LMFDB - Embedded newform 370.2.n.c.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.269
Dual form			370.2.n.c.359.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(1.23205 - 1.86603i) q^{10} +4.73205 q^{11} +(4.73205 - 2.73205i) q^{13} +0.732051 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(2.36603 + 4.09808i) q^{19} +(2.00000 - 1.00000i) q^{20} +(4.09808 + 2.36603i) q^{22} -5.46410i q^{23} +(-4.96410 - 0.598076i) q^{25} +5.46410 q^{26} +(0.633975 + 0.366025i) q^{28} -1.73205 q^{29} -9.66025 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.866025 - 1.50000i) q^{34} +(-0.732051 - 1.46410i) q^{35} -3.00000 q^{36} +(-2.59808 + 5.50000i) q^{37} +4.73205i q^{38} +(2.23205 + 0.133975i) q^{40} +(3.96410 + 6.86603i) q^{41} -5.26795i q^{43} +(2.36603 + 4.09808i) q^{44} +(5.59808 + 3.69615i) q^{45} +(2.73205 - 4.73205i) q^{46} +3.26795i q^{47} +(-3.23205 + 5.59808i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(4.73205 + 2.73205i) q^{52} +(-10.7321 - 6.19615i) q^{53} +(0.633975 - 10.5622i) q^{55} +(0.366025 + 0.633975i) q^{56} +(-1.50000 - 0.866025i) q^{58} +(-1.26795 + 2.19615i) q^{59} +(-2.13397 - 3.69615i) q^{61} +(-8.36603 - 4.83013i) q^{62} +2.19615i q^{63} -1.00000 q^{64} +(-5.46410 - 10.9282i) q^{65} +(4.56218 - 2.63397i) q^{67} -1.73205i q^{68} +(0.0980762 - 1.63397i) q^{70} +(-7.56218 - 13.0981i) q^{71} +(-2.59808 - 1.50000i) q^{72} +15.8564i q^{73} +(-5.00000 + 3.46410i) q^{74} +(-2.36603 + 4.09808i) q^{76} +(3.00000 - 1.73205i) q^{77} +(-0.830127 - 1.43782i) q^{79} +(1.86603 + 1.23205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +7.92820i q^{82} +(8.19615 + 4.73205i) q^{83} +(-2.13397 + 3.23205i) q^{85} +(2.63397 - 4.56218i) q^{86} +4.73205i q^{88} +(0.232051 - 0.401924i) q^{89} +(3.00000 + 6.00000i) q^{90} +(2.00000 - 3.46410i) q^{91} +(4.73205 - 2.73205i) q^{92} +(-1.63397 + 2.83013i) q^{94} +(9.46410 - 4.73205i) q^{95} +3.19615i q^{97} +(-5.59808 + 3.23205i) q^{98} +(-7.09808 + 12.2942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 6 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 + 6 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} + 4 q^{5} + 6 q^{7} - 6 q^{9} - 2 q^{10} + 12 q^{11} + 12 q^{13} - 4 q^{14} - 2 q^{16} - 6 q^{17} + 6 q^{19} + 8 q^{20} + 6 q^{22} - 6 q^{25} + 8 q^{26} + 6 q^{28} - 4 q^{31} + 4 q^{35} - 12 q^{36} + 2 q^{40} + 2 q^{41} + 6 q^{44} + 12 q^{45} + 4 q^{46} - 6 q^{49} - 16 q^{50} + 12 q^{52} - 36 q^{53} + 6 q^{55} - 2 q^{56} - 6 q^{58} - 12 q^{59} - 12 q^{61} - 30 q^{62} - 4 q^{64} - 8 q^{65} - 6 q^{67} - 10 q^{70} - 6 q^{71} - 20 q^{74} - 6 q^{76} + 12 q^{77} + 14 q^{79} + 4 q^{80} - 18 q^{81} + 12 q^{83} - 12 q^{85} + 14 q^{86} - 6 q^{89} + 12 q^{90} + 8 q^{91} + 12 q^{92} - 10 q^{94} + 24 q^{95} - 12 q^{98} - 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 6 * q^7 - 6 * q^9 - 2 * q^10 + 12 * q^11 + 12 * q^13 - 4 * q^14 - 2 * q^16 - 6 * q^17 + 6 * q^19 + 8 * q^20 + 6 * q^22 - 6 * q^25 + 8 * q^26 + 6 * q^28 - 4 * q^31 + 4 * q^35 - 12 * q^36 + 2 * q^40 + 2 * q^41 + 6 * q^44 + 12 * q^45 + 4 * q^46 - 6 * q^49 - 16 * q^50 + 12 * q^52 - 36 * q^53 + 6 * q^55 - 2 * q^56 - 6 * q^58 - 12 * q^59 - 12 * q^61 - 30 * q^62 - 4 * q^64 - 8 * q^65 - 6 * q^67 - 10 * q^70 - 6 * q^71 - 20 * q^74 - 6 * q^76 + 12 * q^77 + 14 * q^79 + 4 * q^80 - 18 * q^81 + 12 * q^83 - 12 * q^85 + 14 * q^86 - 6 * q^89 + 12 * q^90 + 8 * q^91 + 12 * q^92 - 10 * q^94 + 24 * q^95 - 12 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$6$		0			0
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	−0.375382	−	0.926870i	$-0.622489\pi$
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	0.615002	+	0.788526i	$0.289155\pi$
$8$			1.00000i			0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	1.23205	−	1.86603i	0.389609	−	0.590089i
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$		0			0
$13$	4.73205	−	2.73205i	1.31243	−	0.757735i	0.329936	−	0.944003i	$-0.392973\pi$
$13$	4.73205	−	2.73205i	1.31243	−	0.757735i	0.982499	+	0.186269i	$0.0596395\pi$
$14$	0.732051			0.195649
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	0.306944	−	0.951727i	$-0.400693\pi$
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	−0.670748	+	0.741685i	$0.734027\pi$
$18$	−2.59808	+	1.50000i	−0.612372	+	0.353553i
$19$	2.36603	+	4.09808i	0.542803	+	0.940163i	0.998742	+	0.0501517i	$0.0159705\pi$
$19$	2.36603	+	4.09808i	0.542803	+	0.940163i	−0.455938	+	0.890011i	$0.650696\pi$
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$		0			0
$22$	4.09808	+	2.36603i	0.873713	+	0.504438i
$23$		−	5.46410i		−	1.13934i	−0.821872	−	0.569672i	$-0.807070\pi$
$23$		−	5.46410i		−	1.13934i	0.821872	−	0.569672i	$-0.192930\pi$
$24$		0			0
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	5.46410			1.07160
$27$		0			0
$28$	0.633975	+	0.366025i	0.119810	+	0.0691723i
$29$	−1.73205			−0.321634			−0.160817	−	0.986984i	$-0.551413\pi$
$29$	−1.73205			−0.321634			−0.160817	+	0.986984i	$0.551413\pi$
$30$		0			0
$31$	−9.66025			−1.73503			−0.867516	−	0.497409i	$-0.834285\pi$
$31$	−9.66025			−1.73503			−0.867516	+	0.497409i	$0.834285\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−0.866025	−	1.50000i	−0.148522	−	0.257248i
$35$	−0.732051	−	1.46410i	−0.123739	−	0.247478i
$36$	−3.00000			−0.500000
$37$	−2.59808	+	5.50000i	−0.427121	+	0.904194i
$37$	−2.59808	+	5.50000i	−0.427121	+	0.904194i
$38$			4.73205i			0.767640i
$39$		0			0
$40$	2.23205	+	0.133975i	0.352918	+	0.0211832i
$41$	3.96410	+	6.86603i	0.619089	+	1.07229i	0.989652	+	0.143486i	$0.0458312\pi$
$41$	3.96410	+	6.86603i	0.619089	+	1.07229i	−0.370564	+	0.928807i	$0.620835\pi$
$42$		0			0
$43$		−	5.26795i		−	0.803355i	−0.915781	−	0.401677i	$-0.868427\pi$
$43$		−	5.26795i		−	0.803355i	0.915781	−	0.401677i	$-0.131573\pi$
$44$	2.36603	+	4.09808i	0.356692	+	0.617808i
$45$	5.59808	+	3.69615i	0.834512	+	0.550990i
$46$	2.73205	−	4.73205i	0.402819	−	0.697703i
$47$			3.26795i			0.476679i	0.971182	+	0.238340i	$0.0766032\pi$
$47$			3.26795i			0.476679i	−0.971182	+	0.238340i	$0.923397\pi$
$48$		0			0
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$	4.73205	+	2.73205i	0.656217	+	0.378867i
$53$	−10.7321	−	6.19615i	−1.47416	−	0.851107i	−0.474584	−	0.880210i	$-0.657402\pi$
$53$	−10.7321	−	6.19615i	−1.47416	−	0.851107i	−0.999576	+	0.0291032i	$0.990735\pi$
$54$		0			0
$55$	0.633975	−	10.5622i	0.0854851	−	1.42420i
$56$	0.366025	+	0.633975i	0.0489122	+	0.0847184i
$57$		0			0
$58$	−1.50000	−	0.866025i	−0.196960	−	0.113715i
$59$	−1.26795	+	2.19615i	−0.165073	+	0.285915i	−0.936681	−	0.350183i	$-0.886119\pi$
$59$	−1.26795	+	2.19615i	−0.165073	+	0.285915i	0.771608	+	0.636098i	$0.219453\pi$
$60$		0			0
$61$	−2.13397	−	3.69615i	−0.273227	−	0.473244i	0.696459	−	0.717597i	$-0.254758\pi$
$61$	−2.13397	−	3.69615i	−0.273227	−	0.473244i	−0.969686	+	0.244353i	$0.921424\pi$
$62$	−8.36603	−	4.83013i	−1.06249	−	0.613427i
$63$			2.19615i			0.276689i
$64$	−1.00000			−0.125000
$65$	−5.46410	−	10.9282i	−0.677738	−	1.35548i
$66$		0			0
$67$	4.56218	−	2.63397i	0.557359	−	0.321791i	−0.194726	−	0.980858i	$-0.562382\pi$
$67$	4.56218	−	2.63397i	0.557359	−	0.321791i	0.752085	+	0.659066i	$0.229048\pi$
$68$		−	1.73205i		−	0.210042i
$69$		0			0
$70$	0.0980762	−	1.63397i	0.0117223	−	0.195297i
$71$	−7.56218	−	13.0981i	−0.897465	−	1.55446i	−0.830723	−	0.556685i	$-0.812073\pi$
$71$	−7.56218	−	13.0981i	−0.897465	−	1.55446i	−0.0667420	−	0.997770i	$-0.521260\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$			15.8564i			1.85585i	0.372764	+	0.927926i	$0.378410\pi$
$73$			15.8564i			1.85585i	−0.372764	+	0.927926i	$0.621590\pi$
$74$	−5.00000	+	3.46410i	−0.581238	+	0.402694i
$75$		0			0
$76$	−2.36603	+	4.09808i	−0.271402	+	0.470082i
$77$	3.00000	−	1.73205i	0.341882	−	0.197386i
$78$		0			0
$79$	−0.830127	−	1.43782i	−0.0933966	−	0.161768i	0.815542	−	0.578698i	$-0.196439\pi$
$79$	−0.830127	−	1.43782i	−0.0933966	−	0.161768i	−0.908938	+	0.416931i	$0.863106\pi$
$80$	1.86603	+	1.23205i	0.208628	+	0.137747i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$			7.92820i			0.875524i
$83$	8.19615	+	4.73205i	0.899645	+	0.519410i	0.877085	−	0.480335i	$-0.159485\pi$
$83$	8.19615	+	4.73205i	0.899645	+	0.519410i	0.0225597	+	0.999745i	$0.492818\pi$
$84$		0			0
$85$	−2.13397	+	3.23205i	−0.231462	+	0.350565i
$86$	2.63397	−	4.56218i	0.284029	−	0.491952i
$87$		0			0
$88$			4.73205i			0.504438i
$89$	0.232051	−	0.401924i	0.0245973	−	0.0426038i	−0.853465	−	0.521151i	$-0.825503\pi$
$89$	0.232051	−	0.401924i	0.0245973	−	0.0426038i	0.878062	+	0.478547i	$0.158836\pi$
$90$	3.00000	+	6.00000i	0.316228	+	0.632456i
$91$	2.00000	−	3.46410i	0.209657	−	0.363137i
$92$	4.73205	−	2.73205i	0.493350	−	0.284836i
$93$		0			0
$94$	−1.63397	+	2.83013i	−0.168532	+	0.291905i
$95$	9.46410	−	4.73205i	0.970996	−	0.485498i
$96$		0			0
$97$			3.19615i			0.324520i	0.986748	+	0.162260i	$0.0518783\pi$
$97$			3.19615i			0.324520i	−0.986748	+	0.162260i	$0.948122\pi$
$98$	−5.59808	+	3.23205i	−0.565491	+	0.326486i
$99$	−7.09808	+	12.2942i	−0.713384	+	1.23562i
$100$	−1.96410	−	4.59808i	−0.196410	−	0.459808i
$101$	3.73205			0.371353			0.185676	−	0.982611i	$-0.440552\pi$
$101$	3.73205			0.371353			0.185676	+	0.982611i	$0.440552\pi$
$102$		0			0
$103$		−	14.1962i		−	1.39879i	−0.714736	−	0.699394i	$-0.753453\pi$
$103$		−	14.1962i		−	1.39879i	0.714736	−	0.699394i	$-0.246547\pi$
$104$	2.73205	+	4.73205i	0.267900	+	0.464016i
$105$		0			0
$106$	−6.19615	−	10.7321i	−0.601824	−	1.04239i
$107$	−3.63397	+	2.09808i	−0.351310	+	0.202829i	−0.665262	−	0.746610i	$-0.731680\pi$
$107$	−3.63397	+	2.09808i	−0.351310	+	0.202829i	0.313952	+	0.949439i	$0.398347\pi$
$108$		0			0
$109$	−6.59808	+	11.4282i	−0.631981	+	1.09462i	0.355165	+	0.934804i	$0.384425\pi$
$109$	−6.59808	+	11.4282i	−0.631981	+	1.09462i	−0.987146	+	0.159820i	$0.948909\pi$
$110$	5.83013	−	8.83013i	0.555881	−	0.841920i
$111$		0			0
$112$			0.732051i			0.0691723i
$113$	2.66025	+	1.53590i	0.250256	+	0.144485i	0.619881	−	0.784696i	$-0.287181\pi$
$113$	2.66025	+	1.53590i	0.250256	+	0.144485i	−0.369626	+	0.929181i	$0.620514\pi$
$114$		0			0
$115$	−12.1962	−	0.732051i	−1.13730	−	0.0682641i
$116$	−0.866025	−	1.50000i	−0.0804084	−	0.139272i
$117$			16.3923i			1.51547i
$118$	−2.19615	+	1.26795i	−0.202172	+	0.116724i
$119$	−1.26795			−0.116233
$120$		0			0
$121$	11.3923			1.03566
$122$		−	4.26795i		−	0.386402i
$123$		0			0
$124$	−4.83013	−	8.36603i	−0.433758	−	0.751291i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−1.09808	+	1.90192i	−0.0978244	+	0.169437i
$127$	−2.53590	−	1.46410i	−0.225025	−	0.129918i	0.383250	−	0.923645i	$-0.374805\pi$
$127$	−2.53590	−	1.46410i	−0.225025	−	0.129918i	−0.608275	+	0.793727i	$0.708138\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	0.732051	−	12.1962i	0.0642051	−	1.06967i
$131$	5.46410	−	9.46410i	0.477401	−	0.826882i	−0.522264	−	0.852784i	$-0.674912\pi$
$131$	5.46410	−	9.46410i	0.477401	−	0.826882i	0.999664	+	0.0259016i	$0.00824567\pi$
$132$		0			0
$133$	3.00000	+	1.73205i	0.260133	+	0.150188i
$134$	5.26795			0.455081
$135$		0			0
$136$	0.866025	−	1.50000i	0.0742611	−	0.128624i
$137$		−	1.73205i		−	0.147979i	−0.997259	−	0.0739895i	$-0.976427\pi$
$137$		−	1.73205i		−	0.147979i	0.997259	−	0.0739895i	$-0.0235731\pi$
$138$		0			0
$139$	−1.46410	+	2.53590i	−0.124183	+	0.215092i	−0.921413	−	0.388584i	$-0.872964\pi$
$139$	−1.46410	+	2.53590i	−0.124183	+	0.215092i	0.797230	+	0.603676i	$0.206298\pi$
$140$	0.901924	−	1.36603i	0.0762265	−	0.115450i
$141$		0			0
$142$		−	15.1244i		−	1.26921i
$143$	22.3923	−	12.9282i	1.87254	−	1.08111i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−0.232051	+	3.86603i	−0.0192708	+	0.321056i
$146$	−7.92820	+	13.7321i	−0.656143	+	1.13647i
$147$		0			0
$148$	−6.06218	+	0.500000i	−0.498308	+	0.0410997i
$149$	19.5885			1.60475			0.802374	−	0.596821i	$-0.203570\pi$
$149$	19.5885			1.60475			0.802374	+	0.596821i	$0.203570\pi$
$150$		0			0
$151$	8.73205	+	15.1244i	0.710604	+	1.23080i	0.964631	+	0.263605i	$0.0849117\pi$
$151$	8.73205	+	15.1244i	0.710604	+	1.23080i	−0.254026	+	0.967197i	$0.581755\pi$
$152$	−4.09808	+	2.36603i	−0.332398	+	0.191910i
$153$	4.50000	−	2.59808i	0.363803	−	0.210042i
$154$	3.46410			0.279145
$155$	−1.29423	+	21.5622i	−0.103955	+	1.73192i
$156$		0			0
$157$	−14.7224	−	8.50000i	−1.17498	−	0.678374i	−0.220131	−	0.975470i	$-0.570648\pi$
$157$	−14.7224	−	8.50000i	−1.17498	−	0.678374i	−0.954847	+	0.297097i	$0.903982\pi$
$158$		−	1.66025i		−	0.132083i
$159$		0			0
$160$	1.00000	+	2.00000i	0.0790569	+	0.158114i
$161$	−2.00000	−	3.46410i	−0.157622	−	0.273009i
$162$		−	9.00000i		−	0.707107i
$163$	−13.0981	−	7.56218i	−1.02592	−	0.592315i	−0.110107	−	0.993920i	$-0.535119\pi$
$163$	−13.0981	−	7.56218i	−1.02592	−	0.592315i	−0.915813	+	0.401604i	$0.868453\pi$
$164$	−3.96410	+	6.86603i	−0.309544	+	0.536147i
$165$		0			0
$166$	4.73205	+	8.19615i	0.367278	+	0.636145i
$167$	8.53590	−	4.92820i	0.660528	−	0.381356i	−0.131950	−	0.991256i	$-0.542124\pi$
$167$	8.53590	−	4.92820i	0.660528	−	0.381356i	0.792478	+	0.609901i	$0.208791\pi$
$168$		0			0
$169$	8.42820	−	14.5981i	0.648323	−	1.12293i
$170$	−3.46410	+	1.73205i	−0.265684	+	0.132842i
$171$	−14.1962			−1.08561
$172$	4.56218	−	2.63397i	0.347863	−	0.200839i
$173$	12.0622	+	6.96410i	0.917070	+	0.529471i	0.882699	−	0.469938i	$-0.155724\pi$
$173$	12.0622	+	6.96410i	0.917070	+	0.529471i	0.0343711	+	0.999409i	$0.489057\pi$
$174$		0			0
$175$	−3.36603	+	1.43782i	−0.254448	+	0.108689i
$176$	−2.36603	+	4.09808i	−0.178346	+	0.308904i
$177$		0			0
$178$	0.401924	−	0.232051i	0.0301255	−	0.0173929i
$179$	1.07180			0.0801099			0.0400549	−	0.999197i	$-0.487247\pi$
$179$	1.07180			0.0801099			0.0400549	+	0.999197i	$0.487247\pi$
$180$	−0.401924	+	6.69615i	−0.0299576	+	0.499102i
$181$	9.79423	+	16.9641i	0.727999	+	1.26093i	0.957728	+	0.287677i	$0.0928829\pi$
$181$	9.79423	+	16.9641i	0.727999	+	1.26093i	−0.229728	+	0.973255i	$0.573784\pi$
$182$	3.46410	−	2.00000i	0.256776	−	0.148250i
$183$		0			0
$184$	5.46410			0.402819
$185$	11.9282	+	6.53590i	0.876979	+	0.480529i
$186$		0			0
$187$	−7.09808	−	4.09808i	−0.519063	−	0.299681i
$188$	−2.83013	+	1.63397i	−0.206408	+	0.119170i
$189$		0			0
$190$	10.5622	+	0.633975i	0.766261	+	0.0459934i
$191$	15.3205			1.10855			0.554277	−	0.832333i	$-0.312995\pi$
$191$	15.3205			1.10855			0.554277	+	0.832333i	$0.312995\pi$
$192$		0			0
$193$			0.660254i			0.0475261i	0.999718	+	0.0237631i	$0.00756473\pi$
$193$			0.660254i			0.0475261i	−0.999718	+	0.0237631i	$0.992435\pi$
$194$	−1.59808	+	2.76795i	−0.114735	+	0.198727i
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−17.2583	−	9.96410i	−1.22961	−	0.709913i	−0.262658	−	0.964889i	$-0.584599\pi$
$197$	−17.2583	−	9.96410i	−1.22961	−	0.709913i	−0.966947	+	0.254976i	$0.917932\pi$
$198$	−12.2942	+	7.09808i	−0.873713	+	0.504438i
$199$	−12.1962			−0.864562			−0.432281	−	0.901739i	$-0.642291\pi$
$199$	−12.1962			−0.864562			−0.432281	+	0.901739i	$0.642291\pi$
$200$	0.598076	−	4.96410i	0.0422904	−	0.351015i
$201$		0			0
$202$	3.23205	+	1.86603i	0.227406	+	0.131293i
$203$	−1.09808	+	0.633975i	−0.0770698	+	0.0444963i
$204$		0			0
$205$	15.8564	−	7.92820i	1.10746	−	0.553730i
$206$	7.09808	−	12.2942i	0.494546	−	0.856579i
$207$	14.1962	+	8.19615i	0.986701	+	0.569672i
$208$			5.46410i			0.378867i
$209$	11.1962	+	19.3923i	0.774454	+	1.34139i
$210$		0			0
$211$	−20.0526			−1.38048			−0.690238	−	0.723583i	$-0.742494\pi$
$211$	−20.0526			−1.38048			−0.690238	+	0.723583i	$0.742494\pi$
$212$		−	12.3923i		−	0.851107i
$213$		0			0
$214$	−4.19615			−0.286843
$215$	−11.7583	−	0.705771i	−0.801911	−	0.0481332i
$216$		0			0
$217$	−6.12436	+	3.53590i	−0.415748	+	0.240032i
$218$	−11.4282	+	6.59808i	−0.774016	+	0.446878i
$219$		0			0
$220$	9.46410	−	4.73205i	0.638070	−	0.319035i
$221$	−9.46410			−0.636624
$222$		0			0
$223$			14.9282i			0.999666i	0.866122	+	0.499833i	$0.166605\pi$
$223$			14.9282i			0.999666i	−0.866122	+	0.499833i	$0.833395\pi$
$224$	−0.366025	+	0.633975i	−0.0244561	+	0.0423592i
$225$	9.00000	−	12.0000i	0.600000	−	0.800000i
$226$	1.53590	+	2.66025i	0.102166	+	0.176957i
$227$	18.7583	−	10.8301i	1.24503	−	0.718821i	0.274919	−	0.961467i	$-0.411349\pi$
$227$	18.7583	−	10.8301i	1.24503	−	0.718821i	0.970115	+	0.242647i	$0.0780155\pi$
$228$		0			0
$229$	2.79423	+	4.83975i	0.184648	+	0.319819i	0.943458	−	0.331493i	$-0.107552\pi$
$229$	2.79423	+	4.83975i	0.184648	+	0.319819i	−0.758810	+	0.651312i	$0.774219\pi$
$230$	−10.1962	−	6.73205i	−0.672314	−	0.443898i
$231$		0			0
$232$		−	1.73205i		−	0.113715i
$233$			10.2679i			0.672676i	0.941741	+	0.336338i	$0.109188\pi$
$233$			10.2679i			0.672676i	−0.941741	+	0.336338i	$0.890812\pi$
$234$	−8.19615	+	14.1962i	−0.535799	+	0.928032i
$235$	7.29423	+	0.437822i	0.475823	+	0.0285604i
$236$	−2.53590			−0.165073
$237$		0			0
$238$	−1.09808	−	0.633975i	−0.0711777	−	0.0410945i
$239$	8.29423	−	14.3660i	0.536509	−	0.929261i	−0.462580	−	0.886578i	$-0.653076\pi$
$239$	8.29423	−	14.3660i	0.536509	−	0.929261i	0.999089	−	0.0426832i	$-0.0135906\pi$
$240$		0			0
$241$	5.26795	+	9.12436i	0.339338	+	0.587751i	0.984308	−	0.176456i	$-0.0564635\pi$
$241$	5.26795	+	9.12436i	0.339338	+	0.587751i	−0.644970	+	0.764208i	$0.723130\pi$
$242$	9.86603	+	5.69615i	0.634212	+	0.366163i
$243$		0			0
$244$	2.13397	−	3.69615i	0.136614	−	0.236622i
$245$	12.0622	+	7.96410i	0.770624	+	0.508808i
$246$		0			0
$247$	22.3923	+	12.9282i	1.42479	+	0.822602i
$248$		−	9.66025i		−	0.613427i
$249$		0			0
$250$	−7.23205	+	8.52628i	−0.457395	+	0.539249i
$251$	22.1962			1.40101			0.700504	−	0.713648i	$-0.252958\pi$
$251$	22.1962			1.40101			0.700504	+	0.713648i	$0.252958\pi$
$252$	−1.90192	+	1.09808i	−0.119810	+	0.0691723i
$253$		−	25.8564i		−	1.62558i
$254$	−1.46410	−	2.53590i	−0.0918659	−	0.159116i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.0885	−	11.5981i	−1.25308	−	0.723468i	−0.281363	−	0.959601i	$-0.590786\pi$
$257$	−20.0885	−	11.5981i	−1.25308	−	0.723468i	−0.971721	+	0.236133i	$0.924120\pi$
$258$		0			0
$259$	0.366025	+	4.43782i	0.0227437	+	0.275753i
$260$	6.73205	−	10.1962i	0.417504	−	0.632339i
$261$	2.59808	−	4.50000i	0.160817	−	0.278543i
$262$	9.46410	−	5.46410i	0.584694	−	0.337573i
$263$	19.8564	−	11.4641i	1.22440	−	0.706907i	0.258546	−	0.965999i	$-0.416757\pi$
$263$	19.8564	−	11.4641i	1.22440	−	0.706907i	0.965853	+	0.259092i	$0.0834233\pi$
$264$		0			0
$265$	−15.2679	+	23.1244i	−0.937903	+	1.42052i
$266$	1.73205	+	3.00000i	0.106199	+	0.183942i
$267$		0			0
$268$	4.56218	+	2.63397i	0.278679	+	0.160896i
$269$	−9.85641			−0.600956			−0.300478	−	0.953789i	$-0.597146\pi$
$269$	−9.85641			−0.600956			−0.300478	+	0.953789i	$0.597146\pi$
$270$		0			0
$271$	−2.63397	+	4.56218i	−0.160003	+	0.277133i	−0.934869	−	0.354992i	$-0.884484\pi$
$271$	−2.63397	+	4.56218i	−0.160003	+	0.277133i	0.774867	+	0.632125i	$0.217817\pi$
$272$	1.50000	−	0.866025i	0.0909509	−	0.0525105i
$273$		0			0
$274$	0.866025	−	1.50000i	0.0523185	−	0.0906183i
$275$	−23.4904	−	2.83013i	−1.41652	−	0.170663i
$276$		0			0
$277$	−16.7942	+	9.69615i	−1.00907	+	0.582585i	−0.910918	−	0.412586i	$-0.864625\pi$
$277$	−16.7942	+	9.69615i	−1.00907	+	0.582585i	−0.0981489	+	0.995172i	$0.531292\pi$
$278$	−2.53590	+	1.46410i	−0.152093	+	0.0878110i
$279$	14.4904	−	25.0981i	0.867516	−	1.50258i
$280$	1.46410	−	0.732051i	0.0874968	−	0.0437484i
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	−14.0263	+	8.09808i	−0.833776	+	0.481381i	−0.855144	−	0.518391i	$-0.826531\pi$
$283$	−14.0263	+	8.09808i	−0.833776	+	0.481381i	0.0213679	+	0.999772i	$0.493198\pi$
$284$	7.56218	−	13.0981i	0.448733	−	0.777228i
$285$		0			0
$286$	25.8564			1.52892
$287$	5.02628	+	2.90192i	0.296692	+	0.171295i
$288$		−	3.00000i		−	0.176777i
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$	−2.13397	+	3.23205i	−0.125311	+	0.189793i
$291$		0			0
$292$	−13.7321	+	7.92820i	−0.803607	+	0.463963i
$293$	0.990381	−	0.571797i	0.0578587	−	0.0334047i	−0.470792	−	0.882244i	$-0.656032\pi$
$293$	0.990381	−	0.571797i	0.0578587	−	0.0334047i	0.528650	+	0.848840i	$0.322698\pi$
$294$		0			0
$295$	4.73205	+	3.12436i	0.275511	+	0.181907i
$296$	−5.50000	−	2.59808i	−0.319681	−	0.151010i
$297$		0			0
$298$	16.9641	+	9.79423i	0.982704	+	0.567364i
$299$	−14.9282	−	25.8564i	−0.863320	−	1.49531i
$300$		0			0
$301$	−1.92820	−	3.33975i	−0.111140	−	0.192500i
$302$			17.4641i			1.00495i
$303$		0			0
$304$	−4.73205			−0.271402
$305$	−8.53590	+	4.26795i	−0.488764	+	0.244382i
$306$	5.19615			0.297044
$307$		−	31.1244i		−	1.77636i	−0.459495	−	0.888180i	$-0.651970\pi$
$307$		−	31.1244i		−	1.77636i	0.459495	−	0.888180i	$-0.348030\pi$
$308$	3.00000	+	1.73205i	0.170941	+	0.0986928i
$309$		0			0
$310$	−11.9019	+	18.0263i	−0.675984	+	1.02382i
$311$	−0.633975	+	1.09808i	−0.0359494	+	0.0622662i	−0.883440	−	0.468544i	$-0.844779\pi$
$311$	−0.633975	+	1.09808i	−0.0359494	+	0.0622662i	0.847491	+	0.530810i	$0.178112\pi$
$312$		0			0
$313$	11.4282	+	6.59808i	0.645960	+	0.372945i	0.786907	−	0.617072i	$-0.211681\pi$
$313$	11.4282	+	6.59808i	0.645960	+	0.372945i	−0.140947	+	0.990017i	$0.545015\pi$
$314$	−8.50000	−	14.7224i	−0.479683	−	0.830835i
$315$	4.90192	+	0.294229i	0.276192	+	0.0165779i
$316$	0.830127	−	1.43782i	0.0466983	−	0.0808838i
$317$	−17.5981	−	10.1603i	−0.988406	−	0.570657i	−0.0836089	−	0.996499i	$-0.526645\pi$
$317$	−17.5981	−	10.1603i	−0.988406	−	0.570657i	−0.904798	+	0.425842i	$0.859978\pi$
$318$		0			0
$319$	−8.19615			−0.458896
$320$	−0.133975	+	2.23205i	−0.00748941	+	0.124775i
$321$		0			0
$322$		−	4.00000i		−	0.222911i
$323$		−	8.19615i		−	0.456046i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−25.1244	+	10.7321i	−1.39365	+	0.595307i
$326$	−7.56218	−	13.0981i	−0.418830	−	0.725435i
$327$		0			0
$328$	−6.86603	+	3.96410i	−0.379113	+	0.218881i
$329$	1.19615	+	2.07180i	0.0659460	+	0.114222i
$330$		0			0
$331$	−0.196152	+	0.339746i	−0.0107815	+	0.0186741i	−0.871366	−	0.490634i	$-0.836765\pi$
$331$	−0.196152	+	0.339746i	−0.0107815	+	0.0186741i	0.860584	+	0.509308i	$0.170099\pi$
$332$			9.46410i			0.519410i
$333$	−10.3923	−	15.0000i	−0.569495	−	0.821995i
$334$	9.85641			0.539319
$335$	−5.26795	−	10.5359i	−0.287819	−	0.575638i
$336$		0			0
$337$	7.96410	−	4.59808i	0.433832	−	0.250473i	−0.267146	−	0.963656i	$-0.586080\pi$
$337$	7.96410	−	4.59808i	0.433832	−	0.250473i	0.700978	+	0.713183i	$0.252747\pi$
$338$	14.5981	−	8.42820i	0.794031	−	0.458434i
$339$		0			0
$340$	−3.86603	−	0.232051i	−0.209665	−	0.0125847i
$341$	−45.7128			−2.47549
$342$	−12.2942	−	7.09808i	−0.664796	−	0.383820i
$343$			9.85641i			0.532196i
$344$	5.26795			0.284029
$345$		0			0
$346$	6.96410	+	12.0622i	0.374392	+	0.648467i
$347$			27.7128i			1.48770i	0.668346	+	0.743851i	$0.267003\pi$
$347$			27.7128i			1.48770i	−0.668346	+	0.743851i	$0.732997\pi$
$348$		0			0
$349$	1.20577	−	2.08846i	0.0645435	−	0.111793i	−0.831948	−	0.554854i	$-0.812774\pi$
$349$	1.20577	−	2.08846i	0.0645435	−	0.111793i	0.896491	+	0.443061i	$0.146108\pi$
$350$	−3.63397	−	0.437822i	−0.194244	−	0.0234026i
$351$		0			0
$352$	−4.09808	+	2.36603i	−0.218428	+	0.126110i
$353$	8.89230	+	5.13397i	0.473290	+	0.273254i	0.717616	−	0.696439i	$-0.245233\pi$
$353$	8.89230	+	5.13397i	0.473290	+	0.273254i	−0.244326	+	0.969693i	$0.578567\pi$
$354$		0			0
$355$	−30.2487	+	15.1244i	−1.60543	+	0.802717i
$356$	0.464102			0.0245973
$357$		0			0
$358$	0.928203	+	0.535898i	0.0490571	+	0.0283231i
$359$	10.5359			0.556063			0.278032	−	0.960572i	$-0.410318\pi$
$359$	10.5359			0.556063			0.278032	+	0.960572i	$0.410318\pi$
$360$	−3.69615	+	5.59808i	−0.194804	+	0.295045i
$361$	−1.69615	+	2.93782i	−0.0892712	+	0.154622i
$362$			19.5885i			1.02955i
$363$		0			0
$364$	4.00000			0.209657
$365$	35.3923	+	2.12436i	1.85252	+	0.111194i
$366$		0			0
$367$	5.32051	−	3.07180i	0.277728	−	0.160346i	−0.354666	−	0.934993i	$-0.615406\pi$
$367$	5.32051	−	3.07180i	0.277728	−	0.160346i	0.632395	+	0.774646i	$0.282072\pi$
$368$	4.73205	+	2.73205i	0.246675	+	0.142418i
$369$	−23.7846			−1.23818
$370$	7.06218	+	11.6244i	0.367145	+	0.604321i
$371$	−9.07180			−0.470984
$372$		0			0
$373$	−0.866025	+	0.500000i	−0.0448411	+	0.0258890i	−0.522253	−	0.852791i	$-0.674908\pi$
$373$	−0.866025	+	0.500000i	−0.0448411	+	0.0258890i	0.477412	+	0.878680i	$0.341575\pi$
$374$	−4.09808	−	7.09808i	−0.211906	−	0.367033i
$375$		0			0
$376$	−3.26795			−0.168532
$377$	−8.19615	+	4.73205i	−0.422123	+	0.243713i
$378$		0			0
$379$	2.70577	−	4.68653i	0.138986	−	0.240731i	−0.788127	−	0.615513i	$-0.788949\pi$
$379$	2.70577	−	4.68653i	0.138986	−	0.240731i	0.927113	+	0.374782i	$0.122282\pi$
$380$	8.83013	+	5.83013i	0.452976	+	0.299079i
$381$		0			0
$382$	13.2679	+	7.66025i	0.678847	+	0.391933i
$383$	−25.5622	+	14.7583i	−1.30617	+	0.754115i	−0.981454	−	0.191697i	$-0.938601\pi$
$383$	−25.5622	+	14.7583i	−1.30617	+	0.754115i	−0.324712	+	0.945813i	$0.605267\pi$
$384$		0			0
$385$	−3.46410	−	6.92820i	−0.176547	−	0.353094i
$386$	−0.330127	+	0.571797i	−0.0168030	+	0.0291037i
$387$	13.6865	+	7.90192i	0.695726	+	0.401677i
$388$	−2.76795	+	1.59808i	−0.140521	+	0.0811300i
$389$	−5.86603	−	10.1603i	−0.297419	−	0.515145i	0.678125	−	0.734946i	$-0.262793\pi$
$389$	−5.86603	−	10.1603i	−0.297419	−	0.515145i	−0.975545	+	0.219801i	$0.929459\pi$
$390$		0			0
$391$	−4.73205	+	8.19615i	−0.239310	+	0.414497i
$392$	−5.59808	−	3.23205i	−0.282746	−	0.163243i
$393$		0			0
$394$	−9.96410	−	17.2583i	−0.501984	−	0.869462i
$395$	−3.32051	+	1.66025i	−0.167073	+	0.0835364i
$396$	−14.1962			−0.713384
$397$			13.9282i			0.699036i	0.936930	+	0.349518i	$0.113655\pi$
$397$			13.9282i			0.699036i	−0.936930	+	0.349518i	$0.886345\pi$
$398$	−10.5622	−	6.09808i	−0.529434	−	0.305669i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−19.3205			−0.964820			−0.482410	−	0.875946i	$-0.660238\pi$
$401$	−19.3205			−0.964820			−0.482410	+	0.875946i	$0.660238\pi$
$402$		0			0
$403$	−45.7128	+	26.3923i	−2.27712	+	1.31469i
$404$	1.86603	+	3.23205i	0.0928382	+	0.160801i
$405$	−18.0000	+	9.00000i	−0.894427	+	0.447214i
$406$	−1.26795			−0.0629273
$407$	−12.2942	+	26.0263i	−0.609402	+	1.29007i
$408$		0			0
$409$	18.8923	−	32.7224i	0.934164	−	1.61802i	0.158047	−	0.987432i	$-0.449480\pi$
$409$	18.8923	−	32.7224i	0.934164	−	1.61802i	0.776117	−	0.630589i	$-0.217186\pi$
$410$	17.6962	+	1.06218i	0.873951	+	0.0524572i
$411$		0			0
$412$	12.2942	−	7.09808i	0.605693	−	0.349697i
$413$			1.85641i			0.0913478i
$414$	8.19615	+	14.1962i	0.402819	+	0.697703i
$415$	11.6603	−	17.6603i	0.572379	−	0.866908i
$416$	−2.73205	+	4.73205i	−0.133950	+	0.232008i
$417$		0			0
$418$			22.3923i			1.09524i
$419$	8.90192	−	15.4186i	0.434887	−	0.753247i	−0.562399	−	0.826866i	$-0.690121\pi$
$419$	8.90192	−	15.4186i	0.434887	−	0.753247i	0.997286	+	0.0736188i	$0.0234548\pi$
$420$		0			0
$421$	28.5167			1.38982			0.694908	−	0.719098i	$-0.255445\pi$
$421$	28.5167			1.38982			0.694908	+	0.719098i	$0.255445\pi$
$422$	−17.3660	−	10.0263i	−0.845365	−	0.488072i
$423$	−8.49038	−	4.90192i	−0.412816	−	0.238340i
$424$	6.19615	−	10.7321i	0.300912	−	0.521194i
$425$	6.92820	+	5.19615i	0.336067	+	0.252050i
$426$		0			0
$427$	−2.70577	−	1.56218i	−0.130941	−	0.0755991i
$428$	−3.63397	−	2.09808i	−0.175655	−	0.101414i
$429$		0			0
$430$	−9.83013	−	6.49038i	−0.474051	−	0.312994i
$431$	−4.63397	−	8.02628i	−0.223211	−	0.386612i	0.732570	−	0.680691i	$-0.238320\pi$
$431$	−4.63397	−	8.02628i	−0.223211	−	0.386612i	−0.955781	+	0.294079i	$0.904987\pi$
$432$		0			0
$433$		−	40.3731i		−	1.94021i	−0.242694	−	0.970103i	$-0.578031\pi$
$433$		−	40.3731i		−	1.94021i	0.242694	−	0.970103i	$-0.421969\pi$
$434$	−7.07180			−0.339457
$435$		0			0
$436$	−13.1962			−0.631981
$437$	22.3923	−	12.9282i	1.07117	−	0.618440i
$438$		0			0
$439$	−3.07180	−	5.32051i	−0.146609	−	0.253934i	0.783363	−	0.621564i	$-0.213503\pi$
$439$	−3.07180	−	5.32051i	−0.146609	−	0.253934i	−0.929972	+	0.367630i	$0.880169\pi$
$440$	10.5622	+	0.633975i	0.503532	+	0.0302236i
$441$	−9.69615	−	16.7942i	−0.461722	−	0.799725i
$442$	−8.19615	−	4.73205i	−0.389851	−	0.225081i
$443$		−	16.7846i		−	0.797461i	−0.917068	−	0.398730i	$-0.869451\pi$
$443$		−	16.7846i		−	0.797461i	0.917068	−	0.398730i	$-0.130549\pi$
$444$		0			0
$445$	−0.866025	−	0.571797i	−0.0410535	−	0.0271058i
$446$	−7.46410	+	12.9282i	−0.353435	+	0.612168i
$447$		0			0
$448$	−0.633975	+	0.366025i	−0.0299525	+	0.0172931i
$449$	−3.12436	−	5.41154i	−0.147447	−	0.255386i	0.782836	−	0.622228i	$-0.213772\pi$
$449$	−3.12436	−	5.41154i	−0.147447	−	0.255386i	−0.930283	+	0.366842i	$0.880439\pi$
$450$	13.7942	−	5.89230i	0.650266	−	0.277766i
$451$	18.7583	+	32.4904i	0.883295	+	1.52991i
$452$			3.07180i			0.144485i
$453$		0			0
$454$	21.6603			1.01657
$455$	−7.46410	−	4.92820i	−0.349922	−	0.231038i
$456$		0			0
$457$	−16.6244	+	9.59808i	−0.777655	+	0.448979i	−0.835598	−	0.549341i	$-0.814879\pi$
$457$	−16.6244	+	9.59808i	−0.777655	+	0.448979i	0.0579439	+	0.998320i	$0.481546\pi$
$458$			5.58846i			0.261131i
$459$		0			0
$460$	−5.46410	−	10.9282i	−0.254765	−	0.509530i
$461$	10.8564	−	18.8038i	0.505633	−	0.875782i	−0.494346	−	0.869266i	$-0.664592\pi$
$461$	10.8564	−	18.8038i	0.505633	−	0.875782i	0.999979	−	0.00651699i	$-0.00207444\pi$
$462$		0			0
$463$	26.8301	−	15.4904i	1.24690	−	0.719899i	0.276411	−	0.961039i	$-0.410855\pi$
$463$	26.8301	−	15.4904i	1.24690	−	0.719899i	0.970490	+	0.241140i	$0.0775214\pi$
$464$	0.866025	−	1.50000i	0.0402042	−	0.0696358i
$465$		0			0
$466$	−5.13397	+	8.89230i	−0.237827	+	0.411928i
$467$		−	21.4641i		−	0.993240i	−0.867968	−	0.496620i	$-0.834574\pi$
$467$		−	21.4641i		−	0.993240i	0.867968	−	0.496620i	$-0.165426\pi$
$468$	−14.1962	+	8.19615i	−0.656217	+	0.378867i
$469$	1.92820	−	3.33975i	0.0890362	−	0.154215i
$470$	6.09808	+	4.02628i	0.281283	+	0.185718i
$471$		0			0
$472$	−2.19615	−	1.26795i	−0.101086	−	0.0583621i
$473$		−	24.9282i		−	1.14620i
$474$		0			0
$475$	−9.29423	−	21.7583i	−0.426448	−	0.998341i
$476$	−0.633975	−	1.09808i	−0.0290582	−	0.0503302i
$477$	32.1962	−	18.5885i	1.47416	−	0.851107i
$478$	14.3660	−	8.29423i	0.657087	−	0.379369i
$479$	−4.73205	+	8.19615i	−0.216213	+	0.374492i	−0.953647	−	0.300927i	$-0.902704\pi$
$479$	−4.73205	+	8.19615i	−0.216213	+	0.374492i	0.737434	+	0.675419i	$0.236037\pi$
$480$		0			0
$481$	2.73205	+	33.1244i	0.124571	+	1.51034i
$482$			10.5359i			0.479897i
$483$		0			0
$484$	5.69615	+	9.86603i	0.258916	+	0.448456i
$485$	7.13397	+	0.428203i	0.323937	+	0.0194437i
$486$		0			0
$487$			26.5359i			1.20246i	0.799077	+	0.601228i	$0.205322\pi$
$487$			26.5359i			1.20246i	−0.799077	+	0.601228i	$0.794678\pi$
$488$	3.69615	−	2.13397i	0.167317	−	0.0966005i
$489$		0			0
$490$	6.46410	+	12.9282i	0.292018	+	0.584037i
$491$	−12.3397			−0.556885			−0.278442	−	0.960453i	$-0.589818\pi$
$491$	−12.3397			−0.556885			−0.278442	+	0.960453i	$0.589818\pi$
$492$		0			0
$493$	2.59808	+	1.50000i	0.117011	+	0.0675566i
$494$	12.9282	+	22.3923i	0.581667	+	1.00748i
$495$	26.4904	+	17.4904i	1.19065	+	0.786134i
$496$	4.83013	−	8.36603i	0.216879	−	0.375646i
$497$	−9.58846	−	5.53590i	−0.430101	−	0.248319i
$498$		0			0
$499$	18.7583	+	32.4904i	0.839738	+	1.45447i	0.890114	+	0.455739i	$0.150625\pi$
$499$	18.7583	+	32.4904i	0.839738	+	1.45447i	−0.0503753	+	0.998730i	$0.516042\pi$
$500$	−10.5263	+	3.76795i	−0.470750	+	0.168508i
$501$		0			0
$502$	19.2224	+	11.0981i	0.857939	+	0.495331i
$503$	20.8301	+	12.0263i	0.928769	+	0.536225i	0.886422	−	0.462878i	$-0.153183\pi$
$503$	20.8301	+	12.0263i	0.928769	+	0.536225i	0.0423473	+	0.999103i	$0.486516\pi$
$504$	−2.19615			−0.0978244
$505$	0.500000	−	8.33013i	0.0222497	−	0.370686i
$506$	12.9282	−	22.3923i	0.574729	−	0.995459i
$507$		0			0
$508$		−	2.92820i		−	0.129918i
$509$	−2.25833	+	3.91154i	−0.100099	+	0.173376i	−0.911725	−	0.410801i	$-0.865249\pi$
$509$	−2.25833	+	3.91154i	−0.100099	+	0.173376i	0.811626	+	0.584177i	$0.198583\pi$
$510$		0			0
$511$	5.80385	+	10.0526i	0.256747	+	0.444699i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−11.5981	−	20.0885i	−0.511569	−	0.886064i
$515$	−31.6865	−	1.90192i	−1.39628	−	0.0838088i
$516$		0			0
$517$			15.4641i			0.680110i
$518$	−1.90192	+	4.02628i	−0.0835657	+	0.176905i
$519$		0			0
$520$	10.9282	−	5.46410i	0.479233	−	0.239617i
$521$	−7.12436	−	12.3397i	−0.312124	−	0.540614i	0.666698	−	0.745328i	$-0.267707\pi$
$521$	−7.12436	−	12.3397i	−0.312124	−	0.540614i	−0.978822	+	0.204714i	$0.934374\pi$
$522$	4.50000	−	2.59808i	0.196960	−	0.113715i
$523$	7.26795	−	4.19615i	0.317805	−	0.183485i	−0.332609	−	0.943065i	$-0.607929\pi$
$523$	7.26795	−	4.19615i	0.317805	−	0.183485i	0.650414	+	0.759580i	$0.274595\pi$
$524$	10.9282			0.477401
$525$		0			0
$526$	22.9282			0.999717
$527$	14.4904	+	8.36603i	0.631211	+	0.364430i
$528$		0			0
$529$	−6.85641			−0.298105
$530$	−24.7846	+	12.3923i	−1.07657	+	0.538287i
$531$	−3.80385	−	6.58846i	−0.165073	−	0.285915i
$532$			3.46410i			0.150188i
$533$	37.5167	+	21.6603i	1.62503	+	0.938210i
$534$		0			0
$535$	4.19615	+	8.39230i	0.181415	+	0.362831i
$536$	2.63397	+	4.56218i	0.113770	+	0.197056i
$537$		0			0
$538$	−8.53590	−	4.92820i	−0.368009	−	0.212470i
$539$	−15.2942	+	26.4904i	−0.658769	+	1.14102i
$540$		0			0
$541$	27.7321			1.19229			0.596147	−	0.802875i	$-0.296698\pi$
$541$	27.7321			1.19229			0.596147	+	0.802875i	$0.296698\pi$
$542$	−4.56218	+	2.63397i	−0.195962	+	0.113139i
$543$		0			0
$544$	1.73205			0.0742611
$545$	24.6244	+	16.2583i	1.05479	+	0.696430i
$546$		0			0
$547$		−	29.3731i		−	1.25590i	−0.778253	−	0.627951i	$-0.783894\pi$
$547$		−	29.3731i		−	1.25590i	0.778253	−	0.627951i	$-0.216106\pi$
$548$	1.50000	−	0.866025i	0.0640768	−	0.0369948i
$549$	12.8038			0.546455
$550$	−18.9282	−	14.1962i	−0.807101	−	0.605326i
$551$	−4.09808	−	7.09808i	−0.174584	−	0.302388i
$552$		0			0
$553$	−1.05256	−	0.607695i	−0.0447594	−	0.0258418i
$554$	−19.3923			−0.823900
$555$		0			0
$556$	−2.92820			−0.124183
$557$	−1.79423	−	1.03590i	−0.0760239	−	0.0438924i	0.461506	−	0.887137i	$-0.347309\pi$
$557$	−1.79423	−	1.03590i	−0.0760239	−	0.0438924i	−0.537530	+	0.843245i	$0.680643\pi$
$558$	25.0981	−	14.4904i	1.06249	−	0.613427i
$559$	−14.3923	−	24.9282i	−0.608730	−	1.05435i
$560$	1.63397	+	0.0980762i	0.0690480	+	0.00414448i
$561$		0			0
$562$	2.59808	−	1.50000i	0.109593	−	0.0632737i
$563$			21.8564i			0.921138i	0.887624	+	0.460569i	$0.152355\pi$
$563$			21.8564i			0.921138i	−0.887624	+	0.460569i	$0.847645\pi$
$564$		0			0
$565$	3.78461	−	5.73205i	0.159220	−	0.241149i
$566$	−16.1962			−0.680775
$567$	−5.70577	−	3.29423i	−0.239620	−	0.138345i
$568$	13.0981	−	7.56218i	0.549583	−	0.317302i
$569$	33.1051			1.38784			0.693919	−	0.720053i	$-0.255882\pi$
$569$	33.1051			1.38784			0.693919	+	0.720053i	$0.255882\pi$
$570$		0			0
$571$	−11.1244	+	19.2679i	−0.465540	+	0.806339i	−0.999226	−	0.0393442i	$-0.987473\pi$
$571$	−11.1244	+	19.2679i	−0.465540	+	0.806339i	0.533686	+	0.845683i	$0.320806\pi$
$572$	22.3923	+	12.9282i	0.936269	+	0.540555i
$573$		0			0
$574$	2.90192	+	5.02628i	0.121124	+	0.209793i
$575$	−3.26795	+	27.1244i	−0.136283	+	1.13116i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−1.73205	−	1.00000i	−0.0721062	−	0.0416305i	0.463513	−	0.886090i	$-0.346589\pi$
$577$	−1.73205	−	1.00000i	−0.0721062	−	0.0416305i	−0.535620	+	0.844459i	$0.679922\pi$
$578$		−	14.0000i		−	0.582323i
$579$		0			0
$580$	−3.46410	+	1.73205i	−0.143839	+	0.0719195i
$581$	6.92820			0.287430
$582$		0			0
$583$	−50.7846	−	29.3205i	−2.10328	−	1.21433i
$584$	−15.8564			−0.656143
$585$	36.5885	+	2.19615i	1.51275	+	0.0907997i
$586$	1.14359			0.0472414
$587$	−4.39230	+	2.53590i	−0.181290	+	0.104668i	−0.587899	−	0.808935i	$-0.700045\pi$
$587$	−4.39230	+	2.53590i	−0.181290	+	0.104668i	0.406609	+	0.913602i	$0.366711\pi$
$588$		0			0
$589$	−22.8564	−	39.5885i	−0.941782	−	1.63121i
$590$	2.53590	+	5.07180i	0.104401	+	0.208803i
$591$		0			0
$592$	−3.46410	−	5.00000i	−0.142374	−	0.205499i
$593$			16.2679i			0.668045i	0.942565	+	0.334022i	$0.108406\pi$
$593$			16.2679i			0.668045i	−0.942565	+	0.334022i	$0.891594\pi$
$594$		0			0
$595$	−0.169873	+	2.83013i	−0.00696411	+	0.116024i
$596$	9.79423	+	16.9641i	0.401187	+	0.694877i
$597$		0			0
$598$		−	29.8564i		−	1.22092i
$599$	19.0263	+	32.9545i	0.777393	+	1.34648i	0.933440	+	0.358734i	$0.116791\pi$
$599$	19.0263	+	32.9545i	0.777393	+	1.34648i	−0.156047	+	0.987750i	$0.549875\pi$
$600$		0			0
$601$	5.62436	−	9.74167i	0.229422	−	0.397371i	−0.728215	−	0.685349i	$-0.759650\pi$
$601$	5.62436	−	9.74167i	0.229422	−	0.397371i	0.957637	+	0.287978i	$0.0929830\pi$
$602$		−	3.85641i		−	0.157175i
$603$			15.8038i			0.643582i
$604$	−8.73205	+	15.1244i	−0.355302	+	0.615401i
$605$	1.52628	−	25.4282i	0.0620521	−	1.03380i
$606$		0			0
$607$	28.0981	+	16.2224i	1.14047	+	0.658448i	0.946546	−	0.322569i	$-0.104546\pi$
$607$	28.0981	+	16.2224i	1.14047	+	0.658448i	0.193920	+	0.981017i	$0.437880\pi$
$608$	−4.09808	−	2.36603i	−0.166199	−	0.0959550i
$609$		0			0
$610$	−9.52628	−	0.571797i	−0.385708	−	0.0231514i
$611$	8.92820	+	15.4641i	0.361196	+	0.625611i
$612$	4.50000	+	2.59808i	0.181902	+	0.105021i
$613$	−2.00962	−	1.16025i	−0.0811677	−	0.0468622i	0.458867	−	0.888505i	$-0.348256\pi$
$613$	−2.00962	−	1.16025i	−0.0811677	−	0.0468622i	−0.540035	+	0.841643i	$0.681589\pi$
$614$	15.5622	−	26.9545i	0.628038	−	1.08779i
$615$		0			0
$616$	1.73205	+	3.00000i	0.0697863	+	0.120873i
$617$	7.60770	+	4.39230i	0.306274	+	0.176828i	0.645258	−	0.763965i	$-0.276750\pi$
$617$	7.60770	+	4.39230i	0.306274	+	0.176828i	−0.338984	+	0.940792i	$0.610083\pi$
$618$		0			0
$619$	28.4449			1.14330			0.571648	−	0.820499i	$-0.306304\pi$
$619$	28.4449			1.14330			0.571648	+	0.820499i	$0.306304\pi$
$620$	−19.3205	+	9.66025i	−0.775930	+	0.387965i
$621$		0			0
$622$	−1.09808	+	0.633975i	−0.0440288	+	0.0254201i
$623$		−	0.339746i		−	0.0136116i
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	6.59808	+	11.4282i	0.263712	+	0.456763i
$627$		0			0
$628$		−	17.0000i		−	0.678374i
$629$	8.66025	−	6.00000i	0.345307	−	0.239236i
$630$	4.09808	+	2.70577i	0.163271	+	0.107801i
$631$	14.3923	−	24.9282i	0.572949	−	0.992376i	−0.423313	−	0.905984i	$-0.639133\pi$
$631$	14.3923	−	24.9282i	0.572949	−	0.992376i	0.996261	−	0.0863924i	$-0.0275339\pi$
$632$	1.43782	−	0.830127i	0.0571935	−	0.0330207i
$633$		0			0
$634$	−10.1603	−	17.5981i	−0.403515	−	0.698909i
$635$	−3.60770	+	5.46410i	−0.143167	+	0.216836i
$636$		0			0
$637$			35.3205i			1.39945i
$638$	−7.09808	−	4.09808i	−0.281016	−	0.162244i
$639$	45.3731			1.79493
$640$	−1.23205	+	1.86603i	−0.0487011	+	0.0737611i
$641$	−13.3564	+	23.1340i	−0.527546	+	0.913737i	0.471938	+	0.881632i	$0.343555\pi$
$641$	−13.3564	+	23.1340i	−0.527546	+	0.913737i	−0.999484	+	0.0321054i	$0.989779\pi$
$642$		0			0
$643$			22.3397i			0.880994i	0.897754	+	0.440497i	$0.145198\pi$
$643$			22.3397i			0.880994i	−0.897754	+	0.440497i	$0.854802\pi$
$644$	2.00000	−	3.46410i	0.0788110	−	0.136505i
$645$		0			0
$646$	4.09808	−	7.09808i	0.161237	−	0.279270i
$647$	15.7583	−	9.09808i	0.619524	−	0.357682i	−0.157160	−	0.987573i	$-0.550234\pi$
$647$	15.7583	−	9.09808i	0.619524	−	0.357682i	0.776684	+	0.629891i	$0.216900\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$	−27.1244	−	3.26795i	−1.06390	−	0.128180i
$651$		0			0
$652$		−	15.1244i		−	0.592315i
$653$	−6.65064	+	3.83975i	−0.260259	+	0.150261i	−0.624453	−	0.781062i	$-0.714678\pi$
$653$	−6.65064	+	3.83975i	−0.260259	+	0.150261i	0.364193	+	0.931323i	$0.381345\pi$
$654$		0			0
$655$	−20.3923	−	13.4641i	−0.796793	−	0.526086i
$656$	−7.92820			−0.309544
$657$	−41.1962	−	23.7846i	−1.60721	−	0.927926i
$658$			2.39230i			0.0932618i
$659$	−10.7321	−	18.5885i	−0.418061	−	0.724103i	0.577683	−	0.816261i	$-0.303957\pi$
$659$	−10.7321	−	18.5885i	−0.418061	−	0.724103i	−0.995744	+	0.0921577i	$0.970624\pi$
$660$		0			0
$661$	20.8660	+	36.1410i	0.811594	+	1.40572i	0.911748	+	0.410751i	$0.134733\pi$
$661$	20.8660	+	36.1410i	0.811594	+	1.40572i	−0.100153	+	0.994972i	$0.531933\pi$
$662$	−0.339746	+	0.196152i	−0.0132046	+	0.00762368i
$663$		0			0
$664$	−4.73205	+	8.19615i	−0.183639	+	0.318072i
$665$	4.26795	−	6.46410i	0.165504	−	0.250667i
$666$	−1.50000	−	18.1865i	−0.0581238	−	0.704714i
$667$			9.46410i			0.366451i
$668$	8.53590	+	4.92820i	0.330264	+	0.190678i
$669$		0			0
$670$	0.705771	−	11.7583i	0.0272663	−	0.454264i
$671$	−10.0981	−	17.4904i	−0.389832	−	0.675209i
$672$		0			0
$673$	−2.41154	+	1.39230i	−0.0929581	+	0.0536694i	−0.545758	−	0.837943i	$-0.683758\pi$
$673$	−2.41154	+	1.39230i	−0.0929581	+	0.0536694i	0.452800	+	0.891612i	$0.350425\pi$
$674$	9.19615			0.354223
$675$		0			0
$676$	16.8564			0.648323
$677$		−	39.0000i		−	1.49889i	−0.662066	−	0.749446i	$-0.730320\pi$
$677$		−	39.0000i		−	1.49889i	0.662066	−	0.749446i	$-0.269680\pi$
$678$		0			0
$679$	1.16987	+	2.02628i	0.0448956	+	0.0777615i
$680$	−3.23205	−	2.13397i	−0.123943	−	0.0818342i
$681$		0			0
$682$	−39.5885	−	22.8564i	−1.51592	−	0.875217i
$683$	1.43782	+	0.830127i	0.0550167	+	0.0317639i	0.527256	−	0.849706i	$-0.323221\pi$
$683$	1.43782	+	0.830127i	0.0550167	+	0.0317639i	−0.472239	+	0.881470i	$0.656554\pi$
$684$	−7.09808	−	12.2942i	−0.271402	−	0.470082i
$685$	−3.86603	−	0.232051i	−0.147713	−	0.00886621i
$686$	−4.92820	+	8.53590i	−0.188160	+	0.325902i
$687$		0			0
$688$	4.56218	+	2.63397i	0.173931	+	0.100419i
$689$	−67.7128			−2.57965
$690$		0			0
$691$	11.0981	−	19.2224i	0.422191	−	0.731256i	−0.573963	−	0.818881i	$-0.694595\pi$
$691$	11.0981	−	19.2224i	0.422191	−	0.731256i	0.996153	+	0.0876256i	$0.0279279\pi$
$692$			13.9282i			0.529471i
$693$			10.3923i			0.394771i
$694$	−13.8564	+	24.0000i	−0.525982	+	0.911028i
$695$	5.46410	+	3.60770i	0.207265	+	0.136848i
$696$		0			0
$697$		−	13.7321i		−	0.520139i
$698$	2.08846	−	1.20577i	0.0790493	−	0.0456391i
$699$		0			0
$700$	−2.92820	−	2.19615i	−0.110676	−	0.0830068i
$701$	−5.39230	+	9.33975i	−0.203665	+	0.352757i	−0.949706	−	0.313142i	$-0.898619\pi$
$701$	−5.39230	+	9.33975i	−0.203665	+	0.352757i	0.746042	+	0.665899i	$0.231952\pi$
$702$		0			0
$703$	−28.6865	+	2.36603i	−1.08193	+	0.0892363i
$704$	−4.73205			−0.178346
$705$		0			0
$706$	5.13397	+	8.89230i	0.193220	+	0.334666i
$707$	2.36603	−	1.36603i	0.0889835	−	0.0513747i
$708$		0			0
$709$	−14.9282			−0.560640			−0.280320	−	0.959907i	$-0.590441\pi$
$709$	−14.9282			−0.560640			−0.280320	+	0.959907i	$0.590441\pi$
$710$	−33.7583	−	2.02628i	−1.26693	−	0.0760449i
$711$	4.98076			0.186793
$712$	0.401924	+	0.232051i	0.0150627	+	0.00869647i
$713$			52.7846i			1.97680i
$714$		0			0
$715$	−25.8564	−	51.7128i	−0.966975	−	1.93395i
$716$	0.535898	+	0.928203i	0.0200275	+	0.0346886i
$717$		0			0
$718$	9.12436	+	5.26795i	0.340518	+	0.196598i
$719$	−4.19615	+	7.26795i	−0.156490	+	0.271049i	−0.933601	−	0.358315i	$-0.883351\pi$
$719$	−4.19615	+	7.26795i	−0.156490	+	0.271049i	0.777111	+	0.629364i	$0.216685\pi$
$720$	−6.00000	+	3.00000i	−0.223607	+	0.111803i
$721$	−5.19615	−	9.00000i	−0.193515	−	0.335178i
$722$	−2.93782	+	1.69615i	−0.109334	+	0.0631243i
$723$		0			0
$724$	−9.79423	+	16.9641i	−0.364000	+	0.630466i
$725$	8.59808	+	1.03590i	0.319325	+	0.0384723i
$726$		0			0
$727$	−8.87564	+	5.12436i	−0.329179	+	0.190052i	−0.655477	−	0.755215i	$-0.727532\pi$
$727$	−8.87564	+	5.12436i	−0.329179	+	0.190052i	0.326297	+	0.945267i	$0.394199\pi$
$728$	3.46410	+	2.00000i	0.128388	+	0.0741249i
$729$	27.0000			1.00000
$730$	29.5885	+	19.5359i	1.09512	+	0.723056i
$731$	−4.56218	+	7.90192i	−0.168738	+	0.292263i
$732$		0			0
$733$	−9.12436	+	5.26795i	−0.337016	+	0.194576i	−0.658952	−	0.752185i	$-0.729000\pi$
$733$	−9.12436	+	5.26795i	−0.337016	+	0.194576i	0.321936	+	0.946761i	$0.395666\pi$
$734$	6.14359			0.226764
$735$		0			0
$736$	2.73205	+	4.73205i	0.100705	+	0.174426i
$737$	21.5885	−	12.4641i	0.795221	−	0.459121i
$738$	−20.5981	−	11.8923i	−0.758226	−	0.437762i
$739$	−17.0718			−0.627996			−0.313998	−	0.949424i	$-0.601669\pi$
$739$	−17.0718			−0.627996			−0.313998	+	0.949424i	$0.601669\pi$
$740$	0.303848	+	13.5981i	0.0111697	+	0.499875i
$741$		0			0
$742$	−7.85641	−	4.53590i	−0.288418	−	0.166518i
$743$	7.22243	−	4.16987i	0.264965	−	0.152978i	−0.361632	−	0.932321i	$-0.617780\pi$
$743$	7.22243	−	4.16987i	0.264965	−	0.152978i	0.626597	+	0.779343i	$0.284447\pi$
$744$		0			0
$745$	2.62436	−	43.7224i	0.0961490	−	1.60187i
$746$	−1.00000			−0.0366126
$747$	−24.5885	+	14.1962i	−0.899645	+	0.519410i
$748$		−	8.19615i		−	0.299681i
$749$	−1.53590	+	2.66025i	−0.0561205	+	0.0972036i
$750$		0			0
$751$	19.8038			0.722653			0.361326	−	0.932439i	$-0.382324\pi$
$751$	19.8038			0.722653			0.361326	+	0.932439i	$0.382324\pi$
$752$	−2.83013	−	1.63397i	−0.103204	−	0.0595849i
$753$		0			0
$754$	−9.46410			−0.344662
$755$	34.9282	−	17.4641i	1.27117	−	0.635584i
$756$		0			0
$757$	7.33013	+	4.23205i	0.266418	+	0.153817i	0.627259	−	0.778811i	$-0.284177\pi$
$757$	7.33013	+	4.23205i	0.266418	+	0.153817i	−0.360841	+	0.932627i	$0.617510\pi$
$758$	4.68653	−	2.70577i	0.170223	−	0.0982780i
$759$		0			0
$760$	4.73205	+	9.46410i	0.171650	+	0.343299i
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	−0.874946	−	0.484221i	$-0.839103\pi$
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	0.856821	+	0.515615i	$0.172436\pi$
$762$		0			0
$763$			9.66025i			0.349725i
$764$	7.66025	+	13.2679i	0.277138	+	0.480018i
$765$	−5.19615	−	10.3923i	−0.187867	−	0.375735i
$766$	−29.5167			−1.06648
$767$			13.8564i			0.500326i
$768$		0			0
$769$	24.3923			0.879609			0.439805	−	0.898094i	$-0.355048\pi$
$769$	24.3923			0.879609			0.439805	+	0.898094i	$0.355048\pi$
$770$	0.464102	−	7.73205i	0.0167251	−	0.278644i
$771$		0			0
$772$	−0.571797	+	0.330127i	−0.0205794	+	0.0118815i
$773$	−11.3827	+	6.57180i	−0.409407	+	0.236371i	−0.690535	−	0.723299i	$-0.742625\pi$
$773$	−11.3827	+	6.57180i	−0.409407	+	0.236371i	0.281128	+	0.959670i	$0.409291\pi$
$774$	7.90192	+	13.6865i	0.284029	+	0.491952i
$775$	47.9545	+	5.77757i	1.72258	+	0.207536i
$776$	−3.19615			−0.114735
$777$		0			0
$778$		−	11.7321i		−	0.420614i
$779$	−18.7583	+	32.4904i	−0.672087	+	1.16409i
$780$		0			0
$781$	−35.7846	−	61.9808i	−1.28047	−	2.21785i
$782$	−8.19615	+	4.73205i	−0.293094	+	0.169218i
$783$		0			0
$784$	−3.23205	−	5.59808i	−0.115430	−	0.199931i
$785$	−20.9449	+	31.7224i	−0.747554	+	1.13222i
$786$		0			0
$787$			37.5692i			1.33920i	0.742723	+	0.669599i	$0.233534\pi$
$787$			37.5692i			1.33920i	−0.742723	+	0.669599i	$0.766466\pi$
$788$		−	19.9282i		−	0.709913i
$789$		0			0
$790$	−3.70577	−	0.222432i	−0.131845	−	0.00791377i
$791$	2.24871			0.0799550
$792$	−12.2942	−	7.09808i	−0.436856	−	0.252219i
$793$	−20.1962	−	11.6603i	−0.717186	−	0.414068i
$794$	−6.96410	+	12.0622i	−0.247147	+	0.428071i
$795$		0			0
$796$	−6.09808	−	10.5622i	−0.216141	−	0.374366i
$797$	−28.9808	−	16.7321i	−1.02655	−	0.592680i	−0.110556	−	0.993870i	$-0.535263\pi$
$797$	−28.9808	−	16.7321i	−1.02655	−	0.592680i	−0.915995	+	0.401190i	$0.868597\pi$
$798$		0			0
$799$	2.83013	−	4.90192i	0.100123	−	0.173418i
$800$	4.59808	−	1.96410i	0.162567	−	0.0694415i
$801$	0.696152	+	1.20577i	0.0245973	+	0.0426038i
$802$	−16.7321	−	9.66025i	−0.590829	−	0.341115i
$803$			75.0333i			2.64787i
$804$		0			0
$805$	−8.00000	+	4.00000i	−0.281963	+	0.140981i
$806$	−52.7846			−1.85926
$807$		0			0
$808$			3.73205i			0.131293i
$809$	−11.6603	−	20.1962i	−0.409953	−	0.710059i	0.584931	−	0.811083i	$-0.301121\pi$
$809$	−11.6603	−	20.1962i	−0.409953	−	0.710059i	−0.994884	+	0.101024i	$0.967788\pi$
$810$	−20.0885	−	1.20577i	−0.705836	−	0.0423665i
$811$	9.80385	+	16.9808i	0.344260	+	0.596275i	0.985219	−	0.171300i	$-0.0547966\pi$
$811$	9.80385	+	16.9808i	0.344260	+	0.596275i	−0.640959	+	0.767575i	$0.721463\pi$
$812$	−1.09808	−	0.633975i	−0.0385349	−	0.0222481i
$813$		0			0
$814$	−23.6603	+	16.3923i	−0.829291	+	0.574550i
$815$	−18.6340	+	28.2224i	−0.652720	+	0.988589i
$816$		0			0
$817$	21.5885	−	12.4641i	0.755285	−	0.436064i
$818$	32.7224	−	18.8923i	1.14411	−	0.660554i
$819$	6.00000	+	10.3923i	0.209657	+	0.363137i
$820$	14.7942	+	9.76795i	0.516637	+	0.341112i
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	0.511311	−	0.859396i	$-0.329160\pi$
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	−0.999914	+	0.0131101i	$0.995827\pi$
$822$		0			0
$823$	−14.4449	−	8.33975i	−0.503516	−	0.290705i	0.226648	−	0.973977i	$-0.427223\pi$
$823$	−14.4449	−	8.33975i	−0.503516	−	0.290705i	−0.730164	+	0.683271i	$0.760557\pi$
$824$	14.1962			0.494546
$825$		0			0
$826$	−0.928203	+	1.60770i	−0.0322963	+	0.0559389i
$827$	−3.21539	+	1.85641i	−0.111810	+	0.0645536i	−0.554862	−	0.831942i	$-0.687229\pi$
$827$	−3.21539	+	1.85641i	−0.111810	+	0.0645536i	0.443052	+	0.896496i	$0.353896\pi$
$828$			16.3923i			0.569672i
$829$	−15.5359	+	26.9090i	−0.539584	+	0.934587i	0.459342	+	0.888259i	$0.348085\pi$
$829$	−15.5359	+	26.9090i	−0.539584	+	0.934587i	−0.998926	+	0.0463276i	$0.985248\pi$
$830$	18.9282	−	9.46410i	0.657008	−	0.328504i
$831$		0			0
$832$	−4.73205	+	2.73205i	−0.164054	+	0.0947168i
$833$	9.69615	−	5.59808i	0.335952	−	0.193962i
$834$		0			0
$835$	−9.85641	−	19.7128i	−0.341095	−	0.682190i
$836$	−11.1962	+	19.3923i	−0.387227	+	0.670697i
$837$		0			0
$838$	15.4186	−	8.90192i	0.532626	−	0.307512i
$839$	−15.8038	+	27.3731i	−0.545609	+	0.945023i	0.452959	+	0.891531i	$0.350368\pi$
$839$	−15.8038	+	27.3731i	−0.545609	+	0.945023i	−0.998568	+	0.0534918i	$0.982965\pi$
$840$		0			0
$841$	−26.0000			−0.896552
$842$	24.6962	+	14.2583i	0.851086	+	0.491375i
$843$		0			0
$844$	−10.0263	−	17.3660i	−0.345119	−	0.597763i
$845$	−31.4545	−	20.7679i	−1.08207	−	0.714439i
$846$	−4.90192	−	8.49038i	−0.168532	−	0.291905i
$847$	7.22243	−	4.16987i	0.248166	−	0.143279i
$848$	10.7321	−	6.19615i	0.368540	−	0.212777i
$849$		0			0
$850$	3.40192	+	7.96410i	0.116685	+	0.273166i
$851$	30.0526	+	14.1962i	1.03019	+	0.486638i
$852$		0			0
$853$	21.7750	+	12.5718i	0.745561	+	0.430450i	0.824088	−	0.566462i	$-0.191688\pi$
$853$	21.7750	+	12.5718i	0.745561	+	0.430450i	−0.0785264	+	0.996912i	$0.525022\pi$
$854$	−1.56218	−	2.70577i	−0.0534566	−	0.0925896i
$855$	−1.90192	+	31.6865i	−0.0650444	+	1.08366i
$856$	−2.09808	−	3.63397i	−0.0717108	−	0.124207i
$857$			12.5167i			0.427561i	0.976882	+	0.213780i	$0.0685777\pi$
$857$			12.5167i			0.427561i	−0.976882	+	0.213780i	$0.931422\pi$
$858$		0			0
$859$	0.0525589			0.00179329			0.000896643	−	1.00000i	$-0.499715\pi$
$859$	0.0525589			0.00179329			0.000896643		1.00000i	$0.499715\pi$
$860$	−5.26795	−	10.5359i	−0.179636	−	0.359271i
$861$		0			0
$862$		−	9.26795i		−	0.315668i
$863$	−26.1962	−	15.1244i	−0.891727	−	0.514839i	−0.0172203	−	0.999852i	$-0.505482\pi$
$863$	−26.1962	−	15.1244i	−0.891727	−	0.514839i	−0.874507	+	0.485013i	$0.838815\pi$
$864$		0			0
$865$	17.1603	−	25.9904i	0.583466	−	0.883699i
$866$	20.1865	−	34.9641i	0.685966	−	1.18813i
$867$		0			0
$868$	−6.12436	−	3.53590i	−0.207874	−	0.120016i
$869$	−3.92820	−	6.80385i	−0.133255	−	0.230805i
$870$		0			0
$871$	14.3923	−	24.9282i	0.487665	−	0.844660i
$872$	−11.4282	−	6.59808i	−0.387008	−	0.223439i
$873$	−8.30385	−	4.79423i	−0.281043	−	0.162260i
$874$	25.8564			0.874606
$875$	2.75833	+	7.70577i	0.0932486	+	0.260503i
$876$		0			0
$877$		−	49.1051i		−	1.65816i	−0.559129	−	0.829081i	$-0.688864\pi$
$877$		−	49.1051i		−	1.65816i	0.559129	−	0.829081i	$-0.311136\pi$
$878$		−	6.14359i		−	0.207336i
$879$		0			0
$880$	8.83013	+	5.83013i	0.297664	+	0.196534i
$881$	−12.2321	−	21.1865i	−0.412108	−	0.713792i	0.583012	−	0.812464i	$-0.301874\pi$
$881$	−12.2321	−	21.1865i	−0.412108	−	0.713792i	−0.995120	+	0.0986712i	$0.968541\pi$
$882$		−	19.3923i		−	0.652973i
$883$	0.339746	−	0.196152i	0.0114334	−	0.00660105i	−0.494272	−	0.869307i	$-0.664565\pi$
$883$	0.339746	−	0.196152i	0.0114334	−	0.00660105i	0.505706	+	0.862706i	$0.331232\pi$
$884$	−4.73205	−	8.19615i	−0.159156	−	0.275666i
$885$		0			0
$886$	8.39230	−	14.5359i	0.281945	−	0.488343i
$887$		−	1.46410i		−	0.0491597i	−0.999698	−	0.0245799i	$-0.992175\pi$
$887$		−	1.46410i		−	0.0491597i	0.999698	−	0.0245799i	$-0.00782480\pi$
$888$		0			0
$889$	−2.14359			−0.0718938
$890$	−0.464102	−	0.928203i	−0.0155567	−	0.0311134i
$891$	−21.2942	−	36.8827i	−0.713384	−	1.23562i
$892$	−12.9282	+	7.46410i	−0.432868	+	0.249917i
$893$	−13.3923	+	7.73205i	−0.448156	+	0.258743i
$894$		0			0
$895$	0.143594	−	2.39230i	0.00479980	−	0.0799659i
$896$	−0.732051			−0.0244561
$897$		0			0
$898$		−	6.24871i		−	0.208522i
$899$	16.7321			0.558045
$900$	14.8923	+	1.79423i	0.496410	+	0.0598076i
$901$	10.7321	+	18.5885i	0.357536	+	0.619271i
$902$			37.5167i			1.24917i
$903$		0			0
$904$	−1.53590	+	2.66025i	−0.0510832	+	0.0884787i
$905$	39.1769	−	19.5885i	1.30228	−	0.651142i
$906$		0			0
$907$	5.83013	−	3.36603i	0.193586	−	0.111767i	−0.400074	−	0.916483i	$-0.631016\pi$
$907$	5.83013	−	3.36603i	0.193586	−	0.111767i	0.593660	+	0.804716i	$0.297682\pi$
$908$	18.7583	+	10.8301i	0.622517	+	0.359410i
$909$	−5.59808	+	9.69615i	−0.185676	+	0.321601i
$910$	−4.00000	−	8.00000i	−0.132599	−	0.265197i
$911$	5.07180			0.168036			0.0840181	−	0.996464i	$-0.473225\pi$
$911$	5.07180			0.168036			0.0840181	+	0.996464i	$0.473225\pi$
$912$		0			0
$913$	38.7846	+	22.3923i	1.28358	+	0.741077i
$914$	−19.1962			−0.634952
$915$		0			0
$916$	−2.79423	+	4.83975i	−0.0923239	+	0.159910i
$917$		−	8.00000i		−	0.264183i
$918$		0			0
$919$	−35.0333			−1.15564			−0.577821	−	0.816163i	$-0.696097\pi$
$919$	−35.0333			−1.15564			−0.577821	+	0.816163i	$0.696097\pi$
$920$	0.732051	−	12.1962i	0.0241350	−	0.402095i
$921$		0			0
$922$	18.8038	−	10.8564i	0.619272	−	0.357537i
$923$	−71.5692	−	41.3205i	−2.35573	−	1.36008i
$924$		0			0
$925$	16.1865	−	25.7487i	0.532210	−	0.846612i
$926$	30.9808			1.01809
$927$	36.8827	+	21.2942i	1.21139	+	0.699394i
$928$	1.50000	−	0.866025i	0.0492399	−	0.0284287i
$929$	18.2321	+	31.5788i	0.598174	+	1.03607i	0.993091	+	0.117351i	$0.0374402\pi$
$929$	18.2321	+	31.5788i	0.598174	+	1.03607i	−0.394916	+	0.918717i	$0.629226\pi$
$930$		0			0
$931$	−30.5885			−1.00250
$932$	−8.89230	+	5.13397i	−0.291277	+	0.168169i
$933$		0			0
$934$	10.7321	−	18.5885i	0.351163	−	0.608233i
$935$	−10.0981	+	15.2942i	−0.330242	+	0.500175i
$936$	−16.3923			−0.535799
$937$	16.7487	+	9.66987i	0.547157	+	0.315901i	0.747974	−	0.663728i	$-0.231027\pi$
$937$	16.7487	+	9.66987i	0.547157	+	0.315901i	−0.200818	+	0.979629i	$0.564360\pi$
$938$	3.33975	−	1.92820i	0.109047	−	0.0629581i
$939$		0			0
$940$	3.26795	+	6.53590i	0.106589	+	0.213177i
$941$	0.669873	−	1.16025i	0.0218372	−	0.0378232i	−0.854900	−	0.518792i	$-0.826382\pi$
$941$	0.669873	−	1.16025i	0.0218372	−	0.0378232i	0.876738	+	0.480969i	$0.159715\pi$
$942$		0			0
$943$	37.5167	−	21.6603i	1.22171	−	0.705355i
$944$	−1.26795	−	2.19615i	−0.0412682	−	0.0714787i
$945$		0			0
$946$	12.4641	−	21.5885i	0.405243	−	0.701901i
$947$	−24.9282	−	14.3923i	−0.810058	−	0.467687i	0.0369182	−	0.999318i	$-0.488246\pi$
$947$	−24.9282	−	14.3923i	−0.810058	−	0.467687i	−0.846976	+	0.531631i	$0.821579\pi$
$948$		0			0
$949$	43.3205	+	75.0333i	1.40624	+	2.43568i
$950$	2.83013	−	23.4904i	0.0918214	−	0.762129i
$951$		0			0
$952$		−	1.26795i		−	0.0410945i
$953$	0.803848	+	0.464102i	0.0260392	+	0.0150337i	0.512963	−	0.858411i	$-0.328548\pi$
$953$	0.803848	+	0.464102i	0.0260392	+	0.0150337i	−0.486924	+	0.873444i	$0.661881\pi$
$954$	37.1769			1.20365
$955$	2.05256	−	34.1962i	0.0664192	−	1.10656i
$956$	16.5885			0.536509
$957$		0			0
$958$	−8.19615	+	4.73205i	−0.264806	+	0.152886i
$959$	−0.633975	−	1.09808i	−0.0204721	−	0.0354587i
$960$		0			0
$961$	62.3205			2.01034
$962$	−14.1962	+	30.0526i	−0.457702	+	0.968933i
$963$		−	12.5885i		−	0.405657i
$964$	−5.26795	+	9.12436i	−0.169669	+	0.293876i
$965$	1.47372	+	0.0884573i	0.0474407	+	0.00284754i
$966$		0			0
$967$	37.8564	−	21.8564i	1.21738	−	0.702855i	0.253023	−	0.967460i	$-0.418575\pi$
$967$	37.8564	−	21.8564i	1.21738	−	0.702855i	0.964357	+	0.264606i	$0.0852418\pi$
$968$			11.3923i			0.366163i
$969$		0			0
$970$	5.96410	+	3.93782i	0.191496	+	0.126436i
$971$	−21.3205	+	36.9282i	−0.684208	+	1.18508i	0.289477	+	0.957185i	$0.406518\pi$
$971$	−21.3205	+	36.9282i	−0.684208	+	1.18508i	−0.973685	+	0.227898i	$0.926815\pi$
$972$		0			0
$973$			2.14359i			0.0687205i
$974$	−13.2679	+	22.9808i	−0.425133	+	0.736351i
$975$		0			0
$976$	4.26795			0.136614
$977$	−48.3731	−	27.9282i	−1.54759	−	0.893502i	−0.998325	−	0.0578552i	$-0.981574\pi$
$977$	−48.3731	−	27.9282i	−1.54759	−	0.893502i	−0.549267	−	0.835647i	$-0.685093\pi$
$978$		0			0
$979$	1.09808	−	1.90192i	0.0350947	−	0.0607857i
$980$	−0.866025	+	14.4282i	−0.0276642	+	0.460892i
$981$	−19.7942	−	34.2846i	−0.631981	−	1.09462i
$982$	−10.6865	−	6.16987i	−0.341021	−	0.196889i
$983$	30.6340	+	17.6865i	0.977072	+	0.564113i	0.901385	−	0.433019i	$-0.142552\pi$
$983$	30.6340	+	17.6865i	0.977072	+	0.564113i	0.0756872	+	0.997132i	$0.475885\pi$
$984$		0			0
$985$	−24.5526	+	37.1865i	−0.782310	+	1.18486i
$986$	1.50000	+	2.59808i	0.0477697	+	0.0827396i
$987$		0			0
$988$			25.8564i			0.822602i
$989$	−28.7846			−0.915297
$990$	14.1962	+	28.3923i	0.451183	+	0.902367i
$991$	22.7321			0.722107			0.361054	−	0.932545i	$-0.382417\pi$
$991$	22.7321			0.722107			0.361054	+	0.932545i	$0.382417\pi$
$992$	8.36603	−	4.83013i	0.265622	−	0.153357i
$993$		0			0
$994$	−5.53590	−	9.58846i	−0.175588	−	0.304127i
$995$	−1.63397	+	27.2224i	−0.0518005	+	0.863009i
$996$		0			0
$997$	7.26795	+	4.19615i	0.230178	+	0.132893i	0.610654	−	0.791897i	$-0.290907\pi$
$997$	7.26795	+	4.19615i	0.230178	+	0.132893i	−0.380476	+	0.924791i	$0.624240\pi$
$998$			37.5167i			1.18757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.c.269.2	yes	4
5.4	even	2		370.2.n.a.269.1	✓	4
37.26	even	3		370.2.n.a.359.1	yes	4
185.174	even	6	inner	370.2.n.c.359.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.a.269.1	✓	4	5.4	even	2
370.2.n.a.359.1	yes	4	37.26	even	3
370.2.n.c.269.2	yes	4	1.1	even	1	trivial
370.2.n.c.359.2	yes	4	185.174	even	6	inner

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(1.23205 - 1.86603i) q^{10} +4.73205 q^{11} +(4.73205 - 2.73205i) q^{13} +0.732051 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(2.36603 + 4.09808i) q^{19} +(2.00000 - 1.00000i) q^{20} +(4.09808 + 2.36603i) q^{22} -5.46410i q^{23} +(-4.96410 - 0.598076i) q^{25} +5.46410 q^{26} +(0.633975 + 0.366025i) q^{28} -1.73205 q^{29} -9.66025 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.866025 - 1.50000i) q^{34} +(-0.732051 - 1.46410i) q^{35} -3.00000 q^{36} +(-2.59808 + 5.50000i) q^{37} +4.73205i q^{38} +(2.23205 + 0.133975i) q^{40} +(3.96410 + 6.86603i) q^{41} -5.26795i q^{43} +(2.36603 + 4.09808i) q^{44} +(5.59808 + 3.69615i) q^{45} +(2.73205 - 4.73205i) q^{46} +3.26795i q^{47} +(-3.23205 + 5.59808i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(4.73205 + 2.73205i) q^{52} +(-10.7321 - 6.19615i) q^{53} +(0.633975 - 10.5622i) q^{55} +(0.366025 + 0.633975i) q^{56} +(-1.50000 - 0.866025i) q^{58} +(-1.26795 + 2.19615i) q^{59} +(-2.13397 - 3.69615i) q^{61} +(-8.36603 - 4.83013i) q^{62} +2.19615i q^{63} -1.00000 q^{64} +(-5.46410 - 10.9282i) q^{65} +(4.56218 - 2.63397i) q^{67} -1.73205i q^{68} +(0.0980762 - 1.63397i) q^{70} +(-7.56218 - 13.0981i) q^{71} +(-2.59808 - 1.50000i) q^{72} +15.8564i q^{73} +(-5.00000 + 3.46410i) q^{74} +(-2.36603 + 4.09808i) q^{76} +(3.00000 - 1.73205i) q^{77} +(-0.830127 - 1.43782i) q^{79} +(1.86603 + 1.23205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +7.92820i q^{82} +(8.19615 + 4.73205i) q^{83} +(-2.13397 + 3.23205i) q^{85} +(2.63397 - 4.56218i) q^{86} +4.73205i q^{88} +(0.232051 - 0.401924i) q^{89} +(3.00000 + 6.00000i) q^{90} +(2.00000 - 3.46410i) q^{91} +(4.73205 - 2.73205i) q^{92} +(-1.63397 + 2.83013i) q^{94} +(9.46410 - 4.73205i) q^{95} +3.19615i q^{97} +(-5.59808 + 3.23205i) q^{98} +(-7.09808 + 12.2942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 6 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 + 6 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} + 4 q^{5} + 6 q^{7} - 6 q^{9} - 2 q^{10} + 12 q^{11} + 12 q^{13} - 4 q^{14} - 2 q^{16} - 6 q^{17} + 6 q^{19} + 8 q^{20} + 6 q^{22} - 6 q^{25} + 8 q^{26} + 6 q^{28} - 4 q^{31} + 4 q^{35} - 12 q^{36} + 2 q^{40} + 2 q^{41} + 6 q^{44} + 12 q^{45} + 4 q^{46} - 6 q^{49} - 16 q^{50} + 12 q^{52} - 36 q^{53} + 6 q^{55} - 2 q^{56} - 6 q^{58} - 12 q^{59} - 12 q^{61} - 30 q^{62} - 4 q^{64} - 8 q^{65} - 6 q^{67} - 10 q^{70} - 6 q^{71} - 20 q^{74} - 6 q^{76} + 12 q^{77} + 14 q^{79} + 4 q^{80} - 18 q^{81} + 12 q^{83} - 12 q^{85} + 14 q^{86} - 6 q^{89} + 12 q^{90} + 8 q^{91} + 12 q^{92} - 10 q^{94} + 24 q^{95} - 12 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 6 * q^7 - 6 * q^9 - 2 * q^10 + 12 * q^11 + 12 * q^13 - 4 * q^14 - 2 * q^16 - 6 * q^17 + 6 * q^19 + 8 * q^20 + 6 * q^22 - 6 * q^25 + 8 * q^26 + 6 * q^28 - 4 * q^31 + 4 * q^35 - 12 * q^36 + 2 * q^40 + 2 * q^41 + 6 * q^44 + 12 * q^45 + 4 * q^46 - 6 * q^49 - 16 * q^50 + 12 * q^52 - 36 * q^53 + 6 * q^55 - 2 * q^56 - 6 * q^58 - 12 * q^59 - 12 * q^61 - 30 * q^62 - 4 * q^64 - 8 * q^65 - 6 * q^67 - 10 * q^70 - 6 * q^71 - 20 * q^74 - 6 * q^76 + 12 * q^77 + 14 * q^79 + 4 * q^80 - 18 * q^81 + 12 * q^83 - 12 * q^85 + 14 * q^86 - 6 * q^89 + 12 * q^90 + 8 * q^91 + 12 * q^92 - 10 * q^94 + 24 * q^95 - 12 * q^98 - 18 * q^99

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