LMFDB - Embedded newform 546.2.bi.e.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.31411 + 1.12832i) q^{3} +1.00000 q^{4} +(1.62172 - 0.936303i) q^{5} +(1.31411 - 1.12832i) q^{6} +(2.04281 - 1.68135i) q^{7} -1.00000 q^{8} +(0.453768 - 2.96548i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.31411 + 1.12832i) q^{3} +1.00000 q^{4} +(1.62172 - 0.936303i) q^{5} +(1.31411 - 1.12832i) q^{6} +(2.04281 - 1.68135i) q^{7} -1.00000 q^{8} +(0.453768 - 2.96548i) q^{9} +(-1.62172 + 0.936303i) q^{10} +(-2.54994 - 4.41662i) q^{11} +(-1.31411 + 1.12832i) q^{12} +(-3.20727 + 1.64725i) q^{13} +(-2.04281 + 1.68135i) q^{14} +(-1.07467 + 3.06024i) q^{15} +1.00000 q^{16} -2.96212 q^{17} +(-0.453768 + 2.96548i) q^{18} +(-1.30077 + 2.25300i) q^{19} +(1.62172 - 0.936303i) q^{20} +(-0.787372 + 4.51443i) q^{21} +(2.54994 + 4.41662i) q^{22} -6.06950i q^{23} +(1.31411 - 1.12832i) q^{24} +(-0.746672 + 1.29327i) q^{25} +(3.20727 - 1.64725i) q^{26} +(2.74973 + 4.40897i) q^{27} +(2.04281 - 1.68135i) q^{28} +(-7.30144 - 4.21549i) q^{29} +(1.07467 - 3.06024i) q^{30} +(4.09797 - 7.09789i) q^{31} -1.00000 q^{32} +(8.33428 + 2.92677i) q^{33} +2.96212 q^{34} +(1.73863 - 4.63937i) q^{35} +(0.453768 - 2.96548i) q^{36} +6.37656i q^{37} +(1.30077 - 2.25300i) q^{38} +(2.35607 - 5.78351i) q^{39} +(-1.62172 + 0.936303i) q^{40} +(-4.85500 - 2.80304i) q^{41} +(0.787372 - 4.51443i) q^{42} +(-4.87733 - 8.44778i) q^{43} +(-2.54994 - 4.41662i) q^{44} +(-2.04071 - 5.23406i) q^{45} +6.06950i q^{46} +(2.70708 - 1.56293i) q^{47} +(-1.31411 + 1.12832i) q^{48} +(1.34615 - 6.86934i) q^{49} +(0.746672 - 1.29327i) q^{50} +(3.89256 - 3.34224i) q^{51} +(-3.20727 + 1.64725i) q^{52} +(8.21797 + 4.74465i) q^{53} +(-2.74973 - 4.40897i) q^{54} +(-8.27059 - 4.77503i) q^{55} +(-2.04281 + 1.68135i) q^{56} +(-0.832761 - 4.42838i) q^{57} +(7.30144 + 4.21549i) q^{58} -2.20283i q^{59} +(-1.07467 + 3.06024i) q^{60} +(5.11154 + 2.95115i) q^{61} +(-4.09797 + 7.09789i) q^{62} +(-4.05904 - 6.82086i) q^{63} +1.00000 q^{64} +(-3.65898 + 5.67436i) q^{65} +(-8.33428 - 2.92677i) q^{66} +(9.56582 - 5.52283i) q^{67} -2.96212 q^{68} +(6.84837 + 7.97599i) q^{69} +(-1.73863 + 4.63937i) q^{70} +(7.27923 + 12.6080i) q^{71} +(-0.453768 + 2.96548i) q^{72} +(1.99779 - 3.46027i) q^{73} -6.37656i q^{74} +(-0.478024 - 2.54199i) q^{75} +(-1.30077 + 2.25300i) q^{76} +(-12.6349 - 4.73499i) q^{77} +(-2.35607 + 5.78351i) q^{78} +(-5.14630 - 8.91365i) q^{79} +(1.62172 - 0.936303i) q^{80} +(-8.58819 - 2.69128i) q^{81} +(4.85500 + 2.80304i) q^{82} +9.63409i q^{83} +(-0.787372 + 4.51443i) q^{84} +(-4.80375 + 2.77345i) q^{85} +(4.87733 + 8.44778i) q^{86} +(14.3513 - 2.69878i) q^{87} +(2.54994 + 4.41662i) q^{88} -14.7628i q^{89} +(2.04071 + 5.23406i) q^{90} +(-3.78224 + 8.75755i) q^{91} -6.06950i q^{92} +(2.62354 + 13.9512i) q^{93} +(-2.70708 + 1.56293i) q^{94} +4.87167i q^{95} +(1.31411 - 1.12832i) q^{96} +(5.83860 + 10.1127i) q^{97} +(-1.34615 + 6.86934i) q^{98} +(-14.2545 + 5.55768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.31411	+	1.12832i	−0.758701	+	0.651438i
$3$	−1.31411	+	1.12832i	−0.758701	+	0.651438i
$4$	1.00000			0.500000
$5$	1.62172	−	0.936303i	0.725257	−	0.418728i	−0.0914273	−	0.995812i	$-0.529143\pi$
$5$	1.62172	−	0.936303i	0.725257	−	0.418728i	0.816685	+	0.577084i	$0.195810\pi$
$6$	1.31411	−	1.12832i	0.536483	−	0.460637i
$7$	2.04281	−	1.68135i	0.772110	−	0.635489i
$7$	2.04281	−	1.68135i	0.772110	−	0.635489i
$8$	−1.00000			−0.353553
$9$	0.453768	−	2.96548i	0.151256	−	0.988495i
$10$	−1.62172	+	0.936303i	−0.512834	+	0.296085i
$11$	−2.54994	−	4.41662i	−0.768835	−	1.33166i	−0.938195	−	0.346107i	$-0.887503\pi$
$11$	−2.54994	−	4.41662i	−0.768835	−	1.33166i	0.169360	−	0.985554i	$-0.445830\pi$
$12$	−1.31411	+	1.12832i	−0.379351	+	0.325719i
$13$	−3.20727	+	1.64725i	−0.889536	+	0.456865i
$13$	−3.20727	+	1.64725i	−0.889536	+	0.456865i
$14$	−2.04281	+	1.68135i	−0.545964	+	0.449359i
$15$	−1.07467	+	3.06024i	−0.277479	+	0.790150i
$16$	1.00000			0.250000
$17$	−2.96212			−0.718421			−0.359210	−	0.933257i	$-0.616954\pi$
$17$	−2.96212			−0.718421			−0.359210	+	0.933257i	$0.616954\pi$
$18$	−0.453768	+	2.96548i	−0.106954	+	0.698971i
$19$	−1.30077	+	2.25300i	−0.298417	+	0.516874i	−0.975774	−	0.218781i	$-0.929792\pi$
$19$	−1.30077	+	2.25300i	−0.298417	+	0.516874i	0.677357	+	0.735655i	$0.263125\pi$
$20$	1.62172	−	0.936303i	0.362629	−	0.209364i
$21$	−0.787372	+	4.51443i	−0.171819	+	0.985129i
$22$	2.54994	+	4.41662i	0.543648	+	0.941627i
$23$		−	6.06950i		−	1.26558i	−0.774324	−	0.632789i	$-0.781910\pi$
$23$		−	6.06950i		−	1.26558i	0.774324	−	0.632789i	$-0.218090\pi$
$24$	1.31411	−	1.12832i	0.268241	−	0.230318i
$25$	−0.746672	+	1.29327i	−0.149334	+	0.258655i
$26$	3.20727	−	1.64725i	0.628997	−	0.323053i
$27$	2.74973	+	4.40897i	0.529185	+	0.848506i
$28$	2.04281	−	1.68135i	0.386055	−	0.317745i
$29$	−7.30144	−	4.21549i	−1.35584	−	0.782796i	−0.366782	−	0.930307i	$-0.619541\pi$
$29$	−7.30144	−	4.21549i	−1.35584	−	0.782796i	−0.989060	+	0.147511i	$0.952874\pi$
$30$	1.07467	−	3.06024i	0.196207	−	0.558720i
$31$	4.09797	−	7.09789i	0.736017	−	1.27482i	−0.218258	−	0.975891i	$-0.570038\pi$
$31$	4.09797	−	7.09789i	0.736017	−	1.27482i	0.954276	−	0.298928i	$-0.0966291\pi$
$32$	−1.00000			−0.176777
$33$	8.33428	+	2.92677i	1.45081	+	0.509485i
$34$	2.96212			0.508000
$35$	1.73863	−	4.63937i	0.293881	−	0.784197i
$36$	0.453768	−	2.96548i	0.0756279	−	0.494247i
$37$			6.37656i			1.04830i	0.851626	+	0.524150i	$0.175617\pi$
$37$			6.37656i			1.04830i	−0.851626	+	0.524150i	$0.824383\pi$
$38$	1.30077	−	2.25300i	0.211013	−	0.365485i
$39$	2.35607	−	5.78351i	0.377273	−	0.926102i
$40$	−1.62172	+	0.936303i	−0.256417	+	0.148043i
$41$	−4.85500	−	2.80304i	−0.758223	−	0.437761i	0.0704341	−	0.997516i	$-0.477562\pi$
$41$	−4.85500	−	2.80304i	−0.758223	−	0.437761i	−0.828658	+	0.559756i	$0.810895\pi$
$42$	0.787372	−	4.51443i	0.121494	−	0.696591i
$43$	−4.87733	−	8.44778i	−0.743786	−	1.28827i	−0.950760	−	0.309928i	$-0.899695\pi$
$43$	−4.87733	−	8.44778i	−0.743786	−	1.28827i	0.206974	−	0.978346i	$-0.433638\pi$
$44$	−2.54994	−	4.41662i	−0.384417	−	0.665831i
$45$	−2.04071	−	5.23406i	−0.304211	−	0.780248i
$46$			6.06950i			0.894899i
$47$	2.70708	−	1.56293i	0.394868	−	0.227977i	−0.289400	−	0.957208i	$-0.593456\pi$
$47$	2.70708	−	1.56293i	0.394868	−	0.227977i	0.684267	+	0.729232i	$0.260122\pi$
$48$	−1.31411	+	1.12832i	−0.189675	+	0.162860i
$49$	1.34615	−	6.86934i	0.192307	−	0.981335i
$50$	0.746672	−	1.29327i	0.105595	−	0.182897i
$51$	3.89256	−	3.34224i	0.545067	−	0.468007i
$52$	−3.20727	+	1.64725i	−0.444768	+	0.228433i
$53$	8.21797	+	4.74465i	1.12883	+	0.651728i	0.943639	−	0.330976i	$-0.107378\pi$
$53$	8.21797	+	4.74465i	1.12883	+	0.651728i	0.185186	+	0.982703i	$0.440711\pi$
$54$	−2.74973	−	4.40897i	−0.374191	−	0.599985i
$55$	−8.27059	−	4.77503i	−1.11521	−	0.643865i
$56$	−2.04281	+	1.68135i	−0.272982	+	0.224679i
$57$	−0.832761	−	4.42838i	−0.110302	−	0.586554i
$58$	7.30144	+	4.21549i	0.958726	+	0.553520i
$59$		−	2.20283i		−	0.286784i	−0.989666	−	0.143392i	$-0.954199\pi$
$59$		−	2.20283i		−	0.286784i	0.989666	−	0.143392i	$-0.0458009\pi$
$60$	−1.07467	+	3.06024i	−0.138739	+	0.395075i
$61$	5.11154	+	2.95115i	0.654466	+	0.377856i	0.790165	−	0.612894i	$-0.209995\pi$
$61$	5.11154	+	2.95115i	0.654466	+	0.377856i	−0.135699	+	0.990750i	$0.543328\pi$
$62$	−4.09797	+	7.09789i	−0.520443	+	0.901433i
$63$	−4.05904	−	6.82086i	−0.511392	−	0.859348i
$64$	1.00000			0.125000
$65$	−3.65898	+	5.67436i	−0.453840	+	0.703818i
$66$	−8.33428	−	2.92677i	−1.02588	−	0.360260i
$67$	9.56582	−	5.52283i	1.16865	−	0.674721i	0.215289	−	0.976550i	$-0.430931\pi$
$67$	9.56582	−	5.52283i	1.16865	−	0.674721i	0.953362	+	0.301830i	$0.0975975\pi$
$68$	−2.96212			−0.359210
$69$	6.84837	+	7.97599i	0.824447	+	0.960196i
$70$	−1.73863	+	4.63937i	−0.207806	+	0.554511i
$71$	7.27923	+	12.6080i	0.863886	+	1.49629i	0.868149	+	0.496303i	$0.165310\pi$
$71$	7.27923	+	12.6080i	0.863886	+	1.49629i	−0.00426326	+	0.999991i	$0.501357\pi$
$72$	−0.453768	+	2.96548i	−0.0534770	+	0.349486i
$73$	1.99779	−	3.46027i	0.233823	−	0.404994i	−0.725107	−	0.688636i	$-0.758210\pi$
$73$	1.99779	−	3.46027i	0.233823	−	0.404994i	0.958930	+	0.283643i	$0.0915429\pi$
$74$		−	6.37656i		−	0.741260i
$75$	−0.478024	−	2.54199i	−0.0551975	−	0.293524i
$76$	−1.30077	+	2.25300i	−0.149209	+	0.258437i
$77$	−12.6349	−	4.73499i	−1.43988	−	0.539602i
$78$	−2.35607	+	5.78351i	−0.266772	+	0.654853i
$79$	−5.14630	−	8.91365i	−0.579004	−	1.00286i	−0.995594	−	0.0937696i	$-0.970108\pi$
$79$	−5.14630	−	8.91365i	−0.579004	−	1.00286i	0.416590	−	0.909094i	$-0.363225\pi$
$80$	1.62172	−	0.936303i	0.181314	−	0.104682i
$81$	−8.58819	−	2.69128i	−0.954243	−	0.299031i
$82$	4.85500	+	2.80304i	0.536145	+	0.309543i
$83$			9.63409i			1.05748i	0.848784	+	0.528739i	$0.177335\pi$
$83$			9.63409i			1.05748i	−0.848784	+	0.528739i	$0.822665\pi$
$84$	−0.787372	+	4.51443i	−0.0859094	+	0.492564i
$85$	−4.80375	+	2.77345i	−0.521040	+	0.300823i
$86$	4.87733	+	8.44778i	0.525936	+	0.910948i
$87$	14.3513	−	2.69878i	1.53862	−	0.289340i
$88$	2.54994	+	4.41662i	0.271824	+	0.470813i
$89$		−	14.7628i		−	1.56486i	−0.622741	−	0.782428i	$-0.713981\pi$
$89$		−	14.7628i		−	1.56486i	0.622741	−	0.782428i	$-0.286019\pi$
$90$	2.04071	+	5.23406i	0.215109	+	0.551719i
$91$	−3.78224	+	8.75755i	−0.396486	+	0.918041i
$92$		−	6.06950i		−	0.632789i
$93$	2.62354	+	13.9512i	0.272049	+	1.44668i
$94$	−2.70708	+	1.56293i	−0.279214	+	0.161204i
$95$			4.87167i			0.499822i
$96$	1.31411	−	1.12832i	0.134121	−	0.115159i
$97$	5.83860	+	10.1127i	0.592820	+	1.02679i	0.993851	+	0.110729i	$0.0353187\pi$
$97$	5.83860	+	10.1127i	0.592820	+	1.02679i	−0.401031	+	0.916065i	$0.631348\pi$
$98$	−1.34615	+	6.86934i	−0.135982	+	0.693909i
$99$	−14.2545	+	5.55768i	−1.43263	+	0.558568i
$100$	−0.746672	+	1.29327i	−0.0746672	+	0.129327i
$101$	3.15026	+	5.45640i	0.313462	+	0.542932i	0.979109	−	0.203334i	$-0.0651778\pi$
$101$	3.15026	+	5.45640i	0.313462	+	0.542932i	−0.665647	+	0.746267i	$0.731844\pi$
$102$	−3.89256	+	3.34224i	−0.385420	+	0.330931i
$103$	4.99182	−	2.88203i	0.491859	−	0.283975i	−0.233486	−	0.972360i	$-0.575013\pi$
$103$	4.99182	−	2.88203i	0.491859	−	0.283975i	0.725345	+	0.688385i	$0.241680\pi$
$104$	3.20727	−	1.64725i	0.314498	−	0.161526i
$105$	2.94997	+	8.05838i	0.287888	+	0.786417i
$106$	−8.21797	−	4.74465i	−0.798200	−	0.460841i
$107$		−	6.14671i		−	0.594225i	−0.954842	−	0.297113i	$-0.903976\pi$
$107$		−	6.14671i		−	0.594225i	0.954842	−	0.297113i	$-0.0960237\pi$
$108$	2.74973	+	4.40897i	0.264593	+	0.424253i
$109$	−10.8967	−	6.29124i	−1.04372	−	0.602591i	−0.122834	−	0.992427i	$-0.539198\pi$
$109$	−10.8967	−	6.29124i	−1.04372	−	0.602591i	−0.920884	+	0.389836i	$0.872532\pi$
$110$	8.27059	+	4.77503i	0.788570	+	0.455281i
$111$	−7.19483	−	8.37950i	−0.682903	−	0.795347i
$112$	2.04281	−	1.68135i	0.193027	−	0.158872i
$113$	−1.92741	+	1.11279i	−0.181316	+	0.104683i	−0.587911	−	0.808926i	$-0.700049\pi$
$113$	−1.92741	+	1.11279i	−0.181316	+	0.104683i	0.406595	+	0.913609i	$0.366716\pi$
$114$	0.832761	+	4.42838i	0.0779953	+	0.414756i
$115$	−5.68289	−	9.84306i	−0.529933	−	0.917870i
$116$	−7.30144	−	4.21549i	−0.677921	−	0.391398i
$117$	3.42954	+	10.2586i	0.317061	+	0.948405i
$118$			2.20283i			0.202787i
$119$	−6.05106	+	4.98036i	−0.554700	+	0.456549i
$120$	1.07467	−	3.06024i	0.0981035	−	0.279360i
$121$	−7.50436	+	12.9979i	−0.682214	+	1.18163i
$122$	−5.11154	−	2.95115i	−0.462777	−	0.267185i
$123$	9.54273	−	1.79452i	0.860439	−	0.161806i
$124$	4.09797	−	7.09789i	0.368009	−	0.637410i
$125$			12.1595i			1.08758i
$126$	4.05904	+	6.82086i	0.361608	+	0.607651i
$127$	−3.67232	+	6.36064i	−0.325866	+	0.564416i	−0.981687	−	0.190500i	$-0.938989\pi$
$127$	−3.67232	+	6.36064i	−0.325866	+	0.564416i	0.655822	+	0.754916i	$0.272322\pi$
$128$	−1.00000			−0.0883883
$129$	15.9412	+	5.59810i	1.40354	+	0.492885i
$130$	3.65898	−	5.67436i	0.320914	−	0.497675i
$131$	0.465541	+	0.806340i	0.0406745	+	0.0704503i	0.885646	−	0.464361i	$-0.153716\pi$
$131$	0.465541	+	0.806340i	0.0406745	+	0.0704503i	−0.844971	+	0.534811i	$0.820383\pi$
$132$	8.33428	+	2.92677i	0.725406	+	0.254742i
$133$	1.13085	+	6.78950i	0.0980569	+	0.588725i
$134$	−9.56582	+	5.52283i	−0.826361	+	0.477100i
$135$	8.58743	+	4.57555i	0.739089	+	0.393801i
$136$	2.96212			0.254000
$137$	−2.15714			−0.184297			−0.0921483	−	0.995745i	$-0.529373\pi$
$137$	−2.15714			−0.184297			−0.0921483	+	0.995745i	$0.529373\pi$
$138$	−6.84837	−	7.97599i	−0.582972	−	0.678961i
$139$	7.18997	−	4.15113i	0.609845	−	0.352094i	−0.163060	−	0.986616i	$-0.552136\pi$
$139$	7.18997	−	4.15113i	0.609845	−	0.352094i	0.772905	+	0.634522i	$0.218803\pi$
$140$	1.73863	−	4.63937i	0.146941	−	0.392098i
$141$	−1.79390	+	5.10832i	−0.151074	+	0.430198i
$142$	−7.27923	−	12.6080i	−0.610860	−	1.05804i
$143$	15.4536	+	9.96490i	1.29230	+	0.833307i
$144$	0.453768	−	2.96548i	0.0378140	−	0.247124i
$145$	−15.7879			−1.31111
$146$	−1.99779	+	3.46027i	−0.165338	+	0.286374i
$147$	5.98186	+	10.5460i	0.493376	+	0.869816i
$148$			6.37656i			0.524150i
$149$	1.97912	−	3.42793i	0.162136	−	0.280827i	−0.773499	−	0.633798i	$-0.781495\pi$
$149$	1.97912	−	3.42793i	0.162136	−	0.280827i	0.935634	+	0.352971i	$0.114828\pi$
$150$	0.478024	+	2.54199i	0.0390305	+	0.207553i
$151$	4.82241	+	2.78422i	0.392442	+	0.226576i	0.683218	−	0.730215i	$-0.260580\pi$
$151$	4.82241	+	2.78422i	0.392442	+	0.226576i	−0.290776	+	0.956791i	$0.593913\pi$
$152$	1.30077	−	2.25300i	0.105506	−	0.182743i
$153$	−1.34412	+	8.78413i	−0.108665	+	0.710155i
$154$	12.6349	+	4.73499i	1.01815	+	0.381556i
$155$		−	15.3478i		−	1.23276i
$156$	2.35607	−	5.78351i	0.188636	−	0.463051i
$157$	6.31098	+	3.64365i	0.503671	+	0.290795i	0.730228	−	0.683203i	$-0.239414\pi$
$157$	6.31098	+	3.64365i	0.503671	+	0.290795i	−0.226557	+	0.973998i	$0.572747\pi$
$158$	5.14630	+	8.91365i	0.409418	+	0.709132i
$159$	−16.1528	+	3.03755i	−1.28100	+	0.240894i
$160$	−1.62172	+	0.936303i	−0.128209	+	0.0740213i
$161$	−10.2049	−	12.3988i	−0.804262	−	0.977166i
$162$	8.58819	+	2.69128i	0.674752	+	0.211447i
$163$	−17.1552	−	9.90456i	−1.34370	−	0.775785i	−0.356351	−	0.934352i	$-0.615979\pi$
$163$	−17.1552	−	9.90456i	−1.34370	−	0.775785i	−0.987348	+	0.158567i	$0.949313\pi$
$164$	−4.85500	−	2.80304i	−0.379112	−	0.218880i
$165$	16.2562	−	3.05700i	1.26555	−	0.237987i
$166$		−	9.63409i		−	0.747750i
$167$	13.0891	+	7.55698i	1.01286	+	0.584777i	0.912029	−	0.410126i	$-0.134515\pi$
$167$	13.0891	+	7.55698i	1.01286	+	0.584777i	0.100834	+	0.994903i	$0.467849\pi$
$168$	0.787372	−	4.51443i	0.0607471	−	0.348296i
$169$	7.57313	−	10.5663i	0.582548	−	0.812796i
$170$	4.80375	−	2.77345i	0.368431	−	0.212714i
$171$	6.09099	+	4.87976i	0.465790	+	0.373164i
$172$	−4.87733	−	8.44778i	−0.371893	−	0.644137i
$173$	9.62713	−	16.6747i	0.731937	−	1.26775i	−0.224117	−	0.974562i	$-0.571950\pi$
$173$	9.62713	−	16.6747i	0.731937	−	1.26775i	0.956054	−	0.293190i	$-0.0947169\pi$
$174$	−14.3513	+	2.69878i	−1.08797	+	0.204594i
$175$	0.649132	+	3.89733i	0.0490698	+	0.294610i
$176$	−2.54994	−	4.41662i	−0.192209	−	0.332915i
$177$	2.48551	+	2.89476i	0.186822	+	0.217583i
$178$			14.7628i			1.10652i
$179$	−4.65318	+	2.68651i	−0.347795	+	0.200800i	−0.663714	−	0.747987i	$-0.731021\pi$
$179$	−4.65318	+	2.68651i	−0.347795	+	0.200800i	0.315919	+	0.948786i	$0.397687\pi$
$180$	−2.04071	−	5.23406i	−0.152105	−	0.390124i
$181$			11.3131i			0.840893i	0.907317	+	0.420446i	$0.138126\pi$
$181$			11.3131i			0.840893i	−0.907317	+	0.420446i	$0.861874\pi$
$182$	3.78224	−	8.75755i	0.280358	−	0.649153i
$183$	−10.0470	+	1.88934i	−0.742694	+	0.139664i
$184$			6.06950i			0.447450i
$185$	5.97039	+	10.3410i	0.438952	+	0.760287i
$186$	−2.62354	−	13.9512i	−0.192368	−	1.02296i
$187$	7.55323	+	13.0826i	0.552347	+	0.956693i
$188$	2.70708	−	1.56293i	0.197434	−	0.113988i
$189$	13.0302	+	4.38344i	0.947806	+	0.318848i
$190$		−	4.87167i		−	0.353428i
$191$	−2.74863	−	1.58692i	−0.198884	−	0.114826i	0.397251	−	0.917710i	$-0.369964\pi$
$191$	−2.74863	−	1.58692i	−0.198884	−	0.114826i	−0.596135	+	0.802884i	$0.703298\pi$
$192$	−1.31411	+	1.12832i	−0.0948377	+	0.0814298i
$193$	0.181273	−	0.104658i	0.0130483	−	0.00753344i	−0.493462	−	0.869768i	$-0.664269\pi$
$193$	0.181273	−	0.104658i	0.0130483	−	0.00753344i	0.506510	+	0.862234i	$0.330935\pi$
$194$	−5.83860	−	10.1127i	−0.419187	−	0.726053i
$195$	−1.59422	−	11.5852i	−0.114165	−	0.829637i
$196$	1.34615	−	6.86934i	0.0961535	−	0.490667i
$197$	−9.71998	+	16.8355i	−0.692520	+	1.19948i	0.278490	+	0.960439i	$0.410166\pi$
$197$	−9.71998	+	16.8355i	−0.692520	+	1.19948i	−0.971010	+	0.239040i	$0.923167\pi$
$198$	14.2545	−	5.55768i	1.01302	−	0.394967i
$199$		−	14.4539i		−	1.02461i	−0.858803	−	0.512306i	$-0.828791\pi$
$199$		−	14.4539i		−	1.02461i	0.858803	−	0.512306i	$-0.171209\pi$
$200$	0.746672	−	1.29327i	0.0527977	−	0.0914483i
$201$	−6.33899	+	18.0509i	−0.447118	+	1.27322i
$202$	−3.15026	−	5.45640i	−0.221651	−	0.383911i
$203$	−22.0031	+	3.66480i	−1.54432	+	0.257219i
$204$	3.89256	−	3.34224i	0.272533	−	0.234003i
$205$	−10.4980			−0.733210
$206$	−4.99182	+	2.88203i	−0.347797	+	0.200801i
$207$	−17.9990	−	2.75414i	−1.25102	−	0.191426i
$208$	−3.20727	+	1.64725i	−0.222384	+	0.114216i
$209$	13.2675			0.917735
$210$	−2.94997	−	8.05838i	−0.203567	−	0.556081i
$211$	5.78954	−	10.0278i	0.398568	−	0.690341i	−0.594981	−	0.803740i	$-0.702840\pi$
$211$	5.78954	−	10.0278i	0.398568	−	0.690341i	0.993550	+	0.113399i	$0.0361738\pi$
$212$	8.21797	+	4.74465i	0.564413	+	0.325864i
$213$	−23.7916	−	8.35496i	−1.63018	−	0.572472i
$214$			6.14671i			0.420181i
$215$	−15.8194	−	9.13332i	−1.07887	−	0.622887i
$216$	−2.74973	−	4.40897i	−0.187095	−	0.299992i
$217$	−3.56264	−	21.3898i	−0.241848	−	1.45203i
$218$	10.8967	+	6.29124i	0.738020	+	0.426096i
$219$	1.27900	+	6.80132i	0.0864265	+	0.459591i
$220$	−8.27059	−	4.77503i	−0.557603	−	0.321932i
$221$	9.50032	−	4.87936i	0.639061	−	0.328221i
$222$	7.19483	+	8.37950i	0.482885	+	0.562395i
$223$	−3.33759	+	5.78088i	−0.223502	+	0.387116i	−0.955869	−	0.293794i	$-0.905082\pi$
$223$	−3.33759	+	5.78088i	−0.223502	+	0.387116i	0.732367	+	0.680910i	$0.238416\pi$
$224$	−2.04281	+	1.68135i	−0.136491	+	0.112340i
$225$	3.49637	+	2.80109i	0.233091	+	0.186739i
$226$	1.92741	−	1.11279i	0.128210	−	0.0740219i
$227$			18.4820i			1.22669i	0.789814	+	0.613346i	$0.210177\pi$
$227$			18.4820i			1.22669i	−0.789814	+	0.613346i	$0.789823\pi$
$228$	−0.832761	−	4.42838i	−0.0551510	−	0.293277i
$229$	−0.100542	−	0.174145i	−0.00664403	−	0.0115078i	0.862684	−	0.505743i	$-0.168782\pi$
$229$	−0.100542	−	0.174145i	−0.00664403	−	0.0115078i	−0.869328	+	0.494235i	$0.835448\pi$
$230$	5.68289	+	9.84306i	0.374719	+	0.649032i
$231$	21.9463	−	8.03398i	1.44396	−	0.528597i
$232$	7.30144	+	4.21549i	0.479363	+	0.276760i
$233$	11.1073	−	6.41280i	0.727663	−	0.420116i	−0.0899037	−	0.995950i	$-0.528656\pi$
$233$	11.1073	−	6.41280i	0.727663	−	0.420116i	0.817567	+	0.575834i	$0.195323\pi$
$234$	−3.42954	−	10.2586i	−0.224196	−	0.670624i
$235$	2.92675	−	5.06929i	0.190920	−	0.330684i
$236$		−	2.20283i		−	0.143392i
$237$	16.8203	+	5.90682i	1.09260	+	0.383689i
$238$	6.05106	−	4.98036i	0.392232	−	0.322829i
$239$	−30.2795			−1.95862			−0.979311	−	0.202363i	$-0.935138\pi$
$239$	−30.2795			−1.95862			−0.979311	+	0.202363i	$0.935138\pi$
$240$	−1.07467	+	3.06024i	−0.0693697	+	0.197537i
$241$	8.34511			0.537556			0.268778	−	0.963202i	$-0.413380\pi$
$241$	8.34511			0.537556			0.268778	+	0.963202i	$0.413380\pi$
$242$	7.50436	−	12.9979i	0.482398	−	0.835538i
$243$	14.3225	−	6.15363i	0.918786	−	0.394755i
$244$	5.11154	+	2.95115i	0.327233	+	0.188928i
$245$	−4.24871	−	12.4006i	−0.271440	−	0.792245i
$246$	−9.54273	+	1.79452i	−0.608422	+	0.114414i
$247$	0.460662	−	9.36868i	0.0293112	−	0.596115i
$248$	−4.09797	+	7.09789i	−0.260221	+	0.450717i
$249$	−10.8704	−	12.6602i	−0.688882	−	0.802311i
$250$		−	12.1595i		−	0.769033i
$251$	−0.325183	−	0.563233i	−0.0205253	−	0.0355509i	0.855580	−	0.517670i	$-0.173201\pi$
$251$	−0.325183	−	0.563233i	−0.0205253	−	0.0355509i	−0.876106	+	0.482119i	$0.839867\pi$
$252$	−4.05904	−	6.82086i	−0.255696	−	0.429674i
$253$	−26.8067	+	15.4768i	−1.68532	+	0.973021i
$254$	3.67232	−	6.36064i	0.230422	−	0.399102i
$255$	3.18331	−	9.06480i	0.199346	−	0.567660i
$256$	1.00000			0.0625000
$257$	7.41850			0.462753			0.231377	−	0.972864i	$-0.425677\pi$
$257$	7.41850			0.462753			0.231377	+	0.972864i	$0.425677\pi$
$258$	−15.9412	−	5.59810i	−0.992455	−	0.348522i
$259$	10.7212	+	13.0261i	0.666183	+	0.809403i
$260$	−3.65898	+	5.67436i	−0.226920	+	0.351909i
$261$	−15.8141	+	19.7394i	−0.978869	+	1.22184i
$262$	−0.465541	−	0.806340i	−0.0287612	−	0.0498159i
$263$	17.3650	−	10.0257i	1.07077	−	0.618209i	0.142378	−	0.989812i	$-0.454525\pi$
$263$	17.3650	−	10.0257i	1.07077	−	0.618209i	0.928392	+	0.371603i	$0.121192\pi$
$264$	−8.33428	−	2.92677i	−0.512939	−	0.180130i
$265$	17.7697			1.09159
$266$	−1.13085	−	6.78950i	−0.0693367	−	0.416291i
$267$	16.6573	+	19.4000i	1.01941	+	1.18726i
$268$	9.56582	−	5.52283i	0.584325	−	0.337360i
$269$	−12.4850			−0.761225			−0.380612	−	0.924735i	$-0.624287\pi$
$269$	−12.4850			−0.761225			−0.380612	+	0.924735i	$0.624287\pi$
$270$	−8.58743	−	4.57555i	−0.522615	−	0.278459i
$271$	−2.87931			−0.174906			−0.0874530	−	0.996169i	$-0.527873\pi$
$271$	−2.87931			−0.174906			−0.0874530	+	0.996169i	$0.527873\pi$
$272$	−2.96212			−0.179605
$273$	−4.91108	−	15.7760i	−0.297232	−	0.954805i
$274$	2.15714			0.130317
$275$	7.61587			0.459254
$276$	6.84837	+	7.97599i	0.412223	+	0.480098i
$277$	8.00292			0.480849			0.240424	−	0.970668i	$-0.422713\pi$
$277$	8.00292			0.480849			0.240424	+	0.970668i	$0.422713\pi$
$278$	−7.18997	+	4.15113i	−0.431226	+	0.248968i
$279$	−19.1892	−	15.3733i	−1.14883	−	0.920373i
$280$	−1.73863	+	4.63937i	−0.103903	+	0.277255i
$281$	6.16209			0.367599			0.183800	−	0.982964i	$-0.441160\pi$
$281$	6.16209			0.367599			0.183800	+	0.982964i	$0.441160\pi$
$282$	1.79390	−	5.10832i	0.106825	−	0.304196i
$283$	−11.9016	+	6.87141i	−0.707478	+	0.408463i	−0.810127	−	0.586255i	$-0.800602\pi$
$283$	−11.9016	+	6.87141i	−0.707478	+	0.408463i	0.102648	+	0.994718i	$0.467268\pi$
$284$	7.27923	+	12.6080i	0.431943	+	0.748147i
$285$	−5.49682	−	6.40190i	−0.325604	−	0.379216i
$286$	−15.4536	−	9.96490i	−0.913791	−	0.589237i
$287$	−14.6307	+	2.43687i	−0.863624	+	0.143844i
$288$	−0.453768	+	2.96548i	−0.0267385	+	0.174743i
$289$	−8.22582			−0.483872
$290$	15.7879			0.927097
$291$	−19.0830	−	6.70142i	−1.11867	−	0.392844i
$292$	1.99779	−	3.46027i	0.116912	−	0.202497i
$293$	4.43117	−	2.55834i	0.258872	−	0.149460i	−0.364948	−	0.931028i	$-0.618913\pi$
$293$	4.43117	−	2.55834i	0.258872	−	0.149460i	0.623820	+	0.781568i	$0.285580\pi$
$294$	−5.98186	−	10.5460i	−0.348869	−	0.615053i
$295$	−2.06252	−	3.57238i	−0.120084	−	0.207992i
$296$		−	6.37656i		−	0.370630i
$297$	12.4611	−	23.3871i	0.723067	−	1.35706i
$298$	−1.97912	+	3.42793i	−0.114647	+	0.198575i
$299$	9.99799	+	19.4665i	0.578199	+	1.12578i
$300$	−0.478024	−	2.54199i	−0.0275987	−	0.146762i
$301$	−24.1671	−	9.05674i	−1.39297	−	0.522022i
$302$	−4.82241	−	2.78422i	−0.277498	−	0.160214i
$303$	−10.2964	−	3.61580i	−0.591511	−	0.207722i
$304$	−1.30077	+	2.25300i	−0.0746044	+	0.129219i
$305$	11.0527			0.632875
$306$	1.34412	−	8.78413i	0.0768380	−	0.502155i
$307$	1.12751			0.0643502			0.0321751	−	0.999482i	$-0.489757\pi$
$307$	1.12751			0.0643502			0.0321751	+	0.999482i	$0.489757\pi$
$308$	−12.6349	−	4.73499i	−0.719941	−	0.269801i
$309$	−3.30794	+	9.41970i	−0.188182	+	0.535868i
$310$			15.3478i			0.871695i
$311$	5.59744	−	9.69505i	0.317402	−	0.549756i	−0.662543	−	0.749023i	$-0.730523\pi$
$311$	5.59744	−	9.69505i	0.317402	−	0.549756i	0.979945	+	0.199268i	$0.0638563\pi$
$312$	−2.35607	+	5.78351i	−0.133386	+	0.327427i
$313$	28.1564	−	16.2561i	1.59150	−	0.918850i	0.598444	−	0.801165i	$-0.295786\pi$
$313$	28.1564	−	16.2561i	1.59150	−	0.918850i	0.993051	−	0.117686i	$-0.0375475\pi$
$314$	−6.31098	−	3.64365i	−0.356149	−	0.205623i
$315$	−12.9690	−	7.26106i	−0.730723	−	0.409115i
$316$	−5.14630	−	8.91365i	−0.289502	−	0.501432i
$317$	12.7161	+	22.0249i	0.714206	+	1.23704i	0.963265	+	0.268553i	$0.0865456\pi$
$317$	12.7161	+	22.0249i	0.714206	+	1.23704i	−0.249058	+	0.968488i	$0.580121\pi$
$318$	16.1528	−	3.03755i	0.905805	−	0.170337i
$319$			42.9969i			2.40736i
$320$	1.62172	−	0.936303i	0.0906572	−	0.0523409i
$321$	6.93549	+	8.07745i	0.387101	+	0.450840i
$322$	10.2049	+	12.3988i	0.568699	+	0.690960i
$323$	3.85305	−	6.67367i	0.214389	−	0.371333i
$324$	−8.58819	−	2.69128i	−0.477122	−	0.149516i
$325$	0.264430	−	5.37783i	0.0146680	−	0.298309i
$326$	17.1552	+	9.90456i	0.950139	+	0.548563i
$327$	21.4181	−	4.02769i	1.18442	−	0.222732i
$328$	4.85500	+	2.80304i	0.268072	+	0.154772i
$329$	2.90221	−	7.74430i	0.160004	−	0.426957i
$330$	−16.2562	+	3.05700i	−0.894877	+	0.168282i
$331$	−6.22337	−	3.59306i	−0.342067	−	0.197493i	0.319119	−	0.947715i	$-0.396613\pi$
$331$	−6.22337	−	3.59306i	−0.342067	−	0.197493i	−0.661186	+	0.750222i	$0.729947\pi$
$332$			9.63409i			0.528739i
$333$	18.9096	+	2.89348i	1.03624	+	0.158561i
$334$	−13.0891	−	7.55698i	−0.716202	−	0.413500i
$335$	10.3421	−	17.9130i	0.565048	−	0.978692i
$336$	−0.787372	+	4.51443i	−0.0429547	+	0.246282i
$337$	19.2711			1.04976			0.524882	−	0.851175i	$-0.324109\pi$
$337$	19.2711			1.04976			0.524882	+	0.851175i	$0.324109\pi$
$338$	−7.57313	+	10.5663i	−0.411924	+	0.574734i
$339$	1.27724	−	3.63708i	0.0693703	−	0.197539i
$340$	−4.80375	+	2.77345i	−0.260520	+	0.150411i
$341$	−41.7983			−2.26350
$342$	−6.09099	−	4.87976i	−0.329363	−	0.263867i
$343$	−8.79982	−	16.2961i	−0.475146	−	0.879907i
$344$	4.87733	+	8.44778i	0.262968	+	0.455474i
$345$	18.5741	+	6.52271i	0.999997	+	0.351171i
$346$	−9.62713	+	16.6747i	−0.517558	+	0.896436i
$347$		−	7.79589i		−	0.418505i	−0.977862	−	0.209253i	$-0.932897\pi$
$347$		−	7.79589i		−	0.418505i	0.977862	−	0.209253i	$-0.0671031\pi$
$348$	14.3513	−	2.69878i	0.769312	−	0.144670i
$349$	7.17103	−	12.4206i	0.383857	−	0.664859i	−0.607753	−	0.794126i	$-0.707929\pi$
$349$	7.17103	−	12.4206i	0.383857	−	0.664859i	0.991610	+	0.129267i	$0.0412623\pi$
$350$	−0.649132	−	3.89733i	−0.0346976	−	0.208321i
$351$	−16.0818	−	9.61125i	−0.858382	−	0.513010i
$352$	2.54994	+	4.41662i	0.135912	+	0.235407i
$353$	−22.0306	+	12.7194i	−1.17257	+	0.676985i	−0.954285	−	0.298900i	$-0.903380\pi$
$353$	−22.0306	+	12.7194i	−1.17257	+	0.676985i	−0.218288	+	0.975884i	$0.570047\pi$
$354$	−2.48551	−	2.89476i	−0.132103	−	0.153855i
$355$	23.6098	+	13.6311i	1.25308	+	0.723466i
$356$		−	14.7628i		−	0.782428i
$357$	2.33229	−	13.3723i	0.123438	−	0.707737i
$358$	4.65318	−	2.68651i	0.245928	−	0.141987i
$359$	−4.87490	−	8.44358i	−0.257288	−	0.445635i	0.708227	−	0.705985i	$-0.249495\pi$
$359$	−4.87490	−	8.44358i	−0.257288	−	0.445635i	−0.965514	+	0.260350i	$0.916162\pi$
$360$	2.04071	+	5.23406i	0.107555	+	0.275859i
$361$	6.11599	+	10.5932i	0.321894	+	0.557537i
$362$		−	11.3131i		−	0.594601i
$363$	−4.80433	−	25.5481i	−0.252162	−	1.34092i
$364$	−3.78224	+	8.75755i	−0.198243	+	0.459020i
$365$		−	7.48214i		−	0.391633i
$366$	10.0470	−	1.88934i	0.525164	−	0.0987576i
$367$	−12.5943	+	7.27133i	−0.657418	+	0.379560i	−0.791292	−	0.611438i	$-0.790591\pi$
$367$	−12.5943	+	7.27133i	−0.657418	+	0.379560i	0.133875	+	0.990998i	$0.457258\pi$
$368$		−	6.06950i		−	0.316395i
$369$	−10.5154	+	13.1255i	−0.547410	+	0.683286i
$370$	−5.97039	−	10.3410i	−0.310386	−	0.537604i
$371$	24.7652	−	4.12484i	1.28574	−	0.214151i
$372$	2.62354	+	13.9512i	0.136024	+	0.723339i
$373$	6.87679	−	11.9109i	0.356067	−	0.616725i	−0.631233	−	0.775593i	$-0.717451\pi$
$373$	6.87679	−	11.9109i	0.356067	−	0.616725i	0.987300	+	0.158868i	$0.0507843\pi$
$374$	−7.55323	−	13.0826i	−0.390568	−	0.676484i
$375$	−13.7198	−	15.9789i	−0.708489	−	0.825146i
$376$	−2.70708	+	1.56293i	−0.139607	+	0.0806020i
$377$	30.3616	+	1.49289i	1.56370	+	0.0768879i
$378$	−13.0302	−	4.38344i	−0.670200	−	0.225460i
$379$	25.1138	+	14.4995i	1.29001	+	0.744788i	0.978656	−	0.205505i	$-0.0658838\pi$
$379$	25.1138	+	14.4995i	1.29001	+	0.744788i	0.311355	+	0.950294i	$0.399217\pi$
$380$			4.87167i			0.249911i
$381$	−2.35104	−	12.5022i	−0.120447	−	0.640505i
$382$	2.74863	+	1.58692i	0.140632	+	0.0811939i
$383$	4.84882	+	2.79947i	0.247763	+	0.143046i	0.618740	−	0.785596i	$-0.287644\pi$
$383$	4.84882	+	2.79947i	0.247763	+	0.143046i	−0.370977	+	0.928642i	$0.620977\pi$
$384$	1.31411	−	1.12832i	0.0670604	−	0.0575796i
$385$	−24.9237	+	4.15125i	−1.27023	+	0.211567i
$386$	−0.181273	+	0.104658i	−0.00922654	+	0.00532695i
$387$	−27.2649	+	10.6303i	−1.38595	+	0.540369i
$388$	5.83860	+	10.1127i	0.296410	+	0.513397i
$389$	4.31018	+	2.48848i	0.218535	+	0.126171i	0.605272	−	0.796019i	$-0.293065\pi$
$389$	4.31018	+	2.48848i	0.218535	+	0.126171i	−0.386737	+	0.922190i	$0.626398\pi$
$390$	1.59422	+	11.5852i	0.0807267	+	0.586642i
$391$			17.9786i			0.909218i
$392$	−1.34615	+	6.86934i	−0.0679908	+	0.346954i
$393$	−1.52158	−	0.534338i	−0.0767538	−	0.0269538i
$394$	9.71998	−	16.8355i	0.489685	−	0.848160i
$395$	−16.6918	−	9.63699i	−0.839854	−	0.484890i
$396$	−14.2545	+	5.55768i	−0.716315	+	0.279284i
$397$	8.11912	−	14.0627i	0.407487	−	0.705788i	−0.587120	−	0.809500i	$-0.699738\pi$
$397$	8.11912	−	14.0627i	0.407487	−	0.705788i	0.994607	+	0.103711i	$0.0330718\pi$
$398$			14.4539i			0.724510i
$399$	−9.14682	−	7.64619i	−0.457914	−	0.382788i
$400$	−0.746672	+	1.29327i	−0.0373336	+	0.0646637i
$401$	6.92045			0.345591			0.172795	−	0.984958i	$-0.444720\pi$
$401$	6.92045			0.345591			0.172795	+	0.984958i	$0.444720\pi$
$402$	6.33899	−	18.0509i	0.316160	−	0.900299i
$403$	−1.45128	+	29.5152i	−0.0722932	+	1.47026i
$404$	3.15026	+	5.45640i	0.156731	+	0.271466i
$405$	−16.4475	+	3.67663i	−0.817285	+	0.182693i
$406$	22.0031	−	3.66480i	1.09200	−	0.181881i
$407$	28.1628	−	16.2598i	1.39598	−	0.805970i
$408$	−3.89256	+	3.34224i	−0.192710	+	0.165465i
$409$	11.3829			0.562849			0.281425	−	0.959583i	$-0.409193\pi$
$409$	11.3829			0.562849			0.281425	+	0.959583i	$0.409193\pi$
$410$	10.4980			0.518457
$411$	2.83471	−	2.43395i	0.139826	−	0.120058i
$412$	4.99182	−	2.88203i	0.245930	−	0.141987i
$413$	−3.70372	−	4.49996i	−0.182248	−	0.221429i
$414$	17.9990	+	2.75414i	0.884603	+	0.135359i
$415$	9.02043	+	15.6238i	0.442795	+	0.766944i
$416$	3.20727	−	1.64725i	0.157249	−	0.0807631i
$417$	−4.76458	+	13.5677i	−0.233323	+	0.664411i
$418$	−13.2675			−0.648937
$419$	−4.51941	+	7.82784i	−0.220788	+	0.382415i	−0.955047	−	0.296453i	$-0.904196\pi$
$419$	−4.51941	+	7.82784i	−0.220788	+	0.382415i	0.734260	+	0.678869i	$0.237529\pi$
$420$	2.94997	+	8.05838i	0.143944	+	0.393209i
$421$			3.07453i			0.149844i	0.997189	+	0.0749218i	$0.0238707\pi$
$421$			3.07453i			0.149844i	−0.997189	+	0.0749218i	$0.976129\pi$
$422$	−5.78954	+	10.0278i	−0.281830	+	0.488145i
$423$	−3.40646	−	8.73700i	−0.165628	−	0.424807i
$424$	−8.21797	−	4.74465i	−0.399100	−	0.230421i
$425$	2.21174	−	3.83084i	0.107285	−	0.185823i
$426$	23.7916	+	8.35496i	1.15271	+	0.404799i
$427$	15.4038	−	2.56563i	0.745443	−	0.124160i
$428$		−	6.14671i		−	0.297113i
$429$	−31.5514	+	4.34172i	−1.52331	+	0.209620i
$430$	15.8194	+	9.13332i	0.762878	+	0.440448i
$431$	11.6404	+	20.1618i	0.560700	+	0.971160i	0.997436	+	0.0715705i	$0.0228011\pi$
$431$	11.6404	+	20.1618i	0.560700	+	0.971160i	−0.436736	+	0.899590i	$0.643866\pi$
$432$	2.74973	+	4.40897i	0.132296	+	0.212127i
$433$	−23.9459	+	13.8252i	−1.15077	+	0.664396i	−0.949074	−	0.315053i	$-0.897978\pi$
$433$	−23.9459	+	13.8252i	−1.15077	+	0.664396i	−0.201693	+	0.979449i	$0.564644\pi$
$434$	3.56264	+	21.3898i	0.171012	+	1.02674i
$435$	20.7470	−	17.8139i	0.994744	−	0.854110i
$436$	−10.8967	−	6.29124i	−0.521859	−	0.301296i
$437$	13.6746	+	7.89503i	0.654145	+	0.377671i
$438$	−1.27900	−	6.80132i	−0.0611128	−	0.324980i
$439$			4.37253i			0.208690i	0.994541	+	0.104345i	$0.0332746\pi$
$439$			4.37253i			0.208690i	−0.994541	+	0.104345i	$0.966725\pi$
$440$	8.27059	+	4.77503i	0.394285	+	0.227641i
$441$	−19.7601	−	7.10907i	−0.940957	−	0.338527i
$442$	−9.50032	+	4.87936i	−0.451884	+	0.232088i
$443$	−2.31071	+	1.33409i	−0.109785	+	0.0633846i	−0.553887	−	0.832592i	$-0.686856\pi$
$443$	−2.31071	+	1.33409i	−0.109785	+	0.0633846i	0.444102	+	0.895976i	$0.353523\pi$
$444$	−7.19483	−	8.37950i	−0.341451	−	0.397673i
$445$	−13.8225	−	23.9412i	−0.655248	−	1.13492i
$446$	3.33759	−	5.78088i	0.158040	−	0.273733i
$447$	1.26704	+	6.73777i	0.0599291	+	0.318685i
$448$	2.04281	−	1.68135i	0.0965137	−	0.0794361i
$449$	−7.64162	−	13.2357i	−0.360630	−	0.624630i	0.627434	−	0.778670i	$-0.284105\pi$
$449$	−7.64162	−	13.2357i	−0.360630	−	0.624630i	−0.988065	+	0.154039i	$0.950772\pi$
$450$	−3.49637	−	2.80109i	−0.164820	−	0.132045i
$451$			28.5903i			1.34626i
$452$	−1.92741	+	1.11279i	−0.0906580	+	0.0523414i
$453$	−9.47867	+	1.78247i	−0.445347	+	0.0837478i
$454$		−	18.4820i		−	0.867402i
$455$	2.06597	+	17.7437i	0.0968541	+	0.831835i
$456$	0.832761	+	4.42838i	0.0389976	+	0.207378i
$457$			6.93705i			0.324502i	0.986750	+	0.162251i	$0.0518754\pi$
$457$			6.93705i			0.324502i	−0.986750	+	0.162251i	$0.948125\pi$
$458$	0.100542	+	0.174145i	0.00469804	+	0.00813724i
$459$	−8.14504	−	13.0599i	−0.380178	−	0.609584i
$460$	−5.68289	−	9.84306i	−0.264966	−	0.458935i
$461$	−17.6491	+	10.1897i	−0.822001	+	0.474582i	−0.851106	−	0.524994i	$-0.824068\pi$
$461$	−17.6491	+	10.1897i	−0.822001	+	0.474582i	0.0291053	+	0.999576i	$0.490734\pi$
$462$	−21.9463	+	8.03398i	−1.02103	+	0.373774i
$463$		−	22.4244i		−	1.04215i	−0.853511	−	0.521075i	$-0.825531\pi$
$463$		−	22.4244i		−	1.04215i	0.853511	−	0.521075i	$-0.174469\pi$
$464$	−7.30144	−	4.21549i	−0.338961	−	0.195699i
$465$	17.3173	+	20.1687i	0.803069	+	0.935299i
$466$	−11.1073	+	6.41280i	−0.514535	+	0.297067i
$467$	9.83436	+	17.0336i	0.455080	+	0.788221i	0.998693	−	0.0511146i	$-0.0162774\pi$
$467$	9.83436	+	17.0336i	0.455080	+	0.788221i	−0.543613	+	0.839336i	$0.682944\pi$
$468$	3.42954	+	10.2586i	0.158531	+	0.474203i
$469$	10.2554	−	27.3655i	0.473549	−	1.26362i
$470$	−2.92675	+	5.06929i	−0.135001	+	0.233829i
$471$	−12.4045	+	2.33268i	−0.571571	+	0.107484i
$472$			2.20283i			0.101393i
$473$	−24.8738	+	43.0826i	−1.14370	+	1.98094i
$474$	−16.8203	−	5.90682i	−0.772582	−	0.271309i
$475$	−1.94250	−	3.36451i	−0.0891280	−	0.154374i
$476$	−6.05106	+	4.98036i	−0.277350	+	0.228274i
$477$	17.7992	−	22.2173i	0.814971	−	1.01726i
$478$	30.2795			1.38495
$479$	16.4723	−	9.51026i	0.752637	−	0.434535i	−0.0740090	−	0.997258i	$-0.523579\pi$
$479$	16.4723	−	9.51026i	0.752637	−	0.434535i	0.826646	+	0.562722i	$0.190246\pi$
$480$	1.07467	−	3.06024i	0.0490518	−	0.139680i
$481$	−10.5038	−	20.4513i	−0.478932	−	0.932500i
$482$	−8.34511			−0.380109
$483$	27.4003	+	4.77896i	1.24676	+	0.217450i
$484$	−7.50436	+	12.9979i	−0.341107	+	0.590815i
$485$	18.9372	+	10.9334i	0.859894	+	0.496460i
$486$	−14.3225	+	6.15363i	−0.649680	+	0.279134i
$487$		−	22.4738i		−	1.01838i	−0.860653	−	0.509192i	$-0.829944\pi$
$487$		−	22.4738i		−	1.01838i	0.860653	−	0.509192i	$-0.170056\pi$
$488$	−5.11154	−	2.95115i	−0.231389	−	0.133592i
$489$	33.7194	−	6.34096i	1.52484	−	0.286748i
$490$	4.24871	+	12.4006i	0.191937	+	0.560201i
$491$	−25.7148	−	14.8464i	−1.16049	−	0.670010i	−0.209069	−	0.977901i	$-0.567043\pi$
$491$	−25.7148	−	14.8464i	−1.16049	−	0.670010i	−0.951422	+	0.307891i	$0.900377\pi$
$492$	9.54273	−	1.79452i	0.430220	−	0.0809032i
$493$	21.6278	+	12.4868i	0.974065	+	0.562377i
$494$	−0.460662	+	9.36868i	−0.0207261	+	0.421517i
$495$	−17.9132	+	22.3596i	−0.805138	+	1.00499i
$496$	4.09797	−	7.09789i	0.184004	−	0.318705i
$497$	36.0685	+	13.5168i	1.61789	+	0.606313i
$498$	10.8704	+	12.6602i	0.487113	+	0.567319i
$499$	6.50477	−	3.75553i	0.291193	−	0.168121i	−0.347287	−	0.937759i	$-0.612897\pi$
$499$	6.50477	−	3.75553i	0.291193	−	0.168121i	0.638480	+	0.769638i	$0.279564\pi$
$500$			12.1595i			0.543788i
$501$	−25.7272	+	4.83802i	−1.14941	+	0.216147i
$502$	0.325183	+	0.563233i	0.0145136	+	0.0251383i
$503$	14.6024	+	25.2921i	0.651089	+	1.12772i	0.982859	+	0.184358i	$0.0590207\pi$
$503$	14.6024	+	25.2921i	0.651089	+	1.12772i	−0.331770	+	0.943360i	$0.607646\pi$
$504$	4.05904	+	6.82086i	0.180804	+	0.303825i
$505$	10.2177	+	5.89919i	0.454682	+	0.262511i
$506$	26.8067	−	15.4768i	1.19170	−	0.688030i
$507$	1.97035	+	22.4303i	0.0875063	+	0.996164i
$508$	−3.67232	+	6.36064i	−0.162933	+	0.282208i
$509$			38.2320i			1.69460i	0.531113	+	0.847301i	$0.321774\pi$
$509$			38.2320i			1.69460i	−0.531113	+	0.847301i	$0.678226\pi$
$510$	−3.18331	+	9.06480i	−0.140959	+	0.401396i
$511$	−1.73681	−	10.4276i	−0.0768320	−	0.461292i
$512$	−1.00000			−0.0441942
$513$	−13.5102	+	0.460084i	−0.596489	+	0.0203132i
$514$	−7.41850			−0.327216
$515$	5.39691	−	9.34772i	0.237816	−	0.411910i
$516$	15.9412	+	5.59810i	0.701771	+	0.246443i
$517$	−13.8057	−	7.97075i	−0.607176	−	0.350553i
$518$	−10.7212	−	13.0261i	−0.471063	−	0.572334i
$519$	6.16335	+	32.7749i	0.270541	+	1.43866i
$520$	3.65898	−	5.67436i	0.160457	−	0.248837i
$521$	−1.01347	+	1.75537i	−0.0444008	+	0.0769044i	−0.887372	−	0.461055i	$-0.847471\pi$
$521$	−1.01347	+	1.75537i	−0.0444008	+	0.0769044i	0.842971	+	0.537959i	$0.180805\pi$
$522$	15.8141	−	19.7394i	0.692165	−	0.863972i
$523$			14.9844i			0.655221i	0.944813	+	0.327610i	$0.106243\pi$
$523$			14.9844i			0.655221i	−0.944813	+	0.327610i	$0.893757\pi$
$524$	0.465541	+	0.806340i	0.0203372	+	0.0352251i
$525$	−5.25048	−	4.38909i	−0.229150	−	0.191555i
$526$	−17.3650	+	10.0257i	−0.757149	+	0.437140i
$527$	−12.1387	+	21.0248i	−0.528770	+	0.915856i
$528$	8.33428	+	2.92677i	0.362703	+	0.127371i
$529$	−13.8389			−0.601690
$530$	−17.7697			−0.771867
$531$	−6.53245	−	0.999572i	−0.283484	−	0.0433777i
$532$	1.13085	+	6.78950i	0.0490285	+	0.294362i
$533$	20.1886	+	0.992681i	0.874465	+	0.0429978i
$534$	−16.6573	−	19.4000i	−0.720830	−	0.839518i
$535$	−5.75519	−	9.96828i	−0.248818	−	0.430966i
$536$	−9.56582	+	5.52283i	−0.413180	+	0.238550i
$537$	3.08353	−	8.78067i	0.133064	−	0.378914i
$538$	12.4850			0.538267
$539$	−33.7719	+	11.5710i	−1.45466	+	0.498397i
$540$	8.58743	+	4.57555i	0.369544	+	0.196900i
$541$	−0.930484	+	0.537215i	−0.0400046	+	0.0230967i	−0.519869	−	0.854246i	$-0.674019\pi$
$541$	−0.930484	+	0.537215i	−0.0400046	+	0.0230967i	0.479864	+	0.877343i	$0.340686\pi$
$542$	2.87931			0.123677
$543$	−12.7648	−	14.8666i	−0.547790	−	0.637986i
$544$	2.96212			0.127000
$545$	−23.5620			−1.00929
$546$	4.91108	+	15.7760i	0.210175	+	0.675149i
$547$	−26.8765			−1.14916			−0.574578	−	0.818450i	$-0.694834\pi$
$547$	−26.8765			−1.14916			−0.574578	+	0.818450i	$0.694834\pi$
$548$	−2.15714			−0.0921483
$549$	11.0710	−	13.8191i	0.472500	−	0.589783i
$550$	−7.61587			−0.324742
$551$	18.9950	−	10.9668i	0.809214	−	0.467200i
$552$	−6.84837	−	7.97599i	−0.291486	−	0.339481i
$553$	−25.4998	−	9.55619i	−1.08436	−	0.406370i
$554$	−8.00292			−0.340011
$555$	−19.5138	−	6.85270i	−0.828314	−	0.290881i
$556$	7.18997	−	4.15113i	0.304922	−	0.176047i
$557$	13.5744	+	23.5116i	0.575167	+	0.996219i	0.996023	+	0.0890918i	$0.0283965\pi$
$557$	13.5744	+	23.5116i	0.575167	+	0.996219i	−0.420856	+	0.907127i	$0.638270\pi$
$558$	19.1892	+	15.3733i	0.812342	+	0.650802i
$559$	29.5585	+	19.0601i	1.25019	+	0.806157i
$560$	1.73863	−	4.63937i	0.0734704	−	0.196049i
$561$	−24.6872	−	8.66945i	−1.04229	−	0.366024i
$562$	−6.16209			−0.259932
$563$	−16.3087			−0.687329			−0.343664	−	0.939093i	$-0.611668\pi$
$563$	−16.3087			−0.687329			−0.343664	+	0.939093i	$0.611668\pi$
$564$	−1.79390	+	5.10832i	−0.0755368	+	0.215099i
$565$	−2.08382	+	3.60929i	−0.0876671	+	0.151844i
$566$	11.9016	−	6.87141i	0.500263	−	0.288827i
$567$	−22.0690	+	8.94195i	−0.926812	+	0.375526i
$568$	−7.27923	−	12.6080i	−0.305430	−	0.529020i
$569$		−	26.1439i		−	1.09601i	−0.836475	−	0.548005i	$-0.815388\pi$
$569$		−	26.1439i		−	1.09601i	0.836475	−	0.548005i	$-0.184612\pi$
$570$	5.49682	+	6.40190i	0.230236	+	0.268146i
$571$	−0.114124	+	0.197668i	−0.00477593	+	0.00827215i	−0.868403	−	0.495858i	$-0.834854\pi$
$571$	−0.114124	+	0.197668i	−0.00477593	+	0.00827215i	0.863628	+	0.504130i	$0.168187\pi$
$572$	15.4536	+	9.96490i	0.646148	+	0.416653i
$573$	5.40256	−	1.01596i	0.225695	−	0.0424422i
$574$	14.6307	−	2.43687i	0.610674	−	0.101713i
$575$	7.84953	+	4.53193i	0.327348	+	0.188995i
$576$	0.453768	−	2.96548i	0.0189070	−	0.123562i
$577$	−8.82331	+	15.2824i	−0.367319	+	0.636215i	−0.989145	−	0.146940i	$-0.953058\pi$
$577$	−8.82331	+	15.2824i	−0.367319	+	0.636215i	0.621826	+	0.783155i	$0.286391\pi$
$578$	8.22582			0.342149
$579$	−0.120124	+	0.342066i	−0.00499219	+	0.0142158i
$580$	−15.7879			−0.655557
$581$	16.1982	+	19.6806i	0.672016	+	0.816490i
$582$	19.0830	+	6.70142i	0.791016	+	0.277783i
$583$		−	48.3942i		−	2.00428i
$584$	−1.99779	+	3.46027i	−0.0826690	+	0.143187i
$585$	15.1669	+	13.4255i	0.627074	+	0.555075i
$586$	−4.43117	+	2.55834i	−0.183050	+	0.105684i
$587$	−13.2115	−	7.62767i	−0.545298	−	0.314828i	0.201926	−	0.979401i	$-0.435280\pi$
$587$	−13.2115	−	7.62767i	−0.545298	−	0.314828i	−0.747223	+	0.664573i	$0.768613\pi$
$588$	5.98186	+	10.5460i	0.246688	+	0.434908i
$589$	10.6610	+	18.4655i	0.439281	+	0.760857i
$590$	2.06252	+	3.57238i	0.0849124	+	0.147073i
$591$	−6.22279	−	33.0910i	−0.255971	−	1.36118i
$592$			6.37656i			0.262075i
$593$	−0.0222995	+	0.0128746i	−0.000915730	+	0.000528697i	−0.500458	−	0.865761i	$-0.666835\pi$
$593$	−0.0222995	+	0.0128746i	−0.000915730	+	0.000528697i	0.499542	+	0.866290i	$0.333502\pi$
$594$	−12.4611	+	23.3871i	−0.511285	+	0.959584i
$595$	−5.15003	+	13.7424i	−0.211131	+	0.563383i
$596$	1.97912	−	3.42793i	0.0810678	−	0.140414i
$597$	16.3087	+	18.9940i	0.667471	+	0.777374i
$598$	−9.99799	−	19.4665i	−0.408848	−	0.796045i
$599$	−21.8300	−	12.6035i	−0.891949	−	0.514967i	−0.0173692	−	0.999849i	$-0.505529\pi$
$599$	−21.8300	−	12.6035i	−0.891949	−	0.514967i	−0.874579	+	0.484882i	$0.838862\pi$
$600$	0.478024	+	2.54199i	0.0195153	+	0.103776i
$601$	−15.4945	−	8.94574i	−0.632033	−	0.364904i	0.149506	−	0.988761i	$-0.452232\pi$
$601$	−15.4945	−	8.94574i	−0.632033	−	0.364904i	−0.781539	+	0.623856i	$0.785565\pi$
$602$	24.1671	+	9.05674i	0.984978	+	0.369125i
$603$	−12.0372	−	30.8734i	−0.490192	−	1.25726i
$604$	4.82241	+	2.78422i	0.196221	+	0.113288i
$605$			28.1054i			1.14265i
$606$	10.2964	+	3.61580i	0.418262	+	0.146882i
$607$	−22.8924	−	13.2169i	−0.929175	−	0.536459i	−0.0426244	−	0.999091i	$-0.513572\pi$
$607$	−22.8924	−	13.2169i	−0.929175	−	0.536459i	−0.886551	+	0.462632i	$0.846905\pi$
$608$	1.30077	−	2.25300i	0.0527532	−	0.0913713i
$609$	24.7795	−	29.6426i	1.00411	−	1.20118i
$610$	−11.0527			−0.447510
$611$	−6.10778	+	9.47197i	−0.247094	+	0.383195i
$612$	−1.34412	+	8.78413i	−0.0543327	+	0.355077i
$613$	−7.14521	+	4.12529i	−0.288593	+	0.166619i	−0.637307	−	0.770610i	$-0.719952\pi$
$613$	−7.14521	+	4.12529i	−0.288593	+	0.166619i	0.348714	+	0.937229i	$0.386618\pi$
$614$	−1.12751			−0.0455024
$615$	13.7955	−	11.8451i	0.556287	−	0.477641i
$616$	12.6349	+	4.73499i	0.509075	+	0.190778i
$617$	−2.53770	−	4.39542i	−0.102164	−	0.176953i	0.810412	−	0.585860i	$-0.199243\pi$
$617$	−2.53770	−	4.39542i	−0.102164	−	0.176953i	−0.912576	+	0.408907i	$0.865910\pi$
$618$	3.30794	−	9.41970i	0.133065	−	0.378916i
$619$	14.6995	−	25.4603i	0.590822	−	1.02333i	−0.403300	−	0.915068i	$-0.632137\pi$
$619$	14.6995	−	25.4603i	0.590822	−	1.02333i	0.994122	−	0.108266i	$-0.0345298\pi$
$620$		−	15.3478i		−	0.616381i
$621$	26.7602	−	16.6895i	1.07385	−	0.669726i
$622$	−5.59744	+	9.69505i	−0.224437	+	0.388736i
$623$	−24.8214	−	30.1576i	−0.994449	−	1.20824i
$624$	2.35607	−	5.78351i	0.0943182	−	0.231526i
$625$	7.65160	+	13.2530i	0.306064	+	0.530118i
$626$	−28.1564	+	16.2561i	−1.12536	+	0.649725i
$627$	−17.4350	+	14.9701i	−0.696287	+	0.597848i
$628$	6.31098	+	3.64365i	0.251836	+	0.145397i
$629$		−	18.8882i		−	0.753120i
$630$	12.9690	+	7.26106i	0.516699	+	0.289288i
$631$	31.4596	−	18.1632i	1.25239	−	0.723066i	0.280804	−	0.959765i	$-0.409399\pi$
$631$	31.4596	−	18.1632i	1.25239	−	0.723066i	0.971583	+	0.236699i	$0.0760655\pi$
$632$	5.14630	+	8.91365i	0.204709	+	0.354566i
$633$	3.70650	+	19.7101i	0.147320	+	0.783405i
$634$	−12.7161	−	22.0249i	−0.505020	−	0.874721i
$635$			13.7536i			0.545796i
$636$	−16.1528	+	3.03755i	−0.640501	+	0.120447i
$637$	6.99807	+	24.2493i	0.277274	+	0.960791i
$638$		−	42.9969i		−	1.70226i
$639$	40.6919	−	15.8653i	1.60975	−	0.627623i
$640$	−1.62172	+	0.936303i	−0.0641043	+	0.0370106i
$641$		−	0.739636i		−	0.0292139i	−0.999893	−	0.0146069i	$-0.995350\pi$
$641$		−	0.739636i		−	0.0292139i	0.999893	−	0.0146069i	$-0.00464970\pi$
$642$	−6.93549	−	8.07745i	−0.273722	−	0.318792i
$643$	−2.41482	−	4.18259i	−0.0952313	−	0.164945i	0.814474	−	0.580200i	$-0.197026\pi$
$643$	−2.41482	−	4.18259i	−0.0952313	−	0.164945i	−0.909705	+	0.415255i	$0.863692\pi$
$644$	−10.2049	−	12.3988i	−0.402131	−	0.488583i
$645$	31.0937	−	5.84720i	1.22431	−	0.230233i
$646$	−3.85305	+	6.67367i	−0.151596	+	0.262572i
$647$	−2.02071	−	3.49997i	−0.0794422	−	0.137598i	0.823567	−	0.567219i	$-0.191981\pi$
$647$	−2.02071	−	3.49997i	−0.0794422	−	0.137598i	−0.903009	+	0.429621i	$0.858647\pi$
$648$	8.58819	+	2.69128i	0.337376	+	0.105723i
$649$	−9.72906	+	5.61707i	−0.381899	+	0.220489i
$650$	−0.264430	+	5.37783i	−0.0103718	+	0.210936i
$651$	28.8163	+	24.0887i	1.12940	+	0.944109i
$652$	−17.1552	−	9.90456i	−0.671849	−	0.387892i
$653$		−	46.7035i		−	1.82765i	−0.406108	−	0.913825i	$-0.633114\pi$
$653$		−	46.7035i		−	1.82765i	0.406108	−	0.913825i	$-0.366886\pi$
$654$	−21.4181	+	4.02769i	−0.837513	+	0.157495i
$655$	1.50996	+	0.871775i	0.0589989	+	0.0340631i
$656$	−4.85500	−	2.80304i	−0.189556	−	0.109440i
$657$	−9.35484	−	7.49456i	−0.364967	−	0.292391i
$658$	−2.90221	+	7.74430i	−0.113140	+	0.301904i
$659$	40.3288	−	23.2838i	1.57099	−	0.907009i	0.574937	−	0.818198i	$-0.305027\pi$
$659$	40.3288	−	23.2838i	1.57099	−	0.907009i	0.996048	−	0.0888111i	$-0.0283067\pi$
$660$	16.2562	−	3.05700i	0.632773	−	0.118994i
$661$	−22.2936	−	38.6137i	−0.867122	−	1.50190i	−0.864924	−	0.501902i	$-0.832634\pi$
$661$	−22.2936	−	38.6137i	−0.867122	−	1.50190i	−0.00219813	−	0.999998i	$-0.500700\pi$
$662$	6.22337	+	3.59306i	0.241878	+	0.139648i
$663$	−6.97896	+	17.1315i	−0.271040	+	0.665331i
$664$		−	9.63409i		−	0.373875i
$665$	8.19096	+	9.95189i	0.317632	+	0.385918i
$666$	−18.9096	−	2.89348i	−0.732731	−	0.112120i
$667$	−25.5859	+	44.3161i	−0.990690	+	1.71593i
$668$	13.0891	+	7.55698i	0.506432	+	0.292388i
$669$	−2.13675	−	11.3626i	−0.0826114	−	0.439303i
$670$	−10.3421	+	17.9130i	−0.399549	+	0.692040i
$671$		−	30.1010i		−	1.16204i
$672$	0.787372	−	4.51443i	0.0303735	−	0.174148i
$673$	−7.92610	+	13.7284i	−0.305529	+	0.529191i	−0.977379	−	0.211496i	$-0.932166\pi$
$673$	−7.92610	+	13.7284i	−0.305529	+	0.529191i	0.671850	+	0.740687i	$0.265500\pi$
$674$	−19.2711			−0.742295
$675$	−7.75515	+	0.264099i	−0.298496	+	0.0101652i
$676$	7.57313	−	10.5663i	0.291274	−	0.406398i
$677$	2.65460	+	4.59790i	0.102024	+	0.176711i	0.912519	−	0.409035i	$-0.134135\pi$
$677$	2.65460	+	4.59790i	0.102024	+	0.176711i	−0.810494	+	0.585747i	$0.800801\pi$
$678$	−1.27724	+	3.63708i	−0.0490522	+	0.139681i
$679$	28.9302	+	10.8417i	1.11024	+	0.416067i
$680$	4.80375	−	2.77345i	0.184215	−	0.106357i
$681$	−20.8537	−	24.2873i	−0.799114	−	0.930693i
$682$	41.7983			1.60054
$683$	−11.9713			−0.458070			−0.229035	−	0.973418i	$-0.573557\pi$
$683$	−11.9713			−0.458070			−0.229035	+	0.973418i	$0.573557\pi$
$684$	6.09099	+	4.87976i	0.232895	+	0.186582i
$685$	−3.49828	+	2.01973i	−0.133662	+	0.0771701i
$686$	8.79982	+	16.2961i	0.335979	+	0.622188i
$687$	0.328615	+	0.115401i	0.0125375	+	0.00440280i
$688$	−4.87733	−	8.44778i	−0.185946	−	0.322069i
$689$	−34.1729	−	1.68029i	−1.30188	−	0.0640141i
$690$	−18.5741	−	6.52271i	−0.707104	−	0.248315i
$691$	38.9891			1.48322			0.741608	−	0.670834i	$-0.234064\pi$
$691$	38.9891			1.48322			0.741608	+	0.670834i	$0.234064\pi$
$692$	9.62713	−	16.6747i	0.365969	−	0.633876i
$693$	−19.7749	+	35.3200i	−0.751184	+	1.34170i
$694$			7.79589i			0.295928i
$695$	7.77343	−	13.4640i	0.294863	−	0.510718i
$696$	−14.3513	+	2.69878i	−0.543986	+	0.102297i
$697$	14.3811	+	8.30294i	0.544723	+	0.314496i
$698$	−7.17103	+	12.4206i	−0.271428	+	0.470127i
$699$	−7.36048	+	20.9597i	−0.278399	+	0.792771i
$700$	0.649132	+	3.89733i	0.0245349	+	0.147305i
$701$		−	41.8339i		−	1.58005i	−0.613078	−	0.790023i	$-0.710069\pi$
$701$		−	41.8339i		−	1.58005i	0.613078	−	0.790023i	$-0.289931\pi$
$702$	16.0818	+	9.61125i	0.606968	+	0.362753i
$703$	−14.3664	−	8.29444i	−0.541839	−	0.312831i
$704$	−2.54994	−	4.41662i	−0.0961044	−	0.166458i
$705$	1.87373	+	9.96393i	0.0705686	+	0.375263i
$706$	22.0306	−	12.7194i	0.829134	−	0.478701i
$707$	15.6095	+	5.84973i	0.587055	+	0.220002i
$708$	2.48551	+	2.89476i	0.0934110	+	0.108792i
$709$	9.91254	+	5.72301i	0.372273	+	0.214932i	0.674451	−	0.738320i	$-0.264380\pi$
$709$	9.91254	+	5.72301i	0.372273	+	0.214932i	−0.302178	+	0.953252i	$0.597714\pi$
$710$	−23.6098	−	13.6311i	−0.886061	−	0.511567i
$711$	−28.7685	+	11.2165i	−1.07890	+	0.420653i
$712$			14.7628i			0.553260i
$713$	−43.0807	−	24.8726i	−1.61338	−	0.931488i
$714$	−2.33229	+	13.3723i	−0.0872839	+	0.500445i
$715$	34.3917	+	1.69105i	1.28618	+	0.0632418i
$716$	−4.65318	+	2.68651i	−0.173897	+	0.100400i
$717$	39.7906	−	34.1652i	1.48601	−	1.27592i
$718$	4.87490	+	8.44358i	0.181930	+	0.315112i
$719$	16.1498	−	27.9723i	0.602286	−	1.04319i	−0.390188	−	0.920735i	$-0.627590\pi$
$719$	16.1498	−	27.9723i	0.602286	−	1.04319i	0.992474	−	0.122455i	$-0.0390768\pi$
$720$	−2.04071	−	5.23406i	−0.0760526	−	0.195062i
$721$	5.35166	−	14.2804i	0.199306	−	0.531831i
$722$	−6.11599	−	10.5932i	−0.227614	−	0.394238i
$723$	−10.9664	+	9.41599i	−0.407844	+	0.350184i
$724$			11.3131i			0.420446i
$725$	10.9036	−	6.29518i	0.404948	−	0.233797i
$726$	4.80433	+	25.5481i	0.178306	+	0.948177i
$727$		−	35.0984i		−	1.30173i	−0.759195	−	0.650863i	$-0.774407\pi$
$727$		−	35.0984i		−	1.30173i	0.759195	−	0.650863i	$-0.225593\pi$
$728$	3.78224	−	8.75755i	0.140179	−	0.324576i
$729$	−11.8780	+	24.2469i	−0.439926	+	0.898034i
$730$			7.48214i			0.276926i
$731$	14.4473	+	25.0234i	0.534351	+	0.925523i
$732$	−10.0470	+	1.88934i	−0.371347	+	0.0698321i
$733$	1.14358	+	1.98073i	0.0422389	+	0.0731600i	0.886372	−	0.462974i	$-0.153218\pi$
$733$	1.14358	+	1.98073i	0.0422389	+	0.0731600i	−0.844133	+	0.536134i	$0.819884\pi$
$734$	12.5943	−	7.27133i	0.464864	−	0.268390i
$735$	19.5752	+	11.5018i	0.722040	+	0.424251i
$736$			6.06950i			0.223725i
$737$	−48.7845	−	28.1657i	−1.79700	−	1.03750i
$738$	10.5154	−	13.1255i	0.387077	−	0.483156i
$739$	−5.64299	+	3.25798i	−0.207581	+	0.119847i	−0.600186	−	0.799860i	$-0.704907\pi$
$739$	−5.64299	+	3.25798i	−0.207581	+	0.119847i	0.392606	+	0.919707i	$0.371574\pi$
$740$	5.97039	+	10.3410i	0.219476	+	0.380144i
$741$	9.96555	+	12.8312i	0.366094	+	0.471367i
$742$	−24.7652	+	4.12484i	−0.909158	+	0.151428i
$743$	−14.5039	+	25.1215i	−0.532097	+	0.921620i	0.467201	+	0.884151i	$0.345263\pi$
$743$	−14.5039	+	25.1215i	−0.532097	+	0.921620i	−0.999298	+	0.0374682i	$0.988071\pi$
$744$	−2.62354	−	13.9512i	−0.0961838	−	0.511478i
$745$		−	7.41222i		−	0.271563i
$746$	−6.87679	+	11.9109i	−0.251777	+	0.436091i
$747$	28.5697	+	4.37164i	1.04531	+	0.159950i
$748$	7.55323	+	13.0826i	0.276173	+	0.478346i
$749$	−10.3348	−	12.5566i	−0.377624	−	0.458807i
$750$	13.7198	+	15.9789i	0.500978	+	0.583466i
$751$	30.8433			1.12549			0.562744	−	0.826631i	$-0.309746\pi$
$751$	30.8433			1.12549			0.562744	+	0.826631i	$0.309746\pi$
$752$	2.70708	−	1.56293i	0.0987169	−	0.0569942i
$753$	1.06283	+	0.373238i	0.0387318	+	0.0136015i
$754$	−30.3616	−	1.49289i	−1.10571	−	0.0543680i
$755$	10.4275			0.379495
$756$	13.0302	+	4.38344i	0.473903	+	0.159424i
$757$	−10.6357	+	18.4215i	−0.386560	+	0.669542i	−0.991984	−	0.126361i	$-0.959670\pi$
$757$	−10.6357	+	18.4215i	−0.386560	+	0.669542i	0.605424	+	0.795903i	$0.293004\pi$
$758$	−25.1138	−	14.4995i	−0.912176	−	0.526645i
$759$	17.7640	−	50.5849i	0.644793	−	1.83612i
$760$		−	4.87167i		−	0.176714i
$761$	−21.3492	−	12.3260i	−0.773908	−	0.446816i	0.0603590	−	0.998177i	$-0.480775\pi$
$761$	−21.3492	−	12.3260i	−0.773908	−	0.446816i	−0.834267	+	0.551361i	$0.814109\pi$
$762$	2.35104	+	12.5022i	0.0851692	+	0.452905i
$763$	−32.8377	+	5.46939i	−1.18881	+	0.198005i
$764$	−2.74863	−	1.58692i	−0.0994418	−	0.0574128i
$765$	6.04482	+	15.5039i	0.218551	+	0.560546i
$766$	−4.84882	−	2.79947i	−0.175195	−	0.101149i
$767$	3.62861	+	7.06506i	0.131022	+	0.255105i
$768$	−1.31411	+	1.12832i	−0.0474188	+	0.0407149i
$769$	6.30372	−	10.9184i	0.227318	−	0.393726i	−0.729694	−	0.683773i	$-0.760338\pi$
$769$	6.30372	−	10.9184i	0.227318	−	0.393726i	0.957012	+	0.290047i	$0.0936710\pi$
$770$	24.9237	−	4.15125i	0.898189	−	0.149601i
$771$	−9.74872	+	8.37047i	−0.351092	+	0.301455i
$772$	0.181273	−	0.104658i	0.00652415	−	0.00376672i
$773$		−	20.1987i		−	0.726496i	−0.931692	−	0.363248i	$-0.881668\pi$
$773$		−	20.1987i		−	0.726496i	0.931692	−	0.363248i	$-0.118332\pi$
$774$	27.2649	−	10.6303i	0.980018	−	0.382099i
$775$	6.11968	+	10.5996i	0.219826	+	0.380749i
$776$	−5.83860	−	10.1127i	−0.209593	−	0.363026i
$777$	−28.7865	−	5.02073i	−1.03271	−	0.180118i
$778$	−4.31018	−	2.48848i	−0.154527	−	0.0892164i
$779$	12.6305	−	7.29222i	0.452534	−	0.261271i
$780$	−1.59422	−	11.5852i	−0.0570824	−	0.414818i
$781$	37.1232	−	64.2992i	1.32837	−	2.30081i
$782$		−	17.9786i		−	0.642914i
$783$	−1.49102	−	43.7832i	−0.0532848	−	1.56469i
$784$	1.34615	−	6.86934i	0.0480767	−	0.245334i
$785$	13.6462			0.487055
$786$	1.52158	+	0.534338i	0.0542731	+	0.0190592i
$787$	17.5342			0.625026			0.312513	−	0.949913i	$-0.398829\pi$
$787$	17.5342			0.625026			0.312513	+	0.949913i	$0.398829\pi$
$788$	−9.71998	+	16.8355i	−0.346260	+	0.599740i
$789$	−11.5073	+	32.7682i	−0.409669	+	1.16658i
$790$	16.6918	+	9.63699i	0.593866	+	0.342869i
$791$	−2.06635	+	5.51388i	−0.0734710	+	0.196051i
$792$	14.2545	−	5.55768i	0.506511	−	0.197483i
$793$	−21.2554	−	1.04513i	−0.754800	−	0.0371138i
$794$	−8.11912	+	14.0627i	−0.288137	+	0.499068i
$795$	−23.3514	+	20.0500i	−0.828187	+	0.711101i
$796$		−	14.4539i		−	0.512306i
$797$	−24.3061	−	42.0995i	−0.860968	−	1.49124i	−0.870996	−	0.491290i	$-0.836525\pi$
$797$	−24.3061	−	42.0995i	−0.860968	−	1.49124i	0.0100279	−	0.999950i	$-0.496808\pi$
$798$	9.14682	+	7.64619i	0.323794	+	0.270672i
$799$	−8.01869	+	4.62959i	−0.283681	+	0.163783i
$800$	0.746672	−	1.29327i	0.0263989	−	0.0457242i
$801$	−43.7789	−	6.69889i	−1.54685	−	0.236694i
$802$	−6.92045			−0.244370
$803$	−20.3769			−0.719086
$804$	−6.33899	+	18.0509i	−0.223559	+	0.636608i
$805$	−28.1587	−	10.5526i	−0.992463	−	0.371930i
$806$	1.45128	−	29.5152i	0.0511190	−	1.03963i
$807$	16.4067	−	14.0871i	0.577542	−	0.495891i
$808$	−3.15026	−	5.45640i	−0.110826	−	0.191956i
$809$	−7.20663	+	4.16075i	−0.253372	+	0.146284i	−0.621307	−	0.783567i	$-0.713398\pi$
$809$	−7.20663	+	4.16075i	−0.253372	+	0.146284i	0.367936	+	0.929851i	$0.380065\pi$
$810$	16.4475	−	3.67663i	0.577907	−	0.129184i
$811$	21.9549			0.770941			0.385470	−	0.922720i	$-0.374039\pi$
$811$	21.9549			0.770941			0.385470	+	0.922720i	$0.374039\pi$
$812$	−22.0031	+	3.66480i	−0.772159	+	0.128609i
$813$	3.78373	−	3.24880i	0.132701	−	0.113940i
$814$	−28.1628	+	16.2598i	−0.987107	+	0.569907i
$815$	−37.0947			−1.29937
$816$	3.89256	−	3.34224i	0.136267	−	0.117002i
$817$	25.3772			0.887834
$818$	−11.3829			−0.397995
$819$	24.2541	+	15.1901i	0.847507	+	0.530784i
$820$	−10.4980			−0.366605
$821$	27.3330			0.953929			0.476964	−	0.878923i	$-0.341737\pi$
$821$	27.3330			0.953929			0.476964	+	0.878923i	$0.341737\pi$
$822$	−2.83471	+	2.43395i	−0.0988720	+	0.0848938i
$823$	12.7593			0.444760			0.222380	−	0.974960i	$-0.428618\pi$
$823$	12.7593			0.444760			0.222380	+	0.974960i	$0.428618\pi$
$824$	−4.99182	+	2.88203i	−0.173898	+	0.100400i
$825$	−10.0081	+	8.59317i	−0.348437	+	0.299176i
$826$	3.70372	+	4.49996i	0.128869	+	0.156574i
$827$	43.7556			1.52153			0.760766	−	0.649027i	$-0.224824\pi$
$827$	43.7556			1.52153			0.760766	+	0.649027i	$0.224824\pi$
$828$	−17.9990	−	2.75414i	−0.625509	−	0.0957131i
$829$	−35.5899	+	20.5478i	−1.23609	+	0.713656i	−0.968292	−	0.249819i	$-0.919629\pi$
$829$	−35.5899	+	20.5478i	−1.23609	+	0.713656i	−0.267796	+	0.963476i	$0.586295\pi$
$830$	−9.02043	−	15.6238i	−0.313104	−	0.542311i
$831$	−10.5167	+	9.02989i	−0.364821	+	0.313243i
$832$	−3.20727	+	1.64725i	−0.111192	+	0.0571082i
$833$	−3.98746	+	20.3478i	−0.138157	+	0.705011i
$834$	4.76458	−	13.5677i	0.164984	−	0.469809i
$835$	28.3025			0.979449
$836$	13.2675			0.458867
$837$	42.5627	−	1.44946i	1.47118	−	0.0501005i
$838$	4.51941	−	7.82784i	0.156120	−	0.270408i
$839$	19.7685	−	11.4133i	0.682484	−	0.394032i	−0.118306	−	0.992977i	$-0.537747\pi$
$839$	19.7685	−	11.4133i	0.682484	−	0.394032i	0.800790	+	0.598945i	$0.204413\pi$
$840$	−2.94997	−	8.05838i	−0.101784	−	0.278040i
$841$	21.0407	+	36.4435i	0.725540	+	1.25667i
$842$		−	3.07453i		−	0.105955i
$843$	−8.09766	+	6.95284i	−0.278898	+	0.239468i
$844$	5.78954	−	10.0278i	0.199284	−	0.345170i
$845$	2.38822	−	24.2265i	0.0821574	−	0.833415i
$846$	3.40646	+	8.73700i	0.117117	+	0.300384i
$847$	6.52404	+	39.1697i	0.224169	+	1.34589i
$848$	8.21797	+	4.74465i	0.282206	+	0.162932i
$849$	7.88686	−	22.4587i	0.270676	−	0.770780i
$850$	−2.21174	+	3.83084i	−0.0758619	+	0.131397i
$851$	38.7025			1.32671
$852$	−23.7916	−	8.35496i	−0.815088	−	0.286236i
$853$	−4.19858			−0.143757			−0.0718783	−	0.997413i	$-0.522899\pi$
$853$	−4.19858			−0.143757			−0.0718783	+	0.997413i	$0.522899\pi$
$854$	−15.4038	+	2.56563i	−0.527108	+	0.0877941i
$855$	14.4468	+	2.21060i	0.494072	+	0.0756011i
$856$			6.14671i			0.210090i
$857$	4.09187	−	7.08733i	0.139776	−	0.242099i	−0.787636	−	0.616141i	$-0.788695\pi$
$857$	4.09187	−	7.08733i	0.139776	−	0.242099i	0.927412	+	0.374042i	$0.122028\pi$
$858$	31.5514	−	4.34172i	1.07715	−	0.148224i
$859$	−42.2454	+	24.3904i	−1.44139	+	0.832189i	−0.997943	−	0.0641096i	$-0.979579\pi$
$859$	−42.2454	+	24.3904i	−1.44139	+	0.832189i	−0.443451	+	0.896299i	$0.646246\pi$
$860$	−15.8194	−	9.13332i	−0.539436	−	0.311444i
$861$	16.4768	−	19.7105i	0.561527	−	0.671732i
$862$	−11.6404	−	20.1618i	−0.396475	−	0.686714i
$863$	0.899862	+	1.55861i	0.0306316	+	0.0530556i	0.880935	−	0.473238i	$-0.156915\pi$
$863$	0.899862	+	1.55861i	0.0306316	+	0.0530556i	−0.850303	+	0.526293i	$0.823581\pi$
$864$	−2.74973	−	4.40897i	−0.0935476	−	0.149996i
$865$		−	36.0557i		−	1.22593i
$866$	23.9459	−	13.8252i	0.813715	−	0.469799i
$867$	10.8096	−	9.28140i	0.367114	−	0.315213i
$868$	−3.56264	−	21.3898i	−0.120924	−	0.726016i
$869$	−26.2455	+	45.4585i	−0.890317	+	1.54207i
$870$	−20.7470	+	17.8139i	−0.703390	+	0.603947i
$871$	−21.5826	+	33.4705i	−0.731300	+	1.13410i
$872$	10.8967	+	6.29124i	0.369010	+	0.213048i
$873$	32.6386	−	12.7254i	1.10465	−	0.430691i
$874$	−13.6746	−	7.89503i	−0.462550	−	0.267054i
$875$	20.4443	+	24.8395i	0.691143	+	0.839729i
$876$	1.27900	+	6.80132i	0.0432132	+	0.229795i
$877$	−34.6606	−	20.0113i	−1.17040	−	0.675733i	−0.216629	−	0.976254i	$-0.569506\pi$
$877$	−34.6606	−	20.0113i	−1.17040	−	0.675733i	−0.953775	+	0.300521i	$0.902839\pi$
$878$		−	4.37253i		−	0.147566i
$879$	−2.93641	+	8.36174i	−0.0990426	+	0.282034i
$880$	−8.27059	−	4.77503i	−0.278802	−	0.160966i
$881$	−1.57402	+	2.72629i	−0.0530302	+	0.0918510i	−0.891322	−	0.453371i	$-0.850221\pi$
$881$	−1.57402	+	2.72629i	−0.0530302	+	0.0918510i	0.838292	+	0.545222i	$0.183555\pi$
$882$	19.7601	+	7.10907i	0.665357	+	0.239375i
$883$	−5.79510			−0.195021			−0.0975103	−	0.995235i	$-0.531088\pi$
$883$	−5.79510			−0.195021			−0.0975103	+	0.995235i	$0.531088\pi$
$884$	9.50032	−	4.87936i	0.319530	−	0.164111i
$885$	6.74118	+	2.36731i	0.226602	+	0.0795764i
$886$	2.31071	−	1.33409i	0.0776299	−	0.0448196i
$887$	−48.8111			−1.63892			−0.819458	−	0.573139i	$-0.805725\pi$
$887$	−48.8111			−1.63892			−0.819458	+	0.573139i	$0.805725\pi$
$888$	7.19483	+	8.37950i	0.241443	+	0.281197i
$889$	3.19259	+	19.1680i	0.107076	+	0.642875i
$890$	13.8225	+	23.9412i	0.463330	+	0.802512i
$891$	10.0130	+	44.7934i	0.335447	+	1.50063i
$892$	−3.33759	+	5.78088i	−0.111751	+	0.193558i
$893$			8.13206i			0.272129i
$894$	−1.26704	−	6.73777i	−0.0423763	−	0.225345i
$895$	−5.03078	+	8.71357i	−0.168161	+	0.291263i
$896$	−2.04281	+	1.68135i	−0.0682455	+	0.0561698i
$897$	−35.1030	−	14.3002i	−1.17206	−	0.477468i
$898$	7.64162	+	13.2357i	0.255004	+	0.441680i
$899$	−59.8421	+	34.5499i	−1.99585	+	1.15230i
$900$	3.49637	+	2.80109i	0.116546	+	0.0933697i
$901$	−24.3427	−	14.0542i	−0.810972	−	0.468215i
$902$		−	28.5903i		−	0.951951i
$903$	41.9772	−	15.3668i	1.39691	−	0.511375i
$904$	1.92741	−	1.11279i	0.0641049	−	0.0370110i
$905$	10.5924	+	18.3467i	0.352105	+	0.609864i
$906$	9.47867	−	1.78247i	0.314908	−	0.0592187i
$907$	11.9759	+	20.7429i	0.397653	+	0.688756i	0.993436	−	0.114390i	$-0.0364913\pi$
$907$	11.9759	+	20.7429i	0.397653	+	0.688756i	−0.595783	+	0.803146i	$0.703158\pi$
$908$			18.4820i			0.613346i
$909$	17.6104	−	6.86609i	0.584099	−	0.227734i
$910$	−2.06597	−	17.7437i	−0.0684862	−	0.588197i
$911$		−	51.9614i		−	1.72156i	−0.508979	−	0.860779i	$-0.669977\pi$
$911$		−	51.9614i		−	1.72156i	0.508979	−	0.860779i	$-0.330023\pi$
$912$	−0.832761	−	4.42838i	−0.0275755	−	0.146638i
$913$	42.5501	−	24.5663i	1.40820	−	0.813026i
$914$		−	6.93705i		−	0.229457i
$915$	−14.5244	+	12.4710i	−0.480163	+	0.412279i
$916$	−0.100542	−	0.174145i	−0.00332201	−	0.00575390i
$917$	2.30675	+	0.864465i	0.0761756	+	0.0285471i
$918$	8.14504	+	13.0599i	0.268826	+	0.431041i
$919$	18.8651	−	32.6754i	0.622303	−	1.07786i	−0.366753	−	0.930319i	$-0.619530\pi$
$919$	18.8651	−	32.6754i	0.622303	−	1.07786i	0.989056	−	0.147542i	$-0.0471363\pi$
$920$	5.68289	+	9.84306i	0.187359	+	0.324516i
$921$	−1.48167	+	1.27219i	−0.0488226	+	0.0419202i
$922$	17.6491	−	10.1897i	0.581242	−	0.335580i
$923$	−44.1150	−	28.4465i	−1.45206	−	0.936328i
$924$	21.9463	−	8.03398i	0.721979	−	0.264298i
$925$	−8.24664	−	4.76120i	−0.271148	−	0.156547i
$926$			22.4244i			0.736912i
$927$	−6.28149	−	16.1109i	−0.206311	−	0.529153i
$928$	7.30144	+	4.21549i	0.239681	+	0.138380i
$929$	20.9701	+	12.1071i	0.688006	+	0.397220i	0.802865	−	0.596162i	$-0.203308\pi$
$929$	20.9701	+	12.1071i	0.688006	+	0.397220i	−0.114859	+	0.993382i	$0.536642\pi$
$930$	−17.3173	−	20.1687i	−0.567856	−	0.661356i
$931$	13.7256	+	11.9683i	0.449839	+	0.392246i
$932$	11.1073	−	6.41280i	0.363831	−	0.210058i
$933$	3.58351	+	19.0561i	0.117319	+	0.623868i
$934$	−9.83436	−	17.0336i	−0.321790	−	0.557357i
$935$	24.4985	+	14.1442i	0.801187	+	0.462566i
$936$	−3.42954	−	10.2586i	−0.112098	−	0.335312i
$937$			25.9178i			0.846698i	0.905967	+	0.423349i	$0.139146\pi$
$937$			25.9178i			0.846698i	−0.905967	+	0.423349i	$0.860854\pi$
$938$	−10.2554	+	27.3655i	−0.334849	+	0.893516i
$939$	−18.6584	+	53.1319i	−0.608895	+	1.73389i
$940$	2.92675	−	5.06929i	0.0954602	−	0.165342i
$941$	51.6878	+	29.8420i	1.68498	+	0.972821i	0.958267	+	0.285875i	$0.0922843\pi$
$941$	51.6878	+	29.8420i	1.68498	+	0.972821i	0.726709	+	0.686946i	$0.241049\pi$
$942$	12.4045	−	2.33268i	0.404162	−	0.0760030i
$943$	−17.0130	+	29.4674i	−0.554020	+	0.959592i
$944$		−	2.20283i		−	0.0716960i
$945$	25.2356	−	5.09146i	0.820914	−	0.165625i
$946$	24.8738	−	43.0826i	0.808716	−	1.40074i
$947$	−21.8964			−0.711538			−0.355769	−	0.934574i	$-0.615781\pi$
$947$	−21.8964			−0.711538			−0.355769	+	0.934574i	$0.615781\pi$
$948$	16.8203	+	5.90682i	0.546298	+	0.191845i
$949$	−0.707506	+	14.3889i	−0.0229666	+	0.467082i
$950$	1.94250	+	3.36451i	0.0630230	+	0.109159i
$951$	−41.5616	−	14.5953i	−1.34773	−	0.473284i
$952$	6.05106	−	4.98036i	0.196116	−	0.161414i
$953$	5.23975	−	3.02517i	0.169732	−	0.0979949i	−0.412727	−	0.910855i	$-0.635424\pi$
$953$	5.23975	−	3.02517i	0.169732	−	0.0979949i	0.582459	+	0.812860i	$0.302090\pi$
$954$	−17.7992	+	22.2173i	−0.576271	+	0.719312i
$955$	−5.94335			−0.192322
$956$	−30.2795			−0.979311
$957$	−48.5145	−	56.5026i	−1.56825	−	1.82647i
$958$	−16.4723	+	9.51026i	−0.532195	+	0.307263i
$959$	−4.40662	+	3.62689i	−0.142297	+	0.117119i
$960$	−1.07467	+	3.06024i	−0.0346848	+	0.0987687i
$961$	−18.0867	−	31.3271i	−0.583443	−	1.01055i
$962$	10.5038	+	20.4513i	0.338656	+	0.659377i
$963$	−18.2280	−	2.78918i	−0.587388	−	0.0898800i
$964$	8.34511			0.268778
$965$	0.195983	−	0.339453i	0.00630892	−	0.0109274i
$966$	−27.4003	−	4.77896i	−0.881591	−	0.153760i
$967$		−	17.1921i		−	0.552862i	−0.961034	−	0.276431i	$-0.910848\pi$
$967$		−	17.1921i		−	0.552862i	0.961034	−	0.276431i	$-0.0891518\pi$
$968$	7.50436	−	12.9979i	0.241199	−	0.417769i
$969$	2.46674	+	13.1174i	0.0792432	+	0.421392i
$970$	−18.9372	−	10.9334i	−0.608037	−	0.351050i
$971$	−20.6939	+	35.8429i	−0.664100	+	1.15025i	0.315429	+	0.948949i	$0.397852\pi$
$971$	−20.6939	+	35.8429i	−0.664100	+	1.15025i	−0.979529	+	0.201305i	$0.935482\pi$
$972$	14.3225	−	6.15363i	0.459393	−	0.197378i
$973$	7.70825	−	20.5688i	0.247115	−	0.659405i
$974$			22.4738i			0.720107i
$975$	5.72045	+	7.36543i	0.183201	+	0.235882i
$976$	5.11154	+	2.95115i	0.163616	+	0.0944640i
$977$	−19.9713	−	34.5912i	−0.638937	−	1.10667i	−0.985666	−	0.168706i	$-0.946041\pi$
$977$	−19.9713	−	34.5912i	−0.638937	−	1.10667i	0.346729	−	0.937965i	$-0.387292\pi$
$978$	−33.7194	+	6.34096i	−1.07823	+	0.202761i
$979$	−65.2018	+	37.6443i	−2.08386	+	1.20312i
$980$	−4.24871	−	12.4006i	−0.135720	−	0.396122i
$981$	−23.6011	+	29.4594i	−0.753527	+	0.940565i
$982$	25.7148	+	14.8464i	0.820591	+	0.473768i
$983$	−3.96116	−	2.28698i	−0.126342	−	0.0729433i	0.435497	−	0.900190i	$-0.356573\pi$
$983$	−3.96116	−	2.28698i	−0.126342	−	0.0729433i	−0.561839	+	0.827247i	$0.689906\pi$
$984$	−9.54273	+	1.79452i	−0.304211	+	0.0572072i
$985$			36.4034i			1.15991i
$986$	−21.6278	−	12.4868i	−0.688768	−	0.397661i
$987$	4.92426	+	13.4515i	0.156741	+	0.428166i
$988$	0.460662	−	9.36868i	0.0146556	−	0.298057i
$989$	−51.2738	+	29.6030i	−1.63041	+	0.941319i
$990$	17.9132	−	22.3596i	0.569319	−	0.710633i
$991$	9.02683	+	15.6349i	0.286747	+	0.496660i	0.973031	−	0.230673i	$-0.0740929\pi$
$991$	9.02683	+	15.6349i	0.286747	+	0.496660i	−0.686285	+	0.727333i	$0.740760\pi$
$992$	−4.09797	+	7.09789i	−0.130111	+	0.225358i
$993$	12.2323	−	2.30030i	0.388181	−	0.0729978i
$994$	−36.0685	−	13.5168i	−1.14402	−	0.428728i
$995$	−13.5333	−	23.4403i	−0.429033	−	0.743107i
$996$	−10.8704	−	12.6602i	−0.344441	−	0.401155i
$997$		−	42.3940i		−	1.34263i	−0.741171	−	0.671316i	$-0.765729\pi$
$997$		−	42.3940i		−	1.34263i	0.741171	−	0.671316i	$-0.234271\pi$
$998$	−6.50477	+	3.75553i	−0.205905	+	0.118879i
$999$	−28.1140	+	17.5338i	−0.889489	+	0.554745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.17.4	✓	34
3.2	odd	2		546.2.bi.f.17.3	yes	34
7.5	odd	6		546.2.bn.f.173.10	yes	34
13.10	even	6		546.2.bn.e.101.8	yes	34
21.5	even	6		546.2.bn.e.173.8	yes	34
39.23	odd	6		546.2.bn.f.101.10	yes	34
91.75	odd	6		546.2.bi.f.257.3	yes	34
273.257	even	6	inner	546.2.bi.e.257.4	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.4	✓	34	1.1	even	1	trivial
546.2.bi.e.257.4	yes	34	273.257	even	6	inner
546.2.bi.f.17.3	yes	34	3.2	odd	2
546.2.bi.f.257.3	yes	34	91.75	odd	6
546.2.bn.e.101.8	yes	34	13.10	even	6
546.2.bn.e.173.8	yes	34	21.5	even	6
546.2.bn.f.101.10	yes	34	39.23	odd	6
546.2.bn.f.173.10	yes	34	7.5	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.31411 + 1.12832i) q^{3} +1.00000 q^{4} +(1.62172 - 0.936303i) q^{5} +(1.31411 - 1.12832i) q^{6} +(2.04281 - 1.68135i) q^{7} -1.00000 q^{8} +(0.453768 - 2.96548i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.31411 + 1.12832i) q^{3} +1.00000 q^{4} +(1.62172 - 0.936303i) q^{5} +(1.31411 - 1.12832i) q^{6} +(2.04281 - 1.68135i) q^{7} -1.00000 q^{8} +(0.453768 - 2.96548i) q^{9} +(-1.62172 + 0.936303i) q^{10} +(-2.54994 - 4.41662i) q^{11} +(-1.31411 + 1.12832i) q^{12} +(-3.20727 + 1.64725i) q^{13} +(-2.04281 + 1.68135i) q^{14} +(-1.07467 + 3.06024i) q^{15} +1.00000 q^{16} -2.96212 q^{17} +(-0.453768 + 2.96548i) q^{18} +(-1.30077 + 2.25300i) q^{19} +(1.62172 - 0.936303i) q^{20} +(-0.787372 + 4.51443i) q^{21} +(2.54994 + 4.41662i) q^{22} -6.06950i q^{23} +(1.31411 - 1.12832i) q^{24} +(-0.746672 + 1.29327i) q^{25} +(3.20727 - 1.64725i) q^{26} +(2.74973 + 4.40897i) q^{27} +(2.04281 - 1.68135i) q^{28} +(-7.30144 - 4.21549i) q^{29} +(1.07467 - 3.06024i) q^{30} +(4.09797 - 7.09789i) q^{31} -1.00000 q^{32} +(8.33428 + 2.92677i) q^{33} +2.96212 q^{34} +(1.73863 - 4.63937i) q^{35} +(0.453768 - 2.96548i) q^{36} +6.37656i q^{37} +(1.30077 - 2.25300i) q^{38} +(2.35607 - 5.78351i) q^{39} +(-1.62172 + 0.936303i) q^{40} +(-4.85500 - 2.80304i) q^{41} +(0.787372 - 4.51443i) q^{42} +(-4.87733 - 8.44778i) q^{43} +(-2.54994 - 4.41662i) q^{44} +(-2.04071 - 5.23406i) q^{45} +6.06950i q^{46} +(2.70708 - 1.56293i) q^{47} +(-1.31411 + 1.12832i) q^{48} +(1.34615 - 6.86934i) q^{49} +(0.746672 - 1.29327i) q^{50} +(3.89256 - 3.34224i) q^{51} +(-3.20727 + 1.64725i) q^{52} +(8.21797 + 4.74465i) q^{53} +(-2.74973 - 4.40897i) q^{54} +(-8.27059 - 4.77503i) q^{55} +(-2.04281 + 1.68135i) q^{56} +(-0.832761 - 4.42838i) q^{57} +(7.30144 + 4.21549i) q^{58} -2.20283i q^{59} +(-1.07467 + 3.06024i) q^{60} +(5.11154 + 2.95115i) q^{61} +(-4.09797 + 7.09789i) q^{62} +(-4.05904 - 6.82086i) q^{63} +1.00000 q^{64} +(-3.65898 + 5.67436i) q^{65} +(-8.33428 - 2.92677i) q^{66} +(9.56582 - 5.52283i) q^{67} -2.96212 q^{68} +(6.84837 + 7.97599i) q^{69} +(-1.73863 + 4.63937i) q^{70} +(7.27923 + 12.6080i) q^{71} +(-0.453768 + 2.96548i) q^{72} +(1.99779 - 3.46027i) q^{73} -6.37656i q^{74} +(-0.478024 - 2.54199i) q^{75} +(-1.30077 + 2.25300i) q^{76} +(-12.6349 - 4.73499i) q^{77} +(-2.35607 + 5.78351i) q^{78} +(-5.14630 - 8.91365i) q^{79} +(1.62172 - 0.936303i) q^{80} +(-8.58819 - 2.69128i) q^{81} +(4.85500 + 2.80304i) q^{82} +9.63409i q^{83} +(-0.787372 + 4.51443i) q^{84} +(-4.80375 + 2.77345i) q^{85} +(4.87733 + 8.44778i) q^{86} +(14.3513 - 2.69878i) q^{87} +(2.54994 + 4.41662i) q^{88} -14.7628i q^{89} +(2.04071 + 5.23406i) q^{90} +(-3.78224 + 8.75755i) q^{91} -6.06950i q^{92} +(2.62354 + 13.9512i) q^{93} +(-2.70708 + 1.56293i) q^{94} +4.87167i q^{95} +(1.31411 - 1.12832i) q^{96} +(5.83860 + 10.1127i) q^{97} +(-1.34615 + 6.86934i) q^{98} +(-14.2545 + 5.55768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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