LMFDB - Embedded newform 546.2.bn.f.101.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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			101.10
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.320103 - 1.70221i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.62172 - 0.936303i) q^{5} +(-1.31411 - 1.12832i) q^{6} +(2.47749 + 0.928453i) q^{7} -1.00000 q^{8} +(-2.79507 - 1.08977i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.320103 - 1.70221i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.62172 - 0.936303i) q^{5} +(-1.31411 - 1.12832i) q^{6} +(2.47749 + 0.928453i) q^{7} -1.00000 q^{8} +(-2.79507 - 1.08977i) q^{9} -1.87261i q^{10} +5.09987 q^{11} +(-1.63421 + 0.573890i) q^{12} +(3.20727 + 1.64725i) q^{13} +(2.04281 - 1.68135i) q^{14} +(-1.07467 - 3.06024i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.48106 - 2.56527i) q^{17} +(-2.34130 + 1.87572i) q^{18} -2.60154 q^{19} +(-1.62172 - 0.936303i) q^{20} +(2.37348 - 3.92003i) q^{21} +(2.54994 - 4.41662i) q^{22} +(-5.25634 - 3.03475i) q^{23} +(-0.320103 + 1.70221i) q^{24} +(-0.746672 + 1.29327i) q^{25} +(3.03019 - 1.95395i) q^{26} +(-2.74973 + 4.40897i) q^{27} +(-0.434683 - 2.60980i) q^{28} +(-7.30144 + 4.21549i) q^{29} +(-3.18758 - 0.599427i) q^{30} +(-4.09797 + 7.09789i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.63248 - 8.68108i) q^{33} -2.96212 q^{34} +(4.88713 - 0.813991i) q^{35} +(0.453768 + 2.96548i) q^{36} +(5.52226 + 3.18828i) q^{37} +(-1.30077 + 2.25300i) q^{38} +(3.83063 - 4.93217i) q^{39} +(-1.62172 + 0.936303i) q^{40} +(4.85500 - 2.80304i) q^{41} +(-2.20810 - 4.01551i) q^{42} +(-4.87733 + 8.44778i) q^{43} +(-2.54994 - 4.41662i) q^{44} +(-5.55318 + 0.849728i) q^{45} +(-5.25634 + 3.03475i) q^{46} +(2.70708 - 1.56293i) q^{47} +(1.31411 + 1.12832i) q^{48} +(5.27595 + 4.60047i) q^{49} +(0.746672 + 1.29327i) q^{50} +(-4.84074 + 1.69993i) q^{51} +(-0.177072 - 3.60120i) q^{52} +(-8.21797 - 4.74465i) q^{53} +(2.44341 + 4.58582i) q^{54} +(8.27059 - 4.77503i) q^{55} +(-2.47749 - 0.928453i) q^{56} +(-0.832761 + 4.42838i) q^{57} +8.43097i q^{58} +(-1.90771 + 1.10141i) q^{59} +(-2.11291 + 2.46081i) q^{60} -5.90230i q^{61} +(4.09797 + 7.09789i) q^{62} +(-5.91297 - 5.29498i) q^{63} +1.00000 q^{64} +(6.74363 - 0.331587i) q^{65} +(-6.70179 - 5.75431i) q^{66} -11.0457i q^{67} +(-1.48106 + 2.56527i) q^{68} +(-6.84837 + 7.97599i) q^{69} +(1.73863 - 4.63937i) q^{70} +(7.27923 - 12.6080i) q^{71} +(2.79507 + 1.08977i) q^{72} +(-1.99779 + 3.46027i) q^{73} +(5.52226 - 3.18828i) q^{74} +(1.96242 + 1.68498i) 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} +1.87261i q^{80} +(6.62481 + 6.09195i) q^{81} -5.60607i q^{82} +9.63409i q^{83} +(-4.58158 - 0.0954798i) q^{84} +(-4.80375 - 2.77345i) q^{85} +(4.87733 + 8.44778i) q^{86} +(4.83845 + 13.7780i) q^{87} -5.09987 q^{88} +(12.7850 + 7.38141i) q^{89} +(-2.04071 + 5.23406i) q^{90} +(6.41659 + 7.05885i) q^{91} +6.06950i q^{92} +(10.7704 + 9.24768i) q^{93} -3.12586i q^{94} +(-4.21899 + 2.43583i) q^{95} +(1.63421 - 0.573890i) q^{96} +(-5.83860 + 10.1127i) q^{97} +(6.62210 - 2.26887i) q^{98} +(-14.2545 - 5.55768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.320103	−	1.70221i	0.184812	−	0.982774i
$3$	0.320103	−	1.70221i	0.184812	−	0.982774i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	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
$7$	2.47749	+	0.928453i	0.936405	+	0.350922i
$7$	2.47749	+	0.928453i	0.936405	+	0.350922i
$8$	−1.00000			−0.353553
$9$	−2.79507	−	1.08977i	−0.931689	−	0.363256i
$10$		−	1.87261i		−	0.592170i
$11$	5.09987			1.53767			0.768835	−	0.639447i	$-0.220837\pi$
$11$	5.09987			1.53767			0.768835	+	0.639447i	$0.220837\pi$
$12$	−1.63421	+	0.573890i	−0.471756	+	0.165668i
$13$	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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.48106	−	2.56527i	−0.359210	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$17$	−1.48106	−	2.56527i	−0.359210	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$18$	−2.34130	+	1.87572i	−0.551850	+	0.442111i
$19$	−2.60154			−0.596835			−0.298417	−	0.954435i	$-0.596459\pi$
$19$	−2.60154			−0.596835			−0.298417	+	0.954435i	$0.596459\pi$
$20$	−1.62172	−	0.936303i	−0.362629	−	0.209364i
$21$	2.37348	−	3.92003i	0.517935	−	0.855420i
$22$	2.54994	−	4.41662i	0.543648	−	0.941627i
$23$	−5.25634	−	3.03475i	−1.09602	−	0.632789i	−0.160850	−	0.986979i	$-0.551423\pi$
$23$	−5.25634	−	3.03475i	−1.09602	−	0.632789i	−0.935174	+	0.354190i	$0.884757\pi$
$24$	−0.320103	+	1.70221i	−0.0653407	+	0.347463i
$25$	−0.746672	+	1.29327i	−0.149334	+	0.258655i
$26$	3.03019	−	1.95395i	0.594270	−	0.383201i
$27$	−2.74973	+	4.40897i	−0.529185	+	0.848506i
$28$	−0.434683	−	2.60980i	−0.0821475	−	0.493206i
$29$	−7.30144	+	4.21549i	−1.35584	+	0.782796i	−0.989060	−	0.147511i	$-0.952874\pi$
$29$	−7.30144	+	4.21549i	−1.35584	+	0.782796i	−0.366782	+	0.930307i	$0.619541\pi$
$30$	−3.18758	−	0.599427i	−0.581969	−	0.109440i
$31$	−4.09797	+	7.09789i	−0.736017	+	1.27482i	0.218258	+	0.975891i	$0.429962\pi$
$31$	−4.09797	+	7.09789i	−0.736017	+	1.27482i	−0.954276	+	0.298928i	$0.903371\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.63248	−	8.68108i	0.284179	−	1.51118i
$34$	−2.96212			−0.508000
$35$	4.88713	−	0.813991i	0.826075	−	0.137590i
$36$	0.453768	+	2.96548i	0.0756279	+	0.494247i
$37$	5.52226	+	3.18828i	0.907854	+	0.524150i	0.879740	−	0.475455i	$-0.157716\pi$
$37$	5.52226	+	3.18828i	0.907854	+	0.524150i	0.0281141	+	0.999605i	$0.491050\pi$
$38$	−1.30077	+	2.25300i	−0.211013	+	0.365485i
$39$	3.83063	−	4.93217i	0.613392	−	0.789779i
$40$	−1.62172	+	0.936303i	−0.256417	+	0.148043i
$41$	4.85500	−	2.80304i	0.758223	−	0.437761i	−0.0704341	−	0.997516i	$-0.522438\pi$
$41$	4.85500	−	2.80304i	0.758223	−	0.437761i	0.828658	+	0.559756i	$0.189105\pi$
$42$	−2.20810	−	4.01551i	−0.340718	−	0.619606i
$43$	−4.87733	+	8.44778i	−0.743786	+	1.28827i	0.206974	+	0.978346i	$0.433638\pi$
$43$	−4.87733	+	8.44778i	−0.743786	+	1.28827i	−0.950760	+	0.309928i	$0.899695\pi$
$44$	−2.54994	−	4.41662i	−0.384417	−	0.665831i
$45$	−5.55318	+	0.849728i	−0.827820	+	0.126670i
$46$	−5.25634	+	3.03475i	−0.775006	+	0.447450i
$47$	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
$49$	5.27595	+	4.60047i	0.753707	+	0.657210i
$50$	0.746672	+	1.29327i	0.105595	+	0.182897i
$51$	−4.84074	+	1.69993i	−0.677839	+	0.238038i
$52$	−0.177072	−	3.60120i	−0.0245555	−	0.499397i
$53$	−8.21797	−	4.74465i	−1.12883	−	0.651728i	−0.185186	−	0.982703i	$-0.559289\pi$
$53$	−8.21797	−	4.74465i	−1.12883	−	0.651728i	−0.943639	+	0.330976i	$0.892622\pi$
$54$	2.44341	+	4.58582i	0.332507	+	0.624051i
$55$	8.27059	−	4.77503i	1.11521	−	0.643865i
$56$	−2.47749	−	0.928453i	−0.331069	−	0.124070i
$57$	−0.832761	+	4.42838i	−0.110302	+	0.586554i
$58$			8.43097i			1.10704i
$59$	−1.90771	+	1.10141i	−0.248362	+	0.143392i	−0.619014	−	0.785380i	$-0.712468\pi$
$59$	−1.90771	+	1.10141i	−0.248362	+	0.143392i	0.370652	+	0.928772i	$0.379134\pi$
$60$	−2.11291	+	2.46081i	−0.272775	+	0.317689i
$61$		−	5.90230i		−	0.755712i	−0.925864	−	0.377856i	$-0.876661\pi$
$61$		−	5.90230i		−	0.755712i	0.925864	−	0.377856i	$-0.123339\pi$
$62$	4.09797	+	7.09789i	0.520443	+	0.901433i
$63$	−5.91297	−	5.29498i	−0.744964	−	0.667105i
$64$	1.00000			0.125000
$65$	6.74363	−	0.331587i	0.836445	−	0.0411283i
$66$	−6.70179	−	5.75431i	−0.824934	−	0.708307i
$67$		−	11.0457i		−	1.34944i	−0.738073	−	0.674721i	$-0.764264\pi$
$67$		−	11.0457i		−	1.34944i	0.738073	−	0.674721i	$-0.235736\pi$
$68$	−1.48106	+	2.56527i	−0.179605	+	0.311085i
$69$	−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	−0.00426326	−	0.999991i	$-0.501357\pi$
$71$	7.27923	−	12.6080i	0.863886	−	1.49629i	0.868149	−	0.496303i	$-0.165310\pi$
$72$	2.79507	+	1.08977i	0.329402	+	0.128430i
$73$	−1.99779	+	3.46027i	−0.233823	+	0.404994i	−0.958930	−	0.283643i	$-0.908457\pi$
$73$	−1.99779	+	3.46027i	−0.233823	+	0.404994i	0.725107	+	0.688636i	$0.241790\pi$
$74$	5.52226	−	3.18828i	0.641950	−	0.370630i
$75$	1.96242	+	1.68498i	0.226601	+	0.194564i
$76$	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	$-0.363225\pi$
$80$			1.87261i			0.209364i
$81$	6.62481	+	6.09195i	0.736090	+	0.676883i
$82$		−	5.60607i		−	0.619087i
$83$			9.63409i			1.05748i	0.848784	+	0.528739i	$0.177335\pi$
$83$			9.63409i			1.05748i	−0.848784	+	0.528739i	$0.822665\pi$
$84$	−4.58158	−	0.0954798i	−0.499891	−	0.0104177i
$85$	−4.80375	−	2.77345i	−0.521040	−	0.300823i
$86$	4.87733	+	8.44778i	0.525936	+	0.910948i
$87$	4.83845	+	13.7780i	0.518736	+	1.47716i
$88$	−5.09987			−0.543648
$89$	12.7850	+	7.38141i	1.35520	+	0.782428i	0.988973	−	0.148096i	$-0.0473144\pi$
$89$	12.7850	+	7.38141i	1.35520	+	0.782428i	0.366232	+	0.930524i	$0.380648\pi$
$90$	−2.04071	+	5.23406i	−0.215109	+	0.551719i
$91$	6.41659	+	7.05885i	0.672642	+	0.739969i
$92$			6.06950i			0.632789i
$93$	10.7704	+	9.24768i	1.11683	+	0.958940i
$94$		−	3.12586i		−	0.322408i
$95$	−4.21899	+	2.43583i	−0.432859	+	0.249911i
$96$	1.63421	−	0.573890i	0.166791	−	0.0585724i
$97$	−5.83860	+	10.1127i	−0.592820	+	1.02679i	0.401031	+	0.916065i	$0.368652\pi$
$97$	−5.83860	+	10.1127i	−0.592820	+	1.02679i	−0.993851	+	0.110729i	$0.964681\pi$
$98$	6.62210	−	2.26887i	0.668933	−	0.229191i
$99$	−14.2545	−	5.55768i	−1.43263	−	0.558568i
$100$	1.49334			0.149334
$101$	6.30051			0.626924			0.313462	−	0.949601i	$-0.398511\pi$
$101$	6.30051			0.626924			0.313462	+	0.949601i	$0.398511\pi$
$102$	−0.948185	+	5.04217i	−0.0938843	+	0.499249i
$103$	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
$105$	0.178796	−	8.57950i	0.0174487	−	0.837273i
$106$	−8.21797	+	4.74465i	−0.798200	+	0.460841i
$107$	−5.32321	−	3.07336i	−0.514614	−	0.297113i	0.220114	−	0.975474i	$-0.429357\pi$
$107$	−5.32321	−	3.07336i	−0.514614	−	0.297113i	−0.734728	+	0.678362i	$0.762690\pi$
$108$	5.19314	+	0.176850i	0.499710	+	0.0170174i
$109$	10.8967	+	6.29124i	1.04372	+	0.602591i	0.920884	−	0.389836i	$-0.127468\pi$
$109$	10.8967	+	6.29124i	1.04372	+	0.602591i	0.122834	+	0.992427i	$0.460802\pi$
$110$		−	9.55006i		−	0.910562i
$111$	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	0.406595	−	0.913609i	$-0.366716\pi$
$113$	−1.92741	−	1.11279i	−0.181316	−	0.104683i	−0.587911	+	0.808926i	$0.700049\pi$
$114$	3.41871	+	2.93538i	0.320192	+	0.274924i
$115$	−11.3658			−1.05987
$116$	7.30144	+	4.21549i	0.677921	+	0.391398i
$117$	−7.16941	−	8.09936i	−0.662812	−	0.748786i
$118$			2.20283i			0.202787i
$119$	−1.28759	−	7.73055i	−0.118033	−	0.708658i
$120$	1.07467	+	3.06024i	0.0981035	+	0.279360i
$121$	15.0087			1.36443
$122$	−5.11154	−	2.95115i	−0.462777	−	0.267185i
$123$	−3.21727	−	9.16151i	−0.290091	−	0.826066i
$124$	8.19594			0.736017
$125$			12.1595i			1.08758i
$126$	−7.54207	+	2.47329i	−0.671901	+	0.220338i
$127$	−3.67232	−	6.36064i	−0.325866	−	0.564416i	0.655822	−	0.754916i	$-0.272322\pi$
$127$	−3.67232	−	6.36064i	−0.325866	−	0.564416i	−0.981687	+	0.190500i	$0.938989\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	12.8187	+	11.0064i	1.12862	+	0.969061i
$130$	3.08465	−	6.00595i	0.270542	−	0.526757i
$131$	−0.465541	−	0.806340i	−0.0406745	−	0.0704503i	0.844971	−	0.534811i	$-0.179617\pi$
$131$	−0.465541	−	0.806340i	−0.0406745	−	0.0704503i	−0.885646	+	0.464361i	$0.846284\pi$
$132$	−8.33428	+	2.92677i	−0.725406	+	0.254742i
$133$	−6.44531	−	2.41541i	−0.558879	−	0.209443i
$134$	−9.56582	−	5.52283i	−0.826361	−	0.477100i
$135$	−0.331171	+	9.72471i	−0.0285027	+	0.836970i
$136$	1.48106	+	2.56527i	0.127000	+	0.219970i
$137$	1.07857	+	1.86814i	0.0921483	+	0.159606i	0.908415	−	0.418070i	$-0.137293\pi$
$137$	1.07857	+	1.86814i	0.0921483	+	0.159606i	−0.816267	+	0.577675i	$0.803960\pi$
$138$	3.48323	+	9.91886i	0.296512	+	0.844349i
$139$	−7.18997	−	4.15113i	−0.609845	−	0.352094i	0.163060	−	0.986616i	$-0.447864\pi$
$139$	−7.18997	−	4.15113i	−0.609845	−	0.352094i	−0.772905	+	0.634522i	$0.781197\pi$
$140$	−3.14850	−	3.82538i	−0.266097	−	0.323304i
$141$	−1.79390	−	5.10832i	−0.151074	−	0.430198i
$142$	−7.27923	−	12.6080i	−0.610860	−	1.05804i
$143$	16.3567	+	8.40077i	1.36781	+	0.702508i
$144$	2.34130	−	1.87572i	0.195108	−	0.156310i
$145$	−7.89395	+	13.6727i	−0.655557	+	1.13546i
$146$	1.99779	+	3.46027i	0.165338	+	0.286374i
$147$	9.51984	−	7.50818i	0.785183	−	0.619264i
$148$		−	6.37656i		−	0.524150i
$149$	−3.95824			−0.324271			−0.162136	−	0.986768i	$-0.551838\pi$
$149$	−3.95824			−0.324271			−0.162136	+	0.986768i	$0.551838\pi$
$150$	2.44044	−	0.857016i	0.199261	−	0.0699750i
$151$	−4.82241	−	2.78422i	−0.392442	−	0.226576i	0.290776	−	0.956791i	$-0.406087\pi$
$151$	−4.82241	−	2.78422i	−0.392442	−	0.226576i	−0.683218	+	0.730215i	$0.739420\pi$
$152$	2.60154			0.211013
$153$	1.34412	+	8.78413i	0.108665	+	0.710155i
$154$	10.4181	−	8.57465i	0.839512	−	0.690965i
$155$			15.3478i			1.23276i
$156$	−6.18670	−	0.851340i	−0.495332	−	0.0681617i
$157$	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	$0.572747\pi$
$158$	−10.2926			−0.818835
$159$	−10.7070	+	12.4700i	−0.849121	+	0.988934i
$160$	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
$163$		−	19.8091i		−	1.55157i	−0.630997	−	0.775785i	$-0.717354\pi$
$163$		−	19.8091i		−	1.55157i	0.630997	−	0.775785i	$-0.282646\pi$
$164$	−4.85500	−	2.80304i	−0.379112	−	0.218880i
$165$	−5.48068	−	15.6068i	−0.426671	−	1.21499i
$166$	8.34337	+	4.81704i	0.647571	+	0.373875i
$167$	−13.0891	+	7.55698i	−1.01286	+	0.584777i	−0.912029	−	0.410126i	$-0.865485\pi$
$167$	−13.0891	+	7.55698i	−1.01286	+	0.584777i	−0.100834	+	0.994903i	$0.532151\pi$
$168$	−2.37348	+	3.92003i	−0.183118	+	0.302437i
$169$	7.57313	+	10.5663i	0.582548	+	0.812796i
$170$	−4.80375	+	2.77345i	−0.368431	+	0.212714i
$171$	7.27149	+	2.83508i	0.556065	+	0.216804i
$172$	9.75466			0.743786
$173$	19.2543			1.46387			0.731937	−	0.681372i	$-0.238616\pi$
$173$	19.2543			1.46387			0.731937	+	0.681372i	$0.238616\pi$
$174$	14.3513	+	2.69878i	1.08797	+	0.204594i
$175$	−3.05062	+	2.51083i	−0.230605	+	0.189801i
$176$	−2.54994	+	4.41662i	−0.192209	+	0.332915i
$177$	1.26418	+	3.59989i	0.0950217	+	0.270584i
$178$	12.7850	−	7.38141i	0.958275	−	0.553260i
$179$			5.37303i			0.401599i	0.979632	+	0.200800i	$0.0643540\pi$
$179$			5.37303i			0.401599i	−0.979632	+	0.200800i	$0.935646\pi$
$180$	3.51248	+	4.38433i	0.261805	+	0.326789i
$181$			11.3131i			0.840893i	0.907317	+	0.420446i	$0.138126\pi$
$181$			11.3131i			0.840893i	−0.907317	+	0.420446i	$0.861874\pi$
$182$	9.32144	−	2.02751i	0.690951	−	0.150289i
$183$	−10.0470	−	1.88934i	−0.742694	−	0.139664i
$184$	5.25634	+	3.03475i	0.387503	+	0.223725i
$185$	11.9408			0.877904
$186$	13.3939	−	4.70357i	0.982089	−	0.344882i
$187$	−7.55323	−	13.0826i	−0.552347	−	0.956693i
$188$	−2.70708	−	1.56293i	−0.197434	−	0.113988i
$189$	−10.9060	+	8.37020i	−0.793291	+	0.608842i
$190$			4.87167i			0.353428i
$191$		−	3.17384i		−	0.229651i	−0.993386	−	0.114826i	$-0.963369\pi$
$191$		−	3.17384i		−	0.229651i	0.993386	−	0.114826i	$-0.0366309\pi$
$192$	0.320103	−	1.70221i	0.0231014	−	0.122847i
$193$		−	0.209316i		−	0.0150669i	−0.999972	−	0.00753344i	$-0.997602\pi$
$193$		−	0.209316i		−	0.0150669i	0.999972	−	0.00753344i	$-0.00239799\pi$
$194$	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	−0.971010	−	0.239040i	$-0.923167\pi$
$197$	−9.71998	−	16.8355i	−0.692520	−	1.19948i	0.278490	−	0.960439i	$-0.410166\pi$
$198$	−11.9403	+	9.56592i	−0.848563	+	0.679820i
$199$	−12.5175	+	7.22696i	−0.887339	+	0.512306i	−0.873071	−	0.487593i	$-0.837875\pi$
$199$	−12.5175	+	7.22696i	−0.887339	+	0.512306i	−0.0142681	+	0.999898i	$0.504542\pi$
$200$	0.746672	−	1.29327i	0.0527977	−	0.0914483i
$201$	−18.8021	−	3.53575i	−1.32620	−	0.249392i
$202$	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
$205$	5.24898	−	9.09150i	0.366605	−	0.634978i
$206$		−	5.76406i		−	0.401601i
$207$	11.3847	+	14.2105i	0.791289	+	0.987700i
$208$	−3.03019	+	1.95395i	−0.210106	+	0.135482i
$209$	−13.2675			−0.917735
$210$	−7.34067	−	4.44459i	−0.506554	−	0.306706i
$211$	5.78954	+	10.0278i	0.398568	+	0.690341i	0.993550	−	0.113399i	$-0.0361738\pi$
$211$	5.78954	+	10.0278i	0.398568	+	0.690341i	−0.594981	+	0.803740i	$0.702840\pi$
$212$			9.48930i			0.651728i
$213$	−19.1314	−	16.4267i	−1.31086	−	1.12554i
$214$	−5.32321	+	3.07336i	−0.363887	+	0.210090i
$215$			18.2666i			1.24577i
$216$	2.74973	−	4.40897i	0.187095	−	0.299992i
$217$	−16.7428	+	13.7802i	−1.13657	+	0.935462i
$218$	10.8967	−	6.29124i	0.738020	−	0.426096i
$219$	5.25062	+	4.50830i	0.354804	+	0.304643i
$220$	−8.27059	−	4.77503i	−0.557603	−	0.321932i
$221$	−0.524511	−	10.6672i	−0.0352824	−	0.717554i
$222$	−3.65944	−	10.4207i	−0.245606	−	0.699388i
$223$	3.33759	+	5.78088i	0.223502	+	0.387116i	0.955869	−	0.293794i	$-0.0949178\pi$
$223$	3.33759	+	5.78088i	0.223502	+	0.387116i	−0.732367	+	0.680910i	$0.761584\pi$
$224$	0.434683	+	2.60980i	0.0290435	+	0.174375i
$225$	3.49637	−	2.80109i	0.233091	−	0.186739i
$226$	−1.92741	+	1.11279i	−0.128210	+	0.0740219i
$227$	16.0059	−	9.24099i	1.06235	−	0.613346i	0.136266	−	0.990672i	$-0.456490\pi$
$227$	16.0059	−	9.24099i	1.06235	−	0.613346i	0.926080	+	0.377327i	$0.123157\pi$
$228$	4.25147	−	1.49300i	0.281561	−	0.0988763i
$229$	0.100542	+	0.174145i	0.00664403	+	0.0115078i	0.869328	−	0.494235i	$-0.164552\pi$
$229$	0.100542	+	0.174145i	0.00664403	+	0.0115078i	−0.862684	+	0.505743i	$0.831218\pi$
$230$	−5.68289	+	9.84306i	−0.374719	+	0.649032i
$231$	12.1044	−	19.9916i	0.796414	−	1.31535i
$232$	7.30144	−	4.21549i	0.479363	−	0.276760i
$233$	−11.1073	+	6.41280i	−0.727663	+	0.420116i	−0.817567	−	0.575834i	$-0.804677\pi$
$233$	−11.1073	+	6.41280i	−0.727663	+	0.420116i	0.0899037	+	0.995950i	$0.471344\pi$
$234$	−10.5990	+	2.15921i	−0.692875	+	0.141152i
$235$	2.92675	−	5.06929i	0.190920	−	0.330684i
$236$	1.90771	+	1.10141i	0.124181	+	0.0716960i
$237$	−16.8203	+	5.90682i	−1.09260	+	0.383689i
$238$	−7.33864	−	2.75019i	−0.475694	−	0.178268i
$239$	−30.2795			−1.95862			−0.979311	−	0.202363i	$-0.935138\pi$
$239$	−30.2795			−1.95862			−0.979311	+	0.202363i	$0.935138\pi$
$240$	3.18758	+	0.599427i	0.205757	+	0.0386928i
$241$	4.17255	+	7.22708i	0.268778	+	0.465537i	0.968546	−	0.248833i	$-0.0800469\pi$
$241$	4.17255	+	7.22708i	0.268778	+	0.465537i	−0.699769	+	0.714370i	$0.746714\pi$
$242$	7.50436	−	12.9979i	0.482398	−	0.835538i
$243$	12.4904	−	9.32680i	0.801261	−	0.598315i
$244$	−5.11154	+	2.95115i	−0.327233	+	0.188928i
$245$	12.8636	+	2.52081i	0.821824	+	0.161048i
$246$	−9.54273	−	1.79452i	−0.608422	−	0.114414i
$247$	−8.34384	−	4.28539i	−0.530906	−	0.272673i
$248$	4.09797	−	7.09789i	0.260221	−	0.450717i
$249$	16.3993	+	3.08390i	1.03926	+	0.195434i
$250$	10.5304	+	6.07974i	0.666002	+	0.384517i
$251$	0.325183	−	0.563233i	0.0205253	−	0.0355509i	−0.855580	−	0.517670i	$-0.826799\pi$
$251$	0.325183	−	0.563233i	0.0205253	−	0.0355509i	0.876106	+	0.482119i	$0.160133\pi$
$252$	−1.62910	+	7.76827i	−0.102624	+	0.489355i
$253$	−26.8067	−	15.4768i	−1.68532	−	0.973021i
$254$	−7.34464			−0.460844
$255$	−6.25870	+	7.28922i	−0.391935	+	0.456469i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.70925	−	6.42461i	0.231377	−	0.400756i	−0.726837	−	0.686810i	$-0.759010\pi$
$257$	3.70925	−	6.42461i	0.231377	−	0.400756i	0.958213	+	0.286054i	$0.0923437\pi$
$258$	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
$261$	25.0019	−	3.82570i	1.54758	−	0.236805i
$262$	−0.931081			−0.0575224
$263$		−	20.0513i		−	1.23642i	−0.786013	−	0.618209i	$-0.787858\pi$
$263$		−	20.0513i		−	1.23642i	0.786013	−	0.618209i	$-0.212142\pi$
$264$	−1.63248	+	8.68108i	−0.100472	+	0.534283i
$265$	−17.7697			−1.09159
$266$	−5.31446	+	4.37409i	−0.325850	+	0.268193i
$267$	16.6573	−	19.4000i	1.01941	−	1.18726i
$268$	−9.56582	+	5.52283i	−0.584325	+	0.337360i
$269$	−6.24251	−	10.8123i	−0.380612	−	0.659240i	0.610538	−	0.791987i	$-0.290953\pi$
$269$	−6.24251	−	10.8123i	−0.380612	−	0.659240i	−0.991150	+	0.132747i	$0.957620\pi$
$270$	8.25626	+	5.14916i	0.502460	+	0.313368i
$271$	−1.43966	+	2.49356i	−0.0874530	+	0.151473i	−0.906434	−	0.422348i	$-0.861206\pi$
$271$	−1.43966	+	2.49356i	−0.0874530	+	0.151473i	0.818981	+	0.573821i	$0.194539\pi$
$272$	2.96212			0.179605
$273$	14.0696	−	8.66286i	0.851534	−	0.524300i
$274$	2.15714			0.130317
$275$	−3.80794	+	6.59554i	−0.229627	+	0.397726i
$276$	10.3316	+	1.94287i	0.621889	+	0.116947i
$277$	−4.00146	−	6.93073i	−0.240424	−	0.416427i	0.720411	−	0.693548i	$-0.243953\pi$
$277$	−4.00146	−	6.93073i	−0.240424	−	0.416427i	−0.960835	+	0.277120i	$0.910620\pi$
$278$	−7.18997	+	4.15113i	−0.431226	+	0.248968i
$279$	19.1892	−	15.3733i	1.14883	−	0.920373i
$280$	−4.88713	+	0.813991i	−0.292062	+	0.0486453i
$281$	6.16209			0.367599			0.183800	−	0.982964i	$-0.441160\pi$
$281$	6.16209			0.367599			0.183800	+	0.982964i	$0.441160\pi$
$282$	−5.32089	−	1.00060i	−0.316854	−	0.0595847i
$283$		−	13.7428i		−	0.816926i	−0.912775	−	0.408463i	$-0.866065\pi$
$283$		−	13.7428i		−	0.816926i	0.912775	−	0.408463i	$-0.133935\pi$
$284$	−14.5585			−0.863886
$285$	2.79580	+	7.96134i	0.165609	+	0.471589i
$286$	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
$289$	4.11291	−	7.12377i	0.241936	−	0.419045i
$290$	7.89395	+	13.6727i	0.463549	+	0.802890i
$291$	15.3451	+	13.1757i	0.899546	+	0.772371i
$292$	3.99557			0.233823
$293$	−4.43117	−	2.55834i	−0.258872	−	0.149460i	0.364948	−	0.931028i	$-0.381087\pi$
$293$	−4.43117	−	2.55834i	−0.258872	−	0.149460i	−0.623820	+	0.781568i	$0.714420\pi$
$294$	−1.74235	−	11.9985i	−0.101616	−	0.699767i
$295$	−2.06252	+	3.57238i	−0.120084	+	0.207992i
$296$	−5.52226	−	3.18828i	−0.320975	−	0.185315i
$297$	−14.0233	+	22.4852i	−0.813712	+	1.30472i
$298$	−1.97912	+	3.42793i	−0.114647	+	0.198575i
$299$	−11.8595	−	18.3918i	−0.685853	−	1.06362i
$300$	0.478024	−	2.54199i	0.0275987	−	0.146762i
$301$	−19.9269	+	16.4010i	−1.14857	+	0.945335i
$302$	−4.82241	+	2.78422i	−0.277498	+	0.160214i
$303$	2.01681	−	10.7248i	0.115863	−	0.616125i
$304$	1.30077	−	2.25300i	0.0746044	−	0.129219i
$305$	−5.52634	−	9.57191i	−0.316437	−	0.548086i
$306$	8.27934	+	3.22803i	0.473298	+	0.184534i
$307$	−1.12751			−0.0643502			−0.0321751	−	0.999482i	$-0.510243\pi$
$307$	−1.12751			−0.0643502			−0.0321751	+	0.999482i	$0.510243\pi$
$308$	−2.21683	−	13.3096i	−0.126316	−	0.758387i
$309$	−3.30794	−	9.41970i	−0.188182	−	0.535868i
$310$	13.2916	+	7.67389i	0.754910	+	0.435847i
$311$	−5.59744	+	9.69505i	−0.317402	+	0.549756i	−0.979945	−	0.199268i	$-0.936144\pi$
$311$	−5.59744	+	9.69505i	−0.317402	+	0.549756i	0.662543	+	0.749023i	$0.269477\pi$
$312$	−3.83063	+	4.93217i	−0.216867	+	0.279229i
$313$	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
$315$	−14.5469	−	3.05067i	−0.819626	−	0.171886i
$316$	−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	$0.580121\pi$
$318$	5.44581	+	15.5075i	0.305386	+	0.869619i
$319$	−37.2364	+	21.4984i	−2.08484	+	1.20368i
$320$	1.62172	−	0.936303i	0.0906572	−	0.0523409i
$321$	−6.93549	+	8.07745i	−0.387101	+	0.450840i
$322$	−15.8402	+	2.63831i	−0.882739	+	0.147027i
$323$	3.85305	+	6.67367i	0.214389	+	0.371333i
$324$	1.96338	−	8.78323i	0.109077	−	0.487957i
$325$	−4.52513	+	2.91792i	−0.251009	+	0.161857i
$326$	−17.1552	−	9.90456i	−0.950139	−	0.548563i
$327$	14.1971	−	16.5347i	0.785102	−	0.914374i
$328$	−4.85500	+	2.80304i	−0.268072	+	0.154772i
$329$	8.15787	−	1.35876i	0.449758	−	0.0749109i
$330$	−16.2562	−	3.05700i	−0.894877	−	0.168282i
$331$		−	7.18613i		−	0.394985i	−0.980304	−	0.197493i	$-0.936720\pi$
$331$		−	7.18613i		−	0.394985i	0.980304	−	0.197493i	$-0.0632798\pi$
$332$	8.34337	−	4.81704i	0.457902	−	0.264370i
$333$	−11.9606	−	14.9294i	−0.655438	−	0.818128i
$334$			15.1140i			0.826999i
$335$	−10.3421	−	17.9130i	−0.565048	−	0.978692i
$336$	2.20810	+	4.01551i	0.120462	+	0.219064i
$337$	19.2711			1.04976			0.524882	−	0.851175i	$-0.324109\pi$
$337$	19.2711			1.04976			0.524882	+	0.851175i	$0.324109\pi$
$338$	12.9373	−	1.27535i	0.703696	−	0.0693697i
$339$	−2.51118	+	2.92466i	−0.136389	+	0.158846i
$340$			5.54689i			0.300823i
$341$	−20.8991	+	36.1984i	−1.13175	+	1.96025i
$342$	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
$345$	−3.63822	+	19.3470i	−0.195875	+	1.04161i
$346$	9.62713	−	16.6747i	0.517558	−	0.896436i
$347$	6.75144	−	3.89795i	0.362436	−	0.209253i	−0.307713	−	0.951479i	$-0.599564\pi$
$347$	6.75144	−	3.89795i	0.362436	−	0.209253i	0.670149	+	0.742227i	$0.266230\pi$
$348$	9.51287	−	11.0792i	0.509944	−	0.593909i
$349$	−7.17103	−	12.4206i	−0.383857	−	0.664859i	0.607753	−	0.794126i	$-0.292071\pi$
$349$	−7.17103	−	12.4206i	−0.383857	−	0.664859i	−0.991610	+	0.129267i	$0.958738\pi$
$350$	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
$353$		−	25.4388i		−	1.35397i	−0.735997	−	0.676985i	$-0.763286\pi$
$353$		−	25.4388i		−	1.35397i	0.735997	−	0.676985i	$-0.236714\pi$
$354$	3.74969	+	0.705132i	0.199294	+	0.0374773i
$355$		−	27.2623i		−	1.44693i
$356$		−	14.7628i		−	0.782428i
$357$	−13.5712	−	0.282823i	−0.718265	−	0.0149686i
$358$	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	$0.916162\pi$
$360$	5.55318	−	0.849728i	0.292679	−	0.0447846i
$361$	−12.2320			−0.643788
$362$	9.79739	+	5.65653i	0.514939	+	0.297300i
$363$	4.80433	−	25.5481i	0.252162	−	1.34092i
$364$	2.90485	−	9.08636i	0.152255	−	0.476254i
$365$			7.48214i			0.391633i
$366$	−6.65971	+	7.75627i	−0.348109	+	0.405427i
$367$		−	14.5427i		−	0.759120i	−0.925167	−	0.379560i	$-0.876075\pi$
$367$		−	14.5427i		−	0.759120i	0.925167	−	0.379560i	$-0.123925\pi$
$368$	5.25634	−	3.03475i	0.274006	−	0.158197i
$369$	−16.6247	+	2.54385i	−0.865448	+	0.132428i
$370$	5.97039	−	10.3410i	0.310386	−	0.537604i
$371$	−15.9548	−	19.3848i	−0.828332	−	1.00641i
$372$	2.62354	−	13.9512i	0.136024	−	0.723339i
$373$	−13.7536			−0.712133			−0.356067	−	0.934461i	$-0.615882\pi$
$373$	−13.7536			−0.712133			−0.356067	+	0.934461i	$0.615882\pi$
$374$	−15.1065			−0.781136
$375$	20.6980	+	3.89229i	1.06884	+	0.200997i
$376$	−2.70708	+	1.56293i	−0.139607	+	0.0806020i
$377$	−30.3616	+	1.49289i	−1.56370	+	0.0768879i
$378$	1.79583	+	13.6299i	0.0923675	+	0.701048i
$379$	25.1138	−	14.4995i	1.29001	−	0.744788i	0.311355	−	0.950294i	$-0.399217\pi$
$379$	25.1138	−	14.4995i	1.29001	−	0.744788i	0.978656	+	0.205505i	$0.0658838\pi$
$380$	4.21899	+	2.43583i	0.216429	+	0.124956i
$381$	−12.0027	+	4.21501i	−0.614917	+	0.215942i
$382$	−2.74863	−	1.58692i	−0.140632	−	0.0811939i
$383$		−	5.59893i		−	0.286092i	−0.989716	−	0.143046i	$-0.954310\pi$
$383$		−	5.59893i		−	0.286092i	0.989716	−	0.143046i	$-0.0456897\pi$
$384$	−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
$387$	22.8386	−	18.2970i	1.16095	−	0.930087i
$388$	11.6772			0.592820
$389$	−4.31018	−	2.48848i	−0.218535	−	0.126171i	0.386737	−	0.922190i	$-0.373602\pi$
$389$	−4.31018	−	2.48848i	−0.218535	−	0.126171i	−0.605272	+	0.796019i	$0.706935\pi$
$390$	−9.23601	−	7.17326i	−0.467683	−	0.363232i
$391$			17.9786i			0.909218i
$392$	−5.27595	−	4.60047i	−0.266476	−	0.232359i
$393$	−1.52158	+	0.534338i	−0.0767538	+	0.0269538i
$394$	−19.4400			−0.979371
$395$	−16.6918	−	9.63699i	−0.839854	−	0.484890i
$396$	2.31416	+	15.1236i	0.116291	+	0.759989i
$397$	16.2382			0.814974			0.407487	−	0.913211i	$-0.366405\pi$
$397$	16.2382			0.814974			0.407487	+	0.913211i	$0.366405\pi$
$398$			14.4539i			0.724510i
$399$	−6.17471	+	10.1981i	−0.309122	+	0.510544i
$400$	−0.746672	−	1.29327i	−0.0373336	−	0.0646637i
$401$	−3.46023	+	5.99329i	−0.172795	+	0.299290i	−0.939396	−	0.342834i	$-0.888613\pi$
$401$	−3.46023	+	5.99329i	−0.172795	+	0.299290i	0.766601	+	0.642124i	$0.221947\pi$
$402$	−12.4631	+	14.5152i	−0.621602	+	0.723952i
$403$	−24.8353	+	16.0145i	−1.23713	+	0.797737i
$404$	−3.15026	−	5.45640i	−0.156731	−	0.271466i
$405$	16.4475	+	3.67663i	0.817285	+	0.182693i
$406$	−7.82776	+	20.8877i	−0.388485	+	1.03664i
$407$	28.1628	+	16.2598i	1.39598	+	0.805970i
$408$	4.84074	−	1.69993i	0.239652	−	0.0841592i
$409$	5.69146	+	9.85790i	0.281425	+	0.487442i	0.971736	−	0.236071i	$-0.0758597\pi$
$409$	5.69146	+	9.85790i	0.281425	+	0.487442i	−0.690311	+	0.723513i	$0.742526\pi$
$410$	−5.24898	−	9.09150i	−0.259229	−	0.448997i
$411$	3.52522	−	1.23796i	0.173886	−	0.0610640i
$412$	−4.99182	−	2.88203i	−0.245930	−	0.141987i
$413$	−5.74894	+	0.957533i	−0.282887	+	0.0471171i
$414$	17.9990	−	2.75414i	0.884603	−	0.135359i
$415$	9.02043	+	15.6238i	0.442795	+	0.766944i
$416$	0.177072	+	3.60120i	0.00868169	+	0.176563i
$417$	−9.36764	+	10.9101i	−0.458735	+	0.534269i
$418$	−6.63377	+	11.4900i	−0.324468	+	0.561996i
$419$	4.51941	+	7.82784i	0.220788	+	0.382415i	0.955047	−	0.296453i	$-0.0958039\pi$
$419$	4.51941	+	7.82784i	0.220788	+	0.382415i	−0.734260	+	0.678869i	$0.762471\pi$
$420$	−7.51946	+	4.13491i	−0.366912	+	0.201763i
$421$		−	3.07453i		−	0.149844i	−0.997189	−	0.0749218i	$-0.976129\pi$
$421$		−	3.07453i		−	0.149844i	0.997189	−	0.0749218i	$-0.0238707\pi$
$422$	11.5791			0.563661
$423$	−9.26969	+	1.41841i	−0.450708	+	0.0689657i
$424$	8.21797	+	4.74465i	0.399100	+	0.230421i
$425$	4.42347			0.214570
$426$	−23.7916	+	8.35496i	−1.15271	+	0.404799i
$427$	5.48000	−	14.6229i	0.265196	−	0.707652i
$428$			6.14671i			0.297113i
$429$	19.5357	−	25.1534i	0.943194	−	1.21442i
$430$	15.8194	+	9.13332i	0.762878	+	0.440448i
$431$	−23.2809			−1.12140			−0.560700	−	0.828019i	$-0.689468\pi$
$431$	−23.2809			−1.12140			−0.560700	+	0.828019i	$0.689468\pi$
$432$	−2.44341	−	4.58582i	−0.117559	−	0.220635i
$433$	23.9459	+	13.8252i	1.15077	+	0.664396i	0.949074	−	0.315053i	$-0.102022\pi$
$433$	23.9459	+	13.8252i	1.15077	+	0.664396i	0.201693	+	0.979449i	$0.435356\pi$
$434$	3.56264	+	21.3898i	0.171012	+	1.02674i
$435$	20.7470	+	17.8139i	0.994744	+	0.854110i
$436$		−	12.5825i		−	0.602591i
$437$	13.6746	+	7.89503i	0.654145	+	0.377671i
$438$	6.52962	−	2.29302i	0.311997	−	0.109565i
$439$	−3.78672	−	2.18627i	−0.180731	−	0.104345i	0.406905	−	0.913470i	$-0.366608\pi$
$439$	−3.78672	−	2.18627i	−0.180731	−	0.104345i	−0.587636	+	0.809126i	$0.699941\pi$
$440$	−8.27059	+	4.77503i	−0.394285	+	0.227641i
$441$	−9.73320	−	18.6082i	−0.463486	−	0.886104i
$442$	−9.50032	−	4.87936i	−0.451884	−	0.232088i
$443$	2.31071	−	1.33409i	0.109785	−	0.0633846i	−0.444102	−	0.895976i	$-0.646477\pi$
$443$	2.31071	−	1.33409i	0.109785	−	0.0633846i	0.553887	+	0.832592i	$0.313144\pi$
$444$	−10.8543	−	2.04116i	−0.515121	−	0.0968689i
$445$	27.6450			1.31050
$446$	6.67519			0.316079
$447$	−1.26704	+	6.73777i	−0.0599291	+	0.318685i
$448$	2.47749	+	0.928453i	0.117051	+	0.0438653i
$449$	−7.64162	+	13.2357i	−0.360630	+	0.624630i	−0.988065	−	0.154039i	$-0.950772\pi$
$449$	−7.64162	+	13.2357i	−0.360630	+	0.624630i	0.627434	+	0.778670i	$0.284105\pi$
$450$	−0.677631	−	4.42849i	−0.0319439	−	0.208761i
$451$	24.7599	−	14.2951i	1.16590	−	0.673131i
$452$			2.22559i			0.104683i
$453$	−6.28300	+	7.31753i	−0.295201	+	0.343808i
$454$		−	18.4820i		−	0.867402i
$455$	17.0152	+	5.43964i	0.797683	+	0.255014i
$456$	0.832761	−	4.42838i	0.0389976	−	0.207378i
$457$	6.00766	+	3.46853i	0.281027	+	0.162251i	0.633888	−	0.773425i	$-0.281458\pi$
$457$	6.00766	+	3.46853i	0.281027	+	0.162251i	−0.352861	+	0.935676i	$0.614791\pi$
$458$	0.201085			0.00939607
$459$	15.3827	+	0.523853i	0.718004	+	0.0244514i
$460$	5.68289	+	9.84306i	0.264966	+	0.458935i
$461$	17.6491	+	10.1897i	0.822001	+	0.474582i	0.851106	−	0.524994i	$-0.175932\pi$
$461$	17.6491	+	10.1897i	0.822001	+	0.474582i	−0.0291053	+	0.999576i	$0.509266\pi$
$462$	−11.2610	−	20.4786i	−0.523911	−	0.952749i
$463$			22.4244i			1.04215i	0.853511	+	0.521075i	$0.174469\pi$
$463$			22.4244i			1.04215i	−0.853511	+	0.521075i	$0.825531\pi$
$464$		−	8.43097i		−	0.391398i
$465$	26.1252	+	4.91287i	1.21153	+	0.227829i
$466$			12.8256i			0.594134i
$467$	−9.83436	−	17.0336i	−0.455080	−	0.788221i	0.543613	−	0.839336i	$-0.317056\pi$
$467$	−9.83436	−	17.0336i	−0.455080	−	0.788221i	−0.998693	+	0.0511146i	$0.983723\pi$
$468$	−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
$471$	8.22243	−	9.57630i	0.378870	−	0.441253i
$472$	1.90771	−	1.10141i	0.0878093	−	0.0506967i
$473$	−24.8738	+	43.0826i	−1.14370	+	1.98094i
$474$	−3.29469	+	17.5202i	−0.151330	+	0.804730i
$475$	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
$478$	−15.1398	+	26.2229i	−0.692477	+	1.19941i
$479$			19.0205i			0.869070i	0.900655	+	0.434535i	$0.143087\pi$
$479$			19.0205i			0.869070i	−0.900655	+	0.434535i	$0.856913\pi$
$480$	2.11291	−	2.46081i	0.0964406	−	0.112320i
$481$	12.4595	+	19.3222i	0.568103	+	0.881017i
$482$	8.34511			0.380109
$483$	−24.3721	+	13.4021i	−1.10897	+	0.609816i
$484$	−7.50436	−	12.9979i	−0.341107	−	0.590815i
$485$			21.8668i			0.992920i
$486$	−1.83203	−	15.4804i	−0.0831027	−	0.702206i
$487$	19.4629	−	11.2369i	0.881947	−	0.509192i	0.0106472	−	0.999943i	$-0.496611\pi$
$487$	19.4629	−	11.2369i	0.881947	−	0.509192i	0.871300	+	0.490751i	$0.163277\pi$
$488$			5.90230i			0.267185i
$489$	−33.7194	−	6.34096i	−1.52484	−	0.286748i
$490$	8.61487	−	9.87978i	0.389180	−	0.446323i
$491$	−25.7148	+	14.8464i	−1.16049	+	0.670010i	−0.951422	−	0.307891i	$-0.900377\pi$
$491$	−25.7148	+	14.8464i	−1.16049	+	0.670010i	−0.209069	+	0.977901i	$0.567043\pi$
$492$	−6.32547	+	7.36699i	−0.285174	+	0.332130i
$493$	21.6278	+	12.4868i	0.974065	+	0.562377i
$494$	−7.88318	+	5.08328i	−0.354681	+	0.228708i
$495$	−28.3205	+	4.33351i	−1.27291	+	0.194777i
$496$	−4.09797	−	7.09789i	−0.184004	−	0.318705i
$497$	29.7402	−	24.4778i	1.33403	−	1.09798i
$498$	10.8704	−	12.6602i	0.487113	−	0.567319i
$499$	−6.50477	+	3.75553i	−0.291193	+	0.168121i	−0.638480	−	0.769638i	$-0.720436\pi$
$499$	−6.50477	+	3.75553i	−0.291193	+	0.168121i	0.347287	+	0.937759i	$0.387103\pi$
$500$	10.5304	−	6.07974i	0.470935	−	0.271894i
$501$	8.67375	+	24.6994i	0.387515	+	1.10349i
$502$	−0.325183	−	0.563233i	−0.0145136	−	0.0251383i
$503$	−14.6024	+	25.2921i	−0.651089	+	1.12772i	0.331770	+	0.943360i	$0.392354\pi$
$503$	−14.6024	+	25.2921i	−0.651089	+	1.12772i	−0.982859	+	0.184358i	$0.940979\pi$
$504$	5.91297	+	5.29498i	0.263384	+	0.235857i
$505$	10.2177	−	5.89919i	0.454682	−	0.262511i
$506$	−26.8067	+	15.4768i	−1.19170	+	0.688030i
$507$	20.4104	−	9.50877i	0.906456	−	0.422299i
$508$	−3.67232	+	6.36064i	−0.162933	+	0.282208i
$509$	−33.1098	−	19.1160i	−1.46757	−	0.847301i	−0.468227	−	0.883608i	$-0.655107\pi$
$509$	−33.1098	−	19.1160i	−1.46757	−	0.847301i	−0.999341	+	0.0363071i	$0.988441\pi$
$510$	3.18331	+	9.06480i	0.140959	+	0.401396i
$511$	−8.16220	+	6.71794i	−0.361075	+	0.297184i
$512$	−1.00000			−0.0441942
$513$	7.15353	−	11.4701i	0.315836	−	0.506418i
$514$	−3.70925	−	6.42461i	−0.163608	−	0.283377i
$515$	5.39691	−	9.34772i	0.237816	−	0.411910i
$516$	3.12249	−	16.6045i	0.137460	−	0.730973i
$517$	13.8057	−	7.97075i	0.607176	−	0.350553i
$518$	16.6415	−	2.77178i	0.731187	−	0.121785i
$519$	6.16335	−	32.7749i	0.270541	−	1.43866i
$520$	−6.74363	+	0.331587i	−0.295728	+	0.0145411i
$521$	1.01347	−	1.75537i	0.0444008	−	0.0769044i	−0.842971	−	0.537959i	$-0.819195\pi$
$521$	1.01347	−	1.75537i	0.0444008	−	0.0769044i	0.887372	+	0.461055i	$0.152529\pi$
$522$	9.18780	−	23.5651i	0.402139	−	1.03142i
$523$	−12.9768	−	7.49219i	−0.567438	−	0.327610i	0.188687	−	0.982037i	$-0.439577\pi$
$523$	−12.9768	−	7.49219i	−0.567438	−	0.327610i	−0.756125	+	0.654427i	$0.772910\pi$
$524$	−0.465541	+	0.806340i	−0.0203372	+	0.0352251i
$525$	3.29746	+	5.99653i	0.143913	+	0.261710i
$526$	−17.3650	−	10.0257i	−0.757149	−	0.437140i
$527$	24.2774			1.05754
$528$	6.70179	+	5.75431i	0.291658	+	0.250424i
$529$	6.91943	+	11.9848i	0.300845	+	0.521078i
$530$	−8.88486	+	15.3890i	−0.385934	+	0.668457i
$531$	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
$534$	−8.47223	−	24.1256i	−0.366629	−	1.04402i
$535$	−11.5104			−0.497637
$536$			11.0457i			0.477100i
$537$	9.14605	+	1.71992i	0.394681	+	0.0742201i
$538$	−12.4850			−0.538267
$539$	26.9067	+	23.4618i	1.15895	+	1.01057i
$540$	8.58743	−	4.57555i	0.369544	−	0.196900i
$541$	0.930484	−	0.537215i	0.0400046	−	0.0230967i	−0.479864	−	0.877343i	$-0.659314\pi$
$541$	0.930484	−	0.537215i	0.0400046	−	0.0230967i	0.519869	+	0.854246i	$0.325981\pi$
$542$	1.43966	+	2.49356i	0.0618386	+	0.107108i
$543$	19.2572	+	3.62134i	0.826407	+	0.155407i
$544$	1.48106	−	2.56527i	0.0635000	−	0.109985i
$545$	23.5620			1.00929
$546$	−0.467430	−	16.5161i	−0.0200042	−	0.706824i
$547$	−26.8765			−1.14916			−0.574578	−	0.818450i	$-0.694834\pi$
$547$	−26.8765			−1.14916			−0.574578	+	0.818450i	$0.694834\pi$
$548$	1.07857	−	1.86814i	0.0460742	−	0.0798028i
$549$	−6.43214	+	16.4973i	−0.274517	+	0.704089i
$550$	3.80794	+	6.59554i	0.162371	+	0.281235i
$551$	18.9950	−	10.9668i	0.809214	−	0.467200i
$552$	6.84837	−	7.97599i	0.291486	−	0.339481i
$553$	−4.47402	−	26.8616i	−0.190255	−	1.14227i
$554$	−8.00292			−0.340011
$555$	3.82228	−	20.3258i	0.162247	−	0.862781i
$556$			8.30226i			0.352094i
$557$	−27.1489			−1.15033			−0.575167	−	0.818036i	$-0.695063\pi$
$557$	−27.1489			−1.15033			−0.575167	+	0.818036i	$0.695063\pi$
$558$	−3.71905	−	24.3049i	−0.157440	−	1.02891i
$559$	−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
$562$	3.08104	−	5.33653i	0.129966	−	0.225108i
$563$	−8.15434	−	14.1237i	−0.343664	−	0.595244i	0.641446	−	0.767168i	$-0.278335\pi$
$563$	−8.15434	−	14.1237i	−0.343664	−	0.595244i	−0.985110	+	0.171924i	$0.945002\pi$
$564$	−3.52699	+	4.10772i	−0.148513	+	0.172966i
$565$	−4.16765			−0.175334
$566$	−11.9016	−	6.87141i	−0.500263	−	0.288827i
$567$	10.7568	+	21.2436i	0.451745	+	0.892147i
$568$	−7.27923	+	12.6080i	−0.305430	+	0.529020i
$569$	−22.6413	−	13.0720i	−0.949172	−	0.548005i	−0.0563486	−	0.998411i	$-0.517946\pi$
$569$	−22.6413	−	13.0720i	−0.949172	−	0.548005i	−0.892824	+	0.450406i	$0.851279\pi$
$570$	8.29262	+	1.55943i	0.347340	+	0.0653175i
$571$	−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	$0.168187\pi$
$572$	−0.903047	−	18.3657i	−0.0377583	−	0.767907i
$573$	−5.40256	−	1.01596i	−0.225695	−	0.0424422i
$574$	5.20497	−	13.8890i	0.217251	−	0.579716i
$575$	7.84953	−	4.53193i	0.327348	−	0.188995i
$576$	−2.79507	−	1.08977i	−0.116461	−	0.0454070i
$577$	8.82331	−	15.2824i	0.367319	−	0.636215i	−0.621826	−	0.783155i	$-0.713609\pi$
$577$	8.82331	−	15.2824i	0.367319	−	0.636215i	0.989145	+	0.146940i	$0.0469424\pi$
$578$	−4.11291	−	7.12377i	−0.171075	−	0.296310i
$579$	−0.356300	−	0.0670026i	−0.0148073	−	0.00278453i
$580$	15.7879			0.655557
$581$	−8.94479	+	23.8684i	−0.371093	+	0.990228i
$582$	19.0830	−	6.70142i	0.791016	−	0.277783i
$583$	−41.9106	−	24.1971i	−1.73576	−	1.00214i
$584$	1.99779	−	3.46027i	0.0826690	−	0.143187i
$585$	−19.2103	−	6.42218i	−0.794247	−	0.265525i
$586$	−4.43117	+	2.55834i	−0.183050	+	0.105684i
$587$	13.2115	−	7.62767i	0.545298	−	0.314828i	−0.201926	−	0.979401i	$-0.564720\pi$
$587$	13.2115	−	7.62767i	0.545298	−	0.314828i	0.747223	+	0.664573i	$0.231387\pi$
$588$	−11.2622	−	4.49033i	−0.464445	−	0.185178i
$589$	10.6610	−	18.4655i	0.439281	−	0.760857i
$590$	2.06252	+	3.57238i	0.0849124	+	0.147073i
$591$	−31.7690	+	11.1564i	−1.30680	+	0.458913i
$592$	−5.52226	+	3.18828i	−0.226964	+	0.131037i
$593$	−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
$595$	−9.32625	−	11.3313i	−0.382339	−	0.464536i
$596$	1.97912	+	3.42793i	0.0810678	+	0.140414i
$597$	8.29496	+	23.6208i	0.339490	+	0.966734i
$598$	−21.8575	+	1.07474i	−0.893819	+	0.0439495i
$599$	21.8300	+	12.6035i	0.891949	+	0.514967i	0.874579	−	0.484882i	$-0.161138\pi$
$599$	21.8300	+	12.6035i	0.891949	+	0.514967i	0.0173692	+	0.999849i	$0.494471\pi$
$600$	−1.96242	−	1.68498i	−0.0801154	−	0.0687889i
$601$	15.4945	−	8.94574i	0.632033	−	0.364904i	−0.149506	−	0.988761i	$-0.547768\pi$
$601$	15.4945	−	8.94574i	0.632033	−	0.364904i	0.781539	+	0.623856i	$0.214435\pi$
$602$	4.24019	+	25.4577i	0.172817	+	1.03758i
$603$	−12.0372	+	30.8734i	−0.490192	+	1.25726i
$604$			5.56843i			0.226576i
$605$	24.3400	−	14.0527i	0.989562	−	0.571324i
$606$	−8.27956	−	7.10902i	−0.336334	−	0.288784i
$607$			26.4339i			1.07292i	0.843926	+	0.536459i	$0.180239\pi$
$607$			26.4339i			1.07292i	−0.843926	+	0.536459i	$0.819761\pi$
$608$	−1.30077	−	2.25300i	−0.0527532	−	0.0913713i
$609$	−0.804988	+	38.6272i	−0.0326198	+	1.56525i
$610$	−11.0527			−0.447510
$611$	11.2569	−	0.553504i	0.455404	−	0.0223924i
$612$	6.93522	−	5.55610i	0.280340	−	0.224592i
$613$			8.25058i			0.333238i	0.986021	+	0.166619i	$0.0532850\pi$
$613$			8.25058i			0.333238i	−0.986021	+	0.166619i	$0.946715\pi$
$614$	−0.563753	+	0.976449i	−0.0227512	+	0.0394063i
$615$	−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	−0.912576	−	0.408907i	$-0.865910\pi$
$617$	−2.53770	+	4.39542i	−0.102164	+	0.176953i	0.810412	+	0.585860i	$0.199243\pi$
$618$	−9.81167	−	1.84509i	−0.394683	−	0.0742205i
$619$	−14.6995	+	25.4603i	−0.590822	+	1.02333i	0.403300	+	0.915068i	$0.367863\pi$
$619$	−14.6995	+	25.4603i	−0.590822	+	1.02333i	−0.994122	+	0.108266i	$0.965470\pi$
$620$	13.2916	−	7.67389i	0.533802	−	0.308191i
$621$	27.8336	−	14.8303i	1.11693	−	0.595120i
$622$	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
$626$		−	32.5122i		−	1.29945i
$627$	−4.24698	+	22.5842i	−0.169608	+	0.901926i
$628$		−	7.28729i		−	0.290795i
$629$		−	18.8882i		−	0.753120i
$630$	−9.91542	+	11.0727i	−0.395040	+	0.441145i
$631$	31.4596	+	18.1632i	1.25239	+	0.723066i	0.971583	−	0.236699i	$-0.0760655\pi$
$631$	31.4596	+	18.1632i	1.25239	+	0.723066i	0.280804	+	0.959765i	$0.409399\pi$
$632$	5.14630	+	8.91365i	0.204709	+	0.354566i
$633$	18.9227	−	6.64512i	0.752109	−	0.264120i
$634$	25.4322			1.01004
$635$	−11.9110	−	6.87681i	−0.472673	−	0.272898i
$636$	16.1528	+	3.03755i	0.640501	+	0.120447i
$637$	9.34326	+	23.4458i	0.370193	+	0.928955i
$638$			42.9969i			1.70226i
$639$	−34.0857	+	27.3075i	−1.34841	+	1.08027i
$640$		−	1.87261i		−	0.0740213i
$641$	0.640544	−	0.369818i	0.0253000	−	0.0146069i	−0.487297	−	0.873236i	$-0.662017\pi$
$641$	0.640544	−	0.369818i	0.0253000	−	0.0146069i	0.512597	+	0.858630i	$0.328684\pi$
$642$	3.52754	+	10.0450i	0.139221	+	0.396446i
$643$	2.41482	−	4.18259i	0.0952313	−	0.164945i	−0.814474	−	0.580200i	$-0.802974\pi$
$643$	2.41482	−	4.18259i	0.0952313	−	0.164945i	0.909705	+	0.415255i	$0.136308\pi$
$644$	−5.63524	+	15.0372i	−0.222060	+	0.592547i
$645$	31.0937	+	5.84720i	1.22431	+	0.230233i
$646$	7.70609			0.303192
$647$	−4.04141			−0.158884			−0.0794422	−	0.996839i	$-0.525314\pi$
$647$	−4.04141			−0.158884			−0.0794422	+	0.996839i	$0.525314\pi$
$648$	−6.62481	−	6.09195i	−0.260247	−	0.239314i
$649$	−9.72906	+	5.61707i	−0.381899	+	0.220489i
$650$	0.264430	+	5.37783i	0.0103718	+	0.210936i
$651$	18.0975	+	32.9108i	0.709296	+	1.28988i
$652$	−17.1552	+	9.90456i	−0.671849	+	0.387892i
$653$	−40.4464	−	23.3518i	−1.58279	−	0.913825i	−0.994450	−	0.105213i	$-0.966448\pi$
$653$	−40.4464	−	23.3518i	−1.58279	−	0.913825i	−0.588342	−	0.808612i	$-0.700219\pi$
$654$	−7.22095	−	20.5624i	−0.282362	−	0.804055i
$655$	−1.50996	−	0.871775i	−0.0589989	−	0.0340631i
$656$			5.60607i			0.218880i
$657$	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	0.996048	+	0.0888111i	$0.0283067\pi$
$659$	40.3288	+	23.2838i	1.57099	+	0.907009i	0.574937	+	0.818198i	$0.305027\pi$
$660$	−10.7756	+	12.5498i	−0.419438	+	0.488501i
$661$	−44.5873			−1.73424			−0.867122	−	0.498095i	$-0.834033\pi$
$661$	−44.5873			−1.73424			−0.867122	+	0.498095i	$0.834033\pi$
$662$	−6.22337	−	3.59306i	−0.241878	−	0.139648i
$663$	−18.3258	−	2.52177i	−0.711714	−	0.0979376i
$664$		−	9.63409i		−	0.373875i
$665$	−12.7141	+	2.11763i	−0.493030	+	0.0821183i
$666$	−18.9096	+	2.89348i	−0.732731	+	0.112120i
$667$	51.1718			1.98138
$668$	13.0891	+	7.55698i	0.506432	+	0.292388i
$669$	10.9087	−	3.83082i	0.421754	−	0.148108i
$670$	−20.6842			−0.799099
$671$		−	30.1010i		−	1.16204i
$672$	4.58158	+	0.0954798i	0.176738	+	0.00368321i
$673$	−7.92610	−	13.7284i	−0.305529	−	0.529191i	0.671850	−	0.740687i	$-0.265500\pi$
$673$	−7.92610	−	13.7284i	−0.305529	−	0.529191i	−0.977379	+	0.211496i	$0.932166\pi$
$674$	9.63555	−	16.6893i	0.371148	−	0.642847i
$675$	−3.64886	−	6.84821i	−0.140445	−	0.263588i
$676$	5.36416	−	11.8417i	0.206314	−	0.455450i
$677$	−2.65460	−	4.59790i	−0.102024	−	0.176711i	0.810494	−	0.585747i	$-0.199199\pi$
$677$	−2.65460	−	4.59790i	−0.102024	−	0.176711i	−0.912519	+	0.409035i	$0.865865\pi$
$678$	1.27724	+	3.63708i	0.0490522	+	0.139681i
$679$	−23.8543	+	19.6334i	−0.915444	+	0.753461i
$680$	4.80375	+	2.77345i	0.184215	+	0.106357i
$681$	−10.6066	−	30.2035i	−0.406447	−	1.15740i
$682$	20.8991	+	36.1984i	0.800269	+	1.38611i
$683$	5.98567	+	10.3675i	0.229035	+	0.396701i	0.957522	−	0.288359i	$-0.0931096\pi$
$683$	5.98567	+	10.3675i	0.229035	+	0.396701i	−0.728487	+	0.685059i	$0.759776\pi$
$684$	−1.18050	−	7.71483i	−0.0451374	−	0.294984i
$685$	3.49828	+	2.01973i	0.133662	+	0.0771701i
$686$	18.5128	+	0.527188i	0.706820	+	0.0201281i
$687$	0.328615	−	0.115401i	0.0125375	−	0.00440280i
$688$	−4.87733	−	8.44778i	−0.185946	−	0.322069i
$689$	−18.5416	−	28.7544i	−0.706379	−	1.09546i
$690$	14.9359	+	12.8243i	0.568600	+	0.488213i
$691$	19.4945	−	33.7655i	0.741608	−	1.28450i	−0.210156	−	0.977668i	$-0.567397\pi$
$691$	19.4945	−	33.7655i	0.741608	−	1.28450i	0.951763	−	0.306834i	$-0.0992696\pi$
$692$	−9.62713	−	16.6747i	−0.365969	−	0.633876i
$693$	−30.1554	−	27.0037i	−1.14551	−	1.02579i
$694$		−	7.79589i		−	0.295928i
$695$	−15.5469			−0.589726
$696$	−4.83845	−	13.7780i	−0.183401	−	0.522254i
$697$	−14.3811	−	8.30294i	−0.544723	−	0.314496i
$698$	−14.3421			−0.542855
$699$	7.36048	+	20.9597i	0.278399	+	0.792771i
$700$	3.69975	+	1.38650i	0.139838	+	0.0524048i
$701$			41.8339i			1.58005i	0.613078	+	0.790023i	$0.289931\pi$
$701$			41.8339i			1.58005i	−0.613078	+	0.790023i	$0.710069\pi$
$702$	0.282689	+	18.7329i	0.0106694	+	0.707026i
$703$	−14.3664	−	8.29444i	−0.541839	−	0.312831i
$704$	5.09987			0.192209
$705$	−7.69215	−	6.60466i	−0.289703	−	0.248746i
$706$	−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
$709$			11.4460i			0.429864i	0.976629	+	0.214932i	$0.0689530\pi$
$709$			11.4460i			0.429864i	−0.976629	+	0.214932i	$0.931047\pi$
$710$	−23.6098	−	13.6311i	−0.886061	−	0.511567i
$711$	4.67045	+	30.5225i	0.175155	+	1.14468i
$712$	−12.7850	−	7.38141i	−0.479137	−	0.276630i
$713$	43.0807	−	24.8726i	1.61338	−	0.931488i
$714$	−7.03054	+	11.6116i	−0.263111	+	0.434553i
$715$	34.3917	−	1.69105i	1.28618	−	0.0632418i
$716$	4.65318	−	2.68651i	0.173897	−	0.100400i
$717$	−9.69257	+	51.5423i	−0.361976	+	1.92488i
$718$	−9.74981			−0.363860
$719$	32.2996			1.20457			0.602286	−	0.798280i	$-0.294257\pi$
$719$	32.2996			1.20457			0.602286	+	0.798280i	$0.294257\pi$
$720$	2.04071	−	5.23406i	0.0760526	−	0.195062i
$721$	15.0430	−	2.50554i	0.560232	−	0.0933113i
$722$	−6.11599	+	10.5932i	−0.227614	+	0.394238i
$723$	13.6377	−	4.78917i	0.507191	−	0.178111i
$724$	9.79739	−	5.65653i	0.364117	−	0.210223i
$725$		−	12.5904i		−	0.467594i
$726$	−19.7231	−	16.9347i	−0.731993	−	0.628506i
$727$		−	35.0984i		−	1.30173i	−0.759195	−	0.650863i	$-0.774407\pi$
$727$		−	35.0984i		−	1.30173i	0.759195	−	0.650863i	$-0.225593\pi$
$728$	−6.41659	−	7.05885i	−0.237815	−	0.261618i
$729$	−11.8780	−	24.2469i	−0.439926	−	0.898034i
$730$	6.47972	+	3.74107i	0.239825	+	0.138463i
$731$	28.8945			1.06870
$732$	3.38727	+	9.64561i	0.125197	+	0.356512i
$733$	−1.14358	−	1.98073i	−0.0422389	−	0.0731600i	0.844133	−	0.536134i	$-0.180116\pi$
$733$	−1.14358	−	1.98073i	−0.0422389	−	0.0731600i	−0.886372	+	0.462974i	$0.846782\pi$
$734$	−12.5943	−	7.27133i	−0.464864	−	0.268390i
$735$	8.40862	−	21.0897i	0.310157	−	0.777903i
$736$		−	6.06950i		−	0.223725i
$737$		−	56.3314i		−	2.07500i
$738$	−6.10931	+	15.6693i	−0.224887	+	0.576797i
$739$			6.51596i			0.239693i	0.992792	+	0.119847i	$0.0382403\pi$
$739$			6.51596i			0.239693i	−0.992792	+	0.119847i	$0.961760\pi$
$740$	−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	−0.999298	−	0.0374682i	$-0.988071\pi$
$743$	−14.5039	−	25.1215i	−0.532097	−	0.921620i	0.467201	−	0.884151i	$-0.345263\pi$
$744$	−10.7704	−	9.24768i	−0.394861	−	0.339036i
$745$	−6.41917	+	3.70611i	−0.235180	+	0.135781i
$746$	−6.87679	+	11.9109i	−0.251777	+	0.436091i
$747$	10.4989	−	26.9279i	0.384135	−	0.985242i
$748$	−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
$751$	−15.4217	+	26.7111i	−0.562744	+	0.974701i	0.434512	+	0.900666i	$0.356921\pi$
$751$	−15.4217	+	26.7111i	−0.562744	+	0.974701i	−0.997256	+	0.0740350i	$0.976412\pi$
$752$			3.12586i			0.113988i
$753$	−0.854651	−	0.733823i	−0.0311452	−	0.0267420i
$754$	−13.8879	+	27.0404i	−0.505769	+	0.984753i
$755$	−10.4275			−0.379495
$756$	12.7018	+	5.25973i	0.461959	+	0.191295i
$757$	−10.6357	−	18.4215i	−0.386560	−	0.669542i	0.605424	−	0.795903i	$-0.293004\pi$
$757$	−10.6357	−	18.4215i	−0.386560	−	0.669542i	−0.991984	+	0.126361i	$0.959670\pi$
$758$		−	28.9990i		−	1.05329i
$759$	−34.9258	+	40.6765i	−1.26773	+	1.47647i
$760$	4.21899	−	2.43583i	0.153039	−	0.0883569i
$761$			24.6519i			0.893632i	0.894626	+	0.446816i	$0.147442\pi$
$761$			24.6519i			0.893632i	−0.894626	+	0.446816i	$0.852558\pi$
$762$	−2.35104	+	12.5022i	−0.0851692	+	0.452905i
$763$	21.1555	+	25.7036i	0.765880	+	0.930533i
$764$	−2.74863	+	1.58692i	−0.0994418	+	0.0574128i
$765$	10.4044	+	12.9869i	0.376172	+	0.469544i
$766$	−4.84882	−	2.79947i	−0.175195	−	0.101149i
$767$	−7.93283	+	0.390060i	−0.286438	+	0.0140843i
$768$	−1.63421	+	0.573890i	−0.0589696	+	0.0207085i
$769$	−6.30372	−	10.9184i	−0.227318	−	0.393726i	0.729694	−	0.683773i	$-0.239662\pi$
$769$	−6.30372	−	10.9184i	−0.227318	−	0.393726i	−0.957012	+	0.290047i	$0.906329\pi$
$770$	8.86677	−	23.6602i	0.319536	−	0.852655i
$771$	−9.74872	−	8.37047i	−0.351092	−	0.301455i
$772$	−0.181273	+	0.104658i	−0.00652415	+	0.00376672i
$773$	−17.4926	+	10.0993i	−0.629164	+	0.363248i	−0.780428	−	0.625245i	$-0.784999\pi$
$773$	−17.4926	+	10.0993i	−0.629164	+	0.363248i	0.151264	+	0.988493i	$0.451666\pi$
$774$	−4.42635	−	28.9273i	−0.159102	−	1.03977i
$775$	−6.11968	−	10.5996i	−0.219826	−	0.380749i
$776$	5.83860	−	10.1127i	0.209593	−	0.363026i
$777$	25.6051	−	14.0801i	0.918578	−	0.505121i
$778$	−4.31018	+	2.48848i	−0.154527	+	0.0892164i
$779$	−12.6305	+	7.29222i	−0.452534	+	0.261271i
$780$	−10.8302	+	4.41199i	−0.387785	+	0.157974i
$781$	37.1232	−	64.2992i	1.32837	−	2.30081i
$782$	15.5699	+	8.98931i	0.556780	+	0.321457i
$783$	1.49102	−	43.7832i	0.0532848	−	1.56469i
$784$	−6.62210	+	2.26887i	−0.236504	+	0.0810312i
$785$	13.6462			0.487055
$786$	−0.298042	+	1.58490i	−0.0106308	+	0.0565315i
$787$	8.76709	+	15.1850i	0.312513	+	0.541288i	0.978906	−	0.204313i	$-0.0654959\pi$
$787$	8.76709	+	15.1850i	0.312513	+	0.541288i	−0.666393	+	0.745601i	$0.732163\pi$
$788$	−9.71998	+	16.8355i	−0.346260	+	0.599740i
$789$	−34.1317	−	6.41849i	−1.21512	−	0.228504i
$790$	−16.6918	+	9.63699i	−0.593866	+	0.342869i
$791$	−3.74198	−	4.54645i	−0.133050	−	0.161653i
$792$	14.2545	+	5.55768i	0.506511	+	0.197483i
$793$	9.72257	−	18.9303i	0.345259	−	0.672233i
$794$	8.11912	−	14.0627i	0.288137	−	0.499068i
$795$	−5.68814	+	30.2479i	−0.201738	+	1.07278i
$796$	12.5175	+	7.22696i	0.443670	+	0.256153i
$797$	24.3061	−	42.0995i	0.860968	−	1.49124i	−0.0100279	−	0.999950i	$-0.503192\pi$
$797$	24.3061	−	42.0995i	0.860968	−	1.49124i	0.870996	−	0.491290i	$-0.163475\pi$
$798$	5.74447	+	10.4465i	0.203352	+	0.369802i
$799$	−8.01869	−	4.62959i	−0.283681	−	0.163783i
$800$	−1.49334			−0.0527977
$801$	−27.6909	−	34.5642i	−0.978408	−	1.22127i
$802$	3.46023	+	5.99329i	0.122185	+	0.211630i
$803$	−10.1885	+	17.6469i	−0.359543	+	0.622747i
$804$	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
$807$	−20.4032	+	7.16502i	−0.718225	+	0.252221i
$808$	−6.30051			−0.221651
$809$			8.32150i			0.292568i	0.989243	+	0.146284i	$0.0467314\pi$
$809$			8.32150i			0.292568i	−0.989243	+	0.146284i	$0.953269\pi$
$810$	11.4078	−	12.4057i	0.400830	−	0.435891i
$811$	−21.9549			−0.770941			−0.385470	−	0.922720i	$-0.625961\pi$
$811$	−21.9549			−0.770941			−0.385470	+	0.922720i	$0.625961\pi$
$812$	14.1754	+	17.2229i	0.497459	+	0.604405i
$813$	3.78373	+	3.24880i	0.132701	+	0.113940i
$814$	28.1628	−	16.2598i	0.987107	−	0.569907i
$815$	−18.5473	−	32.1249i	−0.649685	−	1.12529i
$816$	0.948185	−	5.04217i	0.0331931	−	0.176511i
$817$	12.6886	−	21.9773i	0.443917	−	0.768887i
$818$	11.3829			0.397995
$819$	−10.2423	−	26.7226i	−0.357895	−	0.933762i
$820$	−10.4980			−0.366605
$821$	−13.6665	+	23.6711i	−0.476964	+	0.826127i	−0.999652	−	0.0263980i	$-0.991596\pi$
$821$	−13.6665	+	23.6711i	−0.476964	+	0.826127i	0.522687	+	0.852525i	$0.324930\pi$
$822$	0.690506	−	3.67191i	0.0240842	−	0.128073i
$823$	−6.37963	−	11.0498i	−0.222380	−	0.385173i	0.733150	−	0.680067i	$-0.238049\pi$
$823$	−6.37963	−	11.0498i	−0.222380	−	0.385173i	−0.955530	+	0.294894i	$0.904716\pi$
$824$	−4.99182	+	2.88203i	−0.173898	+	0.100400i
$825$	10.0081	+	8.59317i	0.348437	+	0.299176i
$826$	−2.04522	+	5.45749i	−0.0711624	+	0.189891i
$827$	43.7556			1.52153			0.760766	−	0.649027i	$-0.224824\pi$
$827$	43.7556			1.52153			0.760766	+	0.649027i	$0.224824\pi$
$828$	6.61435	−	16.9647i	0.229864	−	0.589563i
$829$		−	41.0957i		−	1.42731i	−0.700496	−	0.713656i	$-0.747038\pi$
$829$		−	41.0957i		−	1.42731i	0.700496	−	0.713656i	$-0.252962\pi$
$830$	18.0409			0.626207
$831$	−13.0785	+	4.59279i	−0.453687	+	0.159322i
$832$	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
$835$	−14.1513	+	24.5107i	−0.489724	+	0.848227i
$836$	6.63377	+	11.4900i	0.229434	+	0.397391i
$837$	−20.0261	−	37.5851i	−0.692203	−	1.29913i
$838$	9.03882			0.312241
$839$	−19.7685	−	11.4133i	−0.682484	−	0.394032i	0.118306	−	0.992977i	$-0.462253\pi$
$839$	−19.7685	−	11.4133i	−0.682484	−	0.394032i	−0.800790	+	0.598945i	$0.795587\pi$
$840$	−0.178796	+	8.57950i	−0.00616905	+	0.296021i
$841$	21.0407	−	36.4435i	0.725540	−	1.25667i
$842$	−2.66263	−	1.53727i	−0.0917601	−	0.0529777i
$843$	1.97250	−	10.4892i	0.0679366	−	0.361267i
$844$	5.78954	−	10.0278i	0.199284	−	0.345170i
$845$	22.1748	+	10.0450i	0.762838	+	0.345557i
$846$	−3.40646	+	8.73700i	−0.117117	+	0.300384i
$847$	37.1840	+	13.9349i	1.27766	+	0.478808i
$848$	8.21797	−	4.74465i	0.282206	−	0.162932i
$849$	−23.3932	−	4.39912i	−0.802853	−	0.150977i
$850$	2.21174	−	3.83084i	0.0758619	−	0.131397i
$851$	−19.3513	−	33.5174i	−0.663353	−	1.14896i
$852$	−4.66021	+	24.7816i	−0.159656	+	0.849005i
$853$	4.19858			0.143757			0.0718783	−	0.997413i	$-0.477101\pi$
$853$	4.19858			0.143757			0.0718783	+	0.997413i	$0.477101\pi$
$854$	−9.92381	−	12.0573i	−0.339586	−	0.412592i
$855$	14.4468	−	2.21060i	0.494072	−	0.0756011i
$856$	5.32321	+	3.07336i	0.181944	+	0.105045i
$857$	−4.09187	+	7.08733i	−0.139776	+	0.242099i	−0.927412	−	0.374042i	$-0.877972\pi$
$857$	−4.09187	+	7.08733i	−0.139776	+	0.242099i	0.787636	+	0.616141i	$0.211305\pi$
$858$	−12.0156	−	29.4952i	−0.410207	−	1.00695i
$859$	−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
$861$	0.535267	−	25.6847i	0.0182418	−	0.875331i
$862$	−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	$0.823581\pi$
$864$	−5.19314	−	0.176850i	−0.176674	−	0.00601657i
$865$	31.2251	−	18.0278i	1.06169	−	0.612964i
$866$	23.9459	−	13.8252i	0.813715	−	0.469799i
$867$	−10.8096	−	9.28140i	−0.367114	−	0.315213i
$868$	20.3054	+	7.60954i	0.689210	+	0.258285i
$869$	−26.2455	−	45.4585i	−0.890317	−	1.54207i
$870$	25.8008	−	9.06051i	0.874728	−	0.307180i
$871$	18.1950	−	35.4264i	0.616513	−	1.20038i
$872$	−10.8967	−	6.29124i	−0.369010	−	0.213048i
$873$	27.3398	−	21.9031i	0.925313	−	0.741308i
$874$	13.6746	−	7.89503i	0.462550	−	0.267054i
$875$	−11.2895	+	30.1250i	−0.381655	+	1.01841i
$876$	1.27900	−	6.80132i	0.0432132	−	0.229795i
$877$		−	40.0226i		−	1.35147i	−0.737146	−	0.675733i	$-0.763827\pi$
$877$		−	40.0226i		−	1.35147i	0.737146	−	0.675733i	$-0.236173\pi$
$878$	−3.78672	+	2.18627i	−0.127796	+	0.0737829i
$879$	−5.77327	+	6.72387i	−0.194728	+	0.226791i
$880$			9.55006i			0.321932i
$881$	1.57402	+	2.72629i	0.0530302	+	0.0918510i	0.891322	−	0.453371i	$-0.149779\pi$
$881$	1.57402	+	2.72629i	0.0530302	+	0.0918510i	−0.838292	+	0.545222i	$0.816445\pi$
$882$	−20.9818	−	0.874897i	−0.706493	−	0.0294593i
$883$	−5.79510			−0.195021			−0.0975103	−	0.995235i	$-0.531088\pi$
$883$	−5.79510			−0.195021			−0.0975103	+	0.995235i	$0.531088\pi$
$884$	−8.97581	+	5.78784i	−0.301889	+	0.194666i
$885$	5.42074	+	4.65437i	0.182216	+	0.156455i
$886$		−	2.66818i		−	0.0896393i
$887$	−24.4055	+	42.2716i	−0.819458	+	1.41934i	0.0866241	+	0.996241i	$0.472392\pi$
$887$	−24.4055	+	42.2716i	−0.819458	+	1.41934i	−0.906082	+	0.423102i	$0.860941\pi$
$888$	−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
$891$	33.7857	+	31.0682i	1.13186	+	1.04082i
$892$	3.33759	−	5.78088i	0.111751	−	0.193558i
$893$	−7.04257	+	4.06603i	−0.235671	+	0.136065i
$894$	5.20156	+	4.46618i	0.173966	+	0.149371i
$895$	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
$899$		−	69.0998i		−	2.30461i
$900$	−4.17400	−	1.62740i	−0.139133	−	0.0542466i
$901$			28.1085i			0.936429i
$902$		−	28.5903i		−	0.951951i
$903$	21.5393	+	39.1699i	0.716782	+	1.30349i
$904$	1.92741	+	1.11279i	0.0641049	+	0.0370110i
$905$	10.5924	+	18.3467i	0.352105	+	0.609864i
$906$	3.19567	+	9.10000i	0.106169	+	0.302327i
$907$	−23.9518			−0.795307			−0.397653	−	0.917536i	$-0.630175\pi$
$907$	−23.9518			−0.795307			−0.397653	+	0.917536i	$0.630175\pi$
$908$	−16.0059	−	9.24099i	−0.531173	−	0.306673i
$909$	−17.6104	−	6.86609i	−0.584099	−	0.227734i
$910$	13.2184	−	12.0157i	0.438187	−	0.398318i
$911$			51.9614i			1.72156i	0.508979	+	0.860779i	$0.330023\pi$
$911$			51.9614i			1.72156i	−0.508979	+	0.860779i	$0.669977\pi$
$912$	−3.41871	−	2.93538i	−0.113205	−	0.0972003i
$913$			49.1326i			1.62605i
$914$	6.00766	−	3.46853i	0.198716	−	0.114729i
$915$	−18.0624	+	6.34302i	−0.597126	+	0.209694i
$916$	0.100542	−	0.174145i	0.00332201	−	0.00575390i
$917$	−0.404726	−	2.42994i	−0.0133652	−	0.0802435i
$918$	8.14504	−	13.0599i	0.268826	−	0.431041i
$919$	−37.7303			−1.24461			−0.622303	−	0.782776i	$-0.713803\pi$
$919$	−37.7303			−1.24461			−0.622303	+	0.782776i	$0.713803\pi$
$920$	11.3658			0.374719
$921$	−0.360918	+	1.91926i	−0.0118926	+	0.0632417i
$922$	17.6491	−	10.1897i	0.581242	−	0.335580i
$923$	44.1150	−	28.4465i	1.45206	−	0.936328i
$924$	−23.3655	−	0.486935i	−0.768668	−	0.0160190i
$925$	−8.24664	+	4.76120i	−0.271148	+	0.156547i
$926$	19.4201	+	11.2122i	0.638184	+	0.368456i
$927$	−17.0932	+	2.61554i	−0.561415	+	0.0859058i
$928$	−7.30144	−	4.21549i	−0.239681	−	0.138380i
$929$		−	24.2142i		−	0.794441i	−0.917723	−	0.397220i	$-0.869975\pi$
$929$		−	24.2142i		−	0.794441i	0.917723	−	0.397220i	$-0.130025\pi$
$930$	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
$933$	14.7113	+	12.6315i	0.481626	+	0.413535i
$934$	−19.6687			−0.643580
$935$	−24.4985	−	14.1442i	−0.801187	−	0.462566i
$936$	7.16941	+	8.09936i	0.234340	+	0.264736i
$937$			25.9178i			0.846698i	0.905967	+	0.423349i	$0.139146\pi$
$937$			25.9178i			0.846698i	−0.905967	+	0.423349i	$0.860854\pi$
$938$	−18.5716	−	22.5642i	−0.606383	−	0.736746i
$939$	−18.6584	−	53.1319i	−0.608895	−	1.73389i
$940$	−5.85351			−0.190920
$941$	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	$0.241049\pi$
$942$	−4.18211	−	11.9090i	−0.136260	−	0.388016i
$943$	−34.0261			−1.10804
$944$		−	2.20283i		−	0.0716960i
$945$	−9.84941	+	23.7854i	−0.320401	+	0.773740i
$946$	24.8738	+	43.0826i	0.808716	+	1.40074i
$947$	10.9482	−	18.9628i	0.355769	−	0.616210i	−0.631480	−	0.775392i	$-0.717552\pi$
$947$	10.9482	−	18.9628i	0.355769	−	0.616210i	0.987249	+	0.159182i	$0.0508857\pi$
$948$	13.5256	+	11.6134i	0.439291	+	0.377185i
$949$	−12.1074	+	7.80715i	−0.393022	+	0.253431i
$950$	−1.94250	−	3.36451i	−0.0630230	−	0.109159i
$951$	41.5616	−	14.5953i	1.34773	−	0.473284i
$952$	1.28759	+	7.73055i	0.0417309	+	0.250549i
$953$	5.23975	+	3.02517i	0.169732	+	0.0979949i	0.582459	−	0.812860i	$-0.302090\pi$
$953$	5.23975	+	3.02517i	0.169732	+	0.0979949i	−0.412727	+	0.910855i	$0.635424\pi$
$954$	28.1404	−	4.30594i	0.911078	−	0.139410i
$955$	−2.97168	−	5.14710i	−0.0961612	−	0.166556i
$956$	15.1398	+	26.2229i	0.489655	+	0.848108i
$957$	24.6755	+	70.2661i	0.797645	+	2.27138i
$958$	16.4723	+	9.51026i	0.532195	+	0.307263i
$959$	0.937672	+	5.62969i	0.0302790	+	0.181792i
$960$	−1.07467	−	3.06024i	−0.0346848	−	0.0987687i
$961$	−18.0867	−	31.3271i	−0.583443	−	1.01055i
$962$	22.9633	−	1.12911i	0.740365	−	0.0364041i
$963$	11.5295	+	14.3913i	0.371533	+	0.463753i
$964$	4.17255	−	7.22708i	0.134389	−	0.232768i
$965$	−0.195983	−	0.339453i	−0.00630892	−	0.0109274i
$966$	−0.579515	+	27.8079i	−0.0186456	+	0.894705i
$967$			17.1921i			0.552862i	0.961034	+	0.276431i	$0.0891518\pi$
$967$			17.1921i			0.552862i	−0.961034	+	0.276431i	$0.910848\pi$
$968$	−15.0087			−0.482398
$969$	12.5934	−	4.42245i	0.404558	−	0.142070i
$970$	18.9372	+	10.9334i	0.608037	+	0.351050i
$971$	−41.3879			−1.32820			−0.664100	−	0.747644i	$-0.731185\pi$
$971$	−41.3879			−1.32820			−0.664100	+	0.747644i	$0.731185\pi$
$972$	−14.3225	−	6.15363i	−0.459393	−	0.197378i
$973$	−13.9590	−	16.9599i	−0.447504	−	0.543711i
$974$		−	22.4738i		−	0.720107i
$975$	3.51842	+	8.63677i	0.112680	+	0.276598i
$976$	5.11154	+	2.95115i	0.163616	+	0.0944640i
$977$	39.9425			1.27787			0.638937	−	0.769259i	$-0.279374\pi$
$977$	39.9425			1.27787			0.638937	+	0.769259i	$0.279374\pi$
$978$	−22.3511	+	26.0313i	−0.714710	+	0.832391i
$979$	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
$982$			29.6928i			0.947537i
$983$	−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	$0.689906\pi$
$984$	3.21727	+	9.16151i	0.102563	+	0.292058i
$985$	−31.5263	−	18.2017i	−1.00451	−	0.579954i
$986$	21.6278	−	12.4868i	0.688768	−	0.397661i
$987$	0.298457	−	14.3214i	0.00949998	−	0.455855i
$988$	0.460662	+	9.36868i	0.0146556	+	0.298057i
$989$	51.2738	−	29.6030i	1.63041	−	0.941319i
$990$	−10.4073	+	26.6931i	−0.330767	+	0.848361i
$991$	−18.0537			−0.573493			−0.286747	−	0.958006i	$-0.592574\pi$
$991$	−18.0537			−0.573493			−0.286747	+	0.958006i	$0.592574\pi$
$992$	−8.19594			−0.260221
$993$	−12.2323	−	2.30030i	−0.388181	−	0.0729978i
$994$	−6.32832	−	37.9947i	−0.200722	−	1.20512i
$995$	−13.5333	+	23.4403i	−0.429033	+	0.743107i
$996$	−5.52891	−	15.7441i	−0.175190	−	0.498872i
$997$	−36.7143	+	21.1970i	−1.16275	+	0.671316i	−0.951962	−	0.306215i	$-0.900937\pi$
$997$	−36.7143	+	21.1970i	−1.16275	+	0.671316i	−0.210791	+	0.977531i	$0.567604\pi$
$998$			7.51106i			0.237758i
$999$	−29.2417	+	15.5806i	−0.925168	+	0.492948i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.4	✓	34	39.17	odd	6
546.2.bi.e.257.4	yes	34	7.5	odd	6
546.2.bi.f.17.3	yes	34	13.4	even	6
546.2.bi.f.257.3	yes	34	21.5	even	6
546.2.bn.e.101.8	yes	34	3.2	odd	2
546.2.bn.e.173.8	yes	34	91.82	odd	6
546.2.bn.f.101.10	yes	34	1.1	even	1	trivial
546.2.bn.f.173.10	yes	34	273.173	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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.320103 - 1.70221i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.62172 - 0.936303i) q^{5} +(-1.31411 - 1.12832i) q^{6} +(2.47749 + 0.928453i) q^{7} -1.00000 q^{8} +(-2.79507 - 1.08977i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.320103 - 1.70221i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.62172 - 0.936303i) q^{5} +(-1.31411 - 1.12832i) q^{6} +(2.47749 + 0.928453i) q^{7} -1.00000 q^{8} +(-2.79507 - 1.08977i) q^{9} -1.87261i q^{10} +5.09987 q^{11} +(-1.63421 + 0.573890i) q^{12} +(3.20727 + 1.64725i) q^{13} +(2.04281 - 1.68135i) q^{14} +(-1.07467 - 3.06024i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.48106 - 2.56527i) q^{17} +(-2.34130 + 1.87572i) q^{18} -2.60154 q^{19} +(-1.62172 - 0.936303i) q^{20} +(2.37348 - 3.92003i) q^{21} +(2.54994 - 4.41662i) q^{22} +(-5.25634 - 3.03475i) q^{23} +(-0.320103 + 1.70221i) q^{24} +(-0.746672 + 1.29327i) q^{25} +(3.03019 - 1.95395i) q^{26} +(-2.74973 + 4.40897i) q^{27} +(-0.434683 - 2.60980i) q^{28} +(-7.30144 + 4.21549i) q^{29} +(-3.18758 - 0.599427i) q^{30} +(-4.09797 + 7.09789i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.63248 - 8.68108i) q^{33} -2.96212 q^{34} +(4.88713 - 0.813991i) q^{35} +(0.453768 + 2.96548i) q^{36} +(5.52226 + 3.18828i) q^{37} +(-1.30077 + 2.25300i) q^{38} +(3.83063 - 4.93217i) q^{39} +(-1.62172 + 0.936303i) q^{40} +(4.85500 - 2.80304i) q^{41} +(-2.20810 - 4.01551i) q^{42} +(-4.87733 + 8.44778i) q^{43} +(-2.54994 - 4.41662i) q^{44} +(-5.55318 + 0.849728i) q^{45} +(-5.25634 + 3.03475i) q^{46} +(2.70708 - 1.56293i) q^{47} +(1.31411 + 1.12832i) q^{48} +(5.27595 + 4.60047i) q^{49} +(0.746672 + 1.29327i) q^{50} +(-4.84074 + 1.69993i) q^{51} +(-0.177072 - 3.60120i) q^{52} +(-8.21797 - 4.74465i) q^{53} +(2.44341 + 4.58582i) q^{54} +(8.27059 - 4.77503i) q^{55} +(-2.47749 - 0.928453i) q^{56} +(-0.832761 + 4.42838i) q^{57} +8.43097i q^{58} +(-1.90771 + 1.10141i) q^{59} +(-2.11291 + 2.46081i) q^{60} -5.90230i q^{61} +(4.09797 + 7.09789i) q^{62} +(-5.91297 - 5.29498i) q^{63} +1.00000 q^{64} +(6.74363 - 0.331587i) q^{65} +(-6.70179 - 5.75431i) q^{66} -11.0457i q^{67} +(-1.48106 + 2.56527i) q^{68} +(-6.84837 + 7.97599i) q^{69} +(1.73863 - 4.63937i) q^{70} +(7.27923 - 12.6080i) q^{71} +(2.79507 + 1.08977i) q^{72} +(-1.99779 + 3.46027i) q^{73} +(5.52226 - 3.18828i) q^{74} +(1.96242 + 1.68498i) 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} +1.87261i q^{80} +(6.62481 + 6.09195i) q^{81} -5.60607i q^{82} +9.63409i q^{83} +(-4.58158 - 0.0954798i) q^{84} +(-4.80375 - 2.77345i) q^{85} +(4.87733 + 8.44778i) q^{86} +(4.83845 + 13.7780i) q^{87} -5.09987 q^{88} +(12.7850 + 7.38141i) q^{89} +(-2.04071 + 5.23406i) q^{90} +(6.41659 + 7.05885i) q^{91} +6.06950i q^{92} +(10.7704 + 9.24768i) q^{93} -3.12586i q^{94} +(-4.21899 + 2.43583i) q^{95} +(1.63421 - 0.573890i) q^{96} +(-5.83860 + 10.1127i) q^{97} +(6.62210 - 2.26887i) q^{98} +(-14.2545 - 5.55768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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