LMFDB - Embedded newform 546.2.by.b.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			115.1
Character	$\chi$	$=$	546.115
Dual form			546.2.by.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-4.03777 - 1.08192i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-0.0127227 - 2.64572i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-4.03777 - 1.08192i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-0.0127227 - 2.64572i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +4.18021 q^{10} +(-0.447823 + 0.447823i) q^{11} +(0.500000 + 0.866025i) q^{12} +(1.96448 + 3.02338i) q^{13} +(0.697052 + 2.55228i) q^{14} +(1.08192 - 4.03777i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.95862 + 5.12448i) q^{17} +(0.965926 - 0.258819i) q^{18} +(1.74728 - 1.74728i) q^{19} +(-4.03777 + 1.08192i) q^{20} +(2.64572 - 0.0127227i) q^{21} +(0.316659 - 0.548469i) q^{22} +(4.45906 + 2.57444i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(10.8029 + 6.23707i) q^{25} +(-2.68005 - 2.41192i) q^{26} -1.00000i q^{27} +(-1.33388 - 2.28490i) q^{28} +(-0.692966 - 1.20025i) q^{29} +4.18021i q^{30} +(1.43576 + 5.35833i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.447823 - 0.447823i) q^{33} +(-4.18412 - 4.18412i) q^{34} +(-2.81108 + 10.6966i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.583233 - 2.17666i) q^{37} +(-1.23551 + 2.13997i) q^{38} +(-3.02338 + 1.96448i) q^{39} +(3.62017 - 2.09010i) q^{40} +(1.22233 + 0.327523i) q^{41} +(-2.55228 + 0.697052i) q^{42} +(-2.40764 - 1.39005i) q^{43} +(-0.163915 + 0.611738i) q^{44} +(4.03777 + 1.08192i) q^{45} +(-4.97344 - 1.33263i) q^{46} +(0.859880 - 3.20911i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-6.99968 + 0.0673217i) q^{49} +(-12.0491 - 3.22855i) q^{50} +(-5.12448 + 2.95862i) q^{51} +(3.21298 + 1.63609i) q^{52} +(5.96016 - 10.3233i) q^{53} +(0.258819 + 0.965926i) q^{54} +(2.29272 - 1.32370i) q^{55} +(1.87980 + 1.86181i) q^{56} +(1.74728 + 1.74728i) q^{57} +(0.980002 + 0.980002i) q^{58} +(-3.12406 + 11.6591i) q^{59} +(-1.08192 - 4.03777i) q^{60} +12.3857i q^{61} +(-2.77367 - 4.80415i) q^{62} +(0.0127227 + 2.64572i) q^{63} -1.00000i q^{64} +(-4.66106 - 14.3331i) q^{65} +(0.548469 + 0.316659i) q^{66} +(4.49136 + 4.49136i) q^{67} +(5.12448 + 2.95862i) q^{68} +(-2.57444 + 4.45906i) q^{69} +(-0.0531837 - 11.0597i) q^{70} +(14.8816 - 3.98751i) q^{71} +(0.707107 - 0.707107i) q^{72} +(8.01215 - 2.14685i) q^{73} +(1.12672 + 1.95154i) q^{74} +(-6.23707 + 10.8029i) q^{75} +(0.639550 - 2.38683i) q^{76} +(1.19051 + 1.17912i) q^{77} +(2.41192 - 2.68005i) q^{78} +(-0.213699 - 0.370137i) q^{79} +(-2.95585 + 2.95585i) q^{80} +1.00000 q^{81} -1.26545 q^{82} +(-5.72801 + 5.72801i) q^{83} +(2.28490 - 1.33388i) q^{84} +(-6.40196 - 23.8925i) q^{85} +(2.68538 + 0.719544i) q^{86} +(1.20025 - 0.692966i) q^{87} -0.633318i q^{88} +(-1.62138 + 0.434447i) q^{89} -4.18021 q^{90} +(7.97403 - 5.23592i) q^{91} +5.14888 q^{92} +(-5.35833 + 1.43576i) q^{93} +3.32232i q^{94} +(-8.94554 + 5.16471i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(1.95617 + 7.30052i) q^{97} +(6.74374 - 1.87668i) q^{98} +(0.447823 - 0.447823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−4.03777	−	1.08192i	−1.80575	−	0.483848i	−0.810895	−	0.585192i	$-0.801019\pi$
$5$	−4.03777	−	1.08192i	−1.80575	−	0.483848i	−0.994851	+	0.101343i	$0.967686\pi$
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	−0.0127227	−	2.64572i	−0.00480875	−	0.999988i
$7$	−0.0127227	−	2.64572i	−0.00480875	−	0.999988i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	4.18021			1.32190
$11$	−0.447823	+	0.447823i	−0.135024	+	0.135024i	−0.771388	−	0.636365i	$-0.780437\pi$
$11$	−0.447823	+	0.447823i	−0.135024	+	0.135024i	0.636365	+	0.771388i	$0.280437\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.96448	+	3.02338i	0.544848	+	0.838535i
$13$	1.96448	+	3.02338i	0.544848	+	0.838535i
$14$	0.697052	+	2.55228i	0.186295	+	0.682125i
$15$	1.08192	−	4.03777i	0.279350	−	1.04255i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.95862	+	5.12448i	0.717570	+	1.24287i	0.961960	+	0.273191i	$0.0880792\pi$
$17$	2.95862	+	5.12448i	0.717570	+	1.24287i	−0.244389	+	0.969677i	$0.578587\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	1.74728	−	1.74728i	0.400854	−	0.400854i	−0.477680	−	0.878534i	$-0.658522\pi$
$19$	1.74728	−	1.74728i	0.400854	−	0.400854i	0.878534	+	0.477680i	$0.158522\pi$
$20$	−4.03777	+	1.08192i	−0.902873	+	0.241924i
$21$	2.64572	−	0.0127227i	0.577344	−	0.00277633i
$22$	0.316659	−	0.548469i	0.0675119	−	0.116934i
$23$	4.45906	+	2.57444i	0.929779	+	0.536808i	0.886742	−	0.462265i	$-0.152963\pi$
$23$	4.45906	+	2.57444i	0.929779	+	0.536808i	0.0430374	+	0.999073i	$0.486297\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	10.8029	+	6.23707i	2.16059	+	1.24741i
$26$	−2.68005	−	2.41192i	−0.525600	−	0.473016i
$27$		−	1.00000i		−	0.192450i
$28$	−1.33388	−	2.28490i	−0.252079	−	0.431806i
$29$	−0.692966	−	1.20025i	−0.128681	−	0.222881i	0.794485	−	0.607284i	$-0.207741\pi$
$29$	−0.692966	−	1.20025i	−0.128681	−	0.222881i	−0.923166	+	0.384402i	$0.874408\pi$
$30$			4.18021i			0.763198i
$31$	1.43576	+	5.35833i	0.257870	+	0.962384i	0.966471	+	0.256775i	$0.0826599\pi$
$31$	1.43576	+	5.35833i	0.257870	+	0.962384i	−0.708601	+	0.705609i	$0.750673\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.447823	−	0.447823i	−0.0779560	−	0.0779560i
$34$	−4.18412	−	4.18412i	−0.717570	−	0.717570i
$35$	−2.81108	+	10.6966i	−0.475159	+	1.80805i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−0.583233	−	2.17666i	−0.0958830	−	0.357840i	0.901269	−	0.433260i	$-0.142637\pi$
$37$	−0.583233	−	2.17666i	−0.0958830	−	0.357840i	−0.997152	+	0.0754201i	$0.975970\pi$
$38$	−1.23551	+	2.13997i	−0.200427	+	0.347150i
$39$	−3.02338	+	1.96448i	−0.484128	+	0.314568i
$40$	3.62017	−	2.09010i	0.572399	−	0.330475i
$41$	1.22233	+	0.327523i	0.190896	+	0.0511505i	0.353000	−	0.935623i	$-0.385161\pi$
$41$	1.22233	+	0.327523i	0.190896	+	0.0511505i	−0.162104	+	0.986774i	$0.551828\pi$
$42$	−2.55228	+	0.697052i	−0.393825	+	0.107557i
$43$	−2.40764	−	1.39005i	−0.367162	−	0.211981i	0.305056	−	0.952334i	$-0.401325\pi$
$43$	−2.40764	−	1.39005i	−0.367162	−	0.211981i	−0.672218	+	0.740353i	$0.734658\pi$
$44$	−0.163915	+	0.611738i	−0.0247111	+	0.0922230i
$45$	4.03777	+	1.08192i	0.601915	+	0.161283i
$46$	−4.97344	−	1.33263i	−0.733294	−	0.196485i
$47$	0.859880	−	3.20911i	0.125426	−	0.468097i	−0.874428	−	0.485155i	$-0.838763\pi$
$47$	0.859880	−	3.20911i	0.125426	−	0.468097i	0.999855	+	0.0170575i	$0.00542984\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−6.99968	+	0.0673217i	−0.999954	+	0.00961738i
$50$	−12.0491	−	3.22855i	−1.70400	−	0.456585i
$51$	−5.12448	+	2.95862i	−0.717570	+	0.414289i
$52$	3.21298	+	1.63609i	0.445560	+	0.226884i
$53$	5.96016	−	10.3233i	0.818690	−	1.41801i	−0.0879571	−	0.996124i	$-0.528034\pi$
$53$	5.96016	−	10.3233i	0.818690	−	1.41801i	0.906647	−	0.421889i	$-0.138633\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	2.29272	−	1.32370i	0.309150	−	0.178488i
$56$	1.87980	+	1.86181i	0.251199	+	0.248795i
$57$	1.74728	+	1.74728i	0.231433	+	0.231433i
$58$	0.980002	+	0.980002i	0.128681	+	0.128681i
$59$	−3.12406	+	11.6591i	−0.406718	+	1.51789i	0.394148	+	0.919047i	$0.371040\pi$
$59$	−3.12406	+	11.6591i	−0.406718	+	1.51789i	−0.800866	+	0.598844i	$0.795627\pi$
$60$	−1.08192	−	4.03777i	−0.139675	−	0.521274i
$61$			12.3857i			1.58583i	0.609331	+	0.792916i	$0.291438\pi$
$61$			12.3857i			1.58583i	−0.609331	+	0.792916i	$0.708562\pi$
$62$	−2.77367	−	4.80415i	−0.352257	−	0.610127i
$63$	0.0127227	+	2.64572i	0.00160292	+	0.333329i
$64$		−	1.00000i		−	0.125000i
$65$	−4.66106	−	14.3331i	−0.578133	−	1.77781i
$66$	0.548469	+	0.316659i	0.0675119	+	0.0389780i
$67$	4.49136	+	4.49136i	0.548707	+	0.548707i	0.926067	−	0.377359i	$-0.123168\pi$
$67$	4.49136	+	4.49136i	0.548707	+	0.548707i	−0.377359	+	0.926067i	$0.623168\pi$
$68$	5.12448	+	2.95862i	0.621434	+	0.358785i
$69$	−2.57444	+	4.45906i	−0.309926	+	0.536808i
$70$	−0.0531837	−	11.0597i	−0.00635667	−	1.32188i
$71$	14.8816	−	3.98751i	1.76612	−	0.473231i	0.778178	−	0.628044i	$-0.216144\pi$
$71$	14.8816	−	3.98751i	1.76612	−	0.473231i	0.987944	+	0.154813i	$0.0494776\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	8.01215	−	2.14685i	0.937752	−	0.251270i	0.242595	−	0.970128i	$-0.422002\pi$
$73$	8.01215	−	2.14685i	0.937752	−	0.251270i	0.695157	+	0.718858i	$0.255335\pi$
$74$	1.12672	+	1.95154i	0.130979	+	0.226862i
$75$	−6.23707	+	10.8029i	−0.720195	+	1.24741i
$76$	0.639550	−	2.38683i	0.0733614	−	0.273788i
$77$	1.19051	+	1.17912i	0.135672	+	0.134373i
$78$	2.41192	−	2.68005i	0.273096	−	0.303456i
$79$	−0.213699	−	0.370137i	−0.0240430	−	0.0416437i	0.853754	−	0.520677i	$-0.174321\pi$
$79$	−0.213699	−	0.370137i	−0.0240430	−	0.0416437i	−0.877797	+	0.479034i	$0.840987\pi$
$80$	−2.95585	+	2.95585i	−0.330475	+	0.330475i
$81$	1.00000			0.111111
$82$	−1.26545			−0.139746
$83$	−5.72801	+	5.72801i	−0.628731	+	0.628731i	−0.947749	−	0.319018i	$-0.896647\pi$
$83$	−5.72801	+	5.72801i	−0.628731	+	0.628731i	0.319018	+	0.947749i	$0.396647\pi$
$84$	2.28490	−	1.33388i	0.249303	−	0.145538i
$85$	−6.40196	−	23.8925i	−0.694390	−	2.59150i
$86$	2.68538	+	0.719544i	0.289571	+	0.0775904i
$87$	1.20025	−	0.692966i	0.128681	−	0.0742937i
$88$		−	0.633318i		−	0.0675119i
$89$	−1.62138	+	0.434447i	−0.171866	+	0.0460513i	−0.343726	−	0.939070i	$-0.611689\pi$
$89$	−1.62138	+	0.434447i	−0.171866	+	0.0460513i	0.171860	+	0.985121i	$0.445022\pi$
$90$	−4.18021			−0.440633
$91$	7.97403	−	5.23592i	0.835905	−	0.548874i
$92$	5.14888			0.536808
$93$	−5.35833	+	1.43576i	−0.555633	+	0.148881i
$94$			3.32232i			0.342671i
$95$	−8.94554	+	5.16471i	−0.917793	+	0.529888i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	1.95617	+	7.30052i	0.198619	+	0.741256i	0.991300	+	0.131620i	$0.0420178\pi$
$97$	1.95617	+	7.30052i	0.198619	+	0.741256i	−0.792681	+	0.609636i	$0.791316\pi$
$98$	6.74374	−	1.87668i	0.681221	−	0.189573i
$99$	0.447823	−	0.447823i	0.0450079	−	0.0450079i
$100$	12.4741			1.24741
$101$	4.20030			0.417946			0.208973	−	0.977921i	$-0.432988\pi$
$101$	4.20030			0.417946			0.208973	+	0.977921i	$0.432988\pi$
$102$	4.18412	−	4.18412i	0.414289	−	0.414289i
$103$	0.712002	+	1.23322i	0.0701556	+	0.121513i	0.898969	−	0.438011i	$-0.144317\pi$
$103$	0.712002	+	1.23322i	0.0701556	+	0.121513i	−0.828814	+	0.559525i	$0.810984\pi$
$104$	−3.52695	−	0.748759i	−0.345846	−	0.0734219i
$105$	−10.6966	−	2.81108i	−1.04388	−	0.274333i
$106$	−3.08520	+	11.5141i	−0.299661	+	1.11835i
$107$	5.47839	−	9.48886i	0.529616	−	0.917322i	−0.469787	−	0.882780i	$-0.655669\pi$
$107$	5.47839	−	9.48886i	0.529616	−	0.917322i	0.999403	−	0.0345425i	$-0.0109974\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.12234	−	0.300729i	0.107500	−	0.0288046i	−0.204668	−	0.978831i	$-0.565611\pi$
$109$	1.12234	−	0.300729i	0.107500	−	0.0288046i	0.312168	+	0.950027i	$0.398945\pi$
$110$	−1.87200	+	1.87200i	−0.178488	+	0.178488i
$111$	2.17666	−	0.583233i	0.206599	−	0.0553581i
$112$	−2.29762	−	1.31184i	−0.217105	−	0.123957i
$113$	−8.19504	+	14.1942i	−0.770925	+	1.33528i	0.166132	+	0.986104i	$0.446872\pi$
$113$	−8.19504	+	14.1942i	−0.770925	+	1.33528i	−0.937057	+	0.349177i	$0.886461\pi$
$114$	−2.13997	−	1.23551i	−0.200427	−	0.115717i
$115$	−15.2193	−	15.2193i	−1.41921	−	1.41921i
$116$	−1.20025	−	0.692966i	−0.111441	−	0.0643403i
$117$	−1.96448	−	3.02338i	−0.181616	−	0.279512i
$118$		−	12.0704i		−	1.11117i
$119$	13.5203	−	7.89288i	1.23940	−	0.723539i
$120$	2.09010	+	3.62017i	0.190800	+	0.330475i
$121$			10.5989i			0.963537i
$122$	−3.20567	−	11.9637i	−0.290227	−	1.08314i
$123$	−0.327523	+	1.22233i	−0.0295318	+	0.110214i
$124$	3.92257	+	3.92257i	0.352257	+	0.352257i
$125$	−22.0925	−	22.0925i	−1.97601	−	1.97601i
$126$	−0.697052	−	2.55228i	−0.0620983	−	0.227375i
$127$	15.9441	−	9.20531i	1.41481	−	0.816839i	0.418971	−	0.908000i	$-0.362391\pi$
$127$	15.9441	−	9.20531i	1.41481	−	0.816839i	0.995836	+	0.0911603i	$0.0290576\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	1.39005	−	2.40764i	0.122387	−	0.211981i
$130$	8.21192	+	12.6384i	0.720233	+	1.10846i
$131$	9.34579	−	5.39580i	0.816546	−	0.471433i	−0.0326781	−	0.999466i	$-0.510404\pi$
$131$	9.34579	−	5.39580i	0.816546	−	0.471433i	0.849224	+	0.528033i	$0.177070\pi$
$132$	−0.611738	−	0.163915i	−0.0532450	−	0.0142669i
$133$	−4.64505	−	4.60059i	−0.402777	−	0.398922i
$134$	−5.50077	−	3.17587i	−0.475195	−	0.274354i
$135$	−1.08192	+	4.03777i	−0.0931166	+	0.347516i
$136$	−5.71561	−	1.53149i	−0.490110	−	0.131325i
$137$	−14.3833	−	3.85400i	−1.22885	−	0.329269i	−0.414718	−	0.909950i	$-0.636120\pi$
$137$	−14.3833	−	3.85400i	−1.22885	−	0.329269i	−0.814131	+	0.580681i	$0.802787\pi$
$138$	1.33263	−	4.97344i	0.113441	−	0.423367i
$139$	−8.18822	−	4.72747i	−0.694516	−	0.400979i	0.110786	−	0.993844i	$-0.464663\pi$
$139$	−8.18822	−	4.72747i	−0.694516	−	0.400979i	−0.805302	+	0.592865i	$0.797997\pi$
$140$	2.91382	+	10.6691i	0.246263	+	0.901699i
$141$	3.20911	+	0.859880i	0.270256	+	0.0724149i
$142$	−13.3425	+	7.70329i	−1.11968	+	0.646445i
$143$	−2.23368	−	0.474203i	−0.186790	−	0.0396548i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.49946	+	5.59608i	0.124524	+	0.464729i
$146$	−7.18350	+	4.14740i	−0.594511	+	0.343241i
$147$	−0.0673217	−	6.99968i	−0.00555260	−	0.577324i
$148$	−1.59342	−	1.59342i	−0.130979	−	0.130979i
$149$	−9.91933	−	9.91933i	−0.812623	−	0.812623i	0.172403	−	0.985026i	$-0.444847\pi$
$149$	−9.91933	−	9.91933i	−0.812623	−	0.812623i	−0.985026	+	0.172403i	$0.944847\pi$
$150$	3.22855	−	12.0491i	0.263610	−	0.983805i
$151$	1.90212	+	7.09882i	0.154793	+	0.577694i	0.999123	+	0.0418710i	$0.0133319\pi$
$151$	1.90212	+	7.09882i	0.154793	+	0.577694i	−0.844330	+	0.535823i	$0.820001\pi$
$152$			2.47103i			0.200427i
$153$	−2.95862	−	5.12448i	−0.239190	−	0.414289i
$154$	−1.45513	−	0.830813i	−0.117257	−	0.0669488i
$155$		−	23.1891i		−	1.86259i
$156$	−1.63609	+	3.21298i	−0.130992	+	0.257244i
$157$	−18.5419	−	10.7052i	−1.47980	−	0.854365i	−0.480065	−	0.877233i	$-0.659387\pi$
$157$	−18.5419	−	10.7052i	−1.47980	−	0.854365i	−0.999738	+	0.0228679i	$0.992720\pi$
$158$	0.302216	+	0.302216i	0.0240430	+	0.0240430i
$159$	10.3233	+	5.96016i	0.818690	+	0.472671i
$160$	2.09010	−	3.62017i	0.165237	−	0.286199i
$161$	6.75452	−	11.8302i	0.532331	−	0.932350i
$162$	−0.965926	+	0.258819i	−0.0758903	+	0.0203347i
$163$	−0.157580	+	0.157580i	−0.0123426	+	0.0123426i	−0.713251	−	0.700909i	$-0.752778\pi$
$163$	−0.157580	+	0.157580i	−0.0123426	+	0.0123426i	0.700909	+	0.713251i	$0.252778\pi$
$164$	1.22233	−	0.327523i	0.0954481	−	0.0255753i
$165$	1.32370	+	2.29272i	0.103050	+	0.178488i
$166$	4.05032	−	7.01535i	0.314366	−	0.544497i
$167$	−4.93109	+	18.4031i	−0.381579	+	1.42407i	0.461909	+	0.886927i	$0.347165\pi$
$167$	−4.93109	+	18.4031i	−0.381579	+	1.42407i	−0.843489	+	0.537147i	$0.819502\pi$
$168$	−1.86181	+	1.87980i	−0.143642	+	0.145030i
$169$	−5.28167	+	11.8787i	−0.406282	+	0.913748i
$170$	12.3676	+	21.4214i	0.948555	+	1.64295i
$171$	−1.74728	+	1.74728i	−0.133618	+	0.133618i
$172$	−2.78010			−0.211981
$173$	15.2038			1.15592			0.577962	−	0.816064i	$-0.303848\pi$
$173$	15.2038			1.15592			0.577962	+	0.816064i	$0.303848\pi$
$174$	−0.980002	+	0.980002i	−0.0742937	+	0.0742937i
$175$	16.3641	−	28.6609i	1.23701	−	2.16656i
$176$	0.163915	+	0.611738i	0.0123555	+	0.0461115i
$177$	−11.6591	−	3.12406i	−0.876354	−	0.234818i
$178$	1.45369	−	0.839287i	0.108959	−	0.0629072i
$179$			20.7926i			1.55411i	0.629434	+	0.777054i	$0.283287\pi$
$179$			20.7926i			1.55411i	−0.629434	+	0.777054i	$0.716713\pi$
$180$	4.03777	−	1.08192i	0.300958	−	0.0806414i
$181$	−19.5707			−1.45468			−0.727340	−	0.686278i	$-0.759243\pi$
$181$	−19.5707			−1.45468			−0.727340	+	0.686278i	$0.759243\pi$
$182$	−6.34716	+	7.12134i	−0.470483	+	0.527869i
$183$	−12.3857			−0.915580
$184$	−4.97344	+	1.33263i	−0.366647	+	0.0982427i
$185$			9.41985i			0.692561i
$186$	4.80415	−	2.77367i	0.352257	−	0.203376i
$187$	−3.61980	−	0.969922i	−0.264706	−	0.0709278i
$188$	−0.859880	−	3.20911i	−0.0627132	−	0.234049i
$189$	−2.64572	+	0.0127227i	−0.192448	+	0.000925443i
$190$	7.30400	−	7.30400i	0.529888	−	0.529888i
$191$	5.27268			0.381518			0.190759	−	0.981637i	$-0.438905\pi$
$191$	5.27268			0.381518			0.190759	+	0.981637i	$0.438905\pi$
$192$	1.00000			0.0721688
$193$	9.66089	−	9.66089i	0.695406	−	0.695406i	−0.268010	−	0.963416i	$-0.586366\pi$
$193$	9.66089	−	9.66089i	0.695406	−	0.695406i	0.963416	+	0.268010i	$0.0863660\pi$
$194$	−3.77903	−	6.54547i	−0.271319	−	0.469937i
$195$	14.3331	−	4.66106i	1.02642	−	0.333785i
$196$	−6.02824	+	3.55814i	−0.430588	+	0.254153i
$197$	3.27692	−	12.2296i	0.233471	−	0.871325i	−0.745362	−	0.666660i	$-0.767723\pi$
$197$	3.27692	−	12.2296i	0.233471	−	0.871325i	0.978832	−	0.204664i	$-0.0656102\pi$
$198$	−0.316659	+	0.548469i	−0.0225040	+	0.0389780i
$199$	−2.99838	−	5.19335i	−0.212549	−	0.368147i	0.739962	−	0.672648i	$-0.234843\pi$
$199$	−2.99838	−	5.19335i	−0.212549	−	0.368147i	−0.952512	+	0.304502i	$0.901510\pi$
$200$	−12.0491	+	3.22855i	−0.852000	+	0.228293i
$201$	−4.49136	+	4.49136i	−0.316796	+	0.316796i
$202$	−4.05718	+	1.08712i	−0.285462	+	0.0764893i
$203$	−3.16672	+	1.84866i	−0.222260	+	0.129751i
$204$	−2.95862	+	5.12448i	−0.207145	+	0.358785i
$205$	−4.58115	−	2.64493i	−0.319961	−	0.184730i
$206$	−1.00692	−	1.00692i	−0.0701556	−	0.0701556i
$207$	−4.45906	−	2.57444i	−0.309926	−	0.178936i
$208$	3.60056	−	0.189595i	0.249654	−	0.0131461i
$209$			1.56495i			0.108250i
$210$	11.0597	−	0.0531837i	0.763189	−	0.00367003i
$211$	10.5594	+	18.2895i	0.726941	+	1.25910i	0.958170	+	0.286199i	$0.0923918\pi$
$211$	10.5594	+	18.2895i	0.726941	+	1.25910i	−0.231230	+	0.972899i	$0.574275\pi$
$212$		−	11.9203i		−	0.818690i
$213$	3.98751	+	14.8816i	0.273220	+	1.01967i
$214$	−2.83583	+	10.5834i	−0.193853	+	0.723469i
$215$	8.21758	+	8.21758i	0.560435	+	0.560435i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	14.1584	−	3.86679i	0.961133	−	0.262495i
$218$	−1.00626	+	0.580963i	−0.0681524	+	0.0393478i
$219$	2.14685	+	8.01215i	0.145071	+	0.541411i
$220$	1.32370	−	2.29272i	0.0892439	−	0.154575i
$221$	−9.68112	+	19.0119i	−0.651222	+	1.27888i
$222$	−1.95154	+	1.12672i	−0.130979	+	0.0756205i
$223$	18.8580	+	5.05298i	1.26282	+	0.338373i	0.827277	−	0.561794i	$-0.189888\pi$
$223$	18.8580	+	5.05298i	1.26282	+	0.338373i	0.435547	+	0.900166i	$0.356555\pi$
$224$	2.55886	+	0.672474i	0.170971	+	0.0449315i
$225$	−10.8029	−	6.23707i	−0.720195	−	0.415805i
$226$	4.24207	−	15.8316i	0.282178	−	1.05310i
$227$	19.5147	+	5.22895i	1.29524	+	0.347057i	0.839647	−	0.543133i	$-0.182762\pi$
$227$	19.5147	+	5.22895i	1.29524	+	0.347057i	0.455589	+	0.890190i	$0.349429\pi$
$228$	2.38683	+	0.639550i	0.158072	+	0.0423552i
$229$	−0.488972	+	1.82487i	−0.0323122	+	0.120591i	−0.980198	−	0.198019i	$-0.936549\pi$
$229$	−0.488972	+	1.82487i	−0.0323122	+	0.120591i	0.947886	+	0.318610i	$0.103216\pi$
$230$	18.6398	+	10.7617i	1.22907	+	0.709606i
$231$	−1.17912	+	1.19051i	−0.0775803	+	0.0783300i
$232$	1.33871	+	0.358706i	0.0878904	+	0.0235502i
$233$	−0.334379	+	0.193054i	−0.0219059	+	0.0126474i	−0.510913	−	0.859632i	$-0.670693\pi$
$233$	−0.334379	+	0.193054i	−0.0219059	+	0.0126474i	0.489007	+	0.872280i	$0.337359\pi$
$234$	2.68005	+	2.41192i	0.175200	+	0.157672i
$235$	−6.94400	+	12.0274i	−0.452976	+	0.784578i
$236$	3.12406	+	11.6591i	0.203359	+	0.758945i
$237$	0.370137	−	0.213699i	0.0240430	−	0.0138812i
$238$	−11.0168	+	11.1232i	−0.714112	+	0.721013i
$239$	4.60738	+	4.60738i	0.298027	+	0.298027i	0.840241	−	0.542214i	$-0.182414\pi$
$239$	4.60738	+	4.60738i	0.298027	+	0.298027i	−0.542214	+	0.840241i	$0.682414\pi$
$240$	−2.95585	−	2.95585i	−0.190800	−	0.190800i
$241$	−3.87262	+	14.4528i	−0.249457	+	0.930987i	0.721633	+	0.692276i	$0.243392\pi$
$241$	−3.87262	+	14.4528i	−0.249457	+	0.930987i	−0.971091	+	0.238712i	$0.923275\pi$
$242$	−2.74320	−	10.2378i	−0.176340	−	0.658108i
$243$			1.00000i			0.0641500i
$244$	6.19287	+	10.7264i	0.396458	+	0.686685i
$245$	28.3359	+	7.30124i	1.81032	+	0.466459i
$246$		−	1.26545i		−	0.0806823i
$247$	8.71519	+	1.85021i	0.554534	+	0.117726i
$248$	−4.80415	−	2.77367i	−0.305064	−	0.176129i
$249$	−5.72801	−	5.72801i	−0.362998	−	0.362998i
$250$	27.0577	+	15.6217i	1.71128	+	0.988006i
$251$	−7.83244	+	13.5662i	−0.494379	+	0.856290i	−0.999979	−	0.00647817i	$-0.997938\pi$
$251$	−7.83244	+	13.5662i	−0.494379	+	0.856290i	0.505600	+	0.862768i	$0.331271\pi$
$252$	1.33388	+	2.28490i	0.0840265	+	0.143935i
$253$	−3.14977	+	0.843978i	−0.198024	+	0.0530604i
$254$	−13.0183	+	13.0183i	−0.816839	+	0.816839i
$255$	23.8925	−	6.40196i	1.49620	−	0.400907i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.3488	−	24.8529i	0.895055	−	1.55028i	0.0613182	−	0.998118i	$-0.480470\pi$
$257$	14.3488	−	24.8529i	0.895055	−	1.55028i	0.833737	−	0.552162i	$-0.186197\pi$
$258$	−0.719544	+	2.68538i	−0.0447969	+	0.167184i
$259$	−5.75140	+	1.57077i	−0.357375	+	0.0976026i
$260$	−11.2032	−	10.0823i	−0.694790	−	0.625279i
$261$	0.692966	+	1.20025i	0.0428935	+	0.0742937i
$262$	−7.63081	+	7.63081i	−0.471433	+	0.471433i
$263$	12.0503			0.743056			0.371528	−	0.928422i	$-0.378834\pi$
$263$	12.0503			0.743056			0.371528	+	0.928422i	$0.378834\pi$
$264$	0.633318			0.0389780
$265$	−35.2347	+	35.2347i	−2.16445	+	2.16445i
$266$	5.67749	+	3.24160i	0.348110	+	0.198755i
$267$	−0.434447	−	1.62138i	−0.0265877	−	0.0992268i
$268$	6.13532	+	1.64395i	0.374774	+	0.100420i
$269$	1.58759	−	0.916594i	0.0967969	−	0.0558857i	−0.450820	−	0.892615i	$-0.648868\pi$
$269$	1.58759	−	0.916594i	0.0967969	−	0.0558857i	0.547617	+	0.836729i	$0.315535\pi$
$270$		−	4.18021i		−	0.254399i
$271$	−14.4803	+	3.87999i	−0.879616	+	0.235692i	−0.670242	−	0.742143i	$-0.733810\pi$
$271$	−14.4803	+	3.87999i	−0.879616	+	0.235692i	−0.209375	+	0.977835i	$0.567143\pi$
$272$	5.91724			0.358785
$273$	5.23592	+	7.97403i	0.316892	+	0.482610i
$274$	14.8907			0.899580
$275$	−7.63091	+	2.04470i	−0.460161	+	0.123300i
$276$			5.14888i			0.309926i
$277$	−5.04887	+	2.91497i	−0.303357	+	0.175143i	−0.643950	−	0.765068i	$-0.722706\pi$
$277$	−5.04887	+	2.91497i	−0.303357	+	0.175143i	0.340593	+	0.940211i	$0.389372\pi$
$278$	9.13277	+	2.44712i	0.547747	+	0.146768i
$279$	−1.43576	−	5.35833i	−0.0859567	−	0.320795i
$280$	−5.57589	−	9.55136i	−0.333223	−	0.570803i
$281$	−17.7789	+	17.7789i	−1.06060	+	1.06060i	−0.0625584	+	0.998041i	$0.519926\pi$
$281$	−17.7789	+	17.7789i	−1.06060	+	1.06060i	−0.998041	+	0.0625584i	$0.980074\pi$
$282$	−3.32232			−0.197841
$283$	−13.7870			−0.819550			−0.409775	−	0.912187i	$-0.634393\pi$
$283$	−13.7870			−0.819550			−0.409775	+	0.912187i	$0.634393\pi$
$284$	10.8941	−	10.8941i	0.646445	−	0.646445i
$285$	−5.16471	−	8.94554i	−0.305931	−	0.529888i
$286$	2.28030	−	0.120074i	0.134837	−	0.00710013i
$287$	0.850983	−	3.23812i	0.0502319	−	0.191140i
$288$	0.258819	−	0.965926i	0.0152511	−	0.0569177i
$289$	−9.00685	+	15.6003i	−0.529815	+	0.917666i
$290$	−2.89674	−	5.01730i	−0.170103	−	0.294626i
$291$	−7.30052	+	1.95617i	−0.427964	+	0.114673i
$292$	5.86530	−	5.86530i	0.343241	−	0.343241i
$293$	3.06465	−	0.821170i	0.179039	−	0.0479733i	−0.168186	−	0.985755i	$-0.553791\pi$
$293$	3.06465	−	0.821170i	0.179039	−	0.0479733i	0.347224	+	0.937782i	$0.387124\pi$
$294$	1.87668	+	6.74374i	0.109450	+	0.393303i
$295$	25.2285	−	43.6970i	1.46886	−	2.54414i
$296$	1.95154	+	1.12672i	0.113431	+	0.0654893i
$297$	0.447823	+	0.447823i	0.0259853	+	0.0259853i
$298$	12.1486	+	7.01402i	0.703752	+	0.406311i
$299$	0.976204	+	18.5389i	0.0564553	+	1.07213i
$300$			12.4741i			0.720195i
$301$	−3.64706	+	6.38763i	−0.210213	+	0.368177i
$302$	−3.67462	−	6.36463i	−0.211451	−	0.366243i
$303$			4.20030i			0.241301i
$304$	−0.639550	−	2.38683i	−0.0366807	−	0.136894i
$305$	13.4004	−	50.0108i	0.767302	−	2.86361i
$306$	4.18412	+	4.18412i	0.239190	+	0.239190i
$307$	−10.5351	−	10.5351i	−0.601271	−	0.601271i	0.339378	−	0.940650i	$-0.389783\pi$
$307$	−10.5351	−	10.5351i	−0.601271	−	0.601271i	−0.940650	+	0.339378i	$0.889783\pi$
$308$	1.62057	+	0.425890i	0.0923408	+	0.0242673i
$309$	−1.23322	+	0.712002i	−0.0701556	+	0.0405044i
$310$	6.00178	+	22.3989i	0.340878	+	1.27217i
$311$	16.6841	−	28.8977i	0.946069	−	1.63864i	0.192473	−	0.981302i	$-0.438349\pi$
$311$	16.6841	−	28.8977i	0.946069	−	1.63864i	0.753596	−	0.657338i	$-0.228317\pi$
$312$	0.748759	−	3.52695i	0.0423901	−	0.199674i
$313$	1.72540	−	0.996161i	0.0975254	−	0.0563063i	−0.450444	−	0.892805i	$-0.648734\pi$
$313$	1.72540	−	0.996161i	0.0975254	−	0.0563063i	0.547969	+	0.836498i	$0.315401\pi$
$314$	20.6808	+	5.54140i	1.16708	+	0.312719i
$315$	2.81108	−	10.6966i	0.158386	−	0.602684i
$316$	−0.370137	−	0.213699i	−0.0208218	−	0.0120215i
$317$	5.48586	−	20.4735i	0.308116	−	1.14991i	−0.622113	−	0.782927i	$-0.713726\pi$
$317$	5.48586	−	20.4735i	0.308116	−	1.14991i	0.930229	−	0.366979i	$-0.119608\pi$
$318$	−11.5141	−	3.08520i	−0.645681	−	0.173010i
$319$	0.847827	+	0.227175i	0.0474692	+	0.0127193i
$320$	−1.08192	+	4.03777i	−0.0604810	+	0.225718i
$321$	9.48886	+	5.47839i	0.529616	+	0.305774i
$322$	−3.46249	+	13.1753i	−0.192957	+	0.734230i
$323$	14.1234	+	3.78437i	0.785850	+	0.210568i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	2.36504	+	44.9140i	0.131189	+	2.49138i
$326$	0.111426	−	0.192995i	0.00617131	−	0.0106890i
$327$	0.300729	+	1.12234i	0.0166303	+	0.0620653i
$328$	−1.09591	+	0.632726i	−0.0605117	+	0.0349364i
$329$	−8.50136	−	2.23417i	−0.468695	−	0.123174i
$330$	−1.87200	−	1.87200i	−0.103050	−	0.103050i
$331$	6.63821	+	6.63821i	0.364869	+	0.364869i	0.865602	−	0.500733i	$-0.166936\pi$
$331$	6.63821	+	6.63821i	0.364869	+	0.364869i	−0.500733	+	0.865602i	$0.666936\pi$
$332$	−2.09660	+	7.82461i	−0.115066	+	0.429431i
$333$	0.583233	+	2.17666i	0.0319610	+	0.119280i
$334$		−	19.0523i		−	1.04249i
$335$	−13.2758	−	22.9944i	−0.725335	−	1.25632i
$336$	1.31184	−	2.29762i	0.0715669	−	0.125346i
$337$		−	15.7627i		−	0.858648i	−0.903151	−	0.429324i	$-0.858752\pi$
$337$		−	15.7627i		−	0.858648i	0.903151	−	0.429324i	$-0.141248\pi$
$338$	2.02726	−	12.8410i	0.110269	−	0.698456i
$339$	−14.1942	−	8.19504i	−0.770925	−	0.445094i
$340$	−17.4905	−	17.4905i	−0.948555	−	0.948555i
$341$	−3.04255	−	1.75662i	−0.164763	−	0.0951262i
$342$	1.23551	−	2.13997i	0.0668090	−	0.115717i
$343$	0.267169	+	18.5183i	0.0144258	+	0.999896i
$344$	2.68538	−	0.719544i	0.144786	−	0.0387952i
$345$	15.2193	−	15.2193i	0.819382	−	0.819382i
$346$	−14.6857	+	3.93503i	−0.789510	+	0.211549i
$347$	−3.44525	−	5.96735i	−0.184951	−	0.320344i	0.758609	−	0.651546i	$-0.225879\pi$
$347$	−3.44525	−	5.96735i	−0.184951	−	0.320344i	−0.943560	+	0.331202i	$0.892546\pi$
$348$	0.692966	−	1.20025i	0.0371469	−	0.0643403i
$349$	5.86607	−	21.8925i	0.314004	−	1.17188i	−0.610910	−	0.791700i	$-0.709196\pi$
$349$	5.86607	−	21.8925i	0.314004	−	1.17188i	0.924913	−	0.380178i	$-0.124137\pi$
$350$	−8.38854	+	31.9196i	−0.448386	+	1.70618i
$351$	3.02338	−	1.96448i	0.161376	−	0.104856i
$352$	−0.316659	−	0.548469i	−0.0168780	−	0.0292335i
$353$	−0.656622	+	0.656622i	−0.0349484	+	0.0349484i	−0.724365	−	0.689417i	$-0.757867\pi$
$353$	−0.656622	+	0.656622i	−0.0349484	+	0.0349484i	0.689417	+	0.724365i	$0.257867\pi$
$354$	12.0704			0.641536
$355$	−64.4027			−3.41814
$356$	−1.18693	+	1.18693i	−0.0629072	+	0.0629072i
$357$	7.89288	+	13.5203i	0.417735	+	0.715570i
$358$	−5.38151	−	20.0841i	−0.284422	−	1.06148i
$359$	6.27110	+	1.68034i	0.330976	+	0.0886847i	0.420480	−	0.907302i	$-0.361862\pi$
$359$	6.27110	+	1.68034i	0.330976	+	0.0886847i	−0.0895044	+	0.995986i	$0.528528\pi$
$360$	−3.62017	+	2.09010i	−0.190800	+	0.110158i
$361$			12.8940i			0.678632i
$362$	18.9039	−	5.06527i	0.993564	−	0.266225i
$363$	−10.5989			−0.556298
$364$	4.28775	−	8.52145i	0.224739	−	0.446646i
$365$	−34.6740			−1.81492
$366$	11.9637	−	3.20567i	0.625353	−	0.167563i
$367$			26.0077i			1.35759i	0.734328	+	0.678794i	$0.237497\pi$
$367$			26.0077i			1.35759i	−0.734328	+	0.678794i	$0.762503\pi$
$368$	4.45906	−	2.57444i	0.232445	−	0.134202i
$369$	−1.22233	−	0.327523i	−0.0636321	−	0.0170502i
$370$	−2.43804	−	9.09888i	−0.126748	−	0.473028i
$371$	−27.3884	−	15.6376i	−1.42193	−	0.811862i
$372$	−3.92257	+	3.92257i	−0.203376	+	0.203376i
$373$	−25.7204			−1.33175			−0.665876	−	0.746063i	$-0.731942\pi$
$373$	−25.7204			−1.33175			−0.665876	+	0.746063i	$0.731942\pi$
$374$	3.74749			0.193778
$375$	22.0925	−	22.0925i	1.14085	−	1.14085i
$376$	1.66116	+	2.87721i	0.0856678	+	0.148381i
$377$	2.26751	−	4.45297i	0.116782	−	0.229339i
$378$	2.55228	−	0.697052i	0.131275	−	0.0358525i
$379$	−7.60010	+	28.3640i	−0.390391	+	1.45696i	0.439100	+	0.898438i	$0.355297\pi$
$379$	−7.60010	+	28.3640i	−0.390391	+	1.45696i	−0.829491	+	0.558520i	$0.811369\pi$
$380$	−5.16471	+	8.94554i	−0.264944	+	0.458897i
$381$	9.20531	+	15.9441i	0.471602	+	0.816839i
$382$	−5.09302	+	1.36467i	−0.260582	+	0.0698226i
$383$	−8.93303	+	8.93303i	−0.456457	+	0.456457i	−0.897490	−	0.441034i	$-0.854612\pi$
$383$	−8.93303	+	8.93303i	−0.456457	+	0.456457i	0.441034	+	0.897490i	$0.354612\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	−3.53131	−	6.04905i	−0.179972	−	0.308288i
$386$	−6.83128	+	11.8321i	−0.347703	+	0.602239i
$387$	2.40764	+	1.39005i	0.122387	+	0.0706603i
$388$	5.34435	+	5.34435i	0.271319	+	0.271319i
$389$	12.5800	+	7.26305i	0.637830	+	0.368251i	0.783778	−	0.621041i	$-0.213290\pi$
$389$	12.5800	+	7.26305i	0.637830	+	0.368251i	−0.145948	+	0.989292i	$0.546623\pi$
$390$	−12.6384	+	8.21192i	−0.639969	+	0.415827i
$391$			30.4672i			1.54079i
$392$	4.90191	−	4.99712i	0.247584	−	0.252393i
$393$	5.39580	+	9.34579i	0.272182	+	0.471433i
$394$			12.6610i			0.637854i
$395$	0.462409	+	1.72573i	0.0232663	+	0.0868311i
$396$	0.163915	−	0.611738i	0.00823703	−	0.0307410i
$397$	3.82079	+	3.82079i	0.191760	+	0.191760i	0.796456	−	0.604696i	$-0.206705\pi$
$397$	3.82079	+	3.82079i	0.191760	+	0.191760i	−0.604696	+	0.796456i	$0.706705\pi$
$398$	4.24035	+	4.24035i	0.212549	+	0.212549i
$399$	4.60059	−	4.64505i	0.230318	−	0.232543i
$400$	10.8029	−	6.23707i	0.540146	−	0.311854i
$401$	−1.06062	−	3.95830i	−0.0529650	−	0.197668i	0.934374	−	0.356295i	$-0.115960\pi$
$401$	−1.06062	−	3.95830i	−0.0529650	−	0.197668i	−0.987339	+	0.158627i	$0.949293\pi$
$402$	3.17587	−	5.50077i	0.158398	−	0.274354i
$403$	−13.3798	+	14.8672i	−0.666493	+	0.740586i
$404$	3.63757	−	2.10015i	0.180976	−	0.104486i
$405$	−4.03777	−	1.08192i	−0.200638	−	0.0537609i
$406$	2.58034	−	2.60528i	0.128060	−	0.129298i
$407$	1.23594	+	0.713572i	0.0612634	+	0.0353705i
$408$	1.53149	−	5.71561i	0.0758202	−	0.282965i
$409$	0.120382	+	0.0322563i	0.00595252	+	0.00159497i	0.261794	−	0.965124i	$-0.415686\pi$
$409$	0.120382	+	0.0322563i	0.00595252	+	0.00159497i	−0.255842	+	0.966719i	$0.582353\pi$
$410$	5.10961	+	1.36911i	0.252345	+	0.0676158i
$411$	3.85400	−	14.3833i	0.190104	−	0.709477i
$412$	1.23322	+	0.712002i	0.0607566	+	0.0350778i
$413$	30.8866	+	8.11705i	1.51983	+	0.399414i
$414$	4.97344	+	1.33263i	0.244431	+	0.0654951i
$415$	29.3256	−	16.9312i	1.43954	−	0.831118i
$416$	−3.42881	+	1.11503i	−0.168111	+	0.0546688i
$417$	4.72747	−	8.18822i	0.231505	−	0.400979i
$418$	−0.405038	−	1.51162i	−0.0198111	−	0.0739359i
$419$	3.80264	−	2.19546i	0.185771	−	0.107255i	−0.404230	−	0.914657i	$-0.632461\pi$
$419$	3.80264	−	2.19546i	0.185771	−	0.107255i	0.590001	+	0.807402i	$0.299127\pi$
$420$	−10.6691	+	2.91382i	−0.520596	+	0.142180i
$421$	−22.1184	−	22.1184i	−1.07799	−	1.07799i	−0.996690	−	0.0812959i	$-0.974094\pi$
$421$	−22.1184	−	22.1184i	−1.07799	−	1.07799i	−0.0812959	−	0.996690i	$-0.525906\pi$
$422$	−14.9333	−	14.9333i	−0.726941	−	0.726941i
$423$	−0.859880	+	3.20911i	−0.0418088	+	0.156032i
$424$	3.08520	+	11.5141i	0.149831	+	0.559176i
$425$			73.8125i			3.58043i
$426$	−7.70329	−	13.3425i	−0.373225	−	0.646445i
$427$	32.7692	−	0.157581i	1.58581	−	0.00762586i
$428$		−	10.9568i		−	0.529616i
$429$	0.474203	−	2.23368i	0.0228947	−	0.107843i
$430$	−10.0644	−	5.81071i	−0.485351	−	0.280217i
$431$	−8.10063	−	8.10063i	−0.390194	−	0.390194i	0.484563	−	0.874756i	$-0.338979\pi$
$431$	−8.10063	−	8.10063i	−0.390194	−	0.390194i	−0.874756	+	0.484563i	$0.838979\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	5.94636	−	10.2994i	0.285764	−	0.494958i	−0.687030	−	0.726629i	$-0.741086\pi$
$433$	5.94636	−	10.2994i	0.285764	−	0.494958i	0.972794	+	0.231671i	$0.0744194\pi$
$434$	−12.6751	+	7.39949i	−0.608426	+	0.355187i
$435$	−5.59608	+	1.49946i	−0.268311	+	0.0718938i
$436$	0.821606	−	0.821606i	0.0393478	−	0.0393478i
$437$	12.2895	−	3.29297i	0.587887	−	0.157524i
$438$	−4.14740	−	7.18350i	−0.198170	−	0.343241i
$439$	4.30988	−	7.46493i	0.205699	−	0.356281i	−0.744656	−	0.667448i	$-0.767386\pi$
$439$	4.30988	−	7.46493i	0.205699	−	0.356281i	0.950355	+	0.311167i	$0.100720\pi$
$440$	−0.685198	+	2.55719i	−0.0326655	+	0.121909i
$441$	6.99968	−	0.0673217i	0.333318	−	0.00320579i
$442$	4.43059	−	20.8698i	0.210742	−	0.992675i
$443$	−4.22436	−	7.31680i	−0.200705	−	0.347632i	0.748051	−	0.663642i	$-0.230990\pi$
$443$	−4.22436	−	7.31680i	−0.200705	−	0.347632i	−0.948756	+	0.316010i	$0.897657\pi$
$444$	1.59342	−	1.59342i	0.0756205	−	0.0756205i
$445$	7.01679			0.332628
$446$	−19.5232			−0.924451
$447$	9.91933	−	9.91933i	0.469168	−	0.469168i
$448$	−2.64572	+	0.0127227i	−0.124999	+	0.000601093i
$449$	−2.32879	−	8.69115i	−0.109902	−	0.410161i	0.888953	−	0.457999i	$-0.151434\pi$
$449$	−2.32879	−	8.69115i	−0.109902	−	0.410161i	−0.998855	+	0.0478379i	$0.984767\pi$
$450$	12.0491	+	3.22855i	0.568000	+	0.152195i
$451$	−0.694062	+	0.400717i	−0.0326821	+	0.0188690i
$452$			16.3901i			0.770925i
$453$	−7.09882	+	1.90212i	−0.333532	+	0.0893696i
$454$	−20.2031			−0.948178
$455$	−37.8621	+	12.5142i	−1.77500	+	0.586675i
$456$	−2.47103			−0.115717
$457$	17.8938	−	4.79464i	0.837039	−	0.224284i	0.185257	−	0.982690i	$-0.440688\pi$
$457$	17.8938	−	4.79464i	0.837039	−	0.224284i	0.651782	+	0.758406i	$0.274022\pi$
$458$		−	1.88924i		−	0.0882785i
$459$	5.12448	−	2.95862i	0.239190	−	0.138096i
$460$	−20.7900	−	5.57067i	−0.969340	−	0.259734i
$461$	10.7940	+	40.2836i	0.502725	+	1.87620i	0.481548	+	0.876420i	$0.340075\pi$
$461$	10.7940	+	40.2836i	0.502725	+	1.87620i	0.0211769	+	0.999776i	$0.493259\pi$
$462$	0.830813	−	1.45513i	0.0386529	−	0.0676986i
$463$	−12.7149	+	12.7149i	−0.590912	+	0.590912i	−0.937878	−	0.346966i	$-0.887212\pi$
$463$	−12.7149	+	12.7149i	−0.590912	+	0.590912i	0.346966	+	0.937878i	$0.387212\pi$
$464$	−1.38593			−0.0643403
$465$	23.1891			1.07537
$466$	0.273020	−	0.273020i	0.0126474	−	0.0126474i
$467$	−0.419923	−	0.727328i	−0.0194317	−	0.0336567i	0.856146	−	0.516734i	$-0.172852\pi$
$467$	−0.419923	−	0.727328i	−0.0194317	−	0.0336567i	−0.875578	+	0.483077i	$0.839519\pi$
$468$	−3.21298	−	1.63609i	−0.148520	−	0.0756282i
$469$	11.8258	−	11.9400i	0.546062	−	0.551340i
$470$	3.59448	−	13.4148i	0.165801	−	0.618777i
$471$	10.7052	−	18.5419i	0.493268	−	0.854365i
$472$	−6.03521	−	10.4533i	−0.277793	−	0.481152i
$473$	1.70070	−	0.455700i	0.0781981	−	0.0209531i
$474$	−0.302216	+	0.302216i	−0.0138812	+	0.0138812i
$475$	29.7737	−	7.97784i	1.36611	−	0.366048i
$476$	7.76248	−	13.5956i	0.355793	−	0.623152i
$477$	−5.96016	+	10.3233i	−0.272897	+	0.472671i
$478$	−5.64287	−	3.25791i	−0.258099	−	0.149013i
$479$	−17.5587	−	17.5587i	−0.802277	−	0.802277i	0.181174	−	0.983451i	$-0.442010\pi$
$479$	−17.5587	−	17.5587i	−0.802277	−	0.802277i	−0.983451	+	0.181174i	$0.942010\pi$
$480$	3.62017	+	2.09010i	0.165237	+	0.0953998i
$481$	5.43511	−	6.03932i	0.247820	−	0.275370i
$482$		−	14.9626i		−	0.681530i
$483$	11.8302	+	6.75452i	0.538292	+	0.307341i
$484$	5.29945	+	9.17892i	0.240884	+	0.417224i
$485$		−	31.5943i		−	1.43462i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	9.73144	−	36.3182i	0.440974	−	1.64574i	−0.285380	−	0.958414i	$-0.592120\pi$
$487$	9.73144	−	36.3182i	0.440974	−	1.64574i	0.726354	−	0.687321i	$-0.241213\pi$
$488$	−8.75804	−	8.75804i	−0.396458	−	0.396458i
$489$	−0.157580	−	0.157580i	−0.00712601	−	0.00712601i
$490$	−29.2601	+	0.281419i	−1.32184	+	0.0127132i
$491$	−20.0647	+	11.5844i	−0.905507	+	0.522795i	−0.878983	−	0.476853i	$-0.841777\pi$
$491$	−20.0647	+	11.5844i	−0.905507	+	0.522795i	−0.0265243	+	0.999648i	$0.508444\pi$
$492$	0.327523	+	1.22233i	0.0147659	+	0.0551070i
$493$	4.10044	−	7.10218i	0.184675	−	0.319866i
$494$	−8.89710	+	0.468496i	−0.400299	+	0.0210786i
$495$	−2.29272	+	1.32370i	−0.103050	+	0.0594959i
$496$	5.35833	+	1.43576i	0.240596	+	0.0644675i
$497$	−10.7392	−	39.3218i	−0.481718	−	1.76383i
$498$	7.01535	+	4.05032i	0.314366	+	0.181499i
$499$	5.12214	−	19.1161i	0.229299	−	0.855754i	−0.751338	−	0.659918i	$-0.770591\pi$
$499$	5.12214	−	19.1161i	0.229299	−	0.855754i	0.980637	−	0.195836i	$-0.0627422\pi$
$500$	−30.1789	−	8.08641i	−1.34964	−	0.361635i
$501$	−18.4031	−	4.93109i	−0.822189	−	0.220305i
$502$	4.05437	−	15.1311i	0.180955	−	0.675335i
$503$	1.87260	+	1.08114i	0.0834949	+	0.0482058i	0.541166	−	0.840916i	$-0.317983\pi$
$503$	1.87260	+	1.08114i	0.0834949	+	0.0482058i	−0.457671	+	0.889121i	$0.651316\pi$
$504$	−1.87980	−	1.86181i	−0.0837331	−	0.0829316i
$505$	−16.9599	−	4.54438i	−0.754704	−	0.202222i
$506$	2.82400	−	1.63044i	0.125542	−	0.0724819i
$507$	−11.8787	−	5.28167i	−0.527552	−	0.234567i
$508$	9.20531	−	15.9441i	0.408420	−	0.707404i
$509$	6.78091	+	25.3067i	0.300559	+	1.12170i	0.936702	+	0.350129i	$0.113862\pi$
$509$	6.78091	+	25.3067i	0.300559	+	1.12170i	−0.636143	+	0.771571i	$0.719471\pi$
$510$	−21.4214	+	12.3676i	−0.948555	+	0.547649i
$511$	−5.78190	−	21.1706i	−0.255776	−	0.936532i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.74728	−	1.74728i	−0.0771444	−	0.0771444i
$514$	−7.42750	+	27.7198i	−0.327613	+	1.22267i
$515$	−1.54065	−	5.74980i	−0.0678894	−	0.253367i
$516$		−	2.78010i		−	0.122387i
$517$	1.05204	+	1.82219i	0.0462688	+	0.0801399i
$518$	5.14889	−	3.00582i	0.226229	−	0.132068i
$519$			15.2038i			0.667373i
$520$	13.4309	+	6.83919i	0.588985	+	0.299918i
$521$	6.95625	+	4.01619i	0.304759	+	0.175952i	0.644579	−	0.764538i	$-0.277033\pi$
$521$	6.95625	+	4.01619i	0.304759	+	0.175952i	−0.339820	+	0.940490i	$0.610366\pi$
$522$	−0.980002	−	0.980002i	−0.0428935	−	0.0428935i
$523$	−7.14193	−	4.12339i	−0.312295	−	0.180303i	0.335658	−	0.941984i	$-0.391041\pi$
$523$	−7.14193	−	4.12339i	−0.312295	−	0.180303i	−0.647953	+	0.761680i	$0.724375\pi$
$524$	5.39580	−	9.34579i	0.235716	−	0.408273i
$525$	28.6609	+	16.3641i	1.25086	+	0.714188i
$526$	−11.6397	+	3.11886i	−0.507516	+	0.135989i
$527$	−23.2108	+	23.2108i	−1.01108	+	1.01108i
$528$	−0.611738	+	0.163915i	−0.0266225	+	0.00713347i
$529$	1.75550	+	3.04062i	0.0763261	+	0.132201i
$530$	24.9147	−	43.1535i	1.08223	−	1.87447i
$531$	3.12406	−	11.6591i	0.135573	−	0.505963i
$532$	−6.32303	−	1.66170i	−0.274138	−	0.0720439i
$533$	1.41102	+	4.33899i	0.0611179	+	0.187942i
$534$	0.839287	+	1.45369i	0.0363195	+	0.0629072i
$535$	−32.3867	+	32.3867i	−1.40020	+	1.40020i
$536$	−6.35175			−0.274354
$537$	−20.7926			−0.897265
$538$	−1.29626	+	1.29626i	−0.0558857	+	0.0558857i
$539$	3.10447	−	3.16477i	0.133719	−	0.136316i
$540$	1.08192	+	4.03777i	0.0465583	+	0.173758i
$541$	−27.0933	−	7.25962i	−1.16483	−	0.312116i	−0.375937	−	0.926645i	$-0.622679\pi$
$541$	−27.0933	−	7.25962i	−1.16483	−	0.312116i	−0.788894	+	0.614530i	$0.789346\pi$
$542$	12.9827	−	7.49556i	0.557654	−	0.321962i
$543$		−	19.5707i		−	0.839859i
$544$	−5.71561	+	1.53149i	−0.245055	+	0.0656623i
$545$	−4.85710			−0.208055
$546$	−7.12134	−	6.34716i	−0.304765	−	0.271634i
$547$	33.9957			1.45355			0.726776	−	0.686875i	$-0.241018\pi$
$547$	33.9957			1.45355			0.726776	+	0.686875i	$0.241018\pi$
$548$	−14.3833	+	3.85400i	−0.614425	+	0.164635i
$549$		−	12.3857i		−	0.528610i
$550$	6.84169	−	3.95005i	0.291731	−	0.168431i
$551$	−3.30799	−	0.886372i	−0.140925	−	0.0377607i
$552$	−1.33263	−	4.97344i	−0.0567205	−	0.211684i
$553$	−0.976561	+	0.570096i	−0.0415276	+	0.0242430i
$554$	4.12239	−	4.12239i	0.175143	−	0.175143i
$555$	−9.41985			−0.399850
$556$	−9.45494			−0.400979
$557$	−10.7205	+	10.7205i	−0.454240	+	0.454240i	−0.896759	−	0.442519i	$-0.854085\pi$
$557$	−10.7205	+	10.7205i	−0.454240	+	0.454240i	0.442519	+	0.896759i	$0.354085\pi$
$558$	2.77367	+	4.80415i	0.117419	+	0.203376i
$559$	−0.527095	−	10.0099i	−0.0222937	−	0.423375i
$560$	7.85797	+	7.78276i	0.332060	+	0.328882i
$561$	0.969922	−	3.61980i	0.0409502	−	0.152828i
$562$	12.5716	−	21.7746i	0.530300	−	0.918506i
$563$	9.71160	+	16.8210i	0.409295	+	0.708920i	0.994811	−	0.101741i	$-0.0324412\pi$
$563$	9.71160	+	16.8210i	0.409295	+	0.708920i	−0.585516	+	0.810661i	$0.699108\pi$
$564$	3.20911	−	0.859880i	0.135128	−	0.0362075i
$565$	48.4467	−	48.4467i	2.03817	−	2.03817i
$566$	13.3172	−	3.56833i	0.559763	−	0.149988i
$567$	−0.0127227	−	2.64572i	−0.000534305	−	0.111110i
$568$	−7.70329	+	13.3425i	−0.323223	+	0.559838i
$569$	−38.9709	−	22.4999i	−1.63374	−	0.943243i	−0.982924	−	0.184012i	$-0.941092\pi$
$569$	−38.9709	−	22.4999i	−1.63374	−	0.943243i	−0.650821	−	0.759231i	$-0.725575\pi$
$570$	7.30400	+	7.30400i	0.305931	+	0.305931i
$571$	24.2146	+	13.9803i	1.01335	+	0.585058i	0.912171	−	0.409810i	$-0.134405\pi$
$571$	24.2146	+	13.9803i	1.01335	+	0.585058i	0.101180	+	0.994868i	$0.467738\pi$
$572$	−2.17152	+	0.706168i	−0.0907960	+	0.0295264i
$573$			5.27268i			0.220270i
$574$	0.0161000	+	3.34803i	0.000672002	+	0.139744i
$575$	32.1140	+	55.6230i	1.33924	+	2.31964i
$576$			1.00000i			0.0416667i
$577$	−11.2866	−	42.1222i	−0.469868	−	1.75357i	−0.640224	−	0.768188i	$-0.721159\pi$
$577$	−11.2866	−	42.1222i	−0.469868	−	1.75357i	0.170356	−	0.985383i	$-0.445508\pi$
$578$	4.66229	−	17.3999i	0.193926	−	0.723740i
$579$	9.66089	+	9.66089i	0.401493	+	0.401493i
$580$	4.09661	+	4.09661i	0.170103	+	0.170103i
$581$	15.2276	+	15.0818i	0.631747	+	0.625700i
$582$	6.54547	−	3.77903i	0.271319	−	0.156646i
$583$	1.95391	+	7.29211i	0.0809229	+	0.302008i
$584$	−4.14740	+	7.18350i	−0.171620	+	0.297255i
$585$	4.66106	+	14.3331i	0.192711	+	0.592602i
$586$	−2.74769	+	1.58638i	−0.113506	+	0.0655327i
$587$	9.26294	+	2.48200i	0.382322	+	0.102443i	0.444861	−	0.895600i	$-0.353253\pi$
$587$	9.26294	+	2.48200i	0.382322	+	0.102443i	−0.0625387	+	0.998043i	$0.519920\pi$
$588$	−3.55814	−	6.02824i	−0.146735	−	0.248600i
$589$	11.8712	+	6.85383i	0.489144	+	0.282407i
$590$	−13.0592	+	48.7376i	−0.537639	+	2.00650i
$591$	12.2296	+	3.27692i	0.503059	+	0.134794i
$592$	−2.17666	−	0.583233i	−0.0894600	−	0.0239707i
$593$	1.28640	−	4.80089i	0.0528259	−	0.197149i	−0.934470	−	0.356042i	$-0.884126\pi$
$593$	1.28640	−	4.80089i	0.0528259	−	0.197149i	0.987296	+	0.158893i	$0.0507926\pi$
$594$	−0.548469	−	0.316659i	−0.0225040	−	0.0129927i
$595$	−63.1313	+	17.2418i	−2.58813	+	0.706844i
$596$	−13.5501	−	3.63073i	−0.555032	−	0.148720i
$597$	5.19335	−	2.99838i	0.212549	−	0.122716i
$598$	−5.74116	−	17.6545i	−0.234773	−	0.721947i
$599$	−11.6073	+	20.1044i	−0.474260	+	0.821443i	−0.999566	−	0.0294711i	$-0.990618\pi$
$599$	−11.6073	+	20.1044i	−0.474260	+	0.821443i	0.525305	+	0.850914i	$0.323951\pi$
$600$	−3.22855	−	12.0491i	−0.131805	−	0.491902i
$601$	29.9917	−	17.3157i	1.22339	−	0.706322i	0.257748	−	0.966212i	$-0.417020\pi$
$601$	29.9917	−	17.3157i	1.22339	−	0.706322i	0.965638	+	0.259890i	$0.0836862\pi$
$602$	1.86955	−	7.11391i	0.0761971	−	0.289941i
$603$	−4.49136	−	4.49136i	−0.182902	−	0.182902i
$604$	5.19670	+	5.19670i	0.211451	+	0.211451i
$605$	11.4671	−	42.7960i	0.466206	−	1.73990i
$606$	−1.08712	−	4.05718i	−0.0441611	−	0.164812i
$607$		−	37.4675i		−	1.52076i	−0.649479	−	0.760380i	$-0.725013\pi$
$607$		−	37.4675i		−	1.52076i	0.649479	−	0.760380i	$-0.274987\pi$
$608$	1.23551	+	2.13997i	0.0501067	+	0.0867874i
$609$	−1.84866	−	3.16672i	−0.0749117	−	0.128322i
$610$			51.7750i			2.09631i
$611$	11.3916	−	3.70448i	0.460854	−	0.149867i
$612$	−5.12448	−	2.95862i	−0.207145	−	0.119595i
$613$	8.48376	+	8.48376i	0.342656	+	0.342656i	0.857365	−	0.514709i	$-0.172100\pi$
$613$	8.48376	+	8.48376i	0.342656	+	0.342656i	−0.514709	+	0.857365i	$0.672100\pi$
$614$	12.9028	+	7.44946i	0.520716	+	0.300636i
$615$	2.64493	−	4.58115i	0.106654	−	0.184730i
$616$	−1.67558	+	0.00805754i	−0.0675111	+	0.000324648i
$617$	−1.90489	+	0.510413i	−0.0766879	+	0.0205485i	−0.296959	−	0.954890i	$-0.595972\pi$
$617$	−1.90489	+	0.510413i	−0.0766879	+	0.0205485i	0.220271	+	0.975439i	$0.429306\pi$
$618$	1.00692	−	1.00692i	0.0405044	−	0.0405044i
$619$	18.6069	−	4.98570i	0.747874	−	0.200392i	0.135299	−	0.990805i	$-0.456800\pi$
$619$	18.6069	−	4.98570i	0.747874	−	0.200392i	0.612575	+	0.790413i	$0.290134\pi$
$620$	−11.5945	−	20.0823i	−0.465648	−	0.806526i
$621$	2.57444	−	4.45906i	0.103309	−	0.178936i
$622$	−8.63633	+	32.2312i	−0.346285	+	1.29235i
$623$	1.17005	+	4.28419i	0.0468772	+	0.171642i
$624$	0.189595	+	3.60056i	0.00758989	+	0.144138i
$625$	34.1168	+	59.0920i	1.36467	+	2.36368i
$626$	−1.40878	+	1.40878i	−0.0563063	+	0.0563063i
$627$	−1.56495			−0.0624980
$628$	−21.4103			−0.854365
$629$	9.42866	−	9.42866i	0.375945	−	0.375945i
$630$	0.0531837	+	11.0597i	0.00211889	+	0.440628i
$631$	8.30437	+	30.9923i	0.330592	+	1.23378i	0.908570	+	0.417733i	$0.137175\pi$
$631$	8.30437	+	30.9923i	0.330592	+	1.23378i	−0.577978	+	0.816052i	$0.696158\pi$
$632$	0.412834	+	0.110619i	0.0164217	+	0.00440017i
$633$	−18.2895	+	10.5594i	−0.726941	+	0.419699i
$634$			21.1957i			0.841790i
$635$	−74.3379	+	19.9188i	−2.95001	+	0.790453i
$636$	11.9203			0.472671
$637$	−13.9542	−	21.0304i	−0.552887	−	0.833256i
$638$	−0.877735			−0.0347499
$639$	−14.8816	+	3.98751i	−0.588707	+	0.157744i
$640$		−	4.18021i		−	0.165237i
$641$	29.2441	−	16.8841i	1.15507	−	0.666882i	0.204955	−	0.978771i	$-0.434295\pi$
$641$	29.2441	−	16.8841i	1.15507	−	0.666882i	0.950118	+	0.311889i	$0.100962\pi$
$642$	−10.5834	−	2.83583i	−0.417695	−	0.111921i
$643$	9.13754	+	34.1018i	0.360349	+	1.34484i	0.873617	+	0.486614i	$0.161768\pi$
$643$	9.13754	+	34.1018i	0.360349	+	1.34484i	−0.513268	+	0.858228i	$0.671565\pi$
$644$	−0.0655079	−	13.6225i	−0.00258137	−	0.536802i
$645$	−8.21758	+	8.21758i	−0.323567	+	0.323567i
$646$	−14.6217			−0.575282
$647$	−13.5488			−0.532659			−0.266330	−	0.963882i	$-0.585811\pi$
$647$	−13.5488			−0.532659			−0.266330	+	0.963882i	$0.585811\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−3.82221	−	6.62026i	−0.150035	−	0.259868i
$650$	−13.9090	−	42.7714i	−0.545557	−	1.67763i
$651$	3.86679	+	14.1584i	0.151552	+	0.554910i
$652$	−0.0576783	+	0.215258i	−0.00225886	+	0.00843016i
$653$	1.97187	−	3.41538i	0.0771652	−	0.133654i	−0.824861	−	0.565336i	$-0.808746\pi$
$653$	1.97187	−	3.41538i	0.0771652	−	0.133654i	0.902026	+	0.431682i	$0.142080\pi$
$654$	−0.580963	−	1.00626i	−0.0227175	−	0.0393478i
$655$	−43.5740	+	11.6756i	−1.70258	+	0.456204i
$656$	0.894810	−	0.894810i	0.0349364	−	0.0349364i
$657$	−8.01215	+	2.14685i	−0.312584	+	0.0837566i
$658$	8.78993	−	0.0422690i	0.342667	−	0.00164782i
$659$	2.53663	−	4.39357i	0.0988130	−	0.171149i	−0.812381	−	0.583128i	$-0.801829\pi$
$659$	2.53663	−	4.39357i	0.0988130	−	0.171149i	0.911194	+	0.411978i	$0.135162\pi$
$660$	2.29272	+	1.32370i	0.0892439	+	0.0515250i
$661$	−31.1021	−	31.1021i	−1.20973	−	1.20973i	−0.971113	−	0.238619i	$-0.923305\pi$
$661$	−31.1021	−	31.1021i	−1.20973	−	1.20973i	−0.238619	−	0.971113i	$-0.576695\pi$
$662$	−8.13012	−	4.69393i	−0.315986	−	0.182435i
$663$	−19.0119	−	9.68112i	−0.738363	−	0.375983i
$664$		−	8.10063i		−	0.314366i
$665$	13.7782	+	23.6017i	0.534295	+	0.915234i
$666$	−1.12672	−	1.95154i	−0.0436595	−	0.0756205i
$667$		−	7.13600i		−	0.276307i
$668$	4.93109	+	18.4031i	0.190790	+	0.712037i
$669$	−5.05298	+	18.8580i	−0.195360	+	0.729092i
$670$	18.7748	+	18.7748i	0.725335	+	0.725335i
$671$	−5.54662	−	5.54662i	−0.214125	−	0.214125i
$672$	−0.672474	+	2.55886i	−0.0259412	+	0.0987103i
$673$	38.3345	−	22.1325i	1.47769	−	0.853144i	0.478006	−	0.878356i	$-0.341360\pi$
$673$	38.3345	−	22.1325i	1.47769	−	0.853144i	0.999682	+	0.0252127i	$0.00802631\pi$
$674$	4.07968	+	15.2256i	0.157144	+	0.586468i
$675$	6.23707	−	10.8029i	0.240065	−	0.415805i
$676$	1.36530	+	12.9281i	0.0525115	+	0.497235i
$677$	−28.1133	+	16.2312i	−1.08048	+	0.623818i	−0.931027	−	0.364951i	$-0.881086\pi$
$677$	−28.1133	+	16.2312i	−1.08048	+	0.623818i	−0.149457	+	0.988768i	$0.547753\pi$
$678$	15.8316	+	4.24207i	0.608009	+	0.162916i
$679$	19.2903	−	5.26836i	0.740292	−	0.202181i
$680$	21.4214	+	12.3676i	0.821473	+	0.474278i
$681$	−5.22895	+	19.5147i	−0.200374	+	0.747805i
$682$	3.39353	+	0.909292i	0.129945	+	0.0348186i
$683$	21.4370	+	5.74402i	0.820263	+	0.219789i	0.644462	−	0.764637i	$-0.277082\pi$
$683$	21.4370	+	5.74402i	0.820263	+	0.219789i	0.175802	+	0.984426i	$0.443748\pi$
$684$	−0.639550	+	2.38683i	−0.0244538	+	0.0912628i
$685$	53.9068	+	31.1231i	2.05967	+	1.18915i
$686$	−5.05096	−	17.8182i	−0.192847	−	0.680302i
$687$	−1.82487	−	0.488972i	−0.0696230	−	0.0186554i
$688$	−2.40764	+	1.39005i	−0.0917905	+	0.0529953i
$689$	42.9198	−	2.26004i	1.63512	−	0.0861005i
$690$	−10.7617	+	18.6398i	−0.409691	+	0.709606i
$691$	−5.37626	−	20.0645i	−0.204522	−	0.763288i	−0.989595	−	0.143884i	$-0.954041\pi$
$691$	−5.37626	−	20.0645i	−0.204522	−	0.763288i	0.785072	−	0.619404i	$-0.212626\pi$
$692$	13.1669	−	7.60190i	0.500530	−	0.288981i
$693$	−1.19051	−	1.17912i	−0.0452239	−	0.0447910i
$694$	4.87232	+	4.87232i	0.184951	+	0.184951i
$695$	27.9474	+	27.9474i	1.06011	+	1.06011i
$696$	−0.358706	+	1.33871i	−0.0135967	+	0.0507436i
$697$	1.93803	+	7.23283i	0.0734082	+	0.273963i
$698$			22.6648i			0.857874i
$699$	−0.193054	−	0.334379i	−0.00730198	−	0.0126474i
$700$	−0.158705	−	33.0031i	−0.00599850	−	1.24740i
$701$		−	14.0967i		−	0.532426i	−0.963914	−	0.266213i	$-0.914228\pi$
$701$		−	14.0967i		−	0.532426i	0.963914	−	0.266213i	$-0.0857725\pi$
$702$	−2.41192	+	2.68005i	−0.0910320	+	0.101152i
$703$	−4.82231	−	2.78416i	−0.181877	−	0.105007i
$704$	0.447823	+	0.447823i	0.0168780	+	0.0168780i
$705$	−12.0274	−	6.94400i	−0.452976	−	0.261526i
$706$	0.464302	−	0.804194i	0.0174742	−	0.0302662i
$707$	−0.0534394	−	11.1128i	−0.00200979	−	0.417941i
$708$	−11.6591	+	3.12406i	−0.438177	+	0.117409i
$709$	11.3741	−	11.3741i	0.427165	−	0.427165i	−0.460497	−	0.887661i	$-0.652329\pi$
$709$	11.3741	−	11.3741i	0.427165	−	0.427165i	0.887661	+	0.460497i	$0.152329\pi$
$710$	62.2082	−	16.6686i	2.33463	−	0.625563i
$711$	0.213699	+	0.370137i	0.00801433	+	0.0138812i
$712$	0.839287	−	1.45369i	0.0314536	−	0.0544793i
$713$	−7.39256	+	27.5894i	−0.276854	+	1.03323i
$714$	−11.1232	−	11.0168i	−0.416277	−	0.412292i
$715$	8.50604	+	4.33138i	0.318108	+	0.161984i
$716$	10.3963	+	18.0069i	0.388527	+	0.672949i
$717$	−4.60738	+	4.60738i	−0.172066	+	0.172066i
$718$	−6.49232			−0.242291
$719$	52.3571			1.95259			0.976296	−	0.216440i	$-0.0694446\pi$
$719$	52.3571			1.95259			0.976296	+	0.216440i	$0.0694446\pi$
$720$	2.95585	−	2.95585i	0.110158	−	0.110158i
$721$	3.25371	−	1.89945i	0.121174	−	0.0707391i
$722$	−3.33722	−	12.4547i	−0.124198	−	0.463514i
$723$	−14.4528	−	3.87262i	−0.537506	−	0.144024i
$724$	−16.9487	+	9.78535i	−0.629895	+	0.363670i
$725$		−	17.2883i		−	0.642072i
$726$	10.2378	−	2.74320i	0.379959	−	0.101810i
$727$	−14.4888			−0.537359			−0.268680	−	0.963230i	$-0.586587\pi$
$727$	−14.4888			−0.537359			−0.268680	+	0.963230i	$0.586587\pi$
$728$	−1.93614	+	9.34084i	−0.0717580	+	0.346195i
$729$	−1.00000			−0.0370370
$730$	33.4925	−	8.97428i	1.23961	−	0.332153i
$731$		−	16.4505i		−	0.608445i
$732$	−10.7264	+	6.19287i	−0.396458	+	0.228895i
$733$	−2.32989	−	0.624291i	−0.0860563	−	0.0230587i	0.215534	−	0.976496i	$-0.430851\pi$
$733$	−2.32989	−	0.624291i	−0.0860563	−	0.0230587i	−0.301590	+	0.953438i	$0.597517\pi$
$734$	−6.73128	−	25.1215i	−0.248456	−	0.927250i
$735$	−7.30124	+	28.3359i	−0.269310	+	1.04519i
$736$	−3.64081	+	3.64081i	−0.134202	+	0.134202i
$737$	−4.02268			−0.148177
$738$	1.26545			0.0465819
$739$	−24.8592	+	24.8592i	−0.914462	+	0.914462i	−0.996619	−	0.0821576i	$-0.973819\pi$
$739$	−24.8592	+	24.8592i	−0.914462	+	0.914462i	0.0821576	+	0.996619i	$0.473819\pi$
$740$	4.70993	+	8.15783i	0.173140	+	0.299888i
$741$	−1.85021	+	8.71519i	−0.0679690	+	0.320161i
$742$	30.5024	+	8.01610i	1.11978	+	0.294280i
$743$	−4.80877	+	17.9466i	−0.176417	+	0.658396i	0.819889	+	0.572522i	$0.194035\pi$
$743$	−4.80877	+	17.9466i	−0.176417	+	0.658396i	−0.996306	+	0.0858740i	$0.972632\pi$
$744$	2.77367	−	4.80415i	0.101688	−	0.176129i
$745$	29.3201	+	50.7839i	1.07420	+	1.86058i
$746$	24.8440	−	6.65693i	0.909603	−	0.243727i
$747$	5.72801	−	5.72801i	0.209577	−	0.209577i
$748$	−3.61980	+	0.969922i	−0.132353	+	0.0354639i
$749$	−25.1746	−	14.3736i	−0.919859	−	0.525199i
$750$	−15.6217	+	27.0577i	−0.570426	+	0.988006i
$751$	−13.9680	−	8.06445i	−0.509701	−	0.294276i	0.223010	−	0.974816i	$-0.428412\pi$
$751$	−13.9680	−	8.06445i	−0.509701	−	0.294276i	−0.732711	+	0.680540i	$0.761745\pi$
$752$	−2.34923	−	2.34923i	−0.0856678	−	0.0856678i
$753$	−13.5662	−	7.83244i	−0.494379	−	0.285430i
$754$	−1.03773	+	4.88811i	−0.0377919	+	0.178014i
$755$		−	30.7214i		−	1.11806i
$756$	−2.28490	+	1.33388i	−0.0831010	+	0.0485127i
$757$	−0.821968	−	1.42369i	−0.0298749	−	0.0517449i	0.850701	−	0.525649i	$-0.176178\pi$
$757$	−0.821968	−	1.42369i	−0.0298749	−	0.0517449i	−0.880576	+	0.473904i	$0.842844\pi$
$758$		−	29.3645i		−	1.06657i
$759$	−0.843978	−	3.14977i	−0.0306345	−	0.114329i
$760$	2.67345	−	9.97745i	0.0969763	−	0.361920i
$761$	−37.4447	−	37.4447i	−1.35737	−	1.35737i	−0.877146	−	0.480224i	$-0.840555\pi$
$761$	−37.4447	−	37.4447i	−1.35737	−	1.35737i	−0.480224	−	0.877146i	$-0.659445\pi$
$762$	−13.0183	−	13.0183i	−0.471602	−	0.471602i
$763$	−0.809924	−	2.96556i	−0.0293212	−	0.107360i
$764$	4.56628	−	2.63634i	0.165202	−	0.0953795i
$765$	6.40196	+	23.8925i	0.231463	+	0.863834i
$766$	6.31661	−	10.9407i	0.228228	−	0.395303i
$767$	−41.3872	+	13.4589i	−1.49440	+	0.485972i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−2.73506	−	0.732858i	−0.0986289	−	0.0264275i	0.209167	−	0.977880i	$-0.432925\pi$
$769$	−2.73506	−	0.732858i	−0.0986289	−	0.0264275i	−0.307796	+	0.951452i	$0.599591\pi$
$770$	4.97659	+	4.92896i	0.179344	+	0.177627i
$771$	24.8529	+	14.3488i	0.895055	+	0.516760i
$772$	3.53613	−	13.1970i	0.127268	−	0.474971i
$773$	−12.4952	−	3.34809i	−0.449422	−	0.120422i	0.0270069	−	0.999635i	$-0.491402\pi$
$773$	−12.4952	−	3.34809i	−0.449422	−	0.120422i	−0.476429	+	0.879213i	$0.658069\pi$
$774$	−2.68538	−	0.719544i	−0.0965238	−	0.0258635i
$775$	−17.9099	+	66.8406i	−0.643342	+	2.40098i
$776$	−6.54547	−	3.77903i	−0.234969	−	0.135659i
$777$	−1.57077	−	5.75140i	−0.0563509	−	0.206330i
$778$	−14.0311	−	3.75963i	−0.503041	−	0.134789i
$779$	2.70803	−	1.56348i	0.0970254	−	0.0560177i
$780$	10.0823	−	11.2032i	0.361005	−	0.401137i
$781$	−4.87863	+	8.45003i	−0.174571	+	0.302366i
$782$	−7.88548	−	29.4290i	−0.281984	−	1.05238i
$783$	−1.20025	+	0.692966i	−0.0428935	+	0.0247646i
$784$	−3.44154	+	6.09556i	−0.122912	+	0.217699i
$785$	63.2858	+	63.2858i	2.25877	+	2.25877i
$786$	−7.63081	−	7.63081i	−0.272182	−	0.272182i
$787$	13.5642	−	50.6221i	0.483510	−	1.80448i	−0.103167	−	0.994664i	$-0.532898\pi$
$787$	13.5642	−	50.6221i	0.483510	−	1.80448i	0.586677	−	0.809821i	$-0.300436\pi$
$788$	−3.27692	−	12.2296i	−0.116735	−	0.435662i
$789$			12.0503i			0.429003i
$790$	−0.893306	−	1.54725i	−0.0317824	−	0.0550487i
$791$	37.6582	+	21.5012i	1.33897	+	0.764495i
$792$			0.633318i			0.0225040i
$793$	−37.4468	+	24.3315i	−1.32978	+	0.864036i
$794$	−4.67949	−	2.70171i	−0.166069	−	0.0958800i
$795$	−35.2347	−	35.2347i	−1.24965	−	1.24965i
$796$	−5.19335	−	2.99838i	−0.184073	−	0.106275i
$797$	−18.1260	+	31.3952i	−0.642057	+	1.11208i	0.342916	+	0.939366i	$0.388585\pi$
$797$	−18.1260	+	31.3952i	−0.642057	+	1.11208i	−0.984973	+	0.172709i	$0.944748\pi$
$798$	−3.24160	+	5.67749i	−0.114751	+	0.200981i
$799$	18.9891	−	5.08811i	0.671786	−	0.180004i
$800$	−8.82055	+	8.82055i	−0.311854	+	0.311854i
$801$	1.62138	−	0.434447i	0.0572886	−	0.0153504i
$802$	2.04897	+	3.54892i	0.0723515	+	0.125317i
$803$	−2.62662	+	4.54944i	−0.0926914	+	0.160546i
$804$	−1.64395	+	6.13532i	−0.0579778	+	0.216376i
$805$	−40.0725	+	40.4598i	−1.41237	+	1.42602i
$806$	9.07595	−	17.8235i	0.319687	−	0.627806i
$807$	0.916594	+	1.58759i	0.0322656	+	0.0558857i
$808$	−2.97006	+	2.97006i	−0.104486	+	0.104486i
$809$	−24.2939			−0.854127			−0.427064	−	0.904222i	$-0.640452\pi$
$809$	−24.2939			−0.854127			−0.427064	+	0.904222i	$0.640452\pi$
$810$	4.18021			0.146878
$811$	14.0616	−	14.0616i	0.493771	−	0.493771i	−0.415721	−	0.909492i	$-0.636471\pi$
$811$	14.0616	−	14.0616i	0.493771	−	0.493771i	0.909492	+	0.415721i	$0.136471\pi$
$812$	−1.81812	+	3.18435i	−0.0638036	+	0.111749i
$813$	−3.87999	−	14.4803i	−0.136077	−	0.507847i
$814$	−1.37852	−	0.369372i	−0.0483169	−	0.0129465i
$815$	0.806761	−	0.465783i	0.0282596	−	0.0163157i
$816$			5.91724i			0.207145i
$817$	−6.63564	+	1.77801i	−0.232152	+	0.0622049i
$818$	−0.124629			−0.00435754
$819$	−7.97403	+	5.23592i	−0.278635	+	0.182958i
$820$	−5.28985			−0.184730
$821$	−25.2559	+	6.76730i	−0.881437	+	0.236180i	−0.671027	−	0.741433i	$-0.734147\pi$
$821$	−25.2559	+	6.76730i	−0.881437	+	0.236180i	−0.210410	+	0.977613i	$0.567480\pi$
$822$			14.8907i			0.519373i
$823$	33.0038	−	19.0548i	1.15044	−	0.664207i	0.201446	−	0.979500i	$-0.435436\pi$
$823$	33.0038	−	19.0548i	1.15044	−	0.664207i	0.948994	+	0.315293i	$0.102103\pi$
$824$	−1.37548	−	0.368559i	−0.0479172	−	0.0128394i
$825$	−2.04470	−	7.63091i	−0.0711872	−	0.265674i
$826$	−31.9350	+	0.153569i	−1.11116	+	0.00534335i
$827$	5.83374	−	5.83374i	0.202859	−	0.202859i	−0.598365	−	0.801224i	$-0.704183\pi$
$827$	5.83374	−	5.83374i	0.202859	−	0.202859i	0.801224	+	0.598365i	$0.204183\pi$
$828$	−5.14888			−0.178936
$829$	−11.3812			−0.395285			−0.197643	−	0.980274i	$-0.563329\pi$
$829$	−11.3812			−0.395285			−0.197643	+	0.980274i	$0.563329\pi$
$830$	−23.9443	+	23.9443i	−0.831118	+	0.831118i
$831$	−2.91497	−	5.04887i	−0.101119	−	0.175143i
$832$	3.02338	−	1.96448i	0.104817	−	0.0681059i
$833$	−21.0544	−	35.6705i	−0.729490	−	1.23591i
$834$	−2.44712	+	9.13277i	−0.0847368	+	0.316242i
$835$	39.8213	−	68.9724i	1.37807	−	2.38689i
$836$	0.782474	+	1.35528i	0.0270624	+	0.0468735i
$837$	5.35833	−	1.43576i	0.185211	−	0.0496271i
$838$	−3.10484	+	3.10484i	−0.107255	+	0.107255i
$839$	22.2461	−	5.96083i	0.768021	−	0.205791i	0.146524	−	0.989207i	$-0.453191\pi$
$839$	22.2461	−	5.96083i	0.768021	−	0.205791i	0.621497	+	0.783416i	$0.286525\pi$
$840$	9.55136	−	5.57589i	0.329553	−	0.192387i
$841$	13.5396	−	23.4513i	0.466883	−	0.808664i
$842$	27.0894	+	15.6401i	0.933563	+	0.538993i
$843$	−17.7789	−	17.7789i	−0.612338	−	0.612338i
$844$	18.2895	+	10.5594i	0.629549	+	0.363470i
$845$	34.1780	−	42.2492i	1.17576	−	1.45342i
$846$		−	3.32232i		−	0.114224i
$847$	28.0418	−	0.134847i	0.963526	−	0.00463340i
$848$	−5.96016	−	10.3233i	−0.204673	−	0.354503i
$849$		−	13.7870i		−	0.473167i
$850$	−19.1041	−	71.2974i	−0.655264	−	2.44548i
$851$	3.00300	−	11.2073i	0.102942	−	0.384183i
$852$	10.8941	+	10.8941i	0.373225	+	0.373225i
$853$	23.4705	+	23.4705i	0.803613	+	0.803613i	0.983658	−	0.180045i	$-0.0576244\pi$
$853$	23.4705	+	23.4705i	0.803613	+	0.803613i	−0.180045	+	0.983658i	$0.557624\pi$
$854$	−31.6118	+	8.63351i	−1.08173	+	0.295433i
$855$	8.94554	−	5.16471i	0.305931	−	0.176629i
$856$	2.83583	+	10.5834i	0.0969265	+	0.361735i
$857$	−9.42125	+	16.3181i	−0.321824	+	0.557415i	−0.980864	−	0.194692i	$-0.937629\pi$
$857$	−9.42125	+	16.3181i	−0.321824	+	0.557415i	0.659041	+	0.752107i	$0.270962\pi$
$858$	0.120074	+	2.28030i	0.00409926	+	0.0778482i
$859$	25.2668	−	14.5878i	0.862094	−	0.497730i	−0.00261917	−	0.999997i	$-0.500834\pi$
$859$	25.2668	−	14.5878i	0.862094	−	0.497730i	0.864713	+	0.502267i	$0.167500\pi$
$860$	11.2254	+	3.00784i	0.382784	+	0.102567i
$861$	3.23812	+	0.850983i	0.110355	+	0.0290014i
$862$	9.92121	+	5.72801i	0.337918	+	0.195097i
$863$	−6.37398	+	23.7880i	−0.216973	+	0.809753i	0.768490	+	0.639862i	$0.221008\pi$
$863$	−6.37398	+	23.7880i	−0.216973	+	0.809753i	−0.985463	+	0.169892i	$0.945658\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	−61.3895	−	16.4493i	−2.08730	−	0.559292i
$866$	−3.07806	+	11.4875i	−0.104597	+	0.390361i
$867$	−15.6003	−	9.00685i	−0.529815	−	0.305889i
$868$	10.3281	−	10.4279i	0.350559	−	0.353947i
$869$	0.261455	+	0.0700568i	0.00886927	+	0.00237651i
$870$	5.01730	−	2.89674i	0.170103	−	0.0982088i
$871$	−4.75593	+	22.4023i	−0.161149	+	0.759072i
$872$	−0.580963	+	1.00626i	−0.0196739	+	0.0340762i
$873$	−1.95617	−	7.30052i	−0.0662063	−	0.247085i
$874$	−11.0185	+	6.36152i	−0.372706	+	0.215182i
$875$	−58.1695	+	58.7316i	−1.96649	+	1.98549i
$876$	5.86530	+	5.86530i	0.198170	+	0.198170i
$877$	21.8313	+	21.8313i	0.737191	+	0.737191i	0.972033	−	0.234843i	$-0.0754575\pi$
$877$	21.8313	+	21.8313i	0.737191	+	0.737191i	−0.234843	+	0.972033i	$0.575457\pi$
$878$	−2.23096	+	8.32604i	−0.0752911	+	0.280990i
$879$	0.821170	+	3.06465i	0.0276974	+	0.103368i
$880$		−	2.64740i		−	0.0892439i
$881$	10.9949	+	19.0437i	0.370428	+	0.641600i	0.989631	−	0.143631i	$-0.0458777\pi$
$881$	10.9949	+	19.0437i	0.370428	+	0.641600i	−0.619203	+	0.785231i	$0.712544\pi$
$882$	−6.74374	+	1.87668i	−0.227074	+	0.0631910i
$883$			4.16764i			0.140252i	0.997538	+	0.0701262i	$0.0223402\pi$
$883$			4.16764i			0.140252i	−0.997538	+	0.0701262i	$0.977660\pi$
$884$	1.12188	+	21.3054i	0.0377329	+	0.716578i
$885$	43.6970	+	25.2285i	1.46886	+	0.848045i
$886$	5.97414	+	5.97414i	0.200705	+	0.200705i
$887$	−38.4314	−	22.1884i	−1.29040	−	0.745013i	−0.311675	−	0.950189i	$-0.600890\pi$
$887$	−38.4314	−	22.1884i	−1.29040	−	0.745013i	−0.978725	+	0.205176i	$0.934223\pi$
$888$	−1.12672	+	1.95154i	−0.0378103	+	0.0654893i
$889$	−24.5575	−	42.0664i	−0.823633	−	1.41086i
$890$	−6.77770	+	1.81608i	−0.227189	+	0.0608751i
$891$	−0.447823	+	0.447823i	−0.0150026	+	0.0150026i
$892$	18.8580	−	5.05298i	0.631412	−	0.169186i
$893$	−4.10478	−	7.10968i	−0.137361	−	0.237916i
$894$	−7.01402	+	12.1486i	−0.234584	+	0.406311i
$895$	22.4958	−	83.9556i	0.751953	−	2.80633i
$896$	2.55228	−	0.697052i	0.0852656	−	0.0232869i
$897$	−18.5389	+	0.976204i	−0.618995	+	0.0325945i
$898$	4.49887	+	7.79227i	0.150129	+	0.260032i
$899$	5.43641	−	5.43641i	0.181315	−	0.181315i
$900$	−12.4741			−0.415805
$901$	70.5353			2.34987
$902$	0.566699	−	0.566699i	0.0188690	−	0.0188690i
$903$	−6.38763	−	3.64706i	−0.212567	−	0.121367i
$904$	−4.24207	−	15.8316i	−0.141089	−	0.526551i
$905$	79.0221	+	21.1739i	2.62678	+	0.703844i
$906$	6.36463	−	3.67462i	0.211451	−	0.122081i
$907$		−	8.91779i		−	0.296110i	−0.988979	−	0.148055i	$-0.952699\pi$
$907$		−	8.91779i		−	0.296110i	0.988979	−	0.148055i	$-0.0473013\pi$
$908$	19.5147	−	5.22895i	0.647618	−	0.173529i
$909$	−4.20030			−0.139315
$910$	33.3331	−	21.8872i	1.10498	−	0.725555i
$911$	−28.1929			−0.934072			−0.467036	−	0.884238i	$-0.654678\pi$
$911$	−28.1929			−0.934072			−0.467036	+	0.884238i	$0.654678\pi$
$912$	2.38683	−	0.639550i	0.0790359	−	0.0211776i
$913$		−	5.13028i		−	0.169787i
$914$	−16.0432	+	9.26253i	−0.530661	+	0.306377i
$915$	50.0108	+	13.4004i	1.65331	+	0.443002i
$916$	0.488972	+	1.82487i	0.0161561	+	0.0602953i
$917$	−14.3947	−	24.6577i	−0.475354	−	0.814269i
$918$	−4.18412	+	4.18412i	−0.138096	+	0.138096i
$919$	−11.1928			−0.369216			−0.184608	−	0.982812i	$-0.559102\pi$
$919$	−11.1928			−0.369216			−0.184608	+	0.982812i	$0.559102\pi$
$920$	21.5234			0.709606
$921$	10.5351	−	10.5351i	0.347144	−	0.347144i
$922$	−20.8523	−	36.1173i	−0.686735	−	1.18946i
$923$	41.2903	+	37.1594i	1.35909	+	1.22312i
$924$	−0.425890	+	1.62057i	−0.0140107	+	0.0533130i
$925$	7.27534	−	27.1519i	0.239212	−	0.892750i
$926$	8.99080	−	15.5725i	0.295456	−	0.511745i
$927$	−0.712002	−	1.23322i	−0.0233852	−	0.0405044i
$928$	1.33871	−	0.358706i	0.0439452	−	0.0117751i
$929$	15.5378	−	15.5378i	0.509778	−	0.509778i	−0.404680	−	0.914458i	$-0.632617\pi$
$929$	15.5378	−	15.5378i	0.509778	−	0.509778i	0.914458	+	0.404680i	$0.132617\pi$
$930$	−22.3989	+	6.00178i	−0.734490	+	0.196806i
$931$	−12.1128	+	12.3480i	−0.396980	+	0.404691i
$932$	−0.193054	+	0.334379i	−0.00632370	+	0.0109530i
$933$	28.8977	+	16.6841i	0.946069	+	0.546213i
$934$	0.593861	+	0.593861i	0.0194317	+	0.0194317i
$935$	13.5665	+	7.83265i	0.443674	+	0.256155i
$936$	3.52695	+	0.748759i	0.115282	+	0.0244740i
$937$		−	26.1389i		−	0.853920i	−0.904270	−	0.426960i	$-0.859584\pi$
$937$		−	26.1389i		−	0.853920i	0.904270	−	0.426960i	$-0.140416\pi$
$938$	−8.33249	+	14.5939i	−0.272065	+	0.476508i
$939$	0.996161	+	1.72540i	0.0325085	+	0.0563063i
$940$			13.8880i			0.452976i
$941$	−1.86336	−	6.95414i	−0.0607437	−	0.226699i	0.928880	−	0.370380i	$-0.120773\pi$
$941$	−1.86336	−	6.95414i	−0.0607437	−	0.226699i	−0.989624	+	0.143682i	$0.954106\pi$
$942$	−5.54140	+	20.6808i	−0.180549	+	0.673816i
$943$	4.60727	+	4.60727i	0.150033	+	0.150033i
$944$	8.53508	+	8.53508i	0.277793	+	0.277793i
$945$	10.6966	+	2.81108i	0.347960	+	0.0914445i
$946$	−1.52480	+	0.880345i	−0.0495756	+	0.0286225i
$947$	2.69653	+	10.0636i	0.0876255	+	0.327023i	0.995798	−	0.0915724i	$-0.0291893\pi$
$947$	2.69653	+	10.0636i	0.0876255	+	0.327023i	−0.908173	+	0.418595i	$0.862523\pi$
$948$	0.213699	−	0.370137i	0.00694061	−	0.0120215i
$949$	22.2304	+	20.0064i	0.721630	+	0.649434i
$950$	−26.6944	+	15.4120i	−0.866079	+	0.500031i
$951$	20.4735	+	5.48586i	0.663898	+	0.177891i
$952$	−3.97919	+	15.1414i	−0.128966	+	0.490736i
$953$	12.2353	+	7.06405i	0.396340	+	0.228827i	0.684904	−	0.728634i	$-0.259844\pi$
$953$	12.2353	+	7.06405i	0.396340	+	0.228827i	−0.288563	+	0.957461i	$0.593178\pi$
$954$	3.08520	−	11.5141i	0.0998872	−	0.372784i
$955$	−21.2899	−	5.70461i	−0.688925	−	0.184597i
$956$	6.29380	+	1.68642i	0.203556	+	0.0545427i
$957$	−0.227175	+	0.847827i	−0.00734351	+	0.0274064i
$958$	21.5049	+	12.4159i	0.694792	+	0.401138i
$959$	−10.0136	+	38.1033i	−0.323356	+	1.23042i
$960$	−4.03777	−	1.08192i	−0.130319	−	0.0349187i
$961$	0.196509	−	0.113454i	0.00633899	−	0.00365982i
$962$	−3.68682	+	7.24025i	−0.118868	+	0.233435i
$963$	−5.47839	+	9.48886i	−0.176539	+	0.305774i
$964$	3.87262	+	14.4528i	0.124729	+	0.465494i
$965$	−49.4608	+	28.5562i	−1.59220	+	0.919256i
$966$	−13.1753	−	3.46249i	−0.423908	−	0.111404i
$967$	6.47081	+	6.47081i	0.208087	+	0.208087i	0.803454	−	0.595367i	$-0.202993\pi$
$967$	6.47081	+	6.47081i	0.208087	+	0.208087i	−0.595367	+	0.803454i	$0.702993\pi$
$968$	−7.49456	−	7.49456i	−0.240884	−	0.240884i
$969$	−3.78437	+	14.1234i	−0.121571	+	0.453711i
$970$	8.17720	+	30.5177i	0.262554	+	0.979865i
$971$		−	12.8612i		−	0.412736i	−0.978474	−	0.206368i	$-0.933836\pi$
$971$		−	12.8612i		−	0.412736i	0.978474	−	0.206368i	$-0.0661644\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−12.4034	+	21.7239i	−0.397635	+	0.696436i
$974$			37.5994i			1.20476i
$975$	−44.9140	+	2.36504i	−1.43840	+	0.0757419i
$976$	10.7264	+	6.19287i	0.343343	+	0.198229i
$977$	12.0821	+	12.0821i	0.386540	+	0.386540i	0.873451	−	0.486911i	$-0.161877\pi$
$977$	12.0821	+	12.0821i	0.386540	+	0.386540i	−0.486911	+	0.873451i	$0.661877\pi$
$978$	0.192995	+	0.111426i	0.00617131	+	0.00356301i
$979$	0.531536	−	0.920647i	0.0169880	−	0.0294240i
$980$	28.1903	−	7.84490i	0.900505	−	0.250596i
$981$	−1.12234	+	0.300729i	−0.0358334	+	0.00960153i
$982$	16.3828	−	16.3828i	0.522795	−	0.522795i
$983$	40.0769	−	10.7386i	1.27826	−	0.342507i	0.445067	−	0.895497i	$-0.353180\pi$
$983$	40.0769	−	10.7386i	1.27826	−	0.342507i	0.833188	+	0.552990i	$0.186513\pi$
$984$	−0.632726	−	1.09591i	−0.0201706	−	0.0349364i
$985$	−26.4629	+	45.8351i	−0.843178	+	1.46043i
$986$	−2.12255	+	7.92145i	−0.0675956	+	0.252270i
$987$	2.23417	−	8.50136i	0.0711145	−	0.270601i
$988$	8.47268	−	2.75527i	0.269552	−	0.0876568i
$989$	−7.15722	−	12.3967i	−0.227586	−	0.394191i
$990$	1.87200	−	1.87200i	0.0594959	−	0.0594959i
$991$	−20.0390			−0.636559			−0.318280	−	0.947997i	$-0.603105\pi$
$991$	−20.0390			−0.636559			−0.318280	+	0.947997i	$0.603105\pi$
$992$	−5.54735			−0.176129
$993$	−6.63821	+	6.63821i	−0.210657	+	0.210657i
$994$	20.5505	+	35.2025i	0.651822	+	1.11655i
$995$	6.48800	+	24.2135i	0.205683	+	0.767621i
$996$	−7.82461	−	2.09660i	−0.247932	−	0.0664333i
$997$	12.5168	−	7.22659i	0.396411	−	0.228868i	−0.288523	−	0.957473i	$-0.593164\pi$
$997$	12.5168	−	7.22659i	0.396411	−	0.228868i	0.684934	+	0.728605i	$0.259831\pi$
$998$			19.7904i			0.626455i
$999$	−2.17666	+	0.583233i	−0.0688664	+	0.0184527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.115.1	yes	40
7.5	odd	6		546.2.cg.b.271.6	yes	40
13.6	odd	12		546.2.cg.b.409.6	yes	40
91.19	even	12	inner	546.2.by.b.19.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.1	✓	40	91.19	even	12	inner
546.2.by.b.115.1	yes	40	1.1	even	1	trivial
546.2.cg.b.271.6	yes	40	7.5	odd	6
546.2.cg.b.409.6	yes	40	13.6	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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-4.03777 - 1.08192i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-0.0127227 - 2.64572i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-4.03777 - 1.08192i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-0.0127227 - 2.64572i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +4.18021 q^{10} +(-0.447823 + 0.447823i) q^{11} +(0.500000 + 0.866025i) q^{12} +(1.96448 + 3.02338i) q^{13} +(0.697052 + 2.55228i) q^{14} +(1.08192 - 4.03777i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.95862 + 5.12448i) q^{17} +(0.965926 - 0.258819i) q^{18} +(1.74728 - 1.74728i) q^{19} +(-4.03777 + 1.08192i) q^{20} +(2.64572 - 0.0127227i) q^{21} +(0.316659 - 0.548469i) q^{22} +(4.45906 + 2.57444i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(10.8029 + 6.23707i) q^{25} +(-2.68005 - 2.41192i) q^{26} -1.00000i q^{27} +(-1.33388 - 2.28490i) q^{28} +(-0.692966 - 1.20025i) q^{29} +4.18021i q^{30} +(1.43576 + 5.35833i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.447823 - 0.447823i) q^{33} +(-4.18412 - 4.18412i) q^{34} +(-2.81108 + 10.6966i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.583233 - 2.17666i) q^{37} +(-1.23551 + 2.13997i) q^{38} +(-3.02338 + 1.96448i) q^{39} +(3.62017 - 2.09010i) q^{40} +(1.22233 + 0.327523i) q^{41} +(-2.55228 + 0.697052i) q^{42} +(-2.40764 - 1.39005i) q^{43} +(-0.163915 + 0.611738i) q^{44} +(4.03777 + 1.08192i) q^{45} +(-4.97344 - 1.33263i) q^{46} +(0.859880 - 3.20911i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-6.99968 + 0.0673217i) q^{49} +(-12.0491 - 3.22855i) q^{50} +(-5.12448 + 2.95862i) q^{51} +(3.21298 + 1.63609i) q^{52} +(5.96016 - 10.3233i) q^{53} +(0.258819 + 0.965926i) q^{54} +(2.29272 - 1.32370i) q^{55} +(1.87980 + 1.86181i) q^{56} +(1.74728 + 1.74728i) q^{57} +(0.980002 + 0.980002i) q^{58} +(-3.12406 + 11.6591i) q^{59} +(-1.08192 - 4.03777i) q^{60} +12.3857i q^{61} +(-2.77367 - 4.80415i) q^{62} +(0.0127227 + 2.64572i) q^{63} -1.00000i q^{64} +(-4.66106 - 14.3331i) q^{65} +(0.548469 + 0.316659i) q^{66} +(4.49136 + 4.49136i) q^{67} +(5.12448 + 2.95862i) q^{68} +(-2.57444 + 4.45906i) q^{69} +(-0.0531837 - 11.0597i) q^{70} +(14.8816 - 3.98751i) q^{71} +(0.707107 - 0.707107i) q^{72} +(8.01215 - 2.14685i) q^{73} +(1.12672 + 1.95154i) q^{74} +(-6.23707 + 10.8029i) q^{75} +(0.639550 - 2.38683i) q^{76} +(1.19051 + 1.17912i) q^{77} +(2.41192 - 2.68005i) q^{78} +(-0.213699 - 0.370137i) q^{79} +(-2.95585 + 2.95585i) q^{80} +1.00000 q^{81} -1.26545 q^{82} +(-5.72801 + 5.72801i) q^{83} +(2.28490 - 1.33388i) q^{84} +(-6.40196 - 23.8925i) q^{85} +(2.68538 + 0.719544i) q^{86} +(1.20025 - 0.692966i) q^{87} -0.633318i q^{88} +(-1.62138 + 0.434447i) q^{89} -4.18021 q^{90} +(7.97403 - 5.23592i) q^{91} +5.14888 q^{92} +(-5.35833 + 1.43576i) q^{93} +3.32232i q^{94} +(-8.94554 + 5.16471i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(1.95617 + 7.30052i) q^{97} +(6.74374 - 1.87668i) q^{98} +(0.447823 - 0.447823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more