LMFDB - Embedded newform 546.2.u.a.425.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.14
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.896713 + 1.48186i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.277881 + 0.481304i) q^{5} +(-1.51751 - 0.834971i) q^{6} +(-0.887101 - 2.49260i) q^{7} +1.00000i q^{8} +(-1.39181 + 2.65760i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.896713 + 1.48186i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.277881 + 0.481304i) q^{5} +(-1.51751 - 0.834971i) q^{6} +(-0.887101 - 2.49260i) q^{7} +1.00000i q^{8} +(-1.39181 + 2.65760i) q^{9} -0.555761i q^{10} +3.61740i q^{11} +(1.73168 - 0.0356471i) q^{12} +(-3.35317 - 1.32525i) q^{13} +(2.01455 + 1.71510i) q^{14} +(-0.962403 + 0.0198113i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.94735 + 3.37291i) q^{17} +(-0.123459 - 2.99746i) q^{18} +5.48202i q^{19} +(0.277881 + 0.481304i) q^{20} +(2.89821 - 3.54970i) q^{21} +(-1.80870 - 3.13276i) q^{22} +(-6.60113 + 3.81117i) q^{23} +(-1.48186 + 0.896713i) q^{24} +(2.34556 + 4.06264i) q^{25} +(3.56655 - 0.528884i) q^{26} +(-5.18625 + 0.320643i) q^{27} +(-2.60220 - 0.478048i) q^{28} +(5.62758 + 3.24909i) q^{29} +(0.823560 - 0.498359i) q^{30} +(3.71833 - 2.14678i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.36048 + 3.24377i) q^{33} -3.89470i q^{34} +(1.44621 + 0.265681i) q^{35} +(1.60565 + 2.53415i) q^{36} +(-3.88657 - 6.73173i) q^{37} +(-2.74101 - 4.74757i) q^{38} +(-1.04300 - 6.15728i) q^{39} +(-0.481304 - 0.277881i) q^{40} +(-1.45390 + 2.51823i) q^{41} +(-0.735067 + 4.52324i) q^{42} +(0.175343 + 0.303703i) q^{43} +(3.13276 + 1.80870i) q^{44} +(-0.892357 - 1.40838i) q^{45} +(3.81117 - 6.60113i) q^{46} +(6.28286 - 10.8822i) q^{47} +(0.834971 - 1.51751i) q^{48} +(-5.42611 + 4.42237i) q^{49} +(-4.06264 - 2.34556i) q^{50} +(-6.74439 + 0.138835i) q^{51} +(-2.82428 + 2.24130i) q^{52} +(1.56709 - 0.904762i) q^{53} +(4.33110 - 2.87081i) q^{54} +(-1.74107 - 1.00521i) q^{55} +(2.49260 - 0.887101i) q^{56} +(-8.12358 + 4.91580i) q^{57} -6.49817 q^{58} +(-0.697122 + 1.20745i) q^{59} +(-0.464044 + 0.843371i) q^{60} +0.579410i q^{61} +(-2.14678 + 3.71833i) q^{62} +(7.85902 + 1.11166i) q^{63} -1.00000 q^{64} +(1.56963 - 1.24563i) q^{65} +(3.02042 - 5.48943i) q^{66} +7.89218 q^{67} +(1.94735 + 3.37291i) q^{68} +(-11.5669 - 6.36442i) q^{69} +(-1.38529 + 0.493016i) q^{70} +(-9.91300 + 5.72327i) q^{71} +(-2.65760 - 1.39181i) q^{72} +(8.01069 - 4.62497i) q^{73} +(6.73173 + 3.88657i) q^{74} +(-3.91696 + 7.11882i) q^{75} +(4.74757 + 2.74101i) q^{76} +(9.01673 - 3.20900i) q^{77} +(3.98190 + 4.81087i) q^{78} +(-6.41273 + 11.1072i) q^{79} +0.555761 q^{80} +(-5.12573 - 7.39776i) q^{81} -2.90780i q^{82} -0.175313 q^{83} +(-1.62503 - 4.28477i) q^{84} +(-1.08226 - 1.87453i) q^{85} +(-0.303703 - 0.175343i) q^{86} +(0.231641 + 11.2528i) q^{87} -3.61740 q^{88} +(-3.93114 - 6.80894i) q^{89} +(1.47699 + 0.773515i) q^{90} +(-0.328719 + 9.53373i) q^{91} +7.62233i q^{92} +(6.51550 + 3.58499i) q^{93} +12.5657i q^{94} +(-2.63852 - 1.52335i) q^{95} +(0.0356471 + 1.73168i) q^{96} +(2.76030 - 1.59366i) q^{97} +(2.48796 - 6.54294i) q^{98} +(-9.61363 - 5.03474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.896713	+	1.48186i	0.517718	+	0.855552i
$3$	0.896713	+	1.48186i	0.517718	+	0.855552i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.277881	+	0.481304i	−0.124272	+	0.215245i	−0.921448	−	0.388501i	$-0.872993\pi$
$5$	−0.277881	+	0.481304i	−0.124272	+	0.215245i	0.797176	+	0.603747i	$0.206326\pi$
$6$	−1.51751	−	0.834971i	−0.619519	−	0.340875i
$7$	−0.887101	−	2.49260i	−0.335293	−	0.942114i
$7$	−0.887101	−	2.49260i	−0.335293	−	0.942114i
$8$			1.00000i			0.353553i
$9$	−1.39181	+	2.65760i	−0.463937	+	0.885868i
$10$		−	0.555761i		−	0.175747i
$11$			3.61740i			1.09069i	0.838212	+	0.545344i	$0.183601\pi$
$11$			3.61740i			1.09069i	−0.838212	+	0.545344i	$0.816399\pi$
$12$	1.73168	−	0.0356471i	0.499894	−	0.0102904i
$13$	−3.35317	−	1.32525i	−0.930001	−	0.367558i
$13$	−3.35317	−	1.32525i	−0.930001	−	0.367558i
$14$	2.01455	+	1.71510i	0.538412	+	0.458381i
$15$	−0.962403	+	0.0198113i	−0.248491	+	0.00511526i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.94735	+	3.37291i	−0.472302	+	0.818050i	−0.999498	−	0.0316934i	$-0.989910\pi$
$17$	−1.94735	+	3.37291i	−0.472302	+	0.818050i	0.527196	+	0.849744i	$0.323243\pi$
$18$	−0.123459	−	2.99746i	−0.0290996	−	0.706508i
$19$			5.48202i			1.25766i	0.777542	+	0.628831i	$0.216466\pi$
$19$			5.48202i			1.25766i	−0.777542	+	0.628831i	$0.783534\pi$
$20$	0.277881	+	0.481304i	0.0621360	+	0.107623i
$21$	2.89821	−	3.54970i	0.632440	−	0.774609i
$22$	−1.80870	−	3.13276i	−0.385616	−	0.667907i
$23$	−6.60113	+	3.81117i	−1.37643	+	0.794683i	−0.991728	−	0.128357i	$-0.959030\pi$
$23$	−6.60113	+	3.81117i	−1.37643	+	0.794683i	−0.384703	+	0.923040i	$0.625696\pi$
$24$	−1.48186	+	0.896713i	−0.302483	+	0.183041i
$25$	2.34556	+	4.06264i	0.469113	+	0.812527i
$26$	3.56655	−	0.528884i	0.699458	−	0.103723i
$27$	−5.18625	+	0.320643i	−0.998094	+	0.0617078i
$28$	−2.60220	−	0.478048i	−0.491770	−	0.0903426i
$29$	5.62758	+	3.24909i	1.04502	+	0.603340i	0.921250	−	0.388971i	$-0.127169\pi$
$29$	5.62758	+	3.24909i	1.04502	+	0.603340i	0.123766	+	0.992311i	$0.460503\pi$
$30$	0.823560	−	0.498359i	0.150361	−	0.0909874i
$31$	3.71833	−	2.14678i	0.667832	−	0.385573i	−0.127423	−	0.991848i	$-0.540671\pi$
$31$	3.71833	−	2.14678i	0.667832	−	0.385573i	0.795255	+	0.606276i	$0.207337\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.36048	+	3.24377i	−0.933140	+	0.564668i
$34$		−	3.89470i		−	0.667935i
$35$	1.44621	+	0.265681i	0.244453	+	0.0449082i
$36$	1.60565	+	2.53415i	0.267608	+	0.422358i
$37$	−3.88657	−	6.73173i	−0.638948	−	1.10669i	−0.985664	−	0.168720i	$-0.946037\pi$
$37$	−3.88657	−	6.73173i	−0.638948	−	1.10669i	0.346716	−	0.937970i	$-0.387297\pi$
$38$	−2.74101	−	4.74757i	−0.444651	−	0.770157i
$39$	−1.04300	−	6.15728i	−0.167013	−	0.985955i
$40$	−0.481304	−	0.277881i	−0.0761008	−	0.0439368i
$41$	−1.45390	+	2.51823i	−0.227061	+	0.393281i	−0.956936	−	0.290300i	$-0.906245\pi$
$41$	−1.45390	+	2.51823i	−0.227061	+	0.393281i	0.729875	+	0.683581i	$0.239578\pi$
$42$	−0.735067	+	4.52324i	−0.113423	+	0.697951i
$43$	0.175343	+	0.303703i	0.0267396	+	0.0463143i	0.879086	−	0.476664i	$-0.158154\pi$
$43$	0.175343	+	0.303703i	0.0267396	+	0.0463143i	−0.852346	+	0.522978i	$0.824821\pi$
$44$	3.13276	+	1.80870i	0.472282	+	0.272672i
$45$	−0.892357	−	1.40838i	−0.133025	−	0.209949i
$46$	3.81117	−	6.60113i	0.561926	−	0.973284i
$47$	6.28286	−	10.8822i	0.916449	−	1.58734i	0.111682	−	0.993744i	$-0.464376\pi$
$47$	6.28286	−	10.8822i	0.916449	−	1.58734i	0.804766	−	0.593592i	$-0.202291\pi$
$48$	0.834971	−	1.51751i	0.120518	−	0.219033i
$49$	−5.42611	+	4.42237i	−0.775158	+	0.631768i
$50$	−4.06264	−	2.34556i	−0.574544	−	0.331713i
$51$	−6.74439	+	0.138835i	−0.944403	+	0.0194408i
$52$	−2.82428	+	2.24130i	−0.391657	+	0.310813i
$53$	1.56709	−	0.904762i	0.215257	−	0.124279i	−0.388495	−	0.921451i	$-0.627005\pi$
$53$	1.56709	−	0.904762i	0.215257	−	0.124279i	0.603752	+	0.797172i	$0.293672\pi$
$54$	4.33110	−	2.87081i	0.589388	−	0.390668i
$55$	−1.74107	−	1.00521i	−0.234766	−	0.135542i
$56$	2.49260	−	0.887101i	0.333088	−	0.118544i
$57$	−8.12358	+	4.91580i	−1.07599	+	0.651114i
$58$	−6.49817			−0.853252
$59$	−0.697122	+	1.20745i	−0.0907576	+	0.157197i	−0.907830	−	0.419338i	$-0.862262\pi$
$59$	−0.697122	+	1.20745i	−0.0907576	+	0.157197i	0.817073	+	0.576535i	$0.195596\pi$
$60$	−0.464044	+	0.843371i	−0.0599079	+	0.108879i
$61$			0.579410i			0.0741859i	0.999312	+	0.0370929i	$0.0118098\pi$
$61$			0.579410i			0.0741859i	−0.999312	+	0.0370929i	$0.988190\pi$
$62$	−2.14678	+	3.71833i	−0.272641	+	0.472228i
$63$	7.85902	+	1.11166i	0.990144	+	0.140056i
$64$	−1.00000			−0.125000
$65$	1.56963	−	1.24563i	0.194688	−	0.154501i
$66$	3.02042	−	5.48943i	0.371789	−	0.675702i
$67$	7.89218			0.964183			0.482092	−	0.876121i	$-0.339877\pi$
$67$	7.89218			0.964183			0.482092	+	0.876121i	$0.339877\pi$
$68$	1.94735	+	3.37291i	0.236151	+	0.409025i
$69$	−11.5669	−	6.36442i	−1.39250	−	0.766187i
$70$	−1.38529	+	0.493016i	−0.165574	+	0.0589267i
$71$	−9.91300	+	5.72327i	−1.17646	+	0.679228i	−0.955192	−	0.295986i	$-0.904352\pi$
$71$	−9.91300	+	5.72327i	−1.17646	+	0.679228i	−0.221265	+	0.975214i	$0.571018\pi$
$72$	−2.65760	−	1.39181i	−0.313202	−	0.164026i
$73$	8.01069	−	4.62497i	0.937580	−	0.541312i	0.0483794	−	0.998829i	$-0.484594\pi$
$73$	8.01069	−	4.62497i	0.937580	−	0.541312i	0.889201	+	0.457517i	$0.151261\pi$
$74$	6.73173	+	3.88657i	0.782548	+	0.451804i
$75$	−3.91696	+	7.11882i	−0.452291	+	0.822010i
$76$	4.74757	+	2.74101i	0.544583	+	0.314415i
$77$	9.01673	−	3.20900i	1.02755	−	0.365699i
$78$	3.98190	+	4.81087i	0.450862	+	0.544723i
$79$	−6.41273	+	11.1072i	−0.721489	+	1.24966i	0.238914	+	0.971041i	$0.423209\pi$
$79$	−6.41273	+	11.1072i	−0.721489	+	1.24966i	−0.960403	+	0.278615i	$0.910125\pi$
$80$	0.555761			0.0621360
$81$	−5.12573	−	7.39776i	−0.569525	−	0.821974i
$82$		−	2.90780i		−	0.321112i
$83$	−0.175313			−0.0192431			−0.00962155	−	0.999954i	$-0.503063\pi$
$83$	−0.175313			−0.0192431			−0.00962155	+	0.999954i	$0.503063\pi$
$84$	−1.62503	−	4.28477i	−0.177306	−	0.467507i
$85$	−1.08226	−	1.87453i	−0.117388	−	0.203322i
$86$	−0.303703	−	0.175343i	−0.0327492	−	0.0189077i
$87$	0.231641	+	11.2528i	0.0248345	+	1.20642i
$88$	−3.61740			−0.385616
$89$	−3.93114	−	6.80894i	−0.416700	−	0.721746i	0.578905	−	0.815395i	$-0.303480\pi$
$89$	−3.93114	−	6.80894i	−0.416700	−	0.721746i	−0.995605	+	0.0936489i	$0.970147\pi$
$90$	1.47699	+	0.773515i	0.155689	+	0.0815356i
$91$	−0.328719	+	9.53373i	−0.0344591	+	0.999406i
$92$			7.62233i			0.794683i
$93$	6.51550	+	3.58499i	0.675626	+	0.371747i
$94$			12.5657i			1.29605i
$95$	−2.63852	−	1.52335i	−0.270706	−	0.156292i
$96$	0.0356471	+	1.73168i	0.00363822	+	0.176739i
$97$	2.76030	−	1.59366i	0.280266	−	0.161812i	−0.353278	−	0.935518i	$-0.614933\pi$
$97$	2.76030	−	1.59366i	0.280266	−	0.161812i	0.633544	+	0.773707i	$0.281600\pi$
$98$	2.48796	−	6.54294i	0.251322	−	0.660937i
$99$	−9.61363	−	5.03474i	−0.966206	−	0.506010i
$100$	4.69113			0.469113
$101$	15.4791			1.54023			0.770113	−	0.637908i	$-0.220200\pi$
$101$	15.4791			1.54023			0.770113	+	0.637908i	$0.220200\pi$
$102$	5.77139	−	3.49243i	0.571453	−	0.345802i
$103$	16.5688	+	9.56598i	1.63257	+	0.942564i	0.983297	+	0.182007i	$0.0582595\pi$
$103$	16.5688	+	9.56598i	1.63257	+	0.942564i	0.649272	+	0.760557i	$0.275074\pi$
$104$	1.32525	−	3.35317i	0.129951	−	0.328805i
$105$	0.903130	+	2.38131i	0.0881365	+	0.232392i
$106$	−0.904762	+	1.56709i	−0.0878782	+	0.152210i
$107$	1.43461	−	0.828270i	0.138689	−	0.0800719i	−0.429050	−	0.903281i	$-0.641152\pi$
$107$	1.43461	−	0.828270i	0.138689	−	0.0800719i	0.567739	+	0.823209i	$0.307818\pi$
$108$	−2.31544	+	4.65175i	−0.222803	+	0.447614i
$109$	−9.65592	−	16.7245i	−0.924869	−	1.60192i	−0.791772	−	0.610817i	$-0.790841\pi$
$109$	−9.65592	−	16.7245i	−0.924869	−	1.60192i	−0.133097	−	0.991103i	$-0.542492\pi$
$110$	2.01041			0.191685
$111$	6.49034	−	11.7958i	0.616036	−	1.11961i
$112$	−1.71510	+	2.01455i	−0.162062	+	0.190357i
$113$	1.46966	−	0.848506i	0.138254	−	0.0798207i	−0.429278	−	0.903172i	$-0.641232\pi$
$113$	1.46966	−	0.848506i	0.138254	−	0.0798207i	0.567531	+	0.823352i	$0.307899\pi$
$114$	4.57733	−	8.31900i	0.428706	−	0.779146i
$115$		−	4.23620i		−	0.395027i
$116$	5.62758	−	3.24909i	0.522508	−	0.301670i
$117$	8.18896	−	7.06689i	0.757069	−	0.653334i
$118$		−	1.39424i		−	0.128351i
$119$	10.1348	+	1.86185i	0.929056	+	0.170676i
$120$	−0.0198113	−	0.962403i	−0.00180852	−	0.0878550i
$121$	−2.08560			−0.189600
$122$	−0.289705	−	0.501784i	−0.0262287	−	0.0454294i
$123$	−5.03538	+	0.103655i	−0.454025	+	0.00934622i
$124$		−	4.29356i		−	0.385573i
$125$	−5.38596			−0.481735
$126$	−7.36194	+	2.96678i	−0.655854	+	0.264302i
$127$	−5.98419	+	10.3649i	−0.531011	+	0.919738i	0.468334	+	0.883551i	$0.344854\pi$
$127$	−5.98419	+	10.3649i	−0.531011	+	0.919738i	−0.999345	+	0.0361862i	$0.988479\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.292813	+	0.532168i	−0.0257807	+	0.0468548i
$130$	−0.736522	+	1.86356i	−0.0645972	+	0.163445i
$131$	3.41067	−	5.90746i	0.297992	−	0.516137i	−0.677684	−	0.735353i	$-0.737016\pi$
$131$	3.41067	−	5.90746i	0.297992	−	0.516137i	0.975676	+	0.219216i	$0.0703498\pi$
$132$	0.128950	+	6.26420i	0.0112237	+	0.545228i
$133$	13.6645	−	4.86310i	1.18486	−	0.421685i
$134$	−6.83483	+	3.94609i	−0.590439	+	0.340890i
$135$	1.28683	−	2.58526i	0.110753	−	0.222504i
$136$	−3.37291	−	1.94735i	−0.289224	−	0.166984i
$137$	5.93695	+	3.42770i	0.507228	+	0.292848i	0.731693	−	0.681634i	$-0.238730\pi$
$137$	5.93695	+	3.42770i	0.507228	+	0.292848i	−0.224466	+	0.974482i	$0.572064\pi$
$138$	13.1995	−	0.271714i	1.12361	−	0.0231299i
$139$	0.958211	−	0.553223i	0.0812744	−	0.0469238i	−0.458812	−	0.888533i	$-0.651725\pi$
$139$	0.958211	−	0.553223i	0.0812744	−	0.0469238i	0.540086	+	0.841610i	$0.318392\pi$
$140$	0.953189	−	1.11961i	0.0805592	−	0.0946243i
$141$	21.7598	−	0.447932i	1.83251	−	0.0377226i
$142$	5.72327	−	9.91300i	0.480287	−	0.831881i
$143$	4.79396	−	12.1297i	0.400891	−	1.01434i
$144$	2.99746	−	0.123459i	0.249788	−	0.0102883i
$145$	−3.12759	+	1.80572i	−0.259732	+	0.149957i
$146$	−4.62497	+	8.01069i	−0.382766	+	0.662969i
$147$	−11.4190	−	4.07512i	−0.941823	−	0.336110i
$148$	−7.77313			−0.638948
$149$		−	0.506197i		−	0.0414693i	−0.999785	−	0.0207346i	$-0.993399\pi$
$149$		−	0.506197i		−	0.0414693i	0.999785	−	0.0207346i	$-0.00660052\pi$
$150$	−0.167225	−	8.12355i	−0.0136539	−	0.663285i
$151$	10.6608	+	18.4650i	0.867561	+	1.50266i	0.864481	+	0.502665i	$0.167647\pi$
$151$	10.6608	+	18.4650i	0.867561	+	1.50266i	0.00307963	+	0.999995i	$0.499020\pi$
$152$	−5.48202			−0.444651
$153$	−6.25351	−	9.86973i	−0.505567	−	0.797921i
$154$	−6.20422	+	7.28744i	−0.499950	+	0.587239i
$155$			2.38619i			0.191664i
$156$	−5.85386	−	2.17538i	−0.468684	−	0.174170i
$157$	9.44004	−	5.45021i	0.753397	−	0.434974i	−0.0735227	−	0.997294i	$-0.523424\pi$
$157$	9.44004	−	5.45021i	0.753397	−	0.434974i	0.826920	+	0.562319i	$0.190091\pi$
$158$		−	12.8255i		−	1.02034i
$159$	2.74596	+	1.51090i	0.217769	+	0.119822i
$160$	−0.481304	+	0.277881i	−0.0380504	+	0.0219684i
$161$	15.3556	+	13.0731i	1.21019	+	1.03030i
$162$	8.13789	+	3.84379i	0.639373	+	0.301997i
$163$	23.6900			1.85554			0.927770	−	0.373152i	$-0.121723\pi$
$163$	23.6900			1.85554			0.927770	+	0.373152i	$0.121723\pi$
$164$	1.45390	+	2.51823i	0.113530	+	0.196640i
$165$	−0.0716654	−	3.48140i	−0.00557915	−	0.271027i
$166$	0.151825	−	0.0876565i	0.0117839	−	0.00680346i
$167$	−5.41827	+	9.38472i	−0.419278	+	0.726211i	−0.995867	−	0.0908233i	$-0.971050\pi$
$167$	−5.41827	+	9.38472i	−0.419278	+	0.726211i	0.576589	+	0.817034i	$0.304383\pi$
$168$	3.54970	+	2.89821i	0.273866	+	0.223601i
$169$	9.48743	+	8.88755i	0.729803	+	0.683658i
$170$	1.87453	+	1.08226i	0.143770	+	0.0830057i
$171$	−14.5690	−	7.62993i	−1.11412	−	0.583476i
$172$	0.350686			0.0267396
$173$	−9.63552			−0.732575			−0.366287	−	0.930502i	$-0.619371\pi$
$173$	−9.63552			−0.732575			−0.366287	+	0.930502i	$0.619371\pi$
$174$	−5.82700	−	9.62937i	−0.441744	−	0.730001i
$175$	8.04578	−	9.45052i	0.608203	−	0.714392i
$176$	3.13276	−	1.80870i	0.236141	−	0.136336i
$177$	−2.41439	+	0.0497008i	−0.181477	+	0.00373574i
$178$	6.80894	+	3.93114i	0.510352	+	0.294652i
$179$			18.7722i			1.40310i	0.712619	+	0.701552i	$0.247509\pi$
$179$			18.7722i			1.40310i	−0.712619	+	0.701552i	$0.752491\pi$
$180$	−1.66587	+	0.0686138i	−0.124167	+	0.00511417i
$181$		−	1.79237i		−	0.133226i	−0.997779	−	0.0666129i	$-0.978781\pi$
$181$		−	1.79237i		−	0.133226i	0.997779	−	0.0666129i	$-0.0212193\pi$
$182$	−4.48218	−	8.42081i	−0.332242	−	0.624192i
$183$	−0.858604	+	0.519565i	−0.0634698	+	0.0384073i
$184$	−3.81117	−	6.60113i	−0.280963	−	0.486642i
$185$	4.32001			0.317613
$186$	−7.43508	+	0.153053i	−0.545167	+	0.0112224i
$187$	−12.2012	−	7.04434i	−0.892237	−	0.515134i
$188$	−6.28286	−	10.8822i	−0.458224	−	0.793668i
$189$	5.39996	+	12.6428i	0.392789	+	0.919628i
$190$	3.04670			0.221031
$191$			0.303911i			0.0219902i	0.999940	+	0.0109951i	$0.00349992\pi$
$191$			0.303911i			0.0219902i	−0.999940	+	0.0109951i	$0.996500\pi$
$192$	−0.896713	−	1.48186i	−0.0647147	−	0.106944i
$193$	11.7410			0.845137			0.422568	−	0.906331i	$-0.361129\pi$
$193$	11.7410			0.845137			0.422568	+	0.906331i	$0.361129\pi$
$194$	−1.59366	+	2.76030i	−0.114418	+	0.198178i
$195$	3.25335	+	1.20899i	0.232977	+	0.0865778i
$196$	1.11684	+	6.91033i	0.0797739	+	0.493595i
$197$	−12.6942	−	7.32902i	−0.904427	−	0.522171i	−0.0257931	−	0.999667i	$-0.508211\pi$
$197$	−12.6942	−	7.32902i	−0.904427	−	0.522171i	−0.878634	+	0.477496i	$0.841544\pi$
$198$	10.8430	−	0.446601i	0.770579	−	0.0317386i
$199$	−11.6741	−	6.74005i	−0.827556	−	0.477790i	0.0254591	−	0.999676i	$-0.491895\pi$
$199$	−11.6741	−	6.74005i	−0.827556	−	0.477790i	−0.853015	+	0.521886i	$0.825229\pi$
$200$	−4.06264	+	2.34556i	−0.287272	+	0.165856i
$201$	7.07702	+	11.6951i	0.499175	+	0.824909i
$202$	−13.4053	+	7.73954i	−0.943192	+	0.544552i
$203$	3.10644	−	16.9096i	0.218029	−	1.18682i
$204$	−3.25196	+	5.91023i	−0.227683	+	0.413799i
$205$	−0.808021	−	1.39953i	−0.0564346	−	0.0977476i
$206$	−19.1320			−1.33299
$207$	−0.941046	−	22.8476i	−0.0654073	−	1.58802i
$208$	0.528884	+	3.56655i	0.0366715	+	0.247296i
$209$	−19.8307			−1.37172
$210$	−1.97279	−	1.61071i	−0.136135	−	0.111150i
$211$	−0.786213	+	1.36176i	−0.0541251	+	0.0937474i	−0.891819	−	0.452393i	$-0.850570\pi$
$211$	−0.786213	+	1.36176i	−0.0541251	+	0.0937474i	0.837693	+	0.546141i	$0.183904\pi$
$212$		−	1.80952i		−	0.124279i
$213$	−17.3702	−	9.55753i	−1.19019	−	0.654871i
$214$	−0.828270	+	1.43461i	−0.0566194	+	0.0980676i
$215$	−0.194898			−0.0132919
$216$	−0.320643	−	5.18625i	−0.0218170	−	0.352880i
$217$	−8.64959	−	7.36390i	−0.587173	−	0.499894i
$218$	16.7245	+	9.65592i	1.13273	+	0.653981i
$219$	14.0369	+	7.72344i	0.948523	+	0.521901i
$220$	−1.74107	+	1.00521i	−0.117383	+	0.0677710i
$221$	10.9997	−	8.72919i	0.739922	−	0.587189i
$222$	0.277090	+	13.4606i	0.0185971	+	0.903417i
$223$	−0.686501	−	0.396352i	−0.0459715	−	0.0265417i	0.476838	−	0.878991i	$-0.341783\pi$
$223$	−0.686501	−	0.396352i	−0.0459715	−	0.0265417i	−0.522810	+	0.852449i	$0.675116\pi$
$224$	0.478048	−	2.60220i	0.0319409	−	0.173867i
$225$	−14.0615	+	0.579163i	−0.937431	+	0.0386108i
$226$	−0.848506	+	1.46966i	−0.0564418	+	0.0977600i
$227$	−6.07037	+	10.5142i	−0.402905	+	0.697851i	−0.994075	−	0.108695i	$-0.965333\pi$
$227$	−6.07037	+	10.5142i	−0.402905	+	0.697851i	0.591170	+	0.806547i	$0.298666\pi$
$228$	0.195418	+	9.49313i	0.0129419	+	0.628698i
$229$	−14.6485	−	8.45733i	−0.968002	−	0.558876i	−0.0693752	−	0.997591i	$-0.522101\pi$
$229$	−14.6485	−	8.45733i	−0.968002	−	0.558876i	−0.898626	+	0.438715i	$0.855434\pi$
$230$	2.11810	+	3.66865i	0.139663	+	0.241904i
$231$	12.8407	+	10.4840i	0.844857	+	0.689795i
$232$	−3.24909	+	5.62758i	−0.213313	+	0.369469i
$233$	−10.0101	−	5.77933i	−0.655783	−	0.378617i	0.134885	−	0.990861i	$-0.456933\pi$
$233$	−10.0101	−	5.77933i	−0.655783	−	0.378617i	−0.790668	+	0.612245i	$0.790267\pi$
$234$	−3.55840	+	10.2146i	−0.232620	+	0.667748i
$235$	3.49177	+	6.04792i	0.227778	+	0.394523i
$236$	0.697122	+	1.20745i	0.0453788	+	0.0785984i
$237$	−22.2097	+	0.457191i	−1.44267	+	0.0296978i
$238$	−9.70792	+	3.45499i	−0.629271	+	0.223954i
$239$			28.9533i			1.87283i	0.350893	+	0.936415i	$0.385878\pi$
$239$			28.9533i			1.87283i	−0.350893	+	0.936415i	$0.614122\pi$
$240$	0.498359	+	0.823560i	0.0321689	+	0.0531606i
$241$	5.42282	+	3.13087i	0.349314	+	0.201677i	0.664383	−	0.747392i	$-0.268694\pi$
$241$	5.42282	+	3.13087i	0.349314	+	0.201677i	−0.315069	+	0.949069i	$0.602028\pi$
$242$	1.80618	−	1.04280i	0.116106	−	0.0670336i
$243$	6.36613	−	14.2293i	0.408388	−	0.912809i
$244$	0.501784	+	0.289705i	0.0321234	+	0.0185465i
$245$	−0.620694	−	3.84050i	−0.0396547	−	0.245360i
$246$	4.30894	−	2.60746i	0.274728	−	0.166246i
$247$	7.26504	−	18.3821i	0.462263	−	1.16963i
$248$	2.14678	+	3.71833i	0.136321	+	0.236114i
$249$	−0.157205	−	0.259789i	−0.00996249	−	0.0164635i
$250$	4.66437	−	2.69298i	0.295001	−	0.170319i
$251$	−4.51440	−	7.81917i	−0.284946	−	0.493542i	0.687650	−	0.726043i	$-0.258642\pi$
$251$	−4.51440	−	7.81917i	−0.284946	−	0.493542i	−0.972596	+	0.232501i	$0.925309\pi$
$252$	4.89224	−	6.25028i	0.308182	−	0.393731i
$253$	−13.7865	−	23.8790i	−0.866751	−	1.50126i
$254$		−	11.9684i		−	0.750963i
$255$	1.80731	−	3.28468i	0.113178	−	0.205694i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.17253	−	15.8873i	−0.572166	−	0.991021i	−0.996343	−	0.0854419i	$-0.972770\pi$
$257$	−9.17253	−	15.8873i	−0.572166	−	0.991021i	0.424177	−	0.905579i	$-0.360564\pi$
$258$	−0.0125010	−	0.607278i	−0.000778276	−	0.0378075i
$259$	−13.3317	+	15.6594i	−0.828394	+	0.973026i
$260$	−0.293933	−	1.98215i	−0.0182290	−	0.122928i
$261$	−16.4673	+	10.4338i	−1.01930	+	0.645835i
$262$			6.82135i			0.421424i
$263$			20.4487i			1.26092i	0.776222	+	0.630459i	$0.217133\pi$
$263$			20.4487i			1.26092i	−0.776222	+	0.630459i	$0.782867\pi$
$264$	−3.24377	−	5.36048i	−0.199640	−	0.329915i
$265$			1.00566i			0.0617774i
$266$	−9.40224	+	11.0438i	−0.576488	+	0.677140i
$267$	6.56478	−	11.9311i	0.401758	−	0.730169i
$268$	3.94609	−	6.83483i	0.241046	−	0.417504i
$269$	13.5740	−	23.5109i	0.827623	−	1.43348i	−0.0722757	−	0.997385i	$-0.523026\pi$
$269$	13.5740	−	23.5109i	0.827623	−	1.43348i	0.899898	−	0.436100i	$-0.143641\pi$
$270$	0.178201	+	2.88232i	0.0108450	+	0.175412i
$271$	−9.23798	+	5.33355i	−0.561167	+	0.323990i	−0.753614	−	0.657317i	$-0.771691\pi$
$271$	−9.23798	+	5.33355i	−0.561167	+	0.323990i	0.192447	+	0.981307i	$0.438358\pi$
$272$	3.89470			0.236151
$273$	−14.4224	+	8.06190i	−0.872884	+	0.487929i
$274$	−6.85540			−0.414150
$275$	−14.6962	+	8.48485i	−0.886214	+	0.511656i
$276$	−11.2952	+	6.83505i	−0.679892	+	0.411421i
$277$	−9.52004	+	16.4892i	−0.572004	+	0.990740i	0.424356	+	0.905495i	$0.360501\pi$
$277$	−9.52004	+	16.4892i	−0.572004	+	0.990740i	−0.996360	+	0.0852446i	$0.972833\pi$
$278$	−0.553223	+	0.958211i	−0.0331801	+	0.0574697i
$279$	0.530079	+	12.8698i	0.0317350	+	0.770492i
$280$	−0.265681	+	1.44621i	−0.0158775	+	0.0864273i
$281$		−	3.32671i		−	0.198455i	−0.995065	−	0.0992275i	$-0.968363\pi$
$281$		−	3.32671i		−	0.198455i	0.995065	−	0.0992275i	$-0.0316372\pi$
$282$	−18.6206	+	11.2678i	−1.10884	+	0.670990i
$283$			18.6287i			1.10736i	0.832728	+	0.553682i	$0.186778\pi$
$283$			18.6287i			1.10736i	−0.832728	+	0.553682i	$0.813222\pi$
$284$			11.4465i			0.679228i
$285$	−0.108606	−	5.27591i	−0.00643326	−	0.312518i
$286$	1.91319	+	12.9016i	0.113129	+	0.762890i
$287$	7.56668	+	1.39007i	0.446647	+	0.0820530i
$288$	−2.53415	+	1.60565i	−0.149326	+	0.0946137i
$289$	0.915663	+	1.58597i	0.0538625	+	0.0932926i
$290$	1.80572	−	3.12759i	0.106035	−	0.183659i
$291$	4.83677	+	2.66132i	0.283537	+	0.156009i
$292$		−	9.24995i		−	0.541312i
$293$	11.9791	+	20.7484i	0.699826	+	1.21213i	0.968527	+	0.248910i	$0.0800723\pi$
$293$	11.9791	+	20.7484i	0.699826	+	1.21213i	−0.268701	+	0.963224i	$0.586594\pi$
$294$	11.9267	−	2.18034i	0.695579	−	0.127160i
$295$	−0.387434	−	0.671055i	−0.0225573	−	0.0390703i
$296$	6.73173	−	3.88657i	0.391274	−	0.225902i
$297$	−1.15989	−	18.7608i	−0.0673039	−	1.08861i
$298$	0.253099	+	0.438380i	0.0146616	+	0.0253947i
$299$	27.1854	−	4.03133i	1.57217	−	0.233138i
$300$	4.20660	+	6.95159i	0.242868	+	0.401350i
$301$	0.601463	−	0.706475i	0.0346678	−	0.0407206i
$302$	−18.4650	−	10.6608i	−1.06254	−	0.613458i
$303$	13.8803	+	22.9378i	0.797402	+	1.31774i
$304$	4.74757	−	2.74101i	0.272292	−	0.157208i
$305$	−0.278872	−	0.161007i	−0.0159682	−	0.00921923i
$306$	10.3506	+	5.42068i	0.591703	+	0.309880i
$307$		−	9.95255i		−	0.568022i	−0.958821	−	0.284011i	$-0.908335\pi$
$307$		−	9.95255i		−	0.568022i	0.958821	−	0.284011i	$-0.0916652\pi$
$308$	1.72929	−	9.41322i	0.0985356	−	0.536368i
$309$	0.681999	+	33.1305i	0.0387976	+	1.88473i
$310$	−1.19310	−	2.06650i	−0.0677633	−	0.117370i
$311$	7.68799	+	13.3160i	0.435946	+	0.755081i	0.997372	−	0.0724462i	$-0.0230805\pi$
$311$	7.68799	+	13.3160i	0.435946	+	0.755081i	−0.561426	+	0.827527i	$0.689747\pi$
$312$	6.15728	−	1.04300i	0.348588	−	0.0590481i
$313$	−11.7829	−	6.80287i	−0.666010	−	0.384521i	0.128553	−	0.991703i	$-0.458967\pi$
$313$	−11.7829	−	6.80287i	−0.666010	−	0.384521i	−0.794563	+	0.607181i	$0.792300\pi$
$314$	−5.45021	+	9.44004i	−0.307573	+	0.532732i
$315$	−2.71892	+	3.47366i	−0.153194	+	0.195719i
$316$	6.41273	+	11.1072i	0.360744	+	0.624828i
$317$	−10.4205	−	6.01626i	−0.585272	−	0.337907i	0.177954	−	0.984039i	$-0.443052\pi$
$317$	−10.4205	−	6.01626i	−0.585272	−	0.337907i	−0.763226	+	0.646132i	$0.776386\pi$
$318$	−3.13352	+	0.0645043i	−0.175719	+	0.00361722i
$319$	−11.7532	+	20.3572i	−0.658056	+	1.13979i
$320$	0.277881	−	0.481304i	0.0155340	−	0.0269057i
$321$	2.51381	+	1.38316i	0.140307	+	0.0772006i
$322$	−19.8349	−	3.64384i	−1.10535	−	0.203063i
$323$	−18.4903	−	10.6754i	−1.02883	−	0.593996i
$324$	−8.96952	+	0.740127i	−0.498306	+	0.0411182i
$325$	−2.48106	−	16.7311i	−0.137625	−	0.928077i
$326$	−20.5161	+	11.8450i	−1.13628	+	0.656033i
$327$	16.1248	−	29.3058i	0.891704	−	1.62062i
$328$	−2.51823	−	1.45390i	−0.139046	−	0.0802781i
$329$	−32.6986	−	6.00701i	−1.80273	−	0.331177i
$330$	1.80276	+	2.97915i	0.0992389	+	0.163997i
$331$	17.3739			0.954958			0.477479	−	0.878643i	$-0.341551\pi$
$331$	17.3739			0.954958			0.477479	+	0.878643i	$0.341551\pi$
$332$	−0.0876565	+	0.151825i	−0.00481077	+	0.00833250i
$333$	23.2996	−	0.959664i	1.27681	−	0.0525893i
$334$		−	10.8365i		−	0.592949i
$335$	−2.19308	+	3.79853i	−0.119821	+	0.207536i
$336$	−4.52324	−	0.735067i	−0.246763	−	0.0401012i
$337$	11.9191			0.649274			0.324637	−	0.945839i	$-0.394758\pi$
$337$	11.9191			0.649274			0.324637	+	0.945839i	$0.394758\pi$
$338$	−12.6601	−	2.95313i	−0.688621	−	0.160629i
$339$	2.57523	+	1.41696i	0.139867	+	0.0769584i
$340$	−2.16452			−0.117388
$341$	7.76576	+	13.4507i	0.420540	+	0.728396i
$342$	16.4321	−	0.676805i	0.888548	−	0.0365974i
$343$	15.8367	+	9.60202i	0.855102	+	0.518460i
$344$	−0.303703	+	0.175343i	−0.0163746	+	0.00945387i
$345$	6.27745	−	3.79865i	0.337966	−	0.204513i
$346$	8.34460	−	4.81776i	0.448609	−	0.259004i
$347$	−14.8209	−	8.55683i	−0.795626	−	0.459355i	0.0463133	−	0.998927i	$-0.485253\pi$
$347$	−14.8209	−	8.55683i	−0.795626	−	0.459355i	−0.841939	+	0.539572i	$0.818586\pi$
$348$	9.86101	+	5.42578i	0.528606	+	0.290852i
$349$	−0.660860	−	0.381547i	−0.0353750	−	0.0204238i	0.482208	−	0.876057i	$-0.339835\pi$
$349$	−0.660860	−	0.381547i	−0.0353750	−	0.0204238i	−0.517583	+	0.855633i	$0.673168\pi$
$350$	−2.24259	+	12.2073i	−0.119871	+	0.652507i
$351$	17.8153	+	5.79790i	0.950910	+	0.309469i
$352$	−1.80870	+	3.13276i	−0.0964041	+	0.166977i
$353$	9.11766			0.485284			0.242642	−	0.970116i	$-0.421986\pi$
$353$	9.11766			0.485284			0.242642	+	0.970116i	$0.421986\pi$
$354$	2.06607	−	1.25024i	0.109811	−	0.0664494i
$355$		−	6.36155i		−	0.337636i
$356$	−7.86229			−0.416700
$357$	6.32901	+	16.6879i	0.334967	+	0.883217i
$358$	−9.38612	−	16.2572i	−0.496072	−	0.859222i
$359$	−8.53982	−	4.93047i	−0.450715	−	0.260220i	0.257417	−	0.966300i	$-0.417128\pi$
$359$	−8.53982	−	4.93047i	−0.450715	−	0.260220i	−0.708132	+	0.706080i	$0.750462\pi$
$360$	1.40838	−	0.892357i	0.0742282	−	0.0470314i
$361$	−11.0525			−0.581713
$362$	0.896185	+	1.55224i	0.0471024	+	0.0815838i
$363$	−1.87018	−	3.09056i	−0.0981591	−	0.162212i
$364$	8.09209	+	5.05154i	0.424141	+	0.264773i
$365$			5.14076i			0.269080i
$366$	0.483791	−	0.879258i	0.0252881	−	0.0459596i
$367$		−	22.6445i		−	1.18203i	−0.806660	−	0.591016i	$-0.798727\pi$
$367$		−	22.6445i		−	1.18203i	0.806660	−	0.591016i	$-0.201273\pi$
$368$	6.60113	+	3.81117i	0.344108	+	0.198671i
$369$	−4.66890	−	7.36878i	−0.243053	−	0.383603i
$370$	−3.74124	+	2.16000i	−0.194498	+	0.112293i
$371$	−3.64538	−	3.10352i	−0.189259	−	0.161127i
$372$	6.36245	−	3.85009i	0.329877	−	0.199618i
$373$	−2.65410			−0.137424			−0.0687121	−	0.997637i	$-0.521889\pi$
$373$	−2.65410			−0.137424			−0.0687121	+	0.997637i	$0.521889\pi$
$374$	14.0887			0.728509
$375$	−4.82966	−	7.98123i	−0.249402	−	0.412149i
$376$	10.8822	+	6.28286i	0.561208	+	0.324014i
$377$	−14.5644	−	18.3527i	−0.750103	−	0.945210i
$378$	−10.9979	−	8.24901i	−0.565671	−	0.424283i
$379$	4.91414	−	8.51153i	0.252422	−	0.437208i	−0.711770	−	0.702413i	$-0.752106\pi$
$379$	4.91414	−	8.51153i	0.252422	−	0.437208i	0.964192	+	0.265205i	$0.0854395\pi$
$380$	−2.63852	+	1.52335i	−0.135353	+	0.0781461i
$381$	−20.7254	+	0.426638i	−1.06180	+	0.0218573i
$382$	−0.151955	−	0.263194i	−0.00777471	−	0.0134662i
$383$	−36.2432			−1.85194			−0.925970	−	0.377596i	$-0.876751\pi$
$383$	−36.2432			−1.85194			−0.925970	+	0.377596i	$0.876751\pi$
$384$	1.51751	+	0.834971i	0.0774399	+	0.0426094i
$385$	−0.961074	+	5.23151i	−0.0489809	+	0.266622i
$386$	−10.1680	+	5.87051i	−0.517538	+	0.298801i
$387$	−1.05117	+	0.0432954i	−0.0534338	+	0.00220083i
$388$		−	3.18732i		−	0.161812i
$389$	−11.4567	+	6.61455i	−0.580880	+	0.335371i	−0.761483	−	0.648185i	$-0.775528\pi$
$389$	−11.4567	+	6.61455i	−0.580880	+	0.335371i	0.180603	+	0.983556i	$0.442195\pi$
$390$	−3.42198	+	0.579657i	−0.173279	+	0.0293521i
$391$		−	29.6867i		−	1.50132i
$392$	−4.42237	−	5.42611i	−0.223364	−	0.274060i
$393$	11.8124	−	0.243161i	0.595858	−	0.0122659i
$394$	14.6580			0.738461
$395$	−3.56395	−	6.17294i	−0.179322	−	0.310594i
$396$	−9.16702	+	5.80827i	−0.460660	+	0.291877i
$397$		−	1.74991i		−	0.0878256i	−0.999035	−	0.0439128i	$-0.986018\pi$
$397$		−	1.74991i		−	0.0878256i	0.999035	−	0.0439128i	$-0.0139824\pi$
$398$	13.4801			0.675697
$399$	19.4596	+	15.8880i	0.974196	+	0.795396i
$400$	2.34556	−	4.06264i	0.117278	−	0.203132i
$401$	−8.88833	+	5.13168i	−0.443862	+	0.256264i	−0.705234	−	0.708974i	$-0.749158\pi$
$401$	−8.88833	+	5.13168i	−0.443862	+	0.256264i	0.261372	+	0.965238i	$0.415825\pi$
$402$	−11.9764	−	6.58974i	−0.597330	−	0.328666i
$403$	−15.3132	+	2.27079i	−0.762804	+	0.113116i
$404$	7.73954	−	13.4053i	0.385056	−	0.666937i
$405$	4.98491	−	0.411334i	0.247702	−	0.0204394i
$406$	5.76453	+	16.1973i	0.286089	+	0.803860i
$407$	24.3514	−	14.0593i	1.20705	−	0.696892i
$408$	−0.138835	−	6.74439i	−0.00687335	−	0.333897i
$409$	−12.6206	−	7.28652i	−0.624050	−	0.360295i	0.154394	−	0.988009i	$-0.450657\pi$
$409$	−12.6206	−	7.28652i	−0.624050	−	0.360295i	−0.778444	+	0.627714i	$0.783991\pi$
$410$	1.39953	+	0.808021i	0.0691180	+	0.0399053i
$411$	0.244375	+	11.8714i	0.0120541	+	0.585572i
$412$	16.5688	−	9.56598i	0.816284	−	0.471282i
$413$	3.62811	+	0.666516i	0.178528	+	0.0327971i
$414$	12.2388	+	19.3161i	0.601503	+	0.949334i
$415$	0.0487161	−	0.0843787i	0.00239138	−	0.00414199i
$416$	−2.24130	−	2.82428i	−0.109889	−	0.138472i
$417$	1.67904	+	0.923851i	0.0822229	+	0.0452412i
$418$	17.1739	−	9.91534i	0.840001	−	0.484975i
$419$	17.3685	−	30.0831i	0.848505	−	1.46965i	−0.0340367	−	0.999421i	$-0.510836\pi$
$419$	17.3685	−	30.0831i	0.848505	−	1.46965i	0.882542	−	0.470234i	$-0.155830\pi$
$420$	2.51384	+	0.408522i	0.122663	+	0.0199338i
$421$	31.5971			1.53995			0.769973	−	0.638076i	$-0.220269\pi$
$421$	31.5971			1.53995			0.769973	+	0.638076i	$0.220269\pi$
$422$		−	1.57243i		−	0.0765445i
$423$	20.1761	+	31.8433i	0.980996	+	1.54828i
$424$	0.904762	+	1.56709i	0.0439391	+	0.0761048i
$425$	−18.2705			−0.886251
$426$	19.8218	−	0.408037i	0.960370	−	0.0197694i
$427$	1.44424	−	0.513995i	0.0698916	−	0.0248740i
$428$		−	1.65654i		−	0.0800719i
$429$	22.2734	−	3.77294i	1.07537	−	0.182159i
$430$	0.168786	−	0.0974489i	0.00813961	−	0.00469940i
$431$		−	22.9238i		−	1.10420i	−0.833778	−	0.552100i	$-0.813827\pi$
$431$		−	22.9238i		−	1.10420i	0.833778	−	0.552100i	$-0.186173\pi$
$432$	2.87081	+	4.33110i	0.138122	+	0.208380i
$433$	17.3262	−	10.0033i	0.832643	−	0.480727i	−0.0221138	−	0.999755i	$-0.507040\pi$
$433$	17.3262	−	10.0033i	0.832643	−	0.480727i	0.854757	+	0.519029i	$0.173706\pi$
$434$	11.1727	+	2.05253i	0.536307	+	0.0985244i
$435$	−5.48037	−	3.01544i	−0.262764	−	0.144579i
$436$	−19.3118			−0.924869
$437$	−20.8929	−	36.1875i	−0.999442	−	1.73108i
$438$	−16.0180	+	0.329734i	−0.765369	+	0.0157553i
$439$	12.0087	−	6.93320i	0.573142	−	0.330904i	−0.185261	−	0.982689i	$-0.559313\pi$
$439$	12.0087	−	6.93320i	0.573142	−	0.330904i	0.758403	+	0.651786i	$0.225980\pi$
$440$	1.00521	−	1.74107i	0.0479213	−	0.0830022i
$441$	−4.20081	−	20.5755i	−0.200039	−	0.979788i
$442$	−5.16144	+	13.0596i	−0.245505	+	0.621180i
$443$	30.9904	+	17.8923i	1.47240	+	0.850089i	0.999518	−	0.0310388i	$-0.00988154\pi$
$443$	30.9904	+	17.8923i	1.47240	+	0.850089i	0.472879	+	0.881128i	$0.343215\pi$
$444$	−6.97027	−	11.5187i	−0.330795	−	0.546653i
$445$	4.36956			0.207137
$446$	0.792703			0.0375356
$447$	0.750113	−	0.453914i	0.0354791	−	0.0214694i
$448$	0.887101	+	2.49260i	0.0419116	+	0.117764i
$449$	8.26617	−	4.77247i	0.390105	−	0.225227i	−0.292101	−	0.956388i	$-0.594354\pi$
$449$	8.26617	−	4.77247i	0.390105	−	0.225227i	0.682205	+	0.731161i	$0.261021\pi$
$450$	11.8880	−	7.53230i	0.560406	−	0.355076i
$451$	−9.10943	−	5.25933i	−0.428947	−	0.247652i
$452$		−	1.69701i		−	0.0798207i
$453$	−17.8029	+	32.3556i	−0.836451	+	1.52020i
$454$		−	12.1407i		−	0.569793i
$455$	−4.49727	−	2.80745i	−0.210835	−	0.131615i
$456$	−4.91580	−	8.12358i	−0.230203	−	0.380421i
$457$	3.28026	+	5.68157i	0.153444	+	0.265773i	0.932491	−	0.361192i	$-0.117630\pi$
$457$	3.28026	+	5.68157i	0.153444	+	0.265773i	−0.779047	+	0.626965i	$0.784297\pi$
$458$	16.9147			0.790370
$459$	9.01794	−	18.1171i	0.420921	−	0.845636i
$460$	−3.66865	−	2.11810i	−0.171052	−	0.0987569i
$461$	1.37324	+	2.37852i	0.0639581	+	0.110779i	0.896231	−	0.443587i	$-0.146294\pi$
$461$	1.37324	+	2.37852i	0.0639581	+	0.110779i	−0.832273	+	0.554366i	$0.812961\pi$
$462$	−16.3624	−	2.65903i	−0.761246	−	0.123709i
$463$	3.40968			0.158461			0.0792306	−	0.996856i	$-0.474754\pi$
$463$	3.40968			0.158461			0.0792306	+	0.996856i	$0.474754\pi$
$464$		−	6.49817i		−	0.301670i
$465$	−3.53600	+	2.13973i	−0.163978	+	0.0992277i
$466$	11.5587			0.535445
$467$	2.17534	−	3.76781i	0.100663	−	0.174353i	−0.811295	−	0.584637i	$-0.801237\pi$
$467$	2.17534	−	3.76781i	0.100663	−	0.174353i	0.911958	+	0.410284i	$0.134570\pi$
$468$	−2.02563	−	10.6253i	−0.0936348	−	0.491154i
$469$	−7.00116	−	19.6720i	−0.323283	−	0.908371i
$470$	−6.04792	−	3.49177i	−0.278970	−	0.161063i
$471$	16.5415	+	9.10153i	0.762190	+	0.419377i
$472$	−1.20745	−	0.697122i	−0.0555775	−	0.0320877i
$473$	−1.09862	+	0.634286i	−0.0505144	+	0.0291645i
$474$	19.0055	−	11.5008i	0.872953	−	0.528248i
$475$	−22.2715	+	12.8584i	−1.02188	+	0.589985i
$476$	6.67981	−	7.84607i	0.306169	−	0.359624i
$477$	0.223402	+	5.42397i	0.0102289	+	0.248347i
$478$	−14.4766	−	25.0743i	−0.662146	−	1.14687i
$479$	38.5085			1.75950			0.879748	−	0.475440i	$-0.157711\pi$
$479$	38.5085			1.75950			0.879748	+	0.475440i	$0.157711\pi$
$480$	−0.843371	−	0.464044i	−0.0384945	−	0.0211806i
$481$	4.11108	+	27.7233i	0.187449	+	1.26407i
$482$	−6.26173			−0.285214
$483$	−5.60293	+	34.4776i	−0.254942	+	1.56879i
$484$	−1.04280	+	1.80618i	−0.0473999	+	0.0820991i
$485$			1.77139i			0.0804346i
$486$	1.60140	+	15.5060i	0.0726412	+	0.703366i
$487$	−4.44243	+	7.69451i	−0.201306	+	0.348672i	−0.948949	−	0.315428i	$-0.897852\pi$
$487$	−4.44243	+	7.69451i	−0.201306	+	0.348672i	0.747644	+	0.664100i	$0.231185\pi$
$488$	−0.579410			−0.0262287
$489$	21.2431	+	35.1052i	0.960646	+	1.58751i
$490$	2.45778	+	3.01562i	0.111031	+	0.136232i
$491$	−9.49716	−	5.48319i	−0.428601	−	0.247453i	0.270149	−	0.962818i	$-0.412927\pi$
$491$	−9.49716	−	5.48319i	−0.428601	−	0.247453i	−0.698750	+	0.715366i	$0.746260\pi$
$492$	−2.42792	+	4.41260i	−0.109459	+	0.198935i
$493$	−21.9177	+	12.6542i	−0.987125	+	0.569917i
$494$	2.89935	+	19.5519i	0.130448	+	0.879682i
$495$	5.09468	−	3.22801i	0.228989	−	0.145088i
$496$	−3.71833	−	2.14678i	−0.166958	−	0.0963932i
$497$	23.0597	+	19.6320i	1.03437	+	0.880617i
$498$	0.266038	+	0.146381i	0.0119215	+	0.00655950i
$499$	−12.9437	+	22.4192i	−0.579441	+	1.00362i	0.416102	+	0.909318i	$0.363396\pi$
$499$	−12.9437	+	22.4192i	−0.579441	+	1.00362i	−0.995543	+	0.0943038i	$0.969938\pi$
$500$	−2.69298	+	4.66437i	−0.120434	+	0.208597i
$501$	−18.7655	+	0.386291i	−0.838379	+	0.0172582i
$502$	7.81917	+	4.51440i	0.348987	+	0.201488i
$503$	6.97090	+	12.0739i	0.310817	+	0.538351i	0.978539	−	0.206060i	$-0.0660641\pi$
$503$	6.97090	+	12.0739i	0.310817	+	0.538351i	−0.667723	+	0.744410i	$0.732731\pi$
$504$	−1.11166	+	7.85902i	−0.0495174	+	0.350069i
$505$	−4.30134	+	7.45013i	−0.191407	+	0.331527i
$506$	23.8790	+	13.7865i	1.06155	+	0.612886i
$507$	−4.66259	+	22.0286i	−0.207073	+	0.978325i
$508$	5.98419	+	10.3649i	0.265505	+	0.459869i
$509$	−7.30056	−	12.6449i	−0.323592	−	0.560477i	0.657635	−	0.753337i	$-0.271557\pi$
$509$	−7.30056	−	12.6449i	−0.323592	−	0.560477i	−0.981226	+	0.192860i	$0.938224\pi$
$510$	0.0771590	+	3.74827i	0.00341666	+	0.165976i
$511$	−18.6345	−	15.8646i	−0.824342	−	0.701810i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.75777	−	28.4311i	−0.0776075	−	1.25526i
$514$	15.8873	+	9.17253i	0.700758	+	0.404583i
$515$	−9.20828	+	5.31640i	−0.405765	+	0.234269i
$516$	0.314465	+	0.519667i	0.0138435	+	0.0228771i
$517$	39.3654	+	22.7276i	1.73129	+	0.999559i
$518$	3.71593	−	20.2273i	0.163269	−	0.888736i
$519$	−8.64030	−	14.2785i	−0.379267	−	0.626755i
$520$	1.24563	+	1.56963i	0.0546245	+	0.0688327i
$521$	17.7206	+	30.6930i	0.776355	+	1.34469i	0.934030	+	0.357196i	$0.116267\pi$
$521$	17.7206	+	30.6930i	0.776355	+	1.34469i	−0.157674	+	0.987491i	$0.550400\pi$
$522$	9.04422	−	17.2696i	0.395855	−	0.755869i
$523$	−15.5606	+	8.98390i	−0.680417	+	0.392839i	−0.800012	−	0.599984i	$-0.795174\pi$
$523$	−15.5606	+	8.98390i	−0.680417	+	0.392839i	0.119595	+	0.992823i	$0.461840\pi$
$524$	−3.41067	−	5.90746i	−0.148996	−	0.258069i
$525$	21.2191	+	3.44829i	0.926077	+	0.150496i
$526$	−10.2243	−	17.7091i	−0.445802	−	0.772152i
$527$			16.7221i			0.728427i
$528$	5.48943	+	3.02042i	0.238897	+	0.131447i
$529$	17.5500	−	30.3974i	0.763042	−	1.32163i
$530$	−0.502832	−	0.870930i	−0.0218416	−	0.0378308i
$531$	−2.23867	−	3.53322i	−0.0971499	−	0.153329i
$532$	2.62067	−	14.2653i	0.113620	−	0.618481i
$533$	8.21244	−	6.51725i	0.355720	−	0.282293i
$534$	0.280268	+	13.6150i	0.0121284	+	0.589178i
$535$			0.920641i			0.0398028i
$536$			7.89218i			0.340890i
$537$	−27.8178	+	16.8333i	−1.20043	+	0.726411i
$538$			27.1480i			1.17044i
$539$	−15.9975	−	19.6284i	−0.689061	−	0.845455i
$540$	−1.59549	−	2.40706i	−0.0686588	−	0.103583i
$541$	−5.65426	+	9.79347i	−0.243096	+	0.421054i	−0.961594	−	0.274474i	$-0.911496\pi$
$541$	−5.65426	+	9.79347i	−0.243096	+	0.421054i	0.718499	+	0.695528i	$0.244830\pi$
$542$	5.33355	−	9.23798i	0.229096	−	0.396805i
$543$	2.65604	−	1.60724i	0.113982	−	0.0689733i
$544$	−3.37291	+	1.94735i	−0.144612	+	0.0834919i
$545$	10.7328			0.459741
$546$	8.45921	−	14.1930i	0.362021	−	0.607405i
$547$	−18.1327			−0.775298			−0.387649	−	0.921807i	$-0.626713\pi$
$547$	−18.1327			−0.775298			−0.387649	+	0.921807i	$0.626713\pi$
$548$	5.93695	−	3.42770i	0.253614	−	0.146424i
$549$	−1.53984	−	0.806429i	−0.0657189	−	0.0344176i
$550$	8.48485	−	14.6962i	0.361795	−	0.626648i
$551$	−17.8116	+	30.8505i	−0.758798	+	1.31428i
$552$	6.36442	−	11.5669i	0.270888	−	0.492321i
$553$	33.3745	+	6.13119i	1.41923	+	0.260725i
$554$		−	19.0401i		−	0.808936i
$555$	3.87381	+	6.40164i	0.164434	+	0.271735i
$556$		−	1.10645i		−	0.0469238i
$557$		−	6.59941i		−	0.279626i	−0.990178	−	0.139813i	$-0.955350\pi$
$557$		−	6.59941i		−	0.279626i	0.990178	−	0.139813i	$-0.0446502\pi$
$558$	−6.89394	−	10.8805i	−0.291844	−	0.460608i
$559$	−0.185472	−	1.25074i	−0.00784464	−	0.0529007i
$560$	−0.493016	−	1.38529i	−0.0208337	−	0.0585392i
$561$	−0.502221	−	24.3972i	−0.0212038	−	1.03005i
$562$	1.66336	+	2.88102i	0.0701645	+	0.121528i
$563$	16.4714	−	28.5293i	0.694187	−	1.20237i	−0.276267	−	0.961081i	$-0.589098\pi$
$563$	16.4714	−	28.5293i	0.694187	−	1.20237i	0.970454	−	0.241286i	$-0.0775691\pi$
$564$	10.4920	−	19.0685i	0.441793	−	0.802930i
$565$			0.943134i			0.0396779i
$566$	−9.31437	−	16.1330i	−0.391512	−	0.678119i
$567$	−13.8926	+	19.3389i	−0.583436	+	0.812159i
$568$	−5.72327	−	9.91300i	−0.240143	−	0.415940i
$569$	−3.33368	+	1.92470i	−0.139755	+	0.0806876i	−0.568247	−	0.822858i	$-0.692378\pi$
$569$	−3.33368	+	1.92470i	−0.139755	+	0.0806876i	0.428492	+	0.903545i	$0.359045\pi$
$570$	2.73201	+	4.51477i	0.114431	+	0.189103i
$571$	5.78822	+	10.0255i	0.242229	+	0.419554i	0.961349	−	0.275333i	$-0.0887880\pi$
$571$	5.78822	+	10.0255i	0.242229	+	0.419554i	−0.719120	+	0.694886i	$0.755455\pi$
$572$	−8.10769	−	10.2166i	−0.339000	−	0.427176i
$573$	−0.450353	+	0.272521i	−0.0188138	+	0.0113847i
$574$	−7.24797	+	2.57951i	−0.302525	+	0.107667i
$575$	−30.9668	−	17.8787i	−1.29140	−	0.745592i
$576$	1.39181	−	2.65760i	0.0579921	−	0.110734i
$577$	−11.3976	+	6.58040i	−0.474487	+	0.273945i	−0.718116	−	0.695923i	$-0.754995\pi$
$577$	−11.3976	+	6.58040i	−0.474487	+	0.273945i	0.243629	+	0.969869i	$0.421662\pi$
$578$	−1.58597	−	0.915663i	−0.0659678	−	0.0380865i
$579$	10.5283	+	17.3985i	0.437542	+	0.723058i
$580$			3.61143i			0.149957i
$581$	0.155520	+	0.436985i	0.00645207	+	0.0181292i
$582$	−5.51943	+	0.113619i	−0.228788	+	0.00470965i
$583$	3.27289	+	5.66881i	0.135549	+	0.234778i
$584$	4.62497	+	8.01069i	0.191383	+	0.331485i
$585$	1.12577	+	5.90513i	0.0465447	+	0.244147i
$586$	−20.7484	−	11.9791i	−0.857108	−	0.494851i
$587$	8.67657	−	15.0283i	0.358120	−	0.620283i	−0.629526	−	0.776979i	$-0.716751\pi$
$587$	8.67657	−	15.0283i	0.358120	−	0.620283i	0.987647	+	0.156696i	$0.0500844\pi$
$588$	−9.23865	+	7.85158i	−0.380996	+	0.323794i
$589$	11.7687	+	20.3840i	0.484920	+	0.839906i
$590$	0.671055	+	0.387434i	0.0276269	+	0.0159504i
$591$	−0.522517	−	25.3831i	−0.0214935	−	1.04412i
$592$	−3.88657	+	6.73173i	−0.159737	+	0.276672i
$593$	15.6405	−	27.0901i	0.642278	−	1.11246i	−0.342645	−	0.939465i	$-0.611323\pi$
$593$	15.6405	−	27.0901i	0.642278	−	1.11246i	0.984923	−	0.172994i	$-0.0553440\pi$
$594$	10.3849	+	15.6673i	0.426097	+	0.642839i
$595$	−3.71238	+	4.36054i	−0.152193	+	0.178765i
$596$	−0.438380	−	0.253099i	−0.0179567	−	0.0103673i
$597$	−0.480527	−	23.3433i	−0.0196667	−	0.955377i
$598$	−21.5276	+	17.0839i	−0.880329	+	0.698615i
$599$	−8.02273	+	4.63192i	−0.327800	+	0.189255i	−0.654864	−	0.755747i	$-0.727274\pi$
$599$	−8.02273	+	4.63192i	−0.327800	+	0.189255i	0.327064	+	0.945002i	$0.393941\pi$
$600$	−7.11882	−	3.91696i	−0.290624	−	0.159909i
$601$	−9.30956	−	5.37488i	−0.379745	−	0.219246i	0.297962	−	0.954578i	$-0.403693\pi$
$601$	−9.30956	−	5.37488i	−0.379745	−	0.219246i	−0.677707	+	0.735332i	$0.737026\pi$
$602$	−0.167645	+	0.912557i	−0.00683269	+	0.0371931i
$603$	−10.9844	+	20.9743i	−0.447320	+	0.854139i
$604$	21.3215			0.867561
$605$	0.579547	−	1.00381i	0.0235619	−	0.0408105i
$606$	−23.4896	−	12.9246i	−0.954199	−	0.525025i
$607$			15.9971i			0.649302i	0.945834	+	0.324651i	$0.105247\pi$
$607$			15.9971i			0.649302i	−0.945834	+	0.324651i	$0.894753\pi$
$608$	−2.74101	+	4.74757i	−0.111163	+	0.192539i
$609$	27.8432	−	10.5597i	1.12826	−	0.427902i
$610$	0.322014			0.0130380
$611$	−35.4891	+	28.1636i	−1.43574	+	1.13938i
$612$	−11.6742	+	0.480836i	−0.471901	+	0.0194366i
$613$	−14.5909			−0.589321			−0.294661	−	0.955602i	$-0.595207\pi$
$613$	−14.5909			−0.589321			−0.294661	+	0.955602i	$0.595207\pi$
$614$	4.97628	+	8.61916i	0.200826	+	0.347841i
$615$	1.34935	−	2.45235i	0.0544109	−	0.0988884i
$616$	3.20900	+	9.01673i	0.129294	+	0.363295i
$617$	−20.8367	+	12.0301i	−0.838853	+	0.484312i	−0.856874	−	0.515525i	$-0.827597\pi$
$617$	−20.8367	+	12.0301i	−0.838853	+	0.484312i	0.0180211	+	0.999838i	$0.494263\pi$
$618$	−17.1559	−	28.3509i	−0.690111	−	1.14044i
$619$	−11.1088	+	6.41367i	−0.446500	+	0.257787i	−0.706351	−	0.707862i	$-0.749660\pi$
$619$	−11.1088	+	6.41367i	−0.446500	+	0.257787i	0.259851	+	0.965649i	$0.416327\pi$
$620$	2.06650	+	1.19310i	0.0829928	+	0.0479159i
$621$	33.0131	−	21.8823i	1.32477	−	0.878105i
$622$	−13.3160	−	7.68799i	−0.533923	−	0.308260i
$623$	−13.4846	+	15.8390i	−0.540251	+	0.634575i
$624$	−4.81087	+	3.98190i	−0.192589	+	0.159404i
$625$	−10.2312	+	17.7209i	−0.409247	+	0.708836i
$626$	13.6057			0.543795
$627$	−17.7824	−	29.3863i	−0.710162	−	1.17357i
$628$		−	10.9004i		−	0.434974i
$629$	30.2740			1.20710
$630$	0.617820	−	4.36774i	0.0246145	−	0.174015i
$631$	10.0431	+	17.3952i	0.399810	+	0.692491i	0.993702	−	0.112053i	$-0.0357428\pi$
$631$	10.0431	+	17.3952i	0.399810	+	0.692491i	−0.593892	+	0.804545i	$0.702409\pi$
$632$	−11.1072	−	6.41273i	−0.441820	−	0.255085i
$633$	−2.72294	+	0.0560524i	−0.108227	+	0.00222788i
$634$	12.0325			0.477873
$635$	−3.32578	−	5.76042i	−0.131980	−	0.228595i
$636$	2.68146	−	1.62262i	0.106327	−	0.0643412i
$637$	24.0554	−	7.63801i	0.953108	−	0.302629i
$638$		−	23.5065i		−	0.930631i
$639$	−1.41318	−	34.3106i	−0.0559046	−	1.35730i
$640$			0.555761i			0.0219684i
$641$	34.0138	+	19.6379i	1.34347	+	0.775651i	0.987314	−	0.158778i	$-0.0507553\pi$
$641$	34.0138	+	19.6379i	1.34347	+	0.775651i	0.356152	+	0.934428i	$0.384089\pi$
$642$	−2.86860	+	0.0590509i	−0.113215	+	0.00233055i
$643$	12.0836	−	6.97645i	0.476529	−	0.275124i	−0.242440	−	0.970166i	$-0.577948\pi$
$643$	12.0836	−	6.97645i	0.476529	−	0.275124i	0.718969	+	0.695042i	$0.244614\pi$
$644$	18.9994	−	6.76178i	0.748682	−	0.266451i
$645$	−0.174767	−	0.288811i	−0.00688146	−	0.0113719i
$646$	21.3508			0.840037
$647$	4.16946			0.163918			0.0819591	−	0.996636i	$-0.473882\pi$
$647$	4.16946			0.163918			0.0819591	+	0.996636i	$0.473882\pi$
$648$	7.39776	−	5.12573i	0.290612	−	0.201358i
$649$	−4.36784	−	2.52177i	−0.171453	−	0.0989882i
$650$	10.5142	+	13.2491i	0.412402	+	0.519671i
$651$	3.15605	−	19.4208i	0.123695	−	0.761160i
$652$	11.8450	−	20.5161i	0.463885	−	0.803473i
$653$	25.1589	−	14.5255i	0.984545	−	0.568427i	0.0809055	−	0.996722i	$-0.474219\pi$
$653$	25.1589	−	14.5255i	0.984545	−	0.568427i	0.903639	+	0.428295i	$0.140885\pi$
$654$	0.688411	+	33.4420i	0.0269190	+	1.30769i
$655$	1.89552	+	3.28314i	0.0740641	+	0.128283i
$656$	2.90780			0.113530
$657$	1.14199	+	27.7263i	0.0445533	+	1.08171i
$658$	31.3213	−	11.1470i	1.22103	−	0.434557i
$659$	2.25922	−	1.30436i	0.0880069	−	0.0508108i	−0.455351	−	0.890312i	$-0.650486\pi$
$659$	2.25922	−	1.30436i	0.0880069	−	0.0508108i	0.543358	+	0.839501i	$0.317153\pi$
$660$	−3.05081	−	1.67864i	−0.118753	−	0.0653408i
$661$			11.1882i			0.435172i	0.976041	+	0.217586i	$0.0698183\pi$
$661$			11.1882i			0.435172i	−0.976041	+	0.217586i	$0.930182\pi$
$662$	−15.0463	+	8.68697i	−0.584790	+	0.337629i
$663$	22.7990	+	8.47245i	0.885441	+	0.329043i
$664$		−	0.175313i		−	0.00680346i
$665$	−1.45647	+	7.92813i	−0.0564794	+	0.307440i
$666$	−19.6983	+	12.4809i	−0.763292	+	0.483626i
$667$	−49.5312			−1.91786
$668$	5.41827	+	9.38472i	0.209639	+	0.363106i
$669$	−0.0282576	−	1.37271i	−0.00109250	−	0.0530721i
$670$		−	4.38617i		−	0.169453i
$671$	−2.09596			−0.0809136
$672$	4.28477	−	1.62503i	0.165289	−	0.0626870i
$673$	−3.63204	+	6.29087i	−0.140005	+	0.242495i	−0.927498	−	0.373828i	$-0.878045\pi$
$673$	−3.63204	+	6.29087i	−0.140005	+	0.242495i	0.787493	+	0.616323i	$0.211378\pi$
$674$	−10.3222	+	5.95954i	−0.397597	+	0.229553i
$675$	−13.4673	−	20.3178i	−0.518358	−	0.782031i
$676$	12.4406	−	3.77258i	0.478483	−	0.145099i
$677$	−13.7448	+	23.8066i	−0.528254	+	0.914962i	0.471204	+	0.882024i	$0.343820\pi$
$677$	−13.7448	+	23.8066i	−0.528254	+	0.914962i	−0.999457	+	0.0329380i	$0.989514\pi$
$678$	−2.93869	+	0.0604936i	−0.112860	+	0.00232324i
$679$	−6.42102	−	5.46658i	−0.246416	−	0.209788i
$680$	1.87453	−	1.08226i	0.0718850	−	0.0415028i
$681$	−21.0239	+	0.432783i	−0.805639	+	0.0165843i
$682$	−13.4507	−	7.76576i	−0.515054	−	0.297366i
$683$	−22.6569	−	13.0810i	−0.866944	−	0.500530i	−0.000612290	−	1.00000i	$-0.500195\pi$
$683$	−22.6569	−	13.0810i	−0.866944	−	0.500530i	−0.866331	+	0.499470i	$0.833528\pi$
$684$	−13.8922	+	8.80219i	−0.531183	+	0.336560i
$685$	−3.29953	+	1.90498i	−0.126068	+	0.0727857i
$686$	−18.5160	−	0.397237i	−0.706944	−	0.0151666i
$687$	−0.602959	−	29.2908i	−0.0230043	−	1.11752i
$688$	0.175343	−	0.303703i	0.00668489	−	0.0115786i
$689$	−6.45376	+	0.957028i	−0.245869	+	0.0364598i
$690$	−3.53710	+	6.42846i	−0.134655	+	0.244727i
$691$	−32.3970	+	18.7044i	−1.23244	+	0.711550i	−0.967538	−	0.252725i	$-0.918673\pi$
$691$	−32.3970	+	18.7044i	−1.23244	+	0.711550i	−0.264903	+	0.964275i	$0.585340\pi$
$692$	−4.81776	+	8.34460i	−0.183144	+	0.317214i
$693$	−4.02133	+	28.4292i	−0.152758	+	1.07994i
$694$	17.1137			0.649626
$695$			0.614921i			0.0233253i
$696$	−11.2528	+	0.231641i	−0.426536	+	0.00878034i
$697$	−5.66249	−	9.80773i	−0.214482	−	0.371494i
$698$	0.763095			0.0288836
$699$	−0.412033	−	20.0159i	−0.0155845	−	0.757073i
$700$	−4.16150	−	11.6931i	−0.157290	−	0.441958i
$701$			16.0516i			0.606262i	0.952949	+	0.303131i	$0.0980320\pi$
$701$			16.0516i			0.606262i	−0.952949	+	0.303131i	$0.901968\pi$
$702$	−18.3274	+	3.88651i	−0.691725	+	0.146687i
$703$	36.9035	−	21.3062i	1.39184	−	0.803580i
$704$		−	3.61740i		−	0.136336i
$705$	−5.83105	+	10.5976i	−0.219610	+	0.399127i
$706$	−7.89612	+	4.55883i	−0.297174	+	0.171574i
$707$	−13.7315	−	38.5831i	−0.516426	−	1.45107i
$708$	−1.16415	+	2.11577i	−0.0437516	+	0.0795157i
$709$	−0.916642			−0.0344252			−0.0172126	−	0.999852i	$-0.505479\pi$
$709$	−0.916642			−0.0344252			−0.0172126	+	0.999852i	$0.505479\pi$
$710$	3.18078	+	5.50926i	0.119372	+	0.206759i
$711$	−20.5932	−	32.5016i	−0.772305	−	1.21891i
$712$	6.80894	−	3.93114i	0.255176	−	0.147326i
$713$	−16.3635	+	28.3423i	−0.612816	+	1.06143i
$714$	−13.8250	−	11.2876i	−0.517389	−	0.422429i
$715$	4.50594	+	5.67797i	0.168513	+	0.212344i
$716$	16.2572	+	9.38612i	0.607561	+	0.350776i
$717$	−42.9046	+	25.9628i	−1.60230	+	0.969598i
$718$	9.86094			0.368007
$719$	34.1378			1.27313			0.636563	−	0.771225i	$-0.280355\pi$
$719$	34.1378			1.27313			0.636563	+	0.771225i	$0.280355\pi$
$720$	−0.773515	+	1.47699i	−0.0288272	+	0.0550443i
$721$	9.14600	−	49.7853i	0.340615	−	1.85410i
$722$	9.57178	−	5.52627i	0.356225	−	0.205667i
$723$	0.223213	+	10.8433i	0.00830137	+	0.403268i
$724$	−1.55224	−	0.896185i	−0.0576885	−	0.0333064i
$725$			30.4838i			1.13214i
$726$	3.16491	+	1.74141i	0.117461	+	0.0646299i
$727$			10.1792i			0.377524i	0.982023	+	0.188762i	$0.0604475\pi$
$727$			10.1792i			0.377524i	−0.982023	+	0.188762i	$0.939553\pi$
$728$	−9.53373	−	0.328719i	−0.353343	−	0.0121831i
$729$	26.7944	−	3.32587i	0.992384	−	0.123180i
$730$	−2.57038	−	4.45203i	−0.0951341	−	0.164777i
$731$	−1.36582			−0.0505166
$732$	0.0206543	+	1.00336i	0.000763405	+	0.0370851i
$733$	−26.5104	−	15.3058i	−0.979184	−	0.565332i	−0.0771605	−	0.997019i	$-0.524585\pi$
$733$	−26.5104	−	15.3058i	−0.979184	−	0.565332i	−0.902024	+	0.431686i	$0.857919\pi$
$734$	11.3222	+	19.6107i	0.417912	+	0.723844i
$735$	5.13449	−	4.36360i	0.189388	−	0.160954i
$736$	−7.62233			−0.280963
$737$			28.5492i			1.05162i
$738$	7.72777	+	4.04710i	0.284463	+	0.148976i
$739$	−11.7820			−0.433406			−0.216703	−	0.976238i	$-0.569530\pi$
$739$	−11.7820			−0.433406			−0.216703	+	0.976238i	$0.569530\pi$
$740$	2.16000	−	3.74124i	0.0794033	−	0.137531i
$741$	33.7544	−	5.71773i	1.24000	−	0.210046i
$742$	4.70875	+	0.865039i	0.172864	+	0.0317566i
$743$	4.29201	+	2.47799i	0.157459	+	0.0909088i	0.576659	−	0.816985i	$-0.304356\pi$
$743$	4.29201	+	2.47799i	0.157459	+	0.0909088i	−0.419200	+	0.907894i	$0.637689\pi$
$744$	−3.58499	+	6.51550i	−0.131432	+	0.238870i
$745$	0.243635	+	0.140662i	0.00892608	+	0.00515347i
$746$	2.29852	−	1.32705i	0.0841548	−	0.0485868i
$747$	0.244002	−	0.465912i	0.00892758	−	0.0170468i
$748$	−12.2012	+	7.04434i	−0.446119	+	0.257567i
$749$	−3.33718	−	2.84114i	−0.121938	−	0.103813i
$750$	8.17322	+	4.49711i	0.298444	+	0.164211i
$751$	−5.08516	−	8.80775i	−0.185560	−	0.321399i	0.758205	−	0.652016i	$-0.226077\pi$
$751$	−5.08516	−	8.80775i	−0.185560	−	0.321399i	−0.943765	+	0.330617i	$0.892743\pi$
$752$	−12.5657			−0.458224
$753$	7.53878	−	13.7013i	0.274729	−	0.499302i
$754$	21.7894	+	8.61169i	0.793525	+	0.313619i
$755$	−11.8497			−0.431254
$756$	13.6490	+	1.64490i	0.496408	+	0.0598244i
$757$	22.3721	−	38.7497i	0.813129	−	1.40838i	−0.0975349	−	0.995232i	$-0.531096\pi$
$757$	22.3721	−	38.7497i	0.813129	−	1.40838i	0.910664	−	0.413148i	$-0.135571\pi$
$758$			9.82827i			0.356979i
$759$	23.0227	−	41.8422i	0.835670	−	1.51878i
$760$	1.52335	−	2.63852i	0.0552576	−	0.0957090i
$761$	14.3187			0.519053			0.259526	−	0.965736i	$-0.416434\pi$
$761$	14.3187			0.519053			0.259526	+	0.965736i	$0.416434\pi$
$762$	17.7354	−	10.7322i	0.642487	−	0.388787i
$763$	−33.1218	+	38.9047i	−1.19909	+	1.40844i
$764$	0.263194	+	0.151955i	0.00952204	+	0.00549755i
$765$	6.48807	−	0.267230i	0.234577	−	0.00966173i
$766$	31.3875	−	18.1216i	1.13408	−	0.654760i
$767$	3.93774	−	3.12492i	0.142184	−	0.112834i
$768$	−1.73168	+	0.0356471i	−0.0624868	+	0.00128631i
$769$	−8.87410	−	5.12346i	−0.320008	−	0.184757i	0.331388	−	0.943495i	$-0.392483\pi$
$769$	−8.87410	−	5.12346i	−0.320008	−	0.184757i	−0.651396	+	0.758738i	$0.725816\pi$
$770$	−1.78344	−	5.01115i	−0.0642706	−	0.180589i
$771$	15.3176	−	27.8387i	0.551649	−	1.00259i
$772$	5.87051	−	10.1680i	0.211284	−	0.365955i
$773$	−25.9345	+	44.9198i	−0.932798	+	1.61565i	−0.154283	+	0.988027i	$0.549307\pi$
$773$	−25.9345	+	44.9198i	−0.932798	+	1.61565i	−0.778515	+	0.627626i	$0.784027\pi$
$774$	0.888690	−	0.563079i	0.0319433	−	0.0202394i
$775$	17.4432	+	10.0708i	0.626577	+	0.361754i
$776$	1.59366	+	2.76030i	0.0572090	+	0.0990889i
$777$	−35.1597	−	5.71378i	−1.26135	−	0.204981i
$778$	6.61455	−	11.4567i	0.237143	−	0.410744i
$779$	−13.8050	−	7.97030i	−0.494614	−	0.285566i
$780$	2.67369	−	2.21299i	0.0957336	−	0.0792377i
$781$	−20.7034	−	35.8593i	−0.740825	−	1.28315i
$782$	14.8433	+	25.7094i	0.530797	+	0.919367i
$783$	−30.2278	−	15.0461i	−1.08025	−	0.537705i
$784$	6.54294	+	2.48796i	0.233676	+	0.0888556i
$785$			6.05803i			0.216221i
$786$	−10.1083	+	6.11679i	−0.360550	+	0.218179i
$787$	−8.17673	−	4.72084i	−0.291469	−	0.168280i	0.347135	−	0.937815i	$-0.387154\pi$
$787$	−8.17673	−	4.72084i	−0.291469	−	0.168280i	−0.638604	+	0.769535i	$0.720488\pi$
$788$	−12.6942	+	7.32902i	−0.452213	+	0.261086i
$789$	−30.3020	+	18.3366i	−1.07878	+	0.652800i
$790$	6.17294	+	3.56395i	0.219623	+	0.126800i
$791$	−3.41872	−	2.91055i	−0.121556	−	0.103487i
$792$	5.03474	−	9.61363i	0.178902	−	0.341605i
$793$	0.767863	−	1.94286i	0.0272676	−	0.0689929i
$794$	0.874957	+	1.51547i	0.0310510	+	0.0537820i
$795$	−1.49025	+	0.901792i	−0.0528538	+	0.0319833i
$796$	−11.6741	+	6.74005i	−0.413778	+	0.238895i
$797$	−12.5043	−	21.6580i	−0.442924	−	0.767167i	0.554981	−	0.831863i	$-0.312725\pi$
$797$	−12.5043	−	21.6580i	−0.442924	−	0.767167i	−0.997905	+	0.0646962i	$0.979392\pi$
$798$	−24.7965	−	4.02965i	−0.877786	−	0.142648i
$799$	24.4698	+	42.3830i	0.865680	+	1.49940i
$800$			4.69113i			0.165856i
$801$	23.5669	−	0.970671i	0.832695	−	0.0342970i
$802$	5.13168	−	8.88833i	0.181206	−	0.313858i
$803$	16.7304	+	28.9779i	0.590403	+	1.02261i
$804$	13.6668	−	0.281334i	0.481990	−	0.00992187i
$805$	−10.5591	+	3.75793i	−0.372161	+	0.132450i
$806$	12.1262	−	9.62316i	0.427128	−	0.338961i
$807$	47.0118	−	0.967750i	1.65489	−	0.0340664i
$808$			15.4791i			0.544552i
$809$			5.26148i			0.184984i	0.995713	+	0.0924919i	$0.0294832\pi$
$809$			5.26148i			0.184984i	−0.995713	+	0.0924919i	$0.970517\pi$
$810$	−4.11139	+	2.84868i	−0.144460	+	0.100092i
$811$			15.6340i			0.548982i	0.961590	+	0.274491i	$0.0885094\pi$
$811$			15.6340i			0.548982i	−0.961590	+	0.274491i	$0.911491\pi$
$812$	−13.0909	−	11.1450i	−0.459401	−	0.391114i
$813$	−16.1874	−	8.90671i	−0.567716	−	0.312372i
$814$	−14.0593	+	24.3514i	−0.492777	+	0.853515i
$815$	−6.58298	+	11.4021i	−0.230592	+	0.399397i
$816$	3.49243	+	5.77139i	0.122259	+	0.202039i
$817$	−1.66491	+	0.961234i	−0.0582477	+	0.0336293i
$818$	14.5730			0.509534
$819$	−24.8794	−	14.1427i	−0.869355	−	0.494188i
$820$	−1.61604			−0.0564346
$821$	24.8857	−	14.3678i	0.868518	−	0.501439i	0.00166256	−	0.999999i	$-0.499471\pi$
$821$	24.8857	−	14.3678i	0.868518	−	0.501439i	0.866855	+	0.498559i	$0.166137\pi$
$822$	−6.14733	−	10.1587i	−0.214413	−	0.354327i
$823$	17.8932	−	30.9920i	0.623719	−	1.08031i	−0.365068	−	0.930981i	$-0.618954\pi$
$823$	17.8932	−	30.9920i	0.623719	−	1.08031i	0.988787	−	0.149332i	$-0.0477125\pi$
$824$	−9.56598	+	16.5688i	−0.333247	+	0.577200i
$825$	−25.7516	−	14.1692i	−0.896556	−	0.493308i
$826$	−3.47529	+	1.23684i	−0.120921	+	0.0430350i
$827$		−	32.7339i		−	1.13827i	−0.822244	−	0.569135i	$-0.807278\pi$
$827$		−	32.7339i		−	1.13827i	0.822244	−	0.569135i	$-0.192722\pi$
$828$	−20.2571	−	10.6088i	−0.703984	−	0.368683i
$829$			33.6176i			1.16759i	0.811902	+	0.583794i	$0.198432\pi$
$829$			33.6176i			1.16759i	−0.811902	+	0.583794i	$0.801568\pi$
$830$			0.0974322i			0.00338192i
$831$	−32.9714	+	0.678725i	−1.14377	+	0.0235447i
$832$	3.35317	+	1.32525i	0.116250	+	0.0459447i
$833$	−4.34974	−	26.9137i	−0.150709	−	0.932503i
$834$	−1.91602	+	0.0394417i	−0.0663462	+	0.00136575i
$835$	−3.01126	−	5.21566i	−0.104209	−	0.180495i
$836$	−9.91534	+	17.1739i	−0.342929	+	0.593971i
$837$	−18.5958	+	12.3260i	−0.642766	+	0.426048i
$838$			34.7369i			1.19997i
$839$	15.5856	+	26.9950i	0.538073	+	0.931970i	0.999008	+	0.0445360i	$0.0141809\pi$
$839$	15.5856	+	26.9950i	0.538073	+	0.931970i	−0.460935	+	0.887434i	$0.652486\pi$
$840$	−2.38131	+	0.903130i	−0.0821630	+	0.0311609i
$841$	6.61312	+	11.4543i	0.228039	+	0.394974i
$842$	−27.3639	+	15.7985i	−0.943021	+	0.544453i
$843$	4.92972	−	2.98311i	0.169789	−	0.102744i
$844$	0.786213	+	1.36176i	0.0270626	+	0.0468737i
$845$	−6.91399	+	2.09665i	−0.237848	+	0.0721271i
$846$	−33.3947	−	17.4891i	−1.14813	−	0.601287i
$847$	1.85013	+	5.19856i	0.0635714	+	0.178625i
$848$	−1.56709	−	0.904762i	−0.0538142	−	0.0310696i
$849$	−27.6052	+	16.7046i	−0.947406	+	0.573302i
$850$	15.8227	−	9.13527i	0.542716	−	0.313337i
$851$	51.3115	+	29.6247i	1.75894	+	1.01552i
$852$	−16.9622	+	10.2643i	−0.581114	+	0.351648i
$853$			3.55010i			0.121553i	0.998151	+	0.0607765i	$0.0193577\pi$
$853$			3.55010i			0.121553i	−0.998151	+	0.0607765i	$0.980642\pi$
$854$	−0.993749	+	1.16725i	−0.0340054	+	0.0399425i
$855$	7.72077	−	4.89192i	0.264045	−	0.167300i
$856$	0.828270	+	1.43461i	0.0283097	+	0.0490338i
$857$	12.7969	+	22.1648i	0.437133	+	0.757136i	0.997467	−	0.0711307i	$-0.0226607\pi$
$857$	12.7969	+	22.1648i	0.437133	+	0.757136i	−0.560334	+	0.828266i	$0.689327\pi$
$858$	−17.4028	+	14.4041i	−0.594123	+	0.491750i
$859$	−2.65051	−	1.53027i	−0.0904341	−	0.0522122i	0.454101	−	0.890950i	$-0.349961\pi$
$859$	−2.65051	−	1.53027i	−0.0904341	−	0.0522122i	−0.544535	+	0.838738i	$0.683294\pi$
$860$	−0.0974489	+	0.168786i	−0.00332298	+	0.00575557i
$861$	4.72526	+	12.4592i	0.161036	+	0.424610i
$862$	11.4619	+	19.8526i	0.390393	+	0.676181i
$863$	18.9157	+	10.9210i	0.643896	+	0.371754i	0.786114	−	0.618082i	$-0.212090\pi$
$863$	18.9157	+	10.9210i	0.643896	+	0.371754i	−0.142218	+	0.989835i	$0.545423\pi$
$864$	−4.65175	−	2.31544i	−0.158256	−	0.0787729i
$865$	2.67752	−	4.63761i	0.0910386	−	0.157683i
$866$	−10.0033	+	17.3262i	−0.339925	+	0.588767i
$867$	−1.52910	+	2.77905i	−0.0519311	+	0.0943814i
$868$	−10.7021	+	3.80882i	−0.363254	+	0.129280i
$869$	−40.1791	−	23.1974i	−1.36298	−	0.786919i
$870$	6.25386	−	0.128737i	0.212026	−	0.00436460i
$871$	−26.4638	−	10.4591i	−0.896691	−	0.354393i
$872$	16.7245	−	9.65592i	0.566364	−	0.326991i
$873$	0.393504	+	9.55385i	0.0133181	+	0.323349i
$874$	36.1875	+	20.8929i	1.22406	+	0.706712i
$875$	4.77788	+	13.4250i	0.161522	+	0.453849i
$876$	13.7071	−	8.29455i	0.463121	−	0.280247i
$877$	24.6449			0.832200			0.416100	−	0.909319i	$-0.363397\pi$
$877$	24.6449			0.832200			0.416100	+	0.909319i	$0.363397\pi$
$878$	−6.93320	+	12.0087i	−0.233984	+	0.405272i
$879$	−20.0044	+	36.3567i	−0.674731	+	1.22628i
$880$			2.01041i			0.0677710i
$881$	13.1270	−	22.7365i	0.442258	−	0.766014i	−0.555599	−	0.831451i	$-0.687511\pi$
$881$	13.1270	−	22.7365i	0.442258	−	0.766014i	0.997857	+	0.0654371i	$0.0208442\pi$
$882$	13.9258	+	15.7185i	0.468905	+	0.529271i
$883$	−36.3198			−1.22226			−0.611129	−	0.791531i	$-0.709285\pi$
$883$	−36.3198			−1.22226			−0.611129	+	0.791531i	$0.709285\pi$
$884$	−2.05984	−	13.8906i	−0.0692800	−	0.467193i
$885$	0.646992	−	1.17587i	0.0217484	−	0.0395263i
$886$	−35.7846			−1.20221
$887$	−7.55346	−	13.0830i	−0.253620	−	0.439283i	0.710900	−	0.703294i	$-0.248288\pi$
$887$	−7.55346	−	13.0830i	−0.253620	−	0.439283i	−0.964520	+	0.264010i	$0.914955\pi$
$888$	11.7958	+	6.49034i	0.395840	+	0.217802i
$889$	31.1442	+	5.72146i	1.04454	+	0.191892i
$890$	−3.78415	+	2.18478i	−0.126845	+	0.0732339i
$891$	26.7607	−	18.5418i	0.896517	−	0.621174i
$892$	−0.686501	+	0.396352i	−0.0229858	+	0.0132708i
$893$	59.6566	+	34.4427i	1.99633	+	1.15258i
$894$	−0.422660	+	0.768157i	−0.0141359	+	0.0256910i
$895$	−9.03514	−	5.21644i	−0.302012	−	0.174366i
$896$	−2.01455	−	1.71510i	−0.0673014	−	0.0572976i
$897$	30.3514	+	36.6700i	1.01340	+	1.22438i
$898$	−4.77247	+	8.26617i	−0.159260	+	0.275846i
$899$	27.9003			0.930526
$900$	−6.52916	+	12.4672i	−0.217639	+	0.415572i
$901$			7.04755i			0.234788i
$902$	10.5187			0.350233
$903$	1.58624	+	0.257778i	0.0527867	+	0.00857831i
$904$	0.848506	+	1.46966i	0.0282209	+	0.0488800i
$905$	0.862674	+	0.498065i	0.0286762	+	0.0165562i
$906$	−0.760052	−	36.9222i	−0.0252510	−	1.22666i
$907$	27.9143			0.926878			0.463439	−	0.886129i	$-0.346615\pi$
$907$	27.9143			0.926878			0.463439	+	0.886129i	$0.346615\pi$
$908$	6.07037	+	10.5142i	0.201452	+	0.348926i
$909$	−21.5439	+	41.1373i	−0.714567	+	1.36444i
$910$	5.29848	+	0.182689i	0.175643	+	0.00605609i
$911$		−	51.9732i		−	1.72195i	−0.508649	−	0.860974i	$-0.669855\pi$
$911$		−	51.9732i		−	1.72195i	0.508649	−	0.860974i	$-0.330145\pi$
$912$	8.31900	+	4.57733i	0.275470	+	0.151570i
$913$		−	0.634177i		−	0.0209882i
$914$	−5.68157	−	3.28026i	−0.187930	−	0.108501i
$915$	−0.0114789	−	0.557626i	−0.000379480	−	0.0184346i
$916$	−14.6485	+	8.45733i	−0.484001	+	0.279438i
$917$	−17.7505	−	3.26093i	−0.586175	−	0.107685i
$918$	1.24881	+	20.1989i	0.0412168	+	0.666662i
$919$	−29.3355			−0.967688			−0.483844	−	0.875154i	$-0.660760\pi$
$919$	−29.3355			−0.967688			−0.483844	+	0.875154i	$0.660760\pi$
$920$	4.23620			0.139663
$921$	14.7483	−	8.92459i	0.485972	−	0.294075i
$922$	−2.37852	−	1.37324i	−0.0783323	−	0.0452252i
$923$	40.8247	−	6.05389i	1.34376	−	0.199266i
$924$	15.4997	−	5.87839i	0.509904	−	0.193385i
$925$	18.2324	−	31.5794i	0.599477	−	1.03833i
$926$	−2.95287	+	1.70484i	−0.0970373	+	0.0560245i
$927$	−48.4832	+	30.7192i	−1.59240	+	1.00895i
$928$	3.24909	+	5.62758i	0.106656	+	0.184734i
$929$	43.0116			1.41116			0.705582	−	0.708628i	$-0.250686\pi$
$929$	43.0116			1.41116			0.705582	+	0.708628i	$0.250686\pi$
$930$	1.99240	−	3.62106i	0.0653334	−	0.118739i
$931$	−24.2435	−	29.7460i	−0.794550	−	0.974886i
$932$	−10.0101	+	5.77933i	−0.327892	+	0.189308i
$933$	−12.8385	+	23.3331i	−0.420313	+	0.763893i
$934$			4.35069i			0.142359i
$935$	6.78094	−	3.91497i	0.221760	−	0.128033i
$936$	7.06689	+	8.18896i	0.230989	+	0.267664i
$937$			33.0171i			1.07862i	0.842107	+	0.539311i	$0.181315\pi$
$937$			33.0171i			1.07862i	−0.842107	+	0.539311i	$0.818685\pi$
$938$	15.8992	+	13.5359i	0.519127	+	0.441963i
$939$	−0.485006	−	23.5609i	−0.0158276	−	0.768879i
$940$	6.98354			0.227778
$941$	−4.19320	−	7.26284i	−0.136694	−	0.236762i	0.789549	−	0.613687i	$-0.210315\pi$
$941$	−4.19320	−	7.26284i	−0.136694	−	0.236762i	−0.926243	+	0.376926i	$0.876981\pi$
$942$	−18.8761	+	0.388569i	−0.615016	+	0.0126603i
$943$		−	22.1642i		−	0.721765i
$944$	1.39424			0.0453788
$945$	−7.58557	−	0.914171i	−0.246759	−	0.0297380i
$946$	0.634286	−	1.09862i	0.0206224	−	0.0357191i
$947$	−41.7374	+	24.0971i	−1.35628	+	0.783051i	−0.989121	−	0.147105i	$-0.953004\pi$
$947$	−41.7374	+	24.0971i	−1.35628	+	0.783051i	−0.367164	+	0.930156i	$0.619671\pi$
$948$	−10.7089	+	19.4627i	−0.347809	+	0.632120i
$949$	−32.9904	+	4.89215i	−1.07091	+	0.158806i
$950$	12.8584	−	22.2715i	0.417183	−	0.722582i
$951$	−0.428925	−	20.8365i	−0.0139089	−	0.675671i
$952$	−1.86185	+	10.1348i	−0.0603430	+	0.328471i
$953$	31.4101	−	18.1346i	1.01747	−	0.587439i	0.104103	−	0.994567i	$-0.466803\pi$
$953$	31.4101	−	18.1346i	1.01747	−	0.587439i	0.913371	+	0.407128i	$0.133470\pi$
$954$	−2.90546	−	4.58560i	−0.0940677	−	0.148464i
$955$	−0.146273	−	0.0844509i	−0.00473329	−	0.00273277i
$956$	25.0743	+	14.4766i	0.810960	+	0.468208i
$957$	−40.7058	+	0.837939i	−1.31583	+	0.0270867i
$958$	−33.3493	+	19.2542i	−1.07747	+	0.622076i
$959$	3.27721	−	17.8392i	0.105827	−	0.576056i
$960$	0.962403	−	0.0198113i	0.0310614	−	0.000639407i
$961$	−6.28268	+	10.8819i	−0.202667	+	0.351030i
$962$	−17.4219	−	21.9535i	−0.561706	−	0.707810i
$963$	0.204515	+	4.96541i	0.00659040	+	0.160008i
$964$	5.42282	−	3.13087i	0.174657	−	0.100838i
$965$	−3.26260	+	5.65099i	−0.105027	+	0.181912i
$966$	−12.3865	−	32.6600i	−0.398530	−	1.05082i
$967$	−39.9177			−1.28367			−0.641833	−	0.766845i	$-0.721826\pi$
$967$	−39.9177			−1.28367			−0.641833	+	0.766845i	$0.721826\pi$
$968$		−	2.08560i		−	0.0670336i
$969$	−0.761095	−	36.9729i	−0.0244499	−	1.18774i
$970$	−0.885694	−	1.53407i	−0.0284379	−	0.0492559i
$971$	−30.1800			−0.968523			−0.484262	−	0.874923i	$-0.660912\pi$
$971$	−30.1800			−0.968523			−0.484262	+	0.874923i	$0.660912\pi$
$972$	−9.13985	−	12.6279i	−0.293161	−	0.405039i
$973$	−2.22899	−	1.89767i	−0.0714583	−	0.0608366i
$974$		−	8.88486i		−	0.284689i
$975$	22.5684	−	18.6796i	0.722767	−	0.598227i
$976$	0.501784	−	0.289705i	0.0160617	−	0.00927323i
$977$			19.0462i			0.609341i	0.952458	+	0.304670i	$0.0985463\pi$
$977$			19.0462i			0.609341i	−0.952458	+	0.304670i	$0.901454\pi$
$978$	−35.9496	−	19.7804i	−1.14954	−	0.632508i
$979$	24.6307	−	14.2205i	0.787200	−	0.454490i
$980$	−3.63631	−	1.38271i	−0.116158	−	0.0441691i
$981$	57.8864	−	2.38422i	1.84817	−	0.0761224i
$982$	10.9664			0.349951
$983$	25.9081	+	44.8742i	0.826340	+	1.43126i	0.900891	+	0.434046i	$0.142915\pi$
$983$	25.9081	+	44.8742i	0.826340	+	1.43126i	−0.0745500	+	0.997217i	$0.523752\pi$
$984$	−0.103655	−	5.03538i	−0.00330439	−	0.160522i
$985$	7.05497	−	4.07319i	0.224790	−	0.129783i
$986$	12.6542	−	21.9177i	0.402992	−	0.698003i
$987$	−20.4197	−	53.8412i	−0.649966	−	1.71378i
$988$	−12.2869	−	15.4828i	−0.390897	−	0.492572i
$989$	−2.31493	−	1.33652i	−0.0736104	−	0.0424990i
$990$	−2.79811	+	5.34288i	−0.0889299	+	0.169808i
$991$	−28.1865			−0.895373			−0.447687	−	0.894191i	$-0.647752\pi$
$991$	−28.1865			−0.895373			−0.447687	+	0.894191i	$0.647752\pi$
$992$	4.29356			0.136321
$993$	15.5794	+	25.7457i	0.494399	+	0.817016i
$994$	−29.7863	−	5.47200i	−0.944763	−	0.173561i
$995$	6.48802	−	3.74586i	0.205684	−	0.118752i
$996$	−0.303587	+	0.00624940i	−0.00961951	+	0.000198020i
$997$	−24.8391	−	14.3409i	−0.786663	−	0.454180i	0.0521234	−	0.998641i	$-0.483401\pi$
$997$	−24.8391	−	14.3409i	−0.786663	−	0.454180i	−0.838786	+	0.544461i	$0.816734\pi$
$998$		−	25.8875i		−	0.819454i
$999$	22.3152	+	33.6662i	0.706021	+	1.06515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.14	yes	76
3.2	odd	2	inner	546.2.u.a.425.25	yes	76
7.3	odd	6		546.2.bb.a.269.7	yes	76
13.3	even	3		546.2.bb.a.341.1	yes	76
21.17	even	6		546.2.bb.a.269.20	yes	76
39.29	odd	6		546.2.bb.a.341.26	yes	76
91.3	odd	6	inner	546.2.u.a.185.25	yes	76
273.185	even	6	inner	546.2.u.a.185.14	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.14	✓	76	273.185	even	6	inner
546.2.u.a.185.25	yes	76	91.3	odd	6	inner
546.2.u.a.425.14	yes	76	1.1	even	1	trivial
546.2.u.a.425.25	yes	76	3.2	odd	2	inner
546.2.bb.a.269.7	yes	76	7.3	odd	6
546.2.bb.a.269.20	yes	76	21.17	even	6
546.2.bb.a.341.1	yes	76	13.3	even	3
546.2.bb.a.341.26	yes	76	39.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.896713 + 1.48186i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.277881 + 0.481304i) q^{5} +(-1.51751 - 0.834971i) q^{6} +(-0.887101 - 2.49260i) q^{7} +1.00000i q^{8} +(-1.39181 + 2.65760i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.896713 + 1.48186i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.277881 + 0.481304i) q^{5} +(-1.51751 - 0.834971i) q^{6} +(-0.887101 - 2.49260i) q^{7} +1.00000i q^{8} +(-1.39181 + 2.65760i) q^{9} -0.555761i q^{10} +3.61740i q^{11} +(1.73168 - 0.0356471i) q^{12} +(-3.35317 - 1.32525i) q^{13} +(2.01455 + 1.71510i) q^{14} +(-0.962403 + 0.0198113i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.94735 + 3.37291i) q^{17} +(-0.123459 - 2.99746i) q^{18} +5.48202i q^{19} +(0.277881 + 0.481304i) q^{20} +(2.89821 - 3.54970i) q^{21} +(-1.80870 - 3.13276i) q^{22} +(-6.60113 + 3.81117i) q^{23} +(-1.48186 + 0.896713i) q^{24} +(2.34556 + 4.06264i) q^{25} +(3.56655 - 0.528884i) q^{26} +(-5.18625 + 0.320643i) q^{27} +(-2.60220 - 0.478048i) q^{28} +(5.62758 + 3.24909i) q^{29} +(0.823560 - 0.498359i) q^{30} +(3.71833 - 2.14678i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.36048 + 3.24377i) q^{33} -3.89470i q^{34} +(1.44621 + 0.265681i) q^{35} +(1.60565 + 2.53415i) q^{36} +(-3.88657 - 6.73173i) q^{37} +(-2.74101 - 4.74757i) q^{38} +(-1.04300 - 6.15728i) q^{39} +(-0.481304 - 0.277881i) q^{40} +(-1.45390 + 2.51823i) q^{41} +(-0.735067 + 4.52324i) q^{42} +(0.175343 + 0.303703i) q^{43} +(3.13276 + 1.80870i) q^{44} +(-0.892357 - 1.40838i) q^{45} +(3.81117 - 6.60113i) q^{46} +(6.28286 - 10.8822i) q^{47} +(0.834971 - 1.51751i) q^{48} +(-5.42611 + 4.42237i) q^{49} +(-4.06264 - 2.34556i) q^{50} +(-6.74439 + 0.138835i) q^{51} +(-2.82428 + 2.24130i) q^{52} +(1.56709 - 0.904762i) q^{53} +(4.33110 - 2.87081i) q^{54} +(-1.74107 - 1.00521i) q^{55} +(2.49260 - 0.887101i) q^{56} +(-8.12358 + 4.91580i) q^{57} -6.49817 q^{58} +(-0.697122 + 1.20745i) q^{59} +(-0.464044 + 0.843371i) q^{60} +0.579410i q^{61} +(-2.14678 + 3.71833i) q^{62} +(7.85902 + 1.11166i) q^{63} -1.00000 q^{64} +(1.56963 - 1.24563i) q^{65} +(3.02042 - 5.48943i) q^{66} +7.89218 q^{67} +(1.94735 + 3.37291i) q^{68} +(-11.5669 - 6.36442i) q^{69} +(-1.38529 + 0.493016i) q^{70} +(-9.91300 + 5.72327i) q^{71} +(-2.65760 - 1.39181i) q^{72} +(8.01069 - 4.62497i) q^{73} +(6.73173 + 3.88657i) q^{74} +(-3.91696 + 7.11882i) q^{75} +(4.74757 + 2.74101i) q^{76} +(9.01673 - 3.20900i) q^{77} +(3.98190 + 4.81087i) q^{78} +(-6.41273 + 11.1072i) q^{79} +0.555761 q^{80} +(-5.12573 - 7.39776i) q^{81} -2.90780i q^{82} -0.175313 q^{83} +(-1.62503 - 4.28477i) q^{84} +(-1.08226 - 1.87453i) q^{85} +(-0.303703 - 0.175343i) q^{86} +(0.231641 + 11.2528i) q^{87} -3.61740 q^{88} +(-3.93114 - 6.80894i) q^{89} +(1.47699 + 0.773515i) q^{90} +(-0.328719 + 9.53373i) q^{91} +7.62233i q^{92} +(6.51550 + 3.58499i) q^{93} +12.5657i q^{94} +(-2.63852 - 1.52335i) q^{95} +(0.0356471 + 1.73168i) q^{96} +(2.76030 - 1.59366i) q^{97} +(2.48796 - 6.54294i) q^{98} +(-9.61363 - 5.03474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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