LMFDB - Embedded newform 630.2.bk.b.131.4

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			131.4
Character	$\chi$	$=$	630.131
Dual form			630.2.bk.b.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.352560 - 1.69579i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.69579 - 0.352560i) q^{6} +(2.55256 + 0.696025i) q^{7} +1.00000i q^{8} +(-2.75140 - 1.19573i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.352560 - 1.69579i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.69579 - 0.352560i) q^{6} +(2.55256 + 0.696025i) q^{7} +1.00000i q^{8} +(-2.75140 - 1.19573i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(1.26877 + 0.732523i) q^{11} +(-0.352560 + 1.69579i) q^{12} +(-6.03529 - 3.48448i) q^{13} +(0.696025 - 2.55256i) q^{14} +(-1.64488 + 0.542569i) q^{15} +1.00000 q^{16} +(-3.30332 - 5.72151i) q^{17} +(-1.19573 + 2.75140i) q^{18} +(-3.08388 - 1.78048i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.08024 - 4.08321i) q^{21} +(0.732523 - 1.26877i) q^{22} +(5.51016 - 3.18129i) q^{23} +(1.69579 + 0.352560i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.48448 + 6.03529i) q^{26} +(-2.99775 + 4.24423i) q^{27} +(-2.55256 - 0.696025i) q^{28} +(1.49409 - 0.862614i) q^{29} +(0.542569 + 1.64488i) q^{30} +7.84985i q^{31} -1.00000i q^{32} +(1.68952 - 1.89330i) q^{33} +(-5.72151 + 3.30332i) q^{34} +(-0.673503 - 2.55859i) q^{35} +(2.75140 + 1.19573i) q^{36} +(-2.75951 + 4.77962i) q^{37} +(-1.78048 + 3.08388i) q^{38} +(-8.03674 + 9.00610i) q^{39} +(0.866025 - 0.500000i) q^{40} +(0.632413 - 1.09537i) q^{41} +(-4.08321 - 2.08024i) q^{42} +(-3.24581 - 5.62191i) q^{43} +(-1.26877 - 0.732523i) q^{44} +(0.340166 + 2.98065i) q^{45} +(-3.18129 - 5.51016i) q^{46} +5.39759 q^{47} +(0.352560 - 1.69579i) q^{48} +(6.03110 + 3.55329i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-10.8671 + 3.58455i) q^{51} +(6.03529 + 3.48448i) q^{52} +(5.60809 - 3.23783i) q^{53} +(4.24423 + 2.99775i) q^{54} -1.46505i q^{55} +(-0.696025 + 2.55256i) q^{56} +(-4.10657 + 4.60189i) q^{57} +(-0.862614 - 1.49409i) q^{58} -1.49328 q^{59} +(1.64488 - 0.542569i) q^{60} +3.73592i q^{61} +7.84985 q^{62} +(-6.19085 - 4.96723i) q^{63} -1.00000 q^{64} +6.96896i q^{65} +(-1.89330 - 1.68952i) q^{66} +12.5498 q^{67} +(3.30332 + 5.72151i) q^{68} +(-3.45214 - 10.4657i) q^{69} +(-2.55859 + 0.673503i) q^{70} -14.2133i q^{71} +(1.19573 - 2.75140i) q^{72} +(-1.11022 + 0.640987i) q^{73} +(4.77962 + 2.75951i) q^{74} +(1.29232 + 1.15322i) q^{75} +(3.08388 + 1.78048i) q^{76} +(2.72875 + 2.75290i) q^{77} +(9.00610 + 8.03674i) q^{78} +0.994011 q^{79} +(-0.500000 - 0.866025i) q^{80} +(6.14044 + 6.57989i) q^{81} +(-1.09537 - 0.632413i) q^{82} +(-5.93463 - 10.2791i) q^{83} +(-2.08024 + 4.08321i) q^{84} +(-3.30332 + 5.72151i) q^{85} +(-5.62191 + 3.24581i) q^{86} +(-0.936056 - 2.83779i) q^{87} +(-0.732523 + 1.26877i) q^{88} +(2.18741 - 3.78871i) q^{89} +(2.98065 - 0.340166i) q^{90} +(-12.9801 - 13.0950i) q^{91} +(-5.51016 + 3.18129i) q^{92} +(13.3117 + 2.76754i) q^{93} -5.39759i q^{94} +3.56096i q^{95} +(-1.69579 - 0.352560i) q^{96} +(9.04933 - 5.22463i) q^{97} +(3.55329 - 6.03110i) q^{98} +(-2.61499 - 3.53258i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.352560	−	1.69579i	0.203550	−	0.979064i
$3$	0.352560	−	1.69579i	0.203550	−	0.979064i
$4$	−1.00000			−0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.69579	−	0.352560i	−0.692303	−	0.143932i
$7$	2.55256	+	0.696025i	0.964776	+	0.263073i
$7$	2.55256	+	0.696025i	0.964776	+	0.263073i
$8$			1.00000i			0.353553i
$9$	−2.75140	−	1.19573i	−0.917134	−	0.398578i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	1.26877	+	0.732523i	0.382548	+	0.220864i	0.678926	−	0.734206i	$-0.262446\pi$
$11$	1.26877	+	0.732523i	0.382548	+	0.220864i	−0.296378	+	0.955071i	$0.595779\pi$
$12$	−0.352560	+	1.69579i	−0.101775	+	0.489532i
$13$	−6.03529	−	3.48448i	−1.67389	−	0.966420i	−0.965428	−	0.260671i	$-0.916056\pi$
$13$	−6.03529	−	3.48448i	−1.67389	−	0.966420i	−0.708461	−	0.705750i	$-0.750610\pi$
$14$	0.696025	−	2.55256i	0.186020	−	0.682200i
$15$	−1.64488	+	0.542569i	−0.424705	+	0.140091i
$16$	1.00000			0.250000
$17$	−3.30332	−	5.72151i	−0.801172	−	1.38767i	−0.918845	−	0.394618i	$-0.870877\pi$
$17$	−3.30332	−	5.72151i	−0.801172	−	1.38767i	0.117673	−	0.993052i	$-0.462456\pi$
$18$	−1.19573	+	2.75140i	−0.281837	+	0.648512i
$19$	−3.08388	−	1.78048i	−0.707491	−	0.408470i	0.102640	−	0.994719i	$-0.467271\pi$
$19$	−3.08388	−	1.78048i	−0.707491	−	0.408470i	−0.810131	+	0.586249i	$0.800604\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	2.08024	−	4.08321i	0.453946	−	0.891029i
$22$	0.732523	−	1.26877i	0.156175	−	0.270502i
$23$	5.51016	−	3.18129i	1.14895	−	0.663346i	0.200318	−	0.979731i	$-0.435803\pi$
$23$	5.51016	−	3.18129i	1.14895	−	0.663346i	0.948631	+	0.316385i	$0.102469\pi$
$24$	1.69579	+	0.352560i	0.346152	+	0.0719660i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.48448	+	6.03529i	−0.683362	+	1.18362i
$27$	−2.99775	+	4.24423i	−0.576917	+	0.816803i
$28$	−2.55256	−	0.696025i	−0.482388	−	0.131536i
$29$	1.49409	−	0.862614i	0.277446	−	0.160183i	−0.354821	−	0.934934i	$-0.615458\pi$
$29$	1.49409	−	0.862614i	0.277446	−	0.160183i	0.632267	+	0.774751i	$0.282125\pi$
$30$	0.542569	+	1.64488i	0.0990591	+	0.300312i
$31$			7.84985i			1.40987i	0.709269	+	0.704937i	$0.249025\pi$
$31$			7.84985i			1.40987i	−0.709269	+	0.704937i	$0.750975\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.68952	−	1.89330i	0.294108	−	0.329582i
$34$	−5.72151	+	3.30332i	−0.981231	+	0.566514i
$35$	−0.673503	−	2.55859i	−0.113843	−	0.432481i
$36$	2.75140	+	1.19573i	0.458567	+	0.199289i
$37$	−2.75951	+	4.77962i	−0.453661	+	0.785764i	−0.998610	−	0.0527049i	$-0.983216\pi$
$37$	−2.75951	+	4.77962i	−0.453661	+	0.785764i	0.544949	+	0.838469i	$0.316549\pi$
$38$	−1.78048	+	3.08388i	−0.288832	+	0.500272i
$39$	−8.03674	+	9.00610i	−1.28691	+	1.44213i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	0.632413	−	1.09537i	0.0987663	−	0.171068i	−0.812408	−	0.583089i	$-0.801844\pi$
$41$	0.632413	−	1.09537i	0.0987663	−	0.171068i	0.911174	+	0.412021i	$0.135177\pi$
$42$	−4.08321	−	2.08024i	−0.630053	−	0.320988i
$43$	−3.24581	−	5.62191i	−0.494981	−	0.857333i	0.505002	−	0.863118i	$-0.331492\pi$
$43$	−3.24581	−	5.62191i	−0.494981	−	0.857333i	−0.999983	+	0.00578540i	$0.998158\pi$
$44$	−1.26877	−	0.732523i	−0.191274	−	0.110432i
$45$	0.340166	+	2.98065i	0.0507089	+	0.444329i
$46$	−3.18129	−	5.51016i	−0.469056	−	0.812429i
$47$	5.39759			0.787320			0.393660	−	0.919256i	$-0.371209\pi$
$47$	5.39759			0.787320			0.393660	+	0.919256i	$0.371209\pi$
$48$	0.352560	−	1.69579i	0.0508876	−	0.244766i
$49$	6.03110	+	3.55329i	0.861586	+	0.507612i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−10.8671	+	3.58455i	−1.52170	+	0.501938i
$52$	6.03529	+	3.48448i	0.836945	+	0.483210i
$53$	5.60809	−	3.23783i	0.770331	−	0.444751i	−0.0626620	−	0.998035i	$-0.519959\pi$
$53$	5.60809	−	3.23783i	0.770331	−	0.444751i	0.832993	+	0.553284i	$0.186626\pi$
$54$	4.24423	+	2.99775i	0.577567	+	0.407942i
$55$		−	1.46505i		−	0.197547i
$56$	−0.696025	+	2.55256i	−0.0930102	+	0.341100i
$57$	−4.10657	+	4.60189i	−0.543929	+	0.609535i
$58$	−0.862614	−	1.49409i	−0.113267	−	0.196184i
$59$	−1.49328			−0.194409			−0.0972045	−	0.995264i	$-0.530990\pi$
$59$	−1.49328			−0.194409			−0.0972045	+	0.995264i	$0.530990\pi$
$60$	1.64488	−	0.542569i	0.212353	−	0.0700454i
$61$			3.73592i			0.478335i	0.970978	+	0.239167i	$0.0768745\pi$
$61$			3.73592i			0.478335i	−0.970978	+	0.239167i	$0.923126\pi$
$62$	7.84985			0.996932
$63$	−6.19085	−	4.96723i	−0.779974	−	0.625812i
$64$	−1.00000			−0.125000
$65$			6.96896i			0.864393i
$66$	−1.89330	−	1.68952i	−0.233050	−	0.207966i
$67$	12.5498			1.53320			0.766602	−	0.642123i	$-0.221946\pi$
$67$	12.5498			1.53320			0.766602	+	0.642123i	$0.221946\pi$
$68$	3.30332	+	5.72151i	0.400586	+	0.693835i
$69$	−3.45214	−	10.4657i	−0.415589	−	1.25992i
$70$	−2.55859	+	0.673503i	−0.305810	+	0.0804991i
$71$		−	14.2133i		−	1.68681i	−0.537281	−	0.843403i	$-0.680549\pi$
$71$		−	14.2133i		−	1.68681i	0.537281	−	0.843403i	$-0.319451\pi$
$72$	1.19573	−	2.75140i	0.140919	−	0.324256i
$73$	−1.11022	+	0.640987i	−0.129942	+	0.0750218i	−0.563562	−	0.826074i	$-0.690569\pi$
$73$	−1.11022	+	0.640987i	−0.129942	+	0.0750218i	0.433620	+	0.901096i	$0.357236\pi$
$74$	4.77962	+	2.75951i	0.555619	+	0.320787i
$75$	1.29232	+	1.15322i	0.149224	+	0.133162i
$76$	3.08388	+	1.78048i	0.353745	+	0.204235i
$77$	2.72875	+	2.75290i	0.310970	+	0.313722i
$78$	9.00610	+	8.03674i	1.01974	+	0.909982i
$79$	0.994011			0.111835			0.0559175	−	0.998435i	$-0.482192\pi$
$79$	0.994011			0.111835			0.0559175	+	0.998435i	$0.482192\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	6.14044	+	6.57989i	0.682271	+	0.731099i
$82$	−1.09537	−	0.632413i	−0.120964	−	0.0698383i
$83$	−5.93463	−	10.2791i	−0.651411	−	1.12828i	−0.982781	−	0.184776i	$-0.940844\pi$
$83$	−5.93463	−	10.2791i	−0.651411	−	1.12828i	0.331370	−	0.943501i	$-0.392489\pi$
$84$	−2.08024	+	4.08321i	−0.226973	+	0.445515i
$85$	−3.30332	+	5.72151i	−0.358295	+	0.620585i
$86$	−5.62191	+	3.24581i	−0.606226	+	0.350005i
$87$	−0.936056	−	2.83779i	−0.100356	−	0.304243i
$88$	−0.732523	+	1.26877i	−0.0780873	+	0.135251i
$89$	2.18741	−	3.78871i	0.231865	−	0.401602i	−0.726492	−	0.687175i	$-0.758851\pi$
$89$	2.18741	−	3.78871i	0.231865	−	0.401602i	0.958357	+	0.285573i	$0.0921839\pi$
$90$	2.98065	−	0.340166i	0.314188	−	0.0358566i
$91$	−12.9801	−	13.0950i	−1.36069	−	1.37273i
$92$	−5.51016	+	3.18129i	−0.574474	+	0.331673i
$93$	13.3117	+	2.76754i	1.38036	+	0.286981i
$94$		−	5.39759i		−	0.556719i
$95$			3.56096i			0.365347i
$96$	−1.69579	−	0.352560i	−0.173076	−	0.0359830i
$97$	9.04933	−	5.22463i	0.918820	−	0.530481i	0.0355618	−	0.999367i	$-0.488678\pi$
$97$	9.04933	−	5.22463i	0.918820	−	0.530481i	0.883259	+	0.468886i	$0.155345\pi$
$98$	3.55329	−	6.03110i	0.358936	−	0.609233i
$99$	−2.61499	−	3.53258i	−0.262816	−	0.355037i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.01983	+	1.76640i	−0.101477	+	0.175763i	−0.912293	−	0.409537i	$-0.865690\pi$
$101$	−1.01983	+	1.76640i	−0.101477	+	0.175763i	0.810816	+	0.585301i	$0.199023\pi$
$102$	3.58455	+	10.8671i	0.354924	+	1.07600i
$103$	−2.75430	+	1.59020i	−0.271389	+	0.156687i	−0.629519	−	0.776985i	$-0.716748\pi$
$103$	−2.75430	+	1.59020i	−0.271389	+	0.156687i	0.358130	+	0.933672i	$0.383415\pi$
$104$	3.48448	−	6.03529i	0.341681	−	0.591809i
$105$	−4.57628	+	0.240063i	−0.446600	+	0.0234278i
$106$	−3.23783	−	5.60809i	−0.314486	−	0.544706i
$107$	13.7903	+	7.96185i	1.33316	+	0.769701i	0.985783	−	0.168024i	$-0.0537385\pi$
$107$	13.7903	+	7.96185i	1.33316	+	0.769701i	0.347379	+	0.937725i	$0.387072\pi$
$108$	2.99775	−	4.24423i	0.288458	−	0.408401i
$109$	−3.60853	−	6.25017i	−0.345635	−	0.598657i	0.639834	−	0.768513i	$-0.279003\pi$
$109$	−3.60853	−	6.25017i	−0.345635	−	0.598657i	−0.985469	+	0.169856i	$0.945670\pi$
$110$	−1.46505			−0.139687
$111$	7.13233	+	6.36466i	0.676971	+	0.604106i
$112$	2.55256	+	0.696025i	0.241194	+	0.0657682i
$113$	5.42707	+	3.13332i	0.510536	+	0.294758i	0.733054	−	0.680170i	$-0.238094\pi$
$113$	5.42707	+	3.13332i	0.510536	+	0.294758i	−0.222518	+	0.974929i	$0.571428\pi$
$114$	4.60189	+	4.10657i	0.431006	+	0.384616i
$115$	−5.51016	−	3.18129i	−0.513825	−	0.296657i
$116$	−1.49409	+	0.862614i	−0.138723	+	0.0800917i
$117$	12.4390	+	16.8038i	1.14999	+	1.55351i
$118$			1.49328i			0.137468i
$119$	−4.44959	−	16.9037i	−0.407893	−	1.54956i
$120$	−0.542569	−	1.64488i	−0.0495295	−	0.150156i
$121$	−4.42682	−	7.66748i	−0.402438	−	0.697043i
$122$	3.73592			0.338234
$123$	−1.63456	−	1.45862i	−0.147383	−	0.131520i
$124$		−	7.84985i		−	0.704937i
$125$	1.00000			0.0894427
$126$	−4.96723	+	6.19085i	−0.442516	+	0.551525i
$127$	−0.914380			−0.0811381			−0.0405691	−	0.999177i	$-0.512917\pi$
$127$	−0.914380			−0.0811381			−0.0405691	+	0.999177i	$0.512917\pi$
$128$			1.00000i			0.0883883i
$129$	−10.6779	+	3.52215i	−0.940138	+	0.310108i
$130$	6.96896			0.611218
$131$	4.94937	+	8.57256i	0.432429	+	0.748988i	0.997082	−	0.0763399i	$-0.0243234\pi$
$131$	4.94937	+	8.57256i	0.432429	+	0.748988i	−0.564653	+	0.825328i	$0.690990\pi$
$132$	−1.68952	+	1.89330i	−0.147054	+	0.164791i
$133$	−6.63252	−	6.69123i	−0.575113	−	0.580204i
$134$		−	12.5498i		−	1.08414i
$135$	5.17449	+	0.474009i	0.445349	+	0.0407962i
$136$	5.72151	−	3.30332i	0.490616	−	0.283257i
$137$	10.4341	+	6.02412i	0.891444	+	0.514675i	0.874414	−	0.485180i	$-0.161246\pi$
$137$	10.4341	+	6.02412i	0.891444	+	0.514675i	0.0170294	+	0.999855i	$0.494579\pi$
$138$	−10.4657	+	3.45214i	−0.890897	+	0.293866i
$139$	−15.6077	−	9.01113i	−1.32383	−	0.764314i	−0.339494	−	0.940608i	$-0.610256\pi$
$139$	−15.6077	−	9.01113i	−1.32383	−	0.764314i	−0.984338	+	0.176294i	$0.943589\pi$
$140$	0.673503	+	2.55859i	0.0569214	+	0.216240i
$141$	1.90297	−	9.15318i	0.160259	−	0.770837i
$142$	−14.2133			−1.19275
$143$	−5.10492	−	8.84199i	−0.426895	−	0.739404i
$144$	−2.75140	−	1.19573i	−0.229284	−	0.0996445i
$145$	−1.49409	−	0.862614i	−0.124078	−	0.0716362i
$146$	0.640987	+	1.11022i	0.0530484	+	0.0918826i
$147$	8.15195	−	8.97473i	0.672361	−	0.740223i
$148$	2.75951	−	4.77962i	0.226831	−	0.392882i
$149$	−7.44381	+	4.29769i	−0.609821	+	0.352080i	−0.772895	−	0.634534i	$-0.781192\pi$
$149$	−7.44381	+	4.29769i	−0.609821	+	0.352080i	0.163075	+	0.986614i	$0.447859\pi$
$150$	1.15322	−	1.29232i	0.0941600	−	0.105517i
$151$	1.30386	−	2.25835i	0.106106	−	0.183782i	−0.808083	−	0.589068i	$-0.799495\pi$
$151$	1.30386	−	2.25835i	0.106106	−	0.183782i	0.914190	+	0.405287i	$0.132828\pi$
$152$	1.78048	−	3.08388i	0.144416	−	0.250136i
$153$	2.24735	+	19.6921i	0.181687	+	1.59201i
$154$	2.75290	−	2.72875i	0.221835	−	0.219889i
$155$	6.79817	−	3.92493i	0.546042	−	0.315258i
$156$	8.03674	−	9.00610i	0.643454	−	0.721065i
$157$			7.79034i			0.621737i	0.950453	+	0.310868i	$0.100620\pi$
$157$			7.79034i			0.621737i	−0.950453	+	0.310868i	$0.899380\pi$
$158$		−	0.994011i		−	0.0790793i
$159$	−3.51350	−	10.6517i	−0.278638	−	0.844732i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	16.2793	−	4.28523i	1.28299	−	0.337723i
$162$	6.57989	−	6.14044i	0.516965	−	0.482439i
$163$	−4.14705	+	7.18290i	−0.324822	+	0.562608i	−0.981476	−	0.191584i	$-0.938638\pi$
$163$	−4.14705	+	7.18290i	−0.324822	+	0.562608i	0.656654	+	0.754192i	$0.271971\pi$
$164$	−0.632413	+	1.09537i	−0.0493832	+	0.0855342i
$165$	−2.48441	−	0.516517i	−0.193411	−	0.0402108i
$166$	−10.2791	+	5.93463i	−0.797812	+	0.460617i
$167$	6.88497	−	11.9251i	0.532775	−	0.922793i	−0.466493	−	0.884525i	$-0.654483\pi$
$167$	6.88497	−	11.9251i	0.532775	−	0.922793i	0.999268	−	0.0382680i	$-0.0121841\pi$
$168$	4.08321	+	2.08024i	0.315026	+	0.160494i
$169$	17.7832	+	30.8014i	1.36794	+	2.36934i
$170$	5.72151	+	3.30332i	0.438820	+	0.253353i
$171$	6.35602	+	8.58632i	0.486057	+	0.656612i
$172$	3.24581	+	5.62191i	0.247491	+	0.428666i
$173$	11.6394			0.884929			0.442464	−	0.896786i	$-0.354104\pi$
$173$	11.6394			0.884929			0.442464	+	0.896786i	$0.354104\pi$
$174$	−2.83779	+	0.936056i	−0.215132	+	0.0709622i
$175$	−1.87905	+	1.86257i	−0.142043	+	0.140797i
$176$	1.26877	+	0.732523i	0.0956370	+	0.0552160i
$177$	−0.526472	+	2.53230i	−0.0395720	+	0.190339i
$178$	−3.78871	−	2.18741i	−0.283976	−	0.163953i
$179$	1.21808	−	0.703262i	0.0910439	−	0.0525642i	−0.453787	−	0.891110i	$-0.649927\pi$
$179$	1.21808	−	0.703262i	0.0910439	−	0.0525642i	0.544831	+	0.838546i	$0.316594\pi$
$180$	−0.340166	−	2.98065i	−0.0253544	−	0.222165i
$181$		−	10.1582i		−	0.755054i	−0.925998	−	0.377527i	$-0.876774\pi$
$181$		−	10.1582i		−	0.755054i	0.925998	−	0.377527i	$-0.123226\pi$
$182$	−13.0950	+	12.9801i	−0.970669	+	0.962153i
$183$	6.33533	+	1.31713i	0.468321	+	0.0973653i
$184$	3.18129	+	5.51016i	0.234528	+	0.406215i
$185$	5.51903			0.405767
$186$	2.76754	−	13.3117i	0.202926	−	0.976061i
$187$		−	9.67903i		−	0.707801i
$188$	−5.39759			−0.393660
$189$	−10.6060	+	8.74714i	−0.771474	+	0.636261i
$190$	3.56096			0.258339
$191$			17.1243i			1.23907i	0.784968	+	0.619536i	$0.212679\pi$
$191$			17.1243i			1.23907i	−0.784968	+	0.619536i	$0.787321\pi$
$192$	−0.352560	+	1.69579i	−0.0254438	+	0.122383i
$193$	1.93306			0.139144			0.0695722	−	0.997577i	$-0.477837\pi$
$193$	1.93306			0.139144			0.0695722	+	0.997577i	$0.477837\pi$
$194$	−5.22463	−	9.04933i	−0.375107	−	0.649704i
$195$	11.8179	+	2.45697i	0.846296	+	0.175948i
$196$	−6.03110	−	3.55329i	−0.430793	−	0.253806i
$197$		−	22.0136i		−	1.56840i	−0.620508	−	0.784200i	$-0.713073\pi$
$197$		−	22.0136i		−	1.56840i	0.620508	−	0.784200i	$-0.286927\pi$
$198$	−3.53258	+	2.61499i	−0.251049	+	0.185839i
$199$	23.0430	−	13.3039i	1.63348	−	0.943088i	0.650468	−	0.759534i	$-0.274573\pi$
$199$	23.0430	−	13.3039i	1.63348	−	0.943088i	0.983010	−	0.183554i	$-0.0587604\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	4.42456	−	21.2818i	0.312084	−	1.50110i
$202$	1.76640	+	1.01983i	0.124283	+	0.0717550i
$203$	4.41416	−	1.16195i	0.309813	−	0.0815527i
$204$	10.8671	−	3.58455i	0.760849	−	0.250969i
$205$	−1.26483			−0.0883393
$206$	1.59020	+	2.75430i	0.110794	+	0.191901i
$207$	−18.9647	+	2.16433i	−1.31814	+	0.150432i
$208$	−6.03529	−	3.48448i	−0.418472	−	0.241605i
$209$	−2.60849	−	4.51803i	−0.180433	−	0.312519i
$210$	0.240063	+	4.57628i	0.0165660	+	0.315794i
$211$	−3.44298	+	5.96341i	−0.237024	+	0.410538i	−0.959859	−	0.280483i	$-0.909505\pi$
$211$	−3.44298	+	5.96341i	−0.237024	+	0.410538i	0.722835	+	0.691021i	$0.242839\pi$
$212$	−5.60809	+	3.23783i	−0.385165	+	0.222375i
$213$	−24.1027	−	5.01103i	−1.65149	−	0.343350i
$214$	7.96185	−	13.7903i	0.544261	−	0.942688i
$215$	−3.24581	+	5.62191i	−0.221362	+	0.383411i
$216$	−4.24423	−	2.99775i	−0.288783	−	0.203971i
$217$	−5.46369	+	20.0372i	−0.370900	+	1.36021i
$218$	−6.25017	+	3.60853i	−0.423315	+	0.244401i
$219$	0.695559	+	2.10869i	0.0470015	+	0.142492i
$220$			1.46505i			0.0987734i
$221$			46.0413i			3.09708i
$222$	6.36466	−	7.13233i	0.427168	−	0.478691i
$223$	11.6938	−	6.75140i	0.783072	−	0.452107i	−0.0544458	−	0.998517i	$-0.517339\pi$
$223$	11.6938	−	6.75140i	0.783072	−	0.452107i	0.837518	+	0.546410i	$0.184006\pi$
$224$	0.696025	−	2.55256i	0.0465051	−	0.170550i
$225$	2.41124	−	1.78492i	0.160749	−	0.118995i
$226$	3.13332	−	5.42707i	0.208426	−	0.361004i
$227$	−10.7490	+	18.6179i	−0.713438	+	1.23571i	0.250120	+	0.968215i	$0.419530\pi$
$227$	−10.7490	+	18.6179i	−0.713438	+	1.23571i	−0.963559	+	0.267497i	$0.913803\pi$
$228$	4.10657	−	4.60189i	0.271964	−	0.304767i
$229$	19.4936	−	11.2546i	1.28817	−	0.743727i	0.309845	−	0.950787i	$-0.399723\pi$
$229$	19.4936	−	11.2546i	1.28817	−	0.743727i	0.978328	+	0.207060i	$0.0663896\pi$
$230$	−3.18129	+	5.51016i	−0.209768	+	0.363329i
$231$	5.63039	−	3.65682i	0.370452	−	0.240601i
$232$	0.862614	+	1.49409i	0.0566334	+	0.0980919i
$233$	−15.4408	−	8.91477i	−1.01156	−	0.584026i	−0.0999142	−	0.994996i	$-0.531857\pi$
$233$	−15.4408	−	8.91477i	−1.01156	−	0.584026i	−0.911649	+	0.410970i	$0.865190\pi$
$234$	16.8038	−	12.4390i	1.09850	−	0.813164i
$235$	−2.69880	−	4.67445i	−0.176050	−	0.304928i
$236$	1.49328			0.0972045
$237$	0.350448	−	1.68563i	0.0227641	−	0.109494i
$238$	−16.9037	+	4.44959i	−1.09570	+	0.288424i
$239$	13.7144	+	7.91804i	0.887114	+	0.512175i	0.872997	−	0.487725i	$-0.162173\pi$
$239$	13.7144	+	7.91804i	0.887114	+	0.512175i	0.0141164	+	0.999900i	$0.495506\pi$
$240$	−1.64488	+	0.542569i	−0.106176	+	0.0350227i
$241$	22.8842	+	13.2122i	1.47410	+	0.851073i	0.999575	−	0.0291688i	$-0.00928603\pi$
$241$	22.8842	+	13.2122i	1.47410	+	0.851073i	0.474526	+	0.880241i	$0.342619\pi$
$242$	−7.66748	+	4.42682i	−0.492884	+	0.284567i
$243$	13.3230	−	8.09309i	0.854670	−	0.519172i
$244$		−	3.73592i		−	0.239167i
$245$	0.0616877	−	6.99973i	0.00394109	−	0.447196i
$246$	−1.45862	+	1.63456i	−0.0929984	+	0.104215i
$247$	12.4081	+	21.4914i	0.789507	+	1.36747i
$248$	−7.84985			−0.498466
$249$	−19.5235	+	6.43990i	−1.23725	+	0.408112i
$250$		−	1.00000i		−	0.0632456i
$251$	−27.9912			−1.76679			−0.883395	−	0.468628i	$-0.844748\pi$
$251$	−27.9912			−1.76679			−0.883395	+	0.468628i	$0.844748\pi$
$252$	6.19085	+	4.96723i	0.389987	+	0.312906i
$253$	9.32149			0.586037
$254$			0.914380i			0.0573733i
$255$	8.53786	+	7.61890i	0.534662	+	0.477114i
$256$	1.00000			0.0625000
$257$	−7.21520	−	12.4971i	−0.450072	−	0.779547i	0.548318	−	0.836270i	$-0.315268\pi$
$257$	−7.21520	−	12.4971i	−0.450072	−	0.779547i	−0.998390	+	0.0567229i	$0.981935\pi$
$258$	3.52215	+	10.6779i	0.219280	+	0.664778i
$259$	−10.3706	+	10.2796i	−0.644395	+	0.638741i
$260$		−	6.96896i		−	0.432196i
$261$	−5.14231	+	0.586863i	−0.318301	+	0.0363259i
$262$	8.57256	−	4.94937i	0.529615	−	0.305773i
$263$	−1.39555	−	0.805722i	−0.0860534	−	0.0496830i	0.456356	−	0.889797i	$-0.349154\pi$
$263$	−1.39555	−	0.805722i	−0.0860534	−	0.0496830i	−0.542409	+	0.840114i	$0.682488\pi$
$264$	1.89330	+	1.68952i	0.116525	+	0.103983i
$265$	−5.60809	−	3.23783i	−0.344502	−	0.198898i
$266$	−6.69123	+	6.63252i	−0.410266	+	0.406666i
$267$	−5.65366	−	5.04514i	−0.345998	−	0.308757i
$268$	−12.5498			−0.766602
$269$	2.06266	+	3.57264i	0.125763	+	0.217828i	0.922031	−	0.387116i	$-0.126529\pi$
$269$	2.06266	+	3.57264i	0.125763	+	0.217828i	−0.796268	+	0.604944i	$0.793196\pi$
$270$	0.474009	−	5.17449i	0.0288473	−	0.314909i
$271$	−4.02680	−	2.32488i	−0.244611	−	0.141226i	0.372683	−	0.927959i	$-0.378438\pi$
$271$	−4.02680	−	2.32488i	−0.244611	−	0.141226i	−0.617294	+	0.786732i	$0.711771\pi$
$272$	−3.30332	−	5.72151i	−0.200293	−	0.346918i
$273$	−26.7827	+	17.3948i	−1.62096	+	1.05278i
$274$	6.02412	−	10.4341i	0.363930	−	0.630346i
$275$	−1.26877	+	0.732523i	−0.0765096	+	0.0441728i
$276$	3.45214	+	10.4657i	0.207795	+	0.629959i
$277$	−11.7120	+	20.2858i	−0.703705	+	1.21885i	0.263452	+	0.964673i	$0.415139\pi$
$277$	−11.7120	+	20.2858i	−0.703705	+	1.21885i	−0.967157	+	0.254180i	$0.918194\pi$
$278$	−9.01113	+	15.6077i	−0.540452	+	0.936090i
$279$	9.38633	−	21.5981i	0.561945	−	1.29304i
$280$	2.55859	−	0.673503i	0.152905	−	0.0402495i
$281$	−17.5671	+	10.1424i	−1.04797	+	0.605043i	−0.922079	−	0.387001i	$-0.873511\pi$
$281$	−17.5671	+	10.1424i	−1.04797	+	0.605043i	−0.125887	+	0.992045i	$0.540178\pi$
$282$	−9.15318	−	1.90297i	−0.545064	−	0.113320i
$283$		−	5.74367i		−	0.341426i	−0.985321	−	0.170713i	$-0.945393\pi$
$283$		−	5.74367i		−	0.341426i	0.985321	−	0.170713i	$-0.0546071\pi$
$284$			14.2133i			0.843403i
$285$	6.03864	+	1.25545i	0.357698	+	0.0743665i
$286$	−8.84199	+	5.10492i	−0.522838	+	0.301860i
$287$	2.37668	−	2.35582i	0.140291	−	0.139060i
$288$	−1.19573	+	2.75140i	−0.0704593	+	0.162128i
$289$	−13.3238	+	23.0775i	−0.783753	+	1.35750i
$290$	−0.862614	+	1.49409i	−0.0506545	+	0.0877361i
$291$	−5.66945	−	17.1878i	−0.332349	−	1.00756i
$292$	1.11022	−	0.640987i	0.0649708	−	0.0375109i
$293$	10.7874	−	18.6844i	0.630209	−	1.09155i	−0.357300	−	0.933990i	$-0.616303\pi$
$293$	10.7874	−	18.6844i	0.630209	−	1.09155i	0.987509	−	0.157564i	$-0.0503640\pi$
$294$	−8.97473	−	8.15195i	−0.523417	−	0.475431i
$295$	0.746642	+	1.29322i	0.0434712	+	0.0752943i
$296$	−4.77962	−	2.75951i	−0.277810	−	0.160393i
$297$	−6.91244	+	3.18903i	−0.401101	+	0.185046i
$298$	4.29769	+	7.44381i	0.248958	+	0.431208i
$299$	−44.3406			−2.56428
$300$	−1.29232	−	1.15322i	−0.0746119	−	0.0665812i
$301$	−4.37213	−	16.6094i	−0.252005	−	0.957350i
$302$	−2.25835	−	1.30386i	−0.129953	−	0.0750285i
$303$	2.63589	+	2.35218i	0.151428	+	0.135129i
$304$	−3.08388	−	1.78048i	−0.176873	−	0.102117i
$305$	3.23540	−	1.86796i	0.185258	−	0.106959i
$306$	19.6921	−	2.24735i	1.12572	−	0.128472i
$307$		−	5.22295i		−	0.298090i	−0.988830	−	0.149045i	$-0.952380\pi$
$307$		−	5.22295i		−	0.298090i	0.988830	−	0.149045i	$-0.0476199\pi$
$308$	−2.72875	−	2.75290i	−0.155485	−	0.156861i
$309$	1.72558	+	5.23135i	0.0981649	+	0.297601i
$310$	−3.92493	−	6.79817i	−0.222921	−	0.386110i
$311$	−13.2357			−0.750526			−0.375263	−	0.926918i	$-0.622448\pi$
$311$	−13.2357			−0.750526			−0.375263	+	0.926918i	$0.622448\pi$
$312$	−9.00610	−	8.03674i	−0.509870	−	0.454991i
$313$			30.9549i			1.74968i	0.484416	+	0.874838i	$0.339032\pi$
$313$			30.9549i			1.74968i	−0.484416	+	0.874838i	$0.660968\pi$
$314$	7.79034			0.439634
$315$	−1.20632	+	7.84505i	−0.0679682	+	0.442018i
$316$	−0.994011			−0.0559175
$317$		−	15.1480i		−	0.850796i	−0.905006	−	0.425398i	$-0.860134\pi$
$317$		−	15.1480i		−	0.850796i	0.905006	−	0.425398i	$-0.139866\pi$
$318$	−10.6517	+	3.51350i	−0.597316	+	0.197027i
$319$	2.52754			0.141515
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	18.3635	−	20.5785i	1.02495	−	1.14858i
$322$	−4.28523	−	16.2793i	−0.238806	−	0.907208i
$323$			23.5259i			1.30902i
$324$	−6.14044	−	6.57989i	−0.341136	−	0.365550i
$325$	6.03529	−	3.48448i	0.334778	−	0.193284i
$326$	7.18290	+	4.14705i	0.397824	+	0.229684i
$327$	−11.8712	+	3.91576i	−0.656478	+	0.216542i
$328$	1.09537	+	0.632413i	0.0604818	+	0.0349192i
$329$	13.7777	+	3.75686i	0.759587	+	0.207122i
$330$	−0.516517	+	2.48441i	−0.0284333	+	0.136762i
$331$	1.30322			0.0716313			0.0358157	−	0.999358i	$-0.488597\pi$
$331$	1.30322			0.0716313			0.0358157	+	0.999358i	$0.488597\pi$
$332$	5.93463	+	10.2791i	0.325705	+	0.564138i
$333$	13.3077	−	9.85101i	0.729257	−	0.539832i
$334$	−11.9251	−	6.88497i	−0.652513	−	0.376729i
$335$	−6.27490	−	10.8685i	−0.342835	−	0.593807i
$336$	2.08024	−	4.08321i	0.113486	−	0.222757i
$337$	8.12095	−	14.0659i	0.442377	−	0.766219i	−0.555489	−	0.831524i	$-0.687469\pi$
$337$	8.12095	−	14.0659i	0.442377	−	0.766219i	0.997865	+	0.0653053i	$0.0208021\pi$
$338$	30.8014	−	17.7832i	1.67537	−	0.967277i
$339$	7.22682	−	8.09849i	0.392507	−	0.439850i
$340$	3.30332	−	5.72151i	0.179147	−	0.310293i
$341$	−5.75020	+	9.95964i	−0.311391	+	0.539345i
$342$	8.58632	−	6.35602i	0.464295	−	0.343694i
$343$	12.9215	+	13.2678i	0.697698	+	0.716392i
$344$	5.62191	−	3.24581i	0.303113	−	0.175002i
$345$	−7.33747	+	8.22248i	−0.395036	+	0.442683i
$346$		−	11.6394i		−	0.625739i
$347$		−	5.07209i		−	0.272284i	−0.990689	−	0.136142i	$-0.956530\pi$
$347$		−	5.07209i		−	0.272284i	0.990689	−	0.136142i	$-0.0434703\pi$
$348$	0.936056	+	2.83779i	0.0501778	+	0.152121i
$349$	−20.4996	+	11.8354i	−1.09732	+	0.633536i	−0.935515	−	0.353287i	$-0.885064\pi$
$349$	−20.4996	+	11.8354i	−1.09732	+	0.633536i	−0.161802	+	0.986823i	$0.551731\pi$
$350$	1.86257	+	1.87905i	0.0995584	+	0.100440i
$351$	32.8812	−	15.1696i	1.75507	−	0.809694i
$352$	0.732523	−	1.26877i	0.0390436	−	0.0676255i
$353$	0.272379	−	0.471774i	0.0144973	−	0.0251100i	−0.858686	−	0.512502i	$-0.828719\pi$
$353$	0.272379	−	0.471774i	0.0144973	−	0.0251100i	0.873183	+	0.487392i	$0.162052\pi$
$354$	2.53230	+	0.526472i	0.134590	+	0.0279817i
$355$	−12.3091	+	7.10664i	−0.653297	+	0.377181i
$356$	−2.18741	+	3.78871i	−0.115933	+	0.200801i
$357$	−30.2338	+	1.58601i	−1.60014	+	0.0839406i
$358$	−0.703262	−	1.21808i	−0.0371685	−	0.0643778i
$359$	5.44862	+	3.14576i	0.287567	+	0.166027i	0.636844	−	0.770993i	$-0.280239\pi$
$359$	5.44862	+	3.14576i	0.287567	+	0.166027i	−0.349277	+	0.937019i	$0.613573\pi$
$360$	−2.98065	+	0.340166i	−0.157094	+	0.0179283i
$361$	−3.15979	−	5.47291i	−0.166305	−	0.288048i
$362$	−10.1582			−0.533904
$363$	−14.5631	+	4.80371i	−0.764367	+	0.252129i
$364$	12.9801	+	13.0950i	0.680345	+	0.686367i
$365$	1.11022	+	0.640987i	0.0581117	+	0.0335508i
$366$	1.31713	−	6.33533i	0.0688477	−	0.331153i
$367$	21.0875	+	12.1749i	1.10076	+	0.635522i	0.936420	−	0.350882i	$-0.114118\pi$
$367$	21.0875	+	12.1749i	1.10076	+	0.635522i	0.164337	+	0.986404i	$0.447452\pi$
$368$	5.51016	−	3.18129i	0.287237	−	0.165836i
$369$	−3.04980	+	2.25761i	−0.158766	+	0.117527i
$370$		−	5.51903i		−	0.286921i
$371$	16.5686	−	4.36138i	0.860198	−	0.226432i
$372$	−13.3117	−	2.76754i	−0.690179	−	0.143490i
$373$	−1.08878	−	1.88581i	−0.0563746	−	0.0976437i	0.836461	−	0.548027i	$-0.184621\pi$
$373$	−1.08878	−	1.88581i	−0.0563746	−	0.0976437i	−0.892835	+	0.450383i	$0.851287\pi$
$374$	−9.67903			−0.500491
$375$	0.352560	−	1.69579i	0.0182061	−	0.0875702i
$376$			5.39759i			0.278360i
$377$	−12.0230			−0.619218
$378$	8.74714	+	10.6060i	0.449904	+	0.545514i
$379$	−22.5954			−1.16065			−0.580323	−	0.814387i	$-0.697074\pi$
$379$	−22.5954			−1.16065			−0.580323	+	0.814387i	$0.697074\pi$
$380$		−	3.56096i		−	0.182673i
$381$	−0.322374	+	1.55060i	−0.0165157	+	0.0794395i
$382$	17.1243			0.876156
$383$	3.26282	+	5.65138i	0.166723	+	0.288772i	0.937266	−	0.348616i	$-0.113348\pi$
$383$	3.26282	+	5.65138i	0.166723	+	0.288772i	−0.770543	+	0.637388i	$0.780015\pi$
$384$	1.69579	+	0.352560i	0.0865379	+	0.0179915i
$385$	1.01971	−	3.73962i	0.0519692	−	0.190588i
$386$		−	1.93306i		−	0.0983900i
$387$	2.20823	+	19.3493i	0.112250	+	0.983578i
$388$	−9.04933	+	5.22463i	−0.459410	+	0.265241i
$389$	−30.0342	−	17.3402i	−1.52279	−	0.879184i	−0.999637	−	0.0269467i	$-0.991422\pi$
$389$	−30.0342	−	17.3402i	−1.52279	−	0.879184i	−0.523155	−	0.852238i	$-0.675245\pi$
$390$	2.45697	−	11.8179i	0.124414	−	0.598422i
$391$	−36.4036	−	21.0176i	−1.84101	−	1.06291i
$392$	−3.55329	+	6.03110i	−0.179468	+	0.304616i
$393$	16.2822	−	5.37075i	0.821329	−	0.270919i
$394$	−22.0136			−1.10903
$395$	−0.497005	−	0.860839i	−0.0250071	−	0.0433135i
$396$	2.61499	+	3.53258i	0.131408	+	0.177519i
$397$	23.8417	+	13.7650i	1.19658	+	0.690845i	0.959791	−	0.280717i	$-0.0905721\pi$
$397$	23.8417	+	13.7650i	1.19658	+	0.690845i	0.236788	+	0.971561i	$0.423905\pi$
$398$	−13.3039	−	23.0430i	−0.666864	−	1.15504i
$399$	−13.6853	+	8.88831i	−0.685121	+	0.444972i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	12.1926	−	7.03938i	0.608868	−	0.351530i	−0.163655	−	0.986518i	$-0.552328\pi$
$401$	12.1926	−	7.03938i	0.608868	−	0.351530i	0.772522	+	0.634988i	$0.218995\pi$
$402$	−21.2818	−	4.42456i	−1.06144	−	0.220677i
$403$	27.3526	−	47.3762i	1.36253	−	2.35997i
$404$	1.01983	−	1.76640i	0.0507385	−	0.0878816i
$405$	2.62813	−	8.60772i	0.130593	−	0.427721i
$406$	−1.16195	−	4.41416i	−0.0576665	−	0.219071i
$407$	−7.00236	+	4.04282i	−0.347094	+	0.200395i
$408$	−3.58455	−	10.8671i	−0.177462	−	0.538001i
$409$			32.7642i			1.62009i	0.586371	+	0.810043i	$0.300556\pi$
$409$			32.7642i			1.62009i	−0.586371	+	0.810043i	$0.699444\pi$
$410$			1.26483i			0.0624653i
$411$	13.8943	−	15.5701i	0.685354	−	0.768019i
$412$	2.75430	−	1.59020i	0.135695	−	0.0783433i
$413$	−3.81169	−	1.03936i	−0.187561	−	0.0511437i
$414$	2.16433	+	18.9647i	0.106371	+	0.932062i
$415$	−5.93463	+	10.2791i	−0.291320	+	0.504581i
$416$	−3.48448	+	6.03529i	−0.170841	+	0.295905i
$417$	−20.7836	+	23.2905i	−1.01778	+	1.14054i
$418$	−4.51803	+	2.60849i	−0.220984	+	0.127585i
$419$	−5.81259	+	10.0677i	−0.283964	+	0.491839i	−0.972357	−	0.233498i	$-0.924983\pi$
$419$	−5.81259	+	10.0677i	−0.283964	+	0.491839i	0.688394	+	0.725337i	$0.258316\pi$
$420$	4.57628	−	0.240063i	0.223300	−	0.0117139i
$421$	11.4508	+	19.8333i	0.558076	+	0.966615i	0.997657	+	0.0684126i	$0.0217934\pi$
$421$	11.4508	+	19.8333i	0.558076	+	0.966615i	−0.439582	+	0.898203i	$0.644873\pi$
$422$	5.96341	+	3.44298i	0.290294	+	0.167601i
$423$	−14.8509	−	6.45408i	−0.722078	−	0.313808i
$424$	3.23783	+	5.60809i	0.157243	+	0.272353i
$425$	6.60663			0.320469
$426$	−5.01103	+	24.1027i	−0.242785	+	1.16778i
$427$	−2.60029	+	9.53614i	−0.125837	+	0.461486i
$428$	−13.7903	−	7.96185i	−0.666581	−	0.384851i
$429$	−16.7939	+	5.53955i	−0.810819	+	0.267452i
$430$	5.62191	+	3.24581i	0.271112	+	0.156527i
$431$	−8.34407	+	4.81745i	−0.401920	+	0.232048i	−0.687312	−	0.726362i	$-0.741209\pi$
$431$	−8.34407	+	4.81745i	−0.401920	+	0.232048i	0.285392	+	0.958411i	$0.407876\pi$
$432$	−2.99775	+	4.24423i	−0.144229	+	0.204201i
$433$			37.8458i			1.81875i	0.415972	+	0.909377i	$0.363441\pi$
$433$			37.8458i			1.81875i	−0.415972	+	0.909377i	$0.636559\pi$
$434$	20.0372	+	5.46369i	0.961816	+	0.262266i
$435$	−1.98957	+	2.22954i	−0.0953925	+	0.106898i
$436$	3.60853	+	6.25017i	0.172817	+	0.299329i
$437$	−22.6569			−1.08383
$438$	2.10869	−	0.695559i	0.100757	−	0.0332351i
$439$		−	32.3974i		−	1.54624i	−0.634257	−	0.773122i	$-0.718694\pi$
$439$		−	32.3974i		−	1.54624i	0.634257	−	0.773122i	$-0.281306\pi$
$440$	1.46505			0.0698434
$441$	−12.3452	−	16.9881i	−0.587867	−	0.808958i
$442$	46.0413			2.18996
$443$			21.9018i			1.04059i	0.853988	+	0.520293i	$0.174177\pi$
$443$			21.9018i			1.04059i	−0.853988	+	0.520293i	$0.825823\pi$
$444$	−7.13233	−	6.36466i	−0.338486	−	0.302053i
$445$	−4.37482			−0.207387
$446$	−6.75140	−	11.6938i	−0.319688	−	0.553716i
$447$	4.66358	+	14.1383i	0.220580	+	0.668720i
$448$	−2.55256	−	0.696025i	−0.120597	−	0.0328841i
$449$			25.8522i			1.22004i	0.792385	+	0.610021i	$0.208839\pi$
$449$			25.8522i			1.22004i	−0.792385	+	0.610021i	$0.791161\pi$
$450$	−1.78492	−	2.41124i	−0.0841418	−	0.113667i
$451$	1.60477	−	0.926515i	0.0755657	−	0.0436279i
$452$	−5.42707	−	3.13332i	−0.255268	−	0.147379i
$453$	−3.36999	−	3.00727i	−0.158336	−	0.141294i
$454$	18.6179	+	10.7490i	0.873780	+	0.504477i
$455$	−4.85057	+	17.7887i	−0.227398	+	0.833945i
$456$	−4.60189	−	4.10657i	−0.215503	−	0.192308i
$457$	−22.2463			−1.04064			−0.520318	−	0.853973i	$-0.674187\pi$
$457$	−22.2463			−1.04064			−0.520318	+	0.853973i	$0.674187\pi$
$458$	−11.2546	−	19.4936i	−0.525894	−	0.910876i
$459$	34.1859	+	3.13160i	1.59566	+	0.146171i
$460$	5.51016	+	3.18129i	0.256913	+	0.148329i
$461$	7.05369	+	12.2173i	0.328523	+	0.569018i	0.982219	−	0.187739i	$-0.0601158\pi$
$461$	7.05369	+	12.2173i	0.328523	+	0.569018i	−0.653696	+	0.756757i	$0.726783\pi$
$462$	−3.65682	−	5.63039i	−0.170131	−	0.261949i
$463$	3.33243	−	5.77194i	0.154871	−	0.268245i	−0.778141	−	0.628090i	$-0.783837\pi$
$463$	3.33243	−	5.77194i	0.154871	−	0.268245i	0.933012	+	0.359845i	$0.117170\pi$
$464$	1.49409	−	0.862614i	0.0693615	−	0.0400459i
$465$	−4.25909	−	12.9120i	−0.197510	−	0.598781i
$466$	−8.91477	+	15.4408i	−0.412969	+	0.715283i
$467$	−1.75717	+	3.04350i	−0.0813119	+	0.140836i	−0.903814	−	0.427926i	$-0.859244\pi$
$467$	−1.75717	+	3.04350i	−0.0813119	+	0.140836i	0.822502	+	0.568763i	$0.192578\pi$
$468$	−12.4390	−	16.8038i	−0.574994	−	0.776756i
$469$	32.0341	+	8.73498i	1.47920	+	0.403344i
$470$	−4.67445	+	2.69880i	−0.215616	+	0.124486i
$471$	13.2108	+	2.74656i	0.608721	+	0.126555i
$472$		−	1.49328i		−	0.0687340i
$473$		−	9.51053i		−	0.437294i
$474$	−1.68563	−	0.350448i	−0.0774237	−	0.0160966i
$475$	3.08388	−	1.78048i	0.141498	−	0.0816940i
$476$	4.44959	+	16.9037i	0.203947	+	0.774779i
$477$	−19.3017	+	2.20280i	−0.883764	+	0.100859i
$478$	7.91804	−	13.7144i	0.362163	−	0.627284i
$479$	−0.500486	+	0.866868i	−0.0228678	+	0.0396082i	−0.877233	−	0.480065i	$-0.840613\pi$
$479$	−0.500486	+	0.866868i	−0.0228678	+	0.0396082i	0.854365	+	0.519673i	$0.173946\pi$
$480$	0.542569	+	1.64488i	0.0247648	+	0.0750780i
$481$	33.3089	−	19.2309i	1.51876	−	0.876855i
$482$	13.2122	−	22.8842i	0.601799	−	1.04235i
$483$	−1.52742	−	29.1170i	−0.0695002	−	1.32487i
$484$	4.42682	+	7.66748i	0.201219	+	0.348522i
$485$	−9.04933	−	5.22463i	−0.410909	−	0.237238i
$486$	−8.09309	−	13.3230i	−0.367110	−	0.604343i
$487$	−14.4755	−	25.0723i	−0.655948	−	1.13613i	−0.981655	−	0.190664i	$-0.938936\pi$
$487$	−14.4755	−	25.0723i	−0.655948	−	1.13613i	0.325708	−	0.945471i	$-0.394397\pi$
$488$	−3.73592			−0.169117
$489$	10.7186	+	9.56492i	0.484712	+	0.432541i
$490$	−6.99973	−	0.0616877i	−0.316215	−	0.00278677i
$491$	30.6555	+	17.6990i	1.38346	+	0.798743i	0.992568	−	0.121691i	$-0.0388318\pi$
$491$	30.6555	+	17.6990i	1.38346	+	0.798743i	0.390896	+	0.920435i	$0.372165\pi$
$492$	1.63456	+	1.45862i	0.0736915	+	0.0657598i
$493$	−9.87092	−	5.69898i	−0.444564	−	0.256669i
$494$	21.4914	−	12.4081i	0.966945	−	0.558266i
$495$	−1.75181	+	4.03093i	−0.0787378	+	0.181177i
$496$			7.84985i			0.352469i
$497$	9.89280	−	36.2802i	0.443753	−	1.62739i
$498$	6.43990	+	19.5235i	0.288579	+	0.874868i
$499$	−8.31844	−	14.4080i	−0.372384	−	0.644989i	0.617547	−	0.786534i	$-0.288126\pi$
$499$	−8.31844	−	14.4080i	−0.372384	−	0.644989i	−0.989932	+	0.141545i	$0.954793\pi$
$500$	−1.00000			−0.0447214
$501$	−17.7951	−	15.8798i	−0.795027	−	0.709456i
$502$			27.9912i			1.24931i
$503$	12.7352			0.567834			0.283917	−	0.958849i	$-0.408366\pi$
$503$	12.7352			0.567834			0.283917	+	0.958849i	$0.408366\pi$
$504$	4.96723	−	6.19085i	0.221258	−	0.275763i
$505$	2.03966			0.0907638
$506$		−	9.32149i		−	0.414391i
$507$	58.5022	−	19.2972i	2.59818	−	0.857019i
$508$	0.914380			0.0405691
$509$	−4.73445	−	8.20032i	−0.209851	−	0.363473i	0.741816	−	0.670603i	$-0.233965\pi$
$509$	−4.73445	−	8.20032i	−0.209851	−	0.363473i	−0.951667	+	0.307130i	$0.900631\pi$
$510$	7.61890	−	8.53786i	0.337371	−	0.378063i
$511$	−3.28005	+	0.863414i	−0.145101	+	0.0381952i
$512$		−	1.00000i		−	0.0441942i
$513$	16.8015	−	7.75128i	0.741803	−	0.342227i
$514$	−12.4971	+	7.21520i	−0.551223	+	0.318249i
$515$	2.75430	+	1.59020i	0.121369	+	0.0700724i
$516$	10.6779	−	3.52215i	0.470069	−	0.155054i
$517$	6.84829	+	3.95386i	0.301187	+	0.173891i
$518$	10.2796	+	10.3706i	0.451658	+	0.455656i
$519$	4.10359	−	19.7380i	0.180128	−	0.866402i
$520$	−6.96896			−0.305609
$521$	−2.37330	−	4.11068i	−0.103976	−	0.180092i	0.809343	−	0.587336i	$-0.199823\pi$
$521$	−2.37330	−	4.11068i	−0.103976	−	0.180092i	−0.913320	+	0.407244i	$0.866490\pi$
$522$	0.586863	+	5.14231i	0.0256863	+	0.225073i
$523$	30.1376	+	17.3999i	1.31782	+	0.760846i	0.983378	−	0.181569i	$-0.0581176\pi$
$523$	30.1376	+	17.3999i	1.31782	+	0.760846i	0.334446	+	0.942415i	$0.391451\pi$
$524$	−4.94937	−	8.57256i	−0.216214	−	0.374494i
$525$	2.49604	+	3.84315i	0.108936	+	0.167729i
$526$	−0.805722	+	1.39555i	−0.0351312	+	0.0608490i
$527$	44.9130	−	25.9305i	1.95644	−	1.12955i
$528$	1.68952	−	1.89330i	0.0735270	−	0.0823955i
$529$	8.74127	−	15.1403i	0.380055	−	0.658275i
$530$	−3.23783	+	5.60809i	−0.140642	+	0.243600i
$531$	4.10863	+	1.78557i	0.178299	+	0.0774872i
$532$	6.63252	+	6.69123i	0.287556	+	0.290102i
$533$	−7.63360	+	4.40726i	−0.330648	+	0.190900i
$534$	−5.04514	+	5.65366i	−0.218324	+	0.244658i
$535$		−	15.9237i		−	0.688442i
$536$			12.5498i			0.542069i
$537$	−0.763136	−	2.31356i	−0.0329317	−	0.0998373i
$538$	3.57264	−	2.06266i	0.154027	−	0.0889277i
$539$	5.04920	+	8.92622i	0.217484	+	0.384479i
$540$	−5.17449	−	0.474009i	−0.222674	−	0.0203981i
$541$	−0.542248	+	0.939202i	−0.0233131	+	0.0403794i	−0.877447	−	0.479674i	$-0.840755\pi$
$541$	−0.542248	+	0.939202i	−0.0233131	+	0.0403794i	0.854133	+	0.520054i	$0.174088\pi$
$542$	−2.32488	+	4.02680i	−0.0998620	+	0.172966i
$543$	−17.2262	−	3.58138i	−0.739247	−	0.153692i
$544$	−5.72151	+	3.30332i	−0.245308	+	0.141629i
$545$	−3.60853	+	6.25017i	−0.154573	+	0.267728i
$546$	17.3948	+	26.7827i	0.744429	+	1.14619i
$547$	−8.77785	−	15.2037i	−0.375314	−	0.650063i	0.615060	−	0.788480i	$-0.289132\pi$
$547$	−8.77785	−	15.2037i	−0.375314	−	0.650063i	−0.990374	+	0.138417i	$0.955798\pi$
$548$	−10.4341	−	6.02412i	−0.445722	−	0.257338i
$549$	4.46716	−	10.2790i	0.190654	−	0.438697i
$550$	0.732523	+	1.26877i	0.0312349	+	0.0541004i
$551$	−6.14347			−0.261721
$552$	10.4657	−	3.45214i	0.445449	−	0.146933i
$553$	2.53727	+	0.691856i	0.107896	+	0.0294207i
$554$	20.2858	+	11.7120i	0.861859	+	0.497595i
$555$	1.94579	−	9.35911i	0.0825941	−	0.397272i
$556$	15.6077	+	9.01113i	0.661916	+	0.382157i
$557$	27.9379	−	16.1300i	1.18377	−	0.683449i	0.226885	−	0.973922i	$-0.427146\pi$
$557$	27.9379	−	16.1300i	1.18377	−	0.683449i	0.956883	+	0.290472i	$0.0938124\pi$
$558$	−21.5981	−	9.38633i	−0.914321	−	0.397355i
$559$			45.2398i			1.91344i
$560$	−0.673503	−	2.55859i	−0.0284607	−	0.108120i
$561$	−16.4136	−	3.41243i	−0.692982	−	0.144073i
$562$	10.1424	+	17.5671i	0.427830	+	0.741024i
$563$	−35.5704			−1.49911			−0.749557	−	0.661940i	$-0.769733\pi$
$563$	−35.5704			−1.49911			−0.749557	+	0.661940i	$0.769733\pi$
$564$	−1.90297	+	9.15318i	−0.0801296	+	0.385418i
$565$		−	6.26664i		−	0.263640i
$566$	−5.74367			−0.241425
$567$	11.0941	+	21.0695i	0.465907	+	0.884834i
$568$	14.2133			0.596376
$569$			41.9657i			1.75929i	0.475627	+	0.879647i	$0.342221\pi$
$569$			41.9657i			1.75929i	−0.475627	+	0.879647i	$0.657779\pi$
$570$	1.25545	−	6.03864i	0.0525850	−	0.252931i
$571$	6.77247			0.283419			0.141709	−	0.989908i	$-0.454740\pi$
$571$	6.77247			0.283419			0.141709	+	0.989908i	$0.454740\pi$
$572$	5.10492	+	8.84199i	0.213448	+	0.369702i
$573$	29.0392	+	6.03734i	1.21313	+	0.252214i
$574$	−2.35582	−	2.37668i	−0.0983302	−	0.0992006i
$575$			6.36259i			0.265338i
$576$	2.75140	+	1.19573i	0.114642	+	0.0498223i
$577$	−30.1675	+	17.4172i	−1.25589	+	0.725087i	−0.972273	−	0.233851i	$-0.924867\pi$
$577$	−30.1675	+	17.4172i	−1.25589	+	0.725087i	−0.283616	+	0.958938i	$0.591534\pi$
$578$	23.0775	+	13.3238i	0.959897	+	0.554197i
$579$	0.681518	−	3.27806i	0.0283229	−	0.136231i
$580$	1.49409	+	0.862614i	0.0620388	+	0.0358181i
$581$	−7.99399	−	30.3686i	−0.331647	−	1.25990i
$582$	−17.1878	+	5.66945i	−0.712455	+	0.235006i
$583$	9.48715			0.392918
$584$	−0.640987	−	1.11022i	−0.0265242	−	0.0459413i
$585$	8.33302	−	19.1744i	0.344528	−	0.792764i
$586$	−18.6844	−	10.7874i	−0.771845	−	0.445625i
$587$	−20.1646	−	34.9261i	−0.832281	−	1.44155i	−0.896225	−	0.443599i	$-0.853701\pi$
$587$	−20.1646	−	34.9261i	−0.832281	−	1.44155i	0.0639444	−	0.997953i	$-0.479632\pi$
$588$	−8.15195	+	8.97473i	−0.336181	+	0.370111i
$589$	13.9765	−	24.2080i	0.575892	−	0.997474i
$590$	1.29322	−	0.746642i	0.0532411	−	0.0307388i
$591$	−37.3304	−	7.76109i	−1.53557	−	0.319249i
$592$	−2.75951	+	4.77962i	−0.113415	+	0.196441i
$593$	13.7783	−	23.8647i	0.565806	−	0.980005i	−0.431168	−	0.902272i	$-0.641898\pi$
$593$	13.7783	−	23.8647i	0.565806	−	0.980005i	0.996974	−	0.0777332i	$-0.0247682\pi$
$594$	3.18903	+	6.91244i	0.130847	+	0.283621i
$595$	−12.4142	+	12.3053i	−0.508933	+	0.504468i
$596$	7.44381	−	4.29769i	0.304910	−	0.176040i
$597$	−14.4366	−	43.7665i	−0.590849	−	1.79125i
$598$			44.3406i			1.81322i
$599$		−	14.1442i		−	0.577917i	−0.957342	−	0.288959i	$-0.906691\pi$
$599$		−	14.1442i		−	0.577917i	0.957342	−	0.288959i	$-0.0933090\pi$
$600$	−1.15322	+	1.29232i	−0.0470800	+	0.0527586i
$601$	10.7893	−	6.22920i	0.440104	−	0.254094i	−0.263537	−	0.964649i	$-0.584889\pi$
$601$	10.7893	−	6.22920i	0.440104	−	0.254094i	0.703642	+	0.710555i	$0.251556\pi$
$602$	−16.6094	+	4.37213i	−0.676949	+	0.178195i
$603$	−34.5296	−	15.0062i	−1.40615	−	0.611101i
$604$	−1.30386	+	2.25835i	−0.0530532	+	0.0918908i
$605$	−4.42682	+	7.66748i	−0.179976	+	0.311727i
$606$	2.35218	−	2.63589i	0.0955508	−	0.107076i
$607$	6.89996	−	3.98369i	0.280061	−	0.161693i	−0.353390	−	0.935476i	$-0.614971\pi$
$607$	6.89996	−	3.98369i	0.280061	−	0.161693i	0.633451	+	0.773783i	$0.281638\pi$
$608$	−1.78048	+	3.08388i	−0.0722080	+	0.125068i
$609$	−0.414164	−	7.89514i	−0.0167828	−	0.319927i
$610$	−1.86796	−	3.23540i	−0.0756314	−	0.130997i
$611$	−32.5760	−	18.8078i	−1.31789	−	0.760882i
$612$	−2.24735	−	19.6921i	−0.0908437	−	0.796005i
$613$	3.28676	+	5.69283i	0.132751	+	0.229931i	0.924736	−	0.380609i	$-0.124286\pi$
$613$	3.28676	+	5.69283i	0.132751	+	0.229931i	−0.791985	+	0.610540i	$0.790952\pi$
$614$	−5.22295			−0.210781
$615$	−0.445927	+	2.14488i	−0.0179815	+	0.0864899i
$616$	−2.75290	+	2.72875i	−0.110918	+	0.109944i
$617$	−6.77484	−	3.91146i	−0.272745	−	0.157469i	0.357389	−	0.933955i	$-0.383667\pi$
$617$	−6.77484	−	3.91146i	−0.272745	−	0.157469i	−0.630134	+	0.776486i	$0.717000\pi$
$618$	5.23135	−	1.72558i	0.210436	−	0.0694131i
$619$	39.8161	+	22.9878i	1.60034	+	0.923959i	0.991418	+	0.130732i	$0.0417327\pi$
$619$	39.8161	+	22.9878i	1.60034	+	0.923959i	0.608926	+	0.793227i	$0.291601\pi$
$620$	−6.79817	+	3.92493i	−0.273021	+	0.157629i
$621$	−3.01592	+	32.9231i	−0.121025	+	1.32116i
$622$			13.2357i			0.530702i
$623$	8.22053	−	8.14840i	0.329349	−	0.326459i
$624$	−8.03674	+	9.00610i	−0.321727	+	0.360532i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	30.9549			1.23721
$627$	−8.58127	+	2.83057i	−0.342703	+	0.113042i
$628$		−	7.79034i		−	0.310868i
$629$	36.4622			1.45384
$630$	7.84505	+	1.20632i	0.312554	+	0.0480608i
$631$	−24.0931			−0.959131			−0.479566	−	0.877506i	$-0.659206\pi$
$631$	−24.0931			−0.959131			−0.479566	+	0.877506i	$0.659206\pi$
$632$			0.994011i			0.0395396i
$633$	8.89883	+	7.94102i	0.353697	+	0.315627i
$634$	−15.1480			−0.601604
$635$	0.457190	+	0.791877i	0.0181430	+	0.0314247i
$636$	3.51350	+	10.6517i	0.139319	+	0.422366i
$637$	−24.0181	−	42.4604i	−0.951632	−	1.68234i
$638$		−	2.52754i		−	0.100066i
$639$	−16.9953	+	39.1065i	−0.672324	+	1.54703i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	20.6665	+	11.9318i	0.816279	+	0.471279i	0.849132	−	0.528181i	$-0.177126\pi$
$641$	20.6665	+	11.9318i	0.816279	+	0.471279i	−0.0328524	+	0.999460i	$0.510459\pi$
$642$	−20.5785	−	18.3635i	−0.812167	−	0.724751i
$643$	−12.9563	−	7.48033i	−0.510947	−	0.294996i	0.222276	−	0.974984i	$-0.428652\pi$
$643$	−12.9563	−	7.48033i	−0.510947	−	0.294996i	−0.733223	+	0.679988i	$0.761985\pi$
$644$	−16.2793	+	4.28523i	−0.641493	+	0.168862i
$645$	8.38923	+	7.48627i	0.330326	+	0.294771i
$646$	23.5259			0.925616
$647$	−3.99382	−	6.91751i	−0.157013	−	0.271955i	0.776777	−	0.629776i	$-0.216853\pi$
$647$	−3.99382	−	6.91751i	−0.157013	−	0.271955i	−0.933790	+	0.357821i	$0.883520\pi$
$648$	−6.57989	+	6.14044i	−0.258483	+	0.241219i
$649$	−1.89463	−	1.09387i	−0.0743708	−	0.0429380i
$650$	−3.48448	−	6.03529i	−0.136672	−	0.236724i
$651$	32.0526	+	16.3296i	1.25624	+	0.640007i
$652$	4.14705	−	7.18290i	0.162411	−	0.281304i
$653$	24.4998	−	14.1449i	0.958750	−	0.553535i	0.0629620	−	0.998016i	$-0.479945\pi$
$653$	24.4998	−	14.1449i	0.958750	−	0.553535i	0.895788	+	0.444481i	$0.146612\pi$
$654$	3.91576	+	11.8712i	0.153118	+	0.464200i
$655$	4.94937	−	8.57256i	0.193388	−	0.334958i
$656$	0.632413	−	1.09537i	0.0246916	−	0.0427671i
$657$	3.82112	−	0.436083i	0.149076	−	0.0170132i
$658$	3.75686	−	13.7777i	0.146458	−	0.537109i
$659$	−0.349881	+	0.202004i	−0.0136294	+	0.00786894i	−0.506799	−	0.862064i	$-0.669171\pi$
$659$	−0.349881	+	0.202004i	−0.0136294	+	0.00786894i	0.493170	+	0.869933i	$0.335838\pi$
$660$	2.48441	+	0.516517i	0.0967056	+	0.0201054i
$661$		−	3.41898i		−	0.132983i	−0.997787	−	0.0664915i	$-0.978819\pi$
$661$		−	3.41898i		−	0.132983i	0.997787	−	0.0664915i	$-0.0211805\pi$
$662$		−	1.30322i		−	0.0506510i
$663$	78.0764	+	16.2323i	3.03224	+	0.630411i
$664$	10.2791	−	5.93463i	0.398906	−	0.230308i
$665$	−2.47852	+	9.08955i	−0.0961127	+	0.352478i
$666$	−9.85101	−	13.3077i	−0.381719	−	0.515662i
$667$	5.48846	−	9.50629i	0.212514	−	0.368085i
$668$	−6.88497	+	11.9251i	−0.266387	+	0.461397i
$669$	−7.32620	−	22.2104i	−0.283247	−	0.858705i
$670$	−10.8685	+	6.27490i	−0.419885	+	0.242421i
$671$	−2.73665	+	4.74001i	−0.105647	+	0.182986i
$672$	−4.08321	−	2.08024i	−0.157513	−	0.0802470i
$673$	9.47604	+	16.4130i	0.365274	+	0.632674i	0.988820	−	0.149113i	$-0.0476418\pi$
$673$	9.47604	+	16.4130i	0.365274	+	0.632674i	−0.623546	+	0.781787i	$0.714309\pi$
$674$	−14.0659	−	8.12095i	−0.541798	−	0.312807i
$675$	−2.17674	−	4.71824i	−0.0837828	−	0.181605i
$676$	−17.7832	−	30.8014i	−0.683968	−	1.18467i
$677$	−15.3569			−0.590214			−0.295107	−	0.955464i	$-0.595355\pi$
$677$	−15.3569			−0.590214			−0.295107	+	0.955464i	$0.595355\pi$
$678$	−8.09849	−	7.22682i	−0.311021	−	0.277544i
$679$	26.7354	−	7.03762i	1.02601	−	0.270079i
$680$	−5.72151	−	3.30332i	−0.219410	−	0.126676i
$681$	27.7823	+	24.7920i	1.06462	+	0.950032i
$682$	9.95964	+	5.75020i	0.381374	+	0.220187i
$683$	−26.9763	+	15.5748i	−1.03222	+	0.595951i	−0.917619	−	0.397460i	$-0.869892\pi$
$683$	−26.9763	+	15.5748i	−1.03222	+	0.595951i	−0.114599	+	0.993412i	$0.536558\pi$
$684$	−6.35602	−	8.58632i	−0.243028	−	0.328306i
$685$		−	12.0482i		−	0.460340i
$686$	13.2678	−	12.9215i	0.506566	−	0.493347i
$687$	−12.2128	−	37.0250i	−0.465948	−	1.41259i
$688$	−3.24581	−	5.62191i	−0.123745	−	0.214333i
$689$	−45.1286			−1.71926
$690$	8.22248	+	7.33747i	0.313024	+	0.279333i
$691$			26.8062i			1.01976i	0.860247	+	0.509878i	$0.170309\pi$
$691$			26.8062i			1.01976i	−0.860247	+	0.509878i	$0.829691\pi$
$692$	−11.6394			−0.442464
$693$	−4.21615	−	10.8372i	−0.160158	−	0.411671i
$694$	−5.07209			−0.192534
$695$			18.0223i			0.683624i
$696$	2.83779	−	0.936056i	0.107566	−	0.0354811i
$697$	−8.35624			−0.316515
$698$	11.8354	+	20.4996i	0.447978	+	0.775921i
$699$	−20.5614	+	23.0414i	−0.777703	+	0.871507i
$700$	1.87905	−	1.86257i	0.0710216	−	0.0703984i
$701$		−	9.39873i		−	0.354985i	−0.984122	−	0.177493i	$-0.943201\pi$
$701$		−	9.39873i		−	0.354985i	0.984122	−	0.177493i	$-0.0567985\pi$
$702$	−15.1696	−	32.8812i	−0.572540	−	1.24102i
$703$	17.0200	−	9.82652i	0.641922	−	0.370614i
$704$	−1.26877	−	0.732523i	−0.0478185	−	0.0276080i
$705$	−8.87837	+	2.92857i	−0.334379	+	0.110296i
$706$	−0.471774	−	0.272379i	−0.0177554	−	0.0102511i
$707$	−3.83263	+	3.79901i	−0.144141	+	0.142876i
$708$	0.526472	−	2.53230i	0.0197860	−	0.0951695i
$709$	20.2298			0.759745			0.379873	−	0.925039i	$-0.375968\pi$
$709$	20.2298			0.759745			0.379873	+	0.925039i	$0.375968\pi$
$710$	7.10664	+	12.3091i	0.266707	+	0.461951i
$711$	−2.73493	−	1.18857i	−0.102568	−	0.0445750i
$712$	3.78871	+	2.18741i	0.141988	+	0.0819767i
$713$	24.9727	+	43.2540i	0.935234	+	1.61987i
$714$	1.58601	+	30.2338i	0.0593550	+	1.13147i
$715$	−5.10492	+	8.84199i	−0.190913	+	0.330672i
$716$	−1.21808	+	0.703262i	−0.0455220	+	0.0262821i
$717$	18.2625	−	20.4652i	0.682025	−	0.764288i
$718$	3.14576	−	5.44862i	0.117399	−	0.203341i
$719$	−0.154148	+	0.266992i	−0.00574874	+	0.00995710i	−0.868885	−	0.495013i	$-0.835163\pi$
$719$	−0.154148	+	0.266992i	−0.00574874	+	0.00995710i	0.863137	+	0.504970i	$0.168497\pi$
$720$	0.340166	+	2.98065i	0.0126772	+	0.111082i
$721$	−8.13732	+	2.14200i	−0.303050	+	0.0797724i
$722$	−5.47291	+	3.15979i	−0.203681	+	0.117595i
$723$	30.4732	−	34.1487i	1.13331	−	1.27000i
$724$			10.1582i			0.377527i
$725$			1.72523i			0.0640734i
$726$	4.80371	+	14.5631i	0.178282	+	0.540489i
$727$	3.69340	−	2.13238i	0.136980	−	0.0790857i	−0.429944	−	0.902856i	$-0.641467\pi$
$727$	3.69340	−	2.13238i	0.136980	−	0.0790857i	0.566924	+	0.823770i	$0.308133\pi$
$728$	13.0950	−	12.9801i	0.485335	−	0.481076i
$729$	−9.02702	−	25.4463i	−0.334334	−	0.942455i
$730$	0.640987	−	1.11022i	0.0237240	−	0.0410911i
$731$	−21.4439	+	37.1419i	−0.793130	+	1.37374i
$732$	−6.33533	−	1.31713i	−0.234160	−	0.0486826i
$733$	2.60873	−	1.50615i	0.0963558	−	0.0556310i	−0.451048	−	0.892500i	$-0.648950\pi$
$733$	2.60873	−	1.50615i	0.0963558	−	0.0556310i	0.547404	+	0.836869i	$0.315616\pi$
$734$	12.1749	−	21.0875i	0.449382	−	0.778353i
$735$	−11.8483	−	2.57243i	−0.437032	−	0.0948856i
$736$	−3.18129	−	5.51016i	−0.117264	−	0.203107i
$737$	15.9228	+	9.19303i	0.586524	+	0.338630i
$738$	2.25761	+	3.04980i	0.0831038	+	0.112265i
$739$	9.01920	+	15.6217i	0.331776	+	0.574654i	0.982860	−	0.184352i	$-0.0590187\pi$
$739$	9.01920	+	15.6217i	0.331776	+	0.574654i	−0.651084	+	0.759006i	$0.725685\pi$
$740$	−5.51903			−0.202884
$741$	40.8195	−	13.4645i	1.49954	−	0.494630i
$742$	−4.36138	−	16.5686i	−0.160111	−	0.608252i
$743$	1.82145	+	1.05161i	0.0668225	+	0.0385800i	0.533039	−	0.846091i	$-0.321050\pi$
$743$	1.82145	+	1.05161i	0.0668225	+	0.0385800i	−0.466217	+	0.884671i	$0.654383\pi$
$744$	−2.76754	+	13.3117i	−0.101463	+	0.488030i
$745$	7.44381	+	4.29769i	0.272720	+	0.157455i
$746$	−1.88581	+	1.08878i	−0.0690445	+	0.0398629i
$747$	4.03752	+	35.3782i	0.147725	+	1.29442i
$748$			9.67903i			0.353900i
$749$	29.6590	+	29.9215i	1.08371	+	1.09331i
$750$	−1.69579	−	0.352560i	−0.0619215	−	0.0128737i
$751$	3.40069	+	5.89017i	0.124093	+	0.214935i	0.921378	−	0.388668i	$-0.127065\pi$
$751$	3.40069	+	5.89017i	0.124093	+	0.214935i	−0.797285	+	0.603603i	$0.793731\pi$
$752$	5.39759			0.196830
$753$	−9.86858	+	47.4672i	−0.359631	+	1.72980i
$754$			12.0230i			0.437853i
$755$	−2.60771			−0.0949044
$756$	10.6060	−	8.74714i	0.385737	−	0.318130i
$757$	−26.9017			−0.977761			−0.488880	−	0.872351i	$-0.662595\pi$
$757$	−26.9017			−0.977761			−0.488880	+	0.872351i	$0.662595\pi$
$758$			22.5954i			0.820700i
$759$	3.28638	−	15.8073i	0.119288	−	0.573768i
$760$	−3.56096			−0.129170
$761$	2.08165	+	3.60553i	0.0754598	+	0.130700i	0.901286	−	0.433224i	$-0.142624\pi$
$761$	2.08165	+	3.60553i	0.0754598	+	0.130700i	−0.825826	+	0.563925i	$0.809291\pi$
$762$	1.55060	+	0.322374i	0.0561722	+	0.0116784i
$763$	−4.86072	−	18.4655i	−0.175970	−	0.668497i
$764$		−	17.1243i		−	0.619536i
$765$	15.9302	−	11.7923i	0.575956	−	0.426351i
$766$	5.65138	−	3.26282i	0.204193	−	0.117891i
$767$	9.01241	+	5.20332i	0.325419	+	0.187881i
$768$	0.352560	−	1.69579i	0.0127219	−	0.0611915i
$769$	−15.1341	−	8.73768i	−0.545750	−	0.315089i	0.201656	−	0.979456i	$-0.435368\pi$
$769$	−15.1341	−	8.73768i	−0.545750	−	0.315089i	−0.747406	+	0.664368i	$0.768701\pi$
$770$	−3.73962	−	1.01971i	−0.134766	−	0.0367478i
$771$	−23.7362	+	7.82948i	−0.854839	+	0.281972i
$772$	−1.93306			−0.0695722
$773$	9.80159	+	16.9768i	0.352539	+	0.610615i	0.986694	−	0.162591i	$-0.0519852\pi$
$773$	9.80159	+	16.9768i	0.352539	+	0.610615i	−0.634155	+	0.773206i	$0.718652\pi$
$774$	19.3493	−	2.20823i	0.695495	−	0.0793730i
$775$	−6.79817	−	3.92493i	−0.244197	−	0.140987i
$776$	5.22463	+	9.04933i	0.187553	+	0.324852i
$777$	13.7757	+	21.2104i	0.494202	+	0.760920i
$778$	−17.3402	+	30.0342i	−0.621677	+	1.07678i
$779$	−3.90057	+	2.25200i	−0.139753	+	0.0806862i
$780$	−11.8179	−	2.45697i	−0.423148	−	0.0879738i
$781$	10.4116	−	18.0334i	0.372555	−	0.645284i
$782$	−21.0176	+	36.4036i	−0.751589	+	1.30179i
$783$	−0.817774	+	8.92717i	−0.0292248	+	0.319031i
$784$	6.03110	+	3.55329i	0.215396	+	0.126903i
$785$	6.74663	−	3.89517i	0.240798	−	0.139025i
$786$	−5.37075	−	16.2822i	−0.191568	−	0.580767i
$787$		−	29.0422i		−	1.03524i	−0.855610	−	0.517620i	$-0.826818\pi$
$787$		−	29.0422i		−	1.03524i	0.855610	−	0.517620i	$-0.173182\pi$
$788$			22.0136i			0.784200i
$789$	−1.85835	+	2.08250i	−0.0661590	+	0.0741389i
$790$	−0.860839	+	0.497005i	−0.0306273	+	0.0176827i
$791$	11.6720	+	11.7754i	0.415010	+	0.418684i
$792$	3.53258	−	2.61499i	0.125525	−	0.0929196i
$793$	13.0177	−	22.5473i	0.462273	−	0.800680i
$794$	13.7650	−	23.8417i	0.488501	−	0.846109i
$795$	−7.46787	+	8.36861i	−0.264858	+	0.296804i
$796$	−23.0430	+	13.3039i	−0.816739	+	0.471544i
$797$	−14.0345	+	24.3085i	−0.497129	+	0.861052i	−0.999995	−	0.00331218i	$-0.998946\pi$
$797$	−14.0345	+	24.3085i	−0.497129	+	0.861052i	0.502866	+	0.864365i	$0.332279\pi$
$798$	8.88831	+	13.6853i	0.314643	+	0.484454i
$799$	−17.8300	−	30.8824i	−0.630778	−	1.09254i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−10.5487	+	7.80870i	−0.372721	+	0.275907i
$802$	−7.03938	−	12.1926i	−0.248569	−	0.430534i
$803$	−1.87815			−0.0662785
$804$	−4.42456	+	21.2818i	−0.156042	+	0.750552i
$805$	−11.8507	−	11.9556i	−0.417684	−	0.421381i
$806$	−47.3762	−	27.3526i	−1.66875	−	0.963455i
$807$	6.78565	−	2.23827i	0.238866	−	0.0787910i
$808$	−1.76640	−	1.01983i	−0.0621417	−	0.0358775i
$809$	−2.46533	+	1.42336i	−0.0866764	+	0.0500427i	−0.542712	−	0.839919i	$-0.682602\pi$
$809$	−2.46533	+	1.42336i	−0.0866764	+	0.0500427i	0.456035	+	0.889962i	$0.349269\pi$
$810$	−8.60772	−	2.62813i	−0.302445	−	0.0923432i
$811$			5.05522i			0.177513i	0.996053	+	0.0887564i	$0.0282893\pi$
$811$			5.05522i			0.177513i	−0.996053	+	0.0887564i	$0.971711\pi$
$812$	−4.41416	+	1.16195i	−0.154907	+	0.0407764i
$813$	−5.36219	+	6.00895i	−0.188060	+	0.210743i
$814$	4.04282	+	7.00236i	0.141701	+	0.245433i
$815$	8.29410			0.290530
$816$	−10.8671	+	3.58455i	−0.380424	+	0.125484i
$817$			23.1164i			0.808740i
$818$	32.7642			1.14557
$819$	20.0554	+	51.5506i	0.700793	+	1.80132i
$820$	1.26483			0.0441696
$821$		−	39.0748i		−	1.36372i	−0.731482	−	0.681861i	$-0.761171\pi$
$821$		−	39.0748i		−	1.36372i	0.731482	−	0.681861i	$-0.238829\pi$
$822$	−15.5701	−	13.8943i	−0.543071	−	0.484619i
$823$	−32.7968			−1.14322			−0.571612	−	0.820524i	$-0.693682\pi$
$823$	−32.7968			−1.14322			−0.571612	+	0.820524i	$0.693682\pi$
$824$	−1.59020	−	2.75430i	−0.0553971	−	0.0959506i
$825$	0.794889	+	2.40982i	0.0276745	+	0.0838992i
$826$	−1.03936	+	3.81169i	−0.0361641	+	0.132626i
$827$		−	53.3096i		−	1.85376i	−0.375361	−	0.926879i	$-0.622481\pi$
$827$		−	53.3096i		−	1.85376i	0.375361	−	0.926879i	$-0.377519\pi$
$828$	18.9647	−	2.16433i	0.659068	−	0.0752158i
$829$	39.1781	−	22.6195i	1.36071	−	0.785607i	0.370992	−	0.928636i	$-0.379018\pi$
$829$	39.1781	−	22.6195i	1.36071	−	0.785607i	0.989718	+	0.143029i	$0.0456844\pi$
$830$	10.2791	+	5.93463i	0.356792	+	0.205994i
$831$	30.2712	+	27.0130i	1.05010	+	0.937071i
$832$	6.03529	+	3.48448i	0.209236	+	0.120803i
$833$	0.407548	−	46.2446i	0.0141207	−	1.60228i
$834$	23.2905	+	20.7836i	0.806483	+	0.719679i
$835$	−13.7699			−0.476528
$836$	2.60849	+	4.51803i	0.0902164	+	0.156259i
$837$	−33.3166	−	23.5319i	−1.15159	−	0.813380i
$838$	10.0677	+	5.81259i	0.347783	+	0.200793i
$839$	−19.1888	−	33.2360i	−0.662472	−	1.14744i	−0.979964	−	0.199175i	$-0.936174\pi$
$839$	−19.1888	−	33.2360i	−0.662472	−	1.14744i	0.317492	−	0.948261i	$-0.397159\pi$
$840$	−0.240063	−	4.57628i	−0.00828298	−	0.157897i
$841$	−13.0118	+	22.5371i	−0.448683	+	0.777141i
$842$	19.8333	−	11.4508i	0.683500	−	0.394619i
$843$	11.0059	+	33.3659i	0.379063	+	1.14918i
$844$	3.44298	−	5.96341i	0.118512	−	0.205269i
$845$	17.7832	−	30.8014i	0.611760	−	1.05960i
$846$	−6.45408	+	14.8509i	−0.221896	+	0.510586i
$847$	−5.96296	−	22.6528i	−0.204890	−	0.778361i
$848$	5.60809	−	3.23783i	0.192583	−	0.111188i
$849$	−9.74006	−	2.02499i	−0.334278	−	0.0694974i
$850$		−	6.60663i		−	0.226606i
$851$			35.1153i			1.20374i
$852$	24.1027	+	5.01103i	0.825746	+	0.171675i
$853$	−43.3554	+	25.0313i	−1.48446	+	0.857054i	−0.999844	−	0.0176720i	$-0.994375\pi$
$853$	−43.3554	+	25.0313i	−1.48446	+	0.857054i	−0.484618	+	0.874726i	$0.661041\pi$
$854$	9.53614	+	2.60029i	0.326320	+	0.0889801i
$855$	4.25796	−	9.79763i	0.145619	−	0.335072i
$856$	−7.96185	+	13.7903i	−0.272130	+	0.471344i
$857$	15.7216	−	27.2305i	0.537038	−	0.930178i	−0.462023	−	0.886868i	$-0.652876\pi$
$857$	15.7216	−	27.2305i	0.537038	−	0.930178i	0.999062	−	0.0433100i	$-0.0137903\pi$
$858$	5.53955	+	16.7939i	0.189117	+	0.573336i
$859$	−26.1528	+	15.0993i	−0.892323	+	0.515183i	−0.874702	−	0.484662i	$-0.838943\pi$
$859$	−26.1528	+	15.0993i	−0.892323	+	0.515183i	−0.0176215	+	0.999845i	$0.505609\pi$
$860$	3.24581	−	5.62191i	0.110681	−	0.191705i
$861$	−3.15706	−	4.86091i	−0.107592	−	0.165659i
$862$	4.81745	+	8.34407i	0.164083	+	0.284200i
$863$	13.8288	+	7.98404i	0.470736	+	0.271780i	0.716548	−	0.697538i	$-0.245721\pi$
$863$	13.8288	+	7.98404i	0.470736	+	0.271780i	−0.245812	+	0.969318i	$0.579054\pi$
$864$	4.24423	+	2.99775i	0.144392	+	0.101985i
$865$	−5.81971	−	10.0800i	−0.197876	−	0.342731i
$866$	37.8458			1.28605
$867$	34.4371	+	30.7306i	1.16955	+	1.04366i
$868$	5.46369	−	20.0372i	0.185450	−	0.680107i
$869$	1.26117	+	0.728136i	0.0427822	+	0.0247003i
$870$	2.22954	+	1.98957i	0.0755886	+	0.0674527i
$871$	−75.7418	−	43.7295i	−2.56641	−	1.48172i
$872$	6.25017	−	3.60853i	0.211657	−	0.122200i
$873$	−31.1456	+	3.55448i	−1.05412	+	0.120301i
$874$			22.6569i			0.766382i
$875$	2.55256	+	0.696025i	0.0862922	+	0.0235299i
$876$	−0.695559	−	2.10869i	−0.0235008	−	0.0712460i
$877$	−25.2758	−	43.7790i	−0.853503	−	1.47831i	−0.878027	−	0.478611i	$-0.841140\pi$
$877$	−25.2758	−	43.7790i	−0.853503	−	1.47831i	0.0245242	−	0.999699i	$-0.492193\pi$
$878$	−32.3974			−1.09336
$879$	−27.8816	−	24.8806i	−0.940422	−	0.839201i
$880$		−	1.46505i		−	0.0493867i
$881$	−7.58608			−0.255581			−0.127791	−	0.991801i	$-0.540789\pi$
$881$	−7.58608			−0.255581			−0.127791	+	0.991801i	$0.540789\pi$
$882$	−16.9881	+	12.3452i	−0.572020	+	0.415684i
$883$	−19.9066			−0.669910			−0.334955	−	0.942234i	$-0.608721\pi$
$883$	−19.9066			−0.669910			−0.334955	+	0.942234i	$0.608721\pi$
$884$		−	46.0413i		−	1.54854i
$885$	2.45627	−	0.810210i	0.0825665	−	0.0272349i
$886$	21.9018			0.735806
$887$	−17.5255	−	30.3551i	−0.588449	−	1.01922i	−0.994436	−	0.105345i	$-0.966405\pi$
$887$	−17.5255	−	30.3551i	−0.588449	−	1.01922i	0.405987	−	0.913879i	$-0.366928\pi$
$888$	−6.36466	+	7.13233i	−0.213584	+	0.239345i
$889$	−2.33401	−	0.636431i	−0.0782801	−	0.0213452i
$890$			4.37482i			0.146644i
$891$	2.97087	+	12.8464i	0.0995278	+	0.430370i
$892$	−11.6938	+	6.75140i	−0.391536	+	0.226053i
$893$	−16.6455	−	9.61030i	−0.557021	−	0.321596i
$894$	14.1383	−	4.66358i	0.472856	−	0.155974i
$895$	−1.21808	−	0.703262i	−0.0407161	−	0.0235074i
$896$	−0.696025	+	2.55256i	−0.0232526	+	0.0852750i
$897$	−15.6327	+	75.1923i	−0.521961	+	2.51060i
$898$	25.8522			0.862700
$899$	6.77139	+	11.7284i	0.225839	+	0.391164i
$900$	−2.41124	+	1.78492i	−0.0803746	+	0.0594973i
$901$	−37.0506	−	21.3912i	−1.23433	−	0.712643i
$902$	−0.926515	−	1.60477i	−0.0308496	−	0.0534330i
$903$	−29.7075	+	1.55840i	−0.988603	+	0.0518603i
$904$	−3.13332	+	5.42707i	−0.104213	+	0.180502i
$905$	−8.79728	+	5.07911i	−0.292431	+	0.168835i
$906$	−3.00727	+	3.36999i	−0.0999098	+	0.111960i
$907$	−2.06535	+	3.57729i	−0.0685789	+	0.118782i	−0.898276	−	0.439432i	$-0.855180\pi$
$907$	−2.06535	+	3.57729i	−0.0685789	+	0.118782i	0.829697	+	0.558214i	$0.188513\pi$
$908$	10.7490	−	18.6179i	0.356719	−	0.617856i
$909$	4.91811	−	3.64063i	0.163123	−	0.120752i
$910$	17.7887	+	4.85057i	0.589688	+	0.160795i
$911$	−22.0418	+	12.7258i	−0.730276	+	0.421625i	−0.818523	−	0.574474i	$-0.805207\pi$
$911$	−22.0418	+	12.7258i	−0.730276	+	0.421625i	0.0882472	+	0.996099i	$0.471873\pi$
$912$	−4.10657	+	4.60189i	−0.135982	+	0.152384i
$913$		−	17.3890i		−	0.575493i
$914$			22.2463i			0.735841i
$915$	−2.02699	−	6.14512i	−0.0670103	−	0.203151i
$916$	−19.4936	+	11.2546i	−0.644086	+	0.371863i
$917$	6.66684	+	25.3268i	0.220158	+	0.836366i
$918$	3.13160	−	34.1859i	0.103358	−	1.12830i
$919$	3.41703	−	5.91848i	0.112718	−	0.195232i	−0.804148	−	0.594430i	$-0.797378\pi$
$919$	3.41703	−	5.91848i	0.112718	−	0.195232i	0.916865	+	0.399197i	$0.130711\pi$
$920$	3.18129	−	5.51016i	0.104884	−	0.181665i
$921$	−8.85703	−	1.84140i	−0.291849	−	0.0606763i
$922$	12.2173	−	7.05369i	0.402357	−	0.232301i
$923$	−49.5259	+	85.7813i	−1.63016	+	2.82353i
$924$	−5.63039	+	3.65682i	−0.185226	+	0.120301i
$925$	−2.75951	−	4.77962i	−0.0907323	−	0.157153i
$926$	−5.77194	−	3.33243i	−0.189678	−	0.109510i
$927$	9.47964	−	1.08186i	0.311352	−	0.0355329i
$928$	−0.862614	−	1.49409i	−0.0283167	−	0.0490460i
$929$	36.1564			1.18625			0.593126	−	0.805110i	$-0.297894\pi$
$929$	36.1564			1.18625			0.593126	+	0.805110i	$0.297894\pi$
$930$	−12.9120	+	4.25909i	−0.423402	+	0.139661i
$931$	−12.2726	−	21.6962i	−0.402219	−	0.711063i
$932$	15.4408	+	8.91477i	0.505782	+	0.292013i
$933$	−4.66637	+	22.4449i	−0.152770	+	0.734814i
$934$	3.04350	+	1.75717i	0.0995864	+	0.0574962i
$935$	−8.38228	+	4.83951i	−0.274130	+	0.158269i
$936$	−16.8038	+	12.4390i	−0.549250	+	0.406582i
$937$		−	25.1125i		−	0.820391i	−0.911998	−	0.410195i	$-0.865461\pi$
$937$		−	25.1125i		−	0.820391i	0.911998	−	0.410195i	$-0.134539\pi$
$938$	8.73498	−	32.0341i	0.285207	−	1.04595i
$939$	52.4930	+	10.9135i	1.71305	+	0.356147i
$940$	2.69880	+	4.67445i	0.0880250	+	0.152464i
$941$	2.72207			0.0887370			0.0443685	−	0.999015i	$-0.485872\pi$
$941$	2.72207			0.0887370			0.0443685	+	0.999015i	$0.485872\pi$
$942$	2.74656	−	13.2108i	0.0894878	−	0.430430i
$943$		−	8.04757i		−	0.262065i
$944$	−1.49328			−0.0486023
$945$	12.8783	+	4.81151i	0.418930	+	0.156518i
$946$	−9.51053			−0.309214
$947$		−	4.50181i		−	0.146289i	−0.997321	−	0.0731446i	$-0.976697\pi$
$947$		−	4.50181i		−	0.146289i	0.997321	−	0.0731446i	$-0.0233034\pi$
$948$	−0.350448	+	1.68563i	−0.0113820	+	0.0547468i
$949$	8.93402			0.290010
$950$	−1.78048	−	3.08388i	−0.0577664	−	0.100054i
$951$	−25.6878	−	5.34057i	−0.832984	−	0.173180i
$952$	16.9037	−	4.44959i	0.547851	−	0.144212i
$953$			18.8442i			0.610423i	0.952285	+	0.305211i	$0.0987271\pi$
$953$			18.8442i			0.610423i	−0.952285	+	0.305211i	$0.901273\pi$
$954$	2.20280	+	19.3017i	0.0713182	+	0.624916i
$955$	14.8301	−	8.56216i	0.479890	−	0.277065i
$956$	−13.7144	−	7.91804i	−0.443557	−	0.256088i
$957$	0.891109	−	4.28618i	0.0288055	−	0.138552i
$958$	0.866868	+	0.500486i	0.0280072	+	0.0161700i
$959$	22.4407	+	22.6393i	0.724647	+	0.731061i
$960$	1.64488	−	0.542569i	0.0530882	−	0.0175113i
$961$	−30.6202			−0.987747
$962$	−19.2309	−	33.3089i	−0.620030	−	1.07392i
$963$	−28.4225	−	38.3958i	−0.915902	−	1.23729i
$964$	−22.8842	−	13.2122i	−0.737050	−	0.425536i
$965$	−0.966528	−	1.67408i	−0.0311136	−	0.0538904i
$966$	−29.1170	+	1.52742i	−0.936824	+	0.0491441i
$967$	−17.7127	+	30.6793i	−0.569602	+	0.986579i	0.427003	+	0.904250i	$0.359569\pi$
$967$	−17.7127	+	30.6793i	−0.569602	+	0.986579i	−0.996605	+	0.0823294i	$0.973764\pi$
$968$	7.66748	−	4.42682i	0.246442	−	0.142283i
$969$	39.8951	+	8.29430i	1.28161	+	0.266451i
$970$	−5.22463	+	9.04933i	−0.167753	+	0.290556i
$971$	−0.536311	+	0.928919i	−0.0172111	+	0.0298104i	−0.874503	−	0.485021i	$-0.838812\pi$
$971$	−0.536311	+	0.928919i	−0.0172111	+	0.0298104i	0.857292	+	0.514831i	$0.172145\pi$
$972$	−13.3230	+	8.09309i	−0.427335	+	0.259586i
$973$	−33.5677	−	33.8648i	−1.07613	−	1.08566i
$974$	−25.0723	+	14.4755i	−0.803368	+	0.463825i
$975$	−3.78114	−	11.4631i	−0.121093	−	0.367112i
$976$			3.73592i			0.119584i
$977$		−	7.75308i		−	0.248043i	−0.992280	−	0.124021i	$-0.960421\pi$
$977$		−	7.75308i		−	0.248043i	0.992280	−	0.124021i	$-0.0395792\pi$
$978$	9.56492	−	10.7186i	0.305852	−	0.342743i
$979$	5.55063	−	3.20466i	0.177399	−	0.102421i
$980$	−0.0616877	+	6.99973i	−0.00197054	+	0.223598i
$981$	2.45500	+	21.5116i	0.0783821	+	0.686812i
$982$	17.6990	−	30.6555i	0.564797	−	0.978257i
$983$	−10.7940	+	18.6958i	−0.344275	+	0.596302i	−0.985222	−	0.171283i	$-0.945209\pi$
$983$	−10.7940	+	18.6958i	−0.344275	+	0.596302i	0.640947	+	0.767585i	$0.278542\pi$
$984$	1.45862	−	1.63456i	0.0464992	−	0.0521077i
$985$	−19.0643	+	11.0068i	−0.607439	+	0.350705i
$986$	−5.69898	+	9.87092i	−0.181492	+	0.314354i
$987$	11.2283	−	22.0395i	0.357400	−	0.701525i
$988$	−12.4081	−	21.4914i	−0.394754	−	0.683733i
$989$	−35.7699	−	20.6518i	−1.13742	−	0.656687i
$990$	4.03093	+	1.75181i	0.128112	+	0.0556761i
$991$	−3.97525	−	6.88534i	−0.126278	−	0.218720i	0.795954	−	0.605357i	$-0.206970\pi$
$991$	−3.97525	−	6.88534i	−0.126278	−	0.218720i	−0.922232	+	0.386637i	$0.873636\pi$
$992$	7.84985			0.249233
$993$	0.459462	−	2.20998i	0.0145806	−	0.0701317i
$994$	−36.2802	−	9.89280i	−1.15074	−	0.313780i
$995$	−23.0430	−	13.3039i	−0.730513	−	0.421762i
$996$	19.5235	−	6.43990i	0.618625	−	0.204056i
$997$	49.5700	+	28.6192i	1.56990	+	0.906380i	0.996180	+	0.0873264i	$0.0278323\pi$
$997$	49.5700	+	28.6192i	1.56990	+	0.906380i	0.573717	+	0.819054i	$0.305501\pi$
$998$	−14.4080	+	8.31844i	−0.456076	+	0.263316i
$999$	−12.0135	−	26.0401i	−0.380090	−	0.823873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.131.4	yes	28
3.2	odd	2		1890.2.bk.b.341.5		28
7.3	odd	6		630.2.t.b.311.14	✓	28
9.2	odd	6		630.2.t.b.551.14	yes	28
9.7	even	3		1890.2.t.b.1601.3		28
21.17	even	6		1890.2.t.b.1151.3		28
63.38	even	6	inner	630.2.bk.b.101.11	yes	28
63.52	odd	6		1890.2.bk.b.521.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.14	✓	28	7.3	odd	6
630.2.t.b.551.14	yes	28	9.2	odd	6
630.2.bk.b.101.11	yes	28	63.38	even	6	inner
630.2.bk.b.131.4	yes	28	1.1	even	1	trivial
1890.2.t.b.1151.3		28	21.17	even	6
1890.2.t.b.1601.3		28	9.7	even	3
1890.2.bk.b.341.5		28	3.2	odd	2
1890.2.bk.b.521.5		28	63.52	odd	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.352560 - 1.69579i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.69579 - 0.352560i) q^{6} +(2.55256 + 0.696025i) q^{7} +1.00000i q^{8} +(-2.75140 - 1.19573i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.352560 - 1.69579i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.69579 - 0.352560i) q^{6} +(2.55256 + 0.696025i) q^{7} +1.00000i q^{8} +(-2.75140 - 1.19573i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(1.26877 + 0.732523i) q^{11} +(-0.352560 + 1.69579i) q^{12} +(-6.03529 - 3.48448i) q^{13} +(0.696025 - 2.55256i) q^{14} +(-1.64488 + 0.542569i) q^{15} +1.00000 q^{16} +(-3.30332 - 5.72151i) q^{17} +(-1.19573 + 2.75140i) q^{18} +(-3.08388 - 1.78048i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.08024 - 4.08321i) q^{21} +(0.732523 - 1.26877i) q^{22} +(5.51016 - 3.18129i) q^{23} +(1.69579 + 0.352560i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.48448 + 6.03529i) q^{26} +(-2.99775 + 4.24423i) q^{27} +(-2.55256 - 0.696025i) q^{28} +(1.49409 - 0.862614i) q^{29} +(0.542569 + 1.64488i) q^{30} +7.84985i q^{31} -1.00000i q^{32} +(1.68952 - 1.89330i) q^{33} +(-5.72151 + 3.30332i) q^{34} +(-0.673503 - 2.55859i) q^{35} +(2.75140 + 1.19573i) q^{36} +(-2.75951 + 4.77962i) q^{37} +(-1.78048 + 3.08388i) q^{38} +(-8.03674 + 9.00610i) q^{39} +(0.866025 - 0.500000i) q^{40} +(0.632413 - 1.09537i) q^{41} +(-4.08321 - 2.08024i) q^{42} +(-3.24581 - 5.62191i) q^{43} +(-1.26877 - 0.732523i) q^{44} +(0.340166 + 2.98065i) q^{45} +(-3.18129 - 5.51016i) q^{46} +5.39759 q^{47} +(0.352560 - 1.69579i) q^{48} +(6.03110 + 3.55329i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-10.8671 + 3.58455i) q^{51} +(6.03529 + 3.48448i) q^{52} +(5.60809 - 3.23783i) q^{53} +(4.24423 + 2.99775i) q^{54} -1.46505i q^{55} +(-0.696025 + 2.55256i) q^{56} +(-4.10657 + 4.60189i) q^{57} +(-0.862614 - 1.49409i) q^{58} -1.49328 q^{59} +(1.64488 - 0.542569i) q^{60} +3.73592i q^{61} +7.84985 q^{62} +(-6.19085 - 4.96723i) q^{63} -1.00000 q^{64} +6.96896i q^{65} +(-1.89330 - 1.68952i) q^{66} +12.5498 q^{67} +(3.30332 + 5.72151i) q^{68} +(-3.45214 - 10.4657i) q^{69} +(-2.55859 + 0.673503i) q^{70} -14.2133i q^{71} +(1.19573 - 2.75140i) q^{72} +(-1.11022 + 0.640987i) q^{73} +(4.77962 + 2.75951i) q^{74} +(1.29232 + 1.15322i) q^{75} +(3.08388 + 1.78048i) q^{76} +(2.72875 + 2.75290i) q^{77} +(9.00610 + 8.03674i) q^{78} +0.994011 q^{79} +(-0.500000 - 0.866025i) q^{80} +(6.14044 + 6.57989i) q^{81} +(-1.09537 - 0.632413i) q^{82} +(-5.93463 - 10.2791i) q^{83} +(-2.08024 + 4.08321i) q^{84} +(-3.30332 + 5.72151i) q^{85} +(-5.62191 + 3.24581i) q^{86} +(-0.936056 - 2.83779i) q^{87} +(-0.732523 + 1.26877i) q^{88} +(2.18741 - 3.78871i) q^{89} +(2.98065 - 0.340166i) q^{90} +(-12.9801 - 13.0950i) q^{91} +(-5.51016 + 3.18129i) q^{92} +(13.3117 + 2.76754i) q^{93} -5.39759i q^{94} +3.56096i q^{95} +(-1.69579 - 0.352560i) q^{96} +(9.04933 - 5.22463i) q^{97} +(3.55329 - 6.03110i) q^{98} +(-2.61499 - 3.53258i) 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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