LMFDB - Embedded newform 546.2.bz.a.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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			73.4
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.a.187.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.698266 + 0.187100i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.63839 + 0.197219i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.698266 + 0.187100i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.63839 + 0.197219i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.361449 + 0.626048i) q^{10} +(-0.746421 - 2.78568i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.55895 + 0.577792i) q^{13} +(-0.873365 + 2.49745i) q^{14} +(-0.511166 - 0.511166i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.82443 - 4.89206i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(5.58733 + 1.49712i) q^{19} +(-0.511166 - 0.511166i) q^{20} +(-2.18630 - 1.48999i) q^{21} +2.88395 q^{22} +(1.48698 - 0.858506i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(-3.87756 - 2.23871i) q^{25} +(0.363021 - 3.58723i) q^{26} -1.00000i q^{27} +(-2.18630 - 1.48999i) q^{28} +7.04840 q^{29} +(0.626048 - 0.361449i) q^{30} +(1.87444 + 6.99549i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.746421 + 2.78568i) q^{33} +(3.99435 + 3.99435i) q^{34} +(1.80540 + 0.631353i) q^{35} -1.00000i q^{36} +(8.55470 + 2.29223i) q^{37} +(-2.89221 + 5.00946i) q^{38} +(3.37104 + 1.27909i) q^{39} +(0.626048 - 0.361449i) q^{40} +(8.34830 - 8.34830i) q^{41} +(2.00508 - 1.72617i) q^{42} -1.32786i q^{43} +(-0.746421 + 2.78568i) q^{44} +(0.187100 + 0.698266i) q^{45} +(0.444395 + 1.65851i) q^{46} +(-1.67003 + 6.23265i) q^{47} -1.00000i q^{48} +(6.92221 + 1.04068i) q^{49} +(3.16601 - 3.16601i) q^{50} +(-4.89206 + 2.82443i) q^{51} +(3.37104 + 1.27909i) q^{52} +(3.51393 - 6.08630i) q^{53} +(0.965926 + 0.258819i) q^{54} -2.08480i q^{55} +(2.00508 - 1.72617i) q^{56} +(-4.09021 - 4.09021i) q^{57} +(-1.82426 + 6.80823i) q^{58} +(-9.10726 + 2.44028i) q^{59} +(0.187100 + 0.698266i) q^{60} +(-10.1452 + 5.85736i) q^{61} -7.24226 q^{62} +(1.14840 + 2.38352i) q^{63} -1.00000i q^{64} +(-2.59320 - 0.262427i) q^{65} +(-2.49757 - 1.44197i) q^{66} +(-3.02156 + 0.809626i) q^{67} +(-4.89206 + 2.82443i) q^{68} -1.71701 q^{69} +(-1.07711 + 1.58047i) q^{70} +(-5.64157 - 5.64157i) q^{71} +(0.965926 + 0.258819i) q^{72} +(10.5654 - 2.83100i) q^{73} +(-4.42824 + 7.66994i) q^{74} +(2.23871 + 3.87756i) q^{75} +(-4.09021 - 4.09021i) q^{76} +(-1.41996 - 7.49692i) q^{77} +(-2.10800 + 2.92512i) q^{78} +(-4.87553 - 8.44467i) q^{79} +(0.187100 + 0.698266i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.90314 + 10.2245i) q^{82} +(-0.644239 + 0.644239i) q^{83} +(1.14840 + 2.38352i) q^{84} +(2.88750 - 2.88750i) q^{85} +(1.28262 + 0.343676i) q^{86} +(-6.10409 - 3.52420i) q^{87} +(-2.49757 - 1.44197i) q^{88} +(0.574488 - 2.14402i) q^{89} -0.722898 q^{90} +(-9.50386 + 0.822548i) q^{91} -1.71701 q^{92} +(1.87444 - 6.99549i) q^{93} +(-5.58804 - 3.22626i) q^{94} +(3.62133 + 2.09078i) q^{95} +(0.965926 + 0.258819i) q^{96} +(0.870136 - 0.870136i) q^{97} +(-2.79682 + 6.41699i) q^{98} +(2.03926 - 2.03926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 + 20 * q^9	$ 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−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
$5$	0.698266	+	0.187100i	0.312274	+	0.0836735i	0.411552	−	0.911386i	$-0.364987\pi$
$5$	0.698266	+	0.187100i	0.312274	+	0.0836735i	−0.0992784	+	0.995060i	$0.531653\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	2.63839	+	0.197219i	0.997218	+	0.0745418i
$7$	2.63839	+	0.197219i	0.997218	+	0.0745418i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.361449	+	0.626048i	−0.114300	+	0.197974i
$11$	−0.746421	−	2.78568i	−0.225054	−	0.839914i	−0.982383	−	0.186880i	$-0.940162\pi$
$11$	−0.746421	−	2.78568i	−0.225054	−	0.839914i	0.757329	−	0.653034i	$-0.226504\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.55895	+	0.577792i	−0.987076	+	0.160251i
$13$	−3.55895	+	0.577792i	−0.987076	+	0.160251i
$14$	−0.873365	+	2.49745i	−0.233417	+	0.667470i
$15$	−0.511166	−	0.511166i	−0.131982	−	0.131982i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.82443	−	4.89206i	0.685025	−	1.18650i	−0.288404	−	0.957509i	$-0.593125\pi$
$17$	2.82443	−	4.89206i	0.685025	−	1.18650i	0.973429	−	0.228989i	$-0.0735421\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	5.58733	+	1.49712i	1.28182	+	0.343463i	0.834548	−	0.550934i	$-0.185729\pi$
$19$	5.58733	+	1.49712i	1.28182	+	0.343463i	0.447273	+	0.894398i	$0.352395\pi$
$20$	−0.511166	−	0.511166i	−0.114300	−	0.114300i
$21$	−2.18630	−	1.48999i	−0.477091	−	0.325143i
$22$	2.88395			0.614860
$23$	1.48698	−	0.858506i	0.310056	−	0.179011i	−0.336896	−	0.941542i	$-0.609377\pi$
$23$	1.48698	−	0.858506i	0.310056	−	0.179011i	0.646951	+	0.762531i	$0.276044\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	−3.87756	−	2.23871i	−0.775512	−	0.447742i
$26$	0.363021	−	3.58723i	0.0711942	−	0.703514i
$27$		−	1.00000i		−	0.192450i
$28$	−2.18630	−	1.48999i	−0.413173	−	0.281582i
$29$	7.04840			1.30885			0.654427	−	0.756125i	$-0.272910\pi$
$29$	7.04840			1.30885			0.654427	+	0.756125i	$0.272910\pi$
$30$	0.626048	−	0.361449i	0.114300	−	0.0659912i
$31$	1.87444	+	6.99549i	0.336659	+	1.25643i	0.902060	+	0.431611i	$0.142055\pi$
$31$	1.87444	+	6.99549i	0.336659	+	1.25643i	−0.565401	+	0.824816i	$0.691279\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.746421	+	2.78568i	−0.129935	+	0.484925i
$34$	3.99435	+	3.99435i	0.685025	+	0.685025i
$35$	1.80540	+	0.631353i	0.305168	+	0.106718i
$36$		−	1.00000i		−	0.166667i
$37$	8.55470	+	2.29223i	1.40638	+	0.376840i	0.880633	−	0.473799i	$-0.157118\pi$
$37$	8.55470	+	2.29223i	1.40638	+	0.376840i	0.525751	+	0.850638i	$0.323784\pi$
$38$	−2.89221	+	5.00946i	−0.469179	+	0.812642i
$39$	3.37104	+	1.27909i	0.539799	+	0.204819i
$40$	0.626048	−	0.361449i	0.0989868	−	0.0571501i
$41$	8.34830	−	8.34830i	1.30378	−	1.30378i	0.377965	−	0.925820i	$-0.376624\pi$
$41$	8.34830	−	8.34830i	1.30378	−	1.30378i	0.925820	−	0.377965i	$-0.123376\pi$
$42$	2.00508	−	1.72617i	0.309390	−	0.266354i
$43$		−	1.32786i		−	0.202497i	−0.994861	−	0.101249i	$-0.967716\pi$
$43$		−	1.32786i		−	0.202497i	0.994861	−	0.101249i	$-0.0322837\pi$
$44$	−0.746421	+	2.78568i	−0.112527	+	0.419957i
$45$	0.187100	+	0.698266i	0.0278912	+	0.104091i
$46$	0.444395	+	1.65851i	0.0655225	+	0.244533i
$47$	−1.67003	+	6.23265i	−0.243600	+	0.909126i	0.730483	+	0.682931i	$0.239295\pi$
$47$	−1.67003	+	6.23265i	−0.243600	+	0.909126i	−0.974082	+	0.226195i	$0.927371\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.92221	+	1.04068i	0.988887	+	0.148669i
$50$	3.16601	−	3.16601i	0.447742	−	0.447742i
$51$	−4.89206	+	2.82443i	−0.685025	+	0.395499i
$52$	3.37104	+	1.27909i	0.467479	+	0.177378i
$53$	3.51393	−	6.08630i	0.482675	−	0.836018i	−0.517127	−	0.855909i	$-0.672999\pi$
$53$	3.51393	−	6.08630i	0.482675	−	0.836018i	0.999802	+	0.0198910i	$0.00633191\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$		−	2.08480i		−	0.281114i
$56$	2.00508	−	1.72617i	0.267940	−	0.230669i
$57$	−4.09021	−	4.09021i	−0.541761	−	0.541761i
$58$	−1.82426	+	6.80823i	−0.239537	+	0.893964i
$59$	−9.10726	+	2.44028i	−1.18566	+	0.317698i	−0.797171	−	0.603754i	$-0.793671\pi$
$59$	−9.10726	+	2.44028i	−1.18566	+	0.317698i	−0.388494	+	0.921451i	$0.627004\pi$
$60$	0.187100	+	0.698266i	0.0241545	+	0.0901457i
$61$	−10.1452	+	5.85736i	−1.29897	+	0.749958i	−0.980225	−	0.197884i	$-0.936593\pi$
$61$	−10.1452	+	5.85736i	−1.29897	+	0.749958i	−0.318740	+	0.947842i	$0.603260\pi$
$62$	−7.24226			−0.919768
$63$	1.14840	+	2.38352i	0.144685	+	0.300296i
$64$		−	1.00000i		−	0.125000i
$65$	−2.59320	−	0.262427i	−0.321647	−	0.0325500i
$66$	−2.49757	−	1.44197i	−0.307430	−	0.177495i
$67$	−3.02156	+	0.809626i	−0.369143	+	0.0989115i	−0.438621	−	0.898672i	$-0.644533\pi$
$67$	−3.02156	+	0.809626i	−0.369143	+	0.0989115i	0.0694786	+	0.997583i	$0.477866\pi$
$68$	−4.89206	+	2.82443i	−0.593249	+	0.342513i
$69$	−1.71701			−0.206704
$70$	−1.07711	+	1.58047i	−0.128739	+	0.188903i
$71$	−5.64157	−	5.64157i	−0.669531	−	0.669531i	0.288077	−	0.957607i	$-0.406984\pi$
$71$	−5.64157	−	5.64157i	−0.669531	−	0.669531i	−0.957607	+	0.288077i	$0.906984\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	10.5654	−	2.83100i	1.23659	−	0.331343i	0.419447	−	0.907780i	$-0.362224\pi$
$73$	10.5654	−	2.83100i	1.23659	−	0.331343i	0.817142	+	0.576437i	$0.195557\pi$
$74$	−4.42824	+	7.66994i	−0.514772	+	0.891612i
$75$	2.23871	+	3.87756i	0.258504	+	0.447742i
$76$	−4.09021	−	4.09021i	−0.469179	−	0.469179i
$77$	−1.41996	−	7.49692i	−0.161819	−	0.854353i
$78$	−2.10800	+	2.92512i	−0.238684	+	0.331205i
$79$	−4.87553	−	8.44467i	−0.548540	−	0.950100i	−0.998375	−	0.0569880i	$-0.981850\pi$
$79$	−4.87553	−	8.44467i	−0.548540	−	0.950100i	0.449834	−	0.893112i	$-0.351483\pi$
$80$	0.187100	+	0.698266i	0.0209184	+	0.0780685i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.90314	+	10.2245i	0.651892	+	1.12911i
$83$	−0.644239	+	0.644239i	−0.0707145	+	0.0707145i	−0.741579	−	0.670865i	$-0.765923\pi$
$83$	−0.644239	+	0.644239i	−0.0707145	+	0.0707145i	0.670865	+	0.741579i	$0.265923\pi$
$84$	1.14840	+	2.38352i	0.125301	+	0.260064i
$85$	2.88750	−	2.88750i	0.313194	−	0.313194i
$86$	1.28262	+	0.343676i	0.138308	+	0.0370595i
$87$	−6.10409	−	3.52420i	−0.654427	−	0.377834i
$88$	−2.49757	−	1.44197i	−0.266242	−	0.153715i
$89$	0.574488	−	2.14402i	0.0608956	−	0.227266i	−0.928771	−	0.370655i	$-0.879133\pi$
$89$	0.574488	−	2.14402i	0.0608956	−	0.227266i	0.989666	+	0.143389i	$0.0458000\pi$
$90$	−0.722898			−0.0762001
$91$	−9.50386	+	0.822548i	−0.996276	+	0.0862265i
$92$	−1.71701			−0.179011
$93$	1.87444	−	6.99549i	0.194370	−	0.725398i
$94$	−5.58804	−	3.22626i	−0.576363	−	0.332763i
$95$	3.62133	+	2.09078i	0.371541	+	0.214509i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	0.870136	−	0.870136i	0.0883489	−	0.0883489i	−0.661551	−	0.749900i	$-0.730102\pi$
$97$	0.870136	−	0.870136i	0.0883489	−	0.0883489i	0.749900	+	0.661551i	$0.230102\pi$
$98$	−2.79682	+	6.41699i	−0.282522	+	0.648214i
$99$	2.03926	−	2.03926i	0.204953	−	0.204953i
$100$	2.23871	+	3.87756i	0.223871	+	0.387756i
$101$	−7.50447	+	12.9981i	−0.746722	+	1.29336i	0.202663	+	0.979248i	$0.435040\pi$
$101$	−7.50447	+	12.9981i	−0.746722	+	1.29336i	−0.949386	+	0.314113i	$0.898293\pi$
$102$	−1.46203	−	5.45638i	−0.144763	−	0.540262i
$103$	8.61714	+	14.9253i	0.849072	+	1.47064i	0.882038	+	0.471179i	$0.156171\pi$
$103$	8.61714	+	14.9253i	0.849072	+	1.47064i	−0.0329656	+	0.999456i	$0.510495\pi$
$104$	−2.10800	+	2.92512i	−0.206706	+	0.286832i
$105$	−1.24784	−	1.44947i	−0.121777	−	0.141453i
$106$	4.96944	+	4.96944i	0.482675	+	0.482675i
$107$	−10.0439	−	17.3965i	−0.970977	−	1.68178i	−0.692618	−	0.721305i	$-0.743543\pi$
$107$	−10.0439	−	17.3965i	−0.970977	−	1.68178i	−0.278360	−	0.960477i	$-0.589791\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.57071	+	0.956768i	−0.342012	+	0.0916418i	−0.425737	−	0.904847i	$-0.639985\pi$
$109$	−3.57071	+	0.956768i	−0.342012	+	0.0916418i	0.0837248	+	0.996489i	$0.473318\pi$
$110$	2.01376	+	0.539586i	0.192005	+	0.0514475i
$111$	−6.26248	−	6.26248i	−0.594408	−	0.594408i
$112$	1.14840	+	2.38352i	0.108513	+	0.225222i
$113$	−3.07632			−0.289396			−0.144698	−	0.989476i	$-0.546221\pi$
$113$	−3.07632			−0.289396			−0.144698	+	0.989476i	$0.546221\pi$
$114$	5.00946	−	2.89221i	0.469179	−	0.270881i
$115$	1.19893	−	0.321252i	0.111801	−	0.0299569i
$116$	−6.10409	−	3.52420i	−0.566751	−	0.327214i
$117$	−2.27986	−	2.79325i	−0.210773	−	0.258236i
$118$		−	9.42853i		−	0.867967i
$119$	8.41676	−	12.3501i	0.771563	−	1.13213i
$120$	−0.722898			−0.0659912
$121$	2.32341	−	1.34142i	0.211219	−	0.121948i
$122$	−3.03199	−	11.3155i	−0.274504	−	1.02446i
$123$	−11.4040	+	3.05569i	−1.02826	+	0.275522i
$124$	1.87444	−	6.99549i	0.168329	−	0.628213i
$125$	−4.84453	−	4.84453i	−0.433308	−	0.433308i
$126$	−2.59953	+	0.492367i	−0.231585	+	0.0438635i
$127$			1.74796i			0.155106i	0.996988	+	0.0775532i	$0.0247108\pi$
$127$			1.74796i			0.155106i	−0.996988	+	0.0775532i	$0.975289\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−0.663931	+	1.14996i	−0.0584559	+	0.101249i
$130$	0.924654	−	2.43692i	0.0810976	−	0.213732i
$131$	−13.9083	+	8.02995i	−1.21517	+	0.701580i	−0.963881	−	0.266332i	$-0.914188\pi$
$131$	−13.9083	+	8.02995i	−1.21517	+	0.701580i	−0.251291	+	0.967912i	$0.580855\pi$
$132$	2.03926	−	2.03926i	0.177495	−	0.177495i
$133$	14.4463	+	5.05192i	1.25265	+	0.438057i
$134$		−	3.12815i		−	0.270231i
$135$	0.187100	−	0.698266i	0.0161030	−	0.0600971i
$136$	−1.46203	−	5.45638i	−0.125368	−	0.467881i
$137$	1.47111	+	5.49027i	0.125686	+	0.469065i	0.999863	−	0.0165413i	$-0.00526549\pi$
$137$	1.47111	+	5.49027i	0.125686	+	0.469065i	−0.874178	+	0.485606i	$0.838599\pi$
$138$	0.444395	−	1.65851i	0.0378294	−	0.141181i
$139$			14.6325i			1.24111i	0.784162	+	0.620556i	$0.213093\pi$
$139$			14.6325i			1.24111i	−0.784162	+	0.620556i	$0.786907\pi$
$140$	−1.24784	−	1.44947i	−0.105462	−	0.122502i
$141$	4.56262	−	4.56262i	0.384242	−	0.384242i
$142$	6.90948	−	3.98919i	0.579831	−	0.334765i
$143$	4.26602	+	9.48283i	0.356743	+	0.792994i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.92165	+	1.31875i	0.408721	+	0.109516i
$146$			10.9381i			0.905246i
$147$	−5.47447	−	4.36236i	−0.451527	−	0.359802i
$148$	−6.26248	−	6.26248i	−0.514772	−	0.514772i
$149$	−0.0517473	+	0.193124i	−0.00423930	+	0.0158213i	−0.968013	−	0.250900i	$-0.919274\pi$
$149$	−0.0517473	+	0.193124i	−0.00423930	+	0.0158213i	0.963774	+	0.266721i	$0.0859402\pi$
$150$	−4.32485	+	1.15884i	−0.353123	+	0.0946190i
$151$	−0.197692	−	0.737797i	−0.0160880	−	0.0600411i	0.957415	−	0.288715i	$-0.0932279\pi$
$151$	−0.197692	−	0.737797i	−0.0160880	−	0.0600411i	−0.973503	+	0.228673i	$0.926561\pi$
$152$	5.00946	−	2.89221i	0.406321	−	0.234590i
$153$	5.64886			0.456683
$154$	7.60898	+	0.568769i	0.613149	+	0.0458327i
$155$			5.23542i			0.420519i
$156$	−2.27986	−	2.79325i	−0.182535	−	0.223639i
$157$	−6.80179	−	3.92701i	−0.542842	−	0.313410i	0.203388	−	0.979098i	$-0.434805\pi$
$157$	−6.80179	−	3.92701i	−0.542842	−	0.313410i	−0.746230	+	0.665688i	$0.768138\pi$
$158$	9.41881	−	2.52376i	0.749320	−	0.200780i
$159$	−6.08630	+	3.51393i	−0.482675	+	0.278673i
$160$	−0.722898			−0.0571501
$161$	4.09254	−	1.97181i	0.322537	−	0.155401i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−18.5431	−	4.96861i	−1.45241	−	0.389172i	−0.555548	−	0.831484i	$-0.687492\pi$
$163$	−18.5431	−	4.96861i	−1.45241	−	0.389172i	−0.896861	+	0.442313i	$0.854158\pi$
$164$	−11.4040	+	3.05569i	−0.890502	+	0.238609i
$165$	−1.04240	+	1.80549i	−0.0811507	+	0.140557i
$166$	−0.455546	−	0.789029i	−0.0353572	−	0.0612405i
$167$	−11.8056	−	11.8056i	−0.913548	−	0.913548i	0.0830018	−	0.996549i	$-0.473549\pi$
$167$	−11.8056	−	11.8056i	−0.913548	−	0.913548i	−0.996549	+	0.0830018i	$0.973549\pi$
$168$	−2.59953	+	0.492367i	−0.200558	+	0.0379869i
$169$	12.3323	−	4.11267i	0.948639	−	0.316359i
$170$	2.04177	+	3.53646i	0.156597	+	0.271234i
$171$	1.49712	+	5.58733i	0.114488	+	0.427274i
$172$	−0.663931	+	1.14996i	−0.0506243	+	0.0876838i
$173$	−4.34201	−	7.52059i	−0.330117	−	0.571780i	0.652417	−	0.757860i	$-0.273755\pi$
$173$	−4.34201	−	7.52059i	−0.330117	−	0.571780i	−0.982535	+	0.186080i	$0.940422\pi$
$174$	4.98397	−	4.98397i	0.377834	−	0.377834i
$175$	−9.78900	−	6.67132i	−0.739979	−	0.504304i
$176$	2.03926	−	2.03926i	0.153715	−	0.153715i
$177$	9.10726	+	2.44028i	0.684544	+	0.183423i
$178$	1.92228	+	1.10983i	0.144081	+	0.0831850i
$179$	22.2968	+	12.8730i	1.66654	+	0.962177i	0.969483	+	0.245160i	$0.0788404\pi$
$179$	22.2968	+	12.8730i	1.66654	+	0.962177i	0.697056	+	0.717017i	$0.254493\pi$
$180$	0.187100	−	0.698266i	0.0139456	−	0.0520456i
$181$	−22.3929			−1.66445			−0.832227	−	0.554435i	$-0.812934\pi$
$181$	−22.3929			−1.66445			−0.832227	+	0.554435i	$0.812934\pi$
$182$	1.66526	−	9.39292i	0.123437	−	0.696249i
$183$	11.7147			0.865977
$184$	0.444395	−	1.65851i	0.0327613	−	0.122267i
$185$	5.54458	+	3.20116i	0.407646	+	0.235354i
$186$	6.27198	+	3.62113i	0.459884	+	0.265514i
$187$	−15.7359	−	4.21643i	−1.15072	−	0.308336i
$188$	4.56262	−	4.56262i	0.332763	−	0.332763i
$189$	0.197219	−	2.63839i	0.0143456	−	0.191915i
$190$	−2.95680	+	2.95680i	−0.214509	+	0.214509i
$191$	11.4338	+	19.8039i	0.827318	+	1.43296i	0.900135	+	0.435611i	$0.143468\pi$
$191$	11.4338	+	19.8039i	0.827318	+	1.43296i	−0.0728173	+	0.997345i	$0.523199\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−6.21156	−	23.1818i	−0.447118	−	1.66867i	−0.710284	−	0.703915i	$-0.751433\pi$
$193$	−6.21156	−	23.1818i	−0.447118	−	1.66867i	0.263166	−	0.964750i	$-0.415233\pi$
$194$	0.615279	+	1.06569i	0.0441744	+	0.0765124i
$195$	2.11456	+	1.52387i	0.151427	+	0.109126i
$196$	−5.47447	−	4.36236i	−0.391033	−	0.311597i
$197$	−4.17271	−	4.17271i	−0.297293	−	0.297293i	0.542659	−	0.839953i	$-0.317417\pi$
$197$	−4.17271	−	4.17271i	−0.297293	−	0.297293i	−0.839953	+	0.542659i	$0.817417\pi$
$198$	1.44197	+	2.49757i	0.102477	+	0.177495i
$199$	−3.51164	+	6.08235i	−0.248934	+	0.431166i	−0.963230	−	0.268677i	$-0.913414\pi$
$199$	−3.51164	+	6.08235i	−0.248934	+	0.431166i	0.714296	+	0.699843i	$0.246747\pi$
$200$	−4.32485	+	1.15884i	−0.305813	+	0.0819425i
$201$	3.02156	+	0.809626i	0.213125	+	0.0571066i
$202$	−10.6129	−	10.6129i	−0.746722	−	0.746722i
$203$	18.5964	+	1.39008i	1.30521	+	0.0975643i
$204$	5.64886			0.395499
$205$	7.39129	−	4.26736i	0.516230	−	0.298046i
$206$	−16.6470	+	4.46056i	−1.15985	+	0.310782i
$207$	1.48698	+	0.858506i	0.103352	+	0.0596703i
$208$	−2.27986	−	2.79325i	−0.158080	−	0.193677i
$209$		−	16.6820i		−	1.15392i
$210$	1.72304	−	0.830175i	0.118901	−	0.0572875i
$211$	8.59561			0.591746			0.295873	−	0.955227i	$-0.404389\pi$
$211$	8.59561			0.591746			0.295873	+	0.955227i	$0.404389\pi$
$212$	−6.08630	+	3.51393i	−0.418009	+	0.241337i
$213$	2.06496	+	7.70652i	0.141488	+	0.528042i
$214$	19.4033	−	5.19909i	1.32638	−	0.355402i
$215$	0.248443	−	0.927201i	0.0169436	−	0.0632346i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	3.56585	+	18.8265i	0.242066	+	1.27803i
$218$		−	3.69667i		−	0.250370i
$219$	−10.5654	−	2.83100i	−0.713945	−	0.191301i
$220$	−1.04240	+	1.80549i	−0.0702786	+	0.121726i
$221$	−7.22543	+	19.0425i	−0.486035	+	1.28094i
$222$	7.66994	−	4.42824i	0.514772	−	0.297204i
$223$	−8.00353	+	8.00353i	−0.535956	+	0.535956i	−0.922339	−	0.386382i	$-0.873724\pi$
$223$	−8.00353	+	8.00353i	−0.535956	+	0.535956i	0.386382	+	0.922339i	$0.373724\pi$
$224$	−2.59953	+	0.492367i	−0.173689	+	0.0328976i
$225$		−	4.47742i		−	0.298495i
$226$	0.796210	−	2.97150i	0.0529631	−	0.197661i
$227$	2.15876	+	8.05661i	0.143282	+	0.534736i	0.999826	+	0.0186618i	$0.00594057\pi$
$227$	2.15876	+	8.05661i	0.143282	+	0.534736i	−0.856544	+	0.516074i	$0.827393\pi$
$228$	1.49712	+	5.58733i	0.0991492	+	0.370030i
$229$	−6.16451	+	23.0063i	−0.407362	+	1.52030i	0.392295	+	0.919840i	$0.371681\pi$
$229$	−6.16451	+	23.0063i	−0.407362	+	1.52030i	−0.799657	+	0.600457i	$0.794985\pi$
$230$			1.24122i			0.0818439i
$231$	−2.51874	+	7.20250i	−0.165721	+	0.473890i
$232$	4.98397	−	4.98397i	0.327214	−	0.327214i
$233$	−6.85122	+	3.95555i	−0.448838	+	0.259137i	−0.707339	−	0.706874i	$-0.750105\pi$
$233$	−6.85122	+	3.95555i	−0.448838	+	0.259137i	0.258501	+	0.966011i	$0.416771\pi$
$234$	3.28814	−	1.47923i	0.214953	−	0.0967003i
$235$	−2.33226	+	4.03958i	−0.152140	+	0.263513i
$236$	9.10726	+	2.44028i	0.592832	+	0.158849i
$237$			9.75107i			0.633400i
$238$	9.75089	+	11.3264i	0.632056	+	0.734182i
$239$	7.88669	+	7.88669i	0.510148	+	0.510148i	0.914572	−	0.404424i	$-0.132528\pi$
$239$	7.88669	+	7.88669i	0.510148	+	0.510148i	−0.404424	+	0.914572i	$0.632528\pi$
$240$	0.187100	−	0.698266i	0.0120772	−	0.0450728i
$241$	16.4477	−	4.40715i	1.05949	−	0.283890i	0.313322	−	0.949647i	$-0.398558\pi$
$241$	16.4477	−	4.40715i	1.05949	−	0.283890i	0.746168	+	0.665757i	$0.231891\pi$
$242$	0.694372	+	2.59143i	0.0446359	+	0.166584i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	11.7147			0.749958
$245$	4.63883	+	2.02182i	0.296364	+	0.129169i
$246$		−	11.8063i		−	0.752741i
$247$	−20.7501	−	2.09987i	−1.32030	−	0.133611i
$248$	6.27198	+	3.62113i	0.398271	+	0.229942i
$249$	0.880047	−	0.235808i	0.0557707	−	0.0149437i
$250$	5.93332	−	3.42560i	0.375256	−	0.216654i
$251$	5.49507			0.346846			0.173423	−	0.984847i	$-0.444517\pi$
$251$	5.49507			0.346846			0.173423	+	0.984847i	$0.444517\pi$
$252$	0.197219	−	2.63839i	0.0124236	−	0.166203i
$253$	−3.50143	−	3.50143i	−0.220133	−	0.220133i
$254$	−1.68840	−	0.452406i	−0.105940	−	0.0283865i
$255$	−3.94440	+	1.05690i	−0.247008	+	0.0661857i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.0184575	+	0.0319693i	0.00115135	+	0.00199419i	0.866601	−	0.499003i	$-0.166300\pi$
$257$	0.0184575	+	0.0319693i	0.00115135	+	0.00199419i	−0.865449	+	0.500997i	$0.832967\pi$
$258$	−0.938941	−	0.938941i	−0.0584559	−	0.0584559i
$259$	22.1186	+	7.73494i	1.37438	+	0.480626i
$260$	2.11456	+	1.52387i	0.131140	+	0.0945063i
$261$	3.52420	+	6.10409i	0.218142	+	0.377834i
$262$	−4.15661	−	15.5127i	−0.256796	−	0.958376i
$263$	−2.81870	+	4.88214i	−0.173809	+	0.301046i	−0.939748	−	0.341867i	$-0.888941\pi$
$263$	−2.81870	+	4.88214i	−0.173809	+	0.301046i	0.765940	+	0.642913i	$0.222274\pi$
$264$	1.44197	+	2.49757i	0.0887473	+	0.153715i
$265$	3.59240	−	3.59240i	0.220679	−	0.220679i
$266$	−8.61875	+	12.6465i	−0.528450	+	0.775408i
$267$	−1.56953	+	1.56953i	−0.0960537	+	0.0960537i
$268$	3.02156	+	0.809626i	0.184571	+	0.0494558i
$269$	1.94041	+	1.12030i	0.118309	+	0.0683056i	0.557987	−	0.829850i	$-0.311574\pi$
$269$	1.94041	+	1.12030i	0.118309	+	0.0683056i	−0.439678	+	0.898156i	$0.644907\pi$
$270$	0.626048	+	0.361449i	0.0381001	+	0.0219971i
$271$	−1.83253	+	6.83910i	−0.111318	+	0.415446i	−0.998985	−	0.0450406i	$-0.985658\pi$
$271$	−1.83253	+	6.83910i	−0.111318	+	0.415446i	0.887667	+	0.460486i	$0.152325\pi$
$272$	5.64886			0.342513
$273$	8.64186	+	4.03958i	0.523029	+	0.244487i
$274$	−5.68394			−0.343380
$275$	−3.34204	+	12.4727i	−0.201532	+	0.752129i
$276$	1.48698	+	0.858506i	0.0895054	+	0.0516760i
$277$	−0.00567934	−	0.00327897i	−0.000341238	−	0.000197014i	0.499829	−	0.866124i	$-0.333396\pi$
$277$	−0.00567934	−	0.00327897i	−0.000341238	−	0.000197014i	−0.500171	+	0.865927i	$0.666729\pi$
$278$	−14.1339	−	3.78717i	−0.847695	−	0.227139i
$279$	−5.12105	+	5.12105i	−0.306589	+	0.306589i
$280$	1.72304	−	0.830175i	0.102972	−	0.0496124i
$281$	3.79861	−	3.79861i	0.226606	−	0.226606i	−0.584667	−	0.811273i	$-0.698775\pi$
$281$	3.79861	−	3.79861i	0.226606	−	0.226606i	0.811273	+	0.584667i	$0.198775\pi$
$282$	3.22626	+	5.58804i	0.192121	+	0.332763i
$283$	7.43230	−	12.8731i	0.441804	−	0.765228i	−0.556019	−	0.831170i	$-0.687672\pi$
$283$	7.43230	−	12.8731i	0.441804	−	0.765228i	0.997823	+	0.0659418i	$0.0210052\pi$
$284$	2.06496	+	7.70652i	0.122533	+	0.457298i
$285$	−2.09078	−	3.62133i	−0.123847	−	0.214509i
$286$	−10.2638	+	1.66632i	−0.606913	+	0.0985317i
$287$	23.6725	−	20.3796i	1.39734	−	1.20297i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	−7.45481	−	12.9121i	−0.438519	−	0.759536i
$290$	−2.54763	+	4.41263i	−0.149602	+	0.259119i
$291$	−1.18863	+	0.318492i	−0.0696786	+	0.0186703i
$292$	−10.5654	−	2.83100i	−0.618294	−	0.165671i
$293$	14.8878	+	14.8878i	0.869757	+	0.869757i	0.992445	−	0.122689i	$-0.0391517\pi$
$293$	14.8878	+	14.8878i	0.869757	+	0.869757i	−0.122689	+	0.992445i	$0.539152\pi$
$294$	5.63061	−	4.15887i	0.328384	−	0.242550i
$295$	−6.81586			−0.396835
$296$	7.66994	−	4.42824i	0.445806	−	0.257386i
$297$	−2.78568	+	0.746421i	−0.161642	+	0.0433117i
$298$	−0.173150	−	0.0999681i	−0.0100303	−	0.00579100i
$299$	−4.79604	+	3.91455i	−0.277362	+	0.226384i
$300$		−	4.47742i		−	0.258504i
$301$	0.261880	−	3.50342i	0.0150945	−	0.201934i
$302$	0.763824			0.0439531
$303$	12.9981	−	7.50447i	0.746722	−	0.431120i
$304$	1.49712	+	5.58733i	0.0858658	+	0.320455i
$305$	−8.17998	+	2.19182i	−0.468384	+	0.125503i
$306$	−1.46203	+	5.45638i	−0.0835789	+	0.311921i
$307$	−4.42730	−	4.42730i	−0.252680	−	0.252680i	0.569389	−	0.822068i	$-0.307180\pi$
$307$	−4.42730	−	4.42730i	−0.252680	−	0.252680i	−0.822068	+	0.569389i	$0.807180\pi$
$308$	−2.51874	+	7.20250i	−0.143518	+	0.410401i
$309$		−	17.2343i		−	0.980424i
$310$	−5.05702	−	1.35503i	−0.287220	−	0.0769603i
$311$	1.34306	−	2.32625i	0.0761579	−	0.131909i	−0.825431	−	0.564503i	$-0.809068\pi$
$311$	1.34306	−	2.32625i	0.0761579	−	0.131909i	0.901589	+	0.432593i	$0.142401\pi$
$312$	3.28814	−	1.47923i	0.186154	−	0.0837449i
$313$	−7.95117	+	4.59061i	−0.449427	+	0.259477i	−0.707588	−	0.706625i	$-0.750217\pi$
$313$	−7.95117	+	4.59061i	−0.449427	+	0.259477i	0.258161	+	0.966102i	$0.416883\pi$
$314$	5.55364	−	5.55364i	0.313410	−	0.313410i
$315$	0.355931	+	1.87920i	0.0200544	+	0.105881i
$316$			9.75107i			0.548540i
$317$	0.967304	−	3.61003i	0.0543292	−	0.202759i	−0.933426	−	0.358769i	$-0.883197\pi$
$317$	0.967304	−	3.61003i	0.0543292	−	0.202759i	0.987755	+	0.156010i	$0.0498632\pi$
$318$	−1.81894	−	6.78839i	−0.102001	−	0.380674i
$319$	−5.26107	−	19.6346i	−0.294563	−	1.09932i
$320$	0.187100	−	0.698266i	0.0104592	−	0.0390342i
$321$			20.0877i			1.12119i
$322$	0.845399	+	4.46343i	0.0471123	+	0.248737i
$323$	23.1050	−	23.1050i	1.28560	−	1.28560i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	15.0936	+	5.72704i	0.837240	+	0.317679i
$326$	9.59862	−	16.6253i	0.531619	−	0.920790i
$327$	3.57071	+	0.956768i	0.197461	+	0.0529094i
$328$		−	11.8063i		−	0.651892i
$329$	−5.63540	+	16.1148i	−0.310690	+	0.888438i
$330$	−1.47418	−	1.47418i	−0.0811507	−	0.0811507i
$331$	−2.45623	+	9.16677i	−0.135007	+	0.503851i	0.864991	+	0.501787i	$0.167324\pi$
$331$	−2.45623	+	9.16677i	−0.135007	+	0.503851i	−0.999998	+	0.00206457i	$0.999343\pi$
$332$	0.880047	−	0.235808i	0.0482989	−	0.0129416i
$333$	2.29223	+	8.55470i	0.125613	+	0.468795i
$334$	14.4589	−	8.34785i	0.791155	−	0.456774i
$335$	−2.26134			−0.123550
$336$	0.197219	−	2.63839i	0.0107592	−	0.143936i
$337$			23.7000i			1.29102i	0.763751	+	0.645510i	$0.223355\pi$
$337$			23.7000i			1.29102i	−0.763751	+	0.645510i	$0.776645\pi$
$338$	0.780700	+	12.9765i	0.0424645	+	0.705831i
$339$	2.66417	+	1.53816i	0.144698	+	0.0835414i
$340$	−3.94440	+	1.05690i	−0.213915	+	0.0573185i
$341$	18.0881	−	10.4432i	0.979524	−	0.565528i
$342$	−5.78443			−0.312786
$343$	18.0582	+	4.11092i	0.975054	+	0.221969i
$344$	−0.938941	−	0.938941i	−0.0506243	−	0.0506243i
$345$	−1.19893	−	0.321252i	−0.0645482	−	0.0172956i
$346$	8.38813	−	2.24759i	0.450948	−	0.120831i
$347$	−10.8283	+	18.7552i	−0.581295	+	1.00683i	0.414031	+	0.910263i	$0.364120\pi$
$347$	−10.8283	+	18.7552i	−0.581295	+	1.00683i	−0.995326	+	0.0965700i	$0.969213\pi$
$348$	3.52420	+	6.10409i	0.188917	+	0.327214i
$349$	−2.15099	−	2.15099i	−0.115140	−	0.115140i	0.647189	−	0.762329i	$-0.275944\pi$
$349$	−2.15099	−	2.15099i	−0.115140	−	0.115140i	−0.762329	+	0.647189i	$0.775944\pi$
$350$	8.97758	−	7.72878i	0.479872	−	0.413121i
$351$	0.577792	+	3.55895i	0.0308403	+	0.189963i
$352$	1.44197	+	2.49757i	0.0768575	+	0.133121i
$353$	−3.29456	−	12.2955i	−0.175352	−	0.654422i	−0.996491	−	0.0836945i	$-0.973328\pi$
$353$	−3.29456	−	12.2955i	−0.175352	−	0.654422i	0.821140	−	0.570727i	$-0.193339\pi$
$354$	−4.71427	+	8.16535i	−0.250560	+	0.433983i
$355$	−2.88378	−	4.99485i	−0.153055	−	0.265099i
$356$	−1.56953	+	1.56953i	−0.0831850	+	0.0831850i
$357$	−13.4642	+	6.48714i	−0.712600	+	0.343336i
$358$	−18.2052	+	18.2052i	−0.962177	+	0.962177i
$359$	−17.4586	−	4.67803i	−0.921432	−	0.246897i	−0.233235	−	0.972421i	$-0.574931\pi$
$359$	−17.4586	−	4.67803i	−0.921432	−	0.246897i	−0.688197	+	0.725524i	$0.741598\pi$
$360$	0.626048	+	0.361449i	0.0329956	+	0.0190500i
$361$	12.5224	+	7.22981i	0.659074	+	0.380517i
$362$	5.79572	−	21.6299i	0.304616	−	1.13684i
$363$	−2.68285			−0.140813
$364$	8.64186	+	4.03958i	0.452957	+	0.211732i
$365$	7.90715			0.413879
$366$	−3.03199	+	11.3155i	−0.158485	+	0.591473i
$367$	5.49280	+	3.17127i	0.286722	+	0.165539i	0.636463	−	0.771308i	$-0.280397\pi$
$367$	5.49280	+	3.17127i	0.286722	+	0.165539i	−0.349741	+	0.936847i	$0.613730\pi$
$368$	1.48698	+	0.858506i	0.0775140	+	0.0447527i
$369$	11.4040	+	3.05569i	0.593668	+	0.159073i
$370$	−4.52713	+	4.52713i	−0.235354	+	0.235354i
$371$	10.4714	−	15.3650i	0.543650	−	0.797712i
$372$	−5.12105	+	5.12105i	−0.265514	+	0.265514i
$373$	−14.5737	−	25.2424i	−0.754598	−	1.30700i	−0.945574	−	0.325408i	$-0.894498\pi$
$373$	−14.5737	−	25.2424i	−0.754598	−	1.30700i	0.190975	−	0.981595i	$-0.438835\pi$
$374$	8.14551	−	14.1084i	0.421194	−	0.729530i
$375$	1.77322	+	6.61776i	0.0915688	+	0.341739i
$376$	3.22626	+	5.58804i	0.166382	+	0.288181i
$377$	−25.0849	+	4.07251i	−1.29194	+	0.209745i
$378$	2.49745	+	0.873365i	0.128455	+	0.0449210i
$379$	−5.60418	−	5.60418i	−0.287868	−	0.287868i	0.548369	−	0.836236i	$-0.315249\pi$
$379$	−5.60418	−	5.60418i	−0.287868	−	0.287868i	−0.836236	+	0.548369i	$0.815249\pi$
$380$	−2.09078	−	3.62133i	−0.107255	−	0.185770i
$381$	0.873980	−	1.51378i	0.0447754	−	0.0775532i
$382$	−22.0883	+	5.91855i	−1.13014	+	0.302819i
$383$	−19.9262	−	5.33920i	−1.01818	−	0.272820i	−0.289136	−	0.957288i	$-0.593368\pi$
$383$	−19.9262	−	5.33920i	−1.01818	−	0.272820i	−0.729043	+	0.684468i	$0.760035\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	0.411162	−	5.50051i	0.0209548	−	0.280332i
$386$	23.9996			1.22155
$387$	1.14996	−	0.663931i	0.0584559	−	0.0337495i
$388$	−1.18863	+	0.318492i	−0.0603434	+	0.0161690i
$389$	27.9439	+	16.1334i	1.41681	+	0.817997i	0.996017	−	0.0891580i	$-0.0284176\pi$
$389$	27.9439	+	16.1334i	1.41681	+	0.817997i	0.420796	+	0.907155i	$0.361751\pi$
$390$	−2.01923	+	1.64811i	−0.102248	+	0.0834551i
$391$		−	9.69916i		−	0.490508i
$392$	5.63061	−	4.15887i	0.284389	−	0.210055i
$393$	16.0599			0.810115
$394$	5.11051	−	2.95055i	0.257464	−	0.148647i
$395$	−1.82442	−	6.80884i	−0.0917966	−	0.342590i
$396$	−2.78568	+	0.746421i	−0.139986	+	0.0375090i
$397$	7.82616	−	29.2076i	0.392784	−	1.46589i	−0.432739	−	0.901519i	$-0.642453\pi$
$397$	7.82616	−	29.2076i	0.392784	−	1.46589i	0.825522	−	0.564369i	$-0.190881\pi$
$398$	−4.96621	−	4.96621i	−0.248934	−	0.248934i
$399$	−9.98490	−	11.5982i	−0.499870	−	0.580638i
$400$		−	4.47742i		−	0.223871i
$401$	−17.4489	−	4.67543i	−0.871358	−	0.233480i	−0.204683	−	0.978828i	$-0.565616\pi$
$401$	−17.4489	−	4.67543i	−0.871358	−	0.233480i	−0.666675	+	0.745349i	$0.732283\pi$
$402$	−1.56408	+	2.70906i	−0.0780091	+	0.135116i
$403$	−10.7130	−	23.8136i	−0.533651	−	1.18624i
$404$	12.9981	−	7.50447i	0.646681	−	0.373361i
$405$	−0.511166	+	0.511166i	−0.0254000	+	0.0254000i
$406$	−6.15582	+	17.6030i	−0.305508	+	0.873621i
$407$		−	25.5416i		−	1.26605i
$408$	−1.46203	+	5.45638i	−0.0723814	+	0.270131i
$409$	1.50703	+	5.62433i	0.0745180	+	0.278105i	0.993124	−	0.117071i	$-0.0373504\pi$
$409$	1.50703	+	5.62433i	0.0745180	+	0.278105i	−0.918606	+	0.395176i	$0.870684\pi$
$410$	2.20895	+	8.24391i	0.109092	+	0.407138i
$411$	1.47111	−	5.49027i	0.0725646	−	0.270815i
$412$		−	17.2343i		−	0.849072i
$413$	−24.5098	+	4.64230i	−1.20605	+	0.228432i
$414$	−1.21411	+	1.21411i	−0.0596703	+	0.0596703i
$415$	−0.570387	+	0.329313i	−0.0279992	+	0.0161653i
$416$	3.28814	−	1.47923i	0.161214	−	0.0725252i
$417$	7.31625	−	12.6721i	0.358278	−	0.620556i
$418$	16.1136	+	4.31762i	0.788140	+	0.211182i
$419$			14.2075i			0.694079i	0.937850	+	0.347040i	$0.112813\pi$
$419$			14.2075i			0.694079i	−0.937850	+	0.347040i	$0.887187\pi$
$420$	0.355931	+	1.87920i	0.0173676	+	0.0916954i
$421$	−11.6299	−	11.6299i	−0.566809	−	0.566809i	0.364424	−	0.931233i	$-0.381266\pi$
$421$	−11.6299	−	11.6299i	−0.566809	−	0.566809i	−0.931233	+	0.364424i	$0.881266\pi$
$422$	−2.22471	+	8.30273i	−0.108297	+	0.404170i
$423$	−6.23265	+	1.67003i	−0.303042	+	0.0811999i
$424$	−1.81894	−	6.78839i	−0.0883357	−	0.329673i
$425$	−21.9038	+	12.6462i	−1.06249	+	0.613429i
$426$	−7.97838			−0.386554
$427$	−27.9223	+	13.4532i	−1.35125	+	0.651044i
$428$			20.0877i			0.970977i
$429$	1.04693	−	10.3454i	0.0505464	−	0.499480i
$430$	0.831305	+	0.479954i	0.0400891	+	0.0231455i
$431$	29.9639	−	8.02879i	1.44331	−	0.386733i	0.549617	−	0.835416i	$-0.314773\pi$
$431$	29.9639	−	8.02879i	1.44331	−	0.386733i	0.893691	+	0.448683i	$0.148107\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	32.8606			1.57918			0.789589	−	0.613636i	$-0.210294\pi$
$433$	32.8606			1.57918			0.789589	+	0.613636i	$0.210294\pi$
$434$	−19.1079	−	1.42831i	−0.917209	−	0.0685612i
$435$	−3.60290	−	3.60290i	−0.172746	−	0.172746i
$436$	3.57071	+	0.956768i	0.171006	+	0.0458209i
$437$	9.59351	−	2.57057i	0.458920	−	0.122967i
$438$	5.46906	−	9.47270i	0.261322	−	0.452623i
$439$	19.6143	+	33.9730i	0.936140	+	1.62144i	0.772588	+	0.634908i	$0.218962\pi$
$439$	19.6143	+	33.9730i	0.936140	+	1.62144i	0.163553	+	0.986535i	$0.447705\pi$
$440$	−1.47418	−	1.47418i	−0.0702786	−	0.0702786i
$441$	2.55985	+	6.51515i	0.121898	+	0.310245i
$442$	−16.5236	−	11.9078i	−0.785948	−	0.566396i
$443$	7.50488	+	12.9988i	0.356568	+	0.617593i	0.987385	−	0.158338i	$-0.0506136\pi$
$443$	7.50488	+	12.9988i	0.356568	+	0.617593i	−0.630817	+	0.775931i	$0.717280\pi$
$444$	2.29223	+	8.55470i	0.108784	+	0.405988i
$445$	0.802291	−	1.38961i	0.0380322	−	0.0658737i
$446$	−5.65935	−	9.80229i	−0.267978	−	0.464152i
$447$	0.141376	−	0.141376i	0.00668687	−	0.00668687i
$448$	0.197219	−	2.63839i	0.00931772	−	0.124652i
$449$	4.04136	−	4.04136i	0.190723	−	0.190723i	−0.605285	−	0.796009i	$-0.706941\pi$
$449$	4.04136	−	4.04136i	0.190723	−	0.190723i	0.796009	+	0.605285i	$0.206941\pi$
$450$	4.32485	+	1.15884i	0.203876	+	0.0546283i
$451$	−29.4870	−	17.0243i	−1.38849	−	0.801645i
$452$	2.66417	+	1.53816i	0.125312	+	0.0723489i
$453$	−0.197692	+	0.737797i	−0.00928839	+	0.0346647i
$454$	−8.34082			−0.391454
$455$	−6.79012	−	1.20381i	−0.318326	−	0.0564356i
$456$	−5.78443			−0.270881
$457$	3.55537	−	13.2688i	0.166313	−	0.620690i	−0.831556	−	0.555441i	$-0.812549\pi$
$457$	3.55537	−	13.2688i	0.166313	−	0.620690i	0.997869	−	0.0652486i	$-0.0207840\pi$
$458$	−20.6269	−	11.9089i	−0.963830	−	0.556467i
$459$	−4.89206	−	2.82443i	−0.228342	−	0.131833i
$460$	−1.19893	−	0.321252i	−0.0559004	−	0.0149785i
$461$	−9.71313	+	9.71313i	−0.452385	+	0.452385i	−0.896146	−	0.443760i	$-0.853644\pi$
$461$	−9.71313	+	9.71313i	−0.452385	+	0.452385i	0.443760	+	0.896146i	$0.353644\pi$
$462$	−6.30518	−	4.29706i	−0.293344	−	0.199917i
$463$	−18.4992	+	18.4992i	−0.859729	+	0.859729i	−0.991306	−	0.131577i	$-0.957996\pi$
$463$	−18.4992	+	18.4992i	−0.859729	+	0.859729i	0.131577	+	0.991306i	$0.457996\pi$
$464$	3.52420	+	6.10409i	0.163607	+	0.283375i
$465$	2.61771	−	4.53400i	0.121393	−	0.210259i
$466$	−2.04755	−	7.64154i	−0.0948507	−	0.353988i
$467$	−13.2642	−	22.9743i	−0.613794	−	1.06312i	−0.990595	−	0.136828i	$-0.956309\pi$
$467$	−13.2642	−	22.9743i	−0.613794	−	1.06312i	0.376801	−	0.926294i	$-0.377024\pi$
$468$	0.577792	+	3.55895i	0.0267085	+	0.164513i
$469$	−8.13174	+	1.54020i	−0.375489	+	0.0711198i
$470$	−3.29831	−	3.29831i	−0.152140	−	0.152140i
$471$	3.92701	+	6.80179i	0.180947	+	0.313410i
$472$	−4.71427	+	8.16535i	−0.216992	+	0.375841i
$473$	−3.69900	+	0.991144i	−0.170080	+	0.0455728i
$474$	−9.41881	−	2.52376i	−0.432620	−	0.115920i
$475$	−18.3136	−	18.3136i	−0.840285	−	0.840285i
$476$	−13.4642	+	6.48714i	−0.617130	+	0.297338i
$477$	7.02785			0.321783
$478$	−9.65919	+	5.57673i	−0.441801	+	0.255074i
$479$	16.5965	−	4.44703i	0.758315	−	0.203190i	0.141112	−	0.989994i	$-0.454932\pi$
$479$	16.5965	−	4.44703i	0.758315	−	0.203190i	0.617203	+	0.786804i	$0.288266\pi$
$480$	0.626048	+	0.361449i	0.0285750	+	0.0164978i
$481$	−31.7702	−	3.21509i	−1.44860	−	0.146595i
$482$			17.0279i			0.775601i
$483$	−4.53015	−	0.338627i	−0.206129	−	0.0154081i
$484$	−2.68285			−0.121948
$485$	0.770388	−	0.444784i	0.0349815	−	0.0201966i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	15.4134	−	4.13000i	0.698447	−	0.187148i	0.107912	−	0.994160i	$-0.465584\pi$
$487$	15.4134	−	4.13000i	0.698447	−	0.187148i	0.590535	+	0.807012i	$0.298917\pi$
$488$	−3.03199	+	11.3155i	−0.137252	+	0.512231i
$489$	13.5745	+	13.5745i	0.613860	+	0.613860i
$490$	−3.15354	+	3.95748i	−0.142462	+	0.178781i
$491$			5.71587i			0.257954i	0.991648	+	0.128977i	$0.0411693\pi$
$491$			5.71587i			0.257954i	−0.991648	+	0.128977i	$0.958831\pi$
$492$	11.4040	+	3.05569i	0.514131	+	0.137761i
$493$	19.9077	−	34.4812i	0.896598	−	1.55295i
$494$	7.39883	−	19.4996i	0.332889	−	0.877326i
$495$	1.80549	−	1.04240i	0.0811507	−	0.0468524i
$496$	−5.12105	+	5.12105i	−0.229942	+	0.229942i
$497$	−13.7720	−	15.9973i	−0.617760	−	0.717576i
$498$			0.911092i			0.0408270i
$499$	−8.09395	+	30.2070i	−0.362335	+	1.35225i	0.508663	+	0.860966i	$0.330140\pi$
$499$	−8.09395	+	30.2070i	−0.362335	+	1.35225i	−0.870998	+	0.491286i	$0.836527\pi$
$500$	1.77322	+	6.61776i	0.0793009	+	0.295955i
$501$	4.32116	+	16.1268i	0.193055	+	0.720492i
$502$	−1.42223	+	5.30783i	−0.0634772	+	0.236900i
$503$		−	7.08784i		−	0.316031i	−0.987437	−	0.158016i	$-0.949490\pi$
$503$		−	7.08784i		−	0.316031i	0.987437	−	0.158016i	$-0.0505096\pi$
$504$	2.49745	+	0.873365i	0.111245	+	0.0389028i
$505$	−7.67205	+	7.67205i	−0.341402	+	0.341402i
$506$	4.28836	−	2.47589i	0.190641	−	0.110067i
$507$	−12.7364	−	2.60448i	−0.565645	−	0.115669i
$508$	0.873980	−	1.51378i	0.0387766	−	0.0671631i
$509$	7.83496	+	2.09937i	0.347278	+	0.0930530i	0.428242	−	0.903664i	$-0.359133\pi$
$509$	7.83496	+	2.09937i	0.347278	+	0.0930530i	−0.0809636	+	0.996717i	$0.525800\pi$
$510$		−	4.08355i		−	0.180823i
$511$	28.4340	−	5.38557i	1.25785	−	0.238244i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.49712	−	5.58733i	0.0660995	−	0.246687i
$514$	−0.0356571	+	0.00955429i	−0.00157277	+	0.000421422i
$515$	3.22453	+	12.0341i	0.142090	+	0.530286i
$516$	1.14996	−	0.663931i	0.0506243	−	0.0292279i
$517$	18.6087			0.818411
$518$	−13.1961	+	19.3630i	−0.579803	+	0.850759i
$519$			8.68403i			0.381187i
$520$	−2.01923	+	1.64811i	−0.0885492	+	0.0722742i
$521$	−22.3462	−	12.9016i	−0.979006	−	0.565229i	−0.0770358	−	0.997028i	$-0.524546\pi$
$521$	−22.3462	−	12.9016i	−0.979006	−	0.565229i	−0.901970	+	0.431799i	$0.857879\pi$
$522$	−6.80823	+	1.82426i	−0.297988	+	0.0798457i
$523$	−2.53760	+	1.46508i	−0.110961	+	0.0640636i	−0.554454	−	0.832215i	$-0.687073\pi$
$523$	−2.53760	+	1.46508i	−0.110961	+	0.0640636i	0.443492	+	0.896278i	$0.353739\pi$
$524$	16.0599			0.701580
$525$	5.14186	+	10.6720i	0.224409	+	0.465766i
$526$	−3.98625	−	3.98625i	−0.173809	−	0.173809i
$527$	39.5165	+	10.5884i	1.72137	+	0.461239i
$528$	−2.78568	+	0.746421i	−0.121231	+	0.0324838i
$529$	−10.0259	+	17.3654i	−0.435910	+	0.755019i
$530$	2.54021	+	4.39977i	0.110340	+	0.191114i
$531$	−6.66698	−	6.66698i	−0.289322	−	0.289322i
$532$	−9.98490	−	11.5982i	−0.432900	−	0.502847i
$533$	−24.8876	+	34.5348i	−1.07800	+	1.49587i
$534$	−1.10983	−	1.92228i	−0.0480269	−	0.0831850i
$535$	−3.75841	−	14.0266i	−0.162490	−	0.606422i
$536$	−1.56408	+	2.70906i	−0.0675578	+	0.117014i
$537$	−12.8730	−	22.2968i	−0.555513	−	0.962177i
$538$	−1.58434	+	1.58434i	−0.0683056	+	0.0683056i
$539$	−2.26787	−	20.0598i	−0.0976842	−	0.864039i
$540$	−0.511166	+	0.511166i	−0.0219971	+	0.0219971i
$541$	−12.1228	−	3.24829i	−0.521199	−	0.139655i	−0.0113777	−	0.999935i	$-0.503622\pi$
$541$	−12.1228	−	3.24829i	−0.521199	−	0.139655i	−0.509821	+	0.860281i	$0.670288\pi$
$542$	−6.13177	−	3.54018i	−0.263382	−	0.152064i
$543$	19.3929	+	11.1965i	0.832227	+	0.480486i
$544$	−1.46203	+	5.45638i	−0.0626841	+	0.233940i
$545$	−2.67231			−0.114469
$546$	−6.13862	+	7.30188i	−0.262709	+	0.312491i
$547$	−30.7957			−1.31673			−0.658364	−	0.752699i	$-0.728751\pi$
$547$	−30.7957			−1.31673			−0.658364	+	0.752699i	$0.728751\pi$
$548$	1.47111	−	5.49027i	0.0628428	−	0.234533i
$549$	−10.1452	−	5.85736i	−0.432988	−	0.249986i
$550$	−11.1827	−	6.45632i	−0.476831	−	0.275298i
$551$	39.3817	+	10.5523i	1.67772	+	0.449543i
$552$	−1.21411	+	1.21411i	−0.0516760	+	0.0516760i
$553$	−11.1981	−	23.2419i	−0.476192	−	0.988346i
$554$	0.00463716	−	0.00463716i	0.000197014	−	0.000197014i
$555$	−3.20116	−	5.54458i	−0.135882	−	0.235354i
$556$	7.31625	−	12.6721i	0.310278	−	0.537417i
$557$	−9.88575	−	36.8941i	−0.418873	−	1.56325i	−0.776950	−	0.629562i	$-0.783234\pi$
$557$	−9.88575	−	36.8941i	−0.418873	−	1.56325i	0.358077	−	0.933692i	$-0.383432\pi$
$558$	−3.62113	−	6.27198i	−0.153295	−	0.265514i
$559$	0.767229	+	4.72580i	0.0324503	+	0.199880i
$560$	0.355931	+	1.87920i	0.0150408	+	0.0794106i
$561$	11.5195	+	11.5195i	0.486353	+	0.486353i
$562$	2.68602	+	4.65232i	0.113303	+	0.196246i
$563$	−7.34970	+	12.7301i	−0.309753	+	0.536508i	−0.978308	−	0.207154i	$-0.933580\pi$
$563$	−7.34970	+	12.7301i	−0.309753	+	0.536508i	0.668555	+	0.743663i	$0.266913\pi$
$564$	−6.23265	+	1.67003i	−0.262442	+	0.0703211i
$565$	−2.14809	−	0.575578i	−0.0903707	−	0.0242148i
$566$	10.5109	+	10.5109i	0.441804	+	0.441804i
$567$	−1.48999	+	2.18630i	−0.0625738	+	0.0918161i
$568$	−7.97838			−0.334765
$569$	−6.11807	+	3.53227i	−0.256483	+	0.148081i	−0.622729	−	0.782437i	$-0.713976\pi$
$569$	−6.11807	+	3.53227i	−0.256483	+	0.148081i	0.366246	+	0.930518i	$0.380643\pi$
$570$	4.03907	−	1.08227i	0.169178	−	0.0453311i
$571$	1.42925	+	0.825176i	0.0598121	+	0.0345325i	0.529608	−	0.848243i	$-0.322339\pi$
$571$	1.42925	+	0.825176i	0.0598121	+	0.0345325i	−0.469796	+	0.882775i	$0.655672\pi$
$572$	1.04693	−	10.3454i	0.0437744	−	0.432562i
$573$		−	22.8675i		−	0.955304i
$574$	13.5583	+	28.1405i	0.565913	+	1.17456i
$575$	−7.68778			−0.320603
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	2.61721	+	9.76754i	0.108956	+	0.406628i	0.998764	−	0.0497066i	$-0.0158286\pi$
$577$	2.61721	+	9.76754i	0.108956	+	0.406628i	−0.889808	+	0.456335i	$0.849162\pi$
$578$	14.4016	−	3.85890i	0.599027	−	0.160509i
$579$	−6.21156	+	23.1818i	−0.258144	+	0.963405i
$580$	−3.60290	−	3.60290i	−0.149602	−	0.149602i
$581$	−1.82681	+	1.57270i	−0.0757889	+	0.0652465i
$582$		−	1.23056i		−	0.0510083i
$583$	−19.5773	−	5.24573i	−0.810811	−	0.217256i
$584$	5.46906	−	9.47270i	0.226311	−	0.391983i
$585$	−1.06933	−	2.37699i	−0.0442114	−	0.0982765i
$586$	−18.2338	+	10.5273i	−0.753231	+	0.434878i
$587$	−8.39198	+	8.39198i	−0.346374	+	0.346374i	−0.858757	−	0.512383i	$-0.828763\pi$
$587$	−8.39198	+	8.39198i	−0.346374	+	0.346374i	0.512383	+	0.858757i	$0.328763\pi$
$588$	2.55985	+	6.51515i	0.105566	+	0.268680i
$589$			41.8924i			1.72614i
$590$	1.76408	−	6.58362i	0.0726258	−	0.271043i
$591$	1.52732	+	5.70003i	0.0628255	+	0.234468i
$592$	2.29223	+	8.55470i	0.0942099	+	0.351596i
$593$	−2.19262	+	8.18297i	−0.0900401	+	0.336034i	−0.996221	−	0.0868564i	$-0.972318\pi$
$593$	−2.19262	+	8.18297i	−0.0900401	+	0.336034i	0.906181	+	0.422891i	$0.138985\pi$
$594$		−	2.88395i		−	0.118330i
$595$	8.18784	−	7.04889i	0.335669	−	0.288977i
$596$	0.141376	−	0.141376i	0.00579100	−	0.00579100i
$597$	6.08235	−	3.51164i	0.248934	−	0.143722i
$598$	−2.53985	−	5.64578i	−0.103862	−	0.230873i
$599$	−16.1318	+	27.9411i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$599$	−16.1318	+	27.9411i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$600$	4.32485	+	1.15884i	0.176561	+	0.0473095i
$601$			10.4463i			0.426115i	0.977040	+	0.213058i	$0.0683422\pi$
$601$			10.4463i			0.426115i	−0.977040	+	0.213058i	$0.931658\pi$
$602$	3.31626	+	1.15971i	0.135161	+	0.0472662i
$603$	−2.21194	−	2.21194i	−0.0900771	−	0.0900771i
$604$	−0.197692	+	0.737797i	−0.00804398	+	0.0300205i
$605$	1.87334	−	0.501960i	0.0761621	−	0.0204076i
$606$	3.88460	+	14.4975i	0.157801	+	0.588921i
$607$	21.8700	−	12.6266i	0.887676	−	0.512500i	0.0144941	−	0.999895i	$-0.495386\pi$
$607$	21.8700	−	12.6266i	0.887676	−	0.512500i	0.873181	+	0.487395i	$0.162053\pi$
$608$	−5.78443			−0.234590
$609$	−15.4099	−	10.5021i	−0.624442	−	0.425565i
$610$		−	8.46854i		−	0.342881i
$611$	2.34240	−	23.1467i	0.0947633	−	0.936414i
$612$	−4.89206	−	2.82443i	−0.197750	−	0.114171i
$613$	6.90428	−	1.85000i	0.278861	−	0.0747206i	−0.116678	−	0.993170i	$-0.537224\pi$
$613$	6.90428	−	1.85000i	0.278861	−	0.0747206i	0.395539	+	0.918449i	$0.370558\pi$
$614$	5.42232	−	3.13058i	0.218827	−	0.126340i
$615$	−8.53473			−0.344153
$616$	−6.30518	−	4.29706i	−0.254043	−	0.173133i
$617$	−15.5964	−	15.5964i	−0.627888	−	0.627888i	0.319649	−	0.947536i	$-0.396435\pi$
$617$	−15.5964	−	15.5964i	−0.627888	−	0.627888i	−0.947536	+	0.319649i	$0.896435\pi$
$618$	16.6470	+	4.46056i	0.669642	+	0.179430i
$619$	11.1684	−	2.99258i	0.448898	−	0.120282i	−0.0272858	−	0.999628i	$-0.508686\pi$
$619$	11.1684	−	2.99258i	0.448898	−	0.120282i	0.476184	+	0.879346i	$0.342020\pi$
$620$	2.61771	−	4.53400i	0.105130	−	0.182090i
$621$	−0.858506	−	1.48698i	−0.0344506	−	0.0596703i
$622$	1.89937	+	1.89937i	0.0761579	+	0.0761579i
$623$	1.93857	−	5.54346i	0.0776670	−	0.222094i
$624$	0.577792	+	3.55895i	0.0231302	+	0.142472i
$625$	8.71719	+	15.0986i	0.348687	+	0.603944i
$626$	−2.37627	−	8.86837i	−0.0949750	−	0.354452i
$627$	−8.34100	+	14.4470i	−0.333107	+	0.576959i
$628$	3.92701	+	6.80179i	0.156705	+	0.271421i
$629$	35.3759	−	35.3759i	1.41053	−	1.41053i
$630$	−1.90729	−	0.142569i	−0.0759881	−	0.00568009i
$631$	23.3434	−	23.3434i	0.929287	−	0.929287i	−0.0683731	−	0.997660i	$-0.521781\pi$
$631$	23.3434	−	23.3434i	0.929287	−	0.929287i	0.997660	+	0.0683731i	$0.0217808\pi$
$632$	−9.41881	−	2.52376i	−0.374660	−	0.100390i
$633$	−7.44402	−	4.29781i	−0.295873	−	0.170822i
$634$	3.23666	+	1.86869i	0.128544	+	0.0742151i
$635$	−0.327043	+	1.22054i	−0.0129783	+	0.0484357i
$636$	7.02785			0.278673
$637$	−25.2371	+	0.295861i	−0.999931	+	0.0117224i
$638$	20.3272			0.804762
$639$	2.06496	−	7.70652i	0.0816884	−	0.304865i
$640$	0.626048	+	0.361449i	0.0247467	+	0.0142875i
$641$	−23.2772	−	13.4391i	−0.919393	−	0.530812i	−0.0359514	−	0.999354i	$-0.511446\pi$
$641$	−23.2772	−	13.4391i	−0.919393	−	0.530812i	−0.883441	+	0.468542i	$0.844779\pi$
$642$	−19.4033	−	5.19909i	−0.765786	−	0.205192i
$643$	−2.14970	+	2.14970i	−0.0847758	+	0.0847758i	−0.748223	−	0.663447i	$-0.769093\pi$
$643$	−2.14970	+	2.14970i	−0.0847758	+	0.0847758i	0.663447	+	0.748223i	$0.269093\pi$
$644$	−4.53015	−	0.338627i	−0.178513	−	0.0133438i
$645$	−0.678758	+	0.678758i	−0.0267261	+	0.0267261i
$646$	16.3377	+	28.2978i	0.642799	+	1.11336i
$647$	−4.96893	+	8.60645i	−0.195349	+	0.338354i	−0.947015	−	0.321190i	$-0.895917\pi$
$647$	−4.96893	+	8.60645i	−0.195349	+	0.338354i	0.751666	+	0.659544i	$0.229251\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	13.5957	+	23.5484i	0.533678	+	0.924357i
$650$	−9.43840	+	13.0970i	−0.370204	+	0.513706i
$651$	6.32514	−	18.0872i	0.247902	−	0.708892i
$652$	13.5745	+	13.5745i	0.531619	+	0.531619i
$653$	−0.104045	−	0.180212i	−0.00407161	−	0.00705223i	0.863982	−	0.503522i	$-0.167963\pi$
$653$	−0.104045	−	0.180212i	−0.00407161	−	0.00705223i	−0.868054	+	0.496470i	$0.834629\pi$
$654$	−1.84833	+	3.20141i	−0.0722756	+	0.125185i
$655$	−11.2141	+	3.00480i	−0.438170	+	0.117407i
$656$	11.4040	+	3.05569i	0.445251	+	0.119305i
$657$	7.73442	+	7.73442i	0.301749	+	0.301749i
$658$	−14.1072	−	9.61420i	−0.549955	−	0.374801i
$659$	−24.5644			−0.956893			−0.478447	−	0.878117i	$-0.658800\pi$
$659$	−24.5644			−0.956893			−0.478447	+	0.878117i	$0.658800\pi$
$660$	1.80549	−	1.04240i	0.0702786	−	0.0405753i
$661$	28.3265	−	7.59006i	1.10177	−	0.295219i	0.338286	−	0.941043i	$-0.390153\pi$
$661$	28.3265	−	7.59006i	1.10177	−	0.295219i	0.763486	+	0.645824i	$0.223486\pi$
$662$	−8.21870	−	4.74507i	−0.319429	−	0.184422i
$663$	15.7787	−	12.8786i	0.612793	−	0.500164i
$664$			0.911092i			0.0353572i
$665$	9.14214	+	6.23048i	0.354517	+	0.241608i
$666$	−8.85648			−0.343182
$667$	10.4808	−	6.05109i	0.405818	−	0.234299i
$668$	4.32116	+	16.1268i	0.167191	+	0.623965i
$669$	10.9330	−	2.92950i	0.422695	−	0.113261i
$670$	0.585277	−	2.18428i	0.0226112	−	0.0843862i
$671$	23.8893	+	23.8893i	0.922238	+	0.922238i
$672$	2.49745	+	0.873365i	0.0963411	+	0.0336908i
$673$			3.61720i			0.139433i	0.997567	+	0.0697164i	$0.0222094\pi$
$673$			3.61720i			0.139433i	−0.997567	+	0.0697164i	$0.977791\pi$
$674$	−22.8924	−	6.13401i	−0.881784	−	0.236273i
$675$	−2.23871	+	3.87756i	−0.0861680	+	0.149247i
$676$	−12.7364	−	2.60448i	−0.489863	−	0.100172i
$677$	−10.8597	+	6.26986i	−0.417373	+	0.240970i	−0.693953	−	0.720021i	$-0.744132\pi$
$677$	−10.8597	+	6.26986i	−0.417373	+	0.240970i	0.276580	+	0.960991i	$0.410799\pi$
$678$	−2.17529	+	2.17529i	−0.0835414	+	0.0835414i
$679$	2.46737	−	2.12415i	0.0946888	−	0.0815174i
$680$		−	4.08355i		−	0.156597i
$681$	2.15876	−	8.05661i	0.0827240	−	0.308730i
$682$	5.40577	+	20.1746i	0.206998	+	0.772526i
$683$	4.97429	+	18.5643i	0.190336	+	0.710344i	0.993425	+	0.114485i	$0.0365217\pi$
$683$	4.97429	+	18.5643i	0.190336	+	0.710344i	−0.803089	+	0.595859i	$0.796812\pi$
$684$	1.49712	−	5.58733i	0.0572438	−	0.213637i
$685$			4.10891i			0.156993i
$686$	−8.64466	+	16.3789i	−0.330055	+	0.625351i
$687$	16.8418	−	16.8418i	0.642553	−	0.642553i
$688$	1.14996	−	0.663931i	0.0438419	−	0.0253121i
$689$	−8.98929	+	23.6912i	−0.342465	+	0.902562i
$690$	0.620612	−	1.07493i	0.0236263	−	0.0409219i
$691$	−34.5833	−	9.26656i	−1.31561	−	0.352517i	−0.468279	−	0.883581i	$-0.655126\pi$
$691$	−34.5833	−	9.26656i	−1.31561	−	0.352517i	−0.847332	+	0.531064i	$0.821792\pi$
$692$			8.68403i			0.330117i
$693$	5.78254	−	4.97818i	0.219661	−	0.189105i
$694$	−15.3136	−	15.3136i	−0.581295	−	0.581295i
$695$	−2.73773	+	10.2174i	−0.103848	+	0.387567i
$696$	−6.80823	+	1.82426i	−0.258065	+	0.0691484i
$697$	−17.2612	−	64.4195i	−0.653813	−	2.44006i
$698$	2.63441	−	1.52098i	0.0997141	−	0.0575699i
$699$	7.91111			0.299226
$700$	5.14186	+	10.6720i	0.194344	+	0.403365i
$701$			42.5421i			1.60679i	0.595445	+	0.803396i	$0.296976\pi$
$701$			42.5421i			1.60679i	−0.595445	+	0.803396i	$0.703024\pi$
$702$	−3.58723	−	0.363021i	−0.135391	−	0.0137013i
$703$	44.3662	+	25.6148i	1.67330	+	0.966082i
$704$	−2.78568	+	0.746421i	−0.104989	+	0.0281318i
$705$	4.03958	−	2.33226i	0.152140	−	0.0878378i
$706$	12.7292			0.479070
$707$	−22.3632	+	32.8141i	−0.841054	+	1.23410i
$708$	−6.66698	−	6.66698i	−0.250560	−	0.250560i
$709$	17.5507	+	4.70270i	0.659131	+	0.176614i	0.572854	−	0.819658i	$-0.305836\pi$
$709$	17.5507	+	4.70270i	0.659131	+	0.176614i	0.0862771	+	0.996271i	$0.472503\pi$
$710$	5.57103	−	1.49275i	0.209077	−	0.0560220i
$711$	4.87553	−	8.44467i	0.182847	−	0.316700i
$712$	−1.10983	−	1.92228i	−0.0415925	−	0.0720403i
$713$	8.79291	+	8.79291i	0.329297	+	0.329297i
$714$	−2.78131	−	14.6844i	−0.104088	−	0.549550i
$715$	1.20458	+	7.41970i	0.0450488	+	0.277481i
$716$	−12.8730	−	22.2968i	−0.481088	−	0.833269i
$717$	−2.88673	−	10.7734i	−0.107807	−	0.402341i
$718$	9.03726	−	15.6530i	0.337267	−	0.584164i
$719$	−4.16889	−	7.22074i	−0.155474	−	0.269288i	0.777758	−	0.628564i	$-0.216357\pi$
$719$	−4.16889	−	7.22074i	−0.155474	−	0.269288i	−0.933231	+	0.359276i	$0.883024\pi$
$720$	−0.511166	+	0.511166i	−0.0190500	+	0.0190500i
$721$	19.7918	+	41.0783i	0.737086	+	1.52984i
$722$	−10.2245	+	10.2245i	−0.380517	+	0.380517i
$723$	−16.4477	−	4.40715i	−0.611697	−	0.163904i
$724$	19.3929	+	11.1965i	0.720730	+	0.416113i
$725$	−27.3306	−	15.7793i	−1.01503	−	0.586029i
$726$	0.694372	−	2.59143i	0.0257706	−	0.0961770i
$727$	−0.198078			−0.00734630			−0.00367315	−	0.999993i	$-0.501169\pi$
$727$	−0.198078			−0.00734630			−0.00367315	+	0.999993i	$0.501169\pi$
$728$	−6.13862	+	7.30188i	−0.227512	+	0.270626i
$729$	−1.00000			−0.0370370
$730$	−2.04652	+	7.63772i	−0.0757451	+	0.282685i
$731$	−6.49598	−	3.75046i	−0.240262	−	0.138716i
$732$	−10.1452	−	5.85736i	−0.374979	−	0.216494i
$733$	13.8836	+	3.72009i	0.512801	+	0.137405i	0.505935	−	0.862572i	$-0.331148\pi$
$733$	13.8836	+	3.72009i	0.512801	+	0.137405i	0.00686629	+	0.999976i	$0.497814\pi$
$734$	−4.48486	+	4.48486i	−0.165539	+	0.165539i
$735$	−3.00644	−	4.07036i	−0.110894	−	0.150137i
$736$	−1.21411	+	1.21411i	−0.0447527	+	0.0447527i
$737$	4.51072	+	7.81279i	0.166154	+	0.287788i
$738$	−5.90314	+	10.2245i	−0.217297	+	0.376370i
$739$	−4.80710	−	17.9404i	−0.176832	−	0.659947i	−0.996232	−	0.0867246i	$-0.972360\pi$
$739$	−4.80710	−	17.9404i	−0.176832	−	0.659947i	0.819400	−	0.573222i	$-0.194307\pi$
$740$	−3.20116	−	5.54458i	−0.117677	−	0.203823i
$741$	16.9202	+	12.1936i	0.621578	+	0.447942i
$742$	12.1313	+	14.0914i	0.445353	+	0.517312i
$743$	−17.6068	−	17.6068i	−0.645931	−	0.645931i	0.306076	−	0.952007i	$-0.400984\pi$
$743$	−17.6068	−	17.6068i	−0.645931	−	0.645931i	−0.952007	+	0.306076i	$0.900984\pi$
$744$	−3.62113	−	6.27198i	−0.132757	−	0.229942i
$745$	−0.0722667	+	0.125170i	−0.00264765	+	0.00458586i
$746$	28.1543	−	7.54391i	1.03080	−	0.276202i
$747$	−0.880047	−	0.235808i	−0.0321992	−	0.00862776i
$748$	11.5195	+	11.5195i	0.421194	+	0.421194i
$749$	−23.0687	−	47.8796i	−0.842913	−	1.74948i
$750$	−6.85120			−0.250171
$751$	18.8179	−	10.8645i	0.686674	−	0.396452i	−0.115691	−	0.993285i	$-0.536908\pi$
$751$	18.8179	−	10.8645i	0.686674	−	0.396452i	0.802365	+	0.596834i	$0.203575\pi$
$752$	−6.23265	+	1.67003i	−0.227282	+	0.0608999i
$753$	−4.75887	−	2.74754i	−0.173423	−	0.100126i
$754$	2.55871	−	25.2842i	0.0931828	−	0.920797i
$755$		−	0.552167i		−	0.0200954i
$756$	−1.48999	+	2.18630i	−0.0541905	+	0.0795151i
$757$	43.2335			1.57135			0.785675	−	0.618640i	$-0.212316\pi$
$757$	43.2335			1.57135			0.785675	+	0.618640i	$0.212316\pi$
$758$	6.86369	−	3.96276i	0.249301	−	0.143934i
$759$	1.28161	+	4.78304i	0.0465196	+	0.173613i
$760$	4.03907	−	1.08227i	0.146512	−	0.0392579i
$761$	−4.17307	+	15.5741i	−0.151274	+	0.564561i	0.848122	+	0.529801i	$0.177733\pi$
$761$	−4.17307	+	15.5741i	−0.151274	+	0.564561i	−0.999396	+	0.0347602i	$0.988933\pi$
$762$	1.23600	+	1.23600i	0.0447754	+	0.0447754i
$763$	−9.60961	+	1.82012i	−0.347891	+	0.0658927i
$764$		−	22.8675i		−	0.827318i
$765$	3.94440	+	1.05690i	0.142610	+	0.0382123i
$766$	10.3145	−	17.8653i	0.372679	−	0.645500i
$767$	31.0024	−	13.9470i	1.11943	−	0.503596i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	15.8362	−	15.8362i	0.571069	−	0.571069i	−0.361358	−	0.932427i	$-0.617687\pi$
$769$	15.8362	−	15.8362i	0.571069	−	0.571069i	0.932427	+	0.361358i	$0.117687\pi$
$770$	5.20667	+	1.82079i	0.187635	+	0.0656167i
$771$		−	0.0369149i		−	0.00132946i
$772$	−6.21156	+	23.1818i	−0.223559	+	0.834333i
$773$	1.84042	+	6.86856i	0.0661954	+	0.247045i	0.991093	−	0.133172i	$-0.0425162\pi$
$773$	1.84042	+	6.86856i	0.0661954	+	0.247045i	−0.924898	+	0.380216i	$0.875849\pi$
$774$	0.343676	+	1.28262i	0.0123532	+	0.0461027i
$775$	8.39263	−	31.3217i	0.301472	−	1.12511i
$776$		−	1.23056i		−	0.0441744i
$777$	−15.2878	−	17.7579i	−0.548446	−	0.637063i
$778$	−22.8161	+	22.8161i	−0.817997	+	0.817997i
$779$	59.1431	−	34.1463i	2.11902	−	1.22342i
$780$	−1.06933	−	2.37699i	−0.0382882	−	0.0851099i
$781$	−11.5046	+	19.9266i	−0.411667	+	0.713029i
$782$	9.36867	+	2.51033i	0.335023	+	0.0897691i
$783$		−	7.04840i		−	0.251889i
$784$	2.55985	+	6.51515i	0.0914231	+	0.232684i
$785$	−4.01471	−	4.01471i	−0.143291	−	0.143291i
$786$	−4.15661	+	15.5127i	−0.148261	+	0.553319i
$787$	38.7445	−	10.3816i	1.38109	−	0.370062i	0.509574	−	0.860427i	$-0.329803\pi$
$787$	38.7445	−	10.3816i	1.38109	−	0.370062i	0.871518	+	0.490364i	$0.163136\pi$
$788$	1.52732	+	5.70003i	0.0544085	+	0.203055i
$789$	4.88214	−	2.81870i	0.173809	−	0.100349i
$790$	7.04903			0.250793
$791$	−8.11653	−	0.606709i	−0.288591	−	0.0215721i
$792$		−	2.88395i		−	0.102477i
$793$	32.7221	−	26.7079i	1.16200	−	0.948426i
$794$	26.1868	+	15.1190i	0.929336	+	0.536553i
$795$	−4.90731	+	1.31491i	−0.174044	+	0.0466350i
$796$	6.08235	−	3.51164i	0.215583	−	0.124467i
$797$	−6.58690			−0.233320			−0.116660	−	0.993172i	$-0.537219\pi$
$797$	−6.58690			−0.233320			−0.116660	+	0.993172i	$0.537219\pi$
$798$	13.7873	−	6.64283i	0.488066	−	0.235154i
$799$	25.7736	+	25.7736i	0.911804	+	0.911804i
$800$	4.32485	+	1.15884i	0.152907	+	0.0409712i
$801$	2.14402	−	0.574488i	0.0757552	−	0.0202985i
$802$	9.03223	−	15.6443i	0.318939	−	0.552419i
$803$	−15.7725	−	27.3188i	−0.556599	−	0.964058i
$804$	−2.21194	−	2.21194i	−0.0780091	−	0.0780091i
$805$	3.22660	−	0.611137i	0.113723	−	0.0215398i
$806$	25.7749	−	4.18452i	0.907882	−	0.147394i
$807$	−1.12030	−	1.94041i	−0.0394363	−	0.0683056i
$808$	3.88460	+	14.4975i	0.136660	+	0.510021i
$809$	−10.0105	+	17.3386i	−0.351949	+	0.609593i	−0.986591	−	0.163213i	$-0.947814\pi$
$809$	−10.0105	+	17.3386i	−0.351949	+	0.609593i	0.634642	+	0.772806i	$0.281148\pi$
$810$	−0.361449	−	0.626048i	−0.0127000	−	0.0219971i
$811$	−18.9902	+	18.9902i	−0.666836	+	0.666836i	−0.956982	−	0.290146i	$-0.906296\pi$
$811$	−18.9902	+	18.9902i	−0.666836	+	0.666836i	0.290146	+	0.956982i	$0.406296\pi$
$812$	−15.4099	−	10.5021i	−0.540783	−	0.368550i
$813$	5.00657	−	5.00657i	0.175588	−	0.175588i
$814$	24.6713	+	6.61066i	0.864729	+	0.231703i
$815$	−12.0184	−	6.93882i	−0.420986	−	0.243056i
$816$	−4.89206	−	2.82443i	−0.171256	−	0.0988748i
$817$	1.98797	−	7.41921i	0.0695503	−	0.259565i
$818$	−5.82273			−0.203587
$819$	−5.46428	−	7.81931i	−0.190937	−	0.273229i
$820$	−8.53473			−0.298046
$821$	−5.34509	+	19.9481i	−0.186545	+	0.696195i	0.807750	+	0.589526i	$0.200685\pi$
$821$	−5.34509	+	19.9481i	−0.186545	+	0.696195i	−0.994295	+	0.106669i	$0.965981\pi$
$822$	4.92244	+	2.84197i	0.171690	+	0.0991251i
$823$	16.2183	+	9.36362i	0.565333	+	0.326395i	0.755283	−	0.655398i	$-0.227499\pi$
$823$	16.2183	+	9.36362i	0.565333	+	0.326395i	−0.189950	+	0.981794i	$0.560833\pi$
$824$	16.6470	+	4.46056i	0.579927	+	0.155391i
$825$	9.13062	−	9.13062i	0.317887	−	0.317887i
$826$	1.85949	−	24.8762i	0.0646998	−	0.865552i
$827$	15.9405	−	15.9405i	0.554305	−	0.554305i	−0.373375	−	0.927680i	$-0.621800\pi$
$827$	15.9405	−	15.9405i	0.554305	−	0.554305i	0.927680	+	0.373375i	$0.121800\pi$
$828$	−0.858506	−	1.48698i	−0.0298351	−	0.0516760i
$829$	−17.4933	+	30.2993i	−0.607568	+	1.05234i	0.384072	+	0.923303i	$0.374521\pi$
$829$	−17.4933	+	30.2993i	−0.607568	+	1.05234i	−0.991640	+	0.129035i	$0.958812\pi$
$830$	−0.170465	−	0.636184i	−0.00591693	−	0.0220823i
$831$	0.00327897	+	0.00567934i	0.000113746	+	0.000197014i
$832$	0.577792	+	3.55895i	0.0200313	+	0.123385i
$833$	24.6424	−	30.9245i	0.853808	−	1.07147i
$834$	10.3467	+	10.3467i	0.358278	+	0.358278i
$835$	−6.03464	−	10.4523i	−0.208837	−	0.361717i
$836$	−8.34100	+	14.4470i	−0.288479	+	0.499661i
$837$	6.99549	−	1.87444i	0.241799	−	0.0647900i
$838$	−13.7233	−	3.67716i	−0.474065	−	0.127025i
$839$	−15.8295	−	15.8295i	−0.546496	−	0.546496i	0.378930	−	0.925425i	$-0.376292\pi$
$839$	−15.8295	−	15.8295i	−0.546496	−	0.546496i	−0.925425	+	0.378930i	$0.876292\pi$
$840$	−1.90729	−	0.142569i	−0.0658076	−	0.00491910i
$841$	20.6799			0.713099
$842$	14.2437	−	8.22362i	0.490871	−	0.283405i
$843$	−5.18899	+	1.39039i	−0.178718	+	0.0478875i
$844$	−7.44402	−	4.29781i	−0.256234	−	0.147937i
$845$	9.38071	−	0.564366i	0.322706	−	0.0194148i
$846$		−	6.45252i		−	0.221842i
$847$	6.39463	−	3.08098i	0.219722	−	0.105864i
$848$	7.02785			0.241337
$849$	−12.8731	+	7.43230i	−0.441804	+	0.255076i
$850$	−6.54613	−	24.4305i	−0.224531	−	0.837959i
$851$	14.6885	−	3.93578i	0.503516	−	0.134917i
$852$	2.06496	−	7.70652i	0.0707442	−	0.264021i
$853$	36.3102	+	36.3102i	1.24324	+	1.24324i	0.958651	+	0.284585i	$0.0918559\pi$
$853$	36.3102	+	36.3102i	1.24324	+	1.24324i	0.284585	+	0.958651i	$0.408144\pi$
$854$	−5.76794	−	30.4528i	−0.197375	−	1.04207i
$855$			4.18155i			0.143006i
$856$	−19.4033	−	5.19909i	−0.663190	−	0.177701i
$857$	26.7597	−	46.3492i	0.914094	−	1.58326i	0.105872	−	0.994380i	$-0.466237\pi$
$857$	26.7597	−	46.3492i	0.914094	−	1.58326i	0.808222	−	0.588878i	$-0.200430\pi$
$858$	9.72190	+	3.68884i	0.331900	+	0.125935i
$859$	−7.68423	+	4.43649i	−0.262183	+	0.151371i	−0.625330	−	0.780361i	$-0.715036\pi$
$859$	−7.68423	+	4.43649i	−0.262183	+	0.151371i	0.363147	+	0.931732i	$0.381702\pi$
$860$	−0.678758	+	0.678758i	−0.0231455	+	0.0231455i
$861$	−30.6908	+	5.81302i	−1.04594	+	0.198107i
$862$			31.0209i			1.05658i
$863$	−9.75143	+	36.3928i	−0.331943	+	1.23883i	0.575203	+	0.818010i	$0.304923\pi$
$863$	−9.75143	+	36.3928i	−0.331943	+	1.23883i	−0.907146	+	0.420816i	$0.861744\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	−1.62478	−	6.06376i	−0.0552441	−	0.206174i
$866$	−8.50494	+	31.7409i	−0.289010	+	1.07860i
$867$			14.9096i			0.506358i
$868$	6.32514	−	18.0872i	0.214689	−	0.613918i
$869$	−19.8850	+	19.8850i	−0.674551	+	0.674551i
$870$	4.41263	−	2.54763i	0.149602	−	0.0863729i
$871$	10.2858	−	4.62726i	0.348522	−	0.156789i
$872$	−1.84833	+	3.20141i	−0.0625925	+	0.108413i
$873$	1.18863	+	0.318492i	0.0402289	+	0.0107793i
$874$			9.93193i			0.335953i
$875$	−11.8263	−	13.7372i	−0.399803	−	0.464402i
$876$	7.73442	+	7.73442i	0.261322	+	0.261322i
$877$	−4.92447	+	18.3784i	−0.166287	+	0.620593i	0.831585	+	0.555397i	$0.187434\pi$
$877$	−4.92447	+	18.3784i	−0.166287	+	0.620593i	−0.997872	+	0.0651958i	$0.979233\pi$
$878$	−37.8920	+	10.1531i	−1.27879	+	0.342651i
$879$	−5.44933	−	20.3372i	−0.183801	−	0.685955i
$880$	1.80549	−	1.04240i	0.0608630	−	0.0351393i
$881$	−6.26100			−0.210939			−0.105469	−	0.994423i	$-0.533634\pi$
$881$	−6.26100			−0.210939			−0.105469	+	0.994423i	$0.533634\pi$
$882$	−6.95569	+	0.786378i	−0.234210	+	0.0264787i
$883$			20.5024i			0.689961i	0.938610	+	0.344981i	$0.112115\pi$
$883$			20.5024i			0.689961i	−0.938610	+	0.344981i	$0.887885\pi$
$884$	15.7787	−	12.8786i	0.530694	−	0.433155i
$885$	5.90271	+	3.40793i	0.198417	+	0.114556i
$886$	−14.4983	+	3.88481i	−0.487080	+	0.130513i
$887$	2.64508	−	1.52714i	0.0888130	−	0.0512762i	−0.454936	−	0.890524i	$-0.650338\pi$
$887$	2.64508	−	1.52714i	0.0888130	−	0.0512762i	0.543749	+	0.839248i	$0.317004\pi$
$888$	−8.85648			−0.297204
$889$	−0.344731	+	4.61180i	−0.0115619	+	0.154675i
$890$	1.13461	+	1.13461i	0.0380322	+	0.0380322i
$891$	2.78568	+	0.746421i	0.0933238	+	0.0250060i
$892$	10.9330	−	2.92950i	0.366065	−	0.0980868i
$893$	−18.6621	+	32.3237i	−0.624502	+	1.08167i
$894$	0.0999681	+	0.173150i	0.00334343	+	0.00579100i
$895$	13.1605	+	13.1605i	0.439908	+	0.439908i
$896$	2.49745	+	0.873365i	0.0834338	+	0.0291771i
$897$	6.11077	−	0.992076i	0.204033	−	0.0331245i
$898$	2.85767	+	4.94963i	0.0953617	+	0.165171i
$899$	13.2118	+	49.3070i	0.440637	+	1.64448i
$900$	−2.23871	+	3.87756i	−0.0746236	+	0.129252i
$901$	−19.8497	−	34.3807i	−0.661289	−	1.14539i
$902$	24.0760	−	24.0760i	0.801645	−	0.801645i
$903$	−1.97850	+	2.90311i	−0.0658405	+	0.0966095i
$904$	−2.17529	+	2.17529i	−0.0723489	+	0.0723489i
$905$	−15.6362	−	4.18971i	−0.519765	−	0.139271i
$906$	−0.661491	−	0.381912i	−0.0219766	−	0.0126882i
$907$	−4.79921	−	2.77083i	−0.159355	−	0.0920038i	0.418202	−	0.908354i	$-0.362661\pi$
$907$	−4.79921	−	2.77083i	−0.159355	−	0.0920038i	−0.577557	+	0.816350i	$0.695994\pi$
$908$	2.15876	−	8.05661i	0.0716411	−	0.267368i
$909$	−15.0089			−0.497815
$910$	2.92021	−	6.24718i	0.0968039	−	0.207092i
$911$	−9.44622			−0.312967			−0.156484	−	0.987681i	$-0.550016\pi$
$911$	−9.44622			−0.312967			−0.156484	+	0.987681i	$0.550016\pi$
$912$	1.49712	−	5.58733i	0.0495746	−	0.185015i
$913$	2.27552	+	1.31377i	0.0753086	+	0.0434795i
$914$	11.8965	+	6.86846i	0.393502	+	0.227188i
$915$	8.17998	+	2.19182i	0.270422	+	0.0724593i
$916$	16.8418	−	16.8418i	0.556467	−	0.556467i
$917$	−38.2791	+	18.4432i	−1.26409	+	0.609047i
$918$	3.99435	−	3.99435i	0.131833	−	0.131833i
$919$	−7.11485	−	12.3233i	−0.234697	−	0.406507i	0.724488	−	0.689288i	$-0.242076\pi$
$919$	−7.11485	−	12.3233i	−0.234697	−	0.406507i	−0.959185	+	0.282781i	$0.908743\pi$
$920$	0.620612	−	1.07493i	0.0204610	−	0.0354394i
$921$	1.62051	+	6.04781i	0.0533975	+	0.199282i
$922$	−6.86822	−	11.8961i	−0.226193	−	0.391777i
$923$	23.3377	+	16.8184i	0.768171	+	0.553585i
$924$	5.78254	−	4.97818i	0.190232	−	0.163770i
$925$	−28.0397	−	28.0397i	−0.921941	−	0.921941i
$926$	−13.0809	−	22.6567i	−0.429864	−	0.744547i
$927$	−8.61714	+	14.9253i	−0.283024	+	0.490212i
$928$	−6.80823	+	1.82426i	−0.223491	+	0.0598842i
$929$	−22.7973	−	6.10853i	−0.747957	−	0.200414i	−0.135345	−	0.990799i	$-0.543214\pi$
$929$	−22.7973	−	6.10853i	−0.747957	−	0.200414i	−0.612612	+	0.790384i	$0.709881\pi$
$930$	3.70200	+	3.70200i	0.121393	+	0.121393i
$931$	37.1186	+	16.1780i	1.21651	+	0.530213i
$932$	7.91111			0.259137
$933$	−2.32625	+	1.34306i	−0.0761579	+	0.0439698i
$934$	25.6245	−	6.86605i	0.838458	−	0.224664i
$935$	−10.1990	−	5.88837i	−0.333542	−	0.192570i
$936$	−3.58723	−	0.363021i	−0.117252	−	0.0118657i
$937$			56.4405i			1.84383i	0.387390	+	0.921916i	$0.373377\pi$
$937$			56.4405i			1.84383i	−0.387390	+	0.921916i	$0.626623\pi$
$938$	0.616931	−	8.25329i	0.0201435	−	0.269480i
$939$	9.18122			0.299618
$940$	4.03958	−	2.33226i	0.131757	−	0.0760698i
$941$	5.99326	+	22.3671i	0.195375	+	0.729148i	0.992170	+	0.124898i	$0.0398605\pi$
$941$	5.99326	+	22.3671i	0.195375	+	0.729148i	−0.796795	+	0.604250i	$0.793473\pi$
$942$	−7.58641	+	2.03277i	−0.247178	+	0.0662313i
$943$	5.24665	−	19.5808i	0.170854	−	0.637638i
$944$	−6.66698	−	6.66698i	−0.216992	−	0.216992i
$945$	0.631353	−	1.80540i	0.0205379	−	0.0587296i
$946$		−	3.82949i		−	0.124507i
$947$	15.0518	+	4.03313i	0.489119	+	0.131059i	0.494945	−	0.868924i	$-0.335188\pi$
$947$	15.0518	+	4.03313i	0.489119	+	0.131059i	−0.00582672	+	0.999983i	$0.501855\pi$
$948$	4.87553	−	8.44467i	0.158350	−	0.274270i
$949$	−35.9661	+	16.1800i	−1.16751	+	0.525225i
$950$	22.4295	−	12.9497i	0.727708	−	0.420142i
$951$	−2.64272	+	2.64272i	−0.0856962	+	0.0856962i
$952$	−2.78131	−	14.6844i	−0.0901428	−	0.475924i
$953$			22.5166i			0.729384i	0.931128	+	0.364692i	$0.118826\pi$
$953$			22.5166i			0.729384i	−0.931128	+	0.364692i	$0.881174\pi$
$954$	−1.81894	+	6.78839i	−0.0588904	+	0.219782i
$955$	4.27851	+	15.9676i	0.138449	+	0.516699i
$956$	−2.88673	−	10.7734i	−0.0933635	−	0.348437i
$957$	−5.26107	+	19.6346i	−0.170066	+	0.634696i
$958$			17.1820i			0.555125i
$959$	2.79858	+	14.7756i	0.0903710	+	0.477129i
$960$	−0.511166	+	0.511166i	−0.0164978	+	0.0164978i
$961$	−18.5766	+	10.7252i	−0.599244	+	0.345974i
$962$	11.3283	−	29.8556i	0.365238	−	0.962582i
$963$	10.0439	−	17.3965i	0.323659	−	0.560594i
$964$	−16.4477	−	4.40715i	−0.529745	−	0.141945i
$965$		−	17.3493i		−	0.558493i
$966$	1.49958	−	4.28814i	0.0482481	−	0.137969i
$967$	−24.7711	−	24.7711i	−0.796584	−	0.796584i	0.185972	−	0.982555i	$-0.440457\pi$
$967$	−24.7711	−	24.7711i	−0.796584	−	0.796584i	−0.982555	+	0.185972i	$0.940457\pi$
$968$	0.694372	−	2.59143i	0.0223180	−	0.0832918i
$969$	−31.5621	+	8.45703i	−1.01392	+	0.271679i
$970$	0.230237	+	0.859256i	0.00739246	+	0.0275890i
$971$	18.6308	−	10.7565i	0.597892	−	0.345193i	−0.170320	−	0.985389i	$-0.554480\pi$
$971$	18.6308	−	10.7565i	0.597892	−	0.345193i	0.768212	+	0.640196i	$0.221147\pi$
$972$	−1.00000			−0.0320750
$973$	−2.88581	+	38.6062i	−0.0925147	+	1.23766i
$974$			15.9571i			0.511299i
$975$	−10.2079	−	12.5065i	−0.326914	−	0.400530i
$976$	−10.1452	−	5.85736i	−0.324741	−	0.187489i
$977$	−40.6321	+	10.8873i	−1.29994	+	0.348317i	−0.841426	−	0.540373i	$-0.818283\pi$
$977$	−40.6321	+	10.8873i	−1.29994	+	0.348317i	−0.458510	+	0.888689i	$0.651617\pi$
$978$	−16.6253	+	9.59862i	−0.531619	+	0.306930i
$979$	−6.40136			−0.204588
$980$	−3.00644	−	4.07036i	−0.0960371	−	0.130023i
$981$	−2.61394	−	2.61394i	−0.0834567	−	0.0834567i
$982$	−5.52111	−	1.47938i	−0.176186	−	0.0472088i
$983$	29.3438	−	7.86266i	0.935923	−	0.250780i	0.241544	−	0.970390i	$-0.422346\pi$
$983$	29.3438	−	7.86266i	0.935923	−	0.250780i	0.694378	+	0.719610i	$0.255679\pi$
$984$	−5.90314	+	10.2245i	−0.188185	+	0.325946i
$985$	−2.13295	−	3.69438i	−0.0679614	−	0.117713i
$986$	28.1537	+	28.1537i	0.896598	+	0.896598i
$987$	12.9378	−	11.1381i	0.411815	−	0.354531i
$988$	16.9202	+	12.1936i	0.538302	+	0.387929i
$989$	−1.13998	−	1.97450i	−0.0362492	−	0.0627854i
$990$	0.539586	+	2.01376i	0.0171492	+	0.0640015i
$991$	23.9432	−	41.4708i	0.760579	−	1.31736i	−0.181973	−	0.983304i	$-0.558248\pi$
$991$	23.9432	−	41.4708i	0.760579	−	1.31736i	0.942552	−	0.334059i	$-0.108418\pi$
$992$	−3.62113	−	6.27198i	−0.114971	−	0.199136i
$993$	6.71054	−	6.71054i	0.212953	−	0.212953i
$994$	19.0166	−	9.16236i	0.603171	−	0.290612i
$995$	−3.59006	+	3.59006i	−0.113813	+	0.113813i
$996$	−0.880047	−	0.235808i	−0.0278854	−	0.00747186i
$997$	−18.6023	−	10.7400i	−0.589139	−	0.340140i	0.175618	−	0.984458i	$-0.443808\pi$
$997$	−18.6023	−	10.7400i	−0.589139	−	0.340140i	−0.764757	+	0.644319i	$0.777141\pi$
$998$	−27.0829	−	15.6363i	−0.857293	−	0.494959i
$999$	2.29223	−	8.55470i	0.0725228	−	0.270659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.a.73.4	✓	40
7.5	odd	6		546.2.bz.b.229.9	yes	40
13.5	odd	4		546.2.bz.b.31.9	yes	40
91.5	even	12	inner	546.2.bz.a.187.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.4	✓	40	1.1	even	1	trivial
546.2.bz.a.187.4	yes	40	91.5	even	12	inner
546.2.bz.b.31.9	yes	40	13.5	odd	4
546.2.bz.b.229.9	yes	40	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.698266 + 0.187100i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.63839 + 0.197219i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.698266 + 0.187100i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.63839 + 0.197219i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.361449 + 0.626048i) q^{10} +(-0.746421 - 2.78568i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.55895 + 0.577792i) q^{13} +(-0.873365 + 2.49745i) q^{14} +(-0.511166 - 0.511166i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.82443 - 4.89206i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(5.58733 + 1.49712i) q^{19} +(-0.511166 - 0.511166i) q^{20} +(-2.18630 - 1.48999i) q^{21} +2.88395 q^{22} +(1.48698 - 0.858506i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(-3.87756 - 2.23871i) q^{25} +(0.363021 - 3.58723i) q^{26} -1.00000i q^{27} +(-2.18630 - 1.48999i) q^{28} +7.04840 q^{29} +(0.626048 - 0.361449i) q^{30} +(1.87444 + 6.99549i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.746421 + 2.78568i) q^{33} +(3.99435 + 3.99435i) q^{34} +(1.80540 + 0.631353i) q^{35} -1.00000i q^{36} +(8.55470 + 2.29223i) q^{37} +(-2.89221 + 5.00946i) q^{38} +(3.37104 + 1.27909i) q^{39} +(0.626048 - 0.361449i) q^{40} +(8.34830 - 8.34830i) q^{41} +(2.00508 - 1.72617i) q^{42} -1.32786i q^{43} +(-0.746421 + 2.78568i) q^{44} +(0.187100 + 0.698266i) q^{45} +(0.444395 + 1.65851i) q^{46} +(-1.67003 + 6.23265i) q^{47} -1.00000i q^{48} +(6.92221 + 1.04068i) q^{49} +(3.16601 - 3.16601i) q^{50} +(-4.89206 + 2.82443i) q^{51} +(3.37104 + 1.27909i) q^{52} +(3.51393 - 6.08630i) q^{53} +(0.965926 + 0.258819i) q^{54} -2.08480i q^{55} +(2.00508 - 1.72617i) q^{56} +(-4.09021 - 4.09021i) q^{57} +(-1.82426 + 6.80823i) q^{58} +(-9.10726 + 2.44028i) q^{59} +(0.187100 + 0.698266i) q^{60} +(-10.1452 + 5.85736i) q^{61} -7.24226 q^{62} +(1.14840 + 2.38352i) q^{63} -1.00000i q^{64} +(-2.59320 - 0.262427i) q^{65} +(-2.49757 - 1.44197i) q^{66} +(-3.02156 + 0.809626i) q^{67} +(-4.89206 + 2.82443i) q^{68} -1.71701 q^{69} +(-1.07711 + 1.58047i) q^{70} +(-5.64157 - 5.64157i) q^{71} +(0.965926 + 0.258819i) q^{72} +(10.5654 - 2.83100i) q^{73} +(-4.42824 + 7.66994i) q^{74} +(2.23871 + 3.87756i) q^{75} +(-4.09021 - 4.09021i) q^{76} +(-1.41996 - 7.49692i) q^{77} +(-2.10800 + 2.92512i) q^{78} +(-4.87553 - 8.44467i) q^{79} +(0.187100 + 0.698266i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.90314 + 10.2245i) q^{82} +(-0.644239 + 0.644239i) q^{83} +(1.14840 + 2.38352i) q^{84} +(2.88750 - 2.88750i) q^{85} +(1.28262 + 0.343676i) q^{86} +(-6.10409 - 3.52420i) q^{87} +(-2.49757 - 1.44197i) q^{88} +(0.574488 - 2.14402i) q^{89} -0.722898 q^{90} +(-9.50386 + 0.822548i) q^{91} -1.71701 q^{92} +(1.87444 - 6.99549i) q^{93} +(-5.58804 - 3.22626i) q^{94} +(3.62133 + 2.09078i) q^{95} +(0.965926 + 0.258819i) q^{96} +(0.870136 - 0.870136i) q^{97} +(-2.79682 + 6.41699i) q^{98} +(2.03926 - 2.03926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 + 20 * q^9	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

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