LMFDB - Embedded newform 990.2.t.b.461.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			461.15
Character	$\chi$	$=$	990.461
Dual form			990.2.t.b.131.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.713195 - 1.57840i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.01034 - 1.40685i) q^{6} +(3.86969 + 2.23417i) q^{7} -1.00000 q^{8} +(-1.98271 - 2.25142i) q^{9} -1.00000i q^{10} +(0.273477 - 3.30533i) q^{11} +(-1.72353 + 0.171556i) q^{12} +(-5.39534 + 3.11500i) q^{13} +(3.86969 - 2.23417i) q^{14} +(-0.171556 - 1.72353i) q^{15} +(-0.500000 + 0.866025i) q^{16} +6.51011 q^{17} +(-2.94114 + 0.591365i) q^{18} -7.19244i q^{19} +(-0.866025 - 0.500000i) q^{20} +(6.28626 - 4.51453i) q^{21} +(-2.72576 - 1.88950i) q^{22} +(0.160698 - 0.0927788i) q^{23} +(-0.713195 + 1.57840i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.23000i q^{26} +(-4.96770 + 1.52381i) q^{27} -4.46833i q^{28} +(1.39115 - 2.40954i) q^{29} +(-1.57840 - 0.713195i) q^{30} +(-3.41217 - 5.91006i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.02210 - 2.78900i) q^{33} +(3.25505 - 5.63792i) q^{34} +4.46833 q^{35} +(-0.958432 + 2.84278i) q^{36} -2.21332 q^{37} +(-6.22884 - 3.59622i) q^{38} +(1.06879 + 10.7376i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.73582 + 3.00653i) q^{41} +(-0.766569 - 7.70132i) q^{42} +(2.68449 + 1.54989i) q^{43} +(-2.99924 + 1.41583i) q^{44} +(-2.84278 - 0.958432i) q^{45} -0.185558i q^{46} +(9.56050 + 5.51975i) q^{47} +(1.01034 + 1.40685i) q^{48} +(6.48300 + 11.2289i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.64298 - 10.2756i) q^{51} +(5.39534 + 3.11500i) q^{52} +6.08358i q^{53} +(-1.16419 + 5.06405i) q^{54} +(-1.41583 - 2.99924i) q^{55} +(-3.86969 - 2.23417i) q^{56} +(-11.3526 - 5.12961i) q^{57} +(-1.39115 - 2.40954i) q^{58} +(-11.5172 + 6.64945i) q^{59} +(-1.40685 + 1.01034i) q^{60} +(2.19952 + 1.26989i) q^{61} -6.82435 q^{62} +(-2.64241 - 13.1420i) q^{63} +1.00000 q^{64} +(-3.11500 + 5.39534i) q^{65} +(-4.92640 + 2.95476i) q^{66} +(-5.67108 - 9.82260i) q^{67} +(-3.25505 - 5.63792i) q^{68} +(-0.0318335 - 0.319815i) q^{69} +(2.23417 - 3.86969i) q^{70} +1.30192i q^{71} +(1.98271 + 2.25142i) q^{72} +5.48124i q^{73} +(-1.10666 + 1.91679i) q^{74} +(-1.01034 - 1.40685i) q^{75} +(-6.22884 + 3.59622i) q^{76} +(8.44293 - 12.1796i) q^{77} +(9.83344 + 4.44321i) q^{78} +(8.26376 + 4.77108i) q^{79} +1.00000i q^{80} +(-1.13776 + 8.92779i) q^{81} +3.47164 q^{82} +(-2.06298 + 3.57318i) q^{83} +(-7.05283 - 3.18679i) q^{84} +(5.63792 - 3.25505i) q^{85} +(2.68449 - 1.54989i) q^{86} +(-2.81107 - 3.91427i) q^{87} +(-0.273477 + 3.30533i) q^{88} -10.3192i q^{89} +(-2.25142 + 1.98271i) q^{90} -27.8377 q^{91} +(-0.160698 - 0.0927788i) q^{92} +(-11.7620 + 1.17076i) q^{93} +(9.56050 - 5.51975i) q^{94} +(-3.59622 - 6.22884i) q^{95} +(1.72353 - 0.171556i) q^{96} +(-2.61299 + 4.52583i) q^{97} +12.9660 q^{98} +(-7.98390 + 5.93779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.713195	−	1.57840i	0.411763	−	0.911291i
$3$	0.713195	−	1.57840i	0.411763	−	0.911291i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.01034	−	1.40685i	−0.412469	−	0.574343i
$7$	3.86969	+	2.23417i	1.46261	+	0.844436i	0.999131	−	0.0416747i	$-0.0132693\pi$
$7$	3.86969	+	2.23417i	1.46261	+	0.844436i	0.463474	+	0.886110i	$0.346603\pi$
$8$	−1.00000			−0.353553
$9$	−1.98271	−	2.25142i	−0.660902	−	0.750472i
$10$		−	1.00000i		−	0.316228i
$11$	0.273477	−	3.30533i	0.0824564	−	0.996595i
$11$	0.273477	−	3.30533i	0.0824564	−	0.996595i
$12$	−1.72353	+	0.171556i	−0.497541	+	0.0495239i
$13$	−5.39534	+	3.11500i	−1.49640	+	0.863945i	−0.999991	−	0.00414513i	$-0.998681\pi$
$13$	−5.39534	+	3.11500i	−1.49640	+	0.863945i	−0.496406	+	0.868091i	$0.665347\pi$
$14$	3.86969	−	2.23417i	1.03422	−	0.597106i
$15$	−0.171556	−	1.72353i	−0.0442955	−	0.445015i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.51011			1.57893			0.789467	−	0.613794i	$-0.210357\pi$
$17$	6.51011			1.57893			0.789467	+	0.613794i	$0.210357\pi$
$18$	−2.94114	+	0.591365i	−0.693233	+	0.139386i
$19$		−	7.19244i		−	1.65006i	−0.565090	−	0.825030i	$-0.691158\pi$
$19$		−	7.19244i		−	1.65006i	0.565090	−	0.825030i	$-0.308842\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	6.28626	−	4.51453i	1.37177	−	0.985151i
$22$	−2.72576	−	1.88950i	−0.581134	−	0.402843i
$23$	0.160698	−	0.0927788i	0.0335078	−	0.0193457i	−0.483153	−	0.875536i	$-0.660508\pi$
$23$	0.160698	−	0.0927788i	0.0335078	−	0.0193457i	0.516660	+	0.856190i	$0.327175\pi$
$24$	−0.713195	+	1.57840i	−0.145580	+	0.322190i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			6.23000i			1.22180i
$27$	−4.96770	+	1.52381i	−0.956034	+	0.293257i
$28$		−	4.46833i		−	0.844436i
$29$	1.39115	−	2.40954i	0.258330	−	0.447441i	−0.707465	−	0.706749i	$-0.750161\pi$
$29$	1.39115	−	2.40954i	0.258330	−	0.447441i	0.965795	+	0.259308i	$0.0834944\pi$
$30$	−1.57840	−	0.713195i	−0.288175	−	0.130211i
$31$	−3.41217	−	5.91006i	−0.612845	−	1.06148i	−0.990759	−	0.135637i	$-0.956692\pi$
$31$	−3.41217	−	5.91006i	−0.612845	−	1.06148i	0.377914	−	0.925841i	$-0.376641\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−5.02210	−	2.78900i	−0.874235	−	0.485503i
$34$	3.25505	−	5.63792i	0.558237	−	0.966895i
$35$	4.46833			0.755286
$36$	−0.958432	+	2.84278i	−0.159739	+	0.473797i
$37$	−2.21332			−0.363868			−0.181934	−	0.983311i	$-0.558236\pi$
$37$	−2.21332			−0.363868			−0.181934	+	0.983311i	$0.558236\pi$
$38$	−6.22884	−	3.59622i	−1.01045	−	0.583384i
$39$	1.06879	+	10.7376i	0.171144	+	1.71939i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	1.73582	+	3.00653i	0.271089	+	0.469541i	0.969141	−	0.246507i	$-0.0792827\pi$
$41$	1.73582	+	3.00653i	0.271089	+	0.469541i	−0.698052	+	0.716047i	$0.745949\pi$
$42$	−0.766569	−	7.70132i	−0.118284	−	1.18834i
$43$	2.68449	+	1.54989i	0.409380	+	0.236356i	0.690524	−	0.723310i	$-0.257380\pi$
$43$	2.68449	+	1.54989i	0.409380	+	0.236356i	−0.281143	+	0.959666i	$0.590714\pi$
$44$	−2.99924	+	1.41583i	−0.452152	+	0.213444i
$45$	−2.84278	−	0.958432i	−0.423777	−	0.142875i
$46$		−	0.185558i		−	0.0273590i
$47$	9.56050	+	5.51975i	1.39454	+	0.805139i	0.993814	−	0.111058i	$-0.0354240\pi$
$47$	9.56050	+	5.51975i	1.39454	+	0.805139i	0.400728	+	0.916197i	$0.368757\pi$
$48$	1.01034	+	1.40685i	0.145830	+	0.203061i
$49$	6.48300	+	11.2289i	0.926143	+	1.60413i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	4.64298	−	10.2756i	0.650147	−	1.43887i
$52$	5.39534	+	3.11500i	0.748199	+	0.431973i
$53$			6.08358i			0.835644i	0.908529	+	0.417822i	$0.137206\pi$
$53$			6.08358i			0.835644i	−0.908529	+	0.417822i	$0.862794\pi$
$54$	−1.16419	+	5.06405i	−0.158427	+	0.689131i
$55$	−1.41583	−	2.99924i	−0.190910	−	0.404417i
$56$	−3.86969	−	2.23417i	−0.517109	−	0.298553i
$57$	−11.3526	−	5.12961i	−1.50368	−	0.679434i
$58$	−1.39115	−	2.40954i	−0.182667	−	0.316389i
$59$	−11.5172	+	6.64945i	−1.49941	+	0.865684i	−1.00000		0.000681823i	$-0.999783\pi$
$59$	−11.5172	+	6.64945i	−1.49941	+	0.865684i	−0.499409	+	0.866366i	$0.666450\pi$
$60$	−1.40685	+	1.01034i	−0.181623	+	0.130434i
$61$	2.19952	+	1.26989i	0.281619	+	0.162593i	0.634156	−	0.773205i	$-0.281348\pi$
$61$	2.19952	+	1.26989i	0.281619	+	0.162593i	−0.352537	+	0.935798i	$0.614681\pi$
$62$	−6.82435			−0.866693
$63$	−2.64241	−	13.1420i	−0.332913	−	1.65573i
$64$	1.00000			0.125000
$65$	−3.11500	+	5.39534i	−0.386368	+	0.669209i
$66$	−4.92640	+	2.95476i	−0.606397	+	0.363706i
$67$	−5.67108	−	9.82260i	−0.692833	−	1.20002i	−0.970906	−	0.239462i	$-0.923029\pi$
$67$	−5.67108	−	9.82260i	−0.692833	−	1.20002i	0.278073	−	0.960560i	$-0.410304\pi$
$68$	−3.25505	−	5.63792i	−0.394733	−	0.683698i
$69$	−0.0318335	−	0.319815i	−0.00383230	−	0.0385012i
$70$	2.23417	−	3.86969i	0.267034	−	0.462516i
$71$			1.30192i			0.154509i	0.997011	+	0.0772546i	$0.0246154\pi$
$71$			1.30192i			0.154509i	−0.997011	+	0.0772546i	$0.975385\pi$
$72$	1.98271	+	2.25142i	0.233664	+	0.265332i
$73$			5.48124i			0.641531i	0.947159	+	0.320765i	$0.103940\pi$
$73$			5.48124i			0.641531i	−0.947159	+	0.320765i	$0.896060\pi$
$74$	−1.10666	+	1.91679i	−0.128647	+	0.222823i
$75$	−1.01034	−	1.40685i	−0.116664	−	0.162449i
$76$	−6.22884	+	3.59622i	−0.714497	+	0.412515i
$77$	8.44293	−	12.1796i	0.962161	−	1.38800i
$78$	9.83344	+	4.44321i	1.11342	+	0.503094i
$79$	8.26376	+	4.77108i	0.929745	+	0.536789i	0.886731	−	0.462286i	$-0.152971\pi$
$79$	8.26376	+	4.77108i	0.929745	+	0.536789i	0.0430142	+	0.999074i	$0.486304\pi$
$80$			1.00000i			0.111803i
$81$	−1.13776	+	8.92779i	−0.126418	+	0.991977i
$82$	3.47164			0.383378
$83$	−2.06298	+	3.57318i	−0.226441	+	0.392208i	−0.956751	−	0.290909i	$-0.906042\pi$
$83$	−2.06298	+	3.57318i	−0.226441	+	0.392208i	0.730310	+	0.683116i	$0.239376\pi$
$84$	−7.05283	−	3.18679i	−0.769526	−	0.347708i
$85$	5.63792	−	3.25505i	0.611518	−	0.353060i
$86$	2.68449	−	1.54989i	0.289476	−	0.167129i
$87$	−2.81107	−	3.91427i	−0.301378	−	0.419654i
$88$	−0.273477	+	3.30533i	−0.0291528	+	0.352349i
$89$		−	10.3192i		−	1.09384i	−0.837186	−	0.546919i	$-0.815801\pi$
$89$		−	10.3192i		−	1.09384i	0.837186	−	0.546919i	$-0.184199\pi$
$90$	−2.25142	+	1.98271i	−0.237320	+	0.208995i
$91$	−27.8377			−2.91819
$92$	−0.160698	−	0.0927788i	−0.0167539	−	0.00967286i
$93$	−11.7620	+	1.17076i	−1.21966	+	0.121402i
$94$	9.56050	−	5.51975i	0.986090	−	0.569319i
$95$	−3.59622	−	6.22884i	−0.368964	−	0.639065i
$96$	1.72353	−	0.171556i	0.175907	−	0.0175093i
$97$	−2.61299	+	4.52583i	−0.265309	+	0.459528i	−0.967644	−	0.252318i	$-0.918807\pi$
$97$	−2.61299	+	4.52583i	−0.265309	+	0.459528i	0.702336	+	0.711846i	$0.252141\pi$
$98$	12.9660			1.30976
$99$	−7.98390	+	5.93779i	−0.802412	+	0.596770i
$100$	−1.00000			−0.100000
$101$	−5.63537	+	9.76075i	−0.560740	+	0.971230i	0.436692	+	0.899611i	$0.356150\pi$
$101$	−5.63537	+	9.76075i	−0.560740	+	0.971230i	−0.997432	+	0.0716193i	$0.977183\pi$
$102$	−6.57741	−	9.15872i	−0.651261	−	0.906848i
$103$	−1.19221	−	2.06496i	−0.117472	−	0.203467i	0.801293	−	0.598272i	$-0.204146\pi$
$103$	−1.19221	−	2.06496i	−0.117472	−	0.203467i	−0.918765	+	0.394805i	$0.870812\pi$
$104$	5.39534	−	3.11500i	0.529056	−	0.305451i
$105$	3.18679	−	7.05283i	0.310999	−	0.688285i
$106$	5.26853	+	3.04179i	0.511725	+	0.295445i
$107$	3.84087			0.371310			0.185655	−	0.982615i	$-0.440559\pi$
$107$	3.84087			0.371310			0.185655	+	0.982615i	$0.440559\pi$
$108$	3.80350	+	3.54025i	0.365992	+	0.340661i
$109$			16.7684i			1.60612i	0.595898	+	0.803060i	$0.296796\pi$
$109$			16.7684i			1.60612i	−0.595898	+	0.803060i	$0.703204\pi$
$110$	−3.30533	−	0.273477i	−0.315151	−	0.0260750i
$111$	−1.57853	+	3.49351i	−0.149827	+	0.331589i
$112$	−3.86969	+	2.23417i	−0.365651	+	0.211109i
$113$	3.81940	−	2.20513i	0.359299	−	0.207442i	−0.309474	−	0.950908i	$-0.600153\pi$
$113$	3.81940	−	2.20513i	0.359299	−	0.207442i	0.668773	+	0.743466i	$0.266820\pi$
$114$	−10.1187	+	7.26680i	−0.947699	+	0.680598i
$115$	0.0927788	−	0.160698i	0.00865167	−	0.0149851i
$116$	−2.78230			−0.258330
$117$	17.7105	+	5.97103i	1.63734	+	0.552022i
$118$			13.2989i			1.22426i
$119$	25.1921	+	14.5447i	2.30936	+	1.33331i
$120$	0.171556	+	1.72353i	0.0156608	+	0.157336i
$121$	−10.8504	−	1.80786i	−0.986402	−	0.164351i
$122$	2.19952	−	1.26989i	0.199135	−	0.114971i
$123$	5.98349	−	0.595580i	0.539513	−	0.0537016i
$124$	−3.41217	+	5.91006i	−0.306422	+	0.530739i
$125$		−	1.00000i		−	0.0894427i
$126$	−12.7025	−	4.28259i	−1.13163	−	0.381524i
$127$			8.81589i			0.782283i	0.920330	+	0.391142i	$0.127920\pi$
$127$			8.81589i			0.782283i	−0.920330	+	0.391142i	$0.872080\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.36091	−	3.13183i	0.383957	−	0.275742i
$130$	3.11500	+	5.39534i	0.273204	+	0.473202i
$131$	0.765387	+	1.32569i	0.0668721	+	0.115826i	0.897523	−	0.440968i	$-0.145365\pi$
$131$	0.765387	+	1.32569i	0.0668721	+	0.115826i	−0.830651	+	0.556794i	$0.812031\pi$
$132$	0.0957018	+	5.74377i	0.00832977	+	0.499931i
$133$	16.0691	−	27.8325i	1.39337	−	2.41339i
$134$	−11.3422			−0.979814
$135$	−3.54025	+	3.80350i	−0.304696	+	0.327353i
$136$	−6.51011			−0.558237
$137$	3.27041	+	1.88817i	0.279410	+	0.161317i	0.633156	−	0.774024i	$-0.281759\pi$
$137$	3.27041	+	1.88817i	0.279410	+	0.161317i	−0.353746	+	0.935341i	$0.615092\pi$
$138$	−0.292885	−	0.132339i	−0.0249320	−	0.0112654i
$139$	13.1784	−	7.60855i	1.11778	−	0.645348i	0.176944	−	0.984221i	$-0.443379\pi$
$139$	13.1784	−	7.60855i	1.11778	−	0.645348i	0.940832	+	0.338872i	$0.110046\pi$
$140$	−2.23417	−	3.86969i	−0.188822	−	0.327049i
$141$	15.5309	−	11.1536i	1.30794	−	0.939306i
$142$	1.12749	+	0.650958i	0.0946171	+	0.0546272i
$143$	8.82060	+	18.6853i	0.737616	+	1.56254i
$144$	2.94114	−	0.591365i	0.245095	−	0.0492804i
$145$		−	2.78230i		−	0.231058i
$146$	4.74690	+	2.74062i	0.392856	+	0.226815i
$147$	22.3473	−	2.22439i	1.84318	−	0.183465i
$148$	1.10666	+	1.91679i	0.0909670	+	0.157559i
$149$	0.882237	+	1.52808i	0.0722756	+	0.125185i	0.899898	−	0.436100i	$-0.143641\pi$
$149$	0.882237	+	1.52808i	0.0722756	+	0.125185i	−0.827623	+	0.561285i	$0.810307\pi$
$150$	−1.72353	+	0.171556i	−0.140726	+	0.0140075i
$151$	−2.89704	−	1.67260i	−0.235757	−	0.136115i	0.377468	−	0.926023i	$-0.376795\pi$
$151$	−2.89704	−	1.67260i	−0.235757	−	0.136115i	−0.613225	+	0.789908i	$0.710128\pi$
$152$			7.19244i			0.583384i
$153$	−12.9076	−	14.6570i	−1.04352	−	1.18495i
$154$	−6.32639	−	13.4016i	−0.509795	−	1.07993i
$155$	−5.91006	−	3.41217i	−0.474707	−	0.274072i
$156$	8.76465	−	6.29441i	0.701734	−	0.503956i
$157$	−3.74238	−	6.48200i	−0.298675	−	0.517320i	0.677158	−	0.735837i	$-0.263211\pi$
$157$	−3.74238	−	6.48200i	−0.298675	−	0.517320i	−0.975833	+	0.218517i	$0.929878\pi$
$158$	8.26376	−	4.77108i	0.657429	−	0.379567i
$159$	9.60233	+	4.33878i	0.761514	+	0.344088i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	0.829134			0.0653449
$162$	7.16282	+	5.44923i	0.562764	+	0.428132i
$163$	16.5821			1.29881			0.649404	−	0.760444i	$-0.275019\pi$
$163$	16.5821			1.29881			0.649404	+	0.760444i	$0.275019\pi$
$164$	1.73582	−	3.00653i	0.135545	−	0.234770i
$165$	−5.74377	+	0.0957018i	−0.447152	+	0.00745037i
$166$	2.06298	+	3.57318i	0.160118	+	0.277333i
$167$	11.2138	+	19.4229i	0.867753	+	1.50299i	0.864287	+	0.502998i	$0.167770\pi$
$167$	11.2138	+	19.4229i	0.867753	+	1.50299i	0.00346574	+	0.999994i	$0.498897\pi$
$168$	−6.28626	+	4.51453i	−0.484995	+	0.348304i
$169$	12.9064	−	22.3546i	0.992803	−	1.71959i
$170$		−	6.51011i		−	0.499303i
$171$	−16.1932	+	14.2605i	−1.23832	+	1.09053i
$172$		−	3.09978i		−	0.236356i
$173$	5.54207	−	9.59914i	0.421356	−	0.729809i	−0.574717	−	0.818352i	$-0.694888\pi$
$173$	5.54207	−	9.59914i	0.421356	−	0.729809i	0.996072	+	0.0885432i	$0.0282211\pi$
$174$	−4.79539	+	0.477320i	−0.363538	+	0.0361855i
$175$	3.86969	−	2.23417i	0.292521	−	0.168887i
$176$	2.72576	+	1.88950i	0.205462	+	0.142427i
$177$	2.28150	+	22.9211i	0.171488	+	1.72285i
$178$	−8.93672	−	5.15962i	−0.669836	−	0.386730i
$179$			9.22904i			0.689811i	0.938637	+	0.344906i	$0.112089\pi$
$179$			9.22904i			0.689811i	−0.938637	+	0.344906i	$0.887911\pi$
$180$	0.591365	+	2.94114i	0.0440777	+	0.219219i
$181$	−9.22757			−0.685880			−0.342940	−	0.939357i	$-0.611423\pi$
$181$	−9.22757			−0.685880			−0.342940	+	0.939357i	$0.611423\pi$
$182$	−13.9189	+	24.1082i	−1.03173	+	1.78702i
$183$	3.57309	−	2.56604i	0.264130	−	0.189687i
$184$	−0.160698	+	0.0927788i	−0.0118468	+	0.00683975i
$185$	−1.91679	+	1.10666i	−0.140925	+	0.0813633i
$186$	−4.86709	+	10.7716i	−0.356872	+	0.789809i
$187$	1.78037	−	21.5181i	0.130193	−	1.57356i
$188$		−	11.0395i		−	0.805139i
$189$	−22.6279	−	5.20201i	−1.64594	−	0.378390i
$190$	−7.19244			−0.521794
$191$	11.3633	+	6.56060i	0.822219	+	0.474708i	0.851181	−	0.524872i	$-0.175887\pi$
$191$	11.3633	+	6.56060i	0.822219	+	0.474708i	−0.0289622	+	0.999581i	$0.509220\pi$
$192$	0.713195	−	1.57840i	0.0514704	−	0.113911i
$193$	−18.9691	+	10.9518i	−1.36542	+	0.788328i	−0.990340	−	0.138663i	$-0.955720\pi$
$193$	−18.9691	+	10.9518i	−1.36542	+	0.788328i	−0.375084	+	0.926991i	$0.622386\pi$
$194$	2.61299	+	4.52583i	0.187602	+	0.324936i
$195$	6.29441	+	8.76465i	0.450752	+	0.627650i
$196$	6.48300	−	11.2289i	0.463072	−	0.802064i
$197$	5.97983			0.426045			0.213023	−	0.977047i	$-0.431669\pi$
$197$	5.97983			0.426045			0.213023	+	0.977047i	$0.431669\pi$
$198$	1.15032	+	9.88316i	0.0817498	+	0.702365i
$199$	−5.82491			−0.412917			−0.206458	−	0.978455i	$-0.566194\pi$
$199$	−5.82491			−0.412917			−0.206458	+	0.978455i	$0.566194\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−19.5486	+	1.94581i	−1.37885	+	0.137247i
$202$	5.63537	+	9.76075i	0.396503	+	0.686764i
$203$	10.7666	−	6.21613i	0.755670	−	0.436286i
$204$	−11.2204	+	1.11685i	−0.785585	+	0.0781949i
$205$	3.00653	+	1.73582i	0.209985	+	0.121235i
$206$	−2.38442			−0.166130
$207$	−0.527500	−	0.177844i	−0.0366638	−	0.0123610i
$208$		−	6.23000i		−	0.431973i
$209$	−23.7734	−	1.96697i	−1.64444	−	0.136058i
$210$	−4.51453	−	6.28626i	−0.311532	−	0.433793i
$211$	11.9574	−	6.90362i	0.823183	−	0.475265i	−0.0283299	−	0.999599i	$-0.509019\pi$
$211$	11.9574	−	6.90362i	0.823183	−	0.475265i	0.851513	+	0.524334i	$0.175686\pi$
$212$	5.26853	−	3.04179i	0.361844	−	0.208911i
$213$	2.05495	+	0.928521i	0.140803	+	0.0636212i
$214$	1.92043	−	3.32629i	0.131278	−	0.227380i
$215$	3.09978			0.211403
$216$	4.96770	−	1.52381i	0.338009	−	0.103682i
$217$		−	30.4935i		−	2.07003i
$218$	14.5218	+	8.38419i	0.983543	+	0.567849i
$219$	8.65160	+	3.90920i	0.584621	+	0.264159i
$220$	−1.88950	+	2.72576i	−0.127390	+	0.183771i
$221$	−35.1242	+	20.2790i	−2.36271	+	1.36411i
$222$	2.23620	+	3.11380i	0.150084	+	0.208985i
$223$	−2.63579	+	4.56532i	−0.176506	+	0.305717i	−0.940681	−	0.339292i	$-0.889813\pi$
$223$	−2.63579	+	4.56532i	−0.176506	+	0.305717i	0.764176	+	0.645008i	$0.223146\pi$
$224$			4.46833i			0.298553i
$225$	−2.94114	+	0.591365i	−0.196076	+	0.0394243i
$226$		−	4.41027i		−	0.293367i
$227$	−1.05021	+	1.81901i	−0.0697047	+	0.120732i	−0.898771	−	0.438418i	$-0.855539\pi$
$227$	−1.05021	+	1.81901i	−0.0697047	+	0.120732i	0.829067	+	0.559150i	$0.188872\pi$
$228$	1.23391	+	12.3964i	0.0817174	+	0.820973i
$229$	−3.58056	−	6.20171i	−0.236610	−	0.409820i	0.723129	−	0.690713i	$-0.242703\pi$
$229$	−3.58056	−	6.20171i	−0.236610	−	0.409820i	−0.959739	+	0.280892i	$0.909370\pi$
$230$	−0.0927788	−	0.160698i	−0.00611765	−	0.0105961i
$231$	−13.2029	−	22.0128i	−0.868685	−	1.44833i
$232$	−1.39115	+	2.40954i	−0.0913335	+	0.158194i
$233$	−12.7300			−0.833968			−0.416984	−	0.908914i	$-0.636913\pi$
$233$	−12.7300			−0.833968			−0.416984	+	0.908914i	$0.636913\pi$
$234$	14.0263	−	12.3523i	0.916930	−	0.807492i
$235$	11.0395			0.720138
$236$	11.5172	+	6.64945i	0.749705	+	0.432842i
$237$	13.4244	−	9.64082i	0.872005	−	0.626238i
$238$	25.1921	−	14.5447i	1.63296	−	0.942791i
$239$	6.09733	+	10.5609i	0.394404	+	0.683127i	0.993025	−	0.117905i	$-0.0376179\pi$
$239$	6.09733	+	10.5609i	0.394404	+	0.683127i	−0.598621	+	0.801032i	$0.704285\pi$
$240$	1.57840	+	0.713195i	0.101885	+	0.0460365i
$241$	0.253838	+	0.146553i	0.0163511	+	0.00944033i	0.508153	−	0.861267i	$-0.330328\pi$
$241$	0.253838	+	0.146553i	0.0163511	+	0.00944033i	−0.491802	+	0.870707i	$0.663662\pi$
$242$	−6.99087	+	8.49281i	−0.449390	+	0.545938i
$243$	13.2802	+	8.16310i	0.851925	+	0.523663i
$244$		−	2.53978i		−	0.162593i
$245$	11.2289	+	6.48300i	0.717387	+	0.414184i
$246$	2.47596	−	5.47964i	0.157861	−	0.349369i
$247$	22.4044	+	38.8056i	1.42556	+	2.46914i
$248$	3.41217	+	5.91006i	0.216673	+	0.375289i
$249$	4.16861	+	5.80458i	0.264175	+	0.367850i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$		−	2.65840i		−	0.167797i	−0.996474	−	0.0838984i	$-0.973263\pi$
$251$		−	2.65840i		−	0.167797i	0.996474	−	0.0838984i	$-0.0267371\pi$
$252$	−10.0601	+	8.85939i	−0.633726	+	0.558089i
$253$	−0.262718	−	0.556532i	−0.0165169	−	0.0349889i
$254$	7.63478	+	4.40794i	0.479049	+	0.276579i
$255$	−1.11685	−	11.2204i	−0.0699397	−	0.702648i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	16.8547	−	9.73109i	1.05137	−	0.607009i	0.128337	−	0.991731i	$-0.459036\pi$
$257$	16.8547	−	9.73109i	1.05137	−	0.607009i	0.923032	+	0.384722i	$0.125703\pi$
$258$	−0.531785	−	5.34257i	−0.0331075	−	0.332614i
$259$	−8.56487	−	4.94493i	−0.532195	−	0.307263i
$260$	6.23000			0.386368
$261$	−8.18313	+	1.64535i	−0.506523	+	0.101845i
$262$	1.53077			0.0945715
$263$	6.85063	−	11.8656i	0.422428	−	0.731667i	−0.573748	−	0.819032i	$-0.694511\pi$
$263$	6.85063	−	11.8656i	0.422428	−	0.731667i	0.996176	+	0.0873648i	$0.0278446\pi$
$264$	5.02210	+	2.78900i	0.309089	+	0.171651i
$265$	3.04179	+	5.26853i	0.186856	+	0.323643i
$266$	−16.0691	−	27.8325i	−0.985261	−	1.70652i
$267$	−16.2879	−	7.35963i	−0.996804	−	0.450402i
$268$	−5.67108	+	9.82260i	−0.346417	+	0.600011i
$269$			4.96103i			0.302479i	0.988497	+	0.151240i	$0.0483265\pi$
$269$			4.96103i			0.302479i	−0.988497	+	0.151240i	$0.951674\pi$
$270$	1.52381	+	4.96770i	0.0927359	+	0.302324i
$271$		−	17.2923i		−	1.05043i	−0.850970	−	0.525215i	$-0.823985\pi$
$271$		−	17.2923i		−	1.05043i	0.850970	−	0.525215i	$-0.176015\pi$
$272$	−3.25505	+	5.63792i	−0.197367	+	0.341849i
$273$	−19.8537	+	43.9391i	−1.20160	+	2.65932i
$274$	3.27041	−	1.88817i	0.197573	−	0.114069i
$275$	−2.72576	−	1.88950i	−0.164370	−	0.113941i
$276$	−0.261051	+	0.187476i	−0.0157134	+	0.0112847i
$277$	−17.8388	−	10.2992i	−1.07183	−	0.618821i	−0.143148	−	0.989701i	$-0.545723\pi$
$277$	−17.8388	−	10.2992i	−1.07183	−	0.618821i	−0.928681	+	0.370881i	$0.879056\pi$
$278$		−	15.2171i		−	0.912661i
$279$	−6.54067	+	19.4001i	−0.391580	+	1.16146i
$280$	−4.46833			−0.267034
$281$	7.83774	−	13.5754i	0.467561	−	0.809839i	−0.531752	−	0.846900i	$-0.678466\pi$
$281$	7.83774	−	13.5754i	0.467561	−	0.809839i	0.999313	+	0.0370611i	$0.0117996\pi$
$282$	−1.89389	−	19.0270i	−0.112780	−	1.13304i
$283$	−13.6333	+	7.87118i	−0.810415	+	0.467893i	−0.847100	−	0.531434i	$-0.821653\pi$
$283$	−13.6333	+	7.87118i	−0.810415	+	0.467893i	0.0366852	+	0.999327i	$0.488320\pi$
$284$	1.12749	−	0.650958i	0.0669044	−	0.0386273i
$285$	−12.3964	+	1.23391i	−0.734300	+	0.0730902i
$286$	20.5922	+	1.70376i	1.21764	+	0.100746i
$287$			15.5124i			0.915671i
$288$	0.958432	−	2.84278i	0.0564761	−	0.167513i
$289$	25.3815			1.49303
$290$	−2.40954	−	1.39115i	−0.141493	−	0.0816912i
$291$	5.28001	+	7.35215i	0.309519	+	0.430990i
$292$	4.74690	−	2.74062i	0.277791	−	0.160383i
$293$	−1.95371	−	3.38393i	−0.114137	−	0.197691i	0.803297	−	0.595578i	$-0.203077\pi$
$293$	−1.95371	−	3.38393i	−0.114137	−	0.197691i	−0.917435	+	0.397887i	$0.869744\pi$
$294$	9.24729	−	20.4656i	0.539313	−	1.19358i
$295$	−6.64945	+	11.5172i	−0.387146	+	0.670556i
$296$	2.21332			0.128647
$297$	3.67813	+	16.8366i	0.213427	+	0.976959i
$298$	1.76447			0.102213
$299$	−0.578012	+	1.00115i	−0.0334273	+	0.0578978i
$300$	−0.713195	+	1.57840i	−0.0411763	+	0.0911291i
$301$	6.92542	+	11.9952i	0.399175	+	0.691391i
$302$	−2.89704	+	1.67260i	−0.166706	+	0.0962476i
$303$	11.3873	+	15.8562i	0.654181	+	0.910915i
$304$	6.22884	+	3.59622i	0.357248	+	0.206257i
$305$	2.53978			0.145428
$306$	−19.1471	+	3.84985i	−1.09457	+	0.220081i
$307$			25.4448i			1.45221i	0.687582	+	0.726107i	$0.258672\pi$
$307$			25.4448i			1.45221i	−0.687582	+	0.726107i	$0.741328\pi$
$308$	−14.7693	−	1.22199i	−0.841560	−	0.0696292i
$309$	−4.10962	+	0.409060i	−0.233788	+	0.0232706i
$310$	−5.91006	+	3.41217i	−0.335669	+	0.193798i
$311$	22.9819	−	13.2686i	1.30318	−	0.752393i	0.322235	−	0.946660i	$-0.395566\pi$
$311$	22.9819	−	13.2686i	1.30318	−	0.752393i	0.980949	+	0.194267i	$0.0622327\pi$
$312$	−1.06879	−	10.7376i	−0.0605085	−	0.607898i
$313$	11.9671	−	20.7277i	0.676422	−	1.17160i	−0.299629	−	0.954056i	$-0.596863\pi$
$313$	11.9671	−	20.7277i	0.676422	−	1.17160i	0.976051	−	0.217542i	$-0.0698038\pi$
$314$	−7.48477			−0.422390
$315$	−8.85939	−	10.0601i	−0.499170	−	0.566821i
$316$		−	9.54216i		−	0.536789i
$317$	3.04029	+	1.75531i	0.170759	+	0.0985880i	0.582944	−	0.812512i	$-0.301901\pi$
$317$	3.04029	+	1.75531i	0.170759	+	0.0985880i	−0.412184	+	0.911100i	$0.635234\pi$
$318$	8.55866	−	6.14647i	0.479946	−	0.344677i
$319$	−7.58389	−	5.25717i	−0.424616	−	0.294345i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	2.73929	−	6.06243i	0.152892	−	0.338372i
$322$	0.414567	−	0.718051i	0.0231029	−	0.0400154i
$323$		−	46.8236i		−	2.60533i
$324$	8.30058	−	3.47857i	0.461143	−	0.193254i
$325$			6.23000i			0.345578i
$326$	8.29103	−	14.3605i	0.459198	−	0.795354i
$327$	26.4672	+	11.9591i	1.46364	+	0.661341i
$328$	−1.73582	−	3.00653i	−0.0958446	−	0.166008i
$329$	24.6641	+	42.7195i	1.35978	+	2.35520i
$330$	−2.78900	+	5.02210i	−0.153530	+	0.276457i
$331$	−11.2820	+	19.5410i	−0.620114	+	1.07407i	0.369350	+	0.929290i	$0.379580\pi$
$331$	−11.2820	+	19.5410i	−0.620114	+	1.07407i	−0.989464	+	0.144779i	$0.953753\pi$
$332$	4.12595			0.226441
$333$	4.38837	+	4.98311i	0.240481	+	0.273073i
$334$	22.4277			1.22719
$335$	−9.82260	−	5.67108i	−0.536666	−	0.309844i
$336$	0.766569	+	7.70132i	0.0418198	+	0.420142i
$337$	−18.0791	+	10.4380i	−0.984832	+	0.568593i	−0.903725	−	0.428113i	$-0.859179\pi$
$337$	−18.0791	+	10.4380i	−0.984832	+	0.568593i	−0.0811062	+	0.996705i	$0.525845\pi$
$338$	−12.9064	−	22.3546i	−0.702018	−	1.21593i
$339$	−0.756607	−	7.60125i	−0.0410933	−	0.412843i
$340$	−5.63792	−	3.25505i	−0.305759	−	0.176530i
$341$	−20.4678	+	9.66210i	−1.10840	+	0.523232i
$342$	4.25335	+	21.1540i	0.229995	+	1.14387i
$343$			26.6581i			1.43940i
$344$	−2.68449	−	1.54989i	−0.144738	−	0.0835644i
$345$	−0.187476	−	0.261051i	−0.0100934	−	0.0140545i
$346$	−5.54207	−	9.59914i	−0.297943	−	0.516053i
$347$	−11.0408	−	19.1233i	−0.592704	−	1.02659i	−0.993867	−	0.110586i	$-0.964727\pi$
$347$	−11.0408	−	19.1233i	−0.592704	−	1.02659i	0.401163	−	0.916007i	$-0.368606\pi$
$348$	−1.98432	+	4.39159i	−0.106371	+	0.235414i
$349$	−7.46543	−	4.31017i	−0.399615	−	0.230718i	0.286703	−	0.958020i	$-0.407441\pi$
$349$	−7.46543	−	4.31017i	−0.399615	−	0.230718i	−0.686318	+	0.727302i	$0.740774\pi$
$350$		−	4.46833i		−	0.238842i
$351$	22.0557	−	23.6958i	1.17725	−	1.26479i
$352$	2.99924	−	1.41583i	0.159860	−	0.0754638i
$353$	−26.3805	−	15.2308i	−1.40409	−	0.810653i	−0.409282	−	0.912408i	$-0.634221\pi$
$353$	−26.3805	−	15.2308i	−1.40409	−	0.810653i	−0.994809	+	0.101755i	$0.967554\pi$
$354$	20.9910	+	9.48471i	1.11566	+	0.504106i
$355$	0.650958	+	1.12749i	0.0345493	+	0.0598411i
$356$	−8.93672	+	5.15962i	−0.473645	+	0.273459i
$357$	40.9242	−	29.3901i	2.16594	−	1.55549i
$358$	7.99259	+	4.61452i	0.422421	+	0.243885i
$359$	1.88380			0.0994231			0.0497115	−	0.998764i	$-0.484170\pi$
$359$	1.88380			0.0994231			0.0497115	+	0.998764i	$0.484170\pi$
$360$	2.84278	+	0.958432i	0.149828	+	0.0505138i
$361$	−32.7312			−1.72269
$362$	−4.61378	+	7.99131i	−0.242495	+	0.420014i
$363$	−10.5920	+	15.8370i	−0.555936	+	0.831225i
$364$	13.9189	+	24.1082i	0.729546	+	1.26361i
$365$	2.74062	+	4.74690i	0.143451	+	0.248464i
$366$	−0.435715	−	4.37740i	−0.0227752	−	0.228811i
$367$	0.821032	−	1.42207i	0.0428575	−	0.0742314i	−0.843801	−	0.536656i	$-0.819687\pi$
$367$	0.821032	−	1.42207i	0.0428575	−	0.0742314i	0.886658	+	0.462425i	$0.153021\pi$
$368$			0.185558i			0.00967286i
$369$	3.32733	−	9.86911i	0.173214	−	0.513766i
$370$			2.21332i			0.115065i
$371$	−13.5917	+	23.5416i	−0.705647	+	1.22222i
$372$	6.89490	+	9.60081i	0.357484	+	0.497779i
$373$	−5.84178	+	3.37275i	−0.302476	+	0.174634i	−0.643555	−	0.765400i	$-0.722541\pi$
$373$	−5.84178	+	3.37275i	−0.302476	+	0.174634i	0.341079	+	0.940035i	$0.389208\pi$
$374$	−17.7450	−	12.3009i	−0.917572	−	0.636063i
$375$	−1.57840	−	0.713195i	−0.0815083	−	0.0368292i
$376$	−9.56050	−	5.51975i	−0.493045	−	0.284660i
$377$			17.3337i			0.892733i
$378$	−15.8190	+	16.9953i	−0.813642	+	0.874145i
$379$	−34.6496			−1.77983			−0.889916	−	0.456125i	$-0.849237\pi$
$379$	−34.6496			−1.77983			−0.889916	+	0.456125i	$0.849237\pi$
$380$	−3.59622	+	6.22884i	−0.184482	+	0.319533i
$381$	13.9150	+	6.28745i	0.712888	+	0.322116i
$382$	11.3633	−	6.56060i	0.581396	−	0.335669i
$383$	−4.20967	+	2.43045i	−0.215104	+	0.124190i	−0.603681	−	0.797226i	$-0.706300\pi$
$383$	−4.20967	+	2.43045i	−0.215104	+	0.124190i	0.388577	+	0.921416i	$0.372967\pi$
$384$	−1.01034	−	1.40685i	−0.0515586	−	0.0717928i
$385$	1.22199	−	14.7693i	0.0622782	−	0.752714i
$386$			21.9036i			1.11486i
$387$	−1.83310	−	9.11688i	−0.0931817	−	0.463437i
$388$	5.22598			0.265309
$389$	17.0439	+	9.84029i	0.864159	+	0.498922i	0.865403	−	0.501077i	$-0.167063\pi$
$389$	17.0439	+	9.84029i	0.864159	+	0.498922i	−0.00124401	+	0.999999i	$0.500396\pi$
$390$	10.7376	−	1.06879i	0.543720	−	0.0541204i
$391$	1.04616	−	0.604000i	0.0529065	−	0.0305456i
$392$	−6.48300	−	11.2289i	−0.327441	−	0.567145i
$393$	2.63834	−	0.262613i	0.133087	−	0.0132471i
$394$	2.98992	−	5.17869i	0.150630	−	0.260898i
$395$	9.54216			0.480118
$396$	9.13422	+	3.94537i	0.459012	+	0.198262i
$397$	−23.5740			−1.18315			−0.591573	−	0.806251i	$-0.701493\pi$
$397$	−23.5740			−1.18315			−0.591573	+	0.806251i	$0.701493\pi$
$398$	−2.91245	+	5.04452i	−0.145988	+	0.252859i
$399$	−32.4705	−	45.2135i	−1.62556	−	2.26351i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	7.42060	−	4.28429i	0.370567	−	0.213947i	−0.303139	−	0.952946i	$-0.598035\pi$
$401$	7.42060	−	4.28429i	0.370567	−	0.213947i	0.673706	+	0.738999i	$0.264701\pi$
$402$	−8.08918	+	17.9025i	−0.403452	+	0.892895i
$403$	36.8197	+	21.2578i	1.83412	+	1.05893i
$404$	11.2707			0.560740
$405$	3.47857	+	8.30058i	0.172851	+	0.412459i
$406$		−	12.4323i		−	0.617002i
$407$	−0.605293	+	7.31576i	−0.0300033	+	0.362629i
$408$	−4.64298	+	10.2756i	−0.229862	+	0.508716i
$409$	−23.7276	+	13.6991i	−1.17325	+	0.677379i	−0.954444	−	0.298389i	$-0.903551\pi$
$409$	−23.7276	+	13.6991i	−1.17325	+	0.677379i	−0.218810	+	0.975768i	$0.570217\pi$
$410$	3.00653	−	1.73582i	0.148482	−	0.0857260i
$411$	5.31274	−	3.81539i	0.262058	−	0.188199i
$412$	−1.19221	+	2.06496i	−0.0587359	+	0.101734i
$413$	−59.4239			−2.92406
$414$	−0.417768	+	0.367906i	−0.0205322	+	0.0180816i
$415$			4.12595i			0.202535i
$416$	−5.39534	−	3.11500i	−0.264528	−	0.152725i
$417$	−2.61058	−	26.2272i	−0.127841	−	1.28435i
$418$	−13.5901	+	19.6049i	−0.664716	+	0.958906i
$419$	−5.87748	+	3.39337i	−0.287134	+	0.165777i	−0.636649	−	0.771154i	$-0.719680\pi$
$419$	−5.87748	+	3.39337i	−0.287134	+	0.165777i	0.349515	+	0.936931i	$0.386346\pi$
$420$	−7.70132	+	0.766569i	−0.375786	+	0.0374047i
$421$	−5.06935	+	8.78038i	−0.247065	+	0.427929i	−0.962710	−	0.270535i	$-0.912800\pi$
$421$	−5.06935	+	8.78038i	−0.247065	+	0.427929i	0.715645	+	0.698464i	$0.246133\pi$
$422$		−	13.8072i		−	0.672126i
$423$	−6.52837	−	32.4687i	−0.317420	−	1.57868i
$424$		−	6.08358i		−	0.295445i
$425$	3.25505	−	5.63792i	0.157893	−	0.273479i
$426$	1.83160	−	1.31538i	0.0887412	−	0.0637302i
$427$	5.67430	+	9.82818i	0.274599	+	0.475619i
$428$	−1.92043	−	3.32629i	−0.0928276	−	0.160782i
$429$	35.7837	−	0.596222i	1.72765	−	0.0287859i
$430$	1.54989	−	2.68449i	0.0747423	−	0.129457i
$431$	12.9017			0.621452			0.310726	−	0.950500i	$-0.399428\pi$
$431$	12.9017			0.621452			0.310726	+	0.950500i	$0.399428\pi$
$432$	1.16419	−	5.06405i	0.0560123	−	0.243644i
$433$	−15.2943			−0.734996			−0.367498	−	0.930024i	$-0.619786\pi$
$433$	−15.2943			−0.734996			−0.367498	+	0.930024i	$0.619786\pi$
$434$	−26.4081	−	15.2467i	−1.26763	−	0.731867i
$435$	−4.39159	−	1.98432i	−0.210561	−	0.0951410i
$436$	14.5218	−	8.38419i	0.695470	−	0.401530i
$437$	−0.667306	−	1.15581i	−0.0319216	−	0.0552898i
$438$	7.71127	−	5.53791i	0.368459	−	0.264612i
$439$	−7.38524	−	4.26387i	−0.352478	−	0.203503i	0.313298	−	0.949655i	$-0.398566\pi$
$439$	−7.38524	−	4.26387i	−0.352478	−	0.203503i	−0.665776	+	0.746151i	$0.731899\pi$
$440$	1.41583	+	2.99924i	0.0674969	+	0.142983i
$441$	12.4270	−	36.8595i	0.591763	−	1.75522i
$442$			40.5580i			1.92915i
$443$	−32.3016	−	18.6493i	−1.53470	−	0.886057i	−0.999136	−	0.0415596i	$-0.986767\pi$
$443$	−32.3016	−	18.6493i	−1.53470	−	0.886057i	−0.535560	−	0.844497i	$-0.679899\pi$
$444$	3.81474	−	0.379708i	0.181039	−	0.0180202i
$445$	−5.15962	−	8.93672i	−0.244589	−	0.423641i
$446$	2.63579	+	4.56532i	0.124808	+	0.216174i
$447$	3.04113	−	0.302706i	0.143840	−	0.0143175i
$448$	3.86969	+	2.23417i	0.182826	+	0.105554i
$449$		−	25.4460i		−	1.20087i	−0.799673	−	0.600436i	$-0.794994\pi$
$449$		−	25.4460i		−	1.20087i	0.799673	−	0.600436i	$-0.205006\pi$
$450$	−0.958432	+	2.84278i	−0.0451809	+	0.134010i
$451$	10.4123	−	4.91524i	0.490295	−	0.231450i
$452$	−3.81940	−	2.20513i	−0.179650	−	0.103721i
$453$	−4.70619	+	3.37979i	−0.221116	+	0.158797i
$454$	1.05021	+	1.81901i	0.0492887	+	0.0853705i
$455$	−24.1082	+	13.9189i	−1.13021	+	0.652526i
$456$	11.3526	+	5.12961i	0.531632	+	0.240216i
$457$	5.17553	+	2.98810i	0.242101	+	0.139777i	0.616142	−	0.787635i	$-0.288695\pi$
$457$	5.17553	+	2.98810i	0.242101	+	0.139777i	−0.374041	+	0.927412i	$0.622028\pi$
$458$	−7.16111			−0.334617
$459$	−32.3402	+	9.92014i	−1.50951	+	0.463033i
$460$	−0.185558			−0.00865167
$461$	−0.426816	+	0.739267i	−0.0198788	+	0.0344311i	−0.875794	−	0.482686i	$-0.839661\pi$
$461$	−0.426816	+	0.739267i	−0.0198788	+	0.0344311i	0.855915	+	0.517117i	$0.172995\pi$
$462$	−25.6651	+	0.427627i	−1.19405	+	0.0198950i
$463$	7.04476	+	12.2019i	0.327398	+	0.567070i	0.981995	−	0.188908i	$-0.0604949\pi$
$463$	7.04476	+	12.2019i	0.327398	+	0.567070i	−0.654597	+	0.755978i	$0.727162\pi$
$464$	1.39115	+	2.40954i	0.0645825	+	0.111860i
$465$	−9.60081	+	6.89490i	−0.445227	+	0.319743i
$466$	−6.36499	+	11.0245i	−0.294852	+	0.510699i
$467$			27.8323i			1.28792i	0.765057	+	0.643962i	$0.222711\pi$
$467$			27.8323i			1.28792i	−0.765057	+	0.643962i	$0.777289\pi$
$468$	−3.68420	−	18.3233i	−0.170302	−	0.846994i
$469$		−	50.6806i		−	2.34021i
$470$	5.51975	−	9.56050i	0.254607	−	0.440993i
$471$	−12.9003	+	1.28406i	−0.594412	+	0.0591662i
$472$	11.5172	−	6.64945i	0.530121	−	0.306066i
$473$	5.85704	−	8.44926i	0.269307	−	0.388497i
$474$	−1.63701	−	16.4462i	−0.0751905	−	0.755401i
$475$	−6.22884	−	3.59622i	−0.285799	−	0.165006i
$476$		−	29.0893i		−	1.33331i
$477$	13.6967	−	12.0619i	0.627128	−	0.552278i
$478$	12.1947			0.557771
$479$	−12.6144	+	21.8489i	−0.576369	+	0.998300i	0.419523	+	0.907745i	$0.362197\pi$
$479$	−12.6144	+	21.8489i	−0.576369	+	0.998300i	−0.995891	+	0.0905552i	$0.971136\pi$
$480$	1.40685	−	1.01034i	0.0642134	−	0.0461154i
$481$	11.9416	−	6.89450i	0.544491	−	0.314362i
$482$	0.253838	−	0.146553i	0.0115620	−	0.00667532i
$483$	0.591334	−	1.30871i	0.0269066	−	0.0595482i
$484$	3.85955	+	10.3007i	0.175434	+	0.468212i
$485$			5.22598i			0.237299i
$486$	13.7096	−	7.41944i	0.621878	−	0.336553i
$487$	16.7796			0.760358			0.380179	−	0.924913i	$-0.375862\pi$
$487$	16.7796			0.760358			0.380179	+	0.924913i	$0.375862\pi$
$488$	−2.19952	−	1.26989i	−0.0995675	−	0.0574853i
$489$	11.8262	−	26.1732i	0.534801	−	1.18359i
$490$	11.2289	−	6.48300i	0.507270	−	0.292872i
$491$	−1.98545	−	3.43889i	−0.0896019	−	0.155195i	0.817741	−	0.575586i	$-0.195226\pi$
$491$	−1.98545	−	3.43889i	−0.0896019	−	0.155195i	−0.907343	+	0.420391i	$0.861893\pi$
$492$	−3.50753	−	4.88406i	−0.158132	−	0.220191i
$493$	9.05654	−	15.6864i	0.407886	−	0.706479i
$494$	44.8089			2.01605
$495$	−3.94537	+	9.13422i	−0.177331	+	0.410553i
$496$	6.82435			0.306422
$497$	−2.90870	+	5.03802i	−0.130473	+	0.225986i
$498$	7.11122	−	0.707831i	0.318661	−	0.0317187i
$499$	−14.4656	−	25.0552i	−0.647570	−	1.12162i	−0.983701	−	0.179809i	$-0.942452\pi$
$499$	−14.4656	−	25.0552i	−0.647570	−	1.12162i	0.336131	−	0.941815i	$-0.390881\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	38.6549	−	3.84760i	1.72697	−	0.171898i
$502$	−2.30224	−	1.32920i	−0.102754	−	0.0593252i
$503$	15.4145			0.687298			0.343649	−	0.939098i	$-0.388337\pi$
$503$	15.4145			0.687298			0.343649	+	0.939098i	$0.388337\pi$
$504$	2.64241	+	13.1420i	0.117702	+	0.585390i
$505$			11.2707i			0.501541i
$506$	−0.613329	−	0.0507458i	−0.0272658	−	0.00225592i
$507$	−26.0798	−	36.3148i	−1.15824	−	1.61280i
$508$	7.63478	−	4.40794i	0.338739	−	0.195571i
$509$	−27.9273	+	16.1238i	−1.23785	+	0.714675i	−0.968655	−	0.248409i	$-0.920092\pi$
$509$	−27.9273	+	16.1238i	−1.23785	+	0.714675i	−0.269199	+	0.963085i	$0.586759\pi$
$510$	−10.2756	−	4.64298i	−0.455010	−	0.205595i
$511$	−12.2460	+	21.2107i	−0.541732	+	0.938307i
$512$	−1.00000			−0.0441942
$513$	10.9599	+	35.7299i	0.483891	+	1.57751i
$514$		−	19.4622i		−	0.858440i
$515$	−2.06496	−	1.19221i	−0.0909932	−	0.0525350i
$516$	−4.89270	−	2.21075i	−0.215389	−	0.0973227i
$517$	20.8592	−	30.0911i	0.917386	−	1.32340i
$518$	−8.56487	+	4.94493i	−0.376319	+	0.217268i
$519$	−11.1987	−	15.5937i	−0.491570	−	0.684486i
$520$	3.11500	−	5.39534i	0.136602	−	0.236601i
$521$		−	7.77937i		−	0.340820i	−0.985373	−	0.170410i	$-0.945491\pi$
$521$		−	7.77937i		−	0.340820i	0.985373	−	0.170410i	$-0.0545093\pi$
$522$	−2.66665	+	7.90948i	−0.116716	+	0.346188i
$523$			5.17131i			0.226125i	0.993588	+	0.113063i	$0.0360661\pi$
$523$			5.17131i			0.226125i	−0.993588	+	0.113063i	$0.963934\pi$
$524$	0.765387	−	1.32569i	0.0334361	−	0.0579130i
$525$	−0.766569	−	7.70132i	−0.0334558	−	0.336113i
$526$	−6.85063	−	11.8656i	−0.298702	−	0.517367i
$527$	−22.2136	−	38.4751i	−0.967641	−	1.67600i
$528$	4.92640	−	2.95476i	0.214394	−	0.128590i
$529$	−11.4828	+	19.8888i	−0.499251	+	0.864729i
$530$	6.08358			0.264254
$531$	37.8059	+	12.7461i	1.64063	+	0.553133i
$532$	−32.1382			−1.39337
$533$	−18.7307	−	10.8142i	−0.811315	−	0.468413i
$534$	−14.5176	+	10.4259i	−0.628237	+	0.451174i
$535$	3.32629	−	1.92043i	0.143808	−	0.0830275i
$536$	5.67108	+	9.82260i	0.244953	+	0.424272i
$537$	14.5671	+	6.58211i	0.628618	+	0.284039i
$538$	4.29637	+	2.48051i	0.185230	+	0.106942i
$539$	38.8881	−	18.3576i	1.67503	−	0.790719i
$540$	5.06405	+	1.16419i	0.217922	+	0.0500989i
$541$		−	21.8272i		−	0.938425i	−0.883085	−	0.469212i	$-0.844538\pi$
$541$		−	21.8272i		−	0.938425i	0.883085	−	0.469212i	$-0.155462\pi$
$542$	−14.9755	−	8.64613i	−0.643254	−	0.371383i
$543$	−6.58105	+	14.5648i	−0.282420	+	0.625036i
$544$	3.25505	+	5.63792i	0.139559	+	0.241724i
$545$	8.38419	+	14.5218i	0.359139	+	0.622047i
$546$	28.1255	+	39.1634i	1.20366	+	1.67604i
$547$	30.5007	+	17.6096i	1.30412	+	0.752933i	0.981108	−	0.193463i	$-0.0619719\pi$
$547$	30.5007	+	17.6096i	1.30412	+	0.752933i	0.323010	+	0.946396i	$0.395305\pi$
$548$		−	3.77635i		−	0.161317i
$549$	−1.50194	−	7.46985i	−0.0641012	−	0.318806i
$550$	−2.99924	+	1.41583i	−0.127888	+	0.0603711i
$551$	−17.3305	−	10.0058i	−0.738304	−	0.426260i
$552$	0.0318335	+	0.319815i	0.00135492	+	0.0136122i
$553$	21.3188	+	36.9252i	0.906567	+	1.57022i
$554$	−17.8388	+	10.2992i	−0.757897	+	0.437572i
$555$	0.379708	+	3.81474i	0.0161177	+	0.161926i
$556$	−13.1784	−	7.60855i	−0.558888	−	0.322674i
$557$	25.8765			1.09642			0.548210	−	0.836341i	$-0.315309\pi$
$557$	25.8765			1.09642			0.548210	+	0.836341i	$0.315309\pi$
$558$	13.5307	+	15.3645i	0.572799	+	0.650429i
$559$	−19.3116			−0.816794
$560$	−2.23417	+	3.86969i	−0.0944108	+	0.163524i
$561$	−32.6944	−	18.1567i	−1.38036	−	0.766577i
$562$	−7.83774	−	13.5754i	−0.330615	−	0.572643i
$563$	10.0401	+	17.3900i	0.423140	+	0.732900i	0.996245	−	0.0865825i	$-0.0275946\pi$
$563$	10.0401	+	17.3900i	0.423140	+	0.732900i	−0.573105	+	0.819482i	$0.694261\pi$
$564$	−17.4248	−	7.87332i	−0.733716	−	0.331527i
$565$	2.20513	−	3.81940i	0.0927707	−	0.160684i
$566$			15.7424i			0.661701i
$567$	−24.3490	+	32.0059i	−1.02256	+	1.34412i
$568$		−	1.30192i		−	0.0546272i
$569$	9.36179	−	16.2151i	0.392467	−	0.679772i	−0.600307	−	0.799769i	$-0.704955\pi$
$569$	9.36179	−	16.2151i	0.392467	−	0.679772i	0.992774	+	0.119997i	$0.0382884\pi$
$570$	−5.12961	+	11.3526i	−0.214856	+	0.475507i
$571$	−29.5922	+	17.0851i	−1.23839	+	0.714987i	−0.968766	−	0.247977i	$-0.920234\pi$
$571$	−29.5922	+	17.0851i	−1.23839	+	0.714987i	−0.269628	+	0.962964i	$0.586901\pi$
$572$	11.7716	−	16.9815i	0.492195	−	0.710032i
$573$	18.4595	−	13.2569i	0.771157	−	0.553813i
$574$	13.4342	+	7.75622i	0.560731	+	0.323738i
$575$		−	0.185558i		−	0.00773829i
$576$	−1.98271	−	2.25142i	−0.0826127	−	0.0938091i
$577$	−32.5436			−1.35481			−0.677405	−	0.735611i	$-0.736895\pi$
$577$	−32.5436			−1.35481			−0.677405	+	0.735611i	$0.736895\pi$
$578$	12.6908	−	21.9810i	0.527866	−	0.914290i
$579$	3.75769	+	37.7516i	0.156164	+	1.56890i
$580$	−2.40954	+	1.39115i	−0.100051	+	0.0577644i
$581$	−15.9662	+	9.21807i	−0.662388	+	0.382430i
$582$	9.00715	−	0.896547i	0.373358	−	0.0371631i
$583$	20.1082	+	1.66372i	0.832798	+	0.0689042i
$584$		−	5.48124i		−	0.226815i
$585$	18.3233	−	3.68420i	0.757574	−	0.152323i
$586$	−3.90743			−0.161414
$587$	−2.17550	−	1.25602i	−0.0897924	−	0.0518417i	0.454431	−	0.890782i	$-0.349842\pi$
$587$	−2.17550	−	1.25602i	−0.0897924	−	0.0518417i	−0.544224	+	0.838940i	$0.683176\pi$
$588$	−13.1001	−	18.2412i	−0.540237	−	0.752253i
$589$	−42.5077	+	24.5419i	−1.75150	+	1.01123i
$590$	6.64945	+	11.5172i	0.273753	+	0.474155i
$591$	4.26479	−	9.43858i	0.175430	−	0.388251i
$592$	1.10666	−	1.91679i	0.0454835	−	0.0787797i
$593$	41.4676			1.70287			0.851434	−	0.524461i	$-0.175733\pi$
$593$	41.4676			1.70287			0.851434	+	0.524461i	$0.175733\pi$
$594$	16.4200	+	5.23295i	0.673721	+	0.214710i
$595$	29.0893			1.19255
$596$	0.882237	−	1.52808i	0.0361378	−	0.0625925i
$597$	−4.15429	+	9.19404i	−0.170024	+	0.376287i
$598$	0.578012	+	1.00115i	0.0236367	+	0.0409399i
$599$	−18.6905	+	10.7910i	−0.763673	+	0.440907i	−0.830613	−	0.556850i	$-0.812010\pi$
$599$	−18.6905	+	10.7910i	−0.763673	+	0.440907i	0.0669402	+	0.997757i	$0.478676\pi$
$600$	1.01034	+	1.40685i	0.0412469	+	0.0574343i
$601$	−14.8004	−	8.54500i	−0.603720	−	0.348558i	0.166784	−	0.985993i	$-0.446662\pi$
$601$	−14.8004	−	8.54500i	−0.603720	−	0.348558i	−0.770503	+	0.637436i	$0.779995\pi$
$602$	13.8508			0.564518
$603$	−10.8707	+	32.2433i	−0.442689	+	1.31305i
$604$			3.34521i			0.136115i
$605$	−10.3007	+	3.85955i	−0.418782	+	0.156913i
$606$	19.4255	−	1.93356i	0.789107	−	0.0785455i
$607$	−17.2613	+	9.96583i	−0.700616	+	0.404501i	−0.807577	−	0.589762i	$-0.799221\pi$
$607$	−17.2613	+	9.96583i	−0.700616	+	0.404501i	0.106961	+	0.994263i	$0.465888\pi$
$608$	6.22884	−	3.59622i	0.252613	−	0.145846i
$609$	−2.13283	−	21.4274i	−0.0864264	−	0.868282i
$610$	1.26989	−	2.19952i	0.0514164	−	0.0890559i
$611$	−68.7761			−2.78238
$612$	−6.23950	+	18.5068i	−0.252217	+	0.748094i
$613$		−	37.6979i		−	1.52260i	−0.648398	−	0.761302i	$-0.724561\pi$
$613$		−	37.6979i		−	1.52260i	0.648398	−	0.761302i	$-0.275439\pi$
$614$	22.0359	+	12.7224i	0.889295	+	0.513435i
$615$	4.88406	−	3.50753i	0.196944	−	0.141437i
$616$	−8.44293	+	12.1796i	−0.340175	+	0.490731i
$617$	42.3208	−	24.4339i	1.70377	−	0.983672i	0.761898	−	0.647696i	$-0.224267\pi$
$617$	42.3208	−	24.4339i	1.70377	−	0.983672i	0.941871	−	0.335975i	$-0.109066\pi$
$618$	−1.70055	+	3.76357i	−0.0684063	+	0.151393i
$619$	4.72461	−	8.18326i	0.189898	−	0.328913i	−0.755318	−	0.655358i	$-0.772518\pi$
$619$	4.72461	−	8.18326i	0.189898	−	0.328913i	0.945216	+	0.326445i	$0.105851\pi$
$620$			6.82435i			0.274072i
$621$	−0.656920	+	0.705769i	−0.0263613	+	0.0283215i
$622$		−	26.5372i		−	1.06404i
$623$	23.0549	−	39.9323i	0.923675	−	1.59985i
$624$	−9.83344	−	4.44321i	−0.393653	−	0.177871i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.9671	−	20.7277i	−0.478303	−	0.828445i
$627$	−20.0597	+	36.1211i	−0.801109	+	1.44254i
$628$	−3.74238	+	6.48200i	−0.149337	+	0.258660i
$629$	−14.4090			−0.574523
$630$	−13.1420	+	2.64241i	−0.523589	+	0.105276i
$631$	−4.98202			−0.198331			−0.0991656	−	0.995071i	$-0.531617\pi$
$631$	−4.98202			−0.198331			−0.0991656	+	0.995071i	$0.531617\pi$
$632$	−8.26376	−	4.77108i	−0.328715	−	0.189783i
$633$	−2.36871	−	23.7972i	−0.0941479	−	0.945856i
$634$	3.04029	−	1.75531i	0.120745	−	0.0697122i
$635$	4.40794	+	7.63478i	0.174924	+	0.302977i
$636$	−1.04367	−	10.4853i	−0.0413843	−	0.415767i
$637$	−69.9560	−	40.3891i	−2.77176	−	1.60027i
$638$	−8.34479	+	3.93926i	−0.330373	+	0.155957i
$639$	2.93116	−	2.58132i	0.115955	−	0.102115i
$640$		−	1.00000i		−	0.0395285i
$641$	6.10134	+	3.52261i	0.240988	+	0.139135i	0.615631	−	0.788035i	$-0.288901\pi$
$641$	6.10134	+	3.52261i	0.240988	+	0.139135i	−0.374643	+	0.927169i	$0.622235\pi$
$642$	−3.88057	−	5.40351i	−0.153154	−	0.213259i
$643$	11.2538	+	19.4922i	0.443808	+	0.768697i	0.997968	−	0.0637125i	$-0.0202941\pi$
$643$	11.2538	+	19.4922i	0.443808	+	0.768697i	−0.554161	+	0.832410i	$0.686961\pi$
$644$	−0.414567	−	0.718051i	−0.0163362	−	0.0282952i
$645$	2.21075	−	4.89270i	0.0870481	−	0.192650i
$646$	−40.5504	−	23.4118i	−1.59543	−	0.921124i
$647$		−	26.0058i		−	1.02239i	−0.859464	−	0.511197i	$-0.829202\pi$
$647$		−	26.0058i		−	1.02239i	0.859464	−	0.511197i	$-0.170798\pi$
$648$	1.13776	−	8.92779i	0.0446954	−	0.350717i
$649$	18.8289	+	39.8866i	0.739100	+	1.56568i
$650$	5.39534	+	3.11500i	0.211623	+	0.122180i
$651$	−48.1309	−	21.7478i	−1.88640	−	0.852363i
$652$	−8.29103	−	14.3605i	−0.324702	−	0.562400i
$653$	−16.5486	+	9.55431i	−0.647595	+	0.373889i	−0.787534	−	0.616271i	$-0.788643\pi$
$653$	−16.5486	+	9.55431i	−0.647595	+	0.373889i	0.139939	+	0.990160i	$0.455309\pi$
$654$	23.5905	−	16.9417i	0.922463	−	0.662475i
$655$	1.32569	+	0.765387i	0.0517989	+	0.0299061i
$656$	−3.47164			−0.135545
$657$	12.3406	−	10.8677i	0.481451	−	0.423989i
$658$	49.3282			1.92301
$659$	15.7811	−	27.3337i	0.614746	−	1.06477i	−0.375684	−	0.926748i	$-0.622592\pi$
$659$	15.7811	−	27.3337i	0.614746	−	1.06477i	0.990429	−	0.138023i	$-0.0440746\pi$
$660$	2.95476	+	4.92640i	0.115014	+	0.191760i
$661$	−3.11575	−	5.39663i	−0.121188	−	0.209905i	0.799048	−	0.601267i	$-0.205337\pi$
$661$	−3.11575	−	5.39663i	−0.121188	−	0.209905i	−0.920237	+	0.391362i	$0.872004\pi$
$662$	11.2820	+	19.5410i	0.438487	+	0.759482i
$663$	6.95796	+	69.9030i	0.270225	+	2.71481i
$664$	2.06298	−	3.57318i	0.0800590	−	0.138666i
$665$		−	32.1382i		−	1.24627i
$666$	6.50968	−	1.30888i	0.252245	−	0.0507181i
$667$		−	0.516277i		−	0.0199903i
$668$	11.2138	−	19.4229i	0.433877	−	0.751496i
$669$	5.32608	+	7.41630i	0.205918	+	0.286731i
$670$	−9.82260	+	5.67108i	−0.379480	+	0.219093i
$671$	4.79893	−	6.92285i	0.185261	−	0.267254i
$672$	7.05283	+	3.18679i	0.272069	+	0.122933i
$673$	−1.56534	−	0.903752i	−0.0603396	−	0.0348371i	0.469527	−	0.882918i	$-0.344425\pi$
$673$	−1.56534	−	0.903752i	−0.0603396	−	0.0348371i	−0.529866	+	0.848081i	$0.677758\pi$
$674$			20.8760i			0.804112i
$675$	−1.16419	+	5.06405i	−0.0448098	+	0.194916i
$676$	−25.8129			−0.992803
$677$	7.44454	−	12.8943i	0.286117	−	0.495569i	−0.686763	−	0.726882i	$-0.740969\pi$
$677$	7.44454	−	12.8943i	0.286117	−	0.495569i	0.972879	+	0.231313i	$0.0743021\pi$
$678$	−6.96117	−	3.14538i	−0.267342	−	0.120798i
$679$	−20.2229	+	11.6757i	−0.776084	+	0.448072i
$680$	−5.63792	+	3.25505i	−0.216204	+	0.124826i
$681$	2.12213	+	2.95496i	0.0813202	+	0.113234i
$682$	−1.86630	+	22.5567i	−0.0714644	+	0.863742i
$683$		−	21.7548i		−	0.832425i	−0.909267	−	0.416212i	$-0.863357\pi$
$683$		−	21.7548i		−	0.832425i	0.909267	−	0.416212i	$-0.136643\pi$
$684$	20.4465	+	6.89346i	0.781793	+	0.263578i
$685$	3.77635			0.144287
$686$	23.0866	+	13.3291i	0.881450	+	0.508906i
$687$	−12.3424	+	1.22853i	−0.470893	+	0.0468714i
$688$	−2.68449	+	1.54989i	−0.102345	+	0.0590890i
$689$	−18.9503	−	32.8230i	−0.721951	−	1.25046i
$690$	−0.319815	+	0.0318335i	−0.0121751	+	0.00121188i
$691$	22.7709	−	39.4403i	0.866244	−	1.50038i	0.000437616	−	1.00000i	$-0.499861\pi$
$691$	22.7709	−	39.4403i	0.866244	−	1.50038i	0.865807	−	0.500379i	$-0.166806\pi$
$692$	−11.0841			−0.421356
$693$	−44.1612	+	5.14002i	−1.67755	+	0.195253i
$694$	−22.0817			−0.838210
$695$	7.60855	−	13.1784i	0.288609	−	0.499885i
$696$	2.81107	+	3.91427i	0.106553	+	0.148370i
$697$	11.3004	+	19.5728i	0.428032	+	0.741373i
$698$	−7.46543	+	4.31017i	−0.282571	+	0.163142i
$699$	−9.07896	+	20.0930i	−0.343398	+	0.759988i
$700$	−3.86969	−	2.23417i	−0.146261	−	0.0844436i
$701$	13.2942			0.502115			0.251058	−	0.967972i	$-0.419222\pi$
$701$	13.2942			0.502115			0.251058	+	0.967972i	$0.419222\pi$
$702$	−9.49331	−	30.9487i	−0.358302	−	1.16809i
$703$			15.9192i			0.600404i
$704$	0.273477	−	3.30533i	0.0103071	−	0.124574i
$705$	7.87332	−	17.4248i	0.296527	−	0.656255i
$706$	−26.3805	+	15.2308i	−0.992843	+	0.573218i
$707$	−43.6143	+	25.1807i	−1.64028	+	0.947018i
$708$	18.7095	−	13.4364i	0.703146	−	0.504970i
$709$	−24.3088	+	42.1040i	−0.912934	+	1.58125i	−0.103037	+	0.994678i	$0.532856\pi$
$709$	−24.3088	+	42.1040i	−0.912934	+	1.58125i	−0.809898	+	0.586571i	$0.800477\pi$
$710$	1.30192			0.0488601
$711$	−5.64290	−	28.0648i	−0.211625	−	1.05251i
$712$			10.3192i			0.386730i
$713$	−1.09666	−	0.633155i	−0.0410701	−	0.0237118i
$714$	−4.99045	−	50.1365i	−0.186763	−	1.87631i
$715$	16.9815	+	11.7716i	0.635072	+	0.440233i
$716$	7.99259	−	4.61452i	0.298697	−	0.172453i
$717$	21.0179	−	2.09207i	0.784928	−	0.0781296i
$718$	0.941899	−	1.63142i	0.0351514	−	0.0608840i
$719$		−	2.19593i		−	0.0818944i	−0.999161	−	0.0409472i	$-0.986962\pi$
$719$		−	2.19593i		−	0.0818944i	0.999161	−	0.0409472i	$-0.0130375\pi$
$720$	2.25142	−	1.98271i	0.0839054	−	0.0738911i
$721$		−	10.6544i		−	0.396789i
$722$	−16.3656	+	28.3461i	−0.609065	+	1.05493i
$723$	0.412356	−	0.296137i	0.0153357	−	0.0110134i
$724$	4.61378	+	7.99131i	0.171470	+	0.296995i
$725$	−1.39115	−	2.40954i	−0.0516660	−	0.0894882i
$726$	8.41921	+	17.0914i	0.312466	+	0.634322i
$727$	3.76607	−	6.52302i	0.139676	−	0.241926i	−0.787698	−	0.616061i	$-0.788727\pi$
$727$	3.76607	−	6.52302i	0.139676	−	0.241926i	0.927374	+	0.374136i	$0.122061\pi$
$728$	27.8377			1.03173
$729$	22.3560	−	15.1396i	0.828001	−	0.560726i
$730$	5.48124			0.202870
$731$	17.4763	+	10.0899i	0.646384	+	0.373190i
$732$	−4.00880	−	1.81136i	−0.148170	−	0.0669499i
$733$	−13.8911	+	8.02005i	−0.513081	+	0.296227i	−0.734099	−	0.679042i	$-0.762395\pi$
$733$	−13.8911	+	8.02005i	−0.513081	+	0.296227i	0.221019	+	0.975270i	$0.429062\pi$
$734$	−0.821032	−	1.42207i	−0.0303048	−	0.0524895i
$735$	18.2412	−	13.1001i	0.672836	−	0.483203i
$736$	0.160698	+	0.0927788i	0.00592339	+	0.00341987i
$737$	−34.0179	+	16.0585i	−1.25306	+	0.591524i
$738$	−6.88324	−	7.81611i	−0.253375	−	0.287715i
$739$		−	27.6759i		−	1.01808i	−0.860744	−	0.509038i	$-0.830001\pi$
$739$		−	27.6759i		−	1.01808i	0.860744	−	0.509038i	$-0.169999\pi$
$740$	1.91679	+	1.10666i	0.0704627	+	0.0406817i
$741$	77.2296	−	7.68723i	2.83710	−	0.282397i
$742$	13.5917	+	23.5416i	0.498968	+	0.864238i
$743$	3.88600	+	6.73075i	0.142564	+	0.246927i	0.928461	−	0.371429i	$-0.121132\pi$
$743$	3.88600	+	6.73075i	0.142564	+	0.246927i	−0.785898	+	0.618356i	$0.787799\pi$
$744$	11.7620	−	1.17076i	0.431216	−	0.0429220i
$745$	1.52808	+	0.882237i	0.0559845	+	0.0323226i
$746$			6.74550i			0.246970i
$747$	12.1350	−	2.43994i	0.443996	−	0.0892728i
$748$	−19.5254	+	9.21719i	−0.713918	+	0.337014i
$749$	14.8630	+	8.58113i	0.543081	+	0.313548i
$750$	−1.40685	+	1.01034i	−0.0513708	+	0.0368923i
$751$	−15.5601	−	26.9510i	−0.567798	−	0.983455i	−0.996783	−	0.0801434i	$-0.974462\pi$
$751$	−15.5601	−	26.9510i	−0.567798	−	0.983455i	0.428985	−	0.903311i	$-0.358871\pi$
$752$	−9.56050	+	5.51975i	−0.348635	+	0.201285i
$753$	−4.19603	−	1.89596i	−0.152912	−	0.0690926i
$754$	15.0115	+	8.66687i	0.546685	+	0.315629i
$755$	−3.34521			−0.121745
$756$	6.80887	+	22.1973i	0.247636	+	0.807309i
$757$	3.74337			0.136055			0.0680276	−	0.997683i	$-0.478329\pi$
$757$	3.74337			0.136055			0.0680276	+	0.997683i	$0.478329\pi$
$758$	−17.3248	+	30.0074i	−0.629265	+	1.08992i
$759$	−1.06580	+	0.0177582i	−0.0386861	+	0.000644582i
$760$	3.59622	+	6.22884i	0.130449	+	0.225944i
$761$	23.2308	+	40.2370i	0.842117	+	1.45859i	0.888101	+	0.459648i	$0.152024\pi$
$761$	23.2308	+	40.2370i	0.842117	+	1.45859i	−0.0459839	+	0.998942i	$0.514642\pi$
$762$	12.4026	−	8.90703i	0.449299	−	0.322668i
$763$	−37.4634	+	64.8884i	−1.35626	+	2.34912i
$764$		−	13.1212i		−	0.474708i
$765$	−18.5068	−	6.23950i	−0.669115	−	0.225589i
$766$			4.86091i			0.175632i
$767$	41.4260	−	71.7520i	1.49581	−	2.59082i
$768$	−1.72353	+	0.171556i	−0.0621927	+	0.00619049i
$769$	2.20738	−	1.27443i	0.0796001	−	0.0459571i	−0.459672	−	0.888089i	$-0.652033\pi$
$769$	2.20738	−	1.27443i	0.0796001	−	0.0459571i	0.539272	+	0.842132i	$0.318700\pi$
$770$	−12.1796	−	8.44293i	−0.438923	−	0.304262i
$771$	−3.33885	−	33.5437i	−0.120246	−	1.20805i
$772$	18.9691	+	10.9518i	0.682712	+	0.394164i
$773$			3.21790i			0.115740i	0.998324	+	0.0578699i	$0.0184309\pi$
$773$			3.21790i			0.115740i	−0.998324	+	0.0578699i	$0.981569\pi$
$774$	−8.81200	−	2.97093i	−0.316741	−	0.106788i
$775$	−6.82435			−0.245138
$776$	2.61299	−	4.52583i	0.0938008	−	0.162468i
$777$	−13.9135	+	9.99211i	−0.499144	+	0.358465i
$778$	17.0439	−	9.84029i	0.611052	−	0.352791i
$779$	21.6243	−	12.4848i	0.774770	−	0.447314i
$780$	4.44321	−	9.83344i	0.159092	−	0.352094i
$781$	4.30327	+	0.356044i	0.153983	+	0.0127403i
$782$		−	1.20800i		−	0.0431980i
$783$	−3.23914	+	14.0897i	−0.115757	+	0.503526i
$784$	−12.9660			−0.463072
$785$	−6.48200	−	3.74238i	−0.231353	−	0.133571i
$786$	1.09174	−	2.41618i	0.0389411	−	0.0861821i
$787$	23.4260	−	13.5250i	0.835045	−	0.482114i	−0.0205317	−	0.999789i	$-0.506536\pi$
$787$	23.4260	−	13.5250i	0.835045	−	0.482114i	0.855577	+	0.517676i	$0.173203\pi$
$788$	−2.98992	−	5.17869i	−0.106511	−	0.184483i
$789$	−13.8429	−	19.2756i	−0.492821	−	0.686228i
$790$	4.77108	−	8.26376i	0.169747	−	0.294011i
$791$	19.7065			0.700684
$792$	7.98390	−	5.93779i	0.283696	−	0.210990i
$793$	−15.8229			−0.561886
$794$	−11.7870	+	20.4157i	−0.418305	+	0.724526i
$795$	10.4853	−	1.04367i	0.371874	−	0.0370153i
$796$	2.91245	+	5.04452i	0.103229	+	0.178798i
$797$	−37.9622	+	21.9175i	−1.34469	+	0.776357i	−0.987492	−	0.157672i	$-0.949601\pi$
$797$	−37.9622	+	21.9175i	−1.34469	+	0.776357i	−0.357198	+	0.934029i	$0.616268\pi$
$798$	−55.3913	+	5.51350i	−1.96083	+	0.195176i
$799$	62.2399	+	35.9342i	2.20189	+	1.27126i
$800$	1.00000			0.0353553
$801$	−23.2329	+	20.4600i	−0.820895	+	0.722919i
$802$		−	8.56857i		−	0.302567i
$803$	18.1173	+	1.49899i	0.639346	+	0.0528984i
$804$	11.4594	+	15.9567i	0.404143	+	0.562749i
$805$	0.718051	−	0.414567i	0.0253080	−	0.0146116i
$806$	36.8197	−	21.2578i	1.29692	−	0.748775i
$807$	7.83049	+	3.53818i	0.275646	+	0.124550i
$808$	5.63537	−	9.76075i	0.198252	−	0.343382i
$809$	−40.2796			−1.41615			−0.708077	−	0.706135i	$-0.750437\pi$
$809$	−40.2796			−1.41615			−0.708077	+	0.706135i	$0.750437\pi$
$810$	8.92779	+	1.13776i	0.313691	+	0.0399768i
$811$			52.0619i			1.82814i	0.405557	+	0.914070i	$0.367078\pi$
$811$			52.0619i			1.82814i	−0.405557	+	0.914070i	$0.632922\pi$
$812$	−10.7666	−	6.21613i	−0.377835	−	0.218143i
$813$	−27.2941	−	12.3328i	−0.957247	−	0.432528i
$814$	6.03299	+	4.18208i	0.211456	+	0.146582i
$815$	14.3605	−	8.29103i	0.503026	−	0.290422i
$816$	6.57741	+	9.15872i	0.230256	+	0.320619i
$817$	11.1475	−	19.3080i	0.390001	−	0.675502i
$818$			27.3983i			0.957958i
$819$	55.1940	+	62.6743i	1.92863	+	2.19002i
$820$		−	3.47164i		−	0.121235i
$821$	4.69477	−	8.13159i	0.163849	−	0.283794i	−0.772397	−	0.635140i	$-0.780942\pi$
$821$	4.69477	−	8.13159i	0.163849	−	0.283794i	0.936246	+	0.351346i	$0.114276\pi$
$822$	−0.647854	−	6.50866i	−0.0225965	−	0.227016i
$823$	−2.12640	−	3.68303i	−0.0741217	−	0.128383i	0.826582	−	0.562816i	$-0.190282\pi$
$823$	−2.12640	−	3.68303i	−0.0741217	−	0.128383i	−0.900704	+	0.434433i	$0.856949\pi$
$824$	1.19221	+	2.06496i	0.0415325	+	0.0719365i
$825$	−4.92640	+	2.95476i	−0.171515	+	0.102872i
$826$	−29.7119	+	51.4626i	−1.03381	+	1.79061i
$827$	−30.6848			−1.06702			−0.533508	−	0.845795i	$-0.679127\pi$
$827$	−30.6848			−1.06702			−0.533508	+	0.845795i	$0.679127\pi$
$828$	0.109732	+	0.545751i	0.00381346	+	0.0189661i
$829$	53.4661			1.85696			0.928478	−	0.371388i	$-0.121118\pi$
$829$	53.4661			1.85696			0.928478	+	0.371388i	$0.121118\pi$
$830$	3.57318	+	2.06298i	0.124027	+	0.0716070i
$831$	−28.9789	+	20.8114i	−1.00527	+	0.721940i
$832$	−5.39534	+	3.11500i	−0.187050	+	0.107993i
$833$	42.2050	+	73.1013i	1.46232	+	2.53281i
$834$	−24.0187	−	10.8528i	−0.831699	−	0.375800i
$835$	19.4229	+	11.2138i	0.672159	+	0.388071i
$836$	10.1833	+	21.5718i	0.352195	+	0.746078i
$837$	25.9564	+	24.1599i	0.897185	+	0.835088i
$838$			6.78673i			0.234444i
$839$	11.9826	+	6.91814i	0.413684	+	0.238841i	0.692371	−	0.721541i	$-0.256566\pi$
$839$	11.9826	+	6.91814i	0.413684	+	0.238841i	−0.278687	+	0.960382i	$0.589899\pi$
$840$	−3.18679	+	7.05283i	−0.109955	+	0.243346i
$841$	10.6294	+	18.4107i	0.366531	+	0.634850i
$842$	5.06935	+	8.78038i	0.174701	+	0.302592i
$843$	−15.8376	−	22.0530i	−0.545474	−	0.759546i
$844$	−11.9574	−	6.90362i	−0.411591	−	0.237632i
$845$		−	25.8129i		−	0.887990i
$846$	−31.3829	−	10.5806i	−1.07897	−	0.363769i
$847$	−37.9487	−	31.2375i	−1.30393	−	1.07333i
$848$	−5.26853	−	3.04179i	−0.180922	−	0.104455i
$849$	2.70069	+	27.1325i	0.0926876	+	0.931185i
$850$	−3.25505	−	5.63792i	−0.111647	−	0.193379i
$851$	−0.355676	+	0.205349i	−0.0121924	+	0.00703929i
$852$	−0.223351	−	2.24390i	−0.00765189	−	0.0768747i
$853$	−10.5606	−	6.09719i	−0.361589	−	0.208764i	0.308188	−	0.951325i	$-0.400277\pi$
$853$	−10.5606	−	6.09719i	−0.361589	−	0.208764i	−0.669778	+	0.742562i	$0.733611\pi$
$854$	11.3486			0.388341
$855$	−6.89346	+	20.4465i	−0.235752	+	0.699257i
$856$	−3.84087			−0.131278
$857$	6.74214	−	11.6777i	0.230307	−	0.398903i	−0.727591	−	0.686011i	$-0.759360\pi$
$857$	6.74214	−	11.6777i	0.230307	−	0.398903i	0.957898	+	0.287107i	$0.0926936\pi$
$858$	17.3755	−	31.2877i	0.593189	−	1.06814i
$859$	12.0624	+	20.8926i	0.411563	+	0.712848i	0.995061	−	0.0992669i	$-0.0316498\pi$
$859$	12.0624	+	20.8926i	0.411563	+	0.712848i	−0.583498	+	0.812115i	$0.698316\pi$
$860$	−1.54989	−	2.68449i	−0.0528508	−	0.0915403i
$861$	24.4849	+	11.0634i	0.834442	+	0.377040i
$862$	6.45084	−	11.1732i	0.219716	−	0.380560i
$863$			0.104469i			0.00355615i	0.999998	+	0.00177808i	$0.000565980\pi$
$863$			0.104469i			0.00355615i	−0.999998	+	0.00177808i	$0.999434\pi$
$864$	−3.80350	−	3.54025i	−0.129398	−	0.120442i
$865$		−	11.0841i		−	0.376872i
$866$	−7.64714	+	13.2452i	−0.259860	+	0.450091i
$867$	18.1020	−	40.0622i	0.614775	−	1.36058i
$868$	−26.4081	+	15.2467i	−0.896350	+	0.517508i
$869$	18.0299	−	26.0097i	0.611624	−	0.882317i
$870$	−3.91427	+	2.81107i	−0.132706	+	0.0953041i
$871$	61.1948	+	35.3308i	2.07351	+	1.19714i
$872$		−	16.7684i		−	0.567849i
$873$	15.3703	−	3.09046i	0.520206	−	0.104596i
$874$	−1.33461			−0.0451439
$875$	2.23417	−	3.86969i	0.0755286	−	0.130819i
$876$	−0.940339	−	9.44711i	−0.0317711	−	0.319188i
$877$	38.7882	−	22.3944i	1.30978	−	0.756204i	0.327724	−	0.944774i	$-0.393718\pi$
$877$	38.7882	−	22.3944i	1.30978	−	0.756204i	0.982060	+	0.188569i	$0.0603851\pi$
$878$	−7.38524	+	4.26387i	−0.249240	+	0.143899i
$879$	−6.73458	+	0.670342i	−0.227152	+	0.0226101i
$880$	3.30533	+	0.273477i	0.111423	+	0.00921891i
$881$			23.1144i			0.778745i	0.921080	+	0.389372i	$0.127308\pi$
$881$			23.1144i			0.778745i	−0.921080	+	0.389372i	$0.872692\pi$
$882$	−25.7078	−	29.1919i	−0.865626	−	0.982942i
$883$	19.9876			0.672635			0.336317	−	0.941749i	$-0.390819\pi$
$883$	19.9876			0.672635			0.336317	+	0.941749i	$0.390819\pi$
$884$	35.1242	+	20.2790i	1.18136	+	0.682056i
$885$	13.4364	+	18.7095i	0.451659	+	0.628913i
$886$	−32.3016	+	18.6493i	−1.08519	+	0.626537i
$887$	−3.75290	−	6.50021i	−0.126010	−	0.218256i	0.796117	−	0.605142i	$-0.206884\pi$
$887$	−3.75290	−	6.50021i	−0.126010	−	0.218256i	−0.922127	+	0.386887i	$0.873550\pi$
$888$	1.57853	−	3.49351i	0.0529720	−	0.117235i
$889$	−19.6962	+	34.1147i	−0.660588	+	1.14417i
$890$	−10.3192			−0.345902
$891$	29.1982	+	6.20222i	0.978175	+	0.207782i
$892$	5.27158			0.176506
$893$	39.7005	−	68.7633i	1.32853	−	2.30108i
$894$	1.25841	−	2.78505i	0.0420877	−	0.0931459i
$895$	4.61452	+	7.99259i	0.154246	+	0.267163i
$896$	3.86969	−	2.23417i	0.129277	−	0.0746383i
$897$	1.16798	+	1.62635i	0.0389976	+	0.0543022i
$898$	−22.0369	−	12.7230i	−0.735381	−	0.424572i
$899$	−18.9874			−0.633265
$900$	1.98271	+	2.25142i	0.0660902	+	0.0750472i
$901$			39.6048i			1.31943i
$902$	0.949414	−	11.4749i	0.0316120	−	0.382073i
$903$	23.8724	−	2.37619i	0.794424	−	0.0790748i
$904$	−3.81940	+	2.20513i	−0.127031	+	0.0733417i
$905$	−7.99131	+	4.61378i	−0.265640	+	0.153367i
$906$	0.573890	+	5.76558i	0.0190662	+	0.191549i
$907$	22.0196	−	38.1391i	0.731150	−	1.26639i	−0.225242	−	0.974303i	$-0.572317\pi$
$907$	22.0196	−	38.1391i	0.731150	−	1.26639i	0.956392	−	0.292086i	$-0.0943494\pi$
$908$	2.10041			0.0697047
$909$	33.1488	−	6.66512i	1.09948	−	0.221068i
$910$			27.8377i			0.922811i
$911$	21.6344	+	12.4906i	0.716780	+	0.413833i	0.813566	−	0.581472i	$-0.197523\pi$
$911$	21.6344	+	12.4906i	0.716780	+	0.413833i	−0.0967866	+	0.995305i	$0.530856\pi$
$912$	10.1187	−	7.26680i	0.335062	−	0.240628i
$913$	11.2464	+	7.79600i	0.372200	+	0.258010i
$914$	5.17553	−	2.98810i	0.171191	−	0.0988374i
$915$	1.81136	−	4.00880i	0.0598818	−	0.132527i
$916$	−3.58056	+	6.20171i	−0.118305	+	0.204910i
$917$			6.84001i			0.225877i
$918$	−7.57903	+	32.9675i	−0.250145	+	1.08809i
$919$			2.66014i			0.0877498i	0.999037	+	0.0438749i	$0.0139703\pi$
$919$			2.66014i			0.0877498i	−0.999037	+	0.0438749i	$0.986030\pi$
$920$	−0.0927788	+	0.160698i	−0.00305883	+	0.00529804i
$921$	40.1622	+	18.1471i	1.32339	+	0.597968i
$922$	0.426816	+	0.739267i	0.0140564	+	0.0243465i
$923$	−4.05547	−	7.02428i	−0.133487	−	0.231207i
$924$	−12.4622	+	22.4404i	−0.409976	+	0.738235i
$925$	−1.10666	+	1.91679i	−0.0363868	+	0.0630238i
$926$	14.0895			0.463010
$927$	−2.28530	+	6.77837i	−0.0750591	+	0.222631i
$928$	2.78230			0.0913335
$929$	−10.3580	−	5.98018i	−0.339834	−	0.196203i	0.320365	−	0.947294i	$-0.396195\pi$
$929$	−10.3580	−	5.98018i	−0.339834	−	0.196203i	−0.660199	+	0.751091i	$0.729528\pi$
$930$	1.17076	+	11.7620i	0.0383906	+	0.385691i
$931$	80.7631	−	46.6286i	2.64690	−	1.52819i
$932$	6.36499	+	11.0245i	0.208492	+	0.361119i
$933$	−4.55261	−	45.7378i	−0.149046	−	1.49739i
$934$	24.1035	+	13.9161i	0.788690	+	0.455350i
$935$	−9.21719	−	19.5254i	−0.301434	−	0.638548i
$936$	−17.7105	−	5.97103i	−0.578887	−	0.195169i
$937$			13.5206i			0.441699i	0.975308	+	0.220849i	$0.0708829\pi$
$937$			13.5206i			0.441699i	−0.975308	+	0.220849i	$0.929117\pi$
$938$	−43.8907	−	25.3403i	−1.43308	−	0.827390i
$939$	−24.1817	−	33.6718i	−0.789140	−	1.09884i
$940$	−5.51975	−	9.56050i	−0.180035	−	0.311829i
$941$	−8.60762	−	14.9088i	−0.280600	−	0.486014i	0.690932	−	0.722919i	$-0.257200\pi$
$941$	−8.60762	−	14.9088i	−0.280600	−	0.486014i	−0.971533	+	0.236905i	$0.923867\pi$
$942$	−5.33810	+	11.8140i	−0.173925	+	0.384920i
$943$	0.557884	+	0.322095i	0.0181672	+	0.0104888i
$944$		−	13.2989i		−	0.432842i
$945$	−22.1973	+	6.80887i	−0.722079	+	0.221493i
$946$	−4.38875	−	9.29698i	−0.142691	−	0.302271i
$947$	−24.1209	−	13.9262i	−0.783823	−	0.452540i	0.0539604	−	0.998543i	$-0.482816\pi$
$947$	−24.1209	−	13.9262i	−0.783823	−	0.452540i	−0.837783	+	0.546003i	$0.816149\pi$
$948$	−15.0614	−	6.80542i	−0.489170	−	0.221030i
$949$	−17.0741	−	29.5732i	−0.554248	−	0.959985i
$950$	−6.22884	+	3.59622i	−0.202090	+	0.116677i
$951$	4.93890	−	3.54691i	0.160155	−	0.115017i
$952$	−25.1921	−	14.5447i	−0.816481	−	0.471395i
$953$	−24.0669			−0.779603			−0.389801	−	0.920899i	$-0.627456\pi$
$953$	−24.0669			−0.779603			−0.389801	+	0.920899i	$0.627456\pi$
$954$	−3.59761	−	17.8926i	−0.116477	−	0.579296i
$955$	13.1212			0.424592
$956$	6.09733	−	10.5609i	0.197202	−	0.341564i
$957$	−13.7067	+	8.22104i	−0.443075	+	0.265749i
$958$	12.6144	+	21.8489i	0.407554	+	0.705905i
$959$	8.43699	+	14.6133i	0.272444	+	0.471888i
$960$	−0.171556	−	1.72353i	−0.00553694	−	0.0556268i
$961$	−7.78586	+	13.4855i	−0.251157	+	0.435016i
$962$		−	13.7890i		−	0.444575i
$963$	−7.61530	−	8.64739i	−0.245400	−	0.278658i
$964$		−	0.293107i		−	0.00944033i
$965$	−10.9518	+	18.9691i	−0.352551	+	0.610636i
$966$	−0.837706	−	1.16646i	−0.0269527	−	0.0375303i
$967$	−38.3222	+	22.1253i	−1.23236	+	0.711503i	−0.967521	−	0.252790i	$-0.918652\pi$
$967$	−38.3222	+	22.1253i	−1.23236	+	0.711503i	−0.264838	+	0.964293i	$0.585318\pi$
$968$	10.8504	+	1.80786i	0.348746	+	0.0581070i
$969$	−73.9064	−	33.3943i	−2.37422	−	1.07278i
$970$	4.52583	+	2.61299i	0.145316	+	0.0838980i
$971$			50.9680i			1.63564i	0.575474	+	0.817820i	$0.304817\pi$
$971$			50.9680i			1.63564i	−0.575474	+	0.817820i	$0.695183\pi$
$972$	0.429351	−	15.5825i	0.0137714	−	0.499810i
$973$	67.9950			2.17982
$974$	8.38982	−	14.5316i	0.268827	−	0.465622i
$975$	9.83344	+	4.44321i	0.314922	+	0.142296i
$976$	−2.19952	+	1.26989i	−0.0704048	+	0.0406483i
$977$	−17.0529	+	9.84550i	−0.545571	+	0.314985i	−0.747334	−	0.664449i	$-0.768666\pi$
$977$	−17.0529	+	9.84550i	−0.545571	+	0.314985i	0.201763	+	0.979434i	$0.435333\pi$
$978$	−16.7535	−	23.3284i	−0.535718	−	0.745960i
$979$	−34.1085	−	2.82208i	−1.09011	−	0.0901939i
$980$		−	12.9660i		−	0.414184i
$981$	37.7526	−	33.2468i	1.20535	−	1.06149i
$982$	−3.97089			−0.126716
$983$	−41.8597	−	24.1677i	−1.33512	−	0.770830i	−0.349039	−	0.937108i	$-0.613492\pi$
$983$	−41.8597	−	24.1677i	−1.33512	−	0.770830i	−0.986079	+	0.166278i	$0.946825\pi$
$984$	−5.98349	+	0.595580i	−0.190747	+	0.0189864i
$985$	5.17869	−	2.98992i	0.165007	−	0.0952666i
$986$	−9.05654	−	15.6864i	−0.288419	−	0.499556i
$987$	85.0188	−	8.46254i	2.70618	−	0.269366i
$988$	22.4044	−	38.8056i	0.712780	−	1.23457i
$989$	0.575188			0.0182899
$990$	5.93779	+	7.98390i	0.188715	+	0.253745i
$991$	15.2863			0.485584			0.242792	−	0.970078i	$-0.421937\pi$
$991$	15.2863			0.485584			0.242792	+	0.970078i	$0.421937\pi$
$992$	3.41217	−	5.91006i	0.108337	−	0.187645i
$993$	22.7973	+	31.7440i	0.723449	+	1.00737i
$994$	2.90870	+	5.03802i	0.0922583	+	0.159796i
$995$	−5.04452	+	2.91245i	−0.159922	+	0.0923310i
$996$	2.94261	−	6.51241i	0.0932402	−	0.206354i
$997$	−0.290474	−	0.167705i	−0.00919941	−	0.00531128i	0.495393	−	0.868669i	$-0.335024\pi$
$997$	−0.290474	−	0.167705i	−0.00919941	−	0.00531128i	−0.504593	+	0.863358i	$0.668357\pi$
$998$	−28.9312			−0.915803
$999$	10.9951	−	3.37267i	0.347870	−	0.106707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.b.461.15	yes	48
3.2	odd	2		2970.2.t.a.791.2		48
9.4	even	3		2970.2.t.b.2771.2		48
9.5	odd	6		990.2.t.a.131.15	✓	48
11.10	odd	2		990.2.t.a.461.15	yes	48
33.32	even	2		2970.2.t.b.791.2		48
99.32	even	6	inner	990.2.t.b.131.15	yes	48
99.76	odd	6		2970.2.t.a.2771.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.15	✓	48	9.5	odd	6
990.2.t.a.461.15	yes	48	11.10	odd	2
990.2.t.b.131.15	yes	48	99.32	even	6	inner
990.2.t.b.461.15	yes	48	1.1	even	1	trivial
2970.2.t.a.791.2		48	3.2	odd	2
2970.2.t.a.2771.2		48	99.76	odd	6
2970.2.t.b.791.2		48	33.32	even	2
2970.2.t.b.2771.2		48	9.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.713195 - 1.57840i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.01034 - 1.40685i) q^{6} +(3.86969 + 2.23417i) q^{7} -1.00000 q^{8} +(-1.98271 - 2.25142i) q^{9} -1.00000i q^{10} +(0.273477 - 3.30533i) q^{11} +(-1.72353 + 0.171556i) q^{12} +(-5.39534 + 3.11500i) q^{13} +(3.86969 - 2.23417i) q^{14} +(-0.171556 - 1.72353i) q^{15} +(-0.500000 + 0.866025i) q^{16} +6.51011 q^{17} +(-2.94114 + 0.591365i) q^{18} -7.19244i q^{19} +(-0.866025 - 0.500000i) q^{20} +(6.28626 - 4.51453i) q^{21} +(-2.72576 - 1.88950i) q^{22} +(0.160698 - 0.0927788i) q^{23} +(-0.713195 + 1.57840i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.23000i q^{26} +(-4.96770 + 1.52381i) q^{27} -4.46833i q^{28} +(1.39115 - 2.40954i) q^{29} +(-1.57840 - 0.713195i) q^{30} +(-3.41217 - 5.91006i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.02210 - 2.78900i) q^{33} +(3.25505 - 5.63792i) q^{34} +4.46833 q^{35} +(-0.958432 + 2.84278i) q^{36} -2.21332 q^{37} +(-6.22884 - 3.59622i) q^{38} +(1.06879 + 10.7376i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.73582 + 3.00653i) q^{41} +(-0.766569 - 7.70132i) q^{42} +(2.68449 + 1.54989i) q^{43} +(-2.99924 + 1.41583i) q^{44} +(-2.84278 - 0.958432i) q^{45} -0.185558i q^{46} +(9.56050 + 5.51975i) q^{47} +(1.01034 + 1.40685i) q^{48} +(6.48300 + 11.2289i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.64298 - 10.2756i) q^{51} +(5.39534 + 3.11500i) q^{52} +6.08358i q^{53} +(-1.16419 + 5.06405i) q^{54} +(-1.41583 - 2.99924i) q^{55} +(-3.86969 - 2.23417i) q^{56} +(-11.3526 - 5.12961i) q^{57} +(-1.39115 - 2.40954i) q^{58} +(-11.5172 + 6.64945i) q^{59} +(-1.40685 + 1.01034i) q^{60} +(2.19952 + 1.26989i) q^{61} -6.82435 q^{62} +(-2.64241 - 13.1420i) q^{63} +1.00000 q^{64} +(-3.11500 + 5.39534i) q^{65} +(-4.92640 + 2.95476i) q^{66} +(-5.67108 - 9.82260i) q^{67} +(-3.25505 - 5.63792i) q^{68} +(-0.0318335 - 0.319815i) q^{69} +(2.23417 - 3.86969i) q^{70} +1.30192i q^{71} +(1.98271 + 2.25142i) q^{72} +5.48124i q^{73} +(-1.10666 + 1.91679i) q^{74} +(-1.01034 - 1.40685i) q^{75} +(-6.22884 + 3.59622i) q^{76} +(8.44293 - 12.1796i) q^{77} +(9.83344 + 4.44321i) q^{78} +(8.26376 + 4.77108i) q^{79} +1.00000i q^{80} +(-1.13776 + 8.92779i) q^{81} +3.47164 q^{82} +(-2.06298 + 3.57318i) q^{83} +(-7.05283 - 3.18679i) q^{84} +(5.63792 - 3.25505i) q^{85} +(2.68449 - 1.54989i) q^{86} +(-2.81107 - 3.91427i) q^{87} +(-0.273477 + 3.30533i) q^{88} -10.3192i q^{89} +(-2.25142 + 1.98271i) q^{90} -27.8377 q^{91} +(-0.160698 - 0.0927788i) q^{92} +(-11.7620 + 1.17076i) q^{93} +(9.56050 - 5.51975i) q^{94} +(-3.59622 - 6.22884i) q^{95} +(1.72353 - 0.171556i) q^{96} +(-2.61299 + 4.52583i) q^{97} +12.9660 q^{98} +(-7.98390 + 5.93779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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