LMFDB - Embedded newform 280.2.bv.c.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(117,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 3, 10]))

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

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

chi := DirichletCharacter("280.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bv (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:	$2.23581125660$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.157
Dual form			280.2.bv.c.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.633975 + 0.366025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.633975 + 0.366025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.36603 - 1.36603i) q^{9} +(1.00000 - 3.00000i) q^{10} +(-2.36603 - 1.36603i) q^{11} +(0.732051 + 0.732051i) q^{12} +(3.00000 - 3.00000i) q^{13} +(-3.09808 + 2.09808i) q^{14} +(0.366025 - 1.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.09808 - 4.09808i) q^{17} +(-2.73205 - 2.73205i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(-4.46410 - 0.267949i) q^{20} +(-1.13397 + 0.767949i) q^{21} +(-1.00000 + 3.73205i) q^{22} +(5.59808 + 1.50000i) q^{23} +(0.732051 - 1.26795i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-5.19615 - 3.00000i) q^{26} +(-2.09808 - 2.09808i) q^{27} +(4.00000 + 3.46410i) q^{28} -2.46410 q^{29} +(-1.63397 - 0.0980762i) q^{30} +(-0.169873 - 0.0980762i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-0.366025 + 1.36603i) q^{33} +(-5.19615 + 3.00000i) q^{34} +(1.46410 - 5.73205i) q^{35} +(-2.73205 + 4.73205i) q^{36} +(-1.73205 - 0.464102i) q^{37} +(3.46410 + 3.46410i) q^{38} +(-1.90192 - 1.09808i) q^{39} +(1.26795 + 6.19615i) q^{40} +6.46410i q^{41} +(1.46410 + 1.26795i) q^{42} +(-0.633975 - 0.633975i) q^{43} +5.46410 q^{44} +(6.09808 + 0.366025i) q^{45} -8.19615i q^{46} +(8.83013 + 2.36603i) q^{47} +(-2.00000 - 0.535898i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(5.56218 - 4.36603i) q^{50} +(-1.90192 + 1.09808i) q^{51} +(-2.19615 + 8.19615i) q^{52} +(11.1962 - 3.00000i) q^{53} +(-2.09808 + 3.63397i) q^{54} +(-2.73205 - 5.46410i) q^{55} +(3.26795 - 6.73205i) q^{56} +(1.26795 + 1.26795i) q^{57} +(0.901924 + 3.36603i) q^{58} +(-4.26795 - 2.46410i) q^{59} +(0.464102 + 2.26795i) q^{60} +(1.96410 + 3.40192i) q^{61} +(-0.0717968 + 0.267949i) q^{62} +(-5.46410 - 4.73205i) q^{63} +8.00000i q^{64} +(9.29423 - 1.90192i) q^{65} +2.00000 q^{66} +(2.13397 + 7.96410i) q^{67} +(6.00000 + 6.00000i) q^{68} -3.00000i q^{69} +(-8.36603 + 0.0980762i) q^{70} +8.53590 q^{71} +(7.46410 + 2.00000i) q^{72} +(-10.8301 + 2.90192i) q^{73} +2.53590i q^{74} +(2.03590 - 1.59808i) q^{75} +(3.46410 - 6.00000i) q^{76} +(-1.36603 + 7.09808i) q^{77} +(-0.803848 + 3.00000i) q^{78} +(0.803848 - 0.464102i) q^{79} +(8.00000 - 4.00000i) q^{80} +(3.33013 - 5.76795i) q^{81} +(8.83013 - 2.36603i) q^{82} +(-7.56218 + 7.56218i) q^{83} +(1.19615 - 2.46410i) q^{84} +(3.00000 - 9.00000i) q^{85} +(-0.633975 + 1.09808i) q^{86} +(0.330127 + 1.23205i) q^{87} +(-2.00000 - 7.46410i) q^{88} +(3.40192 + 5.89230i) q^{89} +(-1.73205 - 8.46410i) q^{90} +(-10.0981 - 4.90192i) q^{91} +(-11.1962 + 3.00000i) q^{92} +(-0.0262794 + 0.0980762i) q^{93} -12.9282i q^{94} +(-7.73205 - 0.464102i) q^{95} +2.92820i q^{96} +(-9.73205 + 9.73205i) q^{97} +(7.92820 + 5.92820i) q^{98} -7.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{5} - 6 q^{6} + 8 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^5 - 6 * q^6 + 8 * q^8 + 6 * q^9	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{5} - 6 q^{6} + 8 q^{8} + 6 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 6 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} + 12 q^{23} - 4 q^{24} - 6 q^{25} + 2 q^{27} + 16 q^{28} + 4 q^{29} - 10 q^{30} - 18 q^{31} - 8 q^{32} + 2 q^{33} - 8 q^{35} - 4 q^{36} - 18 q^{39} + 12 q^{40} - 8 q^{42} - 6 q^{43} + 8 q^{44} + 14 q^{45} + 18 q^{47} - 8 q^{48} - 22 q^{49} - 2 q^{50} - 18 q^{51} + 12 q^{52} + 24 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 12 q^{57} + 14 q^{58} - 24 q^{59} - 12 q^{60} - 6 q^{61} - 28 q^{62} - 8 q^{63} + 6 q^{65} + 8 q^{66} + 12 q^{67} + 24 q^{68} - 30 q^{70} + 48 q^{71} + 16 q^{72} - 26 q^{73} + 22 q^{75} - 2 q^{77} - 24 q^{78} + 24 q^{79} + 32 q^{80} - 4 q^{81} + 18 q^{82} - 6 q^{83} - 16 q^{84} + 12 q^{85} - 6 q^{86} - 16 q^{87} - 8 q^{88} + 24 q^{89} - 30 q^{91} - 24 q^{92} + 38 q^{93} - 24 q^{95} - 32 q^{97} + 4 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^5 - 6 * q^6 + 8 * q^8 + 6 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 6 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 + 12 * q^23 - 4 * q^24 - 6 * q^25 + 2 * q^27 + 16 * q^28 + 4 * q^29 - 10 * q^30 - 18 * q^31 - 8 * q^32 + 2 * q^33 - 8 * q^35 - 4 * q^36 - 18 * q^39 + 12 * q^40 - 8 * q^42 - 6 * q^43 + 8 * q^44 + 14 * q^45 + 18 * q^47 - 8 * q^48 - 22 * q^49 - 2 * q^50 - 18 * q^51 + 12 * q^52 + 24 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 12 * q^57 + 14 * q^58 - 24 * q^59 - 12 * q^60 - 6 * q^61 - 28 * q^62 - 8 * q^63 + 6 * q^65 + 8 * q^66 + 12 * q^67 + 24 * q^68 - 30 * q^70 + 48 * q^71 + 16 * q^72 - 26 * q^73 + 22 * q^75 - 2 * q^77 - 24 * q^78 + 24 * q^79 + 32 * q^80 - 4 * q^81 + 18 * q^82 - 6 * q^83 - 16 * q^84 + 12 * q^85 - 6 * q^86 - 16 * q^87 - 8 * q^88 + 24 * q^89 - 30 * q^91 - 24 * q^92 + 38 * q^93 - 24 * q^95 - 32 * q^97 + 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$	−0.133975	−	0.500000i	−0.0773503	−	0.288675i	0.916406	−	0.400251i	$-0.131077\pi$
$3$	−0.133975	−	0.500000i	−0.0773503	−	0.288675i	−0.993756	+	0.111576i	$0.964410\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$	−0.633975	+	0.366025i	−0.258819	+	0.149429i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	2.36603	−	1.36603i	0.788675	−	0.455342i
$10$	1.00000	−	3.00000i	0.316228	−	0.948683i
$11$	−2.36603	−	1.36603i	−0.713384	−	0.411872i	0.0989291	−	0.995094i	$-0.468458\pi$
$11$	−2.36603	−	1.36603i	−0.713384	−	0.411872i	−0.812313	+	0.583222i	$0.801792\pi$
$12$	0.732051	+	0.732051i	0.211325	+	0.211325i
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	−0.155747	−	0.987797i	$-0.549778\pi$
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	0.987797	+	0.155747i	$0.0497784\pi$
$14$	−3.09808	+	2.09808i	−0.827996	+	0.560734i
$15$	0.366025	−	1.09808i	0.0945074	−	0.283522i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.09808	−	4.09808i	−0.266323	−	0.993929i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.09808	−	4.09808i	−0.266323	−	0.993929i	0.695113	−	0.718900i	$-0.255354\pi$
$18$	−2.73205	−	2.73205i	−0.643951	−	0.643951i
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$	−4.46410	−	0.267949i	−0.998203	−	0.0599153i
$21$	−1.13397	+	0.767949i	−0.247454	+	0.167580i
$22$	−1.00000	+	3.73205i	−0.213201	+	0.795676i
$23$	5.59808	+	1.50000i	1.16728	+	0.312772i	0.789870	−	0.613275i	$-0.210148\pi$
$23$	5.59808	+	1.50000i	1.16728	+	0.312772i	0.377410	+	0.926046i	$0.376815\pi$
$24$	0.732051	−	1.26795i	0.149429	−	0.258819i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	−5.19615	−	3.00000i	−1.01905	−	0.588348i
$27$	−2.09808	−	2.09808i	−0.403775	−	0.403775i
$28$	4.00000	+	3.46410i	0.755929	+	0.654654i
$29$	−2.46410			−0.457572			−0.228786	−	0.973477i	$-0.573476\pi$
$29$	−2.46410			−0.457572			−0.228786	+	0.973477i	$0.573476\pi$
$30$	−1.63397	−	0.0980762i	−0.298322	−	0.0179062i
$31$	−0.169873	−	0.0980762i	−0.0305101	−	0.0176150i	0.484667	−	0.874699i	$-0.338941\pi$
$31$	−0.169873	−	0.0980762i	−0.0305101	−	0.0176150i	−0.515177	+	0.857084i	$0.672274\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$	−0.366025	+	1.36603i	−0.0637168	+	0.237795i
$34$	−5.19615	+	3.00000i	−0.891133	+	0.514496i
$35$	1.46410	−	5.73205i	0.247478	−	0.968893i
$36$	−2.73205	+	4.73205i	−0.455342	+	0.788675i
$37$	−1.73205	−	0.464102i	−0.284747	−	0.0762978i	0.113618	−	0.993524i	$-0.463756\pi$
$37$	−1.73205	−	0.464102i	−0.284747	−	0.0762978i	−0.398366	+	0.917227i	$0.630423\pi$
$38$	3.46410	+	3.46410i	0.561951	+	0.561951i
$39$	−1.90192	−	1.09808i	−0.304552	−	0.175833i
$40$	1.26795	+	6.19615i	0.200480	+	0.979698i
$41$			6.46410i			1.00952i	0.863259	+	0.504762i	$0.168420\pi$
$41$			6.46410i			1.00952i	−0.863259	+	0.504762i	$0.831580\pi$
$42$	1.46410	+	1.26795i	0.225916	+	0.195649i
$43$	−0.633975	−	0.633975i	−0.0966802	−	0.0966802i	0.657112	−	0.753793i	$-0.271778\pi$
$43$	−0.633975	−	0.633975i	−0.0966802	−	0.0966802i	−0.753793	+	0.657112i	$0.771778\pi$
$44$	5.46410			0.823744
$45$	6.09808	+	0.366025i	0.909048	+	0.0545638i
$46$		−	8.19615i		−	1.20846i
$47$	8.83013	+	2.36603i	1.28801	+	0.345120i	0.836903	−	0.547351i	$-0.184364\pi$
$47$	8.83013	+	2.36603i	1.28801	+	0.345120i	0.451103	+	0.892472i	$0.351031\pi$
$48$	−2.00000	−	0.535898i	−0.288675	−	0.0773503i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	5.56218	−	4.36603i	0.786611	−	0.617449i
$51$	−1.90192	+	1.09808i	−0.266323	+	0.153761i
$52$	−2.19615	+	8.19615i	−0.304552	+	1.13660i
$53$	11.1962	−	3.00000i	1.53791	−	0.412082i	0.612320	−	0.790610i	$-0.290236\pi$
$53$	11.1962	−	3.00000i	1.53791	−	0.412082i	0.925590	+	0.378528i	$0.123570\pi$
$54$	−2.09808	+	3.63397i	−0.285512	+	0.494521i
$55$	−2.73205	−	5.46410i	−0.368390	−	0.736779i
$56$	3.26795	−	6.73205i	0.436698	−	0.899608i
$57$	1.26795	+	1.26795i	0.167944	+	0.167944i
$58$	0.901924	+	3.36603i	0.118428	+	0.441981i
$59$	−4.26795	−	2.46410i	−0.555640	−	0.320799i	0.195754	−	0.980653i	$-0.437285\pi$
$59$	−4.26795	−	2.46410i	−0.555640	−	0.320799i	−0.751394	+	0.659854i	$0.770618\pi$
$60$	0.464102	+	2.26795i	0.0599153	+	0.292791i
$61$	1.96410	+	3.40192i	0.251477	+	0.435572i	0.963933	−	0.266146i	$-0.0857502\pi$
$61$	1.96410	+	3.40192i	0.251477	+	0.435572i	−0.712455	+	0.701717i	$0.752417\pi$
$62$	−0.0717968	+	0.267949i	−0.00911820	+	0.0340296i
$63$	−5.46410	−	4.73205i	−0.688412	−	0.596182i
$64$			8.00000i			1.00000i
$65$	9.29423	−	1.90192i	1.15281	−	0.235905i
$66$	2.00000			0.246183
$67$	2.13397	+	7.96410i	0.260706	+	0.972970i	0.964826	+	0.262889i	$0.0846752\pi$
$67$	2.13397	+	7.96410i	0.260706	+	0.972970i	−0.704120	+	0.710081i	$0.748658\pi$
$68$	6.00000	+	6.00000i	0.727607	+	0.727607i
$69$		−	3.00000i		−	0.361158i
$70$	−8.36603	+	0.0980762i	−0.999931	+	0.0117223i
$71$	8.53590			1.01302			0.506512	−	0.862233i	$-0.330934\pi$
$71$	8.53590			1.01302			0.506512	+	0.862233i	$0.330934\pi$
$72$	7.46410	+	2.00000i	0.879653	+	0.235702i
$73$	−10.8301	+	2.90192i	−1.26757	+	0.339644i	−0.829100	−	0.559101i	$-0.811146\pi$
$73$	−10.8301	+	2.90192i	−1.26757	+	0.339644i	−0.438471	+	0.898745i	$0.644480\pi$
$74$			2.53590i			0.294792i
$75$	2.03590	−	1.59808i	0.235085	−	0.184530i
$76$	3.46410	−	6.00000i	0.397360	−	0.688247i
$77$	−1.36603	+	7.09808i	−0.155673	+	0.808901i
$78$	−0.803848	+	3.00000i	−0.0910178	+	0.339683i
$79$	0.803848	−	0.464102i	0.0904399	−	0.0522155i	−0.454098	−	0.890952i	$-0.650038\pi$
$79$	0.803848	−	0.464102i	0.0904399	−	0.0522155i	0.544538	+	0.838736i	$0.316705\pi$
$80$	8.00000	−	4.00000i	0.894427	−	0.447214i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$	8.83013	−	2.36603i	0.975124	−	0.261284i
$83$	−7.56218	+	7.56218i	−0.830057	+	0.830057i	−0.987524	−	0.157467i	$-0.949667\pi$
$83$	−7.56218	+	7.56218i	−0.830057	+	0.830057i	0.157467	+	0.987524i	$0.449667\pi$
$84$	1.19615	−	2.46410i	0.130511	−	0.268856i
$85$	3.00000	−	9.00000i	0.325396	−	0.976187i
$86$	−0.633975	+	1.09808i	−0.0683632	+	0.118409i
$87$	0.330127	+	1.23205i	0.0353933	+	0.132090i
$88$	−2.00000	−	7.46410i	−0.213201	−	0.795676i
$89$	3.40192	+	5.89230i	0.360603	+	0.624583i	0.988060	−	0.154068i	$-0.0492375\pi$
$89$	3.40192	+	5.89230i	0.360603	+	0.624583i	−0.627457	+	0.778651i	$0.715904\pi$
$90$	−1.73205	−	8.46410i	−0.182574	−	0.892195i
$91$	−10.0981	−	4.90192i	−1.05857	−	0.513861i
$92$	−11.1962	+	3.00000i	−1.16728	+	0.312772i
$93$	−0.0262794	+	0.0980762i	−0.00272505	+	0.0101700i
$94$		−	12.9282i		−	1.33344i
$95$	−7.73205	−	0.464102i	−0.793292	−	0.0476158i
$96$			2.92820i			0.298858i
$97$	−9.73205	+	9.73205i	−0.988140	+	0.988140i	−0.999930	−	0.0117904i	$-0.996247\pi$
$97$	−9.73205	+	9.73205i	−0.988140	+	0.988140i	0.0117904	+	0.999930i	$0.496247\pi$
$98$	7.92820	+	5.92820i	0.800869	+	0.598839i
$99$	−7.46410			−0.750170
$100$	−8.00000	−	6.00000i	−0.800000	−	0.600000i
$101$	−7.06218	+	12.2321i	−0.702713	+	1.21713i	0.264798	+	0.964304i	$0.414695\pi$
$101$	−7.06218	+	12.2321i	−0.702713	+	1.21713i	−0.967511	+	0.252831i	$0.918638\pi$
$102$	2.19615	+	2.19615i	0.217451	+	0.217451i
$103$	−1.42820	+	5.33013i	−0.140725	+	0.525193i	0.859183	+	0.511668i	$0.170972\pi$
$103$	−1.42820	+	5.33013i	−0.140725	+	0.525193i	−0.999909	+	0.0135254i	$0.995695\pi$
$104$	12.0000			1.17670
$105$	−3.06218	+	0.0358984i	−0.298838	+	0.00350332i
$106$	−8.19615	−	14.1962i	−0.796081	−	1.37885i
$107$	12.4282	+	3.33013i	1.20148	+	0.321936i	0.803414	−	0.595421i	$-0.203015\pi$
$107$	12.4282	+	3.33013i	1.20148	+	0.321936i	0.398066	+	0.917357i	$0.369681\pi$
$108$	5.73205	+	1.53590i	0.551567	+	0.147792i
$109$	−3.86603	+	6.69615i	−0.370298	+	0.641375i	−0.989611	−	0.143769i	$-0.954078\pi$
$109$	−3.86603	+	6.69615i	−0.370298	+	0.641375i	0.619313	+	0.785144i	$0.287411\pi$
$110$	−6.46410	+	5.73205i	−0.616328	+	0.546530i
$111$			0.928203i			0.0881012i
$112$	−10.3923	−	2.00000i	−0.981981	−	0.188982i
$113$	9.46410	−	9.46410i	0.890308	−	0.890308i	−0.104244	−	0.994552i	$-0.533242\pi$
$113$	9.46410	−	9.46410i	0.890308	−	0.890308i	0.994552	+	0.104244i	$0.0332423\pi$
$114$	1.26795	−	2.19615i	0.118754	−	0.205689i
$115$	8.59808	+	9.69615i	0.801775	+	0.904171i
$116$	4.26795	−	2.46410i	0.396269	−	0.228786i
$117$	3.00000	−	11.1962i	0.277350	−	1.03508i
$118$	−1.80385	+	6.73205i	−0.166058	+	0.619736i
$119$	−9.29423	+	6.29423i	−0.852001	+	0.576991i
$120$	2.92820	−	1.46410i	0.267307	−	0.133654i
$121$	−1.76795	−	3.06218i	−0.160723	−	0.278380i
$122$	3.92820	−	3.92820i	0.355643	−	0.355643i
$123$	3.23205	−	0.866025i	0.291424	−	0.0780869i
$124$	0.392305			0.0352300
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−4.46410	+	9.19615i	−0.397694	+	0.819258i
$127$	−11.0000	−	11.0000i	−0.976092	−	0.976092i	0.0236286	−	0.999721i	$-0.492478\pi$
$127$	−11.0000	−	11.0000i	−0.976092	−	0.976092i	−0.999721	+	0.0236286i	$0.992478\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$	−0.232051	+	0.401924i	−0.0204309	+	0.0353874i
$130$	−6.00000	−	12.0000i	−0.526235	−	1.05247i
$131$	−0.267949	−	0.464102i	−0.0234108	−	0.0405487i	0.854083	−	0.520137i	$-0.174119\pi$
$131$	−0.267949	−	0.464102i	−0.0234108	−	0.0405487i	−0.877493	+	0.479589i	$0.840786\pi$
$132$	−0.732051	−	2.73205i	−0.0637168	−	0.237795i
$133$	6.92820	+	6.00000i	0.600751	+	0.520266i
$134$	10.0981	−	5.83013i	0.872341	−	0.503646i
$135$	−1.33013	−	6.50000i	−0.114479	−	0.559431i
$136$	6.00000	−	10.3923i	0.514496	−	0.891133i
$137$	−8.19615	+	2.19615i	−0.700245	+	0.187630i	−0.591340	−	0.806422i	$-0.701401\pi$
$137$	−8.19615	+	2.19615i	−0.700245	+	0.187630i	−0.108904	+	0.994052i	$0.534734\pi$
$138$	−4.09808	+	1.09808i	−0.348851	+	0.0934745i
$139$		−	4.73205i		−	0.401367i	−0.979656	−	0.200684i	$-0.935684\pi$
$139$		−	4.73205i		−	0.401367i	0.979656	−	0.200684i	$-0.0643163\pi$
$140$	3.19615	+	11.3923i	0.270124	+	0.962825i
$141$		−	4.73205i		−	0.398511i
$142$	−3.12436	−	11.6603i	−0.262190	−	0.978507i
$143$	−11.1962	+	3.00000i	−0.936269	+	0.250873i
$144$		−	10.9282i		−	0.910684i
$145$	−4.59808	−	3.03590i	−0.381849	−	0.252118i
$146$	7.92820	+	13.7321i	0.656143	+	1.13647i
$147$	2.90192	+	2.16987i	0.239347	+	0.178968i
$148$	3.46410	−	0.928203i	0.284747	−	0.0762978i
$149$	−2.66987	−	4.62436i	−0.218725	−	0.378842i	0.735694	−	0.677314i	$-0.236856\pi$
$149$	−2.66987	−	4.62436i	−0.218725	−	0.378842i	−0.954418	+	0.298472i	$0.903523\pi$
$150$	−2.92820	−	2.19615i	−0.239087	−	0.179315i
$151$	−12.0981	+	20.9545i	−0.984527	+	1.70525i	−0.340510	+	0.940241i	$0.610600\pi$
$151$	−12.0981	+	20.9545i	−0.984527	+	1.70525i	−0.644018	+	0.765011i	$0.722734\pi$
$152$	−9.46410	−	2.53590i	−0.767640	−	0.205689i
$153$	−8.19615	−	8.19615i	−0.662620	−	0.662620i
$154$	10.1962	−	0.732051i	0.821629	−	0.0589903i
$155$	−0.196152	−	0.392305i	−0.0157553	−	0.0315107i
$156$	4.39230			0.351666
$157$	−7.56218	+	2.02628i	−0.603527	+	0.161715i	−0.547628	−	0.836722i	$-0.684469\pi$
$157$	−7.56218	+	2.02628i	−0.603527	+	0.161715i	−0.0558992	+	0.998436i	$0.517803\pi$
$158$	−0.928203	−	0.928203i	−0.0738439	−	0.0738439i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	−8.39230	−	9.46410i	−0.663470	−	0.748203i
$161$	−1.09808	−	15.2942i	−0.0865405	−	1.20535i
$162$	−9.09808	−	2.43782i	−0.714812	−	0.191533i
$163$	5.36603	−	20.0263i	0.420300	−	1.56858i	−0.353679	−	0.935367i	$-0.615069\pi$
$163$	5.36603	−	20.0263i	0.420300	−	1.56858i	0.773978	−	0.633212i	$-0.218264\pi$
$164$	−6.46410	−	11.1962i	−0.504762	−	0.874273i
$165$	−2.36603	+	2.09808i	−0.184195	+	0.163335i
$166$	13.0981	+	7.56218i	1.01661	+	0.586939i
$167$	12.2942	−	12.2942i	0.951356	−	0.951356i	−0.0475146	−	0.998871i	$-0.515130\pi$
$167$	12.2942	−	12.2942i	0.951356	−	0.951356i	0.998871	+	0.0475146i	$0.0151301\pi$
$168$	−3.80385	−	0.732051i	−0.293473	−	0.0564789i
$169$		−	5.00000i		−	0.384615i
$170$	−13.3923	−	0.803848i	−1.02714	−	0.0616523i
$171$	−4.73205	+	8.19615i	−0.361869	+	0.626775i
$172$	1.73205	+	0.464102i	0.132068	+	0.0353874i
$173$	−24.1244	−	6.46410i	−1.83414	−	0.491457i	−0.835800	−	0.549034i	$-0.814996\pi$
$173$	−24.1244	−	6.46410i	−1.83414	−	0.491457i	−0.998341	+	0.0575778i	$0.981662\pi$
$174$	1.56218	−	0.901924i	0.118428	−	0.0683747i
$175$	9.79423	−	8.89230i	0.740374	−	0.672195i
$176$	−9.46410	+	5.46410i	−0.713384	+	0.411872i
$177$	−0.660254	+	2.46410i	−0.0496277	+	0.185213i
$178$	6.80385	−	6.80385i	0.509970	−	0.509970i
$179$	12.0263	−	20.8301i	0.898886	−	1.55692i	0.0699665	−	0.997549i	$-0.477711\pi$
$179$	12.0263	−	20.8301i	0.898886	−	1.55692i	0.828920	−	0.559367i	$-0.188956\pi$
$180$	−10.9282	+	5.46410i	−0.814540	+	0.407270i
$181$	22.5167			1.67365			0.836825	−	0.547470i	$-0.184409\pi$
$181$	22.5167			1.67365			0.836825	+	0.547470i	$0.184409\pi$
$182$	−3.00000	+	15.5885i	−0.222375	+	1.15549i
$183$	1.43782	−	1.43782i	0.106287	−	0.106287i
$184$	8.19615	+	14.1962i	0.604228	+	1.04655i
$185$	−2.66025	−	3.00000i	−0.195586	−	0.220564i
$186$	0.143594			0.0105288
$187$	−3.00000	+	11.1962i	−0.219382	+	0.818744i
$188$	−17.6603	+	4.73205i	−1.28801	+	0.345120i
$189$	−3.42820	+	7.06218i	−0.249365	+	0.513698i
$190$	2.19615	+	10.7321i	0.159326	+	0.778585i
$191$	10.5622	+	18.2942i	0.764252	+	1.32372i	0.940641	+	0.339403i	$0.110225\pi$
$191$	10.5622	+	18.2942i	0.764252	+	1.32372i	−0.176389	+	0.984321i	$0.556442\pi$
$192$	4.00000	−	1.07180i	0.288675	−	0.0773503i
$193$	0.562178	+	2.09808i	0.0404664	+	0.151023i	0.983203	−	0.182516i	$-0.0584240\pi$
$193$	0.562178	+	2.09808i	0.0404664	+	0.151023i	−0.942737	+	0.333538i	$0.891757\pi$
$194$	16.8564	+	9.73205i	1.21022	+	0.698721i
$195$	−2.19615	−	4.39230i	−0.157270	−	0.314539i
$196$	5.19615	−	13.0000i	0.371154	−	0.928571i
$197$	12.4641	−	12.4641i	0.888030	−	0.888030i	−0.106303	−	0.994334i	$-0.533901\pi$
$197$	12.4641	−	12.4641i	0.888030	−	0.888030i	0.994334	+	0.106303i	$0.0339014\pi$
$198$	2.73205	+	10.1962i	0.194158	+	0.724609i
$199$	−1.73205	+	3.00000i	−0.122782	+	0.212664i	−0.920864	−	0.389885i	$-0.872515\pi$
$199$	−1.73205	+	3.00000i	−0.122782	+	0.212664i	0.798082	+	0.602549i	$0.205848\pi$
$200$	−5.26795	+	13.1244i	−0.372500	+	0.928032i
$201$	3.69615	−	2.13397i	0.260706	−	0.150519i
$202$	19.2942	+	5.16987i	1.35754	+	0.363751i
$203$	2.13397	+	6.16025i	0.149776	+	0.432365i
$204$	2.19615	−	3.80385i	0.153761	−	0.266323i
$205$	−7.96410	+	12.0622i	−0.556237	+	0.842459i
$206$	7.80385			0.543720
$207$	15.2942	−	4.09808i	1.06302	−	0.284836i
$208$	−4.39230	−	16.3923i	−0.304552	−	1.13660i
$209$	9.46410			0.654646
$210$	1.16987	+	4.16987i	0.0807289	+	0.287749i
$211$			27.4641i			1.89071i	0.326048	+	0.945353i	$0.394283\pi$
$211$			27.4641i			1.89071i	−0.326048	+	0.945353i	$0.605717\pi$
$212$	−16.3923	+	16.3923i	−1.12583	+	1.12583i
$213$	−1.14359	−	4.26795i	−0.0783577	−	0.292435i
$214$		−	18.1962i		−	1.24386i
$215$	−0.401924	−	1.96410i	−0.0274110	−	0.133951i
$216$		−	8.39230i		−	0.571024i
$217$	−0.0980762	+	0.509619i	−0.00665785	+	0.0345952i
$218$	10.5622	+	2.83013i	0.715361	+	0.191680i
$219$	2.90192	+	5.02628i	0.196094	+	0.339644i
$220$	10.1962	+	6.73205i	0.687424	+	0.453875i
$221$	−15.5885	−	9.00000i	−1.04859	−	0.605406i
$222$	1.26795	−	0.339746i	0.0850992	−	0.0228023i
$223$	5.92820	+	5.92820i	0.396982	+	0.396982i	0.877167	−	0.480185i	$-0.159431\pi$
$223$	5.92820	+	5.92820i	0.396982	+	0.396982i	−0.480185	+	0.877167i	$0.659431\pi$
$224$	1.07180	+	14.9282i	0.0716124	+	0.997433i
$225$	10.9282	+	8.19615i	0.728547	+	0.546410i
$226$	−16.3923	−	9.46410i	−1.09040	−	0.629543i
$227$	15.5622	−	4.16987i	1.03290	−	0.276764i	0.297731	−	0.954650i	$-0.403770\pi$
$227$	15.5622	−	4.16987i	1.03290	−	0.276764i	0.735167	+	0.677886i	$0.237104\pi$
$228$	−3.46410	−	0.928203i	−0.229416	−	0.0614718i
$229$	7.39230	−	4.26795i	0.488497	−	0.282034i	−0.235454	−	0.971886i	$-0.575658\pi$
$229$	7.39230	−	4.26795i	0.488497	−	0.282034i	0.723951	+	0.689852i	$0.242324\pi$
$230$	10.0981	−	15.2942i	0.665847	−	1.00847i
$231$	3.73205	−	0.267949i	0.245551	−	0.0176298i
$232$	−4.92820	−	4.92820i	−0.323552	−	0.323552i
$233$	−7.09808	−	1.90192i	−0.465010	−	0.124599i	0.0187040	−	0.999825i	$-0.494046\pi$
$233$	−7.09808	−	1.90192i	−0.465010	−	0.124599i	−0.483714	+	0.875226i	$0.660713\pi$
$234$	−16.3923			−1.07160
$235$	13.5622	+	15.2942i	0.884699	+	0.997685i
$236$	9.85641			0.641597
$237$	−0.339746	−	0.339746i	−0.0220689	−	0.0220689i
$238$	12.0000	+	10.3923i	0.777844	+	0.673633i
$239$			1.26795i			0.0820168i	0.999159	+	0.0410084i	$0.0130570\pi$
$239$			1.26795i			0.0820168i	−0.999159	+	0.0410084i	$0.986943\pi$
$240$	−3.07180	−	3.46410i	−0.198284	−	0.223607i
$241$	−0.339746	−	0.196152i	−0.0218850	−	0.0126353i	0.489018	−	0.872274i	$-0.337355\pi$
$241$	−0.339746	−	0.196152i	−0.0218850	−	0.0126353i	−0.510903	+	0.859639i	$0.670689\pi$
$242$	−3.53590	+	3.53590i	−0.227296	+	0.227296i
$243$	−11.9282	−	3.19615i	−0.765195	−	0.205033i
$244$	−6.80385	−	3.92820i	−0.435572	−	0.251477i
$245$	−15.5981	+	1.30385i	−0.996525	+	0.0832998i
$246$	−2.36603	−	4.09808i	−0.150852	−	0.261284i
$247$	−3.80385	+	14.1962i	−0.242033	+	0.903280i
$248$	−0.143594	−	0.535898i	−0.00911820	−	0.0340296i
$249$	4.79423	+	2.76795i	0.303822	+	0.175412i
$250$	15.7583	−	1.29423i	0.996644	−	0.0818542i
$251$	2.33975			0.147683			0.0738417	−	0.997270i	$-0.476474\pi$
$251$	2.33975			0.147683			0.0738417	+	0.997270i	$0.476474\pi$
$252$	14.1962	+	2.73205i	0.894274	+	0.172103i
$253$	−11.1962	−	11.1962i	−0.703896	−	0.703896i
$254$	−11.0000	+	19.0526i	−0.690201	+	1.19546i
$255$	−4.90192	−	0.294229i	−0.306970	−	0.0184253i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−6.92820	−	1.85641i	−0.432169	−	0.115799i	0.0361749	−	0.999345i	$-0.488483\pi$
$257$	−6.92820	−	1.85641i	−0.432169	−	0.115799i	−0.468344	+	0.883546i	$0.655149\pi$
$258$	0.633975	+	0.169873i	0.0394695	+	0.0105758i
$259$	0.339746	+	4.73205i	0.0211108	+	0.294035i
$260$	−14.1962	+	12.5885i	−0.880408	+	0.780703i
$261$	−5.83013	+	3.36603i	−0.360876	+	0.208352i
$262$	−0.535898	+	0.535898i	−0.0331079	+	0.0331079i
$263$	5.59808	+	20.8923i	0.345192	+	1.28827i	0.892388	+	0.451270i	$0.149029\pi$
$263$	5.59808	+	20.8923i	0.345192	+	1.28827i	−0.547195	+	0.837005i	$0.684305\pi$
$264$	−3.46410	+	2.00000i	−0.213201	+	0.123091i
$265$	24.5885	+	8.19615i	1.51046	+	0.503486i
$266$	5.66025	−	11.6603i	0.347052	−	0.714936i
$267$	2.49038	−	2.49038i	0.152409	−	0.152409i
$268$	−11.6603	−	11.6603i	−0.712263	−	0.712263i
$269$	−9.06218	−	5.23205i	−0.552531	−	0.319004i	0.197611	−	0.980280i	$-0.436682\pi$
$269$	−9.06218	−	5.23205i	−0.552531	−	0.319004i	−0.750142	+	0.661277i	$0.770015\pi$
$270$	−8.39230	+	4.19615i	−0.510739	+	0.255370i
$271$	−10.3923	+	6.00000i	−0.631288	+	0.364474i	−0.781251	−	0.624218i	$-0.785418\pi$
$271$	−10.3923	+	6.00000i	−0.631288	+	0.364474i	0.149963	+	0.988692i	$0.452085\pi$
$272$	−16.3923	−	4.39230i	−0.993929	−	0.266323i
$273$	−1.09808	+	5.70577i	−0.0664586	+	0.345329i
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$	1.63397	−	13.5622i	0.0985324	−	0.817830i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−3.75833	−	14.0263i	−0.225816	−	0.842757i	−0.982076	−	0.188486i	$-0.939642\pi$
$277$	−3.75833	−	14.0263i	−0.225816	−	0.842757i	0.756260	−	0.654272i	$-0.227025\pi$
$278$	−6.46410	+	1.73205i	−0.387691	+	0.103882i
$279$	−0.535898			−0.0320834
$280$	14.3923	−	8.53590i	0.860105	−	0.510117i
$281$	24.2487			1.44656			0.723278	−	0.690557i	$-0.242634\pi$
$281$	24.2487			1.44656			0.723278	+	0.690557i	$0.242634\pi$
$282$	−6.46410	+	1.73205i	−0.384932	+	0.103142i
$283$	−1.43782	−	5.36603i	−0.0854697	−	0.318977i	0.909933	−	0.414755i	$-0.136133\pi$
$283$	−1.43782	−	5.36603i	−0.0854697	−	0.318977i	−0.995403	+	0.0957780i	$0.969466\pi$
$284$	−14.7846	+	8.53590i	−0.877305	+	0.506512i
$285$	0.803848	+	3.92820i	0.0476158	+	0.232687i
$286$	8.19615	+	14.1962i	0.484649	+	0.839436i
$287$	16.1603	−	5.59808i	0.953910	−	0.330444i
$288$	−14.9282	+	4.00000i	−0.879653	+	0.235702i
$289$	−0.866025	+	0.500000i	−0.0509427	+	0.0294118i
$290$	−2.46410	+	7.39230i	−0.144697	+	0.434091i
$291$	6.16987	+	3.56218i	0.361684	+	0.208819i
$292$	15.8564	−	15.8564i	0.927926	−	0.927926i
$293$	6.19615	−	6.19615i	0.361983	−	0.361983i	−0.502560	−	0.864543i	$-0.667608\pi$
$293$	6.19615	−	6.19615i	0.361983	−	0.361983i	0.864543	+	0.502560i	$0.167608\pi$
$294$	1.90192	−	4.75833i	0.110922	−	0.277511i
$295$	−4.92820	−	9.85641i	−0.286931	−	0.573862i
$296$	−2.53590	−	4.39230i	−0.147396	−	0.255298i
$297$	2.09808	+	7.83013i	0.121743	+	0.454350i
$298$	−5.33975	+	5.33975i	−0.309323	+	0.309323i
$299$	21.2942	−	12.2942i	1.23148	−	0.710994i
$300$	−1.92820	+	4.80385i	−0.111325	+	0.277350i
$301$	−1.03590	+	2.13397i	−0.0597082	+	0.123000i
$302$	33.0526	+	8.85641i	1.90196	+	0.509629i
$303$	7.06218	+	1.89230i	0.405712	+	0.108710i
$304$			13.8564i			0.794719i
$305$	−0.526279	+	8.76795i	−0.0301347	+	0.502051i
$306$	−8.19615	+	14.1962i	−0.468543	+	0.811540i
$307$	−21.7583	−	21.7583i	−1.24181	−	1.24181i	−0.959248	−	0.282565i	$-0.908815\pi$
$307$	−21.7583	−	21.7583i	−1.24181	−	1.24181i	−0.282565	−	0.959248i	$-0.591185\pi$
$308$	−4.73205	−	13.6603i	−0.269634	−	0.778365i
$309$	2.85641			0.162495
$310$	−0.464102	+	0.411543i	−0.0263592	+	0.0233741i
$311$	−9.58846	−	5.53590i	−0.543712	−	0.313912i	0.202870	−	0.979206i	$-0.434973\pi$
$311$	−9.58846	−	5.53590i	−0.543712	−	0.313912i	−0.746582	+	0.665294i	$0.768306\pi$
$312$	−1.60770	−	6.00000i	−0.0910178	−	0.339683i
$313$	8.12436	−	30.3205i	0.459216	−	1.71382i	−0.216173	−	0.976355i	$-0.569358\pi$
$313$	8.12436	−	30.3205i	0.459216	−	1.71382i	0.675389	−	0.737461i	$-0.263976\pi$
$314$	5.53590	+	9.58846i	0.312409	+	0.541108i
$315$	−4.36603	−	15.5622i	−0.245998	−	0.876829i
$316$	−0.928203	+	1.60770i	−0.0522155	+	0.0904399i
$317$	−9.83013	−	2.63397i	−0.552115	−	0.147939i	−0.0280336	−	0.999607i	$-0.508925\pi$
$317$	−9.83013	−	2.63397i	−0.552115	−	0.147939i	−0.524081	+	0.851668i	$0.675591\pi$
$318$	−6.00000	+	6.00000i	−0.336463	+	0.336463i
$319$	5.83013	+	3.36603i	0.326424	+	0.188461i
$320$	−9.85641	+	14.9282i	−0.550990	+	0.834512i
$321$		−	6.66025i		−	0.371739i
$322$	−20.4904	+	7.09808i	−1.14188	+	0.395560i
$323$	10.3923	+	10.3923i	0.578243	+	0.578243i
$324$			13.3205i			0.740028i
$325$	19.6865	+	7.90192i	1.09201	+	0.438320i
$326$	−29.3205			−1.62391
$327$	3.86603	+	1.03590i	0.213792	+	0.0572853i
$328$	−12.9282	+	12.9282i	−0.713841	+	0.713841i
$329$	−1.73205	−	24.1244i	−0.0954911	−	1.33002i
$330$	3.73205	+	2.46410i	0.205443	+	0.135644i
$331$	9.29423	−	5.36603i	0.510857	−	0.294943i	−0.222329	−	0.974972i	$-0.571366\pi$
$331$	9.29423	−	5.36603i	0.510857	−	0.294943i	0.733186	+	0.680028i	$0.238033\pi$
$332$	5.53590	−	20.6603i	0.303822	−	1.13388i
$333$	−4.73205	+	1.26795i	−0.259315	+	0.0694832i
$334$	−21.2942	−	12.2942i	−1.16517	−	0.672710i
$335$	−5.83013	+	17.4904i	−0.318534	+	0.955602i
$336$	0.392305	+	5.46410i	0.0214020	+	0.298091i
$337$	−2.33975	−	2.33975i	−0.127454	−	0.127454i	0.640502	−	0.767956i	$-0.278726\pi$
$337$	−2.33975	−	2.33975i	−0.127454	−	0.127454i	−0.767956	+	0.640502i	$0.778726\pi$
$338$	−6.83013	+	1.83013i	−0.371510	+	0.0995458i
$339$	−6.00000	−	3.46410i	−0.325875	−	0.188144i
$340$	3.80385	+	18.5885i	0.206293	+	1.00810i
$341$	0.267949	+	0.464102i	0.0145103	+	0.0251325i
$342$	12.9282	+	3.46410i	0.699077	+	0.187317i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		−	2.53590i		−	0.136726i
$345$	3.69615	−	5.59808i	0.198994	−	0.301390i
$346$			35.3205i			1.89884i
$347$	4.91858	+	18.3564i	0.264043	+	0.985424i	0.962833	+	0.270096i	$0.0870556\pi$
$347$	4.91858	+	18.3564i	0.264043	+	0.985424i	−0.698790	+	0.715327i	$0.746278\pi$
$348$	−1.80385	−	1.80385i	−0.0966964	−	0.0966964i
$349$			31.9808i			1.71189i	0.517066	+	0.855945i	$0.327024\pi$
$349$			31.9808i			1.71189i	−0.517066	+	0.855945i	$0.672976\pi$
$350$	−15.7321	−	10.1244i	−0.840913	−	0.541170i
$351$	−12.5885			−0.671922
$352$	10.9282	+	10.9282i	0.582475	+	0.582475i
$353$	−17.1962	+	4.60770i	−0.915259	+	0.245243i	−0.685558	−	0.728018i	$-0.740442\pi$
$353$	−17.1962	+	4.60770i	−0.915259	+	0.245243i	−0.229701	+	0.973261i	$0.573775\pi$
$354$	3.60770			0.191747
$355$	15.9282	+	10.5167i	0.845381	+	0.558166i
$356$	−11.7846	−	6.80385i	−0.624583	−	0.360603i
$357$	4.39230	+	3.80385i	0.232465	+	0.201321i
$358$	−32.8564	−	8.80385i	−1.73652	−	0.465298i
$359$	1.09808	−	0.633975i	0.0579542	−	0.0334599i	−0.470743	−	0.882270i	$-0.656014\pi$
$359$	1.09808	−	0.633975i	0.0579542	−	0.0334599i	0.528697	+	0.848811i	$0.322681\pi$
$360$	11.4641	+	12.9282i	0.604211	+	0.681376i
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	−8.24167	−	30.7583i	−0.433173	−	1.61662i
$363$	−1.29423	+	1.29423i	−0.0679294	+	0.0679294i
$364$	22.3923	−	1.60770i	1.17368	−	0.0842661i
$365$	−23.7846	−	7.92820i	−1.24494	−	0.414981i
$366$	−2.49038	−	1.43782i	−0.130174	−	0.0751562i
$367$	−4.06218	−	15.1603i	−0.212044	−	0.791359i	−0.987186	−	0.159572i	$-0.948989\pi$
$367$	−4.06218	−	15.1603i	−0.212044	−	0.791359i	0.775142	−	0.631787i	$-0.217678\pi$
$368$	16.3923	−	16.3923i	0.854508	−	0.854508i
$369$	8.83013	+	15.2942i	0.459678	+	0.796186i
$370$	−3.12436	+	4.73205i	−0.162428	+	0.246008i
$371$	−17.1962	−	25.3923i	−0.892780	−	1.31830i
$372$	−0.0525589	−	0.196152i	−0.00272505	−	0.0101700i
$373$	2.53590	−	9.46410i	0.131304	−	0.490033i	−0.868682	−	0.495370i	$-0.835032\pi$
$373$	2.53590	−	9.46410i	0.131304	−	0.490033i	0.999986	+	0.00533769i	$0.00169905\pi$
$374$	16.3923			0.847626
$375$	5.76795	−	0.473721i	0.297856	−	0.0244628i
$376$	12.9282	+	22.3923i	0.666721	+	1.15479i
$377$	−7.39230	+	7.39230i	−0.380723	+	0.380723i
$378$	10.9019	+	2.09808i	0.560734	+	0.107913i
$379$	−18.2487			−0.937373			−0.468687	−	0.883364i	$-0.655273\pi$
$379$	−18.2487			−0.937373			−0.468687	+	0.883364i	$0.655273\pi$
$380$	13.8564	−	6.92820i	0.710819	−	0.355409i
$381$	−4.02628	+	6.97372i	−0.206273	+	0.357275i
$382$	21.1244	−	21.1244i	1.08082	−	1.08082i
$383$	1.33013	−	4.96410i	0.0679663	−	0.253654i	−0.923580	−	0.383405i	$-0.874751\pi$
$383$	1.33013	−	4.96410i	0.0679663	−	0.253654i	0.991547	+	0.129751i	$0.0414179\pi$
$384$	−2.92820	−	5.07180i	−0.149429	−	0.258819i
$385$	−11.2942	+	11.5622i	−0.575607	+	0.589263i
$386$	2.66025	−	1.53590i	0.135403	−	0.0781752i
$387$	−2.36603	−	0.633975i	−0.120272	−	0.0322267i
$388$	7.12436	−	26.5885i	0.361684	−	1.34982i
$389$	14.4641	−	25.0526i	0.733359	−	1.27022i	−0.222080	−	0.975028i	$-0.571285\pi$
$389$	14.4641	−	25.0526i	0.733359	−	1.27022i	0.955440	−	0.295187i	$-0.0953819\pi$
$390$	−5.19615	+	4.60770i	−0.263117	+	0.233320i
$391$		−	24.5885i		−	1.24349i
$392$	−19.6603	−	2.33975i	−0.992993	−	0.118175i
$393$	−0.196152	+	0.196152i	−0.00989458	+	0.00989458i
$394$	−21.5885	−	12.4641i	−1.08761	−	0.627932i
$395$	2.07180	+	0.124356i	0.104243	+	0.00625701i
$396$	12.9282	−	7.46410i	0.649667	−	0.375085i
$397$	−0.758330	+	2.83013i	−0.0380595	+	0.142040i	−0.982341	−	0.187099i	$-0.940092\pi$
$397$	−0.758330	+	2.83013i	−0.0380595	+	0.142040i	0.944282	+	0.329139i	$0.106758\pi$
$398$	4.73205	+	1.26795i	0.237196	+	0.0635566i
$399$	2.07180	−	4.26795i	0.103720	−	0.213665i
$400$	19.8564	+	2.39230i	0.992820	+	0.119615i
$401$	−12.3564	−	21.4019i	−0.617049	−	1.06876i	−0.990021	−	0.140918i	$-0.954994\pi$
$401$	−12.3564	−	21.4019i	−0.617049	−	1.06876i	0.372972	−	0.927843i	$-0.378339\pi$
$402$	−4.26795	−	4.26795i	−0.212866	−	0.212866i
$403$	−0.803848	+	0.215390i	−0.0400425	+	0.0107294i
$404$		−	28.2487i		−	1.40543i
$405$	13.3205	−	6.66025i	0.661901	−	0.330951i
$406$	7.63397	−	5.16987i	0.378868	−	0.256576i
$407$	3.46410	+	3.46410i	0.171709	+	0.171709i
$408$	−6.00000	−	1.60770i	−0.297044	−	0.0795928i
$409$	4.69615	−	8.13397i	0.232210	−	0.402199i	−0.726248	−	0.687432i	$-0.758738\pi$
$409$	4.69615	−	8.13397i	0.232210	−	0.402199i	0.958458	+	0.285233i	$0.0920711\pi$
$410$	19.3923	+	6.46410i	0.957718	+	0.319239i
$411$	2.19615	+	3.80385i	0.108328	+	0.187630i
$412$	−2.85641	−	10.6603i	−0.140725	−	0.525193i
$413$	−2.46410	+	12.8038i	−0.121251	+	0.630036i
$414$	−11.1962	−	19.3923i	−0.550261	−	0.953080i
$415$	−23.4282	+	4.79423i	−1.15005	+	0.235339i
$416$	−20.7846	+	12.0000i	−1.01905	+	0.588348i
$417$	−2.36603	+	0.633975i	−0.115865	+	0.0310459i
$418$	−3.46410	−	12.9282i	−0.169435	−	0.632339i
$419$			18.3923i			0.898523i	0.893400	+	0.449261i	$0.148313\pi$
$419$			18.3923i			0.898523i	−0.893400	+	0.449261i	$0.851687\pi$
$420$	5.26795	−	3.12436i	0.257050	−	0.152453i
$421$		−	5.87564i		−	0.286361i	−0.989697	−	0.143181i	$-0.954267\pi$
$421$		−	5.87564i		−	0.286361i	0.989697	−	0.143181i	$-0.0457330\pi$
$422$	37.5167	−	10.0526i	1.82628	−	0.489351i
$423$	24.1244	−	6.46410i	1.17297	−	0.314295i
$424$	28.3923	+	16.3923i	1.37885	+	0.796081i
$425$	16.6865	−	13.0981i	0.809416	−	0.635350i
$426$	−5.41154	+	3.12436i	−0.262190	+	0.151376i
$427$	6.80385	−	7.85641i	0.329261	−	0.380198i
$428$	−24.8564	+	6.66025i	−1.20148	+	0.321936i
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$	−2.53590	+	1.26795i	−0.122292	+	0.0611459i
$431$	8.36603	−	14.4904i	0.402977	−	0.697977i	−0.591106	−	0.806594i	$-0.701309\pi$
$431$	8.36603	−	14.4904i	0.402977	−	0.697977i	0.994084	+	0.108616i	$0.0346420\pi$
$432$	−11.4641	+	3.07180i	−0.551567	+	0.147792i
$433$	4.53590	+	4.53590i	0.217981	+	0.217981i	0.807647	−	0.589666i	$-0.200741\pi$
$433$	4.53590	+	4.53590i	0.217981	+	0.217981i	−0.589666	+	0.807647i	$0.700741\pi$
$434$	0.732051	−	0.0525589i	0.0351396	−	0.00252291i
$435$	−0.901924	+	2.70577i	−0.0432439	+	0.129732i
$436$		−	15.4641i		−	0.740596i
$437$	−19.3923	+	5.19615i	−0.927660	+	0.248566i
$438$	5.80385	−	5.80385i	0.277319	−	0.277319i
$439$	−14.6603	−	25.3923i	−0.699696	−	1.21191i	−0.968572	−	0.248734i	$-0.919986\pi$
$439$	−14.6603	−	25.3923i	−0.699696	−	1.21191i	0.268876	−	0.963175i	$-0.413348\pi$
$440$	5.46410	−	16.3923i	0.260491	−	0.781472i
$441$	−7.09808	+	17.7583i	−0.338004	+	0.845635i
$442$	−6.58846	+	24.5885i	−0.313381	+	1.16955i
$443$	−5.64359	+	21.0622i	−0.268135	+	1.00069i	0.692168	+	0.721736i	$0.256656\pi$
$443$	−5.64359	+	21.0622i	−0.268135	+	1.00069i	−0.960303	+	0.278958i	$0.910011\pi$
$444$	−0.928203	−	1.60770i	−0.0440506	−	0.0762978i
$445$	−0.911543	+	15.1865i	−0.0432113	+	0.719911i
$446$	5.92820	−	10.2679i	0.280709	−	0.486201i
$447$	−1.95448	+	1.95448i	−0.0924439	+	0.0924439i
$448$	20.0000	−	6.92820i	0.944911	−	0.327327i
$449$			12.8038i			0.604251i	0.953268	+	0.302125i	$0.0976962\pi$
$449$			12.8038i			0.604251i	−0.953268	+	0.302125i	$0.902304\pi$
$450$	7.19615	−	17.9282i	0.339230	−	0.845144i
$451$	8.83013	−	15.2942i	0.415794	−	0.720177i
$452$	−6.92820	+	25.8564i	−0.325875	+	1.21618i
$453$	12.0981	+	3.24167i	0.568417	+	0.152307i
$454$	−11.3923	−	19.7321i	−0.534667	−	0.926071i
$455$	−12.8038	−	21.5885i	−0.600254	−	1.01208i
$456$			5.07180i			0.237509i
$457$	0.0717968	−	0.267949i	0.00335851	−	0.0125341i	−0.964226	−	0.265081i	$-0.914601\pi$
$457$	0.0717968	−	0.267949i	0.00335851	−	0.0125341i	0.967585	+	0.252547i	$0.0812681\pi$
$458$	−8.53590	−	8.53590i	−0.398856	−	0.398856i
$459$	−6.29423	+	10.9019i	−0.293789	+	0.508858i
$460$	−24.5885	−	8.19615i	−1.14644	−	0.382148i
$461$	39.8564			1.85630			0.928149	−	0.372209i	$-0.121400\pi$
$461$	39.8564			1.85630			0.928149	+	0.372209i	$0.121400\pi$
$462$	−1.73205	−	5.00000i	−0.0805823	−	0.232621i
$463$	−7.83013	+	7.83013i	−0.363897	+	0.363897i	−0.865245	−	0.501349i	$-0.832837\pi$
$463$	−7.83013	+	7.83013i	−0.363897	+	0.363897i	0.501349	+	0.865245i	$0.332837\pi$
$464$	−4.92820	+	8.53590i	−0.228786	+	0.396269i
$465$	−0.169873	+	0.150635i	−0.00787767	+	0.00698554i
$466$			10.3923i			0.481414i
$467$	−2.76795	+	10.3301i	−0.128085	+	0.478021i	−0.999931	−	0.0117598i	$-0.996257\pi$
$467$	−2.76795	+	10.3301i	−0.128085	+	0.478021i	0.871845	+	0.489781i	$0.162923\pi$
$468$	6.00000	+	22.3923i	0.277350	+	1.03508i
$469$	18.0622	−	12.2321i	0.834034	−	0.564824i
$470$	15.9282	−	24.1244i	0.734713	−	1.11277i
$471$	2.02628	+	3.50962i	0.0933660	+	0.161715i
$472$	−3.60770	−	13.4641i	−0.166058	−	0.619736i
$473$	0.633975	+	2.36603i	0.0291502	+	0.108790i
$474$	−0.339746	+	0.588457i	−0.0156050	+	0.0270287i
$475$	−13.8564	−	10.3923i	−0.635776	−	0.476832i
$476$	9.80385	−	20.1962i	0.449359	−	0.925689i
$477$	22.3923	−	22.3923i	1.02527	−	1.02527i
$478$	1.73205	−	0.464102i	0.0792222	−	0.0212275i
$479$	−7.09808	+	12.2942i	−0.324319	+	0.561738i	−0.981374	−	0.192105i	$-0.938469\pi$
$479$	−7.09808	+	12.2942i	−0.324319	+	0.561738i	0.657055	+	0.753843i	$0.271802\pi$
$480$	−3.60770	+	5.46410i	−0.164668	+	0.249401i
$481$	−6.58846	+	3.80385i	−0.300408	+	0.173441i
$482$	−0.143594	+	0.535898i	−0.00654051	+	0.0244095i
$483$	−7.50000	+	2.59808i	−0.341262	+	0.118217i
$484$	6.12436	+	3.53590i	0.278380	+	0.160723i
$485$	−30.1506	+	6.16987i	−1.36907	+	0.280160i
$486$			17.4641i			0.792188i
$487$	−0.0980762	+	0.0262794i	−0.00444426	+	0.00119084i	−0.261040	−	0.965328i	$-0.584066\pi$
$487$	−0.0980762	+	0.0262794i	−0.00444426	+	0.00119084i	0.256596	+	0.966519i	$0.417399\pi$
$488$	−2.87564	+	10.7321i	−0.130174	+	0.485817i
$489$	−10.7321			−0.485320
$490$	7.49038	+	20.8301i	0.338381	+	0.941009i
$491$		−	1.80385i		−	0.0814065i	−0.999171	−	0.0407033i	$-0.987040\pi$
$491$		−	1.80385i		−	0.0814065i	0.999171	−	0.0407033i	$-0.0129598\pi$
$492$	−4.73205	+	4.73205i	−0.213337	+	0.213337i
$493$	2.70577	+	10.0981i	0.121862	+	0.454794i
$494$	20.7846			0.935144
$495$	−13.9282	−	9.19615i	−0.626026	−	0.413336i
$496$	−0.679492	+	0.392305i	−0.0305101	+	0.0176150i
$497$	−7.39230	−	21.3397i	−0.331590	−	0.957218i
$498$	2.02628	−	7.56218i	0.0907998	−	0.338869i
$499$	15.7583	+	27.2942i	0.705440	+	1.22186i	0.966533	+	0.256544i	$0.0825838\pi$
$499$	15.7583	+	27.2942i	0.705440	+	1.22186i	−0.261093	+	0.965314i	$0.584083\pi$
$500$	−7.53590	−	21.0526i	−0.337016	−	0.941499i
$501$	−7.79423	−	4.50000i	−0.348220	−	0.201045i
$502$	−0.856406	−	3.19615i	−0.0382233	−	0.142651i
$503$	−13.6865	−	13.6865i	−0.610252	−	0.610252i	0.332759	−	0.943012i	$-0.392020\pi$
$503$	−13.6865	−	13.6865i	−0.610252	−	0.610252i	−0.943012	+	0.332759i	$0.892020\pi$
$504$	−1.46410	−	20.3923i	−0.0652163	−	0.908345i
$505$	−28.2487	+	14.1244i	−1.25705	+	0.628526i
$506$	−11.1962	+	19.3923i	−0.497730	+	0.862093i
$507$	−2.50000	+	0.669873i	−0.111029	+	0.0297501i
$508$	30.0526	+	8.05256i	1.33337	+	0.357275i
$509$	−23.4282	+	13.5263i	−1.03844	+	0.599542i	−0.919390	−	0.393347i	$-0.871317\pi$
$509$	−23.4282	+	13.5263i	−1.03844	+	0.599542i	−0.119047	+	0.992889i	$0.537984\pi$
$510$	1.39230	+	6.80385i	0.0616523	+	0.301279i
$511$	16.6340	+	24.5622i	0.735844	+	1.08657i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	9.92820	+	2.66025i	0.438341	+	0.117453i
$514$			10.1436i			0.447415i
$515$	−9.23205	+	8.18653i	−0.406813	+	0.360742i
$516$		−	0.928203i		−	0.0408619i
$517$	−17.6603	−	17.6603i	−0.776697	−	0.776697i
$518$	6.33975	−	2.19615i	0.278552	−	0.0964934i
$519$			12.9282i			0.567485i
$520$	22.3923	+	14.7846i	0.981968	+	0.648348i
$521$	−13.3923	−	7.73205i	−0.586728	−	0.338747i	0.177075	−	0.984197i	$-0.443337\pi$
$521$	−13.3923	−	7.73205i	−0.586728	−	0.338747i	−0.763802	+	0.645450i	$0.776670\pi$
$522$	6.73205	+	6.73205i	0.294654	+	0.294654i
$523$	−32.4904	−	8.70577i	−1.42071	−	0.380677i	−0.534971	−	0.844870i	$-0.679678\pi$
$523$	−32.4904	−	8.70577i	−1.42071	−	0.380677i	−0.885734	+	0.464193i	$0.846344\pi$
$524$	0.928203	+	0.535898i	0.0405487	+	0.0234108i
$525$	−5.75833	−	3.70577i	−0.251314	−	0.161733i
$526$	26.4904	−	15.2942i	1.15504	−	0.666860i
$527$	−0.215390	+	0.803848i	−0.00938255	+	0.0350162i
$528$	4.00000	+	4.00000i	0.174078	+	0.174078i
$529$	9.16987	+	5.29423i	0.398690	+	0.230184i
$530$	2.19615	−	36.5885i	0.0953948	−	1.58930i
$531$	−13.4641			−0.584292
$532$	−18.0000	−	3.46410i	−0.780399	−	0.150188i
$533$	19.3923	+	19.3923i	0.839974	+	0.839974i
$534$	−4.31347	−	2.49038i	−0.186662	−	0.107769i
$535$	19.0885	+	21.5263i	0.825266	+	0.930662i
$536$	−11.6603	+	20.1962i	−0.503646	+	0.872341i
$537$	−12.0263	−	3.22243i	−0.518972	−	0.139058i
$538$	−3.83013	+	14.2942i	−0.165129	+	0.616268i
$539$	18.9282	−	2.73205i	0.815295	−	0.117678i
$540$	8.80385	+	9.92820i	0.378857	+	0.427242i
$541$	13.7942	−	7.96410i	0.593060	−	0.342403i	−0.173246	−	0.984879i	$-0.555426\pi$
$541$	13.7942	−	7.96410i	0.593060	−	0.342403i	0.766307	+	0.642475i	$0.222092\pi$
$542$	12.0000	+	12.0000i	0.515444	+	0.515444i
$543$	−3.01666	−	11.2583i	−0.129457	−	0.483141i
$544$			24.0000i			1.02899i
$545$	−15.4641	+	7.73205i	−0.662409	+	0.331205i
$546$	8.19615	−	0.588457i	0.350763	−	0.0251836i
$547$	−11.4904	+	11.4904i	−0.491293	+	0.491293i	−0.908714	−	0.417420i	$-0.862934\pi$
$547$	−11.4904	+	11.4904i	−0.491293	+	0.491293i	0.417420	+	0.908714i	$0.362934\pi$
$548$	12.0000	−	12.0000i	0.512615	−	0.512615i
$549$	9.29423	+	5.36603i	0.396668	+	0.229016i
$550$	−19.1244	+	2.73205i	−0.815465	+	0.116495i
$551$	7.39230	−	4.26795i	0.314923	−	0.181821i
$552$	6.00000	−	6.00000i	0.255377	−	0.255377i
$553$	−1.85641	−	1.60770i	−0.0789424	−	0.0683662i
$554$	−17.7846	+	10.2679i	−0.755596	+	0.436243i
$555$	−1.14359	+	1.73205i	−0.0485428	+	0.0735215i
$556$	4.73205	+	8.19615i	0.200684	+	0.347594i
$557$	8.24167	+	30.7583i	0.349211	+	1.30327i	0.887615	+	0.460586i	$0.152361\pi$
$557$	8.24167	+	30.7583i	0.349211	+	1.30327i	−0.538404	+	0.842687i	$0.680973\pi$
$558$	0.196152	+	0.732051i	0.00830379	+	0.0309902i
$559$	−3.80385			−0.160886
$560$	−16.9282	−	16.5359i	−0.715347	−	0.698769i
$561$	6.00000			0.253320
$562$	−8.87564	−	33.1244i	−0.374396	−	1.39727i
$563$	−1.35641	−	5.06218i	−0.0571657	−	0.213345i	0.931435	−	0.363909i	$-0.118558\pi$
$563$	−1.35641	−	5.06218i	−0.0571657	−	0.213345i	−0.988600	+	0.150563i	$0.951891\pi$
$564$	4.73205	+	8.19615i	0.199255	+	0.345120i
$565$	29.3205	−	6.00000i	1.23352	−	0.252422i
$566$	−6.80385	+	3.92820i	−0.285987	+	0.165115i
$567$	−17.3038	−	3.33013i	−0.726693	−	0.139852i
$568$	17.0718	+	17.0718i	0.716317	+	0.716317i
$569$	−29.1962	+	16.8564i	−1.22397	+	0.706657i	−0.965761	−	0.259433i	$-0.916464\pi$
$569$	−29.1962	+	16.8564i	−1.22397	+	0.706657i	−0.258205	+	0.966090i	$0.583131\pi$
$570$	5.07180	−	2.53590i	0.212434	−	0.106217i
$571$	−26.7846	−	15.4641i	−1.12090	−	0.647153i	−0.179270	−	0.983800i	$-0.557374\pi$
$571$	−26.7846	−	15.4641i	−1.12090	−	0.647153i	−0.941631	+	0.336647i	$0.890707\pi$
$572$	16.3923	−	16.3923i	0.685397	−	0.685397i
$573$	7.73205	−	7.73205i	0.323011	−	0.323011i
$574$	−13.5622	−	20.0263i	−0.566074	−	0.835881i
$575$	4.09808	+	28.6865i	0.170902	+	1.19631i
$576$	10.9282	+	18.9282i	0.455342	+	0.788675i
$577$	9.49038	+	35.4186i	0.395090	+	1.47449i	0.821627	+	0.570025i	$0.193067\pi$
$577$	9.49038	+	35.4186i	0.395090	+	1.47449i	−0.426538	+	0.904470i	$0.640267\pi$
$578$	1.00000	+	1.00000i	0.0415945	+	0.0415945i
$579$	0.973721	−	0.562178i	0.0404664	−	0.0233633i
$580$	11.0000	+	0.660254i	0.456750	+	0.0274156i
$581$	25.4545	+	12.3564i	1.05603	+	0.512630i
$582$	2.60770	−	9.73205i	0.108092	−	0.403406i
$583$	−30.5885	−	8.19615i	−1.26684	−	0.339450i
$584$	−27.4641	−	15.8564i	−1.13647	−	0.656143i
$585$	19.3923	−	17.1962i	0.801773	−	0.710973i
$586$	−10.7321	−	6.19615i	−0.443337	−	0.255961i
$587$	−9.00000	−	9.00000i	−0.371470	−	0.371470i	0.496543	−	0.868012i	$-0.334603\pi$
$587$	−9.00000	−	9.00000i	−0.371470	−	0.371470i	−0.868012	+	0.496543i	$0.834603\pi$
$588$	−7.19615	−	0.856406i	−0.296764	−	0.0353176i
$589$	0.679492			0.0279980
$590$	−11.6603	+	10.3397i	−0.480045	+	0.425681i
$591$	−7.90192	−	4.56218i	−0.325042	−	0.187663i
$592$	−5.07180	+	5.07180i	−0.208450	+	0.208450i
$593$	−3.80385	+	14.1962i	−0.156205	+	0.582966i	0.842794	+	0.538237i	$0.180909\pi$
$593$	−3.80385	+	14.1962i	−0.156205	+	0.582966i	−0.998999	+	0.0447296i	$0.985757\pi$
$594$	9.92820	−	5.73205i	0.407359	−	0.235189i
$595$	−25.0981	+	0.294229i	−1.02892	+	0.0120622i
$596$	9.24871	+	5.33975i	0.378842	+	0.218725i
$597$	1.73205	+	0.464102i	0.0708881	+	0.0189944i
$598$	−24.5885	−	24.5885i	−1.00550	−	1.00550i
$599$	−21.0000	−	12.1244i	−0.858037	−	0.495388i	0.00531761	−	0.999986i	$-0.498307\pi$
$599$	−21.0000	−	12.1244i	−0.858037	−	0.495388i	−0.863354	+	0.504598i	$0.831641\pi$
$600$	7.26795	+	0.875644i	0.296713	+	0.0357480i
$601$			7.60770i			0.310324i	0.987889	+	0.155162i	$0.0495900\pi$
$601$			7.60770i			0.310324i	−0.987889	+	0.155162i	$0.950410\pi$
$602$	3.29423	+	0.633975i	0.134263	+	0.0258389i
$603$	15.9282	+	15.9282i	0.648647	+	0.648647i
$604$		−	48.3923i		−	1.96905i
$605$	0.473721	−	7.89230i	0.0192595	−	0.320868i
$606$		−	10.3397i		−	0.420023i
$607$	11.1603	+	2.99038i	0.452981	+	0.121376i	0.478094	−	0.878309i	$-0.341328\pi$
$607$	11.1603	+	2.99038i	0.452981	+	0.121376i	−0.0251130	+	0.999685i	$0.507995\pi$
$608$	18.9282	−	5.07180i	0.767640	−	0.205689i
$609$	2.79423	−	1.89230i	0.113228	−	0.0766801i
$610$	12.1699	−	2.49038i	0.492744	−	0.100833i
$611$	33.5885	−	19.3923i	1.35884	−	0.784529i
$612$	22.3923	+	6.00000i	0.905155	+	0.242536i
$613$	13.5622	−	3.63397i	0.547771	−	0.146775i	0.0256889	−	0.999670i	$-0.491822\pi$
$613$	13.5622	−	3.63397i	0.547771	−	0.146775i	0.522082	+	0.852895i	$0.325155\pi$
$614$	−21.7583	+	37.6865i	−0.878095	+	1.52090i
$615$	7.09808	+	2.36603i	0.286222	+	0.0954074i
$616$	−16.9282	+	11.4641i	−0.682057	+	0.461902i
$617$	12.9282	+	12.9282i	0.520470	+	0.520470i	0.917713	−	0.397243i	$-0.130033\pi$
$617$	12.9282	+	12.9282i	0.520470	+	0.520470i	−0.397243	+	0.917713i	$0.630033\pi$
$618$	−1.04552	−	3.90192i	−0.0420569	−	0.156958i
$619$	0.294229	+	0.169873i	0.0118260	+	0.00682777i	0.505901	−	0.862591i	$-0.331160\pi$
$619$	0.294229	+	0.169873i	0.0118260	+	0.00682777i	−0.494075	+	0.869419i	$0.664493\pi$
$620$	0.732051	+	0.483340i	0.0293999	+	0.0194114i
$621$	−8.59808	−	14.8923i	−0.345029	−	0.597608i
$622$	−4.05256	+	15.1244i	−0.162493	+	0.606431i
$623$	11.7846	−	13.6077i	0.472140	−	0.545181i
$624$	−7.60770	+	4.39230i	−0.304552	+	0.175833i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−44.3923			−1.77427
$627$	−1.26795	−	4.73205i	−0.0506370	−	0.188980i
$628$	11.0718	−	11.0718i	0.441813	−	0.441813i
$629$			7.60770i			0.303339i
$630$	−19.6603	+	11.6603i	−0.783283	+	0.464556i
$631$	−10.7321			−0.427236			−0.213618	−	0.976917i	$-0.568525\pi$
$631$	−10.7321			−0.427236			−0.213618	+	0.976917i	$0.568525\pi$
$632$	2.53590	+	0.679492i	0.100873	+	0.0270287i
$633$	13.7321	−	3.67949i	0.545800	−	0.146247i
$634$			14.3923i			0.571591i
$635$	−6.97372	−	34.0788i	−0.276744	−	1.35238i
$636$	10.3923	+	6.00000i	0.412082	+	0.237915i
$637$	−3.50962	+	29.4904i	−0.139056	+	1.16845i
$638$	2.46410	−	9.19615i	0.0975547	−	0.364079i
$639$	20.1962	−	11.6603i	0.798947	−	0.461273i
$640$	24.0000	+	8.00000i	0.948683	+	0.316228i
$641$	7.66987	−	13.2846i	0.302942	−	0.524711i	−0.673859	−	0.738860i	$-0.735365\pi$
$641$	7.66987	−	13.2846i	0.302942	−	0.524711i	0.976801	+	0.214149i	$0.0686979\pi$
$642$	−9.09808	+	2.43782i	−0.359072	+	0.0962132i
$643$	−9.00000	+	9.00000i	−0.354925	+	0.354925i	−0.861938	−	0.507013i	$-0.830750\pi$
$643$	−9.00000	+	9.00000i	−0.354925	+	0.354925i	0.507013	+	0.861938i	$0.330750\pi$
$644$	17.1962	+	25.3923i	0.677623	+	1.00060i
$645$	−0.928203	+	0.464102i	−0.0365480	+	0.0182740i
$646$	10.3923	−	18.0000i	0.408880	−	0.708201i
$647$	3.74167	+	13.9641i	0.147100	+	0.548985i	0.999653	+	0.0263442i	$0.00838660\pi$
$647$	3.74167	+	13.9641i	0.147100	+	0.548985i	−0.852553	+	0.522641i	$0.824947\pi$
$648$	18.1962	−	4.87564i	0.714812	−	0.191533i
$649$	6.73205	+	11.6603i	0.264256	+	0.457705i
$650$	3.58846	−	29.7846i	0.140751	−	1.16825i
$651$	0.267949	−	0.0192379i	0.0105018	−	0.000753992i
$652$	10.7321	+	40.0526i	0.420300	+	1.56858i
$653$	−8.41858	+	31.4186i	−0.329445	+	1.22950i	0.580323	+	0.814386i	$0.302926\pi$
$653$	−8.41858	+	31.4186i	−0.329445	+	1.22950i	−0.909768	+	0.415118i	$0.863740\pi$
$654$		−	5.66025i		−	0.221333i
$655$	0.0717968	−	1.19615i	0.00280533	−	0.0467375i
$656$	22.3923	+	12.9282i	0.874273	+	0.504762i
$657$	−21.6603	+	21.6603i	−0.845047	+	0.845047i
$658$	−32.3205	+	11.1962i	−1.25998	+	0.436471i
$659$	−4.67949			−0.182287			−0.0911436	−	0.995838i	$-0.529052\pi$
$659$	−4.67949			−0.182287			−0.0911436	+	0.995838i	$0.529052\pi$
$660$	2.00000	−	6.00000i	0.0778499	−	0.233550i
$661$	13.0359	−	22.5788i	0.507038	−	0.878215i	−0.492929	−	0.870069i	$-0.664074\pi$
$661$	13.0359	−	22.5788i	0.507038	−	0.878215i	0.999967	−	0.00814557i	$-0.00259284\pi$
$662$	−10.7321	−	10.7321i	−0.417113	−	0.417113i
$663$	−2.41154	+	9.00000i	−0.0936566	+	0.349531i
$664$	−30.2487			−1.17388
$665$	5.53590	+	19.7321i	0.214673	+	0.765176i
$666$	3.46410	+	6.00000i	0.134231	+	0.232495i
$667$	−13.7942	−	3.69615i	−0.534115	−	0.143116i
$668$	−9.00000	+	33.5885i	−0.348220	+	1.29958i
$669$	2.16987	−	3.75833i	0.0838921	−	0.145305i
$670$	26.0263	+	1.56218i	1.00548	+	0.0603522i
$671$		−	10.7321i		−	0.414306i
$672$	7.32051	−	2.53590i	0.282395	−	0.0978244i
$673$	0.196152	−	0.196152i	0.00756112	−	0.00756112i	−0.703316	−	0.710877i	$-0.748298\pi$
$673$	0.196152	−	0.196152i	0.00756112	−	0.00756112i	0.710877	+	0.703316i	$0.248298\pi$
$674$	−2.33975	+	4.05256i	−0.0901236	+	0.156099i
$675$	5.52628	−	13.7679i	0.212707	−	0.529929i
$676$	5.00000	+	8.66025i	0.192308	+	0.333087i
$677$	−7.56218	+	28.2224i	−0.290638	+	1.08468i	0.653982	+	0.756510i	$0.273097\pi$
$677$	−7.56218	+	28.2224i	−0.290638	+	1.08468i	−0.944620	+	0.328166i	$0.893569\pi$
$678$	−2.53590	+	9.46410i	−0.0973906	+	0.363467i
$679$	32.7583	+	15.9019i	1.25715	+	0.610260i
$680$	24.0000	−	12.0000i	0.920358	−	0.460179i
$681$	−4.16987	−	7.22243i	−0.159790	−	0.276764i
$682$	0.535898	−	0.535898i	0.0205206	−	0.0205206i
$683$	−6.13397	+	1.64359i	−0.234710	+	0.0628904i	−0.374257	−	0.927325i	$-0.622102\pi$
$683$	−6.13397	+	1.64359i	−0.234710	+	0.0628904i	0.139547	+	0.990215i	$0.455435\pi$
$684$		−	18.9282i		−	0.723738i
$685$	−18.0000	−	6.00000i	−0.687745	−	0.229248i
$686$	7.95448	−	24.9545i	0.303704	−	0.952767i
$687$	−3.12436	−	3.12436i	−0.119202	−	0.119202i
$688$	−3.46410	+	0.928203i	−0.132068	+	0.0353874i
$689$	24.5885	−	42.5885i	0.936746	−	1.62249i
$690$	−9.00000	−	3.00000i	−0.342624	−	0.114208i
$691$	0.758330	+	1.31347i	0.0288482	+	0.0499666i	0.880089	−	0.474809i	$-0.157483\pi$
$691$	0.758330	+	1.31347i	0.0288482	+	0.0499666i	−0.851241	+	0.524775i	$0.824149\pi$
$692$	48.2487	−	12.9282i	1.83414	−	0.491457i
$693$	6.46410	+	18.6603i	0.245551	+	0.708844i
$694$	23.2750	−	13.4378i	0.883507	−	0.510093i
$695$	5.83013	−	8.83013i	0.221149	−	0.334946i
$696$	−1.80385	+	3.12436i	−0.0683747	+	0.118428i
$697$	26.4904	−	7.09808i	1.00339	−	0.268859i
$698$	43.6865	−	11.7058i	1.65356	−	0.443070i
$699$			3.80385i			0.143875i
$700$	−8.07180	+	25.1962i	−0.305085	+	0.952325i
$701$			17.9808i			0.679124i	0.940584	+	0.339562i	$0.110279\pi$
$701$			17.9808i			0.679124i	−0.940584	+	0.339562i	$0.889721\pi$
$702$	4.60770	+	17.1962i	0.173906	+	0.649027i
$703$	6.00000	−	1.60770i	0.226294	−	0.0606354i
$704$	10.9282	−	18.9282i	0.411872	−	0.713384i
$705$	5.83013	−	8.83013i	0.219575	−	0.332562i
$706$	12.5885	+	21.8038i	0.473773	+	0.820599i
$707$	36.6962	+	7.06218i	1.38010	+	0.265601i
$708$	−1.32051	−	4.92820i	−0.0496277	−	0.185213i
$709$	−1.03590	−	1.79423i	−0.0389040	−	0.0673837i	0.845918	−	0.533313i	$-0.179053\pi$
$709$	−1.03590	−	1.79423i	−0.0389040	−	0.0673837i	−0.884822	+	0.465930i	$0.845720\pi$
$710$	8.53590	−	25.6077i	0.320347	−	0.961040i
$711$	1.26795	−	2.19615i	0.0475518	−	0.0823622i
$712$	−4.98076	+	18.5885i	−0.186662	+	0.696632i
$713$	−0.803848	−	0.803848i	−0.0301043	−	0.0301043i
$714$	3.58846	−	7.39230i	0.134295	−	0.276650i
$715$	−24.5885	−	8.19615i	−0.919556	−	0.306519i
$716$			48.1051i			1.79777i
$717$	0.633975	−	0.169873i	0.0236762	−	0.00634402i
$718$	−1.26795	−	1.26795i	−0.0473194	−	0.0473194i
$719$	3.63397	+	6.29423i	0.135524	+	0.234735i	0.925798	−	0.378019i	$-0.123395\pi$
$719$	3.63397	+	6.29423i	0.135524	+	0.234735i	−0.790273	+	0.612755i	$0.790061\pi$
$720$	13.4641	−	20.3923i	0.501777	−	0.759976i
$721$	14.5622	−	1.04552i	0.542324	−	0.0389371i
$722$	9.56218	+	2.56218i	0.355867	+	0.0953544i
$723$	−0.0525589	+	0.196152i	−0.00195469	+	0.00729499i
$724$	−39.0000	+	22.5167i	−1.44942	+	0.836825i
$725$	−4.83975	−	11.3301i	−0.179744	−	0.420790i
$726$	2.24167	+	1.29423i	0.0831962	+	0.0480333i
$727$	1.70577	−	1.70577i	0.0632636	−	0.0632636i	−0.674767	−	0.738031i	$-0.735756\pi$
$727$	1.70577	−	1.70577i	0.0632636	−	0.0632636i	0.738031	+	0.674767i	$0.235756\pi$
$728$	−10.3923	−	30.0000i	−0.385164	−	1.11187i
$729$		−	13.5885i		−	0.503276i
$730$	−2.12436	+	35.3923i	−0.0786259	+	1.30993i
$731$	−1.90192	+	3.29423i	−0.0703452	+	0.121841i
$732$	−1.05256	+	3.92820i	−0.0389037	+	0.145191i
$733$	21.2942	+	5.70577i	0.786520	+	0.210747i	0.629657	−	0.776873i	$-0.283195\pi$
$733$	21.2942	+	5.70577i	0.786520	+	0.210747i	0.156863	+	0.987620i	$0.449862\pi$
$734$	−19.2224	+	11.0981i	−0.709513	+	0.409637i
$735$	2.74167	+	7.62436i	0.101128	+	0.281229i
$736$	−28.3923	−	16.3923i	−1.04655	−	0.604228i
$737$	5.83013	−	21.7583i	0.214755	−	0.801478i
$738$	17.6603	−	17.6603i	0.650083	−	0.650083i
$739$	2.83013	−	4.90192i	0.104108	−	0.180320i	−0.809265	−	0.587443i	$-0.800135\pi$
$739$	2.83013	−	4.90192i	0.104108	−	0.180320i	0.913373	+	0.407123i	$0.133468\pi$
$740$	7.60770	+	2.53590i	0.279664	+	0.0932215i
$741$	7.60770			0.279476
$742$	−28.3923	+	32.7846i	−1.04231	+	1.20356i
$743$	6.41858	−	6.41858i	0.235475	−	0.235475i	−0.579498	−	0.814973i	$-0.696751\pi$
$743$	6.41858	−	6.41858i	0.235475	−	0.235475i	0.814973	+	0.579498i	$0.196751\pi$
$744$	−0.248711	+	0.143594i	−0.00911820	+	0.00526439i
$745$	0.715390	−	11.9186i	0.0262099	−	0.436663i
$746$	−13.8564			−0.507319
$747$	−7.56218	+	28.2224i	−0.276686	+	1.03260i
$748$	−6.00000	−	22.3923i	−0.219382	−	0.818744i
$749$	−2.43782	−	33.9545i	−0.0890761	−	1.24067i
$750$	−2.75833	−	7.70577i	−0.100720	−	0.281375i
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	0.755510	−	0.655137i	$-0.227389\pi$
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	−0.945120	+	0.326722i	$0.894056\pi$
$752$	25.8564	−	25.8564i	0.942886	−	0.942886i
$753$	−0.313467	−	1.16987i	−0.0114234	−	0.0426325i
$754$	12.8038	+	7.39230i	0.466289	+	0.269212i
$755$	−48.3923	+	24.1962i	−1.76118	+	0.880588i
$756$	−1.12436	−	15.6603i	−0.0408924	−	0.569558i
$757$	1.05256	−	1.05256i	0.0382559	−	0.0382559i	−0.687720	−	0.725976i	$-0.741388\pi$
$757$	1.05256	−	1.05256i	0.0382559	−	0.0382559i	0.725976	+	0.687720i	$0.241388\pi$
$758$	6.67949	+	24.9282i	0.242610	+	0.905433i
$759$	−4.09808	+	7.09808i	−0.148751	+	0.257644i
$760$	−14.5359	−	16.3923i	−0.527272	−	0.594611i
$761$	−41.1962	+	23.7846i	−1.49336	+	0.862191i	−0.999971	−	0.00761770i	$-0.997575\pi$
$761$	−41.1962	+	23.7846i	−1.49336	+	0.862191i	−0.493388	+	0.869809i	$0.664242\pi$
$762$	11.0000	+	2.94744i	0.398488	+	0.106775i
$763$	20.0885	+	3.86603i	0.727251	+	0.139960i
$764$	−36.5885	−	21.1244i	−1.32372	−	0.764252i
$765$	−5.19615	−	25.3923i	−0.187867	−	0.918061i
$766$	−7.26795			−0.262602
$767$	−20.1962	+	5.41154i	−0.729241	+	0.195399i
$768$	−5.85641	+	5.85641i	−0.211325	+	0.211325i
$769$	46.6410			1.68192			0.840959	−	0.541099i	$-0.181992\pi$
$769$	46.6410			1.68192			0.840959	+	0.541099i	$0.181992\pi$
$770$	19.9282	+	11.1962i	0.718163	+	0.403481i
$771$			3.71281i			0.133714i
$772$	−3.07180	−	3.07180i	−0.110556	−	0.110556i
$773$	−7.90192	−	29.4904i	−0.284212	−	1.06070i	−0.949413	−	0.314030i	$-0.898321\pi$
$773$	−7.90192	−	29.4904i	−0.284212	−	1.06070i	0.665200	−	0.746665i	$-0.268346\pi$
$774$			3.46410i			0.124515i
$775$	0.117314	−	0.973721i	0.00421405	−	0.0349771i
$776$	−38.9282			−1.39744
$777$	2.32051	−	0.803848i	0.0832478	−	0.0288379i
$778$	−39.5167	−	10.5885i	−1.41674	−	0.379615i
$779$	−11.1962	−	19.3923i	−0.401144	−	0.694801i
$780$	8.19615	+	5.41154i	0.293469	+	0.193764i
$781$	−20.1962	−	11.6603i	−0.722675	−	0.417237i
$782$	−33.5885	+	9.00000i	−1.20112	+	0.321839i
$783$	5.16987	+	5.16987i	0.184756	+	0.184756i
$784$	4.00000	+	27.7128i	0.142857	+	0.989743i
$785$	−16.6077	−	5.53590i	−0.592754	−	0.197585i
$786$	0.339746	+	0.196152i	0.0121183	+	0.00699653i
$787$	−26.7224	+	7.16025i	−0.952552	+	0.255235i	−0.701445	−	0.712724i	$-0.747461\pi$
$787$	−26.7224	+	7.16025i	−0.952552	+	0.255235i	−0.251107	+	0.967959i	$0.580795\pi$
$788$	−9.12436	+	34.0526i	−0.325042	+	1.21307i
$789$	9.69615	−	5.59808i	0.345192	−	0.199297i
$790$	−0.588457	−	2.87564i	−0.0209364	−	0.102311i
$791$	−31.8564	−	15.4641i	−1.13268	−	0.549840i
$792$	−14.9282	−	14.9282i	−0.530451	−	0.530451i
$793$	16.0981	+	4.31347i	0.571659	+	0.153176i
$794$	4.14359			0.147051
$795$	0.803848	−	13.3923i	0.0285095	−	0.474976i
$796$		−	6.92820i		−	0.245564i
$797$	−12.9282	−	12.9282i	−0.457940	−	0.457940i	0.440038	−	0.897979i	$-0.354965\pi$
$797$	−12.9282	−	12.9282i	−0.457940	−	0.457940i	−0.897979	+	0.440038i	$0.854965\pi$
$798$	−6.58846	−	1.26795i	−0.233229	−	0.0448849i
$799$		−	38.7846i		−	1.37210i
$800$	−4.00000	−	28.0000i	−0.141421	−	0.989949i
$801$	16.0981	+	9.29423i	0.568798	+	0.328395i
$802$	−24.7128	+	24.7128i	−0.872640	+	0.872640i
$803$	29.5885	+	7.92820i	1.04415	+	0.279780i
$804$	−4.26795	+	7.39230i	−0.150519	+	0.260706i
$805$	16.7942	−	29.8923i	0.591919	−	1.05357i
$806$	0.588457	+	1.01924i	0.0207275	+	0.0359011i
$807$	−1.40192	+	5.23205i	−0.0493501	+	0.184177i
$808$	−38.5885	+	10.3397i	−1.35754	+	0.363751i
$809$	−16.5788	−	9.57180i	−0.582881	−	0.336526i	0.179397	−	0.983777i	$-0.442585\pi$
$809$	−16.5788	−	9.57180i	−0.582881	−	0.336526i	−0.762277	+	0.647250i	$0.775919\pi$
$810$	−13.9737	−	15.7583i	−0.490986	−	0.553691i
$811$	47.6603			1.67358			0.836789	−	0.547526i	$-0.184430\pi$
$811$	47.6603			1.67358			0.836789	+	0.547526i	$0.184430\pi$
$812$	−9.85641	−	8.53590i	−0.345892	−	0.299551i
$813$	4.39230	+	4.39230i	0.154045	+	0.154045i
$814$	3.46410	−	6.00000i	0.121417	−	0.210300i
$815$	34.6865	−	30.7583i	1.21502	−	1.07742i
$816$			8.78461i			0.307523i
$817$	3.00000	+	0.803848i	0.104957	+	0.0281231i
$818$	−12.8301	−	3.43782i	−0.448595	−	0.120201i
$819$	−30.5885	+	2.19615i	−1.06885	+	0.0767398i
$820$	1.73205	−	28.8564i	0.0604858	−	1.00771i
$821$	3.92820	−	2.26795i	0.137095	−	0.0791520i	−0.429884	−	0.902884i	$-0.641445\pi$
$821$	3.92820	−	2.26795i	0.137095	−	0.0791520i	0.566979	+	0.823732i	$0.308112\pi$
$822$	4.39230	−	4.39230i	0.153199	−	0.153199i
$823$	−3.30385	−	12.3301i	−0.115165	−	0.429801i	0.884134	−	0.467233i	$-0.154749\pi$
$823$	−3.30385	−	12.3301i	−0.115165	−	0.429801i	−0.999299	+	0.0374316i	$0.988082\pi$
$824$	−13.5167	+	7.80385i	−0.470875	+	0.271860i
$825$	−7.00000	+	1.00000i	−0.243709	+	0.0348155i
$826$	18.3923	−	1.32051i	0.639950	−	0.0459464i
$827$	26.1506	−	26.1506i	0.909347	−	0.909347i	−0.0868727	−	0.996219i	$-0.527687\pi$
$827$	26.1506	−	26.1506i	0.909347	−	0.909347i	0.996219	+	0.0868727i	$0.0276874\pi$
$828$	−22.3923	+	22.3923i	−0.778186	+	0.778186i
$829$	−2.19615	−	1.26795i	−0.0762755	−	0.0440377i	0.461377	−	0.887204i	$-0.347356\pi$
$829$	−2.19615	−	1.26795i	−0.0762755	−	0.0440377i	−0.537653	+	0.843166i	$0.680689\pi$
$830$	15.1244	+	30.2487i	0.524974	+	1.04995i
$831$	−6.50962	+	3.75833i	−0.225816	+	0.130375i
$832$	24.0000	+	24.0000i	0.832050	+	0.832050i
$833$	23.7846	+	17.7846i	0.824088	+	0.616200i
$834$	1.73205	+	3.00000i	0.0599760	+	0.103882i
$835$	38.0885	−	7.79423i	1.31811	−	0.269730i
$836$	−16.3923	+	9.46410i	−0.566940	+	0.327323i
$837$	0.150635	+	0.562178i	0.00520671	+	0.0194317i
$838$	25.1244	−	6.73205i	0.867906	−	0.232555i
$839$	−3.80385			−0.131323			−0.0656617	−	0.997842i	$-0.520916\pi$
$839$	−3.80385			−0.131323			−0.0656617	+	0.997842i	$0.520916\pi$
$840$	−6.19615	−	6.05256i	−0.213788	−	0.208833i
$841$	−22.9282			−0.790628
$842$	−8.02628	+	2.15064i	−0.276604	+	0.0741158i
$843$	−3.24871	−	12.1244i	−0.111892	−	0.417585i
$844$	−27.4641	−	47.5692i	−0.945353	−	1.63740i
$845$	6.16025	−	9.33013i	0.211919	−	0.320966i
$846$	−17.6603	−	30.5885i	−0.607172	−	1.05165i
$847$	−6.12436	+	7.07180i	−0.210435	+	0.242990i
$848$	12.0000	−	44.7846i	0.412082	−	1.53791i
$849$	−2.49038	+	1.43782i	−0.0854697	+	0.0493459i
$850$	−24.0000	−	18.0000i	−0.823193	−	0.617395i
$851$	−9.00000	−	5.19615i	−0.308516	−	0.178122i
$852$	6.24871	+	6.24871i	0.214077	+	0.214077i
$853$	−5.32051	+	5.32051i	−0.182171	+	0.182171i	−0.792301	−	0.610130i	$-0.791117\pi$
$853$	−5.32051	+	5.32051i	−0.182171	+	0.182171i	0.610130	+	0.792301i	$0.291117\pi$
$854$	−13.2224	−	6.41858i	−0.452462	−	0.219639i
$855$	−18.9282	+	9.46410i	−0.647331	+	0.323665i
$856$	18.1962	+	31.5167i	0.621932	+	1.07722i
$857$	−6.75833	−	25.2224i	−0.230860	−	0.861582i	−0.979972	−	0.199138i	$-0.936186\pi$
$857$	−6.75833	−	25.2224i	−0.230860	−	0.861582i	0.749111	−	0.662444i	$-0.230481\pi$
$858$	6.00000	−	6.00000i	0.204837	−	0.204837i
$859$	−3.80385	+	2.19615i	−0.129786	+	0.0749318i	−0.563487	−	0.826125i	$-0.690541\pi$
$859$	−3.80385	+	2.19615i	−0.129786	+	0.0749318i	0.433702	+	0.901057i	$0.357207\pi$
$860$	2.66025	+	3.00000i	0.0907139	+	0.102299i
$861$	−4.96410	−	7.33013i	−0.169176	−	0.249810i
$862$	−22.8564	−	6.12436i	−0.778492	−	0.208596i
$863$	2.76795	+	0.741670i	0.0942221	+	0.0252467i	0.305622	−	0.952153i	$-0.401136\pi$
$863$	2.76795	+	0.741670i	0.0942221	+	0.0252467i	−0.211400	+	0.977400i	$0.567802\pi$
$864$	8.39230	+	14.5359i	0.285512	+	0.494521i
$865$	−37.0526	−	41.7846i	−1.25982	−	1.42072i
$866$	4.53590	−	7.85641i	0.154136	−	0.266972i
$867$	0.366025	+	0.366025i	0.0124309	+	0.0124309i
$868$	−0.339746	−	0.980762i	−0.0115317	−	0.0332892i
$869$	−2.53590			−0.0860245
$870$	4.02628	+	0.241670i	0.136504	+	0.00819337i
$871$	30.2942	+	17.4904i	1.02648	+	0.592639i
$872$	−21.1244	+	5.66025i	−0.715361	+	0.191680i
$873$	−9.73205	+	36.3205i	−0.329380	+	1.22926i
$874$	14.1962	+	24.5885i	0.480192	+	0.831717i
$875$	29.2321	−	4.52628i	0.988224	−	0.153016i
$876$	−10.0526	−	5.80385i	−0.339644	−	0.196094i
$877$	−5.19615	−	1.39230i	−0.175462	−	0.0470148i	0.170018	−	0.985441i	$-0.445617\pi$
$877$	−5.19615	−	1.39230i	−0.175462	−	0.0470148i	−0.345480	+	0.938426i	$0.612284\pi$
$878$	−29.3205	+	29.3205i	−0.989519	+	0.989519i
$879$	−3.92820	−	2.26795i	−0.132495	−	0.0764960i
$880$	−24.3923	−	1.46410i	−0.822264	−	0.0493549i
$881$		−	21.2487i		−	0.715887i	−0.933743	−	0.357944i	$-0.883478\pi$
$881$		−	21.2487i		−	0.715887i	0.933743	−	0.357944i	$-0.116522\pi$
$882$	26.8564	+	3.19615i	0.904302	+	0.107620i
$883$	33.2487	+	33.2487i	1.11891	+	1.11891i	0.991902	+	0.127006i	$0.0405368\pi$
$883$	33.2487	+	33.2487i	1.11891	+	1.11891i	0.127006	+	0.991902i	$0.459463\pi$
$884$	36.0000			1.21081
$885$	−4.26795	+	3.78461i	−0.143466	+	0.127218i
$886$	30.8372			1.03599
$887$	33.8205	+	9.06218i	1.13558	+	0.304278i	0.777173	−	0.629287i	$-0.216653\pi$
$887$	33.8205	+	9.06218i	1.13558	+	0.304278i	0.358408	+	0.933565i	$0.383320\pi$
$888$	−1.85641	+	1.85641i	−0.0622969	+	0.0622969i
$889$	−17.9737	+	37.0263i	−0.602819	+	1.24182i
$890$	21.0788	−	4.31347i	0.706564	−	0.144588i
$891$	−15.7583	+	9.09808i	−0.527924	+	0.304797i
$892$	−16.1962	−	4.33975i	−0.542287	−	0.145305i
$893$	−30.5885	+	8.19615i	−1.02360	+	0.274274i
$894$	3.38526	+	1.95448i	0.113220	+	0.0653677i
$895$	48.1051	−	24.0526i	1.60798	−	0.803988i
$896$	−16.7846	−	24.7846i	−0.560734	−	0.827996i
$897$	−9.00000	−	9.00000i	−0.300501	−	0.300501i
$898$	17.4904	−	4.68653i	0.583662	−	0.156392i
$899$	0.418584	+	0.241670i	0.0139606	+	0.00806014i
$900$	−27.1244	−	3.26795i	−0.904145	−	0.108932i
$901$	−24.5885	−	42.5885i	−0.819160	−	1.41883i
$902$	−24.1244	−	6.46410i	−0.803253	−	0.215231i
$903$	1.20577	+	0.232051i	0.0401256	+	0.00772217i
$904$	37.8564			1.25909
$905$	42.0167	+	27.7417i	1.39668	+	0.922164i
$906$		−	17.7128i		−	0.588469i
$907$	−4.50000	−	16.7942i	−0.149420	−	0.557643i	−0.999519	−	0.0310198i	$-0.990124\pi$
$907$	−4.50000	−	16.7942i	−0.149420	−	0.557643i	0.850099	−	0.526623i	$-0.176542\pi$
$908$	−22.7846	+	22.7846i	−0.756134	+	0.756134i
$909$			38.5885i			1.27990i
$910$	−24.8038	+	25.3923i	−0.822240	+	0.841747i
$911$	−2.19615			−0.0727618			−0.0363809	−	0.999338i	$-0.511583\pi$
$911$	−2.19615			−0.0727618			−0.0363809	+	0.999338i	$0.511583\pi$
$912$	6.92820	−	1.85641i	0.229416	−	0.0614718i
$913$	28.2224	−	7.56218i	0.934026	−	0.250272i
$914$	−0.392305			−0.0129763
$915$	4.45448	−	0.911543i	0.147261	−	0.0301347i
$916$	−8.53590	+	14.7846i	−0.282034	+	0.488497i
$917$	−0.928203	+	1.07180i	−0.0306520	+	0.0353938i
$918$	17.1962	+	4.60770i	0.567558	+	0.152077i
$919$	39.0000	−	22.5167i	1.28649	−	0.742756i	0.308465	−	0.951236i	$-0.400185\pi$
$919$	39.0000	−	22.5167i	1.28649	−	0.742756i	0.978027	+	0.208480i	$0.0668515\pi$
$920$	−2.19615	+	36.5885i	−0.0724050	+	1.20629i
$921$	−7.96410	+	13.7942i	−0.262426	+	0.454535i
$922$	−14.5885	−	54.4449i	−0.480445	−	1.79305i
$923$	25.6077	−	25.6077i	0.842888	−	0.842888i
$924$	−6.19615	+	4.19615i	−0.203838	+	0.138043i
$925$	−1.26795	−	8.87564i	−0.0416899	−	0.291829i
$926$	13.5622	+	7.83013i	0.445681	+	0.257314i
$927$	3.90192	+	14.5622i	0.128156	+	0.478285i
$928$	13.4641	+	3.60770i	0.441981	+	0.118428i
$929$	−13.1603	−	22.7942i	−0.431774	−	0.747854i	0.565252	−	0.824918i	$-0.308779\pi$
$929$	−13.1603	−	22.7942i	−0.431774	−	0.747854i	−0.997026	+	0.0770637i	$0.975446\pi$
$930$	0.267949	+	0.176915i	0.00878640	+	0.00580126i
$931$	9.00000	−	22.5167i	0.294963	−	0.737954i
$932$	14.1962	−	3.80385i	0.465010	−	0.124599i
$933$	−1.48334	+	5.53590i	−0.0485624	+	0.181237i
$934$	15.1244			0.494884
$935$	−19.3923	+	17.1962i	−0.634196	+	0.562374i
$936$	28.3923	−	16.3923i	0.928032	−	0.535799i
$937$	20.3923	−	20.3923i	0.666188	−	0.666188i	−0.290644	−	0.956831i	$-0.593869\pi$
$937$	20.3923	−	20.3923i	0.666188	−	0.666188i	0.956831	+	0.290644i	$0.0938695\pi$
$938$	−23.3205	−	20.1962i	−0.761442	−	0.659428i
$939$	−16.2487			−0.530257
$940$	−38.7846	−	12.9282i	−1.26501	−	0.421671i
$941$	−6.26795	+	10.8564i	−0.204329	+	0.353909i	−0.949919	−	0.312497i	$-0.898835\pi$
$941$	−6.26795	+	10.8564i	−0.204329	+	0.353909i	0.745590	+	0.666405i	$0.232168\pi$
$942$	4.05256	−	4.05256i	0.132040	−	0.132040i
$943$	−9.69615	+	36.1865i	−0.315750	+	1.17840i
$944$	−17.0718	+	9.85641i	−0.555640	+	0.320799i
$945$	−15.0981	+	8.95448i	−0.491140	+	0.291289i
$946$	3.00000	−	1.73205i	0.0975384	−	0.0563138i
$947$	−51.0167	−	13.6699i	−1.65782	−	0.444211i	−0.696032	−	0.718011i	$-0.745053\pi$
$947$	−51.0167	−	13.6699i	−1.65782	−	0.444211i	−0.961787	+	0.273800i	$0.911719\pi$
$948$	0.928203	+	0.248711i	0.0301466	+	0.00807777i
$949$	−23.7846	+	41.1962i	−0.772081	+	1.33728i
$950$	−9.12436	+	22.7321i	−0.296033	+	0.737525i
$951$			5.26795i			0.170825i
$952$	−31.1769	−	6.00000i	−1.01045	−	0.194461i
$953$	−3.46410	+	3.46410i	−0.112213	+	0.112213i	−0.760984	−	0.648771i	$-0.775283\pi$
$953$	−3.46410	+	3.46410i	−0.112213	+	0.112213i	0.648771	+	0.760984i	$0.275283\pi$
$954$	−38.7846	−	22.3923i	−1.25570	−	0.724978i
$955$	−2.83013	+	47.1506i	−0.0915808	+	1.52576i
$956$	−1.26795	−	2.19615i	−0.0410084	−	0.0710286i
$957$	0.901924	−	3.36603i	0.0291551	−	0.108808i
$958$	19.3923	+	5.19615i	0.626537	+	0.167880i
$959$	12.5885	+	18.5885i	0.406502	+	0.600253i
$960$	8.78461	+	2.92820i	0.283522	+	0.0945074i
$961$	−15.4808	−	26.8135i	−0.499379	−	0.864951i
$962$	7.60770	+	7.60770i	0.245282	+	0.245282i
$963$	33.9545	−	9.09808i	1.09417	−	0.293181i
$964$	0.784610			0.0252706
$965$	−1.53590	+	4.60770i	−0.0494423	+	0.148327i
$966$	6.29423	+	9.29423i	0.202513	+	0.299037i
$967$	−36.4904	−	36.4904i	−1.17345	−	1.17345i	−0.981381	−	0.192070i	$-0.938480\pi$
$967$	−36.4904	−	36.4904i	−1.17345	−	1.17345i	−0.192070	−	0.981381i	$-0.561520\pi$
$968$	2.58846	−	9.66025i	0.0831962	−	0.310492i
$969$	3.80385	−	6.58846i	0.122197	−	0.211652i
$970$	19.4641	+	38.9282i	0.624955	+	1.24991i
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	0.980677	−	0.195633i	$-0.0626762\pi$
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	−0.659762	+	0.751475i	$0.729343\pi$
$972$	23.8564	−	6.39230i	0.765195	−	0.205033i
$973$	−11.8301	+	4.09808i	−0.379256	+	0.131378i
$974$	0.0717968	+	0.124356i	0.00230052	+	0.00398461i
$975$	1.31347	−	10.9019i	0.0420646	−	0.349141i
$976$	15.7128			0.502955
$977$	−3.63397	+	0.973721i	−0.116261	+	0.0311521i	−0.316481	−	0.948599i	$-0.602501\pi$
$977$	−3.63397	+	0.973721i	−0.116261	+	0.0311521i	0.200219	+	0.979751i	$0.435835\pi$
$978$	3.92820	+	14.6603i	0.125610	+	0.468783i
$979$		−	18.5885i		−	0.594090i
$980$	25.7128	−	17.8564i	0.821366	−	0.570402i
$981$			21.1244i			0.674449i
$982$	−2.46410	+	0.660254i	−0.0786326	+	0.0210696i
$983$	32.7224	−	8.76795i	1.04368	−	0.279654i	0.304044	−	0.952658i	$-0.401663\pi$
$983$	32.7224	−	8.76795i	1.04368	−	0.279654i	0.739639	+	0.673004i	$0.234996\pi$
$984$	8.19615	+	4.73205i	0.261284	+	0.150852i
$985$	38.6147	−	7.90192i	1.23037	−	0.251776i
$986$	12.8038	−	7.39230i	0.407758	−	0.235419i
$987$	−11.8301	+	4.09808i	−0.376557	+	0.130443i
$988$	−7.60770	−	28.3923i	−0.242033	−	0.903280i
$989$	−2.59808	−	4.50000i	−0.0826140	−	0.143092i
$990$	−7.46410	+	22.3923i	−0.237225	+	0.711674i
$991$	18.6865	−	32.3660i	0.593597	−	1.02814i	−0.400146	−	0.916451i	$-0.631041\pi$
$991$	18.6865	−	32.3660i	0.593597	−	1.02814i	0.993743	−	0.111689i	$-0.0356261\pi$
$992$	0.784610	+	0.784610i	0.0249114	+	0.0249114i
$993$	−3.92820	−	3.92820i	−0.124658	−	0.124658i
$994$	−26.4449	+	17.9090i	−0.838780	+	0.568038i
$995$	−6.92820	+	3.46410i	−0.219639	+	0.109819i
$996$	−11.0718			−0.350823
$997$	−3.00000	+	0.803848i	−0.0950110	+	0.0254581i	−0.306011	−	0.952028i	$-0.598995\pi$
$997$	−3.00000	+	0.803848i	−0.0950110	+	0.0254581i	0.211000	+	0.977486i	$0.432328\pi$
$998$	31.5167	−	31.5167i	0.997642	−	0.997642i
$999$	2.66025	+	4.60770i	0.0841667	+	0.145781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bv.c.157.1	yes	4
5.3	odd	4		280.2.bv.b.213.1	yes	4
7.5	odd	6		280.2.bv.a.117.1	✓	4
8.5	even	2		280.2.bv.d.157.1	yes	4
35.33	even	12		280.2.bv.d.173.1	yes	4
40.13	odd	4		280.2.bv.a.213.1	yes	4
56.5	odd	6		280.2.bv.b.117.1	yes	4
280.173	even	12	inner	280.2.bv.c.173.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bv.a.117.1	✓	4	7.5	odd	6
280.2.bv.a.213.1	yes	4	40.13	odd	4
280.2.bv.b.117.1	yes	4	56.5	odd	6
280.2.bv.b.213.1	yes	4	5.3	odd	4
280.2.bv.c.157.1	yes	4	1.1	even	1	trivial
280.2.bv.c.173.1	yes	4	280.173	even	12	inner
280.2.bv.d.157.1	yes	4	8.5	even	2
280.2.bv.d.173.1	yes	4	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.633975 + 0.366025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.633975 + 0.366025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.36603 - 1.36603i) q^{9} +(1.00000 - 3.00000i) q^{10} +(-2.36603 - 1.36603i) q^{11} +(0.732051 + 0.732051i) q^{12} +(3.00000 - 3.00000i) q^{13} +(-3.09808 + 2.09808i) q^{14} +(0.366025 - 1.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.09808 - 4.09808i) q^{17} +(-2.73205 - 2.73205i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(-4.46410 - 0.267949i) q^{20} +(-1.13397 + 0.767949i) q^{21} +(-1.00000 + 3.73205i) q^{22} +(5.59808 + 1.50000i) q^{23} +(0.732051 - 1.26795i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-5.19615 - 3.00000i) q^{26} +(-2.09808 - 2.09808i) q^{27} +(4.00000 + 3.46410i) q^{28} -2.46410 q^{29} +(-1.63397 - 0.0980762i) q^{30} +(-0.169873 - 0.0980762i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-0.366025 + 1.36603i) q^{33} +(-5.19615 + 3.00000i) q^{34} +(1.46410 - 5.73205i) q^{35} +(-2.73205 + 4.73205i) q^{36} +(-1.73205 - 0.464102i) q^{37} +(3.46410 + 3.46410i) q^{38} +(-1.90192 - 1.09808i) q^{39} +(1.26795 + 6.19615i) q^{40} +6.46410i q^{41} +(1.46410 + 1.26795i) q^{42} +(-0.633975 - 0.633975i) q^{43} +5.46410 q^{44} +(6.09808 + 0.366025i) q^{45} -8.19615i q^{46} +(8.83013 + 2.36603i) q^{47} +(-2.00000 - 0.535898i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(5.56218 - 4.36603i) q^{50} +(-1.90192 + 1.09808i) q^{51} +(-2.19615 + 8.19615i) q^{52} +(11.1962 - 3.00000i) q^{53} +(-2.09808 + 3.63397i) q^{54} +(-2.73205 - 5.46410i) q^{55} +(3.26795 - 6.73205i) q^{56} +(1.26795 + 1.26795i) q^{57} +(0.901924 + 3.36603i) q^{58} +(-4.26795 - 2.46410i) q^{59} +(0.464102 + 2.26795i) q^{60} +(1.96410 + 3.40192i) q^{61} +(-0.0717968 + 0.267949i) q^{62} +(-5.46410 - 4.73205i) q^{63} +8.00000i q^{64} +(9.29423 - 1.90192i) q^{65} +2.00000 q^{66} +(2.13397 + 7.96410i) q^{67} +(6.00000 + 6.00000i) q^{68} -3.00000i q^{69} +(-8.36603 + 0.0980762i) q^{70} +8.53590 q^{71} +(7.46410 + 2.00000i) q^{72} +(-10.8301 + 2.90192i) q^{73} +2.53590i q^{74} +(2.03590 - 1.59808i) q^{75} +(3.46410 - 6.00000i) q^{76} +(-1.36603 + 7.09808i) q^{77} +(-0.803848 + 3.00000i) q^{78} +(0.803848 - 0.464102i) q^{79} +(8.00000 - 4.00000i) q^{80} +(3.33013 - 5.76795i) q^{81} +(8.83013 - 2.36603i) q^{82} +(-7.56218 + 7.56218i) q^{83} +(1.19615 - 2.46410i) q^{84} +(3.00000 - 9.00000i) q^{85} +(-0.633975 + 1.09808i) q^{86} +(0.330127 + 1.23205i) q^{87} +(-2.00000 - 7.46410i) q^{88} +(3.40192 + 5.89230i) q^{89} +(-1.73205 - 8.46410i) q^{90} +(-10.0981 - 4.90192i) q^{91} +(-11.1962 + 3.00000i) q^{92} +(-0.0262794 + 0.0980762i) q^{93} -12.9282i q^{94} +(-7.73205 - 0.464102i) q^{95} +2.92820i q^{96} +(-9.73205 + 9.73205i) q^{97} +(7.92820 + 5.92820i) q^{98} -7.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{5} - 6 q^{6} + 8 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^5 - 6 * q^6 + 8 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{5} - 6 q^{6} + 8 q^{8} + 6 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 6 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} + 12 q^{23} - 4 q^{24} - 6 q^{25} + 2 q^{27} + 16 q^{28} + 4 q^{29} - 10 q^{30} - 18 q^{31} - 8 q^{32} + 2 q^{33} - 8 q^{35} - 4 q^{36} - 18 q^{39} + 12 q^{40} - 8 q^{42} - 6 q^{43} + 8 q^{44} + 14 q^{45} + 18 q^{47} - 8 q^{48} - 22 q^{49} - 2 q^{50} - 18 q^{51} + 12 q^{52} + 24 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 12 q^{57} + 14 q^{58} - 24 q^{59} - 12 q^{60} - 6 q^{61} - 28 q^{62} - 8 q^{63} + 6 q^{65} + 8 q^{66} + 12 q^{67} + 24 q^{68} - 30 q^{70} + 48 q^{71} + 16 q^{72} - 26 q^{73} + 22 q^{75} - 2 q^{77} - 24 q^{78} + 24 q^{79} + 32 q^{80} - 4 q^{81} + 18 q^{82} - 6 q^{83} - 16 q^{84} + 12 q^{85} - 6 q^{86} - 16 q^{87} - 8 q^{88} + 24 q^{89} - 30 q^{91} - 24 q^{92} + 38 q^{93} - 24 q^{95} - 32 q^{97} + 4 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^5 - 6 * q^6 + 8 * q^8 + 6 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 6 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 + 12 * q^23 - 4 * q^24 - 6 * q^25 + 2 * q^27 + 16 * q^28 + 4 * q^29 - 10 * q^30 - 18 * q^31 - 8 * q^32 + 2 * q^33 - 8 * q^35 - 4 * q^36 - 18 * q^39 + 12 * q^40 - 8 * q^42 - 6 * q^43 + 8 * q^44 + 14 * q^45 + 18 * q^47 - 8 * q^48 - 22 * q^49 - 2 * q^50 - 18 * q^51 + 12 * q^52 + 24 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 12 * q^57 + 14 * q^58 - 24 * q^59 - 12 * q^60 - 6 * q^61 - 28 * q^62 - 8 * q^63 + 6 * q^65 + 8 * q^66 + 12 * q^67 + 24 * q^68 - 30 * q^70 + 48 * q^71 + 16 * q^72 - 26 * q^73 + 22 * q^75 - 2 * q^77 - 24 * q^78 + 24 * q^79 + 32 * q^80 - 4 * q^81 + 18 * q^82 - 6 * q^83 - 16 * q^84 + 12 * q^85 - 6 * q^86 - 16 * q^87 - 8 * q^88 + 24 * q^89 - 30 * q^91 - 24 * q^92 + 38 * q^93 - 24 * q^95 - 32 * q^97 + 4 * q^98 - 16 * q^99

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