LMFDB - Embedded newform 630.2.t.b.551.13

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

Embedding invariants

Embedding label			551.13
Character	$\chi$	$=$	630.551
Dual form			630.2.t.b.311.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.11018 - 1.32948i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.296702 - 1.70645i) q^{6} +(-0.142082 + 2.64193i) q^{7} -1.00000i q^{8} +(-0.535019 - 2.95191i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.11018 - 1.32948i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.296702 - 1.70645i) q^{6} +(-0.142082 + 2.64193i) q^{7} -1.00000i q^{8} +(-0.535019 - 2.95191i) q^{9} +(-0.866025 + 0.500000i) q^{10} -4.86026i q^{11} +(-0.596273 - 1.62618i) q^{12} +(3.42136 - 1.97532i) q^{13} +(1.19792 + 2.35902i) q^{14} +(-1.11018 + 1.32948i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.25228 - 2.16902i) q^{17} +(-1.93929 - 2.28892i) q^{18} +(-0.962409 - 0.555647i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.35465 + 3.12191i) q^{21} +(-2.43013 - 4.20911i) q^{22} -3.30404i q^{23} +(-1.32948 - 1.11018i) q^{24} +1.00000 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} +(-0.296702 + 1.70645i) q^{30} +(6.40644 + 3.69876i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-6.46161 - 5.39575i) 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} -1.11129 q^{38} +(1.17216 - 6.74157i) q^{39} +1.00000i q^{40} +(3.91000 + 6.77231i) q^{41} +(4.46617 + 1.02632i) q^{42} +(-3.62690 + 6.28198i) q^{43} +(-4.20911 - 2.43013i) q^{44} +(0.535019 + 2.95191i) q^{45} +(-1.65202 - 2.86139i) q^{46} +(5.84258 + 10.1196i) q^{47} +(-1.70645 - 0.296702i) q^{48} +(-6.95963 - 0.750744i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-4.27391 - 0.743110i) q^{51} -3.95064i q^{52} +(-4.92292 + 2.84225i) q^{53} +(-5.19602 + 0.0371456i) q^{54} +4.86026i q^{55} +(2.64193 + 0.142082i) q^{56} +(-1.80716 + 0.662634i) q^{57} +4.28150 q^{58} +(-0.696461 + 1.20631i) q^{59} +(0.596273 + 1.62618i) q^{60} +(-7.97067 + 4.60187i) q^{61} +7.39752 q^{62} +(7.87476 - 0.994070i) q^{63} -1.00000 q^{64} +(-3.42136 + 1.97532i) q^{65} +(-8.29379 - 1.44205i) q^{66} +(-3.00724 + 5.20869i) q^{67} -2.50457 q^{68} +(-4.39265 - 3.66807i) q^{69} +(-1.19792 - 2.35902i) q^{70} -9.66386i q^{71} +(-2.95191 + 0.535019i) q^{72} +(12.0570 - 6.96114i) q^{73} +3.64170i q^{74} +(1.11018 - 1.32948i) q^{75} +(-0.962409 + 0.555647i) q^{76} +(12.8405 + 0.690557i) q^{77} +(-2.35566 - 6.42445i) q^{78} +(3.91911 + 6.78809i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.42751 + 3.15865i) q^{81} +(6.77231 + 3.91000i) q^{82} +(-0.393868 + 0.682199i) q^{83} +(4.38098 - 1.34426i) q^{84} +(1.25228 + 2.16902i) q^{85} +7.25381i q^{86} +(6.96248 - 2.55294i) q^{87} -4.86026 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} +(12.0297 - 4.41094i) q^{93} +(10.1196 + 5.84258i) q^{94} +(0.962409 + 0.555647i) q^{95} +(-1.62618 + 0.596273i) 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} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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
$3$	1.11018	−	1.32948i	0.640960	−	0.767574i
$3$	1.11018	−	1.32948i	0.640960	−	0.767574i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.296702	−	1.70645i	0.121128	−	0.696655i
$7$	−0.142082	+	2.64193i	−0.0537021	+	0.998557i
$7$	−0.142082	+	2.64193i	−0.0537021	+	0.998557i
$8$		−	1.00000i		−	0.353553i
$9$	−0.535019	−	2.95191i	−0.178340	−	0.983969i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$		−	4.86026i		−	1.46542i	−0.680539	−	0.732712i	$-0.738254\pi$
$11$		−	4.86026i		−	1.46542i	0.680539	−	0.732712i	$-0.261746\pi$
$12$	−0.596273	−	1.62618i	−0.172129	−	0.469437i
$13$	3.42136	−	1.97532i	0.948914	−	0.547856i	0.0561705	−	0.998421i	$-0.482111\pi$
$13$	3.42136	−	1.97532i	0.948914	−	0.547856i	0.892743	+	0.450566i	$0.148778\pi$
$14$	1.19792	+	2.35902i	0.320158	+	0.630475i
$15$	−1.11018	+	1.32948i	−0.286646	+	0.343270i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.25228	−	2.16902i	−0.303723	−	0.526064i	0.673253	−	0.739412i	$-0.264896\pi$
$17$	−1.25228	−	2.16902i	−0.303723	−	0.526064i	−0.976976	+	0.213348i	$0.931563\pi$
$18$	−1.93929	−	2.28892i	−0.457096	−	0.539503i
$19$	−0.962409	−	0.555647i	−0.220792	−	0.127474i	0.385525	−	0.922697i	$-0.374020\pi$
$19$	−0.962409	−	0.555647i	−0.220792	−	0.127474i	−0.606317	+	0.795223i	$0.707354\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	3.35465	+	3.12191i	0.732045	+	0.681256i
$22$	−2.43013	−	4.20911i	−0.518106	−	0.897385i
$23$		−	3.30404i		−	0.688941i	−0.938797	−	0.344470i	$-0.888059\pi$
$23$		−	3.30404i		−	0.688941i	0.938797	−	0.344470i	$-0.111941\pi$
$24$	−1.32948	−	1.11018i	−0.271378	−	0.226614i
$25$	1.00000			0.200000
$26$	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	$0.536535\pi$
$30$	−0.296702	+	1.70645i	−0.0541701	+	0.311554i
$31$	6.40644	+	3.69876i	1.15063	+	0.664317i	0.949041	−	0.315153i	$-0.102056\pi$
$31$	6.40644	+	3.69876i	1.15063	+	0.664317i	0.201590	+	0.979470i	$0.435389\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−6.46161	−	5.39575i	−1.12482	−	0.939279i
$34$	−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	−0.975986	−	0.217832i	$-0.930102\pi$
$37$	−1.82085	+	3.15380i	−0.299345	+	0.518482i	0.676641	+	0.736313i	$0.263435\pi$
$38$	−1.11129			−0.180276
$39$	1.17216	−	6.74157i	0.187696	−	1.07952i
$40$			1.00000i			0.158114i
$41$	3.91000	+	6.77231i	0.610639	+	1.05766i	0.991133	+	0.132874i	$0.0424206\pi$
$41$	3.91000	+	6.77231i	0.610639	+	1.05766i	−0.380494	+	0.924783i	$0.624246\pi$
$42$	4.46617	+	1.02632i	0.689145	+	0.158365i
$43$	−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
$45$	0.535019	+	2.95191i	0.0797559	+	0.440044i
$46$	−1.65202	−	2.86139i	−0.243577	−	0.421888i
$47$	5.84258	+	10.1196i	0.852227	+	1.47610i	0.879194	+	0.476465i	$0.158082\pi$
$47$	5.84258	+	10.1196i	0.852227	+	1.47610i	−0.0269662	+	0.999636i	$0.508585\pi$
$48$	−1.70645	−	0.296702i	−0.246305	−	0.0428252i
$49$	−6.95963	−	0.750744i	−0.994232	−	0.107249i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−4.27391	−	0.743110i	−0.598468	−	0.104056i
$52$		−	3.95064i		−	0.547856i
$53$	−4.92292	+	2.84225i	−0.676216	+	0.390413i	−0.798428	−	0.602091i	$-0.794335\pi$
$53$	−4.92292	+	2.84225i	−0.676216	+	0.390413i	0.122212	+	0.992504i	$0.461001\pi$
$54$	−5.19602	+	0.0371456i	−0.707089	+	0.00505487i
$55$			4.86026i			0.655358i
$56$	2.64193	+	0.142082i	0.353043	+	0.0189866i
$57$	−1.80716	+	0.662634i	−0.239365	+	0.0877681i
$58$	4.28150			0.562188
$59$	−0.696461	+	1.20631i	−0.0906716	+	0.157048i	−0.907794	−	0.419417i	$-0.862235\pi$
$59$	−0.696461	+	1.20631i	−0.0906716	+	0.157048i	0.817122	+	0.576464i	$0.195568\pi$
$60$	0.596273	+	1.62618i	0.0769785	+	0.209939i
$61$	−7.97067	+	4.60187i	−1.02054	+	0.589209i	−0.914260	−	0.405127i	$-0.867227\pi$
$61$	−7.97067	+	4.60187i	−1.02054	+	0.589209i	−0.106280	+	0.994336i	$0.533894\pi$
$62$	7.39752			0.939486
$63$	7.87476	−	0.994070i	0.992126	−	0.125241i
$64$	−1.00000			−0.125000
$65$	−3.42136	+	1.97532i	−0.424367	+	0.245008i
$66$	−8.29379	−	1.44205i	−1.02090	−	0.177504i
$67$	−3.00724	+	5.20869i	−0.367393	+	0.636343i	−0.989157	−	0.146861i	$-0.953083\pi$
$67$	−3.00724	+	5.20869i	−0.367393	+	0.636343i	0.621764	+	0.783204i	$0.286416\pi$
$68$	−2.50457			−0.303723
$69$	−4.39265	−	3.66807i	−0.528813	−	0.441584i
$70$	−1.19792	−	2.35902i	−0.143179	−	0.281957i
$71$		−	9.66386i		−	1.14689i	−0.819244	−	0.573445i	$-0.805607\pi$
$71$		−	9.66386i		−	1.14689i	0.819244	−	0.573445i	$-0.194393\pi$
$72$	−2.95191	+	0.535019i	−0.347886	+	0.0630526i
$73$	12.0570	−	6.96114i	1.41117	−	0.814739i	0.415671	−	0.909515i	$-0.363547\pi$
$73$	12.0570	−	6.96114i	1.41117	−	0.814739i	0.995499	+	0.0947757i	$0.0302134\pi$
$74$			3.64170i			0.423338i
$75$	1.11018	−	1.32948i	0.128192	−	0.153515i
$76$	−0.962409	+	0.555647i	−0.110396	+	0.0637371i
$77$	12.8405	+	0.690557i	1.46331	+	0.0786963i
$78$	−2.35566	−	6.42445i	−0.266726	−	0.727426i
$79$	3.91911	+	6.78809i	0.440934	+	0.763720i	0.997759	−	0.0669097i	$-0.0213140\pi$
$79$	3.91911	+	6.78809i	0.440934	+	0.763720i	−0.556825	+	0.830630i	$0.687981\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−8.42751	+	3.15865i	−0.936390	+	0.350961i
$82$	6.77231	+	3.91000i	0.747877	+	0.431787i
$83$	−0.393868	+	0.682199i	−0.0432326	+	0.0748811i	−0.886832	−	0.462092i	$-0.847099\pi$
$83$	−0.393868	+	0.682199i	−0.0432326	+	0.0748811i	0.843599	+	0.536973i	$0.180432\pi$
$84$	4.38098	−	1.34426i	0.478004	−	0.146671i
$85$	1.25228	+	2.16902i	0.135829	+	0.235263i
$86$			7.25381i			0.782198i
$87$	6.96248	−	2.55294i	0.746456	−	0.273704i
$88$	−4.86026			−0.518106
$89$	7.49361	−	12.9793i	0.794321	−	1.37580i	−0.128949	−	0.991651i	$-0.541160\pi$
$89$	7.49361	−	12.9793i	0.794321	−	1.37580i	0.923270	−	0.384153i	$-0.125506\pi$
$90$	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
$93$	12.0297	−	4.41094i	1.24742	−	0.457393i
$94$	10.1196	+	5.84258i	1.04376	+	0.602616i
$95$	0.962409	+	0.555647i	0.0987410	+	0.0570082i
$96$	−1.62618	+	0.596273i	−0.165971	+	0.0608569i
$97$	14.9781	+	8.64760i	1.52079	+	0.878031i	0.999699	+	0.0245323i	$0.00780966\pi$
$97$	14.9781	+	8.64760i	1.52079	+	0.878031i	0.521095	+	0.853499i	$0.325524\pi$
$98$	−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
$101$	2.93286			0.291831			0.145915	−	0.989297i	$-0.453387\pi$
$101$	2.93286			0.291831			0.145915	+	0.989297i	$0.453387\pi$
$102$	−4.07287	+	1.49340i	−0.403274	+	0.147869i
$103$			2.58519i			0.254727i	0.991856	+	0.127363i	$0.0406514\pi$
$103$			2.58519i			0.254727i	−0.991856	+	0.127363i	$0.959349\pi$
$104$	−1.97532	−	3.42136i	−0.193696	−	0.335492i
$105$	−3.35465	−	3.12191i	−0.327381	−	0.304667i
$106$	−2.84225	+	4.92292i	−0.276064	+	0.478157i
$107$	−6.46896	−	3.73486i	−0.625378	−	0.361062i	0.153582	−	0.988136i	$-0.450919\pi$
$107$	−6.46896	−	3.73486i	−0.625378	−	0.361062i	−0.778960	+	0.627074i	$0.784252\pi$
$108$	−4.48131	+	2.63018i	−0.431214	+	0.253089i
$109$	−8.23189	−	14.2581i	−0.788472	−	1.36567i	−0.926903	−	0.375302i	$-0.877539\pi$
$109$	−8.23189	−	14.2581i	−0.788472	−	1.36567i	0.138430	−	0.990372i	$-0.455794\pi$
$110$	2.43013	+	4.20911i	0.231704	+	0.401323i
$111$	2.17144	+	5.92205i	0.206104	+	0.562096i
$112$	2.35902	−	1.19792i	0.222907	−	0.113193i
$113$	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	$0.282646\pi$
$114$	−1.23373	+	1.47744i	−0.115550	+	0.138375i
$115$			3.30404i			0.308104i
$116$	3.70789	−	2.14075i	0.344269	−	0.198764i
$117$	−7.66146	−	9.04269i	−0.708302	−	0.835997i
$118$			1.39292i			0.128229i
$119$	5.90833	−	3.00027i	0.541615	−	0.275034i
$120$	1.32948	+	1.11018i	0.121364	+	0.101345i
$121$	−12.6222			−1.14747
$122$	−4.60187	+	7.97067i	−0.416634	+	0.721631i
$123$	13.3444	+	2.32021i	1.20323	+	0.209206i
$124$	6.40644	−	3.69876i	0.575315	−	0.332158i
$125$	−1.00000			−0.0894427
$126$	6.32271	−	4.79827i	0.563271	−	0.427464i
$127$	14.4595			1.28307			0.641535	−	0.767093i	$-0.278298\pi$
$127$	14.4595			1.28307			0.641535	+	0.767093i	$0.278298\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.32525	+	11.7960i	0.380817	+	1.03858i
$130$	−1.97532	+	3.42136i	−0.173247	+	0.300073i
$131$	−13.1850			−1.15198			−0.575988	−	0.817458i	$-0.695382\pi$
$131$	−13.1850			−1.15198			−0.575988	+	0.817458i	$0.695382\pi$
$132$	−7.90366	+	2.89804i	−0.687925	+	0.252242i
$133$	1.60472	−	2.46367i	0.139147	−	0.213627i
$134$			6.01448i			0.519572i
$135$	4.51846	+	2.56584i	0.388887	+	0.220832i
$136$	−2.16902	+	1.25228i	−0.185992	+	0.107382i
$137$			10.3775i			0.886614i	0.896370	+	0.443307i	$0.146195\pi$
$137$			10.3775i			0.886614i	−0.896370	+	0.443307i	$0.853805\pi$
$138$	−5.63818	−	0.980316i	−0.479954	−	0.0834501i
$139$	−7.92494	+	4.57547i	−0.672185	+	0.388086i	−0.796904	−	0.604106i	$-0.793530\pi$
$139$	−7.92494	+	4.57547i	−0.672185	+	0.388086i	0.124719	+	0.992192i	$0.460197\pi$
$140$	−2.21694	−	1.44401i	−0.187366	−	0.122041i
$141$	19.9401	+	3.46701i	1.67926	+	0.291975i
$142$	−4.83193	−	8.36915i	−0.405487	−	0.702324i
$143$	−9.60058	−	16.6287i	−0.802841	−	1.39056i
$144$	−2.28892	+	1.93929i	−0.190743	+	0.161608i
$145$	−3.70789	−	2.14075i	−0.307923	−	0.177780i
$146$	6.96114	−	12.0570i	0.576108	−	0.997848i
$147$	−8.72451	+	8.41920i	−0.719585	+	0.694404i
$148$	1.82085	+	3.15380i	0.149673	+	0.259241i
$149$		−	24.1838i		−	1.98121i	−0.136746	−	0.990606i	$-0.543664\pi$
$149$		−	24.1838i		−	1.98121i	0.136746	−	0.990606i	$-0.456336\pi$
$150$	0.296702	−	1.70645i	0.0242256	−	0.139331i
$151$	−22.9956			−1.87136			−0.935679	−	0.352851i	$-0.885212\pi$
$151$	−22.9956			−1.87136			−0.935679	+	0.352851i	$0.885212\pi$
$152$	−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
$156$	−5.25229	−	4.38591i	−0.420520	−	0.351154i
$157$	7.00637	+	4.04513i	0.559169	+	0.322836i	0.752812	−	0.658236i	$-0.228697\pi$
$157$	7.00637	+	4.04513i	0.559169	+	0.322836i	−0.193643	+	0.981072i	$0.562030\pi$
$158$	6.78809	+	3.91911i	0.540032	+	0.311787i
$159$	−1.68660	+	9.70031i	−0.133756	+	0.769285i
$160$	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	−0.889168	−	0.457582i	$-0.848716\pi$
$163$	−0.616736	+	1.06822i	−0.0483065	+	0.0836693i	0.840861	+	0.541251i	$0.182049\pi$
$164$	7.81999			0.610639
$165$	6.46161	+	5.39575i	0.503036	+	0.420058i
$166$			0.787736i			0.0611401i
$167$	5.43643	+	9.41617i	0.420683	+	0.728645i	0.996006	−	0.0892813i	$-0.0284570\pi$
$167$	5.43643	+	9.41617i	0.420683	+	0.728645i	−0.575323	+	0.817926i	$0.695124\pi$
$168$	3.12191	−	3.35465i	0.240860	−	0.258817i
$169$	1.30379	−	2.25823i	0.100292	−	0.173710i
$170$	2.16902	+	1.25228i	0.166356	+	0.0960457i
$171$	−1.12531	+	3.13822i	−0.0860547	+	0.239986i
$172$	3.62690	+	6.28198i	0.276549	+	0.478997i
$173$	2.88695	+	5.00034i	0.219491	+	0.380169i	0.954652	−	0.297723i	$-0.0962271\pi$
$173$	2.88695	+	5.00034i	0.219491	+	0.380169i	−0.735162	+	0.677892i	$0.762894\pi$
$174$	4.75322	−	5.69215i	0.360340	−	0.431521i
$175$	−0.142082	+	2.64193i	−0.0107404	+	0.199711i
$176$	−4.20911	+	2.43013i	−0.317274	+	0.183178i
$177$	0.830562	+	2.26514i	0.0624289	+	0.170259i
$178$		−	14.9872i		−	1.12334i
$179$	−4.85812	+	2.80484i	−0.363113	+	0.209643i	−0.670445	−	0.741959i	$-0.733897\pi$
$179$	−4.85812	+	2.80484i	−0.363113	+	0.209643i	0.307332	+	0.951602i	$0.400564\pi$
$180$	2.82394	+	1.01261i	0.210484	+	0.0754758i
$181$			24.0589i			1.78828i	0.447784	+	0.894142i	$0.352213\pi$
$181$			24.0589i			1.78828i	−0.447784	+	0.894142i	$0.647787\pi$
$182$	8.75834	+	5.70478i	0.649211	+	0.422867i
$183$	−2.73077	+	15.7057i	−0.201864	+	1.16100i
$184$	−3.30404			−0.243577
$185$	1.82085	−	3.15380i	0.133871	−	0.231872i
$186$	8.21255	−	9.83483i	0.602173	−	0.721125i
$187$	−10.5420	+	6.08642i	−0.770907	+	0.445083i
$188$	11.6852			0.852227
$189$	7.42077	−	11.5729i	0.539782	−	0.841805i
$190$	1.11129			0.0806217
$191$	20.9885	−	12.1177i	1.51867	−	0.876807i	0.518916	−	0.854826i	$-0.326336\pi$
$191$	20.9885	−	12.1177i	1.51867	−	0.876807i	0.999758	−	0.0219813i	$-0.00699743\pi$
$192$	−1.11018	+	1.32948i	−0.0801200	+	0.0959467i
$193$	0.308738	−	0.534750i	0.0222235	−	0.0384921i	−0.854700	−	0.519123i	$-0.826259\pi$
$193$	0.308738	−	0.534750i	0.0222235	−	0.0384921i	0.876923	+	0.480630i	$0.159592\pi$
$194$	17.2952			1.24172
$195$	−1.17216	+	6.74157i	−0.0839404	+	0.482774i
$196$	−4.12998	+	5.65184i	−0.294998	+	0.403703i
$197$		−	2.28650i		−	0.162906i	−0.996677	−	0.0814531i	$-0.974044\pi$
$197$		−	2.28650i		−	0.162906i	0.996677	−	0.0814531i	$-0.0259561\pi$
$198$	−11.1247	+	9.42548i	−0.790601	+	0.669839i
$199$	−3.60562	+	2.08171i	−0.255596	+	0.147568i	−0.622324	−	0.782760i	$-0.713811\pi$
$199$	−3.60562	+	2.08171i	−0.255596	+	0.147568i	0.366728	+	0.930328i	$0.380478\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	3.58627	+	9.78062i	0.252956	+	0.689872i
$202$	2.53993	−	1.46643i	0.178709	−	0.103178i
$203$	−6.18254	+	9.49182i	−0.433929	+	0.666195i
$204$	−2.78051	+	3.32976i	−0.194675	+	0.233130i
$205$	−3.91000	−	6.77231i	−0.273086	−	0.472999i
$206$	1.29260	+	2.23884i	0.0900595	+	0.155988i
$207$	−9.75323	+	1.76773i	−0.677896	+	0.122865i
$208$	−3.42136	−	1.97532i	−0.237228	−	0.136964i
$209$	−2.70059	+	4.67756i	−0.186804	+	0.323554i
$210$	−4.46617	−	1.02632i	−0.308195	−	0.0708230i
$211$	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	$0.805562\pi$
$212$			5.68450i			0.390413i
$213$	−12.8479	−	10.7286i	−0.880323	−	0.735111i
$214$	−7.46971			−0.510619
$215$	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
$219$	4.13077	−	23.7576i	0.279131	−	1.60539i
$220$	4.20911	+	2.43013i	0.283778	+	0.163839i
$221$	−8.56901	−	4.94732i	−0.576414	−	0.332793i
$222$	4.84155	+	4.04292i	0.324944	+	0.271343i
$223$	−9.62445	−	5.55668i	−0.644501	−	0.372103i	0.141845	−	0.989889i	$-0.454696\pi$
$223$	−9.62445	−	5.55668i	−0.644501	−	0.372103i	−0.786346	+	0.617786i	$0.788030\pi$
$224$	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
$227$	−11.5284			−0.765168			−0.382584	−	0.923921i	$-0.624966\pi$
$227$	−11.5284			−0.765168			−0.382584	+	0.923921i	$0.624966\pi$
$228$	−0.329723	+	1.89637i	−0.0218364	+	0.125590i
$229$		−	26.2564i		−	1.73507i	−0.497376	−	0.867535i	$-0.665703\pi$
$229$		−	26.2564i		−	1.73507i	0.497376	−	0.867535i	$-0.334297\pi$
$230$	1.65202	+	2.86139i	0.108931	+	0.188674i
$231$	15.1733	−	16.3045i	0.998329	−	1.07276i
$232$	2.14075	−	3.70789i	0.140547	−	0.243435i
$233$	−0.657636	−	0.379686i	−0.0430832	−	0.0248741i	0.478304	−	0.878194i	$-0.341252\pi$
$233$	−0.657636	−	0.379686i	−0.0430832	−	0.0248741i	−0.521387	+	0.853320i	$0.674585\pi$
$234$	−11.1564	−	4.00048i	−0.729314	−	0.261519i
$235$	−5.84258	−	10.1196i	−0.381128	−	0.660132i
$236$	0.696461	+	1.20631i	0.0453358	+	0.0785239i
$237$	13.3755	+	2.32561i	0.868833	+	0.151065i
$238$	3.61663	−	5.55247i	0.234431	−	0.359913i
$239$	−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	$0.626009\pi$
$240$	1.70645	+	0.296702i	0.110151	+	0.0191520i
$241$			13.4712i			0.867754i	0.900972	+	0.433877i	$0.142855\pi$
$241$			13.4712i			0.867754i	−0.900972	+	0.433877i	$0.857145\pi$
$242$	−10.9311	+	6.31108i	−0.702678	+	0.405691i
$243$	−5.15666	+	14.7108i	−0.330800	+	0.943701i
$244$			9.20374i			0.589209i
$245$	6.95963	+	0.750744i	0.444634	+	0.0479633i
$246$	12.7167	−	4.66285i	0.810788	−	0.297292i
$247$	−4.39033			−0.279350
$248$	3.69876	−	6.40644i	0.234871	−	0.406809i
$249$	0.469705	+	1.28100i	0.0297664	+	0.0811800i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−1.02268			−0.0645513			−0.0322756	−	0.999479i	$-0.510275\pi$
$251$	−1.02268			−0.0645513			−0.0322756	+	0.999479i	$0.510275\pi$
$252$	3.07649	−	7.31678i	0.193801	−	0.460914i
$253$	−16.0585			−1.00959
$254$	12.5223	−	7.22974i	0.785717	−	0.453634i
$255$	4.27391	+	0.743110i	0.267643	+	0.0465353i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.8069			1.48503			0.742517	−	0.669827i	$-0.233632\pi$
$257$	23.8069			1.48503			0.742517	+	0.669827i	$0.233632\pi$
$258$	9.64377	+	8.05300i	0.600395	+	0.501358i
$259$	−8.07342	−	5.25866i	−0.501658	−	0.326757i
$260$			3.95064i			0.245008i
$261$	4.33550	−	12.0907i	0.268361	−	0.748394i
$262$	−11.4185	+	6.59248i	−0.705438	+	0.407285i
$263$			7.59726i			0.468467i	0.972180	+	0.234234i	$0.0752580\pi$
$263$			7.59726i			0.468467i	−0.972180	+	0.234234i	$0.924742\pi$
$264$	−5.39575	+	6.46161i	−0.332085	+	0.397684i
$265$	4.92292	−	2.84225i	0.302413	−	0.174598i
$266$	0.157895	−	2.93596i	0.00968118	−	0.180016i
$267$	−8.93647	−	24.3719i	−0.546903	−	1.49154i
$268$	3.00724	+	5.20869i	0.183696	+	0.318172i
$269$	−3.58635	−	6.21175i	−0.218664	−	0.378737i	0.735736	−	0.677269i	$-0.236836\pi$
$269$	−3.58635	−	6.21175i	−0.218664	−	0.378737i	−0.954400	+	0.298532i	$0.903503\pi$
$270$	5.19602	−	0.0371456i	0.316220	−	0.00226061i
$271$	−3.19806	−	1.84640i	−0.194268	−	0.112161i	0.399711	−	0.916641i	$-0.369111\pi$
$271$	−3.19806	−	1.84640i	−0.194268	−	0.112161i	−0.593979	+	0.804480i	$0.702444\pi$
$272$	−1.25228	+	2.16902i	−0.0759308	+	0.131516i
$273$	17.6442	+	4.05464i	1.06788	+	0.245398i
$274$	5.18877	+	8.98722i	0.313465	+	0.542938i
$275$		−	4.86026i		−	0.293085i
$276$	−5.37297	+	1.97011i	−0.323415	+	0.118587i
$277$	24.9090			1.49663			0.748317	−	0.663341i	$-0.230862\pi$
$277$	24.9090			1.49663			0.748317	+	0.663341i	$0.230862\pi$
$278$	−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	$0.810607\pi$
$282$	19.0022	−	6.96754i	1.13156	−	0.414911i
$283$	5.49922	+	3.17497i	0.326895	+	0.188733i	0.654462	−	0.756095i	$-0.272895\pi$
$283$	5.49922	+	3.17497i	0.326895	+	0.188733i	−0.327567	+	0.944828i	$0.606229\pi$
$284$	−8.36915	−	4.83193i	−0.496618	−	0.286722i
$285$	1.80716	−	0.662634i	0.107047	−	0.0392511i
$286$	−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
$290$	−4.28150			−0.251418
$291$	28.1251	−	10.3127i	1.64872	−	0.604539i
$292$		−	13.9223i		−	0.814739i
$293$	1.79507	+	3.10915i	0.104869	+	0.181638i	0.913685	−	0.406424i	$-0.133224\pi$
$293$	1.79507	+	3.10915i	0.104869	+	0.181638i	−0.808816	+	0.588062i	$0.799891\pi$
$294$	−3.34604	+	11.6535i	−0.195145	+	0.679646i
$295$	0.696461	−	1.20631i	0.0405496	−	0.0702339i
$296$	3.15380	+	1.82085i	0.183311	+	0.105835i
$297$	−12.4707	+	21.9609i	−0.723621	+	1.27430i
$298$	−12.0919	−	20.9438i	−0.700464	−	1.21324i
$299$	−6.52655	−	11.3043i	−0.377440	−	0.653745i
$300$	−0.596273	−	1.62618i	−0.0344258	−	0.0938875i
$301$	−16.0813	−	10.4746i	−0.926908	−	0.603746i
$302$	−19.9148	+	11.4978i	−1.14597	+	0.661625i
$303$	3.25599	−	3.89917i	0.187052	−	0.224001i
$304$			1.11129i			0.0637371i
$305$	7.97067	−	4.60187i	0.456399	−	0.263502i
$306$	−2.53616	+	7.07273i	−0.144982	+	0.404321i
$307$			11.0589i			0.631166i	0.948898	+	0.315583i	$0.102200\pi$
$307$			11.0589i			0.631166i	−0.948898	+	0.315583i	$0.897800\pi$
$308$	7.01829	−	10.7749i	0.399904	−	0.613958i
$309$	3.43696	+	2.87002i	0.195522	+	0.163270i
$310$	−7.39752			−0.420151
$311$	−6.97233	+	12.0764i	−0.395364	+	0.684791i	−0.993148	−	0.116867i	$-0.962715\pi$
$311$	−6.97233	+	12.0764i	−0.395364	+	0.684791i	0.597783	+	0.801658i	$0.296048\pi$
$312$	−6.74157	−	1.17216i	−0.381666	−	0.0663607i
$313$	11.4932	−	6.63558i	0.649632	−	0.375065i	−0.138683	−	0.990337i	$-0.544287\pi$
$313$	11.4932	−	6.63558i	0.649632	−	0.375065i	0.788315	+	0.615272i	$0.210954\pi$
$314$	8.09026			0.456560
$315$	−7.87476	+	0.994070i	−0.443692	+	0.0560095i
$316$	7.83821			0.440934
$317$	3.85429	−	2.22528i	0.216478	−	0.124984i	−0.387840	−	0.921727i	$-0.626779\pi$
$317$	3.85429	−	2.22528i	0.216478	−	0.124984i	0.604319	+	0.796743i	$0.293445\pi$
$318$	3.38952	+	9.24402i	0.190075	+	0.518379i
$319$	10.4046	−	18.0213i	0.582546	−	1.00900i
$320$	1.00000			0.0559017
$321$	−12.1471	+	4.45399i	−0.677984	+	0.248597i
$322$	7.79431	−	3.95798i	0.434360	−	0.220570i
$323$			2.78331i			0.154867i
$324$	−1.47828	+	8.87776i	−0.0821268	+	0.493209i
$325$	3.42136	−	1.97532i	0.189783	−	0.109571i
$326$			1.23347i			0.0683157i
$327$	−28.0946	−	4.88484i	−1.55364	−	0.270132i
$328$	6.77231	−	3.91000i	0.373938	−	0.215893i
$329$	−27.5655	+	13.9979i	−1.51974	+	0.771728i
$330$	8.29379	+	1.44205i	0.456558	+	0.0793822i
$331$	−3.91980	−	6.78928i	−0.215451	−	0.373173i	0.737961	−	0.674844i	$-0.235789\pi$
$331$	−3.91980	−	6.78928i	−0.215451	−	0.373173i	−0.953412	+	0.301671i	$0.902456\pi$
$332$	0.393868	+	0.682199i	0.0216163	+	0.0374405i
$333$	10.2839	+	3.68763i	0.563555	+	0.202081i
$334$	9.41617	+	5.43643i	0.515230	+	0.297468i
$335$	3.00724	−	5.20869i	0.164303	−	0.284581i
$336$	1.02632	−	4.46617i	0.0559905	−	0.243649i
$337$	−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	$0.915037\pi$
$338$		−	2.60758i		−	0.141834i
$339$	1.00023	−	5.75274i	0.0543253	−	0.312446i
$340$	2.50457			0.135829
$341$	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
$345$	4.39265	+	3.66807i	0.236492	+	0.197482i
$346$	5.00034	+	2.88695i	0.268820	+	0.155203i
$347$	−25.6810	−	14.8269i	−1.37863	−	0.795951i	−0.386633	−	0.922234i	$-0.626362\pi$
$347$	−25.6810	−	14.8269i	−1.37863	−	0.795951i	−0.991994	+	0.126283i	$0.959695\pi$
$348$	1.27033	−	7.30616i	0.0680968	−	0.391651i
$349$	28.0322	+	16.1844i	1.50053	+	0.866330i	1.00000		0.000609911i	$0.000194141\pi$
$349$	28.0322	+	16.1844i	1.50053	+	0.866330i	0.500528	+	0.865720i	$0.333139\pi$
$350$	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
$353$	6.05699			0.322381			0.161191	−	0.986923i	$-0.448467\pi$
$353$	6.05699			0.322381			0.161191	+	0.986923i	$0.448467\pi$
$354$	1.85186	+	1.54639i	0.0984252	+	0.0821897i
$355$			9.66386i			0.512905i
$356$	−7.49361	−	12.9793i	−0.397160	−	0.687902i
$357$	2.57049	−	11.1858i	0.136045	−	0.592016i
$358$	−2.80484	+	4.85812i	−0.148240	+	0.256760i
$359$	11.4661	+	6.61995i	0.605157	+	0.349388i	0.771068	−	0.636753i	$-0.219723\pi$
$359$	11.4661	+	6.61995i	0.605157	+	0.349388i	−0.165911	+	0.986141i	$0.553056\pi$
$360$	2.95191	−	0.535019i	0.155579	−	0.0281980i
$361$	−8.88251	−	15.3850i	−0.467501	−	0.809735i
$362$	12.0294	+	20.8356i	0.632254	+	1.09510i
$363$	−14.0128	+	16.7809i	−0.735482	+	0.880767i
$364$	10.4373	+	0.561317i	0.547065	+	0.0294210i
$365$	−12.0570	+	6.96114i	−0.631094	+	0.364362i
$366$	5.48794	+	14.9669i	0.286859	+	0.782334i
$367$		−	17.8999i		−	0.934366i	−0.884161	−	0.467183i	$-0.845269\pi$
$367$		−	17.8999i		−	0.934366i	0.884161	−	0.467183i	$-0.154731\pi$
$368$	−2.86139	+	1.65202i	−0.149160	+	0.0861176i
$369$	17.8993	−	15.1653i	0.931801	−	0.789472i
$370$		−	3.64170i		−	0.189323i
$371$	−6.80958	−	13.4099i	−0.353536	−	0.696206i
$372$	2.19486	−	12.6235i	0.113798	−	0.654497i
$373$	−4.52467			−0.234279			−0.117139	−	0.993115i	$-0.537372\pi$
$373$	−4.52467			−0.234279			−0.117139	+	0.993115i	$0.537372\pi$
$374$	−6.08642	+	10.5420i	−0.314721	+	0.545114i
$375$	−1.11018	+	1.32948i	−0.0573292	+	0.0686539i
$376$	10.1196	−	5.84258i	0.521881	−	0.301308i
$377$	16.9147			0.871150
$378$	0.640127	−	13.7328i	0.0329246	−	0.706340i
$379$	−7.47021			−0.383719			−0.191860	−	0.981422i	$-0.561452\pi$
$379$	−7.47021			−0.383719			−0.191860	+	0.981422i	$0.561452\pi$
$380$	0.962409	−	0.555647i	0.0493705	−	0.0285041i
$381$	16.0526	−	19.2235i	0.822398	−	0.984852i
$382$	12.1177	−	20.9885i	0.619996	−	1.07386i
$383$	−33.0831			−1.69047			−0.845234	−	0.534396i	$-0.820539\pi$
$383$	−33.0831			−1.69047			−0.845234	+	0.534396i	$0.820539\pi$
$384$	−0.296702	+	1.70645i	−0.0151410	+	0.0870819i
$385$	−12.8405	−	0.690557i	−0.654412	−	0.0351941i
$386$		−	0.617476i		−	0.0314287i
$387$	20.4843	+	7.34530i	1.04127	+	0.373383i
$388$	14.9781	−	8.64760i	0.760397	−	0.439015i
$389$			36.4482i			1.84800i	0.382395	+	0.923999i	$0.375099\pi$
$389$			36.4482i			1.84800i	−0.382395	+	0.923999i	$0.624901\pi$
$390$	2.35566	+	6.42445i	0.119284	+	0.325315i
$391$	−7.16653	+	4.13760i	−0.362427	+	0.209247i
$392$	−0.750744	+	6.95963i	−0.0379183	+	0.351514i
$393$	−14.6376	+	17.5291i	−0.738370	+	0.884226i
$394$	−1.14325	−	1.98016i	−0.0575960	−	0.0997593i
$395$	−3.91911	−	6.78809i	−0.197192	−	0.341546i
$396$	−4.92157	+	13.7251i	−0.247318	+	0.689711i
$397$	−13.3331	−	7.69789i	−0.669171	−	0.386346i	0.126592	−	0.991955i	$-0.459596\pi$
$397$	−13.3331	−	7.69789i	−0.669171	−	0.386346i	−0.795762	+	0.605609i	$0.792930\pi$
$398$	−2.08171	+	3.60562i	−0.104346	+	0.180733i
$399$	−1.49387	−	4.86855i	−0.0747871	−	0.243732i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	16.4073i		−	0.819341i	−0.912234	−	0.409670i	$-0.865644\pi$
$401$		−	16.4073i		−	0.819341i	0.912234	−	0.409670i	$-0.134356\pi$
$402$	7.99611	+	6.67713i	0.398810	+	0.333025i
$403$	29.2250			1.45580
$404$	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
$408$	−0.743110	+	4.27391i	−0.0367894	+	0.211590i
$409$	−18.3018	−	10.5665i	−0.904964	−	0.522481i	−0.0261565	−	0.999658i	$-0.508327\pi$
$409$	−18.3018	−	10.5665i	−0.904964	−	0.522481i	−0.878807	+	0.477177i	$0.841660\pi$
$410$	−6.77231	−	3.91000i	−0.334461	−	0.193101i
$411$	13.7967	+	11.5209i	0.680541	+	0.568284i
$412$	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
$416$	−3.95064			−0.193696
$417$	−2.71510	+	15.6156i	−0.132959	+	0.764699i
$418$			5.40118i			0.264180i
$419$	2.31087	+	4.00254i	0.112893	+	0.195537i	0.916936	−	0.399035i	$-0.130655\pi$
$419$	2.31087	+	4.00254i	0.112893	+	0.195537i	−0.804042	+	0.594572i	$0.797322\pi$
$420$	−4.38098	+	1.34426i	−0.213770	+	0.0655933i
$421$	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
$423$	26.7463	−	22.6609i	1.30045	−	1.10181i
$424$	2.84225	+	4.92292i	0.138032	+	0.239078i
$425$	−1.25228	−	2.16902i	−0.0607446	−	0.105213i
$426$	−16.4909	−	2.86729i	−0.798986	−	0.138921i
$427$	−11.0253	−	21.7118i	−0.533554	−	1.05071i
$428$	−6.46896	+	3.73486i	−0.312689	+	0.180531i
$429$	−32.7658	−	5.69702i	−1.58195	−	0.275055i
$430$		−	7.25381i		−	0.349810i
$431$	−21.3345	+	12.3175i	−1.02765	+	0.593313i	−0.916310	−	0.400469i	$-0.868847\pi$
$431$	−21.3345	+	12.3175i	−1.02765	+	0.593313i	−0.111338	+	0.993783i	$0.535514\pi$
$432$	0.0371456	+	5.19602i	0.00178717	+	0.249994i
$433$			6.55773i			0.315144i	0.987507	+	0.157572i	$0.0503667\pi$
$433$			6.55773i			0.315144i	−0.987507	+	0.157572i	$0.949633\pi$
$434$	−1.05106	+	19.5438i	−0.0504523	+	0.938130i
$435$	−6.96248	+	2.55294i	−0.333825	+	0.122404i
$436$	−16.4638			−0.788472
$437$	−1.83588	+	3.17984i	−0.0878221	+	0.152112i
$438$	−8.30147	−	22.6401i	−0.396660	−	1.08179i
$439$	28.0844	−	16.2145i	1.34040	−	0.773878i	0.353531	−	0.935423i	$-0.384981\pi$
$439$	28.0844	−	16.2145i	1.34040	−	0.773878i	0.986865	+	0.161545i	$0.0516477\pi$
$440$	4.86026			0.231704
$441$	1.50740	+	20.9458i	0.0717811	+	0.997420i
$442$	−9.89465			−0.470640
$443$	0.204110	−	0.117843i	0.00969755	−	0.00559888i	−0.495143	−	0.868811i	$-0.664884\pi$
$443$	0.204110	−	0.117843i	0.00969755	−	0.00559888i	0.504841	+	0.863212i	$0.331551\pi$
$444$	6.21437	+	1.08050i	0.294921	+	0.0512782i
$445$	−7.49361	+	12.9793i	−0.355231	+	0.615278i
$446$	−11.1134			−0.526233
$447$	−32.1518	−	26.8482i	−1.52073	−	1.26988i
$448$	0.142082	−	2.64193i	0.00671276	−	0.124820i
$449$			18.8068i			0.887549i	0.896139	+	0.443774i	$0.146361\pi$
$449$			18.8068i			0.887549i	−0.896139	+	0.443774i	$0.853639\pi$
$450$	−1.93929	−	2.28892i	−0.0914192	−	0.107901i
$451$	32.9152	−	19.0036i	1.54992	−	0.894845i
$452$		−	3.37117i		−	0.158567i
$453$	−25.5292	+	30.5722i	−1.19947	+	1.43641i
$454$	−9.98390	+	5.76421i	−0.468568	+	0.270528i
$455$	−4.73255	−	9.31966i	−0.221866	−	0.436912i
$456$	0.662634	+	1.80716i	0.0310307	+	0.0846282i
$457$	9.30583	+	16.1182i	0.435308	+	0.753976i	0.997321	−	0.0731525i	$-0.0233060\pi$
$457$	9.30583	+	16.1182i	0.435308	+	0.753976i	−0.562012	+	0.827129i	$0.689973\pi$
$458$	−13.1282	−	22.7387i	−0.613440	−	1.06251i
$459$	0.0930335	+	13.0138i	0.00434243	+	0.607431i
$460$	2.86139	+	1.65202i	0.133413	+	0.0770259i
$461$	13.7720	−	23.8538i	0.641426	−	1.11098i	−0.343689	−	0.939084i	$-0.611677\pi$
$461$	13.7720	−	23.8538i	0.641426	−	1.11098i	0.985115	−	0.171898i	$-0.0549901\pi$
$462$	4.98820	−	21.7068i	0.232072	−	1.00989i
$463$	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	$0.829795\pi$
$464$		−	4.28150i		−	0.198764i
$465$	−12.0297	+	4.41094i	−0.557863	+	0.204552i
$466$	−0.759373			−0.0351773
$467$	−6.08486	+	10.5393i	−0.281574	+	0.487700i	−0.971773	−	0.235920i	$-0.924190\pi$
$467$	−6.08486	+	10.5393i	−0.281574	+	0.487700i	0.690199	+	0.723620i	$0.257523\pi$
$468$	−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
$471$	13.1562	−	4.82400i	0.606206	−	0.222278i
$472$	1.20631	+	0.696461i	0.0555248	+	0.0320572i
$473$	30.5321	+	17.6277i	1.40387	+	0.810523i
$474$	12.7463	−	4.67372i	0.585459	−	0.214671i
$475$	−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
$479$	−40.3538			−1.84381			−0.921906	−	0.387413i	$-0.873369\pi$
$479$	−40.3538			−1.84381			−0.921906	+	0.387413i	$0.873369\pi$
$480$	1.62618	−	0.596273i	0.0742246	−	0.0272160i
$481$			14.3870i			0.655992i
$482$	6.73558	+	11.6664i	0.306797	+	0.531389i
$483$	10.3149	−	11.0839i	0.469345	−	0.504336i
$484$	−6.31108	+	10.9311i	−0.286867	+	0.496868i
$485$	−14.9781	−	8.64760i	−0.680120	−	0.392667i
$486$	2.88962	+	15.3183i	0.131076	+	0.694852i
$487$	−4.11277	−	7.12353i	−0.186367	−	0.322798i	0.757669	−	0.652639i	$-0.226338\pi$
$487$	−4.11277	−	7.12353i	−0.186367	−	0.322798i	−0.944036	+	0.329841i	$0.893005\pi$
$488$	4.60187	+	7.97067i	0.208317	+	0.360815i
$489$	0.735486	+	2.00585i	0.0332598	+	0.0907075i
$490$	6.40258	−	2.82965i	0.289239	−	0.127831i
$491$	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	$0.257016\pi$
$492$	8.68157	−	10.3965i	0.391395	−	0.468710i
$493$		−	10.7233i		−	0.482953i
$494$	−3.80213	+	2.19516i	−0.171066	+	0.0987650i
$495$	14.3470	−	2.60033i	0.644852	−	0.116876i
$496$		−	7.39752i		−	0.332158i
$497$	25.5313	+	1.37306i	1.14523	+	0.0615904i
$498$	1.04728	+	0.874525i	0.0469296	+	0.0391884i
$499$	0.850484			0.0380729			0.0190364	−	0.999819i	$-0.493940\pi$
$499$	0.850484			0.0380729			0.0190364	+	0.999819i	$0.493940\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	18.5540	+	3.22600i	0.828930	+	0.144127i
$502$	−0.885671	+	0.511342i	−0.0395294	+	0.0228223i
$503$	−21.5476			−0.960759			−0.480380	−	0.877061i	$-0.659501\pi$
$503$	−21.5476			−0.960759			−0.480380	+	0.877061i	$0.659501\pi$
$504$	−0.994070	−	7.87476i	−0.0442794	−	0.350770i
$505$	−2.93286			−0.130511
$506$	−13.9071	+	8.02926i	−0.618245	+	0.356944i
$507$	−1.55483	−	4.24039i	−0.0690524	−	0.188323i
$508$	7.22974	−	12.5223i	0.320768	−	0.555586i
$509$	−2.20898			−0.0979113			−0.0489556	−	0.998801i	$-0.515589\pi$
$509$	−2.20898			−0.0979113			−0.0489556	+	0.998801i	$0.515589\pi$
$510$	4.07287	−	1.49340i	0.180350	−	0.0661291i
$511$	16.6778	+	32.8430i	0.737781	+	1.45289i
$512$			1.00000i			0.0441942i
$513$	2.92290	+	4.98005i	0.129049	+	0.219875i
$514$	20.6174	−	11.9035i	0.909394	−	0.525039i
$515$		−	2.58519i		−	0.113917i
$516$	12.3783	+	2.15222i	0.544922	+	0.0947462i
$517$	49.1841	−	28.3965i	2.16311	−	1.24887i
$518$	−9.62112	−	0.517421i	−0.422728	−	0.0227342i
$519$	9.85286	+	1.71313i	0.432493	+	0.0751979i
$520$	1.97532	+	3.42136i	0.0866236	+	0.150036i
$521$	−12.0872	−	20.9356i	−0.529548	−	0.917204i	−0.999406	−	0.0344623i	$-0.989028\pi$
$521$	−12.0872	−	20.9356i	−0.529548	−	0.917204i	0.469858	−	0.882742i	$-0.344305\pi$
$522$	−2.29068	−	12.6386i	−0.100260	−	0.553176i
$523$	−10.3393	−	5.96937i	−0.452104	−	0.261022i	0.256614	−	0.966514i	$-0.417393\pi$
$523$	−10.3393	−	5.96937i	−0.452104	−	0.261022i	−0.708718	+	0.705492i	$0.750726\pi$
$524$	−6.59248	+	11.4185i	−0.287994	+	0.498820i
$525$	3.35465	+	3.12191i	0.146409	+	0.136251i
$526$	3.79863	+	6.57942i	0.165628	+	0.286876i
$527$		−	18.5276i		−	0.807074i
$528$	−1.44205	+	8.29379i	−0.0627572	+	0.360941i
$529$	12.0833			0.525361
$530$	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
$534$	−19.9252	−	16.6384i	−0.862246	−	0.720016i
$535$	6.46896	+	3.73486i	0.279678	+	0.161472i
$536$	5.20869	+	3.00724i	0.224981	+	0.129893i
$537$	−1.66440	+	9.57262i	−0.0718242	+	0.413089i
$538$	−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	−0.663411	−	0.748255i	$-0.730892\pi$
$541$	7.35700	−	12.7427i	0.316302	−	0.547852i	0.979713	+	0.200403i	$0.0642253\pi$
$542$	−3.69280			−0.158620
$543$	31.9857	+	26.7096i	1.37264	+	1.14622i
$544$			2.50457i			0.107382i
$545$	8.23189	+	14.2581i	0.352616	+	0.610748i
$546$	17.3077	−	5.31070i	0.740700	−	0.227277i
$547$	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
$549$	17.8488	+	21.0666i	0.761766	+	0.899100i
$550$	−2.43013	−	4.20911i	−0.103621	−	0.179477i
$551$	−2.37900	−	4.12055i	−0.101349	−	0.175541i
$552$	−3.66807	+	4.39265i	−0.156123	+	0.186964i
$553$	−18.4905	+	9.38955i	−0.786297	+	0.399284i
$554$	21.5718	−	12.4545i	0.916498	−	0.529140i
$555$	−2.17144	−	5.92205i	−0.0921727	−	0.251377i
$556$			9.15093i			0.388086i
$557$	−16.7457	+	9.66812i	−0.709537	+	0.409652i	−0.810890	−	0.585199i	$-0.801016\pi$
$557$	−16.7457	+	9.66812i	−0.709537	+	0.409652i	0.101352	+	0.994851i	$0.467683\pi$
$558$	−3.95781	−	21.8368i	−0.167548	−	0.924425i
$559$			28.6572i			1.21207i
$560$	−2.35902	+	1.19792i	−0.0996869	+	0.0506214i
$561$	−3.61171	+	20.7723i	−0.152486	+	0.877009i
$562$	−14.6491			−0.617935
$563$	−12.0323	+	20.8406i	−0.507103	+	0.878327i	0.492864	+	0.870107i	$0.335950\pi$
$563$	−12.0323	+	20.8406i	−0.507103	+	0.878327i	−0.999966	+	0.00822091i	$0.997383\pi$
$564$	12.9726	−	15.5351i	0.546244	−	0.654148i
$565$	−2.91952	+	1.68559i	−0.122825	+	0.0709132i
$566$	6.34995			0.266908
$567$	−7.14755	−	22.7137i	−0.300169	−	0.953886i
$568$	−9.66386			−0.405487
$569$	−32.2967	+	18.6465i	−1.35395	+	0.781703i	−0.988800	−	0.149246i	$-0.952315\pi$
$569$	−32.2967	+	18.6465i	−1.35395	+	0.781703i	−0.365149	+	0.930949i	$0.618982\pi$
$570$	1.23373	−	1.47744i	0.0516753	−	0.0618831i
$571$	−3.82570	+	6.62630i	−0.160100	+	0.277302i	−0.934905	−	0.354899i	$-0.884515\pi$
$571$	−3.82570	+	6.62630i	−0.160100	+	0.277302i	0.774804	+	0.632201i	$0.217848\pi$
$572$	−19.2012			−0.802841
$573$	7.19070	−	41.3565i	0.300396	−	1.72769i
$574$	−11.2922	+	17.3365i	−0.471326	+	0.723610i
$575$		−	3.30404i		−	0.137788i
$576$	0.535019	+	2.95191i	0.0222925	+	0.122996i
$577$	34.5692	−	19.9585i	1.43913	−	0.830884i	0.441344	−	0.897338i	$-0.354502\pi$
$577$	34.5692	−	19.9585i	1.43913	−	0.830884i	0.997789	+	0.0664543i	$0.0211687\pi$
$578$		−	10.7272i		−	0.446191i
$579$	−0.368184	−	1.00413i	−0.0153012	−	0.0417301i
$580$	−3.70789	+	2.14075i	−0.153962	+	0.0888898i
$581$	−1.74636	−	1.13750i	−0.0724513	−	0.0471915i
$582$	19.2007	−	22.9936i	0.795895	−	0.953114i
$583$	13.8141	+	23.9267i	0.572121	+	0.990943i
$584$	−6.96114	−	12.0570i	−0.288054	−	0.498924i
$585$	7.66146	+	9.04269i	0.316762	+	0.373869i
$586$	3.10915	+	1.79507i	0.128438	+	0.0741535i
$587$	−12.0540	+	20.8782i	−0.497523	+	0.861734i	−0.999996	−	0.00285838i	$-0.999090\pi$
$587$	−12.0540	+	20.8782i	−0.497523	+	0.861734i	0.502473	+	0.864593i	$0.332423\pi$
$588$	2.92899	+	11.7652i	0.120790	+	0.485191i
$589$	−4.11041	−	7.11944i	−0.169366	−	0.293351i
$590$		−	1.39292i		−	0.0573457i
$591$	−3.03985	−	2.53841i	−0.125043	−	0.104416i
$592$	3.64170			0.149673
$593$	−7.23840	+	12.5373i	−0.297246	+	0.514844i	−0.975505	−	0.219978i	$-0.929401\pi$
$593$	−7.23840	+	12.5373i	−0.297246	+	0.514844i	0.678259	+	0.734823i	$0.262735\pi$
$594$	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
$597$	−1.23529	+	7.10465i	−0.0505571	+	0.290774i
$598$	−11.3043	−	6.52655i	−0.462268	−	0.266890i
$599$	14.7387	+	8.50937i	0.602205	+	0.347683i	0.769909	−	0.638154i	$-0.220302\pi$
$599$	14.7387	+	8.50937i	0.602205	+	0.347683i	−0.167703	+	0.985838i	$0.553635\pi$
$600$	−1.32948	−	1.11018i	−0.0542757	−	0.0453227i
$601$	−23.0713	−	13.3202i	−0.941099	−	0.543344i	−0.0507942	−	0.998709i	$-0.516175\pi$
$601$	−23.0713	−	13.3202i	−0.941099	−	0.543344i	−0.890305	+	0.455365i	$0.849509\pi$
$602$	−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
$605$	12.6222			0.513164
$606$	0.870185	−	5.00478i	0.0353489	−	0.203305i
$607$			30.2436i			1.22755i	0.789482	+	0.613774i	$0.210349\pi$
$607$			30.2436i			1.22755i	−0.789482	+	0.613774i	$0.789651\pi$
$608$	0.555647	+	0.962409i	0.0225345	+	0.0390308i
$609$	5.75546	+	18.7571i	0.233223	+	0.760078i
$610$	4.60187	−	7.97067i	0.186324	−	0.322723i
$611$	39.9791	+	23.0819i	1.61738	+	0.933795i
$612$	1.33999	+	7.39324i	0.0541659	+	0.298854i
$613$	−10.5704	−	18.3085i	−0.426934	−	0.739472i	0.569665	−	0.821877i	$-0.307073\pi$
$613$	−10.5704	−	18.3085i	−0.426934	−	0.739472i	−0.996599	+	0.0824054i	$0.973740\pi$
$614$	5.52946	+	9.57730i	0.223151	+	0.386508i
$615$	−13.3444	−	2.32021i	−0.538099	−	0.0935598i
$616$	0.690557	−	12.8405i	0.0278234	−	0.517358i
$617$	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	$0.117354\pi$
$618$	4.41150	+	0.767032i	0.177457	+	0.0308546i
$619$			17.3939i			0.699119i	0.936914	+	0.349559i	$0.113669\pi$
$619$			17.3939i			0.699119i	−0.936914	+	0.349559i	$0.886331\pi$
$620$	−6.40644	+	3.69876i	−0.257289	+	0.148546i
$621$	−8.47765	+	14.9292i	−0.340196	+	0.599087i
$622$			13.9447i			0.559130i
$623$	33.2258	+	21.6417i	1.33116	+	0.867058i
$624$	−6.42445	+	2.35566i	−0.257184	+	0.0943019i
$625$	1.00000			0.0400000
$626$	6.63558	−	11.4932i	0.265211	−	0.459359i
$627$	3.22058	+	8.78329i	0.128617	+	0.350771i
$628$	7.00637	−	4.04513i	0.279584	−	0.161418i
$629$	9.12086			0.363673
$630$	−6.32271	+	4.79827i	−0.251903	+	0.191168i
$631$	−2.59501			−0.103306			−0.0516529	−	0.998665i	$-0.516449\pi$
$631$	−2.59501			−0.103306			−0.0516529	+	0.998665i	$0.516449\pi$
$632$	6.78809	−	3.91911i	0.270016	−	0.155894i
$633$	4.31981	+	0.751089i	0.171697	+	0.0298531i
$634$	2.22528	−	3.85429i	0.0883770	−	0.153073i
$635$	−14.4595			−0.573807
$636$	7.55742	+	6.31080i	0.299671	+	0.250239i
$637$	−25.2943	+	11.1789i	−1.00220	+	0.442925i
$638$		−	20.8092i		−	0.823844i
$639$	−28.5268	+	5.17035i	−1.12850	+	0.204536i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$		−	5.38544i		−	0.212712i	−0.994328	−	0.106356i	$-0.966082\pi$
$641$		−	5.38544i		−	0.212712i	0.994328	−	0.106356i	$-0.0339183\pi$
$642$	−8.29269	+	9.93081i	−0.327287	+	0.391938i
$643$	−16.1682	+	9.33469i	−0.637610	+	0.368124i	−0.783693	−	0.621148i	$-0.786667\pi$
$643$	−16.1682	+	9.33469i	−0.637610	+	0.368124i	0.146083	+	0.989272i	$0.453333\pi$
$644$	4.77108	−	7.32487i	0.188007	−	0.288640i
$645$	−4.32525	−	11.7960i	−0.170307	−	0.464467i
$646$	1.39165	+	2.41042i	0.0547539	+	0.0948365i
$647$	−2.10117	−	3.63934i	−0.0826056	−	0.143077i	0.821763	−	0.569830i	$-0.192991\pi$
$647$	−2.10117	−	3.63934i	−0.0826056	−	0.143077i	−0.904368	+	0.426753i	$0.859658\pi$
$648$	3.15865	+	8.42751i	0.124084	+	0.331064i
$649$	5.86297	+	3.38499i	0.230142	+	0.132872i
$650$	1.97532	−	3.42136i	0.0774785	−	0.134197i
$651$	9.94420	+	32.4084i	0.389744	+	1.27018i
$652$	0.616736	+	1.06822i	0.0241532	+	0.0418346i
$653$			26.6081i			1.04126i	0.853783	+	0.520628i	$0.174302\pi$
$653$			26.6081i			1.04126i	−0.853783	+	0.520628i	$0.825698\pi$
$654$	−26.7731	+	9.81691i	−1.04691	+	0.383872i
$655$	13.1850			0.515179
$656$	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	$0.376901\pi$
$660$	7.90366	−	2.89804i	0.307649	−	0.112806i
$661$	−24.0371	−	13.8778i	−0.934936	−	0.539785i	−0.0465665	−	0.998915i	$-0.514828\pi$
$661$	−24.0371	−	13.8778i	−0.934936	−	0.539785i	−0.888369	+	0.459130i	$0.848161\pi$
$662$	−6.78928	−	3.91980i	−0.263873	−	0.152347i
$663$	−16.0905	+	5.89991i	−0.624902	+	0.229134i
$664$	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
$668$	10.8729			0.420683
$669$	−18.0723	+	6.62659i	−0.698716	+	0.256199i
$670$		−	6.01448i		−	0.232360i
$671$	22.3663	+	38.7396i	0.863441	+	1.49552i
$672$	−1.34426	−	4.38098i	−0.0518560	−	0.169000i
$673$	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
$675$	−4.51846	−	2.56584i	−0.173916	−	0.0987593i
$676$	−1.30379	−	2.25823i	−0.0501458	−	0.0868551i
$677$	−19.0123	−	32.9302i	−0.730700	−	1.26561i	−0.956584	−	0.291456i	$-0.905860\pi$
$677$	−19.0123	−	32.9302i	−0.730700	−	1.26561i	0.225884	−	0.974154i	$-0.427473\pi$
$678$	−2.01014	−	5.48213i	−0.0771990	−	0.210540i
$679$	−24.9745	+	38.3424i	−0.958434	+	1.47145i
$680$	2.16902	−	1.25228i	0.0831780	−	0.0480229i
$681$	−12.7986	+	15.3268i	−0.490442	+	0.587323i
$682$		−	35.9539i		−	1.37675i
$683$	−27.3258	+	15.7765i	−1.04559	+	0.603673i	−0.921412	−	0.388587i	$-0.872963\pi$
$683$	−27.3258	+	15.7765i	−1.04559	+	0.603673i	−0.124180	+	0.992260i	$0.539630\pi$
$684$	2.15512	+	2.54366i	0.0824033	+	0.0972592i
$685$		−	10.3775i		−	0.396506i
$686$	−6.56605	−	17.3172i	−0.250693	−	0.661175i
$687$	−34.9073	−	29.1492i	−1.33179	−	1.11211i
$688$	7.25381			0.276549
$689$	−11.2287	+	19.4487i	−0.427780	+	0.740937i
$690$	5.63818	+	0.980316i	0.214642	+	0.0373200i
$691$	−41.9888	+	24.2422i	−1.59733	+	0.922218i	−0.605329	+	0.795976i	$0.706958\pi$
$691$	−41.9888	+	24.2422i	−1.59733	+	0.922218i	−0.991999	+	0.126242i	$0.959708\pi$
$692$	5.77390			0.219491
$693$	−4.83144	−	38.2734i	−0.183531	−	1.45389i
$694$	−29.6538			−1.12564
$695$	7.92494	−	4.57547i	0.300610	−	0.173557i
$696$	−2.55294	−	6.96248i	−0.0967690	−	0.263912i
$697$	9.79284	−	16.9617i	0.370930	−	0.642470i
$698$	32.3688			1.22518
$699$	−1.23488	+	0.452793i	−0.0467073	+	0.0171262i
$700$	2.21694	+	1.44401i	0.0837925	+	0.0545786i
$701$			48.2125i			1.82096i	0.413553	+	0.910480i	$0.364288\pi$
$701$			48.2125i			1.82096i	−0.413553	+	0.910480i	$0.635712\pi$
$702$	−17.7041	+	10.3909i	−0.668197	+	0.392179i
$703$	3.50480	−	2.02350i	0.132186	−	0.0763176i
$704$			4.86026i			0.183178i
$705$	−19.9401	−	3.46701i	−0.750988	−	0.130575i
$706$	5.24551	−	3.02849i	0.197417	−	0.113979i
$707$	−0.416708	+	7.74842i	−0.0156719	+	0.291409i
$708$	2.37695	+	0.413283i	0.0893313	+	0.0155321i
$709$	−19.3691	−	33.5483i	−0.727422	−	1.25993i	−0.957969	−	0.286871i	$-0.907385\pi$
$709$	−19.3691	−	33.5483i	−0.727422	−	1.25993i	0.230547	−	0.973061i	$-0.425948\pi$
$710$	4.83193	+	8.36915i	0.181339	+	0.314089i
$711$	17.9410	−	15.2006i	0.672841	−	0.570067i
$712$	−12.9793	−	7.49361i	−0.486420	−	0.280835i
$713$	12.2209	−	21.1672i	0.457675	−	0.792716i
$714$	−3.36679	−	10.9724i	−0.125999	−	0.410633i
$715$	9.60058	+	16.6287i	0.359041	+	0.621878i
$716$			5.60968i			0.209643i
$717$	−7.29574	+	41.9606i	−0.272464	+	1.56705i
$718$	13.2399			0.494109
$719$	8.83033	−	15.2946i	0.329316	−	0.570392i	−0.653060	−	0.757306i	$-0.726515\pi$
$719$	8.83033	−	15.2946i	0.329316	−	0.570392i	0.982376	+	0.186914i	$0.0598486\pi$
$720$	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
$723$	17.9096	+	14.9554i	0.666065	+	0.556196i
$724$	20.8356	+	12.0294i	0.774349	+	0.447071i
$725$	3.70789	+	2.14075i	0.137707	+	0.0795054i
$726$	−3.74502	+	21.5391i	−0.138991	+	0.799390i
$727$	15.3445	+	8.85913i	0.569094	+	0.328567i	0.756788	−	0.653661i	$-0.226768\pi$
$727$	15.3445	+	8.85913i	0.569094	+	0.328567i	−0.187693	+	0.982228i	$0.560101\pi$
$728$	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
$731$	18.1676			0.671954
$732$	12.2362	+	10.2178i	0.452262	+	0.377660i
$733$			38.6147i			1.42627i	0.701028	+	0.713133i	$0.252725\pi$
$733$			38.6147i			1.42627i	−0.701028	+	0.713133i	$0.747275\pi$
$734$	−8.94994	−	15.5018i	−0.330348	−	0.572180i
$735$	8.72451	−	8.41920i	0.321808	−	0.310547i
$736$	−1.65202	+	2.86139i	−0.0608943	+	0.105472i
$737$	25.3156	+	14.6160i	0.932513	+	0.538386i
$738$	7.91863	−	22.0832i	0.291489	−	0.812892i
$739$	18.1858	+	31.4988i	0.668976	+	1.15870i	0.978191	+	0.207708i	$0.0666004\pi$
$739$	18.1858	+	31.4988i	0.668976	+	1.15870i	−0.309215	+	0.950992i	$0.600066\pi$
$740$	−1.82085	−	3.15380i	−0.0669357	−	0.115936i
$741$	−4.87403	+	5.83684i	−0.179052	+	0.214422i
$742$	−12.6022	−	8.20850i	−0.462642	−	0.301344i
$743$	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	$0.128949\pi$
$744$	−4.41094	−	12.0297i	−0.161713	−	0.441030i
$745$			24.1838i			0.886025i
$746$	−3.91848	+	2.26234i	−0.143466	+	0.0828300i
$747$	2.22451	+	0.797672i	0.0813907	+	0.0291853i
$748$			12.1728i			0.445083i
$749$	10.7864	−	16.5599i	0.394125	−	0.605086i
$750$	−0.296702	+	1.70645i	−0.0108340	+	0.0623107i
$751$	12.3870			0.452008			0.226004	−	0.974126i	$-0.427434\pi$
$751$	12.3870			0.452008			0.226004	+	0.974126i	$0.427434\pi$
$752$	5.84258	−	10.1196i	0.213057	−	0.369025i
$753$	−1.13536	+	1.35964i	−0.0413748	+	0.0495479i
$754$	14.6485	−	8.45733i	0.533468	−	0.307998i
$755$	22.9956			0.836897
$756$	−6.31204	−	12.2130i	−0.229567	−	0.444184i
$757$	39.2473			1.42647			0.713234	−	0.700926i	$-0.247230\pi$
$757$	39.2473			1.42647			0.713234	+	0.700926i	$0.247230\pi$
$758$	−6.46940	+	3.73511i	−0.234979	+	0.135665i
$759$	−17.8278	+	21.3494i	−0.647108	+	0.774935i
$760$	0.555647	−	0.962409i	0.0201554	−	0.0349102i
$761$	−14.0678			−0.509957			−0.254979	−	0.966947i	$-0.582068\pi$
$761$	−14.0678			−0.509957			−0.254979	+	0.966947i	$0.582068\pi$
$762$	4.29016	−	24.6744i	0.155416	−	0.893858i
$763$	38.8384	−	19.7223i	1.40605	−	0.713995i
$764$		−	24.2354i		−	0.876807i
$765$	5.73274	−	4.85709i	0.207268	−	0.175608i
$766$	−28.6508	+	16.5416i	−1.03520	+	0.597671i
$767$			5.50294i			0.198700i
$768$	0.596273	+	1.62618i	0.0215161	+	0.0586797i
$769$	−12.1581	+	7.01950i	−0.438434	+	0.253130i	−0.702933	−	0.711256i	$-0.748127\pi$
$769$	−12.1581	+	7.01950i	−0.438434	+	0.253130i	0.264499	+	0.964386i	$0.414793\pi$
$770$	−11.4655	+	5.82221i	−0.413187	+	0.209818i
$771$	26.4299	−	31.6507i	0.951848	−	1.13987i
$772$	−0.308738	−	0.534750i	−0.0111117	−	0.0192461i
$773$	−8.57207	−	14.8473i	−0.308316	−	0.534019i	0.669678	−	0.742652i	$-0.266432\pi$
$773$	−8.57207	−	14.8473i	−0.308316	−	0.534019i	−0.977994	+	0.208632i	$0.933099\pi$
$774$	21.4126	−	3.88092i	0.769659	−	0.139497i
$775$	6.40644	+	3.69876i	0.230126	+	0.132863i
$776$	8.64760	−	14.9781i	0.310431	−	0.537682i
$777$	−15.9542	+	4.89539i	−0.572353	+	0.175621i
$778$	18.2241	+	31.5651i	0.653366	+	1.13166i
$779$		−	8.69031i		−	0.311363i
$780$	5.25229	+	4.38591i	0.188062	+	0.157041i
$781$	−46.9689			−1.68068
$782$	−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
$786$	−3.91200	+	22.4995i	−0.139537	+	0.802529i
$787$	28.6382	+	16.5343i	1.02084	+	0.589384i	0.914348	−	0.404929i	$-0.132704\pi$
$787$	28.6382	+	16.5343i	1.02084	+	0.589384i	0.106495	+	0.994313i	$0.466037\pi$
$788$	−1.98016	−	1.14325i	−0.0705405	−	0.0407266i
$789$	10.1004	+	8.43429i	0.359583	+	0.300269i
$790$	−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
$794$	−15.3958			−0.546375
$795$	1.68660	−	9.70031i	0.0598177	−	0.344035i
$796$			4.16341i			0.147568i
$797$	−9.84860	−	17.0583i	−0.348855	−	0.604235i	0.637191	−	0.770706i	$-0.280096\pi$
$797$	−9.84860	−	17.0583i	−0.348855	−	0.604235i	−0.986046	+	0.166471i	$0.946763\pi$
$798$	−3.72801	−	3.46936i	−0.131970	−	0.122814i
$799$	14.6331	−	25.3453i	0.517682	−	0.896652i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−42.3229	−	15.1763i	−1.49541	−	0.536227i
$802$	−8.20364	−	14.2091i	−0.289681	−	0.501742i
$803$	−33.8329	−	58.6004i	−1.19394	−	2.06796i
$804$	10.2634	+	1.78451i	0.361962	+	0.0629348i
$805$	−8.72906	−	0.469446i	−0.307659	−	0.0165458i
$806$	25.3096	−	14.6125i	0.891491	−	0.514703i
$807$	−12.2399	−	2.12816i	−0.430863	−	0.0749146i
$808$		−	2.93286i		−	0.103178i
$809$	21.6772	−	12.5154i	0.762131	−	0.440017i	−0.0679294	−	0.997690i	$-0.521639\pi$
$809$	21.6772	−	12.5154i	0.762131	−	0.440017i	0.830060	+	0.557674i	$0.188306\pi$
$810$	5.71911	−	6.94923i	0.200949	−	0.244171i
$811$		−	12.0504i		−	0.423146i	−0.977362	−	0.211573i	$-0.932141\pi$
$811$		−	12.0504i		−	0.423146i	0.977362	−	0.211573i	$-0.0678586\pi$
$812$	5.12889	+	10.1001i	0.179989	+	0.354446i
$813$	−6.00516	+	2.20192i	−0.210610	+	0.0772247i
$814$	17.6996			0.620370
$815$	0.616736	−	1.06822i	0.0216033	−	0.0374180i
$816$	1.49340	+	4.07287i	0.0522796	+	0.142579i
$817$	6.98113	−	4.03056i	0.244239	−	0.141011i
$818$	−21.1331			−0.738900
$819$	24.9788	−	18.9563i	0.872828	−	0.662385i
$820$	−7.81999			−0.273086
$821$	−36.2762	+	20.9441i	−1.26605	+	0.730953i	−0.974238	−	0.225523i	$-0.927591\pi$
$821$	−36.2762	+	20.9441i	−1.26605	+	0.730953i	−0.291811	+	0.956476i	$0.594258\pi$
$822$	17.7088	+	3.07904i	0.617664	+	0.107394i
$823$	−13.8411	+	23.9735i	−0.482470	+	0.835663i	−0.999797	−	0.0201248i	$-0.993594\pi$
$823$	−13.8411	+	23.9735i	−0.482470	+	0.835663i	0.517327	+	0.855788i	$0.326927\pi$
$824$	2.58519			0.0900595
$825$	−6.46161	−	5.39575i	−0.224964	−	0.187856i
$826$	−3.68001	−	0.197910i	−0.128044	−	0.00688616i
$827$		−	36.8335i		−	1.28083i	−0.768031	−	0.640413i	$-0.778763\pi$
$827$		−	36.8335i		−	1.28083i	0.768031	−	0.640413i	$-0.221237\pi$
$828$	−3.34572	+	9.33041i	−0.116272	+	0.324254i
$829$	44.8357	−	25.8859i	1.55721	−	0.899055i	0.559687	−	0.828704i	$-0.310921\pi$
$829$	44.8357	−	25.8859i	1.55721	−	0.899055i	0.997522	−	0.0703515i	$-0.0224121\pi$
$830$		−	0.787736i		−	0.0273427i
$831$	27.6533	−	33.1159i	0.959284	−	1.14878i
$832$	−3.42136	+	1.97532i	−0.118614	+	0.0684820i
$833$	7.08704	+	16.0357i	0.245551	+	0.555604i
$834$	5.45645	+	14.8811i	0.188942	+	0.515289i
$835$	−5.43643	−	9.41617i	−0.188135	−	0.325860i
$836$	2.70059	+	4.67756i	0.0934019	+	0.161777i
$837$	−19.4568	−	33.1506i	−0.672525	−	1.14585i
$838$	4.00254	+	2.31087i	0.138265	+	0.0798276i
$839$	4.77807	−	8.27587i	0.164957	−	0.285715i	−0.771683	−	0.636008i	$-0.780585\pi$
$839$	4.77807	−	8.27587i	0.164957	−	0.285715i	0.936640	+	0.350293i	$0.113918\pi$
$840$	−3.12191	+	3.35465i	−0.107716	+	0.115747i
$841$	−5.33439	−	9.23943i	−0.183944	−	0.318601i
$842$		−	2.31111i		−	0.0796461i
$843$	−23.8221	+	8.73486i	−0.820475	+	0.300845i
$844$	2.53146			0.0871365
$845$	−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
$849$	10.3262	−	3.78630i	0.354393	−	0.129946i
$850$	−2.16902	−	1.25228i	−0.0743967	−	0.0429529i
$851$	10.4203	+	6.01616i	0.357203	+	0.206231i
$852$	−15.7152	+	5.76230i	−0.538393	+	0.197413i
$853$	6.13810	+	3.54384i	0.210165	+	0.121339i	0.601388	−	0.798957i	$-0.294615\pi$
$853$	6.13810	+	3.54384i	0.210165	+	0.121339i	−0.391223	+	0.920296i	$0.627948\pi$
$854$	−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
$857$	−37.5025			−1.28106			−0.640531	−	0.767932i	$-0.721286\pi$
$857$	−37.5025			−1.28106			−0.640531	+	0.767932i	$0.721286\pi$
$858$	−31.2245	+	11.4491i	−1.06599	+	0.390867i
$859$		−	11.6835i		−	0.398636i	−0.979935	−	0.199318i	$-0.936127\pi$
$859$		−	11.6835i		−	0.398636i	0.979935	−	0.199318i	$-0.0638726\pi$
$860$	−3.62690	−	6.28198i	−0.123676	−	0.214214i
$861$	−8.02584	+	34.9254i	−0.273520	+	1.19025i
$862$	−12.3175	+	21.3345i	−0.419536	+	0.726657i
$863$	41.4770	+	23.9467i	1.41189	+	0.815157i	0.995567	−	0.0940587i	$-0.0299841\pi$
$863$	41.4770	+	23.9467i	1.41189	+	0.815157i	0.416326	+	0.909215i	$0.363317\pi$
$864$	2.63018	+	4.48131i	0.0894805	+	0.152457i
$865$	−2.88695	−	5.00034i	−0.0981592	−	0.170017i
$866$	3.27886	+	5.67916i	0.111420	+	0.192986i
$867$	−6.39631	−	17.4443i	−0.217230	−	0.592438i
$868$	8.86163	+	17.4509i	0.300783	+	0.592323i
$869$	32.9919	−	19.0479i	1.11917	−	0.646155i
$870$	−4.75322	+	5.69215i	−0.161149	+	0.192982i
$871$			23.7611i			0.805113i
$872$	−14.2581	+	8.23189i	−0.482839	+	0.278767i
$873$	17.5134	−	48.8405i	0.592737	−	1.65300i
$874$			3.67176i			0.124199i
$875$	0.142082	−	2.64193i	0.00480326	−	0.0893137i
$876$	−18.5093	−	15.4562i	−0.625373	−	0.522216i
$877$	−33.2605			−1.12313			−0.561564	−	0.827433i	$-0.689800\pi$
$877$	−33.2605			−1.12313			−0.561564	+	0.827433i	$0.689800\pi$
$878$	16.2145	−	28.0844i	0.547214	−	0.947803i
$879$	6.12638	+	1.06520i	0.206638	+	0.0359283i
$880$	4.20911	−	2.43013i	0.141889	−	0.0819197i
$881$	−39.7345			−1.33869			−0.669344	−	0.742953i	$-0.733425\pi$
$881$	−39.7345			−1.33869			−0.669344	+	0.742953i	$0.733425\pi$
$882$	11.7784	+	17.3859i	0.396598	+	0.585414i
$883$	−20.3226			−0.683910			−0.341955	−	0.939716i	$-0.611089\pi$
$883$	−20.3226			−0.683910			−0.341955	+	0.939716i	$0.611089\pi$
$884$	−8.56901	+	4.94732i	−0.288207	+	0.166396i
$885$	−0.830562	−	2.26514i	−0.0279190	−	0.0761419i
$886$	0.117843	−	0.204110i	0.00395901	−	0.00685720i
$887$	−2.71826			−0.0912703			−0.0456351	−	0.998958i	$-0.514531\pi$
$887$	−2.71826			−0.0912703			−0.0456351	+	0.998958i	$0.514531\pi$
$888$	5.92205	−	2.17144i	0.198731	−	0.0728689i
$889$	−2.05444	+	38.2010i	−0.0689036	+	1.28122i
$890$			14.9872i			0.502373i
$891$	15.3519	+	40.9599i	0.514307	+	1.37221i
$892$	−9.62445	+	5.55668i	−0.322250	+	0.186051i
$893$		−	12.9856i		−	0.434548i
$894$	−41.2684	−	7.17538i	−1.38022	−	0.239980i
$895$	4.85812	−	2.80484i	0.162389	−	0.0937554i
$896$	−1.19792	−	2.35902i	−0.0400197	−	0.0788094i
$897$	−22.2744	−	3.87288i	−0.743722	−	0.129312i
$898$	9.40341	+	16.2872i	0.313796	+	0.543510i
$899$	15.8362	+	27.4292i	0.528168	+	0.914813i
$900$	−2.82394	−	1.01261i	−0.0941312	−	0.0337538i
$901$	12.3298	+	7.11861i	0.410765	+	0.237155i
$902$	19.0036	−	32.9152i	0.632751	−	1.09596i
$903$	−31.7788	+	9.75102i	−1.05753	+	0.324494i
$904$	−1.68559	−	2.91952i	−0.0560618	−	0.0971019i
$905$		−	24.0589i		−	0.799744i
$906$	−6.82285	+	39.2409i	−0.226674	+	1.30369i
$907$	−46.2654			−1.53622			−0.768109	−	0.640320i	$-0.778802\pi$
$907$	−46.2654			−1.53622			−0.768109	+	0.640320i	$0.778802\pi$
$908$	−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	$0.890669\pi$
$912$	1.47744	+	1.23373i	0.0489229	+	0.0408529i
$913$	3.31567	+	1.91430i	0.109733	+	0.0633541i
$914$	16.1182	+	9.30583i	0.533142	+	0.307810i
$915$	2.73077	−	15.7057i	0.0902764	−	0.519215i
$916$	−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	−0.335324	−	0.942103i	$-0.608846\pi$
$919$	19.6509	−	34.0363i	0.648223	−	1.12276i	0.983547	−	0.180652i	$-0.0578209\pi$
$920$	3.30404			0.108931
$921$	14.7026	+	12.2773i	0.484466	+	0.404552i
$922$		−	27.5440i		−	0.907113i
$923$	−19.0892	−	33.0635i	−0.628330	−	1.08830i
$924$	−6.53347	−	21.2927i	−0.214935	−	0.700478i
$925$	−1.82085	+	3.15380i	−0.0598691	+	0.103696i
$926$	0.414241	+	0.239162i	0.0136128	+	0.00785935i
$927$	7.63125	−	1.38313i	0.250643	−	0.0454279i
$928$	−2.14075	−	3.70789i	−0.0702735	−	0.121717i
$929$	22.8771	+	39.6243i	0.750574	+	1.30003i	0.947545	+	0.319622i	$0.103556\pi$
$929$	22.8771	+	39.6243i	0.750574	+	1.30003i	−0.196971	+	0.980409i	$0.563111\pi$
$930$	−8.21255	+	9.83483i	−0.269300	+	0.322497i
$931$	6.28085	+	4.58962i	0.205847	+	0.150419i
$932$	−0.657636	+	0.379686i	−0.0215416	+	0.0124370i
$933$	8.31482	+	22.6765i	0.272215	+	0.742395i
$934$			12.1697i			0.398205i
$935$	10.5420	−	6.08642i	0.344760	−	0.199047i
$936$	−9.04269	+	7.66146i	−0.295570	+	0.250423i
$937$		−	52.1498i		−	1.70366i	−0.523819	−	0.851830i	$-0.675493\pi$
$937$		−	52.1498i		−	1.70366i	0.523819	−	0.851830i	$-0.324507\pi$
$938$	−15.8899	−	0.854551i	−0.518822	−	0.0279021i
$939$	3.93758	−	22.6465i	0.128498	−	0.739042i
$940$	−11.6852			−0.381128
$941$	13.3755	−	23.1671i	0.436029	−	0.755224i	−0.561350	−	0.827579i	$-0.689718\pi$
$941$	13.3755	−	23.1671i	0.436029	−	0.755224i	0.997379	+	0.0723541i	$0.0230512\pi$
$942$	8.98161	−	10.7558i	0.292637	−	0.350443i
$943$	22.3760	−	12.9188i	0.728663	−	0.420694i
$944$	1.39292			0.0453358
$945$	−7.42077	+	11.5729i	−0.241398	+	0.376467i
$946$	35.2554			1.14625
$947$	8.53441	−	4.92734i	0.277331	−	0.160117i	−0.354884	−	0.934911i	$-0.615479\pi$
$947$	8.53441	−	4.92734i	0.277331	−	0.160117i	0.632214	+	0.774793i	$0.282146\pi$
$948$	8.70180	−	10.4207i	0.282621	−	0.338449i
$949$	27.5010	−	47.6331i	0.892719	−	1.54623i
$950$	−1.11129			−0.0360551
$951$	1.32049	−	7.59464i	0.0428197	−	0.246273i
$952$	−3.00027	−	5.90833i	−0.0972393	−	0.191490i
$953$			18.8568i			0.610830i	0.952219	+	0.305415i	$0.0987952\pi$
$953$			18.8568i			0.610830i	−0.952219	+	0.305415i	$0.901205\pi$
$954$	16.0527	+	5.75621i	0.519724	+	0.186364i
$955$	−20.9885	+	12.1177i	−0.679172	+	0.392120i
$956$			24.5895i			0.795280i
$957$	−12.4080	−	33.8395i	−0.401093	−	1.09388i
$958$	−34.9474	+	20.1769i	−1.12910	+	0.651886i
$959$	−27.4168	−	1.47447i	−0.885334	−	0.0476130i
$960$	1.11018	−	1.32948i	0.0358308	−	0.0429087i
$961$	11.8616	+	20.5450i	0.382633	+	0.662741i
$962$	7.19352	+	12.4595i	0.231928	+	0.401712i
$963$	−7.56393	+	21.0940i	−0.243744	+	0.679744i
$964$	11.6664	+	6.73558i	0.375749	+	0.216939i
$965$	−0.308738	+	0.534750i	−0.00993863	+	0.0172142i
$966$	3.39102	−	14.7564i	0.109104	−	0.474780i
$967$	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	$0.481596\pi$
$968$			12.6222i			0.405691i
$969$	3.70034	+	3.08996i	0.118872	+	0.0992639i
$970$	−17.2952			−0.555316
$971$	26.8589	−	46.5210i	0.861944	−	1.49293i	−0.00810628	−	0.999967i	$-0.502580\pi$
$971$	26.8589	−	46.5210i	0.861944	−	1.49293i	0.870050	−	0.492963i	$-0.164086\pi$
$972$	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
$975$	1.17216	−	6.74157i	0.0375393	−	0.215903i
$976$	7.97067	+	4.60187i	0.255135	+	0.147302i
$977$	14.8925	+	8.59820i	0.476454	+	0.275081i	0.718937	−	0.695075i	$-0.244629\pi$
$977$	14.8925	+	8.59820i	0.476454	+	0.275081i	−0.242484	+	0.970155i	$0.577962\pi$
$978$	1.63987	+	1.36937i	0.0524373	+	0.0437876i
$979$	−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
$983$	−28.5735			−0.911352			−0.455676	−	0.890146i	$-0.650602\pi$
$983$	−28.5735			−0.911352			−0.455676	+	0.890146i	$0.650602\pi$
$984$	2.32021	−	13.3444i	0.0739655	−	0.425404i
$985$			2.28650i			0.0728539i
$986$	−5.36165	−	9.28664i	−0.170750	−	0.295747i
$987$	−11.9927	+	52.1879i	−0.381733	+	1.66116i
$988$	−2.19516	+	3.80213i	−0.0698374	+	0.120962i
$989$	20.7559	+	11.9834i	0.660001	+	0.381052i
$990$	11.1247	−	9.42548i	0.353567	−	0.299561i
$991$	−9.29023	−	16.0912i	−0.295114	−	0.511152i	0.679897	−	0.733307i	$-0.262024\pi$
$991$	−9.29023	−	16.0912i	−0.295114	−	0.511152i	−0.975011	+	0.222155i	$0.928691\pi$
$992$	−3.69876	−	6.40644i	−0.117436	−	0.203405i
$993$	−13.3779	−	2.32602i	−0.424534	−	0.0738141i
$994$	22.7973	−	11.5765i	0.723086	−	0.367185i
$995$	3.60562	−	2.08171i	0.114306	−	0.0659945i
$996$	1.34423	+	0.233723i	0.0425936	+	0.00740579i
$997$			7.73126i			0.244851i	0.992478	+	0.122426i	$0.0390673\pi$
$997$			7.73126i			0.244851i	−0.992478	+	0.122426i	$0.960933\pi$
$998$	0.736540	−	0.425242i	0.0233148	−	0.0134608i
$999$	16.3196	−	9.57831i	0.516328	−	0.303044i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.13	✓	28	63.59	even	6	inner
630.2.t.b.551.13	yes	28	1.1	even	1	trivial
630.2.bk.b.101.14	yes	28	7.3	odd	6
630.2.bk.b.131.7	yes	28	9.5	odd	6
1890.2.t.b.1151.7		28	63.31	odd	6
1890.2.t.b.1601.7		28	3.2	odd	2
1890.2.bk.b.341.3		28	9.4	even	3
1890.2.bk.b.521.3		28	21.17	even	6

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.11018 - 1.32948i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.296702 - 1.70645i) q^{6} +(-0.142082 + 2.64193i) q^{7} -1.00000i q^{8} +(-0.535019 - 2.95191i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.11018 - 1.32948i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.296702 - 1.70645i) q^{6} +(-0.142082 + 2.64193i) q^{7} -1.00000i q^{8} +(-0.535019 - 2.95191i) q^{9} +(-0.866025 + 0.500000i) q^{10} -4.86026i q^{11} +(-0.596273 - 1.62618i) q^{12} +(3.42136 - 1.97532i) q^{13} +(1.19792 + 2.35902i) q^{14} +(-1.11018 + 1.32948i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.25228 - 2.16902i) q^{17} +(-1.93929 - 2.28892i) q^{18} +(-0.962409 - 0.555647i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.35465 + 3.12191i) q^{21} +(-2.43013 - 4.20911i) q^{22} -3.30404i q^{23} +(-1.32948 - 1.11018i) q^{24} +1.00000 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} +(-0.296702 + 1.70645i) q^{30} +(6.40644 + 3.69876i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-6.46161 - 5.39575i) 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} -1.11129 q^{38} +(1.17216 - 6.74157i) q^{39} +1.00000i q^{40} +(3.91000 + 6.77231i) q^{41} +(4.46617 + 1.02632i) q^{42} +(-3.62690 + 6.28198i) q^{43} +(-4.20911 - 2.43013i) q^{44} +(0.535019 + 2.95191i) q^{45} +(-1.65202 - 2.86139i) q^{46} +(5.84258 + 10.1196i) q^{47} +(-1.70645 - 0.296702i) q^{48} +(-6.95963 - 0.750744i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-4.27391 - 0.743110i) q^{51} -3.95064i q^{52} +(-4.92292 + 2.84225i) q^{53} +(-5.19602 + 0.0371456i) q^{54} +4.86026i q^{55} +(2.64193 + 0.142082i) q^{56} +(-1.80716 + 0.662634i) q^{57} +4.28150 q^{58} +(-0.696461 + 1.20631i) q^{59} +(0.596273 + 1.62618i) q^{60} +(-7.97067 + 4.60187i) q^{61} +7.39752 q^{62} +(7.87476 - 0.994070i) q^{63} -1.00000 q^{64} +(-3.42136 + 1.97532i) q^{65} +(-8.29379 - 1.44205i) q^{66} +(-3.00724 + 5.20869i) q^{67} -2.50457 q^{68} +(-4.39265 - 3.66807i) q^{69} +(-1.19792 - 2.35902i) q^{70} -9.66386i q^{71} +(-2.95191 + 0.535019i) q^{72} +(12.0570 - 6.96114i) q^{73} +3.64170i q^{74} +(1.11018 - 1.32948i) q^{75} +(-0.962409 + 0.555647i) q^{76} +(12.8405 + 0.690557i) q^{77} +(-2.35566 - 6.42445i) q^{78} +(3.91911 + 6.78809i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.42751 + 3.15865i) q^{81} +(6.77231 + 3.91000i) q^{82} +(-0.393868 + 0.682199i) q^{83} +(4.38098 - 1.34426i) q^{84} +(1.25228 + 2.16902i) q^{85} +7.25381i q^{86} +(6.96248 - 2.55294i) q^{87} -4.86026 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} +(12.0297 - 4.41094i) q^{93} +(10.1196 + 5.84258i) q^{94} +(0.962409 + 0.555647i) q^{95} +(-1.62618 + 0.596273i) q^{96} +(14.9781 + 8.64760i) q^{97} +(-6.40258 + 2.82965i) q^{98} +(-14.3470 + 2.60033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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