LMFDB - Embedded newform 180.2.n.b.119.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(59,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("180.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, 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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	180.119
Dual form			180.2.n.b.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.792893 - 2.09077i) q^{5} +2.44949i q^{6} +(-1.50000 + 2.59808i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.792893 - 2.09077i) q^{5} +2.44949i q^{6} +(-1.50000 + 2.59808i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.00000 + 2.44949i) q^{10} +(2.12132 - 3.67423i) q^{11} +(-3.00000 - 1.73205i) q^{12} +(2.12132 - 1.22474i) q^{13} +(-2.12132 - 3.67423i) q^{14} +(-0.621320 - 3.82282i) q^{15} +(-2.00000 + 3.46410i) q^{16} +1.41421 q^{17} +(2.12132 + 3.67423i) q^{18} +7.34847i q^{19} +(-4.41421 + 0.717439i) q^{20} +5.19615i q^{21} +(3.00000 + 5.19615i) q^{22} +(-4.50000 + 2.59808i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-3.74264 - 3.31552i) q^{25} +3.46410i q^{26} -5.19615i q^{27} +6.00000 q^{28} +(1.50000 + 0.866025i) q^{29} +(5.12132 + 1.94218i) q^{30} +(-6.36396 + 3.67423i) q^{31} +(-2.82843 - 4.89898i) q^{32} -7.34847i q^{33} +(-1.00000 + 1.73205i) q^{34} +(4.24264 + 5.19615i) q^{35} -6.00000 q^{36} +2.44949i q^{37} +(-9.00000 - 5.19615i) q^{38} +(2.12132 - 3.67423i) q^{39} +(2.24264 - 5.91359i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-6.36396 - 3.67423i) q^{42} +(3.00000 - 5.19615i) q^{43} -8.48528 q^{44} +(-4.24264 - 5.19615i) q^{45} -7.34847i q^{46} +(4.50000 + 2.59808i) q^{47} +6.92820i q^{48} +(-1.00000 - 1.73205i) q^{49} +(6.70711 - 2.23936i) q^{50} +(2.12132 - 1.22474i) q^{51} +(-4.24264 - 2.44949i) q^{52} -5.65685 q^{53} +(6.36396 + 3.67423i) q^{54} +(-6.00000 - 7.34847i) q^{55} +(-4.24264 + 7.34847i) q^{56} +(6.36396 + 11.0227i) q^{57} +(-2.12132 + 1.22474i) q^{58} +(-6.00000 + 4.89898i) q^{60} +(-3.50000 + 6.06218i) q^{61} -10.3923i q^{62} +(4.50000 + 7.79423i) q^{63} +8.00000 q^{64} +(-0.878680 - 5.40629i) q^{65} +(9.00000 + 5.19615i) q^{66} +(-1.50000 - 2.59808i) q^{67} +(-1.41421 - 2.44949i) q^{68} +(-4.50000 + 7.79423i) q^{69} +(-9.36396 + 1.52192i) q^{70} +4.24264 q^{71} +(4.24264 - 7.34847i) q^{72} +4.89898i q^{73} +(-3.00000 - 1.73205i) q^{74} +(-8.48528 - 1.73205i) q^{75} +(12.7279 - 7.34847i) q^{76} +(6.36396 + 11.0227i) q^{77} +(3.00000 + 5.19615i) q^{78} +(5.65685 + 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} -7.34847i q^{82} +(-4.50000 - 2.59808i) q^{83} +(9.00000 - 5.19615i) q^{84} +(1.12132 - 2.95680i) q^{85} +(4.24264 + 7.34847i) q^{86} +3.00000 q^{87} +(6.00000 - 10.3923i) q^{88} -8.66025i q^{89} +(9.36396 - 1.52192i) q^{90} +7.34847i q^{91} +(9.00000 + 5.19615i) q^{92} +(-6.36396 + 11.0227i) q^{93} +(-6.36396 + 3.67423i) q^{94} +(15.3640 + 5.82655i) q^{95} +(-8.48528 - 4.89898i) q^{96} +(12.7279 + 7.34847i) q^{97} +2.82843 q^{98} +(-6.36396 - 11.0227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5 - 6 * q^7 + 6 * q^9	$ 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5} - 6 q^{7} + 6 q^{9} + 8 q^{10} - 12 q^{12} + 6 q^{15} - 8 q^{16} - 12 q^{20} + 12 q^{22} - 18 q^{23} + 2 q^{25} + 24 q^{28} + 6 q^{29} + 12 q^{30} - 4 q^{34} - 24 q^{36} - 36 q^{38} - 8 q^{40} - 18 q^{41} + 12 q^{43} + 18 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{55} - 24 q^{60} - 14 q^{61} + 18 q^{63} + 32 q^{64} - 12 q^{65} + 36 q^{66} - 6 q^{67} - 18 q^{69} - 12 q^{70} - 12 q^{74} + 12 q^{78} - 18 q^{81} - 18 q^{83} + 36 q^{84} - 4 q^{85} + 12 q^{87} + 24 q^{88} + 12 q^{90} + 36 q^{92} + 36 q^{95}+O(q^{100}) $ 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5 - 6 * q^7 + 6 * q^9 + 8 * q^10 - 12 * q^12 + 6 * q^15 - 8 * q^16 - 12 * q^20 + 12 * q^22 - 18 * q^23 + 2 * q^25 + 24 * q^28 + 6 * q^29 + 12 * q^30 - 4 * q^34 - 24 * q^36 - 36 * q^38 - 8 * q^40 - 18 * q^41 + 12 * q^43 + 18 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^55 - 24 * q^60 - 14 * q^61 + 18 * q^63 + 32 * q^64 - 12 * q^65 + 36 * q^66 - 6 * q^67 - 18 * q^69 - 12 * q^70 - 12 * q^74 + 12 * q^78 - 18 * q^81 - 18 * q^83 + 36 * q^84 - 4 * q^85 + 12 * q^87 + 24 * q^88 + 12 * q^90 + 36 * q^92 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	0.792893	−	2.09077i	0.354593	−	0.935021i
$5$	0.792893	−	2.09077i	0.354593	−	0.935021i
$6$			2.44949i			1.00000i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	2.82843			1.00000
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	2.00000	+	2.44949i	0.632456	+	0.774597i
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$	−3.00000	−	1.73205i	−0.866025	−	0.500000i
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$	−2.12132	−	3.67423i	−0.566947	−	0.981981i
$15$	−0.621320	−	3.82282i	−0.160424	−	0.987048i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	1.41421			0.342997			0.171499	−	0.985184i	$-0.445139\pi$
$17$	1.41421			0.342997			0.171499	+	0.985184i	$0.445139\pi$
$18$	2.12132	+	3.67423i	0.500000	+	0.866025i
$19$			7.34847i			1.68585i	0.538028	+	0.842927i	$0.319170\pi$
$19$			7.34847i			1.68585i	−0.538028	+	0.842927i	$0.680830\pi$
$20$	−4.41421	+	0.717439i	−0.987048	+	0.160424i
$21$			5.19615i			1.13389i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−4.50000	+	2.59808i	−0.938315	+	0.541736i	−0.889432	−	0.457068i	$-0.848900\pi$
$23$	−4.50000	+	2.59808i	−0.938315	+	0.541736i	−0.0488832	+	0.998805i	$0.515566\pi$
$24$	4.24264	−	2.44949i	0.866025	−	0.500000i
$25$	−3.74264	−	3.31552i	−0.748528	−	0.663103i
$26$			3.46410i			0.679366i
$27$		−	5.19615i		−	1.00000i
$28$	6.00000			1.13389
$29$	1.50000	+	0.866025i	0.278543	+	0.160817i	0.632764	−	0.774345i	$-0.281920\pi$
$29$	1.50000	+	0.866025i	0.278543	+	0.160817i	−0.354221	+	0.935162i	$0.615254\pi$
$30$	5.12132	+	1.94218i	0.935021	+	0.354593i
$31$	−6.36396	+	3.67423i	−1.14300	+	0.659912i	−0.947172	−	0.320726i	$-0.896073\pi$
$31$	−6.36396	+	3.67423i	−1.14300	+	0.659912i	−0.195829	+	0.980638i	$0.562740\pi$
$32$	−2.82843	−	4.89898i	−0.500000	−	0.866025i
$33$		−	7.34847i		−	1.27920i
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	4.24264	+	5.19615i	0.717137	+	0.878310i
$36$	−6.00000			−1.00000
$37$			2.44949i			0.402694i	0.979520	+	0.201347i	$0.0645318\pi$
$37$			2.44949i			0.402694i	−0.979520	+	0.201347i	$0.935468\pi$
$38$	−9.00000	−	5.19615i	−1.45999	−	0.842927i
$39$	2.12132	−	3.67423i	0.339683	−	0.588348i
$40$	2.24264	−	5.91359i	0.354593	−	0.935021i
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$	−6.36396	−	3.67423i	−0.981981	−	0.566947i
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$	−8.48528			−1.27920
$45$	−4.24264	−	5.19615i	−0.632456	−	0.774597i
$46$		−	7.34847i		−	1.08347i
$47$	4.50000	+	2.59808i	0.656392	+	0.378968i	0.790901	−	0.611944i	$-0.209612\pi$
$47$	4.50000	+	2.59808i	0.656392	+	0.378968i	−0.134509	+	0.990912i	$0.542946\pi$
$48$			6.92820i			1.00000i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	6.70711	−	2.23936i	0.948528	−	0.316693i
$51$	2.12132	−	1.22474i	0.297044	−	0.171499i
$52$	−4.24264	−	2.44949i	−0.588348	−	0.339683i
$53$	−5.65685			−0.777029			−0.388514	−	0.921443i	$-0.627012\pi$
$53$	−5.65685			−0.777029			−0.388514	+	0.921443i	$0.627012\pi$
$54$	6.36396	+	3.67423i	0.866025	+	0.500000i
$55$	−6.00000	−	7.34847i	−0.809040	−	0.990867i
$56$	−4.24264	+	7.34847i	−0.566947	+	0.981981i
$57$	6.36396	+	11.0227i	0.842927	+	1.45999i
$58$	−2.12132	+	1.22474i	−0.278543	+	0.160817i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−6.00000	+	4.89898i	−0.774597	+	0.632456i
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		−	10.3923i		−	1.31982i
$63$	4.50000	+	7.79423i	0.566947	+	0.981981i
$64$	8.00000			1.00000
$65$	−0.878680	−	5.40629i	−0.108987	−	0.670567i
$66$	9.00000	+	5.19615i	1.10782	+	0.639602i
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$	−1.41421	−	2.44949i	−0.171499	−	0.297044i
$69$	−4.50000	+	7.79423i	−0.541736	+	0.938315i
$70$	−9.36396	+	1.52192i	−1.11921	+	0.181904i
$71$	4.24264			0.503509			0.251754	−	0.967791i	$-0.418992\pi$
$71$	4.24264			0.503509			0.251754	+	0.967791i	$0.418992\pi$
$72$	4.24264	−	7.34847i	0.500000	−	0.866025i
$73$			4.89898i			0.573382i	0.958023	+	0.286691i	$0.0925553\pi$
$73$			4.89898i			0.573382i	−0.958023	+	0.286691i	$0.907445\pi$
$74$	−3.00000	−	1.73205i	−0.348743	−	0.201347i
$75$	−8.48528	−	1.73205i	−0.979796	−	0.200000i
$76$	12.7279	−	7.34847i	1.45999	−	0.842927i
$77$	6.36396	+	11.0227i	0.725241	+	1.25615i
$78$	3.00000	+	5.19615i	0.339683	+	0.588348i
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	5.65685	+	6.92820i	0.632456	+	0.774597i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		−	7.34847i		−	0.811503i
$83$	−4.50000	−	2.59808i	−0.493939	−	0.285176i	0.232268	−	0.972652i	$-0.425385\pi$
$83$	−4.50000	−	2.59808i	−0.493939	−	0.285176i	−0.726207	+	0.687476i	$0.758719\pi$
$84$	9.00000	−	5.19615i	0.981981	−	0.566947i
$85$	1.12132	−	2.95680i	0.121624	−	0.320710i
$86$	4.24264	+	7.34847i	0.457496	+	0.792406i
$87$	3.00000			0.321634
$88$	6.00000	−	10.3923i	0.639602	−	1.10782i
$89$		−	8.66025i		−	0.917985i	−0.888440	−	0.458993i	$-0.848210\pi$
$89$		−	8.66025i		−	0.917985i	0.888440	−	0.458993i	$-0.151790\pi$
$90$	9.36396	−	1.52192i	0.987048	−	0.160424i
$91$			7.34847i			0.770329i
$92$	9.00000	+	5.19615i	0.938315	+	0.541736i
$93$	−6.36396	+	11.0227i	−0.659912	+	1.14300i
$94$	−6.36396	+	3.67423i	−0.656392	+	0.378968i
$95$	15.3640	+	5.82655i	1.57631	+	0.597792i
$96$	−8.48528	−	4.89898i	−0.866025	−	0.500000i
$97$	12.7279	+	7.34847i	1.29232	+	0.746124i	0.979066	−	0.203544i	$-0.0652459\pi$
$97$	12.7279	+	7.34847i	1.29232	+	0.746124i	0.313259	+	0.949668i	$0.398579\pi$
$98$	2.82843			0.285714
$99$	−6.36396	−	11.0227i	−0.639602	−	1.10782i
$100$	−2.00000	+	9.79796i	−0.200000	+	0.979796i
$101$	9.00000	+	5.19615i	0.895533	+	0.517036i	0.875748	−	0.482768i	$-0.160368\pi$
$101$	9.00000	+	5.19615i	0.895533	+	0.517036i	0.0197851	+	0.999804i	$0.493702\pi$
$102$			3.46410i			0.342997i
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	0.679525	−	0.733652i	$-0.262186\pi$
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	−0.975124	+	0.221660i	$0.928852\pi$
$104$	6.00000	−	3.46410i	0.588348	−	0.339683i
$105$	10.8640	+	4.11999i	1.06021	+	0.402070i
$106$	4.00000	−	6.92820i	0.388514	−	0.672927i
$107$			5.19615i			0.502331i	0.967944	+	0.251166i	$0.0808138\pi$
$107$			5.19615i			0.502331i	−0.967944	+	0.251166i	$0.919186\pi$
$108$	−9.00000	+	5.19615i	−0.866025	+	0.500000i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$	13.2426	−	2.15232i	1.26264	−	0.205215i
$111$	2.12132	+	3.67423i	0.201347	+	0.348743i
$112$	−6.00000	−	10.3923i	−0.566947	−	0.981981i
$113$	1.41421	+	2.44949i	0.133038	+	0.230429i	0.924846	−	0.380341i	$-0.124193\pi$
$113$	1.41421	+	2.44949i	0.133038	+	0.230429i	−0.791808	+	0.610770i	$0.790860\pi$
$114$	−18.0000			−1.68585
$115$	1.86396	+	11.4685i	0.173815	+	1.06944i
$116$		−	3.46410i		−	0.321634i
$117$		−	7.34847i		−	0.679366i
$118$		0			0
$119$	−2.12132	+	3.67423i	−0.194461	+	0.336817i
$120$	−1.75736	−	10.8126i	−0.160424	−	0.987048i
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	−4.94975	−	8.57321i	−0.448129	−	0.776182i
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	12.7279	+	7.34847i	1.14300	+	0.659912i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$	−12.7279			−1.13389
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$		−	10.3923i		−	0.914991i
$130$	7.24264	+	2.74666i	0.635222	+	0.240898i
$131$	−8.48528	−	14.6969i	−0.741362	−	1.28408i	−0.951875	−	0.306486i	$-0.900847\pi$
$131$	−8.48528	−	14.6969i	−0.741362	−	1.28408i	0.210513	−	0.977591i	$-0.432487\pi$
$132$	−12.7279	+	7.34847i	−1.10782	+	0.639602i
$133$	−19.0919	−	11.0227i	−1.65548	−	0.955790i
$134$	4.24264			0.366508
$135$	−10.8640	−	4.11999i	−0.935021	−	0.354593i
$136$	4.00000			0.342997
$137$	2.82843	−	4.89898i	0.241649	−	0.418548i	−0.719535	−	0.694456i	$-0.755645\pi$
$137$	2.82843	−	4.89898i	0.241649	−	0.418548i	0.961184	+	0.275908i	$0.0889785\pi$
$138$	−6.36396	−	11.0227i	−0.541736	−	0.938315i
$139$	12.7279	−	7.34847i	1.07957	−	0.623289i	0.148788	−	0.988869i	$-0.452463\pi$
$139$	12.7279	−	7.34847i	1.07957	−	0.623289i	0.930780	+	0.365580i	$0.119129\pi$
$140$	4.75736	−	12.5446i	0.402070	−	1.06021i
$141$	9.00000			0.757937
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$		−	10.3923i		−	0.869048i
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$	3.00000	−	2.44949i	0.249136	−	0.203419i
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$	−3.00000	−	1.73205i	−0.247436	−	0.142857i
$148$	4.24264	−	2.44949i	0.348743	−	0.201347i
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.988492	−	0.151272i	$-0.951663\pi$
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.363241	+	0.931695i	$0.618330\pi$
$150$	8.12132	−	9.16756i	0.663103	−	0.748528i
$151$	−6.36396	−	3.67423i	−0.517892	−	0.299005i	0.218180	−	0.975909i	$-0.429988\pi$
$151$	−6.36396	−	3.67423i	−0.517892	−	0.299005i	−0.736072	+	0.676904i	$0.763321\pi$
$152$			20.7846i			1.68585i
$153$	2.12132	−	3.67423i	0.171499	−	0.297044i
$154$	−18.0000			−1.45048
$155$	2.63604	+	16.2189i	0.211732	+	1.30273i
$156$	−8.48528			−0.679366
$157$	−8.48528	+	4.89898i	−0.677199	+	0.390981i	−0.798799	−	0.601598i	$-0.794531\pi$
$157$	−8.48528	+	4.89898i	−0.677199	+	0.390981i	0.121600	+	0.992579i	$0.461198\pi$
$158$		0			0
$159$	−8.48528	+	4.89898i	−0.672927	+	0.388514i
$160$	−12.4853	+	2.02922i	−0.987048	+	0.160424i
$161$		−	15.5885i		−	1.22854i
$162$	12.7279			1.00000
$163$	18.0000			1.40987			0.704934	−	0.709273i	$-0.250976\pi$
$163$	18.0000			1.40987			0.704934	+	0.709273i	$0.250976\pi$
$164$	9.00000	+	5.19615i	0.702782	+	0.405751i
$165$	−15.3640	−	5.82655i	−1.19608	−	0.453596i
$166$	6.36396	−	3.67423i	0.493939	−	0.285176i
$167$	4.50000	−	2.59808i	0.348220	−	0.201045i	−0.315681	−	0.948865i	$-0.602233\pi$
$167$	4.50000	−	2.59808i	0.348220	−	0.201045i	0.663901	+	0.747820i	$0.268900\pi$
$168$			14.6969i			1.13389i
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$	2.82843	+	3.46410i	0.216930	+	0.265684i
$171$	19.0919	+	11.0227i	1.45999	+	0.842927i
$172$	−12.0000			−0.914991
$173$	9.89949	−	17.1464i	0.752645	−	1.30362i	−0.193892	−	0.981023i	$-0.562111\pi$
$173$	9.89949	−	17.1464i	0.752645	−	1.30362i	0.946537	−	0.322596i	$-0.104555\pi$
$174$	−2.12132	+	3.67423i	−0.160817	+	0.278543i
$175$	14.2279	−	4.75039i	1.07553	−	0.359096i
$176$	8.48528	+	14.6969i	0.639602	+	1.10782i
$177$		0			0
$178$	10.6066	+	6.12372i	0.794998	+	0.458993i
$179$	−4.24264			−0.317110			−0.158555	−	0.987350i	$-0.550683\pi$
$179$	−4.24264			−0.317110			−0.158555	+	0.987350i	$0.550683\pi$
$180$	−4.75736	+	12.5446i	−0.354593	+	0.935021i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−9.00000	−	5.19615i	−0.667124	−	0.385164i
$183$			12.1244i			0.896258i
$184$	−12.7279	+	7.34847i	−0.938315	+	0.541736i
$185$	5.12132	+	1.94218i	0.376527	+	0.142792i
$186$	−9.00000	−	15.5885i	−0.659912	−	1.14300i
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$		−	10.3923i		−	0.757937i
$189$	13.5000	+	7.79423i	0.981981	+	0.566947i
$190$	−18.0000	+	14.6969i	−1.30586	+	1.06623i
$191$	6.36396	−	11.0227i	0.460480	−	0.797575i	−0.538505	−	0.842622i	$-0.681011\pi$
$191$	6.36396	−	11.0227i	0.460480	−	0.797575i	0.998985	+	0.0450476i	$0.0143439\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	14.8492	−	8.57321i	1.06887	−	0.617113i	0.140999	−	0.990010i	$-0.454969\pi$
$193$	14.8492	−	8.57321i	1.06887	−	0.617113i	0.927873	+	0.372896i	$0.121635\pi$
$194$	−18.0000	+	10.3923i	−1.29232	+	0.746124i
$195$	−6.00000	−	7.34847i	−0.429669	−	0.526235i
$196$	−2.00000	+	3.46410i	−0.142857	+	0.247436i
$197$	−14.1421			−1.00759			−0.503793	−	0.863825i	$-0.668062\pi$
$197$	−14.1421			−1.00759			−0.503793	+	0.863825i	$0.668062\pi$
$198$	18.0000			1.27920
$199$		−	22.0454i		−	1.56276i	−0.624057	−	0.781379i	$-0.714517\pi$
$199$		−	22.0454i		−	1.56276i	0.624057	−	0.781379i	$-0.285483\pi$
$200$	−10.5858	−	9.37769i	−0.748528	−	0.663103i
$201$	−4.50000	−	2.59808i	−0.317406	−	0.183254i
$202$	−12.7279	+	7.34847i	−0.895533	+	0.517036i
$203$	−4.50000	+	2.59808i	−0.315838	+	0.182349i
$204$	−4.24264	−	2.44949i	−0.297044	−	0.171499i
$205$	1.86396	+	11.4685i	0.130185	+	0.800992i
$206$	8.48528			0.591198
$207$			15.5885i			1.08347i
$208$			9.79796i			0.679366i
$209$	27.0000	+	15.5885i	1.86763	+	1.07828i
$210$	−12.7279	+	10.3923i	−0.878310	+	0.717137i
$211$	−19.0919	+	11.0227i	−1.31434	+	0.758834i	−0.982812	−	0.184611i	$-0.940897\pi$
$211$	−19.0919	+	11.0227i	−1.31434	+	0.758834i	−0.331528	+	0.943445i	$0.607564\pi$
$212$	5.65685	+	9.79796i	0.388514	+	0.672927i
$213$	6.36396	−	3.67423i	0.436051	−	0.251754i
$214$	−6.36396	−	3.67423i	−0.435031	−	0.251166i
$215$	−8.48528	−	10.3923i	−0.578691	−	0.708749i
$216$		−	14.6969i		−	1.00000i
$217$		−	22.0454i		−	1.49654i
$218$	−3.53553	+	6.12372i	−0.239457	+	0.414751i
$219$	4.24264	+	7.34847i	0.286691	+	0.496564i
$220$	−6.72792	+	17.7408i	−0.453596	+	1.19608i
$221$	3.00000	−	1.73205i	0.201802	−	0.116510i
$222$	−6.00000			−0.402694
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	−0.675098	−	0.737728i	$-0.735899\pi$
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	0.976440	+	0.215788i	$0.0692320\pi$
$224$	16.9706			1.13389
$225$	−14.2279	+	4.75039i	−0.948528	+	0.316693i
$226$	−4.00000			−0.266076
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	0.170648	−	0.985332i	$-0.445414\pi$
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	−0.767999	+	0.640451i	$0.778747\pi$
$228$	12.7279	−	22.0454i	0.842927	−	1.45999i
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	−15.3640	−	5.82655i	−1.01307	−	0.384191i
$231$	19.0919	+	11.0227i	1.25615	+	0.725241i
$232$	4.24264	+	2.44949i	0.278543	+	0.160817i
$233$	−1.41421			−0.0926482			−0.0463241	−	0.998926i	$-0.514751\pi$
$233$	−1.41421			−0.0926482			−0.0463241	+	0.998926i	$0.514751\pi$
$234$	9.00000	+	5.19615i	0.588348	+	0.339683i
$235$	9.00000	−	7.34847i	0.587095	−	0.479361i
$236$		0			0
$237$		0			0
$238$	−3.00000	−	5.19615i	−0.194461	−	0.336817i
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	0.998353	+	0.0573782i	$0.0182741\pi$
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	−0.449485	+	0.893288i	$0.648393\pi$
$240$	14.4853	+	5.49333i	0.935021	+	0.354593i
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	9.89949			0.636364
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	14.0000			0.896258
$245$	−4.41421	+	0.717439i	−0.282014	+	0.0458355i
$246$	−6.36396	−	11.0227i	−0.405751	−	0.702782i
$247$	9.00000	+	15.5885i	0.572656	+	0.991870i
$248$	−18.0000	+	10.3923i	−1.14300	+	0.659912i
$249$	−9.00000			−0.570352
$250$	0.636039	−	15.7986i	0.0402266	−	0.999191i
$251$	−29.6985			−1.87455			−0.937276	−	0.348589i	$-0.886661\pi$
$251$	−29.6985			−1.87455			−0.937276	+	0.348589i	$0.886661\pi$
$252$	9.00000	−	15.5885i	0.566947	−	0.981981i
$253$			22.0454i			1.38598i
$254$	6.36396	−	11.0227i	0.399310	−	0.691626i
$255$	−0.878680	−	5.40629i	−0.0550251	−	0.338555i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−1.41421	−	2.44949i	−0.0882162	−	0.152795i	0.818541	−	0.574448i	$-0.194783\pi$
$257$	−1.41421	−	2.44949i	−0.0882162	−	0.152795i	−0.906757	+	0.421653i	$0.861450\pi$
$258$	12.7279	+	7.34847i	0.792406	+	0.457496i
$259$	−6.36396	−	3.67423i	−0.395437	−	0.228306i
$260$	−8.48528	+	6.92820i	−0.526235	+	0.429669i
$261$	4.50000	−	2.59808i	0.278543	−	0.160817i
$262$	24.0000			1.48272
$263$	−18.0000	−	10.3923i	−1.10993	−	0.640817i	−0.171117	−	0.985251i	$-0.554738\pi$
$263$	−18.0000	−	10.3923i	−1.10993	−	0.640817i	−0.938811	+	0.344434i	$0.888071\pi$
$264$		−	20.7846i		−	1.27920i
$265$	−4.48528	+	11.8272i	−0.275529	+	0.726538i
$266$	27.0000	−	15.5885i	1.65548	−	0.955790i
$267$	−7.50000	−	12.9904i	−0.458993	−	0.794998i
$268$	−3.00000	+	5.19615i	−0.183254	+	0.317406i
$269$		−	22.5167i		−	1.37287i	−0.727194	−	0.686433i	$-0.759176\pi$
$269$		−	22.5167i		−	1.37287i	0.727194	−	0.686433i	$-0.240824\pi$
$270$	12.7279	−	10.3923i	0.774597	−	0.632456i
$271$			7.34847i			0.446388i	0.974774	+	0.223194i	$0.0716483\pi$
$271$			7.34847i			0.446388i	−0.974774	+	0.223194i	$0.928352\pi$
$272$	−2.82843	+	4.89898i	−0.171499	+	0.297044i
$273$	6.36396	+	11.0227i	0.385164	+	0.667124i
$274$	4.00000	+	6.92820i	0.241649	+	0.418548i
$275$	−20.1213	+	6.71807i	−1.21336	+	0.405115i
$276$	18.0000			1.08347
$277$	6.36396	+	3.67423i	0.382373	+	0.220763i	0.678850	−	0.734277i	$-0.262478\pi$
$277$	6.36396	+	3.67423i	0.382373	+	0.220763i	−0.296477	+	0.955040i	$0.595812\pi$
$278$			20.7846i			1.24658i
$279$			22.0454i			1.31982i
$280$	12.0000	+	14.6969i	0.717137	+	0.878310i
$281$	−19.5000	−	11.2583i	−1.16327	−	0.671616i	−0.211186	−	0.977446i	$-0.567733\pi$
$281$	−19.5000	−	11.2583i	−1.16327	−	0.671616i	−0.952086	+	0.305830i	$0.901066\pi$
$282$	−6.36396	+	11.0227i	−0.378968	+	0.656392i
$283$	10.5000	+	18.1865i	0.624160	+	1.08108i	0.988703	+	0.149890i	$0.0478921\pi$
$283$	10.5000	+	18.1865i	0.624160	+	1.08108i	−0.364542	+	0.931187i	$0.618775\pi$
$284$	−4.24264	−	7.34847i	−0.251754	−	0.436051i
$285$	28.0919	−	4.56575i	1.66402	−	0.270452i
$286$	12.7279	+	7.34847i	0.752618	+	0.434524i
$287$		−	15.5885i		−	0.920158i
$288$	−16.9706			−1.00000
$289$	−15.0000			−0.882353
$290$	0.878680	+	5.40629i	0.0515978	+	0.317468i
$291$	25.4558			1.49225
$292$	8.48528	−	4.89898i	0.496564	−	0.286691i
$293$	7.77817	+	13.4722i	0.454406	+	0.787054i	0.998654	−	0.0518704i	$-0.0165183\pi$
$293$	7.77817	+	13.4722i	0.454406	+	0.787054i	−0.544248	+	0.838924i	$0.683185\pi$
$294$	4.24264	−	2.44949i	0.247436	−	0.142857i
$295$		0			0
$296$			6.92820i			0.402694i
$297$	−19.0919	−	11.0227i	−1.10782	−	0.639602i
$298$		−	26.9444i		−	1.56085i
$299$	−6.36396	+	11.0227i	−0.368037	+	0.637459i
$300$	5.48528	+	16.4290i	0.316693	+	0.948528i
$301$	9.00000	+	15.5885i	0.518751	+	0.898504i
$302$	9.00000	−	5.19615i	0.517892	−	0.299005i
$303$	18.0000			1.03407
$304$	−25.4558	−	14.6969i	−1.45999	−	0.842927i
$305$	9.89949	+	12.1244i	0.566843	+	0.694239i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	21.0000			1.19853			0.599267	−	0.800549i	$-0.295459\pi$
$307$	21.0000			1.19853			0.599267	+	0.800549i	$0.295459\pi$
$308$	12.7279	−	22.0454i	0.725241	−	1.25615i
$309$	−9.00000	−	5.19615i	−0.511992	−	0.295599i
$310$	−21.7279	−	8.23999i	−1.23406	−	0.468000i
$311$	−14.8492	−	25.7196i	−0.842023	−	1.45843i	−0.888181	−	0.459493i	$-0.848031\pi$
$311$	−14.8492	−	25.7196i	−0.842023	−	1.45843i	0.0461581	−	0.998934i	$-0.485302\pi$
$312$	6.00000	−	10.3923i	0.339683	−	0.588348i
$313$	2.12132	+	1.22474i	0.119904	+	0.0692267i	0.558753	−	0.829334i	$-0.311280\pi$
$313$	2.12132	+	1.22474i	0.119904	+	0.0692267i	−0.438848	+	0.898561i	$0.644613\pi$
$314$		−	13.8564i		−	0.781962i
$315$	19.8640	−	3.22848i	1.11921	−	0.181904i
$316$		0			0
$317$	3.53553	−	6.12372i	0.198575	−	0.343943i	−0.749491	−	0.662014i	$-0.769702\pi$
$317$	3.53553	−	6.12372i	0.198575	−	0.343943i	0.948067	+	0.318071i	$0.103035\pi$
$318$		−	13.8564i		−	0.777029i
$319$	6.36396	−	3.67423i	0.356313	−	0.205718i
$320$	6.34315	−	16.7262i	0.354593	−	0.935021i
$321$	4.50000	+	7.79423i	0.251166	+	0.435031i
$322$	19.0919	+	11.0227i	1.06395	+	0.614271i
$323$			10.3923i			0.578243i
$324$	−9.00000	+	15.5885i	−0.500000	+	0.866025i
$325$	−12.0000	−	2.44949i	−0.665640	−	0.135873i
$326$	−12.7279	+	22.0454i	−0.704934	+	1.22098i
$327$	7.50000	−	4.33013i	0.414751	−	0.239457i
$328$	−12.7279	+	7.34847i	−0.702782	+	0.405751i
$329$	−13.5000	+	7.79423i	−0.744279	+	0.429710i
$330$	18.0000	−	14.6969i	0.990867	−	0.809040i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$			10.3923i			0.570352i
$333$	6.36396	+	3.67423i	0.348743	+	0.201347i
$334$			7.34847i			0.402090i
$335$	−6.62132	+	1.07616i	−0.361761	+	0.0587968i
$336$	−18.0000	−	10.3923i	−0.981981	−	0.566947i
$337$	−25.4558	+	14.6969i	−1.38667	+	0.800593i	−0.992938	−	0.118633i	$-0.962149\pi$
$337$	−25.4558	+	14.6969i	−1.38667	+	0.800593i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	−4.94975	−	8.57321i	−0.269231	−	0.466321i
$339$	4.24264	+	2.44949i	0.230429	+	0.133038i
$340$	−6.24264	+	1.01461i	−0.338555	+	0.0550251i
$341$			31.1769i			1.68832i
$342$	−27.0000	+	15.5885i	−1.45999	+	0.842927i
$343$	−15.0000			−0.809924
$344$	8.48528	−	14.6969i	0.457496	−	0.792406i
$345$	12.7279	+	15.5885i	0.685248	+	0.839254i
$346$	14.0000	+	24.2487i	0.752645	+	1.30362i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	9.50000	−	16.4545i	0.508523	−	0.880788i	−0.491428	−	0.870918i	$-0.663525\pi$
$349$	9.50000	−	16.4545i	0.508523	−	0.880788i	0.999951	−	0.00987003i	$-0.00314178\pi$
$350$	−4.24264	+	20.7846i	−0.226779	+	1.11098i
$351$	−6.36396	−	11.0227i	−0.339683	−	0.588348i
$352$	−24.0000			−1.27920
$353$	−14.1421	+	24.4949i	−0.752710	+	1.30373i	0.193795	+	0.981042i	$0.437920\pi$
$353$	−14.1421	+	24.4949i	−0.752710	+	1.30373i	−0.946505	+	0.322690i	$0.895413\pi$
$354$		0			0
$355$	3.36396	−	8.87039i	0.178541	−	0.470791i
$356$	−15.0000	+	8.66025i	−0.794998	+	0.458993i
$357$			7.34847i			0.388922i
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	21.2132			1.11959			0.559795	−	0.828631i	$-0.310880\pi$
$359$	21.2132			1.11959			0.559795	+	0.828631i	$0.310880\pi$
$360$	−12.0000	−	14.6969i	−0.632456	−	0.774597i
$361$	−35.0000			−1.84211
$362$	−4.94975	+	8.57321i	−0.260153	+	0.450598i
$363$	−10.5000	−	6.06218i	−0.551107	−	0.318182i
$364$	12.7279	−	7.34847i	0.667124	−	0.385164i
$365$	10.2426	+	3.88437i	0.536124	+	0.203317i
$366$	−14.8492	−	8.57321i	−0.776182	−	0.448129i
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	−0.999404	−	0.0345320i	$-0.989006\pi$
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$368$		−	20.7846i		−	1.08347i
$369$			15.5885i			0.811503i
$370$	−6.00000	+	4.89898i	−0.311925	+	0.254686i
$371$	8.48528	−	14.6969i	0.440534	−	0.763027i
$372$	25.4558			1.31982
$373$	12.7279	−	7.34847i	0.659027	−	0.380489i	−0.132879	−	0.991132i	$-0.542422\pi$
$373$	12.7279	−	7.34847i	0.659027	−	0.380489i	0.791906	+	0.610643i	$0.209089\pi$
$374$	4.24264	+	7.34847i	0.219382	+	0.379980i
$375$	−10.3492	+	16.3674i	−0.534433	+	0.845211i
$376$	12.7279	+	7.34847i	0.656392	+	0.378968i
$377$	4.24264			0.218507
$378$	−19.0919	+	11.0227i	−0.981981	+	0.566947i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−5.27208	−	32.4377i	−0.270452	−	1.66402i
$381$	−13.5000	+	7.79423i	−0.691626	+	0.399310i
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.0361995	−	0.999345i	$-0.488475\pi$
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.883558	+	0.468323i	$0.155141\pi$
$384$			19.5959i			1.00000i
$385$	28.0919	−	4.56575i	1.43169	−	0.232692i
$386$			24.2487i			1.23423i
$387$	−9.00000	−	15.5885i	−0.457496	−	0.792406i
$388$		−	29.3939i		−	1.49225i
$389$	−13.5000	−	7.79423i	−0.684477	−	0.395183i	0.117063	−	0.993125i	$-0.462652\pi$
$389$	−13.5000	−	7.79423i	−0.684477	−	0.395183i	−0.801540	+	0.597941i	$0.795986\pi$
$390$	13.2426	−	2.15232i	0.670567	−	0.108987i
$391$	−6.36396	+	3.67423i	−0.321839	+	0.185814i
$392$	−2.82843	−	4.89898i	−0.142857	−	0.247436i
$393$	−25.4558	−	14.6969i	−1.28408	−	0.741362i
$394$	10.0000	−	17.3205i	0.503793	−	0.872595i
$395$		0			0
$396$	−12.7279	+	22.0454i	−0.639602	+	1.10782i
$397$		−	24.4949i		−	1.22936i	−0.788775	−	0.614682i	$-0.789284\pi$
$397$		−	24.4949i		−	1.22936i	0.788775	−	0.614682i	$-0.210716\pi$
$398$	27.0000	+	15.5885i	1.35339	+	0.781379i
$399$	−38.1838			−1.91158
$400$	18.9706	−	6.33386i	0.948528	−	0.316693i
$401$	15.0000	−	8.66025i	0.749064	−	0.432472i	−0.0762914	−	0.997086i	$-0.524308\pi$
$401$	15.0000	−	8.66025i	0.749064	−	0.432472i	0.825356	+	0.564613i	$0.190975\pi$
$402$	6.36396	−	3.67423i	0.317406	−	0.183254i
$403$	−9.00000	+	15.5885i	−0.448322	+	0.776516i
$404$		−	20.7846i		−	1.03407i
$405$	−19.8640	+	3.22848i	−0.987048	+	0.160424i
$406$		−	7.34847i		−	0.364698i
$407$	9.00000	+	5.19615i	0.446113	+	0.257564i
$408$	6.00000	−	3.46410i	0.297044	−	0.171499i
$409$	14.0000	+	24.2487i	0.692255	+	1.19902i	0.971097	+	0.238685i	$0.0767162\pi$
$409$	14.0000	+	24.2487i	0.692255	+	1.19902i	−0.278842	+	0.960337i	$0.589950\pi$
$410$	−15.3640	−	5.82655i	−0.758772	−	0.287753i
$411$		−	9.79796i		−	0.483298i
$412$	−6.00000	+	10.3923i	−0.295599	+	0.511992i
$413$		0			0
$414$	−19.0919	−	11.0227i	−0.938315	−	0.541736i
$415$	−9.00000	+	7.34847i	−0.441793	+	0.360722i
$416$	−12.0000	−	6.92820i	−0.588348	−	0.339683i
$417$	12.7279	−	22.0454i	0.623289	−	1.07957i
$418$	−38.1838	+	22.0454i	−1.86763	+	1.07828i
$419$	2.12132	+	3.67423i	0.103633	+	0.179498i	0.913179	−	0.407559i	$-0.133620\pi$
$419$	2.12132	+	3.67423i	0.103633	+	0.179498i	−0.809546	+	0.587057i	$0.800287\pi$
$420$	−3.72792	−	22.9369i	−0.181904	−	1.11921i
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	−0.999895	−	0.0145228i	$-0.995377\pi$
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	0.512524	+	0.858673i	$0.328710\pi$
$422$		−	31.1769i		−	1.51767i
$423$	13.5000	−	7.79423i	0.656392	−	0.378968i
$424$	−16.0000			−0.777029
$425$	−5.29289	−	4.68885i	−0.256743	−	0.227442i
$426$			10.3923i			0.503509i
$427$	−10.5000	−	18.1865i	−0.508131	−	0.880108i
$428$	9.00000	−	5.19615i	0.435031	−	0.251166i
$429$	−9.00000	−	15.5885i	−0.434524	−	0.752618i
$430$	18.7279	−	3.04384i	0.903141	−	0.146787i
$431$	25.4558			1.22616			0.613082	−	0.790019i	$-0.289929\pi$
$431$	25.4558			1.22616			0.613082	+	0.790019i	$0.289929\pi$
$432$	18.0000	+	10.3923i	0.866025	+	0.500000i
$433$			12.2474i			0.588575i	0.955717	+	0.294287i	$0.0950823\pi$
$433$			12.2474i			0.588575i	−0.955717	+	0.294287i	$0.904918\pi$
$434$	27.0000	+	15.5885i	1.29604	+	0.748270i
$435$	2.37868	−	6.27231i	0.114049	−	0.300734i
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$	−19.0919	−	33.0681i	−0.913289	−	1.58186i
$438$	−12.0000			−0.573382
$439$	12.7279	+	7.34847i	0.607471	+	0.350723i	0.771975	−	0.635653i	$-0.219269\pi$
$439$	12.7279	+	7.34847i	0.607471	+	0.350723i	−0.164504	+	0.986376i	$0.552602\pi$
$440$	−16.9706	−	20.7846i	−0.809040	−	0.990867i
$441$	−6.00000			−0.285714
$442$			4.89898i			0.233021i
$443$	31.5000	+	18.1865i	1.49661	+	0.864068i	0.999992	−	0.00390106i	$-0.00124175\pi$
$443$	31.5000	+	18.1865i	1.49661	+	0.864068i	0.496618	+	0.867969i	$0.334575\pi$
$444$	4.24264	−	7.34847i	0.201347	−	0.348743i
$445$	−18.1066	−	6.86666i	−0.858335	−	0.325511i
$446$	6.36396	+	11.0227i	0.301342	+	0.521940i
$447$	−16.5000	+	28.5788i	−0.780423	+	1.35173i
$448$	−12.0000	+	20.7846i	−0.566947	+	0.981981i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	4.24264	−	20.7846i	0.200000	−	0.979796i
$451$			22.0454i			1.03808i
$452$	2.82843	−	4.89898i	0.133038	−	0.230429i
$453$	−12.7279			−0.598010
$454$	12.7279	−	7.34847i	0.597351	−	0.344881i
$455$	15.3640	+	5.82655i	0.720274	+	0.273153i
$456$	18.0000	+	31.1769i	0.842927	+	1.45999i
$457$	−14.8492	−	8.57321i	−0.694618	−	0.401038i	0.110722	−	0.993851i	$-0.464684\pi$
$457$	−14.8492	−	8.57321i	−0.694618	−	0.401038i	−0.805340	+	0.592813i	$0.798017\pi$
$458$	1.41421			0.0660819
$459$		−	7.34847i		−	0.342997i
$460$	18.0000	−	14.6969i	0.839254	−	0.685248i
$461$	4.50000	+	2.59808i	0.209586	+	0.121004i	0.601119	−	0.799160i	$-0.294722\pi$
$461$	4.50000	+	2.59808i	0.209586	+	0.121004i	−0.391533	+	0.920164i	$0.628055\pi$
$462$	−27.0000	+	15.5885i	−1.25615	+	0.725241i
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	−0.892778	−	0.450497i	$-0.851247\pi$
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	0.0562469	−	0.998417i	$-0.482087\pi$
$464$	−6.00000	+	3.46410i	−0.278543	+	0.160817i
$465$	18.0000	+	22.0454i	0.834730	+	1.02233i
$466$	1.00000	−	1.73205i	0.0463241	−	0.0802357i
$467$			20.7846i			0.961797i	0.876776	+	0.480899i	$0.159689\pi$
$467$			20.7846i			0.961797i	−0.876776	+	0.480899i	$0.840311\pi$
$468$	−12.7279	+	7.34847i	−0.588348	+	0.339683i
$469$	9.00000			0.415581
$470$	2.63604	+	16.2189i	0.121591	+	0.748120i
$471$	−8.48528	+	14.6969i	−0.390981	+	0.677199i
$472$		0			0
$473$	−12.7279	−	22.0454i	−0.585230	−	1.01365i
$474$		0			0
$475$	24.3640	−	27.5027i	1.11790	−	1.26191i
$476$	8.48528			0.388922
$477$	−8.48528	+	14.6969i	−0.388514	+	0.672927i
$478$	−24.0000			−1.09773
$479$	4.24264	−	7.34847i	0.193851	−	0.335760i	−0.752672	−	0.658396i	$-0.771235\pi$
$479$	4.24264	−	7.34847i	0.193851	−	0.335760i	0.946523	+	0.322635i	$0.104569\pi$
$480$	−16.9706	+	13.8564i	−0.774597	+	0.632456i
$481$	3.00000	+	5.19615i	0.136788	+	0.236924i
$482$	17.6777	+	30.6186i	0.805196	+	1.39464i
$483$	−13.5000	−	23.3827i	−0.614271	−	1.06395i
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	25.4558	−	20.7846i	1.15589	−	0.943781i
$486$	19.0919	−	11.0227i	0.866025	−	0.500000i
$487$	−12.0000			−0.543772			−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$	−9.89949	+	17.1464i	−0.448129	+	0.776182i
$489$	27.0000	−	15.5885i	1.22098	−	0.704934i
$490$	2.24264	−	5.91359i	0.101312	−	0.267149i
$491$	8.48528	+	14.6969i	0.382935	+	0.663264i	0.991480	−	0.130256i	$-0.0415799\pi$
$491$	8.48528	+	14.6969i	0.382935	+	0.663264i	−0.608545	+	0.793519i	$0.708247\pi$
$492$	18.0000			0.811503
$493$	2.12132	+	1.22474i	0.0955395	+	0.0551597i
$494$	−25.4558			−1.14531
$495$	−28.0919	+	4.56575i	−1.26264	+	0.205215i
$496$		−	29.3939i		−	1.31982i
$497$	−6.36396	+	11.0227i	−0.285463	+	0.494436i
$498$	6.36396	−	11.0227i	0.285176	−	0.493939i
$499$	−12.7279	+	7.34847i	−0.569780	+	0.328963i	−0.757061	−	0.653344i	$-0.773366\pi$
$499$	−12.7279	+	7.34847i	−0.569780	+	0.328963i	0.187281	+	0.982306i	$0.440032\pi$
$500$	18.8995	+	11.9503i	0.845211	+	0.534433i
$501$	4.50000	−	7.79423i	0.201045	−	0.348220i
$502$	21.0000	−	36.3731i	0.937276	−	1.62341i
$503$			25.9808i			1.15842i	0.815177	+	0.579212i	$0.196640\pi$
$503$			25.9808i			1.15842i	−0.815177	+	0.579212i	$0.803360\pi$
$504$	12.7279	+	22.0454i	0.566947	+	0.981981i
$505$	18.0000	−	14.6969i	0.800989	−	0.654005i
$506$	−27.0000	−	15.5885i	−1.20030	−	0.692991i
$507$			12.1244i			0.538462i
$508$	9.00000	+	15.5885i	0.399310	+	0.691626i
$509$	13.5000	−	7.79423i	0.598377	−	0.345473i	−0.170026	−	0.985440i	$-0.554385\pi$
$509$	13.5000	−	7.79423i	0.598377	−	0.345473i	0.768403	+	0.639966i	$0.221052\pi$
$510$	7.24264	+	2.74666i	0.320710	+	0.121624i
$511$	−12.7279	−	7.34847i	−0.563050	−	0.325077i
$512$	22.6274			1.00000
$513$	38.1838			1.68585
$514$	4.00000			0.176432
$515$	−13.2426	+	2.15232i	−0.583540	+	0.0948424i
$516$	−18.0000	+	10.3923i	−0.792406	+	0.457496i
$517$	19.0919	−	11.0227i	0.839660	−	0.484778i
$518$	9.00000	−	5.19615i	0.395437	−	0.228306i
$519$		−	34.2929i		−	1.50529i
$520$	−2.48528	−	15.2913i	−0.108987	−	0.670567i
$521$			25.9808i			1.13824i	0.822255	+	0.569119i	$0.192716\pi$
$521$			25.9808i			1.13824i	−0.822255	+	0.569119i	$0.807284\pi$
$522$			7.34847i			0.321634i
$523$	−27.0000			−1.18063			−0.590314	−	0.807174i	$-0.700996\pi$
$523$	−27.0000			−1.18063			−0.590314	+	0.807174i	$0.700996\pi$
$524$	−16.9706	+	29.3939i	−0.741362	+	1.28408i
$525$	17.2279	−	19.4473i	0.751888	−	0.848751i
$526$	25.4558	−	14.6969i	1.10993	−	0.640817i
$527$	−9.00000	+	5.19615i	−0.392046	+	0.226348i
$528$	25.4558	+	14.6969i	1.10782	+	0.639602i
$529$	2.00000	−	3.46410i	0.0869565	−	0.150613i
$530$	−11.3137	−	13.8564i	−0.491436	−	0.601884i
$531$		0			0
$532$			44.0908i			1.91158i
$533$	−6.36396	+	11.0227i	−0.275654	+	0.477446i
$534$	21.2132			0.917985
$535$	10.8640	+	4.11999i	0.469690	+	0.178123i
$536$	−4.24264	−	7.34847i	−0.183254	−	0.317406i
$537$	−6.36396	+	3.67423i	−0.274625	+	0.158555i
$538$	27.5772	+	15.9217i	1.18894	+	0.686433i
$539$	−8.48528			−0.365487
$540$	3.72792	+	22.9369i	0.160424	+	0.987048i
$541$	31.0000			1.33279			0.666397	−	0.745597i	$-0.267836\pi$
$541$	31.0000			1.33279			0.666397	+	0.745597i	$0.267836\pi$
$542$	−9.00000	−	5.19615i	−0.386583	−	0.223194i
$543$	10.5000	−	6.06218i	0.450598	−	0.260153i
$544$	−4.00000	−	6.92820i	−0.171499	−	0.297044i
$545$	3.96447	−	10.4539i	0.169819	−	0.447794i
$546$	−18.0000			−0.770329
$547$	13.5000	−	23.3827i	0.577218	−	0.999771i	−0.418578	−	0.908181i	$-0.637471\pi$
$547$	13.5000	−	23.3827i	0.577218	−	0.999771i	0.995797	−	0.0915908i	$-0.0291952\pi$
$548$	−11.3137			−0.483298
$549$	10.5000	+	18.1865i	0.448129	+	0.776182i
$550$	6.00000	−	29.3939i	0.255841	−	1.25336i
$551$	−6.36396	+	11.0227i	−0.271114	+	0.469583i
$552$	−12.7279	+	22.0454i	−0.541736	+	0.938315i
$553$		0			0
$554$	−9.00000	+	5.19615i	−0.382373	+	0.220763i
$555$	9.36396	−	1.52192i	0.397478	−	0.0646018i
$556$	−25.4558	−	14.6969i	−1.07957	−	0.623289i
$557$	14.1421			0.599222			0.299611	−	0.954062i	$-0.403143\pi$
$557$	14.1421			0.599222			0.299611	+	0.954062i	$0.403143\pi$
$558$	−27.0000	−	15.5885i	−1.14300	−	0.659912i
$559$		−	14.6969i		−	0.621614i
$560$	−26.4853	+	4.30463i	−1.11921	+	0.181904i
$561$		−	10.3923i		−	0.438763i
$562$	27.5772	−	15.9217i	1.16327	−	0.671616i
$563$	13.5000	−	7.79423i	0.568957	−	0.328488i	−0.187776	−	0.982212i	$-0.560128\pi$
$563$	13.5000	−	7.79423i	0.568957	−	0.328488i	0.756733	+	0.653724i	$0.226794\pi$
$564$	−9.00000	−	15.5885i	−0.378968	−	0.656392i
$565$	6.24264	−	1.01461i	0.262630	−	0.0426850i
$566$	−29.6985			−1.24832
$567$	27.0000			1.13389
$568$	12.0000			0.503509
$569$	21.0000	+	12.1244i	0.880366	+	0.508279i	0.870779	−	0.491675i	$-0.163615\pi$
$569$	21.0000	+	12.1244i	0.880366	+	0.508279i	0.00958679	+	0.999954i	$0.496948\pi$
$570$	−14.2721	+	37.6339i	−0.597792	+	1.57631i
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$	−18.0000	+	10.3923i	−0.752618	+	0.434524i
$573$		−	22.0454i		−	0.920960i
$574$	19.0919	+	11.0227i	0.796880	+	0.460079i
$575$	25.4558	+	5.19615i	1.06158	+	0.216695i
$576$	12.0000	−	20.7846i	0.500000	−	0.866025i
$577$			4.89898i			0.203947i	0.994787	+	0.101974i	$0.0325157\pi$
$577$			4.89898i			0.203947i	−0.994787	+	0.101974i	$0.967484\pi$
$578$	10.6066	−	18.3712i	0.441176	−	0.764140i
$579$	14.8492	−	25.7196i	0.617113	−	1.06887i
$580$	−7.24264	−	2.74666i	−0.300734	−	0.114049i
$581$	13.5000	−	7.79423i	0.560074	−	0.323359i
$582$	−18.0000	+	31.1769i	−0.746124	+	1.29232i
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$			13.8564i			0.573382i
$585$	−15.3640	−	5.82655i	−0.635222	−	0.240898i
$586$	−22.0000			−0.908812
$587$	−4.50000	−	2.59808i	−0.185735	−	0.107234i	0.404249	−	0.914649i	$-0.367533\pi$
$587$	−4.50000	−	2.59808i	−0.185735	−	0.107234i	−0.589984	+	0.807415i	$0.700866\pi$
$588$			6.92820i			0.285714i
$589$	−27.0000	−	46.7654i	−1.11252	−	1.92693i
$590$		0			0
$591$	−21.2132	+	12.2474i	−0.872595	+	0.503793i
$592$	−8.48528	−	4.89898i	−0.348743	−	0.201347i
$593$	26.8701			1.10342			0.551711	−	0.834036i	$-0.313975\pi$
$593$	26.8701			1.10342			0.551711	+	0.834036i	$0.313975\pi$
$594$	27.0000	−	15.5885i	1.10782	−	0.639602i
$595$	6.00000	+	7.34847i	0.245976	+	0.301258i
$596$	33.0000	+	19.0526i	1.35173	+	0.780423i
$597$	−19.0919	−	33.0681i	−0.781379	−	1.35339i
$598$	−9.00000	−	15.5885i	−0.368037	−	0.637459i
$599$	−4.24264	−	7.34847i	−0.173350	−	0.300250i	0.766239	−	0.642555i	$-0.222126\pi$
$599$	−4.24264	−	7.34847i	−0.173350	−	0.300250i	−0.939589	+	0.342305i	$0.888792\pi$
$600$	−24.0000	−	4.89898i	−0.979796	−	0.200000i
$601$	−8.00000	+	13.8564i	−0.326327	+	0.565215i	−0.981780	−	0.190021i	$-0.939144\pi$
$601$	−8.00000	+	13.8564i	−0.326327	+	0.565215i	0.655453	+	0.755236i	$0.272478\pi$
$602$	−25.4558			−1.03750
$603$	−9.00000			−0.366508
$604$			14.6969i			0.598010i
$605$	−15.4497	+	2.51104i	−0.628122	+	0.102088i
$606$	−12.7279	+	22.0454i	−0.517036	+	0.895533i
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	−0.998415	−	0.0562808i	$-0.982076\pi$
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	0.450467	−	0.892793i	$-0.351258\pi$
$608$	36.0000	−	20.7846i	1.45999	−	0.842927i
$609$	−4.50000	+	7.79423i	−0.182349	+	0.315838i
$610$	−21.8492	+	3.55114i	−0.884650	+	0.143782i
$611$	12.7279			0.514917
$612$	−8.48528			−0.342997
$613$			7.34847i			0.296802i	0.988927	+	0.148401i	$0.0474126\pi$
$613$			7.34847i			0.296802i	−0.988927	+	0.148401i	$0.952587\pi$
$614$	−14.8492	+	25.7196i	−0.599267	+	1.03796i
$615$	12.7279	+	15.5885i	0.513239	+	0.628587i
$616$	18.0000	+	31.1769i	0.725241	+	1.25615i
$617$	1.41421	+	2.44949i	0.0569341	+	0.0986127i	0.893088	−	0.449883i	$-0.148534\pi$
$617$	1.41421	+	2.44949i	0.0569341	+	0.0986127i	−0.836154	+	0.548495i	$0.815201\pi$
$618$	12.7279	−	7.34847i	0.511992	−	0.295599i
$619$	19.0919	+	11.0227i	0.767368	+	0.443040i	0.831935	−	0.554873i	$-0.187233\pi$
$619$	19.0919	+	11.0227i	0.767368	+	0.443040i	−0.0645672	+	0.997913i	$0.520567\pi$
$620$	25.4558	−	20.7846i	1.02233	−	0.834730i
$621$	13.5000	+	23.3827i	0.541736	+	0.938315i
$622$	42.0000			1.68405
$623$	22.5000	+	12.9904i	0.901443	+	0.520449i
$624$	8.48528	+	14.6969i	0.339683	+	0.588348i
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	−3.00000	+	1.73205i	−0.119904	+	0.0692267i
$627$	54.0000			2.15655
$628$	16.9706	+	9.79796i	0.677199	+	0.390981i
$629$			3.46410i			0.138123i
$630$	−10.0919	+	26.6112i	−0.402070	+	1.06021i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	−19.0919	+	33.0681i	−0.758834	+	1.31434i
$634$	5.00000	+	8.66025i	0.198575	+	0.343943i
$635$	−7.13604	+	18.8169i	−0.283185	+	0.746727i
$636$	16.9706	+	9.79796i	0.672927	+	0.388514i
$637$	−4.24264	−	2.44949i	−0.168100	−	0.0970523i
$638$			10.3923i			0.411435i
$639$	6.36396	−	11.0227i	0.251754	−	0.436051i
$640$	16.0000	+	19.5959i	0.632456	+	0.774597i
$641$	−34.5000	−	19.9186i	−1.36267	−	0.786737i	−0.372690	−	0.927956i	$-0.621564\pi$
$641$	−34.5000	−	19.9186i	−1.36267	−	0.786737i	−0.989978	+	0.141219i	$0.954898\pi$
$642$	−12.7279			−0.502331
$643$	16.5000	+	28.5788i	0.650696	+	1.12704i	0.982954	+	0.183851i	$0.0588563\pi$
$643$	16.5000	+	28.5788i	0.650696	+	1.12704i	−0.332258	+	0.943189i	$0.607810\pi$
$644$	−27.0000	+	15.5885i	−1.06395	+	0.614271i
$645$	−21.7279	−	8.23999i	−0.855536	−	0.324449i
$646$	−12.7279	−	7.34847i	−0.500773	−	0.289122i
$647$		−	25.9808i		−	1.02141i	−0.859756	−	0.510705i	$-0.829385\pi$
$647$		−	25.9808i		−	1.02141i	0.859756	−	0.510705i	$-0.170615\pi$
$648$	−12.7279	−	22.0454i	−0.500000	−	0.866025i
$649$		0			0
$650$	11.4853	−	12.9649i	0.450490	−	0.508525i
$651$	−19.0919	−	33.0681i	−0.748270	−	1.29604i
$652$	−18.0000	−	31.1769i	−0.704934	−	1.22098i
$653$	0.707107	+	1.22474i	0.0276712	+	0.0479280i	0.879529	−	0.475845i	$-0.157858\pi$
$653$	0.707107	+	1.22474i	0.0276712	+	0.0479280i	−0.851858	+	0.523773i	$0.824524\pi$
$654$			12.2474i			0.478913i
$655$	−37.4558	+	6.08767i	−1.46352	+	0.237865i
$656$		−	20.7846i		−	0.811503i
$657$	12.7279	+	7.34847i	0.496564	+	0.286691i
$658$		−	22.0454i		−	0.859419i
$659$	8.48528	−	14.6969i	0.330540	−	0.572511i	−0.652078	−	0.758152i	$-0.726103\pi$
$659$	8.48528	−	14.6969i	0.330540	−	0.572511i	0.982618	+	0.185640i	$0.0594359\pi$
$660$	5.27208	+	32.4377i	0.205215	+	1.26264i
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	−0.998636	−	0.0522143i	$-0.983372\pi$
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	0.454099	−	0.890951i	$-0.349961\pi$
$662$		0			0
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$	−12.7279	−	7.34847i	−0.493939	−	0.285176i
$665$	−38.1838	+	31.1769i	−1.48070	+	1.20899i
$666$	−9.00000	+	5.19615i	−0.348743	+	0.201347i
$667$	−9.00000			−0.348481
$668$	−9.00000	−	5.19615i	−0.348220	−	0.201045i
$669$		−	15.5885i		−	0.602685i
$670$	3.36396	−	8.87039i	0.129961	−	0.342693i
$671$	14.8492	+	25.7196i	0.573249	+	0.992896i
$672$	25.4558	−	14.6969i	0.981981	−	0.566947i
$673$	−40.3051	−	23.2702i	−1.55365	−	0.896998i	−0.997840	−	0.0656868i	$-0.979076\pi$
$673$	−40.3051	−	23.2702i	−1.55365	−	0.896998i	−0.555807	−	0.831312i	$-0.687591\pi$
$674$		−	41.5692i		−	1.60119i
$675$	−17.2279	+	19.4473i	−0.663103	+	0.748528i
$676$	14.0000			0.538462
$677$	−4.94975	+	8.57321i	−0.190234	+	0.329495i	−0.945328	−	0.326122i	$-0.894258\pi$
$677$	−4.94975	+	8.57321i	−0.190234	+	0.329495i	0.755094	+	0.655617i	$0.227591\pi$
$678$	−6.00000	+	3.46410i	−0.230429	+	0.133038i
$679$	−38.1838	+	22.0454i	−1.46536	+	0.846025i
$680$	3.17157	−	8.36308i	0.121624	−	0.320710i
$681$	−18.0000			−0.689761
$682$	−38.1838	−	22.0454i	−1.46213	−	0.844162i
$683$		−	20.7846i		−	0.795301i	−0.917537	−	0.397650i	$-0.869826\pi$
$683$		−	20.7846i		−	0.795301i	0.917537	−	0.397650i	$-0.130174\pi$
$684$		−	44.0908i		−	1.68585i
$685$	−8.00000	−	9.79796i	−0.305664	−	0.374361i
$686$	10.6066	−	18.3712i	0.404962	−	0.701415i
$687$	−1.50000	−	0.866025i	−0.0572286	−	0.0330409i
$688$	12.0000	+	20.7846i	0.457496	+	0.792406i
$689$	−12.0000	+	6.92820i	−0.457164	+	0.263944i
$690$	−28.0919	+	4.56575i	−1.06944	+	0.173815i
$691$	12.7279	+	7.34847i	0.484193	+	0.279549i	0.722162	−	0.691724i	$-0.243148\pi$
$691$	12.7279	+	7.34847i	0.484193	+	0.279549i	−0.237969	+	0.971273i	$0.576482\pi$
$692$	−39.5980			−1.50529
$693$	38.1838			1.45048
$694$		0			0
$695$	−5.27208	−	32.4377i	−0.199981	−	1.23043i
$696$	8.48528			0.321634
$697$	−6.36396	+	3.67423i	−0.241052	+	0.139172i
$698$	13.4350	+	23.2702i	0.508523	+	0.880788i
$699$	−2.12132	+	1.22474i	−0.0802357	+	0.0463241i
$700$	−22.4558	−	19.8931i	−0.848751	−	0.751888i
$701$		−	12.1244i		−	0.457931i	−0.973435	−	0.228965i	$-0.926466\pi$
$701$		−	12.1244i		−	0.457931i	0.973435	−	0.228965i	$-0.0735342\pi$
$702$	18.0000			0.679366
$703$	−18.0000			−0.678883
$704$	16.9706	−	29.3939i	0.639602	−	1.10782i
$705$	7.13604	−	18.8169i	0.268759	−	0.708687i
$706$	−20.0000	−	34.6410i	−0.752710	−	1.30373i
$707$	−27.0000	+	15.5885i	−1.01544	+	0.586264i
$708$		0			0
$709$	−21.5000	+	37.2391i	−0.807449	+	1.39854i	0.107176	+	0.994240i	$0.465819\pi$
$709$	−21.5000	+	37.2391i	−0.807449	+	1.39854i	−0.914625	+	0.404303i	$0.867514\pi$
$710$	8.48528	+	10.3923i	0.318447	+	0.390016i
$711$		0			0
$712$		−	24.4949i		−	0.917985i
$713$	19.0919	−	33.0681i	0.714997	−	1.23841i
$714$	−9.00000	−	5.19615i	−0.336817	−	0.194461i
$715$	−21.7279	−	8.23999i	−0.812578	−	0.308158i
$716$	4.24264	+	7.34847i	0.158555	+	0.274625i
$717$	25.4558	+	14.6969i	0.950666	+	0.548867i
$718$	−15.0000	+	25.9808i	−0.559795	+	0.969593i
$719$	−16.9706			−0.632895			−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$	26.4853	−	4.30463i	0.987048	−	0.160424i
$721$	18.0000			0.670355
$722$	24.7487	−	42.8661i	0.921053	−	1.59531i
$723$		−	43.3013i		−	1.61039i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	−2.74264	−	8.21449i	−0.101859	−	0.305079i
$726$	14.8492	−	8.57321i	0.551107	−	0.318182i
$727$	4.50000	−	7.79423i	0.166896	−	0.289072i	−0.770431	−	0.637523i	$-0.779959\pi$
$727$	4.50000	−	7.79423i	0.166896	−	0.289072i	0.937327	+	0.348451i	$0.113292\pi$
$728$			20.7846i			0.770329i
$729$	−27.0000			−1.00000
$730$	−12.0000	+	9.79796i	−0.444140	+	0.362639i
$731$	4.24264	−	7.34847i	0.156920	−	0.271793i
$732$	21.0000	−	12.1244i	0.776182	−	0.448129i
$733$	38.1838	−	22.0454i	1.41035	−	0.814266i	0.414929	−	0.909854i	$-0.363807\pi$
$733$	38.1838	−	22.0454i	1.41035	−	0.814266i	0.995421	+	0.0955883i	$0.0304732\pi$
$734$	−12.7279	−	22.0454i	−0.469796	−	0.813711i
$735$	−6.00000	+	4.89898i	−0.221313	+	0.180702i
$736$	25.4558	+	14.6969i	0.938315	+	0.541736i
$737$	−12.7279			−0.468839
$738$	−19.0919	−	11.0227i	−0.702782	−	0.405751i
$739$			44.0908i			1.62191i	0.585111	+	0.810953i	$0.301051\pi$
$739$			44.0908i			1.62191i	−0.585111	+	0.810953i	$0.698949\pi$
$740$	−1.75736	−	10.8126i	−0.0646018	−	0.397478i
$741$	27.0000	+	15.5885i	0.991870	+	0.572656i
$742$	12.0000	+	20.7846i	0.440534	+	0.763027i
$743$	−22.5000	+	12.9904i	−0.825445	+	0.476571i	−0.852291	−	0.523069i	$-0.824787\pi$
$743$	−22.5000	+	12.9904i	−0.825445	+	0.476571i	0.0268456	+	0.999640i	$0.491454\pi$
$744$	−18.0000	+	31.1769i	−0.659912	+	1.14300i
$745$	6.83452	+	42.0510i	0.250398	+	1.54063i
$746$			20.7846i			0.760979i
$747$	−13.5000	+	7.79423i	−0.493939	+	0.285176i
$748$	−12.0000			−0.438763
$749$	−13.5000	−	7.79423i	−0.493279	−	0.284795i
$750$	−12.7279	−	24.2487i	−0.464758	−	0.885438i
$751$	31.8198	−	18.3712i	1.16112	−	0.670374i	0.209549	−	0.977798i	$-0.432801\pi$
$751$	31.8198	−	18.3712i	1.16112	−	0.670374i	0.951572	+	0.307425i	$0.0994672\pi$
$752$	−18.0000	+	10.3923i	−0.656392	+	0.378968i
$753$	−44.5477	+	25.7196i	−1.62341	+	0.937276i
$754$	−3.00000	+	5.19615i	−0.109254	+	0.189233i
$755$	−12.7279	+	10.3923i	−0.463217	+	0.378215i
$756$		−	31.1769i		−	1.13389i
$757$			51.4393i			1.86959i	0.355184	+	0.934796i	$0.384418\pi$
$757$			51.4393i			1.86959i	−0.355184	+	0.934796i	$0.615582\pi$
$758$		0			0
$759$	19.0919	+	33.0681i	0.692991	+	1.20030i
$760$	43.4558	+	16.4800i	1.57631	+	0.597792i
$761$	−7.50000	+	4.33013i	−0.271875	+	0.156967i	−0.629739	−	0.776807i	$-0.716838\pi$
$761$	−7.50000	+	4.33013i	−0.271875	+	0.156967i	0.357865	+	0.933774i	$0.383505\pi$
$762$		−	22.0454i		−	0.798621i
$763$	−7.50000	+	12.9904i	−0.271518	+	0.470283i
$764$	−25.4558			−0.920960
$765$	−6.00000	−	7.34847i	−0.216930	−	0.265684i
$766$			29.3939i			1.06204i
$767$		0			0
$768$	−24.0000	−	13.8564i	−0.866025	−	0.500000i
$769$	18.5000	+	32.0429i	0.667127	+	1.15550i	0.978704	+	0.205277i	$0.0658095\pi$
$769$	18.5000	+	32.0429i	0.667127	+	1.15550i	−0.311577	+	0.950221i	$0.600857\pi$
$770$	−14.2721	+	37.6339i	−0.514330	+	1.35623i
$771$	−4.24264	−	2.44949i	−0.152795	−	0.0882162i
$772$	−29.6985	−	17.1464i	−1.06887	−	0.617113i
$773$	11.3137			0.406926			0.203463	−	0.979083i	$-0.434780\pi$
$773$	11.3137			0.406926			0.203463	+	0.979083i	$0.434780\pi$
$774$	25.4558			0.914991
$775$	36.0000	+	7.34847i	1.29316	+	0.263965i
$776$	36.0000	+	20.7846i	1.29232	+	0.746124i
$777$	−12.7279			−0.456612
$778$	19.0919	−	11.0227i	0.684477	−	0.395183i
$779$	−19.0919	−	33.0681i	−0.684038	−	1.18479i
$780$	−6.72792	+	17.7408i	−0.240898	+	0.635222i
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		−	10.3923i		−	0.371628i
$783$	4.50000	−	7.79423i	0.160817	−	0.278543i
$784$	8.00000			0.285714
$785$	3.51472	+	21.6251i	0.125446	+	0.771834i
$786$	36.0000	−	20.7846i	1.28408	−	0.741362i
$787$	21.0000	+	36.3731i	0.748569	+	1.29656i	0.948509	+	0.316752i	$0.102592\pi$
$787$	21.0000	+	36.3731i	0.748569	+	1.29656i	−0.199939	+	0.979808i	$0.564075\pi$
$788$	14.1421	+	24.4949i	0.503793	+	0.872595i
$789$	−36.0000			−1.28163
$790$		0			0
$791$	−8.48528			−0.301702
$792$	−18.0000	−	31.1769i	−0.639602	−	1.10782i
$793$			17.1464i			0.608888i
$794$	30.0000	+	17.3205i	1.06466	+	0.614682i
$795$	3.51472	+	21.6251i	0.124654	+	0.766965i
$796$	−38.1838	+	22.0454i	−1.35339	+	0.781379i
$797$	17.6777	+	30.6186i	0.626175	+	1.08457i	0.988312	+	0.152442i	$0.0487139\pi$
$797$	17.6777	+	30.6186i	0.626175	+	1.08457i	−0.362137	+	0.932125i	$0.617953\pi$
$798$	27.0000	−	46.7654i	0.955790	−	1.65548i
$799$	6.36396	+	3.67423i	0.225141	+	0.129985i
$800$	−5.65685	+	27.7128i	−0.200000	+	0.979796i
$801$	−22.5000	−	12.9904i	−0.794998	−	0.458993i
$802$			24.4949i			0.864945i
$803$	18.0000	+	10.3923i	0.635206	+	0.366736i
$804$			10.3923i			0.366508i
$805$	−32.5919	−	12.3600i	−1.14871	−	0.435632i
$806$	−12.7279	−	22.0454i	−0.448322	−	0.776516i
$807$	−19.5000	−	33.7750i	−0.686433	−	1.18894i
$808$	25.4558	+	14.6969i	0.895533	+	0.517036i
$809$		−	3.46410i		−	0.121791i	−0.998144	−	0.0608957i	$-0.980604\pi$
$809$		−	3.46410i		−	0.121791i	0.998144	−	0.0608957i	$-0.0193957\pi$
$810$	10.0919	−	26.6112i	0.354593	−	0.935021i
$811$		−	29.3939i		−	1.03216i	−0.856541	−	0.516079i	$-0.827391\pi$
$811$		−	29.3939i		−	1.03216i	0.856541	−	0.516079i	$-0.172609\pi$
$812$	9.00000	+	5.19615i	0.315838	+	0.182349i
$813$	6.36396	+	11.0227i	0.223194	+	0.386583i
$814$	−12.7279	+	7.34847i	−0.446113	+	0.257564i
$815$	14.2721	−	37.6339i	0.499929	−	1.31826i
$816$			9.79796i			0.342997i
$817$	38.1838	+	22.0454i	1.33588	+	0.771271i
$818$	−39.5980			−1.38451
$819$	19.0919	+	11.0227i	0.667124	+	0.385164i
$820$	18.0000	−	14.6969i	0.628587	−	0.513239i
$821$	10.5000	+	6.06218i	0.366453	+	0.211571i	0.671908	−	0.740635i	$-0.265475\pi$
$821$	10.5000	+	6.06218i	0.366453	+	0.211571i	−0.305455	+	0.952207i	$0.598809\pi$
$822$	12.0000	+	6.92820i	0.418548	+	0.241649i
$823$	−1.50000	−	2.59808i	−0.0522867	−	0.0905632i	0.838697	−	0.544598i	$-0.183318\pi$
$823$	−1.50000	−	2.59808i	−0.0522867	−	0.0905632i	−0.890984	+	0.454034i	$0.849984\pi$
$824$	−8.48528	−	14.6969i	−0.295599	−	0.511992i
$825$	−24.3640	+	27.5027i	−0.848244	+	0.957520i
$826$		0			0
$827$			36.3731i			1.26482i	0.774636	+	0.632408i	$0.217933\pi$
$827$			36.3731i			1.26482i	−0.774636	+	0.632408i	$0.782067\pi$
$828$	27.0000	−	15.5885i	0.938315	−	0.541736i
$829$	11.0000			0.382046			0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000			0.382046			0.191023	+	0.981586i	$0.438820\pi$
$830$	−2.63604	−	16.2189i	−0.0914982	−	0.562965i
$831$	12.7279			0.441527
$832$	16.9706	−	9.79796i	0.588348	−	0.339683i
$833$	−1.41421	−	2.44949i	−0.0489996	−	0.0848698i
$834$	18.0000	+	31.1769i	0.623289	+	1.07957i
$835$	−1.86396	−	11.4685i	−0.0645050	−	0.396883i
$836$		−	62.3538i		−	2.15655i
$837$	19.0919	+	33.0681i	0.659912	+	1.14300i
$838$	−6.00000			−0.207267
$839$	−2.12132	+	3.67423i	−0.0732361	+	0.126849i	−0.900318	−	0.435233i	$-0.856666\pi$
$839$	−2.12132	+	3.67423i	−0.0732361	+	0.126849i	0.827082	+	0.562082i	$0.189999\pi$
$840$	30.7279	+	11.6531i	1.06021	+	0.402070i
$841$	−13.0000	−	22.5167i	−0.448276	−	0.776437i
$842$	−14.1421	−	24.4949i	−0.487370	−	0.844150i
$843$	−39.0000			−1.34323
$844$	38.1838	+	22.0454i	1.31434	+	0.758834i
$845$	9.89949	+	12.1244i	0.340553	+	0.417091i
$846$			22.0454i			0.757937i
$847$	21.0000			0.721569
$848$	11.3137	−	19.5959i	0.388514	−	0.672927i
$849$	31.5000	+	18.1865i	1.08108	+	0.624160i
$850$	9.48528	−	3.16693i	0.325342	−	0.108625i
$851$	−6.36396	−	11.0227i	−0.218154	−	0.377853i
$852$	−12.7279	−	7.34847i	−0.436051	−	0.251754i
$853$	−31.8198	−	18.3712i	−1.08949	−	0.629017i	−0.156049	−	0.987749i	$-0.549876\pi$
$853$	−31.8198	−	18.3712i	−1.08949	−	0.629017i	−0.933440	+	0.358732i	$0.883209\pi$
$854$	29.6985			1.01626
$855$	38.1838	−	31.1769i	1.30586	−	1.06623i
$856$			14.6969i			0.502331i
$857$	−9.19239	+	15.9217i	−0.314006	+	0.543874i	−0.979226	−	0.202773i	$-0.935005\pi$
$857$	−9.19239	+	15.9217i	−0.314006	+	0.543874i	0.665220	+	0.746648i	$0.268338\pi$
$858$	25.4558			0.869048
$859$	6.36396	−	3.67423i	0.217136	−	0.125363i	−0.387488	−	0.921875i	$-0.626657\pi$
$859$	6.36396	−	3.67423i	0.217136	−	0.125363i	0.604623	+	0.796512i	$0.293324\pi$
$860$	−9.51472	+	25.0892i	−0.324449	+	0.855536i
$861$	−13.5000	−	23.3827i	−0.460079	−	0.796880i
$862$	−18.0000	+	31.1769i	−0.613082	+	1.06189i
$863$			5.19615i			0.176879i	0.996082	+	0.0884395i	$0.0281880\pi$
$863$			5.19615i			0.176879i	−0.996082	+	0.0884395i	$0.971812\pi$
$864$	−25.4558	+	14.6969i	−0.866025	+	0.500000i
$865$	−28.0000	−	34.2929i	−0.952029	−	1.16599i
$866$	−15.0000	−	8.66025i	−0.509721	−	0.294287i
$867$	−22.5000	+	12.9904i	−0.764140	+	0.441176i
$868$	−38.1838	+	22.0454i	−1.29604	+	0.748270i
$869$		0			0
$870$	6.00000	+	7.34847i	0.203419	+	0.249136i
$871$	−6.36396	−	3.67423i	−0.215635	−	0.124497i
$872$	14.1421			0.478913
$873$	38.1838	−	22.0454i	1.29232	−	0.746124i
$874$	54.0000			1.82658
$875$	1.34924	−	33.5139i	0.0456127	−	1.13298i
$876$	8.48528	−	14.6969i	0.286691	−	0.496564i
$877$	27.5772	−	15.9217i	0.931215	−	0.537637i	0.0440191	−	0.999031i	$-0.485984\pi$
$877$	27.5772	−	15.9217i	0.931215	−	0.537637i	0.887196	+	0.461394i	$0.152650\pi$
$878$	−18.0000	+	10.3923i	−0.607471	+	0.350723i
$879$	23.3345	+	13.4722i	0.787054	+	0.454406i
$880$	37.4558	−	6.08767i	1.26264	−	0.205215i
$881$		−	25.9808i		−	0.875314i	−0.899142	−	0.437657i	$-0.855808\pi$
$881$		−	25.9808i		−	0.875314i	0.899142	−	0.437657i	$-0.144192\pi$
$882$	4.24264	−	7.34847i	0.142857	−	0.247436i
$883$	33.0000			1.11054			0.555269	−	0.831671i	$-0.312615\pi$
$883$	33.0000			1.11054			0.555269	+	0.831671i	$0.312615\pi$
$884$	−6.00000	−	3.46410i	−0.201802	−	0.116510i
$885$		0			0
$886$	−44.5477	+	25.7196i	−1.49661	+	0.864068i
$887$	18.0000	−	10.3923i	0.604381	−	0.348939i	−0.166382	−	0.986061i	$-0.553209\pi$
$887$	18.0000	−	10.3923i	0.604381	−	0.348939i	0.770763	+	0.637122i	$0.219875\pi$
$888$	6.00000	+	10.3923i	0.201347	+	0.348743i
$889$	13.5000	−	23.3827i	0.452775	−	0.784230i
$890$	21.2132	−	17.3205i	0.711068	−	0.580585i
$891$	−38.1838			−1.27920
$892$	−18.0000			−0.602685
$893$	−19.0919	+	33.0681i	−0.638886	+	1.10658i
$894$	−23.3345	−	40.4166i	−0.780423	−	1.35173i
$895$	−3.36396	+	8.87039i	−0.112445	+	0.296504i
$896$	−16.9706	−	29.3939i	−0.566947	−	0.981981i
$897$			22.0454i			0.736075i
$898$		0			0
$899$	−12.7279			−0.424500
$900$	22.4558	+	19.8931i	0.748528	+	0.663103i
$901$	−8.00000			−0.266519
$902$	−27.0000	−	15.5885i	−0.899002	−	0.519039i
$903$	27.0000	+	15.5885i	0.898504	+	0.518751i
$904$	4.00000	+	6.92820i	0.133038	+	0.230429i
$905$	5.55025	−	14.6354i	0.184497	−	0.486497i
$906$	9.00000	−	15.5885i	0.299005	−	0.517892i
$907$	−4.50000	+	7.79423i	−0.149420	+	0.258803i	−0.931013	−	0.364985i	$-0.881074\pi$
$907$	−4.50000	+	7.79423i	−0.149420	+	0.258803i	0.781593	+	0.623788i	$0.214407\pi$
$908$			20.7846i			0.689761i
$909$	27.0000	−	15.5885i	0.895533	−	0.517036i
$910$	−18.0000	+	14.6969i	−0.596694	+	0.487199i
$911$	−21.2132	+	36.7423i	−0.702825	+	1.21733i	0.264646	+	0.964346i	$0.414745\pi$
$911$	−21.2132	+	36.7423i	−0.702825	+	1.21733i	−0.967471	+	0.252983i	$0.918588\pi$
$912$	−50.9117			−1.68585
$913$	−19.0919	+	11.0227i	−0.631849	+	0.364798i
$914$	21.0000	−	12.1244i	0.694618	−	0.401038i
$915$	25.3492	+	9.61332i	0.838020	+	0.317807i
$916$	−1.00000	+	1.73205i	−0.0330409	+	0.0572286i
$917$	50.9117			1.68125
$918$	9.00000	+	5.19615i	0.297044	+	0.171499i
$919$			14.6969i			0.484807i	0.970175	+	0.242404i	$0.0779358\pi$
$919$			14.6969i			0.484807i	−0.970175	+	0.242404i	$0.922064\pi$
$920$	5.27208	+	32.4377i	0.173815	+	1.06944i
$921$	31.5000	−	18.1865i	1.03796	−	0.599267i
$922$	−6.36396	+	3.67423i	−0.209586	+	0.121004i
$923$	9.00000	−	5.19615i	0.296239	−	0.171033i
$924$		−	44.0908i		−	1.45048i
$925$	8.12132	−	9.16756i	0.267027	−	0.301428i
$926$	50.9117			1.67306
$927$	−18.0000			−0.591198
$928$		−	9.79796i		−	0.321634i
$929$	−15.0000	−	8.66025i	−0.492134	−	0.284134i	0.233325	−	0.972399i	$-0.425039\pi$
$929$	−15.0000	−	8.66025i	−0.492134	−	0.284134i	−0.725459	+	0.688265i	$0.758373\pi$
$930$	−39.7279	+	6.45695i	−1.30273	+	0.211732i
$931$	12.7279	−	7.34847i	0.417141	−	0.240836i
$932$	1.41421	+	2.44949i	0.0463241	+	0.0802357i
$933$	−44.5477	−	25.7196i	−1.45843	−	0.842023i
$934$	−25.4558	−	14.6969i	−0.832941	−	0.480899i
$935$	−8.48528	−	10.3923i	−0.277498	−	0.339865i
$936$		−	20.7846i		−	0.679366i
$937$		−	4.89898i		−	0.160043i	−0.996793	−	0.0800213i	$-0.974501\pi$
$937$		−	4.89898i		−	0.160043i	0.996793	−	0.0800213i	$-0.0254988\pi$
$938$	−6.36396	+	11.0227i	−0.207791	+	0.359904i
$939$	4.24264			0.138453
$940$	−21.7279	−	8.23999i	−0.708687	−	0.268759i
$941$	7.50000	−	4.33013i	0.244493	−	0.141158i	−0.372747	−	0.927933i	$-0.621584\pi$
$941$	7.50000	−	4.33013i	0.244493	−	0.141158i	0.617240	+	0.786775i	$0.288251\pi$
$942$	−12.0000	−	20.7846i	−0.390981	−	0.677199i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$		0			0
$945$	27.0000	−	22.0454i	0.878310	−	0.717137i
$946$	36.0000			1.17046
$947$	−31.5000	−	18.1865i	−1.02361	−	0.590983i	−0.108464	−	0.994100i	$-0.534593\pi$
$947$	−31.5000	−	18.1865i	−1.02361	−	0.590983i	−0.915148	+	0.403117i	$0.867927\pi$
$948$		0			0
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	16.4558	+	49.2870i	0.533898	+	1.59908i
$951$		−	12.2474i		−	0.397151i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	−24.0416			−0.778785			−0.389392	−	0.921072i	$-0.627315\pi$
$953$	−24.0416			−0.778785			−0.389392	+	0.921072i	$0.627315\pi$
$954$	−12.0000	−	20.7846i	−0.388514	−	0.672927i
$955$	−18.0000	−	22.0454i	−0.582466	−	0.713373i
$956$	16.9706	−	29.3939i	0.548867	−	0.950666i
$957$	6.36396	−	11.0227i	0.205718	−	0.356313i
$958$	6.00000	+	10.3923i	0.193851	+	0.335760i
$959$	8.48528	+	14.6969i	0.274004	+	0.474589i
$960$	−4.97056	−	30.5826i	−0.160424	−	0.987048i
$961$	11.5000	−	19.9186i	0.370968	−	0.642535i
$962$	−8.48528			−0.273576
$963$	13.5000	+	7.79423i	0.435031	+	0.251166i
$964$	−50.0000			−1.61039
$965$	−6.15076	−	37.8440i	−0.198000	−	1.21824i
$966$	38.1838			1.22854
$967$	13.5000	+	23.3827i	0.434131	+	0.751936i	0.997224	−	0.0744567i	$-0.0237223\pi$
$967$	13.5000	+	23.3827i	0.434131	+	0.751936i	−0.563094	+	0.826393i	$0.690389\pi$
$968$	−9.89949	−	17.1464i	−0.318182	−	0.551107i
$969$	9.00000	+	15.5885i	0.289122	+	0.500773i
$970$	7.45584	+	45.8739i	0.239393	+	1.47292i
$971$	12.7279			0.408458			0.204229	−	0.978923i	$-0.434531\pi$
$971$	12.7279			0.408458			0.204229	+	0.978923i	$0.434531\pi$
$972$			31.1769i			1.00000i
$973$			44.0908i			1.41349i
$974$	8.48528	−	14.6969i	0.271886	−	0.470920i
$975$	−20.1213	+	6.71807i	−0.644398	+	0.215150i
$976$	−14.0000	−	24.2487i	−0.448129	−	0.776182i
$977$	−0.707107	−	1.22474i	−0.0226224	−	0.0391831i	0.854493	−	0.519464i	$-0.173868\pi$
$977$	−0.707107	−	1.22474i	−0.0226224	−	0.0391831i	−0.877115	+	0.480281i	$0.840535\pi$
$978$			44.0908i			1.40987i
$979$	−31.8198	−	18.3712i	−1.01697	−	0.587145i
$980$	5.65685	+	6.92820i	0.180702	+	0.221313i
$981$	7.50000	−	12.9904i	0.239457	−	0.414751i
$982$	−24.0000			−0.765871
$983$	−40.5000	−	23.3827i	−1.29175	−	0.745792i	−0.312785	−	0.949824i	$-0.601262\pi$
$983$	−40.5000	−	23.3827i	−1.29175	−	0.745792i	−0.978964	+	0.204032i	$0.934595\pi$
$984$	−12.7279	+	22.0454i	−0.405751	+	0.702782i
$985$	−11.2132	+	29.5680i	−0.357282	+	0.942113i
$986$	−3.00000	+	1.73205i	−0.0955395	+	0.0551597i
$987$	−13.5000	+	23.3827i	−0.429710	+	0.744279i
$988$	18.0000	−	31.1769i	0.572656	−	0.991870i
$989$			31.1769i			0.991368i
$990$	14.2721	−	37.6339i	0.453596	−	1.19608i
$991$		−	58.7878i		−	1.86745i	−0.357985	−	0.933727i	$-0.616536\pi$
$991$		−	58.7878i		−	1.86745i	0.357985	−	0.933727i	$-0.383464\pi$
$992$	36.0000	+	20.7846i	1.14300	+	0.659912i
$993$		0			0
$994$	−9.00000	−	15.5885i	−0.285463	−	0.494436i
$995$	−46.0919	−	17.4797i	−1.46121	−	0.554142i
$996$	9.00000	+	15.5885i	0.285176	+	0.493939i
$997$	−33.9411	−	19.5959i	−1.07493	−	0.620609i	−0.145403	−	0.989373i	$-0.546448\pi$
$997$	−33.9411	−	19.5959i	−1.07493	−	0.620609i	−0.929523	+	0.368764i	$0.879781\pi$
$998$		−	20.7846i		−	0.657925i
$999$	12.7279			0.402694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.b.119.1	yes	4
3.2	odd	2		540.2.n.a.359.2		4
4.3	odd	2		180.2.n.a.119.1	yes	4
5.2	odd	4		900.2.r.b.551.1		8
5.3	odd	4		900.2.r.b.551.4		8
5.4	even	2		180.2.n.a.119.2	yes	4
9.4	even	3		540.2.n.a.179.1		4
9.5	odd	6	inner	180.2.n.b.59.2	yes	4
12.11	even	2		540.2.n.b.359.2		4
15.14	odd	2		540.2.n.b.359.1		4
20.3	even	4		900.2.r.b.551.3		8
20.7	even	4		900.2.r.b.551.2		8
20.19	odd	2	inner	180.2.n.b.119.2	yes	4
36.23	even	6		180.2.n.a.59.2	yes	4
36.31	odd	6		540.2.n.b.179.1		4
45.4	even	6		540.2.n.b.179.2		4
45.14	odd	6		180.2.n.a.59.1	✓	4
45.23	even	12		900.2.r.b.851.3		8
45.32	even	12		900.2.r.b.851.2		8
60.59	even	2		540.2.n.a.359.1		4
180.23	odd	12		900.2.r.b.851.4		8
180.59	even	6	inner	180.2.n.b.59.1	yes	4
180.139	odd	6		540.2.n.a.179.2		4
180.167	odd	12		900.2.r.b.851.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.a.59.1	✓	4	45.14	odd	6
180.2.n.a.59.2	yes	4	36.23	even	6
180.2.n.a.119.1	yes	4	4.3	odd	2
180.2.n.a.119.2	yes	4	5.4	even	2
180.2.n.b.59.1	yes	4	180.59	even	6	inner
180.2.n.b.59.2	yes	4	9.5	odd	6	inner
180.2.n.b.119.1	yes	4	1.1	even	1	trivial
180.2.n.b.119.2	yes	4	20.19	odd	2	inner
540.2.n.a.179.1		4	9.4	even	3
540.2.n.a.179.2		4	180.139	odd	6
540.2.n.a.359.1		4	60.59	even	2
540.2.n.a.359.2		4	3.2	odd	2
540.2.n.b.179.1		4	36.31	odd	6
540.2.n.b.179.2		4	45.4	even	6
540.2.n.b.359.1		4	15.14	odd	2
540.2.n.b.359.2		4	12.11	even	2
900.2.r.b.551.1		8	5.2	odd	4
900.2.r.b.551.2		8	20.7	even	4
900.2.r.b.551.3		8	20.3	even	4
900.2.r.b.551.4		8	5.3	odd	4
900.2.r.b.851.1		8	180.167	odd	12
900.2.r.b.851.2		8	45.32	even	12
900.2.r.b.851.3		8	45.23	even	12
900.2.r.b.851.4		8	180.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.792893 - 2.09077i) q^{5} +2.44949i q^{6} +(-1.50000 + 2.59808i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.792893 - 2.09077i) q^{5} +2.44949i q^{6} +(-1.50000 + 2.59808i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.00000 + 2.44949i) q^{10} +(2.12132 - 3.67423i) q^{11} +(-3.00000 - 1.73205i) q^{12} +(2.12132 - 1.22474i) q^{13} +(-2.12132 - 3.67423i) q^{14} +(-0.621320 - 3.82282i) q^{15} +(-2.00000 + 3.46410i) q^{16} +1.41421 q^{17} +(2.12132 + 3.67423i) q^{18} +7.34847i q^{19} +(-4.41421 + 0.717439i) q^{20} +5.19615i q^{21} +(3.00000 + 5.19615i) q^{22} +(-4.50000 + 2.59808i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-3.74264 - 3.31552i) q^{25} +3.46410i q^{26} -5.19615i q^{27} +6.00000 q^{28} +(1.50000 + 0.866025i) q^{29} +(5.12132 + 1.94218i) q^{30} +(-6.36396 + 3.67423i) q^{31} +(-2.82843 - 4.89898i) q^{32} -7.34847i q^{33} +(-1.00000 + 1.73205i) q^{34} +(4.24264 + 5.19615i) q^{35} -6.00000 q^{36} +2.44949i q^{37} +(-9.00000 - 5.19615i) q^{38} +(2.12132 - 3.67423i) q^{39} +(2.24264 - 5.91359i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-6.36396 - 3.67423i) q^{42} +(3.00000 - 5.19615i) q^{43} -8.48528 q^{44} +(-4.24264 - 5.19615i) q^{45} -7.34847i q^{46} +(4.50000 + 2.59808i) q^{47} +6.92820i q^{48} +(-1.00000 - 1.73205i) q^{49} +(6.70711 - 2.23936i) q^{50} +(2.12132 - 1.22474i) q^{51} +(-4.24264 - 2.44949i) q^{52} -5.65685 q^{53} +(6.36396 + 3.67423i) q^{54} +(-6.00000 - 7.34847i) q^{55} +(-4.24264 + 7.34847i) q^{56} +(6.36396 + 11.0227i) q^{57} +(-2.12132 + 1.22474i) q^{58} +(-6.00000 + 4.89898i) q^{60} +(-3.50000 + 6.06218i) q^{61} -10.3923i q^{62} +(4.50000 + 7.79423i) q^{63} +8.00000 q^{64} +(-0.878680 - 5.40629i) q^{65} +(9.00000 + 5.19615i) q^{66} +(-1.50000 - 2.59808i) q^{67} +(-1.41421 - 2.44949i) q^{68} +(-4.50000 + 7.79423i) q^{69} +(-9.36396 + 1.52192i) q^{70} +4.24264 q^{71} +(4.24264 - 7.34847i) q^{72} +4.89898i q^{73} +(-3.00000 - 1.73205i) q^{74} +(-8.48528 - 1.73205i) q^{75} +(12.7279 - 7.34847i) q^{76} +(6.36396 + 11.0227i) q^{77} +(3.00000 + 5.19615i) q^{78} +(5.65685 + 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} -7.34847i q^{82} +(-4.50000 - 2.59808i) q^{83} +(9.00000 - 5.19615i) q^{84} +(1.12132 - 2.95680i) q^{85} +(4.24264 + 7.34847i) q^{86} +3.00000 q^{87} +(6.00000 - 10.3923i) q^{88} -8.66025i q^{89} +(9.36396 - 1.52192i) q^{90} +7.34847i q^{91} +(9.00000 + 5.19615i) q^{92} +(-6.36396 + 11.0227i) q^{93} +(-6.36396 + 3.67423i) q^{94} +(15.3640 + 5.82655i) q^{95} +(-8.48528 - 4.89898i) q^{96} +(12.7279 + 7.34847i) q^{97} +2.82843 q^{98} +(-6.36396 - 11.0227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5 - 6 * q^7 + 6 * q^9	\( 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5} - 6 q^{7} + 6 q^{9} + 8 q^{10} - 12 q^{12} + 6 q^{15} - 8 q^{16} - 12 q^{20} + 12 q^{22} - 18 q^{23} + 2 q^{25} + 24 q^{28} + 6 q^{29} + 12 q^{30} - 4 q^{34} - 24 q^{36} - 36 q^{38} - 8 q^{40} - 18 q^{41} + 12 q^{43} + 18 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{55} - 24 q^{60} - 14 q^{61} + 18 q^{63} + 32 q^{64} - 12 q^{65} + 36 q^{66} - 6 q^{67} - 18 q^{69} - 12 q^{70} - 12 q^{74} + 12 q^{78} - 18 q^{81} - 18 q^{83} + 36 q^{84} - 4 q^{85} + 12 q^{87} + 24 q^{88} + 12 q^{90} + 36 q^{92} + 36 q^{95}+O(q^{100}) \) 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5 - 6 * q^7 + 6 * q^9 + 8 * q^10 - 12 * q^12 + 6 * q^15 - 8 * q^16 - 12 * q^20 + 12 * q^22 - 18 * q^23 + 2 * q^25 + 24 * q^28 + 6 * q^29 + 12 * q^30 - 4 * q^34 - 24 * q^36 - 36 * q^38 - 8 * q^40 - 18 * q^41 + 12 * q^43 + 18 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^55 - 24 * q^60 - 14 * q^61 + 18 * q^63 + 32 * q^64 - 12 * q^65 + 36 * q^66 - 6 * q^67 - 18 * q^69 - 12 * q^70 - 12 * q^74 + 12 * q^78 - 18 * q^81 - 18 * q^83 + 36 * q^84 - 4 * q^85 + 12 * q^87 + 24 * q^88 + 12 * q^90 + 36 * q^92 + 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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