LMFDB - Embedded newform 132.2.j.a.79.1

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			79.1
Character	$\chi$	$=$	132.79
Dual form			132.2.j.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 0.00375312i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.99997 + 0.0106154i) q^{4} +(0.907723 + 2.79369i) q^{5} +(-0.828215 - 1.14632i) q^{6} +(-2.11823 - 1.53899i) q^{7} +(-2.82834 - 0.0225185i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.41421 - 0.00375312i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.99997 + 0.0106154i) q^{4} +(0.907723 + 2.79369i) q^{5} +(-0.828215 - 1.14632i) q^{6} +(-2.11823 - 1.53899i) q^{7} +(-2.82834 - 0.0225185i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.27323 - 3.95426i) q^{10} +(0.900319 + 3.19209i) q^{11} +(1.16697 + 1.62425i) q^{12} +(4.58403 + 1.48944i) q^{13} +(2.98984 + 2.18440i) q^{14} +(-1.72659 + 2.37645i) q^{15} +(3.99977 + 0.0424609i) q^{16} +(-1.58673 + 0.515561i) q^{17} +(0.440584 - 1.34383i) q^{18} +(-1.68276 + 1.22260i) q^{19} +(1.78577 + 5.59693i) q^{20} -2.61828i q^{21} +(-1.26126 - 4.51766i) q^{22} -7.78585i q^{23} +(-1.64424 - 2.30141i) q^{24} +(-2.93563 + 2.13286i) q^{25} +(-6.47719 - 2.12359i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-4.22007 - 3.10041i) q^{28} +(3.53447 - 4.86478i) q^{29} +(2.45068 - 3.35432i) q^{30} +(4.86049 + 1.57927i) q^{31} +(-5.65636 - 0.0750602i) q^{32} +(-2.05326 + 2.60464i) q^{33} +(2.24591 - 0.723155i) q^{34} +(2.37667 - 7.31464i) q^{35} +(-0.628121 + 1.89881i) q^{36} +(-7.62856 - 5.54247i) q^{37} +(2.38437 - 1.72269i) q^{38} +(1.48944 + 4.58403i) q^{39} +(-2.50444 - 7.92192i) q^{40} +(-0.990482 - 1.36328i) q^{41} +(-0.00982670 + 3.70279i) q^{42} +6.84645 q^{43} +(1.76673 + 6.39364i) q^{44} -2.93745 q^{45} +(-0.0292212 + 11.0108i) q^{46} +(-2.67005 - 3.67500i) q^{47} +(2.31666 + 3.26084i) q^{48} +(-0.0446905 - 0.137543i) q^{49} +(4.15960 - 3.00529i) q^{50} +(-1.34976 - 0.980655i) q^{51} +(9.15212 + 3.02750i) q^{52} +(1.23354 - 3.79644i) q^{53} +(1.34615 - 0.433445i) q^{54} +(-8.10045 + 5.41274i) q^{55} +(5.95642 + 4.40047i) q^{56} +(-1.97821 - 0.642759i) q^{57} +(-5.01673 + 6.86654i) q^{58} +(-3.88186 + 5.34292i) q^{59} +(-3.47836 + 4.73451i) q^{60} +(-0.319198 + 0.103714i) q^{61} +(-6.86782 - 2.25166i) q^{62} +(2.11823 - 1.53899i) q^{63} +(7.99899 + 0.127380i) q^{64} +14.1583i q^{65} +(2.91351 - 3.67579i) q^{66} +0.0794202i q^{67} +(-3.17889 + 1.01426i) q^{68} +(6.29889 - 4.57641i) q^{69} +(-3.38856 + 10.3355i) q^{70} +(12.0346 - 3.91027i) q^{71} +(0.895421 - 2.68295i) q^{72} +(4.24927 - 5.84861i) q^{73} +(10.7676 + 7.86684i) q^{74} +(-3.45104 - 1.12131i) q^{75} +(-3.37846 + 2.42730i) q^{76} +(3.00549 - 8.14716i) q^{77} +(-2.08918 - 6.48837i) q^{78} +(-2.97160 + 9.14565i) q^{79} +(3.51207 + 11.2127i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.39563 + 1.93168i) q^{82} +(1.35246 + 4.16246i) q^{83} +(0.0277940 - 5.23648i) q^{84} +(-2.88063 - 3.96485i) q^{85} +(-9.68231 - 0.0256955i) q^{86} +6.01319 q^{87} +(-2.47452 - 9.04858i) q^{88} +6.42078 q^{89} +(4.15417 + 0.0110246i) q^{90} +(-7.41781 - 10.2097i) q^{91} +(0.0826498 - 15.5715i) q^{92} +(1.57927 + 4.86049i) q^{93} +(3.76221 + 5.20724i) q^{94} +(-4.94304 - 3.59133i) q^{95} +(-3.26400 - 4.62021i) q^{96} +(-4.48438 + 13.8015i) q^{97} +(0.0626854 + 0.194682i) q^{98} +(-3.31407 - 0.130155i) 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 $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41421	−	0.00375312i	−0.999996	−	0.00265385i
$2$	−1.41421	−	0.00375312i	−0.999996	−	0.00265385i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	1.99997	+	0.0106154i	0.999986	+	0.00530769i
$5$	0.907723	+	2.79369i	0.405946	+	1.24937i	0.920103	+	0.391677i	$0.128105\pi$
$5$	0.907723	+	2.79369i	0.405946	+	1.24937i	−0.514156	+	0.857696i	$0.671895\pi$
$6$	−0.828215	−	1.14632i	−0.338117	−	0.467985i
$7$	−2.11823	−	1.53899i	−0.800616	−	0.581682i	0.110479	−	0.993878i	$-0.464762\pi$
$7$	−2.11823	−	1.53899i	−0.800616	−	0.581682i	−0.911095	+	0.412197i	$0.864762\pi$
$8$	−2.82834	−	0.0225185i	−0.999968	−	0.00796149i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−1.27323	−	3.95426i	−0.402629	−	1.25045i
$11$	0.900319	+	3.19209i	0.271456	+	0.962451i
$11$	0.900319	+	3.19209i	0.271456	+	0.962451i
$12$	1.16697	+	1.62425i	0.336874	+	0.468881i
$13$	4.58403	+	1.48944i	1.27138	+	0.413097i	0.865537	−	0.500845i	$-0.166977\pi$
$13$	4.58403	+	1.48944i	1.27138	+	0.413097i	0.405845	+	0.913942i	$0.366977\pi$
$14$	2.98984	+	2.18440i	0.799070	+	0.583804i
$15$	−1.72659	+	2.37645i	−0.445804	+	0.613597i
$16$	3.99977	+	0.0424609i	0.999944	+	0.0106152i
$17$	−1.58673	+	0.515561i	−0.384839	+	0.125042i	−0.495046	−	0.868867i	$-0.664849\pi$
$17$	−1.58673	+	0.515561i	−0.384839	+	0.125042i	0.110207	+	0.993909i	$0.464849\pi$
$18$	0.440584	−	1.34383i	0.103847	−	0.316744i
$19$	−1.68276	+	1.22260i	−0.386052	+	0.280484i	−0.763836	−	0.645410i	$-0.776686\pi$
$19$	−1.68276	+	1.22260i	−0.386052	+	0.280484i	0.377783	+	0.925894i	$0.376686\pi$
$20$	1.78577	+	5.59693i	0.399309	+	1.25151i
$21$		−	2.61828i		−	0.571355i
$22$	−1.26126	−	4.51766i	−0.268901	−	0.963168i
$23$		−	7.78585i		−	1.62346i	−0.584031	−	0.811731i	$-0.698526\pi$
$23$		−	7.78585i		−	1.62346i	0.584031	−	0.811731i	$-0.301474\pi$
$24$	−1.64424	−	2.30141i	−0.335629	−	0.469773i
$25$	−2.93563	+	2.13286i	−0.587126	+	0.426572i
$26$	−6.47719	−	2.12359i	−1.27028	−	0.416469i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−4.22007	−	3.10041i	−0.797517	−	0.585923i
$29$	3.53447	−	4.86478i	0.656334	−	0.903366i	−0.343019	−	0.939328i	$-0.611450\pi$
$29$	3.53447	−	4.86478i	0.656334	−	0.903366i	0.999353	+	0.0359621i	$0.0114495\pi$
$30$	2.45068	−	3.35432i	0.447431	−	0.612412i
$31$	4.86049	+	1.57927i	0.872970	+	0.283645i	0.711035	−	0.703156i	$-0.248227\pi$
$31$	4.86049	+	1.57927i	0.872970	+	0.283645i	0.161935	+	0.986801i	$0.448227\pi$
$32$	−5.65636	−	0.0750602i	−0.999912	−	0.0132689i
$33$	−2.05326	+	2.60464i	−0.357427	+	0.453409i
$34$	2.24591	−	0.723155i	0.385170	−	0.124020i
$35$	2.37667	−	7.31464i	0.401731	−	1.23640i
$36$	−0.628121	+	1.89881i	−0.104687	+	0.316468i
$37$	−7.62856	−	5.54247i	−1.25413	−	0.911177i	−0.255673	−	0.966763i	$-0.582297\pi$
$37$	−7.62856	−	5.54247i	−1.25413	−	0.911177i	−0.998454	+	0.0555864i	$0.982297\pi$
$38$	2.38437	−	1.72269i	0.386795	−	0.279458i
$39$	1.48944	+	4.58403i	0.238502	+	0.734032i
$40$	−2.50444	−	7.92192i	−0.395986	−	1.25257i
$41$	−0.990482	−	1.36328i	−0.154687	−	0.212909i	0.724639	−	0.689129i	$-0.242007\pi$
$41$	−0.990482	−	1.36328i	−0.154687	−	0.212909i	−0.879326	+	0.476220i	$0.842007\pi$
$42$	−0.00982670	+	3.70279i	−0.00151629	+	0.571353i
$43$	6.84645			1.04407			0.522037	−	0.852923i	$-0.325172\pi$
$43$	6.84645			1.04407			0.522037	+	0.852923i	$0.325172\pi$
$44$	1.76673	+	6.39364i	0.266344	+	0.963878i
$45$	−2.93745			−0.437890
$46$	−0.0292212	+	11.0108i	−0.00430843	+	1.62346i
$47$	−2.67005	−	3.67500i	−0.389466	−	0.536054i	0.568595	−	0.822618i	$-0.307487\pi$
$47$	−2.67005	−	3.67500i	−0.389466	−	0.536054i	−0.958061	+	0.286563i	$0.907487\pi$
$48$	2.31666	+	3.26084i	0.334381	+	0.470662i
$49$	−0.0446905	−	0.137543i	−0.00638435	−	0.0196490i
$50$	4.15960	−	3.00529i	0.588256	−	0.425012i
$51$	−1.34976	−	0.980655i	−0.189004	−	0.137319i
$52$	9.15212	+	3.02750i	1.26917	+	0.419839i
$53$	1.23354	−	3.79644i	0.169439	−	0.521481i	−0.829897	−	0.557917i	$-0.811601\pi$
$53$	1.23354	−	3.79644i	0.169439	−	0.521481i	0.999336	+	0.0364363i	$0.0116006\pi$
$54$	1.34615	−	0.433445i	0.183188	−	0.0589844i
$55$	−8.10045	+	5.41274i	−1.09226	+	0.729854i
$56$	5.95642	+	4.40047i	0.795960	+	0.588037i
$57$	−1.97821	−	0.642759i	−0.262020	−	0.0851354i
$58$	−5.01673	+	6.86654i	−0.658729	+	0.901621i
$59$	−3.88186	+	5.34292i	−0.505375	+	0.695589i	−0.983131	−	0.182903i	$-0.941450\pi$
$59$	−3.88186	+	5.34292i	−0.505375	+	0.695589i	0.477756	+	0.878493i	$0.341450\pi$
$60$	−3.47836	+	4.73451i	−0.449055	+	0.611222i
$61$	−0.319198	+	0.103714i	−0.0408691	+	0.0132792i	−0.329380	−	0.944197i	$-0.606840\pi$
$61$	−0.319198	+	0.103714i	−0.0408691	+	0.0132792i	0.288511	+	0.957477i	$0.406840\pi$
$62$	−6.86782	−	2.25166i	−0.872214	−	0.285961i
$63$	2.11823	−	1.53899i	0.266872	−	0.193894i
$64$	7.99899	+	0.127380i	0.999873	+	0.0159225i
$65$			14.1583i			1.75613i
$66$	2.91351	−	3.67579i	0.358629	−	0.452459i
$67$			0.0794202i			0.00970273i	0.999988	+	0.00485136i	$0.00154424\pi$
$67$			0.0794202i			0.00970273i	−0.999988	+	0.00485136i	$0.998456\pi$
$68$	−3.17889	+	1.01426i	−0.385497	+	0.122997i
$69$	6.29889	−	4.57641i	0.758297	−	0.550935i
$70$	−3.38856	+	10.3355i	−0.405011	+	1.23533i
$71$	12.0346	−	3.91027i	1.42824	−	0.464064i	0.510031	−	0.860156i	$-0.329634\pi$
$71$	12.0346	−	3.91027i	1.42824	−	0.464064i	0.918211	+	0.396092i	$0.129634\pi$
$72$	0.895421	−	2.68295i	0.105526	−	0.316189i
$73$	4.24927	−	5.84861i	0.497339	−	0.684529i	−0.484381	−	0.874857i	$-0.660955\pi$
$73$	4.24927	−	5.84861i	0.497339	−	0.684529i	0.981720	+	0.190328i	$0.0609553\pi$
$74$	10.7676	+	7.86684i	1.25170	+	0.914502i
$75$	−3.45104	−	1.12131i	−0.398492	−	0.129478i
$76$	−3.37846	+	2.42730i	−0.387536	+	0.278431i
$77$	3.00549	−	8.14716i	0.342508	−	0.928455i
$78$	−2.08918	−	6.48837i	−0.236553	−	0.734663i
$79$	−2.97160	+	9.14565i	−0.334331	+	1.02897i	0.632719	+	0.774381i	$0.281939\pi$
$79$	−2.97160	+	9.14565i	−0.334331	+	1.02897i	−0.967050	+	0.254585i	$0.918061\pi$
$80$	3.51207	+	11.2127i	0.392661	+	1.25361i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.39563	+	1.93168i	0.154122	+	0.213318i
$83$	1.35246	+	4.16246i	0.148452	+	0.456889i	0.997439	−	0.0715253i	$-0.0227867\pi$
$83$	1.35246	+	4.16246i	0.148452	+	0.456889i	−0.848986	+	0.528415i	$0.822787\pi$
$84$	0.0277940	−	5.23648i	0.00303258	−	0.571347i
$85$	−2.88063	−	3.96485i	−0.312448	−	0.430048i
$86$	−9.68231	−	0.0256955i	−1.04407	−	0.00277082i
$87$	6.01319			0.644682
$88$	−2.47452	−	9.04858i	−0.263785	−	0.964581i
$89$	6.42078			0.680601			0.340301	−	0.940317i	$-0.389471\pi$
$89$	6.42078			0.680601			0.340301	+	0.940317i	$0.389471\pi$
$90$	4.15417	+	0.0110246i	0.437888	+	0.00116210i
$91$	−7.41781	−	10.2097i	−0.777598	−	1.07027i
$92$	0.0826498	−	15.5715i	0.00861683	−	1.62344i
$93$	1.57927	+	4.86049i	0.163763	+	0.504010i
$94$	3.76221	+	5.20724i	0.388042	+	0.537086i
$95$	−4.94304	−	3.59133i	−0.507145	−	0.368463i
$96$	−3.26400	−	4.62021i	−0.333130	−	0.471548i
$97$	−4.48438	+	13.8015i	−0.455319	+	1.40133i	0.415440	+	0.909620i	$0.363627\pi$
$97$	−4.48438	+	13.8015i	−0.455319	+	1.40133i	−0.870760	+	0.491709i	$0.836373\pi$
$98$	0.0626854	+	0.194682i	0.00633218	+	0.0196659i
$99$	−3.31407	−	0.130155i	−0.333077	−	0.0130811i
$100$	−5.89382	+	4.23450i	−0.589382	+	0.423450i
$101$	−17.0807	−	5.54985i	−1.69959	−	0.552230i	−0.711044	−	0.703148i	$-0.751777\pi$
$101$	−17.0807	−	5.54985i	−1.69959	−	0.552230i	−0.988546	+	0.150917i	$0.951777\pi$
$102$	1.90516	+	1.39192i	0.188638	+	0.137820i
$103$	−6.00236	+	8.26154i	−0.591430	+	0.814034i	−0.994890	−	0.100963i	$-0.967808\pi$
$103$	−6.00236	+	8.26154i	−0.591430	+	0.814034i	0.403460	+	0.914997i	$0.367808\pi$
$104$	−12.9316	−	4.31587i	−1.26805	−	0.423206i
$105$	7.31464	−	2.37667i	0.713836	−	0.231939i
$106$	−1.75873	+	5.36433i	−0.170823	+	0.521030i
$107$	−5.56260	+	4.04147i	−0.537757	+	0.390704i	−0.823251	−	0.567677i	$-0.807842\pi$
$107$	−5.56260	+	4.04147i	−0.537757	+	0.390704i	0.285494	+	0.958380i	$0.407842\pi$
$108$	−1.90537	+	0.607929i	−0.183344	+	0.0584980i
$109$		−	3.44430i		−	0.329904i	−0.986302	−	0.164952i	$-0.947253\pi$
$109$		−	3.44430i		−	0.329904i	0.986302	−	0.164952i	$-0.0527469\pi$
$110$	11.4760	−	7.62434i	1.09420	−	0.726952i
$111$		−	9.42942i		−	0.895001i
$112$	−8.40710	−	6.24554i	−0.794396	−	0.590148i
$113$	−2.73400	+	1.98637i	−0.257193	+	0.186862i	−0.708909	−	0.705300i	$-0.750812\pi$
$113$	−2.73400	+	1.98637i	−0.257193	+	0.186862i	0.451716	+	0.892162i	$0.350812\pi$
$114$	2.79519	+	0.916419i	0.261793	+	0.0858305i
$115$	21.7512	−	7.06740i	2.02831	−	0.659038i
$116$	7.12048	−	9.69190i	0.661120	−	0.899870i
$117$	−2.83309	+	3.89941i	−0.261919	+	0.360501i
$118$	5.50981	−	7.54144i	0.507219	−	0.694246i
$119$	4.15451	+	1.34988i	0.380843	+	0.123743i
$120$	4.93690	−	6.68252i	0.450675	−	0.610028i
$121$	−9.37885	+	5.74779i	−0.852623	+	0.522527i
$122$	0.451801	−	0.145475i	0.0409042	−	0.0131707i
$123$	0.520727	−	1.60263i	0.0469524	−	0.144505i
$124$	9.70408	+	3.21009i	0.871452	+	0.288275i
$125$	3.25897	+	2.36778i	0.291491	+	0.211781i
$126$	−3.00140	+	2.16850i	−0.267386	+	0.193185i
$127$	−4.49554	−	13.8358i	−0.398914	−	1.22773i	−0.925871	−	0.377840i	$-0.876667\pi$
$127$	−4.49554	−	13.8358i	−0.398914	−	1.22773i	0.526956	−	0.849892i	$-0.323333\pi$
$128$	−11.3118	−	0.210163i	−0.999827	−	0.0185759i
$129$	4.02424	+	5.53890i	0.354315	+	0.487673i
$130$	0.0531379	−	20.0228i	0.00466050	−	1.75612i
$131$	−5.02290			−0.438853			−0.219426	−	0.975629i	$-0.570419\pi$
$131$	−5.02290			−0.438853			−0.219426	+	0.975629i	$0.570419\pi$
$132$	−4.13411	+	5.18740i	−0.359828	+	0.451505i
$133$	5.44604			0.472232
$134$	0.000298073	−	0.112317i	2.57496e−5	−	0.00970269i
$135$	−1.72659	−	2.37645i	−0.148601	−	0.204532i
$136$	4.49943	−	1.42245i	0.385823	−	0.121974i
$137$	1.93609	+	5.95868i	0.165412	+	0.509085i	0.999066	−	0.0432013i	$-0.0137557\pi$
$137$	1.93609	+	5.95868i	0.165412	+	0.509085i	−0.833655	+	0.552286i	$0.813756\pi$
$138$	−8.92511	+	6.44836i	−0.759756	+	0.548920i
$139$	15.3236	+	11.1333i	1.29973	+	0.944310i	0.999953	−	0.00969859i	$-0.00308721\pi$
$139$	15.3236	+	11.1333i	1.29973	+	0.944310i	0.299779	+	0.954009i	$0.403087\pi$
$140$	4.83092	−	14.6039i	0.408288	−	1.23425i
$141$	1.40373	−	4.32023i	0.118215	−	0.363829i
$142$	−17.0341	+	5.48477i	−1.42947	+	0.460272i
$143$	−0.627340	+	15.9736i	−0.0524608	+	1.33578i
$144$	−1.27638	+	3.79089i	−0.106365	+	0.315908i
$145$	16.7990	+	5.45832i	1.39508	+	0.453289i
$146$	−6.03130	+	8.25521i	−0.499154	+	0.683206i
$147$	0.0850063	−	0.117001i	0.00701120	−	0.00965009i
$148$	−15.1981	−	11.1658i	−1.24927	−	0.917820i
$149$	9.78716	−	3.18004i	0.801795	−	0.260519i	0.120676	−	0.992692i	$-0.461494\pi$
$149$	9.78716	−	3.18004i	0.801795	−	0.260519i	0.681119	+	0.732173i	$0.261494\pi$
$150$	4.87628	+	1.59872i	0.398147	+	0.130535i
$151$	−4.95528	+	3.60022i	−0.403255	+	0.292982i	−0.770865	−	0.636998i	$-0.780176\pi$
$151$	−4.95528	+	3.60022i	−0.403255	+	0.292982i	0.367611	+	0.929980i	$0.380176\pi$
$152$	4.78695	−	3.42003i	0.388273	−	0.277401i
$153$		−	1.66839i		−	0.134881i
$154$	−4.28097	+	11.5105i	−0.344970	+	0.927543i
$155$			15.0122i			1.20581i
$156$	2.93018	+	9.18374i	0.234602	+	0.735288i
$157$	12.1045	−	8.79443i	0.966044	−	0.701872i	0.0114972	−	0.999934i	$-0.496340\pi$
$157$	12.1045	−	8.79443i	0.966044	−	0.701872i	0.954546	+	0.298062i	$0.0963403\pi$
$158$	4.23679	−	12.9227i	0.337061	−	1.02808i
$159$	3.79644	−	1.23354i	0.301077	−	0.0978259i
$160$	−4.92471	−	15.8702i	−0.389333	−	1.25465i
$161$	−11.9823	+	16.4922i	−0.944338	+	1.29977i
$162$	1.14191	+	0.834287i	0.0897171	+	0.0655478i
$163$	−16.1476	−	5.24667i	−1.26478	−	0.410951i	−0.401582	−	0.915823i	$-0.631540\pi$
$163$	−16.1476	−	5.24667i	−1.26478	−	0.410951i	−0.863194	+	0.504872i	$0.831540\pi$
$164$	−1.96646	−	2.73704i	−0.153555	−	0.213727i
$165$	−9.14032	−	3.37187i	−0.711573	−	0.262500i
$166$	−1.89705	−	5.89166i	−0.147239	−	0.457282i
$167$	−1.98709	+	6.11564i	−0.153766	+	0.473242i	−0.998034	−	0.0626789i	$-0.980036\pi$
$167$	−1.98709	+	6.11564i	−0.153766	+	0.473242i	0.844268	+	0.535921i	$0.180036\pi$
$168$	−0.0589597	+	7.40537i	−0.00454884	+	0.571337i
$169$	8.27768	+	6.01409i	0.636744	+	0.462622i
$170$	4.05893	+	5.61793i	0.311306	+	0.430876i
$171$	−0.642759	−	1.97821i	−0.0491530	−	0.151277i
$172$	13.6927	+	0.0726777i	1.04406	+	0.00554162i
$173$	4.97174	+	6.84301i	0.377994	+	0.520264i	0.955052	−	0.296439i	$-0.0957992\pi$
$173$	4.97174	+	6.84301i	0.377994	+	0.520264i	−0.577058	+	0.816703i	$0.695799\pi$
$174$	−8.50391	−	0.0225682i	−0.644680	−	0.00171089i
$175$	9.50078			0.718192
$176$	3.46553	+	12.8059i	0.261224	+	0.965278i
$177$	−6.60422			−0.496403
$178$	−9.08032	−	0.0240979i	−0.680599	−	0.00180622i
$179$	−10.5401	−	14.5072i	−0.787803	−	1.08432i	−0.994378	−	0.105887i	$-0.966232\pi$
$179$	−10.5401	−	14.5072i	−0.787803	−	1.08432i	0.206576	−	0.978431i	$-0.433768\pi$
$180$	−5.87483	−	0.0311822i	−0.437884	−	0.00232418i
$181$	0.405753	+	1.24878i	0.0301594	+	0.0928211i	0.965003	−	0.262238i	$-0.0844606\pi$
$181$	0.405753	+	1.24878i	0.0301594	+	0.0928211i	−0.934844	+	0.355059i	$0.884461\pi$
$182$	10.4520	+	14.4665i	0.774754	+	1.07233i
$183$	−0.271526	−	0.197275i	−0.0200718	−	0.0145830i
$184$	−0.175326	+	22.0210i	−0.0129252	+	1.62341i
$185$	8.55930	−	26.3428i	0.629292	−	1.93676i
$186$	−2.21517	−	6.87968i	−0.162424	−	0.504442i
$187$	−3.07428	−	4.60082i	−0.224814	−	0.336445i
$188$	−5.30101	−	7.37825i	−0.386616	−	0.538114i
$189$	2.49013	+	0.809092i	0.181130	+	0.0588528i
$190$	6.97701	+	5.09744i	0.506166	+	0.369807i
$191$	3.23956	−	4.45887i	0.234406	−	0.322632i	−0.675568	−	0.737298i	$-0.736101\pi$
$191$	3.23956	−	4.45887i	0.234406	−	0.322632i	0.909974	+	0.414666i	$0.136101\pi$
$192$	4.59863	+	6.54619i	0.331878	+	0.472430i
$193$	−20.6434	+	6.70745i	−1.48594	+	0.482813i	−0.935883	−	0.352311i	$-0.885396\pi$
$193$	−20.6434	+	6.70745i	−1.48594	+	0.482813i	−0.550062	+	0.835124i	$0.685396\pi$
$194$	6.39364	−	19.5014i	0.459037	−	1.40012i
$195$	−11.4543	+	8.32206i	−0.820262	+	0.595955i
$196$	−0.0879196	−	0.275557i	−0.00627997	−	0.0196826i
$197$			5.91198i			0.421211i	0.977571	+	0.210606i	$0.0675436\pi$
$197$			5.91198i			0.421211i	−0.977571	+	0.210606i	$0.932456\pi$
$198$	4.68630	+	0.196505i	0.333041	+	0.0139650i
$199$		−	6.54654i		−	0.464072i	−0.972707	−	0.232036i	$-0.925461\pi$
$199$		−	6.54654i		−	0.464072i	0.972707	−	0.232036i	$-0.0745387\pi$
$200$	8.35098	−	5.96634i	0.590504	−	0.421884i
$201$	−0.0642523	+	0.0466820i	−0.00453201	+	0.00329270i
$202$	24.1348	+	7.91275i	1.69812	+	0.556739i
$203$	−14.9736	+	4.86523i	−1.05094	+	0.341472i
$204$	−2.68906	−	1.97561i	−0.188272	−	0.138320i
$205$	2.90949	−	4.00458i	0.203208	−	0.279692i
$206$	8.51960	−	11.6610i	0.593589	−	0.812462i
$207$	7.40478	+	2.40596i	0.514668	+	0.167226i
$208$	18.2718	+	6.15207i	1.26692	+	0.426570i
$209$	−5.41767	−	4.27080i	−0.374748	−	0.295417i
$210$	−10.3534	+	3.33366i	−0.714449	+	0.230044i
$211$	4.79963	−	14.7718i	0.330420	−	1.01693i	−0.638514	−	0.769610i	$-0.720450\pi$
$211$	4.79963	−	14.7718i	0.330420	−	1.01693i	0.968934	−	0.247319i	$-0.0795495\pi$
$212$	2.50734	−	7.57968i	0.172205	−	0.520574i
$213$	10.2372	+	7.43778i	0.701443	+	0.509628i
$214$	7.88185	−	5.69460i	0.538792	−	0.389275i
$215$	6.21468	+	19.1268i	0.423838	+	1.30444i
$216$	2.69687	−	0.852588i	0.183499	−	0.0580113i
$217$	−7.86517	−	10.8255i	−0.533923	−	0.734882i
$218$	−0.0129269	+	4.87096i	−0.000875517	+	0.329903i
$219$	7.22929			0.488510
$220$	−16.2581	+	10.7393i	−1.09612	+	0.724046i
$221$	−8.04153			−0.540932
$222$	−0.0353897	+	13.3352i	−0.00237520	+	0.894997i
$223$	−9.05026	−	12.4566i	−0.606050	−	0.834156i	0.390195	−	0.920732i	$-0.372408\pi$
$223$	−9.05026	−	12.4566i	−0.606050	−	0.834156i	−0.996245	+	0.0865757i	$0.972408\pi$
$224$	11.8660	+	8.86404i	0.792827	+	0.592254i
$225$	−1.12131	−	3.45104i	−0.0747541	−	0.230069i
$226$	3.87390	−	2.79887i	0.257688	−	0.186178i
$227$	11.6225	+	8.44423i	0.771412	+	0.560463i	0.902389	−	0.430922i	$-0.141812\pi$
$227$	11.6225	+	8.44423i	0.771412	+	0.560463i	−0.130978	+	0.991385i	$0.541812\pi$
$228$	−3.94954	−	1.30650i	−0.261564	−	0.0865250i
$229$	−5.64581	+	17.3760i	−0.373085	+	1.14824i	0.571676	+	0.820480i	$0.306294\pi$
$229$	−5.64581	+	17.3760i	−0.373085	+	1.14824i	−0.944761	+	0.327759i	$0.893706\pi$
$230$	−30.7873	+	9.91314i	−2.03005	+	0.653653i
$231$	8.35777	−	2.35728i	0.549901	−	0.155098i
$232$	−10.1062	+	13.6796i	−0.663505	+	0.898112i
$233$	−2.35544	−	0.765328i	−0.154310	−	0.0501383i	0.230844	−	0.972991i	$-0.425851\pi$
$233$	−2.35544	−	0.765328i	−0.154310	−	0.0501383i	−0.385153	+	0.922853i	$0.625851\pi$
$234$	4.02121	−	5.50395i	0.262875	−	0.359804i
$235$	7.84314	−	10.7952i	0.511630	−	0.704198i
$236$	−7.82033	+	10.6445i	−0.509060	+	0.692897i
$237$	−9.14565	+	2.97160i	−0.594074	+	0.193026i
$238$	−5.87027	−	1.92461i	−0.380513	−	0.124754i
$239$	−3.59979	+	2.61540i	−0.232851	+	0.169176i	−0.698092	−	0.716008i	$-0.745968\pi$
$239$	−3.59979	+	2.61540i	−0.232851	+	0.169176i	0.465241	+	0.885184i	$0.345968\pi$
$240$	−7.00689	+	9.43195i	−0.452293	+	0.608830i
$241$		−	24.2622i		−	1.56287i	−0.623988	−	0.781434i	$-0.714489\pi$
$241$		−	24.2622i		−	1.56287i	0.623988	−	0.781434i	$-0.285511\pi$
$242$	13.2852	−	8.09338i	0.854007	−	0.520262i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.639487	+	0.204036i	−0.0409390	+	0.0130621i
$245$	0.343686	−	0.249702i	0.0219573	−	0.0159529i
$246$	−0.742431	+	2.26450i	−0.0473357	+	0.144379i
$247$	−9.53483	+	3.09805i	−0.606687	+	0.197124i
$248$	−13.7116	−	4.57616i	−0.870684	−	0.290586i
$249$	−2.57254	+	3.54080i	−0.163028	+	0.224389i
$250$	−4.59998	−	3.36077i	−0.290928	−	0.212554i
$251$	7.20387	+	2.34068i	0.454704	+	0.147742i	0.527410	−	0.849611i	$-0.323163\pi$
$251$	7.20387	+	2.34068i	0.454704	+	0.147742i	−0.0727054	+	0.997353i	$0.523163\pi$
$252$	4.25274	−	3.05544i	0.267897	−	0.192475i
$253$	24.8531	−	7.00975i	1.56250	−	0.440699i
$254$	6.30570	+	19.5836i	0.395655	+	1.22879i
$255$	1.51444	−	4.66096i	0.0948377	−	0.291880i
$256$	15.9964	+	0.339668i	0.999775	+	0.0212293i
$257$	−17.3631	−	12.6150i	−1.08308	−	0.786905i	−0.104864	−	0.994487i	$-0.533441\pi$
$257$	−17.3631	−	12.6150i	−1.08308	−	0.786905i	−0.978218	+	0.207582i	$0.933441\pi$
$258$	−5.67033	−	7.84826i	−0.353019	−	0.488611i
$259$	7.62927	+	23.4805i	0.474060	+	1.45901i
$260$	−0.150296	+	28.3163i	−0.00932097	+	1.75610i
$261$	3.53447	+	4.86478i	0.218778	+	0.301122i
$262$	7.10343	+	0.0188515i	0.438851	+	0.00116465i
$263$	17.2377			1.06292			0.531462	−	0.847082i	$-0.321643\pi$
$263$	17.2377			1.06292			0.531462	+	0.847082i	$0.321643\pi$
$264$	5.86596	−	7.32055i	0.361025	−	0.450549i
$265$	11.7258			0.720308
$266$	−7.70184	−	0.0204396i	−0.472230	−	0.00125324i
$267$	3.77404	+	5.19452i	0.230968	+	0.317900i
$268$	−0.000843076		0.158838i	−5.14991e−5		0.00970259i
$269$	−7.37177	−	22.6880i	−0.449464	−	1.38331i	−0.877513	−	0.479553i	$-0.840799\pi$
$269$	−7.37177	−	22.6880i	−0.449464	−	1.38331i	0.428048	−	0.903756i	$-0.359201\pi$
$270$	2.43284	+	3.36728i	0.148058	+	0.204926i
$271$	−6.72506	−	4.88604i	−0.408518	−	0.296806i	0.364483	−	0.931210i	$-0.381246\pi$
$271$	−6.72506	−	4.88604i	−0.408518	−	0.296806i	−0.773002	+	0.634404i	$0.781246\pi$
$272$	−6.36846	+	1.99475i	−0.386145	+	0.120950i
$273$	3.89977	−	12.0023i	0.236025	−	0.726410i
$274$	−2.71568	−	8.43409i	−0.164060	−	0.509522i
$275$	−9.45128	−	7.45054i	−0.569934	−	0.449284i
$276$	12.6462	−	9.08582i	0.761210	−	0.546902i
$277$	−1.88287	−	0.611782i	−0.113131	−	0.0367584i	0.251905	−	0.967752i	$-0.418943\pi$
$277$	−1.88287	−	0.611782i	−0.113131	−	0.0367584i	−0.365035	+	0.930994i	$0.618943\pi$
$278$	−21.6290	−	15.8023i	−1.29722	−	0.947756i
$279$	−3.00395	+	4.13458i	−0.179842	+	0.247531i
$280$	−6.88674	+	20.6348i	−0.411562	+	1.23316i
$281$	3.71271	−	1.20633i	0.221482	−	0.0719638i	−0.196174	−	0.980569i	$-0.562852\pi$
$281$	3.71271	−	1.20633i	0.221482	−	0.0719638i	0.417656	+	0.908605i	$0.362852\pi$
$282$	−2.00138	+	6.10443i	−0.119180	+	0.363514i
$283$	10.4319	−	7.57919i	0.620110	−	0.450536i	−0.232850	−	0.972513i	$-0.574805\pi$
$283$	10.4319	−	7.57919i	0.620110	−	0.450536i	0.852960	+	0.521976i	$0.174805\pi$
$284$	24.1103	−	7.69268i	1.43069	−	0.456477i
$285$		−	6.10994i		−	0.361921i
$286$	0.947141	−	22.5876i	0.0560056	−	1.33564i
$287$			4.41208i			0.260437i
$288$	1.81930	−	5.35632i	0.107203	−	0.315624i
$289$	−11.5014	+	8.35624i	−0.676551	+	0.491543i
$290$	−23.7368	−	7.78225i	−1.39387	−	0.456989i
$291$	−13.8015	+	4.48438i	−0.809058	+	0.262879i
$292$	8.56050	−	11.6520i	0.500965	−	0.681879i
$293$	−11.2819	+	15.5282i	−0.659097	+	0.907169i	−0.999451	−	0.0331283i	$-0.989453\pi$
$293$	−11.2819	+	15.5282i	−0.659097	+	0.907169i	0.340354	+	0.940297i	$0.389453\pi$
$294$	−0.120656	+	0.165145i	−0.00703679	+	0.00963145i
$295$	−18.4501	−	5.99480i	−1.07421	−	0.349031i
$296$	21.4513	+	15.8478i	1.24683	+	0.921133i
$297$	−1.84266	−	2.75764i	−0.106922	−	0.160015i
$298$	−13.8530	+	4.46051i	−0.802484	+	0.258390i
$299$	11.5966	−	35.6906i	0.670647	−	2.06404i
$300$	−6.89008	−	2.27922i	−0.397799	−	0.131591i
$301$	−14.5024	−	10.5366i	−0.835902	−	0.607319i
$302$	7.02131	−	5.07286i	0.404031	−	0.291910i
$303$	−5.54985	−	17.0807i	−0.318830	−	0.981259i
$304$	−6.78259	+	4.81867i	−0.389008	+	0.276370i
$305$	−0.579486	−	0.797595i	−0.0331813	−	0.0456701i
$306$	−0.00626166	+	2.35945i	−0.000357955	+	0.134881i
$307$	4.20914			0.240228			0.120114	−	0.992760i	$-0.461674\pi$
$307$	4.20914			0.240228			0.120114	+	0.992760i	$0.461674\pi$
$308$	6.09739	−	16.2622i	0.347431	−	0.926624i
$309$	−10.2118			−0.580931
$310$	0.0563426	−	21.2304i	0.00320005	−	1.20581i
$311$	−1.10861	−	1.52587i	−0.0628637	−	0.0865244i	0.776428	−	0.630206i	$-0.217030\pi$
$311$	−1.10861	−	1.52587i	−0.0628637	−	0.0865244i	−0.839291	+	0.543682i	$0.817030\pi$
$312$	−4.10942	−	12.9987i	−0.232650	−	0.735908i
$313$	−1.50551	−	4.63350i	−0.0850967	−	0.261901i	0.899450	−	0.437024i	$-0.143968\pi$
$313$	−1.50551	−	4.63350i	−0.0850967	−	0.261901i	−0.984546	+	0.175123i	$0.943968\pi$
$314$	−17.1513	+	12.3917i	−0.967903	+	0.699306i
$315$	6.22221	+	4.52070i	0.350582	+	0.254712i
$316$	−6.04021	+	18.2595i	−0.339788	+	1.02718i
$317$	−4.28567	+	13.1899i	−0.240707	+	0.740821i	0.755605	+	0.655027i	$0.227343\pi$
$317$	−4.28567	+	13.1899i	−0.240707	+	0.740821i	−0.996313	+	0.0857943i	$0.972657\pi$
$318$	−5.37359	+	1.73023i	−0.301336	+	0.0970266i
$319$	18.7109	+	6.90248i	1.04761	+	0.386465i
$320$	6.90501	+	22.4623i	0.386002	+	1.25568i
$321$	−6.53923	−	2.12473i	−0.364984	−	0.118591i
$322$	17.0074	−	23.2785i	0.947784	−	1.29726i
$323$	2.03977	−	2.80751i	0.113496	−	0.156214i
$324$	−1.61177	−	1.18414i	−0.0895429	−	0.0657857i
$325$	−16.6338	+	5.40465i	−0.922677	+	0.299796i
$326$	22.8164	+	7.48049i	1.26368	+	0.414306i
$327$	2.78650	−	2.02451i	0.154094	−	0.111956i
$328$	2.77072	+	3.87812i	0.152987	+	0.214133i
$329$			11.8937i			0.655719i
$330$	12.9137	+	4.80283i	0.710874	+	0.264387i
$331$		−	1.25177i		−	0.0688037i	−0.999408	−	0.0344018i	$-0.989047\pi$
$331$		−	1.25177i		−	0.0688037i	0.999408	−	0.0344018i	$-0.0109526\pi$
$332$	2.66071	+	8.33916i	0.146025	+	0.457671i
$333$	7.62856	−	5.54247i	0.418042	−	0.303726i
$334$	2.83311	−	8.64133i	0.155021	−	0.472833i
$335$	−0.221875	+	0.0720916i	−0.0121223	+	0.00393878i
$336$	0.111175	−	10.4725i	0.00606507	−	0.571323i
$337$	2.98651	−	4.11058i	0.162686	−	0.223917i	−0.719890	−	0.694088i	$-0.755808\pi$
$337$	2.98651	−	4.11058i	0.162686	−	0.223917i	0.882575	+	0.470171i	$0.155808\pi$
$338$	−11.6838	−	8.53624i	−0.635515	−	0.464310i
$339$	−3.21401	−	1.04429i	−0.174561	−	0.0567183i
$340$	−5.71909	−	7.96016i	−0.310161	−	0.431700i
$341$	−0.665175	+	16.9370i	−0.0360213	+	0.917188i
$342$	0.901570	+	2.80001i	0.0487513	+	0.151407i
$343$	−5.78066	+	17.7910i	−0.312126	+	0.960626i
$344$	−19.3641	−	0.154172i	−1.04404	−	0.00831238i
$345$	18.5027	+	13.4430i	0.996151	+	0.723746i
$346$	−7.00539	−	9.69610i	−0.376612	−	0.521266i
$347$	−1.36812	−	4.21064i	−0.0734446	−	0.226039i	0.907595	−	0.419847i	$-0.137916\pi$
$347$	−1.36812	−	4.21064i	−0.0734446	−	0.226039i	−0.981040	+	0.193808i	$0.937916\pi$
$348$	12.0262	+	0.0638324i	0.644673	+	0.00342177i
$349$	−10.1683	−	13.9954i	−0.544296	−	0.749159i	0.444929	−	0.895566i	$-0.353229\pi$
$349$	−10.1683	−	13.9954i	−0.544296	−	0.749159i	−0.989224	+	0.146407i	$0.953229\pi$
$350$	−13.4361	−	0.0356576i	−0.718189	−	0.00190598i
$351$	−4.81993			−0.257269
$352$	−4.85293	−	18.1232i	−0.258662	−	0.965968i
$353$	30.4382			1.62006			0.810031	−	0.586387i	$-0.199450\pi$
$353$	30.4382			1.62006			0.810031	+	0.586387i	$0.199450\pi$
$354$	9.33974	+	0.0247864i	0.496402	+	0.00131738i
$355$	21.8481	+	30.0714i	1.15958	+	1.59602i
$356$	12.8414	+	0.0681590i	0.680592	+	0.00361242i
$357$	1.34988	+	4.15451i	0.0714433	+	0.219880i
$358$	14.8514	+	20.5557i	0.784922	+	1.08640i
$359$	−23.5641	−	17.1203i	−1.24367	−	0.903576i	−0.245828	−	0.969313i	$-0.579060\pi$
$359$	−23.5641	−	17.1203i	−1.24367	−	0.903576i	−0.997837	+	0.0657377i	$0.979060\pi$
$360$	8.30811	+	0.0661470i	0.437876	+	0.00348626i
$361$	−4.53438	+	13.9554i	−0.238652	+	0.734494i
$362$	−0.569133	−	1.76756i	−0.0299130	−	0.0929008i
$363$	−10.1628	−	4.20918i	−0.533409	−	0.220925i
$364$	−14.7270	−	20.4979i	−0.771906	−	1.07438i
$365$	20.1963	+	6.56219i	1.05713	+	0.343481i
$366$	0.383254	+	0.280007i	0.0200330	+	0.0146362i
$367$	−5.92305	+	8.15237i	−0.309180	+	0.425550i	−0.935125	−	0.354317i	$-0.884713\pi$
$367$	−5.92305	+	8.15237i	−0.309180	+	0.425550i	0.625945	+	0.779867i	$0.284713\pi$
$368$	0.330594	−	31.1416i	0.0172334	−	1.62337i
$369$	1.60263	−	0.520727i	0.0834297	−	0.0271080i
$370$	−12.2035	+	37.2221i	−0.634430	+	1.93509i
$371$	−8.45558	+	6.14334i	−0.438992	+	0.318946i
$372$	3.10690	+	9.73761i	0.161085	+	0.504872i
$373$			31.8003i			1.64656i	0.567637	+	0.823279i	$0.307858\pi$
$373$			31.8003i			1.64656i	−0.567637	+	0.823279i	$0.692142\pi$
$374$	4.33041	+	6.51806i	0.223920	+	0.337041i
$375$			4.02831i			0.208021i
$376$	7.46904	+	10.4543i	0.385186	+	0.539138i
$377$	23.4479	−	17.0359i	1.20763	−	0.877394i
$378$	−3.51853	−	1.15357i	−0.180973	−	0.0593333i
$379$	−32.1586	+	10.4490i	−1.65188	+	0.536728i	−0.979146	−	0.203158i	$-0.934879\pi$
$379$	−32.1586	+	10.4490i	−1.65188	+	0.536728i	−0.672732	+	0.739886i	$0.734879\pi$
$380$	−9.84782	−	7.23503i	−0.505183	−	0.371149i
$381$	8.55102	−	11.7695i	0.438082	−	0.602968i
$382$	−4.59814	+	6.29361i	−0.235261	+	0.322009i
$383$	12.5258	+	4.06988i	0.640038	+	0.207961i	0.611017	−	0.791618i	$-0.290761\pi$
$383$	12.5258	+	4.06988i	0.640038	+	0.207961i	0.0290216	+	0.999579i	$0.490761\pi$
$384$	−6.47886	−	9.27493i	−0.330623	−	0.473309i
$385$	25.4887	+	1.00103i	1.29903	+	0.0510174i
$386$	29.2193	−	9.40825i	1.48722	−	0.478867i
$387$	−2.11567	+	6.51136i	−0.107546	+	0.330991i
$388$	−9.11513	+	27.5550i	−0.462751	+	1.39889i
$389$	11.5897	+	8.42041i	0.587621	+	0.426932i	0.841464	−	0.540314i	$-0.181694\pi$
$389$	11.5897	+	8.42041i	0.587621	+	0.426932i	−0.253842	+	0.967246i	$0.581694\pi$
$390$	16.2301	−	11.7261i	0.821841	−	0.593776i
$391$	4.01408	+	12.3541i	0.203001	+	0.624772i
$392$	0.123302	+	0.390025i	0.00622771	+	0.0196992i
$393$	−2.95239	−	4.06361i	−0.148928	−	0.204982i
$394$	0.0221884	−	8.36078i	0.00111783	−	0.421210i
$395$	−28.2475			−1.42128
$396$	−6.62666	−	0.295487i	−0.333002	−	0.0148488i
$397$	1.63555			0.0820859			0.0410429	−	0.999157i	$-0.486932\pi$
$397$	1.63555			0.0820859			0.0410429	+	0.999157i	$0.486932\pi$
$398$	−0.0245699	+	9.25817i	−0.00123158	+	0.464070i
$399$	3.20110	+	4.40594i	0.160256	+	0.220573i
$400$	−11.8324	+	8.40631i	−0.591621	+	0.420315i
$401$	−1.87150	−	5.75988i	−0.0934582	−	0.287635i	0.893391	−	0.449281i	$-0.148320\pi$
$401$	−1.87150	−	5.75988i	−0.0934582	−	0.287635i	−0.986849	+	0.161646i	$0.948320\pi$
$402$	0.0910414	−	0.0657770i	0.00454073	−	0.00328066i
$403$	19.9284	+	14.4788i	0.992705	+	0.721242i
$404$	−34.1019	−	11.2809i	−1.69664	−	0.561243i
$405$	0.907723	−	2.79369i	0.0451051	−	0.138819i
$406$	21.1941	−	6.82425i	1.05185	−	0.338682i
$407$	10.8239	−	29.3410i	0.536522	−	1.45438i
$408$	3.79548	+	2.80402i	0.187904	+	0.138820i
$409$	17.8745	+	5.80777i	0.883836	+	0.287176i	0.715549	−	0.698562i	$-0.246176\pi$
$409$	17.8745	+	5.80777i	0.883836	+	0.287176i	0.168287	+	0.985738i	$0.446176\pi$
$410$	−4.12966	+	5.65238i	−0.203949	+	0.279151i
$411$	−3.68267	+	5.06876i	−0.181653	+	0.250023i
$412$	−12.0923	+	16.4591i	−0.595743	+	0.810884i
$413$	16.4454	−	5.34342i	0.809223	−	0.262933i
$414$	−10.4629	−	3.43032i	−0.514222	−	0.168591i
$415$	−10.4009	+	7.55672i	−0.510562	+	0.370945i
$416$	−25.8171	−	8.76889i	−1.26579	−	0.429930i
$417$			18.9410i			0.927546i
$418$	7.64568	+	6.06014i	0.373963	+	0.296411i
$419$		−	16.4782i		−	0.805013i	−0.915417	−	0.402507i	$-0.868139\pi$
$419$		−	16.4782i		−	0.805013i	0.915417	−	0.402507i	$-0.131861\pi$
$420$	14.6543	−	4.67563i	0.715057	−	0.228147i
$421$	−31.5438	+	22.9179i	−1.53735	+	1.11695i	−0.585385	+	0.810756i	$0.699056\pi$
$421$	−31.5438	+	22.9179i	−1.53735	+	1.11695i	−0.951968	+	0.306197i	$0.900944\pi$
$422$	−6.84312	+	20.8723i	−0.333118	+	1.01605i
$423$	4.32023	−	1.40373i	0.210057	−	0.0682515i
$424$	−3.57435	+	10.7098i	−0.173586	+	0.520116i
$425$	3.55844	−	4.89777i	0.172610	−	0.237577i
$426$	−14.4497	−	10.5570i	−0.700088	−	0.511488i
$427$	0.835748	+	0.271551i	0.0404447	+	0.0131413i
$428$	−11.1680	+	8.02377i	−0.539823	+	0.387844i
$429$	−13.2917	+	8.88152i	−0.641727	+	0.428804i
$430$	−8.71707	−	27.0726i	−0.420375	−	1.30556i
$431$	−1.39738	+	4.30071i	−0.0673097	+	0.207158i	−0.979054	−	0.203600i	$-0.934736\pi$
$431$	−1.39738	+	4.30071i	−0.0673097	+	0.207158i	0.911745	+	0.410758i	$0.134736\pi$
$432$	−3.81713	+	1.19562i	−0.183652	+	0.0575241i
$433$	0.365311	+	0.265414i	0.0175557	+	0.0127550i	0.596529	−	0.802592i	$-0.296546\pi$
$433$	0.365311	+	0.265414i	0.0175557	+	0.0127550i	−0.578973	+	0.815347i	$0.696546\pi$
$434$	11.0824	+	15.3390i	0.531971	+	0.736296i
$435$	5.45832	+	16.7990i	0.261706	+	0.805449i
$436$	0.0365625	−	6.88850i	0.00175103	−	0.329899i
$437$	9.51898	+	13.1017i	0.455354	+	0.626742i
$438$	−10.2237	−	0.0271324i	−0.488508	−	0.00129643i
$439$	−19.3289			−0.922519			−0.461260	−	0.887265i	$-0.652602\pi$
$439$	−19.3289			−0.922519			−0.461260	+	0.887265i	$0.652602\pi$
$440$	23.0327	−	15.1266i	1.09804	−	0.721135i
$441$	0.144621			0.00688673
$442$	11.3724	+	0.0301808i	0.540930	+	0.00143555i
$443$	12.1114	+	16.6700i	0.575431	+	0.792013i	0.993185	−	0.116547i	$-0.0371826\pi$
$443$	12.1114	+	16.6700i	0.575431	+	0.792013i	−0.417754	+	0.908560i	$0.637183\pi$
$444$	0.100097	−	18.8586i	0.00475039	−	0.894988i
$445$	5.82829	+	17.9376i	0.276288	+	0.850326i
$446$	12.7522	+	17.6502i	0.603834	+	0.835762i
$447$	8.32546	+	6.04880i	0.393781	+	0.286098i
$448$	−16.7477	−	12.5801i	−0.791253	−	0.594356i
$449$	0.896385	−	2.75879i	0.0423030	−	0.130195i	−0.927675	−	0.373390i	$-0.878195\pi$
$449$	0.896385	−	2.75879i	0.0423030	−	0.130195i	0.969978	+	0.243195i	$0.0781954\pi$
$450$	1.57282	+	4.88470i	0.0741432	+	0.230267i
$451$	3.45996	−	4.38909i	0.162923	−	0.206674i
$452$	−5.48900	+	3.94365i	−0.258181	+	0.185494i
$453$	−5.82528	−	1.89275i	−0.273695	−	0.0889290i
$454$	−16.4049	−	11.9855i	−0.769922	−	0.562509i
$455$	21.7895	−	29.9906i	1.02151	−	1.40598i
$456$	5.58056	+	1.86248i	0.261334	+	0.0872188i
$457$	18.8634	−	6.12909i	0.882392	−	0.286707i	0.167442	−	0.985882i	$-0.446449\pi$
$457$	18.8634	−	6.12909i	0.882392	−	0.286707i	0.714950	+	0.699175i	$0.246449\pi$
$458$	8.04956	−	24.5521i	0.376131	−	1.14724i
$459$	1.34976	−	0.980655i	0.0630012	−	0.0457730i
$460$	43.5768	−	13.9037i	2.03178	−	0.648263i
$461$		−	9.47905i		−	0.441483i	−0.975332	−	0.220742i	$-0.929152\pi$
$461$		−	9.47905i		−	0.441483i	0.975332	−	0.220742i	$-0.0708478\pi$
$462$	−11.8285	+	3.30232i	−0.550311	+	0.153638i
$463$			11.7115i			0.544279i	0.962258	+	0.272140i	$0.0877313\pi$
$463$			11.7115i			0.544279i	−0.962258	+	0.272140i	$0.912269\pi$
$464$	14.3436	−	19.3079i	0.665887	−	0.896348i
$465$	−12.1451	+	8.82396i	−0.563218	+	0.409202i
$466$	3.32821	+	1.09117i	0.154176	+	0.0505476i
$467$	22.4911	−	7.30782i	1.04077	−	0.338165i	0.261728	−	0.965142i	$-0.415708\pi$
$467$	22.4911	−	7.30782i	1.04077	−	0.338165i	0.779038	+	0.626976i	$0.215708\pi$
$468$	−5.70749	+	7.76863i	−0.263829	+	0.359105i
$469$	0.122227	−	0.168230i	0.00564390	−	0.00776816i
$470$	−11.1323	+	15.2372i	−0.513497	+	0.702838i
$471$	14.2297	+	4.62350i	0.655669	+	0.213040i
$472$	11.0995	−	15.0242i	0.510897	−	0.691544i
$473$	6.16399	+	21.8545i	0.283420	+	1.00487i
$474$	12.9450	−	4.16814i	0.594584	−	0.191449i
$475$	2.33234	−	7.17820i	0.107015	−	0.329358i
$476$	8.29457	+	2.74383i	0.380181	+	0.125763i
$477$	3.22944	+	2.34633i	0.147866	+	0.107431i
$478$	5.10067	−	3.68521i	0.233299	−	0.168558i
$479$	−6.32093	−	19.4538i	−0.288811	−	0.888867i	−0.985231	−	0.171233i	$-0.945225\pi$
$479$	−6.32093	−	19.4538i	−0.288811	−	0.888867i	0.696420	−	0.717634i	$-0.254775\pi$
$480$	9.94460	−	13.3125i	0.453907	−	0.607628i
$481$	−26.7144	−	36.7692i	−1.21807	−	1.67653i
$482$	−0.0910590	+	34.3119i	−0.00414762	+	1.56286i
$483$	−20.3855			−0.927573
$484$	−18.8185	+	11.3959i	−0.855384	+	0.517994i
$485$	−42.6276			−1.93562
$486$	−0.00375312	+	1.41421i	−0.000170245	+	0.0641498i
$487$	−13.9547	−	19.2070i	−0.632347	−	0.870350i	0.365832	−	0.930681i	$-0.380785\pi$
$487$	−13.9547	−	19.2070i	−0.632347	−	0.870350i	−0.998178	+	0.0603306i	$0.980785\pi$
$488$	0.905134	−	0.286149i	0.0409735	−	0.0129534i
$489$	−5.24667	−	16.1476i	−0.237263	−	0.730219i
$490$	−0.486980	+	0.351841i	−0.0219995	+	0.0158946i
$491$	25.7264	+	18.6914i	1.16102	+	0.843529i	0.989906	−	0.141723i	$-0.0452642\pi$
$491$	25.7264	+	18.6914i	1.16102	+	0.843529i	0.171112	+	0.985252i	$0.445264\pi$
$492$	1.05845	−	3.19969i	0.0477187	−	0.144253i
$493$	−3.10017	+	9.54133i	−0.139625	+	0.429720i
$494$	13.4959	−	4.34551i	0.607208	−	0.195514i
$495$	−2.64465	−	9.37661i	−0.118868	−	0.421447i
$496$	19.3738	+	6.52310i	0.869910	+	0.292896i
$497$	−31.5099	−	10.2382i	−1.41341	−	0.459245i
$498$	3.65140	−	4.99777i	0.163623	−	0.223956i
$499$	10.3285	−	14.2160i	0.462368	−	0.636395i	−0.512630	−	0.858610i	$-0.671329\pi$
$499$	10.3285	−	14.2160i	0.462368	−	0.636395i	0.974998	+	0.222215i	$0.0713286\pi$
$500$	6.49272	+	4.77009i	0.290363	+	0.213325i
$501$	−6.11564	+	1.98709i	−0.273227	+	0.0887767i
$502$	−10.1790	−	3.33725i	−0.454311	−	0.148949i
$503$	4.25136	−	3.08879i	0.189559	−	0.137722i	−0.488958	−	0.872307i	$-0.662623\pi$
$503$	4.25136	−	3.08879i	0.189559	−	0.137722i	0.678517	+	0.734585i	$0.262623\pi$
$504$	−6.02573	+	4.30507i	−0.268407	+	0.191763i
$505$		−	52.7557i		−	2.34760i
$506$	−35.1738	+	9.81997i	−1.56367	+	0.436551i
$507$			10.2318i			0.454409i
$508$	−8.84407	−	27.7190i	−0.392392	−	1.22983i
$509$	−3.51383	+	2.55295i	−0.155748	+	0.113158i	−0.662930	−	0.748682i	$-0.730687\pi$
$509$	−3.51383	+	2.55295i	−0.155748	+	0.113158i	0.507182	+	0.861839i	$0.330687\pi$
$510$	−2.15922	+	6.58588i	−0.0956119	+	0.291628i
$511$	−18.0019	+	5.84916i	−0.796355	+	0.258752i
$512$	−22.6210	−	0.540398i	−0.999715	−	0.0238825i
$513$	1.22260	−	1.68276i	0.0539791	−	0.0742958i
$514$	24.5077	+	17.9055i	1.08099	+	0.789776i
$515$	−28.5286	−	9.26952i	−1.25712	−	0.408464i
$516$	7.98957	+	11.1204i	0.351721	+	0.489546i
$517$	9.32704	−	11.8317i	0.410203	−	0.520357i
$518$	−10.7013	−	33.2349i	−0.470186	−	1.46026i
$519$	−2.61380	+	8.04444i	−0.114733	+	0.353112i
$520$	0.318824	−	40.0446i	0.0139814	−	1.75607i
$521$	−5.69229	−	4.13569i	−0.249384	−	0.181188i	0.456070	−	0.889944i	$-0.349257\pi$
$521$	−5.69229	−	4.13569i	−0.249384	−	0.181188i	−0.705454	+	0.708756i	$0.749257\pi$
$522$	−4.98022	−	6.89307i	−0.217978	−	0.301702i
$523$	−12.4768	−	38.3995i	−0.545570	−	1.67909i	−0.719630	−	0.694358i	$-0.755689\pi$
$523$	−12.4768	−	38.3995i	−0.545570	−	1.67909i	0.174060	−	0.984735i	$-0.444311\pi$
$524$	−10.0457	−	0.0533200i	−0.438847	−	0.00232929i
$525$	5.58442	+	7.68629i	0.243724	+	0.335457i
$526$	−24.3777	−	0.0646952i	−1.06292	−	0.00282084i
$527$	−8.52651			−0.371421
$528$	−8.32317	+	10.3308i	−0.362219	+	0.449589i
$529$	−37.6195			−1.63563
$530$	−16.5827	−	0.0440082i	−0.720306	−	0.00191159i
$531$	−3.88186	−	5.34292i	−0.168458	−	0.231863i
$532$	10.8919	+	0.0578118i	0.472225	+	0.00250646i
$533$	−2.50987	−	7.72459i	−0.108715	−	0.334589i
$534$	−5.31778	−	7.36030i	−0.230123	−	0.318511i
$535$	−16.3399	−	11.8716i	−0.706435	−	0.513255i
$536$	0.00178842	−	0.224627i	7.72482e−5	−	0.00970242i
$537$	5.54125	−	17.0542i	0.239123	−	0.735943i
$538$	10.3401	+	32.1132i	0.445792	+	1.38450i
$539$	0.398814	−	0.266489i	0.0171781	−	0.0114785i
$540$	−3.42791	−	4.77116i	−0.147514	−	0.205318i
$541$	15.2257	+	4.94712i	0.654603	+	0.212693i	0.617443	−	0.786616i	$-0.288169\pi$
$541$	15.2257	+	4.94712i	0.654603	+	0.212693i	0.0371603	+	0.999309i	$0.488169\pi$
$542$	9.49230	+	6.93512i	0.407729	+	0.297889i
$543$	−0.771788	+	1.06228i	−0.0331206	+	0.0455866i
$544$	9.01382	−	2.79709i	0.386465	−	0.119924i
$545$	9.62228	−	3.12647i	0.412173	−	0.133923i
$546$	−5.56014	+	16.9591i	−0.237952	+	0.725781i
$547$	32.2294	−	23.4161i	1.37803	−	1.00120i	0.380970	−	0.924587i	$-0.375590\pi$
$547$	32.2294	−	23.4161i	1.37803	−	1.00120i	0.997061	−	0.0766105i	$-0.0244098\pi$
$548$	3.80888	+	11.9377i	0.162707	+	0.509955i
$549$		−	0.335624i		−	0.0143241i
$550$	13.3381	+	10.5721i	0.568739	+	0.450795i
$551$			12.5075i			0.532838i
$552$	−17.9184	+	12.8018i	−0.762659	+	0.544880i
$553$	20.3696	−	14.7994i	0.866202	−	0.629333i
$554$	2.66048	+	0.872254i	0.113033	+	0.0370585i
$555$	26.3428	−	8.55930i	1.11819	−	0.363322i
$556$	30.5286	+	22.4289i	1.29470	+	0.951195i
$557$	0.384067	−	0.528623i	0.0162734	−	0.0223985i	−0.800803	−	0.598928i	$-0.795593\pi$
$557$	0.384067	−	0.528623i	0.0162734	−	0.0223985i	0.817076	+	0.576530i	$0.195593\pi$
$558$	4.26373	−	5.83589i	0.180498	−	0.247053i
$559$	31.3843	+	10.1974i	1.32742	+	0.431304i
$560$	9.81674	−	29.1560i	0.414833	−	1.23207i
$561$	1.91513	−	5.19144i	0.0808567	−	0.219183i
$562$	−5.25507	+	1.69207i	−0.221672	+	0.0713757i
$563$	−13.6791	+	42.1000i	−0.576507	+	1.77430i	0.0544842	+	0.998515i	$0.482649\pi$
$563$	−13.6791	+	42.1000i	−0.576507	+	1.77430i	−0.630991	+	0.775790i	$0.717351\pi$
$564$	2.85327	−	8.62543i	0.120144	−	0.363196i
$565$	−8.03099	−	5.83486i	−0.337866	−	0.245474i
$566$	−14.7813	+	10.6794i	−0.621303	+	0.448889i
$567$	0.809092	+	2.49013i	0.0339787	+	0.104576i
$568$	−34.1259	+	10.7886i	−1.43189	+	0.452678i
$569$	8.67120	+	11.9349i	0.363516	+	0.500336i	0.951124	−	0.308809i	$-0.0999305\pi$
$569$	8.67120	+	11.9349i	0.363516	+	0.500336i	−0.587608	+	0.809145i	$0.699930\pi$
$570$	−0.0229313	+	8.64072i	−0.000960487	+	0.361920i
$571$	−1.61906			−0.0677554			−0.0338777	−	0.999426i	$-0.510786\pi$
$571$	−1.61906			−0.0677554			−0.0338777	+	0.999426i	$0.510786\pi$
$572$	−1.42423	+	31.9401i	−0.0595500	+	1.33548i
$573$	5.51146			0.230245
$574$	0.0165591	−	6.23960i	0.000691162	−	0.260436i
$575$	16.6061	+	22.8564i	0.692523	+	0.953177i
$576$	−2.59297	+	7.56813i	−0.108040	+	0.315339i
$577$	8.07820	+	24.8621i	0.336300	+	1.03502i	0.966078	+	0.258250i	$0.0831457\pi$
$577$	8.07820	+	24.8621i	0.336300	+	1.03502i	−0.629778	+	0.776775i	$0.716854\pi$
$578$	16.2967	−	11.7743i	0.677853	−	0.489746i
$579$	−17.5603	−	12.7583i	−0.729782	−	0.530218i
$580$	33.5395	+	11.0948i	1.39265	+	0.460687i
$581$	3.54113	−	10.8985i	0.146911	−	0.452145i
$582$	19.5350	−	6.29004i	0.809752	−	0.260731i
$583$	13.2291	+	0.519556i	0.547895	+	0.0215178i
$584$	−12.1501	+	16.4462i	−0.502773	+	0.680547i
$585$	−13.4654	−	4.37517i	−0.556725	−	0.180891i
$586$	16.0133	−	21.9178i	0.661502	−	0.905417i
$587$	−17.0789	+	23.5071i	−0.704923	+	0.970243i	0.294968	+	0.955507i	$0.404691\pi$
$587$	−17.0789	+	23.5071i	−0.704923	+	0.970243i	−0.999891	+	0.0147364i	$0.995309\pi$
$588$	0.171252	−	0.233097i	0.00706232	−	0.00961274i
$589$	−10.1099	+	3.28490i	−0.416570	+	0.135352i
$590$	26.0698	+	8.54714i	1.07328	+	0.351880i
$591$	−4.78290	+	3.47498i	−0.196742	+	0.142941i
$592$	−30.2772	−	22.4926i	−1.24438	−	0.924438i
$593$		−	20.8976i		−	0.858164i	−0.903266	−	0.429082i	$-0.858837\pi$
$593$		−	20.8976i		−	0.858164i	0.903266	−	0.429082i	$-0.141163\pi$
$594$	2.59556	+	3.90680i	0.106497	+	0.160298i
$595$			12.8317i			0.526049i
$596$	19.6078	−	6.25610i	0.803167	−	0.256260i
$597$	5.29626	−	3.84796i	0.216762	−	0.157486i
$598$	−16.5339	+	50.4304i	−0.676122	+	2.06225i
$599$	−3.94466	+	1.28170i	−0.161174	+	0.0523687i	−0.388493	−	0.921452i	$-0.627004\pi$
$599$	−3.94466	+	1.28170i	−0.161174	+	0.0523687i	0.227318	+	0.973820i	$0.427004\pi$
$600$	9.73546	+	3.24916i	0.397448	+	0.132646i
$601$	14.8397	−	20.4251i	0.605323	−	0.833156i	−0.390859	−	0.920450i	$-0.627822\pi$
$601$	14.8397	−	20.4251i	0.605323	−	0.833156i	0.996183	+	0.0872946i	$0.0278221\pi$
$602$	20.4698	+	14.9554i	0.834288	+	0.609535i
$603$	−0.0755331	−	0.0245422i	−0.00307595	−	0.000999436i
$604$	−9.94863	+	7.14773i	−0.404804	+	0.290837i
$605$	−24.5709	−	20.9842i	−0.998950	−	0.853127i
$606$	7.78453	+	24.1765i	0.316225	+	0.982102i
$607$	−7.58932	+	23.3575i	−0.308041	+	0.948053i	0.670484	+	0.741924i	$0.266087\pi$
$607$	−7.58932	+	23.3575i	−0.308041	+	0.948053i	−0.978525	+	0.206129i	$0.933913\pi$
$608$	9.61008	−	6.78915i	0.389740	−	0.275336i
$609$	−12.7373	−	9.25422i	−0.516143	−	0.375000i
$610$	0.816521	+	1.13014i	0.0330600	+	0.0457580i
$611$	−6.76587	−	20.8232i	−0.273718	−	0.842417i
$612$	0.0177106	−	3.33673i	0.000715908	−	0.134879i
$613$	20.2384	+	27.8557i	0.817419	+	1.12508i	0.990136	+	0.140110i	$0.0447455\pi$
$613$	20.2384	+	27.8557i	0.817419	+	1.12508i	−0.172717	+	0.984972i	$0.555254\pi$
$614$	−5.95261	−	0.0157974i	−0.240228	−	0.000637531i
$615$	4.94993			0.199600
$616$	−8.68401	+	22.9752i	−0.349889	+	0.925699i
$617$	−29.8450			−1.20151			−0.600757	−	0.799432i	$-0.705134\pi$
$617$	−29.8450			−1.20151			−0.600757	+	0.799432i	$0.705134\pi$
$618$	14.4417	+	0.0383262i	0.580929	+	0.00154171i
$619$	11.6079	+	15.9769i	0.466561	+	0.642166i	0.975853	−	0.218428i	$-0.0700928\pi$
$619$	11.6079	+	15.9769i	0.466561	+	0.642166i	−0.509292	+	0.860594i	$0.670093\pi$
$620$	−0.159361	+	30.0240i	−0.00640007	+	1.20579i
$621$	2.40596	+	7.40478i	0.0965479	+	0.297144i
$622$	1.56208	+	2.16207i	0.0626338	+	0.0866909i
$623$	−13.6007	−	9.88149i	−0.544900	−	0.395893i
$624$	5.76279	+	18.3983i	0.230696	+	0.736523i
$625$	−9.26315	+	28.5090i	−0.370526	+	1.14036i
$626$	2.11172	+	6.55838i	0.0844014	+	0.262126i
$627$	0.270724	−	6.89330i	0.0108117	−	0.275292i
$628$	24.3020	−	17.4601i	0.969755	−	0.696734i
$629$	14.9620	+	4.86144i	0.596573	+	0.193838i
$630$	−8.78253	−	6.41656i	−0.349904	−	0.255642i
$631$	9.51464	−	13.0958i	0.378772	−	0.521335i	−0.576487	−	0.817106i	$-0.695577\pi$
$631$	9.51464	−	13.0958i	0.378772	−	0.521335i	0.955259	+	0.295772i	$0.0955768\pi$
$632$	8.61064	−	25.8001i	0.342513	−	1.02627i
$633$	14.7718	−	4.79963i	0.587124	−	0.190768i
$634$	6.11034	−	18.6373i	0.242673	−	0.740180i
$635$	34.5723	−	25.1182i	1.37196	−	0.996787i
$636$	7.60587	−	2.42674i	0.301592	−	0.0962265i
$637$		−	0.697066i		−	0.0276187i
$638$	−26.4353	−	9.83177i	−1.04658	−	0.389244i
$639$			12.6539i			0.500581i
$640$	−9.68082	−	31.7923i	−0.382668	−	1.25670i
$641$	−23.3781	+	16.9852i	−0.923381	+	0.670875i	−0.944363	−	0.328905i	$-0.893321\pi$
$641$	−23.3781	+	16.9852i	−0.923381	+	0.670875i	0.0209826	+	0.999780i	$0.493321\pi$
$642$	9.23987	+	3.02935i	0.364668	+	0.119559i
$643$	11.9135	−	3.87093i	0.469822	−	0.152654i	−0.0645312	−	0.997916i	$-0.520555\pi$
$643$	11.9135	−	3.87093i	0.469822	−	0.152654i	0.534353	+	0.845261i	$0.320555\pi$
$644$	−24.1393	+	32.8568i	−0.951224	+	1.29474i
$645$	−11.8210	+	16.2703i	−0.465453	+	0.640641i
$646$	−2.89520	+	3.96274i	−0.113910	+	0.155912i
$647$	17.0975	+	5.55533i	0.672173	+	0.218402i	0.625166	−	0.780492i	$-0.285031\pi$
$647$	17.0975	+	5.55533i	0.672173	+	0.218402i	0.0470078	+	0.998895i	$0.485031\pi$
$648$	2.27494	+	1.68067i	0.0893680	+	0.0660231i
$649$	−20.5500	−	7.58091i	−0.806658	−	0.297577i
$650$	23.5439	−	7.58087i	0.923469	−	0.297346i
$651$	4.13497	−	12.7261i	0.162062	−	0.498776i
$652$	−32.2390	−	10.6646i	−1.26258	−	0.417658i
$653$	7.37486	+	5.35815i	0.288600	+	0.209681i	0.722660	−	0.691204i	$-0.242919\pi$
$653$	7.37486	+	5.35815i	0.288600	+	0.209681i	−0.434060	+	0.900884i	$0.642919\pi$
$654$	−3.94828	+	2.85262i	−0.154390	+	0.111546i
$655$	−4.55940	−	14.0324i	−0.178151	−	0.548291i
$656$	−3.90382	−	5.49487i	−0.152418	−	0.214539i
$657$	4.24927	+	5.84861i	0.165780	+	0.228176i
$658$	0.0446383	−	16.8201i	0.00174018	−	0.655717i
$659$	−33.9827			−1.32378			−0.661890	−	0.749601i	$-0.730245\pi$
$659$	−33.9827			−1.32378			−0.661890	+	0.749601i	$0.730245\pi$
$660$	−18.2446	−	6.84068i	−0.710170	−	0.266273i
$661$	43.3261			1.68519			0.842595	−	0.538547i	$-0.181027\pi$
$661$	43.3261			1.68519			0.842595	+	0.538547i	$0.181027\pi$
$662$	−0.00469805	+	1.77027i	−0.000182595	+	0.0688035i
$663$	−4.72669	−	6.50573i	−0.183570	−	0.252662i
$664$	−3.73150	−	11.8033i	−0.144810	−	0.458057i
$665$	4.94350	+	15.2145i	0.191701	+	0.589994i
$666$	−10.8092	+	7.80958i	−0.418847	+	0.302615i
$667$	−37.8764	−	27.5188i	−1.46658	−	1.06553i
$668$	−4.03905	+	12.2100i	−0.156275	+	0.472419i
$669$	4.75800	−	14.6436i	0.183955	−	0.566155i
$670$	0.314048	−	0.101120i	0.0121327	−	0.00390660i
$671$	−0.618443	−	0.925532i	−0.0238747	−	0.0357298i
$672$	−0.196529	+	14.8099i	−0.00758125	+	0.571305i
$673$	−3.91966	−	1.27357i	−0.151092	−	0.0490927i	0.232495	−	0.972598i	$-0.425311\pi$
$673$	−3.91966	−	1.27357i	−0.151092	−	0.0490927i	−0.383586	+	0.923505i	$0.625311\pi$
$674$	−4.23898	+	5.80201i	−0.163279	+	0.223485i
$675$	2.13286	−	2.93563i	0.0820938	−	0.112992i
$676$	16.4913	+	12.1159i	0.634280	+	0.465995i
$677$	−18.6238	+	6.05124i	−0.715771	+	0.232568i	−0.644189	−	0.764867i	$-0.722805\pi$
$677$	−18.6238	+	6.05124i	−0.715771	+	0.232568i	−0.0715823	+	0.997435i	$0.522805\pi$
$678$	4.54136	+	1.48891i	0.174410	+	0.0571813i
$679$	30.7392	−	22.3334i	1.17966	−	0.857076i
$680$	8.05811	+	11.2788i	0.309014	+	0.432522i
$681$			14.3662i			0.550513i
$682$	1.00426	−	23.9499i	0.0384552	−	0.917089i
$683$			19.6447i			0.751683i	0.926684	+	0.375842i	$0.122646\pi$
$683$			19.6447i			0.751683i	−0.926684	+	0.375842i	$0.877354\pi$
$684$	−1.26450	−	3.96318i	−0.0483493	−	0.151536i
$685$	−14.8892	+	10.8177i	−0.568889	+	0.413322i
$686$	8.24183	−	25.1385i	0.314674	−	0.959794i
$687$	−17.3760	+	5.64581i	−0.662936	+	0.215401i
$688$	27.3843	+	0.290707i	1.04402	+	0.0110831i
$689$	11.3092	−	15.5657i	0.430844	−	0.593006i
$690$	−26.1162	−	19.0806i	−0.994227	−	0.726387i
$691$	−13.9758	−	4.54102i	−0.531666	−	0.172749i	0.0308673	−	0.999523i	$-0.490173\pi$
$691$	−13.9758	−	4.54102i	−0.531666	−	0.172749i	−0.562533	+	0.826775i	$0.690173\pi$
$692$	9.87069	+	13.7386i	0.375227	+	0.522263i
$693$	6.81966	+	5.37600i	0.259057	+	0.204217i
$694$	1.91901	+	5.95986i	0.0728444	+	0.226233i
$695$	−17.1932	+	52.9153i	−0.652176	+	2.00719i
$696$	−17.0073	−	0.135408i	−0.644662	−	0.00513263i
$697$	2.27448	+	1.65251i	0.0861522	+	0.0625932i
$698$	14.3275	+	19.8306i	0.542306	+	0.750601i
$699$	−0.765328	−	2.35544i	−0.0289474	−	0.0890908i
$700$	19.0013	+	0.100854i	0.718182	+	0.00381194i
$701$	13.1330	+	18.0761i	0.496028	+	0.682723i	0.981485	−	0.191537i	$-0.0613471\pi$
$701$	13.1330	+	18.0761i	0.496028	+	0.682723i	−0.485458	+	0.874260i	$0.661347\pi$
$702$	6.81639	+	0.0180898i	0.257268	+	0.000682755i
$703$	19.6133			0.739729
$704$	6.79503	+	25.6481i	0.256097	+	0.966651i
$705$	13.3435			0.502547
$706$	−43.0460	−	0.114238i	−1.62006	−	0.00429941i
$707$	27.6397	+	38.0428i	1.03950	+	1.43075i
$708$	−13.2082	−	0.0701063i	−0.496396	−	0.00263476i
$709$	−8.78470	−	27.0365i	−0.329916	−	1.01538i	−0.969172	−	0.246384i	$-0.920758\pi$
$709$	−8.78470	−	27.0365i	−0.329916	−	1.01538i	0.639256	−	0.768994i	$-0.279242\pi$
$710$	−30.7850	−	42.6092i	−1.15534	−	1.59910i
$711$	−7.77976	−	5.65232i	−0.291764	−	0.211979i
$712$	−18.1601	−	0.144586i	−0.680580	−	0.00541860i
$713$	12.2960	−	37.8431i	0.460487	−	1.41723i
$714$	−1.89342	−	5.88041i	−0.0708595	−	0.220069i
$715$	−45.1947	+	12.7470i	−1.69018	+	0.476711i
$716$	−20.9259	−	29.1258i	−0.782036	−	1.08848i
$717$	−4.23181	−	1.37500i	−0.158040	−	0.0513502i
$718$	33.2603	+	24.3001i	1.24126	+	0.906873i
$719$	8.80477	−	12.1187i	0.328363	−	0.451952i	−0.612635	−	0.790366i	$-0.709890\pi$
$719$	8.80477	−	12.1187i	0.328363	−	0.451952i	0.940997	+	0.338414i	$0.109890\pi$
$720$	−11.7492	−	0.124727i	−0.437865	−	0.00464830i
$721$	25.4288	−	8.26231i	0.947018	−	0.307705i
$722$	6.46493	−	19.7188i	0.240600	−	0.733858i
$723$	19.6286	−	14.2610i	0.729994	−	0.530372i
$724$	0.798239	+	2.50183i	0.0296663	+	0.0929798i
$725$			21.8197i			0.810364i
$726$	14.3565	+	5.99080i	0.532821	+	0.222340i
$727$		−	6.15713i		−	0.228355i	−0.993460	−	0.114178i	$-0.963577\pi$
$727$		−	6.15713i		−	0.228355i	0.993460	−	0.114178i	$-0.0364233\pi$
$728$	20.7502	+	29.0436i	0.769052	+	1.07643i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−28.5372	−	9.35611i	−1.05621	−	0.346285i
$731$	−10.8635	+	3.52976i	−0.401801	+	0.130553i
$732$	−0.540950	−	0.397427i	−0.0199941	−	0.0146893i
$733$	2.01958	−	2.77971i	0.0745949	−	0.102671i	−0.770089	−	0.637936i	$-0.779788\pi$
$733$	2.01958	−	2.77971i	0.0745949	−	0.102671i	0.844684	+	0.535265i	$0.179788\pi$
$734$	8.40702	−	11.5069i	0.310309	−	0.424728i
$735$	0.404027	+	0.131276i	0.0149027	+	0.00484220i
$736$	−0.584408	+	44.0395i	−0.0215416	+	1.62332i
$737$	−0.253516	+	0.0715035i	−0.00933840	+	0.00263387i
$738$	−2.26841	+	0.730402i	−0.0835014	+	0.0268865i
$739$	5.73506	−	17.6507i	0.210967	−	0.649291i	−0.788448	−	0.615102i	$-0.789115\pi$
$739$	5.73506	−	17.6507i	0.210967	−	0.649291i	0.999415	−	0.0341895i	$-0.0108850\pi$
$740$	17.3980	−	52.5940i	0.639563	−	1.93340i
$741$	−8.11081	−	5.89285i	−0.297958	−	0.216479i
$742$	11.9810	−	8.65623i	0.439837	−	0.317780i
$743$	3.06915	+	9.44587i	0.112596	+	0.346535i	0.991438	−	0.130578i	$-0.0416832\pi$
$743$	3.06915	+	9.44587i	0.112596	+	0.346535i	−0.878842	+	0.477113i	$0.841683\pi$
$744$	−4.35726	−	13.7827i	−0.159745	−	0.505297i
$745$	17.7681	+	24.4556i	0.650972	+	0.895986i
$746$	0.119350	−	44.9723i	0.00436972	−	1.64655i
$747$	−4.37667			−0.160134
$748$	−6.09964	−	9.23415i	−0.223025	−	0.337634i
$749$	18.0026			0.657802
$750$	0.0151187	−	5.69687i	0.000552058	−	0.208020i
$751$	23.5204	+	32.3731i	0.858273	+	1.18131i	0.981979	+	0.188992i	$0.0605221\pi$
$751$	23.5204	+	32.3731i	0.858273	+	1.18131i	−0.123706	+	0.992319i	$0.539478\pi$
$752$	−10.5235	−	14.8126i	−0.383754	−	0.540158i
$753$	2.34068	+	7.20387i	0.0852991	+	0.262524i
$754$	−33.2242	+	24.0043i	−1.20995	+	0.874186i
$755$	−14.5559	−	10.5755i	−0.529743	−	0.384881i
$756$	4.97160	+	1.64460i	0.180815	+	0.0598134i
$757$	8.78945	−	27.0511i	0.319458	−	0.983190i	−0.654423	−	0.756129i	$-0.727088\pi$
$757$	8.78945	−	27.0511i	0.319458	−	0.983190i	0.973881	−	0.227061i	$-0.0729117\pi$
$758$	45.5182	−	14.6563i	1.65330	−	0.532342i
$759$	20.2793	+	15.9864i	0.736092	+	0.580268i
$760$	13.8997	+	10.2688i	0.504196	+	0.372489i
$761$	−19.9531	−	6.48316i	−0.723300	−	0.235014i	−0.0758465	−	0.997120i	$-0.524166\pi$
$761$	−19.9531	−	6.48316i	−0.723300	−	0.235014i	−0.647453	+	0.762105i	$0.724166\pi$
$762$	−12.1371	+	16.6124i	−0.439681	+	0.601803i
$763$	−5.30072	+	7.29582i	−0.191899	+	0.264126i
$764$	6.52635	−	8.88322i	0.236115	−	0.321383i
$765$	4.66096	−	1.51444i	0.168517	−	0.0547546i
$766$	−17.6988	−	5.80267i	−0.639484	−	0.209659i
$767$	−25.7525	+	18.7103i	−0.929870	+	0.675590i
$768$	9.12765	+	13.1410i	0.329366	+	0.474185i
$769$			31.2417i			1.12661i	0.826250	+	0.563303i	$0.190470\pi$
$769$			31.2417i			1.12661i	−0.826250	+	0.563303i	$0.809530\pi$
$770$	−36.0427	−	1.51133i	−1.29889	−	0.0544647i
$771$		−	21.4620i		−	0.772935i
$772$	−41.3574	+	13.1956i	−1.48849	+	0.474919i
$773$	2.11543	−	1.53695i	0.0760868	−	0.0552803i	−0.549092	−	0.835762i	$-0.685026\pi$
$773$	2.11543	−	1.53695i	0.0760868	−	0.0552803i	0.625178	+	0.780482i	$0.285026\pi$
$774$	3.01644	−	9.20048i	0.108424	−	0.330705i
$775$	−17.6370	+	5.73060i	−0.633539	+	0.205849i
$776$	12.9941	−	38.9343i	0.466462	−	1.39766i
$777$	−14.5117	+	19.9737i	−0.520605	+	0.716552i
$778$	−16.3587	−	11.9517i	−0.586486	−	0.428490i
$779$	3.33349	+	1.08312i	0.119435	+	0.0388067i
$780$	−22.9967	+	16.5223i	−0.823414	+	0.591593i
$781$	23.3169	+	34.8950i	0.834344	+	1.24864i
$782$	−5.63038	−	17.4863i	−0.201342	−	0.625308i
$783$	−1.85818	+	5.71889i	−0.0664059	+	0.204376i
$784$	−0.172912	−	0.552039i	−0.00617541	−	0.0197157i
$785$	35.5564	+	25.8332i	1.26906	+	0.922028i
$786$	4.16004	+	5.75787i	0.148384	+	0.205377i
$787$	−7.42627	−	22.8557i	−0.264718	−	0.814718i	−0.991758	−	0.128123i	$-0.959105\pi$
$787$	−7.42627	−	22.8557i	−0.264718	−	0.814718i	0.727040	−	0.686595i	$-0.240895\pi$
$788$	−0.0627580	+	11.8238i	−0.00223566	+	0.421206i
$789$	10.1321	+	13.9456i	0.360712	+	0.496477i
$790$	39.9478	+	0.106016i	1.42128	+	0.00377188i
$791$	8.84823			0.314607
$792$	9.37038	+	0.442751i	0.332962	+	0.0157325i
$793$	−1.61769			−0.0574458
$794$	−2.31301	−	0.00613841i	−0.0820856	−	0.000217844i
$795$	6.89223	+	9.48635i	0.244442	+	0.336446i
$796$	0.0694940	−	13.0929i	0.00246315	−	0.464065i
$797$	5.45531	+	16.7897i	0.193237	+	0.594722i	0.999993	+	0.00383710i	$0.00122139\pi$
$797$	5.45531	+	16.7897i	0.193237	+	0.594722i	−0.806756	+	0.590885i	$0.798779\pi$
$798$	−4.51049	−	6.24294i	−0.159670	−	0.220998i
$799$	6.13134	+	4.45468i	0.216911	+	0.157595i
$800$	16.7651	−	11.8439i	0.592734	−	0.418744i
$801$	−1.98413	+	6.10653i	−0.0701058	+	0.215763i
$802$	2.62507	+	8.15270i	0.0926945	+	0.287882i
$803$	22.4950	+	8.29842i	0.793831	+	0.292845i
$804$	−0.128998	+	0.0926807i	−0.00454942	+	0.00326860i
$805$	−56.9507	−	18.5044i	−2.00725	−	0.652195i
$806$	−28.1286	−	20.5509i	−0.990788	−	0.723874i
$807$	14.0219	−	19.2995i	0.493595	−	0.679376i
$808$	48.1849	+	16.0815i	1.69514	+	0.565744i
$809$	−20.0987	+	6.53045i	−0.706632	+	0.229599i	−0.640218	−	0.768194i	$-0.721156\pi$
$809$	−20.0987	+	6.53045i	−0.706632	+	0.229599i	−0.0664141	+	0.997792i	$0.521156\pi$
$810$	−1.29420	+	3.94745i	−0.0454734	+	0.138699i
$811$	−9.32169	+	6.77260i	−0.327329	+	0.237818i	−0.739296	−	0.673380i	$-0.764842\pi$
$811$	−9.32169	+	6.77260i	−0.327329	+	0.237818i	0.411968	+	0.911199i	$0.364842\pi$
$812$	−29.9985	+	9.57137i	−1.05274	+	0.335889i
$813$		−	8.31263i		−	0.291537i
$814$	−15.4174	+	41.4537i	−0.540380	+	1.45295i
$815$		−	49.8738i		−	1.74700i
$816$	−5.35708	−	3.97971i	−0.187535	−	0.139318i
$817$	−11.5210	+	8.37047i	−0.403067	+	0.292846i
$818$	−25.2565	−	8.28049i	−0.883071	−	0.289520i
$819$	12.0023	−	3.89977i	0.419393	−	0.136269i
$820$	5.86142	−	7.97815i	0.204690	−	0.278609i
$821$	24.1507	−	33.2406i	0.842867	−	1.16011i	−0.142523	−	0.989791i	$-0.545522\pi$
$821$	24.1507	−	33.2406i	0.842867	−	1.16011i	0.985390	−	0.170315i	$-0.0544785\pi$
$822$	5.22708	−	7.15446i	0.182316	−	0.249540i
$823$	−32.9520	−	10.7068i	−1.14864	−	0.373214i	−0.328006	−	0.944676i	$-0.606377\pi$
$823$	−32.9520	−	10.7068i	−1.14864	−	0.373214i	−0.820629	+	0.571461i	$0.806377\pi$
$824$	17.1627	−	23.2313i	0.597893	−	0.809300i
$825$	0.472287	−	12.0256i	0.0164429	−	0.418676i
$826$	−23.2772	+	7.49499i	−0.809918	+	0.260784i
$827$	9.86519	−	30.3619i	0.343046	−	1.05579i	−0.619575	−	0.784937i	$-0.712695\pi$
$827$	9.86519	−	30.3619i	0.343046	−	1.05579i	0.962621	−	0.270850i	$-0.0873049\pi$
$828$	14.7838	+	4.89046i	0.513773	+	0.169955i
$829$	−19.4097	−	14.1019i	−0.674125	−	0.489781i	0.197278	−	0.980348i	$-0.436790\pi$
$829$	−19.4097	−	14.1019i	−0.674125	−	0.489781i	−0.871403	+	0.490567i	$0.836790\pi$
$830$	14.7375	−	10.6477i	0.511545	−	0.369589i
$831$	−0.611782	−	1.88287i	−0.0212225	−	0.0653161i
$832$	36.4779	+	12.4979i	1.26464	+	0.433288i
$833$	0.141824	+	0.195204i	0.00491390	+	0.00676340i
$834$	0.0710879	−	26.7866i	0.00246157	−	0.927543i
$835$	−18.8889			−0.653677
$836$	−10.7898	−	8.59899i	−0.373175	−	0.297402i
$837$	−5.11062			−0.176649
$838$	−0.0618446	+	23.3036i	−0.00213639	+	0.805010i
$839$	−16.7139	−	23.0047i	−0.577027	−	0.794209i	0.416339	−	0.909210i	$-0.363313\pi$
$839$	−16.7139	−	23.0047i	−0.577027	−	0.794209i	−0.993365	+	0.115000i	$0.963313\pi$
$840$	−20.7418	+	6.55732i	−0.715660	+	0.226249i
$841$	−2.21210	−	6.80815i	−0.0762794	−	0.234764i
$842$	44.6956	−	32.2924i	1.54031	−	1.11287i
$843$	3.15822	+	2.29458i	0.108775	+	0.0790296i
$844$	9.75594	−	29.4921i	0.335813	−	1.01516i
$845$	−9.28762	+	28.5844i	−0.319504	+	0.983332i
$846$	−6.11497	+	1.96895i	−0.210237	+	0.0676938i
$847$	28.7123	+	2.25876i	0.986568	+	0.0776118i
$848$	5.09507	−	15.1325i	0.174966	−	0.519653i
$849$	12.2634	+	3.98462i	0.420879	+	0.136752i
$850$	−5.05076	+	6.91312i	−0.173240	+	0.237118i
$851$	−43.1529	+	59.3948i	−1.47926	+	2.03603i
$852$	20.3952	+	14.9840i	0.698728	+	0.513344i
$853$	13.9203	−	4.52297i	0.476621	−	0.154864i	−0.0608478	−	0.998147i	$-0.519380\pi$
$853$	13.9203	−	4.52297i	0.476621	−	0.154864i	0.537469	+	0.843283i	$0.319380\pi$
$854$	−1.18090	−	0.387166i	−0.0404097	−	0.0132486i
$855$	4.94304	−	3.59133i	0.169048	−	0.122821i
$856$	15.8239	−	11.3054i	0.540851	−	0.386410i
$857$		−	32.1273i		−	1.09745i	−0.836004	−	0.548724i	$-0.815114\pi$
$857$		−	32.1273i		−	1.09745i	0.836004	−	0.548724i	$-0.184886\pi$
$858$	18.8305	−	12.5104i	0.642863	−	0.427099i
$859$			32.2330i			1.09978i	0.835239	+	0.549888i	$0.185329\pi$
$859$			32.2330i			1.09978i	−0.835239	+	0.549888i	$0.814671\pi$
$860$	12.2262	+	38.3191i	0.416908	+	1.30667i
$861$	−3.56945	+	2.59336i	−0.121646	+	0.0883813i
$862$	1.99233	−	6.07685i	0.0678592	−	0.206978i
$863$	−51.3427	+	16.6823i	−1.74773	+	0.567870i	−0.995815	−	0.0913946i	$-0.970868\pi$
$863$	−51.3427	+	16.6823i	−1.74773	+	0.567870i	−0.751911	+	0.659265i	$0.770868\pi$
$864$	5.40271	−	1.67652i	0.183804	−	0.0570365i
$865$	−14.6042	+	20.1010i	−0.496559	+	0.683455i
$866$	−0.515630	−	0.376722i	−0.0175218	−	0.0128015i
$867$	−13.5207	−	4.39313i	−0.459186	−	0.149199i
$868$	−15.6152	−	21.7342i	−0.530015	−	0.737705i
$869$	−31.8691	−	1.25161i	−1.08109	−	0.0424581i
$870$	−7.65615	−	23.7777i	−0.259568	−	0.806141i
$871$	−0.118292	+	0.364065i	−0.00400817	+	0.0123359i
$872$	−0.0775604	+	9.74164i	−0.00262653	+	0.329893i
$873$	−11.7402	−	8.52979i	−0.397347	−	0.288690i
$874$	−13.4126	−	18.5643i	−0.453690	−	0.627948i
$875$	−3.25928	−	10.0310i	−0.110184	−	0.339110i
$876$	14.4584	+	0.0767416i	0.488503	+	0.00259286i
$877$	−17.6007	−	24.2252i	−0.594332	−	0.818028i	0.400842	−	0.916147i	$-0.368718\pi$
$877$	−17.6007	−	24.2252i	−0.594332	−	0.818028i	−0.995175	+	0.0981187i	$0.968718\pi$
$878$	27.3351	+	0.0725437i	0.922516	+	0.00244823i
$879$	−19.1939			−0.647396
$880$	−32.6298	+	21.3058i	−1.09995	+	0.718218i
$881$	27.5799			0.929189			0.464595	−	0.885523i	$-0.346200\pi$
$881$	27.5799			0.929189			0.464595	+	0.885523i	$0.346200\pi$
$882$	−0.204525		0.000542781i	−0.00688671		1.82764e-5i
$883$	24.4976	+	33.7180i	0.824409	+	1.13470i	0.988938	+	0.148330i	$0.0473897\pi$
$883$	24.4976	+	33.7180i	0.824409	+	1.13470i	−0.164529	+	0.986372i	$0.552610\pi$
$884$	−16.0828	−	0.0853639i	−0.540924	−	0.00287110i
$885$	−5.99480	−	18.4501i	−0.201513	−	0.620193i
$886$	−17.0655	−	23.6202i	−0.573327	−	0.793538i
$887$	13.5564	+	9.84933i	0.455181	+	0.330708i	0.791638	−	0.610991i	$-0.209229\pi$
$887$	13.5564	+	9.84933i	0.455181	+	0.330708i	−0.336457	+	0.941699i	$0.609229\pi$
$888$	−0.212336	+	26.6696i	−0.00712554	+	0.894972i
$889$	−11.7706	+	36.2261i	−0.394772	+	1.21498i
$890$	−8.17510	−	25.3894i	−0.274030	−	0.851056i
$891$	1.14789	−	3.11165i	0.0384557	−	0.104244i
$892$	−17.9680	−	25.0089i	−0.601614	−	0.837361i
$893$	8.98611	+	2.91976i	0.300709	+	0.0977062i
$894$	−11.7512	−	8.58551i	−0.393020	−	0.287142i
$895$	30.9610	−	42.6142i	1.03491	−	1.42443i
$896$	23.6375	+	17.8538i	0.789673	+	0.596454i
$897$	35.6906	−	11.5966i	1.19167	−	0.387198i
$898$	−1.27803	+	3.89814i	−0.0426484	+	0.130083i
$899$	24.8620	−	18.0633i	0.829196	−	0.602446i
$900$	−2.20596	−	6.91389i	−0.0735319	−	0.230463i
$901$			6.65990i			0.221873i
$902$	−4.90958	+	6.19411i	−0.163471	+	0.206241i
$903$		−	17.9259i		−	0.596537i
$904$	7.77740	−	5.55655i	0.258672	−	0.184808i
$905$	−3.12039	+	2.26709i	−0.103725	+	0.0753607i
$906$	8.23105	+	2.69860i	0.273458	+	0.0896550i
$907$	31.3735	−	10.1939i	1.04174	−	0.338482i	0.262319	−	0.964981i	$-0.415513\pi$
$907$	31.3735	−	10.1939i	1.04174	−	0.338482i	0.779422	+	0.626499i	$0.215513\pi$
$908$	23.1550	+	17.0116i	0.768426	+	0.564550i
$909$	10.5564	−	14.5297i	0.350135	−	0.481919i
$910$	−30.9274	+	42.3312i	−1.02523	+	1.40327i
$911$	−0.842197	−	0.273646i	−0.0279032	−	0.00906631i	0.295032	−	0.955487i	$-0.404670\pi$
$911$	−0.842197	−	0.273646i	−0.0279032	−	0.00906631i	−0.322935	+	0.946421i	$0.604670\pi$
$912$	−7.88509	−	2.65489i	−0.261101	−	0.0879121i
$913$	−12.0693	+	8.06473i	−0.399435	+	0.266904i
$914$	−26.6998	+	8.59701i	−0.883150	+	0.284364i
$915$	0.304654	−	0.937629i	0.0100716	−	0.0309970i
$916$	−11.4759	+	34.6916i	−0.379175	+	1.14624i
$917$	10.6397	+	7.73017i	0.351353	+	0.255273i
$918$	−1.91252	+	1.38178i	−0.0631224	+	0.0456057i
$919$	12.1497	+	37.3931i	0.400783	+	1.23348i	0.924365	+	0.381509i	$0.124595\pi$
$919$	12.1497	+	37.3931i	0.400783	+	1.23348i	−0.523582	+	0.851975i	$0.675405\pi$
$920$	−61.6789	+	19.4992i	−2.03349	+	0.642869i
$921$	2.47407	+	3.40527i	0.0815234	+	0.112207i
$922$	−0.0355760	+	13.4054i	−0.00117163	+	0.441482i
$923$	60.9910			2.00754
$924$	16.7403	−	4.62578i	0.550717	−	0.152177i
$925$	34.2159			1.12501
$926$	0.0439546	−	16.5625i	0.00144444	−	0.544278i
$927$	−6.00236	−	8.26154i	−0.197143	−	0.271345i
$928$	−20.3574	+	27.2516i	−0.668263	+	0.894578i
$929$	8.68203	+	26.7205i	0.284848	+	0.876673i	0.986444	+	0.164098i	$0.0524712\pi$
$929$	8.68203	+	26.7205i	0.284848	+	0.876673i	−0.701596	+	0.712575i	$0.747529\pi$
$930$	17.2089	−	12.4333i	0.564302	−	0.407705i
$931$	0.243364	+	0.176814i	0.00797592	+	0.00579485i
$932$	−4.70268	−	1.55564i	−0.154042	−	0.0509566i
$933$	0.582832	−	1.79377i	0.0190811	−	0.0587255i
$934$	−31.8346	+	10.2504i	−1.04166	+	0.335402i
$935$	10.0627	−	12.7648i	0.329084	−	0.417455i
$936$	8.10073	−	10.9650i	0.264781	−	0.358404i
$937$	13.5396	+	4.39929i	0.442320	+	0.143718i	0.521706	−	0.853125i	$-0.325296\pi$
$937$	13.5396	+	4.39929i	0.442320	+	0.143718i	−0.0793858	+	0.996844i	$0.525296\pi$
$938$	−0.173485	+	0.237454i	−0.00566449	+	0.00775315i
$939$	2.86366	−	3.94149i	0.0934520	−	0.128626i
$940$	15.8006	−	21.5067i	0.515360	−	0.701473i
$941$	−10.5653	+	3.43289i	−0.344420	+	0.111909i	−0.476119	−	0.879381i	$-0.657957\pi$
$941$	−10.5653	+	3.43289i	−0.344420	+	0.111909i	0.131699	+	0.991290i	$0.457957\pi$
$942$	−20.1064	−	6.59201i	−0.655102	−	0.214779i
$943$	−10.6143	+	7.71174i	−0.345649	+	0.251129i
$944$	−15.7534	+	21.2057i	−0.512731	+	0.690186i
$945$			7.69107i			0.250191i
$946$	−8.63514	−	30.9299i	−0.280753	−	1.00562i
$947$			4.07650i			0.132468i	0.997804	+	0.0662342i	$0.0210985\pi$
$947$			4.07650i			0.132468i	−0.997804	+	0.0662342i	$0.978902\pi$
$948$	−18.3226	+	5.84604i	−0.595090	+	0.189870i
$949$	28.1899	−	20.4812i	0.915084	−	0.664848i
$950$	−3.32535	+	10.1427i	−0.107889	+	0.329073i
$951$	−13.1899	+	4.28567i	−0.427713	+	0.138972i
$952$	−11.7200	−	3.91147i	−0.379846	−	0.126772i
$953$	−15.9477	+	21.9502i	−0.516598	+	0.711036i	−0.985014	−	0.172472i	$-0.944825\pi$
$953$	−15.9477	+	21.9502i	−0.516598	+	0.711036i	0.468416	+	0.883508i	$0.344825\pi$
$954$	−4.55830	−	3.33032i	−0.147580	−	0.107823i
$955$	15.3973	+	5.00288i	0.498244	+	0.161889i
$956$	−7.22724	+	5.19251i	−0.233746	+	0.167938i
$957$	5.41379	+	19.1946i	0.175003	+	0.620475i
$958$	8.86610	+	27.5355i	0.286451	+	0.889631i
$959$	5.06923	−	15.6015i	0.163694	−	0.503798i
$960$	−14.1137	+	18.7893i	−0.455518	+	0.606421i
$961$	−3.94923	−	2.86929i	−0.127395	−	0.0925576i
$962$	37.6417	+	52.0995i	1.21362	+	1.67976i
$963$	−2.12473	−	6.53923i	−0.0684683	−	0.210724i
$964$	0.257553	−	48.5238i	0.00829522	−	1.56285i
$965$	−37.4770	−	51.5827i	−1.20643	−	1.66050i
$966$	28.8294	+	0.0765093i	0.927570	+	0.00246164i
$967$	−46.9882			−1.51104			−0.755519	−	0.655126i	$-0.772615\pi$
$967$	−46.9882			−1.51104			−0.755519	+	0.655126i	$0.772615\pi$
$968$	26.6560	−	16.0455i	0.856756	−	0.515722i
$969$	3.47027			0.111481
$970$	60.2843	+	0.159986i	1.93561	+	0.00513685i
$971$	12.7173	+	17.5039i	0.408118	+	0.561726i	0.962758	−	0.270364i	$-0.0871441\pi$
$971$	12.7173	+	17.5039i	0.408118	+	0.561726i	−0.554640	+	0.832090i	$0.687144\pi$
$972$	0.0106154	−	1.99997i	0.000340489	−	0.0641491i
$973$	−15.3250	−	47.1656i	−0.491298	−	1.51206i
$974$	19.6627	+	27.2150i	0.630035	+	0.872025i
$975$	−14.1495	−	10.2802i	−0.453148	−	0.329231i
$976$	−1.28112	+	0.401278i	−0.0410077	+	0.0128446i
$977$	−12.2562	+	37.7208i	−0.392111	+	1.20679i	0.539077	+	0.842256i	$0.318773\pi$
$977$	−12.2562	+	37.7208i	−0.392111	+	1.20679i	−0.931188	+	0.364538i	$0.881227\pi$
$978$	7.35928	+	22.8557i	0.235324	+	0.730846i
$979$	5.78075	+	20.4957i	0.184754	+	0.655045i
$980$	0.690012	−	0.495749i	0.0220416	−	0.0158361i
$981$	3.27572	+	1.06435i	0.104586	+	0.0339820i
$982$	−36.3124	−	26.5300i	−1.15878	−	0.846607i
$983$	−21.0988	+	29.0400i	−0.672947	+	0.926232i	−0.999823	−	0.0188351i	$-0.994004\pi$
$983$	−21.0988	+	29.0400i	−0.672947	+	0.926232i	0.326875	+	0.945067i	$0.394004\pi$
$984$	−1.50888	+	4.52106i	−0.0481014	+	0.144126i
$985$	−16.5162	+	5.36645i	−0.526251	+	0.170989i
$986$	4.42009	−	13.4818i	0.140764	−	0.429348i
$987$	−9.62218	+	6.99092i	−0.306277	+	0.222523i
$988$	−19.1023	+	6.09481i	−0.607724	+	0.193902i
$989$		−	53.3054i		−	1.69501i
$990$	3.70489	+	13.2704i	0.117749	+	0.421761i
$991$		−	20.6125i		−	0.654779i	−0.944890	−	0.327389i	$-0.893831\pi$
$991$		−	20.6125i		−	0.654779i	0.944890	−	0.327389i	$-0.106169\pi$
$992$	−27.3741	−	9.29774i	−0.869130	−	0.295204i
$993$	1.01271	−	0.735774i	0.0321373	−	0.0233491i
$994$	44.5231	+	14.5972i	1.41219	+	0.462995i
$995$	18.2890	−	5.94245i	0.579799	−	0.188388i
$996$	−5.18260	+	7.05419i	−0.164217	+	0.223521i
$997$	4.77732	−	6.57542i	0.151299	−	0.208246i	−0.726639	−	0.687020i	$-0.758919\pi$
$997$	4.77732	−	6.57542i	0.151299	−	0.208246i	0.877938	+	0.478774i	$0.158919\pi$
$998$	−14.6600	+	20.0656i	−0.464055	+	0.635166i
$999$	8.96791	+	2.91385i	0.283732	+	0.0921901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.79.1	✓	48
3.2	odd	2		396.2.r.b.343.12		48
4.3	odd	2	inner	132.2.j.a.79.2	yes	48
11.6	odd	10	inner	132.2.j.a.127.2	yes	48
12.11	even	2		396.2.r.b.343.11		48
33.17	even	10		396.2.r.b.127.11		48
44.39	even	10	inner	132.2.j.a.127.1	yes	48
132.83	odd	10		396.2.r.b.127.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.79.1	✓	48	1.1	even	1	trivial
132.2.j.a.79.2	yes	48	4.3	odd	2	inner
132.2.j.a.127.1	yes	48	44.39	even	10	inner
132.2.j.a.127.2	yes	48	11.6	odd	10	inner
396.2.r.b.127.11		48	33.17	even	10
396.2.r.b.127.12		48	132.83	odd	10
396.2.r.b.343.11		48	12.11	even	2
396.2.r.b.343.12		48	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 0.00375312i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.99997 + 0.0106154i) q^{4} +(0.907723 + 2.79369i) q^{5} +(-0.828215 - 1.14632i) q^{6} +(-2.11823 - 1.53899i) q^{7} +(-2.82834 - 0.0225185i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.41421 - 0.00375312i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.99997 + 0.0106154i) q^{4} +(0.907723 + 2.79369i) q^{5} +(-0.828215 - 1.14632i) q^{6} +(-2.11823 - 1.53899i) q^{7} +(-2.82834 - 0.0225185i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.27323 - 3.95426i) q^{10} +(0.900319 + 3.19209i) q^{11} +(1.16697 + 1.62425i) q^{12} +(4.58403 + 1.48944i) q^{13} +(2.98984 + 2.18440i) q^{14} +(-1.72659 + 2.37645i) q^{15} +(3.99977 + 0.0424609i) q^{16} +(-1.58673 + 0.515561i) q^{17} +(0.440584 - 1.34383i) q^{18} +(-1.68276 + 1.22260i) q^{19} +(1.78577 + 5.59693i) q^{20} -2.61828i q^{21} +(-1.26126 - 4.51766i) q^{22} -7.78585i q^{23} +(-1.64424 - 2.30141i) q^{24} +(-2.93563 + 2.13286i) q^{25} +(-6.47719 - 2.12359i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-4.22007 - 3.10041i) q^{28} +(3.53447 - 4.86478i) q^{29} +(2.45068 - 3.35432i) q^{30} +(4.86049 + 1.57927i) q^{31} +(-5.65636 - 0.0750602i) q^{32} +(-2.05326 + 2.60464i) q^{33} +(2.24591 - 0.723155i) q^{34} +(2.37667 - 7.31464i) q^{35} +(-0.628121 + 1.89881i) q^{36} +(-7.62856 - 5.54247i) q^{37} +(2.38437 - 1.72269i) q^{38} +(1.48944 + 4.58403i) q^{39} +(-2.50444 - 7.92192i) q^{40} +(-0.990482 - 1.36328i) q^{41} +(-0.00982670 + 3.70279i) q^{42} +6.84645 q^{43} +(1.76673 + 6.39364i) q^{44} -2.93745 q^{45} +(-0.0292212 + 11.0108i) q^{46} +(-2.67005 - 3.67500i) q^{47} +(2.31666 + 3.26084i) q^{48} +(-0.0446905 - 0.137543i) q^{49} +(4.15960 - 3.00529i) q^{50} +(-1.34976 - 0.980655i) q^{51} +(9.15212 + 3.02750i) q^{52} +(1.23354 - 3.79644i) q^{53} +(1.34615 - 0.433445i) q^{54} +(-8.10045 + 5.41274i) q^{55} +(5.95642 + 4.40047i) q^{56} +(-1.97821 - 0.642759i) q^{57} +(-5.01673 + 6.86654i) q^{58} +(-3.88186 + 5.34292i) q^{59} +(-3.47836 + 4.73451i) q^{60} +(-0.319198 + 0.103714i) q^{61} +(-6.86782 - 2.25166i) q^{62} +(2.11823 - 1.53899i) q^{63} +(7.99899 + 0.127380i) q^{64} +14.1583i q^{65} +(2.91351 - 3.67579i) q^{66} +0.0794202i q^{67} +(-3.17889 + 1.01426i) q^{68} +(6.29889 - 4.57641i) q^{69} +(-3.38856 + 10.3355i) q^{70} +(12.0346 - 3.91027i) q^{71} +(0.895421 - 2.68295i) q^{72} +(4.24927 - 5.84861i) q^{73} +(10.7676 + 7.86684i) q^{74} +(-3.45104 - 1.12131i) q^{75} +(-3.37846 + 2.42730i) q^{76} +(3.00549 - 8.14716i) q^{77} +(-2.08918 - 6.48837i) q^{78} +(-2.97160 + 9.14565i) q^{79} +(3.51207 + 11.2127i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.39563 + 1.93168i) q^{82} +(1.35246 + 4.16246i) q^{83} +(0.0277940 - 5.23648i) q^{84} +(-2.88063 - 3.96485i) q^{85} +(-9.68231 - 0.0256955i) q^{86} +6.01319 q^{87} +(-2.47452 - 9.04858i) q^{88} +6.42078 q^{89} +(4.15417 + 0.0110246i) q^{90} +(-7.41781 - 10.2097i) q^{91} +(0.0826498 - 15.5715i) q^{92} +(1.57927 + 4.86049i) q^{93} +(3.76221 + 5.20724i) q^{94} +(-4.94304 - 3.59133i) q^{95} +(-3.26400 - 4.62021i) q^{96} +(-4.48438 + 13.8015i) q^{97} +(0.0626854 + 0.194682i) q^{98} +(-3.31407 - 0.130155i) 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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