LMFDB - Embedded newform 546.2.bx.a.223.9

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			223.9
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.a.475.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.14071 + 1.14071i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56426 - 0.651604i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.14071 + 1.14071i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56426 - 0.651604i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.806606 + 1.39708i) q^{10} +(-0.325835 + 1.21603i) q^{11} +1.00000 q^{12} +(-3.51375 - 0.808446i) q^{13} +(2.64553 + 0.0342770i) q^{14} +(1.55824 + 0.417530i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.338413 - 0.586148i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-5.48248 + 1.46903i) q^{19} +(0.417530 + 1.55824i) q^{20} +(1.89491 - 1.84643i) q^{21} +(-0.629465 + 1.09026i) q^{22} +(2.30399 - 1.33021i) q^{23} +(0.965926 + 0.258819i) q^{24} -2.39755i q^{25} +(-3.18478 - 1.69032i) q^{26} -1.00000i q^{27} +(2.54651 + 0.717822i) q^{28} +(1.92256 + 3.32997i) q^{29} +(1.39708 + 0.806606i) q^{30} +(-0.505667 - 0.505667i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.325835 + 1.21603i) q^{33} +(0.478588 - 0.478588i) q^{34} +(3.66837 + 2.18179i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.16343 + 4.34198i) q^{37} -5.67588 q^{38} +(-3.44722 + 1.05674i) q^{39} +1.61321i q^{40} +(1.69965 - 6.34318i) q^{41} +(2.30823 - 1.29308i) q^{42} +(-1.12959 - 0.652168i) q^{43} +(-0.890197 + 0.890197i) q^{44} +(1.55824 - 0.417530i) q^{45} +(2.56977 - 0.688566i) q^{46} +(-0.433654 + 0.433654i) q^{47} +(0.866025 + 0.500000i) q^{48} +(6.15082 - 3.34176i) q^{49} +(0.620531 - 2.31585i) q^{50} -0.676826i q^{51} +(-2.63877 - 2.45701i) q^{52} -4.52858 q^{53} +(0.258819 - 0.965926i) q^{54} +(-1.75883 + 1.01546i) q^{55} +(2.27396 + 1.35245i) q^{56} +(-4.01345 + 4.01345i) q^{57} +(0.995188 + 3.71409i) q^{58} +(1.06551 + 3.97652i) q^{59} +(1.14071 + 1.14071i) q^{60} +(2.66960 + 1.54130i) q^{61} +(-0.357560 - 0.619313i) q^{62} +(0.717822 - 2.54651i) q^{63} +1.00000i q^{64} +(-3.08597 - 4.93038i) q^{65} +1.25893i q^{66} +(-13.6367 - 3.65393i) q^{67} +(0.586148 - 0.338413i) q^{68} +(1.33021 - 2.30399i) q^{69} +(2.97869 + 3.05689i) q^{70} +(-2.97844 - 11.1157i) q^{71} +(0.965926 - 0.258819i) q^{72} +(0.598200 - 0.598200i) q^{73} +(-2.24758 + 3.89292i) q^{74} +(-1.19877 - 2.07634i) q^{75} +(-5.48248 - 1.46903i) q^{76} +(-0.0431523 + 3.33053i) q^{77} +(-3.60326 + 0.128526i) q^{78} -9.59048 q^{79} +(-0.417530 + 1.55824i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.28347 - 5.68714i) q^{82} +(0.963254 + 0.963254i) q^{83} +(2.56426 - 0.651604i) q^{84} +(1.05466 - 0.282595i) q^{85} +(-0.922305 - 0.922305i) q^{86} +(3.32997 + 1.92256i) q^{87} +(-1.09026 + 0.629465i) q^{88} +(8.80699 + 2.35983i) q^{89} +1.61321 q^{90} +(-9.53693 + 0.216510i) q^{91} +2.66042 q^{92} +(-0.690754 - 0.185087i) q^{93} +(-0.531116 + 0.306640i) q^{94} +(-7.92967 - 4.57820i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-13.9265 + 3.73159i) q^{97} +(6.80615 - 1.63594i) q^{98} +(0.890197 + 0.890197i) 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
$5$	1.14071	+	1.14071i	0.510142	+	0.510142i	0.914570	−	0.404428i	$-0.132529\pi$
$5$	1.14071	+	1.14071i	0.510142	+	0.510142i	−0.404428	+	0.914570i	$0.632529\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	2.56426	−	0.651604i	0.969198	−	0.246283i
$7$	2.56426	−	0.651604i	0.969198	−	0.246283i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.806606	+	1.39708i	0.255071	+	0.441796i
$11$	−0.325835	+	1.21603i	−0.0982429	+	0.366648i	−0.997491	−	0.0707911i	$-0.977448\pi$
$11$	−0.325835	+	1.21603i	−0.0982429	+	0.366648i	0.899248	+	0.437439i	$0.144114\pi$
$12$	1.00000			0.288675
$13$	−3.51375	−	0.808446i	−0.974538	−	0.224223i
$13$	−3.51375	−	0.808446i	−0.974538	−	0.224223i
$14$	2.64553	+	0.0342770i	0.707047	+	0.00916091i
$15$	1.55824	+	0.417530i	0.402337	+	0.107806i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.338413	−	0.586148i	0.0820772	−	0.142162i	−0.822065	−	0.569394i	$-0.807178\pi$
$17$	0.338413	−	0.586148i	0.0820772	−	0.142162i	0.904142	+	0.427232i	$0.140511\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−5.48248	+	1.46903i	−1.25777	+	0.337018i	−0.825332	−	0.564647i	$-0.809012\pi$
$19$	−5.48248	+	1.46903i	−1.25777	+	0.337018i	−0.432435	+	0.901665i	$0.642345\pi$
$20$	0.417530	+	1.55824i	0.0933625	+	0.348434i
$21$	1.89491	−	1.84643i	0.413503	−	0.402925i
$22$	−0.629465	+	1.09026i	−0.134202	+	0.232445i
$23$	2.30399	−	1.33021i	0.480415	−	0.277368i	−0.240175	−	0.970730i	$-0.577205\pi$
$23$	2.30399	−	1.33021i	0.480415	−	0.277368i	0.720589	+	0.693362i	$0.243871\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$		−	2.39755i		−	0.479510i
$26$	−3.18478	−	1.69032i	−0.624586	−	0.331500i
$27$		−	1.00000i		−	0.192450i
$28$	2.54651	+	0.717822i	0.481246	+	0.135656i
$29$	1.92256	+	3.32997i	0.357010	+	0.618359i	0.987460	−	0.157871i	$-0.0504630\pi$
$29$	1.92256	+	3.32997i	0.357010	+	0.618359i	−0.630450	+	0.776230i	$0.717130\pi$
$30$	1.39708	+	0.806606i	0.255071	+	0.147265i
$31$	−0.505667	−	0.505667i	−0.0908204	−	0.0908204i	0.660237	−	0.751057i	$-0.270456\pi$
$31$	−0.505667	−	0.505667i	−0.0908204	−	0.0908204i	−0.751057	+	0.660237i	$0.770456\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.325835	+	1.21603i	0.0567206	+	0.211684i
$34$	0.478588	−	0.478588i	0.0820772	−	0.0820772i
$35$	3.66837	+	2.18179i	0.620068	+	0.368789i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−1.16343	+	4.34198i	−0.191267	+	0.713818i	0.801935	+	0.597411i	$0.203804\pi$
$37$	−1.16343	+	4.34198i	−0.191267	+	0.713818i	−0.993202	+	0.116406i	$0.962863\pi$
$38$	−5.67588			−0.920749
$39$	−3.44722	+	1.05674i	−0.551996	+	0.169214i
$40$			1.61321i			0.255071i
$41$	1.69965	−	6.34318i	0.265441	−	0.990639i	−0.696539	−	0.717519i	$-0.745278\pi$
$41$	1.69965	−	6.34318i	0.265441	−	0.990639i	0.961980	−	0.273120i	$-0.0880556\pi$
$42$	2.30823	−	1.29308i	0.356168	−	0.199527i
$43$	−1.12959	−	0.652168i	−0.172261	−	0.0994547i	0.411391	−	0.911459i	$-0.365043\pi$
$43$	−1.12959	−	0.652168i	−0.172261	−	0.0994547i	−0.583651	+	0.812004i	$0.698376\pi$
$44$	−0.890197	+	0.890197i	−0.134202	+	0.134202i
$45$	1.55824	−	0.417530i	0.232289	−	0.0622417i
$46$	2.56977	−	0.688566i	0.378891	−	0.101524i
$47$	−0.433654	+	0.433654i	−0.0632549	+	0.0632549i	−0.738027	−	0.674772i	$-0.764242\pi$
$47$	−0.433654	+	0.433654i	−0.0632549	+	0.0632549i	0.674772	+	0.738027i	$0.264242\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	6.15082	−	3.34176i	0.878689	−	0.477394i
$50$	0.620531	−	2.31585i	0.0877564	−	0.327511i
$51$		−	0.676826i		−	0.0947746i
$52$	−2.63877	−	2.45701i	−0.365932	−	0.340726i
$53$	−4.52858			−0.622048			−0.311024	−	0.950402i	$-0.600672\pi$
$53$	−4.52858			−0.622048			−0.311024	+	0.950402i	$0.600672\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−1.75883	+	1.01546i	−0.237160	+	0.136925i
$56$	2.27396	+	1.35245i	0.303870	+	0.180729i
$57$	−4.01345	+	4.01345i	−0.531595	+	0.531595i
$58$	0.995188	+	3.71409i	0.130675	+	0.487684i
$59$	1.06551	+	3.97652i	0.138717	+	0.517699i	0.999955	+	0.00949697i	$0.00302302\pi$
$59$	1.06551	+	3.97652i	0.138717	+	0.517699i	−0.861238	+	0.508202i	$0.830310\pi$
$60$	1.14071	+	1.14071i	0.147265	+	0.147265i
$61$	2.66960	+	1.54130i	0.341808	+	0.197343i	0.661071	−	0.750323i	$-0.270102\pi$
$61$	2.66960	+	1.54130i	0.341808	+	0.197343i	−0.319263	+	0.947666i	$0.603435\pi$
$62$	−0.357560	−	0.619313i	−0.0454102	−	0.0786528i
$63$	0.717822	−	2.54651i	0.0904371	−	0.320831i
$64$			1.00000i			0.125000i
$65$	−3.08597	−	4.93038i	−0.382768	−	0.611538i
$66$			1.25893i			0.154963i
$67$	−13.6367	−	3.65393i	−1.66598	−	0.446399i	−0.701959	−	0.712217i	$-0.747691\pi$
$67$	−13.6367	−	3.65393i	−1.66598	−	0.446399i	−0.964023	+	0.265818i	$0.914358\pi$
$68$	0.586148	−	0.338413i	0.0710809	−	0.0410386i
$69$	1.33021	−	2.30399i	0.160138	−	0.277368i
$70$	2.97869	+	3.05689i	0.356021	+	0.365368i
$71$	−2.97844	−	11.1157i	−0.353475	−	1.31919i	−0.882392	−	0.470515i	$-0.844068\pi$
$71$	−2.97844	−	11.1157i	−0.353475	−	1.31919i	0.528917	−	0.848674i	$-0.322598\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	0.598200	−	0.598200i	0.0700140	−	0.0700140i	−0.671233	−	0.741247i	$-0.734235\pi$
$73$	0.598200	−	0.598200i	0.0700140	−	0.0700140i	0.741247	+	0.671233i	$0.234235\pi$
$74$	−2.24758	+	3.89292i	−0.261275	+	0.452542i
$75$	−1.19877	−	2.07634i	−0.138423	−	0.239755i
$76$	−5.48248	−	1.46903i	−0.628884	−	0.168509i
$77$	−0.0431523	+	3.33053i	−0.00491766	+	0.379550i
$78$	−3.60326	+	0.128526i	−0.407989	+	0.0145527i
$79$	−9.59048			−1.07901			−0.539507	−	0.841981i	$-0.681389\pi$
$79$	−9.59048			−1.07901			−0.539507	+	0.841981i	$0.681389\pi$
$80$	−0.417530	+	1.55824i	−0.0466813	+	0.174217i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.28347	−	5.68714i	0.362599	−	0.628040i
$83$	0.963254	+	0.963254i	0.105731	+	0.105731i	0.757993	−	0.652262i	$-0.226180\pi$
$83$	0.963254	+	0.963254i	0.105731	+	0.105731i	−0.652262	+	0.757993i	$0.726180\pi$
$84$	2.56426	−	0.651604i	0.279783	−	0.0710959i
$85$	1.05466	−	0.282595i	0.114394	−	0.0306517i
$86$	−0.922305	−	0.922305i	−0.0994547	−	0.0994547i
$87$	3.32997	+	1.92256i	0.357010	+	0.206120i
$88$	−1.09026	+	0.629465i	−0.116223	+	0.0671012i
$89$	8.80699	+	2.35983i	0.933539	+	0.250141i	0.693363	−	0.720588i	$-0.256128\pi$
$89$	8.80699	+	2.35983i	0.933539	+	0.250141i	0.240176	+	0.970729i	$0.422795\pi$
$90$	1.61321			0.170047
$91$	−9.53693	+	0.216510i	−0.999742	+	0.0226964i
$92$	2.66042			0.277368
$93$	−0.690754	−	0.185087i	−0.0716278	−	0.0191926i
$94$	−0.531116	+	0.306640i	−0.0547804	+	0.0316275i
$95$	−7.92967	−	4.57820i	−0.813567	−	0.469713i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−13.9265	+	3.73159i	−1.41402	+	0.378885i	−0.883358	−	0.468698i	$-0.844723\pi$
$97$	−13.9265	+	3.73159i	−1.41402	+	0.378885i	−0.530662	+	0.847584i	$0.678056\pi$
$98$	6.80615	−	1.63594i	0.687525	−	0.165255i
$99$	0.890197	+	0.890197i	0.0894682	+	0.0894682i
$100$	1.19877	−	2.07634i	0.119877	−	0.207634i
$101$	4.47828	+	7.75660i	0.445605	+	0.771811i	0.998094	−	0.0617093i	$-0.0196552\pi$
$101$	4.47828	+	7.75660i	0.445605	+	0.771811i	−0.552489	+	0.833520i	$0.686322\pi$
$102$	0.175175	−	0.653764i	0.0173450	−	0.0647322i
$103$	−2.91347			−0.287072			−0.143536	−	0.989645i	$-0.545847\pi$
$103$	−2.91347			−0.287072			−0.143536	+	0.989645i	$0.545847\pi$
$104$	−1.91294	−	3.05625i	−0.187579	−	0.299690i
$105$	4.26780	+	0.0552961i	0.416495	+	0.00539634i
$106$	−4.37427	−	1.17208i	−0.424867	−	0.113843i
$107$	1.11825	+	1.93687i	0.108106	+	0.187245i	0.915003	−	0.403447i	$-0.132188\pi$
$107$	1.11825	+	1.93687i	0.108106	+	0.187245i	−0.806897	+	0.590692i	$0.798855\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−8.57616	+	8.57616i	−0.821447	+	0.821447i	−0.986316	−	0.164868i	$-0.947280\pi$
$109$	−8.57616	+	8.57616i	−0.821447	+	0.821447i	0.164868	+	0.986316i	$0.447280\pi$
$110$	−1.96172	+	0.525641i	−0.187042	+	0.0501179i
$111$	1.16343	+	4.34198i	0.110428	+	0.412123i
$112$	1.84643	+	1.89491i	0.174472	+	0.179052i
$113$	1.10711	−	1.91757i	0.104148	−	0.180389i	−0.809242	−	0.587476i	$-0.800122\pi$
$113$	1.10711	−	1.91757i	0.104148	−	0.180389i	0.913390	+	0.407086i	$0.133455\pi$
$114$	−4.91546	+	2.83794i	−0.460375	+	0.265797i
$115$	4.14558	+	1.11080i	0.386577	+	0.103583i
$116$			3.84511i			0.357010i
$117$	−2.45701	+	2.63877i	−0.227150	+	0.243954i
$118$			4.11680i			0.378982i
$119$	0.485841	−	1.72355i	0.0445369	−	0.157997i
$120$	0.806606	+	1.39708i	0.0736327	+	0.127536i
$121$	8.15371	+	4.70755i	0.741247	+	0.427959i
$122$	2.17972	+	2.17972i	0.197343	+	0.197343i
$123$	−1.69965	−	6.34318i	−0.153252	−	0.571945i
$124$	−0.185087	−	0.690754i	−0.0166213	−	0.0620315i
$125$	8.43848	−	8.43848i	0.754760	−	0.754760i
$126$	1.35245	−	2.27396i	0.120486	−	0.202580i
$127$	3.80920	−	2.19924i	0.338012	−	0.195151i	−0.321381	−	0.946950i	$-0.604147\pi$
$127$	3.80920	−	2.19924i	0.338012	−	0.195151i	0.659392	+	0.751799i	$0.270814\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−1.30434			−0.114840
$130$	−1.70474	−	5.56109i	−0.149516	−	0.487740i
$131$		−	5.76533i		−	0.503719i	−0.967764	−	0.251860i	$-0.918958\pi$
$131$		−	5.76533i		−	0.503719i	0.967764	−	0.251860i	$-0.0810421\pi$
$132$	−0.325835	+	1.21603i	−0.0283603	+	0.105842i
$133$	−13.1013	+	7.33937i	−1.13602	+	0.636404i
$134$	−12.2263	−	7.05885i	−1.05619	−	0.609792i
$135$	1.14071	−	1.14071i	0.0981769	−	0.0981769i
$136$	0.653764	−	0.175175i	0.0560598	−	0.0150212i
$137$	−11.1130	+	2.97771i	−0.949445	+	0.254403i	−0.700127	−	0.714019i	$-0.746873\pi$
$137$	−11.1130	+	2.97771i	−0.949445	+	0.254403i	−0.249318	+	0.968422i	$0.580206\pi$
$138$	1.88120	−	1.88120i	0.160138	−	0.160138i
$139$	−0.570520	−	0.329390i	−0.0483909	−	0.0279385i	0.475609	−	0.879657i	$-0.342228\pi$
$139$	−0.570520	−	0.329390i	−0.0483909	−	0.0279385i	−0.524000	+	0.851718i	$0.675561\pi$
$140$	2.08601	+	3.72367i	0.176300	+	0.314708i
$141$	−0.158728	+	0.592382i	−0.0133673	+	0.0498876i
$142$		−	11.5078i		−	0.965713i
$143$	2.12800	−	4.00941i	0.177952	−	0.335284i
$144$	1.00000			0.0833333
$145$	−1.60545	+	5.99162i	−0.133325	+	0.497577i
$146$	0.732642	−	0.422991i	0.0606339	−	0.0350070i
$147$	3.65589	−	5.96946i	0.301533	−	0.492353i
$148$	−3.17855	+	3.17855i	−0.261275	+	0.261275i
$149$	5.09002	+	18.9962i	0.416991	+	1.55623i	0.780814	+	0.624763i	$0.214804\pi$
$149$	5.09002	+	18.9962i	0.416991	+	1.55623i	−0.363824	+	0.931468i	$0.618529\pi$
$150$	−0.620531	−	2.31585i	−0.0506662	−	0.189089i
$151$	−12.4806	−	12.4806i	−1.01566	−	1.01566i	−0.999875	−	0.0157803i	$-0.994977\pi$
$151$	−12.4806	−	12.4806i	−1.01566	−	1.01566i	−0.0157803	−	0.999875i	$-0.505023\pi$
$152$	−4.91546	−	2.83794i	−0.398696	−	0.230187i
$153$	−0.338413	−	0.586148i	−0.0273591	−	0.0473873i
$154$	−0.903688	+	3.20588i	−0.0728212	+	0.258337i
$155$		−	1.15364i		−	0.0926627i
$156$	−3.51375	−	0.808446i	−0.281325	−	0.0647275i
$157$		−	18.7135i		−	1.49350i	−0.665107	−	0.746748i	$-0.731614\pi$
$157$		−	18.7135i		−	1.49350i	0.665107	−	0.746748i	$-0.268386\pi$
$158$	−9.26369	−	2.48220i	−0.736980	−	0.197473i
$159$	−3.92187	+	2.26429i	−0.311024	+	0.179570i
$160$	−0.806606	+	1.39708i	−0.0637678	+	0.110449i
$161$	5.04125	−	4.91228i	0.397306	−	0.387142i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	6.40360	−	1.71584i	0.501568	−	0.134395i	0.000840552	−	1.00000i	$-0.499732\pi$
$163$	6.40360	−	1.71584i	0.501568	−	0.134395i	0.500728	+	0.865605i	$0.333066\pi$
$164$	4.64353	−	4.64353i	0.362599	−	0.362599i
$165$	−1.01546	+	1.75883i	−0.0790534	+	0.136925i
$166$	0.681123	+	1.17974i	0.0528654	+	0.0915656i
$167$	20.4602	+	5.48230i	1.58326	+	0.424233i	0.939933	−	0.341359i	$-0.110887\pi$
$167$	20.4602	+	5.48230i	1.58326	+	0.424233i	0.643326	+	0.765592i	$0.277554\pi$
$168$	2.64553	+	0.0342770i	0.204107	+	0.00264453i
$169$	11.6928	+	5.68135i	0.899448	+	0.437027i
$170$	1.09186			0.0837421
$171$	−1.46903	+	5.48248i	−0.112339	+	0.419256i
$172$	−0.652168	−	1.12959i	−0.0497273	−	0.0861303i
$173$	7.82956	−	13.5612i	0.595270	−	1.03104i	−0.398238	−	0.917282i	$-0.630378\pi$
$173$	7.82956	−	13.5612i	0.595270	−	1.03104i	0.993509	−	0.113756i	$-0.0362884\pi$
$174$	2.71891	+	2.71891i	0.206120	+	0.206120i
$175$	−1.56225	−	6.14793i	−0.118095	−	0.464740i
$176$	−1.21603	+	0.325835i	−0.0916619	+	0.0245607i
$177$	2.91102	+	2.91102i	0.218805	+	0.218805i
$178$	7.89613	+	4.55883i	0.591840	+	0.341699i
$179$	−10.7044	+	6.18019i	−0.800085	+	0.461929i	−0.843501	−	0.537128i	$-0.819509\pi$
$179$	−10.7044	+	6.18019i	−0.800085	+	0.461929i	0.0434159	+	0.999057i	$0.486176\pi$
$180$	1.55824	+	0.417530i	0.116145	+	0.0311208i
$181$	−10.0595			−0.747718			−0.373859	−	0.927486i	$-0.621966\pi$
$181$	−10.0595			−0.747718			−0.373859	+	0.927486i	$0.621966\pi$
$182$	−9.26801	−	2.25921i	−0.686990	−	0.167464i
$183$	3.08259			0.227872
$184$	2.56977	+	0.688566i	0.189446	+	0.0507618i
$185$	−6.28010	+	3.62582i	−0.461722	+	0.266575i
$186$	−0.619313	−	0.357560i	−0.0454102	−	0.0262176i
$187$	0.602509	+	0.602509i	0.0440598	+	0.0440598i
$188$	−0.592382	+	0.158728i	−0.0432039	+	0.0115765i
$189$	−0.651604	−	2.56426i	−0.0473972	−	0.186522i
$190$	−6.47455	−	6.47455i	−0.469713	−	0.469713i
$191$	9.75519	−	16.8965i	0.705861	−	1.22259i	−0.260519	−	0.965469i	$-0.583894\pi$
$191$	9.75519	−	16.8965i	0.705861	−	1.22259i	0.966380	−	0.257118i	$-0.0827729\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−3.64787	+	13.6140i	−0.262579	+	0.979959i	0.701136	+	0.713027i	$0.252676\pi$
$193$	−3.64787	+	13.6140i	−0.262579	+	0.979959i	−0.963715	+	0.266932i	$0.913990\pi$
$194$	−14.4178			−1.03513
$195$	−5.13772	−	2.72685i	−0.367920	−	0.195274i
$196$	6.99765	+	0.181362i	0.499832	+	0.0129544i
$197$	20.8117	+	5.57649i	1.48277	+	0.397308i	0.907290	−	0.420505i	$-0.138147\pi$
$197$	20.8117	+	5.57649i	1.48277	+	0.397308i	0.575484	+	0.817813i	$0.304814\pi$
$198$	0.629465	+	1.09026i	0.0447341	+	0.0774817i
$199$	6.03194	−	10.4476i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$199$	6.03194	−	10.4476i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$200$	1.69532	−	1.69532i	0.119877	−	0.119877i
$201$	−13.6367	+	3.65393i	−0.961855	+	0.257728i
$202$	2.31813	+	8.65137i	0.163103	+	0.608708i
$203$	7.09975	+	7.28614i	0.498305	+	0.511387i
$204$	0.338413	−	0.586148i	0.0236936	−	0.0410386i
$205$	9.17456	−	5.29694i	0.640779	−	0.369954i
$206$	−2.81419	−	0.754060i	−0.196074	−	0.0525379i
$207$		−	2.66042i		−	0.184912i
$208$	−1.05674	−	3.44722i	−0.0732716	−	0.239021i
$209$		−	7.14553i		−	0.494267i
$210$	4.10807	+	1.15800i	0.283483	+	0.0799096i
$211$	1.74542	+	3.02315i	0.120160	+	0.208122i	0.919830	−	0.392316i	$-0.128326\pi$
$211$	1.74542	+	3.02315i	0.120160	+	0.208122i	−0.799671	+	0.600439i	$0.794993\pi$
$212$	−3.92187	−	2.26429i	−0.269355	−	0.155512i
$213$	−8.13724	−	8.13724i	−0.557555	−	0.557555i
$214$	0.578851	+	2.16030i	0.0395694	+	0.147675i
$215$	−0.544599	−	2.03247i	−0.0371414	−	0.138613i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−1.62615	−	0.967165i	−0.110391	−	0.0656554i
$218$	−10.5036	+	6.06426i	−0.711394	+	0.410724i
$219$	0.218956	−	0.817156i	0.0147957	−	0.0552183i
$220$	−2.03092			−0.136925
$221$	−1.66297	+	1.78599i	−0.111863	+	0.120139i
$222$			4.49515i			0.301695i
$223$	−7.49967	+	27.9892i	−0.502215	+	1.87429i	−0.0170782	+	0.999854i	$0.505436\pi$
$223$	−7.49967	+	27.9892i	−0.502215	+	1.87429i	−0.485137	+	0.874438i	$0.661230\pi$
$224$	1.29308	+	2.30823i	0.0863975	+	0.154225i
$225$	−2.07634	−	1.19877i	−0.138423	−	0.0799183i
$226$	1.56569	−	1.56569i	0.104148	−	0.104148i
$227$	−12.1746	+	3.26218i	−0.808058	+	0.216518i	−0.639119	−	0.769108i	$-0.720701\pi$
$227$	−12.1746	+	3.26218i	−0.808058	+	0.216518i	−0.168939	+	0.985626i	$0.554034\pi$
$228$	−5.48248	+	1.46903i	−0.363086	+	0.0972886i
$229$	18.2974	−	18.2974i	1.20912	−	1.20912i	0.237812	−	0.971311i	$-0.423570\pi$
$229$	18.2974	−	18.2974i	1.20912	−	1.20912i	0.971311	−	0.237812i	$-0.0764303\pi$
$230$	3.71682	+	2.14591i	0.245080	+	0.141497i
$231$	1.62790	+	2.90590i	0.107108	+	0.191194i
$232$	−0.995188	+	3.71409i	−0.0653373	+	0.243842i
$233$			4.11691i			0.269708i	0.990866	+	0.134854i	$0.0430565\pi$
$233$			4.11691i			0.269708i	−0.990866	+	0.134854i	$0.956944\pi$
$234$	−3.05625	+	1.91294i	−0.199793	+	0.125053i
$235$	−0.989349			−0.0645380
$236$	−1.06551	+	3.97652i	−0.0693585	+	0.258850i
$237$	−8.30560	+	4.79524i	−0.539507	+	0.311484i
$238$	0.915373	−	1.53907i	0.0593348	−	0.0997633i
$239$	0.430732	−	0.430732i	0.0278617	−	0.0278617i	−0.693039	−	0.720900i	$-0.743729\pi$
$239$	0.430732	−	0.430732i	0.0278617	−	0.0278617i	0.720900	+	0.693039i	$0.243729\pi$
$240$	0.417530	+	1.55824i	0.0269514	+	0.100584i
$241$	4.25787	+	15.8906i	0.274273	+	1.02360i	0.956327	+	0.292300i	$0.0944205\pi$
$241$	4.25787	+	15.8906i	0.274273	+	1.02360i	−0.682053	+	0.731302i	$0.738913\pi$
$242$	6.65748	+	6.65748i	0.427959	+	0.427959i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.54130	+	2.66960i	0.0986713	+	0.170904i
$245$	10.8283	+	3.20433i	0.691796	+	0.204717i
$246$		−	6.56695i		−	0.418693i
$247$	20.4517	−	0.729497i	1.30131	−	0.0464168i
$248$		−	0.715121i		−	0.0454102i
$249$	1.31583	+	0.352575i	0.0833873	+	0.0223435i
$250$	10.3350	−	5.96691i	0.653642	−	0.377380i
$251$	9.83489	−	17.0345i	0.620773	−	1.07521i	−0.368570	−	0.929600i	$-0.620152\pi$
$251$	9.83489	−	17.0345i	0.620773	−	1.07521i	0.989342	−	0.145609i	$-0.0465143\pi$
$252$	1.89491	−	1.84643i	0.119368	−	0.116314i
$253$	0.866857	+	3.23515i	0.0544988	+	0.203392i
$254$	4.24861	−	1.13841i	0.266581	−	0.0714303i
$255$	0.772064	−	0.772064i	0.0483485	−	0.0483485i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.3076	+	24.7815i	0.892483	+	1.54583i	0.836890	+	0.547372i	$0.184372\pi$
$257$	14.3076	+	24.7815i	0.892483	+	1.54583i	0.0555928	+	0.998454i	$0.482295\pi$
$258$	−1.25989	−	0.337587i	−0.0784374	−	0.0210172i
$259$	−0.154080	+	11.8921i	−0.00957408	+	0.738936i
$260$	−0.207339	−	5.81282i	−0.0128586	−	0.360496i
$261$	3.84511			0.238006
$262$	1.49218	−	5.56888i	0.0921870	−	0.344047i
$263$	−8.48891	−	14.7032i	−0.523449	−	0.906639i	−0.999628	−	0.0272911i	$-0.991312\pi$
$263$	−8.48891	−	14.7032i	−0.523449	−	0.906639i	0.476179	−	0.879348i	$-0.342021\pi$
$264$	−0.629465	+	1.09026i	−0.0387409	+	0.0671012i
$265$	−5.16581	−	5.16581i	−0.317333	−	0.317333i
$266$	−14.5544	+	3.69843i	−0.892388	+	0.226765i
$267$	8.80699	−	2.35983i	0.538979	−	0.144419i
$268$	−9.98272	−	9.98272i	−0.609792	−	0.609792i
$269$	0.379010	+	0.218822i	0.0231087	+	0.0133418i	0.511510	−	0.859277i	$-0.329086\pi$
$269$	0.379010	+	0.218822i	0.0231087	+	0.0133418i	−0.488401	+	0.872619i	$0.662420\pi$
$270$	1.39708	−	0.806606i	0.0850237	−	0.0490885i
$271$	29.7621	+	7.97473i	1.80792	+	0.484430i	0.995168	−	0.0981826i	$-0.0313029\pi$
$271$	29.7621	+	7.97473i	1.80792	+	0.484430i	0.812750	+	0.582613i	$0.197970\pi$
$272$	0.676826			0.0410386
$273$	−8.15097	+	4.95597i	−0.493319	+	0.299949i
$274$	−11.5050			−0.695042
$275$	2.91550	+	0.781205i	0.175811	+	0.0471084i
$276$	2.30399	−	1.33021i	0.138684	−	0.0800691i
$277$	−0.253608	−	0.146421i	−0.0152378	−	0.00879757i	0.492362	−	0.870391i	$-0.336134\pi$
$277$	−0.253608	−	0.146421i	−0.0152378	−	0.00879757i	−0.507600	+	0.861593i	$0.669467\pi$
$278$	−0.465828	−	0.465828i	−0.0279385	−	0.0279385i
$279$	−0.690754	+	0.185087i	−0.0413543	+	0.0110809i
$280$	1.05118	+	4.13669i	0.0628198	+	0.247214i
$281$	16.3447	+	16.3447i	0.975043	+	0.975043i	0.999696	−	0.0246533i	$-0.00784818\pi$
$281$	16.3447	+	16.3447i	0.975043	+	0.975043i	−0.0246533	+	0.999696i	$0.507848\pi$
$282$	−0.306640	+	0.531116i	−0.0182601	+	0.0316275i
$283$	−4.29246	−	7.43476i	−0.255160	−	0.441950i	0.709779	−	0.704425i	$-0.248795\pi$
$283$	−4.29246	−	7.43476i	−0.255160	−	0.441950i	−0.964939	+	0.262474i	$0.915462\pi$
$284$	2.97844	−	11.1157i	0.176738	−	0.659594i
$285$	−9.15640			−0.542378
$286$	3.09320	−	3.32203i	0.182905	−	0.196436i
$287$	0.225095	−	17.3730i	0.0132869	−	1.02550i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	8.27095	+	14.3257i	0.486527	+	0.842689i
$290$	−3.10149	+	5.37194i	−0.182126	+	0.315451i
$291$	−10.1949	+	10.1949i	−0.597635	+	0.597635i
$292$	0.817156	−	0.218956i	0.0478205	−	0.0128135i
$293$	7.75194	+	28.9306i	0.452873	+	1.69015i	0.694266	+	0.719718i	$0.255729\pi$
$293$	7.75194	+	28.9306i	0.452873	+	1.69015i	−0.241393	+	0.970427i	$0.577604\pi$
$294$	5.07633	−	4.81984i	0.296057	−	0.281099i
$295$	−3.32063	+	5.75151i	−0.193335	+	0.334866i
$296$	−3.89292	+	2.24758i	−0.226271	+	0.130638i
$297$	1.21603	+	0.325835i	0.0705614	+	0.0189069i
$298$			19.6663i			1.13924i
$299$	−9.17103	+	2.81136i	−0.530375	+	0.162585i
$300$		−	2.39755i		−	0.138423i
$301$	−3.32151	−	0.936282i	−0.191449	−	0.0539664i
$302$	−8.82511	−	15.2855i	−0.507828	−	0.879584i
$303$	7.75660	+	4.47828i	0.445605	+	0.257270i
$304$	−4.01345	−	4.01345i	−0.230187	−	0.230187i
$305$	1.28707	+	4.80343i	0.0736977	+	0.275043i
$306$	−0.175175	−	0.653764i	−0.0100141	−	0.0373732i
$307$	5.90984	−	5.90984i	0.337292	−	0.337292i	−0.518055	−	0.855347i	$-0.673344\pi$
$307$	5.90984	−	5.90984i	0.337292	−	0.337292i	0.855347	+	0.518055i	$0.173344\pi$
$308$	−1.70264	+	2.86275i	−0.0970168	+	0.163120i
$309$	−2.52314	+	1.45673i	−0.143536	+	0.0828706i
$310$	0.298584	−	1.11433i	0.0169585	−	0.0632898i
$311$	−29.9039			−1.69569			−0.847847	−	0.530241i	$-0.822101\pi$
$311$	−29.9039			−1.69569			−0.847847	+	0.530241i	$0.822101\pi$
$312$	−3.18478	−	1.69032i	−0.180303	−	0.0956957i
$313$		−	10.0266i		−	0.566736i	−0.959011	−	0.283368i	$-0.908548\pi$
$313$		−	10.0266i		−	0.566736i	0.959011	−	0.283368i	$-0.0914517\pi$
$314$	4.84340	−	18.0758i	0.273329	−	1.02008i
$315$	3.72367	−	2.08601i	0.209805	−	0.117533i
$316$	−8.30560	−	4.79524i	−0.467227	−	0.269753i
$317$	15.4584	−	15.4584i	0.868229	−	0.868229i	−0.124048	−	0.992276i	$-0.539588\pi$
$317$	15.4584	−	15.4584i	0.868229	−	0.868229i	0.992276	+	0.124048i	$0.0395875\pi$
$318$	−4.37427	+	1.17208i	−0.245297	+	0.0657272i
$319$	−4.67578	+	1.25287i	−0.261793	+	0.0701473i
$320$	−1.14071	+	1.14071i	−0.0637678	+	0.0637678i
$321$	1.93687	+	1.11825i	0.108106	+	0.0624149i
$322$	6.14086	−	3.44013i	0.342217	−	0.191711i
$323$	−0.994275	+	3.71068i	−0.0553229	+	0.206468i
$324$		−	1.00000i		−	0.0555556i
$325$	−1.93829	+	8.42438i	−0.107517	+	0.467300i
$326$	6.62949			0.367173
$327$	−3.13909	+	11.7153i	−0.173592	+	0.647855i
$328$	5.68714	−	3.28347i	0.314020	−	0.181299i
$329$	−0.829429	+	1.39457i	−0.0457279	+	0.0768852i
$330$	−1.43608	+	1.43608i	−0.0790534	+	0.0790534i
$331$	0.659555	+	2.46149i	0.0362524	+	0.135296i	0.981680	−	0.190536i	$-0.0610225\pi$
$331$	0.659555	+	2.46149i	0.0362524	+	0.135296i	−0.945428	+	0.325831i	$0.894356\pi$
$332$	0.352575	+	1.31583i	0.0193501	+	0.0722155i
$333$	3.17855	+	3.17855i	0.174184	+	0.174184i
$334$	18.3441	+	10.5910i	1.00375	+	0.579513i
$335$	−11.3874	−	19.7236i	−0.622161	−	1.07762i
$336$	2.54651	+	0.717822i	0.138924	+	0.0391604i
$337$		−	10.4586i		−	0.569715i	−0.958570	−	0.284858i	$-0.908054\pi$
$337$		−	10.4586i		−	0.569715i	0.958570	−	0.284858i	$-0.0919463\pi$
$338$	9.82397	+	8.51409i	0.534353	+	0.463105i
$339$		−	2.21422i		−	0.120260i
$340$	1.05466	+	0.282595i	0.0571969	+	0.0153259i
$341$	0.779671	−	0.450143i	0.0422216	−	0.0243766i
$342$	−2.83794	+	4.91546i	−0.153458	+	0.265797i
$343$	13.5948	−	12.5770i	0.734049	−	0.679096i
$344$	−0.337587	−	1.25989i	−0.0182015	−	0.0679288i
$345$	4.14558	−	1.11080i	0.223190	−	0.0598036i
$346$	11.0727	−	11.0727i	0.595270	−	0.595270i
$347$	3.47714	−	6.02258i	0.186663	−	0.323309i	−0.757473	−	0.652867i	$-0.773566\pi$
$347$	3.47714	−	6.02258i	0.186663	−	0.323309i	0.944136	+	0.329557i	$0.106900\pi$
$348$	1.92256	+	3.32997i	0.103060	+	0.178505i
$349$	11.5437	+	3.09314i	0.617922	+	0.165572i	0.554183	−	0.832395i	$-0.313031\pi$
$349$	11.5437	+	3.09314i	0.617922	+	0.165572i	0.0637391	+	0.997967i	$0.479697\pi$
$350$	0.0821808	−	6.34278i	0.00439275	−	0.339036i
$351$	−0.808446	+	3.51375i	−0.0431517	+	0.187550i
$352$	−1.25893			−0.0671012
$353$	−9.34528	+	34.8771i	−0.497399	+	1.85632i	0.0187575	+	0.999824i	$0.494029\pi$
$353$	−9.34528	+	34.8771i	−0.497399	+	1.85632i	−0.516157	+	0.856494i	$0.672638\pi$
$354$	2.05840	+	3.56525i	0.109403	+	0.189491i
$355$	9.28226	−	16.0773i	0.492651	−	0.853297i
$356$	6.44716	+	6.44716i	0.341699	+	0.341699i
$357$	−0.441023	−	1.73556i	−0.0233414	−	0.0918553i
$358$	−11.9392	+	3.19910i	−0.631007	+	0.169078i
$359$	17.2168	+	17.2168i	0.908668	+	0.908668i	0.996165	−	0.0874967i	$-0.0278867\pi$
$359$	17.2168	+	17.2168i	0.908668	+	0.908668i	−0.0874967	+	0.996165i	$0.527887\pi$
$360$	1.39708	+	0.806606i	0.0736327	+	0.0425119i
$361$	11.4451	−	6.60781i	0.602372	−	0.347780i
$362$	−9.71674	−	2.60359i	−0.510701	−	0.136842i
$363$	9.41510			0.494164
$364$	−8.36748	−	4.58096i	−0.438575	−	0.240108i
$365$	1.36475			0.0714342
$366$	2.97755	+	0.797833i	0.155639	+	0.0417034i
$367$	21.1130	−	12.1896i	1.10209	−	0.636291i	0.165319	−	0.986240i	$-0.447135\pi$
$367$	21.1130	−	12.1896i	1.10209	−	0.636291i	0.936769	+	0.349949i	$0.113801\pi$
$368$	2.30399	+	1.33021i	0.120104	+	0.0693419i
$369$	−4.64353	−	4.64353i	−0.241733	−	0.241733i
$370$	−7.00454	+	1.87686i	−0.364149	+	0.0975733i
$371$	−11.6124	+	2.95084i	−0.602888	+	0.153200i
$372$	−0.505667	−	0.505667i	−0.0262176	−	0.0262176i
$373$	5.79040	−	10.0293i	0.299816	−	0.519296i	−0.676278	−	0.736647i	$-0.736408\pi$
$373$	5.79040	−	10.0293i	0.299816	−	0.519296i	0.976094	+	0.217350i	$0.0697414\pi$
$374$	0.426038	+	0.737919i	0.0220299	+	0.0381569i
$375$	3.08870	−	11.5272i	0.159500	−	0.595261i
$376$	−0.613279			−0.0316275
$377$	−4.06328	−	13.2549i	−0.209269	−	0.682664i
$378$	0.0342770	−	2.64553i	0.00176302	−	0.136071i
$379$	14.8453	+	3.97777i	0.762550	+	0.204325i	0.619078	−	0.785330i	$-0.287507\pi$
$379$	14.8453	+	3.97777i	0.762550	+	0.204325i	0.143472	+	0.989654i	$0.454173\pi$
$380$	−4.57820	−	7.92967i	−0.234857	−	0.406784i
$381$	2.19924	−	3.80920i	0.112671	−	0.195151i
$382$	13.7959	−	13.7959i	0.705861	−	0.705861i
$383$	−33.2528	+	8.91007i	−1.69914	+	0.455283i	−0.972723	−	0.231971i	$-0.925483\pi$
$383$	−33.2528	+	8.91007i	−1.69914	+	0.455283i	−0.726417	+	0.687254i	$0.758816\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−3.84841	+	3.74996i	−0.196133	+	0.191116i
$386$	−7.04714	+	12.2060i	−0.358690	+	0.621269i
$387$	−1.12959	+	0.652168i	−0.0574202	+	0.0331516i
$388$	−13.9265	−	3.73159i	−0.707010	−	0.189443i
$389$			14.6992i			0.745280i	0.927976	+	0.372640i	$0.121547\pi$
$389$			14.6992i			0.745280i	−0.927976	+	0.372640i	$0.878453\pi$
$390$	−4.25690	−	3.96367i	−0.215556	−	0.200708i
$391$		−	1.80064i		−	0.0910622i
$392$	6.71227	+	1.98631i	0.339021	+	0.100324i
$393$	−2.88267	−	4.99292i	−0.145411	−	0.251860i
$394$	18.6593	+	10.7729i	0.940041	+	0.542733i
$395$	−10.9400	−	10.9400i	−0.550450	−	0.550450i
$396$	0.325835	+	1.21603i	0.0163738	+	0.0611079i
$397$	−3.62070	−	13.5126i	−0.181718	−	0.678180i	−0.995309	−	0.0967433i	$-0.969157\pi$
$397$	−3.62070	−	13.5126i	−0.181718	−	0.678180i	0.813592	−	0.581437i	$-0.197509\pi$
$398$	8.53046	−	8.53046i	0.427593	−	0.427593i
$399$	−7.67634	+	12.9067i	−0.384298	+	0.646144i
$400$	2.07634	−	1.19877i	0.103817	−	0.0599387i
$401$	2.90448	−	10.8397i	0.145043	−	0.541307i	−0.854711	−	0.519105i	$-0.826265\pi$
$401$	2.90448	−	10.8397i	0.145043	−	0.541307i	0.999753	−	0.0222025i	$-0.00706787\pi$
$402$	−14.1177			−0.704127
$403$	1.36798	+	2.18559i	0.0681440	+	0.108872i
$404$			8.95655i			0.445605i
$405$	0.417530	−	1.55824i	0.0207472	−	0.0774297i
$406$	4.97204	+	8.87542i	0.246758	+	0.440480i
$407$	−4.90091	−	2.82954i	−0.242929	−	0.140255i
$408$	0.478588	−	0.478588i	0.0236936	−	0.0236936i
$409$	25.7020	−	6.88684i	1.27088	−	0.340532i	0.440515	−	0.897745i	$-0.354796\pi$
$409$	25.7020	−	6.88684i	1.27088	−	0.340532i	0.830370	+	0.557213i	$0.188129\pi$
$410$	10.2329	−	2.74190i	0.505367	−	0.135413i
$411$	−8.13525	+	8.13525i	−0.401283	+	0.401283i
$412$	−2.52314	−	1.45673i	−0.124306	−	0.0717681i
$413$	5.32335	+	9.50253i	0.261945	+	0.467589i
$414$	0.688566	−	2.56977i	0.0338412	−	0.126297i
$415$			2.19759i			0.107876i
$416$	−0.128526	−	3.60326i	−0.00630149	−	0.176664i
$417$	−0.658780			−0.0322606
$418$	1.84940	−	6.90205i	0.0904571	−	0.337591i
$419$	−12.3466	+	7.12833i	−0.603173	+	0.348242i	−0.770289	−	0.637695i	$-0.779888\pi$
$419$	−12.3466	+	7.12833i	−0.603173	+	0.348242i	0.167116	+	0.985937i	$0.446555\pi$
$420$	3.66837	+	2.18179i	0.178998	+	0.106460i
$421$	7.03263	−	7.03263i	0.342749	−	0.342749i	−0.514651	−	0.857400i	$-0.672078\pi$
$421$	7.03263	−	7.03263i	0.342749	−	0.342749i	0.857400	+	0.514651i	$0.172078\pi$
$422$	0.903495	+	3.37189i	0.0439815	+	0.164141i
$423$	0.158728	+	0.592382i	0.00771764	+	0.0288026i
$424$	−3.20219	−	3.20219i	−0.155512	−	0.155512i
$425$	−1.40532	−	0.811361i	−0.0681680	−	0.0393568i
$426$	−5.75390	−	9.96604i	−0.278777	−	0.482856i
$427$	7.84986	+	2.21275i	0.379881	+	0.107083i
$428$			2.23651i			0.108106i
$429$	−0.161805	−	4.53625i	−0.00781201	−	0.219012i
$430$		−	2.10417i		−	0.101472i
$431$	−15.2675	−	4.09092i	−0.735411	−	0.197053i	−0.128373	−	0.991726i	$-0.540976\pi$
$431$	−15.2675	−	4.09092i	−0.735411	−	0.197053i	−0.607037	+	0.794673i	$0.707642\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	1.12053	−	1.94081i	0.0538492	−	0.0932695i	−0.837844	−	0.545909i	$-0.816184\pi$
$433$	1.12053	−	1.94081i	0.0538492	−	0.0932695i	0.891693	+	0.452640i	$0.149518\pi$
$434$	−1.32042	−	1.35509i	−0.0633824	−	0.0650464i
$435$	1.60545	+	5.99162i	0.0769754	+	0.287276i
$436$	−11.7153	+	3.13909i	−0.561059	+	0.150335i
$437$	−10.6775	+	10.6775i	−0.510772	+	0.510772i
$438$	0.422991	−	0.732642i	0.0202113	−	0.0350070i
$439$	7.43138	+	12.8715i	0.354680	+	0.614325i	0.987063	−	0.160331i	$-0.0512563\pi$
$439$	7.43138	+	12.8715i	0.354680	+	0.614325i	−0.632383	+	0.774656i	$0.717923\pi$
$440$	−1.96172	−	0.525641i	−0.0935212	−	0.0250589i
$441$	0.181362	−	6.99765i	0.00863627	−	0.333221i
$442$	−2.06855	+	1.29472i	−0.0983909	+	0.0615838i
$443$	12.1078			0.575258			0.287629	−	0.957742i	$-0.407133\pi$
$443$	12.1078			0.575258			0.287629	+	0.957742i	$0.407133\pi$
$444$	−1.16343	+	4.34198i	−0.0552140	+	0.206061i
$445$	7.35436	+	12.7381i	0.348630	+	0.603845i
$446$	−14.4883	+	25.0944i	−0.686039	+	1.18825i
$447$	13.9062	+	13.9062i	0.657741	+	0.657741i
$448$	0.651604	+	2.56426i	0.0307854	+	0.121150i
$449$	−19.4403	+	5.20902i	−0.917446	+	0.245829i	−0.686493	−	0.727136i	$-0.740851\pi$
$449$	−19.4403	+	5.20902i	−0.917446	+	0.245829i	−0.230953	+	0.972965i	$0.574184\pi$
$450$	−1.69532	−	1.69532i	−0.0799183	−	0.0799183i
$451$	7.15971	+	4.13366i	0.337138	+	0.194646i
$452$	1.91757	−	1.10711i	0.0901947	−	0.0520740i
$453$	−17.0488	−	4.56821i	−0.801022	−	0.214633i
$454$	−12.6041			−0.591539
$455$	−11.1259	−	10.6319i	−0.521589	−	0.498433i
$456$	−5.67588			−0.265797
$457$	−11.7774	−	3.15575i	−0.550925	−	0.147620i	−0.0273911	−	0.999625i	$-0.508720\pi$
$457$	−11.7774	−	3.15575i	−0.550925	−	0.147620i	−0.523534	+	0.852005i	$0.675387\pi$
$458$	22.4096	−	12.9382i	1.04713	−	0.604562i
$459$	−0.586148	−	0.338413i	−0.0273591	−	0.0157958i
$460$	3.03477	+	3.03477i	0.141497	+	0.141497i
$461$	27.9434	−	7.48740i	1.30145	−	0.348723i	0.459453	−	0.888202i	$-0.348045\pi$
$461$	27.9434	−	7.48740i	1.30145	−	0.348723i	0.841999	+	0.539479i	$0.181379\pi$
$462$	0.820324	+	3.22822i	0.0381649	+	0.150190i
$463$	−19.1635	−	19.1635i	−0.890604	−	0.890604i	0.103976	−	0.994580i	$-0.466844\pi$
$463$	−19.1635	−	19.1635i	−0.890604	−	0.890604i	−0.994580	+	0.103976i	$0.966844\pi$
$464$	−1.92256	+	3.32997i	−0.0892524	+	0.154590i
$465$	−0.576821	−	0.999083i	−0.0267494	−	0.0463313i
$466$	−1.06553	+	3.97663i	−0.0493599	+	0.184214i
$467$	−18.2994			−0.846794			−0.423397	−	0.905944i	$-0.639162\pi$
$467$	−18.2994			−0.846794			−0.423397	+	0.905944i	$0.639162\pi$
$468$	−3.44722	+	1.05674i	−0.159348	+	0.0488478i
$469$	−37.3488	−	0.483913i	−1.72461	−	0.0223450i
$470$	−0.955638	−	0.256062i	−0.0440803	−	0.0118113i
$471$	−9.35673	−	16.2063i	−0.431135	−	0.746748i
$472$	−2.05840	+	3.56525i	−0.0947455	+	0.164104i
$473$	1.16112	−	1.16112i	0.0533882	−	0.0533882i
$474$	−9.26369	+	2.48220i	−0.425496	+	0.114011i
$475$	3.52206	+	13.1445i	0.161603	+	0.603111i
$476$	1.28252	−	1.24971i	0.0587844	−	0.0572806i
$477$	−2.26429	+	3.92187i	−0.103675	+	0.179570i
$478$	0.527537	−	0.304573i	0.0241290	−	0.0139309i
$479$	−18.1880	−	4.87347i	−0.831033	−	0.222675i	−0.181869	−	0.983323i	$-0.558215\pi$
$479$	−18.1880	−	4.87347i	−0.831033	−	0.222675i	−0.649164	+	0.760648i	$0.724881\pi$
$480$			1.61321i			0.0736327i
$481$	7.59826	−	14.3161i	0.346451	−	0.652756i
$482$			16.4511i			0.749329i
$483$	1.90971	−	6.77479i	0.0868947	−	0.308263i
$484$	4.70755	+	8.15371i	0.213979	+	0.370623i
$485$	−20.1428	−	11.6294i	−0.914637	−	0.528066i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−11.1917	−	41.7681i	−0.507146	−	1.89270i	−0.447065	−	0.894502i	$-0.647531\pi$
$487$	−11.1917	−	41.7681i	−0.507146	−	1.89270i	−0.0600816	−	0.998193i	$-0.519136\pi$
$488$	0.797833	+	2.97755i	0.0361162	+	0.134788i
$489$	4.68776	−	4.68776i	0.211988	−	0.211988i
$490$	9.63001	+	5.89772i	0.435039	+	0.266432i
$491$	−21.2865	+	12.2898i	−0.960647	+	0.554630i	−0.896372	−	0.443303i	$-0.853807\pi$
$491$	−21.2865	+	12.2898i	−0.960647	+	0.554630i	−0.0642746	+	0.997932i	$0.520473\pi$
$492$	1.69965	−	6.34318i	0.0766262	−	0.285973i
$493$	2.60247			0.117209
$494$	19.9436	+	4.58864i	0.897305	+	0.206453i
$495$			2.03092i			0.0912830i
$496$	0.185087	−	0.690754i	0.00831065	−	0.0310158i
$497$	−14.8805	−	26.5627i	−0.667482	−	1.19150i
$498$	1.17974	+	0.681123i	0.0528654	+	0.0305219i
$499$	−25.0509	+	25.0509i	−1.12143	+	1.12143i	−0.129905	+	0.991526i	$0.541467\pi$
$499$	−25.0509	+	25.0509i	−1.12143	+	1.12143i	−0.991526	+	0.129905i	$0.958533\pi$
$500$	11.5272	−	3.08870i	0.515511	−	0.138131i
$501$	20.4602	−	5.48230i	0.914095	−	0.244931i
$502$	13.9086	−	13.9086i	0.620773	−	0.620773i
$503$	−3.51019	−	2.02661i	−0.156512	−	0.0903621i	0.419699	−	0.907664i	$-0.362136\pi$
$503$	−3.51019	−	2.02661i	−0.156512	−	0.0903621i	−0.576210	+	0.817301i	$0.695469\pi$
$504$	2.30823	−	1.29308i	0.102817	−	0.0575984i
$505$	−3.73963	+	13.9565i	−0.166411	+	0.621056i
$506$			3.34928i			0.148893i
$507$	12.9670	−	0.926223i	0.575883	−	0.0411350i
$508$	4.39848			0.195151
$509$	−5.59731	+	20.8894i	−0.248096	+	0.925908i	0.723706	+	0.690109i	$0.242437\pi$
$509$	−5.59731	+	20.8894i	−0.248096	+	0.925908i	−0.971802	+	0.235799i	$0.924229\pi$
$510$	0.945581	−	0.545932i	0.0418710	−	0.0241743i
$511$	1.14415	−	1.92373i	0.0506141	−	0.0851007i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.46903	+	5.48248i	0.0648591	+	0.242057i
$514$	7.40615	+	27.6401i	0.326671	+	1.21915i
$515$	−3.32343	−	3.32343i	−0.146448	−	0.146448i
$516$	−1.12959	−	0.652168i	−0.0497273	−	0.0287101i
$517$	−0.386038	−	0.668637i	−0.0169779	−	0.0294066i
$518$	−3.22672	+	11.4470i	−0.141774	+	0.502951i
$519$		−	15.6591i		−	0.687359i
$520$	1.30419	−	5.66842i	0.0571927	−	0.248577i
$521$		−	33.4299i		−	1.46459i	−0.680988	−	0.732295i	$-0.738449\pi$
$521$		−	33.4299i		−	1.46459i	0.680988	−	0.732295i	$-0.261551\pi$
$522$	3.71409	+	0.995188i	0.162561	+	0.0435582i
$523$	33.6310	−	19.4168i	1.47058	−	0.849039i	0.471125	−	0.882067i	$-0.343848\pi$
$523$	33.6310	−	19.4168i	1.47058	−	0.849039i	0.999454	+	0.0330274i	$0.0105149\pi$
$524$	2.88267	−	4.99292i	0.125930	−	0.218117i
$525$	−4.42691	−	4.54314i	−0.193206	−	0.198279i
$526$	−4.39418	−	16.3993i	−0.191595	−	0.715044i
$527$	−0.467520	+	0.125272i	−0.0203655	+	0.00545692i
$528$	−0.890197	+	0.890197i	−0.0387409	+	0.0387409i
$529$	−7.96109	+	13.7890i	−0.346134	+	0.599522i
$530$	−3.65278	−	6.32680i	−0.158667	−	0.274819i
$531$	3.97652	+	1.06551i	0.172566	+	0.0462390i
$532$	−15.0157	−	0.194552i	−0.651014	−	0.00843491i
$533$	−11.1003	+	20.9143i	−0.480806	+	0.905897i
$534$	9.11766			0.394560
$535$	−0.933809	+	3.48502i	−0.0403721	+	0.150671i
$536$	−7.05885	−	12.2263i	−0.304896	−	0.528095i
$537$	−6.18019	+	10.7044i	−0.266695	+	0.461929i
$538$	0.309461	+	0.309461i	0.0133418	+	0.0133418i
$539$	2.05954	+	8.56846i	0.0887105	+	0.369070i
$540$	1.55824	−	0.417530i	0.0670561	−	0.0179676i
$541$	−29.7301	−	29.7301i	−1.27820	−	1.27820i	−0.941676	−	0.336522i	$-0.890749\pi$
$541$	−29.7301	−	29.7301i	−1.27820	−	1.27820i	−0.336522	−	0.941676i	$-0.609251\pi$
$542$	26.6840	+	15.4060i	1.14617	+	0.661744i
$543$	−8.71180	+	5.02976i	−0.373859	+	0.215848i
$544$	0.653764	+	0.175175i	0.0280299	+	0.00751058i
$545$	−19.5659			−0.838110
$546$	−9.15593	+	2.67747i	−0.391838	+	0.114585i
$547$	5.37130			0.229660			0.114830	−	0.993385i	$-0.463368\pi$
$547$	5.37130			0.229660			0.114830	+	0.993385i	$0.463368\pi$
$548$	−11.1130	−	2.97771i	−0.474722	−	0.127201i
$549$	2.66960	−	1.54130i	0.113936	−	0.0657809i
$550$	2.61396	+	1.50917i	0.111460	+	0.0643513i
$551$	−15.4322	−	15.4322i	−0.657433	−	0.657433i
$552$	2.56977	−	0.688566i	0.109376	−	0.0293073i
$553$	−24.5925	+	6.24920i	−1.04578	+	0.265743i
$554$	−0.207070	−	0.207070i	−0.00879757	−	0.00879757i
$555$	−3.62582	+	6.28010i	−0.153907	+	0.266575i
$556$	−0.329390	−	0.570520i	−0.0139692	−	0.0241955i
$557$	11.1852	−	41.7436i	0.473930	−	1.76873i	−0.151505	−	0.988456i	$-0.548412\pi$
$557$	11.1852	−	41.7436i	0.473930	−	1.76873i	0.625436	−	0.780276i	$-0.284921\pi$
$558$	−0.715121			−0.0302735
$559$	3.44184	+	3.20476i	0.145574	+	0.135547i
$560$	−0.0552961	+	4.26780i	−0.00233668	+	0.180347i
$561$	0.823042	+	0.220533i	0.0347489	+	0.00931093i
$562$	11.5574	+	20.0181i	0.487521	+	0.844412i
$563$	−16.0744	+	27.8417i	−0.677457	+	1.17339i	0.298288	+	0.954476i	$0.403585\pi$
$563$	−16.0744	+	27.8417i	−0.677457	+	1.17339i	−0.975744	+	0.218913i	$0.929749\pi$
$564$	−0.433654	+	0.433654i	−0.0182601	+	0.0182601i
$565$	3.45028	−	0.924501i	0.145155	−	0.0388941i
$566$	−2.22194	−	8.29239i	−0.0933951	−	0.348555i
$567$	−1.84643	−	1.89491i	−0.0775429	−	0.0795787i
$568$	5.75390	−	9.96604i	0.241428	−	0.418166i
$569$	−33.9613	+	19.6076i	−1.42373	+	0.821993i	−0.996616	−	0.0822032i	$-0.973804\pi$
$569$	−33.9613	+	19.6076i	−1.42373	+	0.821993i	−0.427118	+	0.904196i	$0.640471\pi$
$570$	−8.84440	−	2.36985i	−0.370451	−	0.0992621i
$571$			9.23258i			0.386371i	0.981162	+	0.193186i	$0.0618820\pi$
$571$			9.23258i			0.386371i	−0.981162	+	0.193186i	$0.938118\pi$
$572$	3.84760	−	2.40825i	0.160876	−	0.100694i
$573$		−	19.5104i		−	0.815058i
$574$	4.71390	−	16.7228i	0.196754	−	0.697997i
$575$	−3.18924	−	5.52392i	−0.133000	−	0.230364i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	5.57617	+	5.57617i	0.232139	+	0.232139i	0.813585	−	0.581446i	$-0.197513\pi$
$577$	5.57617	+	5.57617i	0.232139	+	0.232139i	−0.581446	+	0.813585i	$0.697513\pi$
$578$	4.28136	+	15.9783i	0.178081	+	0.664608i
$579$	3.64787	+	13.6140i	0.151600	+	0.565780i
$580$	−4.38617	+	4.38617i	−0.182126	+	0.182126i
$581$	3.09769	+	1.84237i	0.128514	+	0.0764343i
$582$	−12.4861	+	7.20888i	−0.517567	+	0.298818i
$583$	1.47557	−	5.50690i	0.0611119	−	0.228073i
$584$	0.845982			0.0350070
$585$	−5.81282	+	0.207339i	−0.240331	+	0.00857242i
$586$			29.9512i			1.23727i
$587$	−3.26923	+	12.2009i	−0.134935	+	0.503586i	0.865063	+	0.501664i	$0.167279\pi$
$587$	−3.26923	+	12.2009i	−0.134935	+	0.503586i	−0.999998	+	0.00192225i	$0.999388\pi$
$588$	6.15082	−	3.34176i	0.253656	−	0.137812i
$589$	3.51515	+	2.02947i	0.144839	+	0.0836229i
$590$	−4.69608	+	4.69608i	−0.193335	+	0.193335i
$591$	20.8117	−	5.57649i	0.856080	−	0.229386i
$592$	−4.34198	+	1.16343i	−0.178454	+	0.0478167i
$593$	24.2459	−	24.2459i	0.995660	−	0.995660i	−0.00433041	−	0.999991i	$-0.501378\pi$
$593$	24.2459	−	24.2459i	0.995660	−	0.995660i	0.999991	+	0.00433041i	$0.00137842\pi$
$594$	1.09026	+	0.629465i	0.0447341	+	0.0258272i
$595$	2.52028	−	1.41187i	0.103321	−	0.0578809i
$596$	−5.09002	+	18.9962i	−0.208495	+	0.778115i
$597$		−	12.0639i		−	0.493742i
$598$	−9.58617	+	0.341932i	−0.392008	+	0.0139826i
$599$	−1.17565			−0.0480357			−0.0240179	−	0.999712i	$-0.507646\pi$
$599$	−1.17565			−0.0480357			−0.0240179	+	0.999712i	$0.507646\pi$
$600$	0.620531	−	2.31585i	0.0253331	−	0.0945443i
$601$	−28.7400	+	16.5930i	−1.17233	+	0.676843i	−0.954227	−	0.299083i	$-0.903319\pi$
$601$	−28.7400	+	16.5930i	−1.17233	+	0.676843i	−0.218100	+	0.975926i	$0.569986\pi$
$602$	−2.96600	−	1.76405i	−0.120885	−	0.0718972i
$603$	−9.98272	+	9.98272i	−0.406528	+	0.406528i
$604$	−4.56821	−	17.0488i	−0.185878	−	0.693706i
$605$	3.93108	+	14.6710i	0.159821	+	0.596461i
$606$	6.33324	+	6.33324i	0.257270	+	0.257270i
$607$	−6.21402	−	3.58767i	−0.252219	−	0.145619i	0.368561	−	0.929604i	$-0.379851\pi$
$607$	−6.21402	−	3.58767i	−0.252219	−	0.145619i	−0.620780	+	0.783985i	$0.713184\pi$
$608$	−2.83794	−	4.91546i	−0.115094	−	0.199348i
$609$	9.79163	+	2.76011i	0.396777	+	0.111845i
$610$			4.97287i			0.201346i
$611$	1.87434	−	1.17316i	0.0758275	−	0.0474612i
$612$		−	0.676826i		−	0.0273591i
$613$	−2.54565	−	0.682106i	−0.102818	−	0.0275500i	0.207043	−	0.978332i	$-0.433616\pi$
$613$	−2.54565	−	0.682106i	−0.102818	−	0.0275500i	−0.309861	+	0.950782i	$0.600283\pi$
$614$	7.23805	−	4.17889i	0.292104	−	0.168646i
$615$	5.29694	−	9.17456i	0.213593	−	0.369954i
$616$	−2.38556	+	2.32453i	−0.0961168	+	0.0936580i
$617$	0.444260	+	1.65800i	0.0178852	+	0.0667486i	0.974292	−	0.225290i	$-0.0723330\pi$
$617$	0.444260	+	1.65800i	0.0178852	+	0.0667486i	−0.956406	+	0.292039i	$0.905666\pi$
$618$	−2.81419	+	0.754060i	−0.113203	+	0.0303328i
$619$	−9.88120	+	9.88120i	−0.397159	+	0.397159i	−0.877230	−	0.480071i	$-0.840611\pi$
$619$	−9.88120	+	9.88120i	−0.397159	+	0.397159i	0.480071	+	0.877230i	$0.340611\pi$
$620$	0.576821	−	0.999083i	0.0231657	−	0.0401241i
$621$	−1.33021	−	2.30399i	−0.0533794	−	0.0924559i
$622$	−28.8849	−	7.73969i	−1.15818	−	0.310333i
$623$	24.1210	+	0.312526i	0.966389	+	0.0125211i
$624$	−2.63877	−	2.45701i	−0.105635	−	0.0983590i
$625$	7.26402			0.290561
$626$	2.59507	−	9.68493i	0.103720	−	0.387088i
$627$	−3.57277	−	6.18821i	−0.142683	−	0.247133i
$628$	9.35673	−	16.2063i	0.373374	−	0.646703i
$629$	2.15133	+	2.15133i	0.0857790	+	0.0857790i
$630$	4.13669	−	1.05118i	0.164810	−	0.0418798i
$631$	−10.2068	+	2.73490i	−0.406325	+	0.108874i	−0.456192	−	0.889881i	$-0.650787\pi$
$631$	−10.2068	+	2.73490i	−0.406325	+	0.108874i	0.0498669	+	0.998756i	$0.484120\pi$
$632$	−6.78150	−	6.78150i	−0.269753	−	0.269753i
$633$	3.02315	+	1.74542i	0.120160	+	0.0693742i
$634$	18.9326	−	10.9307i	0.751908	−	0.434114i
$635$	6.85390	+	1.83650i	0.271989	+	0.0728792i
$636$	−4.52858			−0.179570
$637$	−24.3141	+	6.76949i	−0.963358	+	0.268217i
$638$	−4.84072			−0.191646
$639$	−11.1157	−	2.97844i	−0.439729	−	0.117825i
$640$	−1.39708	+	0.806606i	−0.0552245	+	0.0318839i
$641$	28.5856	+	16.5039i	1.12906	+	0.651865i	0.943699	−	0.330805i	$-0.107320\pi$
$641$	28.5856	+	16.5039i	1.12906	+	0.651865i	0.185364	+	0.982670i	$0.440654\pi$
$642$	1.58145	+	1.58145i	0.0624149	+	0.0624149i
$643$	−21.0179	+	5.63174i	−0.828866	+	0.222094i	−0.648219	−	0.761454i	$-0.724486\pi$
$643$	−21.0179	+	5.63174i	−0.828866	+	0.222094i	−0.180647	+	0.983548i	$0.557819\pi$
$644$	6.82199	−	1.73354i	0.268824	−	0.0683110i
$645$	−1.48787	−	1.48787i	−0.0585849	−	0.0585849i
$646$	−1.92079	+	3.32691i	−0.0755725	+	0.130895i
$647$	−22.1507	−	38.3662i	−0.870835	−	1.50833i	−0.861134	−	0.508378i	$-0.830245\pi$
$647$	−22.1507	−	38.3662i	−0.870835	−	1.50833i	−0.00970138	−	0.999953i	$-0.503088\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−5.18276			−0.203441
$650$	−4.05263	+	7.63566i	−0.158957	+	0.299495i
$651$	−1.89187	−	0.0245122i	−0.0741484	−	0.000960709i
$652$	6.40360	+	1.71584i	0.250784	+	0.0671974i
$653$	−6.62523	−	11.4752i	−0.259265	−	0.449061i	0.706780	−	0.707433i	$-0.250147\pi$
$653$	−6.62523	−	11.4752i	−0.259265	−	0.449061i	−0.966045	+	0.258373i	$0.916814\pi$
$654$	−6.06426	+	10.5036i	−0.237131	+	0.410724i
$655$	6.57659	−	6.57659i	0.256969	−	0.256969i
$656$	6.34318	−	1.69965i	0.247660	−	0.0663602i
$657$	−0.218956	−	0.817156i	−0.00854230	−	0.0318803i
$658$	−1.16211	+	1.13238i	−0.0453037	+	0.0441448i
$659$	−0.814057	+	1.40999i	−0.0317112	+	0.0549254i	−0.881445	−	0.472286i	$-0.843429\pi$
$659$	−0.814057	+	1.40999i	−0.0317112	+	0.0549254i	0.849734	+	0.527211i	$0.176762\pi$
$660$	−1.75883	+	1.01546i	−0.0684623	+	0.0395267i
$661$	12.7530	+	3.41716i	0.496035	+	0.132912i	0.498159	−	0.867086i	$-0.334010\pi$
$661$	12.7530	+	3.41716i	0.496035	+	0.132912i	−0.00212431	+	0.999998i	$0.500676\pi$
$662$			2.54832i			0.0990434i
$663$	−0.547177	+	2.37819i	−0.0212506	+	0.0923614i
$664$			1.36225i			0.0528654i
$665$	−23.3169	−	6.57267i	−0.904190	−	0.254877i
$666$	2.24758	+	3.89292i	0.0870918	+	0.150847i
$667$	8.85909	+	5.11480i	0.343025	+	0.198046i
$668$	14.9779	+	14.9779i	0.579513	+	0.579513i
$669$	7.49967	+	27.9892i	0.289954	+	1.08212i
$670$	−5.89456	−	21.9988i	−0.227727	−	0.849888i
$671$	−2.74412	+	2.74412i	−0.105935	+	0.105935i
$672$	2.27396	+	1.35245i	0.0877198	+	0.0521719i
$673$	19.6542	−	11.3474i	0.757615	−	0.437409i	−0.0708236	−	0.997489i	$-0.522563\pi$
$673$	19.6542	−	11.3474i	0.757615	−	0.437409i	0.828439	+	0.560079i	$0.189229\pi$
$674$	2.70688	−	10.1022i	0.104265	−	0.389123i
$675$	−2.39755			−0.0922817
$676$	7.28561	+	10.7666i	0.280216	+	0.414100i
$677$			16.6317i			0.639210i	0.947551	+	0.319605i	$0.103550\pi$
$677$			16.6317i			0.639210i	−0.947551	+	0.319605i	$0.896450\pi$
$678$	0.573081	−	2.13877i	0.0220090	−	0.0821389i
$679$	−33.2795	+	18.6433i	−1.27715	+	0.715464i
$680$	0.945581	+	0.545932i	0.0362614	+	0.0209355i
$681$	−8.91244	+	8.91244i	−0.341525	+	0.341525i
$682$	0.869610	−	0.233011i	0.0332991	−	0.00892246i
$683$	17.7429	−	4.75421i	0.678915	−	0.181915i	0.0971477	−	0.995270i	$-0.469028\pi$
$683$	17.7429	−	4.75421i	0.678915	−	0.181915i	0.581767	+	0.813355i	$0.302361\pi$
$684$	−4.01345	+	4.01345i	−0.153458	+	0.153458i
$685$	−16.0734	−	9.27999i	−0.614134	−	0.354570i
$686$	16.3867	−	8.62990i	0.625648	−	0.329491i
$687$	6.69730	−	24.9947i	0.255518	−	0.953606i
$688$		−	1.30434i		−	0.0497273i
$689$	15.9123	+	3.66111i	0.606210	+	0.139477i
$690$	4.29182			0.163387
$691$	−4.10071	+	15.3041i	−0.155999	+	0.582195i	0.843019	+	0.537883i	$0.180776\pi$
$691$	−4.10071	+	15.3041i	−0.155999	+	0.582195i	−0.999018	+	0.0443111i	$0.985891\pi$
$692$	13.5612	−	7.82956i	0.515519	−	0.297635i
$693$	2.86275	+	1.70264i	0.108747	+	0.0646779i
$694$	4.91742	−	4.91742i	0.186663	−	0.186663i
$695$	−0.275060	−	1.02654i	−0.0104336	−	0.0389389i
$696$	0.995188	+	3.71409i	0.0377225	+	0.140782i
$697$	−3.14286	−	3.14286i	−0.119044	−	0.119044i
$698$	10.3498	+	5.97548i	0.391747	+	0.226175i
$699$	2.05845	+	3.56535i	0.0778578	+	0.134854i
$700$	1.72101	−	6.10539i	0.0650482	−	0.230762i
$701$		−	23.1026i		−	0.872572i	−0.899808	−	0.436286i	$-0.856294\pi$
$701$		−	23.1026i		−	0.872572i	0.899808	−	0.436286i	$-0.143706\pi$
$702$	−1.69032	+	3.18478i	−0.0637971	+	0.120202i
$703$		−	25.5139i		−	0.962277i
$704$	−1.21603	−	0.325835i	−0.0458309	−	0.0122804i
$705$	−0.856802	+	0.494675i	−0.0322690	+	0.0186305i
$706$	−18.0537	+	31.2699i	−0.679460	+	1.17686i
$707$	16.5377	+	16.9719i	0.621964	+	0.638292i
$708$	1.06551	+	3.97652i	0.0400442	+	0.149447i
$709$	−19.2247	+	5.15124i	−0.721999	+	0.193459i	−0.601063	−	0.799201i	$-0.705256\pi$
$709$	−19.2247	+	5.15124i	−0.721999	+	0.193459i	−0.120935	+	0.992660i	$0.538589\pi$
$710$	13.1271	−	13.1271i	0.492651	−	0.492651i
$711$	−4.79524	+	8.30560i	−0.179836	+	0.311484i
$712$	4.55883	+	7.89613i	0.170849	+	0.295920i
$713$	−1.83769	−	0.492408i	−0.0688221	−	0.0184408i
$714$	0.0231996	−	1.79056i	0.000868222	−	0.0670101i
$715$	7.00102	−	2.14615i	0.261823	−	0.0802615i
$716$	−12.3604			−0.461929
$717$	0.157659	−	0.588391i	0.00588788	−	0.0219738i
$718$	12.1741	+	21.0862i	0.454334	+	0.786930i
$719$	17.3814	−	30.1054i	0.648216	−	1.12274i	−0.335332	−	0.942100i	$-0.608849\pi$
$719$	17.3814	−	30.1054i	0.648216	−	1.12274i	0.983549	−	0.180644i	$-0.0578181\pi$
$720$	1.14071	+	1.14071i	0.0425119	+	0.0425119i
$721$	−7.47087	+	1.89843i	−0.278230	+	0.0707011i
$722$	12.7653	−	3.42046i	0.475076	−	0.127296i
$723$	11.6327	+	11.6327i	0.432625	+	0.432625i
$724$	−8.71180	−	5.02976i	−0.323771	−	0.186929i
$725$	7.98375	−	4.60942i	0.296509	−	0.171190i
$726$	9.09429	+	2.43681i	0.337521	+	0.0904384i
$727$	−20.5762			−0.763130			−0.381565	−	0.924342i	$-0.624615\pi$
$727$	−20.5762			−0.763130			−0.381565	+	0.924342i	$0.624615\pi$
$728$	−6.89673	−	6.59054i	−0.255610	−	0.244262i
$729$	−1.00000			−0.0370370
$730$	1.31825	+	0.353223i	0.0487905	+	0.0130734i
$731$	−0.764534	+	0.441404i	−0.0282773	+	0.0163259i
$732$	2.66960	+	1.54130i	0.0986713	+	0.0569679i
$733$	−24.8116	−	24.8116i	−0.916439	−	0.916439i	0.0803296	−	0.996768i	$-0.474403\pi$
$733$	−24.8116	−	24.8116i	−0.916439	−	0.916439i	−0.996768	+	0.0803296i	$0.974403\pi$
$734$	23.5485	−	6.30979i	0.869189	−	0.232899i
$735$	10.9798	−	2.63912i	0.404995	−	0.0973455i
$736$	1.88120	+	1.88120i	0.0693419	+	0.0693419i
$737$	8.88660	−	15.3920i	0.327342	−	0.566973i
$738$	−3.28347	−	5.68714i	−0.120866	−	0.209347i
$739$	−2.25700	+	8.42323i	−0.0830250	+	0.309854i	−0.994933	−	0.100541i	$-0.967942\pi$
$739$	−2.25700	+	8.42323i	−0.0830250	+	0.309854i	0.911908	+	0.410395i	$0.134609\pi$
$740$	−7.25163			−0.266575
$741$	17.3469	−	10.8576i	0.637255	−	0.398864i
$742$	−11.9805	−	0.155226i	−0.439818	−	0.00569853i
$743$	43.4660	+	11.6467i	1.59461	+	0.427275i	0.943410	−	0.331628i	$-0.107598\pi$
$743$	43.4660	+	11.6467i	1.59461	+	0.427275i	0.651203	+	0.758904i	$0.274265\pi$
$744$	−0.357560	−	0.619313i	−0.0131088	−	0.0227051i
$745$	−15.8630	+	27.4755i	−0.581175	+	1.00662i
$746$	8.18887	−	8.18887i	0.299816	−	0.299816i
$747$	1.31583	−	0.352575i	0.0481437	−	0.0129001i
$748$	0.220533	+	0.823042i	0.00806350	+	0.0300934i
$749$	4.12956	+	4.23798i	0.150891	+	0.154852i
$750$	5.96691	−	10.3350i	0.217881	−	0.377380i
$751$	14.9462	−	8.62922i	0.545396	−	0.314885i	−0.201867	−	0.979413i	$-0.564701\pi$
$751$	14.9462	−	8.62922i	0.545396	−	0.314885i	0.747263	+	0.664528i	$0.231367\pi$
$752$	−0.592382	−	0.158728i	−0.0216020	−	0.00578823i
$753$		−	19.6698i		−	0.716806i
$754$	−0.494196	−	13.8549i	−0.0179975	−	0.504567i
$755$		−	28.4735i		−	1.03626i
$756$	0.717822	−	2.54651i	0.0261069	−	0.0926158i
$757$	8.50009	+	14.7226i	0.308941	+	0.535101i	0.978131	−	0.207990i	$-0.0666921\pi$
$757$	8.50009	+	14.7226i	0.308941	+	0.535101i	−0.669190	+	0.743091i	$0.733359\pi$
$758$	13.3099	+	7.68447i	0.483437	+	0.279113i
$759$	2.36830	+	2.36830i	0.0859637	+	0.0859637i
$760$	−2.36985	−	8.84440i	−0.0859635	−	0.320820i
$761$	−1.85372	−	6.91816i	−0.0671971	−	0.250783i	0.924154	−	0.382021i	$-0.124772\pi$
$761$	−1.85372	−	6.91816i	−0.0671971	−	0.250783i	−0.991351	+	0.131237i	$0.958105\pi$
$762$	3.11020	−	3.11020i	0.112671	−	0.112671i
$763$	−16.4032	+	27.5797i	−0.593836	+	0.998454i
$764$	16.8965	−	9.75519i	0.611293	−	0.352930i
$765$	0.282595	−	1.05466i	0.0102172	−	0.0381313i
$766$	−34.4259			−1.24386
$767$	−0.529114	−	14.8339i	−0.0191052	−	0.535621i
$768$			1.00000i			0.0360844i
$769$	−0.609923	+	2.27626i	−0.0219944	+	0.0820841i	−0.976051	−	0.217543i	$-0.930196\pi$
$769$	−0.609923	+	2.27626i	−0.0219944	+	0.0820841i	0.954056	+	0.299627i	$0.0968624\pi$
$770$	−4.68784	+	2.62614i	−0.168938	+	0.0946396i
$771$	24.7815	+	14.3076i	0.892483	+	0.515275i
$772$	−9.96616	+	9.96616i	−0.358690	+	0.358690i
$773$	23.7814	−	6.37222i	0.855359	−	0.229193i	0.195613	−	0.980681i	$-0.437330\pi$
$773$	23.7814	−	6.37222i	0.855359	−	0.229193i	0.659746	+	0.751489i	$0.270664\pi$
$774$	−1.25989	+	0.337587i	−0.0452859	+	0.0121343i
$775$	−1.21236	+	1.21236i	−0.0435493	+	0.0435493i
$776$	−12.4861	−	7.20888i	−0.448226	−	0.258784i
$777$	5.81259	+	10.3759i	0.208526	+	0.372232i
$778$	−3.80444	+	14.1983i	−0.136396	+	0.509035i
$779$			37.2732i			1.33545i
$780$	−3.08597	−	4.93038i	−0.110495	−	0.176536i
$781$	14.4875			0.518404
$782$	0.466040	−	1.73928i	0.0166655	−	0.0621966i
$783$	3.32997	−	1.92256i	0.119003	−	0.0687066i
$784$	5.96946	+	3.65589i	0.213195	+	0.130567i
$785$	21.3467	−	21.3467i	0.761896	−	0.761896i
$786$	−1.49218	−	5.56888i	−0.0532242	−	0.198635i
$787$	4.86775	+	18.1667i	0.173517	+	0.647573i	0.996800	+	0.0799416i	$0.0254734\pi$
$787$	4.86775	+	18.1667i	0.173517	+	0.647573i	−0.823283	+	0.567631i	$0.807860\pi$
$788$	15.2352	+	15.2352i	0.542733	+	0.542733i
$789$	−14.7032	−	8.48891i	−0.523449	−	0.302213i
$790$	−7.73574	−	13.3987i	−0.275225	−	0.476704i
$791$	1.58941	−	5.63853i	0.0565130	−	0.200483i
$792$			1.25893i			0.0447341i
$793$	−8.13425	−	7.57395i	−0.288856	−	0.268959i
$794$		−	13.9893i		−	0.496462i
$795$	−7.05663	−	1.89082i	−0.250273	−	0.0670604i
$796$	10.4476	−	6.03194i	0.370307	−	0.213797i
$797$	−0.264056	+	0.457358i	−0.00935334	+	0.0162005i	−0.870664	−	0.491878i	$-0.836311\pi$
$797$	−0.264056	+	0.457358i	−0.00935334	+	0.0162005i	0.861311	+	0.508078i	$0.169644\pi$
$798$	−10.7553	+	10.4801i	−0.380733	+	0.370993i
$799$	0.107431	+	0.400940i	0.00380065	+	0.0141842i
$800$	2.31585	−	0.620531i	0.0818778	−	0.0219391i
$801$	6.44716	−	6.44716i	0.227799	−	0.227799i
$802$	5.61103	−	9.71858i	0.198132	−	0.343175i
$803$	0.532516	+	0.922345i	0.0187921	+	0.0325488i
$804$	−13.6367	−	3.65393i	−0.480928	−	0.128864i
$805$	11.3541	+	0.147111i	0.400180	+	0.00518497i
$806$	0.755696	+	2.46518i	0.0266182	+	0.0868321i
$807$	0.437643			0.0154058
$808$	−2.31813	+	8.65137i	−0.0815514	+	0.304354i
$809$	22.7839	+	39.4629i	0.801040	+	1.38744i	0.918932	+	0.394416i	$0.129053\pi$
$809$	22.7839	+	39.4629i	0.801040	+	1.38744i	−0.117892	+	0.993026i	$0.537614\pi$
$810$	0.806606	−	1.39708i	0.0283412	−	0.0490885i
$811$	24.8555	+	24.8555i	0.872796	+	0.872796i	0.992776	−	0.119980i	$-0.0382831\pi$
$811$	24.8555	+	24.8555i	0.872796	+	0.872796i	−0.119980	+	0.992776i	$0.538283\pi$
$812$	2.50549	+	9.85985i	0.0879255	+	0.346013i
$813$	29.7621	−	7.97473i	1.04380	−	0.279686i
$814$	−4.00157	−	4.00157i	−0.140255	−	0.140255i
$815$	9.26194	+	5.34739i	0.324432	+	0.187311i
$816$	0.586148	−	0.338413i	0.0205193	−	0.0118468i
$817$	7.15100	+	1.91610i	0.250182	+	0.0670360i
$818$	26.6087			0.930352
$819$	−4.58096	+	8.36748i	−0.160072	+	0.292384i
$820$	10.5939			0.369954
$821$	−15.6730	−	4.19958i	−0.546993	−	0.146566i	−0.0252688	−	0.999681i	$-0.508044\pi$
$821$	−15.6730	−	4.19958i	−0.546993	−	0.146566i	−0.521724	+	0.853114i	$0.674711\pi$
$822$	−9.96361	+	5.75249i	−0.347521	+	0.200641i
$823$	38.6613	+	22.3211i	1.34765	+	0.778065i	0.987916	−	0.154991i	$-0.0495349\pi$
$823$	38.6613	+	22.3211i	1.34765	+	0.778065i	0.359732	+	0.933056i	$0.382868\pi$
$824$	−2.06013	−	2.06013i	−0.0717681	−	0.0717681i
$825$	2.91550	−	0.781205i	0.101505	−	0.0271981i
$826$	2.68252	+	10.5565i	0.0933369	+	0.367309i
$827$	7.82684	+	7.82684i	0.272166	+	0.272166i	0.829972	−	0.557806i	$-0.188357\pi$
$827$	7.82684	+	7.82684i	0.272166	+	0.272166i	−0.557806	+	0.829972i	$0.688357\pi$
$828$	1.33021	−	2.30399i	0.0462279	−	0.0800691i
$829$	−19.1506	−	33.1699i	−0.665129	−	1.15204i	−0.979250	−	0.202655i	$-0.935043\pi$
$829$	−19.1506	−	33.1699i	−0.665129	−	1.15204i	0.314121	−	0.949383i	$-0.398290\pi$
$830$	−0.568779	+	2.12271i	−0.0197426	+	0.0736804i
$831$	−0.292842			−0.0101586
$832$	0.808446	−	3.51375i	0.0280278	−	0.121817i
$833$	0.122750	−	4.73619i	0.00425304	−	0.164099i
$834$	−0.636333	−	0.170505i	−0.0220344	−	0.00590410i
$835$	17.0855	+	29.5930i	0.591268	+	1.02411i
$836$	3.57277	−	6.18821i	0.123567	−	0.214024i
$837$	−0.505667	+	0.505667i	−0.0174784	+	0.0174784i
$838$	−13.7709	+	3.68990i	−0.475707	+	0.127465i
$839$	7.49795	+	27.9827i	0.258858	+	0.966071i	0.965903	+	0.258903i	$0.0833610\pi$
$839$	7.49795	+	27.9827i	0.258858	+	0.966071i	−0.707045	+	0.707168i	$0.749972\pi$
$840$	2.97869	+	3.05689i	0.102775	+	0.105473i
$841$	7.10756	−	12.3106i	0.245088	−	0.424505i
$842$	8.61318	−	4.97282i	0.296830	−	0.171375i
$843$	22.3273	+	5.98257i	0.768992	+	0.206051i
$844$			3.49084i			0.120160i
$845$	6.85737	+	19.8190i	0.235901	+	0.681793i
$846$			0.613279i			0.0210850i
$847$	23.9757	+	6.75837i	0.823814	+	0.232220i
$848$	−2.26429	−	3.92187i	−0.0777561	−	0.134677i
$849$	−7.43476	−	4.29246i	−0.255160	−	0.147317i
$850$	−1.14744	−	1.14744i	−0.0393568	−	0.0393568i
$851$	3.09521	+	11.5515i	0.106102	+	0.395980i
$852$	−2.97844	−	11.1157i	−0.102040	−	0.380817i
$853$	0.922075	−	0.922075i	0.0315713	−	0.0315713i	−0.691145	−	0.722716i	$-0.742893\pi$
$853$	0.922075	−	0.922075i	0.0315713	−	0.0315713i	0.722716	+	0.691145i	$0.242893\pi$
$854$	7.00968	+	4.16905i	0.239866	+	0.142662i
$855$	−7.92967	+	4.57820i	−0.271189	+	0.156571i
$856$	−0.578851	+	2.16030i	−0.0197847	+	0.0738376i
$857$	27.0048			0.922466			0.461233	−	0.887279i	$-0.347407\pi$
$857$	27.0048			0.922466			0.461233	+	0.887279i	$0.347407\pi$
$858$	1.01778	−	4.42356i	0.0347463	−	0.151018i
$859$		−	9.90847i		−	0.338073i	−0.985610	−	0.169036i	$-0.945934\pi$
$859$		−	9.90847i		−	0.338073i	0.985610	−	0.169036i	$-0.0540655\pi$
$860$	0.544599	−	2.03247i	0.0185707	−	0.0693067i
$861$	−8.49158	−	15.1580i	−0.289392	−	0.516585i
$862$	−13.6885	−	7.90305i	−0.466232	−	0.269179i
$863$	−9.05583	+	9.05583i	−0.308264	+	0.308264i	−0.844236	−	0.535972i	$-0.819945\pi$
$863$	−9.05583	+	9.05583i	−0.308264	+	0.308264i	0.535972	+	0.844236i	$0.319945\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	24.4007	−	6.53815i	0.829649	−	0.222304i
$866$	1.58467	−	1.58467i	0.0538492	−	0.0538492i
$867$	14.3257	+	8.27095i	0.486527	+	0.280896i
$868$	−0.924708	−	1.65067i	−0.0313866	−	0.0560273i
$869$	3.12491	−	11.6623i	0.106005	−	0.395618i
$870$			6.20298i			0.210301i
$871$	44.9617	+	23.8635i	1.52347	+	0.808583i
$872$	−12.1285			−0.410724
$873$	−3.73159	+	13.9265i	−0.126295	+	0.471340i
$874$	−13.0772	+	7.55010i	−0.442342	+	0.255386i
$875$	16.1399	−	27.1370i	0.545627	−	0.917397i
$876$	0.598200	−	0.598200i	0.0202113	−	0.0202113i
$877$	−7.72320	−	28.8234i	−0.260794	−	0.973297i	−0.964775	−	0.263078i	$-0.915263\pi$
$877$	−7.72320	−	28.8234i	−0.260794	−	0.973297i	0.703981	−	0.710219i	$-0.251404\pi$
$878$	3.84677	+	14.3563i	0.129822	+	0.484503i
$879$	21.1787	+	21.1787i	0.714340	+	0.714340i
$880$	−1.75883	−	1.01546i	−0.0592901	−	0.0342311i
$881$	−14.1819	−	24.5638i	−0.477800	−	0.827574i	0.521876	−	0.853021i	$-0.325232\pi$
$881$	−14.1819	−	24.5638i	−0.477800	−	0.827574i	−0.999676	+	0.0254474i	$0.991899\pi$
$882$	1.98631	−	6.71227i	0.0668824	−	0.226014i
$883$			26.2301i			0.882714i	0.897332	+	0.441357i	$0.145503\pi$
$883$			26.2301i			0.882714i	−0.897332	+	0.441357i	$0.854497\pi$
$884$	−2.33317	+	0.715228i	−0.0784728	+	0.0240557i
$885$			6.64127i			0.223244i
$886$	11.6952	+	3.13373i	0.392909	+	0.105280i
$887$	−13.9684	+	8.06468i	−0.469014	+	0.270785i	−0.715827	−	0.698278i	$-0.753950\pi$
$887$	−13.9684	+	8.06468i	−0.469014	+	0.270785i	0.246813	+	0.969063i	$0.420617\pi$
$888$	−2.24758	+	3.89292i	−0.0754237	+	0.130638i
$889$	8.33472	−	8.12151i	0.279538	−	0.272387i
$890$	3.80690	+	14.2075i	0.127607	+	0.476238i
$891$	1.21603	−	0.325835i	0.0407386	−	0.0109159i
$892$	−20.4895	+	20.4895i	−0.686039	+	0.686039i
$893$	1.74045	−	3.01455i	0.0582420	−	0.100878i
$894$	9.83317	+	17.0315i	0.328870	+	0.569620i
$895$	−19.2605	−	5.16083i	−0.643807	−	0.172508i
$896$	−0.0342770	+	2.64553i	−0.00114511	+	0.0883809i
$897$	−6.53666	+	7.02023i	−0.218253	+	0.234399i
$898$	−20.1261			−0.671617
$899$	0.711680	−	2.65603i	0.0237359	−	0.0885834i
$900$	−1.19877	−	2.07634i	−0.0399591	−	0.0692113i
$901$	−1.53253	+	2.65442i	−0.0510560	+	0.0884316i
$902$	5.84588	+	5.84588i	0.194646	+	0.194646i
$903$	−3.34465	+	0.849911i	−0.111303	+	0.0282833i
$904$	2.13877	−	0.573081i	0.0711344	−	0.0190604i
$905$	−11.4750	−	11.4750i	−0.381443	−	0.381443i
$906$	−15.2855	−	8.82511i	−0.507828	−	0.293195i
$907$	47.8336	−	27.6167i	1.58829	−	0.916999i	0.594699	−	0.803949i	$-0.297271\pi$
$907$	47.8336	−	27.6167i	1.58829	−	0.916999i	0.993589	−	0.113050i	$-0.0360620\pi$
$908$	−12.1746	−	3.26218i	−0.404029	−	0.108259i
$909$	8.95655			0.297070
$910$	−7.99503	−	13.1492i	−0.265033	−	0.435893i
$911$	47.3683			1.56938			0.784691	−	0.619887i	$-0.212822\pi$
$911$	47.3683			1.56938			0.784691	+	0.619887i	$0.212822\pi$
$912$	−5.48248	−	1.46903i	−0.181543	−	0.0486443i
$913$	−1.48521	+	0.857486i	−0.0491532	+	0.0283786i
$914$	−10.5594	−	6.09645i	−0.349272	−	0.201652i
$915$	3.51635	+	3.51635i	0.116247	+	0.116247i
$916$	24.9947	−	6.69730i	0.825847	−	0.221285i
$917$	−3.75671	−	14.7838i	−0.124058	−	0.488204i
$918$	−0.478588	−	0.478588i	−0.0157958	−	0.0157958i
$919$	−9.23745	+	15.9997i	−0.304715	+	0.527782i	−0.977198	−	0.212331i	$-0.931895\pi$
$919$	−9.23745	+	15.9997i	−0.304715	+	0.527782i	0.672483	+	0.740113i	$0.265228\pi$
$920$	2.14591	+	3.71682i	0.0707485	+	0.122540i
$921$	2.16315	−	8.07299i	0.0712783	−	0.266014i
$922$	28.9291			0.952729
$923$	1.47905	+	41.4656i	0.0486834	+	1.36486i
$924$	−0.0431523	+	3.33053i	−0.00141961	+	0.109567i
$925$	10.4101	+	2.78938i	0.342282	+	0.0917143i
$926$	−13.5507	−	23.4704i	−0.445302	−	0.771286i
$927$	−1.45673	+	2.52314i	−0.0478454	+	0.0828706i
$928$	−2.71891	+	2.71891i	−0.0892524	+	0.0892524i
$929$	−27.4563	+	7.35689i	−0.900812	+	0.241372i	−0.679365	−	0.733801i	$-0.737745\pi$
$929$	−27.4563	+	7.35689i	−0.900812	+	0.241372i	−0.221447	+	0.975172i	$0.571078\pi$
$930$	−0.298584	−	1.11433i	−0.00979097	−	0.0365404i
$931$	−28.8126	+	27.3569i	−0.944296	+	0.896585i
$932$	−2.05845	+	3.56535i	−0.0674269	+	0.116787i
$933$	−25.8975	+	14.9519i	−0.847847	+	0.489505i
$934$	−17.6758	−	4.73623i	−0.578371	−	0.154974i
$935$			1.37458i			0.0449535i
$936$	−3.60326	+	0.128526i	−0.117776	+	0.00420099i
$937$		−	46.0058i		−	1.50294i	−0.659765	−	0.751472i	$-0.729344\pi$
$937$		−	46.0058i		−	1.50294i	0.659765	−	0.751472i	$-0.270656\pi$
$938$	−35.9509	−	10.1340i	−1.17384	−	0.330887i
$939$	−5.01329	−	8.68327i	−0.163603	−	0.283368i
$940$	−0.856802	−	0.494675i	−0.0279458	−	0.0161345i
$941$	−20.5795	−	20.5795i	−0.670873	−	0.670873i	0.287044	−	0.957917i	$-0.407327\pi$
$941$	−20.5795	−	20.5795i	−0.670873	−	0.670873i	−0.957917	+	0.287044i	$0.907327\pi$
$942$	−4.84340	−	18.0758i	−0.157806	−	0.588942i
$943$	−4.52178	−	16.8755i	−0.147249	−	0.549542i
$944$	−2.91102	+	2.91102i	−0.0947455	+	0.0947455i
$945$	2.18179	−	3.66837i	0.0709735	−	0.119332i
$946$	1.42207	−	0.821033i	0.0462355	−	0.0266941i
$947$	−11.1510	+	41.6162i	−0.362360	+	1.35235i	0.508605	+	0.861000i	$0.330161\pi$
$947$	−11.1510	+	41.6162i	−0.362360	+	1.35235i	−0.870965	+	0.491345i	$0.836505\pi$
$948$	−9.59048			−0.311484
$949$	−2.58554	+	1.61831i	−0.0839300	+	0.0525326i
$950$			13.6082i			0.441508i
$951$	5.65816	−	21.1165i	0.183478	−	0.684750i
$952$	1.56227	−	0.875190i	0.0506335	−	0.0283651i
$953$	−5.67202	−	3.27474i	−0.183735	−	0.106079i	0.405311	−	0.914179i	$-0.367163\pi$
$953$	−5.67202	−	3.27474i	−0.183735	−	0.106079i	−0.589046	+	0.808099i	$0.700496\pi$
$954$	−3.20219	+	3.20219i	−0.103675	+	0.103675i
$955$	30.4019	−	8.14617i	0.983783	−	0.263604i
$956$	0.588391	−	0.157659i	0.0190299	−	0.00509905i
$957$	−3.42291	+	3.42291i	−0.110647	+	0.110647i
$958$	−16.3070	−	9.41483i	−0.526854	−	0.304179i
$959$	−26.5562	+	14.8769i	−0.857545	+	0.480399i
$960$	−0.417530	+	1.55824i	−0.0134757	+	0.0502921i
$961$		−	30.4886i		−	0.983503i
$962$	11.0446	−	11.8617i	0.356093	−	0.382436i
$963$	2.23651			0.0720705
$964$	−4.25787	+	15.8906i	−0.137137	+	0.511801i
$965$	−19.6909	+	11.3685i	−0.633871	+	0.365966i
$966$	3.59808	−	6.04967i	0.115766	−	0.194645i
$967$	13.1121	−	13.1121i	0.421656	−	0.421656i	−0.464117	−	0.885774i	$-0.653628\pi$
$967$	13.1121	−	13.1121i	0.421656	−	0.421656i	0.885774	+	0.464117i	$0.153628\pi$
$968$	2.43681	+	9.09429i	0.0783219	+	0.292301i
$969$	0.994275	+	3.71068i	0.0319407	+	0.119204i
$970$	−16.4465	−	16.4465i	−0.528066	−	0.528066i
$971$	−13.6113	−	7.85851i	−0.436809	−	0.252192i	0.265434	−	0.964129i	$-0.414485\pi$
$971$	−13.6113	−	7.85851i	−0.436809	−	0.252192i	−0.702243	+	0.711937i	$0.747818\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−1.67759	−	0.472887i	−0.0537811	−	0.0151601i
$974$		−	43.2416i		−	1.38555i
$975$	2.53358	+	8.26487i	0.0811395	+	0.264688i
$976$			3.08259i			0.0986713i
$977$	26.8519	+	7.19494i	0.859068	+	0.230187i	0.661355	−	0.750073i	$-0.269982\pi$
$977$	26.8519	+	7.19494i	0.859068	+	0.230187i	0.197713	+	0.980260i	$0.436648\pi$
$978$	5.74131	−	3.31474i	0.183587	−	0.105994i
$979$	−5.73925	+	9.94067i	−0.183427	+	0.317705i
$980$	7.77543	+	8.18919i	0.248377	+	0.261594i
$981$	3.13909	+	11.7153i	0.100224	+	0.374039i
$982$	−23.7420	+	6.36165i	−0.757638	+	0.203009i
$983$	−32.3866	+	32.3866i	−1.03297	+	1.03297i	−0.0335344	+	0.999438i	$0.510676\pi$
$983$	−32.3866	+	32.3866i	−1.03297	+	1.03297i	−0.999438	+	0.0335344i	$0.989324\pi$
$984$	3.28347	−	5.68714i	0.104673	−	0.181299i
$985$	17.3790	+	30.1014i	0.553742	+	0.959110i
$986$	2.51379	+	0.673569i	0.0800555	+	0.0214508i
$987$	−0.0210214	+	1.62245i	−0.000669118	+	0.0516431i
$988$	18.0764	+	9.59407i	0.575087	+	0.305228i
$989$	−3.47008			−0.110342
$990$	−0.525641	+	1.96172i	−0.0167060	+	0.0623475i
$991$	0.0261986	+	0.0453774i	0.000832227	+	0.00144146i	0.866441	−	0.499279i	$-0.166402\pi$
$991$	0.0261986	+	0.0453774i	0.000832227	+	0.00144146i	−0.865609	+	0.500721i	$0.833068\pi$
$992$	0.357560	−	0.619313i	0.0113526	−	0.0196632i
$993$	1.80194	+	1.80194i	0.0571828	+	0.0571828i
$994$	−7.49853	−	29.5089i	−0.237839	−	0.935967i
$995$	18.7985	−	5.03703i	0.595951	−	0.159685i
$996$	0.963254	+	0.963254i	0.0305219	+	0.0305219i
$997$	−38.1644	−	22.0342i	−1.20868	−	0.697831i	−0.246208	−	0.969217i	$-0.579185\pi$
$997$	−38.1644	−	22.0342i	−1.20868	−	0.697831i	−0.962471	+	0.271386i	$0.912518\pi$
$998$	−30.6809	+	17.7137i	−0.971188	+	0.560716i
$999$	4.34198	+	1.16343i	0.137374	+	0.0368093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.223.9	✓	40
7.6	odd	2		546.2.bx.b.223.7	yes	40
13.7	odd	12		546.2.bx.b.475.7	yes	40
91.20	even	12	inner	546.2.bx.a.475.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.9	✓	40	1.1	even	1	trivial
546.2.bx.a.475.9	yes	40	91.20	even	12	inner
546.2.bx.b.223.7	yes	40	7.6	odd	2
546.2.bx.b.475.7	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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.14071 + 1.14071i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56426 - 0.651604i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.14071 + 1.14071i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56426 - 0.651604i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.806606 + 1.39708i) q^{10} +(-0.325835 + 1.21603i) q^{11} +1.00000 q^{12} +(-3.51375 - 0.808446i) q^{13} +(2.64553 + 0.0342770i) q^{14} +(1.55824 + 0.417530i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.338413 - 0.586148i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-5.48248 + 1.46903i) q^{19} +(0.417530 + 1.55824i) q^{20} +(1.89491 - 1.84643i) q^{21} +(-0.629465 + 1.09026i) q^{22} +(2.30399 - 1.33021i) q^{23} +(0.965926 + 0.258819i) q^{24} -2.39755i q^{25} +(-3.18478 - 1.69032i) q^{26} -1.00000i q^{27} +(2.54651 + 0.717822i) q^{28} +(1.92256 + 3.32997i) q^{29} +(1.39708 + 0.806606i) q^{30} +(-0.505667 - 0.505667i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.325835 + 1.21603i) q^{33} +(0.478588 - 0.478588i) q^{34} +(3.66837 + 2.18179i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.16343 + 4.34198i) q^{37} -5.67588 q^{38} +(-3.44722 + 1.05674i) q^{39} +1.61321i q^{40} +(1.69965 - 6.34318i) q^{41} +(2.30823 - 1.29308i) q^{42} +(-1.12959 - 0.652168i) q^{43} +(-0.890197 + 0.890197i) q^{44} +(1.55824 - 0.417530i) q^{45} +(2.56977 - 0.688566i) q^{46} +(-0.433654 + 0.433654i) q^{47} +(0.866025 + 0.500000i) q^{48} +(6.15082 - 3.34176i) q^{49} +(0.620531 - 2.31585i) q^{50} -0.676826i q^{51} +(-2.63877 - 2.45701i) q^{52} -4.52858 q^{53} +(0.258819 - 0.965926i) q^{54} +(-1.75883 + 1.01546i) q^{55} +(2.27396 + 1.35245i) q^{56} +(-4.01345 + 4.01345i) q^{57} +(0.995188 + 3.71409i) q^{58} +(1.06551 + 3.97652i) q^{59} +(1.14071 + 1.14071i) q^{60} +(2.66960 + 1.54130i) q^{61} +(-0.357560 - 0.619313i) q^{62} +(0.717822 - 2.54651i) q^{63} +1.00000i q^{64} +(-3.08597 - 4.93038i) q^{65} +1.25893i q^{66} +(-13.6367 - 3.65393i) q^{67} +(0.586148 - 0.338413i) q^{68} +(1.33021 - 2.30399i) q^{69} +(2.97869 + 3.05689i) q^{70} +(-2.97844 - 11.1157i) q^{71} +(0.965926 - 0.258819i) q^{72} +(0.598200 - 0.598200i) q^{73} +(-2.24758 + 3.89292i) q^{74} +(-1.19877 - 2.07634i) q^{75} +(-5.48248 - 1.46903i) q^{76} +(-0.0431523 + 3.33053i) q^{77} +(-3.60326 + 0.128526i) q^{78} -9.59048 q^{79} +(-0.417530 + 1.55824i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.28347 - 5.68714i) q^{82} +(0.963254 + 0.963254i) q^{83} +(2.56426 - 0.651604i) q^{84} +(1.05466 - 0.282595i) q^{85} +(-0.922305 - 0.922305i) q^{86} +(3.32997 + 1.92256i) q^{87} +(-1.09026 + 0.629465i) q^{88} +(8.80699 + 2.35983i) q^{89} +1.61321 q^{90} +(-9.53693 + 0.216510i) q^{91} +2.66042 q^{92} +(-0.690754 - 0.185087i) q^{93} +(-0.531116 + 0.306640i) q^{94} +(-7.92967 - 4.57820i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-13.9265 + 3.73159i) q^{97} +(6.80615 - 1.63594i) q^{98} +(0.890197 + 0.890197i) 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

Introduction

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