LMFDB - Embedded newform 144.2.x.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(13,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("144.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.x (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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			61.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	144.61
Dual form			144.2.x.a.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-1.86603 - 0.500000i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-1.86603 - 0.500000i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(2.36603 - 1.36603i) q^{10} +(-0.500000 - 1.86603i) q^{11} -3.46410i q^{12} +(-0.598076 + 2.23205i) q^{13} +(-6.09808 + 1.63397i) q^{14} +(-3.23205 - 0.866025i) q^{15} -4.00000 q^{16} +4.00000 q^{17} +(-3.00000 + 3.00000i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 + 3.73205i) q^{20} +(6.69615 + 3.86603i) q^{21} +(2.36603 + 1.36603i) q^{22} +(-5.59808 + 3.23205i) q^{23} +(3.46410 + 3.46410i) q^{24} +(-1.09808 - 0.633975i) q^{25} +(-1.63397 - 2.83013i) q^{26} +5.19615 q^{27} +(4.46410 - 7.73205i) q^{28} +(-0.866025 + 0.232051i) q^{29} +(4.09808 - 2.36603i) q^{30} +(-4.59808 - 7.96410i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.866025 - 3.23205i) q^{33} +(-4.00000 + 4.00000i) q^{34} +(-6.09808 - 6.09808i) q^{35} -6.00000i q^{36} +(-4.26795 + 4.26795i) q^{37} +6.00000 q^{38} +(-1.03590 + 3.86603i) q^{39} +(-2.73205 - 4.73205i) q^{40} +(0.696152 - 0.401924i) q^{41} +(-10.5622 + 2.83013i) q^{42} +(-1.69615 - 6.33013i) q^{43} +(-3.73205 + 1.00000i) q^{44} +(-5.59808 - 1.50000i) q^{45} +(2.36603 - 8.83013i) q^{46} +(-0.598076 + 1.03590i) q^{47} -6.92820 q^{48} +(6.46410 + 11.1962i) q^{49} +(1.73205 - 0.464102i) q^{50} +6.92820 q^{51} +(4.46410 + 1.19615i) q^{52} +(5.73205 - 5.73205i) q^{53} +(-5.19615 + 5.19615i) q^{54} +3.73205i q^{55} +(3.26795 + 12.1962i) q^{56} +(-5.19615 - 5.19615i) q^{57} +(0.633975 - 1.09808i) q^{58} +(-1.50000 - 0.401924i) q^{59} +(-1.73205 + 6.46410i) q^{60} +(-2.13397 + 0.571797i) q^{61} +(12.5622 + 3.36603i) q^{62} +(11.5981 + 6.69615i) q^{63} +8.00000i q^{64} +(2.23205 - 3.86603i) q^{65} +(4.09808 + 2.36603i) q^{66} +(-2.23205 + 8.33013i) q^{67} -8.00000i q^{68} +(-9.69615 + 5.59808i) q^{69} +12.1962 q^{70} -2.92820i q^{71} +(6.00000 + 6.00000i) q^{72} +7.46410i q^{73} -8.53590i q^{74} +(-1.90192 - 1.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(2.23205 - 8.33013i) q^{77} +(-2.83013 - 4.90192i) q^{78} +(-0.866025 + 1.50000i) q^{79} +(7.46410 + 2.00000i) q^{80} +9.00000 q^{81} +(-0.294229 + 1.09808i) q^{82} +(-14.1603 + 3.79423i) q^{83} +(7.73205 - 13.3923i) q^{84} +(-7.46410 - 2.00000i) q^{85} +(8.02628 + 4.63397i) q^{86} +(-1.50000 + 0.401924i) q^{87} +(2.73205 - 4.73205i) q^{88} +15.8564i q^{89} +(7.09808 - 4.09808i) q^{90} +(-7.29423 + 7.29423i) q^{91} +(6.46410 + 11.1962i) q^{92} +(-7.96410 - 13.7942i) q^{93} +(-0.437822 - 1.63397i) q^{94} +(4.09808 + 7.09808i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-17.6603 - 4.73205i) q^{98} +(-1.50000 - 5.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{5} + 12 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^5 + 12 * q^7 + 8 * q^8 + 12 * q^9	$ 4 q - 4 q^{2} - 4 q^{5} + 12 q^{7} + 8 q^{8} + 12 q^{9} + 6 q^{10} - 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{15} - 16 q^{16} + 16 q^{17} - 12 q^{18} - 12 q^{19} - 4 q^{20} + 6 q^{21} + 6 q^{22} - 12 q^{23} + 6 q^{25} - 10 q^{26} + 4 q^{28} + 6 q^{30} - 8 q^{31} + 16 q^{32} - 16 q^{34} - 14 q^{35} - 24 q^{37} + 24 q^{38} - 18 q^{39} - 4 q^{40} - 18 q^{41} - 18 q^{42} + 14 q^{43} - 8 q^{44} - 12 q^{45} + 6 q^{46} + 8 q^{47} + 12 q^{49} + 4 q^{52} + 16 q^{53} + 20 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} + 26 q^{62} + 36 q^{63} + 2 q^{65} + 6 q^{66} - 2 q^{67} - 18 q^{69} + 28 q^{70} + 24 q^{72} - 18 q^{75} - 24 q^{76} + 2 q^{77} + 6 q^{78} + 16 q^{80} + 36 q^{81} + 30 q^{82} - 22 q^{83} + 24 q^{84} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 4 q^{88} + 18 q^{90} + 2 q^{91} + 12 q^{92} - 18 q^{93} - 26 q^{94} + 6 q^{95} - 2 q^{97} - 36 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^5 + 12 * q^7 + 8 * q^8 + 12 * q^9 + 6 * q^10 - 2 * q^11 + 8 * q^13 - 14 * q^14 - 6 * q^15 - 16 * q^16 + 16 * q^17 - 12 * q^18 - 12 * q^19 - 4 * q^20 + 6 * q^21 + 6 * q^22 - 12 * q^23 + 6 * q^25 - 10 * q^26 + 4 * q^28 + 6 * q^30 - 8 * q^31 + 16 * q^32 - 16 * q^34 - 14 * q^35 - 24 * q^37 + 24 * q^38 - 18 * q^39 - 4 * q^40 - 18 * q^41 - 18 * q^42 + 14 * q^43 - 8 * q^44 - 12 * q^45 + 6 * q^46 + 8 * q^47 + 12 * q^49 + 4 * q^52 + 16 * q^53 + 20 * q^56 + 6 * q^58 - 6 * q^59 - 12 * q^61 + 26 * q^62 + 36 * q^63 + 2 * q^65 + 6 * q^66 - 2 * q^67 - 18 * q^69 + 28 * q^70 + 24 * q^72 - 18 * q^75 - 24 * q^76 + 2 * q^77 + 6 * q^78 + 16 * q^80 + 36 * q^81 + 30 * q^82 - 22 * q^83 + 24 * q^84 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 4 * q^88 + 18 * q^90 + 2 * q^91 + 12 * q^92 - 18 * q^93 - 26 * q^94 + 6 * q^95 - 2 * q^97 - 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$		−	2.00000i		−	1.00000i
$5$	−1.86603	−	0.500000i	−0.834512	−	0.223607i	−0.183831	−	0.982958i	$-0.558850\pi$
$5$	−1.86603	−	0.500000i	−0.834512	−	0.223607i	−0.650681	+	0.759351i	$0.725517\pi$
$6$	−1.73205	+	1.73205i	−0.707107	+	0.707107i
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.999068	−	0.0431647i	$-0.0137440\pi$
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.462152	+	0.886801i	$0.347077\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	3.00000			1.00000
$10$	2.36603	−	1.36603i	0.748203	−	0.431975i
$11$	−0.500000	−	1.86603i	−0.150756	−	0.562628i	−0.999432	−	0.0337145i	$-0.989266\pi$
$11$	−0.500000	−	1.86603i	−0.150756	−	0.562628i	0.848676	−	0.528913i	$-0.177400\pi$
$12$		−	3.46410i		−	1.00000i
$13$	−0.598076	+	2.23205i	−0.165876	+	0.619060i	0.832050	+	0.554700i	$0.187167\pi$
$13$	−0.598076	+	2.23205i	−0.165876	+	0.619060i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	−6.09808	+	1.63397i	−1.62978	+	0.436698i
$15$	−3.23205	−	0.866025i	−0.834512	−	0.223607i
$16$	−4.00000			−1.00000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	−3.00000	+	3.00000i	−0.707107	+	0.707107i
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	−1.00000	+	3.73205i	−0.223607	+	0.834512i
$21$	6.69615	+	3.86603i	1.46122	+	0.843636i
$22$	2.36603	+	1.36603i	0.504438	+	0.291238i
$23$	−5.59808	+	3.23205i	−1.16728	+	0.673929i	−0.953038	−	0.302851i	$-0.902061\pi$
$23$	−5.59808	+	3.23205i	−1.16728	+	0.673929i	−0.214242	+	0.976781i	$0.568728\pi$
$24$	3.46410	+	3.46410i	0.707107	+	0.707107i
$25$	−1.09808	−	0.633975i	−0.219615	−	0.126795i
$26$	−1.63397	−	2.83013i	−0.320449	−	0.555034i
$27$	5.19615			1.00000
$28$	4.46410	−	7.73205i	0.843636	−	1.46122i
$29$	−0.866025	+	0.232051i	−0.160817	+	0.0430908i	−0.338329	−	0.941028i	$-0.609862\pi$
$29$	−0.866025	+	0.232051i	−0.160817	+	0.0430908i	0.177512	+	0.984119i	$0.443195\pi$
$30$	4.09808	−	2.36603i	0.748203	−	0.431975i
$31$	−4.59808	−	7.96410i	−0.825839	−	1.43039i	−0.901277	−	0.433244i	$-0.857369\pi$
$31$	−4.59808	−	7.96410i	−0.825839	−	1.43039i	0.0754376	−	0.997151i	$-0.475965\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−0.866025	−	3.23205i	−0.150756	−	0.562628i
$34$	−4.00000	+	4.00000i	−0.685994	+	0.685994i
$35$	−6.09808	−	6.09808i	−1.03076	−	1.03076i
$36$		−	6.00000i		−	1.00000i
$37$	−4.26795	+	4.26795i	−0.701647	+	0.701647i	−0.964764	−	0.263117i	$-0.915249\pi$
$37$	−4.26795	+	4.26795i	−0.701647	+	0.701647i	0.263117	+	0.964764i	$0.415249\pi$
$38$	6.00000			0.973329
$39$	−1.03590	+	3.86603i	−0.165876	+	0.619060i
$40$	−2.73205	−	4.73205i	−0.431975	−	0.748203i
$41$	0.696152	−	0.401924i	0.108721	−	0.0627700i	−0.444654	−	0.895703i	$-0.646673\pi$
$41$	0.696152	−	0.401924i	0.108721	−	0.0627700i	0.553374	+	0.832933i	$0.313340\pi$
$42$	−10.5622	+	2.83013i	−1.62978	+	0.436698i
$43$	−1.69615	−	6.33013i	−0.258661	−	0.965335i	−0.966017	−	0.258478i	$-0.916779\pi$
$43$	−1.69615	−	6.33013i	−0.258661	−	0.965335i	0.707356	−	0.706857i	$-0.249888\pi$
$44$	−3.73205	+	1.00000i	−0.562628	+	0.150756i
$45$	−5.59808	−	1.50000i	−0.834512	−	0.223607i
$46$	2.36603	−	8.83013i	0.348851	−	1.30193i
$47$	−0.598076	+	1.03590i	−0.0872384	+	0.151101i	−0.906343	−	0.422543i	$-0.861138\pi$
$47$	−0.598076	+	1.03590i	−0.0872384	+	0.151101i	0.819104	+	0.573644i	$0.194471\pi$
$48$	−6.92820			−1.00000
$49$	6.46410	+	11.1962i	0.923443	+	1.59945i
$50$	1.73205	−	0.464102i	0.244949	−	0.0656339i
$51$	6.92820			0.970143
$52$	4.46410	+	1.19615i	0.619060	+	0.165876i
$53$	5.73205	−	5.73205i	0.787358	−	0.787358i	−0.193703	−	0.981060i	$-0.562050\pi$
$53$	5.73205	−	5.73205i	0.787358	−	0.787358i	0.981060	+	0.193703i	$0.0620497\pi$
$54$	−5.19615	+	5.19615i	−0.707107	+	0.707107i
$55$			3.73205i			0.503230i
$56$	3.26795	+	12.1962i	0.436698	+	1.62978i
$57$	−5.19615	−	5.19615i	−0.688247	−	0.688247i
$58$	0.633975	−	1.09808i	0.0832449	−	0.144184i
$59$	−1.50000	−	0.401924i	−0.195283	−	0.0523260i	0.159852	−	0.987141i	$-0.448898\pi$
$59$	−1.50000	−	0.401924i	−0.195283	−	0.0523260i	−0.355135	+	0.934815i	$0.615565\pi$
$60$	−1.73205	+	6.46410i	−0.223607	+	0.834512i
$61$	−2.13397	+	0.571797i	−0.273227	+	0.0732111i	−0.392831	−	0.919611i	$-0.628504\pi$
$61$	−2.13397	+	0.571797i	−0.273227	+	0.0732111i	0.119604	+	0.992822i	$0.461838\pi$
$62$	12.5622	+	3.36603i	1.59540	+	0.427486i
$63$	11.5981	+	6.69615i	1.46122	+	0.843636i
$64$			8.00000i			1.00000i
$65$	2.23205	−	3.86603i	0.276852	−	0.479521i
$66$	4.09808	+	2.36603i	0.504438	+	0.291238i
$67$	−2.23205	+	8.33013i	−0.272688	+	1.01769i	0.684686	+	0.728838i	$0.259939\pi$
$67$	−2.23205	+	8.33013i	−0.272688	+	1.01769i	−0.957375	+	0.288849i	$0.906727\pi$
$68$		−	8.00000i		−	0.970143i
$69$	−9.69615	+	5.59808i	−1.16728	+	0.673929i
$70$	12.1962			1.45772
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$	6.00000	+	6.00000i	0.707107	+	0.707107i
$73$			7.46410i			0.873607i	0.899557	+	0.436804i	$0.143889\pi$
$73$			7.46410i			0.873607i	−0.899557	+	0.436804i	$0.856111\pi$
$74$		−	8.53590i		−	0.992278i
$75$	−1.90192	−	1.09808i	−0.219615	−	0.126795i
$76$	−6.00000	+	6.00000i	−0.688247	+	0.688247i
$77$	2.23205	−	8.33013i	0.254366	−	0.949306i
$78$	−2.83013	−	4.90192i	−0.320449	−	0.555034i
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	−0.910622	−	0.413239i	$-0.864397\pi$
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	0.813187	+	0.582003i	$0.197731\pi$
$80$	7.46410	+	2.00000i	0.834512	+	0.223607i
$81$	9.00000			1.00000
$82$	−0.294229	+	1.09808i	−0.0324921	+	0.121262i
$83$	−14.1603	+	3.79423i	−1.55429	+	0.416471i	−0.930850	−	0.365401i	$-0.880932\pi$
$83$	−14.1603	+	3.79423i	−1.55429	+	0.416471i	−0.623440	+	0.781872i	$0.714265\pi$
$84$	7.73205	−	13.3923i	0.843636	−	1.46122i
$85$	−7.46410	−	2.00000i	−0.809595	−	0.216930i
$86$	8.02628	+	4.63397i	0.865496	+	0.499694i
$87$	−1.50000	+	0.401924i	−0.160817	+	0.0430908i
$88$	2.73205	−	4.73205i	0.291238	−	0.504438i
$89$			15.8564i			1.68078i	0.541985	+	0.840388i	$0.317673\pi$
$89$			15.8564i			1.68078i	−0.541985	+	0.840388i	$0.682327\pi$
$90$	7.09808	−	4.09808i	0.748203	−	0.431975i
$91$	−7.29423	+	7.29423i	−0.764643	+	0.764643i
$92$	6.46410	+	11.1962i	0.673929	+	1.16728i
$93$	−7.96410	−	13.7942i	−0.825839	−	1.43039i
$94$	−0.437822	−	1.63397i	−0.0451579	−	0.168532i
$95$	4.09808	+	7.09808i	0.420454	+	0.728247i
$96$	6.92820	−	6.92820i	0.707107	−	0.707107i
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$	−17.6603	−	4.73205i	−1.78396	−	0.478009i
$99$	−1.50000	−	5.59808i	−0.150756	−	0.562628i
$100$	−1.26795	+	2.19615i	−0.126795	+	0.219615i
$101$	−0.133975	−	0.500000i	−0.0133310	−	0.0497519i	0.958940	−	0.283609i	$-0.0915318\pi$
$101$	−0.133975	−	0.500000i	−0.0133310	−	0.0497519i	−0.972271	+	0.233857i	$0.924865\pi$
$102$	−6.92820	+	6.92820i	−0.685994	+	0.685994i
$103$	13.7942	−	7.96410i	1.35919	−	0.784726i	0.369672	−	0.929162i	$-0.379470\pi$
$103$	13.7942	−	7.96410i	1.35919	−	0.784726i	0.989514	+	0.144436i	$0.0461369\pi$
$104$	−5.66025	+	3.26795i	−0.555034	+	0.320449i
$105$	−10.5622	−	10.5622i	−1.03076	−	1.03076i
$106$			11.4641i			1.11349i
$107$	9.39230	−	9.39230i	0.907988	−	0.907988i	−0.0881214	−	0.996110i	$-0.528086\pi$
$107$	9.39230	−	9.39230i	0.907988	−	0.907988i	0.996110	+	0.0881214i	$0.0280863\pi$
$108$		−	10.3923i		−	1.00000i
$109$	−1.73205	−	1.73205i	−0.165900	−	0.165900i	0.619274	−	0.785175i	$-0.287427\pi$
$109$	−1.73205	−	1.73205i	−0.165900	−	0.165900i	−0.785175	+	0.619274i	$0.787427\pi$
$110$	−3.73205	−	3.73205i	−0.355837	−	0.355837i
$111$	−7.39230	+	7.39230i	−0.701647	+	0.701647i
$112$	−15.4641	−	8.92820i	−1.46122	−	0.843636i
$113$	−6.23205	−	10.7942i	−0.586262	−	1.01544i	−0.994717	−	0.102657i	$-0.967266\pi$
$113$	−6.23205	−	10.7942i	−0.586262	−	1.01544i	0.408455	−	0.912779i	$-0.366068\pi$
$114$	10.3923			0.973329
$115$	12.0622	−	3.23205i	1.12480	−	0.301390i
$116$	0.464102	+	1.73205i	0.0430908	+	0.160817i
$117$	−1.79423	+	6.69615i	−0.165876	+	0.619060i
$118$	1.90192	−	1.09808i	0.175086	−	0.101086i
$119$	15.4641	+	8.92820i	1.41759	+	0.818447i
$120$	−4.73205	−	8.19615i	−0.431975	−	0.748203i
$121$	6.29423	−	3.63397i	0.572203	−	0.330361i
$122$	1.56218	−	2.70577i	0.141433	−	0.244969i
$123$	1.20577	−	0.696152i	0.108721	−	0.0627700i
$124$	−15.9282	+	9.19615i	−1.43039	+	0.825839i
$125$	8.56218	+	8.56218i	0.765824	+	0.765824i
$126$	−18.2942	+	4.90192i	−1.62978	+	0.436698i
$127$	0.392305			0.0348114			0.0174057	−	0.999849i	$-0.494459\pi$
$127$	0.392305			0.0348114			0.0174057	+	0.999849i	$0.494459\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	−2.93782	−	10.9641i	−0.258661	−	0.965335i
$130$	1.63397	+	6.09808i	0.143309	+	0.534837i
$131$	1.30385	−	4.86603i	0.113918	−	0.425147i	−0.885286	−	0.465047i	$-0.846037\pi$
$131$	1.30385	−	4.86603i	0.113918	−	0.425147i	0.999204	+	0.0399004i	$0.0127041\pi$
$132$	−6.46410	+	1.73205i	−0.562628	+	0.150756i
$133$	−4.90192	−	18.2942i	−0.425051	−	1.58631i
$134$	−6.09808	−	10.5622i	−0.526794	−	0.912433i
$135$	−9.69615	−	2.59808i	−0.834512	−	0.223607i
$136$	8.00000	+	8.00000i	0.685994	+	0.685994i
$137$	−0.571797	−	0.330127i	−0.0488519	−	0.0282047i	0.475375	−	0.879783i	$-0.342312\pi$
$137$	−0.571797	−	0.330127i	−0.0488519	−	0.0282047i	−0.524227	+	0.851579i	$0.675646\pi$
$138$	4.09808	−	15.2942i	0.348851	−	1.30193i
$139$	16.1603	+	4.33013i	1.37069	+	0.367277i	0.867732	−	0.497032i	$-0.165577\pi$
$139$	16.1603	+	4.33013i	1.37069	+	0.367277i	0.502962	+	0.864308i	$0.332243\pi$
$140$	−12.1962	+	12.1962i	−1.03076	+	1.03076i
$141$	−1.03590	+	1.79423i	−0.0872384	+	0.151101i
$142$	2.92820	+	2.92820i	0.245729	+	0.245729i
$143$	4.46410			0.373307
$144$	−12.0000			−1.00000
$145$	1.73205			0.143839
$146$	−7.46410	−	7.46410i	−0.617733	−	0.617733i
$147$	11.1962	+	19.3923i	0.923443	+	1.59945i
$148$	8.53590	+	8.53590i	0.701647	+	0.701647i
$149$	16.0622	+	4.30385i	1.31586	+	0.352585i	0.847427	−	0.530912i	$-0.178150\pi$
$149$	16.0622	+	4.30385i	1.31586	+	0.352585i	0.468438	+	0.883497i	$0.344817\pi$
$150$	3.00000	−	0.803848i	0.244949	−	0.0656339i
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	0.232623	−	0.972567i	$-0.425269\pi$
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	−0.725956	+	0.687741i	$0.758602\pi$
$152$		−	12.0000i		−	0.973329i
$153$	12.0000			0.970143
$154$	6.09808	+	10.5622i	0.491397	+	0.851125i
$155$	4.59808	+	17.1603i	0.369326	+	1.37834i
$156$	7.73205	+	2.07180i	0.619060	+	0.165876i
$157$	−0.866025	+	3.23205i	−0.0691164	+	0.257946i	−0.991835	−	0.127529i	$-0.959296\pi$
$157$	−0.866025	+	3.23205i	−0.0691164	+	0.257946i	0.922719	+	0.385474i	$0.125962\pi$
$158$	−0.633975	−	2.36603i	−0.0504363	−	0.188231i
$159$	9.92820	−	9.92820i	0.787358	−	0.787358i
$160$	−9.46410	+	5.46410i	−0.748203	+	0.431975i
$161$	−28.8564			−2.27420
$162$	−9.00000	+	9.00000i	−0.707107	+	0.707107i
$163$	−1.92820	−	1.92820i	−0.151029	−	0.151029i	0.627549	−	0.778577i	$-0.284058\pi$
$163$	−1.92820	−	1.92820i	−0.151029	−	0.151029i	−0.778577	+	0.627549i	$0.784058\pi$
$164$	−0.803848	−	1.39230i	−0.0627700	−	0.108721i
$165$			6.46410i			0.503230i
$166$	10.3660	−	17.9545i	0.804560	−	1.39354i
$167$	−14.2583	+	8.23205i	−1.10334	+	0.637015i	−0.937097	−	0.349069i	$-0.886498\pi$
$167$	−14.2583	+	8.23205i	−1.10334	+	0.637015i	−0.166246	+	0.986084i	$0.553165\pi$
$168$	5.66025	+	21.1244i	0.436698	+	1.62978i
$169$	6.63397	+	3.83013i	0.510306	+	0.294625i
$170$	9.46410	−	5.46410i	0.725863	−	0.419077i
$171$	−9.00000	−	9.00000i	−0.688247	−	0.688247i
$172$	−12.6603	+	3.39230i	−0.965335	+	0.258661i
$173$	7.59808	−	2.03590i	0.577671	−	0.154786i	0.0418586	−	0.999124i	$-0.486672\pi$
$173$	7.59808	−	2.03590i	0.577671	−	0.154786i	0.535812	+	0.844337i	$0.320005\pi$
$174$	1.09808	−	1.90192i	0.0832449	−	0.144184i
$175$	−2.83013	−	4.90192i	−0.213937	−	0.370551i
$176$	2.00000	+	7.46410i	0.150756	+	0.562628i
$177$	−2.59808	−	0.696152i	−0.195283	−	0.0523260i
$178$	−15.8564	−	15.8564i	−1.18849	−	1.18849i
$179$	−5.92820	−	5.92820i	−0.443095	−	0.443095i	0.449956	−	0.893051i	$-0.351440\pi$
$179$	−5.92820	−	5.92820i	−0.443095	−	0.443095i	−0.893051	+	0.449956i	$0.851440\pi$
$180$	−3.00000	+	11.1962i	−0.223607	+	0.834512i
$181$	−7.73205	+	7.73205i	−0.574719	+	0.574719i	−0.933443	−	0.358725i	$-0.883212\pi$
$181$	−7.73205	+	7.73205i	−0.574719	+	0.574719i	0.358725	+	0.933443i	$0.383212\pi$
$182$		−	14.5885i		−	1.08137i
$183$	−3.69615	+	0.990381i	−0.273227	+	0.0732111i
$184$	−17.6603	−	4.73205i	−1.30193	−	0.348851i
$185$	10.0981	−	5.83013i	0.742425	−	0.428639i
$186$	21.7583	+	5.83013i	1.59540	+	0.427486i
$187$	−2.00000	−	7.46410i	−0.146254	−	0.545829i
$188$	2.07180	+	1.19615i	0.151101	+	0.0872384i
$189$	20.0885	+	11.5981i	1.46122	+	0.843636i
$190$	−11.1962	−	3.00000i	−0.812254	−	0.217643i
$191$	1.40192	−	2.42820i	0.101440	−	0.175699i	−0.810838	−	0.585270i	$-0.800988\pi$
$191$	1.40192	−	2.42820i	0.101440	−	0.175699i	0.912278	+	0.409572i	$0.134322\pi$
$192$			13.8564i			1.00000i
$193$	2.23205	+	3.86603i	0.160667	+	0.278283i	0.935108	−	0.354363i	$-0.115302\pi$
$193$	2.23205	+	3.86603i	0.160667	+	0.278283i	−0.774441	+	0.632646i	$0.781969\pi$
$194$	−0.366025	−	1.36603i	−0.0262791	−	0.0980749i
$195$	3.86603	−	6.69615i	0.276852	−	0.479521i
$196$	22.3923	−	12.9282i	1.59945	−	0.923443i
$197$	3.53590	−	3.53590i	0.251922	−	0.251922i	−0.569836	−	0.821758i	$-0.692993\pi$
$197$	3.53590	−	3.53590i	0.251922	−	0.251922i	0.821758	+	0.569836i	$0.192993\pi$
$198$	7.09808	+	4.09808i	0.504438	+	0.291238i
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$	−0.928203	−	3.46410i	−0.0656339	−	0.244949i
$201$	−3.86603	+	14.4282i	−0.272688	+	1.01769i
$202$	0.633975	+	0.366025i	0.0446063	+	0.0257535i
$203$	−3.86603	−	1.03590i	−0.271342	−	0.0727058i
$204$		−	13.8564i		−	0.970143i
$205$	−1.50000	+	0.401924i	−0.104765	+	0.0280716i
$206$	−5.83013	+	21.7583i	−0.406204	+	1.51597i
$207$	−16.7942	+	9.69615i	−1.16728	+	0.673929i
$208$	2.39230	−	8.92820i	0.165876	−	0.619060i
$209$	−4.09808	+	7.09808i	−0.283470	+	0.490984i
$210$	21.1244			1.45772
$211$	−4.96410	+	18.5263i	−0.341743	+	1.27540i	0.554629	+	0.832098i	$0.312860\pi$
$211$	−4.96410	+	18.5263i	−0.341743	+	1.27540i	−0.896371	+	0.443304i	$0.853806\pi$
$212$	−11.4641	−	11.4641i	−0.787358	−	0.787358i
$213$		−	5.07180i		−	0.347514i
$214$			18.7846i			1.28409i
$215$			12.6603i			0.863422i
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$		−	41.0526i		−	2.78683i
$218$	3.46410			0.234619
$219$			12.9282i			0.873607i
$220$	7.46410			0.503230
$221$	−2.39230	+	8.92820i	−0.160924	+	0.600576i
$222$		−	14.7846i		−	0.992278i
$223$	7.79423	−	13.5000i	0.521940	−	0.904027i	−0.477734	−	0.878504i	$-0.658542\pi$
$223$	7.79423	−	13.5000i	0.521940	−	0.904027i	0.999674	−	0.0255224i	$-0.00812491\pi$
$224$	24.3923	−	6.53590i	1.62978	−	0.436698i
$225$	−3.29423	−	1.90192i	−0.219615	−	0.126795i
$226$	17.0263	+	4.56218i	1.13257	+	0.303472i
$227$	19.6244	−	5.25833i	1.30251	−	0.349008i	0.460114	−	0.887860i	$-0.347809\pi$
$227$	19.6244	−	5.25833i	1.30251	−	0.349008i	0.842400	+	0.538852i	$0.181142\pi$
$228$	−10.3923	+	10.3923i	−0.688247	+	0.688247i
$229$	16.5263	+	4.42820i	1.09209	+	0.292624i	0.759539	−	0.650462i	$-0.225425\pi$
$229$	16.5263	+	4.42820i	1.09209	+	0.292624i	0.332549	+	0.943086i	$0.392091\pi$
$230$	−8.83013	+	15.2942i	−0.582241	+	1.00847i
$231$	3.86603	−	14.4282i	0.254366	−	0.949306i
$232$	−2.19615	−	1.26795i	−0.144184	−	0.0832449i
$233$			9.07180i			0.594313i	0.954829	+	0.297157i	$0.0960383\pi$
$233$			9.07180i			0.594313i	−0.954829	+	0.297157i	$0.903962\pi$
$234$	−4.90192	−	8.49038i	−0.320449	−	0.555034i
$235$	1.63397	−	1.63397i	0.106589	−	0.106589i
$236$	−0.803848	+	3.00000i	−0.0523260	+	0.195283i
$237$	−1.50000	+	2.59808i	−0.0974355	+	0.168763i
$238$	−24.3923	+	6.53590i	−1.58112	+	0.423659i
$239$	−0.401924	−	0.696152i	−0.0259983	−	0.0450304i	0.852734	−	0.522346i	$-0.174943\pi$
$239$	−0.401924	−	0.696152i	−0.0259983	−	0.0450304i	−0.878732	+	0.477316i	$0.841610\pi$
$240$	12.9282	+	3.46410i	0.834512	+	0.223607i
$241$	−2.76795	+	4.79423i	−0.178299	+	0.308823i	−0.941298	−	0.337576i	$-0.890393\pi$
$241$	−2.76795	+	4.79423i	−0.178299	+	0.308823i	0.762999	+	0.646400i	$0.223726\pi$
$242$	−2.66025	+	9.92820i	−0.171008	+	0.638209i
$243$	15.5885			1.00000
$244$	1.14359	+	4.26795i	0.0732111	+	0.273227i
$245$	−6.46410	−	24.1244i	−0.412976	−	1.54125i
$246$	−0.509619	+	1.90192i	−0.0324921	+	0.121262i
$247$	8.49038	−	4.90192i	0.540230	−	0.311902i
$248$	6.73205	−	25.1244i	0.427486	−	1.59540i
$249$	−24.5263	+	6.57180i	−1.55429	+	0.416471i
$250$	−17.1244			−1.08304
$251$	−13.3923	+	13.3923i	−0.845315	+	0.845315i	−0.989544	−	0.144229i	$-0.953930\pi$
$251$	−13.3923	+	13.3923i	−0.845315	+	0.845315i	0.144229	+	0.989544i	$0.453930\pi$
$252$	13.3923	−	23.1962i	0.843636	−	1.46122i
$253$	8.83013	+	8.83013i	0.555145	+	0.555145i
$254$	−0.392305	+	0.392305i	−0.0246154	+	0.0246154i
$255$	−12.9282	−	3.46410i	−0.809595	−	0.216930i
$256$	16.0000			1.00000
$257$	12.1603	+	21.0622i	0.758536	+	1.31382i	0.943597	+	0.331096i	$0.107418\pi$
$257$	12.1603	+	21.0622i	0.758536	+	1.31382i	−0.185061	+	0.982727i	$0.559248\pi$
$258$	13.9019	+	8.02628i	0.865496	+	0.499694i
$259$	−26.0263	+	6.97372i	−1.61719	+	0.433326i
$260$	−7.73205	−	4.46410i	−0.479521	−	0.276852i
$261$	−2.59808	+	0.696152i	−0.160817	+	0.0430908i
$262$	3.56218	+	6.16987i	0.220072	+	0.381176i
$263$	−8.59808	−	4.96410i	−0.530180	−	0.306100i	0.210910	−	0.977506i	$-0.432357\pi$
$263$	−8.59808	−	4.96410i	−0.530180	−	0.306100i	−0.741090	+	0.671406i	$0.765691\pi$
$264$	4.73205	−	8.19615i	0.291238	−	0.504438i
$265$	−13.5622	+	7.83013i	−0.833118	+	0.481001i
$266$	23.1962	+	13.3923i	1.42225	+	0.821135i
$267$			27.4641i			1.68078i
$268$	16.6603	+	4.46410i	1.01769	+	0.272688i
$269$	4.26795	+	4.26795i	0.260221	+	0.260221i	0.825144	−	0.564923i	$-0.191094\pi$
$269$	4.26795	+	4.26795i	0.260221	+	0.260221i	−0.564923	+	0.825144i	$0.691094\pi$
$270$	12.2942	−	7.09808i	0.748203	−	0.431975i
$271$	−1.07180			−0.0651070			−0.0325535	−	0.999470i	$-0.510364\pi$
$271$	−1.07180			−0.0651070			−0.0325535	+	0.999470i	$0.510364\pi$
$272$	−16.0000			−0.970143
$273$	−12.6340	+	12.6340i	−0.764643	+	0.764643i
$274$	0.901924	−	0.241670i	0.0544872	−	0.0145998i
$275$	−0.633975	+	2.36603i	−0.0382301	+	0.142677i
$276$	11.1962	+	19.3923i	0.673929	+	1.16728i
$277$	−1.79423	−	6.69615i	−0.107805	−	0.402333i	0.890844	−	0.454310i	$-0.150114\pi$
$277$	−1.79423	−	6.69615i	−0.107805	−	0.402333i	−0.998648	+	0.0519775i	$0.983448\pi$
$278$	−20.4904	+	11.8301i	−1.22893	+	0.709524i
$279$	−13.7942	−	23.8923i	−0.825839	−	1.43039i
$280$		−	24.3923i		−	1.45772i
$281$	−10.0359	−	5.79423i	−0.598692	−	0.345655i	0.169835	−	0.985472i	$-0.445676\pi$
$281$	−10.0359	−	5.79423i	−0.598692	−	0.345655i	−0.768527	+	0.639818i	$0.779010\pi$
$282$	−0.758330	−	2.83013i	−0.0451579	−	0.168532i
$283$	−13.1603	−	3.52628i	−0.782296	−	0.209616i	−0.154499	−	0.987993i	$-0.549376\pi$
$283$	−13.1603	−	3.52628i	−0.782296	−	0.209616i	−0.627797	+	0.778377i	$0.716043\pi$
$284$	−5.85641			−0.347514
$285$	7.09808	+	12.2942i	0.420454	+	0.728247i
$286$	−4.46410	+	4.46410i	−0.263968	+	0.263968i
$287$	3.58846			0.211820
$288$	12.0000	−	12.0000i	0.707107	−	0.707107i
$289$	−1.00000			−0.0588235
$290$	−1.73205	+	1.73205i	−0.101710	+	0.101710i
$291$	−0.866025	+	1.50000i	−0.0507673	+	0.0879316i
$292$	14.9282			0.873607
$293$	2.13397	+	0.571797i	0.124668	+	0.0334047i	0.320614	−	0.947210i	$-0.396111\pi$
$293$	2.13397	+	0.571797i	0.124668	+	0.0334047i	−0.195945	+	0.980615i	$0.562778\pi$
$294$	−30.5885	−	8.19615i	−1.78396	−	0.478009i
$295$	2.59808	+	1.50000i	0.151266	+	0.0873334i
$296$	−17.0718			−0.992278
$297$	−2.59808	−	9.69615i	−0.150756	−	0.562628i
$298$	−20.3660	+	11.7583i	−1.17977	+	0.681142i
$299$	−3.86603	−	14.4282i	−0.223578	−	0.834405i
$300$	−2.19615	+	3.80385i	−0.126795	+	0.219615i
$301$	7.57180	−	28.2583i	0.436431	−	1.62878i
$302$	9.56218	−	2.56218i	0.550242	−	0.147437i
$303$	−0.232051	−	0.866025i	−0.0133310	−	0.0497519i
$304$	12.0000	+	12.0000i	0.688247	+	0.688247i
$305$	4.26795			0.244382
$306$	−12.0000	+	12.0000i	−0.685994	+	0.685994i
$307$	7.92820	+	7.92820i	0.452486	+	0.452486i	0.896179	−	0.443693i	$-0.146332\pi$
$307$	7.92820	+	7.92820i	0.452486	+	0.452486i	−0.443693	+	0.896179i	$0.646332\pi$
$308$	−16.6603	−	4.46410i	−0.949306	−	0.254366i
$309$	23.8923	−	13.7942i	1.35919	−	0.784726i
$310$	−21.7583	−	12.5622i	−1.23579	−	0.713484i
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	−0.216391	−	0.976307i	$-0.569428\pi$
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	0.737311	+	0.675553i	$0.236095\pi$
$312$	−9.80385	+	5.66025i	−0.555034	+	0.320449i
$313$	25.1603	+	14.5263i	1.42214	+	0.821074i	0.996482	−	0.0838094i	$-0.0267087\pi$
$313$	25.1603	+	14.5263i	1.42214	+	0.821074i	0.425660	+	0.904883i	$0.360042\pi$
$314$	−2.36603	−	4.09808i	−0.133523	−	0.231268i
$315$	−18.2942	−	18.2942i	−1.03076	−	1.03076i
$316$	3.00000	+	1.73205i	0.168763	+	0.0974355i
$317$	−33.4545	+	8.96410i	−1.87899	+	0.503474i	−0.879364	+	0.476150i	$0.842032\pi$
$317$	−33.4545	+	8.96410i	−1.87899	+	0.503474i	−0.999627	+	0.0273246i	$0.991301\pi$
$318$			19.8564i			1.11349i
$319$	0.866025	+	1.50000i	0.0484881	+	0.0839839i
$320$	4.00000	−	14.9282i	0.223607	−	0.834512i
$321$	16.2679	−	16.2679i	0.907988	−	0.907988i
$322$	28.8564	−	28.8564i	1.60810	−	1.60810i
$323$	−12.0000	−	12.0000i	−0.667698	−	0.667698i
$324$		−	18.0000i		−	1.00000i
$325$	2.07180	−	2.07180i	0.114923	−	0.114923i
$326$	3.85641			0.213587
$327$	−3.00000	−	3.00000i	−0.165900	−	0.165900i
$328$	2.19615	+	0.588457i	0.121262	+	0.0324921i
$329$	−4.62436	+	2.66987i	−0.254949	+	0.147195i
$330$	−6.46410	−	6.46410i	−0.355837	−	0.355837i
$331$	1.35641	+	5.06218i	0.0745548	+	0.278242i	0.993132	−	0.116999i	$-0.0373275\pi$
$331$	1.35641	+	5.06218i	0.0745548	+	0.278242i	−0.918577	+	0.395242i	$0.870661\pi$
$332$	7.58846	+	28.3205i	0.416471	+	1.55429i
$333$	−12.8038	+	12.8038i	−0.701647	+	0.701647i
$334$	6.02628	−	22.4904i	0.329743	−	1.23062i
$335$	8.33013	−	14.4282i	0.455123	−	0.788297i
$336$	−26.7846	−	15.4641i	−1.46122	−	0.843636i
$337$	−9.69615	−	16.7942i	−0.528183	−	0.914840i	−0.999460	−	0.0328547i	$-0.989540\pi$
$337$	−9.69615	−	16.7942i	−0.528183	−	0.914840i	0.471277	−	0.881985i	$-0.343793\pi$
$338$	−10.4641	+	2.80385i	−0.569172	+	0.152509i
$339$	−10.7942	−	18.6962i	−0.586262	−	1.01544i
$340$	−4.00000	+	14.9282i	−0.216930	+	0.809595i
$341$	−12.5622	+	12.5622i	−0.680280	+	0.680280i
$342$	18.0000			0.973329
$343$			26.4641i			1.42893i
$344$	9.26795	−	16.0526i	0.499694	−	0.865496i
$345$	20.8923	−	5.59808i	1.12480	−	0.301390i
$346$	−5.56218	+	9.63397i	−0.299025	+	0.517926i
$347$	−1.76795	−	0.473721i	−0.0949085	−	0.0254307i	0.211052	−	0.977475i	$-0.432311\pi$
$347$	−1.76795	−	0.473721i	−0.0949085	−	0.0254307i	−0.305961	+	0.952044i	$0.598978\pi$
$348$	0.803848	+	3.00000i	0.0430908	+	0.160817i
$349$	−3.86603	+	1.03590i	−0.206944	+	0.0554504i	−0.360802	−	0.932643i	$-0.617497\pi$
$349$	−3.86603	+	1.03590i	−0.206944	+	0.0554504i	0.153858	+	0.988093i	$0.450830\pi$
$350$	7.73205	+	2.07180i	0.413296	+	0.110742i
$351$	−3.10770	+	11.5981i	−0.165876	+	0.619060i
$352$	−9.46410	−	5.46410i	−0.504438	−	0.291238i
$353$	−11.7679	+	20.3827i	−0.626345	+	1.08486i	0.361934	+	0.932204i	$0.382116\pi$
$353$	−11.7679	+	20.3827i	−0.626345	+	1.08486i	−0.988279	+	0.152657i	$0.951217\pi$
$354$	3.29423	−	1.90192i	0.175086	−	0.101086i
$355$	−1.46410	+	5.46410i	−0.0777064	+	0.290004i
$356$	31.7128			1.68078
$357$	26.7846	+	15.4641i	1.41759	+	0.818447i
$358$	11.8564			0.626631
$359$		−	28.9282i		−	1.52677i	−0.645942	−	0.763386i	$-0.723535\pi$
$359$		−	28.9282i		−	1.52677i	0.645942	−	0.763386i	$-0.276465\pi$
$360$	−8.19615	−	14.1962i	−0.431975	−	0.748203i
$361$		−	1.00000i		−	0.0526316i
$362$		−	15.4641i		−	0.812775i
$363$	10.9019	−	6.29423i	0.572203	−	0.330361i
$364$	14.5885	+	14.5885i	0.764643	+	0.764643i
$365$	3.73205	−	13.9282i	0.195344	−	0.729035i
$366$	2.70577	−	4.68653i	0.141433	−	0.244969i
$367$	−17.4545	+	30.2321i	−0.911117	+	1.57810i	−0.0986270	+	0.995124i	$0.531445\pi$
$367$	−17.4545	+	30.2321i	−0.911117	+	1.57810i	−0.812490	+	0.582976i	$0.801888\pi$
$368$	22.3923	−	12.9282i	1.16728	−	0.673929i
$369$	2.08846	−	1.20577i	0.108721	−	0.0627700i
$370$	−4.26795	+	15.9282i	−0.221880	+	0.828068i
$371$	34.9545	−	9.36603i	1.81475	−	0.486260i
$372$	−27.5885	+	15.9282i	−1.43039	+	0.825839i
$373$	−1.59808	−	0.428203i	−0.0827452	−	0.0221715i	0.217209	−	0.976125i	$-0.430305\pi$
$373$	−1.59808	−	0.428203i	−0.0827452	−	0.0221715i	−0.299954	+	0.953954i	$0.596971\pi$
$374$	9.46410	+	5.46410i	0.489377	+	0.282542i
$375$	14.8301	+	14.8301i	0.765824	+	0.765824i
$376$	−3.26795	+	0.875644i	−0.168532	+	0.0451579i
$377$		−	2.07180i		−	0.106703i
$378$	−31.6865	+	8.49038i	−1.62978	+	0.436698i
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	−0.983209	−	0.182484i	$-0.941586\pi$
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	0.182484	+	0.983209i	$0.441586\pi$
$380$	14.1962	−	8.19615i	0.728247	−	0.420454i
$381$	0.679492			0.0348114
$382$	1.02628	+	3.83013i	0.0525090	+	0.195966i
$383$	3.66987	+	6.35641i	0.187522	+	0.324797i	0.944423	−	0.328732i	$-0.106621\pi$
$383$	3.66987	+	6.35641i	0.187522	+	0.324797i	−0.756902	+	0.653529i	$0.773288\pi$
$384$	−13.8564	−	13.8564i	−0.707107	−	0.707107i
$385$	−8.33013	+	14.4282i	−0.424543	+	0.735329i
$386$	−6.09808	−	1.63397i	−0.310384	−	0.0831671i
$387$	−5.08846	−	18.9904i	−0.258661	−	0.965335i
$388$	1.73205	+	1.00000i	0.0879316	+	0.0507673i
$389$	2.40192	+	8.96410i	0.121782	+	0.454498i	0.999705	−	0.0243053i	$-0.00773738\pi$
$389$	2.40192	+	8.96410i	0.121782	+	0.454498i	−0.877922	+	0.478803i	$0.841071\pi$
$390$	2.83013	+	10.5622i	0.143309	+	0.534837i
$391$	−22.3923	+	12.9282i	−1.13243	+	0.653807i
$392$	−9.46410	+	35.3205i	−0.478009	+	1.78396i
$393$	2.25833	−	8.42820i	0.113918	−	0.425147i
$394$			7.07180i			0.356272i
$395$	2.36603	−	2.36603i	0.119048	−	0.119048i
$396$	−11.1962	+	3.00000i	−0.562628	+	0.150756i
$397$	17.0526	+	17.0526i	0.855843	+	0.855843i	0.990845	−	0.135002i	$-0.0431041\pi$
$397$	17.0526	+	17.0526i	0.855843	+	0.855843i	−0.135002	+	0.990845i	$0.543104\pi$
$398$	21.8564	+	21.8564i	1.09556	+	1.09556i
$399$	−8.49038	−	31.6865i	−0.425051	−	1.58631i
$400$	4.39230	+	2.53590i	0.219615	+	0.126795i
$401$	−16.1603	−	27.9904i	−0.807005	−	1.39777i	−0.914929	−	0.403614i	$-0.867754\pi$
$401$	−16.1603	−	27.9904i	−0.807005	−	1.39777i	0.107925	−	0.994159i	$-0.465579\pi$
$402$	−10.5622	−	18.2942i	−0.526794	−	0.912433i
$403$	20.5263	−	5.50000i	1.02249	−	0.273975i
$404$	−1.00000	+	0.267949i	−0.0497519	+	0.0133310i
$405$	−16.7942	−	4.50000i	−0.834512	−	0.223607i
$406$	4.90192	−	2.83013i	0.243278	−	0.140457i
$407$	10.0981	+	5.83013i	0.500543	+	0.288989i
$408$	13.8564	+	13.8564i	0.685994	+	0.685994i
$409$	−19.6244	+	11.3301i	−0.970362	+	0.560239i	−0.899347	−	0.437236i	$-0.855957\pi$
$409$	−19.6244	+	11.3301i	−0.970362	+	0.560239i	−0.0710154	+	0.997475i	$0.522624\pi$
$410$	1.09808	−	1.90192i	0.0542301	−	0.0939293i
$411$	−0.990381	−	0.571797i	−0.0488519	−	0.0282047i
$412$	−15.9282	−	27.5885i	−0.784726	−	1.35919i
$413$	−4.90192	−	4.90192i	−0.241208	−	0.241208i
$414$	7.09808	−	26.4904i	0.348851	−	1.30193i
$415$	28.3205			1.39020
$416$	6.53590	+	11.3205i	0.320449	+	0.555034i
$417$	27.9904	+	7.50000i	1.37069	+	0.367277i
$418$	−3.00000	−	11.1962i	−0.146735	−	0.547622i
$419$	−4.96410	+	18.5263i	−0.242512	+	0.905068i	0.732105	+	0.681191i	$0.238538\pi$
$419$	−4.96410	+	18.5263i	−0.242512	+	0.905068i	−0.974618	+	0.223876i	$0.928129\pi$
$420$	−21.1244	+	21.1244i	−1.03076	+	1.03076i
$421$	−4.79423	−	17.8923i	−0.233656	−	0.872018i	−0.978750	−	0.205058i	$-0.934262\pi$
$421$	−4.79423	−	17.8923i	−0.233656	−	0.872018i	0.745094	−	0.666960i	$-0.232405\pi$
$422$	−13.5622	−	23.4904i	−0.660196	−	1.14349i
$423$	−1.79423	+	3.10770i	−0.0872384	+	0.151101i
$424$	22.9282			1.11349
$425$	−4.39230	−	2.53590i	−0.213058	−	0.123009i
$426$	5.07180	+	5.07180i	0.245729	+	0.245729i
$427$	−9.52628	−	2.55256i	−0.461009	−	0.123527i
$428$	−18.7846	−	18.7846i	−0.907988	−	0.907988i
$429$	7.73205			0.373307
$430$	−12.6603	−	12.6603i	−0.610532	−	0.610532i
$431$	−3.32051			−0.159943			−0.0799716	−	0.996797i	$-0.525483\pi$
$431$	−3.32051			−0.159943			−0.0799716	+	0.996797i	$0.525483\pi$
$432$	−20.7846			−1.00000
$433$	3.60770			0.173375			0.0866874	−	0.996236i	$-0.472372\pi$
$433$	3.60770			0.173375			0.0866874	+	0.996236i	$0.472372\pi$
$434$	41.0526	+	41.0526i	1.97059	+	1.97059i
$435$	3.00000			0.143839
$436$	−3.46410	+	3.46410i	−0.165900	+	0.165900i
$437$	26.4904	+	7.09808i	1.26721	+	0.339547i
$438$	−12.9282	−	12.9282i	−0.617733	−	0.617733i
$439$	5.93782	+	3.42820i	0.283397	+	0.163619i	0.634960	−	0.772545i	$-0.281016\pi$
$439$	5.93782	+	3.42820i	0.283397	+	0.163619i	−0.351563	+	0.936164i	$0.614350\pi$
$440$	−7.46410	+	7.46410i	−0.355837	+	0.355837i
$441$	19.3923	+	33.5885i	0.923443	+	1.59945i
$442$	−6.53590	−	11.3205i	−0.310881	−	0.538462i
$443$	−1.16025	−	4.33013i	−0.0551253	−	0.205731i	0.932870	−	0.360213i	$-0.117296\pi$
$443$	−1.16025	−	4.33013i	−0.0551253	−	0.205731i	−0.987996	+	0.154482i	$0.950629\pi$
$444$	14.7846	+	14.7846i	0.701647	+	0.701647i
$445$	7.92820	−	29.5885i	0.375833	−	1.40263i
$446$	5.70577	+	21.2942i	0.270176	+	1.00831i
$447$	27.8205	+	7.45448i	1.31586	+	0.352585i
$448$	−17.8564	+	30.9282i	−0.843636	+	1.46122i
$449$	35.3205			1.66688			0.833439	−	0.552612i	$-0.186369\pi$
$449$	35.3205			1.66688			0.833439	+	0.552612i	$0.186369\pi$
$450$	5.19615	−	1.39230i	0.244949	−	0.0656339i
$451$	−1.09808	−	1.09808i	−0.0517064	−	0.0517064i
$452$	−21.5885	+	12.4641i	−1.01544	+	0.586262i
$453$	−10.5000	−	6.06218i	−0.493333	−	0.284826i
$454$	−14.3660	+	24.8827i	−0.674231	+	1.16780i
$455$	17.2583	−	9.96410i	0.809083	−	0.467124i
$456$		−	20.7846i		−	0.973329i
$457$	25.9641	+	14.9904i	1.21455	+	0.701220i	0.963747	−	0.266818i	$-0.0859722\pi$
$457$	25.9641	+	14.9904i	1.21455	+	0.701220i	0.250802	+	0.968038i	$0.419306\pi$
$458$	−20.9545	+	12.0981i	−0.979139	+	0.565306i
$459$	20.7846			0.970143
$460$	−6.46410	−	24.1244i	−0.301390	−	1.12480i
$461$	4.59808	−	1.23205i	0.214154	−	0.0573823i	−0.150147	−	0.988664i	$-0.547975\pi$
$461$	4.59808	−	1.23205i	0.214154	−	0.0573823i	0.364301	+	0.931281i	$0.381308\pi$
$462$	10.5622	+	18.2942i	0.491397	+	0.851125i
$463$	−5.33013	−	9.23205i	−0.247712	−	0.429050i	0.715179	−	0.698942i	$-0.246345\pi$
$463$	−5.33013	−	9.23205i	−0.247712	−	0.429050i	−0.962891	+	0.269892i	$0.913012\pi$
$464$	3.46410	−	0.928203i	0.160817	−	0.0430908i
$465$	7.96410	+	29.7224i	0.369326	+	1.37834i
$466$	−9.07180	−	9.07180i	−0.420243	−	0.420243i
$467$	21.7846	+	21.7846i	1.00807	+	1.00807i	0.999967	+	0.00810436i	$0.00257972\pi$
$467$	21.7846	+	21.7846i	1.00807	+	1.00807i	0.00810436	+	0.999967i	$0.497420\pi$
$468$	13.3923	+	3.58846i	0.619060	+	0.165876i
$469$	−27.2224	+	27.2224i	−1.25702	+	1.25702i
$470$			3.26795i			0.150739i
$471$	−1.50000	+	5.59808i	−0.0691164	+	0.257946i
$472$	−2.19615	−	3.80385i	−0.101086	−	0.175086i
$473$	−10.9641	+	6.33013i	−0.504130	+	0.291060i
$474$	−1.09808	−	4.09808i	−0.0504363	−	0.188231i
$475$	1.39230	+	5.19615i	0.0638833	+	0.238416i
$476$	17.8564	−	30.9282i	0.818447	−	1.41759i
$477$	17.1962	−	17.1962i	0.787358	−	0.787358i
$478$	1.09808	+	0.294229i	0.0502248	+	0.0134577i
$479$	9.33013	−	16.1603i	0.426304	−	0.738381i	−0.570237	−	0.821480i	$-0.693149\pi$
$479$	9.33013	−	16.1603i	0.426304	−	0.738381i	0.996541	+	0.0830995i	$0.0264819\pi$
$480$	−16.3923	+	9.46410i	−0.748203	+	0.431975i
$481$	−6.97372	−	12.0788i	−0.317974	−	0.550748i
$482$	−2.02628	−	7.56218i	−0.0922945	−	0.344448i
$483$	−49.9808			−2.27420
$484$	−7.26795	−	12.5885i	−0.330361	−	0.572203i
$485$	1.36603	−	1.36603i	0.0620280	−	0.0620280i
$486$	−15.5885	+	15.5885i	−0.707107	+	0.707107i
$487$		−	6.78461i		−	0.307440i	−0.988114	−	0.153720i	$-0.950875\pi$
$487$		−	6.78461i		−	0.307440i	0.988114	−	0.153720i	$-0.0491254\pi$
$488$	−5.41154	−	3.12436i	−0.244969	−	0.141433i
$489$	−3.33975	−	3.33975i	−0.151029	−	0.151029i
$490$	30.5885	+	17.6603i	1.38185	+	0.797809i
$491$	0.500000	+	0.133975i	0.0225647	+	0.00604619i	0.270084	−	0.962837i	$-0.412949\pi$
$491$	0.500000	+	0.133975i	0.0225647	+	0.00604619i	−0.247519	+	0.968883i	$0.579615\pi$
$492$	−1.39230	−	2.41154i	−0.0627700	−	0.108721i
$493$	−3.46410	+	0.928203i	−0.156015	+	0.0418042i
$494$	−3.58846	+	13.3923i	−0.161452	+	0.602548i
$495$			11.1962i			0.503230i
$496$	18.3923	+	31.8564i	0.825839	+	1.43039i
$497$	6.53590	−	11.3205i	0.293175	−	0.507794i
$498$	17.9545	−	31.0981i	0.804560	−	1.39354i
$499$	−2.50000	+	9.33013i	−0.111915	+	0.417674i	−0.999038	−	0.0438606i	$-0.986034\pi$
$499$	−2.50000	+	9.33013i	−0.111915	+	0.417674i	0.887122	+	0.461534i	$0.152701\pi$
$500$	17.1244	−	17.1244i	0.765824	−	0.765824i
$501$	−24.6962	+	14.2583i	−1.10334	+	0.637015i
$502$		−	26.7846i		−	1.19546i
$503$			13.8564i			0.617827i	0.951090	+	0.308913i	$0.0999653\pi$
$503$			13.8564i			0.617827i	−0.951090	+	0.308913i	$0.900035\pi$
$504$	9.80385	+	36.5885i	0.436698	+	1.62978i
$505$			1.00000i			0.0444994i
$506$	−17.6603			−0.785094
$507$	11.4904	+	6.63397i	0.510306	+	0.294625i
$508$		−	0.784610i		−	0.0348114i
$509$	1.25833	−	4.69615i	0.0557745	−	0.208153i	−0.932415	−	0.361389i	$-0.882303\pi$
$509$	1.25833	−	4.69615i	0.0557745	−	0.208153i	0.988190	+	0.153236i	$0.0489693\pi$
$510$	16.3923	−	9.46410i	0.725863	−	0.419077i
$511$	−16.6603	+	28.8564i	−0.737006	+	1.27653i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−15.5885	−	15.5885i	−0.688247	−	0.688247i
$514$	−33.2224	−	8.90192i	−1.46538	−	0.392647i
$515$	−29.7224	+	7.96410i	−1.30973	+	0.350940i
$516$	−21.9282	+	5.87564i	−0.965335	+	0.258661i
$517$	2.23205	+	0.598076i	0.0981655	+	0.0263034i
$518$	19.0526	−	33.0000i	0.837121	−	1.44994i
$519$	13.1603	−	3.52628i	0.577671	−	0.154786i
$520$	12.1962	−	3.26795i	0.534837	−	0.143309i
$521$		−	41.8564i		−	1.83376i	−0.399160	−	0.916881i	$-0.630698\pi$
$521$		−	41.8564i		−	1.83376i	0.399160	−	0.916881i	$-0.369302\pi$
$522$	1.90192	−	3.29423i	0.0832449	−	0.144184i
$523$	22.1244	−	22.1244i	0.967431	−	0.967431i	−0.0320556	−	0.999486i	$-0.510205\pi$
$523$	22.1244	−	22.1244i	0.967431	−	0.967431i	0.999486	+	0.0320556i	$0.0102054\pi$
$524$	−9.73205	−	2.60770i	−0.425147	−	0.113918i
$525$	−4.90192	−	8.49038i	−0.213937	−	0.370551i
$526$	13.5622	−	3.63397i	0.591339	−	0.158449i
$527$	−18.3923	−	31.8564i	−0.801181	−	1.38769i
$528$	3.46410	+	12.9282i	0.150756	+	0.562628i
$529$	9.39230	−	16.2679i	0.408361	−	0.707302i
$530$	5.73205	−	21.3923i	0.248984	−	0.929222i
$531$	−4.50000	−	1.20577i	−0.195283	−	0.0523260i
$532$	−36.5885	+	9.80385i	−1.58631	+	0.425051i
$533$	0.480762	+	1.79423i	0.0208241	+	0.0777167i
$534$	−27.4641	−	27.4641i	−1.18849	−	1.18849i
$535$	−22.2224	+	12.8301i	−0.960760	+	0.554695i
$536$	−21.1244	+	12.1962i	−0.912433	+	0.526794i
$537$	−10.2679	−	10.2679i	−0.443095	−	0.443095i
$538$	−8.53590			−0.368009
$539$	17.6603	−	17.6603i	0.760681	−	0.760681i
$540$	−5.19615	+	19.3923i	−0.223607	+	0.834512i
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	0.306856	−	0.951756i	$-0.400723\pi$
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	−0.951756	+	0.306856i	$0.900723\pi$
$542$	1.07180	−	1.07180i	0.0460376	−	0.0460376i
$543$	−13.3923	+	13.3923i	−0.574719	+	0.574719i
$544$	16.0000	−	16.0000i	0.685994	−	0.685994i
$545$	2.36603	+	4.09808i	0.101349	+	0.175542i
$546$		−	25.2679i		−	1.08137i
$547$	21.4282	−	5.74167i	0.916204	−	0.245496i	0.230242	−	0.973133i	$-0.426048\pi$
$547$	21.4282	−	5.74167i	0.916204	−	0.245496i	0.685962	+	0.727637i	$0.259382\pi$
$548$	−0.660254	+	1.14359i	−0.0282047	+	0.0488519i
$549$	−6.40192	+	1.71539i	−0.273227	+	0.0732111i
$550$	−1.73205	−	3.00000i	−0.0738549	−	0.127920i
$551$	3.29423	+	1.90192i	0.140339	+	0.0810247i
$552$	−30.5885	−	8.19615i	−1.30193	−	0.348851i
$553$	−6.69615	+	3.86603i	−0.284749	+	0.164400i
$554$	8.49038	+	4.90192i	0.360722	+	0.208263i
$555$	17.4904	−	10.0981i	0.742425	−	0.428639i
$556$	8.66025	−	32.3205i	0.367277	−	1.37069i
$557$	−23.9808	−	23.9808i	−1.01610	−	1.01610i	−0.999868	−	0.0162292i	$-0.994834\pi$
$557$	−23.9808	−	23.9808i	−1.01610	−	1.01610i	−0.0162292	−	0.999868i	$-0.505166\pi$
$558$	37.6865	+	10.0981i	1.59540	+	0.427486i
$559$	15.1436			0.640506
$560$	24.3923	+	24.3923i	1.03076	+	1.03076i
$561$	−3.46410	−	12.9282i	−0.146254	−	0.545829i
$562$	15.8301	−	4.24167i	0.667754	−	0.178924i
$563$	−1.64359	+	6.13397i	−0.0692692	+	0.258516i	−0.991873	−	0.127233i	$-0.959390\pi$
$563$	−1.64359	+	6.13397i	−0.0692692	+	0.258516i	0.922604	+	0.385749i	$0.126057\pi$
$564$	3.58846	+	2.07180i	0.151101	+	0.0872384i
$565$	6.23205	+	23.2583i	0.262184	+	0.978485i
$566$	16.6865	−	9.63397i	0.701387	−	0.404946i
$567$	34.7942	+	20.0885i	1.46122	+	0.843636i
$568$	5.85641	−	5.85641i	0.245729	−	0.245729i
$569$	−27.4808	−	15.8660i	−1.15205	−	0.665138i	−0.202667	−	0.979248i	$-0.564961\pi$
$569$	−27.4808	−	15.8660i	−1.15205	−	0.665138i	−0.949387	+	0.314109i	$0.898294\pi$
$570$	−19.3923	−	5.19615i	−0.812254	−	0.217643i
$571$	39.5526	+	10.5981i	1.65522	+	0.443516i	0.961068	−	0.276310i	$-0.0891117\pi$
$571$	39.5526	+	10.5981i	1.65522	+	0.443516i	0.694155	+	0.719826i	$0.255778\pi$
$572$		−	8.92820i		−	0.373307i
$573$	2.42820	−	4.20577i	0.101440	−	0.175699i
$574$	−3.58846	+	3.58846i	−0.149779	+	0.149779i
$575$	8.19615			0.341803
$576$			24.0000i			1.00000i
$577$	−25.1769			−1.04813			−0.524064	−	0.851679i	$-0.675585\pi$
$577$	−25.1769			−1.04813			−0.524064	+	0.851679i	$0.675585\pi$
$578$	1.00000	−	1.00000i	0.0415945	−	0.0415945i
$579$	3.86603	+	6.69615i	0.160667	+	0.278283i
$580$		−	3.46410i		−	0.143839i
$581$	−63.2128	−	16.9378i	−2.62251	−	0.702699i
$582$	−0.633975	−	2.36603i	−0.0262791	−	0.0980749i
$583$	−13.5622	−	7.83013i	−0.561688	−	0.324291i
$584$	−14.9282	+	14.9282i	−0.617733	+	0.617733i
$585$	6.69615	−	11.5981i	0.276852	−	0.479521i
$586$	−2.70577	+	1.56218i	−0.111774	+	0.0645330i
$587$	3.96410	+	14.7942i	0.163616	+	0.610623i	0.998213	+	0.0597617i	$0.0190341\pi$
$587$	3.96410	+	14.7942i	0.163616	+	0.610623i	−0.834597	+	0.550861i	$0.814299\pi$
$588$	38.7846	−	22.3923i	1.59945	−	0.923443i
$589$	−10.0981	+	37.6865i	−0.416084	+	1.55285i
$590$	−4.09808	+	1.09808i	−0.168715	+	0.0452071i
$591$	6.12436	−	6.12436i	0.251922	−	0.251922i
$592$	17.0718	−	17.0718i	0.701647	−	0.701647i
$593$	−5.46410			−0.224384			−0.112192	−	0.993687i	$-0.535787\pi$
$593$	−5.46410			−0.224384			−0.112192	+	0.993687i	$0.535787\pi$
$594$	12.2942	+	7.09808i	0.504438	+	0.291238i
$595$	−24.3923	−	24.3923i	−0.999987	−	0.999987i
$596$	8.60770	−	32.1244i	0.352585	−	1.31586i
$597$		−	37.8564i		−	1.54936i
$598$	18.2942	+	10.5622i	0.748107	+	0.431920i
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.968781	−	0.247917i	$-0.920254\pi$
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.269688	+	0.962948i	$0.586921\pi$
$600$	−1.60770	−	6.00000i	−0.0656339	−	0.244949i
$601$	−26.7679	−	15.4545i	−1.09189	−	0.630401i	−0.157809	−	0.987470i	$-0.550443\pi$
$601$	−26.7679	−	15.4545i	−1.09189	−	0.630401i	−0.934078	+	0.357068i	$0.883776\pi$
$602$	20.6865	+	35.8301i	0.843120	+	1.46033i
$603$	−6.69615	+	24.9904i	−0.272688	+	1.01769i
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$	−13.5622	+	3.63397i	−0.551381	+	0.147742i
$606$	1.09808	+	0.633975i	0.0446063	+	0.0257535i
$607$	0.598076	+	1.03590i	0.0242752	+	0.0420458i	0.877908	−	0.478830i	$-0.158939\pi$
$607$	0.598076	+	1.03590i	0.0242752	+	0.0420458i	−0.853633	+	0.520876i	$0.825606\pi$
$608$	−24.0000			−0.973329
$609$	−6.69615	−	1.79423i	−0.271342	−	0.0727058i
$610$	−4.26795	+	4.26795i	−0.172804	+	0.172804i
$611$	−1.95448	−	1.95448i	−0.0790699	−	0.0790699i
$612$		−	24.0000i		−	0.970143i
$613$	23.5885	−	23.5885i	0.952729	−	0.952729i	−0.0462032	−	0.998932i	$-0.514712\pi$
$613$	23.5885	−	23.5885i	0.952729	−	0.952729i	0.998932	+	0.0462032i	$0.0147122\pi$
$614$	−15.8564			−0.639912
$615$	−2.59808	+	0.696152i	−0.104765	+	0.0280716i
$616$	21.1244	−	12.1962i	0.851125	−	0.491397i
$617$	23.0885	−	13.3301i	0.929506	−	0.536651i	0.0428509	−	0.999081i	$-0.486356\pi$
$617$	23.0885	−	13.3301i	0.929506	−	0.536651i	0.886655	+	0.462431i	$0.153023\pi$
$618$	−10.0981	+	37.6865i	−0.406204	+	1.51597i
$619$	−1.91154	−	7.13397i	−0.0768314	−	0.286739i	0.916811	−	0.399322i	$-0.130754\pi$
$619$	−1.91154	−	7.13397i	−0.0768314	−	0.286739i	−0.993642	+	0.112583i	$0.964088\pi$
$620$	34.3205	−	9.19615i	1.37834	−	0.369326i
$621$	−29.0885	+	16.7942i	−1.16728	+	0.673929i
$622$	−3.88269	+	14.4904i	−0.155682	+	0.581011i
$623$	−35.3923	+	61.3013i	−1.41796	+	2.45598i
$624$	4.14359	−	15.4641i	0.165876	−	0.619060i
$625$	−8.52628	−	14.7679i	−0.341051	−	0.590718i
$626$	−39.6865	+	10.6340i	−1.58619	+	0.425019i
$627$	−7.09808	+	12.2942i	−0.283470	+	0.490984i
$628$	6.46410	+	1.73205i	0.257946	+	0.0691164i
$629$	−17.0718	+	17.0718i	−0.680697	+	0.680697i
$630$	36.5885			1.45772
$631$			16.2487i			0.646851i	0.946254	+	0.323425i	$0.104835\pi$
$631$			16.2487i			0.646851i	−0.946254	+	0.323425i	$0.895165\pi$
$632$	−4.73205	+	1.26795i	−0.188231	+	0.0504363i
$633$	−8.59808	+	32.0885i	−0.341743	+	1.27540i
$634$	24.4904	−	42.4186i	0.972637	−	1.68466i
$635$	−0.732051	−	0.196152i	−0.0290506	−	0.00778407i
$636$	−19.8564	−	19.8564i	−0.787358	−	0.787358i
$637$	−28.8564	+	7.73205i	−1.14333	+	0.306355i
$638$	−2.36603	−	0.633975i	−0.0936718	−	0.0250993i
$639$		−	8.78461i		−	0.347514i
$640$	10.9282	+	18.9282i	0.431975	+	0.748203i
$641$	9.23205	−	15.9904i	0.364644	−	0.631582i	−0.624075	−	0.781365i	$-0.714524\pi$
$641$	9.23205	−	15.9904i	0.364644	−	0.631582i	0.988719	+	0.149782i	$0.0478573\pi$
$642$			32.5359i			1.28409i
$643$	7.96410	−	29.7224i	0.314074	−	1.17214i	−0.610776	−	0.791804i	$-0.709142\pi$
$643$	7.96410	−	29.7224i	0.314074	−	1.17214i	0.924849	−	0.380334i	$-0.124191\pi$
$644$			57.7128i			2.27420i
$645$			21.9282i			0.863422i
$646$	24.0000			0.944267
$647$			25.6077i			1.00674i	0.864070	+	0.503371i	$0.167907\pi$
$647$			25.6077i			1.00674i	−0.864070	+	0.503371i	$0.832093\pi$
$648$	18.0000	+	18.0000i	0.707107	+	0.707107i
$649$			3.00000i			0.117760i
$650$			4.14359i			0.162525i
$651$		−	71.1051i		−	2.78683i
$652$	−3.85641	+	3.85641i	−0.151029	+	0.151029i
$653$	−12.6699	+	47.2846i	−0.495810	+	1.85039i	0.0296324	+	0.999561i	$0.490566\pi$
$653$	−12.6699	+	47.2846i	−0.495810	+	1.85039i	−0.525443	+	0.850829i	$0.676100\pi$
$654$	6.00000			0.234619
$655$	−4.86603	+	8.42820i	−0.190131	+	0.329317i
$656$	−2.78461	+	1.60770i	−0.108721	+	0.0627700i
$657$			22.3923i			0.873607i
$658$	1.95448	−	7.29423i	0.0761937	−	0.284359i
$659$	1.23205	−	0.330127i	0.0479939	−	0.0128599i	−0.234742	−	0.972058i	$-0.575425\pi$
$659$	1.23205	−	0.330127i	0.0479939	−	0.0128599i	0.282736	+	0.959198i	$0.408758\pi$
$660$	12.9282			0.503230
$661$	19.7942	+	5.30385i	0.769906	+	0.206296i	0.622330	−	0.782755i	$-0.286186\pi$
$661$	19.7942	+	5.30385i	0.769906	+	0.206296i	0.147576	+	0.989051i	$0.452853\pi$
$662$	−6.41858	−	3.70577i	−0.249465	−	0.144029i
$663$	−4.14359	+	15.4641i	−0.160924	+	0.600576i
$664$	−35.9090	−	20.7321i	−1.39354	−	0.804560i
$665$			36.5885i			1.41884i
$666$		−	25.6077i		−	0.992278i
$667$	4.09808	−	4.09808i	0.158678	−	0.158678i
$668$	16.4641	+	28.5167i	0.637015	+	1.10334i
$669$	13.5000	−	23.3827i	0.521940	−	0.904027i
$670$	6.09808	+	22.7583i	0.235589	+	0.879231i
$671$	2.13397	+	3.69615i	0.0823812	+	0.142688i
$672$	42.2487	−	11.3205i	1.62978	−	0.436698i
$673$	21.1603	−	36.6506i	0.815668	−	1.41278i	−0.0931795	−	0.995649i	$-0.529703\pi$
$673$	21.1603	−	36.6506i	0.815668	−	1.41278i	0.908847	−	0.417129i	$-0.136964\pi$
$674$	26.4904	+	7.09808i	1.02037	+	0.273408i
$675$	−5.70577	−	3.29423i	−0.219615	−	0.126795i
$676$	7.66025	−	13.2679i	0.294625	−	0.510306i
$677$	2.34936	+	8.76795i	0.0902934	+	0.336980i	0.996264	−	0.0863612i	$-0.0275239\pi$
$677$	2.34936	+	8.76795i	0.0902934	+	0.336980i	−0.905970	+	0.423341i	$0.860857\pi$
$678$	29.4904	+	7.90192i	1.13257	+	0.303472i
$679$	−3.86603	+	2.23205i	−0.148364	+	0.0856582i
$680$	−10.9282	−	18.9282i	−0.419077	−	0.725863i
$681$	33.9904	−	9.10770i	1.30251	−	0.349008i
$682$		−	25.1244i		−	0.962061i
$683$	15.3923	−	15.3923i	0.588970	−	0.588970i	−0.348382	−	0.937353i	$-0.613269\pi$
$683$	15.3923	−	15.3923i	0.588970	−	0.588970i	0.937353	+	0.348382i	$0.113269\pi$
$684$	−18.0000	+	18.0000i	−0.688247	+	0.688247i
$685$	0.901924	+	0.901924i	0.0344607	+	0.0344607i
$686$	−26.4641	−	26.4641i	−1.01040	−	1.01040i
$687$	28.6244	+	7.66987i	1.09209	+	0.292624i
$688$	6.78461	+	25.3205i	0.258661	+	0.965335i
$689$	9.36603	+	16.2224i	0.356817	+	0.618025i
$690$	−15.2942	+	26.4904i	−0.582241	+	1.00847i
$691$	−1.96410	+	0.526279i	−0.0747179	+	0.0200206i	−0.295984	−	0.955193i	$-0.595648\pi$
$691$	−1.96410	+	0.526279i	−0.0747179	+	0.0200206i	0.221266	+	0.975213i	$0.428981\pi$
$692$	−4.07180	−	15.1962i	−0.154786	−	0.577671i
$693$	6.69615	−	24.9904i	0.254366	−	0.949306i
$694$	2.24167	−	1.29423i	0.0850926	−	0.0491282i
$695$	−27.9904	−	16.1603i	−1.06174	−	0.612993i
$696$	−3.80385	−	2.19615i	−0.144184	−	0.0832449i
$697$	2.78461	−	1.60770i	0.105475	−	0.0608958i
$698$	2.83013	−	4.90192i	0.107122	−	0.185541i
$699$			15.7128i			0.594313i
$700$	−9.80385	+	5.66025i	−0.370551	+	0.213937i
$701$	17.0526	+	17.0526i	0.644066	+	0.644066i	0.951553	−	0.307486i	$-0.0994878\pi$
$701$	17.0526	+	17.0526i	0.644066	+	0.644066i	−0.307486	+	0.951553i	$0.599488\pi$
$702$	−8.49038	−	14.7058i	−0.320449	−	0.555034i
$703$	25.6077			0.965813
$704$	14.9282	−	4.00000i	0.562628	−	0.150756i
$705$	2.83013	−	2.83013i	0.106589	−	0.106589i
$706$	−8.61474	−	32.1506i	−0.324220	−	1.21001i
$707$	0.598076	−	2.23205i	0.0224930	−	0.0839449i
$708$	−1.39230	+	5.19615i	−0.0523260	+	0.195283i
$709$	10.1147	+	37.7487i	0.379867	+	1.41768i	0.846102	+	0.533022i	$0.178944\pi$
$709$	10.1147	+	37.7487i	0.379867	+	1.41768i	−0.466235	+	0.884661i	$0.654390\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$	−2.59808	+	4.50000i	−0.0974355	+	0.168763i
$712$	−31.7128	+	31.7128i	−1.18849	+	1.18849i
$713$	51.4808	+	29.7224i	1.92797	+	1.11311i
$714$	−42.2487	+	11.3205i	−1.58112	+	0.423659i
$715$	−8.33013	−	2.23205i	−0.311529	−	0.0834740i
$716$	−11.8564	+	11.8564i	−0.443095	+	0.443095i
$717$	−0.696152	−	1.20577i	−0.0259983	−	0.0450304i
$718$	28.9282	+	28.9282i	1.07959	+	1.07959i
$719$	−11.3205			−0.422184			−0.211092	−	0.977466i	$-0.567702\pi$
$719$	−11.3205			−0.422184			−0.211092	+	0.977466i	$0.567702\pi$
$720$	22.3923	+	6.00000i	0.834512	+	0.223607i
$721$	71.1051			2.64809
$722$	1.00000	+	1.00000i	0.0372161	+	0.0372161i
$723$	−4.79423	+	8.30385i	−0.178299	+	0.308823i
$724$	15.4641	+	15.4641i	0.574719	+	0.574719i
$725$	1.09808	+	0.294229i	0.0407815	+	0.0109274i
$726$	−4.60770	+	17.1962i	−0.171008	+	0.638209i
$727$	3.06218	+	1.76795i	0.113570	+	0.0655696i	0.555709	−	0.831377i	$-0.312447\pi$
$727$	3.06218	+	1.76795i	0.113570	+	0.0655696i	−0.442139	+	0.896947i	$0.645780\pi$
$728$	−29.1769			−1.08137
$729$	27.0000			1.00000
$730$	10.1962	+	17.6603i	0.377377	+	0.653635i
$731$	−6.78461	−	25.3205i	−0.250938	−	0.936513i
$732$	1.98076	+	7.39230i	0.0732111	+	0.273227i
$733$	8.47372	−	31.6244i	0.312984	−	1.16807i	−0.612868	−	0.790185i	$-0.709984\pi$
$733$	8.47372	−	31.6244i	0.312984	−	1.16807i	0.925852	−	0.377887i	$-0.123349\pi$
$734$	−12.7776	−	47.6865i	−0.471629	−	1.76014i
$735$	−11.1962	−	41.7846i	−0.412976	−	1.54125i
$736$	−9.46410	+	35.3205i	−0.348851	+	1.30193i
$737$	16.6603			0.613688
$738$	−0.882686	+	3.29423i	−0.0324921	+	0.121262i
$739$	−26.2679	−	26.2679i	−0.966282	−	0.966282i	0.0331677	−	0.999450i	$-0.489440\pi$
$739$	−26.2679	−	26.2679i	−0.966282	−	0.966282i	−0.999450	+	0.0331677i	$0.989440\pi$
$740$	−11.6603	−	20.1962i	−0.428639	−	0.742425i
$741$	14.7058	−	8.49038i	0.540230	−	0.311902i
$742$	−25.5885	+	44.3205i	−0.939382	+	1.62706i
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.0372984	−	0.999304i	$-0.488125\pi$
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.884072	+	0.467351i	$0.154791\pi$
$744$	11.6603	−	43.5167i	0.427486	−	1.59540i
$745$	−27.8205	−	16.0622i	−1.01926	−	0.588473i
$746$	2.02628	−	1.16987i	0.0741874	−	0.0428321i
$747$	−42.4808	+	11.3827i	−1.55429	+	0.416471i
$748$	−14.9282	+	4.00000i	−0.545829	+	0.146254i
$749$	57.2750	−	15.3468i	2.09278	−	0.560759i
$750$	−29.6603			−1.08304
$751$	−24.7224	−	42.8205i	−0.902134	−	1.56254i	−0.824718	−	0.565544i	$-0.808666\pi$
$751$	−24.7224	−	42.8205i	−0.902134	−	1.56254i	−0.0774160	−	0.996999i	$-0.524667\pi$
$752$	2.39230	−	4.14359i	0.0872384	−	0.151101i
$753$	−23.1962	+	23.1962i	−0.845315	+	0.845315i
$754$	2.07180	+	2.07180i	0.0754504	+	0.0754504i
$755$	9.56218	+	9.56218i	0.348003	+	0.348003i
$756$	23.1962	−	40.1769i	0.843636	−	1.46122i
$757$	1.53590	−	1.53590i	0.0558232	−	0.0558232i	−0.678644	−	0.734467i	$-0.737432\pi$
$757$	1.53590	−	1.53590i	0.0558232	−	0.0558232i	0.734467	+	0.678644i	$0.237432\pi$
$758$		−	31.1769i		−	1.13240i
$759$	15.2942	+	15.2942i	0.555145	+	0.555145i
$760$	−6.00000	+	22.3923i	−0.217643	+	0.812254i
$761$	−16.2846	+	9.40192i	−0.590317	+	0.340819i	−0.765223	−	0.643766i	$-0.777371\pi$
$761$	−16.2846	+	9.40192i	−0.590317	+	0.340819i	0.174906	+	0.984585i	$0.444038\pi$
$762$	−0.679492	+	0.679492i	−0.0246154	+	0.0246154i
$763$	−2.83013	−	10.5622i	−0.102457	−	0.382377i
$764$	−4.85641	−	2.80385i	−0.175699	−	0.101440i
$765$	−22.3923	−	6.00000i	−0.809595	−	0.216930i
$766$	−10.0263	−	2.68653i	−0.362264	−	0.0970684i
$767$	1.79423	−	3.10770i	0.0647858	−	0.112212i
$768$	27.7128			1.00000
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	0.795993	−	0.605305i	$-0.206949\pi$
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	−0.922207	+	0.386698i	$0.873616\pi$
$770$	−6.09808	−	22.7583i	−0.219759	−	0.820153i
$771$	21.0622	+	36.4808i	0.758536	+	1.31382i
$772$	7.73205	−	4.46410i	0.278283	−	0.160667i
$773$	−23.5885	+	23.5885i	−0.848418	+	0.848418i	−0.989936	−	0.141518i	$-0.954802\pi$
$773$	−23.5885	+	23.5885i	−0.848418	+	0.848418i	0.141518	+	0.989936i	$0.454802\pi$
$774$	24.0788	+	13.9019i	0.865496	+	0.499694i
$775$			11.6603i			0.418849i
$776$	−2.73205	+	0.732051i	−0.0980749	+	0.0262791i
$777$	−45.0788	+	12.0788i	−1.61719	+	0.433326i
$778$	−11.3660	−	6.56218i	−0.407492	−	0.235265i
$779$	−3.29423	−	0.882686i	−0.118028	−	0.0316255i
$780$	−13.3923	−	7.73205i	−0.479521	−	0.276852i
$781$	−5.46410	+	1.46410i	−0.195521	+	0.0523897i
$782$	9.46410	−	35.3205i	0.338436	−	1.26306i
$783$	−4.50000	+	1.20577i	−0.160817	+	0.0430908i
$784$	−25.8564	−	44.7846i	−0.923443	−	1.59945i
$785$	3.23205	−	5.59808i	0.115357	−	0.199804i
$786$	6.16987	+	10.6865i	0.220072	+	0.381176i
$787$	0.820508	−	3.06218i	0.0292480	−	0.109155i	−0.949759	−	0.312983i	$-0.898672\pi$
$787$	0.820508	−	3.06218i	0.0292480	−	0.109155i	0.979007	+	0.203828i	$0.0653384\pi$
$788$	−7.07180	−	7.07180i	−0.251922	−	0.251922i
$789$	−14.8923	−	8.59808i	−0.530180	−	0.306100i
$790$			4.73205i			0.168359i
$791$		−	55.6410i		−	1.97837i
$792$	8.19615	−	14.1962i	0.291238	−	0.504438i
$793$		−	5.10512i		−	0.181288i
$794$	−34.1051			−1.21035
$795$	−23.4904	+	13.5622i	−0.833118	+	0.481001i
$796$	−43.7128			−1.54936
$797$	11.0622	−	41.2846i	0.391842	−	1.46238i	−0.435250	−	0.900310i	$-0.643340\pi$
$797$	11.0622	−	41.2846i	0.391842	−	1.46238i	0.827092	−	0.562066i	$-0.189993\pi$
$798$	40.1769	+	23.1962i	1.42225	+	0.821135i
$799$	−2.39230	+	4.14359i	−0.0846337	+	0.146590i
$800$	−6.92820	+	1.85641i	−0.244949	+	0.0656339i
$801$			47.5692i			1.68078i
$802$	44.1506	+	11.8301i	1.55901	+	0.417736i
$803$	13.9282	−	3.73205i	0.491516	−	0.131701i
$804$	28.8564	+	7.73205i	1.01769	+	0.272688i
$805$	53.8468	+	14.4282i	1.89785	+	0.508527i
$806$	−15.0263	+	26.0263i	−0.529278	+	0.916737i
$807$	7.39230	+	7.39230i	0.260221	+	0.260221i
$808$	0.732051	−	1.26795i	0.0257535	−	0.0446063i
$809$		−	36.6410i		−	1.28823i	−0.764929	−	0.644115i	$-0.777226\pi$
$809$		−	36.6410i		−	1.28823i	0.764929	−	0.644115i	$-0.222774\pi$
$810$	21.2942	−	12.2942i	0.748203	−	0.431975i
$811$	−18.4641	+	18.4641i	−0.648362	+	0.648362i	−0.952597	−	0.304235i	$-0.901599\pi$
$811$	−18.4641	+	18.4641i	−0.648362	+	0.648362i	0.304235	+	0.952597i	$0.401599\pi$
$812$	−2.07180	+	7.73205i	−0.0727058	+	0.271342i
$813$	−1.85641			−0.0651070
$814$	−15.9282	+	4.26795i	−0.558283	+	0.149592i
$815$	2.63397	+	4.56218i	0.0922641	+	0.159806i
$816$	−27.7128			−0.970143
$817$	−13.9019	+	24.0788i	−0.486367	+	0.842412i
$818$	8.29423	−	30.9545i	0.290001	−	1.08230i
$819$	−21.8827	+	21.8827i	−0.764643	+	0.764643i
$820$	0.803848	+	3.00000i	0.0280716	+	0.104765i
$821$	10.7224	+	40.0167i	0.374215	+	1.39659i	0.854488	+	0.519472i	$0.173871\pi$
$821$	10.7224	+	40.0167i	0.374215	+	1.39659i	−0.480272	+	0.877119i	$0.659462\pi$
$822$	1.56218	−	0.418584i	0.0544872	−	0.0145998i
$823$	36.6506	−	21.1603i	1.27756	−	0.737600i	0.301162	−	0.953573i	$-0.402626\pi$
$823$	36.6506	−	21.1603i	1.27756	−	0.737600i	0.976399	+	0.215973i	$0.0692923\pi$
$824$	43.5167	+	11.6603i	1.51597	+	0.406204i
$825$	−1.09808	+	4.09808i	−0.0382301	+	0.142677i
$826$	9.80385			0.341119
$827$	−31.3923	+	31.3923i	−1.09162	+	1.09162i	−0.0962613	+	0.995356i	$0.530688\pi$
$827$	−31.3923	+	31.3923i	−1.09162	+	1.09162i	−0.995356	+	0.0962613i	$0.969312\pi$
$828$	19.3923	+	33.5885i	0.673929	+	1.16728i
$829$	−14.2679	−	14.2679i	−0.495546	−	0.495546i	0.414502	−	0.910048i	$-0.363956\pi$
$829$	−14.2679	−	14.2679i	−0.495546	−	0.495546i	−0.910048	+	0.414502i	$0.863956\pi$
$830$	−28.3205	+	28.3205i	−0.983019	+	0.983019i
$831$	−3.10770	−	11.5981i	−0.107805	−	0.402333i
$832$	−17.8564	−	4.78461i	−0.619060	−	0.165876i
$833$	25.8564	+	44.7846i	0.895871	+	1.55169i
$834$	−35.4904	+	20.4904i	−1.22893	+	0.709524i
$835$	30.7224	−	8.23205i	1.06319	−	0.284882i
$836$	14.1962	+	8.19615i	0.490984	+	0.283470i
$837$	−23.8923	−	41.3827i	−0.825839	−	1.43039i
$838$	−13.5622	−	23.4904i	−0.468498	−	0.811462i
$839$	6.74167	+	3.89230i	0.232748	+	0.134377i	0.611839	−	0.790982i	$-0.290430\pi$
$839$	6.74167	+	3.89230i	0.232748	+	0.134377i	−0.379091	+	0.925359i	$0.623763\pi$
$840$		−	42.2487i		−	1.45772i
$841$	−24.4186	+	14.0981i	−0.842020	+	0.486141i
$842$	22.6865	+	13.0981i	0.781830	+	0.451390i
$843$	−17.3827	−	10.0359i	−0.598692	−	0.345655i
$844$	37.0526	+	9.92820i	1.27540	+	0.341743i
$845$	−10.4641	−	10.4641i	−0.359976	−	0.359976i
$846$	−1.31347	−	4.90192i	−0.0451579	−	0.168532i
$847$	32.4449			1.11482
$848$	−22.9282	+	22.9282i	−0.787358	+	0.787358i
$849$	−22.7942	−	6.10770i	−0.782296	−	0.209616i
$850$	6.92820	−	1.85641i	0.237635	−	0.0636742i
$851$	10.0981	−	37.6865i	0.346158	−	1.29188i
$852$	−10.1436			−0.347514
$853$	−2.06218	−	7.69615i	−0.0706076	−	0.263511i	0.921594	−	0.388156i	$-0.126888\pi$
$853$	−2.06218	−	7.69615i	−0.0706076	−	0.263511i	−0.992201	+	0.124644i	$0.960221\pi$
$854$	12.0788	−	6.97372i	0.413329	−	0.238636i
$855$	12.2942	+	21.2942i	0.420454	+	0.728247i
$856$	37.5692			1.28409
$857$	14.6436	+	8.45448i	0.500216	+	0.288800i	0.728803	−	0.684724i	$-0.240077\pi$
$857$	14.6436	+	8.45448i	0.500216	+	0.288800i	−0.228587	+	0.973523i	$0.573411\pi$
$858$	−7.73205	+	7.73205i	−0.263968	+	0.263968i
$859$	−4.50000	−	1.20577i	−0.153538	−	0.0411404i	0.181231	−	0.983440i	$-0.441992\pi$
$859$	−4.50000	−	1.20577i	−0.153538	−	0.0411404i	−0.334769	+	0.942300i	$0.608658\pi$
$860$	25.3205			0.863422
$861$	6.21539			0.211820
$862$	3.32051	−	3.32051i	0.113097	−	0.113097i
$863$	−26.5359			−0.903292			−0.451646	−	0.892197i	$-0.649163\pi$
$863$	−26.5359			−0.903292			−0.451646	+	0.892197i	$0.649163\pi$
$864$	20.7846	−	20.7846i	0.707107	−	0.707107i
$865$	−15.1962			−0.516685
$866$	−3.60770	+	3.60770i	−0.122594	+	0.122594i
$867$	−1.73205			−0.0588235
$868$	−82.1051			−2.78683
$869$	3.23205	+	0.866025i	0.109640	+	0.0293779i
$870$	−3.00000	+	3.00000i	−0.101710	+	0.101710i
$871$	−17.2583	−	9.96410i	−0.584776	−	0.337621i
$872$		−	6.92820i		−	0.234619i
$873$	−1.50000	+	2.59808i	−0.0507673	+	0.0879316i
$874$	−33.5885	+	19.3923i	−1.13615	+	0.655954i
$875$	13.9904	+	52.2128i	0.472961	+	1.76512i
$876$	25.8564			0.873607
$877$	−13.3827	+	49.9449i	−0.451901	+	1.68652i	0.245140	+	0.969488i	$0.421166\pi$
$877$	−13.3827	+	49.9449i	−0.451901	+	1.68652i	−0.697042	+	0.717031i	$0.745501\pi$
$878$	−9.36603	+	2.50962i	−0.316088	+	0.0846955i
$879$	3.69615	+	0.990381i	0.124668	+	0.0334047i
$880$		−	14.9282i		−	0.503230i
$881$	31.3205			1.05521			0.527607	−	0.849488i	$-0.323089\pi$
$881$	31.3205			1.05521			0.527607	+	0.849488i	$0.323089\pi$
$882$	−52.9808	−	14.1962i	−1.78396	−	0.478009i
$883$	−3.00000	−	3.00000i	−0.100958	−	0.100958i	0.654824	−	0.755782i	$-0.272743\pi$
$883$	−3.00000	−	3.00000i	−0.100958	−	0.100958i	−0.755782	+	0.654824i	$0.772743\pi$
$884$	17.8564	+	4.78461i	0.600576	+	0.160924i
$885$	4.50000	+	2.59808i	0.151266	+	0.0873334i
$886$	5.49038	+	3.16987i	0.184453	+	0.106494i
$887$	8.93782	−	5.16025i	0.300103	−	0.173264i	−0.342386	−	0.939559i	$-0.611235\pi$
$887$	8.93782	−	5.16025i	0.300103	−	0.173264i	0.642489	+	0.766295i	$0.277902\pi$
$888$	−29.5692			−0.992278
$889$	1.51666	+	0.875644i	0.0508672	+	0.0293682i
$890$	21.6603	+	37.5167i	0.726053	+	1.25756i
$891$	−4.50000	−	16.7942i	−0.150756	−	0.562628i
$892$	−27.0000	−	15.5885i	−0.904027	−	0.521940i
$893$	4.90192	−	1.31347i	0.164037	−	0.0439535i
$894$	−35.2750	+	20.3660i	−1.17977	+	0.681142i
$895$	8.09808	+	14.0263i	0.270689	+	0.468847i
$896$	−13.0718	−	48.7846i	−0.436698	−	1.62978i
$897$	−6.69615	−	24.9904i	−0.223578	−	0.834405i
$898$	−35.3205	+	35.3205i	−1.17866	+	1.17866i
$899$	5.83013	+	5.83013i	0.194446	+	0.194446i
$900$	−3.80385	+	6.58846i	−0.126795	+	0.219615i
$901$	22.9282	−	22.9282i	0.763849	−	0.763849i
$902$	2.19615			0.0731239
$903$	13.1147	−	48.9449i	0.436431	−	1.62878i
$904$	9.12436	−	34.0526i	0.303472	−	1.13257i
$905$	18.2942	−	10.5622i	0.608121	−	0.351099i
$906$	16.5622	−	4.43782i	0.550242	−	0.147437i
$907$	−2.42820	−	9.06218i	−0.0806272	−	0.300905i	0.913823	−	0.406112i	$-0.133116\pi$
$907$	−2.42820	−	9.06218i	−0.0806272	−	0.300905i	−0.994450	+	0.105208i	$0.966449\pi$
$908$	−10.5167	−	39.2487i	−0.349008	−	1.30251i
$909$	−0.401924	−	1.50000i	−0.0133310	−	0.0497519i
$910$	−7.29423	+	27.2224i	−0.241801	+	0.902415i
$911$	−4.13397	+	7.16025i	−0.136965	+	0.237230i	−0.926346	−	0.376673i	$-0.877068\pi$
$911$	−4.13397	+	7.16025i	−0.136965	+	0.237230i	0.789382	+	0.613903i	$0.210401\pi$
$912$	20.7846	+	20.7846i	0.688247	+	0.688247i
$913$	14.1603	+	24.5263i	0.468636	+	0.811701i
$914$	−40.9545	+	10.9737i	−1.35465	+	0.362978i
$915$	7.39230			0.244382
$916$	8.85641	−	33.0526i	0.292624	−	1.09209i
$917$	15.9019	−	15.9019i	0.525128	−	0.525128i
$918$	−20.7846	+	20.7846i	−0.685994	+	0.685994i
$919$		−	36.5359i		−	1.20521i	−0.798040	−	0.602604i	$-0.794130\pi$
$919$		−	36.5359i		−	1.20521i	0.798040	−	0.602604i	$-0.205870\pi$
$920$	30.5885	+	17.6603i	1.00847	+	0.582241i
$921$	13.7321	+	13.7321i	0.452486	+	0.452486i
$922$	−3.36603	+	5.83013i	−0.110854	+	0.192005i
$923$	6.53590	+	1.75129i	0.215132	+	0.0576444i
$924$	−28.8564	−	7.73205i	−0.949306	−	0.254366i
$925$	7.39230	−	1.98076i	0.243057	−	0.0651271i
$926$	14.5622	+	3.90192i	0.478543	+	0.128225i
$927$	41.3827	−	23.8923i	1.35919	−	0.784726i
$928$	−2.53590	+	4.39230i	−0.0832449	+	0.144184i
$929$	9.35641	−	16.2058i	0.306974	−	0.531694i	−0.670725	−	0.741706i	$-0.734017\pi$
$929$	9.35641	−	16.2058i	0.306974	−	0.531694i	0.977699	+	0.210012i	$0.0673503\pi$
$930$	−37.6865	−	21.7583i	−1.23579	−	0.713484i
$931$	14.1962	−	52.9808i	0.465260	−	1.73637i
$932$	18.1436			0.594313
$933$	15.9115	−	9.18653i	0.520921	−	0.300754i
$934$	−43.5692			−1.42563
$935$			14.9282i			0.488204i
$936$	−16.9808	+	9.80385i	−0.555034	+	0.320449i
$937$			19.0718i			0.623048i	0.950238	+	0.311524i	$0.100840\pi$
$937$			19.0718i			0.623048i	−0.950238	+	0.311524i	$0.899160\pi$
$938$		−	54.4449i		−	1.77769i
$939$	43.5788	+	25.1603i	1.42214	+	0.821074i
$940$	−3.26795	−	3.26795i	−0.106589	−	0.106589i
$941$	9.13397	−	34.0885i	0.297759	−	1.11125i	−0.641242	−	0.767338i	$-0.721581\pi$
$941$	9.13397	−	34.0885i	0.297759	−	1.11125i	0.939001	−	0.343913i	$-0.111753\pi$
$942$	−4.09808	−	7.09808i	−0.133523	−	0.231268i
$943$	−2.59808	+	4.50000i	−0.0846050	+	0.146540i
$944$	6.00000	+	1.60770i	0.195283	+	0.0523260i
$945$	−31.6865	−	31.6865i	−1.03076	−	1.03076i
$946$	4.63397	−	17.2942i	0.150664	−	0.562284i
$947$	−41.0167	+	10.9904i	−1.33286	+	0.357139i	−0.853782	−	0.520631i	$-0.825697\pi$
$947$	−41.0167	+	10.9904i	−1.33286	+	0.357139i	−0.479081	+	0.877771i	$0.659030\pi$
$948$	5.19615	+	3.00000i	0.168763	+	0.0974355i
$949$	−16.6603	−	4.46410i	−0.540815	−	0.144911i
$950$	−6.58846	−	3.80385i	−0.213758	−	0.123413i
$951$	−57.9449	+	15.5263i	−1.87899	+	0.503474i
$952$	13.0718	+	48.7846i	0.423659	+	1.58112i
$953$		−	32.5359i		−	1.05394i	−0.849884	−	0.526971i	$-0.823328\pi$
$953$		−	32.5359i		−	1.05394i	0.849884	−	0.526971i	$-0.176672\pi$
$954$			34.3923i			1.11349i
$955$	−3.83013	+	3.83013i	−0.123940	+	0.123940i
$956$	−1.39230	+	0.803848i	−0.0450304	+	0.0259983i
$957$	1.50000	+	2.59808i	0.0484881	+	0.0839839i
$958$	6.83013	+	25.4904i	0.220671	+	0.823557i
$959$	−1.47372	−	2.55256i	−0.0475889	−	0.0824264i
$960$	6.92820	−	25.8564i	0.223607	−	0.834512i
$961$	−26.7846	+	46.3923i	−0.864020	+	1.49653i
$962$	19.0526	+	5.10512i	0.614279	+	0.164596i
$963$	28.1769	−	28.1769i	0.907988	−	0.907988i
$964$	9.58846	+	5.53590i	0.308823	+	0.178299i
$965$	−2.23205	−	8.33013i	−0.0718523	−	0.268156i
$966$	49.9808	−	49.9808i	1.60810	−	1.60810i
$967$	−27.0622	+	15.6244i	−0.870261	+	0.502445i	−0.867435	−	0.497551i	$-0.834233\pi$
$967$	−27.0622	+	15.6244i	−0.870261	+	0.502445i	−0.00282602	+	0.999996i	$0.500900\pi$
$968$	19.8564	+	5.32051i	0.638209	+	0.171008i
$969$	−20.7846	−	20.7846i	−0.667698	−	0.667698i
$970$			2.73205i			0.0877209i
$971$	−23.9808	+	23.9808i	−0.769579	+	0.769579i	−0.978032	−	0.208453i	$-0.933157\pi$
$971$	−23.9808	+	23.9808i	−0.769579	+	0.769579i	0.208453	+	0.978032i	$0.433157\pi$
$972$		−	31.1769i		−	1.00000i
$973$	52.8109	+	52.8109i	1.69304	+	1.69304i
$974$	6.78461	+	6.78461i	0.217393	+	0.217393i
$975$	3.58846	−	3.58846i	0.114923	−	0.114923i
$976$	8.53590	−	2.28719i	0.273227	−	0.0732111i
$977$	−24.2846	−	42.0622i	−0.776933	−	1.34569i	−0.933701	−	0.358053i	$-0.883441\pi$
$977$	−24.2846	−	42.0622i	−0.776933	−	1.34569i	0.156768	−	0.987635i	$-0.449893\pi$
$978$	6.67949			0.213587
$979$	29.5885	−	7.92820i	0.945651	−	0.253386i
$980$	−48.2487	+	12.9282i	−1.54125	+	0.412976i
$981$	−5.19615	−	5.19615i	−0.165900	−	0.165900i
$982$	−0.633975	+	0.366025i	−0.0202309	+	0.0116803i
$983$	−1.08142	−	0.624356i	−0.0344918	−	0.0199139i	0.482655	−	0.875811i	$-0.339673\pi$
$983$	−1.08142	−	0.624356i	−0.0344918	−	0.0199139i	−0.517147	+	0.855897i	$0.673006\pi$
$984$	3.80385	+	1.01924i	0.121262	+	0.0324921i
$985$	−8.36603	+	4.83013i	−0.266564	+	0.153901i
$986$	2.53590	−	4.39230i	0.0807595	−	0.139879i
$987$	−8.00962	+	4.62436i	−0.254949	+	0.147195i
$988$	−9.80385	−	16.9808i	−0.311902	−	0.540230i
$989$	29.9545	+	29.9545i	0.952497	+	0.952497i
$990$	−11.1962	−	11.1962i	−0.355837	−	0.355837i
$991$	−44.3923			−1.41017			−0.705084	−	0.709124i	$-0.749091\pi$
$991$	−44.3923			−1.41017			−0.705084	+	0.709124i	$0.749091\pi$
$992$	−50.2487	−	13.4641i	−1.59540	−	0.427486i
$993$	2.34936	+	8.76795i	0.0745548	+	0.278242i
$994$	4.78461	+	17.8564i	0.151759	+	0.566371i
$995$	−10.9282	+	40.7846i	−0.346447	+	1.29296i
$996$	13.1436	+	49.0526i	0.416471	+	1.55429i
$997$	−1.06218	−	3.96410i	−0.0336395	−	0.125544i	0.947064	−	0.321044i	$-0.104034\pi$
$997$	−1.06218	−	3.96410i	−0.0336395	−	0.125544i	−0.980704	+	0.195500i	$0.937367\pi$
$998$	−6.83013	−	11.8301i	−0.216204	−	0.374476i
$999$	−22.1769	+	22.1769i	−0.701647	+	0.701647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.x.a.61.1	✓	4
3.2	odd	2		432.2.y.d.397.1		4
4.3	odd	2		576.2.bb.a.529.1		4
9.4	even	3		144.2.x.d.13.1	yes	4
9.5	odd	6		432.2.y.a.253.1		4
12.11	even	2		1728.2.bc.c.721.1		4
16.5	even	4		144.2.x.d.133.1	yes	4
16.11	odd	4		576.2.bb.b.241.1		4
36.23	even	6		1728.2.bc.b.145.1		4
36.31	odd	6		576.2.bb.b.337.1		4
48.5	odd	4		432.2.y.a.181.1		4
48.11	even	4		1728.2.bc.b.1585.1		4
144.5	odd	12		432.2.y.d.37.1		4
144.59	even	12		1728.2.bc.c.1009.1		4
144.85	even	12	inner	144.2.x.a.85.1	yes	4
144.139	odd	12		576.2.bb.a.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.61.1	✓	4	1.1	even	1	trivial
144.2.x.a.85.1	yes	4	144.85	even	12	inner
144.2.x.d.13.1	yes	4	9.4	even	3
144.2.x.d.133.1	yes	4	16.5	even	4
432.2.y.a.181.1		4	48.5	odd	4
432.2.y.a.253.1		4	9.5	odd	6
432.2.y.d.37.1		4	144.5	odd	12
432.2.y.d.397.1		4	3.2	odd	2
576.2.bb.a.49.1		4	144.139	odd	12
576.2.bb.a.529.1		4	4.3	odd	2
576.2.bb.b.241.1		4	16.11	odd	4
576.2.bb.b.337.1		4	36.31	odd	6
1728.2.bc.b.145.1		4	36.23	even	6
1728.2.bc.b.1585.1		4	48.11	even	4
1728.2.bc.c.721.1		4	12.11	even	2
1728.2.bc.c.1009.1		4	144.59	even	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-1.86603 - 0.500000i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-1.86603 - 0.500000i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(2.36603 - 1.36603i) q^{10} +(-0.500000 - 1.86603i) q^{11} -3.46410i q^{12} +(-0.598076 + 2.23205i) q^{13} +(-6.09808 + 1.63397i) q^{14} +(-3.23205 - 0.866025i) q^{15} -4.00000 q^{16} +4.00000 q^{17} +(-3.00000 + 3.00000i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 + 3.73205i) q^{20} +(6.69615 + 3.86603i) q^{21} +(2.36603 + 1.36603i) q^{22} +(-5.59808 + 3.23205i) q^{23} +(3.46410 + 3.46410i) q^{24} +(-1.09808 - 0.633975i) q^{25} +(-1.63397 - 2.83013i) q^{26} +5.19615 q^{27} +(4.46410 - 7.73205i) q^{28} +(-0.866025 + 0.232051i) q^{29} +(4.09808 - 2.36603i) q^{30} +(-4.59808 - 7.96410i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.866025 - 3.23205i) q^{33} +(-4.00000 + 4.00000i) q^{34} +(-6.09808 - 6.09808i) q^{35} -6.00000i q^{36} +(-4.26795 + 4.26795i) q^{37} +6.00000 q^{38} +(-1.03590 + 3.86603i) q^{39} +(-2.73205 - 4.73205i) q^{40} +(0.696152 - 0.401924i) q^{41} +(-10.5622 + 2.83013i) q^{42} +(-1.69615 - 6.33013i) q^{43} +(-3.73205 + 1.00000i) q^{44} +(-5.59808 - 1.50000i) q^{45} +(2.36603 - 8.83013i) q^{46} +(-0.598076 + 1.03590i) q^{47} -6.92820 q^{48} +(6.46410 + 11.1962i) q^{49} +(1.73205 - 0.464102i) q^{50} +6.92820 q^{51} +(4.46410 + 1.19615i) q^{52} +(5.73205 - 5.73205i) q^{53} +(-5.19615 + 5.19615i) q^{54} +3.73205i q^{55} +(3.26795 + 12.1962i) q^{56} +(-5.19615 - 5.19615i) q^{57} +(0.633975 - 1.09808i) q^{58} +(-1.50000 - 0.401924i) q^{59} +(-1.73205 + 6.46410i) q^{60} +(-2.13397 + 0.571797i) q^{61} +(12.5622 + 3.36603i) q^{62} +(11.5981 + 6.69615i) q^{63} +8.00000i q^{64} +(2.23205 - 3.86603i) q^{65} +(4.09808 + 2.36603i) q^{66} +(-2.23205 + 8.33013i) q^{67} -8.00000i q^{68} +(-9.69615 + 5.59808i) q^{69} +12.1962 q^{70} -2.92820i q^{71} +(6.00000 + 6.00000i) q^{72} +7.46410i q^{73} -8.53590i q^{74} +(-1.90192 - 1.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(2.23205 - 8.33013i) q^{77} +(-2.83013 - 4.90192i) q^{78} +(-0.866025 + 1.50000i) q^{79} +(7.46410 + 2.00000i) q^{80} +9.00000 q^{81} +(-0.294229 + 1.09808i) q^{82} +(-14.1603 + 3.79423i) q^{83} +(7.73205 - 13.3923i) q^{84} +(-7.46410 - 2.00000i) q^{85} +(8.02628 + 4.63397i) q^{86} +(-1.50000 + 0.401924i) q^{87} +(2.73205 - 4.73205i) q^{88} +15.8564i q^{89} +(7.09808 - 4.09808i) q^{90} +(-7.29423 + 7.29423i) q^{91} +(6.46410 + 11.1962i) q^{92} +(-7.96410 - 13.7942i) q^{93} +(-0.437822 - 1.63397i) q^{94} +(4.09808 + 7.09808i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-17.6603 - 4.73205i) q^{98} +(-1.50000 - 5.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{5} + 12 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^5 + 12 * q^7 + 8 * q^8 + 12 * q^9	\( 4 q - 4 q^{2} - 4 q^{5} + 12 q^{7} + 8 q^{8} + 12 q^{9} + 6 q^{10} - 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{15} - 16 q^{16} + 16 q^{17} - 12 q^{18} - 12 q^{19} - 4 q^{20} + 6 q^{21} + 6 q^{22} - 12 q^{23} + 6 q^{25} - 10 q^{26} + 4 q^{28} + 6 q^{30} - 8 q^{31} + 16 q^{32} - 16 q^{34} - 14 q^{35} - 24 q^{37} + 24 q^{38} - 18 q^{39} - 4 q^{40} - 18 q^{41} - 18 q^{42} + 14 q^{43} - 8 q^{44} - 12 q^{45} + 6 q^{46} + 8 q^{47} + 12 q^{49} + 4 q^{52} + 16 q^{53} + 20 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} + 26 q^{62} + 36 q^{63} + 2 q^{65} + 6 q^{66} - 2 q^{67} - 18 q^{69} + 28 q^{70} + 24 q^{72} - 18 q^{75} - 24 q^{76} + 2 q^{77} + 6 q^{78} + 16 q^{80} + 36 q^{81} + 30 q^{82} - 22 q^{83} + 24 q^{84} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 4 q^{88} + 18 q^{90} + 2 q^{91} + 12 q^{92} - 18 q^{93} - 26 q^{94} + 6 q^{95} - 2 q^{97} - 36 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^5 + 12 * q^7 + 8 * q^8 + 12 * q^9 + 6 * q^10 - 2 * q^11 + 8 * q^13 - 14 * q^14 - 6 * q^15 - 16 * q^16 + 16 * q^17 - 12 * q^18 - 12 * q^19 - 4 * q^20 + 6 * q^21 + 6 * q^22 - 12 * q^23 + 6 * q^25 - 10 * q^26 + 4 * q^28 + 6 * q^30 - 8 * q^31 + 16 * q^32 - 16 * q^34 - 14 * q^35 - 24 * q^37 + 24 * q^38 - 18 * q^39 - 4 * q^40 - 18 * q^41 - 18 * q^42 + 14 * q^43 - 8 * q^44 - 12 * q^45 + 6 * q^46 + 8 * q^47 + 12 * q^49 + 4 * q^52 + 16 * q^53 + 20 * q^56 + 6 * q^58 - 6 * q^59 - 12 * q^61 + 26 * q^62 + 36 * q^63 + 2 * q^65 + 6 * q^66 - 2 * q^67 - 18 * q^69 + 28 * q^70 + 24 * q^72 - 18 * q^75 - 24 * q^76 + 2 * q^77 + 6 * q^78 + 16 * q^80 + 36 * q^81 + 30 * q^82 - 22 * q^83 + 24 * q^84 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 4 * q^88 + 18 * q^90 + 2 * q^91 + 12 * q^92 - 18 * q^93 - 26 * q^94 + 6 * q^95 - 2 * q^97 - 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more