LMFDB - Embedded newform 650.2.n.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(49,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("650.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.49
Dual form			650.2.n.a.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.633975 + 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.633975 + 0.366025i) q^{6} +(-1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.633975 + 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.633975 + 0.366025i) q^{6} +(-1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-1.23205 + 2.13397i) q^{9} +(2.59808 - 1.50000i) q^{11} -0.732051i q^{12} +(0.866025 - 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-7.09808 - 4.09808i) q^{17} +2.46410 q^{18} +(0.401924 + 0.232051i) q^{19} -2.19615i q^{21} +(-2.59808 - 1.50000i) q^{22} +(-8.19615 + 4.73205i) q^{23} +(-0.633975 + 0.366025i) q^{24} +(-3.46410 + 1.00000i) q^{26} -4.00000i q^{27} +(-1.50000 - 2.59808i) q^{28} +(-1.26795 - 2.19615i) q^{29} -4.73205i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.09808 + 1.90192i) q^{33} +8.19615i q^{34} +(-1.23205 - 2.13397i) q^{36} +(-0.401924 - 0.696152i) q^{37} -0.464102i q^{38} +(0.732051 + 2.53590i) q^{39} +(-9.00000 + 5.19615i) q^{41} +(-1.90192 + 1.09808i) q^{42} +(1.73205 + 1.00000i) q^{43} +3.00000i q^{44} +(8.19615 + 4.73205i) q^{46} +3.00000 q^{47} +(0.633975 + 0.366025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +6.00000 q^{51} +(2.59808 + 2.50000i) q^{52} -0.464102i q^{53} +(-3.46410 + 2.00000i) q^{54} +(-1.50000 + 2.59808i) q^{56} -0.339746 q^{57} +(-1.26795 + 2.19615i) q^{58} +(-9.00000 - 5.19615i) q^{59} +(-3.09808 + 5.36603i) q^{61} +(-4.09808 + 2.36603i) q^{62} +(-3.69615 - 6.40192i) q^{63} +1.00000 q^{64} +2.19615 q^{66} +(7.09808 - 4.09808i) q^{68} +(3.46410 - 6.00000i) q^{69} +(-5.19615 - 3.00000i) q^{71} +(-1.23205 + 2.13397i) q^{72} -11.6603 q^{73} +(-0.401924 + 0.696152i) q^{74} +(-0.401924 + 0.232051i) q^{76} +9.00000i q^{77} +(1.83013 - 1.90192i) q^{78} +4.19615 q^{79} +(-2.23205 - 3.86603i) q^{81} +(9.00000 + 5.19615i) q^{82} +8.19615 q^{83} +(1.90192 + 1.09808i) q^{84} -2.00000i q^{86} +(1.60770 + 0.928203i) q^{87} +(2.59808 - 1.50000i) q^{88} +(-5.89230 + 3.40192i) q^{89} +(7.79423 + 7.50000i) q^{91} -9.46410i q^{92} +(1.73205 + 3.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} -0.732051i q^{96} +(-4.56218 + 7.90192i) q^{97} +(-1.00000 + 1.73205i) q^{98} +7.39230i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9} + 12 q^{14} - 2 q^{16} - 18 q^{17} - 4 q^{18} + 12 q^{19} - 12 q^{23} - 6 q^{24} - 6 q^{28} - 12 q^{29} - 2 q^{32} + 6 q^{33} + 2 q^{36} - 12 q^{37} - 4 q^{39} - 36 q^{41} - 18 q^{42} + 12 q^{46} + 12 q^{47} + 6 q^{48} - 4 q^{49} + 24 q^{51} - 6 q^{56} - 36 q^{57} - 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} + 6 q^{63} + 4 q^{64} - 12 q^{66} + 18 q^{68} + 2 q^{72} - 12 q^{73} - 12 q^{74} - 12 q^{76} - 10 q^{78} - 4 q^{79} - 2 q^{81} + 36 q^{82} + 12 q^{83} + 18 q^{84} + 48 q^{87} + 18 q^{89} - 6 q^{94} + 6 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9 + 12 * q^14 - 2 * q^16 - 18 * q^17 - 4 * q^18 + 12 * q^19 - 12 * q^23 - 6 * q^24 - 6 * q^28 - 12 * q^29 - 2 * q^32 + 6 * q^33 + 2 * q^36 - 12 * q^37 - 4 * q^39 - 36 * q^41 - 18 * q^42 + 12 * q^46 + 12 * q^47 + 6 * q^48 - 4 * q^49 + 24 * q^51 - 6 * q^56 - 36 * q^57 - 12 * q^58 - 36 * q^59 - 2 * q^61 - 6 * q^62 + 6 * q^63 + 4 * q^64 - 12 * q^66 + 18 * q^68 + 2 * q^72 - 12 * q^73 - 12 * q^74 - 12 * q^76 - 10 * q^78 - 4 * q^79 - 2 * q^81 + 36 * q^82 + 12 * q^83 + 18 * q^84 + 48 * q^87 + 18 * q^89 - 6 * q^94 + 6 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.633975	+	0.366025i	−0.366025	+	0.211325i	−0.671721	−	0.740805i	$-0.734444\pi$
$3$	−0.633975	+	0.366025i	−0.366025	+	0.211325i	0.305695	+	0.952129i	$0.401111\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.633975	+	0.366025i	0.258819	+	0.149429i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	1.00000			0.353553
$9$	−1.23205	+	2.13397i	−0.410684	+	0.711325i
$10$		0			0
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$12$		−	0.732051i		−	0.211325i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−7.09808	−	4.09808i	−1.72154	−	0.993929i	−0.915778	−	0.401685i	$-0.868425\pi$
$17$	−7.09808	−	4.09808i	−1.72154	−	0.993929i	−0.805759	−	0.592244i	$-0.798242\pi$
$18$	2.46410			0.580794
$19$	0.401924	+	0.232051i	0.0922076	+	0.0532361i	0.545395	−	0.838179i	$-0.316380\pi$
$19$	0.401924	+	0.232051i	0.0922076	+	0.0532361i	−0.453187	+	0.891415i	$0.649713\pi$
$20$		0			0
$21$		−	2.19615i		−	0.479240i
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	−8.19615	+	4.73205i	−1.70902	+	0.986701i	−0.773234	+	0.634120i	$0.781362\pi$
$23$	−8.19615	+	4.73205i	−1.70902	+	0.986701i	−0.935781	+	0.352581i	$0.885304\pi$
$24$	−0.633975	+	0.366025i	−0.129410	+	0.0747146i
$25$		0			0
$26$	−3.46410	+	1.00000i	−0.679366	+	0.196116i
$27$		−	4.00000i		−	0.769800i
$28$	−1.50000	−	2.59808i	−0.283473	−	0.490990i
$29$	−1.26795	−	2.19615i	−0.235452	−	0.407815i	0.723952	−	0.689851i	$-0.242324\pi$
$29$	−1.26795	−	2.19615i	−0.235452	−	0.407815i	−0.959404	+	0.282035i	$0.908990\pi$
$30$		0			0
$31$		−	4.73205i		−	0.849901i	−0.905216	−	0.424951i	$-0.860291\pi$
$31$		−	4.73205i		−	0.849901i	0.905216	−	0.424951i	$-0.139709\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.09808	+	1.90192i	−0.191151	+	0.331082i
$34$			8.19615i			1.40563i
$35$		0			0
$36$	−1.23205	−	2.13397i	−0.205342	−	0.355662i
$37$	−0.401924	−	0.696152i	−0.0660759	−	0.114447i	0.831095	−	0.556131i	$-0.187715\pi$
$37$	−0.401924	−	0.696152i	−0.0660759	−	0.114447i	−0.897171	+	0.441684i	$0.854381\pi$
$38$		−	0.464102i		−	0.0752872i
$39$	0.732051	+	2.53590i	0.117222	+	0.406069i
$40$		0			0
$41$	−9.00000	+	5.19615i	−1.40556	+	0.811503i	−0.994956	−	0.100309i	$-0.968017\pi$
$41$	−9.00000	+	5.19615i	−1.40556	+	0.811503i	−0.410608	+	0.911812i	$0.634683\pi$
$42$	−1.90192	+	1.09808i	−0.293473	+	0.169437i
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	8.19615	+	4.73205i	1.20846	+	0.697703i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	0.633975	+	0.366025i	0.0915064	+	0.0528312i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$	6.00000			0.840168
$52$	2.59808	+	2.50000i	0.360288	+	0.346688i
$53$		−	0.464102i		−	0.0637493i	−0.999492	−	0.0318746i	$-0.989852\pi$
$53$		−	0.464102i		−	0.0637493i	0.999492	−	0.0318746i	$-0.0101477\pi$
$54$	−3.46410	+	2.00000i	−0.471405	+	0.272166i
$55$		0			0
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$	−0.339746			−0.0450005
$58$	−1.26795	+	2.19615i	−0.166490	+	0.288369i
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.217620	−	0.976034i	$-0.569829\pi$
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.954080	+	0.299552i	$0.903163\pi$
$60$		0			0
$61$	−3.09808	+	5.36603i	−0.396668	+	0.687049i	−0.993313	−	0.115456i	$-0.963167\pi$
$61$	−3.09808	+	5.36603i	−0.396668	+	0.687049i	0.596645	+	0.802506i	$0.296500\pi$
$62$	−4.09808	+	2.36603i	−0.520456	+	0.300486i
$63$	−3.69615	−	6.40192i	−0.465671	−	0.806567i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.19615			0.270328
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	7.09808	−	4.09808i	0.860768	−	0.496965i
$69$	3.46410	−	6.00000i	0.417029	−	0.722315i
$70$		0			0
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	0.158901	−	0.987294i	$-0.449205\pi$
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	−0.775571	+	0.631260i	$0.782538\pi$
$72$	−1.23205	+	2.13397i	−0.145199	+	0.251491i
$73$	−11.6603			−1.36473			−0.682365	−	0.731012i	$-0.739048\pi$
$73$	−11.6603			−1.36473			−0.682365	+	0.731012i	$0.739048\pi$
$74$	−0.401924	+	0.696152i	−0.0467227	+	0.0809261i
$75$		0			0
$76$	−0.401924	+	0.232051i	−0.0461038	+	0.0266181i
$77$			9.00000i			1.02565i
$78$	1.83013	−	1.90192i	0.207221	−	0.215350i
$79$	4.19615			0.472104			0.236052	−	0.971740i	$-0.424146\pi$
$79$	4.19615			0.472104			0.236052	+	0.971740i	$0.424146\pi$
$80$		0			0
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	9.00000	+	5.19615i	0.993884	+	0.573819i
$83$	8.19615			0.899645			0.449822	−	0.893118i	$-0.351487\pi$
$83$	8.19615			0.899645			0.449822	+	0.893118i	$0.351487\pi$
$84$	1.90192	+	1.09808i	0.207517	+	0.119810i
$85$		0			0
$86$		−	2.00000i		−	0.215666i
$87$	1.60770	+	0.928203i	0.172363	+	0.0995138i
$88$	2.59808	−	1.50000i	0.276956	−	0.159901i
$89$	−5.89230	+	3.40192i	−0.624583	+	0.360603i	−0.778651	−	0.627457i	$-0.784096\pi$
$89$	−5.89230	+	3.40192i	−0.624583	+	0.360603i	0.154068	+	0.988060i	$0.450762\pi$
$90$		0			0
$91$	7.79423	+	7.50000i	0.817057	+	0.786214i
$92$		−	9.46410i		−	0.986701i
$93$	1.73205	+	3.00000i	0.179605	+	0.311086i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$		−	0.732051i		−	0.0747146i
$97$	−4.56218	+	7.90192i	−0.463219	+	0.802319i	−0.999119	−	0.0419625i	$-0.986639\pi$
$97$	−4.56218	+	7.90192i	−0.463219	+	0.802319i	0.535900	+	0.844281i	$0.319972\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$			7.39230i			0.742955i
$100$		0			0
$101$	−5.36603	−	9.29423i	−0.533939	−	0.924810i	−0.999214	−	0.0396438i	$-0.987378\pi$
$101$	−5.36603	−	9.29423i	−0.533939	−	0.924810i	0.465274	−	0.885167i	$-0.345956\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$			9.19615i			0.906124i	0.891479	+	0.453062i	$0.149668\pi$
$103$			9.19615i			0.906124i	−0.891479	+	0.453062i	$0.850332\pi$
$104$	0.866025	−	3.50000i	0.0849208	−	0.343203i
$105$		0			0
$106$	−0.401924	+	0.232051i	−0.0390383	+	0.0225388i
$107$	15.2942	−	8.83013i	1.47855	−	0.853641i	0.478843	−	0.877900i	$-0.341056\pi$
$107$	15.2942	−	8.83013i	1.47855	−	0.853641i	0.999706	+	0.0242598i	$0.00772291\pi$
$108$	3.46410	+	2.00000i	0.333333	+	0.192450i
$109$		−	8.53590i		−	0.817591i	−0.912626	−	0.408795i	$-0.865949\pi$
$109$		−	8.53590i		−	0.817591i	0.912626	−	0.408795i	$-0.134051\pi$
$110$		0			0
$111$	0.509619	+	0.294229i	0.0483709	+	0.0279269i
$112$	3.00000			0.283473
$113$	6.00000	+	3.46410i	0.564433	+	0.325875i	0.754923	−	0.655814i	$-0.227674\pi$
$113$	6.00000	+	3.46410i	0.564433	+	0.325875i	−0.190490	+	0.981689i	$0.561008\pi$
$114$	0.169873	+	0.294229i	0.0159101	+	0.0275570i
$115$		0			0
$116$	2.53590			0.235452
$117$	6.40192	+	6.16025i	0.591858	+	0.569516i
$118$			10.3923i			0.956689i
$119$	21.2942	−	12.2942i	1.95204	−	1.12701i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	6.19615			0.560973
$123$	3.80385	−	6.58846i	0.342981	−	0.594061i
$124$	4.09808	+	2.36603i	0.368018	+	0.212475i
$125$		0			0
$126$	−3.69615	+	6.40192i	−0.329279	+	0.570329i
$127$	9.35641	−	5.40192i	0.830247	−	0.479343i	−0.0236904	−	0.999719i	$-0.507542\pi$
$127$	9.35641	−	5.40192i	0.830247	−	0.479343i	0.853937	+	0.520376i	$0.174208\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.46410			−0.128907
$130$		0			0
$131$	6.12436			0.535087			0.267544	−	0.963546i	$-0.413788\pi$
$131$	6.12436			0.535087			0.267544	+	0.963546i	$0.413788\pi$
$132$	−1.09808	−	1.90192i	−0.0955753	−	0.165541i
$133$	−1.20577	+	0.696152i	−0.104554	+	0.0603641i
$134$		0			0
$135$		0			0
$136$	−7.09808	−	4.09808i	−0.608655	−	0.351407i
$137$	−1.09808	+	1.90192i	−0.0938150	+	0.162492i	−0.909113	−	0.416549i	$-0.863240\pi$
$137$	−1.09808	+	1.90192i	−0.0938150	+	0.162492i	0.815298	+	0.579041i	$0.196573\pi$
$138$	−6.92820			−0.589768
$139$	0.598076	−	1.03590i	0.0507282	−	0.0878638i	−0.839546	−	0.543288i	$-0.817179\pi$
$139$	0.598076	−	1.03590i	0.0507282	−	0.0878638i	0.890274	+	0.455424i	$0.150512\pi$
$140$		0			0
$141$	−1.90192	+	1.09808i	−0.160171	+	0.0924747i
$142$			6.00000i			0.503509i
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$	2.46410			0.205342
$145$		0			0
$146$	5.83013	+	10.0981i	0.482505	+	0.835723i
$147$	1.26795	+	0.732051i	0.104579	+	0.0603785i
$148$	0.803848			0.0660759
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$		0			0
$151$			23.6603i			1.92544i	0.270492	+	0.962722i	$0.412813\pi$
$151$			23.6603i			1.92544i	−0.270492	+	0.962722i	$0.587187\pi$
$152$	0.401924	+	0.232051i	0.0326003	+	0.0188218i
$153$	17.4904	−	10.0981i	1.41401	−	0.816381i
$154$	7.79423	−	4.50000i	0.628077	−	0.362620i
$155$		0			0
$156$	−2.56218	−	0.633975i	−0.205138	−	0.0507586i
$157$		−	13.0000i		−	1.03751i	−0.854922	−	0.518756i	$-0.826395\pi$
$157$		−	13.0000i		−	1.03751i	0.854922	−	0.518756i	$-0.173605\pi$
$158$	−2.09808	−	3.63397i	−0.166914	−	0.289103i
$159$	0.169873	+	0.294229i	0.0134718	+	0.0233338i
$160$		0			0
$161$		−	28.3923i		−	2.23763i
$162$	−2.23205	+	3.86603i	−0.175366	+	0.303744i
$163$	−5.36603	+	9.29423i	−0.420300	+	0.727980i	−0.995969	−	0.0897026i	$-0.971408\pi$
$163$	−5.36603	+	9.29423i	−0.420300	+	0.727980i	0.575669	+	0.817683i	$0.304742\pi$
$164$		−	10.3923i		−	0.811503i
$165$		0			0
$166$	−4.09808	−	7.09808i	−0.318072	−	0.550918i
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$		−	2.19615i		−	0.169437i
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$	−0.990381	+	0.571797i	−0.0757363	+	0.0437264i
$172$	−1.73205	+	1.00000i	−0.132068	+	0.0762493i
$173$	−12.9904	−	7.50000i	−0.987640	−	0.570214i	−0.0830722	−	0.996544i	$-0.526473\pi$
$173$	−12.9904	−	7.50000i	−0.987640	−	0.570214i	−0.904568	+	0.426329i	$0.859807\pi$
$174$		−	1.85641i		−	0.140734i
$175$		0			0
$176$	−2.59808	−	1.50000i	−0.195837	−	0.113067i
$177$	7.60770			0.571829
$178$	5.89230	+	3.40192i	0.441647	+	0.254985i
$179$	−4.73205	−	8.19615i	−0.353690	−	0.612609i	0.633203	−	0.773986i	$-0.281740\pi$
$179$	−4.73205	−	8.19615i	−0.353690	−	0.612609i	−0.986893	+	0.161377i	$0.948407\pi$
$180$		0			0
$181$	14.5885			1.08435			0.542176	−	0.840265i	$-0.317601\pi$
$181$	14.5885			1.08435			0.542176	+	0.840265i	$0.317601\pi$
$182$	2.59808	−	10.5000i	0.192582	−	0.778312i
$183$		−	4.53590i		−	0.335303i
$184$	−8.19615	+	4.73205i	−0.604228	+	0.348851i
$185$		0			0
$186$	1.73205	−	3.00000i	0.127000	−	0.219971i
$187$	−24.5885			−1.79809
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	10.3923	+	6.00000i	0.755929	+	0.436436i
$190$		0			0
$191$	11.3660	−	19.6865i	0.822417	−	1.42447i	−0.0814609	−	0.996677i	$-0.525959\pi$
$191$	11.3660	−	19.6865i	0.822417	−	1.42447i	0.903878	−	0.427791i	$-0.140708\pi$
$192$	−0.633975	+	0.366025i	−0.0457532	+	0.0264156i
$193$	8.19615	+	14.1962i	0.589972	+	1.02186i	0.994235	+	0.107219i	$0.0341945\pi$
$193$	8.19615	+	14.1962i	0.589972	+	1.02186i	−0.404263	+	0.914643i	$0.632472\pi$
$194$	9.12436			0.655091
$195$		0			0
$196$	2.00000			0.142857
$197$	10.7942	+	18.6962i	0.769057	+	1.33205i	0.938075	+	0.346433i	$0.112607\pi$
$197$	10.7942	+	18.6962i	0.769057	+	1.33205i	−0.169018	+	0.985613i	$0.554060\pi$
$198$	6.40192	−	3.69615i	0.454965	−	0.262674i
$199$	−3.19615	+	5.53590i	−0.226569	+	0.392429i	−0.956789	−	0.290783i	$-0.906084\pi$
$199$	−3.19615	+	5.53590i	−0.226569	+	0.392429i	0.730220	+	0.683212i	$0.239418\pi$
$200$		0			0
$201$		0			0
$202$	−5.36603	+	9.29423i	−0.377552	+	0.653940i
$203$	7.60770			0.533956
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$		0			0
$206$	7.96410	−	4.59808i	0.554885	−	0.320363i
$207$		−	23.3205i		−	1.62089i
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$	1.39230			0.0963077
$210$		0			0
$211$	8.79423	+	15.2321i	0.605420	+	1.04862i	0.991985	+	0.126356i	$0.0403280\pi$
$211$	8.79423	+	15.2321i	0.605420	+	1.04862i	−0.386565	+	0.922262i	$0.626339\pi$
$212$	0.401924	+	0.232051i	0.0276042	+	0.0159373i
$213$	4.39230			0.300956
$214$	−15.2942	−	8.83013i	−1.04549	−	0.603615i
$215$		0			0
$216$		−	4.00000i		−	0.272166i
$217$	12.2942	+	7.09808i	0.834587	+	0.481849i
$218$	−7.39230	+	4.26795i	−0.500670	+	0.289062i
$219$	7.39230	−	4.26795i	0.499526	−	0.288401i
$220$		0			0
$221$	−20.4904	+	21.2942i	−1.37833	+	1.43240i
$222$		−	0.588457i		−	0.0394947i
$223$	3.23205	+	5.59808i	0.216434	+	0.374875i	0.953715	−	0.300711i	$-0.0972240\pi$
$223$	3.23205	+	5.59808i	0.216434	+	0.374875i	−0.737281	+	0.675586i	$0.763891\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$		0			0
$226$		−	6.92820i		−	0.460857i
$227$	−8.19615	+	14.1962i	−0.543998	+	0.942232i	0.454672	+	0.890659i	$0.349757\pi$
$227$	−8.19615	+	14.1962i	−0.543998	+	0.942232i	−0.998669	+	0.0515725i	$0.983577\pi$
$228$	0.169873	−	0.294229i	0.0112501	−	0.0194858i
$229$		−	1.26795i		−	0.0837884i	−0.999122	−	0.0418942i	$-0.986661\pi$
$229$		−	1.26795i		−	0.0837884i	0.999122	−	0.0418942i	$-0.0133392\pi$
$230$		0			0
$231$	−3.29423	−	5.70577i	−0.216744	−	0.375412i
$232$	−1.26795	−	2.19615i	−0.0832449	−	0.144184i
$233$		−	4.73205i		−	0.310007i	−0.987914	−	0.155003i	$-0.950461\pi$
$233$		−	4.73205i		−	0.310007i	0.987914	−	0.155003i	$-0.0495389\pi$
$234$	2.13397	−	8.62436i	0.139502	−	0.563792i
$235$		0			0
$236$	9.00000	−	5.19615i	0.585850	−	0.338241i
$237$	−2.66025	+	1.53590i	−0.172802	+	0.0997673i
$238$	−21.2942	−	12.2942i	−1.38030	−	0.796916i
$239$			2.19615i			0.142057i	0.997474	+	0.0710286i	$0.0226282\pi$
$239$			2.19615i			0.142057i	−0.997474	+	0.0710286i	$0.977372\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$	2.00000			0.128565
$243$	13.2224	+	7.63397i	0.848219	+	0.489720i
$244$	−3.09808	−	5.36603i	−0.198334	−	0.343525i
$245$		0			0
$246$	−7.60770			−0.485049
$247$	1.16025	−	1.20577i	0.0738252	−	0.0767214i
$248$		−	4.73205i		−	0.300486i
$249$	−5.19615	+	3.00000i	−0.329293	+	0.190117i
$250$		0			0
$251$	−8.59808	+	14.8923i	−0.542706	+	0.939994i	0.456042	+	0.889958i	$0.349267\pi$
$251$	−8.59808	+	14.8923i	−0.542706	+	0.939994i	−0.998747	+	0.0500355i	$0.984067\pi$
$252$	7.39230			0.465671
$253$	−14.1962	+	24.5885i	−0.892504	+	1.54586i
$254$	−9.35641	−	5.40192i	−0.587073	−	0.338947i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.0000	+	6.92820i	−0.748539	+	0.432169i	−0.825166	−	0.564890i	$-0.808918\pi$
$257$	−12.0000	+	6.92820i	−0.748539	+	0.432169i	0.0766265	+	0.997060i	$0.475585\pi$
$258$	0.732051	+	1.26795i	0.0455755	+	0.0789391i
$259$	2.41154			0.149846
$260$		0			0
$261$	6.24871			0.386786
$262$	−3.06218	−	5.30385i	−0.189182	−	0.327673i
$263$	−3.10770	+	1.79423i	−0.191629	+	0.110637i	−0.592745	−	0.805390i	$-0.701956\pi$
$263$	−3.10770	+	1.79423i	−0.191629	+	0.110637i	0.401116	+	0.916027i	$0.368622\pi$
$264$	−1.09808	+	1.90192i	−0.0675819	+	0.117055i
$265$		0			0
$266$	1.20577	+	0.696152i	0.0739306	+	0.0426838i
$267$	2.49038	−	4.31347i	0.152409	−	0.263980i
$268$		0			0
$269$	−13.5622	+	23.4904i	−0.826901	+	1.43223i	0.0735575	+	0.997291i	$0.476565\pi$
$269$	−13.5622	+	23.4904i	−0.826901	+	1.43223i	−0.900458	+	0.434943i	$0.856769\pi$
$270$		0			0
$271$	8.19615	−	4.73205i	0.497881	−	0.287452i	−0.229957	−	0.973201i	$-0.573859\pi$
$271$	8.19615	−	4.73205i	0.497881	−	0.287452i	0.727838	+	0.685749i	$0.240525\pi$
$272$			8.19615i			0.496965i
$273$	−7.68653	−	1.90192i	−0.465210	−	0.115110i
$274$	2.19615			0.132674
$275$		0			0
$276$	3.46410	+	6.00000i	0.208514	+	0.361158i
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	0.525792	−	0.850613i	$-0.323769\pi$
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	−0.473757	+	0.880656i	$0.657103\pi$
$278$	−1.19615			−0.0717405
$279$	10.0981	+	5.83013i	0.604556	+	0.349041i
$280$		0			0
$281$			10.3923i			0.619953i	0.950744	+	0.309976i	$0.100321\pi$
$281$			10.3923i			0.619953i	−0.950744	+	0.309976i	$0.899679\pi$
$282$	1.90192	+	1.09808i	0.113258	+	0.0653895i
$283$	8.32051	−	4.80385i	0.494603	−	0.285559i	−0.231879	−	0.972745i	$-0.574487\pi$
$283$	8.32051	−	4.80385i	0.494603	−	0.285559i	0.726482	+	0.687186i	$0.241154\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$	−7.50000	+	7.79423i	−0.443484	+	0.460882i
$287$		−	31.1769i		−	1.84032i
$288$	−1.23205	−	2.13397i	−0.0725993	−	0.125746i
$289$	25.0885	+	43.4545i	1.47579	+	2.55615i
$290$		0			0
$291$		−	6.67949i		−	0.391559i
$292$	5.83013	−	10.0981i	0.341182	−	0.590945i
$293$	5.59808	−	9.69615i	0.327043	−	0.566455i	−0.654881	−	0.755732i	$-0.727281\pi$
$293$	5.59808	−	9.69615i	0.327043	−	0.566455i	0.981924	+	0.189277i	$0.0606144\pi$
$294$		−	1.46410i		−	0.0853881i
$295$		0			0
$296$	−0.401924	−	0.696152i	−0.0233613	−	0.0404630i
$297$	−6.00000	−	10.3923i	−0.348155	−	0.603023i
$298$			6.00000i			0.347571i
$299$	9.46410	+	32.7846i	0.547323	+	1.89598i
$300$		0			0
$301$	−5.19615	+	3.00000i	−0.299501	+	0.172917i
$302$	20.4904	−	11.8301i	1.17909	−	0.680747i
$303$	6.80385	+	3.92820i	0.390871	+	0.225669i
$304$		−	0.464102i		−	0.0266181i
$305$		0			0
$306$	−17.4904	−	10.0981i	−0.999859	−	0.577269i
$307$	−27.4641			−1.56746			−0.783730	−	0.621102i	$-0.786685\pi$
$307$	−27.4641			−1.56746			−0.783730	+	0.621102i	$0.786685\pi$
$308$	−7.79423	−	4.50000i	−0.444117	−	0.256411i
$309$	−3.36603	−	5.83013i	−0.191486	−	0.331664i
$310$		0			0
$311$	−9.12436			−0.517395			−0.258697	−	0.965958i	$-0.583293\pi$
$311$	−9.12436			−0.517395			−0.258697	+	0.965958i	$0.583293\pi$
$312$	0.732051	+	2.53590i	0.0414442	+	0.143567i
$313$		−	26.3923i		−	1.49178i	−0.666068	−	0.745891i	$-0.732024\pi$
$313$		−	26.3923i		−	1.49178i	0.666068	−	0.745891i	$-0.267976\pi$
$314$	−11.2583	+	6.50000i	−0.635344	+	0.366816i
$315$		0			0
$316$	−2.09808	+	3.63397i	−0.118026	+	0.204427i
$317$	−23.1962			−1.30283			−0.651413	−	0.758723i	$-0.725823\pi$
$317$	−23.1962			−1.30283			−0.651413	+	0.758723i	$0.725823\pi$
$318$	0.169873	−	0.294229i	0.00952600	−	0.0164995i
$319$	−6.58846	−	3.80385i	−0.368883	−	0.212975i
$320$		0			0
$321$	−6.46410	+	11.1962i	−0.360791	+	0.624908i
$322$	−24.5885	+	14.1962i	−1.37026	+	0.791121i
$323$	−1.90192	−	3.29423i	−0.105826	−	0.183296i
$324$	4.46410			0.248006
$325$		0			0
$326$	10.7321			0.594393
$327$	3.12436	+	5.41154i	0.172777	+	0.299259i
$328$	−9.00000	+	5.19615i	−0.496942	+	0.286910i
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	11.1962	+	6.46410i	0.615396	+	0.355299i	0.775074	−	0.631870i	$-0.217712\pi$
$331$	11.1962	+	6.46410i	0.615396	+	0.355299i	−0.159678	+	0.987169i	$0.551046\pi$
$332$	−4.09808	+	7.09808i	−0.224911	+	0.389558i
$333$	1.98076			0.108545
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$		0			0
$336$	−1.90192	+	1.09808i	−0.103758	+	0.0599050i
$337$			6.19615i			0.337526i	0.985657	+	0.168763i	$0.0539772\pi$
$337$			6.19615i			0.337526i	−0.985657	+	0.168763i	$0.946023\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	−5.07180			−0.275462
$340$		0			0
$341$	−7.09808	−	12.2942i	−0.384382	−	0.665770i
$342$	0.990381	+	0.571797i	0.0535537	+	0.0309192i
$343$	−15.0000			−0.809924
$344$	1.73205	+	1.00000i	0.0933859	+	0.0539164i
$345$		0			0
$346$			15.0000i			0.806405i
$347$	24.8827	+	14.3660i	1.33577	+	0.771209i	0.986178	−	0.165692i	$-0.0529858\pi$
$347$	24.8827	+	14.3660i	1.33577	+	0.771209i	0.349595	+	0.936901i	$0.386319\pi$
$348$	−1.60770	+	0.928203i	−0.0861815	+	0.0497569i
$349$	3.50962	−	2.02628i	0.187866	−	0.108464i	−0.403117	−	0.915148i	$-0.632073\pi$
$349$	3.50962	−	2.02628i	0.187866	−	0.108464i	0.590983	+	0.806684i	$0.298740\pi$
$350$		0			0
$351$	−14.0000	−	3.46410i	−0.747265	−	0.184900i
$352$			3.00000i			0.159901i
$353$	−4.90192	−	8.49038i	−0.260903	−	0.451897i	0.705579	−	0.708631i	$-0.250687\pi$
$353$	−4.90192	−	8.49038i	−0.260903	−	0.451897i	−0.966482	+	0.256734i	$0.917354\pi$
$354$	−3.80385	−	6.58846i	−0.202172	−	0.350173i
$355$		0			0
$356$		−	6.80385i		−	0.360603i
$357$	−9.00000	+	15.5885i	−0.476331	+	0.825029i
$358$	−4.73205	+	8.19615i	−0.250097	+	0.433180i
$359$			1.60770i			0.0848509i	0.999100	+	0.0424255i	$0.0135085\pi$
$359$			1.60770i			0.0848509i	−0.999100	+	0.0424255i	$0.986492\pi$
$360$		0			0
$361$	−9.39230	−	16.2679i	−0.494332	−	0.856208i
$362$	−7.29423	−	12.6340i	−0.383376	−	0.664027i
$363$		−	1.46410i		−	0.0768454i
$364$	−10.3923	+	3.00000i	−0.544705	+	0.157243i
$365$		0			0
$366$	−3.92820	+	2.26795i	−0.205330	+	0.118548i
$367$	−4.85641	+	2.80385i	−0.253502	+	0.146360i	−0.621367	−	0.783520i	$-0.713422\pi$
$367$	−4.85641	+	2.80385i	−0.253502	+	0.146360i	0.367865	+	0.929879i	$0.380089\pi$
$368$	8.19615	+	4.73205i	0.427254	+	0.246675i
$369$		−	25.6077i		−	1.33308i
$370$		0			0
$371$	1.20577	+	0.696152i	0.0626005	+	0.0361424i
$372$	−3.46410			−0.179605
$373$	−0.339746	−	0.196152i	−0.0175914	−	0.0101564i	0.491179	−	0.871059i	$-0.336566\pi$
$373$	−0.339746	−	0.196152i	−0.0175914	−	0.0101564i	−0.508770	+	0.860903i	$0.669900\pi$
$374$	12.2942	+	21.2942i	0.635719	+	1.10110i
$375$		0			0
$376$	3.00000			0.154713
$377$	−8.78461	+	2.53590i	−0.452430	+	0.130605i
$378$		−	12.0000i		−	0.617213i
$379$	−25.7942	+	14.8923i	−1.32496	+	0.764966i	−0.984515	−	0.175298i	$-0.943911\pi$
$379$	−25.7942	+	14.8923i	−1.32496	+	0.764966i	−0.340445	+	0.940264i	$0.610578\pi$
$380$		0			0
$381$	−3.95448	+	6.84936i	−0.202594	+	0.350904i
$382$	−22.7321			−1.16307
$383$	11.1962	−	19.3923i	0.572097	−	0.990900i	−0.424254	−	0.905543i	$-0.639464\pi$
$383$	11.1962	−	19.3923i	0.572097	−	0.990900i	0.996350	−	0.0853571i	$-0.0272031\pi$
$384$	0.633975	+	0.366025i	0.0323524	+	0.0186787i
$385$		0			0
$386$	8.19615	−	14.1962i	0.417173	−	0.722565i
$387$	−4.26795	+	2.46410i	−0.216952	+	0.125257i
$388$	−4.56218	−	7.90192i	−0.231609	−	0.401159i
$389$	−22.7321			−1.15256			−0.576280	−	0.817252i	$-0.695496\pi$
$389$	−22.7321			−1.15256			−0.576280	+	0.817252i	$0.695496\pi$
$390$		0			0
$391$	77.5692			3.92284
$392$	−1.00000	−	1.73205i	−0.0505076	−	0.0874818i
$393$	−3.88269	+	2.24167i	−0.195856	+	0.113077i
$394$	10.7942	−	18.6962i	0.543805	−	0.941899i
$395$		0			0
$396$	−6.40192	−	3.69615i	−0.321709	−	0.185739i
$397$	5.59808	−	9.69615i	0.280959	−	0.486636i	−0.690662	−	0.723178i	$-0.742681\pi$
$397$	5.59808	−	9.69615i	0.280959	−	0.486636i	0.971621	+	0.236542i	$0.0760140\pi$
$398$	6.39230			0.320417
$399$	0.509619	−	0.882686i	0.0255129	−	0.0441896i
$400$		0			0
$401$	−4.50000	+	2.59808i	−0.224719	+	0.129742i	−0.608134	−	0.793835i	$-0.708081\pi$
$401$	−4.50000	+	2.59808i	−0.224719	+	0.129742i	0.383414	+	0.923576i	$0.374748\pi$
$402$		0			0
$403$	−16.5622	−	4.09808i	−0.825021	−	0.204140i
$404$	10.7321			0.533939
$405$		0			0
$406$	−3.80385	−	6.58846i	−0.188782	−	0.326980i
$407$	−2.08846	−	1.20577i	−0.103521	−	0.0597679i
$408$	6.00000			0.297044
$409$	14.0885	+	8.13397i	0.696629	+	0.402199i	0.806091	−	0.591792i	$-0.201579\pi$
$409$	14.0885	+	8.13397i	0.696629	+	0.402199i	−0.109461	+	0.993991i	$0.534913\pi$
$410$		0			0
$411$		−	1.60770i		−	0.0793018i
$412$	−7.96410	−	4.59808i	−0.392363	−	0.226531i
$413$	27.0000	−	15.5885i	1.32858	−	0.767058i
$414$	−20.1962	+	11.6603i	−0.992587	+	0.573070i
$415$		0			0
$416$	2.59808	+	2.50000i	0.127381	+	0.122573i
$417$			0.875644i			0.0428805i
$418$	−0.696152	−	1.20577i	−0.0340499	−	0.0589762i
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	0.573158	−	0.819445i	$-0.305718\pi$
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	−0.996239	+	0.0866469i	$0.972385\pi$
$420$		0			0
$421$		−	2.87564i		−	0.140150i	−0.997542	−	0.0700752i	$-0.977676\pi$
$421$		−	2.87564i		−	0.140150i	0.997542	−	0.0700752i	$-0.0223239\pi$
$422$	8.79423	−	15.2321i	0.428096	−	0.741485i
$423$	−3.69615	+	6.40192i	−0.179713	+	0.311272i
$424$		−	0.464102i		−	0.0225388i
$425$		0			0
$426$	−2.19615	−	3.80385i	−0.106404	−	0.184297i
$427$	−9.29423	−	16.0981i	−0.449779	−	0.779041i
$428$			17.6603i			0.853641i
$429$	5.70577	+	5.49038i	0.275477	+	0.265078i
$430$		0			0
$431$	−7.09808	+	4.09808i	−0.341902	+	0.197397i	−0.661113	−	0.750286i	$-0.729916\pi$
$431$	−7.09808	+	4.09808i	−0.341902	+	0.197397i	0.319211	+	0.947684i	$0.396582\pi$
$432$	−3.46410	+	2.00000i	−0.166667	+	0.0962250i
$433$	7.26795	+	4.19615i	0.349275	+	0.201654i	0.664366	−	0.747407i	$-0.268702\pi$
$433$	7.26795	+	4.19615i	0.349275	+	0.201654i	−0.315091	+	0.949062i	$0.602035\pi$
$434$		−	14.1962i		−	0.681437i
$435$		0			0
$436$	7.39230	+	4.26795i	0.354027	+	0.204398i
$437$	−4.39230			−0.210112
$438$	−7.39230	−	4.26795i	−0.353218	−	0.203931i
$439$	−1.70577	−	2.95448i	−0.0814120	−	0.141010i	0.822445	−	0.568845i	$-0.192610\pi$
$439$	−1.70577	−	2.95448i	−0.0814120	−	0.141010i	−0.903857	+	0.427835i	$0.859276\pi$
$440$		0			0
$441$	4.92820			0.234676
$442$	28.6865	+	7.09808i	1.36448	+	0.337621i
$443$			22.3923i			1.06389i	0.846779	+	0.531945i	$0.178539\pi$
$443$			22.3923i			1.06389i	−0.846779	+	0.531945i	$0.821461\pi$
$444$	−0.509619	+	0.294229i	−0.0241854	+	0.0139635i
$445$		0			0
$446$	3.23205	−	5.59808i	0.153042	−	0.265077i
$447$	4.39230			0.207749
$448$	−1.50000	+	2.59808i	−0.0708683	+	0.122748i
$449$	−13.5000	−	7.79423i	−0.637104	−	0.367832i	0.146394	−	0.989226i	$-0.453233\pi$
$449$	−13.5000	−	7.79423i	−0.637104	−	0.367832i	−0.783498	+	0.621394i	$0.786567\pi$
$450$		0			0
$451$	−15.5885	+	27.0000i	−0.734032	+	1.27138i
$452$	−6.00000	+	3.46410i	−0.282216	+	0.162938i
$453$	−8.66025	−	15.0000i	−0.406894	−	0.704761i
$454$	16.3923			0.769329
$455$		0			0
$456$	−0.339746			−0.0159101
$457$	9.16987	+	15.8827i	0.428949	+	0.742961i	0.996780	−	0.0801841i	$-0.0255508\pi$
$457$	9.16987	+	15.8827i	0.428949	+	0.742961i	−0.567832	+	0.823145i	$0.692217\pi$
$458$	−1.09808	+	0.633975i	−0.0513097	+	0.0296237i
$459$	−16.3923	+	28.3923i	−0.765127	+	1.32524i
$460$		0			0
$461$	−26.4904	−	15.2942i	−1.23378	−	0.712323i	−0.265964	−	0.963983i	$-0.585690\pi$
$461$	−26.4904	−	15.2942i	−1.23378	−	0.712323i	−0.967816	+	0.251660i	$0.919024\pi$
$462$	−3.29423	+	5.70577i	−0.153261	+	0.265457i
$463$	−12.9282			−0.600825			−0.300412	−	0.953809i	$-0.597124\pi$
$463$	−12.9282			−0.600825			−0.300412	+	0.953809i	$0.597124\pi$
$464$	−1.26795	+	2.19615i	−0.0588631	+	0.101954i
$465$		0			0
$466$	−4.09808	+	2.36603i	−0.189840	+	0.109604i
$467$		−	37.8564i		−	1.75179i	−0.482506	−	0.875893i	$-0.660273\pi$
$467$		−	37.8564i		−	1.75179i	0.482506	−	0.875893i	$-0.339727\pi$
$468$	−8.53590	+	2.46410i	−0.394572	+	0.113903i
$469$		0			0
$470$		0			0
$471$	4.75833	+	8.24167i	0.219252	+	0.379756i
$472$	−9.00000	−	5.19615i	−0.414259	−	0.239172i
$473$	6.00000			0.275880
$474$	2.66025	+	1.53590i	0.122190	+	0.0705461i
$475$		0			0
$476$			24.5885i			1.12701i
$477$	0.990381	+	0.571797i	0.0453464	+	0.0261808i
$478$	1.90192	−	1.09808i	0.0869920	−	0.0502248i
$479$	35.4904	−	20.4904i	1.62160	−	0.936229i	0.635104	−	0.772427i	$-0.280957\pi$
$479$	35.4904	−	20.4904i	1.62160	−	0.936229i	0.986493	−	0.163803i	$-0.0523760\pi$
$480$		0			0
$481$	−2.78461	+	0.803848i	−0.126967	+	0.0366523i
$482$			8.66025i			0.394464i
$483$	10.3923	+	18.0000i	0.472866	+	0.819028i
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$		−	15.2679i		−	0.692568i
$487$	7.62436	−	13.2058i	0.345493	−	0.598411i	−0.639951	−	0.768416i	$-0.721045\pi$
$487$	7.62436	−	13.2058i	0.345493	−	0.598411i	0.985443	+	0.170005i	$0.0543785\pi$
$488$	−3.09808	+	5.36603i	−0.140243	+	0.242909i
$489$		−	7.85641i		−	0.355279i
$490$		0			0
$491$	−10.3301	−	17.8923i	−0.466192	−	0.807468i	0.533062	−	0.846076i	$-0.321041\pi$
$491$	−10.3301	−	17.8923i	−0.466192	−	0.807468i	−0.999254	+	0.0386076i	$0.987708\pi$
$492$	3.80385	+	6.58846i	0.171491	+	0.297031i
$493$			20.7846i			0.936092i
$494$	−1.62436	−	0.401924i	−0.0730832	−	0.0180834i
$495$		0			0
$496$	−4.09808	+	2.36603i	−0.184009	+	0.106238i
$497$	15.5885	−	9.00000i	0.699238	−	0.403705i
$498$	5.19615	+	3.00000i	0.232845	+	0.134433i
$499$			25.8564i			1.15749i	0.815508	+	0.578746i	$0.196458\pi$
$499$			25.8564i			1.15749i	−0.815508	+	0.578746i	$0.803542\pi$
$500$		0			0
$501$	−1.90192	−	1.09808i	−0.0849717	−	0.0490584i
$502$	17.1962			0.767502
$503$	−23.0885	−	13.3301i	−1.02946	−	0.594361i	−0.112633	−	0.993637i	$-0.535928\pi$
$503$	−23.0885	−	13.3301i	−1.02946	−	0.594361i	−0.916831	+	0.399276i	$0.869262\pi$
$504$	−3.69615	−	6.40192i	−0.164640	−	0.285164i
$505$		0			0
$506$	28.3923			1.26219
$507$	9.50962	−	0.366025i	0.422337	−	0.0162558i
$508$			10.8038i			0.479343i
$509$	19.3923	−	11.1962i	0.859549	−	0.496261i	−0.00431237	−	0.999991i	$-0.501373\pi$
$509$	19.3923	−	11.1962i	0.859549	−	0.496261i	0.863861	+	0.503730i	$0.168039\pi$
$510$		0			0
$511$	17.4904	−	30.2942i	0.773729	−	1.34014i
$512$	1.00000			0.0441942
$513$	0.928203	−	1.60770i	0.0409812	−	0.0709815i
$514$	12.0000	+	6.92820i	0.529297	+	0.305590i
$515$		0			0
$516$	0.732051	−	1.26795i	0.0322267	−	0.0558184i
$517$	7.79423	−	4.50000i	0.342790	−	0.197910i
$518$	−1.20577	−	2.08846i	−0.0529786	−	0.0917615i
$519$	10.9808			0.482002
$520$		0			0
$521$	6.46410			0.283197			0.141599	−	0.989924i	$-0.454776\pi$
$521$	6.46410			0.283197			0.141599	+	0.989924i	$0.454776\pi$
$522$	−3.12436	−	5.41154i	−0.136749	−	0.236857i
$523$	2.07180	−	1.19615i	0.0905933	−	0.0523041i	−0.454019	−	0.890992i	$-0.650010\pi$
$523$	2.07180	−	1.19615i	0.0905933	−	0.0523041i	0.544612	+	0.838688i	$0.316677\pi$
$524$	−3.06218	+	5.30385i	−0.133772	+	0.231700i
$525$		0			0
$526$	3.10770	+	1.79423i	0.135502	+	0.0782321i
$527$	−19.3923	+	33.5885i	−0.844742	+	1.46314i
$528$	2.19615			0.0955753
$529$	33.2846	−	57.6506i	1.44716	−	2.50655i
$530$		0			0
$531$	22.1769	−	12.8038i	0.962396	−	0.555640i
$532$		−	1.39230i		−	0.0603641i
$533$	10.3923	+	36.0000i	0.450141	+	1.55933i
$534$	−4.98076			−0.215539
$535$		0			0
$536$		0			0
$537$	6.00000	+	3.46410i	0.258919	+	0.149487i
$538$	27.1244			1.16941
$539$	−5.19615	−	3.00000i	−0.223814	−	0.129219i
$540$		0			0
$541$		−	22.0526i		−	0.948114i	−0.880494	−	0.474057i	$-0.842789\pi$
$541$		−	22.0526i		−	0.948114i	0.880494	−	0.474057i	$-0.157211\pi$
$542$	−8.19615	−	4.73205i	−0.352055	−	0.203259i
$543$	−9.24871	+	5.33975i	−0.396900	+	0.229150i
$544$	7.09808	−	4.09808i	0.304328	−	0.175704i
$545$		0			0
$546$	2.19615	+	7.60770i	0.0939866	+	0.325579i
$547$		−	6.78461i		−	0.290089i	−0.989425	−	0.145044i	$-0.953667\pi$
$547$		−	6.78461i		−	0.290089i	0.989425	−	0.145044i	$-0.0463325\pi$
$548$	−1.09808	−	1.90192i	−0.0469075	−	0.0812462i
$549$	−7.63397	−	13.2224i	−0.325810	−	0.564320i
$550$		0			0
$551$		−	1.17691i		−	0.0501382i
$552$	3.46410	−	6.00000i	0.147442	−	0.255377i
$553$	−6.29423	+	10.9019i	−0.267658	+	0.463597i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	0.598076	+	1.03590i	0.0253641	+	0.0439319i
$557$	−3.40192	−	5.89230i	−0.144144	−	0.249665i	0.784909	−	0.619611i	$-0.212710\pi$
$557$	−3.40192	−	5.89230i	−0.144144	−	0.249665i	−0.929053	+	0.369946i	$0.879376\pi$
$558$		−	11.6603i		−	0.493618i
$559$	5.00000	−	5.19615i	0.211477	−	0.219774i
$560$		0			0
$561$	15.5885	−	9.00000i	0.658145	−	0.379980i
$562$	9.00000	−	5.19615i	0.379642	−	0.219186i
$563$	12.5885	+	7.26795i	0.530540	+	0.306308i	0.741236	−	0.671244i	$-0.234240\pi$
$563$	12.5885	+	7.26795i	0.530540	+	0.306308i	−0.210696	+	0.977552i	$0.567573\pi$
$564$		−	2.19615i		−	0.0924747i
$565$		0			0
$566$	−8.32051	−	4.80385i	−0.349737	−	0.201921i
$567$	13.3923			0.562424
$568$	−5.19615	−	3.00000i	−0.218026	−	0.125877i
$569$	−13.6244	−	23.5981i	−0.571163	−	0.989283i	−0.996447	−	0.0842230i	$-0.973159\pi$
$569$	−13.6244	−	23.5981i	−0.571163	−	0.989283i	0.425284	−	0.905060i	$-0.360174\pi$
$570$		0			0
$571$	−38.3731			−1.60586			−0.802931	−	0.596071i	$-0.796728\pi$
$571$	−38.3731			−1.60586			−0.802931	+	0.596071i	$0.796728\pi$
$572$	10.5000	+	2.59808i	0.439027	+	0.108631i
$573$			16.6410i			0.695188i
$574$	−27.0000	+	15.5885i	−1.12696	+	0.650650i
$575$		0			0
$576$	−1.23205	+	2.13397i	−0.0513355	+	0.0889156i
$577$	−26.4449			−1.10091			−0.550457	−	0.834863i	$-0.685547\pi$
$577$	−26.4449			−1.10091			−0.550457	+	0.834863i	$0.685547\pi$
$578$	25.0885	−	43.4545i	1.04354	−	1.80747i
$579$	−10.3923	−	6.00000i	−0.431889	−	0.249351i
$580$		0			0
$581$	−12.2942	+	21.2942i	−0.510051	+	0.883433i
$582$	−5.78461	+	3.33975i	−0.239780	+	0.138437i
$583$	−0.696152	−	1.20577i	−0.0288317	−	0.0499379i
$584$	−11.6603			−0.482505
$585$		0			0
$586$	−11.1962			−0.462509
$587$	15.0000	+	25.9808i	0.619116	+	1.07234i	0.989647	+	0.143521i	$0.0458424\pi$
$587$	15.0000	+	25.9808i	0.619116	+	1.07234i	−0.370531	+	0.928820i	$0.620824\pi$
$588$	−1.26795	+	0.732051i	−0.0522893	+	0.0301893i
$589$	1.09808	−	1.90192i	0.0452454	−	0.0783674i
$590$		0			0
$591$	−13.6865	−	7.90192i	−0.562989	−	0.325042i
$592$	−0.401924	+	0.696152i	−0.0165190	+	0.0286117i
$593$	20.7846			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$593$	20.7846			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$594$	−6.00000	+	10.3923i	−0.246183	+	0.426401i
$595$		0			0
$596$	5.19615	−	3.00000i	0.212843	−	0.122885i
$597$		−	4.67949i		−	0.191519i
$598$	23.6603	−	24.5885i	0.967540	−	1.00550i
$599$	19.8564			0.811311			0.405655	−	0.914026i	$-0.367043\pi$
$599$	19.8564			0.811311			0.405655	+	0.914026i	$0.367043\pi$
$600$		0			0
$601$	18.8923	+	32.7224i	0.770633	+	1.33478i	0.937216	+	0.348748i	$0.113393\pi$
$601$	18.8923	+	32.7224i	0.770633	+	1.33478i	−0.166583	+	0.986027i	$0.553273\pi$
$602$	5.19615	+	3.00000i	0.211779	+	0.122271i
$603$		0			0
$604$	−20.4904	−	11.8301i	−0.833742	−	0.481361i
$605$		0			0
$606$		−	7.85641i		−	0.319145i
$607$	32.5526	+	18.7942i	1.32127	+	0.762834i	0.983931	−	0.178550i	$-0.0571406\pi$
$607$	32.5526	+	18.7942i	1.32127	+	0.762834i	0.337337	+	0.941384i	$0.390474\pi$
$608$	−0.401924	+	0.232051i	−0.0163002	+	0.00941090i
$609$	−4.82309	+	2.78461i	−0.195441	+	0.112838i
$610$		0			0
$611$	2.59808	−	10.5000i	0.105107	−	0.424785i
$612$			20.1962i			0.816381i
$613$	−19.4545	−	33.6962i	−0.785759	−	1.36097i	−0.928545	−	0.371221i	$-0.878939\pi$
$613$	−19.4545	−	33.6962i	−0.785759	−	1.36097i	0.142785	−	0.989754i	$-0.454394\pi$
$614$	13.7321	+	23.7846i	0.554180	+	0.959869i
$615$		0			0
$616$			9.00000i			0.362620i
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	−0.988343	−	0.152242i	$-0.951351\pi$
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	0.626017	+	0.779809i	$0.284684\pi$
$618$	−3.36603	+	5.83013i	−0.135401	+	0.234522i
$619$		−	31.3923i		−	1.26176i	−0.775879	−	0.630882i	$-0.782693\pi$
$619$		−	31.3923i		−	1.26176i	0.775879	−	0.630882i	$-0.217307\pi$
$620$		0			0
$621$	18.9282	+	32.7846i	0.759563	+	1.31560i
$622$	4.56218	+	7.90192i	0.182927	+	0.316838i
$623$		−	20.4115i		−	0.817771i
$624$	1.83013	−	1.90192i	0.0732637	−	0.0761379i
$625$		0			0
$626$	−22.8564	+	13.1962i	−0.913526	+	0.527424i
$627$	−0.882686	+	0.509619i	−0.0352511	+	0.0203522i
$628$	11.2583	+	6.50000i	0.449256	+	0.259378i
$629$			6.58846i			0.262699i
$630$		0			0
$631$	−18.0000	−	10.3923i	−0.716569	−	0.413711i	0.0969198	−	0.995292i	$-0.469101\pi$
$631$	−18.0000	−	10.3923i	−0.716569	−	0.413711i	−0.813488	+	0.581581i	$0.802434\pi$
$632$	4.19615			0.166914
$633$	−11.1506	−	6.43782i	−0.443198	−	0.255880i
$634$	11.5981	+	20.0885i	0.460618	+	0.797815i
$635$		0			0
$636$	−0.339746			−0.0134718
$637$	−6.92820	+	2.00000i	−0.274505	+	0.0792429i
$638$			7.60770i			0.301192i
$639$	12.8038	−	7.39230i	0.506512	−	0.292435i
$640$		0			0
$641$	−16.0359	+	27.7750i	−0.633380	+	1.09705i	0.353476	+	0.935444i	$0.385000\pi$
$641$	−16.0359	+	27.7750i	−0.633380	+	1.09705i	−0.986856	+	0.161603i	$0.948334\pi$
$642$	12.9282			0.510235
$643$	−5.36603	+	9.29423i	−0.211615	+	0.366529i	−0.952220	−	0.305412i	$-0.901206\pi$
$643$	−5.36603	+	9.29423i	−0.211615	+	0.366529i	0.740605	+	0.671941i	$0.234539\pi$
$644$	24.5885	+	14.1962i	0.968921	+	0.559407i
$645$		0			0
$646$	−1.90192	+	3.29423i	−0.0748302	+	0.129610i
$647$	−0.696152	+	0.401924i	−0.0273686	+	0.0158013i	−0.513622	−	0.858017i	$-0.671697\pi$
$647$	−0.696152	+	0.401924i	−0.0273686	+	0.0158013i	0.486253	+	0.873818i	$0.338363\pi$
$648$	−2.23205	−	3.86603i	−0.0876832	−	0.151872i
$649$	−31.1769			−1.22380
$650$		0			0
$651$	−10.3923			−0.407307
$652$	−5.36603	−	9.29423i	−0.210150	−	0.363990i
$653$	−1.20577	+	0.696152i	−0.0471855	+	0.0272425i	−0.523407	−	0.852083i	$-0.675339\pi$
$653$	−1.20577	+	0.696152i	−0.0471855	+	0.0272425i	0.476222	+	0.879325i	$0.342006\pi$
$654$	3.12436	−	5.41154i	0.122172	−	0.211608i
$655$		0			0
$656$	9.00000	+	5.19615i	0.351391	+	0.202876i
$657$	14.3660	−	24.8827i	0.560472	−	0.970766i
$658$	9.00000			0.350857
$659$	−2.66025	+	4.60770i	−0.103629	+	0.179490i	−0.913177	−	0.407563i	$-0.866379\pi$
$659$	−2.66025	+	4.60770i	−0.103629	+	0.179490i	0.809548	+	0.587053i	$0.199712\pi$
$660$		0			0
$661$	31.0981	−	17.9545i	1.20957	−	0.698348i	0.246909	−	0.969039i	$-0.420585\pi$
$661$	31.0981	−	17.9545i	1.20957	−	0.698348i	0.962666	+	0.270690i	$0.0872520\pi$
$662$		−	12.9282i		−	0.502469i
$663$	5.19615	−	21.0000i	0.201802	−	0.815572i
$664$	8.19615			0.318072
$665$		0			0
$666$	−0.990381	−	1.71539i	−0.0383765	−	0.0664700i
$667$	20.7846	+	12.0000i	0.804783	+	0.464642i
$668$	−3.00000			−0.116073
$669$	−4.09808	−	2.36603i	−0.158441	−	0.0914758i
$670$		0			0
$671$			18.5885i			0.717599i
$672$	1.90192	+	1.09808i	0.0733683	+	0.0423592i
$673$	−21.1244	+	12.1962i	−0.814284	+	0.470127i	−0.848441	−	0.529289i	$-0.822459\pi$
$673$	−21.1244	+	12.1962i	−0.814284	+	0.470127i	0.0341573	+	0.999416i	$0.489125\pi$
$674$	5.36603	−	3.09808i	0.206692	−	0.119333i
$675$		0			0
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$		−	25.8564i		−	0.993742i	−0.867824	−	0.496871i	$-0.834482\pi$
$677$		−	25.8564i		−	0.993742i	0.867824	−	0.496871i	$-0.165518\pi$
$678$	2.53590	+	4.39230i	0.0973906	+	0.168685i
$679$	−13.6865	−	23.7058i	−0.525241	−	0.909744i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$	−7.09808	+	12.2942i	−0.271799	+	0.470770i
$683$	15.5885	−	27.0000i	0.596476	−	1.03313i	−0.396861	−	0.917879i	$-0.629901\pi$
$683$	15.5885	−	27.0000i	0.596476	−	1.03313i	0.993337	−	0.115248i	$-0.0367661\pi$
$684$		−	1.14359i		−	0.0437264i
$685$		0			0
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$	0.464102	+	0.803848i	0.0177066	+	0.0306687i
$688$		−	2.00000i		−	0.0762493i
$689$	−1.62436	−	0.401924i	−0.0618830	−	0.0153121i
$690$		0			0
$691$	−31.7942	+	18.3564i	−1.20951	+	0.698311i	−0.962652	−	0.270741i	$-0.912731\pi$
$691$	−31.7942	+	18.3564i	−1.20951	+	0.698311i	−0.246857	+	0.969052i	$0.579398\pi$
$692$	12.9904	−	7.50000i	0.493820	−	0.285107i
$693$	−19.2058	−	11.0885i	−0.729567	−	0.421216i
$694$		−	28.7321i		−	1.09065i
$695$		0			0
$696$	1.60770	+	0.928203i	0.0609395	+	0.0351835i
$697$	85.1769			3.22631
$698$	−3.50962	−	2.02628i	−0.132841	−	0.0766958i
$699$	1.73205	+	3.00000i	0.0655122	+	0.113470i
$700$		0			0
$701$	35.9090			1.35626			0.678131	−	0.734941i	$-0.262790\pi$
$701$	35.9090			1.35626			0.678131	+	0.734941i	$0.262790\pi$
$702$	4.00000	+	13.8564i	0.150970	+	0.522976i
$703$		−	0.373067i		−	0.0140705i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$	−4.90192	+	8.49038i	−0.184486	+	0.319540i
$707$	32.1962			1.21086
$708$	−3.80385	+	6.58846i	−0.142957	+	0.247609i
$709$	−9.50962	−	5.49038i	−0.357141	−	0.206196i	0.310685	−	0.950513i	$-0.399442\pi$
$709$	−9.50962	−	5.49038i	−0.357141	−	0.206196i	−0.667826	+	0.744317i	$0.732775\pi$
$710$		0			0
$711$	−5.16987	+	8.95448i	−0.193885	+	0.335819i
$712$	−5.89230	+	3.40192i	−0.220823	+	0.127492i
$713$	22.3923	+	38.7846i	0.838598	+	1.45250i
$714$	18.0000			0.673633
$715$		0			0
$716$	9.46410			0.353690
$717$	−0.803848	−	1.39230i	−0.0300202	−	0.0519966i
$718$	1.39230	−	0.803848i	0.0519604	−	0.0299993i
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	−0.517649	−	0.855593i	$-0.673193\pi$
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	0.999790	+	0.0205009i	$0.00652609\pi$
$720$		0			0
$721$	−23.8923	−	13.7942i	−0.889796	−	0.513724i
$722$	−9.39230	+	16.2679i	−0.349545	+	0.605430i
$723$	6.33975			0.235778
$724$	−7.29423	+	12.6340i	−0.271088	+	0.469538i
$725$		0			0
$726$	−1.26795	+	0.732051i	−0.0470580	+	0.0271690i
$727$			34.3731i			1.27483i	0.770522	+	0.637413i	$0.219996\pi$
$727$			34.3731i			1.27483i	−0.770522	+	0.637413i	$0.780004\pi$
$728$	7.79423	+	7.50000i	0.288873	+	0.277968i
$729$	2.21539			0.0820515
$730$		0			0
$731$	−8.19615	−	14.1962i	−0.303146	−	0.525064i
$732$	3.92820	+	2.26795i	0.145191	+	0.0838258i
$733$	−14.9090			−0.550675			−0.275338	−	0.961348i	$-0.588790\pi$
$733$	−14.9090			−0.550675			−0.275338	+	0.961348i	$0.588790\pi$
$734$	4.85641	+	2.80385i	0.179253	+	0.103492i
$735$		0			0
$736$		−	9.46410i		−	0.348851i
$737$		0			0
$738$	−22.1769	+	12.8038i	−0.816344	+	0.471316i
$739$	−28.2058	+	16.2846i	−1.03757	+	0.599039i	−0.919143	−	0.393924i	$-0.871117\pi$
$739$	−28.2058	+	16.2846i	−1.03757	+	0.599039i	−0.118423	+	0.992963i	$0.537784\pi$
$740$		0			0
$741$	−0.294229	+	1.18911i	−0.0108088	+	0.0436831i
$742$		−	1.39230i		−	0.0511131i
$743$	6.80385	+	11.7846i	0.249609	+	0.432335i	0.963417	−	0.268006i	$-0.0863646\pi$
$743$	6.80385	+	11.7846i	0.249609	+	0.432335i	−0.713808	+	0.700341i	$0.753031\pi$
$744$	1.73205	+	3.00000i	0.0635001	+	0.109985i
$745$		0			0
$746$			0.392305i			0.0143633i
$747$	−10.0981	+	17.4904i	−0.369469	+	0.639940i
$748$	12.2942	−	21.2942i	0.449522	−	0.778594i
$749$			52.9808i			1.93587i
$750$		0			0
$751$	10.1962	+	17.6603i	0.372063	+	0.644432i	0.989883	−	0.141888i	$-0.0453172\pi$
$751$	10.1962	+	17.6603i	0.372063	+	0.644432i	−0.617820	+	0.786320i	$0.711984\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$		−	12.5885i		−	0.458749i
$754$	6.58846	+	6.33975i	0.239937	+	0.230880i
$755$		0			0
$756$	−10.3923	+	6.00000i	−0.377964	+	0.218218i
$757$	−32.7224	+	18.8923i	−1.18932	+	0.686652i	−0.958151	−	0.286262i	$-0.907587\pi$
$757$	−32.7224	+	18.8923i	−1.18932	+	0.686652i	−0.231166	+	0.972914i	$0.574254\pi$
$758$	25.7942	+	14.8923i	0.936889	+	0.540913i
$759$		−	20.7846i		−	0.754434i
$760$		0			0
$761$	16.2846	+	9.40192i	0.590317	+	0.340819i	0.765223	−	0.643766i	$-0.222629\pi$
$761$	16.2846	+	9.40192i	0.590317	+	0.340819i	−0.174906	+	0.984585i	$0.555962\pi$
$762$	7.90897			0.286512
$763$	22.1769	+	12.8038i	0.802858	+	0.463530i
$764$	11.3660	+	19.6865i	0.411208	+	0.712234i
$765$		0			0
$766$	−22.3923			−0.809067
$767$	−25.9808	+	27.0000i	−0.938111	+	0.974913i
$768$		−	0.732051i		−	0.0264156i
$769$	33.0000	−	19.0526i	1.19001	−	0.687053i	0.231701	−	0.972787i	$-0.425571\pi$
$769$	33.0000	−	19.0526i	1.19001	−	0.687053i	0.958309	+	0.285734i	$0.0922374\pi$
$770$		0			0
$771$	5.07180	−	8.78461i	0.182656	−	0.316370i
$772$	−16.3923			−0.589972
$773$	1.20577	−	2.08846i	0.0433686	−	0.0751166i	−0.843526	−	0.537088i	$-0.819524\pi$
$773$	1.20577	−	2.08846i	0.0433686	−	0.0751166i	0.886895	+	0.461971i	$0.152858\pi$
$774$	4.26795	+	2.46410i	0.153408	+	0.0885703i
$775$		0			0
$776$	−4.56218	+	7.90192i	−0.163773	+	0.283663i
$777$	−1.52886	+	0.882686i	−0.0548474	+	0.0316662i
$778$	11.3660	+	19.6865i	0.407492	+	0.705796i
$779$	−4.82309			−0.172805
$780$		0			0
$781$	−18.0000			−0.644091
$782$	−38.7846	−	67.1769i	−1.38693	−	2.40224i
$783$	−8.78461	+	5.07180i	−0.313936	+	0.181251i
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$		0			0
$786$	3.88269	+	2.24167i	0.138491	+	0.0799577i
$787$	21.4186	−	37.0981i	0.763490	−	1.32240i	−0.177551	−	0.984112i	$-0.556818\pi$
$787$	21.4186	−	37.0981i	0.763490	−	1.32240i	0.941041	−	0.338292i	$-0.109849\pi$
$788$	−21.5885			−0.769057
$789$	1.31347	−	2.27499i	0.0467606	−	0.0809918i
$790$		0			0
$791$	−18.0000	+	10.3923i	−0.640006	+	0.369508i
$792$			7.39230i			0.262674i
$793$	16.0981	+	15.4904i	0.571659	+	0.550080i
$794$	−11.1962			−0.397337
$795$		0			0
$796$	−3.19615	−	5.53590i	−0.113285	−	0.196215i
$797$	11.1962	+	6.46410i	0.396588	+	0.228970i	0.685011	−	0.728533i	$-0.259797\pi$
$797$	11.1962	+	6.46410i	0.396588	+	0.228970i	−0.288423	+	0.957503i	$0.593131\pi$
$798$	−1.01924			−0.0360806
$799$	−21.2942	−	12.2942i	−0.753336	−	0.434939i
$800$		0			0
$801$		−	16.7654i		−	0.592375i
$802$	4.50000	+	2.59808i	0.158901	+	0.0917413i
$803$	−30.2942	+	17.4904i	−1.06906	+	0.617222i
$804$		0			0
$805$		0			0
$806$	4.73205	+	16.3923i	0.166679	+	0.577394i
$807$		−	19.8564i		−	0.698979i
$808$	−5.36603	−	9.29423i	−0.188776	−	0.326970i
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	0.996125	−	0.0879478i	$-0.0280309\pi$
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	−0.574228	+	0.818696i	$0.694698\pi$
$810$		0			0
$811$		−	43.3923i		−	1.52371i	−0.647748	−	0.761855i	$-0.724289\pi$
$811$		−	43.3923i		−	1.52371i	0.647748	−	0.761855i	$-0.275711\pi$
$812$	−3.80385	+	6.58846i	−0.133489	+	0.231210i
$813$	−3.46410	+	6.00000i	−0.121491	+	0.210429i
$814$			2.41154i			0.0845245i
$815$		0			0
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	0.464102	+	0.803848i	0.0162369	+	0.0281231i
$818$		−	16.2679i		−	0.568796i
$819$	−25.6077	+	7.39230i	−0.894805	+	0.258308i
$820$		0			0
$821$	17.4904	−	10.0981i	0.610419	−	0.352425i	−0.162711	−	0.986674i	$-0.552024\pi$
$821$	17.4904	−	10.0981i	0.610419	−	0.352425i	0.773129	+	0.634249i	$0.218690\pi$
$822$	−1.39230	+	0.803848i	−0.0485622	+	0.0280374i
$823$	−23.5526	−	13.5981i	−0.820991	−	0.473999i	0.0297674	−	0.999557i	$-0.490523\pi$
$823$	−23.5526	−	13.5981i	−0.820991	−	0.473999i	−0.850758	+	0.525558i	$0.823857\pi$
$824$			9.19615i			0.320363i
$825$		0			0
$826$	−27.0000	−	15.5885i	−0.939450	−	0.542392i
$827$	−42.5885			−1.48095			−0.740473	−	0.672086i	$-0.765398\pi$
$827$	−42.5885			−1.48095			−0.740473	+	0.672086i	$0.765398\pi$
$828$	20.1962	+	11.6603i	0.701865	+	0.405222i
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	0.638457	−	0.769657i	$-0.279573\pi$
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	−0.985771	+	0.168091i	$0.946240\pi$
$830$		0			0
$831$	−0.732051			−0.0253946
$832$	0.866025	−	3.50000i	0.0300240	−	0.121341i
$833$			16.3923i			0.567960i
$834$	0.758330	−	0.437822i	0.0262588	−	0.0151605i
$835$		0			0
$836$	−0.696152	+	1.20577i	−0.0240769	+	0.0417025i
$837$	−18.9282			−0.654254
$838$	−8.66025	+	15.0000i	−0.299164	+	0.518166i
$839$	−18.8827	−	10.9019i	−0.651903	−	0.376376i	0.137282	−	0.990532i	$-0.456163\pi$
$839$	−18.8827	−	10.9019i	−0.651903	−	0.376376i	−0.789185	+	0.614156i	$0.789497\pi$
$840$		0			0
$841$	11.2846	−	19.5455i	0.389124	−	0.673983i
$842$	−2.49038	+	1.43782i	−0.0858242	+	0.0495506i
$843$	−3.80385	−	6.58846i	−0.131011	−	0.226919i
$844$	−17.5885			−0.605420
$845$		0			0
$846$	7.39230			0.254153
$847$	−3.00000	−	5.19615i	−0.103081	−	0.178542i
$848$	−0.401924	+	0.232051i	−0.0138021	+	0.00796866i
$849$	−3.51666	+	6.09103i	−0.120691	+	0.209044i
$850$		0			0
$851$	6.58846	+	3.80385i	0.225849	+	0.130394i
$852$	−2.19615	+	3.80385i	−0.0752389	+	0.130318i
$853$	−13.8564			−0.474434			−0.237217	−	0.971457i	$-0.576235\pi$
$853$	−13.8564			−0.474434			−0.237217	+	0.971457i	$0.576235\pi$
$854$	−9.29423	+	16.0981i	−0.318042	+	0.550865i
$855$		0			0
$856$	15.2942	−	8.83013i	0.522746	−	0.301808i
$857$		−	16.7321i		−	0.571556i	−0.958296	−	0.285778i	$-0.907748\pi$
$857$		−	16.7321i		−	0.571556i	0.958296	−	0.285778i	$-0.0922520\pi$
$858$	1.90192	−	7.68653i	0.0649306	−	0.262414i
$859$	20.3731			0.695120			0.347560	−	0.937658i	$-0.387010\pi$
$859$	20.3731			0.695120			0.347560	+	0.937658i	$0.387010\pi$
$860$		0			0
$861$	11.4115	+	19.7654i	0.388904	+	0.673602i
$862$	7.09808	+	4.09808i	0.241761	+	0.139581i
$863$	−43.1769			−1.46976			−0.734880	−	0.678198i	$-0.762761\pi$
$863$	−43.1769			−1.46976			−0.734880	+	0.678198i	$0.762761\pi$
$864$	3.46410	+	2.00000i	0.117851	+	0.0680414i
$865$		0			0
$866$		−	8.39230i		−	0.285182i
$867$	−31.8109	−	18.3660i	−1.08035	−	0.623743i
$868$	−12.2942	+	7.09808i	−0.417293	+	0.240924i
$869$	10.9019	−	6.29423i	0.369822	−	0.213517i
$870$		0			0
$871$		0			0
$872$		−	8.53590i		−	0.289062i
$873$	−11.2417	−	19.4711i	−0.380473	−	0.658998i
$874$	2.19615	+	3.80385i	0.0742860	+	0.128667i
$875$		0			0
$876$			8.53590i			0.288401i
$877$	13.7321	−	23.7846i	0.463698	−	0.803149i	−0.535443	−	0.844571i	$-0.679855\pi$
$877$	13.7321	−	23.7846i	0.463698	−	0.803149i	0.999142	+	0.0414220i	$0.0131888\pi$
$878$	−1.70577	+	2.95448i	−0.0575670	+	0.0997090i
$879$			8.19615i			0.276449i
$880$		0			0
$881$	−13.1603	−	22.7942i	−0.443380	−	0.767957i	0.554558	−	0.832145i	$-0.312888\pi$
$881$	−13.1603	−	22.7942i	−0.443380	−	0.767957i	−0.997938	+	0.0641883i	$0.979554\pi$
$882$	−2.46410	−	4.26795i	−0.0829706	−	0.143709i
$883$		−	4.58846i		−	0.154414i	−0.997015	−	0.0772069i	$-0.975400\pi$
$883$		−	4.58846i		−	0.154414i	0.997015	−	0.0772069i	$-0.0246002\pi$
$884$	−8.19615	−	28.3923i	−0.275666	−	0.954937i
$885$		0			0
$886$	19.3923	−	11.1962i	0.651497	−	0.376142i
$887$	−35.3038	+	20.3827i	−1.18539	+	0.684384i	−0.957255	−	0.289246i	$-0.906595\pi$
$887$	−35.3038	+	20.3827i	−1.18539	+	0.684384i	−0.228133	+	0.973630i	$0.573262\pi$
$888$	0.509619	+	0.294229i	0.0171017	+	0.00987367i
$889$			32.4115i			1.08705i
$890$		0			0
$891$	−11.5981	−	6.69615i	−0.388550	−	0.224330i
$892$	−6.46410			−0.216434
$893$	1.20577	+	0.696152i	0.0403496	+	0.0232959i
$894$	−2.19615	−	3.80385i	−0.0734503	−	0.127220i
$895$		0			0
$896$	3.00000			0.100223
$897$	−18.0000	−	17.3205i	−0.601003	−	0.578315i
$898$			15.5885i			0.520194i
$899$	−10.3923	+	6.00000i	−0.346603	+	0.200111i
$900$		0			0
$901$	−1.90192	+	3.29423i	−0.0633623	+	0.109747i
$902$	31.1769			1.03808
$903$	2.19615	−	3.80385i	0.0730834	−	0.126584i
$904$	6.00000	+	3.46410i	0.199557	+	0.115214i
$905$		0			0
$906$	−8.66025	+	15.0000i	−0.287718	+	0.498342i
$907$	3.97372	−	2.29423i	0.131945	−	0.0761786i	−0.432574	−	0.901598i	$-0.642395\pi$
$907$	3.97372	−	2.29423i	0.131945	−	0.0761786i	0.564520	+	0.825420i	$0.309061\pi$
$908$	−8.19615	−	14.1962i	−0.271999	−	0.471116i
$909$	26.4449			0.877121
$910$		0			0
$911$	−21.4641			−0.711137			−0.355569	−	0.934650i	$-0.615713\pi$
$911$	−21.4641			−0.711137			−0.355569	+	0.934650i	$0.615713\pi$
$912$	0.169873	+	0.294229i	0.00562506	+	0.00974288i
$913$	21.2942	−	12.2942i	0.704736	−	0.406880i
$914$	9.16987	−	15.8827i	0.303312	−	0.525353i
$915$		0			0
$916$	1.09808	+	0.633975i	0.0362815	+	0.0209471i
$917$	−9.18653	+	15.9115i	−0.303366	+	0.525445i
$918$	32.7846			1.08205
$919$	15.3923	−	26.6603i	0.507745	−	0.879441i	−0.492215	−	0.870474i	$-0.663812\pi$
$919$	15.3923	−	26.6603i	0.507745	−	0.879441i	0.999960	−	0.00896670i	$-0.00285423\pi$
$920$		0			0
$921$	17.4115	−	10.0526i	0.573730	−	0.331243i
$922$			30.5885i			1.00738i
$923$	−15.0000	+	15.5885i	−0.493731	+	0.513100i
$924$	6.58846			0.216744
$925$		0			0
$926$	6.46410	+	11.1962i	0.212424	+	0.367928i
$927$	−19.6244	−	11.3301i	−0.644548	−	0.372130i
$928$	2.53590			0.0832449
$929$	2.78461	+	1.60770i	0.0913601	+	0.0527468i	0.544984	−	0.838446i	$-0.316536\pi$
$929$	2.78461	+	1.60770i	0.0913601	+	0.0527468i	−0.453624	+	0.891193i	$0.649869\pi$
$930$		0			0
$931$		−	0.928203i		−	0.0304206i
$932$	4.09808	+	2.36603i	0.134237	+	0.0775017i
$933$	5.78461	−	3.33975i	0.189380	−	0.109338i
$934$	−32.7846	+	18.9282i	−1.07275	+	0.619350i
$935$		0			0
$936$	6.40192	+	6.16025i	0.209253	+	0.201354i
$937$		−	9.60770i		−	0.313870i	−0.987609	−	0.156935i	$-0.949839\pi$
$937$		−	9.60770i		−	0.313870i	0.987609	−	0.156935i	$-0.0501613\pi$
$938$		0			0
$939$	9.66025	+	16.7321i	0.315250	+	0.546030i
$940$		0			0
$941$		−	3.21539i		−	0.104819i	−0.998626	−	0.0524094i	$-0.983310\pi$
$941$		−	3.21539i		−	0.104819i	0.998626	−	0.0524094i	$-0.0166901\pi$
$942$	4.75833	−	8.24167i	0.155035	−	0.268528i
$943$	49.1769	−	85.1769i	1.60142	−	2.77374i
$944$			10.3923i			0.338241i
$945$		0			0
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	7.68653	+	13.3135i	0.249779	+	0.432630i	0.963464	−	0.267837i	$-0.0863088\pi$
$947$	7.68653	+	13.3135i	0.249779	+	0.432630i	−0.713686	+	0.700466i	$0.752975\pi$
$948$		−	3.07180i		−	0.0997673i
$949$	−10.0981	+	40.8109i	−0.327797	+	1.32478i
$950$		0			0
$951$	14.7058	−	8.49038i	0.476867	−	0.275319i
$952$	21.2942	−	12.2942i	0.690150	−	0.398458i
$953$	−5.70577	−	3.29423i	−0.184828	−	0.106711i	0.404731	−	0.914436i	$-0.367365\pi$
$953$	−5.70577	−	3.29423i	−0.184828	−	0.106711i	−0.589559	+	0.807725i	$0.700698\pi$
$954$		−	1.14359i		−	0.0370252i
$955$		0			0
$956$	−1.90192	−	1.09808i	−0.0615126	−	0.0355143i
$957$	5.56922			0.180027
$958$	−35.4904	−	20.4904i	−1.14664	−	0.662014i
$959$	−3.29423	−	5.70577i	−0.106376	−	0.184249i
$960$		0			0
$961$	8.60770			0.277668
$962$	2.08846	+	2.00962i	0.0673346	+	0.0647927i
$963$			43.5167i			1.40230i
$964$	7.50000	−	4.33013i	0.241559	−	0.139464i
$965$		0			0
$966$	10.3923	−	18.0000i	0.334367	−	0.579141i
$967$	−44.5692			−1.43325			−0.716625	−	0.697459i	$-0.754314\pi$
$967$	−44.5692			−1.43325			−0.716625	+	0.697459i	$0.754314\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	2.41154	+	1.39230i	0.0774699	+	0.0447273i
$970$		0			0
$971$	−23.3827	+	40.5000i	−0.750386	+	1.29971i	0.197250	+	0.980353i	$0.436799\pi$
$971$	−23.3827	+	40.5000i	−0.750386	+	1.29971i	−0.947636	+	0.319354i	$0.896534\pi$
$972$	−13.2224	+	7.63397i	−0.424110	+	0.244860i
$973$	1.79423	+	3.10770i	0.0575203	+	0.0996281i
$974$	−15.2487			−0.488600
$975$		0			0
$976$	6.19615			0.198334
$977$	8.19615	+	14.1962i	0.262218	+	0.454175i	0.966831	−	0.255417i	$-0.0822127\pi$
$977$	8.19615	+	14.1962i	0.262218	+	0.454175i	−0.704613	+	0.709592i	$0.748879\pi$
$978$	−6.80385	+	3.92820i	−0.217563	+	0.125610i
$979$	−10.2058	+	17.6769i	−0.326178	+	0.564957i
$980$		0			0
$981$	18.2154	+	10.5167i	0.581573	+	0.335771i
$982$	−10.3301	+	17.8923i	−0.329648	+	0.570966i
$983$	−44.5692			−1.42154			−0.710769	−	0.703426i	$-0.751653\pi$
$983$	−44.5692			−1.42154			−0.710769	+	0.703426i	$0.751653\pi$
$984$	3.80385	−	6.58846i	0.121262	−	0.210032i
$985$		0			0
$986$	18.0000	−	10.3923i	0.573237	−	0.330958i
$987$		−	6.58846i		−	0.209713i
$988$	0.464102	+	1.60770i	0.0147650	+	0.0511476i
$989$	−18.9282			−0.601882
$990$		0			0
$991$	5.58846	+	9.67949i	0.177523	+	0.307479i	0.941032	−	0.338319i	$-0.109858\pi$
$991$	5.58846	+	9.67949i	0.177523	+	0.307479i	−0.763508	+	0.645798i	$0.776525\pi$
$992$	4.09808	+	2.36603i	0.130114	+	0.0751214i
$993$	−9.46410			−0.300334
$994$	−15.5885	−	9.00000i	−0.494436	−	0.285463i
$995$		0			0
$996$		−	6.00000i		−	0.190117i
$997$	−35.1340	−	20.2846i	−1.11270	−	0.642420i	−0.173176	−	0.984891i	$-0.555403\pi$
$997$	−35.1340	−	20.2846i	−1.11270	−	0.642420i	−0.939528	+	0.342471i	$0.888736\pi$
$998$	22.3923	−	12.9282i	0.708816	−	0.409235i
$999$	−2.78461	+	1.60770i	−0.0881012	+	0.0508652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.n.a.49.2		4
5.2	odd	4		650.2.m.a.101.2		4
5.3	odd	4		130.2.l.a.101.1	✓	4
5.4	even	2		650.2.n.b.49.1		4
13.4	even	6		650.2.n.b.199.1		4
15.8	even	4		1170.2.bs.c.361.2		4
20.3	even	4		1040.2.da.a.881.2		4
65.2	even	12		8450.2.a.bm.1.1		2
65.3	odd	12		1690.2.d.f.1351.2		4
65.4	even	6	inner	650.2.n.a.199.2		4
65.8	even	4		1690.2.e.l.991.1		4
65.17	odd	12		650.2.m.a.251.2		4
65.18	even	4		1690.2.e.n.991.1		4
65.23	odd	12		1690.2.d.f.1351.4		4
65.28	even	12		1690.2.a.j.1.2		2
65.33	even	12		1690.2.e.l.191.1		4
65.37	even	12		8450.2.a.bf.1.1		2
65.38	odd	4		1690.2.l.g.361.2		4
65.43	odd	12		130.2.l.a.121.1	yes	4
65.48	odd	12		1690.2.l.g.1161.2		4
65.58	even	12		1690.2.e.n.191.1		4
65.63	even	12		1690.2.a.m.1.2		2
195.173	even	12		1170.2.bs.c.901.2		4
260.43	even	12		1040.2.da.a.641.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.1	✓	4	5.3	odd	4
130.2.l.a.121.1	yes	4	65.43	odd	12
650.2.m.a.101.2		4	5.2	odd	4
650.2.m.a.251.2		4	65.17	odd	12
650.2.n.a.49.2		4	1.1	even	1	trivial
650.2.n.a.199.2		4	65.4	even	6	inner
650.2.n.b.49.1		4	5.4	even	2
650.2.n.b.199.1		4	13.4	even	6
1040.2.da.a.641.2		4	260.43	even	12
1040.2.da.a.881.2		4	20.3	even	4
1170.2.bs.c.361.2		4	15.8	even	4
1170.2.bs.c.901.2		4	195.173	even	12
1690.2.a.j.1.2		2	65.28	even	12
1690.2.a.m.1.2		2	65.63	even	12
1690.2.d.f.1351.2		4	65.3	odd	12
1690.2.d.f.1351.4		4	65.23	odd	12
1690.2.e.l.191.1		4	65.33	even	12
1690.2.e.l.991.1		4	65.8	even	4
1690.2.e.n.191.1		4	65.58	even	12
1690.2.e.n.991.1		4	65.18	even	4
1690.2.l.g.361.2		4	65.38	odd	4
1690.2.l.g.1161.2		4	65.48	odd	12
8450.2.a.bf.1.1		2	65.37	even	12
8450.2.a.bm.1.1		2	65.2	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.633975 + 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.633975 + 0.366025i) q^{6} +(-1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.633975 + 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.633975 + 0.366025i) q^{6} +(-1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-1.23205 + 2.13397i) q^{9} +(2.59808 - 1.50000i) q^{11} -0.732051i q^{12} +(0.866025 - 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-7.09808 - 4.09808i) q^{17} +2.46410 q^{18} +(0.401924 + 0.232051i) q^{19} -2.19615i q^{21} +(-2.59808 - 1.50000i) q^{22} +(-8.19615 + 4.73205i) q^{23} +(-0.633975 + 0.366025i) q^{24} +(-3.46410 + 1.00000i) q^{26} -4.00000i q^{27} +(-1.50000 - 2.59808i) q^{28} +(-1.26795 - 2.19615i) q^{29} -4.73205i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.09808 + 1.90192i) q^{33} +8.19615i q^{34} +(-1.23205 - 2.13397i) q^{36} +(-0.401924 - 0.696152i) q^{37} -0.464102i q^{38} +(0.732051 + 2.53590i) q^{39} +(-9.00000 + 5.19615i) q^{41} +(-1.90192 + 1.09808i) q^{42} +(1.73205 + 1.00000i) q^{43} +3.00000i q^{44} +(8.19615 + 4.73205i) q^{46} +3.00000 q^{47} +(0.633975 + 0.366025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +6.00000 q^{51} +(2.59808 + 2.50000i) q^{52} -0.464102i q^{53} +(-3.46410 + 2.00000i) q^{54} +(-1.50000 + 2.59808i) q^{56} -0.339746 q^{57} +(-1.26795 + 2.19615i) q^{58} +(-9.00000 - 5.19615i) q^{59} +(-3.09808 + 5.36603i) q^{61} +(-4.09808 + 2.36603i) q^{62} +(-3.69615 - 6.40192i) q^{63} +1.00000 q^{64} +2.19615 q^{66} +(7.09808 - 4.09808i) q^{68} +(3.46410 - 6.00000i) q^{69} +(-5.19615 - 3.00000i) q^{71} +(-1.23205 + 2.13397i) q^{72} -11.6603 q^{73} +(-0.401924 + 0.696152i) q^{74} +(-0.401924 + 0.232051i) q^{76} +9.00000i q^{77} +(1.83013 - 1.90192i) q^{78} +4.19615 q^{79} +(-2.23205 - 3.86603i) q^{81} +(9.00000 + 5.19615i) q^{82} +8.19615 q^{83} +(1.90192 + 1.09808i) q^{84} -2.00000i q^{86} +(1.60770 + 0.928203i) q^{87} +(2.59808 - 1.50000i) q^{88} +(-5.89230 + 3.40192i) q^{89} +(7.79423 + 7.50000i) q^{91} -9.46410i q^{92} +(1.73205 + 3.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} -0.732051i q^{96} +(-4.56218 + 7.90192i) q^{97} +(-1.00000 + 1.73205i) q^{98} +7.39230i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9} + 12 q^{14} - 2 q^{16} - 18 q^{17} - 4 q^{18} + 12 q^{19} - 12 q^{23} - 6 q^{24} - 6 q^{28} - 12 q^{29} - 2 q^{32} + 6 q^{33} + 2 q^{36} - 12 q^{37} - 4 q^{39} - 36 q^{41} - 18 q^{42} + 12 q^{46} + 12 q^{47} + 6 q^{48} - 4 q^{49} + 24 q^{51} - 6 q^{56} - 36 q^{57} - 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} + 6 q^{63} + 4 q^{64} - 12 q^{66} + 18 q^{68} + 2 q^{72} - 12 q^{73} - 12 q^{74} - 12 q^{76} - 10 q^{78} - 4 q^{79} - 2 q^{81} + 36 q^{82} + 12 q^{83} + 18 q^{84} + 48 q^{87} + 18 q^{89} - 6 q^{94} + 6 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9 + 12 * q^14 - 2 * q^16 - 18 * q^17 - 4 * q^18 + 12 * q^19 - 12 * q^23 - 6 * q^24 - 6 * q^28 - 12 * q^29 - 2 * q^32 + 6 * q^33 + 2 * q^36 - 12 * q^37 - 4 * q^39 - 36 * q^41 - 18 * q^42 + 12 * q^46 + 12 * q^47 + 6 * q^48 - 4 * q^49 + 24 * q^51 - 6 * q^56 - 36 * q^57 - 12 * q^58 - 36 * q^59 - 2 * q^61 - 6 * q^62 + 6 * q^63 + 4 * q^64 - 12 * q^66 + 18 * q^68 + 2 * q^72 - 12 * q^73 - 12 * q^74 - 12 * q^76 - 10 * q^78 - 4 * q^79 - 2 * q^81 + 36 * q^82 + 12 * q^83 + 18 * q^84 + 48 * q^87 + 18 * q^89 - 6 * q^94 + 6 * q^97 - 4 * q^98

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