LMFDB - Embedded newform 546.2.bx.b.223.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.5
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.b.475.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.77438 + 1.77438i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.76783 + 1.96844i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.77438 + 1.77438i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.76783 + 1.96844i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.25468 - 2.17316i) q^{10} +(-0.239338 + 0.893220i) q^{11} -1.00000 q^{12} +(1.53943 + 3.26039i) q^{13} +(-1.19812 - 2.35892i) q^{14} +(-2.42385 - 0.649468i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.62617 - 4.54866i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-1.76219 + 0.472178i) q^{19} +(0.649468 + 2.42385i) q^{20} +(-2.51521 - 0.820805i) q^{21} +(0.462365 - 0.800839i) q^{22} +(-5.27538 + 3.04574i) q^{23} +(0.965926 + 0.258819i) q^{24} +1.29686i q^{25} +(-0.643122 - 3.54773i) q^{26} +1.00000i q^{27} +(0.546766 + 2.58864i) q^{28} +(-3.15163 - 5.45877i) q^{29} +(2.17316 + 1.25468i) q^{30} +(3.75725 + 3.75725i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.239338 - 0.893220i) q^{33} +(-3.71396 + 3.71396i) q^{34} +(-0.355959 + 6.62958i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-0.542304 + 2.02391i) q^{37} +1.82435 q^{38} +(-2.96338 - 2.05387i) q^{39} -2.50935i q^{40} +(-1.84930 + 6.90168i) q^{41} +(2.21707 + 1.44382i) q^{42} +(7.61197 + 4.39478i) q^{43} +(-0.653882 + 0.653882i) q^{44} +(2.42385 - 0.649468i) q^{45} +(5.88392 - 1.57659i) q^{46} +(-2.17165 + 2.17165i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.749536 + 6.95976i) q^{49} +(0.335651 - 1.25267i) q^{50} +5.25234i q^{51} +(-0.297013 + 3.59330i) q^{52} +3.75859 q^{53} +(0.258819 - 0.965926i) q^{54} +(-2.00959 + 1.16024i) q^{55} +(0.141853 - 2.64195i) q^{56} +(1.29001 - 1.29001i) q^{57} +(1.63140 + 6.08847i) q^{58} +(1.46988 + 5.48566i) q^{59} +(-1.77438 - 1.77438i) q^{60} +(3.63362 + 2.09787i) q^{61} +(-2.65678 - 4.60167i) q^{62} +(2.58864 - 0.546766i) q^{63} +1.00000i q^{64} +(-3.05365 + 8.51671i) q^{65} +0.924729i q^{66} +(4.93612 + 1.32263i) q^{67} +(4.54866 - 2.62617i) q^{68} +(3.04574 - 5.27538i) q^{69} +(2.05969 - 6.31155i) q^{70} +(-3.60545 - 13.4557i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(4.41027 - 4.41027i) q^{73} +(1.04765 - 1.81459i) q^{74} +(-0.648428 - 1.12311i) q^{75} +(-1.76219 - 0.472178i) q^{76} +(-2.18136 + 1.10794i) q^{77} +(2.33083 + 2.75086i) q^{78} -13.1469 q^{79} +(-0.649468 + 2.42385i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.57257 - 6.18788i) q^{82} +(-1.26095 - 1.26095i) q^{83} +(-1.76783 - 1.96844i) q^{84} +(12.7309 - 3.41123i) q^{85} +(-6.21515 - 6.21515i) q^{86} +(5.45877 + 3.15163i) q^{87} +(0.800839 - 0.462365i) q^{88} +(-7.69329 - 2.06141i) q^{89} -2.50935 q^{90} +(-3.69645 + 8.79411i) q^{91} -6.09148 q^{92} +(-5.13250 - 1.37525i) q^{93} +(2.65972 - 1.53559i) q^{94} +(-3.96462 - 2.28897i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-2.07866 + 0.556974i) q^{97} +(2.52531 - 6.52861i) q^{98} +(0.653882 + 0.653882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.77438	+	1.77438i	0.793527	+	0.793527i	0.982066	−	0.188539i	$-0.0603750\pi$
$5$	1.77438	+	1.77438i	0.793527	+	0.793527i	−0.188539	+	0.982066i	$0.560375\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	1.76783	+	1.96844i	0.668178	+	0.744002i
$7$	1.76783	+	1.96844i	0.668178	+	0.744002i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.25468	−	2.17316i	−0.396764	−	0.687215i
$11$	−0.239338	+	0.893220i	−0.0721630	+	0.269316i	−0.992575	−	0.121634i	$-0.961187\pi$
$11$	−0.239338	+	0.893220i	−0.0721630	+	0.269316i	0.920412	+	0.390950i	$0.127853\pi$
$12$	−1.00000			−0.288675
$13$	1.53943	+	3.26039i	0.426961	+	0.904270i
$13$	1.53943	+	3.26039i	0.426961	+	0.904270i
$14$	−1.19812	−	2.35892i	−0.320212	−	0.630448i
$15$	−2.42385	−	0.649468i	−0.625835	−	0.167692i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.62617	−	4.54866i	0.636939	−	1.10321i	−0.349161	−	0.937063i	$-0.613533\pi$
$17$	2.62617	−	4.54866i	0.636939	−	1.10321i	0.986101	−	0.166149i	$-0.0531332\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−1.76219	+	0.472178i	−0.404274	+	0.108325i	−0.455225	−	0.890376i	$-0.650441\pi$
$19$	−1.76219	+	0.472178i	−0.404274	+	0.108325i	0.0509513	+	0.998701i	$0.483775\pi$
$20$	0.649468	+	2.42385i	0.145226	+	0.541989i
$21$	−2.51521	−	0.820805i	−0.548864	−	0.179114i
$22$	0.462365	−	0.800839i	0.0985765	−	0.170739i
$23$	−5.27538	+	3.04574i	−1.09999	+	0.635081i	−0.936219	−	0.351417i	$-0.885700\pi$
$23$	−5.27538	+	3.04574i	−1.09999	+	0.635081i	−0.163773	+	0.986498i	$0.552367\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$			1.29686i			0.259371i
$26$	−0.643122	−	3.54773i	−0.126127	−	0.695767i
$27$			1.00000i			0.192450i
$28$	0.546766	+	2.58864i	0.103329	+	0.489207i
$29$	−3.15163	−	5.45877i	−0.585242	−	1.01367i	−0.994845	−	0.101405i	$-0.967666\pi$
$29$	−3.15163	−	5.45877i	−0.585242	−	1.01367i	0.409603	−	0.912264i	$-0.365667\pi$
$30$	2.17316	+	1.25468i	0.396764	+	0.229072i
$31$	3.75725	+	3.75725i	0.674822	+	0.674822i	0.958824	−	0.284002i	$-0.0916622\pi$
$31$	3.75725	+	3.75725i	0.674822	+	0.674822i	−0.284002	+	0.958824i	$0.591662\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.239338	−	0.893220i	−0.0416633	−	0.155490i
$34$	−3.71396	+	3.71396i	−0.636939	+	0.636939i
$35$	−0.355959	+	6.62958i	−0.0601681	+	1.12060i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−0.542304	+	2.02391i	−0.0891543	+	0.332728i	−0.996068	−	0.0885872i	$-0.971765\pi$
$37$	−0.542304	+	2.02391i	−0.0891543	+	0.332728i	0.906914	+	0.421315i	$0.138431\pi$
$38$	1.82435			0.295949
$39$	−2.96338	−	2.05387i	−0.474521	−	0.328882i
$40$		−	2.50935i		−	0.396764i
$41$	−1.84930	+	6.90168i	−0.288812	+	1.07786i	0.657196	+	0.753719i	$0.271742\pi$
$41$	−1.84930	+	6.90168i	−0.288812	+	1.07786i	−0.946008	+	0.324142i	$0.894924\pi$
$42$	2.21707	+	1.44382i	0.342101	+	0.222786i
$43$	7.61197	+	4.39478i	1.16082	+	0.670197i	0.951499	−	0.307651i	$-0.0995429\pi$
$43$	7.61197	+	4.39478i	1.16082	+	0.670197i	0.209316	+	0.977848i	$0.432876\pi$
$44$	−0.653882	+	0.653882i	−0.0985765	+	0.0985765i
$45$	2.42385	−	0.649468i	0.361326	−	0.0968170i
$46$	5.88392	−	1.57659i	0.867536	−	0.232456i
$47$	−2.17165	+	2.17165i	−0.316768	+	0.316768i	−0.847525	−	0.530756i	$-0.821908\pi$
$47$	−2.17165	+	2.17165i	−0.316768	+	0.316768i	0.530756	+	0.847525i	$0.321908\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−0.749536	+	6.95976i	−0.107077	+	0.994251i
$50$	0.335651	−	1.25267i	0.0474682	−	0.177154i
$51$			5.25234i			0.735474i
$52$	−0.297013	+	3.59330i	−0.0411882	+	0.498301i
$53$	3.75859			0.516283			0.258141	−	0.966107i	$-0.416890\pi$
$53$	3.75859			0.516283			0.258141	+	0.966107i	$0.416890\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−2.00959	+	1.16024i	−0.270973	+	0.156446i
$56$	0.141853	−	2.64195i	0.0189559	−	0.353045i
$57$	1.29001	−	1.29001i	0.170866	−	0.170866i
$58$	1.63140	+	6.08847i	0.214213	+	0.799456i
$59$	1.46988	+	5.48566i	0.191362	+	0.714172i	0.993179	+	0.116602i	$0.0372002\pi$
$59$	1.46988	+	5.48566i	0.191362	+	0.714172i	−0.801817	+	0.597570i	$0.796133\pi$
$60$	−1.77438	−	1.77438i	−0.229072	−	0.229072i
$61$	3.63362	+	2.09787i	0.465237	+	0.268605i	0.714244	−	0.699897i	$-0.246771\pi$
$61$	3.63362	+	2.09787i	0.465237	+	0.268605i	−0.249007	+	0.968502i	$0.580104\pi$
$62$	−2.65678	−	4.60167i	−0.337411	−	0.584413i
$63$	2.58864	−	0.546766i	0.326138	−	0.0688861i
$64$			1.00000i			0.125000i
$65$	−3.05365	+	8.51671i	−0.378758	+	1.05637i
$66$			0.924729i			0.113826i
$67$	4.93612	+	1.32263i	0.603043	+	0.161585i	0.547407	−	0.836866i	$-0.315615\pi$
$67$	4.93612	+	1.32263i	0.603043	+	0.161585i	0.0556356	+	0.998451i	$0.482282\pi$
$68$	4.54866	−	2.62617i	0.551606	−	0.318470i
$69$	3.04574	−	5.27538i	0.366664	−	0.635081i
$70$	2.05969	−	6.31155i	0.246180	−	0.754374i
$71$	−3.60545	−	13.4557i	−0.427888	−	1.59690i	−0.757534	−	0.652795i	$-0.773596\pi$
$71$	−3.60545	−	13.4557i	−0.427888	−	1.59690i	0.329646	−	0.944105i	$-0.393071\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	4.41027	−	4.41027i	0.516183	−	0.516183i	−0.400231	−	0.916414i	$-0.631070\pi$
$73$	4.41027	−	4.41027i	0.516183	−	0.516183i	0.916414	+	0.400231i	$0.131070\pi$
$74$	1.04765	−	1.81459i	0.121787	−	0.210941i
$75$	−0.648428	−	1.12311i	−0.0748740	−	0.129686i
$76$	−1.76219	−	0.472178i	−0.202137	−	0.0541625i
$77$	−2.18136	+	1.10794i	−0.248589	+	0.126262i
$78$	2.33083	+	2.75086i	0.263914	+	0.311474i
$79$	−13.1469			−1.47914			−0.739569	−	0.673081i	$-0.764971\pi$
$79$	−13.1469			−1.47914			−0.739569	+	0.673081i	$0.764971\pi$
$80$	−0.649468	+	2.42385i	−0.0726128	+	0.270995i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.57257	−	6.18788i	0.394525	−	0.683337i
$83$	−1.26095	−	1.26095i	−0.138407	−	0.138407i	0.634509	−	0.772916i	$-0.281202\pi$
$83$	−1.26095	−	1.26095i	−0.138407	−	0.138407i	−0.772916	+	0.634509i	$0.781202\pi$
$84$	−1.76783	−	1.96844i	−0.192886	−	0.214775i
$85$	12.7309	−	3.41123i	1.38086	−	0.370000i
$86$	−6.21515	−	6.21515i	−0.670197	−	0.670197i
$87$	5.45877	+	3.15163i	0.585242	+	0.337890i
$88$	0.800839	−	0.462365i	0.0853697	−	0.0492882i
$89$	−7.69329	−	2.06141i	−0.815487	−	0.218509i	−0.173115	−	0.984902i	$-0.555383\pi$
$89$	−7.69329	−	2.06141i	−0.815487	−	0.218509i	−0.642372	+	0.766393i	$0.722050\pi$
$90$	−2.50935			−0.264509
$91$	−3.69645	+	8.79411i	−0.387493	+	0.921873i
$92$	−6.09148			−0.635081
$93$	−5.13250	−	1.37525i	−0.532215	−	0.142607i
$94$	2.65972	−	1.53559i	0.274329	−	0.158384i
$95$	−3.96462	−	2.28897i	−0.406761	−	0.234844i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−2.07866	+	0.556974i	−0.211056	+	0.0565522i	−0.362798	−	0.931868i	$-0.618178\pi$
$97$	−2.07866	+	0.556974i	−0.211056	+	0.0565522i	0.151742	+	0.988420i	$0.451512\pi$
$98$	2.52531	−	6.52861i	0.255095	−	0.659490i
$99$	0.653882	+	0.653882i	0.0657176	+	0.0657176i
$100$	−0.648428	+	1.12311i	−0.0648428	+	0.112311i
$101$	−6.04085	−	10.4631i	−0.601087	−	1.04111i	−0.992657	−	0.120965i	$-0.961401\pi$
$101$	−6.04085	−	10.4631i	−0.601087	−	1.04111i	0.391570	−	0.920148i	$-0.371932\pi$
$102$	1.35940	−	5.07337i	0.134601	−	0.502338i
$103$	−13.8218			−1.36190			−0.680952	−	0.732328i	$-0.738434\pi$
$103$	−13.8218			−1.36190			−0.680952	+	0.732328i	$0.738434\pi$
$104$	1.21691	−	3.39399i	0.119327	−	0.332808i
$105$	−3.00652	−	5.91936i	−0.293406	−	0.577670i
$106$	−3.63052	−	0.972796i	−0.352628	−	0.0944863i
$107$	4.18315	+	7.24543i	0.404401	+	0.700442i	0.994252	−	0.107070i	$-0.0341468\pi$
$107$	4.18315	+	7.24543i	0.404401	+	0.700442i	−0.589851	+	0.807512i	$0.700814\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	6.41880	−	6.41880i	0.614809	−	0.614809i	−0.329386	−	0.944195i	$-0.606842\pi$
$109$	6.41880	−	6.41880i	0.614809	−	0.614809i	0.944195	+	0.329386i	$0.106842\pi$
$110$	2.24140	−	0.600583i	0.213710	−	0.0572633i
$111$	−0.542304	−	2.02391i	−0.0514732	−	0.192101i
$112$	−0.820805	+	2.51521i	−0.0775588	+	0.237665i
$113$	6.80111	−	11.7799i	0.639795	−	1.10816i	−0.345683	−	0.938351i	$-0.612353\pi$
$113$	6.80111	−	11.7799i	0.639795	−	1.10816i	0.985478	−	0.169806i	$-0.0543140\pi$
$114$	−1.57994	+	0.912177i	−0.147975	+	0.0854332i
$115$	−14.7648	−	3.95622i	−1.37683	−	0.368920i
$116$		−	6.30325i		−	0.585242i
$117$	3.59330	+	0.297013i	0.332200	+	0.0274588i
$118$		−	5.67917i		−	0.522810i
$119$	13.5964	−	2.87180i	1.24638	−	0.263258i
$120$	1.25468	+	2.17316i	0.114536	+	0.198382i
$121$	8.78572	+	5.07244i	0.798702	+	0.461131i
$122$	−2.96684	−	2.96684i	−0.268605	−	0.268605i
$123$	−1.84930	−	6.90168i	−0.166746	−	0.622303i
$124$	1.37525	+	5.13250i	0.123501	+	0.460912i
$125$	6.57079	−	6.57079i	0.587709	−	0.587709i
$126$	−2.64195	−	0.141853i	−0.235363	−	0.0126373i
$127$	12.1049	−	6.98879i	1.07414	−	0.620155i	0.144831	−	0.989456i	$-0.453736\pi$
$127$	12.1049	−	6.98879i	1.07414	−	0.620155i	0.929310	+	0.369301i	$0.120403\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−8.78955			−0.773877
$130$	5.15388	−	7.43617i	0.452025	−	0.652195i
$131$			13.4753i			1.17734i	0.808372	+	0.588672i	$0.200349\pi$
$131$			13.4753i			1.17734i	−0.808372	+	0.588672i	$0.799651\pi$
$132$	0.239338	−	0.893220i	0.0208317	−	0.0777448i
$133$	−4.04471	−	2.63404i	−0.350721	−	0.228400i
$134$	−4.42560	−	2.55512i	−0.382314	−	0.220729i
$135$	−1.77438	+	1.77438i	−0.152714	+	0.152714i
$136$	−5.07337	+	1.35940i	−0.435038	+	0.116568i
$137$	14.6762	−	3.93248i	1.25387	−	0.335975i	0.430042	−	0.902809i	$-0.358499\pi$
$137$	14.6762	−	3.93248i	1.25387	−	0.335975i	0.823832	+	0.566834i	$0.191832\pi$
$138$	−4.30733	+	4.30733i	−0.366664	+	0.366664i
$139$	−4.07741	−	2.35409i	−0.345841	−	0.199671i	0.317011	−	0.948422i	$-0.397321\pi$
$139$	−4.07741	−	2.35409i	−0.345841	−	0.199671i	−0.662852	+	0.748750i	$0.730654\pi$
$140$	−3.62306	+	5.56340i	−0.306204	+	0.470193i
$141$	0.794880	−	2.96653i	0.0669410	−	0.249827i
$142$			13.9304i			1.16901i
$143$	−3.28069	+	0.594713i	−0.274345	+	0.0497324i
$144$	1.00000			0.0833333
$145$	4.09376	−	15.2781i	0.339968	−	1.26878i
$146$	−5.40145	+	3.11853i	−0.447027	+	0.258091i
$147$	−2.83076	−	6.40209i	−0.233477	−	0.528036i
$148$	−1.48160	+	1.48160i	−0.121787	+	0.121787i
$149$	2.58363	+	9.64223i	0.211659	+	0.789923i	0.987316	+	0.158768i	$0.0507521\pi$
$149$	2.58363	+	9.64223i	0.211659	+	0.789923i	−0.775657	+	0.631155i	$0.782581\pi$
$150$	0.335651	+	1.25267i	0.0274058	+	0.102280i
$151$	−6.27583	−	6.27583i	−0.510719	−	0.510719i	0.404027	−	0.914747i	$-0.367610\pi$
$151$	−6.27583	−	6.27583i	−0.510719	−	0.510719i	−0.914747	+	0.404027i	$0.867610\pi$
$152$	1.57994	+	0.912177i	0.128150	+	0.0739873i
$153$	−2.62617	−	4.54866i	−0.212313	−	0.367737i
$154$	2.39379	−	0.505611i	0.192897	−	0.0407433i
$155$			13.3336i			1.07098i
$156$	−1.53943	−	3.26039i	−0.123253	−	0.261040i
$157$		−	22.3331i		−	1.78237i	−0.453635	−	0.891187i	$-0.649873\pi$
$157$		−	22.3331i		−	1.78237i	0.453635	−	0.891187i	$-0.350127\pi$
$158$	12.6989	+	3.40266i	1.01027	+	0.270701i
$159$	−3.25504	+	1.87930i	−0.258141	+	0.149038i
$160$	1.25468	−	2.17316i	0.0991909	−	0.171804i
$161$	−15.3213	−	4.99992i	−1.20749	−	0.394049i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	7.13155	−	1.91089i	0.558586	−	0.149673i	0.0315292	−	0.999503i	$-0.489962\pi$
$163$	7.13155	−	1.91089i	0.558586	−	0.149673i	0.527057	+	0.849830i	$0.323296\pi$
$164$	−5.05238	+	5.05238i	−0.394525	+	0.394525i
$165$	1.16024	−	2.00959i	0.0903243	−	0.156446i
$166$	0.891625	+	1.54434i	0.0692035	+	0.119864i
$167$	4.17577	+	1.11890i	0.323131	+	0.0865827i	0.416738	−	0.909026i	$-0.363173\pi$
$167$	4.17577	+	1.11890i	0.323131	+	0.0865827i	−0.0936073	+	0.995609i	$0.529840\pi$
$168$	1.19812	+	2.35892i	0.0924373	+	0.181995i
$169$	−8.26032	+	10.0383i	−0.635409	+	0.772175i
$170$	−13.1800			−1.01086
$171$	−0.472178	+	1.76219i	−0.0361083	+	0.134758i
$172$	4.39478	+	7.61197i	0.335099	+	0.580408i
$173$	−2.15852	+	3.73867i	−0.164109	+	0.284246i	−0.936339	−	0.351098i	$-0.885808\pi$
$173$	−2.15852	+	3.73867i	−0.164109	+	0.284246i	0.772229	+	0.635344i	$0.219142\pi$
$174$	−4.45707	−	4.45707i	−0.337890	−	0.337890i
$175$	−2.55279	+	2.29262i	−0.192972	+	0.173306i
$176$	−0.893220	+	0.239338i	−0.0673290	+	0.0180407i
$177$	−4.01578	−	4.01578i	−0.301845	−	0.301845i
$178$	6.89761	+	3.98234i	0.516998	+	0.298489i
$179$	−9.66418	+	5.57961i	−0.722334	+	0.417040i	−0.815611	−	0.578600i	$-0.803599\pi$
$179$	−9.66418	+	5.57961i	−0.722334	+	0.417040i	0.0932768	+	0.995640i	$0.470266\pi$
$180$	2.42385	+	0.649468i	0.180663	+	0.0484085i
$181$	−2.90491			−0.215920			−0.107960	−	0.994155i	$-0.534432\pi$
$181$	−2.90491			−0.215920			−0.107960	+	0.994155i	$0.534432\pi$
$182$	5.84657	−	7.53774i	0.433377	−	0.558735i
$183$	−4.19574			−0.310158
$184$	5.88392	+	1.57659i	0.433768	+	0.116228i
$185$	−4.55344	+	2.62893i	−0.334775	+	0.193283i
$186$	4.60167	+	2.65678i	0.337411	+	0.194804i
$187$	3.43441	+	3.43441i	0.251149	+	0.251149i
$188$	−2.96653	+	0.794880i	−0.216357	+	0.0579726i
$189$	−1.96844	+	1.76783i	−0.143183	+	0.128591i
$190$	3.23710	+	3.23710i	0.234844	+	0.234844i
$191$	10.1676	−	17.6108i	0.735700	−	1.27427i	−0.218715	−	0.975789i	$-0.570187\pi$
$191$	10.1676	−	17.6108i	0.735700	−	1.27427i	0.954415	−	0.298482i	$-0.0964801\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	5.33209	−	19.8996i	0.383812	−	1.43241i	−0.456219	−	0.889867i	$-0.650797\pi$
$193$	5.33209	−	19.8996i	0.383812	−	1.43241i	0.840031	−	0.542538i	$-0.182537\pi$
$194$	2.15198			0.154503
$195$	−1.61382	−	8.90251i	−0.115568	−	0.637522i
$196$	−4.12899	+	5.65256i	−0.294928	+	0.403754i
$197$	17.7106	+	4.74553i	1.26183	+	0.338105i	0.826894	−	0.562359i	$-0.190106\pi$
$197$	17.7106	+	4.74553i	1.26183	+	0.338105i	0.434932	+	0.900464i	$0.356773\pi$
$198$	−0.462365	−	0.800839i	−0.0328588	−	0.0569132i
$199$	−8.72750	+	15.1165i	−0.618676	+	1.07158i	0.371052	+	0.928612i	$0.378997\pi$
$199$	−8.72750	+	15.1165i	−0.618676	+	1.07158i	−0.989728	+	0.142966i	$0.954336\pi$
$200$	0.917015	−	0.917015i	0.0648428	−	0.0648428i
$201$	−4.93612	+	1.32263i	−0.348167	+	0.0932911i
$202$	3.12697	+	11.6700i	0.220013	+	0.821100i
$203$	5.17374	−	15.8540i	0.363125	−	1.11273i
$204$	−2.62617	+	4.54866i	−0.183869	+	0.318470i
$205$	−15.5276	+	8.96485i	−1.08449	+	0.626132i
$206$	13.3509	+	3.57735i	0.930198	+	0.249246i
$207$			6.09148i			0.423387i
$208$	−2.05387	+	2.96338i	−0.142410	+	0.205473i
$209$		−	1.68703i		−	0.116695i
$210$	1.37203	+	6.49581i	0.0946791	+	0.448253i
$211$	−14.0231	−	24.2888i	−0.965393	−	1.67211i	−0.708555	−	0.705655i	$-0.750653\pi$
$211$	−14.0231	−	24.2888i	−0.965393	−	1.67211i	−0.256838	−	0.966455i	$-0.582681\pi$
$212$	3.25504	+	1.87930i	0.223557	+	0.129071i
$213$	9.85027	+	9.85027i	0.674929	+	0.674929i
$214$	−2.16536	−	8.08123i	−0.148021	−	0.552421i
$215$	5.70854	+	21.3045i	0.389319	+	1.45296i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−0.753743	+	14.0381i	−0.0511674	+	0.952969i
$218$	−7.86139	+	4.53877i	−0.532440	+	0.307405i
$219$	−1.61427	+	6.02454i	−0.109082	+	0.407101i
$220$	−2.32047			−0.156446
$221$	18.8732	+	1.56001i	1.26955	+	0.104938i
$222$			2.09530i			0.140628i
$223$	0.121456	−	0.453279i	0.00813328	−	0.0303538i	−0.961740	−	0.273964i	$-0.911665\pi$
$223$	0.121456	−	0.453279i	0.00813328	−	0.0303538i	0.969873	+	0.243610i	$0.0783318\pi$
$224$	1.44382	−	2.21707i	0.0964694	−	0.148134i
$225$	1.12311	+	0.648428i	0.0748740	+	0.0432285i
$226$	−9.61822	+	9.61822i	−0.639795	+	0.639795i
$227$	26.1459	−	7.00578i	1.73537	−	0.464990i	0.753957	−	0.656923i	$-0.228142\pi$
$227$	26.1459	−	7.00578i	1.73537	−	0.464990i	0.981408	+	0.191933i	$0.0614758\pi$
$228$	1.76219	−	0.472178i	0.116704	−	0.0312707i
$229$	18.1214	−	18.1214i	1.19749	−	1.19749i	0.222578	−	0.974915i	$-0.428553\pi$
$229$	18.1214	−	18.1214i	1.19749	−	1.19749i	0.974915	−	0.222578i	$-0.0714472\pi$
$230$	13.2378	+	7.64284i	0.872874	+	0.503954i
$231$	1.33514	−	2.05019i	0.0878460	−	0.134892i
$232$	−1.63140	+	6.08847i	−0.107107	+	0.399728i
$233$			18.3756i			1.20383i	0.798561	+	0.601914i	$0.205595\pi$
$233$			18.3756i			1.20383i	−0.798561	+	0.601914i	$0.794405\pi$
$234$	−3.39399	−	1.21691i	−0.221872	−	0.0795516i
$235$	−7.70668			−0.502729
$236$	−1.46988	+	5.48566i	−0.0956809	+	0.357086i
$237$	11.3855	−	6.57343i	0.739569	−	0.426990i
$238$	−13.8764	−	0.745060i	−0.899473	−	0.0482951i
$239$	10.8688	−	10.8688i	0.703041	−	0.703041i	−0.262021	−	0.965062i	$-0.584389\pi$
$239$	10.8688	−	10.8688i	0.703041	−	0.703041i	0.965062	+	0.262021i	$0.0843889\pi$
$240$	−0.649468	−	2.42385i	−0.0419230	−	0.156459i
$241$	2.98930	+	11.1562i	0.192558	+	0.718636i	0.992886	+	0.119073i	$0.0379922\pi$
$241$	2.98930	+	11.1562i	0.192558	+	0.718636i	−0.800328	+	0.599563i	$0.795341\pi$
$242$	−7.17351	−	7.17351i	−0.461131	−	0.461131i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.09787	+	3.63362i	0.134302	+	0.232619i
$245$	−13.6792	+	11.0193i	−0.873933	+	0.703997i
$246$			7.14514i			0.455558i
$247$	−4.25225	−	5.01855i	−0.270564	−	0.319323i
$248$		−	5.31355i		−	0.337411i
$249$	1.72249	+	0.461539i	0.109158	+	0.0292489i
$250$	−8.04754	+	4.64625i	−0.508971	+	0.293855i
$251$	−5.54552	+	9.60512i	−0.350030	+	0.606270i	−0.986254	−	0.165234i	$-0.947162\pi$
$251$	−5.54552	+	9.60512i	−0.350030	+	0.606270i	0.636224	+	0.771504i	$0.280495\pi$
$252$	2.51521	+	0.820805i	0.158443	+	0.0517059i
$253$	−1.45792	−	5.44103i	−0.0916586	−	0.342075i
$254$	−13.5013	+	3.61767i	−0.847148	+	0.226993i
$255$	−9.31965	+	9.31965i	−0.583619	+	0.583619i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.72776	+	4.72461i	0.170153	+	0.294713i	0.938473	−	0.345352i	$-0.112241\pi$
$257$	2.72776	+	4.72461i	0.170153	+	0.294713i	−0.768320	+	0.640066i	$0.778907\pi$
$258$	8.49005	+	2.27490i	0.528568	+	0.141629i
$259$	−4.94265	+	2.51043i	−0.307121	+	0.155991i
$260$	−6.90289	+	5.84886i	−0.428099	+	0.362731i
$261$	−6.30325			−0.390161
$262$	3.48767	−	13.0161i	0.215469	−	0.804140i
$263$	−1.94080	−	3.36156i	−0.119675	−	0.207283i	0.799964	−	0.600048i	$-0.204852\pi$
$263$	−1.94080	−	3.36156i	−0.119675	−	0.207283i	−0.919639	+	0.392765i	$0.871519\pi$
$264$	−0.462365	+	0.800839i	−0.0284566	+	0.0492882i
$265$	6.66918	+	6.66918i	0.409684	+	0.409684i
$266$	3.22515	+	3.59114i	0.197747	+	0.220187i
$267$	7.69329	−	2.06141i	0.470822	−	0.126156i
$268$	3.61349	+	3.61349i	0.220729	+	0.220729i
$269$	−6.88733	−	3.97640i	−0.419928	−	0.242446i	0.275118	−	0.961410i	$-0.411283\pi$
$269$	−6.88733	−	3.97640i	−0.419928	−	0.242446i	−0.695047	+	0.718965i	$0.744616\pi$
$270$	2.17316	−	1.25468i	0.132255	−	0.0763572i
$271$	9.22246	+	2.47115i	0.560224	+	0.150112i	0.527809	−	0.849363i	$-0.323014\pi$
$271$	9.22246	+	2.47115i	0.560224	+	0.150112i	0.0324150	+	0.999474i	$0.489680\pi$
$272$	5.25234			0.318470
$273$	−1.19584	−	9.46414i	−0.0723753	−	0.572796i
$274$	−15.1939			−0.917900
$275$	−1.15838	−	0.310386i	−0.0698527	−	0.0187170i
$276$	5.27538	−	3.04574i	0.317540	−	0.183332i
$277$	−10.9550	−	6.32485i	−0.658220	−	0.380024i	0.133378	−	0.991065i	$-0.457417\pi$
$277$	−10.9550	−	6.32485i	−0.658220	−	0.380024i	−0.791598	+	0.611042i	$0.790751\pi$
$278$	3.32919	+	3.32919i	0.199671	+	0.199671i
$279$	5.13250	−	1.37525i	0.307275	−	0.0823340i
$280$	4.93952	−	4.43612i	0.295193	−	0.265109i
$281$	4.99829	+	4.99829i	0.298173	+	0.298173i	0.840298	−	0.542125i	$-0.182380\pi$
$281$	4.99829	+	4.99829i	0.298173	+	0.298173i	−0.542125	+	0.840298i	$0.682380\pi$
$282$	−1.53559	+	2.65972i	−0.0914431	+	0.158384i
$283$	7.69921	+	13.3354i	0.457670	+	0.792708i	0.998837	−	0.0482068i	$-0.0153507\pi$
$283$	7.69921	+	13.3354i	0.457670	+	0.792708i	−0.541167	+	0.840915i	$0.682017\pi$
$284$	3.60545	−	13.4557i	0.213944	−	0.798450i
$285$	4.57795			0.271174
$286$	3.32283	+	0.274656i	0.196483	+	0.0162408i
$287$	−16.8548	+	8.56077i	−0.994908	+	0.505326i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	−5.29352	−	9.16865i	−0.311384	−	0.539333i
$290$	−7.90854	+	13.6980i	−0.464406	+	0.804374i
$291$	1.52168	−	1.52168i	0.0892026	−	0.0892026i
$292$	6.02454	−	1.61427i	0.352559	−	0.0944680i
$293$	3.63669	+	13.5723i	0.212458	+	0.792904i	0.987046	+	0.160438i	$0.0512906\pi$
$293$	3.63669	+	13.5723i	0.212458	+	0.792904i	−0.774588	+	0.632466i	$0.782043\pi$
$294$	1.07732	+	6.91660i	0.0628306	+	0.403384i
$295$	−7.12552	+	12.3418i	−0.414864	+	0.718566i
$296$	1.81459	−	1.04765i	0.105471	−	0.0608935i
$297$	−0.893220	−	0.239338i	−0.0518299	−	0.0138878i
$298$		−	9.98237i		−	0.578263i
$299$	−18.0514	−	12.5111i	−1.04394	−	0.723536i
$300$		−	1.29686i		−	0.0748740i
$301$	4.80583	+	22.7530i	0.277004	+	1.31146i
$302$	4.43768	+	7.68628i	0.255360	+	0.442296i
$303$	10.4631	+	6.04085i	0.601087	+	0.347038i
$304$	−1.29001	−	1.29001i	−0.0739873	−	0.0739873i
$305$	2.72500	+	10.1698i	0.156033	+	0.582324i
$306$	1.35940	+	5.07337i	0.0777120	+	0.290025i
$307$	16.4155	−	16.4155i	0.936880	−	0.936880i	−0.0612428	−	0.998123i	$-0.519506\pi$
$307$	16.4155	−	16.4155i	0.936880	−	0.936880i	0.998123	+	0.0612428i	$0.0195064\pi$
$308$	−2.44308	−	0.131176i	−0.139208	−	0.00747442i
$309$	11.9701	−	6.91091i	0.680952	−	0.393148i
$310$	3.45098	−	12.8793i	0.196003	−	0.731492i
$311$	−8.28375			−0.469729			−0.234864	−	0.972028i	$-0.575465\pi$
$311$	−8.28375			−0.469729			−0.234864	+	0.972028i	$0.575465\pi$
$312$	0.643122	+	3.54773i	0.0364096	+	0.200851i
$313$		−	24.4606i		−	1.38260i	−0.722570	−	0.691298i	$-0.757039\pi$
$313$		−	24.4606i		−	1.38260i	0.722570	−	0.691298i	$-0.242961\pi$
$314$	−5.78023	+	21.5721i	−0.326197	+	1.21738i
$315$	5.56340	+	3.62306i	0.313462	+	0.204136i
$316$	−11.3855	−	6.57343i	−0.640486	−	0.369785i
$317$	−3.36399	+	3.36399i	−0.188941	+	0.188941i	−0.795238	−	0.606297i	$-0.792654\pi$
$317$	−3.36399	+	3.36399i	−0.188941	+	0.188941i	0.606297	+	0.795238i	$0.292654\pi$
$318$	3.63052	−	0.972796i	0.203590	−	0.0545517i
$319$	5.63019	−	1.50860i	0.315230	−	0.0844656i
$320$	−1.77438	+	1.77438i	−0.0991909	+	0.0991909i
$321$	−7.24543	−	4.18315i	−0.404401	−	0.233481i
$322$	13.5052	+	8.79501i	0.752616	+	0.490127i
$323$	−2.48004	+	9.25562i	−0.137993	+	0.514996i
$324$		−	1.00000i		−	0.0555556i
$325$	−4.22826	+	1.99642i	−0.234541	+	0.110741i
$326$	−7.38312			−0.408913
$327$	−2.34944	+	8.76824i	−0.129924	+	0.484885i
$328$	6.18788	−	3.57257i	0.341668	−	0.197262i
$329$	−8.11390	−	0.435656i	−0.447334	−	0.0240185i
$330$	−1.64082	+	1.64082i	−0.0903243	+	0.0903243i
$331$	3.30280	+	12.3262i	0.181539	+	0.677511i	0.995345	+	0.0963752i	$0.0307249\pi$
$331$	3.30280	+	12.3262i	0.181539	+	0.677511i	−0.813807	+	0.581136i	$0.802608\pi$
$332$	−0.461539	−	1.72249i	−0.0253302	−	0.0945338i
$333$	1.48160	+	1.48160i	0.0811913	+	0.0811913i
$334$	−3.74390	−	2.16154i	−0.204857	−	0.118274i
$335$	6.41171	+	11.1054i	0.350309	+	0.606753i
$336$	−0.546766	−	2.58864i	−0.0298286	−	0.141222i
$337$			27.1903i			1.48115i	0.671973	+	0.740576i	$0.265447\pi$
$337$			27.1903i			1.48115i	−0.671973	+	0.740576i	$0.734553\pi$
$338$	10.5770	−	7.55831i	0.575311	−	0.411118i
$339$			13.6022i			0.738771i
$340$	12.7309	+	3.41123i	0.690429	+	0.185000i
$341$	−4.25530	+	2.45680i	−0.230437	+	0.133043i
$342$	0.912177	−	1.57994i	0.0493249	−	0.0854332i
$343$	−15.0249	+	10.8283i	−0.811270	+	0.584671i
$344$	−2.27490	−	8.49005i	−0.122655	−	0.457753i
$345$	14.7648	−	3.95622i	0.794912	−	0.212996i
$346$	3.05261	−	3.05261i	0.164109	−	0.164109i
$347$	16.5096	−	28.5954i	0.886280	−	1.53508i	0.0420407	−	0.999116i	$-0.486614\pi$
$347$	16.5096	−	28.5954i	0.886280	−	1.53508i	0.844239	−	0.535966i	$-0.180053\pi$
$348$	3.15163	+	5.45877i	0.168945	+	0.292621i
$349$	−7.77709	−	2.08387i	−0.416298	−	0.111547i	0.0445891	−	0.999005i	$-0.485802\pi$
$349$	−7.77709	−	2.08387i	−0.416298	−	0.111547i	−0.460887	+	0.887459i	$0.652469\pi$
$350$	3.05918	−	1.55379i	0.163520	−	0.0830538i
$351$	−3.26039	+	1.53943i	−0.174027	+	0.0821686i
$352$	0.924729			0.0492882
$353$	−2.64991	+	9.88959i	−0.141040	+	0.526370i	0.858859	+	0.512211i	$0.171174\pi$
$353$	−2.64991	+	9.88959i	−0.141040	+	0.526370i	−0.999900	+	0.0141585i	$0.995493\pi$
$354$	2.83959	+	4.91831i	0.150922	+	0.261405i
$355$	17.4781	−	30.2730i	0.927643	−	1.60672i
$356$	−5.63188	−	5.63188i	−0.298489	−	0.298489i
$357$	−10.3389	+	9.28525i	−0.547194	+	0.491428i
$358$	10.7790	−	2.88822i	0.569687	−	0.152647i
$359$	−19.7727	−	19.7727i	−1.04356	−	1.04356i	−0.999007	−	0.0445577i	$-0.985812\pi$
$359$	−19.7727	−	19.7727i	−1.04356	−	1.04356i	−0.0445577	−	0.999007i	$-0.514188\pi$
$360$	−2.17316	−	1.25468i	−0.114536	−	0.0661273i
$361$	−13.5721	+	7.83587i	−0.714322	+	0.412414i
$362$	2.80593	+	0.751845i	0.147476	+	0.0395161i
$363$	−10.1449			−0.532468
$364$	−7.59827	+	5.76770i	−0.398258	+	0.302309i
$365$	15.6510			0.819210
$366$	4.05277	+	1.08594i	0.211842	+	0.0567629i
$367$	17.5652	−	10.1413i	0.916895	−	0.529370i	0.0342520	−	0.999413i	$-0.489095\pi$
$367$	17.5652	−	10.1413i	0.916895	−	0.529370i	0.882643	+	0.470044i	$0.155762\pi$
$368$	−5.27538	−	3.04574i	−0.274998	−	0.158770i
$369$	5.05238	+	5.05238i	0.263016	+	0.263016i
$370$	5.07870	−	1.36083i	0.264029	−	0.0707463i
$371$	6.64457	+	7.39858i	0.344969	+	0.384115i
$372$	−3.75725	−	3.75725i	−0.194804	−	0.194804i
$373$	17.9942	−	31.1668i	0.931704	−	1.61376i	0.151295	−	0.988489i	$-0.451656\pi$
$373$	17.9942	−	31.1668i	0.931704	−	1.61376i	0.780409	−	0.625269i	$-0.215011\pi$
$374$	−2.42850	−	4.20628i	−0.125574	−	0.217501i
$375$	−2.40508	+	8.97587i	−0.124198	+	0.463512i
$376$	3.07118			0.158384
$377$	12.9460	−	18.6789i	0.666755	−	0.962014i
$378$	2.35892	−	1.19812i	0.121330	−	0.0616249i
$379$	0.896824	+	0.240303i	0.0460668	+	0.0123436i	0.281779	−	0.959479i	$-0.409076\pi$
$379$	0.896824	+	0.240303i	0.0460668	+	0.0123436i	−0.235712	+	0.971823i	$0.575742\pi$
$380$	−2.28897	−	3.96462i	−0.117422	−	0.203381i
$381$	−6.98879	+	12.1049i	−0.358047	+	0.620155i
$382$	−14.3791	+	14.3791i	−0.735700	+	0.735700i
$383$	−26.8392	+	7.19153i	−1.37142	+	0.367470i	−0.867996	−	0.496571i	$-0.834592\pi$
$383$	−26.8392	+	7.19153i	−1.37142	+	0.367470i	−0.503421	+	0.864041i	$0.667926\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−5.83647	−	1.90466i	−0.297454	−	0.0970703i
$386$	−10.3008	+	17.8415i	−0.524297	+	0.908109i
$387$	7.61197	−	4.39478i	0.386938	−	0.223399i
$388$	−2.07866	−	0.556974i	−0.105528	−	0.0282761i
$389$			25.3359i			1.28458i	0.766462	+	0.642290i	$0.222016\pi$
$389$			25.3359i			1.28458i	−0.766462	+	0.642290i	$0.777984\pi$
$390$	−0.745309	+	9.01685i	−0.0377402	+	0.456586i
$391$			31.9945i			1.61803i
$392$	5.45129	−	4.39129i	0.275332	−	0.221794i
$393$	−6.73765	−	11.6700i	−0.339870	−	0.588672i
$394$	−15.8789	−	9.16766i	−0.799965	−	0.461860i
$395$	−23.3276	−	23.3276i	−1.17374	−	1.17374i
$396$	0.239338	+	0.893220i	0.0120272	+	0.0448860i
$397$	−9.79102	−	36.5406i	−0.491397	−	1.83392i	−0.549340	−	0.835599i	$-0.685121\pi$
$397$	−9.79102	−	36.5406i	−0.491397	−	1.83392i	0.0579431	−	0.998320i	$-0.481546\pi$
$398$	12.3425	−	12.3425i	0.618676	−	0.618676i
$399$	4.81984	+	0.258790i	0.241294	+	0.0129557i
$400$	−1.12311	+	0.648428i	−0.0561555	+	0.0324214i
$401$	1.25562	−	4.68605i	0.0627028	−	0.234010i	−0.927462	−	0.373918i	$-0.878014\pi$
$401$	1.25562	−	4.68605i	0.0627028	−	0.234010i	0.990164	+	0.139908i	$0.0446807\pi$
$402$	5.11025			0.254876
$403$	−6.46609	+	18.0341i	−0.322099	+	0.898344i
$404$		−	12.0817i		−	0.601087i
$405$	0.649468	−	2.42385i	0.0322723	−	0.120442i
$406$	−9.10077	+	13.9747i	−0.451663	+	0.693554i
$407$	−1.67800	−	0.968794i	−0.0831754	−	0.0480213i
$408$	3.71396	−	3.71396i	0.183869	−	0.183869i
$409$	12.7591	−	3.41880i	0.630899	−	0.169049i	0.0708213	−	0.997489i	$-0.477438\pi$
$409$	12.7591	−	3.41880i	0.630899	−	0.169049i	0.560078	+	0.828440i	$0.310771\pi$
$410$	17.3188	−	4.64055i	0.855312	−	0.229180i
$411$	−10.7437	+	10.7437i	−0.529950	+	0.529950i
$412$	−11.9701	−	6.91091i	−0.589722	−	0.340476i
$413$	−8.19971	+	12.5911i	−0.403481	+	0.619567i
$414$	1.57659	−	5.88392i	0.0774852	−	0.289179i
$415$		−	4.47481i		−	0.219660i
$416$	2.75086	−	2.33083i	0.134872	−	0.114278i
$417$	4.70818			0.230561
$418$	−0.436636	+	1.62955i	−0.0213566	+	0.0797039i
$419$	12.7342	−	7.35208i	0.622105	−	0.359172i	−0.155583	−	0.987823i	$-0.549726\pi$
$419$	12.7342	−	7.35208i	0.622105	−	0.359172i	0.777688	+	0.628650i	$0.216392\pi$
$420$	0.355959	−	6.62958i	0.0173690	−	0.323490i
$421$	13.5622	−	13.5622i	0.660983	−	0.660983i	−0.294629	−	0.955612i	$-0.595196\pi$
$421$	13.5622	−	13.5622i	0.660983	−	0.660983i	0.955612	+	0.294629i	$0.0951960\pi$
$422$	7.25891	+	27.0906i	0.353358	+	1.31875i
$423$	0.794880	+	2.96653i	0.0386484	+	0.144238i
$424$	−2.65773	−	2.65773i	−0.129071	−	0.129071i
$425$	5.89895	+	3.40576i	0.286141	+	0.165204i
$426$	−6.96519	−	12.0641i	−0.337465	−	0.584506i
$427$	2.29409	+	10.8613i	0.111019	+	0.525613i
$428$			8.36630i			0.404401i
$429$	2.54380	−	2.15538i	0.122816	−	0.104063i
$430$		−	22.0561i		−	1.06364i
$431$	−23.0033	−	6.16371i	−1.10803	−	0.296895i	−0.341999	−	0.939700i	$-0.611104\pi$
$431$	−23.0033	−	6.16371i	−1.10803	−	0.296895i	−0.766030	+	0.642805i	$0.777771\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−10.1080	+	17.5075i	−0.485758	+	0.841358i	−0.999866	−	0.0163676i	$-0.994790\pi$
$433$	−10.1080	+	17.5075i	−0.485758	+	0.841358i	0.514108	+	0.857726i	$0.328123\pi$
$434$	4.36139	−	13.3647i	0.209354	−	0.641526i
$435$	4.09376	+	15.2781i	0.196281	+	0.732530i
$436$	8.76824	−	2.34944i	0.419922	−	0.112518i
$437$	7.85809	−	7.85809i	0.375903	−	0.375903i
$438$	3.11853	−	5.40145i	0.149009	−	0.258091i
$439$	−9.98522	−	17.2949i	−0.476569	−	0.825441i	0.523071	−	0.852289i	$-0.324786\pi$
$439$	−9.98522	−	17.2949i	−0.476569	−	0.825441i	−0.999640	+	0.0268480i	$0.991453\pi$
$440$	2.24140	+	0.600583i	0.106855	+	0.0286316i
$441$	5.65256	+	4.12899i	0.269169	+	0.196619i
$442$	−17.8264	−	6.39160i	−0.847913	−	0.304017i
$443$	14.9948			0.712427			0.356213	−	0.934405i	$-0.384068\pi$
$443$	14.9948			0.712427			0.356213	+	0.934405i	$0.384068\pi$
$444$	0.542304	−	2.02391i	0.0257366	−	0.0960504i
$445$	−9.99310	−	17.3086i	−0.473718	−	0.820504i
$446$	−0.234634	+	0.406399i	−0.0111103	+	0.0192435i
$447$	−7.05860	−	7.05860i	−0.333861	−	0.333861i
$448$	−1.96844	+	1.76783i	−0.0930002	+	0.0835222i
$449$	−4.65409	+	1.24706i	−0.219640	+	0.0588523i	−0.366961	−	0.930236i	$-0.619602\pi$
$449$	−4.65409	+	1.24706i	−0.219640	+	0.0588523i	0.147321	+	0.989089i	$0.452935\pi$
$450$	−0.917015	−	0.917015i	−0.0432285	−	0.0432285i
$451$	−5.72211	−	3.30366i	−0.269444	−	0.155563i
$452$	11.7799	−	6.80111i	0.554078	−	0.319897i
$453$	8.57294	+	2.29711i	0.402792	+	0.107928i
$454$	−27.0682			−1.27038
$455$	−22.1630	+	9.04519i	−1.03902	+	0.424045i
$456$	−1.82435			−0.0854332
$457$	−39.2598	−	10.5196i	−1.83650	−	0.492088i	−0.837939	−	0.545764i	$-0.816240\pi$
$457$	−39.2598	−	10.5196i	−1.83650	−	0.492088i	−0.998558	+	0.0536755i	$0.982906\pi$
$458$	−22.1940	+	12.8137i	−1.03706	+	0.598746i
$459$	4.54866	+	2.62617i	0.212313	+	0.122579i
$460$	−10.8086	−	10.8086i	−0.503954	−	0.503954i
$461$	−22.0088	+	5.89723i	−1.02505	+	0.274661i	−0.731905	−	0.681406i	$-0.761369\pi$
$461$	−22.0088	+	5.89723i	−1.02505	+	0.274661i	−0.293145	+	0.956068i	$0.594702\pi$
$462$	−1.82028	+	1.63477i	−0.0846869	+	0.0760562i
$463$	−9.48862	−	9.48862i	−0.440974	−	0.440974i	0.451365	−	0.892339i	$-0.350937\pi$
$463$	−9.48862	−	9.48862i	−0.440974	−	0.440974i	−0.892339	+	0.451365i	$0.850937\pi$
$464$	3.15163	−	5.45877i	0.146311	−	0.253417i
$465$	−6.66679	−	11.5472i	−0.309165	−	0.535489i
$466$	4.75596	−	17.7495i	0.220316	−	0.822230i
$467$	39.4343			1.82480			0.912402	−	0.409296i	$-0.134226\pi$
$467$	39.4343			1.82480			0.912402	+	0.409296i	$0.134226\pi$
$468$	2.96338	+	2.05387i	0.136982	+	0.0949401i
$469$	6.12271	+	12.0547i	0.282721	+	0.556632i
$470$	7.44408	+	1.99464i	0.343370	+	0.0920057i
$471$	11.1665	+	19.3410i	0.514527	+	0.891187i
$472$	2.83959	−	4.91831i	0.130703	−	0.226383i
$473$	−5.74733	+	5.74733i	−0.264263	+	0.264263i
$474$	−12.6989	+	3.40266i	−0.583280	+	0.156289i
$475$	−0.612346	−	2.28531i	−0.0280964	−	0.104857i
$476$	13.2107	+	4.31115i	0.605513	+	0.197601i
$477$	1.87930	−	3.25504i	0.0860471	−	0.149038i
$478$	−13.3115	+	7.68537i	−0.608852	+	0.351521i
$479$	28.8414	+	7.72802i	1.31780	+	0.353102i	0.848151	−	0.529754i	$-0.177716\pi$
$479$	28.8414	+	7.72802i	1.31780	+	0.353102i	0.469644	+	0.882856i	$0.344382\pi$
$480$			2.50935i			0.114536i
$481$	−7.43357	+	1.34753i	−0.338942	+	0.0614423i
$482$		−	11.5498i		−	0.526078i
$483$	15.7686	−	3.33062i	0.717498	−	0.151548i
$484$	5.07244	+	8.78572i	0.230565	+	0.399351i
$485$	−4.67661	−	2.70004i	−0.212354	−	0.122603i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	3.80837	+	14.2130i	0.172574	+	0.644055i	0.996952	+	0.0780153i	$0.0248583\pi$
$487$	3.80837	+	14.2130i	0.172574	+	0.644055i	−0.824378	+	0.566039i	$0.808475\pi$
$488$	−1.08594	−	4.05277i	−0.0491581	−	0.183460i
$489$	−5.22065	+	5.22065i	−0.236086	+	0.236086i
$490$	16.0651	−	7.10338i	0.725748	−	0.320898i
$491$	24.1291	−	13.9309i	1.08893	−	0.628693i	0.155638	−	0.987814i	$-0.450257\pi$
$491$	24.1291	−	13.9309i	1.08893	−	0.628693i	0.933291	+	0.359121i	$0.116923\pi$
$492$	1.84930	−	6.90168i	0.0833729	−	0.311152i
$493$	−33.1068			−1.49106
$494$	2.80846	+	5.94811i	0.126359	+	0.267618i
$495$			2.32047i			0.104297i
$496$	−1.37525	+	5.13250i	−0.0617505	+	0.230456i
$497$	20.1130	−	30.8846i	0.902191	−	1.38536i
$498$	−1.54434	−	0.891625i	−0.0692035	−	0.0399547i
$499$	12.4880	−	12.4880i	0.559041	−	0.559041i	−0.369993	−	0.929034i	$-0.620640\pi$
$499$	12.4880	−	12.4880i	0.559041	−	0.559041i	0.929034	+	0.369993i	$0.120640\pi$
$500$	8.97587	−	2.40508i	0.401413	−	0.107558i
$501$	−4.17577	+	1.11890i	−0.186560	+	0.0499886i
$502$	7.84255	−	7.84255i	0.350030	−	0.350030i
$503$	−32.8439	−	18.9624i	−1.46444	−	0.845492i	−0.465224	−	0.885193i	$-0.654026\pi$
$503$	−32.8439	−	18.9624i	−1.46444	−	0.845492i	−0.999212	+	0.0397008i	$0.987360\pi$
$504$	−2.21707	−	1.44382i	−0.0987560	−	0.0643129i
$505$	7.84668	−	29.2842i	0.349173	−	1.30313i
$506$			5.63297i			0.250416i
$507$	2.13451	−	12.8236i	0.0947969	−	0.569515i
$508$	13.9776			0.620155
$509$	−0.166695	+	0.622116i	−0.00738864	+	0.0275748i	−0.969522	−	0.245005i	$-0.921210\pi$
$509$	−0.166695	+	0.622116i	−0.00738864	+	0.0275748i	0.962133	+	0.272580i	$0.0878770\pi$
$510$	11.4142	−	6.58999i	0.505429	−	0.291809i
$511$	16.4780	+	0.884746i	0.728943	+	0.0391388i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.472178	−	1.76219i	−0.0208471	−	0.0778026i
$514$	−1.41199	−	5.26962i	−0.0622803	−	0.232433i
$515$	−24.5252	−	24.5252i	−1.08071	−	1.08071i
$516$	−7.61197	−	4.39478i	−0.335099	−	0.193469i
$517$	−1.42001	−	2.45952i	−0.0624518	−	0.108170i
$518$	5.42398	−	1.14564i	0.238316	−	0.0503366i
$519$		−	4.31704i		−	0.189497i
$520$	8.18148	−	3.86297i	0.358782	−	0.169402i
$521$		−	34.8137i		−	1.52522i	−0.646861	−	0.762608i	$-0.723919\pi$
$521$		−	34.8137i		−	1.52522i	0.646861	−	0.762608i	$-0.276081\pi$
$522$	6.08847	+	1.63140i	0.266485	+	0.0714045i
$523$	−33.0045	+	19.0551i	−1.44318	+	0.833223i	−0.998061	−	0.0622463i	$-0.980174\pi$
$523$	−33.0045	+	19.0551i	−1.44318	+	0.833223i	−0.445124	+	0.895469i	$0.646840\pi$
$524$	−6.73765	+	11.6700i	−0.294336	+	0.509805i
$525$	1.06447	−	3.26186i	0.0464571	−	0.142359i
$526$	1.00463	+	3.74933i	0.0438040	+	0.163479i
$527$	26.9576	−	7.22327i	1.17429	−	0.314651i
$528$	0.653882	−	0.653882i	0.0284566	−	0.0284566i
$529$	7.05307	−	12.2163i	0.306655	−	0.531142i
$530$	−4.71582	−	8.16804i	−0.204842	−	0.354797i
$531$	5.48566	+	1.46988i	0.238057	+	0.0637873i
$532$	−2.18580	−	4.30350i	−0.0947666	−	0.186580i
$533$	−25.3490	+	4.59520i	−1.09799	+	0.199040i
$534$	−7.96468			−0.344665
$535$	−5.43365	+	20.2787i	−0.234917	+	0.876723i
$536$	−2.55512	−	4.42560i	−0.110365	−	0.191157i
$537$	5.57961	−	9.66418i	0.240778	−	0.417040i
$538$	5.62348	+	5.62348i	0.242446	+	0.242446i
$539$	−6.03720	−	2.33523i	−0.260041	−	0.100586i
$540$	−2.42385	+	0.649468i	−0.104306	+	0.0279487i
$541$	−12.1210	−	12.1210i	−0.521121	−	0.521121i	0.396789	−	0.917910i	$-0.370125\pi$
$541$	−12.1210	−	12.1210i	−0.521121	−	0.521121i	−0.917910	+	0.396789i	$0.870125\pi$
$542$	−8.26863	−	4.77390i	−0.355168	−	0.205056i
$543$	2.51572	−	1.45245i	0.107960	−	0.0623308i
$544$	−5.07337	−	1.35940i	−0.217519	−	0.0582840i
$545$	22.7788			0.975736
$546$	−1.29441	+	9.45116i	−0.0553957	+	0.404472i
$547$	16.9129			0.723142			0.361571	−	0.932345i	$-0.382240\pi$
$547$	16.9129			0.723142			0.361571	+	0.932345i	$0.382240\pi$
$548$	14.6762	+	3.93248i	0.626937	+	0.167987i
$549$	3.63362	−	2.09787i	0.155079	−	0.0895349i
$550$	1.03857	+	0.599620i	0.0442849	+	0.0255679i
$551$	8.13127	+	8.13127i	0.346404	+	0.346404i
$552$	−5.88392	+	1.57659i	−0.250436	+	0.0671042i
$553$	−23.2415	−	25.8789i	−0.988328	−	1.10048i
$554$	8.94469	+	8.94469i	0.380024	+	0.380024i
$555$	2.62893	−	4.55344i	0.111592	−	0.193283i
$556$	−2.35409	−	4.07741i	−0.0998357	−	0.172921i
$557$	−8.24415	+	30.7676i	−0.349316	+	1.30366i	0.538173	+	0.842835i	$0.319115\pi$
$557$	−8.24415	+	30.7676i	−0.349316	+	1.30366i	−0.887489	+	0.460830i	$0.847552\pi$
$558$	−5.31355			−0.224941
$559$	−2.61061	+	31.5835i	−0.110417	+	1.33584i
$560$	−5.91936	+	3.00652i	−0.250139	+	0.127049i
$561$	−4.69149	−	1.25708i	−0.198075	−	0.0530740i
$562$	−3.53433	−	6.12163i	−0.149087	−	0.258226i
$563$	−0.192317	+	0.333103i	−0.00810520	+	0.0140386i	−0.870050	−	0.492964i	$-0.835913\pi$
$563$	−0.192317	+	0.333103i	−0.00810520	+	0.0140386i	0.861944	+	0.507003i	$0.169247\pi$
$564$	2.17165	−	2.17165i	0.0914431	−	0.0914431i
$565$	32.9697	−	8.83421i	1.38705	−	0.371658i
$566$	−3.98540	−	14.8737i	−0.167519	−	0.625189i
$567$	0.820805	−	2.51521i	0.0344706	−	0.105629i
$568$	−6.96519	+	12.0641i	−0.292253	+	0.506197i
$569$	22.7812	−	13.1527i	0.955038	−	0.551392i	0.0603959	−	0.998175i	$-0.480764\pi$
$569$	22.7812	−	13.1527i	0.955038	−	0.551392i	0.894642	+	0.446783i	$0.147430\pi$
$570$	−4.42196	−	1.18486i	−0.185215	−	0.0496283i
$571$			34.6841i			1.45149i	0.687966	+	0.725743i	$0.258504\pi$
$571$			34.6841i			1.45149i	−0.687966	+	0.725743i	$0.741496\pi$
$572$	−3.13852	−	1.12531i	−0.131228	−	0.0470515i
$573$			20.3352i			0.849514i
$574$	18.4962	−	3.90672i	0.772016	−	0.163064i
$575$	−3.94988	−	6.84140i	−0.164722	−	0.285306i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	25.0110	+	25.0110i	1.04122	+	1.04122i	0.999113	+	0.0421076i	$0.0134072\pi$
$577$	25.0110	+	25.0110i	1.04122	+	1.04122i	0.0421076	+	0.999113i	$0.486593\pi$
$578$	2.74013	+	10.2263i	0.113974	+	0.425358i
$579$	5.33209	+	19.8996i	0.221594	+	0.827000i
$580$	11.1844	−	11.1844i	0.464406	−	0.464406i
$581$	0.252959	−	4.71125i	0.0104945	−	0.195456i
$582$	−1.86367	+	1.07599i	−0.0772517	+	0.0446013i
$583$	−0.899573	+	3.35725i	−0.0372565	+	0.139043i
$584$	−6.23706			−0.258091
$585$	5.84886	+	6.90289i	0.241821	+	0.285399i
$586$		−	14.0511i		−	0.580446i
$587$	1.52105	−	5.67665i	0.0627806	−	0.234301i	−0.927405	−	0.374059i	$-0.877966\pi$
$587$	1.52105	−	5.67665i	0.0627806	−	0.234301i	0.990186	+	0.139758i	$0.0446325\pi$
$588$	0.749536	−	6.95976i	0.0309103	−	0.287015i
$589$	−8.39508	−	4.84690i	−0.345913	−	0.199713i
$590$	10.0770	−	10.0770i	0.414864	−	0.414864i
$591$	−17.7106	+	4.74553i	−0.728515	+	0.195205i
$592$	−2.02391	+	0.542304i	−0.0831821	+	0.0222886i
$593$	−19.2585	+	19.2585i	−0.790852	+	0.790852i	−0.981633	−	0.190781i	$-0.938898\pi$
$593$	−19.2585	+	19.2585i	−0.790852	+	0.790852i	0.190781	+	0.981633i	$0.438898\pi$
$594$	0.800839	+	0.462365i	0.0328588	+	0.0189711i
$595$	29.2209	+	19.0295i	1.19794	+	0.780134i
$596$	−2.58363	+	9.64223i	−0.105830	+	0.394961i
$597$		−	17.4550i		−	0.714385i
$598$	14.1982	+	16.7568i	0.580607	+	0.685238i
$599$	−12.8007			−0.523021			−0.261511	−	0.965201i	$-0.584221\pi$
$599$	−12.8007			−0.523021			−0.261511	+	0.965201i	$0.584221\pi$
$600$	−0.335651	+	1.25267i	−0.0137029	+	0.0511399i
$601$	−15.0883	+	8.71121i	−0.615463	+	0.355337i	−0.775100	−	0.631838i	$-0.782301\pi$
$601$	−15.0883	+	8.71121i	−0.615463	+	0.355337i	0.159638	+	0.987176i	$0.448967\pi$
$602$	1.24682	−	23.2215i	0.0508168	−	0.946438i
$603$	3.61349	−	3.61349i	0.147153	−	0.147153i
$604$	−2.29711	−	8.57294i	−0.0934681	−	0.348828i
$605$	6.58878	+	24.5897i	0.267872	+	0.999711i
$606$	−8.54305	−	8.54305i	−0.347038	−	0.347038i
$607$	4.00850	+	2.31431i	0.162700	+	0.0939349i	0.579139	−	0.815229i	$-0.303389\pi$
$607$	4.00850	+	2.31431i	0.162700	+	0.0939349i	−0.416439	+	0.909164i	$0.636722\pi$
$608$	0.912177	+	1.57994i	0.0369937	+	0.0640749i
$609$	3.44641	+	16.3168i	0.139655	+	0.661191i
$610$		−	10.5286i		−	0.426290i
$611$	−10.4235	−	3.73734i	−0.421692	−	0.151197i
$612$		−	5.25234i		−	0.212313i
$613$	20.2891	+	5.43644i	0.819467	+	0.219576i	0.644114	−	0.764930i	$-0.277226\pi$
$613$	20.2891	+	5.43644i	0.819467	+	0.219576i	0.175354	+	0.984505i	$0.443893\pi$
$614$	−20.1048	+	11.6075i	−0.811362	+	0.468440i
$615$	8.96485	−	15.5276i	0.361497	−	0.626132i
$616$	2.32589	+	0.759023i	0.0937127	+	0.0305819i
$617$	0.681997	+	2.54525i	0.0274562	+	0.102468i	0.978294	−	0.207221i	$-0.0664419\pi$
$617$	0.681997	+	2.54525i	0.0274562	+	0.102468i	−0.950838	+	0.309689i	$0.899775\pi$
$618$	−13.3509	+	3.57735i	−0.537050	+	0.143902i
$619$	16.4670	−	16.4670i	0.661865	−	0.661865i	−0.293954	−	0.955820i	$-0.594971\pi$
$619$	16.4670	−	16.4670i	0.661865	−	0.661865i	0.955820	+	0.293954i	$0.0949713\pi$
$620$	−6.66679	+	11.5472i	−0.267745	+	0.463748i
$621$	−3.04574	−	5.27538i	−0.122221	−	0.211694i
$622$	8.00149	+	2.14399i	0.320831	+	0.0859663i
$623$	−9.54268	−	18.7880i	−0.382319	−	0.752727i
$624$	0.297013	−	3.59330i	0.0118900	−	0.143847i
$625$	29.8024			1.19210
$626$	−6.33088	+	23.6272i	−0.253033	+	0.944331i
$627$	0.843517	+	1.46101i	0.0336868	+	0.0583473i
$628$	11.1665	−	19.3410i	0.445594	−	0.771791i
$629$	7.78188	+	7.78188i	0.310284	+	0.310284i
$630$	−4.43612	−	4.93952i	−0.176739	−	0.196795i
$631$	17.2926	−	4.63355i	0.688410	−	0.184459i	0.102376	−	0.994746i	$-0.467355\pi$
$631$	17.2926	−	4.63355i	0.688410	−	0.184459i	0.586033	+	0.810287i	$0.300689\pi$
$632$	9.29624	+	9.29624i	0.369785	+	0.369785i
$633$	24.2888	+	14.0231i	0.965393	+	0.557370i
$634$	4.12003	−	2.37870i	0.163627	−	0.0944704i
$635$	33.8796	+	9.07800i	1.34447	+	0.360250i
$636$	−3.75859			−0.149038
$637$	−23.8454	+	8.27026i	−0.944789	+	0.327680i
$638$	−5.82880			−0.230764
$639$	−13.4557	−	3.60545i	−0.532300	−	0.142629i
$640$	2.17316	−	1.25468i	0.0859018	−	0.0495955i
$641$	−18.1530	−	10.4807i	−0.717002	−	0.413961i	0.0966462	−	0.995319i	$-0.469188\pi$
$641$	−18.1530	−	10.4807i	−0.717002	−	0.413961i	−0.813648	+	0.581357i	$0.802522\pi$
$642$	5.91587	+	5.91587i	0.233481	+	0.233481i
$643$	−6.13410	+	1.64363i	−0.241905	+	0.0648183i	−0.377735	−	0.925914i	$-0.623297\pi$
$643$	−6.13410	+	1.64363i	−0.241905	+	0.0648183i	0.135829	+	0.990732i	$0.456630\pi$
$644$	−10.7687	−	11.9907i	−0.424347	−	0.472501i
$645$	−15.5960	−	15.5960i	−0.614092	−	0.614092i
$646$	4.79106	−	8.29836i	0.188502	−	0.326495i
$647$	−16.8621	−	29.2060i	−0.662918	−	1.14821i	−0.979845	−	0.199758i	$-0.935984\pi$
$647$	−16.8621	−	29.2060i	−0.662918	−	1.14821i	0.316927	−	0.948450i	$-0.397349\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−5.25170			−0.206147
$650$	4.60089	−	0.834036i	0.180462	−	0.0327136i
$651$	−6.36630	−	12.5342i	−0.249515	−	0.491256i
$652$	7.13155	+	1.91089i	0.279293	+	0.0748363i
$653$	3.83532	+	6.64296i	0.150088	+	0.259959i	0.931259	−	0.364357i	$-0.118711\pi$
$653$	3.83532	+	6.64296i	0.150088	+	0.259959i	−0.781172	+	0.624316i	$0.785378\pi$
$654$	4.53877	−	7.86139i	0.177480	−	0.307405i
$655$	−23.9103	+	23.9103i	−0.934254	+	0.934254i
$656$	−6.90168	+	1.84930i	−0.269465	+	0.0722030i
$657$	−1.61427	−	6.02454i	−0.0629787	−	0.235040i
$658$	7.72467	+	2.52084i	0.301139	+	0.0982727i
$659$	−16.5777	+	28.7134i	−0.645774	+	1.11851i	0.338348	+	0.941021i	$0.390132\pi$
$659$	−16.5777	+	28.7134i	−0.645774	+	1.11851i	−0.984122	+	0.177493i	$0.943201\pi$
$660$	2.00959	−	1.16024i	0.0782231	−	0.0451621i
$661$	−21.5869	−	5.78418i	−0.839632	−	0.224979i	−0.186721	−	0.982413i	$-0.559786\pi$
$661$	−21.5869	−	5.78418i	−0.839632	−	0.224979i	−0.652911	+	0.757434i	$0.726453\pi$
$662$		−	12.7611i		−	0.495973i
$663$	−17.1247	+	8.08560i	−0.665068	+	0.314019i
$664$			1.78325i			0.0692035i
$665$	−2.50307	−	11.8507i	−0.0970648	−	0.459549i
$666$	−1.04765	−	1.81459i	−0.0405957	−	0.0703138i
$667$	33.2520	+	19.1981i	1.28752	+	0.743352i
$668$	3.05688	+	3.05688i	0.118274	+	0.118274i
$669$	0.121456	+	0.453279i	0.00469575	+	0.0175248i
$670$	−3.31894	−	12.3865i	−0.128222	−	0.478531i
$671$	−2.74352	+	2.74352i	−0.105912	+	0.105912i
$672$	−0.141853	+	2.64195i	−0.00547210	+	0.101915i
$673$	−15.9203	+	9.19157i	−0.613681	+	0.354309i	−0.774405	−	0.632691i	$-0.781951\pi$
$673$	−15.9203	+	9.19157i	−0.613681	+	0.354309i	0.160724	+	0.986999i	$0.448617\pi$
$674$	7.03738	−	26.2638i	0.271070	−	1.01165i
$675$	−1.29686			−0.0499160
$676$	−12.1728	+	4.56324i	−0.468184	+	0.175509i
$677$			38.8560i			1.49336i	0.665186	+	0.746678i	$0.268352\pi$
$677$			38.8560i			1.49336i	−0.665186	+	0.746678i	$0.731648\pi$
$678$	3.52051	−	13.1387i	0.135205	−	0.504590i
$679$	−4.77109	−	3.10708i	−0.183098	−	0.119239i
$680$	−11.4142	−	6.58999i	−0.437714	−	0.252714i
$681$	−19.1401	+	19.1401i	−0.733452	+	0.733452i
$682$	4.74617	−	1.27173i	0.181740	−	0.0486972i
$683$	−33.9480	+	9.09634i	−1.29898	+	0.348062i	−0.841066	−	0.540933i	$-0.818071\pi$
$683$	−33.9480	+	9.09634i	−1.29898	+	0.348062i	−0.457918	+	0.888994i	$0.651405\pi$
$684$	−1.29001	+	1.29001i	−0.0493249	+	0.0493249i
$685$	33.0189	+	19.0635i	1.26159	+	0.728378i
$686$	17.3155	−	6.57056i	0.661110	−	0.250865i
$687$	−6.63288	+	24.7542i	−0.253060	+	0.944433i
$688$			8.78955i			0.335099i
$689$	5.78609	+	12.2545i	0.220432	+	0.466859i
$690$	−15.2857			−0.581916
$691$	11.2504	−	41.9872i	0.427987	−	1.59727i	−0.329327	−	0.944216i	$-0.606822\pi$
$691$	11.2504	−	41.9872i	0.427987	−	1.59727i	0.757313	−	0.653052i	$-0.226512\pi$
$692$	−3.73867	+	2.15852i	−0.142123	+	0.0820547i
$693$	−0.131176	+	2.44308i	−0.00498295	+	0.0928051i
$694$	−23.3481	+	23.3481i	−0.886280	+	0.886280i
$695$	−3.05782	−	11.4119i	−0.115990	−	0.432879i
$696$	−1.63140	−	6.08847i	−0.0618381	−	0.230783i
$697$	26.5368	+	26.5368i	1.00515	+	1.00515i
$698$	6.97275	+	4.02572i	0.263923	+	0.152376i
$699$	−9.18782	−	15.9138i	−0.347515	−	0.601914i
$700$	−3.35709	+	0.709077i	−0.126886	+	0.0268006i
$701$			41.9413i			1.58410i	0.610457	+	0.792050i	$0.290986\pi$
$701$			41.9413i			1.58410i	−0.610457	+	0.792050i	$0.709014\pi$
$702$	3.54773	−	0.643122i	0.133900	−	0.0242731i
$703$		−	3.82257i		−	0.144171i
$704$	−0.893220	−	0.239338i	−0.0336645	−	0.00902037i
$705$	6.67418	−	3.85334i	0.251364	−	0.145125i
$706$	5.11923	−	8.86677i	0.192665	−	0.333705i
$707$	9.91672	−	30.3880i	0.372957	−	1.14286i
$708$	−1.46988	−	5.48566i	−0.0552414	−	0.206164i
$709$	−3.41478	+	0.914988i	−0.128245	+	0.0343631i	−0.322370	−	0.946614i	$-0.604480\pi$
$709$	−3.41478	+	0.914988i	−0.128245	+	0.0343631i	0.194126	+	0.980977i	$0.437813\pi$
$710$	−24.7178	+	24.7178i	−0.927643	+	0.927643i
$711$	−6.57343	+	11.3855i	−0.246523	+	0.426990i
$712$	3.98234	+	6.89761i	0.149244	+	0.258499i
$713$	−31.2645	−	8.37730i	−1.17086	−	0.313732i
$714$	12.3898	−	6.29295i	0.463678	−	0.235508i
$715$	−6.87644	−	4.76595i	−0.257164	−	0.178236i
$716$	−11.1592			−0.417040
$717$	−3.97824	+	14.8470i	−0.148570	+	0.554471i
$718$	13.9814	+	24.2165i	0.521782	+	0.903753i
$719$	−6.46610	+	11.1996i	−0.241145	+	0.417675i	−0.961041	−	0.276407i	$-0.910856\pi$
$719$	−6.46610	+	11.1996i	−0.241145	+	0.417675i	0.719896	+	0.694082i	$0.244190\pi$
$720$	1.77438	+	1.77438i	0.0661273	+	0.0661273i
$721$	−24.4347	−	27.2075i	−0.909995	−	1.01326i
$722$	15.1377	−	4.05614i	0.563368	−	0.150954i
$723$	−8.16693	−	8.16693i	−0.303731	−	0.303731i
$724$	−2.51572	−	1.45245i	−0.0934961	−	0.0539800i
$725$	7.07924	−	4.08720i	0.262916	−	0.151795i
$726$	9.79920	+	2.62569i	0.363682	+	0.0974484i
$727$	−24.5415			−0.910194			−0.455097	−	0.890442i	$-0.650395\pi$
$727$	−24.5415			−0.910194			−0.455097	+	0.890442i	$0.650395\pi$
$728$	8.83215	−	3.60459i	0.327341	−	0.133595i
$729$	−1.00000			−0.0370370
$730$	−15.1177	−	4.05077i	−0.559531	−	0.149926i
$731$	39.9807	−	23.0828i	1.47874	−	0.853750i
$732$	−3.63362	−	2.09787i	−0.134302	−	0.0775395i
$733$	34.1906	+	34.1906i	1.26286	+	1.26286i	0.949702	+	0.313155i	$0.101386\pi$
$733$	34.1906	+	34.1906i	1.26286	+	1.26286i	0.313155	+	0.949702i	$0.398614\pi$
$734$	−19.5914	+	5.24950i	−0.723132	+	0.193763i
$735$	6.33690	−	16.3826i	0.233740	−	0.604281i
$736$	4.30733	+	4.30733i	0.158770	+	0.158770i
$737$	−2.36280	+	4.09248i	−0.0870348	+	0.150749i
$738$	−3.57257	−	6.18788i	−0.131508	−	0.227779i
$739$	−6.16766	+	23.0180i	−0.226881	+	0.846732i	0.754761	+	0.656000i	$0.227753\pi$
$739$	−6.16766	+	23.0180i	−0.226881	+	0.846732i	−0.981642	+	0.190732i	$0.938914\pi$
$740$	−5.25786			−0.193283
$741$	6.19183	+	2.22007i	0.227463	+	0.0815562i
$742$	−4.50327	−	8.86622i	−0.165320	−	0.325489i
$743$	−22.2032	−	5.94933i	−0.814557	−	0.218260i	−0.172591	−	0.984994i	$-0.555214\pi$
$743$	−22.2032	−	5.94933i	−0.814557	−	0.218260i	−0.641965	+	0.766734i	$0.721881\pi$
$744$	2.65678	+	4.60167i	0.0974021	+	0.168705i
$745$	−12.5247	+	21.6933i	−0.458868	+	0.794782i
$746$	−25.4476	+	25.4476i	−0.931704	+	0.931704i
$747$	−1.72249	+	0.461539i	−0.0630225	+	0.0168868i
$748$	1.25708	+	4.69149i	0.0459635	+	0.171538i
$749$	−6.86711	+	21.0430i	−0.250919	+	0.768895i
$750$	4.64625	−	8.04754i	0.169657	−	0.293855i
$751$	21.4771	−	12.3998i	0.783710	−	0.452475i	−0.0540337	−	0.998539i	$-0.517208\pi$
$751$	21.4771	−	12.3998i	0.783710	−	0.452475i	0.837743	+	0.546064i	$0.183875\pi$
$752$	−2.96653	−	0.794880i	−0.108178	−	0.0289863i
$753$		−	11.0910i		−	0.404180i
$754$	−17.3394	+	14.6918i	−0.631463	+	0.535043i
$755$		−	22.2714i		−	0.810540i
$756$	−2.58864	+	0.546766i	−0.0941479	+	0.0198857i
$757$	20.6559	+	35.7771i	0.750752	+	1.30034i	0.947458	+	0.319879i	$0.103642\pi$
$757$	20.6559	+	35.7771i	0.750752	+	1.30034i	−0.196706	+	0.980463i	$0.563024\pi$
$758$	−0.804071	−	0.464230i	−0.0292052	−	0.0168616i
$759$	3.98311	+	3.98311i	0.144578	+	0.144578i
$760$	1.18486	+	4.42196i	0.0429794	+	0.160401i
$761$	8.43835	+	31.4924i	0.305890	+	1.14160i	0.932176	+	0.362004i	$0.117907\pi$
$761$	8.43835	+	31.4924i	0.305890	+	1.14160i	−0.626286	+	0.779593i	$0.715426\pi$
$762$	9.88365	−	9.88365i	0.358047	−	0.358047i
$763$	23.9824	+	1.28768i	0.868221	+	0.0466171i
$764$	17.6108	−	10.1676i	0.637135	−	0.367850i
$765$	3.41123	−	12.7309i	0.123333	−	0.460286i
$766$	27.7859			1.00395
$767$	−15.6226	+	13.2372i	−0.564100	+	0.477966i
$768$		−	1.00000i		−	0.0360844i
$769$	−5.76511	+	21.5157i	−0.207895	+	0.775875i	0.780652	+	0.624965i	$0.214887\pi$
$769$	−5.76511	+	21.5157i	−0.207895	+	0.775875i	−0.988548	+	0.150910i	$0.951780\pi$
$770$	5.14464	+	3.35035i	0.185400	+	0.120738i
$771$	−4.72461	−	2.72776i	−0.170153	−	0.0982378i
$772$	14.5675	−	14.5675i	0.524297	−	0.524297i
$773$	15.0276	−	4.02664i	0.540507	−	0.144828i	0.0217709	−	0.999763i	$-0.493070\pi$
$773$	15.0276	−	4.02664i	0.540507	−	0.144828i	0.518736	+	0.854935i	$0.326403\pi$
$774$	−8.49005	+	2.27490i	−0.305169	+	0.0817697i
$775$	−4.87261	+	4.87261i	−0.175029	+	0.175029i
$776$	1.86367	+	1.07599i	0.0669020	+	0.0386259i
$777$	3.02524	−	4.64542i	0.108530	−	0.166654i
$778$	6.55741	−	24.4726i	0.235095	−	0.877385i
$779$		−	13.0353i		−	0.467037i
$780$	3.05365	−	8.51671i	0.109338	−	0.304947i
$781$	12.8818			0.460948
$782$	8.28079	−	30.9043i	0.296120	−	1.10514i
$783$	5.45877	−	3.15163i	0.195081	−	0.112630i
$784$	−6.40209	+	2.83076i	−0.228646	+	0.101099i
$785$	39.6274	−	39.6274i	1.41436	−	1.41436i
$786$	3.48767	+	13.0161i	0.124401	+	0.464271i
$787$	−0.592801	−	2.21236i	−0.0211311	−	0.0788622i	0.954555	−	0.298034i	$-0.0963310\pi$
$787$	−0.592801	−	2.21236i	−0.0211311	−	0.0788622i	−0.975686	+	0.219172i	$0.929664\pi$
$788$	12.9650	+	12.9650i	0.461860	+	0.461860i
$789$	3.36156	+	1.94080i	0.119675	+	0.0690942i
$790$	16.4951	+	28.5703i	0.586868	+	1.01649i
$791$	35.2112	−	7.43724i	1.25197	−	0.264438i
$792$		−	0.924729i		−	0.0328588i
$793$	−1.24619	+	15.0765i	−0.0442534	+	0.535384i
$794$			37.8296i			1.34252i
$795$	−9.11027	−	2.44109i	−0.323108	−	0.0865765i
$796$	−15.1165	+	8.72750i	−0.535789	+	0.309338i
$797$	1.29492	−	2.24287i	0.0458684	−	0.0794465i	−0.842180	−	0.539197i	$-0.818728\pi$
$797$	1.29492	−	2.24287i	0.0458684	−	0.0794465i	0.888048	+	0.459751i	$0.152061\pi$
$798$	−4.58863	−	1.49744i	−0.162436	−	0.0530088i
$799$	4.17498	+	15.5812i	0.147700	+	0.551225i
$800$	1.25267	−	0.335651i	0.0442884	−	0.0118670i
$801$	−5.63188	+	5.63188i	−0.198993	+	0.198993i
$802$	−2.42568	+	4.20140i	−0.0856536	+	0.148356i
$803$	2.88380	+	4.99488i	0.101767	+	0.176266i
$804$	−4.93612	−	1.32263i	−0.174084	−	0.0466455i
$805$	−18.3141	−	36.0577i	−0.645489	−	1.27087i
$806$	10.9133	−	15.7461i	0.384406	−	0.554632i
$807$	7.95281			0.279952
$808$	−3.12697	+	11.6700i	−0.110007	+	0.410550i
$809$	4.65249	+	8.05834i	0.163573	+	0.283316i	0.936147	−	0.351608i	$-0.114365\pi$
$809$	4.65249	+	8.05834i	0.163573	+	0.283316i	−0.772575	+	0.634924i	$0.781032\pi$
$810$	−1.25468	+	2.17316i	−0.0440848	+	0.0763572i
$811$	−13.9465	−	13.9465i	−0.489727	−	0.489727i	0.418493	−	0.908220i	$-0.362558\pi$
$811$	−13.9465	−	13.9465i	−0.489727	−	0.489727i	−0.908220	+	0.418493i	$0.862558\pi$
$812$	12.4076	−	11.1431i	0.435421	−	0.391046i
$813$	−9.22246	+	2.47115i	−0.323446	+	0.0866670i
$814$	1.37008	+	1.37008i	0.0480213	+	0.0480213i
$815$	16.0447	+	9.26343i	0.562022	+	0.324484i
$816$	−4.54866	+	2.62617i	−0.159235	+	0.0919343i
$817$	−15.4889	−	4.15023i	−0.541887	−	0.145198i
$818$	−13.2092			−0.461850
$819$	5.76770	+	7.59827i	0.201540	+	0.265505i
$820$	−17.9297			−0.626132
$821$	−28.0486	−	7.51560i	−0.978903	−	0.262296i	−0.266321	−	0.963884i	$-0.585808\pi$
$821$	−28.0486	−	7.51560i	−0.978903	−	0.262296i	−0.712583	+	0.701588i	$0.752475\pi$
$822$	13.1583	−	7.59697i	0.458950	−	0.264975i
$823$	−25.9527	−	14.9838i	−0.904653	−	0.522302i	−0.0259463	−	0.999663i	$-0.508260\pi$
$823$	−25.9527	−	14.9838i	−0.904653	−	0.522302i	−0.878707	+	0.477361i	$0.841593\pi$
$824$	9.77351	+	9.77351i	0.340476	+	0.340476i
$825$	1.15838	−	0.310386i	0.0403295	−	0.0108063i
$826$	11.1791	−	10.0398i	0.388972	−	0.349330i
$827$	8.32523	+	8.32523i	0.289497	+	0.289497i	0.836881	−	0.547385i	$-0.184376\pi$
$827$	8.32523	+	8.32523i	0.289497	+	0.289497i	−0.547385	+	0.836881i	$0.684376\pi$
$828$	−3.04574	+	5.27538i	−0.105847	+	0.183332i
$829$	−6.14904	−	10.6504i	−0.213565	−	0.369905i	0.739263	−	0.673417i	$-0.235174\pi$
$829$	−6.14904	−	10.6504i	−0.213565	−	0.369905i	−0.952828	+	0.303512i	$0.901841\pi$
$830$	−1.15816	+	4.32233i	−0.0402005	+	0.150030i
$831$	12.6497			0.438813
$832$	−3.26039	+	1.53943i	−0.113034	+	0.0533701i
$833$	29.6891	+	21.6869i	1.02867	+	0.751406i
$834$	−4.54776	−	1.21857i	−0.157476	−	0.0421955i
$835$	5.42407	+	9.39476i	0.187708	+	0.325119i
$836$	0.843517	−	1.46101i	0.0291736	−	0.0505302i
$837$	−3.75725	+	3.75725i	−0.129870	+	0.129870i
$838$	−14.2031	+	3.80572i	−0.490639	+	0.131466i
$839$	−8.42243	−	31.4330i	−0.290775	−	1.08519i	−0.944515	−	0.328467i	$-0.893468\pi$
$839$	−8.42243	−	31.4330i	−0.290775	−	1.08519i	0.653741	−	0.756719i	$-0.273199\pi$
$840$	−2.05969	+	6.31155i	−0.0710661	+	0.217769i
$841$	−5.36548	+	9.29329i	−0.185017	+	0.320458i
$842$	−16.6103	+	9.58995i	−0.572428	+	0.330491i
$843$	−6.82780	−	1.82950i	−0.235162	−	0.0630114i
$844$		−	28.0463i		−	0.965393i
$845$	−32.4687	+	3.15478i	−1.11696	+	0.108528i
$846$		−	3.07118i		−	0.105589i
$847$	5.54688	+	26.2614i	0.190593	+	0.902353i
$848$	1.87930	+	3.25504i	0.0645353	+	0.111778i
$849$	−13.3354	−	7.69921i	−0.457670	−	0.264236i
$850$	−4.81647	−	4.81647i	−0.165204	−	0.165204i
$851$	−3.30344	−	12.3286i	−0.113240	−	0.422619i
$852$	3.60545	+	13.4557i	0.123521	+	0.460985i
$853$	1.67274	−	1.67274i	0.0572736	−	0.0572736i	−0.677890	−	0.735163i	$-0.737105\pi$
$853$	1.67274	−	1.67274i	0.0572736	−	0.0572736i	0.735163	+	0.677890i	$0.237105\pi$
$854$	0.595178	−	11.0849i	0.0203666	−	0.379318i
$855$	−3.96462	+	2.28897i	−0.135587	+	0.0782813i
$856$	2.16536	−	8.08123i	0.0740104	−	0.276211i
$857$	6.84909			0.233961			0.116980	−	0.993134i	$-0.462679\pi$
$857$	6.84909			0.233961			0.116980	+	0.993134i	$0.462679\pi$
$858$	−3.01498	+	1.42355i	−0.102930	+	0.0485993i
$859$			7.11442i			0.242741i	0.992607	+	0.121371i	$0.0387289\pi$
$859$			7.11442i			0.242741i	−0.992607	+	0.121371i	$0.961271\pi$
$860$	−5.70854	+	21.3045i	−0.194659	+	0.726479i
$861$	10.3163	−	15.8413i	0.351579	−	0.539868i
$862$	20.6242	+	11.9074i	0.702462	+	0.405567i
$863$	−13.4859	+	13.4859i	−0.459066	+	0.459066i	−0.898349	−	0.439283i	$-0.855233\pi$
$863$	−13.4859	+	13.4859i	−0.459066	+	0.459066i	0.439283	+	0.898349i	$0.355233\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−10.4639	+	2.80378i	−0.355782	+	0.0953315i
$866$	14.2948	−	14.2948i	0.485758	−	0.485758i
$867$	9.16865	+	5.29352i	0.311384	+	0.179778i
$868$	−7.67182	+	11.7805i	−0.260399	+	0.399856i
$869$	3.14654	−	11.7430i	0.106739	−	0.398355i
$870$		−	15.8171i		−	0.536249i
$871$	3.28651	+	18.1298i	0.111359	+	0.614304i
$872$	−9.07755			−0.307405
$873$	−0.556974	+	2.07866i	−0.0188507	+	0.0703519i
$874$	−9.62415	+	5.55651i	−0.325542	+	0.187952i
$875$	24.5503	+	1.31817i	0.829951	+	0.0445622i
$876$	−4.41027	+	4.41027i	−0.149009	+	0.149009i
$877$	13.6919	+	51.0990i	0.462344	+	1.72549i	0.665548	+	0.746355i	$0.268198\pi$
$877$	13.6919	+	51.0990i	0.462344	+	1.72549i	−0.203204	+	0.979136i	$0.565135\pi$
$878$	5.16873	+	19.2900i	0.174436	+	0.651005i
$879$	−9.93563	−	9.93563i	−0.335121	−	0.335121i
$880$	−2.00959	−	1.16024i	−0.0677432	−	0.0391116i
$881$	−8.30135	−	14.3784i	−0.279680	−	0.484419i	0.691625	−	0.722256i	$-0.256895\pi$
$881$	−8.30135	−	14.3784i	−0.279680	−	0.484419i	−0.971305	+	0.237837i	$0.923562\pi$
$882$	−4.39129	−	5.45129i	−0.147862	−	0.183555i
$883$		−	41.1888i		−	1.38611i	−0.720884	−	0.693056i	$-0.756264\pi$
$883$		−	41.1888i		−	1.38611i	0.720884	−	0.693056i	$-0.243736\pi$
$884$	15.5647	+	10.7876i	0.523497	+	0.362827i
$885$		−	14.2510i		−	0.479044i
$886$	−14.4839	−	3.88095i	−0.486597	−	0.130383i
$887$	−7.95653	+	4.59370i	−0.267154	+	0.154241i	−0.627594	−	0.778541i	$-0.715960\pi$
$887$	−7.95653	+	4.59370i	−0.267154	+	0.154241i	0.360440	+	0.932783i	$0.382627\pi$
$888$	−1.04765	+	1.81459i	−0.0351569	+	0.0608935i
$889$	35.1566	+	11.4729i	1.17911	+	0.384788i
$890$	5.17281	+	19.3052i	0.173393	+	0.647111i
$891$	0.893220	−	0.239338i	0.0299240	−	0.00801811i
$892$	0.331823	−	0.331823i	0.0111103	−	0.0111103i
$893$	2.80146	−	4.85227i	0.0937473	−	0.162375i
$894$	4.99119	+	8.64499i	0.166930	+	0.289132i
$895$	−27.0483	−	7.24757i	−0.904125	−	0.242259i
$896$	2.35892	−	1.19812i	0.0788059	−	0.0400265i
$897$	21.8885	+	1.80925i	0.730836	+	0.0604090i
$898$	4.81827			0.160788
$899$	8.66854	−	32.3514i	0.289112	−	1.07898i
$900$	0.648428	+	1.12311i	0.0216143	+	0.0374370i
$901$	9.87070	−	17.0966i	0.328841	−	0.569569i
$902$	4.67208	+	4.67208i	0.155563	+	0.155563i
$903$	−15.5385	−	17.3017i	−0.517087	−	0.575766i
$904$	−13.1387	+	3.52051i	−0.436988	+	0.117091i
$905$	−5.15441	−	5.15441i	−0.171338	−	0.171338i
$906$	−7.68628	−	4.43768i	−0.255360	−	0.147432i
$907$	−36.4183	+	21.0261i	−1.20925	+	0.698161i	−0.962596	−	0.270942i	$-0.912665\pi$
$907$	−36.4183	+	21.0261i	−1.20925	+	0.698161i	−0.246655	+	0.969103i	$0.579331\pi$
$908$	26.1459	+	7.00578i	0.867683	+	0.232495i
$909$	−12.0817			−0.400725
$910$	23.7489	−	3.00078i	0.787268	−	0.0994747i
$911$	−10.2895			−0.340908			−0.170454	−	0.985366i	$-0.554523\pi$
$911$	−10.2895			−0.340908			−0.170454	+	0.985366i	$0.554523\pi$
$912$	1.76219	+	0.472178i	0.0583520	+	0.0156354i
$913$	1.42810	−	0.824512i	0.0472631	−	0.0272874i
$914$	35.1994	+	20.3224i	1.16429	+	0.672205i
$915$	−7.44484	−	7.44484i	−0.246119	−	0.246119i
$916$	24.7542	−	6.63288i	0.817903	−	0.219156i
$917$	−26.5254	+	23.8221i	−0.875945	+	0.786675i
$918$	−3.71396	−	3.71396i	−0.122579	−	0.122579i
$919$	3.95773	−	6.85498i	0.130553	−	0.226125i	−0.793337	−	0.608783i	$-0.791658\pi$
$919$	3.95773	−	6.85498i	0.130553	−	0.226125i	0.923890	+	0.382658i	$0.124991\pi$
$920$	7.64284	+	13.2378i	0.251977	+	0.436437i
$921$	−6.00848	+	22.4239i	−0.197986	+	0.738894i
$922$	22.7852			0.750389
$923$	38.3206	−	32.4693i	1.26134	−	1.06874i
$924$	2.18136	−	1.10794i	0.0717615	−	0.0364486i
$925$	−2.62471	−	0.703290i	−0.0863001	−	0.0231240i
$926$	6.70947	+	11.6211i	0.220487	+	0.381894i
$927$	−6.91091	+	11.9701i	−0.226984	+	0.393148i
$928$	−4.45707	+	4.45707i	−0.146311	+	0.146311i
$929$	−43.2298	+	11.5834i	−1.41832	+	0.380039i	−0.884889	−	0.465803i	$-0.845766\pi$
$929$	−43.2298	+	11.5834i	−1.41832	+	0.380039i	−0.533435	+	0.845841i	$0.679099\pi$
$930$	3.45098	+	12.8793i	0.113162	+	0.422327i
$931$	−1.96542	−	12.6183i	−0.0644139	−	0.413549i
$932$	−9.18782	+	15.9138i	−0.300957	+	0.521273i
$933$	7.17394	−	4.14188i	0.234864	−	0.135599i
$934$	−38.0906	−	10.2064i	−1.24636	−	0.333962i
$935$			12.1879i			0.398587i
$936$	−2.33083	−	2.75086i	−0.0761854	−	0.0899148i
$937$			16.1603i			0.527934i	0.964532	+	0.263967i	$0.0850310\pi$
$937$			16.1603i			0.527934i	−0.964532	+	0.263967i	$0.914969\pi$
$938$	−2.79411	−	13.2286i	−0.0912310	−	0.431928i
$939$	12.2303	+	21.1835i	0.399121	+	0.691298i
$940$	−6.67418	−	3.85334i	−0.217688	−	0.125682i
$941$	−29.4696	−	29.4696i	−0.960683	−	0.960683i	0.0385730	−	0.999256i	$-0.487719\pi$
$941$	−29.4696	−	29.4696i	−0.960683	−	0.960683i	−0.999256	+	0.0385730i	$0.987719\pi$
$942$	−5.78023	−	21.5721i	−0.188330	−	0.702857i
$943$	−11.2650	−	42.0414i	−0.366838	−	1.36906i
$944$	−4.01578	+	4.01578i	−0.130703	+	0.130703i
$945$	−6.62958	−	0.355959i	−0.215660	−	0.0115794i
$946$	7.03902	−	4.06398i	0.228858	−	0.132131i
$947$	7.24261	−	27.0298i	0.235353	−	0.878350i	−0.742636	−	0.669695i	$-0.766425\pi$
$947$	7.24261	−	27.0298i	0.235353	−	0.878350i	0.977989	−	0.208655i	$-0.0669085\pi$
$948$	13.1469			0.426990
$949$	21.1685	+	7.58991i	0.687158	+	0.246379i
$950$			2.36592i			0.0767607i
$951$	1.23131	−	4.59530i	0.0399279	−	0.149013i
$952$	−11.6448	−	7.58344i	−0.377409	−	0.245781i
$953$	−36.5842	−	21.1219i	−1.18508	−	0.684205i	−0.227894	−	0.973686i	$-0.573184\pi$
$953$	−36.5842	−	21.1219i	−1.18508	−	0.684205i	−0.957184	+	0.289481i	$0.906517\pi$
$954$	−2.65773	+	2.65773i	−0.0860471	+	0.0860471i
$955$	49.2894	−	13.2070i	1.59497	−	0.427370i
$956$	14.8470	−	3.97824i	0.480186	−	0.128666i
$957$	−4.12158	+	4.12158i	−0.133232	+	0.133232i
$958$	−25.8584	−	14.9294i	−0.835449	−	0.482346i
$959$	33.6860	+	21.9373i	1.08778	+	0.708394i
$960$	0.649468	−	2.42385i	0.0209615	−	0.0782294i
$961$		−	2.76616i		−	0.0892311i
$962$	7.52905	+	0.622331i	0.242746	+	0.0200648i
$963$	8.36630			0.269600
$964$	−2.98930	+	11.1562i	−0.0962789	+	0.359318i
$965$	44.7707	−	25.8483i	1.44122	−	0.832088i
$966$	−16.0934	−	0.864095i	−0.517795	−	0.0278018i
$967$	−21.8284	+	21.8284i	−0.701954	+	0.701954i	−0.964830	−	0.262876i	$-0.915329\pi$
$967$	−21.8284	+	21.8284i	−0.701954	+	0.701954i	0.262876	+	0.964830i	$0.415329\pi$
$968$	−2.62569	−	9.79920i	−0.0843928	−	0.314958i
$969$	−2.48004	−	9.25562i	−0.0796702	−	0.297333i
$970$	3.81844	+	3.81844i	0.122603	+	0.122603i
$971$	−8.86654	−	5.11910i	−0.284541	−	0.164280i	0.350936	−	0.936399i	$-0.385863\pi$
$971$	−8.86654	−	5.11910i	−0.284541	−	0.164280i	−0.635477	+	0.772119i	$0.719197\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−2.57428	−	12.1878i	−0.0825275	−	0.390722i
$974$		−	14.7144i		−	0.471481i
$975$	2.66357	−	3.84307i	0.0853025	−	0.123077i
$976$			4.19574i			0.134302i
$977$	−25.3501	−	6.79254i	−0.811022	−	0.217313i	−0.170604	−	0.985340i	$-0.554572\pi$
$977$	−25.3501	−	6.79254i	−0.811022	−	0.217313i	−0.640417	+	0.768027i	$0.721239\pi$
$978$	6.39397	−	3.69156i	0.204457	−	0.118043i
$979$	3.68259	−	6.37843i	0.117696	−	0.203855i
$980$	−17.3562	+	2.70338i	−0.554423	+	0.0863563i
$981$	−2.34944	−	8.76824i	−0.0750119	−	0.279948i
$982$	−26.9125	+	7.21117i	−0.858811	+	0.230118i
$983$	−4.18287	+	4.18287i	−0.133413	+	0.133413i	−0.770660	−	0.637247i	$-0.780073\pi$
$983$	−4.18287	+	4.18287i	−0.133413	+	0.133413i	0.637247	+	0.770660i	$0.280073\pi$
$984$	−3.57257	+	6.18788i	−0.113889	+	0.197262i
$985$	23.0049	+	39.8457i	0.732997	+	1.26959i
$986$	31.9787	+	8.56867i	1.01841	+	0.272882i
$987$	7.24467	−	3.67966i	0.230600	−	0.117125i
$988$	−1.17328	−	6.47232i	−0.0373271	−	0.205912i
$989$	−53.5414			−1.70252
$990$	0.600583	−	2.24140i	0.0190878	−	0.0712365i
$991$	−7.42046	−	12.8526i	−0.235719	−	0.408277i	0.723763	−	0.690049i	$-0.242411\pi$
$991$	−7.42046	−	12.8526i	−0.235719	−	0.408277i	−0.959481	+	0.281772i	$0.909078\pi$
$992$	2.65678	−	4.60167i	0.0843527	−	0.146103i
$993$	−9.02343	−	9.02343i	−0.286350	−	0.286350i
$994$	−27.4212	+	24.6266i	−0.869747	+	0.781108i
$995$	−42.3083	+	11.3365i	−1.34126	+	0.359390i
$996$	1.26095	+	1.26095i	0.0399547	+	0.0399547i
$997$	7.64344	+	4.41294i	0.242070	+	0.139759i	0.616128	−	0.787646i	$-0.288700\pi$
$997$	7.64344	+	4.41294i	0.242070	+	0.139759i	−0.374058	+	0.927405i	$0.622034\pi$
$998$	−15.2947	+	8.83037i	−0.484144	+	0.279521i
$999$	−2.02391	−	0.542304i	−0.0640336	−	0.0171577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.223.5	yes	40
7.6	odd	2		546.2.bx.a.223.1	✓	40
13.7	odd	12		546.2.bx.a.475.1	yes	40
91.20	even	12	inner	546.2.bx.b.475.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.1	✓	40	7.6	odd	2
546.2.bx.a.475.1	yes	40	13.7	odd	12
546.2.bx.b.223.5	yes	40	1.1	even	1	trivial
546.2.bx.b.475.5	yes	40	91.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.77438 + 1.77438i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.76783 + 1.96844i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.77438 + 1.77438i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.76783 + 1.96844i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.25468 - 2.17316i) q^{10} +(-0.239338 + 0.893220i) q^{11} -1.00000 q^{12} +(1.53943 + 3.26039i) q^{13} +(-1.19812 - 2.35892i) q^{14} +(-2.42385 - 0.649468i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.62617 - 4.54866i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-1.76219 + 0.472178i) q^{19} +(0.649468 + 2.42385i) q^{20} +(-2.51521 - 0.820805i) q^{21} +(0.462365 - 0.800839i) q^{22} +(-5.27538 + 3.04574i) q^{23} +(0.965926 + 0.258819i) q^{24} +1.29686i q^{25} +(-0.643122 - 3.54773i) q^{26} +1.00000i q^{27} +(0.546766 + 2.58864i) q^{28} +(-3.15163 - 5.45877i) q^{29} +(2.17316 + 1.25468i) q^{30} +(3.75725 + 3.75725i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.239338 - 0.893220i) q^{33} +(-3.71396 + 3.71396i) q^{34} +(-0.355959 + 6.62958i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-0.542304 + 2.02391i) q^{37} +1.82435 q^{38} +(-2.96338 - 2.05387i) q^{39} -2.50935i q^{40} +(-1.84930 + 6.90168i) q^{41} +(2.21707 + 1.44382i) q^{42} +(7.61197 + 4.39478i) q^{43} +(-0.653882 + 0.653882i) q^{44} +(2.42385 - 0.649468i) q^{45} +(5.88392 - 1.57659i) q^{46} +(-2.17165 + 2.17165i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.749536 + 6.95976i) q^{49} +(0.335651 - 1.25267i) q^{50} +5.25234i q^{51} +(-0.297013 + 3.59330i) q^{52} +3.75859 q^{53} +(0.258819 - 0.965926i) q^{54} +(-2.00959 + 1.16024i) q^{55} +(0.141853 - 2.64195i) q^{56} +(1.29001 - 1.29001i) q^{57} +(1.63140 + 6.08847i) q^{58} +(1.46988 + 5.48566i) q^{59} +(-1.77438 - 1.77438i) q^{60} +(3.63362 + 2.09787i) q^{61} +(-2.65678 - 4.60167i) q^{62} +(2.58864 - 0.546766i) q^{63} +1.00000i q^{64} +(-3.05365 + 8.51671i) q^{65} +0.924729i q^{66} +(4.93612 + 1.32263i) q^{67} +(4.54866 - 2.62617i) q^{68} +(3.04574 - 5.27538i) q^{69} +(2.05969 - 6.31155i) q^{70} +(-3.60545 - 13.4557i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(4.41027 - 4.41027i) q^{73} +(1.04765 - 1.81459i) q^{74} +(-0.648428 - 1.12311i) q^{75} +(-1.76219 - 0.472178i) q^{76} +(-2.18136 + 1.10794i) q^{77} +(2.33083 + 2.75086i) q^{78} -13.1469 q^{79} +(-0.649468 + 2.42385i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.57257 - 6.18788i) q^{82} +(-1.26095 - 1.26095i) q^{83} +(-1.76783 - 1.96844i) q^{84} +(12.7309 - 3.41123i) q^{85} +(-6.21515 - 6.21515i) q^{86} +(5.45877 + 3.15163i) q^{87} +(0.800839 - 0.462365i) q^{88} +(-7.69329 - 2.06141i) q^{89} -2.50935 q^{90} +(-3.69645 + 8.79411i) q^{91} -6.09148 q^{92} +(-5.13250 - 1.37525i) q^{93} +(2.65972 - 1.53559i) q^{94} +(-3.96462 - 2.28897i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-2.07866 + 0.556974i) q^{97} +(2.52531 - 6.52861i) q^{98} +(0.653882 + 0.653882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

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