LMFDB - Embedded newform 630.2.bk.b.101.14

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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.b.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.70645 + 0.296702i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.296702 + 1.70645i) q^{6} +(-2.21694 + 1.44401i) q^{7} -1.00000i q^{8} +(2.82394 + 1.01261i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.70645 + 0.296702i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.296702 + 1.70645i) q^{6} +(-2.21694 + 1.44401i) q^{7} -1.00000i q^{8} +(2.82394 + 1.01261i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-4.20911 + 2.43013i) q^{11} +(-1.70645 - 0.296702i) q^{12} +(-3.42136 + 1.97532i) q^{13} +(-1.44401 - 2.21694i) q^{14} +(-1.11018 + 1.32948i) q^{15} +1.00000 q^{16} +(1.25228 - 2.16902i) q^{17} +(-1.01261 + 2.82394i) q^{18} +(-0.962409 + 0.555647i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-4.21154 + 1.80636i) q^{21} +(-2.43013 - 4.20911i) q^{22} +(2.86139 + 1.65202i) q^{23} +(0.296702 - 1.70645i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.97532 - 3.42136i) q^{26} +(4.51846 + 2.56584i) q^{27} +(2.21694 - 1.44401i) q^{28} +(3.70789 + 2.14075i) q^{29} +(-1.32948 - 1.11018i) q^{30} +7.39752i q^{31} +1.00000i q^{32} +(-7.90366 + 2.89804i) q^{33} +(2.16902 + 1.25228i) q^{34} +(-0.142082 - 2.64193i) q^{35} +(-2.82394 - 1.01261i) q^{36} +(-1.82085 - 3.15380i) q^{37} +(-0.555647 - 0.962409i) q^{38} +(-6.42445 + 2.35566i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-3.91000 - 6.77231i) q^{41} +(-1.80636 - 4.21154i) q^{42} +(-3.62690 + 6.28198i) q^{43} +(4.20911 - 2.43013i) q^{44} +(-2.28892 + 1.93929i) q^{45} +(-1.65202 + 2.86139i) q^{46} +11.6852 q^{47} +(1.70645 + 0.296702i) q^{48} +(2.82965 - 6.40258i) q^{49} +(0.866025 - 0.500000i) q^{50} +(2.78051 - 3.32976i) q^{51} +(3.42136 - 1.97532i) q^{52} +(4.92292 + 2.84225i) q^{53} +(-2.56584 + 4.51846i) q^{54} -4.86026i q^{55} +(1.44401 + 2.21694i) q^{56} +(-1.80716 + 0.662634i) q^{57} +(-2.14075 + 3.70789i) q^{58} -1.39292 q^{59} +(1.11018 - 1.32948i) q^{60} +9.20374i q^{61} -7.39752 q^{62} +(-7.72273 + 1.83290i) q^{63} -1.00000 q^{64} -3.95064i q^{65} +(-2.89804 - 7.90366i) q^{66} +6.01448 q^{67} +(-1.25228 + 2.16902i) q^{68} +(4.39265 + 3.66807i) q^{69} +(2.64193 - 0.142082i) q^{70} -9.66386i q^{71} +(1.01261 - 2.82394i) q^{72} +(12.0570 + 6.96114i) q^{73} +(3.15380 - 1.82085i) q^{74} +(-0.596273 - 1.62618i) q^{75} +(0.962409 - 0.555647i) q^{76} +(5.82221 - 11.4655i) q^{77} +(-2.35566 - 6.42445i) q^{78} -7.83821 q^{79} +(-0.500000 + 0.866025i) q^{80} +(6.94923 + 5.71911i) q^{81} +(6.77231 - 3.91000i) q^{82} +(0.393868 - 0.682199i) q^{83} +(4.21154 - 1.80636i) q^{84} +(1.25228 + 2.16902i) q^{85} +(-6.28198 - 3.62690i) q^{86} +(5.69215 + 4.75322i) q^{87} +(2.43013 + 4.20911i) q^{88} +(-7.49361 - 12.9793i) q^{89} +(-1.93929 - 2.28892i) q^{90} +(4.73255 - 9.31966i) q^{91} +(-2.86139 - 1.65202i) q^{92} +(-2.19486 + 12.6235i) q^{93} +11.6852i q^{94} -1.11129i q^{95} +(-0.296702 + 1.70645i) q^{96} +(-14.9781 - 8.64760i) q^{97} +(6.40258 + 2.82965i) q^{98} +(-14.3470 + 2.60033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * 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
$3$	1.70645	+	0.296702i	0.985219	+	0.171301i
$3$	1.70645	+	0.296702i	0.985219	+	0.171301i
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.296702	+	1.70645i	−0.121128	+	0.696655i
$7$	−2.21694	+	1.44401i	−0.837925	+	0.545786i
$7$	−2.21694	+	1.44401i	−0.837925	+	0.545786i
$8$		−	1.00000i		−	0.353553i
$9$	2.82394	+	1.01261i	0.941312	+	0.337538i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−4.20911	+	2.43013i	−1.26909	+	0.732712i	−0.974817	−	0.223008i	$-0.928413\pi$
$11$	−4.20911	+	2.43013i	−1.26909	+	0.732712i	−0.294278	+	0.955720i	$0.595079\pi$
$12$	−1.70645	−	0.296702i	−0.492609	−	0.0856505i
$13$	−3.42136	+	1.97532i	−0.948914	+	0.547856i	−0.892743	−	0.450566i	$-0.851222\pi$
$13$	−3.42136	+	1.97532i	−0.948914	+	0.547856i	−0.0561705	+	0.998421i	$0.517889\pi$
$14$	−1.44401	−	2.21694i	−0.385929	−	0.592502i
$15$	−1.11018	+	1.32948i	−0.286646	+	0.343270i
$16$	1.00000			0.250000
$17$	1.25228	−	2.16902i	0.303723	−	0.526064i	−0.673253	−	0.739412i	$-0.735104\pi$
$17$	1.25228	−	2.16902i	0.303723	−	0.526064i	0.976976	+	0.213348i	$0.0684369\pi$
$18$	−1.01261	+	2.82394i	−0.238675	+	0.665608i
$19$	−0.962409	+	0.555647i	−0.220792	+	0.127474i	−0.606317	−	0.795223i	$-0.707354\pi$
$19$	−0.962409	+	0.555647i	−0.220792	+	0.127474i	0.385525	+	0.922697i	$0.374020\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−4.21154	+	1.80636i	−0.919033	+	0.394181i
$22$	−2.43013	−	4.20911i	−0.518106	−	0.897385i
$23$	2.86139	+	1.65202i	0.596640	+	0.344470i	0.767719	−	0.640787i	$-0.221392\pi$
$23$	2.86139	+	1.65202i	0.596640	+	0.344470i	−0.171079	+	0.985257i	$0.554725\pi$
$24$	0.296702	−	1.70645i	0.0605640	−	0.348327i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.97532	−	3.42136i	−0.387392	−	0.670983i
$27$	4.51846	+	2.56584i	0.869578	+	0.493796i
$28$	2.21694	−	1.44401i	0.418962	−	0.272893i
$29$	3.70789	+	2.14075i	0.688537	+	0.397527i	0.803064	−	0.595893i	$-0.203202\pi$
$29$	3.70789	+	2.14075i	0.688537	+	0.397527i	−0.114527	+	0.993420i	$0.536535\pi$
$30$	−1.32948	−	1.11018i	−0.242728	−	0.202689i
$31$			7.39752i			1.32863i	0.747451	+	0.664317i	$0.231277\pi$
$31$			7.39752i			1.32863i	−0.747451	+	0.664317i	$0.768723\pi$
$32$			1.00000i			0.176777i
$33$	−7.90366	+	2.89804i	−1.37585	+	0.504485i
$34$	2.16902	+	1.25228i	0.371983	+	0.214765i
$35$	−0.142082	−	2.64193i	−0.0240163	−	0.446568i
$36$	−2.82394	−	1.01261i	−0.470656	−	0.168769i
$37$	−1.82085	−	3.15380i	−0.299345	−	0.518482i	0.676641	−	0.736313i	$-0.263435\pi$
$37$	−1.82085	−	3.15380i	−0.299345	−	0.518482i	−0.975986	+	0.217832i	$0.930102\pi$
$38$	−0.555647	−	0.962409i	−0.0901378	−	0.156123i
$39$	−6.42445	+	2.35566i	−1.02874	+	0.377208i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−3.91000	−	6.77231i	−0.610639	−	1.05766i	−0.991133	−	0.132874i	$-0.957579\pi$
$41$	−3.91000	−	6.77231i	−0.610639	−	1.05766i	0.380494	−	0.924783i	$-0.375754\pi$
$42$	−1.80636	−	4.21154i	−0.278728	−	0.649854i
$43$	−3.62690	+	6.28198i	−0.553098	+	0.957993i	0.444951	+	0.895555i	$0.353221\pi$
$43$	−3.62690	+	6.28198i	−0.553098	+	0.957993i	−0.998049	+	0.0624384i	$0.980112\pi$
$44$	4.20911	−	2.43013i	0.634547	−	0.366356i
$45$	−2.28892	+	1.93929i	−0.341212	+	0.289093i
$46$	−1.65202	+	2.86139i	−0.243577	+	0.421888i
$47$	11.6852			1.70445			0.852227	−	0.523172i	$-0.175251\pi$
$47$	11.6852			1.70445			0.852227	+	0.523172i	$0.175251\pi$
$48$	1.70645	+	0.296702i	0.246305	+	0.0428252i
$49$	2.82965	−	6.40258i	0.404236	−	0.914655i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	2.78051	−	3.32976i	0.389349	−	0.466260i
$52$	3.42136	−	1.97532i	0.474457	−	0.273928i
$53$	4.92292	+	2.84225i	0.676216	+	0.390413i	0.798428	−	0.602091i	$-0.205665\pi$
$53$	4.92292	+	2.84225i	0.676216	+	0.390413i	−0.122212	+	0.992504i	$0.538999\pi$
$54$	−2.56584	+	4.51846i	−0.349167	+	0.614884i
$55$		−	4.86026i		−	0.655358i
$56$	1.44401	+	2.21694i	0.192964	+	0.296251i
$57$	−1.80716	+	0.662634i	−0.239365	+	0.0877681i
$58$	−2.14075	+	3.70789i	−0.281094	+	0.486869i
$59$	−1.39292			−0.181343			−0.0906716	−	0.995881i	$-0.528901\pi$
$59$	−1.39292			−0.181343			−0.0906716	+	0.995881i	$0.528901\pi$
$60$	1.11018	−	1.32948i	0.143323	−	0.171635i
$61$			9.20374i			1.17842i	0.807981	+	0.589209i	$0.200561\pi$
$61$			9.20374i			1.17842i	−0.807981	+	0.589209i	$0.799439\pi$
$62$	−7.39752			−0.939486
$63$	−7.72273	+	1.83290i	−0.972972	+	0.230923i
$64$	−1.00000			−0.125000
$65$		−	3.95064i		−	0.490017i
$66$	−2.89804	−	7.90366i	−0.356724	−	0.972873i
$67$	6.01448			0.734786			0.367393	−	0.930066i	$-0.380250\pi$
$67$	6.01448			0.734786			0.367393	+	0.930066i	$0.380250\pi$
$68$	−1.25228	+	2.16902i	−0.151862	+	0.263032i
$69$	4.39265	+	3.66807i	0.528813	+	0.441584i
$70$	2.64193	−	0.142082i	0.315771	−	0.0169821i
$71$		−	9.66386i		−	1.14689i	−0.819244	−	0.573445i	$-0.805607\pi$
$71$		−	9.66386i		−	1.14689i	0.819244	−	0.573445i	$-0.194393\pi$
$72$	1.01261	−	2.82394i	0.119338	−	0.332804i
$73$	12.0570	+	6.96114i	1.41117	+	0.814739i	0.995499	−	0.0947757i	$-0.0302134\pi$
$73$	12.0570	+	6.96114i	1.41117	+	0.814739i	0.415671	+	0.909515i	$0.363547\pi$
$74$	3.15380	−	1.82085i	0.366622	−	0.211669i
$75$	−0.596273	−	1.62618i	−0.0688517	−	0.187775i
$76$	0.962409	−	0.555647i	0.110396	−	0.0637371i
$77$	5.82221	−	11.4655i	0.663502	−	1.30661i
$78$	−2.35566	−	6.42445i	−0.266726	−	0.727426i
$79$	−7.83821			−0.881868			−0.440934	−	0.897540i	$-0.645353\pi$
$79$	−7.83821			−0.881868			−0.440934	+	0.897540i	$0.645353\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	6.94923	+	5.71911i	0.772136	+	0.635457i
$82$	6.77231	−	3.91000i	0.747877	−	0.431787i
$83$	0.393868	−	0.682199i	0.0432326	−	0.0748811i	−0.843599	−	0.536973i	$-0.819568\pi$
$83$	0.393868	−	0.682199i	0.0432326	−	0.0748811i	0.886832	+	0.462092i	$0.152901\pi$
$84$	4.21154	−	1.80636i	0.459516	−	0.197091i
$85$	1.25228	+	2.16902i	0.135829	+	0.235263i
$86$	−6.28198	−	3.62690i	−0.677404	−	0.391099i
$87$	5.69215	+	4.75322i	0.610263	+	0.509598i
$88$	2.43013	+	4.20911i	0.259053	+	0.448693i
$89$	−7.49361	−	12.9793i	−0.794321	−	1.37580i	−0.923270	−	0.384153i	$-0.874494\pi$
$89$	−7.49361	−	12.9793i	−0.794321	−	1.37580i	0.128949	−	0.991651i	$-0.458840\pi$
$90$	−1.93929	−	2.28892i	−0.204419	−	0.241273i
$91$	4.73255	−	9.31966i	0.496106	−	0.976966i
$92$	−2.86139	−	1.65202i	−0.298320	−	0.172235i
$93$	−2.19486	+	12.6235i	−0.227596	+	1.30899i
$94$			11.6852i			1.20523i
$95$		−	1.11129i		−	0.114016i
$96$	−0.296702	+	1.70645i	−0.0302820	+	0.174164i
$97$	−14.9781	−	8.64760i	−1.52079	−	0.878031i	−0.999699	−	0.0245323i	$-0.992190\pi$
$97$	−14.9781	−	8.64760i	−1.52079	−	0.878031i	−0.521095	−	0.853499i	$-0.674476\pi$
$98$	6.40258	+	2.82965i	0.646759	+	0.285838i
$99$	−14.3470	+	2.60033i	−1.44193	+	0.261343i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	1.46643	+	2.53993i	0.145915	+	0.252733i	0.929714	−	0.368282i	$-0.120054\pi$
$101$	1.46643	+	2.53993i	0.145915	+	0.252733i	−0.783799	+	0.621015i	$0.786721\pi$
$102$	3.32976	+	2.78051i	0.329696	+	0.275311i
$103$	2.23884	+	1.29260i	0.220600	+	0.127363i	0.606228	−	0.795291i	$-0.292682\pi$
$103$	2.23884	+	1.29260i	0.220600	+	0.127363i	−0.385628	+	0.922654i	$0.626015\pi$
$104$	1.97532	+	3.42136i	0.193696	+	0.335492i
$105$	0.541411	−	4.55048i	0.0528363	−	0.444081i
$106$	−2.84225	+	4.92292i	−0.276064	+	0.478157i
$107$	6.46896	−	3.73486i	0.625378	−	0.361062i	−0.153582	−	0.988136i	$-0.549081\pi$
$107$	6.46896	−	3.73486i	0.625378	−	0.361062i	0.778960	+	0.627074i	$0.215748\pi$
$108$	−4.51846	−	2.56584i	−0.434789	−	0.246898i
$109$	−8.23189	+	14.2581i	−0.788472	+	1.36567i	0.138430	+	0.990372i	$0.455794\pi$
$109$	−8.23189	+	14.2581i	−0.788472	+	1.36567i	−0.926903	+	0.375302i	$0.877539\pi$
$110$	4.86026			0.463408
$111$	−2.17144	−	5.92205i	−0.206104	−	0.562096i
$112$	−2.21694	+	1.44401i	−0.209481	+	0.136446i
$113$	2.91952	−	1.68559i	0.274646	−	0.158567i	−0.356351	−	0.934352i	$-0.615979\pi$
$113$	2.91952	−	1.68559i	0.274646	−	0.158567i	0.630997	+	0.775785i	$0.282646\pi$
$114$	−0.662634	−	1.80716i	−0.0620614	−	0.169256i
$115$	−2.86139	+	1.65202i	−0.266826	+	0.154052i
$116$	−3.70789	−	2.14075i	−0.344269	−	0.198764i
$117$	−11.6619	+	2.11367i	−1.07815	+	0.195409i
$118$		−	1.39292i		−	0.128229i
$119$	0.355855	+	6.61690i	0.0326211	+	0.606570i
$120$	1.32948	+	1.11018i	0.121364	+	0.101345i
$121$	6.31108	−	10.9311i	0.573734	−	0.993737i
$122$	−9.20374			−0.833267
$123$	−4.66285	−	12.7167i	−0.420435	−	1.14663i
$124$		−	7.39752i		−	0.664317i
$125$	1.00000			0.0894427
$126$	−1.83290	−	7.72273i	−0.163288	−	0.687995i
$127$	14.4595			1.28307			0.641535	−	0.767093i	$-0.278298\pi$
$127$	14.4595			1.28307			0.641535	+	0.767093i	$0.278298\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−8.05300	+	9.64377i	−0.709027	+	0.849087i
$130$	3.95064			0.346494
$131$	−6.59248	+	11.4185i	−0.575988	+	0.997640i	0.419946	+	0.907549i	$0.362049\pi$
$131$	−6.59248	+	11.4185i	−0.575988	+	0.997640i	−0.995934	+	0.0900907i	$0.971284\pi$
$132$	7.90366	−	2.89804i	0.687925	−	0.252242i
$133$	1.33124	−	2.62157i	0.115433	−	0.227319i
$134$			6.01448i			0.519572i
$135$	−4.48131	+	2.63018i	−0.385690	+	0.226370i
$136$	−2.16902	−	1.25228i	−0.185992	−	0.107382i
$137$	8.98722	−	5.18877i	0.767830	−	0.443307i	−0.0642701	−	0.997933i	$-0.520472\pi$
$137$	8.98722	−	5.18877i	0.767830	−	0.443307i	0.832100	+	0.554626i	$0.187139\pi$
$138$	−3.66807	+	4.39265i	−0.312247	+	0.373927i
$139$	7.92494	−	4.57547i	0.672185	−	0.388086i	−0.124719	−	0.992192i	$-0.539803\pi$
$139$	7.92494	−	4.57547i	0.672185	−	0.388086i	0.796904	+	0.604106i	$0.206470\pi$
$140$	0.142082	+	2.64193i	0.0120081	+	0.223284i
$141$	19.9401	+	3.46701i	1.67926	+	0.291975i
$142$	9.66386			0.810974
$143$	9.60058	−	16.6287i	0.802841	−	1.39056i
$144$	2.82394	+	1.01261i	0.235328	+	0.0843845i
$145$	−3.70789	+	2.14075i	−0.307923	+	0.177780i
$146$	−6.96114	+	12.0570i	−0.576108	+	0.997848i
$147$	6.72831	−	10.0861i	0.554942	−	0.831889i
$148$	1.82085	+	3.15380i	0.149673	+	0.259241i
$149$	20.9438	+	12.0919i	1.71578	+	0.990606i	0.926263	+	0.376878i	$0.123002\pi$
$149$	20.9438	+	12.0919i	1.71578	+	0.990606i	0.789517	+	0.613728i	$0.210331\pi$
$150$	1.62618	−	0.596273i	0.132777	−	0.0486855i
$151$	11.4978	+	19.9148i	0.935679	+	1.62064i	0.773418	+	0.633897i	$0.218546\pi$
$151$	11.4978	+	19.9148i	0.935679	+	1.62064i	0.162262	+	0.986748i	$0.448121\pi$
$152$	0.555647	+	0.962409i	0.0450689	+	0.0780617i
$153$	5.73274	−	4.85709i	0.463465	−	0.392672i
$154$	11.4655	+	5.82221i	0.923914	+	0.469167i
$155$	−6.40644	−	3.69876i	−0.514578	−	0.297091i
$156$	6.42445	−	2.35566i	0.514368	−	0.188604i
$157$			8.09026i			0.645673i	0.946455	+	0.322836i	$0.104636\pi$
$157$			8.09026i			0.645673i	−0.946455	+	0.322836i	$0.895364\pi$
$158$		−	7.83821i		−	0.623575i
$159$	7.55742	+	6.31080i	0.599342	+	0.500479i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−8.72906	+	0.469446i	−0.687947	+	0.0369975i
$162$	−5.71911	+	6.94923i	−0.449336	+	0.545983i
$163$	−0.616736	−	1.06822i	−0.0483065	−	0.0836693i	0.840861	−	0.541251i	$-0.182049\pi$
$163$	−0.616736	−	1.06822i	−0.0483065	−	0.0836693i	−0.889168	+	0.457582i	$0.848716\pi$
$164$	3.91000	+	6.77231i	0.305319	+	0.528829i
$165$	1.44205	−	8.29379i	0.112263	−	0.645671i
$166$	0.682199	+	0.393868i	0.0529489	+	0.0305701i
$167$	−5.43643	−	9.41617i	−0.420683	−	0.728645i	0.575323	−	0.817926i	$-0.304876\pi$
$167$	−5.43643	−	9.41617i	−0.420683	−	0.728645i	−0.996006	+	0.0892813i	$0.971543\pi$
$168$	1.80636	+	4.21154i	0.139364	+	0.324927i
$169$	1.30379	−	2.25823i	0.100292	−	0.173710i
$170$	−2.16902	+	1.25228i	−0.166356	+	0.0960457i
$171$	−3.28044	+	0.594563i	−0.250861	+	0.0454674i
$172$	3.62690	−	6.28198i	0.276549	−	0.478997i
$173$	5.77390			0.438981			0.219491	−	0.975615i	$-0.429560\pi$
$173$	5.77390			0.438981			0.219491	+	0.975615i	$0.429560\pi$
$174$	−4.75322	+	5.69215i	−0.360340	+	0.431521i
$175$	2.35902	+	1.19792i	0.178325	+	0.0905542i
$176$	−4.20911	+	2.43013i	−0.317274	+	0.183178i
$177$	−2.37695	−	0.413283i	−0.178663	−	0.0310643i
$178$	12.9793	−	7.49361i	0.972840	−	0.561670i
$179$	4.85812	+	2.80484i	0.363113	+	0.209643i	0.670445	−	0.741959i	$-0.266103\pi$
$179$	4.85812	+	2.80484i	0.363113	+	0.209643i	−0.307332	+	0.951602i	$0.599436\pi$
$180$	2.28892	−	1.93929i	0.170606	−	0.144546i
$181$		−	24.0589i		−	1.78828i	−0.447784	−	0.894142i	$-0.647787\pi$
$181$		−	24.0589i		−	1.78828i	0.447784	−	0.894142i	$-0.352213\pi$
$182$	9.31966	+	4.73255i	0.690819	+	0.350800i
$183$	−2.73077	+	15.7057i	−0.201864	+	1.16100i
$184$	1.65202	−	2.86139i	0.121789	−	0.210944i
$185$	3.64170			0.267743
$186$	−12.6235	−	2.19486i	−0.925599	−	0.160935i
$187$			12.1728i			0.890167i
$188$	−11.6852			−0.852227
$189$	−13.7223	+	0.836399i	−0.998148	+	0.0608391i
$190$	1.11129			0.0806217
$191$			24.2354i			1.75361i	0.480843	+	0.876807i	$0.340331\pi$
$191$			24.2354i			1.75361i	−0.480843	+	0.876807i	$0.659669\pi$
$192$	−1.70645	−	0.296702i	−0.123152	−	0.0214126i
$193$	−0.617476			−0.0444469			−0.0222235	−	0.999753i	$-0.507075\pi$
$193$	−0.617476			−0.0444469			−0.0222235	+	0.999753i	$0.507075\pi$
$194$	8.64760	−	14.9781i	0.620862	−	1.07536i
$195$	1.17216	−	6.74157i	0.0839404	−	0.482774i
$196$	−2.82965	+	6.40258i	−0.202118	+	0.457327i
$197$		−	2.28650i		−	0.162906i	−0.996677	−	0.0814531i	$-0.974044\pi$
$197$		−	2.28650i		−	0.162906i	0.996677	−	0.0814531i	$-0.0259561\pi$
$198$	−2.60033	−	14.3470i	−0.184798	−	1.01960i
$199$	−3.60562	−	2.08171i	−0.255596	−	0.147568i	0.366728	−	0.930328i	$-0.380478\pi$
$199$	−3.60562	−	2.08171i	−0.255596	−	0.147568i	−0.622324	+	0.782760i	$0.713811\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	10.2634	+	1.78451i	0.723925	+	0.125870i
$202$	−2.53993	+	1.46643i	−0.178709	+	0.103178i
$203$	−11.3114	+	0.608325i	−0.793907	+	0.0426961i
$204$	−2.78051	+	3.32976i	−0.194675	+	0.233130i
$205$	7.81999			0.546172
$206$	−1.29260	+	2.23884i	−0.0900595	+	0.155988i
$207$	6.40751	+	7.56268i	0.445353	+	0.525643i
$208$	−3.42136	+	1.97532i	−0.237228	+	0.136964i
$209$	2.70059	−	4.67756i	0.186804	−	0.323554i
$210$	4.55048	+	0.541411i	0.314013	+	0.0373609i
$211$	1.26573	+	2.19231i	0.0871365	+	0.150925i	0.906300	−	0.422636i	$-0.138895\pi$
$211$	1.26573	+	2.19231i	0.0871365	+	0.150925i	−0.819163	+	0.573561i	$0.805562\pi$
$212$	−4.92292	−	2.84225i	−0.338108	−	0.195207i
$213$	2.86729	−	16.4909i	0.196463	−	1.12994i
$214$	3.73486	+	6.46896i	0.255309	+	0.442209i
$215$	−3.62690	−	6.28198i	−0.247353	−	0.428428i
$216$	2.56584	−	4.51846i	0.174583	−	0.307442i
$217$	−10.6821	−	16.3999i	−0.725149	−	1.11329i
$218$	−14.2581	−	8.23189i	−0.965677	−	0.557534i
$219$	18.5093	+	15.4562i	1.25075	+	1.04443i
$220$			4.86026i			0.327679i
$221$			9.89465i			0.665586i
$222$	5.92205	−	2.17144i	0.397462	−	0.145738i
$223$	9.62445	+	5.55668i	0.644501	+	0.372103i	0.786346	−	0.617786i	$-0.211970\pi$
$223$	9.62445	+	5.55668i	0.644501	+	0.372103i	−0.141845	+	0.989889i	$0.545304\pi$
$224$	−1.44401	−	2.21694i	−0.0964822	−	0.148126i
$225$	−0.535019	−	2.95191i	−0.0356679	−	0.196794i
$226$	1.68559	+	2.91952i	0.112124	+	0.194204i
$227$	−5.76421	−	9.98390i	−0.382584	−	0.662655i	0.608847	−	0.793288i	$-0.291632\pi$
$227$	−5.76421	−	9.98390i	−0.382584	−	0.662655i	−0.991431	+	0.130633i	$0.958299\pi$
$228$	1.80716	−	0.662634i	0.119682	−	0.0438840i
$229$	−22.7387	−	13.1282i	−1.50262	−	0.867535i	−0.999995	−	0.00302766i	$-0.999036\pi$
$229$	−22.7387	−	13.1282i	−1.50262	−	0.867535i	−0.502620	−	0.864508i	$-0.667630\pi$
$230$	−1.65202	−	2.86139i	−0.108931	−	0.188674i
$231$	13.3371	−	17.8378i	0.877518	−	1.17364i
$232$	2.14075	−	3.70789i	0.140547	−	0.243435i
$233$	0.657636	−	0.379686i	0.0430832	−	0.0248741i	−0.478304	−	0.878194i	$-0.658748\pi$
$233$	0.657636	−	0.379686i	0.0430832	−	0.0248741i	0.521387	+	0.853320i	$0.325415\pi$
$234$	−2.11367	−	11.6619i	−0.138175	−	0.762364i
$235$	−5.84258	+	10.1196i	−0.381128	+	0.660132i
$236$	1.39292			0.0906716
$237$	−13.3755	−	2.32561i	−0.868833	−	0.151065i
$238$	−6.61690	+	0.355855i	−0.428910	+	0.0230666i
$239$	−21.2951	+	12.2947i	−1.37746	+	0.795280i	−0.991854	−	0.127382i	$-0.959343\pi$
$239$	−21.2951	+	12.2947i	−1.37746	+	0.795280i	−0.385611	+	0.922661i	$0.626009\pi$
$240$	−1.11018	+	1.32948i	−0.0716615	+	0.0858174i
$241$	−11.6664	+	6.73558i	−0.751497	+	0.433877i	−0.826235	−	0.563326i	$-0.809521\pi$
$241$	−11.6664	+	6.73558i	−0.751497	+	0.433877i	0.0747375	+	0.997203i	$0.476188\pi$
$242$	10.9311	+	6.31108i	0.702678	+	0.405691i
$243$	10.1616	+	11.8212i	0.651869	+	0.758332i
$244$		−	9.20374i		−	0.589209i
$245$	4.12998	+	5.65184i	0.263854	+	0.361083i
$246$	12.7167	−	4.66285i	0.810788	−	0.297292i
$247$	2.19516	−	3.80213i	0.139675	−	0.241924i
$248$	7.39752			0.469743
$249$	0.874525	−	1.04728i	0.0554208	−	0.0663685i
$250$			1.00000i			0.0632456i
$251$	1.02268			0.0645513			0.0322756	−	0.999479i	$-0.489725\pi$
$251$	1.02268			0.0645513			0.0322756	+	0.999479i	$0.489725\pi$
$252$	7.72273	−	1.83290i	0.486486	−	0.115462i
$253$	−16.0585			−1.00959
$254$			14.4595i			0.907268i
$255$	1.49340	+	4.07287i	0.0935206	+	0.255053i
$256$	1.00000			0.0625000
$257$	11.9035	−	20.6174i	0.742517	−	1.28608i	−0.208829	−	0.977952i	$-0.566965\pi$
$257$	11.9035	−	20.6174i	0.742517	−	1.28608i	0.951346	−	0.308125i	$-0.0997016\pi$
$258$	−9.64377	−	8.05300i	−0.600395	−	0.501358i
$259$	8.59084	+	4.36246i	0.533809	+	0.271070i
$260$			3.95064i			0.245008i
$261$	8.30308	+	9.79999i	0.513948	+	0.606604i
$262$	−11.4185	−	6.59248i	−0.705438	−	0.407285i
$263$	6.57942	−	3.79863i	0.405704	−	0.234234i	−0.283238	−	0.959050i	$-0.591409\pi$
$263$	6.57942	−	3.79863i	0.405704	−	0.234234i	0.688942	+	0.724816i	$0.258075\pi$
$264$	2.89804	+	7.90366i	0.178362	+	0.486437i
$265$	−4.92292	+	2.84225i	−0.302413	+	0.174598i
$266$	2.62157	+	1.33124i	0.160739	+	0.0816236i
$267$	−8.93647	−	24.3719i	−0.546903	−	1.49154i
$268$	−6.01448			−0.367393
$269$	3.58635	−	6.21175i	0.218664	−	0.378737i	−0.735736	−	0.677269i	$-0.763164\pi$
$269$	3.58635	−	6.21175i	0.218664	−	0.378737i	0.954400	+	0.298532i	$0.0964969\pi$
$270$	−2.63018	−	4.48131i	−0.160068	−	0.272724i
$271$	−3.19806	+	1.84640i	−0.194268	+	0.112161i	−0.593979	−	0.804480i	$-0.702444\pi$
$271$	−3.19806	+	1.84640i	−0.194268	+	0.112161i	0.399711	+	0.916641i	$0.369111\pi$
$272$	1.25228	−	2.16902i	0.0759308	−	0.131516i
$273$	10.8410	−	14.4994i	0.656129	−	0.877541i
$274$	5.18877	+	8.98722i	0.313465	+	0.542938i
$275$	4.20911	+	2.43013i	0.253819	+	0.146542i
$276$	−4.39265	−	3.66807i	−0.264406	−	0.220792i
$277$	−12.4545	−	21.5718i	−0.748317	−	1.29612i	−0.948629	−	0.316392i	$-0.897529\pi$
$277$	−12.4545	−	21.5718i	−0.748317	−	1.29612i	0.200311	−	0.979732i	$-0.435805\pi$
$278$	4.57547	+	7.92494i	0.274418	+	0.475306i
$279$	−7.49083	+	20.8901i	−0.448464	+	1.25066i
$280$	−2.64193	+	0.142082i	−0.157886	+	0.00849104i
$281$	−12.6865	−	7.32455i	−0.756813	−	0.436946i	0.0713375	−	0.997452i	$-0.477273\pi$
$281$	−12.6865	−	7.32455i	−0.756813	−	0.436946i	−0.828150	+	0.560506i	$0.810607\pi$
$282$	−3.46701	+	19.9401i	−0.206457	+	1.18742i
$283$			6.34995i			0.377465i	0.982029	+	0.188733i	$0.0604380\pi$
$283$			6.34995i			0.377465i	−0.982029	+	0.188733i	$0.939562\pi$
$284$			9.66386i			0.573445i
$285$	0.329723	−	1.89637i	0.0195311	−	0.112331i
$286$	16.6287	+	9.60058i	0.983275	+	0.567694i
$287$	18.4475	+	9.36772i	1.08892	+	0.552959i
$288$	−1.01261	+	2.82394i	−0.0596688	+	0.166402i
$289$	5.36358	+	9.28999i	0.315504	+	0.546470i
$290$	−2.14075	−	3.70789i	−0.125709	−	0.217735i
$291$	−22.9936	−	19.2007i	−1.34791	−	1.12557i
$292$	−12.0570	−	6.96114i	−0.705585	−	0.407370i
$293$	−1.79507	−	3.10915i	−0.104869	−	0.181638i	0.808816	−	0.588062i	$-0.200109\pi$
$293$	−1.79507	−	3.10915i	−0.104869	−	0.181638i	−0.913685	+	0.406424i	$0.866776\pi$
$294$	10.0861	+	6.72831i	0.588234	+	0.392403i
$295$	0.696461	−	1.20631i	0.0405496	−	0.0702339i
$296$	−3.15380	+	1.82085i	−0.183311	+	0.105835i
$297$	−25.2540	+	0.180537i	−1.46539	+	0.0104758i
$298$	−12.0919	+	20.9438i	−0.700464	+	1.21324i
$299$	−13.0531			−0.754880
$300$	0.596273	+	1.62618i	0.0344258	+	0.0938875i
$301$	−1.03064	−	19.1641i	−0.0594050	−	1.10460i
$302$	−19.9148	+	11.4978i	−1.14597	+	0.661625i
$303$	1.74879	+	4.76936i	0.100465	+	0.273992i
$304$	−0.962409	+	0.555647i	−0.0551979	+	0.0318685i
$305$	−7.97067	−	4.60187i	−0.456399	−	0.263502i
$306$	4.85709	+	5.73274i	0.277661	+	0.327719i
$307$		−	11.0589i		−	0.631166i	−0.948898	−	0.315583i	$-0.897800\pi$
$307$		−	11.0589i		−	0.631166i	0.948898	−	0.315583i	$-0.102200\pi$
$308$	−5.82221	+	11.4655i	−0.331751	+	0.653306i
$309$	3.43696	+	2.87002i	0.195522	+	0.163270i
$310$	3.69876	−	6.40644i	0.210075	−	0.363861i
$311$	−13.9447			−0.790729			−0.395364	−	0.918524i	$-0.629382\pi$
$311$	−13.9447			−0.790729			−0.395364	+	0.918524i	$0.629382\pi$
$312$	2.35566	+	6.42445i	0.133363	+	0.363713i
$313$		−	13.2712i		−	0.750130i	−0.926999	−	0.375065i	$-0.877620\pi$
$313$		−	13.2712i		−	0.750130i	0.926999	−	0.375065i	$-0.122380\pi$
$314$	−8.09026			−0.456560
$315$	2.27403	−	7.60453i	0.128127	−	0.428466i
$316$	7.83821			0.440934
$317$			4.45055i			0.249968i	0.992159	+	0.124984i	$0.0398879\pi$
$317$			4.45055i			0.249968i	−0.992159	+	0.124984i	$0.960112\pi$
$318$	−6.31080	+	7.55742i	−0.353892	+	0.423799i
$319$	−20.8092			−1.16509
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	12.1471	−	4.45399i	0.677984	−	0.248597i
$322$	−0.469446	−	8.72906i	−0.0261612	−	0.486452i
$323$			2.78331i			0.154867i
$324$	−6.94923	−	5.71911i	−0.386068	−	0.317728i
$325$	3.42136	+	1.97532i	0.189783	+	0.109571i
$326$	1.06822	−	0.616736i	0.0591631	−	0.0341578i
$327$	−18.2777	+	21.8882i	−1.01076	+	1.21042i
$328$	−6.77231	+	3.91000i	−0.373938	+	0.215893i
$329$	−25.9053	+	16.8735i	−1.42820	+	0.930267i
$330$	8.29379	+	1.44205i	0.456558	+	0.0793822i
$331$	7.83959			0.430903			0.215451	−	0.976515i	$-0.430878\pi$
$331$	7.83959			0.430903			0.215451	+	0.976515i	$0.430878\pi$
$332$	−0.393868	+	0.682199i	−0.0216163	+	0.0374405i
$333$	−1.94838	−	10.7499i	−0.106770	−	0.589093i
$334$	9.41617	−	5.43643i	0.515230	−	0.297468i
$335$	−3.00724	+	5.20869i	−0.164303	+	0.284581i
$336$	−4.21154	+	1.80636i	−0.229758	+	0.0985453i
$337$	−4.66042	−	8.07208i	−0.253869	−	0.439714i	0.710719	−	0.703476i	$-0.248370\pi$
$337$	−4.66042	−	8.07208i	−0.253869	−	0.439714i	−0.964588	+	0.263762i	$0.915037\pi$
$338$	2.25823	+	1.30379i	0.122832	+	0.0709169i
$339$	5.48213	−	2.01014i	0.297749	−	0.109176i
$340$	−1.25228	−	2.16902i	−0.0679146	−	0.117631i
$341$	−17.9769	−	31.1370i	−0.973506	−	1.68616i
$342$	−0.594563	−	3.28044i	−0.0321503	−	0.177386i
$343$	2.97226	+	18.2802i	0.160487	+	0.987038i
$344$	6.28198	+	3.62690i	0.338702	+	0.195550i
$345$	−5.37297	+	1.97011i	−0.289271	+	0.106067i
$346$			5.77390i			0.310407i
$347$			29.6538i			1.59190i	0.605361	+	0.795951i	$0.293029\pi$
$347$			29.6538i			1.59190i	−0.605361	+	0.795951i	$0.706971\pi$
$348$	−5.69215	−	4.75322i	−0.305131	−	0.254799i
$349$	−28.0322	−	16.1844i	−1.50053	−	0.866330i	−1.00000		0.000609911i	$-0.999806\pi$
$349$	−28.0322	−	16.1844i	−1.50053	−	0.866330i	−0.500528	−	0.865720i	$-0.666861\pi$
$350$	−1.19792	+	2.35902i	−0.0640315	+	0.126095i
$351$	−20.5276	+	0.146749i	−1.09568	+	0.00783288i
$352$	−2.43013	−	4.20911i	−0.129526	−	0.224346i
$353$	3.02849	+	5.24551i	0.161191	+	0.279190i	0.935296	−	0.353867i	$-0.115133\pi$
$353$	3.02849	+	5.24551i	0.161191	+	0.279190i	−0.774105	+	0.633057i	$0.781800\pi$
$354$	0.413283	−	2.37695i	0.0219657	−	0.126334i
$355$	8.36915	+	4.83193i	0.444188	+	0.256452i
$356$	7.49361	+	12.9793i	0.397160	+	0.687902i
$357$	−1.35600	+	11.3970i	−0.0717671	+	0.603192i
$358$	−2.80484	+	4.85812i	−0.148240	+	0.256760i
$359$	−11.4661	+	6.61995i	−0.605157	+	0.349388i	−0.771068	−	0.636753i	$-0.780277\pi$
$359$	−11.4661	+	6.61995i	−0.605157	+	0.349388i	0.165911	+	0.986141i	$0.446944\pi$
$360$	1.93929	+	2.28892i	0.102210	+	0.120637i
$361$	−8.88251	+	15.3850i	−0.467501	+	0.809735i
$362$	24.0589			1.26451
$363$	14.0128	−	16.7809i	0.735482	−	0.880767i
$364$	−4.73255	+	9.31966i	−0.248053	+	0.488483i
$365$	−12.0570	+	6.96114i	−0.631094	+	0.364362i
$366$	−15.7057	−	2.73077i	−0.820951	−	0.142740i
$367$	15.5018	−	8.94994i	0.809185	−	0.467183i	−0.0374878	−	0.999297i	$-0.511936\pi$
$367$	15.5018	−	8.94994i	0.809185	−	0.467183i	0.846673	+	0.532114i	$0.178602\pi$
$368$	2.86139	+	1.65202i	0.149160	+	0.0861176i
$369$	−4.18384	−	23.0839i	−0.217802	−	1.20170i
$370$			3.64170i			0.189323i
$371$	−15.0181	+	0.807668i	−0.779700	+	0.0419320i
$372$	2.19486	−	12.6235i	0.113798	−	0.654497i
$373$	2.26234	−	3.91848i	0.117139	−	0.202891i	−0.801494	−	0.598003i	$-0.795961\pi$
$373$	2.26234	−	3.91848i	0.117139	−	0.202891i	0.918633	+	0.395112i	$0.129294\pi$
$374$	−12.1728			−0.629443
$375$	1.70645	+	0.296702i	0.0881206	+	0.0153216i
$376$		−	11.6852i		−	0.602616i
$377$	−16.9147			−0.871150
$378$	−0.836399	−	13.7223i	−0.0430197	−	0.705797i
$379$	−7.47021			−0.383719			−0.191860	−	0.981422i	$-0.561452\pi$
$379$	−7.47021			−0.383719			−0.191860	+	0.981422i	$0.561452\pi$
$380$			1.11129i			0.0570082i
$381$	24.6744	+	4.29016i	1.26411	+	0.219791i
$382$	−24.2354			−1.23999
$383$	−16.5416	+	28.6508i	−0.845234	+	1.46399i	0.0401839	+	0.999192i	$0.487206\pi$
$383$	−16.5416	+	28.6508i	−0.845234	+	1.46399i	−0.885418	+	0.464796i	$0.846128\pi$
$384$	0.296702	−	1.70645i	0.0151410	−	0.0870819i
$385$	7.01829	+	10.7749i	0.357685	+	0.549140i
$386$		−	0.617476i		−	0.0314287i
$387$	−16.6034	+	14.0673i	−0.843996	+	0.715079i
$388$	14.9781	+	8.64760i	0.760397	+	0.439015i
$389$	31.5651	−	18.2241i	1.60041	−	0.923999i	0.609009	−	0.793163i	$-0.291567\pi$
$389$	31.5651	−	18.2241i	1.60041	−	0.923999i	0.991404	−	0.130836i	$-0.0417661\pi$
$390$	6.74157	+	1.17216i	0.341373	+	0.0593548i
$391$	7.16653	−	4.13760i	0.362427	−	0.209247i
$392$	−6.40258	−	2.82965i	−0.323379	−	0.142919i
$393$	−14.6376	+	17.5291i	−0.738370	+	0.884226i
$394$	2.28650			0.115192
$395$	3.91911	−	6.78809i	0.197192	−	0.341546i
$396$	14.3470	−	2.60033i	0.720966	−	0.130672i
$397$	−13.3331	+	7.69789i	−0.669171	+	0.386346i	−0.795762	−	0.605609i	$-0.792930\pi$
$397$	−13.3331	+	7.69789i	−0.669171	+	0.386346i	0.126592	+	0.991955i	$0.459596\pi$
$398$	2.08171	−	3.60562i	0.104346	−	0.180733i
$399$	3.04952	−	4.07859i	0.152667	−	0.204185i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	14.2091	+	8.20364i	0.709570	+	0.409670i	0.810902	−	0.585182i	$-0.198977\pi$
$401$	14.2091	+	8.20364i	0.709570	+	0.409670i	−0.101332	+	0.994853i	$0.532310\pi$
$402$	−1.78451	+	10.2634i	−0.0890032	+	0.511892i
$403$	−14.6125	−	25.3096i	−0.727899	−	1.26076i
$404$	−1.46643	−	2.53993i	−0.0729576	−	0.126366i
$405$	−8.42751	+	3.15865i	−0.418766	+	0.156955i
$406$	−0.608325	−	11.3114i	−0.0301907	−	0.561377i
$407$	15.3283	+	8.84980i	0.759796	+	0.438668i
$408$	−3.32976	−	2.78051i	−0.164848	−	0.137656i
$409$		−	21.1331i		−	1.04496i	−0.852651	−	0.522481i	$-0.825006\pi$
$409$		−	21.1331i		−	1.04496i	0.852651	−	0.522481i	$-0.174994\pi$
$410$			7.81999i			0.386202i
$411$	16.8757	−	6.18785i	0.832419	−	0.305224i
$412$	−2.23884	−	1.29260i	−0.110300	−	0.0636817i
$413$	3.08803	−	2.01140i	0.151952	−	0.0989745i
$414$	−7.56268	+	6.40751i	−0.371686	+	0.314912i
$415$	0.393868	+	0.682199i	0.0193342	+	0.0334878i
$416$	−1.97532	−	3.42136i	−0.0968481	−	0.167746i
$417$	14.8811	−	5.45645i	0.728728	−	0.267204i
$418$	4.67756	+	2.70059i	0.228787	+	0.132090i
$419$	−2.31087	−	4.00254i	−0.112893	−	0.195537i	0.804042	−	0.594572i	$-0.202678\pi$
$419$	−2.31087	−	4.00254i	−0.112893	−	0.195537i	−0.916936	+	0.399035i	$0.869345\pi$
$420$	−0.541411	+	4.55048i	−0.0264181	+	0.222041i
$421$	1.15555	−	2.00148i	0.0563183	−	0.0975461i	−0.836492	−	0.547979i	$-0.815397\pi$
$421$	1.15555	−	2.00148i	0.0563183	−	0.0975461i	0.892810	+	0.450433i	$0.148731\pi$
$422$	−2.19231	+	1.26573i	−0.106720	+	0.0616148i
$423$	32.9981	+	11.8325i	1.60442	+	0.575318i
$424$	2.84225	−	4.92292i	0.138032	−	0.239078i
$425$	−2.50457			−0.121489
$426$	16.4909	+	2.86729i	0.798986	+	0.138921i
$427$	−13.2903	−	20.4041i	−0.643164	−	0.987426i
$428$	−6.46896	+	3.73486i	−0.312689	+	0.180531i
$429$	21.3167	−	25.5275i	1.02918	−	1.23248i
$430$	6.28198	−	3.62690i	0.302944	−	0.174905i
$431$	21.3345	+	12.3175i	1.02765	+	0.593313i	0.916310	−	0.400469i	$-0.131153\pi$
$431$	21.3345	+	12.3175i	1.02765	+	0.593313i	0.111338	+	0.993783i	$0.464486\pi$
$432$	4.51846	+	2.56584i	0.217394	+	0.123449i
$433$		−	6.55773i		−	0.315144i	−0.987507	−	0.157572i	$-0.949633\pi$
$433$		−	6.55773i		−	0.315144i	0.987507	−	0.157572i	$-0.0503667\pi$
$434$	16.3999	−	10.6821i	0.787218	−	0.512758i
$435$	−6.96248	+	2.55294i	−0.333825	+	0.122404i
$436$	8.23189	−	14.2581i	0.394236	−	0.682837i
$437$	−3.67176			−0.175644
$438$	−15.4562	+	18.5093i	−0.738524	+	0.884411i
$439$		−	32.4291i		−	1.54776i	−0.633335	−	0.773878i	$-0.718314\pi$
$439$		−	32.4291i		−	1.54776i	0.633335	−	0.773878i	$-0.281686\pi$
$440$	−4.86026			−0.231704
$441$	14.4741	−	15.2151i	0.689242	−	0.724531i
$442$	−9.89465			−0.470640
$443$			0.235686i			0.0111978i	0.999984	+	0.00559888i	$0.00178219\pi$
$443$			0.235686i			0.0111978i	−0.999984	+	0.00559888i	$0.998218\pi$
$444$	2.17144	+	5.92205i	0.103052	+	0.281048i
$445$	14.9872			0.710462
$446$	−5.55668	+	9.62445i	−0.263116	+	0.455731i
$447$	32.1518	+	26.8482i	1.52073	+	1.26988i
$448$	2.21694	−	1.44401i	0.104741	−	0.0682232i
$449$			18.8068i			0.887549i	0.896139	+	0.443774i	$0.146361\pi$
$449$			18.8068i			0.887549i	−0.896139	+	0.443774i	$0.853639\pi$
$450$	2.95191	−	0.535019i	0.139154	−	0.0252210i
$451$	32.9152	+	19.0036i	1.54992	+	0.894845i
$452$	−2.91952	+	1.68559i	−0.137323	+	0.0792833i
$453$	13.7117	+	37.3950i	0.644231	+	1.75697i
$454$	9.98390	−	5.76421i	0.468568	−	0.270528i
$455$	5.70478	+	8.75834i	0.267444	+	0.410597i
$456$	0.662634	+	1.80716i	0.0310307	+	0.0846282i
$457$	−18.6117			−0.870617			−0.435308	−	0.900281i	$-0.643361\pi$
$457$	−18.6117			−0.870617			−0.435308	+	0.900281i	$0.643361\pi$
$458$	13.1282	−	22.7387i	0.613440	−	1.06251i
$459$	11.2237	−	6.58746i	0.523879	−	0.307476i
$460$	2.86139	−	1.65202i	0.133413	−	0.0770259i
$461$	−13.7720	+	23.8538i	−0.641426	+	1.11098i	0.343689	+	0.939084i	$0.388323\pi$
$461$	−13.7720	+	23.8538i	−0.641426	+	1.11098i	−0.985115	+	0.171898i	$0.945010\pi$
$462$	17.8378	+	13.3371i	0.829889	+	0.620499i
$463$	0.239162	+	0.414241i	0.0111148	+	0.0192514i	0.871529	−	0.490343i	$-0.163129\pi$
$463$	0.239162	+	0.414241i	0.0111148	+	0.0192514i	−0.860415	+	0.509595i	$0.829795\pi$
$464$	3.70789	+	2.14075i	0.172134	+	0.0993818i
$465$	−9.83483	−	8.21255i	−0.456079	−	0.380848i
$466$	0.379686	+	0.657636i	0.0175886	+	0.0304644i
$467$	6.08486	+	10.5393i	0.281574	+	0.487700i	0.971773	−	0.235920i	$-0.0758103\pi$
$467$	6.08486	+	10.5393i	0.281574	+	0.487700i	−0.690199	+	0.723620i	$0.742477\pi$
$468$	11.6619	−	2.11367i	0.539073	−	0.0977044i
$469$	−13.3337	+	8.68499i	−0.615695	+	0.401036i
$470$	−10.1196	−	5.84258i	−0.466784	−	0.269498i
$471$	−2.40040	+	13.8056i	−0.110604	+	0.636129i
$472$			1.39292i			0.0641145i
$473$		−	35.2554i		−	1.62105i
$474$	2.32561	−	13.3755i	0.106819	−	0.614358i
$475$	0.962409	+	0.555647i	0.0441583	+	0.0254948i
$476$	−0.355855	−	6.61690i	−0.0163106	−	0.303285i
$477$	11.0239	+	13.0114i	0.504751	+	0.595749i
$478$	−12.2947	−	21.2951i	−0.562348	−	0.974015i
$479$	−20.1769	−	34.9474i	−0.921906	−	1.59679i	−0.796462	−	0.604688i	$-0.793298\pi$
$479$	−20.1769	−	34.9474i	−0.921906	−	1.59679i	−0.125444	−	0.992101i	$-0.540036\pi$
$480$	−1.32948	−	1.11018i	−0.0606821	−	0.0506724i
$481$	12.4595	+	7.19352i	0.568106	+	0.327996i
$482$	−6.73558	−	11.6664i	−0.306797	−	0.531389i
$483$	−15.0350	−	1.78884i	−0.684116	−	0.0813952i
$484$	−6.31108	+	10.9311i	−0.286867	+	0.496868i
$485$	14.9781	−	8.64760i	0.680120	−	0.392667i
$486$	−11.8212	+	10.1616i	−0.536222	+	0.460941i
$487$	−4.11277	+	7.12353i	−0.186367	+	0.322798i	−0.944036	−	0.329841i	$-0.893005\pi$
$487$	−4.11277	+	7.12353i	−0.186367	+	0.322798i	0.757669	+	0.652639i	$0.226338\pi$
$488$	9.20374			0.416634
$489$	−0.735486	−	2.00585i	−0.0332598	−	0.0907075i
$490$	−5.65184	+	4.12998i	−0.255324	+	0.186573i
$491$	9.11388	−	5.26190i	0.411303	−	0.237466i	−0.280046	−	0.959987i	$-0.590350\pi$
$491$	9.11388	−	5.26190i	0.411303	−	0.237466i	0.691350	+	0.722520i	$0.257016\pi$
$492$	4.66285	+	12.7167i	0.210218	+	0.573313i
$493$	9.28664	−	5.36165i	0.418249	−	0.241476i
$494$	3.80213	+	2.19516i	0.171066	+	0.0987650i
$495$	4.92157	−	13.7251i	0.221208	−	0.616896i
$496$			7.39752i			0.332158i
$497$	13.9548	+	21.4242i	0.625956	+	0.961007i
$498$	1.04728	+	0.874525i	0.0469296	+	0.0391884i
$499$	−0.425242	+	0.736540i	−0.0190364	+	0.0329721i	−0.875387	−	0.483423i	$-0.839393\pi$
$499$	−0.425242	+	0.736540i	−0.0190364	+	0.0329721i	0.856350	+	0.516395i	$0.172727\pi$
$500$	−1.00000			−0.0447214
$501$	−6.48319	−	17.6812i	−0.289648	−	0.789938i
$502$			1.02268i			0.0456446i
$503$	21.5476			0.960759			0.480380	−	0.877061i	$-0.340499\pi$
$503$	21.5476			0.960759			0.480380	+	0.877061i	$0.340499\pi$
$504$	1.83290	+	7.72273i	0.0816438	+	0.343998i
$505$	−2.93286			−0.130511
$506$		−	16.0585i		−	0.713888i
$507$	2.89487	−	3.46672i	0.128566	−	0.153962i
$508$	−14.4595			−0.641535
$509$	−1.10449	+	1.91303i	−0.0489556	+	0.0847936i	−0.889465	−	0.457004i	$-0.848923\pi$
$509$	−1.10449	+	1.91303i	−0.0489556	+	0.0847936i	0.840509	+	0.541797i	$0.182256\pi$
$510$	−4.07287	+	1.49340i	−0.180350	+	0.0661291i
$511$	−36.7817	+	1.97811i	−1.62713	+	0.0875064i
$512$			1.00000i			0.0441942i
$513$	−5.77430	+	0.0412796i	−0.254942	+	0.00182254i
$514$	20.6174	+	11.9035i	0.909394	+	0.525039i
$515$	−2.23884	+	1.29260i	−0.0986552	+	0.0569586i
$516$	8.05300	−	9.64377i	0.354514	−	0.424543i
$517$	−49.1841	+	28.3965i	−2.16311	+	1.24887i
$518$	−4.36246	+	8.59084i	−0.191675	+	0.377460i
$519$	9.85286	+	1.71313i	0.432493	+	0.0751979i
$520$	−3.95064			−0.173247
$521$	12.0872	−	20.9356i	0.529548	−	0.917204i	−0.469858	−	0.882742i	$-0.655695\pi$
$521$	12.0872	−	20.9356i	0.529548	−	0.917204i	0.999406	−	0.0344623i	$-0.0109719\pi$
$522$	−9.79999	+	8.30308i	−0.428934	+	0.363416i
$523$	−10.3393	+	5.96937i	−0.452104	+	0.261022i	−0.708718	−	0.705492i	$-0.750726\pi$
$523$	−10.3393	+	5.96937i	−0.452104	+	0.261022i	0.256614	+	0.966514i	$0.417393\pi$
$524$	6.59248	−	11.4185i	0.287994	−	0.498820i
$525$	3.67013	+	2.74412i	0.160177	+	0.119763i
$526$	3.79863	+	6.57942i	0.165628	+	0.286876i
$527$	16.0453	+	9.26378i	0.698946	+	0.403537i
$528$	−7.90366	+	2.89804i	−0.343963	+	0.126121i
$529$	−6.04165	−	10.4644i	−0.262680	−	0.454976i
$530$	−2.84225	−	4.92292i	−0.123460	−	0.213838i
$531$	−3.93352	−	1.41049i	−0.170700	−	0.0612102i
$532$	−1.33124	+	2.62157i	−0.0577166	+	0.113659i
$533$	26.7550	+	15.4470i	1.15889	+	0.669084i
$534$	24.3719	−	8.93647i	1.05468	−	0.386719i
$535$			7.46971i			0.322944i
$536$		−	6.01448i		−	0.259786i
$537$	7.45793	+	6.22773i	0.321834	+	0.268746i
$538$	6.21175	+	3.58635i	0.267807	+	0.154619i
$539$	3.64881	+	33.8256i	0.157166	+	1.45697i
$540$	4.48131	−	2.63018i	0.192845	−	0.113185i
$541$	7.35700	+	12.7427i	0.316302	+	0.547852i	0.979713	−	0.200403i	$-0.0642253\pi$
$541$	7.35700	+	12.7427i	0.316302	+	0.547852i	−0.663411	+	0.748255i	$0.730892\pi$
$542$	−1.84640	−	3.19806i	−0.0793098	−	0.137369i
$543$	7.13832	−	41.0553i	0.306335	−	1.76185i
$544$	2.16902	+	1.25228i	0.0929959	+	0.0536912i
$545$	−8.23189	−	14.2581i	−0.352616	−	0.610748i
$546$	14.4994	+	10.8410i	0.620515	+	0.463953i
$547$	8.78526	−	15.2165i	0.375631	−	0.650611i	−0.614791	−	0.788690i	$-0.710759\pi$
$547$	8.78526	−	15.2165i	0.375631	−	0.650611i	0.990421	+	0.138079i	$0.0440928\pi$
$548$	−8.98722	+	5.18877i	−0.383915	+	0.221653i
$549$	−9.31983	+	25.9908i	−0.397761	+	1.10926i
$550$	−2.43013	+	4.20911i	−0.103621	+	0.179477i
$551$	−4.75800			−0.202698
$552$	3.66807	−	4.39265i	0.156123	−	0.186964i
$553$	17.3769	−	11.3185i	0.738939	−	0.481311i
$554$	21.5718	−	12.4545i	0.916498	−	0.529140i
$555$	6.21437	+	1.08050i	0.263785	+	0.0458646i
$556$	−7.92494	+	4.57547i	−0.336092	+	0.194043i
$557$	16.7457	+	9.66812i	0.709537	+	0.409652i	0.810890	−	0.585199i	$-0.198984\pi$
$557$	16.7457	+	9.66812i	0.709537	+	0.409652i	−0.101352	+	0.994851i	$0.532317\pi$
$558$	−20.8901	−	7.49083i	−0.884349	−	0.317112i
$559$		−	28.6572i		−	1.21207i
$560$	−0.142082	−	2.64193i	−0.00600407	−	0.111642i
$561$	−3.61171	+	20.7723i	−0.152486	+	0.877009i
$562$	7.32455	−	12.6865i	0.308968	−	0.535147i
$563$	−24.0647			−1.01421			−0.507103	−	0.861886i	$-0.669283\pi$
$563$	−24.0647			−1.01421			−0.507103	+	0.861886i	$0.669283\pi$
$564$	−19.9401	−	3.46701i	−0.839630	−	0.145987i
$565$			3.37117i			0.141826i
$566$	−6.34995			−0.266908
$567$	−23.6645	−	2.64415i	−0.993816	−	0.111044i
$568$	−9.66386			−0.405487
$569$		−	37.2930i		−	1.56341i	−0.623651	−	0.781703i	$-0.714351\pi$
$569$		−	37.2930i		−	1.56341i	0.623651	−	0.781703i	$-0.285649\pi$
$570$	1.89637	+	0.329723i	0.0794300	+	0.0138106i
$571$	7.65139			0.320201			0.160100	−	0.987101i	$-0.448818\pi$
$571$	7.65139			0.320201			0.160100	+	0.987101i	$0.448818\pi$
$572$	−9.60058	+	16.6287i	−0.401421	+	0.695281i
$573$	−7.19070	+	41.3565i	−0.300396	+	1.72769i
$574$	−9.36772	+	18.4475i	−0.391001	+	0.769985i
$575$		−	3.30404i		−	0.137788i
$576$	−2.82394	−	1.01261i	−0.117664	−	0.0421922i
$577$	34.5692	+	19.9585i	1.43913	+	0.830884i	0.997789	−	0.0664543i	$-0.0211687\pi$
$577$	34.5692	+	19.9585i	1.43913	+	0.830884i	0.441344	+	0.897338i	$0.354502\pi$
$578$	−9.28999	+	5.36358i	−0.386412	+	0.223095i
$579$	−1.05369	−	0.183206i	−0.0437899	−	0.00761380i
$580$	3.70789	−	2.14075i	0.153962	−	0.0888898i
$581$	0.111923	+	2.08115i	0.00464336	+	0.0863404i
$582$	19.2007	−	22.9936i	0.795895	−	0.953114i
$583$	−27.6282			−1.14424
$584$	6.96114	−	12.0570i	0.288054	−	0.498924i
$585$	4.00048	−	11.1564i	0.165399	−	0.461259i
$586$	3.10915	−	1.79507i	0.128438	−	0.0741535i
$587$	12.0540	−	20.8782i	0.497523	−	0.861734i	−0.502473	−	0.864593i	$-0.667577\pi$
$587$	12.0540	−	20.8782i	0.497523	−	0.861734i	0.999996	+	0.00285838i	$0.000909853\pi$
$588$	−6.72831	+	10.0861i	−0.277471	+	0.415945i
$589$	−4.11041	−	7.11944i	−0.169366	−	0.293351i
$590$	1.20631	+	0.696461i	0.0496629	+	0.0286729i
$591$	0.678408	−	3.90179i	0.0279060	−	0.160498i
$592$	−1.82085	−	3.15380i	−0.0748364	−	0.129620i
$593$	7.23840	+	12.5373i	0.297246	+	0.514844i	0.975505	−	0.219978i	$-0.0705987\pi$
$593$	7.23840	+	12.5373i	0.297246	+	0.514844i	−0.678259	+	0.734823i	$0.737265\pi$
$594$	−0.180537	−	25.2540i	−0.00740753	−	1.03619i
$595$	−5.90833	−	3.00027i	−0.242218	−	0.122999i
$596$	−20.9438	−	12.0919i	−0.857890	−	0.495303i
$597$	−5.53516	−	4.62212i	−0.226539	−	0.189171i
$598$		−	13.0531i		−	0.533781i
$599$		−	17.0187i		−	0.695367i	−0.937612	−	0.347683i	$-0.886968\pi$
$599$		−	17.0187i		−	0.695367i	0.937612	−	0.347683i	$-0.113032\pi$
$600$	−1.62618	+	0.596273i	−0.0663885	+	0.0243427i
$601$	23.0713	+	13.3202i	0.941099	+	0.543344i	0.890305	−	0.455365i	$-0.150491\pi$
$601$	23.0713	+	13.3202i	0.941099	+	0.543344i	0.0507942	+	0.998709i	$0.483825\pi$
$602$	19.1641	−	1.03064i	0.781070	−	0.0420057i
$603$	16.9845	+	6.09035i	0.691663	+	0.248018i
$604$	−11.4978	−	19.9148i	−0.467840	−	0.810322i
$605$	6.31108	+	10.9311i	0.256582	+	0.444413i
$606$	−4.76936	+	1.74879i	−0.193742	+	0.0710395i
$607$	26.1917	+	15.1218i	1.06309	+	0.613774i	0.926285	−	0.376824i	$-0.122984\pi$
$607$	26.1917	+	15.1218i	1.06309	+	0.613774i	0.136803	+	0.990598i	$0.456317\pi$
$608$	−0.555647	−	0.962409i	−0.0225345	−	0.0390308i
$609$	−19.4829	−	2.31805i	−0.789486	−	0.0939321i
$610$	4.60187	−	7.97067i	0.186324	−	0.322723i
$611$	−39.9791	+	23.0819i	−1.61738	+	0.933795i
$612$	−5.73274	+	4.85709i	−0.231732	+	0.196336i
$613$	−10.5704	+	18.3085i	−0.426934	+	0.739472i	−0.996599	−	0.0824054i	$-0.973740\pi$
$613$	−10.5704	+	18.3085i	−0.426934	+	0.739472i	0.569665	+	0.821877i	$0.307073\pi$
$614$	11.0589			0.446301
$615$	13.3444	+	2.32021i	0.538099	+	0.0935598i
$616$	−11.4655	−	5.82221i	−0.461957	−	0.234583i
$617$	27.0032	−	15.5903i	1.08711	−	0.627641i	0.154302	−	0.988024i	$-0.450687\pi$
$617$	27.0032	−	15.5903i	1.08711	−	0.627641i	0.932805	+	0.360382i	$0.117354\pi$
$618$	−2.87002	+	3.43696i	−0.115449	+	0.138255i
$619$	−15.0635	+	8.69694i	−0.605455	+	0.349559i	−0.771184	−	0.636612i	$-0.780335\pi$
$619$	−15.0635	+	8.69694i	−0.605455	+	0.349559i	0.165730	+	0.986171i	$0.447002\pi$
$620$	6.40644	+	3.69876i	0.257289	+	0.148546i
$621$	8.69023	+	14.8065i	0.348727	+	0.594162i
$622$		−	13.9447i		−	0.559130i
$623$	35.3552	+	17.9535i	1.41648	+	0.719291i
$624$	−6.42445	+	2.35566i	−0.257184	+	0.0943019i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	13.2712			0.530422
$627$	5.99626	−	7.18075i	0.239468	−	0.286771i
$628$		−	8.09026i		−	0.322836i
$629$	−9.12086			−0.363673
$630$	7.60453	+	2.27403i	0.302972	+	0.0905994i
$631$	−2.59501			−0.103306			−0.0516529	−	0.998665i	$-0.516449\pi$
$631$	−2.59501			−0.103306			−0.0516529	+	0.998665i	$0.516449\pi$
$632$			7.83821i			0.311787i
$633$	1.50944	+	4.11661i	0.0599949	+	0.163620i
$634$	−4.45055			−0.176754
$635$	−7.22974	+	12.5223i	−0.286903	+	0.496931i
$636$	−7.55742	−	6.31080i	−0.299671	−	0.250239i
$637$	2.96592	+	27.4950i	0.117514	+	1.08939i
$638$		−	20.8092i		−	0.823844i
$639$	9.78576	−	27.2901i	0.387119	−	1.07958i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−4.66393	+	2.69272i	−0.184214	+	0.106356i	−0.589271	−	0.807935i	$-0.700585\pi$
$641$	−4.66393	+	2.69272i	−0.184214	+	0.106356i	0.405057	+	0.914291i	$0.367252\pi$
$642$	4.45399	+	12.1471i	0.175785	+	0.479407i
$643$	16.1682	−	9.33469i	0.637610	−	0.368124i	−0.146083	−	0.989272i	$-0.546667\pi$
$643$	16.1682	−	9.33469i	0.637610	−	0.368124i	0.783693	+	0.621148i	$0.213333\pi$
$644$	8.72906	−	0.469446i	0.343973	−	0.0184988i
$645$	−4.32525	−	11.7960i	−0.170307	−	0.464467i
$646$	−2.78331			−0.109508
$647$	2.10117	−	3.63934i	0.0826056	−	0.143077i	−0.821763	−	0.569830i	$-0.807009\pi$
$647$	2.10117	−	3.63934i	0.0826056	−	0.143077i	0.904368	+	0.426753i	$0.140342\pi$
$648$	5.71911	−	6.94923i	0.224668	−	0.272991i
$649$	5.86297	−	3.38499i	0.230142	−	0.132872i
$650$	−1.97532	+	3.42136i	−0.0774785	+	0.134197i
$651$	−13.3626	−	31.1549i	−0.523722	−	1.22106i
$652$	0.616736	+	1.06822i	0.0241532	+	0.0418346i
$653$	−23.0433	−	13.3041i	−0.901755	−	0.520628i	−0.0239858	−	0.999712i	$-0.507636\pi$
$653$	−23.0433	−	13.3041i	−0.901755	−	0.520628i	−0.877769	+	0.479084i	$0.840969\pi$
$654$	−21.8882	−	18.2777i	−0.855897	−	0.714715i
$655$	−6.59248	−	11.4185i	−0.257589	−	0.446158i
$656$	−3.91000	−	6.77231i	−0.152660	−	0.264414i
$657$	26.9994	+	31.8669i	1.05335	+	1.24325i
$658$	−16.8735	−	25.9053i	−0.657798	−	1.00989i
$659$	35.1130	+	20.2725i	1.36781	+	0.789704i	0.990648	−	0.136444i	$-0.0435674\pi$
$659$	35.1130	+	20.2725i	1.36781	+	0.789704i	0.377160	+	0.926148i	$0.376901\pi$
$660$	−1.44205	+	8.29379i	−0.0561317	+	0.322835i
$661$		−	27.7557i		−	1.07957i	−0.841803	−	0.539785i	$-0.818505\pi$
$661$		−	27.7557i		−	1.07957i	0.841803	−	0.539785i	$-0.181495\pi$
$662$			7.83959i			0.304694i
$663$	−2.93576	+	16.8847i	−0.114016	+	0.655748i
$664$	−0.682199	−	0.393868i	−0.0264745	−	0.0152850i
$665$	1.60472	+	2.46367i	0.0622285	+	0.0955371i
$666$	10.7499	−	1.94838i	0.416552	−	0.0754980i
$667$	7.07313	+	12.2510i	0.273873	+	0.474361i
$668$	5.43643	+	9.41617i	0.210342	+	0.364323i
$669$	14.7750	+	12.3378i	0.571233	+	0.477006i
$670$	−5.20869	−	3.00724i	−0.201229	−	0.116180i
$671$	−22.3663	−	38.7396i	−0.863441	−	1.49552i
$672$	−1.80636	−	4.21154i	−0.0696820	−	0.162464i
$673$	19.5469	−	33.8562i	0.753477	−	1.30506i	−0.192650	−	0.981267i	$-0.561708\pi$
$673$	19.5469	−	33.8562i	0.753477	−	1.30506i	0.946128	−	0.323794i	$-0.104958\pi$
$674$	8.07208	−	4.66042i	0.310925	−	0.179513i
$675$	−0.0371456	−	5.19602i	−0.00142973	−	0.199995i
$676$	−1.30379	+	2.25823i	−0.0501458	+	0.0868551i
$677$	−38.0245			−1.46140			−0.730700	−	0.682698i	$-0.760806\pi$
$677$	−38.0245			−1.46140			−0.730700	+	0.682698i	$0.760806\pi$
$678$	2.01014	+	5.48213i	0.0771990	+	0.210540i
$679$	45.6928	−	2.45734i	1.75353	−	0.0943042i
$680$	2.16902	−	1.25228i	0.0831780	−	0.0480229i
$681$	−6.87408	−	18.7473i	−0.263415	−	0.718397i
$682$	31.1370	−	17.9769i	1.19230	−	0.688373i
$683$	27.3258	+	15.7765i	1.04559	+	0.603673i	0.921412	−	0.388587i	$-0.127037\pi$
$683$	27.3258	+	15.7765i	1.04559	+	0.603673i	0.124180	+	0.992260i	$0.460370\pi$
$684$	3.28044	−	0.594563i	0.125431	−	0.0227337i
$685$			10.3775i			0.396506i
$686$	−18.2802	+	2.97226i	−0.697941	+	0.113481i
$687$	−34.9073	−	29.1492i	−1.33179	−	1.11211i
$688$	−3.62690	+	6.28198i	−0.138274	+	0.239498i
$689$	−22.4574			−0.855561
$690$	−1.97011	−	5.37297i	−0.0750009	−	0.204545i
$691$			48.4845i			1.84444i	0.386671	+	0.922218i	$0.373625\pi$
$691$			48.4845i			1.84444i	−0.386671	+	0.922218i	$0.626375\pi$
$692$	−5.77390			−0.219491
$693$	28.0516	−	26.4821i	1.06559	−	1.00597i
$694$	−29.6538			−1.12564
$695$			9.15093i			0.347115i
$696$	4.75322	−	5.69215i	0.180170	−	0.215761i
$697$	−19.5857			−0.741861
$698$	16.1844	−	28.0322i	0.612588	−	1.06103i
$699$	1.23488	−	0.452793i	0.0467073	−	0.0171262i
$700$	−2.35902	−	1.19792i	−0.0891627	−	0.0452771i
$701$			48.2125i			1.82096i	0.413553	+	0.910480i	$0.364288\pi$
$701$			48.2125i			1.82096i	−0.413553	+	0.910480i	$0.635712\pi$
$702$	−0.146749	−	20.5276i	−0.00553868	−	0.774765i
$703$	3.50480	+	2.02350i	0.132186	+	0.0763176i
$704$	4.20911	−	2.43013i	0.158637	−	0.0915890i
$705$	−12.9726	+	15.5351i	−0.488575	+	0.585087i
$706$	−5.24551	+	3.02849i	−0.197417	+	0.113979i
$707$	−6.91868	−	3.51333i	−0.260204	−	0.132132i
$708$	2.37695	+	0.413283i	0.0893313	+	0.0155321i
$709$	38.7382			1.45484			0.727422	−	0.686190i	$-0.240718\pi$
$709$	38.7382			1.45484			0.727422	+	0.686190i	$0.240718\pi$
$710$	−4.83193	+	8.36915i	−0.181339	+	0.314089i
$711$	−22.1346	−	7.93708i	−0.830113	−	0.297664i
$712$	−12.9793	+	7.49361i	−0.486420	+	0.280835i
$713$	−12.2209	+	21.1672i	−0.457675	+	0.792716i
$714$	−11.3970	−	1.35600i	−0.426521	−	0.0507470i
$715$	9.60058	+	16.6287i	0.359041	+	0.621878i
$716$	−4.85812	−	2.80484i	−0.181557	−	0.104822i
$717$	−39.9869	+	14.6620i	−1.49334	+	0.547563i
$718$	−6.61995	−	11.4661i	−0.247054	−	0.427911i
$719$	−8.83033	−	15.2946i	−0.329316	−	0.570392i	0.653060	−	0.757306i	$-0.273485\pi$
$719$	−8.83033	−	15.2946i	−0.329316	−	0.570392i	−0.982376	+	0.186914i	$0.940151\pi$
$720$	−2.28892	+	1.93929i	−0.0853029	+	0.0722732i
$721$	−6.82991	+	0.367310i	−0.254359	+	0.0136794i
$722$	−15.3850	−	8.88251i	−0.572569	−	0.330573i
$723$	−21.9065	+	8.03249i	−0.814713	+	0.298732i
$724$			24.0589i			0.894142i
$725$		−	4.28150i		−	0.159011i
$726$	16.7809	+	14.0128i	0.622796	+	0.520064i
$727$	−15.3445	−	8.85913i	−0.569094	−	0.328567i	0.187693	−	0.982228i	$-0.439899\pi$
$727$	−15.3445	−	8.85913i	−0.569094	−	0.328567i	−0.756788	+	0.653661i	$0.773232\pi$
$728$	−9.31966	−	4.73255i	−0.345409	−	0.175400i
$729$	13.8329	+	23.1873i	0.512330	+	0.858788i
$730$	−6.96114	−	12.0570i	−0.257643	−	0.446251i
$731$	9.08382	+	15.7336i	0.335977	+	0.581930i
$732$	2.73077	−	15.7057i	0.100932	−	0.580500i
$733$	33.4413	+	19.3074i	1.23518	+	0.713133i	0.968106	−	0.250542i	$-0.0806087\pi$
$733$	33.4413	+	19.3074i	1.23518	+	0.713133i	0.267078	+	0.963675i	$0.413942\pi$
$734$	8.94994	+	15.5018i	0.330348	+	0.572180i
$735$	5.37068	+	10.8699i	0.198101	+	0.400944i
$736$	−1.65202	+	2.86139i	−0.0608943	+	0.105472i
$737$	−25.3156	+	14.6160i	−0.932513	+	0.538386i
$738$	23.0839	−	4.18384i	0.849730	−	0.154009i
$739$	18.1858	−	31.4988i	0.668976	−	1.15870i	−0.309215	−	0.950992i	$-0.600066\pi$
$739$	18.1858	−	31.4988i	0.668976	−	1.15870i	0.978191	−	0.207708i	$-0.0666004\pi$
$740$	−3.64170			−0.133871
$741$	4.87403	−	5.83684i	0.179052	−	0.214422i
$742$	−0.807668	−	15.0181i	−0.0296504	−	0.551331i
$743$	28.2741	−	16.3241i	1.03728	−	0.598872i	0.118216	−	0.992988i	$-0.462283\pi$
$743$	28.2741	−	16.3241i	1.03728	−	0.598872i	0.919061	+	0.394116i	$0.128949\pi$
$744$	12.6235	+	2.19486i	0.462799	+	0.0804674i
$745$	−20.9438	+	12.0919i	−0.767320	+	0.443013i
$746$	3.91848	+	2.26234i	0.143466	+	0.0828300i
$747$	1.80306	−	1.52765i	0.0659706	−	0.0558938i
$748$		−	12.1728i		−	0.445083i
$749$	−8.94812	+	17.6212i	−0.326957	+	0.643865i
$750$	−0.296702	+	1.70645i	−0.0108340	+	0.0623107i
$751$	−6.19350	+	10.7274i	−0.226004	+	0.391450i	−0.956620	−	0.291338i	$-0.905900\pi$
$751$	−6.19350	+	10.7274i	−0.226004	+	0.391450i	0.730616	+	0.682788i	$0.239233\pi$
$752$	11.6852			0.426114
$753$	1.74516	+	0.303432i	0.0635971	+	0.0110577i
$754$		−	16.9147i		−	0.615996i
$755$	−22.9956			−0.836897
$756$	13.7223	−	0.836399i	0.499074	−	0.0304195i
$757$	39.2473			1.42647			0.713234	−	0.700926i	$-0.247230\pi$
$757$	39.2473			1.42647			0.713234	+	0.700926i	$0.247230\pi$
$758$		−	7.47021i		−	0.271330i
$759$	−27.4030	−	4.76460i	−0.994668	−	0.172944i
$760$	−1.11129			−0.0403109
$761$	−7.03390	+	12.1831i	−0.254979	+	0.441636i	−0.964890	−	0.262655i	$-0.915402\pi$
$761$	−7.03390	+	12.1831i	−0.254979	+	0.441636i	0.709911	+	0.704291i	$0.248735\pi$
$762$	−4.29016	+	24.6744i	−0.155416	+	0.893858i
$763$	−2.33921	−	43.4962i	−0.0846852	−	1.57467i
$764$		−	24.2354i		−	0.876807i
$765$	1.33999	+	7.39324i	0.0484474	+	0.267303i
$766$	−28.6508	−	16.5416i	−1.03520	−	0.597671i
$767$	4.76569	−	2.75147i	0.172079	−	0.0993498i
$768$	1.70645	+	0.296702i	0.0615762	+	0.0107063i
$769$	12.1581	−	7.01950i	0.438434	−	0.253130i	−0.264499	−	0.964386i	$-0.585207\pi$
$769$	12.1581	−	7.01950i	0.438434	−	0.253130i	0.702933	+	0.711256i	$0.251873\pi$
$770$	−10.7749	+	7.01829i	−0.388301	+	0.252921i
$771$	26.4299	−	31.6507i	0.951848	−	1.13987i
$772$	0.617476			0.0222235
$773$	8.57207	−	14.8473i	0.308316	−	0.534019i	−0.669678	−	0.742652i	$-0.733568\pi$
$773$	8.57207	−	14.8473i	0.308316	−	0.534019i	0.977994	+	0.208632i	$0.0669012\pi$
$774$	−14.0673	−	16.6034i	−0.505637	−	0.596796i
$775$	6.40644	−	3.69876i	0.230126	−	0.132863i
$776$	−8.64760	+	14.9781i	−0.310431	+	0.537682i
$777$	13.3655	+	9.99323i	0.479484	+	0.358505i
$778$	18.2241	+	31.5651i	0.653366	+	1.13166i
$779$	7.52603	+	4.34515i	0.269648	+	0.155681i
$780$	−1.17216	+	6.74157i	−0.0419702	+	0.241387i
$781$	23.4845	+	40.6763i	0.840340	+	1.45551i
$782$	4.13760	+	7.16653i	0.147960	+	0.256275i
$783$	11.2611	+	19.1867i	0.402439	+	0.685678i
$784$	2.82965	−	6.40258i	0.101059	−	0.228664i
$785$	−7.00637	−	4.04513i	−0.250068	−	0.144377i
$786$	−17.5291	−	14.6376i	−0.625242	−	0.522107i
$787$			33.0686i			1.17877i	0.807853	+	0.589384i	$0.200629\pi$
$787$			33.0686i			1.17877i	−0.807853	+	0.589384i	$0.799371\pi$
$788$			2.28650i			0.0814531i
$789$	12.3545	−	4.53004i	0.439832	−	0.161274i
$790$	6.78809	+	3.91911i	0.241509	+	0.139436i
$791$	−4.03840	+	7.95268i	−0.143589	+	0.282765i
$792$	2.60033	+	14.3470i	0.0923988	+	0.509800i
$793$	−18.1803	−	31.4893i	−0.645603	−	1.11822i
$794$	−7.69789	−	13.3331i	−0.273188	−	0.473175i
$795$	−9.24402	+	3.38952i	−0.327852	+	0.120214i
$796$	3.60562	+	2.08171i	0.127798	+	0.0737841i
$797$	9.84860	+	17.0583i	0.348855	+	0.604235i	0.986046	−	0.166471i	$-0.0532371\pi$
$797$	9.84860	+	17.0583i	0.348855	+	0.604235i	−0.637191	+	0.770706i	$0.719904\pi$
$798$	4.07859	+	3.04952i	0.144380	+	0.107952i
$799$	14.6331	−	25.3453i	0.517682	−	0.896652i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−8.01844	−	44.2409i	−0.283318	−	1.56317i
$802$	−8.20364	+	14.2091i	−0.289681	+	0.501742i
$803$	−67.6659			−2.38788
$804$	−10.2634	−	1.78451i	−0.361962	−	0.0629348i
$805$	3.95798	−	7.79431i	0.139500	−	0.274713i
$806$	25.3096	−	14.6125i	0.891491	−	0.514703i
$807$	7.96297	−	9.53595i	0.280310	−	0.335681i
$808$	2.53993	−	1.46643i	0.0893545	−	0.0515888i
$809$	−21.6772	−	12.5154i	−0.762131	−	0.440017i	0.0679294	−	0.997690i	$-0.478361\pi$
$809$	−21.6772	−	12.5154i	−0.762131	−	0.440017i	−0.830060	+	0.557674i	$0.811694\pi$
$810$	−3.15865	−	8.42751i	−0.110984	−	0.296113i
$811$			12.0504i			0.423146i	0.977362	+	0.211573i	$0.0678586\pi$
$811$			12.0504i			0.423146i	−0.977362	+	0.211573i	$0.932141\pi$
$812$	11.3114	−	0.608325i	0.396953	−	0.0213480i
$813$	−6.00516	+	2.20192i	−0.210610	+	0.0772247i
$814$	−8.84980	+	15.3283i	−0.310185	+	0.537257i
$815$	1.23347			0.0432066
$816$	2.78051	−	3.32976i	0.0973373	−	0.116565i
$817$		−	8.06111i		−	0.282023i
$818$	21.1331			0.738900
$819$	22.8016	−	21.5259i	0.796754	−	0.752175i
$820$	−7.81999			−0.273086
$821$		−	41.8882i		−	1.46191i	−0.682427	−	0.730953i	$-0.739076\pi$
$821$		−	41.8882i		−	1.46191i	0.682427	−	0.730953i	$-0.260924\pi$
$822$	6.18785	+	16.8757i	0.215826	+	0.588609i
$823$	27.6822			0.964940			0.482470	−	0.875912i	$-0.339740\pi$
$823$	27.6822			0.964940			0.482470	+	0.875912i	$0.339740\pi$
$824$	1.29260	−	2.23884i	0.0450297	−	0.0779938i
$825$	6.46161	+	5.39575i	0.224964	+	0.187856i
$826$	2.01140	+	3.08803i	0.0699855	+	0.107446i
$827$		−	36.8335i		−	1.28083i	−0.768031	−	0.640413i	$-0.778763\pi$
$827$		−	36.8335i		−	1.28083i	0.768031	−	0.640413i	$-0.221237\pi$
$828$	−6.40751	−	7.56268i	−0.222676	−	0.262821i
$829$	44.8357	+	25.8859i	1.55721	+	0.899055i	0.997522	+	0.0703515i	$0.0224121\pi$
$829$	44.8357	+	25.8859i	1.55721	+	0.899055i	0.559687	+	0.828704i	$0.310921\pi$
$830$	−0.682199	+	0.393868i	−0.0236795	+	0.0136714i
$831$	−14.8525	−	40.5064i	−0.515229	−	1.40515i
$832$	3.42136	−	1.97532i	0.118614	−	0.0684820i
$833$	−10.3438	−	14.1554i	−0.358391	−	0.490456i
$834$	5.45645	+	14.8811i	0.188942	+	0.515289i
$835$	10.8729			0.376271
$836$	−2.70059	+	4.67756i	−0.0934019	+	0.161777i
$837$	−18.9809	+	33.4254i	−0.656074	+	1.15535i
$838$	4.00254	−	2.31087i	0.138265	−	0.0798276i
$839$	−4.77807	+	8.27587i	−0.164957	+	0.285715i	−0.936640	−	0.350293i	$-0.886082\pi$
$839$	−4.77807	+	8.27587i	−0.164957	+	0.285715i	0.771683	+	0.636008i	$0.219415\pi$
$840$	−4.55048	−	0.541411i	−0.157006	−	0.0186804i
$841$	−5.33439	−	9.23943i	−0.183944	−	0.318601i
$842$	2.00148	+	1.15555i	0.0689755	+	0.0398230i
$843$	−19.4756	−	16.2631i	−0.670777	−	0.560130i
$844$	−1.26573	−	2.19231i	−0.0435682	−	0.0754624i
$845$	1.30379	+	2.25823i	0.0448518	+	0.0776855i
$846$	−11.8325	+	32.9981i	−0.406811	+	1.13450i
$847$	1.79339	+	33.3469i	0.0616214	+	1.14581i
$848$	4.92292	+	2.84225i	0.169054	+	0.0976033i
$849$	−1.88404	+	10.8359i	−0.0646602	+	0.371886i
$850$		−	2.50457i		−	0.0859059i
$851$		−	12.0323i		−	0.412463i
$852$	−2.86729	+	16.4909i	−0.0982317	+	0.564969i
$853$	−6.13810	−	3.54384i	−0.210165	−	0.121339i	0.391223	−	0.920296i	$-0.372052\pi$
$853$	−6.13810	−	3.54384i	−0.210165	−	0.121339i	−0.601388	+	0.798957i	$0.705385\pi$
$854$	20.4041	−	13.2903i	0.698215	−	0.454786i
$855$	1.12531	−	3.13822i	0.0384848	−	0.107325i
$856$	−3.73486	−	6.46896i	−0.127655	−	0.221104i
$857$	−18.7513	−	32.4782i	−0.640531	−	1.10943i	−0.985314	−	0.170750i	$-0.945381\pi$
$857$	−18.7513	−	32.4782i	−0.640531	−	1.10943i	0.344783	−	0.938682i	$-0.387952\pi$
$858$	25.5275	+	21.3167i	0.871495	+	0.727739i
$859$	−10.1182	−	5.84175i	−0.345229	−	0.199318i	0.317353	−	0.948307i	$-0.397206\pi$
$859$	−10.1182	−	5.84175i	−0.345229	−	0.199318i	−0.662582	+	0.748990i	$0.730539\pi$
$860$	3.62690	+	6.28198i	0.123676	+	0.214214i
$861$	28.7004	+	21.4590i	0.978106	+	0.731320i
$862$	−12.3175	+	21.3345i	−0.419536	+	0.726657i
$863$	−41.4770	+	23.9467i	−1.41189	+	0.815157i	−0.995567	−	0.0940587i	$-0.970016\pi$
$863$	−41.4770	+	23.9467i	−1.41189	+	0.815157i	−0.416326	+	0.909215i	$0.636683\pi$
$864$	−2.56584	+	4.51846i	−0.0872917	+	0.153721i
$865$	−2.88695	+	5.00034i	−0.0981592	+	0.170017i
$866$	6.55773			0.222841
$867$	6.39631	+	17.4443i	0.217230	+	0.592438i
$868$	10.6821	+	16.3999i	0.362575	+	0.556647i
$869$	32.9919	−	19.0479i	1.11917	−	0.646155i
$870$	−2.55294	−	6.96248i	−0.0865528	−	0.236050i
$871$	−20.5777	+	11.8805i	−0.697248	+	0.402557i
$872$	14.2581	+	8.23189i	0.482839	+	0.278767i
$873$	−33.5405	−	39.5873i	−1.13517	−	1.33983i
$874$		−	3.67176i		−	0.124199i
$875$	−2.21694	+	1.44401i	−0.0749463	+	0.0488166i
$876$	−18.5093	−	15.4562i	−0.625373	−	0.522216i
$877$	16.6303	−	28.8045i	0.561564	−	0.972658i	−0.435796	−	0.900046i	$-0.643533\pi$
$877$	16.6303	−	28.8045i	0.561564	−	0.972658i	0.997360	−	0.0726125i	$-0.0231336\pi$
$878$	32.4291			1.09443
$879$	−2.14070	−	5.83820i	−0.0722040	−	0.196918i
$880$		−	4.86026i		−	0.163839i
$881$	39.7345			1.33869			0.669344	−	0.742953i	$-0.266575\pi$
$881$	39.7345			1.33869			0.669344	+	0.742953i	$0.266575\pi$
$882$	15.2151	+	14.4741i	0.512321	+	0.487368i
$883$	−20.3226			−0.683910			−0.341955	−	0.939716i	$-0.611089\pi$
$883$	−20.3226			−0.683910			−0.341955	+	0.939716i	$0.611089\pi$
$884$		−	9.89465i		−	0.332793i
$885$	1.54639	−	1.85186i	0.0519813	−	0.0622496i
$886$	−0.235686			−0.00791802
$887$	−1.35913	+	2.35408i	−0.0456351	+	0.0790424i	−0.887941	−	0.459958i	$-0.847864\pi$
$887$	−1.35913	+	2.35408i	−0.0456351	+	0.0790424i	0.842306	+	0.539000i	$0.181198\pi$
$888$	−5.92205	+	2.17144i	−0.198731	+	0.0728689i
$889$	−32.0558	+	20.8797i	−1.07512	+	0.700282i
$890$			14.9872i			0.502373i
$891$	−43.1483	−	7.18484i	−1.44552	−	0.240701i
$892$	−9.62445	−	5.55668i	−0.322250	−	0.186051i
$893$	−11.2459	+	6.49282i	−0.376329	+	0.217274i
$894$	−26.8482	+	32.1518i	−0.897940	+	1.07532i
$895$	−4.85812	+	2.80484i	−0.162389	+	0.0937554i
$896$	1.44401	+	2.21694i	0.0482411	+	0.0740628i
$897$	−22.2744	−	3.87288i	−0.743722	−	0.129312i
$898$	−18.8068			−0.627592
$899$	−15.8362	+	27.4292i	−0.528168	+	0.914813i
$900$	0.535019	+	2.95191i	0.0178340	+	0.0983969i
$901$	12.3298	−	7.11861i	0.410765	−	0.237155i
$902$	−19.0036	+	32.9152i	−0.632751	+	1.09596i
$903$	3.92729	−	33.0083i	0.130692	−	1.09845i
$904$	−1.68559	−	2.91952i	−0.0560618	−	0.0971019i
$905$	20.8356	+	12.0294i	0.692599	+	0.399872i
$906$	−37.3950	+	13.7117i	−1.24237	+	0.455540i
$907$	23.1327	+	40.0670i	0.768109	+	1.33040i	0.938587	+	0.345042i	$0.112135\pi$
$907$	23.1327	+	40.0670i	0.768109	+	1.33040i	−0.170479	+	0.985361i	$0.554531\pi$
$908$	5.76421	+	9.98390i	0.191292	+	0.331327i
$909$	1.56914	+	8.65753i	0.0520449	+	0.287152i
$910$	−8.75834	+	5.70478i	−0.290336	+	0.189112i
$911$	−33.8272	−	19.5301i	−1.12074	−	0.647062i	−0.179154	−	0.983821i	$-0.557336\pi$
$911$	−33.8272	−	19.5301i	−1.12074	−	0.647062i	−0.941591	+	0.336759i	$0.890669\pi$
$912$	−1.80716	+	0.662634i	−0.0598411	+	0.0219420i
$913$			3.82860i			0.126708i
$914$		−	18.6117i		−	0.615619i
$915$	−12.2362	−	10.2178i	−0.404515	−	0.337789i
$916$	22.7387	+	13.1282i	0.751308	+	0.433768i
$917$	−1.87335	−	34.8338i	−0.0618635	−	1.15031i
$918$	6.58746	+	11.2237i	0.217418	+	0.370439i
$919$	19.6509	+	34.0363i	0.648223	+	1.12276i	0.983547	+	0.180652i	$0.0578209\pi$
$919$	19.6509	+	34.0363i	0.648223	+	1.12276i	−0.335324	+	0.942103i	$0.608846\pi$
$920$	1.65202	+	2.86139i	0.0544655	+	0.0943371i
$921$	3.28120	−	18.8715i	0.108119	−	0.621836i
$922$	−23.8538	−	13.7720i	−0.785583	−	0.453556i
$923$	19.0892	+	33.0635i	0.628330	+	1.08830i
$924$	−13.3371	+	17.8378i	−0.438759	+	0.586820i
$925$	−1.82085	+	3.15380i	−0.0598691	+	0.103696i
$926$	−0.414241	+	0.239162i	−0.0136128	+	0.00785935i
$927$	5.01345	+	5.91729i	0.164663	+	0.194349i
$928$	−2.14075	+	3.70789i	−0.0702735	+	0.121717i
$929$	45.7542			1.50115			0.750574	−	0.660787i	$-0.229777\pi$
$929$	45.7542			1.50115			0.750574	+	0.660787i	$0.229777\pi$
$930$	8.21255	−	9.83483i	0.269300	−	0.322497i
$931$	0.834297	+	7.73419i	0.0273430	+	0.253478i
$932$	−0.657636	+	0.379686i	−0.0215416	+	0.0124370i
$933$	−23.7958	−	4.13741i	−0.779041	−	0.135453i
$934$	−10.5393	+	6.08486i	−0.344856	+	0.199103i
$935$	−10.5420	−	6.08642i	−0.344760	−	0.199047i
$936$	2.11367	+	11.6619i	0.0690874	+	0.381182i
$937$			52.1498i			1.70366i	0.523819	+	0.851830i	$0.324507\pi$
$937$			52.1498i			1.70366i	−0.523819	+	0.851830i	$0.675493\pi$
$938$	−8.68499	−	13.3337i	−0.283575	−	0.435362i
$939$	3.93758	−	22.6465i	0.128498	−	0.739042i
$940$	5.84258	−	10.1196i	0.190564	−	0.330066i
$941$	26.7510			0.872058			0.436029	−	0.899933i	$-0.356384\pi$
$941$	26.7510			0.872058			0.436029	+	0.899933i	$0.356384\pi$
$942$	−13.8056	−	2.40040i	−0.449811	−	0.0782091i
$943$		−	25.8376i		−	0.841388i
$944$	−1.39292			−0.0453358
$945$	6.13679	−	12.3020i	0.199630	−	0.400185i
$946$	35.2554			1.14625
$947$			9.85468i			0.320234i	0.987098	+	0.160117i	$0.0511872\pi$
$947$			9.85468i			0.320234i	−0.987098	+	0.160117i	$0.948813\pi$
$948$	13.3755	+	2.32561i	0.434416	+	0.0755324i
$949$	−55.0019			−1.78544
$950$	−0.555647	+	0.962409i	−0.0180276	+	0.0312247i
$951$	−1.32049	+	7.59464i	−0.0428197	+	0.246273i
$952$	6.61690	−	0.355855i	0.214455	−	0.0115333i
$953$			18.8568i			0.610830i	0.952219	+	0.305415i	$0.0987952\pi$
$953$			18.8568i			0.610830i	−0.952219	+	0.305415i	$0.901205\pi$
$954$	−13.0114	+	11.0239i	−0.421258	+	0.356913i
$955$	−20.9885	−	12.1177i	−0.679172	−	0.392120i
$956$	21.2951	−	12.2947i	0.688732	−	0.397640i
$957$	−35.5098	−	6.17413i	−1.14787	−	0.199581i
$958$	34.9474	−	20.1769i	1.12910	−	0.651886i
$959$	−12.4315	+	24.4809i	−0.401433	+	0.790528i
$960$	1.11018	−	1.32948i	0.0358308	−	0.0429087i
$961$	−23.7233			−0.765267
$962$	−7.19352	+	12.4595i	−0.231928	+	0.401712i
$963$	22.0499	−	3.99644i	0.710548	−	0.128783i
$964$	11.6664	−	6.73558i	0.375749	−	0.216939i
$965$	0.308738	−	0.534750i	0.00993863	−	0.0172142i
$966$	1.78884	−	15.0350i	0.0575551	−	0.483743i
$967$	27.7839	+	48.1232i	0.893471	+	1.54754i	0.835686	+	0.549208i	$0.185070\pi$
$967$	27.7839	+	48.1232i	0.893471	+	1.54754i	0.0577849	+	0.998329i	$0.481596\pi$
$968$	−10.9311	−	6.31108i	−0.351339	−	0.202846i
$969$	−0.825813	+	4.74957i	−0.0265289	+	0.152578i
$970$	8.64760	+	14.9781i	0.277658	+	0.480917i
$971$	−26.8589	−	46.5210i	−0.861944	−	1.49293i	−0.870050	−	0.492963i	$-0.835914\pi$
$971$	−26.8589	−	46.5210i	−0.861944	−	1.49293i	0.00810628	−	0.999967i	$-0.497420\pi$
$972$	−10.1616	−	11.8212i	−0.325934	−	0.379166i
$973$	−10.9621	+	21.5873i	−0.351428	+	0.692056i
$974$	−7.12353	−	4.11277i	−0.228253	−	0.131782i
$975$	5.25229	+	4.38591i	0.168208	+	0.140462i
$976$			9.20374i			0.294605i
$977$		−	17.1964i		−	0.550162i	−0.961421	−	0.275081i	$-0.911295\pi$
$977$		−	17.1964i		−	0.550162i	0.961421	−	0.275081i	$-0.0887046\pi$
$978$	2.00585	−	0.735486i	0.0641399	−	0.0235182i
$979$	63.0829	+	36.4209i	2.01614	+	1.16402i
$980$	−4.12998	−	5.65184i	−0.131927	−	0.180541i
$981$	−37.6842	+	31.9281i	−1.20317	+	1.01939i
$982$	5.26190	+	9.11388i	0.167914	+	0.290835i
$983$	−14.2867	−	24.7453i	−0.455676	−	0.789254i	0.543051	−	0.839700i	$-0.317269\pi$
$983$	−14.2867	−	24.7453i	−0.455676	−	0.789254i	−0.998727	+	0.0504459i	$0.983936\pi$
$984$	−12.7167	+	4.66285i	−0.405394	+	0.148646i
$985$	1.98016	+	1.14325i	0.0630933	+	0.0364269i
$986$	5.36165	+	9.28664i	0.170750	+	0.295747i
$987$	−49.2125	+	21.1077i	−1.56645	+	0.671864i
$988$	−2.19516	+	3.80213i	−0.0698374	+	0.120962i
$989$	−20.7559	+	11.9834i	−0.660001	+	0.381052i
$990$	13.7251	+	4.92157i	0.436211	+	0.156418i
$991$	−9.29023	+	16.0912i	−0.295114	+	0.511152i	−0.975011	−	0.222155i	$-0.928691\pi$
$991$	−9.29023	+	16.0912i	−0.295114	+	0.511152i	0.679897	+	0.733307i	$0.262024\pi$
$992$	−7.39752			−0.234871
$993$	13.3779	+	2.32602i	0.424534	+	0.0738141i
$994$	−21.4242	+	13.9548i	−0.679535	+	0.442618i
$995$	3.60562	−	2.08171i	0.114306	−	0.0659945i
$996$	−0.874525	+	1.04728i	−0.0277104	+	0.0331842i
$997$	−6.69547	+	3.86563i	−0.212048	+	0.122426i	−0.602263	−	0.798298i	$-0.705734\pi$
$997$	−6.69547	+	3.86563i	−0.212048	+	0.122426i	0.390215	+	0.920724i	$0.372401\pi$
$998$	−0.736540	−	0.425242i	−0.0233148	−	0.0134608i
$999$	−0.135273	−	18.9223i	−0.00427984	−	0.598676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.101.14	yes	28
3.2	odd	2		1890.2.bk.b.521.3		28
7.5	odd	6		630.2.t.b.551.13	yes	28
9.4	even	3		1890.2.t.b.1151.7		28
9.5	odd	6		630.2.t.b.311.13	✓	28
21.5	even	6		1890.2.t.b.1601.7		28
63.5	even	6	inner	630.2.bk.b.131.7	yes	28
63.40	odd	6		1890.2.bk.b.341.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.13	✓	28	9.5	odd	6
630.2.t.b.551.13	yes	28	7.5	odd	6
630.2.bk.b.101.14	yes	28	1.1	even	1	trivial
630.2.bk.b.131.7	yes	28	63.5	even	6	inner
1890.2.t.b.1151.7		28	9.4	even	3
1890.2.t.b.1601.7		28	21.5	even	6
1890.2.bk.b.341.3		28	63.40	odd	6
1890.2.bk.b.521.3		28	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.70645 + 0.296702i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.296702 + 1.70645i) q^{6} +(-2.21694 + 1.44401i) q^{7} -1.00000i q^{8} +(2.82394 + 1.01261i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.70645 + 0.296702i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.296702 + 1.70645i) q^{6} +(-2.21694 + 1.44401i) q^{7} -1.00000i q^{8} +(2.82394 + 1.01261i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-4.20911 + 2.43013i) q^{11} +(-1.70645 - 0.296702i) q^{12} +(-3.42136 + 1.97532i) q^{13} +(-1.44401 - 2.21694i) q^{14} +(-1.11018 + 1.32948i) q^{15} +1.00000 q^{16} +(1.25228 - 2.16902i) q^{17} +(-1.01261 + 2.82394i) q^{18} +(-0.962409 + 0.555647i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-4.21154 + 1.80636i) q^{21} +(-2.43013 - 4.20911i) q^{22} +(2.86139 + 1.65202i) q^{23} +(0.296702 - 1.70645i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.97532 - 3.42136i) q^{26} +(4.51846 + 2.56584i) q^{27} +(2.21694 - 1.44401i) q^{28} +(3.70789 + 2.14075i) q^{29} +(-1.32948 - 1.11018i) q^{30} +7.39752i q^{31} +1.00000i q^{32} +(-7.90366 + 2.89804i) q^{33} +(2.16902 + 1.25228i) q^{34} +(-0.142082 - 2.64193i) q^{35} +(-2.82394 - 1.01261i) q^{36} +(-1.82085 - 3.15380i) q^{37} +(-0.555647 - 0.962409i) q^{38} +(-6.42445 + 2.35566i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-3.91000 - 6.77231i) q^{41} +(-1.80636 - 4.21154i) q^{42} +(-3.62690 + 6.28198i) q^{43} +(4.20911 - 2.43013i) q^{44} +(-2.28892 + 1.93929i) q^{45} +(-1.65202 + 2.86139i) q^{46} +11.6852 q^{47} +(1.70645 + 0.296702i) q^{48} +(2.82965 - 6.40258i) q^{49} +(0.866025 - 0.500000i) q^{50} +(2.78051 - 3.32976i) q^{51} +(3.42136 - 1.97532i) q^{52} +(4.92292 + 2.84225i) q^{53} +(-2.56584 + 4.51846i) q^{54} -4.86026i q^{55} +(1.44401 + 2.21694i) q^{56} +(-1.80716 + 0.662634i) q^{57} +(-2.14075 + 3.70789i) q^{58} -1.39292 q^{59} +(1.11018 - 1.32948i) q^{60} +9.20374i q^{61} -7.39752 q^{62} +(-7.72273 + 1.83290i) q^{63} -1.00000 q^{64} -3.95064i q^{65} +(-2.89804 - 7.90366i) q^{66} +6.01448 q^{67} +(-1.25228 + 2.16902i) q^{68} +(4.39265 + 3.66807i) q^{69} +(2.64193 - 0.142082i) q^{70} -9.66386i q^{71} +(1.01261 - 2.82394i) q^{72} +(12.0570 + 6.96114i) q^{73} +(3.15380 - 1.82085i) q^{74} +(-0.596273 - 1.62618i) q^{75} +(0.962409 - 0.555647i) q^{76} +(5.82221 - 11.4655i) q^{77} +(-2.35566 - 6.42445i) q^{78} -7.83821 q^{79} +(-0.500000 + 0.866025i) q^{80} +(6.94923 + 5.71911i) q^{81} +(6.77231 - 3.91000i) q^{82} +(0.393868 - 0.682199i) q^{83} +(4.21154 - 1.80636i) q^{84} +(1.25228 + 2.16902i) q^{85} +(-6.28198 - 3.62690i) q^{86} +(5.69215 + 4.75322i) q^{87} +(2.43013 + 4.20911i) q^{88} +(-7.49361 - 12.9793i) q^{89} +(-1.93929 - 2.28892i) q^{90} +(4.73255 - 9.31966i) q^{91} +(-2.86139 - 1.65202i) q^{92} +(-2.19486 + 12.6235i) q^{93} +11.6852i q^{94} -1.11129i q^{95} +(-0.296702 + 1.70645i) q^{96} +(-14.9781 - 8.64760i) q^{97} +(6.40258 + 2.82965i) q^{98} +(-14.3470 + 2.60033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

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