LMFDB - Embedded newform 630.2.t.c.311.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 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("630.311");

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.t (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			311.7
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.61729 - 0.619981i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.71060 - 0.271725i) q^{6} +(-2.63727 - 0.211686i) q^{7} -1.00000i q^{8} +(2.23125 - 2.00538i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.61729 - 0.619981i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.71060 - 0.271725i) q^{6} +(-2.63727 - 0.211686i) q^{7} -1.00000i q^{8} +(2.23125 - 2.00538i) q^{9} +(-0.866025 - 0.500000i) q^{10} +4.91498i q^{11} +(1.34556 + 1.09062i) q^{12} +(3.91899 + 2.26263i) q^{13} +(2.17810 + 1.50196i) q^{14} +(1.61729 - 0.619981i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.06626 - 3.57887i) q^{17} +(-2.93500 + 0.621084i) q^{18} +(6.89368 - 3.98007i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.39647 + 1.29270i) q^{21} +(2.45749 - 4.25650i) q^{22} -5.03744i q^{23} +(-0.619981 - 1.61729i) q^{24} +1.00000 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} +(-1.71060 - 0.271725i) q^{30} +(1.36826 - 0.789963i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.04720 + 7.94895i) 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} -7.96013 q^{38} +(7.74094 + 1.22963i) q^{39} -1.00000i q^{40} +(-4.31484 + 7.47352i) q^{41} +(4.45380 + 1.07872i) q^{42} +(-2.88672 - 4.99995i) q^{43} +(-4.25650 + 2.45749i) q^{44} +(2.23125 - 2.00538i) q^{45} +(-2.51872 + 4.36255i) q^{46} +(0.227083 - 0.393319i) q^{47} +(-0.271725 + 1.71060i) q^{48} +(6.91038 + 1.11655i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(1.12291 - 7.06910i) q^{51} +4.52526i q^{52} +(-10.7712 - 6.21874i) q^{53} +(-4.36169 + 2.82412i) q^{54} +4.91498i q^{55} +(-0.211686 + 2.63727i) q^{56} +(8.68150 - 10.7109i) q^{57} +2.85112 q^{58} +(-5.48237 - 9.49575i) q^{59} +(1.34556 + 1.09062i) q^{60} +(3.66392 + 2.11537i) q^{61} -1.57993 q^{62} +(-6.30891 + 4.81640i) q^{63} -1.00000 q^{64} +(3.91899 + 2.26263i) q^{65} +(1.33552 - 8.40759i) q^{66} +(-1.96604 - 3.40527i) q^{67} +4.13252 q^{68} +(-3.12312 - 8.14699i) q^{69} +(2.17810 + 1.50196i) q^{70} +8.14278i q^{71} +(-2.00538 - 2.23125i) q^{72} +(2.06838 + 1.19418i) q^{73} -10.1161i q^{74} +(1.61729 - 0.619981i) q^{75} +(6.89368 + 3.98007i) q^{76} +(1.04044 - 12.9621i) q^{77} +(-6.08903 - 4.93536i) q^{78} +(-4.86467 + 8.42586i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(0.956923 - 8.94898i) q^{81} +(7.47352 - 4.31484i) q^{82} +(-1.42589 - 2.46971i) q^{83} +(-3.31774 - 3.16110i) q^{84} +(2.06626 - 3.57887i) q^{85} +5.77345i q^{86} +(-3.10949 + 3.83636i) q^{87} +4.91498 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} +(1.72310 - 2.12589i) q^{93} +(-0.393319 + 0.227083i) q^{94} +(6.89368 - 3.98007i) q^{95} +(1.09062 - 1.34556i) 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} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.61729	−	0.619981i	0.933742	−	0.357946i
$3$	1.61729	−	0.619981i	0.933742	−	0.357946i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.71060	−	0.271725i	−0.698351	−	0.110931i
$7$	−2.63727	−	0.211686i	−0.996794	−	0.0800100i
$7$	−2.63727	−	0.211686i	−0.996794	−	0.0800100i
$8$		−	1.00000i		−	0.353553i
$9$	2.23125	−	2.00538i	0.743749	−	0.668459i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			4.91498i			1.48192i	0.671548	+	0.740961i	$0.265630\pi$
$11$			4.91498i			1.48192i	−0.671548	+	0.740961i	$0.734370\pi$
$12$	1.34556	+	1.09062i	0.388431	+	0.314836i
$13$	3.91899	+	2.26263i	1.08693	+	0.627541i	0.932758	−	0.360502i	$-0.117395\pi$
$13$	3.91899	+	2.26263i	1.08693	+	0.627541i	0.154175	+	0.988044i	$0.450728\pi$
$14$	2.17810	+	1.50196i	0.582121	+	0.401416i
$15$	1.61729	−	0.619981i	0.417582	−	0.160078i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.06626	−	3.57887i	0.501142	−	0.868003i	−0.498857	−	0.866684i	$-0.666247\pi$
$17$	2.06626	−	3.57887i	0.501142	−	0.868003i	0.999999	−	0.00131881i	$-0.000419790\pi$
$18$	−2.93500	+	0.621084i	−0.691787	+	0.146391i
$19$	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
$21$	−4.39647	+	1.29270i	−0.959388	+	0.282090i
$22$	2.45749	−	4.25650i	0.523939	−	0.907489i
$23$		−	5.03744i		−	1.05038i	−0.850986	−	0.525189i	$-0.823995\pi$
$23$		−	5.03744i		−	1.05038i	0.850986	−	0.525189i	$-0.176005\pi$
$24$	−0.619981	−	1.61729i	−0.126553	−	0.330128i
$25$	1.00000			0.200000
$26$	−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	−0.711417	−	0.702770i	$-0.751946\pi$
$29$	−2.46914	+	1.42556i	−0.458508	+	0.264720i	0.252909	+	0.967490i	$0.418613\pi$
$30$	−1.71060	−	0.271725i	−0.312312	−	0.0496100i
$31$	1.36826	−	0.789963i	0.245746	−	0.141882i	−0.372069	−	0.928205i	$-0.621351\pi$
$31$	1.36826	−	0.789963i	0.245746	−	0.141882i	0.617815	+	0.786324i	$0.288018\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.04720	+	7.94895i	0.530449	+	1.38373i
$34$	−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	$0.520792\pi$
$38$	−7.96013			−1.29130
$39$	7.74094	+	1.22963i	1.23954	+	0.196898i
$40$		−	1.00000i		−	0.158114i
$41$	−4.31484	+	7.47352i	−0.673865	+	1.16717i	0.302935	+	0.953011i	$0.402034\pi$
$41$	−4.31484	+	7.47352i	−0.673865	+	1.16717i	−0.976799	+	0.214156i	$0.931300\pi$
$42$	4.45380	+	1.07872i	0.687237	+	0.166451i
$43$	−2.88672	−	4.99995i	−0.440221	−	0.762486i	0.557484	−	0.830187i	$-0.311767\pi$
$43$	−2.88672	−	4.99995i	−0.440221	−	0.762486i	−0.997706	+	0.0677018i	$0.978433\pi$
$44$	−4.25650	+	2.45749i	−0.641691	+	0.370481i
$45$	2.23125	−	2.00538i	0.332615	−	0.298944i
$46$	−2.51872	+	4.36255i	−0.371365	+	0.643223i
$47$	0.227083	−	0.393319i	0.0331234	−	0.0573714i	−0.848988	−	0.528411i	$-0.822788\pi$
$47$	0.227083	−	0.393319i	0.0331234	−	0.0573714i	0.882112	+	0.471040i	$0.156121\pi$
$48$	−0.271725	+	1.71060i	−0.0392201	+	0.246904i
$49$	6.91038	+	1.11655i	0.987197	+	0.159507i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	1.12291	−	7.06910i	0.157239	−	0.989873i
$52$			4.52526i			0.627541i
$53$	−10.7712	−	6.21874i	−1.47953	−	0.854209i	−0.479802	−	0.877377i	$-0.659292\pi$
$53$	−10.7712	−	6.21874i	−1.47953	−	0.854209i	−0.999732	+	0.0231676i	$0.992625\pi$
$54$	−4.36169	+	2.82412i	−0.593551	+	0.384314i
$55$			4.91498i			0.662736i
$56$	−0.211686	+	2.63727i	−0.0282878	+	0.352420i
$57$	8.68150	−	10.7109i	1.14989	−	1.41869i
$58$	2.85112			0.374370
$59$	−5.48237	−	9.49575i	−0.713744	−	1.23624i	−0.963442	−	0.267917i	$-0.913665\pi$
$59$	−5.48237	−	9.49575i	−0.713744	−	1.23624i	0.249698	−	0.968324i	$-0.419669\pi$
$60$	1.34556	+	1.09062i	0.173712	+	0.140799i
$61$	3.66392	+	2.11537i	0.469117	+	0.270845i	0.715870	−	0.698233i	$-0.246030\pi$
$61$	3.66392	+	2.11537i	0.469117	+	0.270845i	−0.246753	+	0.969078i	$0.579364\pi$
$62$	−1.57993			−0.200651
$63$	−6.30891	+	4.81640i	−0.794848	+	0.606809i
$64$	−1.00000			−0.125000
$65$	3.91899	+	2.26263i	0.486091	+	0.280645i
$66$	1.33552	−	8.40759i	0.164392	−	1.03490i
$67$	−1.96604	−	3.40527i	−0.240189	−	0.416020i	0.720579	−	0.693373i	$-0.243876\pi$
$67$	−1.96604	−	3.40527i	−0.240189	−	0.416020i	−0.960768	+	0.277353i	$0.910543\pi$
$68$	4.13252			0.501142
$69$	−3.12312	−	8.14699i	−0.375979	−	0.980782i
$70$	2.17810	+	1.50196i	0.260333	+	0.179519i
$71$			8.14278i			0.966371i	0.875518	+	0.483185i	$0.160520\pi$
$71$			8.14278i			0.966371i	−0.875518	+	0.483185i	$0.839480\pi$
$72$	−2.00538	−	2.23125i	−0.236336	−	0.262955i
$73$	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	$0.622031\pi$
$74$		−	10.1161i		−	1.17598i
$75$	1.61729	−	0.619981i	0.186748	−	0.0715893i
$76$	6.89368	+	3.98007i	0.790759	+	0.456545i
$77$	1.04044	−	12.9621i	0.118569	−	1.47717i
$78$	−6.08903	−	4.93536i	−0.689447	−	0.558819i
$79$	−4.86467	+	8.42586i	−0.547318	+	0.947983i	0.451139	+	0.892454i	$0.351018\pi$
$79$	−4.86467	+	8.42586i	−0.547318	+	0.947983i	−0.998457	+	0.0555291i	$0.982315\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	0.956923	−	8.94898i	0.106325	−	0.994331i
$82$	7.47352	−	4.31484i	0.825312	−	0.476494i
$83$	−1.42589	−	2.46971i	−0.156512	−	0.271086i	0.777097	−	0.629381i	$-0.216691\pi$
$83$	−1.42589	−	2.46971i	−0.156512	−	0.271086i	−0.933608	+	0.358295i	$0.883358\pi$
$84$	−3.31774	−	3.16110i	−0.361996	−	0.344905i
$85$	2.06626	−	3.57887i	0.224117	−	0.388183i
$86$			5.77345i			0.622567i
$87$	−3.10949	+	3.83636i	−0.333373	+	0.411301i
$88$	4.91498			0.523939
$89$	2.95275	+	5.11432i	0.312991	+	0.542117i	0.979008	−	0.203820i	$-0.0653356\pi$
$89$	2.95275	+	5.11432i	0.312991	+	0.542117i	−0.666017	+	0.745936i	$0.732002\pi$
$90$	−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
$93$	1.72310	−	2.12589i	0.178678	−	0.220445i
$94$	−0.393319	+	0.227083i	−0.0405677	+	0.0234218i
$95$	6.89368	−	3.98007i	0.707276	−	0.408346i
$96$	1.09062	−	1.34556i	0.111311	−	0.137331i
$97$	1.74470	−	1.00730i	0.177147	−	0.102276i	−0.408805	−	0.912622i	$-0.634054\pi$
$97$	1.74470	−	1.00730i	0.177147	−	0.102276i	0.585952	+	0.810346i	$0.300721\pi$
$98$	−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
$101$	−6.47106			−0.643895			−0.321947	−	0.946758i	$-0.604337\pi$
$101$	−6.47106			−0.643895			−0.321947	+	0.946758i	$0.604337\pi$
$102$	−4.50702	+	5.56057i	−0.446261	+	0.550578i
$103$		−	4.11259i		−	0.405226i	−0.979259	−	0.202613i	$-0.935057\pi$
$103$		−	4.11259i		−	0.405226i	0.979259	−	0.202613i	$-0.0649433\pi$
$104$	2.26263	−	3.91899i	0.221869	−	0.384289i
$105$	−4.39647	+	1.29270i	−0.429051	+	0.126155i
$106$	6.21874	+	10.7712i	0.604017	+	1.04619i
$107$	−10.8227	+	6.24846i	−1.04627	+	0.604061i	−0.921601	−	0.388138i	$-0.873119\pi$
$107$	−10.8227	+	6.24846i	−1.04627	+	0.604061i	−0.124664	+	0.992199i	$0.539785\pi$
$108$	5.18939	−	0.264915i	0.499350	−	0.0254915i
$109$	−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	$0.940562\pi$
$110$	2.45749	−	4.25650i	0.234313	−	0.405841i
$111$	13.6119	+	11.0329i	1.29198	+	1.04719i
$112$	1.50196	−	2.17810i	0.141922	−	0.205811i
$113$	14.5943	+	8.42603i	1.37292	+	0.792655i	0.991294	−	0.131663i	$-0.0420318\pi$
$113$	14.5943	+	8.42603i	1.37292	+	0.792655i	0.381623	+	0.924318i	$0.375365\pi$
$114$	−12.8738	+	4.93513i	−1.20574	+	0.462217i
$115$		−	5.03744i		−	0.469743i
$116$	−2.46914	−	1.42556i	−0.229254	−	0.132360i
$117$	13.2817	−	2.81057i	1.22789	−	0.259837i
$118$			10.9647i			1.00939i
$119$	−6.20688	+	9.00104i	−0.568984	+	0.825124i
$120$	−0.619981	−	1.61729i	−0.0565963	−	0.147638i
$121$	−13.1570			−1.19610
$122$	−2.11537	−	3.66392i	−0.191516	−	0.331716i
$123$	−2.34490	+	14.7620i	−0.211432	+	1.33104i
$124$	1.36826	+	0.789963i	0.122873	+	0.0709408i
$125$	1.00000			0.0894427
$126$	7.87187	−	1.01667i	0.701282	−	0.0905718i
$127$	10.8636			0.963991			0.481996	−	0.876174i	$-0.339912\pi$
$127$	10.8636			0.963991			0.481996	+	0.876174i	$0.339912\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−7.76854	−	6.29665i	−0.683982	−	0.554389i
$130$	−2.26263	−	3.91899i	−0.198446	−	0.343719i
$131$	−4.65956			−0.407108			−0.203554	−	0.979064i	$-0.565249\pi$
$131$	−4.65956			−0.407108			−0.203554	+	0.979064i	$0.565249\pi$
$132$	−5.36039	+	6.61342i	−0.466562	+	0.575624i
$133$	−19.0230	+	9.03721i	−1.64950	+	0.783625i
$134$			3.93207i			0.339679i
$135$	2.36527	−	4.62661i	0.203570	−	0.398195i
$136$	−3.57887	−	2.06626i	−0.306885	−	0.177180i
$137$		−	9.91164i		−	0.846808i	−0.905941	−	0.423404i	$-0.860835\pi$
$137$		−	9.91164i		−	0.846808i	0.905941	−	0.423404i	$-0.139165\pi$
$138$	−1.36880	+	8.61706i	−0.116520	+	0.733533i
$139$	0.175478	+	0.101312i	0.0148838	+	0.00859319i	0.507423	−	0.861697i	$-0.330598\pi$
$139$	0.175478	+	0.101312i	0.0148838	+	0.00859319i	−0.492540	+	0.870290i	$0.663931\pi$
$140$	−1.13531	−	2.38979i	−0.0959511	−	0.201974i
$141$	0.123408	−	0.776897i	0.0103928	−	0.0654265i
$142$	4.07139	−	7.05186i	0.341664	−	0.591779i
$143$	−11.1208	+	19.2618i	−0.929968	+	1.61075i
$144$	0.621084	+	2.93500i	0.0517570	+	0.244584i
$145$	−2.46914	+	1.42556i	−0.205051	+	0.118386i
$146$	−1.19418	−	2.06838i	−0.0988311	−	0.171181i
$147$	11.8683	−	2.47852i	0.978882	−	0.204425i
$148$	−5.05807	+	8.76083i	−0.415770	+	0.720136i
$149$		−	3.00122i		−	0.245869i	−0.992415	−	0.122935i	$-0.960769\pi$
$149$		−	3.00122i		−	0.245869i	0.992415	−	0.122935i	$-0.0392305\pi$
$150$	−1.71060	−	0.271725i	−0.139670	−	0.0221863i
$151$	−19.7332			−1.60587			−0.802935	−	0.596067i	$-0.796729\pi$
$151$	−19.7332			−1.60587			−0.802935	+	0.596067i	$0.796729\pi$
$152$	−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
$156$	2.80558	+	7.31866i	0.224626	+	0.585962i
$157$	7.30661	−	4.21847i	0.583131	−	0.336671i	−0.179246	−	0.983804i	$-0.557366\pi$
$157$	7.30661	−	4.21847i	0.583131	−	0.336671i	0.762377	+	0.647134i	$0.224032\pi$
$158$	8.42586	−	4.86467i	0.670325	−	0.387012i
$159$	−21.2756	−	3.37957i	−1.68726	−	0.268018i
$160$	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	$-0.340823\pi$
$164$	−8.62968			−0.673865
$165$	3.04720	+	7.94895i	0.237224	+	0.618825i
$166$			2.85178i			0.221341i
$167$	−8.15100	+	14.1179i	−0.630743	+	1.09248i	0.356657	+	0.934235i	$0.383916\pi$
$167$	−8.15100	+	14.1179i	−0.630743	+	1.09248i	−0.987400	+	0.158243i	$0.949417\pi$
$168$	1.29270	+	4.39647i	0.0997339	+	0.339195i
$169$	3.73901	+	6.47616i	0.287616	+	0.498166i
$170$	−3.57887	+	2.06626i	−0.274487	+	0.158475i
$171$	7.39996	−	22.7049i	0.565889	−	1.73629i
$172$	2.88672	−	4.99995i	0.220111	−	0.381243i
$173$	−10.6052	+	18.3687i	−0.806295	+	1.39654i	0.109119	+	0.994029i	$0.465197\pi$
$173$	−10.6052	+	18.3687i	−0.806295	+	1.39654i	−0.915413	+	0.402515i	$0.868136\pi$
$174$	4.61108	−	1.76764i	0.349565	−	0.134004i
$175$	−2.63727	−	0.211686i	−0.199359	−	0.0160020i
$176$	−4.25650	−	2.45749i	−0.320846	−	0.185240i
$177$	−14.7538	−	11.9584i	−1.10896	−	0.898848i
$178$		−	5.90551i		−	0.442636i
$179$	2.93274	+	1.69322i	0.219203	+	0.126557i	0.605581	−	0.795783i	$-0.292941\pi$
$179$	2.93274	+	1.69322i	0.219203	+	0.126557i	−0.386378	+	0.922341i	$0.626274\pi$
$180$	2.85233	+	0.929628i	0.212600	+	0.0692904i
$181$		−	4.99826i		−	0.371517i	−0.982595	−	0.185759i	$-0.940526\pi$
$181$		−	4.99826i		−	0.371517i	0.982595	−	0.185759i	$-0.0594743\pi$
$182$	5.13757	+	10.8144i	0.380822	+	0.801617i
$183$	7.23711	+	1.14960i	0.534983	+	0.0849806i
$184$	−5.03744			−0.371365
$185$	5.05807	+	8.76083i	0.371876	+	0.644109i
$186$	−2.55520	+	0.979525i	−0.187356	+	0.0718222i
$187$	17.5901	+	10.1556i	1.28631	+	0.742653i
$188$	0.454165			0.0331234
$189$	−7.21725	+	11.7009i	−0.524978	+	0.851116i
$190$	−7.96013			−0.577489
$191$	4.95729	+	2.86209i	0.358697	+	0.207094i	0.668509	−	0.743704i	$-0.266933\pi$
$191$	4.95729	+	2.86209i	0.358697	+	0.207094i	−0.309812	+	0.950798i	$0.600266\pi$
$192$	−1.61729	+	0.619981i	−0.116718	+	0.0447433i
$193$	−2.70156	−	4.67925i	−0.194463	−	0.336820i	0.752261	−	0.658865i	$-0.228963\pi$
$193$	−2.70156	−	4.67925i	−0.194463	−	0.336820i	−0.946724	+	0.322045i	$0.895630\pi$
$194$	−2.01460			−0.144640
$195$	7.74094	+	1.22963i	0.554340	+	0.0880555i
$196$	2.48823	+	6.54284i	0.177731	+	0.467345i
$197$		−	12.5138i		−	0.891571i	−0.895140	−	0.445786i	$-0.852924\pi$
$197$		−	12.5138i		−	0.891571i	0.895140	−	0.445786i	$-0.147076\pi$
$198$	−3.05262	−	14.4255i	−0.216940	−	1.02518i
$199$	−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	$0.885356\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−5.29085	−	4.28840i	−0.373188	−	0.302481i
$202$	5.60410	+	3.23553i	0.394303	+	0.227651i
$203$	6.81356	−	3.23690i	0.478218	−	0.227186i
$204$	6.68348	−	2.56208i	0.467937	−	0.179382i
$205$	−4.31484	+	7.47352i	−0.301361	+	0.521973i
$206$	−2.05630	+	3.56161i	−0.143269	+	0.248149i
$207$	−10.1020	−	11.2398i	−0.702135	−	0.781218i
$208$	−3.91899	+	2.26263i	−0.271733	+	0.156885i
$209$	19.5620	+	33.8823i	1.35313	+	2.34369i
$210$	4.45380	+	1.07872i	0.307342	+	0.0744390i
$211$	−8.73086	+	15.1223i	−0.601057	+	1.04106i	0.391604	+	0.920134i	$0.371920\pi$
$211$	−8.73086	+	15.1223i	−0.601057	+	1.04106i	−0.992661	+	0.120928i	$0.961413\pi$
$212$		−	12.4375i		−	0.854209i
$213$	5.04837	+	13.1692i	0.345909	+	0.902341i
$214$	12.4969			0.854272
$215$	−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
$219$	4.08554	+	0.648978i	0.276075	+	0.0438538i
$220$	−4.25650	+	2.45749i	−0.286973	+	0.165684i
$221$	16.1953	−	9.35037i	1.08942	−	0.628974i
$222$	−6.27181	−	16.3607i	−0.420936	−	1.09806i
$223$	9.84741	−	5.68541i	0.659431	−	0.380723i	−0.132629	−	0.991166i	$-0.542342\pi$
$223$	9.84741	−	5.68541i	0.659431	−	0.380723i	0.792060	+	0.610443i	$0.209008\pi$
$224$	−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
$227$	−7.08592			−0.470309			−0.235155	−	0.971958i	$-0.575560\pi$
$227$	−7.08592			−0.470309			−0.235155	+	0.971958i	$0.575560\pi$
$228$	13.6166	+	2.16297i	0.901784	+	0.143246i
$229$			3.05403i			0.201816i	0.994896	+	0.100908i	$0.0321748\pi$
$229$			3.05403i			0.201816i	−0.994896	+	0.100908i	$0.967825\pi$
$230$	−2.51872	+	4.36255i	−0.166079	+	0.287658i
$231$	−6.35359	−	21.6086i	−0.418036	−	1.42174i
$232$	1.42556	+	2.46914i	0.0935925	+	0.162107i
$233$	18.5443	−	10.7066i	1.21488	−	0.701410i	0.251060	−	0.967972i	$-0.419221\pi$
$233$	18.5443	−	10.7066i	1.21488	−	0.701410i	0.963818	+	0.266562i	$0.0858877\pi$
$234$	−12.9076	−	4.20681i	−0.843793	−	0.275008i
$235$	0.227083	−	0.393319i	0.0148132	−	0.0256573i
$236$	5.48237	−	9.49575i	0.356872	−	0.618120i
$237$	−2.64370	+	16.6430i	−0.171727	+	1.08108i
$238$	9.87584	−	4.69169i	0.640155	−	0.304117i
$239$	−15.7328	−	9.08336i	−1.01767	−	0.587554i	−0.104244	−	0.994552i	$-0.533242\pi$
$239$	−15.7328	−	9.08336i	−1.01767	−	0.587554i	−0.913429	+	0.406998i	$0.866576\pi$
$240$	−0.271725	+	1.71060i	−0.0175398	+	0.110419i
$241$			20.8546i			1.34336i	0.740840	+	0.671681i	$0.234428\pi$
$241$			20.8546i			1.34336i	−0.740840	+	0.671681i	$0.765572\pi$
$242$	11.3943	+	6.57852i	0.732456	+	0.422883i
$243$	−4.00058	−	15.0664i	−0.256637	−	0.966508i
$244$			4.23073i			0.270845i
$245$	6.91038	+	1.11655i	0.441488	+	0.0713337i
$246$	9.41172	−	11.6118i	0.600069	−	0.740340i
$247$	36.0217			2.29201
$248$	−0.789963	−	1.36826i	−0.0501627	−	0.0868844i
$249$	−3.83725	−	3.11021i	−0.243176	−	0.197102i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	−27.8633			−1.75872			−0.879359	−	0.476159i	$-0.842029\pi$
$251$	−27.8633			−1.75872			−0.879359	+	0.476159i	$0.842029\pi$
$252$	−7.32558	−	3.05548i	−0.461468	−	0.192477i
$253$	24.7589			1.55658
$254$	−9.40818	−	5.43182i	−0.590322	−	0.340822i
$255$	1.12291	−	7.06910i	0.0703193	−	0.442685i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−17.0070			−1.06087			−0.530433	−	0.847727i	$-0.677971\pi$
$257$	−17.0070			−1.06087			−0.530433	+	0.847727i	$0.677971\pi$
$258$	3.57943	+	9.33733i	0.222846	+	0.581317i
$259$	−11.4849	−	24.1754i	−0.713639	−	1.50219i
$260$			4.52526i			0.280645i
$261$	−2.65048	+	8.13233i	−0.164060	+	0.503379i
$262$	4.03530	+	2.32978i	0.249302	+	0.143934i
$263$		−	3.06763i		−	0.189158i	−0.995517	−	0.0945791i	$-0.969849\pi$
$263$		−	3.06763i		−	0.189158i	0.995517	−	0.0945791i	$-0.0301505\pi$
$264$	7.94895	−	3.04720i	0.489224	−	0.187542i
$265$	−10.7712	−	6.21874i	−0.661668	−	0.382014i
$266$	20.9930	+	1.68505i	1.28716	+	0.103317i
$267$	7.94624	+	6.44068i	0.486302	+	0.394163i
$268$	1.96604	−	3.40527i	0.120095	−	0.208010i
$269$	−3.48949	+	6.04397i	−0.212758	+	0.368507i	−0.952577	−	0.304299i	$-0.901578\pi$
$269$	−3.48949	+	6.04397i	−0.212758	+	0.368507i	0.739819	+	0.672806i	$0.234911\pi$
$270$	−4.36169	+	2.82412i	−0.265444	+	0.171871i
$271$	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
$273$	−20.1546	−	4.88151i	−1.21981	−	0.295442i
$274$	−4.95582	+	8.58373i	−0.299392	+	0.518562i
$275$			4.91498i			0.296385i
$276$	5.49394	−	6.77819i	0.330696	−	0.407999i
$277$	−28.3005			−1.70042			−0.850208	−	0.526448i	$-0.823524\pi$
$277$	−28.3005			−1.70042			−0.850208	+	0.526448i	$0.823524\pi$
$278$	−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	−0.144959	−	0.989438i	$-0.546305\pi$
$281$	10.7190	−	6.18859i	0.639439	−	0.369180i	0.784399	+	0.620257i	$0.212972\pi$
$282$	−0.495323	+	0.611108i	−0.0294960	+	0.0363910i
$283$	−18.7596	+	10.8309i	−1.11514	+	0.643827i	−0.940156	−	0.340744i	$-0.889321\pi$
$283$	−18.7596	+	10.8309i	−1.11514	+	0.643827i	−0.174985	+	0.984571i	$0.555988\pi$
$284$	−7.05186	+	4.07139i	−0.418451	+	0.241593i
$285$	8.68150	−	10.7109i	0.514248	−	0.634457i
$286$	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
$290$	2.85112			0.167423
$291$	2.19717	−	2.71077i	0.128800	−	0.158908i
$292$			2.38836i			0.139768i
$293$	−1.38901	+	2.40584i	−0.0811469	+	0.140551i	−0.903743	−	0.428076i	$-0.859192\pi$
$293$	−1.38901	+	2.40584i	−0.0811469	+	0.140551i	0.822596	+	0.568626i	$0.192525\pi$
$294$	−11.5175	−	3.78769i	−0.671716	−	0.220903i
$295$	−5.48237	−	9.49575i	−0.319196	−	0.552864i
$296$	8.76083	−	5.05807i	0.509213	−	0.293994i
$297$	22.7397	+	11.6253i	1.31949	+	0.674567i
$298$	−1.50061	+	2.59913i	−0.0869279	+	0.150564i
$299$	11.3979	−	19.7417i	0.659156	−	1.14169i
$300$	1.34556	+	1.09062i	0.0776862	+	0.0629671i
$301$	6.55465	+	13.7973i	0.377804	+	0.795263i
$302$	17.0895	+	9.86662i	0.983390	+	0.567760i
$303$	−10.4656	+	4.01194i	−0.601232	+	0.230480i
$304$			7.96013i			0.456545i
$305$	3.66392	+	2.11537i	0.209796	+	0.121126i
$306$	−3.84170	+	11.7873i	−0.219616	+	0.673836i
$307$			3.67227i			0.209588i	0.994494	+	0.104794i	$0.0334183\pi$
$307$			3.67227i			0.209588i	−0.994494	+	0.104794i	$0.966582\pi$
$308$	11.7458	−	5.58002i	0.669276	−	0.317951i
$309$	−2.54973	−	6.65125i	−0.145049	−	0.378377i
$310$	−1.57993			−0.0897338
$311$	3.66692	+	6.35130i	0.207932	+	0.360149i	0.951063	−	0.308997i	$-0.0999934\pi$
$311$	3.66692	+	6.35130i	0.207932	+	0.360149i	−0.743131	+	0.669146i	$0.766660\pi$
$312$	1.22963	−	7.74094i	0.0696139	−	0.438244i
$313$	−24.7521	−	14.2906i	−1.39907	−	0.807753i	−0.404775	−	0.914417i	$-0.632650\pi$
$313$	−24.7521	−	14.2906i	−1.39907	−	0.807753i	−0.994295	+	0.106663i	$0.965983\pi$
$314$	−8.43694			−0.476124
$315$	−6.30891	+	4.81640i	−0.355467	+	0.271373i
$316$	−9.72934			−0.547318
$317$	5.83771	+	3.37041i	0.327879	+	0.189301i	0.654899	−	0.755717i	$-0.272711\pi$
$317$	5.83771	+	3.37041i	0.327879	+	0.189301i	−0.327020	+	0.945017i	$0.606045\pi$
$318$	16.7354	+	13.5646i	0.938475	+	0.760664i
$319$	−7.00660	−	12.1358i	−0.392294	−	0.679473i
$320$	−1.00000			−0.0559017
$321$	−13.6294	+	16.8154i	−0.760720	+	0.938544i
$322$	7.56603	−	10.9720i	0.421638	−	0.611448i
$323$		−	32.8954i		−	1.83035i
$324$	8.22851	−	3.64577i	0.457139	−	0.202543i
$325$	3.91899	+	2.26263i	0.217387	+	0.125508i
$326$			13.2839i			0.735728i
$327$	−3.69978	+	23.2914i	−0.204598	+	1.28802i
$328$	7.47352	+	4.31484i	0.412656	+	0.238247i
$329$	−0.682138	+	0.989217i	−0.0376075	+	0.0545373i
$330$	1.33552	−	8.40759i	0.0735181	−	0.462822i
$331$	14.4113	−	24.9612i	0.792119	−	1.37199i	−0.132534	−	0.991178i	$-0.542311\pi$
$331$	14.4113	−	24.9612i	0.792119	−	1.37199i	0.924653	−	0.380811i	$-0.124355\pi$
$332$	1.42589	−	2.46971i	0.0782558	−	0.135543i
$333$	28.8546	+	9.40424i	1.58122	+	0.515349i
$334$	14.1179	−	8.15100i	0.772499	−	0.446003i
$335$	−1.96604	−	3.40527i	−0.107416	−	0.186050i
$336$	1.07872	−	4.45380i	0.0588492	−	0.242975i
$337$	12.0913	−	20.9427i	0.658652	−	1.14082i	−0.322312	−	0.946633i	$-0.604460\pi$
$337$	12.0913	−	20.9427i	0.658652	−	1.14082i	0.980965	−	0.194186i	$-0.0622065\pi$
$338$		−	7.47802i		−	0.406751i
$339$	28.8272	+	4.57913i	1.56568	+	0.248704i
$340$	4.13252			0.224117
$341$	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
$345$	−3.12312	−	8.14699i	−0.168143	−	0.438619i
$346$	18.3687	−	10.6052i	0.987505	−	0.570137i
$347$	15.0958	−	8.71559i	0.810387	−	0.467877i	−0.0367033	−	0.999326i	$-0.511686\pi$
$347$	15.0958	−	8.71559i	0.810387	−	0.467877i	0.847090	+	0.531449i	$0.178352\pi$
$348$	−4.87713	−	0.774720i	−0.261442	−	0.0415294i
$349$	31.4274	−	18.1446i	1.68227	−	0.971259i	0.722122	−	0.691766i	$-0.243167\pi$
$349$	31.4274	−	18.1446i	1.68227	−	0.971259i	0.960148	−	0.279493i	$-0.0901665\pi$
$350$	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
$353$	21.7513			1.15770			0.578852	−	0.815432i	$-0.303501\pi$
$353$	21.7513			1.15770			0.578852	+	0.815432i	$0.303501\pi$
$354$	6.79793	+	17.7332i	0.361306	+	0.942507i
$355$			8.14278i			0.432174i
$356$	−2.95275	+	5.11432i	−0.156496	+	0.271058i
$357$	−4.45785	+	18.4054i	−0.235934	+	0.974119i
$358$	−1.69322	−	2.93274i	−0.0894894	−	0.155000i
$359$	19.5772	−	11.3029i	1.03325	−	0.596544i	0.115333	−	0.993327i	$-0.463207\pi$
$359$	19.5772	−	11.3029i	1.03325	−	0.596544i	0.917913	+	0.396783i	$0.129873\pi$
$360$	−2.00538	−	2.23125i	−0.105693	−	0.117597i
$361$	22.1819	−	38.4201i	1.16747	−	2.02211i
$362$	−2.49913	+	4.32862i	−0.131351	+	0.227507i
$363$	−21.2787	+	8.15712i	−1.11684	+	0.428138i
$364$	0.957937	−	11.9343i	0.0502096	−	0.625529i
$365$	2.06838	+	1.19418i	0.108264	+	0.0625063i
$366$	−5.69272	−	4.61413i	−0.297563	−	0.241185i
$367$			12.1778i			0.635676i	0.948145	+	0.317838i	$0.102957\pi$
$367$			12.1778i			0.635676i	−0.948145	+	0.317838i	$0.897043\pi$
$368$	4.36255	+	2.51872i	0.227414	+	0.131297i
$369$	5.35976	+	25.3281i	0.279018	+	1.31853i
$370$		−	10.1161i		−	0.525913i
$371$	27.0900	+	18.6806i	1.40645	+	0.969848i
$372$	2.70263	+	0.429305i	0.140125	+	0.0222585i
$373$	−29.4797			−1.52640			−0.763199	−	0.646163i	$-0.776373\pi$
$373$	−29.4797			−1.52640			−0.763199	+	0.646163i	$0.776373\pi$
$374$	−10.1556	−	17.5901i	−0.525135	−	0.909561i
$375$	1.61729	−	0.619981i	0.0835164	−	0.0320157i
$376$	−0.393319	−	0.227083i	−0.0202839	−	0.0117109i
$377$	−12.9021			−0.664490
$378$	12.1008	−	6.52466i	0.622397	−	0.335592i
$379$	27.9939			1.43795			0.718974	−	0.695037i	$-0.244612\pi$
$379$	27.9939			1.43795			0.718974	+	0.695037i	$0.244612\pi$
$380$	6.89368	+	3.98007i	0.353638	+	0.204173i
$381$	17.5696	−	6.73525i	0.900120	−	0.345057i
$382$	−2.86209	−	4.95729i	−0.146437	−	0.253637i
$383$	−13.6842			−0.699229			−0.349615	−	0.936894i	$-0.613687\pi$
$383$	−13.6842			−0.699229			−0.349615	+	0.936894i	$0.613687\pi$
$384$	1.71060	+	0.271725i	0.0872939	+	0.0138664i
$385$	1.04044	−	12.9621i	0.0530255	−	0.660611i
$386$			5.40313i			0.275012i
$387$	−16.4678	−	5.36716i	−0.837105	−	0.272828i
$388$	1.74470	+	1.00730i	0.0885735	+	0.0511379i
$389$		−	6.87117i		−	0.348382i	−0.984712	−	0.174191i	$-0.944269\pi$
$389$		−	6.87117i		−	0.348382i	0.984712	−	0.174191i	$-0.0557310\pi$
$390$	−6.08903	−	4.93536i	−0.308330	−	0.249911i
$391$	−18.0283	−	10.4087i	−0.911731	−	0.526388i
$392$	1.11655	−	6.91038i	0.0563942	−	0.349027i
$393$	−7.53586	+	2.88884i	−0.380134	+	0.145723i
$394$	−6.25690	+	10.8373i	−0.315218	+	0.545974i
$395$	−4.86467	+	8.42586i	−0.244768	+	0.423951i
$396$	−4.56910	+	14.0192i	−0.229606	+	0.704489i
$397$	−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
$399$	−25.1628	+	26.4097i	−1.25972	+	1.32214i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			8.86214i			0.442554i	0.975211	+	0.221277i	$0.0710225\pi$
$401$			8.86214i			0.442554i	−0.975211	+	0.221277i	$0.928978\pi$
$402$	2.43781	+	6.35929i	0.121587	+	0.317173i
$403$	7.14959			0.356146
$404$	−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
$408$	−7.06910	−	1.12291i	−0.349973	−	0.0555923i
$409$	−2.25993	+	1.30477i	−0.111746	+	0.0645167i	−0.554831	−	0.831963i	$-0.687217\pi$
$409$	−2.25993	+	1.30477i	−0.111746	+	0.0645167i	0.443085	+	0.896480i	$0.353884\pi$
$410$	7.47352	−	4.31484i	0.369091	−	0.213095i
$411$	−6.14503	−	16.0300i	−0.303112	−	0.790701i
$412$	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
$416$	4.52526			0.221869
$417$	0.346610	+	0.0550581i	0.0169736	+	0.00269621i
$418$		−	39.1239i		−	1.91361i
$419$	8.15665	−	14.1277i	0.398478	−	0.690185i	−0.595060	−	0.803681i	$-0.702872\pi$
$419$	8.15665	−	14.1277i	0.398478	−	0.690185i	0.993538	+	0.113496i	$0.0362051\pi$
$420$	−3.31774	−	3.16110i	−0.161889	−	0.154246i
$421$	1.59756	+	2.76706i	0.0778603	+	0.134858i	0.902327	−	0.431053i	$-0.141858\pi$
$421$	1.59756	+	2.76706i	0.0778603	+	0.134858i	−0.824466	+	0.565911i	$0.808525\pi$
$422$	15.1223	−	8.73086i	0.736142	−	0.425012i
$423$	−0.282075	−	1.33298i	−0.0137149	−	0.0648116i
$424$	−6.21874	+	10.7712i	−0.302009	+	0.523094i
$425$	2.06626	−	3.57887i	0.100228	−	0.173601i
$426$	2.21260	−	13.9291i	0.107201	−	0.674866i
$427$	−9.21496	−	6.35440i	−0.445943	−	0.307511i
$428$	−10.8227	−	6.24846i	−0.523133	−	0.302031i
$429$	−6.04360	+	38.0466i	−0.291788	+	1.83690i
$430$			5.77345i			0.278420i
$431$	−17.7856	−	10.2685i	−0.856701	−	0.494616i	0.00620540	−	0.999981i	$-0.498025\pi$
$431$	−17.7856	−	10.2685i	−0.856701	−	0.494616i	−0.862906	+	0.505364i	$0.831358\pi$
$432$	2.82412	+	4.36169i	0.135876	+	0.209852i
$433$			5.62555i			0.270347i	0.990822	+	0.135173i	$0.0431591\pi$
$433$			5.62555i			0.270347i	−0.990822	+	0.135173i	$0.956841\pi$
$434$	4.16669	+	0.334449i	0.200008	+	0.0160541i
$435$	−3.10949	+	3.83636i	−0.149089	+	0.183939i
$436$	−13.6159			−0.652083
$437$	−20.0493	−	34.7265i	−0.959090	−	1.66119i
$438$	−3.21369	−	2.60480i	−0.153556	−	0.124462i
$439$	2.11031	+	1.21839i	0.100720	+	0.0581506i	0.549514	−	0.835485i	$-0.314813\pi$
$439$	2.11031	+	1.21839i	0.100720	+	0.0581506i	−0.448794	+	0.893635i	$0.648146\pi$
$440$	4.91498			0.234313
$441$	17.6579	−	11.3666i	0.840850	−	0.541268i
$442$	−18.7007			−0.889504
$443$	−1.07735	−	0.622006i	−0.0511862	−	0.0295524i	0.474189	−	0.880423i	$-0.342742\pi$
$443$	−1.07735	−	0.622006i	−0.0511862	−	0.0295524i	−0.525375	+	0.850871i	$0.676075\pi$
$444$	−2.74881	+	17.3047i	−0.130453	+	0.821245i
$445$	2.95275	+	5.11432i	0.139974	+	0.242442i
$446$	−11.3708			−0.538424
$447$	−1.86070	−	4.85383i	−0.0880080	−	0.229578i
$448$	2.63727	+	0.211686i	0.124599	+	0.0100012i
$449$		−	17.5222i		−	0.826924i	−0.910521	−	0.413462i	$-0.864319\pi$
$449$		−	17.5222i		−	0.826924i	0.910521	−	0.413462i	$-0.135681\pi$
$450$	−2.93500	+	0.621084i	−0.138357	+	0.0292782i
$451$	−36.7322	−	21.2074i	−1.72965	−	0.998615i
$452$			16.8521i			0.792655i
$453$	−31.9144	+	12.2342i	−1.49947	+	0.574815i
$454$	6.13659	+	3.54296i	0.288004	+	0.166279i
$455$	−9.85647	−	6.79677i	−0.462079	−	0.318637i
$456$	−10.7109	−	8.68150i	−0.501582	−	0.406549i
$457$	−14.3903	+	24.9247i	−0.673150	+	1.16593i	0.303856	+	0.952718i	$0.401726\pi$
$457$	−14.3903	+	24.9247i	−0.673150	+	1.16593i	−0.977006	+	0.213212i	$0.931607\pi$
$458$	1.52702	−	2.64487i	0.0713528	−	0.123587i
$459$	−11.6707	−	18.0248i	−0.544743	−	0.841324i
$460$	4.36255	−	2.51872i	0.203405	−	0.117436i
$461$	17.0159	+	29.4723i	0.792508	+	1.37266i	0.924410	+	0.381401i	$0.124558\pi$
$461$	17.0159	+	29.4723i	0.792508	+	1.37266i	−0.131902	+	0.991263i	$0.542109\pi$
$462$	−5.30191	+	21.8904i	−0.246667	+	1.01843i
$463$	−4.73816	+	8.20674i	−0.220201	+	0.381399i	−0.954869	−	0.297028i	$-0.904005\pi$
$463$	−4.73816	+	8.20674i	−0.220201	+	0.381399i	0.734668	+	0.678427i	$0.237338\pi$
$464$		−	2.85112i		−	0.132360i
$465$	1.72310	−	2.12589i	0.0799070	−	0.0985859i
$466$	−21.4131			−0.991943
$467$	8.13248	+	14.0859i	0.376326	+	0.651816i	0.990525	−	0.137336i	$-0.0438539\pi$
$467$	8.13248	+	14.0859i	0.376326	+	0.651816i	−0.614198	+	0.789152i	$0.710521\pi$
$468$	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
$471$	9.20152	−	11.3524i	0.423984	−	0.523093i
$472$	−9.49575	+	5.48237i	−0.437077	+	0.252347i
$473$	24.5747	−	14.1882i	1.12994	−	0.652374i
$474$	10.6110	−	13.0914i	0.487381	−	0.601310i
$475$	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
$479$	5.87379			0.268380			0.134190	−	0.990956i	$-0.457157\pi$
$479$	5.87379			0.268380			0.134190	+	0.990956i	$0.457157\pi$
$480$	1.09062	−	1.34556i	0.0497799	−	0.0614163i
$481$			45.7782i			2.08731i
$482$	10.4273	−	18.0606i	0.474950	−	0.822638i
$483$	6.51189	+	22.1469i	0.296301	+	1.00772i
$484$	−6.57852	−	11.3943i	−0.299024	−	0.517924i
$485$	1.74470	−	1.00730i	0.0792225	−	0.0457392i
$486$	−4.06858	+	15.0481i	−0.184554	+	0.682598i
$487$	−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	$0.226342\pi$
$488$	2.11537	−	3.66392i	0.0957582	−	0.165858i
$489$	−17.8743	−	14.4877i	−0.808306	−	0.655158i
$490$	−5.42629	−	4.42215i	−0.245135	−	0.199772i
$491$	23.2893	+	13.4461i	1.05103	+	0.606814i	0.922938	−	0.384948i	$-0.125781\pi$
$491$	23.2893	+	13.4461i	1.05103	+	0.606814i	0.128094	+	0.991762i	$0.459114\pi$
$492$	−13.9567	+	5.35024i	−0.629216	+	0.241207i
$493$			11.7823i			0.530648i
$494$	−31.1957	−	18.0109i	−1.40356	−	0.810347i
$495$	9.85639	+	10.9665i	0.443012	+	0.492909i
$496$			1.57993i			0.0709408i
$497$	1.72372	−	21.4747i	0.0773193	−	0.963273i
$498$	1.76805	+	4.61214i	0.0792281	+	0.206675i
$499$	31.1031			1.39237			0.696183	−	0.717865i	$-0.254880\pi$
$499$	31.1031			1.39237			0.696183	+	0.717865i	$0.254880\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−4.42966	+	27.8862i	−0.197903	+	1.24587i
$502$	24.1304	+	13.9317i	1.07699	+	0.621801i
$503$	−3.49948			−0.156034			−0.0780170	−	0.996952i	$-0.524859\pi$
$503$	−3.49948			−0.156034			−0.0780170	+	0.996952i	$0.524859\pi$
$504$	4.81640	+	6.30891i	0.214539	+	0.281021i
$505$	−6.47106			−0.287958
$506$	−21.4418	−	12.3795i	−0.953206	−	0.550334i
$507$	10.0622	+	8.15570i	0.446876	+	0.362207i
$508$	5.43182	+	9.40818i	0.240998	+	0.417421i
$509$	6.83469			0.302942			0.151471	−	0.988462i	$-0.451599\pi$
$509$	6.83469			0.302942			0.151471	+	0.988462i	$0.451599\pi$
$510$	−4.50702	+	5.56057i	−0.199574	+	0.246226i
$511$	−5.20209	−	3.58723i	−0.230127	−	0.158689i
$512$			1.00000i			0.0441942i
$513$	−2.10876	−	41.3083i	−0.0931040	−	1.82380i
$514$	14.7285	+	8.50350i	0.649646	+	0.375073i
$515$		−	4.11259i		−	0.181223i
$516$	1.56879	−	9.87608i	0.0690621	−	0.434770i
$517$	1.93315	+	1.11611i	0.0850200	+	0.0490863i
$518$	−2.14145	+	26.6790i	−0.0940898	+	1.17221i
$519$	−5.76337	+	36.2824i	−0.252984	+	1.59262i
$520$	2.26263	−	3.91899i	0.0992230	−	0.171859i
$521$	8.40753	−	14.5623i	0.368341	−	0.637985i	−0.620966	−	0.783838i	$-0.713259\pi$
$521$	8.40753	−	14.5623i	0.368341	−	0.637985i	0.989306	+	0.145853i	$0.0465927\pi$
$522$	6.36155	−	5.71757i	0.278437	−	0.250251i
$523$	−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
$525$	−4.39647	+	1.29270i	−0.191878	+	0.0564180i
$526$	−1.53381	+	2.65664i	−0.0668775	+	0.115835i
$527$		−	6.52908i		−	0.284411i
$528$	−8.40759	−	1.33552i	−0.365893	−	0.0581212i
$529$	−2.37577			−0.103294
$530$	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
$534$	−3.66130	−	9.55091i	−0.158440	−	0.413308i
$535$	−10.8227	+	6.24846i	−0.467904	+	0.270144i
$536$	−3.40527	+	1.96604i	−0.147085	+	0.0849198i
$537$	5.79286	+	0.920180i	0.249980	+	0.0397087i
$538$	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	$0.948148\pi$
$542$	−2.25377			−0.0968078
$543$	−3.09882	−	8.08362i	−0.132983	−	0.346901i
$544$		−	4.13252i		−	0.177180i
$545$	−6.80795	+	11.7917i	−0.291620	+	0.505101i
$546$	15.0137	+	14.3048i	0.642526	+	0.612190i
$547$	−16.7310	−	28.9790i	−0.715366	−	1.23905i	−0.962818	−	0.270150i	$-0.912927\pi$
$547$	−16.7310	−	28.9790i	−0.715366	−	1.23905i	0.247452	−	0.968900i	$-0.420407\pi$
$548$	8.58373	−	4.95582i	0.366679	−	0.211702i
$549$	12.4172	−	2.62764i	0.529954	−	0.112145i
$550$	2.45749	−	4.25650i	0.104788	−	0.181498i
$551$	−11.3476	+	19.6547i	−0.483426	+	0.837318i
$552$	−8.14699	+	3.12312i	−0.346759	+	0.132929i
$553$	14.6131	−	21.1915i	0.621412	−	0.901153i
$554$	24.5090	+	14.1503i	1.04129	+	0.601188i
$555$	13.6119	+	11.0329i	0.577793	+	0.468320i
$556$			0.202625i			0.00859319i
$557$	−13.5808	−	7.84087i	−0.575436	−	0.332228i	0.183881	−	0.982948i	$-0.441134\pi$
$557$	−13.5808	−	7.84087i	−0.575436	−	0.332228i	−0.759318	+	0.650720i	$0.774467\pi$
$558$	−3.52521	+	3.16835i	−0.149234	+	0.134127i
$559$		−	26.1264i		−	1.10503i
$560$	1.50196	−	2.17810i	0.0634694	−	0.0920415i
$561$	34.7445	+	5.51908i	1.46691	+	0.233016i
$562$	−12.3772			−0.522100
$563$	−3.73368	−	6.46693i	−0.157356	−	0.272548i	0.776558	−	0.630045i	$-0.216964\pi$
$563$	−3.73368	−	6.46693i	−0.157356	−	0.272548i	−0.933914	+	0.357497i	$0.883630\pi$
$564$	0.734516	−	0.281574i	0.0309287	−	0.0118564i
$565$	14.5943	+	8.42603i	0.613988	+	0.354486i
$566$	21.6617			0.910509
$567$	−4.41804	+	23.3983i	−0.185540	+	0.982637i
$568$	8.14278			0.341664
$569$	20.1857	+	11.6542i	0.846229	+	0.488571i	0.859377	−	0.511343i	$-0.170852\pi$
$569$	20.1857	+	11.6542i	0.846229	+	0.488571i	−0.0131477	+	0.999914i	$0.504185\pi$
$570$	−12.8738	+	4.93513i	−0.539226	+	0.206710i
$571$	−1.21978	−	2.11273i	−0.0510463	−	0.0884148i	0.839373	−	0.543556i	$-0.182922\pi$
$571$	−1.21978	−	2.11273i	−0.0510463	−	0.0884148i	−0.890420	+	0.455141i	$0.849589\pi$
$572$	−22.2416			−0.929968
$573$	9.79181	+	1.55540i	0.409059	+	0.0649779i
$574$	−20.6231	+	9.79735i	−0.860791	+	0.408933i
$575$		−	5.03744i		−	0.210076i
$576$	−2.23125	+	2.00538i	−0.0929686	+	0.0835574i
$577$	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	$0.401640\pi$
$578$			0.0777233i			0.00323286i
$579$	−7.27025	−	5.89277i	−0.302141	−	0.244895i
$580$	−2.46914	−	1.42556i	−0.102525	−	0.0591931i
$581$	3.23765	+	6.81513i	0.134320	+	0.282739i
$582$	−3.25819	+	1.24901i	−0.135056	+	0.0517733i
$583$	30.5650	−	52.9401i	1.26587	−	2.19255i
$584$	1.19418	−	2.06838i	0.0494156	−	0.0855903i
$585$	13.2817	−	2.81057i	0.549130	−	0.116203i
$586$	2.40584	−	1.38901i	0.0993842	−	0.0573795i
$587$	6.06540	+	10.5056i	0.250346	+	0.433612i	0.963621	−	0.267272i	$-0.0861223\pi$
$587$	6.06540	+	10.5056i	0.250346	+	0.433612i	−0.713275	+	0.700884i	$0.752789\pi$
$588$	8.08062	+	9.03900i	0.333239	+	0.372762i
$589$	6.28821	−	10.8915i	0.259101	−	0.448777i
$590$			10.9647i			0.451411i
$591$	−7.75832	−	20.2384i	−0.319135	−	0.832498i
$592$	−10.1161			−0.415770
$593$	−15.5440	−	26.9230i	−0.638315	−	1.10559i	−0.985802	−	0.167910i	$-0.946298\pi$
$593$	−15.5440	−	26.9230i	−0.638315	−	1.10559i	0.347487	−	0.937685i	$-0.387035\pi$
$594$	−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
$597$	−30.6101	−	4.86233i	−1.25279	−	0.199002i
$598$	−19.7417	+	11.3979i	−0.807298	+	0.466093i
$599$	1.31153	−	0.757213i	0.0535877	−	0.0309389i	−0.472967	−	0.881080i	$-0.656817\pi$
$599$	1.31153	−	0.757213i	0.0535877	−	0.0309389i	0.526554	+	0.850141i	$0.323484\pi$
$600$	−0.619981	−	1.61729i	−0.0253106	−	0.0660255i
$601$	−28.7908	+	16.6224i	−1.17440	+	0.678040i	−0.954712	−	0.297530i	$-0.903837\pi$
$601$	−28.7908	+	16.6224i	−1.17440	+	0.678040i	−0.219688	+	0.975570i	$0.570504\pi$
$602$	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
$605$	−13.1570			−0.534910
$606$	11.0694	+	1.75835i	0.449665	+	0.0714280i
$607$			16.4368i			0.667150i	0.942724	+	0.333575i	$0.108255\pi$
$607$			16.4368i			0.667150i	−0.942724	+	0.333575i	$0.891745\pi$
$608$	3.98007	−	6.89368i	0.161413	−	0.279576i
$609$	9.01268	−	9.45928i	0.365212	−	0.383309i
$610$	−2.11537	−	3.66392i	−0.0856487	−	0.148348i
$611$	1.77987	−	1.02761i	0.0720058	−	0.0415726i
$612$	9.22067	−	8.28726i	0.372724	−	0.334993i
$613$	−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	$0.246804\pi$
$614$	1.83614	−	3.18028i	0.0741004	−	0.128346i
$615$	−2.34490	+	14.7620i	−0.0945554	+	0.595260i
$616$	−12.9621	−	1.04044i	−0.522259	−	0.0419203i
$617$	−14.9813	−	8.64945i	−0.603124	−	0.348214i	0.167146	−	0.985932i	$-0.446545\pi$
$617$	−14.9813	−	8.64945i	−0.603124	−	0.348214i	−0.770270	+	0.637718i	$0.779878\pi$
$618$	−1.11749	+	7.03502i	−0.0449522	+	0.282990i
$619$			6.35168i			0.255295i	0.991820	+	0.127648i	$0.0407427\pi$
$619$			6.35168i			0.255295i	−0.991820	+	0.127648i	$0.959257\pi$
$620$	1.36826	+	0.789963i	0.0549505	+	0.0317257i
$621$	−23.3062	−	11.9149i	−0.935247	−	0.478129i
$622$		−	7.33384i		−	0.294060i
$623$	−6.70457	−	14.1129i	−0.268613	−	0.565421i
$624$	−4.93536	+	6.08903i	−0.197572	+	0.243756i
$625$	1.00000			0.0400000
$626$	14.2906	+	24.7521i	0.571168	+	0.989292i
$627$	52.6437	+	42.6694i	2.10239	+	1.70405i
$628$	7.30661	+	4.21847i	0.291565	+	0.168335i
$629$	41.8051			1.66688
$630$	7.87187	−	1.01667i	0.313623	−	0.0405049i
$631$	0.419169			0.0166869			0.00834343	−	0.999965i	$-0.497344\pi$
$631$	0.419169			0.0166869			0.00834343	+	0.999965i	$0.497344\pi$
$632$	8.42586	+	4.86467i	0.335163	+	0.193506i
$633$	−4.74479	+	29.8701i	−0.188588	+	1.18723i
$634$	−3.37041	−	5.83771i	−0.133856	−	0.231845i
$635$	10.8636			0.431110
$636$	−7.71100	−	20.1150i	−0.305761	−	0.797611i
$637$	24.5554	+	20.0114i	0.972920	+	0.792880i
$638$			14.0132i			0.554788i
$639$	16.3294	+	18.1686i	0.645979	+	0.718737i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$		−	15.8516i		−	0.626100i	−0.949737	−	0.313050i	$-0.898649\pi$
$641$		−	15.8516i		−	0.626100i	0.949737	−	0.313050i	$-0.101351\pi$
$642$	20.2111	−	7.74786i	0.797670	−	0.305783i
$643$	−21.8689	−	12.6260i	−0.862427	−	0.497923i	0.00239717	−	0.999997i	$-0.499237\pi$
$643$	−21.8689	−	12.6260i	−0.862427	−	0.497923i	−0.864824	+	0.502075i	$0.832570\pi$
$644$	−12.0384	+	5.71905i	−0.474379	+	0.225362i
$645$	−7.76854	−	6.29665i	−0.305886	−	0.247930i
$646$	−16.4477	+	28.4883i	−0.647126	+	1.12086i
$647$	−5.47945	+	9.49068i	−0.215419	+	0.373117i	−0.953402	−	0.301702i	$-0.902445\pi$
$647$	−5.47945	+	9.49068i	−0.215419	+	0.373117i	0.737983	+	0.674819i	$0.235778\pi$
$648$	−8.94898	−	0.956923i	−0.351549	−	0.0375915i
$649$	46.6714	−	26.9458i	1.83201	−	1.05771i
$650$	−2.26263	−	3.91899i	−0.0887477	−	0.153716i
$651$	−4.99431	+	5.24179i	−0.195742	+	0.205442i
$652$	6.64195	−	11.5042i	0.260119	−	0.450539i
$653$			20.7019i			0.810128i	0.914288	+	0.405064i	$0.132751\pi$
$653$			20.7019i			0.810128i	−0.914288	+	0.405064i	$0.867249\pi$
$654$	14.8498	−	18.3211i	0.580673	−	0.716410i
$655$	−4.65956			−0.182064
$656$	−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	−0.0999436	−	0.994993i	$-0.531866\pi$
$659$	18.2719	−	10.5493i	0.711774	−	0.410943i	0.811718	+	0.584050i	$0.198533\pi$
$660$	−5.36039	+	6.61342i	−0.208653	+	0.257427i
$661$	3.90709	−	2.25576i	0.151968	−	0.0877389i	−0.422088	−	0.906555i	$-0.638703\pi$
$661$	3.90709	−	2.25576i	0.151968	−	0.0877389i	0.574056	+	0.818816i	$0.305369\pi$
$662$	−24.9612	+	14.4113i	−0.970143	+	0.560112i
$663$	20.3955	−	25.1631i	0.792094	−	0.977252i
$664$	−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
$668$	−16.3020			−0.630743
$669$	12.4013	−	15.3002i	0.479461	−	0.591538i
$670$			3.93207i			0.151909i
$671$	−10.3970	+	18.0081i	−0.401371	+	0.695196i
$672$	−3.16110	+	3.31774i	−0.121942	+	0.127985i
$673$	0.596334	+	1.03288i	0.0229870	+	0.0398147i	0.877290	−	0.479961i	$-0.159349\pi$
$673$	0.596334	+	1.03288i	0.0229870	+	0.0398147i	−0.854303	+	0.519775i	$0.826016\pi$
$674$	−20.9427	+	12.0913i	−0.806681	+	0.465738i
$675$	2.36527	−	4.62661i	0.0910394	−	0.178078i
$676$	−3.73901	+	6.47616i	−0.143808	+	0.249083i
$677$	11.6201	−	20.1267i	0.446598	−	0.773530i	−0.551564	−	0.834132i	$-0.685969\pi$
$677$	11.6201	−	20.1267i	0.446598	−	0.773530i	0.998162	+	0.0606024i	$0.0193022\pi$
$678$	−22.6755	−	18.3792i	−0.870849	−	0.705851i
$679$	−4.81446	+	2.28719i	−0.184762	+	0.0877745i
$680$	−3.57887	−	2.06626i	−0.137243	−	0.0792375i
$681$	−11.4600	+	4.39314i	−0.439147	+	0.168345i
$682$		−	7.76531i		−	0.297349i
$683$	6.84887	+	3.95420i	0.262065	+	0.151303i	0.625276	−	0.780404i	$-0.284986\pi$
$683$	6.84887	+	3.95420i	0.262065	+	0.151303i	−0.363211	+	0.931707i	$0.618320\pi$
$684$	23.3630	−	4.94391i	0.893308	−	0.189035i
$685$		−	9.91164i		−	0.378704i
$686$	13.3745	+	12.8111i	0.510640	+	0.489129i
$687$	1.89344	+	4.93925i	0.0722393	+	0.188444i
$688$	5.77345			0.220111
$689$	−28.1414	−	48.7424i	−1.07210	−	1.85694i
$690$	−1.36880	+	8.61706i	−0.0521092	+	0.328046i
$691$	11.1512	+	6.43817i	0.424213	+	0.244920i	0.696878	−	0.717189i	$-0.254572\pi$
$691$	11.1512	+	6.43817i	0.424213	+	0.244920i	−0.272665	+	0.962109i	$0.587905\pi$
$692$	−21.2103			−0.806295
$693$	−23.6725	−	31.0082i	−0.899244	−	1.17790i
$694$	−17.4312			−0.661678
$695$	0.175478	+	0.101312i	0.00665626	+	0.00384299i
$696$	3.83636	+	3.10949i	0.145417	+	0.117865i
$697$	17.8312	+	30.8845i	0.675403	+	1.16983i
$698$	−36.2892			−1.37357
$699$	23.3536	−	28.8127i	0.883315	−	1.08980i
$700$	−1.13531	−	2.38979i	−0.0429106	−	0.0903254i
$701$			1.81441i			0.0685292i	0.999413	+	0.0342646i	$0.0109089\pi$
$701$			1.81441i			0.0685292i	−0.999413	+	0.0342646i	$0.989091\pi$
$702$	−23.4834	+	1.19881i	−0.886323	+	0.0452462i
$703$	69.7373	+	40.2629i	2.63019	+	1.51854i
$704$		−	4.91498i		−	0.185240i
$705$	0.123408	−	0.776897i	0.00464781	−	0.0292596i
$706$	−18.8372	−	10.8756i	−0.708946	−	0.409310i
$707$	17.0659	+	1.36984i	0.641830	+	0.0515180i
$708$	2.97939	−	18.7563i	0.111972	−	0.704906i
$709$	−2.21427	+	3.83523i	−0.0831587	+	0.144035i	−0.904605	−	0.426251i	$-0.859834\pi$
$709$	−2.21427	+	3.83523i	−0.0831587	+	0.144035i	0.821446	+	0.570286i	$0.193168\pi$
$710$	4.07139	−	7.05186i	0.152797	−	0.264652i
$711$	6.04274	+	28.5557i	0.226621	+	1.07092i
$712$	5.11432	−	2.95275i	0.191667	−	0.110659i
$713$	−3.97939	−	6.89251i	−0.149029	−	0.258126i
$714$	13.0633	−	13.7106i	0.488883	−	0.513108i
$715$	−11.1208	+	19.2618i	−0.415894	+	0.720350i
$716$			3.38644i			0.126557i
$717$	−31.0761	−	4.93635i	−1.16056	−	0.184351i
$718$	−22.6058			−0.843641
$719$	8.23556	+	14.2644i	0.307134	+	0.531973i	0.977734	−	0.209847i	$-0.0672965\pi$
$719$	8.23556	+	14.2644i	0.307134	+	0.531973i	−0.670600	+	0.741819i	$0.733963\pi$
$720$	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
$723$	12.9295	+	33.7279i	0.480852	+	1.25435i
$724$	4.32862	−	2.49913i	0.160872	−	0.0928793i
$725$	−2.46914	+	1.42556i	−0.0917016	+	0.0529439i
$726$	22.5065	+	3.57510i	0.835294	+	0.132684i
$727$	40.8484	−	23.5838i	1.51498	−	0.874676i	0.515138	−	0.857107i	$-0.327740\pi$
$727$	40.8484	−	23.5838i	1.51498	−	0.874676i	0.999846	−	0.0175695i	$-0.00559284\pi$
$728$	−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
$731$	−23.8589			−0.882453
$732$	2.62298	+	6.84232i	0.0969480	+	0.252899i
$733$			48.2222i			1.78113i	0.454858	+	0.890564i	$0.349690\pi$
$733$			48.2222i			1.78113i	−0.454858	+	0.890564i	$0.650310\pi$
$734$	6.08890	−	10.5463i	0.224745	−	0.389270i
$735$	11.8683	−	2.47852i	0.437769	−	0.0914217i
$736$	−2.51872	−	4.36255i	−0.0928412	−	0.160806i
$737$	16.7369	−	9.66303i	0.616510	−	0.355942i
$738$	8.02239	−	24.6147i	0.295308	−	0.906080i
$739$	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	$-0.0679769\pi$
$740$	−5.05807	+	8.76083i	−0.185938	+	0.322054i
$741$	58.2575	−	22.3328i	2.14014	−	0.820415i
$742$	−14.1204	−	29.7229i	−0.518375	−	1.09116i
$743$	18.6193	+	10.7498i	0.683075	+	0.394373i	0.801013	−	0.598648i	$-0.204295\pi$
$743$	18.6193	+	10.7498i	0.683075	+	0.394373i	−0.117938	+	0.993021i	$0.537628\pi$
$744$	−2.12589	−	1.72310i	−0.0779390	−	0.0631720i
$745$		−	3.00122i		−	0.109956i
$746$	25.5301	+	14.7398i	0.934724	+	0.539663i
$747$	−8.13421	−	2.65109i	−0.297615	−	0.0969983i
$748$			20.3113i			0.742653i
$749$	29.8650	−	14.1879i	1.09124	−	0.518413i
$750$	−1.71060	−	0.271725i	−0.0624624	−	0.00992199i
$751$	16.7351			0.610672			0.305336	−	0.952245i	$-0.401231\pi$
$751$	16.7351			0.610672			0.305336	+	0.952245i	$0.401231\pi$
$752$	0.227083	+	0.393319i	0.00828085	+	0.0143429i
$753$	−45.0631	+	17.2747i	−1.64219	+	0.629527i
$754$	11.1735	+	6.45103i	0.406915	+	0.234933i
$755$	−19.7332			−0.718166
$756$	−13.7419	−	0.399872i	−0.499788	−	0.0145432i
$757$	−33.5973			−1.22112			−0.610558	−	0.791972i	$-0.709055\pi$
$757$	−33.5973			−1.22112			−0.610558	+	0.791972i	$0.709055\pi$
$758$	−24.2434	−	13.9969i	−0.880560	−	0.508392i
$759$	40.0423	−	15.3501i	1.45344	−	0.557172i
$760$	−3.98007	−	6.89368i	−0.144372	−	0.250060i
$761$	28.5379			1.03450			0.517249	−	0.855835i	$-0.326956\pi$
$761$	28.5379			1.03450			0.517249	+	0.855835i	$0.326956\pi$
$762$	−18.5834	−	2.95192i	−0.673205	−	0.106937i
$763$	20.4505	−	29.6568i	0.740359	−	1.07365i
$764$			5.72419i			0.207094i
$765$	−2.56664	−	12.1290i	−0.0927972	−	0.438524i
$766$	11.8509	+	6.84209i	0.428189	+	0.247215i
$767$		−	49.6184i		−	1.79162i
$768$	−1.34556	−	1.09062i	−0.0485539	−	0.0393545i
$769$	4.36339	+	2.51920i	0.157348	+	0.0908448i	0.576606	−	0.817022i	$-0.304377\pi$
$769$	4.36339	+	2.51920i	0.157348	+	0.0908448i	−0.419259	+	0.907867i	$0.637710\pi$
$770$	−7.38211	+	10.7053i	−0.266033	+	0.385793i
$771$	−27.5052	+	10.5440i	−0.990576	+	0.379733i
$772$	2.70156	−	4.67925i	0.0972314	−	0.168410i
$773$	9.36638	−	16.2231i	0.336885	−	0.583503i	−0.646960	−	0.762524i	$-0.723960\pi$
$773$	9.36638	−	16.2231i	0.336885	−	0.583503i	0.983845	+	0.179022i	$0.0572932\pi$
$774$	11.5779	+	12.8820i	0.416161	+	0.463033i
$775$	1.36826	−	0.789963i	0.0491492	−	0.0283763i
$776$	−1.00730	−	1.74470i	−0.0361600	−	0.0626309i
$777$	−33.5627	−	31.9781i	−1.20406	−	1.14721i
$778$	−3.43558	+	5.95061i	−0.123172	+	0.213340i
$779$			68.6934i			2.46120i
$780$	2.80558	+	7.31866i	0.100456	+	0.262050i
$781$	−40.0216			−1.43209
$782$	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
$786$	7.97067	+	1.26612i	0.284304	+	0.0451610i
$787$	−46.4644	+	26.8262i	−1.65628	+	0.956251i	−0.681864	+	0.731479i	$0.738830\pi$
$787$	−46.4644	+	26.8262i	−1.65628	+	0.956251i	−0.974411	+	0.224772i	$0.927836\pi$
$788$	10.8373	−	6.25690i	0.386062	−	0.222893i
$789$	−1.90187	−	4.96124i	−0.0677084	−	0.176625i
$790$	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
$794$	5.13278			0.182155
$795$	−21.2756	−	3.37957i	−0.754567	−	0.119861i
$796$		−	17.8943i		−	0.634247i
$797$	1.34947	−	2.33735i	0.0478007	−	0.0827933i	−0.841135	−	0.540825i	$-0.818112\pi$
$797$	1.34947	−	2.33735i	0.0478007	−	0.0827933i	0.888936	+	0.458032i	$0.151445\pi$
$798$	34.9965	−	10.2901i	1.23886	−	0.364264i
$799$	−0.938423	−	1.62540i	−0.0331990	−	0.0575024i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	16.8445	+	5.48992i	0.595170	+	0.193977i
$802$	4.43107	−	7.67483i	0.156466	−	0.271008i
$803$	−5.86938	+	10.1661i	−0.207126	+	0.358752i
$804$	1.06844	−	6.72621i	0.0376810	−	0.237215i
$805$	−1.06636	+	13.2851i	−0.0375842	+	0.468237i
$806$	−6.19172	−	3.57479i	−0.218094	−	0.125917i
$807$	−1.89636	+	11.9383i	−0.0667551	+	0.420246i
$808$			6.47106i			0.227651i
$809$	−10.1449	−	5.85717i	−0.356676	−	0.205927i	0.310946	−	0.950428i	$-0.399354\pi$
$809$	−10.1449	−	5.85717i	−0.356676	−	0.205927i	−0.667622	+	0.744501i	$0.732688\pi$
$810$	−5.30321	+	7.27159i	−0.186336	+	0.255497i
$811$		−	1.79458i		−	0.0630161i	−0.999503	−	0.0315081i	$-0.989969\pi$
$811$		−	1.79458i		−	0.0630161i	0.999503	−	0.0315081i	$-0.0100310\pi$
$812$	6.21002	+	4.28227i	0.217929	+	0.150278i
$813$	2.45801	−	3.03259i	0.0862063	−	0.106358i
$814$	49.7206			1.74271
$815$	−6.64195	−	11.5042i	−0.232657	−	0.402975i
$816$	5.56057	+	4.50702i	0.194659	+	0.157777i
$817$	−39.8003	−	22.9787i	−1.39244	−	0.803923i
$818$	2.60954			0.0912404
$819$	−35.6223	+	4.60068i	−1.24474	+	0.160761i
$820$	−8.62968			−0.301361
$821$	−24.5051	−	14.1480i	−0.855234	−	0.493769i	0.00717960	−	0.999974i	$-0.497715\pi$
$821$	−24.5051	−	14.1480i	−0.855234	−	0.493769i	−0.862413	+	0.506205i	$0.831048\pi$
$822$	−2.69324	+	16.9549i	−0.0939375	+	0.591369i
$823$	−1.12364	−	1.94620i	−0.0391676	−	0.0678403i	0.845777	−	0.533536i	$-0.179137\pi$
$823$	−1.12364	−	1.94620i	−0.0391676	−	0.0678403i	−0.884945	+	0.465696i	$0.845804\pi$
$824$	−4.11259			−0.143269
$825$	3.04720	+	7.94895i	0.106090	+	0.276747i
$826$	2.32109	−	28.9170i	0.0807610	−	1.00615i
$827$			43.4893i			1.51227i	0.654415	+	0.756136i	$0.272915\pi$
$827$			43.4893i			1.51227i	−0.654415	+	0.756136i	$0.727085\pi$
$828$	4.68294	−	14.3684i	0.162743	−	0.499338i
$829$	−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	$-0.693515\pi$
$830$			2.85178i			0.0989866i
$831$	−45.7702	+	17.5458i	−1.58775	+	0.608657i
$832$	−3.91899	−	2.26263i	−0.135867	−	0.0784427i
$833$	18.2746	−	22.4242i	0.633178	−	0.776954i
$834$	−0.272644	−	0.220987i	−0.00944090	−	0.00765215i
$835$	−8.15100	+	14.1179i	−0.282077	+	0.488571i
$836$	−19.5620	+	33.8823i	−0.676564	+	1.17184i
$837$	−0.418547	−	8.19886i	−0.0144671	−	0.283394i
$838$	−14.1277	+	8.15665i	−0.488034	+	0.281767i
$839$	−21.4923	−	37.2258i	−0.741998	−	1.28518i	−0.951584	−	0.307388i	$-0.900545\pi$
$839$	−21.4923	−	37.2258i	−0.741998	−	1.28518i	0.209586	−	0.977790i	$-0.432788\pi$
$840$	1.29270	+	4.39647i	0.0446024	+	0.151693i
$841$	−10.4356	+	18.0749i	−0.359847	+	0.623273i
$842$		−	3.19512i		−	0.110111i
$843$	13.4988	−	16.6543i	0.464925	−	0.573604i
$844$	−17.4617			−0.601057
$845$	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
$849$	−23.6247	+	29.1472i	−0.810799	+	1.00033i
$850$	−3.57887	+	2.06626i	−0.122754	+	0.0708721i
$851$	44.1321	−	25.4797i	1.51283	−	0.873433i
$852$	−8.88071	+	10.9566i	−0.304248	+	0.375368i
$853$	36.9943	−	21.3587i	1.26666	−	0.731306i	0.292305	−	0.956325i	$-0.405578\pi$
$853$	36.9943	−	21.3587i	1.26666	−	0.731306i	0.974354	+	0.225019i	$0.0722443\pi$
$854$	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
$857$	−39.8521			−1.36132			−0.680661	−	0.732599i	$-0.738307\pi$
$857$	−39.8521			−1.36132			−0.680661	+	0.732599i	$0.738307\pi$
$858$	24.2572	−	29.9275i	0.828127	−	1.02171i
$859$			26.3979i			0.900684i	0.892856	+	0.450342i	$0.148698\pi$
$859$			26.3979i			0.900684i	−0.892856	+	0.450342i	$0.851302\pi$
$860$	2.88672	−	4.99995i	0.0984365	−	0.170497i
$861$	9.30904	−	38.4349i	0.317251	−	1.30986i
$862$	10.2685	+	17.7856i	0.349747	+	0.605779i
$863$	22.4654	−	12.9704i	0.764731	−	0.441517i	−0.0662611	−	0.997802i	$-0.521107\pi$
$863$	22.4654	−	12.9704i	0.764731	−	0.441517i	0.830992	+	0.556285i	$0.187774\pi$
$864$	−0.264915	−	5.18939i	−0.00901260	−	0.176547i
$865$	−10.6052	+	18.3687i	−0.360586	+	0.624553i
$866$	2.81278	−	4.87187i	0.0955820	−	0.165553i
$867$	−0.104582	−	0.0847668i	−0.00355178	−	0.00287883i
$868$	−3.44124	−	2.37299i	−0.116803	−	0.0805444i
$869$	−41.4129	−	23.9098i	−1.40484	−	0.811083i
$870$	4.61108	−	1.76764i	0.156330	−	0.0599286i
$871$		−	17.7937i		−	0.602915i
$872$	11.7917	+	6.80795i	0.399318	+	0.230546i
$873$	1.87283	−	5.74631i	0.0633856	−	0.194483i
$874$			40.0987i			1.35636i
$875$	−2.63727	−	0.211686i	−0.0891560	−	0.00715631i
$876$	1.48074	+	3.86267i	0.0500295	+	0.130508i
$877$	25.0969			0.847462			0.423731	−	0.905788i	$-0.360720\pi$
$877$	25.0969			0.847462			0.423731	+	0.905788i	$0.360720\pi$
$878$	−1.21839	−	2.11031i	−0.0411187	−	0.0712196i
$879$	−0.754858	+	4.75209i	−0.0254607	+	0.160284i
$880$	−4.25650	−	2.45749i	−0.143487	−	0.0828420i
$881$	45.7419			1.54108			0.770541	−	0.637390i	$-0.219986\pi$
$881$	45.7419			1.54108			0.770541	+	0.637390i	$0.219986\pi$
$882$	−20.9755	+	1.01485i	−0.706281	+	0.0341719i
$883$	21.2954			0.716648			0.358324	−	0.933597i	$-0.383348\pi$
$883$	21.2954			0.716648			0.358324	+	0.933597i	$0.383348\pi$
$884$	16.1953	+	9.35037i	0.544708	+	0.314487i
$885$	−14.7538	−	11.9584i	−0.495942	−	0.401977i
$886$	0.622006	+	1.07735i	0.0208967	+	0.0361941i
$887$	15.3159			0.514259			0.257130	−	0.966377i	$-0.417223\pi$
$887$	15.3159			0.514259			0.257130	+	0.966377i	$0.417223\pi$
$888$	11.0329	−	13.6119i	0.370239	−	0.456786i
$889$	−28.6503	−	2.29968i	−0.960901	−	0.0771289i
$890$		−	5.90551i		−	0.197953i
$891$	43.9841	+	4.70326i	1.47352	+	0.157565i
$892$	9.84741	+	5.68541i	0.329716	+	0.190361i
$893$		−	3.61521i		−	0.120979i
$894$	−0.815506	+	5.13389i	−0.0272746	+	0.171703i
$895$	2.93274	+	1.69322i	0.0980308	+	0.0565981i
$896$	−2.17810	−	1.50196i	−0.0727652	−	0.0501770i
$897$	6.19417	−	38.9945i	0.206817	−	1.30199i
$898$	−8.76110	+	15.1747i	−0.292362	+	0.506386i
$899$	−2.25228	+	3.90106i	−0.0751177	+	0.130108i
$900$	2.85233	+	0.929628i	0.0950777	+	0.0309876i
$901$	−44.5121	+	25.6991i	−1.48291	+	0.856160i
$902$	21.2074	+	36.7322i	0.706128	+	1.22305i
$903$	19.1548	+	18.2505i	0.637433	+	0.607337i
$904$	8.42603	−	14.5943i	0.280246	−	0.485400i
$905$		−	4.99826i		−	0.166148i
$906$	33.7558	+	5.36202i	1.12146	+	0.178141i
$907$	−9.70644			−0.322297			−0.161149	−	0.986930i	$-0.551520\pi$
$907$	−9.70644			−0.322297			−0.161149	+	0.986930i	$0.551520\pi$
$908$	−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	−0.584649	−	0.811286i	$-0.698768\pi$
$911$	−5.26323	+	3.03873i	−0.174379	+	0.100677i	0.410270	+	0.911964i	$0.365434\pi$
$912$	4.93513	+	12.8738i	0.163419	+	0.426295i
$913$	12.1386	−	7.00821i	0.401728	−	0.231938i
$914$	24.9247	−	14.3903i	0.824437	−	0.475989i
$915$	7.23711	+	1.14960i	0.239252	+	0.0380045i
$916$	−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	$0.621285\pi$
$920$	−5.03744			−0.166079
$921$	2.27674	+	5.93912i	0.0750211	+	0.195701i
$922$		−	34.0317i		−	1.12077i
$923$	−18.4241	+	31.9115i	−0.606438	+	1.05038i
$924$	15.5368	−	16.3067i	0.511122	−	0.536449i
$925$	5.05807	+	8.76083i	0.166308	+	0.288054i
$926$	8.20674	−	4.73816i	0.269690	−	0.155706i
$927$	−8.24730	−	9.17621i	−0.270877	−	0.301386i
$928$	−1.42556	+	2.46914i	−0.0467963	+	0.0810535i
$929$	6.21064	−	10.7572i	0.203765	−	0.352931i	−0.745974	−	0.665975i	$-0.768016\pi$
$929$	6.21064	−	10.7572i	0.203765	−	0.352931i	0.949738	+	0.313045i	$0.101349\pi$
$930$	−2.55520	+	0.979525i	−0.0837882	+	0.0321199i
$931$	52.0818	−	19.8066i	1.70691	−	0.649136i
$932$	18.5443	+	10.7066i	0.607439	+	0.350705i
$933$	9.86816	+	7.99846i	0.323069	+	0.261858i
$934$		−	16.2650i		−	0.532206i
$935$	17.5901	+	10.1556i	0.575257	+	0.332125i
$936$	−2.81057	−	13.2817i	−0.0918664	−	0.434125i
$937$		−	13.8664i		−	0.452994i	−0.974012	−	0.226497i	$-0.927273\pi$
$937$		−	13.8664i		−	0.452994i	0.974012	−	0.226497i	$-0.0727274\pi$
$938$	0.832366	−	10.3699i	0.0271777	−	0.338590i
$939$	−48.8912	−	7.76623i	−1.59550	−	0.253441i
$940$	0.454165			0.0148132
$941$	28.9912	+	50.2143i	0.945087	+	1.63694i	0.755576	+	0.655061i	$0.227357\pi$
$941$	28.9912	+	50.2143i	0.945087	+	1.63694i	0.189512	+	0.981878i	$0.439310\pi$
$942$	−13.6450	+	5.23075i	−0.444577	+	0.170427i
$943$	37.6474	+	21.7357i	1.22597	+	0.707813i
$944$	10.9647			0.356872
$945$	−7.21725	+	11.7009i	−0.234777	+	0.380631i
$946$	−28.3764			−0.922596
$947$	−12.2744	−	7.08663i	−0.398864	−	0.230284i	0.287130	−	0.957892i	$-0.407299\pi$
$947$	−12.2744	−	7.08663i	−0.398864	−	0.230284i	−0.685994	+	0.727607i	$0.740632\pi$
$948$	−15.7352	+	6.03201i	−0.511054	+	0.195911i
$949$	5.40398	+	9.35998i	0.175421	+	0.303838i
$950$	−7.96013			−0.258261
$951$	11.5309	+	1.83165i	0.373914	+	0.0593952i
$952$	9.00104	+	6.20688i	0.291725	+	0.201166i
$953$		−	10.6995i		−	0.346590i	−0.984870	−	0.173295i	$-0.944559\pi$
$953$		−	10.6995i		−	0.346590i	0.984870	−	0.173295i	$-0.0554414\pi$
$954$	35.4758	+	11.5622i	1.14857	+	0.374341i
$955$	4.95729	+	2.86209i	0.160414	+	0.0926151i
$956$		−	18.1667i		−	0.587554i
$957$	−18.8556	−	15.2831i	−0.609517	−	0.494033i
$958$	−5.08685	−	2.93690i	−0.164349	−	0.0948868i
$959$	−2.09816	+	26.1397i	−0.0677531	+	0.844093i
$960$	−1.61729	+	0.619981i	−0.0521978	+	0.0200098i
$961$	−14.2519	+	24.6850i	−0.459739	+	0.796292i
$962$	22.8891	−	39.6451i	0.737974	−	1.27821i
$963$	−11.6175	+	35.6454i	−0.374368	+	1.14866i
$964$	−18.0606	+	10.4273i	−0.581693	+	0.335841i
$965$	−2.70156	−	4.67925i	−0.0869664	−	0.150630i
$966$	5.43400	−	22.4357i	0.174836	−	0.721858i
$967$	2.27153	−	3.93440i	0.0730474	−	0.126522i	−0.827188	−	0.561925i	$-0.810061\pi$
$967$	2.27153	−	3.93440i	0.0730474	−	0.126522i	0.900235	+	0.435403i	$0.143394\pi$
$968$			13.1570i			0.422883i
$969$	−20.3945	−	53.2014i	−0.655167	−	1.70907i
$970$	−2.01460			−0.0646849
$971$	−12.9286	−	22.3930i	−0.414899	−	0.718627i	0.580518	−	0.814247i	$-0.302850\pi$
$971$	−12.9286	−	22.3930i	−0.414899	−	0.718627i	−0.995418	+	0.0956201i	$0.969517\pi$
$972$	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
$975$	7.74094	+	1.22963i	0.247908	+	0.0393796i
$976$	−3.66392	+	2.11537i	−0.117279	+	0.0677113i
$977$	−8.82069	+	5.09263i	−0.282199	+	0.162928i	−0.634419	−	0.772990i	$-0.718760\pi$
$977$	−8.82069	+	5.09263i	−0.282199	+	0.162928i	0.352220	+	0.935917i	$0.385427\pi$
$978$	8.23577	+	21.4839i	0.263351	+	0.686980i
$979$	−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
$983$	25.7089			0.819987			0.409993	−	0.912088i	$-0.365531\pi$
$983$	25.7089			0.819987			0.409993	+	0.912088i	$0.365531\pi$
$984$	14.7620	+	2.34490i	0.470594	+	0.0747526i
$985$		−	12.5138i		−	0.398723i
$986$	5.89115	−	10.2038i	0.187613	−	0.324954i
$987$	−0.489919	+	2.02276i	−0.0155943	+	0.0643852i
$988$	18.0109	+	31.1957i	0.573002	+	0.992468i
$989$	−25.1869	+	14.5417i	−0.800898	+	0.462399i
$990$	−3.05262	−	14.4255i	−0.0970186	−	0.458472i
$991$	−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	$0.229678\pi$
$992$	0.789963	−	1.36826i	0.0250814	−	0.0434422i
$993$	7.83184	−	49.3042i	0.248536	−	1.56462i
$994$	−12.2301	+	17.7358i	−0.387917	+	0.562545i
$995$	−15.4969	−	8.94715i	−0.491285	−	0.283644i
$996$	0.774899	−	4.87826i	0.0245536	−	0.154574i
$997$			14.7326i			0.466585i	0.972407	+	0.233293i	$0.0749500\pi$
$997$			14.7326i			0.466585i	−0.972407	+	0.233293i	$0.925050\pi$
$998$	−26.9361	−	15.5515i	−0.852646	−	0.492276i
$999$	52.4966	−	2.67992i	1.66092	−	0.0847888i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.7	✓	32	1.1	even	1	trivial
630.2.t.c.551.7	yes	32	63.47	even	6	inner
630.2.bk.c.101.5	yes	32	9.2	odd	6
630.2.bk.c.131.13	yes	32	7.5	odd	6
1890.2.t.c.1151.9		32	3.2	odd	2
1890.2.t.c.1601.9		32	63.61	odd	6
1890.2.bk.c.341.3		32	21.5	even	6
1890.2.bk.c.521.3		32	9.7	even	3

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.61729 - 0.619981i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.71060 - 0.271725i) q^{6} +(-2.63727 - 0.211686i) q^{7} -1.00000i q^{8} +(2.23125 - 2.00538i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.61729 - 0.619981i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.71060 - 0.271725i) q^{6} +(-2.63727 - 0.211686i) q^{7} -1.00000i q^{8} +(2.23125 - 2.00538i) q^{9} +(-0.866025 - 0.500000i) q^{10} +4.91498i q^{11} +(1.34556 + 1.09062i) q^{12} +(3.91899 + 2.26263i) q^{13} +(2.17810 + 1.50196i) q^{14} +(1.61729 - 0.619981i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.06626 - 3.57887i) q^{17} +(-2.93500 + 0.621084i) q^{18} +(6.89368 - 3.98007i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.39647 + 1.29270i) q^{21} +(2.45749 - 4.25650i) q^{22} -5.03744i q^{23} +(-0.619981 - 1.61729i) q^{24} +1.00000 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} +(-1.71060 - 0.271725i) q^{30} +(1.36826 - 0.789963i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.04720 + 7.94895i) 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} -7.96013 q^{38} +(7.74094 + 1.22963i) q^{39} -1.00000i q^{40} +(-4.31484 + 7.47352i) q^{41} +(4.45380 + 1.07872i) q^{42} +(-2.88672 - 4.99995i) q^{43} +(-4.25650 + 2.45749i) q^{44} +(2.23125 - 2.00538i) q^{45} +(-2.51872 + 4.36255i) q^{46} +(0.227083 - 0.393319i) q^{47} +(-0.271725 + 1.71060i) q^{48} +(6.91038 + 1.11655i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(1.12291 - 7.06910i) q^{51} +4.52526i q^{52} +(-10.7712 - 6.21874i) q^{53} +(-4.36169 + 2.82412i) q^{54} +4.91498i q^{55} +(-0.211686 + 2.63727i) q^{56} +(8.68150 - 10.7109i) q^{57} +2.85112 q^{58} +(-5.48237 - 9.49575i) q^{59} +(1.34556 + 1.09062i) q^{60} +(3.66392 + 2.11537i) q^{61} -1.57993 q^{62} +(-6.30891 + 4.81640i) q^{63} -1.00000 q^{64} +(3.91899 + 2.26263i) q^{65} +(1.33552 - 8.40759i) q^{66} +(-1.96604 - 3.40527i) q^{67} +4.13252 q^{68} +(-3.12312 - 8.14699i) q^{69} +(2.17810 + 1.50196i) q^{70} +8.14278i q^{71} +(-2.00538 - 2.23125i) q^{72} +(2.06838 + 1.19418i) q^{73} -10.1161i q^{74} +(1.61729 - 0.619981i) q^{75} +(6.89368 + 3.98007i) q^{76} +(1.04044 - 12.9621i) q^{77} +(-6.08903 - 4.93536i) q^{78} +(-4.86467 + 8.42586i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(0.956923 - 8.94898i) q^{81} +(7.47352 - 4.31484i) q^{82} +(-1.42589 - 2.46971i) q^{83} +(-3.31774 - 3.16110i) q^{84} +(2.06626 - 3.57887i) q^{85} +5.77345i q^{86} +(-3.10949 + 3.83636i) q^{87} +4.91498 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} +(1.72310 - 2.12589i) q^{93} +(-0.393319 + 0.227083i) q^{94} +(6.89368 - 3.98007i) q^{95} +(1.09062 - 1.34556i) q^{96} +(1.74470 - 1.00730i) q^{97} +(-5.42629 - 4.42215i) q^{98} +(9.85639 + 10.9665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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