LMFDB - Embedded newform 144.2.x.d.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("144.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	144.13
Dual form			144.2.x.d.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +1.73205i q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.500000 + 1.86603i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +1.73205i q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.500000 + 1.86603i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +(2.36603 - 1.36603i) q^{10} +(1.86603 + 0.500000i) q^{11} +(-1.73205 - 3.00000i) q^{12} +(2.23205 - 0.598076i) q^{13} +(4.46410 + 4.46410i) q^{14} +(-3.23205 + 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +4.00000 q^{17} +(1.09808 + 4.09808i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(-2.73205 - 2.73205i) q^{20} +(-3.86603 - 6.69615i) q^{21} -2.73205i q^{22} +(5.59808 + 3.23205i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(1.09808 - 0.633975i) q^{25} +(-1.63397 - 2.83013i) q^{26} -5.19615i q^{27} +(4.46410 - 7.73205i) q^{28} +(0.232051 - 0.866025i) q^{29} +(2.36603 + 4.09808i) q^{30} +(-4.59808 + 7.96410i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-0.866025 + 3.23205i) q^{33} +(-1.46410 - 5.46410i) q^{34} +(-6.09808 - 6.09808i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-4.26795 + 4.26795i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(1.03590 + 3.86603i) q^{39} +(-2.73205 + 4.73205i) q^{40} +(-0.696152 - 0.401924i) q^{41} +(-7.73205 + 7.73205i) q^{42} +(6.33013 + 1.69615i) q^{43} +(-3.73205 + 1.00000i) q^{44} +(-1.50000 - 5.59808i) q^{45} +(2.36603 - 8.83013i) q^{46} +(-0.598076 - 1.03590i) q^{47} +(6.00000 + 3.46410i) q^{48} +(6.46410 - 11.1962i) q^{49} +(-1.26795 - 1.26795i) q^{50} +6.92820i q^{51} +(-3.26795 + 3.26795i) q^{52} +(5.73205 - 5.73205i) q^{53} +(-7.09808 + 1.90192i) q^{54} +3.73205i q^{55} +(-12.1962 - 3.26795i) q^{56} +(5.19615 - 5.19615i) q^{57} -1.26795 q^{58} +(0.401924 + 1.50000i) q^{59} +(4.73205 - 4.73205i) q^{60} +(0.571797 - 2.13397i) q^{61} +(12.5622 + 3.36603i) q^{62} +(11.5981 - 6.69615i) q^{63} +8.00000i q^{64} +(2.23205 + 3.86603i) q^{65} +4.73205 q^{66} +(8.33013 - 2.23205i) q^{67} +(-6.92820 + 4.00000i) q^{68} +(-5.59808 + 9.69615i) q^{69} +(-6.09808 + 10.5622i) q^{70} -2.92820i q^{71} +(-6.00000 - 6.00000i) q^{72} +7.46410i q^{73} +(7.39230 + 4.26795i) q^{74} +(1.09808 + 1.90192i) q^{75} +(8.19615 + 2.19615i) q^{76} +(-8.33013 + 2.23205i) q^{77} +(4.90192 - 2.83013i) q^{78} +(-0.866025 - 1.50000i) q^{79} +(7.46410 + 2.00000i) q^{80} +9.00000 q^{81} +(-0.294229 + 1.09808i) q^{82} +(3.79423 - 14.1603i) q^{83} +(13.3923 + 7.73205i) q^{84} +(2.00000 + 7.46410i) q^{85} -9.26795i q^{86} +(1.50000 + 0.401924i) q^{87} +(2.73205 + 4.73205i) q^{88} +15.8564i q^{89} +(-7.09808 + 4.09808i) q^{90} +(-7.29423 + 7.29423i) q^{91} -12.9282 q^{92} +(-13.7942 - 7.96410i) q^{93} +(-1.19615 + 1.19615i) q^{94} +(4.09808 - 7.09808i) q^{95} +(2.53590 - 9.46410i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-17.6603 - 4.73205i) q^{98} +(-5.59808 - 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{5} + 6 q^{6} - 12 q^{7} + 8 q^{8} - 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^5 + 6 * q^6 - 12 * q^7 + 8 * q^8 - 12 * q^9	$ 4 q + 2 q^{2} + 2 q^{5} + 6 q^{6} - 12 q^{7} + 8 q^{8} - 12 q^{9} + 6 q^{10} + 4 q^{11} + 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 16 q^{17} - 6 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{28} - 6 q^{29} + 6 q^{30} - 8 q^{31} - 8 q^{32} + 8 q^{34} - 14 q^{35} - 24 q^{37} - 12 q^{38} + 18 q^{39} - 4 q^{40} + 18 q^{41} - 24 q^{42} + 8 q^{43} - 8 q^{44} - 6 q^{45} + 6 q^{46} + 8 q^{47} + 24 q^{48} + 12 q^{49} - 12 q^{50} - 20 q^{52} + 16 q^{53} - 18 q^{54} - 28 q^{56} - 12 q^{58} + 12 q^{59} + 12 q^{60} + 30 q^{61} + 26 q^{62} + 36 q^{63} + 2 q^{65} + 12 q^{66} + 16 q^{67} - 12 q^{69} - 14 q^{70} - 24 q^{72} - 12 q^{74} - 6 q^{75} + 12 q^{76} - 16 q^{77} + 30 q^{78} + 16 q^{80} + 36 q^{81} + 30 q^{82} - 16 q^{83} + 12 q^{84} + 8 q^{85} + 6 q^{87} + 4 q^{88} - 18 q^{90} + 2 q^{91} - 24 q^{92} - 24 q^{93} + 16 q^{94} + 6 q^{95} + 24 q^{96} - 2 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^5 + 6 * q^6 - 12 * q^7 + 8 * q^8 - 12 * q^9 + 6 * q^10 + 4 * q^11 + 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 16 * q^17 - 6 * q^18 - 12 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^23 - 6 * q^25 - 10 * q^26 + 4 * q^28 - 6 * q^29 + 6 * q^30 - 8 * q^31 - 8 * q^32 + 8 * q^34 - 14 * q^35 - 24 * q^37 - 12 * q^38 + 18 * q^39 - 4 * q^40 + 18 * q^41 - 24 * q^42 + 8 * q^43 - 8 * q^44 - 6 * q^45 + 6 * q^46 + 8 * q^47 + 24 * q^48 + 12 * q^49 - 12 * q^50 - 20 * q^52 + 16 * q^53 - 18 * q^54 - 28 * q^56 - 12 * q^58 + 12 * q^59 + 12 * q^60 + 30 * q^61 + 26 * q^62 + 36 * q^63 + 2 * q^65 + 12 * q^66 + 16 * q^67 - 12 * q^69 - 14 * q^70 - 24 * q^72 - 12 * q^74 - 6 * q^75 + 12 * q^76 - 16 * q^77 + 30 * q^78 + 16 * q^80 + 36 * q^81 + 30 * q^82 - 16 * q^83 + 12 * q^84 + 8 * q^85 + 6 * q^87 + 4 * q^88 - 18 * q^90 + 2 * q^91 - 24 * q^92 - 24 * q^93 + 16 * q^94 + 6 * q^95 + 24 * q^96 - 2 * q^97 - 36 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	0.500000	+	1.86603i	0.223607	+	0.834512i	0.982958	+	0.183831i	$0.0588499\pi$
$5$	0.500000	+	1.86603i	0.223607	+	0.834512i	−0.759351	+	0.650681i	$0.774483\pi$
$6$	2.36603	−	0.633975i	0.965926	−	0.258819i
$7$	−3.86603	+	2.23205i	−1.46122	+	0.843636i	−0.999068	−	0.0431647i	$-0.986256\pi$
$7$	−3.86603	+	2.23205i	−1.46122	+	0.843636i	−0.462152	+	0.886801i	$0.652923\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−3.00000			−1.00000
$10$	2.36603	−	1.36603i	0.748203	−	0.431975i
$11$	1.86603	+	0.500000i	0.562628	+	0.150756i	0.528913	−	0.848676i	$-0.322600\pi$
$11$	1.86603	+	0.500000i	0.562628	+	0.150756i	0.0337145	+	0.999432i	$0.489266\pi$
$12$	−1.73205	−	3.00000i	−0.500000	−	0.866025i
$13$	2.23205	−	0.598076i	0.619060	−	0.165876i	0.0643593	−	0.997927i	$-0.479500\pi$
$13$	2.23205	−	0.598076i	0.619060	−	0.165876i	0.554700	+	0.832050i	$0.312833\pi$
$14$	4.46410	+	4.46410i	1.19308	+	1.19308i
$15$	−3.23205	+	0.866025i	−0.834512	+	0.223607i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	1.09808	+	4.09808i	0.258819	+	0.965926i
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	−2.73205	−	2.73205i	−0.610905	−	0.610905i
$21$	−3.86603	−	6.69615i	−0.843636	−	1.46122i
$22$		−	2.73205i		−	0.582475i
$23$	5.59808	+	3.23205i	1.16728	+	0.673929i	0.953038	−	0.302851i	$-0.0979386\pi$
$23$	5.59808	+	3.23205i	1.16728	+	0.673929i	0.214242	+	0.976781i	$0.431272\pi$
$24$	−3.46410	+	3.46410i	−0.707107	+	0.707107i
$25$	1.09808	−	0.633975i	0.219615	−	0.126795i
$26$	−1.63397	−	2.83013i	−0.320449	−	0.555034i
$27$		−	5.19615i		−	1.00000i
$28$	4.46410	−	7.73205i	0.843636	−	1.46122i
$29$	0.232051	−	0.866025i	0.0430908	−	0.160817i	−0.941028	−	0.338329i	$-0.890138\pi$
$29$	0.232051	−	0.866025i	0.0430908	−	0.160817i	0.984119	+	0.177512i	$0.0568049\pi$
$30$	2.36603	+	4.09808i	0.431975	+	0.748203i
$31$	−4.59808	+	7.96410i	−0.825839	+	1.43039i	0.0754376	+	0.997151i	$0.475965\pi$
$31$	−4.59808	+	7.96410i	−0.825839	+	1.43039i	−0.901277	+	0.433244i	$0.857369\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$	−0.866025	+	3.23205i	−0.150756	+	0.562628i
$34$	−1.46410	−	5.46410i	−0.251091	−	0.937086i
$35$	−6.09808	−	6.09808i	−1.03076	−	1.03076i
$36$	5.19615	−	3.00000i	0.866025	−	0.500000i
$37$	−4.26795	+	4.26795i	−0.701647	+	0.701647i	−0.964764	−	0.263117i	$-0.915249\pi$
$37$	−4.26795	+	4.26795i	−0.701647	+	0.701647i	0.263117	+	0.964764i	$0.415249\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$	1.03590	+	3.86603i	0.165876	+	0.619060i
$40$	−2.73205	+	4.73205i	−0.431975	+	0.748203i
$41$	−0.696152	−	0.401924i	−0.108721	−	0.0627700i	0.444654	−	0.895703i	$-0.353327\pi$
$41$	−0.696152	−	0.401924i	−0.108721	−	0.0627700i	−0.553374	+	0.832933i	$0.686660\pi$
$42$	−7.73205	+	7.73205i	−1.19308	+	1.19308i
$43$	6.33013	+	1.69615i	0.965335	+	0.258661i	0.706857	−	0.707356i	$-0.250112\pi$
$43$	6.33013	+	1.69615i	0.965335	+	0.258661i	0.258478	+	0.966017i	$0.416779\pi$
$44$	−3.73205	+	1.00000i	−0.562628	+	0.150756i
$45$	−1.50000	−	5.59808i	−0.223607	−	0.834512i
$46$	2.36603	−	8.83013i	0.348851	−	1.30193i
$47$	−0.598076	−	1.03590i	−0.0872384	−	0.151101i	0.819104	−	0.573644i	$-0.194471\pi$
$47$	−0.598076	−	1.03590i	−0.0872384	−	0.151101i	−0.906343	+	0.422543i	$0.861138\pi$
$48$	6.00000	+	3.46410i	0.866025	+	0.500000i
$49$	6.46410	−	11.1962i	0.923443	−	1.59945i
$50$	−1.26795	−	1.26795i	−0.179315	−	0.179315i
$51$			6.92820i			0.970143i
$52$	−3.26795	+	3.26795i	−0.453183	+	0.453183i
$53$	5.73205	−	5.73205i	0.787358	−	0.787358i	−0.193703	−	0.981060i	$-0.562050\pi$
$53$	5.73205	−	5.73205i	0.787358	−	0.787358i	0.981060	+	0.193703i	$0.0620497\pi$
$54$	−7.09808	+	1.90192i	−0.965926	+	0.258819i
$55$			3.73205i			0.503230i
$56$	−12.1962	−	3.26795i	−1.62978	−	0.436698i
$57$	5.19615	−	5.19615i	0.688247	−	0.688247i
$58$	−1.26795			−0.166490
$59$	0.401924	+	1.50000i	0.0523260	+	0.195283i	0.987141	−	0.159852i	$-0.0511016\pi$
$59$	0.401924	+	1.50000i	0.0523260	+	0.195283i	−0.934815	+	0.355135i	$0.884435\pi$
$60$	4.73205	−	4.73205i	0.610905	−	0.610905i
$61$	0.571797	−	2.13397i	0.0732111	−	0.273227i	−0.919611	−	0.392831i	$-0.871496\pi$
$61$	0.571797	−	2.13397i	0.0732111	−	0.273227i	0.992822	+	0.119604i	$0.0381624\pi$
$62$	12.5622	+	3.36603i	1.59540	+	0.427486i
$63$	11.5981	−	6.69615i	1.46122	−	0.843636i
$64$			8.00000i			1.00000i
$65$	2.23205	+	3.86603i	0.276852	+	0.479521i
$66$	4.73205			0.582475
$67$	8.33013	−	2.23205i	1.01769	−	0.272688i	0.288849	−	0.957375i	$-0.406727\pi$
$67$	8.33013	−	2.23205i	1.01769	−	0.272688i	0.728838	+	0.684686i	$0.240061\pi$
$68$	−6.92820	+	4.00000i	−0.840168	+	0.485071i
$69$	−5.59808	+	9.69615i	−0.673929	+	1.16728i
$70$	−6.09808	+	10.5622i	−0.728860	+	1.26242i
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$	−6.00000	−	6.00000i	−0.707107	−	0.707107i
$73$			7.46410i			0.873607i	0.899557	+	0.436804i	$0.143889\pi$
$73$			7.46410i			0.873607i	−0.899557	+	0.436804i	$0.856111\pi$
$74$	7.39230	+	4.26795i	0.859338	+	0.496139i
$75$	1.09808	+	1.90192i	0.126795	+	0.219615i
$76$	8.19615	+	2.19615i	0.940163	+	0.251916i
$77$	−8.33013	+	2.23205i	−0.949306	+	0.254366i
$78$	4.90192	−	2.83013i	0.555034	−	0.320449i
$79$	−0.866025	−	1.50000i	−0.0974355	−	0.168763i	0.813187	−	0.582003i	$-0.197731\pi$
$79$	−0.866025	−	1.50000i	−0.0974355	−	0.168763i	−0.910622	+	0.413239i	$0.864397\pi$
$80$	7.46410	+	2.00000i	0.834512	+	0.223607i
$81$	9.00000			1.00000
$82$	−0.294229	+	1.09808i	−0.0324921	+	0.121262i
$83$	3.79423	−	14.1603i	0.416471	−	1.55429i	−0.365401	−	0.930850i	$-0.619068\pi$
$83$	3.79423	−	14.1603i	0.416471	−	1.55429i	0.781872	−	0.623440i	$-0.214265\pi$
$84$	13.3923	+	7.73205i	1.46122	+	0.843636i
$85$	2.00000	+	7.46410i	0.216930	+	0.809595i
$86$		−	9.26795i		−	0.999389i
$87$	1.50000	+	0.401924i	0.160817	+	0.0430908i
$88$	2.73205	+	4.73205i	0.291238	+	0.504438i
$89$			15.8564i			1.68078i	0.541985	+	0.840388i	$0.317673\pi$
$89$			15.8564i			1.68078i	−0.541985	+	0.840388i	$0.682327\pi$
$90$	−7.09808	+	4.09808i	−0.748203	+	0.431975i
$91$	−7.29423	+	7.29423i	−0.764643	+	0.764643i
$92$	−12.9282			−1.34786
$93$	−13.7942	−	7.96410i	−1.43039	−	0.825839i
$94$	−1.19615	+	1.19615i	−0.123374	+	0.123374i
$95$	4.09808	−	7.09808i	0.420454	−	0.728247i
$96$	2.53590	−	9.46410i	0.258819	−	0.965926i
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$	−17.6603	−	4.73205i	−1.78396	−	0.478009i
$99$	−5.59808	−	1.50000i	−0.562628	−	0.150756i
$100$	−1.26795	+	2.19615i	−0.126795	+	0.219615i
$101$	0.500000	+	0.133975i	0.0497519	+	0.0133310i	0.283609	−	0.958940i	$-0.408468\pi$
$101$	0.500000	+	0.133975i	0.0497519	+	0.0133310i	−0.233857	+	0.972271i	$0.575135\pi$
$102$	9.46410	−	2.53590i	0.937086	−	0.251091i
$103$	−13.7942	−	7.96410i	−1.35919	−	0.784726i	−0.369672	−	0.929162i	$-0.620530\pi$
$103$	−13.7942	−	7.96410i	−1.35919	−	0.784726i	−0.989514	+	0.144436i	$0.953863\pi$
$104$	5.66025	+	3.26795i	0.555034	+	0.320449i
$105$	10.5622	−	10.5622i	1.03076	−	1.03076i
$106$	−9.92820	−	5.73205i	−0.964312	−	0.556746i
$107$	9.39230	−	9.39230i	0.907988	−	0.907988i	−0.0881214	−	0.996110i	$-0.528086\pi$
$107$	9.39230	−	9.39230i	0.907988	−	0.907988i	0.996110	+	0.0881214i	$0.0280863\pi$
$108$	5.19615	+	9.00000i	0.500000	+	0.866025i
$109$	−1.73205	−	1.73205i	−0.165900	−	0.165900i	0.619274	−	0.785175i	$-0.287427\pi$
$109$	−1.73205	−	1.73205i	−0.165900	−	0.165900i	−0.785175	+	0.619274i	$0.787427\pi$
$110$	5.09808	−	1.36603i	0.486082	−	0.130245i
$111$	−7.39230	−	7.39230i	−0.701647	−	0.701647i
$112$			17.8564i			1.68727i
$113$	−6.23205	+	10.7942i	−0.586262	+	1.01544i	0.408455	+	0.912779i	$0.366068\pi$
$113$	−6.23205	+	10.7942i	−0.586262	+	1.01544i	−0.994717	+	0.102657i	$0.967266\pi$
$114$	−9.00000	−	5.19615i	−0.842927	−	0.486664i
$115$	−3.23205	+	12.0622i	−0.301390	+	1.12480i
$116$	0.464102	+	1.73205i	0.0430908	+	0.160817i
$117$	−6.69615	+	1.79423i	−0.619060	+	0.165876i
$118$	1.90192	−	1.09808i	0.175086	−	0.101086i
$119$	−15.4641	+	8.92820i	−1.41759	+	0.818447i
$120$	−8.19615	−	4.73205i	−0.748203	−	0.431975i
$121$	−6.29423	−	3.63397i	−0.572203	−	0.330361i
$122$	−3.12436			−0.282866
$123$	0.696152	−	1.20577i	0.0627700	−	0.108721i
$124$		−	18.3923i		−	1.65168i
$125$	8.56218	+	8.56218i	0.765824	+	0.765824i
$126$	−13.3923	−	13.3923i	−1.19308	−	1.19308i
$127$	0.392305			0.0348114			0.0174057	−	0.999849i	$-0.494459\pi$
$127$	0.392305			0.0348114			0.0174057	+	0.999849i	$0.494459\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$	−2.93782	+	10.9641i	−0.258661	+	0.965335i
$130$	4.46410	−	4.46410i	0.391528	−	0.391528i
$131$	−4.86603	+	1.30385i	−0.425147	+	0.113918i	−0.465047	−	0.885286i	$-0.653963\pi$
$131$	−4.86603	+	1.30385i	−0.425147	+	0.113918i	0.0399004	+	0.999204i	$0.487296\pi$
$132$	−1.73205	−	6.46410i	−0.150756	−	0.562628i
$133$	18.2942	+	4.90192i	1.58631	+	0.425051i
$134$	−6.09808	−	10.5622i	−0.526794	−	0.912433i
$135$	9.69615	−	2.59808i	0.834512	−	0.223607i
$136$	8.00000	+	8.00000i	0.685994	+	0.685994i
$137$	0.571797	−	0.330127i	0.0488519	−	0.0282047i	−0.475375	−	0.879783i	$-0.657688\pi$
$137$	0.571797	−	0.330127i	0.0488519	−	0.0282047i	0.524227	+	0.851579i	$0.324354\pi$
$138$	15.2942	+	4.09808i	1.30193	+	0.348851i
$139$	−4.33013	−	16.1603i	−0.367277	−	1.37069i	−0.864308	−	0.502962i	$-0.832243\pi$
$139$	−4.33013	−	16.1603i	−0.367277	−	1.37069i	0.497032	−	0.867732i	$-0.334423\pi$
$140$	16.6603	+	4.46410i	1.40805	+	0.377285i
$141$	1.79423	−	1.03590i	0.151101	−	0.0872384i
$142$	−4.00000	+	1.07180i	−0.335673	+	0.0899432i
$143$	4.46410			0.373307
$144$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$145$	1.73205			0.143839
$146$	10.1962	−	2.73205i	0.843840	−	0.226106i
$147$	19.3923	+	11.1962i	1.59945	+	0.923443i
$148$	3.12436	−	11.6603i	0.256820	−	0.958467i
$149$	−4.30385	−	16.0622i	−0.352585	−	1.31586i	−0.883497	−	0.468438i	$-0.844817\pi$
$149$	−4.30385	−	16.0622i	−0.352585	−	1.31586i	0.530912	−	0.847427i	$-0.321850\pi$
$150$	2.19615	−	2.19615i	0.179315	−	0.179315i
$151$	6.06218	−	3.50000i	0.493333	−	0.284826i	−0.232623	−	0.972567i	$-0.574731\pi$
$151$	6.06218	−	3.50000i	0.493333	−	0.284826i	0.725956	+	0.687741i	$0.241398\pi$
$152$		−	12.0000i		−	0.973329i
$153$	−12.0000			−0.970143
$154$	6.09808	+	10.5622i	0.491397	+	0.851125i
$155$	−17.1603	−	4.59808i	−1.37834	−	0.369326i
$156$	−5.66025	−	5.66025i	−0.453183	−	0.453183i
$157$	3.23205	−	0.866025i	0.257946	−	0.0691164i	−0.127529	−	0.991835i	$-0.540704\pi$
$157$	3.23205	−	0.866025i	0.257946	−	0.0691164i	0.385474	+	0.922719i	$0.374038\pi$
$158$	−1.73205	+	1.73205i	−0.137795	+	0.137795i
$159$	9.92820	+	9.92820i	0.787358	+	0.787358i
$160$		−	10.9282i		−	0.863950i
$161$	−28.8564			−2.27420
$162$	−3.29423	−	12.2942i	−0.258819	−	0.965926i
$163$	−1.92820	−	1.92820i	−0.151029	−	0.151029i	0.627549	−	0.778577i	$-0.284058\pi$
$163$	−1.92820	−	1.92820i	−0.151029	−	0.151029i	−0.778577	+	0.627549i	$0.784058\pi$
$164$	1.60770			0.125540
$165$	−6.46410			−0.503230
$166$	−20.7321			−1.60912
$167$	14.2583	+	8.23205i	1.10334	+	0.637015i	0.937097	−	0.349069i	$-0.113502\pi$
$167$	14.2583	+	8.23205i	1.10334	+	0.637015i	0.166246	+	0.986084i	$0.446835\pi$
$168$	5.66025	−	21.1244i	0.436698	−	1.62978i
$169$	−6.63397	+	3.83013i	−0.510306	+	0.294625i
$170$	9.46410	−	5.46410i	0.725863	−	0.419077i
$171$	9.00000	+	9.00000i	0.688247	+	0.688247i
$172$	−12.6603	+	3.39230i	−0.965335	+	0.258661i
$173$	−2.03590	+	7.59808i	−0.154786	+	0.577671i	0.844337	+	0.535812i	$0.179995\pi$
$173$	−2.03590	+	7.59808i	−0.154786	+	0.577671i	−0.999124	+	0.0418586i	$0.986672\pi$
$174$		−	2.19615i		−	0.166490i
$175$	−2.83013	+	4.90192i	−0.213937	+	0.370551i
$176$	5.46410	−	5.46410i	0.411872	−	0.411872i
$177$	−2.59808	+	0.696152i	−0.195283	+	0.0523260i
$178$	21.6603	−	5.80385i	1.62350	−	0.435017i
$179$	−5.92820	−	5.92820i	−0.443095	−	0.443095i	0.449956	−	0.893051i	$-0.351440\pi$
$179$	−5.92820	−	5.92820i	−0.443095	−	0.443095i	−0.893051	+	0.449956i	$0.851440\pi$
$180$	8.19615	+	8.19615i	0.610905	+	0.610905i
$181$	−7.73205	+	7.73205i	−0.574719	+	0.574719i	−0.933443	−	0.358725i	$-0.883212\pi$
$181$	−7.73205	+	7.73205i	−0.574719	+	0.574719i	0.358725	+	0.933443i	$0.383212\pi$
$182$	12.6340	+	7.29423i	0.936493	+	0.540684i
$183$	3.69615	+	0.990381i	0.273227	+	0.0732111i
$184$	4.73205	+	17.6603i	0.348851	+	1.30193i
$185$	−10.0981	−	5.83013i	−0.742425	−	0.428639i
$186$	−5.83013	+	21.7583i	−0.427486	+	1.59540i
$187$	7.46410	+	2.00000i	0.545829	+	0.146254i
$188$	2.07180	+	1.19615i	0.151101	+	0.0872384i
$189$	11.5981	+	20.0885i	0.843636	+	1.46122i
$190$	−11.1962	−	3.00000i	−0.812254	−	0.217643i
$191$	1.40192	+	2.42820i	0.101440	+	0.175699i	0.912278	−	0.409572i	$-0.134322\pi$
$191$	1.40192	+	2.42820i	0.101440	+	0.175699i	−0.810838	+	0.585270i	$0.800988\pi$
$192$	−13.8564			−1.00000
$193$	2.23205	−	3.86603i	0.160667	−	0.278283i	−0.774441	−	0.632646i	$-0.781969\pi$
$193$	2.23205	−	3.86603i	0.160667	−	0.278283i	0.935108	+	0.354363i	$0.115302\pi$
$194$	−1.00000	+	1.00000i	−0.0717958	+	0.0717958i
$195$	−6.69615	+	3.86603i	−0.479521	+	0.276852i
$196$			25.8564i			1.84689i
$197$	3.53590	−	3.53590i	0.251922	−	0.251922i	−0.569836	−	0.821758i	$-0.692993\pi$
$197$	3.53590	−	3.53590i	0.251922	−	0.251922i	0.821758	+	0.569836i	$0.192993\pi$
$198$			8.19615i			0.582475i
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$	3.46410	+	0.928203i	0.244949	+	0.0656339i
$201$	3.86603	+	14.4282i	0.272688	+	1.01769i
$202$		−	0.732051i		−	0.0515069i
$203$	1.03590	+	3.86603i	0.0727058	+	0.271342i
$204$	−6.92820	−	12.0000i	−0.485071	−	0.840168i
$205$	0.401924	−	1.50000i	0.0280716	−	0.104765i
$206$	−5.83013	+	21.7583i	−0.406204	+	1.51597i
$207$	−16.7942	−	9.69615i	−1.16728	−	0.673929i
$208$	2.39230	−	8.92820i	0.165876	−	0.619060i
$209$	−4.09808	−	7.09808i	−0.283470	−	0.490984i
$210$	−18.2942	−	10.5622i	−1.26242	−	0.728860i
$211$	18.5263	−	4.96410i	1.27540	−	0.341743i	0.443304	−	0.896371i	$-0.353806\pi$
$211$	18.5263	−	4.96410i	1.27540	−	0.341743i	0.832098	+	0.554629i	$0.187140\pi$
$212$	−4.19615	+	15.6603i	−0.288193	+	1.07555i
$213$	5.07180			0.347514
$214$	−16.2679	−	9.39230i	−1.11205	−	0.642045i
$215$			12.6603i			0.863422i
$216$	10.3923	−	10.3923i	0.707107	−	0.707107i
$217$		−	41.0526i		−	2.78683i
$218$	−1.73205	+	3.00000i	−0.117309	+	0.203186i
$219$	−12.9282			−0.873607
$220$	−3.73205	−	6.46410i	−0.251615	−	0.435810i
$221$	8.92820	−	2.39230i	0.600576	−	0.160924i
$222$	−7.39230	+	12.8038i	−0.496139	+	0.859338i
$223$	7.79423	+	13.5000i	0.521940	+	0.904027i	0.999674	+	0.0255224i	$0.00812491\pi$
$223$	7.79423	+	13.5000i	0.521940	+	0.904027i	−0.477734	+	0.878504i	$0.658542\pi$
$224$	24.3923	−	6.53590i	1.62978	−	0.436698i
$225$	−3.29423	+	1.90192i	−0.219615	+	0.126795i
$226$	17.0263	+	4.56218i	1.13257	+	0.303472i
$227$	−5.25833	+	19.6244i	−0.349008	+	1.30251i	0.538852	+	0.842400i	$0.318858\pi$
$227$	−5.25833	+	19.6244i	−0.349008	+	1.30251i	−0.887860	+	0.460114i	$0.847809\pi$
$228$	−3.80385	+	14.1962i	−0.251916	+	0.940163i
$229$	−4.42820	−	16.5263i	−0.292624	−	1.09209i	−0.943086	−	0.332549i	$-0.892091\pi$
$229$	−4.42820	−	16.5263i	−0.292624	−	1.09209i	0.650462	−	0.759539i	$-0.274575\pi$
$230$	17.6603			1.16448
$231$	−3.86603	−	14.4282i	−0.254366	−	0.949306i
$232$	2.19615	−	1.26795i	0.144184	−	0.0832449i
$233$			9.07180i			0.594313i	0.954829	+	0.297157i	$0.0960383\pi$
$233$			9.07180i			0.594313i	−0.954829	+	0.297157i	$0.903962\pi$
$234$	4.90192	+	8.49038i	0.320449	+	0.555034i
$235$	1.63397	−	1.63397i	0.106589	−	0.106589i
$236$	−2.19615	−	2.19615i	−0.142957	−	0.142957i
$237$	2.59808	−	1.50000i	0.168763	−	0.0974355i
$238$	17.8564	+	17.8564i	1.15746	+	1.15746i
$239$	−0.401924	+	0.696152i	−0.0259983	+	0.0450304i	−0.878732	−	0.477316i	$-0.841610\pi$
$239$	−0.401924	+	0.696152i	−0.0259983	+	0.0450304i	0.852734	+	0.522346i	$0.174943\pi$
$240$	−3.46410	+	12.9282i	−0.223607	+	0.834512i
$241$	−2.76795	−	4.79423i	−0.178299	−	0.308823i	0.762999	−	0.646400i	$-0.223726\pi$
$241$	−2.76795	−	4.79423i	−0.178299	−	0.308823i	−0.941298	+	0.337576i	$0.890393\pi$
$242$	−2.66025	+	9.92820i	−0.171008	+	0.638209i
$243$			15.5885i			1.00000i
$244$	1.14359	+	4.26795i	0.0732111	+	0.273227i
$245$	24.1244	+	6.46410i	1.54125	+	0.412976i
$246$	−1.90192	−	0.509619i	−0.121262	−	0.0324921i
$247$	−8.49038	−	4.90192i	−0.540230	−	0.311902i
$248$	−25.1244	+	6.73205i	−1.59540	+	0.427486i
$249$	24.5263	+	6.57180i	1.55429	+	0.416471i
$250$	8.56218	−	14.8301i	0.541520	−	0.937940i
$251$	−13.3923	+	13.3923i	−0.845315	+	0.845315i	−0.989544	−	0.144229i	$-0.953930\pi$
$251$	−13.3923	+	13.3923i	−0.845315	+	0.845315i	0.144229	+	0.989544i	$0.453930\pi$
$252$	−13.3923	+	23.1962i	−0.843636	+	1.46122i
$253$	8.83013	+	8.83013i	0.555145	+	0.555145i
$254$	−0.143594	−	0.535898i	−0.00900986	−	0.0336253i
$255$	−12.9282	+	3.46410i	−0.809595	+	0.216930i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	12.1603	−	21.0622i	0.758536	−	1.31382i	−0.185061	−	0.982727i	$-0.559248\pi$
$257$	12.1603	−	21.0622i	0.758536	−	1.31382i	0.943597	−	0.331096i	$-0.107418\pi$
$258$	16.0526			0.999389
$259$	6.97372	−	26.0263i	0.433326	−	1.61719i
$260$	−7.73205	−	4.46410i	−0.479521	−	0.276852i
$261$	−0.696152	+	2.59808i	−0.0430908	+	0.160817i
$262$	3.56218	+	6.16987i	0.220072	+	0.381176i
$263$	8.59808	−	4.96410i	0.530180	−	0.306100i	−0.210910	−	0.977506i	$-0.567643\pi$
$263$	8.59808	−	4.96410i	0.530180	−	0.306100i	0.741090	+	0.671406i	$0.234309\pi$
$264$	−8.19615	+	4.73205i	−0.504438	+	0.291238i
$265$	13.5622	+	7.83013i	0.833118	+	0.481001i
$266$		−	26.7846i		−	1.64227i
$267$	−27.4641			−1.68078
$268$	−12.1962	+	12.1962i	−0.744999	+	0.744999i
$269$	4.26795	+	4.26795i	0.260221	+	0.260221i	0.825144	−	0.564923i	$-0.191094\pi$
$269$	4.26795	+	4.26795i	0.260221	+	0.260221i	−0.564923	+	0.825144i	$0.691094\pi$
$270$	−7.09808	−	12.2942i	−0.431975	−	0.748203i
$271$	−1.07180			−0.0651070			−0.0325535	−	0.999470i	$-0.510364\pi$
$271$	−1.07180			−0.0651070			−0.0325535	+	0.999470i	$0.510364\pi$
$272$	8.00000	−	13.8564i	0.485071	−	0.840168i
$273$	−12.6340	−	12.6340i	−0.764643	−	0.764643i
$274$	−0.660254	−	0.660254i	−0.0398874	−	0.0398874i
$275$	2.36603	−	0.633975i	0.142677	−	0.0382301i
$276$		−	22.3923i		−	1.34786i
$277$	6.69615	+	1.79423i	0.402333	+	0.107805i	0.454310	−	0.890844i	$-0.349886\pi$
$277$	6.69615	+	1.79423i	0.402333	+	0.107805i	−0.0519775	+	0.998648i	$0.516552\pi$
$278$	−20.4904	+	11.8301i	−1.22893	+	0.709524i
$279$	13.7942	−	23.8923i	0.825839	−	1.43039i
$280$		−	24.3923i		−	1.45772i
$281$	10.0359	−	5.79423i	0.598692	−	0.345655i	−0.169835	−	0.985472i	$-0.554324\pi$
$281$	10.0359	−	5.79423i	0.598692	−	0.345655i	0.768527	+	0.639818i	$0.220990\pi$
$282$	−2.07180	−	2.07180i	−0.123374	−	0.123374i
$283$	3.52628	+	13.1603i	0.209616	+	0.782296i	0.987993	+	0.154499i	$0.0493764\pi$
$283$	3.52628	+	13.1603i	0.209616	+	0.782296i	−0.778377	+	0.627797i	$0.783957\pi$
$284$	2.92820	+	5.07180i	0.173757	+	0.300956i
$285$	12.2942	+	7.09808i	0.728247	+	0.420454i
$286$	−1.63397	−	6.09808i	−0.0966189	−	0.360587i
$287$	3.58846			0.211820
$288$	16.3923	+	4.39230i	0.965926	+	0.258819i
$289$	−1.00000			−0.0588235
$290$	−0.633975	−	2.36603i	−0.0372283	−	0.138938i
$291$	1.50000	−	0.866025i	0.0879316	−	0.0507673i
$292$	−7.46410	−	12.9282i	−0.436804	−	0.756566i
$293$	−0.571797	−	2.13397i	−0.0334047	−	0.124668i	0.947210	−	0.320614i	$-0.103889\pi$
$293$	−0.571797	−	2.13397i	−0.0334047	−	0.124668i	−0.980615	+	0.195945i	$0.937222\pi$
$294$	8.19615	−	30.5885i	0.478009	−	1.78396i
$295$	−2.59808	+	1.50000i	−0.151266	+	0.0873334i
$296$	−17.0718			−0.992278
$297$	2.59808	−	9.69615i	0.150756	−	0.562628i
$298$	−20.3660	+	11.7583i	−1.17977	+	0.681142i
$299$	14.4282	+	3.86603i	0.834405	+	0.223578i
$300$	−3.80385	−	2.19615i	−0.219615	−	0.126795i
$301$	−28.2583	+	7.57180i	−1.62878	+	0.436431i
$302$	−7.00000	−	7.00000i	−0.402805	−	0.402805i
$303$	−0.232051	+	0.866025i	−0.0133310	+	0.0497519i
$304$	−16.3923	+	4.39230i	−0.940163	+	0.251916i
$305$	4.26795			0.244382
$306$	4.39230	+	16.3923i	0.251091	+	0.937086i
$307$	7.92820	+	7.92820i	0.452486	+	0.452486i	0.896179	−	0.443693i	$-0.146332\pi$
$307$	7.92820	+	7.92820i	0.452486	+	0.452486i	−0.443693	+	0.896179i	$0.646332\pi$
$308$	12.1962	−	12.1962i	0.694940	−	0.694940i
$309$	13.7942	−	23.8923i	0.784726	−	1.35919i
$310$			25.1244i			1.42697i
$311$	−9.18653	−	5.30385i	−0.520921	−	0.300754i	0.216391	−	0.976307i	$-0.430572\pi$
$311$	−9.18653	−	5.30385i	−0.520921	−	0.300754i	−0.737311	+	0.675553i	$0.763905\pi$
$312$	−5.66025	+	9.80385i	−0.320449	+	0.555034i
$313$	−25.1603	+	14.5263i	−1.42214	+	0.821074i	−0.996482	−	0.0838094i	$-0.973291\pi$
$313$	−25.1603	+	14.5263i	−1.42214	+	0.821074i	−0.425660	+	0.904883i	$0.639958\pi$
$314$	−2.36603	−	4.09808i	−0.133523	−	0.231268i
$315$	18.2942	+	18.2942i	1.03076	+	1.03076i
$316$	3.00000	+	1.73205i	0.168763	+	0.0974355i
$317$	8.96410	−	33.4545i	0.503474	−	1.87899i	0.0273246	−	0.999627i	$-0.491301\pi$
$317$	8.96410	−	33.4545i	0.503474	−	1.87899i	0.476150	−	0.879364i	$-0.342032\pi$
$318$	9.92820	−	17.1962i	0.556746	−	0.964312i
$319$	0.866025	−	1.50000i	0.0484881	−	0.0839839i
$320$	−14.9282	+	4.00000i	−0.834512	+	0.223607i
$321$	16.2679	+	16.2679i	0.907988	+	0.907988i
$322$	10.5622	+	39.4186i	0.588607	+	2.19671i
$323$	−12.0000	−	12.0000i	−0.667698	−	0.667698i
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$	2.07180	−	2.07180i	0.114923	−	0.114923i
$326$	−1.92820	+	3.33975i	−0.106793	+	0.184971i
$327$	3.00000	−	3.00000i	0.165900	−	0.165900i
$328$	−0.588457	−	2.19615i	−0.0324921	−	0.121262i
$329$	4.62436	+	2.66987i	0.254949	+	0.147195i
$330$	2.36603	+	8.83013i	0.130245	+	0.486082i
$331$	−5.06218	−	1.35641i	−0.278242	−	0.0745548i	0.116999	−	0.993132i	$-0.462672\pi$
$331$	−5.06218	−	1.35641i	−0.278242	−	0.0745548i	−0.395242	+	0.918577i	$0.629339\pi$
$332$	7.58846	+	28.3205i	0.416471	+	1.55429i
$333$	12.8038	−	12.8038i	0.701647	−	0.701647i
$334$	6.02628	−	22.4904i	0.329743	−	1.23062i
$335$	8.33013	+	14.4282i	0.455123	+	0.788297i
$336$	−30.9282			−1.68727
$337$	−9.69615	+	16.7942i	−0.528183	+	0.914840i	0.471277	+	0.881985i	$0.343793\pi$
$337$	−9.69615	+	16.7942i	−0.528183	+	0.914840i	−0.999460	+	0.0328547i	$0.989540\pi$
$338$	7.66025	+	7.66025i	0.416663	+	0.416663i
$339$	−18.6962	−	10.7942i	−1.01544	−	0.586262i
$340$	−10.9282	−	10.9282i	−0.592665	−	0.592665i
$341$	−12.5622	+	12.5622i	−0.680280	+	0.680280i
$342$	9.00000	−	15.5885i	0.486664	−	0.842927i
$343$			26.4641i			1.42893i
$344$	9.26795	+	16.0526i	0.499694	+	0.865496i
$345$	−20.8923	−	5.59808i	−1.12480	−	0.301390i
$346$	11.1244			0.598049
$347$	0.473721	+	1.76795i	0.0254307	+	0.0949085i	0.977475	−	0.211052i	$-0.0676890\pi$
$347$	0.473721	+	1.76795i	0.0254307	+	0.0949085i	−0.952044	+	0.305961i	$0.901022\pi$
$348$	−3.00000	+	0.803848i	−0.160817	+	0.0430908i
$349$	1.03590	−	3.86603i	0.0554504	−	0.206944i	−0.932643	−	0.360802i	$-0.882503\pi$
$349$	1.03590	−	3.86603i	0.0554504	−	0.206944i	0.988093	+	0.153858i	$0.0491698\pi$
$350$	7.73205	+	2.07180i	0.413296	+	0.110742i
$351$	−3.10770	−	11.5981i	−0.165876	−	0.619060i
$352$	−9.46410	−	5.46410i	−0.504438	−	0.291238i
$353$	−11.7679	−	20.3827i	−0.626345	−	1.08486i	−0.988279	−	0.152657i	$-0.951217\pi$
$353$	−11.7679	−	20.3827i	−0.626345	−	1.08486i	0.361934	−	0.932204i	$-0.382116\pi$
$354$	1.90192	+	3.29423i	0.101086	+	0.175086i
$355$	5.46410	−	1.46410i	0.290004	−	0.0777064i
$356$	−15.8564	−	27.4641i	−0.840388	−	1.45559i
$357$	−15.4641	−	26.7846i	−0.818447	−	1.41759i
$358$	−5.92820	+	10.2679i	−0.313315	+	0.542678i
$359$		−	28.9282i		−	1.52677i	−0.645942	−	0.763386i	$-0.723535\pi$
$359$		−	28.9282i		−	1.52677i	0.645942	−	0.763386i	$-0.276465\pi$
$360$	8.19615	−	14.1962i	0.431975	−	0.748203i
$361$		−	1.00000i		−	0.0526316i
$362$	13.3923	+	7.73205i	0.703884	+	0.406388i
$363$	6.29423	−	10.9019i	0.330361	−	0.572203i
$364$	5.33975	−	19.9282i	0.279879	−	1.04452i
$365$	−13.9282	+	3.73205i	−0.729035	+	0.195344i
$366$		−	5.41154i		−	0.282866i
$367$	−17.4545	−	30.2321i	−0.911117	−	1.57810i	−0.812490	−	0.582976i	$-0.801888\pi$
$367$	−17.4545	−	30.2321i	−0.911117	−	1.57810i	−0.0986270	−	0.995124i	$-0.531445\pi$
$368$	22.3923	−	12.9282i	1.16728	−	0.673929i
$369$	2.08846	+	1.20577i	0.108721	+	0.0627700i
$370$	−4.26795	+	15.9282i	−0.221880	+	0.828068i
$371$	−9.36603	+	34.9545i	−0.486260	+	1.81475i
$372$	31.8564			1.65168
$373$	0.428203	+	1.59808i	0.0221715	+	0.0827452i	0.976125	−	0.217209i	$-0.0696953\pi$
$373$	0.428203	+	1.59808i	0.0221715	+	0.0827452i	−0.953954	+	0.299954i	$0.903029\pi$
$374$		−	10.9282i		−	0.565084i
$375$	−14.8301	+	14.8301i	−0.765824	+	0.765824i
$376$	0.875644	−	3.26795i	0.0451579	−	0.168532i
$377$		−	2.07180i		−	0.106703i
$378$	23.1962	−	23.1962i	1.19308	−	1.19308i
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	−0.983209	−	0.182484i	$-0.941586\pi$
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	0.182484	+	0.983209i	$0.441586\pi$
$380$			16.3923i			0.840907i
$381$			0.679492i			0.0348114i
$382$	2.80385	−	2.80385i	0.143457	−	0.143457i
$383$	3.66987	−	6.35641i	0.187522	−	0.324797i	−0.756902	−	0.653529i	$-0.773288\pi$
$383$	3.66987	−	6.35641i	0.187522	−	0.324797i	0.944423	+	0.328732i	$0.106621\pi$
$384$	5.07180	+	18.9282i	0.258819	+	0.965926i
$385$	−8.33013	−	14.4282i	−0.424543	−	0.735329i
$386$	−6.09808	−	1.63397i	−0.310384	−	0.0831671i
$387$	−18.9904	−	5.08846i	−0.965335	−	0.258661i
$388$	1.73205	+	1.00000i	0.0879316	+	0.0507673i
$389$	−8.96410	−	2.40192i	−0.454498	−	0.121782i	0.0243053	−	0.999705i	$-0.492263\pi$
$389$	−8.96410	−	2.40192i	−0.454498	−	0.121782i	−0.478803	+	0.877922i	$0.658929\pi$
$390$	7.73205	+	7.73205i	0.391528	+	0.391528i
$391$	22.3923	+	12.9282i	1.13243	+	0.653807i
$392$	35.3205	−	9.46410i	1.78396	−	0.478009i
$393$	−2.25833	−	8.42820i	−0.113918	−	0.425147i
$394$	−6.12436	−	3.53590i	−0.308541	−	0.178136i
$395$	2.36603	−	2.36603i	0.119048	−	0.119048i
$396$	11.1962	−	3.00000i	0.562628	−	0.150756i
$397$	17.0526	+	17.0526i	0.855843	+	0.855843i	0.990845	−	0.135002i	$-0.0431041\pi$
$397$	17.0526	+	17.0526i	0.855843	+	0.855843i	−0.135002	+	0.990845i	$0.543104\pi$
$398$	−29.8564	+	8.00000i	−1.49657	+	0.401004i
$399$	−8.49038	+	31.6865i	−0.425051	+	1.58631i
$400$		−	5.07180i		−	0.253590i
$401$	−16.1603	+	27.9904i	−0.807005	+	1.39777i	0.107925	+	0.994159i	$0.465579\pi$
$401$	−16.1603	+	27.9904i	−0.807005	+	1.39777i	−0.914929	+	0.403614i	$0.867754\pi$
$402$	18.2942	−	10.5622i	0.912433	−	0.526794i
$403$	−5.50000	+	20.5263i	−0.273975	+	1.02249i
$404$	−1.00000	+	0.267949i	−0.0497519	+	0.0133310i
$405$	4.50000	+	16.7942i	0.223607	+	0.834512i
$406$	4.90192	−	2.83013i	0.243278	−	0.140457i
$407$	−10.0981	+	5.83013i	−0.500543	+	0.288989i
$408$	−13.8564	+	13.8564i	−0.685994	+	0.685994i
$409$	19.6244	+	11.3301i	0.970362	+	0.560239i	0.899347	−	0.437236i	$-0.144043\pi$
$409$	19.6244	+	11.3301i	0.970362	+	0.560239i	0.0710154	+	0.997475i	$0.477376\pi$
$410$	−2.19615			−0.108460
$411$	0.571797	+	0.990381i	0.0282047	+	0.0488519i
$412$	31.8564			1.56945
$413$	−4.90192	−	4.90192i	−0.241208	−	0.241208i
$414$	−7.09808	+	26.4904i	−0.348851	+	1.30193i
$415$	28.3205			1.39020
$416$	−13.0718			−0.640898
$417$	27.9904	−	7.50000i	1.37069	−	0.367277i
$418$	−8.19615	+	8.19615i	−0.400887	+	0.400887i
$419$	18.5263	−	4.96410i	0.905068	−	0.242512i	0.223876	−	0.974618i	$-0.428129\pi$
$419$	18.5263	−	4.96410i	0.905068	−	0.242512i	0.681191	+	0.732105i	$0.261462\pi$
$420$	−7.73205	+	28.8564i	−0.377285	+	1.40805i
$421$	17.8923	+	4.79423i	0.872018	+	0.233656i	0.666960	−	0.745094i	$-0.267595\pi$
$421$	17.8923	+	4.79423i	0.872018	+	0.233656i	0.205058	+	0.978750i	$0.434262\pi$
$422$	−13.5622	−	23.4904i	−0.660196	−	1.14349i
$423$	1.79423	+	3.10770i	0.0872384	+	0.151101i
$424$	22.9282			1.11349
$425$	4.39230	−	2.53590i	0.213058	−	0.123009i
$426$	−1.85641	−	6.92820i	−0.0899432	−	0.335673i
$427$	2.55256	+	9.52628i	0.123527	+	0.461009i
$428$	−6.87564	+	25.6603i	−0.332347	+	1.24034i
$429$			7.73205i			0.373307i
$430$	17.2942	−	4.63397i	0.834002	−	0.223470i
$431$	−3.32051			−0.159943			−0.0799716	−	0.996797i	$-0.525483\pi$
$431$	−3.32051			−0.159943			−0.0799716	+	0.996797i	$0.525483\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	3.60770			0.173375			0.0866874	−	0.996236i	$-0.472372\pi$
$433$	3.60770			0.173375			0.0866874	+	0.996236i	$0.472372\pi$
$434$	−56.0788	+	15.0263i	−2.69187	+	0.721284i
$435$			3.00000i			0.143839i
$436$	4.73205	+	1.26795i	0.226624	+	0.0607238i
$437$	−7.09808	−	26.4904i	−0.339547	−	1.26721i
$438$	4.73205	+	17.6603i	0.226106	+	0.843840i
$439$	−5.93782	+	3.42820i	−0.283397	+	0.163619i	−0.634960	−	0.772545i	$-0.718984\pi$
$439$	−5.93782	+	3.42820i	−0.283397	+	0.163619i	0.351563	+	0.936164i	$0.385650\pi$
$440$	−7.46410	+	7.46410i	−0.355837	+	0.355837i
$441$	−19.3923	+	33.5885i	−0.923443	+	1.59945i
$442$	−6.53590	−	11.3205i	−0.310881	−	0.538462i
$443$	4.33013	+	1.16025i	0.205731	+	0.0551253i	0.360213	−	0.932870i	$-0.382704\pi$
$443$	4.33013	+	1.16025i	0.205731	+	0.0551253i	−0.154482	+	0.987996i	$0.549371\pi$
$444$	20.1962	+	5.41154i	0.958467	+	0.256820i
$445$	−29.5885	+	7.92820i	−1.40263	+	0.375833i
$446$	15.5885	−	15.5885i	0.738135	−	0.738135i
$447$	27.8205	−	7.45448i	1.31586	−	0.352585i
$448$	−17.8564	−	30.9282i	−0.843636	−	1.46122i
$449$	35.3205			1.66688			0.833439	−	0.552612i	$-0.186369\pi$
$449$	35.3205			1.66688			0.833439	+	0.552612i	$0.186369\pi$
$450$	3.80385	+	3.80385i	0.179315	+	0.179315i
$451$	−1.09808	−	1.09808i	−0.0517064	−	0.0517064i
$452$		−	24.9282i		−	1.17252i
$453$	6.06218	+	10.5000i	0.284826	+	0.493333i
$454$	28.7321			1.34846
$455$	−17.2583	−	9.96410i	−0.809083	−	0.467124i
$456$	20.7846			0.973329
$457$	−25.9641	+	14.9904i	−1.21455	+	0.701220i	−0.963747	−	0.266818i	$-0.914028\pi$
$457$	−25.9641	+	14.9904i	−1.21455	+	0.701220i	−0.250802	+	0.968038i	$0.580694\pi$
$458$	−20.9545	+	12.0981i	−0.979139	+	0.565306i
$459$		−	20.7846i		−	0.970143i
$460$	−6.46410	−	24.1244i	−0.301390	−	1.12480i
$461$	−1.23205	+	4.59808i	−0.0573823	+	0.214154i	−0.988664	−	0.150147i	$-0.952025\pi$
$461$	−1.23205	+	4.59808i	−0.0573823	+	0.214154i	0.931281	+	0.364301i	$0.118692\pi$
$462$	−18.2942	+	10.5622i	−0.851125	+	0.491397i
$463$	−5.33013	+	9.23205i	−0.247712	+	0.429050i	−0.962891	−	0.269892i	$-0.913012\pi$
$463$	−5.33013	+	9.23205i	−0.247712	+	0.429050i	0.715179	+	0.698942i	$0.246345\pi$
$464$	−2.53590	−	2.53590i	−0.117726	−	0.117726i
$465$	7.96410	−	29.7224i	0.369326	−	1.37834i
$466$	12.3923	−	3.32051i	0.574062	−	0.153820i
$467$	21.7846	+	21.7846i	1.00807	+	1.00807i	0.999967	+	0.00810436i	$0.00257972\pi$
$467$	21.7846	+	21.7846i	1.00807	+	1.00807i	0.00810436	+	0.999967i	$0.497420\pi$
$468$	9.80385	−	9.80385i	0.453183	−	0.453183i
$469$	−27.2224	+	27.2224i	−1.25702	+	1.25702i
$470$	−2.83013	−	1.63397i	−0.130544	−	0.0753696i
$471$	1.50000	+	5.59808i	0.0691164	+	0.257946i
$472$	−2.19615	+	3.80385i	−0.101086	+	0.175086i
$473$	10.9641	+	6.33013i	0.504130	+	0.291060i
$474$	−3.00000	−	3.00000i	−0.137795	−	0.137795i
$475$	−5.19615	−	1.39230i	−0.238416	−	0.0638833i
$476$	17.8564	−	30.9282i	0.818447	−	1.41759i
$477$	−17.1962	+	17.1962i	−0.787358	+	0.787358i
$478$	1.09808	+	0.294229i	0.0502248	+	0.0134577i
$479$	9.33013	+	16.1603i	0.426304	+	0.738381i	0.996541	−	0.0830995i	$-0.0264819\pi$
$479$	9.33013	+	16.1603i	0.426304	+	0.738381i	−0.570237	+	0.821480i	$0.693149\pi$
$480$	18.9282			0.863950
$481$	−6.97372	+	12.0788i	−0.317974	+	0.550748i
$482$	−5.53590	+	5.53590i	−0.252153	+	0.252153i
$483$		−	49.9808i		−	2.27420i
$484$	14.5359			0.660723
$485$	1.36603	−	1.36603i	0.0620280	−	0.0620280i
$486$	21.2942	−	5.70577i	0.965926	−	0.258819i
$487$		−	6.78461i		−	0.307440i	−0.988114	−	0.153720i	$-0.950875\pi$
$487$		−	6.78461i		−	0.307440i	0.988114	−	0.153720i	$-0.0491254\pi$
$488$	5.41154	−	3.12436i	0.244969	−	0.141433i
$489$	3.33975	−	3.33975i	0.151029	−	0.151029i
$490$		−	35.3205i		−	1.59562i
$491$	−0.133975	−	0.500000i	−0.00604619	−	0.0225647i	0.962837	−	0.270084i	$-0.0870514\pi$
$491$	−0.133975	−	0.500000i	−0.00604619	−	0.0225647i	−0.968883	+	0.247519i	$0.920385\pi$
$492$			2.78461i			0.125540i
$493$	0.928203	−	3.46410i	0.0418042	−	0.156015i
$494$	−3.58846	+	13.3923i	−0.161452	+	0.602548i
$495$		−	11.1962i		−	0.503230i
$496$	18.3923	+	31.8564i	0.825839	+	1.43039i
$497$	6.53590	+	11.3205i	0.293175	+	0.507794i
$498$		−	35.9090i		−	1.60912i
$499$	9.33013	−	2.50000i	0.417674	−	0.111915i	−0.0438606	−	0.999038i	$-0.513966\pi$
$499$	9.33013	−	2.50000i	0.417674	−	0.111915i	0.461534	+	0.887122i	$0.347299\pi$
$500$	−23.3923	−	6.26795i	−1.04614	−	0.280311i
$501$	−14.2583	+	24.6962i	−0.637015	+	1.10334i
$502$	23.1962	+	13.3923i	1.03529	+	0.597728i
$503$			13.8564i			0.617827i	0.951090	+	0.308913i	$0.0999653\pi$
$503$			13.8564i			0.617827i	−0.951090	+	0.308913i	$0.900035\pi$
$504$	36.5885	+	9.80385i	1.62978	+	0.436698i
$505$			1.00000i			0.0444994i
$506$	8.83013	−	15.2942i	0.392547	−	0.679911i
$507$	−6.63397	−	11.4904i	−0.294625	−	0.510306i
$508$	−0.679492	+	0.392305i	−0.0301476	+	0.0174057i
$509$	−4.69615	+	1.25833i	−0.208153	+	0.0557745i	−0.361389	−	0.932415i	$-0.617697\pi$
$509$	−4.69615	+	1.25833i	−0.208153	+	0.0557745i	0.153236	+	0.988190i	$0.451031\pi$
$510$	9.46410	+	16.3923i	0.419077	+	0.725863i
$511$	−16.6603	−	28.8564i	−0.737006	−	1.27653i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−15.5885	+	15.5885i	−0.688247	+	0.688247i
$514$	−33.2224	−	8.90192i	−1.46538	−	0.392647i
$515$	7.96410	−	29.7224i	0.350940	−	1.30973i
$516$	−5.87564	−	21.9282i	−0.258661	−	0.965335i
$517$	−0.598076	−	2.23205i	−0.0263034	−	0.0981655i
$518$	−38.1051			−1.67424
$519$	−13.1603	−	3.52628i	−0.577671	−	0.154786i
$520$	−3.26795	+	12.1962i	−0.143309	+	0.534837i
$521$		−	41.8564i		−	1.83376i	−0.399160	−	0.916881i	$-0.630698\pi$
$521$		−	41.8564i		−	1.83376i	0.399160	−	0.916881i	$-0.369302\pi$
$522$	3.80385			0.166490
$523$	22.1244	−	22.1244i	0.967431	−	0.967431i	−0.0320556	−	0.999486i	$-0.510205\pi$
$523$	22.1244	−	22.1244i	0.967431	−	0.967431i	0.999486	+	0.0320556i	$0.0102054\pi$
$524$	7.12436	−	7.12436i	0.311229	−	0.311229i
$525$	−8.49038	−	4.90192i	−0.370551	−	0.213937i
$526$	−9.92820	−	9.92820i	−0.432890	−	0.432890i
$527$	−18.3923	+	31.8564i	−0.801181	+	1.38769i
$528$	9.46410	+	9.46410i	0.411872	+	0.411872i
$529$	9.39230	+	16.2679i	0.408361	+	0.707302i
$530$	5.73205	−	21.3923i	0.248984	−	0.929222i
$531$	−1.20577	−	4.50000i	−0.0523260	−	0.195283i
$532$	−36.5885	+	9.80385i	−1.58631	+	0.425051i
$533$	−1.79423	−	0.480762i	−0.0777167	−	0.0208241i
$534$	10.0526	+	37.5167i	0.435017	+	1.62350i
$535$	22.2224	+	12.8301i	0.960760	+	0.554695i
$536$	21.1244	+	12.1962i	0.912433	+	0.526794i
$537$	10.2679	−	10.2679i	0.443095	−	0.443095i
$538$	4.26795	−	7.39230i	0.184004	−	0.318705i
$539$	17.6603	−	17.6603i	0.760681	−	0.760681i
$540$	−14.1962	+	14.1962i	−0.610905	+	0.610905i
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	0.306856	−	0.951756i	$-0.400723\pi$
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	−0.951756	+	0.306856i	$0.900723\pi$
$542$	0.392305	+	1.46410i	0.0168509	+	0.0628885i
$543$	−13.3923	−	13.3923i	−0.574719	−	0.574719i
$544$	−21.8564	−	5.85641i	−0.937086	−	0.251091i
$545$	2.36603	−	4.09808i	0.101349	−	0.175542i
$546$	−12.6340	+	21.8827i	−0.540684	+	0.936493i
$547$	−5.74167	+	21.4282i	−0.245496	+	0.916204i	0.727637	+	0.685962i	$0.240618\pi$
$547$	−5.74167	+	21.4282i	−0.245496	+	0.916204i	−0.973133	+	0.230242i	$0.926048\pi$
$548$	−0.660254	+	1.14359i	−0.0282047	+	0.0488519i
$549$	−1.71539	+	6.40192i	−0.0732111	+	0.273227i
$550$	−1.73205	−	3.00000i	−0.0738549	−	0.127920i
$551$	−3.29423	+	1.90192i	−0.140339	+	0.0810247i
$552$	−30.5885	+	8.19615i	−1.30193	+	0.348851i
$553$	6.69615	+	3.86603i	0.284749	+	0.164400i
$554$		−	9.80385i		−	0.416526i
$555$	10.0981	−	17.4904i	0.428639	−	0.742425i
$556$	23.6603	+	23.6603i	1.00342	+	1.00342i
$557$	−23.9808	−	23.9808i	−1.01610	−	1.01610i	−0.999868	−	0.0162292i	$-0.994834\pi$
$557$	−23.9808	−	23.9808i	−1.01610	−	1.01610i	−0.0162292	−	0.999868i	$-0.505166\pi$
$558$	−37.6865	−	10.0981i	−1.59540	−	0.427486i
$559$	15.1436			0.640506
$560$	−33.3205	+	8.92820i	−1.40805	+	0.377285i
$561$	−3.46410	+	12.9282i	−0.146254	+	0.545829i
$562$	−11.5885	−	11.5885i	−0.488830	−	0.488830i
$563$	6.13397	−	1.64359i	0.258516	−	0.0692692i	−0.127233	−	0.991873i	$-0.540610\pi$
$563$	6.13397	−	1.64359i	0.258516	−	0.0692692i	0.385749	+	0.922604i	$0.373943\pi$
$564$	−2.07180	+	3.58846i	−0.0872384	+	0.151101i
$565$	−23.2583	−	6.23205i	−0.978485	−	0.262184i
$566$	16.6865	−	9.63397i	0.701387	−	0.404946i
$567$	−34.7942	+	20.0885i	−1.46122	+	0.843636i
$568$	5.85641	−	5.85641i	0.245729	−	0.245729i
$569$	27.4808	−	15.8660i	1.15205	−	0.665138i	0.202667	−	0.979248i	$-0.435039\pi$
$569$	27.4808	−	15.8660i	1.15205	−	0.665138i	0.949387	+	0.314109i	$0.101706\pi$
$570$	5.19615	−	19.3923i	0.217643	−	0.812254i
$571$	−10.5981	−	39.5526i	−0.443516	−	1.65522i	−0.719826	−	0.694155i	$-0.755778\pi$
$571$	−10.5981	−	39.5526i	−0.443516	−	1.65522i	0.276310	−	0.961068i	$-0.410888\pi$
$572$	−7.73205	+	4.46410i	−0.323293	+	0.186653i
$573$	−4.20577	+	2.42820i	−0.175699	+	0.101440i
$574$	−1.31347	−	4.90192i	−0.0548230	−	0.204602i
$575$	8.19615			0.341803
$576$		−	24.0000i		−	1.00000i
$577$	−25.1769			−1.04813			−0.524064	−	0.851679i	$-0.675585\pi$
$577$	−25.1769			−1.04813			−0.524064	+	0.851679i	$0.675585\pi$
$578$	0.366025	+	1.36603i	0.0152246	+	0.0568192i
$579$	6.69615	+	3.86603i	0.278283	+	0.160667i
$580$	−3.00000	+	1.73205i	−0.124568	+	0.0719195i
$581$	16.9378	+	63.2128i	0.702699	+	2.62251i
$582$	−1.73205	−	1.73205i	−0.0717958	−	0.0717958i
$583$	13.5622	−	7.83013i	0.561688	−	0.324291i
$584$	−14.9282	+	14.9282i	−0.617733	+	0.617733i
$585$	−6.69615	−	11.5981i	−0.276852	−	0.479521i
$586$	−2.70577	+	1.56218i	−0.111774	+	0.0645330i
$587$	−14.7942	−	3.96410i	−0.610623	−	0.163616i	−0.0597617	−	0.998213i	$-0.519034\pi$
$587$	−14.7942	−	3.96410i	−0.610623	−	0.163616i	−0.550861	+	0.834597i	$0.685701\pi$
$588$	−44.7846			−1.84689
$589$	37.6865	−	10.0981i	1.55285	−	0.416084i
$590$	3.00000	+	3.00000i	0.123508	+	0.123508i
$591$	6.12436	+	6.12436i	0.251922	+	0.251922i
$592$	6.24871	+	23.3205i	0.256820	+	0.958467i
$593$	−5.46410			−0.224384			−0.112192	−	0.993687i	$-0.535787\pi$
$593$	−5.46410			−0.224384			−0.112192	+	0.993687i	$0.535787\pi$
$594$	−14.1962			−0.582475
$595$	−24.3923	−	24.3923i	−0.999987	−	0.999987i
$596$	23.5167	+	23.5167i	0.963280	+	0.963280i
$597$	37.8564			1.54936
$598$		−	21.1244i		−	0.863839i
$599$	30.3109	+	17.5000i	1.23847	+	0.715031i	0.968781	−	0.247917i	$-0.0797461\pi$
$599$	30.3109	+	17.5000i	1.23847	+	0.715031i	0.269688	+	0.962948i	$0.413079\pi$
$600$	−1.60770	+	6.00000i	−0.0656339	+	0.244949i
$601$	26.7679	−	15.4545i	1.09189	−	0.630401i	0.157809	−	0.987470i	$-0.449557\pi$
$601$	26.7679	−	15.4545i	1.09189	−	0.630401i	0.934078	+	0.357068i	$0.116224\pi$
$602$	20.6865	+	35.8301i	0.843120	+	1.46033i
$603$	−24.9904	+	6.69615i	−1.01769	+	0.272688i
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$	3.63397	−	13.5622i	0.147742	−	0.551381i
$606$	1.26795			0.0515069
$607$	0.598076	−	1.03590i	0.0242752	−	0.0420458i	−0.853633	−	0.520876i	$-0.825606\pi$
$607$	0.598076	−	1.03590i	0.0242752	−	0.0420458i	0.877908	+	0.478830i	$0.158939\pi$
$608$	12.0000	+	20.7846i	0.486664	+	0.842927i
$609$	−6.69615	+	1.79423i	−0.271342	+	0.0727058i
$610$	−1.56218	−	5.83013i	−0.0632507	−	0.236055i
$611$	−1.95448	−	1.95448i	−0.0790699	−	0.0790699i
$612$	20.7846	−	12.0000i	0.840168	−	0.485071i
$613$	23.5885	−	23.5885i	0.952729	−	0.952729i	−0.0462032	−	0.998932i	$-0.514712\pi$
$613$	23.5885	−	23.5885i	0.952729	−	0.952729i	0.998932	+	0.0462032i	$0.0147122\pi$
$614$	7.92820	−	13.7321i	0.319956	−	0.554180i
$615$	2.59808	+	0.696152i	0.104765	+	0.0280716i
$616$	−21.1244	−	12.1962i	−0.851125	−	0.491397i
$617$	−23.0885	−	13.3301i	−0.929506	−	0.536651i	−0.0428509	−	0.999081i	$-0.513644\pi$
$617$	−23.0885	−	13.3301i	−0.929506	−	0.536651i	−0.886655	+	0.462431i	$0.846977\pi$
$618$	−37.6865	−	10.0981i	−1.51597	−	0.406204i
$619$	7.13397	+	1.91154i	0.286739	+	0.0768314i	0.399322	−	0.916811i	$-0.369246\pi$
$619$	7.13397	+	1.91154i	0.286739	+	0.0768314i	−0.112583	+	0.993642i	$0.535912\pi$
$620$	34.3205	−	9.19615i	1.37834	−	0.369326i
$621$	16.7942	−	29.0885i	0.673929	−	1.16728i
$622$	−3.88269	+	14.4904i	−0.155682	+	0.581011i
$623$	−35.3923	−	61.3013i	−1.41796	−	2.45598i
$624$	15.4641	+	4.14359i	0.619060	+	0.165876i
$625$	−8.52628	+	14.7679i	−0.341051	+	0.590718i
$626$	29.0526	+	29.0526i	1.16117	+	1.16117i
$627$	12.2942	−	7.09808i	0.490984	−	0.283470i
$628$	−4.73205	+	4.73205i	−0.188829	+	0.188829i
$629$	−17.0718	+	17.0718i	−0.680697	+	0.680697i
$630$	18.2942	−	31.6865i	0.728860	−	1.26242i
$631$			16.2487i			0.646851i	0.946254	+	0.323425i	$0.104835\pi$
$631$			16.2487i			0.646851i	−0.946254	+	0.323425i	$0.895165\pi$
$632$	1.26795	−	4.73205i	0.0504363	−	0.188231i
$633$	8.59808	+	32.0885i	0.341743	+	1.27540i
$634$	−48.9808			−1.94527
$635$	0.196152	+	0.732051i	0.00778407	+	0.0290506i
$636$	−27.1244	−	7.26795i	−1.07555	−	0.288193i
$637$	7.73205	−	28.8564i	0.306355	−	1.14333i
$638$	−2.36603	−	0.633975i	−0.0936718	−	0.0250993i
$639$			8.78461i			0.347514i
$640$	10.9282	+	18.9282i	0.431975	+	0.748203i
$641$	9.23205	+	15.9904i	0.364644	+	0.631582i	0.988719	−	0.149782i	$-0.0478573\pi$
$641$	9.23205	+	15.9904i	0.364644	+	0.631582i	−0.624075	+	0.781365i	$0.714524\pi$
$642$	16.2679	−	28.1769i	0.642045	−	1.11205i
$643$	−29.7224	+	7.96410i	−1.17214	+	0.314074i	−0.791804	−	0.610776i	$-0.790858\pi$
$643$	−29.7224	+	7.96410i	−1.17214	+	0.314074i	−0.380334	+	0.924849i	$0.624191\pi$
$644$	49.9808	−	28.8564i	1.96952	−	1.13710i
$645$	−21.9282			−0.863422
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$			25.6077i			1.00674i	0.864070	+	0.503371i	$0.167907\pi$
$647$			25.6077i			1.00674i	−0.864070	+	0.503371i	$0.832093\pi$
$648$	18.0000	+	18.0000i	0.707107	+	0.707107i
$649$			3.00000i			0.117760i
$650$	−3.58846	−	2.07180i	−0.140751	−	0.0812626i
$651$	71.1051			2.78683
$652$	5.26795	+	1.41154i	0.206309	+	0.0552803i
$653$	47.2846	−	12.6699i	1.85039	−	0.495810i	0.850829	−	0.525443i	$-0.176100\pi$
$653$	47.2846	−	12.6699i	1.85039	−	0.495810i	0.999561	+	0.0296324i	$0.00943367\pi$
$654$	−5.19615	−	3.00000i	−0.203186	−	0.117309i
$655$	−4.86603	−	8.42820i	−0.190131	−	0.329317i
$656$	−2.78461	+	1.60770i	−0.108721	+	0.0627700i
$657$		−	22.3923i		−	0.873607i
$658$	1.95448	−	7.29423i	0.0761937	−	0.284359i
$659$	−0.330127	+	1.23205i	−0.0128599	+	0.0479939i	−0.972058	−	0.234742i	$-0.924575\pi$
$659$	−0.330127	+	1.23205i	−0.0128599	+	0.0479939i	0.959198	+	0.282736i	$0.0912421\pi$
$660$	11.1962	−	6.46410i	0.435810	−	0.251615i
$661$	−5.30385	−	19.7942i	−0.206296	−	0.769906i	−0.989051	−	0.147576i	$-0.952853\pi$
$661$	−5.30385	−	19.7942i	−0.206296	−	0.769906i	0.782755	−	0.622330i	$-0.213814\pi$
$662$			7.41154i			0.288058i
$663$	4.14359	+	15.4641i	0.160924	+	0.600576i
$664$	35.9090	−	20.7321i	1.39354	−	0.804560i
$665$			36.5885i			1.41884i
$666$	−22.1769	−	12.8038i	−0.859338	−	0.496139i
$667$	4.09808	−	4.09808i	0.158678	−	0.158678i
$668$	−32.9282			−1.27403
$669$	−23.3827	+	13.5000i	−0.904027	+	0.521940i
$670$	16.6603	−	16.6603i	0.643642	−	0.643642i
$671$	2.13397	−	3.69615i	0.0823812	−	0.142688i
$672$	11.3205	+	42.2487i	0.436698	+	1.62978i
$673$	21.1603	+	36.6506i	0.815668	+	1.41278i	0.908847	+	0.417129i	$0.136964\pi$
$673$	21.1603	+	36.6506i	0.815668	+	1.41278i	−0.0931795	+	0.995649i	$0.529703\pi$
$674$	26.4904	+	7.09808i	1.02037	+	0.273408i
$675$	−3.29423	−	5.70577i	−0.126795	−	0.219615i
$676$	7.66025	−	13.2679i	0.294625	−	0.510306i
$677$	−8.76795	−	2.34936i	−0.336980	−	0.0902934i	0.0863612	−	0.996264i	$-0.472476\pi$
$677$	−8.76795	−	2.34936i	−0.336980	−	0.0902934i	−0.423341	+	0.905970i	$0.639143\pi$
$678$	−7.90192	+	29.4904i	−0.303472	+	1.13257i
$679$	3.86603	+	2.23205i	0.148364	+	0.0856582i
$680$	−10.9282	+	18.9282i	−0.419077	+	0.725863i
$681$	−33.9904	−	9.10770i	−1.30251	−	0.349008i
$682$	21.7583	+	12.5622i	0.833170	+	0.481031i
$683$	15.3923	−	15.3923i	0.588970	−	0.588970i	−0.348382	−	0.937353i	$-0.613269\pi$
$683$	15.3923	−	15.3923i	0.588970	−	0.588970i	0.937353	+	0.348382i	$0.113269\pi$
$684$	−24.5885	−	6.58846i	−0.940163	−	0.251916i
$685$	0.901924	+	0.901924i	0.0344607	+	0.0344607i
$686$	36.1506	−	9.68653i	1.38024	−	0.369834i
$687$	28.6244	−	7.66987i	1.09209	−	0.292624i
$688$	18.5359	−	18.5359i	0.706675	−	0.706675i
$689$	9.36603	−	16.2224i	0.356817	−	0.618025i
$690$			30.5885i			1.16448i
$691$	0.526279	−	1.96410i	0.0200206	−	0.0747179i	−0.955193	−	0.295984i	$-0.904352\pi$
$691$	0.526279	−	1.96410i	0.0200206	−	0.0747179i	0.975213	+	0.221266i	$0.0710190\pi$
$692$	−4.07180	−	15.1962i	−0.154786	−	0.577671i
$693$	24.9904	−	6.69615i	0.949306	−	0.254366i
$694$	2.24167	−	1.29423i	0.0850926	−	0.0491282i
$695$	27.9904	−	16.1603i	1.06174	−	0.612993i
$696$	2.19615	+	3.80385i	0.0832449	+	0.144184i
$697$	−2.78461	−	1.60770i	−0.105475	−	0.0608958i
$698$	−5.66025			−0.214244
$699$	−15.7128			−0.594313
$700$		−	11.3205i		−	0.427875i
$701$	17.0526	+	17.0526i	0.644066	+	0.644066i	0.951553	−	0.307486i	$-0.0994878\pi$
$701$	17.0526	+	17.0526i	0.644066	+	0.644066i	−0.307486	+	0.951553i	$0.599488\pi$
$702$	−14.7058	+	8.49038i	−0.555034	+	0.320449i
$703$	25.6077			0.965813
$704$	−4.00000	+	14.9282i	−0.150756	+	0.562628i
$705$	2.83013	+	2.83013i	0.106589	+	0.106589i
$706$	−23.5359	+	23.5359i	−0.885785	+	0.885785i
$707$	−2.23205	+	0.598076i	−0.0839449	+	0.0224930i
$708$	3.80385	−	3.80385i	0.142957	−	0.142957i
$709$	−37.7487	−	10.1147i	−1.41768	−	0.379867i	−0.533022	−	0.846102i	$-0.678944\pi$
$709$	−37.7487	−	10.1147i	−1.41768	−	0.379867i	−0.884661	+	0.466235i	$0.845610\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$	2.59808	+	4.50000i	0.0974355	+	0.168763i
$712$	−31.7128	+	31.7128i	−1.18849	+	1.18849i
$713$	−51.4808	+	29.7224i	−1.92797	+	1.11311i
$714$	−30.9282	+	30.9282i	−1.15746	+	1.15746i
$715$	2.23205	+	8.33013i	0.0834740	+	0.311529i
$716$	16.1962	+	4.33975i	0.605279	+	0.162184i
$717$	−1.20577	−	0.696152i	−0.0450304	−	0.0259983i
$718$	−39.5167	+	10.5885i	−1.47475	+	0.395158i
$719$	−11.3205			−0.422184			−0.211092	−	0.977466i	$-0.567702\pi$
$719$	−11.3205			−0.422184			−0.211092	+	0.977466i	$0.567702\pi$
$720$	−22.3923	−	6.00000i	−0.834512	−	0.223607i
$721$	71.1051			2.64809
$722$	−1.36603	+	0.366025i	−0.0508382	+	0.0136221i
$723$	8.30385	−	4.79423i	0.308823	−	0.178299i
$724$	5.66025	−	21.1244i	0.210362	−	0.785080i
$725$	−0.294229	−	1.09808i	−0.0109274	−	0.0407815i
$726$	−17.1962	−	4.60770i	−0.638209	−	0.171008i
$727$	−3.06218	+	1.76795i	−0.113570	+	0.0655696i	−0.555709	−	0.831377i	$-0.687553\pi$
$727$	−3.06218	+	1.76795i	−0.113570	+	0.0655696i	0.442139	+	0.896947i	$0.354220\pi$
$728$	−29.1769			−1.08137
$729$	−27.0000			−1.00000
$730$	10.1962	+	17.6603i	0.377377	+	0.653635i
$731$	25.3205	+	6.78461i	0.936513	+	0.250938i
$732$	−7.39230	+	1.98076i	−0.273227	+	0.0732111i
$733$	−31.6244	+	8.47372i	−1.16807	+	0.312984i	−0.790185	−	0.612868i	$-0.790016\pi$
$733$	−31.6244	+	8.47372i	−1.16807	+	0.312984i	−0.377887	+	0.925852i	$0.623349\pi$
$734$	−34.9090	+	34.9090i	−1.28851	+	1.28851i
$735$	−11.1962	+	41.7846i	−0.412976	+	1.54125i
$736$	−25.8564	−	25.8564i	−0.953080	−	0.953080i
$737$	16.6603			0.613688
$738$	0.882686	−	3.29423i	0.0324921	−	0.121262i
$739$	−26.2679	−	26.2679i	−0.966282	−	0.966282i	0.0331677	−	0.999450i	$-0.489440\pi$
$739$	−26.2679	−	26.2679i	−0.966282	−	0.966282i	−0.999450	+	0.0331677i	$0.989440\pi$
$740$	23.3205			0.857279
$741$	8.49038	−	14.7058i	0.311902	−	0.540230i
$742$	51.1769			1.87876
$743$	−25.1147	−	14.5000i	−0.921370	−	0.531953i	−0.0372984	−	0.999304i	$-0.511875\pi$
$743$	−25.1147	−	14.5000i	−0.921370	−	0.531953i	−0.884072	+	0.467351i	$0.845209\pi$
$744$	−11.6603	−	43.5167i	−0.427486	−	1.59540i
$745$	27.8205	−	16.0622i	1.01926	−	0.588473i
$746$	2.02628	−	1.16987i	0.0741874	−	0.0428321i
$747$	−11.3827	+	42.4808i	−0.416471	+	1.55429i
$748$	−14.9282	+	4.00000i	−0.545829	+	0.146254i
$749$	−15.3468	+	57.2750i	−0.560759	+	2.09278i
$750$	25.6865	+	14.8301i	0.937940	+	0.541520i
$751$	−24.7224	+	42.8205i	−0.902134	+	1.56254i	−0.0774160	+	0.996999i	$0.524667\pi$
$751$	−24.7224	+	42.8205i	−0.902134	+	1.56254i	−0.824718	+	0.565544i	$0.808666\pi$
$752$	−4.78461			−0.174477
$753$	−23.1962	−	23.1962i	−0.845315	−	0.845315i
$754$	−2.83013	+	0.758330i	−0.103067	+	0.0276168i
$755$	9.56218	+	9.56218i	0.348003	+	0.348003i
$756$	−40.1769	−	23.1962i	−1.46122	−	0.843636i
$757$	1.53590	−	1.53590i	0.0558232	−	0.0558232i	−0.678644	−	0.734467i	$-0.737432\pi$
$757$	1.53590	−	1.53590i	0.0558232	−	0.0558232i	0.734467	+	0.678644i	$0.237432\pi$
$758$	27.0000	+	15.5885i	0.980684	+	0.566198i
$759$	−15.2942	+	15.2942i	−0.555145	+	0.555145i
$760$	22.3923	−	6.00000i	0.812254	−	0.217643i
$761$	16.2846	+	9.40192i	0.590317	+	0.340819i	0.765223	−	0.643766i	$-0.222629\pi$
$761$	16.2846	+	9.40192i	0.590317	+	0.340819i	−0.174906	+	0.984585i	$0.555962\pi$
$762$	0.928203	−	0.248711i	0.0336253	−	0.00900986i
$763$	10.5622	+	2.83013i	0.382377	+	0.102457i
$764$	−4.85641	−	2.80385i	−0.175699	−	0.101440i
$765$	−6.00000	−	22.3923i	−0.216930	−	0.809595i
$766$	−10.0263	−	2.68653i	−0.362264	−	0.0970684i
$767$	1.79423	+	3.10770i	0.0647858	+	0.112212i
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	−0.922207	−	0.386698i	$-0.873616\pi$
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	0.795993	+	0.605305i	$0.206949\pi$
$770$	−16.6603	+	16.6603i	−0.600394	+	0.600394i
$771$	36.4808	+	21.0622i	1.31382	+	0.758536i
$772$			8.92820i			0.321333i
$773$	−23.5885	+	23.5885i	−0.848418	+	0.848418i	−0.989936	−	0.141518i	$-0.954802\pi$
$773$	−23.5885	+	23.5885i	−0.848418	+	0.848418i	0.141518	+	0.989936i	$0.454802\pi$
$774$			27.8038i			0.999389i
$775$			11.6603i			0.418849i
$776$	0.732051	−	2.73205i	0.0262791	−	0.0980749i
$777$	45.0788	+	12.0788i	1.61719	+	0.433326i
$778$			13.1244i			0.470531i
$779$	0.882686	+	3.29423i	0.0316255	+	0.118028i
$780$	7.73205	−	13.3923i	0.276852	−	0.479521i
$781$	1.46410	−	5.46410i	0.0523897	−	0.195521i
$782$	9.46410	−	35.3205i	0.338436	−	1.26306i
$783$	−4.50000	−	1.20577i	−0.160817	−	0.0430908i
$784$	−25.8564	−	44.7846i	−0.923443	−	1.59945i
$785$	3.23205	+	5.59808i	0.115357	+	0.199804i
$786$	−10.6865	+	6.16987i	−0.381176	+	0.220072i
$787$	−3.06218	+	0.820508i	−0.109155	+	0.0292480i	−0.312983	−	0.949759i	$-0.601328\pi$
$787$	−3.06218	+	0.820508i	−0.109155	+	0.0292480i	0.203828	+	0.979007i	$0.434662\pi$
$788$	−2.58846	+	9.66025i	−0.0922100	+	0.344132i
$789$	8.59808	+	14.8923i	0.306100	+	0.530180i
$790$	−4.09808	−	2.36603i	−0.145803	−	0.0841794i
$791$		−	55.6410i		−	1.97837i
$792$	−8.19615	−	14.1962i	−0.291238	−	0.504438i
$793$		−	5.10512i		−	0.181288i
$794$	17.0526	−	29.5359i	0.605173	−	1.04819i
$795$	−13.5622	+	23.4904i	−0.481001	+	0.833118i
$796$	21.8564	+	37.8564i	0.774680	+	1.34178i
$797$	−41.2846	+	11.0622i	−1.46238	+	0.391842i	−0.900310	−	0.435250i	$-0.856660\pi$
$797$	−41.2846	+	11.0622i	−1.46238	+	0.391842i	−0.562066	+	0.827092i	$0.689993\pi$
$798$	46.3923			1.64227
$799$	−2.39230	−	4.14359i	−0.0846337	−	0.146590i
$800$	−6.92820	+	1.85641i	−0.244949	+	0.0656339i
$801$		−	47.5692i		−	1.68078i
$802$	44.1506	+	11.8301i	1.55901	+	0.417736i
$803$	−3.73205	+	13.9282i	−0.131701	+	0.491516i
$804$	−21.1244	−	21.1244i	−0.744999	−	0.744999i
$805$	−14.4282	−	53.8468i	−0.508527	−	1.89785i
$806$	30.0526			1.05856
$807$	−7.39230	+	7.39230i	−0.260221	+	0.260221i
$808$	0.732051	+	1.26795i	0.0257535	+	0.0446063i
$809$		−	36.6410i		−	1.28823i	−0.764929	−	0.644115i	$-0.777226\pi$
$809$		−	36.6410i		−	1.28823i	0.764929	−	0.644115i	$-0.222774\pi$
$810$	21.2942	−	12.2942i	0.748203	−	0.431975i
$811$	−18.4641	+	18.4641i	−0.648362	+	0.648362i	−0.952597	−	0.304235i	$-0.901599\pi$
$811$	−18.4641	+	18.4641i	−0.648362	+	0.648362i	0.304235	+	0.952597i	$0.401599\pi$
$812$	−5.66025	−	5.66025i	−0.198636	−	0.198636i
$813$		−	1.85641i		−	0.0651070i
$814$	11.6603	+	11.6603i	0.408692	+	0.408692i
$815$	2.63397	−	4.56218i	0.0922641	−	0.159806i
$816$	24.0000	+	13.8564i	0.840168	+	0.485071i
$817$	−13.9019	−	24.0788i	−0.486367	−	0.842412i
$818$	8.29423	−	30.9545i	0.290001	−	1.08230i
$819$	21.8827	−	21.8827i	0.764643	−	0.764643i
$820$	0.803848	+	3.00000i	0.0280716	+	0.104765i
$821$	−40.0167	−	10.7224i	−1.39659	−	0.374215i	−0.519472	−	0.854488i	$-0.673871\pi$
$821$	−40.0167	−	10.7224i	−1.39659	−	0.374215i	−0.877119	+	0.480272i	$0.840538\pi$
$822$	1.14359	−	1.14359i	0.0398874	−	0.0398874i
$823$	−36.6506	−	21.1603i	−1.27756	−	0.737600i	−0.301162	−	0.953573i	$-0.597374\pi$
$823$	−36.6506	−	21.1603i	−1.27756	−	0.737600i	−0.976399	+	0.215973i	$0.930708\pi$
$824$	−11.6603	−	43.5167i	−0.406204	−	1.51597i
$825$	1.09808	+	4.09808i	0.0382301	+	0.142677i
$826$	−4.90192	+	8.49038i	−0.170560	+	0.295418i
$827$	−31.3923	+	31.3923i	−1.09162	+	1.09162i	−0.0962613	+	0.995356i	$0.530688\pi$
$827$	−31.3923	+	31.3923i	−1.09162	+	1.09162i	−0.995356	+	0.0962613i	$0.969312\pi$
$828$	38.7846			1.34786
$829$	−14.2679	−	14.2679i	−0.495546	−	0.495546i	0.414502	−	0.910048i	$-0.363956\pi$
$829$	−14.2679	−	14.2679i	−0.495546	−	0.495546i	−0.910048	+	0.414502i	$0.863956\pi$
$830$	−10.3660	−	38.6865i	−0.359810	−	1.34283i
$831$	−3.10770	+	11.5981i	−0.107805	+	0.402333i
$832$	4.78461	+	17.8564i	0.165876	+	0.619060i
$833$	25.8564	−	44.7846i	0.895871	−	1.55169i
$834$	−20.4904	−	35.4904i	−0.709524	−	1.22893i
$835$	−8.23205	+	30.7224i	−0.284882	+	1.06319i
$836$	14.1962	+	8.19615i	0.490984	+	0.283470i
$837$	41.3827	+	23.8923i	1.43039	+	0.825839i
$838$	−13.5622	−	23.4904i	−0.468498	−	0.811462i
$839$	−6.74167	+	3.89230i	−0.232748	+	0.134377i	−0.611839	−	0.790982i	$-0.709570\pi$
$839$	−6.74167	+	3.89230i	−0.232748	+	0.134377i	0.379091	+	0.925359i	$0.376237\pi$
$840$	42.2487			1.45772
$841$	24.4186	+	14.0981i	0.842020	+	0.486141i
$842$		−	26.1962i		−	0.902779i
$843$	10.0359	+	17.3827i	0.345655	+	0.598692i
$844$	−27.1244	+	27.1244i	−0.933659	+	0.933659i
$845$	−10.4641	−	10.4641i	−0.359976	−	0.359976i
$846$	3.58846	−	3.58846i	0.123374	−	0.123374i
$847$	32.4449			1.11482
$848$	−8.39230	−	31.3205i	−0.288193	−	1.07555i
$849$	−22.7942	+	6.10770i	−0.782296	+	0.209616i
$850$	−5.07180	−	5.07180i	−0.173961	−	0.173961i
$851$	−37.6865	+	10.0981i	−1.29188	+	0.346158i
$852$	−8.78461	+	5.07180i	−0.300956	+	0.173757i
$853$	7.69615	+	2.06218i	0.263511	+	0.0706076i	0.388156	−	0.921594i	$-0.373112\pi$
$853$	7.69615	+	2.06218i	0.263511	+	0.0706076i	−0.124644	+	0.992201i	$0.539779\pi$
$854$	12.0788	−	6.97372i	0.413329	−	0.238636i
$855$	−12.2942	+	21.2942i	−0.420454	+	0.728247i
$856$	37.5692			1.28409
$857$	−14.6436	+	8.45448i	−0.500216	+	0.288800i	−0.728803	−	0.684724i	$-0.759923\pi$
$857$	−14.6436	+	8.45448i	−0.500216	+	0.288800i	0.228587	+	0.973523i	$0.426589\pi$
$858$	10.5622	−	2.83013i	0.360587	−	0.0966189i
$859$	1.20577	+	4.50000i	0.0411404	+	0.153538i	0.983440	−	0.181231i	$-0.0580083\pi$
$859$	1.20577	+	4.50000i	0.0411404	+	0.153538i	−0.942300	+	0.334769i	$0.891342\pi$
$860$	−12.6603	−	21.9282i	−0.431711	−	0.747746i
$861$			6.21539i			0.211820i
$862$	1.21539	+	4.53590i	0.0413964	+	0.154493i
$863$	−26.5359			−0.903292			−0.451646	−	0.892197i	$-0.649163\pi$
$863$	−26.5359			−0.903292			−0.451646	+	0.892197i	$0.649163\pi$
$864$	−7.60770	+	28.3923i	−0.258819	+	0.965926i
$865$	−15.1962			−0.516685
$866$	−1.32051	−	4.92820i	−0.0448727	−	0.167467i
$867$		−	1.73205i		−	0.0588235i
$868$	41.0526	+	71.1051i	1.39341	+	2.41346i
$869$	−0.866025	−	3.23205i	−0.0293779	−	0.109640i
$870$	4.09808	−	1.09808i	0.138938	−	0.0372283i
$871$	17.2583	−	9.96410i	0.584776	−	0.337621i
$872$		−	6.92820i		−	0.234619i
$873$	1.50000	+	2.59808i	0.0507673	+	0.0879316i
$874$	−33.5885	+	19.3923i	−1.13615	+	0.655954i
$875$	−52.2128	−	13.9904i	−1.76512	−	0.472961i
$876$	22.3923	−	12.9282i	0.756566	−	0.436804i
$877$	49.9449	−	13.3827i	1.68652	−	0.451901i	0.717031	−	0.697042i	$-0.245501\pi$
$877$	49.9449	−	13.3827i	1.68652	−	0.451901i	0.969488	+	0.245140i	$0.0788341\pi$
$878$	6.85641	+	6.85641i	0.231393	+	0.231393i
$879$	3.69615	−	0.990381i	0.124668	−	0.0334047i
$880$	12.9282	+	7.46410i	0.435810	+	0.251615i
$881$	31.3205			1.05521			0.527607	−	0.849488i	$-0.323089\pi$
$881$	31.3205			1.05521			0.527607	+	0.849488i	$0.323089\pi$
$882$	52.9808	+	14.1962i	1.78396	+	0.478009i
$883$	−3.00000	−	3.00000i	−0.100958	−	0.100958i	0.654824	−	0.755782i	$-0.272743\pi$
$883$	−3.00000	−	3.00000i	−0.100958	−	0.100958i	−0.755782	+	0.654824i	$0.772743\pi$
$884$	−13.0718	+	13.0718i	−0.439652	+	0.439652i
$885$	−2.59808	−	4.50000i	−0.0873334	−	0.151266i
$886$		−	6.33975i		−	0.212988i
$887$	−8.93782	−	5.16025i	−0.300103	−	0.173264i	0.342386	−	0.939559i	$-0.388765\pi$
$887$	−8.93782	−	5.16025i	−0.300103	−	0.173264i	−0.642489	+	0.766295i	$0.722098\pi$
$888$		−	29.5692i		−	0.992278i
$889$	−1.51666	+	0.875644i	−0.0508672	+	0.0293682i
$890$	21.6603	+	37.5167i	0.726053	+	1.25756i
$891$	16.7942	+	4.50000i	0.562628	+	0.150756i
$892$	−27.0000	−	15.5885i	−0.904027	−	0.521940i
$893$	−1.31347	+	4.90192i	−0.0439535	+	0.164037i
$894$	−20.3660	−	35.2750i	−0.681142	−	1.17977i
$895$	8.09808	−	14.0263i	0.270689	−	0.468847i
$896$	−35.7128	+	35.7128i	−1.19308	+	1.19308i
$897$	−6.69615	+	24.9904i	−0.223578	+	0.834405i
$898$	−12.9282	−	48.2487i	−0.431420	−	1.61008i
$899$	5.83013	+	5.83013i	0.194446	+	0.194446i
$900$	3.80385	−	6.58846i	0.126795	−	0.219615i
$901$	22.9282	−	22.9282i	0.763849	−	0.763849i
$902$	−1.09808	+	1.90192i	−0.0365619	+	0.0633271i
$903$	−13.1147	−	48.9449i	−0.436431	−	1.62878i
$904$	−34.0526	+	9.12436i	−1.13257	+	0.303472i
$905$	−18.2942	−	10.5622i	−0.608121	−	0.351099i
$906$	12.1244	−	12.1244i	0.402805	−	0.402805i
$907$	9.06218	+	2.42820i	0.300905	+	0.0806272i	0.406112	−	0.913823i	$-0.366884\pi$
$907$	9.06218	+	2.42820i	0.300905	+	0.0806272i	−0.105208	+	0.994450i	$0.533551\pi$
$908$	−10.5167	−	39.2487i	−0.349008	−	1.30251i
$909$	−1.50000	−	0.401924i	−0.0497519	−	0.0133310i
$910$	−7.29423	+	27.2224i	−0.241801	+	0.902415i
$911$	−4.13397	−	7.16025i	−0.136965	−	0.237230i	0.789382	−	0.613903i	$-0.210401\pi$
$911$	−4.13397	−	7.16025i	−0.136965	−	0.237230i	−0.926346	+	0.376673i	$0.877068\pi$
$912$	−7.60770	−	28.3923i	−0.251916	−	0.940163i
$913$	14.1603	−	24.5263i	0.468636	−	0.811701i
$914$	29.9808	+	29.9808i	0.991675	+	0.991675i
$915$			7.39230i			0.244382i
$916$	24.1962	+	24.1962i	0.799463	+	0.799463i
$917$	15.9019	−	15.9019i	0.525128	−	0.525128i
$918$	−28.3923	+	7.60770i	−0.937086	+	0.251091i
$919$		−	36.5359i		−	1.20521i	−0.798040	−	0.602604i	$-0.794130\pi$
$919$		−	36.5359i		−	1.20521i	0.798040	−	0.602604i	$-0.205870\pi$
$920$	−30.5885	+	17.6603i	−1.00847	+	0.582241i
$921$	−13.7321	+	13.7321i	−0.452486	+	0.452486i
$922$	6.73205			0.221708
$923$	−1.75129	−	6.53590i	−0.0576444	−	0.215132i
$924$	21.1244	+	21.1244i	0.694940	+	0.694940i
$925$	−1.98076	+	7.39230i	−0.0651271	+	0.243057i
$926$	14.5622	+	3.90192i	0.478543	+	0.128225i
$927$	41.3827	+	23.8923i	1.35919	+	0.784726i
$928$	−2.53590	+	4.39230i	−0.0832449	+	0.144184i
$929$	9.35641	+	16.2058i	0.306974	+	0.531694i	0.977699	−	0.210012i	$-0.0673503\pi$
$929$	9.35641	+	16.2058i	0.306974	+	0.531694i	−0.670725	+	0.741706i	$0.734017\pi$
$930$	−43.5167			−1.42697
$931$	−52.9808	+	14.1962i	−1.73637	+	0.465260i
$932$	−9.07180	−	15.7128i	−0.297157	−	0.514690i
$933$	9.18653	−	15.9115i	0.300754	−	0.520921i
$934$	21.7846	−	37.7321i	0.712814	−	1.23463i
$935$			14.9282i			0.488204i
$936$	−16.9808	−	9.80385i	−0.555034	−	0.320449i
$937$			19.0718i			0.623048i	0.950238	+	0.311524i	$0.100840\pi$
$937$			19.0718i			0.623048i	−0.950238	+	0.311524i	$0.899160\pi$
$938$	47.1506	+	27.2224i	1.53952	+	0.888844i
$939$	−25.1603	−	43.5788i	−0.821074	−	1.42214i
$940$	−1.19615	+	4.46410i	−0.0390142	+	0.145603i
$941$	−34.0885	+	9.13397i	−1.11125	+	0.297759i	−0.767338	−	0.641242i	$-0.778419\pi$
$941$	−34.0885	+	9.13397i	−1.11125	+	0.297759i	−0.343913	+	0.939001i	$0.611753\pi$
$942$	7.09808	−	4.09808i	0.231268	−	0.133523i
$943$	−2.59808	−	4.50000i	−0.0846050	−	0.146540i
$944$	6.00000	+	1.60770i	0.195283	+	0.0523260i
$945$	−31.6865	+	31.6865i	−1.03076	+	1.03076i
$946$	4.63397	−	17.2942i	0.150664	−	0.562284i
$947$	10.9904	−	41.0167i	0.357139	−	1.33286i	−0.520631	−	0.853782i	$-0.674303\pi$
$947$	10.9904	−	41.0167i	0.357139	−	1.33286i	0.877771	−	0.479081i	$-0.159030\pi$
$948$	−3.00000	+	5.19615i	−0.0974355	+	0.168763i
$949$	4.46410	+	16.6603i	0.144911	+	0.540815i
$950$			7.60770i			0.246826i
$951$	57.9449	+	15.5263i	1.87899	+	0.503474i
$952$	−48.7846	−	13.0718i	−1.58112	−	0.423659i
$953$		−	32.5359i		−	1.05394i	−0.849884	−	0.526971i	$-0.823328\pi$
$953$		−	32.5359i		−	1.05394i	0.849884	−	0.526971i	$-0.176672\pi$
$954$	29.7846	+	17.1962i	0.964312	+	0.556746i
$955$	−3.83013	+	3.83013i	−0.123940	+	0.123940i
$956$		−	1.60770i		−	0.0519966i
$957$	2.59808	+	1.50000i	0.0839839	+	0.0484881i
$958$	18.6603	−	18.6603i	0.602885	−	0.602885i
$959$	−1.47372	+	2.55256i	−0.0475889	+	0.0824264i
$960$	−6.92820	−	25.8564i	−0.223607	−	0.834512i
$961$	−26.7846	−	46.3923i	−0.864020	−	1.49653i
$962$	19.0526	+	5.10512i	0.614279	+	0.164596i
$963$	−28.1769	+	28.1769i	−0.907988	+	0.907988i
$964$	9.58846	+	5.53590i	0.308823	+	0.178299i
$965$	8.33013	+	2.23205i	0.268156	+	0.0718523i
$966$	−68.2750	+	18.2942i	−2.19671	+	0.588607i
$967$	27.0622	+	15.6244i	0.870261	+	0.502445i	0.867435	−	0.497551i	$-0.165767\pi$
$967$	27.0622	+	15.6244i	0.870261	+	0.502445i	0.00282602	+	0.999996i	$0.499100\pi$
$968$	−5.32051	−	19.8564i	−0.171008	−	0.638209i
$969$	20.7846	−	20.7846i	0.667698	−	0.667698i
$970$	−2.36603	−	1.36603i	−0.0759685	−	0.0438604i
$971$	−23.9808	+	23.9808i	−0.769579	+	0.769579i	−0.978032	−	0.208453i	$-0.933157\pi$
$971$	−23.9808	+	23.9808i	−0.769579	+	0.769579i	0.208453	+	0.978032i	$0.433157\pi$
$972$	−15.5885	−	27.0000i	−0.500000	−	0.866025i
$973$	52.8109	+	52.8109i	1.69304	+	1.69304i
$974$	−9.26795	+	2.48334i	−0.296964	+	0.0795713i
$975$	3.58846	+	3.58846i	0.114923	+	0.114923i
$976$	−6.24871	−	6.24871i	−0.200016	−	0.200016i
$977$	−24.2846	+	42.0622i	−0.776933	+	1.34569i	0.156768	+	0.987635i	$0.449893\pi$
$977$	−24.2846	+	42.0622i	−0.776933	+	1.34569i	−0.933701	+	0.358053i	$0.883441\pi$
$978$	−5.78461	−	3.33975i	−0.184971	−	0.106793i
$979$	−7.92820	+	29.5885i	−0.253386	+	0.945651i
$980$	−48.2487	+	12.9282i	−1.54125	+	0.412976i
$981$	5.19615	+	5.19615i	0.165900	+	0.165900i
$982$	−0.633975	+	0.366025i	−0.0202309	+	0.0116803i
$983$	1.08142	−	0.624356i	0.0344918	−	0.0199139i	−0.482655	−	0.875811i	$-0.660327\pi$
$983$	1.08142	−	0.624356i	0.0344918	−	0.0199139i	0.517147	+	0.855897i	$0.326994\pi$
$984$	3.80385	−	1.01924i	0.121262	−	0.0324921i
$985$	8.36603	+	4.83013i	0.266564	+	0.153901i
$986$	−5.07180			−0.161519
$987$	−4.62436	+	8.00962i	−0.147195	+	0.254949i
$988$	19.6077			0.623804
$989$	29.9545	+	29.9545i	0.952497	+	0.952497i
$990$	−15.2942	+	4.09808i	−0.486082	+	0.130245i
$991$	−44.3923			−1.41017			−0.705084	−	0.709124i	$-0.749091\pi$
$991$	−44.3923			−1.41017			−0.705084	+	0.709124i	$0.749091\pi$
$992$	36.7846	−	36.7846i	1.16791	−	1.16791i
$993$	2.34936	−	8.76795i	0.0745548	−	0.278242i
$994$	13.0718	−	13.0718i	0.414612	−	0.414612i
$995$	40.7846	−	10.9282i	1.29296	−	0.346447i
$996$	−49.0526	+	13.1436i	−1.55429	+	0.416471i
$997$	3.96410	+	1.06218i	0.125544	+	0.0336395i	0.321044	−	0.947064i	$-0.395966\pi$
$997$	3.96410	+	1.06218i	0.125544	+	0.0336395i	−0.195500	+	0.980704i	$0.562633\pi$
$998$	−6.83013	−	11.8301i	−0.216204	−	0.374476i
$999$	22.1769	+	22.1769i	0.701647	+	0.701647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.x.d.13.1	yes	4
3.2	odd	2		432.2.y.a.253.1		4
4.3	odd	2		576.2.bb.b.337.1		4
9.2	odd	6		432.2.y.d.397.1		4
9.7	even	3		144.2.x.a.61.1	✓	4
12.11	even	2		1728.2.bc.b.145.1		4
16.5	even	4		144.2.x.a.85.1	yes	4
16.11	odd	4		576.2.bb.a.49.1		4
36.7	odd	6		576.2.bb.a.529.1		4
36.11	even	6		1728.2.bc.c.721.1		4
48.5	odd	4		432.2.y.d.37.1		4
48.11	even	4		1728.2.bc.c.1009.1		4
144.11	even	12		1728.2.bc.b.1585.1		4
144.43	odd	12		576.2.bb.b.241.1		4
144.101	odd	12		432.2.y.a.181.1		4
144.133	even	12	inner	144.2.x.d.133.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.61.1	✓	4	9.7	even	3
144.2.x.a.85.1	yes	4	16.5	even	4
144.2.x.d.13.1	yes	4	1.1	even	1	trivial
144.2.x.d.133.1	yes	4	144.133	even	12	inner
432.2.y.a.181.1		4	144.101	odd	12
432.2.y.a.253.1		4	3.2	odd	2
432.2.y.d.37.1		4	48.5	odd	4
432.2.y.d.397.1		4	9.2	odd	6
576.2.bb.a.49.1		4	16.11	odd	4
576.2.bb.a.529.1		4	36.7	odd	6
576.2.bb.b.241.1		4	144.43	odd	12
576.2.bb.b.337.1		4	4.3	odd	2
1728.2.bc.b.145.1		4	12.11	even	2
1728.2.bc.b.1585.1		4	144.11	even	12
1728.2.bc.c.721.1		4	36.11	even	6
1728.2.bc.c.1009.1		4	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +1.73205i q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.500000 + 1.86603i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +1.73205i q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.500000 + 1.86603i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +(2.36603 - 1.36603i) q^{10} +(1.86603 + 0.500000i) q^{11} +(-1.73205 - 3.00000i) q^{12} +(2.23205 - 0.598076i) q^{13} +(4.46410 + 4.46410i) q^{14} +(-3.23205 + 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +4.00000 q^{17} +(1.09808 + 4.09808i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(-2.73205 - 2.73205i) q^{20} +(-3.86603 - 6.69615i) q^{21} -2.73205i q^{22} +(5.59808 + 3.23205i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(1.09808 - 0.633975i) q^{25} +(-1.63397 - 2.83013i) q^{26} -5.19615i q^{27} +(4.46410 - 7.73205i) q^{28} +(0.232051 - 0.866025i) q^{29} +(2.36603 + 4.09808i) q^{30} +(-4.59808 + 7.96410i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-0.866025 + 3.23205i) q^{33} +(-1.46410 - 5.46410i) q^{34} +(-6.09808 - 6.09808i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-4.26795 + 4.26795i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(1.03590 + 3.86603i) q^{39} +(-2.73205 + 4.73205i) q^{40} +(-0.696152 - 0.401924i) q^{41} +(-7.73205 + 7.73205i) q^{42} +(6.33013 + 1.69615i) q^{43} +(-3.73205 + 1.00000i) q^{44} +(-1.50000 - 5.59808i) q^{45} +(2.36603 - 8.83013i) q^{46} +(-0.598076 - 1.03590i) q^{47} +(6.00000 + 3.46410i) q^{48} +(6.46410 - 11.1962i) q^{49} +(-1.26795 - 1.26795i) q^{50} +6.92820i q^{51} +(-3.26795 + 3.26795i) q^{52} +(5.73205 - 5.73205i) q^{53} +(-7.09808 + 1.90192i) q^{54} +3.73205i q^{55} +(-12.1962 - 3.26795i) q^{56} +(5.19615 - 5.19615i) q^{57} -1.26795 q^{58} +(0.401924 + 1.50000i) q^{59} +(4.73205 - 4.73205i) q^{60} +(0.571797 - 2.13397i) q^{61} +(12.5622 + 3.36603i) q^{62} +(11.5981 - 6.69615i) q^{63} +8.00000i q^{64} +(2.23205 + 3.86603i) q^{65} +4.73205 q^{66} +(8.33013 - 2.23205i) q^{67} +(-6.92820 + 4.00000i) q^{68} +(-5.59808 + 9.69615i) q^{69} +(-6.09808 + 10.5622i) q^{70} -2.92820i q^{71} +(-6.00000 - 6.00000i) q^{72} +7.46410i q^{73} +(7.39230 + 4.26795i) q^{74} +(1.09808 + 1.90192i) q^{75} +(8.19615 + 2.19615i) q^{76} +(-8.33013 + 2.23205i) q^{77} +(4.90192 - 2.83013i) q^{78} +(-0.866025 - 1.50000i) q^{79} +(7.46410 + 2.00000i) q^{80} +9.00000 q^{81} +(-0.294229 + 1.09808i) q^{82} +(3.79423 - 14.1603i) q^{83} +(13.3923 + 7.73205i) q^{84} +(2.00000 + 7.46410i) q^{85} -9.26795i q^{86} +(1.50000 + 0.401924i) q^{87} +(2.73205 + 4.73205i) q^{88} +15.8564i q^{89} +(-7.09808 + 4.09808i) q^{90} +(-7.29423 + 7.29423i) q^{91} -12.9282 q^{92} +(-13.7942 - 7.96410i) q^{93} +(-1.19615 + 1.19615i) q^{94} +(4.09808 - 7.09808i) q^{95} +(2.53590 - 9.46410i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-17.6603 - 4.73205i) q^{98} +(-5.59808 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{5} + 6 q^{6} - 12 q^{7} + 8 q^{8} - 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^5 + 6 * q^6 - 12 * q^7 + 8 * q^8 - 12 * q^9	\( 4 q + 2 q^{2} + 2 q^{5} + 6 q^{6} - 12 q^{7} + 8 q^{8} - 12 q^{9} + 6 q^{10} + 4 q^{11} + 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 16 q^{17} - 6 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{28} - 6 q^{29} + 6 q^{30} - 8 q^{31} - 8 q^{32} + 8 q^{34} - 14 q^{35} - 24 q^{37} - 12 q^{38} + 18 q^{39} - 4 q^{40} + 18 q^{41} - 24 q^{42} + 8 q^{43} - 8 q^{44} - 6 q^{45} + 6 q^{46} + 8 q^{47} + 24 q^{48} + 12 q^{49} - 12 q^{50} - 20 q^{52} + 16 q^{53} - 18 q^{54} - 28 q^{56} - 12 q^{58} + 12 q^{59} + 12 q^{60} + 30 q^{61} + 26 q^{62} + 36 q^{63} + 2 q^{65} + 12 q^{66} + 16 q^{67} - 12 q^{69} - 14 q^{70} - 24 q^{72} - 12 q^{74} - 6 q^{75} + 12 q^{76} - 16 q^{77} + 30 q^{78} + 16 q^{80} + 36 q^{81} + 30 q^{82} - 16 q^{83} + 12 q^{84} + 8 q^{85} + 6 q^{87} + 4 q^{88} - 18 q^{90} + 2 q^{91} - 24 q^{92} - 24 q^{93} + 16 q^{94} + 6 q^{95} + 24 q^{96} - 2 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^5 + 6 * q^6 - 12 * q^7 + 8 * q^8 - 12 * q^9 + 6 * q^10 + 4 * q^11 + 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 16 * q^17 - 6 * q^18 - 12 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^23 - 6 * q^25 - 10 * q^26 + 4 * q^28 - 6 * q^29 + 6 * q^30 - 8 * q^31 - 8 * q^32 + 8 * q^34 - 14 * q^35 - 24 * q^37 - 12 * q^38 + 18 * q^39 - 4 * q^40 + 18 * q^41 - 24 * q^42 + 8 * q^43 - 8 * q^44 - 6 * q^45 + 6 * q^46 + 8 * q^47 + 24 * q^48 + 12 * q^49 - 12 * q^50 - 20 * q^52 + 16 * q^53 - 18 * q^54 - 28 * q^56 - 12 * q^58 + 12 * q^59 + 12 * q^60 + 30 * q^61 + 26 * q^62 + 36 * q^63 + 2 * q^65 + 12 * q^66 + 16 * q^67 - 12 * q^69 - 14 * q^70 - 24 * q^72 - 12 * q^74 - 6 * q^75 + 12 * q^76 - 16 * q^77 + 30 * q^78 + 16 * q^80 + 36 * q^81 + 30 * q^82 - 16 * q^83 + 12 * q^84 + 8 * q^85 + 6 * q^87 + 4 * q^88 - 18 * q^90 + 2 * q^91 - 24 * q^92 - 24 * q^93 + 16 * q^94 + 6 * q^95 + 24 * q^96 - 2 * q^97 - 36 * q^98 - 12 * q^99

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