LMFDB - Embedded newform 990.2.t.a.131.15

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			131.15
Character	$\chi$	$=$	990.131
Dual form			990.2.t.a.461.15

$q$-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} +(-2.72576 - 1.88950i) 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} +(-0.273477 + 3.30533i) 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} +(1.03840 - 5.64993i) 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} +(-5.41218 + 1.92569i) 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} +(14.7693 + 1.22199i) 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} +(-2.72576 - 1.88950i) 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} +(9.65844 - 2.39050i) 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} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 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 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * 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 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	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	$-0.986731\pi$
$7$	−3.86969	+	2.23417i	−1.46261	+	0.844436i	−0.463474	+	0.886110i	$0.653397\pi$
$8$	1.00000			0.353553
$9$	−1.98271	+	2.25142i	−0.660902	+	0.750472i
$10$		−	1.00000i		−	0.316228i
$11$	−2.72576	−	1.88950i	−0.821848	−	0.569707i
$11$	−2.72576	−	1.88950i	−0.821848	−	0.569707i
$12$	−1.72353	−	0.171556i	−0.497541	−	0.0495239i
$13$	5.39534	+	3.11500i	1.49640	+	0.863945i	0.999991	−	0.00414513i	$-0.00131944\pi$
$13$	5.39534	+	3.11500i	1.49640	+	0.863945i	0.496406	+	0.868091i	$0.334653\pi$
$14$	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	$-0.789643\pi$
$17$	−6.51011			−1.57893			−0.789467	+	0.613794i	$0.789643\pi$
$18$	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
$22$	−0.273477	+	3.30533i	−0.0583055	+	0.704699i
$23$	0.160698	+	0.0927788i	0.0335078	+	0.0193457i	0.516660	−	0.856190i	$-0.327175\pi$
$23$	0.160698	+	0.0927788i	0.0335078	+	0.0193457i	−0.483153	+	0.875536i	$0.660508\pi$
$24$	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	$-0.249839\pi$
$29$	−1.39115	−	2.40954i	−0.258330	−	0.447441i	−0.965795	+	0.259308i	$0.916506\pi$
$30$	1.57840	−	0.713195i	0.288175	−	0.130211i
$31$	−3.41217	+	5.91006i	−0.612845	+	1.06148i	0.377914	+	0.925841i	$0.376641\pi$
$31$	−3.41217	+	5.91006i	−0.612845	+	1.06148i	−0.990759	+	0.135637i	$0.956692\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.03840	−	5.64993i	0.180762	−	0.983527i
$34$	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	$-0.920717\pi$
$41$	−1.73582	+	3.00653i	−0.271089	+	0.469541i	0.698052	+	0.716047i	$0.254051\pi$
$42$	−0.766569	+	7.70132i	−0.118284	+	1.18834i
$43$	−2.68449	+	1.54989i	−0.409380	+	0.236356i	−0.690524	−	0.723310i	$-0.742620\pi$
$43$	−2.68449	+	1.54989i	−0.409380	+	0.236356i	0.281143	+	0.959666i	$0.409286\pi$
$44$	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	0.400728	−	0.916197i	$-0.368757\pi$
$47$	9.56050	−	5.51975i	1.39454	−	0.805139i	0.993814	+	0.111058i	$0.0354240\pi$
$48$	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	$-0.862794\pi$
$53$		−	6.08358i		−	0.835644i	0.908529	−	0.417822i	$-0.137206\pi$
$54$	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	−0.499409	−	0.866366i	$-0.666450\pi$
$59$	−11.5172	−	6.64945i	−1.49941	−	0.865684i	−1.00000		0.000681823i	$0.999783\pi$
$60$	−1.40685	−	1.01034i	−0.181623	−	0.130434i
$61$	−2.19952	+	1.26989i	−0.281619	+	0.162593i	−0.634156	−	0.773205i	$-0.718652\pi$
$61$	−2.19952	+	1.26989i	−0.281619	+	0.162593i	0.352537	+	0.935798i	$0.385319\pi$
$62$	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
$66$	−5.41218	+	1.92569i	−0.666194	+	0.237036i
$67$	−5.67108	+	9.82260i	−0.692833	+	1.20002i	0.278073	+	0.960560i	$0.410304\pi$
$67$	−5.67108	+	9.82260i	−0.692833	+	1.20002i	−0.970906	+	0.239462i	$0.923029\pi$
$68$	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	$-0.975385\pi$
$71$		−	1.30192i		−	0.154509i	0.997011	−	0.0772546i	$-0.0246154\pi$
$72$	−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
$77$	14.7693	+	1.22199i	1.68312	+	0.139258i
$78$	9.83344	−	4.44321i	1.11342	−	0.503094i
$79$	−8.26376	+	4.77108i	−0.929745	+	0.536789i	−0.886731	−	0.462286i	$-0.847029\pi$
$79$	−8.26376	+	4.77108i	−0.929745	+	0.536789i	−0.0430142	+	0.999074i	$0.513696\pi$
$80$		−	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	$-0.0939576\pi$
$83$	2.06298	+	3.57318i	0.226441	+	0.392208i	−0.730310	+	0.683116i	$0.760624\pi$
$84$	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
$88$	−2.72576	−	1.88950i	−0.290567	−	0.201422i
$89$			10.3192i			1.09384i	0.837186	+	0.546919i	$0.184199\pi$
$89$			10.3192i			1.09384i	−0.837186	+	0.546919i	$0.815801\pi$
$90$	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	0.702336	−	0.711846i	$-0.252141\pi$
$97$	−2.61299	−	4.52583i	−0.265309	−	0.459528i	−0.967644	+	0.252318i	$0.918807\pi$
$98$	−12.9660			−1.30976
$99$	9.65844	−	2.39050i	0.970710	−	0.240254i
$100$	−1.00000			−0.100000
$101$	5.63537	+	9.76075i	0.560740	+	0.971230i	0.997432	+	0.0716193i	$0.0228167\pi$
$101$	5.63537	+	9.76075i	0.560740	+	0.971230i	−0.436692	+	0.899611i	$0.643850\pi$
$102$	−6.57741	+	9.15872i	−0.651261	+	0.906848i
$103$	−1.19221	+	2.06496i	−0.117472	+	0.203467i	−0.918765	−	0.394805i	$-0.870812\pi$
$103$	−1.19221	+	2.06496i	−0.117472	+	0.203467i	0.801293	+	0.598272i	$0.204146\pi$
$104$	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	$-0.559441\pi$
$107$	−3.84087			−0.371310			−0.185655	+	0.982615i	$0.559441\pi$
$108$	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	$0.703204\pi$
$110$	−1.88950	+	2.72576i	−0.180157	+	0.259891i
$111$	−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	0.668773	−	0.743466i	$-0.266820\pi$
$113$	3.81940	+	2.20513i	0.359299	+	0.207442i	−0.309474	+	0.950908i	$0.600153\pi$
$114$	−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
$121$	3.85955	+	10.3007i	0.350869	+	0.936425i
$122$	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	$-0.854635\pi$
$131$	−0.765387	+	1.32569i	−0.0668721	+	0.115826i	0.830651	+	0.556794i	$0.187969\pi$
$132$	4.37379	+	3.72424i	0.380689	+	0.324154i
$133$	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	−0.353746	−	0.935341i	$-0.615092\pi$
$137$	3.27041	−	1.88817i	0.279410	−	0.161317i	0.633156	+	0.774024i	$0.281759\pi$
$138$	0.292885	−	0.132339i	0.0249320	−	0.0112654i
$139$	−13.1784	−	7.60855i	−1.11778	−	0.645348i	−0.176944	−	0.984221i	$-0.556621\pi$
$139$	−13.1784	−	7.60855i	−1.11778	−	0.645348i	−0.940832	+	0.338872i	$0.889954\pi$
$140$	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	$-0.856359\pi$
$149$	−0.882237	+	1.52808i	−0.0722756	+	0.125185i	0.827623	+	0.561285i	$0.189693\pi$
$150$	1.72353	+	0.171556i	0.140726	+	0.0140075i
$151$	2.89704	−	1.67260i	0.235757	−	0.136115i	−0.377468	−	0.926023i	$-0.623205\pi$
$151$	2.89704	−	1.67260i	0.235757	−	0.136115i	0.613225	+	0.789908i	$0.289872\pi$
$152$		−	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	−0.975833	−	0.218517i	$-0.929878\pi$
$157$	−3.74238	+	6.48200i	−0.298675	+	0.517320i	0.677158	+	0.735837i	$0.263211\pi$
$158$	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
$165$	3.72424	−	4.37379i	0.289932	−	0.340499i
$166$	2.06298	−	3.57318i	0.160118	−	0.277333i
$167$	−11.2138	+	19.4229i	−0.867753	+	1.50299i	−0.00346574	+	0.999994i	$0.501103\pi$
$167$	−11.2138	+	19.4229i	−0.867753	+	1.50299i	−0.864287	+	0.502998i	$0.832230\pi$
$168$	−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	$-0.305112\pi$
$173$	−5.54207	−	9.59914i	−0.421356	−	0.729809i	−0.996072	+	0.0885432i	$0.971779\pi$
$174$	−4.79539	−	0.477320i	−0.363538	−	0.0361855i
$175$	−3.86969	−	2.23417i	−0.292521	−	0.168887i
$176$	−0.273477	+	3.30533i	−0.0206141	+	0.249149i
$177$	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	$-0.887911\pi$
$179$		−	9.22904i		−	0.689811i	0.938637	−	0.344906i	$-0.112089\pi$
$180$	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
$187$	17.7450	+	12.3009i	1.29764	+	0.899529i
$188$			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	−0.0289622	−	0.999581i	$-0.509220\pi$
$191$	11.3633	−	6.56060i	0.822219	−	0.474708i	0.851181	+	0.524872i	$0.175887\pi$
$192$	0.713195	+	1.57840i	0.0514704	+	0.113911i
$193$	18.9691	+	10.9518i	1.36542	+	0.788328i	0.990340	−	0.138663i	$-0.0442804\pi$
$193$	18.9691	+	10.9518i	1.36542	+	0.788328i	0.375084	+	0.926991i	$0.377614\pi$
$194$	−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	$-0.568331\pi$
$197$	−5.97983			−0.426045			−0.213023	+	0.977047i	$0.568331\pi$
$198$	−6.89945	−	7.16921i	−0.490323	−	0.509493i
$199$	−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
$209$	−13.5901	+	19.6049i	−0.940050	+	1.35610i
$210$	−4.51453	+	6.28626i	−0.311532	+	0.433793i
$211$	−11.9574	−	6.90362i	−0.823183	−	0.475265i	0.0283299	−	0.999599i	$-0.490981\pi$
$211$	−11.9574	−	6.90362i	−0.823183	−	0.475265i	−0.851513	+	0.524334i	$0.824314\pi$
$212$	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
$220$	3.30533	+	0.273477i	0.222845	+	0.0184378i
$221$	−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	0.764176	−	0.645008i	$-0.223146\pi$
$223$	−2.63579	−	4.56532i	−0.176506	−	0.305717i	−0.940681	+	0.339292i	$0.889813\pi$
$224$		−	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	$-0.144461\pi$
$227$	1.05021	+	1.81901i	0.0697047	+	0.120732i	−0.829067	+	0.559150i	$0.811128\pi$
$228$	−1.23391	+	12.3964i	−0.0817174	+	0.820973i
$229$	−3.58056	+	6.20171i	−0.236610	+	0.409820i	−0.959739	−	0.280892i	$-0.909370\pi$
$229$	−3.58056	+	6.20171i	−0.236610	+	0.409820i	0.723129	+	0.690713i	$0.242703\pi$
$230$	0.0927788	−	0.160698i	0.00611765	−	0.0105961i
$231$	8.60462	+	24.1834i	0.566142	+	1.59115i
$232$	−1.39115	−	2.40954i	−0.0913335	−	0.158194i
$233$	12.7300			0.833968			0.416984	−	0.908914i	$-0.363087\pi$
$233$	12.7300			0.833968			0.416984	+	0.908914i	$0.363087\pi$
$234$	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	$-0.962382\pi$
$239$	−6.09733	+	10.5609i	−0.394404	+	0.683127i	0.598621	+	0.801032i	$0.295715\pi$
$240$	1.57840	−	0.713195i	0.101885	−	0.0460365i
$241$	−0.253838	+	0.146553i	−0.0163511	+	0.00944033i	−0.508153	−	0.861267i	$-0.669672\pi$
$241$	−0.253838	+	0.146553i	−0.0163511	+	0.00944033i	0.491802	+	0.870707i	$0.336338\pi$
$242$	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	$0.0267371\pi$
$251$			2.65840i			0.167797i	−0.996474	+	0.0838984i	$0.973263\pi$
$252$	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	0.923032	−	0.384722i	$-0.125703\pi$
$257$	16.8547	+	9.73109i	1.05137	+	0.607009i	0.128337	+	0.991731i	$0.459036\pi$
$258$	−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	$-0.305489\pi$
$263$	−6.85063	−	11.8656i	−0.422428	−	0.731667i	−0.996176	+	0.0873648i	$0.972155\pi$
$264$	1.03840	−	5.64993i	0.0639088	−	0.347729i
$265$	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	$-0.951674\pi$
$269$		−	4.96103i		−	0.302479i	0.988497	−	0.151240i	$-0.0483265\pi$
$270$	−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
$275$	0.273477	−	3.30533i	0.0164913	−	0.199319i
$276$	−0.261051	−	0.187476i	−0.0157134	−	0.0112847i
$277$	17.8388	−	10.2992i	1.07183	−	0.618821i	0.143148	−	0.989701i	$-0.454277\pi$
$277$	17.8388	−	10.2992i	1.07183	−	0.618821i	0.928681	+	0.370881i	$0.120944\pi$
$278$			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	$-0.321534\pi$
$281$	−7.83774	−	13.5754i	−0.467561	−	0.809839i	−0.999313	+	0.0370611i	$0.988200\pi$
$282$	1.89389	−	19.0270i	0.112780	−	1.13304i
$283$	13.6333	+	7.87118i	0.810415	+	0.467893i	0.847100	−	0.531434i	$-0.178347\pi$
$283$	13.6333	+	7.87118i	0.810415	+	0.467893i	−0.0366852	+	0.999327i	$0.511680\pi$
$284$	1.12749	+	0.650958i	0.0669044	+	0.0386273i
$285$	12.3964	+	1.23391i	0.734300	+	0.0730902i
$286$	−11.7716	+	16.9815i	−0.696070	+	1.00414i
$287$		−	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	$-0.796923\pi$
$293$	1.95371	−	3.38393i	0.114137	−	0.197691i	0.917435	+	0.397887i	$0.130256\pi$
$294$	−9.24729	−	20.4656i	−0.539313	−	1.19358i
$295$	−6.64945	−	11.5172i	−0.387146	−	0.670556i
$296$	−2.21332			−0.128647
$297$	10.6615	+	13.5400i	0.618644	+	0.785671i
$298$	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	$0.741328\pi$
$308$	−8.44293	+	12.1796i	−0.481081	+	0.693998i
$309$	−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	0.980949	−	0.194267i	$-0.0622327\pi$
$311$	22.9819	+	13.2686i	1.30318	+	0.752393i	0.322235	+	0.946660i	$0.395566\pi$
$312$	−1.06879	+	10.7376i	−0.0605085	+	0.607898i
$313$	11.9671	+	20.7277i	0.676422	+	1.17160i	0.976051	+	0.217542i	$0.0698038\pi$
$313$	11.9671	+	20.7277i	0.676422	+	1.17160i	−0.299629	+	0.954056i	$0.596863\pi$
$314$	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	−0.412184	−	0.911100i	$-0.635234\pi$
$317$	3.04029	−	1.75531i	0.170759	−	0.0985880i	0.582944	+	0.812512i	$0.301901\pi$
$318$	−8.55866	−	6.14647i	−0.479946	−	0.344677i
$319$	−0.760896	+	9.19643i	−0.0426020	+	0.514901i
$320$	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
$330$	−5.64993	−	1.03840i	−0.311019	−	0.0571618i
$331$	−11.2820	−	19.5410i	−0.620114	−	1.07407i	−0.989464	−	0.144779i	$-0.953753\pi$
$331$	−11.2820	−	19.5410i	−0.620114	−	1.07407i	0.369350	−	0.929290i	$-0.379580\pi$
$332$	−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	$-0.140821\pi$
$337$	18.0791	+	10.4380i	0.984832	+	0.568593i	0.0811062	+	0.996705i	$0.474155\pi$
$338$	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	−0.401163	−	0.916007i	$-0.631394\pi$
$347$	11.0408	−	19.1233i	0.592704	−	1.02659i	0.993867	−	0.110586i	$-0.0352728\pi$
$348$	1.98432	+	4.39159i	0.106371	+	0.235414i
$349$	7.46543	−	4.31017i	0.399615	−	0.230718i	−0.286703	−	0.958020i	$-0.592559\pi$
$349$	7.46543	−	4.31017i	0.399615	−	0.230718i	0.686318	+	0.727302i	$0.259226\pi$
$350$			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	−0.994809	−	0.101755i	$-0.967554\pi$
$353$	−26.3805	+	15.2308i	−1.40409	+	0.810653i	−0.409282	+	0.912408i	$0.634221\pi$
$354$	−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	$-0.515830\pi$
$359$	−1.88380			−0.0994231			−0.0497115	+	0.998764i	$0.515830\pi$
$360$	−2.84278	+	0.958432i	−0.149828	+	0.0505138i
$361$	−32.7312			−1.72269
$362$	4.61378	+	7.99131i	0.242495	+	0.420014i
$363$	−13.5060	+	13.4383i	−0.708880	+	0.705329i
$364$	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	0.886658	−	0.462425i	$-0.153021\pi$
$367$	0.821032	+	1.42207i	0.0428575	+	0.0742314i	−0.843801	+	0.536656i	$0.819687\pi$
$368$		−	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	$-0.277459\pi$
$373$	5.84178	+	3.37275i	0.302476	+	0.174634i	−0.341079	+	0.940035i	$0.610792\pi$
$374$	1.78037	−	21.5181i	0.0920605	−	1.11267i
$375$	−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	0.388577	−	0.921416i	$-0.372967\pi$
$383$	−4.20967	−	2.43045i	−0.215104	−	0.124190i	−0.603681	+	0.797226i	$0.706300\pi$
$384$	1.01034	−	1.40685i	0.0515586	−	0.0717928i
$385$	12.1796	+	8.44293i	0.620731	+	0.430292i
$386$		−	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	−0.00124401	−	0.999999i	$-0.500396\pi$
$389$	17.0439	−	9.84029i	0.864159	−	0.498922i	0.865403	+	0.501077i	$0.167063\pi$
$390$	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
$396$	−2.75899	+	9.55971i	−0.138644	+	0.480393i
$397$	−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	0.673706	−	0.738999i	$-0.264701\pi$
$401$	7.42060	+	4.28429i	0.370567	+	0.213947i	−0.303139	+	0.952946i	$0.598035\pi$
$402$	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
$407$	6.03299	+	4.18208i	0.299044	+	0.207298i
$408$	−4.64298	−	10.2756i	−0.229862	−	0.508716i
$409$	23.7276	+	13.6991i	1.17325	+	0.677379i	0.954444	−	0.298389i	$-0.0964492\pi$
$409$	23.7276	+	13.6991i	1.17325	+	0.677379i	0.218810	+	0.975768i	$0.429783\pi$
$410$	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
$418$	23.7734	+	1.96697i	1.16279	+	0.0962075i
$419$	−5.87748	−	3.39337i	−0.287134	−	0.165777i	0.349515	−	0.936931i	$-0.386346\pi$
$419$	−5.87748	−	3.39337i	−0.287134	−	0.165777i	−0.636649	+	0.771154i	$0.719680\pi$
$420$	7.70132	+	0.766569i	0.375786	+	0.0374047i
$421$	−5.06935	−	8.78038i	−0.247065	−	0.427929i	0.715645	−	0.698464i	$-0.246133\pi$
$421$	−5.06935	−	8.78038i	−0.247065	−	0.427929i	−0.962710	+	0.270535i	$0.912800\pi$
$422$			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
$429$	23.2020	−	27.2487i	1.12020	−	1.31558i
$430$	1.54989	+	2.68449i	0.0747423	+	0.129457i
$431$	−12.9017			−0.621452			−0.310726	−	0.950500i	$-0.600572\pi$
$431$	−12.9017			−0.621452			−0.310726	+	0.950500i	$0.600572\pi$
$432$	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	$-0.601434\pi$
$439$	7.38524	−	4.26387i	0.352478	−	0.203503i	0.665776	+	0.746151i	$0.268101\pi$
$440$	−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	−0.535560	+	0.844497i	$0.679899\pi$
$443$	−32.3016	+	18.6493i	−1.53470	+	0.886057i	−0.999136	+	0.0415596i	$0.986767\pi$
$444$	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	$0.205006\pi$
$449$			25.4460i			1.20087i	−0.799673	+	0.600436i	$0.794994\pi$
$450$	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	$-0.711305\pi$
$457$	−5.17553	+	2.98810i	−0.242101	+	0.139777i	0.374041	+	0.927412i	$0.377972\pi$
$458$	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	$-0.160339\pi$
$461$	0.426816	+	0.739267i	0.0198788	+	0.0344311i	−0.855915	+	0.517117i	$0.827005\pi$
$462$	16.6412	−	19.5435i	0.774217	−	0.909248i
$463$	7.04476	−	12.2019i	0.327398	−	0.567070i	−0.654597	−	0.755978i	$-0.727162\pi$
$463$	7.04476	−	12.2019i	0.327398	−	0.567070i	0.981995	+	0.188908i	$0.0604949\pi$
$464$	−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	$-0.777289\pi$
$467$		−	27.8323i		−	1.28792i	0.765057	−	0.643962i	$-0.222711\pi$
$468$	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
$473$	10.2458	+	0.847719i	0.471102	+	0.0389781i
$474$	−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	0.995891	+	0.0905552i	$0.0288642\pi$
$479$	12.6144	+	21.8489i	0.576369	+	0.998300i	−0.419523	+	0.907745i	$0.637803\pi$
$480$	−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
$484$	−10.8504	−	1.80786i	−0.493201	−	0.0821757i
$485$		−	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	$-0.804774\pi$
$491$	1.98545	−	3.43889i	0.0896019	−	0.155195i	0.907343	+	0.420391i	$0.138107\pi$
$492$	3.50753	−	4.88406i	0.158132	−	0.220191i
$493$	9.05654	+	15.6864i	0.407886	+	0.706479i
$494$	−44.8089			−2.01605
$495$	9.55971	+	2.75899i	0.429677	+	0.124007i
$496$	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	0.336131	+	0.941815i	$0.390881\pi$
$499$	−14.4656	+	25.0552i	−0.647570	+	1.12162i	−0.983701	+	0.179809i	$0.942452\pi$
$500$	−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	$-0.611663\pi$
$503$	−15.4145			−0.687298			−0.343649	+	0.939098i	$0.611663\pi$
$504$	2.64241	−	13.1420i	0.117702	−	0.585390i
$505$			11.2707i			0.501541i
$506$	−0.350612	+	0.505786i	−0.0155866	+	0.0224849i
$507$	−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	−0.269199	−	0.963085i	$-0.586759\pi$
$509$	−27.9273	−	16.1238i	−1.23785	−	0.714675i	−0.968655	+	0.248409i	$0.920092\pi$
$510$	−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
$517$	−36.4892	−	3.01905i	−1.60479	−	0.132778i
$518$	−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	$0.0545093\pi$
$521$			7.77937i			0.340820i	−0.985373	+	0.170410i	$0.945491\pi$
$522$	−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
$528$	−5.41218	+	1.92569i	−0.235535	+	0.0838049i
$529$	−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	$-0.938028\pi$
$547$	−30.5007	+	17.6096i	−1.30412	+	0.752933i	−0.323010	+	0.946396i	$0.604695\pi$
$548$			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	$-0.684691\pi$
$557$	−25.8765			−1.09642			−0.548210	+	0.836341i	$0.684691\pi$
$558$	−13.5307	+	15.3645i	−0.572799	+	0.650429i
$559$	−19.3116			−0.816794
$560$	2.23417	+	3.86969i	0.0944108	+	0.163524i
$561$	−6.76007	+	36.7817i	−0.285410	+	1.55292i
$562$	−7.83774	+	13.5754i	−0.330615	+	0.572643i
$563$	−10.0401	+	17.3900i	−0.423140	+	0.732900i	−0.996245	−	0.0865825i	$-0.972405\pi$
$563$	−10.0401	+	17.3900i	−0.423140	+	0.732900i	0.573105	+	0.819482i	$0.305739\pi$
$564$	−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	$-0.295045\pi$
$569$	−9.36179	−	16.2151i	−0.392467	−	0.679772i	−0.992774	+	0.119997i	$0.961712\pi$
$570$	−5.12961	−	11.3526i	−0.214856	−	0.475507i
$571$	29.5922	+	17.0851i	1.23839	+	0.714987i	0.968766	−	0.247977i	$-0.0797658\pi$
$571$	29.5922	+	17.0851i	1.23839	+	0.714987i	0.269628	+	0.962964i	$0.413099\pi$
$572$	20.5922	+	1.70376i	0.861003	+	0.0712379i
$573$	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
$583$	−11.4949	+	16.5824i	−0.476072	+	0.686772i
$584$			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	−0.544224	−	0.838940i	$-0.683176\pi$
$587$	−2.17550	+	1.25602i	−0.0897924	+	0.0518417i	0.454431	+	0.890782i	$0.349842\pi$
$588$	−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	$-0.824267\pi$
$593$	−41.4676			−1.70287			−0.851434	+	0.524461i	$0.824267\pi$
$594$	6.39523	−	16.0032i	0.262400	−	0.656617i
$595$	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	0.0669402	−	0.997757i	$-0.478676\pi$
$599$	−18.6905	−	10.7910i	−0.763673	−	0.440907i	−0.830613	+	0.556850i	$0.812010\pi$
$600$	−1.01034	+	1.40685i	−0.0412469	+	0.0574343i
$601$	14.8004	−	8.54500i	0.603720	−	0.348558i	−0.166784	−	0.985993i	$-0.553338\pi$
$601$	14.8004	−	8.54500i	0.603720	−	0.348558i	0.770503	+	0.637436i	$0.220005\pi$
$602$	−13.8508			−0.564518
$603$	−10.8707	−	32.2433i	−0.442689	−	1.31305i
$604$			3.34521i			0.136115i
$605$	−1.80786	+	10.8504i	−0.0735001	+	0.441132i
$606$	19.4255	+	1.93356i	0.789107	+	0.0785455i
$607$	17.2613	+	9.96583i	0.700616	+	0.404501i	0.807577	−	0.589762i	$-0.200779\pi$
$607$	17.2613	+	9.96583i	0.700616	+	0.404501i	−0.106961	+	0.994263i	$0.534112\pi$
$608$	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
$616$	14.7693	+	1.22199i	0.595073	+	0.0492353i
$617$	42.3208	+	24.4339i	1.70377	+	0.983672i	0.941871	+	0.335975i	$0.109066\pi$
$617$	42.3208	+	24.4339i	1.70377	+	0.983672i	0.761898	+	0.647696i	$0.224267\pi$
$618$	1.70055	+	3.76357i	0.0684063	+	0.151393i
$619$	4.72461	+	8.18326i	0.189898	+	0.328913i	0.945216	−	0.326445i	$-0.105851\pi$
$619$	4.72461	+	8.18326i	0.189898	+	0.328913i	−0.755318	+	0.655358i	$0.772518\pi$
$620$		−	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
$627$	−40.6368	−	7.46860i	−1.62288	−	0.298267i
$628$	−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	−0.374643	−	0.927169i	$-0.622235\pi$
$641$	6.10134	−	3.52261i	0.240988	−	0.139135i	0.615631	+	0.788035i	$0.288901\pi$
$642$	−3.88057	+	5.40351i	−0.153154	+	0.213259i
$643$	11.2538	−	19.4922i	0.443808	−	0.768697i	−0.554161	−	0.832410i	$-0.686961\pi$
$643$	11.2538	−	19.4922i	0.443808	−	0.768697i	0.997968	+	0.0637125i	$0.0202941\pi$
$644$	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	$0.170798\pi$
$647$			26.0058i			1.02239i	−0.859464	+	0.511197i	$0.829202\pi$
$648$	−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	0.139939	−	0.990160i	$-0.455309\pi$
$653$	−16.5486	−	9.55431i	−0.647595	−	0.373889i	−0.787534	+	0.616271i	$0.788643\pi$
$654$	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	−0.990429	−	0.138023i	$-0.955925\pi$
$659$	−15.7811	−	27.3337i	−0.614746	−	1.06477i	0.375684	−	0.926748i	$-0.377408\pi$
$660$	1.92569	+	5.41218i	0.0749573	+	0.210669i
$661$	−3.11575	+	5.39663i	−0.121188	+	0.209905i	−0.920237	−	0.391362i	$-0.872004\pi$
$661$	−3.11575	+	5.39663i	−0.121188	+	0.209905i	0.799048	+	0.601267i	$0.205337\pi$
$662$	−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
$671$	8.39483	+	0.694573i	0.324079	+	0.0268137i
$672$	7.05283	−	3.18679i	0.272069	−	0.122933i
$673$	1.56534	−	0.903752i	0.0603396	−	0.0348371i	−0.469527	−	0.882918i	$-0.655575\pi$
$673$	1.56534	−	0.903752i	0.0603396	−	0.0348371i	0.529866	+	0.848081i	$0.322242\pi$
$674$		−	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	$-0.259031\pi$
$677$	−7.44454	−	12.8943i	−0.286117	−	0.495569i	−0.972879	+	0.231313i	$0.925698\pi$
$678$	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
$682$	−18.6015	−	12.8946i	−0.712290	−	0.493761i
$683$			21.7548i			0.832425i	0.909267	+	0.416212i	$0.136643\pi$
$683$			21.7548i			0.832425i	−0.909267	+	0.416212i	$0.863357\pi$
$684$	−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	0.865807	+	0.500379i	$0.166806\pi$
$691$	22.7709	+	39.4403i	0.866244	+	1.50038i	0.000437616		1.00000i	$0.499861\pi$
$692$	11.0841			0.421356
$693$	−32.0344	+	30.8291i	−1.21689	+	1.17110i
$694$	−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	$-0.580778\pi$
$701$	−13.2942			−0.502115			−0.251058	+	0.967972i	$0.580778\pi$
$702$	−9.49331	+	30.9487i	−0.358302	+	1.16809i
$703$			15.9192i			0.600404i
$704$	−2.72576	−	1.88950i	−0.102731	−	0.0712133i
$705$	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	−0.809898	−	0.586571i	$-0.800477\pi$
$709$	−24.3088	−	42.1040i	−0.912934	−	1.58125i	−0.103037	−	0.994678i	$-0.532856\pi$
$710$	−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
$715$	1.70376	−	20.5922i	0.0637171	−	0.770105i
$716$	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	$0.0130375\pi$
$719$			2.19593i			0.0818944i	−0.999161	+	0.0409472i	$0.986962\pi$
$720$	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
$726$	18.3909	+	4.97737i	0.682551	+	0.184727i
$727$	3.76607	+	6.52302i	0.139676	+	0.241926i	0.927374	−	0.374136i	$-0.122061\pi$
$727$	3.76607	+	6.52302i	0.139676	+	0.241926i	−0.787698	+	0.616061i	$0.788727\pi$
$728$	−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	$-0.237605\pi$
$733$	13.8911	+	8.02005i	0.513081	+	0.296227i	−0.221019	+	0.975270i	$0.570938\pi$
$734$	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	$-0.878868\pi$
$743$	−3.88600	+	6.73075i	−0.142564	+	0.246927i	0.785898	+	0.618356i	$0.212201\pi$
$744$	−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	0.428985	+	0.903311i	$0.358871\pi$
$751$	−15.5601	+	26.9510i	−0.567798	+	0.983455i	−0.996783	+	0.0801434i	$0.974462\pi$
$752$	−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
$759$	0.691062	−	0.811590i	0.0250840	−	0.0294588i
$760$	3.59622	−	6.22884i	0.130449	−	0.225944i
$761$	−23.2308	+	40.2370i	−0.842117	+	1.45859i	0.0459839	+	0.998942i	$0.485358\pi$
$761$	−23.2308	+	40.2370i	−0.842117	+	1.45859i	−0.888101	+	0.459648i	$0.847976\pi$
$762$	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	$-0.347967\pi$
$769$	−2.20738	−	1.27443i	−0.0796001	−	0.0459571i	−0.539272	+	0.842132i	$0.681300\pi$
$770$	1.22199	−	14.7693i	0.0440374	−	0.532249i
$771$	−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	$-0.981569\pi$
$773$		−	3.21790i		−	0.115740i	0.998324	−	0.0578699i	$-0.0184309\pi$
$774$	−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
$781$	−2.45998	+	3.54872i	−0.0880249	+	0.126983i
$782$			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	$-0.493464\pi$
$787$	−23.4260	−	13.5250i	−0.835045	−	0.482114i	−0.855577	+	0.517676i	$0.826797\pi$
$788$	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
$792$	9.65844	−	2.39050i	0.343198	−	0.0849427i
$793$	−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	−0.357198	−	0.934029i	$-0.616268\pi$
$797$	−37.9622	−	21.9175i	−1.34469	−	0.776357i	−0.987492	+	0.157672i	$0.949601\pi$
$798$	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
$803$	10.3568	−	14.9406i	0.365485	−	0.527241i
$804$	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	$-0.249563\pi$
$809$	40.2796			1.41615			0.708077	+	0.706135i	$0.249563\pi$
$810$	−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
$814$	0.605293	−	7.31576i	0.0212155	−	0.256417i
$815$	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	$-0.219058\pi$
$821$	−4.69477	−	8.13159i	−0.163849	−	0.283794i	−0.936246	+	0.351346i	$0.885724\pi$
$822$	0.647854	−	6.50866i	0.0225965	−	0.227016i
$823$	−2.12640	+	3.68303i	−0.0741217	+	0.128383i	−0.900704	−	0.434433i	$-0.856949\pi$
$823$	−2.12640	+	3.68303i	−0.0741217	+	0.128383i	0.826582	+	0.562816i	$0.190282\pi$
$824$	−1.19221	+	2.06496i	−0.0415325	+	0.0719365i
$825$	5.41218	−	1.92569i	0.188428	−	0.0670439i
$826$	−29.7119	−	51.4626i	−1.03381	−	1.79061i
$827$	30.6848			1.06702			0.533508	−	0.845795i	$-0.320873\pi$
$827$	30.6848			1.06702			0.533508	+	0.845795i	$0.320873\pi$
$828$	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	−0.278687	−	0.960382i	$-0.589899\pi$
$839$	11.9826	−	6.91814i	0.413684	−	0.238841i	0.692371	+	0.721541i	$0.256566\pi$
$840$	−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	$-0.599723\pi$
$853$	10.5606	−	6.09719i	0.361589	−	0.208764i	0.669778	+	0.742562i	$0.266389\pi$
$854$	−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	$-0.240640\pi$
$857$	−6.74214	−	11.6777i	−0.230307	−	0.398903i	−0.957898	+	0.287107i	$0.907306\pi$
$858$	−35.1991	−	6.46920i	−1.20168	−	0.220855i
$859$	12.0624	−	20.8926i	0.411563	−	0.712848i	−0.583498	−	0.812115i	$-0.698316\pi$
$859$	12.0624	−	20.8926i	0.411563	−	0.712848i	0.995061	+	0.0992669i	$0.0316498\pi$
$860$	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	$-0.999434\pi$
$863$		−	0.104469i		−	0.00355615i	0.999998	−	0.00177808i	$-0.000565980\pi$
$864$	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
$869$	31.5400	+	2.60956i	1.06992	+	0.0885234i
$870$	−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	$-0.606282\pi$
$877$	−38.7882	−	22.3944i	−1.30978	−	0.756204i	−0.982060	+	0.188569i	$0.939615\pi$
$878$	−7.38524	−	4.26387i	−0.249240	−	0.143899i
$879$	6.73458	+	0.670342i	0.227152	+	0.0226101i
$880$	−1.88950	+	2.72576i	−0.0636951	+	0.0918854i
$881$		−	23.1144i		−	0.778745i	−0.921080	−	0.389372i	$-0.872692\pi$
$881$		−	23.1144i		−	0.778745i	0.921080	−	0.389372i	$-0.127308\pi$
$882$	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	$-0.793116\pi$
$887$	3.75290	−	6.50021i	0.126010	−	0.218256i	0.922127	+	0.386887i	$0.126450\pi$
$888$	−1.57853	−	3.49351i	−0.0529720	−	0.117235i
$889$	−19.6962	−	34.1147i	−0.660588	−	1.14417i
$890$	10.3192			0.345902
$891$	−13.7678	+	26.4848i	−0.461240	+	0.887275i
$892$	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
$902$	−9.46286	−	6.55967i	−0.315079	−	0.218413i
$903$	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	0.956392	+	0.292086i	$0.0943494\pi$
$907$	22.0196	+	38.1391i	0.731150	+	1.26639i	−0.225242	+	0.974303i	$0.572317\pi$
$908$	−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	−0.0967866	−	0.995305i	$-0.530856\pi$
$911$	21.6344	−	12.4906i	0.716780	−	0.413833i	0.813566	+	0.581472i	$0.197523\pi$
$912$	−10.1187	−	7.26680i	−0.335062	−	0.240628i
$913$	1.12835	−	13.6376i	0.0373431	−	0.451340i
$914$	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
$924$	−25.2458	−	4.63990i	−0.830525	−	0.152641i
$925$	−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	−0.660199	−	0.751091i	$-0.729528\pi$
$929$	−10.3580	+	5.98018i	−0.339834	+	0.196203i	0.320365	+	0.947294i	$0.396195\pi$
$930$	−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	$-0.742800\pi$
$941$	8.60762	−	14.9088i	0.280600	−	0.486014i	0.971533	+	0.236905i	$0.0761331\pi$
$942$	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	−0.837783	−	0.546003i	$-0.816149\pi$
$947$	−24.1209	+	13.9262i	−0.783823	+	0.452540i	0.0539604	+	0.998543i	$0.482816\pi$
$948$	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	$-0.372544\pi$
$953$	24.0669			0.779603			0.389801	+	0.920899i	$0.372544\pi$
$954$	3.59761	−	17.8926i	0.116477	−	0.579296i
$955$	13.1212			0.424592
$956$	−6.09733	−	10.5609i	−0.197202	−	0.341564i
$957$	−15.0583	+	5.35785i	−0.486766	+	0.173195i
$958$	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	$-0.0813482\pi$
$967$	38.3222	+	22.1253i	1.23236	+	0.711503i	0.264838	+	0.964293i	$0.414682\pi$
$968$	3.85955	+	10.3007i	0.124051	+	0.331076i
$969$	−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	$-0.695183\pi$
$971$		−	50.9680i		−	1.63564i	0.575474	−	0.817820i	$-0.304817\pi$
$972$	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	0.201763	−	0.979434i	$-0.435333\pi$
$977$	−17.0529	−	9.84550i	−0.545571	−	0.314985i	−0.747334	+	0.664449i	$0.768666\pi$
$978$	16.7535	−	23.3284i	0.535718	−	0.745960i
$979$	19.4982	−	28.1278i	0.623166	−	0.898968i
$980$			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	−0.986079	−	0.166278i	$-0.946825\pi$
$983$	−41.8597	+	24.1677i	−1.33512	+	0.770830i	−0.349039	+	0.937108i	$0.613492\pi$
$984$	−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
$990$	−2.39050	−	9.65844i	−0.0759750	−	0.306965i
$991$	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	$-0.664976\pi$
$997$	0.290474	−	0.167705i	0.00919941	−	0.00531128i	0.504593	+	0.863358i	$0.331643\pi$
$998$	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.a.131.15	✓	48
3.2	odd	2		2970.2.t.b.2771.2		48
9.2	odd	6		990.2.t.b.461.15	yes	48
9.7	even	3		2970.2.t.a.791.2		48
11.10	odd	2		990.2.t.b.131.15	yes	48
33.32	even	2		2970.2.t.a.2771.2		48
99.43	odd	6		2970.2.t.b.791.2		48
99.65	even	6	inner	990.2.t.a.461.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.15	✓	48	1.1	even	1	trivial
990.2.t.a.461.15	yes	48	99.65	even	6	inner
990.2.t.b.131.15	yes	48	11.10	odd	2
990.2.t.b.461.15	yes	48	9.2	odd	6
2970.2.t.a.791.2		48	9.7	even	3
2970.2.t.a.2771.2		48	33.32	even	2
2970.2.t.b.791.2		48	99.43	odd	6
2970.2.t.b.2771.2		48	3.2	odd	2

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} +(-2.72576 - 1.88950i) 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} +(-0.273477 + 3.30533i) 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} +(1.03840 - 5.64993i) 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} +(-5.41218 + 1.92569i) 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} +(14.7693 + 1.22199i) 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} +(-2.72576 - 1.88950i) 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} +(9.65844 - 2.39050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * 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 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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