LMFDB - Embedded newform 630.2.t.b.311.14

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			311.14
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.64488 - 0.542569i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.69579 + 0.352560i) q^{6} +(-0.673503 + 2.55859i) q^{7} +1.00000i q^{8} +(2.41124 - 1.78492i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.64488 - 0.542569i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.69579 + 0.352560i) q^{6} +(-0.673503 + 2.55859i) q^{7} +1.00000i q^{8} +(2.41124 - 1.78492i) q^{9} +(-0.866025 - 0.500000i) q^{10} -1.46505i q^{11} +(1.29232 + 1.15322i) q^{12} +(6.03529 + 3.48448i) q^{13} +(-1.86257 + 1.87905i) q^{14} +(-1.64488 + 0.542569i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.30332 - 5.72151i) q^{17} +(2.98065 - 0.340166i) q^{18} +(-3.08388 + 1.78048i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.280383 + 4.57399i) q^{21} +(0.732523 - 1.26877i) q^{22} +6.36259i q^{23} +(0.542569 + 1.64488i) q^{24} +1.00000 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} +(-1.69579 - 0.352560i) q^{30} +(-6.79817 + 3.92493i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.794889 - 2.40982i) 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} -3.56096 q^{38} +(11.8179 + 2.45697i) q^{39} -1.00000i q^{40} +(-0.632413 + 1.09537i) q^{41} +(-2.04418 + 4.10138i) q^{42} +(-3.24581 - 5.62191i) q^{43} +(1.26877 - 0.732523i) q^{44} +(-2.41124 + 1.78492i) q^{45} +(-3.18129 + 5.51016i) q^{46} +(2.69880 - 4.67445i) q^{47} +(-0.352560 + 1.69579i) q^{48} +(-6.09279 - 3.44644i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.32923 - 11.2035i) q^{51} +6.96896i q^{52} +(-5.60809 - 3.23783i) q^{53} +(4.71824 - 2.17674i) q^{54} +1.46505i q^{55} +(-2.55859 - 0.673503i) q^{56} +(-4.10657 + 4.60189i) q^{57} +1.72523 q^{58} +(-0.746642 - 1.29322i) q^{59} +(-1.29232 - 1.15322i) q^{60} +(3.23540 + 1.86796i) q^{61} -7.84985 q^{62} +(2.94290 + 7.37152i) q^{63} -1.00000 q^{64} +(-6.03529 - 3.48448i) q^{65} +(0.516517 - 2.48441i) q^{66} +(-6.27490 - 10.8685i) q^{67} +6.60663 q^{68} +(3.45214 + 10.4657i) q^{69} +(1.86257 - 1.87905i) q^{70} -14.2133i q^{71} +(1.78492 + 2.41124i) q^{72} +(-1.11022 - 0.640987i) q^{73} -5.51903i q^{74} +(1.64488 - 0.542569i) q^{75} +(-3.08388 - 1.78048i) q^{76} +(3.74846 + 0.986714i) q^{77} +(9.00610 + 8.03674i) q^{78} +(-0.497005 + 0.860839i) q^{79} +(0.500000 - 0.866025i) q^{80} +(2.62813 - 8.60772i) q^{81} +(-1.09537 + 0.632413i) q^{82} +(5.93463 + 10.2791i) q^{83} +(-3.82100 + 2.52981i) q^{84} +(-3.30332 + 5.72151i) q^{85} -6.49162i q^{86} +(1.98957 - 2.22954i) q^{87} +1.46505 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} +(-9.05261 + 10.1445i) q^{93} +(4.67445 - 2.69880i) q^{94} +(3.08388 - 1.78048i) q^{95} +(-1.15322 + 1.29232i) 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} + 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.64488	−	0.542569i	0.949670	−	0.313252i
$3$	1.64488	−	0.542569i	0.949670	−	0.313252i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.69579	+	0.352560i	0.692303	+	0.143932i
$7$	−0.673503	+	2.55859i	−0.254560	+	0.967057i
$7$	−0.673503	+	2.55859i	−0.254560	+	0.967057i
$8$			1.00000i			0.353553i
$9$	2.41124	−	1.78492i	0.803746	−	0.594973i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	1.46505i		−	0.441728i	−0.975305	−	0.220864i	$-0.929112\pi$
$11$		−	1.46505i		−	0.441728i	0.975305	−	0.220864i	$-0.0708877\pi$
$12$	1.29232	+	1.15322i	0.373060	+	0.332906i
$13$	6.03529	+	3.48448i	1.67389	+	0.966420i	0.965428	+	0.260671i	$0.0839436\pi$
$13$	6.03529	+	3.48448i	1.67389	+	0.966420i	0.708461	+	0.705750i	$0.249390\pi$
$14$	−1.86257	+	1.87905i	−0.497792	+	0.502198i
$15$	−1.64488	+	0.542569i	−0.424705	+	0.140091i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.30332	−	5.72151i	0.801172	−	1.38767i	−0.117673	−	0.993052i	$-0.537544\pi$
$17$	3.30332	−	5.72151i	0.801172	−	1.38767i	0.918845	−	0.394618i	$-0.129123\pi$
$18$	2.98065	−	0.340166i	0.702546	−	0.0801778i
$19$	−3.08388	+	1.78048i	−0.707491	+	0.408470i	−0.810131	−	0.586249i	$-0.800604\pi$
$19$	−3.08388	+	1.78048i	−0.707491	+	0.408470i	0.102640	+	0.994719i	$0.467271\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	0.280383	+	4.57399i	0.0611845	+	0.998126i
$22$	0.732523	−	1.26877i	0.156175	−	0.270502i
$23$			6.36259i			1.32669i	0.748313	+	0.663346i	$0.230864\pi$
$23$			6.36259i			1.32669i	−0.748313	+	0.663346i	$0.769136\pi$
$24$	0.542569	+	1.64488i	0.110751	+	0.335759i
$25$	1.00000			0.200000
$26$	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	$0.282125\pi$
$30$	−1.69579	−	0.352560i	−0.309607	−	0.0643683i
$31$	−6.79817	+	3.92493i	−1.22099	+	0.704937i	−0.965128	−	0.261777i	$-0.915692\pi$
$31$	−6.79817	+	3.92493i	−1.22099	+	0.704937i	−0.255859	+	0.966714i	$0.582358\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.794889	−	2.40982i	−0.138372	−	0.419496i
$34$	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	0.544949	−	0.838469i	$-0.316549\pi$
$37$	−2.75951	−	4.77962i	−0.453661	−	0.785764i	−0.998610	+	0.0527049i	$0.983216\pi$
$38$	−3.56096			−0.577664
$39$	11.8179	+	2.45697i	1.89238	+	0.393431i
$40$		−	1.00000i		−	0.158114i
$41$	−0.632413	+	1.09537i	−0.0987663	+	0.171068i	−0.911174	−	0.412021i	$-0.864823\pi$
$41$	−0.632413	+	1.09537i	−0.0987663	+	0.171068i	0.812408	+	0.583089i	$0.198156\pi$
$42$	−2.04418	+	4.10138i	−0.315423	+	0.632857i
$43$	−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
$45$	−2.41124	+	1.78492i	−0.359446	+	0.266080i
$46$	−3.18129	+	5.51016i	−0.469056	+	0.812429i
$47$	2.69880	−	4.67445i	0.393660	−	0.681839i	−0.599269	−	0.800547i	$-0.704542\pi$
$47$	2.69880	−	4.67445i	0.393660	−	0.681839i	0.992929	+	0.118709i	$0.0378755\pi$
$48$	−0.352560	+	1.69579i	−0.0508876	+	0.244766i
$49$	−6.09279	−	3.44644i	−0.870398	−	0.492349i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	2.32923	−	11.2035i	0.326158	−	1.56880i
$52$			6.96896i			0.966420i
$53$	−5.60809	−	3.23783i	−0.770331	−	0.444751i	0.0626620	−	0.998035i	$-0.480041\pi$
$53$	−5.60809	−	3.23783i	−0.770331	−	0.444751i	−0.832993	+	0.553284i	$0.813374\pi$
$54$	4.71824	−	2.17674i	0.642071	−	0.296217i
$55$			1.46505i			0.197547i
$56$	−2.55859	−	0.673503i	−0.341906	−	0.0900007i
$57$	−4.10657	+	4.60189i	−0.543929	+	0.609535i
$58$	1.72523			0.226534
$59$	−0.746642	−	1.29322i	−0.0972045	−	0.168363i	0.813322	−	0.581814i	$-0.197657\pi$
$59$	−0.746642	−	1.29322i	−0.0972045	−	0.168363i	−0.910527	+	0.413451i	$0.864323\pi$
$60$	−1.29232	−	1.15322i	−0.166837	−	0.148880i
$61$	3.23540	+	1.86796i	0.414250	+	0.239167i	0.692614	−	0.721308i	$-0.256459\pi$
$61$	3.23540	+	1.86796i	0.414250	+	0.239167i	−0.278364	+	0.960476i	$0.589792\pi$
$62$	−7.84985			−0.996932
$63$	2.94290	+	7.37152i	0.370771	+	0.928724i
$64$	−1.00000			−0.125000
$65$	−6.03529	−	3.48448i	−0.748586	−	0.432196i
$66$	0.516517	−	2.48441i	0.0635788	−	0.305810i
$67$	−6.27490	−	10.8685i	−0.766602	−	1.32779i	−0.939396	−	0.342835i	$-0.888613\pi$
$67$	−6.27490	−	10.8685i	−0.766602	−	1.32779i	0.172794	−	0.984958i	$-0.444720\pi$
$68$	6.60663			0.801172
$69$	3.45214	+	10.4657i	0.415589	+	1.25992i
$70$	1.86257	−	1.87905i	0.222619	−	0.224590i
$71$		−	14.2133i		−	1.68681i	−0.537281	−	0.843403i	$-0.680549\pi$
$71$		−	14.2133i		−	1.68681i	0.537281	−	0.843403i	$-0.319451\pi$
$72$	1.78492	+	2.41124i	0.210355	+	0.284167i
$73$	−1.11022	−	0.640987i	−0.129942	−	0.0750218i	0.433620	−	0.901096i	$-0.357236\pi$
$73$	−1.11022	−	0.640987i	−0.129942	−	0.0750218i	−0.563562	+	0.826074i	$0.690569\pi$
$74$		−	5.51903i		−	0.641574i
$75$	1.64488	−	0.542569i	0.189934	−	0.0626505i
$76$	−3.08388	−	1.78048i	−0.353745	−	0.204235i
$77$	3.74846	+	0.986714i	0.427176	+	0.112447i
$78$	9.00610	+	8.03674i	1.01974	+	0.909982i
$79$	−0.497005	+	0.860839i	−0.0559175	+	0.0968519i	−0.892629	−	0.450792i	$-0.851142\pi$
$79$	−0.497005	+	0.860839i	−0.0559175	+	0.0968519i	0.836712	+	0.547644i	$0.184475\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	2.62813	−	8.60772i	0.292015	−	0.956414i
$82$	−1.09537	+	0.632413i	−0.120964	+	0.0698383i
$83$	5.93463	+	10.2791i	0.651411	+	1.12828i	0.982781	+	0.184776i	$0.0591559\pi$
$83$	5.93463	+	10.2791i	0.651411	+	1.12828i	−0.331370	+	0.943501i	$0.607511\pi$
$84$	−3.82100	+	2.52981i	−0.416905	+	0.276025i
$85$	−3.30332	+	5.72151i	−0.358295	+	0.620585i
$86$		−	6.49162i		−	0.700009i
$87$	1.98957	−	2.22954i	0.213304	−	0.239032i
$88$	1.46505			0.156175
$89$	−2.18741	−	3.78871i	−0.231865	−	0.401602i	0.726492	−	0.687175i	$-0.241149\pi$
$89$	−2.18741	−	3.78871i	−0.231865	−	0.401602i	−0.958357	+	0.285573i	$0.907816\pi$
$90$	−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
$93$	−9.05261	+	10.1445i	−0.938712	+	1.05194i
$94$	4.67445	−	2.69880i	0.482133	−	0.278360i
$95$	3.08388	−	1.78048i	0.316400	−	0.182673i
$96$	−1.15322	+	1.29232i	−0.117700	+	0.131897i
$97$	−9.04933	+	5.22463i	−0.918820	+	0.530481i	−0.883259	−	0.468886i	$-0.844655\pi$
$97$	−9.04933	+	5.22463i	−0.918820	+	0.530481i	−0.0355618	+	0.999367i	$0.511322\pi$
$98$	−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
$101$	−2.03966			−0.202954			−0.101477	−	0.994838i	$-0.532357\pi$
$101$	−2.03966			−0.202954			−0.101477	+	0.994838i	$0.532357\pi$
$102$	7.61890	−	8.53786i	0.754384	−	0.845374i
$103$			3.18039i			0.313373i	0.987648	+	0.156687i	$0.0500813\pi$
$103$			3.18039i			0.313373i	−0.987648	+	0.156687i	$0.949919\pi$
$104$	−3.48448	+	6.03529i	−0.341681	+	0.591809i
$105$	−0.280383	−	4.57399i	−0.0273626	−	0.446376i
$106$	−3.23783	−	5.60809i	−0.314486	−	0.544706i
$107$	−13.7903	+	7.96185i	−1.33316	+	0.769701i	−0.985783	−	0.168024i	$-0.946261\pi$
$107$	−13.7903	+	7.96185i	−1.33316	+	0.769701i	−0.347379	+	0.937725i	$0.612928\pi$
$108$	5.17449	+	0.474009i	0.497915	+	0.0456115i
$109$	−3.60853	+	6.25017i	−0.345635	+	0.598657i	−0.985469	−	0.169856i	$-0.945670\pi$
$109$	−3.60853	+	6.25017i	−0.345635	+	0.598657i	0.639834	+	0.768513i	$0.279003\pi$
$110$	−0.732523	+	1.26877i	−0.0698434	+	0.120972i
$111$	−7.13233	−	6.36466i	−0.676971	−	0.604106i
$112$	−1.87905	−	1.86257i	−0.177554	−	0.175996i
$113$	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	$0.571428\pi$
$114$	−5.85734	+	1.93207i	−0.548590	+	0.180955i
$115$		−	6.36259i		−	0.593314i
$116$	1.49409	+	0.862614i	0.138723	+	0.0800917i
$117$	20.7720	−	2.37060i	1.92038	−	0.219162i
$118$		−	1.49328i		−	0.137468i
$119$	12.4142	+	12.3053i	1.13801	+	1.12802i
$120$	−0.542569	−	1.64488i	−0.0495295	−	0.150156i
$121$	8.85364			0.804876
$122$	1.86796	+	3.23540i	0.169117	+	0.292919i
$123$	−0.445927	+	2.14488i	−0.0402079	+	0.193397i
$124$	−6.79817	−	3.92493i	−0.610494	−	0.352469i
$125$	−1.00000			−0.0894427
$126$	−1.13713	+	7.85538i	−0.101304	+	0.699812i
$127$	−0.914380			−0.0811381			−0.0405691	−	0.999177i	$-0.512917\pi$
$127$	−0.914380			−0.0811381			−0.0405691	+	0.999177i	$0.512917\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−8.38923	−	7.48627i	−0.738630	−	0.659129i
$130$	−3.48448	−	6.03529i	−0.305609	−	0.529330i
$131$	9.89874			0.864857			0.432429	−	0.901668i	$-0.357657\pi$
$131$	9.89874			0.864857			0.432429	+	0.901668i	$0.357657\pi$
$132$	1.68952	−	1.89330i	0.147054	−	0.164791i
$133$	−2.47852	−	9.08955i	−0.214915	−	0.788164i
$134$		−	12.5498i		−	1.08414i
$135$	−2.99775	+	4.24423i	−0.258005	+	0.365285i
$136$	5.72151	+	3.30332i	0.490616	+	0.283257i
$137$		−	12.0482i		−	1.02935i	−0.857385	−	0.514675i	$-0.827912\pi$
$137$		−	12.0482i		−	1.02935i	0.857385	−	0.514675i	$-0.172088\pi$
$138$	−2.24319	+	10.7896i	−0.190953	+	0.918473i
$139$	15.6077	+	9.01113i	1.32383	+	0.764314i	0.984338	−	0.176294i	$-0.0564110\pi$
$139$	15.6077	+	9.01113i	1.32383	+	0.764314i	0.339494	+	0.940608i	$0.389744\pi$
$140$	2.55256	−	0.696025i	0.215730	−	0.0588248i
$141$	1.90297	−	9.15318i	0.160259	−	0.770837i
$142$	7.10664	−	12.3091i	0.596376	−	1.03295i
$143$	5.10492	−	8.84199i	0.426895	−	0.739404i
$144$	0.340166	+	2.98065i	0.0283471	+	0.248388i
$145$	−1.49409	+	0.862614i	−0.124078	+	0.0716362i
$146$	−0.640987	−	1.11022i	−0.0530484	−	0.0918826i
$147$	−11.8918	−	2.36321i	−0.980820	−	0.194915i
$148$	2.75951	−	4.77962i	0.226831	−	0.392882i
$149$		−	8.59537i		−	0.704160i	−0.935970	−	0.352080i	$-0.885474\pi$
$149$		−	8.59537i		−	0.704160i	0.935970	−	0.352080i	$-0.114526\pi$
$150$	1.69579	+	0.352560i	0.138461	+	0.0287864i
$151$	−2.60771			−0.212213			−0.106106	−	0.994355i	$-0.533838\pi$
$151$	−2.60771			−0.212213			−0.106106	+	0.994355i	$0.533838\pi$
$152$	−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
$156$	3.78114	+	11.4631i	0.302733	+	0.917780i
$157$	−6.74663	+	3.89517i	−0.538440	+	0.310868i	−0.744446	−	0.667682i	$-0.767287\pi$
$157$	−6.74663	+	3.89517i	−0.538440	+	0.310868i	0.206006	+	0.978551i	$0.433953\pi$
$158$	−0.860839	+	0.497005i	−0.0684847	+	0.0395396i
$159$	−10.9814	−	2.28306i	−0.870879	−	0.181058i
$160$	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	0.656654	−	0.754192i	$-0.271971\pi$
$163$	−4.14705	−	7.18290i	−0.324822	−	0.562608i	−0.981476	+	0.191584i	$0.938638\pi$
$164$	−1.26483			−0.0987663
$165$	0.794889	+	2.40982i	0.0618820	+	0.187604i
$166$			11.8693i			0.921234i
$167$	−6.88497	+	11.9251i	−0.532775	+	0.922793i	0.466493	+	0.884525i	$0.345517\pi$
$167$	−6.88497	+	11.9251i	−0.532775	+	0.922793i	−0.999268	+	0.0382680i	$0.987816\pi$
$168$	−4.57399	+	0.280383i	−0.352891	+	0.0216320i
$169$	17.7832	+	30.8014i	1.36794	+	2.36934i
$170$	−5.72151	+	3.30332i	−0.438820	+	0.253353i
$171$	−4.25796	+	9.79763i	−0.325614	+	0.749244i
$172$	3.24581	−	5.62191i	0.247491	−	0.428666i
$173$	5.81971	−	10.0800i	0.442464	−	0.766371i	−0.555407	−	0.831578i	$-0.687438\pi$
$173$	5.81971	−	10.0800i	0.442464	−	0.766371i	0.997872	+	0.0652078i	$0.0207710\pi$
$174$	2.83779	−	0.936056i	0.215132	−	0.0709622i
$175$	−0.673503	+	2.55859i	−0.0509121	+	0.193411i
$176$	1.26877	+	0.732523i	0.0956370	+	0.0552160i
$177$	−1.92980	−	1.72209i	−0.145052	−	0.129440i
$178$		−	4.37482i		−	0.327907i
$179$	−1.21808	−	0.703262i	−0.0910439	−	0.0525642i	0.453787	−	0.891110i	$-0.350073\pi$
$179$	−1.21808	−	0.703262i	−0.0910439	−	0.0525642i	−0.544831	+	0.838546i	$0.683406\pi$
$180$	−2.75140	−	1.19573i	−0.205077	−	0.0891248i
$181$			10.1582i			0.755054i	0.925998	+	0.377527i	$0.123226\pi$
$181$			10.1582i			0.755054i	−0.925998	+	0.377527i	$0.876774\pi$
$182$	−17.7887	+	4.85057i	−1.31858	+	0.359548i
$183$	6.33533	+	1.31713i	0.468321	+	0.0973653i
$184$	−6.36259			−0.469056
$185$	2.75951	+	4.77962i	0.202884	+	0.351405i
$186$	−12.9120	+	4.25909i	−0.946756	+	0.312291i
$187$	−8.38228	−	4.83951i	−0.612973	−	0.353900i
$188$	5.39759			0.393660
$189$	8.84027	+	10.5285i	0.643035	+	0.765837i
$190$	3.56096			0.258339
$191$	−14.8301	−	8.56216i	−1.07307	−	0.619536i	−0.144050	−	0.989570i	$-0.546012\pi$
$191$	−14.8301	−	8.56216i	−1.07307	−	0.619536i	−0.929018	+	0.370035i	$0.879346\pi$
$192$	−1.64488	+	0.542569i	−0.118709	+	0.0391565i
$193$	−0.966528	−	1.67408i	−0.0695722	−	0.120503i	0.829141	−	0.559040i	$-0.188830\pi$
$193$	−0.966528	−	1.67408i	−0.0695722	−	0.120503i	−0.898713	+	0.438537i	$0.855497\pi$
$194$	−10.4493			−0.750214
$195$	−11.8179	−	2.45697i	−0.846296	−	0.175948i
$196$	−0.0616877	−	6.99973i	−0.00440627	−	0.499981i
$197$		−	22.0136i		−	1.56840i	−0.620508	−	0.784200i	$-0.713073\pi$
$197$		−	22.0136i		−	1.56840i	0.620508	−	0.784200i	$-0.286927\pi$
$198$	−0.498358	−	4.36679i	−0.0354168	−	0.310335i
$199$	23.0430	+	13.3039i	1.63348	+	0.943088i	0.983010	+	0.183554i	$0.0587604\pi$
$199$	23.0430	+	13.3039i	1.63348	+	0.943088i	0.650468	+	0.759534i	$0.274573\pi$
$200$			1.00000i			0.0707107i
$201$	−16.2183	−	14.4727i	−1.14395	−	1.02083i
$202$	−1.76640	−	1.01983i	−0.124283	−	0.0717550i
$203$	1.20080	+	4.40375i	0.0842798	+	0.309082i
$204$	10.8671	−	3.58455i	0.760849	−	0.250969i
$205$	0.632413	−	1.09537i	0.0441696	−	0.0765041i
$206$	−1.59020	+	2.75430i	−0.110794	+	0.191901i
$207$	11.3567	+	15.3417i	0.789345	+	1.06632i
$208$	−6.03529	+	3.48448i	−0.418472	+	0.241605i
$209$	2.60849	+	4.51803i	0.180433	+	0.312519i
$210$	2.04418	−	4.10138i	0.141062	−	0.283022i
$211$	−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	$0.242839\pi$
$212$		−	6.47567i		−	0.444751i
$213$	−7.71169	−	23.3791i	−0.528396	−	1.60191i
$214$	−15.9237			−1.08852
$215$	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
$219$	−2.17396	−	0.451972i	−0.146902	−	0.0305415i
$220$	−1.26877	+	0.732523i	−0.0855403	+	0.0493867i
$221$	39.8730	−	23.0207i	2.68215	−	1.54854i
$222$	−2.99445	−	9.07812i	−0.200975	−	0.609284i
$223$	−11.6938	+	6.75140i	−0.783072	+	0.452107i	−0.837518	−	0.546410i	$-0.815994\pi$
$223$	−11.6938	+	6.75140i	−0.783072	+	0.452107i	0.0544458	+	0.998517i	$0.482661\pi$
$224$	−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
$227$	−21.4981			−1.42688			−0.713438	−	0.700718i	$-0.752863\pi$
$227$	−21.4981			−1.42688			−0.713438	+	0.700718i	$0.752863\pi$
$228$	−6.03864	−	1.25545i	−0.399918	−	0.0831443i
$229$		−	22.5093i		−	1.48745i	−0.668484	−	0.743727i	$-0.733056\pi$
$229$		−	22.5093i		−	1.48745i	0.668484	−	0.743727i	$-0.266944\pi$
$230$	3.18129	−	5.51016i	0.209768	−	0.363329i
$231$	6.70111	−	0.410774i	0.440901	−	0.0270269i
$232$	0.862614	+	1.49409i	0.0566334	+	0.0980919i
$233$	15.4408	−	8.91477i	1.01156	−	0.584026i	0.0999142	−	0.994996i	$-0.468143\pi$
$233$	15.4408	−	8.91477i	1.01156	−	0.584026i	0.911649	+	0.410970i	$0.134810\pi$
$234$	19.1744	+	8.33302i	1.25347	+	0.544746i
$235$	−2.69880	+	4.67445i	−0.176050	+	0.304928i
$236$	0.746642	−	1.29322i	0.0486023	−	0.0841816i
$237$	−0.350448	+	1.68563i	−0.0227641	+	0.109494i
$238$	4.59838	+	16.8638i	0.298069	+	1.09312i
$239$	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	$0.495506\pi$
$240$	0.352560	−	1.69579i	0.0227576	−	0.109463i
$241$			26.4244i			1.70215i	0.525048	+	0.851073i	$0.324047\pi$
$241$			26.4244i			1.70215i	−0.525048	+	0.851073i	$0.675953\pi$
$242$	7.66748	+	4.42682i	0.492884	+	0.284567i
$243$	−0.347327	−	15.5846i	−0.0222810	−	0.999752i
$244$			3.73592i			0.239167i
$245$	6.09279	+	3.44644i	0.389254	+	0.220185i
$246$	−1.45862	+	1.63456i	−0.0929984	+	0.104215i
$247$	−24.8162			−1.57901
$248$	−3.92493	−	6.79817i	−0.249233	−	0.431684i
$249$	15.3389	+	13.6879i	0.972061	+	0.867434i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	27.9912			1.76679			0.883395	−	0.468628i	$-0.155252\pi$
$251$	27.9912			1.76679			0.883395	+	0.468628i	$0.155252\pi$
$252$	−4.91248	+	6.23439i	−0.309457	+	0.392729i
$253$	9.32149			0.586037
$254$	−0.791877	−	0.457190i	−0.0496868	−	0.0286867i
$255$	−2.32923	+	11.2035i	−0.145862	+	0.701588i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.4304			−0.900143			−0.450072	−	0.892993i	$-0.648602\pi$
$257$	−14.4304			−0.900143			−0.450072	+	0.892993i	$0.648602\pi$
$258$	−3.52215	−	10.6779i	−0.219280	−	0.664778i
$259$	14.0876	−	3.84138i	0.875363	−	0.238692i
$260$		−	6.96896i		−	0.432196i
$261$	2.06291	−	4.74680i	0.127691	−	0.293820i
$262$	8.57256	+	4.94937i	0.529615	+	0.305773i
$263$			1.61144i			0.0993659i	0.998765	+	0.0496830i	$0.0158211\pi$
$263$			1.61144i			0.0993659i	−0.998765	+	0.0496830i	$0.984179\pi$
$264$	2.40982	−	0.794889i	0.148314	−	0.0489220i
$265$	5.60809	+	3.23783i	0.344502	+	0.198898i
$266$	2.39832	−	9.11104i	0.147050	−	0.558634i
$267$	−5.65366	−	5.04514i	−0.345998	−	0.308757i
$268$	6.27490	−	10.8685i	0.383301	−	0.663896i
$269$	−2.06266	+	3.57264i	−0.125763	+	0.217828i	−0.922031	−	0.387116i	$-0.873471\pi$
$269$	−2.06266	+	3.57264i	−0.125763	+	0.217828i	0.796268	+	0.604944i	$0.206804\pi$
$270$	−4.71824	+	2.17674i	−0.287143	+	0.132472i
$271$	−4.02680	+	2.32488i	−0.244611	+	0.141226i	−0.617294	−	0.786732i	$-0.711771\pi$
$271$	−4.02680	+	2.32488i	−0.244611	+	0.141226i	0.372683	+	0.927959i	$0.378438\pi$
$272$	3.30332	+	5.72151i	0.200293	+	0.346918i
$273$	−14.2458	+	28.5824i	−0.862194	+	1.72988i
$274$	6.02412	−	10.4341i	0.363930	−	0.630346i
$275$		−	1.46505i		−	0.0883456i
$276$	−7.33747	+	8.22248i	−0.441664	+	0.494935i
$277$	23.4240			1.40741			0.703705	−	0.710492i	$-0.251528\pi$
$277$	23.4240			1.40741			0.703705	+	0.710492i	$0.251528\pi$
$278$	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	$0.540178\pi$
$282$	6.22461	−	6.97540i	0.370670	−	0.415379i
$283$	4.97417	−	2.87184i	0.295684	−	0.170713i	−0.344819	−	0.938669i	$-0.612060\pi$
$283$	4.97417	−	2.87184i	0.295684	−	0.170713i	0.640502	+	0.767956i	$0.278726\pi$
$284$	12.3091	−	7.10664i	0.730408	−	0.421702i
$285$	4.10657	−	4.60189i	0.243252	−	0.272592i
$286$	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
$290$	−1.72523			−0.101309
$291$	−12.0503	+	13.5038i	−0.706402	+	0.791605i
$292$		−	1.28197i		−	0.0750218i
$293$	−10.7874	+	18.6844i	−0.630209	+	1.09155i	0.357300	+	0.933990i	$0.383697\pi$
$293$	−10.7874	+	18.6844i	−0.630209	+	1.09155i	−0.987509	+	0.157564i	$0.949636\pi$
$294$	−9.11701	−	7.99251i	−0.531715	−	0.466133i
$295$	0.746642	+	1.29322i	0.0434712	+	0.0752943i
$296$	4.77962	−	2.75951i	0.277810	−	0.160393i
$297$	−6.21800	−	4.39184i	−0.360805	−	0.254840i
$298$	4.29769	−	7.44381i	0.248958	−	0.431208i
$299$	−22.1703	+	38.4001i	−1.28214	+	2.22073i
$300$	1.29232	+	1.15322i	0.0746119	+	0.0665812i
$301$	16.5702	−	4.51833i	0.955092	−	0.260432i
$302$	−2.25835	−	1.30386i	−0.129953	−	0.0750285i
$303$	−3.35499	+	1.10666i	−0.192739	+	0.0635758i
$304$		−	3.56096i		−	0.204235i
$305$	−3.23540	−	1.86796i	−0.185258	−	0.106959i
$306$	7.89978	−	18.1775i	0.451600	−	1.03914i
$307$			5.22295i			0.298090i	0.988830	+	0.149045i	$0.0476199\pi$
$307$			5.22295i			0.298090i	−0.988830	+	0.149045i	$0.952380\pi$
$308$	1.01971	+	3.73962i	0.0581033	+	0.213084i
$309$	1.72558	+	5.23135i	0.0981649	+	0.297601i
$310$	7.84985			0.445842
$311$	−6.61784	−	11.4624i	−0.375263	−	0.649975i	0.615103	−	0.788447i	$-0.289114\pi$
$311$	−6.61784	−	11.4624i	−0.375263	−	0.649975i	−0.990366	+	0.138472i	$0.955781\pi$
$312$	−2.45697	+	11.8179i	−0.139099	+	0.669056i
$313$	26.8077	+	15.4775i	1.51526	+	0.874838i	0.999840	+	0.0179024i	$0.00569881\pi$
$313$	26.8077	+	15.4775i	1.51526	+	0.874838i	0.515424	+	0.856935i	$0.327635\pi$
$314$	−7.79034			−0.439634
$315$	−2.94290	−	7.37152i	−0.165814	−	0.415338i
$316$	−0.994011			−0.0559175
$317$	13.1185	+	7.57399i	0.736811	+	0.425398i	0.820909	−	0.571060i	$-0.193467\pi$
$317$	13.1185	+	7.57399i	0.736811	+	0.425398i	−0.0840978	+	0.996458i	$0.526801\pi$
$318$	−8.36861	−	7.46787i	−0.469288	−	0.418777i
$319$	−1.26377	−	2.18891i	−0.0707576	−	0.122556i
$320$	1.00000			0.0559017
$321$	−18.3635	+	20.5785i	−1.02495	+	1.14858i
$322$	−11.9556	−	11.8507i	−0.666262	−	0.660416i
$323$			23.5259i			1.30902i
$324$	8.76857	−	2.02783i	0.487143	−	0.112657i
$325$	6.03529	+	3.48448i	0.334778	+	0.193284i
$326$		−	8.29410i		−	0.459368i
$327$	−2.54445	+	12.2386i	−0.140708	+	0.676798i
$328$	−1.09537	−	0.632413i	−0.0604818	−	0.0349192i
$329$	10.1424	+	10.0534i	0.559167	+	0.554261i
$330$	−0.516517	+	2.48441i	−0.0284333	+	0.136762i
$331$	−0.651609	+	1.12862i	−0.0358157	+	0.0620345i	−0.883378	−	0.468662i	$-0.844736\pi$
$331$	−0.651609	+	1.12862i	−0.0358157	+	0.0620345i	0.847562	+	0.530696i	$0.178070\pi$
$332$	−5.93463	+	10.2791i	−0.325705	+	0.564138i
$333$	−15.1851	−	6.59929i	−0.832137	−	0.361639i
$334$	−11.9251	+	6.88497i	−0.652513	+	0.376729i
$335$	6.27490	+	10.8685i	0.342835	+	0.593807i
$336$	−4.10138	−	2.04418i	−0.223749	−	0.111519i
$337$	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	$0.0208021\pi$
$338$			35.5663i			1.93455i
$339$	10.6269	+	2.20937i	0.577175	+	0.119996i
$340$	−6.60663			−0.358295
$341$	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
$345$	−3.45214	−	10.4657i	−0.185857	−	0.563453i
$346$	10.0800	−	5.81971i	0.541906	−	0.312869i
$347$	−4.39256	+	2.53604i	−0.235805	+	0.136142i	−0.613247	−	0.789891i	$-0.710137\pi$
$347$	−4.39256	+	2.53604i	−0.235805	+	0.136142i	0.377442	+	0.926033i	$0.376804\pi$
$348$	2.92562	+	0.608246i	0.156830	+	0.0326054i
$349$	20.4996	−	11.8354i	1.09732	−	0.633536i	0.161802	−	0.986823i	$-0.448269\pi$
$349$	20.4996	−	11.8354i	1.09732	−	0.633536i	0.935515	+	0.353287i	$0.114936\pi$
$350$	−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
$353$	0.544757			0.0289945			0.0144973	−	0.999895i	$-0.495385\pi$
$353$	0.544757			0.0289945			0.0144973	+	0.999895i	$0.495385\pi$
$354$	−0.810210	−	2.45627i	−0.0430622	−	0.130549i
$355$			14.2133i			0.754363i
$356$	2.18741	−	3.78871i	0.115933	−	0.200801i
$357$	27.0963	+	13.5051i	1.43409	+	0.714767i
$358$	−0.703262	−	1.21808i	−0.0371685	−	0.0643778i
$359$	−5.44862	+	3.14576i	−0.287567	+	0.166027i	−0.636844	−	0.770993i	$-0.719761\pi$
$359$	−5.44862	+	3.14576i	−0.287567	+	0.166027i	0.349277	+	0.937019i	$0.386427\pi$
$360$	−1.78492	−	2.41124i	−0.0940734	−	0.127083i
$361$	−3.15979	+	5.47291i	−0.166305	+	0.288048i
$362$	−5.07911	+	8.79728i	−0.266952	+	0.462375i
$363$	14.5631	−	4.80371i	0.764367	−	0.252129i
$364$	−17.8307	−	4.69362i	−0.934583	−	0.246012i
$365$	1.11022	+	0.640987i	0.0581117	+	0.0335508i
$366$	4.82799	+	4.30833i	0.252363	+	0.225200i
$367$			24.3497i			1.27104i	0.772083	+	0.635522i	$0.219215\pi$
$367$			24.3497i			1.27104i	−0.772083	+	0.635522i	$0.780785\pi$
$368$	−5.51016	−	3.18129i	−0.287237	−	0.165836i
$369$	0.430250	+	3.77001i	0.0223979	+	0.196259i
$370$			5.51903i			0.286921i
$371$	12.0614	−	12.1681i	0.626195	−	0.631738i
$372$	−13.3117	−	2.76754i	−0.690179	−	0.143490i
$373$	2.17755			0.112749			0.0563746	−	0.998410i	$-0.482046\pi$
$373$	2.17755			0.112749			0.0563746	+	0.998410i	$0.482046\pi$
$374$	−4.83951	−	8.38228i	−0.250245	−	0.433438i
$375$	−1.64488	+	0.542569i	−0.0849411	+	0.0280181i
$376$	4.67445	+	2.69880i	0.241066	+	0.139180i
$377$	12.0230			0.619218
$378$	2.39164	+	13.5381i	0.123013	+	0.696325i
$379$	−22.5954			−1.16065			−0.580323	−	0.814387i	$-0.697074\pi$
$379$	−22.5954			−1.16065			−0.580323	+	0.814387i	$0.697074\pi$
$380$	3.08388	+	1.78048i	0.158200	+	0.0913367i
$381$	−1.50404	+	0.496114i	−0.0770544	+	0.0254167i
$382$	−8.56216	−	14.8301i	−0.438078	−	0.758773i
$383$	6.52565			0.333445			0.166723	−	0.986004i	$-0.446682\pi$
$383$	6.52565			0.333445			0.166723	+	0.986004i	$0.446682\pi$
$384$	−1.69579	−	0.352560i	−0.0865379	−	0.0179915i
$385$	−3.74846	−	0.986714i	−0.191039	−	0.0502876i
$386$		−	1.93306i		−	0.0983900i
$387$	−17.8611	−	7.76225i	−0.907929	−	0.394577i
$388$	−9.04933	−	5.22463i	−0.459410	−	0.265241i
$389$			34.6804i			1.75837i	0.476482	+	0.879184i	$0.341912\pi$
$389$			34.6804i			1.75837i	−0.476482	+	0.879184i	$0.658088\pi$
$390$	−9.00610	−	8.03674i	−0.456042	−	0.406956i
$391$	36.4036	+	21.0176i	1.84101	+	1.06291i
$392$	3.44644	−	6.09279i	0.174072	−	0.307732i
$393$	16.2822	−	5.37075i	0.821329	−	0.270919i
$394$	11.0068	−	19.0643i	0.554513	−	0.960445i
$395$	0.497005	−	0.860839i	0.0250071	−	0.0433135i
$396$	1.75181	−	4.03093i	0.0880316	−	0.202562i
$397$	23.8417	−	13.7650i	1.19658	−	0.690845i	0.236788	−	0.971561i	$-0.423905\pi$
$397$	23.8417	−	13.7650i	1.19658	−	0.690845i	0.959791	+	0.280717i	$0.0905721\pi$
$398$	13.3039	+	23.0430i	0.666864	+	1.15504i
$399$	−9.00856	−	13.6064i	−0.450992	−	0.681173i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			14.0788i			0.703060i	0.936177	+	0.351530i	$0.114338\pi$
$401$			14.0788i			0.703060i	−0.936177	+	0.351530i	$0.885662\pi$
$402$	−6.80914	−	20.6429i	−0.339609	−	1.02957i
$403$	−54.7053			−2.72506
$404$	−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
$408$	11.2035	+	2.32923i	0.554654	+	0.115314i
$409$	−28.3746	+	16.3821i	−1.40304	+	0.810043i	−0.994703	−	0.102791i	$-0.967223\pi$
$409$	−28.3746	+	16.3821i	−1.40304	+	0.810043i	−0.408332	+	0.912833i	$0.633890\pi$
$410$	1.09537	−	0.632413i	0.0540965	−	0.0312327i
$411$	−6.53700	−	19.8179i	−0.322447	−	0.977543i
$412$	−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
$416$	−6.96896			−0.341681
$417$	30.5620	+	6.35393i	1.49663	+	0.311153i
$418$			5.21697i			0.255170i
$419$	5.81259	−	10.0677i	0.283964	−	0.491839i	−0.688394	−	0.725337i	$-0.741684\pi$
$419$	5.81259	−	10.0677i	0.283964	−	0.491839i	0.972357	+	0.233498i	$0.0750172\pi$
$420$	3.82100	−	2.52981i	0.186446	−	0.123442i
$421$	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
$423$	−1.83607	−	16.0883i	−0.0892730	−	0.782242i
$424$	3.23783	−	5.60809i	0.157243	−	0.272353i
$425$	3.30332	−	5.72151i	0.160234	−	0.277534i
$426$	5.01103	−	24.1027i	0.242785	−	1.16778i
$427$	−6.95839	+	7.01999i	−0.336740	+	0.339721i
$428$	−13.7903	−	7.96185i	−0.666581	−	0.384851i
$429$	3.59958	−	17.3137i	0.173789	−	0.835916i
$430$			6.49162i			0.313054i
$431$	8.34407	+	4.81745i	0.401920	+	0.232048i	0.687312	−	0.726362i	$-0.258791\pi$
$431$	8.34407	+	4.81745i	0.401920	+	0.232048i	−0.285392	+	0.958411i	$0.592124\pi$
$432$	2.17674	+	4.71824i	0.104728	+	0.227007i
$433$		−	37.8458i		−	1.81875i	−0.415972	−	0.909377i	$-0.636559\pi$
$433$		−	37.8458i		−	1.81875i	0.415972	−	0.909377i	$-0.363441\pi$
$434$	5.28690	−	20.0846i	0.253779	−	0.964090i
$435$	−1.98957	+	2.22954i	−0.0953925	+	0.106898i
$436$	−7.21707			−0.345635
$437$	−11.3285	−	19.6215i	−0.541914	−	0.938622i
$438$	−1.65672	−	1.47840i	−0.0791610	−	0.0706406i
$439$	−28.0570	−	16.1987i	−1.33909	−	0.773122i	−0.352415	−	0.935844i	$-0.614640\pi$
$439$	−28.0570	−	16.1987i	−1.33909	−	0.773122i	−0.986672	+	0.162721i	$0.947973\pi$
$440$	−1.46505			−0.0698434
$441$	−20.8428	+	2.56494i	−0.992513	+	0.122140i
$442$	46.0413			2.18996
$443$	−18.9675	−	10.9509i	−0.901175	−	0.520293i	−0.0235935	−	0.999722i	$-0.507511\pi$
$443$	−18.9675	−	10.9509i	−0.901175	−	0.520293i	−0.877581	+	0.479428i	$0.840844\pi$
$444$	1.94579	−	9.35911i	0.0923430	−	0.444164i
$445$	2.18741	+	3.78871i	0.103693	+	0.179602i
$446$	−13.5028			−0.639376
$447$	−4.66358	−	14.1383i	−0.220580	−	0.668720i
$448$	0.673503	−	2.55859i	0.0318200	−	0.120882i
$449$			25.8522i			1.22004i	0.792385	+	0.610021i	$0.208839\pi$
$449$			25.8522i			1.22004i	−0.792385	+	0.610021i	$0.791161\pi$
$450$	2.98065	−	0.340166i	0.140509	−	0.0160356i
$451$	1.60477	+	0.926515i	0.0755657	+	0.0436279i
$452$			6.26664i			0.294758i
$453$	−4.28937	+	1.41486i	−0.201532	+	0.0664761i
$454$	−18.6179	−	10.7490i	−0.873780	−	0.504477i
$455$	12.9801	−	13.0950i	0.608519	−	0.613905i
$456$	−4.60189	−	4.10657i	−0.215503	−	0.192308i
$457$	11.1231	−	19.2658i	0.520318	−	0.901217i	−0.479403	−	0.877595i	$-0.659147\pi$
$457$	11.1231	−	19.2658i	0.520318	−	0.901217i	0.999721	−	0.0236222i	$-0.00751987\pi$
$458$	11.2546	−	19.4936i	0.525894	−	0.910876i
$459$	−14.3809	−	31.1717i	−0.671244	−	1.45497i
$460$	5.51016	−	3.18129i	0.256913	−	0.148329i
$461$	−7.05369	−	12.2173i	−0.328523	−	0.569018i	0.653696	−	0.756757i	$-0.273217\pi$
$461$	−7.05369	−	12.2173i	−0.328523	−	0.569018i	−0.982219	+	0.187739i	$0.939884\pi$
$462$	6.00872	+	2.99481i	0.279551	+	0.139331i
$463$	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	$0.117170\pi$
$464$			1.72523i			0.0800917i
$465$	9.05261	−	10.1445i	0.419805	−	0.470440i
$466$	17.8295			0.825938
$467$	1.75717	+	3.04350i	0.0813119	+	0.140836i	0.903814	−	0.427926i	$-0.140756\pi$
$467$	1.75717	+	3.04350i	0.0813119	+	0.140836i	−0.822502	+	0.568763i	$0.807422\pi$
$468$	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
$471$	−8.98398	+	10.0676i	−0.413960	+	0.463890i
$472$	1.29322	−	0.746642i	0.0595254	−	0.0343670i
$473$	−8.23636	+	4.75526i	−0.378708	+	0.218647i
$474$	−1.14631	+	1.28458i	−0.0526519	+	0.0590026i
$475$	−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
$479$	−1.00097			−0.0457356			−0.0228678	−	0.999738i	$-0.507280\pi$
$479$	−1.00097			−0.0457356			−0.0228678	+	0.999738i	$0.507280\pi$
$480$	1.15322	−	1.29232i	0.0526371	−	0.0589859i
$481$		−	38.4619i		−	1.75371i
$482$	−13.2122	+	22.8842i	−0.601799	+	1.04235i
$483$	−29.1024	+	1.78396i	−1.32421	+	0.0811730i
$484$	4.42682	+	7.66748i	0.201219	+	0.348522i
$485$	9.04933	−	5.22463i	0.410909	−	0.237238i
$486$	7.49150	−	13.6703i	0.339821	−	0.620098i
$487$	−14.4755	+	25.0723i	−0.655948	+	1.13613i	0.325708	+	0.945471i	$0.394397\pi$
$487$	−14.4755	+	25.0723i	−0.655948	+	1.13613i	−0.981655	+	0.190664i	$0.938936\pi$
$488$	−1.86796	+	3.23540i	−0.0845585	+	0.146460i
$489$	−10.7186	−	9.56492i	−0.484712	−	0.432541i
$490$	3.55329	+	6.03110i	0.160521	+	0.272457i
$491$	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	$0.372165\pi$
$492$	−2.08048	+	0.686255i	−0.0937954	+	0.0309388i
$493$		−	11.3980i		−	0.513338i
$494$	−21.4914	−	12.4081i	−0.966945	−	0.558266i
$495$	2.61499	+	3.53258i	0.117535	+	0.158777i
$496$		−	7.84985i		−	0.352469i
$497$	36.3660	+	9.57269i	1.63124	+	0.429394i
$498$	6.43990	+	19.5235i	0.288579	+	0.874868i
$499$	16.6369			0.744769			0.372384	−	0.928079i	$-0.378540\pi$
$499$	16.6369			0.744769			0.372384	+	0.928079i	$0.378540\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−4.85473	+	23.3509i	−0.216893	+	1.04324i
$502$	24.2411	+	13.9956i	1.08193	+	0.624655i
$503$	−12.7352			−0.567834			−0.283917	−	0.958849i	$-0.591634\pi$
$503$	−12.7352			−0.567834			−0.283917	+	0.958849i	$0.591634\pi$
$504$	−7.37152	+	2.94290i	−0.328354	+	0.131087i
$505$	2.03966			0.0907638
$506$	8.07265	+	4.66075i	0.358873	+	0.207195i
$507$	45.9630	+	41.0158i	2.04129	+	1.82158i
$508$	−0.457190	−	0.791877i	−0.0202845	−	0.0351338i
$509$	−9.46891			−0.419702			−0.209851	−	0.977733i	$-0.567298\pi$
$509$	−9.46891			−0.419702			−0.209851	+	0.977733i	$0.567298\pi$
$510$	−7.61890	+	8.53786i	−0.337371	+	0.378063i
$511$	2.38776	−	2.40890i	0.105628	−	0.106563i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.68793	+	18.4261i	−0.0745238	+	0.813534i
$514$	−12.4971	−	7.21520i	−0.551223	−	0.318249i
$515$		−	3.18039i		−	0.140145i
$516$	2.28868	−	11.0084i	0.100754	−	0.484619i
$517$	−6.84829	−	3.95386i	−0.301187	−	0.173891i
$518$	14.1209	+	3.71708i	0.620439	+	0.163319i
$519$	4.10359	−	19.7380i	0.180128	−	0.866402i
$520$	3.48448	−	6.03529i	0.152804	−	0.264665i
$521$	2.37330	−	4.11068i	0.103976	−	0.180092i	−0.809343	−	0.587336i	$-0.800177\pi$
$521$	2.37330	−	4.11068i	0.103976	−	0.180092i	0.913320	+	0.407244i	$0.133510\pi$
$522$	4.15994	−	3.07939i	0.182075	−	0.134781i
$523$	30.1376	−	17.3999i	1.31782	−	0.760846i	0.334446	−	0.942415i	$-0.391451\pi$
$523$	30.1376	−	17.3999i	1.31782	−	0.760846i	0.983378	+	0.181569i	$0.0581176\pi$
$524$	4.94937	+	8.57256i	0.216214	+	0.374494i
$525$	0.280383	+	4.57399i	0.0122369	+	0.199625i
$526$	−0.805722	+	1.39555i	−0.0351312	+	0.0608490i
$527$			51.8611i			2.25910i
$528$	2.48441	+	0.516517i	0.108120	+	0.0224785i
$529$	−17.4825			−0.760110
$530$	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
$534$	−2.37364	−	7.19604i	−0.102718	−	0.311403i
$535$	13.7903	−	7.96185i	0.596208	−	0.344221i
$536$	10.8685	−	6.27490i	0.469446	−	0.271035i
$537$	−2.38517	−	0.495883i	−0.102928	−	0.0213989i
$538$	−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	0.854133	−	0.520054i	$-0.174088\pi$
$541$	−0.542248	−	0.939202i	−0.0233131	−	0.0403794i	−0.877447	+	0.479674i	$0.840755\pi$
$542$	−4.64975			−0.199724
$543$	5.51153	+	16.7090i	0.236523	+	0.717053i
$544$			6.60663i			0.283257i
$545$	3.60853	−	6.25017i	0.154573	−	0.267728i
$546$	−26.6284	+	17.6302i	−1.13959	+	0.754501i
$547$	−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
$549$	11.1355	−	1.27083i	0.475250	−	0.0542377i
$550$	0.732523	−	1.26877i	0.0312349	−	0.0541004i
$551$	−3.07173	+	5.32040i	−0.130860	+	0.226657i
$552$	−10.4657	+	3.45214i	−0.445449	+	0.146933i
$553$	−1.86780	−	1.85141i	−0.0794269	−	0.0787301i
$554$	20.2858	+	11.7120i	0.861859	+	0.497595i
$555$	7.13233	+	6.36466i	0.302751	+	0.270165i
$556$			18.0223i			0.764314i
$557$	−27.9379	−	16.1300i	−1.18377	−	0.683449i	−0.226885	−	0.973922i	$-0.572854\pi$
$557$	−27.9379	−	16.1300i	−1.18377	−	0.683449i	−0.956883	+	0.290472i	$0.906188\pi$
$558$	−18.9279	+	14.0113i	−0.801280	+	0.593147i
$559$		−	45.2398i		−	1.91344i
$560$	1.87905	+	1.86257i	0.0794045	+	0.0787078i
$561$	−16.4136	−	3.41243i	−0.692982	−	0.144073i
$562$	−20.2848			−0.855661
$563$	−17.7852	−	30.8049i	−0.749557	−	1.29827i	−0.948035	−	0.318165i	$-0.896933\pi$
$563$	−17.7852	−	30.8049i	−0.749557	−	1.29827i	0.198479	−	0.980105i	$-0.436400\pi$
$564$	8.87837	−	2.92857i	0.373847	−	0.123315i
$565$	−5.42707	−	3.13332i	−0.228319	−	0.131820i
$566$	5.74367			0.241425
$567$	20.2536	+	12.5217i	0.850571	+	0.525860i
$568$	14.2133			0.596376
$569$	−36.3434	−	20.9829i	−1.52359	−	0.879647i	−0.999610	−	0.0279186i	$-0.991112\pi$
$569$	−36.3434	−	20.9829i	−1.52359	−	0.879647i	−0.523983	−	0.851729i	$-0.675555\pi$
$570$	5.85734	−	1.93207i	0.245337	−	0.0809253i
$571$	−3.38623	−	5.86513i	−0.141709	−	0.245448i	0.786431	−	0.617678i	$-0.211927\pi$
$571$	−3.38623	−	5.86513i	−0.141709	−	0.245448i	−0.928140	+	0.372230i	$0.878593\pi$
$572$	10.2098			0.426895
$573$	−29.0392	−	6.03734i	−1.21313	−	0.252214i
$574$	−0.880351	−	3.22854i	−0.0367451	−	0.134757i
$575$			6.36259i			0.265338i
$576$	−2.41124	+	1.78492i	−0.100468	+	0.0743716i
$577$	−30.1675	−	17.4172i	−1.25589	−	0.725087i	−0.283616	−	0.958938i	$-0.591534\pi$
$577$	−30.1675	−	17.4172i	−1.25589	−	0.725087i	−0.972273	+	0.233851i	$0.924867\pi$
$578$		−	26.6476i		−	1.10839i
$579$	−2.49812	−	2.22924i	−0.103818	−	0.0926440i
$580$	−1.49409	−	0.862614i	−0.0620388	−	0.0358181i
$581$	−30.2970	+	8.26131i	−1.25693	+	0.342737i
$582$	−17.1878	+	5.66945i	−0.712455	+	0.235006i
$583$	−4.74358	+	8.21612i	−0.196459	+	0.340277i
$584$	0.640987	−	1.11022i	0.0265242	−	0.0459413i
$585$	−20.7720	+	2.37060i	−0.858818	+	0.0980122i
$586$	−18.6844	+	10.7874i	−0.771845	+	0.445625i
$587$	20.1646	+	34.9261i	0.832281	+	1.44155i	0.896225	+	0.443599i	$0.146299\pi$
$587$	20.1646	+	34.9261i	0.832281	+	1.44155i	−0.0639444	+	0.997953i	$0.520368\pi$
$588$	−3.89930	−	11.4802i	−0.160805	−	0.473436i
$589$	13.9765	−	24.2080i	0.575892	−	0.997474i
$590$			1.49328i			0.0614775i
$591$	−11.9439	−	36.2096i	−0.491305	−	1.48946i
$592$	5.51903			0.226831
$593$	−13.7783	−	23.8647i	−0.565806	−	0.980005i	−0.996974	−	0.0777332i	$-0.975232\pi$
$593$	−13.7783	−	23.8647i	−0.565806	−	0.980005i	0.431168	−	0.902272i	$-0.358102\pi$
$594$	−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
$597$	45.1212	+	9.38084i	1.84669	+	0.383932i
$598$	−38.4001	+	22.1703i	−1.57030	+	0.906611i
$599$	−12.2493	+	7.07211i	−0.500491	+	0.288959i	−0.728916	−	0.684603i	$-0.759976\pi$
$599$	−12.2493	+	7.07211i	−0.500491	+	0.288959i	0.228425	+	0.973561i	$0.426642\pi$
$600$	0.542569	+	1.64488i	0.0221503	+	0.0671518i
$601$	−10.7893	+	6.22920i	−0.440104	+	0.254094i	−0.703642	−	0.710555i	$-0.748444\pi$
$601$	−10.7893	+	6.22920i	−0.440104	+	0.254094i	0.263537	+	0.964649i	$0.415111\pi$
$602$	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
$605$	−8.85364			−0.359952
$606$	−3.45884	−	0.719103i	−0.140506	−	0.0292115i
$607$		−	7.96739i		−	0.323386i	−0.986841	−	0.161693i	$-0.948305\pi$
$607$		−	7.96739i		−	0.323386i	0.986841	−	0.161693i	$-0.0516955\pi$
$608$	1.78048	−	3.08388i	0.0722080	−	0.125068i
$609$	4.36451	+	6.59210i	0.176859	+	0.267125i
$610$	−1.86796	−	3.23540i	−0.0756314	−	0.130997i
$611$	32.5760	−	18.8078i	1.31789	−	0.760882i
$612$	15.9302	−	11.7923i	0.643939	−	0.476675i
$613$	3.28676	−	5.69283i	0.132751	−	0.229931i	−0.791985	−	0.610540i	$-0.790952\pi$
$613$	3.28676	−	5.69283i	0.132751	−	0.229931i	0.924736	+	0.380609i	$0.124286\pi$
$614$	−2.61148	+	4.52321i	−0.105391	+	0.182542i
$615$	0.445927	−	2.14488i	0.0179815	−	0.0864899i
$616$	−0.986714	+	3.74846i	−0.0397558	+	0.151030i
$617$	−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	$0.717000\pi$
$618$	−1.12128	+	5.39327i	−0.0451044	+	0.216949i
$619$			45.9757i			1.84792i	0.382492	+	0.923959i	$0.375066\pi$
$619$			45.9757i			1.84792i	−0.382492	+	0.923959i	$0.624934\pi$
$620$	6.79817	+	3.92493i	0.273021	+	0.157629i
$621$	27.0043	+	19.0734i	1.08365	+	0.765390i
$622$		−	13.2357i		−	0.530702i
$623$	11.1670	−	3.04499i	0.447396	−	0.121995i
$624$	−8.03674	+	9.00610i	−0.321727	+	0.360532i
$625$	1.00000			0.0400000
$626$	15.4775	+	26.8077i	0.618604	+	1.07145i
$627$	6.74198	+	6.01632i	0.269249	+	0.240269i
$628$	−6.74663	−	3.89517i	−0.269220	−	0.155434i
$629$	−36.4622			−1.45384
$630$	1.13713	−	7.85538i	0.0453045	−	0.312966i
$631$	−24.0931			−0.959131			−0.479566	−	0.877506i	$-0.659206\pi$
$631$	−24.0931			−0.959131			−0.479566	+	0.877506i	$0.659206\pi$
$632$	−0.860839	−	0.497005i	−0.0342423	−	0.0197698i
$633$	−2.42771	+	11.6771i	−0.0964928	+	0.464124i
$634$	7.57399	+	13.1185i	0.300802	+	0.521004i
$635$	0.914380			0.0362861
$636$	−3.51350	−	10.6517i	−0.139319	−	0.422366i
$637$	−24.7627	−	42.0305i	−0.981134	−	1.66531i
$638$		−	2.52754i		−	0.100066i
$639$	−25.3695	−	34.2716i	−1.00360	−	1.35576i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$		−	23.8637i		−	0.942558i	−0.881984	−	0.471279i	$-0.843792\pi$
$641$		−	23.8637i		−	0.942558i	0.881984	−	0.471279i	$-0.156208\pi$
$642$	−26.1925	+	8.63971i	−1.03374	+	0.340982i
$643$	12.9563	+	7.48033i	0.510947	+	0.294996i	0.733223	−	0.679988i	$-0.238015\pi$
$643$	12.9563	+	7.48033i	0.510947	+	0.294996i	−0.222276	+	0.974984i	$0.571348\pi$
$644$	−4.42852	−	16.2409i	−0.174508	−	0.639980i
$645$	8.38923	+	7.48627i	0.330326	+	0.294771i
$646$	−11.7630	+	20.3741i	−0.462808	+	0.801607i
$647$	3.99382	−	6.91751i	0.157013	−	0.271955i	−0.776777	−	0.629776i	$-0.783147\pi$
$647$	3.99382	−	6.91751i	0.157013	−	0.271955i	0.933790	+	0.357821i	$0.116480\pi$
$648$	8.60772	+	2.62813i	0.338143	+	0.103243i
$649$	−1.89463	+	1.09387i	−0.0743708	+	0.0429380i
$650$	3.48448	+	6.03529i	0.136672	+	0.236724i
$651$	−19.8587	−	29.9943i	−0.778322	−	1.17557i
$652$	4.14705	−	7.18290i	0.162411	−	0.281304i
$653$			28.2899i			1.10707i	0.832826	+	0.553535i	$0.186721\pi$
$653$			28.2899i			1.10707i	−0.832826	+	0.553535i	$0.813279\pi$
$654$	−8.32287	+	9.32674i	−0.325450	+	0.364704i
$655$	−9.89874			−0.386776
$656$	−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	$0.335838\pi$
$660$	−1.68952	+	1.89330i	−0.0657645	+	0.0736968i
$661$	2.96092	−	1.70949i	0.115167	−	0.0664915i	−0.441310	−	0.897355i	$-0.645486\pi$
$661$	2.96092	−	1.70949i	0.115167	−	0.0664915i	0.556477	+	0.830863i	$0.312153\pi$
$662$	−1.12862	+	0.651609i	−0.0438650	+	0.0253255i
$663$	53.0958	−	59.5000i	2.06207	−	2.31079i
$664$	−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
$668$	−13.7699			−0.532775
$669$	−15.5717	+	17.4499i	−0.602036	+	0.674651i
$670$			12.5498i			0.484841i
$671$	2.73665	−	4.74001i	0.105647	−	0.182986i
$672$	−2.52981	−	3.82100i	−0.0975897	−	0.147398i
$673$	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
$675$	2.99775	−	4.24423i	0.115383	−	0.163361i
$676$	−17.7832	+	30.8014i	−0.683968	+	1.18467i
$677$	−7.67846	+	13.2995i	−0.295107	+	0.511141i	−0.975010	−	0.222162i	$-0.928689\pi$
$677$	−7.67846	+	13.2995i	−0.295107	+	0.511141i	0.679903	+	0.733302i	$0.262022\pi$
$678$	8.09849	+	7.22682i	0.311021	+	0.277544i
$679$	−7.27295	−	26.6724i	−0.279110	−	1.02359i
$680$	−5.72151	−	3.30332i	−0.219410	−	0.126676i
$681$	−35.3617	+	11.6642i	−1.35506	+	0.446973i
$682$			11.5004i			0.440373i
$683$	26.9763	+	15.5748i	1.03222	+	0.595951i	0.917619	−	0.397460i	$-0.130108\pi$
$683$	26.9763	+	15.5748i	1.03222	+	0.595951i	0.114599	+	0.993412i	$0.463442\pi$
$684$	−10.6140	+	1.21132i	−0.405836	+	0.0463158i
$685$			12.0482i			0.460340i
$686$	17.8243	−	5.02945i	0.680534	−	0.192025i
$687$	−12.2128	−	37.0250i	−0.465948	−	1.41259i
$688$	6.49162			0.247491
$689$	−22.5643	−	39.0825i	−0.859632	−	1.48893i
$690$	2.24319	−	10.7896i	0.0853969	−	0.410753i
$691$	23.2148	+	13.4031i	0.883134	+	0.509878i	0.871691	−	0.490057i	$-0.163024\pi$
$691$	23.2148	+	13.4031i	0.883134	+	0.509878i	0.0114437	+	0.999935i	$0.496357\pi$
$692$	11.6394			0.442464
$693$	10.7996	−	4.31149i	0.410244	−	0.163780i
$694$	−5.07209			−0.192534
$695$	−15.6077	−	9.01113i	−0.592035	−	0.341812i
$696$	2.22954	+	1.98957i	0.0845106	+	0.0754144i
$697$	4.17812	+	7.23672i	0.158258	+	0.274110i
$698$	23.6709			0.895956
$699$	20.5614	−	23.0414i	0.777703	−	0.871507i
$700$	−2.55256	+	0.696025i	−0.0964776	+	0.0263073i
$701$		−	9.39873i		−	0.354985i	−0.984122	−	0.177493i	$-0.943201\pi$
$701$		−	9.39873i		−	0.354985i	0.984122	−	0.177493i	$-0.0567985\pi$
$702$	36.0608	+	3.30335i	1.36103	+	0.124677i
$703$	17.0200	+	9.82652i	0.641922	+	0.370614i
$704$			1.46505i			0.0552160i
$705$	−1.90297	+	9.15318i	−0.0716701	+	0.344729i
$706$	0.471774	+	0.272379i	0.0177554	+	0.0102511i
$707$	1.37372	−	5.21866i	0.0516640	−	0.196268i
$708$	0.526472	−	2.53230i	0.0197860	−	0.0951695i
$709$	−10.1149	+	17.5195i	−0.379873	+	0.657959i	−0.991043	−	0.133540i	$-0.957366\pi$
$709$	−10.1149	+	17.5195i	−0.379873	+	0.657959i	0.611171	+	0.791499i	$0.290699\pi$
$710$	−7.10664	+	12.3091i	−0.266707	+	0.461951i
$711$	0.338128	+	2.96280i	0.0126808	+	0.111114i
$712$	3.78871	−	2.18741i	0.141988	−	0.0819767i
$713$	−24.9727	−	43.2540i	−0.935234	−	1.61987i
$714$	16.7136	+	25.2439i	0.625489	+	0.944731i
$715$	−5.10492	+	8.84199i	−0.190913	+	0.330672i
$716$		−	1.40652i		−	0.0525642i
$717$	26.8547	+	5.58316i	1.00291	+	0.208507i
$718$	−6.29152			−0.234797
$719$	0.154148	+	0.266992i	0.00574874	+	0.00995710i	0.868885	−	0.495013i	$-0.164837\pi$
$719$	0.154148	+	0.266992i	0.00574874	+	0.00995710i	−0.863137	+	0.504970i	$0.831503\pi$
$720$	−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
$723$	14.3371	+	43.4649i	0.533201	+	1.61648i
$724$	−8.79728	+	5.07911i	−0.326948	+	0.188764i
$725$	1.49409	−	0.862614i	0.0554892	−	0.0320367i
$726$	15.0139	+	3.12144i	0.557218	+	0.115847i
$727$	−3.69340	+	2.13238i	−0.136980	+	0.0790857i	−0.566924	−	0.823770i	$-0.691867\pi$
$727$	−3.69340	+	2.13238i	−0.136980	+	0.0790857i	0.429944	+	0.902856i	$0.358533\pi$
$728$	−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
$731$	−42.8877			−1.58626
$732$	2.02699	+	6.14512i	0.0749198	+	0.227130i
$733$		−	3.01231i		−	0.111262i	−0.998451	−	0.0556310i	$-0.982283\pi$
$733$		−	3.01231i		−	0.111262i	0.998451	−	0.0556310i	$-0.0177171\pi$
$734$	−12.1749	+	21.0875i	−0.449382	+	0.778353i
$735$	11.8918	+	2.36321i	0.438636	+	0.0871684i
$736$	−3.18129	−	5.51016i	−0.117264	−	0.203107i
$737$	−15.9228	+	9.19303i	−0.586524	+	0.338630i
$738$	−1.51240	+	3.48005i	−0.0556721	+	0.128102i
$739$	9.01920	−	15.6217i	0.331776	−	0.574654i	−0.651084	−	0.759006i	$-0.725685\pi$
$739$	9.01920	−	15.6217i	0.331776	−	0.574654i	0.982860	+	0.184352i	$0.0590187\pi$
$740$	−2.75951	+	4.77962i	−0.101442	+	0.175702i
$741$	−40.8195	+	13.4645i	−1.49954	+	0.494630i
$742$	16.5295	−	4.50722i	0.606817	−	0.165465i
$743$	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	$0.654383\pi$
$744$	−10.1445	−	9.05261i	−0.371915	−	0.331885i
$745$			8.59537i			0.314910i
$746$	1.88581	+	1.08878i	0.0690445	+	0.0398629i
$747$	32.6571	+	14.1925i	1.19486	+	0.519276i
$748$		−	9.67903i		−	0.353900i
$749$	−11.0833	−	40.6462i	−0.404975	−	1.48518i
$750$	−1.69579	−	0.352560i	−0.0619215	−	0.0128737i
$751$	−6.80138			−0.248186			−0.124093	−	0.992271i	$-0.539602\pi$
$751$	−6.80138			−0.248186			−0.124093	+	0.992271i	$0.539602\pi$
$752$	2.69880	+	4.67445i	0.0984149	+	0.170460i
$753$	46.0421	−	15.1872i	1.67787	−	0.553451i
$754$	10.4123	+	6.01152i	0.379192	+	0.218927i
$755$	2.60771			0.0949044
$756$	−4.69783	+	12.9202i	−0.170858	+	0.469901i
$757$	−26.9017			−0.977761			−0.488880	−	0.872351i	$-0.662595\pi$
$757$	−26.9017			−0.977761			−0.488880	+	0.872351i	$0.662595\pi$
$758$	−19.5682	−	11.2977i	−0.710747	−	0.410350i
$759$	15.3327	−	5.05755i	0.556542	−	0.183577i
$760$	1.78048	+	3.08388i	0.0645848	+	0.111864i
$761$	4.16330			0.150920			0.0754598	−	0.997149i	$-0.475958\pi$
$761$	4.16330			0.150920			0.0754598	+	0.997149i	$0.475958\pi$
$762$	−1.55060	−	0.322374i	−0.0561722	−	0.0116784i
$763$	−13.5613	−	13.4423i	−0.490951	−	0.486643i
$764$		−	17.1243i		−	0.619536i
$765$	2.24735	+	19.6921i	0.0812531	+	0.711968i
$766$	5.65138	+	3.26282i	0.204193	+	0.117891i
$767$		−	10.4066i		−	0.375762i
$768$	−1.29232	−	1.15322i	−0.0466325	−	0.0416133i
$769$	15.1341	+	8.73768i	0.545750	+	0.315089i	0.747406	−	0.664368i	$-0.231299\pi$
$769$	15.1341	+	8.73768i	0.545750	+	0.315089i	−0.201656	+	0.979456i	$0.564632\pi$
$770$	−2.75290	−	2.72875i	−0.0992077	−	0.0983373i
$771$	−23.7362	+	7.82948i	−0.854839	+	0.281972i
$772$	0.966528	−	1.67408i	0.0347861	−	0.0602513i
$773$	−9.80159	+	16.9768i	−0.352539	+	0.610615i	−0.986694	−	0.162591i	$-0.948015\pi$
$773$	−9.80159	+	16.9768i	−0.352539	+	0.610615i	0.634155	+	0.773206i	$0.281348\pi$
$774$	−11.5870	−	15.6528i	−0.416486	−	0.562630i
$775$	−6.79817	+	3.92493i	−0.244197	+	0.140987i
$776$	−5.22463	−	9.04933i	−0.187553	−	0.324852i
$777$	21.0882	−	13.9621i	0.756535	−	0.500888i
$778$	−17.3402	+	30.0342i	−0.621677	+	1.07678i
$779$		−	4.50399i		−	0.161372i
$780$	−3.78114	−	11.4631i	−0.135387	−	0.410444i
$781$	−20.8231			−0.745110
$782$	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
$786$	16.7862	+	3.48990i	0.598743	+	0.124481i
$787$	25.1512	−	14.5211i	0.896545	−	0.517620i	0.0204673	−	0.999791i	$-0.493485\pi$
$787$	25.1512	−	14.5211i	0.896545	−	0.517620i	0.876078	+	0.482170i	$0.160151\pi$
$788$	19.0643	−	11.0068i	0.679137	−	0.392100i
$789$	0.874320	+	2.65063i	0.0311266	+	0.0943648i
$790$	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
$794$	27.5300			0.977002
$795$	10.9814	+	2.28306i	0.389469	+	0.0809718i
$796$			26.6078i			0.943088i
$797$	14.0345	−	24.3085i	0.497129	−	0.861052i	−0.502866	−	0.864365i	$-0.667721\pi$
$797$	14.0345	−	24.3085i	0.497129	−	0.861052i	0.999995	+	0.00331218i	$0.00105430\pi$
$798$	−0.998432	−	16.2878i	−0.0353441	−	0.576582i
$799$	−17.8300	−	30.8824i	−0.630778	−	1.09254i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−12.0369	−	5.23113i	−0.425303	−	0.184833i
$802$	−7.03938	+	12.1926i	−0.248569	+	0.430534i
$803$	−0.939076	+	1.62653i	−0.0331393	+	0.0573989i
$804$	4.42456	−	21.2818i	0.156042	−	0.750552i
$805$	16.2793	+	4.28523i	0.573769	+	0.151034i
$806$	−47.3762	−	27.3526i	−1.66875	−	0.963455i
$807$	−1.45442	+	6.99569i	−0.0511982	+	0.246260i
$808$		−	2.03966i		−	0.0717550i
$809$	2.46533	+	1.42336i	0.0866764	+	0.0500427i	0.542712	−	0.839919i	$-0.317398\pi$
$809$	2.46533	+	1.42336i	0.0866764	+	0.0500427i	−0.456035	+	0.889962i	$0.650731\pi$
$810$	−6.57989	+	6.14044i	−0.231194	+	0.215753i
$811$		−	5.05522i		−	0.177513i	−0.996053	−	0.0887564i	$-0.971711\pi$
$811$		−	5.05522i		−	0.177513i	0.996053	−	0.0887564i	$-0.0282893\pi$
$812$	−3.21335	+	3.24180i	−0.112767	+	0.113765i
$813$	−5.36219	+	6.00895i	−0.188060	+	0.210743i
$814$	−8.08563			−0.283401
$815$	4.14705	+	7.18290i	0.145265	+	0.251606i
$816$	8.53786	+	7.61890i	0.298885	+	0.266715i
$817$	20.0194	+	11.5582i	0.700389	+	0.404370i
$818$	−32.7642			−1.14557
$819$	−7.92464	+	54.7438i	−0.276909	+	1.91290i
$820$	1.26483			0.0441696
$821$	33.8398	+	19.5374i	1.18102	+	0.681861i	0.956250	−	0.292552i	$-0.0945044\pi$
$821$	33.8398	+	19.5374i	1.18102	+	0.681861i	0.224767	+	0.974412i	$0.427838\pi$
$822$	4.24772	−	20.4313i	0.148156	−	0.712623i
$823$	16.3984	+	28.4028i	0.571612	+	0.990061i	0.996401	+	0.0847683i	$0.0270150\pi$
$823$	16.3984	+	28.4028i	0.571612	+	0.990061i	−0.424789	+	0.905292i	$0.639652\pi$
$824$	−3.18039			−0.110794
$825$	−0.794889	−	2.40982i	−0.0276745	−	0.0838992i
$826$	3.82070	+	1.00573i	0.132939	+	0.0349939i
$827$		−	53.3096i		−	1.85376i	−0.375361	−	0.926879i	$-0.622481\pi$
$827$		−	53.3096i		−	1.85376i	0.375361	−	0.926879i	$-0.377519\pi$
$828$	−7.60796	+	17.5060i	−0.264395	+	0.608377i
$829$	39.1781	+	22.6195i	1.36071	+	0.785607i	0.989718	−	0.143029i	$-0.0456844\pi$
$829$	39.1781	+	22.6195i	1.36071	+	0.785607i	0.370992	+	0.928636i	$0.379018\pi$
$830$		−	11.8693i		−	0.411988i
$831$	38.5295	−	12.7091i	1.33658	−	0.440875i
$832$	−6.03529	−	3.48448i	−0.209236	−	0.120803i
$833$	−39.8453	+	23.4753i	−1.38056	+	0.813370i
$834$	23.2905	+	20.7836i	0.806483	+	0.719679i
$835$	6.88497	−	11.9251i	0.238264	−	0.412686i
$836$	−2.60849	+	4.51803i	−0.0902164	+	0.156259i
$837$	−3.72090	+	40.6190i	−0.128613	+	1.40400i
$838$	10.0677	−	5.81259i	0.347783	−	0.200793i
$839$	19.1888	+	33.2360i	0.662472	+	1.14744i	0.979964	+	0.199175i	$0.0638261\pi$
$839$	19.1888	+	33.2360i	0.662472	+	1.14744i	−0.317492	+	0.948261i	$0.602841\pi$
$840$	4.57399	−	0.280383i	0.157818	−	0.00967412i
$841$	−13.0118	+	22.5371i	−0.448683	+	0.777141i
$842$			22.9015i			0.789238i
$843$	−23.3928	+	26.2143i	−0.805690	+	0.902869i
$844$	−6.88595			−0.237024
$845$	−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
$849$	6.62372	−	7.42265i	0.227326	−	0.254745i
$850$	5.72151	−	3.30332i	0.196246	−	0.113303i
$851$	30.4107	−	17.5577i	1.04247	−	0.601869i
$852$	16.3910	−	18.3681i	0.561548	−	0.629279i
$853$	43.3554	−	25.0313i	1.48446	−	0.857054i	0.484618	−	0.874726i	$-0.338959\pi$
$853$	43.3554	−	25.0313i	1.48446	−	0.857054i	0.999844	+	0.0176720i	$0.00562545\pi$
$854$	−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
$857$	31.4431			1.07408			0.537038	−	0.843558i	$-0.319543\pi$
$857$	31.4431			1.07408			0.537038	+	0.843558i	$0.319543\pi$
$858$	11.7742	−	13.1944i	0.401965	−	0.450448i
$859$			30.1987i			1.03037i	0.857080	+	0.515183i	$0.172276\pi$
$859$			30.1987i			1.03037i	−0.857080	+	0.515183i	$0.827724\pi$
$860$	−3.24581	+	5.62191i	−0.110681	+	0.191705i
$861$	−5.18754	−	2.58553i	−0.176791	−	0.0881146i
$862$	4.81745	+	8.34407i	0.164083	+	0.284200i
$863$	−13.8288	+	7.98404i	−0.470736	+	0.271780i	−0.716548	−	0.697538i	$-0.754279\pi$
$863$	−13.8288	+	7.98404i	−0.470736	+	0.271780i	0.245812	+	0.969318i	$0.420946\pi$
$864$	−0.474009	+	5.17449i	−0.0161261	+	0.176040i
$865$	−5.81971	+	10.0800i	−0.197876	+	0.342731i
$866$	18.9229	−	32.7755i	0.643027	−	1.11376i
$867$	−34.4371	−	30.7306i	−1.16955	−	1.04366i
$868$	14.6209	−	14.7503i	0.496265	−	0.500658i
$869$	1.26117	+	0.728136i	0.0427822	+	0.0247003i
$870$	−2.83779	+	0.936056i	−0.0962100	+	0.0317353i
$871$		−	87.4591i		−	2.96344i
$872$	−6.25017	−	3.60853i	−0.211657	−	0.122200i
$873$	−12.4945	+	28.7501i	−0.422876	+	0.973045i
$874$		−	22.6569i		−	0.766382i
$875$	0.673503	−	2.55859i	0.0227686	−	0.0864962i
$876$	−0.695559	−	2.10869i	−0.0235008	−	0.0712460i
$877$	50.5516			1.70701			0.853503	−	0.521088i	$-0.174474\pi$
$877$	50.5516			1.70701			0.853503	+	0.521088i	$0.174474\pi$
$878$	−16.1987	−	28.0570i	−0.546680	−	0.946878i
$879$	−7.60643	+	36.5864i	−0.256559	+	1.23403i
$880$	−1.26877	−	0.732523i	−0.0427702	−	0.0246934i
$881$	7.58608			0.255581			0.127791	−	0.991801i	$-0.459211\pi$
$881$	7.58608			0.255581			0.127791	+	0.991801i	$0.459211\pi$
$882$	−19.3328	−	8.20009i	−0.650970	−	0.276111i
$883$	−19.9066			−0.669910			−0.334955	−	0.942234i	$-0.608721\pi$
$883$	−19.9066			−0.669910			−0.334955	+	0.942234i	$0.608721\pi$
$884$	39.8730	+	23.0207i	1.34107	+	0.774269i
$885$	1.92980	+	1.72209i	0.0648694	+	0.0578873i
$886$	−10.9509	−	18.9675i	−0.367903	−	0.637227i
$887$	−35.0510			−1.17690			−0.588449	−	0.808534i	$-0.700261\pi$
$887$	−35.0510			−1.17690			−0.588449	+	0.808534i	$0.700261\pi$
$888$	6.36466	−	7.13233i	0.213584	−	0.239345i
$889$	0.615838	−	2.33953i	0.0206546	−	0.0784652i
$890$			4.37482i			0.146644i
$891$	−12.6107	−	3.85034i	−0.422475	−	0.128991i
$892$	−11.6938	−	6.75140i	−0.391536	−	0.226053i
$893$			19.2206i			0.643193i
$894$	3.03038	−	14.5759i	0.101351	−	0.487492i
$895$	1.21808	+	0.703262i	0.0407161	+	0.0235074i
$896$	1.86257	−	1.87905i	0.0622240	−	0.0627748i
$897$	−15.6327	+	75.1923i	−0.521961	+	2.51060i
$898$	−12.9261	+	22.3887i	−0.431350	+	0.747120i
$899$	−6.77139	+	11.7284i	−0.225839	+	0.391164i
$900$	2.75140	+	1.19573i	0.0917134	+	0.0398578i
$901$	−37.0506	+	21.3912i	−1.23433	+	0.712643i
$902$	0.926515	+	1.60477i	0.0308496	+	0.0534330i
$903$	24.8045	−	16.4226i	0.825441	−	0.546509i
$904$	−3.13332	+	5.42707i	−0.104213	+	0.180502i
$905$		−	10.1582i		−	0.337671i
$906$	−4.42213	−	0.919375i	−0.146916	−	0.0305442i
$907$	4.13070			0.137158			0.0685789	−	0.997646i	$-0.478154\pi$
$907$	4.13070			0.137158			0.0685789	+	0.997646i	$0.478154\pi$
$908$	−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	$0.471873\pi$
$912$	−1.93207	−	5.85734i	−0.0639771	−	0.193956i
$913$	15.0593	−	8.69452i	0.498392	−	0.287747i
$914$	19.2658	−	11.1231i	0.637257	−	0.367920i
$915$	−6.33533	−	1.31713i	−0.209439	−	0.0435431i
$916$	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	0.916865	−	0.399197i	$-0.130711\pi$
$919$	3.41703	+	5.91848i	0.112718	+	0.195232i	−0.804148	+	0.594430i	$0.797378\pi$
$920$	6.36259			0.209768
$921$	2.83381	+	8.59111i	0.0933773	+	0.283087i
$922$		−	14.1074i		−	0.464602i
$923$	49.5259	−	85.7813i	1.63016	−	2.82353i
$924$	3.70630	+	5.59794i	0.121928	+	0.184159i
$925$	−2.75951	−	4.77962i	−0.0907323	−	0.157153i
$926$	5.77194	−	3.33243i	0.189678	−	0.109510i
$927$	5.67674	+	7.66868i	0.186448	+	0.251872i
$928$	−0.862614	+	1.49409i	−0.0283167	+	0.0490460i
$929$	18.0782	−	31.3123i	0.593126	−	1.02732i	−0.400682	−	0.916217i	$-0.631227\pi$
$929$	18.0782	−	31.3123i	0.593126	−	1.02732i	0.993808	−	0.111107i	$-0.0354398\pi$
$930$	12.9120	−	4.25909i	0.423402	−	0.139661i
$931$	24.9257	−	0.219668i	0.816908	−	0.00719931i
$932$	15.4408	+	8.91477i	0.505782	+	0.292013i
$933$	−17.1047	−	15.2637i	−0.559982	−	0.499710i
$934$			3.51433i			0.114992i
$935$	8.38228	+	4.83951i	0.274130	+	0.158269i
$936$	2.37060	+	20.7720i	0.0774854	+	0.678955i
$937$			25.1125i			0.820391i	0.911998	+	0.410195i	$0.134539\pi$
$937$			25.1125i			0.820391i	−0.911998	+	0.410195i	$0.865461\pi$
$938$	32.1098	+	8.45234i	1.04842	+	0.275979i
$939$	52.4930	+	10.9135i	1.71305	+	0.356147i
$940$	−5.39759			−0.176050
$941$	1.36104	+	2.35738i	0.0443685	+	0.0768485i	0.887357	−	0.461083i	$-0.152539\pi$
$941$	1.36104	+	2.35738i	0.0443685	+	0.0768485i	−0.842988	+	0.537932i	$0.819206\pi$
$942$	−12.8142	+	4.22680i	−0.417508	+	0.137717i
$943$	−6.96940	−	4.02378i	−0.226955	−	0.131032i
$944$	1.49328			0.0486023
$945$	−8.84027	−	10.5285i	−0.287574	−	0.342493i
$946$	−9.51053			−0.309214
$947$	3.89868	+	2.25090i	0.126690	+	0.0731446i	0.562006	−	0.827133i	$-0.310030\pi$
$947$	3.89868	+	2.25090i	0.126690	+	0.0731446i	−0.435316	+	0.900278i	$0.643363\pi$
$948$	−1.63503	+	0.539320i	−0.0531032	+	0.0175163i
$949$	−4.46701	−	7.73709i	−0.145005	−	0.251156i
$950$	−3.56096			−0.115533
$951$	25.6878	+	5.34057i	0.832984	+	0.173180i
$952$	−12.3053	+	12.4142i	−0.398817	+	0.402347i
$953$			18.8442i			0.610423i	0.952285	+	0.305211i	$0.0987271\pi$
$953$			18.8442i			0.610423i	−0.952285	+	0.305211i	$0.901273\pi$
$954$	−17.8172	−	7.74317i	−0.576852	−	0.250695i
$955$	14.8301	+	8.56216i	0.479890	+	0.277065i
$956$			15.8361i			0.512175i
$957$	−3.26638	−	2.91481i	−0.105587	−	0.0942225i
$958$	−0.866868	−	0.500486i	−0.0280072	−	0.0161700i
$959$	30.8265	+	8.11453i	0.995441	+	0.262032i
$960$	1.64488	−	0.542569i	0.0530882	−	0.0175113i
$961$	15.3101	−	26.5178i	0.493874	−	0.855414i
$962$	19.2309	−	33.3089i	0.620030	−	1.07392i
$963$	−19.0405	+	43.8125i	−0.613572	+	1.41184i
$964$	−22.8842	+	13.2122i	−0.737050	+	0.425536i
$965$	0.966528	+	1.67408i	0.0311136	+	0.0538904i
$966$	−26.0954	−	13.0063i	−0.839606	−	0.418469i
$967$	−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	$0.973764\pi$
$968$			8.85364i			0.284567i
$969$	12.7645	+	38.6973i	0.410053	+	1.24314i
$970$	10.4493			0.335506
$971$	0.536311	+	0.928919i	0.0172111	+	0.0298104i	0.874503	−	0.485021i	$-0.161188\pi$
$971$	0.536311	+	0.928919i	0.0172111	+	0.0298104i	−0.857292	+	0.514831i	$0.827855\pi$
$972$	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
$975$	11.8179	+	2.45697i	0.378475	+	0.0786861i
$976$	−3.23540	+	1.86796i	−0.103563	+	0.0597919i
$977$	−6.71436	+	3.87654i	−0.214811	+	0.124021i	−0.603545	−	0.797329i	$-0.706246\pi$
$977$	−6.71436	+	3.87654i	−0.214811	+	0.124021i	0.388734	+	0.921350i	$0.372912\pi$
$978$	−4.50012	−	13.6428i	−0.143898	−	0.436248i
$979$	−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
$983$	−21.5880			−0.688550			−0.344275	−	0.938869i	$-0.611875\pi$
$983$	−21.5880			−0.688550			−0.344275	+	0.938869i	$0.611875\pi$
$984$	−2.14488	−	0.445927i	−0.0683762	−	0.0142156i
$985$			22.0136i			0.701410i
$986$	5.69898	−	9.87092i	0.181492	−	0.314354i
$987$	22.1376	+	11.0336i	0.704647	+	0.351204i
$988$	−12.4081	−	21.4914i	−0.394754	−	0.683733i
$989$	35.7699	−	20.6518i	1.13742	−	0.656687i
$990$	0.498358	+	4.36679i	0.0158389	+	0.138786i
$991$	−3.97525	+	6.88534i	−0.126278	+	0.218720i	−0.922232	−	0.386637i	$-0.873636\pi$
$991$	−3.97525	+	6.88534i	−0.126278	+	0.218720i	0.795954	+	0.605357i	$0.206970\pi$
$992$	3.92493	−	6.79817i	0.124617	−	0.215842i
$993$	−0.459462	+	2.20998i	−0.0145806	+	0.0701317i
$994$	26.7075	+	26.4732i	0.847111	+	0.839679i
$995$	−23.0430	−	13.3039i	−0.730513	−	0.421762i
$996$	−4.18463	+	20.1278i	−0.132595	+	0.637773i
$997$			57.2385i			1.81276i	0.422463	+	0.906380i	$0.361166\pi$
$997$			57.2385i			1.81276i	−0.422463	+	0.906380i	$0.638834\pi$
$998$	14.4080	+	8.31844i	0.456076	+	0.263316i
$999$	−28.5581	−	2.61607i	−0.903540	−	0.0827687i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.14	✓	28	1.1	even	1	trivial
630.2.t.b.551.14	yes	28	63.47	even	6	inner
630.2.bk.b.101.11	yes	28	9.2	odd	6
630.2.bk.b.131.4	yes	28	7.5	odd	6
1890.2.t.b.1151.3		28	3.2	odd	2
1890.2.t.b.1601.3		28	63.61	odd	6
1890.2.bk.b.341.5		28	21.5	even	6
1890.2.bk.b.521.5		28	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.64488 - 0.542569i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.69579 + 0.352560i) q^{6} +(-0.673503 + 2.55859i) q^{7} +1.00000i q^{8} +(2.41124 - 1.78492i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.64488 - 0.542569i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.69579 + 0.352560i) q^{6} +(-0.673503 + 2.55859i) q^{7} +1.00000i q^{8} +(2.41124 - 1.78492i) q^{9} +(-0.866025 - 0.500000i) q^{10} -1.46505i q^{11} +(1.29232 + 1.15322i) q^{12} +(6.03529 + 3.48448i) q^{13} +(-1.86257 + 1.87905i) q^{14} +(-1.64488 + 0.542569i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.30332 - 5.72151i) q^{17} +(2.98065 - 0.340166i) q^{18} +(-3.08388 + 1.78048i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.280383 + 4.57399i) q^{21} +(0.732523 - 1.26877i) q^{22} +6.36259i q^{23} +(0.542569 + 1.64488i) q^{24} +1.00000 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} +(-1.69579 - 0.352560i) q^{30} +(-6.79817 + 3.92493i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.794889 - 2.40982i) 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} -3.56096 q^{38} +(11.8179 + 2.45697i) q^{39} -1.00000i q^{40} +(-0.632413 + 1.09537i) q^{41} +(-2.04418 + 4.10138i) q^{42} +(-3.24581 - 5.62191i) q^{43} +(1.26877 - 0.732523i) q^{44} +(-2.41124 + 1.78492i) q^{45} +(-3.18129 + 5.51016i) q^{46} +(2.69880 - 4.67445i) q^{47} +(-0.352560 + 1.69579i) q^{48} +(-6.09279 - 3.44644i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.32923 - 11.2035i) q^{51} +6.96896i q^{52} +(-5.60809 - 3.23783i) q^{53} +(4.71824 - 2.17674i) q^{54} +1.46505i q^{55} +(-2.55859 - 0.673503i) q^{56} +(-4.10657 + 4.60189i) q^{57} +1.72523 q^{58} +(-0.746642 - 1.29322i) q^{59} +(-1.29232 - 1.15322i) q^{60} +(3.23540 + 1.86796i) q^{61} -7.84985 q^{62} +(2.94290 + 7.37152i) q^{63} -1.00000 q^{64} +(-6.03529 - 3.48448i) q^{65} +(0.516517 - 2.48441i) q^{66} +(-6.27490 - 10.8685i) q^{67} +6.60663 q^{68} +(3.45214 + 10.4657i) q^{69} +(1.86257 - 1.87905i) q^{70} -14.2133i q^{71} +(1.78492 + 2.41124i) q^{72} +(-1.11022 - 0.640987i) q^{73} -5.51903i q^{74} +(1.64488 - 0.542569i) q^{75} +(-3.08388 - 1.78048i) q^{76} +(3.74846 + 0.986714i) q^{77} +(9.00610 + 8.03674i) q^{78} +(-0.497005 + 0.860839i) q^{79} +(0.500000 - 0.866025i) q^{80} +(2.62813 - 8.60772i) q^{81} +(-1.09537 + 0.632413i) q^{82} +(5.93463 + 10.2791i) q^{83} +(-3.82100 + 2.52981i) q^{84} +(-3.30332 + 5.72151i) q^{85} -6.49162i q^{86} +(1.98957 - 2.22954i) q^{87} +1.46505 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} +(-9.05261 + 10.1445i) q^{93} +(4.67445 - 2.69880i) q^{94} +(3.08388 - 1.78048i) q^{95} +(-1.15322 + 1.29232i) q^{96} +(-9.04933 + 5.22463i) q^{97} +(-3.55329 - 6.03110i) q^{98} +(-2.61499 - 3.53258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 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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