LMFDB - Embedded newform 546.2.cg.b.241.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			241.10
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.b.145.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(2.65393 + 0.711118i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.40673 + 2.24078i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(2.65393 + 0.711118i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.40673 + 2.24078i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.37378 + 2.37945i) q^{10} +(2.14199 + 0.573943i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.354780 - 3.58805i) q^{13} +(-0.589766 + 2.57918i) q^{14} +(-2.65393 + 0.711118i) q^{15} -1.00000 q^{16} -1.67627 q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.0474662 - 0.177146i) q^{19} +(-0.711118 + 2.65393i) q^{20} +(-2.33866 - 1.23721i) q^{21} +(1.10877 + 1.92045i) q^{22} +0.546143i q^{23} +(0.258819 - 0.965926i) q^{24} +(2.20753 + 1.27452i) q^{25} +(2.28627 - 2.78800i) q^{26} +1.00000i q^{27} +(-2.24078 + 1.40673i) q^{28} +(-2.18139 + 3.77828i) q^{29} +(-2.37945 - 1.37378i) q^{30} +(2.02462 + 7.55600i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.14199 + 0.573943i) q^{33} +(-1.18530 - 1.18530i) q^{34} +(2.13990 + 6.94723i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.909963 - 0.909963i) q^{37} +(0.0916976 - 0.158825i) q^{38} +(2.10128 + 2.92996i) q^{39} +(-2.37945 + 1.37378i) q^{40} +(-1.32782 - 4.95550i) q^{41} +(-0.778839 - 2.52852i) q^{42} +(-2.86766 + 1.65565i) q^{43} +(-0.573943 + 2.14199i) q^{44} +(1.94281 - 1.94281i) q^{45} +(-0.386181 + 0.386181i) q^{46} +(2.61197 - 9.74801i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.04223 + 6.30435i) q^{49} +(0.659739 + 2.46218i) q^{50} +(1.45169 - 0.838134i) q^{51} +(3.58805 - 0.354780i) q^{52} +(1.78093 - 3.08467i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(5.27654 + 3.04641i) q^{55} +(-2.57918 - 0.589766i) q^{56} +(0.129680 + 0.129680i) q^{57} +(-4.21412 + 1.12917i) q^{58} +(-1.05173 - 1.05173i) q^{59} +(-0.711118 - 2.65393i) q^{60} +(-11.8307 - 6.83046i) q^{61} +(-3.91127 + 6.77452i) q^{62} +(2.64394 - 0.0978714i) q^{63} -1.00000i q^{64} +(1.60997 - 9.77473i) q^{65} +(-1.92045 - 1.10877i) q^{66} +(-1.82429 + 6.80833i) q^{67} -1.67627i q^{68} +(-0.273071 - 0.472973i) q^{69} +(-3.39930 + 6.42557i) q^{70} +(1.04867 - 3.91368i) q^{71} +(0.258819 + 0.965926i) q^{72} +(8.57385 - 2.29736i) q^{73} +1.28688 q^{74} -2.54903 q^{75} +(0.177146 - 0.0474662i) q^{76} +(1.72711 + 5.60711i) q^{77} +(-0.585966 + 3.55762i) q^{78} +(4.42139 + 7.65808i) q^{79} +(-2.65393 - 0.711118i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.56516 - 4.44298i) q^{82} +(11.3594 - 11.3594i) q^{83} +(1.23721 - 2.33866i) q^{84} +(-4.44870 - 1.19203i) q^{85} +(-3.19846 - 0.857026i) q^{86} -4.36278i q^{87} +(-1.92045 + 1.10877i) q^{88} +(-11.3766 - 11.3766i) q^{89} +2.74755 q^{90} +(7.54097 - 5.84241i) q^{91} -0.546143 q^{92} +(-5.53137 - 5.53137i) q^{93} +(8.73983 - 5.04594i) q^{94} -0.503888i q^{95} +(0.965926 + 0.258819i) q^{96} +(15.6069 + 4.18186i) q^{97} +(-6.60903 + 2.30667i) q^{98} +(1.56804 - 1.56804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$			1.00000i			0.500000i
$5$	2.65393	+	0.711118i	1.18687	+	0.318022i	0.797650	−	0.603121i	$-0.206077\pi$
$5$	2.65393	+	0.711118i	1.18687	+	0.318022i	0.389224	+	0.921143i	$0.372743\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	1.40673	+	2.24078i	0.531694	+	0.846937i
$7$	1.40673	+	2.24078i	0.531694	+	0.846937i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.37378	+	2.37945i	0.434426	+	0.752448i
$11$	2.14199	+	0.573943i	0.645833	+	0.173050i	0.566844	−	0.823825i	$-0.308164\pi$
$11$	2.14199	+	0.573943i	0.645833	+	0.173050i	0.0789889	+	0.996875i	$0.474831\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−0.354780	−	3.58805i	−0.0983982	−	0.995147i
$13$	−0.354780	−	3.58805i	−0.0983982	−	0.995147i
$14$	−0.589766	+	2.57918i	−0.157621	+	0.689315i
$15$	−2.65393	+	0.711118i	−0.685242	+	0.183610i
$16$	−1.00000			−0.250000
$17$	−1.67627			−0.406555			−0.203277	−	0.979121i	$-0.565159\pi$
$17$	−1.67627			−0.406555			−0.203277	+	0.979121i	$0.565159\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−0.0474662	−	0.177146i	−0.0108895	−	0.0406401i	0.960267	−	0.279082i	$-0.0900301\pi$
$19$	−0.0474662	−	0.177146i	−0.0108895	−	0.0406401i	−0.971157	+	0.238442i	$0.923363\pi$
$20$	−0.711118	+	2.65393i	−0.159011	+	0.593437i
$21$	−2.33866	−	1.23721i	−0.510336	−	0.269982i
$22$	1.10877	+	1.92045i	0.236391	+	0.409442i
$23$			0.546143i			0.113879i	0.998378	+	0.0569393i	$0.0181342\pi$
$23$			0.546143i			0.113879i	−0.998378	+	0.0569393i	$0.981866\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$	2.20753	+	1.27452i	0.441506	+	0.254903i
$26$	2.28627	−	2.78800i	0.448374	−	0.546773i
$27$			1.00000i			0.192450i
$28$	−2.24078	+	1.40673i	−0.423468	+	0.265847i
$29$	−2.18139	+	3.77828i	−0.405074	+	0.701609i	−0.994330	−	0.106337i	$-0.966088\pi$
$29$	−2.18139	+	3.77828i	−0.405074	+	0.701609i	0.589256	+	0.807946i	$0.299421\pi$
$30$	−2.37945	−	1.37378i	−0.434426	−	0.250816i
$31$	2.02462	+	7.55600i	0.363633	+	1.35710i	0.869264	+	0.494347i	$0.164593\pi$
$31$	2.02462	+	7.55600i	0.363633	+	1.35710i	−0.505631	+	0.862750i	$0.668740\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.14199	+	0.573943i	−0.372872	+	0.0999107i
$34$	−1.18530	−	1.18530i	−0.203277	−	0.203277i
$35$	2.13990	+	6.94723i	0.361709	+	1.17430i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	0.909963	−	0.909963i	0.149597	−	0.149597i	−0.628341	−	0.777938i	$-0.716266\pi$
$37$	0.909963	−	0.909963i	0.149597	−	0.149597i	0.777938	+	0.628341i	$0.216266\pi$
$38$	0.0916976	−	0.158825i	0.0148753	−	0.0257648i
$39$	2.10128	+	2.92996i	0.336473	+	0.469168i
$40$	−2.37945	+	1.37378i	−0.376224	+	0.217213i
$41$	−1.32782	−	4.95550i	−0.207371	−	0.773919i	−0.988714	−	0.149817i	$-0.952132\pi$
$41$	−1.32782	−	4.95550i	−0.207371	−	0.773919i	0.781343	−	0.624102i	$-0.214535\pi$
$42$	−0.778839	−	2.52852i	−0.120177	−	0.390159i
$43$	−2.86766	+	1.65565i	−0.437315	+	0.252484i	−0.702458	−	0.711725i	$-0.747914\pi$
$43$	−2.86766	+	1.65565i	−0.437315	+	0.252484i	0.265143	+	0.964209i	$0.414581\pi$
$44$	−0.573943	+	2.14199i	−0.0865252	+	0.322917i
$45$	1.94281	−	1.94281i	0.289617	−	0.289617i
$46$	−0.386181	+	0.386181i	−0.0569393	+	0.0569393i
$47$	2.61197	−	9.74801i	0.380995	−	1.42189i	−0.463389	−	0.886155i	$-0.653367\pi$
$47$	2.61197	−	9.74801i	0.380995	−	1.42189i	0.844384	−	0.535738i	$-0.179967\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−3.04223	+	6.30435i	−0.434604	+	0.900622i
$50$	0.659739	+	2.46218i	0.0933011	+	0.348205i
$51$	1.45169	−	0.838134i	0.203277	−	0.117362i
$52$	3.58805	−	0.354780i	0.497574	−	0.0491991i
$53$	1.78093	−	3.08467i	0.244630	−	0.423712i	−0.717397	−	0.696664i	$-0.754667\pi$
$53$	1.78093	−	3.08467i	0.244630	−	0.423712i	0.962028	+	0.272952i	$0.0880002\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	5.27654	+	3.04641i	0.711488	+	0.410778i
$56$	−2.57918	−	0.589766i	−0.344658	−	0.0788107i
$57$	0.129680	+	0.129680i	0.0171765	+	0.0171765i
$58$	−4.21412	+	1.12917i	−0.553342	+	0.148267i
$59$	−1.05173	−	1.05173i	−0.136923	−	0.136923i	0.635323	−	0.772246i	$-0.280867\pi$
$59$	−1.05173	−	1.05173i	−0.136923	−	0.136923i	−0.772246	+	0.635323i	$0.780867\pi$
$60$	−0.711118	−	2.65393i	−0.0918050	−	0.342621i
$61$	−11.8307	−	6.83046i	−1.51477	−	0.874551i	−0.999850	−	0.0173106i	$-0.994490\pi$
$61$	−11.8307	−	6.83046i	−1.51477	−	0.874551i	−0.514917	−	0.857240i	$-0.672177\pi$
$62$	−3.91127	+	6.77452i	−0.496732	+	0.860365i
$63$	2.64394	−	0.0978714i	0.333105	−	0.0123306i
$64$		−	1.00000i		−	0.125000i
$65$	1.60997	−	9.77473i	0.199692	−	1.21241i
$66$	−1.92045	−	1.10877i	−0.236391	−	0.136481i
$67$	−1.82429	+	6.80833i	−0.222872	+	0.831770i	0.760374	+	0.649486i	$0.225016\pi$
$67$	−1.82429	+	6.80833i	−0.222872	+	0.831770i	−0.983246	+	0.182284i	$0.941651\pi$
$68$		−	1.67627i		−	0.203277i
$69$	−0.273071	−	0.472973i	−0.0328739	−	0.0569393i
$70$	−3.39930	+	6.42557i	−0.406294	+	0.768003i
$71$	1.04867	−	3.91368i	0.124454	−	0.464469i	−0.875366	−	0.483462i	$-0.839379\pi$
$71$	1.04867	−	3.91368i	0.124454	−	0.464469i	0.999820	+	0.0189927i	$0.00604594\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	8.57385	−	2.29736i	1.00349	−	0.268885i	0.280585	−	0.959829i	$-0.409471\pi$
$73$	8.57385	−	2.29736i	1.00349	−	0.268885i	0.722908	+	0.690944i	$0.242805\pi$
$74$	1.28688			0.149597
$75$	−2.54903			−0.294337
$76$	0.177146	−	0.0474662i	0.0203201	−	0.00544475i
$77$	1.72711	+	5.60711i	0.196823	+	0.638990i
$78$	−0.585966	+	3.55762i	−0.0663475	+	0.402821i
$79$	4.42139	+	7.65808i	0.497445	+	0.861601i	0.999996	−	0.00294723i	$-0.000938134\pi$
$79$	4.42139	+	7.65808i	0.497445	+	0.861601i	−0.502550	+	0.864548i	$0.667605\pi$
$80$	−2.65393	−	0.711118i	−0.296718	−	0.0795055i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.56516	−	4.44298i	0.283274	−	0.490645i
$83$	11.3594	−	11.3594i	1.24686	−	1.24686i	0.289759	−	0.957100i	$-0.406425\pi$
$83$	11.3594	−	11.3594i	1.24686	−	1.24686i	0.957100	−	0.289759i	$-0.0935751\pi$
$84$	1.23721	−	2.33866i	0.134991	−	0.255168i
$85$	−4.44870	−	1.19203i	−0.482529	−	0.129293i
$86$	−3.19846	−	0.857026i	−0.344899	−	0.0924154i
$87$		−	4.36278i		−	0.467739i
$88$	−1.92045	+	1.10877i	−0.204721	+	0.118196i
$89$	−11.3766	−	11.3766i	−1.20592	−	1.20592i	−0.972338	−	0.233579i	$-0.924956\pi$
$89$	−11.3766	−	11.3766i	−1.20592	−	1.20592i	−0.233579	−	0.972338i	$-0.575044\pi$
$90$	2.74755			0.289617
$91$	7.54097	−	5.84241i	0.790509	−	0.612451i
$92$	−0.546143			−0.0569393
$93$	−5.53137	−	5.53137i	−0.573577	−	0.573577i
$94$	8.73983	−	5.04594i	0.901444	−	0.520449i
$95$		−	0.503888i		−	0.0516978i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	15.6069	+	4.18186i	1.58464	+	0.424603i	0.940358	−	0.340185i	$-0.110490\pi$
$97$	15.6069	+	4.18186i	1.58464	+	0.424603i	0.644282	+	0.764788i	$0.277156\pi$
$98$	−6.60903	+	2.30667i	−0.667613	+	0.233009i
$99$	1.56804	−	1.56804i	0.157594	−	0.157594i
$100$	−1.27452	+	2.20753i	−0.127452	+	0.220753i
$101$	−7.93535	−	13.7444i	−0.789597	−	1.36762i	−0.926214	−	0.376997i	$-0.876957\pi$
$101$	−7.93535	−	13.7444i	−0.789597	−	1.36762i	0.136618	−	0.990624i	$-0.456377\pi$
$102$	1.61915	+	0.433850i	0.160320	+	0.0429576i
$103$	−4.73336	−	8.19841i	−0.466391	−	0.807814i	0.532872	−	0.846196i	$-0.321113\pi$
$103$	−4.73336	−	8.19841i	−0.466391	−	0.807814i	−0.999263	+	0.0383824i	$0.987779\pi$
$104$	2.78800	+	2.28627i	0.273386	+	0.224187i
$105$	−5.32682	−	4.94653i	−0.519845	−	0.482732i
$106$	3.44050	−	0.921879i	0.334171	−	0.0895408i
$107$	3.20890			0.310216			0.155108	−	0.987897i	$-0.450427\pi$
$107$	3.20890			0.310216			0.155108	+	0.987897i	$0.450427\pi$
$108$	−1.00000			−0.0962250
$109$	9.09049	−	2.43579i	0.870711	−	0.233306i	0.204316	−	0.978905i	$-0.434503\pi$
$109$	9.09049	−	2.43579i	0.870711	−	0.233306i	0.666395	+	0.745599i	$0.267836\pi$
$110$	1.57694	+	5.88521i	0.150355	+	0.561133i
$111$	−0.333069	+	1.24303i	−0.0316135	+	0.117983i
$112$	−1.40673	−	2.24078i	−0.132923	−	0.211734i
$113$	1.81014	+	3.13525i	0.170283	+	0.294940i	0.938519	−	0.345228i	$-0.112198\pi$
$113$	1.81014	+	3.13525i	0.170283	+	0.294940i	−0.768235	+	0.640167i	$0.778865\pi$
$114$			0.183395i			0.0171765i
$115$	−0.388372	+	1.44942i	−0.0362159	+	0.135160i
$116$	−3.77828	−	2.18139i	−0.350805	−	0.202537i
$117$	−3.28474	−	1.48678i	−0.303674	−	0.137453i
$118$		−	1.48737i		−	0.136923i
$119$	−2.35806	−	3.75616i	−0.216163	−	0.344326i
$120$	1.37378	−	2.37945i	0.125408	−	0.217213i
$121$	−5.26759	−	3.04124i	−0.478872	−	0.276477i
$122$	−3.53571	−	13.1954i	−0.320108	−	1.19466i
$123$	3.62768	+	3.62768i	0.327097	+	0.327097i
$124$	−7.55600	+	2.02462i	−0.678548	+	0.181817i
$125$	−4.76177	−	4.76177i	−0.425905	−	0.425905i
$126$	1.93875	+	1.80034i	0.172718	+	0.160387i
$127$	11.5855	+	6.68890i	1.02805	+	0.593544i	0.916425	−	0.400207i	$-0.131062\pi$
$127$	11.5855	+	6.68890i	1.02805	+	0.593544i	0.111623	+	0.993751i	$0.464395\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.65565	−	2.86766i	0.145772	−	0.252484i
$130$	8.05020	−	5.77336i	0.706049	−	0.506357i
$131$	16.7924	−	9.69509i	1.46716	−	0.847064i	0.467833	−	0.883817i	$-0.345035\pi$
$131$	16.7924	−	9.69509i	1.46716	−	0.847064i	0.999324	+	0.0367535i	$0.0117016\pi$
$132$	−0.573943	−	2.14199i	−0.0499554	−	0.186436i
$133$	0.330174	−	0.355558i	0.0286297	−	0.0308308i
$134$	−6.10419	+	3.52425i	−0.527321	+	0.304449i
$135$	−0.711118	+	2.65393i	−0.0612033	+	0.228414i
$136$	1.18530	−	1.18530i	0.101639	−	0.101639i
$137$	−9.80752	+	9.80752i	−0.837913	+	0.837913i	−0.988584	−	0.150671i	$-0.951857\pi$
$137$	−9.80752	+	9.80752i	−0.837913	+	0.837913i	0.150671	+	0.988584i	$0.451857\pi$
$138$	0.141352	−	0.527533i	0.0120327	−	0.0449066i
$139$	−13.7082	+	7.91444i	−1.16272	+	0.671294i	−0.951953	−	0.306243i	$-0.900928\pi$
$139$	−13.7082	+	7.91444i	−1.16272	+	0.671294i	−0.210762	+	0.977537i	$0.567595\pi$
$140$	−6.94723	+	2.13990i	−0.587149	+	0.180854i
$141$	2.61197	+	9.74801i	0.219968	+	0.820930i
$142$	3.50891	−	2.02587i	0.294461	−	0.170007i
$143$	1.29941	−	7.88918i	0.108662	−	0.659727i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−8.47606	+	8.47606i	−0.703899	+	0.703899i
$146$	7.68711	+	4.43815i	0.636189	+	0.367304i
$147$	−0.517532	−	6.98084i	−0.0426853	−	0.575770i
$148$	0.909963	+	0.909963i	0.0747985	+	0.0747985i
$149$	13.8974	−	3.72381i	1.13852	−	0.305066i	0.360165	−	0.932888i	$-0.382720\pi$
$149$	13.8974	−	3.72381i	1.13852	−	0.305066i	0.778357	+	0.627822i	$0.216054\pi$
$150$	−1.80244	−	1.80244i	−0.147169	−	0.147169i
$151$	−0.602340	−	2.24796i	−0.0490177	−	0.182937i	0.937076	−	0.349124i	$-0.113521\pi$
$151$	−0.602340	−	2.24796i	−0.0490177	−	0.182937i	−0.986094	+	0.166188i	$0.946854\pi$
$152$	0.158825	+	0.0916976i	0.0128824	+	0.00743766i
$153$	−0.838134	+	1.45169i	−0.0677591	+	0.117362i
$154$	−2.74357	+	5.18608i	−0.221083	+	0.417906i
$155$			21.4928i			1.72635i
$156$	−2.92996	+	2.10128i	−0.234584	+	0.168237i
$157$	4.62239	+	2.66874i	0.368907	+	0.212988i	0.672981	−	0.739660i	$-0.265014\pi$
$157$	4.62239	+	2.66874i	0.368907	+	0.212988i	−0.304074	+	0.952648i	$0.598347\pi$
$158$	−2.28868	+	8.54147i	−0.182078	+	0.679523i
$159$			3.56187i			0.282474i
$160$	−1.37378	−	2.37945i	−0.108606	−	0.188112i
$161$	−1.22379	+	0.768275i	−0.0964480	+	0.0605486i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	1.44909	+	5.40806i	0.113501	+	0.423592i	0.999170	−	0.0407246i	$-0.0129666\pi$
$163$	1.44909	+	5.40806i	0.113501	+	0.423592i	−0.885669	+	0.464317i	$0.846300\pi$
$164$	4.95550	−	1.32782i	0.386960	−	0.103686i
$165$	−6.09282			−0.474326
$166$	16.0646			1.24686
$167$	−6.88324	+	1.84436i	−0.532641	+	0.142721i	−0.515108	−	0.857126i	$-0.672248\pi$
$167$	−6.88324	+	1.84436i	−0.532641	+	0.142721i	−0.0175335	+	0.999846i	$0.505581\pi$
$168$	2.52852	−	0.778839i	0.195080	−	0.0600887i
$169$	−12.7483	+	2.54594i	−0.980636	+	0.195841i
$170$	−2.30282	−	3.98859i	−0.176618	−	0.305911i
$171$	−0.177146	−	0.0474662i	−0.0135467	−	0.00362983i
$172$	−1.65565	−	2.86766i	−0.126242	−	0.218657i
$173$	1.42127	−	2.46170i	0.108057	−	0.187160i	−0.806926	−	0.590652i	$-0.798871\pi$
$173$	1.42127	−	2.46170i	0.108057	−	0.187160i	0.914983	+	0.403492i	$0.132204\pi$
$174$	3.08495	−	3.08495i	0.233870	−	0.233870i
$175$	0.249478	+	6.73949i	0.0188587	+	0.509458i
$176$	−2.14199	−	0.573943i	−0.161458	−	0.0432626i
$177$	1.43669	+	0.384959i	0.107988	+	0.0289353i
$178$		−	16.0889i		−	1.20592i
$179$	−22.1165	+	12.7690i	−1.65307	+	0.954399i	−0.677266	+	0.735738i	$0.736835\pi$
$179$	−22.1165	+	12.7690i	−1.65307	+	0.954399i	−0.975801	+	0.218661i	$0.929831\pi$
$180$	1.94281	+	1.94281i	0.144809	+	0.144809i
$181$	16.1216			1.19831			0.599155	−	0.800633i	$-0.295503\pi$
$181$	16.1216			1.19831			0.599155	+	0.800633i	$0.295503\pi$
$182$	9.46348	+	1.20107i	0.701480	+	0.0890292i
$183$	13.6609			1.00984
$184$	−0.386181	−	0.386181i	−0.0284697	−	0.0284697i
$185$	3.06207	−	1.76789i	0.225128	−	0.129978i
$186$		−	7.82254i		−	0.573577i
$187$	−3.59054	−	0.962083i	−0.262567	−	0.0703545i
$188$	9.74801	+	2.61197i	0.710947	+	0.190498i
$189$	−2.24078	+	1.40673i	−0.162993	+	0.102325i
$190$	0.356302	−	0.356302i	0.0258489	−	0.0258489i
$191$	−0.816556	+	1.41432i	−0.0590839	+	0.102336i	−0.894054	−	0.447958i	$-0.852151\pi$
$191$	−0.816556	+	1.41432i	−0.0590839	+	0.102336i	0.834971	+	0.550295i	$0.185485\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−9.13997	−	2.44905i	−0.657910	−	0.176286i	−0.0856072	−	0.996329i	$-0.527283\pi$
$193$	−9.13997	−	2.44905i	−0.657910	−	0.176286i	−0.572303	+	0.820043i	$0.693950\pi$
$194$	8.07872	+	13.9928i	0.580019	+	1.00462i
$195$	3.49309	+	9.27015i	0.250146	+	0.663849i
$196$	−6.30435	−	3.04223i	−0.450311	−	0.217302i
$197$	10.9689	−	2.93910i	0.781500	−	0.209402i	0.154054	−	0.988062i	$-0.450767\pi$
$197$	10.9689	−	2.93910i	0.781500	−	0.209402i	0.627446	+	0.778660i	$0.284100\pi$
$198$	2.21755			0.157594
$199$	−18.1047			−1.28340			−0.641702	−	0.766954i	$-0.721772\pi$
$199$	−18.1047			−1.28340			−0.641702	+	0.766954i	$0.721772\pi$
$200$	−2.46218	+	0.659739i	−0.174102	+	0.0466506i
$201$	−1.82429	−	6.80833i	−0.128675	−	0.480223i
$202$	4.10764	−	15.3299i	0.289012	−	1.07861i
$203$	−11.5349	+	0.426992i	−0.809594	+	0.0299689i
$204$	0.838134	+	1.45169i	0.0586811	+	0.101639i
$205$		−	14.0958i		−	0.984493i
$206$	2.45017	−	9.14414i	0.170711	−	0.637102i
$207$	0.472973	+	0.273071i	0.0328739	+	0.0189798i
$208$	0.354780	+	3.58805i	0.0245996	+	0.248787i
$209$		−	0.406688i		−	0.0281312i
$210$	−0.268907	−	7.26436i	−0.0185563	−	0.501288i
$211$	0.00906917	−	0.0157083i	0.000624347	−	0.00108140i	−0.865713	−	0.500541i	$-0.833135\pi$
$211$	0.00906917	−	0.0157083i	0.000624347	−	0.00108140i	0.866337	+	0.499459i	$0.166468\pi$
$212$	3.08467	+	1.78093i	0.211856	+	0.122315i
$213$	1.04867	+	3.91368i	0.0718536	+	0.268161i
$214$	2.26904	+	2.26904i	0.155108	+	0.155108i
$215$	−8.78794	+	2.35472i	−0.599332	+	0.160591i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−14.0833	+	15.1660i	−0.956034	+	1.02953i
$218$	8.15031	+	4.70559i	0.552009	+	0.318702i
$219$	−6.27650	+	6.27650i	−0.424126	+	0.424126i
$220$	−3.04641	+	5.27654i	−0.205389	+	0.355744i
$221$	0.594706	+	6.01454i	0.0400043	+	0.404582i
$222$	−1.11447	+	0.643441i	−0.0747985	+	0.0431849i
$223$	3.72027	+	13.8843i	0.249128	+	0.929758i	0.971264	+	0.238007i	$0.0764940\pi$
$223$	3.72027	+	13.8843i	0.249128	+	0.929758i	−0.722136	+	0.691752i	$0.756839\pi$
$224$	0.589766	−	2.57918i	0.0394054	−	0.172329i
$225$	2.20753	−	1.27452i	0.147169	−	0.0849678i
$226$	−0.936996	+	3.49692i	−0.0623281	+	0.232612i
$227$	−2.92840	+	2.92840i	−0.194365	+	0.194365i	−0.797579	−	0.603214i	$-0.793886\pi$
$227$	−2.92840	+	2.92840i	−0.194365	+	0.194365i	0.603214	+	0.797579i	$0.293886\pi$
$228$	−0.129680	+	0.129680i	−0.00858827	+	0.00858827i
$229$	−2.25923	+	8.43158i	−0.149294	+	0.557174i	0.850232	+	0.526408i	$0.176461\pi$
$229$	−2.25923	+	8.43158i	−0.149294	+	0.557174i	−0.999527	+	0.0307665i	$0.990205\pi$
$230$	−1.29952	+	0.750277i	−0.0856877	+	0.0494718i
$231$	−4.29928	−	3.99234i	−0.282872	−	0.262677i
$232$	−1.12917	−	4.21412i	−0.0741337	−	0.276671i
$233$	5.73199	−	3.30937i	0.375515	−	0.216804i	−0.300350	−	0.953829i	$-0.597103\pi$
$233$	5.73199	−	3.30937i	0.375515	−	0.216804i	0.675865	+	0.737025i	$0.263770\pi$
$234$	−1.27135	−	3.37397i	−0.0831106	−	0.220563i
$235$	13.8640	−	24.0131i	0.904386	−	1.56644i
$236$	1.05173	−	1.05173i	0.0684617	−	0.0684617i
$237$	−7.65808	−	4.42139i	−0.497445	−	0.287200i
$238$	0.988606	−	4.32340i	0.0640818	−	0.280244i
$239$	−4.05600	−	4.05600i	−0.262361	−	0.262361i	0.563652	−	0.826013i	$-0.309396\pi$
$239$	−4.05600	−	4.05600i	−0.262361	−	0.262361i	−0.826013	+	0.563652i	$0.809396\pi$
$240$	2.65393	−	0.711118i	0.171310	−	0.0459025i
$241$	6.36407	+	6.36407i	0.409946	+	0.409946i	0.881720	−	0.471774i	$-0.156386\pi$
$241$	6.36407	+	6.36407i	0.409946	+	0.409946i	−0.471774	+	0.881720i	$0.656386\pi$
$242$	−1.57426	−	5.87523i	−0.101197	−	0.377674i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	6.83046	−	11.8307i	0.437275	−	0.757383i
$245$	−12.5570	+	14.5679i	−0.802237	+	0.930711i
$246$			5.13031i			0.327097i
$247$	−0.618770	+	0.233159i	−0.0393714	+	0.0148356i
$248$	−6.77452	−	3.91127i	−0.430183	−	0.248366i
$249$	−4.15784	+	15.5173i	−0.263492	+	0.983366i
$250$		−	6.73415i		−	0.425905i
$251$	−7.77241	−	13.4622i	−0.490590	−	0.849727i	0.509351	−	0.860559i	$-0.329885\pi$
$251$	−7.77241	−	13.4622i	−0.490590	−	0.849727i	−0.999941	+	0.0108317i	$0.996552\pi$
$252$	0.0978714	+	2.64394i	0.00616532	+	0.166553i
$253$	−0.313455	+	1.16983i	−0.0197067	+	0.0735466i
$254$	3.46243	+	12.9220i	0.217252	+	0.810796i
$255$	4.44870	−	1.19203i	0.278588	−	0.0746475i
$256$	1.00000			0.0625000
$257$	7.17059			0.447289			0.223645	−	0.974671i	$-0.428204\pi$
$257$	7.17059			0.447289			0.223645	+	0.974671i	$0.428204\pi$
$258$	3.19846	−	0.857026i	0.199128	−	0.0533561i
$259$	3.31910	+	0.758958i	0.206239	+	0.0471594i
$260$	9.77473	+	1.60997i	0.606203	+	0.0998461i
$261$	2.18139	+	3.77828i	0.135025	+	0.233870i
$262$	18.7295	+	5.01855i	1.15711	+	0.310047i
$263$	−3.61004	−	6.25278i	−0.222605	−	0.385563i	0.732993	−	0.680236i	$-0.238123\pi$
$263$	−3.61004	−	6.25278i	−0.222605	−	0.385563i	−0.955598	+	0.294673i	$0.904789\pi$
$264$	1.10877	−	1.92045i	0.0682403	−	0.118196i
$265$	6.92004	−	6.92004i	0.425094	−	0.425094i
$266$	0.484886	−	0.0179492i	0.0297303	−	0.00110053i
$267$	15.5407	+	4.16412i	0.951077	+	0.254840i
$268$	−6.80833	−	1.82429i	−0.415885	−	0.111436i
$269$			2.01410i			0.122802i	0.998113	+	0.0614010i	$0.0195568\pi$
$269$			2.01410i			0.122802i	−0.998113	+	0.0614010i	$0.980443\pi$
$270$	−2.37945	+	1.37378i	−0.144809	+	0.0836053i
$271$	−16.1973	−	16.1973i	−0.983917	−	0.983917i	0.0159559	−	0.999873i	$-0.494921\pi$
$271$	−16.1973	−	16.1973i	−0.983917	−	0.983917i	−0.999873	+	0.0159559i	$0.994921\pi$
$272$	1.67627			0.101639
$273$	−3.60947	+	8.83016i	−0.218455	+	0.534426i
$274$	−13.8699			−0.837913
$275$	3.99699	+	3.99699i	0.241028	+	0.241028i
$276$	0.472973	−	0.273071i	0.0284697	−	0.0164370i
$277$		−	25.5542i		−	1.53540i	−0.640808	−	0.767702i	$-0.721400\pi$
$277$		−	25.5542i		−	1.53540i	0.640808	−	0.767702i	$-0.278600\pi$
$278$	−15.2895	−	4.09682i	−0.917005	−	0.245711i
$279$	7.55600	+	2.02462i	0.452366	+	0.121211i
$280$	−6.42557	−	3.39930i	−0.384001	−	0.203147i
$281$	−10.1284	+	10.1284i	−0.604210	+	0.604210i	−0.941427	−	0.337217i	$-0.890514\pi$
$281$	−10.1284	+	10.1284i	−0.604210	+	0.604210i	0.337217	+	0.941427i	$0.390514\pi$
$282$	−5.04594	+	8.73983i	−0.300481	+	0.520449i
$283$	15.2040	+	26.3342i	0.903786	+	1.56540i	0.822539	+	0.568709i	$0.192557\pi$
$283$	15.2040	+	26.3342i	0.903786	+	1.56540i	0.0812472	+	0.996694i	$0.474110\pi$
$284$	3.91368	+	1.04867i	0.232234	+	0.0622270i
$285$	0.251944	+	0.436380i	0.0149239	+	0.0258489i
$286$	6.49731	−	4.65968i	0.384194	−	0.275532i
$287$	9.23632	−	9.94641i	0.545203	−	0.587118i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	−14.1901			−0.834713
$290$	−11.9870			−0.703899
$291$	−15.6069	+	4.18186i	−0.914892	+	0.245145i
$292$	2.29736	+	8.57385i	0.134443	+	0.501747i
$293$	−1.88727	+	7.04340i	−0.110256	+	0.411480i	−0.998888	−	0.0471399i	$-0.984989\pi$
$293$	−1.88727	+	7.04340i	−0.110256	+	0.411480i	0.888633	+	0.458620i	$0.151656\pi$
$294$	4.57025	−	5.30215i	0.266542	−	0.309228i
$295$	−2.04331	−	3.53912i	−0.118966	−	0.206055i
$296$			1.28688i			0.0747985i
$297$	−0.573943	+	2.14199i	−0.0333036	+	0.124291i
$298$	12.4601	+	7.19384i	0.721794	+	0.416728i
$299$	1.95959	−	0.193760i	0.113326	−	0.0112055i
$300$		−	2.54903i		−	0.147169i
$301$	−7.74397	−	4.09677i	−0.446355	−	0.236134i
$302$	1.16363	−	2.01547i	0.0669594	−	0.115977i
$303$	13.7444	+	7.93535i	0.789597	+	0.455874i
$304$	0.0474662	+	0.177146i	0.00272237	+	0.0101600i
$305$	−26.5406	−	26.5406i	−1.51971	−	1.51971i
$306$	−1.61915	+	0.433850i	−0.0925607	+	0.0248016i
$307$	1.04129	+	1.04129i	0.0594295	+	0.0594295i	0.736197	−	0.676767i	$-0.236620\pi$
$307$	1.04129	+	1.04129i	0.0594295	+	0.0594295i	−0.676767	+	0.736197i	$0.736620\pi$
$308$	−5.60711	+	1.72711i	−0.319495	+	0.0984113i
$309$	8.19841	+	4.73336i	0.466391	+	0.269271i
$310$	−15.1977	+	15.1977i	−0.863173	+	0.863173i
$311$	−10.3053	+	17.8493i	−0.584360	+	1.01214i	0.410594	+	0.911818i	$0.365321\pi$
$311$	−10.3053	+	17.8493i	−0.584360	+	1.01214i	−0.994955	+	0.100324i	$0.968012\pi$
$312$	−3.55762	−	0.585966i	−0.201410	−	0.0331738i
$313$	−8.86536	+	5.11842i	−0.501100	+	0.289310i	−0.729168	−	0.684335i	$-0.760093\pi$
$313$	−8.86536	+	5.11842i	−0.501100	+	0.289310i	0.228068	+	0.973645i	$0.426759\pi$
$314$	1.38144	+	5.15561i	0.0779592	+	0.290948i
$315$	7.08643	+	1.62041i	0.399275	+	0.0912998i
$316$	−7.65808	+	4.42139i	−0.430800	+	0.248723i
$317$	0.0964049	−	0.359788i	0.00541464	−	0.0202077i	−0.963166	−	0.268909i	$-0.913337\pi$
$317$	0.0964049	−	0.359788i	0.00541464	−	0.0202077i	0.968580	+	0.248701i	$0.0800037\pi$
$318$	−2.51862	+	2.51862i	−0.141237	+	0.141237i
$319$	−6.84103	+	6.84103i	−0.383024	+	0.383024i
$320$	0.711118	−	2.65393i	0.0397527	−	0.148359i
$321$	−2.77899	+	1.60445i	−0.155108	+	0.0895517i
$322$	−1.40860	−	0.322096i	−0.0784983	−	0.0179497i
$323$	0.0795661	+	0.296945i	0.00442718	+	0.0165224i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	3.78985	−	8.37290i	0.210223	−	0.464445i
$326$	−2.79942	+	4.84873i	−0.155045	+	0.268547i
$327$	−6.65470	+	6.65470i	−0.368006	+	0.368006i
$328$	4.44298	+	2.56516i	0.245323	+	0.141637i
$329$	25.5175	−	7.85995i	1.40683	−	0.433333i
$330$	−4.30828	−	4.30828i	−0.237163	−	0.237163i
$331$	12.8651	−	3.44719i	0.707129	−	0.189475i	0.112707	−	0.993628i	$-0.464048\pi$
$331$	12.8651	−	3.44719i	0.707129	−	0.189475i	0.594422	+	0.804154i	$0.297381\pi$
$332$	11.3594	+	11.3594i	0.623429	+	0.623429i
$333$	−0.333069	−	1.24303i	−0.0182521	−	0.0681177i
$334$	−6.17134	−	3.56303i	−0.337681	−	0.194960i
$335$	−9.68306	+	16.7716i	−0.529042	+	0.916328i
$336$	2.33866	+	1.23721i	0.127584	+	0.0674954i
$337$			22.8350i			1.24390i	0.783057	+	0.621950i	$0.213659\pi$
$337$			22.8350i			1.24390i	−0.783057	+	0.621950i	$0.786341\pi$
$338$	−10.8146	−	7.21413i	−0.588239	−	0.392397i
$339$	−3.13525	−	1.81014i	−0.170283	−	0.0983132i
$340$	1.19203	−	4.44870i	0.0646467	−	0.241265i
$341$			17.3469i			0.939385i
$342$	−0.0916976	−	0.158825i	−0.00495844	−	0.00858827i
$343$	−18.4063	+	2.05155i	−0.993846	+	0.110773i
$344$	0.857026	−	3.19846i	0.0462077	−	0.172450i
$345$	−0.388372	−	1.44942i	−0.0209093	−	0.0780344i
$346$	2.74567	−	0.735701i	0.147608	−	0.0395515i
$347$	14.8824			0.798927			0.399463	−	0.916749i	$-0.369196\pi$
$347$	14.8824			0.798927			0.399463	+	0.916749i	$0.369196\pi$
$348$	4.36278			0.233870
$349$	−9.60502	+	2.57366i	−0.514145	+	0.137765i	−0.506557	−	0.862206i	$-0.669082\pi$
$349$	−9.60502	+	2.57366i	−0.514145	+	0.137765i	−0.00758807	+	0.999971i	$0.502415\pi$
$350$	−4.58913	+	4.94195i	−0.245300	+	0.264158i
$351$	3.58805	−	0.354780i	0.191516	−	0.0189367i
$352$	−1.10877	−	1.92045i	−0.0590978	−	0.102360i
$353$	20.9560	+	5.61514i	1.11538	+	0.298864i	0.769011	−	0.639236i	$-0.220749\pi$
$353$	20.9560	+	5.61514i	1.11538	+	0.298864i	0.346365	+	0.938100i	$0.387416\pi$
$354$	0.743684	+	1.28810i	0.0395264	+	0.0684617i
$355$	5.56619	−	9.64092i	0.295422	−	0.511687i
$356$	11.3766	−	11.3766i	0.602958	−	0.602958i
$357$	3.92021	+	2.07390i	0.207480	+	0.109762i
$358$	−24.6678	−	6.60971i	−1.30373	−	0.349334i
$359$	−25.3972	−	6.80517i	−1.34042	−	0.359163i	−0.483827	−	0.875164i	$-0.660754\pi$
$359$	−25.3972	−	6.80517i	−1.34042	−	0.359163i	−0.856588	+	0.516000i	$0.827420\pi$
$360$			2.74755i			0.144809i
$361$	16.4254	−	9.48318i	0.864492	−	0.499115i
$362$	11.3997	+	11.3997i	0.599155	+	0.599155i
$363$	6.08249			0.319248
$364$	5.84241	+	7.54097i	0.306225	+	0.395254i
$365$	24.3881			1.27653
$366$	9.65973	+	9.65973i	0.504922	+	0.504922i
$367$	−7.79817	+	4.50227i	−0.407061	+	0.235017i	−0.689526	−	0.724261i	$-0.742181\pi$
$367$	−7.79817	+	4.50227i	−0.407061	+	0.235017i	0.282465	+	0.959278i	$0.408848\pi$
$368$		−	0.546143i		−	0.0284697i
$369$	−4.95550	−	1.32782i	−0.257973	−	0.0691237i
$370$	3.41529	+	0.915125i	0.177553	+	0.0475751i
$371$	9.41736	−	0.348605i	0.488925	−	0.0180987i
$372$	5.53137	−	5.53137i	0.286788	−	0.286788i
$373$	13.3657	−	23.1501i	0.692049	−	1.19866i	−0.279116	−	0.960257i	$-0.590041\pi$
$373$	13.3657	−	23.1501i	0.692049	−	1.19866i	0.971165	−	0.238407i	$-0.0766253\pi$
$374$	−1.85860	−	3.21919i	−0.0961060	−	0.166461i
$375$	6.50469	+	1.74293i	0.335901	+	0.0900044i
$376$	5.04594	+	8.73983i	0.260225	+	0.450722i
$377$	14.3306	+	6.48649i	0.738063	+	0.334071i
$378$	−2.57918	−	0.589766i	−0.132659	−	0.0303343i
$379$	−10.5843	+	2.83605i	−0.543678	+	0.145678i	−0.520197	−	0.854046i	$-0.674142\pi$
$379$	−10.5843	+	2.83605i	−0.543678	+	0.145678i	−0.0234808	+	0.999724i	$0.507475\pi$
$380$	0.503888			0.0258489
$381$	−13.3778			−0.685365
$382$	−1.57746	+	0.422680i	−0.0807101	+	0.0216262i
$383$	6.03951	+	22.5398i	0.308604	+	1.15173i	0.929798	+	0.368070i	$0.119981\pi$
$383$	6.03951	+	22.5398i	0.308604	+	1.15173i	−0.621193	+	0.783657i	$0.713352\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	0.596313	+	16.1091i	0.0303909	+	0.820994i
$386$	−4.73120	−	8.19468i	−0.240812	−	0.417098i
$387$			3.31129i			0.168322i
$388$	−4.18186	+	15.6069i	−0.212302	+	0.792320i
$389$	24.3558	+	14.0618i	1.23489	+	0.712962i	0.968044	−	0.250779i	$-0.0806866\pi$
$389$	24.3558	+	14.0618i	1.23489	+	0.712962i	0.266842	+	0.963740i	$0.414020\pi$
$390$	−4.08500	+	9.02498i	−0.206852	+	0.456998i
$391$		−	0.915482i		−	0.0462979i
$392$	−2.30667	−	6.60903i	−0.116505	−	0.333806i
$393$	−9.69509	+	16.7924i	−0.489052	+	0.847064i
$394$	9.83442	+	5.67791i	0.495451	+	0.286049i
$395$	6.28827	+	23.4681i	0.316397	+	1.18081i
$396$	1.56804	+	1.56804i	0.0787971	+	0.0787971i
$397$	−21.1092	+	5.65620i	−1.05944	+	0.283877i	−0.746148	−	0.665780i	$-0.768099\pi$
$397$	−21.1092	+	5.65620i	−1.05944	+	0.283877i	−0.313294	+	0.949656i	$0.601432\pi$
$398$	−12.8019	−	12.8019i	−0.641702	−	0.641702i
$399$	−0.108160	+	0.473010i	−0.00541478	+	0.0236801i
$400$	−2.20753	−	1.27452i	−0.110376	−	0.0637259i
$401$	14.5359	−	14.5359i	0.725888	−	0.725888i	−0.243910	−	0.969798i	$-0.578430\pi$
$401$	14.5359	−	14.5359i	0.725888	−	0.725888i	0.969798	+	0.243910i	$0.0784301\pi$
$402$	3.52425	−	6.10419i	0.175774	−	0.304449i
$403$	26.3930	−	9.94517i	1.31473	−	0.495404i
$404$	13.7444	−	7.93535i	0.683811	−	0.394798i
$405$	−0.711118	−	2.65393i	−0.0353358	−	0.131875i
$406$	−8.45836	−	7.85450i	−0.419781	−	0.389812i
$407$	2.47139	−	1.42686i	0.122502	−	0.0707268i
$408$	−0.433850	+	1.61915i	−0.0214788	+	0.0801599i
$409$	−27.9592	+	27.9592i	−1.38249	+	1.38249i	−0.542319	+	0.840173i	$0.682453\pi$
$409$	−27.9592	+	27.9592i	−1.38249	+	1.38249i	−0.840173	+	0.542319i	$0.817547\pi$
$410$	9.96723	−	9.96723i	0.492246	−	0.492246i
$411$	3.58980	−	13.3973i	0.177072	−	0.660841i
$412$	8.19841	−	4.73336i	0.403907	−	0.233196i
$413$	0.877199	−	3.83619i	0.0431641	−	0.188767i
$414$	0.141352	+	0.527533i	0.00694708	+	0.0259269i
$415$	38.2250	−	22.0692i	1.87639	−	1.08334i
$416$	−2.28627	+	2.78800i	−0.112094	+	0.136693i
$417$	7.91444	−	13.7082i	0.387572	−	0.671294i
$418$	0.287572	−	0.287572i	0.0140656	−	0.0140656i
$419$	19.3975	+	11.1991i	0.947629	+	0.547114i	0.892343	−	0.451357i	$-0.149060\pi$
$419$	19.3975	+	11.1991i	0.947629	+	0.547114i	0.0552851	+	0.998471i	$0.482393\pi$
$420$	4.94653	−	5.32682i	0.241366	−	0.259922i
$421$	−5.11816	−	5.11816i	−0.249444	−	0.249444i	0.571299	−	0.820742i	$-0.306440\pi$
$421$	−5.11816	−	5.11816i	−0.249444	−	0.249444i	−0.820742	+	0.571299i	$0.806440\pi$
$422$	0.0175203	−	0.00469455i	0.000852874	−	0.000228527i
$423$	−7.13604	−	7.13604i	−0.346966	−	0.346966i
$424$	0.921879	+	3.44050i	0.0447704	+	0.167085i
$425$	−3.70041	−	2.13643i	−0.179496	−	0.103632i
$426$	−2.02587	+	3.50891i	−0.0981538	+	0.170007i
$427$	−1.33701	−	36.1187i	−0.0647026	−	1.74790i
$428$			3.20890i			0.155108i
$429$	2.81927	+	7.48194i	0.136116	+	0.361231i
$430$	−7.87905	−	4.54897i	−0.379962	−	0.219371i
$431$	−9.76457	+	36.4419i	−0.470343	+	1.75534i	0.168196	+	0.985754i	$0.446206\pi$
$431$	−9.76457	+	36.4419i	−0.470343	+	1.75534i	−0.638539	+	0.769589i	$0.720461\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−18.4530	−	31.9616i	−0.886795	−	1.53597i	−0.843642	−	0.536906i	$-0.819593\pi$
$433$	−18.4530	−	31.9616i	−0.886795	−	1.53597i	−0.0431533	−	0.999068i	$-0.513740\pi$
$434$	−20.6823	+	0.765603i	−0.992784	+	0.0367501i
$435$	3.10245	−	11.5785i	0.148751	−	0.555148i
$436$	2.43579	+	9.09049i	0.116653	+	0.435356i
$437$	0.0967471	−	0.0259233i	0.00462804	−	0.00124008i
$438$	−8.87631			−0.424126
$439$	10.1657			0.485185			0.242592	−	0.970128i	$-0.422002\pi$
$439$	10.1657			0.485185			0.242592	+	0.970128i	$0.422002\pi$
$440$	−5.88521	+	1.57694i	−0.280567	+	0.0751776i
$441$	3.93862	+	5.78682i	0.187553	+	0.275563i
$442$	−3.83240	+	4.67344i	−0.182289	+	0.222293i
$443$	−1.02220	−	1.77050i	−0.0485662	−	0.0841192i	0.840720	−	0.541470i	$-0.182132\pi$
$443$	−1.02220	−	1.77050i	−0.0485662	−	0.0841192i	−0.889287	+	0.457350i	$0.848799\pi$
$444$	−1.24303	−	0.333069i	−0.0589917	−	0.0158068i
$445$	−22.1026	−	38.2828i	−1.04776	−	1.81478i
$446$	−7.18702	+	12.4483i	−0.340315	+	0.589443i
$447$	−10.1736	+	10.1736i	−0.481196	+	0.481196i
$448$	2.24078	−	1.40673i	0.105867	−	0.0664617i
$449$	−19.3298	−	5.17939i	−0.912228	−	0.244431i	−0.227968	−	0.973669i	$-0.573208\pi$
$449$	−19.3298	−	5.17939i	−0.912228	−	0.244431i	−0.684260	+	0.729238i	$0.739875\pi$
$450$	2.46218	+	0.659739i	0.116068	+	0.0311004i
$451$		−	11.3767i		−	0.535708i
$452$	−3.13525	+	1.81014i	−0.147470	+	0.0851417i
$453$	1.64562	+	1.64562i	0.0773181	+	0.0773181i
$454$	−4.14138			−0.194365
$455$	24.1679	−	10.1428i	1.13301	−	0.475502i
$456$	−0.183395			−0.00858827
$457$	−23.3378	−	23.3378i	−1.09170	−	1.09170i	−0.995347	−	0.0963505i	$-0.969283\pi$
$457$	−23.3378	−	23.3378i	−1.09170	−	1.09170i	−0.0963505	−	0.995347i	$-0.530717\pi$
$458$	−7.55955	+	4.36451i	−0.353234	+	0.203940i
$459$		−	1.67627i		−	0.0782415i
$460$	−1.44942	−	0.388372i	−0.0675798	−	0.0181079i
$461$	13.7371	+	3.68085i	0.639801	+	0.171434i	0.564113	−	0.825697i	$-0.309218\pi$
$461$	13.7371	+	3.68085i	0.639801	+	0.171434i	0.0756877	+	0.997132i	$0.475885\pi$
$462$	−0.217034	−	5.86306i	−0.0100974	−	0.272774i
$463$	−15.3894	+	15.3894i	−0.715207	+	0.715207i	−0.967620	−	0.252412i	$-0.918776\pi$
$463$	−15.3894	+	15.3894i	−0.715207	+	0.715207i	0.252412	+	0.967620i	$0.418776\pi$
$464$	2.18139	−	3.77828i	0.101269	−	0.175402i
$465$	−10.7464	−	18.6133i	−0.498353	−	0.863173i
$466$	6.39321	+	1.71305i	0.296160	+	0.0793557i
$467$	−20.4707	−	35.4563i	−0.947272	−	1.64072i	−0.751136	−	0.660147i	$-0.770494\pi$
$467$	−20.4707	−	35.4563i	−0.947272	−	1.64072i	−0.196136	−	0.980577i	$-0.562840\pi$
$468$	1.48678	−	3.28474i	0.0687264	−	0.151837i
$469$	−17.8223	+	5.48965i	−0.822957	+	0.253488i
$470$	26.7831	−	7.17652i	1.23541	−	0.331028i
$471$	−5.33748			−0.245938
$472$	1.48737			0.0684617
$473$	−7.09274	+	1.90049i	−0.326125	+	0.0873848i
$474$	−2.28868	−	8.54147i	−0.105123	−	0.392323i
$475$	0.120993	−	0.451552i	0.00555154	−	0.0207186i
$476$	3.75616	−	2.35806i	0.172163	−	0.108081i
$477$	−1.78093	−	3.08467i	−0.0815433	−	0.141237i
$478$		−	5.73605i		−	0.262361i
$479$	3.00600	−	11.2186i	0.137348	−	0.512589i	−0.862629	−	0.505836i	$-0.831184\pi$
$479$	3.00600	−	11.2186i	0.137348	−	0.512589i	0.999977	−	0.00675234i	$-0.00214935\pi$
$480$	2.37945	+	1.37378i	0.108606	+	0.0627040i
$481$	−3.58783	−	2.94216i	−0.163591	−	0.134151i
$482$			9.00015i			0.409946i
$483$	0.675694	−	1.27724i	0.0307451	−	0.0581164i
$484$	3.04124	−	5.26759i	0.138238	−	0.239436i
$485$	38.4458	+	22.1967i	1.74573	+	1.00790i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	7.41455	+	7.41455i	0.335986	+	0.335986i	0.854854	−	0.518869i	$-0.173647\pi$
$487$	7.41455	+	7.41455i	0.335986	+	0.335986i	−0.518869	+	0.854854i	$0.673647\pi$
$488$	13.1954	−	3.53571i	0.597329	−	0.160054i
$489$	−3.95898	−	3.95898i	−0.179031	−	0.179031i
$490$	−19.1802	+	1.42195i	−0.866474	+	0.0642370i
$491$	−3.98650	−	2.30160i	−0.179908	−	0.103870i	0.407341	−	0.913276i	$-0.366456\pi$
$491$	−3.98650	−	2.30160i	−0.179908	−	0.103870i	−0.587249	+	0.809406i	$0.699789\pi$
$492$	−3.62768	+	3.62768i	−0.163548	+	0.163548i
$493$	3.65660	−	6.33341i	0.164685	−	0.285243i
$494$	−0.602405	−	0.272668i	−0.0271035	−	0.0122679i
$495$	5.27654	−	3.04641i	0.237163	−	0.136926i
$496$	−2.02462	−	7.55600i	−0.0909083	−	0.339274i
$497$	10.2449	−	3.15566i	0.459547	−	0.141550i
$498$	−13.9124	+	8.03232i	−0.623429	+	0.359937i
$499$	3.26150	−	12.1721i	0.146005	−	0.544897i	−0.853704	−	0.520759i	$-0.825649\pi$
$499$	3.26150	−	12.1721i	0.146005	−	0.544897i	0.999709	−	0.0241385i	$-0.00768426\pi$
$500$	4.76177	−	4.76177i	0.212953	−	0.212953i
$501$	5.03888	−	5.03888i	0.225121	−	0.225121i
$502$	4.02329	−	15.0151i	0.179568	−	0.670159i
$503$	−25.3394	+	14.6297i	−1.12983	+	0.652306i	−0.943891	−	0.330256i	$-0.892865\pi$
$503$	−25.3394	+	14.6297i	−1.12983	+	0.652306i	−0.185936	+	0.982562i	$0.559532\pi$
$504$	−1.80034	+	1.93875i	−0.0801936	+	0.0863590i
$505$	−11.2859	−	42.1197i	−0.502218	−	1.87430i
$506$	−1.04884	+	0.605549i	−0.0466267	+	0.0269199i
$507$	9.76735	−	8.57898i	0.433783	−	0.381006i
$508$	−6.68890	+	11.5855i	−0.296772	+	0.514024i
$509$	−17.3157	+	17.3157i	−0.767504	+	0.767504i	−0.977666	−	0.210163i	$-0.932601\pi$
$509$	−17.3157	+	17.3157i	−0.767504	+	0.767504i	0.210163	+	0.977666i	$0.432601\pi$
$510$	3.98859	+	2.30282i	0.176618	+	0.101970i
$511$	17.2090	+	15.9804i	0.761280	+	0.706931i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.177146	−	0.0474662i	0.00782120	−	0.00209568i
$514$	5.07038	+	5.07038i	0.223645	+	0.223645i
$515$	−6.73195	−	25.1240i	−0.296645	−	1.10710i
$516$	2.86766	+	1.65565i	0.126242	+	0.0728858i
$517$	11.1896	−	19.3810i	0.492118	−	0.852374i
$518$	1.81029	+	2.88362i	0.0795397	+	0.126699i
$519$			2.84253i			0.124773i
$520$	5.77336	+	8.05020i	0.253179	+	0.353025i
$521$	7.83904	+	4.52587i	0.343434	+	0.198282i	0.661790	−	0.749690i	$-0.269797\pi$
$521$	7.83904	+	4.52587i	0.343434	+	0.198282i	−0.318355	+	0.947971i	$0.603131\pi$
$522$	−1.12917	+	4.21412i	−0.0494225	+	0.184447i
$523$		−	6.35492i		−	0.277881i	−0.990301	−	0.138941i	$-0.955630\pi$
$523$		−	6.35492i		−	0.277881i	0.990301	−	0.138941i	$-0.0443697\pi$
$524$	9.69509	+	16.7924i	0.423532	+	0.733579i
$525$	−3.58580	−	5.71183i	−0.156497	−	0.249285i
$526$	1.86870	−	6.97407i	0.0814790	−	0.304084i
$527$	−3.39381	−	12.6659i	−0.147837	−	0.551734i
$528$	2.14199	−	0.573943i	0.0932180	−	0.0249777i
$529$	22.7017			0.987032
$530$	9.78641			0.425094
$531$	−1.43669	+	0.384959i	−0.0623469	+	0.0167058i
$532$	0.355558	+	0.330174i	0.0154154	+	0.0143149i
$533$	−17.3095	+	6.52241i	−0.749759	+	0.282517i
$534$	8.04447	+	13.9334i	0.348118	+	0.602958i
$535$	8.51620	+	2.28191i	0.368188	+	0.0986556i
$536$	−3.52425	−	6.10419i	−0.152225	−	0.263661i
$537$	12.7690	−	22.1165i	0.551022	−	0.954399i
$538$	−1.42419	+	1.42419i	−0.0614010	+	0.0614010i
$539$	−10.1347	+	11.7578i	−0.436534	+	0.506443i
$540$	−2.65393	−	0.711118i	−0.114207	−	0.0306017i
$541$	1.59127	+	0.426380i	0.0684142	+	0.0183315i	0.292864	−	0.956154i	$-0.405392\pi$
$541$	1.59127	+	0.426380i	0.0684142	+	0.0183315i	−0.224450	+	0.974486i	$0.572058\pi$
$542$		−	22.9065i		−	0.983917i
$543$	−13.9617	+	8.06081i	−0.599155	+	0.345923i
$544$	1.18530	+	1.18530i	0.0508194	+	0.0508194i
$545$	25.8577			1.10762
$546$	−8.79615	+	3.69158i	−0.376440	+	0.157985i
$547$	30.4255			1.30090			0.650451	−	0.759548i	$-0.274580\pi$
$547$	30.4255			1.30090			0.650451	+	0.759548i	$0.274580\pi$
$548$	−9.80752	−	9.80752i	−0.418956	−	0.418956i
$549$	−11.8307	+	6.83046i	−0.504922	+	0.291517i
$550$			5.65260i			0.241028i
$551$	0.772850	+	0.207085i	0.0329245	+	0.00882210i
$552$	0.527533	+	0.141352i	0.0224533	+	0.00601635i
$553$	−10.9404	+	20.6802i	−0.465233	+	0.879413i
$554$	18.0695	−	18.0695i	0.767702	−	0.767702i
$555$	−1.76789	+	3.06207i	−0.0750426	+	0.129978i
$556$	−7.91444	−	13.7082i	−0.335647	−	0.581358i
$557$	−32.4300	−	8.68959i	−1.37410	−	0.368190i	−0.505127	−	0.863045i	$-0.668555\pi$
$557$	−32.4300	−	8.68959i	−1.37410	−	0.368190i	−0.868976	+	0.494855i	$0.835221\pi$
$558$	3.91127	+	6.77452i	0.165577	+	0.286788i
$559$	6.95794	+	9.70194i	0.294289	+	0.410348i
$560$	−2.13990	−	6.94723i	−0.0904272	−	0.293574i
$561$	3.59054	−	0.962083i	0.151593	−	0.0406192i
$562$	−14.3237			−0.604210
$563$	16.0093			0.674710			0.337355	−	0.941378i	$-0.390468\pi$
$563$	16.0093			0.674710			0.337355	+	0.941378i	$0.390468\pi$
$564$	−9.74801	+	2.61197i	−0.410465	+	0.109984i
$565$	2.57444	+	9.60796i	0.108308	+	0.404210i
$566$	−7.87019	+	29.3719i	−0.330809	+	1.23459i
$567$	1.23721	−	2.33866i	0.0519580	−	0.0982143i
$568$	2.02587	+	3.50891i	0.0850037	+	0.147231i
$569$			4.60867i			0.193205i	0.995323	+	0.0966027i	$0.0307976\pi$
$569$			4.60867i			0.193205i	−0.995323	+	0.0966027i	$0.969202\pi$
$570$	−0.130416	+	0.486718i	−0.00546251	+	0.0203864i
$571$	−22.7993	−	13.1632i	−0.954120	−	0.550861i	−0.0597613	−	0.998213i	$-0.519034\pi$
$571$	−22.7993	−	13.1632i	−0.954120	−	0.550861i	−0.894358	+	0.447352i	$0.852367\pi$
$572$	7.88918	+	1.29941i	0.329863	+	0.0543309i
$573$		−	1.63311i		−	0.0682242i
$574$	13.5642	−	0.502111i	0.566160	−	0.0209577i
$575$	−0.696068	+	1.20563i	−0.0290281	+	0.0502781i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	10.6250	+	39.6530i	0.442324	+	1.65078i	0.722907	+	0.690946i	$0.242806\pi$
$577$	10.6250	+	39.6530i	0.442324	+	1.65078i	−0.280582	+	0.959830i	$0.590528\pi$
$578$	−10.0339	−	10.0339i	−0.417357	−	0.417357i
$579$	9.13997	−	2.44905i	0.379844	−	0.101779i
$580$	−8.47606	−	8.47606i	−0.351949	−	0.351949i
$581$	41.4336	+	9.47438i	1.71896	+	0.393063i
$582$	−13.9928	−	8.07872i	−0.580019	−	0.334874i
$583$	5.58516	−	5.58516i	0.231314	−	0.231314i
$584$	−4.43815	+	7.68711i	−0.183652	+	0.318095i
$585$	−7.66018	−	6.28164i	−0.316710	−	0.259714i
$586$	−6.31494	+	3.64593i	−0.260868	+	0.150612i
$587$	−6.32248	−	23.5958i	−0.260957	−	0.973904i	−0.964679	−	0.263429i	$-0.915147\pi$
$587$	−6.32248	−	23.5958i	−0.260957	−	0.973904i	0.703722	−	0.710475i	$-0.251520\pi$
$588$	6.98084	−	0.517532i	0.287885	−	0.0213427i
$589$	1.24242	−	0.717309i	0.0511928	−	0.0295562i
$590$	1.05770	−	3.94737i	0.0435446	−	0.162511i
$591$	−8.02977	+	8.02977i	−0.330301	+	0.330301i
$592$	−0.909963	+	0.909963i	−0.0373992	+	0.0373992i
$593$	9.55230	−	35.6497i	0.392266	−	1.46396i	−0.434121	−	0.900855i	$-0.642941\pi$
$593$	9.55230	−	35.6497i	0.392266	−	1.46396i	0.826387	−	0.563103i	$-0.190392\pi$
$594$	−1.92045	+	1.10877i	−0.0787971	+	0.0454935i
$595$	−3.58704	−	11.6454i	−0.147054	−	0.477416i
$596$	3.72381	+	13.8974i	0.152533	+	0.569261i
$597$	15.6791	−	9.05233i	0.641702	−	0.370487i
$598$	1.52265	+	1.24863i	0.0622657	+	0.0510603i
$599$	−2.06623	+	3.57882i	−0.0844240	+	0.146227i	−0.905146	−	0.425102i	$-0.860238\pi$
$599$	−2.06623	+	3.57882i	−0.0844240	+	0.146227i	0.820722	+	0.571328i	$0.193572\pi$
$600$	1.80244	−	1.80244i	0.0735843	−	0.0735843i
$601$	−19.4142	−	11.2088i	−0.791923	−	0.457217i	0.0487163	−	0.998813i	$-0.484487\pi$
$601$	−19.4142	−	11.2088i	−0.791923	−	0.457217i	−0.840639	+	0.541596i	$0.817820\pi$
$602$	−2.57896	−	8.37267i	−0.105111	−	0.341244i
$603$	4.98405	+	4.98405i	0.202966	+	0.202966i
$604$	2.24796	−	0.602340i	0.0914683	−	0.0245089i
$605$	−11.8171	−	11.8171i	−0.480434	−	0.480434i
$606$	4.10764	+	15.3299i	0.166861	+	0.622735i
$607$	15.0088	+	8.66532i	0.609187	+	0.351715i	0.772647	−	0.634835i	$-0.218932\pi$
$607$	15.0088	+	8.66532i	0.609187	+	0.351715i	−0.163460	+	0.986550i	$0.552265\pi$
$608$	−0.0916976	+	0.158825i	−0.00371883	+	0.00644120i
$609$	9.77605	−	6.13725i	0.396146	−	0.248694i
$610$		−	37.5341i		−	1.51971i
$611$	−35.9031	−	5.91350i	−1.45248	−	0.239234i
$612$	−1.45169	−	0.838134i	−0.0586811	−	0.0338796i
$613$	−9.95649	+	37.1581i	−0.402139	+	1.50080i	0.407133	+	0.913369i	$0.366529\pi$
$613$	−9.95649	+	37.1581i	−0.402139	+	1.50080i	−0.809272	+	0.587434i	$0.800138\pi$
$614$			1.47260i			0.0594295i
$615$	7.04790	+	12.2073i	0.284199	+	0.492246i
$616$	−5.18608	−	2.74357i	−0.208953	−	0.110542i
$617$	9.83501	−	36.7048i	0.395943	−	1.47768i	−0.424226	−	0.905556i	$-0.639454\pi$
$617$	9.83501	−	36.7048i	0.395943	−	1.47768i	0.820169	−	0.572121i	$-0.193879\pi$
$618$	2.45017	+	9.14414i	0.0985601	+	0.367831i
$619$	−22.9453	+	6.14818i	−0.922250	+	0.247116i	−0.688547	−	0.725192i	$-0.741751\pi$
$619$	−22.9453	+	6.14818i	−0.922250	+	0.247116i	−0.233703	+	0.972308i	$0.575084\pi$
$620$	−21.4928			−0.863173
$621$	−0.546143			−0.0219160
$622$	−19.9083	+	5.33442i	−0.798251	+	0.213891i
$623$	9.48870	−	41.4963i	0.380157	−	1.66251i
$624$	−2.10128	−	2.92996i	−0.0841183	−	0.117292i
$625$	−15.6238	−	27.0612i	−0.624952	−	1.08245i
$626$	−9.88803	−	2.64949i	−0.395205	−	0.105895i
$627$	0.203344	+	0.352202i	0.00812077	+	0.0140656i
$628$	−2.66874	+	4.62239i	−0.106494	+	0.184453i
$629$	−1.52534	+	1.52534i	−0.0608193	+	0.0608193i
$630$	3.86506	+	6.15667i	0.153988	+	0.245287i
$631$	−38.9228	−	10.4293i	−1.54949	−	0.415185i	−0.620173	−	0.784465i	$-0.712937\pi$
$631$	−38.9228	−	10.4293i	−1.54949	−	0.415185i	−0.929318	+	0.369280i	$0.879604\pi$
$632$	−8.54147	−	2.28868i	−0.339762	−	0.0910388i
$633$			0.0181383i			0.000720934i
$634$	0.322577	−	0.186240i	0.0128112	−	0.00739654i
$635$	25.9905	+	25.9905i	1.03140	+	1.03140i
$636$	−3.56187			−0.141237
$637$	23.6997	+	8.67901i	0.939015	+	0.343875i
$638$	−9.67467			−0.383024
$639$	−2.86502	−	2.86502i	−0.113338	−	0.113338i
$640$	2.37945	−	1.37378i	0.0940560	−	0.0543032i
$641$			43.9676i			1.73661i	0.496026	+	0.868307i	$0.334792\pi$
$641$			43.9676i			1.73661i	−0.496026	+	0.868307i	$0.665208\pi$
$642$	−3.09956	−	0.830525i	−0.122330	−	0.0327782i
$643$	25.5889	+	6.85652i	1.00913	+	0.270395i	0.725265	−	0.688470i	$-0.241717\pi$
$643$	25.5889	+	6.85652i	1.00913	+	0.270395i	0.283863	+	0.958865i	$0.408384\pi$
$644$	−0.768275	−	1.22379i	−0.0302743	−	0.0482240i
$645$	6.43322	−	6.43322i	0.253308	−	0.253308i
$646$	−0.153710	+	0.266233i	−0.00604763	+	0.0104748i
$647$	−15.8044	−	27.3741i	−0.621337	−	1.07619i	−0.989237	−	0.146321i	$-0.953257\pi$
$647$	−15.8044	−	27.3741i	−0.621337	−	1.07619i	0.367900	−	0.929865i	$-0.380077\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−1.64915	−	2.85642i	−0.0647350	−	0.112124i
$650$	8.60037	−	3.24071i	0.337334	−	0.127111i
$651$	4.61347	−	20.1758i	0.180816	−	0.790750i
$652$	−5.40806	+	1.44909i	−0.211796	+	0.0567506i
$653$	−0.955783			−0.0374027			−0.0187013	−	0.999825i	$-0.505953\pi$
$653$	−0.955783			−0.0374027			−0.0187013	+	0.999825i	$0.505953\pi$
$654$	−9.41117			−0.368006
$655$	51.4602	−	13.7887i	2.01071	−	0.538769i
$656$	1.32782	+	4.95550i	0.0518428	+	0.193480i
$657$	2.29736	−	8.57385i	0.0896284	−	0.334498i
$658$	23.6014	+	12.4858i	0.920080	+	0.486747i
$659$	−12.1342	−	21.0171i	−0.472681	−	0.818708i	0.526830	−	0.849971i	$-0.323381\pi$
$659$	−12.1342	−	21.0171i	−0.472681	−	0.818708i	−0.999511	+	0.0312626i	$0.990047\pi$
$660$		−	6.09282i		−	0.237163i
$661$	5.48656	−	20.4761i	0.213403	−	0.796429i	−0.773320	−	0.634016i	$-0.781406\pi$
$661$	5.48656	−	20.4761i	0.213403	−	0.796429i	0.986723	−	0.162413i	$-0.0519278\pi$
$662$	11.5345	+	6.65946i	0.448302	+	0.258827i
$663$	−3.52230	−	4.91139i	−0.136795	−	0.190743i
$664$			16.0646i			0.623429i
$665$	1.12910	−	0.708834i	0.0437848	−	0.0274874i
$666$	0.643441	−	1.11447i	0.0249328	−	0.0431849i
$667$	−2.06348	−	1.19135i	−0.0798983	−	0.0461293i
$668$	−1.84436	−	6.88324i	−0.0713604	−	0.266321i
$669$	−10.1640	−	10.1640i	−0.392962	−	0.392962i
$670$	−18.7062	+	5.01232i	−0.722685	+	0.193643i
$671$	−21.4209	−	21.4209i	−0.826945	−	0.826945i
$672$	0.778839	+	2.52852i	0.0300444	+	0.0975398i
$673$	35.5408	+	20.5195i	1.37000	+	0.790969i	0.990927	−	0.134399i	$-0.0429105\pi$
$673$	35.5408	+	20.5195i	1.37000	+	0.790969i	0.379070	+	0.925368i	$0.376244\pi$
$674$	−16.1468	+	16.1468i	−0.621950	+	0.621950i
$675$	−1.27452	+	2.20753i	−0.0490562	+	0.0849678i
$676$	−2.54594	−	12.7483i	−0.0979207	−	0.490318i
$677$	−3.46230	+	1.99896i	−0.133067	+	0.0768264i	−0.565056	−	0.825053i	$-0.691145\pi$
$677$	−3.46230	+	1.99896i	−0.133067	+	0.0768264i	0.431989	+	0.901879i	$0.357812\pi$
$678$	−0.936996	−	3.49692i	−0.0359851	−	0.134298i
$679$	12.5840	+	40.8544i	0.482931	+	1.56785i
$680$	3.98859	−	2.30282i	0.152956	−	0.0883090i
$681$	1.07187	−	4.00027i	0.0410741	−	0.153291i
$682$	−12.2661	+	12.2661i	−0.469692	+	0.469692i
$683$	−8.30922	+	8.30922i	−0.317944	+	0.317944i	−0.847977	−	0.530033i	$-0.822179\pi$
$683$	−8.30922	+	8.30922i	−0.317944	+	0.317944i	0.530033	+	0.847977i	$0.322179\pi$
$684$	0.0474662	−	0.177146i	0.00181492	−	0.00677336i
$685$	−33.0028	+	19.0542i	−1.26097	+	0.728022i
$686$	−14.4659	−	11.5645i	−0.552309	−	0.441536i
$687$	−2.25923	−	8.43158i	−0.0861952	−	0.321685i
$688$	2.86766	−	1.65565i	0.109329	−	0.0631209i
$689$	−11.6998	−	5.29571i	−0.445727	−	0.201750i
$690$	0.750277	−	1.29952i	0.0285626	−	0.0494718i
$691$	20.4063	−	20.4063i	0.776292	−	0.776292i	−0.202906	−	0.979198i	$-0.565039\pi$
$691$	20.4063	−	20.4063i	0.776292	−	0.776292i	0.979198	+	0.202906i	$0.0650385\pi$
$692$	2.46170	+	1.42127i	0.0935799	+	0.0540284i
$693$	5.71946	+	1.30783i	0.217264	+	0.0496805i
$694$	10.5234	+	10.5234i	0.399463	+	0.399463i
$695$	−42.0088	+	11.2562i	−1.59348	+	0.426972i
$696$	3.08495	+	3.08495i	0.116935	+	0.116935i
$697$	2.22579	+	8.30675i	0.0843077	+	0.314641i
$698$	−8.61163	−	4.97193i	−0.325955	−	0.188190i
$699$	−3.30937	+	5.73199i	−0.125172	+	0.216804i
$700$	−6.73949	+	0.249478i	−0.254729	+	0.00942937i
$701$			8.49261i			0.320761i	0.987055	+	0.160381i	$0.0512722\pi$
$701$			8.49261i			0.320761i	−0.987055	+	0.160381i	$0.948728\pi$
$702$	2.78800	+	2.28627i	0.105226	+	0.0862897i
$703$	−0.204389	−	0.118004i	−0.00770867	−	0.00445060i
$704$	0.573943	−	2.14199i	0.0216313	−	0.0807291i
$705$			27.7280i			1.04430i
$706$	10.8476	+	18.7886i	0.408256	+	0.707119i
$707$	19.6354	−	37.1161i	0.738465	−	1.39589i
$708$	−0.384959	+	1.43669i	−0.0144677	+	0.0539940i
$709$	9.84414	+	36.7388i	0.369704	+	1.37976i	0.860930	+	0.508724i	$0.169882\pi$
$709$	9.84414	+	36.7388i	0.369704	+	1.37976i	−0.491225	+	0.871032i	$0.663451\pi$
$710$	10.7530	−	2.88127i	0.403555	−	0.108132i
$711$	8.84278			0.331630
$712$	16.0889			0.602958
$713$	−4.12665	+	1.10573i	−0.154544	+	0.0414100i
$714$	1.30554	+	4.23848i	0.0488587	+	0.158621i
$715$	9.05868	−	20.0133i	0.338775	−	0.748455i
$716$	−12.7690	−	22.1165i	−0.477199	−	0.826534i
$717$	5.54060	+	1.48460i	0.206917	+	0.0554434i
$718$	−13.1466	−	22.7705i	−0.490626	−	0.849789i
$719$	−23.9854	+	41.5439i	−0.894503	+	1.54932i	−0.0600843	+	0.998193i	$0.519137\pi$
$719$	−23.9854	+	41.5439i	−0.894503	+	1.54932i	−0.834419	+	0.551131i	$0.814196\pi$
$720$	−1.94281	+	1.94281i	−0.0724043	+	0.0724043i
$721$	11.7123	−	22.1394i	0.436190	−	0.824513i
$722$	18.3201	+	4.90886i	0.681804	+	0.182689i
$723$	−8.69348	−	2.32941i	−0.323314	−	0.0866317i
$724$			16.1216i			0.599155i
$725$	−9.63097	+	5.56044i	−0.357685	+	0.206510i
$726$	4.30097	+	4.30097i	0.159624	+	0.159624i
$727$	−29.5720			−1.09677			−0.548383	−	0.836227i	$-0.684756\pi$
$727$	−29.5720			−1.09677			−0.548383	+	0.836227i	$0.684756\pi$
$728$	−1.20107	+	9.46348i	−0.0445146	+	0.350740i
$729$	−1.00000			−0.0370370
$730$	17.2450	+	17.2450i	0.638266	+	0.638266i
$731$	4.80697	−	2.77531i	0.177792	−	0.102648i
$732$			13.6609i			0.504922i
$733$	32.8929	+	8.81361i	1.21493	+	0.325538i	0.808693	−	0.588232i	$-0.200176\pi$
$733$	32.8929	+	8.81361i	1.21493	+	0.325538i	0.406233	+	0.913770i	$0.366842\pi$
$734$	−8.69773	−	2.33055i	−0.321039	−	0.0860221i
$735$	3.59071	−	18.8947i	0.132445	−	0.696941i
$736$	0.386181	−	0.386181i	0.0142348	−	0.0142348i
$737$	−7.81520	+	13.5363i	−0.287876	+	0.498617i
$738$	−2.56516	−	4.44298i	−0.0944247	−	0.163548i
$739$	18.6177	+	4.98861i	0.684865	+	0.183509i	0.584441	−	0.811436i	$-0.301314\pi$
$739$	18.6177	+	4.98861i	0.684865	+	0.183509i	0.100423	+	0.994945i	$0.467980\pi$
$740$	1.76789	+	3.06207i	0.0649888	+	0.112564i
$741$	0.419291	−	0.511307i	0.0154030	−	0.0187833i
$742$	6.90558	+	6.41258i	0.253512	+	0.235413i
$743$	−40.9049	+	10.9604i	−1.50065	+	0.402099i	−0.913319	−	0.407245i	$-0.866490\pi$
$743$	−40.9049	+	10.9604i	−1.50065	+	0.402099i	−0.587335	+	0.809344i	$0.699823\pi$
$744$	7.82254			0.286788
$745$	39.5309			1.44830
$746$	25.8205	−	6.91859i	0.945357	−	0.253308i
$747$	−4.15784	−	15.5173i	−0.152127	−	0.567747i
$748$	0.962083	−	3.59054i	0.0351772	−	0.131283i
$749$	4.51406	+	7.19046i	0.164940	+	0.262734i
$750$	3.36708	+	5.83195i	0.122948	+	0.212953i
$751$			1.51788i			0.0553884i	0.999616	+	0.0276942i	$0.00881646\pi$
$751$			1.51788i			0.0553884i	−0.999616	+	0.0276942i	$0.991184\pi$
$752$	−2.61197	+	9.74801i	−0.0952488	+	0.355473i
$753$	13.4622	+	7.77241i	0.490590	+	0.283242i
$754$	5.54661	+	14.7199i	0.201996	+	0.536067i
$755$		−	6.39427i		−	0.232711i
$756$	−1.40673	−	2.24078i	−0.0511623	−	0.0814965i
$757$	10.3621	−	17.9476i	0.376616	−	0.652318i	−0.613951	−	0.789344i	$-0.710421\pi$
$757$	10.3621	−	17.9476i	0.376616	−	0.652318i	0.990568	+	0.137026i	$0.0437542\pi$
$758$	−9.48961	−	5.47883i	−0.344678	−	0.199000i
$759$	−0.313455	−	1.16983i	−0.0113777	−	0.0424621i
$760$	0.356302	+	0.356302i	0.0129244	+	0.0129244i
$761$	10.1812	−	2.72805i	0.369069	−	0.0988918i	−0.0695173	−	0.997581i	$-0.522146\pi$
$761$	10.1812	−	2.72805i	0.369069	−	0.0988918i	0.438587	+	0.898689i	$0.355479\pi$
$762$	−9.45953	−	9.45953i	−0.342683	−	0.342683i
$763$	18.2459	+	16.9433i	0.660547	+	0.613390i
$764$	−1.41432	−	0.816556i	−0.0511682	−	0.0295419i
$765$	−3.25667	+	3.25667i	−0.117745	+	0.117745i
$766$	−11.6674	+	20.2086i	−0.421562	+	0.730166i
$767$	−3.40053	+	4.14679i	−0.122786	+	0.149732i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−1.89366	−	7.06724i	−0.0682871	−	0.254851i	0.923340	−	0.383983i	$-0.125448\pi$
$769$	−1.89366	−	7.06724i	−0.0682871	−	0.254851i	−0.991627	+	0.129132i	$0.958781\pi$
$770$	−10.9692	+	11.8125i	−0.395301	+	0.425692i
$771$	−6.20992	+	3.58530i	−0.223645	+	0.129121i
$772$	2.44905	−	9.13997i	0.0881432	−	0.328955i
$773$	−29.0097	+	29.0097i	−1.04341	+	1.04341i	−0.0443932	+	0.999014i	$0.514135\pi$
$773$	−29.0097	+	29.0097i	−1.04341	+	1.04341i	−0.999014	+	0.0443932i	$0.985865\pi$
$774$	−2.34144	+	2.34144i	−0.0841612	+	0.0841612i
$775$	−5.16083	+	19.2605i	−0.185383	+	0.691857i
$776$	−13.9928	+	8.07872i	−0.502311	+	0.290009i
$777$	−3.25390	+	1.00227i	−0.116733	+	0.0359563i
$778$	7.27893	+	27.1653i	0.260962	+	0.973924i
$779$	−0.814822	+	0.470438i	−0.0291940	+	0.0168552i
$780$	−9.27015	+	3.49309i	−0.331925	+	0.125073i
$781$	4.49247	−	7.78118i	0.160753	−	0.278433i
$782$	0.647343	−	0.647343i	0.0231490	−	0.0231490i
$783$	−3.77828	−	2.18139i	−0.135025	−	0.0779566i
$784$	3.04223	−	6.30435i	0.108651	−	0.225155i
$785$	10.3697	+	10.3697i	0.370111	+	0.370111i
$786$	−18.7295	+	5.01855i	−0.668058	+	0.179006i
$787$	36.8103	+	36.8103i	1.31214	+	1.31214i	0.919832	+	0.392312i	$0.128325\pi$
$787$	36.8103	+	36.8103i	1.31214	+	1.31214i	0.392312	+	0.919832i	$0.371675\pi$
$788$	2.93910	+	10.9689i	0.104701	+	0.390750i
$789$	6.25278	+	3.61004i	0.222605	+	0.128521i
$790$	−12.1480	+	21.0409i	−0.432206	+	0.748603i
$791$	−4.47905	+	8.46658i	−0.159257	+	0.301037i
$792$			2.21755i			0.0787971i
$793$	−20.3108	+	44.8725i	−0.721256	+	1.59347i
$794$	−18.9260	−	10.9269i	−0.671659	−	0.387783i
$795$	−2.53291	+	9.45295i	−0.0898330	+	0.335261i
$796$		−	18.1047i		−	0.641702i
$797$	−9.81837	−	17.0059i	−0.347784	−	0.602380i	0.638071	−	0.769977i	$-0.279733\pi$
$797$	−9.81837	−	17.0059i	−0.347784	−	0.602380i	−0.985856	+	0.167597i	$0.946399\pi$
$798$	−0.410949	+	0.257988i	−0.0145474	+	0.00913266i
$799$	−4.37836	+	16.3403i	−0.154895	+	0.578078i
$800$	−0.659739	−	2.46218i	−0.0233253	−	0.0870511i
$801$	−15.5407	+	4.16412i	−0.549104	+	0.147132i
$802$	20.5569			0.725888
$803$	19.6836			0.694620
$804$	6.80833	−	1.82429i	0.240111	−	0.0643377i
$805$	−3.79418	+	1.16869i	−0.133727	+	0.0411909i
$806$	25.6950	+	11.6304i	0.905067	+	0.409663i
$807$	−1.00705	−	1.74426i	−0.0354499	−	0.0614010i
$808$	15.3299	+	4.10764i	0.539304	+	0.144506i
$809$	7.51268	+	13.0123i	0.264132	+	0.457490i	0.967336	−	0.253498i	$-0.0815813\pi$
$809$	7.51268	+	13.0123i	0.264132	+	0.457490i	−0.703204	+	0.710988i	$0.748248\pi$
$810$	1.37378	−	2.37945i	0.0482695	−	0.0836053i
$811$	−22.5797	+	22.5797i	−0.792880	+	0.792880i	−0.981961	−	0.189081i	$-0.939449\pi$
$811$	−22.5797	+	22.5797i	−0.792880	+	0.792880i	0.189081	+	0.981961i	$0.439449\pi$
$812$	−0.426992	−	11.5349i	−0.0149845	−	0.404797i
$813$	22.1259	+	5.92863i	0.775991	+	0.207926i
$814$	2.75648	+	0.738597i	0.0966146	+	0.0258878i
$815$			15.3831i			0.538846i
$816$	−1.45169	+	0.838134i	−0.0508194	+	0.0293406i
$817$	0.429409	+	0.429409i	0.0150231	+	0.0150231i
$818$	−39.5402			−1.38249
$819$	−1.28918	−	9.45188i	−0.0450478	−	0.330275i
$820$	14.0958			0.492246
$821$	38.8105	+	38.8105i	1.35450	+	1.35450i	0.880558	+	0.473938i	$0.157168\pi$
$821$	38.8105	+	38.8105i	1.35450	+	1.35450i	0.473938	+	0.880558i	$0.342832\pi$
$822$	12.0117	−	6.93496i	0.418956	−	0.241885i
$823$			49.2059i			1.71521i	0.514308	+	0.857606i	$0.328049\pi$
$823$			49.2059i			1.71521i	−0.514308	+	0.857606i	$0.671951\pi$
$824$	9.14414	+	2.45017i	0.318551	+	0.0853555i
$825$	−5.45999	−	1.46300i	−0.190093	−	0.0509352i
$826$	3.33287	−	2.09232i	0.115965	−	0.0728013i
$827$	7.82426	−	7.82426i	0.272076	−	0.272076i	−0.557859	−	0.829936i	$-0.688377\pi$
$827$	7.82426	−	7.82426i	0.272076	−	0.272076i	0.829936	+	0.557859i	$0.188377\pi$
$828$	−0.273071	+	0.472973i	−0.00948989	+	0.0164370i
$829$	−5.52185	−	9.56413i	−0.191782	−	0.332176i	0.754059	−	0.656807i	$-0.228093\pi$
$829$	−5.52185	−	9.56413i	−0.191782	−	0.332176i	−0.945841	+	0.324631i	$0.894760\pi$
$830$	42.6345	+	11.4239i	1.47986	+	0.396528i
$831$	12.7771	+	22.1306i	0.443233	+	0.767702i
$832$	−3.58805	+	0.354780i	−0.124393	+	0.0122998i
$833$	5.09959	−	10.5678i	0.176690	−	0.366152i
$834$	15.2895	−	4.09682i	0.529433	−	0.141861i
$835$	−19.5792			−0.677566
$836$	0.406688			0.0140656
$837$	−7.55600	+	2.02462i	−0.261173	+	0.0699812i
$838$	5.79710	+	21.6351i	0.200257	+	0.747371i
$839$	−0.556614	+	2.07731i	−0.0192164	+	0.0717167i	−0.974868	−	0.222782i	$-0.928486\pi$
$839$	−0.556614	+	2.07731i	−0.0192164	+	0.0717167i	0.955652	+	0.294499i	$0.0951528\pi$
$840$	7.26436	−	0.268907i	0.250644	−	0.00927816i
$841$	4.98306	+	8.63092i	0.171830	+	0.297618i
$842$		−	7.23817i		−	0.249444i
$843$	3.70725	−	13.8356i	0.127684	−	0.476525i
$844$	0.0157083	+	0.00906917i	0.000540701	+	0.000312174i
$845$	−35.6435	−	2.30878i	−1.22617	−	0.0794245i
$846$		−	10.0919i		−	0.346966i
$847$	−0.595301	−	16.0817i	−0.0204548	−	0.552575i
$848$	−1.78093	+	3.08467i	−0.0611575	+	0.105928i
$849$	−26.3342	−	15.2040i	−0.903786	−	0.521801i
$850$	−1.10590	−	4.12727i	−0.0379320	−	0.141564i
$851$	0.496969	+	0.496969i	0.0170359	+	0.0170359i
$852$	−3.91368	+	1.04867i	−0.134081	+	0.0359268i
$853$	27.5693	+	27.5693i	0.943954	+	0.943954i	0.998511	−	0.0545571i	$-0.0173747\pi$
$853$	27.5693	+	27.5693i	0.943954	+	0.943954i	−0.0545571	+	0.998511i	$0.517375\pi$
$854$	24.5943	−	26.4852i	0.841601	−	0.906304i
$855$	−0.436380	−	0.251944i	−0.0149239	−	0.00861630i
$856$	−2.26904	+	2.26904i	−0.0775541	+	0.0775541i
$857$	10.0100	−	17.3379i	0.341936	−	0.592251i	−0.642856	−	0.765987i	$-0.722251\pi$
$857$	10.0100	−	17.3379i	0.341936	−	0.592251i	0.984792	+	0.173736i	$0.0555839\pi$
$858$	−3.29700	+	7.28406i	−0.112558	+	0.248674i
$859$	−22.5936	+	13.0444i	−0.770884	+	0.445070i	−0.833190	−	0.552987i	$-0.813488\pi$
$859$	−22.5936	+	13.0444i	−0.770884	+	0.445070i	0.0623061	+	0.998057i	$0.480155\pi$
$860$	−2.35472	−	8.78794i	−0.0802953	−	0.299666i
$861$	−3.02568	+	13.2320i	−0.103115	+	0.450946i
$862$	−32.6729	+	18.8637i	−1.11284	+	0.642500i
$863$	−9.36095	+	34.9355i	−0.318651	+	1.18922i	0.601892	+	0.798578i	$0.294414\pi$
$863$	−9.36095	+	34.9355i	−0.318651	+	1.18922i	−0.920543	+	0.390642i	$0.872253\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	5.52250	−	5.52250i	0.187771	−	0.187771i
$866$	9.55198	−	35.6485i	0.324590	−	1.21138i
$867$	12.2890	−	7.09506i	0.417357	−	0.240961i
$868$	−15.1660	−	14.0833i	−0.514767	−	0.478017i
$869$	5.07526	+	18.9411i	0.172166	+	0.642533i
$870$	10.3810	−	5.99348i	0.351949	−	0.203198i
$871$	25.0759	+	4.13018i	0.849664	+	0.139946i
$872$	−4.70559	+	8.15031i	−0.159351	+	0.276004i
$873$	11.4250	−	11.4250i	0.386679	−	0.386679i
$874$	0.0867411	+	0.0500800i	0.00293406	+	0.00169398i
$875$	3.97157	−	17.3686i	0.134264	−	0.587166i
$876$	−6.27650	−	6.27650i	−0.212063	−	0.212063i
$877$	−23.6532	+	6.33785i	−0.798711	+	0.214014i	−0.635018	−	0.772497i	$-0.719007\pi$
$877$	−23.6532	+	6.33785i	−0.798711	+	0.214014i	−0.163693	+	0.986511i	$0.552341\pi$
$878$	7.18827	+	7.18827i	0.242592	+	0.242592i
$879$	−1.88727	−	7.04340i	−0.0636562	−	0.237568i
$880$	−5.27654	−	3.04641i	−0.177872	−	0.102694i
$881$	−0.802614	+	1.39017i	−0.0270407	+	0.0468359i	−0.879229	−	0.476399i	$-0.841942\pi$
$881$	−0.802614	+	1.39017i	−0.0270407	+	0.0468359i	0.852188	+	0.523235i	$0.175275\pi$
$882$	−1.30688	+	6.87692i	−0.0440048	+	0.231558i
$883$		−	38.8748i		−	1.30824i	−0.756391	−	0.654120i	$-0.773039\pi$
$883$		−	38.8748i		−	1.30824i	0.756391	−	0.654120i	$-0.226961\pi$
$884$	−6.01454	+	0.594706i	−0.202291	+	0.0200021i
$885$	3.53912	+	2.04331i	0.118966	+	0.0686851i
$886$	0.529130	−	1.97474i	0.0177765	−	0.0663427i
$887$			54.9310i			1.84440i	0.386710	+	0.922201i	$0.373611\pi$
$887$			54.9310i			1.84440i	−0.386710	+	0.922201i	$0.626389\pi$
$888$	−0.643441	−	1.11447i	−0.0215925	−	0.0373992i
$889$	1.30930	+	35.3701i	0.0439126	+	1.18628i
$890$	11.4411	−	42.6989i	0.383508	−	1.43127i
$891$	−0.573943	−	2.14199i	−0.0192278	−	0.0717592i
$892$	−13.8843	+	3.72027i	−0.464879	+	0.124564i
$893$	−1.85080			−0.0619348
$894$	−14.3877			−0.481196
$895$	−67.7760	+	18.1605i	−2.26550	+	0.607039i
$896$	2.57918	+	0.589766i	0.0861644	+	0.0197027i
$897$	−1.60017	+	1.14760i	−0.0534283	+	0.0383171i
$898$	−10.0058	−	17.3306i	−0.333899	−	0.578329i
$899$	−32.9652	−	8.83299i	−1.09945	−	0.294597i
$900$	1.27452	+	2.20753i	0.0424839	+	0.0735843i
$901$	−2.98532	+	5.17073i	−0.0994555	+	0.172262i
$902$	8.04455	−	8.04455i	0.267854	−	0.267854i
$903$	8.75486	−	0.324081i	0.291344	−	0.0107847i
$904$	−3.49692	−	0.936996i	−0.116306	−	0.0311640i
$905$	42.7857	+	11.4644i	1.42224	+	0.381089i
$906$			2.32726i			0.0773181i
$907$	9.42391	−	5.44089i	0.312916	−	0.180662i	−0.335315	−	0.942106i	$-0.608843\pi$
$907$	9.42391	−	5.44089i	0.312916	−	0.180662i	0.648230	+	0.761444i	$0.275509\pi$
$908$	−2.92840	−	2.92840i	−0.0971824	−	0.0971824i
$909$	−15.8707			−0.526398
$910$	24.2613	+	9.91721i	0.804255	+	0.328752i
$911$	−42.6469			−1.41296			−0.706478	−	0.707735i	$-0.749717\pi$
$911$	−42.6469			−1.41296			−0.706478	+	0.707735i	$0.749717\pi$
$912$	−0.129680	−	0.129680i	−0.00429414	−	0.00429414i
$913$	30.8514	−	17.8121i	1.02103	−	0.589493i
$914$		−	33.0047i		−	1.09170i
$915$	36.2551	+	9.71453i	1.19856	+	0.321153i
$916$	−8.43158	−	2.25923i	−0.278587	−	0.0746472i
$917$	45.3469	+	23.9897i	1.49749	+	0.792211i
$918$	1.18530	−	1.18530i	0.0391208	−	0.0391208i
$919$	7.60332	−	13.1693i	0.250810	−	0.434416i	−0.712939	−	0.701226i	$-0.752636\pi$
$919$	7.60332	−	13.1693i	0.250810	−	0.434416i	0.963749	+	0.266810i	$0.0859696\pi$
$920$	−0.750277	−	1.29952i	−0.0247359	−	0.0428439i
$921$	−1.42243	−	0.381138i	−0.0468706	−	0.0125589i
$922$	7.11085	+	12.3164i	0.234183	+	0.405618i
$923$	−14.4146	−	2.37418i	−0.474461	−	0.0781472i
$924$	3.99234	−	4.29928i	0.131338	−	0.141436i
$925$	3.16853	−	0.849005i	0.104181	−	0.0279151i
$926$	−21.7639			−0.715207
$927$	−9.46671			−0.310928
$928$	4.21412	−	1.12917i	0.138335	−	0.0370669i
$929$	3.48112	+	12.9917i	0.114212	+	0.426244i	0.999227	−	0.0393186i	$-0.0125187\pi$
$929$	3.48112	+	12.9917i	0.114212	+	0.426244i	−0.885015	+	0.465562i	$0.845852\pi$
$930$	5.56275	−	20.7605i	0.182410	−	0.680763i
$931$	1.26120	+	0.239675i	0.0413340	+	0.00785503i
$932$	3.30937	+	5.73199i	0.108402	+	0.187758i
$933$		−	20.6106i		−	0.674761i
$934$	10.5964	−	39.5464i	0.346726	−	1.29400i
$935$	−8.84490	−	5.10660i	−0.289259	−	0.167004i
$936$	3.37397	−	1.27135i	0.110282	−	0.0415553i
$937$			24.6205i			0.804315i	0.915570	+	0.402158i	$0.131740\pi$
$937$			24.6205i			0.804315i	−0.915570	+	0.402158i	$0.868260\pi$
$938$	−16.4840	−	8.72049i	−0.538223	−	0.284734i
$939$	5.11842	−	8.86536i	0.167033	−	0.289310i
$940$	24.0131	+	13.8640i	0.783221	+	0.452193i
$941$	0.833574	+	3.11094i	0.0271737	+	0.101414i	0.978181	−	0.207755i	$-0.0666158\pi$
$941$	0.833574	+	3.11094i	0.0271737	+	0.101414i	−0.951007	+	0.309169i	$0.899949\pi$
$942$	−3.77417	−	3.77417i	−0.122969	−	0.122969i
$943$	2.70641	−	0.725181i	0.0881329	−	0.0236151i
$944$	1.05173	+	1.05173i	0.0342308	+	0.0342308i
$945$	−6.94723	+	2.13990i	−0.225994	+	0.0696109i
$946$	−6.35918	−	3.67147i	−0.206755	−	0.119370i
$947$	8.13118	−	8.13118i	0.264228	−	0.264228i	−0.562541	−	0.826769i	$-0.690176\pi$
$947$	8.13118	−	8.13118i	0.264228	−	0.264228i	0.826769	+	0.562541i	$0.190176\pi$
$948$	4.42139	−	7.65808i	0.143600	−	0.248723i
$949$	−11.2849	−	29.9484i	−0.366322	−	0.972166i
$950$	0.404850	−	0.233740i	0.0131351	−	0.00758354i
$951$	0.0964049	+	0.359788i	0.00312614	+	0.0116669i
$952$	4.32340	+	0.988606i	0.140122	+	0.0320409i
$953$	39.2103	−	22.6381i	1.27015	−	0.733319i	0.295130	−	0.955457i	$-0.404637\pi$
$953$	39.2103	−	22.6381i	1.27015	−	0.733319i	0.975015	+	0.222138i	$0.0713037\pi$
$954$	0.921879	−	3.44050i	0.0298469	−	0.111390i
$955$	−3.17283	+	3.17283i	−0.102670	+	0.102670i
$956$	4.05600	−	4.05600i	0.131180	−	0.131180i
$957$	2.50399	−	9.34502i	0.0809425	−	0.302082i
$958$	10.0583	−	5.80715i	0.324968	−	0.187620i
$959$	−35.7731	−	8.18000i	−1.15517	−	0.264146i
$960$	0.711118	+	2.65393i	0.0229512	+	0.0856552i
$961$	−26.1472	+	15.0961i	−0.843458	+	0.486971i
$962$	−0.456560	−	4.61740i	−0.0147201	−	0.148871i
$963$	1.60445	−	2.77899i	0.0517027	−	0.0895517i
$964$	−6.36407	+	6.36407i	−0.204973	+	0.204973i
$965$	−22.5153	−	12.9992i	−0.724793	−	0.418459i
$966$	1.38093	−	0.425357i	0.0444308	−	0.0136856i
$967$	−31.2769	−	31.2769i	−1.00580	−	1.00580i	−0.999983	−	0.00581309i	$-0.998150\pi$
$967$	−31.2769	−	31.2769i	−1.00580	−	1.00580i	−0.00581309	−	0.999983i	$-0.501850\pi$
$968$	5.87523	−	1.57426i	0.188837	−	0.0505987i
$969$	−0.217379	−	0.217379i	−0.00698321	−	0.00698321i
$970$	11.4899	+	42.8807i	0.368917	+	1.37682i
$971$	−15.6210	−	9.01878i	−0.501301	−	0.289426i	0.227950	−	0.973673i	$-0.426798\pi$
$971$	−15.6210	−	9.01878i	−0.501301	−	0.289426i	−0.729251	+	0.684247i	$0.760131\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−37.0183	−	19.5837i	−1.18675	−	0.627824i
$974$			10.4858i			0.335986i
$975$	0.904346	+	9.14607i	0.0289623	+	0.292909i
$976$	11.8307	+	6.83046i	0.378692	+	0.218638i
$977$	−2.68788	+	10.0313i	−0.0859930	+	0.320930i	−0.995500	−	0.0947576i	$-0.969792\pi$
$977$	−2.68788	+	10.0313i	−0.0859930	+	0.320930i	0.909507	+	0.415688i	$0.136459\pi$
$978$		−	5.59884i		−	0.179031i
$979$	−17.8390	−	30.8980i	−0.570136	−	0.987505i
$980$	−14.5679	−	12.5570i	−0.465355	−	0.401118i
$981$	2.43579	−	9.09049i	0.0777688	−	0.290237i
$982$	−1.19140	−	4.44636i	−0.0380190	−	0.141889i
$983$	22.0157	−	5.89909i	0.702192	−	0.188152i	0.109980	−	0.993934i	$-0.464921\pi$
$983$	22.0157	−	5.89909i	0.702192	−	0.188152i	0.592212	+	0.805782i	$0.298255\pi$
$984$	−5.13031			−0.163548
$985$	31.2007			0.994136
$986$	7.06400	−	1.89279i	0.224964	−	0.0602788i
$987$	−18.1688	+	19.5657i	−0.578321	+	0.622782i
$988$	−0.233159	−	0.618770i	−0.00741778	−	0.0196857i
$989$	−0.904219	−	1.56615i	−0.0287525	−	0.0498008i
$990$	5.88521	+	1.57694i	0.187044	+	0.0501184i
$991$	−7.76780	−	13.4542i	−0.246752	−	0.427387i	0.715871	−	0.698233i	$-0.246030\pi$
$991$	−7.76780	−	13.4542i	−0.246752	−	0.427387i	−0.962623	+	0.270846i	$0.912697\pi$
$992$	3.91127	−	6.77452i	0.124183	−	0.215091i
$993$	−9.41790	+	9.41790i	−0.298868	+	0.298868i
$994$	9.47563	+	5.01286i	0.300549	+	0.158998i
$995$	−48.0485	−	12.8746i	−1.52324	−	0.408151i
$996$	−15.5173	−	4.15784i	−0.491683	−	0.131746i
$997$			7.87487i			0.249400i	0.992195	+	0.124700i	$0.0397968\pi$
$997$			7.87487i			0.249400i	−0.992195	+	0.124700i	$0.960203\pi$
$998$	10.9132	−	6.30073i	0.345451	−	0.199446i
$999$	0.909963	+	0.909963i	0.0287899	+	0.0287899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.241.10	yes	40
7.5	odd	6		546.2.by.b.397.10	✓	40
13.2	odd	12		546.2.by.b.535.10	yes	40
91.54	even	12	inner	546.2.cg.b.145.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.10	✓	40	7.5	odd	6
546.2.by.b.535.10	yes	40	13.2	odd	12
546.2.cg.b.145.10	yes	40	91.54	even	12	inner
546.2.cg.b.241.10	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(2.65393 + 0.711118i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.40673 + 2.24078i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(2.65393 + 0.711118i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.40673 + 2.24078i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.37378 + 2.37945i) q^{10} +(2.14199 + 0.573943i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.354780 - 3.58805i) q^{13} +(-0.589766 + 2.57918i) q^{14} +(-2.65393 + 0.711118i) q^{15} -1.00000 q^{16} -1.67627 q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.0474662 - 0.177146i) q^{19} +(-0.711118 + 2.65393i) q^{20} +(-2.33866 - 1.23721i) q^{21} +(1.10877 + 1.92045i) q^{22} +0.546143i q^{23} +(0.258819 - 0.965926i) q^{24} +(2.20753 + 1.27452i) q^{25} +(2.28627 - 2.78800i) q^{26} +1.00000i q^{27} +(-2.24078 + 1.40673i) q^{28} +(-2.18139 + 3.77828i) q^{29} +(-2.37945 - 1.37378i) q^{30} +(2.02462 + 7.55600i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.14199 + 0.573943i) q^{33} +(-1.18530 - 1.18530i) q^{34} +(2.13990 + 6.94723i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.909963 - 0.909963i) q^{37} +(0.0916976 - 0.158825i) q^{38} +(2.10128 + 2.92996i) q^{39} +(-2.37945 + 1.37378i) q^{40} +(-1.32782 - 4.95550i) q^{41} +(-0.778839 - 2.52852i) q^{42} +(-2.86766 + 1.65565i) q^{43} +(-0.573943 + 2.14199i) q^{44} +(1.94281 - 1.94281i) q^{45} +(-0.386181 + 0.386181i) q^{46} +(2.61197 - 9.74801i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.04223 + 6.30435i) q^{49} +(0.659739 + 2.46218i) q^{50} +(1.45169 - 0.838134i) q^{51} +(3.58805 - 0.354780i) q^{52} +(1.78093 - 3.08467i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(5.27654 + 3.04641i) q^{55} +(-2.57918 - 0.589766i) q^{56} +(0.129680 + 0.129680i) q^{57} +(-4.21412 + 1.12917i) q^{58} +(-1.05173 - 1.05173i) q^{59} +(-0.711118 - 2.65393i) q^{60} +(-11.8307 - 6.83046i) q^{61} +(-3.91127 + 6.77452i) q^{62} +(2.64394 - 0.0978714i) q^{63} -1.00000i q^{64} +(1.60997 - 9.77473i) q^{65} +(-1.92045 - 1.10877i) q^{66} +(-1.82429 + 6.80833i) q^{67} -1.67627i q^{68} +(-0.273071 - 0.472973i) q^{69} +(-3.39930 + 6.42557i) q^{70} +(1.04867 - 3.91368i) q^{71} +(0.258819 + 0.965926i) q^{72} +(8.57385 - 2.29736i) q^{73} +1.28688 q^{74} -2.54903 q^{75} +(0.177146 - 0.0474662i) q^{76} +(1.72711 + 5.60711i) q^{77} +(-0.585966 + 3.55762i) q^{78} +(4.42139 + 7.65808i) q^{79} +(-2.65393 - 0.711118i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.56516 - 4.44298i) q^{82} +(11.3594 - 11.3594i) q^{83} +(1.23721 - 2.33866i) q^{84} +(-4.44870 - 1.19203i) q^{85} +(-3.19846 - 0.857026i) q^{86} -4.36278i q^{87} +(-1.92045 + 1.10877i) q^{88} +(-11.3766 - 11.3766i) q^{89} +2.74755 q^{90} +(7.54097 - 5.84241i) q^{91} -0.546143 q^{92} +(-5.53137 - 5.53137i) q^{93} +(8.73983 - 5.04594i) q^{94} -0.503888i q^{95} +(0.965926 + 0.258819i) q^{96} +(15.6069 + 4.18186i) q^{97} +(-6.60903 + 2.30667i) q^{98} +(1.56804 - 1.56804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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