LMFDB - Embedded newform 360.2.bf.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(61,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 0]))

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

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

chi := DirichletCharacter("360.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bf (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.61
Dual form			360.2.bf.a.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.633975 - 2.36603i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.633975 - 2.36603i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.00000i) q^{10} +(-4.33013 - 2.50000i) q^{11} +3.46410i q^{12} +(-5.19615 + 3.00000i) q^{13} +(-1.46410 + 5.46410i) q^{14} +1.73205i q^{15} +(2.00000 - 3.46410i) q^{16} -3.00000 q^{17} +(3.00000 + 3.00000i) q^{18} -7.00000i q^{19} +(1.00000 - 1.73205i) q^{20} +(3.46410 + 6.00000i) q^{21} +(6.83013 + 1.83013i) q^{22} +(-1.00000 - 1.73205i) q^{23} +(-1.26795 - 4.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(6.00000 - 6.00000i) q^{26} +5.19615 q^{27} -8.00000i q^{28} +(-0.633975 - 2.36603i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(7.50000 - 4.33013i) q^{33} +(4.09808 - 1.09808i) q^{34} -4.00000i q^{35} +(-5.19615 - 3.00000i) q^{36} +2.00000i q^{37} +(2.56218 + 9.56218i) q^{38} -10.3923i q^{39} +(-0.732051 + 2.73205i) q^{40} +(2.50000 + 4.33013i) q^{41} +(-6.92820 - 6.92820i) q^{42} +(4.33013 + 2.50000i) q^{43} -10.0000 q^{44} +(-2.59808 - 1.50000i) q^{45} +(2.00000 + 2.00000i) q^{46} +(-1.00000 + 1.73205i) q^{47} +(3.46410 + 6.00000i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.366025 + 1.36603i) q^{50} +(2.59808 - 4.50000i) q^{51} +(-6.00000 + 10.3923i) q^{52} -8.00000i q^{53} +(-7.09808 + 1.90192i) q^{54} -5.00000 q^{55} +(2.92820 + 10.9282i) q^{56} +(10.5000 + 6.06218i) q^{57} +(6.06218 - 3.50000i) q^{59} +(1.73205 + 3.00000i) q^{60} +(3.46410 + 2.00000i) q^{61} +(4.00000 + 4.00000i) q^{62} -12.0000 q^{63} -8.00000i q^{64} +(-3.00000 + 5.19615i) q^{65} +(-8.66025 + 8.66025i) q^{66} +(2.59808 - 1.50000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +3.46410 q^{69} +(1.46410 + 5.46410i) q^{70} +2.00000 q^{71} +(8.19615 + 2.19615i) q^{72} +1.00000 q^{73} +(-0.732051 - 2.73205i) q^{74} +(0.866025 + 1.50000i) q^{75} +(-7.00000 - 12.1244i) q^{76} +(-17.3205 + 10.0000i) q^{77} +(3.80385 + 14.1962i) q^{78} +(-5.00000 + 8.66025i) q^{79} -4.00000i q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 5.00000i) q^{82} +(-10.3923 - 6.00000i) q^{83} +(12.0000 + 6.92820i) q^{84} +(-2.59808 + 1.50000i) q^{85} +(-6.83013 - 1.83013i) q^{86} +(13.6603 - 3.66025i) q^{88} +2.00000 q^{89} +(4.09808 + 1.09808i) q^{90} +24.0000i q^{91} +(-3.46410 - 2.00000i) q^{92} +6.92820 q^{93} +(0.732051 - 2.73205i) q^{94} +(-3.50000 - 6.06218i) q^{95} +(-6.92820 - 6.92820i) q^{96} +(3.50000 - 6.06218i) q^{97} +(9.00000 + 9.00000i) q^{98} +15.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{6} + 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^6 + 8 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 6 q^{6} + 8 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{20} + 10 q^{22} - 4 q^{23} - 12 q^{24} + 2 q^{25} + 24 q^{26} - 6 q^{30} - 8 q^{31} + 8 q^{32} + 30 q^{33} + 6 q^{34} - 14 q^{38} + 4 q^{40} + 10 q^{41} - 40 q^{44} + 8 q^{46} - 4 q^{47} - 18 q^{49} + 2 q^{50} - 24 q^{52} - 18 q^{54} - 20 q^{55} - 16 q^{56} + 42 q^{57} + 16 q^{62} - 48 q^{63} - 12 q^{65} - 8 q^{70} + 8 q^{71} + 12 q^{72} + 4 q^{73} + 4 q^{74} - 28 q^{76} + 36 q^{78} - 20 q^{79} - 18 q^{81} - 20 q^{82} + 48 q^{84} - 10 q^{86} + 20 q^{88} + 8 q^{89} + 6 q^{90} - 4 q^{94} - 14 q^{95} + 14 q^{97} + 36 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^6 + 8 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^17 + 12 * q^18 + 4 * q^20 + 10 * q^22 - 4 * q^23 - 12 * q^24 + 2 * q^25 + 24 * q^26 - 6 * q^30 - 8 * q^31 + 8 * q^32 + 30 * q^33 + 6 * q^34 - 14 * q^38 + 4 * q^40 + 10 * q^41 - 40 * q^44 + 8 * q^46 - 4 * q^47 - 18 * q^49 + 2 * q^50 - 24 * q^52 - 18 * q^54 - 20 * q^55 - 16 * q^56 + 42 * q^57 + 16 * q^62 - 48 * q^63 - 12 * q^65 - 8 * q^70 + 8 * q^71 + 12 * q^72 + 4 * q^73 + 4 * q^74 - 28 * q^76 + 36 * q^78 - 20 * q^79 - 18 * q^81 - 20 * q^82 + 48 * q^84 - 10 * q^86 + 20 * q^88 + 8 * q^89 + 6 * q^90 - 4 * q^94 - 14 * q^95 + 14 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.633975	−	2.36603i	0.258819	−	0.965926i
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$	−4.33013	−	2.50000i	−1.30558	−	0.753778i	−0.324227	−	0.945979i	$-0.605104\pi$
$11$	−4.33013	−	2.50000i	−1.30558	−	0.753778i	−0.981356	+	0.192201i	$0.938437\pi$
$12$			3.46410i			1.00000i
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−1.46410	+	5.46410i	−0.391298	+	1.46034i
$15$			1.73205i			0.447214i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$		−	7.00000i		−	1.60591i	−0.596040	−	0.802955i	$-0.703260\pi$
$19$		−	7.00000i		−	1.60591i	0.596040	−	0.802955i	$-0.296740\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	3.46410	+	6.00000i	0.755929	+	1.30931i
$22$	6.83013	+	1.83013i	1.45619	+	0.390184i
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$	−1.26795	−	4.73205i	−0.258819	−	0.965926i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	6.00000	−	6.00000i	1.17670	−	1.17670i
$27$	5.19615			1.00000
$28$		−	8.00000i		−	1.51186i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	−0.633975	−	2.36603i	−0.115747	−	0.431975i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$	7.50000	−	4.33013i	1.30558	−	0.753778i
$34$	4.09808	−	1.09808i	0.702814	−	0.188319i
$35$		−	4.00000i		−	0.676123i
$36$	−5.19615	−	3.00000i	−0.866025	−	0.500000i
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	2.56218	+	9.56218i	0.415640	+	1.55119i
$39$		−	10.3923i		−	1.66410i
$40$	−0.732051	+	2.73205i	−0.115747	+	0.431975i
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$	−6.92820	−	6.92820i	−1.06904	−	1.06904i
$43$	4.33013	+	2.50000i	0.660338	+	0.381246i	0.792406	−	0.609994i	$-0.208828\pi$
$43$	4.33013	+	2.50000i	0.660338	+	0.381246i	−0.132068	+	0.991241i	$0.542162\pi$
$44$	−10.0000			−1.50756
$45$	−2.59808	−	1.50000i	−0.387298	−	0.223607i
$46$	2.00000	+	2.00000i	0.294884	+	0.294884i
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	−0.929695	−	0.368329i	$-0.879930\pi$
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	0.783830	+	0.620975i	$0.213263\pi$
$48$	3.46410	+	6.00000i	0.500000	+	0.866025i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−0.366025	+	1.36603i	−0.0517638	+	0.193185i
$51$	2.59808	−	4.50000i	0.363803	−	0.630126i
$52$	−6.00000	+	10.3923i	−0.832050	+	1.44115i
$53$		−	8.00000i		−	1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$53$		−	8.00000i		−	1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$54$	−7.09808	+	1.90192i	−0.965926	+	0.258819i
$55$	−5.00000			−0.674200
$56$	2.92820	+	10.9282i	0.391298	+	1.46034i
$57$	10.5000	+	6.06218i	1.39076	+	0.802955i
$58$		0			0
$59$	6.06218	−	3.50000i	0.789228	−	0.455661i	−0.0504625	−	0.998726i	$-0.516070\pi$
$59$	6.06218	−	3.50000i	0.789228	−	0.455661i	0.839691	+	0.543065i	$0.182736\pi$
$60$	1.73205	+	3.00000i	0.223607	+	0.387298i
$61$	3.46410	+	2.00000i	0.443533	+	0.256074i	0.705095	−	0.709113i	$-0.250904\pi$
$61$	3.46410	+	2.00000i	0.443533	+	0.256074i	−0.261562	+	0.965187i	$0.584238\pi$
$62$	4.00000	+	4.00000i	0.508001	+	0.508001i
$63$	−12.0000			−1.51186
$64$		−	8.00000i		−	1.00000i
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$	−8.66025	+	8.66025i	−1.06600	+	1.06600i
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608004\pi$
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$68$	−5.19615	+	3.00000i	−0.630126	+	0.363803i
$69$	3.46410			0.417029
$70$	1.46410	+	5.46410i	0.174994	+	0.653085i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	8.19615	+	2.19615i	0.965926	+	0.258819i
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$	−0.732051	−	2.73205i	−0.0850992	−	0.317594i
$75$	0.866025	+	1.50000i	0.100000	+	0.173205i
$76$	−7.00000	−	12.1244i	−0.802955	−	1.39076i
$77$	−17.3205	+	10.0000i	−1.97386	+	1.13961i
$78$	3.80385	+	14.1962i	0.430701	+	1.60740i
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$		−	4.00000i		−	0.447214i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−5.00000	−	5.00000i	−0.552158	−	0.552158i
$83$	−10.3923	−	6.00000i	−1.14070	−	0.658586i	−0.194099	−	0.980982i	$-0.562178\pi$
$83$	−10.3923	−	6.00000i	−1.14070	−	0.658586i	−0.946605	+	0.322396i	$0.895512\pi$
$84$	12.0000	+	6.92820i	1.30931	+	0.755929i
$85$	−2.59808	+	1.50000i	−0.281801	+	0.162698i
$86$	−6.83013	−	1.83013i	−0.736512	−	0.197348i
$87$		0			0
$88$	13.6603	−	3.66025i	1.45619	−	0.390184i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	4.09808	+	1.09808i	0.431975	+	0.115747i
$91$			24.0000i			2.51588i
$92$	−3.46410	−	2.00000i	−0.361158	−	0.208514i
$93$	6.92820			0.718421
$94$	0.732051	−	2.73205i	0.0755053	−	0.281790i
$95$	−3.50000	−	6.06218i	−0.359092	−	0.621966i
$96$	−6.92820	−	6.92820i	−0.707107	−	0.707107i
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	−0.631810	−	0.775123i	$-0.717688\pi$
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	0.987181	+	0.159602i	$0.0510211\pi$
$98$	9.00000	+	9.00000i	0.909137	+	0.909137i
$99$			15.0000i			1.50756i
$100$		−	2.00000i		−	0.200000i
$101$	12.1244	+	7.00000i	1.20642	+	0.696526i	0.961975	−	0.273138i	$-0.0880614\pi$
$101$	12.1244	+	7.00000i	1.20642	+	0.696526i	0.244443	+	0.969664i	$0.421395\pi$
$102$	−1.90192	+	7.09808i	−0.188319	+	0.702814i
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$	4.39230	−	16.3923i	0.430701	−	1.60740i
$105$	6.00000	+	3.46410i	0.585540	+	0.338062i
$106$	2.92820	+	10.9282i	0.284412	+	1.06144i
$107$		−	13.0000i		−	1.25676i	−0.777908	−	0.628379i	$-0.783719\pi$
$107$		−	13.0000i		−	1.25676i	0.777908	−	0.628379i	$-0.216281\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$	6.83013	−	1.83013i	0.651227	−	0.174496i
$111$	−3.00000	−	1.73205i	−0.284747	−	0.164399i
$112$	−8.00000	−	13.8564i	−0.755929	−	1.30931i
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	−16.5622	−	4.43782i	−1.55119	−	0.415640i
$115$	−1.73205	−	1.00000i	−0.161515	−	0.0932505i
$116$		0			0
$117$	15.5885	+	9.00000i	1.44115	+	0.832050i
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$	−3.46410	−	3.46410i	−0.316228	−	0.316228i
$121$	7.00000	+	12.1244i	0.636364	+	1.10221i
$122$	−5.46410	−	1.46410i	−0.494697	−	0.132554i
$123$	−8.66025			−0.780869
$124$	−6.92820	−	4.00000i	−0.622171	−	0.359211i
$125$		−	1.00000i		−	0.0894427i
$126$	16.3923	−	4.39230i	1.46034	−	0.391298i
$127$	−18.0000			−1.59724			−0.798621	−	0.601834i	$-0.794437\pi$
$127$	−18.0000			−1.59724			−0.798621	+	0.601834i	$0.794437\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	−7.50000	+	4.33013i	−0.660338	+	0.381246i
$130$	2.19615	−	8.19615i	0.192615	−	0.718850i
$131$	10.3923	−	6.00000i	0.907980	−	0.524222i	0.0281993	−	0.999602i	$-0.491023\pi$
$131$	10.3923	−	6.00000i	0.907980	−	0.524222i	0.879781	+	0.475380i	$0.157689\pi$
$132$	8.66025	−	15.0000i	0.753778	−	1.30558i
$133$	−24.2487	−	14.0000i	−2.10263	−	1.21395i
$134$	−3.00000	+	3.00000i	−0.259161	+	0.259161i
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$	6.00000	−	6.00000i	0.514496	−	0.514496i
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$	−4.73205	+	1.26795i	−0.402819	+	0.107935i
$139$	−9.52628	+	5.50000i	−0.808008	+	0.466504i	−0.846264	−	0.532764i	$-0.821153\pi$
$139$	−9.52628	+	5.50000i	−0.808008	+	0.466504i	0.0382553	+	0.999268i	$0.487820\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$	−1.73205	−	3.00000i	−0.145865	−	0.252646i
$142$	−2.73205	+	0.732051i	−0.229269	+	0.0614323i
$143$	30.0000			2.50873
$144$	−12.0000			−1.00000
$145$		0			0
$146$	−1.36603	+	0.366025i	−0.113053	+	0.0302925i
$147$	15.5885			1.28571
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$	−1.73205	−	1.73205i	−0.141421	−	0.141421i
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	14.0000	+	14.0000i	1.13555	+	1.13555i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	20.0000	−	20.0000i	1.61165	−	1.61165i
$155$	−3.46410	−	2.00000i	−0.278243	−	0.160644i
$156$	−10.3923	−	18.0000i	−0.832050	−	1.44115i
$157$	−17.3205	+	10.0000i	−1.38233	+	0.798087i	−0.992435	−	0.122774i	$-0.960821\pi$
$157$	−17.3205	+	10.0000i	−1.38233	+	0.798087i	−0.389892	+	0.920860i	$0.627488\pi$
$158$	3.66025	−	13.6603i	0.291194	−	1.08675i
$159$	12.0000	+	6.92820i	0.951662	+	0.549442i
$160$	1.46410	+	5.46410i	0.115747	+	0.431975i
$161$	−8.00000			−0.630488
$162$	3.29423	−	12.2942i	0.258819	−	0.965926i
$163$		−	20.0000i		−	1.56652i	−0.621694	−	0.783260i	$-0.713555\pi$
$163$		−	20.0000i		−	1.56652i	0.621694	−	0.783260i	$-0.286445\pi$
$164$	8.66025	+	5.00000i	0.676252	+	0.390434i
$165$	4.33013	−	7.50000i	0.337100	−	0.583874i
$166$	16.3923	+	4.39230i	1.27229	+	0.340909i
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	0.726293	−	0.687386i	$-0.241242\pi$
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	−0.958440	+	0.285295i	$0.907908\pi$
$168$	−18.9282	−	5.07180i	−1.46034	−	0.391298i
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$	3.00000	−	3.00000i	0.230089	−	0.230089i
$171$	−18.1865	+	10.5000i	−1.39076	+	0.802955i
$172$	10.0000			0.762493
$173$	6.92820	+	4.00000i	0.526742	+	0.304114i	0.739689	−	0.672949i	$-0.234973\pi$
$173$	6.92820	+	4.00000i	0.526742	+	0.304114i	−0.212947	+	0.977064i	$0.568306\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	−17.3205	+	10.0000i	−1.30558	+	0.753778i
$177$			12.1244i			0.911322i
$178$	−2.73205	+	0.732051i	−0.204776	+	0.0548695i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$	−6.00000			−0.447214
$181$			2.00000i			0.148659i	0.997234	+	0.0743294i	$0.0236816\pi$
$181$			2.00000i			0.148659i	−0.997234	+	0.0743294i	$0.976318\pi$
$182$	−8.78461	−	32.7846i	−0.651159	−	2.43016i
$183$	−6.00000	+	3.46410i	−0.443533	+	0.256074i
$184$	5.46410	+	1.46410i	0.402819	+	0.107935i
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$	−9.46410	+	2.53590i	−0.693942	+	0.185941i
$187$	12.9904	+	7.50000i	0.949951	+	0.548454i
$188$			4.00000i			0.291730i
$189$	10.3923	−	18.0000i	0.755929	−	1.30931i
$190$	7.00000	+	7.00000i	0.507833	+	0.507833i
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	12.0000	+	6.92820i	0.866025	+	0.500000i
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−2.56218	+	9.56218i	−0.183954	+	0.686524i
$195$	−5.19615	−	9.00000i	−0.372104	−	0.644503i
$196$	−15.5885	−	9.00000i	−1.11346	−	0.642857i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$	−5.49038	−	20.4904i	−0.390184	−	1.45619i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	0.732051	+	2.73205i	0.0517638	+	0.193185i
$201$			5.19615i			0.366508i
$202$	−19.1244	−	5.12436i	−1.34558	−	0.360548i
$203$		0			0
$204$		−	10.3923i		−	0.727607i
$205$	4.33013	+	2.50000i	0.302429	+	0.174608i
$206$	−14.0000	−	14.0000i	−0.975426	−	0.975426i
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$			24.0000i			1.66410i
$209$	−17.5000	+	30.3109i	−1.21050	+	2.09665i
$210$	−9.46410	−	2.53590i	−0.653085	−	0.174994i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−8.00000	−	13.8564i	−0.549442	−	0.951662i
$213$	−1.73205	+	3.00000i	−0.118678	+	0.205557i
$214$	4.75833	+	17.7583i	0.325273	+	1.21393i
$215$	5.00000			0.340997
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$	−16.0000			−1.08615
$218$	1.46410	+	5.46410i	0.0991615	+	0.370076i
$219$	−0.866025	+	1.50000i	−0.0585206	+	0.101361i
$220$	−8.66025	+	5.00000i	−0.583874	+	0.337100i
$221$	15.5885	−	9.00000i	1.04859	−	0.605406i
$222$	4.73205	+	1.26795i	0.317594	+	0.0850992i
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	−0.530607	−	0.847618i	$-0.678036\pi$
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	0.999362	+	0.0357107i	$0.0113695\pi$
$224$	16.0000	+	16.0000i	1.06904	+	1.06904i
$225$	−3.00000			−0.200000
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$	7.79423	+	4.50000i	0.517321	+	0.298675i	0.735838	−	0.677158i	$-0.236789\pi$
$227$	7.79423	+	4.50000i	0.517321	+	0.298675i	−0.218517	+	0.975833i	$0.570122\pi$
$228$	24.2487			1.60591
$229$	3.46410	−	2.00000i	0.228914	−	0.132164i	−0.381157	−	0.924510i	$-0.624474\pi$
$229$	3.46410	−	2.00000i	0.228914	−	0.132164i	0.610071	+	0.792347i	$0.291141\pi$
$230$	2.73205	+	0.732051i	0.180146	+	0.0482700i
$231$		−	34.6410i		−	2.27921i
$232$		0			0
$233$	−27.0000			−1.76883			−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000			−1.76883			−0.884414	+	0.466702i	$0.845442\pi$
$234$	−24.5885	−	6.58846i	−1.60740	−	0.430701i
$235$			2.00000i			0.130466i
$236$	7.00000	−	12.1244i	0.455661	−	0.789228i
$237$	−8.66025	−	15.0000i	−0.562544	−	0.974355i
$238$	4.39230	−	16.3923i	0.284711	−	1.06256i
$239$	7.00000	+	12.1244i	0.452792	+	0.784259i	0.998558	−	0.0536783i	$-0.0170946\pi$
$239$	7.00000	+	12.1244i	0.452792	+	0.784259i	−0.545766	+	0.837938i	$0.683761\pi$
$240$	6.00000	+	3.46410i	0.387298	+	0.223607i
$241$	7.50000	−	12.9904i	0.483117	−	0.836784i	−0.516695	−	0.856170i	$-0.672838\pi$
$241$	7.50000	−	12.9904i	0.483117	−	0.836784i	0.999812	+	0.0193858i	$0.00617107\pi$
$242$	−14.0000	−	14.0000i	−0.899954	−	0.899954i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	8.00000			0.512148
$245$	−7.79423	−	4.50000i	−0.497955	−	0.287494i
$246$	11.8301	−	3.16987i	0.754261	−	0.202104i
$247$	21.0000	+	36.3731i	1.33620	+	2.31436i
$248$	10.9282	+	2.92820i	0.693942	+	0.185941i
$249$	18.0000	−	10.3923i	1.14070	−	0.658586i
$250$	0.366025	+	1.36603i	0.0231495	+	0.0863950i
$251$			9.00000i			0.568075i	0.958813	+	0.284037i	$0.0916740\pi$
$251$			9.00000i			0.568075i	−0.958813	+	0.284037i	$0.908326\pi$
$252$	−20.7846	+	12.0000i	−1.30931	+	0.755929i
$253$			10.0000i			0.628695i
$254$	24.5885	−	6.58846i	1.54282	−	0.413397i
$255$		−	5.19615i		−	0.325396i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	0.735972	−	0.677012i	$-0.236726\pi$
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	−0.954296	+	0.298864i	$0.903392\pi$
$258$	8.66025	−	8.66025i	0.539164	−	0.539164i
$259$	6.92820	+	4.00000i	0.430498	+	0.248548i
$260$			12.0000i			0.744208i
$261$		0			0
$262$	−12.0000	+	12.0000i	−0.741362	+	0.741362i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	−6.33975	+	23.6603i	−0.390184	+	1.45619i
$265$	−4.00000	−	6.92820i	−0.245718	−	0.425596i
$266$	38.2487	+	10.2487i	2.34518	+	0.628389i
$267$	−1.73205	+	3.00000i	−0.106000	+	0.183597i
$268$	3.00000	−	5.19615i	0.183254	−	0.317406i
$269$			20.0000i			1.21942i	0.792624	+	0.609711i	$0.208714\pi$
$269$			20.0000i			1.21942i	−0.792624	+	0.609711i	$0.791286\pi$
$270$	−5.19615	+	5.19615i	−0.316228	+	0.316228i
$271$	28.0000			1.70088			0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000			1.70088			0.850439	+	0.526073i	$0.176336\pi$
$272$	−6.00000	+	10.3923i	−0.363803	+	0.630126i
$273$	−36.0000	−	20.7846i	−2.17882	−	1.25794i
$274$	−6.22243	+	23.2224i	−0.375911	+	1.40292i
$275$	−4.33013	+	2.50000i	−0.261116	+	0.150756i
$276$	6.00000	−	3.46410i	0.361158	−	0.208514i
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	0.551131	−	0.834419i	$-0.314196\pi$
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	−0.447062	+	0.894503i	$0.647530\pi$
$278$	11.0000	−	11.0000i	0.659736	−	0.659736i
$279$	−6.00000	+	10.3923i	−0.359211	+	0.622171i
$280$	8.00000	+	8.00000i	0.478091	+	0.478091i
$281$	11.0000	−	19.0526i	0.656205	−	1.13658i	−0.325385	−	0.945582i	$-0.605494\pi$
$281$	11.0000	−	19.0526i	0.656205	−	1.13658i	0.981590	−	0.190999i	$-0.0611727\pi$
$282$	3.46410	+	3.46410i	0.206284	+	0.206284i
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$	3.46410	−	2.00000i	0.205557	−	0.118678i
$285$	12.1244			0.718185
$286$	−40.9808	+	10.9808i	−2.42324	+	0.649306i
$287$	20.0000			1.18056
$288$	16.3923	−	4.39230i	0.965926	−	0.258819i
$289$	−8.00000			−0.470588
$290$		0			0
$291$	6.06218	+	10.5000i	0.355371	+	0.615521i
$292$	1.73205	−	1.00000i	0.101361	−	0.0585206i
$293$	−3.46410	+	2.00000i	−0.202375	+	0.116841i	−0.597763	−	0.801673i	$-0.703944\pi$
$293$	−3.46410	+	2.00000i	−0.202375	+	0.116841i	0.395388	+	0.918514i	$0.370610\pi$
$294$	−21.2942	+	5.70577i	−1.24190	+	0.332767i
$295$	3.50000	−	6.06218i	0.203778	−	0.352954i
$296$	−4.00000	−	4.00000i	−0.232495	−	0.232495i
$297$	−22.5000	−	12.9904i	−1.30558	−	0.753778i
$298$	6.00000	−	6.00000i	0.347571	−	0.347571i
$299$	10.3923	+	6.00000i	0.601003	+	0.346989i
$300$	3.00000	+	1.73205i	0.173205	+	0.100000i
$301$	17.3205	−	10.0000i	0.998337	−	0.576390i
$302$	3.66025	−	13.6603i	0.210624	−	0.786059i
$303$	−21.0000	+	12.1244i	−1.20642	+	0.696526i
$304$	−24.2487	−	14.0000i	−1.39076	−	0.802955i
$305$	4.00000			0.229039
$306$	−9.00000	−	9.00000i	−0.514496	−	0.514496i
$307$			23.0000i			1.31268i	0.754466	+	0.656340i	$0.227896\pi$
$307$			23.0000i			1.31268i	−0.754466	+	0.656340i	$0.772104\pi$
$308$	−20.0000	+	34.6410i	−1.13961	+	1.97386i
$309$	−24.2487			−1.37946
$310$	5.46410	+	1.46410i	0.310340	+	0.0831554i
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	−0.996856	−	0.0792356i	$-0.974752\pi$
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	0.429808	−	0.902920i	$-0.358581\pi$
$312$	20.7846	+	20.7846i	1.17670	+	1.17670i
$313$	4.50000	−	7.79423i	0.254355	−	0.440556i	−0.710365	−	0.703833i	$-0.751470\pi$
$313$	4.50000	−	7.79423i	0.254355	−	0.440556i	0.964720	+	0.263278i	$0.0848035\pi$
$314$	20.0000	−	20.0000i	1.12867	−	1.12867i
$315$	−10.3923	+	6.00000i	−0.585540	+	0.338062i
$316$			20.0000i			1.12509i
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	−18.9282	−	5.07180i	−1.06144	−	0.284412i
$319$		0			0
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	19.5000	+	11.2583i	1.08838	+	0.628379i
$322$	10.9282	−	2.92820i	0.609005	−	0.163182i
$323$			21.0000i			1.16847i
$324$			18.0000i			1.00000i
$325$			6.00000i			0.332820i
$326$	7.32051	+	27.3205i	0.405445	+	1.51314i
$327$	6.00000	+	3.46410i	0.331801	+	0.191565i
$328$	−13.6603	−	3.66025i	−0.754261	−	0.202104i
$329$	4.00000	+	6.92820i	0.220527	+	0.381964i
$330$	−3.16987	+	11.8301i	−0.174496	+	0.651227i
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.0583130	−	0.998298i	$-0.518572\pi$
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.893708	+	0.448649i	$0.851905\pi$
$332$	−24.0000			−1.31717
$333$	5.19615	−	3.00000i	0.284747	−	0.164399i
$334$	6.00000	+	6.00000i	0.328305	+	0.328305i
$335$	1.50000	−	2.59808i	0.0819538	−	0.141948i
$336$	27.7128			1.51186
$337$	−7.50000	−	12.9904i	−0.408551	−	0.707631i	0.586177	−	0.810183i	$-0.300632\pi$
$337$	−7.50000	−	12.9904i	−0.408551	−	0.707631i	−0.994728	+	0.102552i	$0.967299\pi$
$338$	−8.41858	+	31.4186i	−0.457911	+	1.70895i
$339$	10.3923			0.564433
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$			20.0000i			1.08306i
$342$	21.0000	−	21.0000i	1.13555	−	1.13555i
$343$	−8.00000			−0.431959
$344$	−13.6603	+	3.66025i	−0.736512	+	0.197348i
$345$	3.00000	−	1.73205i	0.161515	−	0.0932505i
$346$	−10.9282	−	2.92820i	−0.587504	−	0.157421i
$347$	−16.4545	+	9.50000i	−0.883323	+	0.509987i	−0.871753	−	0.489946i	$-0.837016\pi$
$347$	−16.4545	+	9.50000i	−0.883323	+	0.509987i	−0.0115703	+	0.999933i	$0.503683\pi$
$348$		0			0
$349$	−13.8564	−	8.00000i	−0.741716	−	0.428230i	0.0809766	−	0.996716i	$-0.474196\pi$
$349$	−13.8564	−	8.00000i	−0.741716	−	0.428230i	−0.822693	+	0.568486i	$0.807529\pi$
$350$	4.00000	+	4.00000i	0.213809	+	0.213809i
$351$	−27.0000	+	15.5885i	−1.44115	+	0.832050i
$352$	20.0000	−	20.0000i	1.06600	−	1.06600i
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$	−4.43782	−	16.5622i	−0.235868	−	0.880270i
$355$	1.73205	−	1.00000i	0.0919277	−	0.0530745i
$356$	3.46410	−	2.00000i	0.183597	−	0.106000i
$357$	−10.3923	−	18.0000i	−0.550019	−	0.952661i
$358$	4.39230	+	16.3923i	0.232141	+	0.866360i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$	8.19615	−	2.19615i	0.431975	−	0.115747i
$361$	−30.0000			−1.57895
$362$	−0.732051	−	2.73205i	−0.0384757	−	0.143593i
$363$	−24.2487			−1.27273
$364$	24.0000	+	41.5692i	1.25794	+	2.17882i
$365$	0.866025	−	0.500000i	0.0453298	−	0.0261712i
$366$	6.92820	−	6.92820i	0.362143	−	0.362143i
$367$	−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	$0.322339\pi$
$368$	−8.00000			−0.417029
$369$	7.50000	−	12.9904i	0.390434	−	0.676252i
$370$	−2.00000	−	2.00000i	−0.103975	−	0.103975i
$371$	−27.7128	−	16.0000i	−1.43878	−	0.830679i
$372$	12.0000	−	6.92820i	0.622171	−	0.359211i
$373$	19.0526	−	11.0000i	0.986504	−	0.569558i	0.0822766	−	0.996610i	$-0.473781\pi$
$373$	19.0526	−	11.0000i	0.986504	−	0.569558i	0.904227	+	0.427051i	$0.140448\pi$
$374$	−20.4904	−	5.49038i	−1.05953	−	0.283901i
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$	−1.46410	−	5.46410i	−0.0755053	−	0.281790i
$377$		0			0
$378$	−7.60770	+	28.3923i	−0.391298	+	1.46034i
$379$			3.00000i			0.154100i	0.997027	+	0.0770498i	$0.0245501\pi$
$379$			3.00000i			0.154100i	−0.997027	+	0.0770498i	$0.975450\pi$
$380$	−12.1244	−	7.00000i	−0.621966	−	0.359092i
$381$	15.5885	−	27.0000i	0.798621	−	1.38325i
$382$	−2.92820	+	10.9282i	−0.149820	+	0.559136i
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$	−18.9282	−	5.07180i	−0.965926	−	0.258819i
$385$	−10.0000	+	17.3205i	−0.509647	+	0.882735i
$386$	−23.0000	−	23.0000i	−1.17067	−	1.17067i
$387$		−	15.0000i		−	0.762493i
$388$		−	14.0000i		−	0.710742i
$389$	13.8564	+	8.00000i	0.702548	+	0.405616i	0.808296	−	0.588777i	$-0.200390\pi$
$389$	13.8564	+	8.00000i	0.702548	+	0.405616i	−0.105748	+	0.994393i	$0.533724\pi$
$390$	10.3923	+	10.3923i	0.526235	+	0.526235i
$391$	3.00000	+	5.19615i	0.151717	+	0.262781i
$392$	24.5885	+	6.58846i	1.24190	+	0.332767i
$393$			20.7846i			1.04844i
$394$	2.92820	+	10.9282i	0.147521	+	0.550555i
$395$			10.0000i			0.503155i
$396$	15.0000	+	25.9808i	0.753778	+	1.30558i
$397$		−	26.0000i		−	1.30490i	−0.757831	−	0.652451i	$-0.773741\pi$
$397$		−	26.0000i		−	1.30490i	0.757831	−	0.652451i	$-0.226259\pi$
$398$		0			0
$399$	42.0000	−	24.2487i	2.10263	−	1.21395i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$	−1.90192	−	7.09808i	−0.0948593	−	0.354020i
$403$	20.7846	+	12.0000i	1.03536	+	0.597763i
$404$	28.0000			1.39305
$405$			9.00000i			0.447214i
$406$		0			0
$407$	5.00000	−	8.66025i	0.247841	−	0.429273i
$408$	3.80385	+	14.1962i	0.188319	+	0.702814i
$409$	−7.50000	−	12.9904i	−0.370851	−	0.642333i	0.618846	−	0.785513i	$-0.287601\pi$
$409$	−7.50000	−	12.9904i	−0.370851	−	0.642333i	−0.989697	+	0.143180i	$0.954267\pi$
$410$	−6.83013	−	1.83013i	−0.337316	−	0.0903835i
$411$	14.7224	+	25.5000i	0.726204	+	1.25782i
$412$	24.2487	+	14.0000i	1.19465	+	0.689730i
$413$		−	28.0000i		−	1.37779i
$414$	2.19615	−	8.19615i	0.107935	−	0.402819i
$415$	−12.0000			−0.589057
$416$	−8.78461	−	32.7846i	−0.430701	−	1.60740i
$417$		−	19.0526i		−	0.933008i
$418$	12.8109	−	47.8109i	0.626601	−	2.33851i
$419$	3.46410	−	2.00000i	0.169232	−	0.0977064i	−0.412991	−	0.910735i	$-0.635516\pi$
$419$	3.46410	−	2.00000i	0.169232	−	0.0977064i	0.582224	+	0.813029i	$0.302183\pi$
$420$	13.8564			0.676123
$421$	1.73205	+	1.00000i	0.0844150	+	0.0487370i	0.541613	−	0.840628i	$-0.317814\pi$
$421$	1.73205	+	1.00000i	0.0844150	+	0.0487370i	−0.457198	+	0.889365i	$0.651147\pi$
$422$		0			0
$423$	6.00000			0.291730
$424$	16.0000	+	16.0000i	0.777029	+	0.777029i
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$	1.26795	−	4.73205i	0.0614323	−	0.229269i
$427$	13.8564	−	8.00000i	0.670559	−	0.387147i
$428$	−13.0000	−	22.5167i	−0.628379	−	1.08838i
$429$	−25.9808	+	45.0000i	−1.25436	+	2.17262i
$430$	−6.83013	+	1.83013i	−0.329378	+	0.0882566i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$	10.3923	−	18.0000i	0.500000	−	0.866025i
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$	21.8564	−	5.85641i	1.04914	−	0.281117i
$435$		0			0
$436$	−4.00000	−	6.92820i	−0.191565	−	0.331801i
$437$	−12.1244	+	7.00000i	−0.579987	+	0.334855i
$438$	0.633975	−	2.36603i	0.0302925	−	0.113053i
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.219149	−	0.975691i	$-0.429672\pi$
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.735399	−	0.677634i	$-0.236995\pi$
$440$	10.0000	−	10.0000i	0.476731	−	0.476731i
$441$	−13.5000	+	23.3827i	−0.642857	+	1.11346i
$442$	−18.0000	+	18.0000i	−0.856173	+	0.856173i
$443$	21.6506	+	12.5000i	1.02865	+	0.593893i	0.916598	−	0.399809i	$-0.130924\pi$
$443$	21.6506	+	12.5000i	1.02865	+	0.593893i	0.112054	+	0.993702i	$0.464257\pi$
$444$	−6.92820			−0.328798
$445$	1.73205	−	1.00000i	0.0821071	−	0.0474045i
$446$	−5.12436	+	19.1244i	−0.242645	+	0.905564i
$447$		−	10.3923i		−	0.491539i
$448$	−27.7128	−	16.0000i	−1.30931	−	0.755929i
$449$	−27.0000			−1.27421			−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000			−1.27421			−0.637104	+	0.770778i	$0.719868\pi$
$450$	4.09808	−	1.09808i	0.193185	−	0.0517638i
$451$		−	25.0000i		−	1.17720i
$452$	−10.3923	−	6.00000i	−0.488813	−	0.282216i
$453$	−8.66025	−	15.0000i	−0.406894	−	0.704761i
$454$	−12.2942	−	3.29423i	−0.576997	−	0.154606i
$455$	12.0000	+	20.7846i	0.562569	+	0.974398i
$456$	−33.1244	+	8.87564i	−1.55119	+	0.415640i
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	−0.898974	−	0.438001i	$-0.855687\pi$
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	0.828807	+	0.559534i	$0.189020\pi$
$458$	−4.00000	+	4.00000i	−0.186908	+	0.186908i
$459$	−15.5885			−0.727607
$460$	−4.00000			−0.186501
$461$	12.1244	+	7.00000i	0.564688	+	0.326023i	0.755025	−	0.655696i	$-0.227625\pi$
$461$	12.1244	+	7.00000i	0.564688	+	0.326023i	−0.190337	+	0.981719i	$0.560958\pi$
$462$	12.6795	+	47.3205i	0.589903	+	2.20155i
$463$	−13.0000	−	22.5167i	−0.604161	−	1.04644i	−0.992183	−	0.124788i	$-0.960175\pi$
$463$	−13.0000	−	22.5167i	−0.604161	−	1.04644i	0.388022	−	0.921650i	$-0.373158\pi$
$464$		0			0
$465$	6.00000	−	3.46410i	0.278243	−	0.160644i
$466$	36.8827	−	9.88269i	1.70856	−	0.457807i
$467$		−	13.0000i		−	0.601568i	−0.953692	−	0.300784i	$-0.902752\pi$
$467$		−	13.0000i		−	0.601568i	0.953692	−	0.300784i	$-0.0972484\pi$
$468$	36.0000			1.66410
$469$		−	12.0000i		−	0.554109i
$470$	−0.732051	−	2.73205i	−0.0337670	−	0.126020i
$471$		−	34.6410i		−	1.59617i
$472$	−5.12436	+	19.1244i	−0.235868	+	0.880270i
$473$	−12.5000	−	21.6506i	−0.574751	−	0.995497i
$474$	17.3205	+	17.3205i	0.795557	+	0.795557i
$475$	−6.06218	−	3.50000i	−0.278152	−	0.160591i
$476$			24.0000i			1.10004i
$477$	−20.7846	+	12.0000i	−0.951662	+	0.549442i
$478$	−14.0000	−	14.0000i	−0.640345	−	0.640345i
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$	−9.46410	−	2.53590i	−0.431975	−	0.115747i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−5.49038	+	20.4904i	−0.250080	+	0.933311i
$483$	6.92820	−	12.0000i	0.315244	−	0.546019i
$484$	24.2487	+	14.0000i	1.10221	+	0.636364i
$485$		−	7.00000i		−	0.317854i
$486$	15.5885	+	15.5885i	0.707107	+	0.707107i
$487$	−12.0000			−0.543772			−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$	−10.9282	+	2.92820i	−0.494697	+	0.132554i
$489$	30.0000	+	17.3205i	1.35665	+	0.783260i
$490$	12.2942	+	3.29423i	0.555397	+	0.148818i
$491$	−9.52628	+	5.50000i	−0.429915	+	0.248212i	−0.699310	−	0.714818i	$-0.746509\pi$
$491$	−9.52628	+	5.50000i	−0.429915	+	0.248212i	0.269395	+	0.963030i	$0.413176\pi$
$492$	−15.0000	+	8.66025i	−0.676252	+	0.390434i
$493$		0			0
$494$	−42.0000	−	42.0000i	−1.88967	−	1.88967i
$495$	7.50000	+	12.9904i	0.337100	+	0.583874i
$496$	−16.0000			−0.718421
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$	−20.7846	+	20.7846i	−0.931381	+	0.931381i
$499$	35.5070	−	20.5000i	1.58951	−	0.917706i	0.596127	−	0.802890i	$-0.296706\pi$
$499$	35.5070	−	20.5000i	1.58951	−	0.917706i	0.993387	−	0.114816i	$-0.0366277\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$	10.3923			0.464294
$502$	−3.29423	−	12.2942i	−0.147029	−	0.548718i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$	24.0000	−	24.0000i	1.06904	−	1.06904i
$505$	14.0000			0.622992
$506$	−3.66025	−	13.6603i	−0.162718	−	0.607272i
$507$	19.9186	+	34.5000i	0.884615	+	1.53220i
$508$	−31.1769	+	18.0000i	−1.38325	+	0.798621i
$509$	10.3923	−	6.00000i	0.460631	−	0.265945i	−0.251679	−	0.967811i	$-0.580983\pi$
$509$	10.3923	−	6.00000i	0.460631	−	0.265945i	0.712309	+	0.701866i	$0.247649\pi$
$510$	1.90192	+	7.09808i	0.0842186	+	0.314308i
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		−	36.3731i		−	1.60591i
$514$	7.00000	+	7.00000i	0.308757	+	0.308757i
$515$	12.1244	+	7.00000i	0.534263	+	0.308457i
$516$	−8.66025	+	15.0000i	−0.381246	+	0.660338i
$517$	8.66025	−	5.00000i	0.380878	−	0.219900i
$518$	−10.9282	−	2.92820i	−0.480158	−	0.128658i
$519$	−12.0000	+	6.92820i	−0.526742	+	0.304114i
$520$	−4.39230	−	16.3923i	−0.192615	−	0.718850i
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		0			0
$523$		−	4.00000i		−	0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$		−	4.00000i		−	0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$	12.0000	−	20.7846i	0.524222	−	0.907980i
$525$	6.92820			0.302372
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		−	34.6410i		−	1.50756i
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	8.00000	+	8.00000i	0.347498	+	0.347498i
$531$	−18.1865	−	10.5000i	−0.789228	−	0.455661i
$532$	−56.0000			−2.42791
$533$	−25.9808	−	15.0000i	−1.12535	−	0.649722i
$534$	1.26795	−	4.73205i	0.0548695	−	0.204776i
$535$	−6.50000	−	11.2583i	−0.281020	−	0.486740i
$536$	−2.19615	+	8.19615i	−0.0948593	+	0.354020i
$537$	18.0000	+	10.3923i	0.776757	+	0.448461i
$538$	−7.32051	−	27.3205i	−0.315610	−	1.17787i
$539$			45.0000i			1.93829i
$540$	5.19615	−	9.00000i	0.223607	−	0.387298i
$541$		−	22.0000i		−	0.945854i	−0.881102	−	0.472927i	$-0.843197\pi$
$541$		−	22.0000i		−	0.945854i	0.881102	−	0.472927i	$-0.156803\pi$
$542$	−38.2487	+	10.2487i	−1.64292	+	0.440220i
$543$	−3.00000	−	1.73205i	−0.128742	−	0.0743294i
$544$	4.39230	−	16.3923i	0.188319	−	0.702814i
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$	56.7846	+	15.2154i	2.43016	+	0.651159i
$547$	−11.2583	−	6.50000i	−0.481371	−	0.277920i	0.239616	−	0.970868i	$-0.422978\pi$
$547$	−11.2583	−	6.50000i	−0.481371	−	0.277920i	−0.720988	+	0.692948i	$0.756312\pi$
$548$		−	34.0000i		−	1.45241i
$549$		−	12.0000i		−	0.512148i
$550$	5.00000	−	5.00000i	0.213201	−	0.213201i
$551$		0			0
$552$	−6.92820	+	6.92820i	−0.294884	+	0.294884i
$553$	20.0000	+	34.6410i	0.850487	+	1.47309i
$554$	−2.73205	−	0.732051i	−0.116074	−	0.0311019i
$555$	−3.46410			−0.147043
$556$	−11.0000	+	19.0526i	−0.466504	+	0.808008i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$	4.39230	−	16.3923i	0.185941	−	0.693942i
$559$	−30.0000			−1.26886
$560$	−13.8564	−	8.00000i	−0.585540	−	0.338062i
$561$	−22.5000	+	12.9904i	−0.949951	+	0.548454i
$562$	−8.05256	+	30.0526i	−0.339677	+	1.26769i
$563$	33.7750	−	19.5000i	1.42345	−	0.821827i	0.426855	−	0.904320i	$-0.359622\pi$
$563$	33.7750	−	19.5000i	1.42345	−	0.821827i	0.996592	+	0.0824933i	$0.0262883\pi$
$564$	−6.00000	−	3.46410i	−0.252646	−	0.145865i
$565$	−5.19615	−	3.00000i	−0.218604	−	0.126211i
$566$	−4.00000	+	4.00000i	−0.168133	+	0.168133i
$567$	18.0000	+	31.1769i	0.755929	+	1.30931i
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$	12.5000	−	21.6506i	0.524027	−	0.907642i	−0.475581	−	0.879672i	$-0.657762\pi$
$569$	12.5000	−	21.6506i	0.524027	−	0.907642i	0.999609	−	0.0279702i	$-0.00890434\pi$
$570$	−16.5622	+	4.43782i	−0.693713	+	0.185880i
$571$	−11.2583	+	6.50000i	−0.471146	+	0.272017i	−0.716720	−	0.697362i	$-0.754357\pi$
$571$	−11.2583	+	6.50000i	−0.471146	+	0.272017i	0.245573	+	0.969378i	$0.421024\pi$
$572$	51.9615	−	30.0000i	2.17262	−	1.25436i
$573$	6.92820	+	12.0000i	0.289430	+	0.501307i
$574$	−27.3205	+	7.32051i	−1.14034	+	0.305552i
$575$	−2.00000			−0.0834058
$576$	−20.7846	+	12.0000i	−0.866025	+	0.500000i
$577$	7.00000			0.291414			0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000			0.291414			0.145707	+	0.989328i	$0.453454\pi$
$578$	10.9282	−	2.92820i	0.454553	−	0.121797i
$579$	−39.8372			−1.65558
$580$		0			0
$581$	−41.5692	+	24.0000i	−1.72458	+	0.995688i
$582$	−12.1244	−	12.1244i	−0.502571	−	0.502571i
$583$	−20.0000	+	34.6410i	−0.828315	+	1.43468i
$584$	−2.00000	+	2.00000i	−0.0827606	+	0.0827606i
$585$	18.0000			0.744208
$586$	4.00000	−	4.00000i	0.165238	−	0.165238i
$587$	−23.3827	−	13.5000i	−0.965107	−	0.557205i	−0.0673658	−	0.997728i	$-0.521459\pi$
$587$	−23.3827	−	13.5000i	−0.965107	−	0.557205i	−0.897741	+	0.440524i	$0.854793\pi$
$588$	27.0000	−	15.5885i	1.11346	−	0.642857i
$589$	−24.2487	+	14.0000i	−0.999151	+	0.576860i
$590$	−2.56218	+	9.56218i	−0.105483	+	0.393669i
$591$	12.0000	+	6.92820i	0.493614	+	0.284988i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	34.0000			1.39621			0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000			1.39621			0.698106	+	0.715994i	$0.254026\pi$
$594$	35.4904	+	9.50962i	1.45619	+	0.390184i
$595$			12.0000i			0.491952i
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$		0			0
$598$	−16.3923	−	4.39230i	−0.670331	−	0.179615i
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	0.873799	+	0.486287i	$0.161649\pi$
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	−0.0157622	+	0.999876i	$0.505017\pi$
$600$	−4.73205	−	1.26795i	−0.193185	−	0.0517638i
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$	−20.0000	+	20.0000i	−0.815139	+	0.815139i
$603$	−7.79423	−	4.50000i	−0.317406	−	0.183254i
$604$			20.0000i			0.813788i
$605$	12.1244	+	7.00000i	0.492925	+	0.284590i
$606$	24.2487	−	24.2487i	0.985037	−	0.985037i
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$	38.2487	+	10.2487i	1.55119	+	0.415640i
$609$		0			0
$610$	−5.46410	+	1.46410i	−0.221235	+	0.0592797i
$611$		−	12.0000i		−	0.485468i
$612$	15.5885	+	9.00000i	0.630126	+	0.363803i
$613$			26.0000i			1.05013i	0.851062	+	0.525065i	$0.175959\pi$
$613$			26.0000i			1.05013i	−0.851062	+	0.525065i	$0.824041\pi$
$614$	−8.41858	−	31.4186i	−0.339746	−	1.26795i
$615$	−7.50000	+	4.33013i	−0.302429	+	0.174608i
$616$	14.6410	−	54.6410i	0.589903	−	2.20155i
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$	33.1244	−	8.87564i	1.33246	−	0.357031i
$619$	4.33013	+	2.50000i	0.174042	+	0.100483i	0.584491	−	0.811400i	$-0.301294\pi$
$619$	4.33013	+	2.50000i	0.174042	+	0.100483i	−0.410448	+	0.911884i	$0.634628\pi$
$620$	−8.00000			−0.321288
$621$	−5.19615	−	9.00000i	−0.208514	−	0.361158i
$622$	20.0000	+	20.0000i	0.801927	+	0.801927i
$623$	4.00000	−	6.92820i	0.160257	−	0.277573i
$624$	−36.0000	−	20.7846i	−1.44115	−	0.832050i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.29423	+	12.2942i	−0.131664	+	0.491376i
$627$	−30.3109	−	52.5000i	−1.21050	−	2.09665i
$628$	−20.0000	+	34.6410i	−0.798087	+	1.38233i
$629$		−	6.00000i		−	0.239236i
$630$	12.0000	−	12.0000i	0.478091	−	0.478091i
$631$	−6.00000			−0.238856			−0.119428	−	0.992843i	$-0.538106\pi$
$631$	−6.00000			−0.238856			−0.119428	+	0.992843i	$0.538106\pi$
$632$	−7.32051	−	27.3205i	−0.291194	−	1.08675i
$633$		0			0
$634$	−24.5885	−	6.58846i	−0.976532	−	0.261661i
$635$	−15.5885	+	9.00000i	−0.618609	+	0.357154i
$636$	27.7128			1.09888
$637$	46.7654	+	27.0000i	1.85291	+	1.06978i
$638$		0			0
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	8.00000	+	8.00000i	0.316228	+	0.316228i
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	−0.983625	−	0.180229i	$-0.942316\pi$
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	0.647895	+	0.761730i	$0.275650\pi$
$642$	−30.7583	−	8.24167i	−1.21393	−	0.325273i
$643$	18.1865	−	10.5000i	0.717207	−	0.414080i	−0.0965169	−	0.995331i	$-0.530770\pi$
$643$	18.1865	−	10.5000i	0.717207	−	0.414080i	0.813724	+	0.581252i	$0.197437\pi$
$644$	−13.8564	+	8.00000i	−0.546019	+	0.315244i
$645$	−4.33013	+	7.50000i	−0.170499	+	0.295312i
$646$	−7.68653	−	28.6865i	−0.302423	−	1.12866i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	−6.58846	−	24.5885i	−0.258819	−	0.965926i
$649$	−35.0000			−1.37387
$650$	−2.19615	−	8.19615i	−0.0861402	−	0.321480i
$651$	13.8564	−	24.0000i	0.543075	−	0.940634i
$652$	−20.0000	−	34.6410i	−0.783260	−	1.35665i
$653$	−10.3923	+	6.00000i	−0.406682	+	0.234798i	−0.689363	−	0.724416i	$-0.742110\pi$
$653$	−10.3923	+	6.00000i	−0.406682	+	0.234798i	0.282681	+	0.959214i	$0.408776\pi$
$654$	−9.46410	−	2.53590i	−0.370076	−	0.0991615i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	20.0000			0.780869
$657$	−1.50000	−	2.59808i	−0.0585206	−	0.101361i
$658$	−8.00000	−	8.00000i	−0.311872	−	0.311872i
$659$	−31.1769	−	18.0000i	−1.21448	−	0.701180i	−0.250748	−	0.968052i	$-0.580677\pi$
$659$	−31.1769	−	18.0000i	−1.21448	−	0.701180i	−0.963732	+	0.266872i	$0.914010\pi$
$660$		−	17.3205i		−	0.674200i
$661$	39.8372	−	23.0000i	1.54949	−	0.894596i	0.551306	−	0.834303i	$-0.314130\pi$
$661$	39.8372	−	23.0000i	1.54949	−	0.894596i	0.998181	−	0.0602929i	$-0.0192035\pi$
$662$	27.3205	+	7.32051i	1.06184	+	0.284520i
$663$			31.1769i			1.21081i
$664$	32.7846	−	8.78461i	1.27229	−	0.340909i
$665$	−28.0000			−1.08579
$666$	−6.00000	+	6.00000i	−0.232495	+	0.232495i
$667$		0			0
$668$	−10.3923	−	6.00000i	−0.402090	−	0.232147i
$669$	12.1244	+	21.0000i	0.468755	+	0.811907i
$670$	−1.09808	+	4.09808i	−0.0424224	+	0.158322i
$671$	−10.0000	−	17.3205i	−0.386046	−	0.668651i
$672$	−37.8564	+	10.1436i	−1.46034	+	0.391298i
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	−0.946156	−	0.323711i	$-0.895069\pi$
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	0.753420	+	0.657539i	$0.228403\pi$
$674$	15.0000	+	15.0000i	0.577778	+	0.577778i
$675$	2.59808	−	4.50000i	0.100000	−	0.173205i
$676$		−	46.0000i		−	1.76923i
$677$	13.8564	+	8.00000i	0.532545	+	0.307465i	0.742052	−	0.670342i	$-0.233853\pi$
$677$	13.8564	+	8.00000i	0.532545	+	0.307465i	−0.209507	+	0.977807i	$0.567186\pi$
$678$	−14.1962	+	3.80385i	−0.545200	+	0.146086i
$679$	−14.0000	−	24.2487i	−0.537271	−	0.930580i
$680$	2.19615	−	8.19615i	0.0842186	−	0.314308i
$681$	−13.5000	+	7.79423i	−0.517321	+	0.298675i
$682$	−7.32051	−	27.3205i	−0.280317	−	1.04616i
$683$			51.0000i			1.95146i	0.218975	+	0.975730i	$0.429729\pi$
$683$			51.0000i			1.95146i	−0.218975	+	0.975730i	$0.570271\pi$
$684$	−21.0000	+	36.3731i	−0.802955	+	1.39076i
$685$		−	17.0000i		−	0.649537i
$686$	10.9282	−	2.92820i	0.417241	−	0.111799i
$687$			6.92820i			0.264327i
$688$	17.3205	−	10.0000i	0.660338	−	0.381246i
$689$	24.0000	+	41.5692i	0.914327	+	1.58366i
$690$	−3.46410	+	3.46410i	−0.131876	+	0.131876i
$691$	−10.3923	−	6.00000i	−0.395342	−	0.228251i	0.289130	−	0.957290i	$-0.406634\pi$
$691$	−10.3923	−	6.00000i	−0.395342	−	0.228251i	−0.684472	+	0.729039i	$0.739967\pi$
$692$	16.0000			0.608229
$693$	51.9615	+	30.0000i	1.97386	+	1.13961i
$694$	19.0000	−	19.0000i	0.721230	−	0.721230i
$695$	−5.50000	+	9.52628i	−0.208627	+	0.361352i
$696$		0			0
$697$	−7.50000	−	12.9904i	−0.284083	−	0.492046i
$698$	21.8564	+	5.85641i	0.827277	+	0.221668i
$699$	23.3827	−	40.5000i	0.884414	−	1.53185i
$700$	−6.92820	−	4.00000i	−0.261861	−	0.151186i
$701$			10.0000i			0.377695i	0.982006	+	0.188847i	$0.0604752\pi$
$701$			10.0000i			0.377695i	−0.982006	+	0.188847i	$0.939525\pi$
$702$	31.1769	−	31.1769i	1.17670	−	1.17670i
$703$	14.0000			0.528020
$704$	−20.0000	+	34.6410i	−0.753778	+	1.30558i
$705$	−3.00000	−	1.73205i	−0.112987	−	0.0652328i
$706$	−3.29423	+	12.2942i	−0.123980	+	0.462699i
$707$	48.4974	−	28.0000i	1.82393	−	1.05305i
$708$	12.1244	+	21.0000i	0.455661	+	0.789228i
$709$	27.7128	+	16.0000i	1.04078	+	0.600893i	0.920053	−	0.391794i	$-0.128145\pi$
$709$	27.7128	+	16.0000i	1.04078	+	0.600893i	0.120723	+	0.992686i	$0.461479\pi$
$710$	−2.00000	+	2.00000i	−0.0750587	+	0.0750587i
$711$	30.0000			1.12509
$712$	−4.00000	+	4.00000i	−0.149906	+	0.149906i
$713$	−4.00000	+	6.92820i	−0.149801	+	0.259463i
$714$	20.7846	+	20.7846i	0.777844	+	0.777844i
$715$	25.9808	−	15.0000i	0.971625	−	0.560968i
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$	−24.2487			−0.905585
$718$	16.3923	−	4.39230i	0.611755	−	0.163919i
$719$	−18.0000			−0.671287			−0.335643	−	0.941989i	$-0.608954\pi$
$719$	−18.0000			−0.671287			−0.335643	+	0.941989i	$0.608954\pi$
$720$	−10.3923	+	6.00000i	−0.387298	+	0.223607i
$721$	56.0000			2.08555
$722$	40.9808	−	10.9808i	1.52515	−	0.408662i
$723$	12.9904	+	22.5000i	0.483117	+	0.836784i
$724$	2.00000	+	3.46410i	0.0743294	+	0.128742i
$725$		0			0
$726$	33.1244	−	8.87564i	1.22936	−	0.329406i
$727$	25.0000	−	43.3013i	0.927199	−	1.60596i	0.139212	−	0.990263i	$-0.455543\pi$
$727$	25.0000	−	43.3013i	0.927199	−	1.60596i	0.787986	−	0.615693i	$-0.211124\pi$
$728$	−48.0000	−	48.0000i	−1.77900	−	1.77900i
$729$	27.0000			1.00000
$730$	−1.00000	+	1.00000i	−0.0370117	+	0.0370117i
$731$	−12.9904	−	7.50000i	−0.480467	−	0.277398i
$732$	−6.92820	+	12.0000i	−0.256074	+	0.443533i
$733$	−31.1769	+	18.0000i	−1.15155	+	0.664845i	−0.949263	−	0.314482i	$-0.898169\pi$
$733$	−31.1769	+	18.0000i	−1.15155	+	0.664845i	−0.202282	+	0.979327i	$0.564836\pi$
$734$	6.58846	−	24.5885i	0.243184	−	0.907577i
$735$	13.5000	−	7.79423i	0.497955	−	0.287494i
$736$	10.9282	−	2.92820i	0.402819	−	0.107935i
$737$	−15.0000			−0.552532
$738$	−5.49038	+	20.4904i	−0.202104	+	0.754261i
$739$		−	15.0000i		−	0.551784i	−0.961189	−	0.275892i	$-0.911027\pi$
$739$		−	15.0000i		−	0.551784i	0.961189	−	0.275892i	$-0.0889732\pi$
$740$	3.46410	+	2.00000i	0.127343	+	0.0735215i
$741$	−72.7461			−2.67240
$742$	43.7128	+	11.7128i	1.60475	+	0.429991i
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	−13.8564	+	13.8564i	−0.508001	+	0.508001i
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$	−22.0000	+	22.0000i	−0.805477	+	0.805477i
$747$			36.0000i			1.31717i
$748$	30.0000			1.09691
$749$	−45.0333	−	26.0000i	−1.64548	−	0.950019i
$750$	−2.36603	−	0.633975i	−0.0863950	−	0.0231495i
$751$	23.0000	+	39.8372i	0.839282	+	1.45368i	0.890496	+	0.454991i	$0.150358\pi$
$751$	23.0000	+	39.8372i	0.839282	+	1.45368i	−0.0512140	+	0.998688i	$0.516309\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	−13.5000	−	7.79423i	−0.491967	−	0.284037i
$754$		0			0
$755$			10.0000i			0.363937i
$756$		−	41.5692i		−	1.51186i
$757$		−	4.00000i		−	0.145382i	−0.997354	−	0.0726912i	$-0.976841\pi$
$757$		−	4.00000i		−	0.145382i	0.997354	−	0.0726912i	$-0.0231588\pi$
$758$	−1.09808	−	4.09808i	−0.0398839	−	0.148849i
$759$	−15.0000	−	8.66025i	−0.544466	−	0.314347i
$760$	19.1244	+	5.12436i	0.693713	+	0.185880i
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.819231	+	0.573463i	$0.194400\pi$
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.0870179	+	0.996207i	$0.472266\pi$
$762$	−11.4115	+	42.5885i	−0.413397	+	1.54282i
$763$	−13.8564	−	8.00000i	−0.501636	−	0.289619i
$764$		−	16.0000i		−	0.578860i
$765$	7.79423	+	4.50000i	0.281801	+	0.162698i
$766$	18.0000	+	18.0000i	0.650366	+	0.650366i
$767$	−21.0000	+	36.3731i	−0.758266	+	1.31336i
$768$	27.7128			1.00000
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	0.998852	+	0.0479061i	$0.0152548\pi$
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	−0.457938	+	0.888984i	$0.651412\pi$
$770$	7.32051	−	27.3205i	0.263813	−	0.984563i
$771$	12.1244			0.436648
$772$	39.8372	+	23.0000i	1.43377	+	0.827788i
$773$			42.0000i			1.51064i	0.655359	+	0.755318i	$0.272517\pi$
$773$			42.0000i			1.51064i	−0.655359	+	0.755318i	$0.727483\pi$
$774$	5.49038	+	20.4904i	0.197348	+	0.736512i
$775$	−4.00000			−0.143684
$776$	5.12436	+	19.1244i	0.183954	+	0.686524i
$777$	−12.0000	+	6.92820i	−0.430498	+	0.248548i
$778$	−21.8564	−	5.85641i	−0.783590	−	0.209962i
$779$	30.3109	−	17.5000i	1.08600	−	0.627003i
$780$	−18.0000	−	10.3923i	−0.644503	−	0.372104i
$781$	−8.66025	−	5.00000i	−0.309888	−	0.178914i
$782$	−6.00000	−	6.00000i	−0.214560	−	0.214560i
$783$		0			0
$784$	−36.0000			−1.28571
$785$	−10.0000	+	17.3205i	−0.356915	+	0.618195i
$786$	−7.60770	−	28.3923i	−0.271357	−	1.01272i
$787$	−45.0333	+	26.0000i	−1.60526	+	0.926800i	−0.614855	+	0.788641i	$0.710785\pi$
$787$	−45.0333	+	26.0000i	−1.60526	+	0.926800i	−0.990410	+	0.138159i	$0.955881\pi$
$788$	−8.00000	−	13.8564i	−0.284988	−	0.493614i
$789$		0			0
$790$	−3.66025	−	13.6603i	−0.130226	−	0.486010i
$791$	−24.0000			−0.853342
$792$	−30.0000	−	30.0000i	−1.06600	−	1.06600i
$793$	−24.0000			−0.852265
$794$	9.51666	+	35.5167i	0.337734	+	1.26044i
$795$	13.8564			0.491436
$796$		0			0
$797$	−5.19615	+	3.00000i	−0.184057	+	0.106265i	−0.589197	−	0.807989i	$-0.700556\pi$
$797$	−5.19615	+	3.00000i	−0.184057	+	0.106265i	0.405140	+	0.914255i	$0.367223\pi$
$798$	−48.4974	+	48.4974i	−1.71679	+	1.71679i
$799$	3.00000	−	5.19615i	0.106132	−	0.183827i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−15.0000	−	15.0000i	−0.529668	−	0.529668i
$803$	−4.33013	−	2.50000i	−0.152807	−	0.0882231i
$804$	5.19615	+	9.00000i	0.183254	+	0.317406i
$805$	−6.92820	+	4.00000i	−0.244187	+	0.140981i
$806$	−32.7846	−	8.78461i	−1.15479	−	0.309425i
$807$	−30.0000	−	17.3205i	−1.05605	−	0.609711i
$808$	−38.2487	+	10.2487i	−1.34558	+	0.360548i
$809$	7.00000			0.246107			0.123053	−	0.992400i	$-0.460731\pi$
$809$	7.00000			0.246107			0.123053	+	0.992400i	$0.460731\pi$
$810$	−3.29423	−	12.2942i	−0.115747	−	0.431975i
$811$			1.00000i			0.0351147i	0.999846	+	0.0175574i	$0.00558897\pi$
$811$			1.00000i			0.0351147i	−0.999846	+	0.0175574i	$0.994411\pi$
$812$		0			0
$813$	−24.2487	+	42.0000i	−0.850439	+	1.47300i
$814$	−3.66025	+	13.6603i	−0.128292	+	0.478792i
$815$	−10.0000	−	17.3205i	−0.350285	−	0.606711i
$816$	−10.3923	−	18.0000i	−0.363803	−	0.630126i
$817$	17.5000	−	30.3109i	0.612247	−	1.06044i
$818$	15.0000	+	15.0000i	0.524463	+	0.524463i
$819$	62.3538	−	36.0000i	2.17882	−	1.25794i
$820$	10.0000			0.349215
$821$	−3.46410	−	2.00000i	−0.120898	−	0.0698005i	0.438331	−	0.898813i	$-0.355570\pi$
$821$	−3.46410	−	2.00000i	−0.120898	−	0.0698005i	−0.559229	+	0.829013i	$0.688903\pi$
$822$	−29.4449	−	29.4449i	−1.02701	−	1.02701i
$823$	3.00000	+	5.19615i	0.104573	+	0.181126i	0.913564	−	0.406695i	$-0.133319\pi$
$823$	3.00000	+	5.19615i	0.104573	+	0.181126i	−0.808990	+	0.587822i	$0.799986\pi$
$824$	−38.2487	−	10.2487i	−1.33246	−	0.357031i
$825$		−	8.66025i		−	0.301511i
$826$	10.2487	+	38.2487i	0.356598	+	1.33084i
$827$			16.0000i			0.556375i	0.960527	+	0.278187i	$0.0897336\pi$
$827$			16.0000i			0.556375i	−0.960527	+	0.278187i	$0.910266\pi$
$828$			12.0000i			0.417029i
$829$			8.00000i			0.277851i	0.990303	+	0.138926i	$0.0443649\pi$
$829$			8.00000i			0.277851i	−0.990303	+	0.138926i	$0.955635\pi$
$830$	16.3923	−	4.39230i	0.568985	−	0.152459i
$831$	−3.00000	+	1.73205i	−0.104069	+	0.0600842i
$832$	24.0000	+	41.5692i	0.832050	+	1.44115i
$833$	13.5000	+	23.3827i	0.467747	+	0.810162i
$834$	6.97372	+	26.0263i	0.241480	+	0.901216i
$835$	−5.19615	−	3.00000i	−0.179820	−	0.103819i
$836$			70.0000i			2.42100i
$837$	−10.3923	−	18.0000i	−0.359211	−	0.622171i
$838$	−4.00000	+	4.00000i	−0.138178	+	0.138178i
$839$	−14.0000	+	24.2487i	−0.483334	+	0.837158i	−0.999817	−	0.0191389i	$-0.993908\pi$
$839$	−14.0000	+	24.2487i	−0.483334	+	0.837158i	0.516483	+	0.856297i	$0.327241\pi$
$840$	−18.9282	+	5.07180i	−0.653085	+	0.174994i
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$	−2.73205	−	0.732051i	−0.0941527	−	0.0252281i
$843$	19.0526	+	33.0000i	0.656205	+	1.13658i
$844$		0			0
$845$		−	23.0000i		−	0.791224i
$846$	−8.19615	+	2.19615i	−0.281790	+	0.0755053i
$847$	56.0000			1.92418
$848$	−27.7128	−	16.0000i	−0.951662	−	0.549442i
$849$			6.92820i			0.237775i
$850$	1.09808	−	4.09808i	0.0376637	−	0.140563i
$851$	3.46410	−	2.00000i	0.118748	−	0.0685591i
$852$			6.92820i			0.237356i
$853$	39.8372	+	23.0000i	1.36400	+	0.787505i	0.990153	−	0.139986i	$-0.0447058\pi$
$853$	39.8372	+	23.0000i	1.36400	+	0.787505i	0.373845	+	0.927491i	$0.378039\pi$
$854$	−16.0000	+	16.0000i	−0.547509	+	0.547509i
$855$	−10.5000	+	18.1865i	−0.359092	+	0.621966i
$856$	26.0000	+	26.0000i	0.888662	+	0.888662i
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$	19.0192	−	70.9808i	0.649306	−	2.42324i
$859$	−32.0429	+	18.5000i	−1.09329	+	0.631212i	−0.934451	−	0.356092i	$-0.884109\pi$
$859$	−32.0429	+	18.5000i	−1.09329	+	0.631212i	−0.158840	+	0.987304i	$0.550775\pi$
$860$	8.66025	−	5.00000i	0.295312	−	0.170499i
$861$	−17.3205	+	30.0000i	−0.590281	+	1.02240i
$862$	16.3923	−	4.39230i	0.558324	−	0.149602i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	−7.60770	+	28.3923i	−0.258819	+	0.965926i
$865$	8.00000			0.272008
$866$	−39.6147	+	10.6147i	−1.34616	+	0.360703i
$867$	6.92820	−	12.0000i	0.235294	−	0.407541i
$868$	−27.7128	+	16.0000i	−0.940634	+	0.543075i
$869$	43.3013	−	25.0000i	1.46889	−	0.848067i
$870$		0			0
$871$	−9.00000	+	15.5885i	−0.304953	+	0.528195i
$872$	8.00000	+	8.00000i	0.270914	+	0.270914i
$873$	−21.0000			−0.710742
$874$	14.0000	−	14.0000i	0.473557	−	0.473557i
$875$	−3.46410	−	2.00000i	−0.117108	−	0.0676123i
$876$			3.46410i			0.117041i
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.888640	−	0.458606i	$-0.848349\pi$
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.0471555	+	0.998888i	$0.515016\pi$
$878$	−14.6410	+	54.6410i	−0.494110	+	1.84404i
$879$		−	6.92820i		−	0.233682i
$880$	−10.0000	+	17.3205i	−0.337100	+	0.583874i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	9.88269	−	36.8827i	0.332767	−	1.24190i
$883$		−	41.0000i		−	1.37976i	−0.723924	−	0.689880i	$-0.757663\pi$
$883$		−	41.0000i		−	1.37976i	0.723924	−	0.689880i	$-0.242337\pi$
$884$	18.0000	−	31.1769i	0.605406	−	1.04859i
$885$	6.06218	+	10.5000i	0.203778	+	0.352954i
$886$	−34.1506	−	9.15064i	−1.14731	−	0.307422i
$887$	−11.0000	−	19.0526i	−0.369344	−	0.639722i	0.620119	−	0.784508i	$-0.287084\pi$
$887$	−11.0000	−	19.0526i	−0.369344	−	0.639722i	−0.989463	+	0.144785i	$0.953751\pi$
$888$	9.46410	−	2.53590i	0.317594	−	0.0850992i
$889$	−36.0000	+	62.3538i	−1.20740	+	2.09128i
$890$	−2.00000	+	2.00000i	−0.0670402	+	0.0670402i
$891$	38.9711	−	22.5000i	1.30558	−	0.753778i
$892$		−	28.0000i		−	0.937509i
$893$	12.1244	+	7.00000i	0.405726	+	0.234246i
$894$	3.80385	+	14.1962i	0.127220	+	0.474790i
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$	43.7128	+	11.7128i	1.46034	+	0.391298i
$897$	−18.0000	+	10.3923i	−0.601003	+	0.346989i
$898$	36.8827	−	9.88269i	1.23079	−	0.329789i
$899$		0			0
$900$	−5.19615	+	3.00000i	−0.173205	+	0.100000i
$901$			24.0000i			0.799556i
$902$	9.15064	+	34.1506i	0.304683	+	1.13709i
$903$			34.6410i			1.15278i
$904$	16.3923	+	4.39230i	0.545200	+	0.146086i
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	17.3205	+	17.3205i	0.575435	+	0.575435i
$907$	−21.6506	−	12.5000i	−0.718898	−	0.415056i	0.0954492	−	0.995434i	$-0.469571\pi$
$907$	−21.6506	−	12.5000i	−0.718898	−	0.415056i	−0.814347	+	0.580379i	$0.802905\pi$
$908$	18.0000			0.597351
$909$		−	42.0000i		−	1.39305i
$910$	−24.0000	−	24.0000i	−0.795592	−	0.795592i
$911$	−18.0000	+	31.1769i	−0.596367	+	1.03294i	0.396986	+	0.917825i	$0.370056\pi$
$911$	−18.0000	+	31.1769i	−0.596367	+	1.03294i	−0.993352	+	0.115113i	$0.963277\pi$
$912$	42.0000	−	24.2487i	1.39076	−	0.802955i
$913$	30.0000	+	51.9615i	0.992855	+	1.71968i
$914$	1.09808	−	4.09808i	0.0363211	−	0.135552i
$915$	−3.46410	+	6.00000i	−0.114520	+	0.198354i
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$		−	48.0000i		−	1.58510i
$918$	21.2942	−	5.70577i	0.702814	−	0.188319i
$919$	−26.0000			−0.857661			−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000			−0.857661			−0.428830	+	0.903385i	$0.641074\pi$
$920$	5.46410	−	1.46410i	0.180146	−	0.0482700i
$921$	−34.5000	−	19.9186i	−1.13681	−	0.656340i
$922$	−19.1244	−	5.12436i	−0.629827	−	0.168762i
$923$	−10.3923	+	6.00000i	−0.342067	+	0.197492i
$924$	−34.6410	−	60.0000i	−1.13961	−	1.97386i
$925$	1.73205	+	1.00000i	0.0569495	+	0.0328798i
$926$	26.0000	+	26.0000i	0.854413	+	0.854413i
$927$	21.0000	−	36.3731i	0.689730	−	1.19465i
$928$		0			0
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	−0.0852924	−	0.996356i	$-0.527182\pi$
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	0.905516	−	0.424313i	$-0.139484\pi$
$930$	−6.92820	+	6.92820i	−0.227185	+	0.227185i
$931$	−54.5596	+	31.5000i	−1.78812	+	1.03237i
$932$	−46.7654	+	27.0000i	−1.53185	+	0.884414i
$933$	34.6410			1.13410
$934$	4.75833	+	17.7583i	0.155697	+	0.581070i
$935$	15.0000			0.490552
$936$	−49.1769	+	13.1769i	−1.60740	+	0.430701i
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	4.39230	+	16.3923i	0.143414	+	0.535228i
$939$	7.79423	+	13.5000i	0.254355	+	0.440556i
$940$	2.00000	+	3.46410i	0.0652328	+	0.112987i
$941$	6.92820	−	4.00000i	0.225853	−	0.130396i	−0.382804	−	0.923829i	$-0.625042\pi$
$941$	6.92820	−	4.00000i	0.225853	−	0.130396i	0.608657	+	0.793433i	$0.291708\pi$
$942$	12.6795	+	47.3205i	0.413120	+	1.54179i
$943$	5.00000	−	8.66025i	0.162822	−	0.282017i
$944$		−	28.0000i		−	0.911322i
$945$		−	20.7846i		−	0.676123i
$946$	25.0000	+	25.0000i	0.812820	+	0.812820i
$947$	44.1673	+	25.5000i	1.43524	+	0.828639i	0.997514	−	0.0704677i	$-0.0224492\pi$
$947$	44.1673	+	25.5000i	1.43524	+	0.828639i	0.437730	+	0.899106i	$0.355783\pi$
$948$	−30.0000	−	17.3205i	−0.974355	−	0.562544i
$949$	−5.19615	+	3.00000i	−0.168674	+	0.0973841i
$950$	9.56218	+	2.56218i	0.310238	+	0.0831280i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$	−8.78461	−	32.7846i	−0.284711	−	1.06256i
$953$	−29.0000			−0.939402			−0.469701	−	0.882826i	$-0.655638\pi$
$953$	−29.0000			−0.939402			−0.469701	+	0.882826i	$0.655638\pi$
$954$	24.0000	−	24.0000i	0.777029	−	0.777029i
$955$		−	8.00000i		−	0.258874i
$956$	24.2487	+	14.0000i	0.784259	+	0.452792i
$957$		0			0
$958$	5.85641	−	21.8564i	0.189212	−	0.706148i
$959$	−34.0000	−	58.8897i	−1.09792	−	1.90165i
$960$	13.8564			0.447214
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	12.0000	+	12.0000i	0.386896	+	0.386896i
$963$	−33.7750	+	19.5000i	−1.08838	+	0.628379i
$964$		−	30.0000i		−	0.966235i
$965$	19.9186	+	11.5000i	0.641202	+	0.370198i
$966$	−5.07180	+	18.9282i	−0.163182	+	0.609005i
$967$	−14.0000	−	24.2487i	−0.450210	−	0.779786i	0.548189	−	0.836354i	$-0.315317\pi$
$967$	−14.0000	−	24.2487i	−0.450210	−	0.779786i	−0.998399	+	0.0565684i	$0.981984\pi$
$968$	−38.2487	−	10.2487i	−1.22936	−	0.329406i
$969$	−31.5000	−	18.1865i	−1.01193	−	0.584236i
$970$	2.56218	+	9.56218i	0.0822666	+	0.307023i
$971$		−	36.0000i		−	1.15529i	−0.816286	−	0.577647i	$-0.803971\pi$
$971$		−	36.0000i		−	1.15529i	0.816286	−	0.577647i	$-0.196029\pi$
$972$	−27.0000	−	15.5885i	−0.866025	−	0.500000i
$973$			44.0000i			1.41058i
$974$	16.3923	−	4.39230i	0.525243	−	0.140739i
$975$	−9.00000	−	5.19615i	−0.288231	−	0.166410i
$976$	13.8564	−	8.00000i	0.443533	−	0.256074i
$977$	27.5000	+	47.6314i	0.879803	+	1.52386i	0.851557	+	0.524262i	$0.175659\pi$
$977$	27.5000	+	47.6314i	0.879803	+	1.52386i	0.0282462	+	0.999601i	$0.491008\pi$
$978$	−47.3205	−	12.6795i	−1.51314	−	0.405445i
$979$	−8.66025	−	5.00000i	−0.276783	−	0.159801i
$980$	−18.0000			−0.574989
$981$	−10.3923	+	6.00000i	−0.331801	+	0.191565i
$982$	11.0000	−	11.0000i	0.351024	−	0.351024i
$983$	25.0000	−	43.3013i	0.797376	−	1.38110i	−0.123943	−	0.992289i	$-0.539554\pi$
$983$	25.0000	−	43.3013i	0.797376	−	1.38110i	0.921319	−	0.388807i	$-0.127113\pi$
$984$	17.3205	−	17.3205i	0.552158	−	0.552158i
$985$	−4.00000	−	6.92820i	−0.127451	−	0.220751i
$986$		0			0
$987$	−13.8564			−0.441054
$988$	72.7461	+	42.0000i	2.31436	+	1.33620i
$989$		−	10.0000i		−	0.317982i
$990$	−15.0000	−	15.0000i	−0.476731	−	0.476731i
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	21.8564	−	5.85641i	0.693942	−	0.185941i
$993$	30.0000	−	17.3205i	0.952021	−	0.549650i
$994$	−2.92820	+	10.9282i	−0.0928770	+	0.346622i
$995$		0			0
$996$	20.7846	−	36.0000i	0.658586	−	1.14070i
$997$	−24.2487	−	14.0000i	−0.767964	−	0.443384i	0.0641836	−	0.997938i	$-0.479556\pi$
$997$	−24.2487	−	14.0000i	−0.767964	−	0.443384i	−0.832148	+	0.554554i	$0.812889\pi$
$998$	−41.0000	+	41.0000i	−1.29783	+	1.29783i
$999$			10.3923i			0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bf.a.61.1	✓	4
3.2	odd	2		1080.2.bf.a.181.2		4
4.3	odd	2		1440.2.bv.a.241.2		4
8.3	odd	2		1440.2.bv.a.241.1		4
8.5	even	2	inner	360.2.bf.a.61.2	yes	4
9.4	even	3	inner	360.2.bf.a.301.2	yes	4
9.5	odd	6		1080.2.bf.a.901.1		4
12.11	even	2		4320.2.bv.a.721.1		4
24.5	odd	2		1080.2.bf.a.181.1		4
24.11	even	2		4320.2.bv.a.721.2		4
36.23	even	6		4320.2.bv.a.3601.2		4
36.31	odd	6		1440.2.bv.a.1201.1		4
72.5	odd	6		1080.2.bf.a.901.2		4
72.13	even	6	inner	360.2.bf.a.301.1	yes	4
72.59	even	6		4320.2.bv.a.3601.1		4
72.67	odd	6		1440.2.bv.a.1201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bf.a.61.1	✓	4	1.1	even	1	trivial
360.2.bf.a.61.2	yes	4	8.5	even	2	inner
360.2.bf.a.301.1	yes	4	72.13	even	6	inner
360.2.bf.a.301.2	yes	4	9.4	even	3	inner
1080.2.bf.a.181.1		4	24.5	odd	2
1080.2.bf.a.181.2		4	3.2	odd	2
1080.2.bf.a.901.1		4	9.5	odd	6
1080.2.bf.a.901.2		4	72.5	odd	6
1440.2.bv.a.241.1		4	8.3	odd	2
1440.2.bv.a.241.2		4	4.3	odd	2
1440.2.bv.a.1201.1		4	36.31	odd	6
1440.2.bv.a.1201.2		4	72.67	odd	6
4320.2.bv.a.721.1		4	12.11	even	2
4320.2.bv.a.721.2		4	24.11	even	2
4320.2.bv.a.3601.1		4	72.59	even	6
4320.2.bv.a.3601.2		4	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.633975 - 2.36603i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.633975 - 2.36603i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.00000i) q^{10} +(-4.33013 - 2.50000i) q^{11} +3.46410i q^{12} +(-5.19615 + 3.00000i) q^{13} +(-1.46410 + 5.46410i) q^{14} +1.73205i q^{15} +(2.00000 - 3.46410i) q^{16} -3.00000 q^{17} +(3.00000 + 3.00000i) q^{18} -7.00000i q^{19} +(1.00000 - 1.73205i) q^{20} +(3.46410 + 6.00000i) q^{21} +(6.83013 + 1.83013i) q^{22} +(-1.00000 - 1.73205i) q^{23} +(-1.26795 - 4.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(6.00000 - 6.00000i) q^{26} +5.19615 q^{27} -8.00000i q^{28} +(-0.633975 - 2.36603i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(7.50000 - 4.33013i) q^{33} +(4.09808 - 1.09808i) q^{34} -4.00000i q^{35} +(-5.19615 - 3.00000i) q^{36} +2.00000i q^{37} +(2.56218 + 9.56218i) q^{38} -10.3923i q^{39} +(-0.732051 + 2.73205i) q^{40} +(2.50000 + 4.33013i) q^{41} +(-6.92820 - 6.92820i) q^{42} +(4.33013 + 2.50000i) q^{43} -10.0000 q^{44} +(-2.59808 - 1.50000i) q^{45} +(2.00000 + 2.00000i) q^{46} +(-1.00000 + 1.73205i) q^{47} +(3.46410 + 6.00000i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.366025 + 1.36603i) q^{50} +(2.59808 - 4.50000i) q^{51} +(-6.00000 + 10.3923i) q^{52} -8.00000i q^{53} +(-7.09808 + 1.90192i) q^{54} -5.00000 q^{55} +(2.92820 + 10.9282i) q^{56} +(10.5000 + 6.06218i) q^{57} +(6.06218 - 3.50000i) q^{59} +(1.73205 + 3.00000i) q^{60} +(3.46410 + 2.00000i) q^{61} +(4.00000 + 4.00000i) q^{62} -12.0000 q^{63} -8.00000i q^{64} +(-3.00000 + 5.19615i) q^{65} +(-8.66025 + 8.66025i) q^{66} +(2.59808 - 1.50000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +3.46410 q^{69} +(1.46410 + 5.46410i) q^{70} +2.00000 q^{71} +(8.19615 + 2.19615i) q^{72} +1.00000 q^{73} +(-0.732051 - 2.73205i) q^{74} +(0.866025 + 1.50000i) q^{75} +(-7.00000 - 12.1244i) q^{76} +(-17.3205 + 10.0000i) q^{77} +(3.80385 + 14.1962i) q^{78} +(-5.00000 + 8.66025i) q^{79} -4.00000i q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 5.00000i) q^{82} +(-10.3923 - 6.00000i) q^{83} +(12.0000 + 6.92820i) q^{84} +(-2.59808 + 1.50000i) q^{85} +(-6.83013 - 1.83013i) q^{86} +(13.6603 - 3.66025i) q^{88} +2.00000 q^{89} +(4.09808 + 1.09808i) q^{90} +24.0000i q^{91} +(-3.46410 - 2.00000i) q^{92} +6.92820 q^{93} +(0.732051 - 2.73205i) q^{94} +(-3.50000 - 6.06218i) q^{95} +(-6.92820 - 6.92820i) q^{96} +(3.50000 - 6.06218i) q^{97} +(9.00000 + 9.00000i) q^{98} +15.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{6} + 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^6 + 8 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 6 q^{6} + 8 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{20} + 10 q^{22} - 4 q^{23} - 12 q^{24} + 2 q^{25} + 24 q^{26} - 6 q^{30} - 8 q^{31} + 8 q^{32} + 30 q^{33} + 6 q^{34} - 14 q^{38} + 4 q^{40} + 10 q^{41} - 40 q^{44} + 8 q^{46} - 4 q^{47} - 18 q^{49} + 2 q^{50} - 24 q^{52} - 18 q^{54} - 20 q^{55} - 16 q^{56} + 42 q^{57} + 16 q^{62} - 48 q^{63} - 12 q^{65} - 8 q^{70} + 8 q^{71} + 12 q^{72} + 4 q^{73} + 4 q^{74} - 28 q^{76} + 36 q^{78} - 20 q^{79} - 18 q^{81} - 20 q^{82} + 48 q^{84} - 10 q^{86} + 20 q^{88} + 8 q^{89} + 6 q^{90} - 4 q^{94} - 14 q^{95} + 14 q^{97} + 36 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^6 + 8 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^17 + 12 * q^18 + 4 * q^20 + 10 * q^22 - 4 * q^23 - 12 * q^24 + 2 * q^25 + 24 * q^26 - 6 * q^30 - 8 * q^31 + 8 * q^32 + 30 * q^33 + 6 * q^34 - 14 * q^38 + 4 * q^40 + 10 * q^41 - 40 * q^44 + 8 * q^46 - 4 * q^47 - 18 * q^49 + 2 * q^50 - 24 * q^52 - 18 * q^54 - 20 * q^55 - 16 * q^56 + 42 * q^57 + 16 * q^62 - 48 * q^63 - 12 * q^65 - 8 * q^70 + 8 * q^71 + 12 * q^72 + 4 * q^73 + 4 * q^74 - 28 * q^76 + 36 * q^78 - 20 * q^79 - 18 * q^81 - 20 * q^82 + 48 * q^84 - 10 * q^86 + 20 * q^88 + 8 * q^89 + 6 * q^90 - 4 * q^94 - 14 * q^95 + 14 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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