LMFDB - Embedded newform 630.2.t.c.311.10

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.10
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.55522 + 0.762428i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.72807 - 0.117327i) q^{6} +(1.13965 - 2.38772i) q^{7} +1.00000i q^{8} +(1.83741 - 2.37148i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.55522 + 0.762428i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.72807 - 0.117327i) q^{6} +(1.13965 - 2.38772i) q^{7} +1.00000i q^{8} +(1.83741 - 2.37148i) q^{9} +(0.866025 + 0.500000i) q^{10} +1.06702i q^{11} +(-1.43789 - 0.965644i) q^{12} +(3.43295 + 1.98201i) q^{13} +(2.18082 - 1.49800i) q^{14} +(-1.55522 + 0.762428i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.26688 - 5.65839i) q^{17} +(2.77698 - 1.13506i) q^{18} +(1.00811 - 0.582034i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.0480629 + 4.58232i) q^{21} +(-0.533511 + 0.924068i) q^{22} +7.37575i q^{23} +(-0.762428 - 1.55522i) q^{24} +1.00000 q^{25} +(1.98201 + 3.43295i) q^{26} +(-1.04948 + 5.08907i) q^{27} +(2.63765 - 0.206895i) q^{28} +(-5.89304 + 3.40235i) q^{29} +(-1.72807 - 0.117327i) q^{30} +(3.61632 - 2.08788i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.813528 - 1.65945i) q^{33} +(5.65839 - 3.26688i) q^{34} +(1.13965 - 2.38772i) q^{35} +(2.97247 + 0.405499i) q^{36} +(2.89946 + 5.02202i) q^{37} +1.16407 q^{38} +(-6.85013 - 0.465087i) q^{39} +1.00000i q^{40} +(5.22517 - 9.05026i) q^{41} +(-2.24954 + 3.99244i) q^{42} +(0.665456 + 1.15260i) q^{43} +(-0.924068 + 0.533511i) q^{44} +(1.83741 - 2.37148i) q^{45} +(-3.68787 + 6.38758i) q^{46} +(-6.02991 + 10.4441i) q^{47} +(0.117327 - 1.72807i) q^{48} +(-4.40240 - 5.44232i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.766584 + 11.2908i) q^{51} +3.96403i q^{52} +(7.55453 + 4.36161i) q^{53} +(-3.45341 + 3.88252i) q^{54} +1.06702i q^{55} +(2.38772 + 1.13965i) q^{56} +(-1.12408 + 1.67380i) q^{57} -6.80470 q^{58} +(-4.63478 - 8.02767i) q^{59} +(-1.43789 - 0.965644i) q^{60} +(3.02698 + 1.74763i) q^{61} +4.17577 q^{62} +(-3.56844 - 7.08987i) q^{63} -1.00000 q^{64} +(3.43295 + 1.98201i) q^{65} +(0.125190 - 1.84389i) q^{66} +(-2.98398 - 5.16841i) q^{67} +6.53375 q^{68} +(-5.62348 - 11.4709i) q^{69} +(2.18082 - 1.49800i) q^{70} +0.707493i q^{71} +(2.37148 + 1.83741i) q^{72} +(-6.25109 - 3.60907i) q^{73} +5.79892i q^{74} +(-1.55522 + 0.762428i) q^{75} +(1.00811 + 0.582034i) q^{76} +(2.54775 + 1.21603i) q^{77} +(-5.69984 - 3.82784i) q^{78} +(3.43917 - 5.95682i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.24788 - 8.71476i) q^{81} +(9.05026 - 5.22517i) q^{82} +(2.68887 + 4.65726i) q^{83} +(-3.94438 + 2.33279i) q^{84} +(3.26688 - 5.65839i) q^{85} +1.33091i q^{86} +(6.57092 - 9.78442i) q^{87} -1.06702 q^{88} +(-2.09514 - 3.62889i) q^{89} +(2.77698 - 1.13506i) q^{90} +(8.64485 - 5.93812i) q^{91} +(-6.38758 + 3.68787i) q^{92} +(-4.03230 + 6.00430i) q^{93} +(-10.4441 + 6.02991i) q^{94} +(1.00811 - 0.582034i) q^{95} +(0.965644 - 1.43789i) q^{96} +(4.59071 - 2.65045i) q^{97} +(-1.09143 - 6.91439i) q^{98} +(2.53043 + 1.96055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * 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
$3$	−1.55522	+	0.762428i	−0.897906	+	0.440188i
$3$	−1.55522	+	0.762428i	−0.897906	+	0.440188i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.72807	−	0.117327i	−0.705483	−	0.0478985i
$7$	1.13965	−	2.38772i	0.430747	−	0.902473i
$7$	1.13965	−	2.38772i	0.430747	−	0.902473i
$8$			1.00000i			0.353553i
$9$	1.83741	−	2.37148i	0.612469	−	0.790495i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			1.06702i			0.321719i	0.986977	+	0.160860i	$0.0514266\pi$
$11$			1.06702i			0.321719i	−0.986977	+	0.160860i	$0.948573\pi$
$12$	−1.43789	−	0.965644i	−0.415083	−	0.278757i
$13$	3.43295	+	1.98201i	0.952129	+	0.549712i	0.893742	−	0.448582i	$-0.148071\pi$
$13$	3.43295	+	1.98201i	0.952129	+	0.549712i	0.0583871	+	0.998294i	$0.481404\pi$
$14$	2.18082	−	1.49800i	0.582850	−	0.400358i
$15$	−1.55522	+	0.762428i	−0.401556	+	0.196858i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.26688	−	5.65839i	0.792334	−	1.37236i	−0.132185	−	0.991225i	$-0.542199\pi$
$17$	3.26688	−	5.65839i	0.792334	−	1.37236i	0.924519	−	0.381137i	$-0.124467\pi$
$18$	2.77698	−	1.13506i	0.654541	−	0.267537i
$19$	1.00811	−	0.582034i	0.231277	−	0.133528i	−0.379884	−	0.925034i	$-0.624036\pi$
$19$	1.00811	−	0.582034i	0.231277	−	0.133528i	0.611161	+	0.791506i	$0.290703\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	0.0480629	+	4.58232i	0.0104882	+	0.999945i
$22$	−0.533511	+	0.924068i	−0.113745	+	0.197012i
$23$			7.37575i			1.53795i	0.639279	+	0.768975i	$0.279233\pi$
$23$			7.37575i			1.53795i	−0.639279	+	0.768975i	$0.720767\pi$
$24$	−0.762428	−	1.55522i	−0.155630	−	0.317458i
$25$	1.00000			0.200000
$26$	1.98201	+	3.43295i	0.388705	+	0.673257i
$27$	−1.04948	+	5.08907i	−0.201973	+	0.979391i
$28$	2.63765	−	0.206895i	0.498469	−	0.0390995i
$29$	−5.89304	+	3.40235i	−1.09431	+	0.631800i	−0.934721	−	0.355383i	$-0.884350\pi$
$29$	−5.89304	+	3.40235i	−1.09431	+	0.631800i	−0.159590	+	0.987183i	$0.551017\pi$
$30$	−1.72807	−	0.117327i	−0.315501	−	0.0214208i
$31$	3.61632	−	2.08788i	0.649510	−	0.374995i	−0.138758	−	0.990326i	$-0.544311\pi$
$31$	3.61632	−	2.08788i	0.649510	−	0.374995i	0.788269	+	0.615331i	$0.210978\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.813528	−	1.65945i	−0.141617	−	0.288873i
$34$	5.65839	−	3.26688i	0.970406	−	0.560264i
$35$	1.13965	−	2.38772i	0.192636	−	0.403598i
$36$	2.97247	+	0.405499i	0.495411	+	0.0675831i
$37$	2.89946	+	5.02202i	0.476669	+	0.825614i	0.999643	−	0.0267343i	$-0.00851081\pi$
$37$	2.89946	+	5.02202i	0.476669	+	0.825614i	−0.522974	+	0.852349i	$0.675177\pi$
$38$	1.16407			0.188837
$39$	−6.85013	−	0.465087i	−1.09690	−	0.0744735i
$40$			1.00000i			0.158114i
$41$	5.22517	−	9.05026i	0.816034	−	1.41341i	−0.0925487	−	0.995708i	$-0.529501\pi$
$41$	5.22517	−	9.05026i	0.816034	−	1.41341i	0.908583	−	0.417705i	$-0.137165\pi$
$42$	−2.24954	+	3.99244i	−0.347111	+	0.616047i
$43$	0.665456	+	1.15260i	0.101481	+	0.175770i	0.912295	−	0.409534i	$-0.134309\pi$
$43$	0.665456	+	1.15260i	0.101481	+	0.175770i	−0.810814	+	0.585304i	$0.800975\pi$
$44$	−0.924068	+	0.533511i	−0.139308	+	0.0804298i
$45$	1.83741	−	2.37148i	0.273904	−	0.353520i
$46$	−3.68787	+	6.38758i	−0.543747	+	0.941798i
$47$	−6.02991	+	10.4441i	−0.879553	+	1.52343i	−0.0277210	+	0.999616i	$0.508825\pi$
$47$	−6.02991	+	10.4441i	−0.879553	+	1.52343i	−0.851832	+	0.523815i	$0.824508\pi$
$48$	0.117327	−	1.72807i	0.0169347	−	0.249426i
$49$	−4.40240	−	5.44232i	−0.628915	−	0.777474i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−0.766584	+	11.2908i	−0.107343	+	1.58103i
$52$			3.96403i			0.549712i
$53$	7.55453	+	4.36161i	1.03769	+	0.599113i	0.919179	−	0.393839i	$-0.128853\pi$
$53$	7.55453	+	4.36161i	1.03769	+	0.599113i	0.118515	+	0.992952i	$0.462187\pi$
$54$	−3.45341	+	3.88252i	−0.469950	+	0.528344i
$55$			1.06702i			0.143877i
$56$	2.38772	+	1.13965i	0.319072	+	0.152292i
$57$	−1.12408	+	1.67380i	−0.148887	+	0.221701i
$58$	−6.80470			−0.893501
$59$	−4.63478	−	8.02767i	−0.603397	−	1.04511i	−0.992303	−	0.123836i	$-0.960480\pi$
$59$	−4.63478	−	8.02767i	−0.603397	−	1.04511i	0.388906	−	0.921278i	$-0.372853\pi$
$60$	−1.43789	−	0.965644i	−0.185631	−	0.124664i
$61$	3.02698	+	1.74763i	0.387565	+	0.223761i	0.681105	−	0.732186i	$-0.261500\pi$
$61$	3.02698	+	1.74763i	0.387565	+	0.223761i	−0.293540	+	0.955947i	$0.594833\pi$
$62$	4.17577			0.530323
$63$	−3.56844	−	7.08987i	−0.449581	−	0.893239i
$64$	−1.00000			−0.125000
$65$	3.43295	+	1.98201i	0.425805	+	0.245839i
$66$	0.125190	−	1.84389i	0.0154099	−	0.226967i
$67$	−2.98398	−	5.16841i	−0.364551	−	0.631421i	0.624153	−	0.781302i	$-0.285444\pi$
$67$	−2.98398	−	5.16841i	−0.364551	−	0.631421i	−0.988704	+	0.149881i	$0.952111\pi$
$68$	6.53375			0.792334
$69$	−5.62348	−	11.4709i	−0.676987	−	1.38093i
$70$	2.18082	−	1.49800i	0.260658	−	0.179045i
$71$			0.707493i			0.0839640i	0.999118	+	0.0419820i	$0.0133672\pi$
$71$			0.707493i			0.0839640i	−0.999118	+	0.0419820i	$0.986633\pi$
$72$	2.37148	+	1.83741i	0.279482	+	0.216540i
$73$	−6.25109	−	3.60907i	−0.731635	−	0.422410i	0.0873849	−	0.996175i	$-0.472149\pi$
$73$	−6.25109	−	3.60907i	−0.731635	−	0.422410i	−0.819020	+	0.573765i	$0.805482\pi$
$74$			5.79892i			0.674111i
$75$	−1.55522	+	0.762428i	−0.179581	+	0.0880376i
$76$	1.00811	+	0.582034i	0.115638	+	0.0667639i
$77$	2.54775	+	1.21603i	0.290343	+	0.138579i
$78$	−5.69984	−	3.82784i	−0.645380	−	0.433418i
$79$	3.43917	−	5.95682i	0.386937	−	0.670195i	−0.605099	−	0.796151i	$-0.706866\pi$
$79$	3.43917	−	5.95682i	0.386937	−	0.670195i	0.992036	+	0.125955i	$0.0401996\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−2.24788	−	8.71476i	−0.249764	−	0.968307i
$82$	9.05026	−	5.22517i	0.999434	−	0.577023i
$83$	2.68887	+	4.65726i	0.295142	+	0.511201i	0.975018	−	0.222126i	$-0.0712998\pi$
$83$	2.68887	+	4.65726i	0.295142	+	0.511201i	−0.679876	+	0.733327i	$0.737966\pi$
$84$	−3.94438	+	2.33279i	−0.430367	+	0.254528i
$85$	3.26688	−	5.65839i	0.354342	−	0.613739i
$86$			1.33091i			0.143516i
$87$	6.57092	−	9.78442i	0.704476	−	1.04900i
$88$	−1.06702			−0.113745
$89$	−2.09514	−	3.62889i	−0.222085	−	0.384662i	0.733356	−	0.679845i	$-0.237953\pi$
$89$	−2.09514	−	3.62889i	−0.222085	−	0.384662i	−0.955441	+	0.295183i	$0.904619\pi$
$90$	2.77698	−	1.13506i	0.292720	−	0.119646i
$91$	8.64485	−	5.93812i	0.906226	−	0.622484i
$92$	−6.38758	+	3.68787i	−0.665952	+	0.384487i
$93$	−4.03230	+	6.00430i	−0.418131	+	0.622617i
$94$	−10.4441	+	6.02991i	−1.07723	+	0.621938i
$95$	1.00811	−	0.582034i	0.103430	−	0.0597154i
$96$	0.965644	−	1.43789i	0.0985557	−	0.146754i
$97$	4.59071	−	2.65045i	0.466116	−	0.269112i	−0.248496	−	0.968633i	$-0.579936\pi$
$97$	4.59071	−	2.65045i	0.466116	−	0.269112i	0.714613	+	0.699521i	$0.246603\pi$
$98$	−1.09143	−	6.91439i	−0.110251	−	0.698459i
$99$	2.53043	+	1.96055i	0.254317	+	0.197043i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−14.6847			−1.46118			−0.730589	−	0.682817i	$-0.760754\pi$
$101$	−14.6847			−1.46118			−0.730589	+	0.682817i	$0.760754\pi$
$102$	−6.30928	+	9.39482i	−0.624712	+	0.930226i
$103$		−	13.8207i		−	1.36180i	−0.732377	−	0.680899i	$-0.761589\pi$
$103$		−	13.8207i		−	1.36180i	0.732377	−	0.680899i	$-0.238411\pi$
$104$	−1.98201	+	3.43295i	−0.194352	+	0.336628i
$105$	0.0480629	+	4.58232i	0.00469046	+	0.447189i
$106$	4.36161	+	7.55453i	0.423637	+	0.733761i
$107$	−10.4580	+	6.03792i	−1.01101	+	0.583708i	−0.911488	−	0.411327i	$-0.865065\pi$
$107$	−10.4580	+	6.03792i	−1.01101	+	0.583708i	−0.0995244	+	0.995035i	$0.531732\pi$
$108$	−4.93200	+	1.63566i	−0.474582	+	0.157391i
$109$	6.97867	−	12.0874i	0.668435	−	1.15776i	−0.309906	−	0.950767i	$-0.600298\pi$
$109$	6.97867	−	12.0874i	0.668435	−	1.15776i	0.978342	−	0.206997i	$-0.0663690\pi$
$110$	−0.533511	+	0.924068i	−0.0508683	+	0.0881064i
$111$	−8.33822	−	5.59970i	−0.791429	−	0.531500i
$112$	1.49800	+	2.18082i	0.141548	+	0.206068i
$113$	−5.95078	−	3.43569i	−0.559803	−	0.323202i	0.193264	−	0.981147i	$-0.438093\pi$
$113$	−5.95078	−	3.43569i	−0.559803	−	0.323202i	−0.753066	+	0.657945i	$0.771426\pi$
$114$	−1.81038	+	0.887518i	−0.169558	+	0.0831237i
$115$			7.37575i			0.687792i
$116$	−5.89304	−	3.40235i	−0.547155	−	0.315900i
$117$	11.0080	−	4.49942i	1.01769	−	0.415971i
$118$		−	9.26956i		−	0.853332i
$119$	−9.78757	−	14.2490i	−0.897225	−	1.30620i
$120$	−0.762428	−	1.55522i	−0.0695999	−	0.141971i
$121$	9.86146			0.896497
$122$	1.74763	+	3.02698i	0.158223	+	0.274050i
$123$	−1.22610	+	18.0589i	−0.110554	+	1.62832i
$124$	3.61632	+	2.08788i	0.324755	+	0.187497i
$125$	1.00000			0.0894427
$126$	0.454573	−	7.92423i	0.0404966	−	0.705946i
$127$	−8.69967			−0.771971			−0.385985	−	0.922505i	$-0.626138\pi$
$127$	−8.69967			−0.771971			−0.385985	+	0.922505i	$0.626138\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−1.91371	−	1.28519i	−0.168493	−	0.113154i
$130$	1.98201	+	3.43295i	0.173834	+	0.301090i
$131$	1.16363			0.101667			0.0508335	−	0.998707i	$-0.483812\pi$
$131$	1.16363			0.101667			0.0508335	+	0.998707i	$0.483812\pi$
$132$	1.03036	−	1.53426i	0.0896816	−	0.133540i
$133$	−0.240840	−	3.07040i	−0.0208835	−	0.266238i
$134$		−	5.96796i		−	0.515553i
$135$	−1.04948	+	5.08907i	−0.0903250	+	0.437997i
$136$	5.65839	+	3.26688i	0.485203	+	0.280132i
$137$			6.38560i			0.545558i	0.962077	+	0.272779i	$0.0879428\pi$
$137$			6.38560i			0.545558i	−0.962077	+	0.272779i	$0.912057\pi$
$138$	0.865373	−	12.7458i	0.0736654	−	1.08500i
$139$	−13.7470	−	7.93684i	−1.16601	−	0.673194i	−0.213270	−	0.976993i	$-0.568411\pi$
$139$	−13.7470	−	7.93684i	−1.16601	−	0.673194i	−0.952736	+	0.303799i	$0.901745\pi$
$140$	2.63765	−	0.206895i	0.222922	−	0.0174858i
$141$	1.41494	−	20.8403i	0.119160	−	1.75507i
$142$	−0.353747	+	0.612707i	−0.0296857	+	0.0514172i
$143$	−2.11485	+	3.66303i	−0.176853	+	0.306318i
$144$	1.13506	+	2.77698i	0.0945885	+	0.231415i
$145$	−5.89304	+	3.40235i	−0.489390	+	0.282550i
$146$	−3.60907	−	6.25109i	−0.298689	−	0.517344i
$147$	10.9961	+	5.10748i	0.906941	+	0.421258i
$148$	−2.89946	+	5.02202i	−0.238334	+	0.412807i
$149$			10.2722i			0.841535i	0.907169	+	0.420767i	$0.138239\pi$
$149$			10.2722i			0.841535i	−0.907169	+	0.420767i	$0.861761\pi$
$150$	−1.72807	−	0.117327i	−0.141097	−	0.00957970i
$151$	−18.4715			−1.50319			−0.751596	−	0.659624i	$-0.770716\pi$
$151$	−18.4715			−1.50319			−0.751596	+	0.659624i	$0.770716\pi$
$152$	0.582034	+	1.00811i	0.0472092	+	0.0817687i
$153$	−7.41621	−	18.1441i	−0.599565	−	1.46686i
$154$	1.59840	+	2.32699i	0.128803	+	0.187514i
$155$	3.61632	−	2.08788i	0.290470	−	0.167703i
$156$	−3.02229	−	6.16493i	−0.241977	−	0.493589i
$157$	7.92392	−	4.57487i	0.632397	−	0.365115i	−0.149283	−	0.988795i	$-0.547696\pi$
$157$	7.92392	−	4.57487i	0.632397	−	0.365115i	0.781680	+	0.623680i	$0.214363\pi$
$158$	5.95682	−	3.43917i	0.473899	−	0.273606i
$159$	−15.0744	−	1.02347i	−1.19547	−	0.0811663i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	17.6112	+	8.40575i	1.38796	+	0.662466i
$162$	2.41066	−	8.67114i	0.189400	−	0.681269i
$163$	−0.489557	−	0.847938i	−0.0383451	−	0.0664156i	0.846216	−	0.532840i	$-0.178875\pi$
$163$	−0.489557	−	0.847938i	−0.0383451	−	0.0664156i	−0.884561	+	0.466424i	$0.845542\pi$
$164$	10.4503			0.816034
$165$	−0.813528	−	1.65945i	−0.0633330	−	0.129188i
$166$			5.37774i			0.417394i
$167$	−10.0381	+	17.3864i	−0.776769	+	1.34540i	0.157026	+	0.987594i	$0.449809\pi$
$167$	−10.0381	+	17.3864i	−0.776769	+	1.34540i	−0.933795	+	0.357809i	$0.883524\pi$
$168$	−4.58232	+	0.0480629i	−0.353534	+	0.00370813i
$169$	1.35676	+	2.34997i	0.104366	+	0.180767i
$170$	5.65839	−	3.26688i	0.433979	−	0.250558i
$171$	0.472028	−	3.46016i	0.0360969	−	0.264605i
$172$	−0.665456	+	1.15260i	−0.0507406	+	0.0878852i
$173$	−11.5519	+	20.0084i	−0.878272	+	1.52121i	−0.0250361	+	0.999687i	$0.507970\pi$
$173$	−11.5519	+	20.0084i	−0.878272	+	1.52121i	−0.853236	+	0.521525i	$0.825363\pi$
$174$	10.5828	−	5.18809i	0.802279	−	0.393308i
$175$	1.13965	−	2.38772i	0.0861493	−	0.180495i
$176$	−0.924068	−	0.533511i	−0.0696542	−	0.0402149i
$177$	13.3286	+	8.95110i	1.00184	+	0.672806i
$178$		−	4.19028i		−	0.314075i
$179$	−12.2484	−	7.07161i	−0.915487	−	0.528557i	−0.0332944	−	0.999446i	$-0.510600\pi$
$179$	−12.2484	−	7.07161i	−0.915487	−	0.528557i	−0.882192	+	0.470889i	$0.843933\pi$
$180$	2.97247	+	0.405499i	0.221555	+	0.0302241i
$181$			1.51075i			0.112293i	0.998423	+	0.0561466i	$0.0178814\pi$
$181$			1.51075i			0.112293i	−0.998423	+	0.0561466i	$0.982119\pi$
$182$	10.4557	−	0.820138i	0.775029	−	0.0607927i
$183$	−6.04005	−	0.410087i	−0.446494	−	0.0303145i
$184$	−7.37575			−0.543747
$185$	2.89946	+	5.02202i	0.213173	+	0.369226i
$186$	−6.49423	+	3.18372i	−0.476180	+	0.233442i
$187$	6.03763	+	3.48583i	0.441515	+	0.254909i
$188$	−12.0598			−0.879553
$189$	10.9552	+	8.30561i	0.796875	+	0.604144i
$190$	1.16407			0.0844504
$191$	−0.202055	−	0.116657i	−0.0146202	−	0.00844098i	0.492672	−	0.870215i	$-0.336020\pi$
$191$	−0.202055	−	0.116657i	−0.0146202	−	0.00844098i	−0.507292	+	0.861774i	$0.669354\pi$
$192$	1.55522	−	0.762428i	0.112238	−	0.0550235i
$193$	−0.0930544	−	0.161175i	−0.00669820	−	0.0116016i	0.862657	−	0.505790i	$-0.168799\pi$
$193$	−0.0930544	−	0.161175i	−0.00669820	−	0.0116016i	−0.869355	+	0.494188i	$0.835465\pi$
$194$	5.30090			0.380582
$195$	−6.85013	−	0.465087i	−0.490548	−	0.0333056i
$196$	2.51198	−	6.53375i	0.179427	−	0.466697i
$197$		−	12.3021i		−	0.876485i	−0.898857	−	0.438243i	$-0.855601\pi$
$197$		−	12.3021i		−	0.876485i	0.898857	−	0.438243i	$-0.144399\pi$
$198$	1.21114	+	2.96310i	0.0860717	+	0.210578i
$199$	17.4049	+	10.0487i	1.23380	+	0.712334i	0.967820	−	0.251645i	$-0.0809715\pi$
$199$	17.4049	+	10.0487i	1.23380	+	0.712334i	0.265979	+	0.963979i	$0.414305\pi$
$200$			1.00000i			0.0707107i
$201$	8.58128	+	5.76293i	0.605277	+	0.406486i
$202$	−12.7173	−	7.34233i	−0.894785	−	0.516604i
$203$	1.40786	+	17.9484i	0.0988124	+	1.25973i
$204$	−10.1614	+	4.98152i	−0.711441	+	0.348776i
$205$	5.22517	−	9.05026i	0.364942	−	0.632097i
$206$	6.91037	−	11.9691i	0.481468	−	0.833928i
$207$	17.4915	+	13.5522i	1.21574	+	0.941946i
$208$	−3.43295	+	1.98201i	−0.238032	+	0.137428i
$209$	0.621043	+	1.07568i	0.0429584	+	0.0744062i
$210$	−2.24954	+	3.99244i	−0.155233	+	0.275505i
$211$	−12.4132	+	21.5003i	−0.854561	+	1.48014i	0.0224913	+	0.999747i	$0.492840\pi$
$211$	−12.4132	+	21.5003i	−0.854561	+	1.48014i	−0.877052	+	0.480396i	$0.840493\pi$
$212$			8.72322i			0.599113i
$213$	−0.539413	−	1.10031i	−0.0369599	−	0.0753917i
$214$	−12.0758			−0.825488
$215$	0.665456	+	1.15260i	0.0453837	+	0.0786069i
$216$	−5.08907	−	1.04948i	−0.346267	−	0.0714081i
$217$	−0.863946	−	11.0142i	−0.0586485	−	0.747693i
$218$	12.0874	−	6.97867i	0.818663	−	0.472655i
$219$	12.4735	+	0.846882i	0.842879	+	0.0572269i
$220$	−0.924068	+	0.533511i	−0.0623007	+	0.0359693i
$221$	22.4300	−	12.9500i	1.50881	−	0.871110i
$222$	−4.42126	−	9.01859i	−0.296736	−	0.605288i
$223$	22.1090	−	12.7646i	1.48053	−	0.854782i	0.480770	−	0.876847i	$-0.340357\pi$
$223$	22.1090	−	12.7646i	1.48053	−	0.854782i	0.999757	+	0.0220644i	$0.00702390\pi$
$224$	0.206895	+	2.63765i	0.0138238	+	0.176235i
$225$	1.83741	−	2.37148i	0.122494	−	0.158099i
$226$	−3.43569	−	5.95078i	−0.228538	−	0.395840i
$227$	4.67761			0.310464			0.155232	−	0.987878i	$-0.450387\pi$
$227$	4.67761			0.310464			0.155232	+	0.987878i	$0.450387\pi$
$228$	−2.01159	−	0.136576i	−0.133221	−	0.00904499i
$229$		−	5.56802i		−	0.367945i	−0.982931	−	0.183972i	$-0.941104\pi$
$229$		−	5.56802i		−	0.367945i	0.982931	−	0.183972i	$-0.0588957\pi$
$230$	−3.68787	+	6.38758i	−0.243171	+	0.421185i
$231$	−4.88944	+	0.0512841i	−0.321702	+	0.00337425i
$232$	−3.40235	−	5.89304i	−0.223375	−	0.386897i
$233$	−8.86411	+	5.11770i	−0.580707	+	0.335271i	−0.761414	−	0.648266i	$-0.775495\pi$
$233$	−8.86411	+	5.11770i	−0.580707	+	0.335271i	0.180707	+	0.983537i	$0.442161\pi$
$234$	11.7829	+	1.60741i	0.770275	+	0.105080i
$235$	−6.02991	+	10.4441i	−0.393348	+	0.681299i
$236$	4.63478	−	8.02767i	0.301698	−	0.522557i
$237$	−0.807015	+	11.8863i	−0.0524212	+	0.772097i
$238$	−1.35180	−	17.2337i	−0.0876243	−	1.11710i
$239$	2.42827	+	1.40196i	0.157072	+	0.0906855i	0.576476	−	0.817114i	$-0.304428\pi$
$239$	2.42827	+	1.40196i	0.157072	+	0.0906855i	−0.419404	+	0.907800i	$0.637761\pi$
$240$	0.117327	−	1.72807i	0.00757341	−	0.111547i
$241$			18.5732i			1.19640i	0.801346	+	0.598202i	$0.204118\pi$
$241$			18.5732i			1.19640i	−0.801346	+	0.598202i	$0.795882\pi$
$242$	8.54028	+	4.93073i	0.548990	+	0.316959i
$243$	10.1403	+	11.8395i	0.650502	+	0.759505i
$244$			3.49525i			0.223761i
$245$	−4.40240	−	5.44232i	−0.281259	−	0.347697i
$246$	−10.0913	+	15.0264i	−0.643398	+	0.958051i
$247$	4.61440			0.293607
$248$	2.08788	+	3.61632i	0.132581	+	0.229637i
$249$	−7.73260	−	5.19298i	−0.490034	−	0.329092i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	4.88981			0.308642			0.154321	−	0.988021i	$-0.450681\pi$
$251$	4.88981			0.308642			0.154321	+	0.988021i	$0.450681\pi$
$252$	4.35579	−	6.63529i	0.274389	−	0.417984i
$253$	−7.87008			−0.494788
$254$	−7.53413	−	4.34983i	−0.472734	−	0.272933i
$255$	−0.766584	+	11.2908i	−0.0480054	+	0.707057i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.63605			0.102054			0.0510269	−	0.998697i	$-0.483751\pi$
$257$	1.63605			0.102054			0.0510269	+	0.998697i	$0.483751\pi$
$258$	−1.01473	−	2.06986i	−0.0631740	−	0.128864i
$259$	15.2955	−	1.19977i	0.950418	−	0.0745501i
$260$			3.96403i			0.245839i
$261$	−2.75930	+	20.2268i	−0.170796	+	1.25200i
$262$	1.00773	+	0.581816i	0.0622580	+	0.0359447i
$263$		−	6.48260i		−	0.399734i	−0.979823	−	0.199867i	$-0.935949\pi$
$263$		−	6.48260i		−	0.399734i	0.979823	−	0.199867i	$-0.0640510\pi$
$264$	1.65945	−	0.813528i	0.102132	−	0.0500692i
$265$	7.55453	+	4.36161i	0.464071	+	0.267932i
$266$	1.32663	−	2.77947i	0.0813408	−	0.170420i
$267$	6.02517	+	4.04632i	0.368734	+	0.247631i
$268$	2.98398	−	5.16841i	0.182276	−	0.315711i
$269$	−2.53893	+	4.39756i	−0.154802	+	0.268124i	−0.932987	−	0.359911i	$-0.882807\pi$
$269$	−2.53893	+	4.39756i	−0.154802	+	0.268124i	0.778185	+	0.628035i	$0.216140\pi$
$270$	−3.45341	+	3.88252i	−0.210168	+	0.236283i
$271$	−21.7192	+	12.5396i	−1.31935	+	0.761726i	−0.983624	−	0.180235i	$-0.942314\pi$
$271$	−21.7192	+	12.5396i	−1.31935	+	0.761726i	−0.335724	+	0.941960i	$0.608981\pi$
$272$	3.26688	+	5.65839i	0.198083	+	0.343091i
$273$	−8.91723	+	15.8261i	−0.539695	+	0.957842i
$274$	−3.19280	+	5.53009i	−0.192884	+	0.334085i
$275$			1.06702i			0.0643438i
$276$	7.12235	−	10.6055i	0.428715	−	0.638377i
$277$	−23.9103			−1.43663			−0.718316	−	0.695717i	$-0.755087\pi$
$277$	−23.9103			−1.43663			−0.718316	+	0.695717i	$0.755087\pi$
$278$	−7.93684	−	13.7470i	−0.476020	−	0.824491i
$279$	1.69327	−	12.4123i	0.101373	−	0.743107i
$280$	2.38772	+	1.13965i	0.142694	+	0.0681070i
$281$	−16.7876	+	9.69232i	−1.00146	+	0.578195i	−0.908681	−	0.417491i	$-0.862909\pi$
$281$	−16.7876	+	9.69232i	−1.00146	+	0.578195i	−0.0927826	+	0.995686i	$0.529576\pi$
$282$	11.6455	−	17.3407i	0.693479	−	1.03262i
$283$	7.19135	−	4.15193i	0.427481	−	0.246806i	−0.270792	−	0.962638i	$-0.587285\pi$
$283$	7.19135	−	4.15193i	0.427481	−	0.246806i	0.698273	+	0.715832i	$0.253952\pi$
$284$	−0.612707	+	0.353747i	−0.0363575	+	0.0209910i
$285$	−1.12408	+	1.67380i	−0.0665845	+	0.0991475i
$286$	−3.66303	+	2.11485i	−0.216600	+	0.125054i
$287$	−15.6546	−	22.7903i	−0.924063	−	1.34527i
$288$	−0.405499	+	2.97247i	−0.0238942	+	0.175154i
$289$	−12.8449	−	22.2481i	−0.755585	−	1.30871i
$290$	−6.80470			−0.399586
$291$	−5.11878	+	7.62212i	−0.300068	+	0.446816i
$292$		−	7.21814i		−	0.422410i
$293$	15.6006	−	27.0210i	0.911397	−	1.57859i	0.0993049	−	0.995057i	$-0.468338\pi$
$293$	15.6006	−	27.0210i	0.911397	−	1.57859i	0.812092	−	0.583529i	$-0.198329\pi$
$294$	6.96914	+	9.92124i	0.406449	+	0.578619i
$295$	−4.63478	−	8.02767i	−0.269847	−	0.467389i
$296$	−5.02202	+	2.89946i	−0.291899	+	0.168528i
$297$	−5.43014	−	1.11982i	−0.315089	−	0.0649785i
$298$	−5.13612	+	8.89602i	−0.297528	+	0.515333i
$299$	−14.6188	+	25.3206i	−0.845429	+	1.46433i
$300$	−1.43789	−	0.965644i	−0.0830167	−	0.0557515i
$301$	3.51048	−	0.275359i	0.202341	−	0.0158714i
$302$	−15.9968	−	9.23576i	−0.920513	−	0.531458i
$303$	22.8378	−	11.1960i	1.31200	−	0.643193i
$304$			1.16407i			0.0667639i
$305$	3.02698	+	1.74763i	0.173324	+	0.100069i
$306$	2.64943	−	19.4214i	0.151458	−	1.11025i
$307$		−	11.9251i		−	0.680603i	−0.940316	−	0.340301i	$-0.889471\pi$
$307$		−	11.9251i		−	0.680603i	0.940316	−	0.340301i	$-0.110529\pi$
$308$	0.220762	+	2.81443i	0.0125791	+	0.160367i
$309$	10.5373	+	21.4943i	0.599447	+	1.22277i
$310$	4.17577			0.237168
$311$	−15.2018	−	26.3303i	−0.862017	−	1.49306i	−0.869979	−	0.493088i	$-0.835868\pi$
$311$	−15.2018	−	26.3303i	−0.862017	−	1.49306i	0.00796270	−	0.999968i	$-0.497465\pi$
$312$	0.465087	−	6.85013i	0.0263304	−	0.387812i
$313$	−7.06715	−	4.08022i	−0.399459	−	0.230628i	0.286792	−	0.957993i	$-0.407411\pi$
$313$	−7.06715	−	4.08022i	−0.399459	−	0.230628i	−0.686251	+	0.727365i	$0.740745\pi$
$314$	9.14975			0.516350
$315$	−3.56844	−	7.08987i	−0.201059	−	0.399469i
$316$	6.87835			0.386937
$317$	19.8794	+	11.4774i	1.11654	+	0.644634i	0.940515	−	0.339752i	$-0.110343\pi$
$317$	19.8794	+	11.4774i	1.11654	+	0.644634i	0.176023	+	0.984386i	$0.443677\pi$
$318$	−12.5430	−	8.42353i	−0.703379	−	0.472368i
$319$	−3.63038	−	6.28800i	−0.203262	−	0.352061i
$320$	−1.00000			−0.0559017
$321$	11.6610	−	17.3638i	0.650852	−	0.969150i
$322$	11.0489	+	16.0852i	0.615730	+	0.896393i
$323$		−	7.60573i		−	0.423194i
$324$	6.42327	−	6.30410i	0.356848	−	0.350228i
$325$	3.43295	+	1.98201i	0.190426	+	0.109942i
$326$		−	0.979115i		−	0.0542281i
$327$	−1.63757	+	24.1193i	−0.0905579	+	1.33380i
$328$	9.05026	+	5.22517i	0.499717	+	0.288512i
$329$	18.0656	+	26.3004i	0.995991	+	1.44999i
$330$	0.125190	−	1.84389i	0.00689150	−	0.101503i
$331$	−3.85564	+	6.67816i	−0.211925	+	0.367065i	−0.952317	−	0.305111i	$-0.901307\pi$
$331$	−3.85564	+	6.67816i	−0.211925	+	0.367065i	0.740392	+	0.672175i	$0.234640\pi$
$332$	−2.68887	+	4.65726i	−0.147571	+	0.255600i
$333$	17.2371	+	2.35146i	0.944589	+	0.128859i
$334$	−17.3864	+	10.0381i	−0.951344	+	0.549259i
$335$	−2.98398	−	5.16841i	−0.163032	−	0.282380i
$336$	−3.99244	−	2.24954i	−0.217805	−	0.122722i
$337$	−7.08283	+	12.2678i	−0.385826	+	0.668271i	−0.991883	−	0.127150i	$-0.959417\pi$
$337$	−7.08283	+	12.2678i	−0.385826	+	0.668271i	0.606057	+	0.795421i	$0.292750\pi$
$338$			2.71352i			0.147596i
$339$	11.8742	+	0.806196i	0.644920	+	0.0437866i
$340$	6.53375			0.354342
$341$	2.22782	+	3.85869i	0.120643	+	0.208960i
$342$	2.13887	−	2.76057i	0.115657	−	0.149274i
$343$	−18.0119	+	4.30937i	−0.972552	+	0.232684i
$344$	−1.15260	+	0.665456i	−0.0621442	+	0.0358790i
$345$	−5.62348	−	11.4709i	−0.302758	−	0.617572i
$346$	−20.0084	+	11.5519i	−1.07566	+	0.621032i
$347$	7.85674	−	4.53609i	0.421772	−	0.243510i	−0.274063	−	0.961712i	$-0.588368\pi$
$347$	7.85674	−	4.53609i	0.421772	−	0.243510i	0.695835	+	0.718202i	$0.255034\pi$
$348$	11.7590	+	0.798374i	0.630349	+	0.0427973i
$349$	−10.8602	+	6.27017i	−0.581336	+	0.335634i	−0.761664	−	0.647972i	$-0.775617\pi$
$349$	−10.8602	+	6.27017i	−0.581336	+	0.335634i	0.180328	+	0.983606i	$0.442284\pi$
$350$	2.18082	−	1.49800i	0.116570	−	0.0800715i
$351$	−13.6894	+	15.3904i	−0.730687	+	0.821480i
$352$	−0.533511	−	0.924068i	−0.0284362	−	0.0492530i
$353$	−14.9009			−0.793095			−0.396548	−	0.918014i	$-0.629792\pi$
$353$	−14.9009			−0.793095			−0.396548	+	0.918014i	$0.629792\pi$
$354$	7.06737	+	14.4162i	0.375627	+	0.766212i
$355$			0.707493i			0.0375498i
$356$	2.09514	−	3.62889i	0.111042	−	0.192331i
$357$	26.0856	+	14.6979i	1.38060	+	0.777896i
$358$	−7.07161	−	12.2484i	−0.373746	−	0.647347i
$359$	16.1836	−	9.34360i	0.854137	−	0.493136i	−0.00790764	−	0.999969i	$-0.502517\pi$
$359$	16.1836	−	9.34360i	0.854137	−	0.493136i	0.862045	+	0.506833i	$0.169184\pi$
$360$	2.37148	+	1.83741i	0.124988	+	0.0968398i
$361$	−8.82247	+	15.2810i	−0.464341	+	0.804262i
$362$	−0.755375	+	1.30835i	−0.0397016	+	0.0687652i
$363$	−15.3367	+	7.51866i	−0.804969	+	0.394627i
$364$	9.46498	+	4.51760i	0.496100	+	0.236786i
$365$	−6.25109	−	3.60907i	−0.327197	−	0.188907i
$366$	−5.02580	−	3.37517i	−0.262703	−	0.176423i
$367$			26.8657i			1.40238i	0.712975	+	0.701190i	$0.247348\pi$
$367$			26.8657i			1.40238i	−0.712975	+	0.701190i	$0.752652\pi$
$368$	−6.38758	−	3.68787i	−0.332976	−	0.192244i
$369$	−11.8618	−	29.0204i	−0.617500	−	1.51074i
$370$			5.79892i			0.301472i
$371$	19.0238	−	13.0674i	0.987667	−	0.678425i
$372$	−7.21603	−	0.489929i	−0.374134	−	0.0254017i
$373$	23.8809			1.23651			0.618253	−	0.785979i	$-0.287841\pi$
$373$	23.8809			1.23651			0.618253	+	0.785979i	$0.287841\pi$
$374$	3.48583	+	6.03763i	0.180248	+	0.312198i
$375$	−1.55522	+	0.762428i	−0.0803111	+	0.0393716i
$376$	−10.4441	−	6.02991i	−0.538614	−	0.310969i
$377$	−26.9740			−1.38923
$378$	5.33469	+	12.6705i	0.274387	+	0.651699i
$379$	21.1583			1.08683			0.543415	−	0.839464i	$-0.317131\pi$
$379$	21.1583			1.08683			0.543415	+	0.839464i	$0.317131\pi$
$380$	1.00811	+	0.582034i	0.0517151	+	0.0298577i
$381$	13.5299	−	6.63287i	0.693157	−	0.339812i
$382$	−0.116657	−	0.202055i	−0.00596868	−	0.0103381i
$383$	12.6272			0.645218			0.322609	−	0.946532i	$-0.395440\pi$
$383$	12.6272			0.645218			0.322609	+	0.946532i	$0.395440\pi$
$384$	1.72807	+	0.117327i	0.0881853	+	0.00598731i
$385$	2.54775	+	1.21603i	0.129845	+	0.0619746i
$386$		−	0.186109i		−	0.00947269i
$387$	3.95610	+	0.539683i	0.201100	+	0.0274336i
$388$	4.59071	+	2.65045i	0.233058	+	0.134556i
$389$		−	17.0101i		−	0.862445i	−0.902246	−	0.431222i	$-0.858082\pi$
$389$		−	17.0101i		−	0.862445i	0.902246	−	0.431222i	$-0.141918\pi$
$390$	−5.69984	−	3.82784i	−0.288623	−	0.193830i
$391$	41.7349	+	24.0956i	2.11062	+	1.21857i
$392$	5.44232	−	4.40240i	0.274879	−	0.222355i
$393$	−1.80970	+	0.887185i	−0.0912873	+	0.0447526i
$394$	6.15103	−	10.6539i	0.309884	−	0.536735i
$395$	3.43917	−	5.95682i	0.173044	−	0.299720i
$396$	−0.432676	+	3.17169i	−0.0217428	+	0.159383i
$397$	−8.29364	+	4.78833i	−0.416246	+	0.240320i	−0.693470	−	0.720486i	$-0.743919\pi$
$397$	−8.29364	+	4.78833i	−0.416246	+	0.240320i	0.277224	+	0.960805i	$0.410586\pi$
$398$	10.0487	+	17.4049i	0.503696	+	0.872427i
$399$	2.71552	+	4.59152i	0.135946	+	0.229864i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	23.2837i		−	1.16273i	−0.813641	−	0.581367i	$-0.802518\pi$
$401$		−	23.2837i		−	1.16273i	0.813641	−	0.581367i	$-0.197482\pi$
$402$	4.55014	+	9.28148i	0.226940	+	0.462918i
$403$	16.5529			0.824556
$404$	−7.34233	−	12.7173i	−0.365295	−	0.632709i
$405$	−2.24788	−	8.71476i	−0.111698	−	0.433040i
$406$	−7.75496	+	16.2477i	−0.384872	+	0.806360i
$407$	−5.35860	+	3.09379i	−0.265616	+	0.153353i
$408$	−11.2908	−	0.766584i	−0.558978	−	0.0379516i
$409$	−2.84492	+	1.64251i	−0.140672	+	0.0812170i	−0.568684	−	0.822556i	$-0.692547\pi$
$409$	−2.84492	+	1.64251i	−0.140672	+	0.0812170i	0.428012	+	0.903773i	$0.359214\pi$
$410$	9.05026	−	5.22517i	0.446960	−	0.258053i
$411$	−4.86856	−	9.93099i	−0.240148	−	0.489860i
$412$	11.9691	−	6.91037i	0.589676	−	0.340450i
$413$	−24.4498	+	1.91783i	−1.20310	+	0.0943701i
$414$	8.37193	+	20.4823i	0.411458	+	1.00665i
$415$	2.68887	+	4.65726i	0.131991	+	0.228616i
$416$	−3.96403			−0.194352
$417$	27.4309	+	1.86241i	1.34330	+	0.0912025i
$418$			1.24209i			0.0607524i
$419$	−10.5134	+	18.2098i	−0.513614	+	0.889606i	0.486261	+	0.873814i	$0.338360\pi$
$419$	−10.5134	+	18.2098i	−0.513614	+	0.889606i	−0.999875	+	0.0157922i	$0.994973\pi$
$420$	−3.94438	+	2.33279i	−0.192466	+	0.113828i
$421$	−15.0780	−	26.1158i	−0.734856	−	1.27281i	−0.954787	−	0.297292i	$-0.903916\pi$
$421$	−15.0780	−	26.1158i	−0.734856	−	1.27281i	0.219931	−	0.975515i	$-0.429417\pi$
$422$	−21.5003	+	12.4132i	−1.04662	+	0.604266i
$423$	13.6887	+	33.4899i	0.665565	+	1.62834i
$424$	−4.36161	+	7.55453i	−0.211819	+	0.366881i
$425$	3.26688	−	5.65839i	0.158467	−	0.274472i
$426$	0.0830079	−	1.22260i	0.00402175	−	0.0592351i
$427$	7.62253	−	5.23590i	0.368880	−	0.253383i
$428$	−10.4580	−	6.03792i	−0.505506	−	0.291854i
$429$	0.496258	−	7.30924i	0.0239596	−	0.352893i
$430$			1.33091i			0.0641823i
$431$	−22.4876	−	12.9832i	−1.08319	−	0.625380i	−0.151435	−	0.988467i	$-0.548389\pi$
$431$	−22.4876	−	12.9832i	−1.08319	−	0.625380i	−0.931755	+	0.363087i	$0.881723\pi$
$432$	−3.88252	−	3.45341i	−0.186798	−	0.166152i
$433$			6.96021i			0.334486i	0.985916	+	0.167243i	$0.0534865\pi$
$433$			6.96021i			0.334486i	−0.985916	+	0.167243i	$0.946514\pi$
$434$	4.75890	−	9.97056i	0.228435	−	0.478602i
$435$	6.57092	−	9.78442i	0.315051	−	0.469127i
$436$	13.9573			0.668435
$437$	4.29293	+	7.43558i	0.205359	+	0.355692i
$438$	10.3789	+	6.97016i	0.495923	+	0.333047i
$439$	−17.0980	−	9.87152i	−0.816042	−	0.471142i	0.0330079	−	0.999455i	$-0.489491\pi$
$439$	−17.0980	−	9.87152i	−0.816042	−	0.471142i	−0.849050	+	0.528313i	$0.822825\pi$
$440$	−1.06702			−0.0508683
$441$	−20.9954	+	0.440479i	−0.999780	+	0.0209752i
$442$	25.9000			1.23194
$443$	20.6085	+	11.8983i	0.979140	+	0.565307i	0.902010	−	0.431714i	$-0.142091\pi$
$443$	20.6085	+	11.8983i	0.979140	+	0.565307i	0.0771297	+	0.997021i	$0.475424\pi$
$444$	0.680369	−	10.0210i	0.0322889	−	0.475574i
$445$	−2.09514	−	3.62889i	−0.0993192	−	0.172026i
$446$	25.5292			1.20884
$447$	−7.83185	−	15.9756i	−0.370434	−	0.755619i
$448$	−1.13965	+	2.38772i	−0.0538433	+	0.112809i
$449$			10.6883i			0.504413i	0.967673	+	0.252206i	$0.0811561\pi$
$449$			10.6883i			0.504413i	−0.967673	+	0.252206i	$0.918844\pi$
$450$	2.77698	−	1.13506i	0.130908	−	0.0535074i
$451$	9.65682	+	5.57537i	0.454722	+	0.262534i
$452$		−	6.87137i		−	0.323202i
$453$	28.7273	−	14.0832i	1.34972	−	0.661687i
$454$	4.05093	+	2.33881i	0.190120	+	0.109766i
$455$	8.64485	−	5.93812i	0.405277	−	0.278383i
$456$	−1.67380	−	1.12408i	−0.0783830	−	0.0526397i
$457$	−10.7943	+	18.6962i	−0.504935	+	0.874573i	0.495049	+	0.868865i	$0.335150\pi$
$457$	−10.7943	+	18.6962i	−0.504935	+	0.874573i	−0.999984	+	0.00570788i	$0.998183\pi$
$458$	2.78401	−	4.82204i	0.130088	−	0.225319i
$459$	25.3674	+	22.5637i	1.18405	+	1.05318i
$460$	−6.38758	+	3.68787i	−0.297823	+	0.171948i
$461$	4.36303	+	7.55699i	0.203207	+	0.351964i	0.949560	−	0.313586i	$-0.101530\pi$
$461$	4.36303	+	7.55699i	0.203207	+	0.351964i	−0.746353	+	0.665550i	$0.768197\pi$
$462$	−4.26002	−	2.40031i	−0.198194	−	0.111672i
$463$	−4.86607	+	8.42827i	−0.226145	+	0.391695i	−0.956662	−	0.291199i	$-0.905946\pi$
$463$	−4.86607	+	8.42827i	−0.226145	+	0.391695i	0.730517	+	0.682894i	$0.239279\pi$
$464$		−	6.80470i		−	0.315900i
$465$	−4.03230	+	6.00430i	−0.186994	+	0.278443i
$466$	−10.2354			−0.474145
$467$	−9.84856	−	17.0582i	−0.455737	−	0.789360i	0.542993	−	0.839737i	$-0.317291\pi$
$467$	−9.84856	−	17.0582i	−0.455737	−	0.789360i	−0.998730	+	0.0503774i	$0.983958\pi$
$468$	9.40063	+	7.28353i	0.434544	+	0.336681i
$469$	−15.7414	+	1.23474i	−0.726870	+	0.0570151i
$470$	−10.4441	+	6.02991i	−0.481751	+	0.278139i
$471$	−8.83540	+	13.1563i	−0.407114	+	0.606212i
$472$	8.02767	−	4.63478i	0.369504	−	0.213333i
$473$	−1.22985	+	0.710056i	−0.0565487	+	0.0326484i
$474$	−6.64204	+	9.89032i	−0.305079	+	0.454277i
$475$	1.00811	−	0.582034i	0.0462554	−	0.0267056i
$476$	7.44618	−	15.6008i	0.341295	−	0.715060i
$477$	24.2242	−	9.90140i	1.10915	−	0.453354i
$478$	1.40196	+	2.42827i	0.0641243	+	0.111067i
$479$	−8.15200			−0.372474			−0.186237	−	0.982505i	$-0.559629\pi$
$479$	−8.15200			−0.372474			−0.186237	+	0.982505i	$0.559629\pi$
$480$	0.965644	−	1.43789i	0.0440754	−	0.0656305i
$481$			22.9871i			1.04812i
$482$	−9.28659	+	16.0848i	−0.422992	+	0.732644i
$483$	−33.7981	+	0.354499i	−1.53786	+	0.0161303i
$484$	4.93073	+	8.54028i	0.224124	+	0.388194i
$485$	4.59071	−	2.65045i	0.208454	−	0.120351i
$486$	2.86202	+	15.3235i	0.129824	+	0.695087i
$487$	10.3665	−	17.9553i	0.469751	−	0.813633i	−0.529650	−	0.848216i	$-0.677677\pi$
$487$	10.3665	−	17.9553i	0.469751	−	0.813633i	0.999402	+	0.0345826i	$0.0110102\pi$
$488$	−1.74763	+	3.02698i	−0.0791114	+	0.137025i
$489$	1.40786	+	0.945476i	0.0636656	+	0.0427559i
$490$	−1.09143	−	6.91439i	−0.0493060	−	0.312360i
$491$	21.8030	+	12.5880i	0.983957	+	0.568088i	0.903463	−	0.428667i	$-0.141017\pi$
$491$	21.8030	+	12.5880i	0.983957	+	0.568088i	0.0804947	+	0.996755i	$0.474350\pi$
$492$	−16.2526	+	7.96763i	−0.732722	+	0.359209i
$493$			44.4602i			2.00239i
$494$	3.99619	+	2.30720i	0.179797	+	0.103806i
$495$	2.53043	+	1.96055i	0.113734	+	0.0881203i
$496$			4.17577i			0.187497i
$497$	1.68929	+	0.806293i	0.0757752	+	0.0361672i
$498$	−4.10014	−	8.36356i	−0.183732	−	0.374780i
$499$	19.9748			0.894196			0.447098	−	0.894485i	$-0.352457\pi$
$499$	19.9748			0.894196			0.447098	+	0.894485i	$0.352457\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	2.35547	−	34.6930i	0.105235	−	1.54997i
$502$	4.23470	+	2.44491i	0.189004	+	0.109121i
$503$	10.1758			0.453715			0.226857	−	0.973928i	$-0.427155\pi$
$503$	10.1758			0.453715			0.226857	+	0.973928i	$0.427155\pi$
$504$	7.08987	−	3.56844i	0.315808	−	0.158951i
$505$	−14.6847			−0.653459
$506$	−6.81569	−	3.93504i	−0.302994	−	0.174934i
$507$	−3.90174	−	2.62029i	−0.173282	−	0.116371i
$508$	−4.34983	−	7.53413i	−0.192993	−	0.334273i
$509$	−41.4669			−1.83799			−0.918994	−	0.394272i	$-0.870997\pi$
$509$	−41.4669			−1.83799			−0.918994	+	0.394272i	$0.870997\pi$
$510$	−6.30928	+	9.39482i	−0.279380	+	0.416010i
$511$	−15.7415	+	10.8128i	−0.696363	+	0.478329i
$512$		−	1.00000i		−	0.0441942i
$513$	1.90401	+	5.74118i	0.0840643	+	0.253479i
$514$	1.41686	+	0.818024i	0.0624950	+	0.0360815i
$515$		−	13.8207i		−	0.609015i
$516$	0.156152	−	2.29991i	0.00687420	−	0.101248i
$517$	−11.1441	−	6.43405i	−0.490117	−	0.282969i
$518$	13.8462	+	6.60873i	0.608367	+	0.290371i
$519$	2.71069	−	39.9249i	0.118986	−	1.75251i
$520$	−1.98201	+	3.43295i	−0.0869171	+	0.150545i
$521$	14.6287	−	25.3377i	0.640896	−	1.11006i	−0.344337	−	0.938846i	$-0.611896\pi$
$521$	14.6287	−	25.3377i	0.640896	−	1.11006i	0.985233	−	0.171219i	$-0.0547705\pi$
$522$	−12.5030	+	16.1372i	−0.547241	+	0.706308i
$523$	19.2390	−	11.1076i	0.841262	−	0.485703i	−0.0164309	−	0.999865i	$-0.505230\pi$
$523$	19.2390	−	11.1076i	0.841262	−	0.485703i	0.857693	+	0.514162i	$0.171897\pi$
$524$	0.581816	+	1.00773i	0.0254167	+	0.0440231i
$525$	0.0480629	+	4.58232i	0.00209764	+	0.199989i
$526$	3.24130	−	5.61409i	0.141327	−	0.244786i
$527$		−	27.2834i		−	1.18848i
$528$	1.84389	+	0.125190i	0.0802451	+	0.00544821i
$529$	−31.4016			−1.36529
$530$	4.36161	+	7.55453i	0.189456	+	0.328148i
$531$	−27.5535	−	3.75879i	−1.19572	−	0.163118i
$532$	2.53863	−	1.74378i	0.110063	−	0.0756022i
$533$	35.8755	−	20.7127i	1.55394	−	0.897167i
$534$	3.19479	+	6.51680i	0.138252	+	0.282010i
$535$	−10.4580	+	6.03792i	−0.452138	+	0.261042i
$536$	5.16841	−	2.98398i	0.223241	−	0.128888i
$537$	24.4405	+	1.65938i	1.05469	+	0.0716074i
$538$	−4.39756	+	2.53893i	−0.189592	+	0.109461i
$539$	5.80707	−	4.69746i	0.250128	−	0.202334i
$540$	−4.93200	+	1.63566i	−0.212240	+	0.0703874i
$541$	15.4552	+	26.7692i	0.664470	+	1.15090i	0.979429	+	0.201790i	$0.0646760\pi$
$541$	15.4552	+	26.7692i	0.664470	+	1.15090i	−0.314959	+	0.949105i	$0.601991\pi$
$542$	−25.0792			−1.07724
$543$	−1.15184	−	2.34955i	−0.0494301	−	0.100829i
$544$			6.53375i			0.280132i
$545$	6.97867	−	12.0874i	0.298933	−	0.517768i
$546$	−15.6356	+	9.24723i	−0.669143	+	0.395745i
$547$	−19.3899	−	33.5843i	−0.829053	−	1.43596i	−0.898782	−	0.438396i	$-0.855547\pi$
$547$	−19.3899	−	33.5843i	−0.829053	−	1.43596i	0.0697284	−	0.997566i	$-0.477787\pi$
$548$	−5.53009	+	3.19280i	−0.236234	+	0.136390i
$549$	9.70626	−	3.96733i	0.414253	−	0.169322i
$550$	−0.533511	+	0.924068i	−0.0227490	+	0.0394024i
$551$	−3.96057	+	6.85990i	−0.168726	+	0.292242i
$552$	11.4709	−	5.62348i	0.488234	−	0.239351i
$553$	−10.3038	−	15.0005i	−0.438161	−	0.637885i
$554$	−20.7070	−	11.9552i	−0.879754	−	0.507926i
$555$	−8.33822	−	5.59970i	−0.353938	−	0.237694i
$556$		−	15.8737i		−	0.673194i
$557$	11.3918	+	6.57703i	0.482684	+	0.278678i	0.721534	−	0.692379i	$-0.243437\pi$
$557$	11.3918	+	6.57703i	0.482684	+	0.278678i	−0.238850	+	0.971056i	$0.576770\pi$
$558$	7.67258	−	9.90276i	0.324806	−	0.419217i
$559$			5.27577i			0.223141i
$560$	1.49800	+	2.18082i	0.0633021	+	0.0921566i
$561$	−12.0475	−	0.817962i	−0.508647	−	0.0345344i
$562$	−19.3846			−0.817692
$563$	−15.8508	−	27.4544i	−0.668032	−	1.15706i	−0.978454	−	0.206466i	$-0.933804\pi$
$563$	−15.8508	−	27.4544i	−0.668032	−	1.15706i	0.310422	−	0.950599i	$-0.399530\pi$
$564$	18.7557	−	9.19475i	0.789756	−	0.387169i
$565$	−5.95078	−	3.43569i	−0.250351	−	0.144540i
$566$	8.30385			0.349037
$567$	−23.3702	−	4.56447i	−0.981456	−	0.191690i
$568$	−0.707493			−0.0296857
$569$	−24.6338	−	14.2223i	−1.03270	−	0.596231i	−0.114944	−	0.993372i	$-0.536669\pi$
$569$	−24.6338	−	14.2223i	−1.03270	−	0.596231i	−0.917757	+	0.397141i	$0.870002\pi$
$570$	−1.81038	+	0.887518i	−0.0758285	+	0.0371740i
$571$	9.83999	+	17.0434i	0.411791	+	0.713243i	0.995086	−	0.0990178i	$-0.0315701\pi$
$571$	9.83999	+	17.0434i	0.411791	+	0.713243i	−0.583295	+	0.812261i	$0.698237\pi$
$572$	−4.22970			−0.176853
$573$	0.403183	+	0.0273739i	0.0168432	+	0.00114356i
$574$	−2.16212	−	27.5643i	−0.0902453	−	1.15051i
$575$			7.37575i			0.307590i
$576$	−1.83741	+	2.37148i	−0.0765586	+	0.0988118i
$577$	−23.5232	−	13.5811i	−0.979282	−	0.565389i	−0.0772287	−	0.997013i	$-0.524607\pi$
$577$	−23.5232	−	13.5811i	−0.979282	−	0.565389i	−0.902053	+	0.431625i	$0.857940\pi$
$578$		−	25.6899i		−	1.06856i
$579$	0.267604	+	0.179715i	0.0111213	+	0.00746870i
$580$	−5.89304	−	3.40235i	−0.244695	−	0.141275i
$581$	14.1846	−	1.11263i	0.588476	−	0.0461596i
$582$	−8.24405	+	4.04155i	−0.341727	+	0.167528i
$583$	−4.65393	+	8.06085i	−0.192746	+	0.333846i
$584$	3.60907	−	6.25109i	0.149344	−	0.258672i
$585$	11.0080	−	4.49942i	0.455126	−	0.186028i
$586$	27.0210	−	15.6006i	1.11623	−	0.644455i
$587$	−18.1400	−	31.4194i	−0.748717	−	1.29682i	−0.948438	−	0.316963i	$-0.897337\pi$
$587$	−18.1400	−	31.4194i	−0.748717	−	1.29682i	0.199721	−	0.979853i	$-0.435997\pi$
$588$	1.07483	+	12.0766i	0.0443254	+	0.498031i
$589$	2.43044	−	4.20964i	0.100144	−	0.173455i
$590$		−	9.26956i		−	0.381622i
$591$	9.37943	+	19.1324i	0.385818	+	0.787001i
$592$	−5.79892			−0.238334
$593$	2.54625	+	4.41024i	0.104562	+	0.181107i	0.913559	−	0.406706i	$-0.133323\pi$
$593$	2.54625	+	4.41024i	0.104562	+	0.181107i	−0.808997	+	0.587813i	$0.799989\pi$
$594$	−4.14273	−	3.68486i	−0.169978	−	0.151192i
$595$	−9.78757	−	14.2490i	−0.401251	−	0.584150i
$596$	−8.89602	+	5.13612i	−0.364395	+	0.210384i
$597$	−34.7298	−	2.35797i	−1.42140	−	0.0965051i
$598$	−25.3206	+	14.6188i	−1.03543	+	0.597808i
$599$	16.4231	−	9.48186i	0.671028	−	0.387418i	−0.125438	−	0.992101i	$-0.540034\pi$
$599$	16.4231	−	9.48186i	0.671028	−	0.387418i	0.796466	+	0.604683i	$0.206700\pi$
$600$	−0.762428	−	1.55522i	−0.0311260	−	0.0634915i
$601$	5.21183	−	3.00905i	0.212595	−	0.122742i	−0.389922	−	0.920848i	$-0.627498\pi$
$601$	5.21183	−	3.00905i	0.212595	−	0.122742i	0.602517	+	0.798106i	$0.294165\pi$
$602$	3.17784	+	1.51677i	0.129519	+	0.0618190i
$603$	−17.7396	−	2.42000i	−0.722411	−	0.0985500i
$604$	−9.23576	−	15.9968i	−0.375798	−	0.650901i
$605$	9.86146			0.400926
$606$	25.3762	+	1.72290i	1.03084	+	0.0699882i
$607$			42.0449i			1.70655i	0.521461	+	0.853275i	$0.325387\pi$
$607$			42.0449i			1.70655i	−0.521461	+	0.853275i	$0.674613\pi$
$608$	−0.582034	+	1.00811i	−0.0236046	+	0.0408844i
$609$	−15.8739	−	26.8403i	−0.643243	−	1.08762i
$610$	1.74763	+	3.02698i	0.0707594	+	0.122559i
$611$	−41.4008	+	23.9027i	−1.67490	+	0.967001i
$612$	12.0052	−	15.4947i	0.485280	−	0.626336i
$613$	−6.91836	+	11.9830i	−0.279430	+	0.483987i	−0.971243	−	0.238090i	$-0.923479\pi$
$613$	−6.91836	+	11.9830i	−0.279430	+	0.483987i	0.691813	+	0.722076i	$0.256812\pi$
$614$	5.96256	−	10.3275i	0.240629	−	0.416782i
$615$	−1.22610	+	18.0589i	−0.0494413	+	0.728207i
$616$	−1.21603	+	2.54775i	−0.0489952	+	0.102652i
$617$	13.1926	+	7.61675i	0.531114	+	0.306639i	0.741470	−	0.670986i	$-0.234129\pi$
$617$	13.1926	+	7.61675i	0.531114	+	0.306639i	−0.210356	+	0.977625i	$0.567462\pi$
$618$	−1.62154	+	23.8832i	−0.0652281	+	0.960725i
$619$			12.6914i			0.510111i	0.966926	+	0.255056i	$0.0820938\pi$
$619$			12.6914i			0.510111i	−0.966926	+	0.255056i	$0.917906\pi$
$620$	3.61632	+	2.08788i	0.145235	+	0.0838514i
$621$	−37.5357	−	7.74071i	−1.50625	−	0.310624i
$622$		−	30.4037i		−	1.21908i
$623$	−11.0525	+	0.866949i	−0.442809	+	0.0347336i
$624$	3.82784	−	5.69984i	0.153236	−	0.228176i
$625$	1.00000			0.0400000
$626$	−4.08022	−	7.06715i	−0.163078	−	0.282460i
$627$	−1.78598	−	1.19941i	−0.0713254	−	0.0478999i
$628$	7.92392	+	4.57487i	0.316199	+	0.182557i
$629$	37.8887			1.51072
$630$	0.454573	−	7.92423i	0.0181106	−	0.315709i
$631$	29.0423			1.15616			0.578078	−	0.815982i	$-0.303803\pi$
$631$	29.0423			1.15616			0.578078	+	0.815982i	$0.303803\pi$
$632$	5.95682	+	3.43917i	0.236950	+	0.136803i
$633$	2.91281	−	42.9019i	0.115774	−	1.70520i
$634$	11.4774	+	19.8794i	0.455825	+	0.789512i
$635$	−8.69967			−0.345236
$636$	−6.65083	−	13.5665i	−0.263723	−	0.537947i
$637$	−4.32647	−	27.4088i	−0.171421	−	1.08598i
$638$		−	7.26076i		−	0.287456i
$639$	1.67781	+	1.29995i	0.0663731	+	0.0514253i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	25.2020i		−	0.995420i	−0.867344	−	0.497710i	$-0.834174\pi$
$641$		−	25.2020i		−	0.995420i	0.867344	−	0.497710i	$-0.165826\pi$
$642$	18.7806	−	9.20697i	0.741210	−	0.363370i
$643$	−25.7071	−	14.8420i	−1.01379	−	0.585312i	−0.101491	−	0.994836i	$-0.532361\pi$
$643$	−25.7071	−	14.8420i	−1.01379	−	0.585312i	−0.912299	+	0.409524i	$0.865695\pi$
$644$	1.52601	+	19.4546i	0.0601331	+	0.766620i
$645$	−1.91371	−	1.28519i	−0.0753521	−	0.0506042i
$646$	3.80286	−	6.58675i	0.149622	−	0.259152i
$647$	12.7504	−	22.0843i	0.501269	−	0.868224i	−0.498730	−	0.866758i	$-0.666200\pi$
$647$	12.7504	−	22.0843i	0.501269	−	0.868224i	0.999999	−	0.00146643i	$-0.000466778\pi$
$648$	8.71476	−	2.24788i	0.342348	−	0.0883049i
$649$	8.56570	−	4.94541i	0.336233	−	0.194124i
$650$	1.98201	+	3.43295i	0.0777410	+	0.134651i
$651$	9.74117	+	16.4708i	0.381786	+	0.645541i
$652$	0.489557	−	0.847938i	0.0191725	−	0.0332078i
$653$			39.2157i			1.53463i	0.641270	+	0.767315i	$0.278408\pi$
$653$			39.2157i			1.53463i	−0.641270	+	0.767315i	$0.721592\pi$
$654$	−13.4778	+	20.0691i	−0.527025	+	0.784765i
$655$	1.16363			0.0454668
$656$	5.22517	+	9.05026i	0.204009	+	0.353353i
$657$	−20.0447	+	8.19304i	−0.782016	+	0.319641i
$658$	2.49512	+	31.8096i	0.0972699	+	1.24007i
$659$	18.2859	−	10.5574i	0.712316	−	0.411256i	−0.0996017	−	0.995027i	$-0.531757\pi$
$659$	18.2859	−	10.5574i	0.712316	−	0.411256i	0.811918	+	0.583771i	$0.198424\pi$
$660$	1.03036	−	1.53426i	0.0401068	−	0.0597210i
$661$	−2.29827	+	1.32691i	−0.0893925	+	0.0516108i	−0.544030	−	0.839066i	$-0.683102\pi$
$661$	−2.29827	+	1.32691i	−0.0893925	+	0.0516108i	0.454637	+	0.890677i	$0.349769\pi$
$662$	−6.67816	+	3.85564i	−0.259554	+	0.149854i
$663$	−25.0102	+	37.2413i	−0.971314	+	1.44633i
$664$	−4.65726	+	2.68887i	−0.180737	+	0.104348i
$665$	−0.240840	−	3.07040i	−0.00933938	−	0.119065i
$666$	13.7521	+	10.6550i	0.532881	+	0.412872i
$667$	−25.0949	−	43.4656i	−0.971677	−	1.68299i
$668$	−20.0761			−0.776769
$669$	−24.6522	+	36.7083i	−0.953108	+	1.41922i
$670$		−	5.96796i		−	0.230562i
$671$	−1.86476	+	3.22985i	−0.0719881	+	0.124687i
$672$	−2.33279	−	3.94438i	−0.0899892	−	0.152158i
$673$	17.0840	+	29.5904i	0.658541	+	1.14063i	0.980994	+	0.194040i	$0.0621593\pi$
$673$	17.0840	+	29.5904i	0.658541	+	1.14063i	−0.322453	+	0.946586i	$0.604507\pi$
$674$	−12.2678	+	7.08283i	−0.472539	+	0.272820i
$675$	−1.04948	+	5.08907i	−0.0403945	+	0.195878i
$676$	−1.35676	+	2.34997i	−0.0521830	+	0.0903836i
$677$	4.46860	−	7.73984i	0.171742	−	0.297466i	−0.767287	−	0.641304i	$-0.778394\pi$
$677$	4.46860	−	7.73984i	0.171742	−	0.297466i	0.939029	+	0.343838i	$0.111727\pi$
$678$	9.88029	+	6.63530i	0.379450	+	0.254827i
$679$	−1.09673	−	13.9819i	−0.0420887	−	0.536577i
$680$	5.65839	+	3.26688i	0.216989	+	0.125279i
$681$	−7.27471	+	3.56634i	−0.278767	+	0.136663i
$682$			4.45563i			0.170615i
$683$	1.66557	+	0.961618i	0.0637313	+	0.0367953i	0.531527	−	0.847041i	$-0.321618\pi$
$683$	1.66557	+	0.961618i	0.0637313	+	0.0367953i	−0.467796	+	0.883837i	$0.654952\pi$
$684$	3.23260	−	1.32129i	0.123601	−	0.0505208i
$685$			6.38560i			0.243981i
$686$	−17.7535	−	5.27393i	−0.677831	−	0.201360i
$687$	4.24521	+	8.65948i	0.161965	+	0.330380i
$688$	−1.33091			−0.0507406
$689$	17.2895	+	29.9464i	0.658679	+	1.14087i
$690$	0.865373	−	12.7458i	0.0329442	−	0.485225i
$691$	21.5660	+	12.4511i	0.820408	+	0.473663i	0.850557	−	0.525883i	$-0.176265\pi$
$691$	21.5660	+	12.4511i	0.820408	+	0.473663i	−0.0301494	+	0.999545i	$0.509598\pi$
$692$	−23.1037			−0.878272
$693$	7.56504	−	3.80760i	0.287372	−	0.144639i
$694$	9.07218			0.344375
$695$	−13.7470	−	7.93684i	−0.521454	−	0.301062i
$696$	9.78442	+	6.57092i	0.370877	+	0.249070i
$697$	−34.1399	−	59.1321i	−1.29314	−	2.23979i
$698$	−12.5403			−0.474659
$699$	9.88375	−	14.7174i	0.373838	−	0.556662i
$700$	2.63765	−	0.206895i	0.0996938	−	0.00781990i
$701$			7.54650i			0.285028i	0.989793	+	0.142514i	$0.0455185\pi$
$701$			7.54650i			0.285028i	−0.989793	+	0.142514i	$0.954481\pi$
$702$	−19.5506	+	6.48378i	−0.737889	+	0.244715i
$703$	5.84597	+	3.37517i	0.220485	+	0.127297i
$704$		−	1.06702i		−	0.0402149i
$705$	1.41494	−	20.8403i	0.0532898	−	0.784889i
$706$	−12.9046	−	7.45045i	−0.485670	−	0.280401i
$707$	−16.7353	+	35.0628i	−0.629397	+	1.31867i
$708$	−1.08757	+	16.0185i	−0.0408733	+	0.602011i
$709$	14.2144	−	24.6200i	0.533833	−	0.924625i	−0.465386	−	0.885108i	$-0.654085\pi$
$709$	14.2144	−	24.6200i	0.533833	−	0.924625i	0.999219	−	0.0395175i	$-0.0125821\pi$
$710$	−0.353747	+	0.612707i	−0.0132759	+	0.0229945i
$711$	−7.80735	−	19.1011i	−0.292799	−	0.716345i
$712$	3.62889	−	2.09514i	0.135998	−	0.0785187i
$713$	15.3997	+	26.6731i	0.576723	+	0.998914i
$714$	15.2418	+	25.7716i	0.570411	+	0.964477i
$715$	−2.11485	+	3.66303i	−0.0790910	+	0.136990i
$716$		−	14.1432i		−	0.528557i
$717$	−4.84539	−	0.328976i	−0.180954	−	0.0122858i
$718$	18.6872			0.697400
$719$	−18.9775	−	32.8700i	−0.707742	−	1.22585i	−0.965693	−	0.259687i	$-0.916380\pi$
$719$	−18.9775	−	32.8700i	−0.707742	−	1.22585i	0.257950	−	0.966158i	$-0.416953\pi$
$720$	1.13506	+	2.77698i	0.0423013	+	0.103492i
$721$	−33.0000	−	15.7508i	−1.22899	−	0.586590i
$722$	−15.2810	+	8.82247i	−0.568699	+	0.328338i
$723$	−14.1607	−	28.8853i	−0.526642	−	1.07426i
$724$	−1.30835	+	0.755375i	−0.0486244	+	0.0280733i
$725$	−5.89304	+	3.40235i	−0.218862	+	0.126360i
$726$	−17.0413	−	1.15701i	−0.632463	−	0.0429408i
$727$	−9.90364	+	5.71787i	−0.367306	+	0.212064i	−0.672281	−	0.740296i	$-0.734685\pi$
$727$	−9.90364	+	5.71787i	−0.367306	+	0.212064i	0.304975	+	0.952360i	$0.401352\pi$
$728$	5.93812	+	8.64485i	0.220081	+	0.320399i
$729$	−24.7972	−	10.6818i	−0.918414	−	0.395621i
$730$	−3.60907	−	6.25109i	−0.133578	−	0.231363i
$731$	8.69585			0.321628
$732$	−2.66488	−	5.43588i	−0.0984968	−	0.200916i
$733$		−	11.4016i		−	0.421127i	−0.977580	−	0.210563i	$-0.932470\pi$
$733$		−	11.4016i		−	0.421127i	0.977580	−	0.210563i	$-0.0675298\pi$
$734$	−13.4329	+	23.2664i	−0.495816	+	0.858779i
$735$	10.9961	+	5.10748i	0.405596	+	0.188392i
$736$	−3.68787	−	6.38758i	−0.135937	−	0.235449i
$737$	5.51480	−	3.18397i	0.203140	−	0.117283i
$738$	4.23760	−	31.0633i	0.155988	−	1.14346i
$739$	9.68170	−	16.7692i	0.356147	−	0.616865i	−0.631167	−	0.775647i	$-0.717424\pi$
$739$	9.68170	−	16.7692i	0.356147	−	0.616865i	0.987314	+	0.158783i	$0.0507569\pi$
$740$	−2.89946	+	5.02202i	−0.106586	+	0.184613i
$741$	−7.17639	+	3.51815i	−0.263631	+	0.129242i
$742$	23.0088	−	1.80479i	0.844680	−	0.0662560i
$743$	−15.8903	−	9.17430i	−0.582960	−	0.336572i	0.179349	−	0.983786i	$-0.442601\pi$
$743$	−15.8903	−	9.17430i	−0.582960	−	0.336572i	−0.762309	+	0.647213i	$0.775934\pi$
$744$	−6.00430	−	4.03230i	−0.220128	−	0.147831i
$745$			10.2722i			0.376346i
$746$	20.6815	+	11.9405i	0.757202	+	0.437171i
$747$	15.9852	+	2.18067i	0.584867	+	0.0797864i
$748$			6.97165i			0.254909i
$749$	2.49844	+	31.8519i	0.0912908	+	1.16384i
$750$	−1.72807	−	0.117327i	−0.0631003	−	0.00428417i
$751$	29.2364			1.06685			0.533426	−	0.845847i	$-0.320904\pi$
$751$	29.2364			1.06685			0.533426	+	0.845847i	$0.320904\pi$
$752$	−6.02991	−	10.4441i	−0.219888	−	0.380858i
$753$	−7.60472	+	3.72813i	−0.277132	+	0.135861i
$754$	−23.3602	−	13.4870i	−0.850728	−	0.491168i
$755$	−18.4715			−0.672248
$756$	−1.71526	+	13.6403i	−0.0623834	+	0.496093i
$757$	−29.2582			−1.06341			−0.531705	−	0.846930i	$-0.678448\pi$
$757$	−29.2582			−1.06341			−0.531705	+	0.846930i	$0.678448\pi$
$758$	18.3237	+	10.5792i	0.665545	+	0.384253i
$759$	12.2397	−	6.00037i	0.444273	−	0.217800i
$760$	0.582034	+	1.00811i	0.0211126	+	0.0365681i
$761$	28.9769			1.05041			0.525206	−	0.850975i	$-0.323988\pi$
$761$	28.9769			1.05041			0.525206	+	0.850975i	$0.323988\pi$
$762$	15.0337	+	1.02070i	0.544612	+	0.0369762i
$763$	−20.9081	−	30.4385i	−0.756925	−	1.10195i
$764$		−	0.233313i		−	0.00844098i
$765$	−7.41621	−	18.1441i	−0.268134	−	0.656002i
$766$	10.9355	+	6.31359i	0.395114	+	0.228119i
$767$		−	36.7448i		−	1.32678i
$768$	1.43789	+	0.965644i	0.0518854	+	0.0348447i
$769$	34.9562	+	20.1819i	1.26055	+	0.727780i	0.973181	−	0.230040i	$-0.0738857\pi$
$769$	34.9562	+	20.1819i	1.26055	+	0.727780i	0.287370	+	0.957820i	$0.407219\pi$
$770$	1.59840	+	2.32699i	0.0576023	+	0.0838588i
$771$	−2.54441	+	1.24737i	−0.0916347	+	0.0449229i
$772$	0.0930544	−	0.161175i	0.00334910	−	0.00580081i
$773$	0.661379	−	1.14554i	0.0237882	−	0.0412023i	−0.853886	−	0.520460i	$-0.825761\pi$
$773$	0.661379	−	1.14554i	0.0237882	−	0.0412023i	0.877674	+	0.479257i	$0.159094\pi$
$774$	3.15624	+	2.44543i	0.113449	+	0.0878990i
$775$	3.61632	−	2.08788i	0.129902	−	0.0749990i
$776$	2.65045	+	4.59071i	0.0951456	+	0.164797i
$777$	−22.8731	+	13.5276i	−0.820570	+	0.485302i
$778$	8.50504	−	14.7312i	0.304920	−	0.528137i
$779$		−	12.1649i		−	0.435853i
$780$	−3.02229	−	6.16493i	−0.108215	−	0.220740i
$781$	−0.754911			−0.0270128
$782$	24.0956	+	41.7349i	0.861658	+	1.49244i
$783$	−11.1301	−	33.5608i	−0.397759	−	1.19936i
$784$	6.91439	−	1.09143i	0.246942	−	0.0389798i
$785$	7.92392	−	4.57487i	0.282817	−	0.163284i
$786$	−2.01084	−	0.136525i	−0.0717242	−	0.00486969i
$787$	9.41109	−	5.43349i	0.335469	−	0.193683i	−0.322798	−	0.946468i	$-0.604623\pi$
$787$	9.41109	−	5.43349i	0.335469	−	0.193683i	0.658267	+	0.752785i	$0.271290\pi$
$788$	10.6539	−	6.15103i	0.379529	−	0.219121i
$789$	4.94251	+	10.0819i	0.175958	+	0.358923i
$790$	5.95682	−	3.43917i	0.211934	−	0.122360i
$791$	−14.9853	+	10.2933i	−0.532814	+	0.365988i
$792$	−1.96055	+	2.53043i	−0.0696652	+	0.0899148i
$793$	6.92764	+	11.9990i	0.246008	+	0.426098i
$794$	−9.57667			−0.339863
$795$	−15.0744	−	1.02347i	−0.534632	−	0.0362987i
$796$			20.0974i			0.712334i
$797$	−17.7341	+	30.7164i	−0.628176	+	1.08803i	0.359742	+	0.933052i	$0.382865\pi$
$797$	−17.7341	+	30.7164i	−0.628176	+	1.08803i	−0.987918	+	0.154980i	$0.950469\pi$
$798$	0.0559484	+	5.33414i	0.00198055	+	0.188826i
$799$	39.3979	+	68.2392i	1.39380	+	2.41413i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−12.4555	−	1.69915i	−0.440093	−	0.0600366i
$802$	11.6419	−	20.1643i	0.411089	−	0.712027i
$803$	3.85096	−	6.67005i	0.135897	−	0.235381i
$804$	−0.700202	+	10.3131i	−0.0246942	+	0.363714i
$805$	17.6112	+	8.40575i	0.620713	+	0.296264i
$806$	14.3352	+	8.27643i	0.504936	+	0.291525i
$807$	0.595770	−	8.77492i	0.0209721	−	0.308892i
$808$		−	14.6847i		−	0.516604i
$809$	24.0762	+	13.9004i	0.846474	+	0.488712i	0.859460	−	0.511204i	$-0.170800\pi$
$809$	24.0762	+	13.9004i	0.846474	+	0.488712i	−0.0129857	+	0.999916i	$0.504134\pi$
$810$	2.41066	−	8.67114i	0.0847021	−	0.304673i
$811$		−	3.86695i		−	0.135787i	−0.997693	−	0.0678934i	$-0.978372\pi$
$811$		−	3.86695i		−	0.135787i	0.997693	−	0.0678934i	$-0.0216278\pi$
$812$	−14.8398	+	10.1934i	−0.520777	+	0.357720i
$813$	24.2176	−	36.0611i	0.849347	−	1.26472i
$814$	−6.18758			−0.216875
$815$	−0.489557	−	0.847938i	−0.0171484	−	0.0297020i
$816$	−9.39482	−	6.30928i	−0.328885	−	0.220869i
$817$	1.34171	+	0.774636i	0.0469405	+	0.0271011i
$818$	−3.28503			−0.114858
$819$	1.80194	−	31.4119i	0.0629649	−	1.09762i
$820$	10.4503			0.364942
$821$	43.0387	+	24.8484i	1.50206	+	0.867216i	0.999997	+	0.00238646i	$0.000759636\pi$
$821$	43.0387	+	24.8484i	1.50206	+	0.867216i	0.502065	+	0.864830i	$0.332574\pi$
$822$	0.749202	−	11.0348i	0.0261314	−	0.384882i
$823$	−2.04112	−	3.53533i	−0.0711490	−	0.123234i	0.828256	−	0.560350i	$-0.189333\pi$
$823$	−2.04112	−	3.53533i	−0.0711490	−	0.123234i	−0.899405	+	0.437116i	$0.856000\pi$
$824$	13.8207			0.481468
$825$	−0.813528	−	1.65945i	−0.0283234	−	0.0577747i
$826$	−22.1331	−	10.5640i	−0.770109	−	0.367570i
$827$			21.8951i			0.761368i	0.924705	+	0.380684i	$0.124311\pi$
$827$			21.8951i			0.761368i	−0.924705	+	0.380684i	$0.875689\pi$
$828$	−2.99085	+	21.9242i	−0.103939	+	0.761918i
$829$	16.5716	+	9.56760i	0.575555	+	0.332297i	0.759365	−	0.650665i	$-0.225510\pi$
$829$	16.5716	+	9.56760i	0.575555	+	0.332297i	−0.183810	+	0.982962i	$0.558843\pi$
$830$			5.37774i			0.186664i
$831$	37.1858	−	18.2299i	1.28996	−	0.632389i
$832$	−3.43295	−	1.98201i	−0.119016	−	0.0687140i
$833$	−45.1769	+	7.13116i	−1.56529	+	0.247080i
$834$	22.8246	+	15.3283i	0.790352	+	0.530777i
$835$	−10.0381	+	17.3864i	−0.347382	+	0.601683i
$836$	−0.621043	+	1.07568i	−0.0214792	+	0.0372031i
$837$	6.83012	+	20.5949i	0.236083	+	0.711863i
$838$	−18.2098	+	10.5134i	−0.629046	+	0.363180i
$839$	19.0878	+	33.0610i	0.658984	+	1.14139i	0.980879	+	0.194619i	$0.0623469\pi$
$839$	19.0878	+	33.0610i	0.658984	+	1.14139i	−0.321895	+	0.946775i	$0.604320\pi$
$840$	−4.58232	+	0.0480629i	−0.158105	+	0.00165833i
$841$	8.65196	−	14.9856i	0.298343	−	0.516746i
$842$		−	30.1560i		−	1.03924i
$843$	18.7187	−	27.8730i	0.644705	−	0.959997i
$844$	−24.8264			−0.854561
$845$	1.35676	+	2.34997i	0.0466739	+	0.0808415i
$846$	−4.89024	+	35.8475i	−0.168130	+	1.23246i
$847$	11.2386	−	23.5464i	0.386163	−	0.809064i
$848$	−7.55453	+	4.36161i	−0.259424	+	0.149778i
$849$	−8.01857	+	11.9400i	−0.275197	+	0.409781i
$850$	5.65839	−	3.26688i	0.194081	−	0.112053i
$851$	−37.0411	+	21.3857i	−1.26975	+	0.733092i
$852$	0.683187	−	1.01730i	0.0234056	−	0.0348521i
$853$	31.0491	−	17.9262i	1.06310	−	0.613781i	0.136812	−	0.990597i	$-0.456315\pi$
$853$	31.0491	−	17.9262i	1.06310	−	0.613781i	0.926288	+	0.376816i	$0.122981\pi$
$854$	9.21926	−	0.723151i	0.315476	−	0.0247457i
$855$	0.472028	−	3.46016i	0.0161430	−	0.118335i
$856$	−6.03792	−	10.4580i	−0.206372	−	0.357447i
$857$	−44.4028			−1.51677			−0.758385	−	0.651807i	$-0.774011\pi$
$857$	−44.4028			−1.51677			−0.758385	+	0.651807i	$0.774011\pi$
$858$	4.08439	−	6.08185i	0.139439	−	0.207631i
$859$			21.8209i			0.744518i	0.928129	+	0.372259i	$0.121417\pi$
$859$			21.8209i			0.744518i	−0.928129	+	0.372259i	$0.878583\pi$
$860$	−0.665456	+	1.15260i	−0.0226919	+	0.0393035i
$861$	41.7223	+	23.5084i	1.42189	+	0.801165i
$862$	−12.9832	−	22.4876i	−0.442210	−	0.765931i
$863$	9.78815	−	5.65119i	0.333192	−	0.192369i	−0.324065	−	0.946035i	$-0.605050\pi$
$863$	9.78815	−	5.65119i	0.333192	−	0.192369i	0.657258	+	0.753666i	$0.271716\pi$
$864$	−1.63566	−	4.93200i	−0.0556461	−	0.167790i
$865$	−11.5519	+	20.0084i	−0.392775	+	0.680307i
$866$	−3.48010	+	6.02772i	−0.118259	+	0.204830i
$867$	36.9393	+	24.8073i	1.25452	+	0.842500i
$868$	9.10661	−	6.25530i	0.309098	−	0.212319i
$869$	6.35606	+	3.66967i	0.215615	+	0.124485i
$870$	10.5828	−	5.18809i	0.358790	−	0.175893i
$871$		−	23.6572i		−	0.801592i
$872$	12.0874	+	6.97867i	0.409331	+	0.236328i
$873$	2.14951	−	15.7568i	0.0727498	−	0.533285i
$874$			8.58587i			0.290421i
$875$	1.13965	−	2.38772i	0.0385271	−	0.0807196i
$876$	5.50331	+	11.2258i	0.185940	+	0.379284i
$877$	−3.50324			−0.118296			−0.0591480	−	0.998249i	$-0.518838\pi$
$877$	−3.50324			−0.118296			−0.0591480	+	0.998249i	$0.518838\pi$
$878$	−9.87152	−	17.0980i	−0.333148	−	0.577029i
$879$	−3.66074	+	53.9180i	−0.123474	+	1.81861i
$880$	−0.924068	−	0.533511i	−0.0311503	−	0.0179846i
$881$	54.8735			1.84873			0.924367	−	0.381505i	$-0.124594\pi$
$881$	54.8735			1.84873			0.924367	+	0.381505i	$0.124594\pi$
$882$	−18.4028	−	10.1162i	−0.619654	−	0.340631i
$883$	25.2988			0.851371			0.425685	−	0.904871i	$-0.360033\pi$
$883$	25.2988			0.851371			0.425685	+	0.904871i	$0.360033\pi$
$884$	22.4300	+	12.9500i	0.754403	+	0.435555i
$885$	13.3286	+	8.95110i	0.448037	+	0.300888i
$886$	11.8983	+	20.6085i	0.399732	+	0.692357i
$887$	−0.737555			−0.0247647			−0.0123823	−	0.999923i	$-0.503942\pi$
$887$	−0.737555			−0.0247647			−0.0123823	+	0.999923i	$0.503942\pi$
$888$	5.59970	−	8.33822i	0.187914	−	0.279812i
$889$	−9.91456	+	20.7724i	−0.332524	+	0.696683i
$890$		−	4.19028i		−	0.140459i
$891$	9.29884	−	2.39853i	0.311523	−	0.0803538i
$892$	22.1090	+	12.7646i	0.740263	+	0.427391i
$893$			14.0385i			0.469779i
$894$	1.20521	−	17.7512i	0.0403082	−	0.593688i
$895$	−12.2484	−	7.07161i	−0.409418	−	0.236378i
$896$	−2.18082	+	1.49800i	−0.0728562	+	0.0500447i
$897$	3.43036	−	50.5248i	0.114536	−	1.68697i
$898$	−5.34415	+	9.25635i	−0.178337	+	0.308888i
$899$	−14.2074	+	24.6080i	−0.473844	+	0.820722i
$900$	2.97247	+	0.405499i	0.0990823	+	0.0135166i
$901$	49.3594	−	28.4977i	1.64440	−	0.949395i
$902$	5.57537	+	9.65682i	0.185639	+	0.321537i
$903$	−5.24962	+	3.10473i	−0.174696	+	0.103319i
$904$	3.43569	−	5.95078i	0.114269	−	0.197920i
$905$			1.51075i			0.0502190i
$906$	31.9201	+	2.16721i	1.06048	+	0.0720006i
$907$	13.3636			0.443731			0.221865	−	0.975077i	$-0.428785\pi$
$907$	13.3636			0.443731			0.221865	+	0.975077i	$0.428785\pi$
$908$	2.33881	+	4.05093i	0.0776160	+	0.134435i
$909$	−26.9817	+	34.8244i	−0.894926	+	1.15505i
$910$	10.4557	−	0.820138i	0.346604	−	0.0271873i
$911$	24.9353	−	14.3964i	0.826143	−	0.476974i	−0.0263873	−	0.999652i	$-0.508400\pi$
$911$	24.9353	−	14.3964i	0.826143	−	0.476974i	0.852530	+	0.522678i	$0.175067\pi$
$912$	−0.887518	−	1.81038i	−0.0293887	−	0.0599477i
$913$	−4.96940	+	2.86908i	−0.164463	+	0.0949528i
$914$	−18.6962	+	10.7943i	−0.618417	+	0.357043i
$915$	−6.04005	−	0.410087i	−0.199678	−	0.0135571i
$916$	4.82204	−	2.78401i	0.159325	−	0.0919862i
$917$	1.32613	−	2.77842i	0.0437927	−	0.0917516i
$918$	10.6870	+	32.2245i	0.352722	+	1.06357i
$919$	−27.5655	−	47.7448i	−0.909302	−	1.57496i	−0.815036	−	0.579410i	$-0.803283\pi$
$919$	−27.5655	−	47.7448i	−0.909302	−	1.57496i	−0.0942652	−	0.995547i	$-0.530050\pi$
$920$	−7.37575			−0.243171
$921$	9.09205	+	18.5462i	0.299593	+	0.611117i
$922$			8.72606i			0.287378i
$923$	−1.40226	+	2.42879i	−0.0461560	+	0.0799445i
$924$	−2.48913	−	4.20874i	−0.0818865	−	0.138457i
$925$	2.89946	+	5.02202i	0.0953337	+	0.165123i
$926$	−8.42827	+	4.86607i	−0.276970	+	0.159909i
$927$	−32.7757	−	25.3943i	−1.07649	−	0.834059i
$928$	3.40235	−	5.89304i	0.111688	−	0.193449i
$929$	−20.8456	+	36.1056i	−0.683922	+	1.18459i	0.289852	+	0.957071i	$0.406394\pi$
$929$	−20.8456	+	36.1056i	−0.683922	+	1.18459i	−0.973774	+	0.227516i	$0.926940\pi$
$930$	−6.49423	+	3.18372i	−0.212954	+	0.104398i
$931$	−7.60573	−	2.92412i	−0.249268	−	0.0958342i
$932$	−8.86411	−	5.11770i	−0.290354	−	0.167636i
$933$	43.7172	+	29.3591i	1.43124	+	0.961174i
$934$		−	19.6971i		−	0.644509i
$935$	6.03763	+	3.48583i	0.197452	+	0.113999i
$936$	4.49942	+	11.0080i	0.147068	+	0.359809i
$937$			1.97119i			0.0643961i	0.999482	+	0.0321980i	$0.0102507\pi$
$937$			1.97119i			0.0643961i	−0.999482	+	0.0321980i	$0.989749\pi$
$938$	−14.2498	−	6.80138i	−0.465273	−	0.222073i
$939$	14.1018	+	0.957439i	0.460196	+	0.0312448i
$940$	−12.0598			−0.393348
$941$	−21.6949	−	37.5767i	−0.707233	−	1.22496i	−0.965879	−	0.258992i	$-0.916610\pi$
$941$	−21.6949	−	37.5767i	−0.707233	−	1.22496i	0.258646	−	0.965972i	$-0.416724\pi$
$942$	−14.2299	+	6.97603i	−0.463634	+	0.227291i
$943$	66.7524	+	38.5395i	2.17376	+	1.25502i
$944$	9.26956			0.301698
$945$	10.9552	+	8.30561i	0.356373	+	0.270182i
$946$	−1.42011			−0.0461718
$947$	35.4282	+	20.4545i	1.15126	+	0.664681i	0.949194	−	0.314691i	$-0.101901\pi$
$947$	35.4282	+	20.4545i	1.15126	+	0.664681i	0.202067	+	0.979372i	$0.435234\pi$
$948$	−10.6973	+	5.24425i	−0.347433	+	0.170325i
$949$	−14.3065	−	24.7795i	−0.464407	−	0.804377i
$950$	1.16407			0.0377674
$951$	−39.6675	−	2.69321i	−1.28631	−	0.0873333i
$952$	14.2490	−	9.78757i	0.461811	−	0.317217i
$953$			36.3096i			1.17618i	0.808794	+	0.588092i	$0.200121\pi$
$953$			36.3096i			1.17618i	−0.808794	+	0.588092i	$0.799879\pi$
$954$	25.9295	+	3.53725i	0.839499	+	0.114523i
$955$	−0.202055	−	0.116657i	−0.00653836	−	0.00377492i
$956$			2.80393i			0.0906855i
$957$	10.4402	+	7.01131i	0.337483	+	0.226644i
$958$	−7.05984	−	4.07600i	−0.228093	−	0.131690i
$959$	15.2470	+	7.27733i	0.492352	+	0.234997i
$960$	1.55522	−	0.762428i	0.0501944	−	0.0246073i
$961$	−6.78149	+	11.7459i	−0.218758	+	0.378899i
$962$	−11.4935	+	19.9074i	−0.370567	+	0.641841i
$963$	−4.89674	+	35.8951i	−0.157795	+	1.15670i
$964$	−16.0848	+	9.28659i	−0.518058	+	0.299101i
$965$	−0.0930544	−	0.161175i	−0.00299553	−	0.00518841i
$966$	−29.4472	−	16.5920i	−0.947449	−	0.533839i
$967$	−15.9455	+	27.6184i	−0.512772	+	0.888148i	0.487118	+	0.873336i	$0.338048\pi$
$967$	−15.9455	+	27.6184i	−0.512772	+	0.888148i	−0.999890	+	0.0148116i	$0.995285\pi$
$968$			9.86146i			0.316959i
$969$	5.79882	+	11.8286i	0.186285	+	0.379988i
$970$	5.30090			0.170202
$971$	7.83633	+	13.5729i	0.251480	+	0.435576i	0.963933	−	0.266143i	$-0.0857495\pi$
$971$	7.83633	+	13.5729i	0.251480	+	0.435576i	−0.712454	+	0.701719i	$0.752416\pi$
$972$	−5.18316	+	14.7015i	−0.166250	+	0.471552i
$973$	−34.6177	+	23.7788i	−1.10979	+	0.762313i
$974$	17.9553	−	10.3665i	0.575326	−	0.332164i
$975$	−6.85013	−	0.465087i	−0.219380	−	0.0148947i
$976$	−3.02698	+	1.74763i	−0.0968912	+	0.0559402i
$977$	2.88845	−	1.66765i	0.0924096	−	0.0533527i	−0.453083	−	0.891468i	$-0.649676\pi$
$977$	2.88845	−	1.66765i	0.0924096	−	0.0533527i	0.545493	+	0.838116i	$0.316343\pi$
$978$	0.746505	+	1.52274i	0.0238706	+	0.0486917i
$979$	3.87211	−	2.23556i	0.123753	−	0.0714489i
$980$	2.51198	−	6.53375i	0.0802424	−	0.208713i
$981$	−15.8425	−	38.7593i	−0.505811	−	1.23749i
$982$	12.5880	+	21.8030i	0.401699	+	0.695763i
$983$	14.7214			0.469541			0.234771	−	0.972051i	$-0.424566\pi$
$983$	14.7214			0.469541			0.234771	+	0.972051i	$0.424566\pi$
$984$	−18.0589	−	1.22610i	−0.575698	−	0.0390868i
$985$		−	12.3021i		−	0.391976i
$986$	−22.2301	+	38.5037i	−0.707951	+	1.22621i
$987$	−48.1481	−	27.1290i	−1.53257	−	0.863527i
$988$	2.30720	+	3.99619i	0.0734018	+	0.127136i
$989$	−8.50131	+	4.90823i	−0.270326	+	0.156073i
$990$	1.21114	+	2.96310i	0.0384924	+	0.0941735i
$991$	18.9967	−	32.9033i	0.603450	−	1.04521i	−0.388844	−	0.921303i	$-0.627126\pi$
$991$	18.9967	−	32.9033i	0.603450	−	1.04521i	0.992294	−	0.123903i	$-0.0395411\pi$
$992$	−2.08788	+	3.61632i	−0.0662904	+	0.114818i
$993$	0.904740	−	13.3256i	0.0287110	−	0.422877i
$994$	1.05983	+	1.54292i	0.0336156	+	0.0489384i
$995$	17.4049	+	10.0487i	0.551772	+	0.318565i
$996$	0.630953	−	9.29312i	0.0199925	−	0.294464i
$997$			37.9954i			1.20333i	0.798750	+	0.601664i	$0.205495\pi$
$997$			37.9954i			1.20333i	−0.798750	+	0.601664i	$0.794505\pi$
$998$	17.2987	+	9.98741i	0.547581	+	0.316146i
$999$	−28.6003	+	9.48504i	−0.904874	+	0.300093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.10	✓	32
3.2	odd	2		1890.2.t.c.1151.3		32
7.5	odd	6		630.2.bk.c.131.5	yes	32
9.2	odd	6		630.2.bk.c.101.13	yes	32
9.7	even	3		1890.2.bk.c.521.12		32
21.5	even	6		1890.2.bk.c.341.12		32
63.47	even	6	inner	630.2.t.c.551.10	yes	32
63.61	odd	6		1890.2.t.c.1601.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.10	✓	32	1.1	even	1	trivial
630.2.t.c.551.10	yes	32	63.47	even	6	inner
630.2.bk.c.101.13	yes	32	9.2	odd	6
630.2.bk.c.131.5	yes	32	7.5	odd	6
1890.2.t.c.1151.3		32	3.2	odd	2
1890.2.t.c.1601.3		32	63.61	odd	6
1890.2.bk.c.341.12		32	21.5	even	6
1890.2.bk.c.521.12		32	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.55522 + 0.762428i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.72807 - 0.117327i) q^{6} +(1.13965 - 2.38772i) q^{7} +1.00000i q^{8} +(1.83741 - 2.37148i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.55522 + 0.762428i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.72807 - 0.117327i) q^{6} +(1.13965 - 2.38772i) q^{7} +1.00000i q^{8} +(1.83741 - 2.37148i) q^{9} +(0.866025 + 0.500000i) q^{10} +1.06702i q^{11} +(-1.43789 - 0.965644i) q^{12} +(3.43295 + 1.98201i) q^{13} +(2.18082 - 1.49800i) q^{14} +(-1.55522 + 0.762428i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.26688 - 5.65839i) q^{17} +(2.77698 - 1.13506i) q^{18} +(1.00811 - 0.582034i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.0480629 + 4.58232i) q^{21} +(-0.533511 + 0.924068i) q^{22} +7.37575i q^{23} +(-0.762428 - 1.55522i) q^{24} +1.00000 q^{25} +(1.98201 + 3.43295i) q^{26} +(-1.04948 + 5.08907i) q^{27} +(2.63765 - 0.206895i) q^{28} +(-5.89304 + 3.40235i) q^{29} +(-1.72807 - 0.117327i) q^{30} +(3.61632 - 2.08788i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.813528 - 1.65945i) q^{33} +(5.65839 - 3.26688i) q^{34} +(1.13965 - 2.38772i) q^{35} +(2.97247 + 0.405499i) q^{36} +(2.89946 + 5.02202i) q^{37} +1.16407 q^{38} +(-6.85013 - 0.465087i) q^{39} +1.00000i q^{40} +(5.22517 - 9.05026i) q^{41} +(-2.24954 + 3.99244i) q^{42} +(0.665456 + 1.15260i) q^{43} +(-0.924068 + 0.533511i) q^{44} +(1.83741 - 2.37148i) q^{45} +(-3.68787 + 6.38758i) q^{46} +(-6.02991 + 10.4441i) q^{47} +(0.117327 - 1.72807i) q^{48} +(-4.40240 - 5.44232i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.766584 + 11.2908i) q^{51} +3.96403i q^{52} +(7.55453 + 4.36161i) q^{53} +(-3.45341 + 3.88252i) q^{54} +1.06702i q^{55} +(2.38772 + 1.13965i) q^{56} +(-1.12408 + 1.67380i) q^{57} -6.80470 q^{58} +(-4.63478 - 8.02767i) q^{59} +(-1.43789 - 0.965644i) q^{60} +(3.02698 + 1.74763i) q^{61} +4.17577 q^{62} +(-3.56844 - 7.08987i) q^{63} -1.00000 q^{64} +(3.43295 + 1.98201i) q^{65} +(0.125190 - 1.84389i) q^{66} +(-2.98398 - 5.16841i) q^{67} +6.53375 q^{68} +(-5.62348 - 11.4709i) q^{69} +(2.18082 - 1.49800i) q^{70} +0.707493i q^{71} +(2.37148 + 1.83741i) q^{72} +(-6.25109 - 3.60907i) q^{73} +5.79892i q^{74} +(-1.55522 + 0.762428i) q^{75} +(1.00811 + 0.582034i) q^{76} +(2.54775 + 1.21603i) q^{77} +(-5.69984 - 3.82784i) q^{78} +(3.43917 - 5.95682i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.24788 - 8.71476i) q^{81} +(9.05026 - 5.22517i) q^{82} +(2.68887 + 4.65726i) q^{83} +(-3.94438 + 2.33279i) q^{84} +(3.26688 - 5.65839i) q^{85} +1.33091i q^{86} +(6.57092 - 9.78442i) q^{87} -1.06702 q^{88} +(-2.09514 - 3.62889i) q^{89} +(2.77698 - 1.13506i) q^{90} +(8.64485 - 5.93812i) q^{91} +(-6.38758 + 3.68787i) q^{92} +(-4.03230 + 6.00430i) q^{93} +(-10.4441 + 6.02991i) q^{94} +(1.00811 - 0.582034i) q^{95} +(0.965644 - 1.43789i) q^{96} +(4.59071 - 2.65045i) q^{97} +(-1.09143 - 6.91439i) q^{98} +(2.53043 + 1.96055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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