i
$221$	−0.828544	+	0.478360i	−0.0557339	+	0.0321780i
$222$	11.7995	−	0.594274i	0.791930	−	0.0398851i
$223$		−	27.1756i		−	1.81982i	−0.414811	−	0.909908i	$-0.636152\pi$
$223$		−	27.1756i		−	1.81982i	0.414811	−	0.909908i	$-0.363848\pi$
$224$	−2.82750	−	18.1213i	−0.188920	−	1.21078i
$225$	−4.06978	+	9.04151i	−0.271319	+	0.602767i
$226$	−13.8961	+	24.0688i	−0.924356	+	1.60103i
$227$	−2.42421	−	4.19886i	−0.160901	−	0.278688i	0.774291	−	0.632829i	$-0.218107\pi$
$227$	−2.42421	−	4.19886i	−0.160901	−	0.278688i	−0.935192	+	0.354141i	$0.884773\pi$
$228$	8.99976	−	17.5744i	0.596023	−	1.16389i
$229$	−9.08471	−	5.24506i	−0.600334	−	0.346603i	0.168839	−	0.985644i	$-0.445998\pi$
$229$	−9.08471	−	5.24506i	−0.600334	−	0.346603i	−0.769173	+	0.639040i	$0.779332\pi$
$230$	−6.39112			−0.421418
$231$	−4.98592	+	15.1218i	−0.328049	+	0.994938i
$232$	−1.35483			−0.0889492
$233$	−13.1466	−	7.59021i	−0.861264	−	0.497251i	0.00317138	−	0.999995i	$-0.498991\pi$
$233$	−13.1466	−	7.59021i	−0.861264	−	0.497251i	−0.864435	+	0.502744i	$0.832324\pi$
$234$	−5.56123	+	0.561600i	−0.363549	+	0.0367129i
$235$	6.75584	+	11.7015i	0.440702	+	0.763319i
$236$	−2.32585	+	4.02849i	−0.151400	+	0.262232i
$237$	0.0282395	−	0.0182572i	0.00183435	−	0.00118593i
$238$	−4.39900	−	1.70022i	−0.285145	−	0.110209i
$239$			15.7837i			1.02096i	0.859888	+	0.510482i	$0.170533\pi$
$239$			15.7837i			1.02096i	−0.859888	+	0.510482i	$0.829467\pi$
$240$	0.541919	+	10.7600i	0.0349807	+	0.694553i
$241$	12.1855	−	7.03531i	0.784938	−	0.453184i	−0.0532395	−	0.998582i	$-0.516955\pi$
$241$	12.1855	−	7.03531i	0.784938	−	0.453184i	0.838177	+	0.545398i	$0.183621\pi$
$242$	−1.73087	+	0.999317i	−0.111264	+	0.0642385i
$243$	11.1345	−	10.9098i	0.714275	−	0.699865i
$244$			16.5951i			1.06239i
$245$	−8.68004	+	2.77632i	−0.554547	+	0.177372i
$246$	16.4812	+	25.4925i	1.05081	+	1.62534i
$247$	3.87373	−	6.70949i	0.246479	−	0.426915i
$248$	−0.266995	−	0.462449i	−0.0169542	−	0.0293656i
$249$	−21.1217	−	10.8163i	−1.33853	−	0.685457i
$250$	−17.4462	−	10.0726i	−1.10340	−	0.637046i
$251$	−6.42266			−0.405395			−0.202697	−	0.979241i	$-0.564971\pi$
$251$	−6.42266			−0.405395			−0.202697	+	0.979241i	$0.564971\pi$
$252$	−8.20544	−	8.31069i	−0.516894	−	0.523524i
$253$	−9.15487			−0.575562
$254$	−4.70029	−	2.71372i	−0.294923	−	0.170274i
$255$	1.92021	+	0.983331i	0.120248	+	0.0615786i
$256$	−10.4436	−	18.0889i	−0.652727	−	1.13056i
$257$	2.09925	−	3.63601i	0.130948	−	0.226808i	−0.793094	−	0.609099i	$-0.791531\pi$
$257$	2.09925	−	3.63601i	0.130948	−	0.226808i	0.924042	+	0.382291i	$0.124865\pi$
$258$	−10.6086	−	16.4089i	−0.660463	−	1.02158i
$259$	6.07837	+	7.54150i	0.377691	+	0.468606i
$260$		−	1.91561i		−	0.118801i
$261$	−3.34864	+	2.41214i	−0.207276	+	0.149308i
$262$	−1.08041	+	0.623775i	−0.0667480	+	0.0385370i
$263$	−14.9641	+	8.63952i	−0.922725	+	0.532736i	−0.884503	−	0.466534i	$-0.845503\pi$
$263$	−14.9641	+	8.63952i	−0.922725	+	0.532736i	−0.0382217	+	0.999269i	$0.512169\pi$
$264$	0.298135	+	5.91956i	0.0183489	+	0.364324i
$265$			5.86816i			0.360478i
$266$	37.7344	−	5.88776i	2.31364	−	0.361002i
$267$	−2.46318	+	1.59248i	−0.150744	+	0.0974581i
$268$	−2.80958	+	4.86634i	−0.171623	+	0.297259i
$269$	1.88950	+	3.27272i	0.115205	+	0.199541i	0.917862	−	0.396900i	$-0.129914\pi$
$269$	1.88950	+	3.27272i	0.115205	+	0.199541i	−0.802657	+	0.596441i	$0.796581\pi$
$270$	7.87193	+	9.84347i	0.479070	+	0.599055i
$271$	−19.2185	−	11.0958i	−1.16744	−	0.674023i	−0.214366	−	0.976753i	$-0.568769\pi$
$271$	−19.2185	−	11.0958i	−1.16744	−	0.674023i	−0.953076	+	0.302730i	$0.902102\pi$
$272$	−4.57100			−0.277157
$273$	−3.05155	−	3.41877i	−0.184688	−	0.206914i
$274$	15.9308			0.962416
$275$	−9.94523	−	5.74188i	−0.599720	−	0.346249i
$276$	3.06071	−	5.97683i	0.184233	−	0.359763i
$277$	15.8011	+	27.3683i	0.949396	+	1.64440i	0.746701	+	0.665160i	$0.231637\pi$
$277$	15.8011	+	27.3683i	0.949396	+	1.64440i	0.202695	+	0.979242i	$0.435030\pi$
$278$	−18.0112	+	31.1963i	−1.08024	+	1.87103i
$279$	−1.48325	−	0.667645i	−0.0888001	−	0.0399708i
$280$	−2.64124	+	2.12881i	−0.157844	+	0.127221i
$281$			27.1748i			1.62111i	0.585662	+	0.810555i	$0.300834\pi$
$281$			27.1748i			1.62111i	−0.585662	+	0.810555i	$0.699166\pi$
$282$	−33.4501	+	1.68469i	−1.99193	+	0.100322i
$283$	4.46882	−	2.58008i	0.265644	−	0.153370i	−0.361262	−	0.932464i	$-0.617654\pi$
$283$	4.46882	−	2.58008i	0.265644	−	0.153370i	0.626906	+	0.779095i	$0.284321\pi$
$284$	−21.0098	+	12.1300i	−1.24670	+	0.719784i
$285$	−17.4479	+	0.878754i	−1.03353	+	0.0520529i
$286$		−	6.47373i		−	0.382800i
$287$	−8.97224	+	23.2140i	−0.529615	+	1.37028i
$288$	−18.9637	−	8.53597i	−1.11745	−	0.502987i
$289$	8.04234	−	13.9297i	0.473079	−	0.819397i
$290$	−1.66842	−	2.88979i	−0.0979732	−	0.169695i
$291$	10.6361	−	20.7698i	0.623499	−	1.21755i
$292$	−10.7510	−	6.20711i	−0.629156	−	0.363244i
$293$	29.2385			1.70813			0.854066	−	0.520164i	$-0.174129\pi$
$293$	29.2385			1.70813			0.854066	+	0.520164i	$0.174129\pi$
$294$	3.68166	−	22.2877i	0.214719	−	1.29985i
$295$	4.11580			0.239631
$296$	3.12254	+	1.80280i	0.181494	+	0.104786i
$297$	11.2760	+	14.1001i	0.654302	+	0.818173i
$298$	5.49449	+	9.51673i	0.318287	+	0.551289i
$299$	1.31741	−	2.28181i	0.0761876	−	0.131961i
$300$	7.07358	−	4.57317i	0.408393	−	0.264032i
$301$	5.77523	−	14.9424i	0.332879	−	0.861263i
$302$		−	16.5261i		−	0.950967i
$303$	−0.574477	−	11.4064i	−0.0330029	−	0.655282i
$304$	32.0565	−	18.5078i	1.83856	−	1.06150i
$305$	12.7161	−	7.34163i	0.728121	−	0.420381i
$306$	−4.33907	+	3.12558i	−0.248048	+	0.178677i
$307$		−	4.49689i		−	0.256651i	−0.991732	−	0.128326i	$-0.959040\pi$
$307$		−	4.49689i		−	0.256651i	0.991732	−	0.128326i	$-0.0409603\pi$
$308$	10.5315	−	8.48830i	0.600089	−	0.483666i
$309$	6.41496	+	9.92239i	0.364935	+	0.564465i
$310$	0.657588	−	1.13898i	0.0373485	−	0.0646894i
$311$	−0.646059	−	1.11901i	−0.0366346	−	0.0634531i	0.847127	−	0.531391i	$-0.178330\pi$
$311$	−0.646059	−	1.11901i	−0.0366346	−	0.0634531i	−0.883761	+	0.467938i	$0.844997\pi$
$312$	−1.51833	−	0.777530i	−0.0859585	−	0.0440189i
$313$	2.75796	+	1.59231i	0.155889	+	0.0900025i	0.575915	−	0.817509i	$-0.304646\pi$
$313$	2.75796	+	1.59231i	0.155889	+	0.0900025i	−0.420026	+	0.907512i	$0.637979\pi$
$314$	−2.48541			−0.140260
$315$	−2.73804	+	9.96409i	−0.154271	+	0.561413i
$316$	−0.0285669			−0.00160701
$317$	7.53152	+	4.34833i	0.423012	+	0.244226i	0.696365	−	0.717687i	$-0.254799\pi$
$317$	7.53152	+	4.34833i	0.423012	+	0.244226i	−0.273353	+	0.961914i	$0.588133\pi$
$318$	−12.9470	−	6.63010i	−0.726032	−	0.371798i
$319$	−2.38991	−	4.13944i	−0.133809	−	0.231764i
$320$	2.18724	−	3.78841i	0.122270	−	0.211779i
$321$	2.13398	+	3.30075i	0.119107	+	0.184230i
$322$	12.8330	−	2.00235i	0.715155	−	0.111587i
$323$		−	7.41214i		−	0.412423i
$324$	−12.9753	+	2.64761i	−0.720848	+	0.147090i
$325$	2.86228	−	1.65254i	0.158771	−	0.0916665i
$326$	32.5655	−	18.8017i	1.80363	−	1.04133i
$327$	1.48513	+	29.4878i	0.0821280	+	1.63068i
$328$			9.26426i			0.511533i
$329$	−17.2314	−	21.3792i	−0.949999	−	1.17867i
$330$	−12.2590	+	7.92561i	−0.674835	+	0.436291i
$331$	7.09976	−	12.2972i	0.390238	−	0.675913i	−0.602242	−	0.798313i	$-0.705726\pi$
$331$	7.09976	−	12.2972i	0.390238	−	0.675913i	0.992481	+	0.122401i	$0.0390593\pi$
$332$	10.0796	+	17.4583i	0.553187	+	0.958149i
$333$	10.9274	−	1.10351i	0.598820	−	0.0604718i
$334$	−3.07744	−	1.77676i	−0.168390	−	0.0972202i
$335$	4.97181			0.271639
$336$	−4.45927	−	21.4356i	−0.243273	−	1.16941i
$337$	12.1072			0.659520			0.329760	−	0.944065i	$-0.393032\pi$
$337$	12.1072			0.659520			0.329760	+	0.944065i	$0.393032\pi$
$338$	1.61355	+	0.931585i	0.0877657	+	0.0506716i
$339$	−11.7764	+	22.9964i	−0.639604	+	1.24899i
$340$	−0.916350	−	1.58716i	−0.0496960	−	0.0860761i
$341$	0.941952	−	1.63151i	0.0510096	−	0.0883512i
$342$	17.7746	−	39.4885i	0.961141	−	2.13529i
$343$	16.5592	−	8.29416i	0.894112	−	0.447843i
$344$		−	5.96320i		−	0.321514i
$345$	−5.93382	+	0.298853i	−0.319466	+	0.0160897i
$346$	−26.5310	+	15.3177i	−1.42632	+	0.823485i
$347$	28.8243	−	16.6417i	1.54737	−	0.893373i	0.549027	−	0.835805i	$-0.314999\pi$
$347$	28.8243	−	16.6417i	1.54737	−	0.893373i	0.998342	−	0.0575687i	$-0.0183348\pi$
$348$	3.50148	−	0.176350i	0.187699	−	0.00945334i
$349$		−	18.2529i		−	0.977056i	−0.872548	−	0.488528i	$-0.837534\pi$
$349$		−	18.2529i		−	0.977056i	0.872548	−	0.488528i	$-0.162466\pi$
$350$	15.1968	+	5.87356i	0.812302	+	0.313955i
$351$	−5.13705	+	0.781464i	−0.274196	+	0.0417115i
$352$	12.0430	−	20.8592i	0.641896	−	1.11180i
$353$	1.07945	+	1.86966i	0.0574534	+	0.0995122i	0.893322	−	0.449418i	$-0.148369\pi$
$353$	1.07945	+	1.86966i	0.0574534	+	0.0995122i	−0.835868	+	0.548930i	$0.815035\pi$
$354$	−4.65021	+	9.08075i	−0.247156	+	0.482637i
$355$	18.5894	+	10.7326i	0.986621	+	0.569626i
$356$	2.49174			0.132062
$357$	−4.16375	−	1.37286i	−0.220369	−	0.0726597i
$358$	−7.63508			−0.403527
$359$	−22.7538	−	13.1369i	−1.20090	−	0.693341i	−0.240146	−	0.970737i	$-0.577195\pi$
$359$	−22.7538	−	13.1369i	−1.20090	−	0.693341i	−0.960756	+	0.277396i	$0.910529\pi$
$360$	0.386479	+	3.82710i	0.0203692	+	0.201706i
$361$	20.5115	+	35.5270i	1.07955	+	1.86984i
$362$	9.21235	−	15.9563i	0.484190	−	0.838642i
$363$	−1.56029	+	1.00875i	−0.0818942	+	0.0529457i
$364$	0.600165	+	3.84643i	0.0314572	+	0.201608i
$365$			10.9840i			0.574931i
$366$	1.83077	+	36.3506i	0.0956961	+	1.90007i
$367$	2.53282	−	1.46232i	0.132212	−	0.0763327i	−0.432435	−	0.901665i	$-0.642346\pi$
$367$	2.53282	−	1.46232i	0.132212	−	0.0763327i	0.564647	+	0.825332i	$0.309012\pi$
$368$	10.9020	−	6.29428i	0.568306	−	0.328112i
$369$	16.4940	+	22.8978i	0.858645	+	1.19201i
$370$			8.88030i			0.461665i
$371$	−1.83851	−	11.7829i	−0.0954507	−	0.611739i
$372$	0.750226	+	1.16042i	0.0388974	+	0.0601648i
$373$	−11.2076	+	19.4121i	−0.580306	+	1.00512i	0.415137	+	0.909759i	$0.363734\pi$
$373$	−11.2076	+	19.4121i	−0.580306	+	1.00512i	−0.995443	+	0.0953600i	$0.969600\pi$
$374$	−3.09678	−	5.36377i	−0.160131	−	0.277354i
$375$	−16.6689	−	8.53608i	−0.860780	−	0.440801i
$376$	−8.85201	−	5.11071i	−0.456508	−	0.263565i
$377$	1.37565			0.0708498
$378$	−18.8904	−	17.2988i	−0.971615	−	0.889756i
$379$	−30.2646			−1.55459			−0.777293	−	0.629139i	$-0.783408\pi$
$379$	−30.2646			−1.55459			−0.777293	+	0.629139i	$0.783408\pi$
$380$	12.8527	+	7.42053i	0.659332	+	0.380665i
$381$	−4.49088	−	2.29976i	−0.230075	−	0.117820i
$382$	20.2763	+	35.1196i	1.03743	+	1.79688i
$383$	1.51228	−	2.61935i	0.0772741	−	0.133843i	−0.824799	−	0.565426i	$-0.808712\pi$
$383$	1.51228	−	2.61935i	0.0772741	−	0.133843i	0.902073	+	0.431584i	$0.142045\pi$
$384$	−7.15040	−	11.0599i	−0.364892	−	0.564400i
$385$	−11.1633	−	4.31463i	−0.568936	−	0.219894i
$386$		−	15.3327i		−	0.780416i
$387$	−10.6168	−	14.7388i	−0.539685	−	0.749215i
$388$	−17.1674	+	9.91161i	−0.871543	+	0.503186i
$389$	−1.39609	+	0.806033i	−0.0707846	+	0.0408675i	−0.534975	−	0.844868i	$-0.679679\pi$
$389$	−1.39609	+	0.806033i	−0.0707846	+	0.0408675i	0.464190	+	0.885736i	$0.346345\pi$
$390$	−0.211330	−	4.19602i	−0.0107011	−	0.212474i
$391$		−	2.52078i		−	0.127481i
$392$	4.63650	−	5.10205i	0.234179	−	0.257692i
$393$	−0.973938	+	0.629664i	−0.0491287	+	0.0317624i
$394$	−14.8455	+	25.7132i	−0.747907	+	1.29541i
$395$	0.0126379	+	0.0218895i	0.000635882	+	0.00110138i
$396$	−1.54102	−	15.2599i	−0.0774392	−	0.766840i
$397$	7.52852	+	4.34660i	0.377846	+	0.218149i	0.676881	−	0.736093i	$-0.263331\pi$
$397$	7.52852	+	4.34660i	0.377846	+	0.218149i	−0.299035	+	0.954242i	$0.596665\pi$
$398$	0.735686			0.0368766
$399$	34.7591	−	7.23097i	1.74013	−	0.362001i
$400$	15.7909			0.789547
$401$	22.2992	+	12.8744i	1.11357	+	0.642918i	0.939751	−	0.341860i	$-0.111057\pi$
$401$	22.2992	+	12.8744i	1.11357	+	0.642918i	0.173816	+	0.984778i	$0.444390\pi$
$402$	−5.61736	+	10.9694i	−0.280169	+	0.547103i
$403$	0.271098	+	0.469556i	0.0135044	+	0.0233902i
$404$	−4.85111	+	8.40236i	−0.241352	+	0.418033i
$405$	7.76897	+	8.77106i	0.386043	+	0.435838i
$406$	4.25548	+	5.27982i	0.211196	+	0.262033i
$407$			12.7205i			0.630530i
$408$	−1.62994	+	0.0820910i	−0.0806942	+	0.00406411i
$409$	−18.8027	+	10.8557i	−0.929732	+	0.536781i	−0.886727	−	0.462294i	$-0.847026\pi$
$409$	−18.8027	+	10.8557i	−0.929732	+	0.536781i	−0.0430050	+	0.999075i	$0.513693\pi$
$410$	−19.7602	+	11.4086i	−0.975888	+	0.563429i
$411$	14.7909	−	0.744937i	0.729583	−	0.0367450i
$412$		−	10.0374i		−	0.494509i
$413$	−8.26429	+	1.28949i	−0.406659	+	0.0634517i
$414$	6.04493	−	13.4295i	0.297092	−	0.660026i
$415$	8.91834	−	15.4470i	0.437784	−	0.758264i
$416$	3.46604	+	6.00336i	0.169937	+	0.294339i
$417$	−15.2637	+	29.8064i	−0.747468	+	1.45963i
$418$	43.4354	+	25.0775i	2.12450	+	1.22658i
$419$	−7.03963			−0.343908			−0.171954	−	0.985105i	$-0.555008\pi$
$419$	−7.03963			−0.343908			−0.171954	+	0.985105i	$0.555008\pi$
$420$	6.54903	−	5.84558i	0.319560	−	0.285235i
$421$	−3.33312			−0.162446			−0.0812231	−	0.996696i	$-0.525883\pi$
$421$	−3.33312			−0.162446			−0.0812231	+	0.996696i	$0.525883\pi$
$422$	−11.7977	−	6.81142i	−0.574304	−	0.331575i
$423$	−30.9780	+	3.12831i	−1.50620	+	0.152103i
$424$	−2.21960	−	3.84446i	−0.107793	−	0.186703i
$425$	1.58102	−	2.73841i	0.0766907	−	0.132832i
$426$	−44.6825	+	28.8879i	−2.16487	+	1.39962i
$427$	−23.2330	+	18.7256i	−1.12432	+	0.906193i
$428$		−	3.33902i		−	0.161398i
$429$	−0.302717	−	6.01053i	−0.0146153	−	0.290191i
$430$	12.7192	−	7.34344i	0.613375	−	0.354132i
$431$	31.4183	−	18.1394i	1.51337	−	0.873743i	0.513490	−	0.858096i	$-0.328352\pi$
$431$	31.4183	−	18.1394i	1.51337	−	0.873743i	0.999878	−	0.0156476i	$-0.00498098\pi$
$432$	−23.1223	−	9.03841i	−1.11247	−	0.434860i
$433$			30.5146i			1.46644i	0.679993	+	0.733219i	$0.261983\pi$
$433$			30.5146i			1.46644i	−0.679993	+	0.733219i	$0.738017\pi$
$434$	−0.963554	+	2.49302i	−0.0462521	+	0.119669i
$435$	−1.68417	−	2.60501i	−0.0807500	−	0.124901i
$436$	12.5410	−	21.7217i	0.600606	−	1.04028i
$437$	10.2065	+	17.6782i	0.488245	+	0.845665i
$438$	−24.2342	−	12.4102i	−1.15796	−	0.592984i
$439$	−8.59972	−	4.96505i	−0.410442	−	0.236969i	0.280538	−	0.959843i	$-0.409487\pi$
$439$	−8.59972	−	4.96505i	−0.410442	−	0.236969i	−0.690980	+	0.722874i	$0.742821\pi$
$440$	−4.45506			−0.212387
$441$	2.37604	−	20.8651i	0.113145	−	0.993578i
$442$	1.78253			0.0847864
$443$	27.5184	+	15.8877i	1.30744	+	0.754849i	0.981668	−	0.190600i	$-0.0610434\pi$
$443$	27.5184	+	15.8877i	1.30744	+	0.754849i	0.325769	+	0.945449i	$0.394377\pi$
$444$	−8.30466	−	4.25277i	−0.394121	−	0.201828i
$445$	−1.10234	−	1.90931i	−0.0522558	−	0.0905098i
$446$	−25.3164	+	43.8493i	−1.19877	+	2.07633i
$447$	5.54636	+	8.57887i	0.262334	+	0.405767i
$448$	−3.20493	+	8.29218i	−0.151419	+	0.391769i
$449$		−	40.0170i		−	1.88852i	−0.329204	−	0.944259i	$-0.606780\pi$
$449$		−	40.0170i		−	1.88852i	0.329204	−	0.944259i	$-0.393220\pi$
$450$	14.9897	−	10.7976i	0.706623	−	0.509004i
$451$	−28.3053	+	16.3420i	−1.33284	+	0.769517i
$452$	19.0079	−	10.9742i	0.894054	−	0.516183i
$453$	−0.772770	−	15.3436i	−0.0363079	−	0.720905i
$454$			9.03345i			0.423961i
$455$	2.68183	−	2.16153i	0.125726	−	0.101334i
$456$	11.0984	−	7.17528i	0.519731	−	0.336013i
$457$	5.31734	−	9.20991i	0.248735	−	0.430821i	−0.714440	−	0.699697i	$-0.753319\pi$
$457$	5.31734	−	9.20991i	0.248735	−	0.430821i	0.963175	+	0.268875i	$0.0866519\pi$
$458$	9.77244	+	16.9264i	0.456636	+	0.790917i
$459$	−3.88245	+	3.10484i	−0.181217	+	0.144921i
$460$	4.37106	+	2.52363i	0.203802	+	0.117665i
$461$	−22.4080			−1.04364			−0.521822	−	0.853054i	$-0.674747\pi$
$461$	−22.4080			−1.04364			−0.521822	+	0.853054i	$0.674747\pi$
$462$	22.1322	−	19.7549i	1.02968	−	0.919083i
$463$	22.7448			1.05704			0.528521	−	0.848921i	$-0.322747\pi$
$463$	22.7448			1.05704			0.528521	+	0.848921i	$0.322747\pi$
$464$	5.69201	+	3.28628i	0.264245	+	0.152562i
$465$	0.557277	−	1.08823i	0.0258431	−	0.0504654i
$466$	14.1418	+	24.4944i	0.655108	+	1.13468i
$467$	3.82865	−	6.63141i	0.177169	−	0.306865i	−0.763741	−	0.645523i	$-0.776640\pi$
$467$	3.82865	−	6.63141i	0.177169	−	0.306865i	0.940910	+	0.338658i	$0.109973\pi$
$468$	4.02523	+	1.81184i	0.186066	+	0.0837525i
$469$	−9.98311	+	1.55768i	−0.460977	+	0.0719270i
$470$		−	25.1745i		−	1.16122i
$471$	−2.30758	+	0.116220i	−0.106328	+	0.00535513i
$472$	−2.69642	+	1.55678i	−0.124113	+	0.0716565i
$473$	18.2195	−	10.5190i	0.837732	−	0.483665i
$474$	−0.0625740	+	0.00315150i	−0.00287412	+	0.000144753i
$475$			25.6060i			1.17488i
$476$	2.33724	+	2.89984i	0.107127	+	0.132914i
$477$	−12.3307	−	5.55030i	−0.564582	−	0.254131i
$478$	14.7039	−	25.4679i	0.672540	−	1.16487i
$479$	−11.7971	−	20.4332i	−0.539024	−	0.933617i	−0.998957	−	0.0456635i	$-0.985460\pi$
$479$	−11.7971	−	20.4332i	−0.539024	−	0.933617i	0.459933	−	0.887954i	$-0.347874\pi$
$480$	7.12490	−	13.9132i	0.325205	−	0.635049i
$481$	−3.17052	−	1.83050i	−0.144563	−	0.0834637i
$482$	−26.2160			−1.19410
$483$	11.8211	−	2.45916i	0.537881	−	0.111896i
$484$	1.57838			0.0717447
$485$	15.1896	+	8.76974i	0.689726	+	0.398214i
$486$	−28.1294	+	7.23087i	−1.27598	+	0.327999i
$487$	−13.9941	−	24.2384i	−0.634132	−	1.09835i	−0.986698	−	0.162561i	$-0.948024\pi$
$487$	−13.9941	−	24.2384i	−0.634132	−	1.09835i	0.352567	−	0.935787i	$-0.385309\pi$
$488$	−5.55386	+	9.61957i	−0.251411	+	0.435457i
$489$	29.3562	−	18.9792i	1.32753	−	0.858268i
$490$	16.5921	+	3.60647i	0.749554	+	0.162923i
$491$			0.562924i			0.0254044i	0.999919	+	0.0127022i	$0.00404335\pi$
$491$			0.562924i			0.0254044i	−0.999919	+	0.0127022i	$0.995957\pi$
$492$	−1.20587	−	23.9429i	−0.0543647	−	1.07943i
$493$	1.13979	−	0.658058i	0.0513336	−	0.0296374i
$494$	−12.5009	+	7.21741i	−0.562443	+	0.324727i
$495$	−11.0112	+	7.93176i	−0.494919	+	0.356506i
$496$			2.59049i			0.116317i
$497$	−40.6889	−	15.7263i	−1.82515	−	0.705420i
$498$	24.0047	+	37.1294i	1.07567	+	1.66381i
$499$	−0.624553	+	1.08176i	−0.0279589	+	0.0484262i	−0.879666	−	0.475591i	$-0.842234\pi$
$499$	−0.624553	+	1.08176i	−0.0279589	+	0.0484262i	0.851707	+	0.524018i	$0.175567\pi$
$500$	7.95463	+	13.7778i	0.355742	+	0.616163i
$501$	−2.94033	−	1.50573i	−0.131364	−	0.0672711i
$502$	10.3633	+	5.98325i	0.462537	+	0.267046i
$503$	9.12488			0.406858			0.203429	−	0.979090i	$-0.434791\pi$
$503$	9.12488			0.406858			0.203429	+	0.979090i	$0.434791\pi$
$504$	−1.97507	−	7.56350i	−0.0879765	−	0.336905i
$505$	8.58447			0.382004
$506$	14.7719	+	8.52854i	0.656689	+	0.379140i
$507$	1.54166	+	0.789478i	0.0684676	+	0.0350620i
$508$	2.14311	+	3.71197i	0.0950849	+	0.164692i
$509$	−6.29994	+	10.9118i	−0.279240	+	0.483658i	−0.971196	−	0.238282i	$-0.923416\pi$
$509$	−6.29994	+	10.9118i	−0.279240	+	0.483658i	0.691956	+	0.721939i	$0.256749\pi$
$510$	−2.18231	−	3.37550i	−0.0966341	−	0.149469i
$511$	−3.44133	−	22.0553i	−0.152235	−	0.975670i
$512$			23.7090i			1.04780i
$513$	14.6563	−	37.4942i	0.647092	−	1.65541i
$514$	−6.77451	+	3.91126i	−0.298811	+	0.172518i
$515$	−7.69123	+	4.44053i	−0.338916	+	0.195673i
$516$	0.776191	+	15.4115i	0.0341699	+	0.678453i
$517$		−	36.0609i		−	1.58596i
$518$	−2.78222	−	17.8311i	−0.122244	−	0.783455i
$519$	−23.9165	+	15.4623i	−1.04982	+	0.678721i
$520$	0.641093	−	1.11041i	0.0281138	−	0.0486945i
$521$	−4.24345	−	7.34987i	−0.185909	−	0.322004i	0.757974	−	0.652285i	$-0.226190\pi$
$521$	−4.24345	−	7.34987i	−0.185909	−	0.322004i	−0.943882	+	0.330282i	$0.892856\pi$
$522$	7.65032	−	0.772567i	0.334845	−	0.0338143i
$523$	13.8668	+	8.00601i	0.606354	+	0.350078i	0.771537	−	0.636184i	$-0.219488\pi$
$523$	13.8668	+	8.00601i	0.606354	+	0.350078i	−0.165183	+	0.986263i	$0.552822\pi$
$524$	0.985230			0.0430400
$525$	14.3841	+	4.74269i	0.627773	+	0.206988i
$526$	32.1938			1.40372
$527$	0.449234	+	0.259365i	0.0195689	+	0.0112981i
$528$	13.1059	−	25.5928i	0.570363	−	1.11378i
$529$	−8.02888	−	13.9064i	−0.349082	−	0.604627i
$530$	5.46669	−	9.46859i	0.237458	−	0.411289i
$531$	−3.89286	+	8.64846i	−0.168936	+	0.375311i
$532$	−28.1324	−	10.8732i	−1.21970	−	0.471413i
$533$		−	9.40663i		−	0.407446i
$534$	5.45800	−	0.274889i	0.236191	−	0.0118956i
$535$	−2.55854	+	1.47718i	−0.110615	+	0.0638639i
$536$	−3.25722	+	1.88056i	−0.140691	+	0.0812277i
$537$	−7.08879	+	0.357022i	−0.305904	+	0.0154066i
$538$		−	7.04093i		−	0.303556i
$539$	23.7671	+	5.16603i	1.02372	+	0.222517i
$540$	−1.49698	−	9.84057i	−0.0644196	−	0.423471i
$541$	−6.56009	+	11.3624i	−0.282040	+	0.488508i	−0.971887	−	0.235447i	$-0.924344\pi$
$541$	−6.56009	+	11.3624i	−0.282040	+	0.488508i	0.689847	+	0.723955i	$0.257678\pi$
$542$	20.6734	+	35.8074i	0.887999	+	1.53806i
$543$	7.80707	−	15.2453i	0.335033	−	0.654240i
$544$	5.74354	+	3.31603i	0.246252	+	0.142174i
$545$	−22.1925			−0.950621
$546$	1.73896	+	8.35916i	0.0744207	+	0.357739i
$547$	−10.2040			−0.436293			−0.218147	−	0.975916i	$-0.570001\pi$
$547$	−10.2040			−0.436293			−0.218147	+	0.975916i	$0.570001\pi$
$548$	−10.8955	−	6.29053i	−0.465433	−	0.268718i
$549$	3.39956	+	33.6640i	0.145090	+	1.43675i
$550$	10.6981	+	18.5297i	0.456169	+	0.790108i
$551$	−5.32890	+	9.22993i	−0.227019	+	0.393208i
$552$	3.77444	−	2.44023i	0.160651	−	0.103863i
$553$	−0.0322342	−	0.0399934i	−0.00137074	−	0.00170069i
$554$		−	58.8803i		−	2.50158i
$555$	0.415249	+	8.24490i	0.0176264	+	0.349977i
$556$	24.6367	−	14.2240i	1.04483	−	0.603233i
$557$	5.48064	−	3.16425i	0.232222	−	0.134074i	−0.379375	−	0.925243i	$-0.623861\pi$
$557$	5.48064	−	3.16425i	0.232222	−	0.134074i	0.611597	+	0.791170i	$0.290527\pi$
$558$	1.77134	+	2.45906i	0.0749868	+	0.104100i
$559$			6.05484i			0.256092i
$560$	16.2602	−	2.53711i	0.687119	−	0.107212i
$561$	−3.12601	−	4.83518i	−0.131980	−	0.204142i
$562$	25.3156	−	43.8479i	1.06787	−	1.84961i
$563$	−5.14937	−	8.91897i	−0.217020	−	0.375890i	0.736875	−	0.676029i	$-0.236300\pi$
$563$	−5.14937	−	8.91897i	−0.217020	−	0.375890i	−0.953896	+	0.300139i	$0.902967\pi$
$564$	23.5427	+	12.0561i	0.991326	+	0.507653i
$565$	−16.8181	−	9.70991i	−0.707541	−	0.408499i
$566$	−9.61425			−0.404117
$567$	−18.3476	−	15.1777i	−0.770529	−	0.637406i
$568$	−16.2381			−0.681337
$569$	19.0928	+	11.0232i	0.800410	+	0.462117i	0.843615	−	0.536949i	$-0.180423\pi$
$569$	19.0928	+	11.0232i	0.800410	+	0.462117i	−0.0432043	+	0.999066i	$0.513757\pi$
$570$	28.9718	+	14.8363i	1.21349	+	0.621425i
$571$	−5.40225	−	9.35697i	−0.226077	−	0.391577i	0.730565	−	0.682843i	$-0.239257\pi$
$571$	−5.40225	−	9.35697i	−0.226077	−	0.391577i	−0.956642	+	0.291266i	$0.905923\pi$
$572$	−2.55625	+	4.42756i	−0.106882	+	0.185126i
$573$	20.4677	+	31.6586i	0.855052	+	1.32256i
$574$	36.1030	−	29.0987i	1.50691	−	1.21456i
$575$			8.70827i			0.363160i
$576$	5.89176	+	8.17921i	0.245490	+	0.340800i
$577$	−26.0649	+	15.0486i	−1.08509	+	0.626480i	−0.932266	−	0.361773i	$-0.882172\pi$
$577$	−26.0649	+	15.0486i	−1.08509	+	0.626480i	−0.152829	+	0.988253i	$0.548838\pi$
$578$	−25.9535	+	14.9843i	−1.07952	+	0.623263i
$579$	−0.716970	−	14.2357i	−0.0297963	−	0.591614i
$580$			2.63521i			0.109421i
$581$	−13.0679	+	33.8109i	−0.542149	+	1.40271i
$582$	−36.5107	+	23.6047i	−1.51342	+	0.978446i
$583$	7.83069	−	13.5632i	0.324314	−	0.561728i
$584$	−4.15465	−	7.19606i	−0.171921	−	0.297775i
$585$	−0.392418	−	3.88591i	−0.0162245	−	0.160663i
$586$	−47.1779	−	27.2382i	−1.94890	−	1.12520i
$587$	−15.0550			−0.621385			−0.310693	−	0.950510i	$-0.600561\pi$
$587$	−15.0550			−0.621385			−0.310693	+	0.950510i	$0.600561\pi$
$588$	−11.3186	+	13.7894i	−0.466773	+	0.568666i
$589$	−4.20064			−0.173084
$590$	−6.64106	−	3.83422i	−0.273408	−	0.157852i
$591$	−12.5809	+	24.5676i	−0.517511	+	1.01058i
$592$	−8.74574	−	15.1481i	−0.359448	−	0.622582i
$593$	−4.89393	+	8.47653i	−0.200969	+	0.348089i	−0.948841	−	0.315754i	$-0.897743\pi$
$593$	−4.89393	+	8.47653i	−0.200969	+	0.348089i	0.747872	+	0.663843i	$0.231076\pi$
$594$	−5.05899	−	33.2559i	−0.207573	−	1.36451i
$595$	1.18803	−	3.07380i	0.0487044	−	0.126014i
$596$		−	8.67833i		−	0.355478i
$597$	0.683047	−	0.0344012i	0.0279552	−	0.00140795i
$598$	−4.25141	+	2.45455i	−0.173853	+	0.100374i
$599$	−17.6231	+	10.1747i	−0.720062	+	0.415728i	−0.814775	−	0.579777i	$-0.803140\pi$
$599$	−17.6231	+	10.1747i	−0.720062	+	0.415728i	0.0947136	+	0.995505i	$0.469806\pi$
$600$	5.63079	−	0.283591i	0.229876	−	0.0115776i
$601$			4.67290i			0.190612i	0.995448	+	0.0953058i	$0.0303829\pi$
$601$			4.67290i			0.190612i	−0.995448	+	0.0953058i	$0.969617\pi$
$602$	−23.2387	+	18.7302i	−0.947140	+	0.763385i
$603$	−4.70250	+	10.4472i	−0.191501	+	0.425442i
$604$	−6.52557	+	11.3026i	−0.265522	+	0.459897i
$605$	−0.698273	−	1.20944i	−0.0283888	−	0.0491709i
$606$	−9.69910	+	18.9400i	−0.393999	+	0.769386i
$607$	40.5639	+	23.4196i	1.64644	+	0.950572i	0.978472	+	0.206381i	$0.0661686\pi$
$607$	40.5639	+	23.4196i	1.64644	+	0.950572i	0.667967	+	0.744191i	$0.267165\pi$
$608$	−53.7060			−2.17807
$609$	4.19788	+	4.70305i	0.170107	+	0.190577i
$610$	−27.3574			−1.10767
$611$	8.98805	+	5.18925i	0.363617	+	0.209935i
$612$	4.20179	−	0.424318i	0.169847	−	0.0171520i
$613$	−16.8531	−	29.1904i	−0.680690	−	1.17899i	−0.974771	−	0.223209i	$-0.928347\pi$
$613$	−16.8531	−	29.1904i	−0.680690	−	1.17899i	0.294080	−	0.955781i	$-0.404987\pi$
$614$	−4.18924	+	7.25597i	−0.169064	+	0.292827i
$615$	−17.8129	+	11.5163i	−0.718285	+	0.464381i
$616$	8.94550	−	1.39578i	0.360425	−	0.0562377i
$617$			44.3597i			1.78585i	0.450202	+	0.892927i	$0.351352\pi$
$617$			44.3597i			1.78585i	−0.450202	+	0.892927i	$0.648648\pi$
$618$	−1.10733	−	21.9864i	−0.0445434	−	0.884422i
$619$	30.1275	−	17.3941i	1.21093	−	0.699130i	0.247967	−	0.968769i	$-0.420238\pi$
$619$	30.1275	−	17.3941i	1.21093	−	0.699130i	0.962962	+	0.269639i	$0.0869043\pi$
$620$	−0.899484	+	0.519317i	−0.0361242	+	0.0208563i
$621$	4.98443	−	12.7513i	0.200018	−	0.511692i
$622$			2.40744i			0.0965294i
$623$	2.81162	+	3.48841i	0.112645	+	0.139760i
$624$	4.49293	+	6.94947i	0.179861	+	0.278201i
$625$	−1.22448	+	2.12087i	−0.0489793	+	0.0848346i
$626$	−2.96674	−	5.13854i	−0.118575	−	0.205377i
$627$	41.5002	+	21.2521i	1.65736	+	0.848726i
$628$	1.69984	+	0.981404i	0.0678311	+	0.0391623i
$629$	−3.50256			−0.139656
$630$	13.7004	−	13.5269i	0.545836	−	0.538923i
$631$	23.6044			0.939676			0.469838	−	0.882753i	$-0.344312\pi$
$631$	23.6044			0.939676			0.469838	+	0.882753i	$0.344312\pi$
$632$	−0.0165592	−	0.00956043i	−0.000658688	−	0.000380294i
$633$	−11.2721	−	5.77238i	−0.448025	−	0.229432i
$634$	−8.10167	−	14.0325i	−0.321759	−	0.557302i
$635$	1.89621	−	3.28433i	0.0752488	−	0.130335i
$636$	6.23681	+	9.64684i	0.247306	+	0.382522i
$637$	−4.70775	+	5.18045i	−0.186528	+	0.205257i
$638$			8.90562i			0.352577i
$639$	−40.1346	+	28.9103i	−1.58770	+	1.14367i
$640$	8.57299	−	4.94962i	0.338877	−	0.195651i
$641$	27.8316	−	16.0686i	1.09928	−	0.634671i	0.163250	−	0.986585i	$-0.447802\pi$
$641$	27.8316	−	16.0686i	1.09928	−	0.634671i	0.936032	+	0.351914i	$0.114469\pi$
$642$	−0.368361	−	7.31393i	−0.0145381	−	0.288658i
$643$		−	18.7359i		−	0.738874i	−0.929256	−	0.369437i	$-0.879551\pi$
$643$		−	18.7359i		−	0.738874i	0.929256	−	0.369437i	$-0.120449\pi$
$644$	−9.56749	−	3.69784i	−0.377012	−	0.145715i
$645$	11.4658	−	7.41277i	0.451464	−	0.291878i
$646$	−6.90504	+	11.9599i	−0.271675	+	0.470555i
$647$	−20.4106	−	35.3521i	−0.802422	−	1.38984i	−0.918018	−	0.396539i	$-0.870211\pi$
$647$	−20.4106	−	35.3521i	−0.802422	−	1.38984i	0.115596	−	0.993296i	$-0.463122\pi$
$648$	−8.40735	−	2.80769i	−0.330272	−	0.110297i
$649$	−9.51290	−	5.49227i	−0.373414	−	0.215591i
$650$	−6.15793			−0.241534
$651$	−0.778035	+	2.35970i	−0.0304936	+	0.0924839i
$652$	−29.6965			−1.16301
$653$	13.5824	+	7.84181i	0.531521	+	0.306874i	0.741636	−	0.670803i	$-0.234050\pi$
$653$	13.5824	+	7.84181i	0.531521	+	0.306874i	−0.210115	+	0.977677i	$0.567384\pi$
$654$	25.0740	−	48.9636i	0.980472	−	1.91463i
$655$	−0.435863	−	0.754937i	−0.0170306	−	0.0294978i
$656$	22.4714	−	38.9216i	0.877361	−	1.51963i
$657$	−23.0806	−	10.3891i	−0.900459	−	0.405316i
$658$	7.88725	+	50.5490i	0.307477	+	1.97061i
$659$		−	27.4350i		−	1.06872i	−0.845258	−	0.534359i	$-0.820553\pi$
$659$		−	27.4350i		−	1.06872i	0.845258	−	0.534359i	$-0.179447\pi$
$660$	11.5138	−	0.579886i	0.448174	−	0.0225720i
$661$	−38.6444	+	22.3113i	−1.50309	+	0.867810i	−0.503098	+	0.864230i	$0.667806\pi$
$661$	−38.6444	+	22.3113i	−1.50309	+	0.867810i	−0.999994	+	0.00358060i	$0.998860\pi$
$662$	−22.9117	+	13.2281i	−0.890488	+	0.514124i
$663$	1.65499	−	0.0833526i	0.0642745	−	0.00323715i
$664$			13.4932i			0.523639i
$665$	4.11407	+	26.3669i	0.159537	+	1.02246i
$666$	−18.6600	−	8.39927i	−0.723061	−	0.325465i
$667$	−1.81229	+	3.13899i	−0.0701723	+	0.121542i
$668$	1.40317	+	2.43035i	0.0542901	+	0.0940332i
$669$	−21.4546	+	41.8957i	−0.829482	+	1.61978i
$670$	−8.02228	−	4.63166i	−0.309928	−	0.178937i
$671$	−39.1878			−1.51283
$672$	−9.94733	+	30.1692i	−0.383727	+	1.16380i
$673$	22.0724			0.850828			0.425414	−	0.904999i	$-0.360129\pi$
$673$	22.0724			0.850828			0.425414	+	0.904999i	$0.360129\pi$
$674$	−19.5356	−	11.2789i	−0.752482	−	0.434446i
$675$	13.4123	−	10.7260i	0.516240	−	0.412842i
$676$	−0.735702	−	1.27427i	−0.0282962	−	0.0490105i
$677$	11.3690	−	19.6917i	0.436947	−	0.756814i	−0.560505	−	0.828151i	$-0.689393\pi$
$677$	11.3690	−	19.6917i	0.436947	−	0.756814i	0.997452	+	0.0713366i	$0.0227265\pi$
$678$	40.4249	−	26.1353i	1.55251	−	1.00372i
$679$	−33.2475	−	12.8502i	−1.27592	−	0.493145i
$680$		−	1.22669i		−	0.0470416i
$681$	0.422411	+	8.38710i	0.0161868	+	0.321394i
$682$	−3.03978	+	1.75502i	−0.116399	+	0.0672031i
$683$	14.1921	−	8.19382i	0.543046	−	0.313528i	−0.203267	−	0.979123i	$-0.565156\pi$
$683$	14.1921	−	8.19382i	0.543046	−	0.313528i	0.746312	+	0.665596i	$0.231822\pi$
$684$	−27.7492	+	19.9887i	−1.06102	+	0.764285i
$685$			11.1317i			0.425319i
$686$	−34.4459	−	2.04323i	−1.31515	−	0.0780109i
$687$	9.86470	+	15.2583i	0.376362	+	0.582140i
$688$	−14.4643	+	25.0530i	−0.551448	+	0.955136i
$689$	2.25371	+	3.90354i	0.0858594	+	0.148713i
$690$	9.85295	+	5.04565i	0.375095	+	0.192085i
$691$	17.7667	+	10.2576i	0.675878	+	0.390219i	0.798300	−	0.602260i	$-0.205733\pi$
$691$	17.7667	+	10.2576i	0.675878	+	0.390219i	−0.122422	+	0.992478i	$0.539066\pi$
$692$	24.1937			0.919708
$693$	19.6249	−	19.3764i	0.745488	−	0.736048i
$694$	−62.0127			−2.35397
$695$	−21.7984	−	12.5853i	−0.826862	−	0.477389i
$696$	2.08870	+	1.06961i	0.0791718	+	0.0405435i
$697$	−4.49976	−	7.79381i	−0.170440	−	0.295212i
$698$	−17.0041	+	29.4520i	−0.643617	+	1.11478i
$699$	14.2754	+	22.0805i	0.539944	+	0.835162i
$700$	−8.07422	−	10.0178i	−0.305177	−	0.378636i
$701$			2.09798i			0.0792395i	0.999215	+	0.0396197i	$0.0126147\pi$
$701$			2.09798i			0.0792395i	−0.999215	+	0.0396197i	$0.987385\pi$
$702$	9.01691	+	3.52467i	0.340321	+	0.133030i
$703$	24.5635	−	14.1817i	0.926429	−	0.534874i
$704$	−10.1108	+	5.83746i	−0.381064	+	0.220008i
$705$	−1.17718	−	23.3733i	−0.0443352	−	0.880289i
$706$		−	4.02240i		−	0.151385i
$707$	−17.2371	+	2.68954i	−0.648268	+	0.101150i
$708$	6.76608	−	4.37437i	0.254285	−	0.164399i
$709$	−18.7002	+	32.3897i	−0.702300	+	1.21642i	0.265357	+	0.964150i	$0.414510\pi$
$709$	−18.7002	+	32.3897i	−0.702300	+	1.21642i	−0.967657	+	0.252269i	$0.918823\pi$
$710$	−19.9966	−	34.6351i	−0.750459	−	1.29983i
$711$	−0.0579494	+	0.00585201i	−0.00217327	+	0.000219468i
$712$	1.44437	+	0.833906i	0.0541300	+	0.0312520i
$713$	−1.42859			−0.0535010
$714$	5.43949	+	6.09408i	0.203568	+	0.228065i
$715$	4.52352			0.169170
$716$	5.22184	+	3.01483i	0.195149	+	0.112670i
$717$	12.4609	−	24.3332i	0.465361	−	0.908740i
$718$	24.4763	+	42.3943i	0.913449	+	1.58214i
$719$	−1.74183	+	3.01694i	−0.0649594	+	0.112513i	−0.896676	−	0.442687i	$-0.854025\pi$
$719$	−1.74183	+	3.01694i	−0.0649594	+	0.112513i	0.831717	+	0.555200i	$0.187358\pi$
$720$	7.65930	−	17.0161i	0.285445	−	0.634152i
$721$	14.0523	−	11.3260i	0.523336	−	0.421803i
$722$		−	76.4328i		−	2.84453i
$723$	−24.3402	+	1.22588i	−0.905221	+	0.0455909i
$724$	−12.6012	+	7.27528i	−0.468318	+	0.270384i
$725$	−3.93751	+	2.27332i	−0.146236	+	0.0844291i
$726$	3.45735	−	0.174127i	0.128314	−	0.00646248i
$727$		−	1.79727i		−	0.0666572i	−0.999444	−	0.0333286i	$-0.989389\pi$
$727$		−	1.79727i		−	0.0666572i	0.999444	−	0.0333286i	$-0.0106108\pi$
$728$	−0.939385	+	2.43049i	−0.0348159	+	0.0900799i
$729$	−25.7786	+	8.02884i	−0.954764	+	0.297365i
$730$	10.2326	−	17.7233i	0.378724	−	0.655970i
$731$	2.89639	+	5.01670i	0.107127	+	0.185549i
$732$	13.1015	−	25.5841i	0.484244	−	0.945614i
$733$	−21.2295	−	12.2569i	−0.784129	−	0.452717i	0.0537623	−	0.998554i	$-0.482879\pi$
$733$	−21.2295	−	12.2569i	−0.784129	−	0.452717i	−0.837892	+	0.545836i	$0.816212\pi$
$734$	−5.44911			−0.201130
$735$	15.5735	+	2.57256i	0.574439	+	0.0948903i
$736$	−18.2647			−0.673247
$737$	−11.4914	−	6.63456i	−0.423291	−	0.244387i
$738$	−5.28276	−	52.3124i	−0.194461	−	1.92565i
$739$	20.0212	+	34.6777i	0.736492	+	1.27564i	0.954066	+	0.299597i	$0.0968523\pi$
$739$	20.0212	+	34.6777i	0.736492	+	1.27564i	−0.217574	+	0.976044i	$0.569814\pi$
$740$	3.50652	−	6.07348i	0.128902	−	0.223265i
$741$	−11.2690	+	7.28555i	−0.413976	+	0.267641i
$742$	−8.01027	+	20.7251i	−0.294066	+	0.760843i
$743$			31.6827i			1.16233i	0.813787	+	0.581163i	$0.197402\pi$
$743$			31.6827i			1.16233i	−0.813787	+	0.581163i	$0.802598\pi$
$744$	0.0465230	+	0.923728i	0.00170561	+	0.0338655i
$745$	−6.64982	+	3.83927i	−0.243630	+	0.140660i
$746$	36.1680	−	20.8816i	1.32420	−	0.764530i
$747$	24.0233	+	33.3502i	0.878966	+	1.22022i
$748$			4.89124i			0.178842i
$749$	4.67460	−	3.76768i	0.170806	−	0.137668i
$750$	18.9441	+	29.3019i	0.691741	+	1.06996i
$751$	−5.38435	+	9.32596i	−0.196478	+	0.340309i	−0.947384	−	0.320100i	$-0.896284\pi$
$751$	−5.38435	+	9.32596i	−0.196478	+	0.340309i	0.750906	+	0.660409i	$0.229617\pi$
$752$	24.7931	+	42.9429i	0.904111	+	1.56597i
$753$	9.90157	+	5.07055i	0.360833	+	0.184781i
$754$	−2.21969	−	1.28154i	−0.0808363	−	0.0466709i
$755$	11.5476			0.420260
$756$	6.08892	+	19.2903i	0.221452	+	0.701581i
$757$	20.2177			0.734823			0.367412	−	0.930058i	$-0.380244\pi$
$757$	20.2177			0.734823			0.367412	+	0.930058i	$0.380244\pi$
$758$	48.8335	+	28.1940i	1.77371	+	1.02405i
$759$	14.1137	+	7.22757i	0.512296	+	0.262344i
$760$	4.96684	+	8.60282i	0.180166	+	0.312057i
$761$	9.72745	−	16.8484i	0.352620	−	0.610756i	−0.634088	−	0.773261i	$-0.718624\pi$
$761$	9.72745	−	16.8484i	0.352620	−	0.610756i	0.986708	+	0.162506i	$0.0519575\pi$
$762$	5.10385	+	7.89441i	0.184893	+	0.285984i
$763$	44.5612	−	6.95296i	1.61322	−	0.251714i
$764$		−	32.0257i		−	1.15865i
$765$	−2.18400	−	3.03193i	−0.0789627	−	0.109620i
$766$	−4.88030	+	2.81764i	−0.176332	+	0.101806i
$767$	2.73786	−	1.58070i	0.0988582	−	0.0570758i
$768$	1.81976	+	36.1320i	0.0656651	+	1.30380i
$769$		−	10.8279i		−	0.390463i	−0.980757	−	0.195231i	$-0.937454\pi$
$769$		−	10.8279i		−	0.390463i	0.980757	−	0.195231i	$-0.0625458\pi$
$770$	13.9932	+	17.3615i	0.504279	+	0.625664i
$771$	−6.10689	+	3.94819i	−0.219934	+	0.142191i
$772$	−6.05437	+	10.4865i	−0.217902	+	0.377416i
$773$	16.2689	+	28.1786i	0.585152	+	1.01351i	0.994856	+	0.101295i	$0.0322986\pi$
$773$	16.2689	+	28.1786i	0.585152	+	1.01351i	−0.409704	+	0.912218i	$0.634368\pi$
$774$	3.40040	+	33.6723i	0.122225	+	1.21033i
$775$	−1.55192	−	0.896001i	−0.0557466	−	0.0321853i
$776$	−13.2684			−0.476309
$777$	−3.41695	−	16.4252i	−0.122582	−	0.589250i
$778$	3.00355			0.107683
$779$	63.1137	+	36.4387i	2.26128	+	1.30555i
$780$	−1.51233	+	2.95322i	−0.0541501	+	0.105742i
$781$	−28.6439	−	49.6126i	−1.02496	−	1.77528i
$782$	−2.34832	+	4.06741i	−0.0839758	+	0.145450i
$783$	7.06681	−	1.07502i	0.252547	−	0.0384182i
$784$	−31.8547	+	10.1887i	−1.13767	+	0.363883i
$785$		−	1.73668i		−	0.0619849i
$786$	2.15809	−	0.108691i	0.0769764	−	0.00387687i
$787$	28.0882	−	16.2167i	1.00124	−	0.578063i	0.0926216	−	0.995701i	$-0.470475\pi$
$787$	28.0882	−	16.2167i	1.00124	−	0.578063i	0.908613	+	0.417638i	$0.137142\pi$
$788$	20.3065	−	11.7240i	0.723390	−	0.417649i
$789$	29.8903	−	1.50541i	1.06412	−	0.0535939i
$790$		−	0.0470932i		−	0.00167550i
$791$	36.8118	+	14.2278i	1.30888	+	0.505882i
$792$	4.21374	−	9.36134i	0.149729	−	0.332641i
$793$	5.63921	−	9.76740i	0.200254	−	0.346850i
$794$	−8.09845	−	14.0269i	−0.287403	−	0.497797i
$795$	4.63279	−	9.04673i	0.164308	−	0.320854i
$796$	−0.503156	−	0.290497i	−0.0178339	−	0.0102964i
$797$	46.6147			1.65118			0.825589	−	0.564271i	$-0.190843\pi$
$797$	46.6147			1.65118			0.825589	+	0.564271i	$0.190843\pi$
$798$	−62.8219	−	20.7135i	−2.22387	−	0.733251i
$799$	9.92932			0.351274
$800$	−19.8416	−	11.4556i	−0.701506	−	0.405015i
$801$	5.05462	−	0.510440i	0.178596	−	0.0180355i
$802$	−23.9873	−	41.5471i	−0.847019	−	1.46708i
$803$	14.6575	−	25.3875i	0.517252	−	0.895907i
$804$	8.17330	−	5.28415i	0.288250	−	0.186358i
$805$	1.39915	+	8.96706i	0.0493134	+	0.316047i
$806$		−	1.01020i		−	0.0355829i
$807$	−0.329239	−	6.53715i	−0.0115898	−	0.230118i
$808$	−5.62401	+	3.24703i	−0.197852	+	0.114230i
$809$	2.18884	−	1.26373i	0.0769554	−	0.0444302i	−0.461029	−	0.887385i	$-0.652519\pi$
$809$	2.18884	−	1.26373i	0.0769554	−	0.0444302i	0.537984	+	0.842955i	$0.319186\pi$
$810$	−4.36465	−	21.3900i	−0.153358	−	0.751569i
$811$		−	19.3434i		−	0.679240i	−0.940563	−	0.339620i	$-0.889702\pi$
$811$		−	19.3434i		−	0.679240i	0.940563	−	0.339620i	$-0.110298\pi$
$812$	−0.825619	−	5.29135i	−0.0289735	−	0.185690i
$813$	20.8686	+	32.2786i	0.731893	+	1.13206i
$814$	11.8502	−	20.5251i	0.415349	−	0.719405i
$815$	13.1377	+	22.7551i	0.460193	+	0.797077i
$816$	7.04694	+	3.60870i	0.246692	+	0.126330i
$817$	−40.6249	−	23.4548i	−1.42128	−	0.820579i
$818$	40.4521			1.41437
$819$	2.00542	+	7.67973i	0.0700750	+	0.268352i
$820$	18.0194			0.629265
$821$	−23.2281	−	13.4108i	−0.810667	−	0.468039i	0.0365202	−	0.999333i	$-0.488373\pi$
$821$	−23.2281	−	13.4108i	−0.810667	−	0.468039i	−0.847188	+	0.531294i	$0.821706\pi$
$822$	−24.5599	−	12.5770i	−0.856626	−	0.438674i
$823$	−19.2415	−	33.3273i	−0.670717	−	1.16172i	−0.977701	−	0.210002i	$-0.932653\pi$
$823$	−19.2415	−	33.3273i	−0.670717	−	1.16172i	0.306984	−	0.951715i	$-0.400680\pi$
$824$	3.35921	−	5.81833i	0.117024	−	0.202691i
$825$	10.7991	+	16.7036i	0.375977	+	0.581545i
$826$	14.5361	+	5.61823i	0.505777	+	0.195483i
$827$			19.4439i			0.676130i	0.941123	+	0.338065i	$0.109772\pi$
$827$			19.4439i			0.676130i	−0.941123	+	0.338065i	$0.890228\pi$
$828$	−9.43715	+	6.79790i	−0.327964	+	0.236243i
$829$	14.7653	−	8.52473i	0.512819	−	0.296076i	−0.221173	−	0.975235i	$-0.570988\pi$
$829$	14.7653	−	8.52473i	0.512819	−	0.296076i	0.733992	+	0.679159i	$0.237655\pi$
$830$	−28.7804	+	16.6164i	−0.998983	+	0.576763i
$831$	−2.75329	−	54.6673i	−0.0955104	−	1.89639i
$832$		−	3.36010i		−	0.116490i
$833$	−1.42246	+	6.54423i	−0.0492853	+	0.226744i
$834$	52.3960	−	33.8748i	1.81433	−	1.17299i
$835$	1.24151	−	2.15037i	0.0429644	−	0.0744165i
$836$	−19.8045	−	34.3023i	−0.684951	−	1.18637i
$837$	1.75959	+	2.20028i	0.0608202	+	0.0760528i
$838$	11.3588	+	6.55801i	0.392384	+	0.226543i
$839$	−4.60051			−0.158827			−0.0794136	−	0.996842i	$-0.525305\pi$
$839$	−4.60051			−0.158827			−0.0794136	+	0.996842i	$0.525305\pi$
$840$	5.75256	−	1.19671i	0.198482	−	0.0412904i
$841$	27.1076			0.934744
$842$	5.37816	+	3.10508i	0.185344	+	0.107008i
$843$	21.4539	−	41.8943i	0.738911	−	1.44292i
$844$	5.37919	+	9.31703i	0.185159	+	0.320705i
$845$	−0.650945	+	1.12747i	−0.0223932	+	0.0387862i
$846$	52.8988	+	23.8109i	1.81870	+	0.818636i
$847$	1.78101	+	2.20972i	0.0611964	+	0.0759270i
$848$			21.5354i			0.739530i
$849$	−8.92634	+	0.449569i	−0.306351	+	0.0154292i
$850$	−5.10212	+	2.94571i	−0.175001	+	0.101037i
$851$	8.35374	−	4.82303i	0.286362	−	0.165331i
$852$	41.9664	−	2.11361i	1.43774	−	0.0724111i
$853$			13.0844i			0.448000i	0.974589	+	0.224000i	$0.0719115\pi$
$853$			13.0844i			0.448000i	−0.974589	+	0.224000i	$0.928088\pi$
$854$	54.9321	−	8.57116i	1.87974	−	0.293299i
$855$	27.5926	+	12.4200i	0.943646	+	0.424756i
$856$	1.11747	−	1.93551i	0.0381942	−	0.0661543i
$857$	15.9491	+	27.6246i	0.544809	+	0.943638i	0.998619	+	0.0525389i	$0.0167313\pi$
$857$	15.9491	+	27.6246i	0.544809	+	0.943638i	−0.453809	+	0.891099i	$0.649935\pi$
$858$	−5.11087	+	9.98032i	−0.174482	+	0.340722i
$859$	3.35162	+	1.93506i	0.114356	+	0.0660233i	0.556087	−	0.831124i	$-0.312302\pi$
$859$	3.35162	+	1.93506i	0.114356	+	0.0660233i	−0.441731	+	0.897147i	$0.645635\pi$
$860$	−11.5987			−0.395512
$861$	32.1592	−	28.7048i	1.09598	−	0.978258i
$862$	−67.5935			−2.30224
$863$	−14.8225	−	8.55777i	−0.504563	−	0.291310i	0.226033	−	0.974120i	$-0.427424\pi$
$863$	−14.8225	−	8.55777i	−0.504563	−	0.291310i	−0.730596	+	0.682810i	$0.760758\pi$
$864$	22.4967	+	28.1310i	0.765352	+	0.957036i
$865$	−10.7033	−	18.5386i	−0.363921	−	0.630330i
$866$	28.4269	−	49.2369i	0.965987	−	1.67314i
$867$	−23.3958	+	15.1257i	−0.794563	+	0.513696i
$868$	1.64341	−	1.32457i	0.0557809	−	0.0449588i
$869$		−	0.0674579i		−	0.00228835i
$870$	0.290717	+	5.77227i	0.00985622	+	0.195698i
$871$	3.30728	−	1.90946i	0.112063	−	0.0646995i
$872$	14.5391	−	8.39418i	0.492357	−	0.284263i
$873$	−32.7946	+	23.6230i	−1.10993	+	0.799518i
$874$		−	38.0330i		−	1.28649i
$875$	−10.3130	+	26.6830i	−0.348643	+	0.902051i
$876$	11.6741	+	18.0570i	0.394431	+	0.610089i
$877$	−16.5924	+	28.7389i	−0.560287	+	0.970445i	0.437184	+	0.899372i	$0.355976\pi$
$877$	−16.5924	+	28.7389i	−0.560287	+	0.970445i	−0.997471	+	0.0710734i	$0.977358\pi$
$878$	9.25073	+	16.0227i	0.312197	+	0.540741i
$879$	−45.0759	−	23.0832i	−1.52037	−	0.778576i
$880$	18.7169	+	10.8062i	0.630946	+	0.364277i
$881$	34.9637			1.17796			0.588979	−	0.808148i	$-0.299530\pi$
$881$	34.9637			1.17796			0.588979	+	0.808148i	$0.299530\pi$
$882$	−23.2715	+	31.4535i	−0.783593	+	1.05910i
$883$	36.6775			1.23430			0.617148	−	0.786847i	$-0.288288\pi$
$883$	36.6775			1.23430			0.617148	+	0.786847i	$0.288288\pi$
$884$	−1.21912	−	0.703861i	−0.0410035	−	0.0236734i
$885$	−6.34518	−	3.24934i	−0.213291	−	0.109225i
$886$	−29.6016	−	51.2714i	−0.994484	−	1.72250i
$887$	7.33879	−	12.7112i	0.246412	−	0.426799i	−0.716115	−	0.697982i	$-0.754082\pi$
$887$	7.33879	−	12.7112i	0.246412	−	0.426799i	0.962528	+	0.271183i	$0.0874149\pi$
$888$	−3.39063	−	5.24448i	−0.113782	−	0.175993i
$889$	−2.77849	+	7.18883i	−0.0931875	+	0.241106i
$890$			4.10769i			0.137690i
$891$	−6.25208	−	30.6399i	−0.209453	−	1.02647i
$892$	34.6292	−	19.9932i	1.15947	−	0.669421i
$893$	−69.6344	+	40.2035i	−2.33023	+	1.34536i
$894$	−0.957395	−	19.0094i	−0.0320201	−	0.635768i
$895$		−	5.33502i		−	0.178330i
$896$	−15.6633	+	12.6245i	−0.523275	+	0.421754i
$897$	−3.83244	+	2.47773i	−0.127961	+	0.0827288i
$898$	−37.2792	+	64.5695i	−1.24402	+	2.15471i
$899$	−0.372937	−	0.645946i	−0.0124382	−	0.0215435i
$900$	−14.5155	+	1.46585i	−0.483850	+	0.0488615i
$901$	3.73459	+	2.15617i	0.124417	+	0.0718324i
$902$	60.8960			2.02762
$903$	−20.7001	+	18.4767i	−0.688857	+	0.614865i
$904$	14.6909			0.488611
$905$	11.1494	+	6.43713i	0.370620	+	0.213978i
$906$	−13.0470	+	25.4776i	−0.433456	+	0.846437i
$907$	18.0616	+	31.2836i	0.599725	+	1.03875i	0.992861	+	0.119274i	$0.0380566\pi$
$907$	18.0616	+	31.2836i	0.599725	+	1.03875i	−0.393137	+	0.919480i	$0.628610\pi$
$908$	3.56700	−	6.17822i	0.118375	−	0.205032i
$909$	−8.11947	+	18.0384i	−0.269306	+	0.598296i
$910$	−6.34093	+	0.989386i	−0.210200	+	0.0327978i
$911$			44.3300i			1.46872i	0.678761	+	0.734359i	$0.262517\pi$
$911$			44.3300i			1.46872i	−0.678761	+	0.734359i	$0.737483\pi$
$912$	−64.0317	+	3.22492i	−2.12030	+	0.106788i
$913$	−41.2261	+	23.8019i	−1.36439	+	0.787728i
$914$	−17.1596	+	9.90712i	−0.567590	+	0.327698i
$915$	−25.4000	+	1.27925i	−0.839697	+	0.0422908i
$916$		−	15.4352i		−	0.509993i
$917$	1.11171	+	1.37931i	0.0367120	+	0.0455489i
$918$	9.15697	−	1.39299i	0.302225	−	0.0459754i
$919$	6.67681	−	11.5646i	0.220248	−	0.381480i	−0.734635	−	0.678462i	$-0.762647\pi$
$919$	6.67681	−	11.5646i	0.220248	−	0.381480i	0.954883	+	0.296982i	$0.0959801\pi$
$920$	1.68916	+	2.92571i	0.0556900	+	0.0964579i
$921$	−3.55020	+	6.93269i	−0.116983	+	0.228440i
$922$	36.1565	+	20.8749i	1.19075	+	0.687480i
$923$	16.4877			0.542698
$924$	−22.9374	+	4.77169i	−0.754585	+	0.156977i
$925$	12.0999			0.397843
$926$	−36.7000	−	21.1887i	−1.20604	−	0.696305i
$927$	−2.05620	−	20.3615i	−0.0675345	−	0.668758i
$928$	−4.76807	−	8.25855i	−0.156520	−	0.271100i
$929$	11.0098	−	19.0695i	0.361219	−	0.625649i	−0.626943	−	0.779065i	$-0.715694\pi$
$929$	11.0098	−	19.0695i	0.361219	−	0.625649i	0.988162	+	0.153416i	$0.0490274\pi$
$930$	−1.91297	+	1.23676i	−0.0627289	+	0.0405551i
$931$	−16.5216	−	51.6543i	−0.541475	−	1.69290i
$932$		−	22.3365i		−	0.731657i
$933$	0.112573	+	2.23518i	0.00368549	+	0.0731765i
$934$	−12.3554	+	7.13342i	−0.404283	+	0.233413i
$935$	3.74794	−	2.16387i	0.122571	−	0.0707662i
$936$	1.72691	+	2.39738i	0.0564458	+	0.0783607i
$937$		−	16.1821i		−	0.528647i	−0.964434	−	0.264324i	$-0.914851\pi$
$937$		−	16.1821i		−	0.528647i	0.964434	−	0.264324i	$-0.0851487\pi$
$938$	17.5594	+	6.78671i	0.573334	+	0.221594i
$939$	−2.99475	−	4.63215i	−0.0977299	−	0.151164i
$940$	−9.94056	+	17.2176i	−0.324225	+	0.561575i
$941$	−25.9980	−	45.0299i	−0.847511	−	1.46793i	−0.883423	−	0.468577i	$-0.844767\pi$
$941$	−25.9980	−	45.0299i	−0.847511	−	1.46793i	0.0359117	−	0.999355i	$-0.488566\pi$
$942$	3.83167	+	1.96218i	0.124843	+	0.0639313i
$943$	21.4642	+	12.3924i	0.698970	+	0.403551i
$944$	15.1045			0.491609
$945$	12.0876	−	13.1996i	0.393208	−	0.429384i
$946$	−39.1974			−1.27442
$947$	−25.0095	−	14.4393i	−0.812701	−	0.469213i	0.0351922	−	0.999381i	$-0.488796\pi$
$947$	−25.0095	−	14.4393i	−0.812701	−	0.469213i	−0.847893	+	0.530168i	$0.822129\pi$
$948$	0.0440405	+	0.0225529i	0.00143037	+	0.000732485i
$949$	4.21850	+	7.30665i	0.136938	+	0.237184i
$950$	23.8541	−	41.3166i	0.773930	−	1.34049i
$951$	−8.17816	−	12.6496i	−0.265195	−	0.410192i
$952$	0.384327	+	2.46313i	0.0124561	+	0.0798305i
$953$		−	34.9081i		−	1.13079i	−0.824822	−	0.565393i	$-0.808725\pi$
$953$		−	34.9081i		−	1.13079i	0.824822	−	0.565393i	$-0.191275\pi$
$954$	14.7256	+	20.4428i	0.476759	+	0.661859i
$955$	−24.5398	+	14.1681i	−0.794090	+	0.458468i
$956$	−20.1128	+	11.6121i	−0.650494	+	0.375563i
$957$	0.416433	+	8.26841i	0.0134614	+	0.267280i
$958$			43.9601i			1.42029i
$959$	−3.48758	−	22.3517i	−0.112620	−	0.721775i
$960$	−6.36285	+	4.11367i	−0.205360	+	0.132768i
$961$	−15.3530	+	26.5922i	−0.495258	+	0.857813i
$962$	3.41054	+	5.90723i	0.109960	+	0.190457i
$963$	−0.684010	−	6.77338i	−0.0220419	−	0.218269i
$964$	17.9298	+	10.3518i	0.577480	+	0.333408i
$965$	10.7138			0.344888
$966$	−21.3650	−	7.04441i	−0.687406	−	0.226650i
$967$	−39.5732			−1.27259			−0.636294	−	0.771447i	$-0.719533\pi$
$967$	−39.5732			−1.27259			−0.636294	+	0.771447i	$0.719533\pi$
$968$	0.914931	+	0.528235i	0.0294070	+	0.0169781i
$969$	−5.85173	+	11.4270i	−0.187985	+	0.367089i
$970$	−16.3395	−	28.3009i	−0.524631	−	0.908687i
$971$	−24.0451	+	41.6474i	−0.771644	+	1.33653i	0.165017	+	0.986291i	$0.447232\pi$
$971$	−24.0451	+	41.6474i	−0.771644	+	1.33653i	−0.936661	+	0.350236i	$0.886101\pi$
$972$	22.0937	+	6.16196i	0.708656	+	0.197645i
$973$	47.7130	+	18.4411i	1.52961	+	0.591195i
$974$			52.1466i			1.67089i
$975$	−5.71732	+	0.287949i	−0.183101	+	0.00922176i
$976$	46.6665	−	26.9429i	1.49376	−	0.862421i
$977$	−29.6311	+	17.1075i	−0.947982	+	0.547318i	−0.892454	−	0.451139i	$-0.851018\pi$
$977$	−29.6311	+	17.1075i	−0.947982	+	0.547318i	−0.0555288	+	0.998457i	$0.517684\pi$
$978$	−65.0485	+	3.27613i	−2.08002	+	0.104759i
$979$			5.88400i			0.188053i
$980$	−9.92370	−	9.01820i	−0.317001	−	0.288076i
$981$	20.9904	−	46.6327i	0.670171	−	1.48887i
$982$	0.524412	−	0.908308i	0.0167347	−	0.0289853i
$983$	−26.9763	−	46.7244i	−0.860411	−	1.49028i	−0.871533	−	0.490337i	$-0.836874\pi$
$983$	−26.9763	−	46.7244i	−0.860411	−	1.49028i	0.0111219	−	0.999938i	$-0.496460\pi$
$984$	7.31393	−	14.2824i	0.233160	−	0.455305i
$985$	−17.9671	−	10.3733i	−0.572480	−	0.330521i
$986$	−2.45215			−0.0780923
$987$	9.68662	+	46.5634i	0.308329	+	1.48213i
$988$	11.3996			0.362670
$989$	−13.8160	−	7.97668i	−0.439324	−	0.253644i
$990$	25.1563	−	2.54041i	0.799521	−	0.0807395i
$991$	−2.19788	−	3.80684i	−0.0698179	−	0.120928i	0.829003	−	0.559244i	$-0.188908\pi$
$991$	−2.19788	−	3.80684i	−0.0698179	−	0.120928i	−0.898821	+	0.438316i	$0.855575\pi$
$992$	1.87928	−	3.25500i	0.0596671	−	0.103346i
$993$	−20.6538	+	13.3530i	−0.655428	+	0.423743i
$994$	51.0033	+	63.2804i	1.61773	+	2.00713i
$995$			0.514061i			0.0162968i
$996$	−1.75633	−	34.8724i	−0.0556513	−	1.10497i
$997$	−2.12003	+	1.22400i	−0.0671422	+	0.0387645i	−0.533195	−	0.845992i	$-0.679009\pi$
$997$	−2.12003	+	1.22400i	−0.0671422	+	0.0387645i	0.466053	+	0.884757i	$0.345676\pi$
$998$	2.01550	−	1.16365i	0.0637995	−	0.0368347i
$999$	−17.7176	−	6.92574i	−0.560561	−	0.219121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.131.7	✓	64
3.2	odd	2	inner	273.2.bh.a.131.26	yes	64
7.3	odd	6	inner	273.2.bh.a.248.26	yes	64
21.17	even	6	inner	273.2.bh.a.248.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.7	✓	64	1.1	even	1	trivial
273.2.bh.a.131.26	yes	64	3.2	odd	2	inner
273.2.bh.a.248.7	yes	64	21.17	even	6	inner
273.2.bh.a.248.26	yes	64	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61355 - 0.931585i) q^{2} +(-1.54166 - 0.789478i) q^{3} +(0.735702 + 1.27427i) q^{4} +(0.650945 - 1.12747i) q^{5} +(1.75209 + 2.71005i) q^{6} +(-0.953821 + 2.46784i) q^{7} +0.984865i q^{8} +(1.75345 + 2.43422i) q^{9} +O(q^{10})\)	\(q+(-1.61355 - 0.931585i) q^{2} +(-1.54166 - 0.789478i) q^{3} +(0.735702 + 1.27427i) q^{4} +(0.650945 - 1.12747i) q^{5} +(1.75209 + 2.71005i) q^{6} +(-0.953821 + 2.46784i) q^{7} +0.984865i q^{8} +(1.75345 + 2.43422i) q^{9} +(-2.10067 + 1.21282i) q^{10} +(-3.00907 + 1.73729i) q^{11} +(-0.128193 - 2.54532i) q^{12} -1.00000i q^{13} +(3.83804 - 3.09342i) q^{14} +(-1.89365 + 1.22427i) q^{15} +(2.38889 - 4.13768i) q^{16} +(-0.478360 - 0.828544i) q^{17} +(-0.561600 - 5.56123i) q^{18} +(6.70949 + 3.87373i) q^{19} +1.91561 q^{20} +(3.41877 - 3.05155i) q^{21} +6.47373 q^{22} +(2.28181 + 1.31741i) q^{23} +(0.777530 - 1.51833i) q^{24} +(1.65254 + 2.86228i) q^{25} +(-0.931585 + 1.61355i) q^{26} +(-0.781464 - 5.13705i) q^{27} +(-3.84643 + 0.600165i) q^{28} +1.37565i q^{29} +(4.19602 - 0.211330i) q^{30} +(-0.469556 + 0.271098i) q^{31} +(-6.00336 + 3.46604i) q^{32} +(6.01053 - 0.302717i) q^{33} +1.78253i q^{34} +(2.16153 + 2.68183i) q^{35} +(-1.81184 + 4.02523i) q^{36} +(1.83050 - 3.17052i) q^{37} +(-7.21741 - 12.5009i) q^{38} +(-0.789478 + 1.54166i) q^{39} +(1.11041 + 0.641093i) q^{40} +9.40663 q^{41} +(-8.35916 + 1.73896i) q^{42} -6.05484 q^{43} +(-4.42756 - 2.55625i) q^{44} +(3.88591 - 0.392418i) q^{45} +(-2.45455 - 4.25141i) q^{46} +(-5.18925 + 8.98805i) q^{47} +(-6.94947 + 4.49293i) q^{48} +(-5.18045 - 4.70775i) q^{49} -6.15793i q^{50} +(0.0833526 + 1.65499i) q^{51} +(1.27427 - 0.735702i) q^{52} +(-3.90354 + 2.25371i) q^{53} +(-3.52467 + 9.01691i) q^{54} +4.52352i q^{55} +(-2.43049 - 0.939385i) q^{56} +(-7.28555 - 11.2690i) q^{57} +(1.28154 - 2.21969i) q^{58} +(1.58070 + 2.73786i) q^{59} +(-2.95322 - 1.51233i) q^{60} +(9.76740 + 5.63921i) q^{61} +1.01020 q^{62} +(-7.67973 + 2.00542i) q^{63} +3.36010 q^{64} +(-1.12747 - 0.650945i) q^{65} +(-9.98032 - 5.11087i) q^{66} +(1.90946 + 3.30728i) q^{67} +(0.703861 - 1.21912i) q^{68} +(-2.47773 - 3.83244i) q^{69} +(-0.989386 - 6.34093i) q^{70} +16.4877i q^{71} +(-2.39738 + 1.72691i) q^{72} +(-7.30665 + 4.21850i) q^{73} +(-5.90723 + 3.41054i) q^{74} +(-0.287949 - 5.71732i) q^{75} +11.3996i q^{76} +(-1.41723 - 9.08297i) q^{77} +(2.71005 - 1.75209i) q^{78} +(-0.00970735 + 0.0168136i) q^{79} +(-3.11007 - 5.38680i) q^{80} +(-2.85084 + 8.53655i) q^{81} +(-15.1781 - 8.76308i) q^{82} +13.7006 q^{83} +(6.40371 + 2.11142i) q^{84} -1.24555 q^{85} +(9.76980 + 5.64060i) q^{86} +(1.08605 - 2.12079i) q^{87} +(-1.71100 - 2.96353i) q^{88} +(0.846721 - 1.46656i) q^{89} +(-6.63569 - 2.98687i) q^{90} +(2.46784 + 0.953821i) q^{91} +3.87687i q^{92} +(0.937923 - 0.0472379i) q^{93} +(16.7463 - 9.66846i) q^{94} +(8.73502 - 5.04317i) q^{95} +(11.9915 - 0.603946i) q^{96} +13.4723i q^{97} +(3.97326 + 12.4222i) q^{98} +(-9.50520 - 4.27850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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