LMFDB - Embedded newform 546.2.bx.a.223.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.3
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.a.475.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.781970 - 0.781970i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.20520 + 2.35531i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.781970 - 0.781970i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.20520 + 2.35531i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.552937 + 0.957714i) q^{10} +(0.312928 - 1.16786i) q^{11} +1.00000 q^{12} +(2.62553 - 2.47115i) q^{13} +(1.77373 - 1.96313i) q^{14} +(-1.06819 - 0.286221i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.19466 - 2.06921i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(4.87770 - 1.30697i) q^{19} +(-0.286221 - 1.06819i) q^{20} +(0.133920 + 2.64236i) q^{21} +(-0.604530 + 1.04708i) q^{22} +(5.04730 - 2.91406i) q^{23} +(-0.965926 - 0.258819i) q^{24} -3.77704i q^{25} +(-3.17565 + 1.70741i) q^{26} -1.00000i q^{27} +(-2.22139 + 1.43716i) q^{28} +(-4.18735 - 7.25271i) q^{29} +(0.957714 + 0.552937i) q^{30} +(6.07089 + 6.07089i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.312928 - 1.16786i) q^{33} +(-1.68950 + 1.68950i) q^{34} +(2.78422 - 0.899351i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.63773 + 9.84416i) q^{37} -5.04976 q^{38} +(1.03820 - 3.45284i) q^{39} +1.10587i q^{40} +(0.0706665 - 0.263731i) q^{41} +(0.554536 - 2.58698i) q^{42} +(-9.39867 - 5.42633i) q^{43} +(0.854934 - 0.854934i) q^{44} +(-1.06819 + 0.286221i) q^{45} +(-5.62953 + 1.50843i) q^{46} +(4.79531 - 4.79531i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-4.09498 - 5.67725i) q^{49} +(-0.977571 + 3.64834i) q^{50} -2.38932i q^{51} +(3.50935 - 0.827311i) q^{52} +3.52584 q^{53} +(-0.258819 + 0.965926i) q^{54} +(-1.15793 + 0.668533i) q^{55} +(2.51766 - 0.813250i) q^{56} +(3.57072 - 3.57072i) q^{57} +(2.16753 + 8.08934i) q^{58} +(2.46090 + 9.18419i) q^{59} +(-0.781970 - 0.781970i) q^{60} +(9.83139 + 5.67615i) q^{61} +(-4.29276 - 7.43529i) q^{62} +(1.43716 + 2.22139i) q^{63} +1.00000i q^{64} +(-3.98545 - 0.120724i) q^{65} +1.20906i q^{66} +(-5.76691 - 1.54524i) q^{67} +(2.06921 - 1.19466i) q^{68} +(2.91406 - 5.04730i) q^{69} +(-2.92211 + 0.148099i) q^{70} +(-2.24186 - 8.36673i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(4.16937 - 4.16937i) q^{73} +(5.09571 - 8.82603i) q^{74} +(-1.88852 - 3.27102i) q^{75} +(4.87770 + 1.30697i) q^{76} +(2.37354 + 2.14455i) q^{77} +(-1.89649 + 3.06648i) q^{78} +7.38288 q^{79} +(0.286221 - 1.06819i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.136517 + 0.236455i) q^{82} +(-2.18308 - 2.18308i) q^{83} +(-1.20520 + 2.35531i) q^{84} +(-2.55225 + 0.683873i) q^{85} +(7.67399 + 7.67399i) q^{86} +(-7.25271 - 4.18735i) q^{87} +(-1.04708 + 0.604530i) q^{88} +(-15.1646 - 4.06333i) q^{89} +1.10587 q^{90} +(2.65603 + 9.16218i) q^{91} +5.82812 q^{92} +(8.29298 + 2.22210i) q^{93} +(-5.87303 + 3.39079i) q^{94} +(-4.83623 - 2.79220i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.77794 + 0.476399i) q^{97} +(2.48606 + 6.54366i) q^{98} +(-0.854934 - 0.854934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 + 20 * q^9	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.781970	−	0.781970i	−0.349708	−	0.349708i	0.510293	−	0.860001i	$-0.329537\pi$
$5$	−0.781970	−	0.781970i	−0.349708	−	0.349708i	−0.860001	+	0.510293i	$0.829537\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	−1.20520	+	2.35531i	−0.455523	+	0.890224i
$7$	−1.20520	+	2.35531i	−0.455523	+	0.890224i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.552937	+	0.957714i	0.174854	+	0.302856i
$11$	0.312928	−	1.16786i	0.0943512	−	0.352124i	−0.902569	−	0.430545i	$-0.858321\pi$
$11$	0.312928	−	1.16786i	0.0943512	−	0.352124i	0.996920	+	0.0784215i	$0.0249880\pi$
$12$	1.00000			0.288675
$13$	2.62553	−	2.47115i	0.728192	−	0.685373i
$13$	2.62553	−	2.47115i	0.728192	−	0.685373i
$14$	1.77373	−	1.96313i	0.474051	−	0.524668i
$15$	−1.06819	−	0.286221i	−0.275806	−	0.0739020i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.19466	−	2.06921i	0.289747	−	0.501857i	−0.684002	−	0.729480i	$-0.739762\pi$
$17$	1.19466	−	2.06921i	0.289747	−	0.501857i	0.973749	+	0.227623i	$0.0730954\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	4.87770	−	1.30697i	1.11902	−	0.299841i	0.348533	−	0.937296i	$-0.386680\pi$
$19$	4.87770	−	1.30697i	1.11902	−	0.299841i	0.770487	+	0.637456i	$0.220013\pi$
$20$	−0.286221	−	1.06819i	−0.0640010	−	0.238855i
$21$	0.133920	+	2.64236i	0.0292238	+	0.576610i
$22$	−0.604530	+	1.04708i	−0.128886	+	0.223237i
$23$	5.04730	−	2.91406i	1.05243	−	0.607623i	0.129104	−	0.991631i	$-0.458790\pi$
$23$	5.04730	−	2.91406i	1.05243	−	0.607623i	0.923330	+	0.384008i	$0.125456\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$		−	3.77704i		−	0.755409i
$26$	−3.17565	+	1.70741i	−0.622796	+	0.334850i
$27$		−	1.00000i		−	0.192450i
$28$	−2.22139	+	1.43716i	−0.419803	+	0.271597i
$29$	−4.18735	−	7.25271i	−0.777572	−	1.34679i	−0.933338	−	0.359000i	$-0.883118\pi$
$29$	−4.18735	−	7.25271i	−0.777572	−	1.34679i	0.155766	−	0.987794i	$-0.450216\pi$
$30$	0.957714	+	0.552937i	0.174854	+	0.100952i
$31$	6.07089	+	6.07089i	1.09036	+	1.09036i	0.995489	+	0.0948739i	$0.0302448\pi$
$31$	6.07089	+	6.07089i	1.09036	+	1.09036i	0.0948739	+	0.995489i	$0.469755\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.312928	−	1.16786i	−0.0544737	−	0.203299i
$34$	−1.68950	+	1.68950i	−0.289747	+	0.289747i
$35$	2.78422	−	0.899351i	0.470618	−	0.152018i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−2.63773	+	9.84416i	−0.433641	+	1.61837i	0.310657	+	0.950522i	$0.399451\pi$
$37$	−2.63773	+	9.84416i	−0.433641	+	1.61837i	−0.744298	+	0.667847i	$0.767216\pi$
$38$	−5.04976			−0.819180
$39$	1.03820	−	3.45284i	0.166246	−	0.552898i
$40$			1.10587i			0.174854i
$41$	0.0706665	−	0.263731i	0.0110363	−	0.0411879i	−0.960188	−	0.279354i	$-0.909880\pi$
$41$	0.0706665	−	0.263731i	0.0110363	−	0.0411879i	0.971224	+	0.238166i	$0.0765463\pi$
$42$	0.554536	−	2.58698i	0.0855668	−	0.399180i
$43$	−9.39867	−	5.42633i	−1.43328	−	0.827507i	−0.435915	−	0.899988i	$-0.643575\pi$
$43$	−9.39867	−	5.42633i	−1.43328	−	0.827507i	−0.997370	+	0.0724809i	$0.976908\pi$
$44$	0.854934	−	0.854934i	0.128886	−	0.128886i
$45$	−1.06819	+	0.286221i	−0.159237	+	0.0426673i
$46$	−5.62953	+	1.50843i	−0.830029	+	0.222405i
$47$	4.79531	−	4.79531i	0.699467	−	0.699467i	−0.264828	−	0.964296i	$-0.585315\pi$
$47$	4.79531	−	4.79531i	0.699467	−	0.699467i	0.964296	+	0.264828i	$0.0853153\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−4.09498	−	5.67725i	−0.584997	−	0.811036i
$50$	−0.977571	+	3.64834i	−0.138249	+	0.515954i
$51$		−	2.38932i		−	0.334571i
$52$	3.50935	−	0.827311i	0.486660	−	0.114727i
$53$	3.52584			0.484311			0.242156	−	0.970237i	$-0.422146\pi$
$53$	3.52584			0.484311			0.242156	+	0.970237i	$0.422146\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	−1.15793	+	0.668533i	−0.156136	+	0.0901450i
$56$	2.51766	−	0.813250i	0.336437	−	0.108675i
$57$	3.57072	−	3.57072i	0.472954	−	0.472954i
$58$	2.16753	+	8.08934i	0.284611	+	1.06218i
$59$	2.46090	+	9.18419i	0.320381	+	1.19568i	0.918874	+	0.394551i	$0.129100\pi$
$59$	2.46090	+	9.18419i	0.320381	+	1.19568i	−0.598492	+	0.801129i	$0.704233\pi$
$60$	−0.781970	−	0.781970i	−0.100952	−	0.100952i
$61$	9.83139	+	5.67615i	1.25878	+	0.726757i	0.972837	−	0.231490i	$-0.0743599\pi$
$61$	9.83139	+	5.67615i	1.25878	+	0.726757i	0.285943	+	0.958247i	$0.407693\pi$
$62$	−4.29276	−	7.43529i	−0.545182	−	0.944282i
$63$	1.43716	+	2.22139i	0.181065	+	0.279869i
$64$			1.00000i			0.125000i
$65$	−3.98545	−	0.120724i	−0.494335	−	0.0149740i
$66$			1.20906i			0.148825i
$67$	−5.76691	−	1.54524i	−0.704540	−	0.188781i	−0.111277	−	0.993789i	$-0.535494\pi$
$67$	−5.76691	−	1.54524i	−0.704540	−	0.188781i	−0.593263	+	0.805009i	$0.702161\pi$
$68$	2.06921	−	1.19466i	0.250929	−	0.144874i
$69$	2.91406	−	5.04730i	0.350811	−	0.607623i
$70$	−2.92211	+	0.148099i	−0.349260	+	0.0177012i
$71$	−2.24186	−	8.36673i	−0.266060	−	0.992948i	−0.961599	−	0.274459i	$-0.911501\pi$
$71$	−2.24186	−	8.36673i	−0.266060	−	0.992948i	0.695539	−	0.718488i	$-0.255166\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	4.16937	−	4.16937i	0.487988	−	0.487988i	−0.419683	−	0.907671i	$-0.637859\pi$
$73$	4.16937	−	4.16937i	0.487988	−	0.487988i	0.907671	+	0.419683i	$0.137859\pi$
$74$	5.09571	−	8.82603i	0.592364	−	1.02601i
$75$	−1.88852	−	3.27102i	−0.218068	−	0.377704i
$76$	4.87770	+	1.30697i	0.559510	+	0.149920i
$77$	2.37354	+	2.14455i	0.270490	+	0.244394i
$78$	−1.89649	+	3.06648i	−0.214735	+	0.347211i
$79$	7.38288			0.830639			0.415319	−	0.909676i	$-0.363670\pi$
$79$	7.38288			0.830639			0.415319	+	0.909676i	$0.363670\pi$
$80$	0.286221	−	1.06819i	0.0320005	−	0.119427i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.136517	+	0.236455i	−0.0150758	+	0.0261121i
$83$	−2.18308	−	2.18308i	−0.239624	−	0.239624i	0.577070	−	0.816695i	$-0.304196\pi$
$83$	−2.18308	−	2.18308i	−0.239624	−	0.239624i	−0.816695	+	0.577070i	$0.804196\pi$
$84$	−1.20520	+	2.35531i	−0.131498	+	0.256985i
$85$	−2.55225	+	0.683873i	−0.276830	+	0.0741765i
$86$	7.67399	+	7.67399i	0.827507	+	0.827507i
$87$	−7.25271	−	4.18735i	−0.777572	−	0.448931i
$88$	−1.04708	+	0.604530i	−0.111619	+	0.0644431i
$89$	−15.1646	−	4.06333i	−1.60744	−	0.430712i	−0.660161	−	0.751124i	$-0.729512\pi$
$89$	−15.1646	−	4.06333i	−1.60744	−	0.430712i	−0.947278	+	0.320412i	$0.896179\pi$
$90$	1.10587			0.116569
$91$	2.65603	+	9.16218i	0.278427	+	0.960457i
$92$	5.82812			0.607623
$93$	8.29298	+	2.22210i	0.859942	+	0.230421i
$94$	−5.87303	+	3.39079i	−0.605756	+	0.349734i
$95$	−4.83623	−	2.79220i	−0.496187	−	0.286474i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−1.77794	+	0.476399i	−0.180523	+	0.0483710i	−0.347948	−	0.937514i	$-0.613121\pi$
$97$	−1.77794	+	0.476399i	−0.180523	+	0.0483710i	0.167425	+	0.985885i	$0.446455\pi$
$98$	2.48606	+	6.54366i	0.251130	+	0.661009i
$99$	−0.854934	−	0.854934i	−0.0859241	−	0.0859241i
$100$	1.88852	−	3.27102i	0.188852	−	0.327102i
$101$	3.65414	+	6.32916i	0.363601	+	0.629775i	0.988551	−	0.150890i	$-0.0482140\pi$
$101$	3.65414	+	6.32916i	0.363601	+	0.629775i	−0.624950	+	0.780665i	$0.714881\pi$
$102$	−0.618401	+	2.30790i	−0.0612308	+	0.228517i
$103$	−8.98605			−0.885422			−0.442711	−	0.896664i	$-0.645983\pi$
$103$	−8.98605			−0.885422			−0.442711	+	0.896664i	$0.645983\pi$
$104$	−3.60390	−	0.109166i	−0.353391	−	0.0107046i
$105$	1.96153	−	2.17097i	0.191425	−	0.211865i
$106$	−3.40570	−	0.912554i	−0.330791	−	0.0886351i
$107$	6.95581	+	12.0478i	0.672444	+	1.16471i	0.977209	+	0.212280i	$0.0680887\pi$
$107$	6.95581	+	12.0478i	0.672444	+	1.16471i	−0.304765	+	0.952428i	$0.598578\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−3.22554	+	3.22554i	−0.308951	+	0.308951i	−0.844502	−	0.535552i	$-0.820104\pi$
$109$	−3.22554	+	3.22554i	−0.308951	+	0.308951i	0.535552	+	0.844502i	$0.320104\pi$
$110$	1.29151	−	0.346058i	0.123140	−	0.0329954i
$111$	2.63773	+	9.84416i	0.250363	+	0.934366i
$112$	−2.64236	+	0.133920i	−0.249680	+	0.0126543i
$113$	−10.0372	+	17.3849i	−0.944217	+	1.63543i	−0.186906	+	0.982378i	$0.559846\pi$
$113$	−10.0372	+	17.3849i	−0.944217	+	1.63543i	−0.757311	+	0.653054i	$0.773487\pi$
$114$	−4.37322	+	2.52488i	−0.409590	+	0.236477i
$115$	−6.22554	−	1.66813i	−0.580535	−	0.155554i
$116$		−	8.37471i		−	0.777572i
$117$	−0.827311	−	3.50935i	−0.0764849	−	0.324440i
$118$		−	9.50818i		−	0.875298i
$119$	3.43383	+	5.30761i	0.314778	+	0.486548i
$120$	0.552937	+	0.957714i	0.0504760	+	0.0874270i
$121$	8.26030	+	4.76909i	0.750937	+	0.433553i
$122$	−8.02729	−	8.02729i	−0.726757	−	0.726757i
$123$	−0.0706665	−	0.263731i	−0.00637179	−	0.0237798i
$124$	2.22210	+	8.29298i	0.199550	+	0.744732i
$125$	−6.86339	+	6.86339i	−0.613880	+	0.613880i
$126$	−0.813250	−	2.51766i	−0.0724501	−	0.224291i
$127$	9.65396	−	5.57371i	0.856650	−	0.494587i	−0.00623902	−	0.999981i	$-0.501986\pi$
$127$	9.65396	−	5.57371i	0.856650	−	0.494587i	0.862889	+	0.505393i	$0.168653\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−10.8527			−0.955523
$130$	3.81841	+	1.14812i	0.334897	+	0.100697i
$131$		−	3.86156i		−	0.337386i	−0.985669	−	0.168693i	$-0.946045\pi$
$131$		−	3.86156i		−	0.337386i	0.985669	−	0.168693i	$-0.0539546\pi$
$132$	0.312928	−	1.16786i	0.0272369	−	0.101649i
$133$	−2.80028	+	13.0637i	−0.242815	+	1.13276i
$134$	5.17047	+	2.98517i	0.446660	+	0.257879i
$135$	−0.781970	+	0.781970i	−0.0673013	+	0.0673013i
$136$	−2.30790	+	0.618401i	−0.197901	+	0.0530275i
$137$	−10.7828	+	2.88925i	−0.921240	+	0.246846i	−0.688115	−	0.725601i	$-0.741562\pi$
$137$	−10.7828	+	2.88925i	−0.921240	+	0.246846i	−0.233125	+	0.972447i	$0.574895\pi$
$138$	−4.12110	+	4.12110i	−0.350811	+	0.350811i
$139$	9.33502	+	5.38958i	0.791786	+	0.457138i	0.840591	−	0.541670i	$-0.182208\pi$
$139$	9.33502	+	5.38958i	0.791786	+	0.457138i	−0.0488046	+	0.998808i	$0.515541\pi$
$140$	2.86088	+	0.613247i	0.241788	+	0.0518288i
$141$	1.75520	−	6.55051i	0.147815	−	0.551652i
$142$			8.66187i			0.726888i
$143$	−2.06436	−	3.83955i	−0.172630	−	0.321079i
$144$	1.00000			0.0833333
$145$	−2.39702	+	8.94579i	−0.199061	+	0.742907i
$146$	−5.10642	+	2.94819i	−0.422610	+	0.243994i
$147$	−6.38498	−	2.86915i	−0.526624	−	0.236644i
$148$	−7.20642	+	7.20642i	−0.592364	+	0.592364i
$149$	5.97456	+	22.2974i	0.489455	+	1.82667i	0.559101	+	0.829100i	$0.311147\pi$
$149$	5.97456	+	22.2974i	0.489455	+	1.82667i	−0.0696456	+	0.997572i	$0.522187\pi$
$150$	0.977571	+	3.64834i	0.0798183	+	0.297886i
$151$	2.31792	+	2.31792i	0.188629	+	0.188629i	0.795103	−	0.606474i	$-0.207417\pi$
$151$	2.31792	+	2.31792i	0.188629	+	0.188629i	−0.606474	+	0.795103i	$0.707417\pi$
$152$	−4.37322	−	2.52488i	−0.354715	−	0.204795i
$153$	−1.19466	−	2.06921i	−0.0965825	−	0.167286i
$154$	−1.73761	−	2.68579i	−0.140021	−	0.216427i
$155$		−	9.49451i		−	0.762617i
$156$	2.62553	−	2.47115i	0.210211	−	0.197850i
$157$		−	2.78978i		−	0.222648i	−0.993784	−	0.111324i	$-0.964491\pi$
$157$		−	2.78978i		−	0.222648i	0.993784	−	0.111324i	$-0.0355092\pi$
$158$	−7.13131	−	1.91083i	−0.567337	−	0.152017i
$159$	3.05347	−	1.76292i	0.242156	−	0.139809i
$160$	−0.552937	+	0.957714i	−0.0437135	+	0.0757140i
$161$	0.780502	+	15.4000i	0.0615122	+	1.21369i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	−10.9557	+	2.93557i	−0.858116	+	0.229931i	−0.660942	−	0.750437i	$-0.729843\pi$
$163$	−10.9557	+	2.93557i	−0.858116	+	0.229931i	−0.197174	+	0.980369i	$0.563176\pi$
$164$	0.193065	−	0.193065i	0.0150758	−	0.0150758i
$165$	−0.668533	+	1.15793i	−0.0520452	+	0.0901450i
$166$	1.54367	+	2.67372i	0.119812	+	0.207521i
$167$	5.05024	+	1.35321i	0.390799	+	0.104714i	0.448868	−	0.893598i	$-0.351827\pi$
$167$	5.05024	+	1.35321i	0.390799	+	0.104714i	−0.0580684	+	0.998313i	$0.518494\pi$
$168$	1.77373	−	1.96313i	0.136847	−	0.151458i
$169$	0.786849	−	12.9762i	0.0605268	−	0.998167i
$170$	2.64228			0.202654
$171$	1.30697	−	4.87770i	0.0999469	−	0.373007i
$172$	−5.42633	−	9.39867i	−0.413754	−	0.716642i
$173$	−7.54949	+	13.0761i	−0.573977	+	0.994157i	0.422175	+	0.906514i	$0.361267\pi$
$173$	−7.54949	+	13.0761i	−0.573977	+	0.994157i	−0.996152	+	0.0876430i	$0.972067\pi$
$174$	5.92181	+	5.92181i	0.448931	+	0.448931i
$175$	8.89611	+	4.55210i	0.672483	+	0.344106i
$176$	1.16786	−	0.312928i	0.0880309	−	0.0235878i
$177$	6.72330	+	6.72330i	0.505354	+	0.505354i
$178$	13.5962	+	7.84975i	1.01908	+	0.588364i
$179$	1.52673	−	0.881456i	0.114113	−	0.0658831i	−0.441857	−	0.897085i	$-0.645680\pi$
$179$	1.52673	−	0.881456i	0.114113	−	0.0658831i	0.555970	+	0.831202i	$0.312347\pi$
$180$	−1.06819	−	0.286221i	−0.0796183	−	0.0213337i
$181$	−23.7089			−1.76227			−0.881136	−	0.472863i	$-0.843220\pi$
$181$	−23.7089			−1.76227			−0.881136	+	0.472863i	$0.843220\pi$
$182$	−0.194178	−	9.53742i	−0.0143934	−	0.706960i
$183$	11.3523			0.839187
$184$	−5.62953	−	1.50843i	−0.415014	−	0.111203i
$185$	9.76047	−	5.63521i	0.717604	−	0.414309i
$186$	−7.43529	−	4.29276i	−0.545182	−	0.314761i
$187$	−2.04271	−	2.04271i	−0.149378	−	0.149378i
$188$	6.55051	−	1.75520i	0.477745	−	0.128011i
$189$	2.35531	+	1.20520i	0.171324	+	0.0876655i
$190$	3.94877	+	3.94877i	0.286474	+	0.286474i
$191$	−1.51664	+	2.62689i	−0.109740	+	0.190075i	−0.915665	−	0.401943i	$-0.868335\pi$
$191$	−1.51664	+	2.62689i	−0.109740	+	0.190075i	0.805925	+	0.592018i	$0.201668\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	2.86384	−	10.6880i	0.206144	−	0.769338i	−0.782954	−	0.622079i	$-0.786288\pi$
$193$	2.86384	−	10.6880i	0.206144	−	0.769338i	0.989098	−	0.147259i	$-0.0470451\pi$
$194$	1.84066			0.132152
$195$	−3.51187	+	1.88818i	−0.251490	+	0.135215i
$196$	−0.707730	−	6.96413i	−0.0505521	−	0.497438i
$197$	−19.3179	−	5.17622i	−1.37634	−	0.368790i	−0.506552	−	0.862210i	$-0.669080\pi$
$197$	−19.3179	−	5.17622i	−1.37634	−	0.368790i	−0.869792	+	0.493419i	$0.835747\pi$
$198$	0.604530	+	1.04708i	0.0429621	+	0.0744125i
$199$	3.74351	−	6.48394i	0.265370	−	0.459635i	−0.702290	−	0.711891i	$-0.747839\pi$
$199$	3.74351	−	6.48394i	0.265370	−	0.459635i	0.967661	+	0.252256i	$0.0811725\pi$
$200$	−2.67077	+	2.67077i	−0.188852	+	0.188852i
$201$	−5.76691	+	1.54524i	−0.406766	+	0.108993i
$202$	−1.89152	−	7.05926i	−0.133087	−	0.496688i
$203$	22.1290	−	1.12154i	1.55315	−	0.0787168i
$204$	1.19466	−	2.06921i	0.0836429	−	0.144874i
$205$	−0.261489	+	0.150971i	−0.0182632	+	0.0105443i
$206$	8.67986	+	2.32576i	0.604754	+	0.162043i
$207$		−	5.82812i		−	0.405082i
$208$	3.45284	+	1.03820i	0.239412	+	0.0719865i
$209$		−	6.10546i		−	0.422324i
$210$	−2.45658	+	1.58931i	−0.169520	+	0.109673i
$211$	6.85324	+	11.8702i	0.471797	+	0.817176i	0.999479	−	0.0322660i	$-0.0102724\pi$
$211$	6.85324	+	11.8702i	0.471797	+	0.817176i	−0.527683	+	0.849442i	$0.676939\pi$
$212$	3.05347	+	1.76292i	0.209713	+	0.121078i
$213$	−6.12487	−	6.12487i	−0.419669	−	0.419669i
$214$	−3.60059	−	13.4376i	−0.246132	−	0.918576i
$215$	3.10626	+	11.5927i	0.211845	+	0.790616i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−21.6155	+	6.98218i	−1.46735	+	0.473981i
$218$	3.95046	−	2.28080i	0.267559	−	0.154475i
$219$	1.52610	−	5.69547i	0.103124	−	0.384864i
$220$	−1.33707			−0.0901450
$221$	−1.97671	−	8.38496i	−0.132968	−	0.564033i
$222$		−	10.1914i		−	0.684003i
$223$	−0.473727	+	1.76797i	−0.0317231	+	0.118392i	−0.979972	−	0.199136i	$-0.936186\pi$
$223$	−0.473727	+	1.76797i	−0.0317231	+	0.118392i	0.948249	+	0.317529i	$0.102853\pi$
$224$	2.58698	+	0.554536i	0.172850	+	0.0370515i
$225$	−3.27102	−	1.88852i	−0.218068	−	0.125901i
$226$	14.1947	−	14.1947i	0.944217	−	0.944217i
$227$	−7.87073	+	2.10896i	−0.522399	+	0.139976i	−0.510376	−	0.859951i	$-0.670494\pi$
$227$	−7.87073	+	2.10896i	−0.522399	+	0.139976i	−0.0120228	+	0.999928i	$0.503827\pi$
$228$	4.87770	−	1.30697i	0.323033	−	0.0865565i
$229$	15.5142	−	15.5142i	1.02521	−	1.02521i	0.0255355	−	0.999674i	$-0.491871\pi$
$229$	15.5142	−	15.5142i	1.02521	−	1.02521i	0.999674	−	0.0255355i	$-0.00812908\pi$
$230$	5.58167	+	3.22258i	0.368044	+	0.212491i
$231$	3.12782	+	0.670467i	0.205795	+	0.0441135i
$232$	−2.16753	+	8.08934i	−0.142306	+	0.531091i
$233$		−	22.9719i		−	1.50494i	−0.658628	−	0.752469i	$-0.728863\pi$
$233$		−	22.9719i		−	1.50494i	0.658628	−	0.752469i	$-0.271137\pi$
$234$	−0.109166	+	3.60390i	−0.00713643	+	0.235594i
$235$	−7.49958			−0.489218
$236$	−2.46090	+	9.18419i	−0.160191	+	0.597840i
$237$	6.39376	−	3.69144i	0.415319	−	0.239785i
$238$	−1.94311	−	6.01550i	−0.125953	−	0.389927i
$239$	6.51113	−	6.51113i	0.421170	−	0.421170i	−0.464436	−	0.885606i	$-0.653743\pi$
$239$	6.51113	−	6.51113i	0.421170	−	0.421170i	0.885606	+	0.464436i	$0.153743\pi$
$240$	−0.286221	−	1.06819i	−0.0184755	−	0.0689515i
$241$	−2.09265	−	7.80988i	−0.134800	−	0.503079i	−0.999999	−	0.00165034i	$-0.999475\pi$
$241$	−2.09265	−	7.80988i	−0.134800	−	0.503079i	0.865199	−	0.501429i	$-0.167192\pi$
$242$	−6.74451	−	6.74451i	−0.433553	−	0.433553i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.67615	+	9.83139i	0.363379	+	0.629390i
$245$	−1.23729	+	7.64159i	−0.0790475	+	0.488203i
$246$			0.273034i			0.0174080i
$247$	9.57682	−	15.4850i	0.609359	−	0.985288i
$248$		−	8.58553i		−	0.545182i
$249$	−2.98215	−	0.799063i	−0.188986	−	0.0506386i
$250$	8.40590	−	4.85315i	0.531636	−	0.306940i
$251$	0.625511	−	1.08342i	0.0394819	−	0.0683847i	−0.845609	−	0.533802i	$-0.820763\pi$
$251$	0.625511	−	1.08342i	0.0394819	−	0.0683847i	0.885091	+	0.465418i	$0.154096\pi$
$252$	0.133920	+	2.64236i	0.00843617	+	0.166453i
$253$	−1.82378	−	6.80643i	−0.114660	−	0.427917i
$254$	−10.7676	+	2.88517i	−0.675619	+	0.181031i
$255$	−1.86838	+	1.86838i	−0.117002	+	0.117002i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.98041	−	12.0904i	−0.435426	−	0.754180i	0.561904	−	0.827202i	$-0.310069\pi$
$257$	−6.98041	−	12.0904i	−0.435426	−	0.754180i	−0.997330	+	0.0730222i	$0.976736\pi$
$258$	10.4829	+	2.80887i	0.652634	+	0.174873i
$259$	−20.0070	−	18.0769i	−1.24318	−	1.12324i
$260$	−3.39114	−	2.09728i	−0.210310	−	0.130068i
$261$	−8.37471			−0.518381
$262$	−0.999445	+	3.72998i	−0.0617459	+	0.230439i
$263$	4.41208	+	7.64194i	0.272060	+	0.471222i	0.969389	−	0.245529i	$-0.0789616\pi$
$263$	4.41208	+	7.64194i	0.272060	+	0.471222i	−0.697329	+	0.716751i	$0.745628\pi$
$264$	−0.604530	+	1.04708i	−0.0372062	+	0.0644431i
$265$	−2.75710	−	2.75710i	−0.169367	−	0.169367i
$266$	6.08598	−	11.8938i	0.373156	−	0.729253i
$267$	−15.1646	+	4.06333i	−0.928056	+	0.248672i
$268$	−4.22167	−	4.22167i	−0.257879	−	0.257879i
$269$	4.96802	+	2.86829i	0.302906	+	0.174883i	0.643747	−	0.765238i	$-0.277379\pi$
$269$	4.96802	+	2.86829i	0.302906	+	0.174883i	−0.340842	+	0.940121i	$0.610712\pi$
$270$	0.957714	−	0.552937i	0.0582846	−	0.0336507i
$271$	24.3208	+	6.51674i	1.47738	+	0.395864i	0.905456	−	0.424440i	$-0.139529\pi$
$271$	24.3208	+	6.51674i	1.47738	+	0.395864i	0.571928	+	0.820304i	$0.306196\pi$
$272$	2.38932			0.144874
$273$	6.88128	+	6.60667i	0.416474	+	0.399854i
$274$	11.1632			0.674395
$275$	−4.41107	−	1.18194i	−0.265997	−	0.0712738i
$276$	5.04730	−	2.91406i	0.303812	−	0.175406i
$277$	−12.7981	−	7.38897i	−0.768962	−	0.443960i	0.0635422	−	0.997979i	$-0.479760\pi$
$277$	−12.7981	−	7.38897i	−0.768962	−	0.443960i	−0.832504	+	0.554019i	$0.813094\pi$
$278$	−7.62202	−	7.62202i	−0.457138	−	0.457138i
$279$	8.29298	−	2.22210i	0.496488	−	0.133034i
$280$	−2.60468	−	1.33280i	−0.155659	−	0.0796501i
$281$	10.3251	+	10.3251i	0.615941	+	0.615941i	0.944488	−	0.328547i	$-0.106559\pi$
$281$	10.3251	+	10.3251i	0.615941	+	0.615941i	−0.328547	+	0.944488i	$0.606559\pi$
$282$	−3.39079	+	5.87303i	−0.201919	+	0.349734i
$283$	3.04731	+	5.27810i	0.181144	+	0.313750i	0.942270	−	0.334853i	$-0.108687\pi$
$283$	3.04731	+	5.27810i	0.181144	+	0.313750i	−0.761127	+	0.648603i	$0.775353\pi$
$284$	2.24186	−	8.36673i	0.133030	−	0.496474i
$285$	−5.58440			−0.330791
$286$	1.00027	+	4.24302i	0.0591471	+	0.250895i
$287$	0.536001	+	0.484291i	0.0316391	+	0.0285868i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	5.64558	+	9.77843i	0.332093	+	0.575202i
$290$	4.63068	−	8.02058i	0.271923	−	0.470984i
$291$	−1.30155	+	1.30155i	−0.0762980	+	0.0762980i
$292$	5.69547	−	1.52610i	0.333302	−	0.0893081i
$293$	8.55998	+	31.9463i	0.500079	+	1.86632i	0.499487	+	0.866321i	$0.333522\pi$
$293$	8.55998	+	31.9463i	0.500079	+	1.86632i	0.000592145		1.00000i	$0.499812\pi$
$294$	5.42482	+	4.42394i	0.316382	+	0.258010i
$295$	5.25742	−	9.10612i	0.306099	−	0.530179i
$296$	8.82603	−	5.09571i	0.513003	−	0.296182i
$297$	−1.16786	−	0.312928i	−0.0677662	−	0.0181579i
$298$		−	23.0839i		−	1.33722i
$299$	6.05077	−	20.1236i	0.349925	−	1.16378i
$300$		−	3.77704i		−	0.218068i
$301$	24.1080	−	15.5970i	1.38956	−	0.898995i
$302$	−1.63902	−	2.83886i	−0.0943147	−	0.163358i
$303$	6.32916	+	3.65414i	0.363601	+	0.209925i
$304$	3.57072	+	3.57072i	0.204795	+	0.204795i
$305$	−3.24927	−	12.1264i	−0.186053	−	0.694358i
$306$	0.618401	+	2.30790i	0.0353516	+	0.131934i
$307$	13.1561	−	13.1561i	0.750860	−	0.750860i	−0.223779	−	0.974640i	$-0.571840\pi$
$307$	13.1561	−	13.1561i	0.750860	−	0.750860i	0.974640	+	0.223779i	$0.0718395\pi$
$308$	0.983268	+	3.04400i	0.0560269	+	0.173448i
$309$	−7.78215	+	4.49303i	−0.442711	+	0.255599i
$310$	−2.45736	+	9.17099i	−0.139569	+	0.520877i
$311$	24.1181			1.36761			0.683806	−	0.729664i	$-0.260324\pi$
$311$	24.1181			1.36761			0.683806	+	0.729664i	$0.260324\pi$
$312$	−3.17565	+	1.70741i	−0.179786	+	0.0966630i
$313$		−	0.653940i		−	0.0369629i	−0.999829	−	0.0184814i	$-0.994117\pi$
$313$		−	0.653940i		−	0.0369629i	0.999829	−	0.0184814i	$-0.00588316\pi$
$314$	−0.722048	+	2.69472i	−0.0407475	+	0.152072i
$315$	0.613247	−	2.86088i	0.0345525	−	0.161192i
$316$	6.39376	+	3.69144i	0.359677	+	0.207660i
$317$	−16.2853	+	16.2853i	−0.914672	+	0.914672i	−0.996635	−	0.0819636i	$-0.973881\pi$
$317$	−16.2853	+	16.2853i	−0.914672	+	0.914672i	0.0819636	+	0.996635i	$0.473881\pi$
$318$	−3.40570	+	0.912554i	−0.190982	+	0.0511735i
$319$	−9.78050	+	2.62068i	−0.547603	+	0.146730i
$320$	0.781970	−	0.781970i	0.0437135	−	0.0437135i
$321$	12.0478	+	6.95581i	0.672444	+	0.388236i
$322$	3.23190	−	15.0772i	0.180107	−	0.840222i
$323$	3.12278	−	11.6544i	0.173756	−	0.648466i
$324$		−	1.00000i		−	0.0555556i
$325$	−9.33364	−	9.91676i	−0.517737	−	0.550083i
$326$	11.3422			0.628184
$327$	−1.18063	+	4.40617i	−0.0652890	+	0.243662i
$328$	−0.236455	+	0.136517i	−0.0130560	+	0.00753790i
$329$	5.51513	+	17.0737i	0.304059	+	0.941306i
$330$	0.945449	−	0.945449i	0.0520452	−	0.0520452i
$331$	−3.68510	−	13.7530i	−0.202551	−	0.755931i	−0.990182	−	0.139784i	$-0.955359\pi$
$331$	−3.68510	−	13.7530i	−0.202551	−	0.755931i	0.787631	−	0.616147i	$-0.211307\pi$
$332$	−0.799063	−	2.98215i	−0.0438543	−	0.163666i
$333$	7.20642	+	7.20642i	0.394910	+	0.394910i
$334$	−4.52792	−	2.61420i	−0.247757	−	0.143042i
$335$	3.30122	+	5.71788i	0.180365	+	0.312401i
$336$	−2.22139	+	1.43716i	−0.121187	+	0.0784034i
$337$		−	7.20150i		−	0.392290i	−0.980575	−	0.196145i	$-0.937158\pi$
$337$		−	7.20150i		−	0.392290i	0.980575	−	0.196145i	$-0.0628424\pi$
$338$	−4.11852	+	12.3304i	−0.224018	+	0.670683i
$339$			20.0743i			1.09029i
$340$	−2.55225	−	0.683873i	−0.138415	−	0.0370882i
$341$	8.98970	−	5.19021i	0.486820	−	0.281065i
$342$	−2.52488	+	4.37322i	−0.136530	+	0.236477i
$343$	18.3070	−	2.80271i	0.988483	−	0.151332i
$344$	2.80887	+	10.4829i	0.151444	+	0.565198i
$345$	−6.22554	+	1.66813i	−0.335172	+	0.0898091i
$346$	10.6766	−	10.6766i	0.573977	−	0.573977i
$347$	−11.9217	+	20.6491i	−0.639993	+	1.10850i	0.345441	+	0.938440i	$0.387729\pi$
$347$	−11.9217	+	20.6491i	−0.639993	+	1.10850i	−0.985434	+	0.170059i	$0.945604\pi$
$348$	−4.18735	−	7.25271i	−0.224466	−	0.388786i
$349$	−24.0068	−	6.43260i	−1.28505	−	0.344329i	−0.449275	−	0.893394i	$-0.648318\pi$
$349$	−24.0068	−	6.43260i	−1.28505	−	0.344329i	−0.835780	+	0.549064i	$0.814984\pi$
$350$	−7.41482	−	6.69947i	−0.396339	−	0.358102i
$351$	−2.47115	−	2.62553i	−0.131900	−	0.140141i
$352$	−1.20906			−0.0644431
$353$	−7.04325	+	26.2858i	−0.374874	+	1.39905i	0.478654	+	0.878004i	$0.341125\pi$
$353$	−7.04325	+	26.2858i	−0.374874	+	1.39905i	−0.853528	+	0.521047i	$0.825542\pi$
$354$	−4.75409	−	8.23432i	−0.252677	−	0.437649i
$355$	−4.78947	+	8.29560i	−0.254198	+	0.440285i
$356$	−11.1012	−	11.1012i	−0.588364	−	0.588364i
$357$	5.62759	+	2.87961i	0.297843	+	0.152405i
$358$	−1.70284	+	0.456275i	−0.0899980	+	0.0241149i
$359$	−10.9412	−	10.9412i	−0.577455	−	0.577455i	0.356747	−	0.934201i	$-0.383886\pi$
$359$	−10.9412	−	10.9412i	−0.577455	−	0.577455i	−0.934201	+	0.356747i	$0.883886\pi$
$360$	0.957714	+	0.552937i	0.0504760	+	0.0291423i
$361$	5.62926	−	3.25005i	0.296277	−	0.171055i
$362$	22.9011	+	6.13632i	1.20365	+	0.322518i
$363$	9.53818			0.500624
$364$	−2.28090	+	9.26269i	−0.119552	+	0.485497i
$365$	−6.52066			−0.341307
$366$	−10.9655	−	2.93819i	−0.573175	−	0.153582i
$367$	−18.7743	+	10.8394i	−0.980012	+	0.565810i	−0.902274	−	0.431164i	$-0.858103\pi$
$367$	−18.7743	+	10.8394i	−0.980012	+	0.565810i	−0.0777381	+	0.996974i	$0.524770\pi$
$368$	5.04730	+	2.91406i	0.263108	+	0.151906i
$369$	−0.193065	−	0.193065i	−0.0100505	−	0.0100505i
$370$	−10.8864	+	2.91700i	−0.565956	+	0.151648i
$371$	−4.24935	+	8.30445i	−0.220615	+	0.431145i
$372$	6.07089	+	6.07089i	0.314761	+	0.314761i
$373$	3.42220	−	5.92742i	0.177195	−	0.306910i	−0.763724	−	0.645543i	$-0.776631\pi$
$373$	3.42220	−	5.92742i	0.177195	−	0.306910i	0.940919	+	0.338633i	$0.109964\pi$
$374$	1.44441	+	2.50180i	0.0746889	+	0.129365i
$375$	−2.51217	+	9.37556i	−0.129728	+	0.484152i
$376$	−6.78159			−0.349734
$377$	−28.9166	−	8.69465i	−1.48928	−	0.447797i
$378$	−1.96313	−	1.77373i	−0.100972	−	0.0912311i
$379$	−13.6802	−	3.66560i	−0.702704	−	0.188289i	−0.110263	−	0.993902i	$-0.535169\pi$
$379$	−13.6802	−	3.66560i	−0.702704	−	0.188289i	−0.592442	+	0.805613i	$0.701836\pi$
$380$	−2.79220	−	4.83623i	−0.143237	−	0.248093i
$381$	5.57371	−	9.65396i	0.285550	−	0.494587i
$382$	2.14485	−	2.14485i	0.109740	−	0.109740i
$383$	−6.45564	+	1.72978i	−0.329868	+	0.0883879i	−0.419952	−	0.907546i	$-0.637953\pi$
$383$	−6.45564	+	1.72978i	−0.329868	+	0.0883879i	0.0900840	+	0.995934i	$0.471286\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−0.179060	−	3.53301i	−0.00912575	−	0.180059i
$386$	−5.53251	+	9.58259i	−0.281597	+	0.487741i
$387$	−9.39867	+	5.42633i	−0.477761	+	0.275836i
$388$	−1.77794	−	0.476399i	−0.0902615	−	0.0241855i
$389$		−	14.5487i		−	0.737648i	−0.929499	−	0.368824i	$-0.879760\pi$
$389$		−	14.5487i		−	0.737648i	0.929499	−	0.368824i	$-0.120240\pi$
$390$	3.88090	−	0.914901i	0.196517	−	0.0463278i
$391$		−	13.9252i		−	0.704229i
$392$	−1.11883	+	6.91001i	−0.0565097	+	0.349008i
$393$	−1.93078	−	3.34421i	−0.0973950	−	0.168693i
$394$	17.3200	+	9.99968i	0.872567	+	0.503777i
$395$	−5.77319	−	5.77319i	−0.290481	−	0.290481i
$396$	−0.312928	−	1.16786i	−0.0157252	−	0.0586873i
$397$	2.27144	+	8.47714i	0.114000	+	0.425455i	0.999210	−	0.0397367i	$-0.0126519\pi$
$397$	2.27144	+	8.47714i	0.114000	+	0.425455i	−0.885210	+	0.465192i	$0.845985\pi$
$398$	−5.29412	+	5.29412i	−0.265370	+	0.265370i
$399$	4.10672	+	12.7136i	0.205593	+	0.636476i
$400$	3.27102	−	1.88852i	0.163551	−	0.0944261i
$401$	3.76070	−	14.0351i	0.187801	−	0.700881i	−0.806213	−	0.591625i	$-0.798487\pi$
$401$	3.76070	−	14.0351i	0.187801	−	0.700881i	0.994014	−	0.109256i	$-0.0348468\pi$
$402$	5.97034			0.297774
$403$	30.9414	+	0.937251i	1.54130	+	0.0466878i
$404$			7.30828i			0.363601i
$405$	−0.286221	+	1.06819i	−0.0142224	+	0.0530789i
$406$	−21.6652	−	4.64408i	−1.07523	−	0.230482i
$407$	10.6712	+	6.16102i	0.528951	+	0.305390i
$408$	−1.68950	+	1.68950i	−0.0836429	+	0.0836429i
$409$	−12.4960	+	3.34829i	−0.617887	+	0.165562i	−0.554167	−	0.832405i	$-0.686963\pi$
$409$	−12.4960	+	3.34829i	−0.617887	+	0.165562i	−0.0637202	+	0.997968i	$0.520297\pi$
$410$	0.291653	−	0.0781482i	0.0144037	−	0.00385946i
$411$	−7.89359	+	7.89359i	−0.389362	+	0.389362i
$412$	−7.78215	−	4.49303i	−0.383399	−	0.221355i
$413$	−24.5975	−	5.27263i	−1.21036	−	0.259449i
$414$	−1.50843	+	5.62953i	−0.0741352	+	0.276676i
$415$			3.41421i			0.167597i
$416$	−3.06648	−	1.89649i	−0.150347	−	0.0929831i
$417$	10.7792			0.527858
$418$	−1.58021	+	5.89743i	−0.0772906	+	0.288453i
$419$	5.77665	−	3.33515i	0.282208	−	0.162933i	−0.352215	−	0.935919i	$-0.614571\pi$
$419$	5.77665	−	3.33515i	0.282208	−	0.162933i	0.634423	+	0.772986i	$0.281238\pi$
$420$	2.78422	−	0.899351i	0.135856	−	0.0438839i
$421$	9.25192	−	9.25192i	0.450911	−	0.450911i	−0.444746	−	0.895657i	$-0.646706\pi$
$421$	9.25192	−	9.25192i	0.450911	−	0.450911i	0.895657	+	0.444746i	$0.146706\pi$
$422$	−3.54750	−	13.2394i	−0.172690	−	0.644486i
$423$	−1.75520	−	6.55051i	−0.0853409	−	0.318497i
$424$	−2.49314	−	2.49314i	−0.121078	−	0.121078i
$425$	−7.81550	−	4.51228i	−0.379107	−	0.218878i
$426$	4.33094	+	7.50140i	0.209835	+	0.363444i
$427$	−25.2179	+	16.3151i	−1.22038	+	0.789541i
$428$			13.9116i			0.672444i
$429$	−3.70756	−	2.29297i	−0.179003	−	0.110706i
$430$		−	12.0017i		−	0.578771i
$431$	−0.548540	−	0.146981i	−0.0264222	−	0.00707981i	0.245584	−	0.969375i	$-0.421020\pi$
$431$	−0.548540	−	0.146981i	−0.0264222	−	0.00707981i	−0.272006	+	0.962296i	$0.587687\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−0.449881	+	0.779216i	−0.0216199	+	0.0374467i	−0.876633	−	0.481160i	$-0.840216\pi$
$433$	−0.449881	+	0.779216i	−0.0216199	+	0.0374467i	0.855013	+	0.518607i	$0.173549\pi$
$434$	22.6861	−	1.14977i	1.08897	−	0.0551910i
$435$	2.39702	+	8.94579i	0.114928	+	0.428918i
$436$	−4.40617	+	1.18063i	−0.211017	+	0.0565419i
$437$	20.8106	−	20.8106i	0.995505	−	0.995505i
$438$	−2.94819	+	5.10642i	−0.140870	+	0.243994i
$439$	16.5233	+	28.6192i	0.788613	+	1.36592i	0.926817	+	0.375514i	$0.122534\pi$
$439$	16.5233	+	28.6192i	0.788613	+	1.36592i	−0.138203	+	0.990404i	$0.544133\pi$
$440$	1.29151	+	0.346058i	0.0615702	+	0.0164977i
$441$	−6.96413	+	0.707730i	−0.331625	+	0.0337014i
$442$	−0.260833	+	8.61086i	−0.0124066	+	0.409577i
$443$	7.24534			0.344237			0.172118	−	0.985076i	$-0.444939\pi$
$443$	7.24534			0.344237			0.172118	+	0.985076i	$0.444939\pi$
$444$	−2.63773	+	9.84416i	−0.125181	+	0.467183i
$445$	8.68083	+	15.0356i	0.411511	+	0.712758i
$446$	0.915170	−	1.58512i	0.0433345	−	0.0750576i
$447$	16.3228	+	16.3228i	0.772042	+	0.772042i
$448$	−2.35531	−	1.20520i	−0.111278	−	0.0569404i
$449$	11.8519	−	3.17571i	0.559327	−	0.149871i	0.0319296	−	0.999490i	$-0.489835\pi$
$449$	11.8519	−	3.17571i	0.559327	−	0.149871i	0.527397	+	0.849619i	$0.323168\pi$
$450$	2.67077	+	2.67077i	0.125901	+	0.125901i
$451$	−0.285888	−	0.165057i	−0.0134619	−	0.00777225i
$452$	−17.3849	+	10.0372i	−0.817716	+	0.472109i
$453$	3.16633	+	0.848417i	0.148767	+	0.0398621i
$454$	8.14838			0.382422
$455$	5.08762	−	9.24149i	0.238511	−	0.433248i
$456$	−5.04976			−0.236477
$457$	−31.9182	−	8.55245i	−1.49307	−	0.400067i	−0.582298	−	0.812976i	$-0.697846\pi$
$457$	−31.9182	−	8.55245i	−1.49307	−	0.400067i	−0.910772	+	0.412909i	$0.864513\pi$
$458$	−19.0010	+	10.9702i	−0.887857	+	0.512605i
$459$	−2.06921	−	1.19466i	−0.0965825	−	0.0557619i
$460$	−4.55741	−	4.55741i	−0.212491	−	0.212491i
$461$	−7.33403	+	1.96515i	−0.341580	+	0.0915261i	−0.425531	−	0.904944i	$-0.639913\pi$
$461$	−7.33403	+	1.96515i	−0.341580	+	0.0915261i	0.0839511	+	0.996470i	$0.473246\pi$
$462$	−2.84771	−	1.45716i	−0.132487	−	0.0677932i
$463$	−5.06087	−	5.06087i	−0.235198	−	0.235198i	0.579660	−	0.814858i	$-0.303185\pi$
$463$	−5.06087	−	5.06087i	−0.235198	−	0.235198i	−0.814858	+	0.579660i	$0.803185\pi$
$464$	4.18735	−	7.25271i	0.194393	−	0.336699i
$465$	−4.74725	−	8.22248i	−0.220149	−	0.381309i
$466$	−5.94556	+	22.1891i	−0.275423	+	1.02789i
$467$	−39.0856			−1.80866			−0.904332	−	0.426829i	$-0.859631\pi$
$467$	−39.0856			−1.80866			−0.904332	+	0.426829i	$0.859631\pi$
$468$	1.03820	−	3.45284i	0.0479910	−	0.159608i
$469$	10.5898	−	11.7205i	0.488992	−	0.541204i
$470$	7.24403	+	1.94103i	0.334142	+	0.0895332i
$471$	−1.39489	−	2.41602i	−0.0642731	−	0.111324i
$472$	4.75409	−	8.23432i	0.218825	−	0.379015i
$473$	−9.27831	+	9.27831i	−0.426617	+	0.426617i
$474$	−7.13131	+	1.91083i	−0.327552	+	0.0877673i
$475$	−4.93650	−	18.4233i	−0.226502	−	0.845318i
$476$	0.319978	+	6.31344i	0.0146662	+	0.289376i
$477$	1.76292	−	3.05347i	0.0807185	−	0.139809i
$478$	−7.97447	+	4.60406i	−0.364744	+	0.210585i
$479$	14.9831	+	4.01471i	0.684595	+	0.183437i	0.584320	−	0.811523i	$-0.301361\pi$
$479$	14.9831	+	4.01471i	0.684595	+	0.183437i	0.100274	+	0.994960i	$0.468028\pi$
$480$			1.10587i			0.0504760i
$481$	17.4009	+	32.3644i	0.793413	+	1.47569i
$482$			8.08539i			0.368279i
$483$	8.37592	+	12.9465i	0.381118	+	0.589087i
$484$	4.76909	+	8.26030i	0.216777	+	0.375468i
$485$	1.76283	+	1.01777i	0.0800460	+	0.0462146i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	1.27050	+	4.74157i	0.0575718	+	0.214861i	0.988719	−	0.149783i	$-0.0478574\pi$
$487$	1.27050	+	4.74157i	0.0575718	+	0.214861i	−0.931147	+	0.364644i	$0.881191\pi$
$488$	−2.93819	−	10.9655i	−0.133006	−	0.496384i
$489$	−8.02012	+	8.02012i	−0.362682	+	0.362682i
$490$	3.17292	−	7.06098i	0.143338	−	0.318982i
$491$	11.4684	−	6.62129i	0.517562	−	0.298815i	−0.218374	−	0.975865i	$-0.570075\pi$
$491$	11.4684	−	6.62129i	0.517562	−	0.298815i	0.735937	+	0.677050i	$0.236742\pi$
$492$	0.0706665	−	0.263731i	0.00318589	−	0.0118899i
$493$	−20.0098			−0.901198
$494$	−13.2583	+	12.4787i	−0.596520	+	0.561444i
$495$			1.33707i			0.0600967i
$496$	−2.22210	+	8.29298i	−0.0997752	+	0.372366i
$497$	22.4081	+	4.80332i	1.00514	+	0.215458i
$498$	2.67372	+	1.54367i	0.119812	+	0.0691736i
$499$	3.07331	−	3.07331i	0.137580	−	0.137580i	−0.634963	−	0.772543i	$-0.718985\pi$
$499$	3.07331	−	3.07331i	0.137580	−	0.137580i	0.772543	+	0.634963i	$0.218985\pi$
$500$	−9.37556	+	2.51217i	−0.419288	+	0.112348i
$501$	5.05024	−	1.35321i	0.225628	−	0.0604568i
$502$	−0.884607	+	0.884607i	−0.0394819	+	0.0394819i
$503$	−3.00987	−	1.73775i	−0.134203	−	0.0774824i	0.431395	−	0.902163i	$-0.358021\pi$
$503$	−3.00987	−	1.73775i	−0.134203	−	0.0774824i	−0.565599	+	0.824681i	$0.691355\pi$
$504$	0.554536	−	2.58698i	0.0247010	−	0.115233i
$505$	2.09178	−	7.80664i	0.0930832	−	0.347391i
$506$			7.04654i			0.313257i
$507$	−5.80665	−	11.6311i	−0.257882	−	0.516556i
$508$	11.1474			0.494587
$509$	−4.49134	+	16.7619i	−0.199075	+	0.742958i	0.792099	+	0.610392i	$0.208988\pi$
$509$	−4.49134	+	16.7619i	−0.199075	+	0.742958i	−0.991174	+	0.132566i	$0.957678\pi$
$510$	2.28828	−	1.32114i	0.101327	−	0.0585011i
$511$	4.79524	+	14.8451i	0.212129	+	0.656709i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.30697	−	4.87770i	−0.0577043	−	0.215356i
$514$	3.61333	+	13.4851i	0.159377	+	0.594803i
$515$	7.02683	+	7.02683i	0.309639	+	0.309639i
$516$	−9.39867	−	5.42633i	−0.413754	−	0.238881i
$517$	−4.09967	−	7.10084i	−0.180303	−	0.312295i
$518$	14.6467	+	22.6391i	0.643538	+	0.994706i
$519$			15.0990i			0.662772i
$520$	2.73278	+	2.90351i	0.119840	+	0.127327i
$521$			30.4244i			1.33292i	0.745542	+	0.666458i	$0.232190\pi$
$521$			30.4244i			1.33292i	−0.745542	+	0.666458i	$0.767810\pi$
$522$	8.08934	+	2.16753i	0.354061	+	0.0948704i
$523$	33.0212	−	19.0648i	1.44391	−	0.833644i	0.445806	−	0.895129i	$-0.352917\pi$
$523$	33.0212	−	19.0648i	1.44391	−	0.833644i	0.998108	+	0.0614851i	$0.0195837\pi$
$524$	1.93078	−	3.34421i	0.0843465	−	0.146092i
$525$	9.98031	−	0.505822i	0.435576	−	0.0220759i
$526$	−2.28386	−	8.52348i	−0.0995810	−	0.371641i
$527$	19.8146	−	5.30930i	0.863137	−	0.231277i
$528$	0.854934	−	0.854934i	0.0372062	−	0.0372062i
$529$	5.48347	−	9.49764i	0.238412	−	0.412941i
$530$	1.94957	+	3.37675i	0.0846837	+	0.146677i
$531$	9.18419	+	2.46090i	0.398560	+	0.106794i
$532$	−8.95694	+	9.91332i	−0.388333	+	0.429797i
$533$	−0.466181	−	0.867062i	−0.0201926	−	0.0375566i
$534$	15.6995			0.679384
$535$	3.98180	−	14.8603i	0.172148	−	0.642466i
$536$	2.98517	+	5.17047i	0.128940	+	0.223330i
$537$	0.881456	−	1.52673i	0.0380376	−	0.0658831i
$538$	−4.05637	−	4.05637i	−0.174883	−	0.174883i
$539$	−7.91167	+	3.00580i	−0.340780	+	0.129469i
$540$	−1.06819	+	0.286221i	−0.0459676	+	0.0123170i
$541$	9.06066	+	9.06066i	0.389548	+	0.389548i	0.874526	−	0.484978i	$-0.161172\pi$
$541$	9.06066	+	9.06066i	0.389548	+	0.389548i	−0.484978	+	0.874526i	$0.661172\pi$
$542$	−21.8054	−	12.5894i	−0.936624	−	0.540760i
$543$	−20.5325	+	11.8545i	−0.881136	+	0.508724i
$544$	−2.30790	−	0.618401i	−0.0989506	−	0.0265137i
$545$	5.04455			0.216085
$546$	−4.93687	−	8.16256i	−0.211279	−	0.349325i
$547$	−31.9488			−1.36603			−0.683017	−	0.730403i	$-0.739332\pi$
$547$	−31.9488			−1.36603			−0.683017	+	0.730403i	$0.739332\pi$
$548$	−10.7828	−	2.88925i	−0.460620	−	0.123423i
$549$	9.83139	−	5.67615i	0.419593	−	0.242252i
$550$	3.95485	+	2.28334i	0.168636	+	0.0973618i
$551$	−29.9037	−	29.9037i	−1.27394	−	1.27394i
$552$	−5.62953	+	1.50843i	−0.239609	+	0.0642029i
$553$	−8.89786	+	17.3890i	−0.378375	+	0.739454i
$554$	10.4496	+	10.4496i	0.443960	+	0.443960i
$555$	5.63521	−	9.76047i	0.239201	−	0.414309i
$556$	5.38958	+	9.33502i	0.228569	+	0.395893i
$557$	1.51254	−	5.64488i	0.0640884	−	0.239181i	−0.926450	−	0.376418i	$-0.877156\pi$
$557$	1.51254	−	5.64488i	0.0640884	−	0.239181i	0.990538	+	0.137237i	$0.0438222\pi$
$558$	−8.58553			−0.363454
$559$	−38.0858	+	8.97852i	−1.61086	+	0.379751i
$560$	2.17097	+	1.96153i	0.0917402	+	0.0828896i
$561$	−2.79039	−	0.747684i	−0.117811	−	0.0315672i
$562$	−7.30091	−	12.6456i	−0.307970	−	0.533420i
$563$	6.13173	−	10.6205i	0.258421	−	0.447599i	−0.707398	−	0.706816i	$-0.750131\pi$
$563$	6.13173	−	10.6205i	0.258421	−	0.447599i	0.965819	+	0.259217i	$0.0834643\pi$
$564$	4.79531	−	4.79531i	0.201919	−	0.201919i
$565$	21.4432	−	5.74570i	0.902124	−	0.241723i
$566$	−1.57740	−	5.88695i	−0.0663032	−	0.247447i
$567$	2.64236	−	0.133920i	0.110969	−	0.00562411i
$568$	−4.33094	+	7.50140i	−0.181722	+	0.314752i
$569$	−10.3741	+	5.98948i	−0.434904	+	0.251092i	−0.701434	−	0.712735i	$-0.747456\pi$
$569$	−10.3741	+	5.98948i	−0.434904	+	0.251092i	0.266529	+	0.963827i	$0.414123\pi$
$570$	5.39411	+	1.44535i	0.225935	+	0.0605390i
$571$			33.0802i			1.38436i	0.721723	+	0.692182i	$0.243350\pi$
$571$			33.0802i			1.38436i	−0.721723	+	0.692182i	$0.756650\pi$
$572$	0.131989	−	4.35733i	0.00551872	−	0.182189i
$573$			3.03327i			0.126717i
$574$	−0.392394	−	0.606516i	−0.0163782	−	0.0253155i
$575$	−11.0065	−	19.0639i	−0.459004	−	0.795018i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	12.2625	+	12.2625i	0.510495	+	0.510495i	0.914678	−	0.404183i	$-0.132444\pi$
$577$	12.2625	+	12.2625i	0.510495	+	0.510495i	−0.404183	+	0.914678i	$0.632444\pi$
$578$	−2.92237	−	10.9064i	−0.121554	−	0.453647i
$579$	−2.86384	−	10.6880i	−0.119017	−	0.444178i
$580$	−6.54877	+	6.54877i	−0.271923	+	0.271923i
$581$	7.77289	−	2.51078i	0.322474	−	0.104165i
$582$	1.59406	−	0.920332i	0.0660760	−	0.0381490i
$583$	1.10333	−	4.11769i	0.0456954	−	0.170537i
$584$	−5.89639			−0.243994
$585$	−2.09728	+	3.39114i	−0.0867118	+	0.140207i
$586$		−	33.0732i		−	1.36624i
$587$	10.1586	−	37.9123i	0.419289	−	1.56481i	−0.356796	−	0.934182i	$-0.616131\pi$
$587$	10.1586	−	37.9123i	0.419289	−	1.56481i	0.776086	−	0.630627i	$-0.217202\pi$
$588$	−4.09498	−	5.67725i	−0.168874	−	0.234126i
$589$	37.5464	+	21.6774i	1.54707	+	0.893203i
$590$	−7.43511	+	7.43511i	−0.306099	+	0.306099i
$591$	−19.3179	+	5.17622i	−0.794632	+	0.212921i
$592$	−9.84416	+	2.63773i	−0.404592	+	0.108410i
$593$	−2.17721	+	2.17721i	−0.0894075	+	0.0894075i	−0.750396	−	0.660989i	$-0.770137\pi$
$593$	−2.17721	+	2.17721i	−0.0894075	+	0.0894075i	0.660989	+	0.750396i	$0.270137\pi$
$594$	1.04708	+	0.604530i	0.0429621	+	0.0248042i
$595$	1.46524	−	6.83555i	0.0600690	−	0.280230i
$596$	−5.97456	+	22.2974i	−0.244728	+	0.913336i
$597$		−	7.48701i		−	0.306423i
$598$	−11.0530	+	17.8718i	−0.451989	+	0.730833i
$599$	22.6747			0.926462			0.463231	−	0.886238i	$-0.346690\pi$
$599$	22.6747			0.926462			0.463231	+	0.886238i	$0.346690\pi$
$600$	−0.977571	+	3.64834i	−0.0399092	+	0.148943i
$601$	8.67955	−	5.01114i	0.354046	−	0.204409i	−0.312420	−	0.949944i	$-0.601140\pi$
$601$	8.67955	−	5.01114i	0.354046	−	0.204409i	0.666466	+	0.745535i	$0.267806\pi$
$602$	−27.3233	+	8.82592i	−1.11362	+	0.359718i
$603$	−4.22167	+	4.22167i	−0.171920	+	0.171920i
$604$	0.848417	+	3.16633i	0.0345216	+	0.128836i
$605$	−2.73003	−	10.1886i	−0.110991	−	0.414225i
$606$	−5.16773	−	5.16773i	−0.209925	−	0.209925i
$607$	9.83901	+	5.68056i	0.399353	+	0.230567i	0.686205	−	0.727408i	$-0.259275\pi$
$607$	9.83901	+	5.68056i	0.399353	+	0.230567i	−0.286852	+	0.957975i	$0.592609\pi$
$608$	−2.52488	−	4.37322i	−0.102397	−	0.177358i
$609$	18.6035	−	12.0358i	0.753852	−	0.487714i
$610$			12.5542i			0.508305i
$611$	0.740321	−	24.4401i	0.0299502	−	0.988743i
$612$		−	2.38932i		−	0.0965825i
$613$	27.6878	+	7.41894i	1.11830	+	0.299648i	0.770196	−	0.637807i	$-0.220158\pi$
$613$	27.6878	+	7.41894i	1.11830	+	0.299648i	0.348106	+	0.937455i	$0.386825\pi$
$614$	−16.1129	+	9.30279i	−0.650264	+	0.375430i
$615$	−0.150971	+	0.261489i	−0.00608773	+	0.0105443i
$616$	−0.161917	−	3.19477i	−0.00652384	−	0.128721i
$617$	−5.37234	−	20.0498i	−0.216282	−	0.807176i	−0.985711	−	0.168444i	$-0.946126\pi$
$617$	−5.37234	−	20.0498i	−0.216282	−	0.807176i	0.769429	−	0.638732i	$-0.220541\pi$
$618$	8.67986	−	2.32576i	0.349155	−	0.0935558i
$619$	14.9807	−	14.9807i	0.602125	−	0.602125i	−0.338751	−	0.940876i	$-0.610004\pi$
$619$	14.9807	−	14.9807i	0.602125	−	0.602125i	0.940876	+	0.338751i	$0.110004\pi$
$620$	4.74725	−	8.22248i	0.190654	−	0.330223i
$621$	−2.91406	−	5.04730i	−0.116937	−	0.202541i
$622$	−23.2963	−	6.24222i	−0.934096	−	0.250290i
$623$	27.8468	−	30.8201i	1.11566	−	1.23478i
$624$	3.50935	−	0.827311i	0.140487	−	0.0331189i
$625$	−8.15129			−0.326051
$626$	−0.169252	+	0.631657i	−0.00676467	+	0.0252461i
$627$	−3.05273	−	5.28749i	−0.121914	−	0.211162i
$628$	1.39489	−	2.41602i	0.0556621	−	0.0964096i
$629$	17.2184	+	17.2184i	0.686544	+	0.686544i
$630$	−1.33280	+	2.60468i	−0.0531000	+	0.103773i
$631$	−26.9457	+	7.22008i	−1.07269	+	0.287427i	−0.751598	−	0.659621i	$-0.770717\pi$
$631$	−26.9457	+	7.22008i	−1.07269	+	0.287427i	−0.321093	+	0.947048i	$0.604050\pi$
$632$	−5.22048	−	5.22048i	−0.207660	−	0.207660i
$633$	11.8702	+	6.85324i	0.471797	+	0.272392i
$634$	19.9453	−	11.5154i	0.792129	−	0.457336i
$635$	−11.9076	−	3.19063i	−0.472538	−	0.126616i
$636$	3.52584			0.139809
$637$	−24.7808	−	4.78651i	−0.981852	−	0.189648i
$638$	10.1255			0.400873
$639$	−8.36673	−	2.24186i	−0.330983	−	0.0886865i
$640$	−0.957714	+	0.552937i	−0.0378570	+	0.0218567i
$641$	32.8941	+	18.9914i	1.29924	+	0.750117i	0.980273	−	0.197649i	$-0.0633305\pi$
$641$	32.8941	+	18.9914i	1.29924	+	0.750117i	0.318968	+	0.947766i	$0.396664\pi$
$642$	−9.83701	−	9.83701i	−0.388236	−	0.388236i
$643$	−7.84802	+	2.10287i	−0.309496	+	0.0829292i	−0.410224	−	0.911985i	$-0.634549\pi$
$643$	−7.84802	+	2.10287i	−0.309496	+	0.0829292i	0.100728	+	0.994914i	$0.467883\pi$
$644$	−7.02405	+	13.7270i	−0.276787	+	0.540920i
$645$	8.48646	+	8.48646i	0.334154	+	0.334154i
$646$	−6.03275	+	10.4490i	−0.237355	+	0.411111i
$647$	12.0787	+	20.9209i	0.474863	+	0.822487i	0.999586	−	0.0287863i	$-0.00916422\pi$
$647$	12.0787	+	20.9209i	0.474863	+	0.822487i	−0.524722	+	0.851273i	$0.675831\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	11.4959			0.451255
$650$	6.44896	+	11.9946i	0.252949	+	0.470466i
$651$	−15.2285	+	16.8545i	−0.596850	+	0.660579i
$652$	−10.9557	−	2.93557i	−0.429058	−	0.114966i
$653$	−8.38354	−	14.5207i	−0.328073	−	0.568240i	0.654056	−	0.756446i	$-0.273066\pi$
$653$	−8.38354	−	14.5207i	−0.328073	−	0.568240i	−0.982129	+	0.188206i	$0.939733\pi$
$654$	2.28080	−	3.95046i	0.0891864	−	0.154475i
$655$	−3.01963	+	3.01963i	−0.117987	+	0.117987i
$656$	0.263731	−	0.0706665i	0.0102970	−	0.00275906i
$657$	−1.52610	−	5.69547i	−0.0595387	−	0.222201i
$658$	−0.908191	−	17.9194i	−0.0354050	−	0.698571i
$659$	−14.4094	+	24.9579i	−0.561312	+	0.972221i	0.436070	+	0.899913i	$0.356370\pi$
$659$	−14.4094	+	24.9579i	−0.561312	+	0.972221i	−0.997382	+	0.0723085i	$0.976963\pi$
$660$	−1.15793	+	0.668533i	−0.0450725	+	0.0260226i
$661$	13.0128	+	3.48676i	0.506138	+	0.135619i	0.502847	−	0.864375i	$-0.332286\pi$
$661$	13.0128	+	3.48676i	0.506138	+	0.135619i	0.00329085	+	0.999995i	$0.498952\pi$
$662$			14.2381i			0.553380i
$663$	−5.90436	−	6.27323i	−0.229306	−	0.243632i
$664$			3.08734i			0.119812i
$665$	12.4051	−	8.02566i	0.481050	−	0.311222i
$666$	−5.09571	−	8.82603i	−0.197455	−	0.342002i
$667$	−42.2696	−	24.4044i	−1.63669	−	0.944941i
$668$	3.69703	+	3.69703i	0.143042	+	0.143042i
$669$	0.473727	+	1.76797i	0.0183153	+	0.0683537i
$670$	−1.70884	−	6.37747i	−0.0660182	−	0.246383i
$671$	9.70548	−	9.70548i	0.374676	−	0.374676i
$672$	2.51766	−	0.813250i	0.0971209	−	0.0313718i
$673$	7.61373	−	4.39579i	0.293488	−	0.169445i	−0.346026	−	0.938225i	$-0.612469\pi$
$673$	7.61373	−	4.39579i	0.293488	−	0.169445i	0.639514	+	0.768780i	$0.279136\pi$
$674$	−1.86388	+	6.95611i	−0.0717941	+	0.267939i
$675$	−3.77704			−0.145379
$676$	7.16951	−	10.8443i	0.275751	−	0.417087i
$677$		−	30.0874i		−	1.15635i	−0.815912	−	0.578176i	$-0.803765\pi$
$677$		−	30.0874i		−	1.15635i	0.815912	−	0.578176i	$-0.196235\pi$
$678$	5.19562	−	19.3903i	0.199537	−	0.744681i
$679$	1.02071	−	4.76177i	0.0391714	−	0.182740i
$680$	2.28828	+	1.32114i	0.0877517	+	0.0506635i
$681$	−5.76177	+	5.76177i	−0.220792	+	0.220792i
$682$	−10.0267	+	2.68665i	−0.383943	+	0.102877i
$683$	5.94428	−	1.59276i	0.227451	−	0.0609454i	−0.143293	−	0.989680i	$-0.545769\pi$
$683$	5.94428	−	1.59276i	0.227451	−	0.0609454i	0.370745	+	0.928735i	$0.379103\pi$
$684$	3.57072	−	3.57072i	0.136530	−	0.136530i
$685$	10.6912	+	6.17255i	0.408489	+	0.235841i
$686$	−18.4086	−	2.03098i	−0.702842	−	0.0775430i
$687$	5.67860	−	21.1928i	0.216652	−	0.808557i
$688$		−	10.8527i		−	0.413754i
$689$	9.25721	−	8.71287i	0.352672	−	0.331934i
$690$	6.44516			0.245363
$691$	−8.79499	+	32.8233i	−0.334577	+	1.24866i	0.569750	+	0.821818i	$0.307040\pi$
$691$	−8.79499	+	32.8233i	−0.334577	+	1.24866i	−0.904327	+	0.426841i	$0.859627\pi$
$692$	−13.0761	+	7.54949i	−0.497079	+	0.286988i
$693$	3.04400	−	0.983268i	0.115632	−	0.0373512i
$694$	16.8599	−	16.8599i	0.639993	−	0.639993i
$695$	−3.08522	−	11.5142i	−0.117029	−	0.436759i
$696$	2.16753	+	8.08934i	0.0821601	+	0.306626i
$697$	−0.461293	−	0.461293i	−0.0174727	−	0.0174727i
$698$	21.5239	+	12.4268i	0.814692	+	0.470363i
$699$	−11.4859	−	19.8942i	−0.434438	−	0.752469i
$700$	5.42821	+	8.39029i	0.205167	+	0.317123i
$701$		−	37.8085i		−	1.42801i	−0.700142	−	0.714004i	$-0.746880\pi$
$701$		−	37.8085i		−	1.42801i	0.700142	−	0.714004i	$-0.253120\pi$
$702$	1.70741	+	3.17565i	0.0644420	+	0.119857i
$703$			51.4643i			1.94101i
$704$	1.16786	+	0.312928i	0.0440154	+	0.0117939i
$705$	−6.49482	+	3.74979i	−0.244609	+	0.141225i
$706$	13.6065	−	23.5672i	0.512088	−	0.886962i
$707$	−19.3111	+	0.978726i	−0.726269	+	0.0368088i
$708$	2.46090	+	9.18419i	0.0924862	+	0.345163i
$709$	−21.8936	+	5.86637i	−0.822231	+	0.220316i	−0.645321	−	0.763911i	$-0.723277\pi$
$709$	−21.8936	+	5.86637i	−0.822231	+	0.220316i	−0.176909	+	0.984227i	$0.556610\pi$
$710$	6.77333	−	6.77333i	0.254198	−	0.254198i
$711$	3.69144	−	6.39376i	0.138440	−	0.239785i
$712$	7.84975	+	13.5962i	0.294182	+	0.509538i
$713$	48.3325	+	12.9506i	1.81007	+	0.485005i
$714$	−4.69053	−	4.23802i	−0.175539	−	0.158604i
$715$	−1.38815	+	4.61668i	−0.0519138	+	0.172654i
$716$	1.76291			0.0658831
$717$	2.38324	−	8.89437i	0.0890037	−	0.332166i
$718$	7.73660	+	13.4002i	0.288727	+	0.500090i
$719$	−15.9710	+	27.6626i	−0.595618	+	1.03164i	0.397842	+	0.917454i	$0.369759\pi$
$719$	−15.9710	+	27.6626i	−0.595618	+	1.03164i	−0.993459	+	0.114186i	$0.963574\pi$
$720$	−0.781970	−	0.781970i	−0.0291423	−	0.0291423i
$721$	10.8300	−	21.1649i	0.403330	−	0.788224i
$722$	−6.27862	+	1.68235i	−0.233666	+	0.0626106i
$723$	−5.71723	−	5.71723i	−0.212626	−	0.212626i
$724$	−20.5325	−	11.8545i	−0.763086	−	0.440568i
$725$	−27.3938	+	15.8158i	−1.01738	+	0.587385i
$726$	−9.21317	−	2.46866i	−0.341933	−	0.0916206i
$727$	−1.41270			−0.0523943			−0.0261971	−	0.999657i	$-0.508340\pi$
$727$	−1.41270			−0.0523943			−0.0261971	+	0.999657i	$0.508340\pi$
$728$	4.60055	−	8.35673i	0.170508	−	0.309721i
$729$	−1.00000			−0.0370370
$730$	6.29847	+	1.68767i	0.233117	+	0.0624635i
$731$	−22.4564	+	12.9652i	−0.830581	+	0.479536i
$732$	9.83139	+	5.67615i	0.363379	+	0.209797i
$733$	28.1696	+	28.1696i	1.04047	+	1.04047i	0.999146	+	0.0413211i	$0.0131567\pi$
$733$	28.1696	+	28.1696i	1.04047	+	1.04047i	0.0413211	+	0.999146i	$0.486843\pi$
$734$	20.9400	−	5.61087i	0.772911	−	0.207101i
$735$	2.74927	+	7.23646i	0.101408	+	0.266921i
$736$	−4.12110	−	4.12110i	−0.151906	−	0.151906i
$737$	−3.60925	+	6.25140i	−0.132948	+	0.230273i
$738$	0.136517	+	0.236455i	0.00502527	+	0.00870402i
$739$	−8.26449	+	30.8435i	−0.304014	+	1.13460i	0.629777	+	0.776776i	$0.283146\pi$
$739$	−8.26449	+	30.8435i	−0.304014	+	1.13460i	−0.933791	+	0.357820i	$0.883520\pi$
$740$	11.2704			0.414309
$741$	0.551264	−	18.1988i	0.0202512	−	0.668551i
$742$	6.25390	−	6.92167i	0.229588	−	0.254102i
$743$	33.6460	+	9.01542i	1.23435	+	0.330744i	0.816273	−	0.577667i	$-0.196037\pi$
$743$	33.6460	+	9.01542i	1.23435	+	0.330744i	0.418079	+	0.908411i	$0.362703\pi$
$744$	−4.29276	−	7.43529i	−0.157380	−	0.272591i
$745$	12.7640	−	22.1078i	0.467635	−	0.809968i
$746$	−4.83972	+	4.83972i	−0.177195	+	0.177195i
$747$	−2.98215	+	0.799063i	−0.109111	+	0.0292362i
$748$	−0.747684	−	2.79039i	−0.0273380	−	0.102027i
$749$	−36.7595	+	1.86305i	−1.34316	+	0.0680742i
$750$	4.85315	−	8.40590i	0.177212	−	0.306940i
$751$	8.98109	−	5.18524i	0.327725	−	0.189212i	−0.327106	−	0.944988i	$-0.606073\pi$
$751$	8.98109	−	5.18524i	0.327725	−	0.189212i	0.654831	+	0.755776i	$0.272740\pi$
$752$	6.55051	+	1.75520i	0.238873	+	0.0640057i
$753$		−	1.25102i		−	0.0455898i
$754$	25.6809	+	15.8825i	0.935243	+	0.578408i
$755$		−	3.62509i		−	0.131930i
$756$	1.43716	+	2.22139i	0.0522689	+	0.0807912i
$757$	−0.746201	−	1.29246i	−0.0271211	−	0.0469752i	0.852146	−	0.523304i	$-0.175301\pi$
$757$	−0.746201	−	1.29246i	−0.0271211	−	0.0469752i	−0.879267	+	0.476328i	$0.841967\pi$
$758$	12.2653	+	7.08139i	0.445497	+	0.257208i
$759$	−4.98266	−	4.98266i	−0.180859	−	0.180859i
$760$	1.44535	+	5.39411i	0.0524283	+	0.195665i
$761$	−4.16868	−	15.5577i	−0.151115	−	0.563967i	−0.999407	−	0.0344388i	$-0.989036\pi$
$761$	−4.16868	−	15.5577i	−0.151115	−	0.563967i	0.848292	−	0.529528i	$-0.177631\pi$
$762$	−7.88242	+	7.88242i	−0.285550	+	0.285550i
$763$	−3.70972	−	11.4846i	−0.134301	−	0.415769i
$764$	−2.62689	+	1.51664i	−0.0950376	+	0.0548700i
$765$	−0.683873	+	2.55225i	−0.0247255	+	0.0922768i
$766$	6.68337			0.241480
$767$	29.1567	+	18.0322i	1.05279	+	0.651104i
$768$			1.00000i			0.0360844i
$769$	3.65824	−	13.6528i	0.131920	−	0.492331i	−0.868072	−	0.496438i	$-0.834641\pi$
$769$	3.65824	−	13.6528i	0.131920	−	0.492331i	0.999992	+	0.00410760i	$0.00130749\pi$
$770$	−0.741452	+	3.45897i	−0.0267201	+	0.124653i
$771$	−12.0904	−	6.98041i	−0.435426	−	0.251393i
$772$	7.82415	−	7.82415i	0.281597	−	0.281597i
$773$	−51.3533	+	13.7601i	−1.84705	+	0.494915i	−0.999366	−	0.0355902i	$-0.988669\pi$
$773$	−51.3533	+	13.7601i	−1.84705	+	0.494915i	−0.847682	+	0.530505i	$0.822002\pi$
$774$	10.4829	−	2.80887i	0.376799	−	0.100963i
$775$	22.9300	−	22.9300i	0.823670	−	0.823670i
$776$	1.59406	+	0.920332i	0.0572235	+	0.0330380i
$777$	−26.3650	−	5.65151i	−0.945841	−	0.202747i
$778$	−3.76548	+	14.0530i	−0.134999	+	0.503823i
$779$		−	1.37876i		−	0.0493992i
$780$	−3.98545	−	0.120724i	−0.142702	−	0.00432262i
$781$	−10.4727			−0.374743
$782$	−3.60411	+	13.4507i	−0.128883	+	0.480997i
$783$	−7.25271	+	4.18735i	−0.259191	+	0.149644i
$784$	2.86915	−	6.38498i	0.102470	−	0.228035i
$785$	−2.18152	+	2.18152i	−0.0778619	+	0.0778619i
$786$	0.999445	+	3.72998i	0.0356490	+	0.133044i
$787$	−8.89838	−	33.2092i	−0.317193	−	1.18378i	−0.921930	−	0.387356i	$-0.873389\pi$
$787$	−8.89838	−	33.2092i	−0.317193	−	1.18378i	0.604737	−	0.796425i	$-0.293278\pi$
$788$	−14.1417	−	14.1417i	−0.503777	−	0.503777i
$789$	7.64194	+	4.41208i	0.272060	+	0.157074i
$790$	4.08226	+	7.07069i	0.145240	+	0.251564i
$791$	−28.8500	−	44.5929i	−1.02579	−	1.58554i
$792$			1.20906i			0.0429621i
$793$	39.8393	−	9.39189i	1.41473	−	0.333516i
$794$		−	8.77618i		−	0.311455i
$795$	−3.76627	−	1.00917i	−0.133576	−	0.0357916i
$796$	6.48394	−	3.74351i	0.229817	−	0.132685i
$797$	5.62330	−	9.73984i	0.199188	−	0.345003i	−0.749078	−	0.662482i	$-0.769503\pi$
$797$	5.62330	−	9.73984i	0.199188	−	0.345003i	0.948265	+	0.317479i	$0.102836\pi$
$798$	−0.676265	−	13.3433i	−0.0239395	−	0.472347i
$799$	−4.19374	−	15.6513i	−0.148364	−	0.553702i
$800$	−3.64834	+	0.977571i	−0.128988	+	0.0345624i
$801$	−11.1012	+	11.1012i	−0.392243	+	0.392243i
$802$	−7.26512	+	12.5836i	−0.256540	+	0.444341i
$803$	−3.56454	−	6.17397i	−0.125790	−	0.217875i
$804$	−5.76691	−	1.54524i	−0.203383	−	0.0544963i
$805$	11.4320	−	12.6527i	0.402925	−	0.445948i
$806$	−29.6445	−	8.91353i	−1.04418	−	0.313966i
$807$	5.73658			0.201937
$808$	1.89152	−	7.05926i	0.0665435	−	0.248344i
$809$	−8.95015	−	15.5021i	−0.314671	−	0.545025i	0.664697	−	0.747113i	$-0.268561\pi$
$809$	−8.95015	−	15.5021i	−0.314671	−	0.545025i	−0.979367	+	0.202088i	$0.935227\pi$
$810$	0.552937	−	0.957714i	0.0194282	−	0.0336507i
$811$	2.71012	+	2.71012i	0.0951653	+	0.0951653i	0.753087	−	0.657921i	$-0.228564\pi$
$811$	2.71012	+	2.71012i	0.0951653	+	0.0951653i	−0.657921	+	0.753087i	$0.728564\pi$
$812$	19.7250	+	10.0932i	0.692213	+	0.354202i
$813$	24.3208	−	6.51674i	0.852968	−	0.228552i
$814$	−8.71299	−	8.71299i	−0.305390	−	0.305390i
$815$	10.8626	+	6.27150i	0.380499	+	0.219681i
$816$	2.06921	−	1.19466i	0.0724368	−	0.0418214i
$817$	−52.9360	−	14.1841i	−1.85199	−	0.496240i
$818$	12.9368			0.452325
$819$	9.26269	+	2.28090i	0.323665	+	0.0797012i
$820$	−0.301941			−0.0105443
$821$	3.31759	+	0.888945i	0.115785	+	0.0310244i	0.316246	−	0.948677i	$-0.397577\pi$
$821$	3.31759	+	0.888945i	0.115785	+	0.0310244i	−0.200461	+	0.979702i	$0.564244\pi$
$822$	9.66763	−	5.58161i	0.337197	−	0.194681i
$823$	−28.5856	−	16.5039i	−0.996432	−	0.575290i	−0.0892411	−	0.996010i	$-0.528444\pi$
$823$	−28.5856	−	16.5039i	−0.996432	−	0.575290i	−0.907191	+	0.420720i	$0.861778\pi$
$824$	6.35410	+	6.35410i	0.221355	+	0.221355i
$825$	−4.41107	+	1.18194i	−0.153574	+	0.0411499i
$826$	22.3947	+	11.4593i	0.779212	+	0.398719i
$827$	39.4736	+	39.4736i	1.37263	+	1.37263i	0.856521	+	0.516112i	$0.172621\pi$
$827$	39.4736	+	39.4736i	1.37263	+	1.37263i	0.516112	+	0.856521i	$0.327379\pi$
$828$	2.91406	−	5.04730i	0.101271	−	0.175406i
$829$	26.7186	+	46.2780i	0.927976	+	1.60730i	0.786704	+	0.617331i	$0.211786\pi$
$829$	26.7186	+	46.2780i	0.927976	+	1.60730i	0.141272	+	0.989971i	$0.454881\pi$
$830$	0.883663	−	3.29787i	0.0306724	−	0.114471i
$831$	−14.7779			−0.512641
$832$	2.47115	+	2.62553i	0.0856717	+	0.0910240i
$833$	−16.6395	+	1.69099i	−0.576525	+	0.0585894i
$834$	−10.4119	−	2.78985i	−0.360533	−	0.0966047i
$835$	−2.89097	−	5.00730i	−0.100046	−	0.173285i
$836$	3.05273	−	5.28749i	0.105581	−	0.182872i
$837$	6.07089	−	6.07089i	0.209841	−	0.209841i
$838$	−6.44302	+	1.72640i	−0.222570	+	0.0596376i
$839$	1.84779	+	6.89605i	0.0637928	+	0.238078i	0.990459	−	0.137807i	$-0.0440054\pi$
$839$	1.84779	+	6.89605i	0.0637928	+	0.238078i	−0.926666	+	0.375885i	$0.877339\pi$
$840$	−2.92211	+	0.148099i	−0.100823	+	0.00510989i
$841$	−20.5678	+	35.6246i	−0.709236	+	1.22843i
$842$	−11.3312	+	6.54209i	−0.390500	+	0.225455i
$843$	14.1043	+	3.77923i	0.485777	+	0.130164i
$844$			13.7065i			0.471797i
$845$	−10.7623	+	9.53169i	−0.370233	+	0.327900i
$846$			6.78159i			0.233156i
$847$	−21.1880	+	13.7079i	−0.728029	+	0.471008i
$848$	1.76292	+	3.05347i	0.0605389	+	0.104856i
$849$	5.27810	+	3.04731i	0.181144	+	0.104583i
$850$	6.38133	+	6.38133i	0.218878	+	0.218878i
$851$	15.3730	+	57.3729i	0.526980	+	1.96672i
$852$	−2.24186	−	8.36673i	−0.0768048	−	0.286639i
$853$	−5.08984	+	5.08984i	−0.174273	+	0.174273i	−0.788854	−	0.614581i	$-0.789325\pi$
$853$	−5.08984	+	5.08984i	−0.174273	+	0.174273i	0.614581	+	0.788854i	$0.289325\pi$
$854$	28.5813	−	9.23226i	0.978031	−	0.315922i
$855$	−4.83623	+	2.79220i	−0.165396	+	0.0954912i
$856$	3.60059	−	13.4376i	0.123066	−	0.459288i
$857$	35.4108			1.20961			0.604806	−	0.796373i	$-0.293251\pi$
$857$	35.4108			1.20961			0.604806	+	0.796373i	$0.293251\pi$
$858$	2.98777	+	3.17443i	0.102001	+	0.108373i
$859$			14.6378i			0.499435i	0.968319	+	0.249718i	$0.0803378\pi$
$859$			14.6378i			0.499435i	−0.968319	+	0.249718i	$0.919662\pi$
$860$	−3.10626	+	11.5927i	−0.105923	+	0.395308i
$861$	0.706336	+	0.151407i	0.0240719	+	0.00515995i
$862$	0.491807	+	0.283945i	0.0167510	+	0.00967121i
$863$	10.7015	−	10.7015i	0.364284	−	0.364284i	−0.501104	−	0.865387i	$-0.667072\pi$
$863$	10.7015	−	10.7015i	0.364284	−	0.364284i	0.865387	+	0.501104i	$0.167072\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	16.1286	−	4.32165i	0.548389	−	0.146940i
$866$	0.636227	−	0.636227i	0.0216199	−	0.0216199i
$867$	9.77843	+	5.64558i	0.332093	+	0.191734i
$868$	−22.2106	−	4.76099i	−0.753878	−	0.161598i
$869$	2.31031	−	8.62218i	0.0783718	−	0.292487i
$870$		−	9.26136i		−	0.313990i
$871$	−18.9597	+	10.1938i	−0.642426	+	0.345404i
$872$	4.56160			0.154475
$873$	−0.476399	+	1.77794i	−0.0161237	+	0.0601743i
$874$	−25.4876	+	14.7153i	−0.862133	+	0.497752i
$875$	−7.89365	−	24.4372i	−0.266854	−	0.826128i
$876$	4.16937	−	4.16937i	0.140870	−	0.140870i
$877$	−2.98564	−	11.1426i	−0.100818	−	0.376258i	0.897019	−	0.441991i	$-0.145728\pi$
$877$	−2.98564	−	11.1426i	−0.100818	−	0.376258i	−0.997837	+	0.0657339i	$0.979061\pi$
$878$	−8.55308	−	31.9205i	−0.288652	−	1.07727i
$879$	23.3863	+	23.3863i	0.788800	+	0.788800i
$880$	−1.15793	−	0.668533i	−0.0390339	−	0.0225363i
$881$	8.02315	+	13.8965i	0.270307	+	0.468185i	0.968940	−	0.247295i	$-0.0795416\pi$
$881$	8.02315	+	13.8965i	0.270307	+	0.468185i	−0.698634	+	0.715480i	$0.746208\pi$
$882$	6.91001	+	1.11883i	0.232672	+	0.0376731i
$883$			41.4765i			1.39579i	0.716198	+	0.697897i	$0.245881\pi$
$883$			41.4765i			1.39579i	−0.716198	+	0.697897i	$0.754119\pi$
$884$	2.48060	−	8.24994i	0.0834316	−	0.277476i
$885$		−	10.5148i		−	0.353452i
$886$	−6.99847	−	1.87523i	−0.235118	−	0.0629997i
$887$	46.4648	−	26.8265i	1.56014	−	0.900745i	0.562893	−	0.826530i	$-0.309688\pi$
$887$	46.4648	−	26.8265i	1.56014	−	0.900745i	0.997242	−	0.0742151i	$-0.0236451\pi$
$888$	5.09571	−	8.82603i	0.171001	−	0.296182i
$889$	1.49286	+	29.4555i	0.0500691	+	0.987906i
$890$	−4.49353	−	16.7701i	−0.150623	−	0.562134i
$891$	−1.16786	+	0.312928i	−0.0391248	+	0.0104835i
$892$	−1.29425	+	1.29425i	−0.0433345	+	0.0433345i
$893$	17.1227	−	29.6574i	0.572989	−	0.992447i
$894$	−11.5420	−	19.9913i	−0.386021	−	0.668608i
$895$	−1.88313	−	0.504582i	−0.0629460	−	0.0168663i
$896$	1.96313	+	1.77373i	0.0655834	+	0.0592563i
$897$	−4.82166	−	20.4529i	−0.160991	−	0.682903i
$898$	−12.2700			−0.409455
$899$	18.6094	−	69.4513i	0.620659	−	2.31633i
$900$	−1.88852	−	3.27102i	−0.0629507	−	0.109034i
$901$	4.21218	−	7.29570i	0.140328	−	0.243055i
$902$	0.233426	+	0.233426i	0.00777225	+	0.00777225i
$903$	13.0796	−	25.5614i	0.435263	−	0.850629i
$904$	19.3903	−	5.19562i	0.644912	−	0.172804i
$905$	18.5397	+	18.5397i	0.616280	+	0.616280i
$906$	−2.83886	−	1.63902i	−0.0943147	−	0.0544526i
$907$	−24.5316	+	14.1633i	−0.814558	+	0.470285i	−0.848536	−	0.529138i	$-0.822516\pi$
$907$	−24.5316	+	14.1633i	−0.814558	+	0.470285i	0.0339785	+	0.999423i	$0.489182\pi$
$908$	−7.87073	−	2.10896i	−0.261199	−	0.0699882i
$909$	7.30828			0.242400
$910$	−7.30614	+	7.60982i	−0.242196	+	0.252263i
$911$	−17.1135			−0.566995			−0.283498	−	0.958973i	$-0.591495\pi$
$911$	−17.1135			−0.566995			−0.283498	+	0.958973i	$0.591495\pi$
$912$	4.87770	+	1.30697i	0.161517	+	0.0432783i
$913$	−3.23268	+	1.86639i	−0.106986	+	0.0617685i
$914$	28.6171	+	16.5221i	0.946568	+	0.546502i
$915$	−8.87717	−	8.87717i	−0.293470	−	0.293470i
$916$	21.1928	−	5.67860i	0.700231	−	0.187626i
$917$	9.09517	+	4.65396i	0.300349	+	0.153687i
$918$	1.68950	+	1.68950i	0.0557619	+	0.0557619i
$919$	0.208334	−	0.360845i	0.00687230	−	0.0119032i	−0.862569	−	0.505940i	$-0.831146\pi$
$919$	0.208334	−	0.360845i	0.00687230	−	0.0119032i	0.869441	+	0.494037i	$0.164479\pi$
$920$	3.22258	+	5.58167i	0.106245	+	0.184022i
$921$	4.81548	−	17.9716i	0.158675	−	0.592185i
$922$	7.59275			0.250054
$923$	−26.5615	−	16.4272i	−0.874282	−	0.540706i
$924$	2.37354	+	2.14455i	0.0780836	+	0.0705505i
$925$	37.1818	+	9.96284i	1.22253	+	0.327576i
$926$	3.57857	+	6.19827i	0.117599	+	0.203688i
$927$	−4.49303	+	7.78215i	−0.147570	+	0.255599i
$928$	−5.92181	+	5.92181i	−0.194393	+	0.194393i
$929$	28.6289	−	7.67108i	0.939283	−	0.251680i	0.243474	−	0.969907i	$-0.421713\pi$
$929$	28.6289	−	7.67108i	0.939283	−	0.251680i	0.695809	+	0.718227i	$0.255046\pi$
$930$	2.45736	+	9.17099i	0.0805800	+	0.300729i
$931$	−27.3941	−	22.3399i	−0.897805	−	0.732160i
$932$	11.4859	−	19.8942i	0.376234	−	0.651657i
$933$	20.8869	−	12.0590i	0.683806	−	0.394795i
$934$	37.7538	+	10.1161i	1.23534	+	0.331009i
$935$			3.19468i			0.104477i
$936$	−1.89649	+	3.06648i	−0.0619887	+	0.100231i
$937$		−	35.1676i		−	1.14888i	−0.818548	−	0.574438i	$-0.805221\pi$
$937$		−	35.1676i		−	1.14888i	0.818548	−	0.574438i	$-0.194779\pi$
$938$	−13.2625	+	8.58032i	−0.433035	+	0.280158i
$939$	−0.326970	−	0.566328i	−0.0106703	−	0.0184814i
$940$	−6.49482	−	3.74979i	−0.211838	−	0.122305i
$941$	18.3694	+	18.3694i	0.598825	+	0.598825i	0.940000	−	0.341175i	$-0.110825\pi$
$941$	18.3694	+	18.3694i	0.598825	+	0.598825i	−0.341175	+	0.940000i	$0.610825\pi$
$942$	0.722048	+	2.69472i	0.0235256	+	0.0877987i
$943$	−0.411853	−	1.53705i	−0.0134118	−	0.0500534i
$944$	−6.72330	+	6.72330i	−0.218825	+	0.218825i
$945$	−0.899351	−	2.78422i	−0.0292559	−	0.0905705i
$946$	11.3636	−	6.56075i	0.369461	−	0.213308i
$947$	2.18485	−	8.15396i	0.0709980	−	0.264968i	−0.921298	−	0.388857i	$-0.872870\pi$
$947$	2.18485	−	8.15396i	0.0709980	−	0.264968i	0.992296	+	0.123889i	$0.0395366\pi$
$948$	7.38288			0.239785
$949$	0.643687	−	21.2500i	0.0208950	−	0.689803i
$950$			19.0732i			0.618816i
$951$	−5.96082	+	22.2461i	−0.193293	+	0.721379i
$952$	1.32496	−	6.18113i	0.0429423	−	0.200332i
$953$	−39.7256	−	22.9356i	−1.28684	−	0.742956i	−0.308749	−	0.951144i	$-0.599910\pi$
$953$	−39.7256	−	22.9356i	−1.28684	−	0.742956i	−0.978089	+	0.208188i	$0.933244\pi$
$954$	−2.49314	+	2.49314i	−0.0807185	+	0.0807185i
$955$	3.24012	−	0.868187i	0.104848	−	0.0280939i
$956$	8.89437	−	2.38324i	0.287664	−	0.0770794i
$957$	−7.15982	+	7.15982i	−0.231444	+	0.231444i
$958$	−13.4335	−	7.75581i	−0.434016	−	0.250579i
$959$	6.19041	−	28.8791i	0.199899	−	0.932554i
$960$	0.286221	−	1.06819i	0.00923774	−	0.0344757i
$961$			42.7113i			1.37778i
$962$	−8.43147	−	35.7653i	−0.271842	−	1.15312i
$963$	13.9116			0.448296
$964$	2.09265	−	7.80988i	0.0673998	−	0.251539i
$965$	−10.5971	+	6.11826i	−0.341134	+	0.196954i
$966$	−4.73971	−	14.6732i	−0.152498	−	0.472103i
$967$	−10.2351	+	10.2351i	−0.329140	+	0.329140i	−0.852259	−	0.523119i	$-0.824768\pi$
$967$	−10.2351	+	10.2351i	−0.329140	+	0.329140i	0.523119	+	0.852259i	$0.324768\pi$
$968$	−2.46866	−	9.21317i	−0.0793458	−	0.296122i
$969$	−3.12278	−	11.6544i	−0.100318	−	0.374392i
$970$	−1.43934	−	1.43934i	−0.0462146	−	0.0462146i
$971$	−30.0710	−	17.3615i	−0.965024	−	0.557157i	−0.0673086	−	0.997732i	$-0.521441\pi$
$971$	−30.0710	−	17.3615i	−0.965024	−	0.557157i	−0.897716	+	0.440575i	$0.854775\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−23.9447	+	15.4914i	−0.767633	+	0.496630i
$974$		−	4.90883i		−	0.157289i
$975$	−13.0415	−	3.92134i	−0.417664	−	0.125583i
$976$			11.3523i			0.363379i
$977$	29.7442	+	7.96992i	0.951600	+	0.254980i	0.701041	−	0.713121i	$-0.252719\pi$
$977$	29.7442	+	7.96992i	0.951600	+	0.254980i	0.250559	+	0.968101i	$0.419386\pi$
$978$	9.82260	−	5.67108i	0.314092	−	0.181341i
$979$	−9.49082	+	16.4386i	−0.303328	+	0.525379i
$980$	−4.89232	+	5.99917i	−0.156279	+	0.191636i
$981$	1.18063	+	4.40617i	0.0376946	+	0.140678i
$982$	−12.7914	+	3.42743i	−0.408189	+	0.109374i
$983$	−41.7064	+	41.7064i	−1.33023	+	1.33023i	−0.425067	+	0.905162i	$0.639749\pi$
$983$	−41.7064	+	41.7064i	−1.33023	+	1.33023i	−0.905162	+	0.425067i	$0.860251\pi$
$984$	−0.136517	+	0.236455i	−0.00435201	+	0.00753790i
$985$	11.0584	+	19.1537i	0.352349	+	0.610287i
$986$	19.3280	+	5.17893i	0.615529	+	0.164931i
$987$	13.3131	+	12.0287i	0.423761	+	0.382879i
$988$	16.0363	−	8.62201i	0.510182	−	0.274303i
$989$	−63.2505			−2.01125
$990$	0.346058	−	1.29151i	0.0109985	−	0.0410468i
$991$	26.9472	+	46.6739i	0.856006	+	1.48265i	0.875709	+	0.482840i	$0.160395\pi$
$991$	26.9472	+	46.6739i	0.856006	+	1.48265i	−0.0197025	+	0.999806i	$0.506272\pi$
$992$	4.29276	−	7.43529i	0.136295	−	0.236071i
$993$	−10.0679	−	10.0679i	−0.319494	−	0.319494i
$994$	−20.4014	−	10.4393i	−0.647093	−	0.331115i
$995$	−7.99756	+	2.14294i	−0.253540	+	0.0679358i
$996$	−2.18308	−	2.18308i	−0.0691736	−	0.0691736i
$997$	−2.09912	−	1.21193i	−0.0664799	−	0.0383822i	0.466392	−	0.884578i	$-0.345554\pi$
$997$	−2.09912	−	1.21193i	−0.0664799	−	0.0383822i	−0.532872	+	0.846196i	$0.678887\pi$
$998$	−3.76402	+	2.17316i	−0.119148	+	0.0687901i
$999$	9.84416	+	2.63773i	0.311455	+	0.0834542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.223.3	✓	40
7.6	odd	2		546.2.bx.b.223.3	yes	40
13.7	odd	12		546.2.bx.b.475.3	yes	40
91.20	even	12	inner	546.2.bx.a.475.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.3	✓	40	1.1	even	1	trivial
546.2.bx.a.475.3	yes	40	91.20	even	12	inner
546.2.bx.b.223.3	yes	40	7.6	odd	2
546.2.bx.b.475.3	yes	40	13.7	odd	12

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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.781970 - 0.781970i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.20520 + 2.35531i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.781970 - 0.781970i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.20520 + 2.35531i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.552937 + 0.957714i) q^{10} +(0.312928 - 1.16786i) q^{11} +1.00000 q^{12} +(2.62553 - 2.47115i) q^{13} +(1.77373 - 1.96313i) q^{14} +(-1.06819 - 0.286221i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.19466 - 2.06921i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(4.87770 - 1.30697i) q^{19} +(-0.286221 - 1.06819i) q^{20} +(0.133920 + 2.64236i) q^{21} +(-0.604530 + 1.04708i) q^{22} +(5.04730 - 2.91406i) q^{23} +(-0.965926 - 0.258819i) q^{24} -3.77704i q^{25} +(-3.17565 + 1.70741i) q^{26} -1.00000i q^{27} +(-2.22139 + 1.43716i) q^{28} +(-4.18735 - 7.25271i) q^{29} +(0.957714 + 0.552937i) q^{30} +(6.07089 + 6.07089i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.312928 - 1.16786i) q^{33} +(-1.68950 + 1.68950i) q^{34} +(2.78422 - 0.899351i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.63773 + 9.84416i) q^{37} -5.04976 q^{38} +(1.03820 - 3.45284i) q^{39} +1.10587i q^{40} +(0.0706665 - 0.263731i) q^{41} +(0.554536 - 2.58698i) q^{42} +(-9.39867 - 5.42633i) q^{43} +(0.854934 - 0.854934i) q^{44} +(-1.06819 + 0.286221i) q^{45} +(-5.62953 + 1.50843i) q^{46} +(4.79531 - 4.79531i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-4.09498 - 5.67725i) q^{49} +(-0.977571 + 3.64834i) q^{50} -2.38932i q^{51} +(3.50935 - 0.827311i) q^{52} +3.52584 q^{53} +(-0.258819 + 0.965926i) q^{54} +(-1.15793 + 0.668533i) q^{55} +(2.51766 - 0.813250i) q^{56} +(3.57072 - 3.57072i) q^{57} +(2.16753 + 8.08934i) q^{58} +(2.46090 + 9.18419i) q^{59} +(-0.781970 - 0.781970i) q^{60} +(9.83139 + 5.67615i) q^{61} +(-4.29276 - 7.43529i) q^{62} +(1.43716 + 2.22139i) q^{63} +1.00000i q^{64} +(-3.98545 - 0.120724i) q^{65} +1.20906i q^{66} +(-5.76691 - 1.54524i) q^{67} +(2.06921 - 1.19466i) q^{68} +(2.91406 - 5.04730i) q^{69} +(-2.92211 + 0.148099i) q^{70} +(-2.24186 - 8.36673i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(4.16937 - 4.16937i) q^{73} +(5.09571 - 8.82603i) q^{74} +(-1.88852 - 3.27102i) q^{75} +(4.87770 + 1.30697i) q^{76} +(2.37354 + 2.14455i) q^{77} +(-1.89649 + 3.06648i) q^{78} +7.38288 q^{79} +(0.286221 - 1.06819i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.136517 + 0.236455i) q^{82} +(-2.18308 - 2.18308i) q^{83} +(-1.20520 + 2.35531i) q^{84} +(-2.55225 + 0.683873i) q^{85} +(7.67399 + 7.67399i) q^{86} +(-7.25271 - 4.18735i) q^{87} +(-1.04708 + 0.604530i) q^{88} +(-15.1646 - 4.06333i) q^{89} +1.10587 q^{90} +(2.65603 + 9.16218i) q^{91} +5.82812 q^{92} +(8.29298 + 2.22210i) q^{93} +(-5.87303 + 3.39079i) q^{94} +(-4.83623 - 2.79220i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.77794 + 0.476399i) q^{97} +(2.48606 + 6.54366i) q^{98} +(-0.854934 - 0.854934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 + 20 * q^9	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

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