LMFDB - Embedded newform 630.2.bk.c.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.271725 + 1.71060i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.71060 - 0.271725i) q^{6} +(1.13531 + 2.38979i) q^{7} +1.00000i q^{8} +(-2.85233 + 0.929628i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.271725 + 1.71060i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.71060 - 0.271725i) q^{6} +(1.13531 + 2.38979i) q^{7} +1.00000i q^{8} +(-2.85233 + 0.929628i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-4.25650 + 2.45749i) q^{11} +(-0.271725 - 1.71060i) q^{12} +(-3.91899 + 2.26263i) q^{13} +(2.38979 - 1.13531i) q^{14} +(1.61729 + 0.619981i) q^{15} +1.00000 q^{16} +(-2.06626 + 3.57887i) q^{17} +(0.929628 + 2.85233i) q^{18} +(6.89368 - 3.98007i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.77948 + 2.59143i) q^{21} +(2.45749 + 4.25650i) q^{22} +(-4.36255 - 2.51872i) q^{23} +(-1.71060 + 0.271725i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.26263 + 3.91899i) q^{26} +(-2.36527 - 4.62661i) q^{27} +(-1.13531 - 2.38979i) q^{28} +(-2.46914 - 1.42556i) q^{29} +(0.619981 - 1.61729i) q^{30} +1.57993i q^{31} -1.00000i q^{32} +(-5.36039 - 6.61342i) q^{33} +(3.57887 + 2.06626i) q^{34} +(2.63727 + 0.211686i) q^{35} +(2.85233 - 0.929628i) q^{36} +(5.05807 + 8.76083i) q^{37} +(-3.98007 - 6.89368i) q^{38} +(-4.93536 - 6.08903i) q^{39} +(0.866025 + 0.500000i) q^{40} +(4.31484 + 7.47352i) q^{41} +(2.59143 + 3.77948i) q^{42} +(-2.88672 + 4.99995i) q^{43} +(4.25650 - 2.45749i) q^{44} +(-0.621084 + 2.93500i) q^{45} +(-2.51872 + 4.36255i) q^{46} +0.454165 q^{47} +(0.271725 + 1.71060i) q^{48} +(-4.42215 + 5.42629i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-6.68348 - 2.56208i) q^{51} +(3.91899 - 2.26263i) q^{52} +(10.7712 + 6.21874i) q^{53} +(-4.62661 + 2.36527i) q^{54} +4.91498i q^{55} +(-2.38979 + 1.13531i) q^{56} +(8.68150 + 10.7109i) q^{57} +(-1.42556 + 2.46914i) q^{58} -10.9647 q^{59} +(-1.61729 - 0.619981i) q^{60} -4.23073i q^{61} +1.57993 q^{62} +(-5.45989 - 5.76104i) q^{63} -1.00000 q^{64} +4.52526i q^{65} +(-6.61342 + 5.36039i) q^{66} +3.93207 q^{67} +(2.06626 - 3.57887i) q^{68} +(3.12312 - 8.14699i) q^{69} +(0.211686 - 2.63727i) q^{70} -8.14278i q^{71} +(-0.929628 - 2.85233i) q^{72} +(2.06838 + 1.19418i) q^{73} +(8.76083 - 5.05807i) q^{74} +(1.34556 - 1.09062i) q^{75} +(-6.89368 + 3.98007i) q^{76} +(-10.7053 - 7.38211i) q^{77} +(-6.08903 + 4.93536i) q^{78} +9.72934 q^{79} +(0.500000 - 0.866025i) q^{80} +(7.27159 - 5.30321i) q^{81} +(7.47352 - 4.31484i) q^{82} +(1.42589 - 2.46971i) q^{83} +(3.77948 - 2.59143i) q^{84} +(2.06626 + 3.57887i) q^{85} +(4.99995 + 2.88672i) q^{86} +(1.76764 - 4.61108i) q^{87} +(-2.45749 - 4.25650i) q^{88} +(-2.95275 - 5.11432i) q^{89} +(2.93500 + 0.621084i) q^{90} +(-9.85647 - 6.79677i) q^{91} +(4.36255 + 2.51872i) q^{92} +(-2.70263 + 0.429305i) q^{93} -0.454165i q^{94} -7.96013i q^{95} +(1.71060 - 0.271725i) q^{96} +(-1.74470 - 1.00730i) q^{97} +(5.42629 + 4.42215i) q^{98} +(9.85639 - 10.9665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.271725	+	1.71060i	0.156880	+	0.987618i
$3$	0.271725	+	1.71060i	0.156880	+	0.987618i
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.71060	−	0.271725i	0.698351	−	0.110931i
$7$	1.13531	+	2.38979i	0.429106	+	0.903254i
$7$	1.13531	+	2.38979i	0.429106	+	0.903254i
$8$			1.00000i			0.353553i
$9$	−2.85233	+	0.929628i	−0.950777	+	0.309876i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−4.25650	+	2.45749i	−1.28338	+	0.740961i	−0.977465	−	0.211097i	$-0.932297\pi$
$11$	−4.25650	+	2.45749i	−1.28338	+	0.740961i	−0.305918	+	0.952058i	$0.598963\pi$
$12$	−0.271725	−	1.71060i	−0.0784402	−	0.493809i
$13$	−3.91899	+	2.26263i	−1.08693	+	0.627541i	−0.932758	−	0.360502i	$-0.882605\pi$
$13$	−3.91899	+	2.26263i	−1.08693	+	0.627541i	−0.154175	+	0.988044i	$0.549272\pi$
$14$	2.38979	−	1.13531i	0.638697	−	0.303424i
$15$	1.61729	+	0.619981i	0.417582	+	0.160078i
$16$	1.00000			0.250000
$17$	−2.06626	+	3.57887i	−0.501142	+	0.868003i	0.498857	+	0.866684i	$0.333753\pi$
$17$	−2.06626	+	3.57887i	−0.501142	+	0.868003i	−0.999999	+	0.00131881i	$0.999580\pi$
$18$	0.929628	+	2.85233i	0.219115	+	0.672301i
$19$	6.89368	−	3.98007i	1.58152	−	0.913090i	0.586880	−	0.809674i	$-0.300356\pi$
$19$	6.89368	−	3.98007i	1.58152	−	0.913090i	0.994638	−	0.103416i	$-0.0329772\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−3.77948	+	2.59143i	−0.824751	+	0.565496i
$22$	2.45749	+	4.25650i	0.523939	+	0.907489i
$23$	−4.36255	−	2.51872i	−0.909654	−	0.525189i	−0.0293343	−	0.999570i	$-0.509339\pi$
$23$	−4.36255	−	2.51872i	−0.909654	−	0.525189i	−0.880320	+	0.474381i	$0.842672\pi$
$24$	−1.71060	+	0.271725i	−0.349176	+	0.0554656i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.26263	+	3.91899i	0.443739	+	0.768578i
$27$	−2.36527	−	4.62661i	−0.455197	−	0.890391i
$28$	−1.13531	−	2.38979i	−0.214553	−	0.451627i
$29$	−2.46914	−	1.42556i	−0.458508	−	0.264720i	0.252909	−	0.967490i	$-0.418613\pi$
$29$	−2.46914	−	1.42556i	−0.458508	−	0.264720i	−0.711417	+	0.702770i	$0.751946\pi$
$30$	0.619981	−	1.61729i	0.113193	−	0.295275i
$31$			1.57993i			0.283763i	0.989884	+	0.141882i	$0.0453152\pi$
$31$			1.57993i			0.283763i	−0.989884	+	0.141882i	$0.954685\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.36039	−	6.61342i	−0.933124	−	1.15125i
$34$	3.57887	+	2.06626i	0.613771	+	0.354361i
$35$	2.63727	+	0.211686i	0.445780	+	0.0357815i
$36$	2.85233	−	0.929628i	0.475389	−	0.154938i
$37$	5.05807	+	8.76083i	0.831541	+	1.44027i	0.896816	+	0.442404i	$0.145874\pi$
$37$	5.05807	+	8.76083i	0.831541	+	1.44027i	−0.0652749	+	0.997867i	$0.520792\pi$
$38$	−3.98007	−	6.89368i	−0.645652	−	1.11830i
$39$	−4.93536	−	6.08903i	−0.790289	−	0.975026i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	4.31484	+	7.47352i	0.673865	+	1.16717i	0.976799	+	0.214156i	$0.0687002\pi$
$41$	4.31484	+	7.47352i	0.673865	+	1.16717i	−0.302935	+	0.953011i	$0.597966\pi$
$42$	2.59143	+	3.77948i	0.399866	+	0.583187i
$43$	−2.88672	+	4.99995i	−0.440221	+	0.762486i	−0.997706	−	0.0677018i	$-0.978433\pi$
$43$	−2.88672	+	4.99995i	−0.440221	+	0.762486i	0.557484	+	0.830187i	$0.311767\pi$
$44$	4.25650	−	2.45749i	0.641691	−	0.370481i
$45$	−0.621084	+	2.93500i	−0.0925858	+	0.437525i
$46$	−2.51872	+	4.36255i	−0.371365	+	0.643223i
$47$	0.454165			0.0662468			0.0331234	−	0.999451i	$-0.489455\pi$
$47$	0.454165			0.0662468			0.0331234	+	0.999451i	$0.489455\pi$
$48$	0.271725	+	1.71060i	0.0392201	+	0.246904i
$49$	−4.42215	+	5.42629i	−0.631735	+	0.775184i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−6.68348	−	2.56208i	−0.935874	−	0.358764i
$52$	3.91899	−	2.26263i	0.543467	−	0.313771i
$53$	10.7712	+	6.21874i	1.47953	+	0.854209i	0.999732	−	0.0231676i	$-0.00737512\pi$
$53$	10.7712	+	6.21874i	1.47953	+	0.854209i	0.479802	+	0.877377i	$0.340708\pi$
$54$	−4.62661	+	2.36527i	−0.629601	+	0.321873i
$55$			4.91498i			0.662736i
$56$	−2.38979	+	1.13531i	−0.319349	+	0.151712i
$57$	8.68150	+	10.7109i	1.14989	+	1.41869i
$58$	−1.42556	+	2.46914i	−0.187185	+	0.324214i
$59$	−10.9647			−1.42749			−0.713744	−	0.700407i	$-0.753002\pi$
$59$	−10.9647			−1.42749			−0.713744	+	0.700407i	$0.753002\pi$
$60$	−1.61729	−	0.619981i	−0.208791	−	0.0800392i
$61$		−	4.23073i		−	0.541690i	−0.962623	−	0.270845i	$-0.912697\pi$
$61$		−	4.23073i		−	0.541690i	0.962623	−	0.270845i	$-0.0873031\pi$
$62$	1.57993			0.200651
$63$	−5.45989	−	5.76104i	−0.687881	−	0.725823i
$64$	−1.00000			−0.125000
$65$			4.52526i			0.561290i
$66$	−6.61342	+	5.36039i	−0.814056	+	0.659818i
$67$	3.93207			0.480379			0.240189	−	0.970726i	$-0.422790\pi$
$67$	3.93207			0.480379			0.240189	+	0.970726i	$0.422790\pi$
$68$	2.06626	−	3.57887i	0.250571	−	0.434001i
$69$	3.12312	−	8.14699i	0.375979	−	0.980782i
$70$	0.211686	−	2.63727i	0.0253014	−	0.315214i
$71$		−	8.14278i		−	0.966371i	−0.875518	−	0.483185i	$-0.839480\pi$
$71$		−	8.14278i		−	0.966371i	0.875518	−	0.483185i	$-0.160520\pi$
$72$	−0.929628	−	2.85233i	−0.109558	−	0.336150i
$73$	2.06838	+	1.19418i	0.242086	+	0.139768i	0.616135	−	0.787641i	$-0.288698\pi$
$73$	2.06838	+	1.19418i	0.242086	+	0.139768i	−0.374049	+	0.927409i	$0.622031\pi$
$74$	8.76083	−	5.05807i	1.01843	−	0.587988i
$75$	1.34556	−	1.09062i	0.155372	−	0.125934i
$76$	−6.89368	+	3.98007i	−0.790759	+	0.456545i
$77$	−10.7053	−	7.38211i	−1.21998	−	0.841269i
$78$	−6.08903	+	4.93536i	−0.689447	+	0.558819i
$79$	9.72934			1.09464			0.547318	−	0.836925i	$-0.315649\pi$
$79$	9.72934			1.09464			0.547318	+	0.836925i	$0.315649\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	7.27159	−	5.30321i	0.807954	−	0.589246i
$82$	7.47352	−	4.31484i	0.825312	−	0.476494i
$83$	1.42589	−	2.46971i	0.156512	−	0.271086i	−0.777097	−	0.629381i	$-0.783309\pi$
$83$	1.42589	−	2.46971i	0.156512	−	0.271086i	0.933608	+	0.358295i	$0.116642\pi$
$84$	3.77948	−	2.59143i	0.412376	−	0.282748i
$85$	2.06626	+	3.57887i	0.224117	+	0.388183i
$86$	4.99995	+	2.88672i	0.539159	+	0.311283i
$87$	1.76764	−	4.61108i	0.189511	−	0.494360i
$88$	−2.45749	−	4.25650i	−0.261969	−	0.453744i
$89$	−2.95275	−	5.11432i	−0.312991	−	0.542117i	0.666017	−	0.745936i	$-0.267998\pi$
$89$	−2.95275	−	5.11432i	−0.312991	−	0.542117i	−0.979008	+	0.203820i	$0.934664\pi$
$90$	2.93500	+	0.621084i	0.309377	+	0.0654680i
$91$	−9.85647	−	6.79677i	−1.03324	−	0.712495i
$92$	4.36255	+	2.51872i	0.454827	+	0.262595i
$93$	−2.70263	+	0.429305i	−0.280249	+	0.0445169i
$94$		−	0.454165i		−	0.0468436i
$95$		−	7.96013i		−	0.816692i
$96$	1.71060	−	0.271725i	0.174588	−	0.0277328i
$97$	−1.74470	−	1.00730i	−0.177147	−	0.102276i	0.408805	−	0.912622i	$-0.365946\pi$
$97$	−1.74470	−	1.00730i	−0.177147	−	0.102276i	−0.585952	+	0.810346i	$0.699279\pi$
$98$	5.42629	+	4.42215i	0.548138	+	0.446704i
$99$	9.85639	−	10.9665i	0.990605	−	1.10218i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.23553	−	5.60410i	−0.321947	−	0.557629i	0.658942	−	0.752193i	$-0.271004\pi$
$101$	−3.23553	−	5.60410i	−0.321947	−	0.557629i	−0.980890	+	0.194564i	$0.937671\pi$
$102$	−2.56208	+	6.68348i	−0.253684	+	0.661763i
$103$	3.56161	+	2.05630i	0.350936	+	0.202613i	0.665097	−	0.746757i	$-0.268390\pi$
$103$	3.56161	+	2.05630i	0.350936	+	0.202613i	−0.314161	+	0.949370i	$0.601723\pi$
$104$	−2.26263	−	3.91899i	−0.221869	−	0.384289i
$105$	0.354500	+	4.56884i	0.0345957	+	0.445873i
$106$	6.21874	−	10.7712i	0.604017	−	1.04619i
$107$	10.8227	−	6.24846i	1.04627	−	0.604061i	0.124664	−	0.992199i	$-0.460215\pi$
$107$	10.8227	−	6.24846i	1.04627	−	0.604061i	0.921601	+	0.388138i	$0.126881\pi$
$108$	2.36527	+	4.62661i	0.227599	+	0.445195i
$109$	−6.80795	+	11.7917i	−0.652083	+	1.12944i	0.330533	+	0.943794i	$0.392771\pi$
$109$	−6.80795	+	11.7917i	−0.652083	+	1.12944i	−0.982617	+	0.185647i	$0.940562\pi$
$110$	4.91498			0.468625
$111$	−13.6119	+	11.0329i	−1.29198	+	1.04719i
$112$	1.13531	+	2.38979i	0.107277	+	0.225813i
$113$	14.5943	−	8.42603i	1.37292	−	0.792655i	0.381623	−	0.924318i	$-0.375365\pi$
$113$	14.5943	−	8.42603i	1.37292	−	0.792655i	0.991294	+	0.131663i	$0.0420318\pi$
$114$	10.7109	−	8.68150i	1.00316	−	0.813097i
$115$	−4.36255	+	2.51872i	−0.406810	+	0.234872i
$116$	2.46914	+	1.42556i	0.229254	+	0.132360i
$117$	9.07486	−	10.0970i	0.838971	−	0.933466i
$118$			10.9647i			1.00939i
$119$	−10.8986	−	0.874799i	−0.999070	−	0.0801927i
$120$	−0.619981	+	1.61729i	−0.0565963	+	0.147638i
$121$	6.57852	−	11.3943i	0.598048	−	1.03585i
$122$	−4.23073			−0.383033
$123$	−11.6118	+	9.41172i	−1.04700	+	0.848626i
$124$		−	1.57993i		−	0.141882i
$125$	−1.00000			−0.0894427
$126$	−5.76104	+	5.45989i	−0.513235	+	0.486405i
$127$	10.8636			0.963991			0.481996	−	0.876174i	$-0.339912\pi$
$127$	10.8636			0.963991			0.481996	+	0.876174i	$0.339912\pi$
$128$			1.00000i			0.0883883i
$129$	−9.33733	−	3.57943i	−0.822106	−	0.315151i
$130$	4.52526			0.396892
$131$	−2.32978	+	4.03530i	−0.203554	+	0.352566i	−0.949671	−	0.313249i	$-0.898583\pi$
$131$	−2.32978	+	4.03530i	−0.203554	+	0.352566i	0.746117	+	0.665815i	$0.231916\pi$
$132$	5.36039	+	6.61342i	0.466562	+	0.575624i
$133$	17.3380	+	11.9558i	1.50339	+	1.03670i
$134$		−	3.93207i		−	0.339679i
$135$	−5.18939	−	0.264915i	−0.446632	−	0.0228003i
$136$	−3.57887	−	2.06626i	−0.306885	−	0.177180i
$137$	8.58373	−	4.95582i	0.733357	−	0.423404i	−0.0862918	−	0.996270i	$-0.527502\pi$
$137$	8.58373	−	4.95582i	0.733357	−	0.423404i	0.819649	+	0.572866i	$0.194168\pi$
$138$	−8.14699	−	3.12312i	−0.693518	−	0.265857i
$139$	−0.175478	+	0.101312i	−0.0148838	+	0.00859319i	−0.507423	−	0.861697i	$-0.669402\pi$
$139$	−0.175478	+	0.101312i	−0.0148838	+	0.00859319i	0.492540	+	0.870290i	$0.336069\pi$
$140$	−2.63727	−	0.211686i	−0.222890	−	0.0178908i
$141$	0.123408	+	0.776897i	0.0103928	+	0.0654265i
$142$	−8.14278			−0.683327
$143$	11.1208	−	19.2618i	0.929968	−	1.61075i
$144$	−2.85233	+	0.929628i	−0.237694	+	0.0774690i
$145$	−2.46914	+	1.42556i	−0.205051	+	0.118386i
$146$	1.19418	−	2.06838i	0.0988311	−	0.171181i
$147$	−10.4838	−	6.09009i	−0.864692	−	0.502302i
$148$	−5.05807	−	8.76083i	−0.415770	−	0.720136i
$149$	−2.59913	−	1.50061i	−0.212929	−	0.122935i	0.389743	−	0.920924i	$-0.372564\pi$
$149$	−2.59913	−	1.50061i	−0.212929	−	0.122935i	−0.602672	+	0.797989i	$0.705897\pi$
$150$	−1.09062	−	1.34556i	−0.0890490	−	0.109865i
$151$	9.86662	+	17.0895i	0.802935	+	1.39072i	0.917677	+	0.397328i	$0.130062\pi$
$151$	9.86662	+	17.0895i	0.802935	+	1.39072i	−0.114742	+	0.993395i	$0.536604\pi$
$152$	3.98007	+	6.89368i	0.322826	+	0.559151i
$153$	2.56664	−	12.1290i	0.207501	−	0.980569i
$154$	−7.38211	+	10.7053i	−0.594867	+	0.862659i
$155$	1.36826	+	0.789963i	0.109901	+	0.0634514i
$156$	4.93536	+	6.08903i	0.395145	+	0.487513i
$157$			8.43694i			0.673341i	0.941622	+	0.336671i	$0.109301\pi$
$157$			8.43694i			0.673341i	−0.941622	+	0.336671i	$0.890699\pi$
$158$		−	9.72934i		−	0.774025i
$159$	−7.71100	+	20.1150i	−0.611522	+	1.59522i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	1.06636	−	13.2851i	0.0840407	−	1.04701i
$162$	−5.30321	−	7.27159i	−0.416660	−	0.571310i
$163$	−6.64195	−	11.5042i	−0.520238	−	0.901079i	−0.999723	−	0.0235286i	$-0.992510\pi$
$163$	−6.64195	−	11.5042i	−0.520238	−	0.901079i	0.479485	−	0.877550i	$-0.340823\pi$
$164$	−4.31484	−	7.47352i	−0.336932	−	0.583584i
$165$	−8.40759	+	1.33552i	−0.654530	+	0.103970i
$166$	−2.46971	−	1.42589i	−0.191687	−	0.110670i
$167$	8.15100	+	14.1179i	0.630743	+	1.09248i	0.987400	+	0.158243i	$0.0505831\pi$
$167$	8.15100	+	14.1179i	0.630743	+	1.09248i	−0.356657	+	0.934235i	$0.616084\pi$
$168$	−2.59143	−	3.77948i	−0.199933	−	0.291594i
$169$	3.73901	−	6.47616i	0.287616	−	0.498166i
$170$	3.57887	−	2.06626i	0.274487	−	0.158475i
$171$	−15.9631	+	17.7610i	−1.22073	+	1.35822i
$172$	2.88672	−	4.99995i	0.220111	−	0.381243i
$173$	−21.2103			−1.61259			−0.806295	−	0.591514i	$-0.798530\pi$
$173$	−21.2103			−1.61259			−0.806295	+	0.591514i	$0.798530\pi$
$174$	−4.61108	−	1.76764i	−0.349565	−	0.134004i
$175$	1.50196	−	2.17810i	0.113538	−	0.164649i
$176$	−4.25650	+	2.45749i	−0.320846	+	0.185240i
$177$	−2.97939	−	18.7563i	−0.223945	−	1.40981i
$178$	−5.11432	+	2.95275i	−0.383334	+	0.221318i
$179$	−2.93274	−	1.69322i	−0.219203	−	0.126557i	0.386378	−	0.922341i	$-0.373726\pi$
$179$	−2.93274	−	1.69322i	−0.219203	−	0.126557i	−0.605581	+	0.795783i	$0.707059\pi$
$180$	0.621084	−	2.93500i	0.0462929	−	0.218762i
$181$		−	4.99826i		−	0.371517i	−0.982595	−	0.185759i	$-0.940526\pi$
$181$		−	4.99826i		−	0.371517i	0.982595	−	0.185759i	$-0.0594743\pi$
$182$	−6.79677	+	9.85647i	−0.503810	+	0.730610i
$183$	7.23711	−	1.14960i	0.534983	−	0.0849806i
$184$	2.51872	−	4.36255i	0.185682	−	0.321611i
$185$	10.1161			0.743753
$186$	0.429305	+	2.70263i	0.0314782	+	0.198166i
$187$		−	20.3113i		−	1.48531i
$188$	−0.454165			−0.0331234
$189$	8.37128	−	10.9051i	0.608921	−	0.793231i
$190$	−7.96013			−0.577489
$191$			5.72419i			0.414188i	0.978321	+	0.207094i	$0.0664005\pi$
$191$			5.72419i			0.414188i	−0.978321	+	0.207094i	$0.933599\pi$
$192$	−0.271725	−	1.71060i	−0.0196101	−	0.123452i
$193$	5.40313			0.388926			0.194463	−	0.980910i	$-0.437704\pi$
$193$	5.40313			0.388926			0.194463	+	0.980910i	$0.437704\pi$
$194$	−1.00730	+	1.74470i	−0.0723200	+	0.125262i
$195$	−7.74094	+	1.22963i	−0.554340	+	0.0880555i
$196$	4.42215	−	5.42629i	0.315868	−	0.387592i
$197$			12.5138i			0.891571i	0.895140	+	0.445786i	$0.147076\pi$
$197$			12.5138i			0.891571i	−0.895140	+	0.445786i	$0.852924\pi$
$198$	−10.9665	−	9.85639i	−0.779358	−	0.700463i
$199$	−15.4969	−	8.94715i	−1.09855	−	0.634247i	−0.162708	−	0.986674i	$-0.552023\pi$
$199$	−15.4969	−	8.94715i	−1.09855	−	0.634247i	−0.935839	+	0.352428i	$0.885356\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	1.06844	+	6.72621i	0.0753621	+	0.474431i
$202$	−5.60410	+	3.23553i	−0.394303	+	0.227651i
$203$	0.603543	−	7.51917i	0.0423604	−	0.527742i
$204$	6.68348	+	2.56208i	0.467937	+	0.179382i
$205$	8.62968			0.602723
$206$	2.05630	−	3.56161i	0.143269	−	0.248149i
$207$	14.7849	+	3.12867i	1.02762	+	0.217458i
$208$	−3.91899	+	2.26263i	−0.271733	+	0.156885i
$209$	−19.5620	+	33.8823i	−1.35313	+	2.34369i
$210$	4.56884	−	0.354500i	0.315280	−	0.0244628i
$211$	−8.73086	−	15.1223i	−0.601057	−	1.04106i	−0.992661	−	0.120928i	$-0.961413\pi$
$211$	−8.73086	−	15.1223i	−0.601057	−	1.04106i	0.391604	−	0.920134i	$-0.371920\pi$
$212$	−10.7712	−	6.21874i	−0.739767	−	0.427105i
$213$	13.9291	−	2.21260i	0.954405	−	0.151605i
$214$	−6.24846	−	10.8227i	−0.427136	−	0.739821i
$215$	2.88672	+	4.99995i	0.196873	+	0.340994i
$216$	4.62661	−	2.36527i	0.314801	−	0.160937i
$217$	−3.77568	+	1.79370i	−0.256310	+	0.121765i
$218$	11.7917	+	6.80795i	0.798636	+	0.461092i
$219$	−1.48074	+	3.86267i	−0.100059	+	0.261015i
$220$		−	4.91498i		−	0.331368i
$221$		−	18.7007i		−	1.25795i
$222$	11.0329	+	13.6119i	0.740479	+	0.913571i
$223$	−9.84741	−	5.68541i	−0.659431	−	0.380723i	0.132629	−	0.991166i	$-0.457658\pi$
$223$	−9.84741	−	5.68541i	−0.659431	−	0.380723i	−0.792060	+	0.610443i	$0.790992\pi$
$224$	2.38979	−	1.13531i	0.159674	−	0.0758560i
$225$	2.23125	+	2.00538i	0.148750	+	0.133692i
$226$	−8.42603	−	14.5943i	−0.560491	−	0.970800i
$227$	−3.54296	−	6.13659i	−0.235155	−	0.407300i	0.724163	−	0.689629i	$-0.242226\pi$
$227$	−3.54296	−	6.13659i	−0.235155	−	0.407300i	−0.959318	+	0.282329i	$0.908893\pi$
$228$	−8.68150	−	10.7109i	−0.574946	−	0.709344i
$229$	−2.64487	−	1.52702i	−0.174778	−	0.100908i	0.410059	−	0.912059i	$-0.365508\pi$
$229$	−2.64487	−	1.52702i	−0.174778	−	0.100908i	−0.584837	+	0.811151i	$0.698841\pi$
$230$	2.51872	+	4.36255i	0.166079	+	0.287658i
$231$	9.71896	−	20.3185i	0.639461	−	1.33686i
$232$	1.42556	−	2.46914i	0.0935925	−	0.162107i
$233$	−18.5443	+	10.7066i	−1.21488	+	0.701410i	−0.963818	−	0.266562i	$-0.914112\pi$
$233$	−18.5443	+	10.7066i	−1.21488	+	0.701410i	−0.251060	+	0.967972i	$0.580779\pi$
$234$	−10.0970	−	9.07486i	−0.660060	−	0.593242i
$235$	0.227083	−	0.393319i	0.0148132	−	0.0256573i
$236$	10.9647			0.713744
$237$	2.64370	+	16.6430i	0.171727	+	1.08108i
$238$	−0.874799	+	10.8986i	−0.0567048	+	0.706449i
$239$	−15.7328	+	9.08336i	−1.01767	+	0.587554i	−0.913429	−	0.406998i	$-0.866576\pi$
$239$	−15.7328	+	9.08336i	−1.01767	+	0.587554i	−0.104244	+	0.994552i	$0.533242\pi$
$240$	1.61729	+	0.619981i	0.104396	+	0.0400196i
$241$	18.0606	−	10.4273i	1.16339	−	0.671681i	0.211273	−	0.977427i	$-0.432239\pi$
$241$	18.0606	−	10.4273i	1.16339	−	0.671681i	0.952113	+	0.305746i	$0.0989057\pi$
$242$	−11.3943	−	6.57852i	−0.732456	−	0.422883i
$243$	11.0476	+	10.9978i	0.708702	+	0.705508i
$244$			4.23073i			0.270845i
$245$	2.48823	+	6.54284i	0.158967	+	0.418007i
$246$	9.41172	+	11.6118i	0.600069	+	0.740340i
$247$	−18.0109	+	31.1957i	−1.14600	+	1.98494i
$248$	−1.57993			−0.100325
$249$	4.61214	+	1.76805i	0.292283	+	0.112045i
$250$			1.00000i			0.0632456i
$251$	27.8633			1.75872			0.879359	−	0.476159i	$-0.157971\pi$
$251$	27.8633			1.75872			0.879359	+	0.476159i	$0.157971\pi$
$252$	5.45989	+	5.76104i	0.343941	+	0.362912i
$253$	24.7589			1.55658
$254$		−	10.8636i		−	0.681645i
$255$	−5.56057	+	4.50702i	−0.348216	+	0.282241i
$256$	1.00000			0.0625000
$257$	−8.50350	+	14.7285i	−0.530433	+	0.918738i	0.468936	+	0.883232i	$0.344637\pi$
$257$	−8.50350	+	14.7285i	−0.530433	+	0.918738i	−0.999369	+	0.0355056i	$0.988696\pi$
$258$	−3.57943	+	9.33733i	−0.222846	+	0.581317i
$259$	−15.1940	+	22.0339i	−0.944111	+	1.36912i
$260$		−	4.52526i		−	0.280645i
$261$	8.36805	+	1.77079i	0.517969	+	0.109609i
$262$	4.03530	+	2.32978i	0.249302	+	0.143934i
$263$	2.65664	−	1.53381i	0.163816	−	0.0945791i	−0.415851	−	0.909433i	$-0.636516\pi$
$263$	2.65664	−	1.53381i	0.163816	−	0.0945791i	0.579667	+	0.814854i	$0.303183\pi$
$264$	6.61342	−	5.36039i	0.407028	−	0.329909i
$265$	10.7712	−	6.21874i	0.661668	−	0.382014i
$266$	11.9558	−	17.3380i	0.733057	−	1.06306i
$267$	7.94624	−	6.44068i	0.486302	−	0.394163i
$268$	−3.93207			−0.240189
$269$	3.48949	−	6.04397i	0.212758	−	0.368507i	−0.739819	−	0.672806i	$-0.765089\pi$
$269$	3.48949	−	6.04397i	0.212758	−	0.368507i	0.952577	+	0.304299i	$0.0984222\pi$
$270$	−0.264915	+	5.18939i	−0.0161222	+	0.315817i
$271$	1.95182	−	1.12689i	0.118565	−	0.0684534i	−0.439545	−	0.898221i	$-0.644860\pi$
$271$	1.95182	−	1.12689i	0.118565	−	0.0684534i	0.558110	+	0.829767i	$0.311527\pi$
$272$	−2.06626	+	3.57887i	−0.125285	+	0.217001i
$273$	8.94833	−	18.7074i	0.541577	−	1.13222i
$274$	−4.95582	−	8.58373i	−0.299392	−	0.518562i
$275$	4.25650	+	2.45749i	0.256677	+	0.148192i
$276$	−3.12312	+	8.14699i	−0.187989	+	0.490391i
$277$	14.1503	+	24.5090i	0.850208	+	1.47260i	0.881021	+	0.473077i	$0.156857\pi$
$277$	14.1503	+	24.5090i	0.850208	+	1.47260i	−0.0308133	+	0.999525i	$0.509810\pi$
$278$	0.101312	+	0.175478i	0.00607631	+	0.0105245i
$279$	−1.46874	−	4.50647i	−0.0879314	−	0.269795i
$280$	−0.211686	+	2.63727i	−0.0126507	+	0.157607i
$281$	10.7190	+	6.18859i	0.639439	+	0.369180i	0.784399	−	0.620257i	$-0.212972\pi$
$281$	10.7190	+	6.18859i	0.639439	+	0.369180i	−0.144959	+	0.989438i	$0.546305\pi$
$282$	0.776897	−	0.123408i	0.0462635	−	0.00734884i
$283$		−	21.6617i		−	1.28765i	−0.765171	−	0.643827i	$-0.777346\pi$
$283$		−	21.6617i		−	1.28765i	0.765171	−	0.643827i	$-0.222654\pi$
$284$			8.14278i			0.483185i
$285$	13.6166	−	2.16297i	0.806580	−	0.128123i
$286$	−19.2618	−	11.1208i	−1.13897	−	0.657586i
$287$	−12.9614	+	18.7963i	−0.765089	+	1.10951i
$288$	0.929628	+	2.85233i	0.0547788	+	0.168075i
$289$	−0.0388616	−	0.0673103i	−0.00228598	−	0.00395943i
$290$	1.42556	+	2.46914i	0.0837117	+	0.144993i
$291$	1.24901	−	3.25819i	0.0732185	−	0.190999i
$292$	−2.06838	−	1.19418i	−0.121043	−	0.0698842i
$293$	1.38901	+	2.40584i	0.0811469	+	0.140551i	0.903743	−	0.428076i	$-0.140808\pi$
$293$	1.38901	+	2.40584i	0.0811469	+	0.140551i	−0.822596	+	0.568626i	$0.807475\pi$
$294$	−6.09009	+	10.4838i	−0.355181	+	0.611430i
$295$	−5.48237	+	9.49575i	−0.319196	+	0.552864i
$296$	−8.76083	+	5.05807i	−0.509213	+	0.293994i
$297$	21.4376	+	13.8805i	1.24394	+	0.805428i
$298$	−1.50061	+	2.59913i	−0.0869279	+	0.150564i
$299$	22.7957			1.31831
$300$	−1.34556	+	1.09062i	−0.0776862	+	0.0629671i
$301$	−15.2261	−	1.22216i	−0.877620	−	0.0704442i
$302$	17.0895	−	9.86662i	0.983390	−	0.567760i
$303$	8.70723	−	7.05749i	0.500217	−	0.405442i
$304$	6.89368	−	3.98007i	0.395379	−	0.228272i
$305$	−3.66392	−	2.11537i	−0.209796	−	0.121126i
$306$	−12.1290	−	2.56664i	−0.693367	−	0.146725i
$307$			3.67227i			0.209588i	0.994494	+	0.104794i	$0.0334183\pi$
$307$			3.67227i			0.209588i	−0.994494	+	0.104794i	$0.966582\pi$
$308$	10.7053	+	7.38211i	0.609992	+	0.420635i
$309$	−2.54973	+	6.65125i	−0.145049	+	0.378377i
$310$	0.789963	−	1.36826i	0.0448669	−	0.0777117i
$311$	7.33384			0.415864			0.207932	−	0.978143i	$-0.433327\pi$
$311$	7.33384			0.415864			0.207932	+	0.978143i	$0.433327\pi$
$312$	6.08903	−	4.93536i	0.344724	−	0.279410i
$313$			28.5812i			1.61551i	0.589521	+	0.807753i	$0.299317\pi$
$313$			28.5812i			1.61551i	−0.589521	+	0.807753i	$0.700683\pi$
$314$	8.43694			0.476124
$315$	−7.71915	+	1.84788i	−0.434925	+	0.104116i
$316$	−9.72934			−0.547318
$317$			6.74081i			0.378602i	0.981919	+	0.189301i	$0.0606221\pi$
$317$			6.74081i			0.378602i	−0.981919	+	0.189301i	$0.939378\pi$
$318$	20.1150	+	7.71100i	1.12799	+	0.432411i
$319$	14.0132			0.784588
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	13.6294	+	16.8154i	0.760720	+	0.938544i
$322$	−13.2851	−	1.06636i	−0.740348	−	0.0594258i
$323$			32.8954i			1.83035i
$324$	−7.27159	+	5.30321i	−0.403977	+	0.294623i
$325$	3.91899	+	2.26263i	0.217387	+	0.125508i
$326$	−11.5042	+	6.64195i	−0.637159	+	0.367864i
$327$	−22.0208	−	8.44160i	−1.21776	−	0.466822i
$328$	−7.47352	+	4.31484i	−0.412656	+	0.238247i
$329$	0.515618	+	1.08536i	0.0284269	+	0.0598377i
$330$	1.33552	+	8.40759i	0.0735181	+	0.462822i
$331$	−28.8227			−1.58424			−0.792119	−	0.610367i	$-0.791022\pi$
$331$	−28.8227			−1.58424			−0.792119	+	0.610367i	$0.791022\pi$
$332$	−1.42589	+	2.46971i	−0.0782558	+	0.135543i
$333$	−22.5716	−	20.2867i	−1.23692	−	1.11170i
$334$	14.1179	−	8.15100i	0.772499	−	0.446003i
$335$	1.96604	−	3.40527i	0.107416	−	0.186050i
$336$	−3.77948	+	2.59143i	−0.206188	+	0.141374i
$337$	12.0913	+	20.9427i	0.658652	+	1.14082i	0.980965	+	0.194186i	$0.0622065\pi$
$337$	12.0913	+	20.9427i	0.658652	+	1.14082i	−0.322312	+	0.946633i	$0.604460\pi$
$338$	−6.47616	−	3.73901i	−0.352256	−	0.203375i
$339$	18.3792	+	22.6755i	0.998224	+	1.23157i
$340$	−2.06626	−	3.57887i	−0.112059	−	0.194091i
$341$	−3.88265	−	6.72496i	−0.210258	−	0.364177i
$342$	17.7610	+	15.9631i	0.960406	+	0.863184i
$343$	−17.9882	−	4.40747i	−0.971270	−	0.237981i
$344$	−4.99995	−	2.88672i	−0.269579	−	0.155642i
$345$	−5.49394	−	6.77819i	−0.295784	−	0.364926i
$346$			21.2103i			1.14027i
$347$		−	17.4312i		−	0.935754i	−0.883794	−	0.467877i	$-0.845019\pi$
$347$		−	17.4312i		−	0.935754i	0.883794	−	0.467877i	$-0.154981\pi$
$348$	−1.76764	+	4.61108i	−0.0947554	+	0.247180i
$349$	−31.4274	−	18.1446i	−1.68227	−	0.971259i	−0.960148	−	0.279493i	$-0.909834\pi$
$349$	−31.4274	−	18.1446i	−1.68227	−	0.971259i	−0.722122	−	0.691766i	$-0.756833\pi$
$350$	−2.17810	−	1.50196i	−0.116424	−	0.0802832i
$351$	19.7378	+	12.7799i	1.05353	+	0.682140i
$352$	2.45749	+	4.25650i	0.130985	+	0.226872i
$353$	10.8756	+	18.8372i	0.578852	+	1.00260i	0.995611	+	0.0935846i	$0.0298325\pi$
$353$	10.8756	+	18.8372i	0.578852	+	1.00260i	−0.416759	+	0.909017i	$0.636834\pi$
$354$	−18.7563	+	2.97939i	−0.996888	+	0.158353i
$355$	−7.05186	−	4.07139i	−0.374274	−	0.216087i
$356$	2.95275	+	5.11432i	0.156496	+	0.271058i
$357$	−1.46498	−	18.8808i	−0.0775349	−	0.999280i
$358$	−1.69322	+	2.93274i	−0.0894894	+	0.155000i
$359$	−19.5772	+	11.3029i	−1.03325	+	0.596544i	−0.917913	−	0.396783i	$-0.870127\pi$
$359$	−19.5772	+	11.3029i	−1.03325	+	0.596544i	−0.115333	+	0.993327i	$0.536793\pi$
$360$	−2.93500	−	0.621084i	−0.154688	−	0.0327340i
$361$	22.1819	−	38.4201i	1.16747	−	2.02211i
$362$	−4.99826			−0.262702
$363$	21.2787	+	8.15712i	1.11684	+	0.428138i
$364$	9.85647	+	6.79677i	0.516620	+	0.356247i
$365$	2.06838	−	1.19418i	0.108264	−	0.0625063i
$366$	−1.14960	−	7.23711i	−0.0600904	−	0.378290i
$367$	10.5463	−	6.08890i	0.550512	−	0.317838i	−0.198817	−	0.980037i	$-0.563710\pi$
$367$	10.5463	−	6.08890i	0.550512	−	0.317838i	0.749328	+	0.662199i	$0.230377\pi$
$368$	−4.36255	−	2.51872i	−0.227414	−	0.131297i
$369$	−19.2549	−	17.3058i	−1.00237	−	0.900902i
$370$		−	10.1161i		−	0.525913i
$371$	−2.63284	+	32.8010i	−0.136690	+	1.70294i
$372$	2.70263	−	0.429305i	0.140125	−	0.0222585i
$373$	14.7398	−	25.5301i	0.763199	−	1.32190i	−0.177994	−	0.984032i	$-0.556961\pi$
$373$	14.7398	−	25.5301i	0.763199	−	1.32190i	0.941193	−	0.337868i	$-0.109706\pi$
$374$	−20.3113			−1.05027
$375$	−0.271725	−	1.71060i	−0.0140318	−	0.0883352i
$376$			0.454165i			0.0234218i
$377$	12.9021			0.664490
$378$	−10.9051	−	8.37128i	−0.560899	−	0.430572i
$379$	27.9939			1.43795			0.718974	−	0.695037i	$-0.244612\pi$
$379$	27.9939			1.43795			0.718974	+	0.695037i	$0.244612\pi$
$380$			7.96013i			0.408346i
$381$	2.95192	+	18.5834i	0.151231	+	0.952055i
$382$	5.72419			0.292875
$383$	−6.84209	+	11.8509i	−0.349615	+	0.605550i	−0.986181	−	0.165672i	$-0.947021\pi$
$383$	−6.84209	+	11.8509i	−0.349615	+	0.605550i	0.636566	+	0.771222i	$0.280354\pi$
$384$	−1.71060	+	0.271725i	−0.0872939	+	0.0138664i
$385$	−11.7458	+	5.58002i	−0.598619	+	0.284384i
$386$		−	5.40313i		−	0.275012i
$387$	3.58580	−	16.9451i	0.182276	−	0.861368i
$388$	1.74470	+	1.00730i	0.0885735	+	0.0511379i
$389$	5.95061	−	3.43558i	0.301708	−	0.174191i	−0.341502	−	0.939881i	$-0.610936\pi$
$389$	5.95061	−	3.43558i	0.301708	−	0.174191i	0.643210	+	0.765690i	$0.277602\pi$
$390$	1.22963	+	7.74094i	0.0622646	+	0.391977i
$391$	18.0283	−	10.4087i	0.911731	−	0.526388i
$392$	−5.42629	−	4.42215i	−0.274069	−	0.223352i
$393$	−7.53586	−	2.88884i	−0.380134	−	0.145723i
$394$	12.5138			0.630436
$395$	4.86467	−	8.42586i	0.244768	−	0.423951i
$396$	−9.85639	+	10.9665i	−0.495302	+	0.551089i
$397$	−4.44511	+	2.56639i	−0.223094	+	0.128803i	−0.607382	−	0.794410i	$-0.707780\pi$
$397$	−4.44511	+	2.56639i	−0.223094	+	0.128803i	0.384288	+	0.923213i	$0.374447\pi$
$398$	−8.94715	+	15.4969i	−0.448480	+	0.776790i
$399$	−15.7405	+	32.9071i	−0.788010	+	1.64741i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	7.67483	+	4.43107i	0.383263	+	0.221277i	0.679237	−	0.733919i	$-0.262311\pi$
$401$	7.67483	+	4.43107i	0.383263	+	0.221277i	−0.295974	+	0.955196i	$0.595644\pi$
$402$	6.72621	−	1.06844i	0.335473	−	0.0532890i
$403$	−3.57479	−	6.19172i	−0.178073	−	0.308432i
$404$	3.23553	+	5.60410i	0.160974	+	0.278815i
$405$	−0.956923	−	8.94898i	−0.0475499	−	0.444679i
$406$	−7.51917	−	0.603543i	−0.373170	−	0.0299533i
$407$	−43.0593	−	24.8603i	−2.13437	−	1.23228i
$408$	2.56208	−	6.68348i	0.126842	−	0.330882i
$409$		−	2.60954i		−	0.129033i	−0.997917	−	0.0645167i	$-0.979449\pi$
$409$		−	2.60954i		−	0.129033i	0.997917	−	0.0645167i	$-0.0205506\pi$
$410$		−	8.62968i		−	0.426189i
$411$	10.8099	+	13.3367i	0.533211	+	0.657853i
$412$	−3.56161	−	2.05630i	−0.175468	−	0.101306i
$413$	−12.4484	−	26.2034i	−0.612544	−	1.28938i
$414$	3.12867	−	14.7849i	0.153766	−	0.726638i
$415$	−1.42589	−	2.46971i	−0.0699941	−	0.121233i
$416$	2.26263	+	3.91899i	0.110935	+	0.192144i
$417$	−0.220987	−	0.272644i	−0.0108218	−	0.0133514i
$418$	33.8823	+	19.5620i	1.65724	+	0.956806i
$419$	−8.15665	−	14.1277i	−0.398478	−	0.690185i	0.595060	−	0.803681i	$-0.297128\pi$
$419$	−8.15665	−	14.1277i	−0.398478	−	0.690185i	−0.993538	+	0.113496i	$0.963795\pi$
$420$	−0.354500	−	4.56884i	−0.0172978	−	0.222937i
$421$	1.59756	−	2.76706i	0.0778603	−	0.134858i	−0.824466	−	0.565911i	$-0.808525\pi$
$421$	1.59756	−	2.76706i	0.0778603	−	0.134858i	0.902327	+	0.431053i	$0.141858\pi$
$422$	−15.1223	+	8.73086i	−0.736142	+	0.425012i
$423$	−1.29543	+	0.422204i	−0.0629859	+	0.0205283i
$424$	−6.21874	+	10.7712i	−0.302009	+	0.523094i
$425$	4.13252			0.200457
$426$	−2.21260	−	13.9291i	−0.107201	−	0.674866i
$427$	10.1105	−	4.80319i	0.489284	−	0.232443i
$428$	−10.8227	+	6.24846i	−0.523133	+	0.302031i
$429$	35.9711	+	13.7894i	1.73670	+	0.665757i
$430$	4.99995	−	2.88672i	0.241119	−	0.139210i
$431$	17.7856	+	10.2685i	0.856701	+	0.494616i	0.862906	−	0.505364i	$-0.168642\pi$
$431$	17.7856	+	10.2685i	0.856701	+	0.494616i	−0.00620540	+	0.999981i	$0.501975\pi$
$432$	−2.36527	−	4.62661i	−0.113799	−	0.222598i
$433$			5.62555i			0.270347i	0.990822	+	0.135173i	$0.0431591\pi$
$433$			5.62555i			0.270347i	−0.990822	+	0.135173i	$0.956841\pi$
$434$	1.79370	+	3.77568i	0.0861006	+	0.181239i
$435$	−3.10949	−	3.83636i	−0.149089	−	0.183939i
$436$	6.80795	−	11.7917i	0.326042	−	0.564721i
$437$	−40.0987			−1.91818
$438$	3.86267	+	1.48074i	0.184566	+	0.0707525i
$439$		−	2.43678i		−	0.116301i	−0.998308	−	0.0581506i	$-0.981480\pi$
$439$		−	2.43678i		−	0.116301i	0.998308	−	0.0581506i	$-0.0185204\pi$
$440$	−4.91498			−0.234313
$441$	7.56900	−	19.5885i	0.360429	−	0.932787i
$442$	−18.7007			−0.889504
$443$		−	1.24401i		−	0.0591048i	−0.999563	−	0.0295524i	$-0.990592\pi$
$443$		−	1.24401i		−	0.0591048i	0.999563	−	0.0295524i	$-0.00940818\pi$
$444$	13.6119	−	11.0329i	0.645992	−	0.523597i
$445$	−5.90551			−0.279948
$446$	−5.68541	+	9.84741i	−0.269212	+	0.466288i
$447$	1.86070	−	4.85383i	0.0880080	−	0.229578i
$448$	−1.13531	−	2.38979i	−0.0536383	−	0.112907i
$449$			17.5222i			0.826924i	0.910521	+	0.413462i	$0.135681\pi$
$449$			17.5222i			0.826924i	−0.910521	+	0.413462i	$0.864319\pi$
$450$	2.00538	−	2.23125i	0.0945344	−	0.105182i
$451$	−36.7322	−	21.2074i	−1.72965	−	0.998615i
$452$	−14.5943	+	8.42603i	−0.686459	+	0.396327i
$453$	−26.5523	+	21.5215i	−1.24754	+	1.01117i
$454$	−6.13659	+	3.54296i	−0.288004	+	0.166279i
$455$	−10.8144	+	5.13757i	−0.506987	+	0.240853i
$456$	−10.7109	+	8.68150i	−0.501582	+	0.406549i
$457$	28.7806			1.34630			0.673150	−	0.739506i	$-0.264941\pi$
$457$	28.7806			1.34630			0.673150	+	0.739506i	$0.264941\pi$
$458$	−1.52702	+	2.64487i	−0.0713528	+	0.123587i
$459$	21.4453	+	1.09477i	1.00098	+	0.0510994i
$460$	4.36255	−	2.51872i	0.203405	−	0.117436i
$461$	−17.0159	+	29.4723i	−0.792508	+	1.37266i	0.131902	+	0.991263i	$0.457891\pi$
$461$	−17.0159	+	29.4723i	−0.792508	+	1.37266i	−0.924410	+	0.381401i	$0.875442\pi$
$462$	−20.3185	−	9.71896i	−0.945300	−	0.452167i
$463$	−4.73816	−	8.20674i	−0.220201	−	0.381399i	0.734668	−	0.678427i	$-0.237338\pi$
$463$	−4.73816	−	8.20674i	−0.220201	−	0.381399i	−0.954869	+	0.297028i	$0.904005\pi$
$464$	−2.46914	−	1.42556i	−0.114627	−	0.0661799i
$465$	−0.979525	+	2.55520i	−0.0454244	+	0.118494i
$466$	10.7066	+	18.5443i	0.495972	+	0.859048i
$467$	−8.13248	−	14.0859i	−0.376326	−	0.651816i	0.614198	−	0.789152i	$-0.289479\pi$
$467$	−8.13248	−	14.0859i	−0.376326	−	0.651816i	−0.990525	+	0.137336i	$0.956146\pi$
$468$	−9.07486	+	10.0970i	−0.419486	+	0.466733i
$469$	4.46411	+	9.39680i	0.206134	+	0.433904i
$470$	−0.393319	−	0.227083i	−0.0181424	−	0.0104745i
$471$	−14.4323	+	2.29253i	−0.665004	+	0.105634i
$472$		−	10.9647i		−	0.504693i
$473$		−	28.3764i		−	1.30475i
$474$	16.6430	−	2.64370i	0.764441	−	0.121429i
$475$	−6.89368	−	3.98007i	−0.316304	−	0.182618i
$476$	10.8986	+	0.874799i	0.499535	+	0.0400963i
$477$	−36.5040	−	7.72472i	−1.67141	−	0.353691i
$478$	9.08336	+	15.7328i	0.415463	+	0.719603i
$479$	2.93690	+	5.08685i	0.134190	+	0.232424i	0.925288	−	0.379266i	$-0.123823\pi$
$479$	2.93690	+	5.08685i	0.134190	+	0.232424i	−0.791098	+	0.611690i	$0.790490\pi$
$480$	0.619981	−	1.61729i	0.0282981	−	0.0738188i
$481$	−39.6451	−	22.8891i	−1.80766	−	1.04365i
$482$	−10.4273	−	18.0606i	−0.474950	−	0.822638i
$483$	23.0153	−	1.78577i	1.04723	−	0.0812555i
$484$	−6.57852	+	11.3943i	−0.299024	+	0.517924i
$485$	−1.74470	+	1.00730i	−0.0792225	+	0.0457392i
$486$	10.9978	−	11.0476i	0.498870	−	0.501128i
$487$	−4.11305	+	7.12401i	−0.186380	+	0.322820i	−0.944041	−	0.329829i	$-0.893009\pi$
$487$	−4.11305	+	7.12401i	−0.186380	+	0.322820i	0.757661	+	0.652649i	$0.226342\pi$
$488$	4.23073			0.191516
$489$	17.8743	−	14.4877i	0.808306	−	0.655158i
$490$	6.54284	−	2.48823i	0.295575	−	0.112407i
$491$	23.2893	−	13.4461i	1.05103	−	0.606814i	0.128094	−	0.991762i	$-0.459114\pi$
$491$	23.2893	−	13.4461i	1.05103	−	0.606814i	0.922938	+	0.384948i	$0.125781\pi$
$492$	11.6118	−	9.41172i	0.523500	−	0.424313i
$493$	10.2038	−	5.89115i	0.459555	−	0.265324i
$494$	31.1957	+	18.0109i	1.40356	+	0.810347i
$495$	−4.56910	−	14.0192i	−0.205366	−	0.630114i
$496$			1.57993i			0.0709408i
$497$	19.4595	−	9.24457i	0.872878	−	0.414676i
$498$	1.76805	−	4.61214i	0.0792281	−	0.206675i
$499$	−15.5515	+	26.9361i	−0.696183	+	1.20582i	0.273598	+	0.961844i	$0.411786\pi$
$499$	−15.5515	+	26.9361i	−0.696183	+	1.20582i	−0.969780	+	0.243980i	$0.921547\pi$
$500$	1.00000			0.0447214
$501$	−21.9354	+	17.7793i	−0.980000	+	0.794321i
$502$		−	27.8633i		−	1.24360i
$503$	3.49948			0.156034			0.0780170	−	0.996952i	$-0.475141\pi$
$503$	3.49948			0.156034			0.0780170	+	0.996952i	$0.475141\pi$
$504$	5.76104	−	5.45989i	0.256617	−	0.243203i
$505$	−6.47106			−0.287958
$506$		−	24.7589i		−	1.10067i
$507$	12.0941	+	4.63623i	0.537119	+	0.205902i
$508$	−10.8636			−0.481996
$509$	3.41734	−	5.91901i	0.151471	−	0.262356i	−0.780297	−	0.625409i	$-0.784932\pi$
$509$	3.41734	−	5.91901i	0.151471	−	0.262356i	0.931768	+	0.363053i	$0.118266\pi$
$510$	4.50702	+	5.56057i	0.199574	+	0.246226i
$511$	−0.505584	+	6.29875i	−0.0223657	+	0.278640i
$512$		−	1.00000i		−	0.0441942i
$513$	−34.7196	−	22.4804i	−1.53291	−	0.992533i
$514$	14.7285	+	8.50350i	0.649646	+	0.375073i
$515$	3.56161	−	2.05630i	0.156943	−	0.0906113i
$516$	9.33733	+	3.57943i	0.411053	+	0.157576i
$517$	−1.93315	+	1.11611i	−0.0850200	+	0.0490863i
$518$	22.0339	+	15.1940i	0.968116	+	0.667587i
$519$	−5.76337	−	36.2824i	−0.252984	−	1.59262i
$520$	−4.52526			−0.198446
$521$	−8.40753	+	14.5623i	−0.368341	+	0.637985i	−0.989306	−	0.145853i	$-0.953407\pi$
$521$	−8.40753	+	14.5623i	−0.368341	+	0.637985i	0.620966	+	0.783838i	$0.286741\pi$
$522$	1.77079	−	8.36805i	0.0775052	−	0.366259i
$523$	−5.55234	+	3.20565i	−0.242787	+	0.140173i	−0.616457	−	0.787389i	$-0.711433\pi$
$523$	−5.55234	+	3.20565i	−0.242787	+	0.140173i	0.373670	+	0.927562i	$0.378099\pi$
$524$	2.32978	−	4.03530i	0.101777	−	0.176283i
$525$	4.13398	+	1.97742i	0.180422	+	0.0863015i
$526$	−1.53381	−	2.65664i	−0.0668775	−	0.115835i
$527$	−5.65435	−	3.26454i	−0.246307	−	0.142206i
$528$	−5.36039	−	6.61342i	−0.233281	−	0.287812i
$529$	1.18788	+	2.05748i	0.0516472	+	0.0894555i
$530$	−6.21874	−	10.7712i	−0.270125	−	0.467870i
$531$	31.2751	−	10.1931i	1.35722	−	0.442344i
$532$	−17.3380	−	11.9558i	−0.751696	−	0.518350i
$533$	−33.8197	−	19.5258i	−1.46489	−	0.845756i
$534$	−6.44068	−	7.94624i	−0.278715	−	0.343867i
$535$		−	12.4969i		−	0.540289i
$536$			3.93207i			0.169840i
$537$	2.09953	−	5.47685i	0.0906013	−	0.236344i
$538$	−6.04397	−	3.48949i	−0.260574	−	0.150442i
$539$	5.48781	−	33.9644i	0.236377	−	1.46295i
$540$	5.18939	+	0.264915i	0.223316	+	0.0114001i
$541$	−8.20896	−	14.2183i	−0.352931	−	0.611294i	0.633831	−	0.773472i	$-0.281482\pi$
$541$	−8.20896	−	14.2183i	−0.352931	−	0.611294i	−0.986762	+	0.162178i	$0.948148\pi$
$542$	−1.12689	−	1.95182i	−0.0484039	−	0.0838380i
$543$	8.55003	−	1.35815i	0.366917	−	0.0582838i
$544$	3.57887	+	2.06626i	0.153443	+	0.0885902i
$545$	6.80795	+	11.7917i	0.291620	+	0.505101i
$546$	−18.7074	−	8.94833i	−0.800602	−	0.382953i
$547$	−16.7310	+	28.9790i	−0.715366	+	1.23905i	0.247452	+	0.968900i	$0.420407\pi$
$547$	−16.7310	+	28.9790i	−0.715366	+	1.23905i	−0.962818	+	0.270150i	$0.912927\pi$
$548$	−8.58373	+	4.95582i	−0.366679	+	0.211702i
$549$	3.93301	+	12.0675i	0.167857	+	0.515026i
$550$	2.45749	−	4.25650i	0.104788	−	0.181498i
$551$	−22.6953			−0.966851
$552$	8.14699	+	3.12312i	0.346759	+	0.132929i
$553$	11.0458	+	23.2510i	0.469715	+	0.988735i
$554$	24.5090	−	14.1503i	1.04129	−	0.601188i
$555$	2.74881	+	17.3047i	0.116680	+	0.734543i
$556$	0.175478	−	0.101312i	0.00744192	−	0.00429660i
$557$	13.5808	+	7.84087i	0.575436	+	0.332228i	0.759318	−	0.650720i	$-0.225533\pi$
$557$	13.5808	+	7.84087i	0.575436	+	0.332228i	−0.183881	+	0.982948i	$0.558866\pi$
$558$	−4.50647	+	1.46874i	−0.190774	+	0.0621769i
$559$		−	26.1264i		−	1.10503i
$560$	2.63727	+	0.211686i	0.111445	+	0.00894539i
$561$	34.7445	−	5.51908i	1.46691	−	0.233016i
$562$	6.18859	−	10.7190i	0.261050	−	0.452152i
$563$	−7.46736			−0.314712			−0.157356	−	0.987542i	$-0.550297\pi$
$563$	−7.46736			−0.314712			−0.157356	+	0.987542i	$0.550297\pi$
$564$	−0.123408	−	0.776897i	−0.00519641	−	0.0327132i
$565$		−	16.8521i		−	0.708972i
$566$	−21.6617			−0.910509
$567$	20.9290	+	11.3567i	0.878937	+	0.476938i
$568$	8.14278			0.341664
$569$			23.3084i			0.977141i	0.872524	+	0.488571i	$0.162481\pi$
$569$			23.3084i			0.977141i	−0.872524	+	0.488571i	$0.837519\pi$
$570$	−2.16297	−	13.6166i	−0.0905967	−	0.570338i
$571$	2.43957			0.102093			0.0510463	−	0.998696i	$-0.483744\pi$
$571$	2.43957			0.102093			0.0510463	+	0.998696i	$0.483744\pi$
$572$	−11.1208	+	19.2618i	−0.464984	+	0.805376i
$573$	−9.79181	+	1.55540i	−0.409059	+	0.0649779i
$574$	18.7963	+	12.9614i	0.784542	+	0.541000i
$575$			5.03744i			0.210076i
$576$	2.85233	−	0.929628i	0.118847	−	0.0387345i
$577$	30.7749	+	17.7679i	1.28118	+	0.739688i	0.977064	−	0.212948i	$-0.0683063\pi$
$577$	30.7749	+	17.7679i	1.28118	+	0.739688i	0.304114	+	0.952636i	$0.401640\pi$
$578$	−0.0673103	+	0.0388616i	−0.00279974	+	0.00161643i
$579$	1.46817	+	9.24261i	0.0610149	+	0.384110i
$580$	2.46914	−	1.42556i	0.102525	−	0.0591931i
$581$	7.52090	+	0.603682i	0.312019	+	0.0250450i
$582$	−3.25819	−	1.24901i	−0.135056	−	0.0517733i
$583$	−61.1300			−2.53174
$584$	−1.19418	+	2.06838i	−0.0494156	+	0.0855903i
$585$	−4.20681	−	12.9076i	−0.173930	−	0.533662i
$586$	2.40584	−	1.38901i	0.0993842	−	0.0573795i
$587$	−6.06540	+	10.5056i	−0.250346	+	0.433612i	−0.963621	−	0.267272i	$-0.913878\pi$
$587$	−6.06540	+	10.5056i	−0.250346	+	0.433612i	0.713275	+	0.700884i	$0.247211\pi$
$588$	10.4838	+	6.09009i	0.432346	+	0.251151i
$589$	6.28821	+	10.8915i	0.259101	+	0.448777i
$590$	9.49575	+	5.48237i	0.390934	+	0.225706i
$591$	−21.4061	+	3.40031i	−0.880531	+	0.139870i
$592$	5.05807	+	8.76083i	0.207885	+	0.360068i
$593$	15.5440	+	26.9230i	0.638315	+	1.10559i	0.985802	+	0.167910i	$0.0537017\pi$
$593$	15.5440	+	26.9230i	0.638315	+	1.10559i	−0.347487	+	0.937685i	$0.612965\pi$
$594$	13.8805	−	21.4376i	0.569524	−	0.879597i
$595$	−6.20688	+	9.00104i	−0.254457	+	0.369007i
$596$	2.59913	+	1.50061i	0.106465	+	0.0614673i
$597$	11.0941	−	28.9402i	0.454052	−	1.18445i
$598$		−	22.7957i		−	0.932187i
$599$		−	1.51443i		−	0.0618778i	−0.999521	−	0.0309389i	$-0.990150\pi$
$599$		−	1.51443i		−	0.0618778i	0.999521	−	0.0309389i	$-0.00984972\pi$
$600$	1.09062	+	1.34556i	0.0445245	+	0.0549324i
$601$	28.7908	+	16.6224i	1.17440	+	0.678040i	0.954712	−	0.297530i	$-0.0961629\pi$
$601$	28.7908	+	16.6224i	1.17440	+	0.678040i	0.219688	+	0.975570i	$0.429496\pi$
$602$	−1.22216	+	15.2261i	−0.0498116	+	0.620571i
$603$	−11.2156	+	3.65536i	−0.456733	+	0.148858i
$604$	−9.86662	−	17.0895i	−0.401467	−	0.695362i
$605$	−6.57852	−	11.3943i	−0.267455	−	0.463246i
$606$	−7.05749	−	8.70723i	−0.286691	−	0.353707i
$607$	−14.2347	−	8.21841i	−0.577769	−	0.333575i	0.182477	−	0.983210i	$-0.441588\pi$
$607$	−14.2347	−	8.21841i	−0.577769	−	0.333575i	−0.760246	+	0.649635i	$0.774922\pi$
$608$	−3.98007	−	6.89368i	−0.161413	−	0.279576i
$609$	13.0263	−	1.01072i	0.527853	−	0.0409565i
$610$	−2.11537	+	3.66392i	−0.0856487	+	0.148348i
$611$	−1.77987	+	1.02761i	−0.0720058	+	0.0415726i
$612$	−2.56664	+	12.1290i	−0.103750	+	0.490284i
$613$	−6.16764	+	10.6827i	−0.249109	+	0.431469i	−0.963279	−	0.268503i	$-0.913471\pi$
$613$	−6.16764	+	10.6827i	−0.249109	+	0.431469i	0.714170	+	0.699972i	$0.246804\pi$
$614$	3.67227			0.148201
$615$	2.34490	+	14.7620i	0.0945554	+	0.595260i
$616$	7.38211	−	10.7053i	0.297434	−	0.431329i
$617$	−14.9813	+	8.64945i	−0.603124	+	0.348214i	−0.770270	−	0.637718i	$-0.779878\pi$
$617$	−14.9813	+	8.64945i	−0.603124	+	0.348214i	0.167146	+	0.985932i	$0.446545\pi$
$618$	6.65125	+	2.54973i	0.267553	+	0.102565i
$619$	5.50071	−	3.17584i	0.221092	−	0.127648i	−0.385364	−	0.922765i	$-0.625924\pi$
$619$	5.50071	−	3.17584i	0.221092	−	0.127648i	0.606456	+	0.795117i	$0.292591\pi$
$620$	−1.36826	−	0.789963i	−0.0549505	−	0.0317257i
$621$	−1.33449	+	26.1412i	−0.0535514	+	1.04901i
$622$		−	7.33384i		−	0.294060i
$623$	8.86984	−	12.8628i	0.355362	−	0.515336i
$624$	−4.93536	−	6.08903i	−0.197572	−	0.243756i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	28.5812			1.14234
$627$	−63.2747	−	24.2561i	−2.52695	−	0.968695i
$628$		−	8.43694i		−	0.336671i
$629$	−41.8051			−1.66688
$630$	1.84788	+	7.71915i	0.0736212	+	0.307538i
$631$	0.419169			0.0166869			0.00834343	−	0.999965i	$-0.497344\pi$
$631$	0.419169			0.0166869			0.00834343	+	0.999965i	$0.497344\pi$
$632$			9.72934i			0.387012i
$633$	23.4959	−	19.0441i	0.933876	−	0.756937i
$634$	6.74081			0.267712
$635$	5.43182	−	9.40818i	0.215555	−	0.373352i
$636$	7.71100	−	20.1150i	0.305761	−	0.797611i
$637$	5.05268	−	31.2713i	0.200194	−	1.23901i
$638$		−	14.0132i		−	0.554788i
$639$	7.56976	+	23.2259i	0.299455	+	0.918803i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	13.7279	−	7.92580i	0.542219	−	0.313050i	−0.203759	−	0.979021i	$-0.565316\pi$
$641$	13.7279	−	7.92580i	0.542219	−	0.313050i	0.745978	+	0.665971i	$0.231983\pi$
$642$	16.8154	−	13.6294i	0.663651	−	0.537910i
$643$	21.8689	−	12.6260i	0.862427	−	0.497923i	−0.00239717	−	0.999997i	$-0.500763\pi$
$643$	21.8689	−	12.6260i	0.862427	−	0.497923i	0.864824	+	0.502075i	$0.167430\pi$
$644$	−1.06636	+	13.2851i	−0.0420204	+	0.523505i
$645$	−7.76854	+	6.29665i	−0.305886	+	0.247930i
$646$	32.8954			1.29425
$647$	5.47945	−	9.49068i	0.215419	−	0.373117i	−0.737983	−	0.674819i	$-0.764222\pi$
$647$	5.47945	−	9.49068i	0.215419	−	0.373117i	0.953402	+	0.301702i	$0.0975548\pi$
$648$	5.30321	+	7.27159i	0.208330	+	0.285655i
$649$	46.6714	−	26.9458i	1.83201	−	1.05771i
$650$	2.26263	−	3.91899i	0.0887477	−	0.153716i
$651$	−4.09427	−	5.97131i	−0.160467	−	0.234034i
$652$	6.64195	+	11.5042i	0.260119	+	0.450539i
$653$	17.9284	+	10.3509i	0.701591	+	0.405064i	0.807940	−	0.589265i	$-0.200583\pi$
$653$	17.9284	+	10.3509i	0.701591	+	0.405064i	−0.106348	+	0.994329i	$0.533916\pi$
$654$	−8.44160	+	22.0208i	−0.330093	+	0.861083i
$655$	2.32978	+	4.03530i	0.0910321	+	0.157672i
$656$	4.31484	+	7.47352i	0.168466	+	0.291792i
$657$	−7.00985	−	1.48337i	−0.273480	−	0.0578719i
$658$	1.08536	−	0.515618i	0.0423116	−	0.0201009i
$659$	18.2719	+	10.5493i	0.711774	+	0.410943i	0.811718	−	0.584050i	$-0.198533\pi$
$659$	18.2719	+	10.5493i	0.711774	+	0.410943i	−0.0999436	+	0.994993i	$0.531866\pi$
$660$	8.40759	−	1.33552i	0.327265	−	0.0519852i
$661$			4.51152i			0.175478i	0.996144	+	0.0877389i	$0.0279641\pi$
$661$			4.51152i			0.175478i	−0.996144	+	0.0877389i	$0.972036\pi$
$662$			28.8227i			1.12022i
$663$	31.9896	−	5.08146i	1.24237	−	0.197348i
$664$	2.46971	+	1.42589i	0.0958433	+	0.0553352i
$665$	19.0230	−	9.03721i	0.737681	−	0.350448i
$666$	−20.2867	+	22.5716i	−0.786092	+	0.874631i
$667$	7.18116	+	12.4381i	0.278056	+	0.481607i
$668$	−8.15100	−	14.1179i	−0.315371	−	0.546239i
$669$	7.04969	−	18.3899i	0.272557	−	0.710994i
$670$	−3.40527	−	1.96604i	−0.131557	−	0.0759546i
$671$	10.3970	+	18.0081i	0.401371	+	0.695196i
$672$	2.59143	+	3.77948i	0.0999665	+	0.145797i
$673$	0.596334	−	1.03288i	0.0229870	−	0.0398147i	−0.854303	−	0.519775i	$-0.826016\pi$
$673$	0.596334	−	1.03288i	0.0229870	−	0.0398147i	0.877290	+	0.479961i	$0.159349\pi$
$674$	20.9427	−	12.0913i	0.806681	−	0.465738i
$675$	−2.82412	+	4.36169i	−0.108700	+	0.167882i
$676$	−3.73901	+	6.47616i	−0.143808	+	0.249083i
$677$	23.2403			0.893196			0.446598	−	0.894735i	$-0.352636\pi$
$677$	23.2403			0.893196			0.446598	+	0.894735i	$0.352636\pi$
$678$	22.6755	−	18.3792i	0.870849	−	0.705851i
$679$	0.426464	−	5.31304i	0.0163662	−	0.203896i
$680$	−3.57887	+	2.06626i	−0.137243	+	0.0792375i
$681$	9.53456	−	7.72806i	0.365365	−	0.296140i
$682$	−6.72496	+	3.88265i	−0.257512	+	0.148675i
$683$	−6.84887	−	3.95420i	−0.262065	−	0.151303i	0.363211	−	0.931707i	$-0.381680\pi$
$683$	−6.84887	−	3.95420i	−0.262065	−	0.151303i	−0.625276	+	0.780404i	$0.715014\pi$
$684$	15.9631	−	17.7610i	0.610363	−	0.679110i
$685$		−	9.91164i		−	0.378704i
$686$	−4.40747	+	17.9882i	−0.168278	+	0.686791i
$687$	1.89344	−	4.93925i	0.0722393	−	0.188444i
$688$	−2.88672	+	4.99995i	−0.110055	+	0.190621i
$689$	−56.2829			−2.14421
$690$	−6.77819	+	5.49394i	−0.258041	+	0.209151i
$691$		−	12.8763i		−	0.489839i	−0.969543	−	0.244920i	$-0.921238\pi$
$691$		−	12.8763i		−	0.489839i	0.969543	−	0.244920i	$-0.0787615\pi$
$692$	21.2103			0.806295
$693$	37.3977	+	11.1043i	1.42062	+	0.421816i
$694$	−17.4312			−0.661678
$695$			0.202625i			0.00768599i
$696$	4.61108	+	1.76764i	0.174783	+	0.0670022i
$697$	−35.6623			−1.35081
$698$	−18.1446	+	31.4274i	−0.686784	+	1.18954i
$699$	−23.3536	−	28.8127i	−0.883315	−	1.08980i
$700$	−1.50196	+	2.17810i	−0.0567688	+	0.0823244i
$701$		−	1.81441i		−	0.0685292i	−0.999413	−	0.0342646i	$-0.989091\pi$
$701$		−	1.81441i		−	0.0685292i	0.999413	−	0.0342646i	$-0.0109089\pi$
$702$	12.7799	−	19.7378i	0.482346	−	0.744955i
$703$	69.7373	+	40.2629i	2.63019	+	1.51854i
$704$	4.25650	−	2.45749i	0.160423	−	0.0926202i
$705$	0.734516	+	0.281574i	0.0276635	+	0.0106047i
$706$	18.8372	−	10.8756i	0.708946	−	0.409310i
$707$	9.71928	−	14.0946i	0.365531	−	0.530082i
$708$	2.97939	+	18.7563i	0.111972	+	0.704906i
$709$	4.42854			0.166317			0.0831587	−	0.996536i	$-0.473499\pi$
$709$	4.42854			0.166317			0.0831587	+	0.996536i	$0.473499\pi$
$710$	−4.07139	+	7.05186i	−0.152797	+	0.264652i
$711$	−27.7513	+	9.04466i	−1.04076	+	0.339201i
$712$	5.11432	−	2.95275i	0.191667	−	0.110659i
$713$	3.97939	−	6.89251i	0.149029	−	0.258126i
$714$	−18.8808	+	1.46498i	−0.706598	+	0.0548255i
$715$	−11.1208	−	19.2618i	−0.415894	−	0.720350i
$716$	2.93274	+	1.69322i	0.109602	+	0.0632786i
$717$	−19.8130	−	24.4445i	−0.739931	−	0.912896i
$718$	11.3029	+	19.5772i	0.421821	+	0.730615i
$719$	−8.23556	−	14.2644i	−0.307134	−	0.531973i	0.670600	−	0.741819i	$-0.266037\pi$
$719$	−8.23556	−	14.2644i	−0.307134	−	0.531973i	−0.977734	+	0.209847i	$0.932703\pi$
$720$	−0.621084	+	2.93500i	−0.0231464	+	0.109381i
$721$	−0.870581	+	10.8460i	−0.0324221	+	0.403927i
$722$	−38.4201	−	22.1819i	−1.42985	−	0.825523i
$723$	22.7445	+	28.0612i	0.845877	+	1.04361i
$724$			4.99826i			0.185759i
$725$			2.85112i			0.105888i
$726$	8.15712	−	21.2787i	0.302739	−	0.789728i
$727$	−40.8484	−	23.5838i	−1.51498	−	0.874676i	−0.999846	−	0.0175695i	$-0.994407\pi$
$727$	−40.8484	−	23.5838i	−1.51498	−	0.874676i	−0.515138	−	0.857107i	$-0.672260\pi$
$728$	6.79677	−	9.85647i	0.251905	−	0.365305i
$729$	−15.8110	+	21.8864i	−0.585591	+	0.810607i
$730$	−1.19418	−	2.06838i	−0.0441986	−	0.0765543i
$731$	−11.9294	−	20.6624i	−0.441226	−	0.764227i
$732$	−7.23711	+	1.14960i	−0.267491	+	0.0424903i
$733$	−41.7617	−	24.1111i	−1.54250	−	0.890564i	−0.998680	−	0.0513634i	$-0.983643\pi$
$733$	−41.7617	−	24.1111i	−1.54250	−	0.890564i	−0.543822	−	0.839201i	$-0.683023\pi$
$734$	−6.08890	−	10.5463i	−0.224745	−	0.389270i
$735$	−10.5161	+	6.03423i	−0.387892	+	0.222576i
$736$	−2.51872	+	4.36255i	−0.0928412	+	0.160806i
$737$	−16.7369	+	9.66303i	−0.616510	+	0.355942i
$738$	−17.3058	+	19.2549i	−0.637034	+	0.708784i
$739$	18.2730	−	31.6498i	0.672184	−	1.16426i	−0.305099	−	0.952320i	$-0.598690\pi$
$739$	18.2730	−	31.6498i	0.672184	−	1.16426i	0.977283	−	0.211936i	$-0.0679769\pi$
$740$	−10.1161			−0.371876
$741$	−58.2575	−	22.3328i	−2.14014	−	0.820415i
$742$	32.8010	+	2.63284i	1.20416	+	0.0966548i
$743$	18.6193	−	10.7498i	0.683075	−	0.394373i	−0.117938	−	0.993021i	$-0.537628\pi$
$743$	18.6193	−	10.7498i	0.683075	−	0.394373i	0.801013	+	0.598648i	$0.204295\pi$
$744$	−0.429305	−	2.70263i	−0.0157391	−	0.0990832i
$745$	−2.59913	+	1.50061i	−0.0952247	+	0.0549780i
$746$	−25.5301	−	14.7398i	−0.934724	−	0.539663i
$747$	−1.77119	+	8.36998i	−0.0648046	+	0.306241i
$748$			20.3113i			0.742653i
$749$	27.2195	+	18.7699i	0.994580	+	0.685836i
$750$	−1.71060	+	0.271725i	−0.0624624	+	0.00992199i
$751$	−8.36754	+	14.4930i	−0.305336	+	0.528857i	−0.977336	−	0.211694i	$-0.932102\pi$
$751$	−8.36754	+	14.4930i	−0.305336	+	0.528857i	0.672000	+	0.740551i	$0.265435\pi$
$752$	0.454165			0.0165617
$753$	7.57117	+	47.6631i	0.275909	+	1.73694i
$754$		−	12.9021i		−	0.469865i
$755$	19.7332			0.718166
$756$	−8.37128	+	10.9051i	−0.304460	+	0.396615i
$757$	−33.5973			−1.22112			−0.610558	−	0.791972i	$-0.709055\pi$
$757$	−33.5973			−1.22112			−0.610558	+	0.791972i	$0.709055\pi$
$758$		−	27.9939i		−	1.01678i
$759$	6.72761	+	42.3527i	0.244197	+	1.53731i
$760$	7.96013			0.288744
$761$	14.2690	−	24.7146i	0.517249	−	0.895902i	−0.482550	−	0.875869i	$-0.660289\pi$
$761$	14.2690	−	24.7146i	0.517249	−	0.895902i	0.999799	−	0.0200339i	$-0.00637741\pi$
$762$	18.5834	−	2.95192i	0.673205	−	0.106937i
$763$	−35.9088	−	2.88230i	−1.29999	−	0.104346i
$764$		−	5.72419i		−	0.207094i
$765$	−9.22067	−	8.28726i	−0.333374	−	0.299627i
$766$	11.8509	+	6.84209i	0.428189	+	0.247215i
$767$	42.9708	−	24.8092i	1.55158	−	0.895808i
$768$	0.271725	+	1.71060i	0.00980503	+	0.0617261i
$769$	−4.36339	+	2.51920i	−0.157348	+	0.0908448i	−0.576606	−	0.817022i	$-0.695623\pi$
$769$	−4.36339	+	2.51920i	−0.157348	+	0.0908448i	0.419259	+	0.907867i	$0.362290\pi$
$770$	5.58002	+	11.7458i	0.201090	+	0.423287i
$771$	−27.5052	−	10.5440i	−0.990576	−	0.379733i
$772$	−5.40313			−0.194463
$773$	−9.36638	+	16.2231i	−0.336885	+	0.583503i	−0.983845	−	0.179022i	$-0.942707\pi$
$773$	−9.36638	+	16.2231i	−0.336885	+	0.583503i	0.646960	+	0.762524i	$0.276040\pi$
$774$	−16.9451	−	3.58580i	−0.609079	−	0.128889i
$775$	1.36826	−	0.789963i	0.0491492	−	0.0283763i
$776$	1.00730	−	1.74470i	0.0361600	−	0.0626309i
$777$	−41.8199	−	20.0038i	−1.50028	−	0.717632i
$778$	−3.43558	−	5.95061i	−0.123172	−	0.213340i
$779$	59.4902	+	34.3467i	2.13146	+	1.23060i
$780$	7.74094	−	1.22963i	0.277170	−	0.0440277i
$781$	20.0108	+	34.6598i	0.716043	+	1.24022i
$782$	−10.4087	−	18.0283i	−0.372213	−	0.644691i
$783$	−0.755305	+	14.7956i	−0.0269924	+	0.528751i
$784$	−4.42215	+	5.42629i	−0.157934	+	0.193796i
$785$	7.30661	+	4.21847i	0.260784	+	0.150564i
$786$	−2.88884	+	7.53586i	−0.103042	+	0.268795i
$787$		−	53.6524i		−	1.91250i	−0.292547	−	0.956251i	$-0.594503\pi$
$787$		−	53.6524i		−	1.91250i	0.292547	−	0.956251i	$-0.405497\pi$
$788$		−	12.5138i		−	0.445786i
$789$	3.34563	+	4.12769i	0.119107	+	0.146950i
$790$	−8.42586	−	4.86467i	−0.299779	−	0.173077i
$791$	36.7055	+	25.3111i	1.30510	+	0.899960i
$792$	10.9665	+	9.85639i	0.389679	+	0.350232i
$793$	9.57260	+	16.5802i	0.339933	+	0.588781i
$794$	2.56639	+	4.44511i	0.0910777	+	0.157751i
$795$	13.5646	+	16.7354i	0.481086	+	0.593544i
$796$	15.4969	+	8.94715i	0.549274	+	0.317123i
$797$	−1.34947	−	2.33735i	−0.0478007	−	0.0827933i	0.841135	−	0.540825i	$-0.181888\pi$
$797$	−1.34947	−	2.33735i	−0.0478007	−	0.0827933i	−0.888936	+	0.458032i	$0.848555\pi$
$798$	32.9071	+	15.7405i	1.16490	+	0.557207i
$799$	−0.938423	+	1.62540i	−0.0331990	+	0.0575024i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	13.1766	+	11.8428i	0.465574	+	0.418444i
$802$	4.43107	−	7.67483i	0.156466	−	0.271008i
$803$	−11.7388			−0.414252
$804$	−1.06844	−	6.72621i	−0.0376810	−	0.237215i
$805$	−10.9720	−	7.56603i	−0.386713	−	0.266668i
$806$	−6.19172	+	3.57479i	−0.218094	+	0.125917i
$807$	11.2870	+	4.32683i	0.397322	+	0.152312i
$808$	5.60410	−	3.23553i	0.197152	−	0.113826i
$809$	10.1449	+	5.85717i	0.356676	+	0.205927i	0.667622	−	0.744501i	$-0.267312\pi$
$809$	10.1449	+	5.85717i	0.356676	+	0.205927i	−0.310946	+	0.950428i	$0.600646\pi$
$810$	−8.94898	+	0.956923i	−0.314435	+	0.0336229i
$811$		−	1.79458i		−	0.0630161i	−0.999503	−	0.0315081i	$-0.989969\pi$
$811$		−	1.79458i		−	0.0630161i	0.999503	−	0.0315081i	$-0.0100310\pi$
$812$	−0.603543	+	7.51917i	−0.0211802	+	0.263871i
$813$	2.45801	+	3.03259i	0.0862063	+	0.106358i
$814$	−24.8603	+	43.0593i	−0.871353	+	1.50923i
$815$	−13.2839			−0.465315
$816$	−6.68348	−	2.56208i	−0.233969	−	0.0896909i
$817$			45.9574i			1.60785i
$818$	−2.60954			−0.0912404
$819$	34.4324	+	10.2238i	1.20317	+	0.357248i
$820$	−8.62968			−0.301361
$821$		−	28.2960i		−	0.987539i	−0.869593	−	0.493769i	$-0.835619\pi$
$821$		−	28.2960i		−	0.987539i	0.869593	−	0.493769i	$-0.164381\pi$
$822$	13.3367	−	10.8099i	0.465172	−	0.377037i
$823$	2.24728			0.0783353			0.0391676	−	0.999233i	$-0.487529\pi$
$823$	2.24728			0.0783353			0.0391676	+	0.999233i	$0.487529\pi$
$824$	−2.05630	+	3.56161i	−0.0716345	+	0.124075i
$825$	−3.04720	+	7.94895i	−0.106090	+	0.276747i
$826$	−26.2034	+	12.4484i	−0.911732	+	0.433134i
$827$		−	43.4893i		−	1.51227i	−0.654415	−	0.756136i	$-0.727085\pi$
$827$		−	43.4893i		−	1.51227i	0.654415	−	0.756136i	$-0.272915\pi$
$828$	−14.7849	−	3.12867i	−0.513811	−	0.108729i
$829$	−45.1357	−	26.0591i	−1.56763	−	0.905069i	−0.996445	−	0.0842454i	$-0.973152\pi$
$829$	−45.1357	−	26.0591i	−1.56763	−	0.905069i	−0.571181	−	0.820824i	$-0.693515\pi$
$830$	−2.46971	+	1.42589i	−0.0857249	+	0.0494933i
$831$	−38.0802	+	30.8652i	−1.32099	+	1.07070i
$832$	3.91899	−	2.26263i	0.135867	−	0.0784427i
$833$	−10.2827	−	27.0384i	−0.356273	−	0.936825i
$834$	−0.272644	+	0.220987i	−0.00944090	+	0.00765215i
$835$	16.3020			0.564154
$836$	19.5620	−	33.8823i	0.676564	−	1.17184i
$837$	7.30970	−	3.73696i	0.252660	−	0.129168i
$838$	−14.1277	+	8.15665i	−0.488034	+	0.281767i
$839$	21.4923	−	37.2258i	0.741998	−	1.28518i	−0.209586	−	0.977790i	$-0.567212\pi$
$839$	21.4923	−	37.2258i	0.741998	−	1.28518i	0.951584	−	0.307388i	$-0.0994550\pi$
$840$	−4.56884	+	0.354500i	−0.157640	+	0.0122314i
$841$	−10.4356	−	18.0749i	−0.359847	−	0.623273i
$842$	−2.76706	−	1.59756i	−0.0953590	−	0.0550556i
$843$	−7.67362	+	20.0175i	−0.264294	+	0.689439i
$844$	8.73086	+	15.1223i	0.300529	+	0.520531i
$845$	−3.73901	−	6.47616i	−0.128626	−	0.222787i
$846$	0.422204	+	1.29543i	0.0145157	+	0.0445378i
$847$	34.6987	+	2.78517i	1.19226	+	0.0956995i
$848$	10.7712	+	6.21874i	0.369883	+	0.213552i
$849$	37.0546	−	5.88603i	1.27171	−	0.202008i
$850$		−	4.13252i		−	0.141744i
$851$		−	50.9594i		−	1.74687i
$852$	−13.9291	+	2.21260i	−0.477202	+	0.0758024i
$853$	−36.9943	−	21.3587i	−1.26666	−	0.731306i	−0.292305	−	0.956325i	$-0.594422\pi$
$853$	−36.9943	−	21.3587i	−1.26666	−	0.731306i	−0.974354	+	0.225019i	$0.927756\pi$
$854$	−4.80319	−	10.1105i	−0.164362	−	0.345976i
$855$	7.39996	+	22.7049i	0.253073	+	0.776492i
$856$	6.24846	+	10.8227i	0.213568	+	0.369911i
$857$	−19.9260	−	34.5129i	−0.680661	−	1.17894i	−0.974780	−	0.223170i	$-0.928360\pi$
$857$	−19.9260	−	34.5129i	−0.680661	−	1.17894i	0.294119	−	0.955769i	$-0.404974\pi$
$858$	13.7894	−	35.9711i	0.470761	−	1.22803i
$859$	−22.8612	−	13.1989i	−0.780015	−	0.450342i	0.0564205	−	0.998407i	$-0.482031\pi$
$859$	−22.8612	−	13.1989i	−0.780015	−	0.450342i	−0.836436	+	0.548065i	$0.815365\pi$
$860$	−2.88672	−	4.99995i	−0.0984365	−	0.170497i
$861$	−35.6750	−	17.0645i	−1.21580	−	0.581555i
$862$	10.2685	−	17.7856i	0.349747	−	0.605779i
$863$	−22.4654	+	12.9704i	−0.764731	+	0.441517i	−0.830992	−	0.556285i	$-0.812226\pi$
$863$	−22.4654	+	12.9704i	−0.764731	+	0.441517i	0.0662611	+	0.997802i	$0.478893\pi$
$864$	−4.62661	+	2.36527i	−0.157400	+	0.0804683i
$865$	−10.6052	+	18.3687i	−0.360586	+	0.624553i
$866$	5.62555			0.191164
$867$	0.104582	−	0.0847668i	0.00355178	−	0.00287883i
$868$	3.77568	−	1.79370i	0.128155	−	0.0608823i
$869$	−41.4129	+	23.9098i	−1.40484	+	0.811083i
$870$	−3.83636	+	3.10949i	−0.130065	+	0.105422i
$871$	−15.4098	+	8.89683i	−0.522140	+	0.301458i
$872$	−11.7917	−	6.80795i	−0.399318	−	0.230546i
$873$	5.91286	+	1.25124i	0.200120	+	0.0423480i
$874$			40.0987i			1.35636i
$875$	−1.13531	−	2.38979i	−0.0383804	−	0.0807895i
$876$	1.48074	−	3.86267i	0.0500295	−	0.130508i
$877$	−12.5484	+	21.7345i	−0.423731	+	0.733923i	−0.996301	−	0.0859323i	$-0.972613\pi$
$877$	−12.5484	+	21.7345i	−0.423731	+	0.733923i	0.572570	+	0.819856i	$0.305946\pi$
$878$	−2.43678			−0.0822373
$879$	−3.73801	+	3.02977i	−0.126080	+	0.102192i
$880$			4.91498i			0.165684i
$881$	−45.7419			−1.54108			−0.770541	−	0.637390i	$-0.780014\pi$
$881$	−45.7419			−1.54108			−0.770541	+	0.637390i	$0.780014\pi$
$882$	−19.5885	−	7.56900i	−0.659580	−	0.254862i
$883$	21.2954			0.716648			0.358324	−	0.933597i	$-0.383348\pi$
$883$	21.2954			0.716648			0.358324	+	0.933597i	$0.383348\pi$
$884$			18.7007i			0.628974i
$885$	−17.7332	−	6.79793i	−0.596094	−	0.228510i
$886$	−1.24401			−0.0417934
$887$	7.65797	−	13.2640i	0.257130	−	0.445361i	−0.708342	−	0.705869i	$-0.750557\pi$
$887$	7.65797	−	13.2640i	0.257130	−	0.445361i	0.965472	+	0.260508i	$0.0838900\pi$
$888$	−11.0329	−	13.6119i	−0.370239	−	0.456786i
$889$	12.3336	+	25.9617i	0.413655	+	0.870729i
$890$			5.90551i			0.197953i
$891$	−17.9189	+	40.4430i	−0.600306	+	1.35489i
$892$	9.84741	+	5.68541i	0.329716	+	0.190361i
$893$	3.13087	−	1.80761i	0.104770	−	0.0604893i
$894$	−4.85383	−	1.86070i	−0.162336	−	0.0622310i
$895$	−2.93274	+	1.69322i	−0.0980308	+	0.0565981i
$896$	−2.38979	+	1.13531i	−0.0798371	+	0.0379280i
$897$	6.19417	+	38.9945i	0.206817	+	1.30199i
$898$	17.5222			0.584724
$899$	2.25228	−	3.90106i	0.0751177	−	0.130108i
$900$	−2.23125	−	2.00538i	−0.0743749	−	0.0668459i
$901$	−44.5121	+	25.6991i	−1.48291	+	0.856160i
$902$	−21.2074	+	36.7322i	−0.706128	+	1.22305i
$903$	−2.04669	−	26.3780i	−0.0681095	−	0.877804i
$904$	8.42603	+	14.5943i	0.280246	+	0.485400i
$905$	−4.32862	−	2.49913i	−0.143888	−	0.0830738i
$906$	21.5215	+	26.5523i	0.715005	+	0.882143i
$907$	4.85322	+	8.40603i	0.161149	+	0.279118i	0.935281	−	0.353906i	$-0.115147\pi$
$907$	4.85322	+	8.40603i	0.161149	+	0.279118i	−0.774132	+	0.633024i	$0.781813\pi$
$908$	3.54296	+	6.13659i	0.117577	+	0.203650i
$909$	14.4385	+	12.9769i	0.478896	+	0.430417i
$910$	5.13757	+	10.8144i	0.170309	+	0.358494i
$911$	−5.26323	−	3.03873i	−0.174379	−	0.100677i	0.410270	−	0.911964i	$-0.365434\pi$
$911$	−5.26323	−	3.03873i	−0.174379	−	0.100677i	−0.584649	+	0.811286i	$0.698768\pi$
$912$	8.68150	+	10.7109i	0.287473	+	0.354672i
$913$			14.0164i			0.463876i
$914$		−	28.7806i		−	0.951978i
$915$	2.62298	−	6.84232i	0.0867129	−	0.226200i
$916$	2.64487	+	1.52702i	0.0873889	+	0.0504540i
$917$	−12.2885	−	0.986366i	−0.405803	−	0.0325727i
$918$	1.09477	−	21.4453i	0.0361327	−	0.707800i
$919$	18.7340	+	32.4483i	0.617979	+	1.07037i	0.989854	+	0.142088i	$0.0453817\pi$
$919$	18.7340	+	32.4483i	0.617979	+	1.07037i	−0.371875	+	0.928283i	$0.621285\pi$
$920$	−2.51872	−	4.36255i	−0.0830397	−	0.143829i
$921$	−6.28180	+	0.997848i	−0.206992	+	0.0328802i
$922$	29.4723	+	17.0159i	0.970620	+	0.560387i
$923$	18.4241	+	31.9115i	0.606438	+	1.05038i
$924$	−9.71896	+	20.3185i	−0.319730	+	0.668428i
$925$	5.05807	−	8.76083i	0.166308	−	0.288054i
$926$	−8.20674	+	4.73816i	−0.269690	+	0.155706i
$927$	−12.0705	−	2.55427i	−0.396447	−	0.0838932i
$928$	−1.42556	+	2.46914i	−0.0467963	+	0.0810535i
$929$	12.4213			0.407529			0.203765	−	0.979020i	$-0.434682\pi$
$929$	12.4213			0.407529			0.203765	+	0.979020i	$0.434682\pi$
$930$	2.55520	+	0.979525i	0.0837882	+	0.0321199i
$931$	−8.88787	+	55.0075i	−0.291288	+	1.80280i
$932$	18.5443	−	10.7066i	0.607439	−	0.350705i
$933$	1.99279	+	12.5453i	0.0652410	+	0.410715i
$934$	−14.0859	+	8.13248i	−0.460904	+	0.266103i
$935$	−17.5901	−	10.1556i	−0.575257	−	0.332125i
$936$	10.0970	+	9.07486i	0.330030	+	0.296621i
$937$		−	13.8664i		−	0.452994i	−0.974012	−	0.226497i	$-0.927273\pi$
$937$		−	13.8664i		−	0.452994i	0.974012	−	0.226497i	$-0.0727274\pi$
$938$	9.39680	−	4.46411i	0.306817	−	0.145758i
$939$	−48.8912	+	7.76623i	−1.59550	+	0.253441i
$940$	−0.227083	+	0.393319i	−0.00740662	+	0.0128286i
$941$	57.9825			1.89017			0.945087	−	0.326817i	$-0.105976\pi$
$941$	57.9825			1.89017			0.945087	+	0.326817i	$0.105976\pi$
$942$	2.29253	+	14.4323i	0.0746946	+	0.470229i
$943$		−	43.4715i		−	1.41563i
$944$	−10.9647			−0.356872
$945$	−5.25847	−	12.7023i	−0.171058	−	0.413206i
$946$	−28.3764			−0.922596
$947$		−	14.1733i		−	0.460569i	−0.973123	−	0.230284i	$-0.926034\pi$
$947$		−	14.1733i		−	0.460569i	0.973123	−	0.230284i	$-0.0739656\pi$
$948$	−2.64370	−	16.6430i	−0.0858635	−	0.540541i
$949$	−10.8080			−0.350842
$950$	−3.98007	+	6.89368i	−0.129130	+	0.223660i
$951$	−11.5309	+	1.83165i	−0.373914	+	0.0593952i
$952$	0.874799	−	10.8986i	0.0283524	−	0.353225i
$953$			10.6995i			0.346590i	0.984870	+	0.173295i	$0.0554414\pi$
$953$			10.6995i			0.346590i	−0.984870	+	0.173295i	$0.944559\pi$
$954$	−7.72472	+	36.5040i	−0.250097	+	1.18186i
$955$	4.95729	+	2.86209i	0.160414	+	0.0926151i
$956$	15.7328	−	9.08336i	0.508836	−	0.293777i
$957$	3.80773	+	23.9710i	0.123087	+	0.774873i
$958$	5.08685	−	2.93690i	0.164349	−	0.0948868i
$959$	21.5885	+	14.8869i	0.697130	+	0.480723i
$960$	−1.61729	−	0.619981i	−0.0521978	−	0.0200098i
$961$	28.5038			0.919478
$962$	−22.8891	+	39.6451i	−0.737974	+	1.27821i
$963$	−25.0610	+	27.8837i	−0.807581	+	0.898540i
$964$	−18.0606	+	10.4273i	−0.581693	+	0.335841i
$965$	2.70156	−	4.67925i	0.0869664	−	0.150630i
$966$	−1.78577	−	23.0153i	−0.0574563	−	0.740504i
$967$	2.27153	+	3.93440i	0.0730474	+	0.126522i	0.900235	−	0.435403i	$-0.143394\pi$
$967$	2.27153	+	3.93440i	0.0730474	+	0.126522i	−0.827188	+	0.561925i	$0.810061\pi$
$968$	11.3943	+	6.57852i	0.366228	+	0.211442i
$969$	−56.2710	+	8.93850i	−1.80769	+	0.287146i
$970$	1.00730	+	1.74470i	0.0323425	+	0.0560188i
$971$	12.9286	+	22.3930i	0.414899	+	0.718627i	0.995418	−	0.0956201i	$-0.0304834\pi$
$971$	12.9286	+	22.3930i	0.414899	+	0.718627i	−0.580518	+	0.814247i	$0.697150\pi$
$972$	−11.0476	−	10.9978i	−0.354351	−	0.352754i
$973$	−0.441336	−	0.304334i	−0.0141486	−	0.00975650i
$974$	7.12401	+	4.11305i	0.228268	+	0.131791i
$975$	−2.80558	+	7.31866i	−0.0898504	+	0.234385i
$976$		−	4.23073i		−	0.135423i
$977$			10.1853i			0.325855i	0.986638	+	0.162928i	$0.0520937\pi$
$977$			10.1853i			0.325855i	−0.986638	+	0.162928i	$0.947906\pi$
$978$	−14.4877	−	17.8743i	−0.463266	−	0.571559i
$979$	25.1368	+	14.5127i	0.803375	+	0.463829i
$980$	−2.48823	−	6.54284i	−0.0794836	−	0.209003i
$981$	8.45662	−	39.9627i	0.269999	−	1.27591i
$982$	−13.4461	−	23.2893i	−0.429082	−	0.743192i
$983$	12.8545	+	22.2646i	0.409993	+	0.710130i	0.994889	−	0.100979i	$-0.0321976\pi$
$983$	12.8545	+	22.2646i	0.409993	+	0.710130i	−0.584895	+	0.811109i	$0.698864\pi$
$984$	−9.41172	−	11.6118i	−0.300035	−	0.370170i
$985$	10.8373	+	6.25690i	0.345304	+	0.199361i
$986$	−5.89115	−	10.2038i	−0.187613	−	0.324954i
$987$	−1.71651	+	1.17694i	−0.0546371	+	0.0374623i
$988$	18.0109	−	31.1957i	0.573002	−	0.992468i
$989$	25.1869	−	14.5417i	0.800898	−	0.462399i
$990$	−14.0192	+	4.56910i	−0.445558	+	0.145216i
$991$	−6.19103	+	10.7232i	−0.196665	+	0.340633i	−0.947445	−	0.319919i	$-0.896344\pi$
$991$	−6.19103	+	10.7232i	−0.196665	+	0.340633i	0.750780	+	0.660552i	$0.229678\pi$
$992$	1.57993			0.0501627
$993$	−7.83184	−	49.3042i	−0.248536	−	1.56462i
$994$	−9.24457	−	19.4595i	−0.293220	−	0.617218i
$995$	−15.4969	+	8.94715i	−0.491285	+	0.283644i
$996$	−4.61214	−	1.76805i	−0.146141	−	0.0560227i
$997$	12.7588	−	7.36628i	0.404075	−	0.233293i	−0.284166	−	0.958775i	$-0.591717\pi$
$997$	12.7588	−	7.36628i	0.404075	−	0.233293i	0.688241	+	0.725483i	$0.258383\pi$
$998$	26.9361	+	15.5515i	0.852646	+	0.492276i
$999$	28.5692	−	44.1234i	0.903889	−	1.39600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.101.5	yes	32
3.2	odd	2		1890.2.bk.c.521.3		32
7.5	odd	6		630.2.t.c.551.7	yes	32
9.4	even	3		1890.2.t.c.1151.9		32
9.5	odd	6		630.2.t.c.311.7	✓	32
21.5	even	6		1890.2.t.c.1601.9		32
63.5	even	6	inner	630.2.bk.c.131.13	yes	32
63.40	odd	6		1890.2.bk.c.341.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.7	✓	32	9.5	odd	6
630.2.t.c.551.7	yes	32	7.5	odd	6
630.2.bk.c.101.5	yes	32	1.1	even	1	trivial
630.2.bk.c.131.13	yes	32	63.5	even	6	inner
1890.2.t.c.1151.9		32	9.4	even	3
1890.2.t.c.1601.9		32	21.5	even	6
1890.2.bk.c.341.3		32	63.40	odd	6
1890.2.bk.c.521.3		32	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.271725 + 1.71060i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.71060 - 0.271725i) q^{6} +(1.13531 + 2.38979i) q^{7} +1.00000i q^{8} +(-2.85233 + 0.929628i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.271725 + 1.71060i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.71060 - 0.271725i) q^{6} +(1.13531 + 2.38979i) q^{7} +1.00000i q^{8} +(-2.85233 + 0.929628i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-4.25650 + 2.45749i) q^{11} +(-0.271725 - 1.71060i) q^{12} +(-3.91899 + 2.26263i) q^{13} +(2.38979 - 1.13531i) q^{14} +(1.61729 + 0.619981i) q^{15} +1.00000 q^{16} +(-2.06626 + 3.57887i) q^{17} +(0.929628 + 2.85233i) q^{18} +(6.89368 - 3.98007i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.77948 + 2.59143i) q^{21} +(2.45749 + 4.25650i) q^{22} +(-4.36255 - 2.51872i) q^{23} +(-1.71060 + 0.271725i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.26263 + 3.91899i) q^{26} +(-2.36527 - 4.62661i) q^{27} +(-1.13531 - 2.38979i) q^{28} +(-2.46914 - 1.42556i) q^{29} +(0.619981 - 1.61729i) q^{30} +1.57993i q^{31} -1.00000i q^{32} +(-5.36039 - 6.61342i) q^{33} +(3.57887 + 2.06626i) q^{34} +(2.63727 + 0.211686i) q^{35} +(2.85233 - 0.929628i) q^{36} +(5.05807 + 8.76083i) q^{37} +(-3.98007 - 6.89368i) q^{38} +(-4.93536 - 6.08903i) q^{39} +(0.866025 + 0.500000i) q^{40} +(4.31484 + 7.47352i) q^{41} +(2.59143 + 3.77948i) q^{42} +(-2.88672 + 4.99995i) q^{43} +(4.25650 - 2.45749i) q^{44} +(-0.621084 + 2.93500i) q^{45} +(-2.51872 + 4.36255i) q^{46} +0.454165 q^{47} +(0.271725 + 1.71060i) q^{48} +(-4.42215 + 5.42629i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-6.68348 - 2.56208i) q^{51} +(3.91899 - 2.26263i) q^{52} +(10.7712 + 6.21874i) q^{53} +(-4.62661 + 2.36527i) q^{54} +4.91498i q^{55} +(-2.38979 + 1.13531i) q^{56} +(8.68150 + 10.7109i) q^{57} +(-1.42556 + 2.46914i) q^{58} -10.9647 q^{59} +(-1.61729 - 0.619981i) q^{60} -4.23073i q^{61} +1.57993 q^{62} +(-5.45989 - 5.76104i) q^{63} -1.00000 q^{64} +4.52526i q^{65} +(-6.61342 + 5.36039i) q^{66} +3.93207 q^{67} +(2.06626 - 3.57887i) q^{68} +(3.12312 - 8.14699i) q^{69} +(0.211686 - 2.63727i) q^{70} -8.14278i q^{71} +(-0.929628 - 2.85233i) q^{72} +(2.06838 + 1.19418i) q^{73} +(8.76083 - 5.05807i) q^{74} +(1.34556 - 1.09062i) q^{75} +(-6.89368 + 3.98007i) q^{76} +(-10.7053 - 7.38211i) q^{77} +(-6.08903 + 4.93536i) q^{78} +9.72934 q^{79} +(0.500000 - 0.866025i) q^{80} +(7.27159 - 5.30321i) q^{81} +(7.47352 - 4.31484i) q^{82} +(1.42589 - 2.46971i) q^{83} +(3.77948 - 2.59143i) q^{84} +(2.06626 + 3.57887i) q^{85} +(4.99995 + 2.88672i) q^{86} +(1.76764 - 4.61108i) q^{87} +(-2.45749 - 4.25650i) q^{88} +(-2.95275 - 5.11432i) q^{89} +(2.93500 + 0.621084i) q^{90} +(-9.85647 - 6.79677i) q^{91} +(4.36255 + 2.51872i) q^{92} +(-2.70263 + 0.429305i) q^{93} -0.454165i q^{94} -7.96013i q^{95} +(1.71060 - 0.271725i) q^{96} +(-1.74470 - 1.00730i) q^{97} +(5.42629 + 4.42215i) q^{98} +(9.85639 - 10.9665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

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