LMFDB - Embedded newform 696.2.t.e.389.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [696,2,Mod(365,696)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(696, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("696.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 696 = 2^{3} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	696.t (of order $4$, 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:	$5.55758798068$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			389.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	696.389
Dual form			696.2.t.e.365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} -0.267949i q^{5} +(1.73205 + 1.73205i) q^{6} -3.46410 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} -0.267949i q^{5} +(1.73205 + 1.73205i) q^{6} -3.46410 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.366025 + 0.0980762i) q^{10} +(2.36603 + 2.36603i) q^{11} +(-3.00000 + 1.73205i) q^{12} -5.19615 q^{13} +(1.26795 - 4.73205i) q^{14} +(-0.401924 - 0.232051i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 + 3.00000i) q^{17} +(4.09808 - 1.09808i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(-0.267949 + 0.464102i) q^{20} +(-3.00000 + 5.19615i) q^{21} +(-4.09808 + 2.36603i) q^{22} +1.26795i q^{23} +(-1.26795 - 4.73205i) q^{24} +4.92820 q^{25} +(1.90192 - 7.09808i) q^{26} -5.19615 q^{27} +(6.00000 + 3.46410i) q^{28} +(-2.00000 + 5.00000i) q^{29} +(0.464102 - 0.464102i) q^{30} +(-3.36603 - 3.36603i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(5.59808 - 1.50000i) q^{33} +(-3.00000 - 5.19615i) q^{34} +0.928203i q^{35} +6.00000i q^{36} +(-1.26795 - 1.26795i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-4.50000 + 7.79423i) q^{39} +(-0.535898 - 0.535898i) q^{40} +(4.73205 + 4.73205i) q^{41} +(-6.00000 - 6.00000i) q^{42} +(-0.633975 + 0.633975i) q^{43} +(-1.73205 - 6.46410i) q^{44} +(-0.696152 + 0.401924i) q^{45} +(-1.73205 - 0.464102i) q^{46} +(-6.29423 - 6.29423i) q^{47} +6.92820 q^{48} +5.00000 q^{49} +(-1.80385 + 6.73205i) q^{50} +(1.90192 + 7.09808i) q^{51} +(9.00000 + 5.19615i) q^{52} -3.53590 q^{53} +(1.90192 - 7.09808i) q^{54} +(0.633975 - 0.633975i) q^{55} +(-6.92820 + 6.92820i) q^{56} +(1.90192 + 7.09808i) q^{57} +(-6.09808 - 4.56218i) q^{58} -12.1962 q^{59} +(0.464102 + 0.803848i) q^{60} +(5.19615 - 5.19615i) q^{61} +(5.83013 - 3.36603i) q^{62} +(5.19615 + 9.00000i) q^{63} -8.00000i q^{64} +1.39230i q^{65} +8.19615i q^{66} -12.9282 q^{67} +(8.19615 - 2.19615i) q^{68} +(1.90192 + 1.09808i) q^{69} +(-1.26795 - 0.339746i) q^{70} +1.26795 q^{71} +(-8.19615 - 2.19615i) q^{72} +(7.46410 - 7.46410i) q^{73} +(2.19615 - 1.26795i) q^{74} +(4.26795 - 7.39230i) q^{75} +(8.19615 - 2.19615i) q^{76} +(-8.19615 - 8.19615i) q^{77} +(-9.00000 - 9.00000i) q^{78} +(3.09808 + 3.09808i) q^{79} +(0.928203 - 0.535898i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-8.19615 + 4.73205i) q^{82} -7.12436 q^{83} +(10.3923 - 6.00000i) q^{84} +(0.803848 + 0.803848i) q^{85} +(-0.633975 - 1.09808i) q^{86} +(5.76795 + 7.33013i) q^{87} +9.46410 q^{88} +(10.7321 - 10.7321i) q^{89} +(-0.294229 - 1.09808i) q^{90} +18.0000 q^{91} +(1.26795 - 2.19615i) q^{92} +(-7.96410 + 2.13397i) q^{93} +(10.9019 - 6.29423i) q^{94} +(0.803848 + 0.803848i) q^{95} +(-2.53590 + 9.46410i) q^{96} +(1.46410 - 1.46410i) q^{97} +(-1.83013 + 6.83013i) q^{98} +(2.59808 - 9.69615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 8 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} + 8 q^{8} - 6 q^{9} - 2 q^{10} + 6 q^{11} - 12 q^{12} + 12 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} - 8 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 8 q^{25} + 18 q^{26} + 24 q^{28} - 8 q^{29} - 12 q^{30} - 10 q^{31} - 8 q^{32} + 12 q^{33} - 12 q^{34} - 12 q^{37} - 12 q^{38} - 18 q^{39} - 16 q^{40} + 12 q^{41} - 24 q^{42} - 6 q^{43} + 18 q^{45} + 6 q^{47} + 20 q^{49} - 28 q^{50} + 18 q^{51} + 36 q^{52} - 28 q^{53} + 18 q^{54} + 6 q^{55} + 18 q^{57} - 14 q^{58} - 28 q^{59} - 12 q^{60} + 6 q^{62} - 24 q^{67} + 12 q^{68} + 18 q^{69} - 12 q^{70} + 12 q^{71} - 12 q^{72} + 16 q^{73} - 12 q^{74} + 24 q^{75} + 12 q^{76} - 12 q^{77} - 36 q^{78} + 2 q^{79} - 24 q^{80} - 18 q^{81} - 12 q^{82} + 20 q^{83} + 24 q^{85} - 6 q^{86} + 30 q^{87} + 24 q^{88} + 36 q^{89} + 30 q^{90} + 72 q^{91} + 12 q^{92} - 18 q^{93} + 54 q^{94} + 24 q^{95} - 24 q^{96} - 8 q^{97} + 10 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 8 * q^8 - 6 * q^9 - 2 * q^10 + 6 * q^11 - 12 * q^12 + 12 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 + 6 * q^18 - 12 * q^19 - 8 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 8 * q^25 + 18 * q^26 + 24 * q^28 - 8 * q^29 - 12 * q^30 - 10 * q^31 - 8 * q^32 + 12 * q^33 - 12 * q^34 - 12 * q^37 - 12 * q^38 - 18 * q^39 - 16 * q^40 + 12 * q^41 - 24 * q^42 - 6 * q^43 + 18 * q^45 + 6 * q^47 + 20 * q^49 - 28 * q^50 + 18 * q^51 + 36 * q^52 - 28 * q^53 + 18 * q^54 + 6 * q^55 + 18 * q^57 - 14 * q^58 - 28 * q^59 - 12 * q^60 + 6 * q^62 - 24 * q^67 + 12 * q^68 + 18 * q^69 - 12 * q^70 + 12 * q^71 - 12 * q^72 + 16 * q^73 - 12 * q^74 + 24 * q^75 + 12 * q^76 - 12 * q^77 - 36 * q^78 + 2 * q^79 - 24 * q^80 - 18 * q^81 - 12 * q^82 + 20 * q^83 + 24 * q^85 - 6 * q^86 + 30 * q^87 + 24 * q^88 + 36 * q^89 + 30 * q^90 + 72 * q^91 + 12 * q^92 - 18 * q^93 + 54 * q^94 + 24 * q^95 - 24 * q^96 - 8 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/696\mathbb{Z}\right)^\times$.

$n$	$175$	$233$	$349$	$553$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$3$	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
$5$		−	0.267949i		−	0.119831i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$		−	0.267949i		−	0.119831i	0.998203	−	0.0599153i	$-0.0190830\pi$
$6$	1.73205	+	1.73205i	0.707107	+	0.707107i
$7$	−3.46410			−1.30931			−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−3.46410			−1.30931			−0.654654	+	0.755929i	$0.727186\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	0.366025	+	0.0980762i	0.115747	+	0.0310144i
$11$	2.36603	+	2.36603i	0.713384	+	0.713384i	0.967241	−	0.253858i	$-0.0816996\pi$
$11$	2.36603	+	2.36603i	0.713384	+	0.713384i	−0.253858	+	0.967241i	$0.581700\pi$
$12$	−3.00000	+	1.73205i	−0.866025	+	0.500000i
$13$	−5.19615			−1.44115			−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−5.19615			−1.44115			−0.720577	+	0.693375i	$0.756123\pi$
$14$	1.26795	−	4.73205i	0.338874	−	1.26469i
$15$	−0.401924	−	0.232051i	−0.103776	−	0.0599153i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−3.00000	+	3.00000i	−0.727607	+	0.727607i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−3.00000	+	3.00000i	−0.727607	+	0.727607i	0.242536	+	0.970143i	$0.422021\pi$
$18$	4.09808	−	1.09808i	0.965926	−	0.258819i
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$	−0.267949	+	0.464102i	−0.0599153	+	0.103776i
$21$	−3.00000	+	5.19615i	−0.654654	+	1.13389i
$22$	−4.09808	+	2.36603i	−0.873713	+	0.504438i
$23$			1.26795i			0.264386i	0.991224	+	0.132193i	$0.0422018\pi$
$23$			1.26795i			0.264386i	−0.991224	+	0.132193i	$0.957798\pi$
$24$	−1.26795	−	4.73205i	−0.258819	−	0.965926i
$25$	4.92820			0.985641
$26$	1.90192	−	7.09808i	0.372998	−	1.39205i
$27$	−5.19615			−1.00000
$28$	6.00000	+	3.46410i	1.13389	+	0.654654i
$29$	−2.00000	+	5.00000i	−0.371391	+	0.928477i
$29$	−2.00000	+	5.00000i	−0.371391	+	0.928477i
$30$	0.464102	−	0.464102i	0.0847330	−	0.0847330i
$31$	−3.36603	−	3.36603i	−0.604556	−	0.604556i	0.336962	−	0.941518i	$-0.390601\pi$
$31$	−3.36603	−	3.36603i	−0.604556	−	0.604556i	−0.941518	+	0.336962i	$0.890601\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$	5.59808	−	1.50000i	0.974500	−	0.261116i
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$			0.928203i			0.156895i
$36$			6.00000i			1.00000i
$37$	−1.26795	−	1.26795i	−0.208450	−	0.208450i	0.595159	−	0.803608i	$-0.297089\pi$
$37$	−1.26795	−	1.26795i	−0.208450	−	0.208450i	−0.803608	+	0.595159i	$0.797089\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−4.50000	+	7.79423i	−0.720577	+	1.24808i
$40$	−0.535898	−	0.535898i	−0.0847330	−	0.0847330i
$41$	4.73205	+	4.73205i	0.739022	+	0.739022i	0.972389	−	0.233367i	$-0.0749742\pi$
$41$	4.73205	+	4.73205i	0.739022	+	0.739022i	−0.233367	+	0.972389i	$0.574974\pi$
$42$	−6.00000	−	6.00000i	−0.925820	−	0.925820i
$43$	−0.633975	+	0.633975i	−0.0966802	+	0.0966802i	−0.753793	−	0.657112i	$-0.771778\pi$
$43$	−0.633975	+	0.633975i	−0.0966802	+	0.0966802i	0.657112	+	0.753793i	$0.271778\pi$
$44$	−1.73205	−	6.46410i	−0.261116	−	0.974500i
$45$	−0.696152	+	0.401924i	−0.103776	+	0.0599153i
$46$	−1.73205	−	0.464102i	−0.255377	−	0.0684280i
$47$	−6.29423	−	6.29423i	−0.918108	−	0.918108i	0.0787841	−	0.996892i	$-0.474896\pi$
$47$	−6.29423	−	6.29423i	−0.918108	−	0.918108i	−0.996892	+	0.0787841i	$0.974896\pi$
$48$	6.92820			1.00000
$49$	5.00000			0.714286
$50$	−1.80385	+	6.73205i	−0.255103	+	0.952056i
$51$	1.90192	+	7.09808i	0.266323	+	0.993929i
$52$	9.00000	+	5.19615i	1.24808	+	0.720577i
$53$	−3.53590			−0.485693			−0.242846	−	0.970065i	$-0.578081\pi$
$53$	−3.53590			−0.485693			−0.242846	+	0.970065i	$0.578081\pi$
$54$	1.90192	−	7.09808i	0.258819	−	0.965926i
$55$	0.633975	−	0.633975i	0.0854851	−	0.0854851i
$56$	−6.92820	+	6.92820i	−0.925820	+	0.925820i
$57$	1.90192	+	7.09808i	0.251916	+	0.940163i
$58$	−6.09808	−	4.56218i	−0.800717	−	0.599043i
$59$	−12.1962			−1.58780			−0.793902	−	0.608046i	$-0.791954\pi$
$59$	−12.1962			−1.58780			−0.793902	+	0.608046i	$0.791954\pi$
$60$	0.464102	+	0.803848i	0.0599153	+	0.103776i
$61$	5.19615	−	5.19615i	0.665299	−	0.665299i	−0.291325	−	0.956624i	$-0.594096\pi$
$61$	5.19615	−	5.19615i	0.665299	−	0.665299i	0.956624	+	0.291325i	$0.0940961\pi$
$62$	5.83013	−	3.36603i	0.740427	−	0.427486i
$63$	5.19615	+	9.00000i	0.654654	+	1.13389i
$64$		−	8.00000i		−	1.00000i
$65$			1.39230i			0.172694i
$66$			8.19615i			1.00888i
$67$	−12.9282			−1.57943			−0.789716	−	0.613473i	$-0.789772\pi$
$67$	−12.9282			−1.57943			−0.789716	+	0.613473i	$0.789772\pi$
$68$	8.19615	−	2.19615i	0.993929	−	0.266323i
$69$	1.90192	+	1.09808i	0.228965	+	0.132193i
$70$	−1.26795	−	0.339746i	−0.151549	−	0.0406074i
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	−8.19615	−	2.19615i	−0.965926	−	0.258819i
$73$	7.46410	−	7.46410i	0.873607	−	0.873607i	−0.119256	−	0.992863i	$-0.538051\pi$
$73$	7.46410	−	7.46410i	0.873607	−	0.873607i	0.992863	+	0.119256i	$0.0380511\pi$
$74$	2.19615	−	1.26795i	0.255298	−	0.147396i
$75$	4.26795	−	7.39230i	0.492820	−	0.853590i
$76$	8.19615	−	2.19615i	0.940163	−	0.251916i
$77$	−8.19615	−	8.19615i	−0.934038	−	0.934038i
$78$	−9.00000	−	9.00000i	−1.01905	−	1.01905i
$79$	3.09808	+	3.09808i	0.348561	+	0.348561i	0.859573	−	0.511012i	$-0.170729\pi$
$79$	3.09808	+	3.09808i	0.348561	+	0.348561i	−0.511012	+	0.859573i	$0.670729\pi$
$80$	0.928203	−	0.535898i	0.103776	−	0.0599153i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−8.19615	+	4.73205i	−0.905114	+	0.522568i
$83$	−7.12436			−0.782000			−0.391000	−	0.920391i	$-0.627871\pi$
$83$	−7.12436			−0.782000			−0.391000	+	0.920391i	$0.627871\pi$
$84$	10.3923	−	6.00000i	1.13389	−	0.654654i
$85$	0.803848	+	0.803848i	0.0871895	+	0.0871895i
$86$	−0.633975	−	1.09808i	−0.0683632	−	0.118409i
$87$	5.76795	+	7.33013i	0.618389	+	0.785872i
$88$	9.46410			1.00888
$89$	10.7321	−	10.7321i	1.13760	−	1.13760i	0.148715	−	0.988880i	$-0.452486\pi$
$89$	10.7321	−	10.7321i	1.13760	−	1.13760i	0.988880	−	0.148715i	$-0.0475137\pi$
$90$	−0.294229	−	1.09808i	−0.0310144	−	0.115747i
$91$	18.0000			1.88691
$92$	1.26795	−	2.19615i	0.132193	−	0.228965i
$93$	−7.96410	+	2.13397i	−0.825839	+	0.221283i
$94$	10.9019	−	6.29423i	1.12445	−	0.649200i
$95$	0.803848	+	0.803848i	0.0824730	+	0.0824730i
$96$	−2.53590	+	9.46410i	−0.258819	+	0.965926i
$97$	1.46410	−	1.46410i	0.148657	−	0.148657i	−0.628861	−	0.777518i	$-0.716478\pi$
$97$	1.46410	−	1.46410i	0.148657	−	0.148657i	0.777518	+	0.628861i	$0.216478\pi$
$98$	−1.83013	+	6.83013i	−0.184871	+	0.689947i
$99$	2.59808	−	9.69615i	0.261116	−	0.974500i
$100$	−8.53590	−	4.92820i	−0.853590	−	0.492820i
$101$	0.928203	+	0.928203i	0.0923597	+	0.0923597i	0.751777	−	0.659417i	$-0.229197\pi$
$101$	0.928203	+	0.928203i	0.0923597	+	0.0923597i	−0.659417	+	0.751777i	$0.729197\pi$
$102$	−10.3923			−1.02899
$103$	−4.19615			−0.413459			−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615			−0.413459			−0.206730	+	0.978398i	$0.566282\pi$
$104$	−10.3923	+	10.3923i	−1.01905	+	1.01905i
$105$	1.39230	+	0.803848i	0.135875	+	0.0784475i
$106$	1.29423	−	4.83013i	0.125707	−	0.469143i
$107$	7.46410			0.721582			0.360791	−	0.932647i	$-0.382507\pi$
$107$	7.46410			0.721582			0.360791	+	0.932647i	$0.382507\pi$
$108$	9.00000	+	5.19615i	0.866025	+	0.500000i
$109$	3.92820			0.376254			0.188127	−	0.982145i	$-0.439758\pi$
$109$	3.92820			0.376254			0.188127	+	0.982145i	$0.439758\pi$
$110$	0.633975	+	1.09808i	0.0604471	+	0.104697i
$111$	−3.00000	+	0.803848i	−0.284747	+	0.0762978i
$112$	−6.92820	−	12.0000i	−0.654654	−	1.13389i
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	0.242725	−	0.970095i	$-0.421959\pi$
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	−0.970095	+	0.242725i	$0.921959\pi$
$114$	−10.3923			−0.973329
$115$	0.339746			0.0316815
$116$	8.46410	−	6.66025i	0.785872	−	0.618389i
$117$	7.79423	+	13.5000i	0.720577	+	1.24808i
$118$	4.46410	−	16.6603i	0.410954	−	1.53370i
$119$	10.3923	−	10.3923i	0.952661	−	0.952661i
$120$	−1.26795	+	0.339746i	−0.115747	+	0.0310144i
$121$			0.196152i			0.0178320i
$122$	5.19615	+	9.00000i	0.470438	+	0.814822i
$123$	11.1962	−	3.00000i	1.00952	−	0.270501i
$124$	2.46410	+	9.19615i	0.221283	+	0.825839i
$125$		−	2.66025i		−	0.237940i
$126$	−14.1962	+	3.80385i	−1.26469	+	0.338874i
$127$	−13.9282	−	13.9282i	−1.23593	−	1.23593i	−0.961651	−	0.274278i	$-0.911561\pi$
$127$	−13.9282	−	13.9282i	−1.23593	−	1.23593i	−0.274278	−	0.961651i	$-0.588439\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	0.401924	+	1.50000i	0.0353874	+	0.132068i
$130$	−1.90192	−	0.509619i	−0.166810	−	0.0446965i
$131$	−1.00000	+	1.00000i	−0.0873704	+	0.0873704i	−0.749441	−	0.662071i	$-0.769678\pi$
$131$	−1.00000	+	1.00000i	−0.0873704	+	0.0873704i	0.662071	+	0.749441i	$0.269678\pi$
$132$	−11.1962	−	3.00000i	−0.974500	−	0.261116i
$133$	10.3923	−	10.3923i	0.901127	−	0.901127i
$134$	4.73205	−	17.6603i	0.408787	−	1.52561i
$135$			1.39230i			0.119831i
$136$			12.0000i			1.02899i
$137$	−1.26795	+	1.26795i	−0.108328	+	0.108328i	−0.759193	−	0.650865i	$-0.774406\pi$
$137$	−1.26795	+	1.26795i	−0.108328	+	0.108328i	0.650865	+	0.759193i	$0.274406\pi$
$138$	−2.19615	+	2.19615i	−0.186949	+	0.186949i
$139$		−	4.73205i		−	0.401367i	−0.979656	−	0.200684i	$-0.935684\pi$
$139$		−	4.73205i		−	0.401367i	0.979656	−	0.200684i	$-0.0643163\pi$
$140$	0.928203	−	1.60770i	0.0784475	−	0.135875i
$141$	−14.8923	+	3.99038i	−1.25416	+	0.336051i
$142$	−0.464102	+	1.73205i	−0.0389465	+	0.145350i
$143$	−12.2942	−	12.2942i	−1.02810	−	1.02810i
$144$	6.00000	−	10.3923i	0.500000	−	0.866025i
$145$	1.33975	+	0.535898i	0.111260	+	0.0445039i
$146$	7.46410	+	12.9282i	0.617733	+	1.06995i
$147$	4.33013	−	7.50000i	0.357143	−	0.618590i
$148$	0.928203	+	3.46410i	0.0762978	+	0.284747i
$149$			13.5359i			1.10890i	0.832216	+	0.554452i	$0.187072\pi$
$149$			13.5359i			1.10890i	−0.832216	+	0.554452i	$0.812928\pi$
$150$	8.53590	+	8.53590i	0.696953	+	0.696953i
$151$			12.3923i			1.00847i	0.863566	+	0.504236i	$0.168226\pi$
$151$			12.3923i			1.00847i	−0.863566	+	0.504236i	$0.831774\pi$
$152$			12.0000i			0.973329i
$153$	12.2942	+	3.29423i	0.993929	+	0.266323i
$154$	14.1962	−	8.19615i	1.14396	−	0.660465i
$155$	−0.901924	+	0.901924i	−0.0724443	+	0.0724443i
$156$	15.5885	−	9.00000i	1.24808	−	0.720577i
$157$	12.0000	+	12.0000i	0.957704	+	0.957704i	0.999141	−	0.0414369i	$-0.0131935\pi$
$157$	12.0000	+	12.0000i	0.957704	+	0.957704i	−0.0414369	+	0.999141i	$0.513194\pi$
$158$	−5.36603	+	3.09808i	−0.426898	+	0.246470i
$159$	−3.06218	+	5.30385i	−0.242846	+	0.420622i
$160$	0.392305	+	1.46410i	0.0310144	+	0.115747i
$161$		−	4.39230i		−	0.346162i
$162$	−9.00000	−	9.00000i	−0.707107	−	0.707107i
$163$	−1.43782	−	1.43782i	−0.112619	−	0.112619i	0.648552	−	0.761171i	$-0.275375\pi$
$163$	−1.43782	−	1.43782i	−0.112619	−	0.112619i	−0.761171	+	0.648552i	$0.775375\pi$
$164$	−3.46410	−	12.9282i	−0.270501	−	1.00952i
$165$	−0.401924	−	1.50000i	−0.0312897	−	0.116775i
$166$	2.60770	−	9.73205i	0.202396	−	0.755354i
$167$	24.5885			1.90271			0.951356	−	0.308094i	$-0.0996911\pi$
$167$	24.5885			1.90271			0.951356	+	0.308094i	$0.0996911\pi$
$168$	4.39230	+	16.3923i	0.338874	+	1.26469i
$169$	14.0000			1.07692
$170$	−1.39230	+	0.803848i	−0.106785	+	0.0616523i
$171$	12.2942	+	3.29423i	0.940163	+	0.251916i
$172$	1.73205	−	0.464102i	0.132068	−	0.0353874i
$173$			21.8564i			1.66171i	0.556488	+	0.830856i	$0.312149\pi$
$173$			21.8564i			1.66171i	−0.556488	+	0.830856i	$0.687851\pi$
$174$	−12.1244	+	5.19615i	−0.919145	+	0.393919i
$175$	−17.0718			−1.29051
$176$	−3.46410	+	12.9282i	−0.261116	+	0.974500i
$177$	−10.5622	+	18.2942i	−0.793902	+	1.37508i
$178$	10.7321	+	18.5885i	0.804401	+	1.39326i
$179$			21.6603i			1.61896i	0.587145	+	0.809482i	$0.300252\pi$
$179$			21.6603i			1.61896i	−0.587145	+	0.809482i	$0.699748\pi$
$180$	1.60770			0.119831
$181$			8.32051i			0.618458i	0.950988	+	0.309229i	$0.100071\pi$
$181$			8.32051i			0.618458i	−0.950988	+	0.309229i	$0.899929\pi$
$182$	−6.58846	+	24.5885i	−0.488369	+	1.82262i
$183$	−3.29423	−	12.2942i	−0.243516	−	0.908816i
$184$	2.53590	+	2.53590i	0.186949	+	0.186949i
$185$	−0.339746	+	0.339746i	−0.0249786	+	0.0249786i
$186$		−	11.6603i		−	0.854971i
$187$	−14.1962			−1.03813
$188$	4.60770	+	17.1962i	0.336051	+	1.25416i
$189$	18.0000			1.30931
$190$	−1.39230	+	0.803848i	−0.101008	+	0.0583172i
$191$	−12.4641	+	12.4641i	−0.901871	+	0.901871i	−0.995598	−	0.0937272i	$-0.970122\pi$
$191$	−12.4641	+	12.4641i	−0.901871	+	0.901871i	0.0937272	+	0.995598i	$0.470122\pi$
$192$	−12.0000	−	6.92820i	−0.866025	−	0.500000i
$193$	9.66025	+	9.66025i	0.695360	+	0.695360i	0.963406	−	0.268046i	$-0.0863779\pi$
$193$	9.66025	+	9.66025i	0.695360	+	0.695360i	−0.268046	+	0.963406i	$0.586378\pi$
$194$	1.46410	+	2.53590i	0.105116	+	0.182067i
$195$	2.08846	+	1.20577i	0.149558	+	0.0863471i
$196$	−8.66025	−	5.00000i	−0.618590	−	0.357143i
$197$	−9.85641			−0.702240			−0.351120	−	0.936330i	$-0.614199\pi$
$197$	−9.85641			−0.702240			−0.351120	+	0.936330i	$0.614199\pi$
$198$	12.2942	+	7.09808i	0.873713	+	0.504438i
$199$	−24.7846			−1.75693			−0.878467	−	0.477803i	$-0.841433\pi$
$199$	−24.7846			−1.75693			−0.878467	+	0.477803i	$0.841433\pi$
$200$	9.85641	−	9.85641i	0.696953	−	0.696953i
$201$	−11.1962	+	19.3923i	−0.789716	+	1.36783i
$202$	−1.60770	+	0.928203i	−0.113117	+	0.0653082i
$203$	6.92820	−	17.3205i	0.486265	−	1.21566i
$204$	3.80385	−	14.1962i	0.266323	−	0.993929i
$205$	1.26795	−	1.26795i	0.0885574	−	0.0885574i
$206$	1.53590	−	5.73205i	0.107011	−	0.399371i
$207$	3.29423	−	1.90192i	0.228965	−	0.132193i
$208$	−10.3923	−	18.0000i	−0.720577	−	1.24808i
$209$	−14.1962			−0.981968
$210$	−1.60770	+	1.60770i	−0.110942	+	0.110942i
$211$	−17.8301	−	17.8301i	−1.22748	−	1.22748i	−0.964915	−	0.262561i	$-0.915433\pi$
$211$	−17.8301	−	17.8301i	−1.22748	−	1.22748i	−0.262561	−	0.964915i	$-0.584567\pi$
$212$	6.12436	+	3.53590i	0.420622	+	0.242846i
$213$	1.09808	−	1.90192i	0.0752389	−	0.130318i
$214$	−2.73205	+	10.1962i	−0.186759	+	0.696995i
$215$	0.169873	+	0.169873i	0.0115852	+	0.0115852i
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$	11.6603	+	11.6603i	0.791550	+	0.791550i
$218$	−1.43782	+	5.36603i	−0.0973816	+	0.363433i
$219$	−4.73205	−	17.6603i	−0.319762	−	1.19337i
$220$	−1.73205	+	0.464102i	−0.116775	+	0.0312897i
$221$	15.5885	−	15.5885i	1.04859	−	1.04859i
$222$		−	4.39230i		−	0.294792i
$223$	20.1962			1.35243			0.676217	−	0.736702i	$-0.263618\pi$
$223$	20.1962			1.35243			0.676217	+	0.736702i	$0.263618\pi$
$224$	18.9282	−	5.07180i	1.26469	−	0.338874i
$225$	−7.39230	−	12.8038i	−0.492820	−	0.853590i
$226$	13.3923	−	7.73205i	0.890843	−	0.514328i
$227$	10.1962			0.676742			0.338371	−	0.941013i	$-0.390124\pi$
$227$	10.1962			0.676742			0.338371	+	0.941013i	$0.390124\pi$
$228$	3.80385	−	14.1962i	0.251916	−	0.940163i
$229$	7.26795	+	7.26795i	0.480280	+	0.480280i	0.905221	−	0.424941i	$-0.139705\pi$
$229$	7.26795	+	7.26795i	0.480280	+	0.480280i	−0.424941	+	0.905221i	$0.639705\pi$
$230$	−0.124356	+	0.464102i	−0.00819977	+	0.0306020i
$231$	−19.3923	+	5.19615i	−1.27592	+	0.341882i
$232$	6.00000	+	14.0000i	0.393919	+	0.919145i
$233$			9.58846i			0.628161i	0.949396	+	0.314080i	$0.101696\pi$
$233$			9.58846i			0.628161i	−0.949396	+	0.314080i	$0.898304\pi$
$234$	−21.2942	+	5.70577i	−1.39205	+	0.372998i
$235$	−1.68653	+	1.68653i	−0.110017	+	0.110017i
$236$	21.1244	+	12.1962i	1.37508	+	0.793902i
$237$	7.33013	−	1.96410i	0.476143	−	0.127582i
$238$	10.3923	+	18.0000i	0.673633	+	1.16677i
$239$		−	15.8038i		−	1.02227i	−0.859502	−	0.511133i	$-0.829226\pi$
$239$		−	15.8038i		−	1.02227i	0.859502	−	0.511133i	$-0.170774\pi$
$240$		−	1.85641i		−	0.119831i
$241$		−	25.3923i		−	1.63566i	−0.575458	−	0.817831i	$-0.695176\pi$
$241$		−	25.3923i		−	1.63566i	0.575458	−	0.817831i	$-0.304824\pi$
$242$	−0.267949	−	0.0717968i	−0.0172244	−	0.00461527i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$	−14.1962	+	3.80385i	−0.908816	+	0.243516i
$245$		−	1.33975i		−	0.0855932i
$246$			16.3923i			1.04514i
$247$	15.5885	−	15.5885i	0.991870	−	0.991870i
$248$	−13.4641			−0.854971
$249$	−6.16987	+	10.6865i	−0.391000	+	0.677232i
$250$	3.63397	+	0.973721i	0.229833	+	0.0615835i
$251$	−14.2942	−	14.2942i	−0.902244	−	0.902244i	0.0933862	−	0.995630i	$-0.470231\pi$
$251$	−14.2942	−	14.2942i	−0.902244	−	0.902244i	−0.995630	+	0.0933862i	$0.970231\pi$
$252$		−	20.7846i		−	1.30931i
$253$	−3.00000	+	3.00000i	−0.188608	+	0.188608i
$254$	24.1244	−	13.9282i	1.51370	−	0.873933i
$255$	1.90192	−	0.509619i	0.119103	−	0.0319136i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		−	30.4641i		−	1.90030i	−0.311796	−	0.950149i	$-0.600930\pi$
$257$		−	30.4641i		−	1.90030i	0.311796	−	0.950149i	$-0.399070\pi$
$258$	−2.19615			−0.136726
$259$	4.39230	+	4.39230i	0.272925	+	0.272925i
$260$	1.39230	−	2.41154i	0.0863471	−	0.149558i
$261$	15.9904	−	2.30385i	0.989780	−	0.142605i
$262$	−1.00000	−	1.73205i	−0.0617802	−	0.107006i
$263$	−16.9019	+	16.9019i	−1.04222	+	1.04222i	−0.0431486	+	0.999069i	$0.513739\pi$
$263$	−16.9019	+	16.9019i	−1.04222	+	1.04222i	−0.999069	+	0.0431486i	$0.986261\pi$
$264$	8.19615	−	14.1962i	0.504438	−	0.873713i
$265$			0.947441i			0.0582008i
$266$	10.3923	+	18.0000i	0.637193	+	1.10365i
$267$	−6.80385	−	25.3923i	−0.416389	−	1.55398i
$268$	22.3923	+	12.9282i	1.36783	+	0.789716i
$269$	−3.19615	+	3.19615i	−0.194873	+	0.194873i	−0.797798	−	0.602925i	$-0.794002\pi$
$269$	−3.19615	+	3.19615i	−0.194873	+	0.194873i	0.602925	+	0.797798i	$0.294002\pi$
$270$	−1.90192	−	0.509619i	−0.115747	−	0.0310144i
$271$	8.63397	−	8.63397i	0.524477	−	0.524477i	−0.394444	−	0.918920i	$-0.629063\pi$
$271$	8.63397	−	8.63397i	0.524477	−	0.524477i	0.918920	+	0.394444i	$0.129063\pi$
$272$	−16.3923	−	4.39230i	−0.993929	−	0.266323i
$273$	15.5885	−	27.0000i	0.943456	−	1.63411i
$274$	−1.26795	−	2.19615i	−0.0765996	−	0.132674i
$275$	11.6603	+	11.6603i	0.703140	+	0.703140i
$276$	−2.19615	−	3.80385i	−0.132193	−	0.228965i
$277$			5.07180i			0.304735i	0.988324	+	0.152367i	$0.0486897\pi$
$277$			5.07180i			0.304735i	−0.988324	+	0.152367i	$0.951310\pi$
$278$	6.46410	+	1.73205i	0.387691	+	0.103882i
$279$	−3.69615	+	13.7942i	−0.221283	+	0.825839i
$280$	1.85641	+	1.85641i	0.110942	+	0.110942i
$281$		−	1.73205i		−	0.103325i	−0.998665	−	0.0516627i	$-0.983548\pi$
$281$		−	1.73205i		−	0.103325i	0.998665	−	0.0516627i	$-0.0164521\pi$
$282$		−	21.8038i		−	1.29840i
$283$	3.12436			0.185724			0.0928618	−	0.995679i	$-0.470399\pi$
$283$	3.12436			0.185724			0.0928618	+	0.995679i	$0.470399\pi$
$284$	−2.19615	−	1.26795i	−0.130318	−	0.0752389i
$285$	1.90192	−	0.509619i	0.112660	−	0.0301872i
$286$	21.2942	−	12.2942i	1.25915	−	0.726973i
$287$	−16.3923	−	16.3923i	−0.967607	−	0.967607i
$288$	12.0000	+	12.0000i	0.707107	+	0.707107i
$289$		−	1.00000i		−	0.0588235i
$290$	−1.22243	+	1.63397i	−0.0717837	+	0.0959503i
$291$	−0.928203	−	3.46410i	−0.0544122	−	0.203069i
$292$	−20.3923	+	5.46410i	−1.19337	+	0.319762i
$293$	−15.0000	−	15.0000i	−0.876309	−	0.876309i	0.116841	−	0.993151i	$-0.462723\pi$
$293$	−15.0000	−	15.0000i	−0.876309	−	0.876309i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	8.66025	+	8.66025i	0.505076	+	0.505076i
$295$			3.26795i			0.190267i
$296$	−5.07180			−0.294792
$297$	−12.2942	−	12.2942i	−0.713384	−	0.713384i
$298$	−18.4904	−	4.95448i	−1.07112	−	0.287005i
$299$		−	6.58846i		−	0.381020i
$300$	−14.7846	+	8.53590i	−0.853590	+	0.492820i
$301$	2.19615	−	2.19615i	0.126584	−	0.126584i
$302$	−16.9282	−	4.53590i	−0.974109	−	0.261012i
$303$	2.19615	−	0.588457i	0.126166	−	0.0338060i
$304$	−16.3923	−	4.39230i	−0.940163	−	0.251916i
$305$	−1.39230	−	1.39230i	−0.0797231	−	0.0797231i
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	−12.6340	+	12.6340i	−0.721059	+	0.721059i	−0.968821	−	0.247762i	$-0.920305\pi$
$307$	−12.6340	+	12.6340i	−0.721059	+	0.721059i	0.247762	+	0.968821i	$0.420305\pi$
$308$	6.00000	+	22.3923i	0.341882	+	1.27592i
$309$	−3.63397	+	6.29423i	−0.206730	+	0.358066i
$310$	−0.901924	−	1.56218i	−0.0512258	−	0.0887257i
$311$	6.46410	−	6.46410i	0.366546	−	0.366546i	−0.499670	−	0.866216i	$-0.666545\pi$
$311$	6.46410	−	6.46410i	0.366546	−	0.366546i	0.866216	+	0.499670i	$0.166545\pi$
$312$	6.58846	+	24.5885i	0.372998	+	1.39205i
$313$	−15.1962			−0.858937			−0.429469	−	0.903082i	$-0.641299\pi$
$313$	−15.1962			−0.858937			−0.429469	+	0.903082i	$0.641299\pi$
$314$	−20.7846	+	12.0000i	−1.17294	+	0.677199i
$315$	2.41154	−	1.39230i	0.135875	−	0.0784475i
$316$	−2.26795	−	8.46410i	−0.127582	−	0.476143i
$317$	13.0000	−	13.0000i	0.730153	−	0.730153i	−0.240497	−	0.970650i	$-0.577310\pi$
$317$	13.0000	−	13.0000i	0.730153	−	0.730153i	0.970650	+	0.240497i	$0.0773105\pi$
$318$	−6.12436	−	6.12436i	−0.343437	−	0.343437i
$319$	−16.5622	+	7.09808i	−0.927304	+	0.397416i
$320$	−2.14359			−0.119831
$321$	6.46410	−	11.1962i	0.360791	−	0.624908i
$322$	6.00000	+	1.60770i	0.334367	+	0.0895933i
$323$		−	18.0000i		−	1.00155i
$324$	15.5885	−	9.00000i	0.866025	−	0.500000i
$325$	−25.6077			−1.42046
$326$	2.49038	−	1.43782i	0.137929	−	0.0796336i
$327$	3.40192	−	5.89230i	0.188127	−	0.325845i
$328$	18.9282			1.04514
$329$	21.8038	+	21.8038i	1.20209	+	1.20209i
$330$	2.19615			0.120894
$331$	22.5622	+	22.5622i	1.24013	+	1.24013i	0.959947	+	0.280183i	$0.0903951\pi$
$331$	22.5622	+	22.5622i	1.24013	+	1.24013i	0.280183	+	0.959947i	$0.409605\pi$
$332$	12.3397	+	7.12436i	0.677232	+	0.391000i
$333$	−1.39230	+	5.19615i	−0.0762978	+	0.284747i
$334$	−9.00000	+	33.5885i	−0.492458	+	1.83788i
$335$			3.46410i			0.189264i
$336$	−24.0000			−1.30931
$337$	−21.7846	+	21.7846i	−1.18668	+	1.18668i	−0.208705	+	0.977979i	$0.566925\pi$
$337$	−21.7846	+	21.7846i	−1.18668	+	1.18668i	−0.977979	+	0.208705i	$0.933075\pi$
$338$	−5.12436	+	19.1244i	−0.278728	+	1.04023i
$339$	−18.2942	+	4.90192i	−0.993606	+	0.266236i
$340$	−0.588457	−	2.19615i	−0.0319136	−	0.119103i
$341$		−	15.9282i		−	0.862561i
$342$	−9.00000	+	15.5885i	−0.486664	+	0.842927i
$343$	6.92820			0.374088
$344$			2.53590i			0.136726i
$345$	0.294229	−	0.509619i	0.0158407	−	0.0274370i
$346$	−29.8564	−	8.00000i	−1.60509	−	0.430083i
$347$		−	27.6603i		−	1.48488i	−0.669912	−	0.742440i	$-0.733668\pi$
$347$		−	27.6603i		−	1.48488i	0.669912	−	0.742440i	$-0.266332\pi$
$348$	−2.66025	−	18.4641i	−0.142605	−	0.989780i
$349$		−	13.0526i		−	0.698687i	−0.936995	−	0.349344i	$-0.886405\pi$
$349$		−	13.0526i		−	0.698687i	0.936995	−	0.349344i	$-0.113595\pi$
$350$	6.24871	−	23.3205i	0.334008	−	1.24653i
$351$	27.0000			1.44115
$352$	−16.3923	−	9.46410i	−0.873713	−	0.504438i
$353$	−21.4641			−1.14242			−0.571209	−	0.820804i	$-0.693526\pi$
$353$	−21.4641			−1.14242			−0.571209	+	0.820804i	$0.693526\pi$
$354$	−21.1244	−	21.1244i	−1.12275	−	1.12275i
$355$		−	0.339746i		−	0.0180318i
$356$	−29.3205	+	7.85641i	−1.55398	+	0.416389i
$357$	−6.58846	−	24.5885i	−0.348698	−	1.30136i
$358$	−29.5885	−	7.92820i	−1.56380	−	0.419019i
$359$	5.36603	−	5.36603i	0.283208	−	0.283208i	−0.551179	−	0.834387i	$-0.685822\pi$
$359$	5.36603	−	5.36603i	0.283208	−	0.283208i	0.834387	+	0.551179i	$0.185822\pi$
$360$	−0.588457	+	2.19615i	−0.0310144	+	0.115747i
$361$			1.00000i			0.0526316i
$362$	−11.3660	−	3.04552i	−0.597385	−	0.160069i
$363$	0.294229	+	0.169873i	0.0154430	+	0.00891602i
$364$	−31.1769	−	18.0000i	−1.63411	−	0.943456i
$365$	−2.00000	−	2.00000i	−0.104685	−	0.104685i
$366$	18.0000			0.940875
$367$	15.7321	+	15.7321i	0.821206	+	0.821206i	0.986281	−	0.165075i	$-0.0527865\pi$
$367$	15.7321	+	15.7321i	0.821206	+	0.821206i	−0.165075	+	0.986281i	$0.552787\pi$
$368$	−4.39230	+	2.53590i	−0.228965	+	0.132193i
$369$	5.19615	−	19.3923i	0.270501	−	1.00952i
$370$	−0.339746	−	0.588457i	−0.0176626	−	0.0305924i
$371$	12.2487			0.635921
$372$	15.9282	+	4.26795i	0.825839	+	0.221283i
$373$		−	7.39230i		−	0.382759i	−0.981516	−	0.191380i	$-0.938704\pi$
$373$		−	7.39230i		−	0.382759i	0.981516	−	0.191380i	$-0.0612961\pi$
$374$	5.19615	−	19.3923i	0.268687	−	1.00275i
$375$	−3.99038	−	2.30385i	−0.206062	−	0.118970i
$376$	−25.1769			−1.29840
$377$	10.3923	−	25.9808i	0.535231	−	1.33808i
$378$	−6.58846	+	24.5885i	−0.338874	+	1.26469i
$379$	1.73205	−	1.73205i	0.0889695	−	0.0889695i	−0.661221	−	0.750191i	$-0.729962\pi$
$379$	1.73205	−	1.73205i	0.0889695	−	0.0889695i	0.750191	+	0.661221i	$0.229962\pi$
$380$	−0.588457	−	2.19615i	−0.0301872	−	0.112660i
$381$	−32.9545	+	8.83013i	−1.68831	+	0.452381i
$382$	−12.4641	−	21.5885i	−0.637719	−	1.10456i
$383$	13.8564			0.708029			0.354015	−	0.935240i	$-0.384816\pi$
$383$	13.8564			0.708029			0.354015	+	0.935240i	$0.384816\pi$
$384$	13.8564	−	13.8564i	0.707107	−	0.707107i
$385$	−2.19615	+	2.19615i	−0.111926	+	0.111926i
$386$	−16.7321	+	9.66025i	−0.851639	+	0.491694i
$387$	2.59808	+	0.696152i	0.132068	+	0.0353874i
$388$	−4.00000	+	1.07180i	−0.203069	+	0.0544122i
$389$	−23.6603	+	23.6603i	−1.19962	+	1.19962i	−0.225343	+	0.974279i	$0.572350\pi$
$389$	−23.6603	+	23.6603i	−1.19962	+	1.19962i	−0.974279	+	0.225343i	$0.927650\pi$
$390$	−2.41154	+	2.41154i	−0.122113	+	0.122113i
$391$	−3.80385	−	3.80385i	−0.192369	−	0.192369i
$392$	10.0000	−	10.0000i	0.505076	−	0.505076i
$393$	0.633975	+	2.36603i	0.0319798	+	0.119350i
$394$	3.60770	−	13.4641i	0.181753	−	0.678312i
$395$	0.830127	−	0.830127i	0.0417682	−	0.0417682i
$396$	−14.1962	+	14.1962i	−0.713384	+	0.713384i
$397$		−	23.5359i		−	1.18123i	−0.806952	−	0.590616i	$-0.798885\pi$
$397$		−	23.5359i		−	1.18123i	0.806952	−	0.590616i	$-0.201115\pi$
$398$	9.07180	−	33.8564i	0.454728	−	1.69707i
$399$	−6.58846	−	24.5885i	−0.329835	−	1.23096i
$400$	9.85641	+	17.0718i	0.492820	+	0.853590i
$401$			7.73205i			0.386120i	0.981187	+	0.193060i	$0.0618412\pi$
$401$			7.73205i			0.386120i	−0.981187	+	0.193060i	$0.938159\pi$
$402$	−22.3923	−	22.3923i	−1.11683	−	1.11683i
$403$	17.4904	+	17.4904i	0.871258	+	0.871258i
$404$	−0.679492	−	2.53590i	−0.0338060	−	0.126166i
$405$	2.08846	+	1.20577i	0.103776	+	0.0599153i
$406$	21.1244	+	15.8038i	1.04838	+	0.784332i
$407$		−	6.00000i		−	0.297409i
$408$	18.0000	+	10.3923i	0.891133	+	0.514496i
$409$	−10.1244	−	10.1244i	−0.500617	−	0.500617i	0.411013	−	0.911630i	$-0.365175\pi$
$409$	−10.1244	−	10.1244i	−0.500617	−	0.500617i	−0.911630	+	0.411013i	$0.865175\pi$
$410$	1.26795	+	2.19615i	0.0626195	+	0.108460i
$411$	0.803848	+	3.00000i	0.0396509	+	0.147979i
$412$	7.26795	+	4.19615i	0.358066	+	0.206730i
$413$	42.2487			2.07892
$414$	1.39230	+	5.19615i	0.0684280	+	0.255377i
$415$			1.90897i			0.0937074i
$416$	28.3923	−	7.60770i	1.39205	−	0.372998i
$417$	−7.09808	−	4.09808i	−0.347594	−	0.200684i
$418$	5.19615	−	19.3923i	0.254152	−	0.948509i
$419$			22.5885i			1.10352i	0.834003	+	0.551759i	$0.186043\pi$
$419$			22.5885i			1.10352i	−0.834003	+	0.551759i	$0.813957\pi$
$420$	−1.60770	−	2.78461i	−0.0784475	−	0.135875i
$421$	−15.9282	−	15.9282i	−0.776293	−	0.776293i	0.202905	−	0.979198i	$-0.434962\pi$
$421$	−15.9282	−	15.9282i	−0.776293	−	0.776293i	−0.979198	+	0.202905i	$0.934962\pi$
$422$	30.8827	−	17.8301i	1.50335	−	0.867957i
$423$	−6.91154	+	25.7942i	−0.336051	+	1.25416i
$424$	−7.07180	+	7.07180i	−0.343437	+	0.343437i
$425$	−14.7846	+	14.7846i	−0.717159	+	0.717159i
$426$	2.19615	+	2.19615i	0.106404	+	0.106404i
$427$	−18.0000	+	18.0000i	−0.871081	+	0.871081i
$428$	−12.9282	−	7.46410i	−0.624908	−	0.360791i
$429$	−29.0885	+	7.79423i	−1.40440	+	0.376309i
$430$	−0.294229	+	0.169873i	−0.0141890	+	0.00819200i
$431$			18.3397i			0.883394i	0.897164	+	0.441697i	$0.145623\pi$
$431$			18.3397i			0.883394i	−0.897164	+	0.441697i	$0.854377\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$	−21.3205	+	21.3205i	−1.02460	+	1.02460i	−0.0249085	+	0.999690i	$0.507929\pi$
$433$	−21.3205	+	21.3205i	−1.02460	+	1.02460i	−0.999690	+	0.0249085i	$0.992071\pi$
$434$	−20.1962	+	11.6603i	−0.969446	+	0.559710i
$435$	1.96410	−	1.54552i	0.0941715	−	0.0741019i
$436$	−6.80385	−	3.92820i	−0.325845	−	0.188127i
$437$	−3.80385	−	3.80385i	−0.181963	−	0.181963i
$438$	25.8564			1.23547
$439$		−	4.05256i		−	0.193418i	−0.995313	−	0.0967090i	$-0.969168\pi$
$439$		−	4.05256i		−	0.193418i	0.995313	−	0.0967090i	$-0.0308316\pi$
$440$		−	2.53590i		−	0.120894i
$441$	−7.50000	−	12.9904i	−0.357143	−	0.618590i
$442$	15.5885	+	27.0000i	0.741467	+	1.28426i
$443$	−17.7846	+	17.7846i	−0.844972	+	0.844972i	−0.989501	−	0.144528i	$-0.953834\pi$
$443$	−17.7846	+	17.7846i	−0.844972	+	0.844972i	0.144528	+	0.989501i	$0.453834\pi$
$444$	6.00000	+	1.60770i	0.284747	+	0.0762978i
$445$	−2.87564	−	2.87564i	−0.136319	−	0.136319i
$446$	−7.39230	+	27.5885i	−0.350036	+	1.30635i
$447$	20.3038	+	11.7224i	0.960339	+	0.554452i
$448$			27.7128i			1.30931i
$449$	8.66025	−	8.66025i	0.408703	−	0.408703i	−0.472583	−	0.881286i	$-0.656678\pi$
$449$	8.66025	−	8.66025i	0.408703	−	0.408703i	0.881286	+	0.472583i	$0.156678\pi$
$450$	20.1962	−	5.41154i	0.952056	−	0.255103i
$451$			22.3923i			1.05441i
$452$	5.66025	+	21.1244i	0.266236	+	0.993606i
$453$	18.5885	+	10.7321i	0.873362	+	0.504236i
$454$	−3.73205	+	13.9282i	−0.175154	+	0.653683i
$455$		−	4.82309i		−	0.226110i
$456$	18.0000	+	10.3923i	0.842927	+	0.486664i
$457$			34.0000i			1.59045i	0.606313	+	0.795226i	$0.292648\pi$
$457$			34.0000i			1.59045i	−0.606313	+	0.795226i	$0.707352\pi$
$458$	−12.5885	+	7.26795i	−0.588220	+	0.339609i
$459$	15.5885	−	15.5885i	0.727607	−	0.727607i
$460$	−0.588457	−	0.339746i	−0.0274370	−	0.0158407i
$461$	16.8564	−	16.8564i	0.785081	−	0.785081i	−0.195602	−	0.980683i	$-0.562666\pi$
$461$	16.8564	−	16.8564i	0.785081	−	0.785081i	0.980683	+	0.195602i	$0.0626661\pi$
$462$		−	28.3923i		−	1.32093i
$463$		−	17.8038i		−	0.827415i	−0.910410	−	0.413707i	$-0.864234\pi$
$463$		−	17.8038i		−	0.827415i	0.910410	−	0.413707i	$-0.135766\pi$
$464$	−21.3205	+	3.07180i	−0.989780	+	0.142605i
$465$	0.571797	+	2.13397i	0.0265164	+	0.0989607i
$466$	−13.0981	−	3.50962i	−0.606757	−	0.162580i
$467$	−11.2942	−	11.2942i	−0.522635	−	0.522635i	0.395732	−	0.918366i	$-0.370491\pi$
$467$	−11.2942	−	11.2942i	−0.522635	−	0.522635i	−0.918366	+	0.395732i	$0.870491\pi$
$468$		−	31.1769i		−	1.44115i
$469$	44.7846			2.06796
$470$	−1.68653	−	2.92116i	−0.0777940	−	0.134743i
$471$	28.3923	−	7.60770i	1.30825	−	0.350544i
$472$	−24.3923	+	24.3923i	−1.12275	+	1.12275i
$473$	−3.00000			−0.137940
$474$			10.7321i			0.492939i
$475$	−14.7846	+	14.7846i	−0.678364	+	0.678364i
$476$	−28.3923	+	7.60770i	−1.30136	+	0.348698i
$477$	5.30385	+	9.18653i	0.242846	+	0.420622i
$478$	21.5885	+	5.78461i	0.987433	+	0.264582i
$479$	10.2224	+	10.2224i	0.467075	+	0.467075i	0.900966	−	0.433891i	$-0.142860\pi$
$479$	10.2224	+	10.2224i	0.467075	+	0.467075i	−0.433891	+	0.900966i	$0.642860\pi$
$480$	2.53590	+	0.679492i	0.115747	+	0.0310144i
$481$	6.58846	+	6.58846i	0.300408	+	0.300408i
$482$	34.6865	+	9.29423i	1.57993	+	0.423341i
$483$	−6.58846	−	3.80385i	−0.299785	−	0.173081i
$484$	0.196152	−	0.339746i	0.00891602	−	0.0154430i
$485$	−0.392305	−	0.392305i	−0.0178136	−	0.0178136i
$486$	−21.2942	+	5.70577i	−0.965926	+	0.258819i
$487$	10.7846			0.488697			0.244349	−	0.969687i	$-0.421426\pi$
$487$	10.7846			0.488697			0.244349	+	0.969687i	$0.421426\pi$
$488$		−	20.7846i		−	0.940875i
$489$	−3.40192	+	0.911543i	−0.153840	+	0.0412214i
$490$	1.83013	+	0.490381i	0.0826767	+	0.0221532i
$491$	−12.9019	+	12.9019i	−0.582256	+	0.582256i	−0.935523	−	0.353267i	$-0.885071\pi$
$491$	−12.9019	+	12.9019i	−0.582256	+	0.582256i	0.353267	+	0.935523i	$0.385071\pi$
$492$	−22.3923	−	6.00000i	−1.00952	−	0.270501i
$493$	−9.00000	−	21.0000i	−0.405340	−	0.945792i
$494$	15.5885	+	27.0000i	0.701358	+	1.21479i
$495$	−2.59808	−	0.696152i	−0.116775	−	0.0312897i
$496$	4.92820	−	18.3923i	0.221283	−	0.825839i
$497$	−4.39230			−0.197022
$498$	−12.3397	−	12.3397i	−0.552957	−	0.552957i
$499$	−4.05256			−0.181417			−0.0907087	−	0.995877i	$-0.528913\pi$
$499$	−4.05256			−0.181417			−0.0907087	+	0.995877i	$0.528913\pi$
$500$	−2.66025	+	4.60770i	−0.118970	+	0.206062i
$501$	21.2942	−	36.8827i	0.951356	−	1.64780i
$502$	24.7583	−	14.2942i	1.10502	−	0.637983i
$503$	−14.0263	−	14.0263i	−0.625401	−	0.625401i	0.321506	−	0.946907i	$-0.395811\pi$
$503$	−14.0263	−	14.0263i	−0.625401	−	0.625401i	−0.946907	+	0.321506i	$0.895811\pi$
$504$	28.3923	+	7.60770i	1.26469	+	0.338874i
$505$	0.248711	−	0.248711i	0.0110675	−	0.0110675i
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$	12.1244	−	21.0000i	0.538462	−	0.932643i
$508$	10.1962	+	38.0526i	0.452381	+	1.68831i
$509$	0.0717968			0.00318234			0.00159117	−	0.999999i	$-0.499494\pi$
$509$	0.0717968			0.00318234			0.00159117	+	0.999999i	$0.499494\pi$
$510$			2.78461i			0.123305i
$511$	−25.8564	+	25.8564i	−1.14382	+	1.14382i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	15.5885	−	15.5885i	0.688247	−	0.688247i
$514$	41.6147	+	11.1506i	1.83555	+	0.491833i
$515$			1.12436i			0.0495450i
$516$	0.803848	−	3.00000i	0.0353874	−	0.132068i
$517$		−	29.7846i		−	1.30993i
$518$	−7.60770	+	4.39230i	−0.334263	+	0.192987i
$519$	32.7846	+	18.9282i	1.43908	+	0.830856i
$520$	2.78461	+	2.78461i	0.122113	+	0.122113i
$521$	−4.85641			−0.212763			−0.106382	−	0.994325i	$-0.533926\pi$
$521$	−4.85641			−0.212763			−0.106382	+	0.994325i	$0.533926\pi$
$522$	−2.70577	+	22.6865i	−0.118428	+	0.992963i
$523$		−	12.9282i		−	0.565311i	−0.959222	−	0.282655i	$-0.908785\pi$
$523$		−	12.9282i		−	0.565311i	0.959222	−	0.282655i	$-0.0912153\pi$
$524$	2.73205	−	0.732051i	0.119350	−	0.0319798i
$525$	−14.7846	+	25.6077i	−0.645253	+	1.11761i
$526$	−16.9019	−	29.2750i	−0.736959	−	1.27645i
$527$	20.1962			0.879758
$528$	16.3923	+	16.3923i	0.713384	+	0.713384i
$529$	21.3923			0.930100
$530$	−1.29423	−	0.346788i	−0.0562177	−	0.0150635i
$531$	18.2942	+	31.6865i	0.793902	+	1.37508i
$532$	−28.3923	+	7.60770i	−1.23096	+	0.329835i
$533$	−24.5885	−	24.5885i	−1.06504	−	1.06504i
$534$	37.1769			1.60880
$535$		−	2.00000i		−	0.0864675i
$536$	−25.8564	+	25.8564i	−1.11683	+	1.11683i
$537$	32.4904	+	18.7583i	1.40206	+	0.809482i
$538$	−3.19615	−	5.53590i	−0.137796	−	0.238670i
$539$	11.8301	+	11.8301i	0.509560	+	0.509560i
$540$	1.39230	−	2.41154i	0.0599153	−	0.103776i
$541$	0.928203	−	0.928203i	0.0399066	−	0.0399066i	−0.686872	−	0.726778i	$-0.741017\pi$
$541$	0.928203	−	0.928203i	0.0399066	−	0.0399066i	0.726778	+	0.686872i	$0.241017\pi$
$542$	8.63397	+	14.9545i	0.370861	+	0.642350i
$543$	12.4808	+	7.20577i	0.535601	+	0.309229i
$544$	12.0000	−	20.7846i	0.514496	−	0.891133i
$545$		−	1.05256i		−	0.0450867i
$546$	31.1769	+	31.1769i	1.33425	+	1.33425i
$547$		−	5.32051i		−	0.227488i	−0.993510	−	0.113744i	$-0.963716\pi$
$547$		−	5.32051i		−	0.227488i	0.993510	−	0.113744i	$-0.0362844\pi$
$548$	3.46410	−	0.928203i	0.147979	−	0.0396509i
$549$	−21.2942	−	5.70577i	−0.908816	−	0.243516i
$550$	−20.1962	+	11.6603i	−0.861167	+	0.497195i
$551$	−9.00000	−	21.0000i	−0.383413	−	0.894630i
$552$	6.00000	−	1.60770i	0.255377	−	0.0684280i
$553$	−10.7321	−	10.7321i	−0.456373	−	0.456373i
$554$	−6.92820	−	1.85641i	−0.294351	−	0.0788712i
$555$	0.215390	+	0.803848i	0.00914281	+	0.0341214i
$556$	−4.73205	+	8.19615i	−0.200684	+	0.347594i
$557$			20.9282i			0.886756i	0.896335	+	0.443378i	$0.146220\pi$
$557$			20.9282i			0.886756i	−0.896335	+	0.443378i	$0.853780\pi$
$558$	−17.4904	−	10.0981i	−0.740427	−	0.427486i
$559$	3.29423	−	3.29423i	0.139331	−	0.139331i
$560$	−3.21539	+	1.85641i	−0.135875	+	0.0784475i
$561$	−12.2942	+	21.2942i	−0.519063	+	0.899043i
$562$	2.36603	+	0.633975i	0.0998048	+	0.0267426i
$563$	6.63397	−	6.63397i	0.279589	−	0.279589i	−0.553356	−	0.832945i	$-0.686653\pi$
$563$	6.63397	−	6.63397i	0.279589	−	0.279589i	0.832945	+	0.553356i	$0.186653\pi$
$564$	29.7846	+	7.98076i	1.25416	+	0.336051i
$565$	−2.07180	+	2.07180i	−0.0871611	+	0.0871611i
$566$	−1.14359	+	4.26795i	−0.0480688	+	0.179395i
$567$	15.5885	−	27.0000i	0.654654	−	1.13389i
$568$	2.53590	−	2.53590i	0.106404	−	0.106404i
$569$	28.8564	+	28.8564i	1.20972	+	1.20972i	0.971116	+	0.238607i	$0.0766909\pi$
$569$	28.8564	+	28.8564i	1.20972	+	1.20972i	0.238607	+	0.971116i	$0.423309\pi$
$570$			2.78461i			0.116634i
$571$			12.9282i			0.541028i	0.962716	+	0.270514i	$0.0871937\pi$
$571$			12.9282i			0.541028i	−0.962716	+	0.270514i	$0.912806\pi$
$572$	9.00000	+	33.5885i	0.376309	+	1.40440i
$573$	7.90192	+	29.4904i	0.330108	+	1.23198i
$574$	28.3923	−	16.3923i	1.18507	−	0.684202i
$575$			6.24871i			0.260589i
$576$	−20.7846	+	12.0000i	−0.866025	+	0.500000i
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	−0.382683	−	0.923880i	$-0.625000\pi$
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	0.923880	+	0.382683i	$0.125000\pi$
$578$	1.36603	+	0.366025i	0.0568192	+	0.0152246i
$579$	22.8564	−	6.12436i	0.949880	−	0.254520i
$580$	−1.78461	−	2.26795i	−0.0741019	−	0.0941715i
$581$	24.6795			1.02388
$582$	5.07180			0.210233
$583$	−8.36603	−	8.36603i	−0.346485	−	0.346485i
$584$		−	29.8564i		−	1.23547i
$585$	3.61731	−	2.08846i	0.149558	−	0.0863471i
$586$	25.9808	−	15.0000i	1.07326	−	0.619644i
$587$	−31.6603			−1.30676			−0.653379	−	0.757031i	$-0.726649\pi$
$587$	−31.6603			−1.30676			−0.653379	+	0.757031i	$0.726649\pi$
$588$	−15.0000	+	8.66025i	−0.618590	+	0.357143i
$589$	20.1962			0.832168
$590$	−4.46410	−	1.19615i	−0.183784	−	0.0492448i
$591$	−8.53590	+	14.7846i	−0.351120	+	0.608158i
$592$	1.85641	−	6.92820i	0.0762978	−	0.284747i
$593$	−45.2487			−1.85814			−0.929071	−	0.369902i	$-0.879391\pi$
$593$	−45.2487			−1.85814			−0.929071	+	0.369902i	$0.879391\pi$
$594$	21.2942	−	12.2942i	0.873713	−	0.504438i
$595$	−2.78461	−	2.78461i	−0.114158	−	0.114158i
$596$	13.5359	−	23.4449i	0.554452	−	0.960339i
$597$	−21.4641	+	37.1769i	−0.878467	+	1.52155i
$598$	9.00000	+	2.41154i	0.368037	+	0.0986153i
$599$	−18.2942	+	18.2942i	−0.747482	+	0.747482i	−0.974006	−	0.226524i	$-0.927264\pi$
$599$	−18.2942	+	18.2942i	−0.747482	+	0.747482i	0.226524	+	0.974006i	$0.427264\pi$
$600$	−6.24871	−	23.3205i	−0.255103	−	0.952056i
$601$	−1.46410	−	1.46410i	−0.0597220	−	0.0597220i	0.676615	−	0.736337i	$-0.263446\pi$
$601$	−1.46410	−	1.46410i	−0.0597220	−	0.0597220i	−0.736337	+	0.676615i	$0.763446\pi$
$602$	2.19615	+	3.80385i	0.0895085	+	0.155033i
$603$	19.3923	+	33.5885i	0.789716	+	1.36783i
$604$	12.3923	−	21.4641i	0.504236	−	0.873362i
$605$	0.0525589			0.00213682
$606$			3.21539i			0.130616i
$607$	−7.70577	+	7.70577i	−0.312768	+	0.312768i	−0.845981	−	0.533213i	$-0.820984\pi$
$607$	−7.70577	+	7.70577i	−0.312768	+	0.312768i	0.533213	+	0.845981i	$0.320984\pi$
$608$	12.0000	−	20.7846i	0.486664	−	0.842927i
$609$	−19.9808	−	25.3923i	−0.809661	−	1.02895i
$610$	2.41154	−	1.39230i	0.0976405	−	0.0563728i
$611$	32.7058	+	32.7058i	1.32313	+	1.32313i
$612$	−18.0000	−	18.0000i	−0.727607	−	0.727607i
$613$	16.8564			0.680824			0.340412	−	0.940276i	$-0.389433\pi$
$613$	16.8564			0.680824			0.340412	+	0.940276i	$0.389433\pi$
$614$	−12.6340	−	21.8827i	−0.509866	−	0.883113i
$615$	−0.803848	−	3.00000i	−0.0324143	−	0.120972i
$616$	−32.7846			−1.32093
$617$	13.5167	+	13.5167i	0.544160	+	0.544160i	0.924746	−	0.380585i	$-0.124278\pi$
$617$	13.5167	+	13.5167i	0.544160	+	0.544160i	−0.380585	+	0.924746i	$0.624278\pi$
$618$	−7.26795	−	7.26795i	−0.292360	−	0.292360i
$619$	−8.95448	−	8.95448i	−0.359911	−	0.359911i	0.503869	−	0.863780i	$-0.331909\pi$
$619$	−8.95448	−	8.95448i	−0.359911	−	0.359911i	−0.863780	+	0.503869i	$0.831909\pi$
$620$	2.46410	−	0.660254i	0.0989607	−	0.0265164i
$621$		−	6.58846i		−	0.264386i
$622$	6.46410	+	11.1962i	0.259187	+	0.448925i
$623$	−37.1769	+	37.1769i	−1.48946	+	1.48946i
$624$	−36.0000			−1.44115
$625$	23.9282			0.957128
$626$	5.56218	−	20.7583i	0.222309	−	0.829670i
$627$	−12.2942	+	21.2942i	−0.490984	+	0.850410i
$628$	−8.78461	−	32.7846i	−0.350544	−	1.30825i
$629$	7.60770			0.303339
$630$	1.01924	+	3.80385i	0.0406074	+	0.151549i
$631$			20.8756i			0.831046i	0.909583	+	0.415523i	$0.136401\pi$
$631$			20.8756i			0.831046i	−0.909583	+	0.415523i	$0.863599\pi$
$632$	12.3923			0.492939
$633$	−42.1865	+	11.3038i	−1.67676	+	0.449288i
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	−3.73205	+	3.73205i	−0.148102	+	0.148102i
$636$	10.6077	−	6.12436i	0.420622	−	0.242846i
$637$	−25.9808			−1.02940
$638$	−3.63397	−	25.2224i	−0.143870	−	0.998566i
$639$	−1.90192	−	3.29423i	−0.0752389	−	0.130318i
$640$	0.784610	−	2.92820i	0.0310144	−	0.115747i
$641$	24.1244	−	24.1244i	0.952855	−	0.952855i	−0.0460829	−	0.998938i	$-0.514674\pi$
$641$	24.1244	−	24.1244i	0.952855	−	0.952855i	0.998938	+	0.0460829i	$0.0146738\pi$
$642$	12.9282	+	12.9282i	0.510235	+	0.510235i
$643$	40.3923			1.59292			0.796459	−	0.604693i	$-0.206704\pi$
$643$	40.3923			1.59292			0.796459	+	0.604693i	$0.206704\pi$
$644$	−4.39230	+	7.60770i	−0.173081	+	0.299785i
$645$	0.401924	−	0.107695i	0.0158257	−	0.00424049i
$646$	24.5885	+	6.58846i	0.967420	+	0.259219i
$647$	−37.5167			−1.47493			−0.737466	−	0.675384i	$-0.763978\pi$
$647$	−37.5167			−1.47493			−0.737466	+	0.675384i	$0.763978\pi$
$648$	6.58846	+	24.5885i	0.258819	+	0.965926i
$649$	−28.8564	−	28.8564i	−1.13271	−	1.13271i
$650$	9.37307	−	34.9808i	0.367642	−	1.37206i
$651$	27.5885	−	7.39230i	1.08128	−	0.289727i
$652$	1.05256	+	3.92820i	0.0412214	+	0.153840i
$653$	−13.8564	+	13.8564i	−0.542243	+	0.542243i	−0.924186	−	0.381943i	$-0.875255\pi$
$653$	−13.8564	+	13.8564i	−0.542243	+	0.542243i	0.381943	+	0.924186i	$0.375255\pi$
$654$	6.80385	+	6.80385i	0.266051	+	0.266051i
$655$	0.267949	+	0.267949i	0.0104696	+	0.0104696i
$656$	−6.92820	+	25.8564i	−0.270501	+	1.00952i
$657$	−30.5885	−	8.19615i	−1.19337	−	0.319762i
$658$	−37.7654	+	21.8038i	−1.47225	+	0.850002i
$659$	−16.8827	−	16.8827i	−0.657656	−	0.657656i	0.297169	−	0.954825i	$-0.403958\pi$
$659$	−16.8827	−	16.8827i	−0.657656	−	0.657656i	−0.954825	+	0.297169i	$0.903958\pi$
$660$	−0.803848	+	3.00000i	−0.0312897	+	0.116775i
$661$		−	24.9282i		−	0.969595i	−0.874626	−	0.484797i	$-0.838893\pi$
$661$		−	24.9282i		−	0.969595i	0.874626	−	0.484797i	$-0.161107\pi$
$662$	−39.0788	+	22.5622i	−1.51884	+	0.876904i
$663$	−9.88269	−	36.8827i	−0.383812	−	1.43240i
$664$	−14.2487	+	14.2487i	−0.552957	+	0.552957i
$665$	−2.78461	−	2.78461i	−0.107983	−	0.107983i
$666$	−6.58846	−	3.80385i	−0.255298	−	0.147396i
$667$	−6.33975	−	2.53590i	−0.245476	−	0.0981904i
$668$	−42.5885	−	24.5885i	−1.64780	−	0.951356i
$669$	17.4904	−	30.2942i	0.676217	−	1.17124i
$670$	−4.73205	−	1.26795i	−0.182815	−	0.0489852i
$671$	24.5885			0.949227
$672$	8.78461	−	32.7846i	0.338874	−	1.26469i
$673$			7.00000i			0.269830i	0.990857	+	0.134915i	$0.0430762\pi$
$673$			7.00000i			0.269830i	−0.990857	+	0.134915i	$0.956924\pi$
$674$	−21.7846	−	37.7321i	−0.839112	−	1.45338i
$675$	−25.6077			−0.985641
$676$	−24.2487	−	14.0000i	−0.932643	−	0.538462i
$677$	−5.19615	+	5.19615i	−0.199704	+	0.199704i	−0.799873	−	0.600169i	$-0.795100\pi$
$677$	−5.19615	+	5.19615i	−0.199704	+	0.199704i	0.600169	+	0.799873i	$0.295100\pi$
$678$		−	26.7846i		−	1.02866i
$679$	−5.07180	+	5.07180i	−0.194638	+	0.194638i
$680$	3.21539			0.123305
$681$	8.83013	−	15.2942i	0.338371	−	0.586076i
$682$	21.7583	+	5.83013i	0.833170	+	0.223247i
$683$	0.392305			0.0150111			0.00750556	−	0.999972i	$-0.497611\pi$
$683$	0.392305			0.0150111			0.00750556	+	0.999972i	$0.497611\pi$
$684$	−18.0000	−	18.0000i	−0.688247	−	0.688247i
$685$	0.339746	+	0.339746i	0.0129810	+	0.0129810i
$686$	−2.53590	+	9.46410i	−0.0968211	+	0.361341i
$687$	17.1962	−	4.60770i	0.656074	−	0.175795i
$688$	−3.46410	−	0.928203i	−0.132068	−	0.0353874i
$689$	18.3731			0.699958
$690$	0.588457	+	0.588457i	0.0224022	+	0.0224022i
$691$			23.3205i			0.887154i	0.896236	+	0.443577i	$0.146291\pi$
$691$			23.3205i			0.887154i	−0.896236	+	0.443577i	$0.853709\pi$
$692$	21.8564	−	37.8564i	0.830856	−	1.43908i
$693$	−9.00000	+	33.5885i	−0.341882	+	1.27592i
$694$	37.7846	+	10.1244i	1.43428	+	0.384315i
$695$	−1.26795			−0.0480961
$696$	26.1962	+	3.12436i	0.992963	+	0.118428i
$697$	−28.3923			−1.07544
$698$	17.8301	+	4.77757i	0.674880	+	0.180834i
$699$	14.3827	+	8.30385i	0.544003	+	0.314080i
$700$	29.5692	+	17.0718i	1.11761	+	0.645253i
$701$			25.9282i			0.979295i	0.871921	+	0.489647i	$0.162874\pi$
$701$			25.9282i			0.979295i	−0.871921	+	0.489647i	$0.837126\pi$
$702$	−9.88269	+	36.8827i	−0.372998	+	1.39205i
$703$	7.60770			0.286930
$704$	18.9282	−	18.9282i	0.713384	−	0.713384i
$705$	1.06922	+	3.99038i	0.0402691	+	0.150286i
$706$	7.85641	−	29.3205i	0.295680	−	1.10349i
$707$	−3.21539	−	3.21539i	−0.120927	−	0.120927i
$708$	36.5885	−	21.1244i	1.37508	−	0.793902i
$709$	−4.51666			−0.169627			−0.0848134	−	0.996397i	$-0.527029\pi$
$709$	−4.51666			−0.169627			−0.0848134	+	0.996397i	$0.527029\pi$
$710$	0.464102	+	0.124356i	0.0174174	+	0.00466698i
$711$	3.40192	−	12.6962i	0.127582	−	0.476143i
$712$		−	42.9282i		−	1.60880i
$713$	4.26795	−	4.26795i	0.159836	−	0.159836i
$714$	36.0000			1.34727
$715$	−3.29423	+	3.29423i	−0.123197	+	0.123197i
$716$	21.6603	−	37.5167i	0.809482	−	1.40206i
$717$	−23.7058	−	13.6865i	−0.885308	−	0.511133i
$718$	5.36603	+	9.29423i	0.200258	+	0.346858i
$719$			7.51666i			0.280324i	0.990129	+	0.140162i	$0.0447624\pi$
$719$			7.51666i			0.280324i	−0.990129	+	0.140162i	$0.955238\pi$
$720$	−2.78461	−	1.60770i	−0.103776	−	0.0599153i
$721$	14.5359			0.541345
$722$	−1.36603	−	0.366025i	−0.0508382	−	0.0136221i
$723$	−38.0885	−	21.9904i	−1.41652	−	0.817831i
$724$	8.32051	−	14.4115i	0.309229	−	0.535601i
$725$	−9.85641	+	24.6410i	−0.366058	+	0.915144i
$726$	−0.339746	+	0.339746i	−0.0126092	+	0.0126092i
$727$	−0.320508	−	0.320508i	−0.0118870	−	0.0118870i	0.701138	−	0.713025i	$-0.252676\pi$
$727$	−0.320508	−	0.320508i	−0.0118870	−	0.0118870i	−0.713025	+	0.701138i	$0.752676\pi$
$728$	36.0000	−	36.0000i	1.33425	−	1.33425i
$729$	27.0000			1.00000
$730$	3.46410	−	2.00000i	0.128212	−	0.0740233i
$731$		−	3.80385i		−	0.140690i
$732$	−6.58846	+	24.5885i	−0.243516	+	0.908816i
$733$	28.3923	+	28.3923i	1.04869	+	1.04869i	0.998752	+	0.0499416i	$0.0159035\pi$
$733$	28.3923	+	28.3923i	1.04869	+	1.04869i	0.0499416	+	0.998752i	$0.484096\pi$
$734$	−27.2487	+	15.7321i	−1.00577	+	0.580681i
$735$	−2.00962	−	1.16025i	−0.0741259	−	0.0427966i
$736$	−1.85641	−	6.92820i	−0.0684280	−	0.255377i
$737$	−30.5885	−	30.5885i	−1.12674	−	1.12674i
$738$	24.5885	+	14.1962i	0.905114	+	0.522568i
$739$	−12.4186	+	12.4186i	−0.456825	+	0.456825i	−0.897612	−	0.440787i	$-0.854699\pi$
$739$	−12.4186	+	12.4186i	−0.456825	+	0.456825i	0.440787	+	0.897612i	$0.354699\pi$
$740$	0.928203	−	0.248711i	0.0341214	−	0.00914281i
$741$	−9.88269	−	36.8827i	−0.363050	−	1.35492i
$742$	−4.48334	+	16.7321i	−0.164589	+	0.614253i
$743$	36.4641	+	36.4641i	1.33774	+	1.33774i	0.898247	+	0.439491i	$0.144841\pi$
$743$	36.4641	+	36.4641i	1.33774	+	1.33774i	0.439491	+	0.898247i	$0.355159\pi$
$744$	−11.6603	+	20.1962i	−0.427486	+	0.740427i
$745$	3.62693			0.132881
$746$	10.0981	+	2.70577i	0.369717	+	0.0990653i
$747$	10.6865	+	18.5096i	0.391000	+	0.677232i
$748$	24.5885	+	14.1962i	0.899043	+	0.519063i
$749$	−25.8564			−0.944773
$750$	4.60770	−	4.60770i	0.168249	−	0.168249i
$751$	30.6603	−	30.6603i	1.11881	−	1.11881i	0.126892	−	0.991917i	$-0.459500\pi$
$751$	30.6603	−	30.6603i	1.11881	−	1.11881i	0.991917	−	0.126892i	$-0.0405002\pi$
$752$	9.21539	−	34.3923i	0.336051	−	1.25416i
$753$	−33.8205	+	9.06218i	−1.23249	+	0.330244i
$754$	31.6865	+	23.7058i	1.15396	+	0.863313i
$755$	3.32051			0.120846
$756$	−31.1769	−	18.0000i	−1.13389	−	0.654654i
$757$	15.9282	−	15.9282i	0.578920	−	0.578920i	−0.355685	−	0.934606i	$-0.615753\pi$
$757$	15.9282	−	15.9282i	0.578920	−	0.578920i	0.934606	+	0.355685i	$0.115753\pi$
$758$	1.73205	+	3.00000i	0.0629109	+	0.108965i
$759$	1.90192	+	7.09808i	0.0690355	+	0.257644i
$760$	3.21539			0.116634
$761$			18.9282i			0.686147i	0.939309	+	0.343073i	$0.111468\pi$
$761$			18.9282i			0.686147i	−0.939309	+	0.343073i	$0.888532\pi$
$762$		−	48.2487i		−	1.74787i
$763$	−13.6077			−0.492632
$764$	34.0526	−	9.12436i	1.23198	−	0.330108i
$765$	0.882686	−	3.29423i	0.0319136	−	0.119103i
$766$	−5.07180	+	18.9282i	−0.183251	+	0.683904i
$767$	63.3731			2.28827
$768$	13.8564	+	24.0000i	0.500000	+	0.866025i
$769$	−20.4641	+	20.4641i	−0.737954	+	0.737954i	−0.972182	−	0.234227i	$-0.924744\pi$
$769$	−20.4641	+	20.4641i	−0.737954	+	0.737954i	0.234227	+	0.972182i	$0.424744\pi$
$770$	−2.19615	−	3.80385i	−0.0791438	−	0.137081i
$771$	−45.6962	−	26.3827i	−1.64571	−	0.950149i
$772$	−7.07180	−	26.3923i	−0.254520	−	0.949880i
$773$	26.1962	+	26.1962i	0.942210	+	0.942210i	0.998419	−	0.0562089i	$-0.0179013\pi$
$773$	26.1962	+	26.1962i	0.942210	+	0.942210i	−0.0562089	+	0.998419i	$0.517901\pi$
$774$	−1.90192	+	3.29423i	−0.0683632	+	0.118409i
$775$	−16.5885	−	16.5885i	−0.595875	−	0.595875i
$776$		−	5.85641i		−	0.210233i
$777$	10.3923	−	2.78461i	0.372822	−	0.0998973i
$778$	−23.6603	−	40.9808i	−0.848261	−	1.46923i
$779$	−28.3923			−1.01726
$780$	−2.41154	−	4.17691i	−0.0863471	−	0.149558i
$781$	3.00000	+	3.00000i	0.107348	+	0.107348i
$782$	6.58846	−	3.80385i	0.235603	−	0.136025i
$783$	10.3923	−	25.9808i	0.371391	−	0.928477i
$784$	10.0000	+	17.3205i	0.357143	+	0.618590i
$785$	3.21539	−	3.21539i	0.114762	−	0.114762i
$786$	−3.46410			−0.123560
$787$	−18.3397			−0.653741			−0.326871	−	0.945069i	$-0.605994\pi$
$787$	−18.3397			−0.653741			−0.326871	+	0.945069i	$0.605994\pi$
$788$	17.0718	+	9.85641i	0.608158	+	0.351120i
$789$	10.7154	+	39.9904i	0.381478	+	1.42370i
$790$	0.830127	+	1.43782i	0.0295346	+	0.0511554i
$791$	26.7846	+	26.7846i	0.952351	+	0.952351i
$792$	−14.1962	−	24.5885i	−0.504438	−	0.873713i
$793$	−27.0000	+	27.0000i	−0.958798	+	0.958798i
$794$	32.1506	+	8.61474i	1.14098	+	0.305726i
$795$	1.42116	+	0.820508i	0.0504034	+	0.0291004i
$796$	42.9282	+	24.7846i	1.52155	+	0.878467i
$797$	−26.3205	−	26.3205i	−0.932320	−	0.932320i	0.0655303	−	0.997851i	$-0.479126\pi$
$797$	−26.3205	−	26.3205i	−0.932320	−	0.932320i	−0.997851	+	0.0655303i	$0.979126\pi$
$798$	36.0000			1.27439
$799$	37.7654			1.33604
$800$	−26.9282	+	7.21539i	−0.952056	+	0.255103i
$801$	−43.9808	−	11.7846i	−1.55398	−	0.416389i
$802$	−10.5622	−	2.83013i	−0.372963	−	0.0999353i
$803$	35.3205			1.24643
$804$	38.7846	−	22.3923i	1.36783	−	0.789716i
$805$	−1.17691			−0.0414808
$806$	−30.2942	+	17.4904i	−1.06707	+	0.616072i
$807$	2.02628	+	7.56218i	0.0713284	+	0.266201i
$808$	3.71281			0.130616
$809$	19.5167	+	19.5167i	0.686169	+	0.686169i	0.961383	−	0.275214i	$-0.0887486\pi$
$809$	19.5167	+	19.5167i	0.686169	+	0.686169i	−0.275214	+	0.961383i	$0.588749\pi$
$810$	−2.41154	+	2.41154i	−0.0847330	+	0.0847330i
$811$	8.53590			0.299736			0.149868	−	0.988706i	$-0.452115\pi$
$811$	8.53590			0.299736			0.149868	+	0.988706i	$0.452115\pi$
$812$	−29.3205	+	23.0718i	−1.02895	+	0.809661i
$813$	−5.47372	−	20.4282i	−0.191972	−	0.716448i
$814$	8.19615	+	2.19615i	0.287275	+	0.0769751i
$815$	−0.385263	+	0.385263i	−0.0134952	+	0.0134952i
$816$	−20.7846	+	20.7846i	−0.727607	+	0.727607i
$817$		−	3.80385i		−	0.133080i
$818$	17.5359	−	10.1244i	0.613128	−	0.353990i
$819$	−27.0000	−	46.7654i	−0.943456	−	1.63411i
$820$	−3.46410	+	0.928203i	−0.120972	+	0.0324143i
$821$			14.2154i			0.496121i	0.968745	+	0.248060i	$0.0797931\pi$
$821$			14.2154i			0.496121i	−0.968745	+	0.248060i	$0.920207\pi$
$822$	−4.39230			−0.153199
$823$	−24.8564	−	24.8564i	−0.866440	−	0.866440i	0.125636	−	0.992076i	$-0.459903\pi$
$823$	−24.8564	−	24.8564i	−0.866440	−	0.866440i	−0.992076	+	0.125636i	$0.959903\pi$
$824$	−8.39230	+	8.39230i	−0.292360	+	0.292360i
$825$	27.5885	−	7.39230i	0.960507	−	0.257367i
$826$	−15.4641	+	57.7128i	−0.538065	+	2.00809i
$827$	−2.29423	+	2.29423i	−0.0797781	+	0.0797781i	−0.745870	−	0.666092i	$-0.767966\pi$
$827$	−2.29423	+	2.29423i	−0.0797781	+	0.0797781i	0.666092	+	0.745870i	$0.267966\pi$
$828$	−7.60770			−0.264386
$829$	−7.73205	+	7.73205i	−0.268545	+	0.268545i	−0.828514	−	0.559969i	$-0.810813\pi$
$829$	−7.73205	+	7.73205i	−0.268545	+	0.268545i	0.559969	+	0.828514i	$0.310813\pi$
$830$	−2.60770	−	0.698730i	−0.0905144	−	0.0242533i
$831$	7.60770	+	4.39230i	0.263908	+	0.152367i
$832$			41.5692i			1.44115i
$833$	−15.0000	+	15.0000i	−0.519719	+	0.519719i
$834$	8.19615	−	8.19615i	0.283810	−	0.283810i
$835$		−	6.58846i		−	0.228003i
$836$	24.5885	+	14.1962i	0.850410	+	0.490984i
$837$	17.4904	+	17.4904i	0.604556	+	0.604556i
$838$	−30.8564	−	8.26795i	−1.06592	−	0.285612i
$839$	−8.49038	−	8.49038i	−0.293121	−	0.293121i	0.545191	−	0.838312i	$-0.316457\pi$
$839$	−8.49038	−	8.49038i	−0.293121	−	0.293121i	−0.838312	+	0.545191i	$0.816457\pi$
$840$	4.39230	−	1.17691i	0.151549	−	0.0406074i
$841$	−21.0000	−	20.0000i	−0.724138	−	0.689655i
$842$	27.5885	−	15.9282i	0.950761	−	0.548922i
$843$	−2.59808	−	1.50000i	−0.0894825	−	0.0516627i
$844$	13.0526	+	48.7128i	0.449288	+	1.67676i
$845$		−	3.75129i		−	0.129048i
$846$	−32.7058	−	18.8827i	−1.12445	−	0.649200i
$847$		−	0.679492i		−	0.0233476i
$848$	−7.07180	−	12.2487i	−0.242846	−	0.420622i
$849$	2.70577	−	4.68653i	0.0928618	−	0.160841i
$850$	−14.7846	−	25.6077i	−0.507108	−	0.878337i
$851$	1.60770	−	1.60770i	0.0551111	−	0.0551111i
$852$	−3.80385	+	2.19615i	−0.130318	+	0.0752389i
$853$	2.66025	+	2.66025i	0.0910854	+	0.0910854i	0.751181	−	0.660096i	$-0.229484\pi$
$853$	2.66025	+	2.66025i	0.0910854	+	0.0910854i	−0.660096	+	0.751181i	$0.729484\pi$
$854$	−18.0000	−	31.1769i	−0.615947	−	1.06685i
$855$	0.882686	−	3.29423i	0.0301872	−	0.112660i
$856$	14.9282	−	14.9282i	0.510235	−	0.510235i
$857$		−	3.00000i		−	0.102478i	−0.998686	−	0.0512390i	$-0.983683\pi$
$857$		−	3.00000i		−	0.102478i	0.998686	−	0.0512390i	$-0.0163170\pi$
$858$		−	42.5885i		−	1.45395i
$859$	3.75833	+	3.75833i	0.128233	+	0.128233i	0.768310	−	0.640078i	$-0.221098\pi$
$859$	3.75833	+	3.75833i	0.128233	+	0.128233i	−0.640078	+	0.768310i	$0.721098\pi$
$860$	−0.124356	−	0.464102i	−0.00424049	−	0.0158257i
$861$	−38.7846	+	10.3923i	−1.32178	+	0.354169i
$862$	−25.0526	−	6.71281i	−0.853294	−	0.228639i
$863$	−6.58846			−0.224274			−0.112137	−	0.993693i	$-0.535770\pi$
$863$	−6.58846			−0.224274			−0.112137	+	0.993693i	$0.535770\pi$
$864$	28.3923	−	7.60770i	0.965926	−	0.258819i
$865$	5.85641			0.199124
$866$	−21.3205	−	36.9282i	−0.724500	−	1.25487i
$867$	−1.50000	−	0.866025i	−0.0509427	−	0.0294118i
$868$	−8.53590	−	31.8564i	−0.289727	−	1.08128i
$869$			14.6603i			0.497315i
$870$	1.39230	+	3.24871i	0.0472036	+	0.110142i
$871$	67.1769			2.27620
$872$	7.85641	−	7.85641i	0.266051	−	0.266051i
$873$	−6.00000	−	1.60770i	−0.203069	−	0.0544122i
$874$	6.58846	−	3.80385i	0.222858	−	0.128667i
$875$			9.21539i			0.311537i
$876$	−9.46410	+	35.3205i	−0.319762	+	1.19337i
$877$		−	44.9090i		−	1.51647i	−0.651983	−	0.758234i	$-0.726062\pi$
$877$		−	44.9090i		−	1.51647i	0.651983	−	0.758234i	$-0.273938\pi$
$878$	5.53590	+	1.48334i	0.186828	+	0.0500603i
$879$	−35.4904	+	9.50962i	−1.19706	+	0.320751i
$880$	3.46410	+	0.928203i	0.116775	+	0.0312897i
$881$	−14.0718	+	14.0718i	−0.474091	+	0.474091i	−0.903236	−	0.429145i	$-0.858815\pi$
$881$	−14.0718	+	14.0718i	−0.474091	+	0.474091i	0.429145	+	0.903236i	$0.358815\pi$
$882$	20.4904	−	5.49038i	0.689947	−	0.184871i
$883$	−48.9282			−1.64657			−0.823283	−	0.567632i	$-0.807860\pi$
$883$	−48.9282			−1.64657			−0.823283	+	0.567632i	$0.807860\pi$
$884$	−42.5885	+	11.4115i	−1.43240	+	0.383812i
$885$	4.90192	+	2.83013i	0.164776	+	0.0951337i
$886$	−17.7846	−	30.8038i	−0.597486	−	1.03488i
$887$	−22.2224	+	22.2224i	−0.746156	+	0.746156i	−0.973755	−	0.227599i	$-0.926913\pi$
$887$	−22.2224	+	22.2224i	−0.746156	+	0.746156i	0.227599	+	0.973755i	$0.426913\pi$
$888$	−4.39230	+	7.60770i	−0.147396	+	0.255298i
$889$	48.2487	+	48.2487i	1.61821	+	1.61821i
$890$	4.98076	−	2.87564i	0.166956	−	0.0963918i
$891$	−29.0885	+	7.79423i	−0.974500	+	0.261116i
$892$	−34.9808	−	20.1962i	−1.17124	−	0.676217i
$893$	37.7654			1.26377
$894$	−23.4449	+	23.4449i	−0.784114	+	0.784114i
$895$	5.80385			0.194001
$896$	−37.8564	−	10.1436i	−1.26469	−	0.338874i
$897$	−9.88269	−	5.70577i	−0.329973	−	0.190510i
$898$	8.66025	+	15.0000i	0.288996	+	0.500556i
$899$	23.5622	−	10.0981i	0.785843	−	0.336790i
$900$			29.5692i			0.985641i
$901$	10.6077	−	10.6077i	0.353394	−	0.353394i
$902$	−30.5885	−	8.19615i	−1.01848	−	0.272902i
$903$	−1.39230	−	5.19615i	−0.0463330	−	0.172917i
$904$	−30.9282			−1.02866
$905$	2.22947			0.0741102
$906$	−21.4641	+	21.4641i	−0.713097	+	0.713097i
$907$	10.8564	+	10.8564i	0.360481	+	0.360481i	0.863990	−	0.503509i	$-0.167958\pi$
$907$	10.8564	+	10.8564i	0.360481	+	0.360481i	−0.503509	+	0.863990i	$0.667958\pi$
$908$	−17.6603	−	10.1962i	−0.586076	−	0.338371i
$909$	1.01924	−	3.80385i	0.0338060	−	0.126166i
$910$	6.58846	+	1.76537i	0.218405	+	0.0585215i
$911$	33.2942	+	33.2942i	1.10309	+	1.10309i	0.994036	+	0.109051i	$0.0347811\pi$
$911$	33.2942	+	33.2942i	1.10309	+	1.10309i	0.109051	+	0.994036i	$0.465219\pi$
$912$	−20.7846	+	20.7846i	−0.688247	+	0.688247i
$913$	−16.8564	−	16.8564i	−0.557866	−	0.557866i
$914$	−46.4449	−	12.4449i	−1.53626	−	0.411640i
$915$	−3.29423	+	0.882686i	−0.108904	+	0.0291807i
$916$	−5.32051	−	19.8564i	−0.175795	−	0.656074i
$917$	3.46410	−	3.46410i	0.114395	−	0.114395i
$918$	15.5885	+	27.0000i	0.514496	+	0.891133i
$919$	30.9808			1.02196			0.510981	−	0.859592i	$-0.329282\pi$
$919$	30.9808			1.02196			0.510981	+	0.859592i	$0.329282\pi$
$920$	0.679492	−	0.679492i	0.0224022	−	0.0224022i
$921$	8.00962	+	29.8923i	0.263926	+	0.984985i
$922$	16.8564	+	29.1962i	0.555136	+	0.961524i
$923$	−6.58846			−0.216862
$924$	38.7846	+	10.3923i	1.27592	+	0.341882i
$925$	−6.24871	−	6.24871i	−0.205456	−	0.205456i
$926$	24.3205	+	6.51666i	0.799221	+	0.214151i
$927$	6.29423	+	10.9019i	0.206730	+	0.358066i
$928$	3.60770	−	30.2487i	0.118428	−	0.992963i
$929$			27.7128i			0.909228i	0.890689	+	0.454614i	$0.150223\pi$
$929$			27.7128i			0.909228i	−0.890689	+	0.454614i	$0.849777\pi$
$930$	−3.12436			−0.102452
$931$	−15.0000	+	15.0000i	−0.491605	+	0.491605i
$932$	9.58846	−	16.6077i	0.314080	−	0.544003i
$933$	−4.09808	−	15.2942i	−0.134165	−	0.500711i
$934$	19.5622	−	11.2942i	0.640094	−	0.369558i
$935$			3.80385i			0.124399i
$936$	42.5885	+	11.4115i	1.39205	+	0.372998i
$937$			39.7128i			1.29736i	0.761061	+	0.648681i	$0.224679\pi$
$937$			39.7128i			1.29736i	−0.761061	+	0.648681i	$0.775321\pi$
$938$	−16.3923	+	61.1769i	−0.535228	+	1.99750i
$939$	−13.1603	+	22.7942i	−0.429469	+	0.743862i
$940$	4.60770	−	1.23463i	0.150286	−	0.0402691i
$941$		−	46.1244i		−	1.50361i	−0.659385	−	0.751806i	$-0.729183\pi$
$941$		−	46.1244i		−	1.50361i	0.659385	−	0.751806i	$-0.270817\pi$
$942$			41.5692i			1.35440i
$943$	−6.00000	+	6.00000i	−0.195387	+	0.195387i
$944$	−24.3923	−	42.2487i	−0.793902	−	1.37508i
$945$		−	4.82309i		−	0.156895i
$946$	1.09808	−	4.09808i	0.0357015	−	0.133240i
$947$	9.63397	+	9.63397i	0.313062	+	0.313062i	0.846095	−	0.533033i	$-0.178948\pi$
$947$	9.63397	+	9.63397i	0.313062	+	0.313062i	−0.533033	+	0.846095i	$0.678948\pi$
$948$	−14.6603	−	3.92820i	−0.476143	−	0.127582i
$949$	−38.7846	+	38.7846i	−1.25900	+	1.25900i
$950$	−14.7846	−	25.6077i	−0.479676	−	0.830823i
$951$	−8.24167	−	30.7583i	−0.267254	−	0.997407i
$952$		−	41.5692i		−	1.34727i
$953$		−	22.2679i		−	0.721330i	−0.932695	−	0.360665i	$-0.882550\pi$
$953$		−	22.2679i		−	0.721330i	0.932695	−	0.360665i	$-0.117450\pi$
$954$	−14.4904	+	3.88269i	−0.469143	+	0.125707i
$955$	3.33975	+	3.33975i	0.108072	+	0.108072i
$956$	−15.8038	+	27.3731i	−0.511133	+	0.885308i
$957$	−3.69615	+	30.9904i	−0.119480	+	1.00178i
$958$	−17.7058	+	10.2224i	−0.572048	+	0.330272i
$959$	4.39230	−	4.39230i	0.141835	−	0.141835i
$960$	−1.85641	+	3.21539i	−0.0599153	+	0.103776i
$961$		−	8.33975i		−	0.269024i
$962$	−11.4115	+	6.58846i	−0.367923	+	0.212420i
$963$	−11.1962	−	19.3923i	−0.360791	−	0.624908i
$964$	−25.3923	+	43.9808i	−0.817831	+	1.41652i
$965$	2.58846	−	2.58846i	0.0833254	−	0.0833254i
$966$	7.60770	−	7.60770i	0.244774	−	0.244774i
$967$	7.83013	−	7.83013i	0.251800	−	0.251800i	−0.569908	−	0.821708i	$-0.693021\pi$
$967$	7.83013	−	7.83013i	0.251800	−	0.251800i	0.821708	+	0.569908i	$0.193021\pi$
$968$	0.392305	+	0.392305i	0.0126092	+	0.0126092i
$969$	−27.0000	−	15.5885i	−0.867365	−	0.500773i
$970$	0.679492	−	0.392305i	0.0218172	−	0.0125961i
$971$	20.3205	+	20.3205i	0.652116	+	0.652116i	0.953502	−	0.301386i	$-0.0974493\pi$
$971$	20.3205	+	20.3205i	0.652116	+	0.652116i	−0.301386	+	0.953502i	$0.597449\pi$
$972$		−	31.1769i		−	1.00000i
$973$			16.3923i			0.525513i
$974$	−3.94744	+	14.7321i	−0.126484	+	0.472045i
$975$	−22.1769	+	38.4115i	−0.710230	+	1.23015i
$976$	28.3923	+	7.60770i	0.908816	+	0.243516i
$977$		−	8.07180i		−	0.258240i	−0.991629	−	0.129120i	$-0.958785\pi$
$977$		−	8.07180i		−	0.258240i	0.991629	−	0.129120i	$-0.0412152\pi$
$978$		−	4.98076i		−	0.159267i
$979$	50.7846			1.62308
$980$	−1.33975	+	2.32051i	−0.0427966	+	0.0741259i
$981$	−5.89230	−	10.2058i	−0.188127	−	0.325845i
$982$	−12.9019	−	22.3468i	−0.411717	−	0.713115i
$983$	−26.1506	−	26.1506i	−0.834076	−	0.834076i	0.153996	−	0.988072i	$-0.450786\pi$
$983$	−26.1506	−	26.1506i	−0.834076	−	0.834076i	−0.988072	+	0.153996i	$0.950786\pi$
$984$	16.3923	−	28.3923i	0.522568	−	0.905114i
$985$			2.64102i			0.0841498i
$986$	31.9808	−	4.60770i	1.01847	−	0.146739i
$987$	51.5885	−	13.8231i	1.64208	−	0.439994i
$988$	−42.5885	+	11.4115i	−1.35492	+	0.363050i
$989$	−0.803848	−	0.803848i	−0.0255609	−	0.0255609i
$990$	1.90192	−	3.29423i	0.0604471	−	0.104697i
$991$		−	3.55514i		−	0.112933i	−0.998405	−	0.0564663i	$-0.982017\pi$
$991$		−	3.55514i		−	0.112933i	0.998405	−	0.0564663i	$-0.0179834\pi$
$992$	23.3205	+	13.4641i	0.740427	+	0.427486i
$993$	53.3827	−	14.3038i	1.69405	−	0.453919i
$994$	1.60770	−	6.00000i	0.0509930	−	0.190308i
$995$			6.64102i			0.210534i
$996$	21.3731	−	12.3397i	0.677232	−	0.391000i
$997$	−24.5885	+	24.5885i	−0.778724	+	0.778724i	−0.979614	−	0.200890i	$-0.935617\pi$
$997$	−24.5885	+	24.5885i	−0.778724	+	0.778724i	0.200890	+	0.979614i	$0.435617\pi$
$998$	1.48334	−	5.53590i	0.0469543	−	0.175236i
$999$	6.58846	+	6.58846i	0.208450	+	0.208450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	696.2.t.e.389.1	yes	4
3.2	odd	2		696.2.t.c.389.2	yes	4
8.5	even	2		696.2.t.b.389.1	yes	4
24.5	odd	2		696.2.t.d.389.2	yes	4
29.17	odd	4		696.2.t.d.365.2	yes	4
87.17	even	4		696.2.t.b.365.1	✓	4
232.133	odd	4		696.2.t.c.365.2	yes	4
696.365	even	4	inner	696.2.t.e.365.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
696.2.t.b.365.1	✓	4	87.17	even	4
696.2.t.b.389.1	yes	4	8.5	even	2
696.2.t.c.365.2	yes	4	232.133	odd	4
696.2.t.c.389.2	yes	4	3.2	odd	2
696.2.t.d.365.2	yes	4	29.17	odd	4
696.2.t.d.389.2	yes	4	24.5	odd	2
696.2.t.e.365.1	yes	4	696.365	even	4	inner
696.2.t.e.389.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} -0.267949i q^{5} +(1.73205 + 1.73205i) q^{6} -3.46410 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} -0.267949i q^{5} +(1.73205 + 1.73205i) q^{6} -3.46410 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.366025 + 0.0980762i) q^{10} +(2.36603 + 2.36603i) q^{11} +(-3.00000 + 1.73205i) q^{12} -5.19615 q^{13} +(1.26795 - 4.73205i) q^{14} +(-0.401924 - 0.232051i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 + 3.00000i) q^{17} +(4.09808 - 1.09808i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(-0.267949 + 0.464102i) q^{20} +(-3.00000 + 5.19615i) q^{21} +(-4.09808 + 2.36603i) q^{22} +1.26795i q^{23} +(-1.26795 - 4.73205i) q^{24} +4.92820 q^{25} +(1.90192 - 7.09808i) q^{26} -5.19615 q^{27} +(6.00000 + 3.46410i) q^{28} +(-2.00000 + 5.00000i) q^{29} +(0.464102 - 0.464102i) q^{30} +(-3.36603 - 3.36603i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(5.59808 - 1.50000i) q^{33} +(-3.00000 - 5.19615i) q^{34} +0.928203i q^{35} +6.00000i q^{36} +(-1.26795 - 1.26795i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-4.50000 + 7.79423i) q^{39} +(-0.535898 - 0.535898i) q^{40} +(4.73205 + 4.73205i) q^{41} +(-6.00000 - 6.00000i) q^{42} +(-0.633975 + 0.633975i) q^{43} +(-1.73205 - 6.46410i) q^{44} +(-0.696152 + 0.401924i) q^{45} +(-1.73205 - 0.464102i) q^{46} +(-6.29423 - 6.29423i) q^{47} +6.92820 q^{48} +5.00000 q^{49} +(-1.80385 + 6.73205i) q^{50} +(1.90192 + 7.09808i) q^{51} +(9.00000 + 5.19615i) q^{52} -3.53590 q^{53} +(1.90192 - 7.09808i) q^{54} +(0.633975 - 0.633975i) q^{55} +(-6.92820 + 6.92820i) q^{56} +(1.90192 + 7.09808i) q^{57} +(-6.09808 - 4.56218i) q^{58} -12.1962 q^{59} +(0.464102 + 0.803848i) q^{60} +(5.19615 - 5.19615i) q^{61} +(5.83013 - 3.36603i) q^{62} +(5.19615 + 9.00000i) q^{63} -8.00000i q^{64} +1.39230i q^{65} +8.19615i q^{66} -12.9282 q^{67} +(8.19615 - 2.19615i) q^{68} +(1.90192 + 1.09808i) q^{69} +(-1.26795 - 0.339746i) q^{70} +1.26795 q^{71} +(-8.19615 - 2.19615i) q^{72} +(7.46410 - 7.46410i) q^{73} +(2.19615 - 1.26795i) q^{74} +(4.26795 - 7.39230i) q^{75} +(8.19615 - 2.19615i) q^{76} +(-8.19615 - 8.19615i) q^{77} +(-9.00000 - 9.00000i) q^{78} +(3.09808 + 3.09808i) q^{79} +(0.928203 - 0.535898i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-8.19615 + 4.73205i) q^{82} -7.12436 q^{83} +(10.3923 - 6.00000i) q^{84} +(0.803848 + 0.803848i) q^{85} +(-0.633975 - 1.09808i) q^{86} +(5.76795 + 7.33013i) q^{87} +9.46410 q^{88} +(10.7321 - 10.7321i) q^{89} +(-0.294229 - 1.09808i) q^{90} +18.0000 q^{91} +(1.26795 - 2.19615i) q^{92} +(-7.96410 + 2.13397i) q^{93} +(10.9019 - 6.29423i) q^{94} +(0.803848 + 0.803848i) q^{95} +(-2.53590 + 9.46410i) q^{96} +(1.46410 - 1.46410i) q^{97} +(-1.83013 + 6.83013i) q^{98} +(2.59808 - 9.69615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 8 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} + 8 q^{8} - 6 q^{9} - 2 q^{10} + 6 q^{11} - 12 q^{12} + 12 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} - 8 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 8 q^{25} + 18 q^{26} + 24 q^{28} - 8 q^{29} - 12 q^{30} - 10 q^{31} - 8 q^{32} + 12 q^{33} - 12 q^{34} - 12 q^{37} - 12 q^{38} - 18 q^{39} - 16 q^{40} + 12 q^{41} - 24 q^{42} - 6 q^{43} + 18 q^{45} + 6 q^{47} + 20 q^{49} - 28 q^{50} + 18 q^{51} + 36 q^{52} - 28 q^{53} + 18 q^{54} + 6 q^{55} + 18 q^{57} - 14 q^{58} - 28 q^{59} - 12 q^{60} + 6 q^{62} - 24 q^{67} + 12 q^{68} + 18 q^{69} - 12 q^{70} + 12 q^{71} - 12 q^{72} + 16 q^{73} - 12 q^{74} + 24 q^{75} + 12 q^{76} - 12 q^{77} - 36 q^{78} + 2 q^{79} - 24 q^{80} - 18 q^{81} - 12 q^{82} + 20 q^{83} + 24 q^{85} - 6 q^{86} + 30 q^{87} + 24 q^{88} + 36 q^{89} + 30 q^{90} + 72 q^{91} + 12 q^{92} - 18 q^{93} + 54 q^{94} + 24 q^{95} - 24 q^{96} - 8 q^{97} + 10 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 8 * q^8 - 6 * q^9 - 2 * q^10 + 6 * q^11 - 12 * q^12 + 12 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 + 6 * q^18 - 12 * q^19 - 8 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 8 * q^25 + 18 * q^26 + 24 * q^28 - 8 * q^29 - 12 * q^30 - 10 * q^31 - 8 * q^32 + 12 * q^33 - 12 * q^34 - 12 * q^37 - 12 * q^38 - 18 * q^39 - 16 * q^40 + 12 * q^41 - 24 * q^42 - 6 * q^43 + 18 * q^45 + 6 * q^47 + 20 * q^49 - 28 * q^50 + 18 * q^51 + 36 * q^52 - 28 * q^53 + 18 * q^54 + 6 * q^55 + 18 * q^57 - 14 * q^58 - 28 * q^59 - 12 * q^60 + 6 * q^62 - 24 * q^67 + 12 * q^68 + 18 * q^69 - 12 * q^70 + 12 * q^71 - 12 * q^72 + 16 * q^73 - 12 * q^74 + 24 * q^75 + 12 * q^76 - 12 * q^77 - 36 * q^78 + 2 * q^79 - 24 * q^80 - 18 * q^81 - 12 * q^82 + 20 * q^83 + 24 * q^85 - 6 * q^86 + 30 * q^87 + 24 * q^88 + 36 * q^89 + 30 * q^90 + 72 * q^91 + 12 * q^92 - 18 * q^93 + 54 * q^94 + 24 * q^95 - 24 * q^96 - 8 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more