LMFDB - Embedded newform 546.2.bb.a.269.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (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			269.7
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.834971 + 1.51751i) q^{3} -1.00000 q^{4} +(0.277881 + 0.481304i) q^{5} +(1.51751 + 0.834971i) q^{6} +(-1.71510 - 2.01455i) q^{7} +1.00000i q^{8} +(-1.60565 - 2.53415i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.834971 + 1.51751i) q^{3} -1.00000 q^{4} +(0.277881 + 0.481304i) q^{5} +(1.51751 + 0.834971i) q^{6} +(-1.71510 - 2.01455i) q^{7} +1.00000i q^{8} +(-1.60565 - 2.53415i) q^{9} +(0.481304 - 0.277881i) q^{10} +(3.13276 - 1.80870i) q^{11} +(0.834971 - 1.51751i) q^{12} +(3.35317 + 1.32525i) q^{13} +(-2.01455 + 1.71510i) q^{14} +(-0.962403 + 0.0198113i) q^{15} +1.00000 q^{16} -3.89470 q^{17} +(-2.53415 + 1.60565i) q^{18} +(4.74757 + 2.74101i) q^{19} +(-0.277881 - 0.481304i) q^{20} +(4.48916 - 0.920589i) q^{21} +(-1.80870 - 3.13276i) q^{22} -7.62233i q^{23} +(-1.51751 - 0.834971i) q^{24} +(2.34556 - 4.06264i) q^{25} +(1.32525 - 3.35317i) q^{26} +(5.18625 - 0.320643i) q^{27} +(1.71510 + 2.01455i) q^{28} +(5.62758 + 3.24909i) q^{29} +(0.0198113 + 0.962403i) q^{30} +(3.71833 + 2.14678i) q^{31} -1.00000i q^{32} +(0.128950 + 6.26420i) q^{33} +3.89470i q^{34} +(0.493016 - 1.38529i) q^{35} +(1.60565 + 2.53415i) q^{36} +7.77313 q^{37} +(2.74101 - 4.74757i) q^{38} +(-4.81087 + 3.98190i) q^{39} +(-0.481304 + 0.277881i) q^{40} +(1.45390 - 2.51823i) q^{41} +(-0.920589 - 4.48916i) q^{42} +(0.175343 + 0.303703i) q^{43} +(-3.13276 + 1.80870i) q^{44} +(0.773515 - 1.47699i) q^{45} -7.62233 q^{46} +(-6.28286 - 10.8822i) q^{47} +(-0.834971 + 1.51751i) q^{48} +(-1.11684 + 6.91033i) q^{49} +(-4.06264 - 2.34556i) q^{50} +(3.25196 - 5.91023i) q^{51} +(-3.35317 - 1.32525i) q^{52} +(-1.56709 - 0.904762i) q^{53} +(-0.320643 - 5.18625i) q^{54} +(1.74107 + 1.00521i) q^{55} +(2.01455 - 1.71510i) q^{56} +(-8.12358 + 4.91580i) q^{57} +(3.24909 - 5.62758i) q^{58} -1.39424 q^{59} +(0.962403 - 0.0198113i) q^{60} +(0.501784 + 0.289705i) q^{61} +(2.14678 - 3.71833i) q^{62} +(-2.35131 + 7.58098i) q^{63} -1.00000 q^{64} +(0.293933 + 1.98215i) q^{65} +(6.26420 - 0.128950i) q^{66} +(-3.94609 - 6.83483i) q^{67} +3.89470 q^{68} +(11.5669 + 6.36442i) q^{69} +(-1.38529 - 0.493016i) q^{70} +(-9.91300 + 5.72327i) q^{71} +(2.53415 - 1.60565i) q^{72} +(8.01069 + 4.62497i) q^{73} -7.77313i q^{74} +(4.20660 + 6.95159i) 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} +(0.277881 + 0.481304i) q^{80} +(-3.84379 + 8.13789i) q^{81} +(-2.51823 - 1.45390i) q^{82} +0.175313 q^{83} +(-4.48916 + 0.920589i) q^{84} +(-1.08226 - 1.87453i) q^{85} +(0.303703 - 0.175343i) q^{86} +(-9.62937 + 5.82700i) q^{87} +(1.80870 + 3.13276i) q^{88} -7.86229 q^{89} +(-1.47699 - 0.773515i) q^{90} +(-3.08125 - 9.02806i) q^{91} +7.62233i q^{92} +(-6.36245 + 3.85009i) q^{93} +(-10.8822 + 6.28286i) q^{94} +3.04670i q^{95} +(1.51751 + 0.834971i) q^{96} +(-2.76030 + 1.59366i) q^{97} +(6.91033 + 1.11684i) q^{98} +(-9.61363 - 5.03474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.834971	+	1.51751i	−0.482071	+	0.876132i
$3$	−0.834971	+	1.51751i	−0.482071	+	0.876132i
$4$	−1.00000			−0.500000
$5$	0.277881	+	0.481304i	0.124272	+	0.215245i	0.921448	−	0.388501i	$-0.127007\pi$
$5$	0.277881	+	0.481304i	0.124272	+	0.215245i	−0.797176	+	0.603747i	$0.793674\pi$
$6$	1.51751	+	0.834971i	0.619519	+	0.340875i
$7$	−1.71510	−	2.01455i	−0.648248	−	0.761429i
$7$	−1.71510	−	2.01455i	−0.648248	−	0.761429i
$8$			1.00000i			0.353553i
$9$	−1.60565	−	2.53415i	−0.535216	−	0.844715i
$10$	0.481304	−	0.277881i	0.152202	−	0.0878736i
$11$	3.13276	−	1.80870i	0.944563	−	0.545344i	0.0531754	−	0.998585i	$-0.483066\pi$
$11$	3.13276	−	1.80870i	0.944563	−	0.545344i	0.891388	+	0.453241i	$0.149732\pi$
$12$	0.834971	−	1.51751i	0.241035	−	0.438066i
$13$	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
$16$	1.00000			0.250000
$17$	−3.89470			−0.944603			−0.472302	−	0.881437i	$-0.656577\pi$
$17$	−3.89470			−0.944603			−0.472302	+	0.881437i	$0.656577\pi$
$18$	−2.53415	+	1.60565i	−0.597304	+	0.378455i
$19$	4.74757	+	2.74101i	1.08917	+	0.628831i	0.933355	−	0.358956i	$-0.116867\pi$
$19$	4.74757	+	2.74101i	1.08917	+	0.628831i	0.155812	+	0.987787i	$0.450200\pi$
$20$	−0.277881	−	0.481304i	−0.0621360	−	0.107623i
$21$	4.48916	−	0.920589i	0.979614	−	0.200889i
$22$	−1.80870	−	3.13276i	−0.385616	−	0.667907i
$23$		−	7.62233i		−	1.58937i	−0.607025	−	0.794683i	$-0.707637\pi$
$23$		−	7.62233i		−	1.58937i	0.607025	−	0.794683i	$-0.292363\pi$
$24$	−1.51751	−	0.834971i	−0.309760	−	0.170438i
$25$	2.34556	−	4.06264i	0.469113	−	0.812527i
$26$	1.32525	−	3.35317i	0.259903	−	0.657610i
$27$	5.18625	−	0.320643i	0.998094	−	0.0617078i
$28$	1.71510	+	2.01455i	0.324124	+	0.380714i
$29$	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	$0.460503\pi$
$30$	0.0198113	+	0.962403i	0.00361703	+	0.175710i
$31$	3.71833	+	2.14678i	0.667832	+	0.385573i	0.795255	−	0.606276i	$-0.207337\pi$
$31$	3.71833	+	2.14678i	0.667832	+	0.385573i	−0.127423	+	0.991848i	$0.540671\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.128950	+	6.26420i	0.0224473	+	1.09046i
$34$			3.89470i			0.667935i
$35$	0.493016	−	1.38529i	0.0833350	−	0.234157i
$36$	1.60565	+	2.53415i	0.267608	+	0.422358i
$37$	7.77313			1.27790			0.638948	−	0.769250i	$-0.279370\pi$
$37$	7.77313			1.27790			0.638948	+	0.769250i	$0.279370\pi$
$38$	2.74101	−	4.74757i	0.444651	−	0.770157i
$39$	−4.81087	+	3.98190i	−0.770355	+	0.637615i
$40$	−0.481304	+	0.277881i	−0.0761008	+	0.0439368i
$41$	1.45390	−	2.51823i	0.227061	−	0.393281i	−0.729875	−	0.683581i	$-0.760422\pi$
$41$	1.45390	−	2.51823i	0.227061	−	0.393281i	0.956936	+	0.290300i	$0.0937551\pi$
$42$	−0.920589	−	4.48916i	−0.142050	−	0.692692i
$43$	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
$45$	0.773515	−	1.47699i	0.115309	−	0.220177i
$46$	−7.62233			−1.12385
$47$	−6.28286	−	10.8822i	−0.916449	−	1.58734i	−0.804766	−	0.593592i	$-0.797709\pi$
$47$	−6.28286	−	10.8822i	−0.916449	−	1.58734i	−0.111682	−	0.993744i	$-0.535624\pi$
$48$	−0.834971	+	1.51751i	−0.120518	+	0.219033i
$49$	−1.11684	+	6.91033i	−0.159548	+	0.987190i
$50$	−4.06264	−	2.34556i	−0.574544	−	0.331713i
$51$	3.25196	−	5.91023i	0.455365	−	0.827597i
$52$	−3.35317	−	1.32525i	−0.465000	−	0.183779i
$53$	−1.56709	−	0.904762i	−0.215257	−	0.124279i	0.388495	−	0.921451i	$-0.372995\pi$
$53$	−1.56709	−	0.904762i	−0.215257	−	0.124279i	−0.603752	+	0.797172i	$0.706328\pi$
$54$	−0.320643	−	5.18625i	−0.0436340	−	0.705759i
$55$	1.74107	+	1.00521i	0.234766	+	0.135542i
$56$	2.01455	−	1.71510i	0.269206	−	0.229190i
$57$	−8.12358	+	4.91580i	−1.07599	+	0.651114i
$58$	3.24909	−	5.62758i	0.426626	−	0.738938i
$59$	−1.39424			−0.181515			−0.0907576	−	0.995873i	$-0.528929\pi$
$59$	−1.39424			−0.181515			−0.0907576	+	0.995873i	$0.528929\pi$
$60$	0.962403	−	0.0198113i	0.124246	−	0.00255763i
$61$	0.501784	+	0.289705i	0.0642469	+	0.0370929i	0.531779	−	0.846883i	$-0.321524\pi$
$61$	0.501784	+	0.289705i	0.0642469	+	0.0370929i	−0.467532	+	0.883976i	$0.654857\pi$
$62$	2.14678	−	3.71833i	0.272641	−	0.472228i
$63$	−2.35131	+	7.58098i	−0.296238	+	0.955114i
$64$	−1.00000			−0.125000
$65$	0.293933	+	1.98215i	0.0364579	+	0.245856i
$66$	6.26420	−	0.128950i	0.771069	−	0.0158726i
$67$	−3.94609	−	6.83483i	−0.482092	−	0.835007i	0.517697	−	0.855564i	$-0.326789\pi$
$67$	−3.94609	−	6.83483i	−0.482092	−	0.835007i	−0.999789	+	0.0205567i	$0.993456\pi$
$68$	3.89470			0.472302
$69$	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	$0.571018\pi$
$72$	2.53415	−	1.60565i	0.298652	−	0.189227i
$73$	8.01069	+	4.62497i	0.937580	+	0.541312i	0.889201	−	0.457517i	$-0.151261\pi$
$73$	8.01069	+	4.62497i	0.937580	+	0.541312i	0.0483794	+	0.998829i	$0.484594\pi$
$74$		−	7.77313i		−	0.903609i
$75$	4.20660	+	6.95159i	0.485736	+	0.802701i
$76$	−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	−0.960403	−	0.278615i	$-0.910125\pi$
$79$	−6.41273	−	11.1072i	−0.721489	−	1.24966i	0.238914	−	0.971041i	$-0.423209\pi$
$80$	0.277881	+	0.481304i	0.0310680	+	0.0538114i
$81$	−3.84379	+	8.13789i	−0.427088	+	0.904210i
$82$	−2.51823	−	1.45390i	−0.278091	−	0.160556i
$83$	0.175313			0.0192431			0.00962155	−	0.999954i	$-0.496937\pi$
$83$	0.175313			0.0192431			0.00962155	+	0.999954i	$0.496937\pi$
$84$	−4.48916	+	0.920589i	−0.489807	+	0.100445i
$85$	−1.08226	−	1.87453i	−0.117388	−	0.203322i
$86$	0.303703	−	0.175343i	0.0327492	−	0.0189077i
$87$	−9.62937	+	5.82700i	−1.03238	+	0.624720i
$88$	1.80870	+	3.13276i	0.192808	+	0.333954i
$89$	−7.86229			−0.833401			−0.416700	−	0.909044i	$-0.636814\pi$
$89$	−7.86229			−0.833401			−0.416700	+	0.909044i	$0.636814\pi$
$90$	−1.47699	−	0.773515i	−0.155689	−	0.0815356i
$91$	−3.08125	−	9.02806i	−0.323002	−	0.946398i
$92$			7.62233i			0.794683i
$93$	−6.36245	+	3.85009i	−0.659755	+	0.399236i
$94$	−10.8822	+	6.28286i	−1.12242	+	0.648027i
$95$			3.04670i			0.312584i
$96$	1.51751	+	0.834971i	0.154880	+	0.0852188i
$97$	−2.76030	+	1.59366i	−0.280266	+	0.161812i	−0.633544	−	0.773707i	$-0.718400\pi$
$97$	−2.76030	+	1.59366i	−0.280266	+	0.161812i	0.353278	+	0.935518i	$0.385067\pi$
$98$	6.91033	+	1.11684i	0.698049	+	0.112817i
$99$	−9.61363	−	5.03474i	−0.966206	−	0.506010i
$100$	−2.34556	+	4.06264i	−0.234556	+	0.406264i
$101$	7.73954	+	13.4053i	0.770113	+	1.33387i	0.937501	+	0.347983i	$0.113133\pi$
$101$	7.73954	+	13.4053i	0.770113	+	1.33387i	−0.167388	+	0.985891i	$0.553533\pi$
$102$	−5.91023	−	3.25196i	−0.585200	−	0.321992i
$103$	16.5688	−	9.56598i	1.63257	−	0.942564i	0.649272	−	0.760557i	$-0.275074\pi$
$103$	16.5688	−	9.56598i	1.63257	−	0.942564i	0.983297	−	0.182007i	$-0.0582595\pi$
$104$	−1.32525	+	3.35317i	−0.129951	+	0.328805i
$105$	1.69053	+	1.90483i	0.164979	+	0.185893i
$106$	−0.904762	+	1.56709i	−0.0878782	+	0.152210i
$107$			1.65654i			0.160144i	0.996789	+	0.0800719i	$0.0255150\pi$
$107$			1.65654i			0.160144i	−0.996789	+	0.0800719i	$0.974485\pi$
$108$	−5.18625	+	0.320643i	−0.499047	+	0.0308539i
$109$	−9.65592	+	16.7245i	−0.924869	+	1.60192i	−0.133097	+	0.991103i	$0.542492\pi$
$109$	−9.65592	+	16.7245i	−0.924869	+	1.60192i	−0.791772	+	0.610817i	$0.790841\pi$
$110$	1.00521	−	1.74107i	0.0958427	−	0.166004i
$111$	−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	$0.307899\pi$
$114$	4.91580	+	8.12358i	0.460407	+	0.760843i
$115$	3.66865	−	2.11810i	0.342104	−	0.197514i
$116$	−5.62758	−	3.24909i	−0.522508	−	0.301670i
$117$	−2.02563	−	10.6253i	−0.187270	−	0.982309i
$118$			1.39424i			0.128351i
$119$	6.67981	+	7.84607i	0.612337	+	0.719248i
$120$	−0.0198113	−	0.962403i	−0.00180852	−	0.0878550i
$121$	1.04280	−	1.80618i	0.0947999	−	0.164198i
$122$	0.289705	−	0.501784i	0.0262287	−	0.0454294i
$123$	2.60746	+	4.30894i	0.235107	+	0.388524i
$124$	−3.71833	−	2.14678i	−0.333916	−	0.192786i
$125$	5.38596			0.481735
$126$	7.58098	+	2.35131i	0.675368	+	0.209472i
$127$	−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	$0.988479\pi$
$128$			1.00000i			0.0883883i
$129$	−0.607278	+	0.0125010i	−0.0534678	+	0.00110065i
$130$	1.98215	−	0.293933i	0.173846	−	0.0257796i
$131$	−3.41067	−	5.90746i	−0.297992	−	0.516137i	0.677684	−	0.735353i	$-0.262984\pi$
$131$	−3.41067	−	5.90746i	−0.297992	−	0.516137i	−0.975676	+	0.219216i	$0.929650\pi$
$132$	−0.128950	−	6.26420i	−0.0112237	−	0.545228i
$133$	−2.62067	−	14.2653i	−0.227241	−	1.23696i
$134$	−6.83483	+	3.94609i	−0.590439	+	0.340890i
$135$	1.59549	+	2.40706i	0.137318	+	0.207167i
$136$		−	3.89470i		−	0.333968i
$137$		−	6.85540i		−	0.585696i	−0.956159	−	0.292848i	$-0.905397\pi$
$137$		−	6.85540i		−	0.585696i	0.956159	−	0.292848i	$-0.0946030\pi$
$138$	6.36442	−	11.5669i	0.541776	−	0.984643i
$139$	−0.958211	+	0.553223i	−0.0812744	+	0.0469238i	−0.540086	−	0.841610i	$-0.681608\pi$
$139$	−0.958211	+	0.553223i	−0.0812744	+	0.0469238i	0.458812	+	0.888533i	$0.348275\pi$
$140$	−0.493016	+	1.38529i	−0.0416675	+	0.117078i
$141$	21.7598	−	0.447932i	1.83251	−	0.0377226i
$142$	5.72327	+	9.91300i	0.480287	+	0.831881i
$143$	12.9016	−	1.91319i	1.07889	−	0.159989i
$144$	−1.60565	−	2.53415i	−0.133804	−	0.211179i
$145$			3.61143i			0.299913i
$146$	4.62497	−	8.01069i	0.382766	−	0.662969i
$147$	−9.55394	−	7.46473i	−0.787996	−	0.615680i
$148$	−7.77313			−0.638948
$149$	0.438380	+	0.253099i	0.0359135	+	0.0207346i	0.517849	−	0.855472i	$-0.326733\pi$
$149$	0.438380	+	0.253099i	0.0359135	+	0.0207346i	−0.481936	+	0.876207i	$0.660066\pi$
$150$	6.95159	−	4.20660i	0.567595	−	0.343467i
$151$	10.6608	−	18.4650i	0.867561	−	1.50266i	0.00307963	−	0.999995i	$-0.499020\pi$
$151$	10.6608	−	18.4650i	0.867561	−	1.50266i	0.864481	−	0.502665i	$-0.167647\pi$
$152$	−2.74101	+	4.74757i	−0.222325	+	0.385079i
$153$	6.25351	+	9.86973i	0.505567	+	0.797921i
$154$	−3.20900	+	9.01673i	−0.258589	+	0.726589i
$155$			2.38619i			0.191664i
$156$	4.81087	−	3.98190i	0.385178	−	0.318807i
$157$	9.44004	+	5.45021i	0.753397	+	0.434974i	0.826920	−	0.562319i	$-0.190091\pi$
$157$	9.44004	+	5.45021i	0.753397	+	0.434974i	−0.0735227	+	0.997294i	$0.523424\pi$
$158$	−11.1072	+	6.41273i	−0.883640	+	0.510170i
$159$	2.68146	−	1.62262i	0.212653	−	0.128682i
$160$	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
$163$	−11.8450	+	20.5161i	−0.927770	+	1.60695i	−0.140726	+	0.990049i	$0.544944\pi$
$163$	−11.8450	+	20.5161i	−0.927770	+	1.60695i	−0.787044	+	0.616897i	$0.788390\pi$
$164$	−1.45390	+	2.51823i	−0.113530	+	0.196640i
$165$	−2.97915	+	1.80276i	−0.231926	+	0.140345i
$166$		−	0.175313i		−	0.0136069i
$167$	5.41827	−	9.38472i	0.419278	−	0.726211i	−0.576589	−	0.817034i	$-0.695617\pi$
$167$	5.41827	−	9.38472i	0.419278	−	0.726211i	0.995867	+	0.0908233i	$0.0289499\pi$
$168$	0.920589	+	4.48916i	0.0710250	+	0.346346i
$169$	9.48743	+	8.88755i	0.729803	+	0.683658i
$170$	−1.87453	+	1.08226i	−0.143770	+	0.0830057i
$171$	−0.676805	−	16.4321i	−0.0517566	−	1.25660i
$172$	−0.175343	−	0.303703i	−0.0133698	−	0.0231571i
$173$	−4.81776	+	8.34460i	−0.366287	+	0.634428i	−0.988982	−	0.148037i	$-0.952705\pi$
$173$	−4.81776	+	8.34460i	−0.366287	+	0.634428i	0.622694	+	0.782465i	$0.286038\pi$
$174$	5.82700	+	9.62937i	0.441744	+	0.730001i
$175$	−12.2073	+	2.24259i	−0.922784	+	0.169524i
$176$	3.13276	−	1.80870i	0.236141	−	0.136336i
$177$	1.16415	−	2.11577i	0.0875031	−	0.159031i
$178$			7.86229i			0.589303i
$179$	16.2572	−	9.38612i	1.21512	−	0.701552i	0.251252	−	0.967922i	$-0.419158\pi$
$179$	16.2572	−	9.38612i	1.21512	−	0.701552i	0.963871	+	0.266370i	$0.0858244\pi$
$180$	−0.773515	+	1.47699i	−0.0576544	+	0.110089i
$181$			1.79237i			0.133226i	0.997779	+	0.0666129i	$0.0212193\pi$
$181$			1.79237i			0.133226i	−0.997779	+	0.0666129i	$0.978781\pi$
$182$	−9.02806	+	3.08125i	−0.669205	+	0.228397i
$183$	−0.858604	+	0.519565i	−0.0634698	+	0.0384073i
$184$	7.62233			0.561926
$185$	2.16000	+	3.74124i	0.158807	+	0.275061i
$186$	3.85009	+	6.36245i	0.282302	+	0.466517i
$187$	−12.2012	+	7.04434i	−0.892237	+	0.515134i
$188$	6.28286	+	10.8822i	0.458224	+	0.793668i
$189$	−9.54091	−	9.89803i	−0.693999	−	0.719976i
$190$	3.04670			0.221031
$191$	−0.263194	−	0.151955i	−0.0190441	−	0.0109951i	0.490448	−	0.871471i	$-0.336833\pi$
$191$	−0.263194	−	0.151955i	−0.0190441	−	0.0109951i	−0.509492	+	0.860476i	$0.670167\pi$
$192$	0.834971	−	1.51751i	0.0602588	−	0.109517i
$193$	−5.87051	−	10.1680i	−0.422568	−	0.731910i	0.573622	−	0.819120i	$-0.305538\pi$
$193$	−5.87051	−	10.1680i	−0.422568	−	0.731910i	−0.996190	+	0.0872106i	$0.972205\pi$
$194$	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	$0.841544\pi$
$198$	−5.03474	+	9.61363i	−0.357803	+	0.683211i
$199$		−	13.4801i		−	0.955579i	−0.878474	−	0.477790i	$-0.841438\pi$
$199$		−	13.4801i		−	0.955579i	0.878474	−	0.477790i	$-0.158562\pi$
$200$	4.06264	+	2.34556i	0.287272	+	0.165856i
$201$	13.6668	−	0.281334i	0.963979	−	0.0198437i
$202$	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
$205$	1.61604			0.112869
$206$	−9.56598	−	16.5688i	−0.666493	−	1.15440i
$207$	−19.3161	+	12.2388i	−1.34256	+	0.850654i
$208$	3.35317	+	1.32525i	0.232500	+	0.0918894i
$209$	19.8307			1.37172
$210$	1.90483	−	1.69053i	0.131446	−	0.116658i
$211$	−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	$0.183904\pi$
$212$	1.56709	+	0.904762i	0.107628	+	0.0621393i
$213$	−0.408037	−	19.8218i	−0.0279582	−	1.35817i
$214$	1.65654			0.113239
$215$	−0.0974489	+	0.168786i	−0.00664596	+	0.0115111i
$216$	0.320643	+	5.18625i	0.0218170	+	0.352880i
$217$	−2.05253	−	11.1727i	−0.139335	−	0.758453i
$218$	16.7245	+	9.65592i	1.13273	+	0.653981i
$219$	−13.7071	+	8.29455i	−0.926241	+	0.560494i
$220$	−1.74107	−	1.00521i	−0.117383	−	0.0677710i
$221$	−13.0596	−	5.16144i	−0.878482	−	0.347196i
$222$	11.7958	+	6.49034i	0.791681	+	0.435603i
$223$	0.686501	+	0.396352i	0.0459715	+	0.0265417i	0.522810	−	0.852449i	$-0.324884\pi$
$223$	0.686501	+	0.396352i	0.0459715	+	0.0265417i	−0.476838	+	0.878991i	$0.658217\pi$
$224$	−2.01455	+	1.71510i	−0.134603	+	0.114595i
$225$	−14.0615	+	0.579163i	−0.937431	+	0.0386108i
$226$	−0.848506	−	1.46966i	−0.0564418	−	0.0977600i
$227$	−12.1407			−0.805809			−0.402905	−	0.915242i	$-0.631999\pi$
$227$	−12.1407			−0.805809			−0.402905	+	0.915242i	$0.631999\pi$
$228$	8.12358	−	4.91580i	0.537997	−	0.325557i
$229$	−14.6485	+	8.45733i	−0.968002	+	0.558876i	−0.898626	−	0.438715i	$-0.855434\pi$
$229$	−14.6485	+	8.45733i	−0.968002	+	0.558876i	−0.0693752	+	0.997591i	$0.522101\pi$
$230$	−2.11810	−	3.66865i	−0.139663	−	0.241904i
$231$	12.3984	−	11.0035i	0.815754	−	0.723979i
$232$	−3.24909	+	5.62758i	−0.213313	+	0.369469i
$233$	10.0101	−	5.77933i	0.655783	−	0.378617i	−0.134885	−	0.990861i	$-0.543067\pi$
$233$	10.0101	−	5.77933i	0.655783	−	0.378617i	0.790668	+	0.612245i	$0.209733\pi$
$234$	−10.6253	+	2.02563i	−0.694597	+	0.132420i
$235$	3.49177	−	6.04792i	0.227778	−	0.394523i
$236$	1.39424			0.0907576
$237$	22.2097	−	0.457191i	1.44267	−	0.0296978i
$238$	7.84607	−	6.67981i	0.508585	−	0.432988i
$239$			28.9533i			1.87283i	0.350893	+	0.936415i	$0.385878\pi$
$239$			28.9533i			1.87283i	−0.350893	+	0.936415i	$0.614122\pi$
$240$	−0.962403	+	0.0198113i	−0.0621229	+	0.00127881i
$241$			6.26173i			0.403354i	0.979452	+	0.201677i	$0.0646391\pi$
$241$			6.26173i			0.403354i	−0.979452	+	0.201677i	$0.935361\pi$
$242$	−1.80618	−	1.04280i	−0.116106	−	0.0670336i
$243$	−9.13985	−	12.6279i	−0.586322	−	0.810078i
$244$	−0.501784	−	0.289705i	−0.0321234	−	0.0185465i
$245$	−3.63631	+	1.38271i	−0.232316	+	0.0883382i
$246$	4.30894	−	2.60746i	0.274728	−	0.166246i
$247$	12.2869	+	15.4828i	0.781794	+	0.985145i
$248$	−2.14678	+	3.71833i	−0.136321	+	0.236114i
$249$	−0.146381	+	0.266038i	−0.00927653	+	0.0168595i
$250$		−	5.38596i		−	0.340638i
$251$	4.51440	+	7.81917i	0.284946	+	0.493542i	0.972596	−	0.232501i	$-0.0746909\pi$
$251$	4.51440	+	7.81917i	0.284946	+	0.493542i	−0.687650	+	0.726043i	$0.741358\pi$
$252$	2.35131	−	7.58098i	0.148119	−	0.477557i
$253$	−13.7865	−	23.8790i	−0.866751	−	1.50126i
$254$	10.3649	+	5.98419i	0.650353	+	0.375481i
$255$	3.74827	−	0.0771590i	0.234726	−	0.00483189i
$256$	1.00000			0.0625000
$257$	−18.3451			−1.14433			−0.572166	−	0.820138i	$-0.693897\pi$
$257$	−18.3451			−1.14433			−0.572166	+	0.820138i	$0.693897\pi$
$258$	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
$261$	−0.802259	−	19.4780i	−0.0496586	−	1.20566i
$262$	−5.90746	+	3.41067i	−0.364964	+	0.210712i
$263$	17.7091	−	10.2243i	1.09199	−	0.630459i	0.157883	−	0.987458i	$-0.449533\pi$
$263$	17.7091	−	10.2243i	1.09199	−	0.630459i	0.934105	+	0.356999i	$0.116200\pi$
$264$	−6.26420	+	0.128950i	−0.385535	+	0.00793632i
$265$		−	1.00566i		−	0.0617774i
$266$	−14.2653	+	2.62067i	−0.874664	+	0.160684i
$267$	6.56478	−	11.9311i	0.401758	−	0.730169i
$268$	3.94609	+	6.83483i	0.241046	+	0.417504i
$269$	27.1480			1.65525			0.827623	−	0.561285i	$-0.189693\pi$
$269$	27.1480			1.65525			0.827623	+	0.561285i	$0.189693\pi$
$270$	2.40706	−	1.59549i	0.146489	−	0.0970981i
$271$			10.6671i			0.647980i	0.946060	+	0.323990i	$0.105024\pi$
$271$			10.6671i			0.647980i	−0.946060	+	0.323990i	$0.894976\pi$
$272$	−3.89470			−0.236151
$273$	16.2729	+	2.86236i	0.984880	+	0.173238i
$274$	−6.85540			−0.414150
$275$		−	16.9697i		−	1.02331i
$276$	−11.5669	−	6.36442i	−0.696248	−	0.383093i
$277$	19.0401			1.14401			0.572004	−	0.820251i	$-0.306166\pi$
$277$	19.0401			1.14401			0.572004	+	0.820251i	$0.306166\pi$
$278$	0.553223	+	0.958211i	0.0331801	+	0.0574697i
$279$	−0.530079	−	12.8698i	−0.0317350	−	0.770492i
$280$	1.38529	+	0.493016i	0.0827870	+	0.0294634i
$281$		−	3.32671i		−	0.198455i	−0.995065	−	0.0992275i	$-0.968363\pi$
$281$		−	3.32671i		−	0.198455i	0.995065	−	0.0992275i	$-0.0316372\pi$
$282$	−0.447932	−	21.7598i	−0.0266739	−	1.29578i
$283$	−16.1330	+	9.31437i	−0.959005	+	0.553682i	−0.895867	−	0.444323i	$-0.853444\pi$
$283$	−16.1330	+	9.31437i	−0.959005	+	0.553682i	−0.0631381	+	0.998005i	$0.520111\pi$
$284$	9.91300	−	5.72327i	0.588229	−	0.339614i
$285$	−4.62338	−	2.54390i	−0.273865	−	0.150688i
$286$	−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
$289$	−1.83133			−0.107725
$290$	3.61143			0.212071
$291$	−0.113619	−	5.51943i	−0.00666045	−	0.323555i
$292$	−8.01069	−	4.62497i	−0.468790	−	0.270656i
$293$	−11.9791	−	20.7484i	−0.699826	−	1.21213i	−0.968527	−	0.248910i	$-0.919928\pi$
$293$	−11.9791	−	20.7484i	−0.699826	−	1.21213i	0.268701	−	0.963224i	$-0.413406\pi$
$294$	−7.46473	+	9.55394i	−0.435352	+	0.557197i
$295$	−0.387434	−	0.671055i	−0.0225573	−	0.0390703i
$296$			7.77313i			0.451804i
$297$	15.6673	−	10.3849i	0.909111	−	0.602591i
$298$	0.253099	−	0.438380i	0.0146616	−	0.0253947i
$299$	10.1015	−	25.5589i	0.584184	−	1.47811i
$300$	−4.20660	−	6.95159i	−0.242868	−	0.401350i
$301$	0.311094	−	0.874120i	0.0179312	−	0.0503835i
$302$	−18.4650	−	10.6608i	−1.06254	−	0.613458i
$303$	−26.8049	+	0.551785i	−1.53990	+	0.0316992i
$304$	4.74757	+	2.74101i	0.272292	+	0.157208i
$305$			0.322014i			0.0184385i
$306$	9.86973	−	6.25351i	0.564215	−	0.357490i
$307$			9.95255i			0.568022i	0.958821	+	0.284011i	$0.0916652\pi$
$307$			9.95255i			0.568022i	−0.958821	+	0.284011i	$0.908335\pi$
$308$	9.01673	+	3.20900i	0.513776	+	0.182850i
$309$	0.681999	+	33.1305i	0.0387976	+	1.88473i
$310$	2.38619			0.135527
$311$	−7.68799	+	13.3160i	−0.435946	+	0.755081i	−0.997372	−	0.0724462i	$-0.976919\pi$
$311$	−7.68799	+	13.3160i	−0.435946	+	0.755081i	0.561426	+	0.827527i	$0.310253\pi$
$312$	−3.98190	−	4.81087i	−0.225431	−	0.272362i
$313$	−11.7829	+	6.80287i	−0.666010	+	0.384521i	−0.794563	−	0.607181i	$-0.792300\pi$
$313$	−11.7829	+	6.80287i	−0.666010	+	0.384521i	0.128553	+	0.991703i	$0.458967\pi$
$314$	5.45021	−	9.44004i	0.307573	−	0.532732i
$315$	−4.30214	+	0.974914i	−0.242398	+	0.0549302i
$316$	6.41273	+	11.1072i	0.360744	+	0.624828i
$317$	10.4205	−	6.01626i	0.585272	−	0.337907i	−0.177954	−	0.984039i	$-0.556948\pi$
$317$	10.4205	−	6.01626i	0.585272	−	0.337907i	0.763226	+	0.646132i	$0.223614\pi$
$318$	−1.62262	−	2.68146i	−0.0909922	−	0.150369i
$319$	23.5065			1.31611
$320$	−0.277881	−	0.481304i	−0.0155340	−	0.0269057i
$321$	−2.51381	−	1.38316i	−0.140307	−	0.0772006i
$322$	13.0731	+	15.3556i	0.728535	+	0.855733i
$323$	−18.4903	−	10.6754i	−1.02883	−	0.593996i
$324$	3.84379	−	8.13789i	0.213544	−	0.452105i
$325$	13.2491	−	10.5142i	0.734926	−	0.583225i
$326$	20.5161	+	11.8450i	1.13628	+	0.656033i
$327$	−17.3172	−	28.6174i	−0.957642	−	1.58255i
$328$	2.51823	+	1.45390i	0.139046	+	0.0802781i
$329$	−11.1470	+	31.3213i	−0.614557	+	1.72680i
$330$	1.80276	+	2.97915i	0.0992389	+	0.163997i
$331$	−8.68697	+	15.0463i	−0.477479	+	0.827018i	−0.999667	−	0.0258125i	$-0.991783\pi$
$331$	−8.68697	+	15.0463i	−0.477479	+	0.827018i	0.522188	+	0.852831i	$0.325116\pi$
$332$	−0.175313			−0.00962155
$333$	−12.4809	−	19.6983i	−0.683950	−	1.07946i
$334$	−9.38472	−	5.41827i	−0.513509	−	0.296474i
$335$	2.19308	−	3.79853i	0.119821	−	0.207536i
$336$	4.48916	−	0.920589i	0.244903	−	0.0502223i
$337$	11.9191			0.649274			0.324637	−	0.945839i	$-0.394758\pi$
$337$	11.9191			0.649274			0.324637	+	0.945839i	$0.394758\pi$
$338$	8.88755	−	9.48743i	0.483419	−	0.516048i
$339$	0.0604936	+	2.93869i	0.00328556	+	0.159608i
$340$	1.08226	+	1.87453i	0.0586939	+	0.101661i
$341$	15.5315			0.841079
$342$	−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
$345$	0.151008	+	7.33576i	0.00813001	+	0.394944i
$346$	8.34460	+	4.81776i	0.448609	+	0.259004i
$347$			17.1137i			0.918710i	0.888253	+	0.459355i	$0.151919\pi$
$347$			17.1137i			0.918710i	−0.888253	+	0.459355i	$0.848081\pi$
$348$	9.62937	−	5.82700i	0.516189	−	0.312360i
$349$	0.660860	+	0.381547i	0.0353750	+	0.0204238i	0.517583	−	0.855633i	$-0.326832\pi$
$349$	0.660860	+	0.381547i	0.0353750	+	0.0204238i	−0.482208	+	0.876057i	$0.660165\pi$
$350$	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
$353$	4.55883	+	7.89612i	0.242642	+	0.420268i	0.961466	−	0.274924i	$-0.0886527\pi$
$353$	4.55883	+	7.89612i	0.242642	+	0.420268i	−0.718824	+	0.695192i	$0.755319\pi$
$354$	−2.11577	−	1.16415i	−0.112452	−	0.0618741i
$355$	−5.50926	−	3.18078i	−0.292401	−	0.168818i
$356$	7.86229			0.416700
$357$	−17.4839	+	3.58542i	−0.925346	+	0.189760i
$358$	−9.38612	−	16.2572i	−0.496072	−	0.859222i
$359$	8.53982	−	4.93047i	0.450715	−	0.260220i	−0.257417	−	0.966300i	$-0.582872\pi$
$359$	8.53982	−	4.93047i	0.450715	−	0.260220i	0.708132	+	0.706080i	$0.249538\pi$
$360$	1.47699	+	0.773515i	0.0778444	+	0.0407678i
$361$	5.52627	+	9.57178i	0.290856	+	0.503778i
$362$	1.79237			0.0942048
$363$	1.87018	+	3.09056i	0.0981591	+	0.162212i
$364$	3.08125	+	9.02806i	0.161501	+	0.473199i
$365$			5.14076i			0.269080i
$366$	0.519565	+	0.858604i	0.0271581	+	0.0448800i
$367$	19.6107	−	11.3222i	1.02367	−	0.591016i	0.108505	−	0.994096i	$-0.465394\pi$
$367$	19.6107	−	11.3222i	1.02367	−	0.591016i	0.915165	+	0.403079i	$0.132060\pi$
$368$		−	7.62233i		−	0.397342i
$369$	−8.71600	+	0.358994i	−0.453737	+	0.0186885i
$370$	3.74124	−	2.16000i	0.194498	−	0.112293i
$371$	0.865039	+	4.70875i	0.0449106	+	0.244466i
$372$	6.36245	−	3.85009i	0.329877	−	0.199618i
$373$	1.32705	−	2.29852i	0.0687121	−	0.119013i	−0.829623	−	0.558325i	$-0.811444\pi$
$373$	1.32705	−	2.29852i	0.0687121	−	0.119013i	0.898335	+	0.439312i	$0.144778\pi$
$374$	7.04434	+	12.2012i	0.364254	+	0.630907i
$375$	−4.49711	+	8.17322i	−0.232230	+	0.422063i
$376$	10.8822	−	6.28286i	0.561208	−	0.324014i
$377$	14.5644	+	18.3527i	0.750103	+	0.945210i
$378$	−9.89803	+	9.54091i	−0.509100	+	0.490732i
$379$	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	$0.0854395\pi$
$380$		−	3.04670i		−	0.156292i
$381$	−10.7322	−	17.7354i	−0.549827	−	0.908614i
$382$	−0.151955	+	0.263194i	−0.00777471	+	0.0134662i
$383$	−18.1216	+	31.3875i	−0.925970	+	1.60383i	−0.135977	+	0.990712i	$0.543417\pi$
$383$	−18.1216	+	31.3875i	−0.925970	+	1.60383i	−0.789993	+	0.613116i	$0.789916\pi$
$384$	−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
$387$	0.488089	−	0.931985i	0.0248109	−	0.0473755i
$388$	2.76030	−	1.59366i	0.140133	−	0.0809058i
$389$	11.4567	+	6.61455i	0.580880	+	0.335371i	0.761483	−	0.648185i	$-0.224472\pi$
$389$	11.4567	+	6.61455i	0.580880	+	0.335371i	−0.180603	+	0.983556i	$0.557805\pi$
$390$	−1.20899	+	3.25335i	−0.0612197	+	0.164740i
$391$			29.6867i			1.50132i
$392$	−6.91033	−	1.11684i	−0.349024	−	0.0564087i
$393$	11.8124	−	0.243161i	0.595858	−	0.0122659i
$394$	−7.32902	+	12.6942i	−0.369231	+	0.639526i
$395$	3.56395	−	6.17294i	0.179322	−	0.310594i
$396$	9.61363	+	5.03474i	0.483103	+	0.253005i
$397$	−1.51547	−	0.874957i	−0.0760592	−	0.0439128i	0.461488	−	0.887146i	$-0.347316\pi$
$397$	−1.51547	−	0.874957i	−0.0760592	−	0.0439128i	−0.537547	+	0.843234i	$0.680649\pi$
$398$	−13.4801			−0.675697
$399$	23.8359	+	7.93426i	1.19329	+	0.397210i
$400$	2.34556	−	4.06264i	0.117278	−	0.203132i
$401$		−	10.2634i		−	0.512528i	−0.966607	−	0.256264i	$-0.917508\pi$
$401$		−	10.2634i		−	0.512528i	0.966607	−	0.256264i	$-0.0824916\pi$
$402$	−0.281334	−	13.6668i	−0.0140316	−	0.681636i
$403$	9.62316	+	12.1262i	0.479364	+	0.604050i
$404$	−7.73954	−	13.4053i	−0.385056	−	0.666937i
$405$	−4.98491	+	0.411334i	−0.247702	+	0.0204394i
$406$	−16.9096	+	3.10644i	−0.839208	+	0.154170i
$407$	24.3514	−	14.0593i	1.20705	−	0.696892i
$408$	5.91023	+	3.25196i	0.292600	+	0.160996i
$409$		−	14.5730i		−	0.720590i	−0.932838	−	0.360295i	$-0.882676\pi$
$409$		−	14.5730i		−	0.720590i	0.932838	−	0.360295i	$-0.117324\pi$
$410$		−	1.61604i		−	0.0798106i
$411$	10.4031	+	5.72406i	0.513148	+	0.282347i
$412$	−16.5688	+	9.56598i	−0.816284	+	0.471282i
$413$	2.39128	+	2.80878i	0.117667	+	0.138211i
$414$	12.2388	+	19.3161i	0.601503	+	0.949334i
$415$	0.0487161	+	0.0843787i	0.00239138	+	0.00414199i
$416$	1.32525	−	3.35317i	0.0649757	−	0.164402i
$417$	−0.0394417	−	1.91602i	−0.00193147	−	0.0938277i
$418$		−	19.8307i		−	0.969950i
$419$	−17.3685	+	30.0831i	−0.848505	+	1.46965i	0.0340367	+	0.999421i	$0.489164\pi$
$419$	−17.3685	+	30.0831i	−0.848505	+	1.46965i	−0.882542	+	0.470234i	$0.844170\pi$
$420$	−1.69053	−	1.90483i	−0.0824895	−	0.0929463i
$421$	31.5971			1.53995			0.769973	−	0.638076i	$-0.220269\pi$
$421$	31.5971			1.53995			0.769973	+	0.638076i	$0.220269\pi$
$422$	1.36176	+	0.786213i	0.0662894	+	0.0382722i
$423$	−17.4891	+	33.3947i	−0.850349	+	1.62371i
$424$	0.904762	−	1.56709i	0.0439391	−	0.0761048i
$425$	−9.13527	+	15.8227i	−0.443126	+	0.767516i
$426$	−19.8218	+	0.408037i	−0.960370	+	0.0197694i
$427$	−0.276986	−	1.50774i	−0.0134043	−	0.0729648i
$428$		−	1.65654i		−	0.0800719i
$429$	−7.86923	+	21.1758i	−0.379930	+	1.02238i
$430$	0.168786	+	0.0974489i	0.00813961	+	0.00469940i
$431$	−19.8526	+	11.4619i	−0.956265	+	0.552100i	−0.895021	−	0.446023i	$-0.852840\pi$
$431$	−19.8526	+	11.4619i	−0.956265	+	0.552100i	−0.0612432	+	0.998123i	$0.519507\pi$
$432$	5.18625	−	0.320643i	0.249524	−	0.0154269i
$433$	−17.3262	+	10.0033i	−0.832643	+	0.480727i	−0.854757	−	0.519029i	$-0.826294\pi$
$433$	−17.3262	+	10.0033i	−0.832643	+	0.480727i	0.0221138	+	0.999755i	$0.492960\pi$
$434$	−11.1727	+	2.05253i	−0.536307	+	0.0985244i
$435$	−5.48037	−	3.01544i	−0.262764	−	0.144579i
$436$	9.65592	−	16.7245i	0.462435	−	0.800960i
$437$	20.8929	−	36.1875i	0.999442	−	1.73108i
$438$	8.29455	+	13.7071i	0.396329	+	0.654951i
$439$		−	13.8664i		−	0.661807i	−0.943665	−	0.330904i	$-0.892647\pi$
$439$		−	13.8664i		−	0.661807i	0.943665	−	0.330904i	$-0.107353\pi$
$440$	−1.00521	+	1.74107i	−0.0479213	+	0.0830022i
$441$	19.3050	−	8.26534i	0.919287	−	0.393587i
$442$	−5.16144	+	13.0596i	−0.245505	+	0.621180i
$443$	−30.9904	+	17.8923i	−1.47240	+	0.850089i	−0.999518	−	0.0310388i	$-0.990118\pi$
$443$	−30.9904	+	17.8923i	−1.47240	+	0.850089i	−0.472879	+	0.881128i	$0.656785\pi$
$444$	6.49034	−	11.7958i	0.308018	−	0.559803i
$445$	−2.18478	−	3.78415i	−0.103568	−	0.179386i
$446$	0.396352	−	0.686501i	0.0187678	−	0.0325068i
$447$	−0.750113	+	0.453914i	−0.0354791	+	0.0214694i
$448$	1.71510	+	2.01455i	0.0810311	+	0.0951786i
$449$	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	$0.261021\pi$
$450$	0.579163	+	14.0615i	0.0273020	+	0.662864i
$451$		−	10.5187i		−	0.495305i
$452$	−1.46966	+	0.848506i	−0.0691268	+	0.0399104i
$453$	19.1193	+	31.5955i	0.898303	+	1.48449i
$454$			12.1407i			0.569793i
$455$	3.48902	−	3.99174i	0.163568	−	0.187136i
$456$	−4.91580	−	8.12358i	−0.230203	−	0.380421i
$457$	−6.56051			−0.306888			−0.153444	−	0.988157i	$-0.549036\pi$
$457$	−6.56051			−0.306888			−0.153444	+	0.988157i	$0.549036\pi$
$458$	8.45733	+	14.6485i	0.395185	+	0.684481i
$459$	−20.1989	+	1.24881i	−0.942803	+	0.0582894i
$460$	−3.66865	+	2.11810i	−0.171052	+	0.0987569i
$461$	−1.37324	−	2.37852i	−0.0639581	−	0.110779i	0.832273	−	0.554366i	$-0.187039\pi$
$461$	−1.37324	−	2.37852i	−0.0639581	−	0.110779i	−0.896231	+	0.443587i	$0.853706\pi$
$462$	−11.0035	−	12.3984i	−0.511930	−	0.576825i
$463$	3.40968			0.158461			0.0792306	−	0.996856i	$-0.474754\pi$
$463$	3.40968			0.158461			0.0792306	+	0.996856i	$0.474754\pi$
$464$	5.62758	+	3.24909i	0.261254	+	0.150835i
$465$	−3.62106	−	1.99240i	−0.167923	−	0.0923954i
$466$	−5.77933	−	10.0101i	−0.267722	−	0.463709i
$467$	−2.17534	−	3.76781i	−0.100663	−	0.174353i	0.811295	−	0.584637i	$-0.198763\pi$
$467$	−2.17534	−	3.76781i	−0.100663	−	0.174353i	−0.911958	+	0.410284i	$0.865430\pi$
$468$	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
$471$	−16.1529	+	9.77455i	−0.744286	+	0.450388i
$472$		−	1.39424i		−	0.0641753i
$473$	1.09862	+	0.634286i	0.0505144	+	0.0291645i
$474$	−0.457191	−	22.2097i	−0.0209995	−	1.02012i
$475$	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
$478$	28.9533			1.32429
$479$	19.2542	+	33.3493i	0.879748	+	1.52377i	0.851617	+	0.524164i	$0.175622\pi$
$479$	19.2542	+	33.3493i	0.879748	+	1.52377i	0.0281311	+	0.999604i	$0.491044\pi$
$480$	0.0198113	+	0.962403i	0.000904258	+	0.0439275i
$481$	26.0646	+	10.3013i	1.18844	+	0.469700i
$482$	6.26173			0.285214
$483$	−7.01704	−	34.2178i	−0.319286	−	1.55697i
$484$	−1.04280	+	1.80618i	−0.0473999	+	0.0820991i
$485$	−1.53407	−	0.885694i	−0.0696584	−	0.0402173i
$486$	−12.6279	+	9.13985i	−0.572812	+	0.414592i
$487$	8.88486			0.402611			0.201306	−	0.979528i	$-0.435482\pi$
$487$	8.88486			0.402611			0.201306	+	0.979528i	$0.435482\pi$
$488$	−0.289705	+	0.501784i	−0.0131143	+	0.0227147i
$489$	−21.2431	−	35.1052i	−0.960646	−	1.58751i
$490$	1.38271	+	3.63631i	0.0624645	+	0.164272i
$491$	−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	$0.746260\pi$
$492$	−2.60746	−	4.30894i	−0.117553	−	0.194262i
$493$	−21.9177	−	12.6542i	−0.987125	−	0.569917i
$494$	15.4828	−	12.2869i	0.696603	−	0.552812i
$495$	−0.248204	−	6.02613i	−0.0111559	−	0.270854i
$496$	3.71833	+	2.14678i	0.166958	+	0.0963932i
$497$	28.5317	+	10.1542i	1.27982	+	0.455480i
$498$	0.266038	+	0.146381i	0.0119215	+	0.00655950i
$499$	−12.9437	−	22.4192i	−0.579441	−	1.00362i	−0.995543	−	0.0943038i	$-0.969938\pi$
$499$	−12.9437	−	22.4192i	−0.579441	−	1.00362i	0.416102	−	0.909318i	$-0.363396\pi$
$500$	−5.38596			−0.240867
$501$	9.71727	+	16.0582i	0.434135	+	0.717428i
$502$	7.81917	−	4.51440i	0.348987	−	0.201488i
$503$	−6.97090	−	12.0739i	−0.310817	−	0.538351i	0.667723	−	0.744410i	$-0.267269\pi$
$503$	−6.97090	−	12.0739i	−0.310817	−	0.538351i	−0.978539	+	0.206060i	$0.933936\pi$
$504$	−7.58098	−	2.35131i	−0.337684	−	0.104736i
$505$	−4.30134	+	7.45013i	−0.191407	+	0.331527i
$506$	−23.8790	+	13.7865i	−1.06155	+	0.612886i
$507$	−21.4086	+	6.97639i	−0.950791	+	0.309832i
$508$	5.98419	−	10.3649i	0.265505	−	0.459869i
$509$	−14.6011			−0.647183			−0.323592	−	0.946197i	$-0.604890\pi$
$509$	−14.6011			−0.647183			−0.323592	+	0.946197i	$0.604890\pi$
$510$	−0.0771590	−	3.74827i	−0.00341666	−	0.165976i
$511$	−4.42192	−	24.0703i	−0.195614	−	1.06481i
$512$		−	1.00000i		−	0.0441942i
$513$	25.5010	+	12.6933i	1.12590	+	0.560422i
$514$			18.3451i			0.809166i
$515$	9.20828	+	5.31640i	0.405765	+	0.234269i
$516$	0.607278	−	0.0125010i	0.0267339	−	0.000550324i
$517$	−39.3654	−	22.7276i	−1.73129	−	0.999559i
$518$	−15.6594	+	13.3317i	−0.688034	+	0.585763i
$519$	−8.64030	−	14.2785i	−0.379267	−	0.626755i
$520$	−1.98215	+	0.293933i	−0.0869231	+	0.0128898i
$521$	−17.7206	+	30.6930i	−0.776355	+	1.34469i	0.157674	+	0.987491i	$0.449600\pi$
$521$	−17.7206	+	30.6930i	−0.776355	+	1.34469i	−0.934030	+	0.357196i	$0.883733\pi$
$522$	−19.4780	+	0.802259i	−0.852529	+	0.0351139i
$523$			17.9678i			0.785677i	0.919607	+	0.392839i	$0.128507\pi$
$523$			17.9678i			0.785677i	−0.919607	+	0.392839i	$0.871493\pi$
$524$	3.41067	+	5.90746i	0.148996	+	0.258069i
$525$	6.78958	−	20.3971i	0.296322	−	0.890203i
$526$	−10.2243	−	17.7091i	−0.445802	−	0.772152i
$527$	−14.4818	−	8.36105i	−0.630836	−	0.364213i
$528$	0.128950	+	6.26420i	0.00561183	+	0.272614i
$529$	−35.0999			−1.52608
$530$	−1.00566			−0.0436832
$531$	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
$534$	−11.9311	−	6.56478i	−0.516308	−	0.284086i
$535$	−0.797298	+	0.460320i	−0.0344702	+	0.0199014i
$536$	6.83483	−	3.94609i	0.295220	−	0.170445i
$537$	0.669176	+	32.5076i	0.0288771	+	1.40281i
$538$		−	27.1480i		−	1.17044i
$539$	8.99995	+	23.6684i	0.387655	+	1.01947i
$540$	−1.59549	−	2.40706i	−0.0686588	−	0.103583i
$541$	−5.65426	−	9.79347i	−0.243096	−	0.421054i	0.718499	−	0.695528i	$-0.244830\pi$
$541$	−5.65426	−	9.79347i	−0.243096	−	0.421054i	−0.961594	+	0.274474i	$0.911496\pi$
$542$	10.6671			0.458191
$543$	−2.71993	−	1.49658i	−0.116723	−	0.0642242i
$544$			3.89470i			0.166984i
$545$	−10.7328			−0.459741
$546$	2.86236	−	16.2729i	0.122498	−	0.696415i
$547$	−18.1327			−0.775298			−0.387649	−	0.921807i	$-0.626713\pi$
$547$	−18.1327			−0.775298			−0.387649	+	0.921807i	$0.626713\pi$
$548$			6.85540i			0.292848i
$549$	−0.0715335	−	1.73676i	−0.00305297	−	0.0741230i
$550$	−16.9697			−0.723590
$551$	17.8116	+	30.8505i	0.758798	+	1.31428i
$552$	−6.36442	+	11.5669i	−0.270888	+	0.492321i
$553$	−11.3775	+	31.9688i	−0.483820	+	1.35945i
$554$		−	19.0401i		−	0.808936i
$555$	−7.48089	+	0.153996i	−0.317546	+	0.00653676i
$556$	0.958211	−	0.553223i	0.0406372	−	0.0234619i
$557$	−5.71526	+	3.29971i	−0.242163	+	0.139813i	−0.616171	−	0.787613i	$-0.711317\pi$
$557$	−5.71526	+	3.29971i	−0.242163	+	0.139813i	0.374007	+	0.927426i	$0.377983\pi$
$558$	−12.8698	+	0.530079i	−0.544820	+	0.0224400i
$559$	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
$562$	−3.32671			−0.140329
$563$	32.9428			1.38837			0.694187	−	0.719795i	$-0.255764\pi$
$563$	32.9428			1.38837			0.694187	+	0.719795i	$0.255764\pi$
$564$	−21.7598	+	0.447932i	−0.916255	+	0.0188613i
$565$	0.816778	+	0.471567i	0.0343621	+	0.0198390i
$566$	9.31437	+	16.1330i	0.391512	+	0.678119i
$567$	22.9867	−	6.21382i	0.965351	−	0.260956i
$568$	−5.72327	−	9.91300i	−0.240143	−	0.415940i
$569$		−	3.84940i		−	0.161375i	−0.996739	−	0.0806876i	$-0.974288\pi$
$569$		−	3.84940i		−	0.161375i	0.996739	−	0.0806876i	$-0.0257116\pi$
$570$	−2.54390	+	4.62338i	−0.106552	+	0.193652i
$571$	5.78822	−	10.0255i	0.242229	−	0.419554i	−0.719120	−	0.694886i	$-0.755455\pi$
$571$	5.78822	−	10.0255i	0.242229	−	0.419554i	0.961349	+	0.275333i	$0.0887880\pi$
$572$	−12.9016	+	1.91319i	−0.539445	+	0.0799943i
$573$	0.450353	−	0.272521i	0.0188138	−	0.0113847i
$574$	1.39007	+	7.56668i	0.0580203	+	0.315827i
$575$	−30.9668	−	17.8787i	−1.29140	−	0.745592i
$576$	1.60565	+	2.53415i	0.0669020	+	0.105589i
$577$	−11.3976	−	6.58040i	−0.474487	−	0.273945i	0.243629	−	0.969869i	$-0.421662\pi$
$577$	−11.3976	−	6.58040i	−0.474487	−	0.273945i	−0.718116	+	0.695923i	$0.754995\pi$
$578$			1.83133i			0.0761731i
$579$	20.3317	−	0.418533i	0.844958	−	0.0173937i
$580$		−	3.61143i		−	0.149957i
$581$	−0.300680	−	0.353177i	−0.0124743	−	0.0146522i
$582$	−5.51943	+	0.113619i	−0.228788	+	0.00470965i
$583$	−6.54577			−0.271098
$584$	−4.62497	+	8.01069i	−0.191383	+	0.331485i
$585$	4.55111	−	3.92751i	0.188165	−	0.162382i
$586$	−20.7484	+	11.9791i	−0.857108	+	0.494851i
$587$	−8.67657	+	15.0283i	−0.358120	+	0.620283i	−0.987647	−	0.156696i	$-0.949916\pi$
$587$	−8.67657	+	15.0283i	−0.358120	+	0.620283i	0.629526	+	0.776979i	$0.283249\pi$
$588$	9.55394	+	7.46473i	0.393998	+	0.307840i
$589$	11.7687	+	20.3840i	0.484920	+	0.839906i
$590$	−0.671055	+	0.387434i	−0.0276269	+	0.0159504i
$591$	21.7211	−	13.1441i	0.893489	−	0.540674i
$592$	7.77313			0.319474
$593$	−15.6405	−	27.0901i	−0.642278	−	1.11246i	−0.984923	−	0.172994i	$-0.944656\pi$
$593$	−15.6405	−	27.0901i	−0.642278	−	1.11246i	0.342645	−	0.939465i	$-0.388677\pi$
$594$	−10.3849	−	15.6673i	−0.426097	−	0.642839i
$595$	−1.92015	+	5.39529i	−0.0787185	+	0.221185i
$596$	−0.438380	−	0.253099i	−0.0179567	−	0.0103673i
$597$	20.4561	+	11.2555i	0.837214	+	0.460657i
$598$	−25.5589	−	10.1015i	−1.04518	−	0.413080i
$599$	8.02273	+	4.63192i	0.327800	+	0.189255i	0.654864	−	0.755747i	$-0.272726\pi$
$599$	8.02273	+	4.63192i	0.327800	+	0.189255i	−0.327064	+	0.945002i	$0.606059\pi$
$600$	−6.95159	+	4.20660i	−0.283798	+	0.171734i
$601$	9.30956	+	5.37488i	0.379745	+	0.219246i	0.677707	−	0.735332i	$-0.262974\pi$
$601$	9.30956	+	5.37488i	0.379745	+	0.219246i	−0.297962	+	0.954578i	$0.596307\pi$
$602$	−0.874120	−	0.311094i	−0.0356265	−	0.0126792i
$603$	−10.9844	+	20.9743i	−0.447320	+	0.854139i
$604$	−10.6608	+	18.4650i	−0.433781	+	0.751330i
$605$	1.15909			0.0471239
$606$	0.551785	+	26.8049i	0.0224147	+	1.08887i
$607$	13.8539	+	7.99854i	0.562312	+	0.324651i	0.754073	−	0.656791i	$-0.228087\pi$
$607$	13.8539	+	7.99854i	0.562312	+	0.324651i	−0.191761	+	0.981442i	$0.561420\pi$
$608$	2.74101	−	4.74757i	0.111163	−	0.192539i
$609$	28.2542	+	9.40496i	1.14492	+	0.381108i
$610$	0.322014			0.0130380
$611$	−6.64580	−	44.8162i	−0.268860	−	1.81307i
$612$	−6.25351	−	9.86973i	−0.252783	−	0.398960i
$613$	7.29545	+	12.6361i	0.294661	+	0.510367i	0.974906	−	0.222618i	$-0.0714601\pi$
$613$	7.29545	+	12.6361i	0.294661	+	0.510367i	−0.680245	+	0.732984i	$0.738127\pi$
$614$	9.95255			0.401652
$615$	−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	$0.494263\pi$
$618$	33.1305	−	0.681999i	1.33270	−	0.0274340i
$619$	−11.1088	−	6.41367i	−0.446500	−	0.257787i	0.259851	−	0.965649i	$-0.416327\pi$
$619$	−11.1088	−	6.41367i	−0.446500	−	0.257787i	−0.706351	+	0.707862i	$0.749660\pi$
$620$		−	2.38619i		−	0.0958318i
$621$	−2.44405	−	39.5313i	−0.0980762	−	1.58634i
$622$	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
$626$	6.80287	+	11.7829i	0.271898	+	0.470940i
$627$	−16.5580	+	30.0932i	−0.661264	+	1.20180i
$628$	−9.44004	−	5.45021i	−0.376699	−	0.217487i
$629$	−30.2740			−1.20710
$630$	0.974914	+	4.30214i	0.0388415	+	0.171401i
$631$	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
$633$	−1.41001	−	2.33011i	−0.0560430	−	0.0926136i
$634$	−6.01626	−	10.4205i	−0.238936	−	0.413850i
$635$	−6.65156			−0.263959
$636$	−2.68146	+	1.62262i	−0.106327	+	0.0643412i
$637$	−12.9028	+	21.6914i	−0.511229	+	0.859444i
$638$		−	23.5065i		−	0.930631i
$639$	30.4204	+	15.9314i	1.20341	+	0.630238i
$640$	−0.481304	+	0.277881i	−0.0190252	+	0.0109842i
$641$		−	39.2758i		−	1.55130i	−0.631163	−	0.775651i	$-0.717422\pi$
$641$		−	39.2758i		−	1.55130i	0.631163	−	0.775651i	$-0.282578\pi$
$642$	−1.38316	+	2.51381i	−0.0545890	+	0.0992121i
$643$	−12.0836	+	6.97645i	−0.476529	+	0.275124i	−0.718969	−	0.695042i	$-0.755386\pi$
$643$	−12.0836	+	6.97645i	−0.476529	+	0.275124i	0.242440	+	0.970166i	$0.422052\pi$
$644$	15.3556	−	13.0731i	0.605095	−	0.515152i
$645$	−0.174767	−	0.288811i	−0.00688146	−	0.0113719i
$646$	−10.6754	+	18.4903i	−0.420018	+	0.727493i
$647$	2.08473	+	3.61085i	0.0819591	+	0.141957i	0.904091	−	0.427339i	$-0.140549\pi$
$647$	2.08473	+	3.61085i	0.0819591	+	0.141957i	−0.822132	+	0.569297i	$0.807216\pi$
$648$	−8.13789	−	3.84379i	−0.319687	−	0.150998i
$649$	−4.36784	+	2.52177i	−0.171453	+	0.0989882i
$650$	−10.5142	−	13.2491i	−0.412402	−	0.519671i
$651$	18.6685	+	6.21417i	0.731675	+	0.243552i
$652$	11.8450	−	20.5161i	0.463885	−	0.803473i
$653$			29.0510i			1.13685i	0.822734	+	0.568427i	$0.192448\pi$
$653$			29.0510i			1.13685i	−0.822734	+	0.568427i	$0.807552\pi$
$654$	−28.6174	+	17.3172i	−1.11903	+	0.677155i
$655$	1.89552	−	3.28314i	0.0740641	−	0.128283i
$656$	1.45390	−	2.51823i	0.0567652	−	0.0983202i
$657$	−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	$0.317153\pi$
$660$	2.97915	−	1.80276i	0.115963	−	0.0701725i
$661$	−9.68931	+	5.59412i	−0.376870	+	0.217586i	−0.676456	−	0.736483i	$-0.736485\pi$
$661$	−9.68931	+	5.59412i	−0.376870	+	0.217586i	0.299585	+	0.954070i	$0.403152\pi$
$662$	15.0463	+	8.68697i	0.584790	+	0.337629i
$663$	18.7369	−	15.5083i	0.727680	−	0.602293i
$664$			0.175313i			0.00680346i
$665$	6.13772	−	5.22540i	0.238011	−	0.202632i
$666$	−19.6983	+	12.4809i	−0.763292	+	0.483626i
$667$	24.7656	−	42.8953i	0.958928	−	1.66091i
$668$	−5.41827	+	9.38472i	−0.209639	+	0.363106i
$669$	−1.17467	+	0.710827i	−0.0454155	+	0.0274822i
$670$	−3.79853	−	2.19308i	−0.146750	−	0.0847263i
$671$	2.09596			0.0809136
$672$	−0.920589	−	4.48916i	−0.0355125	−	0.173173i
$673$	−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	$0.211378\pi$
$674$		−	11.9191i		−	0.459106i
$675$	10.8620	−	21.8219i	0.418080	−	0.839927i
$676$	−9.48743	−	8.88755i	−0.364901	−	0.341829i
$677$	13.7448	+	23.8066i	0.528254	+	0.914962i	0.999457	+	0.0329380i	$0.0104864\pi$
$677$	13.7448	+	23.8066i	0.528254	+	0.914962i	−0.471204	+	0.882024i	$0.656180\pi$
$678$	2.93869	−	0.0604936i	0.112860	−	0.00232324i
$679$	7.94471	+	2.82747i	0.304890	+	0.108508i
$680$	1.87453	−	1.08226i	0.0718850	−	0.0415028i
$681$	10.1372	−	18.4236i	0.388457	−	0.705996i
$682$		−	15.5315i		−	0.594733i
$683$			26.1620i			1.00106i	0.865719	+	0.500530i	$0.166862\pi$
$683$			26.1620i			1.00106i	−0.865719	+	0.500530i	$0.833138\pi$
$684$	0.676805	+	16.4321i	0.0258783	+	0.628298i
$685$	3.29953	−	1.90498i	0.126068	−	0.0727857i
$686$	−9.60202	−	15.8367i	−0.366607	−	0.604648i
$687$	−0.602959	−	29.2908i	−0.0230043	−	1.11752i
$688$	0.175343	+	0.303703i	0.00668489	+	0.0115786i
$689$	−4.05569	−	5.11060i	−0.154509	−	0.194699i
$690$	7.33576	−	0.151008i	0.279267	−	0.00574879i
$691$			37.4089i			1.42310i	0.702636	+	0.711550i	$0.252006\pi$
$691$			37.4089i			1.42310i	−0.702636	+	0.711550i	$0.747994\pi$
$692$	4.81776	−	8.34460i	0.183144	−	0.317214i
$693$	6.34563	+	28.0022i	0.241051	+	1.06372i
$694$	17.1137			0.649626
$695$	−0.532537	−	0.307460i	−0.0202003	−	0.0116626i
$696$	−5.82700	−	9.62937i	−0.220872	−	0.365000i
$697$	−5.66249	+	9.80773i	−0.214482	+	0.371494i
$698$	0.381547	−	0.660860i	0.0144418	−	0.0250139i
$699$	0.412033	+	20.0159i	0.0155845	+	0.757073i
$700$	12.2073	−	2.24259i	0.461392	−	0.0847618i
$701$			16.0516i			0.606262i	0.952949	+	0.303131i	$0.0980320\pi$
$701$			16.0516i			0.606262i	−0.952949	+	0.303131i	$0.901968\pi$
$702$	5.79790	−	17.8153i	0.218828	−	0.672395i
$703$	36.9035	+	21.3062i	1.39184	+	0.803580i
$704$	−3.13276	+	1.80870i	−0.118070	+	0.0681680i
$705$	6.26223	+	10.3486i	0.235849	+	0.389751i
$706$	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
$709$	0.458321	−	0.793835i	0.0172126	−	0.0298131i	−0.857291	−	0.514832i	$-0.827854\pi$
$709$	0.458321	−	0.793835i	0.0172126	−	0.0298131i	0.874503	+	0.485019i	$0.161187\pi$
$710$	−3.18078	+	5.50926i	−0.119372	+	0.206759i
$711$	−17.8506	+	34.0850i	−0.669451	+	1.27829i
$712$		−	7.86229i		−	0.294652i
$713$	16.3635	−	28.3423i	0.612816	−	1.06143i
$714$	3.58542	+	17.4839i	0.134181	+	0.654319i
$715$	4.50594	+	5.67797i	0.168513	+	0.212344i
$716$	−16.2572	+	9.38612i	−0.607561	+	0.350776i
$717$	−43.9367	−	24.1751i	−1.64085	−	0.902837i
$718$	−4.93047	−	8.53982i	−0.184003	−	0.318703i
$719$	17.0689	−	29.5642i	0.636563	−	1.10256i	−0.349618	−	0.936892i	$-0.613689\pi$
$719$	17.0689	−	29.5642i	0.636563	−	1.10256i	0.986182	−	0.165668i	$-0.0529779\pi$
$720$	0.773515	−	1.47699i	0.0288272	−	0.0550443i
$721$	−47.6883	−	16.9720i	−1.77601	−	0.632069i
$722$	9.57178	−	5.52627i	0.356225	−	0.205667i
$723$	−9.50221	−	5.22836i	−0.353391	−	0.194445i
$724$		−	1.79237i		−	0.0666129i
$725$	26.3997	−	15.2419i	0.980461	−	0.566069i
$726$	3.09056	−	1.87018i	0.114701	−	0.0694090i
$727$		−	10.1792i		−	0.377524i	−0.982023	−	0.188762i	$-0.939553\pi$
$727$		−	10.1792i		−	0.377524i	0.982023	−	0.188762i	$-0.0604475\pi$
$728$	9.02806	−	3.08125i	0.334602	−	0.114199i
$729$	26.7944	−	3.32587i	0.992384	−	0.123180i
$730$	5.14076			0.190268
$731$	−0.682908	−	1.18283i	−0.0252583	−	0.0437486i
$732$	0.858604	−	0.519565i	0.0317349	−	0.0192037i
$733$	−26.5104	+	15.3058i	−0.979184	+	0.565332i	−0.902024	−	0.431686i	$-0.857919\pi$
$733$	−26.5104	+	15.3058i	−0.979184	+	0.565332i	−0.0771605	+	0.997019i	$0.524585\pi$
$734$	−11.3222	−	19.6107i	−0.417912	−	0.723844i
$735$	0.937943	−	6.67265i	0.0345965	−	0.246124i
$736$	−7.62233			−0.280963
$737$	−24.7243	−	14.2746i	−0.910732	−	0.525812i
$738$	0.358994	+	8.71600i	0.0132148	+	0.320840i
$739$	5.89098	+	10.2035i	0.216703	+	0.375341i	0.953798	−	0.300448i	$-0.0971363\pi$
$739$	5.89098	+	10.2035i	0.216703	+	0.375341i	−0.737095	+	0.675789i	$0.763803\pi$
$740$	−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	$0.637689\pi$
$744$	−3.85009	−	6.36245i	−0.141151	−	0.233259i
$745$			0.281325i			0.0103069i
$746$	−2.29852	−	1.32705i	−0.0841548	−	0.0485868i
$747$	−0.281491	−	0.444268i	−0.0102992	−	0.0162549i
$748$	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
$751$	10.1703			0.371120			0.185560	−	0.982633i	$-0.440590\pi$
$751$	10.1703			0.371120			0.185560	+	0.982633i	$0.440590\pi$
$752$	−6.28286	−	10.8822i	−0.229112	−	0.396834i
$753$	−15.6350	+	0.321851i	−0.569772	+	0.0117289i
$754$	18.3527	−	14.5644i	0.668365	−	0.530403i
$755$	11.8497			0.431254
$756$	9.54091	+	9.89803i	0.347000	+	0.359988i
$757$	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	$-0.135571\pi$
$758$	−8.51153	−	4.91414i	−0.309153	−	0.178489i
$759$	47.7478	−	0.982900i	1.73313	−	0.0356770i
$760$	−3.04670			−0.110515
$761$	7.15935	−	12.4004i	0.259526	−	0.449513i	−0.706589	−	0.707624i	$-0.749767\pi$
$761$	7.15935	−	12.4004i	0.259526	−	0.449513i	0.966115	+	0.258112i	$0.0831002\pi$
$762$	−17.7354	+	10.7322i	−0.642487	+	0.388787i
$763$	50.2533	−	9.23199i	1.81929	−	0.334220i
$764$	0.263194	+	0.151955i	0.00952204	+	0.00549755i
$765$	−3.01261	+	5.75245i	−0.108921	+	0.207980i
$766$	31.3875	+	18.1216i	1.13408	+	0.654760i
$767$	−4.67513	−	1.84772i	−0.168809	−	0.0667173i
$768$	−0.834971	+	1.51751i	−0.0301294	+	0.0547583i
$769$	8.87410	+	5.12346i	0.320008	+	0.184757i	0.651396	−	0.758738i	$-0.274184\pi$
$769$	8.87410	+	5.12346i	0.320008	+	0.184757i	−0.331388	+	0.943495i	$0.607517\pi$
$770$	−5.23151	+	0.961074i	−0.188530	+	0.0346347i
$771$	15.3176	−	27.8387i	0.551649	−	1.00259i
$772$	5.87051	+	10.1680i	0.211284	+	0.365955i
$773$	−51.8689			−1.86560			−0.932798	−	0.360401i	$-0.882640\pi$
$773$	−51.8689			−1.86560			−0.932798	+	0.360401i	$0.882640\pi$
$774$	−0.931985	−	0.488089i	−0.0334995	−	0.0175440i
$775$	17.4432	−	10.0708i	0.626577	−	0.361754i
$776$	−1.59366	−	2.76030i	−0.0572090	−	0.0990889i
$777$	34.8948	−	7.15586i	1.25184	−	0.256715i
$778$	6.61455	−	11.4567i	0.237143	−	0.410744i
$779$	13.8050	−	7.97030i	0.494614	−	0.285566i
$780$	3.25335	+	1.20899i	0.116489	+	0.0432889i
$781$	−20.7034	+	35.8593i	−0.740825	+	1.28315i
$782$	29.6867			1.06159
$783$	30.2278	+	15.0461i	1.08025	+	0.537705i
$784$	−1.11684	+	6.91033i	−0.0398870	+	0.246798i
$785$			6.05803i			0.216221i
$786$	−0.243161	−	11.8124i	−0.00867328	−	0.421335i
$787$		−	9.44167i		−	0.336559i	−0.985739	−	0.168280i	$-0.946179\pi$
$787$		−	9.44167i		−	0.336559i	0.985739	−	0.168280i	$-0.0538212\pi$
$788$	12.6942	+	7.32902i	0.452213	+	0.261086i
$789$	0.728936	+	35.4106i	0.0259508	+	1.26065i
$790$	−6.17294	−	3.56395i	−0.219623	−	0.126800i
$791$	−4.22997	−	1.50542i	−0.150400	−	0.0535266i
$792$	5.03474	−	9.61363i	0.178902	−	0.341605i
$793$	1.29863	+	1.63642i	0.0461158	+	0.0581109i
$794$	−0.874957	+	1.51547i	−0.0310510	+	0.0537820i
$795$	1.52610	+	0.839699i	0.0541252	+	0.0297811i
$796$			13.4801i			0.477790i
$797$	12.5043	+	21.6580i	0.442924	+	0.767167i	0.997905	−	0.0646962i	$-0.0206078\pi$
$797$	12.5043	+	21.6580i	0.442924	+	0.767167i	−0.554981	+	0.831863i	$0.687275\pi$
$798$	7.93426	−	23.8359i	0.280870	−	0.843782i
$799$	24.4698	+	42.3830i	0.865680	+	1.49940i
$800$	−4.06264	−	2.34556i	−0.143636	−	0.0829282i
$801$	12.6241	+	19.9242i	0.446049	+	0.703986i
$802$	−10.2634			−0.362412
$803$	33.4608			1.18081
$804$	−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
$807$	−22.6678	+	41.1973i	−0.797945	+	1.45021i
$808$	−13.4053	+	7.73954i	−0.471596	+	0.272276i
$809$	4.55657	−	2.63074i	0.160201	−	0.0924919i	−0.417756	−	0.908559i	$-0.637183\pi$
$809$	4.55657	−	2.63074i	0.160201	−	0.0924919i	0.577957	+	0.816067i	$0.303850\pi$
$810$	0.411334	+	4.98491i	0.0144528	+	0.175152i
$811$		−	15.6340i		−	0.548982i	−0.961590	−	0.274491i	$-0.911491\pi$
$811$		−	15.6340i		−	0.548982i	0.961590	−	0.274491i	$-0.0885094\pi$
$812$	3.10644	+	16.9096i	0.109015	+	0.593410i
$813$	−16.1874	−	8.90671i	−0.567716	−	0.312372i
$814$	−14.0593	−	24.3514i	−0.492777	−	0.853515i
$815$	−13.1660			−0.461184
$816$	3.25196	−	5.91023i	0.113841	−	0.206899i
$817$			1.92247i			0.0672587i
$818$	−14.5730			−0.509534
$819$	−17.9310	+	22.3042i	−0.626561	+	0.779372i
$820$	−1.61604			−0.0564346
$821$			28.7356i			1.00288i	0.865193	+	0.501439i	$0.167196\pi$
$821$			28.7356i			1.00288i	−0.865193	+	0.501439i	$0.832804\pi$
$822$	5.72406	−	10.4031i	0.199649	−	0.362850i
$823$	−35.7865			−1.24744			−0.623719	−	0.781648i	$-0.714379\pi$
$823$	−35.7865			−1.24744			−0.623719	+	0.781648i	$0.714379\pi$
$824$	9.56598	+	16.5688i	0.333247	+	0.577200i
$825$	25.7516	+	14.1692i	0.896556	+	0.493308i
$826$	2.80878	−	2.39128i	0.0977299	−	0.0832031i
$827$		−	32.7339i		−	1.13827i	−0.822244	−	0.569135i	$-0.807278\pi$
$827$		−	32.7339i		−	1.13827i	0.822244	−	0.569135i	$-0.192722\pi$
$828$	19.3161	−	12.2388i	0.671281	−	0.425327i
$829$	−29.1137	+	16.8088i	−1.01116	+	0.583794i	−0.911531	−	0.411231i	$-0.865099\pi$
$829$	−29.1137	+	16.8088i	−1.01116	+	0.583794i	−0.0996290	+	0.995025i	$0.531766\pi$
$830$	0.0843787	−	0.0487161i	0.00292883	−	0.00169096i
$831$	−15.8979	+	28.8934i	−0.551493	+	1.00230i
$832$	−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
$835$	6.02253			0.208418
$836$	−19.8307			−0.685858
$837$	19.9725	+	9.94147i	0.690352	+	0.343628i
$838$	30.0831	+	17.3685i	1.03920	+	0.599984i
$839$	−15.5856	−	26.9950i	−0.538073	−	0.931970i	−0.999008	−	0.0445360i	$-0.985819\pi$
$839$	−15.5856	−	26.9950i	−0.538073	−	0.931970i	0.460935	−	0.887434i	$-0.347514\pi$
$840$	−1.90483	+	1.69053i	−0.0657230	+	0.0583289i
$841$	6.61312	+	11.4543i	0.228039	+	0.394974i
$842$		−	31.5971i		−	1.08891i
$843$	5.04831	+	2.77771i	0.173873	+	0.0956693i
$844$	0.786213	−	1.36176i	0.0270626	−	0.0468737i
$845$	−1.64124	+	7.03601i	−0.0564602	+	0.242046i
$846$	33.3947	+	17.4891i	1.14813	+	0.601287i
$847$	−5.42715	+	0.997016i	−0.186479	+	0.0342579i
$848$	−1.56709	−	0.904762i	−0.0538142	−	0.0310696i
$849$	−0.664061	−	32.2591i	−0.0227905	−	1.10713i
$850$	15.8227	+	9.13527i	0.542716	+	0.313337i
$851$		−	59.2494i		−	2.03104i
$852$	0.408037	+	19.8218i	0.0139791	+	0.679084i
$853$		−	3.55010i		−	0.121553i	−0.998151	−	0.0607765i	$-0.980642\pi$
$853$		−	3.55010i		−	0.121553i	0.998151	−	0.0607765i	$-0.0193577\pi$
$854$	−1.50774	+	0.276986i	−0.0515939	+	0.00947826i
$855$	7.72077	−	4.89192i	0.264045	−	0.167300i
$856$	−1.65654			−0.0566194
$857$	−12.7969	+	22.1648i	−0.437133	+	0.757136i	−0.997467	−	0.0711307i	$-0.977339\pi$
$857$	−12.7969	+	22.1648i	−0.437133	+	0.757136i	0.560334	+	0.828266i	$0.310673\pi$
$858$	21.1758	+	7.86923i	0.722929	+	0.268651i
$859$	−2.65051	+	1.53027i	−0.0904341	+	0.0522122i	−0.544535	−	0.838738i	$-0.683294\pi$
$859$	−2.65051	+	1.53027i	−0.0904341	+	0.0522122i	0.454101	+	0.890950i	$0.349961\pi$
$860$	0.0974489	−	0.168786i	0.00332298	−	0.00575557i
$861$	4.20852	−	12.6431i	0.143426	−	0.430877i
$862$	11.4619	+	19.8526i	0.390393	+	0.676181i
$863$	−18.9157	+	10.9210i	−0.643896	+	0.371754i	−0.786114	−	0.618082i	$-0.787910\pi$
$863$	−18.9157	+	10.9210i	−0.643896	+	0.371754i	0.142218	+	0.989835i	$0.454577\pi$
$864$	−0.320643	−	5.18625i	−0.0109085	−	0.176440i
$865$	−5.35505			−0.182077
$866$	10.0033	+	17.3262i	0.339925	+	0.588767i
$867$	1.52910	−	2.77905i	0.0519311	−	0.0943814i
$868$	2.05253	+	11.1727i	0.0696673	+	0.379227i
$869$	−40.1791	−	23.1974i	−1.36298	−	0.786919i
$870$	−3.01544	+	5.48037i	−0.102233	+	0.185802i
$871$	−4.17405	−	28.1479i	−0.141432	−	0.953754i
$872$	−16.7245	−	9.65592i	−0.566364	−	0.326991i
$873$	8.47063	+	4.43614i	0.286687	+	0.150141i
$874$	−36.1875	−	20.8929i	−1.22406	−	0.706712i
$875$	−9.23748	−	10.8503i	−0.312284	−	0.366807i
$876$	13.7071	−	8.29455i	0.463121	−	0.280247i
$877$	−12.3225	+	21.3431i	−0.416100	+	0.720706i	−0.995543	−	0.0943062i	$-0.969937\pi$
$877$	−12.3225	+	21.3431i	−0.416100	+	0.720706i	0.579443	+	0.815013i	$0.303270\pi$
$878$	−13.8664			−0.467968
$879$	41.4880	−	0.854040i	1.39935	−	0.0288061i
$880$	1.74107	+	1.00521i	0.0586914	+	0.0338855i
$881$	−13.1270	+	22.7365i	−0.442258	+	0.766014i	−0.997857	−	0.0654371i	$-0.979156\pi$
$881$	−13.1270	+	22.7365i	−0.442258	+	0.766014i	0.555599	+	0.831451i	$0.312489\pi$
$882$	−8.26534	−	19.3050i	−0.278308	−	0.650034i
$883$	−36.3198			−1.22226			−0.611129	−	0.791531i	$-0.709285\pi$
$883$	−36.3198			−1.22226			−0.611129	+	0.791531i	$0.709285\pi$
$884$	13.0596	+	5.16144i	0.439241	+	0.173598i
$885$	1.34183	−	0.0276218i	0.0451050	−	0.000928497i
$886$	17.8923	+	30.9904i	0.601104	+	1.04114i
$887$	−15.1069			−0.507240			−0.253620	−	0.967304i	$-0.581621\pi$
$887$	−15.1069			−0.507240			−0.253620	+	0.967304i	$0.581621\pi$
$888$	−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
$891$	2.67734	+	32.4463i	0.0896942	+	1.08699i
$892$	−0.686501	−	0.396352i	−0.0229858	−	0.0132708i
$893$		−	68.8855i		−	2.30516i
$894$	0.453914	+	0.750113i	0.0151812	+	0.0250875i
$895$	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
$899$	13.9501	+	24.1623i	0.465263	+	0.805859i
$900$	14.0615	−	0.579163i	0.468716	−	0.0193054i
$901$	6.10336	+	3.52377i	0.203332	+	0.117394i
$902$	−10.5187			−0.350233
$903$	1.06673	+	1.20195i	0.0354985	+	0.0399984i
$904$	0.848506	+	1.46966i	0.0282209	+	0.0488800i
$905$	−0.862674	+	0.498065i	−0.0286762	+	0.0165562i
$906$	31.5955	−	19.1193i	1.04969	−	0.635196i
$907$	−13.9571	−	24.1745i	−0.463439	−	0.802700i	0.535691	−	0.844414i	$-0.320051\pi$
$907$	−13.9571	−	24.1745i	−0.463439	−	0.802700i	−0.999130	+	0.0417145i	$0.986718\pi$
$908$	12.1407			0.402905
$909$	21.5439	−	41.1373i	0.714567	−	1.36444i
$910$	−3.99174	−	3.48902i	−0.132325	−	0.115660i
$911$		−	51.9732i		−	1.72195i	−0.508649	−	0.860974i	$-0.669855\pi$
$911$		−	51.9732i		−	1.72195i	0.508649	−	0.860974i	$-0.330145\pi$
$912$	−8.12358	+	4.91580i	−0.268999	+	0.162778i
$913$	0.549214	−	0.317089i	0.0181763	−	0.0104941i
$914$			6.56051i			0.217002i
$915$	−0.488658	−	0.268872i	−0.0161545	−	0.00888864i
$916$	14.6485	−	8.45733i	0.484001	−	0.279438i
$917$	−6.05122	+	17.0029i	−0.199829	+	0.561485i
$918$	1.24881	+	20.1989i	0.0412168	+	0.666662i
$919$	14.6677	−	25.4053i	0.483844	−	0.838042i	−0.515984	−	0.856598i	$-0.672574\pi$
$919$	14.6677	−	25.4053i	0.483844	−	0.838042i	0.999828	+	0.0185560i	$0.00590691\pi$
$920$	2.11810	+	3.66865i	0.0698317	+	0.120952i
$921$	−15.1031	−	8.31009i	−0.497663	−	0.273827i
$922$	−2.37852	+	1.37324i	−0.0783323	+	0.0452252i
$923$	−40.8247	+	6.05389i	−1.34376	+	0.199266i
$924$	−12.3984	+	11.0035i	−0.407877	+	0.361989i
$925$	18.2324	−	31.5794i	0.599477	−	1.03833i
$926$		−	3.40968i		−	0.112049i
$927$	−50.8452	−	26.6281i	−1.66998	−	0.874580i
$928$	3.24909	−	5.62758i	0.106656	−	0.184734i
$929$	21.5058	−	37.2491i	0.705582	−	1.22210i	−0.260899	−	0.965366i	$-0.584019\pi$
$929$	21.5058	−	37.2491i	0.705582	−	1.22210i	0.966481	−	0.256738i	$-0.0826477\pi$
$930$	−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
$933$	−13.7878	−	22.7850i	−0.451394	−	0.745948i
$934$	−3.76781	+	2.17534i	−0.123286	+	0.0711795i
$935$	−6.78094	−	3.91497i	−0.221760	−	0.128033i
$936$	10.6253	−	2.02563i	0.347299	−	0.0662098i
$937$		−	33.0171i		−	1.07862i	−0.842107	−	0.539311i	$-0.818685\pi$
$937$		−	33.0171i		−	1.07862i	0.842107	−	0.539311i	$-0.181315\pi$
$938$	19.6720	+	7.00116i	0.642315	+	0.228596i
$939$	−0.485006	−	23.5609i	−0.0158276	−	0.768879i
$940$	−3.49177	+	6.04792i	−0.113889	+	0.197261i
$941$	4.19320	−	7.26284i	0.136694	−	0.236762i	−0.789549	−	0.613687i	$-0.789685\pi$
$941$	4.19320	−	7.26284i	0.136694	−	0.236762i	0.926243	+	0.376926i	$0.123019\pi$
$942$	9.77455	+	16.1529i	0.318472	+	0.526289i
$943$	−19.1948	−	11.0821i	−0.625067	−	0.360883i
$944$	−1.39424			−0.0453788
$945$	2.11272	−	7.34255i	0.0687268	−	0.238853i
$946$	0.634286	−	1.09862i	0.0206224	−	0.0357191i
$947$		−	48.1942i		−	1.56610i	−0.621957	−	0.783051i	$-0.713662\pi$
$947$		−	48.1942i		−	1.56610i	0.621957	−	0.783051i	$-0.286338\pi$
$948$	−22.2097	+	0.457191i	−0.721336	+	0.0148489i
$949$	20.7319	+	26.1245i	0.672987	+	0.848036i
$950$	−12.8584	−	22.2715i	−0.417183	−	0.722582i
$951$	0.428925	+	20.8365i	0.0139089	+	0.675671i
$952$	−7.84607	+	6.67981i	−0.254293	+	0.216494i
$953$	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	$0.133470\pi$
$954$	5.42397	−	0.223402i	0.175608	−	0.00723291i
$955$		−	0.168902i		−	0.00546554i
$956$		−	28.9533i		−	0.936415i
$957$	−19.6272	+	35.6713i	−0.634458	+	1.15309i
$958$	33.3493	−	19.2542i	1.07747	−	0.622076i
$959$	−13.8106	+	11.7577i	−0.445966	+	0.379677i
$960$	0.962403	−	0.0198113i	0.0310614	−	0.000639407i
$961$	−6.28268	−	10.8819i	−0.202667	−	0.351030i
$962$	10.3013	−	26.0646i	0.332128	−	0.840357i
$963$	4.19791	−	2.65982i	0.135276	−	0.0857115i
$964$		−	6.26173i		−	0.201677i
$965$	3.26260	−	5.65099i	0.105027	−	0.181912i
$966$	−34.2178	+	7.01704i	−1.10094	+	0.225769i
$967$	−39.9177			−1.28367			−0.641833	−	0.766845i	$-0.721826\pi$
$967$	−39.9177			−1.28367			−0.641833	+	0.766845i	$0.721826\pi$
$968$	1.80618	+	1.04280i	0.0580528	+	0.0335168i
$969$	31.6389	−	19.1456i	1.01639	−	0.615044i
$970$	−0.885694	+	1.53407i	−0.0284379	+	0.0492559i
$971$	−15.0900	+	26.1367i	−0.484262	+	0.838766i	−0.999837	−	0.0180788i	$-0.994245\pi$
$971$	−15.0900	+	26.1367i	−0.484262	+	0.838766i	0.515575	+	0.856844i	$0.327578\pi$
$972$	9.13985	+	12.6279i	0.293161	+	0.405039i
$973$	2.75793	+	0.981530i	0.0884152	+	0.0314664i
$974$		−	8.88486i		−	0.284689i
$975$	4.89283	+	28.8846i	0.156696	+	0.925048i
$976$	0.501784	+	0.289705i	0.0160617	+	0.00927323i
$977$	16.4945	−	9.52308i	0.527705	−	0.304670i	−0.212377	−	0.977188i	$-0.568120\pi$
$977$	16.4945	−	9.52308i	0.527705	−	0.304670i	0.740081	+	0.672518i	$0.234787\pi$
$978$	−35.1052	+	21.2431i	−1.12254	+	0.679279i
$979$	−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
$982$	−5.48319	+	9.49716i	−0.174976	+	0.303067i
$983$	−25.9081	+	44.8742i	−0.826340	+	1.43126i	0.0745500	+	0.997217i	$0.476248\pi$
$983$	−25.9081	+	44.8742i	−0.826340	+	1.43126i	−0.900891	+	0.434046i	$0.857085\pi$
$984$	−4.30894	+	2.60746i	−0.137364	+	0.0831228i
$985$		−	8.14637i		−	0.259565i
$986$	−12.6542	+	21.9177i	−0.402992	+	0.698003i
$987$	−38.2228	−	43.0681i	−1.21664	−	1.37087i
$988$	−12.2869	−	15.4828i	−0.390897	−	0.492572i
$989$	2.31493	−	1.33652i	0.0736104	−	0.0424990i
$990$	−6.02613	+	0.248204i	−0.191523	+	0.00788843i
$991$	14.0932	+	24.4102i	0.447687	+	0.775416i	0.998235	−	0.0593874i	$-0.0189147\pi$
$991$	14.0932	+	24.4102i	0.447687	+	0.775416i	−0.550548	+	0.834803i	$0.685581\pi$
$992$	2.14678	−	3.71833i	0.0681603	−	0.118057i
$993$	−15.5794	−	25.7457i	−0.494399	−	0.817016i
$994$	10.1542	−	28.5317i	0.322073	−	0.904969i
$995$	6.48802	−	3.74586i	0.205684	−	0.118752i
$996$	0.146381	−	0.266038i	0.00463826	−	0.00842975i
$997$		−	28.6818i		−	0.908360i	−0.890910	−	0.454180i	$-0.849932\pi$
$997$		−	28.6818i		−	0.908360i	0.890910	−	0.454180i	$-0.150068\pi$
$998$	−22.4192	+	12.9437i	−0.709668	+	0.409727i
$999$	40.3134	−	2.49240i	1.27546	−	0.0788561i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.14	✓	76	39.29	odd	6
546.2.u.a.185.25	yes	76	13.3	even	3
546.2.u.a.425.14	yes	76	7.5	odd	6
546.2.u.a.425.25	yes	76	21.5	even	6
546.2.bb.a.269.7	yes	76	1.1	even	1	trivial
546.2.bb.a.269.20	yes	76	3.2	odd	2	inner
546.2.bb.a.341.1	yes	76	91.68	odd	6	inner
546.2.bb.a.341.26	yes	76	273.68	even	6	inner

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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.834971 + 1.51751i) q^{3} -1.00000 q^{4} +(0.277881 + 0.481304i) q^{5} +(1.51751 + 0.834971i) q^{6} +(-1.71510 - 2.01455i) q^{7} +1.00000i q^{8} +(-1.60565 - 2.53415i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.834971 + 1.51751i) q^{3} -1.00000 q^{4} +(0.277881 + 0.481304i) q^{5} +(1.51751 + 0.834971i) q^{6} +(-1.71510 - 2.01455i) q^{7} +1.00000i q^{8} +(-1.60565 - 2.53415i) q^{9} +(0.481304 - 0.277881i) q^{10} +(3.13276 - 1.80870i) q^{11} +(0.834971 - 1.51751i) q^{12} +(3.35317 + 1.32525i) q^{13} +(-2.01455 + 1.71510i) q^{14} +(-0.962403 + 0.0198113i) q^{15} +1.00000 q^{16} -3.89470 q^{17} +(-2.53415 + 1.60565i) q^{18} +(4.74757 + 2.74101i) q^{19} +(-0.277881 - 0.481304i) q^{20} +(4.48916 - 0.920589i) q^{21} +(-1.80870 - 3.13276i) q^{22} -7.62233i q^{23} +(-1.51751 - 0.834971i) q^{24} +(2.34556 - 4.06264i) q^{25} +(1.32525 - 3.35317i) q^{26} +(5.18625 - 0.320643i) q^{27} +(1.71510 + 2.01455i) q^{28} +(5.62758 + 3.24909i) q^{29} +(0.0198113 + 0.962403i) q^{30} +(3.71833 + 2.14678i) q^{31} -1.00000i q^{32} +(0.128950 + 6.26420i) q^{33} +3.89470i q^{34} +(0.493016 - 1.38529i) q^{35} +(1.60565 + 2.53415i) q^{36} +7.77313 q^{37} +(2.74101 - 4.74757i) q^{38} +(-4.81087 + 3.98190i) q^{39} +(-0.481304 + 0.277881i) q^{40} +(1.45390 - 2.51823i) q^{41} +(-0.920589 - 4.48916i) q^{42} +(0.175343 + 0.303703i) q^{43} +(-3.13276 + 1.80870i) q^{44} +(0.773515 - 1.47699i) q^{45} -7.62233 q^{46} +(-6.28286 - 10.8822i) q^{47} +(-0.834971 + 1.51751i) q^{48} +(-1.11684 + 6.91033i) q^{49} +(-4.06264 - 2.34556i) q^{50} +(3.25196 - 5.91023i) q^{51} +(-3.35317 - 1.32525i) q^{52} +(-1.56709 - 0.904762i) q^{53} +(-0.320643 - 5.18625i) q^{54} +(1.74107 + 1.00521i) q^{55} +(2.01455 - 1.71510i) q^{56} +(-8.12358 + 4.91580i) q^{57} +(3.24909 - 5.62758i) q^{58} -1.39424 q^{59} +(0.962403 - 0.0198113i) q^{60} +(0.501784 + 0.289705i) q^{61} +(2.14678 - 3.71833i) q^{62} +(-2.35131 + 7.58098i) q^{63} -1.00000 q^{64} +(0.293933 + 1.98215i) q^{65} +(6.26420 - 0.128950i) q^{66} +(-3.94609 - 6.83483i) q^{67} +3.89470 q^{68} +(11.5669 + 6.36442i) q^{69} +(-1.38529 - 0.493016i) q^{70} +(-9.91300 + 5.72327i) q^{71} +(2.53415 - 1.60565i) q^{72} +(8.01069 + 4.62497i) q^{73} -7.77313i q^{74} +(4.20660 + 6.95159i) 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} +(0.277881 + 0.481304i) q^{80} +(-3.84379 + 8.13789i) q^{81} +(-2.51823 - 1.45390i) q^{82} +0.175313 q^{83} +(-4.48916 + 0.920589i) q^{84} +(-1.08226 - 1.87453i) q^{85} +(0.303703 - 0.175343i) q^{86} +(-9.62937 + 5.82700i) q^{87} +(1.80870 + 3.13276i) q^{88} -7.86229 q^{89} +(-1.47699 - 0.773515i) q^{90} +(-3.08125 - 9.02806i) q^{91} +7.62233i q^{92} +(-6.36245 + 3.85009i) q^{93} +(-10.8822 + 6.28286i) q^{94} +3.04670i q^{95} +(1.51751 + 0.834971i) q^{96} +(-2.76030 + 1.59366i) q^{97} +(6.91033 + 1.11684i) q^{98} +(-9.61363 - 5.03474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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