LMFDB - Embedded newform 630.2.t.b.551.14

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			551.14
Character	$\chi$	$=$	630.551
Dual form			630.2.t.b.311.14

$q$-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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.64488	+	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	$0.0708877\pi$
$11$			1.46505i			0.441728i	−0.975305	+	0.220864i	$0.929112\pi$
$12$	1.29232	−	1.15322i	0.373060	−	0.332906i
$13$	6.03529	−	3.48448i	1.67389	−	0.966420i	0.708461	−	0.705750i	$-0.249390\pi$
$13$	6.03529	−	3.48448i	1.67389	−	0.966420i	0.965428	−	0.260671i	$-0.0839436\pi$
$14$	−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	0.918845	+	0.394618i	$0.129123\pi$
$17$	3.30332	+	5.72151i	0.801172	+	1.38767i	−0.117673	+	0.993052i	$0.537544\pi$
$18$	2.98065	+	0.340166i	0.702546	+	0.0801778i
$19$	−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
$21$	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	$-0.769136\pi$
$23$		−	6.36259i		−	1.32669i	0.748313	−	0.663346i	$-0.230864\pi$
$24$	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	0.632267	−	0.774751i	$-0.282125\pi$
$29$	1.49409	+	0.862614i	0.277446	+	0.160183i	−0.354821	+	0.934934i	$0.615458\pi$
$30$	−1.69579	+	0.352560i	−0.309607	+	0.0643683i
$31$	−6.79817	−	3.92493i	−1.22099	−	0.704937i	−0.255859	−	0.966714i	$-0.582358\pi$
$31$	−6.79817	−	3.92493i	−1.22099	−	0.704937i	−0.965128	+	0.261777i	$0.915692\pi$
$32$	−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	−0.998610	−	0.0527049i	$-0.983216\pi$
$37$	−2.75951	+	4.77962i	−0.453661	+	0.785764i	0.544949	+	0.838469i	$0.316549\pi$
$38$	−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	0.812408	−	0.583089i	$-0.198156\pi$
$41$	−0.632413	−	1.09537i	−0.0987663	−	0.171068i	−0.911174	+	0.412021i	$0.864823\pi$
$42$	−2.04418	−	4.10138i	−0.315423	−	0.632857i
$43$	−3.24581	+	5.62191i	−0.494981	+	0.857333i	−0.999983	−	0.00578540i	$-0.998158\pi$
$43$	−3.24581	+	5.62191i	−0.494981	+	0.857333i	0.505002	+	0.863118i	$0.331492\pi$
$44$	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	0.992929	−	0.118709i	$-0.0378755\pi$
$47$	2.69880	+	4.67445i	0.393660	+	0.681839i	−0.599269	+	0.800547i	$0.704542\pi$
$48$	−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	−0.832993	−	0.553284i	$-0.813374\pi$
$53$	−5.60809	+	3.23783i	−0.770331	+	0.444751i	0.0626620	+	0.998035i	$0.480041\pi$
$54$	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	−0.910527	−	0.413451i	$-0.864323\pi$
$59$	−0.746642	+	1.29322i	−0.0972045	+	0.168363i	0.813322	+	0.581814i	$0.197657\pi$
$60$	−1.29232	+	1.15322i	−0.166837	+	0.148880i
$61$	3.23540	−	1.86796i	0.414250	−	0.239167i	−0.278364	−	0.960476i	$-0.589792\pi$
$61$	3.23540	−	1.86796i	0.414250	−	0.239167i	0.692614	+	0.721308i	$0.256459\pi$
$62$	−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	0.172794	+	0.984958i	$0.444720\pi$
$67$	−6.27490	+	10.8685i	−0.766602	+	1.32779i	−0.939396	+	0.342835i	$0.888613\pi$
$68$	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	$0.319451\pi$
$71$			14.2133i			1.68681i	−0.537281	+	0.843403i	$0.680549\pi$
$72$	1.78492	−	2.41124i	0.210355	−	0.284167i
$73$	−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	$0.357236\pi$
$74$			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	0.836712	−	0.547644i	$-0.184475\pi$
$79$	−0.497005	−	0.860839i	−0.0559175	−	0.0968519i	−0.892629	+	0.450792i	$0.851142\pi$
$80$	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	−0.331370	−	0.943501i	$-0.607511\pi$
$83$	5.93463	−	10.2791i	0.651411	−	1.12828i	0.982781	−	0.184776i	$-0.0591559\pi$
$84$	−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	−0.958357	−	0.285573i	$-0.907816\pi$
$89$	−2.18741	+	3.78871i	−0.231865	+	0.401602i	0.726492	+	0.687175i	$0.241149\pi$
$90$	−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	−0.0355618	−	0.999367i	$-0.511322\pi$
$97$	−9.04933	−	5.22463i	−0.918820	−	0.530481i	−0.883259	+	0.468886i	$0.844655\pi$
$98$	−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	$-0.949919\pi$
$103$		−	3.18039i		−	0.313373i	0.987648	−	0.156687i	$-0.0500813\pi$
$104$	−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	−0.347379	−	0.937725i	$-0.612928\pi$
$107$	−13.7903	−	7.96185i	−1.33316	−	0.769701i	−0.985783	+	0.168024i	$0.946261\pi$
$108$	5.17449	−	0.474009i	0.497915	−	0.0456115i
$109$	−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	$0.945670\pi$
$110$	−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	−0.222518	−	0.974929i	$-0.571428\pi$
$113$	5.42707	−	3.13332i	0.510536	−	0.294758i	0.733054	+	0.680170i	$0.238094\pi$
$114$	−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	$0.172088\pi$
$137$			12.0482i			1.02935i	−0.857385	+	0.514675i	$0.827912\pi$
$138$	−2.24319	−	10.7896i	−0.190953	−	0.918473i
$139$	15.6077	−	9.01113i	1.32383	−	0.764314i	0.339494	−	0.940608i	$-0.389744\pi$
$139$	15.6077	−	9.01113i	1.32383	−	0.764314i	0.984338	+	0.176294i	$0.0564110\pi$
$140$	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	$0.114526\pi$
$149$			8.59537i			0.704160i	−0.935970	+	0.352080i	$0.885474\pi$
$150$	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	0.206006	−	0.978551i	$-0.433953\pi$
$157$	−6.74663	−	3.89517i	−0.538440	−	0.310868i	−0.744446	+	0.667682i	$0.767287\pi$
$158$	−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	−0.981476	−	0.191584i	$-0.938638\pi$
$163$	−4.14705	+	7.18290i	−0.324822	+	0.562608i	0.656654	+	0.754192i	$0.271971\pi$
$164$	−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	−0.999268	−	0.0382680i	$-0.987816\pi$
$167$	−6.88497	−	11.9251i	−0.532775	−	0.922793i	0.466493	−	0.884525i	$-0.345517\pi$
$168$	−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	0.997872	−	0.0652078i	$-0.0207710\pi$
$173$	5.81971	+	10.0800i	0.442464	+	0.766371i	−0.555407	+	0.831578i	$0.687438\pi$
$174$	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	−0.544831	−	0.838546i	$-0.683406\pi$
$179$	−1.21808	+	0.703262i	−0.0910439	+	0.0525642i	0.453787	+	0.891110i	$0.350073\pi$
$180$	−2.75140	+	1.19573i	−0.205077	+	0.0891248i
$181$		−	10.1582i		−	0.755054i	−0.925998	−	0.377527i	$-0.876774\pi$
$181$		−	10.1582i		−	0.755054i	0.925998	−	0.377527i	$-0.123226\pi$
$182$	−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	−0.929018	−	0.370035i	$-0.879346\pi$
$191$	−14.8301	+	8.56216i	−1.07307	+	0.619536i	−0.144050	+	0.989570i	$0.546012\pi$
$192$	−1.64488	−	0.542569i	−0.118709	−	0.0391565i
$193$	−0.966528	+	1.67408i	−0.0695722	+	0.120503i	−0.898713	−	0.438537i	$-0.855497\pi$
$193$	−0.966528	+	1.67408i	−0.0695722	+	0.120503i	0.829141	+	0.559040i	$0.188830\pi$
$194$	−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	$0.286927\pi$
$197$			22.0136i			1.56840i	−0.620508	+	0.784200i	$0.713073\pi$
$198$	−0.498358	+	4.36679i	−0.0354168	+	0.310335i
$199$	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	$-0.0587604\pi$
$200$		−	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	0.722835	−	0.691021i	$-0.242839\pi$
$211$	−3.44298	−	5.96341i	−0.237024	−	0.410538i	−0.959859	+	0.280483i	$0.909505\pi$
$212$			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	0.0544458	−	0.998517i	$-0.482661\pi$
$223$	−11.6938	−	6.75140i	−0.783072	−	0.452107i	−0.837518	+	0.546410i	$0.815994\pi$
$224$	−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	$0.266944\pi$
$229$			22.5093i			1.48745i	−0.668484	+	0.743727i	$0.733056\pi$
$230$	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	0.911649	−	0.410970i	$-0.134810\pi$
$233$	15.4408	+	8.91477i	1.01156	+	0.584026i	0.0999142	+	0.994996i	$0.468143\pi$
$234$	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	0.0141164	−	0.999900i	$-0.495506\pi$
$239$	13.7144	−	7.91804i	0.887114	−	0.512175i	0.872997	+	0.487725i	$0.162173\pi$
$240$	0.352560	+	1.69579i	0.0227576	+	0.109463i
$241$		−	26.4244i		−	1.70215i	−0.525048	−	0.851073i	$-0.675953\pi$
$241$		−	26.4244i		−	1.70215i	0.525048	−	0.851073i	$-0.324047\pi$
$242$	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	$-0.984179\pi$
$263$		−	1.61144i		−	0.0993659i	0.998765	−	0.0496830i	$-0.0158211\pi$
$264$	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	0.796268	−	0.604944i	$-0.206804\pi$
$269$	−2.06266	−	3.57264i	−0.125763	−	0.217828i	−0.922031	+	0.387116i	$0.873471\pi$
$270$	−4.71824	−	2.17674i	−0.287143	−	0.132472i
$271$	−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
$273$	−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	−0.125887	−	0.992045i	$-0.540178\pi$
$281$	−17.5671	−	10.1424i	−1.04797	−	0.605043i	−0.922079	+	0.387001i	$0.873511\pi$
$282$	6.22461	+	6.97540i	0.370670	+	0.415379i
$283$	4.97417	+	2.87184i	0.295684	+	0.170713i	0.640502	−	0.767956i	$-0.278726\pi$
$283$	4.97417	+	2.87184i	0.295684	+	0.170713i	−0.344819	+	0.938669i	$0.612060\pi$
$284$	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	−0.987509	−	0.157564i	$-0.949636\pi$
$293$	−10.7874	−	18.6844i	−0.630209	−	1.09155i	0.357300	−	0.933990i	$-0.383697\pi$
$294$	−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	$-0.952380\pi$
$307$		−	5.22295i		−	0.298090i	0.988830	−	0.149045i	$-0.0476199\pi$
$308$	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	−0.990366	−	0.138472i	$-0.955781\pi$
$311$	−6.61784	+	11.4624i	−0.375263	+	0.649975i	0.615103	+	0.788447i	$0.289114\pi$
$312$	−2.45697	−	11.8179i	−0.139099	−	0.669056i
$313$	26.8077	−	15.4775i	1.51526	−	0.874838i	0.515424	−	0.856935i	$-0.327635\pi$
$313$	26.8077	−	15.4775i	1.51526	−	0.874838i	0.999840	−	0.0179024i	$-0.00569881\pi$
$314$	−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	−0.0840978	−	0.996458i	$-0.526801\pi$
$317$	13.1185	−	7.57399i	0.736811	−	0.425398i	0.820909	+	0.571060i	$0.193467\pi$
$318$	−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	0.847562	−	0.530696i	$-0.178070\pi$
$331$	−0.651609	−	1.12862i	−0.0358157	−	0.0620345i	−0.883378	+	0.468662i	$0.844736\pi$
$332$	−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	0.997865	−	0.0653053i	$-0.0208021\pi$
$337$	8.12095	+	14.0659i	0.442377	+	0.766219i	−0.555489	+	0.831524i	$0.687469\pi$
$338$		−	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	0.377442	−	0.926033i	$-0.376804\pi$
$347$	−4.39256	−	2.53604i	−0.235805	−	0.136142i	−0.613247	+	0.789891i	$0.710137\pi$
$348$	2.92562	−	0.608246i	0.156830	−	0.0326054i
$349$	20.4996	+	11.8354i	1.09732	+	0.633536i	0.935515	−	0.353287i	$-0.114936\pi$
$349$	20.4996	+	11.8354i	1.09732	+	0.633536i	0.161802	+	0.986823i	$0.448269\pi$
$350$	−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	0.349277	−	0.937019i	$-0.386427\pi$
$359$	−5.44862	−	3.14576i	−0.287567	−	0.166027i	−0.636844	+	0.770993i	$0.719761\pi$
$360$	−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	$-0.780785\pi$
$367$		−	24.3497i		−	1.27104i	0.772083	−	0.635522i	$-0.219215\pi$
$368$	−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	$-0.658088\pi$
$389$		−	34.6804i		−	1.75837i	0.476482	−	0.879184i	$-0.341912\pi$
$390$	−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	0.959791	−	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
$399$	−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	$-0.885662\pi$
$401$		−	14.0788i		−	0.703060i	0.936177	−	0.351530i	$-0.114338\pi$
$402$	−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	−0.408332	−	0.912833i	$-0.633890\pi$
$409$	−28.3746	−	16.3821i	−1.40304	−	0.810043i	−0.994703	+	0.102791i	$0.967223\pi$
$410$	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	0.972357	−	0.233498i	$-0.0750172\pi$
$419$	5.81259	+	10.0677i	0.283964	+	0.491839i	−0.688394	+	0.725337i	$0.741684\pi$
$420$	3.82100	+	2.52981i	0.186446	+	0.123442i
$421$	11.4508	−	19.8333i	0.558076	−	0.966615i	−0.439582	−	0.898203i	$-0.644873\pi$
$421$	11.4508	−	19.8333i	0.558076	−	0.966615i	0.997657	−	0.0684126i	$-0.0217934\pi$
$422$	−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	−0.285392	−	0.958411i	$-0.592124\pi$
$431$	8.34407	−	4.81745i	0.401920	−	0.232048i	0.687312	+	0.726362i	$0.258791\pi$
$432$	2.17674	−	4.71824i	0.104728	−	0.227007i
$433$			37.8458i			1.81875i	0.415972	+	0.909377i	$0.363441\pi$
$433$			37.8458i			1.81875i	−0.415972	+	0.909377i	$0.636559\pi$
$434$	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	−0.986672	−	0.162721i	$-0.947973\pi$
$439$	−28.0570	+	16.1987i	−1.33909	+	0.773122i	−0.352415	+	0.935844i	$0.614640\pi$
$440$	−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	−0.877581	−	0.479428i	$-0.840844\pi$
$443$	−18.9675	+	10.9509i	−0.901175	+	0.520293i	−0.0235935	+	0.999722i	$0.507511\pi$
$444$	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	$-0.791161\pi$
$449$		−	25.8522i		−	1.22004i	0.792385	−	0.610021i	$-0.208839\pi$
$450$	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	0.999721	+	0.0236222i	$0.00751987\pi$
$457$	11.1231	+	19.2658i	0.520318	+	0.901217i	−0.479403	+	0.877595i	$0.659147\pi$
$458$	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	−0.982219	−	0.187739i	$-0.939884\pi$
$461$	−7.05369	+	12.2173i	−0.328523	+	0.569018i	0.653696	+	0.756757i	$0.273217\pi$
$462$	6.00872	−	2.99481i	0.279551	−	0.139331i
$463$	3.33243	+	5.77194i	0.154871	+	0.268245i	0.933012	−	0.359845i	$-0.117170\pi$
$463$	3.33243	+	5.77194i	0.154871	+	0.268245i	−0.778141	+	0.628090i	$0.783837\pi$
$464$		−	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	−0.822502	−	0.568763i	$-0.807422\pi$
$467$	1.75717	−	3.04350i	0.0813119	−	0.140836i	0.903814	+	0.427926i	$0.140756\pi$
$468$	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	−0.981655	−	0.190664i	$-0.938936\pi$
$487$	−14.4755	−	25.0723i	−0.655948	−	1.13613i	0.325708	−	0.945471i	$-0.394397\pi$
$488$	−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	0.390896	−	0.920435i	$-0.372165\pi$
$491$	30.6555	−	17.6990i	1.38346	−	0.798743i	0.992568	+	0.121691i	$0.0388318\pi$
$492$	−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	0.913320	−	0.407244i	$-0.133510\pi$
$521$	2.37330	+	4.11068i	0.103976	+	0.180092i	−0.809343	+	0.587336i	$0.800177\pi$
$522$	4.15994	+	3.07939i	0.182075	+	0.134781i
$523$	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
$525$	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	−0.877447	−	0.479674i	$-0.840755\pi$
$541$	−0.542248	+	0.939202i	−0.0233131	+	0.0403794i	0.854133	+	0.520054i	$0.174088\pi$
$542$	−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	−0.990374	−	0.138417i	$-0.955798\pi$
$547$	−8.77785	+	15.2037i	−0.375314	+	0.650063i	0.615060	+	0.788480i	$0.289132\pi$
$548$	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	−0.956883	−	0.290472i	$-0.906188\pi$
$557$	−27.9379	+	16.1300i	−1.18377	+	0.683449i	−0.226885	+	0.973922i	$0.572854\pi$
$558$	−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	0.198479	+	0.980105i	$0.436400\pi$
$563$	−17.7852	+	30.8049i	−0.749557	+	1.29827i	−0.948035	+	0.318165i	$0.896933\pi$
$564$	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	−0.523983	+	0.851729i	$0.675555\pi$
$569$	−36.3434	+	20.9829i	−1.52359	+	0.879647i	−0.999610	+	0.0279186i	$0.991112\pi$
$570$	5.85734	+	1.93207i	0.245337	+	0.0809253i
$571$	−3.38623	+	5.86513i	−0.141709	+	0.245448i	−0.928140	−	0.372230i	$-0.878593\pi$
$571$	−3.38623	+	5.86513i	−0.141709	+	0.245448i	0.786431	+	0.617678i	$0.211927\pi$
$572$	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	−0.972273	−	0.233851i	$-0.924867\pi$
$577$	−30.1675	+	17.4172i	−1.25589	+	0.725087i	−0.283616	+	0.958938i	$0.591534\pi$
$578$			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	−0.0639444	−	0.997953i	$-0.520368\pi$
$587$	20.1646	−	34.9261i	0.832281	−	1.44155i	0.896225	−	0.443599i	$-0.146299\pi$
$588$	−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	0.431168	+	0.902272i	$0.358102\pi$
$593$	−13.7783	+	23.8647i	−0.565806	+	0.980005i	−0.996974	+	0.0777332i	$0.975232\pi$
$594$	−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	0.228425	−	0.973561i	$-0.426642\pi$
$599$	−12.2493	−	7.07211i	−0.500491	−	0.288959i	−0.728916	+	0.684603i	$0.759976\pi$
$600$	0.542569	−	1.64488i	0.0221503	−	0.0671518i
$601$	−10.7893	−	6.22920i	−0.440104	−	0.254094i	0.263537	−	0.964649i	$-0.415111\pi$
$601$	−10.7893	−	6.22920i	−0.440104	−	0.254094i	−0.703642	+	0.710555i	$0.748444\pi$
$602$	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	$0.0516955\pi$
$607$			7.96739i			0.323386i	−0.986841	+	0.161693i	$0.948305\pi$
$608$	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	0.924736	−	0.380609i	$-0.124286\pi$
$613$	3.28676	+	5.69283i	0.132751	+	0.229931i	−0.791985	+	0.610540i	$0.790952\pi$
$614$	−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	−0.630134	−	0.776486i	$-0.717000\pi$
$617$	−6.77484	+	3.91146i	−0.272745	+	0.157469i	0.357389	+	0.933955i	$0.383667\pi$
$618$	−1.12128	−	5.39327i	−0.0451044	−	0.216949i
$619$		−	45.9757i		−	1.84792i	−0.382492	−	0.923959i	$-0.624934\pi$
$619$		−	45.9757i		−	1.84792i	0.382492	−	0.923959i	$-0.375066\pi$
$620$	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	$0.156208\pi$
$641$			23.8637i			0.942558i	−0.881984	+	0.471279i	$0.843792\pi$
$642$	−26.1925	−	8.63971i	−1.03374	−	0.340982i
$643$	12.9563	−	7.48033i	0.510947	−	0.294996i	−0.222276	−	0.974984i	$-0.571348\pi$
$643$	12.9563	−	7.48033i	0.510947	−	0.294996i	0.733223	+	0.679988i	$0.238015\pi$
$644$	−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	0.933790	−	0.357821i	$-0.116480\pi$
$647$	3.99382	+	6.91751i	0.157013	+	0.271955i	−0.776777	+	0.629776i	$0.783147\pi$
$648$	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	$-0.813279\pi$
$653$		−	28.2899i		−	1.10707i	0.832826	−	0.553535i	$-0.186721\pi$
$654$	−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	0.493170	−	0.869933i	$-0.335838\pi$
$659$	−0.349881	−	0.202004i	−0.0136294	−	0.00786894i	−0.506799	+	0.862064i	$0.669171\pi$
$660$	−1.68952	−	1.89330i	−0.0657645	−	0.0736968i
$661$	2.96092	+	1.70949i	0.115167	+	0.0664915i	0.556477	−	0.830863i	$-0.312153\pi$
$661$	2.96092	+	1.70949i	0.115167	+	0.0664915i	−0.441310	+	0.897355i	$0.645486\pi$
$662$	−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	−0.623546	−	0.781787i	$-0.714309\pi$
$673$	9.47604	−	16.4130i	0.365274	−	0.632674i	0.988820	+	0.149113i	$0.0476418\pi$
$674$	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	0.679903	−	0.733302i	$-0.262022\pi$
$677$	−7.67846	−	13.2995i	−0.295107	−	0.511141i	−0.975010	+	0.222162i	$0.928689\pi$
$678$	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	0.114599	−	0.993412i	$-0.463442\pi$
$683$	26.9763	−	15.5748i	1.03222	−	0.595951i	0.917619	+	0.397460i	$0.130108\pi$
$684$	−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	0.0114437	−	0.999935i	$-0.496357\pi$
$691$	23.2148	−	13.4031i	0.883134	−	0.509878i	0.871691	+	0.490057i	$0.163024\pi$
$692$	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	$0.0567985\pi$
$701$			9.39873i			0.354985i	−0.984122	+	0.177493i	$0.943201\pi$
$702$	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	0.611171	−	0.791499i	$-0.290699\pi$
$709$	−10.1149	−	17.5195i	−0.379873	−	0.657959i	−0.991043	+	0.133540i	$0.957366\pi$
$710$	−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	−0.863137	−	0.504970i	$-0.831503\pi$
$719$	0.154148	−	0.266992i	0.00574874	−	0.00995710i	0.868885	+	0.495013i	$0.164837\pi$
$720$	−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	0.429944	−	0.902856i	$-0.358533\pi$
$727$	−3.69340	−	2.13238i	−0.136980	−	0.0790857i	−0.566924	+	0.823770i	$0.691867\pi$
$728$	−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	$0.0177171\pi$
$733$			3.01231i			0.111262i	−0.998451	+	0.0556310i	$0.982283\pi$
$734$	−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	0.982860	−	0.184352i	$-0.0590187\pi$
$739$	9.01920	+	15.6217i	0.331776	+	0.574654i	−0.651084	+	0.759006i	$0.725685\pi$
$740$	−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	−0.466217	−	0.884671i	$-0.654383\pi$
$743$	1.82145	−	1.05161i	0.0668225	−	0.0385800i	0.533039	+	0.846091i	$0.321050\pi$
$744$	−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	−0.201656	−	0.979456i	$-0.564632\pi$
$769$	15.1341	−	8.73768i	0.545750	−	0.315089i	0.747406	+	0.664368i	$0.231299\pi$
$770$	−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	0.634155	−	0.773206i	$-0.281348\pi$
$773$	−9.80159	−	16.9768i	−0.352539	−	0.610615i	−0.986694	+	0.162591i	$0.948015\pi$
$774$	−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	0.876078	−	0.482170i	$-0.160151\pi$
$787$	25.1512	+	14.5211i	0.896545	+	0.517620i	0.0204673	+	0.999791i	$0.493485\pi$
$788$	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	0.999995	−	0.00331218i	$-0.00105430\pi$
$797$	14.0345	+	24.3085i	0.497129	+	0.861052i	−0.502866	+	0.864365i	$0.667721\pi$
$798$	−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	−0.456035	−	0.889962i	$-0.650731\pi$
$809$	2.46533	−	1.42336i	0.0866764	−	0.0500427i	0.542712	+	0.839919i	$0.317398\pi$
$810$	−6.57989	−	6.14044i	−0.231194	−	0.215753i
$811$			5.05522i			0.177513i	0.996053	+	0.0887564i	$0.0282893\pi$
$811$			5.05522i			0.177513i	−0.996053	+	0.0887564i	$0.971711\pi$
$812$	−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	0.224767	−	0.974412i	$-0.427838\pi$
$821$	33.8398	−	19.5374i	1.18102	−	0.681861i	0.956250	+	0.292552i	$0.0945044\pi$
$822$	4.24772	+	20.4313i	0.148156	+	0.712623i
$823$	16.3984	−	28.4028i	0.571612	−	0.990061i	−0.424789	−	0.905292i	$-0.639652\pi$
$823$	16.3984	−	28.4028i	0.571612	−	0.990061i	0.996401	−	0.0847683i	$-0.0270150\pi$
$824$	−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	$0.377519\pi$
$827$			53.3096i			1.85376i	−0.375361	+	0.926879i	$0.622481\pi$
$828$	−7.60796	−	17.5060i	−0.264395	−	0.608377i
$829$	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	$0.0456844\pi$
$830$			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	−0.317492	−	0.948261i	$-0.602841\pi$
$839$	19.1888	−	33.2360i	0.662472	−	1.14744i	0.979964	−	0.199175i	$-0.0638261\pi$
$840$	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	0.999844	−	0.0176720i	$-0.00562545\pi$
$853$	43.3554	+	25.0313i	1.48446	+	0.857054i	0.484618	+	0.874726i	$0.338959\pi$
$854$	−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	$-0.827724\pi$
$859$		−	30.1987i		−	1.03037i	0.857080	−	0.515183i	$-0.172276\pi$
$860$	−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	0.245812	−	0.969318i	$-0.420946\pi$
$863$	−13.8288	−	7.98404i	−0.470736	−	0.271780i	−0.716548	+	0.697538i	$0.754279\pi$
$864$	−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	0.0882472	−	0.996099i	$-0.471873\pi$
$911$	−22.0418	−	12.7258i	−0.730276	−	0.421625i	−0.818523	+	0.574474i	$0.805207\pi$
$912$	−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	−0.804148	−	0.594430i	$-0.797378\pi$
$919$	3.41703	−	5.91848i	0.112718	−	0.195232i	0.916865	+	0.399197i	$0.130711\pi$
$920$	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	0.993808	+	0.111107i	$0.0354398\pi$
$929$	18.0782	+	31.3123i	0.593126	+	1.02732i	−0.400682	+	0.916217i	$0.631227\pi$
$930$	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	$-0.865461\pi$
$937$		−	25.1125i		−	0.820391i	0.911998	−	0.410195i	$-0.134539\pi$
$938$	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	−0.842988	−	0.537932i	$-0.819206\pi$
$941$	1.36104	−	2.35738i	0.0443685	−	0.0768485i	0.887357	+	0.461083i	$0.152539\pi$
$942$	−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	−0.435316	−	0.900278i	$-0.643363\pi$
$947$	3.89868	−	2.25090i	0.126690	−	0.0731446i	0.562006	+	0.827133i	$0.310030\pi$
$948$	−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	$-0.901273\pi$
$953$		−	18.8442i		−	0.610423i	0.952285	−	0.305211i	$-0.0987271\pi$
$954$	−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	−0.996605	−	0.0823294i	$-0.973764\pi$
$967$	−17.7127	−	30.6793i	−0.569602	−	0.986579i	0.427003	−	0.904250i	$-0.359569\pi$
$968$		−	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	−0.857292	−	0.514831i	$-0.827855\pi$
$971$	0.536311	−	0.928919i	0.0172111	−	0.0298104i	0.874503	+	0.485021i	$0.161188\pi$
$972$	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	0.388734	−	0.921350i	$-0.372912\pi$
$977$	−6.71436	−	3.87654i	−0.214811	−	0.124021i	−0.603545	+	0.797329i	$0.706246\pi$
$978$	−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	0.795954	−	0.605357i	$-0.206970\pi$
$991$	−3.97525	−	6.88534i	−0.126278	−	0.218720i	−0.922232	+	0.386637i	$0.873636\pi$
$992$	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	$-0.638834\pi$
$997$		−	57.2385i		−	1.81276i	0.422463	−	0.906380i	$-0.361166\pi$
$998$	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.551.14	yes	28
3.2	odd	2		1890.2.t.b.1601.3		28
7.3	odd	6		630.2.bk.b.101.11	yes	28
9.4	even	3		1890.2.bk.b.341.5		28
9.5	odd	6		630.2.bk.b.131.4	yes	28
21.17	even	6		1890.2.bk.b.521.5		28
63.31	odd	6		1890.2.t.b.1151.3		28
63.59	even	6	inner	630.2.t.b.311.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.14	✓	28	63.59	even	6	inner
630.2.t.b.551.14	yes	28	1.1	even	1	trivial
630.2.bk.b.101.11	yes	28	7.3	odd	6
630.2.bk.b.131.4	yes	28	9.5	odd	6
1890.2.t.b.1151.3		28	63.31	odd	6
1890.2.t.b.1601.3		28	3.2	odd	2
1890.2.bk.b.341.5		28	9.4	even	3
1890.2.bk.b.521.5		28	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.64488 + 0.542569i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.69579 - 0.352560i) q^{6} +(-0.673503 - 2.55859i) q^{7} -1.00000i q^{8} +(2.41124 + 1.78492i) q^{9} +O(q^{10})\)	\(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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